- FindStat

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Identifier
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
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            []=>[]
[1]=>[1]
[1,2]=>[2]
[2,1]=>[1,1]
[1,2,3]=>[3]
[1,3,2]=>[2,1]
[2,1,3]=>[1,2]
[2,3,1]=>[2,1]
[3,1,2]=>[1,2]
[3,2,1]=>[1,1,1]
[1,2,3,4]=>[4]
[1,2,4,3]=>[3,1]
[1,3,2,4]=>[2,2]
[1,3,4,2]=>[3,1]
[1,4,2,3]=>[2,2]
[1,4,3,2]=>[2,1,1]
[2,1,3,4]=>[1,3]
[2,1,4,3]=>[1,2,1]
[2,3,1,4]=>[2,2]
[2,3,4,1]=>[3,1]
[2,4,1,3]=>[2,2]
[2,4,3,1]=>[2,1,1]
[3,1,2,4]=>[1,3]
[3,1,4,2]=>[1,2,1]
[3,2,1,4]=>[1,1,2]
[3,2,4,1]=>[1,2,1]
[3,4,1,2]=>[2,2]
[3,4,2,1]=>[2,1,1]
[4,1,2,3]=>[1,3]
[4,1,3,2]=>[1,2,1]
[4,2,1,3]=>[1,1,2]
[4,2,3,1]=>[1,2,1]
[4,3,1,2]=>[1,1,2]
[4,3,2,1]=>[1,1,1,1]
[1,2,3,4,5]=>[5]
[1,2,3,5,4]=>[4,1]
[1,2,4,3,5]=>[3,2]
[1,2,4,5,3]=>[4,1]
[1,2,5,3,4]=>[3,2]
[1,2,5,4,3]=>[3,1,1]
[1,3,2,4,5]=>[2,3]
[1,3,2,5,4]=>[2,2,1]
[1,3,4,2,5]=>[3,2]
[1,3,4,5,2]=>[4,1]
[1,3,5,2,4]=>[3,2]
[1,3,5,4,2]=>[3,1,1]
[1,4,2,3,5]=>[2,3]
[1,4,2,5,3]=>[2,2,1]
[1,4,3,2,5]=>[2,1,2]
[1,4,3,5,2]=>[2,2,1]
[1,4,5,2,3]=>[3,2]
[1,4,5,3,2]=>[3,1,1]
[1,5,2,3,4]=>[2,3]
[1,5,2,4,3]=>[2,2,1]
[1,5,3,2,4]=>[2,1,2]
[1,5,3,4,2]=>[2,2,1]
[1,5,4,2,3]=>[2,1,2]
[1,5,4,3,2]=>[2,1,1,1]
[2,1,3,4,5]=>[1,4]
[2,1,3,5,4]=>[1,3,1]
[2,1,4,3,5]=>[1,2,2]
[2,1,4,5,3]=>[1,3,1]
[2,1,5,3,4]=>[1,2,2]
[2,1,5,4,3]=>[1,2,1,1]
[2,3,1,4,5]=>[2,3]
[2,3,1,5,4]=>[2,2,1]
[2,3,4,1,5]=>[3,2]
[2,3,4,5,1]=>[4,1]
[2,3,5,1,4]=>[3,2]
[2,3,5,4,1]=>[3,1,1]
[2,4,1,3,5]=>[2,3]
[2,4,1,5,3]=>[2,2,1]
[2,4,3,1,5]=>[2,1,2]
[2,4,3,5,1]=>[2,2,1]
[2,4,5,1,3]=>[3,2]
[2,4,5,3,1]=>[3,1,1]
[2,5,1,3,4]=>[2,3]
[2,5,1,4,3]=>[2,2,1]
[2,5,3,1,4]=>[2,1,2]
[2,5,3,4,1]=>[2,2,1]
[2,5,4,1,3]=>[2,1,2]
[2,5,4,3,1]=>[2,1,1,1]
[3,1,2,4,5]=>[1,4]
[3,1,2,5,4]=>[1,3,1]
[3,1,4,2,5]=>[1,2,2]
[3,1,4,5,2]=>[1,3,1]
[3,1,5,2,4]=>[1,2,2]
[3,1,5,4,2]=>[1,2,1,1]
[3,2,1,4,5]=>[1,1,3]
[3,2,1,5,4]=>[1,1,2,1]
[3,2,4,1,5]=>[1,2,2]
[3,2,4,5,1]=>[1,3,1]
[3,2,5,1,4]=>[1,2,2]
[3,2,5,4,1]=>[1,2,1,1]
[3,4,1,2,5]=>[2,3]
[3,4,1,5,2]=>[2,2,1]
[3,4,2,1,5]=>[2,1,2]
[3,4,2,5,1]=>[2,2,1]
[3,4,5,1,2]=>[3,2]
[3,4,5,2,1]=>[3,1,1]
[3,5,1,2,4]=>[2,3]
[3,5,1,4,2]=>[2,2,1]
[3,5,2,1,4]=>[2,1,2]
[3,5,2,4,1]=>[2,2,1]
[3,5,4,1,2]=>[2,1,2]
[3,5,4,2,1]=>[2,1,1,1]
[4,1,2,3,5]=>[1,4]
[4,1,2,5,3]=>[1,3,1]
[4,1,3,2,5]=>[1,2,2]
[4,1,3,5,2]=>[1,3,1]
[4,1,5,2,3]=>[1,2,2]
[4,1,5,3,2]=>[1,2,1,1]
[4,2,1,3,5]=>[1,1,3]
[4,2,1,5,3]=>[1,1,2,1]
[4,2,3,1,5]=>[1,2,2]
[4,2,3,5,1]=>[1,3,1]
[4,2,5,1,3]=>[1,2,2]
[4,2,5,3,1]=>[1,2,1,1]
[4,3,1,2,5]=>[1,1,3]
[4,3,1,5,2]=>[1,1,2,1]
[4,3,2,1,5]=>[1,1,1,2]
[4,3,2,5,1]=>[1,1,2,1]
[4,3,5,1,2]=>[1,2,2]
[4,3,5,2,1]=>[1,2,1,1]
[4,5,1,2,3]=>[2,3]
[4,5,1,3,2]=>[2,2,1]
[4,5,2,1,3]=>[2,1,2]
[4,5,2,3,1]=>[2,2,1]
[4,5,3,1,2]=>[2,1,2]
[4,5,3,2,1]=>[2,1,1,1]
[5,1,2,3,4]=>[1,4]
[5,1,2,4,3]=>[1,3,1]
[5,1,3,2,4]=>[1,2,2]
[5,1,3,4,2]=>[1,3,1]
[5,1,4,2,3]=>[1,2,2]
[5,1,4,3,2]=>[1,2,1,1]
[5,2,1,3,4]=>[1,1,3]
[5,2,1,4,3]=>[1,1,2,1]
[5,2,3,1,4]=>[1,2,2]
[5,2,3,4,1]=>[1,3,1]
[5,2,4,1,3]=>[1,2,2]
[5,2,4,3,1]=>[1,2,1,1]
[5,3,1,2,4]=>[1,1,3]
[5,3,1,4,2]=>[1,1,2,1]
[5,3,2,1,4]=>[1,1,1,2]
[5,3,2,4,1]=>[1,1,2,1]
[5,3,4,1,2]=>[1,2,2]
[5,3,4,2,1]=>[1,2,1,1]
[5,4,1,2,3]=>[1,1,3]
[5,4,1,3,2]=>[1,1,2,1]
[5,4,2,1,3]=>[1,1,1,2]
[5,4,2,3,1]=>[1,1,2,1]
[5,4,3,1,2]=>[1,1,1,2]
[5,4,3,2,1]=>[1,1,1,1,1]
[1,2,3,4,5,6]=>[6]
[1,2,3,4,6,5]=>[5,1]
[1,2,3,5,4,6]=>[4,2]
[1,2,3,5,6,4]=>[5,1]
[1,2,3,6,4,5]=>[4,2]
[1,2,3,6,5,4]=>[4,1,1]
[1,2,4,3,5,6]=>[3,3]
[1,2,4,3,6,5]=>[3,2,1]
[1,2,4,5,3,6]=>[4,2]
[1,2,4,5,6,3]=>[5,1]
[1,2,4,6,3,5]=>[4,2]
[1,2,4,6,5,3]=>[4,1,1]
[1,2,5,3,4,6]=>[3,3]
[1,2,5,3,6,4]=>[3,2,1]
[1,2,5,4,3,6]=>[3,1,2]
[1,2,5,4,6,3]=>[3,2,1]
[1,2,5,6,3,4]=>[4,2]
[1,2,5,6,4,3]=>[4,1,1]
[1,2,6,3,4,5]=>[3,3]
[1,2,6,3,5,4]=>[3,2,1]
[1,2,6,4,3,5]=>[3,1,2]
[1,2,6,4,5,3]=>[3,2,1]
[1,2,6,5,3,4]=>[3,1,2]
[1,2,6,5,4,3]=>[3,1,1,1]
[1,3,2,4,5,6]=>[2,4]
[1,3,2,4,6,5]=>[2,3,1]
[1,3,2,5,4,6]=>[2,2,2]
[1,3,2,5,6,4]=>[2,3,1]
[1,3,2,6,4,5]=>[2,2,2]
[1,3,2,6,5,4]=>[2,2,1,1]
[1,3,4,2,5,6]=>[3,3]
[1,3,4,2,6,5]=>[3,2,1]
[1,3,4,5,2,6]=>[4,2]
[1,3,4,5,6,2]=>[5,1]
[1,3,4,6,2,5]=>[4,2]
[1,3,4,6,5,2]=>[4,1,1]
[1,3,5,2,4,6]=>[3,3]
[1,3,5,2,6,4]=>[3,2,1]
[1,3,5,4,2,6]=>[3,1,2]
[1,3,5,4,6,2]=>[3,2,1]
[1,3,5,6,2,4]=>[4,2]
[1,3,5,6,4,2]=>[4,1,1]
[1,3,6,2,4,5]=>[3,3]
[1,3,6,2,5,4]=>[3,2,1]
[1,3,6,4,2,5]=>[3,1,2]
[1,3,6,4,5,2]=>[3,2,1]
[1,3,6,5,2,4]=>[3,1,2]
[1,3,6,5,4,2]=>[3,1,1,1]
[1,4,2,3,5,6]=>[2,4]
[1,4,2,3,6,5]=>[2,3,1]
[1,4,2,5,3,6]=>[2,2,2]
[1,4,2,5,6,3]=>[2,3,1]
[1,4,2,6,3,5]=>[2,2,2]
[1,4,2,6,5,3]=>[2,2,1,1]
[1,4,3,2,5,6]=>[2,1,3]
[1,4,3,2,6,5]=>[2,1,2,1]
[1,4,3,5,2,6]=>[2,2,2]
[1,4,3,5,6,2]=>[2,3,1]
[1,4,3,6,2,5]=>[2,2,2]
[1,4,3,6,5,2]=>[2,2,1,1]
[1,4,5,2,3,6]=>[3,3]
[1,4,5,2,6,3]=>[3,2,1]
[1,4,5,3,2,6]=>[3,1,2]
[1,4,5,3,6,2]=>[3,2,1]
[1,4,5,6,2,3]=>[4,2]
[1,4,5,6,3,2]=>[4,1,1]
[1,4,6,2,3,5]=>[3,3]
[1,4,6,2,5,3]=>[3,2,1]
[1,4,6,3,2,5]=>[3,1,2]
[1,4,6,3,5,2]=>[3,2,1]
[1,4,6,5,2,3]=>[3,1,2]
[1,4,6,5,3,2]=>[3,1,1,1]
[1,5,2,3,4,6]=>[2,4]
[1,5,2,3,6,4]=>[2,3,1]
[1,5,2,4,3,6]=>[2,2,2]
[1,5,2,4,6,3]=>[2,3,1]
[1,5,2,6,3,4]=>[2,2,2]
[1,5,2,6,4,3]=>[2,2,1,1]
[1,5,3,2,4,6]=>[2,1,3]
[1,5,3,2,6,4]=>[2,1,2,1]
[1,5,3,4,2,6]=>[2,2,2]
[1,5,3,4,6,2]=>[2,3,1]
[1,5,3,6,2,4]=>[2,2,2]
[1,5,3,6,4,2]=>[2,2,1,1]
[1,5,4,2,3,6]=>[2,1,3]
[1,5,4,2,6,3]=>[2,1,2,1]
[1,5,4,3,2,6]=>[2,1,1,2]
[1,5,4,3,6,2]=>[2,1,2,1]
[1,5,4,6,2,3]=>[2,2,2]
[1,5,4,6,3,2]=>[2,2,1,1]
[1,5,6,2,3,4]=>[3,3]
[1,5,6,2,4,3]=>[3,2,1]
[1,5,6,3,2,4]=>[3,1,2]
[1,5,6,3,4,2]=>[3,2,1]
[1,5,6,4,2,3]=>[3,1,2]
[1,5,6,4,3,2]=>[3,1,1,1]
[1,6,2,3,4,5]=>[2,4]
[1,6,2,3,5,4]=>[2,3,1]
[1,6,2,4,3,5]=>[2,2,2]
[1,6,2,4,5,3]=>[2,3,1]
[1,6,2,5,3,4]=>[2,2,2]
[1,6,2,5,4,3]=>[2,2,1,1]
[1,6,3,2,4,5]=>[2,1,3]
[1,6,3,2,5,4]=>[2,1,2,1]
[1,6,3,4,2,5]=>[2,2,2]
[1,6,3,4,5,2]=>[2,3,1]
[1,6,3,5,2,4]=>[2,2,2]
[1,6,3,5,4,2]=>[2,2,1,1]
[1,6,4,2,3,5]=>[2,1,3]
[1,6,4,2,5,3]=>[2,1,2,1]
[1,6,4,3,2,5]=>[2,1,1,2]
[1,6,4,3,5,2]=>[2,1,2,1]
[1,6,4,5,2,3]=>[2,2,2]
[1,6,4,5,3,2]=>[2,2,1,1]
[1,6,5,2,3,4]=>[2,1,3]
[1,6,5,2,4,3]=>[2,1,2,1]
[1,6,5,3,2,4]=>[2,1,1,2]
[1,6,5,3,4,2]=>[2,1,2,1]
[1,6,5,4,2,3]=>[2,1,1,2]
[1,6,5,4,3,2]=>[2,1,1,1,1]
[2,1,3,4,5,6]=>[1,5]
[2,1,3,4,6,5]=>[1,4,1]
[2,1,3,5,4,6]=>[1,3,2]
[2,1,3,5,6,4]=>[1,4,1]
[2,1,3,6,4,5]=>[1,3,2]
[2,1,3,6,5,4]=>[1,3,1,1]
[2,1,4,3,5,6]=>[1,2,3]
[2,1,4,3,6,5]=>[1,2,2,1]
[2,1,4,5,3,6]=>[1,3,2]
[2,1,4,5,6,3]=>[1,4,1]
[2,1,4,6,3,5]=>[1,3,2]
[2,1,4,6,5,3]=>[1,3,1,1]
[2,1,5,3,4,6]=>[1,2,3]
[2,1,5,3,6,4]=>[1,2,2,1]
[2,1,5,4,3,6]=>[1,2,1,2]
[2,1,5,4,6,3]=>[1,2,2,1]
[2,1,5,6,3,4]=>[1,3,2]
[2,1,5,6,4,3]=>[1,3,1,1]
[2,1,6,3,4,5]=>[1,2,3]
[2,1,6,3,5,4]=>[1,2,2,1]
[2,1,6,4,3,5]=>[1,2,1,2]
[2,1,6,4,5,3]=>[1,2,2,1]
[2,1,6,5,3,4]=>[1,2,1,2]
[2,1,6,5,4,3]=>[1,2,1,1,1]
[2,3,1,4,5,6]=>[2,4]
[2,3,1,4,6,5]=>[2,3,1]
[2,3,1,5,4,6]=>[2,2,2]
[2,3,1,5,6,4]=>[2,3,1]
[2,3,1,6,4,5]=>[2,2,2]
[2,3,1,6,5,4]=>[2,2,1,1]
[2,3,4,1,5,6]=>[3,3]
[2,3,4,1,6,5]=>[3,2,1]
[2,3,4,5,1,6]=>[4,2]
[2,3,4,5,6,1]=>[5,1]
[2,3,4,6,1,5]=>[4,2]
[2,3,4,6,5,1]=>[4,1,1]
[2,3,5,1,4,6]=>[3,3]
[2,3,5,1,6,4]=>[3,2,1]
[2,3,5,4,1,6]=>[3,1,2]
[2,3,5,4,6,1]=>[3,2,1]
[2,3,5,6,1,4]=>[4,2]
[2,3,5,6,4,1]=>[4,1,1]
[2,3,6,1,4,5]=>[3,3]
[2,3,6,1,5,4]=>[3,2,1]
[2,3,6,4,1,5]=>[3,1,2]
[2,3,6,4,5,1]=>[3,2,1]
[2,3,6,5,1,4]=>[3,1,2]
[2,3,6,5,4,1]=>[3,1,1,1]
[2,4,1,3,5,6]=>[2,4]
[2,4,1,3,6,5]=>[2,3,1]
[2,4,1,5,3,6]=>[2,2,2]
[2,4,1,5,6,3]=>[2,3,1]
[2,4,1,6,3,5]=>[2,2,2]
[2,4,1,6,5,3]=>[2,2,1,1]
[2,4,3,1,5,6]=>[2,1,3]
[2,4,3,1,6,5]=>[2,1,2,1]
[2,4,3,5,1,6]=>[2,2,2]
[2,4,3,5,6,1]=>[2,3,1]
[2,4,3,6,1,5]=>[2,2,2]
[2,4,3,6,5,1]=>[2,2,1,1]
[2,4,5,1,3,6]=>[3,3]
[2,4,5,1,6,3]=>[3,2,1]
[2,4,5,3,1,6]=>[3,1,2]
[2,4,5,3,6,1]=>[3,2,1]
[2,4,5,6,1,3]=>[4,2]
[2,4,5,6,3,1]=>[4,1,1]
[2,4,6,1,3,5]=>[3,3]
[2,4,6,1,5,3]=>[3,2,1]
[2,4,6,3,1,5]=>[3,1,2]
[2,4,6,3,5,1]=>[3,2,1]
[2,4,6,5,1,3]=>[3,1,2]
[2,4,6,5,3,1]=>[3,1,1,1]
[2,5,1,3,4,6]=>[2,4]
[2,5,1,3,6,4]=>[2,3,1]
[2,5,1,4,3,6]=>[2,2,2]
[2,5,1,4,6,3]=>[2,3,1]
[2,5,1,6,3,4]=>[2,2,2]
[2,5,1,6,4,3]=>[2,2,1,1]
[2,5,3,1,4,6]=>[2,1,3]
[2,5,3,1,6,4]=>[2,1,2,1]
[2,5,3,4,1,6]=>[2,2,2]
[2,5,3,4,6,1]=>[2,3,1]
[2,5,3,6,1,4]=>[2,2,2]
[2,5,3,6,4,1]=>[2,2,1,1]
[2,5,4,1,3,6]=>[2,1,3]
[2,5,4,1,6,3]=>[2,1,2,1]
[2,5,4,3,1,6]=>[2,1,1,2]
[2,5,4,3,6,1]=>[2,1,2,1]
[2,5,4,6,1,3]=>[2,2,2]
[2,5,4,6,3,1]=>[2,2,1,1]
[2,5,6,1,3,4]=>[3,3]
[2,5,6,1,4,3]=>[3,2,1]
[2,5,6,3,1,4]=>[3,1,2]
[2,5,6,3,4,1]=>[3,2,1]
[2,5,6,4,1,3]=>[3,1,2]
[2,5,6,4,3,1]=>[3,1,1,1]
[2,6,1,3,4,5]=>[2,4]
[2,6,1,3,5,4]=>[2,3,1]
[2,6,1,4,3,5]=>[2,2,2]
[2,6,1,4,5,3]=>[2,3,1]
[2,6,1,5,3,4]=>[2,2,2]
[2,6,1,5,4,3]=>[2,2,1,1]
[2,6,3,1,4,5]=>[2,1,3]
[2,6,3,1,5,4]=>[2,1,2,1]
[2,6,3,4,1,5]=>[2,2,2]
[2,6,3,4,5,1]=>[2,3,1]
[2,6,3,5,1,4]=>[2,2,2]
[2,6,3,5,4,1]=>[2,2,1,1]
[2,6,4,1,3,5]=>[2,1,3]
[2,6,4,1,5,3]=>[2,1,2,1]
[2,6,4,3,1,5]=>[2,1,1,2]
[2,6,4,3,5,1]=>[2,1,2,1]
[2,6,4,5,1,3]=>[2,2,2]
[2,6,4,5,3,1]=>[2,2,1,1]
[2,6,5,1,3,4]=>[2,1,3]
[2,6,5,1,4,3]=>[2,1,2,1]
[2,6,5,3,1,4]=>[2,1,1,2]
[2,6,5,3,4,1]=>[2,1,2,1]
[2,6,5,4,1,3]=>[2,1,1,2]
[2,6,5,4,3,1]=>[2,1,1,1,1]
[3,1,2,4,5,6]=>[1,5]
[3,1,2,4,6,5]=>[1,4,1]
[3,1,2,5,4,6]=>[1,3,2]
[3,1,2,5,6,4]=>[1,4,1]
[3,1,2,6,4,5]=>[1,3,2]
[3,1,2,6,5,4]=>[1,3,1,1]
[3,1,4,2,5,6]=>[1,2,3]
[3,1,4,2,6,5]=>[1,2,2,1]
[3,1,4,5,2,6]=>[1,3,2]
[3,1,4,5,6,2]=>[1,4,1]
[3,1,4,6,2,5]=>[1,3,2]
[3,1,4,6,5,2]=>[1,3,1,1]
[3,1,5,2,4,6]=>[1,2,3]
[3,1,5,2,6,4]=>[1,2,2,1]
[3,1,5,4,2,6]=>[1,2,1,2]
[3,1,5,4,6,2]=>[1,2,2,1]
[3,1,5,6,2,4]=>[1,3,2]
[3,1,5,6,4,2]=>[1,3,1,1]
[3,1,6,2,4,5]=>[1,2,3]
[3,1,6,2,5,4]=>[1,2,2,1]
[3,1,6,4,2,5]=>[1,2,1,2]
[3,1,6,4,5,2]=>[1,2,2,1]
[3,1,6,5,2,4]=>[1,2,1,2]
[3,1,6,5,4,2]=>[1,2,1,1,1]
[3,2,1,4,5,6]=>[1,1,4]
[3,2,1,4,6,5]=>[1,1,3,1]
[3,2,1,5,4,6]=>[1,1,2,2]
[3,2,1,5,6,4]=>[1,1,3,1]
[3,2,1,6,4,5]=>[1,1,2,2]
[3,2,1,6,5,4]=>[1,1,2,1,1]
[3,2,4,1,5,6]=>[1,2,3]
[3,2,4,1,6,5]=>[1,2,2,1]
[3,2,4,5,1,6]=>[1,3,2]
[3,2,4,5,6,1]=>[1,4,1]
[3,2,4,6,1,5]=>[1,3,2]
[3,2,4,6,5,1]=>[1,3,1,1]
[3,2,5,1,4,6]=>[1,2,3]
[3,2,5,1,6,4]=>[1,2,2,1]
[3,2,5,4,1,6]=>[1,2,1,2]
[3,2,5,4,6,1]=>[1,2,2,1]
[3,2,5,6,1,4]=>[1,3,2]
[3,2,5,6,4,1]=>[1,3,1,1]
[3,2,6,1,4,5]=>[1,2,3]
[3,2,6,1,5,4]=>[1,2,2,1]
[3,2,6,4,1,5]=>[1,2,1,2]
[3,2,6,4,5,1]=>[1,2,2,1]
[3,2,6,5,1,4]=>[1,2,1,2]
[3,2,6,5,4,1]=>[1,2,1,1,1]
[3,4,1,2,5,6]=>[2,4]
[3,4,1,2,6,5]=>[2,3,1]
[3,4,1,5,2,6]=>[2,2,2]
[3,4,1,5,6,2]=>[2,3,1]
[3,4,1,6,2,5]=>[2,2,2]
[3,4,1,6,5,2]=>[2,2,1,1]
[3,4,2,1,5,6]=>[2,1,3]
[3,4,2,1,6,5]=>[2,1,2,1]
[3,4,2,5,1,6]=>[2,2,2]
[3,4,2,5,6,1]=>[2,3,1]
[3,4,2,6,1,5]=>[2,2,2]
[3,4,2,6,5,1]=>[2,2,1,1]
[3,4,5,1,2,6]=>[3,3]
[3,4,5,1,6,2]=>[3,2,1]
[3,4,5,2,1,6]=>[3,1,2]
[3,4,5,2,6,1]=>[3,2,1]
[3,4,5,6,1,2]=>[4,2]
[3,4,5,6,2,1]=>[4,1,1]
[3,4,6,1,2,5]=>[3,3]
[3,4,6,1,5,2]=>[3,2,1]
[3,4,6,2,1,5]=>[3,1,2]
[3,4,6,2,5,1]=>[3,2,1]
[3,4,6,5,1,2]=>[3,1,2]
[3,4,6,5,2,1]=>[3,1,1,1]
[3,5,1,2,4,6]=>[2,4]
[3,5,1,2,6,4]=>[2,3,1]
[3,5,1,4,2,6]=>[2,2,2]
[3,5,1,4,6,2]=>[2,3,1]
[3,5,1,6,2,4]=>[2,2,2]
[3,5,1,6,4,2]=>[2,2,1,1]
[3,5,2,1,4,6]=>[2,1,3]
[3,5,2,1,6,4]=>[2,1,2,1]
[3,5,2,4,1,6]=>[2,2,2]
[3,5,2,4,6,1]=>[2,3,1]
[3,5,2,6,1,4]=>[2,2,2]
[3,5,2,6,4,1]=>[2,2,1,1]
[3,5,4,1,2,6]=>[2,1,3]
[3,5,4,1,6,2]=>[2,1,2,1]
[3,5,4,2,1,6]=>[2,1,1,2]
[3,5,4,2,6,1]=>[2,1,2,1]
[3,5,4,6,1,2]=>[2,2,2]
[3,5,4,6,2,1]=>[2,2,1,1]
[3,5,6,1,2,4]=>[3,3]
[3,5,6,1,4,2]=>[3,2,1]
[3,5,6,2,1,4]=>[3,1,2]
[3,5,6,2,4,1]=>[3,2,1]
[3,5,6,4,1,2]=>[3,1,2]
[3,5,6,4,2,1]=>[3,1,1,1]
[3,6,1,2,4,5]=>[2,4]
[3,6,1,2,5,4]=>[2,3,1]
[3,6,1,4,2,5]=>[2,2,2]
[3,6,1,4,5,2]=>[2,3,1]
[3,6,1,5,2,4]=>[2,2,2]
[3,6,1,5,4,2]=>[2,2,1,1]
[3,6,2,1,4,5]=>[2,1,3]
[3,6,2,1,5,4]=>[2,1,2,1]
[3,6,2,4,1,5]=>[2,2,2]
[3,6,2,4,5,1]=>[2,3,1]
[3,6,2,5,1,4]=>[2,2,2]
[3,6,2,5,4,1]=>[2,2,1,1]
[3,6,4,1,2,5]=>[2,1,3]
[3,6,4,1,5,2]=>[2,1,2,1]
[3,6,4,2,1,5]=>[2,1,1,2]
[3,6,4,2,5,1]=>[2,1,2,1]
[3,6,4,5,1,2]=>[2,2,2]
[3,6,4,5,2,1]=>[2,2,1,1]
[3,6,5,1,2,4]=>[2,1,3]
[3,6,5,1,4,2]=>[2,1,2,1]
[3,6,5,2,1,4]=>[2,1,1,2]
[3,6,5,2,4,1]=>[2,1,2,1]
[3,6,5,4,1,2]=>[2,1,1,2]
[3,6,5,4,2,1]=>[2,1,1,1,1]
[4,1,2,3,5,6]=>[1,5]
[4,1,2,3,6,5]=>[1,4,1]
[4,1,2,5,3,6]=>[1,3,2]
[4,1,2,5,6,3]=>[1,4,1]
[4,1,2,6,3,5]=>[1,3,2]
[4,1,2,6,5,3]=>[1,3,1,1]
[4,1,3,2,5,6]=>[1,2,3]
[4,1,3,2,6,5]=>[1,2,2,1]
[4,1,3,5,2,6]=>[1,3,2]
[4,1,3,5,6,2]=>[1,4,1]
[4,1,3,6,2,5]=>[1,3,2]
[4,1,3,6,5,2]=>[1,3,1,1]
[4,1,5,2,3,6]=>[1,2,3]
[4,1,5,2,6,3]=>[1,2,2,1]
[4,1,5,3,2,6]=>[1,2,1,2]
[4,1,5,3,6,2]=>[1,2,2,1]
[4,1,5,6,2,3]=>[1,3,2]
[4,1,5,6,3,2]=>[1,3,1,1]
[4,1,6,2,3,5]=>[1,2,3]
[4,1,6,2,5,3]=>[1,2,2,1]
[4,1,6,3,2,5]=>[1,2,1,2]
[4,1,6,3,5,2]=>[1,2,2,1]
[4,1,6,5,2,3]=>[1,2,1,2]
[4,1,6,5,3,2]=>[1,2,1,1,1]
[4,2,1,3,5,6]=>[1,1,4]
[4,2,1,3,6,5]=>[1,1,3,1]
[4,2,1,5,3,6]=>[1,1,2,2]
[4,2,1,5,6,3]=>[1,1,3,1]
[4,2,1,6,3,5]=>[1,1,2,2]
[4,2,1,6,5,3]=>[1,1,2,1,1]
[4,2,3,1,5,6]=>[1,2,3]
[4,2,3,1,6,5]=>[1,2,2,1]
[4,2,3,5,1,6]=>[1,3,2]
[4,2,3,5,6,1]=>[1,4,1]
[4,2,3,6,1,5]=>[1,3,2]
[4,2,3,6,5,1]=>[1,3,1,1]
[4,2,5,1,3,6]=>[1,2,3]
[4,2,5,1,6,3]=>[1,2,2,1]
[4,2,5,3,1,6]=>[1,2,1,2]
[4,2,5,3,6,1]=>[1,2,2,1]
[4,2,5,6,1,3]=>[1,3,2]
[4,2,5,6,3,1]=>[1,3,1,1]
[4,2,6,1,3,5]=>[1,2,3]
[4,2,6,1,5,3]=>[1,2,2,1]
[4,2,6,3,1,5]=>[1,2,1,2]
[4,2,6,3,5,1]=>[1,2,2,1]
[4,2,6,5,1,3]=>[1,2,1,2]
[4,2,6,5,3,1]=>[1,2,1,1,1]
[4,3,1,2,5,6]=>[1,1,4]
[4,3,1,2,6,5]=>[1,1,3,1]
[4,3,1,5,2,6]=>[1,1,2,2]
[4,3,1,5,6,2]=>[1,1,3,1]
[4,3,1,6,2,5]=>[1,1,2,2]
[4,3,1,6,5,2]=>[1,1,2,1,1]
[4,3,2,1,5,6]=>[1,1,1,3]
[4,3,2,1,6,5]=>[1,1,1,2,1]
[4,3,2,5,1,6]=>[1,1,2,2]
[4,3,2,5,6,1]=>[1,1,3,1]
[4,3,2,6,1,5]=>[1,1,2,2]
[4,3,2,6,5,1]=>[1,1,2,1,1]
[4,3,5,1,2,6]=>[1,2,3]
[4,3,5,1,6,2]=>[1,2,2,1]
[4,3,5,2,1,6]=>[1,2,1,2]
[4,3,5,2,6,1]=>[1,2,2,1]
[4,3,5,6,1,2]=>[1,3,2]
[4,3,5,6,2,1]=>[1,3,1,1]
[4,3,6,1,2,5]=>[1,2,3]
[4,3,6,1,5,2]=>[1,2,2,1]
[4,3,6,2,1,5]=>[1,2,1,2]
[4,3,6,2,5,1]=>[1,2,2,1]
[4,3,6,5,1,2]=>[1,2,1,2]
[4,3,6,5,2,1]=>[1,2,1,1,1]
[4,5,1,2,3,6]=>[2,4]
[4,5,1,2,6,3]=>[2,3,1]
[4,5,1,3,2,6]=>[2,2,2]
[4,5,1,3,6,2]=>[2,3,1]
[4,5,1,6,2,3]=>[2,2,2]
[4,5,1,6,3,2]=>[2,2,1,1]
[4,5,2,1,3,6]=>[2,1,3]
[4,5,2,1,6,3]=>[2,1,2,1]
[4,5,2,3,1,6]=>[2,2,2]
[4,5,2,3,6,1]=>[2,3,1]
[4,5,2,6,1,3]=>[2,2,2]
[4,5,2,6,3,1]=>[2,2,1,1]
[4,5,3,1,2,6]=>[2,1,3]
[4,5,3,1,6,2]=>[2,1,2,1]
[4,5,3,2,1,6]=>[2,1,1,2]
[4,5,3,2,6,1]=>[2,1,2,1]
[4,5,3,6,1,2]=>[2,2,2]
[4,5,3,6,2,1]=>[2,2,1,1]
[4,5,6,1,2,3]=>[3,3]
[4,5,6,1,3,2]=>[3,2,1]
[4,5,6,2,1,3]=>[3,1,2]
[4,5,6,2,3,1]=>[3,2,1]
[4,5,6,3,1,2]=>[3,1,2]
[4,5,6,3,2,1]=>[3,1,1,1]
[4,6,1,2,3,5]=>[2,4]
[4,6,1,2,5,3]=>[2,3,1]
[4,6,1,3,2,5]=>[2,2,2]
[4,6,1,3,5,2]=>[2,3,1]
[4,6,1,5,2,3]=>[2,2,2]
[4,6,1,5,3,2]=>[2,2,1,1]
[4,6,2,1,3,5]=>[2,1,3]
[4,6,2,1,5,3]=>[2,1,2,1]
[4,6,2,3,1,5]=>[2,2,2]
[4,6,2,3,5,1]=>[2,3,1]
[4,6,2,5,1,3]=>[2,2,2]
[4,6,2,5,3,1]=>[2,2,1,1]
[4,6,3,1,2,5]=>[2,1,3]
[4,6,3,1,5,2]=>[2,1,2,1]
[4,6,3,2,1,5]=>[2,1,1,2]
[4,6,3,2,5,1]=>[2,1,2,1]
[4,6,3,5,1,2]=>[2,2,2]
[4,6,3,5,2,1]=>[2,2,1,1]
[4,6,5,1,2,3]=>[2,1,3]
[4,6,5,1,3,2]=>[2,1,2,1]
[4,6,5,2,1,3]=>[2,1,1,2]
[4,6,5,2,3,1]=>[2,1,2,1]
[4,6,5,3,1,2]=>[2,1,1,2]
[4,6,5,3,2,1]=>[2,1,1,1,1]
[5,1,2,3,4,6]=>[1,5]
[5,1,2,3,6,4]=>[1,4,1]
[5,1,2,4,3,6]=>[1,3,2]
[5,1,2,4,6,3]=>[1,4,1]
[5,1,2,6,3,4]=>[1,3,2]
[5,1,2,6,4,3]=>[1,3,1,1]
[5,1,3,2,4,6]=>[1,2,3]
[5,1,3,2,6,4]=>[1,2,2,1]
[5,1,3,4,2,6]=>[1,3,2]
[5,1,3,4,6,2]=>[1,4,1]
[5,1,3,6,2,4]=>[1,3,2]
[5,1,3,6,4,2]=>[1,3,1,1]
[5,1,4,2,3,6]=>[1,2,3]
[5,1,4,2,6,3]=>[1,2,2,1]
[5,1,4,3,2,6]=>[1,2,1,2]
[5,1,4,3,6,2]=>[1,2,2,1]
[5,1,4,6,2,3]=>[1,3,2]
[5,1,4,6,3,2]=>[1,3,1,1]
[5,1,6,2,3,4]=>[1,2,3]
[5,1,6,2,4,3]=>[1,2,2,1]
[5,1,6,3,2,4]=>[1,2,1,2]
[5,1,6,3,4,2]=>[1,2,2,1]
[5,1,6,4,2,3]=>[1,2,1,2]
[5,1,6,4,3,2]=>[1,2,1,1,1]
[5,2,1,3,4,6]=>[1,1,4]
[5,2,1,3,6,4]=>[1,1,3,1]
[5,2,1,4,3,6]=>[1,1,2,2]
[5,2,1,4,6,3]=>[1,1,3,1]
[5,2,1,6,3,4]=>[1,1,2,2]
[5,2,1,6,4,3]=>[1,1,2,1,1]
[5,2,3,1,4,6]=>[1,2,3]
[5,2,3,1,6,4]=>[1,2,2,1]
[5,2,3,4,1,6]=>[1,3,2]
[5,2,3,4,6,1]=>[1,4,1]
[5,2,3,6,1,4]=>[1,3,2]
[5,2,3,6,4,1]=>[1,3,1,1]
[5,2,4,1,3,6]=>[1,2,3]
[5,2,4,1,6,3]=>[1,2,2,1]
[5,2,4,3,1,6]=>[1,2,1,2]
[5,2,4,3,6,1]=>[1,2,2,1]
[5,2,4,6,1,3]=>[1,3,2]
[5,2,4,6,3,1]=>[1,3,1,1]
[5,2,6,1,3,4]=>[1,2,3]
[5,2,6,1,4,3]=>[1,2,2,1]
[5,2,6,3,1,4]=>[1,2,1,2]
[5,2,6,3,4,1]=>[1,2,2,1]
[5,2,6,4,1,3]=>[1,2,1,2]
[5,2,6,4,3,1]=>[1,2,1,1,1]
[5,3,1,2,4,6]=>[1,1,4]
[5,3,1,2,6,4]=>[1,1,3,1]
[5,3,1,4,2,6]=>[1,1,2,2]
[5,3,1,4,6,2]=>[1,1,3,1]
[5,3,1,6,2,4]=>[1,1,2,2]
[5,3,1,6,4,2]=>[1,1,2,1,1]
[5,3,2,1,4,6]=>[1,1,1,3]
[5,3,2,1,6,4]=>[1,1,1,2,1]
[5,3,2,4,1,6]=>[1,1,2,2]
[5,3,2,4,6,1]=>[1,1,3,1]
[5,3,2,6,1,4]=>[1,1,2,2]
[5,3,2,6,4,1]=>[1,1,2,1,1]
[5,3,4,1,2,6]=>[1,2,3]
[5,3,4,1,6,2]=>[1,2,2,1]
[5,3,4,2,1,6]=>[1,2,1,2]
[5,3,4,2,6,1]=>[1,2,2,1]
[5,3,4,6,1,2]=>[1,3,2]
[5,3,4,6,2,1]=>[1,3,1,1]
[5,3,6,1,2,4]=>[1,2,3]
[5,3,6,1,4,2]=>[1,2,2,1]
[5,3,6,2,1,4]=>[1,2,1,2]
[5,3,6,2,4,1]=>[1,2,2,1]
[5,3,6,4,1,2]=>[1,2,1,2]
[5,3,6,4,2,1]=>[1,2,1,1,1]
[5,4,1,2,3,6]=>[1,1,4]
[5,4,1,2,6,3]=>[1,1,3,1]
[5,4,1,3,2,6]=>[1,1,2,2]
[5,4,1,3,6,2]=>[1,1,3,1]
[5,4,1,6,2,3]=>[1,1,2,2]
[5,4,1,6,3,2]=>[1,1,2,1,1]
[5,4,2,1,3,6]=>[1,1,1,3]
[5,4,2,1,6,3]=>[1,1,1,2,1]
[5,4,2,3,1,6]=>[1,1,2,2]
[5,4,2,3,6,1]=>[1,1,3,1]
[5,4,2,6,1,3]=>[1,1,2,2]
[5,4,2,6,3,1]=>[1,1,2,1,1]
[5,4,3,1,2,6]=>[1,1,1,3]
[5,4,3,1,6,2]=>[1,1,1,2,1]
[5,4,3,2,1,6]=>[1,1,1,1,2]
[5,4,3,2,6,1]=>[1,1,1,2,1]
[5,4,3,6,1,2]=>[1,1,2,2]
[5,4,3,6,2,1]=>[1,1,2,1,1]
[5,4,6,1,2,3]=>[1,2,3]
[5,4,6,1,3,2]=>[1,2,2,1]
[5,4,6,2,1,3]=>[1,2,1,2]
[5,4,6,2,3,1]=>[1,2,2,1]
[5,4,6,3,1,2]=>[1,2,1,2]
[5,4,6,3,2,1]=>[1,2,1,1,1]
[5,6,1,2,3,4]=>[2,4]
[5,6,1,2,4,3]=>[2,3,1]
[5,6,1,3,2,4]=>[2,2,2]
[5,6,1,3,4,2]=>[2,3,1]
[5,6,1,4,2,3]=>[2,2,2]
[5,6,1,4,3,2]=>[2,2,1,1]
[5,6,2,1,3,4]=>[2,1,3]
[5,6,2,1,4,3]=>[2,1,2,1]
[5,6,2,3,1,4]=>[2,2,2]
[5,6,2,3,4,1]=>[2,3,1]
[5,6,2,4,1,3]=>[2,2,2]
[5,6,2,4,3,1]=>[2,2,1,1]
[5,6,3,1,2,4]=>[2,1,3]
[5,6,3,1,4,2]=>[2,1,2,1]
[5,6,3,2,1,4]=>[2,1,1,2]
[5,6,3,2,4,1]=>[2,1,2,1]
[5,6,3,4,1,2]=>[2,2,2]
[5,6,3,4,2,1]=>[2,2,1,1]
[5,6,4,1,2,3]=>[2,1,3]
[5,6,4,1,3,2]=>[2,1,2,1]
[5,6,4,2,1,3]=>[2,1,1,2]
[5,6,4,2,3,1]=>[2,1,2,1]
[5,6,4,3,1,2]=>[2,1,1,2]
[5,6,4,3,2,1]=>[2,1,1,1,1]
[6,1,2,3,4,5]=>[1,5]
[6,1,2,3,5,4]=>[1,4,1]
[6,1,2,4,3,5]=>[1,3,2]
[6,1,2,4,5,3]=>[1,4,1]
[6,1,2,5,3,4]=>[1,3,2]
[6,1,2,5,4,3]=>[1,3,1,1]
[6,1,3,2,4,5]=>[1,2,3]
[6,1,3,2,5,4]=>[1,2,2,1]
[6,1,3,4,2,5]=>[1,3,2]
[6,1,3,4,5,2]=>[1,4,1]
[6,1,3,5,2,4]=>[1,3,2]
[6,1,3,5,4,2]=>[1,3,1,1]
[6,1,4,2,3,5]=>[1,2,3]
[6,1,4,2,5,3]=>[1,2,2,1]
[6,1,4,3,2,5]=>[1,2,1,2]
[6,1,4,3,5,2]=>[1,2,2,1]
[6,1,4,5,2,3]=>[1,3,2]
[6,1,4,5,3,2]=>[1,3,1,1]
[6,1,5,2,3,4]=>[1,2,3]
[6,1,5,2,4,3]=>[1,2,2,1]
[6,1,5,3,2,4]=>[1,2,1,2]
[6,1,5,3,4,2]=>[1,2,2,1]
[6,1,5,4,2,3]=>[1,2,1,2]
[6,1,5,4,3,2]=>[1,2,1,1,1]
[6,2,1,3,4,5]=>[1,1,4]
[6,2,1,3,5,4]=>[1,1,3,1]
[6,2,1,4,3,5]=>[1,1,2,2]
[6,2,1,4,5,3]=>[1,1,3,1]
[6,2,1,5,3,4]=>[1,1,2,2]
[6,2,1,5,4,3]=>[1,1,2,1,1]
[6,2,3,1,4,5]=>[1,2,3]
[6,2,3,1,5,4]=>[1,2,2,1]
[6,2,3,4,1,5]=>[1,3,2]
[6,2,3,4,5,1]=>[1,4,1]
[6,2,3,5,1,4]=>[1,3,2]
[6,2,3,5,4,1]=>[1,3,1,1]
[6,2,4,1,3,5]=>[1,2,3]
[6,2,4,1,5,3]=>[1,2,2,1]
[6,2,4,3,1,5]=>[1,2,1,2]
[6,2,4,3,5,1]=>[1,2,2,1]
[6,2,4,5,1,3]=>[1,3,2]
[6,2,4,5,3,1]=>[1,3,1,1]
[6,2,5,1,3,4]=>[1,2,3]
[6,2,5,1,4,3]=>[1,2,2,1]
[6,2,5,3,1,4]=>[1,2,1,2]
[6,2,5,3,4,1]=>[1,2,2,1]
[6,2,5,4,1,3]=>[1,2,1,2]
[6,2,5,4,3,1]=>[1,2,1,1,1]
[6,3,1,2,4,5]=>[1,1,4]
[6,3,1,2,5,4]=>[1,1,3,1]
[6,3,1,4,2,5]=>[1,1,2,2]
[6,3,1,4,5,2]=>[1,1,3,1]
[6,3,1,5,2,4]=>[1,1,2,2]
[6,3,1,5,4,2]=>[1,1,2,1,1]
[6,3,2,1,4,5]=>[1,1,1,3]
[6,3,2,1,5,4]=>[1,1,1,2,1]
[6,3,2,4,1,5]=>[1,1,2,2]
[6,3,2,4,5,1]=>[1,1,3,1]
[6,3,2,5,1,4]=>[1,1,2,2]
[6,3,2,5,4,1]=>[1,1,2,1,1]
[6,3,4,1,2,5]=>[1,2,3]
[6,3,4,1,5,2]=>[1,2,2,1]
[6,3,4,2,1,5]=>[1,2,1,2]
[6,3,4,2,5,1]=>[1,2,2,1]
[6,3,4,5,1,2]=>[1,3,2]
[6,3,4,5,2,1]=>[1,3,1,1]
[6,3,5,1,2,4]=>[1,2,3]
[6,3,5,1,4,2]=>[1,2,2,1]
[6,3,5,2,1,4]=>[1,2,1,2]
[6,3,5,2,4,1]=>[1,2,2,1]
[6,3,5,4,1,2]=>[1,2,1,2]
[6,3,5,4,2,1]=>[1,2,1,1,1]
[6,4,1,2,3,5]=>[1,1,4]
[6,4,1,2,5,3]=>[1,1,3,1]
[6,4,1,3,2,5]=>[1,1,2,2]
[6,4,1,3,5,2]=>[1,1,3,1]
[6,4,1,5,2,3]=>[1,1,2,2]
[6,4,1,5,3,2]=>[1,1,2,1,1]
[6,4,2,1,3,5]=>[1,1,1,3]
[6,4,2,1,5,3]=>[1,1,1,2,1]
[6,4,2,3,1,5]=>[1,1,2,2]
[6,4,2,3,5,1]=>[1,1,3,1]
[6,4,2,5,1,3]=>[1,1,2,2]
[6,4,2,5,3,1]=>[1,1,2,1,1]
[6,4,3,1,2,5]=>[1,1,1,3]
[6,4,3,1,5,2]=>[1,1,1,2,1]
[6,4,3,2,1,5]=>[1,1,1,1,2]
[6,4,3,2,5,1]=>[1,1,1,2,1]
[6,4,3,5,1,2]=>[1,1,2,2]
[6,4,3,5,2,1]=>[1,1,2,1,1]
[6,4,5,1,2,3]=>[1,2,3]
[6,4,5,1,3,2]=>[1,2,2,1]
[6,4,5,2,1,3]=>[1,2,1,2]
[6,4,5,2,3,1]=>[1,2,2,1]
[6,4,5,3,1,2]=>[1,2,1,2]
[6,4,5,3,2,1]=>[1,2,1,1,1]
[6,5,1,2,3,4]=>[1,1,4]
[6,5,1,2,4,3]=>[1,1,3,1]
[6,5,1,3,2,4]=>[1,1,2,2]
[6,5,1,3,4,2]=>[1,1,3,1]
[6,5,1,4,2,3]=>[1,1,2,2]
[6,5,1,4,3,2]=>[1,1,2,1,1]
[6,5,2,1,3,4]=>[1,1,1,3]
[6,5,2,1,4,3]=>[1,1,1,2,1]
[6,5,2,3,1,4]=>[1,1,2,2]
[6,5,2,3,4,1]=>[1,1,3,1]
[6,5,2,4,1,3]=>[1,1,2,2]
[6,5,2,4,3,1]=>[1,1,2,1,1]
[6,5,3,1,2,4]=>[1,1,1,3]
[6,5,3,1,4,2]=>[1,1,1,2,1]
[6,5,3,2,1,4]=>[1,1,1,1,2]
[6,5,3,2,4,1]=>[1,1,1,2,1]
[6,5,3,4,1,2]=>[1,1,2,2]
[6,5,3,4,2,1]=>[1,1,2,1,1]
[6,5,4,1,2,3]=>[1,1,1,3]
[6,5,4,1,3,2]=>[1,1,1,2,1]
[6,5,4,2,1,3]=>[1,1,1,1,2]
[6,5,4,2,3,1]=>[1,1,1,2,1]
[6,5,4,3,1,2]=>[1,1,1,1,2]
[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[1,2,3,4,5,6,7]=>[7]
[1,2,3,4,5,7,6]=>[6,1]
[1,2,3,4,6,5,7]=>[5,2]
[1,2,3,4,6,7,5]=>[6,1]
[1,2,3,4,7,5,6]=>[5,2]
[1,2,3,4,7,6,5]=>[5,1,1]
[1,2,3,5,4,6,7]=>[4,3]
[1,2,3,5,4,7,6]=>[4,2,1]
[1,2,3,5,6,4,7]=>[5,2]
[1,2,3,5,6,7,4]=>[6,1]
[1,2,3,5,7,4,6]=>[5,2]
[1,2,3,5,7,6,4]=>[5,1,1]
[1,2,3,6,4,5,7]=>[4,3]
[1,2,3,6,4,7,5]=>[4,2,1]
[1,2,3,6,5,4,7]=>[4,1,2]
[1,2,3,6,5,7,4]=>[4,2,1]
[1,2,3,6,7,4,5]=>[5,2]
[1,2,3,6,7,5,4]=>[5,1,1]
[1,2,3,7,4,5,6]=>[4,3]
[1,2,3,7,4,6,5]=>[4,2,1]
[1,2,3,7,5,4,6]=>[4,1,2]
[1,2,3,7,5,6,4]=>[4,2,1]
[1,2,3,7,6,4,5]=>[4,1,2]
[1,2,3,7,6,5,4]=>[4,1,1,1]
[1,2,4,3,5,6,7]=>[3,4]
[1,2,4,3,5,7,6]=>[3,3,1]
[1,2,4,3,6,5,7]=>[3,2,2]
[1,2,4,3,6,7,5]=>[3,3,1]
[1,2,4,3,7,5,6]=>[3,2,2]
[1,2,4,3,7,6,5]=>[3,2,1,1]
[1,2,4,5,3,6,7]=>[4,3]
[1,2,4,5,3,7,6]=>[4,2,1]
[1,2,4,5,6,3,7]=>[5,2]
[1,2,4,5,6,7,3]=>[6,1]
[1,2,4,5,7,3,6]=>[5,2]
[1,2,4,5,7,6,3]=>[5,1,1]
[1,2,4,6,3,5,7]=>[4,3]
[1,2,4,6,3,7,5]=>[4,2,1]
[1,2,4,6,5,3,7]=>[4,1,2]
[1,2,4,6,5,7,3]=>[4,2,1]
[1,2,4,6,7,3,5]=>[5,2]
[1,2,4,6,7,5,3]=>[5,1,1]
[1,2,4,7,3,5,6]=>[4,3]
[1,2,4,7,3,6,5]=>[4,2,1]
[1,2,4,7,5,3,6]=>[4,1,2]
[1,2,4,7,5,6,3]=>[4,2,1]
[1,2,4,7,6,3,5]=>[4,1,2]
[1,2,4,7,6,5,3]=>[4,1,1,1]
[1,2,5,3,4,6,7]=>[3,4]
[1,2,5,3,4,7,6]=>[3,3,1]
[1,2,5,3,6,4,7]=>[3,2,2]
[1,2,5,3,6,7,4]=>[3,3,1]
[1,2,5,3,7,4,6]=>[3,2,2]
[1,2,5,3,7,6,4]=>[3,2,1,1]
[1,2,5,4,3,6,7]=>[3,1,3]
[1,2,5,4,3,7,6]=>[3,1,2,1]
[1,2,5,4,6,3,7]=>[3,2,2]
[1,2,5,4,6,7,3]=>[3,3,1]
[1,2,5,4,7,3,6]=>[3,2,2]
[1,2,5,4,7,6,3]=>[3,2,1,1]
[1,2,5,6,3,4,7]=>[4,3]
[1,2,5,6,3,7,4]=>[4,2,1]
[1,2,5,6,4,3,7]=>[4,1,2]
[1,2,5,6,4,7,3]=>[4,2,1]
[1,2,5,6,7,3,4]=>[5,2]
[1,2,5,6,7,4,3]=>[5,1,1]
[1,2,5,7,3,4,6]=>[4,3]
[1,2,5,7,3,6,4]=>[4,2,1]
[1,2,5,7,4,3,6]=>[4,1,2]
[1,2,5,7,4,6,3]=>[4,2,1]
[1,2,5,7,6,3,4]=>[4,1,2]
[1,2,5,7,6,4,3]=>[4,1,1,1]
[1,2,6,3,4,5,7]=>[3,4]
[1,2,6,3,4,7,5]=>[3,3,1]
[1,2,6,3,5,4,7]=>[3,2,2]
[1,2,6,3,5,7,4]=>[3,3,1]
[1,2,6,3,7,4,5]=>[3,2,2]
[1,2,6,3,7,5,4]=>[3,2,1,1]
[1,2,6,4,3,5,7]=>[3,1,3]
[1,2,6,4,3,7,5]=>[3,1,2,1]
[1,2,6,4,5,3,7]=>[3,2,2]
[1,2,6,4,5,7,3]=>[3,3,1]
[1,2,6,4,7,3,5]=>[3,2,2]
[1,2,6,4,7,5,3]=>[3,2,1,1]
[1,2,6,5,3,4,7]=>[3,1,3]
[1,2,6,5,3,7,4]=>[3,1,2,1]
[1,2,6,5,4,3,7]=>[3,1,1,2]
[1,2,6,5,4,7,3]=>[3,1,2,1]
[1,2,6,5,7,3,4]=>[3,2,2]
[1,2,6,5,7,4,3]=>[3,2,1,1]
[1,2,6,7,3,4,5]=>[4,3]
[1,2,6,7,3,5,4]=>[4,2,1]
[1,2,6,7,4,3,5]=>[4,1,2]
[1,2,6,7,4,5,3]=>[4,2,1]
[1,2,6,7,5,3,4]=>[4,1,2]
[1,2,6,7,5,4,3]=>[4,1,1,1]
[1,2,7,3,4,5,6]=>[3,4]
[1,2,7,3,4,6,5]=>[3,3,1]
[1,2,7,3,5,4,6]=>[3,2,2]
[1,2,7,3,5,6,4]=>[3,3,1]
[1,2,7,3,6,4,5]=>[3,2,2]
[1,2,7,3,6,5,4]=>[3,2,1,1]
[1,2,7,4,3,5,6]=>[3,1,3]
[1,2,7,4,3,6,5]=>[3,1,2,1]
[1,2,7,4,5,3,6]=>[3,2,2]
[1,2,7,4,5,6,3]=>[3,3,1]
[1,2,7,4,6,3,5]=>[3,2,2]
[1,2,7,4,6,5,3]=>[3,2,1,1]
[1,2,7,5,3,4,6]=>[3,1,3]
[1,2,7,5,3,6,4]=>[3,1,2,1]
[1,2,7,5,4,3,6]=>[3,1,1,2]
[1,2,7,5,4,6,3]=>[3,1,2,1]
[1,2,7,5,6,3,4]=>[3,2,2]
[1,2,7,5,6,4,3]=>[3,2,1,1]
[1,2,7,6,3,4,5]=>[3,1,3]
[1,2,7,6,3,5,4]=>[3,1,2,1]
[1,2,7,6,4,3,5]=>[3,1,1,2]
[1,2,7,6,4,5,3]=>[3,1,2,1]
[1,2,7,6,5,3,4]=>[3,1,1,2]
[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[1,3,2,4,5,6,7]=>[2,5]
[1,3,2,4,5,7,6]=>[2,4,1]
[1,3,2,4,6,5,7]=>[2,3,2]
[1,3,2,4,6,7,5]=>[2,4,1]
[1,3,2,4,7,5,6]=>[2,3,2]
[1,3,2,4,7,6,5]=>[2,3,1,1]
[1,3,2,5,4,6,7]=>[2,2,3]
[1,3,2,5,4,7,6]=>[2,2,2,1]
[1,3,2,5,6,4,7]=>[2,3,2]
[1,3,2,5,6,7,4]=>[2,4,1]
[1,3,2,5,7,4,6]=>[2,3,2]
[1,3,2,5,7,6,4]=>[2,3,1,1]
[1,3,2,6,4,5,7]=>[2,2,3]
[1,3,2,6,4,7,5]=>[2,2,2,1]
[1,3,2,6,5,4,7]=>[2,2,1,2]
[1,3,2,6,5,7,4]=>[2,2,2,1]
[1,3,2,6,7,4,5]=>[2,3,2]
[1,3,2,6,7,5,4]=>[2,3,1,1]
[1,3,2,7,4,5,6]=>[2,2,3]
[1,3,2,7,4,6,5]=>[2,2,2,1]
[1,3,2,7,5,4,6]=>[2,2,1,2]
[1,3,2,7,5,6,4]=>[2,2,2,1]
[1,3,2,7,6,4,5]=>[2,2,1,2]
[1,3,2,7,6,5,4]=>[2,2,1,1,1]
[1,3,4,2,5,6,7]=>[3,4]
[1,3,4,2,5,7,6]=>[3,3,1]
[1,3,4,2,6,5,7]=>[3,2,2]
[1,3,4,2,6,7,5]=>[3,3,1]
[1,3,4,2,7,5,6]=>[3,2,2]
[1,3,4,2,7,6,5]=>[3,2,1,1]
[1,3,4,5,2,6,7]=>[4,3]
[1,3,4,5,2,7,6]=>[4,2,1]
[1,3,4,5,6,2,7]=>[5,2]
[1,3,4,5,6,7,2]=>[6,1]
[1,3,4,5,7,2,6]=>[5,2]
[1,3,4,5,7,6,2]=>[5,1,1]
[1,3,4,6,2,5,7]=>[4,3]
[1,3,4,6,2,7,5]=>[4,2,1]
[1,3,4,6,5,2,7]=>[4,1,2]
[1,3,4,6,5,7,2]=>[4,2,1]
[1,3,4,6,7,2,5]=>[5,2]
[1,3,4,6,7,5,2]=>[5,1,1]
[1,3,4,7,2,5,6]=>[4,3]
[1,3,4,7,2,6,5]=>[4,2,1]
[1,3,4,7,5,2,6]=>[4,1,2]
[1,3,4,7,5,6,2]=>[4,2,1]
[1,3,4,7,6,2,5]=>[4,1,2]
[1,3,4,7,6,5,2]=>[4,1,1,1]
[1,3,5,2,4,6,7]=>[3,4]
[1,3,5,2,4,7,6]=>[3,3,1]
[1,3,5,2,6,4,7]=>[3,2,2]
[1,3,5,2,6,7,4]=>[3,3,1]
[1,3,5,2,7,4,6]=>[3,2,2]
[1,3,5,2,7,6,4]=>[3,2,1,1]
[1,3,5,4,2,6,7]=>[3,1,3]
[1,3,5,4,2,7,6]=>[3,1,2,1]
[1,3,5,4,6,2,7]=>[3,2,2]
[1,3,5,4,6,7,2]=>[3,3,1]
[1,3,5,4,7,2,6]=>[3,2,2]
[1,3,5,4,7,6,2]=>[3,2,1,1]
[1,3,5,6,2,4,7]=>[4,3]
[1,3,5,6,2,7,4]=>[4,2,1]
[1,3,5,6,4,2,7]=>[4,1,2]
[1,3,5,6,4,7,2]=>[4,2,1]
[1,3,5,6,7,2,4]=>[5,2]
[1,3,5,6,7,4,2]=>[5,1,1]
[1,3,5,7,2,4,6]=>[4,3]
[1,3,5,7,2,6,4]=>[4,2,1]
[1,3,5,7,4,2,6]=>[4,1,2]
[1,3,5,7,4,6,2]=>[4,2,1]
[1,3,5,7,6,2,4]=>[4,1,2]
[1,3,5,7,6,4,2]=>[4,1,1,1]
[1,3,6,2,4,5,7]=>[3,4]
[1,3,6,2,4,7,5]=>[3,3,1]
[1,3,6,2,5,4,7]=>[3,2,2]
[1,3,6,2,5,7,4]=>[3,3,1]
[1,3,6,2,7,4,5]=>[3,2,2]
[1,3,6,2,7,5,4]=>[3,2,1,1]
[1,3,6,4,2,5,7]=>[3,1,3]
[1,3,6,4,2,7,5]=>[3,1,2,1]
[1,3,6,4,5,2,7]=>[3,2,2]
[1,3,6,4,5,7,2]=>[3,3,1]
[1,3,6,4,7,2,5]=>[3,2,2]
[1,3,6,4,7,5,2]=>[3,2,1,1]
[1,3,6,5,2,4,7]=>[3,1,3]
[1,3,6,5,2,7,4]=>[3,1,2,1]
[1,3,6,5,4,2,7]=>[3,1,1,2]
[1,3,6,5,4,7,2]=>[3,1,2,1]
[1,3,6,5,7,2,4]=>[3,2,2]
[1,3,6,5,7,4,2]=>[3,2,1,1]
[1,3,6,7,2,4,5]=>[4,3]
[1,3,6,7,2,5,4]=>[4,2,1]
[1,3,6,7,4,2,5]=>[4,1,2]
[1,3,6,7,4,5,2]=>[4,2,1]
[1,3,6,7,5,2,4]=>[4,1,2]
[1,3,6,7,5,4,2]=>[4,1,1,1]
[1,3,7,2,4,5,6]=>[3,4]
[1,3,7,2,4,6,5]=>[3,3,1]
[1,3,7,2,5,4,6]=>[3,2,2]
[1,3,7,2,5,6,4]=>[3,3,1]
[1,3,7,2,6,4,5]=>[3,2,2]
[1,3,7,2,6,5,4]=>[3,2,1,1]
[1,3,7,4,2,5,6]=>[3,1,3]
[1,3,7,4,2,6,5]=>[3,1,2,1]
[1,3,7,4,5,2,6]=>[3,2,2]
[1,3,7,4,5,6,2]=>[3,3,1]
[1,3,7,4,6,2,5]=>[3,2,2]
[1,3,7,4,6,5,2]=>[3,2,1,1]
[1,3,7,5,2,4,6]=>[3,1,3]
[1,3,7,5,2,6,4]=>[3,1,2,1]
[1,3,7,5,4,2,6]=>[3,1,1,2]
[1,3,7,5,4,6,2]=>[3,1,2,1]
[1,3,7,5,6,2,4]=>[3,2,2]
[1,3,7,5,6,4,2]=>[3,2,1,1]
[1,3,7,6,2,4,5]=>[3,1,3]
[1,3,7,6,2,5,4]=>[3,1,2,1]
[1,3,7,6,4,2,5]=>[3,1,1,2]
[1,3,7,6,4,5,2]=>[3,1,2,1]
[1,3,7,6,5,2,4]=>[3,1,1,2]
[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[1,4,2,3,5,6,7]=>[2,5]
[1,4,2,3,5,7,6]=>[2,4,1]
[1,4,2,3,6,5,7]=>[2,3,2]
[1,4,2,3,6,7,5]=>[2,4,1]
[1,4,2,3,7,5,6]=>[2,3,2]
[1,4,2,3,7,6,5]=>[2,3,1,1]
[1,4,2,5,3,6,7]=>[2,2,3]
[1,4,2,5,3,7,6]=>[2,2,2,1]
[1,4,2,5,6,3,7]=>[2,3,2]
[1,4,2,5,6,7,3]=>[2,4,1]
[1,4,2,5,7,3,6]=>[2,3,2]
[1,4,2,5,7,6,3]=>[2,3,1,1]
[1,4,2,6,3,5,7]=>[2,2,3]
[1,4,2,6,3,7,5]=>[2,2,2,1]
[1,4,2,6,5,3,7]=>[2,2,1,2]
[1,4,2,6,5,7,3]=>[2,2,2,1]
[1,4,2,6,7,3,5]=>[2,3,2]
[1,4,2,6,7,5,3]=>[2,3,1,1]
[1,4,2,7,3,5,6]=>[2,2,3]
[1,4,2,7,3,6,5]=>[2,2,2,1]
[1,4,2,7,5,3,6]=>[2,2,1,2]
[1,4,2,7,5,6,3]=>[2,2,2,1]
[1,4,2,7,6,3,5]=>[2,2,1,2]
[1,4,2,7,6,5,3]=>[2,2,1,1,1]
[1,4,3,2,5,6,7]=>[2,1,4]
[1,4,3,2,5,7,6]=>[2,1,3,1]
[1,4,3,2,6,5,7]=>[2,1,2,2]
[1,4,3,2,6,7,5]=>[2,1,3,1]
[1,4,3,2,7,5,6]=>[2,1,2,2]
[1,4,3,2,7,6,5]=>[2,1,2,1,1]
[1,4,3,5,2,6,7]=>[2,2,3]
[1,4,3,5,2,7,6]=>[2,2,2,1]
[1,4,3,5,6,2,7]=>[2,3,2]
[1,4,3,5,6,7,2]=>[2,4,1]
[1,4,3,5,7,2,6]=>[2,3,2]
[1,4,3,5,7,6,2]=>[2,3,1,1]
[1,4,3,6,2,5,7]=>[2,2,3]
[1,4,3,6,2,7,5]=>[2,2,2,1]
[1,4,3,6,5,2,7]=>[2,2,1,2]
[1,4,3,6,5,7,2]=>[2,2,2,1]
[1,4,3,6,7,2,5]=>[2,3,2]
[1,4,3,6,7,5,2]=>[2,3,1,1]
[1,4,3,7,2,5,6]=>[2,2,3]
[1,4,3,7,2,6,5]=>[2,2,2,1]
[1,4,3,7,5,2,6]=>[2,2,1,2]
[1,4,3,7,5,6,2]=>[2,2,2,1]
[1,4,3,7,6,2,5]=>[2,2,1,2]
[1,4,3,7,6,5,2]=>[2,2,1,1,1]
[1,4,5,2,3,6,7]=>[3,4]
[1,4,5,2,3,7,6]=>[3,3,1]
[1,4,5,2,6,3,7]=>[3,2,2]
[1,4,5,2,6,7,3]=>[3,3,1]
[1,4,5,2,7,3,6]=>[3,2,2]
[1,4,5,2,7,6,3]=>[3,2,1,1]
[1,4,5,3,2,6,7]=>[3,1,3]
[1,4,5,3,2,7,6]=>[3,1,2,1]
[1,4,5,3,6,2,7]=>[3,2,2]
[1,4,5,3,6,7,2]=>[3,3,1]
[1,4,5,3,7,2,6]=>[3,2,2]
[1,4,5,3,7,6,2]=>[3,2,1,1]
[1,4,5,6,2,3,7]=>[4,3]
[1,4,5,6,2,7,3]=>[4,2,1]
[1,4,5,6,3,2,7]=>[4,1,2]
[1,4,5,6,3,7,2]=>[4,2,1]
[1,4,5,6,7,2,3]=>[5,2]
[1,4,5,6,7,3,2]=>[5,1,1]
[1,4,5,7,2,3,6]=>[4,3]
[1,4,5,7,2,6,3]=>[4,2,1]
[1,4,5,7,3,2,6]=>[4,1,2]
[1,4,5,7,3,6,2]=>[4,2,1]
[1,4,5,7,6,2,3]=>[4,1,2]
[1,4,5,7,6,3,2]=>[4,1,1,1]
[1,4,6,2,3,5,7]=>[3,4]
[1,4,6,2,3,7,5]=>[3,3,1]
[1,4,6,2,5,3,7]=>[3,2,2]
[1,4,6,2,5,7,3]=>[3,3,1]
[1,4,6,2,7,3,5]=>[3,2,2]
[1,4,6,2,7,5,3]=>[3,2,1,1]
[1,4,6,3,2,5,7]=>[3,1,3]
[1,4,6,3,2,7,5]=>[3,1,2,1]
[1,4,6,3,5,2,7]=>[3,2,2]
[1,4,6,3,5,7,2]=>[3,3,1]
[1,4,6,3,7,2,5]=>[3,2,2]
[1,4,6,3,7,5,2]=>[3,2,1,1]
[1,4,6,5,2,3,7]=>[3,1,3]
[1,4,6,5,2,7,3]=>[3,1,2,1]
[1,4,6,5,3,2,7]=>[3,1,1,2]
[1,4,6,5,3,7,2]=>[3,1,2,1]
[1,4,6,5,7,2,3]=>[3,2,2]
[1,4,6,5,7,3,2]=>[3,2,1,1]
[1,4,6,7,2,3,5]=>[4,3]
[1,4,6,7,2,5,3]=>[4,2,1]
[1,4,6,7,3,2,5]=>[4,1,2]
[1,4,6,7,3,5,2]=>[4,2,1]
[1,4,6,7,5,2,3]=>[4,1,2]
[1,4,6,7,5,3,2]=>[4,1,1,1]
[1,4,7,2,3,5,6]=>[3,4]
[1,4,7,2,3,6,5]=>[3,3,1]
[1,4,7,2,5,3,6]=>[3,2,2]
[1,4,7,2,5,6,3]=>[3,3,1]
[1,4,7,2,6,3,5]=>[3,2,2]
[1,4,7,2,6,5,3]=>[3,2,1,1]
[1,4,7,3,2,5,6]=>[3,1,3]
[1,4,7,3,2,6,5]=>[3,1,2,1]
[1,4,7,3,5,2,6]=>[3,2,2]
[1,4,7,3,5,6,2]=>[3,3,1]
[1,4,7,3,6,2,5]=>[3,2,2]
[1,4,7,3,6,5,2]=>[3,2,1,1]
[1,4,7,5,2,3,6]=>[3,1,3]
[1,4,7,5,2,6,3]=>[3,1,2,1]
[1,4,7,5,3,2,6]=>[3,1,1,2]
[1,4,7,5,3,6,2]=>[3,1,2,1]
[1,4,7,5,6,2,3]=>[3,2,2]
[1,4,7,5,6,3,2]=>[3,2,1,1]
[1,4,7,6,2,3,5]=>[3,1,3]
[1,4,7,6,2,5,3]=>[3,1,2,1]
[1,4,7,6,3,2,5]=>[3,1,1,2]
[1,4,7,6,3,5,2]=>[3,1,2,1]
[1,4,7,6,5,2,3]=>[3,1,1,2]
[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[1,5,2,3,4,6,7]=>[2,5]
[1,5,2,3,4,7,6]=>[2,4,1]
[1,5,2,3,6,4,7]=>[2,3,2]
[1,5,2,3,6,7,4]=>[2,4,1]
[1,5,2,3,7,4,6]=>[2,3,2]
[1,5,2,3,7,6,4]=>[2,3,1,1]
[1,5,2,4,3,6,7]=>[2,2,3]
[1,5,2,4,3,7,6]=>[2,2,2,1]
[1,5,2,4,6,3,7]=>[2,3,2]
[1,5,2,4,6,7,3]=>[2,4,1]
[1,5,2,4,7,3,6]=>[2,3,2]
[1,5,2,4,7,6,3]=>[2,3,1,1]
[1,5,2,6,3,4,7]=>[2,2,3]
[1,5,2,6,3,7,4]=>[2,2,2,1]
[1,5,2,6,4,3,7]=>[2,2,1,2]
[1,5,2,6,4,7,3]=>[2,2,2,1]
[1,5,2,6,7,3,4]=>[2,3,2]
[1,5,2,6,7,4,3]=>[2,3,1,1]
[1,5,2,7,3,4,6]=>[2,2,3]
[1,5,2,7,3,6,4]=>[2,2,2,1]
[1,5,2,7,4,3,6]=>[2,2,1,2]
[1,5,2,7,4,6,3]=>[2,2,2,1]
[1,5,2,7,6,3,4]=>[2,2,1,2]
[1,5,2,7,6,4,3]=>[2,2,1,1,1]
[1,5,3,2,4,6,7]=>[2,1,4]
[1,5,3,2,4,7,6]=>[2,1,3,1]
[1,5,3,2,6,4,7]=>[2,1,2,2]
[1,5,3,2,6,7,4]=>[2,1,3,1]
[1,5,3,2,7,4,6]=>[2,1,2,2]
[1,5,3,2,7,6,4]=>[2,1,2,1,1]
[1,5,3,4,2,6,7]=>[2,2,3]
[1,5,3,4,2,7,6]=>[2,2,2,1]
[1,5,3,4,6,2,7]=>[2,3,2]
[1,5,3,4,6,7,2]=>[2,4,1]
[1,5,3,4,7,2,6]=>[2,3,2]
[1,5,3,4,7,6,2]=>[2,3,1,1]
[1,5,3,6,2,4,7]=>[2,2,3]
[1,5,3,6,2,7,4]=>[2,2,2,1]
[1,5,3,6,4,2,7]=>[2,2,1,2]
[1,5,3,6,4,7,2]=>[2,2,2,1]
[1,5,3,6,7,2,4]=>[2,3,2]
[1,5,3,6,7,4,2]=>[2,3,1,1]
[1,5,3,7,2,4,6]=>[2,2,3]
[1,5,3,7,2,6,4]=>[2,2,2,1]
[1,5,3,7,4,2,6]=>[2,2,1,2]
[1,5,3,7,4,6,2]=>[2,2,2,1]
[1,5,3,7,6,2,4]=>[2,2,1,2]
[1,5,3,7,6,4,2]=>[2,2,1,1,1]
[1,5,4,2,3,6,7]=>[2,1,4]
[1,5,4,2,3,7,6]=>[2,1,3,1]
[1,5,4,2,6,3,7]=>[2,1,2,2]
[1,5,4,2,6,7,3]=>[2,1,3,1]
[1,5,4,2,7,3,6]=>[2,1,2,2]
[1,5,4,2,7,6,3]=>[2,1,2,1,1]
[1,5,4,3,2,6,7]=>[2,1,1,3]
[1,5,4,3,2,7,6]=>[2,1,1,2,1]
[1,5,4,3,6,2,7]=>[2,1,2,2]
[1,5,4,3,6,7,2]=>[2,1,3,1]
[1,5,4,3,7,2,6]=>[2,1,2,2]
[1,5,4,3,7,6,2]=>[2,1,2,1,1]
[1,5,4,6,2,3,7]=>[2,2,3]
[1,5,4,6,2,7,3]=>[2,2,2,1]
[1,5,4,6,3,2,7]=>[2,2,1,2]
[1,5,4,6,3,7,2]=>[2,2,2,1]
[1,5,4,6,7,2,3]=>[2,3,2]
[1,5,4,6,7,3,2]=>[2,3,1,1]
[1,5,4,7,2,3,6]=>[2,2,3]
[1,5,4,7,2,6,3]=>[2,2,2,1]
[1,5,4,7,3,2,6]=>[2,2,1,2]
[1,5,4,7,3,6,2]=>[2,2,2,1]
[1,5,4,7,6,2,3]=>[2,2,1,2]
[1,5,4,7,6,3,2]=>[2,2,1,1,1]
[1,5,6,2,3,4,7]=>[3,4]
[1,5,6,2,3,7,4]=>[3,3,1]
[1,5,6,2,4,3,7]=>[3,2,2]
[1,5,6,2,4,7,3]=>[3,3,1]
[1,5,6,2,7,3,4]=>[3,2,2]
[1,5,6,2,7,4,3]=>[3,2,1,1]
[1,5,6,3,2,4,7]=>[3,1,3]
[1,5,6,3,2,7,4]=>[3,1,2,1]
[1,5,6,3,4,2,7]=>[3,2,2]
[1,5,6,3,4,7,2]=>[3,3,1]
[1,5,6,3,7,2,4]=>[3,2,2]
[1,5,6,3,7,4,2]=>[3,2,1,1]
[1,5,6,4,2,3,7]=>[3,1,3]
[1,5,6,4,2,7,3]=>[3,1,2,1]
[1,5,6,4,3,2,7]=>[3,1,1,2]
[1,5,6,4,3,7,2]=>[3,1,2,1]
[1,5,6,4,7,2,3]=>[3,2,2]
[1,5,6,4,7,3,2]=>[3,2,1,1]
[1,5,6,7,2,3,4]=>[4,3]
[1,5,6,7,2,4,3]=>[4,2,1]
[1,5,6,7,3,2,4]=>[4,1,2]
[1,5,6,7,3,4,2]=>[4,2,1]
[1,5,6,7,4,2,3]=>[4,1,2]
[1,5,6,7,4,3,2]=>[4,1,1,1]
[1,5,7,2,3,4,6]=>[3,4]
[1,5,7,2,3,6,4]=>[3,3,1]
[1,5,7,2,4,3,6]=>[3,2,2]
[1,5,7,2,4,6,3]=>[3,3,1]
[1,5,7,2,6,3,4]=>[3,2,2]
[1,5,7,2,6,4,3]=>[3,2,1,1]
[1,5,7,3,2,4,6]=>[3,1,3]
[1,5,7,3,2,6,4]=>[3,1,2,1]
[1,5,7,3,4,2,6]=>[3,2,2]
[1,5,7,3,4,6,2]=>[3,3,1]
[1,5,7,3,6,2,4]=>[3,2,2]
[1,5,7,3,6,4,2]=>[3,2,1,1]
[1,5,7,4,2,3,6]=>[3,1,3]
[1,5,7,4,2,6,3]=>[3,1,2,1]
[1,5,7,4,3,2,6]=>[3,1,1,2]
[1,5,7,4,3,6,2]=>[3,1,2,1]
[1,5,7,4,6,2,3]=>[3,2,2]
[1,5,7,4,6,3,2]=>[3,2,1,1]
[1,5,7,6,2,3,4]=>[3,1,3]
[1,5,7,6,2,4,3]=>[3,1,2,1]
[1,5,7,6,3,2,4]=>[3,1,1,2]
[1,5,7,6,3,4,2]=>[3,1,2,1]
[1,5,7,6,4,2,3]=>[3,1,1,2]
[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[1,6,2,3,4,5,7]=>[2,5]
[1,6,2,3,4,7,5]=>[2,4,1]
[1,6,2,3,5,4,7]=>[2,3,2]
[1,6,2,3,5,7,4]=>[2,4,1]
[1,6,2,3,7,4,5]=>[2,3,2]
[1,6,2,3,7,5,4]=>[2,3,1,1]
[1,6,2,4,3,5,7]=>[2,2,3]
[1,6,2,4,3,7,5]=>[2,2,2,1]
[1,6,2,4,5,3,7]=>[2,3,2]
[1,6,2,4,5,7,3]=>[2,4,1]
[1,6,2,4,7,3,5]=>[2,3,2]
[1,6,2,4,7,5,3]=>[2,3,1,1]
[1,6,2,5,3,4,7]=>[2,2,3]
[1,6,2,5,3,7,4]=>[2,2,2,1]
[1,6,2,5,4,3,7]=>[2,2,1,2]
[1,6,2,5,4,7,3]=>[2,2,2,1]
[1,6,2,5,7,3,4]=>[2,3,2]
[1,6,2,5,7,4,3]=>[2,3,1,1]
[1,6,2,7,3,4,5]=>[2,2,3]
[1,6,2,7,3,5,4]=>[2,2,2,1]
[1,6,2,7,4,3,5]=>[2,2,1,2]
[1,6,2,7,4,5,3]=>[2,2,2,1]
[1,6,2,7,5,3,4]=>[2,2,1,2]
[1,6,2,7,5,4,3]=>[2,2,1,1,1]
[1,6,3,2,4,5,7]=>[2,1,4]
[1,6,3,2,4,7,5]=>[2,1,3,1]
[1,6,3,2,5,4,7]=>[2,1,2,2]
[1,6,3,2,5,7,4]=>[2,1,3,1]
[1,6,3,2,7,4,5]=>[2,1,2,2]
[1,6,3,2,7,5,4]=>[2,1,2,1,1]
[1,6,3,4,2,5,7]=>[2,2,3]
[1,6,3,4,2,7,5]=>[2,2,2,1]
[1,6,3,4,5,2,7]=>[2,3,2]
[1,6,3,4,5,7,2]=>[2,4,1]
[1,6,3,4,7,2,5]=>[2,3,2]
[1,6,3,4,7,5,2]=>[2,3,1,1]
[1,6,3,5,2,4,7]=>[2,2,3]
[1,6,3,5,2,7,4]=>[2,2,2,1]
[1,6,3,5,4,2,7]=>[2,2,1,2]
[1,6,3,5,4,7,2]=>[2,2,2,1]
[1,6,3,5,7,2,4]=>[2,3,2]
[1,6,3,5,7,4,2]=>[2,3,1,1]
[1,6,3,7,2,4,5]=>[2,2,3]
[1,6,3,7,2,5,4]=>[2,2,2,1]
[1,6,3,7,4,2,5]=>[2,2,1,2]
[1,6,3,7,4,5,2]=>[2,2,2,1]
[1,6,3,7,5,2,4]=>[2,2,1,2]
[1,6,3,7,5,4,2]=>[2,2,1,1,1]
[1,6,4,2,3,5,7]=>[2,1,4]
[1,6,4,2,3,7,5]=>[2,1,3,1]
[1,6,4,2,5,3,7]=>[2,1,2,2]
[1,6,4,2,5,7,3]=>[2,1,3,1]
[1,6,4,2,7,3,5]=>[2,1,2,2]
[1,6,4,2,7,5,3]=>[2,1,2,1,1]
[1,6,4,3,2,5,7]=>[2,1,1,3]
[1,6,4,3,2,7,5]=>[2,1,1,2,1]
[1,6,4,3,5,2,7]=>[2,1,2,2]
[1,6,4,3,5,7,2]=>[2,1,3,1]
[1,6,4,3,7,2,5]=>[2,1,2,2]
[1,6,4,3,7,5,2]=>[2,1,2,1,1]
[1,6,4,5,2,3,7]=>[2,2,3]
[1,6,4,5,2,7,3]=>[2,2,2,1]
[1,6,4,5,3,2,7]=>[2,2,1,2]
[1,6,4,5,3,7,2]=>[2,2,2,1]
[1,6,4,5,7,2,3]=>[2,3,2]
[1,6,4,5,7,3,2]=>[2,3,1,1]
[1,6,4,7,2,3,5]=>[2,2,3]
[1,6,4,7,2,5,3]=>[2,2,2,1]
[1,6,4,7,3,2,5]=>[2,2,1,2]
[1,6,4,7,3,5,2]=>[2,2,2,1]
[1,6,4,7,5,2,3]=>[2,2,1,2]
[1,6,4,7,5,3,2]=>[2,2,1,1,1]
[1,6,5,2,3,4,7]=>[2,1,4]
[1,6,5,2,3,7,4]=>[2,1,3,1]
[1,6,5,2,4,3,7]=>[2,1,2,2]
[1,6,5,2,4,7,3]=>[2,1,3,1]
[1,6,5,2,7,3,4]=>[2,1,2,2]
[1,6,5,2,7,4,3]=>[2,1,2,1,1]
[1,6,5,3,2,4,7]=>[2,1,1,3]
[1,6,5,3,2,7,4]=>[2,1,1,2,1]
[1,6,5,3,4,2,7]=>[2,1,2,2]
[1,6,5,3,4,7,2]=>[2,1,3,1]
[1,6,5,3,7,2,4]=>[2,1,2,2]
[1,6,5,3,7,4,2]=>[2,1,2,1,1]
[1,6,5,4,2,3,7]=>[2,1,1,3]
[1,6,5,4,2,7,3]=>[2,1,1,2,1]
[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[1,6,5,4,3,7,2]=>[2,1,1,2,1]
[1,6,5,4,7,2,3]=>[2,1,2,2]
[1,6,5,4,7,3,2]=>[2,1,2,1,1]
[1,6,5,7,2,3,4]=>[2,2,3]
[1,6,5,7,2,4,3]=>[2,2,2,1]
[1,6,5,7,3,2,4]=>[2,2,1,2]
[1,6,5,7,3,4,2]=>[2,2,2,1]
[1,6,5,7,4,2,3]=>[2,2,1,2]
[1,6,5,7,4,3,2]=>[2,2,1,1,1]
[1,6,7,2,3,4,5]=>[3,4]
[1,6,7,2,3,5,4]=>[3,3,1]
[1,6,7,2,4,3,5]=>[3,2,2]
[1,6,7,2,4,5,3]=>[3,3,1]
[1,6,7,2,5,3,4]=>[3,2,2]
[1,6,7,2,5,4,3]=>[3,2,1,1]
[1,6,7,3,2,4,5]=>[3,1,3]
[1,6,7,3,2,5,4]=>[3,1,2,1]
[1,6,7,3,4,2,5]=>[3,2,2]
[1,6,7,3,4,5,2]=>[3,3,1]
[1,6,7,3,5,2,4]=>[3,2,2]
[1,6,7,3,5,4,2]=>[3,2,1,1]
[1,6,7,4,2,3,5]=>[3,1,3]
[1,6,7,4,2,5,3]=>[3,1,2,1]
[1,6,7,4,3,2,5]=>[3,1,1,2]
[1,6,7,4,3,5,2]=>[3,1,2,1]
[1,6,7,4,5,2,3]=>[3,2,2]
[1,6,7,4,5,3,2]=>[3,2,1,1]
[1,6,7,5,2,3,4]=>[3,1,3]
[1,6,7,5,2,4,3]=>[3,1,2,1]
[1,6,7,5,3,2,4]=>[3,1,1,2]
[1,6,7,5,3,4,2]=>[3,1,2,1]
[1,6,7,5,4,2,3]=>[3,1,1,2]
[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[1,7,2,3,4,5,6]=>[2,5]
[1,7,2,3,4,6,5]=>[2,4,1]
[1,7,2,3,5,4,6]=>[2,3,2]
[1,7,2,3,5,6,4]=>[2,4,1]
[1,7,2,3,6,4,5]=>[2,3,2]
[1,7,2,3,6,5,4]=>[2,3,1,1]
[1,7,2,4,3,5,6]=>[2,2,3]
[1,7,2,4,3,6,5]=>[2,2,2,1]
[1,7,2,4,5,3,6]=>[2,3,2]
[1,7,2,4,5,6,3]=>[2,4,1]
[1,7,2,4,6,3,5]=>[2,3,2]
[1,7,2,4,6,5,3]=>[2,3,1,1]
[1,7,2,5,3,4,6]=>[2,2,3]
[1,7,2,5,3,6,4]=>[2,2,2,1]
[1,7,2,5,4,3,6]=>[2,2,1,2]
[1,7,2,5,4,6,3]=>[2,2,2,1]
[1,7,2,5,6,3,4]=>[2,3,2]
[1,7,2,5,6,4,3]=>[2,3,1,1]
[1,7,2,6,3,4,5]=>[2,2,3]
[1,7,2,6,3,5,4]=>[2,2,2,1]
[1,7,2,6,4,3,5]=>[2,2,1,2]
[1,7,2,6,4,5,3]=>[2,2,2,1]
[1,7,2,6,5,3,4]=>[2,2,1,2]
[1,7,2,6,5,4,3]=>[2,2,1,1,1]
[1,7,3,2,4,5,6]=>[2,1,4]
[1,7,3,2,4,6,5]=>[2,1,3,1]
[1,7,3,2,5,4,6]=>[2,1,2,2]
[1,7,3,2,5,6,4]=>[2,1,3,1]
[1,7,3,2,6,4,5]=>[2,1,2,2]
[1,7,3,2,6,5,4]=>[2,1,2,1,1]
[1,7,3,4,2,5,6]=>[2,2,3]
[1,7,3,4,2,6,5]=>[2,2,2,1]
[1,7,3,4,5,2,6]=>[2,3,2]
[1,7,3,4,5,6,2]=>[2,4,1]
[1,7,3,4,6,2,5]=>[2,3,2]
[1,7,3,4,6,5,2]=>[2,3,1,1]
[1,7,3,5,2,4,6]=>[2,2,3]
[1,7,3,5,2,6,4]=>[2,2,2,1]
[1,7,3,5,4,2,6]=>[2,2,1,2]
[1,7,3,5,4,6,2]=>[2,2,2,1]
[1,7,3,5,6,2,4]=>[2,3,2]
[1,7,3,5,6,4,2]=>[2,3,1,1]
[1,7,3,6,2,4,5]=>[2,2,3]
[1,7,3,6,2,5,4]=>[2,2,2,1]
[1,7,3,6,4,2,5]=>[2,2,1,2]
[1,7,3,6,4,5,2]=>[2,2,2,1]
[1,7,3,6,5,2,4]=>[2,2,1,2]
[1,7,3,6,5,4,2]=>[2,2,1,1,1]
[1,7,4,2,3,5,6]=>[2,1,4]
[1,7,4,2,3,6,5]=>[2,1,3,1]
[1,7,4,2,5,3,6]=>[2,1,2,2]
[1,7,4,2,5,6,3]=>[2,1,3,1]
[1,7,4,2,6,3,5]=>[2,1,2,2]
[1,7,4,2,6,5,3]=>[2,1,2,1,1]
[1,7,4,3,2,5,6]=>[2,1,1,3]
[1,7,4,3,2,6,5]=>[2,1,1,2,1]
[1,7,4,3,5,2,6]=>[2,1,2,2]
[1,7,4,3,5,6,2]=>[2,1,3,1]
[1,7,4,3,6,2,5]=>[2,1,2,2]
[1,7,4,3,6,5,2]=>[2,1,2,1,1]
[1,7,4,5,2,3,6]=>[2,2,3]
[1,7,4,5,2,6,3]=>[2,2,2,1]
[1,7,4,5,3,2,6]=>[2,2,1,2]
[1,7,4,5,3,6,2]=>[2,2,2,1]
[1,7,4,5,6,2,3]=>[2,3,2]
[1,7,4,5,6,3,2]=>[2,3,1,1]
[1,7,4,6,2,3,5]=>[2,2,3]
[1,7,4,6,2,5,3]=>[2,2,2,1]
[1,7,4,6,3,2,5]=>[2,2,1,2]
[1,7,4,6,3,5,2]=>[2,2,2,1]
[1,7,4,6,5,2,3]=>[2,2,1,2]
[1,7,4,6,5,3,2]=>[2,2,1,1,1]
[1,7,5,2,3,4,6]=>[2,1,4]
[1,7,5,2,3,6,4]=>[2,1,3,1]
[1,7,5,2,4,3,6]=>[2,1,2,2]
[1,7,5,2,4,6,3]=>[2,1,3,1]
[1,7,5,2,6,3,4]=>[2,1,2,2]
[1,7,5,2,6,4,3]=>[2,1,2,1,1]
[1,7,5,3,2,4,6]=>[2,1,1,3]
[1,7,5,3,2,6,4]=>[2,1,1,2,1]
[1,7,5,3,4,2,6]=>[2,1,2,2]
[1,7,5,3,4,6,2]=>[2,1,3,1]
[1,7,5,3,6,2,4]=>[2,1,2,2]
[1,7,5,3,6,4,2]=>[2,1,2,1,1]
[1,7,5,4,2,3,6]=>[2,1,1,3]
[1,7,5,4,2,6,3]=>[2,1,1,2,1]
[1,7,5,4,3,2,6]=>[2,1,1,1,2]
[1,7,5,4,3,6,2]=>[2,1,1,2,1]
[1,7,5,4,6,2,3]=>[2,1,2,2]
[1,7,5,4,6,3,2]=>[2,1,2,1,1]
[1,7,5,6,2,3,4]=>[2,2,3]
[1,7,5,6,2,4,3]=>[2,2,2,1]
[1,7,5,6,3,2,4]=>[2,2,1,2]
[1,7,5,6,3,4,2]=>[2,2,2,1]
[1,7,5,6,4,2,3]=>[2,2,1,2]
[1,7,5,6,4,3,2]=>[2,2,1,1,1]
[1,7,6,2,3,4,5]=>[2,1,4]
[1,7,6,2,3,5,4]=>[2,1,3,1]
[1,7,6,2,4,3,5]=>[2,1,2,2]
[1,7,6,2,4,5,3]=>[2,1,3,1]
[1,7,6,2,5,3,4]=>[2,1,2,2]
[1,7,6,2,5,4,3]=>[2,1,2,1,1]
[1,7,6,3,2,4,5]=>[2,1,1,3]
[1,7,6,3,2,5,4]=>[2,1,1,2,1]
[1,7,6,3,4,2,5]=>[2,1,2,2]
[1,7,6,3,4,5,2]=>[2,1,3,1]
[1,7,6,3,5,2,4]=>[2,1,2,2]
[1,7,6,3,5,4,2]=>[2,1,2,1,1]
[1,7,6,4,2,3,5]=>[2,1,1,3]
[1,7,6,4,2,5,3]=>[2,1,1,2,1]
[1,7,6,4,3,2,5]=>[2,1,1,1,2]
[1,7,6,4,3,5,2]=>[2,1,1,2,1]
[1,7,6,4,5,2,3]=>[2,1,2,2]
[1,7,6,4,5,3,2]=>[2,1,2,1,1]
[1,7,6,5,2,3,4]=>[2,1,1,3]
[1,7,6,5,2,4,3]=>[2,1,1,2,1]
[1,7,6,5,3,2,4]=>[2,1,1,1,2]
[1,7,6,5,3,4,2]=>[2,1,1,2,1]
[1,7,6,5,4,2,3]=>[2,1,1,1,2]
[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[2,1,3,4,5,6,7]=>[1,6]
[2,1,3,4,5,7,6]=>[1,5,1]
[2,1,3,4,6,5,7]=>[1,4,2]
[2,1,3,4,6,7,5]=>[1,5,1]
[2,1,3,4,7,5,6]=>[1,4,2]
[2,1,3,4,7,6,5]=>[1,4,1,1]
[2,1,3,5,4,6,7]=>[1,3,3]
[2,1,3,5,4,7,6]=>[1,3,2,1]
[2,1,3,5,6,4,7]=>[1,4,2]
[2,1,3,5,6,7,4]=>[1,5,1]
[2,1,3,5,7,4,6]=>[1,4,2]
[2,1,3,5,7,6,4]=>[1,4,1,1]
[2,1,3,6,4,5,7]=>[1,3,3]
[2,1,3,6,4,7,5]=>[1,3,2,1]
[2,1,3,6,5,4,7]=>[1,3,1,2]
[2,1,3,6,5,7,4]=>[1,3,2,1]
[2,1,3,6,7,4,5]=>[1,4,2]
[2,1,3,6,7,5,4]=>[1,4,1,1]
[2,1,3,7,4,5,6]=>[1,3,3]
[2,1,3,7,4,6,5]=>[1,3,2,1]
[2,1,3,7,5,4,6]=>[1,3,1,2]
[2,1,3,7,5,6,4]=>[1,3,2,1]
[2,1,3,7,6,4,5]=>[1,3,1,2]
[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[2,1,4,3,5,6,7]=>[1,2,4]
[2,1,4,3,5,7,6]=>[1,2,3,1]
[2,1,4,3,6,5,7]=>[1,2,2,2]
[2,1,4,3,6,7,5]=>[1,2,3,1]
[2,1,4,3,7,5,6]=>[1,2,2,2]
[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[2,1,4,5,3,6,7]=>[1,3,3]
[2,1,4,5,3,7,6]=>[1,3,2,1]
[2,1,4,5,6,3,7]=>[1,4,2]
[2,1,4,5,6,7,3]=>[1,5,1]
[2,1,4,5,7,3,6]=>[1,4,2]
[2,1,4,5,7,6,3]=>[1,4,1,1]
[2,1,4,6,3,5,7]=>[1,3,3]
[2,1,4,6,3,7,5]=>[1,3,2,1]
[2,1,4,6,5,3,7]=>[1,3,1,2]
[2,1,4,6,5,7,3]=>[1,3,2,1]
[2,1,4,6,7,3,5]=>[1,4,2]
[2,1,4,6,7,5,3]=>[1,4,1,1]
[2,1,4,7,3,5,6]=>[1,3,3]
[2,1,4,7,3,6,5]=>[1,3,2,1]
[2,1,4,7,5,3,6]=>[1,3,1,2]
[2,1,4,7,5,6,3]=>[1,3,2,1]
[2,1,4,7,6,3,5]=>[1,3,1,2]
[2,1,4,7,6,5,3]=>[1,3,1,1,1]
[2,1,5,3,4,6,7]=>[1,2,4]
[2,1,5,3,4,7,6]=>[1,2,3,1]
[2,1,5,3,6,4,7]=>[1,2,2,2]
[2,1,5,3,6,7,4]=>[1,2,3,1]
[2,1,5,3,7,4,6]=>[1,2,2,2]
[2,1,5,3,7,6,4]=>[1,2,2,1,1]
[2,1,5,4,3,6,7]=>[1,2,1,3]
[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[2,1,5,4,6,3,7]=>[1,2,2,2]
[2,1,5,4,6,7,3]=>[1,2,3,1]
[2,1,5,4,7,3,6]=>[1,2,2,2]
[2,1,5,4,7,6,3]=>[1,2,2,1,1]
[2,1,5,6,3,4,7]=>[1,3,3]
[2,1,5,6,3,7,4]=>[1,3,2,1]
[2,1,5,6,4,3,7]=>[1,3,1,2]
[2,1,5,6,4,7,3]=>[1,3,2,1]
[2,1,5,6,7,3,4]=>[1,4,2]
[2,1,5,6,7,4,3]=>[1,4,1,1]
[2,1,5,7,3,4,6]=>[1,3,3]
[2,1,5,7,3,6,4]=>[1,3,2,1]
[2,1,5,7,4,3,6]=>[1,3,1,2]
[2,1,5,7,4,6,3]=>[1,3,2,1]
[2,1,5,7,6,3,4]=>[1,3,1,2]
[2,1,5,7,6,4,3]=>[1,3,1,1,1]
[2,1,6,3,4,5,7]=>[1,2,4]
[2,1,6,3,4,7,5]=>[1,2,3,1]
[2,1,6,3,5,4,7]=>[1,2,2,2]
[2,1,6,3,5,7,4]=>[1,2,3,1]
[2,1,6,3,7,4,5]=>[1,2,2,2]
[2,1,6,3,7,5,4]=>[1,2,2,1,1]
[2,1,6,4,3,5,7]=>[1,2,1,3]
[2,1,6,4,3,7,5]=>[1,2,1,2,1]
[2,1,6,4,5,3,7]=>[1,2,2,2]
[2,1,6,4,5,7,3]=>[1,2,3,1]
[2,1,6,4,7,3,5]=>[1,2,2,2]
[2,1,6,4,7,5,3]=>[1,2,2,1,1]
[2,1,6,5,3,4,7]=>[1,2,1,3]
[2,1,6,5,3,7,4]=>[1,2,1,2,1]
[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[2,1,6,5,4,7,3]=>[1,2,1,2,1]
[2,1,6,5,7,3,4]=>[1,2,2,2]
[2,1,6,5,7,4,3]=>[1,2,2,1,1]
[2,1,6,7,3,4,5]=>[1,3,3]
[2,1,6,7,3,5,4]=>[1,3,2,1]
[2,1,6,7,4,3,5]=>[1,3,1,2]
[2,1,6,7,4,5,3]=>[1,3,2,1]
[2,1,6,7,5,3,4]=>[1,3,1,2]
[2,1,6,7,5,4,3]=>[1,3,1,1,1]
[2,1,7,3,4,5,6]=>[1,2,4]
[2,1,7,3,4,6,5]=>[1,2,3,1]
[2,1,7,3,5,4,6]=>[1,2,2,2]
[2,1,7,3,5,6,4]=>[1,2,3,1]
[2,1,7,3,6,4,5]=>[1,2,2,2]
[2,1,7,3,6,5,4]=>[1,2,2,1,1]
[2,1,7,4,3,5,6]=>[1,2,1,3]
[2,1,7,4,3,6,5]=>[1,2,1,2,1]
[2,1,7,4,5,3,6]=>[1,2,2,2]
[2,1,7,4,5,6,3]=>[1,2,3,1]
[2,1,7,4,6,3,5]=>[1,2,2,2]
[2,1,7,4,6,5,3]=>[1,2,2,1,1]
[2,1,7,5,3,4,6]=>[1,2,1,3]
[2,1,7,5,3,6,4]=>[1,2,1,2,1]
[2,1,7,5,4,3,6]=>[1,2,1,1,2]
[2,1,7,5,4,6,3]=>[1,2,1,2,1]
[2,1,7,5,6,3,4]=>[1,2,2,2]
[2,1,7,5,6,4,3]=>[1,2,2,1,1]
[2,1,7,6,3,4,5]=>[1,2,1,3]
[2,1,7,6,3,5,4]=>[1,2,1,2,1]
[2,1,7,6,4,3,5]=>[1,2,1,1,2]
[2,1,7,6,4,5,3]=>[1,2,1,2,1]
[2,1,7,6,5,3,4]=>[1,2,1,1,2]
[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[2,3,1,4,5,6,7]=>[2,5]
[2,3,1,4,5,7,6]=>[2,4,1]
[2,3,1,4,6,5,7]=>[2,3,2]
[2,3,1,4,6,7,5]=>[2,4,1]
[2,3,1,4,7,5,6]=>[2,3,2]
[2,3,1,4,7,6,5]=>[2,3,1,1]
[2,3,1,5,4,6,7]=>[2,2,3]
[2,3,1,5,4,7,6]=>[2,2,2,1]
[2,3,1,5,6,4,7]=>[2,3,2]
[2,3,1,5,6,7,4]=>[2,4,1]
[2,3,1,5,7,4,6]=>[2,3,2]
[2,3,1,5,7,6,4]=>[2,3,1,1]
[2,3,1,6,4,5,7]=>[2,2,3]
[2,3,1,6,4,7,5]=>[2,2,2,1]
[2,3,1,6,5,4,7]=>[2,2,1,2]
[2,3,1,6,5,7,4]=>[2,2,2,1]
[2,3,1,6,7,4,5]=>[2,3,2]
[2,3,1,6,7,5,4]=>[2,3,1,1]
[2,3,1,7,4,5,6]=>[2,2,3]
[2,3,1,7,4,6,5]=>[2,2,2,1]
[2,3,1,7,5,4,6]=>[2,2,1,2]
[2,3,1,7,5,6,4]=>[2,2,2,1]
[2,3,1,7,6,4,5]=>[2,2,1,2]
[2,3,1,7,6,5,4]=>[2,2,1,1,1]
[2,3,4,1,5,6,7]=>[3,4]
[2,3,4,1,5,7,6]=>[3,3,1]
[2,3,4,1,6,5,7]=>[3,2,2]
[2,3,4,1,6,7,5]=>[3,3,1]
[2,3,4,1,7,5,6]=>[3,2,2]
[2,3,4,1,7,6,5]=>[3,2,1,1]
[2,3,4,5,1,6,7]=>[4,3]
[2,3,4,5,1,7,6]=>[4,2,1]
[2,3,4,5,6,1,7]=>[5,2]
[2,3,4,5,6,7,1]=>[6,1]
[2,3,4,5,7,1,6]=>[5,2]
[2,3,4,5,7,6,1]=>[5,1,1]
[2,3,4,6,1,5,7]=>[4,3]
[2,3,4,6,1,7,5]=>[4,2,1]
[2,3,4,6,5,1,7]=>[4,1,2]
[2,3,4,6,5,7,1]=>[4,2,1]
[2,3,4,6,7,1,5]=>[5,2]
[2,3,4,6,7,5,1]=>[5,1,1]
[2,3,4,7,1,5,6]=>[4,3]
[2,3,4,7,1,6,5]=>[4,2,1]
[2,3,4,7,5,1,6]=>[4,1,2]
[2,3,4,7,5,6,1]=>[4,2,1]
[2,3,4,7,6,1,5]=>[4,1,2]
[2,3,4,7,6,5,1]=>[4,1,1,1]
[2,3,5,1,4,6,7]=>[3,4]
[2,3,5,1,4,7,6]=>[3,3,1]
[2,3,5,1,6,4,7]=>[3,2,2]
[2,3,5,1,6,7,4]=>[3,3,1]
[2,3,5,1,7,4,6]=>[3,2,2]
[2,3,5,1,7,6,4]=>[3,2,1,1]
[2,3,5,4,1,6,7]=>[3,1,3]
[2,3,5,4,1,7,6]=>[3,1,2,1]
[2,3,5,4,6,1,7]=>[3,2,2]
[2,3,5,4,6,7,1]=>[3,3,1]
[2,3,5,4,7,1,6]=>[3,2,2]
[2,3,5,4,7,6,1]=>[3,2,1,1]
[2,3,5,6,1,4,7]=>[4,3]
[2,3,5,6,1,7,4]=>[4,2,1]
[2,3,5,6,4,1,7]=>[4,1,2]
[2,3,5,6,4,7,1]=>[4,2,1]
[2,3,5,6,7,1,4]=>[5,2]
[2,3,5,6,7,4,1]=>[5,1,1]
[2,3,5,7,1,4,6]=>[4,3]
[2,3,5,7,1,6,4]=>[4,2,1]
[2,3,5,7,4,1,6]=>[4,1,2]
[2,3,5,7,4,6,1]=>[4,2,1]
[2,3,5,7,6,1,4]=>[4,1,2]
[2,3,5,7,6,4,1]=>[4,1,1,1]
[2,3,6,1,4,5,7]=>[3,4]
[2,3,6,1,4,7,5]=>[3,3,1]
[2,3,6,1,5,4,7]=>[3,2,2]
[2,3,6,1,5,7,4]=>[3,3,1]
[2,3,6,1,7,4,5]=>[3,2,2]
[2,3,6,1,7,5,4]=>[3,2,1,1]
[2,3,6,4,1,5,7]=>[3,1,3]
[2,3,6,4,1,7,5]=>[3,1,2,1]
[2,3,6,4,5,1,7]=>[3,2,2]
[2,3,6,4,5,7,1]=>[3,3,1]
[2,3,6,4,7,1,5]=>[3,2,2]
[2,3,6,4,7,5,1]=>[3,2,1,1]
[2,3,6,5,1,4,7]=>[3,1,3]
[2,3,6,5,1,7,4]=>[3,1,2,1]
[2,3,6,5,4,1,7]=>[3,1,1,2]
[2,3,6,5,4,7,1]=>[3,1,2,1]
[2,3,6,5,7,1,4]=>[3,2,2]
[2,3,6,5,7,4,1]=>[3,2,1,1]
[2,3,6,7,1,4,5]=>[4,3]
[2,3,6,7,1,5,4]=>[4,2,1]
[2,3,6,7,4,1,5]=>[4,1,2]
[2,3,6,7,4,5,1]=>[4,2,1]
[2,3,6,7,5,1,4]=>[4,1,2]
[2,3,6,7,5,4,1]=>[4,1,1,1]
[2,3,7,1,4,5,6]=>[3,4]
[2,3,7,1,4,6,5]=>[3,3,1]
[2,3,7,1,5,4,6]=>[3,2,2]
[2,3,7,1,5,6,4]=>[3,3,1]
[2,3,7,1,6,4,5]=>[3,2,2]
[2,3,7,1,6,5,4]=>[3,2,1,1]
[2,3,7,4,1,5,6]=>[3,1,3]
[2,3,7,4,1,6,5]=>[3,1,2,1]
[2,3,7,4,5,1,6]=>[3,2,2]
[2,3,7,4,5,6,1]=>[3,3,1]
[2,3,7,4,6,1,5]=>[3,2,2]
[2,3,7,4,6,5,1]=>[3,2,1,1]
[2,3,7,5,1,4,6]=>[3,1,3]
[2,3,7,5,1,6,4]=>[3,1,2,1]
[2,3,7,5,4,1,6]=>[3,1,1,2]
[2,3,7,5,4,6,1]=>[3,1,2,1]
[2,3,7,5,6,1,4]=>[3,2,2]
[2,3,7,5,6,4,1]=>[3,2,1,1]
[2,3,7,6,1,4,5]=>[3,1,3]
[2,3,7,6,1,5,4]=>[3,1,2,1]
[2,3,7,6,4,1,5]=>[3,1,1,2]
[2,3,7,6,4,5,1]=>[3,1,2,1]
[2,3,7,6,5,1,4]=>[3,1,1,2]
[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[2,4,1,3,5,6,7]=>[2,5]
[2,4,1,3,5,7,6]=>[2,4,1]
[2,4,1,3,6,5,7]=>[2,3,2]
[2,4,1,3,6,7,5]=>[2,4,1]
[2,4,1,3,7,5,6]=>[2,3,2]
[2,4,1,3,7,6,5]=>[2,3,1,1]
[2,4,1,5,3,6,7]=>[2,2,3]
[2,4,1,5,3,7,6]=>[2,2,2,1]
[2,4,1,5,6,3,7]=>[2,3,2]
[2,4,1,5,6,7,3]=>[2,4,1]
[2,4,1,5,7,3,6]=>[2,3,2]
[2,4,1,5,7,6,3]=>[2,3,1,1]
[2,4,1,6,3,5,7]=>[2,2,3]
[2,4,1,6,3,7,5]=>[2,2,2,1]
[2,4,1,6,5,3,7]=>[2,2,1,2]
[2,4,1,6,5,7,3]=>[2,2,2,1]
[2,4,1,6,7,3,5]=>[2,3,2]
[2,4,1,6,7,5,3]=>[2,3,1,1]
[2,4,1,7,3,5,6]=>[2,2,3]
[2,4,1,7,3,6,5]=>[2,2,2,1]
[2,4,1,7,5,3,6]=>[2,2,1,2]
[2,4,1,7,5,6,3]=>[2,2,2,1]
[2,4,1,7,6,3,5]=>[2,2,1,2]
[2,4,1,7,6,5,3]=>[2,2,1,1,1]
[2,4,3,1,5,6,7]=>[2,1,4]
[2,4,3,1,5,7,6]=>[2,1,3,1]
[2,4,3,1,6,5,7]=>[2,1,2,2]
[2,4,3,1,6,7,5]=>[2,1,3,1]
[2,4,3,1,7,5,6]=>[2,1,2,2]
[2,4,3,1,7,6,5]=>[2,1,2,1,1]
[2,4,3,5,1,6,7]=>[2,2,3]
[2,4,3,5,1,7,6]=>[2,2,2,1]
[2,4,3,5,6,1,7]=>[2,3,2]
[2,4,3,5,6,7,1]=>[2,4,1]
[2,4,3,5,7,1,6]=>[2,3,2]
[2,4,3,5,7,6,1]=>[2,3,1,1]
[2,4,3,6,1,5,7]=>[2,2,3]
[2,4,3,6,1,7,5]=>[2,2,2,1]
[2,4,3,6,5,1,7]=>[2,2,1,2]
[2,4,3,6,5,7,1]=>[2,2,2,1]
[2,4,3,6,7,1,5]=>[2,3,2]
[2,4,3,6,7,5,1]=>[2,3,1,1]
[2,4,3,7,1,5,6]=>[2,2,3]
[2,4,3,7,1,6,5]=>[2,2,2,1]
[2,4,3,7,5,1,6]=>[2,2,1,2]
[2,4,3,7,5,6,1]=>[2,2,2,1]
[2,4,3,7,6,1,5]=>[2,2,1,2]
[2,4,3,7,6,5,1]=>[2,2,1,1,1]
[2,4,5,1,3,6,7]=>[3,4]
[2,4,5,1,3,7,6]=>[3,3,1]
[2,4,5,1,6,3,7]=>[3,2,2]
[2,4,5,1,6,7,3]=>[3,3,1]
[2,4,5,1,7,3,6]=>[3,2,2]
[2,4,5,1,7,6,3]=>[3,2,1,1]
[2,4,5,3,1,6,7]=>[3,1,3]
[2,4,5,3,1,7,6]=>[3,1,2,1]
[2,4,5,3,6,1,7]=>[3,2,2]
[2,4,5,3,6,7,1]=>[3,3,1]
[2,4,5,3,7,1,6]=>[3,2,2]
[2,4,5,3,7,6,1]=>[3,2,1,1]
[2,4,5,6,1,3,7]=>[4,3]
[2,4,5,6,1,7,3]=>[4,2,1]
[2,4,5,6,3,1,7]=>[4,1,2]
[2,4,5,6,3,7,1]=>[4,2,1]
[2,4,5,6,7,1,3]=>[5,2]
[2,4,5,6,7,3,1]=>[5,1,1]
[2,4,5,7,1,3,6]=>[4,3]
[2,4,5,7,1,6,3]=>[4,2,1]
[2,4,5,7,3,1,6]=>[4,1,2]
[2,4,5,7,3,6,1]=>[4,2,1]
[2,4,5,7,6,1,3]=>[4,1,2]
[2,4,5,7,6,3,1]=>[4,1,1,1]
[2,4,6,1,3,5,7]=>[3,4]
[2,4,6,1,3,7,5]=>[3,3,1]
[2,4,6,1,5,3,7]=>[3,2,2]
[2,4,6,1,5,7,3]=>[3,3,1]
[2,4,6,1,7,3,5]=>[3,2,2]
[2,4,6,1,7,5,3]=>[3,2,1,1]
[2,4,6,3,1,5,7]=>[3,1,3]
[2,4,6,3,1,7,5]=>[3,1,2,1]
[2,4,6,3,5,1,7]=>[3,2,2]
[2,4,6,3,5,7,1]=>[3,3,1]
[2,4,6,3,7,1,5]=>[3,2,2]
[2,4,6,3,7,5,1]=>[3,2,1,1]
[2,4,6,5,1,3,7]=>[3,1,3]
[2,4,6,5,1,7,3]=>[3,1,2,1]
[2,4,6,5,3,1,7]=>[3,1,1,2]
[2,4,6,5,3,7,1]=>[3,1,2,1]
[2,4,6,5,7,1,3]=>[3,2,2]
[2,4,6,5,7,3,1]=>[3,2,1,1]
[2,4,6,7,1,3,5]=>[4,3]
[2,4,6,7,1,5,3]=>[4,2,1]
[2,4,6,7,3,1,5]=>[4,1,2]
[2,4,6,7,3,5,1]=>[4,2,1]
[2,4,6,7,5,1,3]=>[4,1,2]
[2,4,6,7,5,3,1]=>[4,1,1,1]
[2,4,7,1,3,5,6]=>[3,4]
[2,4,7,1,3,6,5]=>[3,3,1]
[2,4,7,1,5,3,6]=>[3,2,2]
[2,4,7,1,5,6,3]=>[3,3,1]
[2,4,7,1,6,3,5]=>[3,2,2]
[2,4,7,1,6,5,3]=>[3,2,1,1]
[2,4,7,3,1,5,6]=>[3,1,3]
[2,4,7,3,1,6,5]=>[3,1,2,1]
[2,4,7,3,5,1,6]=>[3,2,2]
[2,4,7,3,5,6,1]=>[3,3,1]
[2,4,7,3,6,1,5]=>[3,2,2]
[2,4,7,3,6,5,1]=>[3,2,1,1]
[2,4,7,5,1,3,6]=>[3,1,3]
[2,4,7,5,1,6,3]=>[3,1,2,1]
[2,4,7,5,3,1,6]=>[3,1,1,2]
[2,4,7,5,3,6,1]=>[3,1,2,1]
[2,4,7,5,6,1,3]=>[3,2,2]
[2,4,7,5,6,3,1]=>[3,2,1,1]
[2,4,7,6,1,3,5]=>[3,1,3]
[2,4,7,6,1,5,3]=>[3,1,2,1]
[2,4,7,6,3,1,5]=>[3,1,1,2]
[2,4,7,6,3,5,1]=>[3,1,2,1]
[2,4,7,6,5,1,3]=>[3,1,1,2]
[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[2,5,1,3,4,6,7]=>[2,5]
[2,5,1,3,4,7,6]=>[2,4,1]
[2,5,1,3,6,4,7]=>[2,3,2]
[2,5,1,3,6,7,4]=>[2,4,1]
[2,5,1,3,7,4,6]=>[2,3,2]
[2,5,1,3,7,6,4]=>[2,3,1,1]
[2,5,1,4,3,6,7]=>[2,2,3]
[2,5,1,4,3,7,6]=>[2,2,2,1]
[2,5,1,4,6,3,7]=>[2,3,2]
[2,5,1,4,6,7,3]=>[2,4,1]
[2,5,1,4,7,3,6]=>[2,3,2]
[2,5,1,4,7,6,3]=>[2,3,1,1]
[2,5,1,6,3,4,7]=>[2,2,3]
[2,5,1,6,3,7,4]=>[2,2,2,1]
[2,5,1,6,4,3,7]=>[2,2,1,2]
[2,5,1,6,4,7,3]=>[2,2,2,1]
[2,5,1,6,7,3,4]=>[2,3,2]
[2,5,1,6,7,4,3]=>[2,3,1,1]
[2,5,1,7,3,4,6]=>[2,2,3]
[2,5,1,7,3,6,4]=>[2,2,2,1]
[2,5,1,7,4,3,6]=>[2,2,1,2]
[2,5,1,7,4,6,3]=>[2,2,2,1]
[2,5,1,7,6,3,4]=>[2,2,1,2]
[2,5,1,7,6,4,3]=>[2,2,1,1,1]
[2,5,3,1,4,6,7]=>[2,1,4]
[2,5,3,1,4,7,6]=>[2,1,3,1]
[2,5,3,1,6,4,7]=>[2,1,2,2]
[2,5,3,1,6,7,4]=>[2,1,3,1]
[2,5,3,1,7,4,6]=>[2,1,2,2]
[2,5,3,1,7,6,4]=>[2,1,2,1,1]
[2,5,3,4,1,6,7]=>[2,2,3]
[2,5,3,4,1,7,6]=>[2,2,2,1]
[2,5,3,4,6,1,7]=>[2,3,2]
[2,5,3,4,6,7,1]=>[2,4,1]
[2,5,3,4,7,1,6]=>[2,3,2]
[2,5,3,4,7,6,1]=>[2,3,1,1]
[2,5,3,6,1,4,7]=>[2,2,3]
[2,5,3,6,1,7,4]=>[2,2,2,1]
[2,5,3,6,4,1,7]=>[2,2,1,2]
[2,5,3,6,4,7,1]=>[2,2,2,1]
[2,5,3,6,7,1,4]=>[2,3,2]
[2,5,3,6,7,4,1]=>[2,3,1,1]
[2,5,3,7,1,4,6]=>[2,2,3]
[2,5,3,7,1,6,4]=>[2,2,2,1]
[2,5,3,7,4,1,6]=>[2,2,1,2]
[2,5,3,7,4,6,1]=>[2,2,2,1]
[2,5,3,7,6,1,4]=>[2,2,1,2]
[2,5,3,7,6,4,1]=>[2,2,1,1,1]
[2,5,4,1,3,6,7]=>[2,1,4]
[2,5,4,1,3,7,6]=>[2,1,3,1]
[2,5,4,1,6,3,7]=>[2,1,2,2]
[2,5,4,1,6,7,3]=>[2,1,3,1]
[2,5,4,1,7,3,6]=>[2,1,2,2]
[2,5,4,1,7,6,3]=>[2,1,2,1,1]
[2,5,4,3,1,6,7]=>[2,1,1,3]
[2,5,4,3,1,7,6]=>[2,1,1,2,1]
[2,5,4,3,6,1,7]=>[2,1,2,2]
[2,5,4,3,6,7,1]=>[2,1,3,1]
[2,5,4,3,7,1,6]=>[2,1,2,2]
[2,5,4,3,7,6,1]=>[2,1,2,1,1]
[2,5,4,6,1,3,7]=>[2,2,3]
[2,5,4,6,1,7,3]=>[2,2,2,1]
[2,5,4,6,3,1,7]=>[2,2,1,2]
[2,5,4,6,3,7,1]=>[2,2,2,1]
[2,5,4,6,7,1,3]=>[2,3,2]
[2,5,4,6,7,3,1]=>[2,3,1,1]
[2,5,4,7,1,3,6]=>[2,2,3]
[2,5,4,7,1,6,3]=>[2,2,2,1]
[2,5,4,7,3,1,6]=>[2,2,1,2]
[2,5,4,7,3,6,1]=>[2,2,2,1]
[2,5,4,7,6,1,3]=>[2,2,1,2]
[2,5,4,7,6,3,1]=>[2,2,1,1,1]
[2,5,6,1,3,4,7]=>[3,4]
[2,5,6,1,3,7,4]=>[3,3,1]
[2,5,6,1,4,3,7]=>[3,2,2]
[2,5,6,1,4,7,3]=>[3,3,1]
[2,5,6,1,7,3,4]=>[3,2,2]
[2,5,6,1,7,4,3]=>[3,2,1,1]
[2,5,6,3,1,4,7]=>[3,1,3]
[2,5,6,3,1,7,4]=>[3,1,2,1]
[2,5,6,3,4,1,7]=>[3,2,2]
[2,5,6,3,4,7,1]=>[3,3,1]
[2,5,6,3,7,1,4]=>[3,2,2]
[2,5,6,3,7,4,1]=>[3,2,1,1]
[2,5,6,4,1,3,7]=>[3,1,3]
[2,5,6,4,1,7,3]=>[3,1,2,1]
[2,5,6,4,3,1,7]=>[3,1,1,2]
[2,5,6,4,3,7,1]=>[3,1,2,1]
[2,5,6,4,7,1,3]=>[3,2,2]
[2,5,6,4,7,3,1]=>[3,2,1,1]
[2,5,6,7,1,3,4]=>[4,3]
[2,5,6,7,1,4,3]=>[4,2,1]
[2,5,6,7,3,1,4]=>[4,1,2]
[2,5,6,7,3,4,1]=>[4,2,1]
[2,5,6,7,4,1,3]=>[4,1,2]
[2,5,6,7,4,3,1]=>[4,1,1,1]
[2,5,7,1,3,4,6]=>[3,4]
[2,5,7,1,3,6,4]=>[3,3,1]
[2,5,7,1,4,3,6]=>[3,2,2]
[2,5,7,1,4,6,3]=>[3,3,1]
[2,5,7,1,6,3,4]=>[3,2,2]
[2,5,7,1,6,4,3]=>[3,2,1,1]
[2,5,7,3,1,4,6]=>[3,1,3]
[2,5,7,3,1,6,4]=>[3,1,2,1]
[2,5,7,3,4,1,6]=>[3,2,2]
[2,5,7,3,4,6,1]=>[3,3,1]
[2,5,7,3,6,1,4]=>[3,2,2]
[2,5,7,3,6,4,1]=>[3,2,1,1]
[2,5,7,4,1,3,6]=>[3,1,3]
[2,5,7,4,1,6,3]=>[3,1,2,1]
[2,5,7,4,3,1,6]=>[3,1,1,2]
[2,5,7,4,3,6,1]=>[3,1,2,1]
[2,5,7,4,6,1,3]=>[3,2,2]
[2,5,7,4,6,3,1]=>[3,2,1,1]
[2,5,7,6,1,3,4]=>[3,1,3]
[2,5,7,6,1,4,3]=>[3,1,2,1]
[2,5,7,6,3,1,4]=>[3,1,1,2]
[2,5,7,6,3,4,1]=>[3,1,2,1]
[2,5,7,6,4,1,3]=>[3,1,1,2]
[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[2,6,1,3,4,5,7]=>[2,5]
[2,6,1,3,4,7,5]=>[2,4,1]
[2,6,1,3,5,4,7]=>[2,3,2]
[2,6,1,3,5,7,4]=>[2,4,1]
[2,6,1,3,7,4,5]=>[2,3,2]
[2,6,1,3,7,5,4]=>[2,3,1,1]
[2,6,1,4,3,5,7]=>[2,2,3]
[2,6,1,4,3,7,5]=>[2,2,2,1]
[2,6,1,4,5,3,7]=>[2,3,2]
[2,6,1,4,5,7,3]=>[2,4,1]
[2,6,1,4,7,3,5]=>[2,3,2]
[2,6,1,4,7,5,3]=>[2,3,1,1]
[2,6,1,5,3,4,7]=>[2,2,3]
[2,6,1,5,3,7,4]=>[2,2,2,1]
[2,6,1,5,4,3,7]=>[2,2,1,2]
[2,6,1,5,4,7,3]=>[2,2,2,1]
[2,6,1,5,7,3,4]=>[2,3,2]
[2,6,1,5,7,4,3]=>[2,3,1,1]
[2,6,1,7,3,4,5]=>[2,2,3]
[2,6,1,7,3,5,4]=>[2,2,2,1]
[2,6,1,7,4,3,5]=>[2,2,1,2]
[2,6,1,7,4,5,3]=>[2,2,2,1]
[2,6,1,7,5,3,4]=>[2,2,1,2]
[2,6,1,7,5,4,3]=>[2,2,1,1,1]
[2,6,3,1,4,5,7]=>[2,1,4]
[2,6,3,1,4,7,5]=>[2,1,3,1]
[2,6,3,1,5,4,7]=>[2,1,2,2]
[2,6,3,1,5,7,4]=>[2,1,3,1]
[2,6,3,1,7,4,5]=>[2,1,2,2]
[2,6,3,1,7,5,4]=>[2,1,2,1,1]
[2,6,3,4,1,5,7]=>[2,2,3]
[2,6,3,4,1,7,5]=>[2,2,2,1]
[2,6,3,4,5,1,7]=>[2,3,2]
[2,6,3,4,5,7,1]=>[2,4,1]
[2,6,3,4,7,1,5]=>[2,3,2]
[2,6,3,4,7,5,1]=>[2,3,1,1]
[2,6,3,5,1,4,7]=>[2,2,3]
[2,6,3,5,1,7,4]=>[2,2,2,1]
[2,6,3,5,4,1,7]=>[2,2,1,2]
[2,6,3,5,4,7,1]=>[2,2,2,1]
[2,6,3,5,7,1,4]=>[2,3,2]
[2,6,3,5,7,4,1]=>[2,3,1,1]
[2,6,3,7,1,4,5]=>[2,2,3]
[2,6,3,7,1,5,4]=>[2,2,2,1]
[2,6,3,7,4,1,5]=>[2,2,1,2]
[2,6,3,7,4,5,1]=>[2,2,2,1]
[2,6,3,7,5,1,4]=>[2,2,1,2]
[2,6,3,7,5,4,1]=>[2,2,1,1,1]
[2,6,4,1,3,5,7]=>[2,1,4]
[2,6,4,1,3,7,5]=>[2,1,3,1]
[2,6,4,1,5,3,7]=>[2,1,2,2]
[2,6,4,1,5,7,3]=>[2,1,3,1]
[2,6,4,1,7,3,5]=>[2,1,2,2]
[2,6,4,1,7,5,3]=>[2,1,2,1,1]
[2,6,4,3,1,5,7]=>[2,1,1,3]
[2,6,4,3,1,7,5]=>[2,1,1,2,1]
[2,6,4,3,5,1,7]=>[2,1,2,2]
[2,6,4,3,5,7,1]=>[2,1,3,1]
[2,6,4,3,7,1,5]=>[2,1,2,2]
[2,6,4,3,7,5,1]=>[2,1,2,1,1]
[2,6,4,5,1,3,7]=>[2,2,3]
[2,6,4,5,1,7,3]=>[2,2,2,1]
[2,6,4,5,3,1,7]=>[2,2,1,2]
[2,6,4,5,3,7,1]=>[2,2,2,1]
[2,6,4,5,7,1,3]=>[2,3,2]
[2,6,4,5,7,3,1]=>[2,3,1,1]
[2,6,4,7,1,3,5]=>[2,2,3]
[2,6,4,7,1,5,3]=>[2,2,2,1]
[2,6,4,7,3,1,5]=>[2,2,1,2]
[2,6,4,7,3,5,1]=>[2,2,2,1]
[2,6,4,7,5,1,3]=>[2,2,1,2]
[2,6,4,7,5,3,1]=>[2,2,1,1,1]
[2,6,5,1,3,4,7]=>[2,1,4]
[2,6,5,1,3,7,4]=>[2,1,3,1]
[2,6,5,1,4,3,7]=>[2,1,2,2]
[2,6,5,1,4,7,3]=>[2,1,3,1]
[2,6,5,1,7,3,4]=>[2,1,2,2]
[2,6,5,1,7,4,3]=>[2,1,2,1,1]
[2,6,5,3,1,4,7]=>[2,1,1,3]
[2,6,5,3,1,7,4]=>[2,1,1,2,1]
[2,6,5,3,4,1,7]=>[2,1,2,2]
[2,6,5,3,4,7,1]=>[2,1,3,1]
[2,6,5,3,7,1,4]=>[2,1,2,2]
[2,6,5,3,7,4,1]=>[2,1,2,1,1]
[2,6,5,4,1,3,7]=>[2,1,1,3]
[2,6,5,4,1,7,3]=>[2,1,1,2,1]
[2,6,5,4,3,1,7]=>[2,1,1,1,2]
[2,6,5,4,3,7,1]=>[2,1,1,2,1]
[2,6,5,4,7,1,3]=>[2,1,2,2]
[2,6,5,4,7,3,1]=>[2,1,2,1,1]
[2,6,5,7,1,3,4]=>[2,2,3]
[2,6,5,7,1,4,3]=>[2,2,2,1]
[2,6,5,7,3,1,4]=>[2,2,1,2]
[2,6,5,7,3,4,1]=>[2,2,2,1]
[2,6,5,7,4,1,3]=>[2,2,1,2]
[2,6,5,7,4,3,1]=>[2,2,1,1,1]
[2,6,7,1,3,4,5]=>[3,4]
[2,6,7,1,3,5,4]=>[3,3,1]
[2,6,7,1,4,3,5]=>[3,2,2]
[2,6,7,1,4,5,3]=>[3,3,1]
[2,6,7,1,5,3,4]=>[3,2,2]
[2,6,7,1,5,4,3]=>[3,2,1,1]
[2,6,7,3,1,4,5]=>[3,1,3]
[2,6,7,3,1,5,4]=>[3,1,2,1]
[2,6,7,3,4,1,5]=>[3,2,2]
[2,6,7,3,4,5,1]=>[3,3,1]
[2,6,7,3,5,1,4]=>[3,2,2]
[2,6,7,3,5,4,1]=>[3,2,1,1]
[2,6,7,4,1,3,5]=>[3,1,3]
[2,6,7,4,1,5,3]=>[3,1,2,1]
[2,6,7,4,3,1,5]=>[3,1,1,2]
[2,6,7,4,3,5,1]=>[3,1,2,1]
[2,6,7,4,5,1,3]=>[3,2,2]
[2,6,7,4,5,3,1]=>[3,2,1,1]
[2,6,7,5,1,3,4]=>[3,1,3]
[2,6,7,5,1,4,3]=>[3,1,2,1]
[2,6,7,5,3,1,4]=>[3,1,1,2]
[2,6,7,5,3,4,1]=>[3,1,2,1]
[2,6,7,5,4,1,3]=>[3,1,1,2]
[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[2,7,1,3,4,5,6]=>[2,5]
[2,7,1,3,4,6,5]=>[2,4,1]
[2,7,1,3,5,4,6]=>[2,3,2]
[2,7,1,3,5,6,4]=>[2,4,1]
[2,7,1,3,6,4,5]=>[2,3,2]
[2,7,1,3,6,5,4]=>[2,3,1,1]
[2,7,1,4,3,5,6]=>[2,2,3]
[2,7,1,4,3,6,5]=>[2,2,2,1]
[2,7,1,4,5,3,6]=>[2,3,2]
[2,7,1,4,5,6,3]=>[2,4,1]
[2,7,1,4,6,3,5]=>[2,3,2]
[2,7,1,4,6,5,3]=>[2,3,1,1]
[2,7,1,5,3,4,6]=>[2,2,3]
[2,7,1,5,3,6,4]=>[2,2,2,1]
[2,7,1,5,4,3,6]=>[2,2,1,2]
[2,7,1,5,4,6,3]=>[2,2,2,1]
[2,7,1,5,6,3,4]=>[2,3,2]
[2,7,1,5,6,4,3]=>[2,3,1,1]
[2,7,1,6,3,4,5]=>[2,2,3]
[2,7,1,6,3,5,4]=>[2,2,2,1]
[2,7,1,6,4,3,5]=>[2,2,1,2]
[2,7,1,6,4,5,3]=>[2,2,2,1]
[2,7,1,6,5,3,4]=>[2,2,1,2]
[2,7,1,6,5,4,3]=>[2,2,1,1,1]
[2,7,3,1,4,5,6]=>[2,1,4]
[2,7,3,1,4,6,5]=>[2,1,3,1]
[2,7,3,1,5,4,6]=>[2,1,2,2]
[2,7,3,1,5,6,4]=>[2,1,3,1]
[2,7,3,1,6,4,5]=>[2,1,2,2]
[2,7,3,1,6,5,4]=>[2,1,2,1,1]
[2,7,3,4,1,5,6]=>[2,2,3]
[2,7,3,4,1,6,5]=>[2,2,2,1]
[2,7,3,4,5,1,6]=>[2,3,2]
[2,7,3,4,5,6,1]=>[2,4,1]
[2,7,3,4,6,1,5]=>[2,3,2]
[2,7,3,4,6,5,1]=>[2,3,1,1]
[2,7,3,5,1,4,6]=>[2,2,3]
[2,7,3,5,1,6,4]=>[2,2,2,1]
[2,7,3,5,4,1,6]=>[2,2,1,2]
[2,7,3,5,4,6,1]=>[2,2,2,1]
[2,7,3,5,6,1,4]=>[2,3,2]
[2,7,3,5,6,4,1]=>[2,3,1,1]
[2,7,3,6,1,4,5]=>[2,2,3]
[2,7,3,6,1,5,4]=>[2,2,2,1]
[2,7,3,6,4,1,5]=>[2,2,1,2]
[2,7,3,6,4,5,1]=>[2,2,2,1]
[2,7,3,6,5,1,4]=>[2,2,1,2]
[2,7,3,6,5,4,1]=>[2,2,1,1,1]
[2,7,4,1,3,5,6]=>[2,1,4]
[2,7,4,1,3,6,5]=>[2,1,3,1]
[2,7,4,1,5,3,6]=>[2,1,2,2]
[2,7,4,1,5,6,3]=>[2,1,3,1]
[2,7,4,1,6,3,5]=>[2,1,2,2]
[2,7,4,1,6,5,3]=>[2,1,2,1,1]
[2,7,4,3,1,5,6]=>[2,1,1,3]
[2,7,4,3,1,6,5]=>[2,1,1,2,1]
[2,7,4,3,5,1,6]=>[2,1,2,2]
[2,7,4,3,5,6,1]=>[2,1,3,1]
[2,7,4,3,6,1,5]=>[2,1,2,2]
[2,7,4,3,6,5,1]=>[2,1,2,1,1]
[2,7,4,5,1,3,6]=>[2,2,3]
[2,7,4,5,1,6,3]=>[2,2,2,1]
[2,7,4,5,3,1,6]=>[2,2,1,2]
[2,7,4,5,3,6,1]=>[2,2,2,1]
[2,7,4,5,6,1,3]=>[2,3,2]
[2,7,4,5,6,3,1]=>[2,3,1,1]
[2,7,4,6,1,3,5]=>[2,2,3]
[2,7,4,6,1,5,3]=>[2,2,2,1]
[2,7,4,6,3,1,5]=>[2,2,1,2]
[2,7,4,6,3,5,1]=>[2,2,2,1]
[2,7,4,6,5,1,3]=>[2,2,1,2]
[2,7,4,6,5,3,1]=>[2,2,1,1,1]
[2,7,5,1,3,4,6]=>[2,1,4]
[2,7,5,1,3,6,4]=>[2,1,3,1]
[2,7,5,1,4,3,6]=>[2,1,2,2]
[2,7,5,1,4,6,3]=>[2,1,3,1]
[2,7,5,1,6,3,4]=>[2,1,2,2]
[2,7,5,1,6,4,3]=>[2,1,2,1,1]
[2,7,5,3,1,4,6]=>[2,1,1,3]
[2,7,5,3,1,6,4]=>[2,1,1,2,1]
[2,7,5,3,4,1,6]=>[2,1,2,2]
[2,7,5,3,4,6,1]=>[2,1,3,1]
[2,7,5,3,6,1,4]=>[2,1,2,2]
[2,7,5,3,6,4,1]=>[2,1,2,1,1]
[2,7,5,4,1,3,6]=>[2,1,1,3]
[2,7,5,4,1,6,3]=>[2,1,1,2,1]
[2,7,5,4,3,1,6]=>[2,1,1,1,2]
[2,7,5,4,3,6,1]=>[2,1,1,2,1]
[2,7,5,4,6,1,3]=>[2,1,2,2]
[2,7,5,4,6,3,1]=>[2,1,2,1,1]
[2,7,5,6,1,3,4]=>[2,2,3]
[2,7,5,6,1,4,3]=>[2,2,2,1]
[2,7,5,6,3,1,4]=>[2,2,1,2]
[2,7,5,6,3,4,1]=>[2,2,2,1]
[2,7,5,6,4,1,3]=>[2,2,1,2]
[2,7,5,6,4,3,1]=>[2,2,1,1,1]
[2,7,6,1,3,4,5]=>[2,1,4]
[2,7,6,1,3,5,4]=>[2,1,3,1]
[2,7,6,1,4,3,5]=>[2,1,2,2]
[2,7,6,1,4,5,3]=>[2,1,3,1]
[2,7,6,1,5,3,4]=>[2,1,2,2]
[2,7,6,1,5,4,3]=>[2,1,2,1,1]
[2,7,6,3,1,4,5]=>[2,1,1,3]
[2,7,6,3,1,5,4]=>[2,1,1,2,1]
[2,7,6,3,4,1,5]=>[2,1,2,2]
[2,7,6,3,4,5,1]=>[2,1,3,1]
[2,7,6,3,5,1,4]=>[2,1,2,2]
[2,7,6,3,5,4,1]=>[2,1,2,1,1]
[2,7,6,4,1,3,5]=>[2,1,1,3]
[2,7,6,4,1,5,3]=>[2,1,1,2,1]
[2,7,6,4,3,1,5]=>[2,1,1,1,2]
[2,7,6,4,3,5,1]=>[2,1,1,2,1]
[2,7,6,4,5,1,3]=>[2,1,2,2]
[2,7,6,4,5,3,1]=>[2,1,2,1,1]
[2,7,6,5,1,3,4]=>[2,1,1,3]
[2,7,6,5,1,4,3]=>[2,1,1,2,1]
[2,7,6,5,3,1,4]=>[2,1,1,1,2]
[2,7,6,5,3,4,1]=>[2,1,1,2,1]
[2,7,6,5,4,1,3]=>[2,1,1,1,2]
[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[3,1,2,4,5,6,7]=>[1,6]
[3,1,2,4,5,7,6]=>[1,5,1]
[3,1,2,4,6,5,7]=>[1,4,2]
[3,1,2,4,6,7,5]=>[1,5,1]
[3,1,2,4,7,5,6]=>[1,4,2]
[3,1,2,4,7,6,5]=>[1,4,1,1]
[3,1,2,5,4,6,7]=>[1,3,3]
[3,1,2,5,4,7,6]=>[1,3,2,1]
[3,1,2,5,6,4,7]=>[1,4,2]
[3,1,2,5,6,7,4]=>[1,5,1]
[3,1,2,5,7,4,6]=>[1,4,2]
[3,1,2,5,7,6,4]=>[1,4,1,1]
[3,1,2,6,4,5,7]=>[1,3,3]
[3,1,2,6,4,7,5]=>[1,3,2,1]
[3,1,2,6,5,4,7]=>[1,3,1,2]
[3,1,2,6,5,7,4]=>[1,3,2,1]
[3,1,2,6,7,4,5]=>[1,4,2]
[3,1,2,6,7,5,4]=>[1,4,1,1]
[3,1,2,7,4,5,6]=>[1,3,3]
[3,1,2,7,4,6,5]=>[1,3,2,1]
[3,1,2,7,5,4,6]=>[1,3,1,2]
[3,1,2,7,5,6,4]=>[1,3,2,1]
[3,1,2,7,6,4,5]=>[1,3,1,2]
[3,1,2,7,6,5,4]=>[1,3,1,1,1]
[3,1,4,2,5,6,7]=>[1,2,4]
[3,1,4,2,5,7,6]=>[1,2,3,1]
[3,1,4,2,6,5,7]=>[1,2,2,2]
[3,1,4,2,6,7,5]=>[1,2,3,1]
[3,1,4,2,7,5,6]=>[1,2,2,2]
[3,1,4,2,7,6,5]=>[1,2,2,1,1]
[3,1,4,5,2,6,7]=>[1,3,3]
[3,1,4,5,2,7,6]=>[1,3,2,1]
[3,1,4,5,6,2,7]=>[1,4,2]
[3,1,4,5,6,7,2]=>[1,5,1]
[3,1,4,5,7,2,6]=>[1,4,2]
[3,1,4,5,7,6,2]=>[1,4,1,1]
[3,1,4,6,2,5,7]=>[1,3,3]
[3,1,4,6,2,7,5]=>[1,3,2,1]
[3,1,4,6,5,2,7]=>[1,3,1,2]
[3,1,4,6,5,7,2]=>[1,3,2,1]
[3,1,4,6,7,2,5]=>[1,4,2]
[3,1,4,6,7,5,2]=>[1,4,1,1]
[3,1,4,7,2,5,6]=>[1,3,3]
[3,1,4,7,2,6,5]=>[1,3,2,1]
[3,1,4,7,5,2,6]=>[1,3,1,2]
[3,1,4,7,5,6,2]=>[1,3,2,1]
[3,1,4,7,6,2,5]=>[1,3,1,2]
[3,1,4,7,6,5,2]=>[1,3,1,1,1]
[3,1,5,2,4,6,7]=>[1,2,4]
[3,1,5,2,4,7,6]=>[1,2,3,1]
[3,1,5,2,6,4,7]=>[1,2,2,2]
[3,1,5,2,6,7,4]=>[1,2,3,1]
[3,1,5,2,7,4,6]=>[1,2,2,2]
[3,1,5,2,7,6,4]=>[1,2,2,1,1]
[3,1,5,4,2,6,7]=>[1,2,1,3]
[3,1,5,4,2,7,6]=>[1,2,1,2,1]
[3,1,5,4,6,2,7]=>[1,2,2,2]
[3,1,5,4,6,7,2]=>[1,2,3,1]
[3,1,5,4,7,2,6]=>[1,2,2,2]
[3,1,5,4,7,6,2]=>[1,2,2,1,1]
[3,1,5,6,2,4,7]=>[1,3,3]
[3,1,5,6,2,7,4]=>[1,3,2,1]
[3,1,5,6,4,2,7]=>[1,3,1,2]
[3,1,5,6,4,7,2]=>[1,3,2,1]
[3,1,5,6,7,2,4]=>[1,4,2]
[3,1,5,6,7,4,2]=>[1,4,1,1]
[3,1,5,7,2,4,6]=>[1,3,3]
[3,1,5,7,2,6,4]=>[1,3,2,1]
[3,1,5,7,4,2,6]=>[1,3,1,2]
[3,1,5,7,4,6,2]=>[1,3,2,1]
[3,1,5,7,6,2,4]=>[1,3,1,2]
[3,1,5,7,6,4,2]=>[1,3,1,1,1]
[3,1,6,2,4,5,7]=>[1,2,4]
[3,1,6,2,4,7,5]=>[1,2,3,1]
[3,1,6,2,5,4,7]=>[1,2,2,2]
[3,1,6,2,5,7,4]=>[1,2,3,1]
[3,1,6,2,7,4,5]=>[1,2,2,2]
[3,1,6,2,7,5,4]=>[1,2,2,1,1]
[3,1,6,4,2,5,7]=>[1,2,1,3]
[3,1,6,4,2,7,5]=>[1,2,1,2,1]
[3,1,6,4,5,2,7]=>[1,2,2,2]
[3,1,6,4,5,7,2]=>[1,2,3,1]
[3,1,6,4,7,2,5]=>[1,2,2,2]
[3,1,6,4,7,5,2]=>[1,2,2,1,1]
[3,1,6,5,2,4,7]=>[1,2,1,3]
[3,1,6,5,2,7,4]=>[1,2,1,2,1]
[3,1,6,5,4,2,7]=>[1,2,1,1,2]
[3,1,6,5,4,7,2]=>[1,2,1,2,1]
[3,1,6,5,7,2,4]=>[1,2,2,2]
[3,1,6,5,7,4,2]=>[1,2,2,1,1]
[3,1,6,7,2,4,5]=>[1,3,3]
[3,1,6,7,2,5,4]=>[1,3,2,1]
[3,1,6,7,4,2,5]=>[1,3,1,2]
[3,1,6,7,4,5,2]=>[1,3,2,1]
[3,1,6,7,5,2,4]=>[1,3,1,2]
[3,1,6,7,5,4,2]=>[1,3,1,1,1]
[3,1,7,2,4,5,6]=>[1,2,4]
[3,1,7,2,4,6,5]=>[1,2,3,1]
[3,1,7,2,5,4,6]=>[1,2,2,2]
[3,1,7,2,5,6,4]=>[1,2,3,1]
[3,1,7,2,6,4,5]=>[1,2,2,2]
[3,1,7,2,6,5,4]=>[1,2,2,1,1]
[3,1,7,4,2,5,6]=>[1,2,1,3]
[3,1,7,4,2,6,5]=>[1,2,1,2,1]
[3,1,7,4,5,2,6]=>[1,2,2,2]
[3,1,7,4,5,6,2]=>[1,2,3,1]
[3,1,7,4,6,2,5]=>[1,2,2,2]
[3,1,7,4,6,5,2]=>[1,2,2,1,1]
[3,1,7,5,2,4,6]=>[1,2,1,3]
[3,1,7,5,2,6,4]=>[1,2,1,2,1]
[3,1,7,5,4,2,6]=>[1,2,1,1,2]
[3,1,7,5,4,6,2]=>[1,2,1,2,1]
[3,1,7,5,6,2,4]=>[1,2,2,2]
[3,1,7,5,6,4,2]=>[1,2,2,1,1]
[3,1,7,6,2,4,5]=>[1,2,1,3]
[3,1,7,6,2,5,4]=>[1,2,1,2,1]
[3,1,7,6,4,2,5]=>[1,2,1,1,2]
[3,1,7,6,4,5,2]=>[1,2,1,2,1]
[3,1,7,6,5,2,4]=>[1,2,1,1,2]
[3,1,7,6,5,4,2]=>[1,2,1,1,1,1]
[3,2,1,4,5,6,7]=>[1,1,5]
[3,2,1,4,5,7,6]=>[1,1,4,1]
[3,2,1,4,6,5,7]=>[1,1,3,2]
[3,2,1,4,6,7,5]=>[1,1,4,1]
[3,2,1,4,7,5,6]=>[1,1,3,2]
[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[3,2,1,5,4,6,7]=>[1,1,2,3]
[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[3,2,1,5,6,4,7]=>[1,1,3,2]
[3,2,1,5,6,7,4]=>[1,1,4,1]
[3,2,1,5,7,4,6]=>[1,1,3,2]
[3,2,1,5,7,6,4]=>[1,1,3,1,1]
[3,2,1,6,4,5,7]=>[1,1,2,3]
[3,2,1,6,4,7,5]=>[1,1,2,2,1]
[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[3,2,1,6,5,7,4]=>[1,1,2,2,1]
[3,2,1,6,7,4,5]=>[1,1,3,2]
[3,2,1,6,7,5,4]=>[1,1,3,1,1]
[3,2,1,7,4,5,6]=>[1,1,2,3]
[3,2,1,7,4,6,5]=>[1,1,2,2,1]
[3,2,1,7,5,4,6]=>[1,1,2,1,2]
[3,2,1,7,5,6,4]=>[1,1,2,2,1]
[3,2,1,7,6,4,5]=>[1,1,2,1,2]
[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[3,2,4,1,5,6,7]=>[1,2,4]
[3,2,4,1,5,7,6]=>[1,2,3,1]
[3,2,4,1,6,5,7]=>[1,2,2,2]
[3,2,4,1,6,7,5]=>[1,2,3,1]
[3,2,4,1,7,5,6]=>[1,2,2,2]
[3,2,4,1,7,6,5]=>[1,2,2,1,1]
[3,2,4,5,1,6,7]=>[1,3,3]
[3,2,4,5,1,7,6]=>[1,3,2,1]
[3,2,4,5,6,1,7]=>[1,4,2]
[3,2,4,5,6,7,1]=>[1,5,1]
[3,2,4,5,7,1,6]=>[1,4,2]
[3,2,4,5,7,6,1]=>[1,4,1,1]
[3,2,4,6,1,5,7]=>[1,3,3]
[3,2,4,6,1,7,5]=>[1,3,2,1]
[3,2,4,6,5,1,7]=>[1,3,1,2]
[3,2,4,6,5,7,1]=>[1,3,2,1]
[3,2,4,6,7,1,5]=>[1,4,2]
[3,2,4,6,7,5,1]=>[1,4,1,1]
[3,2,4,7,1,5,6]=>[1,3,3]
[3,2,4,7,1,6,5]=>[1,3,2,1]
[3,2,4,7,5,1,6]=>[1,3,1,2]
[3,2,4,7,5,6,1]=>[1,3,2,1]
[3,2,4,7,6,1,5]=>[1,3,1,2]
[3,2,4,7,6,5,1]=>[1,3,1,1,1]
[3,2,5,1,4,6,7]=>[1,2,4]
[3,2,5,1,4,7,6]=>[1,2,3,1]
[3,2,5,1,6,4,7]=>[1,2,2,2]
[3,2,5,1,6,7,4]=>[1,2,3,1]
[3,2,5,1,7,4,6]=>[1,2,2,2]
[3,2,5,1,7,6,4]=>[1,2,2,1,1]
[3,2,5,4,1,6,7]=>[1,2,1,3]
[3,2,5,4,1,7,6]=>[1,2,1,2,1]
[3,2,5,4,6,1,7]=>[1,2,2,2]
[3,2,5,4,6,7,1]=>[1,2,3,1]
[3,2,5,4,7,1,6]=>[1,2,2,2]
[3,2,5,4,7,6,1]=>[1,2,2,1,1]
[3,2,5,6,1,4,7]=>[1,3,3]
[3,2,5,6,1,7,4]=>[1,3,2,1]
[3,2,5,6,4,1,7]=>[1,3,1,2]
[3,2,5,6,4,7,1]=>[1,3,2,1]
[3,2,5,6,7,1,4]=>[1,4,2]
[3,2,5,6,7,4,1]=>[1,4,1,1]
[3,2,5,7,1,4,6]=>[1,3,3]
[3,2,5,7,1,6,4]=>[1,3,2,1]
[3,2,5,7,4,1,6]=>[1,3,1,2]
[3,2,5,7,4,6,1]=>[1,3,2,1]
[3,2,5,7,6,1,4]=>[1,3,1,2]
[3,2,5,7,6,4,1]=>[1,3,1,1,1]
[3,2,6,1,4,5,7]=>[1,2,4]
[3,2,6,1,4,7,5]=>[1,2,3,1]
[3,2,6,1,5,4,7]=>[1,2,2,2]
[3,2,6,1,5,7,4]=>[1,2,3,1]
[3,2,6,1,7,4,5]=>[1,2,2,2]
[3,2,6,1,7,5,4]=>[1,2,2,1,1]
[3,2,6,4,1,5,7]=>[1,2,1,3]
[3,2,6,4,1,7,5]=>[1,2,1,2,1]
[3,2,6,4,5,1,7]=>[1,2,2,2]
[3,2,6,4,5,7,1]=>[1,2,3,1]
[3,2,6,4,7,1,5]=>[1,2,2,2]
[3,2,6,4,7,5,1]=>[1,2,2,1,1]
[3,2,6,5,1,4,7]=>[1,2,1,3]
[3,2,6,5,1,7,4]=>[1,2,1,2,1]
[3,2,6,5,4,1,7]=>[1,2,1,1,2]
[3,2,6,5,4,7,1]=>[1,2,1,2,1]
[3,2,6,5,7,1,4]=>[1,2,2,2]
[3,2,6,5,7,4,1]=>[1,2,2,1,1]
[3,2,6,7,1,4,5]=>[1,3,3]
[3,2,6,7,1,5,4]=>[1,3,2,1]
[3,2,6,7,4,1,5]=>[1,3,1,2]
[3,2,6,7,4,5,1]=>[1,3,2,1]
[3,2,6,7,5,1,4]=>[1,3,1,2]
[3,2,6,7,5,4,1]=>[1,3,1,1,1]
[3,2,7,1,4,5,6]=>[1,2,4]
[3,2,7,1,4,6,5]=>[1,2,3,1]
[3,2,7,1,5,4,6]=>[1,2,2,2]
[3,2,7,1,5,6,4]=>[1,2,3,1]
[3,2,7,1,6,4,5]=>[1,2,2,2]
[3,2,7,1,6,5,4]=>[1,2,2,1,1]
[3,2,7,4,1,5,6]=>[1,2,1,3]
[3,2,7,4,1,6,5]=>[1,2,1,2,1]
[3,2,7,4,5,1,6]=>[1,2,2,2]
[3,2,7,4,5,6,1]=>[1,2,3,1]
[3,2,7,4,6,1,5]=>[1,2,2,2]
[3,2,7,4,6,5,1]=>[1,2,2,1,1]
[3,2,7,5,1,4,6]=>[1,2,1,3]
[3,2,7,5,1,6,4]=>[1,2,1,2,1]
[3,2,7,5,4,1,6]=>[1,2,1,1,2]
[3,2,7,5,4,6,1]=>[1,2,1,2,1]
[3,2,7,5,6,1,4]=>[1,2,2,2]
[3,2,7,5,6,4,1]=>[1,2,2,1,1]
[3,2,7,6,1,4,5]=>[1,2,1,3]
[3,2,7,6,1,5,4]=>[1,2,1,2,1]
[3,2,7,6,4,1,5]=>[1,2,1,1,2]
[3,2,7,6,4,5,1]=>[1,2,1,2,1]
[3,2,7,6,5,1,4]=>[1,2,1,1,2]
[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]
[3,4,1,2,5,6,7]=>[2,5]
[3,4,1,2,5,7,6]=>[2,4,1]
[3,4,1,2,6,5,7]=>[2,3,2]
[3,4,1,2,6,7,5]=>[2,4,1]
[3,4,1,2,7,5,6]=>[2,3,2]
[3,4,1,2,7,6,5]=>[2,3,1,1]
[3,4,1,5,2,6,7]=>[2,2,3]
[3,4,1,5,2,7,6]=>[2,2,2,1]
[3,4,1,5,6,2,7]=>[2,3,2]
[3,4,1,5,6,7,2]=>[2,4,1]
[3,4,1,5,7,2,6]=>[2,3,2]
[3,4,1,5,7,6,2]=>[2,3,1,1]
[3,4,1,6,2,5,7]=>[2,2,3]
[3,4,1,6,2,7,5]=>[2,2,2,1]
[3,4,1,6,5,2,7]=>[2,2,1,2]
[3,4,1,6,5,7,2]=>[2,2,2,1]
[3,4,1,6,7,2,5]=>[2,3,2]
[3,4,1,6,7,5,2]=>[2,3,1,1]
[3,4,1,7,2,5,6]=>[2,2,3]
[3,4,1,7,2,6,5]=>[2,2,2,1]
[3,4,1,7,5,2,6]=>[2,2,1,2]
[3,4,1,7,5,6,2]=>[2,2,2,1]
[3,4,1,7,6,2,5]=>[2,2,1,2]
[3,4,1,7,6,5,2]=>[2,2,1,1,1]
[3,4,2,1,5,6,7]=>[2,1,4]
[3,4,2,1,5,7,6]=>[2,1,3,1]
[3,4,2,1,6,5,7]=>[2,1,2,2]
[3,4,2,1,6,7,5]=>[2,1,3,1]
[3,4,2,1,7,5,6]=>[2,1,2,2]
[3,4,2,1,7,6,5]=>[2,1,2,1,1]
[3,4,2,5,1,6,7]=>[2,2,3]
[3,4,2,5,1,7,6]=>[2,2,2,1]
[3,4,2,5,6,1,7]=>[2,3,2]
[3,4,2,5,6,7,1]=>[2,4,1]
[3,4,2,5,7,1,6]=>[2,3,2]
[3,4,2,5,7,6,1]=>[2,3,1,1]
[3,4,2,6,1,5,7]=>[2,2,3]
[3,4,2,6,1,7,5]=>[2,2,2,1]
[3,4,2,6,5,1,7]=>[2,2,1,2]
[3,4,2,6,5,7,1]=>[2,2,2,1]
[3,4,2,6,7,1,5]=>[2,3,2]
[3,4,2,6,7,5,1]=>[2,3,1,1]
[3,4,2,7,1,5,6]=>[2,2,3]
[3,4,2,7,1,6,5]=>[2,2,2,1]
[3,4,2,7,5,1,6]=>[2,2,1,2]
[3,4,2,7,5,6,1]=>[2,2,2,1]
[3,4,2,7,6,1,5]=>[2,2,1,2]
[3,4,2,7,6,5,1]=>[2,2,1,1,1]
[3,4,5,1,2,6,7]=>[3,4]
[3,4,5,1,2,7,6]=>[3,3,1]
[3,4,5,1,6,2,7]=>[3,2,2]
[3,4,5,1,6,7,2]=>[3,3,1]
[3,4,5,1,7,2,6]=>[3,2,2]
[3,4,5,1,7,6,2]=>[3,2,1,1]
[3,4,5,2,1,6,7]=>[3,1,3]
[3,4,5,2,1,7,6]=>[3,1,2,1]
[3,4,5,2,6,1,7]=>[3,2,2]
[3,4,5,2,6,7,1]=>[3,3,1]
[3,4,5,2,7,1,6]=>[3,2,2]
[3,4,5,2,7,6,1]=>[3,2,1,1]
[3,4,5,6,1,2,7]=>[4,3]
[3,4,5,6,1,7,2]=>[4,2,1]
[3,4,5,6,2,1,7]=>[4,1,2]
[3,4,5,6,2,7,1]=>[4,2,1]
[3,4,5,6,7,1,2]=>[5,2]
[3,4,5,6,7,2,1]=>[5,1,1]
[3,4,5,7,1,2,6]=>[4,3]
[3,4,5,7,1,6,2]=>[4,2,1]
[3,4,5,7,2,1,6]=>[4,1,2]
[3,4,5,7,2,6,1]=>[4,2,1]
[3,4,5,7,6,1,2]=>[4,1,2]
[3,4,5,7,6,2,1]=>[4,1,1,1]
[3,4,6,1,2,5,7]=>[3,4]
[3,4,6,1,2,7,5]=>[3,3,1]
[3,4,6,1,5,2,7]=>[3,2,2]
[3,4,6,1,5,7,2]=>[3,3,1]
[3,4,6,1,7,2,5]=>[3,2,2]
[3,4,6,1,7,5,2]=>[3,2,1,1]
[3,4,6,2,1,5,7]=>[3,1,3]
[3,4,6,2,1,7,5]=>[3,1,2,1]
[3,4,6,2,5,1,7]=>[3,2,2]
[3,4,6,2,5,7,1]=>[3,3,1]
[3,4,6,2,7,1,5]=>[3,2,2]
[3,4,6,2,7,5,1]=>[3,2,1,1]
[3,4,6,5,1,2,7]=>[3,1,3]
[3,4,6,5,1,7,2]=>[3,1,2,1]
[3,4,6,5,2,1,7]=>[3,1,1,2]
[3,4,6,5,2,7,1]=>[3,1,2,1]
[3,4,6,5,7,1,2]=>[3,2,2]
[3,4,6,5,7,2,1]=>[3,2,1,1]
[3,4,6,7,1,2,5]=>[4,3]
[3,4,6,7,1,5,2]=>[4,2,1]
[3,4,6,7,2,1,5]=>[4,1,2]
[3,4,6,7,2,5,1]=>[4,2,1]
[3,4,6,7,5,1,2]=>[4,1,2]
[3,4,6,7,5,2,1]=>[4,1,1,1]
[3,4,7,1,2,5,6]=>[3,4]
[3,4,7,1,2,6,5]=>[3,3,1]
[3,4,7,1,5,2,6]=>[3,2,2]
[3,4,7,1,5,6,2]=>[3,3,1]
[3,4,7,1,6,2,5]=>[3,2,2]
[3,4,7,1,6,5,2]=>[3,2,1,1]
[3,4,7,2,1,5,6]=>[3,1,3]
[3,4,7,2,1,6,5]=>[3,1,2,1]
[3,4,7,2,5,1,6]=>[3,2,2]
[3,4,7,2,5,6,1]=>[3,3,1]
[3,4,7,2,6,1,5]=>[3,2,2]
[3,4,7,2,6,5,1]=>[3,2,1,1]
[3,4,7,5,1,2,6]=>[3,1,3]
[3,4,7,5,1,6,2]=>[3,1,2,1]
[3,4,7,5,2,1,6]=>[3,1,1,2]
[3,4,7,5,2,6,1]=>[3,1,2,1]
[3,4,7,5,6,1,2]=>[3,2,2]
[3,4,7,5,6,2,1]=>[3,2,1,1]
[3,4,7,6,1,2,5]=>[3,1,3]
[3,4,7,6,1,5,2]=>[3,1,2,1]
[3,4,7,6,2,1,5]=>[3,1,1,2]
[3,4,7,6,2,5,1]=>[3,1,2,1]
[3,4,7,6,5,1,2]=>[3,1,1,2]
[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[3,5,1,2,4,6,7]=>[2,5]
[3,5,1,2,4,7,6]=>[2,4,1]
[3,5,1,2,6,4,7]=>[2,3,2]
[3,5,1,2,6,7,4]=>[2,4,1]
[3,5,1,2,7,4,6]=>[2,3,2]
[3,5,1,2,7,6,4]=>[2,3,1,1]
[3,5,1,4,2,6,7]=>[2,2,3]
[3,5,1,4,2,7,6]=>[2,2,2,1]
[3,5,1,4,6,2,7]=>[2,3,2]
[3,5,1,4,6,7,2]=>[2,4,1]
[3,5,1,4,7,2,6]=>[2,3,2]
[3,5,1,4,7,6,2]=>[2,3,1,1]
[3,5,1,6,2,4,7]=>[2,2,3]
[3,5,1,6,2,7,4]=>[2,2,2,1]
[3,5,1,6,4,2,7]=>[2,2,1,2]
[3,5,1,6,4,7,2]=>[2,2,2,1]
[3,5,1,6,7,2,4]=>[2,3,2]
[3,5,1,6,7,4,2]=>[2,3,1,1]
[3,5,1,7,2,4,6]=>[2,2,3]
[3,5,1,7,2,6,4]=>[2,2,2,1]
[3,5,1,7,4,2,6]=>[2,2,1,2]
[3,5,1,7,4,6,2]=>[2,2,2,1]
[3,5,1,7,6,2,4]=>[2,2,1,2]
[3,5,1,7,6,4,2]=>[2,2,1,1,1]
[3,5,2,1,4,6,7]=>[2,1,4]
[3,5,2,1,4,7,6]=>[2,1,3,1]
[3,5,2,1,6,4,7]=>[2,1,2,2]
[3,5,2,1,6,7,4]=>[2,1,3,1]
[3,5,2,1,7,4,6]=>[2,1,2,2]
[3,5,2,1,7,6,4]=>[2,1,2,1,1]
[3,5,2,4,1,6,7]=>[2,2,3]
[3,5,2,4,1,7,6]=>[2,2,2,1]
[3,5,2,4,6,1,7]=>[2,3,2]
[3,5,2,4,6,7,1]=>[2,4,1]
[3,5,2,4,7,1,6]=>[2,3,2]
[3,5,2,4,7,6,1]=>[2,3,1,1]
[3,5,2,6,1,4,7]=>[2,2,3]
[3,5,2,6,1,7,4]=>[2,2,2,1]
[3,5,2,6,4,1,7]=>[2,2,1,2]
[3,5,2,6,4,7,1]=>[2,2,2,1]
[3,5,2,6,7,1,4]=>[2,3,2]
[3,5,2,6,7,4,1]=>[2,3,1,1]
[3,5,2,7,1,4,6]=>[2,2,3]
[3,5,2,7,1,6,4]=>[2,2,2,1]
[3,5,2,7,4,1,6]=>[2,2,1,2]
[3,5,2,7,4,6,1]=>[2,2,2,1]
[3,5,2,7,6,1,4]=>[2,2,1,2]
[3,5,2,7,6,4,1]=>[2,2,1,1,1]
[3,5,4,1,2,6,7]=>[2,1,4]
[3,5,4,1,2,7,6]=>[2,1,3,1]
[3,5,4,1,6,2,7]=>[2,1,2,2]
[3,5,4,1,6,7,2]=>[2,1,3,1]
[3,5,4,1,7,2,6]=>[2,1,2,2]
[3,5,4,1,7,6,2]=>[2,1,2,1,1]
[3,5,4,2,1,6,7]=>[2,1,1,3]
[3,5,4,2,1,7,6]=>[2,1,1,2,1]
[3,5,4,2,6,1,7]=>[2,1,2,2]
[3,5,4,2,6,7,1]=>[2,1,3,1]
[3,5,4,2,7,1,6]=>[2,1,2,2]
[3,5,4,2,7,6,1]=>[2,1,2,1,1]
[3,5,4,6,1,2,7]=>[2,2,3]
[3,5,4,6,1,7,2]=>[2,2,2,1]
[3,5,4,6,2,1,7]=>[2,2,1,2]
[3,5,4,6,2,7,1]=>[2,2,2,1]
[3,5,4,6,7,1,2]=>[2,3,2]
[3,5,4,6,7,2,1]=>[2,3,1,1]
[3,5,4,7,1,2,6]=>[2,2,3]
[3,5,4,7,1,6,2]=>[2,2,2,1]
[3,5,4,7,2,1,6]=>[2,2,1,2]
[3,5,4,7,2,6,1]=>[2,2,2,1]
[3,5,4,7,6,1,2]=>[2,2,1,2]
[3,5,4,7,6,2,1]=>[2,2,1,1,1]
[3,5,6,1,2,4,7]=>[3,4]
[3,5,6,1,2,7,4]=>[3,3,1]
[3,5,6,1,4,2,7]=>[3,2,2]
[3,5,6,1,4,7,2]=>[3,3,1]
[3,5,6,1,7,2,4]=>[3,2,2]
[3,5,6,1,7,4,2]=>[3,2,1,1]
[3,5,6,2,1,4,7]=>[3,1,3]
[3,5,6,2,1,7,4]=>[3,1,2,1]
[3,5,6,2,4,1,7]=>[3,2,2]
[3,5,6,2,4,7,1]=>[3,3,1]
[3,5,6,2,7,1,4]=>[3,2,2]
[3,5,6,2,7,4,1]=>[3,2,1,1]
[3,5,6,4,1,2,7]=>[3,1,3]
[3,5,6,4,1,7,2]=>[3,1,2,1]
[3,5,6,4,2,1,7]=>[3,1,1,2]
[3,5,6,4,2,7,1]=>[3,1,2,1]
[3,5,6,4,7,1,2]=>[3,2,2]
[3,5,6,4,7,2,1]=>[3,2,1,1]
[3,5,6,7,1,2,4]=>[4,3]
[3,5,6,7,1,4,2]=>[4,2,1]
[3,5,6,7,2,1,4]=>[4,1,2]
[3,5,6,7,2,4,1]=>[4,2,1]
[3,5,6,7,4,1,2]=>[4,1,2]
[3,5,6,7,4,2,1]=>[4,1,1,1]
[3,5,7,1,2,4,6]=>[3,4]
[3,5,7,1,2,6,4]=>[3,3,1]
[3,5,7,1,4,2,6]=>[3,2,2]
[3,5,7,1,4,6,2]=>[3,3,1]
[3,5,7,1,6,2,4]=>[3,2,2]
[3,5,7,1,6,4,2]=>[3,2,1,1]
[3,5,7,2,1,4,6]=>[3,1,3]
[3,5,7,2,1,6,4]=>[3,1,2,1]
[3,5,7,2,4,1,6]=>[3,2,2]
[3,5,7,2,4,6,1]=>[3,3,1]
[3,5,7,2,6,1,4]=>[3,2,2]
[3,5,7,2,6,4,1]=>[3,2,1,1]
[3,5,7,4,1,2,6]=>[3,1,3]
[3,5,7,4,1,6,2]=>[3,1,2,1]
[3,5,7,4,2,1,6]=>[3,1,1,2]
[3,5,7,4,2,6,1]=>[3,1,2,1]
[3,5,7,4,6,1,2]=>[3,2,2]
[3,5,7,4,6,2,1]=>[3,2,1,1]
[3,5,7,6,1,2,4]=>[3,1,3]
[3,5,7,6,1,4,2]=>[3,1,2,1]
[3,5,7,6,2,1,4]=>[3,1,1,2]
[3,5,7,6,2,4,1]=>[3,1,2,1]
[3,5,7,6,4,1,2]=>[3,1,1,2]
[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[3,6,1,2,4,5,7]=>[2,5]
[3,6,1,2,4,7,5]=>[2,4,1]
[3,6,1,2,5,4,7]=>[2,3,2]
[3,6,1,2,5,7,4]=>[2,4,1]
[3,6,1,2,7,4,5]=>[2,3,2]
[3,6,1,2,7,5,4]=>[2,3,1,1]
[3,6,1,4,2,5,7]=>[2,2,3]
[3,6,1,4,2,7,5]=>[2,2,2,1]
[3,6,1,4,5,2,7]=>[2,3,2]
[3,6,1,4,5,7,2]=>[2,4,1]
[3,6,1,4,7,2,5]=>[2,3,2]
[3,6,1,4,7,5,2]=>[2,3,1,1]
[3,6,1,5,2,4,7]=>[2,2,3]
[3,6,1,5,2,7,4]=>[2,2,2,1]
[3,6,1,5,4,2,7]=>[2,2,1,2]
[3,6,1,5,4,7,2]=>[2,2,2,1]
[3,6,1,5,7,2,4]=>[2,3,2]
[3,6,1,5,7,4,2]=>[2,3,1,1]
[3,6,1,7,2,4,5]=>[2,2,3]
[3,6,1,7,2,5,4]=>[2,2,2,1]
[3,6,1,7,4,2,5]=>[2,2,1,2]
[3,6,1,7,4,5,2]=>[2,2,2,1]
[3,6,1,7,5,2,4]=>[2,2,1,2]
[3,6,1,7,5,4,2]=>[2,2,1,1,1]
[3,6,2,1,4,5,7]=>[2,1,4]
[3,6,2,1,4,7,5]=>[2,1,3,1]
[3,6,2,1,5,4,7]=>[2,1,2,2]
[3,6,2,1,5,7,4]=>[2,1,3,1]
[3,6,2,1,7,4,5]=>[2,1,2,2]
[3,6,2,1,7,5,4]=>[2,1,2,1,1]
[3,6,2,4,1,5,7]=>[2,2,3]
[3,6,2,4,1,7,5]=>[2,2,2,1]
[3,6,2,4,5,1,7]=>[2,3,2]
[3,6,2,4,5,7,1]=>[2,4,1]
[3,6,2,4,7,1,5]=>[2,3,2]
[3,6,2,4,7,5,1]=>[2,3,1,1]
[3,6,2,5,1,4,7]=>[2,2,3]
[3,6,2,5,1,7,4]=>[2,2,2,1]
[3,6,2,5,4,1,7]=>[2,2,1,2]
[3,6,2,5,4,7,1]=>[2,2,2,1]
[3,6,2,5,7,1,4]=>[2,3,2]
[3,6,2,5,7,4,1]=>[2,3,1,1]
[3,6,2,7,1,4,5]=>[2,2,3]
[3,6,2,7,1,5,4]=>[2,2,2,1]
[3,6,2,7,4,1,5]=>[2,2,1,2]
[3,6,2,7,4,5,1]=>[2,2,2,1]
[3,6,2,7,5,1,4]=>[2,2,1,2]
[3,6,2,7,5,4,1]=>[2,2,1,1,1]
[3,6,4,1,2,5,7]=>[2,1,4]
[3,6,4,1,2,7,5]=>[2,1,3,1]
[3,6,4,1,5,2,7]=>[2,1,2,2]
[3,6,4,1,5,7,2]=>[2,1,3,1]
[3,6,4,1,7,2,5]=>[2,1,2,2]
[3,6,4,1,7,5,2]=>[2,1,2,1,1]
[3,6,4,2,1,5,7]=>[2,1,1,3]
[3,6,4,2,1,7,5]=>[2,1,1,2,1]
[3,6,4,2,5,1,7]=>[2,1,2,2]
[3,6,4,2,5,7,1]=>[2,1,3,1]
[3,6,4,2,7,1,5]=>[2,1,2,2]
[3,6,4,2,7,5,1]=>[2,1,2,1,1]
[3,6,4,5,1,2,7]=>[2,2,3]
[3,6,4,5,1,7,2]=>[2,2,2,1]
[3,6,4,5,2,1,7]=>[2,2,1,2]
[3,6,4,5,2,7,1]=>[2,2,2,1]
[3,6,4,5,7,1,2]=>[2,3,2]
[3,6,4,5,7,2,1]=>[2,3,1,1]
[3,6,4,7,1,2,5]=>[2,2,3]
[3,6,4,7,1,5,2]=>[2,2,2,1]
[3,6,4,7,2,1,5]=>[2,2,1,2]
[3,6,4,7,2,5,1]=>[2,2,2,1]
[3,6,4,7,5,1,2]=>[2,2,1,2]
[3,6,4,7,5,2,1]=>[2,2,1,1,1]
[3,6,5,1,2,4,7]=>[2,1,4]
[3,6,5,1,2,7,4]=>[2,1,3,1]
[3,6,5,1,4,2,7]=>[2,1,2,2]
[3,6,5,1,4,7,2]=>[2,1,3,1]
[3,6,5,1,7,2,4]=>[2,1,2,2]
[3,6,5,1,7,4,2]=>[2,1,2,1,1]
[3,6,5,2,1,4,7]=>[2,1,1,3]
[3,6,5,2,1,7,4]=>[2,1,1,2,1]
[3,6,5,2,4,1,7]=>[2,1,2,2]
[3,6,5,2,4,7,1]=>[2,1,3,1]
[3,6,5,2,7,1,4]=>[2,1,2,2]
[3,6,5,2,7,4,1]=>[2,1,2,1,1]
[3,6,5,4,1,2,7]=>[2,1,1,3]
[3,6,5,4,1,7,2]=>[2,1,1,2,1]
[3,6,5,4,2,1,7]=>[2,1,1,1,2]
[3,6,5,4,2,7,1]=>[2,1,1,2,1]
[3,6,5,4,7,1,2]=>[2,1,2,2]
[3,6,5,4,7,2,1]=>[2,1,2,1,1]
[3,6,5,7,1,2,4]=>[2,2,3]
[3,6,5,7,1,4,2]=>[2,2,2,1]
[3,6,5,7,2,1,4]=>[2,2,1,2]
[3,6,5,7,2,4,1]=>[2,2,2,1]
[3,6,5,7,4,1,2]=>[2,2,1,2]
[3,6,5,7,4,2,1]=>[2,2,1,1,1]
[3,6,7,1,2,4,5]=>[3,4]
[3,6,7,1,2,5,4]=>[3,3,1]
[3,6,7,1,4,2,5]=>[3,2,2]
[3,6,7,1,4,5,2]=>[3,3,1]
[3,6,7,1,5,2,4]=>[3,2,2]
[3,6,7,1,5,4,2]=>[3,2,1,1]
[3,6,7,2,1,4,5]=>[3,1,3]
[3,6,7,2,1,5,4]=>[3,1,2,1]
[3,6,7,2,4,1,5]=>[3,2,2]
[3,6,7,2,4,5,1]=>[3,3,1]
[3,6,7,2,5,1,4]=>[3,2,2]
[3,6,7,2,5,4,1]=>[3,2,1,1]
[3,6,7,4,1,2,5]=>[3,1,3]
[3,6,7,4,1,5,2]=>[3,1,2,1]
[3,6,7,4,2,1,5]=>[3,1,1,2]
[3,6,7,4,2,5,1]=>[3,1,2,1]
[3,6,7,4,5,1,2]=>[3,2,2]
[3,6,7,4,5,2,1]=>[3,2,1,1]
[3,6,7,5,1,2,4]=>[3,1,3]
[3,6,7,5,1,4,2]=>[3,1,2,1]
[3,6,7,5,2,1,4]=>[3,1,1,2]
[3,6,7,5,2,4,1]=>[3,1,2,1]
[3,6,7,5,4,1,2]=>[3,1,1,2]
[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[3,7,1,2,4,5,6]=>[2,5]
[3,7,1,2,4,6,5]=>[2,4,1]
[3,7,1,2,5,4,6]=>[2,3,2]
[3,7,1,2,5,6,4]=>[2,4,1]
[3,7,1,2,6,4,5]=>[2,3,2]
[3,7,1,2,6,5,4]=>[2,3,1,1]
[3,7,1,4,2,5,6]=>[2,2,3]
[3,7,1,4,2,6,5]=>[2,2,2,1]
[3,7,1,4,5,2,6]=>[2,3,2]
[3,7,1,4,5,6,2]=>[2,4,1]
[3,7,1,4,6,2,5]=>[2,3,2]
[3,7,1,4,6,5,2]=>[2,3,1,1]
[3,7,1,5,2,4,6]=>[2,2,3]
[3,7,1,5,2,6,4]=>[2,2,2,1]
[3,7,1,5,4,2,6]=>[2,2,1,2]
[3,7,1,5,4,6,2]=>[2,2,2,1]
[3,7,1,5,6,2,4]=>[2,3,2]
[3,7,1,5,6,4,2]=>[2,3,1,1]
[3,7,1,6,2,4,5]=>[2,2,3]
[3,7,1,6,2,5,4]=>[2,2,2,1]
[3,7,1,6,4,2,5]=>[2,2,1,2]
[3,7,1,6,4,5,2]=>[2,2,2,1]
[3,7,1,6,5,2,4]=>[2,2,1,2]
[3,7,1,6,5,4,2]=>[2,2,1,1,1]
[3,7,2,1,4,5,6]=>[2,1,4]
[3,7,2,1,4,6,5]=>[2,1,3,1]
[3,7,2,1,5,4,6]=>[2,1,2,2]
[3,7,2,1,5,6,4]=>[2,1,3,1]
[3,7,2,1,6,4,5]=>[2,1,2,2]
[3,7,2,1,6,5,4]=>[2,1,2,1,1]
[3,7,2,4,1,5,6]=>[2,2,3]
[3,7,2,4,1,6,5]=>[2,2,2,1]
[3,7,2,4,5,1,6]=>[2,3,2]
[3,7,2,4,5,6,1]=>[2,4,1]
[3,7,2,4,6,1,5]=>[2,3,2]
[3,7,2,4,6,5,1]=>[2,3,1,1]
[3,7,2,5,1,4,6]=>[2,2,3]
[3,7,2,5,1,6,4]=>[2,2,2,1]
[3,7,2,5,4,1,6]=>[2,2,1,2]
[3,7,2,5,4,6,1]=>[2,2,2,1]
[3,7,2,5,6,1,4]=>[2,3,2]
[3,7,2,5,6,4,1]=>[2,3,1,1]
[3,7,2,6,1,4,5]=>[2,2,3]
[3,7,2,6,1,5,4]=>[2,2,2,1]
[3,7,2,6,4,1,5]=>[2,2,1,2]
[3,7,2,6,4,5,1]=>[2,2,2,1]
[3,7,2,6,5,1,4]=>[2,2,1,2]
[3,7,2,6,5,4,1]=>[2,2,1,1,1]
[3,7,4,1,2,5,6]=>[2,1,4]
[3,7,4,1,2,6,5]=>[2,1,3,1]
[3,7,4,1,5,2,6]=>[2,1,2,2]
[3,7,4,1,5,6,2]=>[2,1,3,1]
[3,7,4,1,6,2,5]=>[2,1,2,2]
[3,7,4,1,6,5,2]=>[2,1,2,1,1]
[3,7,4,2,1,5,6]=>[2,1,1,3]
[3,7,4,2,1,6,5]=>[2,1,1,2,1]
[3,7,4,2,5,1,6]=>[2,1,2,2]
[3,7,4,2,5,6,1]=>[2,1,3,1]
[3,7,4,2,6,1,5]=>[2,1,2,2]
[3,7,4,2,6,5,1]=>[2,1,2,1,1]
[3,7,4,5,1,2,6]=>[2,2,3]
[3,7,4,5,1,6,2]=>[2,2,2,1]
[3,7,4,5,2,1,6]=>[2,2,1,2]
[3,7,4,5,2,6,1]=>[2,2,2,1]
[3,7,4,5,6,1,2]=>[2,3,2]
[3,7,4,5,6,2,1]=>[2,3,1,1]
[3,7,4,6,1,2,5]=>[2,2,3]
[3,7,4,6,1,5,2]=>[2,2,2,1]
[3,7,4,6,2,1,5]=>[2,2,1,2]
[3,7,4,6,2,5,1]=>[2,2,2,1]
[3,7,4,6,5,1,2]=>[2,2,1,2]
[3,7,4,6,5,2,1]=>[2,2,1,1,1]
[3,7,5,1,2,4,6]=>[2,1,4]
[3,7,5,1,2,6,4]=>[2,1,3,1]
[3,7,5,1,4,2,6]=>[2,1,2,2]
[3,7,5,1,4,6,2]=>[2,1,3,1]
[3,7,5,1,6,2,4]=>[2,1,2,2]
[3,7,5,1,6,4,2]=>[2,1,2,1,1]
[3,7,5,2,1,4,6]=>[2,1,1,3]
[3,7,5,2,1,6,4]=>[2,1,1,2,1]
[3,7,5,2,4,1,6]=>[2,1,2,2]
[3,7,5,2,4,6,1]=>[2,1,3,1]
[3,7,5,2,6,1,4]=>[2,1,2,2]
[3,7,5,2,6,4,1]=>[2,1,2,1,1]
[3,7,5,4,1,2,6]=>[2,1,1,3]
[3,7,5,4,1,6,2]=>[2,1,1,2,1]
[3,7,5,4,2,1,6]=>[2,1,1,1,2]
[3,7,5,4,2,6,1]=>[2,1,1,2,1]
[3,7,5,4,6,1,2]=>[2,1,2,2]
[3,7,5,4,6,2,1]=>[2,1,2,1,1]
[3,7,5,6,1,2,4]=>[2,2,3]
[3,7,5,6,1,4,2]=>[2,2,2,1]
[3,7,5,6,2,1,4]=>[2,2,1,2]
[3,7,5,6,2,4,1]=>[2,2,2,1]
[3,7,5,6,4,1,2]=>[2,2,1,2]
[3,7,5,6,4,2,1]=>[2,2,1,1,1]
[3,7,6,1,2,4,5]=>[2,1,4]
[3,7,6,1,2,5,4]=>[2,1,3,1]
[3,7,6,1,4,2,5]=>[2,1,2,2]
[3,7,6,1,4,5,2]=>[2,1,3,1]
[3,7,6,1,5,2,4]=>[2,1,2,2]
[3,7,6,1,5,4,2]=>[2,1,2,1,1]
[3,7,6,2,1,4,5]=>[2,1,1,3]
[3,7,6,2,1,5,4]=>[2,1,1,2,1]
[3,7,6,2,4,1,5]=>[2,1,2,2]
[3,7,6,2,4,5,1]=>[2,1,3,1]
[3,7,6,2,5,1,4]=>[2,1,2,2]
[3,7,6,2,5,4,1]=>[2,1,2,1,1]
[3,7,6,4,1,2,5]=>[2,1,1,3]
[3,7,6,4,1,5,2]=>[2,1,1,2,1]
[3,7,6,4,2,1,5]=>[2,1,1,1,2]
[3,7,6,4,2,5,1]=>[2,1,1,2,1]
[3,7,6,4,5,1,2]=>[2,1,2,2]
[3,7,6,4,5,2,1]=>[2,1,2,1,1]
[3,7,6,5,1,2,4]=>[2,1,1,3]
[3,7,6,5,1,4,2]=>[2,1,1,2,1]
[3,7,6,5,2,1,4]=>[2,1,1,1,2]
[3,7,6,5,2,4,1]=>[2,1,1,2,1]
[3,7,6,5,4,1,2]=>[2,1,1,1,2]
[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[4,1,2,3,5,6,7]=>[1,6]
[4,1,2,3,5,7,6]=>[1,5,1]
[4,1,2,3,6,5,7]=>[1,4,2]
[4,1,2,3,6,7,5]=>[1,5,1]
[4,1,2,3,7,5,6]=>[1,4,2]
[4,1,2,3,7,6,5]=>[1,4,1,1]
[4,1,2,5,3,6,7]=>[1,3,3]
[4,1,2,5,3,7,6]=>[1,3,2,1]
[4,1,2,5,6,3,7]=>[1,4,2]
[4,1,2,5,6,7,3]=>[1,5,1]
[4,1,2,5,7,3,6]=>[1,4,2]
[4,1,2,5,7,6,3]=>[1,4,1,1]
[4,1,2,6,3,5,7]=>[1,3,3]
[4,1,2,6,3,7,5]=>[1,3,2,1]
[4,1,2,6,5,3,7]=>[1,3,1,2]
[4,1,2,6,5,7,3]=>[1,3,2,1]
[4,1,2,6,7,3,5]=>[1,4,2]
[4,1,2,6,7,5,3]=>[1,4,1,1]
[4,1,2,7,3,5,6]=>[1,3,3]
[4,1,2,7,3,6,5]=>[1,3,2,1]
[4,1,2,7,5,3,6]=>[1,3,1,2]
[4,1,2,7,5,6,3]=>[1,3,2,1]
[4,1,2,7,6,3,5]=>[1,3,1,2]
[4,1,2,7,6,5,3]=>[1,3,1,1,1]
[4,1,3,2,5,6,7]=>[1,2,4]
[4,1,3,2,5,7,6]=>[1,2,3,1]
[4,1,3,2,6,5,7]=>[1,2,2,2]
[4,1,3,2,6,7,5]=>[1,2,3,1]
[4,1,3,2,7,5,6]=>[1,2,2,2]
[4,1,3,2,7,6,5]=>[1,2,2,1,1]
[4,1,3,5,2,6,7]=>[1,3,3]
[4,1,3,5,2,7,6]=>[1,3,2,1]
[4,1,3,5,6,2,7]=>[1,4,2]
[4,1,3,5,6,7,2]=>[1,5,1]
[4,1,3,5,7,2,6]=>[1,4,2]
[4,1,3,5,7,6,2]=>[1,4,1,1]
[4,1,3,6,2,5,7]=>[1,3,3]
[4,1,3,6,2,7,5]=>[1,3,2,1]
[4,1,3,6,5,2,7]=>[1,3,1,2]
[4,1,3,6,5,7,2]=>[1,3,2,1]
[4,1,3,6,7,2,5]=>[1,4,2]
[4,1,3,6,7,5,2]=>[1,4,1,1]
[4,1,3,7,2,5,6]=>[1,3,3]
[4,1,3,7,2,6,5]=>[1,3,2,1]
[4,1,3,7,5,2,6]=>[1,3,1,2]
[4,1,3,7,5,6,2]=>[1,3,2,1]
[4,1,3,7,6,2,5]=>[1,3,1,2]
[4,1,3,7,6,5,2]=>[1,3,1,1,1]
[4,1,5,2,3,6,7]=>[1,2,4]
[4,1,5,2,3,7,6]=>[1,2,3,1]
[4,1,5,2,6,3,7]=>[1,2,2,2]
[4,1,5,2,6,7,3]=>[1,2,3,1]
[4,1,5,2,7,3,6]=>[1,2,2,2]
[4,1,5,2,7,6,3]=>[1,2,2,1,1]
[4,1,5,3,2,6,7]=>[1,2,1,3]
[4,1,5,3,2,7,6]=>[1,2,1,2,1]
[4,1,5,3,6,2,7]=>[1,2,2,2]
[4,1,5,3,6,7,2]=>[1,2,3,1]
[4,1,5,3,7,2,6]=>[1,2,2,2]
[4,1,5,3,7,6,2]=>[1,2,2,1,1]
[4,1,5,6,2,3,7]=>[1,3,3]
[4,1,5,6,2,7,3]=>[1,3,2,1]
[4,1,5,6,3,2,7]=>[1,3,1,2]
[4,1,5,6,3,7,2]=>[1,3,2,1]
[4,1,5,6,7,2,3]=>[1,4,2]
[4,1,5,6,7,3,2]=>[1,4,1,1]
[4,1,5,7,2,3,6]=>[1,3,3]
[4,1,5,7,2,6,3]=>[1,3,2,1]
[4,1,5,7,3,2,6]=>[1,3,1,2]
[4,1,5,7,3,6,2]=>[1,3,2,1]
[4,1,5,7,6,2,3]=>[1,3,1,2]
[4,1,5,7,6,3,2]=>[1,3,1,1,1]
[4,1,6,2,3,5,7]=>[1,2,4]
[4,1,6,2,3,7,5]=>[1,2,3,1]
[4,1,6,2,5,3,7]=>[1,2,2,2]
[4,1,6,2,5,7,3]=>[1,2,3,1]
[4,1,6,2,7,3,5]=>[1,2,2,2]
[4,1,6,2,7,5,3]=>[1,2,2,1,1]
[4,1,6,3,2,5,7]=>[1,2,1,3]
[4,1,6,3,2,7,5]=>[1,2,1,2,1]
[4,1,6,3,5,2,7]=>[1,2,2,2]
[4,1,6,3,5,7,2]=>[1,2,3,1]
[4,1,6,3,7,2,5]=>[1,2,2,2]
[4,1,6,3,7,5,2]=>[1,2,2,1,1]
[4,1,6,5,2,3,7]=>[1,2,1,3]
[4,1,6,5,2,7,3]=>[1,2,1,2,1]
[4,1,6,5,3,2,7]=>[1,2,1,1,2]
[4,1,6,5,3,7,2]=>[1,2,1,2,1]
[4,1,6,5,7,2,3]=>[1,2,2,2]
[4,1,6,5,7,3,2]=>[1,2,2,1,1]
[4,1,6,7,2,3,5]=>[1,3,3]
[4,1,6,7,2,5,3]=>[1,3,2,1]
[4,1,6,7,3,2,5]=>[1,3,1,2]
[4,1,6,7,3,5,2]=>[1,3,2,1]
[4,1,6,7,5,2,3]=>[1,3,1,2]
[4,1,6,7,5,3,2]=>[1,3,1,1,1]
[4,1,7,2,3,5,6]=>[1,2,4]
[4,1,7,2,3,6,5]=>[1,2,3,1]
[4,1,7,2,5,3,6]=>[1,2,2,2]
[4,1,7,2,5,6,3]=>[1,2,3,1]
[4,1,7,2,6,3,5]=>[1,2,2,2]
[4,1,7,2,6,5,3]=>[1,2,2,1,1]
[4,1,7,3,2,5,6]=>[1,2,1,3]
[4,1,7,3,2,6,5]=>[1,2,1,2,1]
[4,1,7,3,5,2,6]=>[1,2,2,2]
[4,1,7,3,5,6,2]=>[1,2,3,1]
[4,1,7,3,6,2,5]=>[1,2,2,2]
[4,1,7,3,6,5,2]=>[1,2,2,1,1]
[4,1,7,5,2,3,6]=>[1,2,1,3]
[4,1,7,5,2,6,3]=>[1,2,1,2,1]
[4,1,7,5,3,2,6]=>[1,2,1,1,2]
[4,1,7,5,3,6,2]=>[1,2,1,2,1]
[4,1,7,5,6,2,3]=>[1,2,2,2]
[4,1,7,5,6,3,2]=>[1,2,2,1,1]
[4,1,7,6,2,3,5]=>[1,2,1,3]
[4,1,7,6,2,5,3]=>[1,2,1,2,1]
[4,1,7,6,3,2,5]=>[1,2,1,1,2]
[4,1,7,6,3,5,2]=>[1,2,1,2,1]
[4,1,7,6,5,2,3]=>[1,2,1,1,2]
[4,1,7,6,5,3,2]=>[1,2,1,1,1,1]
[4,2,1,3,5,6,7]=>[1,1,5]
[4,2,1,3,5,7,6]=>[1,1,4,1]
[4,2,1,3,6,5,7]=>[1,1,3,2]
[4,2,1,3,6,7,5]=>[1,1,4,1]
[4,2,1,3,7,5,6]=>[1,1,3,2]
[4,2,1,3,7,6,5]=>[1,1,3,1,1]
[4,2,1,5,3,6,7]=>[1,1,2,3]
[4,2,1,5,3,7,6]=>[1,1,2,2,1]
[4,2,1,5,6,3,7]=>[1,1,3,2]
[4,2,1,5,6,7,3]=>[1,1,4,1]
[4,2,1,5,7,3,6]=>[1,1,3,2]
[4,2,1,5,7,6,3]=>[1,1,3,1,1]
[4,2,1,6,3,5,7]=>[1,1,2,3]
[4,2,1,6,3,7,5]=>[1,1,2,2,1]
[4,2,1,6,5,3,7]=>[1,1,2,1,2]
[4,2,1,6,5,7,3]=>[1,1,2,2,1]
[4,2,1,6,7,3,5]=>[1,1,3,2]
[4,2,1,6,7,5,3]=>[1,1,3,1,1]
[4,2,1,7,3,5,6]=>[1,1,2,3]
[4,2,1,7,3,6,5]=>[1,1,2,2,1]
[4,2,1,7,5,3,6]=>[1,1,2,1,2]
[4,2,1,7,5,6,3]=>[1,1,2,2,1]
[4,2,1,7,6,3,5]=>[1,1,2,1,2]
[4,2,1,7,6,5,3]=>[1,1,2,1,1,1]
[4,2,3,1,5,6,7]=>[1,2,4]
[4,2,3,1,5,7,6]=>[1,2,3,1]
[4,2,3,1,6,5,7]=>[1,2,2,2]
[4,2,3,1,6,7,5]=>[1,2,3,1]
[4,2,3,1,7,5,6]=>[1,2,2,2]
[4,2,3,1,7,6,5]=>[1,2,2,1,1]
[4,2,3,5,1,6,7]=>[1,3,3]
[4,2,3,5,1,7,6]=>[1,3,2,1]
[4,2,3,5,6,1,7]=>[1,4,2]
[4,2,3,5,6,7,1]=>[1,5,1]
[4,2,3,5,7,1,6]=>[1,4,2]
[4,2,3,5,7,6,1]=>[1,4,1,1]
[4,2,3,6,1,5,7]=>[1,3,3]
[4,2,3,6,1,7,5]=>[1,3,2,1]
[4,2,3,6,5,1,7]=>[1,3,1,2]
[4,2,3,6,5,7,1]=>[1,3,2,1]
[4,2,3,6,7,1,5]=>[1,4,2]
[4,2,3,6,7,5,1]=>[1,4,1,1]
[4,2,3,7,1,5,6]=>[1,3,3]
[4,2,3,7,1,6,5]=>[1,3,2,1]
[4,2,3,7,5,1,6]=>[1,3,1,2]
[4,2,3,7,5,6,1]=>[1,3,2,1]
[4,2,3,7,6,1,5]=>[1,3,1,2]
[4,2,3,7,6,5,1]=>[1,3,1,1,1]
[4,2,5,1,3,6,7]=>[1,2,4]
[4,2,5,1,3,7,6]=>[1,2,3,1]
[4,2,5,1,6,3,7]=>[1,2,2,2]
[4,2,5,1,6,7,3]=>[1,2,3,1]
[4,2,5,1,7,3,6]=>[1,2,2,2]
[4,2,5,1,7,6,3]=>[1,2,2,1,1]
[4,2,5,3,1,6,7]=>[1,2,1,3]
[4,2,5,3,1,7,6]=>[1,2,1,2,1]
[4,2,5,3,6,1,7]=>[1,2,2,2]
[4,2,5,3,6,7,1]=>[1,2,3,1]
[4,2,5,3,7,1,6]=>[1,2,2,2]
[4,2,5,3,7,6,1]=>[1,2,2,1,1]
[4,2,5,6,1,3,7]=>[1,3,3]
[4,2,5,6,1,7,3]=>[1,3,2,1]
[4,2,5,6,3,1,7]=>[1,3,1,2]
[4,2,5,6,3,7,1]=>[1,3,2,1]
[4,2,5,6,7,1,3]=>[1,4,2]
[4,2,5,6,7,3,1]=>[1,4,1,1]
[4,2,5,7,1,3,6]=>[1,3,3]
[4,2,5,7,1,6,3]=>[1,3,2,1]
[4,2,5,7,3,1,6]=>[1,3,1,2]
[4,2,5,7,3,6,1]=>[1,3,2,1]
[4,2,5,7,6,1,3]=>[1,3,1,2]
[4,2,5,7,6,3,1]=>[1,3,1,1,1]
[4,2,6,1,3,5,7]=>[1,2,4]
[4,2,6,1,3,7,5]=>[1,2,3,1]
[4,2,6,1,5,3,7]=>[1,2,2,2]
[4,2,6,1,5,7,3]=>[1,2,3,1]
[4,2,6,1,7,3,5]=>[1,2,2,2]
[4,2,6,1,7,5,3]=>[1,2,2,1,1]
[4,2,6,3,1,5,7]=>[1,2,1,3]
[4,2,6,3,1,7,5]=>[1,2,1,2,1]
[4,2,6,3,5,1,7]=>[1,2,2,2]
[4,2,6,3,5,7,1]=>[1,2,3,1]
[4,2,6,3,7,1,5]=>[1,2,2,2]
[4,2,6,3,7,5,1]=>[1,2,2,1,1]
[4,2,6,5,1,3,7]=>[1,2,1,3]
[4,2,6,5,1,7,3]=>[1,2,1,2,1]
[4,2,6,5,3,1,7]=>[1,2,1,1,2]
[4,2,6,5,3,7,1]=>[1,2,1,2,1]
[4,2,6,5,7,1,3]=>[1,2,2,2]
[4,2,6,5,7,3,1]=>[1,2,2,1,1]
[4,2,6,7,1,3,5]=>[1,3,3]
[4,2,6,7,1,5,3]=>[1,3,2,1]
[4,2,6,7,3,1,5]=>[1,3,1,2]
[4,2,6,7,3,5,1]=>[1,3,2,1]
[4,2,6,7,5,1,3]=>[1,3,1,2]
[4,2,6,7,5,3,1]=>[1,3,1,1,1]
[4,2,7,1,3,5,6]=>[1,2,4]
[4,2,7,1,3,6,5]=>[1,2,3,1]
[4,2,7,1,5,3,6]=>[1,2,2,2]
[4,2,7,1,5,6,3]=>[1,2,3,1]
[4,2,7,1,6,3,5]=>[1,2,2,2]
[4,2,7,1,6,5,3]=>[1,2,2,1,1]
[4,2,7,3,1,5,6]=>[1,2,1,3]
[4,2,7,3,1,6,5]=>[1,2,1,2,1]
[4,2,7,3,5,1,6]=>[1,2,2,2]
[4,2,7,3,5,6,1]=>[1,2,3,1]
[4,2,7,3,6,1,5]=>[1,2,2,2]
[4,2,7,3,6,5,1]=>[1,2,2,1,1]
[4,2,7,5,1,3,6]=>[1,2,1,3]
[4,2,7,5,1,6,3]=>[1,2,1,2,1]
[4,2,7,5,3,1,6]=>[1,2,1,1,2]
[4,2,7,5,3,6,1]=>[1,2,1,2,1]
[4,2,7,5,6,1,3]=>[1,2,2,2]
[4,2,7,5,6,3,1]=>[1,2,2,1,1]
[4,2,7,6,1,3,5]=>[1,2,1,3]
[4,2,7,6,1,5,3]=>[1,2,1,2,1]
[4,2,7,6,3,1,5]=>[1,2,1,1,2]
[4,2,7,6,3,5,1]=>[1,2,1,2,1]
[4,2,7,6,5,1,3]=>[1,2,1,1,2]
[4,2,7,6,5,3,1]=>[1,2,1,1,1,1]
[4,3,1,2,5,6,7]=>[1,1,5]
[4,3,1,2,5,7,6]=>[1,1,4,1]
[4,3,1,2,6,5,7]=>[1,1,3,2]
[4,3,1,2,6,7,5]=>[1,1,4,1]
[4,3,1,2,7,5,6]=>[1,1,3,2]
[4,3,1,2,7,6,5]=>[1,1,3,1,1]
[4,3,1,5,2,6,7]=>[1,1,2,3]
[4,3,1,5,2,7,6]=>[1,1,2,2,1]
[4,3,1,5,6,2,7]=>[1,1,3,2]
[4,3,1,5,6,7,2]=>[1,1,4,1]
[4,3,1,5,7,2,6]=>[1,1,3,2]
[4,3,1,5,7,6,2]=>[1,1,3,1,1]
[4,3,1,6,2,5,7]=>[1,1,2,3]
[4,3,1,6,2,7,5]=>[1,1,2,2,1]
[4,3,1,6,5,2,7]=>[1,1,2,1,2]
[4,3,1,6,5,7,2]=>[1,1,2,2,1]
[4,3,1,6,7,2,5]=>[1,1,3,2]
[4,3,1,6,7,5,2]=>[1,1,3,1,1]
[4,3,1,7,2,5,6]=>[1,1,2,3]
[4,3,1,7,2,6,5]=>[1,1,2,2,1]
[4,3,1,7,5,2,6]=>[1,1,2,1,2]
[4,3,1,7,5,6,2]=>[1,1,2,2,1]
[4,3,1,7,6,2,5]=>[1,1,2,1,2]
[4,3,1,7,6,5,2]=>[1,1,2,1,1,1]
[4,3,2,1,5,6,7]=>[1,1,1,4]
[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[4,3,2,1,6,7,5]=>[1,1,1,3,1]
[4,3,2,1,7,5,6]=>[1,1,1,2,2]
[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[4,3,2,5,1,6,7]=>[1,1,2,3]
[4,3,2,5,1,7,6]=>[1,1,2,2,1]
[4,3,2,5,6,1,7]=>[1,1,3,2]
[4,3,2,5,6,7,1]=>[1,1,4,1]
[4,3,2,5,7,1,6]=>[1,1,3,2]
[4,3,2,5,7,6,1]=>[1,1,3,1,1]
[4,3,2,6,1,5,7]=>[1,1,2,3]
[4,3,2,6,1,7,5]=>[1,1,2,2,1]
[4,3,2,6,5,1,7]=>[1,1,2,1,2]
[4,3,2,6,5,7,1]=>[1,1,2,2,1]
[4,3,2,6,7,1,5]=>[1,1,3,2]
[4,3,2,6,7,5,1]=>[1,1,3,1,1]
[4,3,2,7,1,5,6]=>[1,1,2,3]
[4,3,2,7,1,6,5]=>[1,1,2,2,1]
[4,3,2,7,5,1,6]=>[1,1,2,1,2]
[4,3,2,7,5,6,1]=>[1,1,2,2,1]
[4,3,2,7,6,1,5]=>[1,1,2,1,2]
[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]
[4,3,5,1,2,6,7]=>[1,2,4]
[4,3,5,1,2,7,6]=>[1,2,3,1]
[4,3,5,1,6,2,7]=>[1,2,2,2]
[4,3,5,1,6,7,2]=>[1,2,3,1]
[4,3,5,1,7,2,6]=>[1,2,2,2]
[4,3,5,1,7,6,2]=>[1,2,2,1,1]
[4,3,5,2,1,6,7]=>[1,2,1,3]
[4,3,5,2,1,7,6]=>[1,2,1,2,1]
[4,3,5,2,6,1,7]=>[1,2,2,2]
[4,3,5,2,6,7,1]=>[1,2,3,1]
[4,3,5,2,7,1,6]=>[1,2,2,2]
[4,3,5,2,7,6,1]=>[1,2,2,1,1]
[4,3,5,6,1,2,7]=>[1,3,3]
[4,3,5,6,1,7,2]=>[1,3,2,1]
[4,3,5,6,2,1,7]=>[1,3,1,2]
[4,3,5,6,2,7,1]=>[1,3,2,1]
[4,3,5,6,7,1,2]=>[1,4,2]
[4,3,5,6,7,2,1]=>[1,4,1,1]
[4,3,5,7,1,2,6]=>[1,3,3]
[4,3,5,7,1,6,2]=>[1,3,2,1]
[4,3,5,7,2,1,6]=>[1,3,1,2]
[4,3,5,7,2,6,1]=>[1,3,2,1]
[4,3,5,7,6,1,2]=>[1,3,1,2]
[4,3,5,7,6,2,1]=>[1,3,1,1,1]
[4,3,6,1,2,5,7]=>[1,2,4]
[4,3,6,1,2,7,5]=>[1,2,3,1]
[4,3,6,1,5,2,7]=>[1,2,2,2]
[4,3,6,1,5,7,2]=>[1,2,3,1]
[4,3,6,1,7,2,5]=>[1,2,2,2]
[4,3,6,1,7,5,2]=>[1,2,2,1,1]
[4,3,6,2,1,5,7]=>[1,2,1,3]
[4,3,6,2,1,7,5]=>[1,2,1,2,1]
[4,3,6,2,5,1,7]=>[1,2,2,2]
[4,3,6,2,5,7,1]=>[1,2,3,1]
[4,3,6,2,7,1,5]=>[1,2,2,2]
[4,3,6,2,7,5,1]=>[1,2,2,1,1]
[4,3,6,5,1,2,7]=>[1,2,1,3]
[4,3,6,5,1,7,2]=>[1,2,1,2,1]
[4,3,6,5,2,1,7]=>[1,2,1,1,2]
[4,3,6,5,2,7,1]=>[1,2,1,2,1]
[4,3,6,5,7,1,2]=>[1,2,2,2]
[4,3,6,5,7,2,1]=>[1,2,2,1,1]
[4,3,6,7,1,2,5]=>[1,3,3]
[4,3,6,7,1,5,2]=>[1,3,2,1]
[4,3,6,7,2,1,5]=>[1,3,1,2]
[4,3,6,7,2,5,1]=>[1,3,2,1]
[4,3,6,7,5,1,2]=>[1,3,1,2]
[4,3,6,7,5,2,1]=>[1,3,1,1,1]
[4,3,7,1,2,5,6]=>[1,2,4]
[4,3,7,1,2,6,5]=>[1,2,3,1]
[4,3,7,1,5,2,6]=>[1,2,2,2]
[4,3,7,1,5,6,2]=>[1,2,3,1]
[4,3,7,1,6,2,5]=>[1,2,2,2]
[4,3,7,1,6,5,2]=>[1,2,2,1,1]
[4,3,7,2,1,5,6]=>[1,2,1,3]
[4,3,7,2,1,6,5]=>[1,2,1,2,1]
[4,3,7,2,5,1,6]=>[1,2,2,2]
[4,3,7,2,5,6,1]=>[1,2,3,1]
[4,3,7,2,6,1,5]=>[1,2,2,2]
[4,3,7,2,6,5,1]=>[1,2,2,1,1]
[4,3,7,5,1,2,6]=>[1,2,1,3]
[4,3,7,5,1,6,2]=>[1,2,1,2,1]
[4,3,7,5,2,1,6]=>[1,2,1,1,2]
[4,3,7,5,2,6,1]=>[1,2,1,2,1]
[4,3,7,5,6,1,2]=>[1,2,2,2]
[4,3,7,5,6,2,1]=>[1,2,2,1,1]
[4,3,7,6,1,2,5]=>[1,2,1,3]
[4,3,7,6,1,5,2]=>[1,2,1,2,1]
[4,3,7,6,2,1,5]=>[1,2,1,1,2]
[4,3,7,6,2,5,1]=>[1,2,1,2,1]
[4,3,7,6,5,1,2]=>[1,2,1,1,2]
[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]
[4,5,1,2,3,6,7]=>[2,5]
[4,5,1,2,3,7,6]=>[2,4,1]
[4,5,1,2,6,3,7]=>[2,3,2]
[4,5,1,2,6,7,3]=>[2,4,1]
[4,5,1,2,7,3,6]=>[2,3,2]
[4,5,1,2,7,6,3]=>[2,3,1,1]
[4,5,1,3,2,6,7]=>[2,2,3]
[4,5,1,3,2,7,6]=>[2,2,2,1]
[4,5,1,3,6,2,7]=>[2,3,2]
[4,5,1,3,6,7,2]=>[2,4,1]
[4,5,1,3,7,2,6]=>[2,3,2]
[4,5,1,3,7,6,2]=>[2,3,1,1]
[4,5,1,6,2,3,7]=>[2,2,3]
[4,5,1,6,2,7,3]=>[2,2,2,1]
[4,5,1,6,3,2,7]=>[2,2,1,2]
[4,5,1,6,3,7,2]=>[2,2,2,1]
[4,5,1,6,7,2,3]=>[2,3,2]
[4,5,1,6,7,3,2]=>[2,3,1,1]
[4,5,1,7,2,3,6]=>[2,2,3]
[4,5,1,7,2,6,3]=>[2,2,2,1]
[4,5,1,7,3,2,6]=>[2,2,1,2]
[4,5,1,7,3,6,2]=>[2,2,2,1]
[4,5,1,7,6,2,3]=>[2,2,1,2]
[4,5,1,7,6,3,2]=>[2,2,1,1,1]
[4,5,2,1,3,6,7]=>[2,1,4]
[4,5,2,1,3,7,6]=>[2,1,3,1]
[4,5,2,1,6,3,7]=>[2,1,2,2]
[4,5,2,1,6,7,3]=>[2,1,3,1]
[4,5,2,1,7,3,6]=>[2,1,2,2]
[4,5,2,1,7,6,3]=>[2,1,2,1,1]
[4,5,2,3,1,6,7]=>[2,2,3]
[4,5,2,3,1,7,6]=>[2,2,2,1]
[4,5,2,3,6,1,7]=>[2,3,2]
[4,5,2,3,6,7,1]=>[2,4,1]
[4,5,2,3,7,1,6]=>[2,3,2]
[4,5,2,3,7,6,1]=>[2,3,1,1]
[4,5,2,6,1,3,7]=>[2,2,3]
[4,5,2,6,1,7,3]=>[2,2,2,1]
[4,5,2,6,3,1,7]=>[2,2,1,2]
[4,5,2,6,3,7,1]=>[2,2,2,1]
[4,5,2,6,7,1,3]=>[2,3,2]
[4,5,2,6,7,3,1]=>[2,3,1,1]
[4,5,2,7,1,3,6]=>[2,2,3]
[4,5,2,7,1,6,3]=>[2,2,2,1]
[4,5,2,7,3,1,6]=>[2,2,1,2]
[4,5,2,7,3,6,1]=>[2,2,2,1]
[4,5,2,7,6,1,3]=>[2,2,1,2]
[4,5,2,7,6,3,1]=>[2,2,1,1,1]
[4,5,3,1,2,6,7]=>[2,1,4]
[4,5,3,1,2,7,6]=>[2,1,3,1]
[4,5,3,1,6,2,7]=>[2,1,2,2]
[4,5,3,1,6,7,2]=>[2,1,3,1]
[4,5,3,1,7,2,6]=>[2,1,2,2]
[4,5,3,1,7,6,2]=>[2,1,2,1,1]
[4,5,3,2,1,6,7]=>[2,1,1,3]
[4,5,3,2,1,7,6]=>[2,1,1,2,1]
[4,5,3,2,6,1,7]=>[2,1,2,2]
[4,5,3,2,6,7,1]=>[2,1,3,1]
[4,5,3,2,7,1,6]=>[2,1,2,2]
[4,5,3,2,7,6,1]=>[2,1,2,1,1]
[4,5,3,6,1,2,7]=>[2,2,3]
[4,5,3,6,1,7,2]=>[2,2,2,1]
[4,5,3,6,2,1,7]=>[2,2,1,2]
[4,5,3,6,2,7,1]=>[2,2,2,1]
[4,5,3,6,7,1,2]=>[2,3,2]
[4,5,3,6,7,2,1]=>[2,3,1,1]
[4,5,3,7,1,2,6]=>[2,2,3]
[4,5,3,7,1,6,2]=>[2,2,2,1]
[4,5,3,7,2,1,6]=>[2,2,1,2]
[4,5,3,7,2,6,1]=>[2,2,2,1]
[4,5,3,7,6,1,2]=>[2,2,1,2]
[4,5,3,7,6,2,1]=>[2,2,1,1,1]
[4,5,6,1,2,3,7]=>[3,4]
[4,5,6,1,2,7,3]=>[3,3,1]
[4,5,6,1,3,2,7]=>[3,2,2]
[4,5,6,1,3,7,2]=>[3,3,1]
[4,5,6,1,7,2,3]=>[3,2,2]
[4,5,6,1,7,3,2]=>[3,2,1,1]
[4,5,6,2,1,3,7]=>[3,1,3]
[4,5,6,2,1,7,3]=>[3,1,2,1]
[4,5,6,2,3,1,7]=>[3,2,2]
[4,5,6,2,3,7,1]=>[3,3,1]
[4,5,6,2,7,1,3]=>[3,2,2]
[4,5,6,2,7,3,1]=>[3,2,1,1]
[4,5,6,3,1,2,7]=>[3,1,3]
[4,5,6,3,1,7,2]=>[3,1,2,1]
[4,5,6,3,2,1,7]=>[3,1,1,2]
[4,5,6,3,2,7,1]=>[3,1,2,1]
[4,5,6,3,7,1,2]=>[3,2,2]
[4,5,6,3,7,2,1]=>[3,2,1,1]
[4,5,6,7,1,2,3]=>[4,3]
[4,5,6,7,1,3,2]=>[4,2,1]
[4,5,6,7,2,1,3]=>[4,1,2]
[4,5,6,7,2,3,1]=>[4,2,1]
[4,5,6,7,3,1,2]=>[4,1,2]
[4,5,6,7,3,2,1]=>[4,1,1,1]
[4,5,7,1,2,3,6]=>[3,4]
[4,5,7,1,2,6,3]=>[3,3,1]
[4,5,7,1,3,2,6]=>[3,2,2]
[4,5,7,1,3,6,2]=>[3,3,1]
[4,5,7,1,6,2,3]=>[3,2,2]
[4,5,7,1,6,3,2]=>[3,2,1,1]
[4,5,7,2,1,3,6]=>[3,1,3]
[4,5,7,2,1,6,3]=>[3,1,2,1]
[4,5,7,2,3,1,6]=>[3,2,2]
[4,5,7,2,3,6,1]=>[3,3,1]
[4,5,7,2,6,1,3]=>[3,2,2]
[4,5,7,2,6,3,1]=>[3,2,1,1]
[4,5,7,3,1,2,6]=>[3,1,3]
[4,5,7,3,1,6,2]=>[3,1,2,1]
[4,5,7,3,2,1,6]=>[3,1,1,2]
[4,5,7,3,2,6,1]=>[3,1,2,1]
[4,5,7,3,6,1,2]=>[3,2,2]
[4,5,7,3,6,2,1]=>[3,2,1,1]
[4,5,7,6,1,2,3]=>[3,1,3]
[4,5,7,6,1,3,2]=>[3,1,2,1]
[4,5,7,6,2,1,3]=>[3,1,1,2]
[4,5,7,6,2,3,1]=>[3,1,2,1]
[4,5,7,6,3,1,2]=>[3,1,1,2]
[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[4,6,1,2,3,5,7]=>[2,5]
[4,6,1,2,3,7,5]=>[2,4,1]
[4,6,1,2,5,3,7]=>[2,3,2]
[4,6,1,2,5,7,3]=>[2,4,1]
[4,6,1,2,7,3,5]=>[2,3,2]
[4,6,1,2,7,5,3]=>[2,3,1,1]
[4,6,1,3,2,5,7]=>[2,2,3]
[4,6,1,3,2,7,5]=>[2,2,2,1]
[4,6,1,3,5,2,7]=>[2,3,2]
[4,6,1,3,5,7,2]=>[2,4,1]
[4,6,1,3,7,2,5]=>[2,3,2]
[4,6,1,3,7,5,2]=>[2,3,1,1]
[4,6,1,5,2,3,7]=>[2,2,3]
[4,6,1,5,2,7,3]=>[2,2,2,1]
[4,6,1,5,3,2,7]=>[2,2,1,2]
[4,6,1,5,3,7,2]=>[2,2,2,1]
[4,6,1,5,7,2,3]=>[2,3,2]
[4,6,1,5,7,3,2]=>[2,3,1,1]
[4,6,1,7,2,3,5]=>[2,2,3]
[4,6,1,7,2,5,3]=>[2,2,2,1]
[4,6,1,7,3,2,5]=>[2,2,1,2]
[4,6,1,7,3,5,2]=>[2,2,2,1]
[4,6,1,7,5,2,3]=>[2,2,1,2]
[4,6,1,7,5,3,2]=>[2,2,1,1,1]
[4,6,2,1,3,5,7]=>[2,1,4]
[4,6,2,1,3,7,5]=>[2,1,3,1]
[4,6,2,1,5,3,7]=>[2,1,2,2]
[4,6,2,1,5,7,3]=>[2,1,3,1]
[4,6,2,1,7,3,5]=>[2,1,2,2]
[4,6,2,1,7,5,3]=>[2,1,2,1,1]
[4,6,2,3,1,5,7]=>[2,2,3]
[4,6,2,3,1,7,5]=>[2,2,2,1]
[4,6,2,3,5,1,7]=>[2,3,2]
[4,6,2,3,5,7,1]=>[2,4,1]
[4,6,2,3,7,1,5]=>[2,3,2]
[4,6,2,3,7,5,1]=>[2,3,1,1]
[4,6,2,5,1,3,7]=>[2,2,3]
[4,6,2,5,1,7,3]=>[2,2,2,1]
[4,6,2,5,3,1,7]=>[2,2,1,2]
[4,6,2,5,3,7,1]=>[2,2,2,1]
[4,6,2,5,7,1,3]=>[2,3,2]
[4,6,2,5,7,3,1]=>[2,3,1,1]
[4,6,2,7,1,3,5]=>[2,2,3]
[4,6,2,7,1,5,3]=>[2,2,2,1]
[4,6,2,7,3,1,5]=>[2,2,1,2]
[4,6,2,7,3,5,1]=>[2,2,2,1]
[4,6,2,7,5,1,3]=>[2,2,1,2]
[4,6,2,7,5,3,1]=>[2,2,1,1,1]
[4,6,3,1,2,5,7]=>[2,1,4]
[4,6,3,1,2,7,5]=>[2,1,3,1]
[4,6,3,1,5,2,7]=>[2,1,2,2]
[4,6,3,1,5,7,2]=>[2,1,3,1]
[4,6,3,1,7,2,5]=>[2,1,2,2]
[4,6,3,1,7,5,2]=>[2,1,2,1,1]
[4,6,3,2,1,5,7]=>[2,1,1,3]
[4,6,3,2,1,7,5]=>[2,1,1,2,1]
[4,6,3,2,5,1,7]=>[2,1,2,2]
[4,6,3,2,5,7,1]=>[2,1,3,1]
[4,6,3,2,7,1,5]=>[2,1,2,2]
[4,6,3,2,7,5,1]=>[2,1,2,1,1]
[4,6,3,5,1,2,7]=>[2,2,3]
[4,6,3,5,1,7,2]=>[2,2,2,1]
[4,6,3,5,2,1,7]=>[2,2,1,2]
[4,6,3,5,2,7,1]=>[2,2,2,1]
[4,6,3,5,7,1,2]=>[2,3,2]
[4,6,3,5,7,2,1]=>[2,3,1,1]
[4,6,3,7,1,2,5]=>[2,2,3]
[4,6,3,7,1,5,2]=>[2,2,2,1]
[4,6,3,7,2,1,5]=>[2,2,1,2]
[4,6,3,7,2,5,1]=>[2,2,2,1]
[4,6,3,7,5,1,2]=>[2,2,1,2]
[4,6,3,7,5,2,1]=>[2,2,1,1,1]
[4,6,5,1,2,3,7]=>[2,1,4]
[4,6,5,1,2,7,3]=>[2,1,3,1]
[4,6,5,1,3,2,7]=>[2,1,2,2]
[4,6,5,1,3,7,2]=>[2,1,3,1]
[4,6,5,1,7,2,3]=>[2,1,2,2]
[4,6,5,1,7,3,2]=>[2,1,2,1,1]
[4,6,5,2,1,3,7]=>[2,1,1,3]
[4,6,5,2,1,7,3]=>[2,1,1,2,1]
[4,6,5,2,3,1,7]=>[2,1,2,2]
[4,6,5,2,3,7,1]=>[2,1,3,1]
[4,6,5,2,7,1,3]=>[2,1,2,2]
[4,6,5,2,7,3,1]=>[2,1,2,1,1]
[4,6,5,3,1,2,7]=>[2,1,1,3]
[4,6,5,3,1,7,2]=>[2,1,1,2,1]
[4,6,5,3,2,1,7]=>[2,1,1,1,2]
[4,6,5,3,2,7,1]=>[2,1,1,2,1]
[4,6,5,3,7,1,2]=>[2,1,2,2]
[4,6,5,3,7,2,1]=>[2,1,2,1,1]
[4,6,5,7,1,2,3]=>[2,2,3]
[4,6,5,7,1,3,2]=>[2,2,2,1]
[4,6,5,7,2,1,3]=>[2,2,1,2]
[4,6,5,7,2,3,1]=>[2,2,2,1]
[4,6,5,7,3,1,2]=>[2,2,1,2]
[4,6,5,7,3,2,1]=>[2,2,1,1,1]
[4,6,7,1,2,3,5]=>[3,4]
[4,6,7,1,2,5,3]=>[3,3,1]
[4,6,7,1,3,2,5]=>[3,2,2]
[4,6,7,1,3,5,2]=>[3,3,1]
[4,6,7,1,5,2,3]=>[3,2,2]
[4,6,7,1,5,3,2]=>[3,2,1,1]
[4,6,7,2,1,3,5]=>[3,1,3]
[4,6,7,2,1,5,3]=>[3,1,2,1]
[4,6,7,2,3,1,5]=>[3,2,2]
[4,6,7,2,3,5,1]=>[3,3,1]
[4,6,7,2,5,1,3]=>[3,2,2]
[4,6,7,2,5,3,1]=>[3,2,1,1]
[4,6,7,3,1,2,5]=>[3,1,3]
[4,6,7,3,1,5,2]=>[3,1,2,1]
[4,6,7,3,2,1,5]=>[3,1,1,2]
[4,6,7,3,2,5,1]=>[3,1,2,1]
[4,6,7,3,5,1,2]=>[3,2,2]
[4,6,7,3,5,2,1]=>[3,2,1,1]
[4,6,7,5,1,2,3]=>[3,1,3]
[4,6,7,5,1,3,2]=>[3,1,2,1]
[4,6,7,5,2,1,3]=>[3,1,1,2]
[4,6,7,5,2,3,1]=>[3,1,2,1]
[4,6,7,5,3,1,2]=>[3,1,1,2]
[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[4,7,1,2,3,5,6]=>[2,5]
[4,7,1,2,3,6,5]=>[2,4,1]
[4,7,1,2,5,3,6]=>[2,3,2]
[4,7,1,2,5,6,3]=>[2,4,1]
[4,7,1,2,6,3,5]=>[2,3,2]
[4,7,1,2,6,5,3]=>[2,3,1,1]
[4,7,1,3,2,5,6]=>[2,2,3]
[4,7,1,3,2,6,5]=>[2,2,2,1]
[4,7,1,3,5,2,6]=>[2,3,2]
[4,7,1,3,5,6,2]=>[2,4,1]
[4,7,1,3,6,2,5]=>[2,3,2]
[4,7,1,3,6,5,2]=>[2,3,1,1]
[4,7,1,5,2,3,6]=>[2,2,3]
[4,7,1,5,2,6,3]=>[2,2,2,1]
[4,7,1,5,3,2,6]=>[2,2,1,2]
[4,7,1,5,3,6,2]=>[2,2,2,1]
[4,7,1,5,6,2,3]=>[2,3,2]
[4,7,1,5,6,3,2]=>[2,3,1,1]
[4,7,1,6,2,3,5]=>[2,2,3]
[4,7,1,6,2,5,3]=>[2,2,2,1]
[4,7,1,6,3,2,5]=>[2,2,1,2]
[4,7,1,6,3,5,2]=>[2,2,2,1]
[4,7,1,6,5,2,3]=>[2,2,1,2]
[4,7,1,6,5,3,2]=>[2,2,1,1,1]
[4,7,2,1,3,5,6]=>[2,1,4]
[4,7,2,1,3,6,5]=>[2,1,3,1]
[4,7,2,1,5,3,6]=>[2,1,2,2]
[4,7,2,1,5,6,3]=>[2,1,3,1]
[4,7,2,1,6,3,5]=>[2,1,2,2]
[4,7,2,1,6,5,3]=>[2,1,2,1,1]
[4,7,2,3,1,5,6]=>[2,2,3]
[4,7,2,3,1,6,5]=>[2,2,2,1]
[4,7,2,3,5,1,6]=>[2,3,2]
[4,7,2,3,5,6,1]=>[2,4,1]
[4,7,2,3,6,1,5]=>[2,3,2]
[4,7,2,3,6,5,1]=>[2,3,1,1]
[4,7,2,5,1,3,6]=>[2,2,3]
[4,7,2,5,1,6,3]=>[2,2,2,1]
[4,7,2,5,3,1,6]=>[2,2,1,2]
[4,7,2,5,3,6,1]=>[2,2,2,1]
[4,7,2,5,6,1,3]=>[2,3,2]
[4,7,2,5,6,3,1]=>[2,3,1,1]
[4,7,2,6,1,3,5]=>[2,2,3]
[4,7,2,6,1,5,3]=>[2,2,2,1]
[4,7,2,6,3,1,5]=>[2,2,1,2]
[4,7,2,6,3,5,1]=>[2,2,2,1]
[4,7,2,6,5,1,3]=>[2,2,1,2]
[4,7,2,6,5,3,1]=>[2,2,1,1,1]
[4,7,3,1,2,5,6]=>[2,1,4]
[4,7,3,1,2,6,5]=>[2,1,3,1]
[4,7,3,1,5,2,6]=>[2,1,2,2]
[4,7,3,1,5,6,2]=>[2,1,3,1]
[4,7,3,1,6,2,5]=>[2,1,2,2]
[4,7,3,1,6,5,2]=>[2,1,2,1,1]
[4,7,3,2,1,5,6]=>[2,1,1,3]
[4,7,3,2,1,6,5]=>[2,1,1,2,1]
[4,7,3,2,5,1,6]=>[2,1,2,2]
[4,7,3,2,5,6,1]=>[2,1,3,1]
[4,7,3,2,6,1,5]=>[2,1,2,2]
[4,7,3,2,6,5,1]=>[2,1,2,1,1]
[4,7,3,5,1,2,6]=>[2,2,3]
[4,7,3,5,1,6,2]=>[2,2,2,1]
[4,7,3,5,2,1,6]=>[2,2,1,2]
[4,7,3,5,2,6,1]=>[2,2,2,1]
[4,7,3,5,6,1,2]=>[2,3,2]
[4,7,3,5,6,2,1]=>[2,3,1,1]
[4,7,3,6,1,2,5]=>[2,2,3]
[4,7,3,6,1,5,2]=>[2,2,2,1]
[4,7,3,6,2,1,5]=>[2,2,1,2]
[4,7,3,6,2,5,1]=>[2,2,2,1]
[4,7,3,6,5,1,2]=>[2,2,1,2]
[4,7,3,6,5,2,1]=>[2,2,1,1,1]
[4,7,5,1,2,3,6]=>[2,1,4]
[4,7,5,1,2,6,3]=>[2,1,3,1]
[4,7,5,1,3,2,6]=>[2,1,2,2]
[4,7,5,1,3,6,2]=>[2,1,3,1]
[4,7,5,1,6,2,3]=>[2,1,2,2]
[4,7,5,1,6,3,2]=>[2,1,2,1,1]
[4,7,5,2,1,3,6]=>[2,1,1,3]
[4,7,5,2,1,6,3]=>[2,1,1,2,1]
[4,7,5,2,3,1,6]=>[2,1,2,2]
[4,7,5,2,3,6,1]=>[2,1,3,1]
[4,7,5,2,6,1,3]=>[2,1,2,2]
[4,7,5,2,6,3,1]=>[2,1,2,1,1]
[4,7,5,3,1,2,6]=>[2,1,1,3]
[4,7,5,3,1,6,2]=>[2,1,1,2,1]
[4,7,5,3,2,1,6]=>[2,1,1,1,2]
[4,7,5,3,2,6,1]=>[2,1,1,2,1]
[4,7,5,3,6,1,2]=>[2,1,2,2]
[4,7,5,3,6,2,1]=>[2,1,2,1,1]
[4,7,5,6,1,2,3]=>[2,2,3]
[4,7,5,6,1,3,2]=>[2,2,2,1]
[4,7,5,6,2,1,3]=>[2,2,1,2]
[4,7,5,6,2,3,1]=>[2,2,2,1]
[4,7,5,6,3,1,2]=>[2,2,1,2]
[4,7,5,6,3,2,1]=>[2,2,1,1,1]
[4,7,6,1,2,3,5]=>[2,1,4]
[4,7,6,1,2,5,3]=>[2,1,3,1]
[4,7,6,1,3,2,5]=>[2,1,2,2]
[4,7,6,1,3,5,2]=>[2,1,3,1]
[4,7,6,1,5,2,3]=>[2,1,2,2]
[4,7,6,1,5,3,2]=>[2,1,2,1,1]
[4,7,6,2,1,3,5]=>[2,1,1,3]
[4,7,6,2,1,5,3]=>[2,1,1,2,1]
[4,7,6,2,3,1,5]=>[2,1,2,2]
[4,7,6,2,3,5,1]=>[2,1,3,1]
[4,7,6,2,5,1,3]=>[2,1,2,2]
[4,7,6,2,5,3,1]=>[2,1,2,1,1]
[4,7,6,3,1,2,5]=>[2,1,1,3]
[4,7,6,3,1,5,2]=>[2,1,1,2,1]
[4,7,6,3,2,1,5]=>[2,1,1,1,2]
[4,7,6,3,2,5,1]=>[2,1,1,2,1]
[4,7,6,3,5,1,2]=>[2,1,2,2]
[4,7,6,3,5,2,1]=>[2,1,2,1,1]
[4,7,6,5,1,2,3]=>[2,1,1,3]
[4,7,6,5,1,3,2]=>[2,1,1,2,1]
[4,7,6,5,2,1,3]=>[2,1,1,1,2]
[4,7,6,5,2,3,1]=>[2,1,1,2,1]
[4,7,6,5,3,1,2]=>[2,1,1,1,2]
[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[5,1,2,3,4,6,7]=>[1,6]
[5,1,2,3,4,7,6]=>[1,5,1]
[5,1,2,3,6,4,7]=>[1,4,2]
[5,1,2,3,6,7,4]=>[1,5,1]
[5,1,2,3,7,4,6]=>[1,4,2]
[5,1,2,3,7,6,4]=>[1,4,1,1]
[5,1,2,4,3,6,7]=>[1,3,3]
[5,1,2,4,3,7,6]=>[1,3,2,1]
[5,1,2,4,6,3,7]=>[1,4,2]
[5,1,2,4,6,7,3]=>[1,5,1]
[5,1,2,4,7,3,6]=>[1,4,2]
[5,1,2,4,7,6,3]=>[1,4,1,1]
[5,1,2,6,3,4,7]=>[1,3,3]
[5,1,2,6,3,7,4]=>[1,3,2,1]
[5,1,2,6,4,3,7]=>[1,3,1,2]
[5,1,2,6,4,7,3]=>[1,3,2,1]
[5,1,2,6,7,3,4]=>[1,4,2]
[5,1,2,6,7,4,3]=>[1,4,1,1]
[5,1,2,7,3,4,6]=>[1,3,3]
[5,1,2,7,3,6,4]=>[1,3,2,1]
[5,1,2,7,4,3,6]=>[1,3,1,2]
[5,1,2,7,4,6,3]=>[1,3,2,1]
[5,1,2,7,6,3,4]=>[1,3,1,2]
[5,1,2,7,6,4,3]=>[1,3,1,1,1]
[5,1,3,2,4,6,7]=>[1,2,4]
[5,1,3,2,4,7,6]=>[1,2,3,1]
[5,1,3,2,6,4,7]=>[1,2,2,2]
[5,1,3,2,6,7,4]=>[1,2,3,1]
[5,1,3,2,7,4,6]=>[1,2,2,2]
[5,1,3,2,7,6,4]=>[1,2,2,1,1]
[5,1,3,4,2,6,7]=>[1,3,3]
[5,1,3,4,2,7,6]=>[1,3,2,1]
[5,1,3,4,6,2,7]=>[1,4,2]
[5,1,3,4,6,7,2]=>[1,5,1]
[5,1,3,4,7,2,6]=>[1,4,2]
[5,1,3,4,7,6,2]=>[1,4,1,1]
[5,1,3,6,2,4,7]=>[1,3,3]
[5,1,3,6,2,7,4]=>[1,3,2,1]
[5,1,3,6,4,2,7]=>[1,3,1,2]
[5,1,3,6,4,7,2]=>[1,3,2,1]
[5,1,3,6,7,2,4]=>[1,4,2]
[5,1,3,6,7,4,2]=>[1,4,1,1]
[5,1,3,7,2,4,6]=>[1,3,3]
[5,1,3,7,2,6,4]=>[1,3,2,1]
[5,1,3,7,4,2,6]=>[1,3,1,2]
[5,1,3,7,4,6,2]=>[1,3,2,1]
[5,1,3,7,6,2,4]=>[1,3,1,2]
[5,1,3,7,6,4,2]=>[1,3,1,1,1]
[5,1,4,2,3,6,7]=>[1,2,4]
[5,1,4,2,3,7,6]=>[1,2,3,1]
[5,1,4,2,6,3,7]=>[1,2,2,2]
[5,1,4,2,6,7,3]=>[1,2,3,1]
[5,1,4,2,7,3,6]=>[1,2,2,2]
[5,1,4,2,7,6,3]=>[1,2,2,1,1]
[5,1,4,3,2,6,7]=>[1,2,1,3]
[5,1,4,3,2,7,6]=>[1,2,1,2,1]
[5,1,4,3,6,2,7]=>[1,2,2,2]
[5,1,4,3,6,7,2]=>[1,2,3,1]
[5,1,4,3,7,2,6]=>[1,2,2,2]
[5,1,4,3,7,6,2]=>[1,2,2,1,1]
[5,1,4,6,2,3,7]=>[1,3,3]
[5,1,4,6,2,7,3]=>[1,3,2,1]
[5,1,4,6,3,2,7]=>[1,3,1,2]
[5,1,4,6,3,7,2]=>[1,3,2,1]
[5,1,4,6,7,2,3]=>[1,4,2]
[5,1,4,6,7,3,2]=>[1,4,1,1]
[5,1,4,7,2,3,6]=>[1,3,3]
[5,1,4,7,2,6,3]=>[1,3,2,1]
[5,1,4,7,3,2,6]=>[1,3,1,2]
[5,1,4,7,3,6,2]=>[1,3,2,1]
[5,1,4,7,6,2,3]=>[1,3,1,2]
[5,1,4,7,6,3,2]=>[1,3,1,1,1]
[5,1,6,2,3,4,7]=>[1,2,4]
[5,1,6,2,3,7,4]=>[1,2,3,1]
[5,1,6,2,4,3,7]=>[1,2,2,2]
[5,1,6,2,4,7,3]=>[1,2,3,1]
[5,1,6,2,7,3,4]=>[1,2,2,2]
[5,1,6,2,7,4,3]=>[1,2,2,1,1]
[5,1,6,3,2,4,7]=>[1,2,1,3]
[5,1,6,3,2,7,4]=>[1,2,1,2,1]
[5,1,6,3,4,2,7]=>[1,2,2,2]
[5,1,6,3,4,7,2]=>[1,2,3,1]
[5,1,6,3,7,2,4]=>[1,2,2,2]
[5,1,6,3,7,4,2]=>[1,2,2,1,1]
[5,1,6,4,2,3,7]=>[1,2,1,3]
[5,1,6,4,2,7,3]=>[1,2,1,2,1]
[5,1,6,4,3,2,7]=>[1,2,1,1,2]
[5,1,6,4,3,7,2]=>[1,2,1,2,1]
[5,1,6,4,7,2,3]=>[1,2,2,2]
[5,1,6,4,7,3,2]=>[1,2,2,1,1]
[5,1,6,7,2,3,4]=>[1,3,3]
[5,1,6,7,2,4,3]=>[1,3,2,1]
[5,1,6,7,3,2,4]=>[1,3,1,2]
[5,1,6,7,3,4,2]=>[1,3,2,1]
[5,1,6,7,4,2,3]=>[1,3,1,2]
[5,1,6,7,4,3,2]=>[1,3,1,1,1]
[5,1,7,2,3,4,6]=>[1,2,4]
[5,1,7,2,3,6,4]=>[1,2,3,1]
[5,1,7,2,4,3,6]=>[1,2,2,2]
[5,1,7,2,4,6,3]=>[1,2,3,1]
[5,1,7,2,6,3,4]=>[1,2,2,2]
[5,1,7,2,6,4,3]=>[1,2,2,1,1]
[5,1,7,3,2,4,6]=>[1,2,1,3]
[5,1,7,3,2,6,4]=>[1,2,1,2,1]
[5,1,7,3,4,2,6]=>[1,2,2,2]
[5,1,7,3,4,6,2]=>[1,2,3,1]
[5,1,7,3,6,2,4]=>[1,2,2,2]
[5,1,7,3,6,4,2]=>[1,2,2,1,1]
[5,1,7,4,2,3,6]=>[1,2,1,3]
[5,1,7,4,2,6,3]=>[1,2,1,2,1]
[5,1,7,4,3,2,6]=>[1,2,1,1,2]
[5,1,7,4,3,6,2]=>[1,2,1,2,1]
[5,1,7,4,6,2,3]=>[1,2,2,2]
[5,1,7,4,6,3,2]=>[1,2,2,1,1]
[5,1,7,6,2,3,4]=>[1,2,1,3]
[5,1,7,6,2,4,3]=>[1,2,1,2,1]
[5,1,7,6,3,2,4]=>[1,2,1,1,2]
[5,1,7,6,3,4,2]=>[1,2,1,2,1]
[5,1,7,6,4,2,3]=>[1,2,1,1,2]
[5,1,7,6,4,3,2]=>[1,2,1,1,1,1]
[5,2,1,3,4,6,7]=>[1,1,5]
[5,2,1,3,4,7,6]=>[1,1,4,1]
[5,2,1,3,6,4,7]=>[1,1,3,2]
[5,2,1,3,6,7,4]=>[1,1,4,1]
[5,2,1,3,7,4,6]=>[1,1,3,2]
[5,2,1,3,7,6,4]=>[1,1,3,1,1]
[5,2,1,4,3,6,7]=>[1,1,2,3]
[5,2,1,4,3,7,6]=>[1,1,2,2,1]
[5,2,1,4,6,3,7]=>[1,1,3,2]
[5,2,1,4,6,7,3]=>[1,1,4,1]
[5,2,1,4,7,3,6]=>[1,1,3,2]
[5,2,1,4,7,6,3]=>[1,1,3,1,1]
[5,2,1,6,3,4,7]=>[1,1,2,3]
[5,2,1,6,3,7,4]=>[1,1,2,2,1]
[5,2,1,6,4,3,7]=>[1,1,2,1,2]
[5,2,1,6,4,7,3]=>[1,1,2,2,1]
[5,2,1,6,7,3,4]=>[1,1,3,2]
[5,2,1,6,7,4,3]=>[1,1,3,1,1]
[5,2,1,7,3,4,6]=>[1,1,2,3]
[5,2,1,7,3,6,4]=>[1,1,2,2,1]
[5,2,1,7,4,3,6]=>[1,1,2,1,2]
[5,2,1,7,4,6,3]=>[1,1,2,2,1]
[5,2,1,7,6,3,4]=>[1,1,2,1,2]
[5,2,1,7,6,4,3]=>[1,1,2,1,1,1]
[5,2,3,1,4,6,7]=>[1,2,4]
[5,2,3,1,4,7,6]=>[1,2,3,1]
[5,2,3,1,6,4,7]=>[1,2,2,2]
[5,2,3,1,6,7,4]=>[1,2,3,1]
[5,2,3,1,7,4,6]=>[1,2,2,2]
[5,2,3,1,7,6,4]=>[1,2,2,1,1]
[5,2,3,4,1,6,7]=>[1,3,3]
[5,2,3,4,1,7,6]=>[1,3,2,1]
[5,2,3,4,6,1,7]=>[1,4,2]
[5,2,3,4,6,7,1]=>[1,5,1]
[5,2,3,4,7,1,6]=>[1,4,2]
[5,2,3,4,7,6,1]=>[1,4,1,1]
[5,2,3,6,1,4,7]=>[1,3,3]
[5,2,3,6,1,7,4]=>[1,3,2,1]
[5,2,3,6,4,1,7]=>[1,3,1,2]
[5,2,3,6,4,7,1]=>[1,3,2,1]
[5,2,3,6,7,1,4]=>[1,4,2]
[5,2,3,6,7,4,1]=>[1,4,1,1]
[5,2,3,7,1,4,6]=>[1,3,3]
[5,2,3,7,1,6,4]=>[1,3,2,1]
[5,2,3,7,4,1,6]=>[1,3,1,2]
[5,2,3,7,4,6,1]=>[1,3,2,1]
[5,2,3,7,6,1,4]=>[1,3,1,2]
[5,2,3,7,6,4,1]=>[1,3,1,1,1]
[5,2,4,1,3,6,7]=>[1,2,4]
[5,2,4,1,3,7,6]=>[1,2,3,1]
[5,2,4,1,6,3,7]=>[1,2,2,2]
[5,2,4,1,6,7,3]=>[1,2,3,1]
[5,2,4,1,7,3,6]=>[1,2,2,2]
[5,2,4,1,7,6,3]=>[1,2,2,1,1]
[5,2,4,3,1,6,7]=>[1,2,1,3]
[5,2,4,3,1,7,6]=>[1,2,1,2,1]
[5,2,4,3,6,1,7]=>[1,2,2,2]
[5,2,4,3,6,7,1]=>[1,2,3,1]
[5,2,4,3,7,1,6]=>[1,2,2,2]
[5,2,4,3,7,6,1]=>[1,2,2,1,1]
[5,2,4,6,1,3,7]=>[1,3,3]
[5,2,4,6,1,7,3]=>[1,3,2,1]
[5,2,4,6,3,1,7]=>[1,3,1,2]
[5,2,4,6,3,7,1]=>[1,3,2,1]
[5,2,4,6,7,1,3]=>[1,4,2]
[5,2,4,6,7,3,1]=>[1,4,1,1]
[5,2,4,7,1,3,6]=>[1,3,3]
[5,2,4,7,1,6,3]=>[1,3,2,1]
[5,2,4,7,3,1,6]=>[1,3,1,2]
[5,2,4,7,3,6,1]=>[1,3,2,1]
[5,2,4,7,6,1,3]=>[1,3,1,2]
[5,2,4,7,6,3,1]=>[1,3,1,1,1]
[5,2,6,1,3,4,7]=>[1,2,4]
[5,2,6,1,3,7,4]=>[1,2,3,1]
[5,2,6,1,4,3,7]=>[1,2,2,2]
[5,2,6,1,4,7,3]=>[1,2,3,1]
[5,2,6,1,7,3,4]=>[1,2,2,2]
[5,2,6,1,7,4,3]=>[1,2,2,1,1]
[5,2,6,3,1,4,7]=>[1,2,1,3]
[5,2,6,3,1,7,4]=>[1,2,1,2,1]
[5,2,6,3,4,1,7]=>[1,2,2,2]
[5,2,6,3,4,7,1]=>[1,2,3,1]
[5,2,6,3,7,1,4]=>[1,2,2,2]
[5,2,6,3,7,4,1]=>[1,2,2,1,1]
[5,2,6,4,1,3,7]=>[1,2,1,3]
[5,2,6,4,1,7,3]=>[1,2,1,2,1]
[5,2,6,4,3,1,7]=>[1,2,1,1,2]
[5,2,6,4,3,7,1]=>[1,2,1,2,1]
[5,2,6,4,7,1,3]=>[1,2,2,2]
[5,2,6,4,7,3,1]=>[1,2,2,1,1]
[5,2,6,7,1,3,4]=>[1,3,3]
[5,2,6,7,1,4,3]=>[1,3,2,1]
[5,2,6,7,3,1,4]=>[1,3,1,2]
[5,2,6,7,3,4,1]=>[1,3,2,1]
[5,2,6,7,4,1,3]=>[1,3,1,2]
[5,2,6,7,4,3,1]=>[1,3,1,1,1]
[5,2,7,1,3,4,6]=>[1,2,4]
[5,2,7,1,3,6,4]=>[1,2,3,1]
[5,2,7,1,4,3,6]=>[1,2,2,2]
[5,2,7,1,4,6,3]=>[1,2,3,1]
[5,2,7,1,6,3,4]=>[1,2,2,2]
[5,2,7,1,6,4,3]=>[1,2,2,1,1]
[5,2,7,3,1,4,6]=>[1,2,1,3]
[5,2,7,3,1,6,4]=>[1,2,1,2,1]
[5,2,7,3,4,1,6]=>[1,2,2,2]
[5,2,7,3,4,6,1]=>[1,2,3,1]
[5,2,7,3,6,1,4]=>[1,2,2,2]
[5,2,7,3,6,4,1]=>[1,2,2,1,1]
[5,2,7,4,1,3,6]=>[1,2,1,3]
[5,2,7,4,1,6,3]=>[1,2,1,2,1]
[5,2,7,4,3,1,6]=>[1,2,1,1,2]
[5,2,7,4,3,6,1]=>[1,2,1,2,1]
[5,2,7,4,6,1,3]=>[1,2,2,2]
[5,2,7,4,6,3,1]=>[1,2,2,1,1]
[5,2,7,6,1,3,4]=>[1,2,1,3]
[5,2,7,6,1,4,3]=>[1,2,1,2,1]
[5,2,7,6,3,1,4]=>[1,2,1,1,2]
[5,2,7,6,3,4,1]=>[1,2,1,2,1]
[5,2,7,6,4,1,3]=>[1,2,1,1,2]
[5,2,7,6,4,3,1]=>[1,2,1,1,1,1]
[5,3,1,2,4,6,7]=>[1,1,5]
[5,3,1,2,4,7,6]=>[1,1,4,1]
[5,3,1,2,6,4,7]=>[1,1,3,2]
[5,3,1,2,6,7,4]=>[1,1,4,1]
[5,3,1,2,7,4,6]=>[1,1,3,2]
[5,3,1,2,7,6,4]=>[1,1,3,1,1]
[5,3,1,4,2,6,7]=>[1,1,2,3]
[5,3,1,4,2,7,6]=>[1,1,2,2,1]
[5,3,1,4,6,2,7]=>[1,1,3,2]
[5,3,1,4,6,7,2]=>[1,1,4,1]
[5,3,1,4,7,2,6]=>[1,1,3,2]
[5,3,1,4,7,6,2]=>[1,1,3,1,1]
[5,3,1,6,2,4,7]=>[1,1,2,3]
[5,3,1,6,2,7,4]=>[1,1,2,2,1]
[5,3,1,6,4,2,7]=>[1,1,2,1,2]
[5,3,1,6,4,7,2]=>[1,1,2,2,1]
[5,3,1,6,7,2,4]=>[1,1,3,2]
[5,3,1,6,7,4,2]=>[1,1,3,1,1]
[5,3,1,7,2,4,6]=>[1,1,2,3]
[5,3,1,7,2,6,4]=>[1,1,2,2,1]
[5,3,1,7,4,2,6]=>[1,1,2,1,2]
[5,3,1,7,4,6,2]=>[1,1,2,2,1]
[5,3,1,7,6,2,4]=>[1,1,2,1,2]
[5,3,1,7,6,4,2]=>[1,1,2,1,1,1]
[5,3,2,1,4,6,7]=>[1,1,1,4]
[5,3,2,1,4,7,6]=>[1,1,1,3,1]
[5,3,2,1,6,4,7]=>[1,1,1,2,2]
[5,3,2,1,6,7,4]=>[1,1,1,3,1]
[5,3,2,1,7,4,6]=>[1,1,1,2,2]
[5,3,2,1,7,6,4]=>[1,1,1,2,1,1]
[5,3,2,4,1,6,7]=>[1,1,2,3]
[5,3,2,4,1,7,6]=>[1,1,2,2,1]
[5,3,2,4,6,1,7]=>[1,1,3,2]
[5,3,2,4,6,7,1]=>[1,1,4,1]
[5,3,2,4,7,1,6]=>[1,1,3,2]
[5,3,2,4,7,6,1]=>[1,1,3,1,1]
[5,3,2,6,1,4,7]=>[1,1,2,3]
[5,3,2,6,1,7,4]=>[1,1,2,2,1]
[5,3,2,6,4,1,7]=>[1,1,2,1,2]
[5,3,2,6,4,7,1]=>[1,1,2,2,1]
[5,3,2,6,7,1,4]=>[1,1,3,2]
[5,3,2,6,7,4,1]=>[1,1,3,1,1]
[5,3,2,7,1,4,6]=>[1,1,2,3]
[5,3,2,7,1,6,4]=>[1,1,2,2,1]
[5,3,2,7,4,1,6]=>[1,1,2,1,2]
[5,3,2,7,4,6,1]=>[1,1,2,2,1]
[5,3,2,7,6,1,4]=>[1,1,2,1,2]
[5,3,2,7,6,4,1]=>[1,1,2,1,1,1]
[5,3,4,1,2,6,7]=>[1,2,4]
[5,3,4,1,2,7,6]=>[1,2,3,1]
[5,3,4,1,6,2,7]=>[1,2,2,2]
[5,3,4,1,6,7,2]=>[1,2,3,1]
[5,3,4,1,7,2,6]=>[1,2,2,2]
[5,3,4,1,7,6,2]=>[1,2,2,1,1]
[5,3,4,2,1,6,7]=>[1,2,1,3]
[5,3,4,2,1,7,6]=>[1,2,1,2,1]
[5,3,4,2,6,1,7]=>[1,2,2,2]
[5,3,4,2,6,7,1]=>[1,2,3,1]
[5,3,4,2,7,1,6]=>[1,2,2,2]
[5,3,4,2,7,6,1]=>[1,2,2,1,1]
[5,3,4,6,1,2,7]=>[1,3,3]
[5,3,4,6,1,7,2]=>[1,3,2,1]
[5,3,4,6,2,1,7]=>[1,3,1,2]
[5,3,4,6,2,7,1]=>[1,3,2,1]
[5,3,4,6,7,1,2]=>[1,4,2]
[5,3,4,6,7,2,1]=>[1,4,1,1]
[5,3,4,7,1,2,6]=>[1,3,3]
[5,3,4,7,1,6,2]=>[1,3,2,1]
[5,3,4,7,2,1,6]=>[1,3,1,2]
[5,3,4,7,2,6,1]=>[1,3,2,1]
[5,3,4,7,6,1,2]=>[1,3,1,2]
[5,3,4,7,6,2,1]=>[1,3,1,1,1]
[5,3,6,1,2,4,7]=>[1,2,4]
[5,3,6,1,2,7,4]=>[1,2,3,1]
[5,3,6,1,4,2,7]=>[1,2,2,2]
[5,3,6,1,4,7,2]=>[1,2,3,1]
[5,3,6,1,7,2,4]=>[1,2,2,2]
[5,3,6,1,7,4,2]=>[1,2,2,1,1]
[5,3,6,2,1,4,7]=>[1,2,1,3]
[5,3,6,2,1,7,4]=>[1,2,1,2,1]
[5,3,6,2,4,1,7]=>[1,2,2,2]
[5,3,6,2,4,7,1]=>[1,2,3,1]
[5,3,6,2,7,1,4]=>[1,2,2,2]
[5,3,6,2,7,4,1]=>[1,2,2,1,1]
[5,3,6,4,1,2,7]=>[1,2,1,3]
[5,3,6,4,1,7,2]=>[1,2,1,2,1]
[5,3,6,4,2,1,7]=>[1,2,1,1,2]
[5,3,6,4,2,7,1]=>[1,2,1,2,1]
[5,3,6,4,7,1,2]=>[1,2,2,2]
[5,3,6,4,7,2,1]=>[1,2,2,1,1]
[5,3,6,7,1,2,4]=>[1,3,3]
[5,3,6,7,1,4,2]=>[1,3,2,1]
[5,3,6,7,2,1,4]=>[1,3,1,2]
[5,3,6,7,2,4,1]=>[1,3,2,1]
[5,3,6,7,4,1,2]=>[1,3,1,2]
[5,3,6,7,4,2,1]=>[1,3,1,1,1]
[5,3,7,1,2,4,6]=>[1,2,4]
[5,3,7,1,2,6,4]=>[1,2,3,1]
[5,3,7,1,4,2,6]=>[1,2,2,2]
[5,3,7,1,4,6,2]=>[1,2,3,1]
[5,3,7,1,6,2,4]=>[1,2,2,2]
[5,3,7,1,6,4,2]=>[1,2,2,1,1]
[5,3,7,2,1,4,6]=>[1,2,1,3]
[5,3,7,2,1,6,4]=>[1,2,1,2,1]
[5,3,7,2,4,1,6]=>[1,2,2,2]
[5,3,7,2,4,6,1]=>[1,2,3,1]
[5,3,7,2,6,1,4]=>[1,2,2,2]
[5,3,7,2,6,4,1]=>[1,2,2,1,1]
[5,3,7,4,1,2,6]=>[1,2,1,3]
[5,3,7,4,1,6,2]=>[1,2,1,2,1]
[5,3,7,4,2,1,6]=>[1,2,1,1,2]
[5,3,7,4,2,6,1]=>[1,2,1,2,1]
[5,3,7,4,6,1,2]=>[1,2,2,2]
[5,3,7,4,6,2,1]=>[1,2,2,1,1]
[5,3,7,6,1,2,4]=>[1,2,1,3]
[5,3,7,6,1,4,2]=>[1,2,1,2,1]
[5,3,7,6,2,1,4]=>[1,2,1,1,2]
[5,3,7,6,2,4,1]=>[1,2,1,2,1]
[5,3,7,6,4,1,2]=>[1,2,1,1,2]
[5,3,7,6,4,2,1]=>[1,2,1,1,1,1]
[5,4,1,2,3,6,7]=>[1,1,5]
[5,4,1,2,3,7,6]=>[1,1,4,1]
[5,4,1,2,6,3,7]=>[1,1,3,2]
[5,4,1,2,6,7,3]=>[1,1,4,1]
[5,4,1,2,7,3,6]=>[1,1,3,2]
[5,4,1,2,7,6,3]=>[1,1,3,1,1]
[5,4,1,3,2,6,7]=>[1,1,2,3]
[5,4,1,3,2,7,6]=>[1,1,2,2,1]
[5,4,1,3,6,2,7]=>[1,1,3,2]
[5,4,1,3,6,7,2]=>[1,1,4,1]
[5,4,1,3,7,2,6]=>[1,1,3,2]
[5,4,1,3,7,6,2]=>[1,1,3,1,1]
[5,4,1,6,2,3,7]=>[1,1,2,3]
[5,4,1,6,2,7,3]=>[1,1,2,2,1]
[5,4,1,6,3,2,7]=>[1,1,2,1,2]
[5,4,1,6,3,7,2]=>[1,1,2,2,1]
[5,4,1,6,7,2,3]=>[1,1,3,2]
[5,4,1,6,7,3,2]=>[1,1,3,1,1]
[5,4,1,7,2,3,6]=>[1,1,2,3]
[5,4,1,7,2,6,3]=>[1,1,2,2,1]
[5,4,1,7,3,2,6]=>[1,1,2,1,2]
[5,4,1,7,3,6,2]=>[1,1,2,2,1]
[5,4,1,7,6,2,3]=>[1,1,2,1,2]
[5,4,1,7,6,3,2]=>[1,1,2,1,1,1]
[5,4,2,1,3,6,7]=>[1,1,1,4]
[5,4,2,1,3,7,6]=>[1,1,1,3,1]
[5,4,2,1,6,3,7]=>[1,1,1,2,2]
[5,4,2,1,6,7,3]=>[1,1,1,3,1]
[5,4,2,1,7,3,6]=>[1,1,1,2,2]
[5,4,2,1,7,6,3]=>[1,1,1,2,1,1]
[5,4,2,3,1,6,7]=>[1,1,2,3]
[5,4,2,3,1,7,6]=>[1,1,2,2,1]
[5,4,2,3,6,1,7]=>[1,1,3,2]
[5,4,2,3,6,7,1]=>[1,1,4,1]
[5,4,2,3,7,1,6]=>[1,1,3,2]
[5,4,2,3,7,6,1]=>[1,1,3,1,1]
[5,4,2,6,1,3,7]=>[1,1,2,3]
[5,4,2,6,1,7,3]=>[1,1,2,2,1]
[5,4,2,6,3,1,7]=>[1,1,2,1,2]
[5,4,2,6,3,7,1]=>[1,1,2,2,1]
[5,4,2,6,7,1,3]=>[1,1,3,2]
[5,4,2,6,7,3,1]=>[1,1,3,1,1]
[5,4,2,7,1,3,6]=>[1,1,2,3]
[5,4,2,7,1,6,3]=>[1,1,2,2,1]
[5,4,2,7,3,1,6]=>[1,1,2,1,2]
[5,4,2,7,3,6,1]=>[1,1,2,2,1]
[5,4,2,7,6,1,3]=>[1,1,2,1,2]
[5,4,2,7,6,3,1]=>[1,1,2,1,1,1]
[5,4,3,1,2,6,7]=>[1,1,1,4]
[5,4,3,1,2,7,6]=>[1,1,1,3,1]
[5,4,3,1,6,2,7]=>[1,1,1,2,2]
[5,4,3,1,6,7,2]=>[1,1,1,3,1]
[5,4,3,1,7,2,6]=>[1,1,1,2,2]
[5,4,3,1,7,6,2]=>[1,1,1,2,1,1]
[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[5,4,3,2,7,1,6]=>[1,1,1,2,2]
[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]
[5,4,3,6,1,2,7]=>[1,1,2,3]
[5,4,3,6,1,7,2]=>[1,1,2,2,1]
[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[5,4,3,6,7,1,2]=>[1,1,3,2]
[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[5,4,3,7,1,2,6]=>[1,1,2,3]
[5,4,3,7,1,6,2]=>[1,1,2,2,1]
[5,4,3,7,2,1,6]=>[1,1,2,1,2]
[5,4,3,7,2,6,1]=>[1,1,2,2,1]
[5,4,3,7,6,1,2]=>[1,1,2,1,2]
[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]
[5,4,6,1,2,3,7]=>[1,2,4]
[5,4,6,1,2,7,3]=>[1,2,3,1]
[5,4,6,1,3,2,7]=>[1,2,2,2]
[5,4,6,1,3,7,2]=>[1,2,3,1]
[5,4,6,1,7,2,3]=>[1,2,2,2]
[5,4,6,1,7,3,2]=>[1,2,2,1,1]
[5,4,6,2,1,3,7]=>[1,2,1,3]
[5,4,6,2,1,7,3]=>[1,2,1,2,1]
[5,4,6,2,3,1,7]=>[1,2,2,2]
[5,4,6,2,3,7,1]=>[1,2,3,1]
[5,4,6,2,7,1,3]=>[1,2,2,2]
[5,4,6,2,7,3,1]=>[1,2,2,1,1]
[5,4,6,3,1,2,7]=>[1,2,1,3]
[5,4,6,3,1,7,2]=>[1,2,1,2,1]
[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[5,4,6,3,7,1,2]=>[1,2,2,2]
[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[5,4,6,7,1,2,3]=>[1,3,3]
[5,4,6,7,1,3,2]=>[1,3,2,1]
[5,4,6,7,2,1,3]=>[1,3,1,2]
[5,4,6,7,2,3,1]=>[1,3,2,1]
[5,4,6,7,3,1,2]=>[1,3,1,2]
[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[5,4,7,1,2,3,6]=>[1,2,4]
[5,4,7,1,2,6,3]=>[1,2,3,1]
[5,4,7,1,3,2,6]=>[1,2,2,2]
[5,4,7,1,3,6,2]=>[1,2,3,1]
[5,4,7,1,6,2,3]=>[1,2,2,2]
[5,4,7,1,6,3,2]=>[1,2,2,1,1]
[5,4,7,2,1,3,6]=>[1,2,1,3]
[5,4,7,2,1,6,3]=>[1,2,1,2,1]
[5,4,7,2,3,1,6]=>[1,2,2,2]
[5,4,7,2,3,6,1]=>[1,2,3,1]
[5,4,7,2,6,1,3]=>[1,2,2,2]
[5,4,7,2,6,3,1]=>[1,2,2,1,1]
[5,4,7,3,1,2,6]=>[1,2,1,3]
[5,4,7,3,1,6,2]=>[1,2,1,2,1]
[5,4,7,3,2,1,6]=>[1,2,1,1,2]
[5,4,7,3,2,6,1]=>[1,2,1,2,1]
[5,4,7,3,6,1,2]=>[1,2,2,2]
[5,4,7,3,6,2,1]=>[1,2,2,1,1]
[5,4,7,6,1,2,3]=>[1,2,1,3]
[5,4,7,6,1,3,2]=>[1,2,1,2,1]
[5,4,7,6,2,1,3]=>[1,2,1,1,2]
[5,4,7,6,2,3,1]=>[1,2,1,2,1]
[5,4,7,6,3,1,2]=>[1,2,1,1,2]
[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]
[5,6,1,2,3,4,7]=>[2,5]
[5,6,1,2,3,7,4]=>[2,4,1]
[5,6,1,2,4,3,7]=>[2,3,2]
[5,6,1,2,4,7,3]=>[2,4,1]
[5,6,1,2,7,3,4]=>[2,3,2]
[5,6,1,2,7,4,3]=>[2,3,1,1]
[5,6,1,3,2,4,7]=>[2,2,3]
[5,6,1,3,2,7,4]=>[2,2,2,1]
[5,6,1,3,4,2,7]=>[2,3,2]
[5,6,1,3,4,7,2]=>[2,4,1]
[5,6,1,3,7,2,4]=>[2,3,2]
[5,6,1,3,7,4,2]=>[2,3,1,1]
[5,6,1,4,2,3,7]=>[2,2,3]
[5,6,1,4,2,7,3]=>[2,2,2,1]
[5,6,1,4,3,2,7]=>[2,2,1,2]
[5,6,1,4,3,7,2]=>[2,2,2,1]
[5,6,1,4,7,2,3]=>[2,3,2]
[5,6,1,4,7,3,2]=>[2,3,1,1]
[5,6,1,7,2,3,4]=>[2,2,3]
[5,6,1,7,2,4,3]=>[2,2,2,1]
[5,6,1,7,3,2,4]=>[2,2,1,2]
[5,6,1,7,3,4,2]=>[2,2,2,1]
[5,6,1,7,4,2,3]=>[2,2,1,2]
[5,6,1,7,4,3,2]=>[2,2,1,1,1]
[5,6,2,1,3,4,7]=>[2,1,4]
[5,6,2,1,3,7,4]=>[2,1,3,1]
[5,6,2,1,4,3,7]=>[2,1,2,2]
[5,6,2,1,4,7,3]=>[2,1,3,1]
[5,6,2,1,7,3,4]=>[2,1,2,2]
[5,6,2,1,7,4,3]=>[2,1,2,1,1]
[5,6,2,3,1,4,7]=>[2,2,3]
[5,6,2,3,1,7,4]=>[2,2,2,1]
[5,6,2,3,4,1,7]=>[2,3,2]
[5,6,2,3,4,7,1]=>[2,4,1]
[5,6,2,3,7,1,4]=>[2,3,2]
[5,6,2,3,7,4,1]=>[2,3,1,1]
[5,6,2,4,1,3,7]=>[2,2,3]
[5,6,2,4,1,7,3]=>[2,2,2,1]
[5,6,2,4,3,1,7]=>[2,2,1,2]
[5,6,2,4,3,7,1]=>[2,2,2,1]
[5,6,2,4,7,1,3]=>[2,3,2]
[5,6,2,4,7,3,1]=>[2,3,1,1]
[5,6,2,7,1,3,4]=>[2,2,3]
[5,6,2,7,1,4,3]=>[2,2,2,1]
[5,6,2,7,3,1,4]=>[2,2,1,2]
[5,6,2,7,3,4,1]=>[2,2,2,1]
[5,6,2,7,4,1,3]=>[2,2,1,2]
[5,6,2,7,4,3,1]=>[2,2,1,1,1]
[5,6,3,1,2,4,7]=>[2,1,4]
[5,6,3,1,2,7,4]=>[2,1,3,1]
[5,6,3,1,4,2,7]=>[2,1,2,2]
[5,6,3,1,4,7,2]=>[2,1,3,1]
[5,6,3,1,7,2,4]=>[2,1,2,2]
[5,6,3,1,7,4,2]=>[2,1,2,1,1]
[5,6,3,2,1,4,7]=>[2,1,1,3]
[5,6,3,2,1,7,4]=>[2,1,1,2,1]
[5,6,3,2,4,1,7]=>[2,1,2,2]
[5,6,3,2,4,7,1]=>[2,1,3,1]
[5,6,3,2,7,1,4]=>[2,1,2,2]
[5,6,3,2,7,4,1]=>[2,1,2,1,1]
[5,6,3,4,1,2,7]=>[2,2,3]
[5,6,3,4,1,7,2]=>[2,2,2,1]
[5,6,3,4,2,1,7]=>[2,2,1,2]
[5,6,3,4,2,7,1]=>[2,2,2,1]
[5,6,3,4,7,1,2]=>[2,3,2]
[5,6,3,4,7,2,1]=>[2,3,1,1]
[5,6,3,7,1,2,4]=>[2,2,3]
[5,6,3,7,1,4,2]=>[2,2,2,1]
[5,6,3,7,2,1,4]=>[2,2,1,2]
[5,6,3,7,2,4,1]=>[2,2,2,1]
[5,6,3,7,4,1,2]=>[2,2,1,2]
[5,6,3,7,4,2,1]=>[2,2,1,1,1]
[5,6,4,1,2,3,7]=>[2,1,4]
[5,6,4,1,2,7,3]=>[2,1,3,1]
[5,6,4,1,3,2,7]=>[2,1,2,2]
[5,6,4,1,3,7,2]=>[2,1,3,1]
[5,6,4,1,7,2,3]=>[2,1,2,2]
[5,6,4,1,7,3,2]=>[2,1,2,1,1]
[5,6,4,2,1,3,7]=>[2,1,1,3]
[5,6,4,2,1,7,3]=>[2,1,1,2,1]
[5,6,4,2,3,1,7]=>[2,1,2,2]
[5,6,4,2,3,7,1]=>[2,1,3,1]
[5,6,4,2,7,1,3]=>[2,1,2,2]
[5,6,4,2,7,3,1]=>[2,1,2,1,1]
[5,6,4,3,1,2,7]=>[2,1,1,3]
[5,6,4,3,1,7,2]=>[2,1,1,2,1]
[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[5,6,4,3,7,1,2]=>[2,1,2,2]
[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[5,6,4,7,1,2,3]=>[2,2,3]
[5,6,4,7,1,3,2]=>[2,2,2,1]
[5,6,4,7,2,1,3]=>[2,2,1,2]
[5,6,4,7,2,3,1]=>[2,2,2,1]
[5,6,4,7,3,1,2]=>[2,2,1,2]
[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[5,6,7,1,2,3,4]=>[3,4]
[5,6,7,1,2,4,3]=>[3,3,1]
[5,6,7,1,3,2,4]=>[3,2,2]
[5,6,7,1,3,4,2]=>[3,3,1]
[5,6,7,1,4,2,3]=>[3,2,2]
[5,6,7,1,4,3,2]=>[3,2,1,1]
[5,6,7,2,1,3,4]=>[3,1,3]
[5,6,7,2,1,4,3]=>[3,1,2,1]
[5,6,7,2,3,1,4]=>[3,2,2]
[5,6,7,2,3,4,1]=>[3,3,1]
[5,6,7,2,4,1,3]=>[3,2,2]
[5,6,7,2,4,3,1]=>[3,2,1,1]
[5,6,7,3,1,2,4]=>[3,1,3]
[5,6,7,3,1,4,2]=>[3,1,2,1]
[5,6,7,3,2,1,4]=>[3,1,1,2]
[5,6,7,3,2,4,1]=>[3,1,2,1]
[5,6,7,3,4,1,2]=>[3,2,2]
[5,6,7,3,4,2,1]=>[3,2,1,1]
[5,6,7,4,1,2,3]=>[3,1,3]
[5,6,7,4,1,3,2]=>[3,1,2,1]
[5,6,7,4,2,1,3]=>[3,1,1,2]
[5,6,7,4,2,3,1]=>[3,1,2,1]
[5,6,7,4,3,1,2]=>[3,1,1,2]
[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[5,7,1,2,3,4,6]=>[2,5]
[5,7,1,2,3,6,4]=>[2,4,1]
[5,7,1,2,4,3,6]=>[2,3,2]
[5,7,1,2,4,6,3]=>[2,4,1]
[5,7,1,2,6,3,4]=>[2,3,2]
[5,7,1,2,6,4,3]=>[2,3,1,1]
[5,7,1,3,2,4,6]=>[2,2,3]
[5,7,1,3,2,6,4]=>[2,2,2,1]
[5,7,1,3,4,2,6]=>[2,3,2]
[5,7,1,3,4,6,2]=>[2,4,1]
[5,7,1,3,6,2,4]=>[2,3,2]
[5,7,1,3,6,4,2]=>[2,3,1,1]
[5,7,1,4,2,3,6]=>[2,2,3]
[5,7,1,4,2,6,3]=>[2,2,2,1]
[5,7,1,4,3,2,6]=>[2,2,1,2]
[5,7,1,4,3,6,2]=>[2,2,2,1]
[5,7,1,4,6,2,3]=>[2,3,2]
[5,7,1,4,6,3,2]=>[2,3,1,1]
[5,7,1,6,2,3,4]=>[2,2,3]
[5,7,1,6,2,4,3]=>[2,2,2,1]
[5,7,1,6,3,2,4]=>[2,2,1,2]
[5,7,1,6,3,4,2]=>[2,2,2,1]
[5,7,1,6,4,2,3]=>[2,2,1,2]
[5,7,1,6,4,3,2]=>[2,2,1,1,1]
[5,7,2,1,3,4,6]=>[2,1,4]
[5,7,2,1,3,6,4]=>[2,1,3,1]
[5,7,2,1,4,3,6]=>[2,1,2,2]
[5,7,2,1,4,6,3]=>[2,1,3,1]
[5,7,2,1,6,3,4]=>[2,1,2,2]
[5,7,2,1,6,4,3]=>[2,1,2,1,1]
[5,7,2,3,1,4,6]=>[2,2,3]
[5,7,2,3,1,6,4]=>[2,2,2,1]
[5,7,2,3,4,1,6]=>[2,3,2]
[5,7,2,3,4,6,1]=>[2,4,1]
[5,7,2,3,6,1,4]=>[2,3,2]
[5,7,2,3,6,4,1]=>[2,3,1,1]
[5,7,2,4,1,3,6]=>[2,2,3]
[5,7,2,4,1,6,3]=>[2,2,2,1]
[5,7,2,4,3,1,6]=>[2,2,1,2]
[5,7,2,4,3,6,1]=>[2,2,2,1]
[5,7,2,4,6,1,3]=>[2,3,2]
[5,7,2,4,6,3,1]=>[2,3,1,1]
[5,7,2,6,1,3,4]=>[2,2,3]
[5,7,2,6,1,4,3]=>[2,2,2,1]
[5,7,2,6,3,1,4]=>[2,2,1,2]
[5,7,2,6,3,4,1]=>[2,2,2,1]
[5,7,2,6,4,1,3]=>[2,2,1,2]
[5,7,2,6,4,3,1]=>[2,2,1,1,1]
[5,7,3,1,2,4,6]=>[2,1,4]
[5,7,3,1,2,6,4]=>[2,1,3,1]
[5,7,3,1,4,2,6]=>[2,1,2,2]
[5,7,3,1,4,6,2]=>[2,1,3,1]
[5,7,3,1,6,2,4]=>[2,1,2,2]
[5,7,3,1,6,4,2]=>[2,1,2,1,1]
[5,7,3,2,1,4,6]=>[2,1,1,3]
[5,7,3,2,1,6,4]=>[2,1,1,2,1]
[5,7,3,2,4,1,6]=>[2,1,2,2]
[5,7,3,2,4,6,1]=>[2,1,3,1]
[5,7,3,2,6,1,4]=>[2,1,2,2]
[5,7,3,2,6,4,1]=>[2,1,2,1,1]
[5,7,3,4,1,2,6]=>[2,2,3]
[5,7,3,4,1,6,2]=>[2,2,2,1]
[5,7,3,4,2,1,6]=>[2,2,1,2]
[5,7,3,4,2,6,1]=>[2,2,2,1]
[5,7,3,4,6,1,2]=>[2,3,2]
[5,7,3,4,6,2,1]=>[2,3,1,1]
[5,7,3,6,1,2,4]=>[2,2,3]
[5,7,3,6,1,4,2]=>[2,2,2,1]
[5,7,3,6,2,1,4]=>[2,2,1,2]
[5,7,3,6,2,4,1]=>[2,2,2,1]
[5,7,3,6,4,1,2]=>[2,2,1,2]
[5,7,3,6,4,2,1]=>[2,2,1,1,1]
[5,7,4,1,2,3,6]=>[2,1,4]
[5,7,4,1,2,6,3]=>[2,1,3,1]
[5,7,4,1,3,2,6]=>[2,1,2,2]
[5,7,4,1,3,6,2]=>[2,1,3,1]
[5,7,4,1,6,2,3]=>[2,1,2,2]
[5,7,4,1,6,3,2]=>[2,1,2,1,1]
[5,7,4,2,1,3,6]=>[2,1,1,3]
[5,7,4,2,1,6,3]=>[2,1,1,2,1]
[5,7,4,2,3,1,6]=>[2,1,2,2]
[5,7,4,2,3,6,1]=>[2,1,3,1]
[5,7,4,2,6,1,3]=>[2,1,2,2]
[5,7,4,2,6,3,1]=>[2,1,2,1,1]
[5,7,4,3,1,2,6]=>[2,1,1,3]
[5,7,4,3,1,6,2]=>[2,1,1,2,1]
[5,7,4,3,2,1,6]=>[2,1,1,1,2]
[5,7,4,3,2,6,1]=>[2,1,1,2,1]
[5,7,4,3,6,1,2]=>[2,1,2,2]
[5,7,4,3,6,2,1]=>[2,1,2,1,1]
[5,7,4,6,1,2,3]=>[2,2,3]
[5,7,4,6,1,3,2]=>[2,2,2,1]
[5,7,4,6,2,1,3]=>[2,2,1,2]
[5,7,4,6,2,3,1]=>[2,2,2,1]
[5,7,4,6,3,1,2]=>[2,2,1,2]
[5,7,4,6,3,2,1]=>[2,2,1,1,1]
[5,7,6,1,2,3,4]=>[2,1,4]
[5,7,6,1,2,4,3]=>[2,1,3,1]
[5,7,6,1,3,2,4]=>[2,1,2,2]
[5,7,6,1,3,4,2]=>[2,1,3,1]
[5,7,6,1,4,2,3]=>[2,1,2,2]
[5,7,6,1,4,3,2]=>[2,1,2,1,1]
[5,7,6,2,1,3,4]=>[2,1,1,3]
[5,7,6,2,1,4,3]=>[2,1,1,2,1]
[5,7,6,2,3,1,4]=>[2,1,2,2]
[5,7,6,2,3,4,1]=>[2,1,3,1]
[5,7,6,2,4,1,3]=>[2,1,2,2]
[5,7,6,2,4,3,1]=>[2,1,2,1,1]
[5,7,6,3,1,2,4]=>[2,1,1,3]
[5,7,6,3,1,4,2]=>[2,1,1,2,1]
[5,7,6,3,2,1,4]=>[2,1,1,1,2]
[5,7,6,3,2,4,1]=>[2,1,1,2,1]
[5,7,6,3,4,1,2]=>[2,1,2,2]
[5,7,6,3,4,2,1]=>[2,1,2,1,1]
[5,7,6,4,1,2,3]=>[2,1,1,3]
[5,7,6,4,1,3,2]=>[2,1,1,2,1]
[5,7,6,4,2,1,3]=>[2,1,1,1,2]
[5,7,6,4,2,3,1]=>[2,1,1,2,1]
[5,7,6,4,3,1,2]=>[2,1,1,1,2]
[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[6,1,2,3,4,5,7]=>[1,6]
[6,1,2,3,4,7,5]=>[1,5,1]
[6,1,2,3,5,4,7]=>[1,4,2]
[6,1,2,3,5,7,4]=>[1,5,1]
[6,1,2,3,7,4,5]=>[1,4,2]
[6,1,2,3,7,5,4]=>[1,4,1,1]
[6,1,2,4,3,5,7]=>[1,3,3]
[6,1,2,4,3,7,5]=>[1,3,2,1]
[6,1,2,4,5,3,7]=>[1,4,2]
[6,1,2,4,5,7,3]=>[1,5,1]
[6,1,2,4,7,3,5]=>[1,4,2]
[6,1,2,4,7,5,3]=>[1,4,1,1]
[6,1,2,5,3,4,7]=>[1,3,3]
[6,1,2,5,3,7,4]=>[1,3,2,1]
[6,1,2,5,4,3,7]=>[1,3,1,2]
[6,1,2,5,4,7,3]=>[1,3,2,1]
[6,1,2,5,7,3,4]=>[1,4,2]
[6,1,2,5,7,4,3]=>[1,4,1,1]
[6,1,2,7,3,4,5]=>[1,3,3]
[6,1,2,7,3,5,4]=>[1,3,2,1]
[6,1,2,7,4,3,5]=>[1,3,1,2]
[6,1,2,7,4,5,3]=>[1,3,2,1]
[6,1,2,7,5,3,4]=>[1,3,1,2]
[6,1,2,7,5,4,3]=>[1,3,1,1,1]
[6,1,3,2,4,5,7]=>[1,2,4]
[6,1,3,2,4,7,5]=>[1,2,3,1]
[6,1,3,2,5,4,7]=>[1,2,2,2]
[6,1,3,2,5,7,4]=>[1,2,3,1]
[6,1,3,2,7,4,5]=>[1,2,2,2]
[6,1,3,2,7,5,4]=>[1,2,2,1,1]
[6,1,3,4,2,5,7]=>[1,3,3]
[6,1,3,4,2,7,5]=>[1,3,2,1]
[6,1,3,4,5,2,7]=>[1,4,2]
[6,1,3,4,5,7,2]=>[1,5,1]
[6,1,3,4,7,2,5]=>[1,4,2]
[6,1,3,4,7,5,2]=>[1,4,1,1]
[6,1,3,5,2,4,7]=>[1,3,3]
[6,1,3,5,2,7,4]=>[1,3,2,1]
[6,1,3,5,4,2,7]=>[1,3,1,2]
[6,1,3,5,4,7,2]=>[1,3,2,1]
[6,1,3,5,7,2,4]=>[1,4,2]
[6,1,3,5,7,4,2]=>[1,4,1,1]
[6,1,3,7,2,4,5]=>[1,3,3]
[6,1,3,7,2,5,4]=>[1,3,2,1]
[6,1,3,7,4,2,5]=>[1,3,1,2]
[6,1,3,7,4,5,2]=>[1,3,2,1]
[6,1,3,7,5,2,4]=>[1,3,1,2]
[6,1,3,7,5,4,2]=>[1,3,1,1,1]
[6,1,4,2,3,5,7]=>[1,2,4]
[6,1,4,2,3,7,5]=>[1,2,3,1]
[6,1,4,2,5,3,7]=>[1,2,2,2]
[6,1,4,2,5,7,3]=>[1,2,3,1]
[6,1,4,2,7,3,5]=>[1,2,2,2]
[6,1,4,2,7,5,3]=>[1,2,2,1,1]
[6,1,4,3,2,5,7]=>[1,2,1,3]
[6,1,4,3,2,7,5]=>[1,2,1,2,1]
[6,1,4,3,5,2,7]=>[1,2,2,2]
[6,1,4,3,5,7,2]=>[1,2,3,1]
[6,1,4,3,7,2,5]=>[1,2,2,2]
[6,1,4,3,7,5,2]=>[1,2,2,1,1]
[6,1,4,5,2,3,7]=>[1,3,3]
[6,1,4,5,2,7,3]=>[1,3,2,1]
[6,1,4,5,3,2,7]=>[1,3,1,2]
[6,1,4,5,3,7,2]=>[1,3,2,1]
[6,1,4,5,7,2,3]=>[1,4,2]
[6,1,4,5,7,3,2]=>[1,4,1,1]
[6,1,4,7,2,3,5]=>[1,3,3]
[6,1,4,7,2,5,3]=>[1,3,2,1]
[6,1,4,7,3,2,5]=>[1,3,1,2]
[6,1,4,7,3,5,2]=>[1,3,2,1]
[6,1,4,7,5,2,3]=>[1,3,1,2]
[6,1,4,7,5,3,2]=>[1,3,1,1,1]
[6,1,5,2,3,4,7]=>[1,2,4]
[6,1,5,2,3,7,4]=>[1,2,3,1]
[6,1,5,2,4,3,7]=>[1,2,2,2]
[6,1,5,2,4,7,3]=>[1,2,3,1]
[6,1,5,2,7,3,4]=>[1,2,2,2]
[6,1,5,2,7,4,3]=>[1,2,2,1,1]
[6,1,5,3,2,4,7]=>[1,2,1,3]
[6,1,5,3,2,7,4]=>[1,2,1,2,1]
[6,1,5,3,4,2,7]=>[1,2,2,2]
[6,1,5,3,4,7,2]=>[1,2,3,1]
[6,1,5,3,7,2,4]=>[1,2,2,2]
[6,1,5,3,7,4,2]=>[1,2,2,1,1]
[6,1,5,4,2,3,7]=>[1,2,1,3]
[6,1,5,4,2,7,3]=>[1,2,1,2,1]
[6,1,5,4,3,2,7]=>[1,2,1,1,2]
[6,1,5,4,3,7,2]=>[1,2,1,2,1]
[6,1,5,4,7,2,3]=>[1,2,2,2]
[6,1,5,4,7,3,2]=>[1,2,2,1,1]
[6,1,5,7,2,3,4]=>[1,3,3]
[6,1,5,7,2,4,3]=>[1,3,2,1]
[6,1,5,7,3,2,4]=>[1,3,1,2]
[6,1,5,7,3,4,2]=>[1,3,2,1]
[6,1,5,7,4,2,3]=>[1,3,1,2]
[6,1,5,7,4,3,2]=>[1,3,1,1,1]
[6,1,7,2,3,4,5]=>[1,2,4]
[6,1,7,2,3,5,4]=>[1,2,3,1]
[6,1,7,2,4,3,5]=>[1,2,2,2]
[6,1,7,2,4,5,3]=>[1,2,3,1]
[6,1,7,2,5,3,4]=>[1,2,2,2]
[6,1,7,2,5,4,3]=>[1,2,2,1,1]
[6,1,7,3,2,4,5]=>[1,2,1,3]
[6,1,7,3,2,5,4]=>[1,2,1,2,1]
[6,1,7,3,4,2,5]=>[1,2,2,2]
[6,1,7,3,4,5,2]=>[1,2,3,1]
[6,1,7,3,5,2,4]=>[1,2,2,2]
[6,1,7,3,5,4,2]=>[1,2,2,1,1]
[6,1,7,4,2,3,5]=>[1,2,1,3]
[6,1,7,4,2,5,3]=>[1,2,1,2,1]
[6,1,7,4,3,2,5]=>[1,2,1,1,2]
[6,1,7,4,3,5,2]=>[1,2,1,2,1]
[6,1,7,4,5,2,3]=>[1,2,2,2]
[6,1,7,4,5,3,2]=>[1,2,2,1,1]
[6,1,7,5,2,3,4]=>[1,2,1,3]
[6,1,7,5,2,4,3]=>[1,2,1,2,1]
[6,1,7,5,3,2,4]=>[1,2,1,1,2]
[6,1,7,5,3,4,2]=>[1,2,1,2,1]
[6,1,7,5,4,2,3]=>[1,2,1,1,2]
[6,1,7,5,4,3,2]=>[1,2,1,1,1,1]
[6,2,1,3,4,5,7]=>[1,1,5]
[6,2,1,3,4,7,5]=>[1,1,4,1]
[6,2,1,3,5,4,7]=>[1,1,3,2]
[6,2,1,3,5,7,4]=>[1,1,4,1]
[6,2,1,3,7,4,5]=>[1,1,3,2]
[6,2,1,3,7,5,4]=>[1,1,3,1,1]
[6,2,1,4,3,5,7]=>[1,1,2,3]
[6,2,1,4,3,7,5]=>[1,1,2,2,1]
[6,2,1,4,5,3,7]=>[1,1,3,2]
[6,2,1,4,5,7,3]=>[1,1,4,1]
[6,2,1,4,7,3,5]=>[1,1,3,2]
[6,2,1,4,7,5,3]=>[1,1,3,1,1]
[6,2,1,5,3,4,7]=>[1,1,2,3]
[6,2,1,5,3,7,4]=>[1,1,2,2,1]
[6,2,1,5,4,3,7]=>[1,1,2,1,2]
[6,2,1,5,4,7,3]=>[1,1,2,2,1]
[6,2,1,5,7,3,4]=>[1,1,3,2]
[6,2,1,5,7,4,3]=>[1,1,3,1,1]
[6,2,1,7,3,4,5]=>[1,1,2,3]
[6,2,1,7,3,5,4]=>[1,1,2,2,1]
[6,2,1,7,4,3,5]=>[1,1,2,1,2]
[6,2,1,7,4,5,3]=>[1,1,2,2,1]
[6,2,1,7,5,3,4]=>[1,1,2,1,2]
[6,2,1,7,5,4,3]=>[1,1,2,1,1,1]
[6,2,3,1,4,5,7]=>[1,2,4]
[6,2,3,1,4,7,5]=>[1,2,3,1]
[6,2,3,1,5,4,7]=>[1,2,2,2]
[6,2,3,1,5,7,4]=>[1,2,3,1]
[6,2,3,1,7,4,5]=>[1,2,2,2]
[6,2,3,1,7,5,4]=>[1,2,2,1,1]
[6,2,3,4,1,5,7]=>[1,3,3]
[6,2,3,4,1,7,5]=>[1,3,2,1]
[6,2,3,4,5,1,7]=>[1,4,2]
[6,2,3,4,5,7,1]=>[1,5,1]
[6,2,3,4,7,1,5]=>[1,4,2]
[6,2,3,4,7,5,1]=>[1,4,1,1]
[6,2,3,5,1,4,7]=>[1,3,3]
[6,2,3,5,1,7,4]=>[1,3,2,1]
[6,2,3,5,4,1,7]=>[1,3,1,2]
[6,2,3,5,4,7,1]=>[1,3,2,1]
[6,2,3,5,7,1,4]=>[1,4,2]
[6,2,3,5,7,4,1]=>[1,4,1,1]
[6,2,3,7,1,4,5]=>[1,3,3]
[6,2,3,7,1,5,4]=>[1,3,2,1]
[6,2,3,7,4,1,5]=>[1,3,1,2]
[6,2,3,7,4,5,1]=>[1,3,2,1]
[6,2,3,7,5,1,4]=>[1,3,1,2]
[6,2,3,7,5,4,1]=>[1,3,1,1,1]
[6,2,4,1,3,5,7]=>[1,2,4]
[6,2,4,1,3,7,5]=>[1,2,3,1]
[6,2,4,1,5,3,7]=>[1,2,2,2]
[6,2,4,1,5,7,3]=>[1,2,3,1]
[6,2,4,1,7,3,5]=>[1,2,2,2]
[6,2,4,1,7,5,3]=>[1,2,2,1,1]
[6,2,4,3,1,5,7]=>[1,2,1,3]
[6,2,4,3,1,7,5]=>[1,2,1,2,1]
[6,2,4,3,5,1,7]=>[1,2,2,2]
[6,2,4,3,5,7,1]=>[1,2,3,1]
[6,2,4,3,7,1,5]=>[1,2,2,2]
[6,2,4,3,7,5,1]=>[1,2,2,1,1]
[6,2,4,5,1,3,7]=>[1,3,3]
[6,2,4,5,1,7,3]=>[1,3,2,1]
[6,2,4,5,3,1,7]=>[1,3,1,2]
[6,2,4,5,3,7,1]=>[1,3,2,1]
[6,2,4,5,7,1,3]=>[1,4,2]
[6,2,4,5,7,3,1]=>[1,4,1,1]
[6,2,4,7,1,3,5]=>[1,3,3]
[6,2,4,7,1,5,3]=>[1,3,2,1]
[6,2,4,7,3,1,5]=>[1,3,1,2]
[6,2,4,7,3,5,1]=>[1,3,2,1]
[6,2,4,7,5,1,3]=>[1,3,1,2]
[6,2,4,7,5,3,1]=>[1,3,1,1,1]
[6,2,5,1,3,4,7]=>[1,2,4]
[6,2,5,1,3,7,4]=>[1,2,3,1]
[6,2,5,1,4,3,7]=>[1,2,2,2]
[6,2,5,1,4,7,3]=>[1,2,3,1]
[6,2,5,1,7,3,4]=>[1,2,2,2]
[6,2,5,1,7,4,3]=>[1,2,2,1,1]
[6,2,5,3,1,4,7]=>[1,2,1,3]
[6,2,5,3,1,7,4]=>[1,2,1,2,1]
[6,2,5,3,4,1,7]=>[1,2,2,2]
[6,2,5,3,4,7,1]=>[1,2,3,1]
[6,2,5,3,7,1,4]=>[1,2,2,2]
[6,2,5,3,7,4,1]=>[1,2,2,1,1]
[6,2,5,4,1,3,7]=>[1,2,1,3]
[6,2,5,4,1,7,3]=>[1,2,1,2,1]
[6,2,5,4,3,1,7]=>[1,2,1,1,2]
[6,2,5,4,3,7,1]=>[1,2,1,2,1]
[6,2,5,4,7,1,3]=>[1,2,2,2]
[6,2,5,4,7,3,1]=>[1,2,2,1,1]
[6,2,5,7,1,3,4]=>[1,3,3]
[6,2,5,7,1,4,3]=>[1,3,2,1]
[6,2,5,7,3,1,4]=>[1,3,1,2]
[6,2,5,7,3,4,1]=>[1,3,2,1]
[6,2,5,7,4,1,3]=>[1,3,1,2]
[6,2,5,7,4,3,1]=>[1,3,1,1,1]
[6,2,7,1,3,4,5]=>[1,2,4]
[6,2,7,1,3,5,4]=>[1,2,3,1]
[6,2,7,1,4,3,5]=>[1,2,2,2]
[6,2,7,1,4,5,3]=>[1,2,3,1]
[6,2,7,1,5,3,4]=>[1,2,2,2]
[6,2,7,1,5,4,3]=>[1,2,2,1,1]
[6,2,7,3,1,4,5]=>[1,2,1,3]
[6,2,7,3,1,5,4]=>[1,2,1,2,1]
[6,2,7,3,4,1,5]=>[1,2,2,2]
[6,2,7,3,4,5,1]=>[1,2,3,1]
[6,2,7,3,5,1,4]=>[1,2,2,2]
[6,2,7,3,5,4,1]=>[1,2,2,1,1]
[6,2,7,4,1,3,5]=>[1,2,1,3]
[6,2,7,4,1,5,3]=>[1,2,1,2,1]
[6,2,7,4,3,1,5]=>[1,2,1,1,2]
[6,2,7,4,3,5,1]=>[1,2,1,2,1]
[6,2,7,4,5,1,3]=>[1,2,2,2]
[6,2,7,4,5,3,1]=>[1,2,2,1,1]
[6,2,7,5,1,3,4]=>[1,2,1,3]
[6,2,7,5,1,4,3]=>[1,2,1,2,1]
[6,2,7,5,3,1,4]=>[1,2,1,1,2]
[6,2,7,5,3,4,1]=>[1,2,1,2,1]
[6,2,7,5,4,1,3]=>[1,2,1,1,2]
[6,2,7,5,4,3,1]=>[1,2,1,1,1,1]
[6,3,1,2,4,5,7]=>[1,1,5]
[6,3,1,2,4,7,5]=>[1,1,4,1]
[6,3,1,2,5,4,7]=>[1,1,3,2]
[6,3,1,2,5,7,4]=>[1,1,4,1]
[6,3,1,2,7,4,5]=>[1,1,3,2]
[6,3,1,2,7,5,4]=>[1,1,3,1,1]
[6,3,1,4,2,5,7]=>[1,1,2,3]
[6,3,1,4,2,7,5]=>[1,1,2,2,1]
[6,3,1,4,5,2,7]=>[1,1,3,2]
[6,3,1,4,5,7,2]=>[1,1,4,1]
[6,3,1,4,7,2,5]=>[1,1,3,2]
[6,3,1,4,7,5,2]=>[1,1,3,1,1]
[6,3,1,5,2,4,7]=>[1,1,2,3]
[6,3,1,5,2,7,4]=>[1,1,2,2,1]
[6,3,1,5,4,2,7]=>[1,1,2,1,2]
[6,3,1,5,4,7,2]=>[1,1,2,2,1]
[6,3,1,5,7,2,4]=>[1,1,3,2]
[6,3,1,5,7,4,2]=>[1,1,3,1,1]
[6,3,1,7,2,4,5]=>[1,1,2,3]
[6,3,1,7,2,5,4]=>[1,1,2,2,1]
[6,3,1,7,4,2,5]=>[1,1,2,1,2]
[6,3,1,7,4,5,2]=>[1,1,2,2,1]
[6,3,1,7,5,2,4]=>[1,1,2,1,2]
[6,3,1,7,5,4,2]=>[1,1,2,1,1,1]
[6,3,2,1,4,5,7]=>[1,1,1,4]
[6,3,2,1,4,7,5]=>[1,1,1,3,1]
[6,3,2,1,5,4,7]=>[1,1,1,2,2]
[6,3,2,1,5,7,4]=>[1,1,1,3,1]
[6,3,2,1,7,4,5]=>[1,1,1,2,2]
[6,3,2,1,7,5,4]=>[1,1,1,2,1,1]
[6,3,2,4,1,5,7]=>[1,1,2,3]
[6,3,2,4,1,7,5]=>[1,1,2,2,1]
[6,3,2,4,5,1,7]=>[1,1,3,2]
[6,3,2,4,5,7,1]=>[1,1,4,1]
[6,3,2,4,7,1,5]=>[1,1,3,2]
[6,3,2,4,7,5,1]=>[1,1,3,1,1]
[6,3,2,5,1,4,7]=>[1,1,2,3]
[6,3,2,5,1,7,4]=>[1,1,2,2,1]
[6,3,2,5,4,1,7]=>[1,1,2,1,2]
[6,3,2,5,4,7,1]=>[1,1,2,2,1]
[6,3,2,5,7,1,4]=>[1,1,3,2]
[6,3,2,5,7,4,1]=>[1,1,3,1,1]
[6,3,2,7,1,4,5]=>[1,1,2,3]
[6,3,2,7,1,5,4]=>[1,1,2,2,1]
[6,3,2,7,4,1,5]=>[1,1,2,1,2]
[6,3,2,7,4,5,1]=>[1,1,2,2,1]
[6,3,2,7,5,1,4]=>[1,1,2,1,2]
[6,3,2,7,5,4,1]=>[1,1,2,1,1,1]
[6,3,4,1,2,5,7]=>[1,2,4]
[6,3,4,1,2,7,5]=>[1,2,3,1]
[6,3,4,1,5,2,7]=>[1,2,2,2]
[6,3,4,1,5,7,2]=>[1,2,3,1]
[6,3,4,1,7,2,5]=>[1,2,2,2]
[6,3,4,1,7,5,2]=>[1,2,2,1,1]
[6,3,4,2,1,5,7]=>[1,2,1,3]
[6,3,4,2,1,7,5]=>[1,2,1,2,1]
[6,3,4,2,5,1,7]=>[1,2,2,2]
[6,3,4,2,5,7,1]=>[1,2,3,1]
[6,3,4,2,7,1,5]=>[1,2,2,2]
[6,3,4,2,7,5,1]=>[1,2,2,1,1]
[6,3,4,5,1,2,7]=>[1,3,3]
[6,3,4,5,1,7,2]=>[1,3,2,1]
[6,3,4,5,2,1,7]=>[1,3,1,2]
[6,3,4,5,2,7,1]=>[1,3,2,1]
[6,3,4,5,7,1,2]=>[1,4,2]
[6,3,4,5,7,2,1]=>[1,4,1,1]
[6,3,4,7,1,2,5]=>[1,3,3]
[6,3,4,7,1,5,2]=>[1,3,2,1]
[6,3,4,7,2,1,5]=>[1,3,1,2]
[6,3,4,7,2,5,1]=>[1,3,2,1]
[6,3,4,7,5,1,2]=>[1,3,1,2]
[6,3,4,7,5,2,1]=>[1,3,1,1,1]
[6,3,5,1,2,4,7]=>[1,2,4]
[6,3,5,1,2,7,4]=>[1,2,3,1]
[6,3,5,1,4,2,7]=>[1,2,2,2]
[6,3,5,1,4,7,2]=>[1,2,3,1]
[6,3,5,1,7,2,4]=>[1,2,2,2]
[6,3,5,1,7,4,2]=>[1,2,2,1,1]
[6,3,5,2,1,4,7]=>[1,2,1,3]
[6,3,5,2,1,7,4]=>[1,2,1,2,1]
[6,3,5,2,4,1,7]=>[1,2,2,2]
[6,3,5,2,4,7,1]=>[1,2,3,1]
[6,3,5,2,7,1,4]=>[1,2,2,2]
[6,3,5,2,7,4,1]=>[1,2,2,1,1]
[6,3,5,4,1,2,7]=>[1,2,1,3]
[6,3,5,4,1,7,2]=>[1,2,1,2,1]
[6,3,5,4,2,1,7]=>[1,2,1,1,2]
[6,3,5,4,2,7,1]=>[1,2,1,2,1]
[6,3,5,4,7,1,2]=>[1,2,2,2]
[6,3,5,4,7,2,1]=>[1,2,2,1,1]
[6,3,5,7,1,2,4]=>[1,3,3]
[6,3,5,7,1,4,2]=>[1,3,2,1]
[6,3,5,7,2,1,4]=>[1,3,1,2]
[6,3,5,7,2,4,1]=>[1,3,2,1]
[6,3,5,7,4,1,2]=>[1,3,1,2]
[6,3,5,7,4,2,1]=>[1,3,1,1,1]
[6,3,7,1,2,4,5]=>[1,2,4]
[6,3,7,1,2,5,4]=>[1,2,3,1]
[6,3,7,1,4,2,5]=>[1,2,2,2]
[6,3,7,1,4,5,2]=>[1,2,3,1]
[6,3,7,1,5,2,4]=>[1,2,2,2]
[6,3,7,1,5,4,2]=>[1,2,2,1,1]
[6,3,7,2,1,4,5]=>[1,2,1,3]
[6,3,7,2,1,5,4]=>[1,2,1,2,1]
[6,3,7,2,4,1,5]=>[1,2,2,2]
[6,3,7,2,4,5,1]=>[1,2,3,1]
[6,3,7,2,5,1,4]=>[1,2,2,2]
[6,3,7,2,5,4,1]=>[1,2,2,1,1]
[6,3,7,4,1,2,5]=>[1,2,1,3]
[6,3,7,4,1,5,2]=>[1,2,1,2,1]
[6,3,7,4,2,1,5]=>[1,2,1,1,2]
[6,3,7,4,2,5,1]=>[1,2,1,2,1]
[6,3,7,4,5,1,2]=>[1,2,2,2]
[6,3,7,4,5,2,1]=>[1,2,2,1,1]
[6,3,7,5,1,2,4]=>[1,2,1,3]
[6,3,7,5,1,4,2]=>[1,2,1,2,1]
[6,3,7,5,2,1,4]=>[1,2,1,1,2]
[6,3,7,5,2,4,1]=>[1,2,1,2,1]
[6,3,7,5,4,1,2]=>[1,2,1,1,2]
[6,3,7,5,4,2,1]=>[1,2,1,1,1,1]
[6,4,1,2,3,5,7]=>[1,1,5]
[6,4,1,2,3,7,5]=>[1,1,4,1]
[6,4,1,2,5,3,7]=>[1,1,3,2]
[6,4,1,2,5,7,3]=>[1,1,4,1]
[6,4,1,2,7,3,5]=>[1,1,3,2]
[6,4,1,2,7,5,3]=>[1,1,3,1,1]
[6,4,1,3,2,5,7]=>[1,1,2,3]
[6,4,1,3,2,7,5]=>[1,1,2,2,1]
[6,4,1,3,5,2,7]=>[1,1,3,2]
[6,4,1,3,5,7,2]=>[1,1,4,1]
[6,4,1,3,7,2,5]=>[1,1,3,2]
[6,4,1,3,7,5,2]=>[1,1,3,1,1]
[6,4,1,5,2,3,7]=>[1,1,2,3]
[6,4,1,5,2,7,3]=>[1,1,2,2,1]
[6,4,1,5,3,2,7]=>[1,1,2,1,2]
[6,4,1,5,3,7,2]=>[1,1,2,2,1]
[6,4,1,5,7,2,3]=>[1,1,3,2]
[6,4,1,5,7,3,2]=>[1,1,3,1,1]
[6,4,1,7,2,3,5]=>[1,1,2,3]
[6,4,1,7,2,5,3]=>[1,1,2,2,1]
[6,4,1,7,3,2,5]=>[1,1,2,1,2]
[6,4,1,7,3,5,2]=>[1,1,2,2,1]
[6,4,1,7,5,2,3]=>[1,1,2,1,2]
[6,4,1,7,5,3,2]=>[1,1,2,1,1,1]
[6,4,2,1,3,5,7]=>[1,1,1,4]
[6,4,2,1,3,7,5]=>[1,1,1,3,1]
[6,4,2,1,5,3,7]=>[1,1,1,2,2]
[6,4,2,1,5,7,3]=>[1,1,1,3,1]
[6,4,2,1,7,3,5]=>[1,1,1,2,2]
[6,4,2,1,7,5,3]=>[1,1,1,2,1,1]
[6,4,2,3,1,5,7]=>[1,1,2,3]
[6,4,2,3,1,7,5]=>[1,1,2,2,1]
[6,4,2,3,5,1,7]=>[1,1,3,2]
[6,4,2,3,5,7,1]=>[1,1,4,1]
[6,4,2,3,7,1,5]=>[1,1,3,2]
[6,4,2,3,7,5,1]=>[1,1,3,1,1]
[6,4,2,5,1,3,7]=>[1,1,2,3]
[6,4,2,5,1,7,3]=>[1,1,2,2,1]
[6,4,2,5,3,1,7]=>[1,1,2,1,2]
[6,4,2,5,3,7,1]=>[1,1,2,2,1]
[6,4,2,5,7,1,3]=>[1,1,3,2]
[6,4,2,5,7,3,1]=>[1,1,3,1,1]
[6,4,2,7,1,3,5]=>[1,1,2,3]
[6,4,2,7,1,5,3]=>[1,1,2,2,1]
[6,4,2,7,3,1,5]=>[1,1,2,1,2]
[6,4,2,7,3,5,1]=>[1,1,2,2,1]
[6,4,2,7,5,1,3]=>[1,1,2,1,2]
[6,4,2,7,5,3,1]=>[1,1,2,1,1,1]
[6,4,3,1,2,5,7]=>[1,1,1,4]
[6,4,3,1,2,7,5]=>[1,1,1,3,1]
[6,4,3,1,5,2,7]=>[1,1,1,2,2]
[6,4,3,1,5,7,2]=>[1,1,1,3,1]
[6,4,3,1,7,2,5]=>[1,1,1,2,2]
[6,4,3,1,7,5,2]=>[1,1,1,2,1,1]
[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[6,4,3,2,1,7,5]=>[1,1,1,1,2,1]
[6,4,3,2,5,1,7]=>[1,1,1,2,2]
[6,4,3,2,5,7,1]=>[1,1,1,3,1]
[6,4,3,2,7,1,5]=>[1,1,1,2,2]
[6,4,3,2,7,5,1]=>[1,1,1,2,1,1]
[6,4,3,5,1,2,7]=>[1,1,2,3]
[6,4,3,5,1,7,2]=>[1,1,2,2,1]
[6,4,3,5,2,1,7]=>[1,1,2,1,2]
[6,4,3,5,2,7,1]=>[1,1,2,2,1]
[6,4,3,5,7,1,2]=>[1,1,3,2]
[6,4,3,5,7,2,1]=>[1,1,3,1,1]
[6,4,3,7,1,2,5]=>[1,1,2,3]
[6,4,3,7,1,5,2]=>[1,1,2,2,1]
[6,4,3,7,2,1,5]=>[1,1,2,1,2]
[6,4,3,7,2,5,1]=>[1,1,2,2,1]
[6,4,3,7,5,1,2]=>[1,1,2,1,2]
[6,4,3,7,5,2,1]=>[1,1,2,1,1,1]
[6,4,5,1,2,3,7]=>[1,2,4]
[6,4,5,1,2,7,3]=>[1,2,3,1]
[6,4,5,1,3,2,7]=>[1,2,2,2]
[6,4,5,1,3,7,2]=>[1,2,3,1]
[6,4,5,1,7,2,3]=>[1,2,2,2]
[6,4,5,1,7,3,2]=>[1,2,2,1,1]
[6,4,5,2,1,3,7]=>[1,2,1,3]
[6,4,5,2,1,7,3]=>[1,2,1,2,1]
[6,4,5,2,3,1,7]=>[1,2,2,2]
[6,4,5,2,3,7,1]=>[1,2,3,1]
[6,4,5,2,7,1,3]=>[1,2,2,2]
[6,4,5,2,7,3,1]=>[1,2,2,1,1]
[6,4,5,3,1,2,7]=>[1,2,1,3]
[6,4,5,3,1,7,2]=>[1,2,1,2,1]
[6,4,5,3,2,1,7]=>[1,2,1,1,2]
[6,4,5,3,2,7,1]=>[1,2,1,2,1]
[6,4,5,3,7,1,2]=>[1,2,2,2]
[6,4,5,3,7,2,1]=>[1,2,2,1,1]
[6,4,5,7,1,2,3]=>[1,3,3]
[6,4,5,7,1,3,2]=>[1,3,2,1]
[6,4,5,7,2,1,3]=>[1,3,1,2]
[6,4,5,7,2,3,1]=>[1,3,2,1]
[6,4,5,7,3,1,2]=>[1,3,1,2]
[6,4,5,7,3,2,1]=>[1,3,1,1,1]
[6,4,7,1,2,3,5]=>[1,2,4]
[6,4,7,1,2,5,3]=>[1,2,3,1]
[6,4,7,1,3,2,5]=>[1,2,2,2]
[6,4,7,1,3,5,2]=>[1,2,3,1]
[6,4,7,1,5,2,3]=>[1,2,2,2]
[6,4,7,1,5,3,2]=>[1,2,2,1,1]
[6,4,7,2,1,3,5]=>[1,2,1,3]
[6,4,7,2,1,5,3]=>[1,2,1,2,1]
[6,4,7,2,3,1,5]=>[1,2,2,2]
[6,4,7,2,3,5,1]=>[1,2,3,1]
[6,4,7,2,5,1,3]=>[1,2,2,2]
[6,4,7,2,5,3,1]=>[1,2,2,1,1]
[6,4,7,3,1,2,5]=>[1,2,1,3]
[6,4,7,3,1,5,2]=>[1,2,1,2,1]
[6,4,7,3,2,1,5]=>[1,2,1,1,2]
[6,4,7,3,2,5,1]=>[1,2,1,2,1]
[6,4,7,3,5,1,2]=>[1,2,2,2]
[6,4,7,3,5,2,1]=>[1,2,2,1,1]
[6,4,7,5,1,2,3]=>[1,2,1,3]
[6,4,7,5,1,3,2]=>[1,2,1,2,1]
[6,4,7,5,2,1,3]=>[1,2,1,1,2]
[6,4,7,5,2,3,1]=>[1,2,1,2,1]
[6,4,7,5,3,1,2]=>[1,2,1,1,2]
[6,4,7,5,3,2,1]=>[1,2,1,1,1,1]
[6,5,1,2,3,4,7]=>[1,1,5]
[6,5,1,2,3,7,4]=>[1,1,4,1]
[6,5,1,2,4,3,7]=>[1,1,3,2]
[6,5,1,2,4,7,3]=>[1,1,4,1]
[6,5,1,2,7,3,4]=>[1,1,3,2]
[6,5,1,2,7,4,3]=>[1,1,3,1,1]
[6,5,1,3,2,4,7]=>[1,1,2,3]
[6,5,1,3,2,7,4]=>[1,1,2,2,1]
[6,5,1,3,4,2,7]=>[1,1,3,2]
[6,5,1,3,4,7,2]=>[1,1,4,1]
[6,5,1,3,7,2,4]=>[1,1,3,2]
[6,5,1,3,7,4,2]=>[1,1,3,1,1]
[6,5,1,4,2,3,7]=>[1,1,2,3]
[6,5,1,4,2,7,3]=>[1,1,2,2,1]
[6,5,1,4,3,2,7]=>[1,1,2,1,2]
[6,5,1,4,3,7,2]=>[1,1,2,2,1]
[6,5,1,4,7,2,3]=>[1,1,3,2]
[6,5,1,4,7,3,2]=>[1,1,3,1,1]
[6,5,1,7,2,3,4]=>[1,1,2,3]
[6,5,1,7,2,4,3]=>[1,1,2,2,1]
[6,5,1,7,3,2,4]=>[1,1,2,1,2]
[6,5,1,7,3,4,2]=>[1,1,2,2,1]
[6,5,1,7,4,2,3]=>[1,1,2,1,2]
[6,5,1,7,4,3,2]=>[1,1,2,1,1,1]
[6,5,2,1,3,4,7]=>[1,1,1,4]
[6,5,2,1,3,7,4]=>[1,1,1,3,1]
[6,5,2,1,4,3,7]=>[1,1,1,2,2]
[6,5,2,1,4,7,3]=>[1,1,1,3,1]
[6,5,2,1,7,3,4]=>[1,1,1,2,2]
[6,5,2,1,7,4,3]=>[1,1,1,2,1,1]
[6,5,2,3,1,4,7]=>[1,1,2,3]
[6,5,2,3,1,7,4]=>[1,1,2,2,1]
[6,5,2,3,4,1,7]=>[1,1,3,2]
[6,5,2,3,4,7,1]=>[1,1,4,1]
[6,5,2,3,7,1,4]=>[1,1,3,2]
[6,5,2,3,7,4,1]=>[1,1,3,1,1]
[6,5,2,4,1,3,7]=>[1,1,2,3]
[6,5,2,4,1,7,3]=>[1,1,2,2,1]
[6,5,2,4,3,1,7]=>[1,1,2,1,2]
[6,5,2,4,3,7,1]=>[1,1,2,2,1]
[6,5,2,4,7,1,3]=>[1,1,3,2]
[6,5,2,4,7,3,1]=>[1,1,3,1,1]
[6,5,2,7,1,3,4]=>[1,1,2,3]
[6,5,2,7,1,4,3]=>[1,1,2,2,1]
[6,5,2,7,3,1,4]=>[1,1,2,1,2]
[6,5,2,7,3,4,1]=>[1,1,2,2,1]
[6,5,2,7,4,1,3]=>[1,1,2,1,2]
[6,5,2,7,4,3,1]=>[1,1,2,1,1,1]
[6,5,3,1,2,4,7]=>[1,1,1,4]
[6,5,3,1,2,7,4]=>[1,1,1,3,1]
[6,5,3,1,4,2,7]=>[1,1,1,2,2]
[6,5,3,1,4,7,2]=>[1,1,1,3,1]
[6,5,3,1,7,2,4]=>[1,1,1,2,2]
[6,5,3,1,7,4,2]=>[1,1,1,2,1,1]
[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[6,5,3,2,1,7,4]=>[1,1,1,1,2,1]
[6,5,3,2,4,1,7]=>[1,1,1,2,2]
[6,5,3,2,4,7,1]=>[1,1,1,3,1]
[6,5,3,2,7,1,4]=>[1,1,1,2,2]
[6,5,3,2,7,4,1]=>[1,1,1,2,1,1]
[6,5,3,4,1,2,7]=>[1,1,2,3]
[6,5,3,4,1,7,2]=>[1,1,2,2,1]
[6,5,3,4,2,1,7]=>[1,1,2,1,2]
[6,5,3,4,2,7,1]=>[1,1,2,2,1]
[6,5,3,4,7,1,2]=>[1,1,3,2]
[6,5,3,4,7,2,1]=>[1,1,3,1,1]
[6,5,3,7,1,2,4]=>[1,1,2,3]
[6,5,3,7,1,4,2]=>[1,1,2,2,1]
[6,5,3,7,2,1,4]=>[1,1,2,1,2]
[6,5,3,7,2,4,1]=>[1,1,2,2,1]
[6,5,3,7,4,1,2]=>[1,1,2,1,2]
[6,5,3,7,4,2,1]=>[1,1,2,1,1,1]
[6,5,4,1,2,3,7]=>[1,1,1,4]
[6,5,4,1,2,7,3]=>[1,1,1,3,1]
[6,5,4,1,3,2,7]=>[1,1,1,2,2]
[6,5,4,1,3,7,2]=>[1,1,1,3,1]
[6,5,4,1,7,2,3]=>[1,1,1,2,2]
[6,5,4,1,7,3,2]=>[1,1,1,2,1,1]
[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[6,5,4,2,1,7,3]=>[1,1,1,1,2,1]
[6,5,4,2,3,1,7]=>[1,1,1,2,2]
[6,5,4,2,3,7,1]=>[1,1,1,3,1]
[6,5,4,2,7,1,3]=>[1,1,1,2,2]
[6,5,4,2,7,3,1]=>[1,1,1,2,1,1]
[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[6,5,4,3,1,7,2]=>[1,1,1,1,2,1]
[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[6,5,4,3,7,1,2]=>[1,1,1,2,2]
[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[6,5,4,7,1,2,3]=>[1,1,2,3]
[6,5,4,7,1,3,2]=>[1,1,2,2,1]
[6,5,4,7,2,1,3]=>[1,1,2,1,2]
[6,5,4,7,2,3,1]=>[1,1,2,2,1]
[6,5,4,7,3,1,2]=>[1,1,2,1,2]
[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[6,5,7,1,2,3,4]=>[1,2,4]
[6,5,7,1,2,4,3]=>[1,2,3,1]
[6,5,7,1,3,2,4]=>[1,2,2,2]
[6,5,7,1,3,4,2]=>[1,2,3,1]
[6,5,7,1,4,2,3]=>[1,2,2,2]
[6,5,7,1,4,3,2]=>[1,2,2,1,1]
[6,5,7,2,1,3,4]=>[1,2,1,3]
[6,5,7,2,1,4,3]=>[1,2,1,2,1]
[6,5,7,2,3,1,4]=>[1,2,2,2]
[6,5,7,2,3,4,1]=>[1,2,3,1]
[6,5,7,2,4,1,3]=>[1,2,2,2]
[6,5,7,2,4,3,1]=>[1,2,2,1,1]
[6,5,7,3,1,2,4]=>[1,2,1,3]
[6,5,7,3,1,4,2]=>[1,2,1,2,1]
[6,5,7,3,2,1,4]=>[1,2,1,1,2]
[6,5,7,3,2,4,1]=>[1,2,1,2,1]
[6,5,7,3,4,1,2]=>[1,2,2,2]
[6,5,7,3,4,2,1]=>[1,2,2,1,1]
[6,5,7,4,1,2,3]=>[1,2,1,3]
[6,5,7,4,1,3,2]=>[1,2,1,2,1]
[6,5,7,4,2,1,3]=>[1,2,1,1,2]
[6,5,7,4,2,3,1]=>[1,2,1,2,1]
[6,5,7,4,3,1,2]=>[1,2,1,1,2]
[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[6,7,1,2,3,4,5]=>[2,5]
[6,7,1,2,3,5,4]=>[2,4,1]
[6,7,1,2,4,3,5]=>[2,3,2]
[6,7,1,2,4,5,3]=>[2,4,1]
[6,7,1,2,5,3,4]=>[2,3,2]
[6,7,1,2,5,4,3]=>[2,3,1,1]
[6,7,1,3,2,4,5]=>[2,2,3]
[6,7,1,3,2,5,4]=>[2,2,2,1]
[6,7,1,3,4,2,5]=>[2,3,2]
[6,7,1,3,4,5,2]=>[2,4,1]
[6,7,1,3,5,2,4]=>[2,3,2]
[6,7,1,3,5,4,2]=>[2,3,1,1]
[6,7,1,4,2,3,5]=>[2,2,3]
[6,7,1,4,2,5,3]=>[2,2,2,1]
[6,7,1,4,3,2,5]=>[2,2,1,2]
[6,7,1,4,3,5,2]=>[2,2,2,1]
[6,7,1,4,5,2,3]=>[2,3,2]
[6,7,1,4,5,3,2]=>[2,3,1,1]
[6,7,1,5,2,3,4]=>[2,2,3]
[6,7,1,5,2,4,3]=>[2,2,2,1]
[6,7,1,5,3,2,4]=>[2,2,1,2]
[6,7,1,5,3,4,2]=>[2,2,2,1]
[6,7,1,5,4,2,3]=>[2,2,1,2]
[6,7,1,5,4,3,2]=>[2,2,1,1,1]
[6,7,2,1,3,4,5]=>[2,1,4]
[6,7,2,1,3,5,4]=>[2,1,3,1]
[6,7,2,1,4,3,5]=>[2,1,2,2]
[6,7,2,1,4,5,3]=>[2,1,3,1]
[6,7,2,1,5,3,4]=>[2,1,2,2]
[6,7,2,1,5,4,3]=>[2,1,2,1,1]
[6,7,2,3,1,4,5]=>[2,2,3]
[6,7,2,3,1,5,4]=>[2,2,2,1]
[6,7,2,3,4,1,5]=>[2,3,2]
[6,7,2,3,4,5,1]=>[2,4,1]
[6,7,2,3,5,1,4]=>[2,3,2]
[6,7,2,3,5,4,1]=>[2,3,1,1]
[6,7,2,4,1,3,5]=>[2,2,3]
[6,7,2,4,1,5,3]=>[2,2,2,1]
[6,7,2,4,3,1,5]=>[2,2,1,2]
[6,7,2,4,3,5,1]=>[2,2,2,1]
[6,7,2,4,5,1,3]=>[2,3,2]
[6,7,2,4,5,3,1]=>[2,3,1,1]
[6,7,2,5,1,3,4]=>[2,2,3]
[6,7,2,5,1,4,3]=>[2,2,2,1]
[6,7,2,5,3,1,4]=>[2,2,1,2]
[6,7,2,5,3,4,1]=>[2,2,2,1]
[6,7,2,5,4,1,3]=>[2,2,1,2]
[6,7,2,5,4,3,1]=>[2,2,1,1,1]
[6,7,3,1,2,4,5]=>[2,1,4]
[6,7,3,1,2,5,4]=>[2,1,3,1]
[6,7,3,1,4,2,5]=>[2,1,2,2]
[6,7,3,1,4,5,2]=>[2,1,3,1]
[6,7,3,1,5,2,4]=>[2,1,2,2]
[6,7,3,1,5,4,2]=>[2,1,2,1,1]
[6,7,3,2,1,4,5]=>[2,1,1,3]
[6,7,3,2,1,5,4]=>[2,1,1,2,1]
[6,7,3,2,4,1,5]=>[2,1,2,2]
[6,7,3,2,4,5,1]=>[2,1,3,1]
[6,7,3,2,5,1,4]=>[2,1,2,2]
[6,7,3,2,5,4,1]=>[2,1,2,1,1]
[6,7,3,4,1,2,5]=>[2,2,3]
[6,7,3,4,1,5,2]=>[2,2,2,1]
[6,7,3,4,2,1,5]=>[2,2,1,2]
[6,7,3,4,2,5,1]=>[2,2,2,1]
[6,7,3,4,5,1,2]=>[2,3,2]
[6,7,3,4,5,2,1]=>[2,3,1,1]
[6,7,3,5,1,2,4]=>[2,2,3]
[6,7,3,5,1,4,2]=>[2,2,2,1]
[6,7,3,5,2,1,4]=>[2,2,1,2]
[6,7,3,5,2,4,1]=>[2,2,2,1]
[6,7,3,5,4,1,2]=>[2,2,1,2]
[6,7,3,5,4,2,1]=>[2,2,1,1,1]
[6,7,4,1,2,3,5]=>[2,1,4]
[6,7,4,1,2,5,3]=>[2,1,3,1]
[6,7,4,1,3,2,5]=>[2,1,2,2]
[6,7,4,1,3,5,2]=>[2,1,3,1]
[6,7,4,1,5,2,3]=>[2,1,2,2]
[6,7,4,1,5,3,2]=>[2,1,2,1,1]
[6,7,4,2,1,3,5]=>[2,1,1,3]
[6,7,4,2,1,5,3]=>[2,1,1,2,1]
[6,7,4,2,3,1,5]=>[2,1,2,2]
[6,7,4,2,3,5,1]=>[2,1,3,1]
[6,7,4,2,5,1,3]=>[2,1,2,2]
[6,7,4,2,5,3,1]=>[2,1,2,1,1]
[6,7,4,3,1,2,5]=>[2,1,1,3]
[6,7,4,3,1,5,2]=>[2,1,1,2,1]
[6,7,4,3,2,1,5]=>[2,1,1,1,2]
[6,7,4,3,2,5,1]=>[2,1,1,2,1]
[6,7,4,3,5,1,2]=>[2,1,2,2]
[6,7,4,3,5,2,1]=>[2,1,2,1,1]
[6,7,4,5,1,2,3]=>[2,2,3]
[6,7,4,5,1,3,2]=>[2,2,2,1]
[6,7,4,5,2,1,3]=>[2,2,1,2]
[6,7,4,5,2,3,1]=>[2,2,2,1]
[6,7,4,5,3,1,2]=>[2,2,1,2]
[6,7,4,5,3,2,1]=>[2,2,1,1,1]
[6,7,5,1,2,3,4]=>[2,1,4]
[6,7,5,1,2,4,3]=>[2,1,3,1]
[6,7,5,1,3,2,4]=>[2,1,2,2]
[6,7,5,1,3,4,2]=>[2,1,3,1]
[6,7,5,1,4,2,3]=>[2,1,2,2]
[6,7,5,1,4,3,2]=>[2,1,2,1,1]
[6,7,5,2,1,3,4]=>[2,1,1,3]
[6,7,5,2,1,4,3]=>[2,1,1,2,1]
[6,7,5,2,3,1,4]=>[2,1,2,2]
[6,7,5,2,3,4,1]=>[2,1,3,1]
[6,7,5,2,4,1,3]=>[2,1,2,2]
[6,7,5,2,4,3,1]=>[2,1,2,1,1]
[6,7,5,3,1,2,4]=>[2,1,1,3]
[6,7,5,3,1,4,2]=>[2,1,1,2,1]
[6,7,5,3,2,1,4]=>[2,1,1,1,2]
[6,7,5,3,2,4,1]=>[2,1,1,2,1]
[6,7,5,3,4,1,2]=>[2,1,2,2]
[6,7,5,3,4,2,1]=>[2,1,2,1,1]
[6,7,5,4,1,2,3]=>[2,1,1,3]
[6,7,5,4,1,3,2]=>[2,1,1,2,1]
[6,7,5,4,2,1,3]=>[2,1,1,1,2]
[6,7,5,4,2,3,1]=>[2,1,1,2,1]
[6,7,5,4,3,1,2]=>[2,1,1,1,2]
[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[7,1,2,3,4,5,6]=>[1,6]
[7,1,2,3,4,6,5]=>[1,5,1]
[7,1,2,3,5,4,6]=>[1,4,2]
[7,1,2,3,5,6,4]=>[1,5,1]
[7,1,2,3,6,4,5]=>[1,4,2]
[7,1,2,3,6,5,4]=>[1,4,1,1]
[7,1,2,4,3,5,6]=>[1,3,3]
[7,1,2,4,3,6,5]=>[1,3,2,1]
[7,1,2,4,5,3,6]=>[1,4,2]
[7,1,2,4,5,6,3]=>[1,5,1]
[7,1,2,4,6,3,5]=>[1,4,2]
[7,1,2,4,6,5,3]=>[1,4,1,1]
[7,1,2,5,3,4,6]=>[1,3,3]
[7,1,2,5,3,6,4]=>[1,3,2,1]
[7,1,2,5,4,3,6]=>[1,3,1,2]
[7,1,2,5,4,6,3]=>[1,3,2,1]
[7,1,2,5,6,3,4]=>[1,4,2]
[7,1,2,5,6,4,3]=>[1,4,1,1]
[7,1,2,6,3,4,5]=>[1,3,3]
[7,1,2,6,3,5,4]=>[1,3,2,1]
[7,1,2,6,4,3,5]=>[1,3,1,2]
[7,1,2,6,4,5,3]=>[1,3,2,1]
[7,1,2,6,5,3,4]=>[1,3,1,2]
[7,1,2,6,5,4,3]=>[1,3,1,1,1]
[7,1,3,2,4,5,6]=>[1,2,4]
[7,1,3,2,4,6,5]=>[1,2,3,1]
[7,1,3,2,5,4,6]=>[1,2,2,2]
[7,1,3,2,5,6,4]=>[1,2,3,1]
[7,1,3,2,6,4,5]=>[1,2,2,2]
[7,1,3,2,6,5,4]=>[1,2,2,1,1]
[7,1,3,4,2,5,6]=>[1,3,3]
[7,1,3,4,2,6,5]=>[1,3,2,1]
[7,1,3,4,5,2,6]=>[1,4,2]
[7,1,3,4,5,6,2]=>[1,5,1]
[7,1,3,4,6,2,5]=>[1,4,2]
[7,1,3,4,6,5,2]=>[1,4,1,1]
[7,1,3,5,2,4,6]=>[1,3,3]
[7,1,3,5,2,6,4]=>[1,3,2,1]
[7,1,3,5,4,2,6]=>[1,3,1,2]
[7,1,3,5,4,6,2]=>[1,3,2,1]
[7,1,3,5,6,2,4]=>[1,4,2]
[7,1,3,5,6,4,2]=>[1,4,1,1]
[7,1,3,6,2,4,5]=>[1,3,3]
[7,1,3,6,2,5,4]=>[1,3,2,1]
[7,1,3,6,4,2,5]=>[1,3,1,2]
[7,1,3,6,4,5,2]=>[1,3,2,1]
[7,1,3,6,5,2,4]=>[1,3,1,2]
[7,1,3,6,5,4,2]=>[1,3,1,1,1]
[7,1,4,2,3,5,6]=>[1,2,4]
[7,1,4,2,3,6,5]=>[1,2,3,1]
[7,1,4,2,5,3,6]=>[1,2,2,2]
[7,1,4,2,5,6,3]=>[1,2,3,1]
[7,1,4,2,6,3,5]=>[1,2,2,2]
[7,1,4,2,6,5,3]=>[1,2,2,1,1]
[7,1,4,3,2,5,6]=>[1,2,1,3]
[7,1,4,3,2,6,5]=>[1,2,1,2,1]
[7,1,4,3,5,2,6]=>[1,2,2,2]
[7,1,4,3,5,6,2]=>[1,2,3,1]
[7,1,4,3,6,2,5]=>[1,2,2,2]
[7,1,4,3,6,5,2]=>[1,2,2,1,1]
[7,1,4,5,2,3,6]=>[1,3,3]
[7,1,4,5,2,6,3]=>[1,3,2,1]
[7,1,4,5,3,2,6]=>[1,3,1,2]
[7,1,4,5,3,6,2]=>[1,3,2,1]
[7,1,4,5,6,2,3]=>[1,4,2]
[7,1,4,5,6,3,2]=>[1,4,1,1]
[7,1,4,6,2,3,5]=>[1,3,3]
[7,1,4,6,2,5,3]=>[1,3,2,1]
[7,1,4,6,3,2,5]=>[1,3,1,2]
[7,1,4,6,3,5,2]=>[1,3,2,1]
[7,1,4,6,5,2,3]=>[1,3,1,2]
[7,1,4,6,5,3,2]=>[1,3,1,1,1]
[7,1,5,2,3,4,6]=>[1,2,4]
[7,1,5,2,3,6,4]=>[1,2,3,1]
[7,1,5,2,4,3,6]=>[1,2,2,2]
[7,1,5,2,4,6,3]=>[1,2,3,1]
[7,1,5,2,6,3,4]=>[1,2,2,2]
[7,1,5,2,6,4,3]=>[1,2,2,1,1]
[7,1,5,3,2,4,6]=>[1,2,1,3]
[7,1,5,3,2,6,4]=>[1,2,1,2,1]
[7,1,5,3,4,2,6]=>[1,2,2,2]
[7,1,5,3,4,6,2]=>[1,2,3,1]
[7,1,5,3,6,2,4]=>[1,2,2,2]
[7,1,5,3,6,4,2]=>[1,2,2,1,1]
[7,1,5,4,2,3,6]=>[1,2,1,3]
[7,1,5,4,2,6,3]=>[1,2,1,2,1]
[7,1,5,4,3,2,6]=>[1,2,1,1,2]
[7,1,5,4,3,6,2]=>[1,2,1,2,1]
[7,1,5,4,6,2,3]=>[1,2,2,2]
[7,1,5,4,6,3,2]=>[1,2,2,1,1]
[7,1,5,6,2,3,4]=>[1,3,3]
[7,1,5,6,2,4,3]=>[1,3,2,1]
[7,1,5,6,3,2,4]=>[1,3,1,2]
[7,1,5,6,3,4,2]=>[1,3,2,1]
[7,1,5,6,4,2,3]=>[1,3,1,2]
[7,1,5,6,4,3,2]=>[1,3,1,1,1]
[7,1,6,2,3,4,5]=>[1,2,4]
[7,1,6,2,3,5,4]=>[1,2,3,1]
[7,1,6,2,4,3,5]=>[1,2,2,2]
[7,1,6,2,4,5,3]=>[1,2,3,1]
[7,1,6,2,5,3,4]=>[1,2,2,2]
[7,1,6,2,5,4,3]=>[1,2,2,1,1]
[7,1,6,3,2,4,5]=>[1,2,1,3]
[7,1,6,3,2,5,4]=>[1,2,1,2,1]
[7,1,6,3,4,2,5]=>[1,2,2,2]
[7,1,6,3,4,5,2]=>[1,2,3,1]
[7,1,6,3,5,2,4]=>[1,2,2,2]
[7,1,6,3,5,4,2]=>[1,2,2,1,1]
[7,1,6,4,2,3,5]=>[1,2,1,3]
[7,1,6,4,2,5,3]=>[1,2,1,2,1]
[7,1,6,4,3,2,5]=>[1,2,1,1,2]
[7,1,6,4,3,5,2]=>[1,2,1,2,1]
[7,1,6,4,5,2,3]=>[1,2,2,2]
[7,1,6,4,5,3,2]=>[1,2,2,1,1]
[7,1,6,5,2,3,4]=>[1,2,1,3]
[7,1,6,5,2,4,3]=>[1,2,1,2,1]
[7,1,6,5,3,2,4]=>[1,2,1,1,2]
[7,1,6,5,3,4,2]=>[1,2,1,2,1]
[7,1,6,5,4,2,3]=>[1,2,1,1,2]
[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]
[7,2,1,3,4,5,6]=>[1,1,5]
[7,2,1,3,4,6,5]=>[1,1,4,1]
[7,2,1,3,5,4,6]=>[1,1,3,2]
[7,2,1,3,5,6,4]=>[1,1,4,1]
[7,2,1,3,6,4,5]=>[1,1,3,2]
[7,2,1,3,6,5,4]=>[1,1,3,1,1]
[7,2,1,4,3,5,6]=>[1,1,2,3]
[7,2,1,4,3,6,5]=>[1,1,2,2,1]
[7,2,1,4,5,3,6]=>[1,1,3,2]
[7,2,1,4,5,6,3]=>[1,1,4,1]
[7,2,1,4,6,3,5]=>[1,1,3,2]
[7,2,1,4,6,5,3]=>[1,1,3,1,1]
[7,2,1,5,3,4,6]=>[1,1,2,3]
[7,2,1,5,3,6,4]=>[1,1,2,2,1]
[7,2,1,5,4,3,6]=>[1,1,2,1,2]
[7,2,1,5,4,6,3]=>[1,1,2,2,1]
[7,2,1,5,6,3,4]=>[1,1,3,2]
[7,2,1,5,6,4,3]=>[1,1,3,1,1]
[7,2,1,6,3,4,5]=>[1,1,2,3]
[7,2,1,6,3,5,4]=>[1,1,2,2,1]
[7,2,1,6,4,3,5]=>[1,1,2,1,2]
[7,2,1,6,4,5,3]=>[1,1,2,2,1]
[7,2,1,6,5,3,4]=>[1,1,2,1,2]
[7,2,1,6,5,4,3]=>[1,1,2,1,1,1]
[7,2,3,1,4,5,6]=>[1,2,4]
[7,2,3,1,4,6,5]=>[1,2,3,1]
[7,2,3,1,5,4,6]=>[1,2,2,2]
[7,2,3,1,5,6,4]=>[1,2,3,1]
[7,2,3,1,6,4,5]=>[1,2,2,2]
[7,2,3,1,6,5,4]=>[1,2,2,1,1]
[7,2,3,4,1,5,6]=>[1,3,3]
[7,2,3,4,1,6,5]=>[1,3,2,1]
[7,2,3,4,5,1,6]=>[1,4,2]
[7,2,3,4,5,6,1]=>[1,5,1]
[7,2,3,4,6,1,5]=>[1,4,2]
[7,2,3,4,6,5,1]=>[1,4,1,1]
[7,2,3,5,1,4,6]=>[1,3,3]
[7,2,3,5,1,6,4]=>[1,3,2,1]
[7,2,3,5,4,1,6]=>[1,3,1,2]
[7,2,3,5,4,6,1]=>[1,3,2,1]
[7,2,3,5,6,1,4]=>[1,4,2]
[7,2,3,5,6,4,1]=>[1,4,1,1]
[7,2,3,6,1,4,5]=>[1,3,3]
[7,2,3,6,1,5,4]=>[1,3,2,1]
[7,2,3,6,4,1,5]=>[1,3,1,2]
[7,2,3,6,4,5,1]=>[1,3,2,1]
[7,2,3,6,5,1,4]=>[1,3,1,2]
[7,2,3,6,5,4,1]=>[1,3,1,1,1]
[7,2,4,1,3,5,6]=>[1,2,4]
[7,2,4,1,3,6,5]=>[1,2,3,1]
[7,2,4,1,5,3,6]=>[1,2,2,2]
[7,2,4,1,5,6,3]=>[1,2,3,1]
[7,2,4,1,6,3,5]=>[1,2,2,2]
[7,2,4,1,6,5,3]=>[1,2,2,1,1]
[7,2,4,3,1,5,6]=>[1,2,1,3]
[7,2,4,3,1,6,5]=>[1,2,1,2,1]
[7,2,4,3,5,1,6]=>[1,2,2,2]
[7,2,4,3,5,6,1]=>[1,2,3,1]
[7,2,4,3,6,1,5]=>[1,2,2,2]
[7,2,4,3,6,5,1]=>[1,2,2,1,1]
[7,2,4,5,1,3,6]=>[1,3,3]
[7,2,4,5,1,6,3]=>[1,3,2,1]
[7,2,4,5,3,1,6]=>[1,3,1,2]
[7,2,4,5,3,6,1]=>[1,3,2,1]
[7,2,4,5,6,1,3]=>[1,4,2]
[7,2,4,5,6,3,1]=>[1,4,1,1]
[7,2,4,6,1,3,5]=>[1,3,3]
[7,2,4,6,1,5,3]=>[1,3,2,1]
[7,2,4,6,3,1,5]=>[1,3,1,2]
[7,2,4,6,3,5,1]=>[1,3,2,1]
[7,2,4,6,5,1,3]=>[1,3,1,2]
[7,2,4,6,5,3,1]=>[1,3,1,1,1]
[7,2,5,1,3,4,6]=>[1,2,4]
[7,2,5,1,3,6,4]=>[1,2,3,1]
[7,2,5,1,4,3,6]=>[1,2,2,2]
[7,2,5,1,4,6,3]=>[1,2,3,1]
[7,2,5,1,6,3,4]=>[1,2,2,2]
[7,2,5,1,6,4,3]=>[1,2,2,1,1]
[7,2,5,3,1,4,6]=>[1,2,1,3]
[7,2,5,3,1,6,4]=>[1,2,1,2,1]
[7,2,5,3,4,1,6]=>[1,2,2,2]
[7,2,5,3,4,6,1]=>[1,2,3,1]
[7,2,5,3,6,1,4]=>[1,2,2,2]
[7,2,5,3,6,4,1]=>[1,2,2,1,1]
[7,2,5,4,1,3,6]=>[1,2,1,3]
[7,2,5,4,1,6,3]=>[1,2,1,2,1]
[7,2,5,4,3,1,6]=>[1,2,1,1,2]
[7,2,5,4,3,6,1]=>[1,2,1,2,1]
[7,2,5,4,6,1,3]=>[1,2,2,2]
[7,2,5,4,6,3,1]=>[1,2,2,1,1]
[7,2,5,6,1,3,4]=>[1,3,3]
[7,2,5,6,1,4,3]=>[1,3,2,1]
[7,2,5,6,3,1,4]=>[1,3,1,2]
[7,2,5,6,3,4,1]=>[1,3,2,1]
[7,2,5,6,4,1,3]=>[1,3,1,2]
[7,2,5,6,4,3,1]=>[1,3,1,1,1]
[7,2,6,1,3,4,5]=>[1,2,4]
[7,2,6,1,3,5,4]=>[1,2,3,1]
[7,2,6,1,4,3,5]=>[1,2,2,2]
[7,2,6,1,4,5,3]=>[1,2,3,1]
[7,2,6,1,5,3,4]=>[1,2,2,2]
[7,2,6,1,5,4,3]=>[1,2,2,1,1]
[7,2,6,3,1,4,5]=>[1,2,1,3]
[7,2,6,3,1,5,4]=>[1,2,1,2,1]
[7,2,6,3,4,1,5]=>[1,2,2,2]
[7,2,6,3,4,5,1]=>[1,2,3,1]
[7,2,6,3,5,1,4]=>[1,2,2,2]
[7,2,6,3,5,4,1]=>[1,2,2,1,1]
[7,2,6,4,1,3,5]=>[1,2,1,3]
[7,2,6,4,1,5,3]=>[1,2,1,2,1]
[7,2,6,4,3,1,5]=>[1,2,1,1,2]
[7,2,6,4,3,5,1]=>[1,2,1,2,1]
[7,2,6,4,5,1,3]=>[1,2,2,2]
[7,2,6,4,5,3,1]=>[1,2,2,1,1]
[7,2,6,5,1,3,4]=>[1,2,1,3]
[7,2,6,5,1,4,3]=>[1,2,1,2,1]
[7,2,6,5,3,1,4]=>[1,2,1,1,2]
[7,2,6,5,3,4,1]=>[1,2,1,2,1]
[7,2,6,5,4,1,3]=>[1,2,1,1,2]
[7,2,6,5,4,3,1]=>[1,2,1,1,1,1]
[7,3,1,2,4,5,6]=>[1,1,5]
[7,3,1,2,4,6,5]=>[1,1,4,1]
[7,3,1,2,5,4,6]=>[1,1,3,2]
[7,3,1,2,5,6,4]=>[1,1,4,1]
[7,3,1,2,6,4,5]=>[1,1,3,2]
[7,3,1,2,6,5,4]=>[1,1,3,1,1]
[7,3,1,4,2,5,6]=>[1,1,2,3]
[7,3,1,4,2,6,5]=>[1,1,2,2,1]
[7,3,1,4,5,2,6]=>[1,1,3,2]
[7,3,1,4,5,6,2]=>[1,1,4,1]
[7,3,1,4,6,2,5]=>[1,1,3,2]
[7,3,1,4,6,5,2]=>[1,1,3,1,1]
[7,3,1,5,2,4,6]=>[1,1,2,3]
[7,3,1,5,2,6,4]=>[1,1,2,2,1]
[7,3,1,5,4,2,6]=>[1,1,2,1,2]
[7,3,1,5,4,6,2]=>[1,1,2,2,1]
[7,3,1,5,6,2,4]=>[1,1,3,2]
[7,3,1,5,6,4,2]=>[1,1,3,1,1]
[7,3,1,6,2,4,5]=>[1,1,2,3]
[7,3,1,6,2,5,4]=>[1,1,2,2,1]
[7,3,1,6,4,2,5]=>[1,1,2,1,2]
[7,3,1,6,4,5,2]=>[1,1,2,2,1]
[7,3,1,6,5,2,4]=>[1,1,2,1,2]
[7,3,1,6,5,4,2]=>[1,1,2,1,1,1]
[7,3,2,1,4,5,6]=>[1,1,1,4]
[7,3,2,1,4,6,5]=>[1,1,1,3,1]
[7,3,2,1,5,4,6]=>[1,1,1,2,2]
[7,3,2,1,5,6,4]=>[1,1,1,3,1]
[7,3,2,1,6,4,5]=>[1,1,1,2,2]
[7,3,2,1,6,5,4]=>[1,1,1,2,1,1]
[7,3,2,4,1,5,6]=>[1,1,2,3]
[7,3,2,4,1,6,5]=>[1,1,2,2,1]
[7,3,2,4,5,1,6]=>[1,1,3,2]
[7,3,2,4,5,6,1]=>[1,1,4,1]
[7,3,2,4,6,1,5]=>[1,1,3,2]
[7,3,2,4,6,5,1]=>[1,1,3,1,1]
[7,3,2,5,1,4,6]=>[1,1,2,3]
[7,3,2,5,1,6,4]=>[1,1,2,2,1]
[7,3,2,5,4,1,6]=>[1,1,2,1,2]
[7,3,2,5,4,6,1]=>[1,1,2,2,1]
[7,3,2,5,6,1,4]=>[1,1,3,2]
[7,3,2,5,6,4,1]=>[1,1,3,1,1]
[7,3,2,6,1,4,5]=>[1,1,2,3]
[7,3,2,6,1,5,4]=>[1,1,2,2,1]
[7,3,2,6,4,1,5]=>[1,1,2,1,2]
[7,3,2,6,4,5,1]=>[1,1,2,2,1]
[7,3,2,6,5,1,4]=>[1,1,2,1,2]
[7,3,2,6,5,4,1]=>[1,1,2,1,1,1]
[7,3,4,1,2,5,6]=>[1,2,4]
[7,3,4,1,2,6,5]=>[1,2,3,1]
[7,3,4,1,5,2,6]=>[1,2,2,2]
[7,3,4,1,5,6,2]=>[1,2,3,1]
[7,3,4,1,6,2,5]=>[1,2,2,2]
[7,3,4,1,6,5,2]=>[1,2,2,1,1]
[7,3,4,2,1,5,6]=>[1,2,1,3]
[7,3,4,2,1,6,5]=>[1,2,1,2,1]
[7,3,4,2,5,1,6]=>[1,2,2,2]
[7,3,4,2,5,6,1]=>[1,2,3,1]
[7,3,4,2,6,1,5]=>[1,2,2,2]
[7,3,4,2,6,5,1]=>[1,2,2,1,1]
[7,3,4,5,1,2,6]=>[1,3,3]
[7,3,4,5,1,6,2]=>[1,3,2,1]
[7,3,4,5,2,1,6]=>[1,3,1,2]
[7,3,4,5,2,6,1]=>[1,3,2,1]
[7,3,4,5,6,1,2]=>[1,4,2]
[7,3,4,5,6,2,1]=>[1,4,1,1]
[7,3,4,6,1,2,5]=>[1,3,3]
[7,3,4,6,1,5,2]=>[1,3,2,1]
[7,3,4,6,2,1,5]=>[1,3,1,2]
[7,3,4,6,2,5,1]=>[1,3,2,1]
[7,3,4,6,5,1,2]=>[1,3,1,2]
[7,3,4,6,5,2,1]=>[1,3,1,1,1]
[7,3,5,1,2,4,6]=>[1,2,4]
[7,3,5,1,2,6,4]=>[1,2,3,1]
[7,3,5,1,4,2,6]=>[1,2,2,2]
[7,3,5,1,4,6,2]=>[1,2,3,1]
[7,3,5,1,6,2,4]=>[1,2,2,2]
[7,3,5,1,6,4,2]=>[1,2,2,1,1]
[7,3,5,2,1,4,6]=>[1,2,1,3]
[7,3,5,2,1,6,4]=>[1,2,1,2,1]
[7,3,5,2,4,1,6]=>[1,2,2,2]
[7,3,5,2,4,6,1]=>[1,2,3,1]
[7,3,5,2,6,1,4]=>[1,2,2,2]
[7,3,5,2,6,4,1]=>[1,2,2,1,1]
[7,3,5,4,1,2,6]=>[1,2,1,3]
[7,3,5,4,1,6,2]=>[1,2,1,2,1]
[7,3,5,4,2,1,6]=>[1,2,1,1,2]
[7,3,5,4,2,6,1]=>[1,2,1,2,1]
[7,3,5,4,6,1,2]=>[1,2,2,2]
[7,3,5,4,6,2,1]=>[1,2,2,1,1]
[7,3,5,6,1,2,4]=>[1,3,3]
[7,3,5,6,1,4,2]=>[1,3,2,1]
[7,3,5,6,2,1,4]=>[1,3,1,2]
[7,3,5,6,2,4,1]=>[1,3,2,1]
[7,3,5,6,4,1,2]=>[1,3,1,2]
[7,3,5,6,4,2,1]=>[1,3,1,1,1]
[7,3,6,1,2,4,5]=>[1,2,4]
[7,3,6,1,2,5,4]=>[1,2,3,1]
[7,3,6,1,4,2,5]=>[1,2,2,2]
[7,3,6,1,4,5,2]=>[1,2,3,1]
[7,3,6,1,5,2,4]=>[1,2,2,2]
[7,3,6,1,5,4,2]=>[1,2,2,1,1]
[7,3,6,2,1,4,5]=>[1,2,1,3]
[7,3,6,2,1,5,4]=>[1,2,1,2,1]
[7,3,6,2,4,1,5]=>[1,2,2,2]
[7,3,6,2,4,5,1]=>[1,2,3,1]
[7,3,6,2,5,1,4]=>[1,2,2,2]
[7,3,6,2,5,4,1]=>[1,2,2,1,1]
[7,3,6,4,1,2,5]=>[1,2,1,3]
[7,3,6,4,1,5,2]=>[1,2,1,2,1]
[7,3,6,4,2,1,5]=>[1,2,1,1,2]
[7,3,6,4,2,5,1]=>[1,2,1,2,1]
[7,3,6,4,5,1,2]=>[1,2,2,2]
[7,3,6,4,5,2,1]=>[1,2,2,1,1]
[7,3,6,5,1,2,4]=>[1,2,1,3]
[7,3,6,5,1,4,2]=>[1,2,1,2,1]
[7,3,6,5,2,1,4]=>[1,2,1,1,2]
[7,3,6,5,2,4,1]=>[1,2,1,2,1]
[7,3,6,5,4,1,2]=>[1,2,1,1,2]
[7,3,6,5,4,2,1]=>[1,2,1,1,1,1]
[7,4,1,2,3,5,6]=>[1,1,5]
[7,4,1,2,3,6,5]=>[1,1,4,1]
[7,4,1,2,5,3,6]=>[1,1,3,2]
[7,4,1,2,5,6,3]=>[1,1,4,1]
[7,4,1,2,6,3,5]=>[1,1,3,2]
[7,4,1,2,6,5,3]=>[1,1,3,1,1]
[7,4,1,3,2,5,6]=>[1,1,2,3]
[7,4,1,3,2,6,5]=>[1,1,2,2,1]
[7,4,1,3,5,2,6]=>[1,1,3,2]
[7,4,1,3,5,6,2]=>[1,1,4,1]
[7,4,1,3,6,2,5]=>[1,1,3,2]
[7,4,1,3,6,5,2]=>[1,1,3,1,1]
[7,4,1,5,2,3,6]=>[1,1,2,3]
[7,4,1,5,2,6,3]=>[1,1,2,2,1]
[7,4,1,5,3,2,6]=>[1,1,2,1,2]
[7,4,1,5,3,6,2]=>[1,1,2,2,1]
[7,4,1,5,6,2,3]=>[1,1,3,2]
[7,4,1,5,6,3,2]=>[1,1,3,1,1]
[7,4,1,6,2,3,5]=>[1,1,2,3]
[7,4,1,6,2,5,3]=>[1,1,2,2,1]
[7,4,1,6,3,2,5]=>[1,1,2,1,2]
[7,4,1,6,3,5,2]=>[1,1,2,2,1]
[7,4,1,6,5,2,3]=>[1,1,2,1,2]
[7,4,1,6,5,3,2]=>[1,1,2,1,1,1]
[7,4,2,1,3,5,6]=>[1,1,1,4]
[7,4,2,1,3,6,5]=>[1,1,1,3,1]
[7,4,2,1,5,3,6]=>[1,1,1,2,2]
[7,4,2,1,5,6,3]=>[1,1,1,3,1]
[7,4,2,1,6,3,5]=>[1,1,1,2,2]
[7,4,2,1,6,5,3]=>[1,1,1,2,1,1]
[7,4,2,3,1,5,6]=>[1,1,2,3]
[7,4,2,3,1,6,5]=>[1,1,2,2,1]
[7,4,2,3,5,1,6]=>[1,1,3,2]
[7,4,2,3,5,6,1]=>[1,1,4,1]
[7,4,2,3,6,1,5]=>[1,1,3,2]
[7,4,2,3,6,5,1]=>[1,1,3,1,1]
[7,4,2,5,1,3,6]=>[1,1,2,3]
[7,4,2,5,1,6,3]=>[1,1,2,2,1]
[7,4,2,5,3,1,6]=>[1,1,2,1,2]
[7,4,2,5,3,6,1]=>[1,1,2,2,1]
[7,4,2,5,6,1,3]=>[1,1,3,2]
[7,4,2,5,6,3,1]=>[1,1,3,1,1]
[7,4,2,6,1,3,5]=>[1,1,2,3]
[7,4,2,6,1,5,3]=>[1,1,2,2,1]
[7,4,2,6,3,1,5]=>[1,1,2,1,2]
[7,4,2,6,3,5,1]=>[1,1,2,2,1]
[7,4,2,6,5,1,3]=>[1,1,2,1,2]
[7,4,2,6,5,3,1]=>[1,1,2,1,1,1]
[7,4,3,1,2,5,6]=>[1,1,1,4]
[7,4,3,1,2,6,5]=>[1,1,1,3,1]
[7,4,3,1,5,2,6]=>[1,1,1,2,2]
[7,4,3,1,5,6,2]=>[1,1,1,3,1]
[7,4,3,1,6,2,5]=>[1,1,1,2,2]
[7,4,3,1,6,5,2]=>[1,1,1,2,1,1]
[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[7,4,3,2,1,6,5]=>[1,1,1,1,2,1]
[7,4,3,2,5,1,6]=>[1,1,1,2,2]
[7,4,3,2,5,6,1]=>[1,1,1,3,1]
[7,4,3,2,6,1,5]=>[1,1,1,2,2]
[7,4,3,2,6,5,1]=>[1,1,1,2,1,1]
[7,4,3,5,1,2,6]=>[1,1,2,3]
[7,4,3,5,1,6,2]=>[1,1,2,2,1]
[7,4,3,5,2,1,6]=>[1,1,2,1,2]
[7,4,3,5,2,6,1]=>[1,1,2,2,1]
[7,4,3,5,6,1,2]=>[1,1,3,2]
[7,4,3,5,6,2,1]=>[1,1,3,1,1]
[7,4,3,6,1,2,5]=>[1,1,2,3]
[7,4,3,6,1,5,2]=>[1,1,2,2,1]
[7,4,3,6,2,1,5]=>[1,1,2,1,2]
[7,4,3,6,2,5,1]=>[1,1,2,2,1]
[7,4,3,6,5,1,2]=>[1,1,2,1,2]
[7,4,3,6,5,2,1]=>[1,1,2,1,1,1]
[7,4,5,1,2,3,6]=>[1,2,4]
[7,4,5,1,2,6,3]=>[1,2,3,1]
[7,4,5,1,3,2,6]=>[1,2,2,2]
[7,4,5,1,3,6,2]=>[1,2,3,1]
[7,4,5,1,6,2,3]=>[1,2,2,2]
[7,4,5,1,6,3,2]=>[1,2,2,1,1]
[7,4,5,2,1,3,6]=>[1,2,1,3]
[7,4,5,2,1,6,3]=>[1,2,1,2,1]
[7,4,5,2,3,1,6]=>[1,2,2,2]
[7,4,5,2,3,6,1]=>[1,2,3,1]
[7,4,5,2,6,1,3]=>[1,2,2,2]
[7,4,5,2,6,3,1]=>[1,2,2,1,1]
[7,4,5,3,1,2,6]=>[1,2,1,3]
[7,4,5,3,1,6,2]=>[1,2,1,2,1]
[7,4,5,3,2,1,6]=>[1,2,1,1,2]
[7,4,5,3,2,6,1]=>[1,2,1,2,1]
[7,4,5,3,6,1,2]=>[1,2,2,2]
[7,4,5,3,6,2,1]=>[1,2,2,1,1]
[7,4,5,6,1,2,3]=>[1,3,3]
[7,4,5,6,1,3,2]=>[1,3,2,1]
[7,4,5,6,2,1,3]=>[1,3,1,2]
[7,4,5,6,2,3,1]=>[1,3,2,1]
[7,4,5,6,3,1,2]=>[1,3,1,2]
[7,4,5,6,3,2,1]=>[1,3,1,1,1]
[7,4,6,1,2,3,5]=>[1,2,4]
[7,4,6,1,2,5,3]=>[1,2,3,1]
[7,4,6,1,3,2,5]=>[1,2,2,2]
[7,4,6,1,3,5,2]=>[1,2,3,1]
[7,4,6,1,5,2,3]=>[1,2,2,2]
[7,4,6,1,5,3,2]=>[1,2,2,1,1]
[7,4,6,2,1,3,5]=>[1,2,1,3]
[7,4,6,2,1,5,3]=>[1,2,1,2,1]
[7,4,6,2,3,1,5]=>[1,2,2,2]
[7,4,6,2,3,5,1]=>[1,2,3,1]
[7,4,6,2,5,1,3]=>[1,2,2,2]
[7,4,6,2,5,3,1]=>[1,2,2,1,1]
[7,4,6,3,1,2,5]=>[1,2,1,3]
[7,4,6,3,1,5,2]=>[1,2,1,2,1]
[7,4,6,3,2,1,5]=>[1,2,1,1,2]
[7,4,6,3,2,5,1]=>[1,2,1,2,1]
[7,4,6,3,5,1,2]=>[1,2,2,2]
[7,4,6,3,5,2,1]=>[1,2,2,1,1]
[7,4,6,5,1,2,3]=>[1,2,1,3]
[7,4,6,5,1,3,2]=>[1,2,1,2,1]
[7,4,6,5,2,1,3]=>[1,2,1,1,2]
[7,4,6,5,2,3,1]=>[1,2,1,2,1]
[7,4,6,5,3,1,2]=>[1,2,1,1,2]
[7,4,6,5,3,2,1]=>[1,2,1,1,1,1]
[7,5,1,2,3,4,6]=>[1,1,5]
[7,5,1,2,3,6,4]=>[1,1,4,1]
[7,5,1,2,4,3,6]=>[1,1,3,2]
[7,5,1,2,4,6,3]=>[1,1,4,1]
[7,5,1,2,6,3,4]=>[1,1,3,2]
[7,5,1,2,6,4,3]=>[1,1,3,1,1]
[7,5,1,3,2,4,6]=>[1,1,2,3]
[7,5,1,3,2,6,4]=>[1,1,2,2,1]
[7,5,1,3,4,2,6]=>[1,1,3,2]
[7,5,1,3,4,6,2]=>[1,1,4,1]
[7,5,1,3,6,2,4]=>[1,1,3,2]
[7,5,1,3,6,4,2]=>[1,1,3,1,1]
[7,5,1,4,2,3,6]=>[1,1,2,3]
[7,5,1,4,2,6,3]=>[1,1,2,2,1]
[7,5,1,4,3,2,6]=>[1,1,2,1,2]
[7,5,1,4,3,6,2]=>[1,1,2,2,1]
[7,5,1,4,6,2,3]=>[1,1,3,2]
[7,5,1,4,6,3,2]=>[1,1,3,1,1]
[7,5,1,6,2,3,4]=>[1,1,2,3]
[7,5,1,6,2,4,3]=>[1,1,2,2,1]
[7,5,1,6,3,2,4]=>[1,1,2,1,2]
[7,5,1,6,3,4,2]=>[1,1,2,2,1]
[7,5,1,6,4,2,3]=>[1,1,2,1,2]
[7,5,1,6,4,3,2]=>[1,1,2,1,1,1]
[7,5,2,1,3,4,6]=>[1,1,1,4]
[7,5,2,1,3,6,4]=>[1,1,1,3,1]
[7,5,2,1,4,3,6]=>[1,1,1,2,2]
[7,5,2,1,4,6,3]=>[1,1,1,3,1]
[7,5,2,1,6,3,4]=>[1,1,1,2,2]
[7,5,2,1,6,4,3]=>[1,1,1,2,1,1]
[7,5,2,3,1,4,6]=>[1,1,2,3]
[7,5,2,3,1,6,4]=>[1,1,2,2,1]
[7,5,2,3,4,1,6]=>[1,1,3,2]
[7,5,2,3,4,6,1]=>[1,1,4,1]
[7,5,2,3,6,1,4]=>[1,1,3,2]
[7,5,2,3,6,4,1]=>[1,1,3,1,1]
[7,5,2,4,1,3,6]=>[1,1,2,3]
[7,5,2,4,1,6,3]=>[1,1,2,2,1]
[7,5,2,4,3,1,6]=>[1,1,2,1,2]
[7,5,2,4,3,6,1]=>[1,1,2,2,1]
[7,5,2,4,6,1,3]=>[1,1,3,2]
[7,5,2,4,6,3,1]=>[1,1,3,1,1]
[7,5,2,6,1,3,4]=>[1,1,2,3]
[7,5,2,6,1,4,3]=>[1,1,2,2,1]
[7,5,2,6,3,1,4]=>[1,1,2,1,2]
[7,5,2,6,3,4,1]=>[1,1,2,2,1]
[7,5,2,6,4,1,3]=>[1,1,2,1,2]
[7,5,2,6,4,3,1]=>[1,1,2,1,1,1]
[7,5,3,1,2,4,6]=>[1,1,1,4]
[7,5,3,1,2,6,4]=>[1,1,1,3,1]
[7,5,3,1,4,2,6]=>[1,1,1,2,2]
[7,5,3,1,4,6,2]=>[1,1,1,3,1]
[7,5,3,1,6,2,4]=>[1,1,1,2,2]
[7,5,3,1,6,4,2]=>[1,1,1,2,1,1]
[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[7,5,3,2,1,6,4]=>[1,1,1,1,2,1]
[7,5,3,2,4,1,6]=>[1,1,1,2,2]
[7,5,3,2,4,6,1]=>[1,1,1,3,1]
[7,5,3,2,6,1,4]=>[1,1,1,2,2]
[7,5,3,2,6,4,1]=>[1,1,1,2,1,1]
[7,5,3,4,1,2,6]=>[1,1,2,3]
[7,5,3,4,1,6,2]=>[1,1,2,2,1]
[7,5,3,4,2,1,6]=>[1,1,2,1,2]
[7,5,3,4,2,6,1]=>[1,1,2,2,1]
[7,5,3,4,6,1,2]=>[1,1,3,2]
[7,5,3,4,6,2,1]=>[1,1,3,1,1]
[7,5,3,6,1,2,4]=>[1,1,2,3]
[7,5,3,6,1,4,2]=>[1,1,2,2,1]
[7,5,3,6,2,1,4]=>[1,1,2,1,2]
[7,5,3,6,2,4,1]=>[1,1,2,2,1]
[7,5,3,6,4,1,2]=>[1,1,2,1,2]
[7,5,3,6,4,2,1]=>[1,1,2,1,1,1]
[7,5,4,1,2,3,6]=>[1,1,1,4]
[7,5,4,1,2,6,3]=>[1,1,1,3,1]
[7,5,4,1,3,2,6]=>[1,1,1,2,2]
[7,5,4,1,3,6,2]=>[1,1,1,3,1]
[7,5,4,1,6,2,3]=>[1,1,1,2,2]
[7,5,4,1,6,3,2]=>[1,1,1,2,1,1]
[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[7,5,4,2,1,6,3]=>[1,1,1,1,2,1]
[7,5,4,2,3,1,6]=>[1,1,1,2,2]
[7,5,4,2,3,6,1]=>[1,1,1,3,1]
[7,5,4,2,6,1,3]=>[1,1,1,2,2]
[7,5,4,2,6,3,1]=>[1,1,1,2,1,1]
[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[7,5,4,3,1,6,2]=>[1,1,1,1,2,1]
[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]
[7,5,4,3,6,1,2]=>[1,1,1,2,2]
[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]
[7,5,4,6,1,2,3]=>[1,1,2,3]
[7,5,4,6,1,3,2]=>[1,1,2,2,1]
[7,5,4,6,2,1,3]=>[1,1,2,1,2]
[7,5,4,6,2,3,1]=>[1,1,2,2,1]
[7,5,4,6,3,1,2]=>[1,1,2,1,2]
[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]
[7,5,6,1,2,3,4]=>[1,2,4]
[7,5,6,1,2,4,3]=>[1,2,3,1]
[7,5,6,1,3,2,4]=>[1,2,2,2]
[7,5,6,1,3,4,2]=>[1,2,3,1]
[7,5,6,1,4,2,3]=>[1,2,2,2]
[7,5,6,1,4,3,2]=>[1,2,2,1,1]
[7,5,6,2,1,3,4]=>[1,2,1,3]
[7,5,6,2,1,4,3]=>[1,2,1,2,1]
[7,5,6,2,3,1,4]=>[1,2,2,2]
[7,5,6,2,3,4,1]=>[1,2,3,1]
[7,5,6,2,4,1,3]=>[1,2,2,2]
[7,5,6,2,4,3,1]=>[1,2,2,1,1]
[7,5,6,3,1,2,4]=>[1,2,1,3]
[7,5,6,3,1,4,2]=>[1,2,1,2,1]
[7,5,6,3,2,1,4]=>[1,2,1,1,2]
[7,5,6,3,2,4,1]=>[1,2,1,2,1]
[7,5,6,3,4,1,2]=>[1,2,2,2]
[7,5,6,3,4,2,1]=>[1,2,2,1,1]
[7,5,6,4,1,2,3]=>[1,2,1,3]
[7,5,6,4,1,3,2]=>[1,2,1,2,1]
[7,5,6,4,2,1,3]=>[1,2,1,1,2]
[7,5,6,4,2,3,1]=>[1,2,1,2,1]
[7,5,6,4,3,1,2]=>[1,2,1,1,2]
[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]
[7,6,1,2,3,4,5]=>[1,1,5]
[7,6,1,2,3,5,4]=>[1,1,4,1]
[7,6,1,2,4,3,5]=>[1,1,3,2]
[7,6,1,2,4,5,3]=>[1,1,4,1]
[7,6,1,2,5,3,4]=>[1,1,3,2]
[7,6,1,2,5,4,3]=>[1,1,3,1,1]
[7,6,1,3,2,4,5]=>[1,1,2,3]
[7,6,1,3,2,5,4]=>[1,1,2,2,1]
[7,6,1,3,4,2,5]=>[1,1,3,2]
[7,6,1,3,4,5,2]=>[1,1,4,1]
[7,6,1,3,5,2,4]=>[1,1,3,2]
[7,6,1,3,5,4,2]=>[1,1,3,1,1]
[7,6,1,4,2,3,5]=>[1,1,2,3]
[7,6,1,4,2,5,3]=>[1,1,2,2,1]
[7,6,1,4,3,2,5]=>[1,1,2,1,2]
[7,6,1,4,3,5,2]=>[1,1,2,2,1]
[7,6,1,4,5,2,3]=>[1,1,3,2]
[7,6,1,4,5,3,2]=>[1,1,3,1,1]
[7,6,1,5,2,3,4]=>[1,1,2,3]
[7,6,1,5,2,4,3]=>[1,1,2,2,1]
[7,6,1,5,3,2,4]=>[1,1,2,1,2]
[7,6,1,5,3,4,2]=>[1,1,2,2,1]
[7,6,1,5,4,2,3]=>[1,1,2,1,2]
[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]
[7,6,2,1,3,4,5]=>[1,1,1,4]
[7,6,2,1,3,5,4]=>[1,1,1,3,1]
[7,6,2,1,4,3,5]=>[1,1,1,2,2]
[7,6,2,1,4,5,3]=>[1,1,1,3,1]
[7,6,2,1,5,3,4]=>[1,1,1,2,2]
[7,6,2,1,5,4,3]=>[1,1,1,2,1,1]
[7,6,2,3,1,4,5]=>[1,1,2,3]
[7,6,2,3,1,5,4]=>[1,1,2,2,1]
[7,6,2,3,4,1,5]=>[1,1,3,2]
[7,6,2,3,4,5,1]=>[1,1,4,1]
[7,6,2,3,5,1,4]=>[1,1,3,2]
[7,6,2,3,5,4,1]=>[1,1,3,1,1]
[7,6,2,4,1,3,5]=>[1,1,2,3]
[7,6,2,4,1,5,3]=>[1,1,2,2,1]
[7,6,2,4,3,1,5]=>[1,1,2,1,2]
[7,6,2,4,3,5,1]=>[1,1,2,2,1]
[7,6,2,4,5,1,3]=>[1,1,3,2]
[7,6,2,4,5,3,1]=>[1,1,3,1,1]
[7,6,2,5,1,3,4]=>[1,1,2,3]
[7,6,2,5,1,4,3]=>[1,1,2,2,1]
[7,6,2,5,3,1,4]=>[1,1,2,1,2]
[7,6,2,5,3,4,1]=>[1,1,2,2,1]
[7,6,2,5,4,1,3]=>[1,1,2,1,2]
[7,6,2,5,4,3,1]=>[1,1,2,1,1,1]
[7,6,3,1,2,4,5]=>[1,1,1,4]
[7,6,3,1,2,5,4]=>[1,1,1,3,1]
[7,6,3,1,4,2,5]=>[1,1,1,2,2]
[7,6,3,1,4,5,2]=>[1,1,1,3,1]
[7,6,3,1,5,2,4]=>[1,1,1,2,2]
[7,6,3,1,5,4,2]=>[1,1,1,2,1,1]
[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[7,6,3,2,1,5,4]=>[1,1,1,1,2,1]
[7,6,3,2,4,1,5]=>[1,1,1,2,2]
[7,6,3,2,4,5,1]=>[1,1,1,3,1]
[7,6,3,2,5,1,4]=>[1,1,1,2,2]
[7,6,3,2,5,4,1]=>[1,1,1,2,1,1]
[7,6,3,4,1,2,5]=>[1,1,2,3]
[7,6,3,4,1,5,2]=>[1,1,2,2,1]
[7,6,3,4,2,1,5]=>[1,1,2,1,2]
[7,6,3,4,2,5,1]=>[1,1,2,2,1]
[7,6,3,4,5,1,2]=>[1,1,3,2]
[7,6,3,4,5,2,1]=>[1,1,3,1,1]
[7,6,3,5,1,2,4]=>[1,1,2,3]
[7,6,3,5,1,4,2]=>[1,1,2,2,1]
[7,6,3,5,2,1,4]=>[1,1,2,1,2]
[7,6,3,5,2,4,1]=>[1,1,2,2,1]
[7,6,3,5,4,1,2]=>[1,1,2,1,2]
[7,6,3,5,4,2,1]=>[1,1,2,1,1,1]
[7,6,4,1,2,3,5]=>[1,1,1,4]
[7,6,4,1,2,5,3]=>[1,1,1,3,1]
[7,6,4,1,3,2,5]=>[1,1,1,2,2]
[7,6,4,1,3,5,2]=>[1,1,1,3,1]
[7,6,4,1,5,2,3]=>[1,1,1,2,2]
[7,6,4,1,5,3,2]=>[1,1,1,2,1,1]
[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[7,6,4,2,1,5,3]=>[1,1,1,1,2,1]
[7,6,4,2,3,1,5]=>[1,1,1,2,2]
[7,6,4,2,3,5,1]=>[1,1,1,3,1]
[7,6,4,2,5,1,3]=>[1,1,1,2,2]
[7,6,4,2,5,3,1]=>[1,1,1,2,1,1]
[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[7,6,4,3,1,5,2]=>[1,1,1,1,2,1]
[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]
[7,6,4,3,5,1,2]=>[1,1,1,2,2]
[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]
[7,6,4,5,1,2,3]=>[1,1,2,3]
[7,6,4,5,1,3,2]=>[1,1,2,2,1]
[7,6,4,5,2,1,3]=>[1,1,2,1,2]
[7,6,4,5,2,3,1]=>[1,1,2,2,1]
[7,6,4,5,3,1,2]=>[1,1,2,1,2]
[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]
[7,6,5,1,2,3,4]=>[1,1,1,4]
[7,6,5,1,2,4,3]=>[1,1,1,3,1]
[7,6,5,1,3,2,4]=>[1,1,1,2,2]
[7,6,5,1,3,4,2]=>[1,1,1,3,1]
[7,6,5,1,4,2,3]=>[1,1,1,2,2]
[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]
[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[7,6,5,2,1,4,3]=>[1,1,1,1,2,1]
[7,6,5,2,3,1,4]=>[1,1,1,2,2]
[7,6,5,2,3,4,1]=>[1,1,1,3,1]
[7,6,5,2,4,1,3]=>[1,1,1,2,2]
[7,6,5,2,4,3,1]=>[1,1,1,2,1,1]
[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[7,6,5,3,1,4,2]=>[1,1,1,1,2,1]
[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]
[7,6,5,3,4,1,2]=>[1,1,1,2,2]
[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]
[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]
[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]
[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]
[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]
[8,6,5,7,4,3,2,1]=>[1,1,2,1,1,1,1]
[8,5,6,7,4,3,2,1]=>[1,3,1,1,1,1]
[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]
[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]
[7,5,6,8,4,3,2,1]=>[1,3,1,1,1,1]
[6,5,7,8,4,3,2,1]=>[1,3,1,1,1,1]
[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]
[7,8,6,4,5,3,2,1]=>[2,1,2,1,1,1]
[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]
[7,6,8,4,5,3,2,1]=>[1,2,2,1,1,1]
[6,7,8,4,5,3,2,1]=>[3,2,1,1,1]
[8,7,5,4,6,3,2,1]=>[1,1,1,2,1,1,1]
[7,8,5,4,6,3,2,1]=>[2,1,2,1,1,1]
[8,7,4,5,6,3,2,1]=>[1,1,3,1,1,1]
[7,8,4,5,6,3,2,1]=>[2,3,1,1,1]
[8,6,5,4,7,3,2,1]=>[1,1,1,2,1,1,1]
[8,5,6,4,7,3,2,1]=>[1,2,2,1,1,1]
[8,6,4,5,7,3,2,1]=>[1,1,3,1,1,1]
[8,5,4,6,7,3,2,1]=>[1,1,3,1,1,1]
[8,4,5,6,7,3,2,1]=>[1,4,1,1,1]
[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]
[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]
[7,5,6,4,8,3,2,1]=>[1,2,2,1,1,1]
[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]
[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]
[7,6,4,5,8,3,2,1]=>[1,1,3,1,1,1]
[6,7,4,5,8,3,2,1]=>[2,3,1,1,1]
[7,5,4,6,8,3,2,1]=>[1,1,3,1,1,1]
[7,4,5,6,8,3,2,1]=>[1,4,1,1,1]
[6,5,4,7,8,3,2,1]=>[1,1,3,1,1,1]
[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]
[6,4,5,7,8,3,2,1]=>[1,4,1,1,1]
[5,4,6,7,8,3,2,1]=>[1,4,1,1,1]
[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]
[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]
[8,6,7,5,3,4,2,1]=>[1,2,1,2,1,1]
[7,6,8,5,3,4,2,1]=>[1,2,1,2,1,1]
[6,7,8,5,3,4,2,1]=>[3,1,2,1,1]
[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]
[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]
[8,6,5,7,3,4,2,1]=>[1,1,2,2,1,1]
[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]
[7,6,5,8,3,4,2,1]=>[1,1,2,2,1,1]
[6,7,5,8,3,4,2,1]=>[2,2,2,1,1]
[6,5,7,8,3,4,2,1]=>[1,3,2,1,1]
[5,6,7,8,3,4,2,1]=>[4,2,1,1]
[8,7,6,4,3,5,2,1]=>[1,1,1,1,2,1,1]
[7,8,6,4,3,5,2,1]=>[2,1,1,2,1,1]
[8,6,7,4,3,5,2,1]=>[1,2,1,2,1,1]
[7,6,8,4,3,5,2,1]=>[1,2,1,2,1,1]
[6,7,8,4,3,5,2,1]=>[3,1,2,1,1]
[8,7,6,3,4,5,2,1]=>[1,1,1,3,1,1]
[7,8,6,3,4,5,2,1]=>[2,1,3,1,1]
[8,6,7,3,4,5,2,1]=>[1,2,3,1,1]
[7,6,8,3,4,5,2,1]=>[1,2,3,1,1]
[6,7,8,3,4,5,2,1]=>[3,3,1,1]
[8,7,5,4,3,6,2,1]=>[1,1,1,1,2,1,1]
[7,8,5,4,3,6,2,1]=>[2,1,1,2,1,1]
[8,7,4,5,3,6,2,1]=>[1,1,2,2,1,1]
[8,7,5,3,4,6,2,1]=>[1,1,1,3,1,1]
[7,8,5,3,4,6,2,1]=>[2,1,3,1,1]
[8,7,4,3,5,6,2,1]=>[1,1,1,3,1,1]
[7,8,4,3,5,6,2,1]=>[2,1,3,1,1]
[8,7,3,4,5,6,2,1]=>[1,1,4,1,1]
[7,8,3,4,5,6,2,1]=>[2,4,1,1]
[8,6,5,4,3,7,2,1]=>[1,1,1,1,2,1,1]
[8,5,6,4,3,7,2,1]=>[1,2,1,2,1,1]
[8,6,4,5,3,7,2,1]=>[1,1,2,2,1,1]
[8,5,4,6,3,7,2,1]=>[1,1,2,2,1,1]
[8,5,6,3,4,7,2,1]=>[1,2,3,1,1]
[8,6,4,3,5,7,2,1]=>[1,1,1,3,1,1]
[8,6,3,4,5,7,2,1]=>[1,1,4,1,1]
[8,5,4,3,6,7,2,1]=>[1,1,1,3,1,1]
[8,5,3,4,6,7,2,1]=>[1,1,4,1,1]
[8,4,3,5,6,7,2,1]=>[1,1,4,1,1]
[8,3,4,5,6,7,2,1]=>[1,5,1,1]
[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]
[7,5,6,4,3,8,2,1]=>[1,2,1,2,1,1]
[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[5,6,7,4,3,8,2,1]=>[3,1,2,1,1]
[7,6,4,5,3,8,2,1]=>[1,1,2,2,1,1]
[6,7,4,5,3,8,2,1]=>[2,2,2,1,1]
[7,5,4,6,3,8,2,1]=>[1,1,2,2,1,1]
[7,4,5,6,3,8,2,1]=>[1,3,2,1,1]
[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]
[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]
[6,4,5,7,3,8,2,1]=>[1,3,2,1,1]
[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]
[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[7,6,5,3,4,8,2,1]=>[1,1,1,3,1,1]
[6,7,5,3,4,8,2,1]=>[2,1,3,1,1]
[6,5,7,3,4,8,2,1]=>[1,2,3,1,1]
[5,6,7,3,4,8,2,1]=>[3,3,1,1]
[7,6,4,3,5,8,2,1]=>[1,1,1,3,1,1]
[7,6,3,4,5,8,2,1]=>[1,1,4,1,1]
[7,5,4,3,6,8,2,1]=>[1,1,1,3,1,1]
[7,5,3,4,6,8,2,1]=>[1,1,4,1,1]
[7,3,4,5,6,8,2,1]=>[1,5,1,1]
[6,5,4,3,7,8,2,1]=>[1,1,1,3,1,1]
[5,6,4,3,7,8,2,1]=>[2,1,3,1,1]
[5,4,6,3,7,8,2,1]=>[1,2,3,1,1]
[4,5,6,3,7,8,2,1]=>[3,3,1,1]
[6,5,3,4,7,8,2,1]=>[1,1,4,1,1]
[6,4,3,5,7,8,2,1]=>[1,1,4,1,1]
[6,3,4,5,7,8,2,1]=>[1,5,1,1]
[5,4,3,6,7,8,2,1]=>[1,1,4,1,1]
[4,5,3,6,7,8,2,1]=>[2,4,1,1]
[5,3,4,6,7,8,2,1]=>[1,5,1,1]
[4,3,5,6,7,8,2,1]=>[1,5,1,1]
[3,4,5,6,7,8,2,1]=>[6,1,1]
[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]
[7,8,6,5,4,2,3,1]=>[2,1,1,1,2,1]
[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]
[7,6,8,5,4,2,3,1]=>[1,2,1,1,2,1]
[8,7,5,6,4,2,3,1]=>[1,1,2,1,2,1]
[8,6,5,7,4,2,3,1]=>[1,1,2,1,2,1]
[8,5,6,7,4,2,3,1]=>[1,3,1,2,1]
[7,6,5,8,4,2,3,1]=>[1,1,2,1,2,1]
[6,7,5,8,4,2,3,1]=>[2,2,1,2,1]
[7,5,6,8,4,2,3,1]=>[1,3,1,2,1]
[6,5,7,8,4,2,3,1]=>[1,3,1,2,1]
[5,6,7,8,4,2,3,1]=>[4,1,2,1]
[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]
[7,8,6,4,5,2,3,1]=>[2,1,2,2,1]
[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]
[7,6,8,4,5,2,3,1]=>[1,2,2,2,1]
[6,7,8,4,5,2,3,1]=>[3,2,2,1]
[8,7,5,4,6,2,3,1]=>[1,1,1,2,2,1]
[8,7,4,5,6,2,3,1]=>[1,1,3,2,1]
[7,8,4,5,6,2,3,1]=>[2,3,2,1]
[8,6,5,4,7,2,3,1]=>[1,1,1,2,2,1]
[8,5,6,4,7,2,3,1]=>[1,2,2,2,1]
[8,6,4,5,7,2,3,1]=>[1,1,3,2,1]
[8,4,5,6,7,2,3,1]=>[1,4,2,1]
[7,6,5,4,8,2,3,1]=>[1,1,1,2,2,1]
[6,7,5,4,8,2,3,1]=>[2,1,2,2,1]
[7,5,6,4,8,2,3,1]=>[1,2,2,2,1]
[6,5,7,4,8,2,3,1]=>[1,2,2,2,1]
[5,6,7,4,8,2,3,1]=>[3,2,2,1]
[7,6,4,5,8,2,3,1]=>[1,1,3,2,1]
[6,7,4,5,8,2,3,1]=>[2,3,2,1]
[7,5,4,6,8,2,3,1]=>[1,1,3,2,1]
[7,4,5,6,8,2,3,1]=>[1,4,2,1]
[6,5,4,7,8,2,3,1]=>[1,1,3,2,1]
[5,6,4,7,8,2,3,1]=>[2,3,2,1]
[6,4,5,7,8,2,3,1]=>[1,4,2,1]
[5,4,6,7,8,2,3,1]=>[1,4,2,1]
[4,5,6,7,8,2,3,1]=>[5,2,1]
[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1]
[7,8,6,5,3,2,4,1]=>[2,1,1,1,2,1]
[8,6,7,5,3,2,4,1]=>[1,2,1,1,2,1]
[7,6,8,5,3,2,4,1]=>[1,2,1,1,2,1]
[6,7,8,5,3,2,4,1]=>[3,1,1,2,1]
[8,7,5,6,3,2,4,1]=>[1,1,2,1,2,1]
[7,8,5,6,3,2,4,1]=>[2,2,1,2,1]
[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]
[8,5,6,7,3,2,4,1]=>[1,3,1,2,1]
[7,6,5,8,3,2,4,1]=>[1,1,2,1,2,1]
[6,7,5,8,3,2,4,1]=>[2,2,1,2,1]
[7,5,6,8,3,2,4,1]=>[1,3,1,2,1]
[6,5,7,8,3,2,4,1]=>[1,3,1,2,1]
[5,6,7,8,3,2,4,1]=>[4,1,2,1]
[8,7,6,5,2,3,4,1]=>[1,1,1,1,3,1]
[8,6,7,5,2,3,4,1]=>[1,2,1,3,1]
[7,6,8,5,2,3,4,1]=>[1,2,1,3,1]
[6,7,8,5,2,3,4,1]=>[3,1,3,1]
[8,7,5,6,2,3,4,1]=>[1,1,2,3,1]
[7,8,5,6,2,3,4,1]=>[2,2,3,1]
[8,6,5,7,2,3,4,1]=>[1,1,2,3,1]
[8,5,6,7,2,3,4,1]=>[1,3,3,1]
[7,6,5,8,2,3,4,1]=>[1,1,2,3,1]
[6,7,5,8,2,3,4,1]=>[2,2,3,1]
[6,5,7,8,2,3,4,1]=>[1,3,3,1]
[5,6,7,8,2,3,4,1]=>[4,3,1]
[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,2,1]
[7,8,6,4,3,2,5,1]=>[2,1,1,1,2,1]
[8,6,7,4,3,2,5,1]=>[1,2,1,1,2,1]
[7,6,8,4,3,2,5,1]=>[1,2,1,1,2,1]
[6,7,8,4,3,2,5,1]=>[3,1,1,2,1]
[8,7,6,3,4,2,5,1]=>[1,1,1,2,2,1]
[7,8,6,3,4,2,5,1]=>[2,1,2,2,1]
[8,6,7,3,4,2,5,1]=>[1,2,2,2,1]
[7,6,8,3,4,2,5,1]=>[1,2,2,2,1]
[6,7,8,3,4,2,5,1]=>[3,2,2,1]
[8,7,6,4,2,3,5,1]=>[1,1,1,1,3,1]
[7,8,6,4,2,3,5,1]=>[2,1,1,3,1]
[8,6,7,4,2,3,5,1]=>[1,2,1,3,1]
[7,6,8,4,2,3,5,1]=>[1,2,1,3,1]
[6,7,8,4,2,3,5,1]=>[3,1,3,1]
[8,7,6,3,2,4,5,1]=>[1,1,1,1,3,1]
[7,8,6,3,2,4,5,1]=>[2,1,1,3,1]
[8,6,7,3,2,4,5,1]=>[1,2,1,3,1]
[6,7,8,3,2,4,5,1]=>[3,1,3,1]
[8,7,6,2,3,4,5,1]=>[1,1,1,4,1]
[7,8,6,2,3,4,5,1]=>[2,1,4,1]
[8,6,7,2,3,4,5,1]=>[1,2,4,1]
[7,6,8,2,3,4,5,1]=>[1,2,4,1]
[6,7,8,2,3,4,5,1]=>[3,4,1]
[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,2,1]
[7,8,5,4,3,2,6,1]=>[2,1,1,1,2,1]
[8,7,5,3,4,2,6,1]=>[1,1,1,2,2,1]
[7,8,5,3,4,2,6,1]=>[2,1,2,2,1]
[8,7,4,3,5,2,6,1]=>[1,1,1,2,2,1]
[7,8,4,3,5,2,6,1]=>[2,1,2,2,1]
[7,8,3,4,5,2,6,1]=>[2,3,2,1]
[8,7,5,4,2,3,6,1]=>[1,1,1,1,3,1]
[7,8,5,4,2,3,6,1]=>[2,1,1,3,1]
[7,8,4,5,2,3,6,1]=>[2,2,3,1]
[8,7,5,3,2,4,6,1]=>[1,1,1,1,3,1]
[7,8,5,2,3,4,6,1]=>[2,1,4,1]
[8,7,4,3,2,5,6,1]=>[1,1,1,1,3,1]
[7,8,4,3,2,5,6,1]=>[2,1,1,3,1]
[8,7,3,4,2,5,6,1]=>[1,1,2,3,1]
[7,8,3,4,2,5,6,1]=>[2,2,3,1]
[7,8,4,2,3,5,6,1]=>[2,1,4,1]
[7,8,3,2,4,5,6,1]=>[2,1,4,1]
[8,7,2,3,4,5,6,1]=>[1,1,5,1]
[7,8,2,3,4,5,6,1]=>[2,5,1]
[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,2,1]
[8,5,6,4,3,2,7,1]=>[1,2,1,1,2,1]
[8,6,4,5,3,2,7,1]=>[1,1,2,1,2,1]
[8,5,4,6,3,2,7,1]=>[1,1,2,1,2,1]
[8,6,5,3,4,2,7,1]=>[1,1,1,2,2,1]
[8,5,6,3,4,2,7,1]=>[1,2,2,2,1]
[8,6,4,3,5,2,7,1]=>[1,1,1,2,2,1]
[8,6,3,4,5,2,7,1]=>[1,1,3,2,1]
[8,5,4,3,6,2,7,1]=>[1,1,1,2,2,1]
[8,4,5,3,6,2,7,1]=>[1,2,2,2,1]
[8,5,3,4,6,2,7,1]=>[1,1,3,2,1]
[8,4,3,5,6,2,7,1]=>[1,1,3,2,1]
[8,3,4,5,6,2,7,1]=>[1,4,2,1]
[8,6,5,4,2,3,7,1]=>[1,1,1,1,3,1]
[8,5,6,4,2,3,7,1]=>[1,2,1,3,1]
[8,6,4,5,2,3,7,1]=>[1,1,2,3,1]
[8,5,4,6,2,3,7,1]=>[1,1,2,3,1]
[8,6,5,3,2,4,7,1]=>[1,1,1,1,3,1]
[8,6,4,3,2,5,7,1]=>[1,1,1,1,3,1]
[8,6,4,2,3,5,7,1]=>[1,1,1,4,1]
[8,6,2,3,4,5,7,1]=>[1,1,5,1]
[8,5,4,3,2,6,7,1]=>[1,1,1,1,3,1]
[8,4,5,3,2,6,7,1]=>[1,2,1,3,1]
[8,5,3,4,2,6,7,1]=>[1,1,2,3,1]
[8,4,3,5,2,6,7,1]=>[1,1,2,3,1]
[8,3,4,5,2,6,7,1]=>[1,3,3,1]
[8,5,4,2,3,6,7,1]=>[1,1,1,4,1]
[8,4,5,2,3,6,7,1]=>[1,2,4,1]
[8,5,2,3,4,6,7,1]=>[1,1,5,1]
[8,4,3,2,5,6,7,1]=>[1,1,1,4,1]
[8,3,4,2,5,6,7,1]=>[1,2,4,1]
[8,4,2,3,5,6,7,1]=>[1,1,5,1]
[8,3,2,4,5,6,7,1]=>[1,1,5,1]
[8,2,3,4,5,6,7,1]=>[1,6,1]
[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]
[6,7,5,4,3,2,8,1]=>[2,1,1,1,2,1]
[7,5,6,4,3,2,8,1]=>[1,2,1,1,2,1]
[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]
[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]
[7,6,4,5,3,2,8,1]=>[1,1,2,1,2,1]
[6,7,4,5,3,2,8,1]=>[2,2,1,2,1]
[7,5,4,6,3,2,8,1]=>[1,1,2,1,2,1]
[7,4,5,6,3,2,8,1]=>[1,3,1,2,1]
[6,5,4,7,3,2,8,1]=>[1,1,2,1,2,1]
[5,6,4,7,3,2,8,1]=>[2,2,1,2,1]
[6,4,5,7,3,2,8,1]=>[1,3,1,2,1]
[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[7,6,5,3,4,2,8,1]=>[1,1,1,2,2,1]
[7,5,6,3,4,2,8,1]=>[1,2,2,2,1]
[6,5,7,3,4,2,8,1]=>[1,2,2,2,1]
[5,6,7,3,4,2,8,1]=>[3,2,2,1]
[7,6,4,3,5,2,8,1]=>[1,1,1,2,2,1]
[6,7,4,3,5,2,8,1]=>[2,1,2,2,1]
[7,6,3,4,5,2,8,1]=>[1,1,3,2,1]
[7,5,4,3,6,2,8,1]=>[1,1,1,2,2,1]
[7,4,5,3,6,2,8,1]=>[1,2,2,2,1]
[7,5,3,4,6,2,8,1]=>[1,1,3,2,1]
[7,3,4,5,6,2,8,1]=>[1,4,2,1]
[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]
[5,6,4,3,7,2,8,1]=>[2,1,2,2,1]
[6,4,5,3,7,2,8,1]=>[1,2,2,2,1]
[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[6,5,3,4,7,2,8,1]=>[1,1,3,2,1]
[5,6,3,4,7,2,8,1]=>[2,3,2,1]
[6,4,3,5,7,2,8,1]=>[1,1,3,2,1]
[6,3,4,5,7,2,8,1]=>[1,4,2,1]
[5,4,3,6,7,2,8,1]=>[1,1,3,2,1]
[4,5,3,6,7,2,8,1]=>[2,3,2,1]
[5,3,4,6,7,2,8,1]=>[1,4,2,1]
[4,3,5,6,7,2,8,1]=>[1,4,2,1]
[3,4,5,6,7,2,8,1]=>[5,2,1]
[7,6,5,4,2,3,8,1]=>[1,1,1,1,3,1]
[6,7,5,4,2,3,8,1]=>[2,1,1,3,1]
[7,5,6,4,2,3,8,1]=>[1,2,1,3,1]
[6,5,7,4,2,3,8,1]=>[1,2,1,3,1]
[5,6,7,4,2,3,8,1]=>[3,1,3,1]
[7,6,4,5,2,3,8,1]=>[1,1,2,3,1]
[6,7,4,5,2,3,8,1]=>[2,2,3,1]
[7,5,4,6,2,3,8,1]=>[1,1,2,3,1]
[7,4,5,6,2,3,8,1]=>[1,3,3,1]
[6,5,4,7,2,3,8,1]=>[1,1,2,3,1]
[5,6,4,7,2,3,8,1]=>[2,2,3,1]
[6,4,5,7,2,3,8,1]=>[1,3,3,1]
[5,4,6,7,2,3,8,1]=>[1,3,3,1]
[4,5,6,7,2,3,8,1]=>[4,3,1]
[6,7,5,3,2,4,8,1]=>[2,1,1,3,1]
[7,5,6,3,2,4,8,1]=>[1,2,1,3,1]
[6,5,7,3,2,4,8,1]=>[1,2,1,3,1]
[7,6,5,2,3,4,8,1]=>[1,1,1,4,1]
[7,5,6,2,3,4,8,1]=>[1,2,4,1]
[5,6,7,2,3,4,8,1]=>[3,4,1]
[7,6,4,3,2,5,8,1]=>[1,1,1,1,3,1]
[6,7,4,3,2,5,8,1]=>[2,1,1,3,1]
[7,6,3,4,2,5,8,1]=>[1,1,2,3,1]
[7,6,4,2,3,5,8,1]=>[1,1,1,4,1]
[6,7,4,2,3,5,8,1]=>[2,1,4,1]
[7,6,3,2,4,5,8,1]=>[1,1,1,4,1]
[6,7,3,2,4,5,8,1]=>[2,1,4,1]
[7,6,2,3,4,5,8,1]=>[1,1,5,1]
[6,7,2,3,4,5,8,1]=>[2,5,1]
[7,5,4,3,2,6,8,1]=>[1,1,1,1,3,1]
[7,4,5,3,2,6,8,1]=>[1,2,1,3,1]
[7,5,3,4,2,6,8,1]=>[1,1,2,3,1]
[7,4,3,5,2,6,8,1]=>[1,1,2,3,1]
[7,3,4,5,2,6,8,1]=>[1,3,3,1]
[7,5,4,2,3,6,8,1]=>[1,1,1,4,1]
[7,4,5,2,3,6,8,1]=>[1,2,4,1]
[7,5,3,2,4,6,8,1]=>[1,1,1,4,1]
[7,5,2,3,4,6,8,1]=>[1,1,5,1]
[7,4,3,2,5,6,8,1]=>[1,1,1,4,1]
[7,3,4,2,5,6,8,1]=>[1,2,4,1]
[7,4,2,3,5,6,8,1]=>[1,1,5,1]
[7,3,2,4,5,6,8,1]=>[1,1,5,1]
[7,2,3,4,5,6,8,1]=>[1,6,1]
[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]
[6,4,5,3,2,7,8,1]=>[1,2,1,3,1]
[5,4,6,3,2,7,8,1]=>[1,2,1,3,1]
[4,5,6,3,2,7,8,1]=>[3,1,3,1]
[6,5,3,4,2,7,8,1]=>[1,1,2,3,1]
[5,6,3,4,2,7,8,1]=>[2,2,3,1]
[6,4,3,5,2,7,8,1]=>[1,1,2,3,1]
[6,3,4,5,2,7,8,1]=>[1,3,3,1]
[5,4,3,6,2,7,8,1]=>[1,1,2,3,1]
[4,5,3,6,2,7,8,1]=>[2,2,3,1]
[4,3,5,6,2,7,8,1]=>[1,3,3,1]
[3,4,5,6,2,7,8,1]=>[4,3,1]
[6,5,4,2,3,7,8,1]=>[1,1,1,4,1]
[5,6,4,2,3,7,8,1]=>[2,1,4,1]
[6,4,5,2,3,7,8,1]=>[1,2,4,1]
[5,4,6,2,3,7,8,1]=>[1,2,4,1]
[4,5,6,2,3,7,8,1]=>[3,4,1]
[6,5,3,2,4,7,8,1]=>[1,1,1,4,1]
[6,5,2,3,4,7,8,1]=>[1,1,5,1]
[6,4,2,3,5,7,8,1]=>[1,1,5,1]
[6,2,3,4,5,7,8,1]=>[1,6,1]
[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]
[4,5,3,2,6,7,8,1]=>[2,1,4,1]
[5,3,4,2,6,7,8,1]=>[1,2,4,1]
[4,3,5,2,6,7,8,1]=>[1,2,4,1]
[3,4,5,2,6,7,8,1]=>[3,4,1]
[5,4,2,3,6,7,8,1]=>[1,1,5,1]
[4,5,2,3,6,7,8,1]=>[2,5,1]
[5,3,2,4,6,7,8,1]=>[1,1,5,1]
[5,2,3,4,6,7,8,1]=>[1,6,1]
[4,3,2,5,6,7,8,1]=>[1,1,5,1]
[3,4,2,5,6,7,8,1]=>[2,5,1]
[4,2,3,5,6,7,8,1]=>[1,6,1]
[3,2,4,5,6,7,8,1]=>[1,6,1]
[2,3,4,5,6,7,8,1]=>[7,1]
[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]
[8,6,7,5,4,3,1,2]=>[1,2,1,1,1,2]
[7,6,8,5,4,3,1,2]=>[1,2,1,1,1,2]
[6,7,8,5,4,3,1,2]=>[3,1,1,1,2]
[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]
[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]
[8,6,5,7,4,3,1,2]=>[1,1,2,1,1,2]
[8,5,6,7,4,3,1,2]=>[1,3,1,1,2]
[7,6,5,8,4,3,1,2]=>[1,1,2,1,1,2]
[6,7,5,8,4,3,1,2]=>[2,2,1,1,2]
[7,5,6,8,4,3,1,2]=>[1,3,1,1,2]
[6,5,7,8,4,3,1,2]=>[1,3,1,1,2]
[5,6,7,8,4,3,1,2]=>[4,1,1,2]
[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]
[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]
[8,6,7,4,5,3,1,2]=>[1,2,2,1,2]
[7,6,8,4,5,3,1,2]=>[1,2,2,1,2]
[6,7,8,4,5,3,1,2]=>[3,2,1,2]
[8,7,5,4,6,3,1,2]=>[1,1,1,2,1,2]
[8,7,4,5,6,3,1,2]=>[1,1,3,1,2]
[7,8,4,5,6,3,1,2]=>[2,3,1,2]
[8,5,6,4,7,3,1,2]=>[1,2,2,1,2]
[8,6,4,5,7,3,1,2]=>[1,1,3,1,2]
[8,5,4,6,7,3,1,2]=>[1,1,3,1,2]
[7,6,5,4,8,3,1,2]=>[1,1,1,2,1,2]
[6,7,5,4,8,3,1,2]=>[2,1,2,1,2]
[7,5,6,4,8,3,1,2]=>[1,2,2,1,2]
[6,5,7,4,8,3,1,2]=>[1,2,2,1,2]
[7,6,4,5,8,3,1,2]=>[1,1,3,1,2]
[6,7,4,5,8,3,1,2]=>[2,3,1,2]
[7,5,4,6,8,3,1,2]=>[1,1,3,1,2]
[7,4,5,6,8,3,1,2]=>[1,4,1,2]
[6,5,4,7,8,3,1,2]=>[1,1,3,1,2]
[5,6,4,7,8,3,1,2]=>[2,3,1,2]
[6,4,5,7,8,3,1,2]=>[1,4,1,2]
[5,4,6,7,8,3,1,2]=>[1,4,1,2]
[4,5,6,7,8,3,1,2]=>[5,1,2]
[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]
[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]
[7,6,8,5,3,4,1,2]=>[1,2,1,2,2]
[6,7,8,5,3,4,1,2]=>[3,1,2,2]
[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]
[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[8,6,5,7,3,4,1,2]=>[1,1,2,2,2]
[8,5,6,7,3,4,1,2]=>[1,3,2,2]
[7,6,5,8,3,4,1,2]=>[1,1,2,2,2]
[6,7,5,8,3,4,1,2]=>[2,2,2,2]
[7,5,6,8,3,4,1,2]=>[1,3,2,2]
[6,5,7,8,3,4,1,2]=>[1,3,2,2]
[5,6,7,8,3,4,1,2]=>[4,2,2]
[8,7,6,4,3,5,1,2]=>[1,1,1,1,2,2]
[7,8,6,4,3,5,1,2]=>[2,1,1,2,2]
[8,6,7,4,3,5,1,2]=>[1,2,1,2,2]
[7,6,8,4,3,5,1,2]=>[1,2,1,2,2]
[6,7,8,4,3,5,1,2]=>[3,1,2,2]
[8,7,6,3,4,5,1,2]=>[1,1,1,3,2]
[7,8,6,3,4,5,1,2]=>[2,1,3,2]
[8,6,7,3,4,5,1,2]=>[1,2,3,2]
[7,6,8,3,4,5,1,2]=>[1,2,3,2]
[6,7,8,3,4,5,1,2]=>[3,3,2]
[8,7,5,4,3,6,1,2]=>[1,1,1,1,2,2]
[7,8,5,4,3,6,1,2]=>[2,1,1,2,2]
[8,7,4,5,3,6,1,2]=>[1,1,2,2,2]
[7,8,4,5,3,6,1,2]=>[2,2,2,2]
[8,7,5,3,4,6,1,2]=>[1,1,1,3,2]
[7,8,5,3,4,6,1,2]=>[2,1,3,2]
[8,7,4,3,5,6,1,2]=>[1,1,1,3,2]
[7,8,4,3,5,6,1,2]=>[2,1,3,2]
[8,7,3,4,5,6,1,2]=>[1,1,4,2]
[7,8,3,4,5,6,1,2]=>[2,4,2]
[8,6,5,4,3,7,1,2]=>[1,1,1,1,2,2]
[8,5,6,3,4,7,1,2]=>[1,2,3,2]
[8,6,4,3,5,7,1,2]=>[1,1,1,3,2]
[8,6,3,4,5,7,1,2]=>[1,1,4,2]
[8,5,4,3,6,7,1,2]=>[1,1,1,3,2]
[8,5,3,4,6,7,1,2]=>[1,1,4,2]
[8,4,3,5,6,7,1,2]=>[1,1,4,2]
[8,3,4,5,6,7,1,2]=>[1,5,2]
[7,6,5,4,3,8,1,2]=>[1,1,1,1,2,2]
[6,7,5,4,3,8,1,2]=>[2,1,1,2,2]
[7,5,6,4,3,8,1,2]=>[1,2,1,2,2]
[6,5,7,4,3,8,1,2]=>[1,2,1,2,2]
[5,6,7,4,3,8,1,2]=>[3,1,2,2]
[7,6,4,5,3,8,1,2]=>[1,1,2,2,2]
[6,7,4,5,3,8,1,2]=>[2,2,2,2]
[7,5,4,6,3,8,1,2]=>[1,1,2,2,2]
[7,4,5,6,3,8,1,2]=>[1,3,2,2]
[6,5,4,7,3,8,1,2]=>[1,1,2,2,2]
[5,6,4,7,3,8,1,2]=>[2,2,2,2]
[6,4,5,7,3,8,1,2]=>[1,3,2,2]
[5,4,6,7,3,8,1,2]=>[1,3,2,2]
[4,5,6,7,3,8,1,2]=>[4,2,2]
[7,6,5,3,4,8,1,2]=>[1,1,1,3,2]
[6,7,5,3,4,8,1,2]=>[2,1,3,2]
[7,5,6,3,4,8,1,2]=>[1,2,3,2]
[6,5,7,3,4,8,1,2]=>[1,2,3,2]
[5,6,7,3,4,8,1,2]=>[3,3,2]
[7,6,4,3,5,8,1,2]=>[1,1,1,3,2]
[6,7,4,3,5,8,1,2]=>[2,1,3,2]
[7,6,3,4,5,8,1,2]=>[1,1,4,2]
[6,7,3,4,5,8,1,2]=>[2,4,2]
[7,5,4,3,6,8,1,2]=>[1,1,1,3,2]
[7,5,3,4,6,8,1,2]=>[1,1,4,2]
[7,3,4,5,6,8,1,2]=>[1,5,2]
[6,5,4,3,7,8,1,2]=>[1,1,1,3,2]
[5,6,4,3,7,8,1,2]=>[2,1,3,2]
[5,4,6,3,7,8,1,2]=>[1,2,3,2]
[4,5,6,3,7,8,1,2]=>[3,3,2]
[6,5,3,4,7,8,1,2]=>[1,1,4,2]
[5,6,3,4,7,8,1,2]=>[2,4,2]
[6,4,3,5,7,8,1,2]=>[1,1,4,2]
[6,3,4,5,7,8,1,2]=>[1,5,2]
[5,4,3,6,7,8,1,2]=>[1,1,4,2]
[4,5,3,6,7,8,1,2]=>[2,4,2]
[5,3,4,6,7,8,1,2]=>[1,5,2]
[4,3,5,6,7,8,1,2]=>[1,5,2]
[3,4,5,6,7,8,1,2]=>[6,2]
[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]
[7,8,6,5,4,2,1,3]=>[2,1,1,1,1,2]
[8,6,7,5,4,2,1,3]=>[1,2,1,1,1,2]
[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]
[6,7,8,5,4,2,1,3]=>[3,1,1,1,2]
[8,7,5,6,4,2,1,3]=>[1,1,2,1,1,2]
[7,8,5,6,4,2,1,3]=>[2,2,1,1,2]
[8,6,5,7,4,2,1,3]=>[1,1,2,1,1,2]
[8,5,6,7,4,2,1,3]=>[1,3,1,1,2]
[7,6,5,8,4,2,1,3]=>[1,1,2,1,1,2]
[6,7,5,8,4,2,1,3]=>[2,2,1,1,2]
[7,5,6,8,4,2,1,3]=>[1,3,1,1,2]
[6,5,7,8,4,2,1,3]=>[1,3,1,1,2]
[5,6,7,8,4,2,1,3]=>[4,1,1,2]
[8,7,6,4,5,2,1,3]=>[1,1,1,2,1,2]
[7,8,6,4,5,2,1,3]=>[2,1,2,1,2]
[8,6,7,4,5,2,1,3]=>[1,2,2,1,2]
[7,6,8,4,5,2,1,3]=>[1,2,2,1,2]
[6,7,8,4,5,2,1,3]=>[3,2,1,2]
[8,7,5,4,6,2,1,3]=>[1,1,1,2,1,2]
[7,8,5,4,6,2,1,3]=>[2,1,2,1,2]
[8,7,4,5,6,2,1,3]=>[1,1,3,1,2]
[7,8,4,5,6,2,1,3]=>[2,3,1,2]
[8,6,5,4,7,2,1,3]=>[1,1,1,2,1,2]
[8,6,4,5,7,2,1,3]=>[1,1,3,1,2]
[8,5,4,6,7,2,1,3]=>[1,1,3,1,2]
[8,4,5,6,7,2,1,3]=>[1,4,1,2]
[7,6,5,4,8,2,1,3]=>[1,1,1,2,1,2]
[6,7,5,4,8,2,1,3]=>[2,1,2,1,2]
[7,5,6,4,8,2,1,3]=>[1,2,2,1,2]
[6,5,7,4,8,2,1,3]=>[1,2,2,1,2]
[5,6,7,4,8,2,1,3]=>[3,2,1,2]
[7,6,4,5,8,2,1,3]=>[1,1,3,1,2]
[6,7,4,5,8,2,1,3]=>[2,3,1,2]
[7,5,4,6,8,2,1,3]=>[1,1,3,1,2]
[7,4,5,6,8,2,1,3]=>[1,4,1,2]
[6,5,4,7,8,2,1,3]=>[1,1,3,1,2]
[5,6,4,7,8,2,1,3]=>[2,3,1,2]
[5,4,6,7,8,2,1,3]=>[1,4,1,2]
[4,5,6,7,8,2,1,3]=>[5,1,2]
[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[7,8,6,5,4,1,2,3]=>[2,1,1,1,3]
[7,6,8,5,4,1,2,3]=>[1,2,1,1,3]
[6,7,8,5,4,1,2,3]=>[3,1,1,3]
[7,8,5,6,4,1,2,3]=>[2,2,1,3]
[8,6,5,7,4,1,2,3]=>[1,1,2,1,3]
[8,5,6,7,4,1,2,3]=>[1,3,1,3]
[7,6,5,8,4,1,2,3]=>[1,1,2,1,3]
[6,7,5,8,4,1,2,3]=>[2,2,1,3]
[7,5,6,8,4,1,2,3]=>[1,3,1,3]
[6,5,7,8,4,1,2,3]=>[1,3,1,3]
[5,6,7,8,4,1,2,3]=>[4,1,3]
[8,7,6,4,5,1,2,3]=>[1,1,1,2,3]
[7,8,6,4,5,1,2,3]=>[2,1,2,3]
[8,6,7,4,5,1,2,3]=>[1,2,2,3]
[6,7,8,4,5,1,2,3]=>[3,2,3]
[8,7,5,4,6,1,2,3]=>[1,1,1,2,3]
[7,8,5,4,6,1,2,3]=>[2,1,2,3]
[8,7,4,5,6,1,2,3]=>[1,1,3,3]
[7,8,4,5,6,1,2,3]=>[2,3,3]
[8,6,5,4,7,1,2,3]=>[1,1,1,2,3]
[8,5,6,4,7,1,2,3]=>[1,2,2,3]
[8,6,4,5,7,1,2,3]=>[1,1,3,3]
[8,5,4,6,7,1,2,3]=>[1,1,3,3]
[8,4,5,6,7,1,2,3]=>[1,4,3]
[7,6,5,4,8,1,2,3]=>[1,1,1,2,3]
[6,7,5,4,8,1,2,3]=>[2,1,2,3]
[7,5,6,4,8,1,2,3]=>[1,2,2,3]
[6,5,7,4,8,1,2,3]=>[1,2,2,3]
[5,6,7,4,8,1,2,3]=>[3,2,3]
[7,6,4,5,8,1,2,3]=>[1,1,3,3]
[6,7,4,5,8,1,2,3]=>[2,3,3]
[7,5,4,6,8,1,2,3]=>[1,1,3,3]
[7,4,5,6,8,1,2,3]=>[1,4,3]
[6,5,4,7,8,1,2,3]=>[1,1,3,3]
[5,6,4,7,8,1,2,3]=>[2,3,3]
[6,4,5,7,8,1,2,3]=>[1,4,3]
[5,4,6,7,8,1,2,3]=>[1,4,3]
[4,5,6,7,8,1,2,3]=>[5,3]
[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]
[7,8,6,5,3,2,1,4]=>[2,1,1,1,1,2]
[8,6,7,5,3,2,1,4]=>[1,2,1,1,1,2]
[7,6,8,5,3,2,1,4]=>[1,2,1,1,1,2]
[6,7,8,5,3,2,1,4]=>[3,1,1,1,2]
[8,7,5,6,3,2,1,4]=>[1,1,2,1,1,2]
[7,8,5,6,3,2,1,4]=>[2,2,1,1,2]
[8,6,5,7,3,2,1,4]=>[1,1,2,1,1,2]
[8,5,6,7,3,2,1,4]=>[1,3,1,1,2]
[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]
[6,7,5,8,3,2,1,4]=>[2,2,1,1,2]
[7,5,6,8,3,2,1,4]=>[1,3,1,1,2]
[6,5,7,8,3,2,1,4]=>[1,3,1,1,2]
[5,6,7,8,3,2,1,4]=>[4,1,1,2]
[8,7,6,5,2,3,1,4]=>[1,1,1,1,2,2]
[7,8,6,5,2,3,1,4]=>[2,1,1,2,2]
[8,6,7,5,2,3,1,4]=>[1,2,1,2,2]
[7,6,8,5,2,3,1,4]=>[1,2,1,2,2]
[6,7,8,5,2,3,1,4]=>[3,1,2,2]
[8,7,5,6,2,3,1,4]=>[1,1,2,2,2]
[7,8,5,6,2,3,1,4]=>[2,2,2,2]
[8,6,5,7,2,3,1,4]=>[1,1,2,2,2]
[8,5,6,7,2,3,1,4]=>[1,3,2,2]
[7,6,5,8,2,3,1,4]=>[1,1,2,2,2]
[6,7,5,8,2,3,1,4]=>[2,2,2,2]
[7,5,6,8,2,3,1,4]=>[1,3,2,2]
[6,5,7,8,2,3,1,4]=>[1,3,2,2]
[5,6,7,8,2,3,1,4]=>[4,2,2]
[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]
[7,8,6,5,3,1,2,4]=>[2,1,1,1,3]
[8,6,7,5,3,1,2,4]=>[1,2,1,1,3]
[7,6,8,5,3,1,2,4]=>[1,2,1,1,3]
[6,7,8,5,3,1,2,4]=>[3,1,1,3]
[8,7,5,6,3,1,2,4]=>[1,1,2,1,3]
[7,8,5,6,3,1,2,4]=>[2,2,1,3]
[8,6,5,7,3,1,2,4]=>[1,1,2,1,3]
[8,5,6,7,3,1,2,4]=>[1,3,1,3]
[7,6,5,8,3,1,2,4]=>[1,1,2,1,3]
[6,7,5,8,3,1,2,4]=>[2,2,1,3]
[7,5,6,8,3,1,2,4]=>[1,3,1,3]
[6,5,7,8,3,1,2,4]=>[1,3,1,3]
[5,6,7,8,3,1,2,4]=>[4,1,3]
[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]
[7,8,6,5,2,1,3,4]=>[2,1,1,1,3]
[8,6,7,5,2,1,3,4]=>[1,2,1,1,3]
[7,6,8,5,2,1,3,4]=>[1,2,1,1,3]
[6,7,8,5,2,1,3,4]=>[3,1,1,3]
[8,7,5,6,2,1,3,4]=>[1,1,2,1,3]
[7,8,5,6,2,1,3,4]=>[2,2,1,3]
[8,6,5,7,2,1,3,4]=>[1,1,2,1,3]
[8,5,6,7,2,1,3,4]=>[1,3,1,3]
[7,6,5,8,2,1,3,4]=>[1,1,2,1,3]
[6,7,5,8,2,1,3,4]=>[2,2,1,3]
[7,5,6,8,2,1,3,4]=>[1,3,1,3]
[6,5,7,8,2,1,3,4]=>[1,3,1,3]
[5,6,7,8,2,1,3,4]=>[4,1,3]
[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[7,8,6,5,1,2,3,4]=>[2,1,1,4]
[8,6,7,5,1,2,3,4]=>[1,2,1,4]
[7,6,8,5,1,2,3,4]=>[1,2,1,4]
[6,7,8,5,1,2,3,4]=>[3,1,4]
[8,7,5,6,1,2,3,4]=>[1,1,2,4]
[7,8,5,6,1,2,3,4]=>[2,2,4]
[8,6,5,7,1,2,3,4]=>[1,1,2,4]
[8,5,6,7,1,2,3,4]=>[1,3,4]
[7,6,5,8,1,2,3,4]=>[1,1,2,4]
[6,7,5,8,1,2,3,4]=>[2,2,4]
[7,5,6,8,1,2,3,4]=>[1,3,4]
[6,5,7,8,1,2,3,4]=>[1,3,4]
[5,6,7,8,1,2,3,4]=>[4,4]
[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]
[7,8,6,4,3,2,1,5]=>[2,1,1,1,1,2]
[8,6,7,4,3,2,1,5]=>[1,2,1,1,1,2]
[7,6,8,4,3,2,1,5]=>[1,2,1,1,1,2]
[6,7,8,4,3,2,1,5]=>[3,1,1,1,2]
[8,7,6,3,4,2,1,5]=>[1,1,1,2,1,2]
[7,8,6,3,4,2,1,5]=>[2,1,2,1,2]
[8,6,7,3,4,2,1,5]=>[1,2,2,1,2]
[6,7,8,3,4,2,1,5]=>[3,2,1,2]
[8,7,6,4,2,3,1,5]=>[1,1,1,1,2,2]
[7,8,6,4,2,3,1,5]=>[2,1,1,2,2]
[8,6,7,4,2,3,1,5]=>[1,2,1,2,2]
[7,6,8,4,2,3,1,5]=>[1,2,1,2,2]
[6,7,8,4,2,3,1,5]=>[3,1,2,2]
[8,7,6,3,2,4,1,5]=>[1,1,1,1,2,2]
[8,6,7,3,2,4,1,5]=>[1,2,1,2,2]
[7,6,8,3,2,4,1,5]=>[1,2,1,2,2]
[6,7,8,3,2,4,1,5]=>[3,1,2,2]
[8,7,6,2,3,4,1,5]=>[1,1,1,3,2]
[7,8,6,2,3,4,1,5]=>[2,1,3,2]
[8,6,7,2,3,4,1,5]=>[1,2,3,2]
[7,6,8,2,3,4,1,5]=>[1,2,3,2]
[6,7,8,2,3,4,1,5]=>[3,3,2]
[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]
[7,8,6,4,3,1,2,5]=>[2,1,1,1,3]
[8,6,7,4,3,1,2,5]=>[1,2,1,1,3]
[7,6,8,4,3,1,2,5]=>[1,2,1,1,3]
[6,7,8,4,3,1,2,5]=>[3,1,1,3]
[8,7,6,3,4,1,2,5]=>[1,1,1,2,3]
[7,8,6,3,4,1,2,5]=>[2,1,2,3]
[8,6,7,3,4,1,2,5]=>[1,2,2,3]
[7,6,8,3,4,1,2,5]=>[1,2,2,3]
[6,7,8,3,4,1,2,5]=>[3,2,3]
[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]
[7,8,6,4,2,1,3,5]=>[2,1,1,1,3]
[8,6,7,4,2,1,3,5]=>[1,2,1,1,3]
[7,6,8,4,2,1,3,5]=>[1,2,1,1,3]
[6,7,8,4,2,1,3,5]=>[3,1,1,3]
[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]
[7,8,6,4,1,2,3,5]=>[2,1,1,4]
[8,6,7,4,1,2,3,5]=>[1,2,1,4]
[7,6,8,4,1,2,3,5]=>[1,2,1,4]
[6,7,8,4,1,2,3,5]=>[3,1,4]
[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]
[7,8,6,3,2,1,4,5]=>[2,1,1,1,3]
[8,6,7,3,2,1,4,5]=>[1,2,1,1,3]
[7,6,8,3,2,1,4,5]=>[1,2,1,1,3]
[6,7,8,3,2,1,4,5]=>[3,1,1,3]
[8,7,6,2,3,1,4,5]=>[1,1,1,2,3]
[7,8,6,2,3,1,4,5]=>[2,1,2,3]
[8,6,7,2,3,1,4,5]=>[1,2,2,3]
[7,6,8,2,3,1,4,5]=>[1,2,2,3]
[6,7,8,2,3,1,4,5]=>[3,2,3]
[8,7,6,3,1,2,4,5]=>[1,1,1,1,4]
[7,8,6,3,1,2,4,5]=>[2,1,1,4]
[8,6,7,3,1,2,4,5]=>[1,2,1,4]
[7,6,8,3,1,2,4,5]=>[1,2,1,4]
[6,7,8,3,1,2,4,5]=>[3,1,4]
[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]
[7,8,6,2,1,3,4,5]=>[2,1,1,4]
[8,6,7,2,1,3,4,5]=>[1,2,1,4]
[7,6,8,2,1,3,4,5]=>[1,2,1,4]
[6,7,8,2,1,3,4,5]=>[3,1,4]
[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[7,8,6,1,2,3,4,5]=>[2,1,5]
[8,6,7,1,2,3,4,5]=>[1,2,5]
[7,6,8,1,2,3,4,5]=>[1,2,5]
[6,7,8,1,2,3,4,5]=>[3,5]
[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]
[7,8,5,4,3,2,1,6]=>[2,1,1,1,1,2]
[8,7,4,5,3,2,1,6]=>[1,1,2,1,1,2]
[7,8,4,5,3,2,1,6]=>[2,2,1,1,2]
[8,7,5,3,4,2,1,6]=>[1,1,1,2,1,2]
[8,7,4,3,5,2,1,6]=>[1,1,1,2,1,2]
[7,8,4,3,5,2,1,6]=>[2,1,2,1,2]
[8,7,3,4,5,2,1,6]=>[1,1,3,1,2]
[7,8,3,4,5,2,1,6]=>[2,3,1,2]
[8,7,5,4,2,3,1,6]=>[1,1,1,1,2,2]
[8,7,4,5,2,3,1,6]=>[1,1,2,2,2]
[7,8,4,5,2,3,1,6]=>[2,2,2,2]
[8,7,5,3,2,4,1,6]=>[1,1,1,1,2,2]
[7,8,5,3,2,4,1,6]=>[2,1,1,2,2]
[8,7,5,2,3,4,1,6]=>[1,1,1,3,2]
[7,8,5,2,3,4,1,6]=>[2,1,3,2]
[8,7,4,3,2,5,1,6]=>[1,1,1,1,2,2]
[7,8,4,3,2,5,1,6]=>[2,1,1,2,2]
[8,7,3,4,2,5,1,6]=>[1,1,2,2,2]
[7,8,3,4,2,5,1,6]=>[2,2,2,2]
[8,7,4,2,3,5,1,6]=>[1,1,1,3,2]
[8,7,3,2,4,5,1,6]=>[1,1,1,3,2]
[7,8,3,2,4,5,1,6]=>[2,1,3,2]
[8,7,2,3,4,5,1,6]=>[1,1,4,2]
[7,8,2,3,4,5,1,6]=>[2,4,2]
[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]
[7,8,5,4,3,1,2,6]=>[2,1,1,1,3]
[8,7,5,3,4,1,2,6]=>[1,1,1,2,3]
[7,8,5,3,4,1,2,6]=>[2,1,2,3]
[8,7,4,3,5,1,2,6]=>[1,1,1,2,3]
[7,8,4,3,5,1,2,6]=>[2,1,2,3]
[8,7,3,4,5,1,2,6]=>[1,1,3,3]
[7,8,3,4,5,1,2,6]=>[2,3,3]
[8,7,5,4,2,1,3,6]=>[1,1,1,1,1,3]
[7,8,5,4,2,1,3,6]=>[2,1,1,1,3]
[7,8,4,5,2,1,3,6]=>[2,2,1,3]
[8,7,5,4,1,2,3,6]=>[1,1,1,1,4]
[7,8,5,4,1,2,3,6]=>[2,1,1,4]
[8,7,4,5,1,2,3,6]=>[1,1,2,4]
[7,8,4,5,1,2,3,6]=>[2,2,4]
[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]
[7,8,5,3,2,1,4,6]=>[2,1,1,1,3]
[8,7,5,2,3,1,4,6]=>[1,1,1,2,3]
[7,8,5,2,3,1,4,6]=>[2,1,2,3]
[8,7,5,3,1,2,4,6]=>[1,1,1,1,4]
[7,8,5,3,1,2,4,6]=>[2,1,1,4]
[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]
[7,8,5,2,1,3,4,6]=>[2,1,1,4]
[8,7,5,1,2,3,4,6]=>[1,1,1,5]
[7,8,5,1,2,3,4,6]=>[2,1,5]
[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,3]
[7,8,4,3,2,1,5,6]=>[2,1,1,1,3]
[8,7,3,4,2,1,5,6]=>[1,1,2,1,3]
[7,8,3,4,2,1,5,6]=>[2,2,1,3]
[7,8,4,2,3,1,5,6]=>[2,1,2,3]
[8,7,3,2,4,1,5,6]=>[1,1,1,2,3]
[7,8,3,2,4,1,5,6]=>[2,1,2,3]
[8,7,2,3,4,1,5,6]=>[1,1,3,3]
[7,8,2,3,4,1,5,6]=>[2,3,3]
[8,7,4,3,1,2,5,6]=>[1,1,1,1,4]
[7,8,4,3,1,2,5,6]=>[2,1,1,4]
[8,7,3,4,1,2,5,6]=>[1,1,2,4]
[7,8,3,4,1,2,5,6]=>[2,2,4]
[8,7,4,2,1,3,5,6]=>[1,1,1,1,4]
[7,8,4,2,1,3,5,6]=>[2,1,1,4]
[8,7,4,1,2,3,5,6]=>[1,1,1,5]
[7,8,4,1,2,3,5,6]=>[2,1,5]
[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]
[7,8,3,2,1,4,5,6]=>[2,1,1,4]
[8,7,2,3,1,4,5,6]=>[1,1,2,4]
[7,8,2,3,1,4,5,6]=>[2,2,4]
[7,8,3,1,2,4,5,6]=>[2,1,5]
[8,7,2,1,3,4,5,6]=>[1,1,1,5]
[7,8,2,1,3,4,5,6]=>[2,1,5]
[8,7,1,2,3,4,5,6]=>[1,1,6]
[7,8,1,2,3,4,5,6]=>[2,6]
[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]
[8,5,6,4,3,2,1,7]=>[1,2,1,1,1,2]
[8,6,4,5,3,2,1,7]=>[1,1,2,1,1,2]
[8,4,5,6,3,2,1,7]=>[1,3,1,1,2]
[8,6,5,3,4,2,1,7]=>[1,1,1,2,1,2]
[8,5,6,3,4,2,1,7]=>[1,2,2,1,2]
[8,6,4,3,5,2,1,7]=>[1,1,1,2,1,2]
[8,5,4,3,6,2,1,7]=>[1,1,1,2,1,2]
[8,4,5,3,6,2,1,7]=>[1,2,2,1,2]
[8,4,3,5,6,2,1,7]=>[1,1,3,1,2]
[8,3,4,5,6,2,1,7]=>[1,4,1,2]
[8,6,5,4,2,3,1,7]=>[1,1,1,1,2,2]
[8,5,6,4,2,3,1,7]=>[1,2,1,2,2]
[8,6,4,5,2,3,1,7]=>[1,1,2,2,2]
[8,4,5,6,2,3,1,7]=>[1,3,2,2]
[8,6,5,3,2,4,1,7]=>[1,1,1,1,2,2]
[8,6,5,2,3,4,1,7]=>[1,1,1,3,2]
[8,5,6,2,3,4,1,7]=>[1,2,3,2]
[8,6,4,3,2,5,1,7]=>[1,1,1,1,2,2]
[8,6,3,4,2,5,1,7]=>[1,1,2,2,2]
[8,6,4,2,3,5,1,7]=>[1,1,1,3,2]
[8,6,3,2,4,5,1,7]=>[1,1,1,3,2]
[8,5,4,3,2,6,1,7]=>[1,1,1,1,2,2]
[8,4,5,3,2,6,1,7]=>[1,2,1,2,2]
[8,5,3,4,2,6,1,7]=>[1,1,2,2,2]
[8,4,3,5,2,6,1,7]=>[1,1,2,2,2]
[8,3,4,5,2,6,1,7]=>[1,3,2,2]
[8,5,4,2,3,6,1,7]=>[1,1,1,3,2]
[8,4,5,2,3,6,1,7]=>[1,2,3,2]
[8,5,3,2,4,6,1,7]=>[1,1,1,3,2]
[8,5,2,3,4,6,1,7]=>[1,1,4,2]
[8,4,3,2,5,6,1,7]=>[1,1,1,3,2]
[8,3,4,2,5,6,1,7]=>[1,2,3,2]
[8,4,2,3,5,6,1,7]=>[1,1,4,2]
[8,3,2,4,5,6,1,7]=>[1,1,4,2]
[8,2,3,4,5,6,1,7]=>[1,5,2]
[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,3]
[8,6,4,5,3,1,2,7]=>[1,1,2,1,3]
[8,5,4,6,3,1,2,7]=>[1,1,2,1,3]
[8,6,5,3,4,1,2,7]=>[1,1,1,2,3]
[8,5,6,3,4,1,2,7]=>[1,2,2,3]
[8,6,4,3,5,1,2,7]=>[1,1,1,2,3]
[8,6,3,4,5,1,2,7]=>[1,1,3,3]
[8,5,4,3,6,1,2,7]=>[1,1,1,2,3]
[8,4,5,3,6,1,2,7]=>[1,2,2,3]
[8,5,3,4,6,1,2,7]=>[1,1,3,3]
[8,4,3,5,6,1,2,7]=>[1,1,3,3]
[8,3,4,5,6,1,2,7]=>[1,4,3]
[8,6,5,4,2,1,3,7]=>[1,1,1,1,1,3]
[8,5,6,4,2,1,3,7]=>[1,2,1,1,3]
[8,6,4,5,2,1,3,7]=>[1,1,2,1,3]
[8,5,4,6,2,1,3,7]=>[1,1,2,1,3]
[8,4,5,6,2,1,3,7]=>[1,3,1,3]
[8,6,5,4,1,2,3,7]=>[1,1,1,1,4]
[8,5,6,4,1,2,3,7]=>[1,2,1,4]
[8,6,4,5,1,2,3,7]=>[1,1,2,4]
[8,5,4,6,1,2,3,7]=>[1,1,2,4]
[8,4,5,6,1,2,3,7]=>[1,3,4]
[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,3]
[8,5,6,3,2,1,4,7]=>[1,2,1,1,3]
[8,6,5,2,3,1,4,7]=>[1,1,1,2,3]
[8,5,6,2,3,1,4,7]=>[1,2,2,3]
[8,6,5,3,1,2,4,7]=>[1,1,1,1,4]
[8,5,6,3,1,2,4,7]=>[1,2,1,4]
[8,6,5,2,1,3,4,7]=>[1,1,1,1,4]
[8,5,6,2,1,3,4,7]=>[1,2,1,4]
[8,6,5,1,2,3,4,7]=>[1,1,1,5]
[8,5,6,1,2,3,4,7]=>[1,2,5]
[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]
[8,6,3,4,2,1,5,7]=>[1,1,2,1,3]
[8,6,4,2,3,1,5,7]=>[1,1,1,2,3]
[8,6,3,2,4,1,5,7]=>[1,1,1,2,3]
[8,6,2,3,4,1,5,7]=>[1,1,3,3]
[8,6,4,3,1,2,5,7]=>[1,1,1,1,4]
[8,6,3,4,1,2,5,7]=>[1,1,2,4]
[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]
[8,6,4,1,2,3,5,7]=>[1,1,1,5]
[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]
[8,6,2,3,1,4,5,7]=>[1,1,2,4]
[8,6,1,2,3,4,5,7]=>[1,1,6]
[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,3]
[8,4,5,3,2,1,6,7]=>[1,2,1,1,3]
[8,4,3,5,2,1,6,7]=>[1,1,2,1,3]
[8,3,4,5,2,1,6,7]=>[1,3,1,3]
[8,5,4,2,3,1,6,7]=>[1,1,1,2,3]
[8,4,5,2,3,1,6,7]=>[1,2,2,3]
[8,5,3,2,4,1,6,7]=>[1,1,1,2,3]
[8,5,2,3,4,1,6,7]=>[1,1,3,3]
[8,4,2,3,5,1,6,7]=>[1,1,3,3]
[8,2,3,4,5,1,6,7]=>[1,4,3]
[8,5,4,3,1,2,6,7]=>[1,1,1,1,4]
[8,5,3,4,1,2,6,7]=>[1,1,2,4]
[8,4,3,5,1,2,6,7]=>[1,1,2,4]
[8,3,4,5,1,2,6,7]=>[1,3,4]
[8,5,4,2,1,3,6,7]=>[1,1,1,1,4]
[8,4,5,2,1,3,6,7]=>[1,2,1,4]
[8,5,4,1,2,3,6,7]=>[1,1,1,5]
[8,4,5,1,2,3,6,7]=>[1,2,5]
[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]
[8,5,2,3,1,4,6,7]=>[1,1,2,4]
[8,5,3,1,2,4,6,7]=>[1,1,1,5]
[8,5,2,1,3,4,6,7]=>[1,1,1,5]
[8,5,1,2,3,4,6,7]=>[1,1,6]
[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]
[8,3,4,2,1,5,6,7]=>[1,2,1,4]
[8,4,2,3,1,5,6,7]=>[1,1,2,4]
[8,3,2,4,1,5,6,7]=>[1,1,2,4]
[8,2,3,4,1,5,6,7]=>[1,3,4]
[8,4,3,1,2,5,6,7]=>[1,1,1,5]
[8,3,4,1,2,5,6,7]=>[1,2,5]
[8,4,2,1,3,5,6,7]=>[1,1,1,5]
[8,4,1,2,3,5,6,7]=>[1,1,6]
[8,3,2,1,4,5,6,7]=>[1,1,1,5]
[8,2,3,1,4,5,6,7]=>[1,2,5]
[8,3,1,2,4,5,6,7]=>[1,1,6]
[8,2,1,3,4,5,6,7]=>[1,1,6]
[8,1,2,3,4,5,6,7]=>[1,7]
[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]
[7,5,6,4,3,2,1,8]=>[1,2,1,1,1,2]
[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]
[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]
[7,6,4,5,3,2,1,8]=>[1,1,2,1,1,2]
[6,7,4,5,3,2,1,8]=>[2,2,1,1,2]
[7,5,4,6,3,2,1,8]=>[1,1,2,1,1,2]
[7,4,5,6,3,2,1,8]=>[1,3,1,1,2]
[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]
[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]
[5,4,6,7,3,2,1,8]=>[1,3,1,1,2]
[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[7,6,5,3,4,2,1,8]=>[1,1,1,2,1,2]
[6,7,5,3,4,2,1,8]=>[2,1,2,1,2]
[7,5,6,3,4,2,1,8]=>[1,2,2,1,2]
[6,5,7,3,4,2,1,8]=>[1,2,2,1,2]
[5,6,7,3,4,2,1,8]=>[3,2,1,2]
[7,6,4,3,5,2,1,8]=>[1,1,1,2,1,2]
[6,7,4,3,5,2,1,8]=>[2,1,2,1,2]
[7,6,3,4,5,2,1,8]=>[1,1,3,1,2]
[7,5,4,3,6,2,1,8]=>[1,1,1,2,1,2]
[7,4,5,3,6,2,1,8]=>[1,2,2,1,2]
[7,3,4,5,6,2,1,8]=>[1,4,1,2]
[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]
[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]
[6,4,5,3,7,2,1,8]=>[1,2,2,1,2]
[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]
[4,5,6,3,7,2,1,8]=>[3,2,1,2]
[5,6,3,4,7,2,1,8]=>[2,3,1,2]
[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[4,5,3,6,7,2,1,8]=>[2,3,1,2]
[3,4,5,6,7,2,1,8]=>[5,1,2]
[7,6,5,4,2,3,1,8]=>[1,1,1,1,2,2]
[6,7,5,4,2,3,1,8]=>[2,1,1,2,2]
[7,5,6,4,2,3,1,8]=>[1,2,1,2,2]
[5,6,7,4,2,3,1,8]=>[3,1,2,2]
[7,6,4,5,2,3,1,8]=>[1,1,2,2,2]
[6,7,4,5,2,3,1,8]=>[2,2,2,2]
[7,5,4,6,2,3,1,8]=>[1,1,2,2,2]
[7,4,5,6,2,3,1,8]=>[1,3,2,2]
[6,5,4,7,2,3,1,8]=>[1,1,2,2,2]
[5,6,4,7,2,3,1,8]=>[2,2,2,2]
[5,4,6,7,2,3,1,8]=>[1,3,2,2]
[4,5,6,7,2,3,1,8]=>[4,2,2]
[7,6,5,3,2,4,1,8]=>[1,1,1,1,2,2]
[7,5,6,3,2,4,1,8]=>[1,2,1,2,2]
[6,5,7,3,2,4,1,8]=>[1,2,1,2,2]
[5,6,7,3,2,4,1,8]=>[3,1,2,2]
[7,6,5,2,3,4,1,8]=>[1,1,1,3,2]
[6,7,5,2,3,4,1,8]=>[2,1,3,2]
[7,5,6,2,3,4,1,8]=>[1,2,3,2]
[6,5,7,2,3,4,1,8]=>[1,2,3,2]
[5,6,7,2,3,4,1,8]=>[3,3,2]
[7,6,4,3,2,5,1,8]=>[1,1,1,1,2,2]
[6,7,4,3,2,5,1,8]=>[2,1,1,2,2]
[6,7,3,4,2,5,1,8]=>[2,2,2,2]
[7,6,4,2,3,5,1,8]=>[1,1,1,3,2]
[6,7,4,2,3,5,1,8]=>[2,1,3,2]
[7,6,3,2,4,5,1,8]=>[1,1,1,3,2]
[6,7,3,2,4,5,1,8]=>[2,1,3,2]
[7,6,2,3,4,5,1,8]=>[1,1,4,2]
[6,7,2,3,4,5,1,8]=>[2,4,2]
[7,5,4,3,2,6,1,8]=>[1,1,1,1,2,2]
[7,4,5,3,2,6,1,8]=>[1,2,1,2,2]
[7,5,3,4,2,6,1,8]=>[1,1,2,2,2]
[7,4,3,5,2,6,1,8]=>[1,1,2,2,2]
[7,3,4,5,2,6,1,8]=>[1,3,2,2]
[7,5,4,2,3,6,1,8]=>[1,1,1,3,2]
[7,4,5,2,3,6,1,8]=>[1,2,3,2]
[7,5,3,2,4,6,1,8]=>[1,1,1,3,2]
[7,5,2,3,4,6,1,8]=>[1,1,4,2]
[7,4,3,2,5,6,1,8]=>[1,1,1,3,2]
[7,4,2,3,5,6,1,8]=>[1,1,4,2]
[7,3,2,4,5,6,1,8]=>[1,1,4,2]
[7,2,3,4,5,6,1,8]=>[1,5,2]
[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]
[5,4,6,3,2,7,1,8]=>[1,2,1,2,2]
[5,6,3,4,2,7,1,8]=>[2,2,2,2]
[6,4,3,5,2,7,1,8]=>[1,1,2,2,2]
[6,3,4,5,2,7,1,8]=>[1,3,2,2]
[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]
[4,5,3,6,2,7,1,8]=>[2,2,2,2]
[5,3,4,6,2,7,1,8]=>[1,3,2,2]
[4,3,5,6,2,7,1,8]=>[1,3,2,2]
[3,4,5,6,2,7,1,8]=>[4,2,2]
[6,4,5,2,3,7,1,8]=>[1,2,3,2]
[5,4,6,2,3,7,1,8]=>[1,2,3,2]
[4,5,6,2,3,7,1,8]=>[3,3,2]
[6,5,3,2,4,7,1,8]=>[1,1,1,3,2]
[5,6,3,2,4,7,1,8]=>[2,1,3,2]
[6,5,2,3,4,7,1,8]=>[1,1,4,2]
[5,6,2,3,4,7,1,8]=>[2,4,2]
[6,3,4,2,5,7,1,8]=>[1,2,3,2]
[6,4,2,3,5,7,1,8]=>[1,1,4,2]
[6,3,2,4,5,7,1,8]=>[1,1,4,2]
[6,2,3,4,5,7,1,8]=>[1,5,2]
[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]
[4,5,3,2,6,7,1,8]=>[2,1,3,2]
[5,3,4,2,6,7,1,8]=>[1,2,3,2]
[3,4,5,2,6,7,1,8]=>[3,3,2]
[5,4,2,3,6,7,1,8]=>[1,1,4,2]
[4,5,2,3,6,7,1,8]=>[2,4,2]
[5,3,2,4,6,7,1,8]=>[1,1,4,2]
[5,2,3,4,6,7,1,8]=>[1,5,2]
[4,3,2,5,6,7,1,8]=>[1,1,4,2]
[3,4,2,5,6,7,1,8]=>[2,4,2]
[4,2,3,5,6,7,1,8]=>[1,5,2]
[3,2,4,5,6,7,1,8]=>[1,5,2]
[2,3,4,5,6,7,1,8]=>[6,2]
[7,6,5,4,3,1,2,8]=>[1,1,1,1,1,3]
[6,7,5,4,3,1,2,8]=>[2,1,1,1,3]
[7,5,6,4,3,1,2,8]=>[1,2,1,1,3]
[6,5,7,4,3,1,2,8]=>[1,2,1,1,3]
[5,6,7,4,3,1,2,8]=>[3,1,1,3]
[7,6,4,5,3,1,2,8]=>[1,1,2,1,3]
[7,5,4,6,3,1,2,8]=>[1,1,2,1,3]
[7,4,5,6,3,1,2,8]=>[1,3,1,3]
[5,4,6,7,3,1,2,8]=>[1,3,1,3]
[4,5,6,7,3,1,2,8]=>[4,1,3]
[7,6,5,3,4,1,2,8]=>[1,1,1,2,3]
[6,7,5,3,4,1,2,8]=>[2,1,2,3]
[7,5,6,3,4,1,2,8]=>[1,2,2,3]
[5,6,7,3,4,1,2,8]=>[3,2,3]
[7,6,4,3,5,1,2,8]=>[1,1,1,2,3]
[6,7,4,3,5,1,2,8]=>[2,1,2,3]
[6,7,3,4,5,1,2,8]=>[2,3,3]
[7,5,4,3,6,1,2,8]=>[1,1,1,2,3]
[7,4,5,3,6,1,2,8]=>[1,2,2,3]
[7,5,3,4,6,1,2,8]=>[1,1,3,3]
[7,4,3,5,6,1,2,8]=>[1,1,3,3]
[7,3,4,5,6,1,2,8]=>[1,4,3]
[6,5,4,3,7,1,2,8]=>[1,1,1,2,3]
[5,6,4,3,7,1,2,8]=>[2,1,2,3]
[5,4,6,3,7,1,2,8]=>[1,2,2,3]
[6,5,3,4,7,1,2,8]=>[1,1,3,3]
[5,6,3,4,7,1,2,8]=>[2,3,3]
[6,4,3,5,7,1,2,8]=>[1,1,3,3]
[6,3,4,5,7,1,2,8]=>[1,4,3]
[4,5,3,6,7,1,2,8]=>[2,3,3]
[5,3,4,6,7,1,2,8]=>[1,4,3]
[4,3,5,6,7,1,2,8]=>[1,4,3]
[3,4,5,6,7,1,2,8]=>[5,3]
[7,6,5,4,2,1,3,8]=>[1,1,1,1,1,3]
[6,7,5,4,2,1,3,8]=>[2,1,1,1,3]
[6,5,7,4,2,1,3,8]=>[1,2,1,1,3]
[5,6,7,4,2,1,3,8]=>[3,1,1,3]
[7,6,4,5,2,1,3,8]=>[1,1,2,1,3]
[6,7,4,5,2,1,3,8]=>[2,2,1,3]
[7,5,4,6,2,1,3,8]=>[1,1,2,1,3]
[7,4,5,6,2,1,3,8]=>[1,3,1,3]
[6,5,4,7,2,1,3,8]=>[1,1,2,1,3]
[5,4,6,7,2,1,3,8]=>[1,3,1,3]
[4,5,6,7,2,1,3,8]=>[4,1,3]
[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]
[6,7,5,4,1,2,3,8]=>[2,1,1,4]
[7,5,6,4,1,2,3,8]=>[1,2,1,4]
[6,5,7,4,1,2,3,8]=>[1,2,1,4]
[5,6,7,4,1,2,3,8]=>[3,1,4]
[7,6,4,5,1,2,3,8]=>[1,1,2,4]
[6,7,4,5,1,2,3,8]=>[2,2,4]
[7,5,4,6,1,2,3,8]=>[1,1,2,4]
[7,4,5,6,1,2,3,8]=>[1,3,4]
[6,5,4,7,1,2,3,8]=>[1,1,2,4]
[5,6,4,7,1,2,3,8]=>[2,2,4]
[6,4,5,7,1,2,3,8]=>[1,3,4]
[5,4,6,7,1,2,3,8]=>[1,3,4]
[4,5,6,7,1,2,3,8]=>[4,4]
[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,3]
[6,7,5,3,2,1,4,8]=>[2,1,1,1,3]
[7,5,6,3,2,1,4,8]=>[1,2,1,1,3]
[5,6,7,3,2,1,4,8]=>[3,1,1,3]
[7,6,5,2,3,1,4,8]=>[1,1,1,2,3]
[6,7,5,2,3,1,4,8]=>[2,1,2,3]
[7,5,6,2,3,1,4,8]=>[1,2,2,3]
[6,5,7,2,3,1,4,8]=>[1,2,2,3]
[5,6,7,2,3,1,4,8]=>[3,2,3]
[7,6,5,3,1,2,4,8]=>[1,1,1,1,4]
[6,7,5,3,1,2,4,8]=>[2,1,1,4]
[7,5,6,3,1,2,4,8]=>[1,2,1,4]
[5,6,7,3,1,2,4,8]=>[3,1,4]
[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]
[6,7,5,2,1,3,4,8]=>[2,1,1,4]
[7,5,6,2,1,3,4,8]=>[1,2,1,4]
[5,6,7,2,1,3,4,8]=>[3,1,4]
[7,6,5,1,2,3,4,8]=>[1,1,1,5]
[6,7,5,1,2,3,4,8]=>[2,1,5]
[7,5,6,1,2,3,4,8]=>[1,2,5]
[6,5,7,1,2,3,4,8]=>[1,2,5]
[5,6,7,1,2,3,4,8]=>[3,5]
[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]
[6,7,4,3,2,1,5,8]=>[2,1,1,1,3]
[7,6,3,4,2,1,5,8]=>[1,1,2,1,3]
[7,6,3,2,4,1,5,8]=>[1,1,1,2,3]
[6,7,3,2,4,1,5,8]=>[2,1,2,3]
[7,6,2,3,4,1,5,8]=>[1,1,3,3]
[6,7,2,3,4,1,5,8]=>[2,3,3]
[7,6,4,3,1,2,5,8]=>[1,1,1,1,4]
[6,7,4,3,1,2,5,8]=>[2,1,1,4]
[7,6,3,4,1,2,5,8]=>[1,1,2,4]
[6,7,3,4,1,2,5,8]=>[2,2,4]
[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]
[7,6,4,1,2,3,5,8]=>[1,1,1,5]
[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]
[6,7,3,2,1,4,5,8]=>[2,1,1,4]
[7,6,2,3,1,4,5,8]=>[1,1,2,4]
[6,7,2,3,1,4,5,8]=>[2,2,4]
[7,6,3,1,2,4,5,8]=>[1,1,1,5]
[6,7,3,1,2,4,5,8]=>[2,1,5]
[6,7,2,1,3,4,5,8]=>[2,1,5]
[7,6,1,2,3,4,5,8]=>[1,1,6]
[6,7,1,2,3,4,5,8]=>[2,6]
[7,5,4,3,2,1,6,8]=>[1,1,1,1,1,3]
[7,4,5,3,2,1,6,8]=>[1,2,1,1,3]
[7,5,3,4,2,1,6,8]=>[1,1,2,1,3]
[7,4,3,5,2,1,6,8]=>[1,1,2,1,3]
[7,3,4,5,2,1,6,8]=>[1,3,1,3]
[7,5,4,2,3,1,6,8]=>[1,1,1,2,3]
[7,4,5,2,3,1,6,8]=>[1,2,2,3]
[7,5,3,2,4,1,6,8]=>[1,1,1,2,3]
[7,5,2,3,4,1,6,8]=>[1,1,3,3]
[7,4,3,2,5,1,6,8]=>[1,1,1,2,3]
[7,4,2,3,5,1,6,8]=>[1,1,3,3]
[7,2,3,4,5,1,6,8]=>[1,4,3]
[7,4,5,3,1,2,6,8]=>[1,2,1,4]
[7,5,3,4,1,2,6,8]=>[1,1,2,4]
[7,4,3,5,1,2,6,8]=>[1,1,2,4]
[7,3,4,5,1,2,6,8]=>[1,3,4]
[7,4,5,2,1,3,6,8]=>[1,2,1,4]
[7,5,4,1,2,3,6,8]=>[1,1,1,5]
[7,4,5,1,2,3,6,8]=>[1,2,5]
[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]
[7,5,2,3,1,4,6,8]=>[1,1,2,4]
[7,5,3,1,2,4,6,8]=>[1,1,1,5]
[7,5,2,1,3,4,6,8]=>[1,1,1,5]
[7,5,1,2,3,4,6,8]=>[1,1,6]
[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]
[7,3,4,2,1,5,6,8]=>[1,2,1,4]
[7,4,2,3,1,5,6,8]=>[1,1,2,4]
[7,3,2,4,1,5,6,8]=>[1,1,2,4]
[7,2,3,4,1,5,6,8]=>[1,3,4]
[7,4,3,1,2,5,6,8]=>[1,1,1,5]
[7,3,4,1,2,5,6,8]=>[1,2,5]
[7,4,1,2,3,5,6,8]=>[1,1,6]
[7,3,2,1,4,5,6,8]=>[1,1,1,5]
[7,2,3,1,4,5,6,8]=>[1,2,5]
[7,3,1,2,4,5,6,8]=>[1,1,6]
[7,2,1,3,4,5,6,8]=>[1,1,6]
[7,1,2,3,4,5,6,8]=>[1,7]
[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[5,6,4,3,2,1,7,8]=>[2,1,1,1,3]
[6,4,5,3,2,1,7,8]=>[1,2,1,1,3]
[5,4,6,3,2,1,7,8]=>[1,2,1,1,3]
[4,5,6,3,2,1,7,8]=>[3,1,1,3]
[6,5,3,4,2,1,7,8]=>[1,1,2,1,3]
[5,6,3,4,2,1,7,8]=>[2,2,1,3]
[6,4,3,5,2,1,7,8]=>[1,1,2,1,3]
[6,3,4,5,2,1,7,8]=>[1,3,1,3]
[5,4,3,6,2,1,7,8]=>[1,1,2,1,3]
[4,5,3,6,2,1,7,8]=>[2,2,1,3]
[4,3,5,6,2,1,7,8]=>[1,3,1,3]
[3,4,5,6,2,1,7,8]=>[4,1,3]
[6,5,4,2,3,1,7,8]=>[1,1,1,2,3]
[5,6,4,2,3,1,7,8]=>[2,1,2,3]
[6,4,5,2,3,1,7,8]=>[1,2,2,3]
[5,4,6,2,3,1,7,8]=>[1,2,2,3]
[4,5,6,2,3,1,7,8]=>[3,2,3]
[6,5,3,2,4,1,7,8]=>[1,1,1,2,3]
[5,6,3,2,4,1,7,8]=>[2,1,2,3]
[6,5,2,3,4,1,7,8]=>[1,1,3,3]
[5,6,2,3,4,1,7,8]=>[2,3,3]
[6,4,3,2,5,1,7,8]=>[1,1,1,2,3]
[6,3,4,2,5,1,7,8]=>[1,2,2,3]
[6,4,2,3,5,1,7,8]=>[1,1,3,3]
[6,3,2,4,5,1,7,8]=>[1,1,3,3]
[6,2,3,4,5,1,7,8]=>[1,4,3]
[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]
[4,5,3,2,6,1,7,8]=>[2,1,2,3]
[4,3,5,2,6,1,7,8]=>[1,2,2,3]
[3,4,5,2,6,1,7,8]=>[3,2,3]
[5,4,2,3,6,1,7,8]=>[1,1,3,3]
[5,3,2,4,6,1,7,8]=>[1,1,3,3]
[5,2,3,4,6,1,7,8]=>[1,4,3]
[4,3,2,5,6,1,7,8]=>[1,1,3,3]
[3,4,2,5,6,1,7,8]=>[2,3,3]
[4,2,3,5,6,1,7,8]=>[1,4,3]
[3,2,4,5,6,1,7,8]=>[1,4,3]
[2,3,4,5,6,1,7,8]=>[5,3]
[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]
[5,6,4,3,1,2,7,8]=>[2,1,1,4]
[6,4,5,3,1,2,7,8]=>[1,2,1,4]
[5,4,6,3,1,2,7,8]=>[1,2,1,4]
[4,5,6,3,1,2,7,8]=>[3,1,4]
[6,5,3,4,1,2,7,8]=>[1,1,2,4]
[5,6,3,4,1,2,7,8]=>[2,2,4]
[6,4,3,5,1,2,7,8]=>[1,1,2,4]
[5,4,3,6,1,2,7,8]=>[1,1,2,4]
[4,5,3,6,1,2,7,8]=>[2,2,4]
[5,3,4,6,1,2,7,8]=>[1,3,4]
[3,4,5,6,1,2,7,8]=>[4,4]
[6,5,4,2,1,3,7,8]=>[1,1,1,1,4]
[5,6,4,2,1,3,7,8]=>[2,1,1,4]
[6,4,5,2,1,3,7,8]=>[1,2,1,4]
[5,4,6,2,1,3,7,8]=>[1,2,1,4]
[4,5,6,2,1,3,7,8]=>[3,1,4]
[6,5,4,1,2,3,7,8]=>[1,1,1,5]
[6,4,5,1,2,3,7,8]=>[1,2,5]
[4,5,6,1,2,3,7,8]=>[3,5]
[6,5,3,2,1,4,7,8]=>[1,1,1,1,4]
[5,6,3,2,1,4,7,8]=>[2,1,1,4]
[6,5,2,3,1,4,7,8]=>[1,1,2,4]
[5,6,2,3,1,4,7,8]=>[2,2,4]
[5,6,3,1,2,4,7,8]=>[2,1,5]
[6,5,2,1,3,4,7,8]=>[1,1,1,5]
[6,5,1,2,3,4,7,8]=>[1,1,6]
[5,6,1,2,3,4,7,8]=>[2,6]
[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]
[6,3,4,2,1,5,7,8]=>[1,2,1,4]
[6,3,2,4,1,5,7,8]=>[1,1,2,4]
[6,2,3,4,1,5,7,8]=>[1,3,4]
[6,4,3,1,2,5,7,8]=>[1,1,1,5]
[6,4,2,1,3,5,7,8]=>[1,1,1,5]
[6,4,1,2,3,5,7,8]=>[1,1,6]
[6,3,2,1,4,5,7,8]=>[1,1,1,5]
[6,2,3,1,4,5,7,8]=>[1,2,5]
[6,3,1,2,4,5,7,8]=>[1,1,6]
[6,2,1,3,4,5,7,8]=>[1,1,6]
[6,1,2,3,4,5,7,8]=>[1,7]
[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[4,5,3,2,1,6,7,8]=>[2,1,1,4]
[5,3,4,2,1,6,7,8]=>[1,2,1,4]
[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[3,4,5,2,1,6,7,8]=>[3,1,4]
[5,4,2,3,1,6,7,8]=>[1,1,2,4]
[4,5,2,3,1,6,7,8]=>[2,2,4]
[5,3,2,4,1,6,7,8]=>[1,1,2,4]
[5,2,3,4,1,6,7,8]=>[1,3,4]
[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[3,4,2,5,1,6,7,8]=>[2,2,4]
[4,2,3,5,1,6,7,8]=>[1,3,4]
[3,2,4,5,1,6,7,8]=>[1,3,4]
[2,3,4,5,1,6,7,8]=>[4,4]
[5,4,3,1,2,6,7,8]=>[1,1,1,5]
[4,5,3,1,2,6,7,8]=>[2,1,5]
[5,3,4,1,2,6,7,8]=>[1,2,5]
[3,4,5,1,2,6,7,8]=>[3,5]
[5,4,2,1,3,6,7,8]=>[1,1,1,5]
[5,4,1,2,3,6,7,8]=>[1,1,6]
[4,5,1,2,3,6,7,8]=>[2,6]
[5,3,2,1,4,6,7,8]=>[1,1,1,5]
[5,2,3,1,4,6,7,8]=>[1,2,5]
[5,3,1,2,4,6,7,8]=>[1,1,6]
[5,2,1,3,4,6,7,8]=>[1,1,6]
[5,1,2,3,4,6,7,8]=>[1,7]
[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[3,4,2,1,5,6,7,8]=>[2,1,5]
[4,2,3,1,5,6,7,8]=>[1,2,5]
[3,2,4,1,5,6,7,8]=>[1,2,5]
[2,3,4,1,5,6,7,8]=>[3,5]
[4,3,1,2,5,6,7,8]=>[1,1,6]
[3,4,1,2,5,6,7,8]=>[2,6]
[4,2,1,3,5,6,7,8]=>[1,1,6]
[4,1,2,3,5,6,7,8]=>[1,7]
[3,2,1,4,5,6,7,8]=>[1,1,6]
[2,3,1,4,5,6,7,8]=>[2,6]
[3,1,2,4,5,6,7,8]=>[1,7]
[2,1,3,4,5,6,7,8]=>[1,7]
[1,2,3,4,5,6,7,8]=>[8]
[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]
[6,5,8,7,4,3,2,1]=>[1,2,1,1,1,1,1]
[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]
[5,7,6,8,4,3,2,1]=>[2,2,1,1,1,1]
[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[4,7,8,6,5,3,2,1]=>[3,1,1,1,1,1]
[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]
[4,7,6,8,5,3,2,1]=>[2,2,1,1,1,1]
[4,6,7,8,5,3,2,1]=>[4,1,1,1,1]
[5,4,8,7,6,3,2,1]=>[1,2,1,1,1,1,1]
[5,4,7,8,6,3,2,1]=>[1,3,1,1,1,1]
[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]
[4,5,7,8,6,3,2,1]=>[4,1,1,1,1]
[6,5,4,8,7,3,2,1]=>[1,1,2,1,1,1,1]
[5,6,4,8,7,3,2,1]=>[2,2,1,1,1,1]
[4,6,5,8,7,3,2,1]=>[2,2,1,1,1,1]
[5,4,6,8,7,3,2,1]=>[1,3,1,1,1,1]
[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
[5,7,6,4,8,3,2,1]=>[2,1,2,1,1,1]
[4,7,6,5,8,3,2,1]=>[2,1,2,1,1,1]
[4,6,7,5,8,3,2,1]=>[3,2,1,1,1]
[5,4,7,6,8,3,2,1]=>[1,2,2,1,1,1]
[4,5,7,6,8,3,2,1]=>[3,2,1,1,1]
[4,6,5,7,8,3,2,1]=>[2,3,1,1,1]
[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[3,7,8,6,5,4,2,1]=>[3,1,1,1,1,1]
[3,6,8,7,5,4,2,1]=>[3,1,1,1,1,1]
[3,7,6,8,5,4,2,1]=>[2,2,1,1,1,1]
[3,6,7,8,5,4,2,1]=>[4,1,1,1,1]
[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]
[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]
[3,6,5,8,7,4,2,1]=>[2,2,1,1,1,1]
[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[3,7,6,5,8,4,2,1]=>[2,1,2,1,1,1]
[3,6,7,5,8,4,2,1]=>[3,2,1,1,1]
[3,5,7,6,8,4,2,1]=>[3,2,1,1,1]
[3,6,5,7,8,4,2,1]=>[2,3,1,1,1]
[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]
[4,3,7,8,6,5,2,1]=>[1,3,1,1,1,1]
[4,3,6,8,7,5,2,1]=>[1,3,1,1,1,1]
[4,3,7,6,8,5,2,1]=>[1,2,2,1,1,1]
[4,3,6,7,8,5,2,1]=>[1,4,1,1,1]
[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[3,4,7,8,6,5,2,1]=>[4,1,1,1,1]
[3,4,6,8,7,5,2,1]=>[4,1,1,1,1]
[3,4,7,6,8,5,2,1]=>[3,2,1,1,1]
[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]
[5,4,3,7,8,6,2,1]=>[1,1,3,1,1,1]
[4,5,3,8,7,6,2,1]=>[2,2,1,1,1,1]
[4,5,3,7,8,6,2,1]=>[2,3,1,1,1]
[3,5,4,8,7,6,2,1]=>[2,2,1,1,1,1]
[3,5,4,7,8,6,2,1]=>[2,3,1,1,1]
[4,3,5,8,7,6,2,1]=>[1,3,1,1,1,1]
[4,3,5,7,8,6,2,1]=>[1,4,1,1,1]
[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[3,4,5,7,8,6,2,1]=>[5,1,1,1]
[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]
[5,6,4,3,8,7,2,1]=>[2,1,2,1,1,1]
[4,6,5,3,8,7,2,1]=>[2,1,2,1,1,1]
[5,4,6,3,8,7,2,1]=>[1,2,2,1,1,1]
[4,5,6,3,8,7,2,1]=>[3,2,1,1,1]
[3,6,5,4,8,7,2,1]=>[2,1,2,1,1,1]
[3,5,6,4,8,7,2,1]=>[3,2,1,1,1]
[4,3,6,5,8,7,2,1]=>[1,2,2,1,1,1]
[3,4,6,5,8,7,2,1]=>[3,2,1,1,1]
[5,4,3,6,8,7,2,1]=>[1,1,3,1,1,1]
[4,5,3,6,8,7,2,1]=>[2,3,1,1,1]
[3,5,4,6,8,7,2,1]=>[2,3,1,1,1]
[4,3,5,6,8,7,2,1]=>[1,4,1,1,1]
[3,4,5,6,8,7,2,1]=>[5,1,1,1]
[5,7,6,4,3,8,2,1]=>[2,1,1,2,1,1]
[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]
[4,6,7,5,3,8,2,1]=>[3,1,2,1,1]
[5,4,7,6,3,8,2,1]=>[1,2,1,2,1,1]
[4,5,7,6,3,8,2,1]=>[3,1,2,1,1]
[4,6,5,7,3,8,2,1]=>[2,2,2,1,1]
[3,7,6,5,4,8,2,1]=>[2,1,1,2,1,1]
[3,6,7,5,4,8,2,1]=>[3,1,2,1,1]
[3,5,7,6,4,8,2,1]=>[3,1,2,1,1]
[3,6,5,7,4,8,2,1]=>[2,2,2,1,1]
[3,5,6,7,4,8,2,1]=>[4,2,1,1]
[4,3,7,6,5,8,2,1]=>[1,2,1,2,1,1]
[4,3,6,7,5,8,2,1]=>[1,3,2,1,1]
[3,4,7,6,5,8,2,1]=>[3,1,2,1,1]
[3,4,6,7,5,8,2,1]=>[4,2,1,1]
[5,4,3,7,6,8,2,1]=>[1,1,2,2,1,1]
[4,5,3,7,6,8,2,1]=>[2,2,2,1,1]
[3,5,4,7,6,8,2,1]=>[2,2,2,1,1]
[4,3,5,7,6,8,2,1]=>[1,3,2,1,1]
[3,4,5,7,6,8,2,1]=>[4,2,1,1]
[4,6,5,3,7,8,2,1]=>[2,1,3,1,1]
[3,6,5,4,7,8,2,1]=>[2,1,3,1,1]
[3,5,6,4,7,8,2,1]=>[3,3,1,1]
[4,3,6,5,7,8,2,1]=>[1,2,3,1,1]
[3,4,6,5,7,8,2,1]=>[3,3,1,1]
[3,5,4,6,7,8,2,1]=>[2,4,1,1]
[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[2,7,8,6,5,4,3,1]=>[3,1,1,1,1,1]
[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]
[2,7,6,8,5,4,3,1]=>[2,2,1,1,1,1]
[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[2,5,8,7,6,4,3,1]=>[3,1,1,1,1,1]
[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]
[2,6,5,8,7,4,3,1]=>[2,2,1,1,1,1]
[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]
[2,7,6,5,8,4,3,1]=>[2,1,2,1,1,1]
[2,6,7,5,8,4,3,1]=>[3,2,1,1,1]
[2,5,7,6,8,4,3,1]=>[3,2,1,1,1]
[2,6,5,7,8,4,3,1]=>[2,3,1,1,1]
[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]
[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[2,5,4,8,7,6,3,1]=>[2,2,1,1,1,1]
[2,5,4,7,8,6,3,1]=>[2,3,1,1,1]
[2,4,5,7,8,6,3,1]=>[5,1,1,1]
[2,6,5,4,8,7,3,1]=>[2,1,2,1,1,1]
[2,5,6,4,8,7,3,1]=>[3,2,1,1,1]
[2,4,6,5,8,7,3,1]=>[3,2,1,1,1]
[2,4,5,6,8,7,3,1]=>[5,1,1,1]
[2,7,6,5,4,8,3,1]=>[2,1,1,2,1,1]
[2,6,7,5,4,8,3,1]=>[3,1,2,1,1]
[2,5,7,6,4,8,3,1]=>[3,1,2,1,1]
[2,6,5,7,4,8,3,1]=>[2,2,2,1,1]
[2,5,6,7,4,8,3,1]=>[4,2,1,1]
[2,4,7,6,5,8,3,1]=>[3,1,2,1,1]
[2,4,6,7,5,8,3,1]=>[4,2,1,1]
[2,5,4,7,6,8,3,1]=>[2,2,2,1,1]
[2,6,5,4,7,8,3,1]=>[2,1,3,1,1]
[2,5,6,4,7,8,3,1]=>[3,3,1,1]
[2,4,6,5,7,8,3,1]=>[3,3,1,1]
[2,5,4,6,7,8,3,1]=>[2,4,1,1]
[2,4,5,6,7,8,3,1]=>[6,1,1]
[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]
[3,2,7,8,6,5,4,1]=>[1,3,1,1,1,1]
[3,2,6,8,7,5,4,1]=>[1,3,1,1,1,1]
[3,2,7,6,8,5,4,1]=>[1,2,2,1,1,1]
[3,2,5,8,7,6,4,1]=>[1,3,1,1,1,1]
[3,2,5,7,8,6,4,1]=>[1,4,1,1,1]
[3,2,6,5,8,7,4,1]=>[1,2,2,1,1,1]
[3,2,5,6,8,7,4,1]=>[1,4,1,1,1]
[3,2,7,6,5,8,4,1]=>[1,2,1,2,1,1]
[3,2,6,7,5,8,4,1]=>[1,3,2,1,1]
[3,2,5,7,6,8,4,1]=>[1,3,2,1,1]
[3,2,6,5,7,8,4,1]=>[1,2,3,1,1]
[3,2,5,6,7,8,4,1]=>[1,5,1,1]
[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[2,3,7,8,6,5,4,1]=>[4,1,1,1,1]
[2,3,6,8,7,5,4,1]=>[4,1,1,1,1]
[2,3,7,6,8,5,4,1]=>[3,2,1,1,1]
[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[2,3,6,5,8,7,4,1]=>[3,2,1,1,1]
[2,3,5,6,8,7,4,1]=>[5,1,1,1]
[2,3,7,6,5,8,4,1]=>[3,1,2,1,1]
[2,3,6,7,5,8,4,1]=>[4,2,1,1]
[2,3,5,7,6,8,4,1]=>[4,2,1,1]
[2,3,6,5,7,8,4,1]=>[3,3,1,1]
[2,3,5,6,7,8,4,1]=>[6,1,1]
[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]
[4,3,2,7,8,6,5,1]=>[1,1,3,1,1,1]
[4,3,2,6,8,7,5,1]=>[1,1,3,1,1,1]
[4,3,2,6,7,8,5,1]=>[1,1,4,1,1]
[3,4,2,8,7,6,5,1]=>[2,2,1,1,1,1]
[3,4,2,7,8,6,5,1]=>[2,3,1,1,1]
[3,4,2,6,8,7,5,1]=>[2,3,1,1,1]
[3,4,2,7,6,8,5,1]=>[2,2,2,1,1]
[3,4,2,6,7,8,5,1]=>[2,4,1,1]
[2,4,3,8,7,6,5,1]=>[2,2,1,1,1,1]
[2,4,3,7,8,6,5,1]=>[2,3,1,1,1]
[2,4,3,6,8,7,5,1]=>[2,3,1,1,1]
[2,4,3,7,6,8,5,1]=>[2,2,2,1,1]
[2,4,3,6,7,8,5,1]=>[2,4,1,1]
[3,2,4,8,7,6,5,1]=>[1,3,1,1,1,1]
[3,2,4,7,8,6,5,1]=>[1,4,1,1,1]
[3,2,4,7,6,8,5,1]=>[1,3,2,1,1]
[3,2,4,6,7,8,5,1]=>[1,5,1,1]
[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[2,3,4,7,8,6,5,1]=>[5,1,1,1]
[2,3,4,6,8,7,5,1]=>[5,1,1,1]
[2,3,4,7,6,8,5,1]=>[4,2,1,1]
[2,3,4,6,7,8,5,1]=>[6,1,1]
[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]
[5,4,3,2,7,8,6,1]=>[1,1,1,3,1,1]
[4,5,3,2,8,7,6,1]=>[2,1,2,1,1,1]
[4,5,3,2,7,8,6,1]=>[2,1,3,1,1]
[3,5,4,2,7,8,6,1]=>[2,1,3,1,1]
[3,4,5,2,8,7,6,1]=>[3,2,1,1,1]
[3,4,5,2,7,8,6,1]=>[3,3,1,1]
[2,5,4,3,8,7,6,1]=>[2,1,2,1,1,1]
[2,5,4,3,7,8,6,1]=>[2,1,3,1,1]
[2,4,5,3,8,7,6,1]=>[3,2,1,1,1]
[2,4,5,3,7,8,6,1]=>[3,3,1,1]
[3,2,5,4,7,8,6,1]=>[1,2,3,1,1]
[2,3,5,4,8,7,6,1]=>[3,2,1,1,1]
[2,3,5,4,7,8,6,1]=>[3,3,1,1]
[4,3,2,5,8,7,6,1]=>[1,1,3,1,1,1]
[4,3,2,5,7,8,6,1]=>[1,1,4,1,1]
[3,4,2,5,8,7,6,1]=>[2,3,1,1,1]
[3,4,2,5,7,8,6,1]=>[2,4,1,1]
[2,4,3,5,8,7,6,1]=>[2,3,1,1,1]
[2,4,3,5,7,8,6,1]=>[2,4,1,1]
[3,2,4,5,7,8,6,1]=>[1,5,1,1]
[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[2,3,4,5,7,8,6,1]=>[6,1,1]
[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]
[5,6,4,3,2,8,7,1]=>[2,1,1,2,1,1]
[4,6,5,3,2,8,7,1]=>[2,1,1,2,1,1]
[5,4,6,3,2,8,7,1]=>[1,2,1,2,1,1]
[4,5,6,3,2,8,7,1]=>[3,1,2,1,1]
[3,6,5,4,2,8,7,1]=>[2,1,1,2,1,1]
[3,5,6,4,2,8,7,1]=>[3,1,2,1,1]
[4,3,6,5,2,8,7,1]=>[1,2,1,2,1,1]
[5,4,3,6,2,8,7,1]=>[1,1,2,2,1,1]
[4,5,3,6,2,8,7,1]=>[2,2,2,1,1]
[3,5,4,6,2,8,7,1]=>[2,2,2,1,1]
[3,4,5,6,2,8,7,1]=>[4,2,1,1]
[2,6,5,4,3,8,7,1]=>[2,1,1,2,1,1]
[2,4,6,5,3,8,7,1]=>[3,1,2,1,1]
[2,4,5,6,3,8,7,1]=>[4,2,1,1]
[3,2,6,5,4,8,7,1]=>[1,2,1,2,1,1]
[2,3,5,6,4,8,7,1]=>[4,2,1,1]
[4,3,2,6,5,8,7,1]=>[1,1,2,2,1,1]
[3,4,2,6,5,8,7,1]=>[2,2,2,1,1]
[2,4,3,6,5,8,7,1]=>[2,2,2,1,1]
[3,2,4,6,5,8,7,1]=>[1,3,2,1,1]
[2,3,4,6,5,8,7,1]=>[4,2,1,1]
[5,4,3,2,6,8,7,1]=>[1,1,1,3,1,1]
[4,5,3,2,6,8,7,1]=>[2,1,3,1,1]
[3,5,4,2,6,8,7,1]=>[2,1,3,1,1]
[4,3,5,2,6,8,7,1]=>[1,2,3,1,1]
[3,4,5,2,6,8,7,1]=>[3,3,1,1]
[2,5,4,3,6,8,7,1]=>[2,1,3,1,1]
[2,4,5,3,6,8,7,1]=>[3,3,1,1]
[3,2,5,4,6,8,7,1]=>[1,2,3,1,1]
[4,3,2,5,6,8,7,1]=>[1,1,4,1,1]
[3,4,2,5,6,8,7,1]=>[2,4,1,1]
[2,4,3,5,6,8,7,1]=>[2,4,1,1]
[3,2,4,5,6,8,7,1]=>[1,5,1,1]
[2,3,4,5,6,8,7,1]=>[6,1,1]
[5,7,6,4,3,2,8,1]=>[2,1,1,1,2,1]
[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]
[4,6,7,5,3,2,8,1]=>[3,1,1,2,1]
[5,4,7,6,3,2,8,1]=>[1,2,1,1,2,1]
[4,5,7,6,3,2,8,1]=>[3,1,1,2,1]
[4,6,5,7,3,2,8,1]=>[2,2,1,2,1]
[3,7,6,5,4,2,8,1]=>[2,1,1,1,2,1]
[3,6,7,5,4,2,8,1]=>[3,1,1,2,1]
[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]
[3,6,5,7,4,2,8,1]=>[2,2,1,2,1]
[3,5,6,7,4,2,8,1]=>[4,1,2,1]
[4,3,7,6,5,2,8,1]=>[1,2,1,1,2,1]
[4,3,6,7,5,2,8,1]=>[1,3,1,2,1]
[3,4,7,6,5,2,8,1]=>[3,1,1,2,1]
[3,4,6,7,5,2,8,1]=>[4,1,2,1]
[5,4,3,7,6,2,8,1]=>[1,1,2,1,2,1]
[4,5,3,7,6,2,8,1]=>[2,2,1,2,1]
[3,5,4,7,6,2,8,1]=>[2,2,1,2,1]
[4,3,5,7,6,2,8,1]=>[1,3,1,2,1]
[3,4,5,7,6,2,8,1]=>[4,1,2,1]
[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]
[3,6,5,4,7,2,8,1]=>[2,1,2,2,1]
[3,5,6,4,7,2,8,1]=>[3,2,2,1]
[4,3,6,5,7,2,8,1]=>[1,2,2,2,1]
[3,4,6,5,7,2,8,1]=>[3,2,2,1]
[3,5,4,6,7,2,8,1]=>[2,3,2,1]
[2,7,6,5,4,3,8,1]=>[2,1,1,1,2,1]
[2,5,7,6,4,3,8,1]=>[3,1,1,2,1]
[2,6,5,7,4,3,8,1]=>[2,2,1,2,1]
[2,5,6,7,4,3,8,1]=>[4,1,2,1]
[2,4,7,6,5,3,8,1]=>[3,1,1,2,1]
[2,4,6,7,5,3,8,1]=>[4,1,2,1]
[2,5,4,7,6,3,8,1]=>[2,2,1,2,1]
[2,4,5,7,6,3,8,1]=>[4,1,2,1]
[2,5,6,4,7,3,8,1]=>[3,2,2,1]
[2,4,6,5,7,3,8,1]=>[3,2,2,1]
[2,5,4,6,7,3,8,1]=>[2,3,2,1]
[2,4,5,6,7,3,8,1]=>[5,2,1]
[3,2,7,6,5,4,8,1]=>[1,2,1,1,2,1]
[3,2,6,7,5,4,8,1]=>[1,3,1,2,1]
[3,2,5,7,6,4,8,1]=>[1,3,1,2,1]
[3,2,6,5,7,4,8,1]=>[1,2,2,2,1]
[3,2,5,6,7,4,8,1]=>[1,4,2,1]
[2,3,7,6,5,4,8,1]=>[3,1,1,2,1]
[2,3,6,7,5,4,8,1]=>[4,1,2,1]
[2,3,5,7,6,4,8,1]=>[4,1,2,1]
[2,3,5,6,7,4,8,1]=>[5,2,1]
[4,3,2,7,6,5,8,1]=>[1,1,2,1,2,1]
[4,3,2,6,7,5,8,1]=>[1,1,3,2,1]
[3,4,2,7,6,5,8,1]=>[2,2,1,2,1]
[3,4,2,6,7,5,8,1]=>[2,3,2,1]
[2,4,3,7,6,5,8,1]=>[2,2,1,2,1]
[2,4,3,6,7,5,8,1]=>[2,3,2,1]
[3,2,4,7,6,5,8,1]=>[1,3,1,2,1]
[3,2,4,6,7,5,8,1]=>[1,4,2,1]
[2,3,4,7,6,5,8,1]=>[4,1,2,1]
[2,3,4,6,7,5,8,1]=>[5,2,1]
[5,4,3,2,7,6,8,1]=>[1,1,1,2,2,1]
[4,5,3,2,7,6,8,1]=>[2,1,2,2,1]
[3,5,4,2,7,6,8,1]=>[2,1,2,2,1]
[4,3,5,2,7,6,8,1]=>[1,2,2,2,1]
[3,4,5,2,7,6,8,1]=>[3,2,2,1]
[2,5,4,3,7,6,8,1]=>[2,1,2,2,1]
[2,4,5,3,7,6,8,1]=>[3,2,2,1]
[3,2,5,4,7,6,8,1]=>[1,2,2,2,1]
[2,3,5,4,7,6,8,1]=>[3,2,2,1]
[4,3,2,5,7,6,8,1]=>[1,1,3,2,1]
[3,4,2,5,7,6,8,1]=>[2,3,2,1]
[2,4,3,5,7,6,8,1]=>[2,3,2,1]
[3,2,4,5,7,6,8,1]=>[1,4,2,1]
[2,3,4,5,7,6,8,1]=>[5,2,1]
[4,6,5,3,2,7,8,1]=>[2,1,1,3,1]
[3,6,5,4,2,7,8,1]=>[2,1,1,3,1]
[3,5,6,4,2,7,8,1]=>[3,1,3,1]
[4,3,6,5,2,7,8,1]=>[1,2,1,3,1]
[3,4,6,5,2,7,8,1]=>[3,1,3,1]
[3,5,4,6,2,7,8,1]=>[2,2,3,1]
[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]
[2,5,6,4,3,7,8,1]=>[3,1,3,1]
[2,4,6,5,3,7,8,1]=>[3,1,3,1]
[2,5,4,6,3,7,8,1]=>[2,2,3,1]
[2,4,5,6,3,7,8,1]=>[4,3,1]
[3,2,5,6,4,7,8,1]=>[1,3,3,1]
[2,3,6,5,4,7,8,1]=>[3,1,3,1]
[2,3,5,6,4,7,8,1]=>[4,3,1]
[4,3,2,6,5,7,8,1]=>[1,1,2,3,1]
[3,4,2,6,5,7,8,1]=>[2,2,3,1]
[2,4,3,6,5,7,8,1]=>[2,2,3,1]
[2,3,4,6,5,7,8,1]=>[4,3,1]
[3,5,4,2,6,7,8,1]=>[2,1,4,1]
[2,5,4,3,6,7,8,1]=>[2,1,4,1]
[2,4,5,3,6,7,8,1]=>[3,4,1]
[3,2,5,4,6,7,8,1]=>[1,2,4,1]
[2,3,5,4,6,7,8,1]=>[3,4,1]
[2,4,3,5,6,7,8,1]=>[2,5,1]
[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[1,7,6,8,5,4,3,2]=>[2,2,1,1,1,1]
[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]
[1,6,5,8,7,4,3,2]=>[2,2,1,1,1,1]
[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]
[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]
[1,5,7,6,8,4,3,2]=>[3,2,1,1,1]
[1,6,5,7,8,4,3,2]=>[2,3,1,1,1]
[1,5,6,7,8,4,3,2]=>[5,1,1,1]
[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]
[1,4,7,6,8,5,3,2]=>[3,2,1,1,1]
[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[1,5,4,8,7,6,3,2]=>[2,2,1,1,1,1]
[1,5,4,7,8,6,3,2]=>[2,3,1,1,1]
[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]
[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[1,6,5,4,8,7,3,2]=>[2,1,2,1,1,1]
[1,4,6,5,8,7,3,2]=>[3,2,1,1,1]
[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]
[1,6,5,7,4,8,3,2]=>[2,2,2,1,1]
[1,5,6,7,4,8,3,2]=>[4,2,1,1]
[1,4,7,6,5,8,3,2]=>[3,1,2,1,1]
[1,4,6,7,5,8,3,2]=>[4,2,1,1]
[1,5,4,7,6,8,3,2]=>[2,2,2,1,1]
[1,4,5,7,6,8,3,2]=>[4,2,1,1]
[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]
[1,5,6,4,7,8,3,2]=>[3,3,1,1]
[1,5,4,6,7,8,3,2]=>[2,4,1,1]
[1,4,5,6,7,8,3,2]=>[6,1,1]
[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[1,3,7,8,6,5,4,2]=>[4,1,1,1,1]
[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]
[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]
[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[1,3,6,5,8,7,4,2]=>[3,2,1,1,1]
[1,3,5,6,8,7,4,2]=>[5,1,1,1]
[1,3,7,6,5,8,4,2]=>[3,1,2,1,1]
[1,3,6,7,5,8,4,2]=>[4,2,1,1]
[1,3,5,7,6,8,4,2]=>[4,2,1,1]
[1,3,6,5,7,8,4,2]=>[3,3,1,1]
[1,3,5,6,7,8,4,2]=>[6,1,1]
[1,4,3,8,7,6,5,2]=>[2,2,1,1,1,1]
[1,4,3,7,8,6,5,2]=>[2,3,1,1,1]
[1,4,3,6,8,7,5,2]=>[2,3,1,1,1]
[1,4,3,7,6,8,5,2]=>[2,2,2,1,1]
[1,4,3,6,7,8,5,2]=>[2,4,1,1]
[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[1,3,4,7,8,6,5,2]=>[5,1,1,1]
[1,3,4,6,8,7,5,2]=>[5,1,1,1]
[1,3,4,7,6,8,5,2]=>[4,2,1,1]
[1,3,4,6,7,8,5,2]=>[6,1,1]
[1,5,4,3,8,7,6,2]=>[2,1,2,1,1,1]
[1,5,4,3,7,8,6,2]=>[2,1,3,1,1]
[1,4,5,3,8,7,6,2]=>[3,2,1,1,1]
[1,4,5,3,7,8,6,2]=>[3,3,1,1]
[1,3,5,4,8,7,6,2]=>[3,2,1,1,1]
[1,3,5,4,7,8,6,2]=>[3,3,1,1]
[1,4,3,5,8,7,6,2]=>[2,3,1,1,1]
[1,4,3,5,7,8,6,2]=>[2,4,1,1]
[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[1,3,4,5,7,8,6,2]=>[6,1,1]
[1,6,5,4,3,8,7,2]=>[2,1,1,2,1,1]
[1,5,6,4,3,8,7,2]=>[3,1,2,1,1]
[1,4,6,5,3,8,7,2]=>[3,1,2,1,1]
[1,5,4,6,3,8,7,2]=>[2,2,2,1,1]
[1,4,5,6,3,8,7,2]=>[4,2,1,1]
[1,3,6,5,4,8,7,2]=>[3,1,2,1,1]
[1,3,5,6,4,8,7,2]=>[4,2,1,1]
[1,4,3,6,5,8,7,2]=>[2,2,2,1,1]
[1,3,4,6,5,8,7,2]=>[4,2,1,1]
[1,5,4,3,6,8,7,2]=>[2,1,3,1,1]
[1,4,5,3,6,8,7,2]=>[3,3,1,1]
[1,3,5,4,6,8,7,2]=>[3,3,1,1]
[1,4,3,5,6,8,7,2]=>[2,4,1,1]
[1,3,4,5,6,8,7,2]=>[6,1,1]
[1,7,6,5,4,3,8,2]=>[2,1,1,1,2,1]
[1,6,7,5,4,3,8,2]=>[3,1,1,2,1]
[1,5,7,6,4,3,8,2]=>[3,1,1,2,1]
[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]
[1,5,6,7,4,3,8,2]=>[4,1,2,1]
[1,4,7,6,5,3,8,2]=>[3,1,1,2,1]
[1,4,6,7,5,3,8,2]=>[4,1,2,1]
[1,5,4,7,6,3,8,2]=>[2,2,1,2,1]
[1,4,5,7,6,3,8,2]=>[4,1,2,1]
[1,6,5,4,7,3,8,2]=>[2,1,2,2,1]
[1,5,6,4,7,3,8,2]=>[3,2,2,1]
[1,4,6,5,7,3,8,2]=>[3,2,2,1]
[1,5,4,6,7,3,8,2]=>[2,3,2,1]
[1,4,5,6,7,3,8,2]=>[5,2,1]
[1,3,5,7,6,4,8,2]=>[4,1,2,1]
[1,3,6,5,7,4,8,2]=>[3,2,2,1]
[1,3,5,6,7,4,8,2]=>[5,2,1]
[1,4,3,6,7,5,8,2]=>[2,3,2,1]
[1,3,4,7,6,5,8,2]=>[4,1,2,1]
[1,3,4,6,7,5,8,2]=>[5,2,1]
[1,5,4,3,7,6,8,2]=>[2,1,2,2,1]
[1,3,5,4,7,6,8,2]=>[3,2,2,1]
[1,4,3,5,7,6,8,2]=>[2,3,2,1]
[1,3,4,5,7,6,8,2]=>[5,2,1]
[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]
[1,4,6,5,3,7,8,2]=>[3,1,3,1]
[1,5,4,6,3,7,8,2]=>[2,2,3,1]
[1,4,5,6,3,7,8,2]=>[4,3,1]
[1,3,5,6,4,7,8,2]=>[4,3,1]
[1,4,3,6,5,7,8,2]=>[2,2,3,1]
[1,3,4,6,5,7,8,2]=>[4,3,1]
[1,5,4,3,6,7,8,2]=>[2,1,4,1]
[1,4,5,3,6,7,8,2]=>[3,4,1]
[1,3,5,4,6,7,8,2]=>[3,4,1]
[1,4,3,5,6,7,8,2]=>[2,5,1]
[1,3,4,5,6,7,8,2]=>[7,1]
[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[2,1,7,8,6,5,4,3]=>[1,3,1,1,1,1]
[2,1,6,8,7,5,4,3]=>[1,3,1,1,1,1]
[2,1,7,6,8,5,4,3]=>[1,2,2,1,1,1]
[2,1,6,7,8,5,4,3]=>[1,4,1,1,1]
[2,1,5,8,7,6,4,3]=>[1,3,1,1,1,1]
[2,1,5,7,8,6,4,3]=>[1,4,1,1,1]
[2,1,6,5,8,7,4,3]=>[1,2,2,1,1,1]
[2,1,5,6,8,7,4,3]=>[1,4,1,1,1]
[2,1,7,6,5,8,4,3]=>[1,2,1,2,1,1]
[2,1,6,7,5,8,4,3]=>[1,3,2,1,1]
[2,1,5,7,6,8,4,3]=>[1,3,2,1,1]
[2,1,6,5,7,8,4,3]=>[1,2,3,1,1]
[2,1,5,6,7,8,4,3]=>[1,5,1,1]
[2,1,4,8,7,6,5,3]=>[1,3,1,1,1,1]
[2,1,4,7,8,6,5,3]=>[1,4,1,1,1]
[2,1,4,6,8,7,5,3]=>[1,4,1,1,1]
[2,1,4,7,6,8,5,3]=>[1,3,2,1,1]
[2,1,4,6,7,8,5,3]=>[1,5,1,1]
[2,1,5,4,8,7,6,3]=>[1,2,2,1,1,1]
[2,1,5,4,7,8,6,3]=>[1,2,3,1,1]
[2,1,4,5,8,7,6,3]=>[1,4,1,1,1]
[2,1,4,5,7,8,6,3]=>[1,5,1,1]
[2,1,6,5,4,8,7,3]=>[1,2,1,2,1,1]
[2,1,5,6,4,8,7,3]=>[1,3,2,1,1]
[2,1,4,6,5,8,7,3]=>[1,3,2,1,1]
[2,1,5,4,6,8,7,3]=>[1,2,3,1,1]
[2,1,4,5,6,8,7,3]=>[1,5,1,1]
[2,1,7,6,5,4,8,3]=>[1,2,1,1,2,1]
[2,1,6,7,5,4,8,3]=>[1,3,1,2,1]
[2,1,5,7,6,4,8,3]=>[1,3,1,2,1]
[2,1,6,5,7,4,8,3]=>[1,2,2,2,1]
[2,1,5,6,7,4,8,3]=>[1,4,2,1]
[2,1,4,7,6,5,8,3]=>[1,3,1,2,1]
[2,1,4,6,7,5,8,3]=>[1,4,2,1]
[2,1,5,4,7,6,8,3]=>[1,2,2,2,1]
[2,1,4,5,7,6,8,3]=>[1,4,2,1]
[2,1,6,5,4,7,8,3]=>[1,2,1,3,1]
[2,1,5,6,4,7,8,3]=>[1,3,3,1]
[2,1,4,6,5,7,8,3]=>[1,3,3,1]
[2,1,5,4,6,7,8,3]=>[1,2,4,1]
[2,1,4,5,6,7,8,3]=>[1,6,1]
[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[1,2,7,8,6,5,4,3]=>[4,1,1,1,1]
[1,2,6,8,7,5,4,3]=>[4,1,1,1,1]
[1,2,7,6,8,5,4,3]=>[3,2,1,1,1]
[1,2,6,7,8,5,4,3]=>[5,1,1,1]
[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[1,2,5,7,8,6,4,3]=>[5,1,1,1]
[1,2,6,5,8,7,4,3]=>[3,2,1,1,1]
[1,2,5,6,8,7,4,3]=>[5,1,1,1]
[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]
[1,2,6,7,5,8,4,3]=>[4,2,1,1]
[1,2,5,7,6,8,4,3]=>[4,2,1,1]
[1,2,6,5,7,8,4,3]=>[3,3,1,1]
[1,2,5,6,7,8,4,3]=>[6,1,1]
[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[1,2,4,7,8,6,5,3]=>[5,1,1,1]
[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[1,2,4,7,6,8,5,3]=>[4,2,1,1]
[1,2,4,6,7,8,5,3]=>[6,1,1]
[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]
[1,2,4,5,8,7,6,3]=>[5,1,1,1]
[1,2,4,5,7,8,6,3]=>[6,1,1]
[1,2,6,5,4,8,7,3]=>[3,1,2,1,1]
[1,2,5,6,4,8,7,3]=>[4,2,1,1]
[1,2,4,6,5,8,7,3]=>[4,2,1,1]
[1,2,5,4,6,8,7,3]=>[3,3,1,1]
[1,2,4,5,6,8,7,3]=>[6,1,1]
[1,2,7,6,5,4,8,3]=>[3,1,1,2,1]
[1,2,6,7,5,4,8,3]=>[4,1,2,1]
[1,2,5,7,6,4,8,3]=>[4,1,2,1]
[1,2,6,5,7,4,8,3]=>[3,2,2,1]
[1,2,5,6,7,4,8,3]=>[5,2,1]
[1,2,4,7,6,5,8,3]=>[4,1,2,1]
[1,2,4,6,7,5,8,3]=>[5,2,1]
[1,2,5,4,7,6,8,3]=>[3,2,2,1]
[1,2,6,5,4,7,8,3]=>[3,1,3,1]
[1,2,5,6,4,7,8,3]=>[4,3,1]
[1,2,4,6,5,7,8,3]=>[4,3,1]
[1,2,5,4,6,7,8,3]=>[3,4,1]
[1,2,4,5,6,7,8,3]=>[7,1]
[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[3,2,1,7,8,6,5,4]=>[1,1,3,1,1,1]
[3,2,1,6,8,7,5,4]=>[1,1,3,1,1,1]
[3,2,1,7,6,8,5,4]=>[1,1,2,2,1,1]
[3,2,1,6,7,8,5,4]=>[1,1,4,1,1]
[3,2,1,5,8,7,6,4]=>[1,1,3,1,1,1]
[3,2,1,5,7,8,6,4]=>[1,1,4,1,1]
[3,2,1,6,5,8,7,4]=>[1,1,2,2,1,1]
[3,2,1,5,6,8,7,4]=>[1,1,4,1,1]
[3,2,1,7,6,5,8,4]=>[1,1,2,1,2,1]
[3,2,1,6,7,5,8,4]=>[1,1,3,2,1]
[3,2,1,5,7,6,8,4]=>[1,1,3,2,1]
[3,2,1,6,5,7,8,4]=>[1,1,2,3,1]
[3,2,1,5,6,7,8,4]=>[1,1,5,1]
[2,3,1,8,7,6,5,4]=>[2,2,1,1,1,1]
[2,3,1,7,8,6,5,4]=>[2,3,1,1,1]
[2,3,1,6,8,7,5,4]=>[2,3,1,1,1]
[2,3,1,7,6,8,5,4]=>[2,2,2,1,1]
[2,3,1,6,7,8,5,4]=>[2,4,1,1]
[2,3,1,5,8,7,6,4]=>[2,3,1,1,1]
[2,3,1,5,7,8,6,4]=>[2,4,1,1]
[2,3,1,6,5,8,7,4]=>[2,2,2,1,1]
[2,3,1,5,6,8,7,4]=>[2,4,1,1]
[2,3,1,7,6,5,8,4]=>[2,2,1,2,1]
[2,3,1,6,7,5,8,4]=>[2,3,2,1]
[2,3,1,5,7,6,8,4]=>[2,3,2,1]
[2,3,1,6,5,7,8,4]=>[2,2,3,1]
[2,3,1,5,6,7,8,4]=>[2,5,1]
[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[1,3,2,7,8,6,5,4]=>[2,3,1,1,1]
[1,3,2,6,8,7,5,4]=>[2,3,1,1,1]
[1,3,2,7,6,8,5,4]=>[2,2,2,1,1]
[1,3,2,6,7,8,5,4]=>[2,4,1,1]
[1,3,2,5,8,7,6,4]=>[2,3,1,1,1]
[1,3,2,5,7,8,6,4]=>[2,4,1,1]
[1,3,2,6,5,8,7,4]=>[2,2,2,1,1]
[1,3,2,5,6,8,7,4]=>[2,4,1,1]
[1,3,2,7,6,5,8,4]=>[2,2,1,2,1]
[1,3,2,6,7,5,8,4]=>[2,3,2,1]
[1,3,2,5,7,6,8,4]=>[2,3,2,1]
[1,3,2,6,5,7,8,4]=>[2,2,3,1]
[1,3,2,5,6,7,8,4]=>[2,5,1]
[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[2,1,3,7,8,6,5,4]=>[1,4,1,1,1]
[2,1,3,6,8,7,5,4]=>[1,4,1,1,1]
[2,1,3,7,6,8,5,4]=>[1,3,2,1,1]
[2,1,3,6,7,8,5,4]=>[1,5,1,1]
[2,1,3,5,8,7,6,4]=>[1,4,1,1,1]
[2,1,3,5,7,8,6,4]=>[1,5,1,1]
[2,1,3,6,5,8,7,4]=>[1,3,2,1,1]
[2,1,3,5,6,8,7,4]=>[1,5,1,1]
[2,1,3,7,6,5,8,4]=>[1,3,1,2,1]
[2,1,3,6,7,5,8,4]=>[1,4,2,1]
[2,1,3,5,7,6,8,4]=>[1,4,2,1]
[2,1,3,6,5,7,8,4]=>[1,3,3,1]
[2,1,3,5,6,7,8,4]=>[1,6,1]
[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[1,2,3,7,6,8,5,4]=>[4,2,1,1]
[1,2,3,6,7,8,5,4]=>[6,1,1]
[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[1,2,3,5,7,8,6,4]=>[6,1,1]
[1,2,3,6,5,8,7,4]=>[4,2,1,1]
[1,2,3,5,6,8,7,4]=>[6,1,1]
[1,2,3,7,6,5,8,4]=>[4,1,2,1]
[1,2,3,6,7,5,8,4]=>[5,2,1]
[1,2,3,5,7,6,8,4]=>[5,2,1]
[1,2,3,6,5,7,8,4]=>[4,3,1]
[1,2,3,5,6,7,8,4]=>[7,1]
[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[4,3,2,1,7,8,6,5]=>[1,1,1,3,1,1]
[4,3,2,1,6,8,7,5]=>[1,1,1,3,1,1]
[4,3,2,1,7,6,8,5]=>[1,1,1,2,2,1]
[4,3,2,1,6,7,8,5]=>[1,1,1,4,1]
[3,4,2,1,8,7,6,5]=>[2,1,2,1,1,1]
[3,4,2,1,7,8,6,5]=>[2,1,3,1,1]
[3,4,2,1,6,8,7,5]=>[2,1,3,1,1]
[3,4,2,1,7,6,8,5]=>[2,1,2,2,1]
[3,4,2,1,6,7,8,5]=>[2,1,4,1]
[2,4,3,1,8,7,6,5]=>[2,1,2,1,1,1]
[2,4,3,1,7,8,6,5]=>[2,1,3,1,1]
[2,4,3,1,6,8,7,5]=>[2,1,3,1,1]
[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]
[2,4,3,1,6,7,8,5]=>[2,1,4,1]
[3,2,4,1,8,7,6,5]=>[1,2,2,1,1,1]
[3,2,4,1,7,8,6,5]=>[1,2,3,1,1]
[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]
[3,2,4,1,7,6,8,5]=>[1,2,2,2,1]
[3,2,4,1,6,7,8,5]=>[1,2,4,1]
[2,3,4,1,8,7,6,5]=>[3,2,1,1,1]
[2,3,4,1,7,8,6,5]=>[3,3,1,1]
[2,3,4,1,6,8,7,5]=>[3,3,1,1]
[2,3,4,1,7,6,8,5]=>[3,2,2,1]
[2,3,4,1,6,7,8,5]=>[3,4,1]
[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[1,4,3,2,7,8,6,5]=>[2,1,3,1,1]
[1,4,3,2,6,8,7,5]=>[2,1,3,1,1]
[1,4,3,2,7,6,8,5]=>[2,1,2,2,1]
[1,4,3,2,6,7,8,5]=>[2,1,4,1]
[1,3,4,2,8,7,6,5]=>[3,2,1,1,1]
[1,3,4,2,7,8,6,5]=>[3,3,1,1]
[1,3,4,2,6,8,7,5]=>[3,3,1,1]
[1,3,4,2,7,6,8,5]=>[3,2,2,1]
[1,3,4,2,6,7,8,5]=>[3,4,1]
[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[2,1,4,3,7,8,6,5]=>[1,2,3,1,1]
[2,1,4,3,6,8,7,5]=>[1,2,3,1,1]
[2,1,4,3,7,6,8,5]=>[1,2,2,2,1]
[2,1,4,3,6,7,8,5]=>[1,2,4,1]
[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[1,2,4,3,7,8,6,5]=>[3,3,1,1]
[1,2,4,3,6,8,7,5]=>[3,3,1,1]
[1,2,4,3,7,6,8,5]=>[3,2,2,1]
[1,2,4,3,6,7,8,5]=>[3,4,1]
[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[3,2,1,4,7,8,6,5]=>[1,1,4,1,1]
[3,2,1,4,6,8,7,5]=>[1,1,4,1,1]
[3,2,1,4,7,6,8,5]=>[1,1,3,2,1]
[3,2,1,4,6,7,8,5]=>[1,1,5,1]
[2,3,1,4,8,7,6,5]=>[2,3,1,1,1]
[2,3,1,4,7,8,6,5]=>[2,4,1,1]
[2,3,1,4,6,8,7,5]=>[2,4,1,1]
[2,3,1,4,7,6,8,5]=>[2,3,2,1]
[2,3,1,4,6,7,8,5]=>[2,5,1]
[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[1,3,2,4,7,8,6,5]=>[2,4,1,1]
[1,3,2,4,6,8,7,5]=>[2,4,1,1]
[1,3,2,4,7,6,8,5]=>[2,3,2,1]
[1,3,2,4,6,7,8,5]=>[2,5,1]
[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[2,1,3,4,7,8,6,5]=>[1,5,1,1]
[2,1,3,4,6,8,7,5]=>[1,5,1,1]
[2,1,3,4,7,6,8,5]=>[1,4,2,1]
[2,1,3,4,6,7,8,5]=>[1,6,1]
[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[1,2,3,4,7,8,6,5]=>[6,1,1]
[1,2,3,4,6,8,7,5]=>[6,1,1]
[1,2,3,4,7,6,8,5]=>[5,2,1]
[1,2,3,4,6,7,8,5]=>[7,1]
[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[5,4,3,2,1,7,8,6]=>[1,1,1,1,3,1]
[4,5,3,2,1,8,7,6]=>[2,1,1,2,1,1]
[4,5,3,2,1,7,8,6]=>[2,1,1,3,1]
[3,5,4,2,1,8,7,6]=>[2,1,1,2,1,1]
[3,5,4,2,1,7,8,6]=>[2,1,1,3,1]
[4,3,5,2,1,8,7,6]=>[1,2,1,2,1,1]
[4,3,5,2,1,7,8,6]=>[1,2,1,3,1]
[3,4,5,2,1,8,7,6]=>[3,1,2,1,1]
[3,4,5,2,1,7,8,6]=>[3,1,3,1]
[2,5,4,3,1,8,7,6]=>[2,1,1,2,1,1]
[2,5,4,3,1,7,8,6]=>[2,1,1,3,1]
[2,4,5,3,1,8,7,6]=>[3,1,2,1,1]
[2,4,5,3,1,7,8,6]=>[3,1,3,1]
[3,2,5,4,1,8,7,6]=>[1,2,1,2,1,1]
[3,2,5,4,1,7,8,6]=>[1,2,1,3,1]
[2,3,5,4,1,8,7,6]=>[3,1,2,1,1]
[2,3,5,4,1,7,8,6]=>[3,1,3,1]
[4,3,2,5,1,8,7,6]=>[1,1,2,2,1,1]
[4,3,2,5,1,7,8,6]=>[1,1,2,3,1]
[3,4,2,5,1,8,7,6]=>[2,2,2,1,1]
[3,4,2,5,1,7,8,6]=>[2,2,3,1]
[2,4,3,5,1,8,7,6]=>[2,2,2,1,1]
[2,4,3,5,1,7,8,6]=>[2,2,3,1]
[3,2,4,5,1,8,7,6]=>[1,3,2,1,1]
[3,2,4,5,1,7,8,6]=>[1,3,3,1]
[2,3,4,5,1,8,7,6]=>[4,2,1,1]
[2,3,4,5,1,7,8,6]=>[4,3,1]
[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]
[1,5,4,3,2,7,8,6]=>[2,1,1,3,1]
[1,4,5,3,2,8,7,6]=>[3,1,2,1,1]
[1,4,5,3,2,7,8,6]=>[3,1,3,1]
[1,3,5,4,2,8,7,6]=>[3,1,2,1,1]
[1,3,5,4,2,7,8,6]=>[3,1,3,1]
[1,4,3,5,2,8,7,6]=>[2,2,2,1,1]
[1,4,3,5,2,7,8,6]=>[2,2,3,1]
[1,3,4,5,2,8,7,6]=>[4,2,1,1]
[1,3,4,5,2,7,8,6]=>[4,3,1]
[2,1,5,4,3,8,7,6]=>[1,2,1,2,1,1]
[2,1,5,4,3,7,8,6]=>[1,2,1,3,1]
[2,1,4,5,3,8,7,6]=>[1,3,2,1,1]
[2,1,4,5,3,7,8,6]=>[1,3,3,1]
[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]
[1,2,5,4,3,7,8,6]=>[3,1,3,1]
[1,2,4,5,3,8,7,6]=>[4,2,1,1]
[1,2,4,5,3,7,8,6]=>[4,3,1]
[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]
[3,2,1,5,4,7,8,6]=>[1,1,2,3,1]
[2,3,1,5,4,7,8,6]=>[2,2,3,1]
[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]
[1,3,2,5,4,7,8,6]=>[2,2,3,1]
[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[2,1,3,5,4,7,8,6]=>[1,3,3,1]
[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[1,2,3,5,4,7,8,6]=>[4,3,1]
[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[4,3,2,1,5,7,8,6]=>[1,1,1,4,1]
[3,4,2,1,5,8,7,6]=>[2,1,3,1,1]
[2,4,3,1,5,8,7,6]=>[2,1,3,1,1]
[2,4,3,1,5,7,8,6]=>[2,1,4,1]
[3,2,4,1,5,8,7,6]=>[1,2,3,1,1]
[3,2,4,1,5,7,8,6]=>[1,2,4,1]
[2,3,4,1,5,8,7,6]=>[3,3,1,1]
[2,3,4,1,5,7,8,6]=>[3,4,1]
[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]
[1,4,3,2,5,7,8,6]=>[2,1,4,1]
[1,3,4,2,5,8,7,6]=>[3,3,1,1]
[1,3,4,2,5,7,8,6]=>[3,4,1]
[2,1,4,3,5,8,7,6]=>[1,2,3,1,1]
[2,1,4,3,5,7,8,6]=>[1,2,4,1]
[1,2,4,3,5,8,7,6]=>[3,3,1,1]
[1,2,4,3,5,7,8,6]=>[3,4,1]
[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[3,2,1,4,5,7,8,6]=>[1,1,5,1]
[2,3,1,4,5,8,7,6]=>[2,4,1,1]
[2,3,1,4,5,7,8,6]=>[2,5,1]
[1,3,2,4,5,8,7,6]=>[2,4,1,1]
[1,3,2,4,5,7,8,6]=>[2,5,1]
[2,1,3,4,5,8,7,6]=>[1,5,1,1]
[2,1,3,4,5,7,8,6]=>[1,6,1]
[1,2,3,4,5,8,7,6]=>[6,1,1]
[1,2,3,4,5,7,8,6]=>[7,1]
[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]
[5,6,4,3,2,1,8,7]=>[2,1,1,1,2,1]
[4,6,5,3,2,1,8,7]=>[2,1,1,1,2,1]
[5,4,6,3,2,1,8,7]=>[1,2,1,1,2,1]
[4,5,6,3,2,1,8,7]=>[3,1,1,2,1]
[3,6,5,4,2,1,8,7]=>[2,1,1,1,2,1]
[3,5,6,4,2,1,8,7]=>[3,1,1,2,1]
[4,3,6,5,2,1,8,7]=>[1,2,1,1,2,1]
[3,4,6,5,2,1,8,7]=>[3,1,1,2,1]
[5,4,3,6,2,1,8,7]=>[1,1,2,1,2,1]
[4,5,3,6,2,1,8,7]=>[2,2,1,2,1]
[3,5,4,6,2,1,8,7]=>[2,2,1,2,1]
[4,3,5,6,2,1,8,7]=>[1,3,1,2,1]
[3,4,5,6,2,1,8,7]=>[4,1,2,1]
[2,6,5,4,3,1,8,7]=>[2,1,1,1,2,1]
[2,5,6,4,3,1,8,7]=>[3,1,1,2,1]
[2,4,6,5,3,1,8,7]=>[3,1,1,2,1]
[2,5,4,6,3,1,8,7]=>[2,2,1,2,1]
[2,4,5,6,3,1,8,7]=>[4,1,2,1]
[3,2,6,5,4,1,8,7]=>[1,2,1,1,2,1]
[3,2,5,6,4,1,8,7]=>[1,3,1,2,1]
[2,3,6,5,4,1,8,7]=>[3,1,1,2,1]
[2,3,5,6,4,1,8,7]=>[4,1,2,1]
[4,3,2,6,5,1,8,7]=>[1,1,2,1,2,1]
[3,4,2,6,5,1,8,7]=>[2,2,1,2,1]
[2,4,3,6,5,1,8,7]=>[2,2,1,2,1]
[3,2,4,6,5,1,8,7]=>[1,3,1,2,1]
[2,3,4,6,5,1,8,7]=>[4,1,2,1]
[5,4,3,2,6,1,8,7]=>[1,1,1,2,2,1]
[4,5,3,2,6,1,8,7]=>[2,1,2,2,1]
[3,5,4,2,6,1,8,7]=>[2,1,2,2,1]
[4,3,5,2,6,1,8,7]=>[1,2,2,2,1]
[3,4,5,2,6,1,8,7]=>[3,2,2,1]
[2,5,4,3,6,1,8,7]=>[2,1,2,2,1]
[2,4,5,3,6,1,8,7]=>[3,2,2,1]
[3,2,5,4,6,1,8,7]=>[1,2,2,2,1]
[4,3,2,5,6,1,8,7]=>[1,1,3,2,1]
[3,4,2,5,6,1,8,7]=>[2,3,2,1]
[2,4,3,5,6,1,8,7]=>[2,3,2,1]
[2,3,4,5,6,1,8,7]=>[5,2,1]
[1,6,5,4,3,2,8,7]=>[2,1,1,1,2,1]
[1,5,6,4,3,2,8,7]=>[3,1,1,2,1]
[1,5,4,6,3,2,8,7]=>[2,2,1,2,1]
[1,4,5,6,3,2,8,7]=>[4,1,2,1]
[1,3,6,5,4,2,8,7]=>[3,1,1,2,1]
[1,3,5,6,4,2,8,7]=>[4,1,2,1]
[1,3,4,6,5,2,8,7]=>[4,1,2,1]
[1,3,4,5,6,2,8,7]=>[5,2,1]
[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]
[2,1,5,6,4,3,8,7]=>[1,3,1,2,1]
[2,1,4,6,5,3,8,7]=>[1,3,1,2,1]
[2,1,5,4,6,3,8,7]=>[1,2,2,2,1]
[2,1,4,5,6,3,8,7]=>[1,4,2,1]
[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]
[1,2,5,6,4,3,8,7]=>[4,1,2,1]
[1,2,4,6,5,3,8,7]=>[4,1,2,1]
[1,2,5,4,6,3,8,7]=>[3,2,2,1]
[1,2,4,5,6,3,8,7]=>[5,2,1]
[3,2,1,6,5,4,8,7]=>[1,1,2,1,2,1]
[3,2,1,5,6,4,8,7]=>[1,1,3,2,1]
[2,3,1,6,5,4,8,7]=>[2,2,1,2,1]
[1,3,2,6,5,4,8,7]=>[2,2,1,2,1]
[1,3,2,5,6,4,8,7]=>[2,3,2,1]
[2,1,3,5,6,4,8,7]=>[1,4,2,1]
[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[1,2,3,5,6,4,8,7]=>[5,2,1]
[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[3,4,2,1,6,5,8,7]=>[2,1,2,2,1]
[2,4,3,1,6,5,8,7]=>[2,1,2,2,1]
[3,2,4,1,6,5,8,7]=>[1,2,2,2,1]
[2,3,4,1,6,5,8,7]=>[3,2,2,1]
[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]
[1,3,4,2,6,5,8,7]=>[3,2,2,1]
[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[2,3,1,4,6,5,8,7]=>[2,3,2,1]
[1,3,2,4,6,5,8,7]=>[2,3,2,1]
[2,1,3,4,6,5,8,7]=>[1,4,2,1]
[1,2,3,4,6,5,8,7]=>[5,2,1]
[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[4,5,3,2,1,6,8,7]=>[2,1,1,3,1]
[3,5,4,2,1,6,8,7]=>[2,1,1,3,1]
[4,3,5,2,1,6,8,7]=>[1,2,1,3,1]
[3,4,5,2,1,6,8,7]=>[3,1,3,1]
[2,5,4,3,1,6,8,7]=>[2,1,1,3,1]
[2,4,5,3,1,6,8,7]=>[3,1,3,1]
[3,2,5,4,1,6,8,7]=>[1,2,1,3,1]
[2,3,5,4,1,6,8,7]=>[3,1,3,1]
[4,3,2,5,1,6,8,7]=>[1,1,2,3,1]
[3,4,2,5,1,6,8,7]=>[2,2,3,1]
[2,4,3,5,1,6,8,7]=>[2,2,3,1]
[3,2,4,5,1,6,8,7]=>[1,3,3,1]
[2,3,4,5,1,6,8,7]=>[4,3,1]
[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]
[1,4,5,3,2,6,8,7]=>[3,1,3,1]
[1,3,5,4,2,6,8,7]=>[3,1,3,1]
[1,4,3,5,2,6,8,7]=>[2,2,3,1]
[1,3,4,5,2,6,8,7]=>[4,3,1]
[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[2,1,4,5,3,6,8,7]=>[1,3,3,1]
[1,2,5,4,3,6,8,7]=>[3,1,3,1]
[1,2,4,5,3,6,8,7]=>[4,3,1]
[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[1,3,2,5,4,6,8,7]=>[2,2,3,1]
[2,1,3,5,4,6,8,7]=>[1,3,3,1]
[1,2,3,5,4,6,8,7]=>[4,3,1]
[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[3,4,2,1,5,6,8,7]=>[2,1,4,1]
[2,4,3,1,5,6,8,7]=>[2,1,4,1]
[3,2,4,1,5,6,8,7]=>[1,2,4,1]
[2,3,4,1,5,6,8,7]=>[3,4,1]
[1,4,3,2,5,6,8,7]=>[2,1,4,1]
[1,3,4,2,5,6,8,7]=>[3,4,1]
[2,1,4,3,5,6,8,7]=>[1,2,4,1]
[1,2,4,3,5,6,8,7]=>[3,4,1]
[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[2,3,1,4,5,6,8,7]=>[2,5,1]
[1,3,2,4,5,6,8,7]=>[2,5,1]
[2,1,3,4,5,6,8,7]=>[1,6,1]
[1,2,3,4,5,6,8,7]=>[7,1]
[5,7,6,4,3,2,1,8]=>[2,1,1,1,1,2]
[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]
[4,6,7,5,3,2,1,8]=>[3,1,1,1,2]
[5,4,7,6,3,2,1,8]=>[1,2,1,1,1,2]
[4,5,7,6,3,2,1,8]=>[3,1,1,1,2]
[4,6,5,7,3,2,1,8]=>[2,2,1,1,2]
[3,7,6,5,4,2,1,8]=>[2,1,1,1,1,2]
[3,5,7,6,4,2,1,8]=>[3,1,1,1,2]
[3,5,6,7,4,2,1,8]=>[4,1,1,2]
[4,3,7,6,5,2,1,8]=>[1,2,1,1,1,2]
[3,4,7,6,5,2,1,8]=>[3,1,1,1,2]
[5,4,3,7,6,2,1,8]=>[1,1,2,1,1,2]
[4,5,3,7,6,2,1,8]=>[2,2,1,1,2]
[3,5,4,7,6,2,1,8]=>[2,2,1,1,2]
[4,3,5,7,6,2,1,8]=>[1,3,1,1,2]
[4,6,5,3,7,2,1,8]=>[2,1,2,1,2]
[3,6,5,4,7,2,1,8]=>[2,1,2,1,2]
[3,5,6,4,7,2,1,8]=>[3,2,1,2]
[4,3,6,5,7,2,1,8]=>[1,2,2,1,2]
[2,7,6,5,4,3,1,8]=>[2,1,1,1,1,2]
[2,6,7,5,4,3,1,8]=>[3,1,1,1,2]
[2,5,7,6,4,3,1,8]=>[3,1,1,1,2]
[2,6,5,7,4,3,1,8]=>[2,2,1,1,2]
[2,5,6,7,4,3,1,8]=>[4,1,1,2]
[2,4,7,6,5,3,1,8]=>[3,1,1,1,2]
[2,4,6,7,5,3,1,8]=>[4,1,1,2]
[2,5,4,7,6,3,1,8]=>[2,2,1,1,2]
[2,4,5,7,6,3,1,8]=>[4,1,1,2]
[2,5,6,4,7,3,1,8]=>[3,2,1,2]
[2,5,4,6,7,3,1,8]=>[2,3,1,2]
[2,4,5,6,7,3,1,8]=>[5,1,2]
[3,2,7,6,5,4,1,8]=>[1,2,1,1,1,2]
[3,2,6,7,5,4,1,8]=>[1,3,1,1,2]
[3,2,5,7,6,4,1,8]=>[1,3,1,1,2]
[3,2,6,5,7,4,1,8]=>[1,2,2,1,2]
[3,2,5,6,7,4,1,8]=>[1,4,1,2]
[2,3,7,6,5,4,1,8]=>[3,1,1,1,2]
[2,3,6,7,5,4,1,8]=>[4,1,1,2]
[2,3,5,7,6,4,1,8]=>[4,1,1,2]
[2,3,6,5,7,4,1,8]=>[3,2,1,2]
[2,3,5,6,7,4,1,8]=>[5,1,2]
[4,3,2,7,6,5,1,8]=>[1,1,2,1,1,2]
[4,3,2,6,7,5,1,8]=>[1,1,3,1,2]
[3,4,2,7,6,5,1,8]=>[2,2,1,1,2]
[3,4,2,6,7,5,1,8]=>[2,3,1,2]
[2,4,3,7,6,5,1,8]=>[2,2,1,1,2]
[3,2,4,7,6,5,1,8]=>[1,3,1,1,2]
[3,2,4,6,7,5,1,8]=>[1,4,1,2]
[2,3,4,7,6,5,1,8]=>[4,1,1,2]
[2,3,4,6,7,5,1,8]=>[5,1,2]
[5,4,3,2,7,6,1,8]=>[1,1,1,2,1,2]
[4,5,3,2,7,6,1,8]=>[2,1,2,1,2]
[3,5,4,2,7,6,1,8]=>[2,1,2,1,2]
[4,3,5,2,7,6,1,8]=>[1,2,2,1,2]
[3,4,5,2,7,6,1,8]=>[3,2,1,2]
[2,5,4,3,7,6,1,8]=>[2,1,2,1,2]
[3,2,5,4,7,6,1,8]=>[1,2,2,1,2]
[2,3,5,4,7,6,1,8]=>[3,2,1,2]
[4,3,2,5,7,6,1,8]=>[1,1,3,1,2]
[3,4,2,5,7,6,1,8]=>[2,3,1,2]
[2,4,3,5,7,6,1,8]=>[2,3,1,2]
[3,2,4,5,7,6,1,8]=>[1,4,1,2]
[2,3,4,5,7,6,1,8]=>[5,1,2]
[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]
[3,5,6,4,2,7,1,8]=>[3,1,2,2]
[4,3,6,5,2,7,1,8]=>[1,2,1,2,2]
[3,4,6,5,2,7,1,8]=>[3,1,2,2]
[3,5,4,6,2,7,1,8]=>[2,2,2,2]
[2,6,5,4,3,7,1,8]=>[2,1,1,2,2]
[2,4,6,5,3,7,1,8]=>[3,1,2,2]
[2,5,4,6,3,7,1,8]=>[2,2,2,2]
[2,4,5,6,3,7,1,8]=>[4,2,2]
[3,2,6,5,4,7,1,8]=>[1,2,1,2,2]
[2,3,5,6,4,7,1,8]=>[4,2,2]
[4,3,2,6,5,7,1,8]=>[1,1,2,2,2]
[3,4,2,6,5,7,1,8]=>[2,2,2,2]
[2,4,3,6,5,7,1,8]=>[2,2,2,2]
[3,2,4,6,5,7,1,8]=>[1,3,2,2]
[2,3,4,6,5,7,1,8]=>[4,2,2]
[3,5,4,2,6,7,1,8]=>[2,1,3,2]
[2,5,4,3,6,7,1,8]=>[2,1,3,2]
[2,4,5,3,6,7,1,8]=>[3,3,2]
[3,2,5,4,6,7,1,8]=>[1,2,3,2]
[2,3,5,4,6,7,1,8]=>[3,3,2]
[2,4,3,5,6,7,1,8]=>[2,4,2]
[1,7,6,5,4,3,2,8]=>[2,1,1,1,1,2]
[1,6,7,5,4,3,2,8]=>[3,1,1,1,2]
[1,5,7,6,4,3,2,8]=>[3,1,1,1,2]
[1,6,5,7,4,3,2,8]=>[2,2,1,1,2]
[1,5,6,7,4,3,2,8]=>[4,1,1,2]
[1,4,7,6,5,3,2,8]=>[3,1,1,1,2]
[1,4,6,7,5,3,2,8]=>[4,1,1,2]
[1,5,4,7,6,3,2,8]=>[2,2,1,1,2]
[1,4,5,7,6,3,2,8]=>[4,1,1,2]
[1,5,6,4,7,3,2,8]=>[3,2,1,2]
[1,4,6,5,7,3,2,8]=>[3,2,1,2]
[1,5,4,6,7,3,2,8]=>[2,3,1,2]
[1,4,5,6,7,3,2,8]=>[5,1,2]
[1,3,7,6,5,4,2,8]=>[3,1,1,1,2]
[1,3,6,7,5,4,2,8]=>[4,1,1,2]
[1,3,5,7,6,4,2,8]=>[4,1,1,2]
[1,3,6,5,7,4,2,8]=>[3,2,1,2]
[1,3,5,6,7,4,2,8]=>[5,1,2]
[1,4,3,7,6,5,2,8]=>[2,2,1,1,2]
[1,3,4,6,7,5,2,8]=>[5,1,2]
[1,4,5,3,7,6,2,8]=>[3,2,1,2]
[1,3,5,4,7,6,2,8]=>[3,2,1,2]
[1,4,3,5,7,6,2,8]=>[2,3,1,2]
[1,3,4,5,7,6,2,8]=>[5,1,2]
[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]
[1,5,6,4,3,7,2,8]=>[3,1,2,2]
[1,4,6,5,3,7,2,8]=>[3,1,2,2]
[1,5,4,6,3,7,2,8]=>[2,2,2,2]
[1,4,5,6,3,7,2,8]=>[4,2,2]
[1,3,6,5,4,7,2,8]=>[3,1,2,2]
[1,3,5,6,4,7,2,8]=>[4,2,2]
[1,4,3,6,5,7,2,8]=>[2,2,2,2]
[1,3,4,6,5,7,2,8]=>[4,2,2]
[1,5,4,3,6,7,2,8]=>[2,1,3,2]
[1,4,5,3,6,7,2,8]=>[3,3,2]
[1,3,5,4,6,7,2,8]=>[3,3,2]
[1,3,4,5,6,7,2,8]=>[6,2]
[2,1,7,6,5,4,3,8]=>[1,2,1,1,1,2]
[2,1,6,7,5,4,3,8]=>[1,3,1,1,2]
[2,1,5,6,7,4,3,8]=>[1,4,1,2]
[2,1,4,7,6,5,3,8]=>[1,3,1,1,2]
[2,1,4,6,7,5,3,8]=>[1,4,1,2]
[2,1,5,4,7,6,3,8]=>[1,2,2,1,2]
[2,1,4,5,7,6,3,8]=>[1,4,1,2]
[2,1,5,4,6,7,3,8]=>[1,2,3,2]
[2,1,4,5,6,7,3,8]=>[1,5,2]
[1,2,7,6,5,4,3,8]=>[3,1,1,1,2]
[1,2,6,7,5,4,3,8]=>[4,1,1,2]
[1,2,5,7,6,4,3,8]=>[4,1,1,2]
[1,2,5,6,7,4,3,8]=>[5,1,2]
[1,2,4,7,6,5,3,8]=>[4,1,1,2]
[1,2,4,6,7,5,3,8]=>[5,1,2]
[1,2,5,4,7,6,3,8]=>[3,2,1,2]
[1,2,4,5,7,6,3,8]=>[5,1,2]
[1,2,5,6,4,7,3,8]=>[4,2,2]
[1,2,4,6,5,7,3,8]=>[4,2,2]
[1,2,5,4,6,7,3,8]=>[3,3,2]
[1,2,4,5,6,7,3,8]=>[6,2]
[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[3,2,1,6,7,5,4,8]=>[1,1,3,1,2]
[3,2,1,5,7,6,4,8]=>[1,1,3,1,2]
[3,2,1,6,5,7,4,8]=>[1,1,2,2,2]
[3,2,1,5,6,7,4,8]=>[1,1,4,2]
[2,3,1,7,6,5,4,8]=>[2,2,1,1,2]
[2,3,1,6,7,5,4,8]=>[2,3,1,2]
[2,3,1,6,5,7,4,8]=>[2,2,2,2]
[2,3,1,5,6,7,4,8]=>[2,4,2]
[1,3,2,7,6,5,4,8]=>[2,2,1,1,2]
[1,3,2,6,7,5,4,8]=>[2,3,1,2]
[1,3,2,5,7,6,4,8]=>[2,3,1,2]
[1,3,2,6,5,7,4,8]=>[2,2,2,2]
[1,3,2,5,6,7,4,8]=>[2,4,2]
[2,1,3,7,6,5,4,8]=>[1,3,1,1,2]
[2,1,3,6,7,5,4,8]=>[1,4,1,2]
[2,1,3,6,5,7,4,8]=>[1,3,2,2]
[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[1,2,3,6,7,5,4,8]=>[5,1,2]
[1,2,3,5,7,6,4,8]=>[5,1,2]
[1,2,3,6,5,7,4,8]=>[4,2,2]
[1,2,3,5,6,7,4,8]=>[6,2]
[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[4,3,2,1,6,7,5,8]=>[1,1,1,3,2]
[3,2,4,1,7,6,5,8]=>[1,2,2,1,2]
[3,2,4,1,6,7,5,8]=>[1,2,3,2]
[2,3,4,1,7,6,5,8]=>[3,2,1,2]
[2,3,4,1,6,7,5,8]=>[3,3,2]
[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[1,4,3,2,6,7,5,8]=>[2,1,3,2]
[1,3,4,2,7,6,5,8]=>[3,2,1,2]
[1,3,4,2,6,7,5,8]=>[3,3,2]
[1,2,4,3,7,6,5,8]=>[3,2,1,2]
[1,2,4,3,6,7,5,8]=>[3,3,2]
[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[3,2,1,4,6,7,5,8]=>[1,1,4,2]
[2,3,1,4,6,7,5,8]=>[2,4,2]
[1,3,2,4,7,6,5,8]=>[2,3,1,2]
[2,1,3,4,6,7,5,8]=>[1,5,2]
[1,2,3,4,7,6,5,8]=>[5,1,2]
[1,2,3,4,6,7,5,8]=>[6,2]
[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]
[4,5,3,2,1,7,6,8]=>[2,1,1,2,2]
[3,5,4,2,1,7,6,8]=>[2,1,1,2,2]
[4,3,5,2,1,7,6,8]=>[1,2,1,2,2]
[3,4,5,2,1,7,6,8]=>[3,1,2,2]
[2,5,4,3,1,7,6,8]=>[2,1,1,2,2]
[2,4,5,3,1,7,6,8]=>[3,1,2,2]
[3,2,5,4,1,7,6,8]=>[1,2,1,2,2]
[2,3,5,4,1,7,6,8]=>[3,1,2,2]
[4,3,2,5,1,7,6,8]=>[1,1,2,2,2]
[3,4,2,5,1,7,6,8]=>[2,2,2,2]
[2,4,3,5,1,7,6,8]=>[2,2,2,2]
[3,2,4,5,1,7,6,8]=>[1,3,2,2]
[2,3,4,5,1,7,6,8]=>[4,2,2]
[1,5,4,3,2,7,6,8]=>[2,1,1,2,2]
[1,4,5,3,2,7,6,8]=>[3,1,2,2]
[1,3,5,4,2,7,6,8]=>[3,1,2,2]
[1,4,3,5,2,7,6,8]=>[2,2,2,2]
[1,3,4,5,2,7,6,8]=>[4,2,2]
[2,1,5,4,3,7,6,8]=>[1,2,1,2,2]
[1,2,5,4,3,7,6,8]=>[3,1,2,2]
[1,2,4,5,3,7,6,8]=>[4,2,2]
[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[2,3,1,5,4,7,6,8]=>[2,2,2,2]
[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[2,1,3,5,4,7,6,8]=>[1,3,2,2]
[1,2,3,5,4,7,6,8]=>[4,2,2]
[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[3,4,2,1,5,7,6,8]=>[2,1,3,2]
[2,4,3,1,5,7,6,8]=>[2,1,3,2]
[3,2,4,1,5,7,6,8]=>[1,2,3,2]
[2,3,4,1,5,7,6,8]=>[3,3,2]
[1,4,3,2,5,7,6,8]=>[2,1,3,2]
[1,3,4,2,5,7,6,8]=>[3,3,2]
[1,2,4,3,5,7,6,8]=>[3,3,2]
[3,2,1,4,5,7,6,8]=>[1,1,4,2]
[2,3,1,4,5,7,6,8]=>[2,4,2]
[1,3,2,4,5,7,6,8]=>[2,4,2]
[2,1,3,4,5,7,6,8]=>[1,5,2]
[1,2,3,4,5,7,6,8]=>[6,2]
[3,6,5,4,2,1,7,8]=>[2,1,1,1,3]
[3,5,6,4,2,1,7,8]=>[3,1,1,3]
[4,3,6,5,2,1,7,8]=>[1,2,1,1,3]
[3,5,4,6,2,1,7,8]=>[2,2,1,3]
[2,4,6,5,3,1,7,8]=>[3,1,1,3]
[2,5,4,6,3,1,7,8]=>[2,2,1,3]
[2,4,5,6,3,1,7,8]=>[4,1,3]
[2,3,6,5,4,1,7,8]=>[3,1,1,3]
[2,3,5,6,4,1,7,8]=>[4,1,3]
[4,3,2,6,5,1,7,8]=>[1,1,2,1,3]
[3,4,2,6,5,1,7,8]=>[2,2,1,3]
[2,4,3,6,5,1,7,8]=>[2,2,1,3]
[2,3,4,6,5,1,7,8]=>[4,1,3]
[3,5,4,2,6,1,7,8]=>[2,1,2,3]
[2,5,4,3,6,1,7,8]=>[2,1,2,3]
[3,2,5,4,6,1,7,8]=>[1,2,2,3]
[2,3,5,4,6,1,7,8]=>[3,2,3]
[2,4,3,5,6,1,7,8]=>[2,3,3]
[1,6,5,4,3,2,7,8]=>[2,1,1,1,3]
[1,5,6,4,3,2,7,8]=>[3,1,1,3]
[1,4,6,5,3,2,7,8]=>[3,1,1,3]
[1,5,4,6,3,2,7,8]=>[2,2,1,3]
[1,4,5,6,3,2,7,8]=>[4,1,3]
[1,3,6,5,4,2,7,8]=>[3,1,1,3]
[1,3,5,6,4,2,7,8]=>[4,1,3]
[1,4,3,6,5,2,7,8]=>[2,2,1,3]
[1,3,4,6,5,2,7,8]=>[4,1,3]
[1,5,4,3,6,2,7,8]=>[2,1,2,3]
[1,4,5,3,6,2,7,8]=>[3,2,3]
[1,3,5,4,6,2,7,8]=>[3,2,3]
[1,4,3,5,6,2,7,8]=>[2,3,3]
[1,3,4,5,6,2,7,8]=>[5,3]
[2,1,5,6,4,3,7,8]=>[1,3,1,3]
[2,1,4,6,5,3,7,8]=>[1,3,1,3]
[2,1,5,4,6,3,7,8]=>[1,2,2,3]
[2,1,4,5,6,3,7,8]=>[1,4,3]
[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[1,2,5,6,4,3,7,8]=>[4,1,3]
[1,2,4,6,5,3,7,8]=>[4,1,3]
[1,2,5,4,6,3,7,8]=>[3,2,3]
[1,2,4,5,6,3,7,8]=>[5,3]
[3,2,1,6,5,4,7,8]=>[1,1,2,1,3]
[3,2,1,5,6,4,7,8]=>[1,1,3,3]
[2,3,1,6,5,4,7,8]=>[2,2,1,3]
[2,3,1,5,6,4,7,8]=>[2,3,3]
[1,3,2,6,5,4,7,8]=>[2,2,1,3]
[1,3,2,5,6,4,7,8]=>[2,3,3]
[2,1,3,6,5,4,7,8]=>[1,3,1,3]
[2,1,3,5,6,4,7,8]=>[1,4,3]
[1,2,3,6,5,4,7,8]=>[4,1,3]
[1,2,3,5,6,4,7,8]=>[5,3]
[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[3,4,2,1,6,5,7,8]=>[2,1,2,3]
[2,4,3,1,6,5,7,8]=>[2,1,2,3]
[3,2,4,1,6,5,7,8]=>[1,2,2,3]
[2,3,4,1,6,5,7,8]=>[3,2,3]
[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[2,1,4,3,6,5,7,8]=>[1,2,2,3]
[1,2,4,3,6,5,7,8]=>[3,2,3]
[3,2,1,4,6,5,7,8]=>[1,1,3,3]
[2,3,1,4,6,5,7,8]=>[2,3,3]
[1,3,2,4,6,5,7,8]=>[2,3,3]
[2,1,3,4,6,5,7,8]=>[1,4,3]
[1,2,3,4,6,5,7,8]=>[5,3]
[3,5,4,2,1,6,7,8]=>[2,1,1,4]
[2,5,4,3,1,6,7,8]=>[2,1,1,4]
[2,4,5,3,1,6,7,8]=>[3,1,4]
[3,2,5,4,1,6,7,8]=>[1,2,1,4]
[2,3,5,4,1,6,7,8]=>[3,1,4]
[2,4,3,5,1,6,7,8]=>[2,2,4]
[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[1,4,5,3,2,6,7,8]=>[3,1,4]
[1,3,5,4,2,6,7,8]=>[3,1,4]
[1,3,4,5,2,6,7,8]=>[4,4]
[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[2,1,4,5,3,6,7,8]=>[1,3,4]
[1,2,5,4,3,6,7,8]=>[3,1,4]
[1,2,4,5,3,6,7,8]=>[4,4]
[3,2,1,5,4,6,7,8]=>[1,1,2,4]
[2,3,1,5,4,6,7,8]=>[2,2,4]
[1,3,2,5,4,6,7,8]=>[2,2,4]
[2,1,3,5,4,6,7,8]=>[1,3,4]
[1,2,3,5,4,6,7,8]=>[4,4]
[2,4,3,1,5,6,7,8]=>[2,1,5]
[1,4,3,2,5,6,7,8]=>[2,1,5]
[1,3,4,2,5,6,7,8]=>[3,5]
[2,1,4,3,5,6,7,8]=>[1,2,5]
[1,2,4,3,5,6,7,8]=>[3,5]
[1,3,2,4,5,6,7,8]=>[2,6]
[1,2,3,4,8,6,7,5]=>[5,2,1]
[1,2,3,5,8,6,7,4]=>[5,2,1]
[1,2,3,7,5,6,4,8]=>[4,2,2]
[1,2,3,7,5,6,8,4]=>[4,3,1]
[1,2,3,8,5,6,7,4]=>[4,3,1]
[1,2,3,8,5,7,6,4]=>[4,2,1,1]
[1,2,3,8,6,5,7,4]=>[4,1,2,1]
[1,2,3,8,6,7,5,4]=>[4,2,1,1]
[1,2,4,3,8,6,7,5]=>[3,2,2,1]
[1,2,4,5,8,6,7,3]=>[5,2,1]
[1,2,4,7,5,6,8,3]=>[4,3,1]
[1,2,4,8,5,6,7,3]=>[4,3,1]
[1,2,4,8,5,7,6,3]=>[4,2,1,1]
[1,2,4,8,6,5,7,3]=>[4,1,2,1]
[1,2,4,8,6,7,5,3]=>[4,2,1,1]
[1,2,5,4,8,6,7,3]=>[3,2,2,1]
[1,2,6,4,5,3,7,8]=>[3,2,3]
[1,2,6,4,5,7,8,3]=>[3,4,1]
[1,2,6,4,5,8,7,3]=>[3,3,1,1]
[1,2,7,4,5,6,3,8]=>[3,3,2]
[1,2,7,4,5,6,8,3]=>[3,4,1]
[1,2,8,4,5,6,7,3]=>[3,4,1]
[1,2,8,4,5,7,6,3]=>[3,3,1,1]
[1,2,7,4,6,5,3,8]=>[3,2,1,2]
[1,2,7,4,6,5,8,3]=>[3,2,2,1]
[1,2,8,4,6,7,5,3]=>[3,3,1,1]
[1,2,8,4,7,6,5,3]=>[3,2,1,1,1]
[1,2,7,5,4,6,3,8]=>[3,1,2,2]
[1,2,7,5,4,6,8,3]=>[3,1,3,1]
[1,2,8,5,4,6,7,3]=>[3,1,3,1]
[1,2,8,5,4,7,6,3]=>[3,1,2,1,1]
[1,2,7,5,6,4,3,8]=>[3,2,1,2]
[1,2,7,5,6,4,8,3]=>[3,2,2,1]
[1,2,8,5,6,4,7,3]=>[3,2,2,1]
[1,2,8,5,6,7,4,3]=>[3,3,1,1]
[1,2,8,5,7,6,4,3]=>[3,2,1,1,1]
[1,2,8,6,5,4,7,3]=>[3,1,1,2,1]
[1,2,8,6,5,7,4,3]=>[3,1,2,1,1]
[1,2,8,7,5,6,4,3]=>[3,1,2,1,1]
[1,3,2,4,8,6,7,5]=>[2,3,2,1]
[1,3,2,5,8,6,7,4]=>[2,3,2,1]
[1,3,2,7,5,6,4,8]=>[2,2,2,2]
[1,3,2,7,5,6,8,4]=>[2,2,3,1]
[1,3,2,8,5,6,7,4]=>[2,2,3,1]
[1,3,2,8,5,7,6,4]=>[2,2,2,1,1]
[1,3,2,8,6,5,7,4]=>[2,2,1,2,1]
[1,3,2,8,6,7,5,4]=>[2,2,2,1,1]
[1,3,4,2,8,6,7,5]=>[3,2,2,1]
[1,3,4,5,8,6,7,2]=>[5,2,1]
[1,3,4,7,5,6,8,2]=>[4,3,1]
[1,3,4,8,5,6,7,2]=>[4,3,1]
[1,3,4,8,6,5,7,2]=>[4,1,2,1]
[1,3,4,8,6,7,5,2]=>[4,2,1,1]
[1,3,6,4,5,2,8,7]=>[3,2,2,1]
[1,3,6,4,5,7,2,8]=>[3,3,2]
[1,3,6,4,5,7,8,2]=>[3,4,1]
[1,3,6,4,5,8,7,2]=>[3,3,1,1]
[1,3,7,4,5,6,2,8]=>[3,3,2]
[1,3,7,4,5,6,8,2]=>[3,4,1]
[1,3,8,4,5,6,7,2]=>[3,4,1]
[1,3,7,4,6,5,2,8]=>[3,2,1,2]
[1,3,8,4,6,5,7,2]=>[3,2,2,1]
[1,3,8,4,6,7,5,2]=>[3,3,1,1]
[1,3,8,4,7,6,5,2]=>[3,2,1,1,1]
[1,3,7,5,4,6,8,2]=>[3,1,3,1]
[1,3,8,5,4,6,7,2]=>[3,1,3,1]
[1,3,8,5,4,7,6,2]=>[3,1,2,1,1]
[1,3,7,5,6,4,2,8]=>[3,2,1,2]
[1,3,8,5,6,4,7,2]=>[3,2,2,1]
[1,3,8,5,6,7,4,2]=>[3,3,1,1]
[1,3,8,5,7,6,4,2]=>[3,2,1,1,1]
[1,3,8,6,5,7,4,2]=>[3,1,2,1,1]
[1,3,8,7,5,6,4,2]=>[3,1,2,1,1]
[1,4,3,2,8,6,7,5]=>[2,1,2,2,1]
[1,4,3,5,8,6,7,2]=>[2,3,2,1]
[1,4,3,7,5,6,2,8]=>[2,2,2,2]
[1,4,3,8,5,6,7,2]=>[2,2,3,1]
[1,4,3,8,5,7,6,2]=>[2,2,2,1,1]
[1,4,3,8,6,5,7,2]=>[2,2,1,2,1]
[1,4,3,8,6,7,5,2]=>[2,2,2,1,1]
[1,5,3,4,2,6,7,8]=>[2,2,4]
[1,5,3,4,2,7,6,8]=>[2,2,2,2]
[1,5,3,4,2,7,8,6]=>[2,2,3,1]
[1,5,3,4,2,8,7,6]=>[2,2,2,1,1]
[1,5,3,4,6,2,7,8]=>[2,3,3]
[1,5,3,4,6,2,8,7]=>[2,3,2,1]
[1,5,3,4,6,7,2,8]=>[2,4,2]
[1,5,3,4,6,7,8,2]=>[2,5,1]
[1,5,3,4,7,6,2,8]=>[2,3,1,2]
[1,5,3,4,7,6,8,2]=>[2,3,2,1]
[1,5,3,4,8,6,7,2]=>[2,3,2,1]
[1,5,3,4,8,7,6,2]=>[2,3,1,1,1]
[1,6,3,4,5,2,7,8]=>[2,3,3]
[1,6,3,4,5,7,2,8]=>[2,4,2]
[1,6,3,4,5,7,8,2]=>[2,5,1]
[1,6,3,4,5,8,7,2]=>[2,4,1,1]
[1,7,3,4,5,6,2,8]=>[2,4,2]
[1,7,3,4,5,6,8,2]=>[2,5,1]
[1,8,3,4,5,6,7,2]=>[2,5,1]
[1,8,3,4,5,7,6,2]=>[2,4,1,1]
[1,7,3,4,6,5,2,8]=>[2,3,1,2]
[1,7,3,4,6,5,8,2]=>[2,3,2,1]
[1,8,3,4,6,5,7,2]=>[2,3,2,1]
[1,8,3,4,6,7,5,2]=>[2,4,1,1]
[1,8,3,4,7,6,5,2]=>[2,3,1,1,1]
[1,6,3,5,4,2,7,8]=>[2,2,1,3]
[1,6,3,5,4,7,2,8]=>[2,2,2,2]
[1,6,3,5,4,7,8,2]=>[2,2,3,1]
[1,6,3,5,4,8,7,2]=>[2,2,2,1,1]
[1,7,3,5,4,6,2,8]=>[2,2,2,2]
[1,8,3,5,4,6,7,2]=>[2,2,3,1]
[1,8,3,5,4,7,6,2]=>[2,2,2,1,1]
[1,7,3,5,6,4,8,2]=>[2,3,2,1]
[1,8,3,5,6,4,7,2]=>[2,3,2,1]
[1,8,3,5,6,7,4,2]=>[2,4,1,1]
[1,8,3,5,7,6,4,2]=>[2,3,1,1,1]
[1,7,3,6,5,4,2,8]=>[2,2,1,1,2]
[1,7,3,6,5,4,8,2]=>[2,2,1,2,1]
[1,8,3,6,5,4,7,2]=>[2,2,1,2,1]
[1,8,3,6,5,7,4,2]=>[2,2,2,1,1]
[1,8,3,7,5,6,4,2]=>[2,2,2,1,1]
[1,8,3,7,6,5,4,2]=>[2,2,1,1,1,1]
[1,6,4,3,5,2,7,8]=>[2,1,2,3]
[1,6,4,3,5,8,7,2]=>[2,1,3,1,1]
[1,8,4,3,5,6,7,2]=>[2,1,4,1]
[1,8,4,3,5,7,6,2]=>[2,1,3,1,1]
[1,7,4,3,6,5,2,8]=>[2,1,2,1,2]
[1,7,4,3,6,5,8,2]=>[2,1,2,2,1]
[1,8,4,3,6,5,7,2]=>[2,1,2,2,1]
[1,8,4,3,6,7,5,2]=>[2,1,3,1,1]
[1,6,4,5,3,2,7,8]=>[2,2,1,3]
[1,6,4,5,3,2,8,7]=>[2,2,1,2,1]
[1,6,4,5,3,8,7,2]=>[2,2,2,1,1]
[1,7,4,5,3,6,8,2]=>[2,2,3,1]
[1,8,4,5,3,6,7,2]=>[2,2,3,1]
[1,8,4,5,3,7,6,2]=>[2,2,2,1,1]
[1,7,4,5,6,3,2,8]=>[2,3,1,2]
[1,7,4,5,6,3,8,2]=>[2,3,2,1]
[1,8,4,5,6,3,7,2]=>[2,3,2,1]
[1,8,4,5,6,7,3,2]=>[2,4,1,1]
[1,8,4,5,7,6,3,2]=>[2,3,1,1,1]
[1,7,4,6,5,3,2,8]=>[2,2,1,1,2]
[1,7,4,6,5,3,8,2]=>[2,2,1,2,1]
[1,8,4,6,5,3,7,2]=>[2,2,1,2,1]
[1,8,4,6,5,7,3,2]=>[2,2,2,1,1]
[1,8,4,7,5,6,3,2]=>[2,2,2,1,1]
[1,8,4,7,6,5,3,2]=>[2,2,1,1,1,1]
[1,7,5,4,3,6,2,8]=>[2,1,1,2,2]
[1,7,5,4,3,6,8,2]=>[2,1,1,3,1]
[1,8,5,4,3,6,7,2]=>[2,1,1,3,1]
[1,8,5,4,3,7,6,2]=>[2,1,1,2,1,1]
[1,7,5,4,6,3,8,2]=>[2,1,2,2,1]
[1,8,5,4,6,3,7,2]=>[2,1,2,2,1]
[1,8,5,4,6,7,3,2]=>[2,1,3,1,1]
[1,8,5,4,7,6,3,2]=>[2,1,2,1,1,1]
[1,7,6,4,5,3,2,8]=>[2,1,2,1,2]
[1,7,6,4,5,3,8,2]=>[2,1,2,2,1]
[1,8,6,4,5,3,7,2]=>[2,1,2,2,1]
[1,8,6,4,5,7,3,2]=>[2,1,3,1,1]
[1,8,7,4,5,6,3,2]=>[2,1,3,1,1]
[1,8,7,4,6,5,3,2]=>[2,1,2,1,1,1]
[1,8,6,5,4,3,7,2]=>[2,1,1,1,2,1]
[1,8,6,5,4,7,3,2]=>[2,1,1,2,1,1]
[1,8,7,5,4,6,3,2]=>[2,1,1,2,1,1]
[1,8,7,5,6,4,3,2]=>[2,1,2,1,1,1]
[2,1,3,4,8,6,7,5]=>[1,4,2,1]
[2,1,3,5,8,6,7,4]=>[1,4,2,1]
[2,1,3,7,5,6,8,4]=>[1,3,3,1]
[2,1,3,8,5,6,7,4]=>[1,3,3,1]
[2,1,3,8,5,7,6,4]=>[1,3,2,1,1]
[2,1,3,8,6,5,7,4]=>[1,3,1,2,1]
[2,1,3,8,6,7,5,4]=>[1,3,2,1,1]
[2,1,4,3,8,6,7,5]=>[1,2,2,2,1]
[2,1,4,5,8,6,7,3]=>[1,4,2,1]
[2,1,4,7,5,6,8,3]=>[1,3,3,1]
[2,1,4,8,5,6,7,3]=>[1,3,3,1]
[2,1,4,8,5,7,6,3]=>[1,3,2,1,1]
[2,1,4,8,6,5,7,3]=>[1,3,1,2,1]
[2,1,4,8,6,7,5,3]=>[1,3,2,1,1]
[2,1,5,4,8,6,7,3]=>[1,2,2,2,1]
[2,1,6,4,5,3,7,8]=>[1,2,2,3]
[2,1,6,4,5,3,8,7]=>[1,2,2,2,1]
[2,1,6,4,5,7,3,8]=>[1,2,3,2]
[2,1,6,4,5,7,8,3]=>[1,2,4,1]
[2,1,6,4,5,8,7,3]=>[1,2,3,1,1]
[2,1,7,4,5,6,8,3]=>[1,2,4,1]
[2,1,8,4,5,6,7,3]=>[1,2,4,1]
[2,1,8,4,5,7,6,3]=>[1,2,3,1,1]
[2,1,7,4,6,5,8,3]=>[1,2,2,2,1]
[2,1,8,4,6,5,7,3]=>[1,2,2,2,1]
[2,1,8,4,6,7,5,3]=>[1,2,3,1,1]
[2,1,8,4,7,6,5,3]=>[1,2,2,1,1,1]
[2,1,7,5,4,6,8,3]=>[1,2,1,3,1]
[2,1,8,5,4,6,7,3]=>[1,2,1,3,1]
[2,1,8,5,4,7,6,3]=>[1,2,1,2,1,1]
[2,1,7,5,6,4,3,8]=>[1,2,2,1,2]
[2,1,7,5,6,4,8,3]=>[1,2,2,2,1]
[2,1,8,5,6,4,7,3]=>[1,2,2,2,1]
[2,1,8,5,6,7,4,3]=>[1,2,3,1,1]
[2,1,8,5,7,6,4,3]=>[1,2,2,1,1,1]
[2,1,8,6,5,4,7,3]=>[1,2,1,1,2,1]
[2,1,8,6,5,7,4,3]=>[1,2,1,2,1,1]
[2,1,8,7,5,6,4,3]=>[1,2,1,2,1,1]
[2,3,1,4,8,6,7,5]=>[2,3,2,1]
[2,3,1,5,8,6,7,4]=>[2,3,2,1]
[2,3,1,7,5,6,4,8]=>[2,2,2,2]
[2,3,1,7,5,6,8,4]=>[2,2,3,1]
[2,3,1,8,5,6,7,4]=>[2,2,3,1]
[2,3,1,8,5,7,6,4]=>[2,2,2,1,1]
[2,3,1,8,6,5,7,4]=>[2,2,1,2,1]
[2,3,1,8,6,7,5,4]=>[2,2,2,1,1]
[2,3,4,1,8,6,7,5]=>[3,2,2,1]
[2,3,4,5,8,6,7,1]=>[5,2,1]
[2,3,4,7,5,6,1,8]=>[4,2,2]
[2,3,4,7,5,6,8,1]=>[4,3,1]
[2,3,4,8,5,6,7,1]=>[4,3,1]
[2,3,4,8,5,7,6,1]=>[4,2,1,1]
[2,3,4,8,6,5,7,1]=>[4,1,2,1]
[2,3,4,8,6,7,5,1]=>[4,2,1,1]
[2,3,5,4,8,6,7,1]=>[3,2,2,1]
[2,3,6,4,5,1,7,8]=>[3,2,3]
[2,3,6,4,5,1,8,7]=>[3,2,2,1]
[2,3,6,4,5,7,8,1]=>[3,4,1]
[2,3,6,4,5,8,7,1]=>[3,3,1,1]
[2,3,7,4,5,6,1,8]=>[3,3,2]
[2,3,7,4,5,6,8,1]=>[3,4,1]
[2,3,8,4,5,6,7,1]=>[3,4,1]
[2,3,8,4,5,7,6,1]=>[3,3,1,1]
[2,3,7,4,6,5,1,8]=>[3,2,1,2]
[2,3,7,4,6,5,8,1]=>[3,2,2,1]
[2,3,8,4,6,5,7,1]=>[3,2,2,1]
[2,3,8,4,6,7,5,1]=>[3,3,1,1]
[2,3,8,4,7,6,5,1]=>[3,2,1,1,1]
[2,3,7,5,4,6,1,8]=>[3,1,2,2]
[2,3,7,5,4,6,8,1]=>[3,1,3,1]
[2,3,8,5,4,6,7,1]=>[3,1,3,1]
[2,3,8,5,4,7,6,1]=>[3,1,2,1,1]
[2,3,7,5,6,4,1,8]=>[3,2,1,2]
[2,3,7,5,6,4,8,1]=>[3,2,2,1]
[2,3,8,5,6,4,7,1]=>[3,2,2,1]
[2,3,8,5,6,7,4,1]=>[3,3,1,1]
[2,3,8,5,7,6,4,1]=>[3,2,1,1,1]
[2,3,8,6,5,4,7,1]=>[3,1,1,2,1]
[2,3,8,6,5,7,4,1]=>[3,1,2,1,1]
[2,3,8,7,5,6,4,1]=>[3,1,2,1,1]
[2,4,3,1,8,6,7,5]=>[2,1,2,2,1]
[2,4,3,5,8,6,7,1]=>[2,3,2,1]
[2,4,3,7,5,6,1,8]=>[2,2,2,2]
[2,4,3,7,5,6,8,1]=>[2,2,3,1]
[2,4,3,8,5,6,7,1]=>[2,2,3,1]
[2,4,3,8,5,7,6,1]=>[2,2,2,1,1]
[2,4,3,8,6,5,7,1]=>[2,2,1,2,1]
[2,4,3,8,6,7,5,1]=>[2,2,2,1,1]
[2,5,3,4,1,6,7,8]=>[2,2,4]
[2,5,3,4,1,7,6,8]=>[2,2,2,2]
[2,5,3,4,1,7,8,6]=>[2,2,3,1]
[2,5,3,4,1,8,7,6]=>[2,2,2,1,1]
[2,5,3,4,6,1,8,7]=>[2,3,2,1]
[2,5,3,4,6,7,1,8]=>[2,4,2]
[2,5,3,4,6,7,8,1]=>[2,5,1]
[2,5,3,4,6,8,7,1]=>[2,4,1,1]
[2,5,3,4,7,6,1,8]=>[2,3,1,2]
[2,5,3,4,7,6,8,1]=>[2,3,2,1]
[2,5,3,4,8,6,7,1]=>[2,3,2,1]
[2,5,3,4,8,7,6,1]=>[2,3,1,1,1]
[2,6,3,4,5,1,7,8]=>[2,3,3]
[2,6,3,4,5,1,8,7]=>[2,3,2,1]
[2,6,3,4,5,7,8,1]=>[2,5,1]
[2,6,3,4,5,8,7,1]=>[2,4,1,1]
[2,7,3,4,5,6,1,8]=>[2,4,2]
[2,7,3,4,5,6,8,1]=>[2,5,1]
[2,8,3,4,5,6,7,1]=>[2,5,1]
[2,8,3,4,5,7,6,1]=>[2,4,1,1]
[2,8,3,4,6,7,5,1]=>[2,4,1,1]
[2,6,3,5,4,1,7,8]=>[2,2,1,3]
[2,6,3,5,4,1,8,7]=>[2,2,1,2,1]
[2,6,3,5,4,7,8,1]=>[2,2,3,1]
[2,6,3,5,4,8,7,1]=>[2,2,2,1,1]
[2,7,3,5,4,6,1,8]=>[2,2,2,2]
[2,7,3,5,4,6,8,1]=>[2,2,3,1]
[2,8,3,5,4,6,7,1]=>[2,2,3,1]
[2,8,3,5,4,7,6,1]=>[2,2,2,1,1]
[2,7,3,5,6,4,1,8]=>[2,3,1,2]
[2,7,3,5,6,4,8,1]=>[2,3,2,1]
[2,8,3,5,6,7,4,1]=>[2,4,1,1]
[2,8,3,5,7,6,4,1]=>[2,3,1,1,1]
[2,7,3,6,5,4,1,8]=>[2,2,1,1,2]
[2,8,3,6,5,4,7,1]=>[2,2,1,2,1]
[2,8,3,6,5,7,4,1]=>[2,2,2,1,1]
[2,8,3,7,5,6,4,1]=>[2,2,2,1,1]
[2,8,3,7,6,5,4,1]=>[2,2,1,1,1,1]
[2,5,4,3,8,6,7,1]=>[2,1,2,2,1]
[2,6,4,3,5,1,7,8]=>[2,1,2,3]
[2,6,4,3,5,1,8,7]=>[2,1,2,2,1]
[2,6,4,3,5,7,8,1]=>[2,1,4,1]
[2,6,4,3,5,8,7,1]=>[2,1,3,1,1]
[2,7,4,3,5,6,8,1]=>[2,1,4,1]
[2,8,4,3,5,6,7,1]=>[2,1,4,1]
[2,8,4,3,5,7,6,1]=>[2,1,3,1,1]
[2,7,4,3,6,5,1,8]=>[2,1,2,1,2]
[2,7,4,3,6,5,8,1]=>[2,1,2,2,1]
[2,8,4,3,6,5,7,1]=>[2,1,2,2,1]
[2,8,4,3,6,7,5,1]=>[2,1,3,1,1]
[2,8,4,3,7,6,5,1]=>[2,1,2,1,1,1]
[2,6,4,5,3,1,7,8]=>[2,2,1,3]
[2,6,4,5,3,1,8,7]=>[2,2,1,2,1]
[2,6,4,5,3,7,8,1]=>[2,2,3,1]
[2,6,4,5,3,8,7,1]=>[2,2,2,1,1]
[2,7,4,5,3,6,1,8]=>[2,2,2,2]
[2,8,4,5,3,6,7,1]=>[2,2,3,1]
[2,7,4,5,6,3,1,8]=>[2,3,1,2]
[2,7,4,5,6,3,8,1]=>[2,3,2,1]
[2,8,4,5,6,3,7,1]=>[2,3,2,1]
[2,8,4,5,6,7,3,1]=>[2,4,1,1]
[2,7,4,6,5,3,1,8]=>[2,2,1,1,2]
[2,7,4,6,5,3,8,1]=>[2,2,1,2,1]
[2,8,4,6,5,3,7,1]=>[2,2,1,2,1]
[2,8,4,6,5,7,3,1]=>[2,2,2,1,1]
[2,8,4,7,5,6,3,1]=>[2,2,2,1,1]
[2,8,4,7,6,5,3,1]=>[2,2,1,1,1,1]
[2,7,5,4,3,6,1,8]=>[2,1,1,2,2]
[2,7,5,4,3,6,8,1]=>[2,1,1,3,1]
[2,8,5,4,3,6,7,1]=>[2,1,1,3,1]
[2,8,5,4,3,7,6,1]=>[2,1,1,2,1,1]
[2,7,5,4,6,3,8,1]=>[2,1,2,2,1]
[2,8,5,4,6,3,7,1]=>[2,1,2,2,1]
[2,8,5,4,6,7,3,1]=>[2,1,3,1,1]
[2,8,5,4,7,6,3,1]=>[2,1,2,1,1,1]
[2,7,6,4,5,3,8,1]=>[2,1,2,2,1]
[2,8,6,4,5,3,7,1]=>[2,1,2,2,1]
[2,8,6,4,5,7,3,1]=>[2,1,3,1,1]
[2,8,7,4,5,6,3,1]=>[2,1,3,1,1]
[2,8,7,4,6,5,3,1]=>[2,1,2,1,1,1]
[2,8,6,5,4,3,7,1]=>[2,1,1,1,2,1]
[2,8,6,5,4,7,3,1]=>[2,1,1,2,1,1]
[2,8,7,5,4,6,3,1]=>[2,1,1,2,1,1]
[2,8,7,5,6,4,3,1]=>[2,1,2,1,1,1]
[3,2,1,4,8,6,7,5]=>[1,1,3,2,1]
[3,2,1,5,8,6,7,4]=>[1,1,3,2,1]
[3,2,1,7,5,6,4,8]=>[1,1,2,2,2]
[3,2,1,7,5,6,8,4]=>[1,1,2,3,1]
[3,2,1,8,5,6,7,4]=>[1,1,2,3,1]
[3,2,1,8,5,7,6,4]=>[1,1,2,2,1,1]
[3,2,1,8,6,5,7,4]=>[1,1,2,1,2,1]
[3,2,1,8,6,7,5,4]=>[1,1,2,2,1,1]
[3,2,4,1,8,6,7,5]=>[1,2,2,2,1]
[3,2,4,5,8,6,7,1]=>[1,4,2,1]
[3,2,4,7,5,6,1,8]=>[1,3,2,2]
[3,2,4,7,5,6,8,1]=>[1,3,3,1]
[3,2,4,8,5,6,7,1]=>[1,3,3,1]
[3,2,4,8,5,7,6,1]=>[1,3,2,1,1]
[3,2,4,8,6,5,7,1]=>[1,3,1,2,1]
[3,2,4,8,6,7,5,1]=>[1,3,2,1,1]
[3,2,5,4,8,6,7,1]=>[1,2,2,2,1]
[3,2,6,4,5,1,8,7]=>[1,2,2,2,1]
[3,2,6,4,5,7,1,8]=>[1,2,3,2]
[3,2,7,4,5,6,1,8]=>[1,2,3,2]
[3,2,8,4,5,6,7,1]=>[1,2,4,1]
[3,2,7,4,6,5,1,8]=>[1,2,2,1,2]
[3,2,7,4,6,5,8,1]=>[1,2,2,2,1]
[3,2,8,4,6,5,7,1]=>[1,2,2,2,1]
[3,2,7,5,4,6,1,8]=>[1,2,1,2,2]
[3,2,8,5,4,6,7,1]=>[1,2,1,3,1]
[3,2,8,5,4,7,6,1]=>[1,2,1,2,1,1]
[3,2,7,5,6,4,1,8]=>[1,2,2,1,2]
[3,2,7,5,6,4,8,1]=>[1,2,2,2,1]
[3,2,8,5,6,4,7,1]=>[1,2,2,2,1]
[3,2,8,5,6,7,4,1]=>[1,2,3,1,1]
[3,2,8,5,7,6,4,1]=>[1,2,2,1,1,1]
[3,2,8,6,5,4,7,1]=>[1,2,1,1,2,1]
[3,2,8,6,5,7,4,1]=>[1,2,1,2,1,1]
[3,2,8,7,5,6,4,1]=>[1,2,1,2,1,1]
[4,2,3,1,5,6,8,7]=>[1,2,4,1]
[4,2,3,1,5,7,6,8]=>[1,2,3,2]
[4,2,3,1,5,7,8,6]=>[1,2,4,1]
[4,2,3,1,5,8,7,6]=>[1,2,3,1,1]
[4,2,3,1,6,5,7,8]=>[1,2,2,3]
[4,2,3,1,6,5,8,7]=>[1,2,2,2,1]
[4,2,3,1,6,7,5,8]=>[1,2,3,2]
[4,2,3,1,6,7,8,5]=>[1,2,4,1]
[4,2,3,1,6,8,7,5]=>[1,2,3,1,1]
[4,2,3,1,7,6,5,8]=>[1,2,2,1,2]
[4,2,3,1,7,6,8,5]=>[1,2,2,2,1]
[4,2,3,1,8,6,7,5]=>[1,2,2,2,1]
[4,2,3,1,8,7,6,5]=>[1,2,2,1,1,1]
[4,2,3,5,1,6,8,7]=>[1,3,3,1]
[4,2,3,5,1,7,6,8]=>[1,3,2,2]
[4,2,3,5,1,7,8,6]=>[1,3,3,1]
[4,2,3,5,1,8,7,6]=>[1,3,2,1,1]
[4,2,3,5,6,1,8,7]=>[1,4,2,1]
[4,2,3,5,6,8,7,1]=>[1,5,1,1]
[4,2,3,5,7,6,1,8]=>[1,4,1,2]
[4,2,3,5,7,6,8,1]=>[1,4,2,1]
[4,2,3,5,8,7,6,1]=>[1,4,1,1,1]
[4,2,3,6,5,1,7,8]=>[1,3,1,3]
[4,2,3,6,5,1,8,7]=>[1,3,1,2,1]
[4,2,3,6,5,8,7,1]=>[1,3,2,1,1]
[4,2,3,7,5,6,1,8]=>[1,3,2,2]
[4,2,3,7,5,6,8,1]=>[1,3,3,1]
[4,2,3,8,5,6,7,1]=>[1,3,3,1]
[4,2,3,8,5,7,6,1]=>[1,3,2,1,1]
[4,2,3,7,6,5,1,8]=>[1,3,1,1,2]
[4,2,3,7,6,5,8,1]=>[1,3,1,2,1]
[4,2,3,8,6,5,7,1]=>[1,3,1,2,1]
[4,2,3,8,6,7,5,1]=>[1,3,2,1,1]
[4,2,3,8,7,6,5,1]=>[1,3,1,1,1,1]
[5,2,3,4,1,6,8,7]=>[1,3,3,1]
[5,2,3,4,1,7,6,8]=>[1,3,2,2]
[5,2,3,4,1,7,8,6]=>[1,3,3,1]
[5,2,3,4,1,8,7,6]=>[1,3,2,1,1]
[5,2,3,4,6,1,8,7]=>[1,4,2,1]
[5,2,3,4,6,8,7,1]=>[1,5,1,1]
[5,2,3,4,7,6,1,8]=>[1,4,1,2]
[5,2,3,4,7,6,8,1]=>[1,4,2,1]
[5,2,3,4,8,6,7,1]=>[1,4,2,1]
[5,2,3,4,8,7,6,1]=>[1,4,1,1,1]
[6,2,3,4,5,1,8,7]=>[1,4,2,1]
[6,2,3,4,5,8,7,1]=>[1,5,1,1]
[8,2,3,4,5,7,6,1]=>[1,5,1,1]
[7,2,3,4,6,5,1,8]=>[1,4,1,2]
[7,2,3,4,6,5,8,1]=>[1,4,2,1]
[8,2,3,4,6,5,7,1]=>[1,4,2,1]
[8,2,3,4,6,7,5,1]=>[1,5,1,1]
[8,2,3,4,7,6,5,1]=>[1,4,1,1,1]
[6,2,3,5,4,1,7,8]=>[1,3,1,3]
[6,2,3,5,4,1,8,7]=>[1,3,1,2,1]
[6,2,3,5,4,7,1,8]=>[1,3,2,2]
[6,2,3,5,4,7,8,1]=>[1,3,3,1]
[6,2,3,5,4,8,7,1]=>[1,3,2,1,1]
[7,2,3,5,4,6,1,8]=>[1,3,2,2]
[8,2,3,5,4,6,7,1]=>[1,3,3,1]
[8,2,3,5,4,7,6,1]=>[1,3,2,1,1]
[7,2,3,5,6,4,1,8]=>[1,4,1,2]
[7,2,3,5,6,4,8,1]=>[1,4,2,1]
[8,2,3,5,6,4,7,1]=>[1,4,2,1]
[8,2,3,5,6,7,4,1]=>[1,5,1,1]
[8,2,3,5,7,6,4,1]=>[1,4,1,1,1]
[7,2,3,6,5,4,1,8]=>[1,3,1,1,2]
[8,2,3,6,5,4,7,1]=>[1,3,1,2,1]
[8,2,3,6,5,7,4,1]=>[1,3,2,1,1]
[8,2,3,7,5,6,4,1]=>[1,3,2,1,1]
[8,2,3,7,6,5,4,1]=>[1,3,1,1,1,1]
[5,2,4,3,1,6,7,8]=>[1,2,1,4]
[5,2,4,3,1,6,8,7]=>[1,2,1,3,1]
[5,2,4,3,1,7,6,8]=>[1,2,1,2,2]
[5,2,4,3,1,7,8,6]=>[1,2,1,3,1]
[5,2,4,3,1,8,7,6]=>[1,2,1,2,1,1]
[5,2,4,3,6,1,7,8]=>[1,2,2,3]
[5,2,4,3,6,1,8,7]=>[1,2,2,2,1]
[5,2,4,3,6,7,1,8]=>[1,2,3,2]
[5,2,4,3,6,7,8,1]=>[1,2,4,1]
[5,2,4,3,7,6,1,8]=>[1,2,2,1,2]
[5,2,4,3,7,6,8,1]=>[1,2,2,2,1]
[5,2,4,3,8,7,6,1]=>[1,2,2,1,1,1]
[6,2,4,3,5,1,8,7]=>[1,2,2,2,1]
[6,2,4,3,5,8,7,1]=>[1,2,3,1,1]
[7,2,4,3,5,6,8,1]=>[1,2,4,1]
[8,2,4,3,5,6,7,1]=>[1,2,4,1]
[8,2,4,3,5,7,6,1]=>[1,2,3,1,1]
[7,2,4,3,6,5,1,8]=>[1,2,2,1,2]
[7,2,4,3,6,5,8,1]=>[1,2,2,2,1]
[8,2,4,3,6,5,7,1]=>[1,2,2,2,1]
[8,2,4,3,6,7,5,1]=>[1,2,3,1,1]
[8,2,4,3,7,6,5,1]=>[1,2,2,1,1,1]
[6,2,4,5,3,1,7,8]=>[1,3,1,3]
[6,2,4,5,3,1,8,7]=>[1,3,1,2,1]
[6,2,4,5,3,7,1,8]=>[1,3,2,2]
[6,2,4,5,3,7,8,1]=>[1,3,3,1]
[6,2,4,5,3,8,7,1]=>[1,3,2,1,1]
[7,2,4,5,3,6,1,8]=>[1,3,2,2]
[7,2,4,5,3,6,8,1]=>[1,3,3,1]
[8,2,4,5,3,6,7,1]=>[1,3,3,1]
[8,2,4,5,3,7,6,1]=>[1,3,2,1,1]
[7,2,4,5,6,3,1,8]=>[1,4,1,2]
[7,2,4,5,6,3,8,1]=>[1,4,2,1]
[8,2,4,5,6,3,7,1]=>[1,4,2,1]
[8,2,4,5,6,7,3,1]=>[1,5,1,1]
[8,2,4,5,7,6,3,1]=>[1,4,1,1,1]
[7,2,4,6,5,3,1,8]=>[1,3,1,1,2]
[7,2,4,6,5,3,8,1]=>[1,3,1,2,1]
[8,2,4,6,5,3,7,1]=>[1,3,1,2,1]
[8,2,4,6,5,7,3,1]=>[1,3,2,1,1]
[8,2,4,7,5,6,3,1]=>[1,3,2,1,1]
[8,2,4,7,6,5,3,1]=>[1,3,1,1,1,1]
[6,2,5,4,3,1,7,8]=>[1,2,1,1,3]
[6,2,5,4,3,1,8,7]=>[1,2,1,1,2,1]
[6,2,5,4,3,7,1,8]=>[1,2,1,2,2]
[6,2,5,4,3,7,8,1]=>[1,2,1,3,1]
[6,2,5,4,3,8,7,1]=>[1,2,1,2,1,1]
[7,2,5,4,3,6,1,8]=>[1,2,1,2,2]
[7,2,5,4,3,6,8,1]=>[1,2,1,3,1]
[8,2,5,4,3,6,7,1]=>[1,2,1,3,1]
[8,2,5,4,3,7,6,1]=>[1,2,1,2,1,1]
[7,2,5,4,6,3,1,8]=>[1,2,2,1,2]
[7,2,5,4,6,3,8,1]=>[1,2,2,2,1]
[8,2,5,4,6,3,7,1]=>[1,2,2,2,1]
[8,2,5,4,6,7,3,1]=>[1,2,3,1,1]
[8,2,5,4,7,6,3,1]=>[1,2,2,1,1,1]
[7,2,6,4,5,3,1,8]=>[1,2,2,1,2]
[7,2,6,4,5,3,8,1]=>[1,2,2,2,1]
[8,2,6,4,5,3,7,1]=>[1,2,2,2,1]
[8,2,6,4,5,7,3,1]=>[1,2,3,1,1]
[8,2,7,4,5,6,3,1]=>[1,2,3,1,1]
[8,2,7,4,6,5,3,1]=>[1,2,2,1,1,1]
[7,2,6,5,4,3,1,8]=>[1,2,1,1,1,2]
[7,2,6,5,4,3,8,1]=>[1,2,1,1,2,1]
[8,2,6,5,4,3,7,1]=>[1,2,1,1,2,1]
[8,2,6,5,4,7,3,1]=>[1,2,1,2,1,1]
[8,2,7,5,4,6,3,1]=>[1,2,1,2,1,1]
[8,2,7,5,6,4,3,1]=>[1,2,2,1,1,1]
[8,2,7,6,5,4,3,1]=>[1,2,1,1,1,1,1]
[4,3,2,1,8,6,7,5]=>[1,1,1,2,2,1]
[4,3,2,7,5,6,1,8]=>[1,1,2,2,2]
[4,3,2,7,5,6,8,1]=>[1,1,2,3,1]
[4,3,2,8,5,6,7,1]=>[1,1,2,3,1]
[4,3,2,8,5,7,6,1]=>[1,1,2,2,1,1]
[4,3,2,8,6,5,7,1]=>[1,1,2,1,2,1]
[4,3,2,8,6,7,5,1]=>[1,1,2,2,1,1]
[5,3,2,4,1,6,8,7]=>[1,1,2,3,1]
[5,3,2,4,1,7,6,8]=>[1,1,2,2,2]
[5,3,2,4,1,7,8,6]=>[1,1,2,3,1]
[5,3,2,4,1,8,7,6]=>[1,1,2,2,1,1]
[5,3,2,4,6,1,8,7]=>[1,1,3,2,1]
[5,3,2,4,6,8,7,1]=>[1,1,4,1,1]
[5,3,2,4,7,6,1,8]=>[1,1,3,1,2]
[5,3,2,4,7,6,8,1]=>[1,1,3,2,1]
[5,3,2,4,8,6,7,1]=>[1,1,3,2,1]
[5,3,2,4,8,7,6,1]=>[1,1,3,1,1,1]
[6,3,2,4,5,1,8,7]=>[1,1,3,2,1]
[6,3,2,4,5,8,7,1]=>[1,1,4,1,1]
[8,3,2,4,5,7,6,1]=>[1,1,4,1,1]
[8,3,2,4,6,5,7,1]=>[1,1,3,2,1]
[8,3,2,4,6,7,5,1]=>[1,1,4,1,1]
[8,3,2,4,7,6,5,1]=>[1,1,3,1,1,1]
[6,3,2,5,4,1,7,8]=>[1,1,2,1,3]
[6,3,2,5,4,1,8,7]=>[1,1,2,1,2,1]
[6,3,2,5,4,7,1,8]=>[1,1,2,2,2]
[6,3,2,5,4,7,8,1]=>[1,1,2,3,1]
[6,3,2,5,4,8,7,1]=>[1,1,2,2,1,1]
[7,3,2,5,4,6,1,8]=>[1,1,2,2,2]
[7,3,2,5,4,6,8,1]=>[1,1,2,3,1]
[8,3,2,5,4,6,7,1]=>[1,1,2,3,1]
[8,3,2,5,4,7,6,1]=>[1,1,2,2,1,1]
[7,3,2,5,6,4,8,1]=>[1,1,3,2,1]
[8,3,2,5,6,4,7,1]=>[1,1,3,2,1]
[8,3,2,5,6,7,4,1]=>[1,1,4,1,1]
[8,3,2,5,7,6,4,1]=>[1,1,3,1,1,1]
[7,3,2,6,5,4,8,1]=>[1,1,2,1,2,1]
[8,3,2,6,5,4,7,1]=>[1,1,2,1,2,1]
[8,3,2,6,5,7,4,1]=>[1,1,2,2,1,1]
[8,3,2,7,5,6,4,1]=>[1,1,2,2,1,1]
[8,3,2,7,6,5,4,1]=>[1,1,2,1,1,1,1]
[5,3,4,2,1,6,8,7]=>[1,2,1,3,1]
[5,3,4,2,1,7,6,8]=>[1,2,1,2,2]
[5,3,4,2,1,7,8,6]=>[1,2,1,3,1]
[5,3,4,2,1,8,7,6]=>[1,2,1,2,1,1]
[5,3,4,2,6,1,8,7]=>[1,2,2,2,1]
[5,3,4,2,7,6,1,8]=>[1,2,2,1,2]
[5,3,4,2,7,6,8,1]=>[1,2,2,2,1]
[5,3,4,2,8,6,7,1]=>[1,2,2,2,1]
[6,3,4,2,5,1,8,7]=>[1,2,2,2,1]
[6,3,4,2,5,8,7,1]=>[1,2,3,1,1]
[8,3,4,2,5,7,6,1]=>[1,2,3,1,1]
[7,3,4,2,6,5,1,8]=>[1,2,2,1,2]
[7,3,4,2,6,5,8,1]=>[1,2,2,2,1]
[8,3,4,2,6,5,7,1]=>[1,2,2,2,1]
[8,3,4,2,6,7,5,1]=>[1,2,3,1,1]
[8,3,4,2,7,6,5,1]=>[1,2,2,1,1,1]
[6,3,4,5,2,1,8,7]=>[1,3,1,2,1]
[6,3,4,5,2,8,7,1]=>[1,3,2,1,1]
[8,3,4,5,2,7,6,1]=>[1,3,2,1,1]
[8,3,4,5,7,6,2,1]=>[1,4,1,1,1]
[7,3,4,6,5,2,1,8]=>[1,3,1,1,2]
[7,3,4,6,5,2,8,1]=>[1,3,1,2,1]
[8,3,4,6,5,2,7,1]=>[1,3,1,2,1]
[8,3,4,6,5,7,2,1]=>[1,3,2,1,1]
[8,3,4,7,5,6,2,1]=>[1,3,2,1,1]
[8,3,4,7,6,5,2,1]=>[1,3,1,1,1,1]
[6,3,5,4,2,1,7,8]=>[1,2,1,1,3]
[6,3,5,4,2,1,8,7]=>[1,2,1,1,2,1]
[6,3,5,4,2,7,1,8]=>[1,2,1,2,2]
[6,3,5,4,2,7,8,1]=>[1,2,1,3,1]
[6,3,5,4,2,8,7,1]=>[1,2,1,2,1,1]
[7,3,5,4,2,6,1,8]=>[1,2,1,2,2]
[7,3,5,4,2,6,8,1]=>[1,2,1,3,1]
[8,3,5,4,2,6,7,1]=>[1,2,1,3,1]
[8,3,5,4,2,7,6,1]=>[1,2,1,2,1,1]
[7,3,5,4,6,2,1,8]=>[1,2,2,1,2]
[7,3,5,4,6,2,8,1]=>[1,2,2,2,1]
[8,3,5,4,6,2,7,1]=>[1,2,2,2,1]
[8,3,5,4,6,7,2,1]=>[1,2,3,1,1]
[8,3,5,4,7,6,2,1]=>[1,2,2,1,1,1]
[7,3,6,4,5,2,1,8]=>[1,2,2,1,2]
[7,3,6,4,5,2,8,1]=>[1,2,2,2,1]
[8,3,6,4,5,2,7,1]=>[1,2,2,2,1]
[8,3,6,4,5,7,2,1]=>[1,2,3,1,1]
[8,3,7,4,5,6,2,1]=>[1,2,3,1,1]
[8,3,7,4,6,5,2,1]=>[1,2,2,1,1,1]
[7,3,6,5,4,2,1,8]=>[1,2,1,1,1,2]
[7,3,6,5,4,2,8,1]=>[1,2,1,1,2,1]
[8,3,6,5,4,2,7,1]=>[1,2,1,1,2,1]
[8,3,6,5,4,7,2,1]=>[1,2,1,2,1,1]
[8,3,7,5,4,6,2,1]=>[1,2,1,2,1,1]
[8,3,7,5,6,4,2,1]=>[1,2,2,1,1,1]
[8,3,7,6,5,4,2,1]=>[1,2,1,1,1,1,1]
[5,4,3,2,8,6,7,1]=>[1,1,1,2,2,1]
[6,4,3,2,5,1,8,7]=>[1,1,1,2,2,1]
[6,4,3,2,5,8,7,1]=>[1,1,1,3,1,1]
[8,4,3,2,5,7,6,1]=>[1,1,1,3,1,1]
[7,4,3,2,6,5,1,8]=>[1,1,1,2,1,2]
[7,4,3,2,6,5,8,1]=>[1,1,1,2,2,1]
[8,4,3,2,6,5,7,1]=>[1,1,1,2,2,1]
[8,4,3,2,6,7,5,1]=>[1,1,1,3,1,1]
[8,4,3,2,7,6,5,1]=>[1,1,1,2,1,1,1]
[6,4,3,5,2,1,8,7]=>[1,1,2,1,2,1]
[6,4,3,5,2,8,7,1]=>[1,1,2,2,1,1]
[8,4,3,5,2,7,6,1]=>[1,1,2,2,1,1]
[8,4,3,5,7,6,2,1]=>[1,1,3,1,1,1]
[7,4,3,6,5,2,1,8]=>[1,1,2,1,1,2]
[7,4,3,6,5,2,8,1]=>[1,1,2,1,2,1]
[8,4,3,6,5,2,7,1]=>[1,1,2,1,2,1]
[8,4,3,6,5,7,2,1]=>[1,1,2,2,1,1]
[8,4,3,7,5,6,2,1]=>[1,1,2,2,1,1]
[8,4,3,7,6,5,2,1]=>[1,1,2,1,1,1,1]
[6,5,3,4,2,1,8,7]=>[1,1,2,1,2,1]
[6,5,3,4,2,8,7,1]=>[1,1,2,2,1,1]
[8,5,3,4,2,7,6,1]=>[1,1,2,2,1,1]
[8,5,3,4,7,6,2,1]=>[1,1,3,1,1,1]
[8,7,3,4,6,5,2,1]=>[1,1,3,1,1,1]
[7,6,3,5,4,2,1,8]=>[1,1,2,1,1,2]
[7,6,3,5,4,2,8,1]=>[1,1,2,1,2,1]
[8,6,3,5,4,2,7,1]=>[1,1,2,1,2,1]
[8,6,3,5,4,7,2,1]=>[1,1,2,2,1,1]
[8,7,3,5,4,6,2,1]=>[1,1,2,2,1,1]
[8,7,3,5,6,4,2,1]=>[1,1,3,1,1,1]
[8,7,3,6,5,4,2,1]=>[1,1,2,1,1,1,1]
[8,5,4,3,2,7,6,1]=>[1,1,1,1,2,1,1]
[8,5,4,3,7,6,2,1]=>[1,1,1,2,1,1,1]
[8,7,4,3,6,5,2,1]=>[1,1,1,2,1,1,1]
[8,7,4,6,5,3,2,1]=>[1,1,2,1,1,1,1]
[2,4,1,3,6,5,8,7]=>[2,3,2,1]
[2,1,4,6,3,5,8,7]=>[1,3,3,1]
[2,4,1,6,3,5,8,7]=>[2,2,3,1]
[2,4,6,1,3,5,8,7]=>[3,4,1]
[2,1,4,3,6,8,5,7]=>[1,2,3,2]
[2,4,1,3,6,8,5,7]=>[2,4,2]
[2,1,4,6,3,8,5,7]=>[1,3,2,2]
[2,4,1,6,3,8,5,7]=>[2,2,2,2]
[2,4,6,1,3,8,5,7]=>[3,3,2]
[2,1,4,6,8,3,5,7]=>[1,4,3]
[2,4,1,6,8,3,5,7]=>[2,3,3]
[2,4,6,1,8,3,5,7]=>[3,2,3]
[2,4,6,8,1,3,5,7]=>[4,4]
[2,4,1,3,6,5,7,8]=>[2,3,3]
[2,1,4,6,3,5,7,8]=>[1,3,4]
[2,4,1,6,3,5,7,8]=>[2,2,4]
[2,4,6,1,3,5,7,8]=>[3,5]
[2,4,1,3,6,7,5,8]=>[2,4,2]
[2,1,4,6,3,7,5,8]=>[1,3,2,2]
[2,4,1,6,3,7,5,8]=>[2,2,2,2]
[2,4,6,1,3,7,5,8]=>[3,3,2]
[2,4,1,6,7,3,5,8]=>[2,3,3]
[2,4,6,7,1,3,5,8]=>[4,4]
[2,4,1,3,6,7,8,5]=>[2,5,1]
[2,1,4,6,3,7,8,5]=>[1,3,3,1]
[2,4,1,6,3,7,8,5]=>[2,2,3,1]
[2,4,6,1,3,7,8,5]=>[3,4,1]
[2,1,4,6,7,3,8,5]=>[1,4,2,1]
[2,4,1,6,7,3,8,5]=>[2,3,2,1]
[2,4,6,1,7,3,8,5]=>[3,2,2,1]
[2,4,6,7,1,3,8,5]=>[4,3,1]
[2,1,4,6,7,8,3,5]=>[1,5,2]
[2,4,1,6,7,8,3,5]=>[2,4,2]
[2,4,6,1,7,8,3,5]=>[3,3,2]
[2,4,6,7,1,8,3,5]=>[4,2,2]
[2,4,6,7,8,1,3,5]=>[5,3]
[2,1,4,3,7,5,8,6]=>[1,2,2,2,1]
[2,4,1,3,7,5,8,6]=>[2,3,2,1]
[2,1,4,7,3,5,8,6]=>[1,3,3,1]
[2,4,1,7,3,5,8,6]=>[2,2,3,1]
[2,4,7,1,3,5,8,6]=>[3,4,1]
[2,1,4,3,7,8,5,6]=>[1,2,3,2]
[2,4,1,3,7,8,5,6]=>[2,4,2]
[2,1,4,7,3,8,5,6]=>[1,3,2,2]
[2,4,1,7,3,8,5,6]=>[2,2,2,2]
[2,4,7,1,3,8,5,6]=>[3,3,2]
[2,1,4,7,8,3,5,6]=>[1,4,3]
[2,4,1,7,8,3,5,6]=>[2,3,3]
[2,4,7,1,8,3,5,6]=>[3,2,3]
[2,4,7,8,1,3,5,6]=>[4,4]
[2,4,1,3,7,5,6,8]=>[2,3,3]
[2,1,4,7,3,5,6,8]=>[1,3,4]
[2,4,7,1,3,5,6,8]=>[3,5]
[2,4,1,3,5,7,6,8]=>[2,4,2]
[2,4,1,5,3,7,6,8]=>[2,2,2,2]
[2,4,5,1,3,7,6,8]=>[3,3,2]
[2,4,5,1,7,3,6,8]=>[3,2,3]
[2,4,1,3,5,7,8,6]=>[2,5,1]
[2,4,1,5,3,7,8,6]=>[2,2,3,1]
[2,4,5,1,3,7,8,6]=>[3,4,1]
[2,1,4,5,7,3,8,6]=>[1,4,2,1]
[2,4,1,5,7,3,8,6]=>[2,3,2,1]
[2,4,5,1,7,3,8,6]=>[3,2,2,1]
[2,4,5,7,1,3,8,6]=>[4,3,1]
[2,1,4,5,7,8,3,6]=>[1,5,2]
[2,4,1,5,7,8,3,6]=>[2,4,2]
[2,4,5,1,7,8,3,6]=>[3,3,2]
[2,4,5,7,1,8,3,6]=>[4,2,2]
[2,4,5,7,8,1,3,6]=>[5,3]
[2,1,4,3,8,5,6,7]=>[1,2,2,3]
[2,4,1,3,8,5,6,7]=>[2,3,3]
[2,1,4,8,3,5,6,7]=>[1,3,4]
[2,4,1,8,3,5,6,7]=>[2,2,4]
[2,4,8,1,3,5,6,7]=>[3,5]
[2,1,4,3,5,8,6,7]=>[1,2,3,2]
[2,4,1,3,5,8,6,7]=>[2,4,2]
[2,4,1,5,3,8,6,7]=>[2,2,2,2]
[2,1,4,5,8,3,6,7]=>[1,4,3]
[2,4,1,5,8,3,6,7]=>[2,3,3]
[2,4,5,1,8,3,6,7]=>[3,2,3]
[2,4,5,8,1,3,6,7]=>[4,4]
[2,4,1,3,5,6,8,7]=>[2,5,1]
[2,4,1,5,3,6,8,7]=>[2,2,3,1]
[2,4,1,5,6,3,8,7]=>[2,3,2,1]
[2,4,5,1,6,3,8,7]=>[3,2,2,1]
[2,4,5,6,1,3,8,7]=>[4,3,1]
[2,1,4,5,6,8,3,7]=>[1,5,2]
[2,4,1,5,6,8,3,7]=>[2,4,2]
[2,4,5,1,6,8,3,7]=>[3,3,2]
[2,4,5,6,1,8,3,7]=>[4,2,2]
[2,4,5,6,8,1,3,7]=>[5,3]
[2,4,1,3,5,6,7,8]=>[2,6]
[2,4,1,5,3,6,7,8]=>[2,2,4]
[2,4,5,1,3,6,7,8]=>[3,5]
[2,4,1,5,6,3,7,8]=>[2,3,3]
[2,4,5,1,6,3,7,8]=>[3,2,3]
[2,4,5,6,1,3,7,8]=>[4,4]
[2,4,1,5,6,7,3,8]=>[2,4,2]
[2,4,5,1,6,7,3,8]=>[3,3,2]
[2,4,5,6,1,7,3,8]=>[4,2,2]
[2,4,5,6,7,1,3,8]=>[5,3]
[2,4,1,5,6,7,8,3]=>[2,5,1]
[2,4,5,1,6,7,8,3]=>[3,4,1]
[2,4,5,6,1,7,8,3]=>[4,3,1]
[2,4,5,6,7,1,8,3]=>[5,2,1]
[2,4,5,6,7,8,1,3]=>[6,2]
[2,1,5,3,6,4,8,7]=>[1,2,2,2,1]
[2,5,1,3,6,4,8,7]=>[2,3,2,1]
[2,1,5,6,3,4,8,7]=>[1,3,3,1]
[2,5,1,6,3,4,8,7]=>[2,2,3,1]
[2,5,6,1,3,4,8,7]=>[3,4,1]
[2,1,5,3,6,8,4,7]=>[1,2,3,2]
[2,5,1,3,6,8,4,7]=>[2,4,2]
[2,5,1,6,3,8,4,7]=>[2,2,2,2]
[2,5,6,1,3,8,4,7]=>[3,3,2]
[2,1,5,6,8,3,4,7]=>[1,4,3]
[2,5,1,6,8,3,4,7]=>[2,3,3]
[2,5,6,1,8,3,4,7]=>[3,2,3]
[2,5,6,8,1,3,4,7]=>[4,4]
[2,1,5,3,6,4,7,8]=>[1,2,2,3]
[2,5,1,3,6,4,7,8]=>[2,3,3]
[2,1,5,6,3,4,7,8]=>[1,3,4]
[2,5,1,6,3,4,7,8]=>[2,2,4]
[2,5,6,1,3,4,7,8]=>[3,5]
[2,1,5,3,6,7,4,8]=>[1,2,3,2]
[2,5,1,3,6,7,4,8]=>[2,4,2]
[2,1,5,6,3,7,4,8]=>[1,3,2,2]
[2,5,1,6,3,7,4,8]=>[2,2,2,2]
[2,5,6,1,3,7,4,8]=>[3,3,2]
[2,1,5,6,7,3,4,8]=>[1,4,3]
[2,5,1,6,7,3,4,8]=>[2,3,3]
[2,5,6,1,7,3,4,8]=>[3,2,3]
[2,5,6,7,1,3,4,8]=>[4,4]
[2,1,5,3,6,7,8,4]=>[1,2,4,1]
[2,5,1,3,6,7,8,4]=>[2,5,1]
[2,1,5,6,3,7,8,4]=>[1,3,3,1]
[2,5,1,6,3,7,8,4]=>[2,2,3,1]
[2,5,6,1,3,7,8,4]=>[3,4,1]
[2,1,5,6,7,3,8,4]=>[1,4,2,1]
[2,5,1,6,7,3,8,4]=>[2,3,2,1]
[2,5,6,1,7,3,8,4]=>[3,2,2,1]
[2,5,6,7,1,3,8,4]=>[4,3,1]
[2,1,5,6,7,8,3,4]=>[1,5,2]
[2,5,1,6,7,8,3,4]=>[2,4,2]
[2,5,6,1,7,8,3,4]=>[3,3,2]
[2,5,6,7,1,8,3,4]=>[4,2,2]
[2,5,6,7,8,1,3,4]=>[5,3]
[2,1,5,3,7,4,8,6]=>[1,2,2,2,1]
[2,5,1,3,7,4,8,6]=>[2,3,2,1]
[2,1,5,7,3,4,8,6]=>[1,3,3,1]
[2,5,1,7,3,4,8,6]=>[2,2,3,1]
[2,5,7,1,3,4,8,6]=>[3,4,1]
[2,1,5,3,7,8,4,6]=>[1,2,3,2]
[2,5,1,3,7,8,4,6]=>[2,4,2]
[2,1,5,7,3,8,4,6]=>[1,3,2,2]
[2,5,1,7,3,8,4,6]=>[2,2,2,2]
[2,5,7,1,3,8,4,6]=>[3,3,2]
[2,1,5,7,8,3,4,6]=>[1,4,3]
[2,5,1,7,8,3,4,6]=>[2,3,3]
[2,5,7,1,8,3,4,6]=>[3,2,3]
[2,5,7,8,1,3,4,6]=>[4,4]
[2,1,5,3,7,4,6,8]=>[1,2,2,3]
[2,5,1,3,7,4,6,8]=>[2,3,3]
[2,1,5,7,3,4,6,8]=>[1,3,4]
[2,5,1,3,4,7,6,8]=>[2,4,2]
[2,3,5,1,4,7,6,8]=>[3,3,2]
[2,3,1,5,7,4,6,8]=>[2,3,3]
[2,3,5,7,1,4,6,8]=>[4,4]
[2,5,1,3,4,7,8,6]=>[2,5,1]
[2,3,5,1,4,7,8,6]=>[3,4,1]
[2,3,5,1,7,4,8,6]=>[3,2,2,1]
[2,3,5,7,1,4,8,6]=>[4,3,1]
[2,1,3,5,7,8,4,6]=>[1,5,2]
[2,3,1,5,7,8,4,6]=>[2,4,2]
[2,3,5,1,7,8,4,6]=>[3,3,2]
[2,3,5,7,1,8,4,6]=>[4,2,2]
[2,3,5,7,8,1,4,6]=>[5,3]
[2,1,5,3,8,4,6,7]=>[1,2,2,3]
[2,5,1,3,8,4,6,7]=>[2,3,3]
[2,1,5,8,3,4,6,7]=>[1,3,4]
[2,5,1,8,3,4,6,7]=>[2,2,4]
[2,5,8,1,3,4,6,7]=>[3,5]
[2,5,1,3,4,8,6,7]=>[2,4,2]
[2,1,3,5,4,8,6,7]=>[1,3,2,2]
[2,3,5,1,4,8,6,7]=>[3,3,2]
[2,1,3,5,8,4,6,7]=>[1,4,3]
[2,3,1,5,8,4,6,7]=>[2,3,3]
[2,3,5,1,8,4,6,7]=>[3,2,3]
[2,3,5,8,1,4,6,7]=>[4,4]
[2,1,5,3,4,6,8,7]=>[1,2,4,1]
[2,3,5,1,6,4,8,7]=>[3,2,2,1]
[2,3,5,6,1,4,8,7]=>[4,3,1]
[2,3,1,5,6,8,4,7]=>[2,4,2]
[2,3,5,1,6,8,4,7]=>[3,3,2]
[2,3,5,6,1,8,4,7]=>[4,2,2]
[2,3,5,6,8,1,4,7]=>[5,3]
[2,1,5,3,4,6,7,8]=>[1,2,5]
[2,5,1,3,4,6,7,8]=>[2,6]
[2,3,5,1,4,6,7,8]=>[3,5]
[2,3,5,1,6,4,7,8]=>[3,2,3]
[2,3,5,6,1,4,7,8]=>[4,4]
[2,3,5,1,6,7,4,8]=>[3,3,2]
[2,3,5,6,1,7,4,8]=>[4,2,2]
[2,3,5,6,7,1,4,8]=>[5,3]
[2,3,5,1,6,7,8,4]=>[3,4,1]
[2,3,5,6,1,7,8,4]=>[4,3,1]
[2,3,5,6,7,1,8,4]=>[5,2,1]
[2,3,5,6,7,8,1,4]=>[6,2]
[2,1,6,3,7,4,8,5]=>[1,2,2,2,1]
[2,6,1,3,7,4,8,5]=>[2,3,2,1]
[2,1,6,7,3,4,8,5]=>[1,3,3,1]
[2,6,1,7,3,4,8,5]=>[2,2,3,1]
[2,6,7,1,3,4,8,5]=>[3,4,1]
[2,1,6,3,7,8,4,5]=>[1,2,3,2]
[2,6,1,3,7,8,4,5]=>[2,4,2]
[2,1,6,7,3,8,4,5]=>[1,3,2,2]
[2,6,1,7,3,8,4,5]=>[2,2,2,2]
[2,6,7,1,3,8,4,5]=>[3,3,2]
[2,1,6,7,8,3,4,5]=>[1,4,3]
[2,6,1,7,8,3,4,5]=>[2,3,3]
[2,6,7,1,8,3,4,5]=>[3,2,3]
[2,6,7,8,1,3,4,5]=>[4,4]
[2,1,6,3,7,4,5,8]=>[1,2,2,3]
[2,6,1,3,7,4,5,8]=>[2,3,3]
[2,1,6,7,3,4,5,8]=>[1,3,4]
[2,6,1,7,3,4,5,8]=>[2,2,4]
[2,6,7,1,3,4,5,8]=>[3,5]
[2,1,6,3,4,7,5,8]=>[1,2,3,2]
[2,6,1,3,4,7,5,8]=>[2,4,2]
[2,3,1,6,4,7,5,8]=>[2,2,2,2]
[2,3,6,1,4,7,5,8]=>[3,3,2]
[2,3,1,6,7,4,5,8]=>[2,3,3]
[2,3,6,1,7,4,5,8]=>[3,2,3]
[2,3,6,7,1,4,5,8]=>[4,4]
[2,1,6,3,4,7,8,5]=>[1,2,4,1]
[2,6,1,3,4,7,8,5]=>[2,5,1]
[2,1,3,6,4,7,8,5]=>[1,3,3,1]
[2,3,1,6,4,7,8,5]=>[2,2,3,1]
[2,3,6,1,4,7,8,5]=>[3,4,1]
[2,1,3,6,7,4,8,5]=>[1,4,2,1]
[2,3,1,6,7,4,8,5]=>[2,3,2,1]
[2,3,6,1,7,4,8,5]=>[3,2,2,1]
[2,3,6,7,1,4,8,5]=>[4,3,1]
[2,1,3,6,7,8,4,5]=>[1,5,2]
[2,3,1,6,7,8,4,5]=>[2,4,2]
[2,3,6,1,7,8,4,5]=>[3,3,2]
[2,3,6,7,1,8,4,5]=>[4,2,2]
[2,3,6,7,8,1,4,5]=>[5,3]
[2,1,6,3,8,4,5,7]=>[1,2,2,3]
[2,6,1,3,8,4,5,7]=>[2,3,3]
[2,1,6,8,3,4,5,7]=>[1,3,4]
[2,6,1,8,3,4,5,7]=>[2,2,4]
[2,6,8,1,3,4,5,7]=>[3,5]
[2,1,6,3,4,8,5,7]=>[1,2,3,2]
[2,6,1,3,4,8,5,7]=>[2,4,2]
[2,1,3,6,4,8,5,7]=>[1,3,2,2]
[2,3,1,6,4,8,5,7]=>[2,2,2,2]
[2,3,6,1,4,8,5,7]=>[3,3,2]
[2,3,1,6,8,4,5,7]=>[2,3,3]
[2,3,6,1,8,4,5,7]=>[3,2,3]
[2,3,6,8,1,4,5,7]=>[4,4]
[2,1,6,3,4,5,8,7]=>[1,2,4,1]
[2,6,1,3,4,5,8,7]=>[2,5,1]
[2,1,3,6,4,5,8,7]=>[1,3,3,1]
[2,3,1,6,4,5,8,7]=>[2,2,3,1]
[2,3,6,1,4,5,8,7]=>[3,4,1]
[2,3,4,6,1,5,8,7]=>[4,3,1]
[2,1,3,4,6,8,5,7]=>[1,5,2]
[2,3,1,4,6,8,5,7]=>[2,4,2]
[2,3,4,1,6,8,5,7]=>[3,3,2]
[2,3,4,6,1,8,5,7]=>[4,2,2]
[2,3,4,6,8,1,5,7]=>[5,3]
[2,1,6,3,4,5,7,8]=>[1,2,5]
[2,6,1,3,4,5,7,8]=>[2,6]
[2,1,3,6,4,5,7,8]=>[1,3,4]
[2,3,1,6,4,5,7,8]=>[2,2,4]
[2,3,6,1,4,5,7,8]=>[3,5]
[2,3,4,6,1,5,7,8]=>[4,4]
[2,3,4,6,1,7,5,8]=>[4,2,2]
[2,3,4,6,7,1,5,8]=>[5,3]
[2,3,4,6,1,7,8,5]=>[4,3,1]
[2,3,4,6,7,1,8,5]=>[5,2,1]
[2,3,4,6,7,8,1,5]=>[6,2]
[2,1,7,3,8,4,5,6]=>[1,2,2,3]
[2,7,1,3,8,4,5,6]=>[2,3,3]
[2,1,7,8,3,4,5,6]=>[1,3,4]
[2,7,1,8,3,4,5,6]=>[2,2,4]
[2,7,8,1,3,4,5,6]=>[3,5]
[2,1,7,3,4,8,5,6]=>[1,2,3,2]
[2,7,1,3,4,8,5,6]=>[2,4,2]
[2,1,3,7,4,8,5,6]=>[1,3,2,2]
[2,3,1,7,4,8,5,6]=>[2,2,2,2]
[2,3,7,1,4,8,5,6]=>[3,3,2]
[2,1,3,7,8,4,5,6]=>[1,4,3]
[2,3,1,7,8,4,5,6]=>[2,3,3]
[2,3,7,1,8,4,5,6]=>[3,2,3]
[2,3,7,8,1,4,5,6]=>[4,4]
[2,1,7,3,4,5,8,6]=>[1,2,4,1]
[2,7,1,3,4,5,8,6]=>[2,5,1]
[2,1,3,7,4,5,8,6]=>[1,3,3,1]
[2,3,1,7,4,5,8,6]=>[2,2,3,1]
[2,3,7,1,4,5,8,6]=>[3,4,1]
[2,1,3,4,7,5,8,6]=>[1,4,2,1]
[2,3,4,1,7,5,8,6]=>[3,2,2,1]
[2,3,4,7,1,5,8,6]=>[4,3,1]
[2,1,3,4,7,8,5,6]=>[1,5,2]
[2,3,1,4,7,8,5,6]=>[2,4,2]
[2,3,4,1,7,8,5,6]=>[3,3,2]
[2,3,4,7,1,8,5,6]=>[4,2,2]
[2,3,4,7,8,1,5,6]=>[5,3]
[2,1,7,3,4,5,6,8]=>[1,2,5]
[2,7,1,3,4,5,6,8]=>[2,6]
[2,1,3,7,4,5,6,8]=>[1,3,4]
[2,3,1,7,4,5,6,8]=>[2,2,4]
[2,3,7,1,4,5,6,8]=>[3,5]
[2,1,3,4,7,5,6,8]=>[1,4,3]
[2,3,1,4,7,5,6,8]=>[2,3,3]
[2,3,4,1,7,5,6,8]=>[3,2,3]
[2,3,4,7,1,5,6,8]=>[4,4]
[2,3,4,5,7,1,6,8]=>[5,3]
[2,3,4,5,7,1,8,6]=>[5,2,1]
[2,3,4,5,7,8,1,6]=>[6,2]
[2,1,8,3,4,5,6,7]=>[1,2,5]
[2,8,1,3,4,5,6,7]=>[2,6]
[2,1,3,8,4,5,6,7]=>[1,3,4]
[2,3,1,8,4,5,6,7]=>[2,2,4]
[2,3,8,1,4,5,6,7]=>[3,5]
[2,1,3,4,8,5,6,7]=>[1,4,3]
[2,3,1,4,8,5,6,7]=>[2,3,3]
[2,3,4,1,8,5,6,7]=>[3,2,3]
[2,3,4,8,1,5,6,7]=>[4,4]
[2,1,3,4,5,8,6,7]=>[1,5,2]
[2,3,1,4,5,8,6,7]=>[2,4,2]
[2,3,4,1,5,8,6,7]=>[3,3,2]
[2,3,4,5,1,8,6,7]=>[4,2,2]
[2,3,4,5,8,1,6,7]=>[5,3]
[2,3,4,5,6,8,1,7]=>[6,2]
[3,1,4,2,6,5,8,7]=>[1,2,2,2,1]
[3,4,1,2,6,5,8,7]=>[2,3,2,1]
[3,1,4,6,2,5,8,7]=>[1,3,3,1]
[3,4,1,6,2,5,8,7]=>[2,2,3,1]
[3,4,6,1,2,5,8,7]=>[3,4,1]
[3,1,4,2,6,8,5,7]=>[1,2,3,2]
[3,4,1,2,6,8,5,7]=>[2,4,2]
[3,1,4,6,2,8,5,7]=>[1,3,2,2]
[3,4,1,6,2,8,5,7]=>[2,2,2,2]
[3,1,4,6,8,2,5,7]=>[1,4,3]
[3,4,1,6,8,2,5,7]=>[2,3,3]
[3,4,6,1,8,2,5,7]=>[3,2,3]
[3,4,6,8,1,2,5,7]=>[4,4]
[3,1,4,2,6,5,7,8]=>[1,2,2,3]
[3,4,1,2,6,5,7,8]=>[2,3,3]
[3,1,4,6,2,5,7,8]=>[1,3,4]
[3,4,1,6,2,5,7,8]=>[2,2,4]
[3,4,6,1,2,5,7,8]=>[3,5]
[3,1,4,2,6,7,5,8]=>[1,2,3,2]
[3,4,1,2,6,7,5,8]=>[2,4,2]
[3,1,4,6,2,7,5,8]=>[1,3,2,2]
[3,4,1,6,2,7,5,8]=>[2,2,2,2]
[3,4,6,1,2,7,5,8]=>[3,3,2]
[3,1,4,6,7,2,5,8]=>[1,4,3]
[3,4,1,6,7,2,5,8]=>[2,3,3]
[3,4,6,1,7,2,5,8]=>[3,2,3]
[3,4,6,7,1,2,5,8]=>[4,4]
[3,1,4,2,6,7,8,5]=>[1,2,4,1]
[3,4,1,2,6,7,8,5]=>[2,5,1]
[3,1,4,6,2,7,8,5]=>[1,3,3,1]
[3,4,1,6,2,7,8,5]=>[2,2,3,1]
[3,4,6,1,2,7,8,5]=>[3,4,1]
[3,1,4,6,7,2,8,5]=>[1,4,2,1]
[3,4,1,6,7,2,8,5]=>[2,3,2,1]
[3,4,6,1,7,2,8,5]=>[3,2,2,1]
[3,4,6,7,1,2,8,5]=>[4,3,1]
[3,1,4,6,7,8,2,5]=>[1,5,2]
[3,4,1,6,7,8,2,5]=>[2,4,2]
[3,4,6,1,7,8,2,5]=>[3,3,2]
[3,4,6,7,1,8,2,5]=>[4,2,2]
[3,4,6,7,8,1,2,5]=>[5,3]
[3,1,4,2,7,5,8,6]=>[1,2,2,2,1]
[3,4,1,2,7,5,8,6]=>[2,3,2,1]
[3,1,4,7,2,5,8,6]=>[1,3,3,1]
[3,4,1,7,2,5,8,6]=>[2,2,3,1]
[3,4,7,1,2,5,8,6]=>[3,4,1]
[3,1,4,2,7,8,5,6]=>[1,2,3,2]
[3,4,1,2,7,8,5,6]=>[2,4,2]
[3,1,4,7,2,8,5,6]=>[1,3,2,2]
[3,4,7,1,2,8,5,6]=>[3,3,2]
[3,4,1,7,8,2,5,6]=>[2,3,3]
[3,4,7,1,8,2,5,6]=>[3,2,3]
[3,4,7,8,1,2,5,6]=>[4,4]
[3,1,4,2,7,5,6,8]=>[1,2,2,3]
[3,4,1,2,7,5,6,8]=>[2,3,3]
[3,1,4,7,2,5,6,8]=>[1,3,4]
[3,4,7,1,2,5,6,8]=>[3,5]
[3,1,4,2,5,7,6,8]=>[1,2,3,2]
[3,4,1,2,5,7,6,8]=>[2,4,2]
[3,1,4,5,2,7,6,8]=>[1,3,2,2]
[3,4,1,5,2,7,6,8]=>[2,2,2,2]
[3,4,5,1,2,7,6,8]=>[3,3,2]
[3,1,4,5,7,2,6,8]=>[1,4,3]
[3,4,1,5,7,2,6,8]=>[2,3,3]
[3,4,5,1,7,2,6,8]=>[3,2,3]
[3,4,5,7,1,2,6,8]=>[4,4]
[3,1,4,2,5,7,8,6]=>[1,2,4,1]
[3,4,1,2,5,7,8,6]=>[2,5,1]
[3,1,4,5,2,7,8,6]=>[1,3,3,1]
[3,4,1,5,2,7,8,6]=>[2,2,3,1]
[3,4,5,1,2,7,8,6]=>[3,4,1]
[3,1,4,5,7,2,8,6]=>[1,4,2,1]
[3,4,1,5,7,2,8,6]=>[2,3,2,1]
[3,4,5,1,7,2,8,6]=>[3,2,2,1]
[3,4,5,7,1,2,8,6]=>[4,3,1]
[3,1,4,5,7,8,2,6]=>[1,5,2]
[3,4,1,5,7,8,2,6]=>[2,4,2]
[3,4,5,1,7,8,2,6]=>[3,3,2]
[3,4,5,7,1,8,2,6]=>[4,2,2]
[3,4,5,7,8,1,2,6]=>[5,3]
[3,1,4,2,8,5,6,7]=>[1,2,2,3]
[3,4,1,2,8,5,6,7]=>[2,3,3]
[3,1,4,8,2,5,6,7]=>[1,3,4]
[3,4,1,8,2,5,6,7]=>[2,2,4]
[3,4,8,1,2,5,6,7]=>[3,5]
[3,1,4,2,5,8,6,7]=>[1,2,3,2]
[3,4,1,2,5,8,6,7]=>[2,4,2]
[3,4,1,5,2,8,6,7]=>[2,2,2,2]
[3,4,5,1,2,8,6,7]=>[3,3,2]
[3,1,4,5,8,2,6,7]=>[1,4,3]
[3,4,1,5,8,2,6,7]=>[2,3,3]
[3,4,5,1,8,2,6,7]=>[3,2,3]
[3,4,5,8,1,2,6,7]=>[4,4]
[3,1,4,2,5,6,8,7]=>[1,2,4,1]
[3,4,1,2,5,6,8,7]=>[2,5,1]
[3,4,1,5,2,6,8,7]=>[2,2,3,1]
[3,4,5,1,2,6,8,7]=>[3,4,1]
[3,1,4,5,6,2,8,7]=>[1,4,2,1]
[3,4,1,5,6,2,8,7]=>[2,3,2,1]
[3,4,5,1,6,2,8,7]=>[3,2,2,1]
[3,4,5,6,1,2,8,7]=>[4,3,1]
[3,1,4,5,6,8,2,7]=>[1,5,2]
[3,4,1,5,6,8,2,7]=>[2,4,2]
[3,4,5,1,6,8,2,7]=>[3,3,2]
[3,4,5,6,1,8,2,7]=>[4,2,2]
[3,4,5,6,8,1,2,7]=>[5,3]
[3,1,4,2,5,6,7,8]=>[1,2,5]
[3,1,4,5,2,6,7,8]=>[1,3,4]
[3,4,1,5,2,6,7,8]=>[2,2,4]
[3,1,4,5,6,2,7,8]=>[1,4,3]
[3,4,1,5,6,2,7,8]=>[2,3,3]
[3,4,5,1,6,2,7,8]=>[3,2,3]
[3,1,4,5,6,7,2,8]=>[1,5,2]
[3,4,1,5,6,7,2,8]=>[2,4,2]
[3,4,5,1,6,7,2,8]=>[3,3,2]
[3,4,5,6,1,7,2,8]=>[4,2,2]
[3,1,4,5,6,7,8,2]=>[1,6,1]
[3,4,1,5,6,7,8,2]=>[2,5,1]
[3,4,5,1,6,7,8,2]=>[3,4,1]
[3,4,5,6,1,7,8,2]=>[4,3,1]
[3,4,5,6,7,1,8,2]=>[5,2,1]
[3,1,5,2,6,4,8,7]=>[1,2,2,2,1]
[3,5,1,2,6,4,8,7]=>[2,3,2,1]
[3,1,5,6,2,4,8,7]=>[1,3,3,1]
[3,5,1,6,2,4,8,7]=>[2,2,3,1]
[3,5,6,1,2,4,8,7]=>[3,4,1]
[3,1,5,2,6,8,4,7]=>[1,2,3,2]
[3,5,1,2,6,8,4,7]=>[2,4,2]
[3,1,5,6,2,8,4,7]=>[1,3,2,2]
[3,5,1,6,2,8,4,7]=>[2,2,2,2]
[3,5,6,1,2,8,4,7]=>[3,3,2]
[3,1,5,6,8,2,4,7]=>[1,4,3]
[3,5,1,6,8,2,4,7]=>[2,3,3]
[3,5,6,1,8,2,4,7]=>[3,2,3]
[3,5,6,8,1,2,4,7]=>[4,4]
[3,1,5,2,6,4,7,8]=>[1,2,2,3]
[3,5,1,2,6,4,7,8]=>[2,3,3]
[3,1,5,6,2,4,7,8]=>[1,3,4]
[3,5,1,6,2,4,7,8]=>[2,2,4]
[3,5,6,1,2,4,7,8]=>[3,5]
[3,1,5,2,6,7,4,8]=>[1,2,3,2]
[3,5,1,2,6,7,4,8]=>[2,4,2]
[3,1,5,6,2,7,4,8]=>[1,3,2,2]
[3,5,1,6,2,7,4,8]=>[2,2,2,2]
[3,5,6,1,2,7,4,8]=>[3,3,2]
[3,1,5,6,7,2,4,8]=>[1,4,3]
[3,5,1,6,7,2,4,8]=>[2,3,3]
[3,5,6,1,7,2,4,8]=>[3,2,3]
[3,5,6,7,1,2,4,8]=>[4,4]
[3,1,5,2,6,7,8,4]=>[1,2,4,1]
[3,5,1,2,6,7,8,4]=>[2,5,1]
[3,1,5,6,2,7,8,4]=>[1,3,3,1]
[3,5,1,6,2,7,8,4]=>[2,2,3,1]
[3,5,6,1,2,7,8,4]=>[3,4,1]
[3,1,5,6,7,2,8,4]=>[1,4,2,1]
[3,5,1,6,7,2,8,4]=>[2,3,2,1]
[3,5,6,1,7,2,8,4]=>[3,2,2,1]
[3,5,6,7,1,2,8,4]=>[4,3,1]
[3,1,5,6,7,8,2,4]=>[1,5,2]
[3,5,1,6,7,8,2,4]=>[2,4,2]
[3,5,6,1,7,8,2,4]=>[3,3,2]
[3,5,6,7,1,8,2,4]=>[4,2,2]
[3,5,6,7,8,1,2,4]=>[5,3]
[3,1,5,2,7,4,8,6]=>[1,2,2,2,1]
[3,5,1,2,7,4,8,6]=>[2,3,2,1]
[3,1,5,7,2,4,8,6]=>[1,3,3,1]
[3,5,1,7,2,4,8,6]=>[2,2,3,1]
[3,5,7,1,2,4,8,6]=>[3,4,1]
[3,1,5,2,7,8,4,6]=>[1,2,3,2]
[3,5,1,2,7,8,4,6]=>[2,4,2]
[3,1,5,7,2,8,4,6]=>[1,3,2,2]
[3,5,1,7,2,8,4,6]=>[2,2,2,2]
[3,5,7,1,2,8,4,6]=>[3,3,2]
[3,1,5,7,8,2,4,6]=>[1,4,3]
[3,5,1,7,8,2,4,6]=>[2,3,3]
[3,5,7,1,8,2,4,6]=>[3,2,3]
[3,5,7,8,1,2,4,6]=>[4,4]
[3,1,5,2,7,4,6,8]=>[1,2,2,3]
[3,5,1,2,7,4,6,8]=>[2,3,3]
[3,1,5,7,2,4,6,8]=>[1,3,4]
[3,5,1,7,2,4,6,8]=>[2,2,4]
[3,5,7,1,2,4,6,8]=>[3,5]
[3,1,5,2,4,7,6,8]=>[1,2,3,2]
[3,5,1,2,4,7,6,8]=>[2,4,2]
[3,1,2,5,4,7,6,8]=>[1,3,2,2]
[1,3,5,2,4,7,6,8]=>[3,3,2]
[3,1,2,5,7,4,6,8]=>[1,4,3]
[1,3,2,5,7,4,6,8]=>[2,3,3]
[1,3,5,2,7,4,6,8]=>[3,2,3]
[1,3,5,7,2,4,6,8]=>[4,4]
[3,1,5,2,4,7,8,6]=>[1,2,4,1]
[3,5,1,2,4,7,8,6]=>[2,5,1]
[1,3,5,2,4,7,8,6]=>[3,4,1]
[3,1,2,5,7,4,8,6]=>[1,4,2,1]
[1,3,2,5,7,4,8,6]=>[2,3,2,1]
[1,3,5,2,7,4,8,6]=>[3,2,2,1]
[1,3,5,7,2,4,8,6]=>[4,3,1]
[3,1,2,5,7,8,4,6]=>[1,5,2]
[1,3,2,5,7,8,4,6]=>[2,4,2]
[1,3,5,2,7,8,4,6]=>[3,3,2]
[1,3,5,7,2,8,4,6]=>[4,2,2]
[1,3,5,7,8,2,4,6]=>[5,3]
[3,1,5,2,8,4,6,7]=>[1,2,2,3]
[3,5,1,2,8,4,6,7]=>[2,3,3]
[3,1,5,8,2,4,6,7]=>[1,3,4]
[3,5,1,8,2,4,6,7]=>[2,2,4]
[3,5,8,1,2,4,6,7]=>[3,5]
[3,1,5,2,4,8,6,7]=>[1,2,3,2]
[3,5,1,2,4,8,6,7]=>[2,4,2]
[1,3,2,5,4,8,6,7]=>[2,2,2,2]
[1,3,5,2,4,8,6,7]=>[3,3,2]
[3,1,2,5,8,4,6,7]=>[1,4,3]
[1,3,2,5,8,4,6,7]=>[2,3,3]
[1,3,5,2,8,4,6,7]=>[3,2,3]
[1,3,5,8,2,4,6,7]=>[4,4]
[3,1,5,2,4,6,8,7]=>[1,2,4,1]
[3,5,1,2,4,6,8,7]=>[2,5,1]
[3,1,2,5,4,6,8,7]=>[1,3,3,1]
[1,3,5,2,4,6,8,7]=>[3,4,1]
[1,3,5,2,6,4,8,7]=>[3,2,2,1]
[1,3,5,6,2,4,8,7]=>[4,3,1]
[3,1,2,5,6,8,4,7]=>[1,5,2]
[1,3,2,5,6,8,4,7]=>[2,4,2]
[1,3,5,2,6,8,4,7]=>[3,3,2]
[1,3,5,6,2,8,4,7]=>[4,2,2]
[1,3,5,6,8,2,4,7]=>[5,3]
[3,1,5,2,4,6,7,8]=>[1,2,5]
[3,5,1,2,4,6,7,8]=>[2,6]
[3,1,2,5,4,6,7,8]=>[1,3,4]
[1,3,5,2,4,6,7,8]=>[3,5]
[3,1,2,5,6,4,7,8]=>[1,4,3]
[1,3,5,2,6,4,7,8]=>[3,2,3]
[1,3,5,6,2,4,7,8]=>[4,4]
[3,1,2,5,6,7,4,8]=>[1,5,2]
[1,3,5,2,6,7,4,8]=>[3,3,2]
[1,3,5,6,2,7,4,8]=>[4,2,2]
[1,3,5,6,7,2,4,8]=>[5,3]
[3,1,2,5,6,7,8,4]=>[1,6,1]
[1,3,5,2,6,7,8,4]=>[3,4,1]
[1,3,5,6,2,7,8,4]=>[4,3,1]
[1,3,5,6,7,2,8,4]=>[5,2,1]
[1,3,5,6,7,8,2,4]=>[6,2]
[3,1,6,2,7,4,8,5]=>[1,2,2,2,1]
[3,6,1,2,7,4,8,5]=>[2,3,2,1]
[3,6,1,7,2,4,8,5]=>[2,2,3,1]
[3,6,7,1,2,4,8,5]=>[3,4,1]
[3,1,6,2,7,8,4,5]=>[1,2,3,2]
[3,6,1,2,7,8,4,5]=>[2,4,2]
[3,1,6,7,2,8,4,5]=>[1,3,2,2]
[3,6,1,7,2,8,4,5]=>[2,2,2,2]
[3,6,7,1,2,8,4,5]=>[3,3,2]
[3,1,6,7,8,2,4,5]=>[1,4,3]
[3,6,1,7,8,2,4,5]=>[2,3,3]
[3,6,7,1,8,2,4,5]=>[3,2,3]
[3,6,7,8,1,2,4,5]=>[4,4]
[3,1,6,2,7,4,5,8]=>[1,2,2,3]
[3,6,1,2,7,4,5,8]=>[2,3,3]
[3,1,6,7,2,4,5,8]=>[1,3,4]
[3,6,1,7,2,4,5,8]=>[2,2,4]
[3,6,7,1,2,4,5,8]=>[3,5]
[3,1,6,2,4,7,5,8]=>[1,2,3,2]
[3,6,1,2,4,7,5,8]=>[2,4,2]
[3,1,2,6,4,7,5,8]=>[1,3,2,2]
[1,3,2,6,4,7,5,8]=>[2,2,2,2]
[1,3,6,2,4,7,5,8]=>[3,3,2]
[3,1,2,6,7,4,5,8]=>[1,4,3]
[1,3,2,6,7,4,5,8]=>[2,3,3]
[1,3,6,2,7,4,5,8]=>[3,2,3]
[1,3,6,7,2,4,5,8]=>[4,4]
[3,1,6,2,4,7,8,5]=>[1,2,4,1]
[3,6,1,2,4,7,8,5]=>[2,5,1]
[3,1,2,6,4,7,8,5]=>[1,3,3,1]
[1,3,2,6,4,7,8,5]=>[2,2,3,1]
[1,3,6,2,4,7,8,5]=>[3,4,1]
[3,1,2,6,7,4,8,5]=>[1,4,2,1]
[1,3,2,6,7,4,8,5]=>[2,3,2,1]
[1,3,6,2,7,4,8,5]=>[3,2,2,1]
[1,3,6,7,2,4,8,5]=>[4,3,1]
[3,1,2,6,7,8,4,5]=>[1,5,2]
[1,3,2,6,7,8,4,5]=>[2,4,2]
[1,3,6,2,7,8,4,5]=>[3,3,2]
[1,3,6,7,2,8,4,5]=>[4,2,2]
[1,3,6,7,8,2,4,5]=>[5,3]
[3,1,6,2,8,4,5,7]=>[1,2,2,3]
[3,6,1,2,8,4,5,7]=>[2,3,3]
[3,1,6,8,2,4,5,7]=>[1,3,4]
[3,6,1,8,2,4,5,7]=>[2,2,4]
[3,6,8,1,2,4,5,7]=>[3,5]
[3,1,6,2,4,8,5,7]=>[1,2,3,2]
[3,6,1,2,4,8,5,7]=>[2,4,2]
[3,1,2,6,4,8,5,7]=>[1,3,2,2]
[1,3,2,6,4,8,5,7]=>[2,2,2,2]
[1,3,6,2,4,8,5,7]=>[3,3,2]
[3,1,2,6,8,4,5,7]=>[1,4,3]
[1,3,2,6,8,4,5,7]=>[2,3,3]
[1,3,6,2,8,4,5,7]=>[3,2,3]
[1,3,6,8,2,4,5,7]=>[4,4]
[3,1,6,2,4,5,8,7]=>[1,2,4,1]
[3,6,1,2,4,5,8,7]=>[2,5,1]
[3,1,2,6,4,5,8,7]=>[1,3,3,1]
[1,3,6,2,4,5,8,7]=>[3,4,1]
[3,1,2,4,6,5,8,7]=>[1,4,2,1]
[1,3,4,6,2,5,8,7]=>[4,3,1]
[3,1,2,4,6,8,5,7]=>[1,5,2]
[1,3,2,4,6,8,5,7]=>[2,4,2]
[1,3,4,2,6,8,5,7]=>[3,3,2]
[1,3,4,6,2,8,5,7]=>[4,2,2]
[1,3,4,6,8,2,5,7]=>[5,3]
[3,1,6,2,4,5,7,8]=>[1,2,5]
[3,6,1,2,4,5,7,8]=>[2,6]
[3,1,2,6,4,5,7,8]=>[1,3,4]
[1,3,2,6,4,5,7,8]=>[2,2,4]
[1,3,6,2,4,5,7,8]=>[3,5]
[1,3,4,6,2,5,7,8]=>[4,4]
[3,1,2,4,6,7,5,8]=>[1,5,2]
[1,3,4,6,2,7,5,8]=>[4,2,2]
[1,3,4,6,7,2,5,8]=>[5,3]
[3,1,2,4,6,7,8,5]=>[1,6,1]
[1,3,4,6,2,7,8,5]=>[4,3,1]
[1,3,4,6,7,2,8,5]=>[5,2,1]
[1,3,4,6,7,8,2,5]=>[6,2]
[3,1,7,2,8,4,5,6]=>[1,2,2,3]
[3,7,1,2,8,4,5,6]=>[2,3,3]
[3,1,7,8,2,4,5,6]=>[1,3,4]
[3,7,1,8,2,4,5,6]=>[2,2,4]
[3,7,8,1,2,4,5,6]=>[3,5]
[3,1,7,2,4,8,5,6]=>[1,2,3,2]
[3,7,1,2,4,8,5,6]=>[2,4,2]
[3,1,2,7,4,8,5,6]=>[1,3,2,2]
[1,3,2,7,4,8,5,6]=>[2,2,2,2]
[1,3,7,2,4,8,5,6]=>[3,3,2]
[3,1,2,7,8,4,5,6]=>[1,4,3]
[1,3,2,7,8,4,5,6]=>[2,3,3]
[1,3,7,2,8,4,5,6]=>[3,2,3]
[1,3,7,8,2,4,5,6]=>[4,4]
[3,1,7,2,4,5,8,6]=>[1,2,4,1]
[3,7,1,2,4,5,8,6]=>[2,5,1]
[3,1,2,7,4,5,8,6]=>[1,3,3,1]
[1,3,2,7,4,5,8,6]=>[2,2,3,1]
[1,3,7,2,4,5,8,6]=>[3,4,1]
[3,1,2,4,7,5,8,6]=>[1,4,2,1]
[1,3,2,4,7,5,8,6]=>[2,3,2,1]
[1,3,4,2,7,5,8,6]=>[3,2,2,1]
[1,3,4,7,2,5,8,6]=>[4,3,1]
[3,1,2,4,7,8,5,6]=>[1,5,2]
[1,3,2,4,7,8,5,6]=>[2,4,2]
[1,3,4,2,7,8,5,6]=>[3,3,2]
[1,3,4,7,2,8,5,6]=>[4,2,2]
[1,3,4,7,8,2,5,6]=>[5,3]
[3,1,7,2,4,5,6,8]=>[1,2,5]
[3,7,1,2,4,5,6,8]=>[2,6]
[3,1,2,7,4,5,6,8]=>[1,3,4]
[1,3,2,7,4,5,6,8]=>[2,2,4]
[1,3,7,2,4,5,6,8]=>[3,5]
[3,1,2,4,7,5,6,8]=>[1,4,3]
[1,3,2,4,7,5,6,8]=>[2,3,3]
[1,3,4,2,7,5,6,8]=>[3,2,3]
[1,3,4,7,2,5,6,8]=>[4,4]
[3,1,2,4,5,7,6,8]=>[1,5,2]
[1,3,4,5,7,2,6,8]=>[5,3]
[3,1,2,4,5,7,8,6]=>[1,6,1]
[1,3,4,5,7,2,8,6]=>[5,2,1]
[1,3,4,5,7,8,2,6]=>[6,2]
[3,1,8,2,4,5,6,7]=>[1,2,5]
[3,8,1,2,4,5,6,7]=>[2,6]
[3,1,2,8,4,5,6,7]=>[1,3,4]
[1,3,2,8,4,5,6,7]=>[2,2,4]
[1,3,8,2,4,5,6,7]=>[3,5]
[3,1,2,4,8,5,6,7]=>[1,4,3]
[1,3,2,4,8,5,6,7]=>[2,3,3]
[1,3,4,2,8,5,6,7]=>[3,2,3]
[1,3,4,8,2,5,6,7]=>[4,4]
[3,1,2,4,5,8,6,7]=>[1,5,2]
[1,3,2,4,5,8,6,7]=>[2,4,2]
[1,3,4,2,5,8,6,7]=>[3,3,2]
[1,3,4,5,2,8,6,7]=>[4,2,2]
[1,3,4,5,8,2,6,7]=>[5,3]
[3,1,2,4,5,6,8,7]=>[1,6,1]
[1,3,4,5,6,8,2,7]=>[6,2]
[4,1,5,2,6,3,8,7]=>[1,2,2,2,1]
[4,5,1,2,6,3,8,7]=>[2,3,2,1]
[4,1,5,6,2,3,8,7]=>[1,3,3,1]
[4,5,1,6,2,3,8,7]=>[2,2,3,1]
[4,5,6,1,2,3,8,7]=>[3,4,1]
[4,1,5,2,6,8,3,7]=>[1,2,3,2]
[4,5,1,2,6,8,3,7]=>[2,4,2]
[4,1,5,6,2,8,3,7]=>[1,3,2,2]
[4,5,1,6,2,8,3,7]=>[2,2,2,2]
[4,5,6,1,2,8,3,7]=>[3,3,2]
[4,1,5,6,8,2,3,7]=>[1,4,3]
[4,5,1,6,8,2,3,7]=>[2,3,3]
[4,5,6,1,8,2,3,7]=>[3,2,3]
[4,5,6,8,1,2,3,7]=>[4,4]
[4,1,5,2,6,3,7,8]=>[1,2,2,3]
[4,1,5,6,2,3,7,8]=>[1,3,4]
[4,5,1,6,2,3,7,8]=>[2,2,4]
[4,1,5,2,6,7,3,8]=>[1,2,3,2]
[4,5,1,2,6,7,3,8]=>[2,4,2]
[4,1,5,6,2,7,3,8]=>[1,3,2,2]
[4,5,1,6,2,7,3,8]=>[2,2,2,2]
[4,5,6,1,2,7,3,8]=>[3,3,2]
[4,1,5,6,7,2,3,8]=>[1,4,3]
[4,5,1,6,7,2,3,8]=>[2,3,3]
[4,5,6,1,7,2,3,8]=>[3,2,3]
[4,1,5,2,6,7,8,3]=>[1,2,4,1]
[4,5,1,2,6,7,8,3]=>[2,5,1]
[4,5,1,6,2,7,8,3]=>[2,2,3,1]
[4,5,6,1,2,7,8,3]=>[3,4,1]
[4,1,5,6,7,2,8,3]=>[1,4,2,1]
[4,5,1,6,7,2,8,3]=>[2,3,2,1]
[4,5,6,1,7,2,8,3]=>[3,2,2,1]
[4,5,6,7,1,2,8,3]=>[4,3,1]
[4,1,5,6,7,8,2,3]=>[1,5,2]
[4,5,1,6,7,8,2,3]=>[2,4,2]
[4,5,6,1,7,8,2,3]=>[3,3,2]
[4,5,6,7,1,8,2,3]=>[4,2,2]
[4,1,5,2,7,3,8,6]=>[1,2,2,2,1]
[4,5,1,2,7,3,8,6]=>[2,3,2,1]
[4,1,5,7,2,3,8,6]=>[1,3,3,1]
[4,5,1,7,2,3,8,6]=>[2,2,3,1]
[4,5,7,1,2,3,8,6]=>[3,4,1]
[4,1,5,2,7,8,3,6]=>[1,2,3,2]
[4,5,1,2,7,8,3,6]=>[2,4,2]
[4,1,5,7,2,8,3,6]=>[1,3,2,2]
[4,5,1,7,2,8,3,6]=>[2,2,2,2]
[4,5,7,1,2,8,3,6]=>[3,3,2]
[4,1,5,7,8,2,3,6]=>[1,4,3]
[4,5,1,7,8,2,3,6]=>[2,3,3]
[4,5,7,1,8,2,3,6]=>[3,2,3]
[4,5,7,8,1,2,3,6]=>[4,4]
[4,1,5,2,7,3,6,8]=>[1,2,2,3]
[4,5,1,2,7,3,6,8]=>[2,3,3]
[4,1,5,7,2,3,6,8]=>[1,3,4]
[4,5,1,7,2,3,6,8]=>[2,2,4]
[4,5,7,1,2,3,6,8]=>[3,5]
[4,1,5,2,3,7,6,8]=>[1,2,3,2]
[4,5,1,2,3,7,6,8]=>[2,4,2]
[4,1,2,5,3,7,6,8]=>[1,3,2,2]
[1,4,2,5,3,7,6,8]=>[2,2,2,2]
[1,4,5,2,3,7,6,8]=>[3,3,2]
[4,1,2,5,7,3,6,8]=>[1,4,3]
[1,4,2,5,7,3,6,8]=>[2,3,3]
[1,4,5,2,7,3,6,8]=>[3,2,3]
[1,4,5,7,2,3,6,8]=>[4,4]
[4,1,5,2,3,7,8,6]=>[1,2,4,1]
[4,5,1,2,3,7,8,6]=>[2,5,1]
[4,1,2,5,3,7,8,6]=>[1,3,3,1]
[1,4,2,5,3,7,8,6]=>[2,2,3,1]
[1,4,5,2,3,7,8,6]=>[3,4,1]
[4,1,2,5,7,3,8,6]=>[1,4,2,1]
[1,4,2,5,7,3,8,6]=>[2,3,2,1]
[1,4,5,2,7,3,8,6]=>[3,2,2,1]
[1,4,5,7,2,3,8,6]=>[4,3,1]
[4,1,2,5,7,8,3,6]=>[1,5,2]
[1,4,2,5,7,8,3,6]=>[2,4,2]
[1,4,5,2,7,8,3,6]=>[3,3,2]
[1,4,5,7,2,8,3,6]=>[4,2,2]
[1,4,5,7,8,2,3,6]=>[5,3]
[4,1,5,2,8,3,6,7]=>[1,2,2,3]
[4,5,1,2,8,3,6,7]=>[2,3,3]
[4,1,5,8,2,3,6,7]=>[1,3,4]
[4,5,1,8,2,3,6,7]=>[2,2,4]
[4,5,8,1,2,3,6,7]=>[3,5]
[4,1,5,2,3,8,6,7]=>[1,2,3,2]
[4,5,1,2,3,8,6,7]=>[2,4,2]
[4,1,2,5,3,8,6,7]=>[1,3,2,2]
[1,4,2,5,3,8,6,7]=>[2,2,2,2]
[1,4,5,2,3,8,6,7]=>[3,3,2]
[4,1,2,5,8,3,6,7]=>[1,4,3]
[1,4,2,5,8,3,6,7]=>[2,3,3]
[1,4,5,2,8,3,6,7]=>[3,2,3]
[1,4,5,8,2,3,6,7]=>[4,4]
[4,1,5,2,3,6,8,7]=>[1,2,4,1]
[4,5,1,2,3,6,8,7]=>[2,5,1]
[1,4,2,5,3,6,8,7]=>[2,2,3,1]
[4,1,2,5,6,3,8,7]=>[1,4,2,1]
[1,4,2,5,6,3,8,7]=>[2,3,2,1]
[1,4,5,2,6,3,8,7]=>[3,2,2,1]
[1,4,5,6,2,3,8,7]=>[4,3,1]
[4,1,2,5,6,8,3,7]=>[1,5,2]
[1,4,2,5,6,8,3,7]=>[2,4,2]
[1,4,5,2,6,8,3,7]=>[3,3,2]
[1,4,5,6,2,8,3,7]=>[4,2,2]
[1,4,5,6,8,2,3,7]=>[5,3]
[4,1,5,2,3,6,7,8]=>[1,2,5]
[4,1,2,5,3,6,7,8]=>[1,3,4]
[1,4,2,5,3,6,7,8]=>[2,2,4]
[1,4,5,2,3,6,7,8]=>[3,5]
[4,1,2,5,6,3,7,8]=>[1,4,3]
[1,4,2,5,6,3,7,8]=>[2,3,3]
[1,4,5,2,6,3,7,8]=>[3,2,3]
[1,4,5,6,2,3,7,8]=>[4,4]
[4,1,2,5,6,7,3,8]=>[1,5,2]
[1,4,2,5,6,7,3,8]=>[2,4,2]
[1,4,5,2,6,7,3,8]=>[3,3,2]
[1,4,5,6,2,7,3,8]=>[4,2,2]
[1,4,5,6,7,2,3,8]=>[5,3]
[4,1,2,5,6,7,8,3]=>[1,6,1]
[1,4,2,5,6,7,8,3]=>[2,5,1]
[1,4,5,2,6,7,8,3]=>[3,4,1]
[1,4,5,6,2,7,8,3]=>[4,3,1]
[1,4,5,6,7,2,8,3]=>[5,2,1]
[1,4,5,6,7,8,2,3]=>[6,2]
[4,1,6,2,7,3,8,5]=>[1,2,2,2,1]
[4,6,1,2,7,3,8,5]=>[2,3,2,1]
[4,1,6,7,2,3,8,5]=>[1,3,3,1]
[4,6,1,7,2,3,8,5]=>[2,2,3,1]
[4,6,7,1,2,3,8,5]=>[3,4,1]
[4,1,6,2,7,8,3,5]=>[1,2,3,2]
[4,6,1,2,7,8,3,5]=>[2,4,2]
[4,1,6,7,2,8,3,5]=>[1,3,2,2]
[4,6,1,7,2,8,3,5]=>[2,2,2,2]
[4,6,7,1,2,8,3,5]=>[3,3,2]
[4,1,6,7,8,2,3,5]=>[1,4,3]
[4,6,1,7,8,2,3,5]=>[2,3,3]
[4,6,7,1,8,2,3,5]=>[3,2,3]
[4,6,7,8,1,2,3,5]=>[4,4]
[4,1,6,2,7,3,5,8]=>[1,2,2,3]
[4,6,1,2,7,3,5,8]=>[2,3,3]
[4,1,6,7,2,3,5,8]=>[1,3,4]
[4,6,1,7,2,3,5,8]=>[2,2,4]
[4,6,7,1,2,3,5,8]=>[3,5]
[4,1,6,2,3,7,5,8]=>[1,2,3,2]
[4,6,1,2,3,7,5,8]=>[2,4,2]
[4,1,2,6,3,7,5,8]=>[1,3,2,2]
[1,4,2,6,3,7,5,8]=>[2,2,2,2]
[1,4,6,2,3,7,5,8]=>[3,3,2]
[4,1,2,6,7,3,5,8]=>[1,4,3]
[1,4,2,6,7,3,5,8]=>[2,3,3]
[1,4,6,2,7,3,5,8]=>[3,2,3]
[1,4,6,7,2,3,5,8]=>[4,4]
[4,1,6,2,3,7,8,5]=>[1,2,4,1]
[4,6,1,2,3,7,8,5]=>[2,5,1]
[4,1,2,6,3,7,8,5]=>[1,3,3,1]
[1,4,2,6,3,7,8,5]=>[2,2,3,1]
[1,4,6,2,3,7,8,5]=>[3,4,1]
[4,1,2,6,7,3,8,5]=>[1,4,2,1]
[1,4,2,6,7,3,8,5]=>[2,3,2,1]
[1,4,6,2,7,3,8,5]=>[3,2,2,1]
[1,4,6,7,2,3,8,5]=>[4,3,1]
[1,4,2,6,7,8,3,5]=>[2,4,2]
[1,4,6,2,7,8,3,5]=>[3,3,2]
[1,4,6,7,2,8,3,5]=>[4,2,2]
[1,4,6,7,8,2,3,5]=>[5,3]
[4,1,6,2,8,3,5,7]=>[1,2,2,3]
[4,6,1,2,8,3,5,7]=>[2,3,3]
[4,1,6,8,2,3,5,7]=>[1,3,4]
[4,6,1,8,2,3,5,7]=>[2,2,4]
[4,6,8,1,2,3,5,7]=>[3,5]
[4,1,6,2,3,8,5,7]=>[1,2,3,2]
[4,6,1,2,3,8,5,7]=>[2,4,2]
[4,1,2,6,3,8,5,7]=>[1,3,2,2]
[1,4,2,6,3,8,5,7]=>[2,2,2,2]
[1,4,6,2,3,8,5,7]=>[3,3,2]
[4,1,2,6,8,3,5,7]=>[1,4,3]
[1,4,2,6,8,3,5,7]=>[2,3,3]
[1,4,6,2,8,3,5,7]=>[3,2,3]
[1,4,6,8,2,3,5,7]=>[4,4]
[4,1,6,2,3,5,8,7]=>[1,2,4,1]
[4,6,1,2,3,5,8,7]=>[2,5,1]
[4,1,2,6,3,5,8,7]=>[1,3,3,1]
[1,4,2,6,3,5,8,7]=>[2,2,3,1]
[1,4,6,2,3,5,8,7]=>[3,4,1]
[4,1,2,3,6,5,8,7]=>[1,4,2,1]
[1,4,2,3,6,5,8,7]=>[2,3,2,1]
[1,2,4,6,3,5,8,7]=>[4,3,1]
[4,1,2,3,6,8,5,7]=>[1,5,2]
[1,4,2,3,6,8,5,7]=>[2,4,2]
[1,2,4,3,6,8,5,7]=>[3,3,2]
[1,2,4,6,3,8,5,7]=>[4,2,2]
[1,2,4,6,8,3,5,7]=>[5,3]
[4,1,6,2,3,5,7,8]=>[1,2,5]
[4,6,1,2,3,5,7,8]=>[2,6]
[4,1,2,6,3,5,7,8]=>[1,3,4]
[1,4,2,6,3,5,7,8]=>[2,2,4]
[1,4,6,2,3,5,7,8]=>[3,5]
[4,1,2,3,6,5,7,8]=>[1,4,3]
[1,4,2,3,6,5,7,8]=>[2,3,3]
[1,2,4,6,3,5,7,8]=>[4,4]
[4,1,2,3,6,7,5,8]=>[1,5,2]
[1,4,2,3,6,7,5,8]=>[2,4,2]
[1,2,4,6,3,7,5,8]=>[4,2,2]
[1,2,4,6,7,3,5,8]=>[5,3]
[4,1,2,3,6,7,8,5]=>[1,6,1]
[1,4,2,3,6,7,8,5]=>[2,5,1]
[1,2,4,6,3,7,8,5]=>[4,3,1]
[1,2,4,6,7,3,8,5]=>[5,2,1]
[1,2,4,6,7,8,3,5]=>[6,2]
[4,1,7,2,8,3,5,6]=>[1,2,2,3]
[4,7,1,2,8,3,5,6]=>[2,3,3]
[4,1,7,8,2,3,5,6]=>[1,3,4]
[4,7,1,8,2,3,5,6]=>[2,2,4]
[4,7,8,1,2,3,5,6]=>[3,5]
[4,1,7,2,3,8,5,6]=>[1,2,3,2]
[4,7,1,2,3,8,5,6]=>[2,4,2]
[4,1,2,7,3,8,5,6]=>[1,3,2,2]
[1,4,2,7,3,8,5,6]=>[2,2,2,2]
[1,4,7,2,3,8,5,6]=>[3,3,2]
[4,1,2,7,8,3,5,6]=>[1,4,3]
[1,4,2,7,8,3,5,6]=>[2,3,3]
[1,4,7,2,8,3,5,6]=>[3,2,3]
[1,4,7,8,2,3,5,6]=>[4,4]
[4,1,7,2,3,5,8,6]=>[1,2,4,1]
[4,7,1,2,3,5,8,6]=>[2,5,1]
[4,1,2,7,3,5,8,6]=>[1,3,3,1]
[1,4,2,7,3,5,8,6]=>[2,2,3,1]
[1,4,7,2,3,5,8,6]=>[3,4,1]
[4,1,2,3,7,5,8,6]=>[1,4,2,1]
[1,4,2,3,7,5,8,6]=>[2,3,2,1]
[1,2,4,3,7,5,8,6]=>[3,2,2,1]
[1,2,4,7,3,5,8,6]=>[4,3,1]
[4,1,2,3,7,8,5,6]=>[1,5,2]
[1,4,2,3,7,8,5,6]=>[2,4,2]
[1,2,4,3,7,8,5,6]=>[3,3,2]
[1,2,4,7,3,8,5,6]=>[4,2,2]
[1,2,4,7,8,3,5,6]=>[5,3]
[4,1,7,2,3,5,6,8]=>[1,2,5]
[4,7,1,2,3,5,6,8]=>[2,6]
[4,1,2,7,3,5,6,8]=>[1,3,4]
[1,4,2,7,3,5,6,8]=>[2,2,4]
[1,4,7,2,3,5,6,8]=>[3,5]
[4,1,2,3,7,5,6,8]=>[1,4,3]
[1,4,2,3,7,5,6,8]=>[2,3,3]
[1,2,4,3,7,5,6,8]=>[3,2,3]
[1,2,4,7,3,5,6,8]=>[4,4]
[4,1,2,3,5,7,6,8]=>[1,5,2]
[1,4,2,3,5,7,6,8]=>[2,4,2]
[1,2,4,5,7,3,6,8]=>[5,3]
[4,1,2,3,5,7,8,6]=>[1,6,1]
[1,4,2,3,5,7,8,6]=>[2,5,1]
[1,2,4,5,7,3,8,6]=>[5,2,1]
[1,2,4,5,7,8,3,6]=>[6,2]
[4,1,8,2,3,5,6,7]=>[1,2,5]
[4,8,1,2,3,5,6,7]=>[2,6]
[4,1,2,8,3,5,6,7]=>[1,3,4]
[1,4,2,8,3,5,6,7]=>[2,2,4]
[1,4,8,2,3,5,6,7]=>[3,5]
[4,1,2,3,8,5,6,7]=>[1,4,3]
[1,4,2,3,8,5,6,7]=>[2,3,3]
[1,2,4,3,8,5,6,7]=>[3,2,3]
[1,2,4,8,3,5,6,7]=>[4,4]
[4,1,2,3,5,8,6,7]=>[1,5,2]
[1,4,2,3,5,8,6,7]=>[2,4,2]
[1,2,4,3,5,8,6,7]=>[3,3,2]
[1,2,4,5,3,8,6,7]=>[4,2,2]
[1,2,4,5,8,3,6,7]=>[5,3]
[4,1,2,3,5,6,8,7]=>[1,6,1]
[1,4,2,3,5,6,8,7]=>[2,5,1]
[1,2,4,5,6,8,3,7]=>[6,2]
[1,4,2,3,5,6,7,8]=>[2,6]
[5,1,6,2,7,3,8,4]=>[1,2,2,2,1]
[5,6,1,2,7,3,8,4]=>[2,3,2,1]
[5,1,6,7,2,3,8,4]=>[1,3,3,1]
[5,6,1,7,2,3,8,4]=>[2,2,3,1]
[5,6,7,1,2,3,8,4]=>[3,4,1]
[5,1,6,2,7,8,3,4]=>[1,2,3,2]
[5,6,1,2,7,8,3,4]=>[2,4,2]
[5,1,6,7,2,8,3,4]=>[1,3,2,2]
[5,6,1,7,2,8,3,4]=>[2,2,2,2]
[5,6,7,1,2,8,3,4]=>[3,3,2]
[5,1,6,7,8,2,3,4]=>[1,4,3]
[5,6,1,7,8,2,3,4]=>[2,3,3]
[5,6,7,1,8,2,3,4]=>[3,2,3]
[5,1,6,2,7,3,4,8]=>[1,2,2,3]
[5,6,1,2,7,3,4,8]=>[2,3,3]
[5,1,6,7,2,3,4,8]=>[1,3,4]
[5,6,1,7,2,3,4,8]=>[2,2,4]
[5,1,6,2,3,7,4,8]=>[1,2,3,2]
[5,6,1,2,3,7,4,8]=>[2,4,2]
[5,1,2,6,3,7,4,8]=>[1,3,2,2]
[1,5,2,6,3,7,4,8]=>[2,2,2,2]
[1,5,6,2,3,7,4,8]=>[3,3,2]
[5,1,2,6,7,3,4,8]=>[1,4,3]
[1,5,2,6,7,3,4,8]=>[2,3,3]
[1,5,6,2,7,3,4,8]=>[3,2,3]
[1,5,6,7,2,3,4,8]=>[4,4]
[5,1,6,2,3,7,8,4]=>[1,2,4,1]
[5,6,1,2,3,7,8,4]=>[2,5,1]
[5,1,2,6,3,7,8,4]=>[1,3,3,1]
[1,5,2,6,3,7,8,4]=>[2,2,3,1]
[1,5,6,2,3,7,8,4]=>[3,4,1]
[5,1,2,6,7,3,8,4]=>[1,4,2,1]
[1,5,2,6,7,3,8,4]=>[2,3,2,1]
[1,5,6,2,7,3,8,4]=>[3,2,2,1]
[1,5,6,7,2,3,8,4]=>[4,3,1]
[5,1,2,6,7,8,3,4]=>[1,5,2]
[1,5,2,6,7,8,3,4]=>[2,4,2]
[1,5,6,2,7,8,3,4]=>[3,3,2]
[1,5,6,7,2,8,3,4]=>[4,2,2]
[1,5,6,7,8,2,3,4]=>[5,3]
[5,1,6,2,8,3,4,7]=>[1,2,2,3]
[5,6,1,2,8,3,4,7]=>[2,3,3]
[5,1,6,8,2,3,4,7]=>[1,3,4]
[5,6,1,8,2,3,4,7]=>[2,2,4]
[5,6,8,1,2,3,4,7]=>[3,5]
[5,1,6,2,3,8,4,7]=>[1,2,3,2]
[5,6,1,2,3,8,4,7]=>[2,4,2]
[5,1,2,6,3,8,4,7]=>[1,3,2,2]
[1,5,2,6,3,8,4,7]=>[2,2,2,2]
[1,5,6,2,3,8,4,7]=>[3,3,2]
[5,1,2,6,8,3,4,7]=>[1,4,3]
[1,5,2,6,8,3,4,7]=>[2,3,3]
[1,5,6,2,8,3,4,7]=>[3,2,3]
[1,5,6,8,2,3,4,7]=>[4,4]
[5,1,6,2,3,4,8,7]=>[1,2,4,1]
[5,6,1,2,3,4,8,7]=>[2,5,1]
[5,1,2,6,3,4,8,7]=>[1,3,3,1]
[1,5,2,6,3,4,8,7]=>[2,2,3,1]
[1,5,6,2,3,4,8,7]=>[3,4,1]
[5,1,2,3,6,4,8,7]=>[1,4,2,1]
[1,5,2,3,6,4,8,7]=>[2,3,2,1]
[1,2,5,3,6,4,8,7]=>[3,2,2,1]
[1,2,5,6,3,4,8,7]=>[4,3,1]
[5,1,2,3,6,8,4,7]=>[1,5,2]
[1,5,2,3,6,8,4,7]=>[2,4,2]
[1,2,5,3,6,8,4,7]=>[3,3,2]
[1,2,5,6,3,8,4,7]=>[4,2,2]
[1,2,5,6,8,3,4,7]=>[5,3]
[5,1,6,2,3,4,7,8]=>[1,2,5]
[5,1,2,6,3,4,7,8]=>[1,3,4]
[1,5,2,6,3,4,7,8]=>[2,2,4]
[1,5,6,2,3,4,7,8]=>[3,5]
[5,1,2,3,6,4,7,8]=>[1,4,3]
[1,5,2,3,6,4,7,8]=>[2,3,3]
[1,2,5,3,6,4,7,8]=>[3,2,3]
[1,2,5,6,3,4,7,8]=>[4,4]
[5,1,2,3,6,7,4,8]=>[1,5,2]
[1,5,2,3,6,7,4,8]=>[2,4,2]
[1,2,5,3,6,7,4,8]=>[3,3,2]
[1,2,5,6,3,7,4,8]=>[4,2,2]
[1,2,5,6,7,3,4,8]=>[5,3]
[5,1,2,3,6,7,8,4]=>[1,6,1]
[1,5,2,3,6,7,8,4]=>[2,5,1]
[1,2,5,3,6,7,8,4]=>[3,4,1]
[1,2,5,6,3,7,8,4]=>[4,3,1]
[1,2,5,6,7,3,8,4]=>[5,2,1]
[1,2,5,6,7,8,3,4]=>[6,2]
[5,1,7,2,8,3,4,6]=>[1,2,2,3]
[5,7,1,2,8,3,4,6]=>[2,3,3]
[5,1,7,8,2,3,4,6]=>[1,3,4]
[5,7,1,8,2,3,4,6]=>[2,2,4]
[5,7,8,1,2,3,4,6]=>[3,5]
[5,1,7,2,3,8,4,6]=>[1,2,3,2]
[5,7,1,2,3,8,4,6]=>[2,4,2]
[5,1,2,7,3,8,4,6]=>[1,3,2,2]
[1,5,2,7,3,8,4,6]=>[2,2,2,2]
[1,5,7,2,3,8,4,6]=>[3,3,2]
[5,1,2,7,8,3,4,6]=>[1,4,3]
[1,5,2,7,8,3,4,6]=>[2,3,3]
[1,5,7,2,8,3,4,6]=>[3,2,3]
[1,5,7,8,2,3,4,6]=>[4,4]
[5,1,7,2,3,4,8,6]=>[1,2,4,1]
[5,7,1,2,3,4,8,6]=>[2,5,1]
[5,1,2,7,3,4,8,6]=>[1,3,3,1]
[1,5,2,7,3,4,8,6]=>[2,2,3,1]
[1,5,7,2,3,4,8,6]=>[3,4,1]
[5,1,2,3,7,4,8,6]=>[1,4,2,1]
[1,5,2,3,7,4,8,6]=>[2,3,2,1]
[1,2,5,3,7,4,8,6]=>[3,2,2,1]
[1,2,5,7,3,4,8,6]=>[4,3,1]
[5,1,2,3,7,8,4,6]=>[1,5,2]
[1,5,2,3,7,8,4,6]=>[2,4,2]
[1,2,5,3,7,8,4,6]=>[3,3,2]
[1,2,5,7,3,8,4,6]=>[4,2,2]
[1,2,5,7,8,3,4,6]=>[5,3]
[5,1,7,2,3,4,6,8]=>[1,2,5]
[5,7,1,2,3,4,6,8]=>[2,6]
[5,1,2,7,3,4,6,8]=>[1,3,4]
[1,5,2,7,3,4,6,8]=>[2,2,4]
[1,5,7,2,3,4,6,8]=>[3,5]
[5,1,2,3,7,4,6,8]=>[1,4,3]
[1,5,2,3,7,4,6,8]=>[2,3,3]
[1,2,5,3,7,4,6,8]=>[3,2,3]
[1,2,5,7,3,4,6,8]=>[4,4]
[5,1,2,3,4,7,6,8]=>[1,5,2]
[1,5,2,3,4,7,6,8]=>[2,4,2]
[1,2,5,3,4,7,6,8]=>[3,3,2]
[1,2,3,5,7,4,6,8]=>[5,3]
[5,1,2,3,4,7,8,6]=>[1,6,1]
[1,5,2,3,4,7,8,6]=>[2,5,1]
[1,2,5,3,4,7,8,6]=>[3,4,1]
[1,2,3,5,7,4,8,6]=>[5,2,1]
[1,2,3,5,7,8,4,6]=>[6,2]
[5,1,8,2,3,4,6,7]=>[1,2,5]
[5,8,1,2,3,4,6,7]=>[2,6]
[5,1,2,8,3,4,6,7]=>[1,3,4]
[1,5,2,8,3,4,6,7]=>[2,2,4]
[1,5,8,2,3,4,6,7]=>[3,5]
[5,1,2,3,8,4,6,7]=>[1,4,3]
[1,5,2,3,8,4,6,7]=>[2,3,3]
[1,2,5,3,8,4,6,7]=>[3,2,3]
[1,2,5,8,3,4,6,7]=>[4,4]
[5,1,2,3,4,8,6,7]=>[1,5,2]
[1,5,2,3,4,8,6,7]=>[2,4,2]
[1,2,5,3,4,8,6,7]=>[3,3,2]
[1,2,3,5,4,8,6,7]=>[4,2,2]
[1,2,3,5,8,4,6,7]=>[5,3]
[5,1,2,3,4,6,8,7]=>[1,6,1]
[1,5,2,3,4,6,8,7]=>[2,5,1]
[1,2,5,3,4,6,8,7]=>[3,4,1]
[1,2,3,5,6,8,4,7]=>[6,2]
[1,5,2,3,4,6,7,8]=>[2,6]
[1,2,5,3,4,6,7,8]=>[3,5]
[6,1,7,2,8,3,4,5]=>[1,2,2,3]
[6,7,1,2,8,3,4,5]=>[2,3,3]
[6,1,7,8,2,3,4,5]=>[1,3,4]
[6,7,1,8,2,3,4,5]=>[2,2,4]
[6,1,7,2,3,8,4,5]=>[1,2,3,2]
[6,7,1,2,3,8,4,5]=>[2,4,2]
[6,1,2,7,3,8,4,5]=>[1,3,2,2]
[1,6,2,7,3,8,4,5]=>[2,2,2,2]
[1,6,7,2,3,8,4,5]=>[3,3,2]
[6,1,2,7,8,3,4,5]=>[1,4,3]
[1,6,2,7,8,3,4,5]=>[2,3,3]
[1,6,7,2,8,3,4,5]=>[3,2,3]
[1,6,7,8,2,3,4,5]=>[4,4]
[6,1,7,2,3,4,8,5]=>[1,2,4,1]
[6,7,1,2,3,4,8,5]=>[2,5,1]
[6,1,2,7,3,4,8,5]=>[1,3,3,1]
[1,6,2,7,3,4,8,5]=>[2,2,3,1]
[1,6,7,2,3,4,8,5]=>[3,4,1]
[6,1,2,3,7,4,8,5]=>[1,4,2,1]
[1,6,2,3,7,4,8,5]=>[2,3,2,1]
[1,2,6,3,7,4,8,5]=>[3,2,2,1]
[1,2,6,7,3,4,8,5]=>[4,3,1]
[6,1,2,3,7,8,4,5]=>[1,5,2]
[1,6,2,3,7,8,4,5]=>[2,4,2]
[1,2,6,3,7,8,4,5]=>[3,3,2]
[1,2,6,7,3,8,4,5]=>[4,2,2]
[1,2,6,7,8,3,4,5]=>[5,3]
[6,1,7,2,3,4,5,8]=>[1,2,5]
[6,1,2,7,3,4,5,8]=>[1,3,4]
[1,6,2,7,3,4,5,8]=>[2,2,4]
[1,6,7,2,3,4,5,8]=>[3,5]
[6,1,2,3,7,4,5,8]=>[1,4,3]
[1,6,2,3,7,4,5,8]=>[2,3,3]
[1,2,6,3,7,4,5,8]=>[3,2,3]
[1,2,6,7,3,4,5,8]=>[4,4]
[6,1,2,3,4,7,5,8]=>[1,5,2]
[1,6,2,3,4,7,5,8]=>[2,4,2]
[1,2,6,3,4,7,5,8]=>[3,3,2]
[1,2,3,6,4,7,5,8]=>[4,2,2]
[1,2,3,6,7,4,5,8]=>[5,3]
[6,1,2,3,4,7,8,5]=>[1,6,1]
[1,6,2,3,4,7,8,5]=>[2,5,1]
[1,2,6,3,4,7,8,5]=>[3,4,1]
[1,2,3,6,4,7,8,5]=>[4,3,1]
[1,2,3,6,7,4,8,5]=>[5,2,1]
[1,2,3,6,7,8,4,5]=>[6,2]
[6,1,8,2,3,4,5,7]=>[1,2,5]
[6,8,1,2,3,4,5,7]=>[2,6]
[6,1,2,8,3,4,5,7]=>[1,3,4]
[1,6,2,8,3,4,5,7]=>[2,2,4]
[1,6,8,2,3,4,5,7]=>[3,5]
[6,1,2,3,8,4,5,7]=>[1,4,3]
[1,6,2,3,8,4,5,7]=>[2,3,3]
[1,2,6,3,8,4,5,7]=>[3,2,3]
[1,2,6,8,3,4,5,7]=>[4,4]
[6,1,2,3,4,8,5,7]=>[1,5,2]
[1,6,2,3,4,8,5,7]=>[2,4,2]
[1,2,6,3,4,8,5,7]=>[3,3,2]
[1,2,3,6,4,8,5,7]=>[4,2,2]
[1,2,3,6,8,4,5,7]=>[5,3]
[6,1,2,3,4,5,8,7]=>[1,6,1]
[1,6,2,3,4,5,8,7]=>[2,5,1]
[1,2,6,3,4,5,8,7]=>[3,4,1]
[1,2,3,6,4,5,8,7]=>[4,3,1]
[1,2,3,4,6,8,5,7]=>[6,2]
[1,6,2,3,4,5,7,8]=>[2,6]
[1,2,6,3,4,5,7,8]=>[3,5]
[1,2,3,6,4,5,7,8]=>[4,4]
[7,1,8,2,3,4,5,6]=>[1,2,5]
[7,1,2,8,3,4,5,6]=>[1,3,4]
[1,7,2,8,3,4,5,6]=>[2,2,4]
[1,7,8,2,3,4,5,6]=>[3,5]
[7,1,2,3,8,4,5,6]=>[1,4,3]
[1,7,2,3,8,4,5,6]=>[2,3,3]
[1,2,7,3,8,4,5,6]=>[3,2,3]
[1,2,7,8,3,4,5,6]=>[4,4]
[7,1,2,3,4,8,5,6]=>[1,5,2]
[1,7,2,3,4,8,5,6]=>[2,4,2]
[1,2,7,3,4,8,5,6]=>[3,3,2]
[1,2,3,7,4,8,5,6]=>[4,2,2]
[1,2,3,7,8,4,5,6]=>[5,3]
[7,1,2,3,4,5,8,6]=>[1,6,1]
[1,7,2,3,4,5,8,6]=>[2,5,1]
[1,2,7,3,4,5,8,6]=>[3,4,1]
[1,2,3,7,4,5,8,6]=>[4,3,1]
[1,2,3,4,7,5,8,6]=>[5,2,1]
[1,2,3,4,7,8,5,6]=>[6,2]
[1,7,2,3,4,5,6,8]=>[2,6]
[1,2,7,3,4,5,6,8]=>[3,5]
[1,2,3,7,4,5,6,8]=>[4,4]
[1,2,3,4,7,5,6,8]=>[5,3]
[1,8,2,3,4,5,6,7]=>[2,6]
[1,2,8,3,4,5,6,7]=>[3,5]
[1,2,3,8,4,5,6,7]=>[4,4]
[1,2,3,4,8,5,6,7]=>[5,3]
[1,2,3,4,5,8,6,7]=>[6,2]
[5,3,2,6,1,4,8,7]=>[1,1,2,3,1]
[7,3,2,5,4,8,1,6]=>[1,1,2,2,2]
[8,4,5,2,3,7,6,1]=>[1,2,3,1,1]
[7,4,5,2,3,8,1,6]=>[1,2,3,2]
[6,4,5,2,3,1,8,7]=>[1,2,2,2,1]
[5,4,6,2,1,3,8,7]=>[1,2,1,3,1]
[3,6,1,5,4,2,8,7]=>[2,2,1,2,1]
[4,6,5,1,3,2,8,7]=>[2,1,2,2,1]
[5,6,4,3,1,2,8,7]=>[2,1,1,3,1]
[7,5,4,3,2,8,1,6]=>[1,1,1,1,2,2]
[8,6,4,3,7,2,5,1]=>[1,1,1,2,2,1]
[7,6,4,3,8,2,1,5]=>[1,1,1,2,1,2]
[6,7,4,3,8,1,2,5]=>[2,1,2,3]
[5,7,4,3,1,8,2,6]=>[2,1,1,2,2]
[4,7,5,1,3,8,2,6]=>[2,1,3,2]
[3,7,1,5,4,8,2,6]=>[2,2,2,2]
[2,1,7,5,4,8,3,6]=>[1,2,1,2,2]
[3,8,1,5,4,7,6,2]=>[2,2,2,1,1]
[4,8,5,1,3,7,6,2]=>[2,1,3,1,1]
[5,8,4,3,1,7,6,2]=>[2,1,1,2,1,1]
[6,8,4,3,7,1,5,2]=>[2,1,2,2,1]
[7,8,4,3,6,5,1,2]=>[2,1,2,1,2]
[6,8,5,7,3,1,4,2]=>[2,2,1,2,1]
[5,8,6,7,1,3,4,2]=>[2,2,3,1]
[4,8,6,1,7,3,5,2]=>[2,1,2,2,1]
[3,8,1,6,7,4,5,2]=>[2,3,2,1]
[2,1,8,6,7,4,5,3]=>[1,2,2,2,1]
[2,1,7,6,8,4,3,5]=>[1,2,2,1,2]
[3,7,1,6,8,4,2,5]=>[2,3,1,2]
[4,7,6,1,8,3,2,5]=>[2,1,2,1,2]
[5,7,6,8,1,3,2,4]=>[2,2,2,2]
[5,4,7,2,1,8,3,6]=>[1,2,1,2,2]
[6,4,7,2,8,1,3,5]=>[1,2,2,3]
[7,4,6,2,8,3,1,5]=>[1,2,2,1,2]
[8,4,6,2,7,3,5,1]=>[1,2,2,2,1]
[8,3,2,6,7,4,5,1]=>[1,1,3,2,1]
[7,3,2,6,8,4,1,5]=>[1,1,3,1,2]
[6,3,2,7,8,1,4,5]=>[1,1,3,3]
[5,3,2,7,1,8,4,6]=>[1,1,2,2,2]
[4,3,2,1,7,8,5,6]=>[1,1,1,3,2]
[3,4,1,2,8,7,6,5]=>[2,3,1,1,1]
[5,3,2,8,1,7,6,4]=>[1,1,2,2,1,1]
[6,3,2,8,7,1,5,4]=>[1,1,2,1,2,1]
[7,3,2,8,6,5,1,4]=>[1,1,2,1,1,2]
[8,4,7,2,6,5,3,1]=>[1,2,2,1,1,1]
[7,4,8,2,6,5,1,3]=>[1,2,2,1,2]
[6,4,8,2,7,1,5,3]=>[1,2,2,2,1]
[5,4,8,2,1,7,6,3]=>[1,2,1,2,1,1]
[4,5,8,1,2,7,6,3]=>[3,3,1,1]
[3,5,1,8,2,7,6,4]=>[2,2,2,1,1]
[2,1,5,8,3,7,6,4]=>[1,3,2,1,1]
[2,1,6,8,7,3,5,4]=>[1,3,1,2,1]
[3,6,1,8,7,2,5,4]=>[2,2,1,2,1]
[4,6,8,1,7,2,5,3]=>[3,2,2,1]
[5,6,8,7,1,2,4,3]=>[3,1,3,1]
[6,5,8,7,2,1,4,3]=>[1,2,1,1,2,1]
[7,5,8,6,2,4,1,3]=>[1,2,1,2,2]
[8,5,7,6,2,4,3,1]=>[1,2,1,2,1,1]
[5,7,8,6,1,4,2,3]=>[3,1,2,2]
[4,7,8,1,6,5,2,3]=>[3,2,1,2]
[3,7,1,8,6,5,2,4]=>[2,2,1,1,2]
[2,1,7,8,6,5,3,4]=>[1,3,1,1,2]
[3,8,1,7,6,5,4,2]=>[2,2,1,1,1,1]
[4,8,7,1,6,5,3,2]=>[2,1,2,1,1,1]
[5,8,7,6,1,4,3,2]=>[2,1,1,2,1,1]
[6,8,7,5,4,1,3,2]=>[2,1,1,1,2,1]
[3,2,5,1,4,6,7,8]=>[1,2,5]
[4,2,5,1,3,6,7,8]=>[1,2,5]
[5,2,4,1,3,6,7,8]=>[1,2,5]
[3,2,6,1,4,5,7,8]=>[1,2,5]
[4,2,6,1,3,5,7,8]=>[1,2,5]
[5,2,6,1,3,4,7,8]=>[1,2,5]
[5,3,6,1,2,4,7,8]=>[1,2,5]
[6,2,4,1,3,5,7,8]=>[1,2,5]
[6,3,5,1,2,4,7,8]=>[1,2,5]
[3,2,7,1,4,5,6,8]=>[1,2,5]
[4,2,7,1,3,5,6,8]=>[1,2,5]
[5,2,7,1,3,4,6,8]=>[1,2,5]
[5,3,7,1,2,4,6,8]=>[1,2,5]
[5,4,7,1,2,3,6,8]=>[1,2,5]
[6,2,7,1,3,4,5,8]=>[1,2,5]
[6,3,7,1,2,4,5,8]=>[1,2,5]
[6,4,7,1,2,3,5,8]=>[1,2,5]
[7,2,5,1,3,4,6,8]=>[1,2,5]
[7,3,5,1,2,4,6,8]=>[1,2,5]
[7,3,6,1,2,4,5,8]=>[1,2,5]
[7,4,6,1,2,3,5,8]=>[1,2,5]
[3,2,8,1,4,5,6,7]=>[1,2,5]
[4,2,8,1,3,5,6,7]=>[1,2,5]
[4,3,8,1,2,5,6,7]=>[1,2,5]
[5,2,8,1,3,4,6,7]=>[1,2,5]
[5,3,8,1,2,4,6,7]=>[1,2,5]
[5,4,8,1,2,3,6,7]=>[1,2,5]
[6,2,8,1,3,4,5,7]=>[1,2,5]
[6,3,8,1,2,4,5,7]=>[1,2,5]
[6,4,8,1,2,3,5,7]=>[1,2,5]
[6,5,8,1,2,3,4,7]=>[1,2,5]
[7,2,8,1,3,4,5,6]=>[1,2,5]
[7,3,8,1,2,4,5,6]=>[1,2,5]
[7,4,8,1,2,3,5,6]=>[1,2,5]
[7,5,8,1,2,3,4,6]=>[1,2,5]
[8,2,4,1,3,5,6,7]=>[1,2,5]
[8,3,5,1,2,4,6,7]=>[1,2,5]
[8,2,6,1,3,4,5,7]=>[1,2,5]
[8,3,6,1,2,4,5,7]=>[1,2,5]
[8,4,6,1,2,3,5,7]=>[1,2,5]
[8,2,7,1,3,4,5,6]=>[1,2,5]
[8,3,7,1,2,4,5,6]=>[1,2,5]
[8,4,7,1,2,3,5,6]=>[1,2,5]
[8,5,7,1,2,3,4,6]=>[1,2,5]
[3,2,5,7,1,4,6,8]=>[1,3,4]
[4,2,5,7,1,3,6,8]=>[1,3,4]
[4,3,5,7,1,2,6,8]=>[1,3,4]
[5,2,4,7,1,3,6,8]=>[1,3,4]
[5,3,4,7,1,2,6,8]=>[1,3,4]
[3,2,6,7,1,4,5,8]=>[1,3,4]
[4,2,6,7,1,3,5,8]=>[1,3,4]
[4,3,6,7,1,2,5,8]=>[1,3,4]
[5,2,6,7,1,3,4,8]=>[1,3,4]
[5,3,6,7,1,2,4,8]=>[1,3,4]
[6,2,4,7,1,3,5,8]=>[1,3,4]
[6,3,4,7,1,2,5,8]=>[1,3,4]
[6,2,5,7,1,3,4,8]=>[1,3,4]
[6,3,5,7,1,2,4,8]=>[1,3,4]
[7,2,4,6,1,3,5,8]=>[1,3,4]
[7,3,4,6,1,2,5,8]=>[1,3,4]
[7,2,5,6,1,3,4,8]=>[1,3,4]
[7,3,5,6,1,2,4,8]=>[1,3,4]
[3,2,5,8,1,4,6,7]=>[1,3,4]
[4,2,5,8,1,3,6,7]=>[1,3,4]
[4,3,5,8,1,2,6,7]=>[1,3,4]
[5,2,4,8,1,3,6,7]=>[1,3,4]
[5,3,4,8,1,2,6,7]=>[1,3,4]
[3,2,6,8,1,4,5,7]=>[1,3,4]
[4,2,6,8,1,3,5,7]=>[1,3,4]
[4,3,6,8,1,2,5,7]=>[1,3,4]
[5,2,6,8,1,3,4,7]=>[1,3,4]
[5,3,6,8,1,2,4,7]=>[1,3,4]
[5,4,6,8,1,2,3,7]=>[1,3,4]
[6,2,4,8,1,3,5,7]=>[1,3,4]
[6,3,4,8,1,2,5,7]=>[1,3,4]
[6,2,5,8,1,3,4,7]=>[1,3,4]
[6,3,5,8,1,2,4,7]=>[1,3,4]
[6,4,5,8,1,2,3,7]=>[1,3,4]
[3,2,7,8,1,4,5,6]=>[1,3,4]
[4,2,7,8,1,3,5,6]=>[1,3,4]
[4,3,7,8,1,2,5,6]=>[1,3,4]
[5,2,7,8,1,3,4,6]=>[1,3,4]
[5,3,7,8,1,2,4,6]=>[1,3,4]
[5,4,7,8,1,2,3,6]=>[1,3,4]
[6,2,7,8,1,3,4,5]=>[1,3,4]
[6,3,7,8,1,2,4,5]=>[1,3,4]
[6,4,7,8,1,2,3,5]=>[1,3,4]
[7,2,4,8,1,3,5,6]=>[1,3,4]
[7,3,4,8,1,2,5,6]=>[1,3,4]
[7,2,5,8,1,3,4,6]=>[1,3,4]
[7,3,5,8,1,2,4,6]=>[1,3,4]
[7,4,5,8,1,2,3,6]=>[1,3,4]
[7,2,6,8,1,3,4,5]=>[1,3,4]
[7,3,6,8,1,2,4,5]=>[1,3,4]
[7,4,6,8,1,2,3,5]=>[1,3,4]
[8,2,4,6,1,3,5,7]=>[1,3,4]
[8,3,4,6,1,2,5,7]=>[1,3,4]
[8,2,5,6,1,3,4,7]=>[1,3,4]
[8,3,5,6,1,2,4,7]=>[1,3,4]
[8,2,4,7,1,3,5,6]=>[1,3,4]
[8,2,5,7,1,3,4,6]=>[1,3,4]
[8,3,5,7,1,2,4,6]=>[1,3,4]
[8,4,5,7,1,2,3,6]=>[1,3,4]
[8,2,6,7,1,3,4,5]=>[1,3,4]
[8,4,6,7,1,2,3,5]=>[1,3,4]
[3,6,2,5,1,4,7,8]=>[2,2,4]
[4,6,2,5,1,3,7,8]=>[2,2,4]
[4,6,3,5,1,2,7,8]=>[2,2,4]
[5,6,2,4,1,3,7,8]=>[2,2,4]
[3,7,2,5,1,4,6,8]=>[2,2,4]
[4,7,2,5,1,3,6,8]=>[2,2,4]
[4,7,3,5,1,2,6,8]=>[2,2,4]
[5,7,2,4,1,3,6,8]=>[2,2,4]
[5,7,3,4,1,2,6,8]=>[2,2,4]
[3,7,2,6,1,4,5,8]=>[2,2,4]
[4,7,2,6,1,3,5,8]=>[2,2,4]
[4,7,3,6,1,2,5,8]=>[2,2,4]
[5,7,2,6,1,3,4,8]=>[2,2,4]
[5,7,3,6,1,2,4,8]=>[2,2,4]
[5,7,4,6,1,2,3,8]=>[2,2,4]
[6,7,2,4,1,3,5,8]=>[2,2,4]
[6,7,2,5,1,3,4,8]=>[2,2,4]
[6,7,3,5,1,2,4,8]=>[2,2,4]
[3,8,2,5,1,4,6,7]=>[2,2,4]
[4,8,2,5,1,3,6,7]=>[2,2,4]
[4,8,3,5,1,2,6,7]=>[2,2,4]
[5,8,2,4,1,3,6,7]=>[2,2,4]
[5,8,3,4,1,2,6,7]=>[2,2,4]
[3,8,2,6,1,4,5,7]=>[2,2,4]
[4,8,2,6,1,3,5,7]=>[2,2,4]
[5,8,2,6,1,3,4,7]=>[2,2,4]
[5,8,3,6,1,2,4,7]=>[2,2,4]
[5,8,4,6,1,2,3,7]=>[2,2,4]
[6,8,2,4,1,3,5,7]=>[2,2,4]
[6,8,3,4,1,2,5,7]=>[2,2,4]
[6,8,3,5,1,2,4,7]=>[2,2,4]
[6,8,4,5,1,2,3,7]=>[2,2,4]
[3,8,2,7,1,4,5,6]=>[2,2,4]
[4,8,2,7,1,3,5,6]=>[2,2,4]
[4,8,3,7,1,2,5,6]=>[2,2,4]
[5,8,2,7,1,3,4,6]=>[2,2,4]
[5,8,3,7,1,2,4,6]=>[2,2,4]
[5,8,4,7,1,2,3,6]=>[2,2,4]
[6,8,2,7,1,3,4,5]=>[2,2,4]
[6,8,3,7,1,2,4,5]=>[2,2,4]
[6,8,4,7,1,2,3,5]=>[2,2,4]
[6,8,5,7,1,2,3,4]=>[2,2,4]
[7,8,2,4,1,3,5,6]=>[2,2,4]
[7,8,2,5,1,3,4,6]=>[2,2,4]
[7,8,3,5,1,2,4,6]=>[2,2,4]
[7,8,2,6,1,3,4,5]=>[2,2,4]
[7,8,4,6,1,2,3,5]=>[2,2,4]
[4,3,2,6,1,5,7,8]=>[1,1,2,4]
[5,3,2,6,1,4,7,8]=>[1,1,2,4]
[5,4,2,6,1,3,7,8]=>[1,1,2,4]
[6,3,2,5,1,4,7,8]=>[1,1,2,4]
[6,4,2,5,1,3,7,8]=>[1,1,2,4]
[6,5,2,4,1,3,7,8]=>[1,1,2,4]
[4,3,2,7,1,5,6,8]=>[1,1,2,4]
[5,3,2,7,1,4,6,8]=>[1,1,2,4]
[5,4,2,7,1,3,6,8]=>[1,1,2,4]
[5,4,3,7,1,2,6,8]=>[1,1,2,4]
[6,3,2,7,1,4,5,8]=>[1,1,2,4]
[6,4,2,7,1,3,5,8]=>[1,1,2,4]
[6,4,3,7,1,2,5,8]=>[1,1,2,4]
[6,5,2,7,1,3,4,8]=>[1,1,2,4]
[6,5,3,7,1,2,4,8]=>[1,1,2,4]
[7,3,2,5,1,4,6,8]=>[1,1,2,4]
[7,4,2,5,1,3,6,8]=>[1,1,2,4]
[7,5,2,4,1,3,6,8]=>[1,1,2,4]
[7,3,2,6,1,4,5,8]=>[1,1,2,4]
[7,4,2,6,1,3,5,8]=>[1,1,2,4]
[7,4,3,6,1,2,5,8]=>[1,1,2,4]
[7,5,2,6,1,3,4,8]=>[1,1,2,4]
[7,5,3,6,1,2,4,8]=>[1,1,2,4]
[7,6,3,5,1,2,4,8]=>[1,1,2,4]
[4,3,2,8,1,5,6,7]=>[1,1,2,4]
[5,3,2,8,1,4,6,7]=>[1,1,2,4]
[5,4,2,8,1,3,6,7]=>[1,1,2,4]
[5,4,3,8,1,2,6,7]=>[1,1,2,4]
[6,3,2,8,1,4,5,7]=>[1,1,2,4]
[6,4,2,8,1,3,5,7]=>[1,1,2,4]
[6,4,3,8,1,2,5,7]=>[1,1,2,4]
[6,5,2,8,1,3,4,7]=>[1,1,2,4]
[6,5,3,8,1,2,4,7]=>[1,1,2,4]
[6,5,4,8,1,2,3,7]=>[1,1,2,4]
[7,3,2,8,1,4,5,6]=>[1,1,2,4]
[7,4,2,8,1,3,5,6]=>[1,1,2,4]
[7,4,3,8,1,2,5,6]=>[1,1,2,4]
[7,5,3,8,1,2,4,6]=>[1,1,2,4]
[7,5,4,8,1,2,3,6]=>[1,1,2,4]
[7,6,2,8,1,3,4,5]=>[1,1,2,4]
[7,6,4,8,1,2,3,5]=>[1,1,2,4]
[8,3,2,5,1,4,6,7]=>[1,1,2,4]
[8,4,2,5,1,3,6,7]=>[1,1,2,4]
[8,5,2,4,1,3,6,7]=>[1,1,2,4]
[8,3,2,6,1,4,5,7]=>[1,1,2,4]
[8,4,2,6,1,3,5,7]=>[1,1,2,4]
[8,5,3,6,1,2,4,7]=>[1,1,2,4]
[8,6,2,4,1,3,5,7]=>[1,1,2,4]
[8,6,2,5,1,3,4,7]=>[1,1,2,4]
[8,6,3,5,1,2,4,7]=>[1,1,2,4]
[8,3,2,7,1,4,5,6]=>[1,1,2,4]
[8,4,2,7,1,3,5,6]=>[1,1,2,4]
[8,4,3,7,1,2,5,6]=>[1,1,2,4]
[8,5,2,7,1,3,4,6]=>[1,1,2,4]
[8,5,3,7,1,2,4,6]=>[1,1,2,4]
[8,5,4,7,1,2,3,6]=>[1,1,2,4]
[8,6,2,7,1,3,4,5]=>[1,1,2,4]
[8,6,3,7,1,2,4,5]=>[1,1,2,4]
[8,6,4,7,1,2,3,5]=>[1,1,2,4]
[8,7,2,4,1,3,5,6]=>[1,1,2,4]
[8,7,2,5,1,3,4,6]=>[1,1,2,4]
[8,7,3,5,1,2,4,6]=>[1,1,2,4]
[8,7,2,6,1,3,4,5]=>[1,1,2,4]
[8,7,3,6,1,2,4,5]=>[1,1,2,4]
[8,7,4,6,1,2,3,5]=>[1,1,2,4]
[3,6,2,5,8,1,4,7]=>[2,3,3]
[4,6,2,5,8,1,3,7]=>[2,3,3]
[4,6,3,5,8,1,2,7]=>[2,3,3]
[5,6,2,4,8,1,3,7]=>[2,3,3]
[5,6,3,4,8,1,2,7]=>[2,3,3]
[3,7,2,5,8,1,4,6]=>[2,3,3]
[4,7,2,5,8,1,3,6]=>[2,3,3]
[4,7,3,5,8,1,2,6]=>[2,3,3]
[5,7,2,4,8,1,3,6]=>[2,3,3]
[5,7,3,4,8,1,2,6]=>[2,3,3]
[3,7,2,6,8,1,4,5]=>[2,3,3]
[4,7,2,6,8,1,3,5]=>[2,3,3]
[4,7,3,6,8,1,2,5]=>[2,3,3]
[5,7,2,6,8,1,3,4]=>[2,3,3]
[5,7,3,6,8,1,2,4]=>[2,3,3]
[5,7,4,6,8,1,2,3]=>[2,3,3]
[6,7,2,4,8,1,3,5]=>[2,3,3]
[6,7,3,4,8,1,2,5]=>[2,3,3]
[6,7,3,5,8,1,2,4]=>[2,3,3]
[3,8,2,5,7,1,4,6]=>[2,3,3]
[4,8,2,5,7,1,3,6]=>[2,3,3]
[4,8,3,5,7,1,2,6]=>[2,3,3]
[5,8,2,4,7,1,3,6]=>[2,3,3]
[3,8,2,6,7,1,4,5]=>[2,3,3]
[4,8,2,6,7,1,3,5]=>[2,3,3]
[4,8,3,6,7,1,2,5]=>[2,3,3]
[5,8,2,6,7,1,3,4]=>[2,3,3]
[5,8,3,6,7,1,2,4]=>[2,3,3]
[6,8,2,4,7,1,3,5]=>[2,3,3]
[6,8,2,5,7,1,3,4]=>[2,3,3]
[6,8,3,5,7,1,2,4]=>[2,3,3]
[6,8,4,5,7,1,2,3]=>[2,3,3]
[7,8,2,4,6,1,3,5]=>[2,3,3]
[7,8,3,4,6,1,2,5]=>[2,3,3]
[7,8,2,5,6,1,3,4]=>[2,3,3]
[7,8,3,5,6,1,2,4]=>[2,3,3]
[4,3,2,6,8,1,5,7]=>[1,1,3,3]
[5,3,2,6,8,1,4,7]=>[1,1,3,3]
[5,4,2,6,8,1,3,7]=>[1,1,3,3]
[5,4,3,6,8,1,2,7]=>[1,1,3,3]
[6,3,2,5,8,1,4,7]=>[1,1,3,3]
[6,4,2,5,8,1,3,7]=>[1,1,3,3]
[6,4,3,5,8,1,2,7]=>[1,1,3,3]
[6,5,2,4,8,1,3,7]=>[1,1,3,3]
[6,5,3,4,8,1,2,7]=>[1,1,3,3]
[4,3,2,7,8,1,5,6]=>[1,1,3,3]
[5,3,2,7,8,1,4,6]=>[1,1,3,3]
[5,4,2,7,8,1,3,6]=>[1,1,3,3]
[5,4,3,7,8,1,2,6]=>[1,1,3,3]
[6,4,2,7,8,1,3,5]=>[1,1,3,3]
[6,4,3,7,8,1,2,5]=>[1,1,3,3]
[6,5,2,7,8,1,3,4]=>[1,1,3,3]
[6,5,3,7,8,1,2,4]=>[1,1,3,3]
[7,3,2,5,8,1,4,6]=>[1,1,3,3]
[7,4,2,5,8,1,3,6]=>[1,1,3,3]
[7,4,3,5,8,1,2,6]=>[1,1,3,3]
[7,5,2,4,8,1,3,6]=>[1,1,3,3]
[7,5,3,4,8,1,2,6]=>[1,1,3,3]
[7,3,2,6,8,1,4,5]=>[1,1,3,3]
[7,4,2,6,8,1,3,5]=>[1,1,3,3]
[7,4,3,6,8,1,2,5]=>[1,1,3,3]
[7,5,2,6,8,1,3,4]=>[1,1,3,3]
[7,5,3,6,8,1,2,4]=>[1,1,3,3]
[7,6,2,4,8,1,3,5]=>[1,1,3,3]
[7,6,3,4,8,1,2,5]=>[1,1,3,3]
[7,6,2,5,8,1,3,4]=>[1,1,3,3]
[7,6,3,5,8,1,2,4]=>[1,1,3,3]
[8,3,2,5,7,1,4,6]=>[1,1,3,3]
[8,4,2,5,7,1,3,6]=>[1,1,3,3]
[8,4,3,5,7,1,2,6]=>[1,1,3,3]
[8,5,2,4,7,1,3,6]=>[1,1,3,3]
[8,5,3,4,7,1,2,6]=>[1,1,3,3]
[8,3,2,6,7,1,4,5]=>[1,1,3,3]
[8,4,2,6,7,1,3,5]=>[1,1,3,3]
[8,4,3,6,7,1,2,5]=>[1,1,3,3]
[8,5,2,6,7,1,3,4]=>[1,1,3,3]
[8,5,3,6,7,1,2,4]=>[1,1,3,3]
[8,6,2,4,7,1,3,5]=>[1,1,3,3]
[8,6,3,4,7,1,2,5]=>[1,1,3,3]
[8,6,2,5,7,1,3,4]=>[1,1,3,3]
[8,6,3,5,7,1,2,4]=>[1,1,3,3]
[8,7,2,4,6,1,3,5]=>[1,1,3,3]
[8,7,3,4,6,1,2,5]=>[1,1,3,3]
[8,7,2,5,6,1,3,4]=>[1,1,3,3]
[8,7,3,5,6,1,2,4]=>[1,1,3,3]
[4,3,7,2,6,1,5,8]=>[1,2,2,3]
[5,3,7,2,6,1,4,8]=>[1,2,2,3]
[5,4,7,2,6,1,3,8]=>[1,2,2,3]
[5,4,7,3,6,1,2,8]=>[1,2,2,3]
[6,3,7,2,5,1,4,8]=>[1,2,2,3]
[6,4,7,2,5,1,3,8]=>[1,2,2,3]
[6,4,7,3,5,1,2,8]=>[1,2,2,3]
[6,5,7,2,4,1,3,8]=>[1,2,2,3]
[7,3,6,2,5,1,4,8]=>[1,2,2,3]
[7,4,6,2,5,1,3,8]=>[1,2,2,3]
[7,4,6,3,5,1,2,8]=>[1,2,2,3]
[7,5,6,2,4,1,3,8]=>[1,2,2,3]
[4,3,8,2,6,1,5,7]=>[1,2,2,3]
[5,3,8,2,6,1,4,7]=>[1,2,2,3]
[5,4,8,2,6,1,3,7]=>[1,2,2,3]
[5,4,8,3,6,1,2,7]=>[1,2,2,3]
[6,3,8,2,5,1,4,7]=>[1,2,2,3]
[6,4,8,2,5,1,3,7]=>[1,2,2,3]
[6,4,8,3,5,1,2,7]=>[1,2,2,3]
[6,5,8,2,4,1,3,7]=>[1,2,2,3]
[6,5,8,3,4,1,2,7]=>[1,2,2,3]
[4,3,8,2,7,1,5,6]=>[1,2,2,3]
[5,3,8,2,7,1,4,6]=>[1,2,2,3]
[5,4,8,2,7,1,3,6]=>[1,2,2,3]
[5,4,8,3,7,1,2,6]=>[1,2,2,3]
[6,3,8,2,7,1,4,5]=>[1,2,2,3]
[6,4,8,2,7,1,3,5]=>[1,2,2,3]
[6,4,8,3,7,1,2,5]=>[1,2,2,3]
[6,5,8,2,7,1,3,4]=>[1,2,2,3]
[6,5,8,3,7,1,2,4]=>[1,2,2,3]
[6,5,8,4,7,1,2,3]=>[1,2,2,3]
[7,3,8,2,5,1,4,6]=>[1,2,2,3]
[7,4,8,2,5,1,3,6]=>[1,2,2,3]
[7,4,8,3,5,1,2,6]=>[1,2,2,3]
[7,5,8,2,4,1,3,6]=>[1,2,2,3]
[7,5,8,3,4,1,2,6]=>[1,2,2,3]
[7,3,8,2,6,1,4,5]=>[1,2,2,3]
[7,4,8,2,6,1,3,5]=>[1,2,2,3]
[7,4,8,3,6,1,2,5]=>[1,2,2,3]
[7,5,8,2,6,1,3,4]=>[1,2,2,3]
[7,5,8,3,6,1,2,4]=>[1,2,2,3]
[7,5,8,4,6,1,2,3]=>[1,2,2,3]
[7,6,8,2,4,1,3,5]=>[1,2,2,3]
[7,6,8,2,5,1,3,4]=>[1,2,2,3]
[7,6,8,3,5,1,2,4]=>[1,2,2,3]
[8,3,6,2,5,1,4,7]=>[1,2,2,3]
[8,4,6,2,5,1,3,7]=>[1,2,2,3]
[8,4,6,3,5,1,2,7]=>[1,2,2,3]
[8,5,6,2,4,1,3,7]=>[1,2,2,3]
[8,3,7,2,5,1,4,6]=>[1,2,2,3]
[8,4,7,3,5,1,2,6]=>[1,2,2,3]
[8,5,7,2,4,1,3,6]=>[1,2,2,3]
[8,3,7,2,6,1,4,5]=>[1,2,2,3]
[8,4,7,2,6,1,3,5]=>[1,2,2,3]
[8,4,7,3,6,1,2,5]=>[1,2,2,3]
[8,5,7,2,6,1,3,4]=>[1,2,2,3]
[8,6,7,2,4,1,3,5]=>[1,2,2,3]
[8,6,7,2,5,1,3,4]=>[1,2,2,3]
[8,6,7,3,5,1,2,4]=>[1,2,2,3]
[5,4,3,2,7,1,6,8]=>[1,1,1,2,3]
[6,4,3,2,7,1,5,8]=>[1,1,1,2,3]
[6,5,3,2,7,1,4,8]=>[1,1,1,2,3]
[6,5,4,2,7,1,3,8]=>[1,1,1,2,3]
[7,5,3,2,6,1,4,8]=>[1,1,1,2,3]
[7,5,4,2,6,1,3,8]=>[1,1,1,2,3]
[7,6,3,2,5,1,4,8]=>[1,1,1,2,3]
[7,6,4,2,5,1,3,8]=>[1,1,1,2,3]
[7,6,5,2,4,1,3,8]=>[1,1,1,2,3]
[5,4,3,2,8,1,6,7]=>[1,1,1,2,3]
[6,5,3,2,8,1,4,7]=>[1,1,1,2,3]
[6,5,4,2,8,1,3,7]=>[1,1,1,2,3]
[6,5,4,3,8,1,2,7]=>[1,1,1,2,3]
[7,4,3,2,8,1,5,6]=>[1,1,1,2,3]
[7,5,3,2,8,1,4,6]=>[1,1,1,2,3]
[7,5,4,2,8,1,3,6]=>[1,1,1,2,3]
[7,5,4,3,8,1,2,6]=>[1,1,1,2,3]
[7,6,3,2,8,1,4,5]=>[1,1,1,2,3]
[7,6,4,3,8,1,2,5]=>[1,1,1,2,3]
[7,6,5,2,8,1,3,4]=>[1,1,1,2,3]
[7,6,5,3,8,1,2,4]=>[1,1,1,2,3]
[8,5,3,2,6,1,4,7]=>[1,1,1,2,3]
[8,5,4,2,6,1,3,7]=>[1,1,1,2,3]
[8,6,4,2,5,1,3,7]=>[1,1,1,2,3]
[8,6,5,2,4,1,3,7]=>[1,1,1,2,3]
[8,5,3,2,7,1,4,6]=>[1,1,1,2,3]
[8,6,3,2,7,1,4,5]=>[1,1,1,2,3]
[8,6,4,2,7,1,3,5]=>[1,1,1,2,3]
[8,6,4,3,7,1,2,5]=>[1,1,1,2,3]
[8,6,5,2,7,1,3,4]=>[1,1,1,2,3]
[8,6,5,3,7,1,2,4]=>[1,1,1,2,3]
[8,7,4,2,5,1,3,6]=>[1,1,1,2,3]
[8,7,5,2,4,1,3,6]=>[1,1,1,2,3]
[8,7,3,2,6,1,4,5]=>[1,1,1,2,3]
[8,7,4,2,6,1,3,5]=>[1,1,1,2,3]
[8,7,4,3,6,1,2,5]=>[1,1,1,2,3]
[8,7,5,2,6,1,3,4]=>[1,1,1,2,3]
[8,7,5,3,6,1,2,4]=>[1,1,1,2,3]
[8,7,6,2,4,1,3,5]=>[1,1,1,2,3]
[8,7,6,2,5,1,3,4]=>[1,1,1,2,3]
[8,7,6,3,5,1,2,4]=>[1,1,1,2,3]
[4,8,3,7,2,6,1,5]=>[2,2,2,2]
[5,8,3,7,2,6,1,4]=>[2,2,2,2]
[5,8,4,7,2,6,1,3]=>[2,2,2,2]
[5,8,4,7,3,6,1,2]=>[2,2,2,2]
[6,8,3,7,2,5,1,4]=>[2,2,2,2]
[6,8,4,7,2,5,1,3]=>[2,2,2,2]
[6,8,4,7,3,5,1,2]=>[2,2,2,2]
[6,8,5,7,2,4,1,3]=>[2,2,2,2]
[6,8,5,7,3,4,1,2]=>[2,2,2,2]
[7,8,3,6,2,5,1,4]=>[2,2,2,2]
[7,8,4,6,2,5,1,3]=>[2,2,2,2]
[7,8,4,6,3,5,1,2]=>[2,2,2,2]
[7,8,5,6,2,4,1,3]=>[2,2,2,2]
[5,4,3,8,2,7,1,6]=>[1,1,2,2,2]
[6,4,3,8,2,7,1,5]=>[1,1,2,2,2]
[6,5,3,8,2,7,1,4]=>[1,1,2,2,2]
[6,5,4,8,2,7,1,3]=>[1,1,2,2,2]
[6,5,4,8,3,7,1,2]=>[1,1,2,2,2]
[7,4,3,8,2,6,1,5]=>[1,1,2,2,2]
[7,5,3,8,2,6,1,4]=>[1,1,2,2,2]
[7,5,4,8,2,6,1,3]=>[1,1,2,2,2]
[7,5,4,8,3,6,1,2]=>[1,1,2,2,2]
[7,6,3,8,2,5,1,4]=>[1,1,2,2,2]
[7,6,4,8,2,5,1,3]=>[1,1,2,2,2]
[7,6,4,8,3,5,1,2]=>[1,1,2,2,2]
[7,6,5,8,2,4,1,3]=>[1,1,2,2,2]
[8,4,3,7,2,6,1,5]=>[1,1,2,2,2]
[8,5,3,7,2,6,1,4]=>[1,1,2,2,2]
[8,5,4,7,2,6,1,3]=>[1,1,2,2,2]
[8,5,4,7,3,6,1,2]=>[1,1,2,2,2]
[8,6,3,7,2,5,1,4]=>[1,1,2,2,2]
[8,6,4,7,2,5,1,3]=>[1,1,2,2,2]
[8,6,4,7,3,5,1,2]=>[1,1,2,2,2]
[8,6,5,7,2,4,1,3]=>[1,1,2,2,2]
[8,7,3,6,2,5,1,4]=>[1,1,2,2,2]
[8,7,4,6,2,5,1,3]=>[1,1,2,2,2]
[8,7,4,6,3,5,1,2]=>[1,1,2,2,2]
[8,7,5,6,2,4,1,3]=>[1,1,2,2,2]
[6,5,4,3,2,8,1,7]=>[1,1,1,1,2,2]
[7,6,4,3,2,8,1,5]=>[1,1,1,1,2,2]
[7,6,5,3,2,8,1,4]=>[1,1,1,1,2,2]
[7,6,5,4,2,8,1,3]=>[1,1,1,1,2,2]
[8,5,4,3,2,7,1,6]=>[1,1,1,1,2,2]
[8,6,4,3,2,7,1,5]=>[1,1,1,1,2,2]
[8,6,5,3,2,7,1,4]=>[1,1,1,1,2,2]
[8,6,5,4,2,7,1,3]=>[1,1,1,1,2,2]
[8,7,4,3,2,6,1,5]=>[1,1,1,1,2,2]
[8,7,5,3,2,6,1,4]=>[1,1,1,1,2,2]
[8,7,5,4,2,6,1,3]=>[1,1,1,1,2,2]
[8,7,6,3,2,5,1,4]=>[1,1,1,1,2,2]
[8,7,6,4,2,5,1,3]=>[1,1,1,1,2,2]
[8,7,6,5,2,4,1,3]=>[1,1,1,1,2,2]
[8,1,2,3,4,7,5,6]=>[1,5,2]
[8,1,2,3,6,4,5,7]=>[1,4,3]
[8,1,2,3,7,4,5,6]=>[1,4,3]
[7,1,2,3,6,4,8,5]=>[1,4,2,1]
[5,1,2,3,8,7,4,6]=>[1,4,1,2]
[8,1,2,3,6,7,4,5]=>[1,5,2]
[4,1,2,8,3,7,5,6]=>[1,3,2,2]
[8,1,2,5,3,4,6,7]=>[1,3,4]
[7,1,2,5,3,4,8,6]=>[1,3,3,1]
[8,1,2,6,3,4,5,7]=>[1,3,4]
[7,1,2,6,3,4,8,5]=>[1,3,3,1]
[6,1,2,5,3,8,4,7]=>[1,3,2,2]
[8,1,2,5,3,7,4,6]=>[1,3,2,2]
[8,1,2,6,3,7,4,5]=>[1,3,2,2]
[6,1,2,5,3,7,8,4]=>[1,3,3,1]
[4,1,2,8,6,3,5,7]=>[1,3,1,3]
[4,1,2,8,7,3,5,6]=>[1,3,1,3]
[4,1,2,7,6,3,8,5]=>[1,3,1,2,1]
[8,1,2,5,6,3,4,7]=>[1,4,3]
[8,1,2,5,7,3,4,6]=>[1,4,3]
[8,1,2,7,6,3,4,5]=>[1,3,1,3]
[7,1,2,5,6,3,8,4]=>[1,4,2,1]
[4,1,2,5,8,7,3,6]=>[1,4,1,2]
[4,1,2,8,6,7,3,5]=>[1,3,2,2]
[8,1,2,5,6,7,3,4]=>[1,5,2]
[3,1,8,2,4,7,5,6]=>[1,2,3,2]
[3,1,8,2,6,4,5,7]=>[1,2,2,3]
[3,1,8,2,7,4,5,6]=>[1,2,2,3]
[3,1,7,2,6,4,8,5]=>[1,2,2,2,1]
[3,1,5,2,8,7,4,6]=>[1,2,2,1,2]
[3,1,8,2,6,7,4,5]=>[1,2,3,2]
[8,1,4,2,3,5,6,7]=>[1,2,5]
[7,1,4,2,3,5,8,6]=>[1,2,4,1]
[6,1,4,2,3,8,5,7]=>[1,2,3,2]
[8,1,4,2,3,7,5,6]=>[1,2,3,2]
[6,1,4,2,3,7,8,5]=>[1,2,4,1]
[8,1,5,2,3,4,6,7]=>[1,2,5]
[7,1,5,2,3,4,8,6]=>[1,2,4,1]
[8,1,7,2,3,4,5,6]=>[1,2,5]
[6,1,5,2,3,8,4,7]=>[1,2,3,2]
[8,1,5,2,3,7,4,6]=>[1,2,3,2]
[6,1,8,2,3,7,4,5]=>[1,2,3,2]
[6,1,5,2,3,7,8,4]=>[1,2,4,1]
[5,1,4,2,8,3,6,7]=>[1,2,2,3]
[5,1,4,2,7,3,8,6]=>[1,2,2,2,1]
[8,1,4,2,6,3,5,7]=>[1,2,2,3]
[8,1,4,2,7,3,5,6]=>[1,2,2,3]
[7,1,4,2,6,3,8,5]=>[1,2,2,2,1]
[8,1,5,2,6,3,4,7]=>[1,2,2,3]
[8,1,5,2,7,3,4,6]=>[1,2,2,3]
[7,1,8,2,6,3,4,5]=>[1,2,2,3]
[7,1,5,2,6,3,8,4]=>[1,2,2,2,1]
[5,1,4,2,6,8,3,7]=>[1,2,3,2]
[5,1,4,2,8,7,3,6]=>[1,2,2,1,2]
[8,1,4,2,6,7,3,5]=>[1,2,3,2]
[8,1,5,2,6,7,3,4]=>[1,2,3,2]
[5,1,4,2,6,7,8,3]=>[1,2,4,1]
[3,1,4,8,2,7,5,6]=>[1,3,2,2]
[3,1,8,5,2,4,6,7]=>[1,2,1,4]
[3,1,7,5,2,4,8,6]=>[1,2,1,3,1]
[3,1,8,6,2,4,5,7]=>[1,2,1,4]
[3,1,7,6,2,4,8,5]=>[1,2,1,3,1]
[3,1,6,5,2,8,4,7]=>[1,2,1,2,2]
[3,1,8,5,2,7,4,6]=>[1,2,1,2,2]
[3,1,8,6,2,7,4,5]=>[1,2,1,2,2]
[3,1,6,5,2,7,8,4]=>[1,2,1,3,1]
[8,1,4,5,2,3,6,7]=>[1,3,4]
[7,1,4,5,2,3,8,6]=>[1,3,3,1]
[8,1,4,6,2,3,5,7]=>[1,3,4]
[7,1,4,8,2,3,5,6]=>[1,3,4]
[7,1,4,6,2,3,8,5]=>[1,3,3,1]
[8,1,6,5,2,3,4,7]=>[1,2,1,4]
[7,1,8,5,2,3,4,6]=>[1,2,1,4]
[7,1,8,6,2,3,4,5]=>[1,2,1,4]
[7,1,6,5,2,3,8,4]=>[1,2,1,3,1]
[6,1,4,5,2,8,3,7]=>[1,3,2,2]
[8,1,4,5,2,7,3,6]=>[1,3,2,2]
[8,1,4,6,2,7,3,5]=>[1,3,2,2]
[8,1,6,5,2,7,3,4]=>[1,2,1,2,2]
[6,1,4,5,2,7,8,3]=>[1,3,3,1]
[3,1,4,8,6,2,5,7]=>[1,3,1,3]
[3,1,4,8,7,2,5,6]=>[1,3,1,3]
[3,1,4,7,6,2,8,5]=>[1,3,1,2,1]
[3,1,8,5,6,2,4,7]=>[1,2,2,3]
[3,1,8,5,7,2,4,6]=>[1,2,2,3]
[3,1,8,7,6,2,4,5]=>[1,2,1,1,3]
[3,1,7,5,6,2,8,4]=>[1,2,2,2,1]
[8,1,4,5,6,2,3,7]=>[1,4,3]
[8,1,4,5,7,2,3,6]=>[1,4,3]
[8,1,4,7,6,2,3,5]=>[1,3,1,3]
[8,1,7,5,6,2,3,4]=>[1,2,2,3]
[7,1,4,5,6,2,8,3]=>[1,4,2,1]
[3,1,4,5,8,7,2,6]=>[1,4,1,2]
[3,1,4,8,6,7,2,5]=>[1,3,2,2]
[3,1,8,5,6,7,2,4]=>[1,2,3,2]
[8,1,4,5,6,7,2,3]=>[1,5,2]
[2,8,1,3,4,7,5,6]=>[2,4,2]
[2,8,1,3,6,4,5,7]=>[2,3,3]
[2,8,1,3,7,4,5,6]=>[2,3,3]
[2,7,1,3,6,4,8,5]=>[2,3,2,1]
[2,5,1,3,8,7,4,6]=>[2,3,1,2]
[2,8,1,3,6,7,4,5]=>[2,4,2]
[2,4,1,8,3,7,5,6]=>[2,2,2,2]
[2,8,1,5,3,4,6,7]=>[2,2,4]
[2,7,1,5,3,4,8,6]=>[2,2,3,1]
[2,8,1,6,3,4,5,7]=>[2,2,4]
[2,7,1,6,3,4,8,5]=>[2,2,3,1]
[2,6,1,5,3,8,4,7]=>[2,2,2,2]
[2,8,1,5,3,7,4,6]=>[2,2,2,2]
[2,8,1,6,3,7,4,5]=>[2,2,2,2]
[2,6,1,5,3,7,8,4]=>[2,2,3,1]
[2,4,1,8,6,3,5,7]=>[2,2,1,3]
[2,4,1,8,7,3,5,6]=>[2,2,1,3]
[2,4,1,7,6,3,8,5]=>[2,2,1,2,1]
[2,8,1,5,6,3,4,7]=>[2,3,3]
[2,8,1,5,7,3,4,6]=>[2,3,3]
[2,8,1,7,6,3,4,5]=>[2,2,1,3]
[2,7,1,5,6,3,8,4]=>[2,3,2,1]
[2,4,1,5,8,7,3,6]=>[2,3,1,2]
[2,4,1,8,6,7,3,5]=>[2,2,2,2]
[2,8,1,5,6,7,3,4]=>[2,4,2]
[7,3,1,2,4,5,8,6]=>[1,1,5,1]
[6,3,1,2,4,8,5,7]=>[1,1,4,2]
[8,3,1,2,4,7,5,6]=>[1,1,4,2]
[6,3,1,2,4,7,8,5]=>[1,1,5,1]
[5,3,1,2,8,4,6,7]=>[1,1,3,3]
[5,3,1,2,7,4,8,6]=>[1,1,3,2,1]
[8,3,1,2,6,4,5,7]=>[1,1,3,3]
[8,3,1,2,7,4,5,6]=>[1,1,3,3]
[7,3,1,2,6,4,8,5]=>[1,1,3,2,1]
[5,3,1,2,6,8,4,7]=>[1,1,4,2]
[5,3,1,2,8,7,4,6]=>[1,1,3,1,2]
[8,3,1,2,6,7,4,5]=>[1,1,4,2]
[5,3,1,2,6,7,8,4]=>[1,1,5,1]
[7,4,1,2,3,5,8,6]=>[1,1,5,1]
[6,4,1,2,3,8,5,7]=>[1,1,4,2]
[8,4,1,2,3,7,5,6]=>[1,1,4,2]
[6,4,1,2,3,7,8,5]=>[1,1,5,1]
[7,6,1,2,3,4,8,5]=>[1,1,5,1]
[5,8,1,2,3,7,4,6]=>[2,4,2]
[8,6,1,2,3,7,4,5]=>[1,1,4,2]
[5,4,1,2,8,3,6,7]=>[1,1,3,3]
[5,4,1,2,7,3,8,6]=>[1,1,3,2,1]
[8,4,1,2,6,3,5,7]=>[1,1,3,3]
[8,4,1,2,7,3,5,6]=>[1,1,3,3]
[7,4,1,2,6,3,8,5]=>[1,1,3,2,1]
[5,8,1,2,6,3,4,7]=>[2,3,3]
[5,8,1,2,7,3,4,6]=>[2,3,3]
[8,7,1,2,6,3,4,5]=>[1,1,3,3]
[5,7,1,2,6,3,8,4]=>[2,3,2,1]
[5,4,1,2,6,8,3,7]=>[1,1,4,2]
[5,4,1,2,8,7,3,6]=>[1,1,3,1,2]
[8,4,1,2,6,7,3,5]=>[1,1,4,2]
[5,8,1,2,6,7,3,4]=>[2,4,2]
[5,4,1,2,6,7,8,3]=>[1,1,5,1]
[4,3,1,8,2,5,6,7]=>[1,1,2,4]
[4,3,1,7,2,5,8,6]=>[1,1,2,3,1]
[4,3,1,6,2,8,5,7]=>[1,1,2,2,2]
[4,3,1,8,2,7,5,6]=>[1,1,2,2,2]
[4,3,1,6,2,7,8,5]=>[1,1,2,3,1]
[8,3,1,5,2,4,6,7]=>[1,1,2,4]
[7,3,1,5,2,4,8,6]=>[1,1,2,3,1]
[8,3,1,6,2,4,5,7]=>[1,1,2,4]
[7,3,1,8,2,4,5,6]=>[1,1,2,4]
[7,3,1,6,2,4,8,5]=>[1,1,2,3,1]
[6,3,1,5,2,8,4,7]=>[1,1,2,2,2]
[8,3,1,5,2,7,4,6]=>[1,1,2,2,2]
[8,3,1,6,2,7,4,5]=>[1,1,2,2,2]
[6,3,1,5,2,7,8,4]=>[1,1,2,3,1]
[8,4,1,5,2,3,6,7]=>[1,1,2,4]
[7,4,1,5,2,3,8,6]=>[1,1,2,3,1]
[8,4,1,6,2,3,5,7]=>[1,1,2,4]
[7,4,1,8,2,3,5,6]=>[1,1,2,4]
[7,4,1,6,2,3,8,5]=>[1,1,2,3,1]
[6,8,1,5,2,3,4,7]=>[2,2,4]
[8,7,1,5,2,3,4,6]=>[1,1,2,4]
[8,7,1,6,2,3,4,5]=>[1,1,2,4]
[6,7,1,5,2,3,8,4]=>[2,2,3,1]
[6,4,1,5,2,8,3,7]=>[1,1,2,2,2]
[8,4,1,5,2,7,3,6]=>[1,1,2,2,2]
[8,4,1,6,2,7,3,5]=>[1,1,2,2,2]
[6,8,1,5,2,7,3,4]=>[2,2,2,2]
[6,4,1,5,2,7,8,3]=>[1,1,2,3,1]
[4,3,1,5,8,2,6,7]=>[1,1,3,3]
[4,3,1,5,7,2,8,6]=>[1,1,3,2,1]
[4,3,1,8,6,2,5,7]=>[1,1,2,1,3]
[4,3,1,8,7,2,5,6]=>[1,1,2,1,3]
[4,3,1,7,6,2,8,5]=>[1,1,2,1,2,1]
[8,3,1,5,6,2,4,7]=>[1,1,3,3]
[8,3,1,5,7,2,4,6]=>[1,1,3,3]
[8,3,1,7,6,2,4,5]=>[1,1,2,1,3]
[7,3,1,5,6,2,8,4]=>[1,1,3,2,1]
[8,4,1,5,6,2,3,7]=>[1,1,3,3]
[8,4,1,5,7,2,3,6]=>[1,1,3,3]
[8,4,1,7,6,2,3,5]=>[1,1,2,1,3]
[7,8,1,5,6,2,3,4]=>[2,3,3]
[7,4,1,5,6,2,8,3]=>[1,1,3,2,1]
[4,3,1,5,6,8,2,7]=>[1,1,4,2]
[4,3,1,5,8,7,2,6]=>[1,1,3,1,2]
[4,3,1,8,6,7,2,5]=>[1,1,2,2,2]
[8,3,1,5,6,7,2,4]=>[1,1,4,2]
[8,4,1,5,6,7,2,3]=>[1,1,4,2]
[4,3,1,5,6,7,8,2]=>[1,1,5,1]
[2,3,8,1,4,7,5,6]=>[3,3,2]
[2,3,8,1,6,4,5,7]=>[3,2,3]
[2,3,8,1,7,4,5,6]=>[3,2,3]
[2,3,7,1,6,4,8,5]=>[3,2,2,1]
[2,3,5,1,8,7,4,6]=>[3,2,1,2]
[2,3,8,1,6,7,4,5]=>[3,3,2]
[2,8,4,1,3,5,6,7]=>[2,1,5]
[2,7,4,1,3,5,8,6]=>[2,1,4,1]
[2,6,4,1,3,8,5,7]=>[2,1,3,2]
[2,8,4,1,3,7,5,6]=>[2,1,3,2]
[2,6,4,1,3,7,8,5]=>[2,1,4,1]
[2,8,5,1,3,4,6,7]=>[2,1,5]
[2,7,5,1,3,4,8,6]=>[2,1,4,1]
[2,8,7,1,3,4,5,6]=>[2,1,5]
[2,6,5,1,3,8,4,7]=>[2,1,3,2]
[2,8,5,1,3,7,4,6]=>[2,1,3,2]
[2,6,8,1,3,7,4,5]=>[3,3,2]
[2,6,5,1,3,7,8,4]=>[2,1,4,1]
[2,5,4,1,8,3,6,7]=>[2,1,2,3]
[2,5,4,1,7,3,8,6]=>[2,1,2,2,1]
[2,8,4,1,6,3,5,7]=>[2,1,2,3]
[2,8,4,1,7,3,5,6]=>[2,1,2,3]
[2,7,4,1,6,3,8,5]=>[2,1,2,2,1]
[2,8,5,1,6,3,4,7]=>[2,1,2,3]
[2,8,5,1,7,3,4,6]=>[2,1,2,3]
[2,7,8,1,6,3,4,5]=>[3,2,3]
[2,7,5,1,6,3,8,4]=>[2,1,2,2,1]
[2,5,4,1,6,8,3,7]=>[2,1,3,2]
[2,5,4,1,8,7,3,6]=>[2,1,2,1,2]
[2,8,4,1,6,7,3,5]=>[2,1,3,2]
[2,8,5,1,6,7,3,4]=>[2,1,3,2]
[2,5,4,1,6,7,8,3]=>[2,1,4,1]
[7,3,4,1,2,5,8,6]=>[1,2,4,1]
[6,3,4,1,2,8,5,7]=>[1,2,3,2]
[8,3,4,1,2,7,5,6]=>[1,2,3,2]
[6,3,4,1,2,7,8,5]=>[1,2,4,1]
[7,3,5,1,2,4,8,6]=>[1,2,4,1]
[6,3,7,1,2,4,8,5]=>[1,2,4,1]
[6,3,5,1,2,8,4,7]=>[1,2,3,2]
[8,3,5,1,2,7,4,6]=>[1,2,3,2]
[6,3,8,1,2,7,4,5]=>[1,2,3,2]
[6,3,5,1,2,7,8,4]=>[1,2,4,1]
[7,5,4,1,2,3,8,6]=>[1,1,1,4,1]
[6,8,4,1,2,3,5,7]=>[2,1,5]
[6,7,4,1,2,3,8,5]=>[2,1,4,1]
[6,8,5,1,2,3,4,7]=>[2,1,5]
[6,7,5,1,2,3,8,4]=>[2,1,4,1]
[6,5,4,1,2,8,3,7]=>[1,1,1,3,2]
[8,5,4,1,2,7,3,6]=>[1,1,1,3,2]
[6,8,4,1,2,7,3,5]=>[2,1,3,2]
[6,8,5,1,2,7,3,4]=>[2,1,3,2]
[6,5,4,1,2,7,8,3]=>[1,1,1,4,1]
[5,3,4,1,8,2,6,7]=>[1,2,2,3]
[5,3,4,1,7,2,8,6]=>[1,2,2,2,1]
[8,3,4,1,6,2,5,7]=>[1,2,2,3]
[8,3,4,1,7,2,5,6]=>[1,2,2,3]
[7,3,4,1,6,2,8,5]=>[1,2,2,2,1]
[8,3,5,1,6,2,4,7]=>[1,2,2,3]
[8,3,5,1,7,2,4,6]=>[1,2,2,3]
[7,3,8,1,6,2,4,5]=>[1,2,2,3]
[7,3,5,1,6,2,8,4]=>[1,2,2,2,1]
[8,5,4,1,6,2,3,7]=>[1,1,1,2,3]
[8,5,4,1,7,2,3,6]=>[1,1,1,2,3]
[7,8,4,1,6,2,3,5]=>[2,1,2,3]
[7,8,5,1,6,2,3,4]=>[2,1,2,3]
[7,5,4,1,6,2,8,3]=>[1,1,1,2,2,1]
[5,3,4,1,6,8,2,7]=>[1,2,3,2]
[5,3,4,1,8,7,2,6]=>[1,2,2,1,2]
[8,3,4,1,6,7,2,5]=>[1,2,3,2]
[8,3,5,1,6,7,2,4]=>[1,2,3,2]
[8,5,4,1,6,7,2,3]=>[1,1,1,3,2]
[5,3,4,1,6,7,8,2]=>[1,2,4,1]
[2,3,4,8,1,7,5,6]=>[4,2,2]
[2,3,8,5,1,4,6,7]=>[3,1,4]
[2,3,7,5,1,4,8,6]=>[3,1,3,1]
[2,3,8,6,1,4,5,7]=>[3,1,4]
[2,3,7,6,1,4,8,5]=>[3,1,3,1]
[2,3,6,5,1,8,4,7]=>[3,1,2,2]
[2,3,8,5,1,7,4,6]=>[3,1,2,2]
[2,3,8,6,1,7,4,5]=>[3,1,2,2]
[2,3,6,5,1,7,8,4]=>[3,1,3,1]
[2,8,4,5,1,3,6,7]=>[2,2,4]
[2,7,4,5,1,3,8,6]=>[2,2,3,1]
[2,8,4,6,1,3,5,7]=>[2,2,4]
[2,7,4,8,1,3,5,6]=>[2,2,4]
[2,7,4,6,1,3,8,5]=>[2,2,3,1]
[2,8,6,5,1,3,4,7]=>[2,1,1,4]
[2,7,8,5,1,3,4,6]=>[3,1,4]
[2,7,8,6,1,3,4,5]=>[3,1,4]
[2,7,6,5,1,3,8,4]=>[2,1,1,3,1]
[2,6,4,5,1,8,3,7]=>[2,2,2,2]
[2,8,4,5,1,7,3,6]=>[2,2,2,2]
[2,8,4,6,1,7,3,5]=>[2,2,2,2]
[2,8,6,5,1,7,3,4]=>[2,1,1,2,2]
[2,6,4,5,1,7,8,3]=>[2,2,3,1]
[7,3,4,5,1,2,8,6]=>[1,3,3,1]
[7,3,4,6,1,2,8,5]=>[1,3,3,1]
[8,3,6,5,1,2,4,7]=>[1,2,1,4]
[7,3,8,5,1,2,4,6]=>[1,2,1,4]
[7,3,8,6,1,2,4,5]=>[1,2,1,4]
[7,3,6,5,1,2,8,4]=>[1,2,1,3,1]
[7,6,4,5,1,2,8,3]=>[1,1,2,3,1]
[6,3,4,5,1,8,2,7]=>[1,3,2,2]
[8,3,4,5,1,7,2,6]=>[1,3,2,2]
[8,3,4,6,1,7,2,5]=>[1,3,2,2]
[8,3,6,5,1,7,2,4]=>[1,2,1,2,2]
[8,6,4,5,1,7,2,3]=>[1,1,2,2,2]
[6,3,4,5,1,7,8,2]=>[1,3,3,1]
[2,3,4,8,6,1,5,7]=>[4,1,3]
[2,3,4,8,7,1,5,6]=>[4,1,3]
[2,3,4,7,6,1,8,5]=>[4,1,2,1]
[2,3,8,5,6,1,4,7]=>[3,2,3]
[2,3,8,5,7,1,4,6]=>[3,2,3]
[2,3,8,7,6,1,4,5]=>[3,1,1,3]
[2,3,7,5,6,1,8,4]=>[3,2,2,1]
[2,8,4,5,6,1,3,7]=>[2,3,3]
[2,8,4,5,7,1,3,6]=>[2,3,3]
[2,8,4,7,6,1,3,5]=>[2,2,1,3]
[2,8,7,5,6,1,3,4]=>[2,1,2,3]
[2,7,4,5,6,1,8,3]=>[2,3,2,1]
[8,3,4,5,7,1,2,6]=>[1,4,3]
[8,3,4,7,6,1,2,5]=>[1,3,1,3]
[8,3,7,5,6,1,2,4]=>[1,2,2,3]
[7,3,4,5,6,1,8,2]=>[1,4,2,1]
[2,3,4,5,8,7,1,6]=>[5,1,2]
[2,3,4,8,6,7,1,5]=>[4,2,2]
[2,3,8,5,6,7,1,4]=>[3,3,2]
[2,8,4,5,6,7,1,3]=>[2,4,2]
[3,5,2,6,1,4,8,7]=>[2,2,3,1]
[3,5,2,6,4,1,8,7]=>[2,2,1,2,1]
[3,5,2,7,4,8,1,6]=>[2,2,2,2]
[3,5,2,7,4,8,6,1]=>[2,2,2,1,1]
[4,5,7,2,3,8,6,1]=>[3,3,1,1]
[4,5,7,2,3,8,1,6]=>[3,3,2]
[4,5,6,2,3,1,8,7]=>[3,2,2,1]
[4,5,6,2,1,3,8,7]=>[3,1,3,1]
[3,5,1,6,4,2,8,7]=>[2,2,1,2,1]
[4,5,6,1,3,2,8,7]=>[3,2,2,1]
[4,5,6,3,1,2,8,7]=>[3,1,3,1]
[4,5,7,3,2,8,1,6]=>[3,1,2,2]
[4,5,7,3,2,8,6,1]=>[3,1,2,1,1]
[4,6,7,3,8,2,5,1]=>[3,2,2,1]
[4,6,7,3,8,2,1,5]=>[3,2,1,2]
[4,6,7,3,8,1,2,5]=>[3,2,3]
[4,5,7,3,1,8,2,6]=>[3,1,2,2]
[4,5,7,1,3,8,2,6]=>[3,3,2]
[3,5,1,7,4,8,2,6]=>[2,2,2,2]
[2,1,5,7,4,8,3,6]=>[1,3,2,2]
[2,1,5,7,4,8,6,3]=>[1,3,2,1,1]
[3,5,1,7,4,8,6,2]=>[2,2,2,1,1]
[4,5,7,1,3,8,6,2]=>[3,3,1,1]
[4,5,7,3,1,8,6,2]=>[3,1,2,1,1]
[4,6,7,3,8,1,5,2]=>[3,2,2,1]
[4,6,7,3,8,5,1,2]=>[3,2,1,2]
[4,6,7,3,8,5,2,1]=>[3,2,1,1,1]
[5,6,7,8,3,1,4,2]=>[4,1,2,1]
[5,6,7,8,1,3,4,2]=>[4,3,1]
[4,6,7,1,8,3,5,2]=>[3,2,2,1]
[3,6,1,7,8,4,5,2]=>[2,3,2,1]
[2,1,6,7,8,4,5,3]=>[1,4,2,1]
[2,1,6,7,8,4,3,5]=>[1,4,1,2]
[3,6,1,7,8,4,2,5]=>[2,3,1,2]
[4,6,7,1,8,3,2,5]=>[3,2,1,2]
[5,6,7,8,1,3,2,4]=>[4,2,2]
[4,5,7,2,1,8,3,6]=>[3,1,2,2]
[4,6,7,2,8,1,3,5]=>[3,2,3]
[4,6,7,2,8,3,1,5]=>[3,2,1,2]
[4,6,7,2,8,3,5,1]=>[3,2,2,1]
[3,6,2,7,8,4,5,1]=>[2,3,2,1]
[3,6,2,7,8,4,1,5]=>[2,3,1,2]
[3,6,2,7,8,1,4,5]=>[2,3,3]
[3,5,2,7,1,8,4,6]=>[2,2,2,2]
[3,4,2,1,7,8,5,6]=>[2,1,3,2]
[3,4,1,2,7,8,6,5]=>[2,4,1,1]
[3,5,2,7,1,8,6,4]=>[2,2,2,1,1]
[3,6,2,7,8,1,5,4]=>[2,3,2,1]
[3,6,2,7,8,5,1,4]=>[2,3,1,2]
[3,6,2,7,8,5,4,1]=>[2,3,1,1,1]
[4,6,7,2,8,5,3,1]=>[3,2,1,1,1]
[4,6,7,2,8,5,1,3]=>[3,2,1,2]
[4,6,7,2,8,1,5,3]=>[3,2,2,1]
[4,5,7,2,1,8,6,3]=>[3,1,2,1,1]
[4,5,7,1,2,8,6,3]=>[3,3,1,1]
[3,5,1,7,2,8,6,4]=>[2,2,2,1,1]
[2,1,5,7,3,8,6,4]=>[1,3,2,1,1]
[2,1,6,7,8,3,5,4]=>[1,4,2,1]
[3,6,1,7,8,2,5,4]=>[2,3,2,1]
[4,6,7,1,8,2,5,3]=>[3,2,2,1]
[5,6,7,8,1,2,4,3]=>[4,3,1]
[5,6,7,8,2,1,4,3]=>[4,1,2,1]
[5,6,7,8,2,4,1,3]=>[4,2,2]
[5,6,7,8,2,4,3,1]=>[4,2,1,1]
[5,6,7,8,1,4,2,3]=>[4,2,2]
[4,6,7,1,8,5,2,3]=>[3,2,1,2]
[3,6,1,7,8,5,2,4]=>[2,3,1,2]
[2,1,6,7,8,5,3,4]=>[1,4,1,2]
[3,6,1,7,8,5,4,2]=>[2,3,1,1,1]
[4,6,7,1,8,5,3,2]=>[3,2,1,1,1]
[5,6,7,8,1,4,3,2]=>[4,2,1,1]
[5,6,7,8,4,1,3,2]=>[4,1,2,1]
[6,5,8,7,3,4,1,2]=>[1,2,1,2,2]
[3,6,7,4,5,8,1,2]=>[3,3,2]
[2,6,7,4,5,1,8,3]=>[3,2,2,1]
[1,6,7,4,5,2,3,8]=>[3,2,3]
[1,5,4,7,6,2,3,8]=>[2,2,1,3]
[2,5,4,7,6,1,8,3]=>[2,2,1,2,1]
[3,5,4,7,6,8,1,2]=>[2,2,2,2]
[4,5,3,7,8,6,1,2]=>[2,3,1,2]
[5,4,3,8,7,6,1,2]=>[1,1,2,1,1,2]
[6,4,8,3,7,5,1,2]=>[1,2,2,1,2]
[6,3,8,4,5,7,1,2]=>[1,2,3,2]
[5,3,4,8,6,7,1,2]=>[1,3,2,2]
[4,3,5,6,8,7,1,2]=>[1,4,1,2]
[3,2,5,6,1,8,7,4]=>[1,3,2,1,1]
[4,2,5,6,8,1,7,3]=>[1,4,2,1]
[5,2,4,8,6,1,7,3]=>[1,3,1,2,1]
[6,2,8,4,5,1,7,3]=>[1,2,2,2,1]
[7,8,2,4,5,1,6,3]=>[2,3,2,1]
[7,8,1,4,5,2,3,6]=>[2,3,3]
[6,1,8,4,5,2,3,7]=>[1,2,2,3]
[5,1,4,8,6,2,3,7]=>[1,3,1,3]
[4,1,3,2,8,6,5,7]=>[1,2,2,1,2]
[5,1,3,8,2,6,4,7]=>[1,3,2,2]
[6,1,8,3,2,5,4,7]=>[1,2,1,2,2]
[7,8,1,3,2,5,4,6]=>[2,2,2,2]
[7,8,2,3,1,5,6,4]=>[2,2,3,1]
[6,2,8,3,1,5,7,4]=>[1,2,1,3,1]
[5,2,3,8,1,6,7,4]=>[1,3,3,1]
[6,3,8,2,1,7,5,4]=>[1,2,1,2,1,1]
[7,8,3,2,1,6,5,4]=>[2,1,1,2,1,1]
[7,8,4,2,6,1,5,3]=>[2,1,2,2,1]
[5,4,2,8,7,1,6,3]=>[1,1,2,1,2,1]
[4,5,2,7,8,1,6,3]=>[2,3,2,1]
[2,5,3,7,1,6,8,4]=>[2,2,3,1]
[1,5,3,7,2,6,4,8]=>[2,2,2,2]
[1,6,7,3,2,5,4,8]=>[3,1,2,2]
[2,6,7,3,1,5,8,4]=>[3,1,3,1]
[3,6,7,2,1,8,5,4]=>[3,1,2,1,1]
[7,8,5,6,2,1,4,3]=>[2,2,1,2,1]
[6,5,8,7,1,2,3,4]=>[1,2,1,4]
[5,4,1,8,7,2,3,6]=>[1,1,2,1,3]
[6,4,8,1,7,2,3,5]=>[1,2,2,3]
[7,8,3,1,2,6,4,5]=>[2,1,3,2]
[5,3,1,8,2,7,4,6]=>[1,1,2,2,2]
[4,3,1,2,8,7,5,6]=>[1,1,3,1,2]
[4,2,1,3,8,5,7,6]=>[1,1,3,2,1]
[5,2,1,8,3,4,7,6]=>[1,1,2,3,1]
[6,2,8,1,3,4,7,5]=>[1,2,4,1]
[7,8,2,1,3,4,6,5]=>[2,1,4,1]
[4,3,1,2,6,5,8,7]=>[1,1,3,2,1]
[5,3,1,6,2,4,8,7]=>[1,1,2,3,1]
[6,3,1,5,2,4,8,7]=>[1,1,2,3,1]
[7,3,1,5,2,8,4,6]=>[1,1,2,2,2]
[8,4,5,1,2,7,3,6]=>[1,2,3,2]
[7,4,5,1,2,8,3,6]=>[1,2,3,2]
[6,4,5,1,2,3,8,7]=>[1,2,4,1]
[5,4,6,1,2,3,8,7]=>[1,2,4,1]
[2,1,6,5,3,4,8,7]=>[1,2,1,3,1]
[3,6,1,5,2,4,8,7]=>[2,2,3,1]
[4,6,5,1,2,3,8,7]=>[2,1,4,1]
[5,6,4,1,2,3,8,7]=>[2,1,4,1]
[6,5,4,1,2,3,8,7]=>[1,1,1,4,1]
[7,5,4,1,2,8,3,6]=>[1,1,1,3,2]
[8,6,4,1,7,2,3,5]=>[1,1,1,2,3]
[7,6,4,1,8,2,3,5]=>[1,1,1,2,3]
[6,7,4,1,8,2,3,5]=>[2,1,2,3]
[5,7,4,1,2,8,3,6]=>[2,1,3,2]
[4,7,5,1,2,8,3,6]=>[2,1,3,2]
[3,7,1,5,2,8,4,6]=>[2,2,2,2]
[2,1,7,5,3,8,4,6]=>[1,2,1,2,2]
[2,1,8,5,3,7,4,6]=>[1,2,1,2,2]
[3,8,1,5,2,7,4,6]=>[2,2,2,2]
[4,8,5,1,2,7,3,6]=>[2,1,3,2]
[5,8,4,1,2,7,3,6]=>[2,1,3,2]
[6,8,4,1,7,2,3,5]=>[2,1,2,3]
[8,7,4,1,6,2,3,5]=>[1,1,1,2,3]
[5,8,6,7,1,2,3,4]=>[2,2,4]
[4,8,6,1,7,2,3,5]=>[2,1,2,3]
[3,8,1,6,7,2,4,5]=>[2,3,3]
[2,1,8,6,7,3,4,5]=>[1,2,2,3]
[2,1,7,6,8,3,4,5]=>[1,2,2,3]
[3,7,1,6,8,2,4,5]=>[2,3,3]
[4,7,6,1,8,2,3,5]=>[2,1,2,3]
[5,7,6,8,1,2,3,4]=>[2,2,4]
[5,4,7,1,2,8,3,6]=>[1,2,3,2]
[6,4,7,1,8,2,3,5]=>[1,2,2,3]
[7,4,6,1,8,2,3,5]=>[1,2,2,3]
[8,4,6,1,7,2,3,5]=>[1,2,2,3]
[8,3,1,6,7,2,4,5]=>[1,1,3,3]
[7,3,1,6,8,2,4,5]=>[1,1,3,3]
[6,3,1,7,8,2,4,5]=>[1,1,3,3]
[5,3,1,7,2,8,4,6]=>[1,1,2,2,2]
[4,3,1,2,7,8,5,6]=>[1,1,4,2]
[2,1,4,3,8,7,5,6]=>[1,2,2,1,2]
[3,4,1,2,8,7,5,6]=>[2,3,1,2]
[6,3,1,8,7,2,4,5]=>[1,1,2,1,3]
[7,3,1,8,6,2,4,5]=>[1,1,2,1,3]
[8,4,7,1,6,2,3,5]=>[1,2,2,3]
[7,4,8,1,6,2,3,5]=>[1,2,2,3]
[5,4,8,1,2,7,3,6]=>[1,2,3,2]
[4,5,8,1,2,7,3,6]=>[3,3,2]
[3,5,1,8,2,7,4,6]=>[2,2,2,2]
[2,1,5,8,3,7,4,6]=>[1,3,2,2]
[2,1,6,8,7,3,4,5]=>[1,3,1,3]
[3,6,1,8,7,2,4,5]=>[2,2,1,3]
[4,6,8,1,7,2,3,5]=>[3,2,3]
[5,6,8,7,1,2,3,4]=>[3,1,4]
[7,5,8,6,1,2,3,4]=>[1,2,1,4]
[8,5,7,6,1,2,3,4]=>[1,2,1,4]
[5,7,8,6,1,2,3,4]=>[3,1,4]
[4,7,8,1,6,2,3,5]=>[3,2,3]
[3,7,1,8,6,2,4,5]=>[2,2,1,3]
[2,1,7,8,6,3,4,5]=>[1,3,1,3]
[2,1,8,7,6,3,4,5]=>[1,2,1,1,3]
[3,8,1,7,6,2,4,5]=>[2,2,1,3]
[4,8,7,1,6,2,3,5]=>[2,1,2,3]
[5,8,7,6,1,2,3,4]=>[2,1,1,4]
[6,8,7,5,1,2,3,4]=>[2,1,1,4]
[6,4,7,3,8,5,1,2]=>[1,2,2,1,2]
[6,4,7,3,5,8,1,2]=>[1,2,3,2]
[6,4,7,2,5,1,8,3]=>[1,2,2,2,1]
[5,4,2,7,6,1,3,8]=>[1,1,2,1,3]
[5,4,2,7,6,1,8,3]=>[1,1,2,1,2,1]
[5,4,3,7,6,8,1,2]=>[1,1,2,2,2]
[5,4,3,7,8,6,1,2]=>[1,1,3,1,2]
[6,4,8,3,5,7,1,2]=>[1,2,3,2]
[5,4,3,8,6,7,1,2]=>[1,1,2,2,2]
[5,4,3,6,8,7,1,2]=>[1,1,3,1,2]
[5,4,2,6,7,1,8,3]=>[1,1,3,2,1]
[5,4,2,6,7,1,3,8]=>[1,1,3,3]
[5,3,2,6,1,7,4,8]=>[1,1,2,2,2]
[5,3,2,6,1,7,8,4]=>[1,1,2,3,1]
[5,3,2,6,1,8,7,4]=>[1,1,2,2,1,1]
[5,4,2,6,8,1,7,3]=>[1,1,3,2,1]
[5,4,2,8,6,1,7,3]=>[1,1,2,1,2,1]
[6,4,8,2,5,1,7,3]=>[1,2,2,2,1]
[7,8,4,2,5,1,6,3]=>[2,1,2,2,1]
[7,8,4,2,5,1,3,6]=>[2,1,2,3]
[5,4,2,8,6,1,3,7]=>[1,1,2,1,3]
[5,3,2,6,1,8,4,7]=>[1,1,2,2,2]
[4,3,2,1,6,8,5,7]=>[1,1,1,3,2]
[4,3,2,1,8,6,5,7]=>[1,1,1,2,1,2]
[5,3,2,8,1,6,4,7]=>[1,1,2,2,2]
[6,3,8,2,1,5,4,7]=>[1,2,1,2,2]
[7,8,3,2,1,5,4,6]=>[2,1,1,2,2]
[7,8,3,2,1,5,6,4]=>[2,1,1,3,1]
[6,3,8,2,1,5,7,4]=>[1,2,1,3,1]
[5,3,2,8,1,6,7,4]=>[1,1,2,3,1]
[5,4,2,7,8,1,6,3]=>[1,1,3,2,1]
[5,3,2,7,1,8,6,4]=>[1,1,2,2,1,1]
[5,3,2,7,1,6,8,4]=>[1,1,2,3,1]
[5,3,2,7,1,6,4,8]=>[1,1,2,2,2]
[6,3,7,2,1,5,4,8]=>[1,2,1,2,2]
[6,3,7,2,1,5,8,4]=>[1,2,1,3,1]
[6,3,7,2,1,8,5,4]=>[1,2,1,2,1,1]
[6,4,7,2,8,1,5,3]=>[1,2,2,2,1]
[6,5,7,8,2,1,4,3]=>[1,3,1,2,1]
[6,5,8,7,2,1,3,4]=>[1,2,1,1,3]
[6,3,7,2,1,8,4,5]=>[1,2,1,2,2]
[6,3,7,2,1,4,8,5]=>[1,2,1,3,1]
[6,3,7,2,1,4,5,8]=>[1,2,1,4]
[5,3,2,7,1,4,8,6]=>[1,1,2,3,1]
[5,4,2,8,7,1,3,6]=>[1,1,2,1,3]
[7,8,4,2,6,1,3,5]=>[2,1,2,3]
[7,8,3,2,1,6,4,5]=>[2,1,1,2,2]
[6,3,8,2,1,7,4,5]=>[1,2,1,2,2]
[5,3,2,8,1,7,4,6]=>[1,1,2,2,2]
[4,3,2,1,8,7,5,6]=>[1,1,1,2,1,2]
[4,3,2,1,7,5,8,6]=>[1,1,1,2,2,1]
[4,3,2,1,7,5,6,8]=>[1,1,1,2,3]
[4,3,2,1,8,5,7,6]=>[1,1,1,2,2,1]
[5,3,2,8,1,4,7,6]=>[1,1,2,3,1]
[6,3,8,2,1,4,7,5]=>[1,2,1,3,1]
[7,8,3,2,1,4,6,5]=>[2,1,1,3,1]
[6,3,8,2,1,4,5,7]=>[1,2,1,4]
[4,3,2,1,8,5,6,7]=>[1,1,1,2,3]
[4,3,2,1,5,8,6,7]=>[1,1,1,3,2]
[7,8,5,6,1,2,4,3]=>[2,2,3,1]
[7,8,4,1,6,2,5,3]=>[2,1,2,2,1]
[7,8,1,4,6,2,5,3]=>[2,3,2,1]
[6,1,8,4,7,2,5,3]=>[1,2,2,2,1]
[1,6,8,4,7,2,5,3]=>[3,2,2,1]
[1,6,8,3,2,7,5,4]=>[3,1,2,1,1]
[6,1,8,3,2,7,5,4]=>[1,2,1,2,1,1]
[7,8,1,3,2,6,5,4]=>[2,2,2,1,1]
[7,8,3,1,2,6,5,4]=>[2,1,3,1,1]
[7,8,3,4,6,5,1,2]=>[2,3,1,2]
[7,8,2,4,6,1,5,3]=>[2,3,2,1]
[7,8,2,3,1,6,5,4]=>[2,2,2,1,1]
[7,8,2,1,3,6,5,4]=>[2,1,3,1,1]
[7,8,1,2,3,6,5,4]=>[2,4,1,1]
[6,1,8,2,3,7,5,4]=>[1,2,3,1,1]
[1,6,8,2,3,7,5,4]=>[3,3,1,1]
[1,5,2,8,3,7,6,4]=>[2,2,2,1,1]
[5,1,2,8,3,7,6,4]=>[1,3,2,1,1]
[5,2,1,8,3,7,6,4]=>[1,1,2,2,1,1]
[6,2,8,1,3,7,5,4]=>[1,2,3,1,1]
[6,2,8,3,1,7,5,4]=>[1,2,1,2,1,1]
[6,2,8,4,7,1,5,3]=>[1,2,2,2,1]
[6,3,8,4,7,5,1,2]=>[1,2,2,1,2]
[3,6,8,4,7,5,1,2]=>[3,2,1,2]
[2,6,8,4,7,1,5,3]=>[3,2,2,1]
[2,6,8,3,1,7,5,4]=>[3,1,2,1,1]
[2,6,8,1,3,7,5,4]=>[3,3,1,1]
[2,5,1,8,3,7,6,4]=>[2,2,2,1,1]
[1,2,5,8,3,7,6,4]=>[4,2,1,1]
[2,4,1,3,8,7,6,5]=>[2,3,1,1,1]
[2,5,3,8,1,7,6,4]=>[2,2,2,1,1]
[2,5,4,8,7,1,6,3]=>[2,2,1,2,1]
[3,5,4,8,7,6,1,2]=>[2,2,1,1,2]
[5,3,4,8,7,6,1,2]=>[1,3,1,1,2]
[5,2,4,8,7,1,6,3]=>[1,3,1,2,1]
[5,2,3,8,1,7,6,4]=>[1,3,2,1,1]
[4,2,1,3,8,7,6,5]=>[1,1,3,1,1,1]
[4,1,2,3,8,7,6,5]=>[1,4,1,1,1]
[1,4,2,3,8,7,6,5]=>[2,3,1,1,1]
[4,1,3,2,8,7,6,5]=>[1,2,2,1,1,1]
[4,3,1,2,8,7,6,5]=>[1,1,3,1,1,1]
[6,3,8,1,2,7,5,4]=>[1,2,3,1,1]
[5,3,1,8,2,7,6,4]=>[1,1,2,2,1,1]
[5,1,3,8,2,7,6,4]=>[1,3,2,1,1]
[1,5,3,8,2,7,6,4]=>[2,2,2,1,1]
[1,5,4,8,7,2,6,3]=>[2,2,1,2,1]
[5,1,4,8,7,2,6,3]=>[1,3,1,2,1]
[5,4,1,8,7,2,6,3]=>[1,1,2,1,2,1]
[6,4,8,1,7,2,5,3]=>[1,2,2,2,1]
[6,5,8,7,1,2,4,3]=>[1,2,1,3,1]
[5,6,8,7,3,4,1,2]=>[3,1,2,2]
[5,6,8,7,2,1,4,3]=>[3,1,1,2,1]
[4,5,1,8,7,2,6,3]=>[2,2,1,2,1]
[4,1,5,8,7,2,6,3]=>[1,3,1,2,1]
[1,4,5,8,7,2,6,3]=>[4,1,2,1]
[1,3,5,8,2,7,6,4]=>[4,2,1,1]
[3,1,5,8,2,7,6,4]=>[1,3,2,1,1]
[3,6,8,1,2,7,5,4]=>[3,3,1,1]
[3,6,8,2,1,7,5,4]=>[3,1,2,1,1]
[4,6,8,2,7,1,5,3]=>[3,2,2,1]
[4,6,8,3,7,5,1,2]=>[3,2,1,2]
[4,5,3,8,7,6,1,2]=>[2,2,1,1,2]
[4,5,2,8,7,1,6,3]=>[2,2,1,2,1]
[3,5,2,8,1,7,6,4]=>[2,2,2,1,1]
[3,1,4,2,8,7,6,5]=>[1,2,2,1,1,1]
[3,1,2,4,8,7,6,5]=>[1,4,1,1,1]
[3,2,5,8,1,7,6,4]=>[1,3,2,1,1]
[4,2,5,8,7,1,6,3]=>[1,3,1,2,1]
[4,3,5,8,7,6,1,2]=>[1,3,1,1,2]
[3,4,5,8,7,6,1,2]=>[4,1,1,2]
[2,4,5,8,7,1,6,3]=>[4,1,2,1]
[2,3,5,8,1,7,6,4]=>[4,2,1,1]
[4,1,3,2,6,5,8,7]=>[1,2,2,2,1]
[5,1,3,2,6,4,8,7]=>[1,2,2,2,1]
[6,1,3,2,5,4,8,7]=>[1,2,2,2,1]
[7,1,3,2,5,4,8,6]=>[1,2,2,2,1]
[8,1,3,2,5,4,7,6]=>[1,2,2,2,1]
[8,1,4,2,5,3,7,6]=>[1,2,2,2,1]
[7,1,4,2,5,3,8,6]=>[1,2,2,2,1]
[6,1,4,2,5,3,8,7]=>[1,2,2,2,1]
[5,1,4,2,6,3,8,7]=>[1,2,2,2,1]
[2,1,6,3,5,4,8,7]=>[1,2,2,2,1]
[3,1,6,2,5,4,8,7]=>[1,2,2,2,1]
[4,1,6,2,5,3,8,7]=>[1,2,2,2,1]
[6,2,5,1,4,3,8,7]=>[1,2,2,2,1]
[5,2,6,1,4,3,8,7]=>[1,2,2,2,1]
[5,2,7,1,4,3,8,6]=>[1,2,2,2,1]
[5,2,8,1,4,3,7,6]=>[1,2,2,2,1]
[6,2,8,1,4,3,7,5]=>[1,2,2,2,1]
[6,2,7,1,4,3,8,5]=>[1,2,2,2,1]
[7,2,6,1,4,3,8,5]=>[1,2,2,2,1]
[7,2,5,1,4,3,8,6]=>[1,2,2,2,1]
[4,1,7,2,5,3,8,6]=>[1,2,2,2,1]
[3,1,7,2,5,4,8,6]=>[1,2,2,2,1]
[2,1,7,3,5,4,8,6]=>[1,2,2,2,1]
[2,1,8,3,5,4,7,6]=>[1,2,2,2,1]
[3,1,8,2,5,4,7,6]=>[1,2,2,2,1]
[4,1,8,2,5,3,7,6]=>[1,2,2,2,1]
[8,2,5,1,4,3,7,6]=>[1,2,2,2,1]
[8,2,6,1,4,3,7,5]=>[1,2,2,2,1]
[7,1,4,3,8,2,6,5]=>[1,2,2,2,1]
[8,1,4,3,7,2,6,5]=>[1,2,2,2,1]
[8,1,5,3,7,2,6,4]=>[1,2,2,2,1]
[7,1,5,3,8,2,6,4]=>[1,2,2,2,1]
[8,2,6,1,5,3,7,4]=>[1,2,2,2,1]
[5,1,8,2,6,3,7,4]=>[1,2,2,2,1]
[4,1,8,2,6,3,7,5]=>[1,2,2,2,1]
[3,1,8,2,6,4,7,5]=>[1,2,2,2,1]
[2,1,8,3,6,4,7,5]=>[1,2,2,2,1]
[2,1,7,3,6,4,8,5]=>[1,2,2,2,1]
[4,1,7,2,6,3,8,5]=>[1,2,2,2,1]
[5,1,7,2,6,3,8,4]=>[1,2,2,2,1]
[7,2,6,1,5,3,8,4]=>[1,2,2,2,1]
[6,2,7,1,5,3,8,4]=>[1,2,2,2,1]
[6,2,8,1,5,3,7,4]=>[1,2,2,2,1]
[8,1,5,2,6,3,7,4]=>[1,2,2,2,1]
[6,1,5,2,7,3,8,4]=>[1,2,2,2,1]
[6,1,4,2,7,3,8,5]=>[1,2,2,2,1]
[8,1,4,2,6,3,7,5]=>[1,2,2,2,1]
[8,1,3,2,6,4,7,5]=>[1,2,2,2,1]
[7,1,3,2,6,4,8,5]=>[1,2,2,2,1]
[6,1,3,2,7,4,8,5]=>[1,2,2,2,1]
[5,1,3,2,7,4,8,6]=>[1,2,2,2,1]
[4,1,3,2,7,5,8,6]=>[1,2,2,2,1]
[2,1,4,3,8,5,7,6]=>[1,2,2,2,1]
[3,1,4,2,8,5,7,6]=>[1,2,2,2,1]
[4,1,3,2,8,5,7,6]=>[1,2,2,2,1]
[5,1,3,2,8,4,7,6]=>[1,2,2,2,1]
[6,1,3,2,8,4,7,5]=>[1,2,2,2,1]
[8,4,7,1,3,2,6,5]=>[1,2,2,2,1]
[7,4,8,1,3,2,6,5]=>[1,2,2,2,1]
[7,3,8,1,4,2,6,5]=>[1,2,2,2,1]
[8,3,7,1,4,2,6,5]=>[1,2,2,2,1]
[6,1,4,2,8,3,7,5]=>[1,2,2,2,1]
[5,1,4,2,8,3,7,6]=>[1,2,2,2,1]
[4,1,5,2,8,3,7,6]=>[1,2,2,2,1]
[3,1,5,2,8,4,7,6]=>[1,2,2,2,1]
[2,1,5,3,8,4,7,6]=>[1,2,2,2,1]
[2,1,6,3,8,4,7,5]=>[1,2,2,2,1]
[3,1,6,2,8,4,7,5]=>[1,2,2,2,1]
[4,1,6,2,8,3,7,5]=>[1,2,2,2,1]
[5,1,6,2,8,3,7,4]=>[1,2,2,2,1]
[6,1,5,2,8,3,7,4]=>[1,2,2,2,1]
[8,3,7,1,5,2,6,4]=>[1,2,2,2,1]
[7,3,8,1,5,2,6,4]=>[1,2,2,2,1]
[6,2,7,3,8,1,5,4]=>[1,2,2,2,1]
[6,2,8,3,7,1,5,4]=>[1,2,2,2,1]
[8,3,7,2,6,1,5,4]=>[1,2,2,2,1]
[5,1,8,3,7,2,6,4]=>[1,2,2,2,1]
[4,1,8,3,7,2,6,5]=>[1,2,2,2,1]
[3,1,8,4,7,2,6,5]=>[1,2,2,2,1]
[2,1,8,4,7,3,6,5]=>[1,2,2,2,1]
[2,1,7,4,8,3,6,5]=>[1,2,2,2,1]
[3,1,7,4,8,2,6,5]=>[1,2,2,2,1]
[4,1,7,3,8,2,6,5]=>[1,2,2,2,1]
[5,1,7,3,8,2,6,4]=>[1,2,2,2,1]
[7,3,8,2,6,1,5,4]=>[1,2,2,2,1]
[8,2,6,3,7,1,5,4]=>[1,2,2,2,1]
[7,2,6,3,8,1,5,4]=>[1,2,2,2,1]
[3,4,2,6,8,1,5,7]=>[2,3,3]
[5,3,6,2,8,1,4,7]=>[1,2,2,3]
[5,3,6,2,4,8,1,7]=>[1,2,3,2]
[5,7,3,8,2,4,1,6]=>[2,2,2,2]
[5,7,3,8,2,4,6,1]=>[2,2,3,1]
[7,4,2,5,8,3,6,1]=>[1,1,3,2,1]
[7,4,2,5,8,3,1,6]=>[1,1,3,1,2]
[4,5,2,6,3,8,1,7]=>[2,2,2,2]
[4,5,2,1,6,8,3,7]=>[2,1,3,2]
[5,3,1,6,8,2,4,7]=>[1,1,3,3]
[5,6,2,8,1,3,4,7]=>[2,2,4]
[3,5,6,1,4,8,2,7]=>[3,3,2]
[4,1,5,6,3,8,2,7]=>[1,3,2,2]
[4,5,1,6,3,8,2,7]=>[2,2,2,2]
[4,5,6,3,2,8,1,7]=>[3,1,2,2]
[7,4,5,3,8,2,1,6]=>[1,2,2,1,2]
[7,4,5,3,8,2,6,1]=>[1,2,2,2,1]
[6,7,4,8,3,2,5,1]=>[2,2,1,2,1]
[6,7,4,8,3,2,1,5]=>[2,2,1,1,2]
[6,7,4,1,8,3,2,5]=>[2,1,2,1,2]
[7,4,5,3,1,8,2,6]=>[1,2,1,2,2]
[4,7,1,5,8,3,2,6]=>[2,3,1,2]
[5,3,7,8,1,4,2,6]=>[1,3,2,2]
[7,5,8,2,4,6,1,3]=>[1,2,3,2]
[7,3,5,8,1,4,6,2]=>[1,3,3,1]
[4,5,1,7,8,3,6,2]=>[2,3,2,1]
[7,4,1,5,8,3,6,2]=>[1,1,3,2,1]
[6,7,4,3,8,1,5,2]=>[2,1,2,2,1]
[6,7,4,8,3,1,5,2]=>[2,2,1,2,1]
[6,7,4,8,3,5,2,1]=>[2,2,2,1,1]
[5,6,7,3,8,4,2,1]=>[3,2,1,1,1]
[5,6,7,3,1,8,4,2]=>[3,1,2,1,1]
[5,6,1,7,3,8,4,2]=>[2,2,2,1,1]
[5,1,6,7,3,8,4,2]=>[1,3,2,1,1]
[6,4,7,1,8,3,5,2]=>[1,2,2,2,1]
[6,7,8,3,1,4,5,2]=>[3,1,3,1]
[6,7,2,8,4,5,1,3]=>[2,2,2,2]
[6,7,2,8,4,1,3,5]=>[2,2,1,3]
[6,1,7,4,8,3,2,5]=>[1,2,2,1,2]
[5,1,6,7,3,2,8,4]=>[1,3,1,2,1]
[5,6,1,7,3,2,8,4]=>[2,2,1,2,1]
[5,6,7,3,2,1,8,4]=>[3,1,1,2,1]
[5,6,7,3,2,8,4,1]=>[3,1,2,1,1]
[5,6,2,7,3,8,4,1]=>[2,2,2,1,1]
[5,6,2,7,3,1,8,4]=>[2,2,1,2,1]
[5,6,2,1,7,3,8,4]=>[2,1,2,2,1]
[6,1,7,4,2,8,3,5]=>[1,2,1,2,2]
[6,7,2,1,8,3,4,5]=>[2,1,2,3]
[7,5,8,2,1,3,4,6]=>[1,2,1,4]
[5,7,3,1,8,2,4,6]=>[2,1,2,3]
[4,7,1,5,2,8,3,6]=>[2,2,2,2]
[7,4,2,5,1,8,3,6]=>[1,1,2,2,2]
[6,7,4,2,1,8,3,5]=>[2,1,1,2,2]
[6,7,4,2,8,3,1,5]=>[2,1,2,1,2]
[6,7,4,2,8,3,5,1]=>[2,1,2,2,1]
[3,6,7,2,8,4,5,1]=>[3,2,2,1]
[3,6,7,2,8,4,1,5]=>[3,2,1,2]
[3,6,7,2,1,8,4,5]=>[3,1,2,2]
[5,7,3,8,2,1,4,6]=>[2,2,1,3]
[3,4,7,8,2,1,5,6]=>[4,1,3]
[3,7,8,1,4,6,2,5]=>[3,3,2]
[3,4,7,8,2,6,1,5]=>[4,2,2]
[5,7,3,8,2,6,1,4]=>[2,2,2,2]
[3,6,7,2,8,5,1,4]=>[3,2,1,2]
[3,6,7,8,5,2,1,4]=>[4,1,1,2]
[3,6,7,8,5,2,4,1]=>[4,1,2,1]
[6,4,7,8,2,5,3,1]=>[1,3,2,1,1]
[6,4,7,8,2,1,5,3]=>[1,3,1,2,1]
[4,1,5,7,8,2,6,3]=>[1,4,2,1]
[5,3,7,8,1,6,2,4]=>[1,3,2,2]
[6,7,2,8,5,1,3,4]=>[2,2,1,3]
[6,4,1,7,8,2,5,3]=>[1,1,3,2,1]
[5,1,6,2,7,8,4,3]=>[1,2,3,1,1]
[5,6,2,1,7,8,4,3]=>[2,1,3,1,1]
[5,6,2,7,1,8,4,3]=>[2,2,2,1,1]
[5,6,2,7,8,4,3,1]=>[2,3,1,1,1]
[5,6,7,2,8,4,3,1]=>[3,2,1,1,1]
[5,6,7,2,1,8,4,3]=>[3,1,2,1,1]
[5,6,1,7,2,8,4,3]=>[2,2,2,1,1]
[5,1,6,7,2,8,4,3]=>[1,3,2,1,1]
[6,4,7,1,8,2,5,3]=>[1,2,2,2,1]
[3,6,7,1,8,5,2,4]=>[3,2,1,2]
[6,7,8,5,2,4,1,3]=>[3,1,2,2]
[6,7,8,3,5,1,4,2]=>[3,2,2,1]
[4,6,7,8,1,5,3,2]=>[4,2,1,1]
[5,1,6,7,8,4,3,2]=>[1,4,1,1,1]
[5,6,1,7,8,4,3,2]=>[2,3,1,1,1]
[5,6,7,1,8,4,3,2]=>[3,2,1,1,1]
[8,6,1,3,4,2,5,7]=>[1,1,3,3]
[8,3,2,5,1,6,4,7]=>[1,1,2,2,2]
[8,5,3,6,2,4,1,7]=>[1,1,2,2,2]
[5,3,2,7,4,1,8,6]=>[1,1,2,1,2,1]
[7,5,3,8,2,4,6,1]=>[1,1,2,3,1]
[7,2,4,5,8,3,6,1]=>[1,4,2,1]
[2,4,5,3,7,1,8,6]=>[3,2,2,1]
[8,2,4,5,6,3,1,7]=>[1,4,1,2]
[8,2,4,5,6,1,3,7]=>[1,4,3]
[8,1,2,4,5,6,3,7]=>[1,5,2]
[8,2,5,1,3,6,4,7]=>[1,2,3,2]
[8,5,6,2,1,4,3,7]=>[1,2,1,2,2]
[8,5,3,6,4,1,2,7]=>[1,1,2,1,3]
[8,4,1,5,6,3,2,7]=>[1,1,3,1,2]
[8,1,4,5,6,3,2,7]=>[1,4,1,2]
[4,5,3,7,2,1,8,6]=>[2,2,1,2,1]
[7,4,5,8,3,2,6,1]=>[1,3,1,2,1]
[4,3,6,7,2,8,5,1]=>[1,3,2,1,1]
[4,3,6,7,2,8,1,5]=>[1,3,2,2]
[1,4,3,6,7,2,8,5]=>[2,3,2,1]
[4,5,3,7,1,8,2,6]=>[2,2,2,2]
[4,1,5,3,7,2,8,6]=>[1,2,2,2,1]
[5,3,4,7,1,2,8,6]=>[1,3,3,1]
[7,5,8,2,1,4,6,3]=>[1,2,1,3,1]
[7,5,3,8,4,1,6,2]=>[1,1,2,1,2,1]
[7,4,5,8,3,6,1,2]=>[1,3,2,2]
[4,3,6,7,8,1,5,2]=>[1,4,2,1]
[1,6,4,7,8,3,5,2]=>[2,3,2,1]
[6,4,7,8,3,5,2,1]=>[1,3,2,1,1]
[3,5,6,7,8,4,1,2]=>[5,1,2]
[3,1,5,6,7,8,4,2]=>[1,5,1,1]
[4,6,1,7,8,3,5,2]=>[2,3,2,1]
[3,6,7,1,4,8,5,2]=>[3,3,1,1]
[6,2,4,1,7,8,5,3]=>[1,2,3,1,1]
[2,6,7,1,4,8,3,5]=>[3,3,2]
[4,3,6,7,8,1,2,5]=>[1,4,3]
[1,5,3,6,7,8,2,4]=>[2,4,2]
[3,5,6,7,8,2,1,4]=>[5,1,2]
[3,5,6,7,8,2,4,1]=>[5,2,1]
[5,2,7,1,3,8,4,6]=>[1,2,3,2]
[5,3,1,7,8,2,4,6]=>[1,1,3,3]
[4,5,2,7,8,1,3,6]=>[2,3,3]
[4,2,6,7,8,3,1,5]=>[1,4,1,2]
[4,2,6,7,8,3,5,1]=>[1,4,2,1]
[3,6,2,7,4,8,5,1]=>[2,2,2,1,1]
[3,6,2,7,4,8,1,5]=>[2,2,2,2]
[3,2,1,6,4,7,8,5]=>[1,1,2,3,1]
[3,7,4,2,1,5,8,6]=>[2,1,1,3,1]
[1,7,3,4,2,5,8,6]=>[2,2,3,1]
[4,7,2,1,3,5,8,6]=>[2,1,4,1]
[7,8,4,2,1,3,6,5]=>[2,1,1,3,1]
[7,8,1,3,4,2,6,5]=>[2,3,2,1]
[7,8,3,4,2,1,6,5]=>[2,2,1,2,1]
[6,3,2,7,1,8,5,4]=>[1,1,2,2,1,1]
[3,6,2,7,1,8,5,4]=>[2,2,2,1,1]
[6,7,3,8,2,5,4,1]=>[2,2,2,1,1]
[6,4,7,8,5,2,3,1]=>[1,3,1,2,1]
[2,6,4,7,8,1,5,3]=>[2,3,2,1]
[4,6,2,7,8,1,5,3]=>[2,3,2,1]
[7,4,5,8,6,2,1,3]=>[1,3,1,1,2]
[7,4,1,5,8,6,2,3]=>[1,1,3,1,2]
[7,5,3,8,6,1,2,4]=>[1,1,2,1,3]
[7,5,8,2,1,6,3,4]=>[1,2,1,2,2]
[6,2,7,1,3,8,5,4]=>[1,2,3,1,1]
[6,3,1,7,8,2,5,4]=>[1,1,3,2,1]
[4,6,1,7,8,5,2,3]=>[2,3,1,2]
[5,1,2,6,7,8,4,3]=>[1,5,1,1]
[5,2,6,7,8,4,1,3]=>[1,4,1,2]
[5,2,6,7,8,4,3,1]=>[1,4,1,1,1]
[2,5,6,7,8,4,1,3]=>[5,1,2]
[1,5,2,6,7,8,4,3]=>[2,4,1,1]
[1,6,4,7,8,5,2,3]=>[2,3,1,2]
[2,6,7,1,3,8,5,4]=>[3,3,1,1]
[6,7,8,2,1,5,4,3]=>[3,1,2,1,1]
[6,7,3,8,5,1,4,2]=>[2,2,1,2,1]
[6,4,7,8,5,3,1,2]=>[1,3,1,1,2]
[4,5,2,3,7,6,1,8]=>[2,3,1,2]
[6,4,3,7,2,5,1,8]=>[1,1,2,2,2]
[8,4,3,6,5,1,2,7]=>[1,1,2,1,3]
[1,5,6,3,4,8,7,2]=>[3,3,1,1]
[4,6,2,7,3,5,1,8]=>[2,2,2,2]
[3,2,6,7,4,5,1,8]=>[1,3,2,2]
[4,7,2,6,5,3,1,8]=>[2,2,1,1,2]
[5,7,6,2,4,3,1,8]=>[2,1,2,1,2]
[1,7,5,4,8,3,6,2]=>[2,1,2,2,1]
[8,7,5,4,1,3,2,6]=>[1,1,1,1,2,2]
[6,8,5,4,2,1,3,7]=>[2,1,1,1,3]
[5,8,6,2,4,1,3,7]=>[2,1,2,3]
[4,8,2,6,5,1,3,7]=>[2,2,1,3]
[3,2,8,6,5,1,4,7]=>[1,2,1,1,3]
[4,1,2,6,5,8,7,3]=>[1,3,2,1,1]
[5,1,6,2,4,8,7,3]=>[1,2,3,1,1]
[6,1,5,4,2,8,7,3]=>[1,2,1,2,1,1]
[7,1,5,4,8,2,6,3]=>[1,2,2,2,1]
[8,1,5,4,7,6,2,3]=>[1,2,2,1,2]
[1,8,6,7,4,5,3,2]=>[2,2,2,1,1]
[8,1,6,7,4,5,2,3]=>[1,3,2,2]
[7,1,6,8,4,2,5,3]=>[1,3,1,2,1]
[6,1,7,8,2,4,5,3]=>[1,3,3,1]
[5,1,7,2,8,4,6,3]=>[1,2,2,2,1]
[4,1,2,7,8,5,6,3]=>[1,4,2,1]
[3,2,1,7,8,5,6,4]=>[1,1,3,2,1]
[3,2,8,7,1,5,4,6]=>[1,2,1,2,2]
[4,8,2,7,1,5,3,6]=>[2,2,2,2]
[5,8,7,2,1,4,3,6]=>[2,1,1,2,2]
[6,8,7,1,2,4,3,5]=>[2,1,3,2]
[7,8,6,1,4,2,3,5]=>[2,1,2,3]
[8,7,6,1,4,3,2,5]=>[1,1,1,2,1,2]
[1,7,6,8,4,3,5,2]=>[2,2,1,2,1]
[1,6,7,8,3,4,5,2]=>[4,3,1]
[8,6,7,1,3,4,2,5]=>[1,2,3,2]
[7,6,8,1,3,2,4,5]=>[1,2,2,3]
[5,7,8,2,1,3,4,6]=>[3,1,4]
[4,7,2,8,1,3,5,6]=>[2,2,4]
[3,2,6,8,4,1,5,7]=>[1,3,1,3]
[4,6,2,8,3,1,5,7]=>[2,2,1,3]
[5,6,8,2,3,1,4,7]=>[3,2,3]
[6,5,8,3,2,1,4,7]=>[1,2,1,1,3]
[7,5,8,3,1,2,4,6]=>[1,2,1,4]
[8,5,7,3,1,4,2,6]=>[1,2,1,2,2]
[1,5,7,3,8,4,6,2]=>[3,2,2,1]
[1,4,3,7,8,5,6,2]=>[2,3,2,1]
[8,4,3,7,1,5,2,6]=>[1,1,2,2,2]
[6,4,3,8,2,1,5,7]=>[1,1,2,1,3]
[4,5,2,3,8,1,6,7]=>[2,3,3]
[3,2,5,4,8,1,6,7]=>[1,2,2,3]
[4,5,2,3,1,8,7,6]=>[2,2,2,1,1]
[6,4,3,1,2,8,7,5]=>[1,1,1,3,1,1]
[7,4,3,1,8,2,6,5]=>[1,1,1,2,2,1]
[8,4,3,1,7,6,2,5]=>[1,1,1,2,1,2]
[1,5,8,3,7,6,4,2]=>[3,2,1,1,1]
[8,5,1,3,7,6,2,4]=>[1,1,3,1,2]
[7,5,1,3,8,2,6,4]=>[1,1,3,2,1]
[6,5,1,3,2,8,7,4]=>[1,1,2,2,1,1]
[5,6,1,2,3,8,7,4]=>[2,4,1,1]
[4,6,2,1,3,8,7,5]=>[2,1,3,1,1]
[3,2,6,1,4,8,7,5]=>[1,2,3,1,1]
[3,2,7,1,8,4,6,5]=>[1,2,2,2,1]
[4,7,2,1,8,3,6,5]=>[2,1,2,2,1]
[5,7,1,2,8,3,6,4]=>[2,3,2,1]
[6,7,1,8,2,3,5,4]=>[2,2,3,1]
[7,6,1,8,3,2,5,4]=>[1,1,2,1,2,1]
[8,6,1,7,3,5,2,4]=>[1,1,2,2,2]
[1,6,8,7,3,5,4,2]=>[3,1,2,1,1]
[1,7,8,6,5,3,4,2]=>[3,1,1,2,1]
[8,7,1,6,5,3,2,4]=>[1,1,2,1,1,2]
[7,8,1,6,5,2,3,4]=>[2,2,1,3]
[6,8,1,7,2,5,3,4]=>[2,2,2,2]
[5,8,1,2,7,6,3,4]=>[2,3,1,2]
[4,8,2,1,7,6,3,5]=>[2,1,2,1,2]
[3,2,8,1,7,6,4,5]=>[1,2,2,1,2]
[4,1,2,8,7,6,5,3]=>[1,3,1,1,1,1]
[5,1,8,2,7,6,4,3]=>[1,2,2,1,1,1]
[6,1,8,7,2,5,4,3]=>[1,2,1,2,1,1]
[7,1,8,6,5,2,4,3]=>[1,2,1,1,2,1]
[8,1,7,6,5,4,2,3]=>[1,2,1,1,1,2]
[3,1,2,6,5,8,7,4]=>[1,3,2,1,1]
[3,1,6,2,4,8,7,5]=>[1,2,3,1,1]
[3,1,5,2,4,8,7,6]=>[1,2,3,1,1]
[4,5,1,2,3,8,7,6]=>[2,4,1,1]
[4,6,1,2,3,8,7,5]=>[2,4,1,1]
[1,6,5,3,4,8,7,2]=>[2,1,3,1,1]
[6,1,5,2,4,8,7,3]=>[1,2,3,1,1]
[6,5,1,2,3,8,7,4]=>[1,1,4,1,1]
[6,4,1,2,3,8,7,5]=>[1,1,4,1,1]
[5,4,1,2,3,8,7,6]=>[1,1,4,1,1]
[5,4,1,2,7,3,6,8]=>[1,1,3,3]
[6,4,1,7,2,3,5,8]=>[1,1,2,4]
[6,4,1,8,2,3,5,7]=>[1,1,2,4]
[7,4,1,2,8,3,6,5]=>[1,1,3,2,1]
[7,5,1,2,8,3,6,4]=>[1,1,3,2,1]
[7,1,5,2,8,4,6,3]=>[1,2,2,2,1]
[1,7,5,3,8,4,6,2]=>[2,1,2,2,1]
[1,8,5,3,7,4,6,2]=>[2,1,2,2,1]
[8,1,5,2,7,4,6,3]=>[1,2,2,2,1]
[8,5,1,2,7,3,6,4]=>[1,1,3,2,1]
[8,4,1,2,7,3,6,5]=>[1,1,3,2,1]
[8,4,1,7,2,3,5,6]=>[1,1,2,4]
[7,4,1,6,2,3,5,8]=>[1,1,2,4]
[8,6,1,7,2,3,5,4]=>[1,1,2,3,1]
[8,1,6,7,2,4,5,3]=>[1,3,3,1]
[1,8,6,7,3,4,5,2]=>[2,2,3,1]
[1,7,6,8,3,4,5,2]=>[2,2,3,1]
[7,1,6,8,2,4,5,3]=>[1,3,3,1]
[7,6,1,8,2,3,5,4]=>[1,1,2,3,1]
[4,7,1,2,8,3,6,5]=>[2,3,2,1]
[3,1,7,2,8,4,6,5]=>[1,2,2,2,1]
[3,1,2,7,8,5,6,4]=>[1,4,2,1]
[1,4,3,8,7,5,6,2]=>[2,2,1,2,1]
[4,1,2,8,7,5,6,3]=>[1,3,1,2,1]
[3,1,2,8,7,5,6,4]=>[1,3,1,2,1]
[3,1,8,2,7,4,6,5]=>[1,2,2,2,1]
[3,1,8,7,2,4,5,6]=>[1,2,1,4]
[3,1,7,6,2,4,5,8]=>[1,2,1,4]
[4,7,1,6,2,3,5,8]=>[2,2,4]
[4,8,1,6,2,3,5,7]=>[2,2,4]
[4,8,1,7,2,3,5,6]=>[2,2,4]
[4,8,1,2,7,3,6,5]=>[2,3,2,1]
[5,8,1,2,7,3,6,4]=>[2,3,2,1]
[5,1,8,2,7,4,6,3]=>[1,2,2,2,1]
[1,5,8,3,7,4,6,2]=>[3,2,2,1]
[1,6,8,7,3,4,5,2]=>[3,1,3,1]
[6,1,8,7,2,4,5,3]=>[1,2,1,3,1]
[6,8,1,7,2,3,5,4]=>[2,2,3,1]
[6,8,7,1,2,3,4,5]=>[2,1,5]
[5,8,7,1,2,3,4,6]=>[2,1,5]
[5,8,6,1,2,3,4,7]=>[2,1,5]
[5,7,6,1,2,3,4,8]=>[2,1,5]
[7,8,1,6,2,3,5,4]=>[2,2,3,1]
[7,1,8,6,2,4,5,3]=>[1,2,1,3,1]
[1,7,8,6,3,4,5,2]=>[3,1,3,1]
[1,8,7,6,3,4,5,2]=>[2,1,1,3,1]
[8,1,7,6,2,4,5,3]=>[1,2,1,3,1]
[8,7,1,6,2,3,5,4]=>[1,1,2,3,1]
[3,2,5,1,6,4,8,7]=>[1,2,2,2,1]
[3,2,5,4,7,1,8,6]=>[1,2,2,2,1]
[4,2,5,3,7,6,8,1]=>[1,2,2,2,1]
[4,2,5,3,7,1,8,6]=>[1,2,2,2,1]
[4,2,5,3,6,1,8,7]=>[1,2,2,2,1]
[4,2,5,1,6,3,8,7]=>[1,2,2,2,1]
[3,1,5,4,6,2,8,7]=>[1,2,2,2,1]
[4,1,5,3,6,2,8,7]=>[1,2,2,2,1]
[4,3,5,1,6,2,8,7]=>[1,2,2,2,1]
[4,3,5,2,7,1,8,6]=>[1,2,2,2,1]
[4,3,6,2,7,5,8,1]=>[1,2,2,2,1]
[4,3,6,2,7,1,8,5]=>[1,2,2,2,1]
[4,3,6,1,7,2,8,5]=>[1,2,2,2,1]
[4,3,5,1,7,2,8,6]=>[1,2,2,2,1]
[3,1,5,4,7,2,8,6]=>[1,2,2,2,1]
[2,1,5,4,7,3,8,6]=>[1,2,2,2,1]
[3,1,5,4,7,6,8,2]=>[1,2,2,2,1]
[4,1,5,3,7,6,8,2]=>[1,2,2,2,1]
[4,3,5,1,7,6,8,2]=>[1,2,2,2,1]
[4,3,6,1,7,5,8,2]=>[1,2,2,2,1]
[4,3,6,5,7,1,8,2]=>[1,2,2,2,1]
[5,3,6,4,7,2,8,1]=>[1,2,2,2,1]
[5,3,6,4,7,1,8,2]=>[1,2,2,2,1]
[5,3,6,1,7,4,8,2]=>[1,2,2,2,1]
[5,1,6,3,7,4,8,2]=>[1,2,2,2,1]
[4,1,6,3,7,5,8,2]=>[1,2,2,2,1]
[3,1,6,4,7,5,8,2]=>[1,2,2,2,1]
[2,1,6,4,7,5,8,3]=>[1,2,2,2,1]
[2,1,6,4,7,3,8,5]=>[1,2,2,2,1]
[3,1,6,4,7,2,8,5]=>[1,2,2,2,1]
[4,1,6,3,7,2,8,5]=>[1,2,2,2,1]
[5,1,6,3,7,2,8,4]=>[1,2,2,2,1]
[5,3,6,1,7,2,8,4]=>[1,2,2,2,1]
[5,3,6,2,7,1,8,4]=>[1,2,2,2,1]
[5,3,6,2,7,4,8,1]=>[1,2,2,2,1]
[5,2,6,3,7,4,8,1]=>[1,2,2,2,1]
[5,2,6,3,7,1,8,4]=>[1,2,2,2,1]
[5,2,6,1,7,3,8,4]=>[1,2,2,2,1]
[4,2,5,1,7,3,8,6]=>[1,2,2,2,1]
[4,2,6,1,7,3,8,5]=>[1,2,2,2,1]
[4,2,6,3,7,1,8,5]=>[1,2,2,2,1]
[4,2,6,3,7,5,8,1]=>[1,2,2,2,1]
[3,2,6,4,7,5,8,1]=>[1,2,2,2,1]
[3,2,6,4,7,1,8,5]=>[1,2,2,2,1]
[3,2,6,1,7,4,8,5]=>[1,2,2,2,1]
[3,2,5,1,7,4,8,6]=>[1,2,2,2,1]
[3,2,4,1,7,5,8,6]=>[1,2,2,2,1]
[3,1,4,2,7,6,8,5]=>[1,2,2,2,1]
[3,2,5,1,7,6,8,4]=>[1,2,2,2,1]
[3,2,6,1,7,5,8,4]=>[1,2,2,2,1]
[3,2,6,5,7,1,8,4]=>[1,2,2,2,1]
[4,2,6,5,7,3,8,1]=>[1,2,2,2,1]
[4,2,6,5,7,1,8,3]=>[1,2,2,2,1]
[4,2,6,1,7,5,8,3]=>[1,2,2,2,1]
[4,2,5,1,7,6,8,3]=>[1,2,2,2,1]
[4,1,5,2,7,6,8,3]=>[1,2,2,2,1]
[3,1,5,2,7,6,8,4]=>[1,2,2,2,1]
[2,1,5,3,7,6,8,4]=>[1,2,2,2,1]
[2,1,6,3,7,5,8,4]=>[1,2,2,2,1]
[3,1,6,2,7,5,8,4]=>[1,2,2,2,1]
[4,1,6,2,7,5,8,3]=>[1,2,2,2,1]
[5,1,6,2,7,4,8,3]=>[1,2,2,2,1]
[5,2,6,1,7,4,8,3]=>[1,2,2,2,1]
[5,2,6,4,7,1,8,3]=>[1,2,2,2,1]
[5,2,6,4,7,3,8,1]=>[1,2,2,2,1]
[5,4,6,2,7,3,8,1]=>[1,2,2,2,1]
[5,4,6,2,7,1,8,3]=>[1,2,2,2,1]
[5,4,6,1,7,2,8,3]=>[1,2,2,2,1]
[5,1,6,4,7,2,8,3]=>[1,2,2,2,1]
[4,1,6,5,7,2,8,3]=>[1,2,2,2,1]
[3,1,6,5,7,2,8,4]=>[1,2,2,2,1]
[2,1,6,5,7,3,8,4]=>[1,2,2,2,1]
[3,1,6,5,7,4,8,2]=>[1,2,2,2,1]
[4,1,6,5,7,3,8,2]=>[1,2,2,2,1]
[5,1,6,4,7,3,8,2]=>[1,2,2,2,1]
[5,4,6,1,7,3,8,2]=>[1,2,2,2,1]
[5,4,6,3,7,1,8,2]=>[1,2,2,2,1]
[8,3,5,2,1,6,4,7]=>[1,2,1,2,2]
[8,6,3,5,2,4,1,7]=>[1,1,2,2,2]
[3,7,5,2,4,1,8,6]=>[2,1,2,2,1]
[8,3,7,5,2,4,6,1]=>[1,2,1,3,1]
[8,2,4,5,7,3,6,1]=>[1,4,2,1]
[2,4,5,7,3,1,8,6]=>[4,1,2,1]
[8,2,4,6,5,3,1,7]=>[1,3,1,1,2]
[8,2,5,4,6,1,3,7]=>[1,2,2,3]
[8,6,3,5,1,4,2,7]=>[1,1,2,2,2]
[8,6,1,4,5,3,2,7]=>[1,1,3,1,2]
[8,1,5,6,4,3,2,7]=>[1,3,1,1,2]
[5,7,4,3,2,1,8,6]=>[2,1,1,1,2,1]
[8,5,7,4,3,2,6,1]=>[1,2,1,1,2,1]
[4,6,8,3,2,7,5,1]=>[3,1,2,1,1]
[4,7,6,3,2,8,1,5]=>[2,1,1,2,2]
[1,4,6,7,3,2,8,5]=>[4,1,2,1]
[5,4,7,3,1,8,2,6]=>[1,2,1,2,2]
[1,7,4,5,3,2,8,6]=>[2,2,1,2,1]
[3,7,5,1,4,2,8,6]=>[2,1,2,2,1]
[5,7,4,2,1,3,8,6]=>[2,1,1,3,1]
[8,5,7,4,2,1,6,3]=>[1,2,1,1,2,1]
[8,3,7,5,1,4,6,2]=>[1,2,1,3,1]
[8,4,1,7,5,3,6,2]=>[1,1,2,1,2,1]
[4,6,3,8,7,1,5,2]=>[2,2,1,2,1]
[1,7,4,8,6,3,5,2]=>[2,2,1,2,1]
[8,4,7,6,3,5,2,1]=>[1,2,1,2,1,1]
[3,6,5,8,7,4,1,2]=>[2,2,1,1,2]
[3,1,5,8,6,7,4,2]=>[1,3,2,1,1]
[4,8,1,6,7,3,5,2]=>[2,3,2,1]
[3,6,4,1,8,7,5,2]=>[2,1,2,1,1,1]
[8,2,6,1,4,7,5,3]=>[1,2,3,1,1]
[2,7,6,8,1,4,3,5]=>[2,2,2,2]
[3,7,1,6,4,8,2,5]=>[2,2,2,2]
[1,7,3,5,6,8,2,4]=>[2,4,2]
[1,3,6,7,5,8,2,4]=>[4,2,2]
[3,7,6,5,8,2,1,4]=>[2,1,2,1,2]
[3,6,8,5,7,2,4,1]=>[3,2,2,1]
[2,3,5,7,6,8,1,4]=>[4,2,2]
[2,1,6,5,7,8,3,4]=>[1,2,3,2]
[4,2,7,6,8,3,1,5]=>[1,2,2,1,2]
[4,2,6,8,7,3,5,1]=>[1,3,1,2,1]
[3,8,2,4,6,7,5,1]=>[2,4,1,1]
[3,7,2,6,4,8,1,5]=>[2,2,2,2]
[3,2,6,1,4,7,8,5]=>[1,2,4,1]
[5,3,7,2,1,8,4,6]=>[1,2,1,2,2]
[4,7,3,2,1,5,8,6]=>[2,1,1,3,1]
[8,7,6,1,3,4,2,5]=>[1,1,1,3,2]
[8,5,7,3,2,1,6,4]=>[1,2,1,1,2,1]
[8,3,6,7,2,1,5,4]=>[1,3,1,2,1]
[3,7,8,6,2,1,5,4]=>[3,1,1,2,1]
[8,7,6,3,5,2,4,1]=>[1,1,1,2,2,1]
[2,7,4,8,1,6,5,3]=>[2,2,2,1,1]
[4,6,8,2,1,7,5,3]=>[3,1,2,1,1]
[8,4,1,5,7,2,6,3]=>[1,1,3,2,1]
[8,5,3,7,1,6,2,4]=>[1,1,2,2,2]
[8,5,7,2,1,3,6,4]=>[1,2,1,3,1]
[8,2,6,7,1,3,5,4]=>[1,3,3,1]
[8,3,6,1,7,5,2,4]=>[1,2,2,1,2]
[4,6,1,8,7,2,5,3]=>[2,2,1,2,1]
[8,1,2,5,6,7,4,3]=>[1,5,1,1]
[8,2,6,5,7,4,1,3]=>[1,2,2,1,2]
[2,1,7,8,5,6,4,3]=>[1,3,2,1,1]
[8,2,5,7,6,4,3,1]=>[1,3,1,1,1,1]
[2,7,6,8,5,4,1,3]=>[2,2,1,1,2]
[1,7,2,5,8,6,4,3]=>[2,3,1,1,1]
[1,7,4,8,2,6,5,3]=>[2,2,2,1,1]
[3,7,8,1,6,5,2,4]=>[3,2,1,2]
[2,7,8,6,1,3,5,4]=>[3,1,3,1]
[8,7,6,3,5,1,4,2]=>[1,1,1,2,2,1]
[8,4,7,6,5,1,3,2]=>[1,2,1,1,2,1]
[8,7,1,5,6,4,3,2]=>[1,1,3,1,1,1]
[8,1,6,7,5,4,3,2]=>[1,3,1,1,1,1]
[6,5,3,1,2,4,8,7]=>[1,1,1,4,1]
[4,6,3,5,1,2,8,7]=>[2,2,3,1]
[8,5,3,7,2,1,4,6]=>[1,1,2,1,3]
[6,8,1,4,5,7,3,2]=>[2,4,1,1]
[8,7,2,4,5,1,3,6]=>[1,1,3,3]
[3,6,2,4,5,1,8,7]=>[2,3,2,1]
[2,6,1,4,5,3,8,7]=>[2,3,2,1]
[6,1,2,4,5,3,8,7]=>[1,4,2,1]
[5,6,3,2,1,4,8,7]=>[2,1,1,3,1]
[5,4,3,6,1,2,8,7]=>[1,1,2,3,1]
[6,3,1,4,5,2,8,7]=>[1,1,3,2,1]
[3,1,6,4,5,2,8,7]=>[1,2,2,2,1]
[8,3,7,4,5,1,2,6]=>[1,2,2,3]
[5,8,7,4,2,6,3,1]=>[2,1,1,2,1,1]
[2,8,7,4,1,6,3,5]=>[2,1,1,2,2]
[8,1,7,4,2,6,3,5]=>[1,2,1,2,2]
[3,7,8,4,5,1,2,6]=>[3,2,3]
[2,1,8,7,5,3,4,6]=>[1,2,1,1,3]
[2,1,6,8,5,7,3,4]=>[1,3,2,2]
[5,6,3,8,1,7,2,4]=>[2,2,2,2]
[7,6,1,4,5,8,3,2]=>[1,1,4,1,1]
[3,7,6,4,5,8,2,1]=>[2,1,3,1,1]
[8,5,7,4,1,6,3,2]=>[1,2,1,2,1,1]
[5,1,8,4,7,6,2,3]=>[1,2,2,1,2]
[2,5,8,4,7,6,1,3]=>[3,2,1,2]
[2,4,8,3,5,6,7,1]=>[3,4,1]
[4,1,8,3,5,6,7,2]=>[1,2,4,1]
[3,8,4,2,5,6,7,1]=>[2,1,4,1]
[8,4,1,3,5,6,7,2]=>[1,1,5,1]
[7,5,8,4,3,6,1,2]=>[1,2,1,2,2]
[6,5,3,8,4,1,7,2]=>[1,1,2,1,2,1]
[2,1,5,8,4,6,7,3]=>[1,3,3,1]
[2,1,4,8,3,6,7,5]=>[1,3,3,1]
[6,4,3,8,2,1,7,5]=>[1,1,2,1,2,1]
[7,3,8,4,2,6,1,5]=>[1,2,1,2,2]
[8,3,1,2,5,6,7,4]=>[1,1,5,1]
[3,1,8,2,5,6,7,4]=>[1,2,4,1]
[2,3,8,1,5,6,7,4]=>[3,4,1]
[4,3,8,2,5,6,7,1]=>[1,2,4,1]
[4,8,2,3,5,6,7,1]=>[2,5,1]
[3,8,2,1,5,6,7,4]=>[2,1,4,1]
[2,8,1,3,5,6,7,4]=>[2,5,1]
[8,1,2,3,5,6,7,4]=>[1,6,1]
[7,8,2,4,3,6,1,5]=>[2,2,2,2]
[6,8,3,2,4,1,7,5]=>[2,1,2,2,1]
[2,1,8,3,4,6,7,5]=>[1,2,4,1]
[2,1,7,8,5,4,3,6]=>[1,3,1,1,2]
[5,7,3,8,1,4,2,6]=>[2,2,2,2]
[7,1,8,4,5,3,2,6]=>[1,2,2,1,2]
[2,7,8,4,5,3,1,6]=>[3,2,1,2]
[8,7,1,4,3,6,2,5]=>[1,1,2,2,2]
[3,8,7,4,2,6,1,5]=>[2,1,1,2,2]
[5,7,8,4,3,6,2,1]=>[3,1,2,1,1]
[5,6,3,8,4,2,7,1]=>[2,2,1,2,1]
[4,8,3,6,2,1,7,5]=>[2,2,1,2,1]
[8,6,3,1,4,2,7,5]=>[1,1,1,2,2,1]
[7,5,3,8,2,4,1,6]=>[1,1,2,2,2]
[2,4,3,1,8,5,7,6]=>[2,1,2,2,1]
[4,1,3,2,6,8,7,5]=>[1,2,3,1,1]
[7,5,3,6,2,8,1,4]=>[1,1,2,2,2]
[8,6,3,5,1,2,7,4]=>[1,1,2,3,1]
[5,8,3,2,6,1,7,4]=>[2,1,2,2,1]
[4,5,3,8,6,2,7,1]=>[2,2,1,2,1]
[3,5,8,4,7,6,2,1]=>[3,2,1,1,1]
[5,8,2,4,7,6,1,3]=>[2,3,1,2]
[8,7,5,4,1,6,2,3]=>[1,1,1,1,2,2]
[2,7,6,4,5,8,1,3]=>[2,1,3,2]
[7,1,6,4,5,8,2,3]=>[1,2,3,2]
[5,7,3,6,1,8,2,4]=>[2,2,2,2]
[2,1,7,6,5,8,3,4]=>[1,2,1,2,2]
[2,1,8,5,3,6,7,4]=>[1,2,1,3,1]
[6,8,3,5,2,1,7,4]=>[2,2,1,2,1]
[7,8,5,4,2,6,1,3]=>[2,1,1,2,2]
[8,1,4,2,5,6,7,3]=>[1,2,4,1]
[2,8,4,1,5,6,7,3]=>[2,1,4,1]
[4,8,1,2,5,6,7,3]=>[2,5,1]
[3,4,8,1,5,6,7,2]=>[3,4,1]
[3,4,2,8,5,6,7,1]=>[2,2,3,1]
[2,4,1,8,5,6,7,3]=>[2,2,3,1]
[4,1,2,8,5,6,7,3]=>[1,3,3,1]
[8,4,2,1,5,6,7,3]=>[1,1,1,4,1]
[7,5,2,4,8,6,1,3]=>[1,1,3,1,2]
[6,5,3,2,8,1,7,4]=>[1,1,1,2,2,1]
[2,1,5,3,8,6,7,4]=>[1,2,2,2,1]
[6,4,3,5,8,1,7,2]=>[1,1,3,2,1]
[7,3,5,4,8,6,1,2]=>[1,2,2,1,2]
[8,3,4,1,5,6,7,2]=>[1,2,4,1]
[4,3,1,8,5,6,7,2]=>[1,1,2,3,1]
[3,1,4,8,5,6,7,2]=>[1,3,3,1]
[6,5,3,7,2,8,4,1]=>[1,1,2,2,1,1]
[6,3,7,4,5,8,2,1]=>[1,2,3,1,1]
[6,7,2,4,5,8,3,1]=>[2,4,1,1]
[5,1,7,4,8,6,3,2]=>[1,2,2,1,1,1]
[2,5,7,4,8,6,3,1]=>[3,2,1,1,1]
[5,6,3,7,1,8,4,2]=>[2,2,2,1,1]
[3,8,7,4,5,2,1,6]=>[2,1,2,1,2]
[3,7,5,4,8,6,2,1]=>[2,1,2,1,1,1]
[5,7,1,4,8,6,2,3]=>[2,3,1,2]
[5,6,3,1,8,2,7,4]=>[2,1,2,2,1]
[4,6,3,5,8,2,7,1]=>[2,3,2,1]
[4,6,3,8,1,2,7,5]=>[2,2,3,1]
[3,7,8,4,1,6,2,5]=>[3,1,2,2]
[3,2,5,1,6,8,4,7]=>[1,2,3,2]
[3,6,2,5,4,8,1,7]=>[2,2,2,2]
[3,5,2,4,7,1,8,6]=>[2,3,2,1]
[3,5,8,2,4,7,6,1]=>[3,3,1,1]
[4,2,5,8,3,7,6,1]=>[1,3,2,1,1]
[4,2,6,5,3,8,1,7]=>[1,2,1,2,2]
[5,4,2,1,6,8,3,7]=>[1,1,1,3,2]
[6,3,5,1,4,8,2,7]=>[1,2,3,2]
[4,6,1,5,3,8,2,7]=>[2,2,2,2]
[5,1,6,4,3,8,2,7]=>[1,2,1,2,2]
[5,4,3,2,7,1,8,6]=>[1,1,1,2,2,1]
[5,4,3,8,2,7,6,1]=>[1,1,2,2,1,1]
[4,3,6,2,8,7,5,1]=>[1,2,2,1,1,1]
[4,3,7,6,2,1,8,5]=>[1,2,1,1,2,1]
[6,4,3,1,7,2,8,5]=>[1,1,1,2,2,1]
[7,5,4,3,1,8,2,6]=>[1,1,1,1,2,2]
[1,4,7,5,8,3,2,6]=>[3,2,1,2]
[7,1,3,5,8,4,2,6]=>[1,4,1,2]
[7,2,5,8,4,1,3,6]=>[1,3,1,3]
[2,8,5,7,4,6,1,3]=>[2,2,2,2]
[3,5,8,7,1,4,6,2]=>[3,1,3,1]
[1,4,5,8,7,3,6,2]=>[4,1,2,1]
[1,5,4,8,7,3,6,2]=>[2,2,1,2,1]
[6,4,3,8,1,7,5,2]=>[1,1,2,2,1,1]
[4,3,7,1,8,6,5,2]=>[1,2,2,1,1,1]
[4,8,3,7,6,5,2,1]=>[2,2,1,1,1,1]
[5,3,8,7,6,4,2,1]=>[1,2,1,1,1,1,1]
[7,5,3,1,8,6,4,2]=>[1,1,1,2,1,1,1]
[1,8,6,5,3,7,4,2]=>[2,1,1,2,1,1]
[1,5,8,6,3,7,4,2]=>[3,1,2,1,1]
[4,6,1,8,7,3,5,2]=>[2,2,1,2,1]
[6,8,7,3,1,4,5,2]=>[2,1,1,3,1]
[6,2,8,7,4,5,1,3]=>[1,2,1,2,2]
[7,6,2,8,4,1,3,5]=>[1,1,2,1,3]
[7,3,1,6,8,4,2,5]=>[1,1,3,1,2]
[1,7,6,4,8,3,2,5]=>[2,1,2,1,2]
[5,7,1,6,3,2,8,4]=>[2,2,1,2,1]
[6,1,7,5,3,2,8,4]=>[1,2,1,1,2,1]
[7,6,5,3,2,1,8,4]=>[1,1,1,1,1,2,1]
[6,5,3,2,8,7,4,1]=>[1,1,1,2,1,1,1]
[5,2,6,3,8,7,4,1]=>[1,2,2,1,1,1]
[5,2,7,6,3,1,8,4]=>[1,2,1,1,2,1]
[6,5,2,1,7,3,8,4]=>[1,1,1,2,2,1]
[5,2,7,4,1,8,3,6]=>[1,2,1,2,2]
[4,7,2,6,3,1,8,5]=>[2,2,1,2,1]
[2,4,8,6,3,7,5,1]=>[3,1,2,1,1]
[3,8,6,2,4,7,5,1]=>[2,1,3,1,1]
[7,3,6,2,4,1,8,5]=>[1,2,2,2,1]
[3,6,7,2,1,4,8,5]=>[3,1,3,1]
[4,3,7,8,2,1,5,6]=>[1,3,1,3]
[8,3,7,1,4,6,2,5]=>[1,2,3,2]
[3,8,2,5,7,1,6,4]=>[2,3,2,1]
[8,3,6,2,7,1,5,4]=>[1,2,2,2,1]
[7,8,3,6,2,1,5,4]=>[2,2,1,2,1]
[8,7,3,6,2,5,4,1]=>[1,1,2,2,1,1]
[4,7,8,2,1,6,5,3]=>[3,1,2,1,1]
[4,2,6,8,1,7,5,3]=>[1,3,2,1,1]
[5,4,8,2,7,1,6,3]=>[1,2,2,2,1]
[4,8,1,5,7,2,6,3]=>[2,3,2,1]
[5,8,3,7,1,6,2,4]=>[2,2,2,2]
[5,8,7,2,6,1,3,4]=>[2,1,2,3]
[8,6,2,7,5,1,3,4]=>[1,1,2,1,3]
[3,6,8,1,7,5,2,4]=>[3,2,1,2]
[5,1,6,8,2,7,4,3]=>[1,3,2,1,1]
[6,5,2,8,1,7,4,3]=>[1,1,2,2,1,1]
[5,2,7,1,8,6,4,3]=>[1,2,2,1,1,1]
[5,8,2,7,6,4,3,1]=>[2,2,1,1,1,1]
[6,2,8,7,5,4,3,1]=>[1,2,1,1,1,1,1]
[7,6,2,1,8,5,4,3]=>[1,1,1,2,1,1,1]
[6,1,7,2,8,5,4,3]=>[1,2,2,1,1,1]
[7,5,1,8,2,6,4,3]=>[1,1,2,2,1,1]
[4,7,1,8,6,2,5,3]=>[2,2,1,2,1]
[7,8,3,1,6,5,2,4]=>[2,1,2,1,2]
[8,7,4,6,1,5,3,2]=>[1,1,2,2,1,1]
[8,5,7,1,6,4,3,2]=>[1,2,2,1,1,1]
[6,8,1,7,5,4,3,2]=>[2,2,1,1,1,1]
[7,1,8,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[5,4,2,3,7,6,1,8]=>[1,1,3,1,2]
[6,4,2,7,3,5,1,8]=>[1,1,2,2,2]
[7,4,2,6,3,5,1,8]=>[1,1,2,2,2]
[8,4,2,6,3,1,5,7]=>[1,1,2,1,3]
[3,2,7,6,4,5,1,8]=>[1,2,1,2,2]
[4,7,2,6,3,5,1,8]=>[2,2,2,2]
[5,7,6,2,3,4,1,8]=>[2,1,3,2]
[1,6,5,2,3,8,4,7]=>[2,1,3,2]
[1,7,5,2,8,3,4,6]=>[2,1,2,3]
[6,8,5,2,3,1,4,7]=>[2,1,2,3]
[5,8,6,2,3,1,4,7]=>[2,1,2,3]
[4,8,2,6,3,1,5,7]=>[2,2,1,3]
[3,2,8,6,4,1,5,7]=>[1,2,1,1,3]
[3,2,1,6,4,8,5,7]=>[1,1,2,2,2]
[7,1,5,2,8,3,4,6]=>[1,2,2,3]
[1,8,5,2,7,3,4,6]=>[2,1,2,3]
[1,8,6,7,2,3,4,5]=>[2,2,4]
[8,1,6,7,2,3,4,5]=>[1,3,4]
[7,1,6,8,2,3,4,5]=>[1,3,4]
[3,2,1,7,8,4,5,6]=>[1,1,3,3]
[3,2,8,7,1,4,5,6]=>[1,2,1,4]
[5,8,7,2,1,3,4,6]=>[2,1,1,4]
[1,7,6,8,2,3,4,5]=>[2,2,4]
[6,5,8,2,3,1,4,7]=>[1,2,2,3]
[8,5,7,2,1,3,4,6]=>[1,2,1,4]
[6,4,2,8,3,1,5,7]=>[1,1,2,1,3]
[5,4,2,3,8,1,6,7]=>[1,1,3,3]
[3,2,5,4,1,8,6,7]=>[1,2,1,2,2]
[4,5,2,3,1,8,6,7]=>[2,2,2,2]
[5,4,2,3,1,8,6,7]=>[1,1,2,2,2]
[6,4,2,1,3,8,5,7]=>[1,1,1,3,2]
[7,4,2,1,8,3,5,6]=>[1,1,1,2,3]
[8,4,2,1,7,3,5,6]=>[1,1,1,2,3]
[1,4,2,8,7,3,5,6]=>[2,2,1,3]
[1,5,8,2,7,3,4,6]=>[3,2,3]
[8,5,1,2,7,3,4,6]=>[1,1,3,3]
[7,5,1,2,8,3,4,6]=>[1,1,3,3]
[6,5,1,2,3,8,4,7]=>[1,1,4,2]
[4,6,2,1,3,8,5,7]=>[2,1,3,2]
[3,2,6,1,4,8,5,7]=>[1,2,3,2]
[3,2,7,1,8,4,5,6]=>[1,2,2,3]
[4,7,2,1,8,3,5,6]=>[2,1,2,3]
[7,6,1,8,2,3,4,5]=>[1,1,2,4]
[8,6,1,7,2,3,4,5]=>[1,1,2,4]
[1,6,8,7,2,3,4,5]=>[3,1,4]
[1,7,8,6,2,3,4,5]=>[3,1,4]
[7,8,1,6,2,3,4,5]=>[2,2,4]
[6,8,1,7,2,3,4,5]=>[2,2,4]
[4,8,2,1,7,3,5,6]=>[2,1,2,3]
[3,2,8,1,7,4,5,6]=>[1,2,2,3]
[3,2,1,8,7,4,5,6]=>[1,1,2,1,3]
[5,1,8,2,7,3,4,6]=>[1,2,2,3]
[6,1,8,7,2,3,4,5]=>[1,2,1,4]
[8,1,7,6,2,3,4,5]=>[1,2,1,4]
[1,8,7,6,2,3,4,5]=>[2,1,1,4]
[6,3,5,1,2,4,8,7]=>[1,2,4,1]
[4,3,5,6,1,2,8,7]=>[1,3,3,1]
[8,3,7,5,2,1,4,6]=>[1,2,1,1,3]
[6,3,7,5,1,8,4,2]=>[1,2,1,2,1,1]
[6,5,2,7,1,8,3,4]=>[1,1,2,2,2]
[8,5,2,7,4,1,3,6]=>[1,1,2,1,3]
[2,6,1,5,4,3,8,7]=>[2,2,1,2,1]
[6,4,3,5,1,2,8,7]=>[1,1,2,3,1]
[5,3,1,4,6,2,8,7]=>[1,1,3,2,1]
[3,1,4,6,5,2,8,7]=>[1,3,1,2,1]
[5,7,4,6,2,8,3,1]=>[2,2,2,1,1]
[8,1,4,7,2,6,3,5]=>[1,3,2,2]
[3,4,7,8,5,2,1,6]=>[4,1,1,2]
[2,1,8,5,7,3,4,6]=>[1,2,2,3]
[8,6,3,5,1,7,4,2]=>[1,1,2,2,1,1]
[5,8,2,4,6,7,3,1]=>[2,4,1,1]
[3,4,8,6,5,7,1,2]=>[3,1,2,2]
[7,5,4,8,1,6,3,2]=>[1,1,2,2,1,1]
[5,1,4,6,8,2,7,3]=>[1,4,2,1]
[2,5,4,6,7,1,8,3]=>[2,3,2,1]
[2,4,6,3,7,5,8,1]=>[3,2,2,1]
[4,1,6,3,8,5,7,2]=>[1,2,2,2,1]
[3,7,4,2,8,6,5,1]=>[2,1,2,1,1,1]
[7,4,1,3,5,8,6,2]=>[1,1,4,1,1]
[6,5,8,4,1,7,3,2]=>[1,2,1,2,1,1]
[8,5,3,7,4,1,6,2]=>[1,1,2,1,2,1]
[2,1,4,8,3,7,6,5]=>[1,3,2,1,1]
[7,4,3,8,2,1,6,5]=>[1,1,2,1,2,1]
[6,3,7,4,1,8,2,5]=>[1,2,1,2,2]
[8,3,1,2,5,7,6,4]=>[1,1,4,1,1]
[3,1,8,2,7,6,5,4]=>[1,2,2,1,1,1]
[2,3,8,1,6,7,5,4]=>[3,3,1,1]
[4,3,7,2,6,8,5,1]=>[1,2,3,1,1]
[4,7,2,3,8,5,6,1]=>[2,3,2,1]
[3,8,2,1,7,5,6,4]=>[2,1,2,2,1]
[2,8,1,3,6,5,7,4]=>[2,3,2,1]
[2,7,8,5,4,3,1,6]=>[3,1,1,1,2]
[8,7,1,6,3,4,2,5]=>[1,1,2,2,2]
[3,8,6,7,2,4,1,5]=>[2,2,2,2]
[5,3,8,7,4,2,6,1]=>[1,2,1,1,2,1]
[4,3,8,7,2,1,6,5]=>[1,2,1,1,2,1]
[8,3,6,1,4,2,7,5]=>[1,2,2,2,1]
[7,3,5,8,2,4,1,6]=>[1,3,2,2]
[2,3,4,1,8,5,7,6]=>[3,2,2,1]
[4,1,3,2,6,7,8,5]=>[1,2,4,1]
[8,3,5,6,2,7,1,4]=>[1,3,2,2]
[5,3,6,1,8,7,2,4]=>[1,2,2,1,2]
[5,6,2,8,7,4,1,3]=>[2,2,1,1,2]
[7,8,5,6,1,4,2,3]=>[2,2,2,2]
[2,8,6,5,4,7,1,3]=>[2,1,1,2,2]
[8,1,6,4,5,7,2,3]=>[1,2,3,2]
[5,8,3,6,1,7,2,4]=>[2,2,2,2]
[2,1,8,6,5,7,3,4]=>[1,2,1,2,2]
[2,1,7,5,3,6,8,4]=>[1,2,1,3,1]
[6,7,3,5,2,1,8,4]=>[2,2,1,2,1]
[7,1,4,2,5,6,8,3]=>[1,2,4,1]
[2,7,4,1,6,5,8,3]=>[2,1,2,2,1]
[4,6,1,2,8,7,3,5]=>[2,3,1,2]
[2,4,1,5,8,7,6,3]=>[2,3,1,1,1]
[4,1,2,5,8,6,7,3]=>[1,4,2,1]
[6,4,2,1,5,8,7,3]=>[1,1,1,3,1,1]
[8,5,2,4,6,1,7,3]=>[1,1,3,2,1]
[7,5,3,2,6,8,1,4]=>[1,1,1,3,2]
[2,1,5,3,6,8,7,4]=>[1,2,3,1,1]
[7,3,5,4,6,1,8,2]=>[1,2,2,2,1]
[6,3,4,1,5,7,8,2]=>[1,2,4,1]
[4,3,1,5,7,6,8,2]=>[1,1,3,2,1]
[3,1,4,5,6,8,7,2]=>[1,5,1,1]
[4,5,2,6,3,1,8,7]=>[2,2,1,2,1]
[6,5,2,1,4,3,8,7]=>[1,1,1,2,2,1]
[6,5,2,7,4,8,3,1]=>[1,1,2,2,1,1]
[8,5,2,7,4,1,6,3]=>[1,1,2,1,2,1]
[8,3,7,5,2,1,6,4]=>[1,2,1,1,2,1]
[6,3,7,5,2,8,4,1]=>[1,2,1,2,1,1]
[3,1,6,5,4,2,8,7]=>[1,2,1,1,2,1]
[5,6,3,2,4,1,8,7]=>[2,1,2,2,1]
[3,6,2,4,1,5,8,7]=>[2,2,3,1]
[2,6,1,3,5,4,8,7]=>[2,3,2,1]
[6,7,2,3,4,8,5,1]=>[2,4,1,1]
[8,7,2,3,4,1,6,5]=>[1,1,3,2,1]
[5,1,7,3,8,4,6,2]=>[1,2,2,2,1]
[2,5,7,3,8,6,4,1]=>[3,2,1,1,1]
[7,6,1,3,5,8,4,2]=>[1,1,4,1,1]
[3,6,7,4,1,8,5,2]=>[3,1,2,1,1]
[5,6,3,7,4,8,1,2]=>[2,2,2,2]
[2,1,6,7,4,8,5,3]=>[1,3,2,1,1]
[2,1,8,7,4,3,6,5]=>[1,2,1,1,2,1]
[5,8,3,7,4,2,6,1]=>[2,2,1,2,1]
[3,8,7,4,1,2,6,5]=>[2,1,1,3,1]
[7,8,1,3,5,2,6,4]=>[2,3,2,1]
[5,8,7,3,2,6,1,4]=>[2,1,1,2,2]
[2,8,6,3,1,5,7,4]=>[2,1,1,3,1]
[8,1,6,3,2,5,4,7]=>[1,2,1,2,2]
[2,8,4,1,6,3,7,5]=>[2,1,2,2,1]
[4,8,1,2,7,6,3,5]=>[2,3,1,2]
[3,8,4,2,5,7,1,6]=>[2,1,3,2]
[6,8,3,5,2,7,4,1]=>[2,2,2,1,1]
[2,1,5,3,8,7,6,4]=>[1,2,2,1,1,1]
[6,5,3,2,8,7,1,4]=>[1,1,1,2,1,2]
[7,5,2,4,8,1,6,3]=>[1,1,3,2,1]
[3,4,2,8,5,7,6,1]=>[2,2,2,1,1]
[2,4,1,8,7,6,5,3]=>[2,2,1,1,1,1]
[8,4,2,1,7,5,3,6]=>[1,1,1,2,1,2]
[4,3,1,8,6,7,5,2]=>[1,1,2,2,1,1]
[3,1,4,8,6,5,7,2]=>[1,3,1,2,1]
[7,1,6,5,4,8,2,3]=>[1,2,1,2,2]
[3,7,5,6,8,4,2,1]=>[2,3,1,1,1]
[5,7,1,6,8,2,4,3]=>[2,3,2,1]
[8,6,2,5,1,7,4,3]=>[1,1,2,2,1,1]
[5,6,2,1,8,7,3,4]=>[2,1,2,1,2]
[4,6,2,5,8,3,7,1]=>[2,3,2,1]
[7,5,2,6,3,8,1,4]=>[1,1,2,2,2]
[4,1,2,3,6,8,7,5]=>[1,5,1,1]
[2,4,3,1,8,5,6,7]=>[2,1,2,3]
[7,5,2,8,3,4,6,1]=>[1,1,2,3,1]
[5,6,2,8,4,3,1,7]=>[2,2,1,1,2]
[4,7,2,8,1,5,3,6]=>[2,2,2,2]
[8,7,2,1,4,5,6,3]=>[1,1,1,4,1]
[3,6,8,7,1,5,4,2]=>[3,1,2,1,1]
[5,7,8,6,3,4,1,2]=>[3,1,2,2]
[7,1,8,5,4,3,6,2]=>[1,2,1,1,2,1]
[2,7,8,4,5,3,6,1]=>[3,2,2,1]
[5,7,3,8,1,4,6,2]=>[2,2,3,1]
[2,1,7,8,5,4,6,3]=>[1,3,1,2,1]
[2,1,5,8,4,6,3,7]=>[1,3,2,2]
[6,5,3,8,4,1,2,7]=>[1,1,2,1,3]
[7,5,8,4,3,6,2,1]=>[1,2,1,2,1,1]
[2,4,8,3,5,6,1,7]=>[3,3,2]
[4,1,8,3,6,5,2,7]=>[1,2,2,1,2]
[3,4,8,1,7,2,5,6]=>[3,2,3]
[8,4,1,3,7,2,6,5]=>[1,1,3,2,1]
[3,1,8,2,4,7,6,5]=>[1,2,3,1,1]
[2,3,8,1,4,6,7,5]=>[3,4,1]
[4,3,8,2,5,1,7,6]=>[1,2,2,2,1]
[6,3,8,4,2,5,7,1]=>[1,2,1,3,1]
[7,4,3,8,2,5,1,6]=>[1,1,2,2,2]
[2,1,4,8,3,5,7,6]=>[1,3,3,1]
[6,8,2,4,3,5,1,7]=>[2,2,2,2]
[4,8,2,3,5,1,6,7]=>[2,3,3]
[3,8,2,1,4,6,5,7]=>[2,1,3,2]
[2,8,1,3,4,5,7,6]=>[2,5,1]
[2,8,4,1,6,5,3,7]=>[2,1,2,1,2]
[2,8,4,1,6,5,7,3]=>[2,1,2,2,1]
[2,8,7,6,1,4,3,5]=>[2,1,1,2,2]
[2,8,5,6,7,4,3,1]=>[2,3,1,1,1]
[7,5,8,6,1,4,2,3]=>[1,2,1,2,2]
[3,5,7,6,1,4,2,8]=>[3,1,2,2]
[3,5,7,2,4,1,6,8]=>[3,2,3]
[7,5,8,2,4,1,6,3]=>[1,2,2,2,1]
[2,8,5,3,4,7,6,1]=>[2,1,3,1,1]
[2,8,5,3,4,1,7,6]=>[2,1,2,2,1]
[2,8,5,3,4,1,6,7]=>[2,1,2,3]
[2,8,7,6,1,4,5,3]=>[2,1,1,3,1]
[2,8,5,3,6,1,7,4]=>[2,1,2,2,1]
[2,8,5,6,7,4,1,3]=>[2,3,1,2]
[2,8,5,3,4,7,1,6]=>[2,1,3,2]
[2,8,5,3,4,6,1,7]=>[2,1,3,2]
[2,8,5,3,4,6,7,1]=>[2,1,4,1]
[3,5,7,2,4,6,1,8]=>[3,3,2]
[6,5,2,7,3,1,4,8]=>[1,1,2,1,3]
[6,5,2,8,3,1,7,4]=>[1,1,2,1,2,1]
[6,5,2,8,3,1,4,7]=>[1,1,2,1,3]
[7,5,8,2,4,6,3,1]=>[1,2,3,1,1]
[7,5,8,6,1,4,3,2]=>[1,2,1,2,1,1]
[6,5,8,2,1,3,7,4]=>[1,2,1,3,1]
[3,5,6,2,1,8,7,4]=>[3,1,2,1,1]
[3,5,7,6,1,4,8,2]=>[3,1,3,1]
[3,5,7,2,4,1,8,6]=>[3,2,2,1]
[3,5,7,2,4,6,8,1]=>[3,4,1]
[6,5,2,7,3,1,8,4]=>[1,1,2,1,2,1]
[4,5,2,6,3,1,7,8]=>[2,2,1,3]
[4,1,2,3,7,6,8,5]=>[1,4,2,1]
[6,5,2,7,3,4,8,1]=>[1,1,2,3,1]
[5,1,6,7,4,3,8,2]=>[1,3,1,2,1]
[5,1,2,6,4,8,7,3]=>[1,3,2,1,1]
[5,1,2,8,6,4,7,3]=>[1,3,1,2,1]
[5,1,6,8,7,3,4,2]=>[1,3,1,2,1]
[6,5,2,8,3,7,4,1]=>[1,1,2,2,1,1]
[4,1,2,3,8,7,5,6]=>[1,4,1,2]
[4,1,2,3,8,6,5,7]=>[1,4,1,2]
[4,1,2,3,8,6,7,5]=>[1,4,2,1]
[4,1,2,3,7,6,5,8]=>[1,4,1,2]
[4,1,2,3,8,5,7,6]=>[1,4,2,1]
[7,1,6,8,4,3,5,2]=>[1,3,1,2,1]
[6,1,2,8,4,5,7,3]=>[1,3,3,1]
[5,6,8,2,3,1,7,4]=>[3,2,2,1]
[6,5,8,2,4,3,1,7]=>[1,2,2,1,2]
[6,5,8,2,4,3,7,1]=>[1,2,2,2,1]
[7,5,2,8,3,4,1,6]=>[1,1,2,2,2]
[6,5,2,8,3,7,1,4]=>[1,1,2,2,2]
[6,5,2,7,3,4,1,8]=>[1,1,2,2,2]
[5,1,6,7,4,3,2,8]=>[1,3,1,1,2]
[5,1,6,8,7,3,2,4]=>[1,3,1,1,2]
[7,1,6,8,4,3,2,5]=>[1,3,1,1,2]
[5,7,8,6,3,4,2,1]=>[3,1,2,1,1]
[4,1,8,3,6,5,7,2]=>[1,2,2,2,1]
[4,1,8,3,6,2,7,5]=>[1,2,2,2,1]
[3,1,4,8,6,2,7,5]=>[1,3,1,2,1]
[3,1,4,8,6,5,2,7]=>[1,3,1,1,2]
[7,1,6,5,8,3,2,4]=>[1,2,2,1,2]
[4,1,6,7,8,3,2,5]=>[1,4,1,2]
[4,1,6,5,7,3,2,8]=>[1,2,2,1,2]
[4,5,2,6,3,7,1,8]=>[2,2,2,2]
[4,5,2,7,3,8,1,6]=>[2,2,2,2]
[3,5,6,2,4,8,7,1]=>[3,3,1,1]
[3,5,6,2,4,8,1,7]=>[3,3,2]
[3,7,5,6,8,4,1,2]=>[2,3,1,2]
[3,6,5,2,8,1,7,4]=>[2,1,2,2,1]
[6,1,2,5,8,4,7,3]=>[1,4,2,1]
[7,1,6,5,8,3,4,2]=>[1,2,2,2,1]
[7,5,2,6,3,8,4,1]=>[1,1,2,2,1,1]
[4,1,2,3,5,8,7,6]=>[1,5,1,1]
[4,1,2,3,7,8,6,5]=>[1,5,1,1]
[4,5,2,7,3,8,6,1]=>[2,2,2,1,1]
[4,1,6,7,8,3,5,2]=>[1,4,2,1]
[4,1,2,6,8,5,7,3]=>[1,4,2,1]
[4,1,2,5,6,8,7,3]=>[1,5,1,1]
[4,5,2,6,3,7,8,1]=>[2,2,3,1]
[7,8,5,6,1,4,3,2]=>[2,2,2,1,1]
[7,8,4,2,1,5,3,6]=>[2,1,1,2,2]
[7,8,2,1,6,5,3,4]=>[2,1,2,1,2]
[6,4,1,2,5,7,3,8]=>[1,1,4,2]
[2,4,8,1,5,7,3,6]=>[3,3,2]
[4,3,8,1,7,2,5,6]=>[1,2,2,3]
[6,3,1,4,7,2,5,8]=>[1,1,3,3]
[7,8,3,4,5,1,6,2]=>[2,3,2,1]
[7,8,3,5,4,2,1,6]=>[2,2,1,1,2]
[7,8,4,1,2,3,6,5]=>[2,1,4,1]
[7,8,3,6,5,4,1,2]=>[2,2,1,1,2]
[7,8,2,1,5,3,4,6]=>[2,1,2,3]
[7,8,2,6,4,1,3,5]=>[2,2,1,3]
[7,8,2,5,6,4,1,3]=>[2,3,1,2]
[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]
[6,2,1,7,5,4,3,8]=>[1,1,2,1,1,2]
[2,1,8,7,5,4,3,6]=>[1,2,1,1,1,2]
[1,3,8,2,6,4,7,5]=>[3,2,2,1]
[5,3,7,1,6,4,8,2]=>[1,2,2,2,1]
[5,3,6,2,7,4,1,8]=>[1,2,2,1,2]
[6,1,2,5,8,7,4,3]=>[1,4,1,1,1]
[6,3,1,8,4,2,7,5]=>[1,1,2,1,2,1]
[6,4,2,1,5,3,8,7]=>[1,1,1,2,2,1]
[6,4,3,7,5,8,1,2]=>[1,1,2,2,2]
[4,3,8,7,5,6,1,2]=>[1,2,1,2,2]
[2,4,7,1,5,3,6,8]=>[3,2,3]
[1,3,7,6,4,2,8,5]=>[3,1,1,2,1]
[2,1,7,5,6,8,4,3]=>[1,2,3,1,1]
[3,7,2,8,6,4,1,5]=>[2,2,1,1,2]
[3,8,1,7,6,4,5,2]=>[2,2,1,2,1]
[1,8,5,7,3,6,4,2]=>[2,2,2,1,1]
[2,7,5,8,3,6,1,4]=>[2,2,2,2]
[1,5,6,8,2,4,7,3]=>[4,3,1]
[2,6,8,5,3,1,4,7]=>[3,1,1,3]
[2,6,1,4,7,3,5,8]=>[2,3,3]
[5,6,7,3,8,4,1,2]=>[3,2,1,2]
[5,2,8,1,4,7,3,6]=>[1,2,3,2]
[4,6,7,5,2,1,3,8]=>[3,1,1,3]
[4,5,6,7,2,8,1,3]=>[4,2,2]
[4,5,7,6,1,8,3,2]=>[3,1,2,1,1]
[1,5,8,6,2,7,3,4]=>[3,1,2,2]
[1,6,5,8,3,2,7,4]=>[2,2,1,2,1]
[4,6,5,7,1,2,8,3]=>[2,2,3,1]
[4,7,5,6,3,1,8,2]=>[2,2,1,2,1]
[5,1,6,3,4,2,8,7]=>[1,2,2,2,1]
[5,7,1,4,2,3,8,6]=>[2,2,3,1]
[5,7,6,4,3,8,1,2]=>[2,1,1,2,2]
[6,3,4,5,8,7,1,2]=>[1,4,1,2]
[6,2,4,1,8,3,7,5]=>[1,2,2,2,1]
[6,2,3,5,4,8,1,7]=>[1,3,2,2]
[6,1,3,4,5,8,7,2]=>[1,5,1,1]
[5,1,4,2,7,6,8,3]=>[1,2,2,2,1]
[1,6,2,4,7,8,3,5]=>[2,4,2]
[5,7,2,4,1,6,3,8]=>[2,2,2,2]
[6,1,4,2,8,5,3,7]=>[1,2,2,1,2]
[6,7,5,8,1,4,3,2]=>[2,2,2,1,1]
[5,8,7,6,3,4,1,2]=>[2,1,1,2,2]
[5,8,7,6,2,3,1,4]=>[2,1,1,2,2]
[4,1,7,2,6,5,3,8]=>[1,2,2,1,2]
[4,8,2,1,5,6,3,7]=>[2,1,3,2]
[4,2,7,8,1,6,3,5]=>[1,3,2,2]
[2,1,8,7,6,5,3,4]=>[1,2,1,1,1,2]
[3,1,4,7,8,2,6,5]=>[1,4,2,1]
[3,1,7,4,5,6,8,2]=>[1,2,4,1]
[4,2,7,1,6,3,8,5]=>[1,2,2,2,1]
[4,3,7,5,6,8,1,2]=>[1,2,3,2]
[4,8,6,3,5,7,1,2]=>[2,1,3,2]
[4,8,1,2,5,3,7,6]=>[2,3,2,1]
[3,8,6,5,2,4,1,7]=>[2,1,1,2,2]
[3,8,5,6,1,4,7,2]=>[2,2,3,1]
[5,3,7,8,2,1,6,4]=>[1,3,1,2,1]
[5,2,8,7,1,6,4,3]=>[1,2,1,2,1,1]
[1,6,8,7,5,2,4,3]=>[3,1,1,2,1]
[3,6,7,8,5,1,4,2]=>[4,1,2,1]
[3,7,6,8,5,2,1,4]=>[2,2,1,1,2]
[3,7,8,5,1,2,4,6]=>[3,1,4]
[3,7,1,6,4,2,5,8]=>[2,2,1,3]
[4,1,8,6,2,3,5,7]=>[1,2,1,4]
[4,7,8,6,3,5,1,2]=>[3,1,2,2]
[3,8,7,6,5,4,1,2]=>[2,1,1,1,1,2]
[2,1,7,6,5,3,4,8]=>[1,2,1,1,3]
[2,8,1,6,4,5,3,7]=>[2,2,2,2]
[2,8,7,5,1,4,3,6]=>[2,1,1,2,2]
[2,8,6,7,5,1,3,4]=>[2,2,1,3]
[2,7,8,6,5,4,1,3]=>[3,1,1,1,2]
[6,3,1,2,7,4,8,5]=>[1,1,3,2,1]
[6,4,2,7,1,3,8,5]=>[1,1,2,3,1]
[7,4,2,5,1,3,8,6]=>[1,1,2,3,1]
[7,5,3,6,1,8,2,4]=>[1,1,2,2,2]
[8,5,3,6,1,7,2,4]=>[1,1,2,2,2]
[7,3,6,2,4,8,1,5]=>[1,2,3,2]
[4,3,7,1,2,5,8,6]=>[1,2,4,1]
[3,6,2,7,1,4,8,5]=>[2,2,3,1]
[5,3,6,7,1,2,8,4]=>[1,3,3,1]
[6,3,7,4,1,2,8,5]=>[1,2,1,3,1]
[4,7,1,5,2,3,8,6]=>[2,2,3,1]
[3,7,5,1,2,4,8,6]=>[2,1,4,1]
[7,6,4,2,3,8,1,5]=>[1,1,1,3,2]
[8,6,4,2,3,7,1,5]=>[1,1,1,3,2]
[4,7,6,3,8,1,2,5]=>[2,1,2,3]
[5,7,4,2,3,8,1,6]=>[2,1,3,2]
[3,7,6,1,4,8,2,5]=>[2,1,3,2]
[5,7,2,6,1,8,3,4]=>[2,2,2,2]
[6,4,7,5,2,8,1,3]=>[1,2,1,2,2]
[7,4,8,5,2,6,1,3]=>[1,2,1,2,2]
[5,8,2,6,3,7,1,4]=>[2,2,2,2]
[3,8,6,1,2,7,4,5]=>[2,1,3,2]
[3,8,6,2,4,7,1,5]=>[2,1,3,2]
[6,8,4,3,7,1,2,5]=>[2,1,2,3]
[6,8,5,3,7,1,2,4]=>[2,1,2,3]
[3,8,5,7,1,2,4,6]=>[2,2,4]
[2,8,5,7,1,3,4,6]=>[2,2,4]
[4,8,6,2,7,1,3,5]=>[2,1,2,3]
[6,3,7,5,8,1,2,4]=>[1,2,2,3]
[2,7,6,4,8,1,3,5]=>[2,1,2,3]
[2,6,5,8,1,3,4,7]=>[2,2,4]
[3,6,5,8,1,2,4,7]=>[2,2,4]
[2,5,7,4,8,1,3,6]=>[3,2,3]
[5,4,6,7,2,8,1,3]=>[1,3,2,2]
[4,6,3,7,1,8,2,5]=>[2,2,2,2]
[3,5,7,1,4,8,2,6]=>[3,3,2]
[5,3,7,2,4,8,1,6]=>[1,2,3,2]
[5,4,7,3,8,1,2,6]=>[1,2,2,3]
[7,4,6,3,8,1,2,5]=>[1,2,2,3]
[8,4,6,3,7,1,2,5]=>[1,2,2,3]
[8,4,1,6,7,2,3,5]=>[1,1,3,3]
[7,4,1,6,8,2,3,5]=>[1,1,3,3]
[5,4,1,7,8,2,3,6]=>[1,1,3,3]
[6,5,3,7,1,8,2,4]=>[1,1,2,2,2]
[6,5,1,2,7,8,3,4]=>[1,1,4,2]
[5,3,6,4,7,8,1,2]=>[1,2,3,2]
[6,3,7,4,8,5,1,2]=>[1,2,2,1,2]
[4,7,1,5,8,6,2,3]=>[2,3,1,2]
[7,5,1,2,8,6,3,4]=>[1,1,3,1,2]
[7,5,3,8,1,6,2,4]=>[1,1,2,2,2]
[7,4,1,8,6,2,3,5]=>[1,1,2,1,3]
[7,6,1,8,5,2,3,4]=>[1,1,2,1,3]
[8,6,1,7,5,2,3,4]=>[1,1,2,1,3]
[5,7,2,8,1,6,3,4]=>[2,2,2,2]
[6,4,7,8,2,5,1,3]=>[1,3,2,2]
[6,3,7,8,5,1,2,4]=>[1,3,1,3]
[3,6,8,2,7,1,4,5]=>[3,2,3]
[2,4,8,7,1,3,5,6]=>[3,1,4]
[4,3,8,7,1,2,5,6]=>[1,2,1,4]
[5,3,8,7,1,2,4,6]=>[1,2,1,4]
[8,3,7,6,1,2,4,5]=>[1,2,1,4]
[8,4,7,6,1,2,3,5]=>[1,2,1,4]
[5,4,8,7,1,2,3,6]=>[1,2,1,4]
[3,5,8,7,1,2,4,6]=>[3,1,4]
[2,5,8,7,1,3,4,6]=>[3,1,4]
[4,6,8,2,7,1,3,5]=>[3,2,3]
[4,7,1,8,6,2,3,5]=>[2,2,1,3]
[7,5,8,6,4,1,2,3]=>[1,2,1,1,3]
[6,8,4,7,5,1,2,3]=>[2,2,1,3]
[5,8,7,1,6,2,3,4]=>[2,1,2,3]
[2,8,7,6,1,3,4,5]=>[2,1,1,4]
[3,8,7,6,1,2,4,5]=>[2,1,1,4]
[4,8,7,6,1,2,3,5]=>[2,1,1,4]
[5,6,3,1,4,2,8,7]=>[2,1,2,2,1]
[7,5,3,8,2,1,6,4]=>[1,1,2,1,2,1]
[3,8,7,4,5,1,6,2]=>[2,1,2,2,1]
[6,7,1,4,5,8,2,3]=>[2,4,2]
[2,1,7,8,5,3,6,4]=>[1,3,1,2,1]
[5,7,3,8,1,2,6,4]=>[2,2,3,1]
[8,7,1,4,5,3,2,6]=>[1,1,3,1,2]
[2,7,8,4,1,6,5,3]=>[3,1,2,1,1]
[7,1,8,4,2,6,5,3]=>[1,2,1,2,1,1]
[7,5,1,4,8,6,3,2]=>[1,1,3,1,1,1]
[6,5,3,1,8,4,7,2]=>[1,1,1,2,2,1]
[6,4,3,8,1,5,7,2]=>[1,1,2,3,1]
[8,6,3,1,2,5,7,4]=>[1,1,1,4,1]
[8,7,1,4,2,6,5,3]=>[1,1,2,2,1,1]
[7,3,8,4,1,6,5,2]=>[1,2,1,2,1,1]
[3,6,4,5,7,2,8,1]=>[2,3,2,1]
[5,3,2,7,4,6,8,1]=>[1,1,2,3,1]
[7,5,3,6,2,4,8,1]=>[1,1,2,3,1]
[6,3,2,5,1,8,4,7]=>[1,1,2,2,2]
[8,5,3,6,2,7,1,4]=>[1,1,2,2,2]
[8,2,6,3,4,7,1,5]=>[1,2,3,2]
[7,2,6,3,4,5,8,1]=>[1,2,4,1]
[6,2,7,3,4,5,8,1]=>[1,2,4,1]
[3,6,2,7,4,5,8,1]=>[2,2,3,1]
[4,2,5,7,3,6,8,1]=>[1,3,3,1]
[5,4,7,6,2,3,8,1]=>[1,2,1,3,1]
[6,7,3,5,2,4,8,1]=>[2,2,3,1]
[3,7,6,2,4,5,8,1]=>[2,1,4,1]
[2,7,6,3,4,5,8,1]=>[2,1,4,1]
[6,5,3,1,2,8,4,7]=>[1,1,1,3,2]
[8,6,5,2,3,7,1,4]=>[1,1,1,3,2]
[8,5,2,1,7,3,4,6]=>[1,1,1,2,3]
[7,5,2,1,8,3,4,6]=>[1,1,1,2,3]
[1,6,3,2,8,4,5,7]=>[2,1,2,3]
[5,6,2,3,1,8,4,7]=>[2,2,2,2]
[4,2,6,5,1,8,3,7]=>[1,2,1,2,2]
[5,4,8,6,2,7,1,3]=>[1,2,1,2,2]
[6,8,3,5,2,7,1,4]=>[2,2,2,2]
[7,8,5,2,3,6,1,4]=>[2,1,3,2]
[6,8,2,1,7,3,4,5]=>[2,1,2,3]
[1,8,6,3,7,2,4,5]=>[2,1,2,3]
[1,8,2,7,3,4,5,6]=>[2,2,4]
[2,8,1,7,3,4,5,6]=>[2,2,4]
[3,8,6,1,7,2,4,5]=>[2,1,2,3]
[4,8,1,5,7,2,3,6]=>[2,3,3]
[4,2,8,3,7,1,5,6]=>[1,2,2,3]
[4,1,7,5,8,2,3,6]=>[1,2,2,3]
[1,7,3,8,2,4,5,6]=>[2,2,4]
[8,1,2,7,3,4,5,6]=>[1,3,4]
[3,6,2,7,1,8,4,5]=>[2,2,2,2]
[6,3,7,1,2,8,4,5]=>[1,2,3,2]
[7,2,6,1,8,3,4,5]=>[1,2,2,3]
[8,2,6,1,7,3,4,5]=>[1,2,2,3]
[7,3,1,5,8,2,4,6]=>[1,1,3,3]
[3,2,1,5,8,4,6,7]=>[1,1,3,3]
[5,4,1,3,6,8,2,7]=>[1,1,4,2]
[1,5,3,4,6,8,2,7]=>[2,4,2]
[4,3,5,1,6,8,2,7]=>[1,2,3,2]
[5,4,6,3,8,7,1,2]=>[1,2,2,1,2]
[3,6,4,5,8,7,1,2]=>[2,3,1,2]
[6,5,3,4,8,7,1,2]=>[1,1,3,1,2]
[5,3,2,8,7,1,4,6]=>[1,1,2,1,3]
[5,3,1,8,7,2,4,6]=>[1,1,2,1,3]
[8,5,3,7,6,1,2,4]=>[1,1,2,1,3]
[6,1,8,3,7,2,4,5]=>[1,2,2,3]
[6,3,8,1,7,2,4,5]=>[1,2,2,3]
[7,6,8,2,3,5,1,4]=>[1,2,3,2]
[3,7,8,2,4,6,1,5]=>[3,3,2]
[6,7,3,8,2,5,1,4]=>[2,2,2,2]
[5,4,7,8,2,6,1,3]=>[1,3,2,2]
[4,2,5,8,7,1,3,6]=>[1,3,1,3]
[3,6,2,8,7,1,4,5]=>[2,2,1,3]
[3,7,8,1,6,2,4,5]=>[3,2,3]
[2,3,8,7,1,4,5,6]=>[3,1,4]
[7,2,8,6,1,3,4,5]=>[1,2,1,4]
[2,1,8,7,3,4,5,6]=>[1,2,1,4]
[8,2,7,6,1,3,4,5]=>[1,2,1,4]
[1,2,8,7,3,4,5,6]=>[3,1,4]
[1,3,8,7,2,4,5,6]=>[3,1,4]
[1,7,8,3,6,2,4,5]=>[3,2,3]
[4,1,5,8,7,2,3,6]=>[1,3,1,3]
[5,4,8,7,6,1,2,3]=>[1,2,1,1,3]
[6,8,3,7,5,1,2,4]=>[2,2,1,3]
[7,8,6,2,5,1,3,4]=>[2,1,2,3]
[8,1,6,7,3,2,5,4]=>[1,3,1,2,1]
[8,1,6,7,3,2,4,5]=>[1,3,1,3]
[8,1,5,3,7,2,4,6]=>[1,2,2,3]
[8,1,5,3,6,2,4,7]=>[1,2,2,3]
[7,5,1,3,6,2,4,8]=>[1,1,3,3]
[7,5,8,3,6,2,4,1]=>[1,2,2,2,1]
[7,4,8,3,2,6,5,1]=>[1,2,1,2,1,1]
[7,4,1,3,2,6,5,8]=>[1,1,2,2,2]
[8,1,4,3,2,6,5,7]=>[1,2,1,2,2]
[8,1,4,3,2,7,5,6]=>[1,2,1,2,2]
[8,1,4,3,2,7,6,5]=>[1,2,1,2,1,1]
[8,1,5,4,6,7,2,3]=>[1,2,3,2]
[8,1,5,3,6,2,7,4]=>[1,2,2,2,1]
[8,1,4,3,2,6,7,5]=>[1,2,1,3,1]
[8,1,4,3,2,5,7,6]=>[1,2,1,3,1]
[8,1,4,3,2,5,6,7]=>[1,2,1,4]
[7,4,1,3,2,5,6,8]=>[1,1,2,4]
[7,4,8,3,2,5,6,1]=>[1,2,1,3,1]
[6,4,3,8,2,5,7,1]=>[1,1,2,3,1]
[6,4,3,1,2,5,8,7]=>[1,1,1,4,1]
[7,4,1,3,2,5,8,6]=>[1,1,2,3,1]
[7,4,1,3,2,6,8,5]=>[1,1,2,3,1]
[7,5,1,3,6,2,8,4]=>[1,1,3,2,1]
[7,5,1,4,6,8,2,3]=>[1,1,4,2]
[7,5,8,3,6,2,1,4]=>[1,2,2,1,2]
[7,4,8,3,2,6,1,5]=>[1,2,1,2,2]
[7,4,8,3,2,5,1,6]=>[1,2,1,2,2]
[6,4,3,8,2,5,1,7]=>[1,1,2,2,2]
[6,4,3,7,2,5,8,1]=>[1,1,2,3,1]
[5,4,3,2,8,6,1,7]=>[1,1,1,2,1,2]
[5,4,3,2,8,7,1,6]=>[1,1,1,2,1,2]
[6,5,3,8,7,2,1,4]=>[1,1,2,1,1,2]
[6,5,4,8,7,1,2,3]=>[1,1,2,1,3]
[6,5,4,1,7,8,2,3]=>[1,1,1,3,2]
[6,5,3,1,7,2,8,4]=>[1,1,1,2,2,1]
[6,4,3,1,2,7,8,5]=>[1,1,1,4,1]
[5,4,3,2,1,8,6,7]=>[1,1,1,1,2,2]
[6,5,3,1,8,2,7,4]=>[1,1,1,2,2,1]
[6,5,4,1,8,7,2,3]=>[1,1,1,2,1,2]
[7,5,1,4,8,6,2,3]=>[1,1,3,1,2]
[7,4,1,3,2,8,6,5]=>[1,1,2,2,1,1]
[7,4,1,3,2,8,5,6]=>[1,1,2,2,2]
[6,4,3,1,2,8,5,7]=>[1,1,1,3,2]
[6,4,3,1,2,7,5,8]=>[1,1,1,3,2]
[6,4,3,8,2,7,5,1]=>[1,1,2,2,1,1]
[6,5,3,8,7,2,4,1]=>[1,1,2,1,2,1]
[6,5,3,1,7,2,4,8]=>[1,1,1,2,3]
[6,5,3,1,8,2,4,7]=>[1,1,1,2,3]
[7,5,1,3,8,2,4,6]=>[1,1,3,3]
[7,6,1,8,3,2,4,5]=>[1,1,2,1,3]
[7,6,1,8,4,5,2,3]=>[1,1,2,2,2]
[7,6,8,1,4,5,2,3]=>[1,2,3,2]
[7,6,8,1,3,2,5,4]=>[1,2,2,2,1]
[6,5,3,7,8,2,4,1]=>[1,1,3,2,1]
[6,4,3,7,2,8,5,1]=>[1,1,2,2,1,1]
[6,4,3,7,2,1,5,8]=>[1,1,2,1,3]
[7,4,8,3,2,1,5,6]=>[1,2,1,1,3]
[7,4,8,3,2,1,6,5]=>[1,2,1,1,2,1]
[7,5,8,3,1,2,6,4]=>[1,2,1,3,1]
[7,5,8,4,1,6,2,3]=>[1,2,1,2,2]
[6,5,4,8,1,7,2,3]=>[1,1,2,2,2]
[6,5,3,8,1,2,7,4]=>[1,1,2,3,1]
[5,4,3,2,8,1,7,6]=>[1,1,1,2,2,1]
[6,4,3,7,2,1,8,5]=>[1,1,2,1,2,1]
[6,5,3,7,1,2,8,4]=>[1,1,2,3,1]
[6,5,4,7,1,8,2,3]=>[1,1,2,2,2]
[6,5,3,7,8,2,1,4]=>[1,1,3,1,2]
[6,4,3,7,2,8,1,5]=>[1,1,2,2,2]
[5,4,3,2,7,8,1,6]=>[1,1,1,3,2]
[5,4,3,2,6,8,1,7]=>[1,1,1,3,2]
[5,6,2,1,3,4,8,7]=>[2,1,4,1]
[5,8,2,7,4,1,3,6]=>[2,2,1,3]
[5,3,7,8,2,1,4,6]=>[1,3,1,3]
[7,6,1,2,5,8,3,4]=>[1,1,4,2]
[2,1,7,8,4,3,5,6]=>[1,3,1,3]
[8,3,7,4,1,5,6,2]=>[1,2,1,3,1]
[7,8,1,2,5,4,6,3]=>[2,3,2,1]
[2,6,8,3,1,4,7,5]=>[3,1,3,1]
[6,1,8,3,2,4,5,7]=>[1,2,1,4]
[8,4,1,3,7,6,2,5]=>[1,1,3,1,2]
[5,8,7,4,2,1,6,3]=>[2,1,1,1,2,1]
[7,5,1,6,8,3,4,2]=>[1,1,3,2,1]
[6,5,2,1,8,7,4,3]=>[1,1,1,2,1,1,1]
[4,7,2,8,1,3,6,5]=>[2,2,3,1]
[7,3,8,6,1,2,5,4]=>[1,2,1,3,1]
[3,4,7,1,8,2,6,5]=>[3,2,2,1]
[1,8,2,4,3,5,6,7]=>[2,2,4]
[1,7,2,4,3,5,6,8]=>[2,2,4]
[1,6,2,4,3,5,7,8]=>[2,2,4]
[1,5,2,4,3,6,7,8]=>[2,2,4]
[1,6,2,5,3,4,7,8]=>[2,2,4]
[1,7,2,5,3,4,6,8]=>[2,2,4]
[1,8,2,5,3,4,6,7]=>[2,2,4]
[1,8,2,6,3,4,5,7]=>[2,2,4]
[1,7,2,6,3,4,5,8]=>[2,2,4]
[1,8,2,7,3,5,4,6]=>[2,2,2,2]
[1,7,2,8,3,5,4,6]=>[2,2,2,2]
[1,6,2,8,3,5,4,7]=>[2,2,2,2]
[1,5,2,8,3,6,4,7]=>[2,2,2,2]
[1,4,2,8,3,6,5,7]=>[2,2,2,2]
[1,3,2,8,4,6,5,7]=>[2,2,2,2]
[1,2,3,8,4,6,5,7]=>[4,2,2]
[1,2,3,7,4,6,5,8]=>[4,2,2]
[1,3,2,7,4,6,5,8]=>[2,2,2,2]
[1,4,2,7,3,6,5,8]=>[2,2,2,2]
[1,5,2,7,3,6,4,8]=>[2,2,2,2]
[1,6,2,7,3,5,4,8]=>[2,2,2,2]
[1,7,2,6,3,5,4,8]=>[2,2,2,2]
[1,8,2,6,3,5,4,7]=>[2,2,2,2]
[1,8,2,5,3,6,4,7]=>[2,2,2,2]
[1,7,2,5,3,6,4,8]=>[2,2,2,2]
[1,6,2,5,3,7,4,8]=>[2,2,2,2]
[1,5,2,4,3,7,6,8]=>[2,2,2,2]
[1,6,2,4,3,7,5,8]=>[2,2,2,2]
[1,7,2,4,3,6,5,8]=>[2,2,2,2]
[1,8,2,4,3,6,5,7]=>[2,2,2,2]
[1,8,2,3,4,6,5,7]=>[2,4,2]
[1,7,2,3,4,6,5,8]=>[2,4,2]
[1,8,2,3,4,7,5,6]=>[2,4,2]
[1,8,2,4,3,7,5,6]=>[2,2,2,2]
[1,7,2,4,3,8,5,6]=>[2,2,2,2]
[1,6,2,4,3,8,5,7]=>[2,2,2,2]
[1,5,2,4,3,8,6,7]=>[2,2,2,2]
[1,6,2,5,3,8,4,7]=>[2,2,2,2]
[1,7,2,5,3,8,4,6]=>[2,2,2,2]
[1,8,2,5,3,7,4,6]=>[2,2,2,2]
[1,8,2,6,3,7,4,5]=>[2,2,2,2]
[1,7,2,6,3,8,4,5]=>[2,2,2,2]
[1,2,3,8,4,7,5,6]=>[4,2,2]
[1,3,2,8,4,7,5,6]=>[2,2,2,2]
[1,4,2,8,3,7,5,6]=>[2,2,2,2]
[1,5,2,8,3,7,4,6]=>[2,2,2,2]
[1,6,2,8,3,7,4,5]=>[2,2,2,2]
[1,7,2,8,3,6,4,5]=>[2,2,2,2]
[1,8,2,7,3,6,4,5]=>[2,2,2,2]
[4,6,3,7,2,5,1,8]=>[2,2,2,2]
[4,6,3,7,5,2,1,8]=>[2,2,1,1,2]
[4,6,3,8,5,1,7,2]=>[2,2,1,2,1]
[4,6,3,8,5,1,2,7]=>[2,2,1,3]
[5,6,8,3,4,1,2,7]=>[3,2,3]
[5,6,8,3,4,1,7,2]=>[3,2,2,1]
[4,6,2,7,5,3,1,8]=>[2,2,1,1,2]
[5,6,7,2,4,3,1,8]=>[3,2,1,2]
[5,6,8,4,3,1,7,2]=>[3,1,1,2,1]
[5,6,8,4,3,1,2,7]=>[3,1,1,3]
[5,7,8,4,1,6,2,3]=>[3,1,2,2]
[5,7,8,4,1,6,3,2]=>[3,1,2,1,1]
[5,7,8,4,1,3,6,2]=>[3,1,3,1]
[5,6,8,4,2,1,7,3]=>[3,1,1,2,1]
[5,6,8,2,4,1,7,3]=>[3,2,2,1]
[4,6,2,8,5,1,7,3]=>[2,2,1,2,1]
[3,2,6,8,5,1,7,4]=>[1,3,1,2,1]
[3,2,6,8,5,1,4,7]=>[1,3,1,3]
[4,6,2,8,5,1,3,7]=>[2,2,1,3]
[5,6,8,2,4,1,3,7]=>[3,2,3]
[5,6,8,4,2,1,3,7]=>[3,1,1,3]
[5,7,8,4,1,3,2,6]=>[3,1,2,2]
[5,7,8,4,1,2,6,3]=>[3,1,3,1]
[5,7,8,4,1,2,3,6]=>[3,1,4]
[6,7,8,1,5,2,3,4]=>[3,2,3]
[6,7,8,1,5,2,4,3]=>[3,2,2,1]
[6,7,8,1,5,3,2,4]=>[3,2,1,2]
[6,7,8,1,3,5,2,4]=>[3,3,2]
[5,7,8,2,1,6,3,4]=>[3,1,2,2]
[4,7,2,8,1,6,3,5]=>[2,2,2,2]
[3,2,7,8,1,6,4,5]=>[1,3,2,2]
[3,2,7,8,1,6,5,4]=>[1,3,2,1,1]
[4,7,2,8,1,6,5,3]=>[2,2,2,1,1]
[5,7,8,2,1,6,4,3]=>[3,1,2,1,1]
[6,7,8,1,3,5,4,2]=>[3,3,1,1]
[6,7,8,1,5,3,4,2]=>[3,2,2,1]
[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]
[6,7,8,1,5,4,2,3]=>[3,2,1,2]
[6,7,8,1,4,5,2,3]=>[3,3,2]
[6,7,8,1,4,5,3,2]=>[3,3,1,1]
[6,7,8,1,4,3,5,2]=>[3,2,2,1]
[6,7,8,1,3,4,5,2]=>[3,4,1]
[5,7,8,2,1,4,6,3]=>[3,1,3,1]
[4,7,2,8,1,5,6,3]=>[2,2,3,1]
[3,2,7,8,1,5,6,4]=>[1,3,3,1]
[3,2,6,8,4,1,7,5]=>[1,3,1,2,1]
[4,6,2,8,3,1,7,5]=>[2,2,1,2,1]
[5,6,8,3,2,1,7,4]=>[3,1,1,2,1]
[5,7,8,3,1,4,6,2]=>[3,1,3,1]
[5,7,8,3,1,6,4,2]=>[3,1,2,1,1]
[5,7,8,3,1,6,2,4]=>[3,1,2,2]
[4,7,3,8,1,6,2,5]=>[2,2,2,2]
[4,7,3,8,1,6,5,2]=>[2,2,2,1,1]
[4,7,3,8,1,5,6,2]=>[2,2,3,1]
[4,6,3,8,2,1,7,5]=>[2,2,1,2,1]
[4,5,3,2,8,1,7,6]=>[2,1,2,2,1]
[4,5,2,3,8,1,7,6]=>[2,3,2,1]
[3,2,5,4,8,1,7,6]=>[1,2,2,2,1]
[4,5,3,2,8,1,6,7]=>[2,1,2,3]
[4,6,3,8,2,1,5,7]=>[2,2,1,3]
[4,7,3,8,1,5,2,6]=>[2,2,2,2]
[4,7,3,8,1,2,6,5]=>[2,2,3,1]
[4,7,3,8,1,2,5,6]=>[2,2,4]
[5,7,8,3,1,2,4,6]=>[3,1,4]
[5,7,8,3,1,2,6,4]=>[3,1,3,1]
[5,7,8,3,1,4,2,6]=>[3,1,2,2]
[5,6,8,3,2,1,4,7]=>[3,1,1,3]
[3,2,7,8,1,5,4,6]=>[1,3,2,2]
[5,7,8,2,1,4,3,6]=>[3,1,2,2]
[6,7,8,1,3,4,2,5]=>[3,3,2]
[6,7,8,1,4,3,2,5]=>[3,2,1,2]
[6,7,8,1,4,2,5,3]=>[3,2,2,1]
[6,7,8,1,4,2,3,5]=>[3,2,3]
[6,7,8,1,2,5,3,4]=>[3,3,2]
[6,7,8,1,2,5,4,3]=>[3,3,1,1]
[6,7,8,1,2,4,5,3]=>[3,4,1]
[6,7,8,1,3,2,5,4]=>[3,2,2,1]
[5,7,8,2,1,3,6,4]=>[3,1,3,1]
[3,2,7,8,1,4,6,5]=>[1,3,3,1]
[6,7,8,1,3,2,4,5]=>[3,2,3]
[6,7,8,1,2,4,3,5]=>[3,3,2]
[6,7,8,1,2,3,5,4]=>[3,4,1]
[7,2,8,5,1,6,4,3]=>[1,2,1,2,1,1]
[1,3,7,5,2,6,4,8]=>[3,1,2,2]
[1,3,7,5,4,2,6,8]=>[3,1,1,3]
[7,2,8,5,4,1,6,3]=>[1,2,1,1,2,1]
[2,8,5,4,3,1,7,6]=>[2,1,1,1,2,1]
[2,8,4,5,6,1,7,3]=>[2,3,2,1]
[2,8,6,5,7,3,1,4]=>[2,1,2,1,2]
[2,8,4,5,3,7,1,6]=>[2,2,2,2]
[2,8,4,3,5,6,1,7]=>[2,1,3,2]
[7,2,8,4,5,6,1,3]=>[1,2,3,2]
[1,6,3,7,5,2,4,8]=>[2,2,1,3]
[6,2,3,8,5,1,7,4]=>[1,3,1,2,1]
[6,3,2,8,5,1,4,7]=>[1,1,2,1,3]
[7,4,8,2,5,6,3,1]=>[1,2,3,1,1]
[7,4,8,5,2,1,3,6]=>[1,2,1,1,3]
[6,4,8,5,1,3,7,2]=>[1,2,1,3,1]
[6,3,7,5,2,1,8,4]=>[1,2,1,1,2,1]
[4,3,7,5,1,2,8,6]=>[1,2,1,3,1]
[4,3,7,1,5,6,8,2]=>[1,2,4,1]
[3,6,1,7,5,2,8,4]=>[2,2,1,2,1]
[3,4,1,2,7,6,8,5]=>[2,3,2,1]
[3,4,2,1,7,5,8,6]=>[2,1,2,2,1]
[3,6,5,7,1,4,8,2]=>[2,2,3,1]
[6,5,2,7,4,1,8,3]=>[1,1,2,1,2,1]
[3,5,2,6,4,8,7,1]=>[2,2,2,1,1]
[5,3,1,8,6,4,7,2]=>[1,1,2,1,2,1]
[5,6,1,8,7,2,4,3]=>[2,2,1,2,1]
[6,3,5,8,2,7,4,1]=>[1,3,2,1,1]
[6,5,8,4,2,3,7,1]=>[1,2,1,3,1]
[6,2,5,8,3,7,1,4]=>[1,3,2,2]
[1,6,5,7,3,4,2,8]=>[2,2,2,2]
[1,5,2,7,4,6,3,8]=>[2,2,2,2]
[5,2,1,8,7,6,3,4]=>[1,1,2,1,1,2]
[7,1,3,8,4,6,2,5]=>[1,3,2,2]
[2,3,4,8,6,1,7,5]=>[4,1,2,1]
[2,3,4,8,6,5,1,7]=>[4,1,1,2]
[2,7,3,5,8,6,1,4]=>[2,3,1,2]
[3,2,4,7,8,6,1,5]=>[1,4,1,2]
[1,5,4,6,2,7,3,8]=>[2,2,2,2]
[5,2,4,7,1,8,3,6]=>[1,3,2,2]
[5,3,6,4,1,8,7,2]=>[1,2,1,2,1,1]
[5,3,6,1,4,8,2,7]=>[1,2,3,2]
[7,3,5,6,8,4,2,1]=>[1,4,1,1,1]
[6,3,5,1,8,2,7,4]=>[1,2,2,2,1]
[2,6,1,5,8,4,7,3]=>[2,3,2,1]
[2,7,6,5,8,3,4,1]=>[2,1,2,2,1]
[5,7,1,6,3,8,4,2]=>[2,2,2,1,1]
[3,2,4,1,7,8,5,6]=>[1,2,3,2]
[3,1,4,2,7,8,6,5]=>[1,2,3,1,1]
[5,1,4,7,2,8,6,3]=>[1,3,2,1,1]
[3,6,4,7,8,2,5,1]=>[2,3,2,1]
[3,1,4,6,8,5,7,2]=>[1,4,2,1]
[6,3,4,5,7,1,8,2]=>[1,4,2,1]
[2,5,4,6,1,7,8,3]=>[2,2,3,1]
[7,2,1,4,3,6,5,8]=>[1,1,2,2,2]
[7,3,4,1,2,6,5,8]=>[1,2,3,2]
[7,4,3,2,1,6,5,8]=>[1,1,1,1,2,2]
[7,6,3,2,5,4,1,8]=>[1,1,1,2,1,2]
[6,7,3,2,5,4,8,1]=>[2,1,2,2,1]
[1,8,3,2,5,4,7,6]=>[2,1,2,2,1]
[1,8,4,5,2,3,7,6]=>[2,2,3,1]
[7,3,5,1,6,2,4,8]=>[1,2,2,3]
[7,2,1,5,6,3,4,8]=>[1,1,3,3]
[7,2,1,6,5,4,3,8]=>[1,1,2,1,1,2]
[7,3,6,1,5,4,2,8]=>[1,2,2,1,2]
[7,4,6,5,1,3,2,8]=>[1,2,1,2,2]
[1,8,5,4,3,2,7,6]=>[2,1,1,1,2,1]
[1,8,6,4,3,7,2,5]=>[2,1,1,2,2]
[6,5,7,4,3,1,8,2]=>[1,2,1,1,2,1]
[6,4,7,5,1,3,8,2]=>[1,2,1,3,1]
[6,3,7,1,5,4,8,2]=>[1,2,2,2,1]
[6,2,1,7,5,4,8,3]=>[1,1,2,1,2,1]
[3,2,1,8,5,4,7,6]=>[1,1,2,1,2,1]
[2,3,8,1,5,4,7,6]=>[3,2,2,1]
[2,4,8,5,1,3,7,6]=>[3,1,3,1]
[2,5,8,4,3,1,7,6]=>[3,1,1,2,1]
[2,6,8,4,3,7,1,5]=>[3,1,2,2]
[2,7,8,4,3,6,5,1]=>[3,1,2,1,1]
[1,8,7,4,3,6,5,2]=>[2,1,1,2,1,1]
[1,8,7,5,6,3,4,2]=>[2,1,2,2,1]
[2,7,8,5,6,3,4,1]=>[3,2,2,1]
[2,6,8,5,7,3,1,4]=>[3,2,1,2]
[2,5,8,6,7,1,3,4]=>[3,2,3]
[2,4,8,6,1,7,3,5]=>[3,1,2,2]
[3,2,1,8,6,7,4,5]=>[1,1,2,2,2]
[5,2,1,7,6,8,4,3]=>[1,1,2,2,1,1]
[5,3,7,1,6,8,4,2]=>[1,2,3,1,1]
[5,4,7,6,1,8,3,2]=>[1,2,1,2,1,1]
[4,5,7,6,8,1,3,2]=>[3,2,2,1]
[4,6,7,5,8,3,1,2]=>[3,2,1,2]
[1,8,6,5,7,3,2,4]=>[2,1,2,1,2]
[1,8,5,6,7,2,3,4]=>[2,3,3]
[4,7,5,6,8,2,3,1]=>[2,3,2,1]
[4,6,5,7,8,2,1,3]=>[2,3,1,2]
[5,4,6,7,1,8,2,3]=>[1,3,2,2]
[5,3,6,1,7,8,2,4]=>[1,2,3,2]
[5,2,1,6,7,8,3,4]=>[1,1,4,2]
[6,2,1,5,7,3,8,4]=>[1,1,3,2,1]
[6,3,5,1,7,2,8,4]=>[1,2,2,2,1]
[6,4,5,7,1,2,8,3]=>[1,3,3,1]
[6,5,4,7,2,1,8,3]=>[1,1,2,1,2,1]
[5,6,4,7,2,8,1,3]=>[2,2,2,2]
[1,8,4,6,2,7,3,5]=>[2,2,2,2]
[1,8,3,2,6,7,4,5]=>[2,1,3,2]
[5,7,3,2,6,8,4,1]=>[2,1,3,1,1]
[5,6,3,2,7,8,1,4]=>[2,1,3,2]
[6,5,3,2,7,1,8,4]=>[1,1,1,2,2,1]
[6,4,3,2,1,7,8,5]=>[1,1,1,1,3,1]
[6,2,1,4,3,7,8,5]=>[1,1,2,3,1]
[5,2,1,4,3,8,7,6]=>[1,1,2,2,1,1]
[5,3,4,1,2,8,7,6]=>[1,2,3,1,1]
[4,6,3,2,8,7,1,5]=>[2,1,2,1,2]
[4,7,3,2,8,6,5,1]=>[2,1,2,1,1,1]
[1,8,3,2,7,6,5,4]=>[2,1,2,1,1,1]
[1,8,4,7,2,6,5,3]=>[2,2,2,1,1]
[3,7,4,8,2,6,5,1]=>[2,2,2,1,1]
[3,6,4,8,2,7,1,5]=>[2,2,2,2]
[3,5,4,8,2,1,7,6]=>[2,2,1,2,1]
[3,4,5,8,1,2,7,6]=>[4,3,1]
[4,3,5,1,8,2,7,6]=>[1,2,2,2,1]
[4,2,1,5,8,3,7,6]=>[1,1,3,2,1]
[4,2,1,6,8,7,3,5]=>[1,1,3,1,2]
[4,3,6,1,8,7,2,5]=>[1,2,2,1,2]
[3,4,6,8,1,7,2,5]=>[4,2,2]
[3,5,6,8,7,1,2,4]=>[4,1,3]
[3,6,5,8,7,2,1,4]=>[2,2,1,1,2]
[3,7,5,8,6,2,4,1]=>[2,2,1,2,1]
[1,8,5,7,6,2,4,3]=>[2,2,1,2,1]
[1,8,6,7,5,4,2,3]=>[2,2,1,1,2]
[3,6,7,8,5,4,1,2]=>[4,1,1,2]
[3,5,7,8,6,1,4,2]=>[4,1,2,1]
[3,4,7,8,1,6,5,2]=>[4,2,1,1]
[4,2,1,7,8,6,5,3]=>[1,1,3,1,1,1]
[2,3,8,1,7,6,5,4]=>[3,2,1,1,1]
[2,4,8,7,1,6,5,3]=>[3,1,2,1,1]
[2,5,8,7,6,1,4,3]=>[3,1,1,2,1]
[2,6,8,7,5,4,1,3]=>[3,1,1,1,2]
[7,4,6,1,8,3,5,2]=>[1,2,2,2,1]
[8,3,5,1,7,4,6,2]=>[1,2,2,2,1]
[8,3,4,1,7,5,6,2]=>[1,2,2,2,1]
[4,8,3,1,7,5,6,2]=>[2,1,2,2,1]
[4,6,2,1,7,5,8,3]=>[2,1,2,2,1]
[1,4,6,2,7,5,8,3]=>[3,2,2,1]
[1,7,5,2,6,8,4,3]=>[2,1,3,1,1]
[7,5,2,1,6,8,4,3]=>[1,1,1,3,1,1]
[6,8,4,3,1,7,5,2]=>[2,1,1,2,1,1]
[3,6,8,4,1,7,5,2]=>[3,1,2,1,1]
[3,6,7,5,1,8,4,2]=>[3,1,2,1,1]
[7,5,6,1,8,3,4,2]=>[1,2,2,2,1]
[3,4,6,5,7,1,8,2]=>[3,2,2,1]
[4,7,5,6,1,8,3,2]=>[2,2,2,1,1]
[6,7,5,1,8,4,3,2]=>[2,1,2,1,1,1]
[6,8,4,1,7,5,3,2]=>[2,1,2,1,1,1]
[6,7,5,3,1,8,4,2]=>[2,1,1,2,1,1]
[8,4,2,1,6,7,5,3]=>[1,1,1,3,1,1]
[1,8,4,2,6,7,5,3]=>[2,1,3,1,1]
[1,5,3,2,7,6,8,4]=>[2,1,2,2,1]
[5,3,2,1,7,6,8,4]=>[1,1,1,2,2,1]
[2,5,3,1,7,6,8,4]=>[2,1,2,2,1]
[2,8,4,1,6,7,5,3]=>[2,1,3,1,1]
[2,7,5,1,6,8,4,3]=>[2,1,3,1,1]
[2,4,6,1,7,5,8,3]=>[3,2,2,1]
[4,7,1,6,5,8,2,3]=>[2,2,2,2]
[4,8,2,6,5,7,1,3]=>[2,2,2,2]
[4,6,1,2,7,5,8,3]=>[2,3,2,1]
[7,5,1,2,6,8,4,3]=>[1,1,4,1,1]
[8,4,1,2,6,7,5,3]=>[1,1,4,1,1]
[5,3,1,2,7,6,8,4]=>[1,1,3,2,1]
[1,2,5,3,7,6,8,4]=>[3,2,2,1]
[4,3,1,2,7,6,8,5]=>[1,1,3,2,1]
[3,5,1,2,7,6,8,4]=>[2,3,2,1]
[6,7,1,5,8,2,3,4]=>[2,3,3]
[2,7,6,1,5,8,3,4]=>[2,1,3,2]
[2,3,5,1,7,6,8,4]=>[3,2,2,1]
[7,6,1,5,8,3,2,4]=>[1,1,3,1,2]
[3,6,7,1,5,8,2,4]=>[3,3,2]
[7,1,6,5,8,2,4,3]=>[1,2,2,2,1]
[7,5,1,6,8,4,2,3]=>[1,1,3,1,2]
[8,4,1,6,7,5,2,3]=>[1,1,3,1,2]
[5,2,3,1,7,6,8,4]=>[1,2,2,2,1]
[3,5,2,1,7,6,8,4]=>[2,1,2,2,1]
[1,3,5,2,7,6,8,4]=>[3,2,2,1]
[1,7,6,2,5,8,3,4]=>[2,1,3,2]
[7,6,2,1,5,8,3,4]=>[1,1,1,3,2]
[8,3,1,5,7,6,2,4]=>[1,1,3,1,2]
[6,2,4,1,7,5,8,3]=>[1,2,2,2,1]
[6,2,5,1,7,4,8,3]=>[1,2,2,2,1]
[7,1,6,4,8,2,5,3]=>[1,2,2,2,1]
[8,2,6,4,7,1,5,3]=>[1,2,2,2,1]
[6,1,5,2,7,4,8,3]=>[1,2,2,2,1]
[7,6,2,5,8,3,1,4]=>[1,1,3,1,2]
[8,3,5,7,6,2,1,4]=>[1,3,1,1,2]
[1,8,3,5,7,6,2,4]=>[2,3,1,2]
[1,5,2,3,7,6,8,4]=>[2,3,2,1]
[5,2,1,3,7,6,8,4]=>[1,1,3,2,1]
[7,5,2,6,8,4,1,3]=>[1,1,3,1,2]
[8,4,2,6,7,5,1,3]=>[1,1,3,1,2]
[6,1,4,2,7,5,8,3]=>[1,2,2,2,1]
[8,2,6,5,7,1,4,3]=>[1,2,2,2,1]
[3,6,8,2,5,7,1,4]=>[3,3,2]
[8,3,2,5,7,6,1,4]=>[1,1,3,1,2]
[5,1,3,2,7,6,8,4]=>[1,2,2,2,1]
[4,1,3,2,7,6,8,5]=>[1,2,2,2,1]
[4,2,1,3,7,6,8,5]=>[1,1,3,2,1]
[1,4,2,3,7,6,8,5]=>[2,3,2,1]
[2,4,1,3,7,6,8,5]=>[2,3,2,1]
[2,5,1,3,7,6,8,4]=>[2,3,2,1]
[2,8,3,5,7,6,1,4]=>[2,3,1,2]
[6,8,2,3,5,7,1,4]=>[2,4,2]
[6,7,1,3,5,8,2,4]=>[2,4,2]
[8,3,5,7,6,1,2,4]=>[1,3,1,3]
[5,1,2,3,7,6,8,4]=>[1,4,2,1]
[3,1,2,4,7,6,8,5]=>[1,4,2,1]
[8,1,2,4,3,6,5,7]=>[1,3,2,2]
[8,1,3,5,6,2,7,4]=>[1,4,2,1]
[8,1,3,4,2,6,7,5]=>[1,3,3,1]
[8,1,3,2,4,5,7,6]=>[1,2,4,1]
[2,7,8,3,4,5,6,1]=>[3,4,1]
[2,6,3,8,4,5,7,1]=>[2,2,3,1]
[6,3,2,1,4,5,8,7]=>[1,1,1,4,1]
[7,3,1,4,2,6,8,5]=>[1,1,2,3,1]
[7,4,1,5,6,8,2,3]=>[1,1,4,2]
[4,7,8,5,6,1,2,3]=>[3,2,3]
[3,7,8,5,6,2,1,4]=>[3,2,1,2]
[3,7,8,4,2,6,1,5]=>[3,1,2,2]
[3,7,8,2,4,5,1,6]=>[3,3,2]
[3,6,2,8,4,5,1,7]=>[2,2,2,2]
[2,3,6,7,4,5,8,1]=>[4,3,1]
[3,5,2,4,8,6,1,7]=>[2,3,1,2]
[3,5,4,2,8,7,1,6]=>[2,1,2,1,2]
[4,6,5,8,7,1,2,3]=>[2,2,1,3]
[6,4,5,1,7,8,2,3]=>[1,2,3,2]
[7,4,1,2,3,8,5,6]=>[1,1,4,2]
[6,2,4,1,3,7,5,8]=>[1,2,3,2]
[2,6,4,8,3,7,5,1]=>[2,2,2,1,1]
[2,6,5,8,7,3,4,1]=>[2,2,1,2,1]
[6,2,5,1,7,3,4,8]=>[1,2,2,3]
[6,5,2,1,8,3,4,7]=>[1,1,1,2,3]
[2,5,6,7,8,3,4,1]=>[5,2,1]
[2,4,6,7,3,8,5,1]=>[4,2,1,1]
[4,2,6,7,3,1,5,8]=>[1,3,1,3]
[4,7,8,2,3,1,5,6]=>[3,2,3]
[4,7,8,3,2,1,6,5]=>[3,1,1,2,1]
[5,6,4,8,1,7,2,3]=>[2,2,2,2]
[5,6,3,8,1,2,7,4]=>[2,2,3,1]
[4,2,5,3,7,1,6,8]=>[1,2,2,3]
[4,3,6,7,2,1,8,5]=>[1,3,1,2,1]
[3,4,6,7,2,8,1,5]=>[4,2,2]
[3,4,5,2,7,8,1,6]=>[3,3,2]
[3,4,2,5,6,8,1,7]=>[2,4,2]
[5,2,7,8,6,4,1,3]=>[1,3,1,1,2]
[5,1,2,7,8,6,4,3]=>[1,4,1,1,1]
[4,7,1,8,6,5,2,3]=>[2,2,1,1,2]
[4,7,1,2,8,6,5,3]=>[2,3,1,1,1]
[4,6,8,1,2,7,5,3]=>[3,3,1,1]
[6,8,7,1,5,3,2,4]=>[2,1,2,1,2]
[6,8,7,3,5,1,2,4]=>[2,1,2,3]
[7,8,1,6,3,5,2,4]=>[2,2,2,2]
[7,8,1,3,6,5,2,4]=>[2,3,1,2]
[7,8,3,6,5,2,1,4]=>[2,2,1,1,2]
[4,7,2,8,6,1,5,3]=>[2,2,1,2,1]
[1,7,3,4,8,6,5,2]=>[2,3,1,1,1]
[4,2,7,1,8,6,5,3]=>[1,2,2,1,1,1]
[7,8,2,3,6,5,1,4]=>[2,3,1,2]
[8,5,7,1,6,2,3,4]=>[1,2,2,3]
[8,5,7,1,2,6,3,4]=>[1,2,3,2]
[6,8,2,7,1,3,5,4]=>[2,2,3,1]
[6,8,7,2,5,3,1,4]=>[2,1,2,1,2]
[6,2,4,8,7,1,5,3]=>[1,3,1,2,1]
[1,6,8,3,7,4,5,2]=>[3,2,2,1]
[1,6,8,3,4,7,5,2]=>[3,3,1,1]
[6,2,4,8,1,7,5,3]=>[1,3,2,1,1]
[6,8,7,2,3,5,1,4]=>[2,1,3,2]
[6,8,2,1,7,3,5,4]=>[2,1,2,2,1]
[8,5,7,2,1,6,3,4]=>[1,2,1,2,2]
[8,5,7,1,2,3,6,4]=>[1,2,4,1]
[8,7,6,2,1,4,3,5]=>[1,1,1,1,2,2]
[8,5,7,2,3,1,6,4]=>[1,2,2,2,1]
[5,8,4,2,7,1,6,3]=>[2,1,2,2,1]
[1,8,7,5,3,4,6,2]=>[2,1,1,3,1]
[1,8,7,3,5,4,6,2]=>[2,1,2,2,1]
[8,2,5,4,7,1,6,3]=>[1,2,2,2,1]
[8,5,2,7,3,1,6,4]=>[1,1,2,1,2,1]
[8,7,6,2,4,3,1,5]=>[1,1,1,2,1,2]
[8,7,6,1,2,4,3,5]=>[1,1,1,3,2]
[8,7,6,1,4,2,3,5]=>[1,1,1,2,3]
[8,7,6,4,1,3,2,5]=>[1,1,1,1,2,2]
[5,8,4,7,2,1,6,3]=>[2,2,1,2,1]
[1,8,7,5,4,3,6,2]=>[2,1,1,1,2,1]
[1,6,8,4,3,7,5,2]=>[3,1,2,1,1]
[6,8,7,3,2,5,1,4]=>[2,1,1,2,2]
[6,8,1,7,3,2,5,4]=>[2,2,1,2,1]
[8,5,7,3,1,6,2,4]=>[1,2,1,2,2]
[8,5,7,1,3,2,6,4]=>[1,2,2,2,1]
[8,5,7,3,1,2,6,4]=>[1,2,1,3,1]
[5,8,4,7,1,2,6,3]=>[2,2,3,1]
[5,8,4,1,7,2,6,3]=>[2,1,2,2,1]
[5,8,4,7,1,6,2,3]=>[2,2,2,2]
[8,1,2,6,5,7,4,3]=>[1,3,2,1,1]
[8,2,5,6,7,4,1,3]=>[1,4,1,2]
[4,8,5,7,1,6,2,3]=>[2,2,2,2]
[4,8,5,7,1,2,6,3]=>[2,2,3,1]
[4,8,5,1,7,2,6,3]=>[2,1,2,2,1]
[8,5,3,1,7,2,6,4]=>[1,1,1,2,2,1]
[8,5,3,7,1,2,6,4]=>[1,1,2,3,1]
[6,8,1,3,7,2,5,4]=>[2,3,2,1]
[4,6,2,8,1,7,5,3]=>[2,2,2,1,1]
[1,6,4,8,3,7,5,2]=>[2,2,2,1,1]
[1,8,7,4,5,3,6,2]=>[2,1,2,2,1]
[4,8,5,7,2,1,6,3]=>[2,2,1,2,1]
[8,5,3,7,2,1,6,4]=>[1,1,2,1,2,1]
[8,7,6,3,1,4,2,5]=>[1,1,1,1,2,2]
[8,7,6,1,3,2,4,5]=>[1,1,1,2,3]
[8,5,3,2,7,1,6,4]=>[1,1,1,2,2,1]
[4,8,5,2,7,1,6,3]=>[2,1,2,2,1]
[1,8,7,4,3,5,6,2]=>[2,1,1,3,1]
[1,8,7,3,4,5,6,2]=>[2,1,4,1]
[8,2,4,5,7,1,6,3]=>[1,4,2,1]
[8,5,2,3,7,1,6,4]=>[1,1,3,2,1]
[6,3,1,5,4,2,8,7]=>[1,1,2,1,2,1]
[8,3,1,5,2,7,6,4]=>[1,1,2,2,1,1]
[8,5,4,2,1,7,3,6]=>[1,1,1,1,2,2]
[8,5,4,2,1,7,6,3]=>[1,1,1,1,2,1,1]
[6,5,4,2,1,3,8,7]=>[1,1,1,1,3,1]
[6,5,4,2,3,1,8,7]=>[1,1,1,2,2,1]
[6,3,2,5,1,4,8,7]=>[1,1,2,3,1]
[6,5,4,3,1,2,8,7]=>[1,1,1,1,3,1]
[6,5,4,1,3,2,8,7]=>[1,1,1,2,2,1]
[8,5,4,1,2,7,6,3]=>[1,1,1,3,1,1]
[8,7,4,1,6,3,2,5]=>[1,1,1,2,1,2]
[8,7,4,1,6,3,5,2]=>[1,1,1,2,2,1]
[8,7,4,1,6,5,3,2]=>[1,1,1,2,1,1,1]
[8,5,4,1,3,7,6,2]=>[1,1,1,3,1,1]
[8,5,4,3,1,7,6,2]=>[1,1,1,1,2,1,1]
[8,3,2,5,1,7,6,4]=>[1,1,2,2,1,1]
[2,1,8,5,3,7,6,4]=>[1,2,1,2,1,1]
[8,3,2,5,1,7,4,6]=>[1,1,2,2,2]
[8,5,4,3,1,7,2,6]=>[1,1,1,1,2,2]
[8,5,4,1,3,7,2,6]=>[1,1,1,3,2]
[8,7,4,1,6,5,2,3]=>[1,1,1,2,1,2]
[8,7,4,1,6,2,5,3]=>[1,1,1,2,2,1]
[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1]
[8,7,4,3,6,2,1,5]=>[1,1,1,2,1,2]
[8,3,2,7,6,4,1,5]=>[1,1,2,1,1,2]
[2,1,8,7,6,4,3,5]=>[1,2,1,1,1,2]
[2,1,8,7,6,4,5,3]=>[1,2,1,1,2,1]
[8,3,2,7,6,4,5,1]=>[1,1,2,1,2,1]
[8,7,4,3,6,2,5,1]=>[1,1,1,2,2,1]
[8,7,6,5,2,4,3,1]=>[1,1,1,1,2,1,1]
[8,5,4,2,3,7,6,1]=>[1,1,1,3,1,1]
[8,7,4,2,6,5,3,1]=>[1,1,1,2,1,1,1]
[8,7,4,2,6,3,5,1]=>[1,1,1,2,2,1]
[8,7,4,2,6,3,1,5]=>[1,1,1,2,1,2]
[8,3,1,7,6,4,2,5]=>[1,1,2,1,1,2]
[8,3,1,7,6,4,5,2]=>[1,1,2,1,2,1]
[8,3,1,7,6,5,4,2]=>[1,1,2,1,1,1,1]
[8,3,1,5,4,7,6,2]=>[1,1,2,2,1,1]
[8,3,1,5,4,7,2,6]=>[1,1,2,2,2]
[8,3,1,7,6,5,2,4]=>[1,1,2,1,1,2]
[8,3,1,7,6,2,5,4]=>[1,1,2,1,2,1]
[8,7,4,2,6,1,5,3]=>[1,1,1,2,2,1]
[8,7,4,2,6,5,1,3]=>[1,1,1,2,1,2]
[8,5,4,2,3,7,1,6]=>[1,1,1,3,2]
[8,3,2,5,4,7,1,6]=>[1,1,2,2,2]
[2,1,8,5,4,7,3,6]=>[1,2,1,2,2]
[8,3,2,7,6,5,1,4]=>[1,1,2,1,1,2]
[8,7,4,3,6,5,1,2]=>[1,1,1,2,1,2]
[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,2,1]
[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2]
[8,7,6,5,1,3,4,2]=>[1,1,1,1,3,1]
[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]
[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]
[8,7,4,3,6,1,5,2]=>[1,1,1,2,2,1]
[8,3,2,7,6,1,5,4]=>[1,1,2,1,2,1]
[2,1,8,7,6,3,5,4]=>[1,2,1,1,2,1]
[8,3,2,7,6,1,4,5]=>[1,1,2,1,3]
[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2]
[8,7,6,5,1,2,4,3]=>[1,1,1,1,3,1]
[7,3,5,1,8,4,6,2]=>[1,2,2,2,1]
[7,3,4,1,8,5,6,2]=>[1,2,2,2,1]
[4,5,6,2,1,8,7,3]=>[3,1,2,1,1]
[1,6,5,2,7,4,3,8]=>[2,1,2,1,2]
[7,4,3,1,8,6,5,2]=>[1,1,1,2,1,1,1]
[7,6,5,1,8,4,3,2]=>[1,1,1,2,1,1,1]
[7,6,4,1,8,5,3,2]=>[1,1,1,2,1,1,1]
[6,4,2,1,8,7,5,3]=>[1,1,1,2,1,1,1]
[1,6,4,2,7,5,3,8]=>[2,1,2,1,2]
[1,5,3,2,7,6,4,8]=>[2,1,2,1,2]
[5,3,2,1,8,7,6,4]=>[1,1,1,2,1,1,1]
[2,5,3,1,7,8,6,4]=>[2,1,3,1,1]
[2,6,4,1,7,8,5,3]=>[2,1,3,1,1]
[2,6,5,1,7,8,4,3]=>[2,1,3,1,1]
[4,5,7,1,6,8,2,3]=>[3,3,2]
[6,5,1,2,8,4,3,7]=>[1,1,3,1,2]
[6,4,1,2,8,5,3,7]=>[1,1,3,1,2]
[5,3,1,2,8,6,4,7]=>[1,1,3,1,2]
[4,3,1,2,8,6,5,7]=>[1,1,3,1,2]
[6,1,2,5,8,3,4,7]=>[1,4,3]
[7,1,3,4,8,2,5,6]=>[1,4,3]
[7,1,5,6,8,2,3,4]=>[1,4,3]
[2,6,1,5,7,8,3,4]=>[2,4,2]
[7,4,1,6,8,5,2,3]=>[1,1,3,1,2]
[5,2,3,1,8,6,7,4]=>[1,2,2,2,1]
[3,5,2,1,6,8,7,4]=>[2,1,3,1,1]
[1,6,2,5,7,3,4,8]=>[2,3,3]
[6,2,1,5,8,7,3,4]=>[1,1,3,1,2]
[7,3,1,5,8,6,2,4]=>[1,1,3,1,2]
[6,2,4,1,8,5,7,3]=>[1,2,2,2,1]
[6,2,5,1,8,4,7,3]=>[1,2,2,2,1]
[7,3,1,4,8,6,2,5]=>[1,1,3,1,2]
[6,2,1,4,8,7,3,5]=>[1,1,3,1,2]
[1,6,2,4,7,3,5,8]=>[2,3,3]
[5,2,1,3,8,7,4,6]=>[1,1,3,1,2]
[7,4,1,3,8,5,2,6]=>[1,1,3,1,2]
[7,5,1,3,8,4,2,6]=>[1,1,3,1,2]
[3,6,7,1,4,8,2,5]=>[3,3,2]
[7,6,1,4,8,3,2,5]=>[1,1,3,1,2]
[4,2,1,3,8,7,5,6]=>[1,1,3,1,2]
[2,6,1,4,7,8,3,5]=>[2,4,2]
[7,1,4,6,8,2,3,5]=>[1,4,3]
[7,1,3,5,8,2,4,6]=>[1,4,3]
[6,1,2,4,8,3,5,7]=>[1,4,3]
[5,2,3,1,6,4,8,7]=>[1,2,2,2,1]
[7,4,5,2,3,1,8,6]=>[1,2,2,2,1]
[8,6,7,3,5,2,4,1]=>[1,2,2,2,1]
[7,3,5,2,4,1,8,6]=>[1,2,2,2,1]
[6,3,5,2,4,1,8,7]=>[1,2,2,2,1]
[5,2,4,1,6,3,8,7]=>[1,2,2,2,1]
[4,1,6,3,5,2,8,7]=>[1,2,2,2,1]
[6,3,4,1,5,2,8,7]=>[1,2,2,2,1]
[5,2,6,3,4,1,8,7]=>[1,2,2,2,1]
[5,2,7,3,4,1,8,6]=>[1,2,2,2,1]
[5,2,8,6,7,3,4,1]=>[1,2,2,2,1]
[6,2,8,5,7,3,4,1]=>[1,2,2,2,1]
[6,2,7,3,4,1,8,5]=>[1,2,2,2,1]
[7,3,4,1,5,2,8,6]=>[1,2,2,2,1]
[4,1,7,3,5,2,8,6]=>[1,2,2,2,1]
[3,1,7,4,5,2,8,6]=>[1,2,2,2,1]
[2,1,7,4,5,3,8,6]=>[1,2,2,2,1]
[3,1,8,6,7,4,5,2]=>[1,2,2,2,1]
[4,1,8,6,7,3,5,2]=>[1,2,2,2,1]
[8,6,7,3,4,1,5,2]=>[1,2,2,2,1]
[8,5,7,3,4,1,6,2]=>[1,2,2,2,1]
[8,5,6,2,7,3,4,1]=>[1,2,2,2,1]
[8,4,7,3,5,1,6,2]=>[1,2,2,2,1]
[5,1,8,4,7,3,6,2]=>[1,2,2,2,1]
[4,1,8,5,7,3,6,2]=>[1,2,2,2,1]
[3,1,8,5,7,4,6,2]=>[1,2,2,2,1]
[2,1,8,5,7,4,6,3]=>[1,2,2,2,1]
[2,1,7,4,6,3,8,5]=>[1,2,2,2,1]
[3,1,7,4,6,2,8,5]=>[1,2,2,2,1]
[4,1,7,3,6,2,8,5]=>[1,2,2,2,1]
[5,1,7,3,6,2,8,4]=>[1,2,2,2,1]
[6,2,7,3,5,1,8,4]=>[1,2,2,2,1]
[6,2,8,4,7,3,5,1]=>[1,2,2,2,1]
[8,4,7,3,6,2,5,1]=>[1,2,2,2,1]
[7,3,6,2,5,1,8,4]=>[1,2,2,2,1]
[6,2,5,1,7,3,8,4]=>[1,2,2,2,1]
[5,2,4,1,7,3,8,6]=>[1,2,2,2,1]
[6,2,4,1,7,3,8,5]=>[1,2,2,2,1]
[8,5,7,3,6,2,4,1]=>[1,2,2,2,1]
[8,5,7,4,6,2,3,1]=>[1,2,2,2,1]
[7,4,6,2,3,1,8,5]=>[1,2,2,2,1]
[6,2,3,1,7,4,8,5]=>[1,2,2,2,1]
[5,2,3,1,7,4,8,6]=>[1,2,2,2,1]
[4,2,3,1,7,5,8,6]=>[1,2,2,2,1]
[3,1,4,2,8,6,7,5]=>[1,2,2,2,1]
[6,2,3,1,8,5,7,4]=>[1,2,2,2,1]
[8,5,6,2,3,1,7,4]=>[1,2,2,2,1]
[7,4,8,5,6,2,3,1]=>[1,2,2,2,1]
[7,3,8,5,6,2,4,1]=>[1,2,2,2,1]
[8,5,6,2,4,1,7,3]=>[1,2,2,2,1]
[5,2,4,1,8,6,7,3]=>[1,2,2,2,1]
[4,1,5,2,8,6,7,3]=>[1,2,2,2,1]
[3,1,5,2,8,6,7,4]=>[1,2,2,2,1]
[2,1,6,3,8,5,7,4]=>[1,2,2,2,1]
[3,1,6,2,8,5,7,4]=>[1,2,2,2,1]
[4,1,6,2,8,5,7,3]=>[1,2,2,2,1]
[5,1,6,2,8,4,7,3]=>[1,2,2,2,1]
[8,4,6,2,5,1,7,3]=>[1,2,2,2,1]
[7,3,8,4,6,2,5,1]=>[1,2,2,2,1]
[6,2,7,3,8,4,5,1]=>[1,2,2,2,1]
[8,4,5,1,6,2,7,3]=>[1,2,2,2,1]
[5,1,8,4,6,2,7,3]=>[1,2,2,2,1]
[4,1,8,5,6,2,7,3]=>[1,2,2,2,1]
[3,1,8,5,6,2,7,4]=>[1,2,2,2,1]
[2,1,8,5,6,3,7,4]=>[1,2,2,2,1]
[2,1,7,4,8,5,6,3]=>[1,2,2,2,1]
[3,1,7,4,8,5,6,2]=>[1,2,2,2,1]
[4,1,7,3,8,5,6,2]=>[1,2,2,2,1]
[7,3,8,4,5,1,6,2]=>[1,2,2,2,1]
[8,4,5,1,7,3,6,2]=>[1,2,2,2,1]
[7,3,6,2,8,4,5,1]=>[1,2,2,2,1]
[7,8,5,6,1,3,4,2]=>[2,2,3,1]
[7,8,1,3,6,2,5,4]=>[2,3,2,1]
[1,3,8,4,7,2,5,6]=>[3,2,3]
[3,6,1,4,7,2,5,8]=>[2,3,3]
[4,6,1,2,5,7,3,8]=>[2,4,2]
[1,4,8,2,5,7,3,6]=>[3,3,2]
[7,8,2,4,5,6,1,3]=>[2,4,2]
[7,8,1,5,4,6,3,2]=>[2,2,2,1,1]
[7,8,2,1,6,3,4,5]=>[2,1,2,3]
[7,8,3,5,6,4,1,2]=>[2,3,1,2]
[7,8,1,4,2,3,6,5]=>[2,2,3,1]
[7,8,5,1,4,2,6,3]=>[2,1,2,2,1]
[7,8,4,5,3,1,6,2]=>[2,2,1,2,1]
[1,5,8,4,3,2,7,6]=>[3,1,1,2,1]
[5,6,1,4,3,2,7,8]=>[2,2,1,3]
[2,6,4,8,3,7,1,5]=>[2,2,2,2]
[1,4,6,8,3,7,5,2]=>[4,2,1,1]
[2,4,8,5,3,1,6,7]=>[3,1,1,3]
[2,5,8,1,4,7,6,3]=>[3,3,1,1]
[3,5,8,4,7,6,1,2]=>[3,2,1,2]
[1,6,2,4,7,3,8,5]=>[2,3,2,1]
[5,6,2,1,4,7,8,3]=>[2,1,4,1]
[4,6,2,5,3,1,8,7]=>[2,2,1,2,1]
[4,7,5,1,3,6,8,2]=>[2,1,4,1]
[7,5,3,6,2,4,1,8]=>[1,1,2,2,2]
[5,7,3,6,1,4,8,2]=>[2,2,3,1]
[5,3,6,7,2,1,8,4]=>[1,3,1,2,1]
[6,1,7,5,2,4,8,3]=>[1,2,1,3,1]
[6,3,1,2,4,5,8,7]=>[1,1,5,1]
[1,4,7,2,5,3,8,6]=>[3,2,2,1]
[4,6,7,8,3,5,1,2]=>[4,2,2]
[3,6,1,8,4,2,5,7]=>[2,2,1,3]
[1,6,7,5,8,2,4,3]=>[3,2,2,1]
[3,5,6,7,8,1,4,2]=>[5,2,1]
[3,6,5,7,8,2,1,4]=>[2,3,1,2]
[5,2,7,6,1,4,3,8]=>[1,2,1,2,2]
[2,5,7,6,8,1,3,4]=>[3,2,3]
[2,7,5,6,8,4,1,3]=>[2,3,1,2]
[2,1,6,8,4,5,3,7]=>[1,3,2,2]
[2,7,1,8,5,3,4,6]=>[2,2,1,3]
[3,7,6,8,5,4,1,2]=>[2,2,1,1,2]
[4,3,8,5,6,7,1,2]=>[1,2,3,2]
[4,2,8,1,6,3,7,5]=>[1,2,2,2,1]
[3,1,8,5,4,6,7,2]=>[1,2,1,3,1]
[3,2,8,4,5,6,1,7]=>[1,2,3,2]
[3,4,2,8,6,1,7,5]=>[2,2,1,2,1]
[3,4,7,1,5,2,6,8]=>[3,2,3]
[4,3,7,8,1,2,6,5]=>[1,3,3,1]
[1,7,3,8,5,2,6,4]=>[2,2,1,2,1]
[4,1,8,3,6,2,5,7]=>[1,2,2,3]
[5,7,8,6,3,2,1,4]=>[3,1,1,1,2]
[5,7,8,6,1,3,4,2]=>[3,1,3,1]
[7,6,5,8,1,3,4,2]=>[1,1,2,3,1]
[1,6,4,3,8,2,5,7]=>[2,1,2,3]
[7,1,3,4,8,2,6,5]=>[1,4,2,1]
[3,6,5,4,1,2,7,8]=>[2,1,1,4]
[2,4,5,1,7,8,6,3]=>[3,3,1,1]
[2,6,3,4,5,8,1,7]=>[2,4,2]
[2,6,4,1,8,3,7,5]=>[2,1,2,2,1]
[7,3,6,4,8,5,1,2]=>[1,2,2,1,2]
[7,2,1,4,8,3,5,6]=>[1,1,3,3]
[7,1,6,5,3,8,4,2]=>[1,2,1,2,1,1]
[7,2,5,6,3,8,1,4]=>[1,3,2,2]
[6,5,2,7,1,8,4,3]=>[1,1,2,2,1,1]
[5,6,2,7,3,1,4,8]=>[2,2,1,3]
[5,6,7,4,2,8,1,3]=>[3,1,2,2]
[5,7,6,4,1,8,3,2]=>[2,1,1,2,1,1]
[6,7,1,5,2,8,3,4]=>[2,2,2,2]
[1,7,5,2,4,8,3,6]=>[2,1,3,2]
[6,1,5,2,8,3,4,7]=>[1,2,2,3]
[6,7,5,3,8,4,1,2]=>[2,1,2,1,2]
[1,6,5,4,2,3,8,7]=>[2,1,1,3,1]
[7,1,5,3,4,2,8,6]=>[1,2,2,2,1]
[7,6,1,5,3,2,8,4]=>[1,1,2,1,2,1]
[7,5,6,4,1,2,8,3]=>[1,2,1,3,1]
[6,7,5,4,3,1,8,2]=>[2,1,1,1,2,1]
[7,5,2,4,3,1,6,8]=>[1,1,2,1,3]
[7,4,6,1,2,5,3,8]=>[1,2,3,2]
[7,1,4,2,5,3,6,8]=>[1,2,2,3]
[6,8,1,4,2,5,7,3]=>[2,2,3,1]
[1,6,4,2,5,7,3,8]=>[2,1,3,2]
[1,6,3,7,5,4,2,8]=>[2,2,1,1,2]
[6,8,1,3,7,5,4,2]=>[2,3,1,1,1]
[7,1,3,5,6,4,2,8]=>[1,4,1,2]
[7,3,1,6,4,5,2,8]=>[1,1,2,2,2]
[7,4,2,6,5,1,3,8]=>[1,1,2,1,3]
[7,4,6,3,1,5,2,8]=>[1,2,1,2,2]
[7,2,4,1,5,3,6,8]=>[1,2,2,3]
[7,2,3,5,4,1,6,8]=>[1,3,1,3]
[6,8,1,2,3,4,7,5]=>[2,5,1]
[1,5,7,2,3,8,6,4]=>[3,3,1,1]
[5,1,8,2,3,6,7,4]=>[1,2,4,1]
[5,8,2,3,7,6,4,1]=>[2,3,1,1,1]
[6,2,8,1,3,7,4,5]=>[1,2,3,2]
[6,8,2,3,5,4,7,1]=>[2,3,2,1]
[6,8,2,4,1,5,7,3]=>[2,2,3,1]
[6,8,3,1,2,4,7,5]=>[2,1,4,1]
[2,6,4,1,5,7,3,8]=>[2,1,3,2]
[2,6,3,5,7,1,4,8]=>[2,3,3]
[2,5,1,7,8,3,6,4]=>[2,3,2,1]
[2,5,3,6,8,4,7,1]=>[2,3,2,1]
[2,1,4,7,8,5,6,3]=>[1,4,2,1]
[2,4,7,6,8,5,1,3]=>[3,2,1,2]
[2,5,3,7,6,1,8,4]=>[2,2,1,2,1]
[2,5,7,8,1,4,6,3]=>[4,3,1]
[3,5,7,4,1,6,2,8]=>[3,1,2,2]
[5,3,4,1,8,6,7,2]=>[1,2,2,2,1]
[5,2,8,4,6,1,7,3]=>[1,2,2,2,1]
[5,2,1,8,6,3,7,4]=>[1,1,2,1,2,1]
[4,2,8,6,5,3,7,1]=>[1,2,1,1,2,1]
[4,2,8,5,7,6,3,1]=>[1,2,2,1,1,1]
[1,4,2,7,5,8,6,3]=>[2,2,2,1,1]
[4,1,8,6,7,5,3,2]=>[1,2,2,1,1,1]
[5,3,8,7,6,2,4,1]=>[1,2,1,1,2,1]
[5,8,4,7,6,2,1,3]=>[2,2,1,1,2]
[5,8,7,4,3,6,1,2]=>[2,1,1,2,2]
[6,4,8,3,1,7,2,5]=>[1,2,1,2,2]
[6,4,2,8,7,1,3,5]=>[1,1,2,1,3]
[6,3,8,7,2,5,1,4]=>[1,2,1,2,2]
[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]
[5,1,3,8,6,7,2,4]=>[1,3,2,2]
[1,5,3,7,8,6,2,4]=>[2,3,1,2]
[1,5,7,6,4,2,8,3]=>[3,1,1,2,1]
[5,8,7,4,1,6,2,3]=>[2,1,1,2,2]
[6,4,8,1,2,7,3,5]=>[1,2,3,2]
[6,8,5,1,2,3,7,4]=>[2,1,4,1]
[6,8,5,2,4,3,7,1]=>[2,1,2,2,1]
[6,8,5,3,1,2,7,4]=>[2,1,1,3,1]
[4,5,1,2,7,6,3,8]=>[2,3,1,2]
[4,5,1,2,6,8,7,3]=>[2,4,1,1]
[3,5,6,1,8,4,7,2]=>[3,2,2,1]
[3,5,7,1,2,8,6,4]=>[3,3,1,1]
[3,6,2,7,5,1,4,8]=>[2,2,1,3]
[4,2,6,1,7,3,5,8]=>[1,2,2,3]
[4,6,3,1,2,7,5,8]=>[2,1,3,2]
[4,5,3,1,7,6,2,8]=>[2,1,2,1,2]
[4,2,5,7,1,6,3,8]=>[1,3,2,2]
[3,5,2,7,8,1,6,4]=>[2,3,2,1]
[3,1,4,7,5,6,2,8]=>[1,3,2,2]
[3,4,6,5,8,7,1,2]=>[3,2,1,2]
[3,1,4,5,8,6,7,2]=>[1,4,2,1]
[3,4,6,8,5,2,7,1]=>[4,1,2,1]
[3,5,6,2,8,4,7,1]=>[3,2,2,1]
[4,2,5,6,1,8,7,3]=>[1,3,2,1,1]
[4,5,3,1,6,8,7,2]=>[2,1,3,1,1]
[2,1,7,5,8,6,4,3]=>[1,2,2,1,1,1]
[1,2,7,5,3,8,6,4]=>[3,1,2,1,1]
[4,1,2,7,3,8,6,5]=>[1,3,2,1,1]
[6,4,1,7,5,2,3,8]=>[1,1,2,1,3]
[6,1,3,7,5,2,4,8]=>[1,3,1,3]
[3,1,2,6,8,5,4,7]=>[1,4,1,2]
[3,7,1,2,5,4,8,6]=>[2,3,2,1]
[1,3,7,2,4,8,6,5]=>[3,3,1,1]
[2,4,1,7,8,6,5,3]=>[2,3,1,1,1]
[3,4,7,5,1,8,6,2]=>[3,1,2,1,1]
[2,7,4,1,5,8,6,3]=>[2,1,3,1,1]
[2,3,7,1,5,8,6,4]=>[3,3,1,1]
[5,2,8,1,3,7,4,6]=>[1,2,3,2]
[2,1,6,8,3,4,7,5]=>[1,3,3,1]
[2,6,8,3,1,5,7,4]=>[3,1,3,1]
[2,8,6,4,1,5,7,3]=>[2,1,1,3,1]
[3,6,4,8,5,1,7,2]=>[2,2,1,2,1]
[6,3,7,4,5,1,8,2]=>[1,2,2,2,1]
[2,6,3,7,5,8,1,4]=>[2,2,2,2]
[5,2,1,7,8,3,4,6]=>[1,1,3,3]
[4,7,2,3,6,8,1,5]=>[2,4,2]
[5,2,7,3,6,8,1,4]=>[1,2,3,2]
[5,7,4,6,2,8,1,3]=>[2,2,2,2]
[5,7,3,4,6,1,8,2]=>[2,3,2,1]
[5,3,8,4,6,1,7,2]=>[1,2,2,2,1]
[8,5,2,4,1,6,7,3]=>[1,1,2,3,1]
[8,2,3,5,1,6,7,4]=>[1,3,3,1]
[4,2,8,3,6,7,1,5]=>[1,2,3,2]
[2,4,8,1,7,3,5,6]=>[3,2,3]
[8,4,1,3,6,2,5,7]=>[1,1,3,3]
[4,8,3,1,7,2,5,6]=>[2,1,2,3]
[5,2,8,4,7,1,6,3]=>[1,2,2,2,1]
[5,8,4,7,3,1,6,2]=>[2,2,1,2,1]
[4,6,8,3,1,7,5,2]=>[3,1,2,1,1]
[6,3,8,2,7,1,5,4]=>[1,2,2,2,1]
[6,3,1,8,2,4,7,5]=>[1,1,2,3,1]
[5,3,8,1,2,6,4,7]=>[1,2,3,2]
[5,7,4,1,6,2,3,8]=>[2,1,2,3]
[8,5,4,1,2,6,3,7]=>[1,1,1,3,2]
[5,1,8,4,2,7,3,6]=>[1,2,1,2,2]
[1,6,2,8,5,3,7,4]=>[2,2,1,2,1]
[6,8,5,3,1,7,4,2]=>[2,1,1,2,1,1]
[8,4,5,1,2,6,3,7]=>[1,2,3,2]
[5,6,3,7,1,2,4,8]=>[2,2,4]
[1,6,3,7,2,8,4,5]=>[2,2,2,2]
[6,3,2,7,8,5,1,4]=>[1,1,3,1,2]
[4,5,7,8,3,1,6,2]=>[4,1,2,1]
[4,7,2,5,8,1,6,3]=>[2,3,2,1]
[8,1,3,4,6,2,5,7]=>[1,4,3]
[3,8,2,4,6,7,1,5]=>[2,4,2]
[3,5,6,8,2,7,1,4]=>[4,2,2]
[2,4,5,6,8,1,7,3]=>[5,2,1]
[4,8,3,5,6,1,7,2]=>[2,3,2,1]
[5,6,2,3,7,8,1,4]=>[2,4,2]
[5,8,7,3,4,1,2,6]=>[2,1,2,3]
[6,8,7,3,4,1,2,5]=>[2,1,2,3]
[6,8,4,7,1,5,3,2]=>[2,2,2,1,1]
[6,8,4,7,2,5,3,1]=>[2,2,2,1,1]
[5,4,8,7,2,6,3,1]=>[1,2,1,2,1,1]
[5,4,8,7,1,6,3,2]=>[1,2,1,2,1,1]
[5,3,8,7,6,1,2,4]=>[1,2,1,1,3]
[4,3,8,7,6,1,2,5]=>[1,2,1,1,3]
[4,8,3,7,5,1,2,6]=>[2,2,1,3]
[8,3,4,6,5,1,2,7]=>[1,3,1,3]
[3,8,4,7,5,1,2,6]=>[2,2,1,3]
[3,4,8,7,6,1,2,5]=>[3,1,1,3]
[3,5,8,7,6,1,2,4]=>[3,1,1,3]
[4,5,8,7,6,1,2,3]=>[3,1,1,3]
[4,5,8,7,1,6,3,2]=>[3,1,2,1,1]
[4,5,8,7,2,6,3,1]=>[3,1,2,1,1]
[3,5,8,2,7,6,4,1]=>[3,2,1,1,1]
[3,5,8,1,7,6,4,2]=>[3,2,1,1,1]
[2,5,8,1,7,6,4,3]=>[3,2,1,1,1]
[2,5,8,7,1,6,3,4]=>[3,1,2,2]
[2,4,8,7,1,6,3,5]=>[3,1,2,2]
[2,8,4,7,1,5,3,6]=>[2,2,2,2]
[8,2,4,6,1,5,3,7]=>[1,3,2,2]
[8,1,4,6,2,5,3,7]=>[1,3,2,2]
[1,8,4,7,2,5,3,6]=>[2,2,2,2]
[1,4,8,7,2,6,3,5]=>[3,1,2,2]
[1,5,8,7,2,6,3,4]=>[3,1,2,2]
[1,5,8,2,7,6,4,3]=>[3,2,1,1,1]
[2,5,8,3,7,6,4,1]=>[3,2,1,1,1]
[1,4,2,8,7,6,5,3]=>[2,2,1,1,1,1]
[1,3,8,2,7,6,4,5]=>[3,2,1,2]
[1,8,3,2,7,5,4,6]=>[2,1,2,1,2]
[8,1,3,2,6,5,4,7]=>[1,2,2,1,2]
[8,2,3,1,6,5,4,7]=>[1,2,2,1,2]
[2,8,3,1,7,5,4,6]=>[2,1,2,1,2]
[2,3,8,1,7,6,4,5]=>[3,2,1,2]
[3,4,1,8,7,6,5,2]=>[2,2,1,1,1,1]
[4,3,1,8,7,6,5,2]=>[1,1,2,1,1,1,1]
[4,2,1,8,7,6,5,3]=>[1,1,2,1,1,1,1]
[3,8,2,1,7,5,4,6]=>[2,1,2,1,2]
[8,3,2,1,6,5,4,7]=>[1,1,1,2,1,2]
[8,4,2,6,1,5,3,7]=>[1,1,2,2,2]
[4,2,8,7,1,6,3,5]=>[1,2,1,2,2]
[5,2,8,7,1,6,3,4]=>[1,2,1,2,2]
[5,2,8,1,7,6,4,3]=>[1,2,2,1,1,1]
[5,3,8,1,7,6,4,2]=>[1,2,2,1,1,1]
[5,3,8,2,7,6,4,1]=>[1,2,2,1,1,1]
[6,8,3,2,7,5,4,1]=>[2,1,2,1,1,1]
[6,8,3,1,7,5,4,2]=>[2,1,2,1,1,1]
[6,8,2,1,7,5,4,3]=>[2,1,2,1,1,1]
[6,8,2,7,1,5,3,4]=>[2,2,2,2]
[6,8,7,2,1,4,3,5]=>[2,1,1,2,2]
[8,5,6,1,2,4,3,7]=>[1,2,3,2]
[5,8,7,1,2,4,3,6]=>[2,1,3,2]
[6,8,1,2,7,5,4,3]=>[2,3,1,1,1]
[6,8,2,3,7,5,4,1]=>[2,3,1,1,1]
[5,2,8,3,7,6,4,1]=>[1,2,2,1,1,1]
[5,1,8,3,7,6,4,2]=>[1,2,2,1,1,1]
[5,1,8,7,2,6,3,4]=>[1,2,1,2,2]
[4,1,8,7,2,6,3,5]=>[1,2,1,2,2]
[4,8,1,7,2,5,3,6]=>[2,2,2,2]
[8,4,1,6,2,5,3,7]=>[1,1,2,2,2]
[8,3,1,2,6,5,4,7]=>[1,1,3,1,2]
[3,8,1,2,7,5,4,6]=>[2,3,1,2]
[3,1,8,2,7,6,4,5]=>[1,2,2,1,2]
[3,1,2,8,7,6,5,4]=>[1,3,1,1,1,1]
[4,1,3,8,7,6,5,2]=>[1,3,1,1,1,1]
[3,1,4,8,7,6,5,2]=>[1,3,1,1,1,1]
[2,1,8,3,7,6,4,5]=>[1,2,2,1,2]
[2,8,1,3,7,5,4,6]=>[2,3,1,2]
[8,2,1,3,6,5,4,7]=>[1,1,3,1,2]
[8,1,2,3,6,5,4,7]=>[1,4,1,2]
[1,8,2,3,7,5,4,6]=>[2,3,1,2]
[1,2,8,3,7,6,4,5]=>[3,2,1,2]
[1,4,3,6,8,2,5,7]=>[2,3,3]
[3,1,6,2,5,8,4,7]=>[1,2,3,2]
[3,5,1,8,2,4,7,6]=>[2,2,3,1]
[1,4,5,2,8,3,7,6]=>[3,2,2,1]
[1,4,2,6,5,8,3,7]=>[2,2,2,2]
[1,5,4,2,6,8,3,7]=>[2,1,3,2]
[3,1,6,5,8,2,4,7]=>[1,2,2,3]
[1,6,4,2,5,8,3,7]=>[2,1,3,2]
[1,5,2,6,4,8,3,7]=>[2,2,2,2]
[1,2,6,5,4,8,3,7]=>[3,1,2,2]
[1,2,5,4,7,3,8,6]=>[3,2,2,1]
[4,1,2,6,3,8,7,5]=>[1,3,2,1,1]
[7,1,5,4,2,8,3,6]=>[1,2,1,2,2]
[1,4,7,5,2,8,3,6]=>[3,1,2,2]
[7,1,3,5,2,8,4,6]=>[1,3,2,2]
[7,2,5,1,8,3,4,6]=>[1,2,2,3]
[1,4,5,2,8,7,3,6]=>[3,2,1,2]
[1,6,4,2,8,3,7,5]=>[2,1,2,2,1]
[1,4,2,8,3,7,6,5]=>[2,2,2,1,1]
[1,2,5,3,8,7,6,4]=>[3,2,1,1,1]
[1,2,8,6,5,3,7,4]=>[3,1,1,2,1]
[1,5,2,8,6,3,7,4]=>[2,2,1,2,1]
[1,6,4,2,8,7,3,5]=>[2,1,2,1,2]
[6,2,1,8,7,3,4,5]=>[1,1,2,1,3]
[7,6,2,1,8,3,4,5]=>[1,1,1,2,3]
[7,3,1,6,2,8,4,5]=>[1,1,2,2,2]
[1,7,6,4,2,8,3,5]=>[2,1,1,2,2]
[1,7,5,2,6,3,8,4]=>[2,1,2,2,1]
[1,6,2,7,5,3,8,4]=>[2,2,1,2,1]
[1,2,7,6,5,3,8,4]=>[3,1,1,2,1]
[1,2,6,5,3,8,7,4]=>[3,1,2,1,1]
[1,5,2,6,3,8,7,4]=>[2,2,2,1,1]
[1,5,2,7,6,3,8,4]=>[2,2,1,2,1]
[1,6,5,2,7,3,8,4]=>[2,1,2,2,1]
[1,5,7,4,2,8,3,6]=>[3,1,2,2]
[4,1,2,8,6,3,7,5]=>[1,3,1,2,1]
[3,1,8,6,2,4,7,5]=>[1,2,1,3,1]
[4,3,7,1,8,2,5,6]=>[1,2,2,3]
[8,3,1,6,2,4,7,5]=>[1,1,2,3,1]
[7,1,8,3,2,4,6,5]=>[1,2,1,3,1]
[1,8,7,3,2,4,6,5]=>[2,1,1,3,1]
[1,4,2,8,7,3,6,5]=>[2,2,1,2,1]
[1,7,4,2,8,3,6,5]=>[2,1,2,2,1]
[8,1,5,4,2,7,3,6]=>[1,2,1,2,2]
[1,4,8,5,2,7,3,6]=>[3,1,2,2]
[8,5,3,1,7,2,4,6]=>[1,1,1,2,3]
[8,6,2,1,7,3,4,5]=>[1,1,1,2,3]
[1,8,6,4,2,7,3,5]=>[2,1,1,2,2]
[1,8,5,2,6,3,7,4]=>[2,1,2,2,1]
[1,5,2,7,3,8,6,4]=>[2,2,2,1,1]
[1,2,8,5,3,7,6,4]=>[3,1,2,1,1]
[1,2,6,3,8,7,5,4]=>[3,2,1,1,1]
[1,2,7,6,3,8,5,4]=>[3,1,2,1,1]
[1,6,2,7,3,8,5,4]=>[2,2,2,1,1]
[1,7,2,8,5,3,6,4]=>[2,2,1,2,1]
[1,7,4,2,8,6,3,5]=>[2,1,2,1,2]
[7,1,8,3,2,6,4,5]=>[1,2,1,2,2]
[7,2,1,8,6,3,4,5]=>[1,1,2,1,3]
[1,8,7,3,2,6,4,5]=>[2,1,1,2,2]
[1,4,2,8,7,6,3,5]=>[2,2,1,1,2]
[1,2,8,7,5,3,6,4]=>[3,1,1,2,1]
[1,2,8,6,3,7,5,4]=>[3,1,2,1,1]
[1,2,7,3,8,6,5,4]=>[3,2,1,1,1]
[4,1,7,3,6,5,8,2]=>[1,2,2,2,1]
[5,1,8,7,6,2,4,3]=>[1,2,1,1,2,1]
[8,1,7,6,3,4,5,2]=>[1,2,1,3,1]
[5,7,8,6,2,4,1,3]=>[3,1,2,2]
[5,7,1,6,2,4,3,8]=>[2,2,2,2]
[6,4,1,5,2,7,3,8]=>[1,1,2,2,2]
[8,1,4,5,3,7,6,2]=>[1,3,2,1,1]
[6,1,4,5,3,8,7,2]=>[1,3,2,1,1]
[6,1,4,5,3,7,8,2]=>[1,3,3,1]
[5,1,7,8,6,2,4,3]=>[1,3,1,2,1]
[6,1,4,8,3,5,7,2]=>[1,3,3,1]
[7,1,8,6,3,4,5,2]=>[1,2,1,3,1]
[7,1,4,5,3,8,6,2]=>[1,3,2,1,1]
[7,1,4,5,3,6,8,2]=>[1,3,3,1]
[8,1,4,5,3,6,7,2]=>[1,3,3,1]
[7,4,1,5,2,6,3,8]=>[1,1,2,2,2]
[6,3,5,7,2,1,4,8]=>[1,3,1,3]
[6,3,5,8,2,1,7,4]=>[1,3,1,2,1]
[6,3,5,7,2,1,8,4]=>[1,3,1,2,1]
[8,4,5,7,3,6,1,2]=>[1,3,2,2]
[6,4,5,8,3,7,2,1]=>[1,3,2,1,1]
[5,8,7,6,2,4,1,3]=>[2,1,1,2,2]
[5,4,8,6,3,1,7,2]=>[1,2,1,1,2,1]
[5,4,1,8,2,3,7,6]=>[1,1,2,3,1]
[5,8,1,6,2,4,3,7]=>[2,2,2,2]
[8,4,1,5,2,6,3,7]=>[1,1,2,2,2]
[6,3,5,8,2,1,4,7]=>[1,3,1,3]
[2,3,4,1,8,6,5,7]=>[3,2,1,2]
[8,3,5,6,2,1,4,7]=>[1,3,1,3]
[2,3,8,5,1,4,7,6]=>[3,1,3,1]
[2,3,8,6,1,5,7,4]=>[3,1,3,1]
[2,8,6,7,1,3,5,4]=>[2,2,3,1]
[8,3,5,7,2,1,6,4]=>[1,3,1,2,1]
[2,3,8,5,6,1,7,4]=>[3,2,2,1]
[7,4,5,6,3,1,8,2]=>[1,3,1,2,1]
[8,4,5,6,3,1,7,2]=>[1,3,1,2,1]
[7,3,5,6,2,8,1,4]=>[1,3,2,2]
[7,3,5,8,2,1,6,4]=>[1,3,1,2,1]
[7,3,5,6,2,1,4,8]=>[1,3,1,3]
[2,7,6,5,1,3,4,8]=>[2,1,1,4]
[2,7,6,8,1,3,5,4]=>[2,2,3,1]
[2,7,6,5,8,3,1,4]=>[2,1,2,1,2]
[8,7,5,6,1,4,2,3]=>[1,1,2,2,2]
[2,6,4,1,8,5,7,3]=>[2,1,2,2,1]
[2,6,1,3,8,5,7,4]=>[2,3,2,1]
[2,7,1,3,6,5,8,4]=>[2,3,2,1]
[2,7,6,8,4,3,1,5]=>[2,2,1,1,2]
[2,7,6,1,8,3,4,5]=>[2,1,2,3]
[2,7,6,1,4,3,5,8]=>[2,1,2,3]
[7,3,5,1,2,8,4,6]=>[1,2,3,2]
[8,4,1,5,2,3,7,6]=>[1,1,2,3,1]
[7,8,1,6,3,4,2,5]=>[2,2,2,2]
[6,4,1,8,3,2,7,5]=>[1,1,2,1,2,1]
[2,3,8,6,4,1,7,5]=>[3,1,1,2,1]
[2,8,6,7,4,3,1,5]=>[2,2,1,1,2]
[8,3,5,7,2,4,1,6]=>[1,3,2,2]
[2,3,4,1,8,7,5,6]=>[3,2,1,2]
[2,8,6,1,7,3,4,5]=>[2,1,2,3]
[2,3,8,1,6,4,7,5]=>[3,2,2,1]
[2,3,8,1,4,5,7,6]=>[3,4,1]
[2,8,6,1,4,3,5,7]=>[2,1,2,3]
[8,4,3,6,5,1,7,2]=>[1,1,2,1,2,1]
[8,5,6,3,4,1,7,2]=>[1,2,2,2,1]
[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,2,1]
[1,7,6,5,4,2,3,8]=>[2,1,1,1,3]
[1,8,6,5,2,7,3,4]=>[2,1,1,2,2]
[8,7,5,4,1,6,3,2]=>[1,1,1,1,2,1,1]
[7,8,5,4,1,3,6,2]=>[2,1,1,3,1]
[6,8,5,4,2,1,7,3]=>[2,1,1,1,2,1]
[5,8,6,2,4,1,7,3]=>[2,1,2,2,1]
[4,8,2,6,5,1,7,3]=>[2,2,1,2,1]
[3,2,8,6,5,1,7,4]=>[1,2,1,1,2,1]
[3,2,1,7,6,4,5,8]=>[1,1,2,1,3]
[4,1,3,7,6,2,5,8]=>[1,3,1,3]
[5,1,7,3,6,2,4,8]=>[1,2,2,3]
[6,1,7,5,3,2,4,8]=>[1,2,1,1,3]
[7,1,6,5,2,4,3,8]=>[1,2,1,2,2]
[8,1,6,5,2,3,7,4]=>[1,2,1,3,1]
[1,2,7,6,3,4,5,8]=>[3,1,4]
[1,2,8,3,7,4,5,6]=>[3,2,3]
[8,1,7,2,6,3,5,4]=>[1,2,2,2,1]
[7,1,8,2,6,4,3,5]=>[1,2,2,1,2]
[6,1,8,2,4,7,3,5]=>[1,2,3,2]
[5,1,8,3,2,7,4,6]=>[1,2,1,2,2]
[4,1,3,8,2,7,5,6]=>[1,3,2,2]
[3,2,1,8,4,7,5,6]=>[1,1,2,2,2]
[3,2,8,7,1,6,5,4]=>[1,2,1,2,1,1]
[4,8,2,7,1,6,5,3]=>[2,2,2,1,1]
[5,8,7,2,1,6,4,3]=>[2,1,1,2,1,1]
[6,8,7,1,3,5,4,2]=>[2,1,3,1,1]
[7,8,6,1,5,3,4,2]=>[2,1,2,2,1]
[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]
[1,8,7,2,6,5,3,4]=>[2,1,2,1,2]
[1,7,8,2,5,6,3,4]=>[3,3,2]
[8,6,7,1,4,5,3,2]=>[1,2,3,1,1]
[7,6,8,1,4,3,5,2]=>[1,2,2,2,1]
[6,5,8,3,2,1,7,4]=>[1,2,1,1,2,1]
[7,5,8,3,1,4,6,2]=>[1,2,1,3,1]
[8,5,7,3,1,6,4,2]=>[1,2,1,2,1,1]
[1,6,8,4,2,7,3,5]=>[3,1,2,2]
[1,5,4,8,2,7,3,6]=>[2,2,2,2]
[8,4,3,7,1,6,5,2]=>[1,1,2,2,1,1]
[7,4,3,8,1,5,6,2]=>[1,1,2,3,1]
[6,4,3,1,5,2,7,8]=>[1,1,1,2,3]
[7,4,3,1,2,6,5,8]=>[1,1,1,3,2]
[8,4,3,1,2,5,7,6]=>[1,1,1,4,1]
[1,5,4,2,3,6,7,8]=>[2,1,5]
[8,5,1,4,2,3,7,6]=>[1,1,2,3,1]
[7,5,1,4,2,6,3,8]=>[1,1,2,2,2]
[6,5,1,4,3,2,7,8]=>[1,1,2,1,3]
[5,6,1,3,4,2,7,8]=>[2,3,3]
[4,6,2,1,5,3,7,8]=>[2,1,2,3]
[3,2,6,1,5,4,7,8]=>[1,2,2,3]
[3,2,7,1,4,6,5,8]=>[1,2,3,2]
[4,7,2,1,3,6,5,8]=>[2,1,3,2]
[5,7,1,3,2,6,4,8]=>[2,2,2,2]
[6,7,1,2,4,5,3,8]=>[2,4,2]
[7,6,1,2,5,4,3,8]=>[1,1,3,1,2]
[8,6,1,2,5,3,7,4]=>[1,1,3,2,1]
[1,7,2,3,6,4,5,8]=>[2,3,3]
[8,7,1,2,3,6,5,4]=>[1,1,4,1,1]
[7,8,1,2,3,5,6,4]=>[2,5,1]
[6,8,1,2,4,3,7,5]=>[2,3,2,1]
[5,8,1,3,2,4,7,6]=>[2,2,3,1]
[4,8,2,1,3,5,7,6]=>[2,1,4,1]
[3,2,8,1,4,5,7,6]=>[1,2,4,1]
[4,1,3,2,5,6,7,8]=>[1,2,5]
[5,1,2,4,3,6,7,8]=>[1,3,4]
[6,1,2,3,5,4,7,8]=>[1,4,3]
[7,1,2,3,4,6,5,8]=>[1,5,2]
[8,1,2,3,4,5,7,6]=>[1,6,1]
[6,7,3,8,5,1,2,4]=>[2,2,1,3]
[6,7,4,5,1,8,3,2]=>[2,2,2,1,1]
[5,4,7,6,8,1,2,3]=>[1,2,2,3]
[5,3,7,8,6,1,2,4]=>[1,3,1,3]
[3,8,4,5,7,1,2,6]=>[2,3,3]
[3,4,8,6,7,1,2,5]=>[3,2,3]
[4,5,6,7,1,8,3,2]=>[4,2,1,1]
[3,5,6,2,7,4,8,1]=>[3,2,2,1]
[3,5,6,1,7,8,4,2]=>[3,3,1,1]
[2,5,6,1,8,7,4,3]=>[3,2,1,1,1]
[2,5,6,8,1,7,3,4]=>[4,2,2]
[8,2,4,5,1,6,3,7]=>[1,3,2,2]
[1,4,8,6,2,3,7,5]=>[3,1,3,1]
[1,5,6,8,2,3,7,4]=>[4,3,1]
[1,5,6,2,8,4,7,3]=>[3,2,2,1]
[2,5,6,3,4,7,8,1]=>[3,4,1]
[1,4,2,6,8,5,7,3]=>[2,3,2,1]
[8,1,3,2,5,4,6,7]=>[1,2,2,3]
[8,2,3,1,5,6,4,7]=>[1,2,3,2]
[2,8,3,1,5,7,4,6]=>[2,1,3,2]
[2,4,1,6,8,7,5,3]=>[2,3,1,1,1]
[3,4,1,6,7,8,5,2]=>[2,4,1,1]
[4,3,1,7,6,8,5,2]=>[1,1,2,2,1,1]
[5,2,7,8,1,6,3,4]=>[1,3,2,2]
[5,3,7,2,6,4,8,1]=>[1,2,2,2,1]
[6,7,3,1,5,8,4,2]=>[2,1,3,1,1]
[6,7,2,1,8,5,4,3]=>[2,1,2,1,1,1]
[6,7,2,8,1,5,3,4]=>[2,2,2,2]
[6,7,8,2,1,4,3,5]=>[3,1,2,2]
[6,7,1,2,8,4,5,3]=>[2,3,2,1]
[6,7,1,3,4,8,5,2]=>[2,4,1,1]
[5,2,7,3,4,6,8,1]=>[1,2,4,1]
[5,1,7,3,4,8,6,2]=>[1,2,3,1,1]
[5,1,7,8,2,3,6,4]=>[1,3,3,1]
[4,1,8,7,2,3,6,5]=>[1,2,1,3,1]
[3,8,1,2,7,4,5,6]=>[2,3,3]
[4,1,3,7,5,8,6,2]=>[1,3,2,1,1]
[3,1,4,5,7,8,6,2]=>[1,5,1,1]
[2,1,8,3,4,7,6,5]=>[1,2,3,1,1]
[8,2,1,3,4,6,5,7]=>[1,1,4,2]
[1,8,2,3,4,5,7,6]=>[2,5,1]
[1,2,8,3,4,6,7,5]=>[3,4,1]
[4,2,1,6,5,8,7,3]=>[1,1,2,2,1,1]
[5,2,6,1,4,8,7,3]=>[1,2,3,1,1]
[5,2,6,4,1,8,7,3]=>[1,2,1,2,1,1]
[5,2,7,4,8,1,6,3]=>[1,2,2,2,1]
[5,2,7,4,8,6,1,3]=>[1,2,2,1,2]
[5,7,2,3,8,6,1,4]=>[2,3,1,2]
[5,7,2,3,8,1,6,4]=>[2,3,2,1]
[5,6,2,3,1,8,7,4]=>[2,2,2,1,1]
[5,6,2,1,3,8,7,4]=>[2,1,3,1,1]
[5,1,6,4,2,8,7,3]=>[1,2,1,2,1,1]
[5,6,1,3,2,8,7,4]=>[2,2,2,1,1]
[5,6,3,1,2,8,7,4]=>[2,1,3,1,1]
[5,6,3,2,1,8,7,4]=>[2,1,1,2,1,1]
[5,7,3,2,8,1,6,4]=>[2,1,2,2,1]
[5,7,3,2,8,6,1,4]=>[2,1,2,1,2]
[6,7,3,8,2,1,5,4]=>[2,2,1,2,1]
[6,7,3,8,1,2,5,4]=>[2,2,3,1]
[5,7,3,1,8,2,6,4]=>[2,1,2,2,1]
[5,7,1,3,8,2,6,4]=>[2,3,2,1]
[5,1,7,4,8,2,6,3]=>[1,2,2,2,1]
[1,5,7,4,8,3,6,2]=>[3,2,2,1]
[1,5,7,4,8,6,3,2]=>[3,2,1,1,1]
[5,1,7,4,8,6,2,3]=>[1,2,2,1,2]
[5,7,1,3,8,6,2,4]=>[2,3,1,2]
[5,7,3,1,8,6,2,4]=>[2,1,2,1,2]
[6,7,3,8,1,5,2,4]=>[2,2,2,2]
[6,7,3,8,5,2,1,4]=>[2,2,1,1,2]
[6,7,8,3,1,4,2,5]=>[3,1,2,2]
[6,7,1,8,3,5,2,4]=>[2,2,2,2]
[6,1,7,8,4,5,2,3]=>[1,3,2,2]
[1,6,7,8,4,5,3,2]=>[4,2,1,1]
[1,6,7,8,4,3,5,2]=>[4,1,2,1]
[6,1,7,8,4,2,5,3]=>[1,3,1,2,1]
[6,7,1,8,3,2,5,4]=>[2,2,1,2,1]
[5,7,2,1,8,3,6,4]=>[2,1,2,2,1]
[6,7,2,8,1,3,5,4]=>[2,2,3,1]
[6,7,2,8,3,1,5,4]=>[2,2,1,2,1]
[6,7,2,8,3,5,1,4]=>[2,2,2,2]
[6,2,7,8,4,5,1,3]=>[1,3,2,2]
[6,2,7,8,4,1,5,3]=>[1,3,1,2,1]
[6,2,7,8,1,4,5,3]=>[1,3,3,1]
[5,2,7,1,8,4,6,3]=>[1,2,2,2,1]
[4,2,1,7,8,5,6,3]=>[1,1,3,2,1]
[4,1,2,7,8,6,5,3]=>[1,4,1,1,1]
[6,2,7,8,1,5,4,3]=>[1,3,2,1,1]
[6,2,7,8,5,1,4,3]=>[1,3,1,2,1]
[6,2,7,8,5,4,1,3]=>[1,3,1,1,2]
[6,7,2,8,5,3,1,4]=>[2,2,1,1,2]
[5,7,2,1,8,6,3,4]=>[2,1,2,1,2]
[5,7,1,2,8,6,3,4]=>[2,3,1,2]
[5,1,7,2,8,6,4,3]=>[1,2,2,1,1,1]
[1,5,7,3,8,6,4,2]=>[3,2,1,1,1]
[1,6,7,8,3,5,4,2]=>[4,2,1,1]
[6,1,7,8,2,5,4,3]=>[1,3,2,1,1]
[6,7,1,8,2,5,3,4]=>[2,2,2,2]
[6,7,8,2,4,1,3,5]=>[3,2,3]
[6,7,8,2,4,3,1,5]=>[3,2,1,2]
[6,7,1,8,5,2,3,4]=>[2,2,1,3]
[6,1,7,8,5,2,4,3]=>[1,3,1,2,1]
[1,6,7,8,5,3,4,2]=>[4,1,2,1]
[6,1,7,8,5,4,2,3]=>[1,3,1,1,2]
[6,7,1,8,5,3,2,4]=>[2,2,1,1,2]
[6,7,8,4,1,3,2,5]=>[3,1,2,2]
[6,3,8,5,2,7,4,1]=>[1,2,1,2,1,1]
[6,5,2,8,4,7,3,1]=>[1,1,2,2,1,1]
[6,3,4,5,8,7,2,1]=>[1,4,1,1,1]
[3,8,4,7,5,2,1,6]=>[2,2,1,1,2]
[5,8,1,4,7,2,3,6]=>[2,3,3]
[5,6,1,4,8,7,3,2]=>[2,3,1,1,1]
[3,6,4,8,5,7,1,2]=>[2,2,2,2]
[5,1,4,8,6,3,7,2]=>[1,3,1,2,1]
[3,4,7,1,8,6,5,2]=>[3,2,1,1,1]
[6,3,8,4,2,7,1,5]=>[1,2,1,2,2]
[3,6,8,7,1,4,2,5]=>[3,1,2,2]
[5,3,7,1,6,8,2,4]=>[1,2,3,2]
[4,3,8,5,6,7,2,1]=>[1,2,3,1,1]
[5,8,1,7,6,2,4,3]=>[2,2,1,2,1]
[4,6,1,2,7,8,5,3]=>[2,4,1,1]
[3,6,4,2,8,7,5,1]=>[2,1,2,1,1,1]
[6,3,7,5,2,8,1,4]=>[1,2,1,2,2]
[6,5,2,7,4,8,1,3]=>[1,1,2,2,2]
[5,7,1,4,8,3,2,6]=>[2,3,1,2]
[7,8,3,5,1,4,6,2]=>[2,2,3,1]
[5,8,1,4,6,7,2,3]=>[2,4,2]
[6,5,8,4,3,7,2,1]=>[1,2,1,2,1,1]
[6,3,7,4,2,8,5,1]=>[1,2,1,2,1,1]
[8,7,1,6,2,4,5,3]=>[1,1,2,3,1]
[3,8,6,7,1,4,5,2]=>[2,2,3,1]
[5,3,8,7,4,1,2,6]=>[1,2,1,1,3]
[4,3,8,7,1,5,6,2]=>[1,2,1,3,1]
[8,3,6,1,2,5,7,4]=>[1,2,4,1]
[5,6,1,8,7,3,2,4]=>[2,2,1,1,2]
[5,4,2,7,3,6,8,1]=>[1,1,2,3,1]
[7,5,3,6,4,2,8,1]=>[1,1,2,1,2,1]
[6,4,1,5,3,8,2,7]=>[1,1,2,2,2]
[8,2,6,3,4,7,5,1]=>[1,2,3,1,1]
[7,2,6,3,5,4,8,1]=>[1,2,2,2,1]
[6,2,7,4,3,5,8,1]=>[1,2,1,3,1]
[5,7,3,6,4,2,8,1]=>[2,2,1,2,1]
[3,7,6,4,5,2,8,1]=>[2,1,2,2,1]
[2,7,6,5,3,4,8,1]=>[2,1,1,3,1]
[6,5,4,3,1,8,2,7]=>[1,1,1,1,2,2]
[8,6,5,4,2,7,3,1]=>[1,1,1,1,2,1,1]
[8,5,4,1,7,2,6,3]=>[1,1,1,2,2,1]
[7,5,4,1,8,3,2,6]=>[1,1,1,2,1,2]
[1,6,5,2,8,3,4,7]=>[2,1,2,3]
[1,6,5,3,4,8,2,7]=>[2,1,3,2]
[5,4,6,3,1,8,2,7]=>[1,2,1,2,2]
[6,5,8,4,2,7,3,1]=>[1,2,1,2,1,1]
[5,8,2,6,4,7,3,1]=>[2,2,2,1,1]
[3,8,6,2,5,7,4,1]=>[2,1,3,1,1]
[7,8,5,3,2,6,4,1]=>[2,1,1,2,1,1]
[6,8,3,1,7,2,5,4]=>[2,1,2,2,1]
[1,8,6,3,7,5,2,4]=>[2,1,2,1,2]
[8,7,5,2,6,4,3,1]=>[1,1,1,2,1,1,1]
[8,7,1,6,2,5,4,3]=>[1,1,2,2,1,1]
[7,8,1,6,3,2,5,4]=>[2,2,1,2,1]
[2,8,1,7,3,5,6,4]=>[2,2,3,1]
[3,8,6,1,7,4,5,2]=>[2,1,2,2,1]
[4,8,1,3,7,2,6,5]=>[2,3,2,1]
[4,2,8,5,7,3,6,1]=>[1,2,2,2,1]
[5,1,7,6,8,3,2,4]=>[1,2,2,1,2]
[3,7,1,5,8,4,2,6]=>[2,3,1,2]
[6,7,3,1,8,4,2,5]=>[2,1,2,1,2]
[1,7,3,8,4,5,2,6]=>[2,2,2,2]
[1,7,2,8,5,3,4,6]=>[2,2,1,3]
[7,6,1,8,4,3,2,5]=>[1,1,2,1,1,2]
[8,6,1,7,4,2,5,3]=>[1,1,2,1,2,1]
[8,1,2,7,3,4,6,5]=>[1,3,3,1]
[7,1,2,8,3,5,4,6]=>[1,3,2,2]
[7,2,6,1,8,4,3,5]=>[1,2,2,1,2]
[8,2,6,1,7,3,5,4]=>[1,2,2,2,1]
[8,3,1,4,7,5,6,2]=>[1,1,3,2,1]
[7,3,1,5,8,4,2,6]=>[1,1,3,1,2]
[4,2,1,5,8,3,6,7]=>[1,1,3,3]
[5,4,2,7,1,8,3,6]=>[1,1,2,2,2]
[5,4,3,1,6,8,2,7]=>[1,1,1,3,2]
[4,7,5,6,8,3,2,1]=>[2,3,1,1,1]
[6,5,4,8,2,7,3,1]=>[1,1,2,2,1,1]
[6,5,1,8,7,4,2,3]=>[1,1,2,1,1,2]
[8,6,4,7,5,3,2,1]=>[1,1,2,1,1,1,1]
[5,1,8,3,7,6,2,4]=>[1,2,2,1,2]
[5,4,8,1,7,2,6,3]=>[1,2,2,2,1]
[7,5,8,3,2,6,4,1]=>[1,2,1,2,1,1]
[3,6,8,2,4,7,5,1]=>[3,3,1,1]
[5,7,3,8,2,6,4,1]=>[2,2,2,1,1]
[5,4,6,8,2,7,3,1]=>[1,3,2,1,1]
[5,2,6,8,7,3,4,1]=>[1,3,1,2,1]
[4,7,2,8,6,3,5,1]=>[2,2,1,2,1]
[3,6,8,1,7,2,5,4]=>[3,2,2,1]
[2,3,8,7,4,5,6,1]=>[3,1,3,1]
[7,2,8,6,4,3,5,1]=>[1,2,1,1,2,1]
[2,1,8,7,5,6,3,4]=>[1,2,1,2,2]
[8,2,7,6,3,5,4,1]=>[1,2,1,2,1,1]
[8,1,7,6,5,2,4,3]=>[1,2,1,1,2,1]
[7,1,8,6,5,3,2,4]=>[1,2,1,1,1,2]
[1,2,8,7,6,3,4,5]=>[3,1,1,3]
[1,3,8,7,4,6,2,5]=>[3,1,2,2]
[1,5,8,3,7,6,2,4]=>[3,2,1,2]
[5,1,6,8,7,4,2,3]=>[1,3,1,1,2]
[6,8,4,7,5,3,2,1]=>[2,2,1,1,1,1]
[6,8,7,2,5,4,3,1]=>[2,1,2,1,1,1]
[3,8,7,6,4,5,2,1]=>[2,1,1,2,1,1]
[2,8,7,6,5,3,4,1]=>[2,1,1,1,2,1]
[1,8,7,6,5,4,2,3]=>[2,1,1,1,1,2]
[5,8,6,7,3,4,1,2]=>[2,2,2,2]
[4,8,6,7,3,5,1,2]=>[2,2,2,2]
[3,8,6,7,4,5,1,2]=>[2,2,2,2]
[2,8,6,7,4,5,1,3]=>[2,2,2,2]
[1,8,6,7,4,5,2,3]=>[2,2,2,2]
[1,8,5,7,4,6,2,3]=>[2,2,2,2]
[3,8,5,7,4,6,1,2]=>[2,2,2,2]
[4,8,5,7,3,6,1,2]=>[2,2,2,2]
[7,8,3,6,4,5,1,2]=>[2,2,2,2]
[6,8,3,7,4,5,1,2]=>[2,2,2,2]
[5,8,3,7,4,6,1,2]=>[2,2,2,2]
[3,7,4,8,5,6,1,2]=>[2,2,2,2]
[4,7,3,8,5,6,1,2]=>[2,2,2,2]
[4,7,2,8,5,6,1,3]=>[2,2,2,2]
[4,7,1,8,5,6,2,3]=>[2,2,2,2]
[3,7,1,8,5,6,2,4]=>[2,2,2,2]
[3,7,2,8,5,6,1,4]=>[2,2,2,2]
[2,7,3,8,5,6,1,4]=>[2,2,2,2]
[2,7,4,8,5,6,1,3]=>[2,2,2,2]
[5,8,2,7,4,6,1,3]=>[2,2,2,2]
[6,8,2,7,4,5,1,3]=>[2,2,2,2]
[7,8,2,6,4,5,1,3]=>[2,2,2,2]
[7,8,1,6,4,5,2,3]=>[2,2,2,2]
[6,8,1,7,4,5,2,3]=>[2,2,2,2]
[5,8,1,7,4,6,2,3]=>[2,2,2,2]
[1,7,4,8,5,6,2,3]=>[2,2,2,2]
[1,7,3,8,5,6,2,4]=>[2,2,2,2]
[2,8,5,6,1,7,3,4]=>[2,2,2,2]
[1,8,5,6,2,7,3,4]=>[2,2,2,2]
[1,7,3,8,4,6,2,5]=>[2,2,2,2]
[4,8,1,7,3,6,2,5]=>[2,2,2,2]
[5,8,1,7,3,6,2,4]=>[2,2,2,2]
[6,8,1,7,3,5,2,4]=>[2,2,2,2]
[7,8,2,6,3,5,1,4]=>[2,2,2,2]
[6,8,2,7,3,5,1,4]=>[2,2,2,2]
[5,8,2,7,3,6,1,4]=>[2,2,2,2]
[4,8,2,7,3,6,1,5]=>[2,2,2,2]
[2,7,3,8,4,6,1,5]=>[2,2,2,2]
[3,7,2,8,4,6,1,5]=>[2,2,2,2]
[3,7,1,8,4,6,2,5]=>[2,2,2,2]
[1,8,4,7,3,6,2,5]=>[2,2,2,2]
[2,8,4,7,3,6,1,5]=>[2,2,2,2]
[3,8,4,7,2,6,1,5]=>[2,2,2,2]
[4,8,5,7,2,6,1,3]=>[2,2,2,2]
[3,8,5,7,2,6,1,4]=>[2,2,2,2]
[2,8,5,7,3,6,1,4]=>[2,2,2,2]
[1,8,5,7,3,6,2,4]=>[2,2,2,2]
[1,8,6,7,3,5,2,4]=>[2,2,2,2]
[2,8,6,7,3,5,1,4]=>[2,2,2,2]
[3,8,6,7,2,5,1,4]=>[2,2,2,2]
[4,8,6,7,2,5,1,3]=>[2,2,2,2]
[5,8,6,7,2,4,1,3]=>[2,2,2,2]
[6,8,5,7,1,4,2,3]=>[2,2,2,2]
[5,8,6,7,1,4,2,3]=>[2,2,2,2]
[4,8,6,7,1,5,2,3]=>[2,2,2,2]
[3,8,6,7,1,5,2,4]=>[2,2,2,2]
[1,5,2,8,6,7,3,4]=>[2,2,2,2]
[2,5,1,8,6,7,3,4]=>[2,2,2,2]
[2,6,1,8,5,7,3,4]=>[2,2,2,2]
[1,6,2,8,5,7,3,4]=>[2,2,2,2]
[3,8,5,7,1,6,2,4]=>[2,2,2,2]
[6,8,4,7,1,5,2,3]=>[2,2,2,2]
[7,8,4,6,1,5,2,3]=>[2,2,2,2]
[7,8,3,6,1,5,2,4]=>[2,2,2,2]
[6,8,3,7,1,5,2,4]=>[2,2,2,2]
[4,8,3,7,1,6,2,5]=>[2,2,2,2]
[3,8,4,7,1,6,2,5]=>[2,2,2,2]
[1,6,2,8,4,7,3,5]=>[2,2,2,2]
[2,6,1,8,4,7,3,5]=>[2,2,2,2]
[3,7,2,6,1,8,4,5]=>[2,2,2,2]
[3,7,1,6,2,8,4,5]=>[2,2,2,2]
[4,8,1,6,2,7,3,5]=>[2,2,2,2]
[5,8,1,6,2,7,3,4]=>[2,2,2,2]
[7,8,1,5,2,6,3,4]=>[2,2,2,2]
[7,8,2,5,1,6,3,4]=>[2,2,2,2]
[6,8,2,5,1,7,3,4]=>[2,2,2,2]
[5,8,2,6,1,7,3,4]=>[2,2,2,2]
[4,8,2,6,1,7,3,5]=>[2,2,2,2]
[1,7,3,6,2,8,4,5]=>[2,2,2,2]
[2,7,3,6,1,8,4,5]=>[2,2,2,2]
[6,7,4,8,3,5,1,2]=>[2,2,2,2]
[6,7,4,5,2,8,1,3]=>[2,2,2,2]
[5,7,4,6,2,3,1,8]=>[2,2,2,2]
[5,7,4,6,3,8,1,2]=>[2,2,2,2]
[5,7,4,8,3,6,1,2]=>[2,2,2,2]
[6,8,4,5,3,7,1,2]=>[2,2,2,2]
[5,8,4,6,3,7,1,2]=>[2,2,2,2]
[5,6,4,8,3,7,1,2]=>[2,2,2,2]
[5,6,3,7,2,4,1,8]=>[2,2,2,2]
[5,6,3,7,2,8,1,4]=>[2,2,2,2]
[5,6,3,8,2,7,1,4]=>[2,2,2,2]
[5,6,4,8,2,7,1,3]=>[2,2,2,2]
[5,8,4,6,2,7,1,3]=>[2,2,2,2]
[6,8,4,5,2,7,1,3]=>[2,2,2,2]
[7,8,4,5,2,6,1,3]=>[2,2,2,2]
[6,8,4,5,2,3,1,7]=>[2,2,2,2]
[5,8,4,6,2,3,1,7]=>[2,2,2,2]
[5,6,4,8,2,3,1,7]=>[2,2,2,2]
[5,6,3,8,2,4,1,7]=>[2,2,2,2]
[5,6,3,4,2,8,1,7]=>[2,2,2,2]
[4,6,3,5,2,7,1,8]=>[2,2,2,2]
[4,6,3,5,2,8,1,7]=>[2,2,2,2]
[4,6,3,8,2,5,1,7]=>[2,2,2,2]
[4,8,3,6,2,5,1,7]=>[2,2,2,2]
[5,8,3,6,2,4,1,7]=>[2,2,2,2]
[6,8,3,5,2,4,1,7]=>[2,2,2,2]
[7,8,3,5,2,4,1,6]=>[2,2,2,2]
[7,8,3,5,2,6,1,4]=>[2,2,2,2]
[5,8,3,6,2,7,1,4]=>[2,2,2,2]
[4,8,3,6,2,7,1,5]=>[2,2,2,2]
[4,6,3,8,2,7,1,5]=>[2,2,2,2]
[4,6,3,7,2,8,1,5]=>[2,2,2,2]
[4,7,3,6,2,5,1,8]=>[2,2,2,2]
[4,7,3,6,2,8,1,5]=>[2,2,2,2]
[4,7,3,8,2,6,1,5]=>[2,2,2,2]
[5,7,4,8,2,6,1,3]=>[2,2,2,2]
[5,7,3,6,2,8,1,4]=>[2,2,2,2]
[5,7,3,6,2,4,1,8]=>[2,2,2,2]
[6,7,3,5,2,4,1,8]=>[2,2,2,2]
[6,7,3,5,2,8,1,4]=>[2,2,2,2]
[6,7,4,8,2,5,1,3]=>[2,2,2,2]
[6,7,5,8,2,4,1,3]=>[2,2,2,2]
[6,8,5,7,2,3,1,4]=>[2,2,2,2]
[6,7,4,8,2,3,1,5]=>[2,2,2,2]
[6,7,3,8,2,4,1,5]=>[2,2,2,2]
[6,7,3,4,2,8,1,5]=>[2,2,2,2]
[5,7,3,4,2,6,1,8]=>[2,2,2,2]
[5,7,3,4,2,8,1,6]=>[2,2,2,2]
[5,7,4,8,2,3,1,6]=>[2,2,2,2]
[5,8,4,7,2,3,1,6]=>[2,2,2,2]
[6,8,4,7,2,3,1,5]=>[2,2,2,2]
[7,8,4,6,2,3,1,5]=>[2,2,2,2]
[7,8,3,6,2,4,1,5]=>[2,2,2,2]
[6,8,3,7,2,4,1,5]=>[2,2,2,2]
[5,8,3,7,2,4,1,6]=>[2,2,2,2]
[4,8,3,7,2,5,1,6]=>[2,2,2,2]
[4,7,3,8,2,5,1,6]=>[2,2,2,2]
[4,7,3,5,2,8,1,6]=>[2,2,2,2]
[4,7,3,5,2,6,1,8]=>[2,2,2,2]
[4,5,3,7,2,6,1,8]=>[2,2,2,2]
[4,5,3,7,2,8,1,6]=>[2,2,2,2]
[4,5,3,8,2,7,1,6]=>[2,2,2,2]
[4,8,3,5,2,7,1,6]=>[2,2,2,2]
[5,8,3,4,2,7,1,6]=>[2,2,2,2]
[6,8,3,4,2,7,1,5]=>[2,2,2,2]
[7,8,3,4,2,6,1,5]=>[2,2,2,2]
[6,8,3,4,2,5,1,7]=>[2,2,2,2]
[5,8,3,4,2,6,1,7]=>[2,2,2,2]
[4,8,3,5,2,6,1,7]=>[2,2,2,2]
[4,5,3,8,2,6,1,7]=>[2,2,2,2]
[4,5,3,6,2,8,1,7]=>[2,2,2,2]
[4,7,5,2,1,8,3,6]=>[2,1,1,2,2]
[4,8,5,2,1,7,6,3]=>[2,1,1,2,1,1]
[4,6,5,2,1,3,8,7]=>[2,1,1,3,1]
[5,6,4,2,3,1,8,7]=>[2,1,2,2,1]
[6,4,5,3,1,2,8,7]=>[1,2,1,3,1]
[5,4,6,1,3,2,8,7]=>[1,2,2,2,1]
[4,6,8,1,7,3,2,5]=>[3,2,1,2]
[4,7,8,1,6,3,5,2]=>[3,2,2,1]
[7,4,8,1,6,5,3,2]=>[1,2,2,1,1,1]
[5,4,8,1,3,7,6,2]=>[1,2,3,1,1]
[8,4,5,3,1,7,6,2]=>[1,2,1,2,1,1]
[5,4,7,1,3,8,2,6]=>[1,2,3,2]
[6,4,8,1,7,5,2,3]=>[1,2,2,1,2]
[5,6,8,7,2,1,3,4]=>[3,1,1,3]
[8,5,7,6,4,2,1,3]=>[1,2,1,1,1,2]
[8,4,6,3,7,2,1,5]=>[1,2,2,1,2]
[6,3,2,8,7,4,1,5]=>[1,1,2,1,1,2]
[2,1,6,8,7,4,3,5]=>[1,3,1,1,2]
[2,1,7,8,6,4,5,3]=>[1,3,1,2,1]
[7,3,2,8,6,4,5,1]=>[1,1,2,1,2,1]
[7,6,8,5,2,4,3,1]=>[1,2,1,2,1,1]
[5,7,8,6,2,3,1,4]=>[3,1,2,2]
[5,8,7,6,3,2,1,4]=>[2,1,1,1,1,2]
[6,8,7,5,3,2,4,1]=>[2,1,1,1,2,1]
[5,8,4,2,3,7,6,1]=>[2,1,3,1,1]
[7,8,4,2,6,5,3,1]=>[2,1,2,1,1,1]
[4,8,7,2,6,3,5,1]=>[2,1,2,2,1]
[4,8,6,2,7,3,1,5]=>[2,1,2,1,2]
[3,6,1,8,7,4,2,5]=>[2,2,1,1,2]
[3,7,1,8,6,4,5,2]=>[2,2,1,2,1]
[3,8,1,6,7,5,2,4]=>[2,3,1,2]
[3,7,1,6,8,2,5,4]=>[2,3,2,1]
[4,7,6,2,8,1,3,5]=>[2,1,2,3]
[6,7,4,2,8,1,5,3]=>[2,1,2,2,1]
[6,8,4,2,7,5,1,3]=>[2,1,2,1,2]
[2,1,8,6,7,5,3,4]=>[1,2,2,1,2]
[8,3,2,6,7,5,1,4]=>[1,1,3,1,2]
[8,6,4,3,7,5,1,2]=>[1,1,1,2,1,2]
[5,8,6,7,3,1,2,4]=>[2,2,1,3]
[6,7,5,8,1,3,4,2]=>[2,2,3,1]
[7,6,5,8,1,4,3,2]=>[1,1,2,2,1,1]
[8,6,5,7,4,1,3,2]=>[1,1,2,1,2,1]
[7,6,4,3,8,1,5,2]=>[1,1,1,2,2,1]
[7,3,2,6,8,1,5,4]=>[1,1,3,2,1]
[2,1,7,6,8,3,5,4]=>[1,2,2,2,1]
[7,5,6,8,1,4,2,3]=>[1,3,2,2]
[6,5,7,8,1,2,4,3]=>[1,3,3,1]
[8,1,3,7,4,6,5,2]=>[1,3,2,1,1]
[5,2,8,7,4,6,1,3]=>[1,2,1,2,2]
[1,6,2,5,4,7,3,8]=>[2,2,2,2]
[6,2,7,5,4,8,3,1]=>[1,2,1,2,1,1]
[8,1,3,5,4,7,6,2]=>[1,3,2,1,1]
[6,1,5,4,3,8,7,2]=>[1,2,1,2,1,1]
[6,1,8,3,4,5,7,2]=>[1,2,4,1]
[7,1,5,3,4,8,6,2]=>[1,2,3,1,1]
[7,1,4,3,5,6,8,2]=>[1,2,4,1]
[8,1,3,4,5,6,7,2]=>[1,6,1]
[1,7,2,4,5,6,3,8]=>[2,4,2]
[6,3,2,7,5,1,8,4]=>[1,1,2,1,2,1]
[8,4,7,2,5,6,1,3]=>[1,2,3,2]
[6,5,8,2,4,7,3,1]=>[1,2,3,1,1]
[8,5,2,1,4,3,7,6]=>[1,1,1,2,2,1]
[6,5,2,8,4,1,3,7]=>[1,1,2,1,3]
[5,6,2,1,4,8,3,7]=>[2,1,3,2]
[3,6,1,8,5,2,4,7]=>[2,2,1,3]
[1,2,6,3,5,4,7,8]=>[3,2,3]
[3,4,1,2,8,6,5,7]=>[2,3,1,2]
[4,3,1,2,6,8,5,7]=>[1,1,4,2]
[5,8,1,6,3,2,4,7]=>[2,2,1,3]
[6,3,8,5,2,1,4,7]=>[1,2,1,1,3]
[8,3,1,5,2,4,7,6]=>[1,1,2,3,1]
[3,8,2,6,1,5,7,4]=>[2,2,3,1]
[3,8,6,7,2,1,5,4]=>[2,2,1,2,1]
[8,5,6,4,2,1,7,3]=>[1,2,1,1,2,1]
[7,2,5,8,3,1,6,4]=>[1,3,1,2,1]
[1,7,5,6,3,2,4,8]=>[2,2,1,3]
[6,1,2,3,8,5,7,4]=>[1,4,2,1]
[7,1,2,3,6,5,8,4]=>[1,4,2,1]
[7,2,1,3,8,6,4,5]=>[1,1,3,1,2]
[1,5,7,3,2,4,6,8]=>[3,1,4]
[5,2,7,3,1,8,4,6]=>[1,2,1,2,2]
[5,8,2,4,1,3,7,6]=>[2,2,3,1]
[8,7,2,6,3,4,1,5]=>[1,1,2,2,2]
[4,8,1,6,3,2,7,5]=>[2,2,1,2,1]
[3,1,8,6,4,2,7,5]=>[1,2,1,1,2,1]
[8,1,6,7,4,3,2,5]=>[1,3,1,1,2]
[3,5,8,7,2,4,1,6]=>[3,1,2,2]
[4,2,1,3,7,8,5,6]=>[1,1,4,2]
[2,4,1,3,8,7,5,6]=>[2,3,1,2]
[2,5,8,3,1,7,4,6]=>[3,1,2,2]
[8,6,1,3,7,2,4,5]=>[1,1,3,3]
[2,8,1,3,6,4,7,5]=>[2,3,2,1]
[6,8,2,3,4,1,5,7]=>[2,3,3]
[5,1,8,3,2,4,6,7]=>[1,2,1,4]
[1,4,2,7,8,6,3,5]=>[2,3,1,2]
[1,6,2,4,8,5,3,7]=>[2,3,1,2]
[1,6,2,4,7,5,3,8]=>[2,3,1,2]
[1,7,3,8,5,2,4,6]=>[2,2,1,3]
[1,7,3,2,8,6,4,5]=>[2,1,2,1,2]
[4,2,5,7,8,6,1,3]=>[1,4,1,2]
[7,2,3,1,8,5,6,4]=>[1,2,2,2,1]
[8,2,5,1,7,3,4,6]=>[1,2,2,3]
[6,2,1,8,3,4,7,5]=>[1,1,2,3,1]
[6,2,8,3,5,1,7,4]=>[1,2,2,2,1]
[6,2,4,8,5,7,1,3]=>[1,3,2,2]
[1,3,6,4,8,5,7,2]=>[3,2,2,1]
[1,3,6,4,7,5,8,2]=>[3,2,2,1]
[6,2,4,7,5,8,1,3]=>[1,3,2,2]
[6,2,1,3,7,8,4,5]=>[1,1,4,2]
[7,8,2,1,4,3,5,6]=>[2,1,2,3]
[7,6,4,2,3,1,8,5]=>[1,1,1,2,2,1]
[5,7,2,3,1,6,8,4]=>[2,2,3,1]
[7,5,4,2,6,8,1,3]=>[1,1,1,3,2]
[1,7,5,3,4,6,8,2]=>[2,1,4,1]
[8,2,5,4,6,7,1,3]=>[1,2,3,2]
[5,2,6,3,1,8,7,4]=>[1,2,1,2,1,1]
[8,2,6,4,3,1,7,5]=>[1,2,1,1,2,1]
[8,2,7,4,1,3,5,6]=>[1,2,1,4]
[1,2,8,4,3,5,6,7]=>[3,1,4]
[1,7,4,2,3,5,6,8]=>[2,1,5]
[6,8,4,1,3,2,5,7]=>[2,1,2,3]
[1,8,7,4,3,2,5,6]=>[2,1,1,1,3]
[1,6,3,8,2,4,7,5]=>[2,2,3,1]
[5,3,8,1,2,7,4,6]=>[1,2,3,2]
[5,1,8,3,2,6,4,7]=>[1,2,1,2,2]
[5,7,3,1,2,6,4,8]=>[2,1,3,2]
[1,7,5,4,2,6,3,8]=>[2,1,1,2,2]
[1,5,8,2,4,6,3,7]=>[3,3,2]
[1,5,8,4,2,7,3,6]=>[3,1,2,2]
[1,4,6,2,8,3,7,5]=>[3,2,2,1]
[5,3,1,6,7,2,4,8]=>[1,1,3,3]
[5,3,6,1,2,8,4,7]=>[1,2,3,2]
[1,6,3,2,7,8,4,5]=>[2,1,3,2]
[1,7,4,5,3,8,6,2]=>[2,2,2,1,1]
[6,3,4,1,2,5,8,7]=>[1,2,4,1]
[6,3,1,4,2,7,5,8]=>[1,1,2,2,2]
[1,8,3,2,4,5,6,7]=>[2,1,5]
[8,6,3,2,4,1,7,5]=>[1,1,1,2,2,1]
[8,5,3,2,6,7,1,4]=>[1,1,1,3,2]
[4,5,2,6,8,1,7,3]=>[2,3,2,1]
[4,2,5,6,7,8,1,3]=>[1,5,2]
[5,2,3,6,7,1,8,4]=>[1,4,2,1]
[6,2,3,4,1,7,8,5]=>[1,3,3,1]
[7,2,3,1,4,5,8,6]=>[1,2,4,1]
[8,6,1,4,3,2,5,7]=>[1,1,2,1,3]
[8,3,1,6,5,2,4,7]=>[1,1,2,1,3]
[3,7,5,1,8,2,4,6]=>[2,1,2,3]
[4,1,5,2,8,7,3,6]=>[1,2,2,1,2]
[8,1,2,4,6,5,3,7]=>[1,4,1,2]
[8,1,2,5,4,6,3,7]=>[1,3,2,2]
[8,2,6,5,1,3,4,7]=>[1,2,1,4]
[8,3,1,6,2,5,4,7]=>[1,1,2,2,2]
[8,1,2,6,4,5,3,7]=>[1,3,2,2]
[8,1,2,5,6,4,3,7]=>[1,4,1,2]
[8,1,2,6,5,4,3,7]=>[1,3,1,1,2]
[1,7,5,4,2,8,3,6]=>[2,1,1,2,2]
[5,1,4,8,2,7,3,6]=>[1,3,2,2]
[1,4,6,8,2,7,3,5]=>[4,2,2]
[1,4,7,6,2,8,3,5]=>[3,1,2,2]
[5,1,4,7,2,8,3,6]=>[1,3,2,2]
[1,7,4,5,2,8,3,6]=>[2,2,2,2]
[3,7,5,1,2,8,4,6]=>[2,1,3,2]
[5,7,2,8,1,3,4,6]=>[2,2,4]
[5,2,8,7,1,3,4,6]=>[1,2,1,4]
[4,1,5,8,2,7,3,6]=>[1,3,2,2]
[1,4,6,2,8,7,3,5]=>[3,2,1,2]
[1,4,2,8,6,7,3,5]=>[2,2,2,2]
[3,1,2,6,4,8,7,5]=>[1,3,2,1,1]
[2,1,7,6,3,4,8,5]=>[1,2,1,3,1]
[3,1,2,7,4,6,8,5]=>[1,3,3,1]
[1,4,7,2,6,8,3,5]=>[3,3,2]
[1,2,3,6,8,5,7,4]=>[5,2,1]
[5,1,4,2,7,8,3,6]=>[1,2,3,2]
[1,4,2,7,6,8,3,5]=>[2,2,2,2]
[1,4,2,6,8,7,3,5]=>[2,3,1,2]
[3,1,2,8,4,6,7,5]=>[1,3,3,1]
[3,1,2,7,6,4,8,5]=>[1,3,1,2,1]
[5,3,7,1,8,2,4,6]=>[1,2,2,3]
[1,7,4,3,2,5,8,6]=>[2,1,1,3,1]
[4,8,7,2,1,3,5,6]=>[2,1,1,4]
[1,8,7,3,4,2,5,6]=>[2,1,2,3]
[3,1,7,8,2,6,4,5]=>[1,3,2,2]
[1,4,2,7,8,3,6,5]=>[2,3,2,1]
[5,2,8,1,3,4,7,6]=>[1,2,4,1]
[2,1,8,6,3,4,7,5]=>[1,2,1,3,1]
[1,4,2,6,8,3,7,5]=>[2,3,2,1]
[1,2,3,7,8,5,6,4]=>[5,2,1]
[1,2,3,7,5,8,6,4]=>[4,2,1,1]
[1,4,2,7,3,8,6,5]=>[2,2,2,1,1]
[3,1,7,2,8,6,4,5]=>[1,2,2,1,2]
[2,1,7,8,3,4,6,5]=>[1,3,3,1]
[1,2,3,8,7,5,6,4]=>[4,1,2,1]
[4,7,8,5,6,2,1,3]=>[3,2,1,2]
[5,7,8,4,2,6,1,3]=>[3,1,2,2]
[6,7,8,4,2,5,1,3]=>[3,1,2,2]
[8,6,3,7,2,1,5,4]=>[1,1,2,1,2,1]
[7,6,3,8,2,1,5,4]=>[1,1,2,1,2,1]
[6,7,8,3,2,1,5,4]=>[3,1,1,2,1]
[5,7,8,3,2,1,6,4]=>[3,1,1,2,1]
[2,7,8,4,3,5,6,1]=>[3,1,3,1]
[3,7,8,4,2,5,1,6]=>[3,1,2,2]
[4,7,8,3,2,1,5,6]=>[3,1,1,3]
[5,7,8,3,2,1,4,6]=>[3,1,1,3]
[7,6,3,8,2,1,4,5]=>[1,1,2,1,3]
[8,6,3,7,2,1,4,5]=>[1,1,2,1,3]
[5,6,3,8,2,1,4,7]=>[2,2,1,3]
[3,6,4,8,2,5,1,7]=>[2,2,2,2]
[2,6,4,8,3,5,7,1]=>[2,2,3,1]
[2,6,4,7,3,5,8,1]=>[2,2,3,1]
[3,6,4,7,2,5,1,8]=>[2,2,2,2]
[4,6,3,7,2,1,5,8]=>[2,2,1,3]
[5,6,3,7,2,1,4,8]=>[2,2,1,3]
[8,4,3,2,1,6,5,7]=>[1,1,1,1,2,2]
[6,4,3,2,1,7,5,8]=>[1,1,1,1,2,2]
[4,5,3,2,7,1,6,8]=>[2,1,2,3]
[3,5,4,2,8,6,1,7]=>[2,1,2,1,2]
[6,4,3,2,1,8,5,7]=>[1,1,1,1,2,2]
[7,4,3,2,1,8,5,6]=>[1,1,1,1,2,2]
[8,4,3,2,1,7,5,6]=>[1,1,1,1,2,2]
[8,4,3,2,1,7,6,5]=>[1,1,1,1,2,1,1]
[7,4,3,2,1,8,6,5]=>[1,1,1,1,2,1,1]
[6,4,3,2,1,8,7,5]=>[1,1,1,1,2,1,1]
[5,6,3,8,2,1,7,4]=>[2,2,1,2,1]
[7,5,3,2,8,1,6,4]=>[1,1,1,2,2,1]
[8,5,4,2,7,6,1,3]=>[1,1,1,2,1,2]
[7,5,4,2,8,6,1,3]=>[1,1,1,2,1,2]
[6,5,4,2,8,7,1,3]=>[1,1,1,2,1,2]
[4,6,5,8,7,2,1,3]=>[2,2,1,1,2]
[2,6,5,7,8,3,4,1]=>[2,3,2,1]
[6,5,4,2,7,8,1,3]=>[1,1,1,3,2]
[8,5,4,2,6,7,1,3]=>[1,1,1,3,2]
[8,5,3,2,6,1,7,4]=>[1,1,1,2,2,1]
[7,5,3,2,6,1,8,4]=>[1,1,1,2,2,1]
[5,6,3,7,2,1,8,4]=>[2,2,1,2,1]
[4,6,3,7,2,1,8,5]=>[2,2,1,2,1]
[3,6,4,7,2,8,1,5]=>[2,2,2,2]
[2,6,4,7,3,8,5,1]=>[2,2,2,1,1]
[3,5,4,2,7,8,1,6]=>[2,1,3,2]
[4,5,3,2,7,1,8,6]=>[2,1,2,2,1]
[7,4,3,2,1,6,8,5]=>[1,1,1,1,3,1]
[8,4,3,2,1,6,7,5]=>[1,1,1,1,3,1]
[8,4,3,2,1,5,7,6]=>[1,1,1,1,3,1]
[7,4,3,2,1,5,8,6]=>[1,1,1,1,3,1]
[6,4,3,2,1,5,8,7]=>[1,1,1,1,3,1]
[3,5,4,2,6,8,1,7]=>[2,1,3,2]
[5,6,3,4,1,2,8,7]=>[2,2,3,1]
[8,5,3,7,2,6,4,1]=>[1,1,2,2,1,1]
[8,5,7,4,2,6,3,1]=>[1,2,1,2,1,1]
[7,5,8,4,2,6,1,3]=>[1,2,1,2,2]
[2,1,7,8,5,6,3,4]=>[1,3,2,2]
[6,8,3,7,5,1,4,2]=>[2,2,1,2,1]
[5,7,3,8,1,6,2,4]=>[2,2,2,2]
[3,2,6,4,8,5,1,7]=>[1,2,2,1,2]
[3,2,5,8,4,6,1,7]=>[1,3,2,2]
[3,5,2,4,1,7,6,8]=>[2,2,2,2]
[4,2,1,5,7,3,6,8]=>[1,1,3,3]
[4,2,5,3,8,1,6,7]=>[1,2,2,3]
[4,2,5,8,3,1,6,7]=>[1,3,1,3]
[3,1,5,4,2,8,6,7]=>[1,2,1,2,2]
[4,1,5,3,8,2,6,7]=>[1,2,2,3]
[4,1,5,8,3,2,6,7]=>[1,3,1,3]
[4,3,8,5,2,1,6,7]=>[1,2,1,1,3]
[4,7,3,5,2,1,6,8]=>[2,2,1,3]
[4,3,2,7,5,1,6,8]=>[1,1,2,1,3]
[4,3,6,2,5,1,7,8]=>[1,2,2,3]
[4,6,3,2,5,1,7,8]=>[2,1,2,3]
[4,5,1,7,3,2,6,8]=>[2,2,1,3]
[3,5,1,4,2,7,6,8]=>[2,2,2,2]
[2,5,1,4,3,7,8,6]=>[2,2,3,1]
[5,2,1,4,3,7,8,6]=>[1,1,2,3,1]
[5,3,1,4,2,7,6,8]=>[1,1,2,2,2]
[4,3,1,5,7,2,6,8]=>[1,1,3,3]
[4,3,1,7,5,2,6,8]=>[1,1,2,1,3]
[4,3,6,1,5,2,7,8]=>[1,2,2,3]
[4,6,3,1,5,2,7,8]=>[2,1,2,3]
[5,3,6,4,1,2,7,8]=>[1,2,1,4]
[4,3,6,1,7,2,5,8]=>[1,2,2,3]
[6,2,4,1,3,7,8,5]=>[1,2,4,1]
[3,6,4,1,2,7,5,8]=>[2,1,3,2]
[4,6,3,1,7,2,5,8]=>[2,1,2,3]
[5,3,6,2,1,4,7,8]=>[1,2,1,4]
[5,6,2,7,1,3,4,8]=>[2,2,4]
[4,5,2,7,3,1,6,8]=>[2,2,1,3]
[4,6,7,2,3,1,5,8]=>[3,2,3]
[4,6,2,1,7,3,5,8]=>[2,1,2,3]
[3,2,6,1,4,7,5,8]=>[1,2,3,2]
[3,5,2,7,4,6,1,8]=>[2,2,2,2]
[3,7,2,4,8,5,1,6]=>[2,3,1,2]
[7,2,1,4,6,3,8,5]=>[1,1,3,2,1]
[7,3,1,4,6,8,2,5]=>[1,1,4,2]
[3,2,6,1,5,7,4,8]=>[1,2,3,2]
[6,3,2,1,5,7,4,8]=>[1,1,1,3,2]
[6,4,2,1,5,3,7,8]=>[1,1,1,2,3]
[4,2,6,1,5,3,7,8]=>[1,2,2,3]
[4,2,1,7,5,3,6,8]=>[1,1,2,1,3]
[7,4,1,5,6,2,3,8]=>[1,1,3,3]
[7,3,1,5,2,6,4,8]=>[1,1,2,2,2]
[7,2,1,5,3,6,8,4]=>[1,1,2,3,1]
[6,2,5,1,3,7,8,4]=>[1,2,4,1]
[6,3,5,1,2,7,4,8]=>[1,2,3,2]
[6,4,5,1,7,2,3,8]=>[1,2,2,3]
[5,2,6,4,1,3,7,8]=>[1,2,1,4]
[3,6,5,1,2,7,4,8]=>[2,1,3,2]
[6,5,2,1,4,7,8,3]=>[1,1,1,4,1]
[6,5,3,1,4,7,2,8]=>[1,1,1,3,2]
[2,3,1,8,5,4,7,6]=>[2,2,1,2,1]
[2,4,1,5,8,3,7,6]=>[2,3,2,1]
[2,4,1,5,3,8,7,6]=>[2,2,2,1,1]
[3,4,5,1,2,8,7,6]=>[3,3,1,1]
[3,4,5,1,8,2,7,6]=>[3,2,2,1]
[1,8,4,5,3,2,7,6]=>[2,2,1,2,1]
[2,4,8,5,3,1,7,6]=>[3,1,1,2,1]
[3,4,5,8,2,1,7,6]=>[4,1,2,1]
[3,4,5,2,8,1,7,6]=>[3,2,2,1]
[3,4,6,2,1,7,8,5]=>[3,1,3,1]
[3,4,6,2,1,7,5,8]=>[3,1,2,2]
[3,5,6,2,7,1,4,8]=>[3,2,3]
[3,5,6,2,7,1,8,4]=>[3,2,2,1]
[3,5,6,2,7,8,1,4]=>[3,3,2]
[3,4,6,2,8,7,1,5]=>[3,2,1,2]
[3,4,6,8,2,7,1,5]=>[4,2,2]
[2,4,8,6,3,7,1,5]=>[3,1,2,2]
[1,8,4,6,3,7,2,5]=>[2,2,2,2]
[1,8,4,6,3,7,5,2]=>[2,2,2,1,1]
[3,4,6,8,2,7,5,1]=>[4,2,1,1]
[3,4,6,2,8,7,5,1]=>[3,2,1,1,1]
[3,5,6,2,7,8,4,1]=>[3,3,1,1]
[3,5,6,2,7,4,1,8]=>[3,2,1,2]
[4,5,6,7,2,8,3,1]=>[4,2,1,1]
[3,5,6,8,7,2,4,1]=>[4,1,2,1]
[2,5,8,6,7,3,4,1]=>[3,2,2,1]
[1,8,5,6,7,3,4,2]=>[2,3,2,1]
[1,8,5,6,7,3,2,4]=>[2,3,1,2]
[2,5,8,6,7,3,1,4]=>[3,2,1,2]
[3,5,6,8,7,2,1,4]=>[4,1,1,2]
[4,5,6,7,2,1,8,3]=>[4,1,2,1]
[3,4,6,1,8,7,2,5]=>[3,2,1,2]
[2,4,1,6,8,7,3,5]=>[2,3,1,2]
[2,3,1,8,6,7,4,5]=>[2,2,2,2]
[1,8,3,2,6,7,5,4]=>[2,1,3,1,1]
[2,5,1,6,7,8,4,3]=>[2,4,1,1]
[2,5,1,6,7,4,8,3]=>[2,3,2,1]
[2,5,1,6,7,4,3,8]=>[2,3,1,2]
[3,5,6,1,7,4,2,8]=>[3,2,1,2]
[3,5,6,1,7,4,8,2]=>[3,2,2,1]
[3,4,6,1,8,7,5,2]=>[3,2,1,1,1]
[3,4,6,8,1,7,5,2]=>[4,2,1,1]
[2,4,8,6,1,7,5,3]=>[3,1,2,1,1]
[1,8,4,6,2,7,5,3]=>[2,2,2,1,1]
[1,8,5,6,7,2,4,3]=>[2,3,2,1]
[2,5,8,6,7,1,4,3]=>[3,2,2,1]
[3,5,6,8,7,1,4,2]=>[4,1,2,1]
[4,5,6,7,8,1,3,2]=>[5,2,1]
[4,5,6,7,1,3,8,2]=>[4,3,1]
[4,5,6,7,1,3,2,8]=>[4,2,2]
[4,5,6,7,3,1,8,2]=>[4,1,2,1]
[3,5,6,8,7,4,1,2]=>[4,1,1,2]
[2,5,8,6,7,4,1,3]=>[3,2,1,2]
[1,8,5,6,7,4,2,3]=>[2,3,1,2]
[1,8,5,6,7,4,3,2]=>[2,3,1,1,1]
[2,5,8,6,7,4,3,1]=>[3,2,1,1,1]
[8,2,5,3,7,1,6,4]=>[1,2,2,2,1]
[8,2,4,3,7,1,6,5]=>[1,2,2,2,1]
[5,8,2,4,3,7,1,6]=>[2,2,2,2]
[4,2,5,6,1,8,3,7]=>[1,3,2,2]
[4,2,5,6,1,7,3,8]=>[1,3,2,2]
[6,1,5,7,3,2,4,8]=>[1,3,1,3]
[6,1,5,8,3,2,4,7]=>[1,3,1,3]
[3,8,2,4,7,1,5,6]=>[2,3,3]
[3,6,8,2,4,7,1,5]=>[3,3,2]
[4,3,5,6,7,1,8,2]=>[1,4,2,1]
[3,7,1,5,6,8,2,4]=>[2,4,2]
[3,7,1,5,8,2,4,6]=>[2,3,3]
[8,3,2,4,6,1,5,7]=>[1,1,3,3]
[7,3,2,4,6,1,5,8]=>[1,1,3,3]
[3,2,5,1,7,4,6,8]=>[1,2,2,3]
[3,2,5,1,8,4,6,7]=>[1,2,2,3]
[3,2,5,1,7,8,4,6]=>[1,2,3,2]
[7,8,3,2,4,6,1,5]=>[2,1,3,2]
[6,1,5,7,8,3,2,4]=>[1,4,1,2]
[4,2,5,6,1,7,8,3]=>[1,3,3,1]
[5,7,6,1,8,3,4,2]=>[2,1,2,2,1]
[5,8,6,1,7,3,4,2]=>[2,1,2,2,1]
[6,1,5,8,7,3,2,4]=>[1,3,1,1,2]
[8,7,3,2,4,6,1,5]=>[1,1,1,3,2]
[3,2,5,1,8,7,4,6]=>[1,2,2,1,2]
[3,2,5,1,6,4,7,8]=>[1,2,2,3]
[3,2,4,1,8,7,5,6]=>[1,2,2,1,2]
[3,2,5,1,6,8,7,4]=>[1,2,3,1,1]
[3,8,6,5,1,7,4,2]=>[2,1,1,2,1,1]
[3,7,6,5,1,8,4,2]=>[2,1,1,2,1,1]
[6,5,1,7,8,4,2,3]=>[1,1,3,1,2]
[3,2,5,1,6,7,8,4]=>[1,2,4,1]
[3,2,4,1,8,5,6,7]=>[1,2,2,3]
[3,2,4,1,7,5,6,8]=>[1,2,2,3]
[3,2,4,1,6,8,5,7]=>[1,2,3,2]
[3,2,4,1,8,5,7,6]=>[1,2,2,2,1]
[8,3,2,4,7,6,1,5]=>[1,1,3,1,2]
[3,2,5,1,8,4,7,6]=>[1,2,2,2,1]
[3,2,5,1,6,7,4,8]=>[1,2,3,2]
[6,5,1,7,4,2,3,8]=>[1,1,2,1,3]
[6,5,1,8,4,2,3,7]=>[1,1,2,1,3]
[8,4,2,3,7,5,1,6]=>[1,1,3,1,2]
[4,2,6,1,8,3,7,5]=>[1,2,2,2,1]
[5,2,6,1,8,3,7,4]=>[1,2,2,2,1]
[8,4,6,1,7,3,5,2]=>[1,2,2,2,1]
[5,2,6,1,8,4,7,3]=>[1,2,2,2,1]
[7,4,2,3,8,5,1,6]=>[1,1,3,1,2]
[8,5,1,6,4,2,3,7]=>[1,1,2,1,3]
[7,5,1,6,4,2,3,8]=>[1,1,2,1,3]
[3,2,5,1,7,6,4,8]=>[1,2,2,1,2]
[3,2,5,1,8,6,4,7]=>[1,2,2,1,2]
[7,3,2,4,8,6,1,5]=>[1,1,3,1,2]
[8,6,1,5,7,3,2,4]=>[1,1,3,1,2]
[4,2,6,1,8,5,7,3]=>[1,2,2,2,1]
[8,5,6,1,7,3,4,2]=>[1,2,2,2,1]
[3,6,8,5,1,7,4,2]=>[3,1,2,1,1]
[8,5,1,6,7,4,2,3]=>[1,1,3,1,2]
[3,2,5,1,8,6,7,4]=>[1,2,2,2,1]
[3,2,4,1,8,6,5,7]=>[1,2,2,1,2]
[3,2,4,1,5,8,6,7]=>[1,2,3,2]
[3,2,5,1,7,8,6,4]=>[1,2,3,1,1]
[7,8,5,1,6,4,2,3]=>[2,1,2,1,2]
[3,8,5,1,7,6,4,2]=>[2,1,2,1,1,1]
[3,7,5,1,8,6,4,2]=>[2,1,2,1,1,1]
[8,7,5,1,6,4,2,3]=>[1,1,1,2,1,2]
[3,2,5,1,8,7,6,4]=>[1,2,2,1,1,1]
[6,5,7,3,1,8,4,2]=>[1,2,1,2,1,1]
[4,6,3,7,1,8,5,2]=>[2,2,2,1,1]
[4,6,3,7,5,1,8,2]=>[2,2,1,2,1]
[4,2,6,1,7,5,3,8]=>[1,2,2,1,2]
[2,5,7,4,1,6,3,8]=>[3,1,2,2]
[2,5,7,4,1,6,8,3]=>[3,1,3,1]
[5,4,7,3,6,1,8,2]=>[1,2,2,2,1]
[5,4,7,8,3,1,6,2]=>[1,3,1,2,1]
[4,3,7,5,1,8,6,2]=>[1,2,1,2,1,1]
[6,4,3,8,5,1,7,2]=>[1,1,2,1,2,1]
[5,8,4,3,6,1,7,2]=>[2,1,2,2,1]
[5,4,8,3,6,1,7,2]=>[1,2,2,2,1]
[5,4,3,6,7,1,8,2]=>[1,1,3,2,1]
[2,5,4,6,1,7,3,8]=>[2,2,2,2]
[3,2,5,8,1,6,7,4]=>[1,3,3,1]
[2,5,4,6,8,1,7,3]=>[2,3,2,1]
[5,2,8,4,1,6,7,3]=>[1,2,1,3,1]
[4,6,2,1,8,5,7,3]=>[2,1,2,2,1]
[2,4,1,7,5,8,6,3]=>[2,2,2,1,1]
[2,4,1,7,5,3,8,6]=>[2,2,1,2,1]
[2,6,4,1,8,5,3,7]=>[2,1,2,1,2]
[5,4,8,2,1,6,3,7]=>[1,2,1,2,2]
[2,5,8,4,1,6,3,7]=>[3,1,2,2]
[3,2,5,6,1,8,4,7]=>[1,3,2,2]
[4,8,3,2,6,1,5,7]=>[2,1,2,3]
[3,5,2,8,1,6,4,7]=>[2,2,2,2]
[3,2,1,6,8,5,4,7]=>[1,1,3,1,2]
[3,2,7,1,5,4,8,6]=>[1,2,2,2,1]
[3,2,7,1,5,8,6,4]=>[1,2,3,1,1]
[3,8,2,5,1,6,7,4]=>[2,2,3,1]
[4,8,3,2,6,7,1,5]=>[2,1,3,2]
[4,3,8,2,6,7,1,5]=>[1,2,3,2]
[4,3,2,6,7,8,1,5]=>[1,1,4,2]
[4,3,2,6,7,1,5,8]=>[1,1,3,3]
[4,3,7,2,6,8,1,5]=>[1,2,3,2]
[4,3,7,8,2,6,1,5]=>[1,3,2,2]
[2,5,7,4,8,1,6,3]=>[3,2,2,1]
[3,2,5,7,8,1,6,4]=>[1,4,2,1]
[3,2,5,7,1,6,8,4]=>[1,3,3,1]
[3,2,5,7,1,6,4,8]=>[1,3,2,2]
[6,3,2,7,1,5,4,8]=>[1,1,2,2,2]
[6,3,2,7,1,5,8,4]=>[1,1,2,3,1]
[6,3,2,7,8,1,5,4]=>[1,1,3,2,1]
[4,2,6,1,7,8,5,3]=>[1,2,3,1,1]
[6,5,2,1,7,8,4,3]=>[1,1,1,3,1,1]
[2,1,7,5,3,8,6,4]=>[1,2,1,2,1,1]
[6,2,1,8,5,3,7,4]=>[1,1,2,1,2,1]
[6,3,2,7,1,4,8,5]=>[1,1,2,3,1]
[6,3,2,1,4,7,8,5]=>[1,1,1,4,1]
[6,3,2,1,4,7,5,8]=>[1,1,1,3,2]
[3,5,2,1,7,4,6,8]=>[2,1,2,3]
[3,5,2,1,7,8,4,6]=>[2,1,3,2]
[5,8,4,2,1,7,3,6]=>[2,1,1,2,2]
[4,6,2,1,8,3,7,5]=>[2,1,2,2,1]
[2,4,1,7,3,8,6,5]=>[2,2,2,1,1]
[3,2,7,1,4,8,6,5]=>[1,2,3,1,1]
[3,5,8,2,1,7,4,6]=>[3,1,2,2]
[4,8,3,7,2,1,5,6]=>[2,2,1,3]
[4,3,7,2,8,1,5,6]=>[1,2,2,3]
[4,3,7,2,1,5,6,8]=>[1,2,1,4]
[4,8,3,2,7,1,5,6]=>[2,1,2,3]
[3,5,2,8,1,7,4,6]=>[2,2,2,2]
[6,3,2,8,1,4,7,5]=>[1,1,2,3,1]
[3,2,1,4,7,5,8,6]=>[1,1,3,2,1]
[5,3,2,1,8,4,6,7]=>[1,1,1,2,3]
[4,8,3,2,1,5,6,7]=>[2,1,1,4]
[4,3,8,2,1,5,6,7]=>[1,2,1,4]
[6,2,3,1,5,4,8,7]=>[1,2,2,2,1]
[8,4,5,2,3,1,7,6]=>[1,2,2,2,1]
[8,6,7,2,5,3,4,1]=>[1,2,2,2,1]
[8,2,5,3,4,1,7,6]=>[1,2,2,2,1]
[6,2,5,3,4,1,8,7]=>[1,2,2,2,1]
[6,1,5,2,4,3,8,7]=>[1,2,2,2,1]
[6,4,5,1,3,2,8,7]=>[1,2,2,2,1]
[6,1,5,3,4,2,8,7]=>[1,2,2,2,1]
[6,3,5,1,4,2,8,7]=>[1,2,2,2,1]
[8,3,5,2,4,1,7,6]=>[1,2,2,2,1]
[8,3,7,5,6,2,4,1]=>[1,2,2,2,1]
[8,3,7,2,4,1,6,5]=>[1,2,2,2,1]
[8,3,5,1,4,2,7,6]=>[1,2,2,2,1]
[8,1,5,3,4,2,7,6]=>[1,2,2,2,1]
[8,4,5,1,3,2,7,6]=>[1,2,2,2,1]
[2,1,8,4,5,3,7,6]=>[1,2,2,2,1]
[8,6,7,4,5,1,3,2]=>[1,2,2,2,1]
[8,6,7,1,5,3,4,2]=>[1,2,2,2,1]
[8,6,7,3,5,1,4,2]=>[1,2,2,2,1]
[8,3,7,5,6,1,4,2]=>[1,2,2,2,1]
[8,5,7,3,6,1,4,2]=>[1,2,2,2,1]
[8,3,7,4,6,2,5,1]=>[1,2,2,2,1]
[8,3,7,4,6,1,5,2]=>[1,2,2,2,1]
[8,3,7,1,6,4,5,2]=>[1,2,2,2,1]
[8,1,7,3,6,4,5,2]=>[1,2,2,2,1]
[8,1,7,5,6,3,4,2]=>[1,2,2,2,1]
[8,4,7,5,6,1,3,2]=>[1,2,2,2,1]
[2,1,8,4,7,5,6,3]=>[1,2,2,2,1]
[8,1,7,3,4,2,6,5]=>[1,2,2,2,1]
[8,1,7,3,6,2,5,4]=>[1,2,2,2,1]
[8,3,7,1,6,2,5,4]=>[1,2,2,2,1]
[8,3,7,2,6,4,5,1]=>[1,2,2,2,1]
[8,2,7,3,6,4,5,1]=>[1,2,2,2,1]
[8,2,7,3,6,1,5,4]=>[1,2,2,2,1]
[8,2,7,1,6,3,5,4]=>[1,2,2,2,1]
[8,1,7,2,4,3,6,5]=>[1,2,2,2,1]
[8,1,3,2,7,4,6,5]=>[1,2,2,2,1]
[2,1,8,3,7,4,6,5]=>[1,2,2,2,1]
[8,1,5,2,4,3,7,6]=>[1,2,2,2,1]
[8,2,7,1,4,3,6,5]=>[1,2,2,2,1]
[8,2,7,3,4,1,6,5]=>[1,2,2,2,1]
[8,2,7,5,6,3,4,1]=>[1,2,2,2,1]
[8,4,7,5,6,2,3,1]=>[1,2,2,2,1]
[8,4,7,2,3,1,6,5]=>[1,2,2,2,1]
[8,2,3,1,7,4,6,5]=>[1,2,2,2,1]
[8,2,3,1,5,4,7,6]=>[1,2,2,2,1]
[4,2,3,1,8,5,7,6]=>[1,2,2,2,1]
[4,1,3,2,8,6,7,5]=>[1,2,2,2,1]
[8,6,7,2,3,1,5,4]=>[1,2,2,2,1]
[8,2,3,1,7,5,6,4]=>[1,2,2,2,1]
[8,5,7,2,6,3,4,1]=>[1,2,2,2,1]
[8,5,7,2,6,1,4,3]=>[1,2,2,2,1]
[8,2,7,5,6,1,4,3]=>[1,2,2,2,1]
[8,6,7,2,5,1,4,3]=>[1,2,2,2,1]
[8,6,7,1,5,2,4,3]=>[1,2,2,2,1]
[8,6,7,1,3,2,5,4]=>[1,2,2,2,1]
[2,1,8,6,7,3,5,4]=>[1,2,2,2,1]
[2,1,8,3,7,5,6,4]=>[1,2,2,2,1]
[8,1,3,2,7,5,6,4]=>[1,2,2,2,1]
[8,1,7,5,6,2,4,3]=>[1,2,2,2,1]
[8,1,7,2,6,4,5,3]=>[1,2,2,2,1]
[8,2,7,1,6,4,5,3]=>[1,2,2,2,1]
[8,2,7,4,6,1,5,3]=>[1,2,2,2,1]
[8,2,7,4,6,3,5,1]=>[1,2,2,2,1]
[8,4,7,2,6,3,5,1]=>[1,2,2,2,1]
[8,4,7,2,6,1,5,3]=>[1,2,2,2,1]
[8,4,7,1,6,2,5,3]=>[1,2,2,2,1]
[8,1,7,4,6,2,5,3]=>[1,2,2,2,1]
[8,5,7,1,6,2,4,3]=>[1,2,2,2,1]
[2,1,8,5,7,3,6,4]=>[1,2,2,2,1]
[8,5,7,4,6,1,3,2]=>[1,2,2,2,1]
[8,5,7,1,6,3,4,2]=>[1,2,2,2,1]
[8,1,7,4,6,3,5,2]=>[1,2,2,2,1]
[8,4,7,1,6,3,5,2]=>[1,2,2,2,1]
[8,4,7,3,6,1,5,2]=>[1,2,2,2,1]
[2,4,8,3,6,1,7,5]=>[3,2,2,1]
[6,5,8,1,3,2,7,4]=>[1,2,2,2,1]
[4,5,8,6,3,2,7,1]=>[3,1,1,2,1]
[6,5,8,7,3,1,2,4]=>[1,2,1,1,3]
[1,5,8,7,3,6,2,4]=>[3,1,2,2]
[1,7,2,8,4,6,5,3]=>[2,2,2,1,1]
[6,7,2,8,4,1,5,3]=>[2,2,1,2,1]
[3,6,2,8,4,5,7,1]=>[2,2,3,1]
[2,6,1,8,4,5,7,3]=>[2,2,3,1]
[2,8,4,6,1,5,7,3]=>[2,2,3,1]
[6,3,1,8,4,5,7,2]=>[1,1,2,3,1]
[3,1,6,8,4,5,7,2]=>[1,3,3,1]
[2,3,6,8,4,5,7,1]=>[4,3,1]
[6,3,7,8,4,1,5,2]=>[1,3,1,2,1]
[1,3,7,8,4,6,5,2]=>[4,2,1,1]
[1,5,7,8,2,4,6,3]=>[4,3,1]
[5,1,7,8,2,4,6,3]=>[1,3,3,1]
[3,6,7,8,4,2,5,1]=>[4,1,2,1]
[7,6,1,8,4,2,5,3]=>[1,1,2,1,2,1]
[5,6,8,7,3,2,1,4]=>[3,1,1,1,2]
[2,8,3,7,1,6,5,4]=>[2,2,2,1,1]
[5,2,8,7,3,6,1,4]=>[1,2,1,2,2]
[7,2,1,8,4,6,5,3]=>[1,1,2,2,1,1]
[3,2,7,8,4,6,5,1]=>[1,3,2,1,1]
[5,2,7,8,1,4,6,3]=>[1,3,3,1]
[1,2,7,8,5,4,6,3]=>[4,1,2,1]
[4,2,1,3,8,5,6,7]=>[1,1,3,3]
[7,2,5,8,3,4,6,1]=>[1,3,3,1]
[6,2,8,5,4,3,1,7]=>[1,2,1,1,1,2]
[2,8,3,5,4,1,6,7]=>[2,2,1,3]
[2,8,4,5,3,1,6,7]=>[2,2,1,3]
[6,4,8,5,2,3,1,7]=>[1,2,1,2,2]
[7,3,5,8,2,4,6,1]=>[1,3,3,1]
[4,3,1,2,8,5,6,7]=>[1,1,3,3]
[3,4,2,1,8,5,6,7]=>[2,1,2,3]
[2,7,6,8,4,3,5,1]=>[2,2,1,2,1]
[5,7,1,8,3,4,6,2]=>[2,2,3,1]
[3,7,5,8,1,4,6,2]=>[2,2,3,1]
[1,7,5,8,3,4,6,2]=>[2,2,3,1]
[1,6,8,5,4,3,2,7]=>[3,1,1,1,2]
[4,6,8,5,1,3,2,7]=>[3,1,2,2]
[5,6,8,1,4,3,2,7]=>[3,2,1,2]
[7,5,8,6,3,4,2,1]=>[1,2,1,2,1,1]
[2,4,8,3,6,5,1,7]=>[3,2,1,2]
[2,8,4,1,5,6,3,7]=>[2,1,3,2]
[4,1,8,3,5,6,2,7]=>[1,2,3,2]
[5,6,8,4,1,3,2,7]=>[3,1,2,2]
[4,6,8,1,5,3,2,7]=>[3,2,1,2]
[1,6,8,4,5,3,2,7]=>[3,2,1,2]
[1,7,3,8,5,4,6,2]=>[2,2,1,2,1]
[3,7,1,8,5,4,6,2]=>[2,2,1,2,1]
[2,7,3,8,4,6,5,1]=>[2,2,2,1,1]
[7,1,3,8,4,6,5,2]=>[1,3,2,1,1]
[5,7,8,4,3,6,1,2]=>[3,1,2,2]
[2,8,7,4,1,6,5,3]=>[2,1,1,2,1,1]
[2,8,5,4,3,1,6,7]=>[2,1,1,1,3]
[6,5,8,4,2,3,1,7]=>[1,2,1,2,2]
[4,1,3,2,8,5,6,7]=>[1,2,2,3]
[1,4,3,2,8,5,6,7]=>[2,1,2,3]
[7,3,2,8,5,4,6,1]=>[1,1,2,1,2,1]
[6,4,8,2,5,3,1,7]=>[1,2,2,1,2]
[2,8,4,3,5,1,6,7]=>[2,1,2,3]
[2,8,3,4,5,1,6,7]=>[2,3,3]
[6,2,8,4,5,3,1,7]=>[1,2,2,1,2]
[7,2,3,8,5,4,6,1]=>[1,3,1,2,1]
[4,2,3,1,8,5,6,7]=>[1,2,2,3]
[3,2,1,4,8,5,6,7]=>[1,1,3,3]
[5,1,3,2,4,8,6,7]=>[1,2,3,2]
[2,8,1,5,3,4,7,6]=>[2,2,3,1]
[1,2,8,4,5,3,7,6]=>[3,2,2,1]
[1,4,2,8,5,3,6,7]=>[2,2,1,3]
[1,8,4,2,5,3,6,7]=>[2,1,2,3]
[8,1,5,3,2,4,6,7]=>[1,2,1,4]
[3,8,1,5,2,4,6,7]=>[2,2,4]
[3,5,1,4,8,2,6,7]=>[2,3,3]
[1,5,2,8,4,3,6,7]=>[2,2,1,3]
[1,2,8,5,4,3,6,7]=>[3,1,1,3]
[1,2,5,4,3,8,6,7]=>[3,1,2,2]
[1,2,4,8,5,3,7,6]=>[4,1,2,1]
[1,2,7,4,8,5,3,6]=>[3,2,1,2]
[1,5,2,7,8,4,3,6]=>[2,3,1,2]
[5,1,2,7,4,8,3,6]=>[1,3,2,2]
[8,3,5,1,4,7,2,6]=>[1,2,3,2]
[2,8,1,5,4,7,3,6]=>[2,2,2,2]
[1,2,8,5,7,4,3,6]=>[3,2,1,2]
[1,2,4,8,7,5,3,6]=>[4,1,1,2]
[2,8,1,4,3,7,6,5]=>[2,2,2,1,1]
[6,1,2,8,7,4,3,5]=>[1,3,1,1,2]
[6,4,1,2,8,7,3,5]=>[1,1,3,1,2]
[3,6,4,8,1,7,2,5]=>[2,2,2,2]
[7,6,1,4,2,8,3,5]=>[1,1,2,2,2]
[7,1,6,2,8,4,3,5]=>[1,2,2,1,2]
[1,6,7,2,8,4,3,5]=>[3,2,1,2]
[6,7,1,4,2,8,3,5]=>[2,2,2,2]
[6,3,7,1,4,8,2,5]=>[1,2,3,2]
[3,7,8,1,5,2,4,6]=>[3,2,3]
[7,1,2,8,5,3,4,6]=>[1,3,1,3]
[1,7,2,8,4,5,3,6]=>[2,2,2,2]
[1,4,2,7,8,5,3,6]=>[2,3,1,2]
[6,1,2,8,4,3,7,5]=>[1,3,1,2,1]
[6,4,1,2,8,3,7,5]=>[1,1,3,2,1]
[7,6,1,3,2,4,8,5]=>[1,1,2,3,1]
[6,7,1,3,2,4,8,5]=>[2,2,3,1]
[1,2,7,3,5,8,4,6]=>[3,3,2]
[1,2,7,5,8,3,4,6]=>[3,2,3]
[5,8,1,3,7,2,4,6]=>[2,3,3]
[1,2,5,8,7,3,4,6]=>[4,1,3]
[1,2,5,8,3,7,4,6]=>[4,2,2]
[2,8,1,7,3,5,4,6]=>[2,2,2,2]
[8,6,1,3,2,4,7,5]=>[1,1,2,3,1]
[4,2,8,1,7,3,6,5]=>[1,2,2,2,1]
[2,8,1,7,4,3,6,5]=>[2,2,1,2,1]
[7,1,2,8,4,3,6,5]=>[1,3,1,2,1]
[1,2,8,4,7,5,3,6]=>[3,2,1,2]
[1,2,8,7,4,5,3,6]=>[3,1,2,2]
[2,8,1,7,5,3,4,6]=>[2,2,1,3]
[8,3,7,1,5,2,4,6]=>[1,2,2,3]
[3,8,6,1,4,7,2,5]=>[2,1,3,2]
[8,6,1,4,2,7,3,5]=>[1,1,2,2,2]
[8,1,6,2,7,4,3,5]=>[1,2,2,1,2]
[7,1,2,8,6,4,3,5]=>[1,3,1,1,2]
[7,4,1,2,8,6,3,5]=>[1,1,3,1,2]
[3,7,4,8,1,6,2,5]=>[2,2,2,2]
[3,4,8,7,1,6,2,5]=>[3,1,2,2]
[4,2,8,1,7,6,3,5]=>[1,2,2,1,2]
[2,8,1,7,6,4,3,5]=>[2,2,1,1,2]
[7,8,3,4,1,5,2,6]=>[2,2,2,2]
[7,8,3,4,1,6,2,5]=>[2,2,2,2]
[6,8,3,4,1,7,2,5]=>[2,2,2,2]
[6,7,3,4,1,8,2,5]=>[2,2,2,2]
[5,7,3,4,1,8,2,6]=>[2,2,2,2]
[5,8,3,4,1,7,2,6]=>[2,2,2,2]
[5,8,3,4,1,6,2,7]=>[2,2,2,2]
[6,8,3,4,1,5,2,7]=>[2,2,2,2]
[6,7,3,4,1,5,2,8]=>[2,2,2,2]
[5,7,3,4,1,6,2,8]=>[2,2,2,2]
[5,6,2,8,3,4,1,7]=>[2,2,2,2]
[5,6,2,7,3,4,1,8]=>[2,2,2,2]
[4,6,2,8,3,5,1,7]=>[2,2,2,2]
[4,7,3,5,1,6,2,8]=>[2,2,2,2]
[4,8,3,5,1,6,2,7]=>[2,2,2,2]
[4,8,3,5,1,7,2,6]=>[2,2,2,2]
[4,7,3,5,1,8,2,6]=>[2,2,2,2]
[5,6,2,3,1,7,4,8]=>[2,2,2,2]
[5,6,2,4,1,8,3,7]=>[2,2,2,2]
[5,6,2,4,1,7,3,8]=>[2,2,2,2]
[4,6,2,5,1,7,3,8]=>[2,2,2,2]
[4,6,2,5,1,8,3,7]=>[2,2,2,2]
[4,5,1,8,3,7,2,6]=>[2,2,2,2]
[4,5,1,7,3,8,2,6]=>[2,2,2,2]
[4,6,2,7,3,8,1,5]=>[2,2,2,2]
[5,6,2,7,3,8,1,4]=>[2,2,2,2]
[5,6,2,7,4,8,1,3]=>[2,2,2,2]
[5,6,3,8,4,7,1,2]=>[2,2,2,2]
[5,6,2,8,4,7,1,3]=>[2,2,2,2]
[5,6,2,8,3,7,1,4]=>[2,2,2,2]
[4,6,2,8,3,7,1,5]=>[2,2,2,2]
[4,5,1,7,3,6,2,8]=>[2,2,2,2]
[4,5,1,8,3,6,2,7]=>[2,2,2,2]
[6,5,3,2,1,4,8,7]=>[1,1,1,1,3,1]
[4,6,3,5,2,1,8,7]=>[2,2,1,2,1]
[8,7,3,5,2,4,1,6]=>[1,1,2,2,2]
[6,8,2,4,5,7,3,1]=>[2,4,1,1]
[8,7,2,4,5,3,1,6]=>[1,1,3,1,2]
[3,6,1,4,5,2,8,7]=>[2,3,2,1]
[8,3,7,4,5,2,1,6]=>[1,2,2,1,2]
[6,3,8,4,5,7,2,1]=>[1,2,3,1,1]
[5,8,7,4,3,6,2,1]=>[2,1,1,2,1,1]
[2,8,7,4,3,6,1,5]=>[2,1,1,2,2]
[8,1,7,4,3,6,2,5]=>[1,2,1,2,2]
[8,7,3,5,1,4,2,6]=>[1,1,2,2,2]
[2,1,6,8,5,7,4,3]=>[1,3,2,1,1]
[6,8,3,5,1,7,4,2]=>[2,2,2,1,1]
[5,1,8,4,7,6,3,2]=>[1,2,2,1,1,1]
[2,5,8,4,7,6,3,1]=>[3,2,1,1,1]
[4,3,8,1,5,6,7,2]=>[1,2,4,1]
[4,8,1,3,5,6,7,2]=>[2,5,1]
[5,8,7,4,1,6,3,2]=>[2,1,1,2,1,1]
[5,8,3,6,1,4,7,2]=>[2,2,3,1]
[4,8,3,6,1,2,7,5]=>[2,2,3,1]
[3,8,7,4,1,6,2,5]=>[2,1,1,2,2]
[3,8,1,2,5,6,7,4]=>[2,5,1]
[8,7,1,4,2,6,3,5]=>[1,1,2,2,2]
[8,6,3,1,2,4,7,5]=>[1,1,1,4,1]
[8,1,7,4,5,2,3,6]=>[1,2,2,3]
[2,8,7,4,5,1,3,6]=>[2,1,2,3]
[8,7,2,4,1,6,3,5]=>[1,1,2,2,2]
[5,8,3,6,2,4,7,1]=>[2,2,3,1]
[8,6,3,2,1,4,7,5]=>[1,1,1,1,3,1]
[8,7,3,5,2,1,4,6]=>[1,1,2,1,3]
[5,8,3,6,2,1,7,4]=>[2,2,1,2,1]
[5,8,7,4,2,6,1,3]=>[2,1,1,2,2]
[2,6,8,4,5,7,1,3]=>[3,3,2]
[6,1,8,4,5,7,2,3]=>[1,2,3,2]
[6,8,3,5,1,7,2,4]=>[2,2,2,2]
[2,1,5,8,3,6,7,4]=>[1,3,3,1]
[5,8,3,6,1,2,7,4]=>[2,2,3,1]
[4,1,8,2,5,6,7,3]=>[1,2,4,1]
[2,4,8,1,5,6,7,3]=>[3,4,1]
[4,8,2,1,5,6,7,3]=>[2,1,4,1]
[3,4,8,2,5,6,7,1]=>[3,4,1]
[5,8,1,4,7,6,2,3]=>[2,3,1,2]
[5,8,3,1,6,2,7,4]=>[2,1,2,2,1]
[4,5,3,8,6,1,7,2]=>[2,2,1,2,1]
[3,4,1,8,5,6,7,2]=>[2,2,3,1]
[4,5,7,6,2,3,8,1]=>[3,1,3,1]
[3,5,7,2,6,4,8,1]=>[3,2,2,1]
[2,5,7,3,6,4,8,1]=>[3,2,2,1]
[1,5,7,3,6,8,4,2]=>[3,3,1,1]
[8,4,3,7,6,1,5,2]=>[1,1,2,1,2,1]
[6,7,2,3,5,4,8,1]=>[2,3,2,1]
[5,2,7,3,6,4,8,1]=>[1,2,2,2,1]
[8,3,4,7,6,1,5,2]=>[1,3,1,2,1]
[8,2,4,7,1,6,5,3]=>[1,3,2,1,1]
[3,1,4,7,6,8,5,2]=>[1,3,2,1,1]
[4,1,3,7,6,8,5,2]=>[1,3,2,1,1]
[5,1,7,3,6,8,4,2]=>[1,2,3,1,1]
[6,7,1,3,5,8,4,2]=>[2,4,1,1]
[5,8,7,3,6,1,4,2]=>[2,1,2,2,1]
[4,8,3,7,6,1,5,2]=>[2,2,1,2,1]
[3,8,4,7,6,1,5,2]=>[2,2,1,2,1]
[2,8,4,7,1,6,5,3]=>[2,2,2,1,1]
[8,1,4,7,2,6,5,3]=>[1,3,2,1,1]
[8,1,3,2,7,6,5,4]=>[1,2,2,1,1,1]
[2,8,3,1,7,6,5,4]=>[2,1,2,1,1,1]
[3,8,2,1,7,6,5,4]=>[2,1,2,1,1,1]
[6,7,1,2,8,5,4,3]=>[2,3,1,1,1]
[8,2,3,1,7,6,5,4]=>[1,2,2,1,1,1]
[8,3,2,1,7,6,5,4]=>[1,1,1,2,1,1,1]
[3,4,1,7,6,8,5,2]=>[2,2,2,1,1]
[1,4,2,7,8,6,5,3]=>[2,3,1,1,1]
[8,4,2,7,1,6,5,3]=>[1,1,2,2,1,1]
[8,5,7,2,1,6,4,3]=>[1,2,1,2,1,1]
[1,5,7,2,8,6,4,3]=>[3,2,1,1,1]
[2,5,7,1,8,6,4,3]=>[3,2,1,1,1]
[3,5,7,1,6,8,4,2]=>[3,3,1,1]
[6,7,4,5,8,1,3,2]=>[2,3,2,1]
[5,4,7,6,8,1,3,2]=>[1,2,2,2,1]
[2,5,7,8,1,6,4,3]=>[4,2,1,1]
[1,5,7,8,2,6,4,3]=>[4,2,1,1]
[8,5,7,1,2,6,4,3]=>[1,2,3,1,1]
[8,4,1,7,2,6,5,3]=>[1,1,2,2,1,1]
[1,4,8,7,2,6,5,3]=>[3,1,2,1,1]
[3,4,8,7,6,1,5,2]=>[3,1,1,2,1]
[4,3,8,7,6,1,5,2]=>[1,2,1,1,2,1]
[5,3,7,8,6,1,4,2]=>[1,3,1,2,1]
[6,7,2,8,1,5,4,3]=>[2,2,2,1,1]
[5,2,7,8,1,6,4,3]=>[1,3,2,1,1]
[4,2,8,7,1,6,5,3]=>[1,2,1,2,1,1]
[3,2,8,1,7,6,5,4]=>[1,2,2,1,1,1]
[1,3,8,2,7,6,5,4]=>[3,2,1,1,1]
[8,3,1,2,7,6,5,4]=>[1,1,3,1,1,1]
[8,2,1,3,7,6,5,4]=>[1,1,3,1,1,1]
[1,2,8,3,7,6,5,4]=>[3,2,1,1,1]
[2,1,8,3,7,6,5,4]=>[1,2,2,1,1,1]
[4,1,8,7,2,6,5,3]=>[1,2,1,2,1,1]
[5,1,7,8,2,6,4,3]=>[1,3,2,1,1]
[6,7,1,8,2,5,4,3]=>[2,2,2,1,1]
[5,8,7,1,2,6,4,3]=>[2,1,3,1,1]
[4,8,1,7,2,6,5,3]=>[2,2,2,1,1]
[3,8,1,2,7,6,5,4]=>[2,3,1,1,1]
[2,8,1,3,7,6,5,4]=>[2,3,1,1,1]
[1,8,2,3,7,6,5,4]=>[2,3,1,1,1]
[8,1,2,3,7,6,5,4]=>[1,4,1,1,1]
[6,7,1,8,4,5,2,3]=>[2,2,2,2]
[3,7,1,5,8,2,6,4]=>[2,3,2,1]
[2,7,1,5,8,3,6,4]=>[2,3,2,1]
[2,6,5,1,8,3,7,4]=>[2,1,2,2,1]
[3,6,5,1,8,2,7,4]=>[2,1,2,2,1]
[4,6,5,1,8,7,2,3]=>[2,1,2,1,2]
[5,6,4,1,8,7,2,3]=>[2,1,2,1,2]
[8,1,4,5,7,6,2,3]=>[1,4,1,2]
[6,4,5,1,8,7,2,3]=>[1,2,2,1,2]
[5,4,6,1,8,7,2,3]=>[1,2,2,1,2]
[4,5,6,1,8,7,2,3]=>[3,2,1,2]
[3,5,6,1,8,2,7,4]=>[3,2,2,1]
[2,5,6,1,8,3,7,4]=>[3,2,2,1]
[2,4,6,1,3,8,7,5]=>[3,3,1,1]
[3,4,6,1,2,8,7,5]=>[3,3,1,1]
[4,3,6,1,2,8,7,5]=>[1,2,3,1,1]
[5,3,6,1,8,2,7,4]=>[1,2,2,2,1]
[7,3,1,5,8,2,6,4]=>[1,1,3,2,1]
[8,1,3,5,7,2,6,4]=>[1,4,2,1]
[8,1,2,5,7,3,6,4]=>[1,4,2,1]
[7,2,1,5,8,3,6,4]=>[1,1,3,2,1]
[6,2,5,1,8,3,7,4]=>[1,2,2,2,1]
[4,2,6,1,3,8,7,5]=>[1,2,3,1,1]
[2,3,6,1,4,8,7,5]=>[3,3,1,1]
[4,2,5,3,1,8,7,6]=>[1,2,1,2,1,1]
[6,2,4,1,3,8,7,5]=>[1,2,3,1,1]
[7,2,1,4,3,8,6,5]=>[1,1,2,2,1,1]
[8,1,2,4,3,7,6,5]=>[1,3,2,1,1]
[8,1,3,4,2,7,6,5]=>[1,3,2,1,1]
[7,3,1,4,2,8,6,5]=>[1,1,2,2,1,1]
[6,3,4,1,2,8,7,5]=>[1,2,3,1,1]
[4,6,3,1,2,8,7,5]=>[2,1,3,1,1]
[3,6,4,1,2,8,7,5]=>[2,1,3,1,1]
[2,6,4,1,3,8,7,5]=>[2,1,3,1,1]
[2,7,1,4,3,8,6,5]=>[2,2,2,1,1]
[3,7,1,4,2,8,6,5]=>[2,2,2,1,1]
[4,7,1,3,2,8,6,5]=>[2,2,2,1,1]
[8,1,6,7,2,3,5,4]=>[1,3,3,1]
[4,7,1,2,3,8,6,5]=>[2,4,1,1]
[3,7,1,2,4,8,6,5]=>[2,4,1,1]
[2,7,1,3,4,8,6,5]=>[2,4,1,1]
[2,6,3,1,4,8,7,5]=>[2,1,3,1,1]
[3,6,2,1,4,8,7,5]=>[2,1,3,1,1]
[5,6,2,1,8,3,7,4]=>[2,1,2,2,1]
[6,5,2,1,8,3,7,4]=>[1,1,1,2,2,1]
[8,1,5,2,7,3,6,4]=>[1,2,2,2,1]
[8,1,4,2,3,7,6,5]=>[1,2,3,1,1]
[7,4,1,2,3,8,6,5]=>[1,1,4,1,1]
[6,4,2,1,3,8,7,5]=>[1,1,1,3,1,1]
[5,4,2,3,1,8,7,6]=>[1,1,2,2,1,1]
[3,5,2,4,1,8,7,6]=>[2,2,2,1,1]
[6,3,2,1,4,8,7,5]=>[1,1,1,3,1,1]
[7,3,1,2,4,8,6,5]=>[1,1,4,1,1]
[8,1,3,2,4,7,6,5]=>[1,2,3,1,1]
[8,1,2,3,4,7,6,5]=>[1,5,1,1]
[7,2,1,3,4,8,6,5]=>[1,1,4,1,1]
[6,2,3,1,4,8,7,5]=>[1,2,3,1,1]
[2,4,3,6,1,5,8,7]=>[2,2,3,1]
[2,4,3,6,5,8,1,7]=>[2,2,2,2]
[2,4,6,3,5,8,7,1]=>[3,3,1,1]
[2,4,6,3,5,8,1,7]=>[3,3,2]
[2,4,6,3,5,1,8,7]=>[3,2,2,1]
[2,4,6,3,1,5,8,7]=>[3,1,3,1]
[2,4,1,6,5,3,8,7]=>[2,2,1,2,1]
[2,4,6,1,5,3,8,7]=>[3,2,2,1]
[4,2,6,5,3,1,8,7]=>[1,2,1,1,2,1]
[4,2,6,5,1,3,8,7]=>[1,2,1,3,1]
[4,2,6,5,1,8,7,3]=>[1,2,1,2,1,1]
[4,2,6,5,8,1,7,3]=>[1,2,2,2,1]
[4,2,6,5,8,1,3,7]=>[1,2,2,3]
[4,2,6,5,8,3,1,7]=>[1,2,2,1,2]
[2,4,6,1,5,8,3,7]=>[3,3,2]
[2,4,1,6,5,8,3,7]=>[2,2,2,2]
[2,1,4,6,5,8,3,7]=>[1,3,2,2]
[2,4,1,6,5,8,7,3]=>[2,2,2,1,1]
[2,4,6,1,5,8,7,3]=>[3,3,1,1]
[4,2,6,5,3,8,7,1]=>[1,2,1,2,1,1]
[4,2,6,5,8,3,7,1]=>[1,2,2,2,1]
[2,6,4,3,8,7,1,5]=>[2,1,2,1,2]
[2,6,4,3,8,7,5,1]=>[2,1,2,1,1,1]
[4,2,6,8,5,3,7,1]=>[1,3,1,2,1]
[2,4,6,8,1,5,7,3]=>[4,3,1]
[2,4,6,1,8,5,7,3]=>[3,2,2,1]
[2,4,1,6,8,5,7,3]=>[2,3,2,1]
[2,1,4,6,8,5,7,3]=>[1,4,2,1]
[2,1,4,6,8,5,3,7]=>[1,4,1,2]
[2,4,1,6,8,5,3,7]=>[2,3,1,2]
[2,4,6,1,8,5,3,7]=>[3,2,1,2]
[2,4,6,8,1,5,3,7]=>[4,2,2]
[4,2,6,8,5,3,1,7]=>[1,3,1,1,2]
[4,2,6,8,5,1,3,7]=>[1,3,1,3]
[4,2,6,8,5,1,7,3]=>[1,3,1,2,1]
[2,4,6,8,3,5,7,1]=>[4,3,1]
[2,4,6,8,3,5,1,7]=>[4,2,2]
[2,4,6,8,3,1,5,7]=>[4,1,3]
[2,4,6,3,1,8,5,7]=>[3,1,2,2]
[2,4,6,3,8,1,5,7]=>[3,2,3]
[2,4,6,3,8,5,1,7]=>[3,2,1,2]
[2,4,6,3,8,5,7,1]=>[3,2,2,1]
[2,4,3,6,8,5,7,1]=>[2,3,2,1]
[2,4,3,6,8,5,1,7]=>[2,3,1,2]
[2,4,3,6,8,1,5,7]=>[2,3,3]
[2,4,3,6,1,8,5,7]=>[2,2,2,2]
[2,4,3,1,6,8,5,7]=>[2,1,3,2]
[2,4,1,3,6,8,7,5]=>[2,4,1,1]
[2,4,3,6,1,8,7,5]=>[2,2,2,1,1]
[2,4,3,6,8,1,7,5]=>[2,3,2,1]
[4,6,5,2,8,7,3,1]=>[2,1,2,1,1,1]
[4,6,5,2,8,7,1,3]=>[2,1,2,1,2]
[4,6,2,5,8,7,1,3]=>[2,3,1,2]
[4,6,2,5,8,7,3,1]=>[2,3,1,1,1]
[2,4,6,3,8,1,7,5]=>[3,2,2,1]
[2,4,6,3,1,8,7,5]=>[3,1,2,1,1]
[2,4,1,6,3,8,7,5]=>[2,2,2,1,1]
[2,1,4,6,3,8,7,5]=>[1,3,2,1,1]
[2,1,4,6,8,3,7,5]=>[1,4,2,1]
[2,4,1,6,8,3,7,5]=>[2,3,2,1]
[2,4,6,1,8,3,7,5]=>[3,2,2,1]
[2,4,6,8,1,3,7,5]=>[4,3,1]
[2,4,6,8,3,1,7,5]=>[4,1,2,1]
[4,6,2,8,5,7,3,1]=>[2,2,2,1,1]
[4,6,2,8,5,7,1,3]=>[2,2,2,2]
[6,2,4,8,7,1,3,5]=>[1,3,1,3]
[6,4,2,8,7,5,3,1]=>[1,1,2,1,1,1,1]
[2,6,4,8,1,7,5,3]=>[2,2,2,1,1]
[2,6,4,1,8,7,5,3]=>[2,1,2,1,1,1]
[2,6,1,4,8,7,5,3]=>[2,3,1,1,1]
[2,1,6,4,8,7,5,3]=>[1,2,2,1,1,1]
[2,1,6,4,8,7,3,5]=>[1,2,2,1,2]
[2,6,1,4,8,7,3,5]=>[2,3,1,2]
[2,6,4,1,8,7,3,5]=>[2,1,2,1,2]
[2,6,4,8,1,7,3,5]=>[2,2,2,2]
[6,4,2,8,7,5,1,3]=>[1,1,2,1,1,2]
[6,2,4,8,7,3,5,1]=>[1,3,1,2,1]
[6,2,4,8,7,3,1,5]=>[1,3,1,1,2]
[1,6,4,7,3,8,2,5]=>[2,2,2,2]
[1,3,7,4,5,8,2,6]=>[3,3,2]
[5,2,4,7,3,6,8,1]=>[1,3,3,1]
[1,7,6,3,4,8,2,5]=>[2,1,3,2]
[8,1,6,3,7,2,4,5]=>[1,2,2,3]
[7,1,6,3,8,2,4,5]=>[1,2,2,3]
[1,2,7,4,8,3,5,6]=>[3,2,3]
[6,1,7,3,4,8,2,5]=>[1,2,3,2]
[2,1,7,4,5,8,3,6]=>[1,2,3,2]
[5,1,4,7,3,8,2,6]=>[1,3,2,2]
[4,3,1,7,5,8,2,6]=>[1,1,2,2,2]
[2,8,6,3,7,1,4,5]=>[2,1,2,3]
[6,8,1,3,7,2,4,5]=>[2,3,3]
[5,8,2,1,7,3,4,6]=>[2,1,2,3]
[5,7,2,1,8,3,4,6]=>[2,1,2,3]
[6,7,1,3,8,2,4,5]=>[2,3,3]
[5,1,2,4,8,3,6,7]=>[1,4,3]
[4,3,6,1,5,8,2,7]=>[1,2,3,2]
[2,6,1,4,5,8,3,7]=>[2,4,2]
[6,5,1,3,4,8,2,7]=>[1,1,4,2]
[1,6,2,4,8,3,5,7]=>[2,3,3]
[8,5,1,3,7,2,4,6]=>[1,1,3,3]
[1,5,3,2,8,4,6,7]=>[2,1,2,3]
[6,4,2,1,5,8,3,7]=>[1,1,1,3,2]
[2,5,3,4,1,8,6,7]=>[2,2,2,2]
[4,3,5,2,1,8,6,7]=>[1,2,1,2,2]
[2,6,4,8,7,1,3,5]=>[2,2,1,3]
[1,6,4,8,7,2,3,5]=>[2,2,1,3]
[2,7,8,3,6,1,4,5]=>[3,2,3]
[4,3,2,8,7,1,5,6]=>[1,1,2,1,3]
[5,2,4,8,7,1,3,6]=>[1,3,1,3]
[6,2,8,3,7,1,4,5]=>[1,2,2,3]
[5,1,4,8,7,2,3,6]=>[1,3,1,3]
[4,8,2,5,1,3,7,6]=>[2,2,3,1]
[4,7,2,5,1,3,8,6]=>[2,2,3,1]
[3,7,2,1,5,4,8,6]=>[2,1,2,2,1]
[3,8,2,1,5,4,7,6]=>[2,1,2,2,1]
[8,3,2,1,5,4,6,7]=>[1,1,1,2,3]
[8,3,2,1,6,4,5,7]=>[1,1,1,2,3]
[8,4,2,5,1,6,3,7]=>[1,1,2,2,2]
[8,3,2,1,5,6,4,7]=>[1,1,1,3,2]
[8,3,2,1,4,6,5,7]=>[1,1,1,3,2]
[3,8,2,1,4,5,7,6]=>[2,1,4,1]
[3,7,2,1,4,5,8,6]=>[2,1,4,1]
[3,2,7,1,4,6,8,5]=>[1,2,4,1]
[3,2,8,1,4,6,7,5]=>[1,2,4,1]
[3,2,8,1,4,7,6,5]=>[1,2,3,1,1]
[3,8,2,1,4,7,5,6]=>[2,1,3,2]
[3,8,2,1,5,7,4,6]=>[2,1,3,2]
[4,8,2,5,1,7,3,6]=>[2,2,2,2]
[4,7,2,5,1,8,3,6]=>[2,2,2,2]
[3,7,2,1,5,8,4,6]=>[2,1,3,2]
[3,7,2,1,4,8,5,6]=>[2,1,3,2]
[3,2,1,7,5,8,6,4]=>[1,1,2,2,1,1]
[3,2,7,1,6,8,4,5]=>[1,2,3,2]
[4,2,7,6,1,8,3,5]=>[1,2,1,2,2]
[4,3,7,6,8,1,2,5]=>[1,2,2,3]
[4,3,8,6,7,1,2,5]=>[1,2,2,3]
[4,2,8,6,1,7,3,5]=>[1,2,1,2,2]
[3,2,8,1,6,7,4,5]=>[1,2,3,2]
[3,2,1,8,7,5,6,4]=>[1,1,2,1,2,1]
[3,8,2,1,7,4,5,6]=>[2,1,2,3]
[3,2,8,1,7,4,6,5]=>[1,2,2,2,1]
[3,2,8,1,6,4,7,5]=>[1,2,2,2,1]
[3,2,7,1,6,4,8,5]=>[1,2,2,2,1]
[4,2,7,6,1,3,8,5]=>[1,2,1,3,1]
[4,2,8,6,1,3,7,5]=>[1,2,1,3,1]
[4,2,8,7,1,3,6,5]=>[1,2,1,3,1]
[5,7,8,3,4,1,2,6]=>[3,2,3]
[4,2,7,8,1,3,6,5]=>[1,3,3,1]
[4,2,6,8,1,3,7,5]=>[1,3,3,1]
[4,2,6,7,1,3,8,5]=>[1,3,3,1]
[3,2,6,1,8,4,7,5]=>[1,2,2,2,1]
[3,7,2,1,8,4,5,6]=>[2,1,2,3]
[3,7,2,1,8,5,4,6]=>[2,1,2,1,2]
[4,7,3,8,5,1,2,6]=>[2,2,1,3]
[4,3,7,8,6,1,2,5]=>[1,3,1,3]
[3,2,7,1,8,6,4,5]=>[1,2,2,1,2]
[3,2,1,6,8,5,7,4]=>[1,1,3,2,1]
[3,2,6,1,8,7,4,5]=>[1,2,2,1,2]
[4,2,6,8,1,7,3,5]=>[1,3,2,2]
[4,3,6,8,7,1,2,5]=>[1,3,1,3]
[4,2,6,7,1,8,3,5]=>[1,3,2,2]
[3,2,6,1,7,8,4,5]=>[1,2,3,2]
[3,4,6,8,7,5,1,2]=>[4,1,1,2]
[5,3,6,4,8,7,1,2]=>[1,2,2,1,2]
[1,4,6,2,7,8,5,3]=>[3,3,1,1]
[3,1,8,5,4,2,6,7]=>[1,2,1,1,3]
[1,2,7,5,4,8,6,3]=>[3,1,2,1,1]
[6,3,7,5,4,8,1,2]=>[1,2,1,2,2]
[7,3,8,5,4,6,1,2]=>[1,2,1,2,2]
[3,8,7,5,4,6,1,2]=>[2,1,1,2,2]
[4,3,6,7,8,5,1,2]=>[1,4,1,2]
[4,5,6,3,8,7,1,2]=>[3,2,1,2]
[3,6,8,5,4,7,1,2]=>[3,1,2,2]
[6,8,3,5,4,7,1,2]=>[2,2,2,2]
[7,6,3,5,4,8,1,2]=>[1,1,2,2,2]
[1,6,2,5,4,8,7,3]=>[2,2,2,1,1]
[7,1,2,5,8,3,6,4]=>[1,4,2,1]
[1,8,2,5,7,3,6,4]=>[2,3,2,1]
[6,2,1,5,4,8,7,3]=>[1,1,2,2,1,1]
[4,1,6,2,8,7,5,3]=>[1,2,2,1,1,1]
[7,8,1,2,4,6,5,3]=>[2,4,1,1]
[7,8,3,1,4,2,6,5]=>[2,1,2,2,1]
[4,3,6,1,8,2,7,5]=>[1,2,2,2,1]
[2,3,8,5,4,1,6,7]=>[3,1,1,3]
[4,8,1,5,2,3,7,6]=>[2,2,3,1]
[7,5,1,6,4,3,2,8]=>[1,1,2,1,1,2]
[5,8,1,6,4,3,2,7]=>[2,2,1,1,2]
[6,1,5,7,4,3,2,8]=>[1,3,1,1,2]
[1,5,8,6,4,3,2,7]=>[3,1,1,1,2]
[3,4,6,1,5,8,2,7]=>[3,3,2]
[7,8,4,1,5,3,2,6]=>[2,1,2,1,2]
[7,8,5,1,6,3,2,4]=>[2,1,2,1,2]
[2,6,1,5,7,3,8,4]=>[2,3,2,1]
[1,6,8,7,4,3,2,5]=>[3,1,1,1,2]
[6,8,1,7,4,3,2,5]=>[2,2,1,1,2]
[5,6,1,7,4,3,2,8]=>[2,2,1,1,2]
[5,1,7,6,4,3,2,8]=>[1,2,1,1,1,2]
[6,1,7,8,4,3,2,5]=>[1,3,1,1,2]
[7,1,8,6,4,3,2,5]=>[1,2,1,1,1,2]
[1,8,7,6,4,3,2,5]=>[2,1,1,1,1,2]
[2,1,7,5,6,3,8,4]=>[1,2,2,2,1]
[3,1,6,7,5,8,2,4]=>[1,3,2,2]
[7,8,1,6,5,3,2,4]=>[2,2,1,1,2]
[7,8,2,1,4,5,6,3]=>[2,1,4,1]
[2,8,1,5,4,6,7,3]=>[2,2,3,1]
[7,2,1,5,4,6,8,3]=>[1,1,2,3,1]
[1,2,8,5,6,3,7,4]=>[3,2,2,1]
[6,1,2,5,7,3,8,4]=>[1,4,2,1]
[4,2,1,5,6,3,7,8]=>[1,1,3,3]
[4,3,6,1,5,7,2,8]=>[1,2,3,2]
[5,1,6,3,7,8,2,4]=>[1,2,3,2]
[1,3,6,8,5,7,2,4]=>[4,2,2]
[2,4,6,3,7,1,8,5]=>[3,2,2,1]
[1,3,6,4,8,7,2,5]=>[3,2,1,2]
[4,1,6,7,3,8,2,5]=>[1,3,2,2]
[5,4,6,1,3,7,2,8]=>[1,2,3,2]
[6,4,1,5,2,3,7,8]=>[1,1,2,4]
[4,1,7,5,2,3,8,6]=>[1,2,1,3,1]
[1,2,4,5,8,3,7,6]=>[5,2,1]
[7,2,3,5,4,1,8,6]=>[1,3,1,2,1]
[2,8,3,5,4,1,7,6]=>[2,2,1,2,1]
[4,2,6,3,8,1,7,5]=>[1,2,2,2,1]
[7,8,2,3,4,1,6,5]=>[2,3,2,1]
[7,8,1,4,6,3,2,5]=>[2,3,1,2]
[3,1,6,4,7,8,2,5]=>[1,2,3,2]
[1,8,5,7,4,3,2,6]=>[2,2,1,1,2]
[7,1,5,8,4,3,2,6]=>[1,3,1,1,2]
[5,1,8,7,4,3,2,6]=>[1,2,1,1,1,2]
[6,5,1,8,4,3,2,7]=>[1,1,2,1,1,2]
[6,5,7,1,4,3,2,8]=>[1,2,2,1,2]
[7,5,8,1,4,3,2,6]=>[1,2,2,1,2]
[5,8,7,1,4,3,2,6]=>[2,1,2,1,2]
[1,5,7,8,4,3,2,6]=>[4,1,1,2]
[2,4,7,5,1,3,8,6]=>[3,1,3,1]
[7,8,4,6,1,3,2,5]=>[2,2,2,2]
[7,8,5,4,1,3,2,6]=>[2,1,1,2,2]
[3,5,6,4,1,8,2,7]=>[3,1,2,2]
[2,6,4,5,1,3,8,7]=>[2,2,3,1]
[1,6,5,8,4,3,2,7]=>[2,2,1,1,2]
[6,8,5,1,4,3,2,7]=>[2,1,2,1,2]
[7,6,5,1,4,3,2,8]=>[1,1,1,2,1,2]
[3,4,6,2,7,1,5,8]=>[3,2,3]
[3,6,2,5,4,1,7,8]=>[2,2,1,3]
[3,2,7,5,4,1,6,8]=>[1,2,1,1,3]
[4,3,6,2,8,1,5,7]=>[1,2,2,3]
[6,1,2,5,4,7,8,3]=>[1,3,3,1]
[6,2,4,5,1,3,7,8]=>[1,3,4]
[4,2,8,5,1,3,7,6]=>[1,2,1,3,1]
[4,3,6,8,1,7,2,5]=>[1,3,2,2]
[5,3,6,4,1,7,2,8]=>[1,2,1,2,2]
[6,2,1,5,8,3,7,4]=>[1,1,3,2,1]
[1,6,7,4,8,3,5,2]=>[3,2,2,1]
[1,4,6,3,7,5,8,2]=>[3,2,2,1]
[4,6,7,2,5,8,1,3]=>[3,3,2]
[2,4,6,1,7,5,3,8]=>[3,2,1,2]
[2,7,5,4,1,6,3,8]=>[2,1,1,2,2]
[7,5,4,6,2,8,1,3]=>[1,1,2,2,2]
[1,7,5,4,3,8,6,2]=>[2,1,1,2,1,1]
[1,4,6,3,5,8,7,2]=>[3,3,1,1]
[1,5,8,4,3,6,7,2]=>[3,1,3,1]
[5,4,6,2,7,8,1,3]=>[1,2,3,2]
[2,5,4,1,6,7,3,8]=>[2,1,3,2]
[5,6,3,2,7,1,4,8]=>[2,1,2,3]
[5,6,3,2,7,1,8,4]=>[2,1,2,2,1]
[8,5,6,3,2,7,1,4]=>[1,2,1,2,2]
[5,4,6,2,8,1,7,3]=>[1,2,2,2,1]
[2,4,1,7,8,5,3,6]=>[2,3,1,2]
[2,5,4,1,6,3,8,7]=>[2,1,2,2,1]
[5,6,3,2,1,8,4,7]=>[2,1,1,2,2]
[3,5,2,1,6,4,7,8]=>[2,1,2,3]
[6,8,4,3,2,1,5,7]=>[2,1,1,1,3]
[5,3,8,2,1,6,4,7]=>[1,2,1,2,2]
[3,7,5,8,2,1,4,6]=>[2,2,1,3]
[7,3,2,8,5,1,6,4]=>[1,1,2,1,2,1]
[8,4,6,3,2,1,7,5]=>[1,2,1,1,2,1]
[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,2,1]
[7,6,4,3,2,1,8,5]=>[1,1,1,1,1,2,1]
[7,8,4,3,2,1,6,5]=>[2,1,1,1,2,1]
[5,4,7,2,1,8,6,3]=>[1,2,1,2,1,1]
[7,5,8,3,2,6,1,4]=>[1,2,1,2,2]
[5,7,3,2,1,6,8,4]=>[2,1,1,3,1]
[5,7,3,2,1,6,4,8]=>[2,1,1,2,2]
[6,3,7,2,5,1,8,4]=>[1,2,2,2,1]
[6,7,8,3,5,2,1,4]=>[3,2,1,2]
[6,2,5,7,8,4,1,3]=>[1,4,1,2]
[2,1,5,7,8,6,3,4]=>[1,4,1,2]
[3,6,7,2,8,1,4,5]=>[3,2,3]
[6,3,7,2,8,1,4,5]=>[1,2,2,3]
[3,2,6,1,7,4,5,8]=>[1,2,2,3]
[3,5,2,1,4,7,6,8]=>[2,1,3,2]
[7,3,5,2,1,8,4,6]=>[1,2,1,2,2]
[2,5,4,1,3,7,8,6]=>[2,1,4,1]
[2,5,8,4,1,3,7,6]=>[3,1,3,1]
[2,4,1,7,8,3,6,5]=>[2,3,2,1]
[3,7,2,8,6,1,4,5]=>[2,2,1,3]
[3,6,8,2,1,7,4,5]=>[3,1,2,2]
[5,3,8,2,1,4,7,6]=>[1,2,1,3,1]
[4,8,7,3,2,1,5,6]=>[2,1,1,1,3]
[4,7,3,2,1,5,6,8]=>[2,1,1,4]
[8,4,7,3,2,1,5,6]=>[1,2,1,1,3]
[8,3,5,2,1,4,7,6]=>[1,2,1,3,1]
[7,3,2,8,6,1,4,5]=>[1,1,2,1,3]
[3,5,2,1,4,6,8,7]=>[2,1,4,1]
[7,8,3,5,4,6,1,2]=>[2,2,2,2]
[8,6,3,7,5,2,4,1]=>[1,1,2,1,2,1]
[5,4,1,6,3,2,8,7]=>[1,1,2,1,2,1]
[5,4,1,6,2,3,8,7]=>[1,1,2,3,1]
[5,7,1,6,2,8,3,4]=>[2,2,2,2]
[5,7,1,6,2,8,4,3]=>[2,2,2,1,1]
[2,7,6,5,1,8,3,4]=>[2,1,1,2,2]
[2,7,6,5,1,8,4,3]=>[2,1,1,2,1,1]
[2,3,6,5,1,4,8,7]=>[3,1,3,1]
[2,3,6,4,1,5,8,7]=>[3,1,3,1]
[2,3,6,1,5,4,8,7]=>[3,2,2,1]
[2,7,6,1,4,8,5,3]=>[2,1,3,1,1]
[2,7,6,1,4,8,3,5]=>[2,1,3,2]
[7,3,5,1,8,4,2,6]=>[1,2,2,1,2]
[7,3,5,1,8,6,4,2]=>[1,2,2,1,1,1]
[2,7,6,1,5,8,4,3]=>[2,1,3,1,1]
[2,7,6,4,1,8,5,3]=>[2,1,1,2,1,1]
[2,1,7,6,3,8,5,4]=>[1,2,1,2,1,1]
[2,1,7,6,3,8,4,5]=>[1,2,1,2,2]
[5,7,3,6,2,8,4,1]=>[2,2,2,1,1]
[2,7,6,4,1,8,3,5]=>[2,1,1,2,2]
[7,3,5,1,8,6,2,4]=>[1,2,2,1,2]
[6,3,5,1,8,2,4,7]=>[1,2,2,3]
[2,3,4,8,7,6,1,5]=>[4,1,1,2]
[2,3,4,8,5,7,1,6]=>[4,2,2]
[7,3,5,4,8,1,2,6]=>[1,2,2,3]
[6,4,3,5,8,7,2,1]=>[1,1,3,1,1,1]
[2,1,4,5,8,7,3,6]=>[1,4,1,2]
[6,4,3,5,8,7,1,2]=>[1,1,3,1,2]
[7,3,5,4,8,1,6,2]=>[1,2,2,2,1]
[2,3,4,8,7,5,6,1]=>[4,1,2,1]
[2,3,4,8,7,5,1,6]=>[4,1,1,2]
[2,7,6,5,4,8,1,3]=>[2,1,1,2,2]
[7,3,5,6,8,4,1,2]=>[1,4,1,2]
[7,3,5,6,8,1,4,2]=>[1,4,2,1]
[7,3,5,6,8,1,2,4]=>[1,4,3]
[6,4,1,5,8,7,2,3]=>[1,1,3,1,2]
[6,4,1,5,8,7,3,2]=>[1,1,3,1,1,1]
[6,4,1,5,8,3,7,2]=>[1,1,3,2,1]
[5,7,1,6,3,8,2,4]=>[2,2,2,2]
[6,4,1,5,8,3,2,7]=>[1,1,3,1,2]
[7,4,1,5,8,2,3,6]=>[1,1,3,3]
[7,4,1,5,8,2,6,3]=>[1,1,3,2,1]
[6,3,5,7,8,2,1,4]=>[1,4,1,2]
[6,3,5,7,8,2,4,1]=>[1,4,2,1]
[2,7,6,4,5,8,3,1]=>[2,1,3,1,1]
[5,7,3,6,1,8,4,2]=>[2,2,2,1,1]
[2,1,4,5,8,6,3,7]=>[1,4,1,2]
[7,3,5,4,8,6,2,1]=>[1,2,2,1,1,1]
[2,3,4,8,5,6,1,7]=>[4,2,2]
[2,3,4,8,7,1,6,5]=>[4,1,2,1]
[2,3,4,8,1,7,6,5]=>[4,2,1,1]
[2,3,4,8,1,6,7,5]=>[4,3,1]
[2,3,4,8,5,1,7,6]=>[4,1,2,1]
[6,3,5,4,8,2,7,1]=>[1,2,2,2,1]
[7,4,3,5,8,2,1,6]=>[1,1,3,1,2]
[2,1,4,5,8,3,7,6]=>[1,4,2,1]
[7,4,3,5,8,2,6,1]=>[1,1,3,2,1]
[6,3,5,4,8,2,1,7]=>[1,2,2,1,2]
[2,3,4,8,5,1,6,7]=>[4,1,3]
[2,3,4,8,1,6,5,7]=>[4,2,2]
[2,3,4,8,1,5,7,6]=>[4,3,1]
[7,8,2,6,1,5,3,4]=>[2,2,2,2]
[7,8,1,6,2,5,3,4]=>[2,2,2,2]
[1,8,6,7,2,5,3,4]=>[2,2,2,2]
[1,8,5,7,2,6,3,4]=>[2,2,2,2]
[5,8,1,7,2,6,3,4]=>[2,2,2,2]
[5,8,2,7,1,6,3,4]=>[2,2,2,2]
[2,8,6,7,1,5,3,4]=>[2,2,2,2]
[2,8,5,7,1,6,3,4]=>[2,2,2,2]
[2,8,1,7,5,6,3,4]=>[2,2,2,2]
[1,8,2,7,5,6,3,4]=>[2,2,2,2]
[1,8,2,7,4,6,3,5]=>[2,2,2,2]
[2,8,1,7,4,6,3,5]=>[2,2,2,2]
[2,8,4,7,1,6,3,5]=>[2,2,2,2]
[4,8,2,7,1,6,3,5]=>[2,2,2,2]
[4,8,1,7,2,6,3,5]=>[2,2,2,2]
[1,8,4,7,2,6,3,5]=>[2,2,2,2]
[4,8,1,7,5,6,2,3]=>[2,2,2,2]
[1,8,4,7,5,6,2,3]=>[2,2,2,2]
[1,8,3,7,5,6,2,4]=>[2,2,2,2]
[3,8,1,7,5,6,2,4]=>[2,2,2,2]
[3,8,1,7,4,6,2,5]=>[2,2,2,2]
[1,8,3,7,4,6,2,5]=>[2,2,2,2]
[1,8,3,7,2,6,4,5]=>[2,2,2,2]
[3,8,1,7,2,6,4,5]=>[2,2,2,2]
[3,8,2,7,1,6,4,5]=>[2,2,2,2]
[3,8,2,7,4,6,1,5]=>[2,2,2,2]
[3,8,2,7,5,6,1,4]=>[2,2,2,2]
[4,8,2,7,5,6,1,3]=>[2,2,2,2]
[4,8,3,7,5,6,1,2]=>[2,2,2,2]
[3,8,4,7,5,6,1,2]=>[2,2,2,2]
[2,8,4,7,5,6,1,3]=>[2,2,2,2]
[2,8,3,7,5,6,1,4]=>[2,2,2,2]
[2,8,3,7,4,6,1,5]=>[2,2,2,2]
[2,8,3,7,1,6,4,5]=>[2,2,2,2]
[2,8,1,7,3,6,4,5]=>[2,2,2,2]
[7,5,2,8,6,4,1,3]=>[1,1,2,1,1,2]
[7,5,1,8,6,2,3,4]=>[1,1,2,1,3]
[7,4,8,6,1,5,2,3]=>[1,2,1,2,2]
[7,1,8,4,5,2,6,3]=>[1,2,2,2,1]
[6,8,1,7,4,2,5,3]=>[2,2,1,2,1]
[1,6,7,4,2,8,5,3]=>[3,1,2,1,1]
[1,6,7,3,8,5,2,4]=>[3,2,1,2]
[7,1,8,3,5,6,2,4]=>[1,2,3,2]
[7,3,8,6,2,5,1,4]=>[1,2,1,2,2]
[7,4,2,8,6,1,3,5]=>[1,1,2,1,3]
[7,3,1,8,4,2,5,6]=>[1,1,2,1,3]
[7,2,8,4,1,5,3,6]=>[1,2,1,2,2]
[7,2,8,3,5,1,6,4]=>[1,2,2,2,1]
[7,2,8,3,4,6,1,5]=>[1,2,3,2]
[1,5,7,8,2,6,3,4]=>[4,2,2]
[6,2,3,8,5,7,4,1]=>[1,3,2,1,1]
[6,2,4,8,5,3,1,7]=>[1,3,1,1,2]
[6,3,1,4,8,5,2,7]=>[1,1,3,1,2]
[2,6,3,7,8,5,4,1]=>[2,3,1,1,1]
[2,6,3,7,8,4,5,1]=>[2,3,2,1]
[2,4,7,3,5,6,8,1]=>[3,4,1]
[2,4,7,3,6,8,5,1]=>[3,3,1,1]
[2,5,3,7,8,1,6,4]=>[2,3,2,1]
[3,1,5,4,7,8,2,6]=>[1,2,3,2]
[5,3,1,4,8,2,6,7]=>[1,1,3,3]
[5,2,4,8,6,1,3,7]=>[1,3,1,3]
[5,2,3,8,4,6,7,1]=>[1,3,3,1]
[4,8,2,3,6,1,7,5]=>[2,3,2,1]
[4,8,2,3,5,7,1,6]=>[2,4,2]
[1,4,7,8,3,6,2,5]=>[4,2,2]
[4,8,1,3,6,7,2,5]=>[2,4,2]
[5,3,8,2,4,7,1,6]=>[1,2,3,2]
[5,4,3,8,1,2,7,6]=>[1,1,2,3,1]
[6,4,2,8,1,3,7,5]=>[1,1,2,3,1]
[6,3,8,2,5,1,7,4]=>[1,2,2,2,1]
[6,3,8,1,4,7,2,5]=>[1,2,3,2]
[5,8,1,3,6,2,7,4]=>[2,3,2,1]
[1,5,7,4,2,6,8,3]=>[3,1,3,1]
[5,8,1,4,2,6,3,7]=>[2,2,2,2]
[5,8,4,1,2,7,6,3]=>[2,1,3,1,1]
[6,5,1,2,8,7,3,4]=>[1,1,3,1,2]
[6,5,3,1,4,2,8,7]=>[1,1,1,2,2,1]
[5,3,1,6,4,2,7,8]=>[1,1,2,1,3]
[5,2,6,4,1,7,3,8]=>[1,2,1,2,2]
[4,6,1,7,5,2,8,3]=>[2,2,1,2,1]
[4,5,1,7,2,6,3,8]=>[2,2,2,2]
[3,5,6,1,2,8,7,4]=>[3,3,1,1]
[3,5,7,1,8,6,2,4]=>[3,2,1,2]
[3,6,2,7,5,1,8,4]=>[2,2,1,2,1]
[4,2,5,7,1,8,6,3]=>[1,3,2,1,1]
[3,4,7,2,8,6,1,5]=>[3,2,1,2]
[3,4,5,8,2,7,1,6]=>[4,2,2]
[3,4,6,2,8,1,5,7]=>[3,2,3]
[3,5,2,6,8,1,7,4]=>[2,3,2,1]
[4,2,5,6,1,3,8,7]=>[1,3,3,1]
[4,3,1,2,5,6,8,7]=>[1,1,5,1]
[5,3,6,8,4,7,2,1]=>[1,3,2,1,1]
[3,7,2,5,4,8,6,1]=>[2,2,2,1,1]
[8,4,2,5,7,3,6,1]=>[1,1,3,2,1]
[4,7,2,5,8,3,6,1]=>[2,3,2,1]
[5,2,6,8,4,3,7,1]=>[1,3,1,2,1]
[3,1,6,5,4,8,2,7]=>[1,2,1,2,2]
[4,1,6,5,8,3,2,7]=>[1,2,2,1,2]
[5,1,6,8,4,3,2,7]=>[1,3,1,1,2]
[8,5,4,7,6,3,2,1]=>[1,1,2,1,1,1,1]
[5,7,1,8,4,3,2,6]=>[2,2,1,1,2]
[2,7,1,5,4,3,8,6]=>[2,2,1,2,1]
[8,2,1,5,4,3,7,6]=>[1,1,2,1,2,1]
[8,4,1,5,7,3,2,6]=>[1,1,3,1,2]
[8,5,6,7,1,3,2,4]=>[1,3,2,2]
[8,4,6,1,7,3,2,5]=>[1,2,2,1,2]
[8,3,6,1,4,7,2,5]=>[1,2,3,2]
[2,7,6,1,4,3,8,5]=>[2,1,2,2,1]
[6,7,8,5,1,3,2,4]=>[3,1,2,2]
[5,7,6,8,2,3,4,1]=>[2,2,3,1]
[5,7,2,8,4,3,6,1]=>[2,2,1,2,1]
[6,7,8,2,4,3,5,1]=>[3,2,2,1]
[4,7,6,2,8,3,5,1]=>[2,1,2,2,1]
[8,3,6,2,4,7,5,1]=>[1,2,3,1,1]
[3,7,6,2,4,8,5,1]=>[2,1,3,1,1]
[5,7,3,8,4,6,2,1]=>[2,2,2,1,1]
[4,7,3,5,8,6,2,1]=>[2,3,1,1,1]
[8,7,2,1,4,3,6,5]=>[1,1,1,2,2,1]
[8,7,3,1,4,6,2,5]=>[1,1,1,3,2]
[8,7,6,3,2,5,4,1]=>[1,1,1,1,2,1,1]
[8,7,3,5,1,6,2,4]=>[1,1,2,2,2]
[8,7,2,5,1,3,6,4]=>[1,1,2,3,1]
[8,2,6,5,1,3,7,4]=>[1,2,1,3,1]
[8,4,6,5,7,1,2,3]=>[1,2,2,3]
[5,7,6,8,4,1,2,3]=>[2,2,1,3]
[4,7,6,5,8,1,2,3]=>[2,1,2,3]
[3,7,6,5,1,8,2,4]=>[2,1,1,2,2]
[3,6,4,8,7,5,1,2]=>[2,2,1,1,2]
[5,6,4,3,8,7,1,2]=>[2,1,2,1,2]
[1,6,2,4,7,8,5,3]=>[2,4,1,1]
[3,6,2,4,8,1,5,7]=>[2,3,3]
[3,4,7,2,8,1,6,5]=>[3,2,2,1]
[1,4,7,2,5,8,6,3]=>[3,3,1,1]
[7,3,8,4,5,6,1,2]=>[1,2,3,2]
[3,5,6,4,8,7,1,2]=>[3,2,1,2]
[4,6,8,5,3,7,1,2]=>[3,1,2,2]
[6,8,5,3,4,7,1,2]=>[2,1,3,2]
[1,6,5,4,2,8,7,3]=>[2,1,1,2,1,1]
[1,8,5,2,7,3,6,4]=>[2,1,2,2,1]
[4,2,7,5,1,8,6,3]=>[1,2,1,2,1,1]
[7,8,1,4,2,6,5,3]=>[2,2,2,1,1]
[1,3,6,4,8,2,5,7]=>[3,2,3]
[4,1,7,5,3,2,6,8]=>[1,2,1,1,3]
[6,5,1,3,4,2,8,7]=>[1,1,3,2,1]
[4,8,5,3,1,7,2,6]=>[2,1,1,2,2]
[7,4,5,3,2,8,1,6]=>[1,2,1,2,2]
[5,8,3,6,1,4,2,7]=>[2,2,2,2]
[2,5,8,6,4,1,3,7]=>[3,1,1,3]
[1,4,6,2,5,8,3,7]=>[3,3,2]
[3,6,2,5,8,1,7,4]=>[2,3,2,1]
[1,6,8,7,4,2,3,5]=>[3,1,1,3]
[6,1,7,8,2,4,3,5]=>[1,3,2,2]
[7,1,8,6,3,4,2,5]=>[1,2,1,2,2]
[7,2,1,4,5,6,8,3]=>[1,1,5,1]
[1,2,8,3,6,5,7,4]=>[3,2,2,1]
[6,1,3,2,7,5,8,4]=>[1,2,2,2,1]
[1,6,3,8,5,7,2,4]=>[2,2,2,2]
[2,6,4,1,7,5,8,3]=>[2,1,2,2,1]
[7,6,5,8,1,4,2,3]=>[1,1,2,2,2]
[5,8,6,7,3,2,1,4]=>[2,2,1,1,2]
[1,6,4,3,7,2,8,5]=>[2,1,2,2,1]
[2,6,3,4,8,7,1,5]=>[2,3,1,2]
[7,1,3,4,5,2,8,6]=>[1,4,2,1]
[1,8,3,5,4,2,7,6]=>[2,2,1,2,1]
[4,1,6,3,8,2,7,5]=>[1,2,2,2,1]
[7,8,2,4,6,3,1,5]=>[2,3,1,2]
[3,2,6,4,7,8,1,5]=>[1,2,3,2]
[2,8,5,7,4,3,1,6]=>[2,2,1,1,2]
[7,2,5,8,3,4,1,6]=>[1,3,2,2]
[5,3,8,7,1,2,6,4]=>[1,2,1,3,1]
[6,5,3,8,2,1,7,4]=>[1,1,2,1,2,1]
[7,5,8,4,1,2,3,6]=>[1,2,1,4]
[5,8,7,4,1,3,2,6]=>[2,1,1,2,2]
[3,5,7,8,4,1,2,6]=>[4,1,3]
[1,4,7,5,3,8,2,6]=>[3,1,2,2]
[2,4,6,7,3,1,8,5]=>[4,1,2,1]
[7,8,4,6,3,1,2,5]=>[2,2,1,3]
[2,6,4,5,3,8,1,7]=>[2,2,2,2]
[3,6,5,8,4,2,1,7]=>[2,2,1,1,2]
[5,6,8,4,2,3,1,7]=>[3,1,2,2]
[6,8,5,4,3,1,2,7]=>[2,1,1,1,3]
[6,1,4,2,8,5,7,3]=>[1,2,2,2,1]
[4,8,6,5,3,2,7,1]=>[2,1,1,1,2,1]
[8,6,5,1,2,4,7,3]=>[1,1,1,4,1]
[6,7,5,8,2,1,4,3]=>[2,2,1,2,1]
[1,7,5,8,2,6,4,3]=>[2,2,2,1,1]
[1,3,8,5,7,6,2,4]=>[3,2,1,2]
[6,3,8,5,7,1,2,4]=>[1,2,2,3]
[8,3,1,5,6,2,7,4]=>[1,1,3,2,1]
[6,8,5,2,1,4,7,3]=>[2,1,1,3,1]
[3,8,2,5,6,1,7,4]=>[2,3,2,1]
[2,8,1,5,6,3,7,4]=>[2,3,2,1]
[8,1,2,5,6,3,7,4]=>[1,4,2,1]
[1,8,2,5,7,6,3,4]=>[2,3,1,2]
[5,1,8,6,2,7,3,4]=>[1,2,1,2,2]
[2,5,8,6,1,7,3,4]=>[3,1,2,2]
[8,6,1,5,7,2,3,4]=>[1,1,3,3]
[3,8,6,5,7,1,2,4]=>[2,1,2,3]
[7,6,5,8,1,2,4,3]=>[1,1,2,3,1]
[5,1,7,6,8,4,2,3]=>[1,2,2,1,2]
[5,1,3,7,8,6,2,4]=>[1,4,1,2]
[7,2,5,8,1,6,4,3]=>[1,3,2,1,1]
[3,2,8,5,7,6,1,4]=>[1,2,2,1,2]
[8,2,1,5,7,6,3,4]=>[1,1,3,1,2]
[5,2,8,6,1,7,3,4]=>[1,2,1,2,2]
[1,2,8,6,5,7,3,4]=>[3,1,2,2]
[4,2,1,3,6,7,8,5]=>[1,1,5,1]
[8,2,5,6,3,7,1,4]=>[1,3,2,2]
[7,2,6,5,4,1,8,3]=>[1,2,1,1,2,1]
[6,1,3,5,4,7,8,2]=>[1,3,3,1]
[6,1,5,3,4,7,8,2]=>[1,2,4,1]
[7,5,6,2,4,1,8,3]=>[1,2,2,2,1]
[8,5,2,6,3,7,1,4]=>[1,1,2,2,2]
[4,3,1,2,6,7,8,5]=>[1,1,5,1]
[8,1,6,5,7,3,2,4]=>[1,2,2,1,2]
[3,5,8,6,2,7,1,4]=>[3,1,2,2]
[5,8,1,6,3,7,2,4]=>[2,2,2,2]
[1,8,5,6,3,7,2,4]=>[2,2,2,2]
[1,7,6,5,4,2,8,3]=>[2,1,1,1,2,1]
[5,7,6,1,4,2,8,3]=>[2,1,2,2,1]
[7,1,4,2,6,5,8,3]=>[1,2,2,2,1]
[4,1,7,3,5,6,8,2]=>[1,2,4,1]
[2,7,4,1,5,6,8,3]=>[2,1,4,1]
[5,7,6,4,1,2,8,3]=>[2,1,1,3,1]
[4,7,6,1,5,2,8,3]=>[2,1,2,2,1]
[1,7,6,4,5,2,8,3]=>[2,1,2,2,1]
[1,8,3,6,5,7,2,4]=>[2,2,2,2]
[3,8,1,6,5,7,2,4]=>[2,2,2,2]
[8,1,3,5,7,6,2,4]=>[1,4,1,2]
[7,8,5,4,1,6,2,3]=>[2,1,1,2,2]
[6,1,5,4,3,7,8,2]=>[1,2,1,3,1]
[7,5,6,4,2,1,8,3]=>[1,2,1,1,2,1]
[8,3,2,6,5,7,1,4]=>[1,1,2,2,2]
[7,4,6,2,5,1,8,3]=>[1,2,2,2,1]
[6,1,4,3,5,7,8,2]=>[1,2,4,1]
[6,1,3,4,5,7,8,2]=>[1,6,1]
[7,2,6,4,5,1,8,3]=>[1,2,2,2,1]
[8,2,3,6,5,7,1,4]=>[1,3,2,2]
[5,4,7,3,6,8,1,2]=>[1,2,3,2]
[3,4,7,8,5,6,1,2]=>[4,2,2]
[3,4,7,2,5,1,6,8]=>[3,2,3]
[1,4,7,2,5,8,3,6]=>[3,3,2]
[3,6,2,4,7,1,5,8]=>[2,3,3]
[6,8,3,4,5,7,1,2]=>[2,4,2]
[4,3,6,7,5,8,1,2]=>[1,3,2,2]
[6,3,7,5,8,4,1,2]=>[1,2,2,1,2]
[7,3,8,6,4,5,1,2]=>[1,2,1,2,2]
[3,2,7,6,5,1,4,8]=>[1,2,1,1,3]
[1,2,7,6,5,8,3,4]=>[3,1,2,2]
[4,8,2,6,1,5,3,7]=>[2,2,2,2]
[2,3,8,6,4,1,5,7]=>[3,1,1,3]
[4,3,6,2,5,1,8,7]=>[1,2,2,2,1]
[7,8,3,2,5,1,4,6]=>[2,1,2,3]
[7,8,1,2,5,6,3,4]=>[2,4,2]
[4,1,6,2,5,7,3,8]=>[1,2,3,2]
[6,1,2,5,8,7,3,4]=>[1,4,1,2]
[2,1,8,6,4,7,3,5]=>[1,2,1,2,2]
[7,1,3,6,8,4,2,5]=>[1,4,1,2]
[1,8,3,6,7,4,5,2]=>[2,3,2,1]
[7,1,5,8,3,6,2,4]=>[1,3,2,2]
[5,1,8,7,2,3,6,4]=>[1,2,1,3,1]
[6,1,5,7,4,2,8,3]=>[1,3,1,2,1]
[3,1,6,4,7,2,5,8]=>[1,2,2,3]
[2,4,7,5,1,8,3,6]=>[3,1,2,2]
[6,5,7,1,4,2,3,8]=>[1,2,2,3]
[5,6,8,1,3,2,4,7]=>[3,2,3]
[6,8,5,1,3,4,2,7]=>[2,1,3,2]
[2,8,3,4,5,1,7,6]=>[2,3,2,1]
[6,2,4,3,1,5,7,8]=>[1,2,1,4]
[4,2,8,3,1,7,5,6]=>[1,2,1,2,2]
[1,3,7,4,8,2,5,6]=>[3,2,3]
[5,3,7,4,1,6,2,8]=>[1,2,1,2,2]
[2,4,7,3,6,1,8,5]=>[3,2,2,1]
[5,8,7,6,3,1,2,4]=>[2,1,1,1,3]
[7,5,6,8,1,4,3,2]=>[1,3,2,1,1]
[2,4,7,1,6,5,3,8]=>[3,2,1,2]
[1,2,7,8,5,4,3,6]=>[4,1,1,2]
[6,3,1,2,8,4,5,7]=>[1,1,3,3]
[4,2,1,3,6,5,8,7]=>[1,1,3,2,1]
[2,8,1,4,5,6,3,7]=>[2,4,2]
[7,2,1,5,4,6,3,8]=>[1,1,2,2,2]
[4,2,6,1,8,5,3,7]=>[1,2,2,1,2]
[7,8,2,1,4,5,3,6]=>[2,1,3,2]
[7,8,4,1,5,3,6,2]=>[2,1,2,2,1]
[3,4,6,1,5,8,7,2]=>[3,3,1,1]
[7,5,1,6,4,3,8,2]=>[1,1,2,1,2,1]
[5,8,1,6,3,4,7,2]=>[2,2,3,1]
[6,5,1,8,2,7,4,3]=>[1,1,2,2,1,1]
[6,8,1,7,5,2,3,4]=>[2,2,1,3]
[7,6,1,8,5,3,2,4]=>[1,1,2,1,1,2]
[5,6,1,7,4,8,2,3]=>[2,2,2,2]
[3,6,1,5,7,4,2,8]=>[2,3,1,2]
[2,5,6,1,7,4,8,3]=>[3,2,2,1]
[3,1,7,5,6,4,8,2]=>[1,2,2,2,1]
[5,1,7,6,4,8,3,2]=>[1,2,1,2,1,1]
[6,1,7,8,5,3,4,2]=>[1,3,1,2,1]
[7,1,8,6,5,4,2,3]=>[1,2,1,1,1,2]
[2,6,5,7,3,4,8,1]=>[2,2,3,1]
[1,6,4,7,5,8,2,3]=>[2,2,2,2]
[8,5,3,6,2,7,4,1]=>[1,1,2,2,1,1]
[1,3,7,4,6,8,2,5]=>[3,3,2]
[4,7,5,6,3,2,8,1]=>[2,2,1,2,1]
[1,7,6,5,4,8,2,3]=>[2,1,1,2,2]
[8,1,6,5,7,2,4,3]=>[1,2,2,2,1]
[1,2,7,6,8,3,4,5]=>[3,2,3]
[6,1,7,5,3,8,2,4]=>[1,2,1,2,2]
[2,1,7,5,6,8,3,4]=>[1,2,3,2]
[5,4,1,7,6,8,2,3]=>[1,1,2,2,2]
[4,8,5,6,2,7,3,1]=>[2,2,2,1,1]
[3,8,6,4,2,7,5,1]=>[2,1,1,2,1,1]
[7,8,5,2,4,6,3,1]=>[2,1,3,1,1]
[2,8,6,3,7,4,5,1]=>[2,1,2,2,1]
[7,8,1,6,2,4,5,3]=>[2,2,3,1]
[6,8,1,4,7,2,5,3]=>[2,3,2,1]
[3,8,4,1,7,2,6,5]=>[2,1,2,2,1]
[5,4,7,1,8,3,2,6]=>[1,2,2,1,2]
[3,7,4,1,8,5,2,6]=>[2,1,2,1,2]
[6,7,1,4,8,3,2,5]=>[2,3,1,2]
[2,7,1,8,4,5,3,6]=>[2,2,2,2]
[6,1,2,8,4,3,5,7]=>[1,3,1,3]
[6,5,1,4,3,8,2,7]=>[1,1,2,2,2]
[1,6,2,5,8,3,4,7]=>[2,3,3]
[8,5,1,3,7,2,6,4]=>[1,1,3,2,1]
[8,4,2,1,7,3,6,5]=>[1,1,1,2,2,1]
[7,4,2,1,8,5,3,6]=>[1,1,1,2,1,2]
[1,5,4,2,8,3,6,7]=>[2,1,2,3]
[6,4,3,1,5,8,2,7]=>[1,1,1,3,2]
[3,7,6,8,4,5,2,1]=>[2,2,2,1,1]
[2,7,6,8,5,3,4,1]=>[2,2,1,2,1]
[1,7,6,8,5,4,2,3]=>[2,2,1,1,2]
[1,4,8,6,7,5,2,3]=>[3,2,1,2]
[2,4,8,6,7,3,5,1]=>[3,2,2,1]
[7,3,8,5,4,6,2,1]=>[1,2,1,2,1,1]
[3,4,8,5,6,7,2,1]=>[3,3,1,1]
[6,3,5,8,4,7,2,1]=>[1,3,2,1,1]
[5,4,3,8,6,7,2,1]=>[1,1,2,2,1,1]
[5,4,2,8,7,3,6,1]=>[1,1,2,1,2,1]
[6,2,5,8,7,3,4,1]=>[1,3,1,2,1]
[3,2,8,5,7,4,6,1]=>[1,2,2,2,1]
[1,3,8,7,5,6,2,4]=>[3,1,2,2]
[2,1,8,7,4,6,3,5]=>[1,2,1,2,2]
[3,1,8,5,7,6,2,4]=>[1,2,2,1,2]
[6,1,5,8,7,4,2,3]=>[1,3,1,1,2]
[5,4,1,8,7,6,2,3]=>[1,1,2,1,1,2]
[5,8,6,7,4,3,2,1]=>[2,2,1,1,1,1]
[4,8,7,5,6,3,2,1]=>[2,1,2,1,1,1]
[4,2,1,6,3,5,8,7]=>[1,1,2,3,1]
[6,2,1,4,3,5,8,7]=>[1,1,2,3,1]
[6,2,1,4,3,8,5,7]=>[1,1,2,2,2]
[8,2,1,4,3,6,5,7]=>[1,1,2,2,2]
[8,2,4,1,3,6,5,7]=>[1,2,3,2]
[6,2,4,1,3,8,5,7]=>[1,2,3,2]
[6,2,4,1,3,5,8,7]=>[1,2,4,1]
[4,2,6,1,3,5,8,7]=>[1,2,4,1]
[2,1,6,4,3,5,8,7]=>[1,2,1,3,1]
[2,6,1,4,3,5,8,7]=>[2,2,3,1]
[2,6,4,1,3,5,8,7]=>[2,1,4,1]
[4,6,2,1,3,5,8,7]=>[2,1,4,1]
[6,4,2,1,3,5,8,7]=>[1,1,1,4,1]
[8,4,2,1,3,6,5,7]=>[1,1,1,3,2]
[8,4,2,1,6,3,5,7]=>[1,1,1,2,3]
[6,4,2,1,8,3,5,7]=>[1,1,1,2,3]
[4,6,2,1,8,3,5,7]=>[2,1,2,3]
[2,6,1,4,3,8,5,7]=>[2,2,2,2]
[2,1,6,4,3,8,5,7]=>[1,2,1,2,2]
[2,1,8,4,3,6,5,7]=>[1,2,1,2,2]
[2,8,1,4,3,6,5,7]=>[2,2,2,2]
[2,8,4,1,3,6,5,7]=>[2,1,3,2]
[4,8,2,1,3,6,5,7]=>[2,1,3,2]
[4,8,2,1,6,3,5,7]=>[2,1,2,3]
[6,8,2,1,4,3,5,7]=>[2,1,2,3]
[8,6,2,1,4,3,5,7]=>[1,1,1,2,3]
[2,8,1,4,6,3,5,7]=>[2,3,3]
[2,1,8,4,6,3,5,7]=>[1,2,2,3]
[2,1,6,4,8,3,5,7]=>[1,2,2,3]
[2,6,1,4,8,3,5,7]=>[2,3,3]
[2,6,4,1,8,3,5,7]=>[2,1,2,3]
[2,6,4,8,1,3,5,7]=>[2,2,4]
[4,6,2,8,1,3,5,7]=>[2,2,4]
[4,2,6,1,3,8,5,7]=>[1,2,3,2]
[4,2,6,1,8,3,5,7]=>[1,2,2,3]
[6,2,4,1,8,3,5,7]=>[1,2,2,3]
[8,2,4,1,6,3,5,7]=>[1,2,2,3]
[8,2,1,4,6,3,5,7]=>[1,1,3,3]
[6,2,1,4,8,3,5,7]=>[1,1,3,3]
[4,2,1,6,8,3,5,7]=>[1,1,3,3]
[4,2,1,6,3,8,5,7]=>[1,1,2,2,2]
[4,2,1,3,6,8,5,7]=>[1,1,4,2]
[2,1,4,3,8,6,5,7]=>[1,2,2,1,2]
[2,4,1,3,8,6,5,7]=>[2,3,1,2]
[4,2,1,3,8,6,5,7]=>[1,1,3,1,2]
[4,2,1,8,3,6,5,7]=>[1,1,2,2,2]
[4,2,1,8,6,3,5,7]=>[1,1,2,1,3]
[6,2,1,8,4,3,5,7]=>[1,1,2,1,3]
[8,2,1,6,4,3,5,7]=>[1,1,2,1,3]
[8,2,6,1,4,3,5,7]=>[1,2,2,3]
[6,2,8,1,4,3,5,7]=>[1,2,2,3]
[4,2,8,1,6,3,5,7]=>[1,2,2,3]
[4,2,8,1,3,6,5,7]=>[1,2,3,2]
[2,4,8,1,3,6,5,7]=>[3,3,2]
[2,4,1,8,3,6,5,7]=>[2,2,2,2]
[2,1,4,8,3,6,5,7]=>[1,3,2,2]
[2,1,4,8,6,3,5,7]=>[1,3,1,3]
[2,4,8,1,6,3,5,7]=>[3,2,3]
[2,4,8,6,1,3,5,7]=>[3,1,4]
[4,2,8,6,1,3,5,7]=>[1,2,1,4]
[6,2,8,4,1,3,5,7]=>[1,2,1,4]
[8,2,6,4,1,3,5,7]=>[1,2,1,4]
[8,4,6,2,1,3,5,7]=>[1,2,1,4]
[6,4,8,2,1,3,5,7]=>[1,2,1,4]
[4,6,8,2,1,3,5,7]=>[3,1,4]
[2,6,8,4,1,3,5,7]=>[3,1,4]
[2,6,8,1,4,3,5,7]=>[3,2,3]
[2,6,1,8,4,3,5,7]=>[2,2,1,3]
[2,1,6,8,4,3,5,7]=>[1,3,1,3]
[2,1,8,6,4,3,5,7]=>[1,2,1,1,3]
[2,8,1,6,4,3,5,7]=>[2,2,1,3]
[2,8,6,4,1,3,5,7]=>[2,1,1,4]
[4,8,6,2,1,3,5,7]=>[2,1,1,4]
[6,8,4,2,1,3,5,7]=>[2,1,1,4]
[3,2,6,1,5,4,8,7]=>[1,2,2,2,1]
[5,2,4,3,8,1,7,6]=>[1,2,2,2,1]
[6,2,4,1,5,3,8,7]=>[1,2,2,2,1]
[4,3,6,1,5,2,8,7]=>[1,2,2,2,1]
[4,3,5,2,8,1,7,6]=>[1,2,2,2,1]
[4,3,7,2,6,5,8,1]=>[1,2,2,2,1]
[4,3,8,2,6,1,7,5]=>[1,2,2,2,1]
[4,3,8,1,7,2,6,5]=>[1,2,2,2,1]
[4,3,8,1,5,2,7,6]=>[1,2,2,2,1]
[5,1,8,3,4,2,7,6]=>[1,2,2,2,1]
[5,4,8,1,3,2,7,6]=>[1,2,2,2,1]
[2,1,5,4,8,3,7,6]=>[1,2,2,2,1]
[5,1,7,6,8,3,4,2]=>[1,2,2,2,1]
[4,3,7,6,8,1,5,2]=>[1,2,2,2,1]
[4,3,7,1,8,5,6,2]=>[1,2,2,2,1]
[4,3,6,5,8,1,7,2]=>[1,2,2,2,1]
[6,3,5,4,7,2,8,1]=>[1,2,2,2,1]
[6,3,5,4,8,1,7,2]=>[1,2,2,2,1]
[7,1,6,3,8,4,5,2]=>[1,2,2,2,1]
[7,4,6,5,8,1,3,2]=>[1,2,2,2,1]
[2,1,8,4,6,3,7,5]=>[1,2,2,2,1]
[8,4,6,1,3,2,7,5]=>[1,2,2,2,1]
[8,1,6,3,4,2,7,5]=>[1,2,2,2,1]
[8,1,6,3,7,2,5,4]=>[1,2,2,2,1]
[8,3,5,1,7,2,6,4]=>[1,2,2,2,1]
[8,3,5,2,6,1,7,4]=>[1,2,2,2,1]
[7,3,5,2,6,4,8,1]=>[1,2,2,2,1]
[8,2,6,3,5,1,7,4]=>[1,2,2,2,1]
[8,2,7,1,5,3,6,4]=>[1,2,2,2,1]
[8,2,4,1,5,3,7,6]=>[1,2,2,2,1]
[8,2,4,1,7,3,6,5]=>[1,2,2,2,1]
[8,2,4,3,6,1,7,5]=>[1,2,2,2,1]
[3,2,8,4,6,1,7,5]=>[1,2,2,2,1]
[3,2,8,1,5,4,7,6]=>[1,2,2,2,1]
[3,2,7,6,8,1,5,4]=>[1,2,2,2,1]
[3,2,7,1,8,5,6,4]=>[1,2,2,2,1]
[3,2,6,5,8,1,7,4]=>[1,2,2,2,1]
[6,5,7,2,4,3,8,1]=>[1,2,2,2,1]
[6,5,8,2,4,1,7,3]=>[1,2,2,2,1]
[7,2,4,1,8,5,6,3]=>[1,2,2,2,1]
[7,6,8,2,4,1,5,3]=>[1,2,2,2,1]
[7,6,8,1,5,2,4,3]=>[1,2,2,2,1]
[2,1,7,3,8,5,6,4]=>[1,2,2,2,1]
[7,1,3,2,8,5,6,4]=>[1,2,2,2,1]
[7,1,8,5,6,2,4,3]=>[1,2,2,2,1]
[7,1,8,2,6,4,5,3]=>[1,2,2,2,1]
[7,2,8,1,5,4,6,3]=>[1,2,2,2,1]
[6,2,7,4,5,3,8,1]=>[1,2,2,2,1]
[5,4,7,2,6,3,8,1]=>[1,2,2,2,1]
[5,4,8,2,6,1,7,3]=>[1,2,2,2,1]
[6,5,8,1,7,2,4,3]=>[1,2,2,2,1]
[2,1,6,5,8,3,7,4]=>[1,2,2,2,1]
[6,5,7,4,8,1,3,2]=>[1,2,2,2,1]
[6,5,7,1,8,3,4,2]=>[1,2,2,2,1]
[6,1,7,4,8,3,5,2]=>[1,2,2,2,1]
[5,4,7,1,8,3,6,2]=>[1,2,2,2,1]
[5,4,6,3,8,1,7,2]=>[1,2,2,2,1]
[2,8,3,1,5,4,6,7]=>[2,1,2,3]
[2,5,3,4,7,1,8,6]=>[2,3,2,1]
[2,4,8,3,5,7,6,1]=>[3,3,1,1]
[4,2,5,3,1,8,6,7]=>[1,2,1,2,2]
[4,2,1,8,5,3,6,7]=>[1,1,2,1,3]
[5,4,1,3,8,2,6,7]=>[1,1,3,3]
[5,1,4,8,3,2,6,7]=>[1,3,1,3]
[1,5,8,4,3,2,6,7]=>[3,1,1,3]
[1,8,5,4,3,2,6,7]=>[2,1,1,1,3]
[1,7,4,3,8,5,2,6]=>[2,1,2,1,2]
[1,5,7,3,8,4,2,6]=>[3,2,1,2]
[5,1,4,7,8,3,2,6]=>[1,4,1,2]
[4,8,1,5,7,3,6,2]=>[2,3,2,1]
[8,1,5,3,7,4,6,2]=>[1,2,2,2,1]
[3,8,4,7,6,5,2,1]=>[2,2,1,1,1,1]
[1,6,8,5,3,7,4,2]=>[3,1,2,1,1]
[6,8,1,7,4,3,5,2]=>[2,2,1,2,1]
[6,4,8,1,7,3,5,2]=>[1,2,2,2,1]
[6,4,8,7,1,5,2,3]=>[1,2,1,2,2]
[7,6,4,1,3,8,2,5]=>[1,1,1,3,2]
[1,7,5,6,3,2,8,4]=>[2,2,1,2,1]
[4,2,1,7,8,5,3,6]=>[1,1,3,1,2]
[2,7,4,6,3,1,8,5]=>[2,2,1,2,1]
[2,6,8,4,3,7,5,1]=>[3,1,2,1,1]
[6,2,4,8,3,7,5,1]=>[1,3,2,1,1]
[7,2,6,3,4,1,8,5]=>[1,2,2,2,1]
[2,6,7,3,1,4,8,5]=>[3,1,3,1]
[2,7,1,8,3,5,4,6]=>[2,2,2,2]
[2,1,7,3,5,8,4,6]=>[1,2,3,2]
[8,7,1,3,6,2,4,5]=>[1,1,3,3]
[8,2,1,7,3,5,6,4]=>[1,1,2,3,1]
[7,8,2,6,3,1,5,4]=>[2,2,1,2,1]
[8,7,2,6,3,5,4,1]=>[1,1,2,2,1,1]
[1,2,8,7,4,5,6,3]=>[3,1,3,1]
[8,3,7,1,5,6,2,4]=>[1,2,3,2]
[8,6,1,2,7,5,3,4]=>[1,1,3,1,2]
[8,1,6,2,7,4,5,3]=>[1,2,2,2,1]
[1,8,5,2,6,7,4,3]=>[2,1,3,1,1]
[5,2,1,8,6,7,4,3]=>[1,1,2,2,1,1]
[2,8,5,7,6,4,3,1]=>[2,2,1,1,1,1]
[1,7,8,5,2,6,4,3]=>[3,1,2,1,1]
[7,8,1,6,4,2,5,3]=>[2,2,1,2,1]
[7,8,6,1,5,3,2,4]=>[2,1,2,1,2]
[7,3,8,6,1,5,2,4]=>[1,2,1,2,2]
[8,7,6,1,5,3,4,2]=>[1,1,1,2,2,1]
[8,7,1,6,4,5,3,2]=>[1,1,2,2,1,1]
[8,1,7,5,6,4,3,2]=>[1,2,2,1,1,1]
[1,8,6,7,5,4,3,2]=>[2,2,1,1,1,1]
[6,3,5,2,1,4,8,7]=>[1,2,1,3,1]
[6,3,5,7,2,8,4,1]=>[1,3,2,1,1]
[8,5,2,7,4,3,1,6]=>[1,1,2,1,1,2]
[4,5,3,6,1,2,8,7]=>[2,2,3,1]
[3,5,1,4,6,2,8,7]=>[2,3,2,1]
[8,3,4,5,7,2,1,6]=>[1,4,1,2]
[5,7,4,6,3,8,2,1]=>[2,2,2,1,1]
[2,8,4,6,3,7,1,5]=>[2,2,2,2]
[8,1,4,7,3,6,2,5]=>[1,3,2,2]
[8,3,4,7,5,1,2,6]=>[1,3,1,3]
[8,5,1,4,7,3,2,6]=>[1,1,3,1,2]
[8,5,3,7,1,4,2,6]=>[1,1,2,2,2]
[2,1,8,5,7,4,3,6]=>[1,2,2,1,2]
[6,5,3,7,1,8,4,2]=>[1,1,2,2,1,1]
[6,5,1,4,7,8,3,2]=>[1,1,4,1,1]
[6,3,4,7,5,8,1,2]=>[1,3,2,2]
[5,1,4,6,8,3,7,2]=>[1,4,2,1]
[4,7,1,3,5,8,6,2]=>[2,4,1,1]
[4,8,3,7,1,2,6,5]=>[2,2,3,1]
[3,8,6,4,1,7,2,5]=>[2,1,1,2,2]
[3,8,1,2,5,7,6,4]=>[2,4,1,1]
[2,8,7,5,4,1,3,6]=>[2,1,1,1,3]
[8,7,2,6,4,1,3,5]=>[1,1,2,1,3]
[3,8,6,7,4,2,1,5]=>[2,2,1,1,2]
[5,7,6,8,4,2,3,1]=>[2,2,1,2,1]
[5,3,7,8,2,4,6,1]=>[1,3,3,1]
[8,3,6,2,1,4,7,5]=>[1,2,1,3,1]
[5,3,7,6,2,1,8,4]=>[1,2,1,1,2,1]
[5,3,6,2,8,7,1,4]=>[1,2,2,1,2]
[5,7,8,6,4,2,1,3]=>[3,1,1,1,2]
[2,6,7,5,4,8,1,3]=>[3,1,2,2]
[6,1,7,4,5,8,2,3]=>[1,2,3,2]
[6,7,3,5,1,8,2,4]=>[2,2,2,2]
[2,1,6,7,5,8,3,4]=>[1,3,2,2]
[2,1,5,7,3,6,8,4]=>[1,3,3,1]
[5,7,3,6,1,2,8,4]=>[2,2,3,1]
[4,1,7,2,5,6,8,3]=>[1,2,4,1]
[2,4,7,1,6,5,8,3]=>[3,2,2,1]
[4,6,2,1,8,7,5,3]=>[2,1,2,1,1,1]
[3,4,6,2,7,8,5,1]=>[3,3,1,1]
[4,6,1,2,5,8,7,3]=>[2,4,1,1]
[5,6,1,4,8,2,7,3]=>[2,3,2,1]
[5,6,3,1,8,7,2,4]=>[2,1,2,1,2]
[3,5,6,4,7,1,8,2]=>[3,2,2,1]
[3,4,6,1,5,7,8,2]=>[3,4,1]
[3,4,1,5,7,6,8,2]=>[2,3,2,1]
[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]
[3,8,2,7,6,1,5,4]=>[2,2,1,2,1]
[3,8,2,7,6,5,1,4]=>[2,2,1,1,2]
[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1]
[4,8,7,2,6,5,3,1]=>[2,1,2,1,1,1]
[4,8,7,2,6,5,1,3]=>[2,1,2,1,2]
[4,8,7,2,6,1,5,3]=>[2,1,2,2,1]
[4,8,7,2,1,6,5,3]=>[2,1,1,2,1,1]
[4,8,7,3,1,6,5,2]=>[2,1,1,2,1,1]
[4,8,7,3,2,1,6,5]=>[2,1,1,1,2,1]
[4,8,7,3,2,6,1,5]=>[2,1,1,2,2]
[4,8,7,3,2,6,5,1]=>[2,1,1,2,1,1]
[4,8,7,3,6,2,5,1]=>[2,1,2,2,1]
[4,8,7,3,6,2,1,5]=>[2,1,2,1,2]
[4,8,7,3,6,1,5,2]=>[2,1,2,2,1]
[4,8,7,3,6,5,1,2]=>[2,1,2,1,2]
[4,8,7,3,6,5,2,1]=>[2,1,2,1,1,1]
[5,8,7,6,3,4,2,1]=>[2,1,1,2,1,1]
[5,8,7,6,3,1,4,2]=>[2,1,1,1,2,1]
[5,8,7,6,3,2,4,1]=>[2,1,1,1,2,1]
[5,8,7,6,2,4,3,1]=>[2,1,1,2,1,1]
[5,8,7,6,2,1,4,3]=>[2,1,1,1,2,1]
[5,8,7,6,4,2,3,1]=>[2,1,1,1,2,1]
[5,8,7,6,4,2,1,3]=>[2,1,1,1,1,2]
[5,8,7,6,4,1,3,2]=>[2,1,1,1,2,1]
[5,8,7,6,4,3,1,2]=>[2,1,1,1,1,2]
[7,3,4,2,1,6,5,8]=>[1,2,1,2,2]
[7,3,5,2,6,1,4,8]=>[1,2,2,3]
[7,3,5,2,6,4,1,8]=>[1,2,2,1,2]
[6,3,5,2,7,4,8,1]=>[1,2,2,2,1]
[7,2,1,5,6,4,3,8]=>[1,1,3,1,2]
[7,3,5,1,6,4,2,8]=>[1,2,2,1,2]
[7,4,5,6,1,3,2,8]=>[1,3,2,2]
[1,4,5,7,3,2,8,6]=>[4,1,2,1]
[1,4,6,7,3,8,2,5]=>[4,2,2]
[6,4,5,7,3,1,8,2]=>[1,3,1,2,1]
[6,4,5,7,1,3,8,2]=>[1,3,3,1]
[6,3,5,1,7,4,8,2]=>[1,2,2,2,1]
[6,2,1,5,7,4,8,3]=>[1,1,3,2,1]
[3,2,1,5,7,4,8,6]=>[1,1,3,2,1]
[2,4,6,7,3,8,1,5]=>[4,2,2]
[1,4,6,7,3,8,5,2]=>[4,2,1,1]
[1,5,6,7,8,3,4,2]=>[5,2,1]
[2,5,6,7,8,3,1,4]=>[5,1,2]
[3,2,1,6,7,8,4,5]=>[1,1,4,2]
[5,2,1,6,7,8,4,3]=>[1,1,4,1,1]
[5,3,6,1,7,8,4,2]=>[1,2,3,1,1]
[5,4,6,7,1,8,3,2]=>[1,3,2,1,1]
[1,5,6,7,8,3,2,4]=>[5,1,2]
[6,4,5,7,2,1,8,3]=>[1,3,1,2,1]
[5,4,6,7,2,8,3,1]=>[1,3,2,1,1]
[5,3,6,2,7,8,4,1]=>[1,2,3,1,1]
[5,3,6,2,7,8,1,4]=>[1,2,3,2]
[6,3,5,2,7,1,8,4]=>[1,2,2,2,1]
[6,3,4,2,1,7,8,5]=>[1,2,1,3,1]
[5,3,4,1,2,7,8,6]=>[1,2,4,1]
[4,3,6,2,7,8,1,5]=>[1,2,3,2]
[4,3,6,2,7,8,5,1]=>[1,2,3,1,1]
[1,3,6,2,7,8,5,4]=>[3,3,1,1]
[1,4,6,7,2,8,5,3]=>[4,2,1,1]
[3,4,6,7,2,8,5,1]=>[4,2,1,1]
[3,4,5,7,2,1,8,6]=>[4,1,2,1]
[4,2,1,5,7,3,8,6]=>[1,1,3,2,1]
[4,2,1,6,7,8,3,5]=>[1,1,4,2]
[4,3,6,1,7,8,2,5]=>[1,2,3,2]
[1,5,6,7,8,2,4,3]=>[5,2,1]
[1,5,6,7,8,4,2,3]=>[5,1,2]
[3,4,6,7,1,8,5,2]=>[4,2,1,1]
[4,3,6,1,7,8,5,2]=>[1,2,3,1,1]
[4,2,1,6,7,8,5,3]=>[1,1,4,1,1]
[2,3,6,1,7,8,5,4]=>[3,3,1,1]
[2,4,6,7,1,8,5,3]=>[4,2,1,1]
[2,5,6,7,8,1,4,3]=>[5,2,1]
[1,4,3,6,2,5,7,8]=>[2,2,4]
[1,4,3,7,2,5,6,8]=>[2,2,4]
[1,4,3,7,6,8,2,5]=>[2,2,2,2]
[1,4,3,7,5,8,2,6]=>[2,2,2,2]
[1,4,3,7,2,6,5,8]=>[2,2,2,2]
[1,5,3,7,4,8,2,6]=>[2,2,2,2]
[1,3,2,6,5,8,4,7]=>[2,2,2,2]
[1,5,4,8,2,6,3,7]=>[2,2,2,2]
[1,5,4,8,3,7,2,6]=>[2,2,2,2]
[1,2,3,6,5,8,4,7]=>[4,2,2]
[6,8,2,4,5,7,1,3]=>[2,4,2]
[3,7,8,4,5,2,6,1]=>[3,2,2,1]
[7,8,1,4,5,3,6,2]=>[2,3,2,1]
[3,8,7,4,1,6,5,2]=>[2,1,1,2,1,1]
[4,8,3,6,1,5,7,2]=>[2,2,3,1]
[5,8,3,1,6,4,7,2]=>[2,1,2,2,1]
[5,8,1,4,7,6,3,2]=>[2,3,1,1,1]
[7,5,1,8,6,2,4,3]=>[1,1,2,1,2,1]
[7,4,1,8,2,6,3,5]=>[1,1,2,2,2]
[7,1,8,4,2,6,3,5]=>[1,2,1,2,2]
[1,6,3,8,5,2,4,7]=>[2,2,1,3]
[6,1,3,8,5,2,4,7]=>[1,3,1,3]
[7,1,8,3,6,2,5,4]=>[1,2,2,2,1]
[7,3,1,8,4,2,6,5]=>[1,1,2,1,2,1]
[7,2,8,4,1,6,5,3]=>[1,2,1,2,1,1]
[7,2,8,3,6,5,1,4]=>[1,2,2,1,2]
[7,2,8,3,6,1,5,4]=>[1,2,2,2,1]
[7,1,8,2,3,6,5,4]=>[1,2,3,1,1]
[6,1,2,8,3,5,4,7]=>[1,3,2,2]
[1,5,2,3,8,4,7,6]=>[2,3,2,1]
[5,1,2,3,8,4,7,6]=>[1,4,2,1]
[5,2,3,8,1,4,7,6]=>[1,3,3,1]
[6,2,8,1,3,5,4,7]=>[1,2,3,2]
[6,2,4,1,8,7,3,5]=>[1,2,2,1,2]
[6,3,1,4,2,8,5,7]=>[1,1,2,2,2]
[3,1,6,4,2,8,5,7]=>[1,2,1,2,2]
[2,6,3,8,7,1,5,4]=>[2,2,1,2,1]
[2,6,3,8,5,1,4,7]=>[2,2,1,3]
[2,5,1,8,3,4,7,6]=>[2,2,3,1]
[2,5,1,3,8,4,7,6]=>[2,3,2,1]
[1,2,5,3,8,4,7,6]=>[3,2,2,1]
[1,2,4,8,3,7,6,5]=>[4,2,1,1]
[2,4,8,1,3,7,6,5]=>[3,3,1,1]
[2,4,8,3,7,1,6,5]=>[3,2,2,1]
[2,4,8,3,7,6,1,5]=>[3,2,1,2]
[2,5,3,8,1,7,4,6]=>[2,2,2,2]
[2,5,4,1,3,8,7,6]=>[2,1,3,1,1]
[3,1,5,4,8,2,7,6]=>[1,2,2,2,1]
[5,3,1,4,8,2,7,6]=>[1,1,3,2,1]
[5,2,3,8,4,7,1,6]=>[1,3,2,2]
[4,8,2,3,7,6,1,5]=>[2,3,1,2]
[4,8,2,3,7,1,6,5]=>[2,3,2,1]
[4,8,1,2,3,7,6,5]=>[2,4,1,1]
[1,4,8,2,3,7,6,5]=>[3,3,1,1]
[1,4,8,3,7,2,6,5]=>[3,2,2,1]
[6,3,8,1,5,2,4,7]=>[1,2,2,3]
[5,3,8,1,2,4,7,6]=>[1,2,4,1]
[5,1,3,8,2,4,7,6]=>[1,3,3,1]
[1,5,3,8,2,4,7,6]=>[2,2,3,1]
[1,5,4,8,2,7,6,3]=>[2,2,2,1,1]
[5,1,4,8,2,7,6,3]=>[1,3,2,1,1]
[5,4,8,1,2,7,6,3]=>[1,2,3,1,1]
[6,5,1,2,8,7,4,3]=>[1,1,3,1,1,1]
[5,3,1,6,4,2,8,7]=>[1,1,2,1,2,1]
[5,1,6,2,8,7,4,3]=>[1,2,2,1,1,1]
[4,1,5,8,2,7,6,3]=>[1,3,2,1,1]
[4,1,2,5,8,7,6,3]=>[1,4,1,1,1]
[1,4,2,5,8,7,6,3]=>[2,3,1,1,1]
[1,3,5,2,8,7,4,6]=>[3,2,1,2]
[3,5,1,2,8,7,4,6]=>[2,3,1,2]
[3,6,2,8,7,5,1,4]=>[2,2,1,1,2]
[4,2,6,1,8,7,3,5]=>[1,2,2,1,2]
[4,3,1,5,8,2,7,6]=>[1,1,3,2,1]
[3,5,2,8,7,1,4,6]=>[2,2,1,3]
[3,4,8,7,2,6,1,5]=>[3,1,2,2]
[3,4,8,7,1,2,6,5]=>[3,1,3,1]
[3,4,8,1,7,2,6,5]=>[3,2,2,1]
[1,3,4,8,7,2,6,5]=>[4,1,2,1]
[1,3,4,8,2,7,6,5]=>[4,2,1,1]
[3,4,8,1,2,7,6,5]=>[3,3,1,1]
[3,4,8,2,7,1,6,5]=>[3,2,2,1]
[3,4,8,2,7,6,1,5]=>[3,2,1,2]
[4,2,5,8,1,7,6,3]=>[1,3,2,1,1]
[4,3,1,2,5,8,7,6]=>[1,1,4,1,1]
[3,1,4,2,5,8,7,6]=>[1,2,3,1,1]
[2,3,5,1,8,7,6,4]=>[3,2,1,1,1]
[7,8,2,1,5,3,6,4]=>[2,1,2,2,1]
[6,4,1,2,7,3,5,8]=>[1,1,3,3]
[2,3,7,5,4,1,8,6]=>[3,1,1,2,1]
[6,3,1,5,4,2,7,8]=>[1,1,2,1,3]
[7,8,1,5,4,2,6,3]=>[2,2,1,2,1]
[7,8,3,5,4,1,6,2]=>[2,2,1,2,1]
[7,8,2,5,4,1,3,6]=>[2,2,1,3]
[7,8,2,5,4,6,1,3]=>[2,2,2,2]
[6,2,1,5,4,7,3,8]=>[1,1,2,2,2]
[5,3,6,1,4,7,8,2]=>[1,2,4,1]
[5,3,6,2,4,7,1,8]=>[1,2,3,2]
[6,4,2,1,7,3,8,5]=>[1,1,1,2,2,1]
[4,3,7,5,8,6,1,2]=>[1,2,2,1,2]
[4,2,7,1,8,3,6,5]=>[1,2,2,2,1]
[3,2,6,7,4,8,1,5]=>[1,3,2,2]
[3,1,6,7,4,8,5,2]=>[1,3,2,1,1]
[1,7,6,5,3,8,4,2]=>[2,1,1,2,1,1]
[2,7,6,5,3,8,1,4]=>[2,1,1,2,2]
[1,7,6,5,2,4,8,3]=>[2,1,1,3,1]
[2,7,6,5,3,1,4,8]=>[2,1,1,1,3]
[2,7,1,4,8,3,5,6]=>[2,3,3]
[3,7,6,4,8,5,1,2]=>[2,1,2,1,2]
[5,7,6,3,8,4,1,2]=>[2,1,2,1,2]
[5,1,6,2,4,8,3,7]=>[1,2,3,2]
[4,7,6,5,2,1,3,8]=>[2,1,1,1,3]
[4,7,6,5,2,8,1,3]=>[2,1,1,2,2]
[4,7,6,5,1,8,3,2]=>[2,1,1,2,1,1]
[1,7,6,5,2,8,3,4]=>[2,1,1,2,2]
[1,7,6,5,3,2,8,4]=>[2,1,1,1,2,1]
[4,7,6,5,1,2,8,3]=>[2,1,1,3,1]
[4,7,6,5,3,1,8,2]=>[2,1,1,1,2,1]
[6,1,3,5,4,8,7,2]=>[1,3,2,1,1]
[5,2,6,3,4,1,7,8]=>[1,2,2,3]
[5,1,6,2,4,7,8,3]=>[1,2,4,1]
[1,2,6,3,4,8,7,5]=>[3,3,1,1]
[1,7,2,4,8,3,6,5]=>[2,3,2,1]
[6,1,4,2,8,3,5,7]=>[1,2,2,3]
[4,1,8,2,6,3,5,7]=>[1,2,2,3]
[4,7,2,1,5,3,6,8]=>[2,1,2,3]
[4,7,1,6,2,3,8,5]=>[2,2,3,1]
[1,7,2,6,8,3,5,4]=>[2,3,2,1]
[1,2,6,7,4,8,5,3]=>[4,2,1,1]
[3,1,6,7,4,2,8,5]=>[1,3,1,2,1]
[3,2,8,5,4,6,1,7]=>[1,2,1,2,2]
[4,7,6,3,5,8,1,2]=>[2,1,3,2]
[4,7,1,2,5,3,8,6]=>[2,3,2,1]
[3,7,6,5,2,4,1,8]=>[2,1,1,2,2]
[3,7,6,5,1,4,8,2]=>[2,1,1,3,1]
[3,7,6,5,2,1,8,4]=>[2,1,1,1,2,1]
[1,7,6,5,8,2,4,3]=>[2,1,2,2,1]
[3,7,6,5,8,1,4,2]=>[2,1,2,2,1]
[3,7,6,5,1,2,4,8]=>[2,1,1,4]
[3,1,6,8,4,2,5,7]=>[1,3,1,3]
[4,7,6,8,3,5,1,2]=>[2,2,2,2]
[2,7,6,5,1,4,3,8]=>[2,1,1,2,2]
[2,7,6,5,8,1,3,4]=>[2,1,2,3]
[2,7,6,5,8,4,1,3]=>[2,1,2,1,2]
[6,3,2,1,7,4,8,5]=>[1,1,1,2,2,1]
[4,2,1,7,3,5,8,6]=>[1,1,2,3,1]
[7,3,1,5,4,2,8,6]=>[1,1,2,1,2,1]
[8,4,1,5,2,7,6,3]=>[1,1,2,2,1,1]
[8,2,5,1,3,7,6,4]=>[1,2,3,1,1]
[4,3,7,2,1,5,8,6]=>[1,2,1,3,1]
[6,3,7,4,2,1,8,5]=>[1,2,1,1,2,1]
[4,7,2,5,3,1,8,6]=>[2,2,1,2,1]
[2,7,5,4,1,3,8,6]=>[2,1,1,3,1]
[7,5,4,3,2,1,8,6]=>[1,1,1,1,1,2,1]
[8,5,3,2,1,7,6,4]=>[1,1,1,1,2,1,1]
[6,5,2,1,8,4,3,7]=>[1,1,1,2,1,2]
[4,6,3,2,8,1,5,7]=>[2,1,2,3]
[5,7,4,3,2,8,1,6]=>[2,1,1,2,2]
[1,7,6,2,4,8,3,5]=>[2,1,3,2]
[2,7,3,6,4,8,1,5]=>[2,2,2,2]
[6,2,7,5,3,8,1,4]=>[1,2,1,2,2]
[7,1,8,5,3,6,4,2]=>[1,2,1,2,1,1]
[5,8,1,6,2,7,4,3]=>[2,2,2,1,1]
[1,8,6,2,3,7,5,4]=>[2,1,3,1,1]
[1,8,6,3,2,7,5,4]=>[2,1,1,2,1,1]
[5,8,3,2,7,1,6,4]=>[2,1,2,2,1]
[8,7,3,1,6,5,4,2]=>[1,1,1,2,1,1,1]
[8,7,2,6,1,5,4,3]=>[1,1,2,2,1,1]
[1,8,5,7,4,3,6,2]=>[2,2,1,2,1]
[1,8,5,7,2,4,6,3]=>[2,2,3,1]
[3,8,6,1,7,2,5,4]=>[2,1,2,2,1]
[7,2,8,5,6,1,4,3]=>[1,2,2,2,1]
[6,3,7,5,8,2,1,4]=>[1,2,2,1,2]
[3,7,2,6,8,4,1,5]=>[2,3,1,2]
[3,6,5,8,1,4,2,7]=>[2,2,2,2]
[2,6,5,8,4,1,3,7]=>[2,2,1,3]
[6,5,4,8,3,2,1,7]=>[1,1,2,1,1,2]
[8,4,3,7,2,1,6,5]=>[1,1,2,1,2,1]
[8,2,4,7,1,3,6,5]=>[1,3,3,1]
[6,2,5,8,1,4,3,7]=>[1,3,2,2]
[4,3,6,8,2,1,5,7]=>[1,3,1,3]
[6,3,5,1,8,4,2,7]=>[1,2,2,1,2]
[8,4,1,5,7,3,6,2]=>[1,1,3,2,1]
[6,4,2,5,8,3,1,7]=>[1,1,3,1,2]
[5,4,1,6,8,2,3,7]=>[1,1,3,3]
[6,5,2,1,7,8,3,4]=>[1,1,1,3,2]
[6,3,7,4,8,5,2,1]=>[1,2,2,1,1,1]
[4,7,2,5,8,6,3,1]=>[2,3,1,1,1]
[6,3,1,8,4,7,5,2]=>[1,1,2,2,1,1]
[6,4,2,8,7,3,5,1]=>[1,1,2,1,2,1]
[6,5,3,8,7,4,1,2]=>[1,1,2,1,1,2]
[5,4,8,1,7,6,2,3]=>[1,2,2,1,2]
[5,2,8,1,7,3,6,4]=>[1,2,2,2,1]
[6,4,8,2,1,7,5,3]=>[1,2,1,2,1,1]
[3,6,8,1,4,7,5,2]=>[3,3,1,1]
[5,7,3,8,1,6,4,2]=>[2,2,2,1,1]
[6,4,7,8,1,5,3,2]=>[1,3,2,1,1]
[2,5,8,7,1,3,6,4]=>[3,1,3,1]
[5,3,8,7,2,1,6,4]=>[1,2,1,1,2,1]
[8,3,7,6,1,5,4,2]=>[1,2,1,2,1,1]
[8,2,7,6,5,1,4,3]=>[1,2,1,1,2,1]
[4,3,8,7,6,2,1,5]=>[1,2,1,1,1,2]
[2,4,8,7,6,1,3,5]=>[3,1,1,3]
[3,5,8,7,2,6,1,4]=>[3,1,2,2]
[4,7,3,8,6,5,1,2]=>[2,2,1,1,2]
[7,5,8,6,4,3,2,1]=>[1,2,1,1,1,1,1]
[5,8,7,3,6,4,2,1]=>[2,1,2,1,1,1]
[4,8,7,6,2,5,3,1]=>[2,1,1,2,1,1]
[3,8,7,6,5,1,4,2]=>[2,1,1,1,2,1]
[2,8,7,6,5,4,1,3]=>[2,1,1,1,1,2]
[3,6,5,1,2,4,8,7]=>[2,1,4,1]
[3,7,5,8,2,4,1,6]=>[2,2,2,2]
[3,8,5,7,2,4,1,6]=>[2,2,2,2]
[5,1,7,8,4,3,2,6]=>[1,3,1,1,2]
[5,1,2,6,4,3,8,7]=>[1,3,1,2,1]
[6,1,2,5,4,3,8,7]=>[1,3,1,2,1]
[5,1,2,4,6,3,8,7]=>[1,4,2,1]
[4,1,2,6,5,3,8,7]=>[1,3,1,2,1]
[4,1,5,7,8,3,2,6]=>[1,4,1,2]
[4,1,5,8,7,3,2,6]=>[1,3,1,1,2]
[4,7,1,8,3,6,2,5]=>[2,2,2,2]
[4,1,7,8,5,2,3,6]=>[1,3,1,3]
[5,1,7,4,8,2,3,6]=>[1,2,2,3]
[7,5,3,8,1,4,2,6]=>[1,1,2,2,2]
[2,1,5,8,7,3,4,6]=>[1,3,1,3]
[5,1,8,4,7,2,3,6]=>[1,2,2,3]
[4,1,8,7,5,2,3,6]=>[1,2,1,1,3]
[4,7,1,6,3,2,8,5]=>[2,2,1,2,1]
[6,1,2,3,7,5,8,4]=>[1,4,2,1]
[7,1,2,3,8,6,5,4]=>[1,4,1,1,1]
[7,1,2,3,5,8,6,4]=>[1,5,1,1]
[6,8,1,4,3,7,2,5]=>[2,2,2,2]
[8,7,3,2,4,1,6,5]=>[1,1,1,2,2,1]
[2,1,7,3,4,8,6,5]=>[1,2,3,1,1]
[7,8,3,2,4,1,6,5]=>[2,1,2,2,1]
[6,7,1,4,3,8,2,5]=>[2,2,2,2]
[8,1,2,3,5,7,6,4]=>[1,5,1,1]
[8,1,2,3,6,7,5,4]=>[1,5,1,1]
[7,1,2,3,6,8,5,4]=>[1,5,1,1]
[7,1,2,3,8,5,6,4]=>[1,4,2,1]
[8,1,2,3,7,5,6,4]=>[1,4,2,1]
[8,1,2,3,6,5,7,4]=>[1,4,2,1]
[7,1,8,5,4,3,2,6]=>[1,2,1,1,1,2]
[7,8,2,6,3,4,1,5]=>[2,2,2,2]
[6,8,2,7,3,4,1,5]=>[2,2,2,2]
[6,7,2,8,3,4,1,5]=>[2,2,2,2]
[3,8,7,1,4,2,6,5]=>[2,1,2,2,1]
[3,7,8,1,4,2,6,5]=>[3,2,2,1]
[3,6,8,1,4,2,7,5]=>[3,2,2,1]
[3,5,7,8,2,4,1,6]=>[4,2,2]
[3,6,7,1,4,2,8,5]=>[3,2,2,1]
[7,6,2,8,3,1,4,5]=>[1,1,2,1,3]
[8,6,2,7,3,1,4,5]=>[1,1,2,1,3]
[8,1,7,5,4,3,2,6]=>[1,2,1,1,1,2]
[8,1,7,4,5,3,2,6]=>[1,2,2,1,2]
[5,8,3,7,1,4,2,6]=>[2,2,2,2]
[2,1,7,3,4,6,8,5]=>[1,2,4,1]
[6,7,3,2,4,1,8,5]=>[2,1,2,2,1]
[8,7,2,4,3,6,1,5]=>[1,1,2,2,2]
[7,1,2,3,5,6,8,4]=>[1,6,1]
[6,1,2,3,8,7,4,5]=>[1,4,1,2]
[5,1,2,3,7,8,6,4]=>[1,5,1,1]
[5,1,2,3,8,7,6,4]=>[1,4,1,1,1]
[5,1,2,3,8,6,7,4]=>[1,4,2,1]
[6,1,2,3,5,8,7,4]=>[1,5,1,1]
[8,6,2,4,3,1,7,5]=>[1,1,2,1,2,1]
[7,6,3,2,4,8,1,5]=>[1,1,1,3,2]
[2,1,6,3,4,8,7,5]=>[1,2,3,1,1]
[8,6,3,2,4,7,1,5]=>[1,1,1,3,2]
[7,6,2,4,3,1,8,5]=>[1,1,2,1,2,1]
[6,1,2,3,5,7,8,4]=>[1,6,1]
[5,1,2,3,6,8,7,4]=>[1,5,1,1]
[7,8,1,2,6,3,5,4]=>[2,3,2,1]
[1,4,8,2,7,3,5,6]=>[3,2,3]
[1,2,8,5,4,7,3,6]=>[3,1,2,2]
[1,3,8,5,4,2,7,6]=>[3,1,1,2,1]
[2,3,6,8,4,7,1,5]=>[4,2,2]
[1,3,6,8,4,7,5,2]=>[4,2,1,1]
[2,4,8,1,7,3,6,5]=>[3,2,2,1]
[3,4,8,5,7,6,1,2]=>[3,2,1,2]
[1,2,6,8,4,5,7,3]=>[4,3,1]
[7,5,1,2,4,3,6,8]=>[1,1,3,3]
[7,4,6,1,5,2,3,8]=>[1,2,2,3]
[7,1,4,2,6,3,5,8]=>[1,2,2,3]
[6,8,1,4,7,2,3,5]=>[2,3,3]
[1,6,4,2,8,3,5,7]=>[2,1,2,3]
[1,6,3,8,5,4,2,7]=>[2,2,1,1,2]
[6,8,1,7,3,5,4,2]=>[2,2,2,1,1]
[7,1,3,6,5,4,2,8]=>[1,3,1,1,2]
[7,3,1,6,5,4,2,8]=>[1,1,2,1,1,2]
[7,2,1,4,6,3,5,8]=>[1,1,3,3]
[7,2,3,6,5,1,4,8]=>[1,3,1,3]
[7,1,2,3,6,5,4,8]=>[1,4,1,2]
[6,8,1,2,7,3,5,4]=>[2,3,2,1]
[1,6,2,3,8,5,4,7]=>[2,3,1,2]
[1,5,8,2,7,6,3,4]=>[3,2,1,2]
[5,1,8,2,7,6,3,4]=>[1,2,2,1,2]
[5,8,2,7,6,3,4,1]=>[2,2,1,2,1]
[6,2,8,1,7,3,5,4]=>[1,2,2,2,1]
[6,8,2,1,7,4,3,5]=>[2,1,2,1,2]
[3,6,4,1,2,8,5,7]=>[2,1,3,2]
[2,1,6,3,8,5,4,7]=>[1,2,2,1,2]
[2,5,1,8,7,6,3,4]=>[2,2,1,1,2]
[2,5,3,8,7,4,6,1]=>[2,2,1,2,1]
[1,2,5,3,8,7,4,6]=>[3,2,1,2]
[2,4,8,7,6,5,1,3]=>[3,1,1,1,2]
[2,5,3,8,7,1,6,4]=>[2,2,1,2,1]
[2,5,8,4,1,7,6,3]=>[3,1,2,1,1]
[3,5,8,7,1,4,2,6]=>[3,1,2,2]
[5,3,8,4,1,7,6,2]=>[1,2,1,2,1,1]
[4,2,8,7,6,3,5,1]=>[1,2,1,1,2,1]
[4,2,8,7,6,5,3,1]=>[1,2,1,1,1,1,1]
[4,1,8,7,6,5,3,2]=>[1,2,1,1,1,1,1]
[4,3,8,7,6,5,1,2]=>[1,2,1,1,1,2]
[6,3,1,8,7,2,5,4]=>[1,1,2,1,2,1]
[5,8,3,7,6,1,4,2]=>[2,2,1,2,1]
[5,1,3,8,7,6,2,4]=>[1,3,1,1,2]
[1,5,3,8,7,6,2,4]=>[2,2,1,1,2]
[1,5,8,4,7,2,6,3]=>[3,2,2,1]
[5,1,8,4,7,2,6,3]=>[1,2,2,2,1]
[5,8,7,4,6,1,2,3]=>[2,1,2,3]
[6,8,5,1,2,4,7,3]=>[2,1,4,1]
[5,6,3,1,2,4,8,7]=>[2,1,4,1]
[5,6,2,4,3,1,8,7]=>[2,2,1,2,1]
[5,6,1,2,4,3,8,7]=>[2,3,2,1]
[4,5,8,1,7,2,3,6]=>[3,2,3]
[4,5,8,1,7,2,6,3]=>[3,2,2,1]
[1,3,2,5,8,7,4,6]=>[2,3,1,2]
[3,5,1,8,7,4,6,2]=>[2,2,1,2,1]
[3,5,1,8,7,2,6,4]=>[2,2,1,2,1]
[4,3,6,1,2,8,5,7]=>[1,2,3,2]
[4,5,8,3,1,7,2,6]=>[3,1,2,2]
[4,5,2,8,7,1,3,6]=>[2,2,1,3]
[3,2,5,8,7,1,6,4]=>[1,3,1,2,1]
[3,4,8,7,6,2,1,5]=>[3,1,1,1,2]
[3,1,4,8,7,6,2,5]=>[1,3,1,1,2]
[3,4,8,7,6,5,1,2]=>[3,1,1,1,2]
[1,3,4,8,7,6,2,5]=>[4,1,1,2]
[3,4,8,7,6,2,5,1]=>[3,1,1,2,1]
[3,2,5,8,7,4,6,1]=>[1,3,1,2,1]
[4,5,8,3,1,7,6,2]=>[3,1,2,1,1]
[2,1,3,5,8,7,4,6]=>[1,4,1,2]
[1,2,7,5,8,6,4,3]=>[3,2,1,1,1]
[7,1,4,8,2,6,5,3]=>[1,3,2,1,1]
[6,8,1,3,7,5,2,4]=>[2,3,1,2]
[3,7,8,1,2,6,5,4]=>[3,3,1,1]
[1,3,7,8,2,6,5,4]=>[4,2,1,1]
[2,3,7,8,1,6,5,4]=>[4,2,1,1]
[2,7,8,1,3,6,5,4]=>[3,3,1,1]
[8,1,2,6,7,3,5,4]=>[1,4,2,1]
[8,1,2,6,7,5,3,4]=>[1,4,1,2]
[8,2,5,7,1,3,6,4]=>[1,3,3,1]
[2,8,1,6,7,3,5,4]=>[2,3,2,1]
[2,6,8,3,7,1,5,4]=>[3,2,2,1]
[2,8,6,4,7,1,5,3]=>[2,1,2,2,1]
[6,8,3,4,1,7,5,2]=>[2,2,2,1,1]
[6,8,3,7,4,1,5,2]=>[2,2,1,2,1]
[2,6,8,3,7,5,1,4]=>[3,2,1,2]
[2,8,1,6,7,5,3,4]=>[2,3,1,2]
[8,2,5,7,1,6,3,4]=>[1,3,2,2]
[8,4,7,2,3,6,1,5]=>[1,2,3,2]
[8,5,7,4,2,6,1,3]=>[1,2,1,2,2]
[8,3,5,7,4,1,6,2]=>[1,3,1,2,1]
[8,5,2,4,7,1,6,3]=>[1,1,3,2,1]
[8,2,3,5,7,1,6,4]=>[1,4,2,1]
[8,2,4,7,3,6,1,5]=>[1,3,2,2]
[8,2,7,1,4,6,3,5]=>[1,2,3,2]
[8,7,1,2,4,6,3,5]=>[1,1,4,2]
[8,7,1,4,6,2,3,5]=>[1,1,3,3]
[8,4,7,1,3,6,2,5]=>[1,2,3,2]
[1,6,8,3,7,2,5,4]=>[3,2,2,1]
[8,3,5,7,1,2,6,4]=>[1,3,3,1]
[5,8,7,1,3,6,2,4]=>[2,1,3,2]
[8,5,4,7,1,6,2,3]=>[1,1,2,2,2]
[8,5,4,7,1,2,6,3]=>[1,1,2,3,1]
[8,5,1,4,7,2,6,3]=>[1,1,3,2,1]
[1,4,6,8,2,7,5,3]=>[4,2,1,1]
[1,6,5,8,2,7,4,3]=>[2,2,2,1,1]
[8,5,6,3,1,7,4,2]=>[1,2,1,2,1,1]
[5,6,2,8,1,7,4,3]=>[2,2,2,1,1]
[1,8,4,5,7,2,6,3]=>[2,3,2,1]
[5,8,7,3,6,1,2,4]=>[2,1,2,3]
[8,3,5,7,1,6,2,4]=>[1,3,2,2]
[1,6,8,3,7,5,2,4]=>[3,2,1,2]
[6,3,8,2,7,5,1,4]=>[1,2,2,1,2]
[6,8,4,2,7,1,5,3]=>[2,1,2,2,1]
[8,6,4,7,3,1,5,2]=>[1,1,2,1,2,1]
[8,4,5,7,3,1,6,2]=>[1,3,1,2,1]
[8,4,2,5,7,1,6,3]=>[1,1,3,2,1]
[8,3,4,7,2,6,1,5]=>[1,3,2,2]
[8,7,1,3,4,6,2,5]=>[1,1,4,2]
[8,3,7,2,4,6,1,5]=>[1,2,3,2]
[2,8,4,5,7,1,6,3]=>[2,3,2,1]
[8,7,3,4,5,1,6,2]=>[1,1,3,2,1]
[8,7,4,5,2,6,1,3]=>[1,1,2,2,2]
[5,8,7,2,3,6,1,4]=>[2,1,3,2]
[8,7,2,3,4,6,1,5]=>[1,1,4,2]
[8,7,2,3,6,1,4,5]=>[1,1,3,3]
[1,3,2,8,5,4,7,6]=>[2,2,1,2,1]
[4,2,8,5,3,7,1,6]=>[1,2,1,2,2]
[5,2,1,8,4,3,7,6]=>[1,1,2,1,2,1]
[6,2,8,4,3,7,5,1]=>[1,2,1,2,1,1]
[7,2,8,4,3,1,6,5]=>[1,2,1,1,2,1]
[7,3,4,8,2,1,6,5]=>[1,3,1,2,1]
[6,3,4,8,2,7,5,1]=>[1,3,2,1,1]
[5,3,4,1,8,2,7,6]=>[1,2,2,2,1]
[8,1,4,5,2,3,7,6]=>[1,3,3,1]
[8,1,5,4,3,2,7,6]=>[1,2,1,1,2,1]
[3,5,4,2,8,1,7,6]=>[2,1,2,2,1]
[4,5,3,2,8,7,1,6]=>[2,1,2,1,2]
[6,4,3,2,8,7,5,1]=>[1,1,1,2,1,1,1]
[6,5,3,2,1,7,8,4]=>[1,1,1,1,3,1]
[5,6,3,2,7,8,4,1]=>[2,1,3,1,1]
[4,1,6,3,2,7,8,5]=>[1,2,1,3,1]
[3,6,4,2,7,8,1,5]=>[2,1,3,2]
[8,1,6,4,3,7,2,5]=>[1,2,1,2,2]
[8,1,7,4,3,6,5,2]=>[1,2,1,2,1,1]
[2,7,4,1,3,6,5,8]=>[2,1,3,2]
[3,7,4,2,6,1,5,8]=>[2,1,2,3]
[4,1,7,3,2,6,5,8]=>[1,2,1,2,2]
[5,7,3,2,6,4,8,1]=>[2,1,2,2,1]
[6,7,3,2,5,4,1,8]=>[2,1,2,1,2]
[7,6,3,2,1,5,4,8]=>[1,1,1,1,2,2]
[4,7,5,6,2,3,8,1]=>[2,2,3,1]
[3,1,7,5,6,2,4,8]=>[1,2,2,3]
[2,7,5,6,1,3,4,8]=>[2,2,4]
[2,6,5,7,1,3,8,4]=>[2,2,3,1]
[4,6,5,7,2,8,1,3]=>[2,2,2,2]
[5,6,4,7,2,8,3,1]=>[2,2,2,1,1]
[6,5,4,1,7,2,8,3]=>[1,1,1,2,2,1]
[7,5,4,6,2,1,8,3]=>[1,1,2,1,2,1]
[6,4,5,7,1,8,2,3]=>[1,3,2,2]
[5,4,6,1,7,8,2,3]=>[1,2,3,2]
[8,1,5,6,7,2,3,4]=>[1,4,3]
[2,1,4,6,8,7,3,5]=>[1,4,1,2]
[3,4,6,8,7,1,2,5]=>[4,1,3]
[4,3,1,6,8,7,2,5]=>[1,1,3,1,2]
[5,3,6,8,7,2,4,1]=>[1,3,1,2,1]
[6,3,5,1,8,7,2,4]=>[1,2,2,1,2]
[7,3,5,8,6,2,1,4]=>[1,3,1,1,2]
[7,2,8,5,6,3,1,4]=>[1,2,2,1,2]
[6,2,8,5,1,7,3,4]=>[1,2,1,2,2]
[4,2,1,8,6,7,3,5]=>[1,1,2,2,2]
[1,3,2,8,6,7,4,5]=>[2,2,2,2]
[2,3,8,6,7,1,4,5]=>[3,2,3]
[8,1,3,2,6,7,4,5]=>[1,2,3,2]
[2,3,8,7,1,6,5,4]=>[3,1,2,1,1]
[4,2,8,7,6,1,5,3]=>[1,2,1,1,2,1]
[5,2,8,7,6,4,1,3]=>[1,2,1,1,1,2]
[7,2,1,8,6,5,4,3]=>[1,1,2,1,1,1,1]
[7,3,6,1,8,5,4,2]=>[1,2,2,1,1,1]
[6,3,7,8,5,4,2,1]=>[1,3,1,1,1,1]
[5,3,7,8,6,4,1,2]=>[1,3,1,1,2]
[4,3,1,7,8,6,5,2]=>[1,1,3,1,1,1]
[3,4,7,8,6,1,5,2]=>[4,1,2,1]
[8,1,5,7,6,2,4,3]=>[1,3,1,2,1]
[3,5,7,6,8,1,4,2]=>[3,2,2,1]
[4,5,7,6,8,3,1,2]=>[3,2,1,2]
[5,4,1,7,6,8,3,2]=>[1,1,2,2,1,1]
[6,4,7,5,8,3,2,1]=>[1,2,2,1,1,1]
[7,4,6,5,1,8,3,2]=>[1,2,1,2,1,1]
[7,5,6,4,3,1,8,2]=>[1,2,1,1,2,1]
[6,5,1,7,4,3,8,2]=>[1,1,2,1,2,1]
[4,6,7,5,3,8,1,2]=>[3,1,2,2]
[3,6,7,5,1,4,8,2]=>[3,1,3,1]
[8,1,6,7,5,4,2,3]=>[1,3,1,1,2]
[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[2,7,6,1,5,4,3,8]=>[2,1,2,1,2]
[3,7,6,5,1,4,2,8]=>[2,1,1,2,2]
[4,7,6,5,3,1,2,8]=>[2,1,1,1,3]
[8,6,4,3,1,5,7,2]=>[1,1,1,1,3,1]
[8,6,4,1,5,2,7,3]=>[1,1,1,2,2,1]
[8,6,5,1,3,2,7,4]=>[1,1,1,2,2,1]
[8,6,3,1,7,2,4,5]=>[1,1,1,2,3]
[8,7,3,1,5,2,4,6]=>[1,1,1,2,3]
[5,3,1,7,2,4,6,8]=>[1,1,2,4]
[8,7,1,2,4,5,3,6]=>[1,1,4,2]
[8,6,1,2,4,7,3,5]=>[1,1,4,2]
[8,5,1,2,6,7,3,4]=>[1,1,4,2]
[8,5,1,6,4,2,7,3]=>[1,1,2,1,2,1]
[8,5,1,3,6,4,7,2]=>[1,1,3,2,1]
[8,6,1,5,3,4,7,2]=>[1,1,2,3,1]
[8,6,1,5,2,4,7,3]=>[1,1,2,3,1]
[8,6,1,2,5,7,3,4]=>[1,1,4,2]
[8,6,1,2,7,4,3,5]=>[1,1,3,1,2]
[8,7,1,2,5,4,3,6]=>[1,1,3,1,2]
[5,1,4,2,3,8,6,7]=>[1,2,3,2]
[5,1,4,2,7,3,6,8]=>[1,2,2,3]
[7,1,5,8,2,6,3,4]=>[1,3,2,2]
[5,7,8,1,2,4,6,3]=>[3,4,1]
[5,7,8,1,3,4,6,2]=>[3,4,1]
[5,8,1,7,3,4,6,2]=>[2,2,3,1]
[8,1,5,7,2,4,6,3]=>[1,3,3,1]
[8,4,1,2,7,6,3,5]=>[1,1,3,1,2]
[1,4,2,3,8,7,5,6]=>[2,3,1,2]
[1,4,2,7,6,3,5,8]=>[2,2,1,3]
[6,1,2,8,7,5,3,4]=>[1,3,1,1,2]
[6,1,2,4,8,7,5,3]=>[1,4,1,1,1]
[3,1,8,4,6,7,5,2]=>[1,2,3,1,1]
[3,1,7,6,4,8,5,2]=>[1,2,1,2,1,1]
[7,1,2,4,6,8,5,3]=>[1,5,1,1]
[7,1,2,6,8,5,3,4]=>[1,4,1,2]
[6,1,2,7,8,5,3,4]=>[1,4,1,2]
[6,1,2,7,4,8,5,3]=>[1,3,2,1,1]
[3,1,6,4,7,8,5,2]=>[1,2,3,1,1]
[5,7,1,3,8,4,6,2]=>[2,3,2,1]
[5,7,1,8,4,2,6,3]=>[2,2,1,2,1]
[7,1,5,3,2,8,6,4]=>[1,2,1,2,1,1]
[7,1,4,5,2,8,6,3]=>[1,3,2,1,1]
[4,7,3,1,5,8,6,2]=>[2,1,3,1,1]
[4,8,7,3,1,5,6,2]=>[2,1,1,3,1]
[8,1,7,4,5,2,6,3]=>[1,2,2,2,1]
[8,1,7,5,3,2,6,4]=>[1,2,1,1,2,1]
[8,3,7,1,2,6,4,5]=>[1,2,3,2]
[3,1,2,8,4,7,5,6]=>[1,3,2,2]
[3,1,2,8,6,4,5,7]=>[1,3,1,3]
[3,1,7,2,6,4,5,8]=>[1,2,2,3]
[1,4,2,3,8,6,5,7]=>[2,3,1,2]
[1,4,2,3,8,5,7,6]=>[2,3,2,1]
[5,8,1,7,2,4,6,3]=>[2,2,3,1]
[5,8,1,3,4,7,6,2]=>[2,4,1,1]
[3,1,8,6,4,7,5,2]=>[1,2,1,2,1,1]
[8,1,2,6,7,4,5,3]=>[1,4,2,1]
[6,1,2,8,7,3,5,4]=>[1,3,1,2,1]
[1,2,3,5,8,4,7,6]=>[5,2,1]
[1,2,3,5,8,6,4,7]=>[5,1,2]
[7,1,2,8,3,6,5,4]=>[1,3,2,1,1]
[7,1,2,8,6,4,5,3]=>[1,3,1,2,1]
[3,1,7,8,4,6,5,2]=>[1,3,2,1,1]
[3,1,8,7,6,4,5,2]=>[1,2,1,1,2,1]
[8,1,2,7,4,6,5,3]=>[1,3,2,1,1]
[8,1,2,7,3,6,5,4]=>[1,3,2,1,1]
[1,2,3,5,8,7,4,6]=>[5,1,2]
[1,2,3,6,8,5,4,7]=>[5,1,2]
[7,8,5,6,3,1,4,2]=>[2,2,1,2,1]
[7,8,5,3,6,1,2,4]=>[2,1,2,3]
[7,5,6,3,1,4,2,8]=>[1,2,1,2,2]
[7,5,8,3,1,4,2,6]=>[1,2,1,2,2]
[7,8,5,3,1,4,2,6]=>[2,1,1,2,2]
[7,8,5,3,1,6,2,4]=>[2,1,1,2,2]
[7,8,5,3,1,6,4,2]=>[2,1,1,2,1,1]
[7,8,5,3,6,1,4,2]=>[2,1,2,2,1]
[7,8,5,3,6,4,1,2]=>[2,1,2,1,2]
[7,8,5,3,4,1,6,2]=>[2,1,2,2,1]
[7,8,5,3,1,4,6,2]=>[2,1,1,3,1]
[7,8,5,3,1,2,6,4]=>[2,1,1,3,1]
[7,5,3,8,1,2,6,4]=>[1,1,2,3,1]
[7,5,8,3,4,1,6,2]=>[1,2,2,2,1]
[7,5,8,3,4,6,1,2]=>[1,2,3,2]
[7,5,6,3,4,1,8,2]=>[1,2,2,2,1]
[7,5,6,3,1,4,8,2]=>[1,2,1,3,1]
[7,5,6,3,1,2,8,4]=>[1,2,1,3,1]
[7,5,3,6,1,2,8,4]=>[1,1,2,3,1]
[7,5,3,4,1,2,8,6]=>[1,1,2,3,1]
[7,5,3,1,4,2,6,8]=>[1,1,1,2,3]
[7,5,3,1,4,2,8,6]=>[1,1,1,2,2,1]
[7,5,3,1,6,2,8,4]=>[1,1,1,2,2,1]
[7,5,3,1,6,4,8,2]=>[1,1,1,2,2,1]
[7,5,3,6,1,4,8,2]=>[1,1,2,3,1]
[7,5,3,6,4,1,8,2]=>[1,1,2,1,2,1]
[7,5,3,6,4,8,1,2]=>[1,1,2,2,2]
[7,5,3,8,4,6,1,2]=>[1,1,2,2,2]
[7,5,3,8,1,4,6,2]=>[1,1,2,3,1]
[7,5,3,1,8,4,6,2]=>[1,1,1,2,2,1]
[7,5,3,1,8,2,6,4]=>[1,1,1,2,2,1]
[7,5,3,1,8,2,4,6]=>[1,1,1,2,3]
[7,5,3,1,6,2,4,8]=>[1,1,1,2,3]
[7,5,3,1,6,4,2,8]=>[1,1,1,2,1,2]
[7,5,3,1,8,4,2,6]=>[1,1,1,2,1,2]
[7,5,3,1,8,6,2,4]=>[1,1,1,2,1,2]
[7,5,3,8,1,6,4,2]=>[1,1,2,2,1,1]
[7,5,3,8,6,1,4,2]=>[1,1,2,1,2,1]
[7,5,3,8,6,4,1,2]=>[1,1,2,1,1,2]
[7,5,8,3,6,4,1,2]=>[1,2,2,1,2]
[7,5,8,3,6,1,4,2]=>[1,2,2,2,1]
[7,5,8,3,1,6,4,2]=>[1,2,1,2,1,1]
[7,5,8,3,1,6,2,4]=>[1,2,1,2,2]
[7,5,3,6,1,4,2,8]=>[1,1,2,2,2]
[7,5,3,6,4,1,2,8]=>[1,1,2,1,3]
[7,5,3,8,4,1,2,6]=>[1,1,2,1,3]
[7,5,8,6,3,1,2,4]=>[1,2,1,1,3]
[7,5,8,6,3,1,4,2]=>[1,2,1,1,2,1]
[7,5,8,6,3,4,1,2]=>[1,2,1,2,2]
[7,5,6,8,3,1,4,2]=>[1,3,1,2,1]
[7,5,6,3,8,1,2,4]=>[1,2,2,3]
[7,5,3,4,1,6,2,8]=>[1,1,2,2,2]
[7,5,3,4,1,8,2,6]=>[1,1,2,2,2]
[7,5,6,3,1,8,2,4]=>[1,2,1,2,2]
[7,5,6,3,1,8,4,2]=>[1,2,1,2,1,1]
[7,5,6,3,8,1,4,2]=>[1,2,2,2,1]
[7,5,6,3,8,4,1,2]=>[1,2,2,1,2]
[7,5,3,6,8,4,1,2]=>[1,1,3,1,2]
[7,5,3,6,8,1,4,2]=>[1,1,3,2,1]
[7,5,3,6,1,8,4,2]=>[1,1,2,2,1,1]
[7,5,3,1,6,8,4,2]=>[1,1,1,3,1,1]
[7,5,3,1,6,8,2,4]=>[1,1,1,3,2]
[7,5,3,1,4,8,2,6]=>[1,1,1,3,2]
[7,5,3,1,4,6,2,8]=>[1,1,1,3,2]
[7,5,3,1,2,6,4,8]=>[1,1,1,3,2]
[7,5,3,1,2,8,4,6]=>[1,1,1,3,2]
[7,5,3,1,2,8,6,4]=>[1,1,1,3,1,1]
[7,5,3,1,4,8,6,2]=>[1,1,1,3,1,1]
[7,5,3,4,1,8,6,2]=>[1,1,2,2,1,1]
[7,5,3,4,8,1,6,2]=>[1,1,3,2,1]
[7,5,3,4,8,6,1,2]=>[1,1,3,1,2]
[7,5,3,4,6,1,8,2]=>[1,1,3,2,1]
[7,5,3,4,1,6,8,2]=>[1,1,2,3,1]
[7,5,3,1,4,6,8,2]=>[1,1,1,4,1]
[7,5,3,1,2,6,8,4]=>[1,1,1,4,1]
[7,5,3,1,2,4,8,6]=>[1,1,1,4,1]
[3,6,2,5,4,1,8,7]=>[2,2,1,2,1]
[3,5,2,8,4,7,6,1]=>[2,2,2,1,1]
[5,4,7,3,2,8,6,1]=>[1,2,1,2,1,1]
[5,4,8,3,2,7,6,1]=>[1,2,1,2,1,1]
[6,4,5,3,2,1,8,7]=>[1,2,1,1,2,1]
[5,3,2,6,4,1,8,7]=>[1,1,2,1,2,1]
[4,5,8,3,2,7,6,1]=>[3,1,2,1,1]
[4,7,6,3,8,5,2,1]=>[2,1,2,1,1,1]
[4,8,6,3,7,5,2,1]=>[2,1,2,1,1,1]
[4,8,5,3,2,7,6,1]=>[2,1,1,2,1,1]
[5,8,4,3,2,7,6,1]=>[2,1,1,2,1,1]
[5,3,2,8,4,7,6,1]=>[1,1,2,2,1,1]
[2,1,5,8,4,7,6,3]=>[1,3,2,1,1]
[5,3,2,7,4,8,6,1]=>[1,1,2,2,1,1]
[5,7,4,3,2,8,6,1]=>[2,1,1,2,1,1]
[4,7,5,3,2,8,6,1]=>[2,1,1,2,1,1]
[4,7,8,3,6,5,2,1]=>[3,2,1,1,1]
[4,6,8,3,7,5,2,1]=>[3,2,1,1,1]
[7,6,4,3,8,5,2,1]=>[1,1,1,2,1,1,1]
[7,3,2,6,8,5,4,1]=>[1,1,3,1,1,1]
[2,1,8,6,7,5,4,3]=>[1,2,2,1,1,1]
[8,3,2,6,7,5,4,1]=>[1,1,3,1,1,1]
[8,6,4,3,7,5,2,1]=>[1,1,1,2,1,1,1]
[8,5,7,6,4,3,2,1]=>[1,2,1,1,1,1,1]
[8,4,5,3,2,7,6,1]=>[1,2,1,2,1,1]
[8,4,7,3,6,5,2,1]=>[1,2,2,1,1,1]
[8,4,6,3,7,5,2,1]=>[1,2,2,1,1,1]
[7,4,6,3,8,5,2,1]=>[1,2,2,1,1,1]
[3,7,2,6,8,5,4,1]=>[2,3,1,1,1]
[3,8,2,6,7,5,4,1]=>[2,3,1,1,1]
[3,8,2,5,4,7,6,1]=>[2,2,2,1,1]
[3,7,2,8,6,5,4,1]=>[2,2,1,1,1,1]
[3,6,2,8,7,5,4,1]=>[2,2,1,1,1,1]
[6,4,7,3,8,5,2,1]=>[1,2,2,1,1,1]
[6,4,8,3,7,5,2,1]=>[1,2,2,1,1,1]
[7,4,8,3,6,5,2,1]=>[1,2,2,1,1,1]
[7,4,5,3,2,8,6,1]=>[1,2,1,2,1,1]
[7,5,4,3,2,8,6,1]=>[1,1,1,1,2,1,1]
[7,3,2,5,4,8,6,1]=>[1,1,2,2,1,1]
[2,1,7,5,4,8,6,3]=>[1,2,1,2,1,1]
[7,3,2,8,6,5,4,1]=>[1,1,2,1,1,1,1]
[7,8,4,3,6,5,2,1]=>[2,1,2,1,1,1]
[6,8,5,7,4,3,2,1]=>[2,2,1,1,1,1]
[6,8,4,3,7,5,2,1]=>[2,1,2,1,1,1]
[6,3,2,8,7,5,4,1]=>[1,1,2,1,1,1,1]
[6,3,2,7,8,5,4,1]=>[1,1,3,1,1,1]
[6,7,4,3,8,5,2,1]=>[2,1,2,1,1,1]
[4,6,8,3,5,7,1,2]=>[3,3,2]
[6,8,1,2,4,5,7,3]=>[2,5,1]
[3,5,8,2,4,7,1,6]=>[3,3,2]
[8,3,5,2,4,1,6,7]=>[1,2,2,3]
[4,2,5,7,3,6,1,8]=>[1,3,2,2]
[4,5,2,8,3,1,6,7]=>[2,2,1,3]
[4,2,5,8,3,7,1,6]=>[1,3,2,2]
[2,1,6,8,4,7,3,5]=>[1,3,2,2]
[1,2,5,8,3,6,7,4]=>[4,3,1]
[5,3,6,8,4,7,1,2]=>[1,3,2,2]
[1,6,5,8,2,4,7,3]=>[2,2,3,1]
[3,1,2,6,8,5,7,4]=>[1,4,2,1]
[1,4,3,8,2,6,7,5]=>[2,2,3,1]
[5,4,8,3,2,1,6,7]=>[1,2,1,1,3]
[5,4,3,7,2,6,1,8]=>[1,1,2,2,2]
[4,3,6,2,7,5,1,8]=>[1,2,2,1,2]
[4,6,3,2,1,8,5,7]=>[2,1,1,2,2]
[4,1,7,3,2,5,8,6]=>[1,2,1,3,1]
[4,3,1,7,8,2,6,5]=>[1,1,3,2,1]
[3,5,1,2,7,8,6,4]=>[2,4,1,1]
[7,5,1,4,8,2,6,3]=>[1,1,3,2,1]
[5,4,7,3,8,6,1,2]=>[1,2,2,1,2]
[5,8,4,7,6,3,1,2]=>[2,2,1,1,2]
[5,8,7,1,4,2,6,3]=>[2,1,2,2,1]
[8,3,5,1,2,7,6,4]=>[1,2,3,1,1]
[4,8,3,1,7,2,6,5]=>[2,1,2,2,1]
[1,8,4,3,5,2,7,6]=>[2,1,2,2,1]
[4,6,3,1,5,2,8,7]=>[2,1,2,2,1]
[4,7,3,6,5,2,1,8]=>[2,2,1,1,2]
[5,3,7,6,4,2,1,8]=>[1,2,1,1,1,2]
[1,6,3,4,2,8,7,5]=>[2,2,2,1,1]
[1,8,3,6,2,7,5,4]=>[2,2,2,1,1]
[1,6,8,7,4,2,5,3]=>[3,1,1,2,1]
[6,4,8,7,5,3,1,2]=>[1,2,1,1,1,2]
[7,6,4,3,8,5,1,2]=>[1,1,1,2,1,2]
[1,7,6,2,8,4,5,3]=>[2,1,2,2,1]
[7,1,3,2,6,8,5,4]=>[1,2,3,1,1]
[1,5,3,2,7,4,8,6]=>[2,1,2,2,1]
[6,3,2,1,8,5,4,7]=>[1,1,1,2,1,2]
[6,5,3,2,7,4,1,8]=>[1,1,1,2,1,2]
[5,2,6,3,7,4,1,8]=>[1,2,2,1,2]
[2,8,5,3,1,6,4,7]=>[2,1,1,2,2]
[2,1,7,3,8,5,4,6]=>[1,2,2,1,2]
[1,6,2,3,7,8,5,4]=>[2,4,1,1]
[1,6,7,2,8,4,5,3]=>[3,2,2,1]
[5,7,1,8,2,4,6,3]=>[2,2,3,1]
[5,1,2,7,8,3,6,4]=>[1,4,2,1]
[2,4,1,7,8,6,3,5]=>[2,3,1,2]
[4,2,1,7,3,8,5,6]=>[1,1,2,2,2]
[6,2,8,4,3,1,5,7]=>[1,2,1,1,3]
[7,3,2,1,8,4,5,6]=>[1,1,1,2,3]
[7,8,3,2,5,6,1,4]=>[2,1,3,2]
[7,1,8,2,4,5,6,3]=>[1,2,4,1]
[8,7,6,1,2,4,5,3]=>[1,1,1,4,1]
[8,3,7,6,2,1,4,5]=>[1,2,1,1,3]
[3,2,8,7,5,1,4,6]=>[1,2,1,1,3]
[8,3,6,5,2,1,4,7]=>[1,2,1,1,3]
[7,6,3,5,2,4,1,8]=>[1,1,2,2,2]
[7,4,6,2,5,3,1,8]=>[1,2,2,1,2]
[8,2,4,1,6,5,3,7]=>[1,2,2,1,2]
[4,2,8,1,7,5,3,6]=>[1,2,2,1,2]
[8,2,4,1,7,6,3,5]=>[1,2,2,1,2]
[8,7,1,5,6,2,4,3]=>[1,1,3,2,1]
[8,5,7,3,6,4,1,2]=>[1,2,2,1,2]
[6,8,3,7,5,4,1,2]=>[2,2,1,1,2]
[8,1,6,7,5,2,4,3]=>[1,3,1,2,1]
[8,1,2,6,4,3,7,5]=>[1,3,1,2,1]
[2,8,1,7,5,4,3,6]=>[2,2,1,1,2]
[2,5,1,8,6,4,3,7]=>[2,2,1,1,2]
[5,7,2,6,4,3,1,8]=>[2,2,1,1,2]
[6,2,7,5,4,3,1,8]=>[1,2,1,1,1,2]
[2,1,8,6,5,4,3,7]=>[1,2,1,1,1,2]
[1,2,7,5,4,3,8,6]=>[3,1,1,2,1]
[1,7,2,4,3,8,6,5]=>[2,2,2,1,1]
[1,7,2,8,3,6,5,4]=>[2,2,2,1,1]
[1,7,8,6,5,2,4,3]=>[3,1,1,2,1]
[7,3,8,6,5,4,1,2]=>[1,2,1,1,1,2]
[1,8,7,6,5,2,4,3]=>[2,1,1,1,2,1]
[8,1,7,3,2,6,5,4]=>[1,2,1,2,1,1]
[5,1,4,3,2,8,7,6]=>[1,2,1,2,1,1]
[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,2,1]
[8,6,3,2,1,7,4,5]=>[1,1,1,1,2,2]
[8,6,5,4,1,7,2,3]=>[1,1,1,1,2,2]
[8,6,5,1,7,3,2,4]=>[1,1,1,2,1,2]
[8,6,1,7,4,3,2,5]=>[1,1,2,1,1,2]
[4,6,3,2,7,5,1,8]=>[2,1,2,1,2]
[1,4,3,7,2,5,8,6]=>[2,2,3,1]
[7,4,8,3,1,6,2,5]=>[1,2,1,2,2]
[7,1,5,8,3,2,6,4]=>[1,3,1,2,1]
[5,7,4,1,8,2,6,3]=>[2,1,2,2,1]
[5,7,4,3,1,8,6,2]=>[2,1,1,2,1,1]
[1,8,7,2,5,4,6,3]=>[2,1,2,2,1]
[1,8,5,3,7,2,6,4]=>[2,1,2,2,1]
[4,3,1,8,7,5,2,6]=>[1,1,2,1,1,2]
[1,4,8,6,3,5,2,7]=>[3,1,2,2]
[7,4,6,3,5,2,1,8]=>[1,2,2,1,2]
[1,3,5,6,8,4,2,7]=>[5,1,2]
[3,5,4,8,7,1,2,6]=>[2,2,1,3]
[3,1,4,6,8,7,2,5]=>[1,4,1,2]
[1,6,3,8,7,2,5,4]=>[2,2,1,2,1]
[1,6,2,4,8,7,5,3]=>[2,3,1,1,1]
[8,4,1,6,7,5,3,2]=>[1,1,3,1,1,1]
[7,1,6,4,8,5,2,3]=>[1,2,2,1,2]
[7,3,6,8,5,1,2,4]=>[1,3,1,3]
[1,3,7,2,6,8,4,5]=>[3,3,2]
[3,6,5,2,8,1,4,7]=>[2,1,2,3]
[3,6,5,7,2,4,1,8]=>[2,2,2,2]
[4,2,6,3,8,1,5,7]=>[1,2,2,3]
[4,2,6,7,3,5,1,8]=>[1,3,2,2]
[3,6,2,4,7,5,1,8]=>[2,3,1,2]
[3,6,2,4,1,8,5,7]=>[2,2,2,2]
[7,3,8,2,1,6,4,5]=>[1,2,1,2,2]
[7,3,5,2,1,8,6,4]=>[1,2,1,2,1,1]
[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,2,1]
[8,7,6,4,1,5,2,3]=>[1,1,1,1,2,2]
[3,8,7,2,1,4,6,5]=>[2,1,1,3,1]
[3,8,2,7,1,5,4,6]=>[2,2,2,2]
[3,6,8,2,1,5,4,7]=>[3,1,2,2]
[2,4,8,1,6,5,3,7]=>[3,2,1,2]
[4,2,8,1,5,7,3,6]=>[1,2,3,2]
[8,5,7,6,1,4,2,3]=>[1,2,1,2,2]
[8,6,1,7,3,5,4,2]=>[1,1,2,2,1,1]
[8,6,1,7,5,4,2,3]=>[1,1,2,1,1,2]
[1,6,2,8,7,3,5,4]=>[2,2,1,2,1]
[1,8,2,4,6,7,3,5]=>[2,4,2]
[2,8,5,4,7,1,3,6]=>[2,1,2,3]
[2,1,5,8,6,4,3,7]=>[1,3,1,1,2]
[7,2,5,6,4,3,1,8]=>[1,3,1,1,2]
[1,2,5,7,8,4,3,6]=>[5,1,2]
[1,2,7,4,8,6,3,5]=>[3,2,1,2]
[1,2,7,8,3,6,5,4]=>[4,2,1,1]
[7,1,8,6,3,5,4,2]=>[1,2,1,2,1,1]
[1,8,7,6,3,5,2,4]=>[2,1,1,2,2]
[1,8,7,4,6,3,2,5]=>[2,1,2,1,2]
[7,1,5,8,3,4,6,2]=>[1,3,3,1]
[7,1,6,4,2,3,5,8]=>[1,2,1,4]
[8,6,2,4,7,3,5,1]=>[1,1,3,2,1]
[8,6,2,4,5,7,3,1]=>[1,1,4,1,1]
[2,7,1,4,5,8,3,6]=>[2,4,2]
[7,1,6,4,5,2,3,8]=>[1,2,2,3]
[7,1,4,5,6,8,2,3]=>[1,5,2]
[7,1,4,6,5,8,3,2]=>[1,3,2,1,1]
[7,1,2,3,8,5,4,6]=>[1,4,1,2]
[7,1,5,4,3,8,2,6]=>[1,2,1,2,2]
[7,1,3,4,2,6,8,5]=>[1,3,3,1]
[7,1,5,4,6,2,8,3]=>[1,2,2,2,1]
[7,1,5,6,4,3,8,2]=>[1,3,1,2,1]
[7,1,6,5,4,3,2,8]=>[1,2,1,1,1,2]
[8,6,2,5,4,3,7,1]=>[1,1,2,1,2,1]
[2,5,1,7,4,3,6,8]=>[2,2,1,3]
[2,5,1,4,7,8,6,3]=>[2,4,1,1]
[3,5,1,4,8,6,2,7]=>[2,3,1,2]
[3,6,2,4,7,8,1,5]=>[2,4,2]
[5,6,2,4,8,7,1,3]=>[2,3,1,2]
[6,3,8,2,4,7,1,5]=>[1,2,3,2]
[6,5,8,7,2,3,1,4]=>[1,2,1,2,2]
[6,5,7,8,2,4,1,3]=>[1,3,2,2]
[6,3,4,2,8,5,1,7]=>[1,2,2,1,2]
[3,4,7,2,5,8,1,6]=>[3,3,2]
[4,6,8,1,3,5,2,7]=>[3,3,2]
[4,3,8,1,2,7,5,6]=>[1,2,3,2]
[3,6,4,1,7,2,5,8]=>[2,1,2,3]
[2,8,3,1,5,6,4,7]=>[2,1,3,2]
[3,8,7,1,5,4,2,6]=>[2,1,2,1,2]
[4,3,1,7,6,8,2,5]=>[1,1,2,2,2]
[3,4,1,7,5,6,8,2]=>[2,2,3,1]
[3,4,1,5,7,6,2,8]=>[2,3,1,2]
[3,7,4,1,6,2,8,5]=>[2,1,2,2,1]
[8,4,7,2,5,3,6,1]=>[1,2,2,2,1]
[4,7,8,1,2,3,6,5]=>[3,4,1]
[2,8,6,1,5,3,7,4]=>[2,1,2,2,1]
[7,6,5,1,3,8,2,4]=>[1,1,1,3,2]
[7,6,5,1,3,4,8,2]=>[1,1,1,4,1]
[7,2,6,4,1,3,8,5]=>[1,2,1,3,1]
[6,7,5,2,1,3,8,4]=>[2,1,1,3,1]
[8,4,5,3,7,2,6,1]=>[1,2,2,2,1]
[4,7,5,2,8,1,6,3]=>[2,1,2,2,1]
[2,6,4,3,1,5,7,8]=>[2,1,1,4]
[7,3,8,4,1,5,2,6]=>[1,2,1,2,2]
[7,2,3,4,1,6,5,8]=>[1,3,2,2]
[4,2,8,3,6,1,5,7]=>[1,2,2,3]
[6,8,5,7,2,1,3,4]=>[2,2,1,3]
[4,8,5,2,7,1,3,6]=>[2,1,2,3]
[6,3,5,2,1,7,4,8]=>[1,2,1,2,2]
[6,8,5,3,1,4,2,7]=>[2,1,1,2,2]
[3,6,5,4,2,8,1,7]=>[2,1,1,2,2]
[1,6,4,7,2,5,3,8]=>[2,2,2,2]
[1,6,4,8,2,5,3,7]=>[2,2,2,2]
[1,6,5,8,2,4,3,7]=>[2,2,2,2]
[1,6,8,2,4,3,7,5]=>[3,2,2,1]
[1,6,2,4,3,7,8,5]=>[2,2,3,1]
[1,5,6,2,4,7,3,8]=>[3,3,2]
[1,5,6,2,4,7,8,3]=>[3,4,1]
[1,5,8,2,4,7,3,6]=>[3,3,2]
[1,5,7,2,4,8,3,6]=>[3,3,2]
[1,6,5,7,2,4,3,8]=>[2,2,2,2]
[1,6,7,2,4,3,8,5]=>[3,2,2,1]
[1,5,6,7,2,4,8,3]=>[4,3,1]
[1,5,8,2,4,6,7,3]=>[3,4,1]
[1,5,7,2,4,6,8,3]=>[3,4,1]
[1,5,7,8,3,2,4,6]=>[4,1,3]
[1,5,8,3,2,4,6,7]=>[3,1,4]
[1,5,6,2,4,8,3,7]=>[3,3,2]
[1,7,6,2,8,3,4,5]=>[2,1,2,3]
[1,7,3,4,2,8,6,5]=>[2,2,2,1,1]
[1,6,2,4,3,8,7,5]=>[2,2,2,1,1]
[1,5,6,2,4,8,7,3]=>[3,3,1,1]
[1,5,8,7,3,2,4,6]=>[3,1,1,3]
[1,4,2,3,5,8,7,6]=>[2,4,1,1]
[1,5,2,3,4,8,7,6]=>[2,4,1,1]
[1,6,5,2,3,8,7,4]=>[2,1,3,1,1]
[1,7,4,2,8,6,5,3]=>[2,1,2,1,1,1]
[1,7,6,5,2,8,4,3]=>[2,1,1,2,1,1]
[1,6,7,5,2,3,8,4]=>[3,1,3,1]
[1,7,5,2,8,4,3,6]=>[2,1,2,1,2]
[1,7,5,6,2,8,3,4]=>[2,2,2,2]
[1,5,7,6,2,4,8,3]=>[3,1,3,1]
[1,5,8,3,2,4,7,6]=>[3,1,3,1]
[1,6,5,2,3,7,4,8]=>[2,1,3,2]
[1,6,5,2,3,7,8,4]=>[2,1,4,1]
[1,6,8,4,2,3,7,5]=>[3,1,3,1]
[1,7,4,6,2,8,3,5]=>[2,2,2,2]
[1,7,3,5,2,8,4,6]=>[2,2,2,2]
[1,6,8,5,2,3,7,4]=>[3,1,3,1]
[1,6,4,2,3,7,8,5]=>[2,1,4,1]
[1,6,4,2,3,7,5,8]=>[2,1,3,2]
[1,5,8,6,2,4,7,3]=>[3,1,3,1]
[1,5,7,3,2,4,8,6]=>[3,1,3,1]
[1,7,3,4,2,8,5,6]=>[2,2,2,2]
[1,7,4,2,8,5,3,6]=>[2,1,2,1,2]
[1,6,7,4,2,3,8,5]=>[3,1,3,1]
[1,6,4,2,3,8,5,7]=>[2,1,3,2]
[1,7,6,4,2,8,5,3]=>[2,1,1,2,1,1]
[1,7,5,2,8,6,4,3]=>[2,1,2,1,1,1]
[1,6,4,2,3,8,7,5]=>[2,1,3,1,1]
[7,3,5,6,1,4,8,2]=>[1,3,3,1]
[3,7,5,6,1,4,8,2]=>[2,2,3,1]
[8,2,4,1,6,7,5,3]=>[1,2,3,1,1]
[8,6,1,4,2,7,5,3]=>[1,1,2,2,1,1]
[3,6,1,4,2,8,5,7]=>[2,2,2,2]
[1,6,7,4,3,5,8,2]=>[3,1,3,1]
[6,7,1,4,3,5,8,2]=>[2,2,3,1]
[7,6,1,4,3,5,8,2]=>[1,1,2,3,1]
[3,5,4,1,6,7,8,2]=>[2,1,4,1]
[4,7,1,6,3,5,8,2]=>[2,2,3,1]
[3,1,4,7,6,5,8,2]=>[1,3,1,2,1]
[6,1,7,4,3,5,8,2]=>[1,2,1,3,1]
[7,1,6,4,3,5,8,2]=>[1,2,1,3,1]
[1,7,6,4,3,5,8,2]=>[2,1,1,3,1]
[8,1,6,4,2,7,5,3]=>[1,2,1,2,1,1]
[8,4,1,3,7,2,5,6]=>[1,1,3,3]
[4,7,1,3,8,2,5,6]=>[2,3,3]
[7,4,1,3,8,2,5,6]=>[1,1,3,3]
[1,3,6,4,2,8,5,7]=>[3,1,2,2]
[4,7,3,1,2,8,5,6]=>[2,1,3,2]
[4,7,8,1,2,6,5,3]=>[3,3,1,1]
[6,8,1,4,2,7,5,3]=>[2,2,2,1,1]
[1,8,6,4,2,7,5,3]=>[2,1,1,2,1,1]
[4,8,1,3,7,2,5,6]=>[2,3,3]
[8,7,1,3,6,2,5,4]=>[1,1,3,2,1]
[6,8,5,7,3,2,1,4]=>[2,2,1,1,2]
[1,8,4,3,7,2,5,6]=>[2,1,2,3]
[2,8,3,4,7,6,1,5]=>[2,3,1,2]
[3,7,8,4,6,2,1,5]=>[3,2,1,2]
[3,7,4,6,8,2,1,5]=>[2,3,1,2]
[2,4,3,7,8,6,1,5]=>[2,3,1,2]
[1,4,7,3,8,2,5,6]=>[3,2,3]
[5,7,6,8,3,2,1,4]=>[2,2,1,1,2]
[2,5,3,4,8,6,1,7]=>[2,3,1,2]
[3,7,5,4,8,2,1,6]=>[2,1,2,1,2]
[7,1,3,4,2,8,5,6]=>[1,3,2,2]
[6,1,4,3,8,2,5,7]=>[1,2,2,3]
[4,1,7,3,8,2,5,6]=>[1,2,2,3]
[8,1,4,3,7,2,5,6]=>[1,2,2,3]
[8,2,3,4,7,6,1,5]=>[1,4,1,2]
[4,2,3,7,8,6,1,5]=>[1,4,1,2]
[5,2,3,4,8,6,1,7]=>[1,4,1,2]
[2,7,5,6,3,8,1,4]=>[2,2,2,2]
[5,7,2,6,3,8,1,4]=>[2,2,2,2]
[5,7,2,6,8,4,1,3]=>[2,3,1,2]
[7,2,5,6,8,4,1,3]=>[1,4,1,2]
[4,2,3,8,5,6,1,7]=>[1,3,2,2]
[5,2,3,8,7,6,1,4]=>[1,3,1,1,2]
[8,2,3,7,5,6,1,4]=>[1,3,2,2]
[6,1,8,3,7,2,5,4]=>[1,2,2,2,1]
[1,7,8,4,2,6,5,3]=>[3,1,2,1,1]
[4,7,1,8,2,5,6,3]=>[2,2,3,1]
[3,7,4,8,5,2,1,6]=>[2,2,1,1,2]
[2,4,3,8,5,6,1,7]=>[2,2,2,2]
[1,4,8,3,6,2,5,7]=>[3,2,3]
[7,5,8,6,3,2,1,4]=>[1,2,1,1,1,2]
[6,5,8,7,3,2,1,4]=>[1,2,1,1,1,2]
[8,5,7,6,3,2,1,4]=>[1,2,1,1,1,2]
[2,5,3,8,7,6,1,4]=>[2,2,1,1,2]
[3,7,5,8,6,2,1,4]=>[2,2,1,1,2]
[3,7,8,6,5,2,1,4]=>[3,1,1,1,2]
[1,8,7,3,6,2,5,4]=>[2,1,2,2,1]
[6,8,7,5,3,2,1,4]=>[2,1,1,1,1,2]
[5,7,6,8,3,4,1,2]=>[2,2,2,2]
[3,7,6,8,4,5,1,2]=>[2,2,2,2]
[1,5,4,7,6,8,2,3]=>[2,2,2,2]
[1,7,4,6,5,8,2,3]=>[2,2,2,2]
[3,7,4,6,5,8,1,2]=>[2,2,2,2]
[3,5,4,8,6,7,1,2]=>[2,2,2,2]
[3,8,4,6,5,7,1,2]=>[2,2,2,2]
[3,6,4,7,5,8,1,2]=>[2,2,2,2]
[1,6,2,7,5,8,3,4]=>[2,2,2,2]
[1,6,4,8,5,7,2,3]=>[2,2,2,2]
[1,8,4,6,5,7,2,3]=>[2,2,2,2]
[1,5,4,8,6,7,2,3]=>[2,2,2,2]
[7,8,1,5,4,6,2,3]=>[2,2,2,2]
[7,8,1,5,2,4,3,6]=>[2,2,2,2]
[1,8,2,6,5,7,3,4]=>[2,2,2,2]
[1,7,2,8,5,6,3,4]=>[2,2,2,2]
[1,7,2,6,5,8,3,4]=>[2,2,2,2]
[1,5,2,7,6,8,3,4]=>[2,2,2,2]
[1,7,6,8,2,5,3,4]=>[2,2,2,2]
[1,7,6,8,4,5,2,3]=>[2,2,2,2]
[5,7,6,8,1,4,2,3]=>[2,2,2,2]
[7,8,5,6,1,3,2,4]=>[2,2,2,2]
[5,8,6,7,1,3,2,4]=>[2,2,2,2]
[1,3,2,7,6,8,4,5]=>[2,2,2,2]
[1,7,6,8,2,4,3,5]=>[2,2,2,2]
[7,8,1,3,2,6,4,5]=>[2,2,2,2]
[7,8,1,6,2,4,3,5]=>[2,2,2,2]
[1,8,6,7,2,4,3,5]=>[2,2,2,2]
[7,8,1,4,2,6,3,5]=>[2,2,2,2]
[7,8,1,4,2,5,3,6]=>[2,2,2,2]
[7,8,2,1,4,3,6,5]=>[2,1,2,2,1]
[7,8,1,2,4,3,5,6]=>[2,3,3]
[4,3,6,5,8,7,1,2]=>[1,2,2,1,2]
[3,4,6,5,7,8,1,2]=>[3,3,2]
[1,6,2,3,8,7,4,5]=>[2,3,1,2]
[1,7,4,3,2,8,6,5]=>[2,1,1,2,1,1]
[1,4,7,6,2,5,8,3]=>[3,1,3,1]
[1,2,6,5,3,7,4,8]=>[3,1,2,2]
[1,2,6,5,3,7,8,4]=>[3,1,3,1]
[1,3,7,5,2,6,8,4]=>[3,1,3,1]
[1,3,7,4,2,6,8,5]=>[3,1,3,1]
[1,2,6,4,3,7,8,5]=>[3,1,3,1]
[1,2,6,4,3,7,5,8]=>[3,1,2,2]
[1,4,7,3,2,5,8,6]=>[3,1,3,1]
[1,4,3,2,5,8,6,7]=>[2,1,3,2]
[1,5,3,2,4,8,6,7]=>[2,1,3,2]
[1,7,5,3,2,8,6,4]=>[2,1,1,2,1,1]
[1,5,3,2,4,8,7,6]=>[2,1,3,1,1]
[7,6,5,4,3,1,8,2]=>[1,1,1,1,1,2,1]
[6,8,5,4,3,2,1,7]=>[2,1,1,1,1,2]
[7,1,5,4,3,8,6,2]=>[1,2,1,2,1,1]
[3,6,5,4,8,1,7,2]=>[2,1,2,2,1]
[6,8,1,4,3,2,7,5]=>[2,2,1,2,1]
[2,8,5,4,3,7,1,6]=>[2,1,1,2,2]
[7,6,1,4,3,8,5,2]=>[1,1,2,2,1,1]
[4,6,5,8,3,1,7,2]=>[2,2,1,2,1]
[6,8,5,1,3,2,7,4]=>[2,1,2,2,1]
[1,8,2,4,3,7,6,5]=>[2,2,2,1,1]
[3,8,5,4,7,2,1,6]=>[2,1,2,1,2]
[7,6,5,1,3,8,4,2]=>[1,1,1,3,1,1]
[1,6,3,4,8,7,5,2]=>[2,3,1,1,1]
[1,4,5,8,3,7,6,2]=>[4,2,1,1]
[6,8,5,4,1,2,7,3]=>[2,1,1,3,1]
[1,8,5,2,3,7,6,4]=>[2,1,3,1,1]
[6,8,2,4,3,7,1,5]=>[2,2,2,2]
[1,8,3,4,7,2,6,5]=>[2,3,2,1]
[7,5,8,4,3,2,1,6]=>[1,2,1,1,1,2]
[4,8,5,7,3,2,1,6]=>[2,2,1,1,2]
[5,1,7,6,8,4,3,2]=>[1,2,2,1,1,1]
[6,4,8,5,2,7,1,3]=>[1,2,1,2,2]
[5,1,8,6,7,4,3,2]=>[1,2,2,1,1,1]
[8,4,7,5,2,6,1,3]=>[1,2,1,2,2]
[5,4,6,8,2,1,7,3]=>[1,3,1,2,1]
[6,4,5,8,1,2,7,3]=>[1,3,3,1]
[7,4,6,5,2,1,8,3]=>[1,2,1,1,2,1]
[8,4,6,5,2,1,7,3]=>[1,2,1,1,2,1]
[4,8,7,5,6,1,3,2]=>[2,1,2,2,1]
[2,7,5,1,8,4,3,6]=>[2,1,2,1,2]
[5,1,8,7,4,2,3,6]=>[1,2,1,1,3]
[2,8,6,7,4,3,5,1]=>[2,2,1,2,1]
[3,6,5,2,4,1,8,7]=>[2,1,2,2,1]
[5,2,3,6,4,1,8,7]=>[1,3,1,2,1]
[6,1,4,5,3,2,8,7]=>[1,3,1,2,1]
[3,8,7,1,4,6,5,2]=>[2,1,3,1,1]
[5,7,1,2,4,3,8,6]=>[2,3,2,1]
[4,3,7,6,8,2,5,1]=>[1,2,2,2,1]
[5,3,6,8,1,7,2,4]=>[1,3,2,2]
[3,2,6,8,5,7,1,4]=>[1,3,2,2]
[6,3,7,2,4,8,5,1]=>[1,2,3,1,1]
[7,4,8,6,5,2,1,3]=>[1,2,1,1,1,2]
[7,1,8,2,5,4,3,6]=>[1,2,2,1,2]
[2,5,3,7,4,1,8,6]=>[2,2,1,2,1]
[3,6,4,7,5,1,8,2]=>[2,2,1,2,1]
[8,4,7,6,2,3,1,5]=>[1,2,1,2,2]
[8,4,7,1,2,5,6,3]=>[1,2,4,1]
[4,2,8,7,3,5,6,1]=>[1,2,1,3,1]
[8,1,7,4,2,5,6,3]=>[1,2,1,3,1]
[7,4,3,8,2,5,6,1]=>[1,1,2,3,1]
[6,4,1,5,8,2,7,3]=>[1,1,3,2,1]
[2,5,8,7,3,6,1,4]=>[3,1,2,2]
[2,1,5,8,7,4,6,3]=>[1,3,1,2,1]
[8,3,5,6,7,4,1,2]=>[1,4,1,2]
[7,4,3,2,8,5,6,1]=>[1,1,1,2,2,1]
[4,2,7,1,8,5,6,3]=>[1,2,2,2,1]
[4,1,7,2,8,5,6,3]=>[1,2,2,2,1]
[2,4,8,7,3,5,6,1]=>[3,1,3,1]
[4,7,8,3,1,5,6,2]=>[3,1,3,1]
[3,4,7,2,8,5,6,1]=>[3,2,2,1]
[3,7,1,4,8,5,6,2]=>[2,3,2,1]
[7,2,3,4,8,5,6,1]=>[1,4,2,1]
[6,1,8,5,2,7,4,3]=>[1,2,1,2,1,1]
[2,1,7,4,5,8,6,3]=>[1,2,3,1,1]
[2,1,8,3,6,7,5,4]=>[1,2,3,1,1]
[8,2,1,6,4,7,5,3]=>[1,1,2,2,1,1]
[7,8,2,6,4,1,5,3]=>[2,2,1,2,1]
[2,6,3,5,8,7,1,4]=>[2,3,1,2]
[7,6,2,1,5,8,4,3]=>[1,1,1,3,1,1]
[4,5,2,7,6,1,8,3]=>[2,2,1,2,1]
[5,1,6,8,4,7,2,3]=>[1,3,2,2]
[3,6,8,7,5,2,1,4]=>[3,1,1,1,2]
[7,4,8,6,5,2,3,1]=>[1,2,1,1,2,1]
[8,1,6,4,7,3,2,5]=>[1,2,2,1,2]
[7,6,4,1,2,3,8,5]=>[1,1,1,4,1]
[2,6,4,8,5,3,7,1]=>[2,2,1,2,1]
[7,3,5,8,4,2,1,6]=>[1,3,1,1,2]
[3,2,5,8,4,1,7,6]=>[1,3,1,2,1]
[8,4,7,1,5,2,3,6]=>[1,2,2,3]
[4,8,7,5,6,1,2,3]=>[2,1,2,3]
[6,1,4,8,7,3,5,2]=>[1,3,1,2,1]
[7,2,8,4,3,5,6,1]=>[1,2,1,3,1]
[4,7,8,1,3,5,6,2]=>[3,4,1]
[8,7,3,4,1,5,6,2]=>[1,1,2,3,1]
[4,8,2,7,3,5,6,1]=>[2,2,3,1]
[3,1,8,7,2,5,6,4]=>[1,2,1,3,1]
[3,8,1,7,2,5,6,4]=>[2,2,3,1]
[8,2,3,7,1,5,6,4]=>[1,3,3,1]
[6,4,8,7,1,3,2,5]=>[1,2,1,2,2]
[2,8,4,6,7,3,1,5]=>[2,3,1,2]
[4,3,8,2,7,6,1,5]=>[1,2,2,1,2]
[6,8,4,2,1,3,7,5]=>[2,1,1,3,1]
[7,8,2,4,3,5,6,1]=>[2,2,3,1]
[2,8,3,7,1,5,6,4]=>[2,2,3,1]
[8,1,2,7,3,5,6,4]=>[1,3,3,1]
[6,4,1,3,2,8,5,7]=>[1,1,2,2,2]
[5,3,8,6,2,1,4,7]=>[1,2,1,1,3]
[4,6,5,2,8,3,1,7]=>[2,1,2,1,2]
[4,3,7,5,1,8,2,6]=>[1,2,1,2,2]
[6,8,5,2,7,4,3,1]=>[2,1,2,1,1,1]
[7,2,5,4,3,8,1,6]=>[1,2,1,2,2]
[3,6,8,1,4,5,2,7]=>[3,3,2]
[6,8,1,2,4,5,3,7]=>[2,4,2]
[8,1,6,2,4,5,3,7]=>[1,2,3,2]
[3,8,6,1,2,5,4,7]=>[2,1,3,2]
[5,8,1,6,2,3,4,7]=>[2,2,4]
[4,1,6,5,8,2,3,7]=>[1,2,2,3]
[4,3,8,6,2,5,1,7]=>[1,2,1,2,2]
[8,3,6,1,4,5,2,7]=>[1,2,3,2]
[2,3,6,8,4,5,1,7]=>[4,2,2]
[2,7,5,4,3,8,1,6]=>[2,1,1,2,2]
[6,3,8,7,4,2,5,1]=>[1,2,1,1,2,1]
[5,8,4,3,7,6,1,2]=>[2,1,2,1,2]
[8,7,4,3,1,6,2,5]=>[1,1,1,1,2,2]
[1,7,4,3,8,6,2,5]=>[2,1,2,1,2]
[7,1,5,3,4,8,2,6]=>[1,2,3,2]
[2,8,6,1,7,4,5,3]=>[2,1,2,2,1]
[4,8,6,5,7,2,1,3]=>[2,1,2,1,2]
[4,7,6,8,2,1,5,3]=>[2,2,1,2,1]
[6,1,8,7,4,3,5,2]=>[1,2,1,1,2,1]
[8,5,4,3,1,6,7,2]=>[1,1,1,1,3,1]
[1,5,8,6,3,4,7,2]=>[3,1,3,1]
[2,5,8,6,3,4,7,1]=>[3,1,3,1]
[4,1,3,8,5,6,7,2]=>[1,3,3,1]
[6,5,8,4,3,1,7,2]=>[1,2,1,1,2,1]
[4,6,5,2,8,1,7,3]=>[2,1,2,2,1]
[7,2,8,1,3,6,4,5]=>[1,2,3,2]
[1,8,5,2,3,6,7,4]=>[2,1,4,1]
[1,8,3,2,5,6,7,4]=>[2,1,4,1]
[2,8,3,1,5,6,7,4]=>[2,1,4,1]
[4,8,3,2,5,6,7,1]=>[2,1,4,1]
[8,2,3,1,5,6,7,4]=>[1,2,4,1]
[2,1,8,3,5,6,7,4]=>[1,2,4,1]
[1,4,8,2,3,6,7,5]=>[3,4,1]
[3,1,2,7,8,6,4,5]=>[1,4,1,2]
[7,5,1,8,2,4,3,6]=>[1,1,2,2,2]
[3,5,8,1,2,4,7,6]=>[3,4,1]
[4,5,8,1,2,3,7,6]=>[3,4,1]
[4,2,7,1,8,6,3,5]=>[1,2,2,1,2]
[3,8,4,1,2,6,7,5]=>[2,1,4,1]
[5,4,8,2,3,6,7,1]=>[1,2,4,1]
[5,8,3,6,7,4,1,2]=>[2,3,1,2]
[2,3,1,6,8,4,7,5]=>[2,3,2,1]
[2,4,3,7,1,8,5,6]=>[2,2,2,2]
[1,4,7,3,2,8,5,6]=>[3,1,2,2]
[2,7,1,4,3,8,5,6]=>[2,2,2,2]
[2,4,1,8,6,3,7,5]=>[2,2,1,2,1]
[8,4,1,3,6,2,7,5]=>[1,1,3,2,1]
[6,8,5,1,7,2,3,4]=>[2,1,2,3]
[7,3,6,5,8,2,1,4]=>[1,2,2,1,2]
[7,6,3,5,8,2,1,4]=>[1,1,3,1,2]
[4,5,8,7,3,6,1,2]=>[3,1,2,2]
[3,5,2,8,6,1,7,4]=>[2,2,1,2,1]
[8,2,5,6,1,4,7,3]=>[1,3,3,1]
[8,6,5,4,1,2,7,3]=>[1,1,1,1,3,1]
[2,6,1,8,3,7,5,4]=>[2,2,2,1,1]
[4,7,1,6,2,8,5,3]=>[2,2,2,1,1]
[6,1,5,3,8,7,2,4]=>[1,2,2,1,2]
[2,8,6,3,7,1,5,4]=>[2,1,2,2,1]
[7,6,1,5,8,2,3,4]=>[1,1,3,3]
[3,6,8,5,1,2,7,4]=>[3,1,3,1]
[6,5,2,4,8,1,7,3]=>[1,1,3,2,1]
[5,1,4,8,2,6,7,3]=>[1,3,3,1]
[4,8,2,5,1,6,7,3]=>[2,2,3,1]
[3,4,8,5,2,6,7,1]=>[3,1,3,1]
[4,2,1,8,5,6,7,3]=>[1,1,2,3,1]
[1,5,4,8,2,6,7,3]=>[2,2,3,1]
[7,2,1,5,8,6,3,4]=>[1,1,3,1,2]
[2,8,4,5,1,6,7,3]=>[2,2,3,1]
[5,4,8,3,7,6,1,2]=>[1,2,2,1,2]
[3,1,5,8,6,2,7,4]=>[1,3,1,2,1]
[6,3,4,8,5,1,7,2]=>[1,3,1,2,1]
[5,3,4,8,1,6,7,2]=>[1,3,3,1]
[7,6,1,2,8,3,5,4]=>[1,1,3,2,1]
[7,5,8,4,1,2,6,3]=>[1,2,1,3,1]
[7,5,8,4,6,1,3,2]=>[1,2,2,2,1]
[6,5,4,8,7,1,3,2]=>[1,1,2,1,2,1]
[6,5,4,8,1,2,7,3]=>[1,1,2,3,1]
[7,5,1,6,2,3,8,4]=>[1,1,2,3,1]
[7,5,1,6,8,2,4,3]=>[1,1,3,2,1]
[6,5,4,1,8,2,7,3]=>[1,1,1,2,2,1]
[6,5,4,7,1,2,8,3]=>[1,1,2,3,1]
[6,5,4,7,8,1,3,2]=>[1,1,3,2,1]
[6,5,3,7,1,4,2,8]=>[1,1,2,2,2]
[6,5,3,1,8,4,2,7]=>[1,1,1,2,1,2]
[7,5,1,4,8,3,2,6]=>[1,1,3,1,2]
[8,1,6,4,7,3,5,2]=>[1,2,2,2,1]
[7,5,1,4,8,3,6,2]=>[1,1,3,2,1]
[6,5,3,7,1,4,8,2]=>[1,1,2,3,1]
[6,4,3,1,5,8,7,2]=>[1,1,1,3,1,1]
[7,4,1,5,3,8,6,2]=>[1,1,2,2,1,1]
[8,1,5,4,3,7,6,2]=>[1,2,1,2,1,1]
[8,1,5,4,3,7,2,6]=>[1,2,1,2,2]
[7,4,1,5,3,8,2,6]=>[1,1,2,2,2]
[7,4,1,5,3,2,6,8]=>[1,1,2,1,3]
[8,1,5,4,3,2,6,7]=>[1,2,1,1,3]
[8,1,6,4,2,5,3,7]=>[1,2,1,2,2]
[6,5,3,1,2,7,4,8]=>[1,1,1,3,2]
[6,5,3,8,1,4,2,7]=>[1,1,2,2,2]
[7,6,8,1,4,3,2,5]=>[1,2,2,1,2]
[8,1,7,2,5,4,3,6]=>[1,2,2,1,2]
[8,1,7,2,5,4,6,3]=>[1,2,2,2,1]
[7,6,1,2,5,4,8,3]=>[1,1,3,2,1]
[6,5,3,8,1,4,7,2]=>[1,1,2,3,1]
[6,5,3,1,2,7,8,4]=>[1,1,1,4,1]
[7,5,1,4,2,6,8,3]=>[1,1,2,3,1]
[8,1,6,4,2,5,7,3]=>[1,2,1,3,1]
[7,4,1,5,3,2,8,6]=>[1,1,2,1,2,1]
[6,4,3,1,5,2,8,7]=>[1,1,1,2,2,1]
[6,4,3,1,5,7,2,8]=>[1,1,1,3,2]
[7,4,1,5,3,6,2,8]=>[1,1,2,2,2]
[8,1,5,4,3,6,2,7]=>[1,2,1,2,2]
[8,1,5,4,3,6,7,2]=>[1,2,1,3,1]
[7,4,1,5,3,6,8,2]=>[1,1,2,3,1]
[6,4,3,1,5,7,8,2]=>[1,1,1,4,1]
[6,7,3,8,4,5,1,2]=>[2,2,2,2]
[6,7,4,5,1,8,2,3]=>[2,2,2,2]
[4,7,5,6,2,3,1,8]=>[2,2,2,2]
[4,7,5,6,1,8,2,3]=>[2,2,2,2]
[4,7,5,6,3,8,1,2]=>[2,2,2,2]
[3,7,5,8,4,6,1,2]=>[2,2,2,2]
[4,5,3,8,6,7,1,2]=>[2,2,2,2]
[4,8,3,6,5,7,1,2]=>[2,2,2,2]
[5,6,4,7,1,8,2,3]=>[2,2,2,2]
[5,6,1,7,3,8,2,4]=>[2,2,2,2]
[5,6,1,8,2,7,3,4]=>[2,2,2,2]
[5,6,1,8,4,7,2,3]=>[2,2,2,2]
[4,8,1,6,5,7,2,3]=>[2,2,2,2]
[4,5,1,8,6,7,2,3]=>[2,2,2,2]
[7,8,4,5,1,6,2,3]=>[2,2,2,2]
[4,8,2,3,1,6,5,7]=>[2,2,2,2]
[5,6,2,8,1,4,3,7]=>[2,2,2,2]
[5,6,3,4,1,8,2,7]=>[2,2,2,2]
[3,6,4,5,2,7,1,8]=>[2,2,2,2]
[3,6,4,5,1,8,2,7]=>[2,2,2,2]
[2,6,4,8,1,5,3,7]=>[2,2,2,2]
[2,8,3,6,1,5,4,7]=>[2,2,2,2]
[2,8,3,4,1,6,5,7]=>[2,2,2,2]
[7,8,2,5,3,4,1,6]=>[2,2,2,2]
[7,8,1,5,3,6,2,4]=>[2,2,2,2]
[1,5,3,8,6,7,2,4]=>[2,2,2,2]
[1,8,3,6,2,7,4,5]=>[2,2,2,2]
[1,6,4,8,2,7,3,5]=>[2,2,2,2]
[2,6,4,7,3,5,1,8]=>[2,2,2,2]
[2,7,3,6,4,5,1,8]=>[2,2,2,2]
[1,7,3,6,4,8,2,5]=>[2,2,2,2]
[1,7,2,8,4,6,3,5]=>[2,2,2,2]
[1,7,5,8,4,6,2,3]=>[2,2,2,2]
[1,7,5,8,2,6,3,4]=>[2,2,2,2]
[1,7,5,6,3,8,2,4]=>[2,2,2,2]
[2,7,5,6,3,4,1,8]=>[2,2,2,2]
[6,7,2,5,3,4,1,8]=>[2,2,2,2]
[6,7,1,5,3,8,2,4]=>[2,2,2,2]
[6,7,5,8,1,4,2,3]=>[2,2,2,2]
[5,8,6,7,2,3,1,4]=>[2,2,2,2]
[6,7,2,3,1,8,4,5]=>[2,2,2,2]
[6,7,2,8,1,4,3,5]=>[2,2,2,2]
[3,4,2,7,5,6,1,8]=>[2,2,2,2]
[3,4,1,7,5,8,2,6]=>[2,2,2,2]
[2,7,5,8,1,4,3,6]=>[2,2,2,2]
[2,3,1,7,5,8,4,6]=>[2,2,2,2]
[2,3,1,8,4,7,5,6]=>[2,2,2,2]
[7,8,2,3,1,6,4,5]=>[2,2,2,2]
[7,8,2,6,1,4,3,5]=>[2,2,2,2]
[2,8,6,7,1,4,3,5]=>[2,2,2,2]
[2,8,1,4,3,7,5,6]=>[2,2,2,2]
[3,7,2,5,4,6,1,8]=>[2,2,2,2]
[4,5,2,7,3,6,1,8]=>[2,2,2,2]
[4,5,1,8,2,7,3,6]=>[2,2,2,2]
[3,4,1,8,2,7,5,6]=>[2,2,2,2]
[3,4,1,8,6,7,2,5]=>[2,2,2,2]
[3,4,2,5,1,8,6,7]=>[2,2,2,2]
[3,4,2,8,1,6,5,7]=>[2,2,2,2]
[3,8,2,5,1,6,4,7]=>[2,2,2,2]
[4,5,2,8,1,6,3,7]=>[2,2,2,2]
[4,5,3,6,1,8,2,7]=>[2,2,2,2]
[7,1,5,8,4,6,2,3]=>[1,3,2,2]
[8,6,7,1,4,2,5,3]=>[1,2,2,2,1]
[8,6,3,7,5,1,2,4]=>[1,1,2,1,3]
[7,6,1,8,3,5,2,4]=>[1,1,2,2,2]
[7,6,1,3,8,5,2,4]=>[1,1,3,1,2]
[7,6,8,2,4,5,1,3]=>[1,2,3,2]
[7,6,2,8,3,5,1,4]=>[1,1,2,2,2]
[7,6,2,3,8,5,1,4]=>[1,1,3,1,2]
[8,7,1,5,2,6,3,4]=>[1,1,2,2,2]
[8,7,1,5,2,3,6,4]=>[1,1,2,3,1]
[8,5,2,3,1,7,6,4]=>[1,1,2,2,1,1]
[8,6,2,3,7,1,5,4]=>[1,1,3,2,1]
[8,6,2,7,3,1,5,4]=>[1,1,2,1,2,1]
[8,6,7,2,4,1,5,3]=>[1,2,2,2,1]
[8,7,2,5,1,6,3,4]=>[1,1,2,2,2]
[8,4,2,1,7,6,3,5]=>[1,1,1,2,1,2]
[8,5,2,7,1,6,3,4]=>[1,1,2,2,2]
[8,5,7,2,1,4,3,6]=>[1,2,1,2,2]
[5,8,7,3,1,4,2,6]=>[2,1,1,2,2]
[5,8,7,3,1,4,6,2]=>[2,1,1,3,1]
[8,5,7,2,1,4,6,3]=>[1,2,1,3,1]
[8,5,2,7,1,3,6,4]=>[1,1,2,3,1]
[8,4,2,1,3,7,6,5]=>[1,1,1,3,1,1]
[8,7,4,1,2,3,6,5]=>[1,1,1,4,1]
[8,7,4,1,2,6,3,5]=>[1,1,1,3,2]
[8,4,3,1,7,2,6,5]=>[1,1,1,2,2,1]
[8,4,3,1,2,7,6,5]=>[1,1,1,3,1,1]
[8,6,1,3,7,2,5,4]=>[1,1,3,2,1]
[8,5,1,3,2,7,6,4]=>[1,1,2,2,1,1]
[8,5,7,4,1,6,2,3]=>[1,2,1,2,2]
[8,1,6,4,7,2,5,3]=>[1,2,2,2,1]
[6,1,5,8,4,2,7,3]=>[1,3,1,2,1]
[5,8,3,6,4,1,2,7]=>[2,2,1,3]
[5,2,8,6,4,1,3,7]=>[1,2,1,1,3]
[8,4,7,5,1,6,2,3]=>[1,2,1,2,2]
[8,4,7,5,1,2,6,3]=>[1,2,1,3,1]
[8,4,7,5,1,2,3,6]=>[1,2,1,4]
[8,7,3,5,1,2,6,4]=>[1,1,2,3,1]
[8,3,2,6,5,1,4,7]=>[1,1,2,1,3]
[4,8,6,3,5,1,2,7]=>[2,1,2,3]
[4,8,7,3,1,5,2,6]=>[2,1,1,2,2]
[8,4,7,2,1,5,3,6]=>[1,2,1,2,2]
[8,3,2,7,1,5,4,6]=>[1,1,2,2,2]
[8,3,2,1,7,6,4,5]=>[1,1,1,2,1,2]
[8,7,3,1,4,2,6,5]=>[1,1,1,2,2,1]
[8,7,3,1,6,2,4,5]=>[1,1,1,2,3]
[8,7,3,1,2,6,4,5]=>[1,1,1,3,2]
[8,7,3,1,2,4,6,5]=>[1,1,1,4,1]
[8,3,2,1,4,7,6,5]=>[1,1,1,3,1,1]
[8,3,2,1,7,4,6,5]=>[1,1,1,2,2,1]
[8,3,2,7,1,5,6,4]=>[1,1,2,3,1]
[8,4,7,2,1,5,6,3]=>[1,2,1,3,1]
[8,7,2,1,6,3,4,5]=>[1,1,1,2,3]
[8,7,2,1,3,6,4,5]=>[1,1,1,3,2]
[8,7,2,1,3,4,6,5]=>[1,1,1,4,1]
[3,6,5,4,1,2,8,7]=>[2,1,1,3,1]
[3,8,5,6,7,4,1,2]=>[2,3,1,2]
[4,7,5,8,6,2,1,3]=>[2,2,1,1,2]
[2,5,7,8,6,3,4,1]=>[4,1,2,1]
[4,8,5,7,6,3,1,2]=>[2,2,1,1,2]
[4,6,3,2,1,5,8,7]=>[2,1,1,3,1]
[6,2,1,5,3,4,8,7]=>[1,1,2,3,1]
[5,8,1,3,7,6,4,2]=>[2,3,1,1,1]
[4,7,2,3,6,1,8,5]=>[2,3,2,1]
[3,7,4,2,8,1,5,6]=>[2,1,2,3]
[4,2,6,8,5,7,3,1]=>[1,3,2,1,1]
[6,4,2,7,3,8,5,1]=>[1,1,2,2,1,1]
[8,1,6,7,5,3,4,2]=>[1,3,1,2,1]
[2,1,5,8,7,6,3,4]=>[1,3,1,1,2]
[2,1,4,7,6,3,8,5]=>[1,3,1,2,1]
[6,4,7,8,5,3,2,1]=>[1,3,1,1,1,1]
[4,1,3,7,6,2,8,5]=>[1,3,1,2,1]
[8,5,1,6,3,2,7,4]=>[1,1,2,1,2,1]
[6,3,7,1,5,2,8,4]=>[1,2,2,2,1]
[3,2,6,8,4,7,5,1]=>[1,3,2,1,1]
[8,4,6,1,3,2,5,7]=>[1,2,2,3]
[4,2,8,6,7,3,1,5]=>[1,2,2,1,2]
[7,4,3,8,2,1,5,6]=>[1,1,2,1,3]
[4,7,5,8,1,6,3,2]=>[2,2,2,1,1]
[6,4,3,2,7,8,1,5]=>[1,1,1,3,2]
[4,2,5,1,6,7,8,3]=>[1,2,4,1]
[2,4,8,5,7,1,3,6]=>[3,2,3]
[3,7,1,4,6,8,5,2]=>[2,4,1,1]
[7,8,2,5,6,1,4,3]=>[2,3,2,1]
[2,4,3,8,7,5,6,1]=>[2,2,1,2,1]
[2,6,7,3,5,1,8,4]=>[3,2,2,1]
[7,6,8,4,2,5,3,1]=>[1,2,1,2,1,1]
[8,5,7,1,6,3,2,4]=>[1,2,2,1,2]
[6,5,7,2,8,4,3,1]=>[1,2,2,1,1,1]
[3,4,8,6,5,2,1,7]=>[3,1,1,1,2]
[2,7,6,1,4,5,8,3]=>[2,1,4,1]
[6,5,8,2,1,7,3,4]=>[1,2,1,2,2]
[7,4,3,5,1,6,8,2]=>[1,1,2,3,1]
[4,1,6,3,5,8,7,2]=>[1,2,3,1,1]
[6,2,5,8,4,3,7,1]=>[1,3,1,2,1]
[8,6,7,1,5,4,3,2]=>[1,2,2,1,1,1]
[2,1,6,5,8,4,7,3]=>[1,2,2,2,1]
[2,1,6,8,5,4,3,7]=>[1,3,1,1,2]
[4,1,8,5,6,2,3,7]=>[1,2,2,3]
[2,6,4,8,7,3,5,1]=>[2,2,1,2,1]
[6,2,8,4,3,5,1,7]=>[1,2,1,2,2]
[4,8,2,7,6,1,3,5]=>[2,2,1,3]
[3,1,8,2,7,5,4,6]=>[1,2,2,1,2]
[3,8,1,2,6,7,4,5]=>[2,4,2]
[5,8,4,3,2,7,1,6]=>[2,1,1,2,2]
[7,4,8,6,3,2,5,1]=>[1,2,1,1,2,1]
[5,8,4,7,2,1,3,6]=>[2,2,1,3]
[2,1,8,4,3,7,5,6]=>[1,2,1,2,2]
[6,3,8,2,4,5,7,1]=>[1,2,4,1]
[5,8,4,2,3,6,1,7]=>[2,1,3,2]
[5,8,2,4,3,1,6,7]=>[2,2,1,3]
[2,8,3,1,6,4,5,7]=>[2,1,2,3]
[8,2,1,3,4,7,5,6]=>[1,1,4,2]
[1,4,8,2,6,3,5,7]=>[3,2,3]
[1,2,7,3,5,4,8,6]=>[3,2,2,1]
[1,2,3,8,4,5,7,6]=>[4,3,1]
[1,2,8,3,4,5,7,6]=>[3,4,1]
[1,3,8,2,6,4,5,7]=>[3,2,3]
[1,5,7,2,3,6,4,8]=>[3,3,2]
[1,7,2,3,5,4,8,6]=>[2,3,2,1]
[1,3,8,2,4,5,7,6]=>[3,4,1]
[1,2,3,8,4,6,7,5]=>[4,3,1]
[1,8,2,3,5,4,6,7]=>[2,3,3]
[1,7,8,2,3,6,4,5]=>[3,3,2]
[1,6,7,8,2,3,5,4]=>[4,3,1]
[1,7,8,2,5,3,6,4]=>[3,2,2,1]
[1,7,8,2,4,5,3,6]=>[3,3,2]
[1,2,8,3,6,4,5,7]=>[3,2,3]
[1,8,2,3,6,4,5,7]=>[2,3,3]
[1,2,8,3,5,4,6,7]=>[3,2,3]
[1,2,7,8,3,6,4,5]=>[4,2,2]
[1,5,2,7,8,3,6,4]=>[2,3,2,1]
[1,3,2,8,4,6,7,5]=>[2,2,3,1]
[1,8,2,3,4,6,7,5]=>[2,5,1]
[1,7,8,2,4,3,6,5]=>[3,2,2,1]
[7,6,3,1,5,2,4,8]=>[1,1,1,2,3]
[6,7,3,1,5,2,8,4]=>[2,1,2,2,1]
[6,8,3,1,5,2,7,4]=>[2,1,2,2,1]
[6,8,4,5,1,2,7,3]=>[2,2,3,1]
[6,7,4,5,1,2,8,3]=>[2,2,3,1]
[7,2,1,6,5,3,4,8]=>[1,1,2,1,3]
[7,3,6,1,5,2,4,8]=>[1,2,2,3]
[7,4,6,5,1,2,3,8]=>[1,2,1,4]
[6,7,5,4,1,2,8,3]=>[2,1,1,3,1]
[5,8,6,4,1,7,2,3]=>[2,1,1,2,2]
[5,7,6,4,1,8,2,3]=>[2,1,1,2,2]
[5,6,7,4,1,8,2,3]=>[3,1,2,2]
[6,5,7,4,1,2,8,3]=>[1,2,1,3,1]
[6,4,7,5,1,2,8,3]=>[1,2,1,3,1]
[6,2,1,7,5,3,8,4]=>[1,1,2,1,2,1]
[6,3,8,1,5,2,7,4]=>[1,2,2,2,1]
[6,4,8,5,1,2,7,3]=>[1,2,1,3,1]
[6,5,8,4,1,2,7,3]=>[1,2,1,3,1]
[5,6,8,4,1,7,2,3]=>[3,1,2,2]
[4,6,8,5,7,1,2,3]=>[3,2,3]
[4,5,8,6,7,1,2,3]=>[3,2,3]
[5,4,8,6,1,7,2,3]=>[1,2,1,2,2]
[5,3,8,1,6,7,2,4]=>[1,2,3,2]
[5,2,1,8,6,7,3,4]=>[1,1,2,2,2]
[5,2,1,7,6,8,3,4]=>[1,1,2,2,2]
[5,4,7,6,1,8,2,3]=>[1,2,1,2,2]
[4,5,7,6,8,1,2,3]=>[3,2,3]
[4,6,7,5,8,1,2,3]=>[3,2,3]
[4,8,6,5,7,1,2,3]=>[2,1,2,3]
[4,8,5,6,7,1,2,3]=>[2,3,3]
[4,7,5,6,8,1,2,3]=>[2,3,3]
[4,6,5,7,8,1,2,3]=>[2,3,3]
[5,7,4,6,1,8,2,3]=>[2,2,2,2]
[5,8,4,6,1,7,2,3]=>[2,2,2,2]
[5,8,3,1,6,7,2,4]=>[2,1,3,2]
[5,7,3,1,6,8,2,4]=>[2,1,3,2]
[5,6,3,1,7,8,2,4]=>[2,1,3,2]
[6,2,1,4,3,8,7,5]=>[1,1,2,2,1,1]
[5,8,3,1,7,6,2,4]=>[2,1,2,1,2]
[5,7,4,8,1,6,2,3]=>[2,2,2,2]
[5,2,1,6,8,7,3,4]=>[1,1,3,1,2]
[5,4,6,8,1,7,2,3]=>[1,3,2,2]
[4,5,6,8,7,1,2,3]=>[4,1,3]
[4,7,5,8,6,1,2,3]=>[2,2,1,3]
[4,8,5,7,6,1,2,3]=>[2,2,1,3]
[4,8,6,7,5,1,2,3]=>[2,2,1,3]
[4,7,6,8,5,1,2,3]=>[2,2,1,3]
[4,6,7,8,5,1,2,3]=>[4,1,3]
[4,5,7,8,6,1,2,3]=>[4,1,3]
[5,4,7,8,1,6,2,3]=>[1,3,2,2]
[5,3,7,1,8,6,2,4]=>[1,2,2,1,2]
[5,2,1,7,8,6,3,4]=>[1,1,3,1,2]
[5,3,8,1,7,6,2,4]=>[1,2,2,1,2]
[5,4,8,7,1,6,2,3]=>[1,2,1,2,2]
[4,6,8,7,5,1,2,3]=>[3,1,1,3]
[4,7,8,6,5,1,2,3]=>[3,1,1,3]
[4,8,7,6,5,1,2,3]=>[2,1,1,1,3]
[2,5,4,7,3,6,1,8]=>[2,2,2,2]
[2,4,6,3,7,5,1,8]=>[3,2,1,2]
[4,2,7,3,6,5,1,8]=>[1,2,2,1,2]
[4,2,6,3,1,5,8,7]=>[1,2,1,3,1]
[2,5,3,1,6,4,8,7]=>[2,1,2,2,1]
[2,5,3,7,6,4,1,8]=>[2,2,1,1,2]
[2,6,5,3,7,4,1,8]=>[2,1,2,1,2]
[4,2,7,6,3,5,1,8]=>[1,2,1,2,2]
[2,7,5,3,6,4,1,8]=>[2,1,2,1,2]
[2,6,3,7,5,4,1,8]=>[2,2,1,1,2]
[1,7,5,2,3,8,4,6]=>[2,1,3,2]
[2,1,3,7,5,4,8,6]=>[1,3,1,2,1]
[2,3,1,8,6,5,4,7]=>[2,2,1,1,2]
[2,5,3,1,8,6,4,7]=>[2,1,2,1,2]
[4,2,8,3,1,6,5,7]=>[1,2,1,2,2]
[8,3,2,6,4,1,5,7]=>[1,1,2,1,3]
[3,6,8,2,1,4,5,7]=>[3,1,4]
[1,5,2,8,3,4,7,6]=>[2,2,3,1]
[1,2,6,3,8,7,4,5]=>[3,2,1,2]
[1,2,8,3,6,4,7,5]=>[3,2,2,1]
[1,2,7,6,3,4,8,5]=>[3,1,3,1]
[2,1,3,8,7,5,4,6]=>[1,3,1,1,2]
[1,2,3,8,6,4,7,5]=>[4,1,2,1]
[1,2,3,7,4,8,6,5]=>[4,2,1,1]
[1,2,7,6,3,8,4,5]=>[3,1,2,2]
[1,2,3,6,4,8,7,5]=>[4,2,1,1]
[1,2,3,7,6,4,8,5]=>[4,1,2,1]
[2,6,3,1,8,5,4,7]=>[2,1,2,1,2]
[2,1,3,8,5,4,7,6]=>[1,3,1,2,1]
[7,1,8,4,2,3,5,6]=>[1,2,1,4]
[2,1,8,4,3,5,7,6]=>[1,2,1,3,1]
[4,2,6,3,1,8,5,7]=>[1,2,1,2,2]
[5,4,2,8,3,1,6,7]=>[1,1,2,1,3]
[3,5,8,2,4,1,6,7]=>[3,2,3]
[2,5,4,8,3,1,6,7]=>[2,2,1,3]
[4,2,1,8,3,5,7,6]=>[1,1,2,3,1]
[1,8,7,4,2,3,5,6]=>[2,1,1,4]
[1,5,2,8,7,3,4,6]=>[2,2,1,3]
[1,2,7,3,6,4,8,5]=>[3,2,2,1]
[1,2,8,6,3,7,4,5]=>[3,1,2,2]
[1,2,7,3,8,6,4,5]=>[3,2,1,2]
[1,2,3,8,4,7,6,5]=>[4,2,1,1]
[1,2,7,3,4,8,6,5]=>[3,3,1,1]
[1,2,6,3,8,4,7,5]=>[3,2,2,1]
[1,5,2,3,8,7,4,6]=>[2,3,1,2]
[4,2,1,8,3,7,5,6]=>[1,1,2,2,2]
[8,3,2,1,7,4,5,6]=>[1,1,1,2,3]
[1,8,4,2,7,3,5,6]=>[2,1,2,3]
[1,2,8,6,3,4,7,5]=>[3,1,3,1]
[1,2,7,3,8,4,6,5]=>[3,2,2,1]
[1,2,3,8,7,4,6,5]=>[4,1,2,1]
[1,2,3,8,7,6,4,5]=>[4,1,1,2]
[2,5,3,8,1,6,4,7]=>[2,2,2,2]
[2,6,4,7,1,5,3,8]=>[2,2,2,2]
[2,6,5,7,1,4,3,8]=>[2,2,2,2]
[3,8,5,7,1,2,6,4]=>[2,2,3,1]
[3,8,5,7,2,6,4,1]=>[2,2,2,1,1]
[3,4,8,6,2,5,7,1]=>[3,1,3,1]
[3,4,8,6,1,2,5,7]=>[3,1,4]
[2,5,7,1,4,8,6,3]=>[3,3,1,1]
[2,4,8,1,5,7,6,3]=>[3,3,1,1]
[2,4,3,8,1,6,5,7]=>[2,2,2,2]
[2,8,1,7,5,6,4,3]=>[2,2,2,1,1]
[2,3,8,1,6,5,7,4]=>[3,2,2,1]
[2,4,8,1,3,5,7,6]=>[3,4,1]
[3,5,7,6,1,2,4,8]=>[3,1,4]
[3,5,7,6,2,4,8,1]=>[3,1,3,1]
[4,8,6,7,2,3,5,1]=>[2,2,3,1]
[4,8,6,7,1,2,3,5]=>[2,2,4]
[4,8,6,7,1,3,5,2]=>[2,2,3,1]
[3,4,8,6,1,5,7,2]=>[3,1,3,1]
[3,8,5,7,1,6,4,2]=>[2,2,2,1,1]
[3,2,8,5,6,1,7,4]=>[1,2,2,2,1]
[3,8,5,7,2,1,6,4]=>[2,2,1,2,1]
[3,4,8,6,2,1,5,7]=>[3,1,1,3]
[3,5,7,6,2,1,4,8]=>[3,1,1,3]
[4,8,6,7,2,1,3,5]=>[2,2,1,3]
[4,8,6,7,3,5,2,1]=>[2,2,2,1,1]
[5,8,6,7,3,4,2,1]=>[2,2,2,1,1]
[5,8,6,7,2,1,3,4]=>[2,2,1,3]
[5,8,6,7,2,1,4,3]=>[2,2,1,2,1]
[4,8,6,7,2,1,5,3]=>[2,2,1,2,1]
[4,3,1,7,5,2,8,6]=>[1,1,2,1,2,1]
[4,3,2,8,5,1,7,6]=>[1,1,2,1,2,1]
[4,3,8,5,1,6,7,2]=>[1,2,1,3,1]
[4,8,6,7,1,5,3,2]=>[2,2,2,1,1]
[5,8,6,7,1,4,3,2]=>[2,2,2,1,1]
[5,8,6,7,2,3,4,1]=>[2,2,3,1]
[5,8,6,7,2,4,3,1]=>[2,2,2,1,1]
[5,8,6,7,1,2,4,3]=>[2,2,3,1]
[4,2,3,8,5,1,6,7]=>[1,3,1,3]
[4,2,8,5,1,7,6,3]=>[1,2,1,2,1,1]
[3,4,2,8,5,6,1,7]=>[2,2,2,2]
[3,2,4,8,6,1,5,7]=>[1,3,1,3]
[3,2,5,7,6,1,4,8]=>[1,3,1,3]
[4,8,6,7,1,3,2,5]=>[2,2,2,2]
[4,8,6,7,1,2,5,3]=>[2,2,3,1]
[4,8,6,7,2,5,3,1]=>[2,2,2,1,1]
[4,3,8,5,2,6,7,1]=>[1,2,1,3,1]
[4,3,8,5,1,2,6,7]=>[1,2,1,4]
[4,2,6,7,5,1,3,8]=>[1,3,1,3]
[3,8,5,7,1,4,2,6]=>[2,2,2,2]
[3,8,4,7,1,5,2,6]=>[2,2,2,2]
[3,5,2,8,4,6,1,7]=>[2,2,2,2]
[3,5,1,7,4,6,2,8]=>[2,2,2,2]
[3,8,4,7,2,5,1,6]=>[2,2,2,2]
[4,1,3,8,5,2,6,7]=>[1,3,1,3]
[4,1,2,6,7,5,3,8]=>[1,4,1,2]
[4,2,6,7,5,3,8,1]=>[1,3,1,2,1]
[4,8,6,7,3,2,5,1]=>[2,2,1,2,1]
[4,8,6,7,3,1,2,5]=>[2,2,1,3]
[3,1,5,7,6,2,4,8]=>[1,3,1,3]
[3,4,1,7,5,6,2,8]=>[2,2,2,2]
[4,1,7,5,2,8,6,3]=>[1,2,1,2,1,1]
[4,1,6,7,5,2,3,8]=>[1,3,1,3]
[4,8,6,7,2,3,1,5]=>[2,2,2,2]
[5,8,6,7,3,2,4,1]=>[2,2,1,2,1]
[5,8,6,7,4,2,3,1]=>[2,2,1,2,1]
[5,8,6,7,4,1,2,3]=>[2,2,1,3]
[5,8,6,7,4,1,3,2]=>[2,2,1,2,1]
[5,8,6,7,3,1,4,2]=>[2,2,1,2,1]
[4,8,6,7,3,1,5,2]=>[2,2,1,2,1]
[4,1,6,7,5,3,8,2]=>[1,3,1,2,1]
[4,1,7,5,3,2,8,6]=>[1,2,1,1,2,1]
[4,2,8,5,3,1,7,6]=>[1,2,1,1,2,1]
[4,2,1,6,7,5,3,8]=>[1,1,3,1,2]
[4,8,6,7,3,2,1,5]=>[2,2,1,1,2]
[5,8,6,7,4,2,1,3]=>[2,2,1,1,2]
[5,8,6,7,4,3,1,2]=>[2,2,1,1,2]
[7,3,5,8,1,4,2,6]=>[1,3,2,2]
[3,8,7,6,1,4,2,5]=>[2,1,1,2,2]
[5,1,8,3,6,7,2,4]=>[1,2,3,2]
[1,4,7,8,5,6,2,3]=>[4,2,2]
[3,4,7,1,5,8,6,2]=>[3,3,1,1]
[3,6,1,4,7,8,5,2]=>[2,4,1,1]
[1,6,8,4,7,5,2,3]=>[3,2,1,2]
[6,8,1,3,5,7,2,4]=>[2,4,2]
[7,6,1,4,3,8,2,5]=>[1,1,2,2,2]
[3,8,1,6,5,4,2,7]=>[2,2,1,1,2]
[4,1,3,7,5,8,2,6]=>[1,3,2,2]
[6,1,7,3,8,4,2,5]=>[1,2,2,1,2]
[7,1,8,6,3,5,2,4]=>[1,2,1,2,2]
[3,1,7,6,5,8,4,2]=>[1,2,1,2,1,1]
[8,2,7,6,5,3,4,1]=>[1,2,1,1,2,1]
[8,4,2,6,7,5,3,1]=>[1,1,3,1,1,1]
[4,8,1,6,7,5,3,2]=>[2,3,1,1,1]
[7,4,1,6,8,2,5,3]=>[1,1,3,2,1]
[1,3,8,6,2,7,5,4]=>[3,1,2,1,1]
[6,1,3,2,7,8,4,5]=>[1,2,3,2]
[1,8,6,2,5,3,4,7]=>[2,1,2,3]
[4,7,2,6,8,1,5,3]=>[2,3,2,1]
[8,7,3,6,4,5,2,1]=>[1,1,2,2,1,1]
[5,7,8,6,2,1,4,3]=>[3,1,1,2,1]
[2,7,4,1,6,8,3,5]=>[2,1,3,2]
[3,7,2,4,5,1,6,8]=>[2,3,3]
[1,8,6,4,5,2,3,7]=>[2,1,2,3]
[2,8,4,6,5,1,3,7]=>[2,2,1,3]
[3,4,1,7,5,2,6,8]=>[2,2,1,3]
[7,5,8,6,1,2,4,3]=>[1,2,1,3,1]
[5,6,8,7,3,1,4,2]=>[3,1,1,2,1]
[2,5,4,3,6,8,1,7]=>[2,1,3,2]
[3,8,5,4,6,2,1,7]=>[2,1,2,1,2]
[4,8,2,1,3,7,5,6]=>[2,1,3,2]
[6,4,1,2,7,5,8,3]=>[1,1,3,2,1]
[4,1,8,3,6,7,5,2]=>[1,2,3,1,1]
[8,3,7,4,5,2,6,1]=>[1,2,2,2,1]
[4,3,7,8,5,1,6,2]=>[1,3,1,2,1]
[5,4,8,2,7,6,1,3]=>[1,2,2,1,2]
[1,2,7,3,6,5,8,4]=>[3,2,2,1]
[2,8,7,6,3,4,1,5]=>[2,1,1,2,2]
[5,8,2,6,3,4,1,7]=>[2,2,2,2]
[4,1,7,5,8,6,2,3]=>[1,2,2,1,2]
[5,1,7,8,4,3,6,2]=>[1,3,1,2,1]
[8,2,7,5,4,3,6,1]=>[1,2,1,1,2,1]
[6,3,8,1,4,7,5,2]=>[1,2,3,1,1]
[3,8,4,5,6,1,2,7]=>[2,3,3]
[1,4,3,5,7,8,2,6]=>[2,4,2]
[6,5,8,7,1,3,4,2]=>[1,2,1,3,1]
[3,6,7,2,4,8,1,5]=>[3,3,2]
[1,5,2,7,4,3,8,6]=>[2,2,1,2,1]
[2,8,5,6,4,3,1,7]=>[2,2,1,1,2]
[1,8,6,5,4,3,2,7]=>[2,1,1,1,1,2]
[6,1,5,2,8,4,7,3]=>[1,2,2,2,1]
[4,6,1,8,5,7,2,3]=>[2,2,2,2]
[4,7,1,2,8,5,6,3]=>[2,3,2,1]
[1,4,7,2,8,5,6,3]=>[3,2,2,1]
[1,7,3,5,8,6,2,4]=>[2,3,1,2]
[7,3,5,8,6,1,2,4]=>[1,3,1,3]
[3,6,8,1,5,7,2,4]=>[3,3,2]
[3,4,6,5,8,1,7,2]=>[3,2,2,1]
[6,8,1,5,7,2,3,4]=>[2,3,3]
[7,1,2,5,8,6,3,4]=>[1,4,1,2]
[1,7,2,5,8,6,3,4]=>[2,3,1,2]
[1,7,6,8,2,3,5,4]=>[2,2,3,1]
[7,6,8,1,2,3,5,4]=>[1,2,4,1]
[2,7,1,5,8,6,3,4]=>[2,3,1,2]
[2,4,7,1,8,5,6,3]=>[3,2,2,1]
[4,7,5,8,3,1,6,2]=>[2,2,1,2,1]
[4,7,2,1,8,5,6,3]=>[2,1,2,2,1]
[7,6,8,2,1,3,5,4]=>[1,2,1,3,1]
[1,2,7,6,8,3,5,4]=>[3,2,2,1]
[3,7,6,8,2,1,5,4]=>[2,2,1,2,1]
[7,4,2,1,6,8,5,3]=>[1,1,1,3,1,1]
[6,7,4,1,8,5,3,2]=>[2,1,2,1,1,1]
[6,7,4,3,1,8,5,2]=>[2,1,1,2,1,1]
[2,7,4,1,6,8,5,3]=>[2,1,3,1,1]
[2,3,7,6,8,1,5,4]=>[3,2,2,1]
[7,4,2,6,8,5,1,3]=>[1,1,3,1,2]
[7,3,2,5,8,6,1,4]=>[1,1,3,1,2]
[3,1,7,6,8,2,5,4]=>[1,2,2,2,1]
[3,7,6,8,1,2,5,4]=>[2,2,3,1]
[1,3,7,6,8,2,5,4]=>[3,2,2,1]
[1,7,4,2,6,8,5,3]=>[2,1,3,1,1]
[7,4,1,2,6,8,5,3]=>[1,1,4,1,1]
[7,1,4,2,8,5,6,3]=>[1,2,2,2,1]
[7,1,8,2,5,4,6,3]=>[1,2,2,2,1]
[7,3,8,4,6,1,5,2]=>[1,2,2,2,1]
[7,2,8,1,6,4,5,3]=>[1,2,2,2,1]
[7,1,6,8,5,4,2,3]=>[1,3,1,1,2]
[7,1,2,6,8,5,4,3]=>[1,4,1,1,1]
[1,7,2,6,8,5,4,3]=>[2,3,1,1,1]
[1,7,6,8,3,2,5,4]=>[2,2,1,2,1]
[7,6,8,3,1,2,5,4]=>[1,2,1,3,1]
[7,1,5,8,6,3,2,4]=>[1,3,1,1,2]
[7,2,5,8,6,3,1,4]=>[1,3,1,1,2]
[3,6,7,1,8,5,4,2]=>[3,2,1,1,1]
[7,2,6,8,5,4,1,3]=>[1,3,1,1,2]
[7,6,8,2,3,1,5,4]=>[1,2,2,2,1]
[2,7,6,8,3,1,5,4]=>[2,2,1,2,1]
[2,7,1,6,8,5,4,3]=>[2,3,1,1,1]
[6,7,3,1,8,5,4,2]=>[2,1,2,1,1,1]
[6,7,1,8,5,4,3,2]=>[2,2,1,1,1,1]
[7,2,1,6,8,5,4,3]=>[1,1,3,1,1,1]
[7,6,8,3,2,1,5,4]=>[1,2,1,1,2,1]
[4,7,8,5,6,1,3,2]=>[3,2,2,1]
[4,6,5,8,7,1,3,2]=>[2,2,1,2,1]
[5,6,4,8,1,2,7,3]=>[2,2,3,1]
[8,1,5,6,7,2,4,3]=>[1,4,2,1]
[6,4,5,1,8,2,7,3]=>[1,2,2,2,1]
[5,4,6,7,1,2,8,3]=>[1,3,3,1]
[4,3,6,7,2,1,5,8]=>[1,3,1,3]
[5,3,6,7,1,4,2,8]=>[1,3,2,2]
[8,1,4,6,7,3,2,5]=>[1,4,1,2]
[8,1,3,6,7,4,5,2]=>[1,4,2,1]
[7,2,1,6,8,4,5,3]=>[1,1,3,2,1]
[5,2,6,7,1,4,8,3]=>[1,3,3,1]
[4,2,6,7,3,1,8,5]=>[1,3,1,2,1]
[6,2,4,1,5,8,7,3]=>[1,2,3,1,1]
[7,2,1,5,4,8,6,3]=>[1,1,2,2,1,1]
[8,1,4,5,3,7,2,6]=>[1,3,2,2]
[7,3,1,5,4,8,2,6]=>[1,1,2,2,2]
[6,3,4,1,5,8,2,7]=>[1,2,3,2]
[5,3,4,2,1,8,6,7]=>[1,2,1,2,2]
[4,3,5,2,7,1,6,8]=>[1,2,2,3]
[5,6,3,8,1,4,2,7]=>[2,2,2,2]
[8,1,7,2,4,5,6,3]=>[1,2,4,1]
[7,6,1,2,4,5,8,3]=>[1,1,5,1]
[4,7,8,2,3,1,6,5]=>[3,2,2,1]
[5,6,2,8,1,4,7,3]=>[2,2,3,1]
[6,5,2,1,3,7,8,4]=>[1,1,1,4,1]
[7,5,1,3,2,6,8,4]=>[1,1,2,3,1]
[8,1,6,3,2,5,7,4]=>[1,2,1,3,1]
[7,4,1,3,5,2,8,6]=>[1,1,3,2,1]
[5,4,2,3,1,6,8,7]=>[1,1,2,3,1]
[7,3,1,4,5,6,2,8]=>[1,1,4,2]
[8,1,4,3,5,6,2,7]=>[1,2,3,2]
[6,2,3,1,5,7,8,4]=>[1,2,4,1]
[7,8,4,2,1,6,5,3]=>[2,1,1,2,1,1]
[7,8,4,2,1,5,6,3]=>[2,1,1,3,1]
[6,2,3,4,8,7,1,5]=>[1,4,1,2]
[6,2,3,4,7,8,1,5]=>[1,5,2]
[7,8,3,4,6,2,1,5]=>[2,3,1,2]
[7,8,3,6,4,2,1,5]=>[2,2,1,1,2]
[7,8,3,5,6,2,1,4]=>[2,3,1,2]
[6,2,3,8,7,5,1,4]=>[1,3,1,1,2]
[6,2,3,7,8,5,1,4]=>[1,4,1,2]
[5,2,6,3,8,1,7,4]=>[1,2,2,2,1]
[6,3,2,5,8,7,1,4]=>[1,1,3,1,2]
[6,3,2,8,4,7,1,5]=>[1,1,2,2,2]
[6,4,3,8,7,5,1,2]=>[1,1,2,1,1,2]
[6,4,3,7,8,5,1,2]=>[1,1,3,1,2]
[6,2,4,1,7,3,5,8]=>[1,2,2,3]
[6,3,2,7,4,8,1,5]=>[1,1,2,2,2]
[6,3,2,5,7,8,1,4]=>[1,1,4,2]
[5,7,2,3,6,1,8,4]=>[2,3,2,1]
[5,8,2,3,6,1,7,4]=>[2,3,2,1]
[4,7,5,8,3,2,1,6]=>[2,2,1,1,2]
[4,5,6,8,3,2,1,7]=>[4,1,1,2]
[4,6,8,5,3,2,1,7]=>[3,1,1,1,2]
[5,6,1,4,2,3,7,8]=>[2,2,4]
[5,6,8,4,3,7,1,2]=>[3,1,2,2]
[5,6,1,4,2,3,8,7]=>[2,2,3,1]
[5,2,8,3,4,1,7,6]=>[1,2,2,2,1]
[4,5,8,6,3,2,1,7]=>[3,1,1,1,2]
[4,6,5,8,3,2,1,7]=>[2,2,1,1,2]
[4,7,5,6,3,2,1,8]=>[2,2,1,1,2]
[6,2,3,4,5,8,1,7]=>[1,5,2]
[5,1,4,3,6,2,8,7]=>[1,2,2,2,1]
[5,1,4,3,7,2,8,6]=>[1,2,2,2,1]
[5,1,4,3,8,2,7,6]=>[1,2,2,2,1]
[5,6,2,4,1,7,8,3]=>[2,2,3,1]
[5,6,2,4,1,8,7,3]=>[2,2,2,1,1]
[5,7,2,4,1,8,6,3]=>[2,2,2,1,1]
[6,1,4,2,8,7,5,3]=>[1,2,2,1,1,1]
[6,1,4,2,7,8,5,3]=>[1,2,3,1,1]
[5,8,2,4,1,7,6,3]=>[2,2,2,1,1]
[5,2,7,4,1,6,8,3]=>[1,2,1,3,1]
[5,4,1,3,7,2,6,8]=>[1,1,3,3]
[5,1,4,3,6,2,7,8]=>[1,2,2,3]
[5,8,6,4,3,7,1,2]=>[2,1,1,2,2]
[5,8,1,4,2,3,7,6]=>[2,2,3,1]
[5,1,6,3,4,2,7,8]=>[1,2,2,3]
[4,8,6,5,3,2,1,7]=>[2,1,1,1,1,2]
[4,8,5,6,3,2,1,7]=>[2,2,1,1,2]
[5,4,7,8,3,2,1,6]=>[1,3,1,1,2]
[5,4,8,7,3,2,1,6]=>[1,2,1,1,1,2]
[4,6,8,7,3,2,1,5]=>[3,1,1,1,2]
[4,6,7,8,3,2,1,5]=>[4,1,1,2]
[4,7,6,8,3,2,1,5]=>[2,2,1,1,2]
[4,7,8,5,3,2,1,6]=>[3,1,1,1,2]
[5,7,1,3,4,2,6,8]=>[2,3,3]
[5,1,8,4,2,3,6,7]=>[1,2,1,4]
[5,1,7,4,2,3,6,8]=>[1,2,1,4]
[5,8,1,3,4,2,6,7]=>[2,3,3]
[4,8,7,5,3,2,1,6]=>[2,1,1,1,1,2]
[4,7,8,6,3,2,1,5]=>[3,1,1,1,2]
[4,8,7,6,3,2,1,5]=>[2,1,1,1,1,2]
[4,8,2,6,3,7,5,1]=>[2,2,2,1,1]
[4,8,2,3,6,7,5,1]=>[2,4,1,1]
[4,8,3,1,6,7,5,2]=>[2,1,3,1,1]
[4,3,8,1,6,2,5,7]=>[1,2,2,3]
[1,4,8,7,3,5,2,6]=>[3,1,2,2]
[4,3,8,7,2,5,1,6]=>[1,2,1,2,2]
[5,8,4,3,7,1,6,2]=>[2,1,2,2,1]
[5,8,1,4,7,2,6,3]=>[2,3,2,1]
[5,8,1,7,4,2,3,6]=>[2,2,1,3]
[6,8,1,2,4,3,5,7]=>[2,3,3]
[5,8,7,1,3,4,2,6]=>[2,1,3,2]
[4,8,7,6,3,1,2,5]=>[2,1,1,1,3]
[5,8,4,7,3,1,2,6]=>[2,2,1,3]
[4,3,8,2,7,5,6,1]=>[1,2,2,2,1]
[1,4,8,3,7,5,6,2]=>[3,2,2,1]
[1,4,3,8,2,6,5,7]=>[2,2,2,2]
[4,3,2,8,1,6,5,7]=>[1,1,2,2,2]
[4,1,3,8,2,6,5,7]=>[1,3,2,2]
[4,1,8,3,7,5,6,2]=>[1,2,2,2,1]
[4,1,8,7,3,5,2,6]=>[1,2,1,2,2]
[3,7,8,1,5,4,2,6]=>[3,2,1,2]
[7,3,8,1,5,4,6,2]=>[1,2,2,2,1]
[3,4,8,1,6,2,5,7]=>[3,2,3]
[3,4,8,7,2,5,1,6]=>[3,1,2,2]
[3,4,8,2,7,5,6,1]=>[3,2,2,1]
[1,2,4,8,3,6,5,7]=>[4,2,2]
[1,2,4,3,8,6,5,7]=>[3,2,1,2]
[3,4,2,1,8,6,5,7]=>[2,1,2,1,2]
[3,4,1,8,2,6,5,7]=>[2,2,2,2]
[3,6,7,8,4,1,2,5]=>[4,1,3]
[4,1,7,8,5,3,2,6]=>[1,3,1,1,2]
[4,1,2,8,3,6,5,7]=>[1,3,2,2]
[1,4,3,2,8,6,5,7]=>[2,1,2,1,2]
[4,2,3,1,8,6,5,7]=>[1,2,2,1,2]
[3,7,6,8,4,2,1,5]=>[2,2,1,1,2]
[4,7,1,8,5,2,3,6]=>[2,2,1,3]
[2,6,8,7,4,3,1,5]=>[3,1,1,1,2]
[3,7,8,6,2,4,1,5]=>[3,1,2,2]
[3,7,8,2,6,4,5,1]=>[3,2,2,1]
[4,2,3,8,1,6,5,7]=>[1,3,2,2]
[4,3,1,8,2,6,5,7]=>[1,1,2,2,2]
[1,4,7,8,5,3,2,6]=>[4,1,1,2]
[4,3,7,8,5,2,1,6]=>[1,3,1,1,2]
[3,7,2,8,4,6,5,1]=>[2,2,2,1,1]
[4,2,8,6,3,1,5,7]=>[1,2,1,1,3]
[2,6,8,4,7,3,1,5]=>[3,2,1,2]
[2,4,8,6,3,1,5,7]=>[3,1,1,3]
[7,3,6,8,4,2,1,5]=>[1,3,1,1,2]
[7,6,2,8,3,5,4,1]=>[1,1,2,2,1,1]
[1,7,3,8,4,6,5,2]=>[2,2,2,1,1]
[1,3,4,8,2,6,5,7]=>[4,2,2]
[3,2,4,8,1,6,5,7]=>[1,3,2,2]
[7,3,8,6,2,4,1,5]=>[1,2,1,2,2]
[7,3,8,2,6,4,5,1]=>[1,2,2,2,1]
[2,4,8,3,6,1,5,7]=>[3,2,3]
[6,2,8,7,4,3,5,1]=>[1,2,1,1,2,1]
[7,4,1,8,5,2,6,3]=>[1,1,2,1,2,1]
[7,3,2,8,4,6,5,1]=>[1,1,2,2,1,1]
[2,4,3,1,8,6,5,7]=>[2,1,2,1,2]
[1,3,4,2,8,6,5,7]=>[3,2,1,2]
[1,3,2,4,8,6,5,7]=>[2,3,1,2]
[3,2,1,4,8,6,5,7]=>[1,1,3,1,2]
[3,1,2,4,8,6,5,7]=>[1,4,1,2]
[3,1,4,2,8,6,5,7]=>[1,2,2,1,2]
[3,1,4,8,2,6,5,7]=>[1,3,2,2]
[7,3,4,8,5,1,6,2]=>[1,3,1,2,1]
[3,7,4,8,5,1,2,6]=>[2,2,1,3]
[6,7,2,8,3,5,4,1]=>[2,2,2,1,1]
[2,3,1,4,8,6,5,7]=>[2,3,1,2]
[2,1,3,4,8,6,5,7]=>[1,4,1,2]
[1,2,3,4,8,6,5,7]=>[5,1,2]
[4,8,3,6,2,1,5,7]=>[2,2,1,3]
[3,5,8,2,6,1,4,7]=>[3,2,3]
[3,6,5,8,2,4,1,7]=>[2,2,2,2]
[5,3,8,7,2,4,6,1]=>[1,2,1,3,1]
[2,8,4,5,7,3,6,1]=>[2,3,2,1]
[2,4,5,7,3,8,1,6]=>[4,2,2]
[6,2,4,5,8,3,1,7]=>[1,4,1,2]
[4,8,1,2,5,6,3,7]=>[2,4,2]
[8,1,3,5,2,6,4,7]=>[1,3,2,2]
[5,2,1,6,3,8,4,7]=>[1,1,2,2,2]
[6,2,5,1,8,4,3,7]=>[1,2,2,1,2]
[3,6,1,5,8,4,2,7]=>[2,3,1,2]
[6,1,4,5,8,3,2,7]=>[1,4,1,2]
[5,6,4,8,1,3,2,7]=>[2,2,2,2]
[6,5,4,3,8,2,1,7]=>[1,1,1,2,1,2]
[5,4,3,7,2,8,1,6]=>[1,1,2,2,2]
[5,8,4,3,7,2,6,1]=>[2,1,2,2,1]
[4,6,8,3,7,2,5,1]=>[3,2,2,1]
[7,4,6,3,2,8,1,5]=>[1,2,1,2,2]
[1,4,3,6,2,7,8,5]=>[2,2,3,1]
[1,5,4,3,7,2,8,6]=>[2,1,2,2,1]
[4,7,8,5,3,1,2,6]=>[3,1,1,3]
[5,7,3,4,1,2,8,6]=>[2,2,3,1]
[8,5,4,7,6,2,1,3]=>[1,1,2,1,1,2]
[8,5,7,4,3,6,1,2]=>[1,2,1,2,2]
[4,3,8,1,6,7,5,2]=>[1,2,3,1,1]
[4,7,8,3,6,1,5,2]=>[3,2,2,1]
[5,3,8,6,7,4,1,2]=>[1,2,2,1,2]
[1,3,8,6,4,7,5,2]=>[3,1,2,1,1]
[8,6,2,7,4,1,5,3]=>[1,1,2,1,2,1]
[7,6,2,1,4,3,8,5]=>[1,1,1,2,2,1]
[7,6,1,3,4,2,8,5]=>[1,1,3,2,1]
[1,5,7,3,2,6,8,4]=>[3,1,3,1]
[1,6,7,3,2,5,8,4]=>[3,1,3,1]
[3,2,6,8,5,7,4,1]=>[1,3,2,1,1]
[5,8,2,3,6,7,4,1]=>[2,4,1,1]
[7,5,2,3,1,6,8,4]=>[1,1,2,3,1]
[1,6,4,7,2,3,8,5]=>[2,2,3,1]
[3,1,7,5,2,8,4,6]=>[1,2,1,2,2]
[2,5,7,4,1,8,3,6]=>[3,1,2,2]
[4,2,6,1,7,8,3,5]=>[1,2,3,2]
[4,2,7,6,3,8,1,5]=>[1,2,1,2,2]
[6,4,8,7,2,3,5,1]=>[1,2,1,3,1]
[3,2,6,8,7,4,5,1]=>[1,3,1,2,1]
[3,2,7,4,1,6,8,5]=>[1,2,1,3,1]
[6,3,2,1,7,8,4,5]=>[1,1,1,3,2]
[3,7,1,8,4,2,5,6]=>[2,2,1,3]
[4,2,1,3,7,5,8,6]=>[1,1,3,2,1]
[8,1,3,7,4,2,6,5]=>[1,3,1,2,1]
[8,4,3,7,6,2,1,5]=>[1,1,2,1,1,2]
[8,3,5,2,7,6,1,4]=>[1,2,2,1,2]
[3,6,2,8,7,1,5,4]=>[2,2,1,2,1]
[7,3,2,8,1,6,5,4]=>[1,1,2,2,1,1]
[3,8,7,2,6,5,4,1]=>[2,1,2,1,1,1]
[4,2,7,8,6,1,5,3]=>[1,3,1,2,1]
[6,8,2,4,7,1,5,3]=>[2,3,2,1]
[5,2,1,8,7,3,6,4]=>[1,1,2,1,2,1]
[8,2,1,6,3,7,5,4]=>[1,1,2,2,1,1]
[6,8,3,1,7,5,2,4]=>[2,1,2,1,2]
[5,8,1,6,7,2,4,3]=>[2,3,2,1]
[6,2,8,1,5,7,4,3]=>[1,2,3,1,1]
[5,7,8,2,6,1,4,3]=>[3,2,2,1]
[8,7,2,5,6,4,3,1]=>[1,1,3,1,1,1]
[8,6,7,5,2,4,3,1]=>[1,2,1,2,1,1]
[7,2,6,8,1,5,4,3]=>[1,3,2,1,1]
[1,2,7,8,5,6,4,3]=>[4,2,1,1]
[7,4,8,1,6,2,5,3]=>[1,2,2,2,1]
[3,7,1,8,2,6,5,4]=>[2,2,2,1,1]
[2,1,7,3,8,6,5,4]=>[1,2,2,1,1,1]
[8,2,1,7,6,5,4,3]=>[1,1,2,1,1,1,1]
[8,1,4,7,6,5,3,2]=>[1,3,1,1,1,1]
[8,6,7,5,1,4,3,2]=>[1,2,1,2,1,1]
[7,8,6,5,4,1,3,2]=>[2,1,1,1,2,1]
[5,8,4,3,2,1,6,7]=>[2,1,1,1,3]
[6,4,7,3,2,1,8,5]=>[1,2,1,1,2,1]
[5,4,7,3,2,1,6,8]=>[1,2,1,1,3]
[6,5,3,7,2,1,4,8]=>[1,1,2,1,3]
[5,8,3,6,2,1,4,7]=>[2,2,1,3]
[6,3,7,8,2,1,4,5]=>[1,3,1,3]
[5,3,7,6,2,1,4,8]=>[1,2,1,1,3]
[3,8,7,6,2,1,4,5]=>[2,1,1,1,3]
[5,8,4,2,6,1,3,7]=>[2,1,2,3]
[4,8,7,2,5,1,3,6]=>[2,1,2,3]
[5,8,3,2,6,1,4,7]=>[2,1,2,3]
[4,8,3,2,5,1,7,6]=>[2,1,2,2,1]
[4,3,7,2,5,1,8,6]=>[1,2,2,2,1]
[3,8,7,2,5,1,4,6]=>[2,1,2,3]
[6,4,2,7,5,1,3,8]=>[1,1,2,1,3]
[6,3,2,7,5,1,4,8]=>[1,1,2,1,3]
[5,3,2,6,7,1,4,8]=>[1,1,3,3]
[3,8,2,6,5,1,4,7]=>[2,2,1,3]
[6,2,7,8,5,1,3,4]=>[1,3,1,3]
[5,2,7,6,8,1,3,4]=>[1,2,2,3]
[4,2,7,6,5,1,3,8]=>[1,2,1,1,3]
[2,8,7,6,5,1,3,4]=>[2,1,1,1,3]
[6,5,4,3,1,7,8,2]=>[1,1,1,1,3,1]
[6,4,7,3,1,5,8,2]=>[1,2,1,3,1]
[5,4,7,3,1,8,6,2]=>[1,2,1,2,1,1]
[6,4,3,7,1,5,8,2]=>[1,1,2,3,1]
[5,4,3,6,1,8,7,2]=>[1,1,2,2,1,1]
[6,3,7,8,1,4,5,2]=>[1,3,3,1]
[5,3,7,6,1,4,8,2]=>[1,2,1,3,1]
[4,3,7,6,1,5,8,2]=>[1,2,1,3,1]
[3,8,7,6,1,4,5,2]=>[2,1,1,3,1]
[6,5,4,2,1,7,3,8]=>[1,1,1,1,2,2]
[6,4,7,2,1,5,3,8]=>[1,2,1,2,2]
[4,8,7,2,1,5,3,6]=>[2,1,1,2,2]
[5,8,3,2,1,4,7,6]=>[2,1,1,3,1]
[4,8,3,2,1,5,7,6]=>[2,1,1,3,1]
[5,3,7,2,1,4,8,6]=>[1,2,1,3,1]
[3,8,7,2,1,4,5,6]=>[2,1,1,4]
[6,5,2,7,1,4,3,8]=>[1,1,2,2,2]
[5,8,2,6,1,4,3,7]=>[2,2,2,2]
[6,4,2,7,1,5,3,8]=>[1,1,2,2,2]
[5,4,2,6,1,8,3,7]=>[1,1,2,2,2]
[4,3,2,6,1,5,8,7]=>[1,1,2,3,1]
[6,2,7,8,1,4,3,5]=>[1,3,2,2]
[4,2,7,6,1,5,3,8]=>[1,2,1,2,2]
[3,2,7,6,1,4,5,8]=>[1,2,1,4]
[6,5,4,1,8,7,3,2]=>[1,1,1,2,1,1,1]
[5,8,4,1,6,7,3,2]=>[2,1,3,1,1]
[6,4,7,1,5,8,3,2]=>[1,2,3,1,1]
[5,4,7,1,6,8,3,2]=>[1,2,3,1,1]
[4,8,7,1,5,6,3,2]=>[2,1,3,1,1]
[5,4,3,1,6,8,7,2]=>[1,1,1,3,1,1]
[4,8,3,1,5,6,7,2]=>[2,1,4,1]
[3,8,7,1,5,4,6,2]=>[2,1,2,2,1]
[5,8,2,1,6,4,3,7]=>[2,1,2,1,2]
[6,3,2,1,5,4,8,7]=>[1,1,1,2,2,1]
[5,3,2,1,6,4,8,7]=>[1,1,1,2,2,1]
[3,8,2,1,5,4,6,7]=>[2,1,2,3]
[6,2,7,1,5,4,3,8]=>[1,2,2,1,2]
[5,2,7,1,6,4,3,8]=>[1,2,2,1,2]
[4,2,7,1,5,6,3,8]=>[1,2,3,2]
[3,2,7,1,5,4,6,8]=>[1,2,2,3]
[2,8,7,1,5,4,3,6]=>[2,1,2,1,2]
[6,5,1,7,8,4,3,2]=>[1,1,3,1,1,1]
[5,8,1,6,7,4,3,2]=>[2,3,1,1,1]
[6,4,1,7,5,8,3,2]=>[1,1,2,2,1,1]
[5,4,1,6,7,8,3,2]=>[1,1,4,1,1]
[4,8,1,6,5,7,3,2]=>[2,2,2,1,1]
[6,3,1,7,5,4,8,2]=>[1,1,2,1,2,1]
[5,3,1,6,7,4,8,2]=>[1,1,3,2,1]
[4,3,1,6,5,7,8,2]=>[1,1,2,3,1]
[3,8,1,6,5,4,7,2]=>[2,2,1,2,1]
[5,2,1,6,7,4,3,8]=>[1,1,3,1,2]
[4,2,1,6,5,7,3,8]=>[1,1,2,2,2]
[2,8,1,6,5,4,3,7]=>[2,2,1,1,2]
[6,1,7,8,5,4,3,2]=>[1,3,1,1,1,1]
[4,1,7,6,5,8,3,2]=>[1,2,1,2,1,1]
[3,1,7,6,5,4,8,2]=>[1,2,1,1,2,1]
[4,5,8,1,2,6,3,7]=>[3,3,2]
[1,4,5,7,2,6,3,8]=>[4,2,2]
[1,7,3,5,6,2,4,8]=>[2,3,3]
[8,1,3,5,7,2,4,6]=>[1,4,3]
[3,6,8,1,7,2,4,5]=>[3,2,3]
[3,4,5,6,8,1,7,2]=>[5,2,1]
[4,5,8,2,6,7,1,3]=>[3,3,2]
[8,2,3,5,6,7,1,4]=>[1,5,2]
[1,7,2,3,5,4,6,8]=>[2,3,3]
[8,1,2,3,5,4,6,7]=>[1,4,3]
[2,7,8,1,3,5,4,6]=>[3,3,2]
[2,7,8,3,5,6,1,4]=>[3,3,2]
[2,4,5,7,8,1,6,3]=>[5,2,1]
[4,5,8,1,7,6,3,2]=>[3,2,1,1,1]
[4,5,8,7,2,1,6,3]=>[3,1,1,2,1]
[8,7,3,5,6,2,1,4]=>[1,1,3,1,2]
[8,7,2,1,3,5,4,6]=>[1,1,1,3,2]
[3,6,8,7,2,1,5,4]=>[3,1,1,2,1]
[8,6,4,1,7,5,3,2]=>[1,1,1,2,1,1,1]
[7,6,4,3,1,8,5,2]=>[1,1,1,1,2,1,1]
[2,3,6,7,8,1,5,4]=>[5,2,1]
[3,6,8,1,2,5,4,7]=>[3,3,2]
[1,3,6,7,2,5,4,8]=>[4,2,2]
[7,4,1,8,5,2,3,6]=>[1,1,2,1,3]
[7,1,4,2,8,3,6,5]=>[1,2,2,2,1]
[7,1,8,2,5,3,6,4]=>[1,2,2,2,1]
[8,1,7,5,4,2,3,6]=>[1,2,1,1,3]
[1,7,2,6,5,4,3,8]=>[2,2,1,1,2]
[1,7,6,3,2,5,4,8]=>[2,1,1,2,2]
[8,6,3,1,2,5,4,7]=>[1,1,1,3,2]
[8,1,7,6,3,2,4,5]=>[1,2,1,1,3]
[8,2,5,7,6,3,1,4]=>[1,3,1,1,2]
[3,6,8,1,7,5,4,2]=>[3,2,1,1,1]
[8,2,6,7,5,4,1,3]=>[1,3,1,1,2]
[2,7,8,6,3,1,5,4]=>[3,1,1,2,1]
[2,7,8,1,6,5,4,3]=>[3,2,1,1,1]
[7,3,1,8,6,5,4,2]=>[1,1,2,1,1,1,1]
[8,7,2,1,6,5,4,3]=>[1,1,1,2,1,1,1]
[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,2,1]
[2,1,8,6,3,7,4,5]=>[1,2,1,2,2]
[8,6,1,5,2,7,4,3]=>[1,1,2,2,1,1]
[8,5,1,7,4,2,6,3]=>[1,1,2,1,2,1]
[2,1,7,5,4,3,8,6]=>[1,2,1,1,2,1]
[2,1,8,4,5,3,6,7]=>[1,2,2,3]
[2,1,7,8,3,6,5,4]=>[1,3,2,1,1]
[2,1,4,8,5,7,3,6]=>[1,3,2,2]
[2,1,5,4,6,8,3,7]=>[1,2,3,2]
[8,5,3,1,6,2,4,7]=>[1,1,1,2,3]
[6,4,1,5,2,3,8,7]=>[1,1,2,3,1]
[8,3,7,5,2,6,1,4]=>[1,2,1,2,2]
[5,3,7,4,6,8,1,2]=>[1,2,3,2]
[5,8,3,7,6,2,1,4]=>[2,2,1,1,2]
[5,2,4,8,6,3,1,7]=>[1,3,1,1,2]
[4,2,6,3,8,5,1,7]=>[1,2,2,1,2]
[4,6,3,2,7,8,1,5]=>[2,1,3,2]
[3,8,2,4,7,5,1,6]=>[2,3,1,2]
[8,5,2,7,4,6,1,3]=>[1,1,2,2,2]
[5,8,2,1,7,6,4,3]=>[2,1,2,1,1,1]
[8,3,2,4,1,7,5,6]=>[1,1,2,2,2]
[7,2,4,3,1,5,8,6]=>[1,2,1,3,1]
[7,8,3,1,5,4,6,2]=>[2,1,2,2,1]
[7,2,8,1,4,6,5,3]=>[1,2,3,1,1]
[6,2,3,1,4,5,8,7]=>[1,2,4,1]
[5,6,1,4,3,2,8,7]=>[2,2,1,2,1]
[6,8,1,4,5,3,2,7]=>[2,3,1,2]
[6,7,1,5,4,3,8,2]=>[2,2,1,2,1]
[8,7,5,1,3,4,2,6]=>[1,1,1,3,2]
[8,2,6,1,4,7,3,5]=>[1,2,3,2]
[5,8,1,6,3,7,4,2]=>[2,2,2,1,1]
[8,3,5,6,1,7,4,2]=>[1,3,2,1,1]
[7,5,4,8,2,1,3,6]=>[1,1,2,1,3]
[7,3,6,5,4,1,8,2]=>[1,2,1,1,2,1]
[8,3,6,4,5,1,2,7]=>[1,2,2,3]
[6,3,5,4,1,2,8,7]=>[1,2,1,3,1]
[2,6,3,5,1,4,8,7]=>[2,2,3,1]
[2,7,8,5,1,6,4,3]=>[3,1,2,1,1]
[8,7,3,6,5,1,4,2]=>[1,1,2,1,2,1]
[2,8,3,4,6,1,5,7]=>[2,3,3]
[2,7,4,3,6,1,8,5]=>[2,1,2,2,1]
[3,4,7,2,8,1,5,6]=>[3,2,3]
[4,2,3,5,8,1,6,7]=>[1,4,3]
[3,2,8,4,7,1,6,5]=>[1,2,2,2,1]
[3,8,4,7,1,6,5,2]=>[2,2,2,1,1]
[3,2,4,6,1,5,8,7]=>[1,3,3,1]
[8,3,4,5,7,6,1,2]=>[1,4,1,2]
[2,3,8,4,6,7,1,5]=>[3,3,2]
[3,2,4,5,6,8,1,7]=>[1,5,2]
[5,6,8,1,4,2,7,3]=>[3,2,2,1]
[1,5,7,8,4,6,2,3]=>[4,2,2]
[1,3,5,7,8,6,2,4]=>[5,1,2]
[3,5,7,8,6,1,2,4]=>[4,1,3]
[3,5,1,6,8,2,7,4]=>[2,3,2,1]
[3,1,5,6,8,2,7,4]=>[1,4,2,1]
[2,3,5,6,8,1,7,4]=>[5,2,1]
[5,6,4,8,2,1,7,3]=>[2,2,1,2,1]
[5,1,6,3,8,4,7,2]=>[1,2,2,2,1]
[2,5,1,6,8,3,7,4]=>[2,3,2,1]
[5,1,2,6,8,3,7,4]=>[1,4,2,1]
[5,7,1,8,6,2,3,4]=>[2,2,1,3]
[1,5,2,7,8,6,3,4]=>[2,3,1,2]
[1,6,7,5,2,8,3,4]=>[3,1,2,2]
[6,1,7,5,2,8,3,4]=>[1,2,1,2,2]
[2,6,7,5,1,8,3,4]=>[3,1,2,2]
[5,7,2,8,6,1,3,4]=>[2,2,1,3]
[3,5,7,8,6,2,1,4]=>[4,1,1,2]
[5,1,7,8,6,3,4,2]=>[1,3,1,2,1]
[5,1,3,7,8,6,4,2]=>[1,4,1,1,1]
[5,2,7,8,4,6,1,3]=>[1,3,2,2]
[3,2,5,7,8,6,1,4]=>[1,4,1,2]
[6,2,7,5,1,8,3,4]=>[1,2,1,2,2]
[1,2,6,7,5,8,3,4]=>[4,2,2]
[6,2,7,5,4,1,8,3]=>[1,2,1,1,2,1]
[6,7,5,2,4,1,8,3]=>[2,1,2,2,1]
[6,7,2,5,3,8,1,4]=>[2,2,2,2]
[6,7,4,5,2,1,8,3]=>[2,2,1,2,1]
[5,1,7,8,6,4,3,2]=>[1,3,1,1,1,1]
[2,5,7,8,6,3,1,4]=>[4,1,1,2]
[5,1,7,8,6,3,2,4]=>[1,3,1,1,2]
[6,3,7,5,1,8,2,4]=>[1,2,1,2,2]
[1,6,7,5,3,8,2,4]=>[3,1,2,2]
[1,6,7,5,4,2,8,3]=>[3,1,1,2,1]
[6,7,5,1,4,2,8,3]=>[2,1,2,2,1]
[5,7,8,6,4,1,2,3]=>[3,1,1,3]
[4,1,7,2,6,5,8,3]=>[1,2,2,2,1]
[2,4,7,1,5,6,8,3]=>[3,4,1]
[6,7,4,1,5,2,8,3]=>[2,1,2,2,1]
[1,6,7,4,5,2,8,3]=>[3,2,2,1]
[1,6,3,7,5,8,2,4]=>[2,2,2,2]
[6,3,1,7,5,8,2,4]=>[1,1,2,2,2]
[2,5,3,7,8,6,1,4]=>[2,3,1,2]
[6,7,5,4,2,1,8,3]=>[2,1,1,1,2,1]
[6,3,2,7,5,8,1,4]=>[1,1,2,2,2]
[6,7,4,2,5,1,8,3]=>[2,1,2,2,1]
[6,2,7,4,5,1,8,3]=>[1,2,2,2,1]
[6,2,3,7,5,8,1,4]=>[1,3,2,2]
[4,5,1,6,3,2,8,7]=>[2,2,1,2,1]
[7,5,1,6,3,8,2,4]=>[1,1,2,2,2]
[7,5,1,6,3,8,4,2]=>[1,1,2,2,1,1]
[2,7,6,1,3,8,4,5]=>[2,1,3,2]
[2,7,6,1,3,8,5,4]=>[2,1,3,1,1]
[7,3,5,1,8,2,6,4]=>[1,2,2,2,1]
[7,3,5,1,8,2,4,6]=>[1,2,2,3]
[3,7,5,1,8,6,2,4]=>[2,1,2,1,2]
[2,6,7,1,5,8,3,4]=>[3,3,2]
[2,6,7,4,1,8,3,5]=>[3,1,2,2]
[2,1,6,7,3,8,5,4]=>[1,3,2,1,1]
[2,6,7,4,1,8,5,3]=>[3,1,2,1,1]
[2,6,7,1,5,8,4,3]=>[3,3,1,1]
[3,6,5,1,8,4,7,2]=>[2,1,2,2,1]
[3,6,5,1,8,4,2,7]=>[2,1,2,1,2]
[3,7,5,4,8,1,6,2]=>[2,1,2,2,1]
[3,7,5,4,8,1,2,6]=>[2,1,2,3]
[4,6,1,5,8,7,3,2]=>[2,3,1,1,1]
[4,6,1,5,8,7,2,3]=>[2,3,1,2]
[4,6,1,5,8,2,7,3]=>[2,3,2,1]
[7,5,1,6,2,8,3,4]=>[1,1,2,2,2]
[7,5,1,6,2,8,4,3]=>[1,1,2,2,1,1]
[4,6,1,5,8,2,3,7]=>[2,3,3]
[4,7,1,5,8,3,6,2]=>[2,3,2,1]
[2,3,4,7,8,1,6,5]=>[5,2,1]
[6,8,5,4,3,2,7,1]=>[2,1,1,1,2,1]
[6,8,5,4,3,7,2,1]=>[2,1,1,2,1,1]
[5,8,4,3,2,1,7,6]=>[2,1,1,1,2,1]
[6,5,4,3,1,8,7,2]=>[1,1,1,1,2,1,1]
[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,2,1]
[8,3,4,6,2,1,5,7]=>[1,3,1,3]
[3,5,6,2,1,8,4,7]=>[3,1,2,2]
[3,5,2,6,8,4,1,7]=>[2,3,1,2]
[7,5,3,2,8,4,1,6]=>[1,1,1,2,1,2]
[7,5,3,2,8,4,6,1]=>[1,1,1,2,2,1]
[2,4,5,7,3,8,6,1]=>[4,2,1,1]
[4,2,5,6,8,3,1,7]=>[1,4,1,2]
[4,2,8,1,5,6,3,7]=>[1,2,3,2]
[2,5,6,1,8,4,3,7]=>[3,2,1,2]
[5,3,6,8,1,4,2,7]=>[1,3,2,2]
[4,5,6,8,1,3,2,7]=>[4,2,2]
[1,4,5,6,8,3,2,7]=>[5,1,2]
[4,5,6,3,8,2,1,7]=>[3,2,1,2]
[4,5,3,7,2,8,6,1]=>[2,2,2,1,1]
[6,4,7,3,2,8,5,1]=>[1,2,1,2,1,1]
[6,1,4,7,3,2,8,5]=>[1,3,1,2,1]
[1,7,8,4,5,3,2,6]=>[3,2,1,2]
[5,1,7,3,8,4,2,6]=>[1,2,2,1,2]
[2,5,1,7,4,3,8,6]=>[2,2,1,2,1]
[2,5,7,4,1,8,6,3]=>[3,1,2,1,1]
[5,3,7,1,4,8,6,2]=>[1,2,3,1,1]
[6,4,3,1,7,8,5,2]=>[1,1,1,3,1,1]
[6,4,1,7,3,8,5,2]=>[1,1,2,2,1,1]
[5,6,3,7,8,4,2,1]=>[2,3,1,1,1]
[5,1,6,3,7,8,4,2]=>[1,2,3,1,1]
[5,6,1,3,7,8,4,2]=>[2,4,1,1]
[5,6,1,7,8,3,4,2]=>[2,3,2,1]
[1,6,3,7,4,8,5,2]=>[2,2,2,1,1]
[6,7,2,4,1,8,5,3]=>[2,2,2,1,1]
[6,7,2,1,4,3,8,5]=>[2,1,2,2,1]
[6,4,7,3,1,2,8,5]=>[1,2,1,3,1]
[5,6,3,1,2,7,8,4]=>[2,1,4,1]
[5,6,1,3,2,7,8,4]=>[2,2,3,1]
[5,6,3,2,1,7,8,4]=>[2,1,1,3,1]
[2,5,6,3,7,8,4,1]=>[3,3,1,1]
[2,5,6,3,1,7,8,4]=>[3,1,3,1]
[2,6,4,7,3,1,8,5]=>[2,2,1,2,1]
[6,3,7,2,8,4,5,1]=>[1,2,2,2,1]
[6,3,7,2,8,4,1,5]=>[1,2,2,1,2]
[6,3,2,7,1,8,4,5]=>[1,1,2,2,2]
[7,5,3,2,1,8,4,6]=>[1,1,1,1,2,2]
[7,3,8,4,2,1,5,6]=>[1,2,1,1,3]
[4,7,2,1,3,8,6,5]=>[2,1,3,1,1]
[1,3,7,8,6,4,2,5]=>[4,1,1,2]
[7,3,8,4,6,2,1,5]=>[1,2,2,1,2]
[5,7,3,8,2,1,6,4]=>[2,2,1,2,1]
[6,3,7,8,5,2,1,4]=>[1,3,1,1,2]
[4,6,2,7,8,5,3,1]=>[2,3,1,1,1]
[4,6,2,1,7,8,5,3]=>[2,1,3,1,1]
[7,4,5,8,1,2,6,3]=>[1,3,3,1]
[2,5,1,7,3,8,6,4]=>[2,2,2,1,1]
[6,7,2,1,3,8,5,4]=>[2,1,3,1,1]
[5,1,6,7,8,2,4,3]=>[1,4,2,1]
[6,3,7,1,8,5,2,4]=>[1,2,2,1,2]
[6,2,1,7,3,8,5,4]=>[1,1,2,2,1,1]
[6,2,7,1,8,5,4,3]=>[1,2,2,1,1,1]
[6,3,1,7,8,5,4,2]=>[1,1,3,1,1,1]
[4,1,3,6,8,2,5,7]=>[1,4,3]
[4,2,3,6,8,1,5,7]=>[1,4,3]
[5,3,2,1,8,4,7,6]=>[1,1,1,2,2,1]
[3,6,5,8,2,1,7,4]=>[2,2,1,2,1]
[4,5,2,1,3,8,7,6]=>[2,1,3,1,1]
[3,2,6,4,5,8,1,7]=>[1,2,3,2]
[2,4,6,5,8,1,3,7]=>[3,2,3]
[1,6,2,4,5,8,3,7]=>[2,4,2]
[5,3,2,1,6,8,4,7]=>[1,1,1,3,2]
[6,2,4,5,8,1,3,7]=>[1,4,3]
[1,3,4,6,5,8,2,7]=>[4,2,2]
[1,6,3,4,5,8,2,7]=>[2,4,2]
[3,4,1,8,5,2,7,6]=>[2,2,1,2,1]
[2,8,4,1,7,6,3,5]=>[2,1,2,1,2]
[8,1,4,2,7,3,6,5]=>[1,2,2,2,1]
[1,5,3,2,8,7,4,6]=>[2,1,2,1,2]
[8,2,1,7,5,3,4,6]=>[1,1,2,1,3]
[1,7,6,4,5,8,3,2]=>[2,1,3,1,1]
[5,8,7,4,1,2,6,3]=>[2,1,1,3,1]
[5,8,7,4,6,2,1,3]=>[2,1,2,1,2]
[3,4,2,5,8,6,7,1]=>[2,3,2,1]
[4,1,3,5,6,8,7,2]=>[1,5,1,1]
[2,4,8,6,7,1,3,5]=>[3,2,3]
[4,3,6,2,8,1,7,5]=>[1,2,2,2,1]
[3,7,4,8,2,1,6,5]=>[2,2,1,2,1]
[2,3,5,8,6,7,1,4]=>[4,2,2]
[3,2,5,6,8,7,1,4]=>[1,4,1,2]
[2,1,8,5,6,7,3,4]=>[1,2,3,2]
[1,2,8,3,5,6,7,4]=>[3,4,1]
[4,2,3,7,1,8,6,5]=>[1,3,2,1,1]
[3,2,6,4,8,1,7,5]=>[1,2,2,2,1]
[8,2,1,6,7,3,4,5]=>[1,1,3,3]
[2,7,8,5,4,1,3,6]=>[3,1,1,3]
[1,7,5,3,8,4,2,6]=>[2,1,2,1,2]
[4,7,5,3,1,2,8,6]=>[2,1,1,3,1]
[7,2,4,8,5,3,1,6]=>[1,3,1,1,2]
[4,8,3,1,2,7,6,5]=>[2,1,3,1,1]
[3,5,2,7,4,1,8,6]=>[2,2,1,2,1]
[8,4,2,3,7,1,5,6]=>[1,1,3,3]
[2,8,4,7,1,3,5,6]=>[2,2,4]
[8,2,4,6,7,1,3,5]=>[1,4,3]
[4,8,2,3,6,7,1,5]=>[2,4,2]
[3,5,2,7,6,1,8,4]=>[2,2,1,2,1]
[1,6,3,2,5,8,7,4]=>[2,1,3,1,1]
[5,8,3,2,1,6,7,4]=>[2,1,1,3,1]
[5,8,7,3,4,6,2,1]=>[2,1,3,1,1]
[5,8,2,7,4,1,6,3]=>[2,2,1,2,1]
[5,1,4,2,8,7,6,3]=>[1,2,2,1,1,1]
[4,7,6,5,8,2,1,3]=>[2,1,2,1,2]
[5,3,7,1,6,2,8,4]=>[1,2,2,2,1]
[5,2,6,8,7,1,3,4]=>[1,3,1,3]
[6,3,2,1,8,5,7,4]=>[1,1,1,2,2,1]
[2,7,5,4,1,8,6,3]=>[2,1,1,2,1,1]
[4,2,5,6,8,7,1,3]=>[1,4,1,2]
[1,8,4,2,5,6,7,3]=>[2,1,4,1]
[3,8,4,1,5,6,7,2]=>[2,1,4,1]
[4,2,8,5,6,7,1,3]=>[1,2,3,2]
[5,2,4,7,1,8,6,3]=>[1,3,2,1,1]
[5,3,4,7,1,8,6,2]=>[1,3,2,1,1]
[8,6,4,1,3,2,5,7]=>[1,1,1,2,3]
[8,1,3,6,5,2,4,7]=>[1,3,1,3]
[8,1,4,3,6,5,2,7]=>[1,2,2,1,2]
[3,6,5,2,1,8,7,4]=>[2,1,1,2,1,1]
[8,3,2,4,6,5,1,7]=>[1,1,3,1,2]
[8,4,2,1,6,5,3,7]=>[1,1,1,2,1,2]
[8,4,1,2,6,5,3,7]=>[1,1,3,1,2]
[8,6,4,2,1,5,3,7]=>[1,1,1,1,2,2]
[8,3,6,4,1,5,2,7]=>[1,2,1,2,2]
[8,2,6,3,4,5,1,7]=>[1,2,3,2]
[1,3,4,8,5,7,2,6]=>[4,2,2]
[5,8,4,7,6,2,3,1]=>[2,2,1,2,1]
[1,3,4,7,5,8,2,6]=>[4,2,2]
[1,3,5,2,4,8,7,6]=>[3,3,1,1]
[2,6,5,1,3,8,7,4]=>[2,1,3,1,1]
[4,7,1,6,5,8,3,2]=>[2,2,2,1,1]
[5,4,8,7,6,3,1,2]=>[1,2,1,1,1,2]
[2,8,5,1,4,7,6,3]=>[2,1,3,1,1]
[4,3,1,5,8,6,7,2]=>[1,1,3,2,1]
[4,1,3,5,8,6,7,2]=>[1,4,2,1]
[6,5,3,8,4,7,1,2]=>[1,1,2,2,2]
[5,4,2,1,6,8,7,3]=>[1,1,1,3,1,1]
[6,8,4,3,2,7,1,5]=>[2,1,1,2,2]
[3,4,7,8,2,1,6,5]=>[4,1,2,1]
[5,1,3,2,8,6,7,4]=>[1,2,2,2,1]
[5,3,1,2,8,6,7,4]=>[1,1,3,2,1]
[5,2,3,1,6,8,7,4]=>[1,2,3,1,1]
[5,3,2,1,8,6,7,4]=>[1,1,1,2,2,1]
[5,2,1,3,6,8,7,4]=>[1,1,4,1,1]
[2,4,7,3,8,1,6,5]=>[3,2,2,1]
[6,3,8,2,7,4,1,5]=>[1,2,2,1,2]
[8,2,1,3,6,4,7,5]=>[1,1,3,2,1]
[3,5,1,7,8,4,2,6]=>[2,3,1,2]
[2,7,4,5,8,3,1,6]=>[2,3,1,2]
[1,8,4,3,7,2,6,5]=>[2,1,2,2,1]
[3,4,8,7,2,1,6,5]=>[3,1,1,2,1]
[5,4,7,8,3,6,2,1]=>[1,3,2,1,1]
[6,4,3,8,7,2,1,5]=>[1,1,2,1,1,2]
[6,3,8,7,4,1,2,5]=>[1,2,1,1,3]
[3,5,7,2,4,8,1,6]=>[3,3,2]
[8,4,7,2,3,1,5,6]=>[1,2,2,3]
[8,4,7,1,3,2,5,6]=>[1,2,2,3]
[8,4,7,2,1,3,5,6]=>[1,2,1,4]
[8,6,4,2,1,3,7,5]=>[1,1,1,1,3,1]
[8,6,4,1,3,2,7,5]=>[1,1,1,2,2,1]
[8,6,4,2,3,1,7,5]=>[1,1,1,2,2,1]
[3,5,7,2,6,1,8,4]=>[3,2,2,1]
[6,1,3,8,5,7,2,4]=>[1,3,2,2]
[5,8,3,2,6,7,1,4]=>[2,1,3,2]
[4,8,5,3,6,2,7,1]=>[2,1,2,2,1]
[2,8,1,5,4,7,6,3]=>[2,2,2,1,1]
[1,5,8,7,4,6,2,3]=>[3,1,2,2]
[2,1,7,6,4,5,8,3]=>[1,2,1,3,1]
[1,7,2,4,6,5,8,3]=>[2,3,2,1]
[3,5,1,7,6,8,2,4]=>[2,2,2,2]
[5,8,2,6,1,3,7,4]=>[2,2,3,1]
[6,3,5,8,7,2,1,4]=>[1,3,1,1,2]
[2,5,7,8,4,1,6,3]=>[4,1,2,1]
[4,2,8,1,5,6,7,3]=>[1,2,4,1]
[4,1,5,2,6,8,7,3]=>[1,2,3,1,1]
[3,4,5,1,6,8,7,2]=>[3,3,1,1]
[4,2,8,5,1,6,7,3]=>[1,2,1,3,1]
[4,1,8,5,2,6,7,3]=>[1,2,1,3,1]
[2,7,1,8,5,4,6,3]=>[2,2,1,2,1]
[5,8,6,2,1,3,7,4]=>[2,1,1,3,1]
[8,2,4,1,5,6,7,3]=>[1,2,4,1]
[4,6,3,5,8,1,7,2]=>[2,3,2,1]
[1,7,8,3,5,4,6,2]=>[3,2,2,1]
[3,4,5,1,8,6,7,2]=>[3,2,2,1]
[3,8,1,4,5,6,7,2]=>[2,5,1]
[3,4,5,6,8,2,1,7]=>[5,1,2]
[3,4,5,7,1,8,6,2]=>[4,2,1,1]
[3,4,5,7,8,2,6,1]=>[5,2,1]
[3,4,6,2,8,5,1,7]=>[3,2,1,2]
[3,4,6,8,1,5,2,7]=>[4,2,2]
[3,4,7,2,1,8,6,5]=>[3,1,2,1,1]
[3,4,7,8,1,5,6,2]=>[4,3,1]
[3,4,8,2,1,5,6,7]=>[3,1,4]
[3,5,2,6,7,8,1,4]=>[2,4,2]
[3,5,2,7,8,4,6,1]=>[2,3,2,1]
[3,5,2,8,4,1,6,7]=>[2,2,1,3]
[3,5,6,2,8,4,1,7]=>[3,2,1,2]
[3,5,6,8,4,1,2,7]=>[4,1,3]
[3,5,7,2,4,8,6,1]=>[3,3,1,1]
[3,5,7,2,8,4,6,1]=>[3,2,2,1]
[3,5,7,8,4,1,6,2]=>[4,1,2,1]
[3,6,2,1,7,8,5,4]=>[2,1,3,1,1]
[3,6,2,1,8,5,4,7]=>[2,1,2,1,2]
[3,6,7,2,4,8,5,1]=>[3,3,1,1]
[3,6,7,2,8,5,4,1]=>[3,2,1,1,1]
[3,6,7,8,4,5,1,2]=>[4,2,2]
[3,6,8,2,4,5,1,7]=>[3,3,2]
[3,7,2,1,4,8,6,5]=>[2,1,3,1,1]
[3,7,2,1,8,5,6,4]=>[2,1,2,2,1]
[3,7,2,8,4,5,6,1]=>[2,2,3,1]
[3,7,8,2,4,5,6,1]=>[3,4,1]
[3,8,2,1,4,5,6,7]=>[2,1,5]
[4,1,5,6,7,8,3,2]=>[1,5,1,1]
[4,1,5,7,3,8,6,2]=>[1,3,2,1,1]
[4,1,6,3,7,8,5,2]=>[1,2,3,1,1]
[4,1,6,3,8,5,2,7]=>[1,2,2,1,2]
[4,1,6,7,3,8,5,2]=>[1,3,2,1,1]
[4,1,6,7,8,5,2,3]=>[1,4,1,2]
[4,1,6,8,3,5,2,7]=>[1,3,2,2]
[4,1,7,3,2,8,6,5]=>[1,2,1,2,1,1]
[4,1,7,8,3,5,6,2]=>[1,3,3,1]
[4,1,8,3,2,5,6,7]=>[1,2,1,4]
[4,5,2,6,7,8,3,1]=>[2,4,1,1]
[4,5,2,6,8,1,3,7]=>[2,3,3]
[4,5,6,3,8,1,2,7]=>[3,2,3]
[4,5,6,8,3,1,2,7]=>[4,1,3]
[4,5,7,3,8,1,6,2]=>[3,2,2,1]
[4,5,8,3,2,1,6,7]=>[3,1,1,3]
[4,6,2,3,7,8,5,1]=>[2,4,1,1]
[4,6,2,3,8,5,1,7]=>[2,3,1,2]
[4,6,2,7,3,8,5,1]=>[2,2,2,1,1]
[4,6,2,7,8,5,1,3]=>[2,3,1,2]
[4,6,7,3,2,8,5,1]=>[3,1,2,1,1]
[4,6,8,3,2,5,1,7]=>[3,1,2,2]
[4,7,2,3,1,8,6,5]=>[2,2,2,1,1]
[4,7,2,8,3,5,6,1]=>[2,2,3,1]
[4,7,8,3,2,5,6,1]=>[3,1,3,1]
[4,8,2,3,1,5,6,7]=>[2,2,4]
[5,1,2,6,8,4,3,7]=>[1,4,1,2]
[5,1,2,7,4,8,6,3]=>[1,3,2,1,1]
[5,1,2,7,8,4,6,3]=>[1,4,2,1]
[5,1,2,8,4,3,6,7]=>[1,3,1,3]
[5,1,6,3,8,4,2,7]=>[1,2,2,1,2]
[5,1,6,7,4,8,2,3]=>[1,3,2,2]
[5,1,6,7,8,4,2,3]=>[1,4,1,2]
[5,1,8,3,4,2,6,7]=>[1,2,2,3]
[5,6,2,3,8,4,1,7]=>[2,3,1,2]
[5,6,2,7,8,4,1,3]=>[2,3,1,2]
[5,6,8,3,4,2,1,7]=>[3,2,1,2]
[5,7,2,3,4,8,6,1]=>[2,4,1,1]
[5,7,2,3,8,4,6,1]=>[2,3,2,1]
[5,7,8,3,4,2,6,1]=>[3,2,2,1]
[5,8,2,3,4,1,6,7]=>[2,3,3]
[6,1,2,3,7,8,5,4]=>[1,5,1,1]
[6,1,2,3,8,5,4,7]=>[1,4,1,2]
[6,1,2,7,8,5,4,3]=>[1,4,1,1,1]
[6,1,2,8,4,5,3,7]=>[1,3,2,2]
[6,1,7,3,4,8,5,2]=>[1,2,3,1,1]
[6,1,7,3,8,5,4,2]=>[1,2,2,1,1,1]
[6,1,7,8,4,5,3,2]=>[1,3,2,1,1]
[6,1,8,3,4,5,2,7]=>[1,2,3,2]
[6,7,2,3,8,5,4,1]=>[2,3,1,1,1]
[6,7,2,8,4,5,3,1]=>[2,2,2,1,1]
[6,8,2,3,4,5,1,7]=>[2,4,2]
[7,1,2,3,4,8,6,5]=>[1,5,1,1]
[7,1,2,8,4,5,6,3]=>[1,3,3,1]
[7,1,8,3,4,5,6,2]=>[1,2,4,1]
[6,4,1,8,2,3,7,5]=>[1,1,2,3,1]
[5,8,1,2,4,3,7,6]=>[2,3,2,1]
[1,3,5,7,2,6,4,8]=>[4,2,2]
[3,5,8,6,1,2,4,7]=>[3,1,4]
[3,1,6,8,2,4,7,5]=>[1,3,3,1]
[3,6,2,8,1,5,7,4]=>[2,2,3,1]
[2,6,1,3,8,4,7,5]=>[2,3,2,1]
[1,7,5,2,3,4,6,8]=>[2,1,5]
[2,7,5,1,3,8,4,6]=>[2,1,3,2]
[8,2,5,7,4,6,1,3]=>[1,3,2,2]
[8,2,1,3,7,6,4,5]=>[1,1,3,1,2]
[8,2,5,1,3,7,4,6]=>[1,2,3,2]
[8,2,7,5,3,1,6,4]=>[1,2,1,1,2,1]
[8,2,6,5,4,7,1,3]=>[1,2,1,2,2]
[7,6,5,2,4,8,1,3]=>[1,1,1,3,2]
[7,8,2,5,3,1,6,4]=>[2,2,1,2,1]
[7,1,8,6,3,2,4,5]=>[1,2,1,1,3]
[6,8,1,5,3,2,4,7]=>[2,2,1,3]
[1,6,7,5,3,2,4,8]=>[3,1,1,3]
[6,5,1,2,4,8,3,7]=>[1,1,4,2]
[7,8,1,6,4,2,3,5]=>[2,2,1,3]
[8,4,1,2,5,6,3,7]=>[1,1,4,2]
[1,7,3,6,5,2,4,8]=>[2,2,1,3]
[8,1,3,7,2,6,4,5]=>[1,3,2,2]
[7,3,2,6,5,1,8,4]=>[1,1,2,1,2,1]
[7,8,4,2,5,6,1,3]=>[2,1,3,2]
[8,2,7,4,5,6,1,3]=>[1,2,3,2]
[8,2,3,6,5,1,7,4]=>[1,3,1,2,1]
[4,8,6,5,7,3,2,1]=>[2,1,2,1,1,1]
[3,8,7,5,4,6,2,1]=>[2,1,1,2,1,1]
[4,8,5,6,7,3,2,1]=>[2,3,1,1,1]
[2,8,7,6,4,3,5,1]=>[2,1,1,1,2,1]
[3,8,7,4,5,6,2,1]=>[2,1,3,1,1]
[1,8,7,6,5,3,2,4]=>[2,1,1,1,1,2]
[2,8,7,6,3,4,5,1]=>[2,1,1,3,1]
[1,8,7,6,5,2,3,4]=>[2,1,1,1,3]
[7,2,8,6,5,4,1,3]=>[1,2,1,1,1,2]
[7,2,8,5,4,6,1,3]=>[1,2,1,2,2]
[6,3,2,8,5,1,7,4]=>[1,1,2,1,2,1]
[8,4,7,2,5,6,3,1]=>[1,2,3,1,1]
[6,8,5,4,3,1,7,2]=>[2,1,1,1,2,1]
[5,8,6,4,1,3,7,2]=>[2,1,1,3,1]
[4,8,6,1,5,3,7,2]=>[2,1,2,2,1]
[3,6,1,8,5,2,7,4]=>[2,2,1,2,1]
[3,4,1,2,8,6,7,5]=>[2,3,2,1]
[6,8,3,5,4,1,7,2]=>[2,2,1,2,1]
[7,2,5,8,3,6,1,4]=>[1,3,2,2]
[1,7,5,6,3,4,2,8]=>[2,2,2,2]
[7,2,6,8,5,3,1,4]=>[1,3,1,1,2]
[7,6,3,8,5,2,1,4]=>[1,1,2,1,1,2]
[7,2,6,4,8,3,1,5]=>[1,2,2,1,2]
[1,5,7,4,2,6,3,8]=>[3,1,2,2]
[4,2,3,1,7,8,5,6]=>[1,2,3,2]
[5,2,8,4,1,7,6,3]=>[1,2,1,2,1,1]
[8,6,3,4,7,2,5,1]=>[1,1,3,2,1]
[6,8,3,4,5,1,7,2]=>[2,3,2,1]
[1,6,3,2,5,8,4,7]=>[2,1,3,2]
[8,3,2,1,5,4,7,6]=>[1,1,1,2,2,1]
[6,3,7,1,5,8,4,2]=>[1,2,3,1,1]
[2,5,1,8,4,3,7,6]=>[2,2,1,2,1]
[6,2,5,4,8,1,3,7]=>[1,2,2,3]
[4,3,1,6,5,8,2,7]=>[1,1,2,2,2]
[1,3,5,4,6,8,2,7]=>[3,3,2]
[6,1,3,4,5,8,2,7]=>[1,5,2]
[8,3,4,1,5,2,7,6]=>[1,2,2,2,1]
[7,5,4,2,6,8,3,1]=>[1,1,1,3,1,1]
[8,2,6,4,1,7,3,5]=>[1,2,1,2,2]
[7,3,8,4,5,2,1,6]=>[1,2,2,1,2]
[7,2,5,1,8,4,3,6]=>[1,2,2,1,2]
[1,7,3,2,5,4,8,6]=>[2,1,2,2,1]
[8,7,2,1,5,3,4,6]=>[1,1,1,2,3]
[3,6,1,5,8,7,4,2]=>[2,3,1,1,1]
[8,3,6,4,5,1,7,2]=>[1,2,2,2,1]
[5,4,6,8,1,2,7,3]=>[1,3,3,1]
[6,4,7,2,3,5,8,1]=>[1,2,4,1]
[6,8,4,1,3,5,7,2]=>[2,1,4,1]
[3,4,7,8,6,2,5,1]=>[4,1,2,1]
[4,1,3,5,7,8,6,2]=>[1,5,1,1]
[6,5,1,8,4,7,3,2]=>[1,1,2,2,1,1]
[5,3,1,8,4,7,6,2]=>[1,1,2,2,1,1]
[8,2,7,4,6,1,3,5]=>[1,2,2,3]
[4,7,3,2,8,1,6,5]=>[2,1,2,2,1]
[6,3,1,4,7,2,8,5]=>[1,1,3,2,1]
[8,7,3,6,1,5,2,4]=>[1,1,2,2,2]
[7,4,3,6,8,2,5,1]=>[1,1,3,2,1]
[2,4,7,3,8,5,6,1]=>[3,2,2,1]
[2,8,6,1,5,7,3,4]=>[2,1,3,2]
[7,8,2,5,4,3,1,6]=>[2,2,1,1,2]
[1,8,3,4,2,7,6,5]=>[2,2,2,1,1]
[8,5,3,7,4,2,6,1]=>[1,1,2,1,2,1]
[5,7,3,2,4,1,8,6]=>[2,1,2,2,1]
[2,8,3,4,7,1,5,6]=>[2,3,3]
[4,1,3,6,7,8,2,5]=>[1,5,2]
[1,7,6,3,2,5,8,4]=>[2,1,1,3,1]
[3,8,1,5,6,2,7,4]=>[2,3,2,1]
[8,2,5,6,1,7,4,3]=>[1,3,2,1,1]
[7,1,5,2,8,6,4,3]=>[1,2,2,1,1,1]
[6,5,4,8,7,2,1,3]=>[1,1,2,1,1,2]
[1,8,6,4,5,2,7,3]=>[2,1,2,2,1]
[1,8,5,3,6,2,7,4]=>[2,1,2,2,1]
[3,6,2,1,7,5,8,4]=>[2,1,2,2,1]
[2,5,4,1,8,7,6,3]=>[2,1,2,1,1,1]
[4,7,2,6,5,8,1,3]=>[2,2,2,2]
[6,8,1,4,2,7,3,5]=>[2,2,2,2]
[6,3,4,7,1,8,2,5]=>[1,3,2,2]
[3,4,7,8,2,5,6,1]=>[4,3,1]
[1,8,2,4,5,6,7,3]=>[2,5,1]
[5,2,4,1,6,8,7,3]=>[1,2,3,1,1]
[3,2,5,7,6,1,8,4]=>[1,3,1,2,1]
[4,3,5,6,1,8,7,2]=>[1,3,2,1,1]
[5,3,4,1,7,6,8,2]=>[1,2,2,2,1]
[3,1,4,6,5,7,8,2]=>[1,3,3,1]
[1,4,7,3,5,6,8,2]=>[3,4,1]
[5,1,3,6,4,8,7,2]=>[1,3,2,1,1]
[1,3,2,7,5,8,6,4]=>[2,2,2,1,1]
[1,4,2,5,8,3,7,6]=>[2,3,2,1]
[1,4,2,7,8,5,6,3]=>[2,3,2,1]
[5,1,2,6,8,4,7,3]=>[1,4,2,1]
[4,1,2,6,8,5,3,7]=>[1,4,1,2]
[1,5,2,4,8,7,6,3]=>[2,3,1,1,1]
[1,2,6,4,8,7,5,3]=>[3,2,1,1,1]
[1,2,7,4,8,6,5,3]=>[3,2,1,1,1]
[1,3,2,7,5,8,4,6]=>[2,2,2,2]
[1,3,2,8,5,7,4,6]=>[2,2,2,2]
[1,4,2,5,8,7,3,6]=>[2,3,1,2]
[1,5,2,4,8,7,3,6]=>[2,3,1,2]
[1,2,6,4,8,7,3,5]=>[3,2,1,2]
[1,2,7,8,5,6,3,4]=>[4,2,2]
[1,2,6,8,5,7,3,4]=>[4,2,2]
[1,5,6,8,2,7,3,4]=>[4,2,2]
[1,3,8,2,6,7,4,5]=>[3,3,2]
[1,4,7,2,8,6,3,5]=>[3,2,1,2]
[1,6,7,8,2,5,3,4]=>[4,2,2]
[1,5,7,8,2,3,6,4]=>[4,3,1]
[1,5,2,7,8,4,6,3]=>[2,3,2,1]
[1,4,7,2,8,3,6,5]=>[3,2,2,1]
[1,3,6,2,4,8,7,5]=>[3,3,1,1]
[1,6,7,3,4,8,5,2]=>[3,3,1,1]
[1,5,3,7,4,8,6,2]=>[2,2,2,1,1]
[2,8,4,1,5,3,7,6]=>[2,1,2,2,1]
[3,8,4,1,5,7,2,6]=>[2,1,3,2]
[1,3,6,4,2,8,7,5]=>[3,1,2,1,1]
[1,3,7,4,2,8,6,5]=>[3,1,2,1,1]
[1,3,8,4,2,7,6,5]=>[3,1,2,1,1]
[1,2,8,4,7,3,6,5]=>[3,2,2,1]
[1,2,7,4,8,3,6,5]=>[3,2,2,1]
[1,2,6,4,8,3,7,5]=>[3,2,2,1]
[1,5,2,4,8,3,7,6]=>[2,3,2,1]
[1,8,4,5,7,2,3,6]=>[2,3,3]
[1,8,3,5,2,7,4,6]=>[2,2,2,2]
[2,8,3,5,1,4,7,6]=>[2,2,3,1]
[1,3,8,6,2,7,4,5]=>[3,1,2,2]
[1,4,8,6,7,2,3,5]=>[3,2,3]
[1,5,6,8,7,2,3,4]=>[4,1,3]
[1,2,6,8,5,3,7,4]=>[4,1,2,1]
[1,2,5,8,7,3,6,4]=>[4,1,2,1]
[1,2,6,8,7,3,5,4]=>[4,1,2,1]
[1,2,7,8,6,3,5,4]=>[4,1,2,1]
[1,6,7,8,5,2,3,4]=>[4,1,3]
[1,5,7,8,6,2,3,4]=>[4,1,3]
[1,4,7,6,8,2,3,5]=>[3,2,3]
[1,3,7,6,2,8,4,5]=>[3,1,2,2]
[2,3,8,7,4,1,6,5]=>[3,1,1,2,1]
[1,2,8,4,7,6,3,5]=>[3,2,1,2]
[1,2,5,8,7,6,3,4]=>[4,1,1,2]
[1,2,6,8,7,5,3,4]=>[4,1,1,2]
[1,2,7,8,6,5,3,4]=>[4,1,1,2]
[5,2,6,7,3,4,8,1]=>[1,3,3,1]
[5,2,4,7,6,3,8,1]=>[1,3,1,2,1]
[5,6,2,1,7,8,3,4]=>[2,1,3,2]
[5,6,2,1,4,8,7,3]=>[2,1,3,1,1]
[2,6,1,4,5,8,7,3]=>[2,4,1,1]
[5,4,2,7,6,3,8,1]=>[1,1,2,1,2,1]
[2,3,7,6,4,5,8,1]=>[3,1,3,1]
[2,6,1,7,5,8,3,4]=>[2,2,2,2]
[2,6,1,7,4,8,5,3]=>[2,2,2,1,1]
[5,1,2,7,8,4,3,6]=>[1,4,1,2]
[2,6,1,7,4,8,3,5]=>[2,2,2,2]
[3,6,4,1,7,8,2,5]=>[2,1,3,2]
[5,4,6,1,3,8,7,2]=>[1,2,3,1,1]
[3,6,4,1,5,8,7,2]=>[2,1,3,1,1]
[2,6,1,5,4,8,7,3]=>[2,2,2,1,1]
[2,6,1,4,7,8,5,3]=>[2,4,1,1]
[5,1,2,4,8,6,7,3]=>[1,4,2,1]
[5,1,2,4,8,7,3,6]=>[1,4,1,2]
[5,1,2,4,8,7,6,3]=>[1,4,1,1,1]
[1,2,3,8,5,4,7,6]=>[4,1,2,1]
[4,3,1,2,8,5,7,6]=>[1,1,3,2,1]
[2,1,5,3,8,6,4,7]=>[1,2,2,1,2]
[1,2,3,8,5,6,4,7]=>[4,2,2]
[1,2,3,8,6,4,5,7]=>[4,1,3]
[1,2,3,8,6,5,4,7]=>[4,1,1,2]
[1,2,3,8,5,4,6,7]=>[4,1,3]
[2,6,1,5,4,8,3,7]=>[2,2,2,2]
[5,1,2,4,8,6,3,7]=>[1,4,1,2]
[5,1,2,4,8,3,7,6]=>[1,4,2,1]
[5,6,3,1,4,8,2,7]=>[2,1,3,2]
[2,5,4,3,1,8,6,7]=>[2,1,1,2,2]
[5,4,6,3,1,8,7,2]=>[1,2,1,2,1,1]
[3,6,4,5,1,8,7,2]=>[2,2,2,1,1]
[3,6,5,4,1,8,7,2]=>[2,1,1,2,1,1]
[5,2,6,1,7,8,4,3]=>[1,2,3,1,1]
[5,1,6,2,8,7,3,4]=>[1,2,2,1,2]
[2,1,3,7,8,6,4,5]=>[1,4,1,2]
[2,1,3,7,8,5,6,4]=>[1,4,2,1]
[5,2,4,1,7,8,6,3]=>[1,2,3,1,1]
[4,3,1,2,8,6,7,5]=>[1,1,3,2,1]
[5,1,4,2,8,6,7,3]=>[1,2,2,2,1]
[2,1,3,6,8,5,7,4]=>[1,4,2,1]
[1,2,3,8,6,7,4,5]=>[4,2,2]
[1,2,3,8,7,5,4,6]=>[4,1,1,2]
[1,2,3,8,7,4,5,6]=>[4,1,3]
[1,2,3,8,5,7,4,6]=>[4,2,2]
[2,1,3,6,8,7,4,5]=>[1,4,1,2]
[5,4,1,2,8,7,6,3]=>[1,1,3,1,1,1]
[3,1,6,2,8,7,5,4]=>[1,2,2,1,1,1]
[1,2,8,4,5,3,6,7]=>[3,2,3]
[1,8,3,4,2,5,6,7]=>[2,2,4]
[1,8,4,3,2,5,6,7]=>[2,1,1,4]
[8,4,7,6,5,3,2,1]=>[1,2,1,1,1,1,1]
[8,4,7,5,6,3,2,1]=>[1,2,2,1,1,1]
[8,5,7,4,6,3,2,1]=>[1,2,2,1,1,1]
[8,7,6,3,5,4,2,1]=>[1,1,1,2,1,1,1]
[8,6,7,3,5,4,2,1]=>[1,2,2,1,1,1]
[8,5,7,3,6,4,2,1]=>[1,2,2,1,1,1]
[8,1,7,4,6,5,3,2]=>[1,2,2,1,1,1]
[8,1,7,3,6,5,4,2]=>[1,2,2,1,1,1]
[8,2,7,3,6,5,4,1]=>[1,2,2,1,1,1]
[8,3,7,2,6,5,4,1]=>[1,2,2,1,1,1]
[8,5,7,2,6,4,3,1]=>[1,2,2,1,1,1]
[8,6,7,2,5,4,3,1]=>[1,2,2,1,1,1]
[8,7,6,2,5,4,3,1]=>[1,1,1,2,1,1,1]
[8,4,7,1,6,5,3,2]=>[1,2,2,1,1,1]
[8,3,7,1,6,5,4,2]=>[1,2,2,1,1,1]
[8,2,7,1,6,5,4,3]=>[1,2,2,1,1,1]
[8,1,7,2,6,5,4,3]=>[1,2,2,1,1,1]
[8,7,6,2,5,3,4,1]=>[1,1,1,2,2,1]
[8,1,7,6,5,3,4,2]=>[1,2,1,1,2,1]
[8,3,7,6,5,2,4,1]=>[1,2,1,1,2,1]
[8,4,7,6,5,2,3,1]=>[1,2,1,1,2,1]
[8,5,7,6,4,2,3,1]=>[1,2,1,1,2,1]
[8,6,7,5,4,1,3,2]=>[1,2,1,1,2,1]
[8,5,7,6,4,1,3,2]=>[1,2,1,1,2,1]
[8,3,7,6,5,1,4,2]=>[1,2,1,1,2,1]
[8,7,6,4,5,1,3,2]=>[1,1,1,2,2,1]
[8,7,6,2,5,1,4,3]=>[1,1,1,2,2,1]
[8,7,6,1,5,2,4,3]=>[1,1,1,2,2,1]
[6,8,1,3,2,5,4,7]=>[2,2,2,2]
[6,8,1,4,2,5,3,7]=>[2,2,2,2]
[7,8,3,6,1,4,2,5]=>[2,2,2,2]
[7,8,2,5,3,6,1,4]=>[2,2,2,2]
[7,8,2,5,1,4,3,6]=>[2,2,2,2]
[7,8,1,4,3,6,2,5]=>[2,2,2,2]
[5,8,1,4,3,7,2,6]=>[2,2,2,2]
[6,8,2,5,1,4,3,7]=>[2,2,2,2]
[6,8,2,5,3,7,1,4]=>[2,2,2,2]
[6,8,2,5,4,7,1,3]=>[2,2,2,2]
[2,5,4,7,6,8,1,3]=>[2,2,2,2]
[2,5,3,7,6,8,1,4]=>[2,2,2,2]
[2,5,1,4,3,7,6,8]=>[2,2,2,2]
[2,6,1,4,3,7,5,8]=>[2,2,2,2]
[2,6,5,8,1,4,3,7]=>[2,2,2,2]
[2,6,1,5,3,7,4,8]=>[2,2,2,2]
[2,6,3,7,4,8,1,5]=>[2,2,2,2]
[2,6,4,7,5,8,1,3]=>[2,2,2,2]
[5,8,3,6,4,7,1,2]=>[2,2,2,2]
[5,8,2,6,4,7,1,3]=>[2,2,2,2]
[4,8,2,6,3,7,1,5]=>[2,2,2,2]
[4,8,1,5,3,7,2,6]=>[2,2,2,2]
[4,8,1,5,2,6,3,7]=>[2,2,2,2]
[4,8,3,7,1,5,2,6]=>[2,2,2,2]
[6,8,3,7,1,4,2,5]=>[2,2,2,2]
[5,8,1,3,2,6,4,7]=>[2,2,2,2]
[5,8,4,7,1,3,2,6]=>[2,2,2,2]
[6,8,4,7,1,3,2,5]=>[2,2,2,2]
[6,8,5,7,1,3,2,4]=>[2,2,2,2]
[5,7,6,8,2,4,1,3]=>[2,2,2,2]
[4,7,6,8,1,3,2,5]=>[2,2,2,2]
[4,7,5,8,1,3,2,6]=>[2,2,2,2]
[4,7,1,3,2,6,5,8]=>[2,2,2,2]
[3,7,1,4,2,6,5,8]=>[2,2,2,2]
[3,7,5,8,1,4,2,6]=>[2,2,2,2]
[3,7,6,8,1,4,2,5]=>[2,2,2,2]
[3,7,6,8,2,5,1,4]=>[2,2,2,2]
[4,7,6,8,2,5,1,3]=>[2,2,2,2]
[4,7,5,8,3,6,1,2]=>[2,2,2,2]
[4,7,5,8,2,6,1,3]=>[2,2,2,2]
[3,7,5,8,2,6,1,4]=>[2,2,2,2]
[3,7,4,8,2,6,1,5]=>[2,2,2,2]
[3,7,4,8,1,5,2,6]=>[2,2,2,2]
[3,7,1,5,2,6,4,8]=>[2,2,2,2]
[3,7,2,6,1,5,4,8]=>[2,2,2,2]
[3,7,2,6,5,8,1,4]=>[2,2,2,2]
[4,7,3,6,5,8,1,2]=>[2,2,2,2]
[3,6,5,8,4,7,1,2]=>[2,2,2,2]
[2,6,5,8,4,7,1,3]=>[2,2,2,2]
[2,6,5,8,3,7,1,4]=>[2,2,2,2]
[2,6,3,7,1,5,4,8]=>[2,2,2,2]
[7,6,4,2,8,5,3,1]=>[1,1,1,2,1,1,1]
[7,6,4,3,8,2,5,1]=>[1,1,1,2,2,1]
[7,6,4,8,5,2,3,1]=>[1,1,2,1,2,1]
[6,8,4,3,7,2,1,5]=>[2,1,2,1,2]
[6,7,4,3,5,1,8,2]=>[2,1,2,2,1]
[6,7,3,5,4,8,2,1]=>[2,2,2,1,1]
[6,8,3,7,5,2,4,1]=>[2,2,1,2,1]
[7,6,8,3,5,2,4,1]=>[1,2,2,2,1]
[7,6,3,5,8,2,4,1]=>[1,1,3,2,1]
[7,6,3,5,2,4,8,1]=>[1,1,2,3,1]
[7,6,4,2,5,1,8,3]=>[1,1,1,2,2,1]
[7,6,2,8,4,1,5,3]=>[1,1,2,1,2,1]
[7,6,3,8,2,4,1,5]=>[1,1,2,2,2]
[7,6,3,4,8,2,5,1]=>[1,1,3,2,1]
[6,8,3,7,4,5,2,1]=>[2,2,2,1,1]
[6,7,3,5,8,4,2,1]=>[2,3,1,1,1]
[5,7,8,3,6,2,1,4]=>[3,2,1,2]
[5,8,3,6,7,2,1,4]=>[2,3,1,2]
[6,3,4,8,7,2,5,1]=>[1,3,1,2,1]
[6,3,8,4,7,2,1,5]=>[1,2,2,1,2]
[6,2,8,4,1,7,5,3]=>[1,2,1,2,1,1]
[6,2,7,4,1,5,3,8]=>[1,2,1,2,2]
[6,3,4,7,5,8,2,1]=>[1,3,2,1,1]
[6,3,5,7,8,4,2,1]=>[1,4,1,1,1]
[5,7,3,6,8,2,1,4]=>[2,3,1,2]
[5,6,8,3,7,2,1,4]=>[3,2,1,2]
[5,6,7,3,4,1,8,2]=>[3,2,2,1]
[4,6,7,8,3,5,2,1]=>[4,2,1,1]
[4,6,8,3,5,7,2,1]=>[3,3,1,1]
[4,7,3,5,6,8,2,1]=>[2,4,1,1]
[4,7,3,5,8,2,6,1]=>[2,3,2,1]
[5,3,4,7,8,2,1,6]=>[1,4,1,2]
[5,3,8,2,4,1,6,7]=>[1,2,2,3]
[5,3,4,8,2,6,1,7]=>[1,3,2,2]
[4,8,3,6,2,5,7,1]=>[2,2,3,1]
[4,8,3,5,7,2,6,1]=>[2,3,2,1]
[4,8,3,5,6,7,2,1]=>[2,4,1,1]
[4,7,8,3,5,6,2,1]=>[3,3,1,1]
[4,7,8,3,6,2,5,1]=>[3,2,2,1]
[4,8,3,6,7,2,5,1]=>[2,3,2,1]
[4,8,3,7,2,5,6,1]=>[2,2,3,1]
[5,3,4,8,2,7,6,1]=>[1,3,2,1,1]
[5,3,8,2,4,1,7,6]=>[1,2,2,2,1]
[5,2,8,4,1,7,3,6]=>[1,2,1,2,2]
[6,4,2,5,1,8,7,3]=>[1,1,2,2,1,1]
[6,4,3,5,8,2,1,7]=>[1,1,3,1,2]
[6,3,5,8,7,2,4,1]=>[1,3,1,2,1]
[5,8,3,7,2,6,4,1]=>[2,2,2,1,1]
[5,7,3,4,8,2,1,6]=>[2,3,1,2]
[5,8,4,2,3,1,6,7]=>[2,1,2,3]
[5,8,4,2,3,1,7,6]=>[2,1,2,2,1]
[6,4,5,3,8,2,1,7]=>[1,2,2,1,2]
[6,4,8,5,3,7,2,1]=>[1,2,1,2,1,1]
[6,4,3,8,5,7,2,1]=>[1,1,2,2,1,1]
[6,4,2,8,5,3,1,7]=>[1,1,2,1,1,2]
[6,4,2,7,3,1,8,5]=>[1,1,2,1,2,1]
[6,4,3,7,8,5,2,1]=>[1,1,3,1,1,1]
[6,4,5,3,7,1,8,2]=>[1,2,2,2,1]
[5,7,4,2,3,1,6,8]=>[2,1,2,3]
[5,6,3,7,1,8,2,4]=>[2,2,2,2]
[5,6,3,4,7,1,8,2]=>[2,3,2,1]
[5,6,3,4,8,2,1,7]=>[2,3,1,2]
[6,3,5,7,4,8,2,1]=>[1,3,2,1,1]
[6,3,5,4,7,8,2,1]=>[1,2,3,1,1]
[6,4,3,5,7,1,8,2]=>[1,1,3,2,1]
[6,4,2,5,1,7,3,8]=>[1,1,2,2,2]
[5,3,7,2,4,1,6,8]=>[1,2,2,3]
[5,3,4,7,2,6,1,8]=>[1,3,2,2]
[4,7,3,6,2,5,8,1]=>[2,2,3,1]
[4,7,3,6,8,2,5,1]=>[2,3,2,1]
[4,6,7,3,5,8,2,1]=>[3,3,1,1]
[4,5,7,8,3,6,2,1]=>[4,2,1,1]
[4,5,8,3,6,7,2,1]=>[3,3,1,1]
[4,5,8,3,7,2,6,1]=>[3,2,2,1]
[5,3,4,6,8,2,1,7]=>[1,4,1,2]
[5,3,6,8,2,1,4,7]=>[1,3,1,3]
[5,3,6,7,1,8,2,4]=>[1,3,2,2]
[5,3,4,6,7,1,8,2]=>[1,4,2,1]
[4,6,3,5,7,8,2,1]=>[2,4,1,1]
[4,5,7,3,6,8,2,1]=>[3,3,1,1]
[4,5,6,8,3,7,2,1]=>[4,2,1,1]
[5,7,4,8,6,3,2,1]=>[2,2,1,1,1,1]
[3,2,6,5,1,8,7,4]=>[1,2,1,2,1,1]
[3,5,6,7,2,8,4,1]=>[4,2,1,1]
[1,6,2,5,3,4,8,7]=>[2,2,3,1]
[1,3,8,2,4,6,5,7]=>[3,3,2]
[1,7,2,3,6,4,8,5]=>[2,3,2,1]
[1,6,8,2,5,3,7,4]=>[3,2,2,1]
[1,8,2,5,3,4,7,6]=>[2,2,3,1]
[1,8,2,3,6,4,7,5]=>[2,3,2,1]
[1,3,5,2,8,4,7,6]=>[3,2,2,1]
[1,2,7,3,5,4,6,8]=>[3,2,3]
[1,8,2,7,3,4,6,5]=>[2,2,3,1]
[1,5,8,2,3,7,4,6]=>[3,3,2]
[1,6,8,2,3,5,4,7]=>[3,3,2]
[5,3,6,1,2,4,8,7]=>[1,2,4,1]
[7,1,5,8,4,2,3,6]=>[1,3,1,3]
[8,1,5,7,4,2,3,6]=>[1,3,1,3]
[7,1,4,5,8,2,3,6]=>[1,4,3]
[7,4,1,6,2,8,3,5]=>[1,1,2,2,2]
[8,4,1,7,2,6,3,5]=>[1,1,2,2,2]
[8,1,4,7,5,2,3,6]=>[1,3,1,3]
[8,1,5,4,7,2,3,6]=>[1,2,2,3]
[2,1,7,5,8,3,4,6]=>[1,2,2,3]
[7,1,5,4,8,2,3,6]=>[1,2,2,3]
[7,1,4,8,5,2,3,6]=>[1,3,1,3]
[6,4,1,7,2,3,8,5]=>[1,1,2,3,1]
[7,8,3,1,2,4,6,5]=>[2,1,4,1]
[8,7,1,6,4,2,3,5]=>[1,1,2,1,3]
[8,6,1,7,4,2,3,5]=>[1,1,2,1,3]
[7,6,1,8,4,2,3,5]=>[1,1,2,1,3]
[7,3,8,1,2,4,6,5]=>[1,2,4,1]
[8,3,7,1,2,4,6,5]=>[1,2,4,1]
[8,3,6,1,2,4,7,5]=>[1,2,4,1]
[8,3,7,5,1,2,4,6]=>[1,2,1,4]
[7,3,6,1,2,4,8,5]=>[1,2,4,1]
[6,7,1,8,4,2,3,5]=>[2,2,1,3]
[6,8,1,7,4,2,3,5]=>[2,2,1,3]
[7,1,8,5,4,2,3,6]=>[1,2,1,1,3]
[7,1,8,4,5,2,3,6]=>[1,2,2,3]
[2,1,7,8,5,3,4,6]=>[1,3,1,3]
[7,6,3,1,2,4,8,5]=>[1,1,1,4,1]
[6,1,2,3,8,7,5,4]=>[1,4,1,1,1]
[6,8,1,4,2,3,7,5]=>[2,2,3,1]
[6,8,3,1,2,7,4,5]=>[2,1,3,2]
[6,7,3,1,2,8,4,5]=>[2,1,3,2]
[6,7,1,4,2,3,8,5]=>[2,2,3,1]
[4,3,6,8,5,7,1,2]=>[1,3,2,2]
[6,1,2,5,4,8,3,7]=>[1,3,2,2]
[3,2,8,5,4,1,7,6]=>[1,2,1,1,2,1]
[7,8,2,1,4,6,3,5]=>[2,1,3,2]
[7,2,1,5,8,3,4,6]=>[1,1,3,3]
[2,4,8,5,1,3,6,7]=>[3,1,4]
[3,5,6,1,8,4,2,7]=>[3,2,1,2]
[1,3,6,8,7,4,2,5]=>[4,1,1,2]
[1,2,8,5,7,3,4,6]=>[3,2,3]
[2,6,1,5,8,3,4,7]=>[2,3,3]
[5,7,1,6,8,4,3,2]=>[2,3,1,1,1]
[4,8,1,2,5,7,3,6]=>[2,4,2]
[8,4,6,2,5,7,3,1]=>[1,2,3,1,1]
[8,3,6,4,7,2,5,1]=>[1,2,2,2,1]
[3,8,1,4,7,2,5,6]=>[2,3,3]
[1,7,8,4,6,2,5,3]=>[3,2,2,1]
[3,7,4,8,5,1,6,2]=>[2,2,1,2,1]
[3,7,1,6,5,4,8,2]=>[2,2,1,2,1]
[2,7,3,1,5,8,4,6]=>[2,1,3,2]
[2,7,4,6,8,1,3,5]=>[2,3,3]
[2,7,5,8,6,4,1,3]=>[2,2,1,1,2]
[8,2,6,7,5,4,3,1]=>[1,3,1,1,1,1]
[3,8,7,1,6,4,5,2]=>[2,1,2,2,1]
[3,6,8,2,7,4,1,5]=>[3,2,1,2]
[1,5,2,8,7,4,6,3]=>[2,2,1,2,1]
[3,4,2,7,8,1,6,5]=>[2,3,2,1]
[4,1,3,7,5,6,8,2]=>[1,3,3,1]
[6,3,8,1,7,4,2,5]=>[1,2,2,1,2]
[6,5,8,7,1,4,2,3]=>[1,2,1,2,2]
[4,1,7,3,8,5,2,6]=>[1,2,2,1,2]
[3,6,1,4,5,8,2,7]=>[2,4,2]
[1,6,7,4,5,3,8,2]=>[3,2,2,1]
[6,1,7,3,5,4,8,2]=>[1,2,2,2,1]
[6,3,1,2,5,8,4,7]=>[1,1,4,2]
[1,4,7,2,8,5,3,6]=>[3,2,1,2]
[5,6,8,7,2,4,1,3]=>[3,1,2,2]
[6,8,5,7,1,2,4,3]=>[2,2,3,1]
[2,8,4,1,7,5,6,3]=>[2,1,2,2,1]
[8,2,4,3,7,5,6,1]=>[1,2,2,2,1]
[6,8,2,1,5,7,3,4]=>[2,1,3,2]
[7,2,8,4,1,6,3,5]=>[1,2,1,2,2]
[1,2,4,8,6,5,3,7]=>[4,1,1,2]
[7,1,5,6,8,4,3,2]=>[1,4,1,1,1]
[2,7,8,1,4,6,3,5]=>[3,3,2]
[4,8,2,5,7,1,6,3]=>[2,3,2,1]
[4,1,6,8,5,3,7,2]=>[1,3,1,2,1]
[5,2,6,4,8,3,1,7]=>[1,2,2,1,2]
[6,7,1,3,4,5,8,2]=>[2,5,1]
[1,7,3,2,4,8,5,6]=>[2,1,3,2]
[1,3,6,5,2,8,4,7]=>[3,1,2,2]
[7,1,6,5,3,4,8,2]=>[1,2,1,3,1]
[6,3,4,2,8,7,5,1]=>[1,2,2,1,1,1]
[4,3,8,7,5,2,6,1]=>[1,2,1,1,2,1]
[6,8,7,4,2,3,5,1]=>[2,1,1,3,1]
[3,6,4,5,2,8,7,1]=>[2,2,2,1,1]
[8,6,1,3,5,4,2,7]=>[1,1,3,1,2]
[5,3,8,6,1,2,4,7]=>[1,2,1,4]
[2,5,6,3,4,8,7,1]=>[3,3,1,1]
[2,5,3,6,8,7,4,1]=>[2,3,1,1,1]
[4,8,7,3,5,2,6,1]=>[2,1,2,2,1]
[3,8,7,2,6,4,5,1]=>[2,1,2,2,1]
[6,3,5,4,8,7,2,1]=>[1,2,2,1,1,1]
[4,3,8,6,1,5,2,7]=>[1,2,1,2,2]
[4,7,6,2,5,3,8,1]=>[2,1,2,2,1]
[7,5,2,6,8,1,4,3]=>[1,1,3,2,1]
[8,5,2,7,1,4,3,6]=>[1,1,2,2,2]
[1,8,5,3,6,2,4,7]=>[2,1,2,3]
[5,1,7,2,4,3,8,6]=>[1,2,2,2,1]
[1,5,3,4,8,6,2,7]=>[2,3,1,2]
[5,4,1,3,8,6,2,7]=>[1,1,3,1,2]
[5,1,8,6,3,4,2,7]=>[1,2,1,2,2]
[4,5,2,8,3,7,6,1]=>[2,2,2,1,1]
[8,2,3,7,6,4,5,1]=>[1,3,1,2,1]
[5,8,2,4,7,6,3,1]=>[2,3,1,1,1]
[6,8,2,5,3,4,7,1]=>[2,2,3,1]
[7,2,5,6,4,8,1,3]=>[1,3,2,2]
[1,6,7,4,8,2,3,5]=>[3,2,3]
[7,1,3,5,8,2,6,4]=>[1,4,2,1]
[8,2,1,3,5,6,7,4]=>[1,1,5,1]
[6,3,1,4,7,5,8,2]=>[1,1,3,2,1]
[4,1,3,8,2,6,7,5]=>[1,3,3,1]
[2,8,3,6,7,5,4,1]=>[2,3,1,1,1]
[3,1,7,2,8,5,4,6]=>[1,2,2,1,2]
[3,6,1,4,7,2,8,5]=>[2,3,2,1]
[1,5,8,4,7,2,3,6]=>[3,2,3]
[7,1,3,6,2,8,4,5]=>[1,3,2,2]
[6,2,7,4,5,8,1,3]=>[1,2,3,2]
[2,1,8,4,5,7,3,6]=>[1,2,3,2]
[1,8,5,7,3,2,4,6]=>[2,2,1,3]
[2,1,8,5,4,3,6,7]=>[1,2,1,1,3]
[2,7,4,1,5,3,8,6]=>[2,1,2,2,1]
[7,4,8,6,2,3,1,5]=>[1,2,1,2,2]
[2,7,1,4,6,3,8,5]=>[2,3,2,1]
[4,7,5,6,8,1,3,2]=>[2,3,2,1]
[7,1,3,2,8,5,4,6]=>[1,2,2,1,2]
[2,8,5,4,1,3,6,7]=>[2,1,1,4]
[5,1,7,4,2,3,8,6]=>[1,2,1,3,1]
[3,8,6,5,1,4,2,7]=>[2,1,1,2,2]
[1,3,4,8,6,5,2,7]=>[4,1,1,2]
[4,1,8,6,5,3,2,7]=>[1,2,1,1,1,2]
[4,8,5,2,7,3,6,1]=>[2,1,2,2,1]
[7,2,8,5,3,6,4,1]=>[1,2,1,2,1,1]
[5,2,8,4,3,7,6,1]=>[1,2,1,2,1,1]
[8,4,7,5,2,3,6,1]=>[1,2,1,3,1]
[7,5,2,8,4,6,1,3]=>[1,1,2,2,2]
[5,7,4,3,6,2,8,1]=>[2,1,2,2,1]
[6,7,5,1,2,8,3,4]=>[2,1,3,2]
[5,2,6,8,3,4,7,1]=>[1,3,3,1]
[7,6,2,4,5,8,3,1]=>[1,1,4,1,1]
[3,6,8,4,7,2,5,1]=>[3,2,2,1]
[7,6,3,8,4,2,5,1]=>[1,1,2,1,2,1]
[2,6,3,8,4,7,5,1]=>[2,2,2,1,1]
[7,2,3,6,5,8,4,1]=>[1,3,2,1,1]
[6,2,7,5,8,3,1,4]=>[1,2,2,1,2]
[2,8,3,6,4,5,7,1]=>[2,2,3,1]
[2,1,5,6,8,3,7,4]=>[1,4,2,1]
[5,8,1,2,6,4,7,3]=>[2,3,2,1]
[1,6,8,3,2,7,4,5]=>[3,1,2,2]
[6,5,7,2,8,4,1,3]=>[1,2,2,1,2]
[7,5,1,2,8,4,6,3]=>[1,1,3,2,1]
[5,4,8,3,6,2,7,1]=>[1,2,2,2,1]
[5,8,2,7,4,3,6,1]=>[2,2,1,2,1]
[6,4,5,8,2,7,3,1]=>[1,3,2,1,1]
[5,7,3,6,4,8,2,1]=>[2,2,2,1,1]
[1,5,6,4,8,2,7,3]=>[3,2,2,1]
[3,1,5,6,4,8,7,2]=>[1,3,2,1,1]
[1,3,6,2,5,7,8,4]=>[3,4,1]
[1,4,6,3,5,7,8,2]=>[3,4,1]
[3,5,1,6,4,7,8,2]=>[2,2,3,1]
[3,6,1,4,2,7,8,5]=>[2,2,3,1]
[2,4,6,3,1,7,8,5]=>[3,1,3,1]
[1,3,6,5,2,7,8,4]=>[3,1,3,1]
[1,2,6,4,3,8,5,7]=>[3,1,2,2]
[1,2,6,3,5,8,7,4]=>[3,3,1,1]
[2,3,5,1,8,4,7,6]=>[3,2,2,1]
[2,3,6,1,8,5,4,7]=>[3,2,1,2]
[1,2,7,4,6,8,3,5]=>[3,3,2]
[2,3,7,5,1,8,4,6]=>[3,1,2,2]
[4,7,2,5,3,8,6,1]=>[2,2,2,1,1]
[3,1,7,5,4,8,6,2]=>[1,2,1,2,1,1]
[1,2,7,6,4,8,5,3]=>[3,1,2,1,1]
[1,2,7,3,6,8,5,4]=>[3,3,1,1]
[2,3,6,1,8,5,7,4]=>[3,2,2,1]
[3,1,5,4,8,7,6,2]=>[1,2,2,1,1,1]
[1,2,5,8,4,7,3,6]=>[4,2,2]
[1,2,6,8,5,4,7,3]=>[4,1,2,1]
[1,3,6,8,5,2,7,4]=>[4,1,2,1]
[3,5,7,4,8,2,1,6]=>[3,2,1,2]
[2,4,7,6,8,3,1,5]=>[3,2,1,2]
[1,4,6,8,3,5,2,7]=>[4,2,2]
[1,3,6,8,5,2,4,7]=>[4,1,3]
[1,2,6,8,5,4,3,7]=>[4,1,1,2]
[1,2,5,8,4,3,7,6]=>[4,1,2,1]
[1,3,5,8,2,4,7,6]=>[4,3,1]
[1,3,6,8,2,5,4,7]=>[4,2,2]
[1,4,6,8,3,2,5,7]=>[4,1,3]
[3,5,7,4,8,1,2,6]=>[3,2,3]
[4,6,1,7,5,8,2,3]=>[2,2,2,2]
[2,3,6,7,5,8,1,4]=>[4,2,2]
[1,3,7,5,6,8,2,4]=>[3,3,2]
[2,3,6,5,8,1,7,4]=>[3,2,2,1]
[3,4,6,2,8,1,7,5]=>[3,2,2,1]
[3,5,4,6,8,2,1,7]=>[2,3,1,2]
[3,5,4,6,8,1,2,7]=>[2,3,3]
[1,2,4,7,5,8,3,6]=>[4,2,2]
[1,2,6,7,4,8,3,5]=>[4,2,2]
[3,6,4,7,1,8,5,2]=>[2,2,2,1,1]
[1,2,6,7,3,8,5,4]=>[4,2,1,1]
[1,2,5,7,3,8,6,4]=>[4,2,1,1]
[3,1,5,7,6,8,4,2]=>[1,3,2,1,1]
[3,5,4,6,8,2,7,1]=>[2,3,2,1]
[4,2,6,1,8,7,5,3]=>[1,2,2,1,1,1]
[3,1,6,5,8,7,4,2]=>[1,2,2,1,1,1]
[2,3,6,5,8,7,1,4]=>[3,2,1,2]
[1,2,7,4,6,8,5,3]=>[3,3,1,1]
[1,2,7,5,6,8,4,3]=>[3,3,1,1]
[3,1,6,7,5,8,4,2]=>[1,3,2,1,1]
[4,6,2,7,5,8,3,1]=>[2,2,2,1,1]
[3,5,7,4,8,2,6,1]=>[3,2,2,1]
[2,4,7,6,8,3,5,1]=>[3,2,2,1]
[1,4,6,8,3,5,7,2]=>[4,3,1]
[1,3,6,8,2,5,7,4]=>[4,3,1]
[1,3,5,8,2,7,4,6]=>[4,2,2]
[1,2,5,8,4,7,6,3]=>[4,2,1,1]
[1,2,4,8,7,3,6,5]=>[4,1,2,1]
[1,2,5,8,7,4,3,6]=>[4,1,1,2]
[1,3,5,8,7,2,4,6]=>[4,1,3]
[2,3,7,6,8,5,1,4]=>[3,2,1,2]
[5,7,1,2,8,6,4,3]=>[2,3,1,1,1]
[3,1,7,6,8,5,4,2]=>[1,2,2,1,1,1]
[1,2,6,8,5,7,4,3]=>[4,2,1,1]
[1,2,5,8,7,4,6,3]=>[4,1,2,1]
[1,2,4,8,7,6,3,5]=>[4,1,1,2]
[6,4,5,7,2,8,1,3]=>[1,3,2,2]
[5,3,4,7,2,8,1,6]=>[1,3,2,2]
[3,2,7,4,6,8,1,5]=>[1,2,3,2]
[5,3,6,2,7,1,4,8]=>[1,2,2,3]
[2,6,3,4,7,1,5,8]=>[2,3,3]
[2,7,3,4,5,8,1,6]=>[2,4,2]
[3,7,4,5,6,8,1,2]=>[2,4,2]
[2,5,7,3,6,8,1,4]=>[3,3,2]
[4,7,6,2,3,8,1,5]=>[2,1,3,2]
[7,3,5,2,4,8,1,6]=>[1,2,3,2]
[7,6,2,4,5,8,1,3]=>[1,1,4,2]
[6,5,2,3,4,8,1,7]=>[1,1,4,2]
[5,3,1,2,8,4,7,6]=>[1,1,3,2,1]
[6,5,2,3,7,1,4,8]=>[1,1,3,3]
[5,2,1,7,3,4,6,8]=>[1,1,2,4]
[5,2,1,8,3,4,6,7]=>[1,1,2,4]
[6,3,2,8,4,5,7,1]=>[1,1,2,3,1]
[7,3,1,2,8,4,6,5]=>[1,1,3,2,1]
[6,4,1,3,8,5,7,2]=>[1,1,3,2,1]
[6,2,3,1,8,4,7,5]=>[1,2,2,2,1]
[8,3,5,2,7,1,4,6]=>[1,2,2,3]
[8,6,2,4,7,1,5,3]=>[1,1,3,2,1]
[8,5,2,3,6,1,4,7]=>[1,1,3,3]
[8,2,1,7,3,4,5,6]=>[1,1,2,4]
[8,6,3,7,2,4,5,1]=>[1,1,2,3,1]
[7,1,6,2,3,4,5,8]=>[1,2,5]
[8,2,7,3,4,5,6,1]=>[1,2,4,1]
[8,1,6,2,3,4,5,7]=>[1,2,5]
[8,1,7,3,4,5,6,2]=>[1,2,4,1]
[8,6,1,7,2,4,5,3]=>[1,1,2,3,1]
[8,1,5,7,2,3,6,4]=>[1,3,3,1]
[1,7,5,8,2,3,6,4]=>[2,2,3,1]
[7,2,1,8,3,4,5,6]=>[1,1,2,4]
[7,3,8,2,4,5,6,1]=>[1,2,4,1]
[7,2,8,3,4,5,6,1]=>[1,2,4,1]
[1,7,8,3,4,5,6,2]=>[3,4,1]
[1,4,5,8,3,6,7,2]=>[4,3,1]
[2,5,7,1,8,3,6,4]=>[3,2,2,1]
[6,2,7,1,8,4,5,3]=>[1,2,2,2,1]
[4,7,1,3,8,5,6,2]=>[2,3,2,1]
[1,6,2,8,4,5,7,3]=>[2,2,3,1]
[4,1,3,6,8,2,7,5]=>[1,4,2,1]
[5,3,4,6,8,2,7,1]=>[1,4,2,1]
[4,6,3,8,7,1,2,5]=>[2,2,1,3]
[6,4,5,8,7,1,2,3]=>[1,3,1,3]
[5,3,4,8,7,1,2,6]=>[1,3,1,3]
[3,2,8,7,1,4,6,5]=>[1,2,1,3,1]
[3,1,8,7,2,4,6,5]=>[1,2,1,3,1]
[5,3,7,6,1,2,4,8]=>[1,2,1,4]
[1,8,3,7,2,4,5,6]=>[2,2,4]
[3,8,1,7,2,4,5,6]=>[2,2,4]
[6,8,2,3,5,1,4,7]=>[2,3,3]
[4,7,8,2,6,1,3,5]=>[3,2,3]
[6,2,8,7,1,4,5,3]=>[1,2,1,3,1]
[3,8,7,1,4,5,6,2]=>[2,1,4,1]
[2,8,6,1,3,4,5,7]=>[2,1,5]
[2,7,6,1,3,4,5,8]=>[2,1,5]
[1,7,6,2,3,4,5,8]=>[2,1,5]
[1,8,6,2,3,4,5,7]=>[2,1,5]
[2,8,7,3,4,5,6,1]=>[2,1,4,1]
[3,8,7,2,4,5,6,1]=>[2,1,4,1]
[7,8,3,6,2,4,5,1]=>[2,2,3,1]
[1,5,8,7,2,3,6,4]=>[3,1,3,1]
[8,7,6,1,3,4,5,2]=>[1,1,1,4,1]
[3,6,2,4,7,1,8,5]=>[2,3,2,1]
[3,4,7,2,5,1,8,6]=>[3,2,2,1]
[2,1,6,4,8,5,3,7]=>[1,2,2,1,2]
[4,1,8,5,3,2,7,6]=>[1,2,1,1,2,1]
[3,6,2,5,7,1,4,8]=>[2,3,3]
[1,2,8,3,7,5,4,6]=>[3,2,1,2]
[6,1,3,2,8,5,4,7]=>[1,2,2,1,2]
[5,6,1,2,8,4,3,7]=>[2,3,1,2]
[1,6,3,8,7,4,2,5]=>[2,2,1,1,2]
[4,3,8,1,2,6,7,5]=>[1,2,4,1]
[3,6,8,7,1,2,5,4]=>[3,1,3,1]
[6,2,8,5,4,7,1,3]=>[1,2,1,2,2]
[6,5,7,2,4,8,1,3]=>[1,2,3,2]
[3,4,1,6,5,8,7,2]=>[2,2,2,1,1]
[3,5,1,2,4,8,7,6]=>[2,4,1,1]
[3,7,5,2,1,4,6,8]=>[2,1,1,4]
[3,8,5,2,7,4,1,6]=>[2,1,2,1,2]
[5,2,8,4,7,3,1,6]=>[1,2,2,1,2]
[5,2,7,4,1,3,6,8]=>[1,2,1,4]
[4,3,5,1,2,8,7,6]=>[1,2,3,1,1]
[3,1,4,6,2,8,7,5]=>[1,3,2,1,1]
[1,4,6,5,2,8,7,3]=>[3,1,2,1,1]
[3,4,5,6,1,8,7,2]=>[4,2,1,1]
[3,4,5,8,7,2,1,6]=>[4,1,1,2]
[1,4,7,2,6,3,5,8]=>[3,2,3]
[8,4,7,5,2,1,6,3]=>[1,2,1,1,2,1]
[8,1,4,7,2,3,6,5]=>[1,3,3,1]
[1,8,5,7,3,4,6,2]=>[2,2,3,1]
[6,3,5,1,7,4,2,8]=>[1,2,2,1,2]
[6,1,4,8,7,3,2,5]=>[1,3,1,1,2]
[6,4,8,5,7,1,2,3]=>[1,2,2,3]
[5,4,8,1,6,3,2,7]=>[1,2,2,1,2]
[1,4,8,6,3,7,2,5]=>[3,1,2,2]
[5,4,7,6,3,8,1,2]=>[1,2,1,2,2]
[4,6,3,7,5,8,1,2]=>[2,2,2,2]
[4,1,3,5,8,6,2,7]=>[1,4,1,2]
[5,7,4,3,8,1,2,6]=>[2,1,2,3]
[1,4,8,3,7,6,5,2]=>[3,2,1,1,1]
[4,3,8,2,1,6,5,7]=>[1,2,1,2,2]
[3,8,4,2,7,1,5,6]=>[2,1,2,3]
[3,1,2,5,7,6,4,8]=>[1,4,1,2]
[1,8,2,7,6,5,4,3]=>[2,2,1,1,1,1]
[3,8,1,6,7,5,4,2]=>[2,3,1,1,1]
[3,7,2,6,8,5,1,4]=>[2,3,1,2]
[7,2,3,8,5,6,1,4]=>[1,3,2,2]
[8,2,1,7,5,6,4,3]=>[1,1,2,2,1,1]
[8,1,3,6,5,7,4,2]=>[1,3,2,1,1]
[8,2,4,3,6,1,5,7]=>[1,2,2,3]
[1,7,8,5,4,3,6,2]=>[3,1,1,2,1]
[1,8,4,5,3,2,6,7]=>[2,2,1,3]
[7,8,5,4,3,1,6,2]=>[2,1,1,1,2,1]
[7,1,6,3,4,2,5,8]=>[1,2,2,3]
[6,8,7,1,4,2,5,3]=>[2,1,2,2,1]
[3,6,1,4,2,7,5,8]=>[2,2,2,2]
[3,4,1,8,5,7,6,2]=>[2,2,2,1,1]
[3,6,5,1,2,8,4,7]=>[2,1,3,2]
[3,8,5,6,7,2,1,4]=>[2,3,1,2]
[8,1,7,6,2,4,3,5]=>[1,2,1,2,2]
[8,5,6,1,4,2,3,7]=>[1,2,2,3]
[8,6,5,4,7,1,3,2]=>[1,1,1,2,2,1]
[1,6,4,5,7,2,3,8]=>[2,3,3]
[8,3,6,1,7,2,4,5]=>[1,2,2,3]
[1,8,6,5,7,3,4,2]=>[2,1,2,2,1]
[1,7,5,3,6,8,4,2]=>[2,1,3,1,1]
[7,4,1,6,5,8,3,2]=>[1,1,2,2,1,1]
[4,1,5,8,7,6,3,2]=>[1,3,1,1,1,1]
[1,2,5,8,6,7,3,4]=>[4,2,2]
[4,2,1,5,8,7,3,6]=>[1,1,3,1,2]
[5,2,4,6,1,7,3,8]=>[1,3,2,2]
[1,5,3,6,8,7,4,2]=>[2,3,1,1,1]
[3,5,4,6,1,8,2,7]=>[2,2,2,2]
[3,1,5,7,6,8,2,4]=>[1,3,2,2]
[1,4,5,6,8,7,2,3]=>[5,1,2]
[1,4,6,3,7,2,8,5]=>[3,2,2,1]
[1,7,3,6,5,2,8,4]=>[2,2,1,2,1]
[8,6,2,5,4,1,7,3]=>[1,1,2,1,2,1]
[3,7,2,6,5,4,1,8]=>[2,2,1,1,2]
[7,6,2,5,4,3,1,8]=>[1,1,2,1,1,2]
[4,7,5,2,6,3,1,8]=>[2,1,2,1,2]
[3,2,6,4,7,5,1,8]=>[1,2,2,1,2]
[6,2,3,7,5,4,1,8]=>[1,3,1,1,2]
[1,3,4,7,6,2,8,5]=>[4,1,2,1]
[2,8,3,6,1,7,5,4]=>[2,2,2,1,1]
[8,7,2,5,1,6,4,3]=>[1,1,2,2,1,1]
[3,8,2,6,5,1,7,4]=>[2,2,1,2,1]
[7,8,2,5,4,1,6,3]=>[2,2,1,2,1]
[4,8,5,2,6,1,7,3]=>[2,1,2,2,1]
[4,5,1,3,7,2,8,6]=>[2,3,2,1]
[6,1,3,7,5,2,8,4]=>[1,3,1,2,1]
[7,1,3,6,2,8,5,4]=>[1,3,2,1,1]
[8,1,3,6,2,7,5,4]=>[1,3,2,1,1]
[1,2,4,7,3,8,6,5]=>[4,2,1,1]
[7,1,8,2,6,5,4,3]=>[1,2,2,1,1,1]
[3,1,8,6,2,7,5,4]=>[1,2,1,2,1,1]
[4,1,7,8,2,6,5,3]=>[1,3,2,1,1]
[5,6,1,8,2,7,4,3]=>[2,2,2,1,1]
[4,2,7,8,1,6,5,3]=>[1,3,2,1,1]
[3,2,8,6,1,7,5,4]=>[1,2,1,2,1,1]
[7,2,8,1,6,5,4,3]=>[1,2,2,1,1,1]
[1,8,7,2,6,5,4,3]=>[2,1,2,1,1,1]
[2,8,7,1,6,5,4,3]=>[2,1,2,1,1,1]
[3,8,7,1,6,5,4,2]=>[2,1,2,1,1,1]
[4,8,7,5,1,6,3,2]=>[2,1,1,2,1,1]
[6,7,8,5,1,4,3,2]=>[3,1,2,1,1]
[5,6,3,8,4,1,7,2]=>[2,2,1,2,1]
[7,3,8,5,4,1,6,2]=>[1,2,1,1,2,1]
[3,4,8,6,5,1,7,2]=>[3,1,1,2,1]
[8,3,7,5,1,6,4,2]=>[1,2,1,2,1,1]
[1,4,8,6,2,7,5,3]=>[3,1,2,1,1]
[8,4,6,7,1,5,3,2]=>[1,3,2,1,1]
[5,6,4,7,8,1,3,2]=>[2,3,2,1]
[3,4,6,5,1,2,8,7]=>[3,1,3,1]
[7,3,5,1,2,8,6,4]=>[1,2,3,1,1]
[1,4,6,2,3,8,7,5]=>[3,3,1,1]
[1,3,2,7,4,8,6,5]=>[2,2,2,1,1]
[7,2,1,6,3,8,5,4]=>[1,1,2,2,1,1]
[2,3,1,7,6,4,8,5]=>[2,2,1,2,1]
[4,5,2,1,7,3,8,6]=>[2,1,2,2,1]
[5,6,7,1,2,8,4,3]=>[3,3,1,1]
[4,7,5,1,2,8,6,3]=>[2,1,3,1,1]
[3,7,1,6,2,8,5,4]=>[2,2,2,1,1]
[7,6,1,2,8,5,4,3]=>[1,1,3,1,1,1]
[2,7,1,3,8,6,5,4]=>[2,3,1,1,1]
[8,6,1,2,7,5,4,3]=>[1,1,3,1,1,1]
[1,7,2,3,8,6,5,4]=>[2,3,1,1,1]
[8,7,1,2,6,5,4,3]=>[1,1,3,1,1,1]
[7,8,1,2,6,5,4,3]=>[2,3,1,1,1]
[3,8,1,6,2,7,5,4]=>[2,2,2,1,1]
[4,8,5,1,2,7,6,3]=>[2,1,3,1,1]
[5,6,8,1,2,7,4,3]=>[3,3,1,1]
[2,1,3,7,4,8,6,5]=>[1,3,2,1,1]
[4,2,7,3,6,8,1,5]=>[1,2,3,2]
[5,3,6,4,2,8,1,7]=>[1,2,1,2,2]
[4,1,5,3,8,2,7,6]=>[1,2,2,2,1]
[5,2,6,4,7,3,1,8]=>[1,2,2,1,2]
[2,6,3,4,7,5,1,8]=>[2,3,1,2]
[2,6,3,5,4,8,1,7]=>[2,2,2,2]
[2,7,4,3,5,8,1,6]=>[2,1,3,2]
[7,3,6,4,2,8,1,5]=>[1,2,1,2,2]
[7,6,4,5,2,8,1,3]=>[1,1,2,2,2]
[5,4,3,1,8,2,7,6]=>[1,1,1,2,2,1]
[6,5,4,2,7,3,1,8]=>[1,1,1,2,1,2]
[5,4,1,7,2,6,3,8]=>[1,1,2,2,2]
[5,4,1,8,3,2,6,7]=>[1,1,2,1,3]
[6,5,2,8,3,4,7,1]=>[1,1,2,3,1]
[7,4,2,1,8,3,6,5]=>[1,1,1,2,2,1]
[6,5,3,4,8,2,7,1]=>[1,1,3,2,1]
[6,1,5,3,8,2,7,4]=>[1,2,2,2,1]
[4,6,3,1,8,2,7,5]=>[2,1,2,2,1]
[5,8,4,2,7,3,1,6]=>[2,1,2,1,2]
[8,2,6,4,7,3,1,5]=>[1,2,2,1,2]
[8,6,2,5,7,4,1,3]=>[1,1,3,1,2]
[8,5,3,2,6,4,1,7]=>[1,1,1,2,1,2]
[8,3,1,7,2,5,4,6]=>[1,1,2,2,2]
[7,5,2,6,4,3,1,8]=>[1,1,2,1,1,2]
[7,1,6,2,5,4,3,8]=>[1,2,2,1,2]
[8,1,7,3,5,6,4,2]=>[1,2,3,1,1]
[8,6,1,7,4,5,2,3]=>[1,1,2,2,2]
[8,1,3,7,2,6,5,4]=>[1,3,2,1,1]
[1,7,6,8,3,2,4,5]=>[2,2,1,3]
[7,1,5,8,4,2,6,3]=>[1,3,1,2,1]
[7,3,8,4,5,2,6,1]=>[1,2,2,2,1]
[7,2,8,5,3,4,6,1]=>[1,2,1,3,1]
[6,1,8,4,3,2,5,7]=>[1,2,1,1,3]
[6,1,7,4,2,5,3,8]=>[1,2,1,2,2]
[1,2,7,3,4,6,5,8]=>[3,3,2]
[1,7,8,4,3,5,6,2]=>[3,1,3,1]
[1,6,2,8,3,5,7,4]=>[2,2,3,1]
[2,6,1,7,3,5,4,8]=>[2,2,2,2]
[3,1,5,8,4,2,6,7]=>[1,3,1,3]
[4,3,1,6,8,2,7,5]=>[1,1,3,2,1]
[5,7,4,8,3,2,1,6]=>[2,2,1,1,2]
[5,4,8,2,7,3,1,6]=>[1,2,2,1,2]
[5,2,8,7,3,4,1,6]=>[1,2,1,2,2]
[6,4,7,5,3,2,1,8]=>[1,2,1,1,1,2]
[1,8,3,7,6,2,4,5]=>[2,2,1,3]
[5,8,3,2,6,4,1,7]=>[2,1,2,1,2]
[6,8,2,4,7,5,1,3]=>[2,3,1,2]
[7,3,8,2,6,4,1,5]=>[1,2,2,1,2]
[4,6,8,2,7,3,1,5]=>[3,2,1,2]
[2,6,8,7,3,4,1,5]=>[3,1,2,2]
[7,2,8,6,3,5,1,4]=>[1,2,1,2,2]
[6,8,1,7,2,5,4,3]=>[2,2,2,1,1]
[3,8,7,4,5,6,1,2]=>[2,1,3,2]
[2,8,6,4,3,5,1,7]=>[2,1,1,2,2]
[2,7,6,3,5,4,1,8]=>[2,1,2,1,2]
[1,7,6,5,2,4,3,8]=>[2,1,1,2,2]
[1,8,6,5,3,2,4,7]=>[2,1,1,1,3]
[3,8,7,4,6,2,5,1]=>[2,1,2,2,1]
[5,8,3,7,6,2,4,1]=>[2,2,1,2,1]
[7,1,8,6,5,2,3,4]=>[1,2,1,1,3]
[8,4,7,5,3,2,1,6]=>[1,2,1,1,1,2]
[8,7,2,5,4,3,1,6]=>[1,1,2,1,1,2]
[6,8,3,2,5,4,7,1]=>[2,1,2,2,1]
[6,8,4,5,2,3,7,1]=>[2,2,3,1]
[1,5,7,8,4,3,6,2]=>[4,1,2,1]
[6,3,8,1,5,4,7,2]=>[1,2,2,2,1]
[6,2,1,8,5,4,7,3]=>[1,1,2,1,2,1]
[2,6,3,1,7,5,4,8]=>[2,1,2,1,2]
[2,6,5,7,4,1,3,8]=>[2,2,1,3]
[2,5,6,8,4,3,7,1]=>[4,1,2,1]
[2,4,7,5,8,1,6,3]=>[3,2,2,1]
[2,5,4,7,1,8,6,3]=>[2,2,2,1,1]
[5,2,1,8,7,6,4,3]=>[1,1,2,1,1,1,1]
[4,8,5,7,6,1,3,2]=>[2,2,1,2,1]
[4,8,6,7,5,3,1,2]=>[2,2,1,1,2]
[4,8,7,5,6,2,3,1]=>[2,1,2,2,1]
[6,5,4,8,2,1,7,3]=>[1,1,2,1,2,1]
[5,8,4,7,2,6,3,1]=>[2,2,2,1,1]
[1,5,7,4,8,2,6,3]=>[3,2,2,1]
[1,5,7,3,2,8,6,4]=>[3,1,2,1,1]
[5,8,3,2,7,6,4,1]=>[2,1,2,1,1,1]
[5,2,1,4,3,6,7,8]=>[1,1,2,4]
[3,5,7,4,2,6,1,8]=>[3,1,2,2]
[3,6,4,5,1,2,7,8]=>[2,2,4]
[4,2,1,6,5,3,7,8]=>[1,1,2,1,3]
[4,2,1,5,7,6,3,8]=>[1,1,3,1,2]
[4,3,5,1,7,6,2,8]=>[1,2,2,1,2]
[3,5,4,7,1,6,2,8]=>[2,2,2,2]
[3,4,7,5,6,1,2,8]=>[3,2,3]
[3,4,5,8,6,7,1,2]=>[4,2,2]
[3,5,4,6,1,8,7,2]=>[2,2,2,1,1]
[4,3,5,1,6,8,7,2]=>[1,2,3,1,1]
[4,2,1,5,6,8,7,3]=>[1,1,4,1,1]
[2,1,7,3,8,4,6,5]=>[1,2,2,2,1]
[4,1,8,2,7,3,6,5]=>[1,2,2,2,1]
[4,1,7,2,8,3,6,5]=>[1,2,2,2,1]
[7,1,3,2,8,4,6,5]=>[1,2,2,2,1]
[7,1,8,2,4,3,6,5]=>[1,2,2,2,1]
[8,1,7,2,5,3,6,4]=>[1,2,2,2,1]
[7,1,5,2,8,3,6,4]=>[1,2,2,2,1]
[5,1,7,2,8,3,6,4]=>[1,2,2,2,1]
[5,1,8,2,7,3,6,4]=>[1,2,2,2,1]
[5,1,8,2,4,3,7,6]=>[1,2,2,2,1]
[8,1,6,2,4,3,7,5]=>[1,2,2,2,1]
[6,1,8,2,4,3,7,5]=>[1,2,2,2,1]
[6,1,8,2,5,3,7,4]=>[1,2,2,2,1]
[8,1,6,2,5,3,7,4]=>[1,2,2,2,1]
[8,1,6,2,7,3,5,4]=>[1,2,2,2,1]
[6,1,8,2,7,3,5,4]=>[1,2,2,2,1]
[6,1,7,2,8,3,5,4]=>[1,2,2,2,1]
[6,1,7,2,5,3,8,4]=>[1,2,2,2,1]
[6,1,7,2,4,3,8,5]=>[1,2,2,2,1]
[5,1,6,2,4,3,8,7]=>[1,2,2,2,1]
[7,1,5,2,4,3,8,6]=>[1,2,2,2,1]
[7,1,6,2,4,3,8,5]=>[1,2,2,2,1]
[7,1,6,2,5,3,8,4]=>[1,2,2,2,1]
[7,1,6,2,8,3,5,4]=>[1,2,2,2,1]
[7,1,8,2,6,3,5,4]=>[1,2,2,2,1]
[1,8,2,7,5,4,6,3]=>[2,2,1,2,1]
[1,8,2,7,4,3,5,6]=>[2,2,1,3]
[1,8,6,4,7,2,3,5]=>[2,1,2,3]
[1,8,4,2,6,3,5,7]=>[2,1,2,3]
[7,4,8,1,5,2,3,6]=>[1,2,2,3]
[4,1,7,2,6,3,5,8]=>[1,2,2,3]
[5,1,7,4,3,6,2,8]=>[1,2,1,2,2]
[7,5,8,3,2,4,1,6]=>[1,2,1,2,2]
[1,8,5,4,3,6,2,7]=>[2,1,1,2,2]
[1,8,5,4,3,7,2,6]=>[2,1,1,2,2]
[1,8,5,4,7,2,6,3]=>[2,1,2,2,1]
[1,8,4,2,5,3,7,6]=>[2,1,2,2,1]
[1,8,5,4,2,6,7,3]=>[2,1,1,3,1]
[7,4,8,2,1,3,5,6]=>[1,2,1,4]
[4,1,7,3,2,5,6,8]=>[1,2,1,4]
[7,5,4,8,2,3,6,1]=>[1,1,2,3,1]
[7,3,8,1,5,6,2,4]=>[1,2,3,2]
[3,1,7,2,6,8,4,5]=>[1,2,3,2]
[5,1,7,4,2,6,8,3]=>[1,2,1,3,1]
[4,1,6,3,2,5,8,7]=>[1,2,1,3,1]
[5,4,3,7,1,2,8,6]=>[1,1,2,3,1]
[4,3,1,6,2,5,7,8]=>[1,1,2,4]
[6,5,4,3,7,1,8,2]=>[1,1,1,2,2,1]
[5,4,2,7,1,6,8,3]=>[1,1,2,3,1]
[6,5,1,7,3,8,2,4]=>[1,1,2,2,2]
[6,3,2,8,5,7,1,4]=>[1,1,2,2,2]
[6,5,4,2,8,3,7,1]=>[1,1,1,2,2,1]
[6,5,4,3,8,2,7,1]=>[1,1,1,2,2,1]
[6,5,4,3,8,7,1,2]=>[1,1,1,2,1,2]
[7,5,4,8,6,1,3,2]=>[1,1,2,1,2,1]
[7,6,3,8,5,4,1,2]=>[1,1,2,1,1,2]
[6,3,8,1,7,5,2,4]=>[1,2,2,1,2]
[6,5,8,3,1,7,4,2]=>[1,2,1,2,1,1]
[5,4,8,2,1,7,3,6]=>[1,2,1,2,2]
[5,4,3,8,1,6,2,7]=>[1,1,2,2,2]
[5,4,3,7,1,6,2,8]=>[1,1,2,2,2]
[6,4,2,8,5,1,3,7]=>[1,1,2,1,3]
[7,6,4,8,5,1,2,3]=>[1,1,2,1,3]
[7,2,8,6,3,1,4,5]=>[1,2,1,1,3]
[7,2,8,6,1,5,3,4]=>[1,2,1,2,2]
[2,1,7,8,3,6,4,5]=>[1,3,2,2]
[6,4,1,7,8,2,3,5]=>[1,1,3,3]
[4,2,1,6,7,3,5,8]=>[1,1,3,3]
[4,3,1,5,2,7,6,8]=>[1,1,2,2,2]
[5,4,2,7,3,8,1,6]=>[1,1,2,2,2]
[4,1,5,3,2,8,6,7]=>[1,2,1,2,2]
[3,1,6,2,8,7,4,5]=>[1,2,2,1,2]
[6,3,1,7,8,5,2,4]=>[1,1,3,1,2]
[5,4,1,7,8,2,6,3]=>[1,1,3,2,1]
[6,5,4,1,7,8,3,2]=>[1,1,1,3,1,1]
[5,4,3,1,6,7,2,8]=>[1,1,1,3,2]
[6,5,4,2,7,8,3,1]=>[1,1,1,3,1,1]
[5,4,2,6,3,8,7,1]=>[1,1,2,2,1,1]
[4,3,1,5,2,6,8,7]=>[1,1,2,3,1]
[5,4,2,1,6,7,8,3]=>[1,1,1,4,1]
[5,4,3,1,6,7,8,2]=>[1,1,1,4,1]
[6,3,8,1,2,5,7,4]=>[1,2,4,1]
[3,6,7,1,2,5,8,4]=>[3,4,1]
[7,8,3,1,2,5,6,4]=>[2,1,4,1]
[7,8,1,3,2,4,6,5]=>[2,2,3,1]
[7,8,2,1,3,5,4,6]=>[2,1,3,2]
[5,2,3,7,1,8,6,4]=>[1,3,2,1,1]
[2,5,3,6,1,8,7,4]=>[2,2,2,1,1]
[2,6,7,3,1,8,4,5]=>[3,1,2,2]
[2,6,7,1,3,5,4,8]=>[3,3,2]
[6,2,8,3,1,7,4,5]=>[1,2,1,2,2]
[3,2,5,7,1,8,4,6]=>[1,3,2,2]
[4,3,1,2,7,8,6,5]=>[1,1,4,1,1]
[5,1,2,7,3,6,4,8]=>[1,3,2,2]
[5,1,4,7,8,2,3,6]=>[1,4,3]
[5,3,4,7,8,6,1,2]=>[1,4,1,2]
[3,5,4,6,8,7,1,2]=>[2,3,1,2]
[1,5,4,6,8,2,3,7]=>[2,3,3]
[1,6,7,3,2,4,8,5]=>[3,1,3,1]
[1,5,3,6,2,7,8,4]=>[2,2,3,1]
[5,1,3,7,2,6,8,4]=>[1,3,3,1]
[5,2,4,7,8,1,6,3]=>[1,4,2,1]
[4,2,5,7,6,1,8,3]=>[1,3,1,2,1]
[4,5,2,8,6,1,7,3]=>[2,2,1,2,1]
[5,3,1,8,2,6,7,4]=>[1,1,2,3,1]
[6,1,8,3,2,4,7,5]=>[1,2,1,3,1]
[4,3,5,7,6,8,1,2]=>[1,3,2,2]
[4,1,5,7,6,2,3,8]=>[1,3,1,3]
[4,5,1,8,6,2,3,7]=>[2,2,1,3]
[5,2,1,8,3,6,4,7]=>[1,1,2,2,2]
[3,4,2,1,8,7,5,6]=>[2,1,2,1,2]
[7,6,5,4,2,1,8,3]=>[1,1,1,1,1,2,1]
[7,6,5,4,8,1,3,2]=>[1,1,1,2,2,1]
[7,6,5,8,2,1,4,3]=>[1,1,2,1,2,1]
[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,2,1]
[7,6,5,4,1,8,3,2]=>[1,1,1,1,2,1,1]
[7,6,5,2,8,1,4,3]=>[1,1,1,2,2,1]
[7,6,5,8,4,1,3,2]=>[1,1,2,1,2,1]
[7,6,8,5,2,1,4,3]=>[1,2,1,1,2,1]
[7,8,6,3,2,1,5,4]=>[2,1,1,1,2,1]
[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,2,1]
[7,8,2,4,5,1,3,6]=>[2,3,3]
[4,6,7,2,5,1,3,8]=>[3,2,3]
[7,8,1,3,2,4,5,6]=>[2,2,4]
[7,8,4,1,5,2,3,6]=>[2,1,2,3]
[3,6,7,2,1,4,5,8]=>[3,1,4]
[5,2,3,6,1,4,7,8]=>[1,3,4]
[2,5,3,6,1,4,7,8]=>[2,2,4]
[2,6,7,3,1,4,5,8]=>[3,1,4]
[4,6,7,1,5,2,3,8]=>[3,2,3]
[4,6,7,3,5,8,1,2]=>[3,3,2]
[6,4,7,1,5,2,3,8]=>[1,2,2,3]
[6,2,7,3,1,4,5,8]=>[1,2,1,4]
[3,2,5,6,1,4,7,8]=>[1,3,4]
[3,5,2,6,1,4,7,8]=>[2,2,4]
[5,1,4,6,7,2,3,8]=>[1,4,3]
[3,5,4,6,7,8,1,2]=>[2,4,2]
[1,5,4,6,7,2,3,8]=>[2,3,3]
[1,6,7,3,2,4,5,8]=>[3,1,4]
[1,5,3,6,2,4,7,8]=>[2,2,4]
[5,1,3,6,2,4,7,8]=>[1,3,4]
[5,2,4,6,7,1,3,8]=>[1,4,3]
[2,5,4,6,7,1,3,8]=>[2,3,3]
[2,6,7,4,5,1,3,8]=>[3,2,3]
[6,2,7,4,5,1,3,8]=>[1,2,2,3]
[4,2,5,6,7,1,3,8]=>[1,4,3]
[4,5,2,6,7,1,3,8]=>[2,3,3]
[5,3,1,6,2,4,7,8]=>[1,1,2,4]
[6,1,7,3,2,4,5,8]=>[1,2,1,4]
[6,1,7,4,5,2,3,8]=>[1,2,2,3]
[6,3,7,4,5,8,1,2]=>[1,2,3,2]
[5,4,1,6,7,2,3,8]=>[1,1,3,3]
[5,2,1,6,3,4,7,8]=>[1,1,2,4]
[7,3,2,5,4,1,6,8]=>[1,1,2,1,3]
[7,3,5,4,2,1,6,8]=>[1,2,1,1,3]
[7,3,5,2,4,1,6,8]=>[1,2,2,3]
[7,6,5,2,1,4,3,8]=>[1,1,1,1,2,2]
[1,3,6,7,5,2,8,4]=>[4,1,2,1]
[7,3,4,1,6,2,5,8]=>[1,2,2,3]
[7,3,4,1,6,5,2,8]=>[1,2,2,1,2]
[7,3,4,1,5,6,2,8]=>[1,2,3,2]
[7,3,2,5,1,6,4,8]=>[1,1,2,2,2]
[7,6,5,4,1,3,2,8]=>[1,1,1,1,2,2]
[7,3,4,1,5,2,6,8]=>[1,2,2,3]
[1,3,6,7,2,5,8,4]=>[4,3,1]
[1,7,4,6,2,8,5,3]=>[2,2,2,1,1]
[4,3,1,7,2,6,8,5]=>[1,1,2,3,1]
[5,6,1,4,7,3,8,2]=>[2,3,2,1]
[5,3,2,1,7,4,8,6]=>[1,1,1,2,2,1]
[1,3,4,5,8,7,2,6]=>[5,1,2]
[6,3,4,5,8,1,7,2]=>[1,4,2,1]
[2,4,5,1,6,8,7,3]=>[3,3,1,1]
[3,1,2,5,6,8,7,4]=>[1,5,1,1]
[4,3,2,5,6,8,1,7]=>[1,1,4,2]
[3,7,5,4,6,8,1,2]=>[2,1,3,2]
[3,1,4,6,5,8,2,7]=>[1,3,2,2]
[2,3,4,5,8,6,1,7]=>[5,1,2]
[2,3,4,5,8,1,7,6]=>[5,2,1]
[3,1,4,6,5,8,7,2]=>[1,3,2,1,1]
[3,7,5,4,6,8,2,1]=>[2,1,3,1,1]
[5,6,1,4,7,2,8,3]=>[2,3,2,1]
[4,3,1,7,5,6,8,2]=>[1,1,2,3,1]
[4,3,1,7,6,5,8,2]=>[1,1,2,1,2,1]
[3,1,4,6,7,8,5,2]=>[1,5,1,1]
[1,4,5,2,6,8,7,3]=>[3,3,1,1]
[3,7,5,2,6,8,1,4]=>[2,1,3,2]
[3,7,5,2,6,8,4,1]=>[2,1,3,1,1]
[5,6,1,2,7,4,8,3]=>[2,3,2,1]
[6,3,5,2,4,7,8,1]=>[1,2,4,1]
[5,3,2,1,4,7,8,6]=>[1,1,1,4,1]
[5,3,1,4,2,7,8,6]=>[1,1,2,3,1]
[5,3,1,2,4,7,8,6]=>[1,1,5,1]
[7,1,5,2,6,8,4,3]=>[1,2,3,1,1]
[7,1,5,2,6,8,3,4]=>[1,2,3,2]
[1,7,4,6,5,8,3,2]=>[2,2,2,1,1]
[2,7,4,6,1,8,3,5]=>[2,2,2,2]
[2,7,4,6,1,8,5,3]=>[2,2,2,1,1]
[2,3,6,7,1,5,8,4]=>[4,3,1]
[2,3,6,7,5,1,8,4]=>[4,1,2,1]
[4,3,2,6,7,1,8,5]=>[1,1,3,2,1]
[7,3,2,5,6,8,1,4]=>[1,1,4,2]
[7,1,5,4,6,8,2,3]=>[1,2,3,2]
[2,7,4,6,5,8,1,3]=>[2,2,2,2]
[7,3,4,5,8,6,1,2]=>[1,4,1,2]
[7,3,4,5,8,1,6,2]=>[1,4,2,1]
[7,3,4,5,8,1,2,6]=>[1,4,3]
[1,3,4,5,8,6,2,7]=>[5,1,2]
[1,3,4,5,8,2,7,6]=>[5,2,1]
[6,3,4,5,8,2,1,7]=>[1,4,1,2]
[6,3,4,5,8,2,7,1]=>[1,4,2,1]
[7,3,4,5,8,6,2,1]=>[1,4,1,1,1]
[2,7,4,6,5,8,3,1]=>[2,2,2,1,1]
[7,1,5,4,6,8,3,2]=>[1,2,3,1,1]
[7,3,2,5,6,8,4,1]=>[1,1,4,1,1]
[5,7,4,6,1,8,3,2]=>[2,2,2,1,1]
[6,3,4,5,8,1,2,7]=>[1,4,3]
[7,3,4,5,8,2,1,6]=>[1,4,1,2]
[7,3,4,5,8,2,6,1]=>[1,4,2,1]
[4,7,6,1,8,2,5,3]=>[2,1,2,2,1]
[4,8,6,1,7,5,2,3]=>[2,1,2,1,2]
[4,7,8,2,6,1,5,3]=>[3,2,2,1]
[7,6,4,2,8,3,5,1]=>[1,1,1,2,2,1]
[8,6,4,2,7,5,3,1]=>[1,1,1,2,1,1,1]
[8,4,7,3,6,5,1,2]=>[1,2,2,1,2]
[8,4,6,1,7,5,3,2]=>[1,2,2,1,1,1]
[6,4,7,1,8,3,2,5]=>[1,2,2,1,2]
[7,4,8,3,6,1,5,2]=>[1,2,2,2,1]
[7,8,4,3,6,2,5,1]=>[2,1,2,2,1]
[6,2,1,7,3,5,4,8]=>[1,1,2,2,2]
[2,1,8,6,3,5,4,7]=>[1,2,1,2,2]
[2,1,7,3,5,8,6,4]=>[1,2,3,1,1]
[2,6,3,1,4,8,5,7]=>[2,1,3,2]
[4,2,1,8,3,6,7,5]=>[1,1,2,3,1]
[2,1,8,6,3,5,7,4]=>[1,2,1,3,1]
[6,2,1,7,3,5,8,4]=>[1,1,2,3,1]
[2,7,3,1,4,8,5,6]=>[2,1,3,2]
[3,2,1,6,4,5,7,8]=>[1,1,2,4]
[3,2,1,5,7,8,4,6]=>[1,1,4,2]
[2,1,7,3,6,8,4,5]=>[1,2,3,2]
[2,7,3,1,5,6,8,4]=>[2,1,4,1]
[4,3,7,5,6,1,8,2]=>[1,2,2,2,1]
[4,3,6,8,5,1,7,2]=>[1,3,1,2,1]
[2,6,1,8,3,5,7,4]=>[2,2,3,1]
[2,1,6,8,3,7,4,5]=>[1,3,2,2]
[2,1,8,3,5,7,4,6]=>[1,2,3,2]
[3,2,1,5,6,8,4,7]=>[1,1,4,2]
[3,2,1,5,7,4,6,8]=>[1,1,3,3]
[8,2,4,1,7,5,6,3]=>[1,2,2,2,1]
[3,8,4,7,5,1,6,2]=>[2,2,1,2,1]
[8,4,3,6,1,7,5,2]=>[1,1,2,2,1,1]
[8,2,1,7,3,5,4,6]=>[1,1,2,2,2]
[5,8,6,3,1,7,4,2]=>[2,1,1,2,1,1]
[2,4,7,1,8,5,3,6]=>[3,2,1,2]
[2,4,8,5,1,6,3,7]=>[3,1,2,2]
[6,2,1,7,3,4,8,5]=>[1,1,2,3,1]
[6,2,1,7,8,3,5,4]=>[1,1,3,2,1]
[2,1,8,3,6,4,5,7]=>[1,2,2,3]
[3,2,1,6,7,4,5,8]=>[1,1,3,3]
[3,2,1,6,8,4,5,7]=>[1,1,3,3]
[2,1,8,3,7,4,5,6]=>[1,2,2,3]
[2,1,8,3,6,7,4,5]=>[1,2,3,2]
[2,4,8,5,1,6,7,3]=>[3,1,3,1]
[4,3,8,5,6,1,7,2]=>[1,2,2,2,1]
[3,2,1,8,4,5,6,7]=>[1,1,2,4]
[1,6,8,3,7,2,4,5]=>[3,2,3]
[3,8,1,5,7,2,4,6]=>[2,3,3]
[1,2,6,8,4,7,3,5]=>[4,2,2]
[6,1,5,8,2,4,7,3]=>[1,3,3,1]
[1,2,4,8,3,6,7,5]=>[4,3,1]
[4,1,2,7,8,3,6,5]=>[1,4,2,1]
[3,5,7,4,8,6,1,2]=>[3,2,1,2]
[5,3,8,4,7,6,1,2]=>[1,2,2,1,2]
[8,7,1,2,5,4,6,3]=>[1,1,3,2,1]
[5,8,1,2,3,7,6,4]=>[2,4,1,1]
[1,2,8,4,3,5,7,6]=>[3,1,3,1]
[1,2,5,3,7,6,4,8]=>[3,2,1,2]
[6,1,2,8,7,4,5,3]=>[1,3,1,2,1]
[7,1,6,2,8,4,5,3]=>[1,2,2,2,1]
[1,2,6,3,8,5,4,7]=>[3,2,1,2]
[1,2,8,5,3,6,4,7]=>[3,1,2,2]
[1,2,7,3,8,5,4,6]=>[3,2,1,2]
[4,1,2,7,8,6,3,5]=>[1,4,1,2]
[1,6,2,8,4,3,5,7]=>[2,2,1,3]
[1,6,4,2,7,3,5,8]=>[2,1,2,3]
[1,8,6,3,2,4,5,7]=>[2,1,1,4]
[1,7,3,2,8,4,5,6]=>[2,1,2,3]
[3,1,7,8,6,2,4,5]=>[1,3,1,3]
[1,8,7,2,4,5,6,3]=>[2,1,4,1]
[1,8,7,3,5,6,2,4]=>[2,1,3,2]
[1,3,2,8,7,4,5,6]=>[2,2,1,3]
[1,8,3,2,6,4,5,7]=>[2,1,2,3]
[1,7,6,3,2,4,5,8]=>[2,1,1,4]
[1,2,8,4,3,7,5,6]=>[3,1,2,2]
[8,5,1,7,2,4,6,3]=>[1,1,2,3,1]
[5,3,8,7,4,6,1,2]=>[1,2,1,2,2]
[3,8,6,4,7,5,1,2]=>[2,1,2,1,2]
[6,1,8,2,7,4,5,3]=>[1,2,2,2,1]
[1,2,5,3,8,6,4,7]=>[3,2,1,2]
[1,2,7,5,3,6,4,8]=>[3,1,2,2]
[1,2,6,3,7,5,4,8]=>[3,2,1,2]
[1,2,3,7,5,4,8,6]=>[4,1,2,1]
[3,7,4,8,6,5,1,2]=>[2,2,1,1,2]
[1,8,2,7,6,4,5,3]=>[2,2,1,2,1]
[2,8,7,6,5,1,4,3]=>[2,1,1,1,2,1]
[7,1,6,3,2,5,4,8]=>[1,2,1,2,2]
[2,7,6,3,1,5,8,4]=>[2,1,1,3,1]
[1,8,4,3,6,5,2,7]=>[2,1,2,1,2]
[1,8,4,6,5,3,2,7]=>[2,2,1,1,2]
[7,4,2,1,6,5,3,8]=>[1,1,1,2,1,2]
[7,6,1,4,3,5,2,8]=>[1,1,2,2,2]
[7,4,1,3,5,2,6,8]=>[1,1,3,3]
[7,3,1,2,4,6,5,8]=>[1,1,4,2]
[1,8,6,3,4,5,2,7]=>[2,1,3,2]
[1,8,6,7,4,2,5,3]=>[2,2,1,2,1]
[3,6,2,1,4,8,5,7]=>[2,1,3,2]
[3,1,7,2,4,6,8,5]=>[1,2,4,1]
[3,4,7,1,5,2,8,6]=>[3,2,2,1]
[3,6,7,4,1,5,8,2]=>[3,1,3,1]
[4,3,2,7,1,5,8,6]=>[1,1,2,3,1]
[3,1,2,8,6,5,4,7]=>[1,3,1,1,2]
[5,4,8,6,1,2,3,7]=>[1,2,1,4]
[5,6,8,7,4,3,1,2]=>[3,1,1,1,2]
[1,8,2,7,4,3,6,5]=>[2,2,1,2,1]
[6,5,8,2,3,7,1,4]=>[1,2,3,2]
[6,4,8,5,3,1,7,2]=>[1,2,1,1,2,1]
[5,7,8,6,1,3,2,4]=>[3,1,2,2]
[2,4,8,1,6,3,7,5]=>[3,2,2,1]
[3,1,2,8,6,4,7,5]=>[1,3,1,2,1]
[5,3,2,6,4,8,1,7]=>[1,1,2,2,2]
[4,1,6,3,5,8,2,7]=>[1,2,3,2]
[2,4,5,3,8,6,1,7]=>[3,2,1,2]
[1,8,5,3,2,7,6,4]=>[2,1,1,2,1,1]
[1,8,4,5,2,6,7,3]=>[2,2,3,1]
[4,1,2,7,6,5,8,3]=>[1,3,1,2,1]
[2,4,1,6,7,8,5,3]=>[2,4,1,1]
[1,8,4,3,6,2,7,5]=>[2,1,2,2,1]
[5,6,7,3,2,8,1,4]=>[3,1,2,2]
[2,5,7,3,6,8,4,1]=>[3,3,1,1]
[5,3,2,1,4,8,6,7]=>[1,1,1,3,2]
[5,3,1,4,2,8,6,7]=>[1,1,2,2,2]
[7,6,1,3,8,5,4,2]=>[1,1,3,1,1,1]
[3,4,7,8,1,2,6,5]=>[4,3,1]
[3,6,7,8,1,4,5,2]=>[4,3,1]
[3,6,2,8,1,5,4,7]=>[2,2,2,2]
[2,3,6,8,5,1,4,7]=>[4,1,3]
[3,1,6,4,8,2,5,7]=>[1,2,2,3]
[7,3,2,6,8,5,1,4]=>[1,1,3,1,2]
[7,3,5,8,4,6,1,2]=>[1,3,2,2]
[7,5,2,8,4,1,6,3]=>[1,1,2,1,2,1]
[7,4,5,8,2,1,3,6]=>[1,3,1,3]
[1,8,5,2,4,6,3,7]=>[2,1,3,2]
[1,8,4,2,3,5,7,6]=>[2,1,4,1]
[6,4,2,8,3,5,1,7]=>[1,1,2,2,2]
[6,3,4,8,2,5,7,1]=>[1,3,3,1]
[7,5,4,8,3,6,2,1]=>[1,1,2,2,1,1]
[2,7,4,8,5,3,6,1]=>[2,2,1,2,1]
[7,1,5,4,8,3,6,2]=>[1,2,2,2,1]
[7,3,2,5,8,4,6,1]=>[1,1,3,2,1]
[8,4,6,3,7,2,5,1]=>[1,2,2,2,1]
[7,4,6,3,8,5,1,2]=>[1,2,2,1,2]
[2,5,6,8,3,4,1,7]=>[4,2,2]
[8,4,6,2,7,5,3,1]=>[1,2,2,1,1,1]
[8,5,6,7,2,4,3,1]=>[1,3,2,1,1]
[2,5,6,8,4,3,1,7]=>[4,1,1,2]
[2,5,7,8,4,1,3,6]=>[4,1,3]
[6,5,7,8,4,1,3,2]=>[1,3,1,2,1]
[7,5,6,8,2,4,1,3]=>[1,3,2,2]
[7,4,6,2,8,5,1,3]=>[1,2,2,1,2]
[4,3,2,6,8,5,1,7]=>[1,1,3,1,2]
[3,5,6,8,2,4,1,7]=>[4,2,2]
[3,5,6,8,4,2,1,7]=>[4,1,1,2]
[2,6,7,8,1,4,5,3]=>[4,3,1]
[3,6,7,8,1,4,2,5]=>[4,2,2]
[3,5,7,8,2,1,4,6]=>[4,1,3]
[2,6,7,8,1,4,3,5]=>[4,2,2]
[6,5,7,8,3,1,4,2]=>[1,3,1,2,1]
[2,5,7,8,3,1,4,6]=>[4,1,3]
[2,4,7,3,8,1,5,6]=>[3,2,3]
[6,4,7,3,8,1,5,2]=>[1,2,2,2,1]
[6,4,7,3,8,1,2,5]=>[1,2,2,3]
[7,4,6,3,8,2,1,5]=>[1,2,2,1,2]
[6,3,2,5,4,8,1,7]=>[1,1,2,2,2]
[6,4,5,2,3,8,1,7]=>[1,2,3,2]
[6,4,5,3,2,8,1,7]=>[1,2,1,2,2]
[5,4,6,3,8,2,1,7]=>[1,2,2,1,2]
[5,4,7,3,8,1,6,2]=>[1,2,2,2,1]
[2,5,7,8,3,1,6,4]=>[4,1,2,1]
[4,5,7,8,3,1,2,6]=>[4,1,3]
[4,5,6,8,2,3,1,7]=>[4,2,2]
[5,4,6,2,8,3,1,7]=>[1,2,2,1,2]
[5,3,2,6,8,4,1,7]=>[1,1,3,1,2]
[5,4,7,2,8,1,3,6]=>[1,2,2,3]
[4,5,7,8,2,1,3,6]=>[4,1,3]
[4,6,7,8,1,3,2,5]=>[4,2,2]
[4,6,7,8,1,3,5,2]=>[4,3,1]
[2,6,7,8,1,3,5,4]=>[4,3,1]
[2,6,7,8,1,5,3,4]=>[4,2,2]
[4,6,7,8,1,5,2,3]=>[4,2,2]
[4,6,7,8,1,2,5,3]=>[4,3,1]
[4,5,7,8,2,1,6,3]=>[4,1,2,1]
[5,4,7,2,8,1,6,3]=>[1,2,2,2,1]
[5,3,2,7,8,1,6,4]=>[1,1,3,2,1]
[4,3,2,7,8,1,6,5]=>[1,1,3,2,1]
[3,5,7,8,2,1,6,4]=>[4,1,2,1]
[3,6,7,8,1,2,5,4]=>[4,3,1]
[3,6,7,8,1,5,2,4]=>[4,2,2]
[3,6,7,8,1,5,4,2]=>[4,2,1,1]
[2,6,7,8,1,5,4,3]=>[4,2,1,1]
[4,2,7,1,5,3,8,6]=>[1,2,2,2,1]
[4,2,8,6,1,5,3,7]=>[1,2,1,2,2]
[3,2,6,7,5,1,4,8]=>[1,3,1,3]
[2,7,1,3,5,4,8,6]=>[2,3,2,1]
[4,7,2,1,5,8,6,3]=>[2,1,3,1,1]
[7,2,1,3,5,8,6,4]=>[1,1,4,1,1]
[2,3,6,4,7,1,5,8]=>[3,2,3]
[1,3,4,8,2,7,5,6]=>[4,2,2]
[3,1,4,8,2,6,7,5]=>[1,3,3,1]
[8,3,1,6,2,5,7,4]=>[1,1,2,3,1]
[4,8,6,2,1,5,7,3]=>[2,1,1,3,1]
[4,8,3,6,5,1,7,2]=>[2,2,1,2,1]
[6,4,7,3,5,1,8,2]=>[1,2,2,2,1]
[6,4,7,5,1,8,2,3]=>[1,2,1,2,2]
[3,6,1,7,5,8,2,4]=>[2,2,2,2]
[7,3,5,1,6,8,2,4]=>[1,2,3,2]
[4,7,3,5,6,1,8,2]=>[2,3,2,1]
[3,4,6,8,5,1,7,2]=>[4,1,2,1]
[4,6,8,2,1,5,7,3]=>[3,1,3,1]
[6,8,2,1,3,5,7,4]=>[2,1,4,1]
[1,8,2,3,5,7,4,6]=>[2,4,2]
[2,7,3,6,1,4,5,8]=>[2,2,4]
[2,6,1,3,5,8,4,7]=>[2,4,2]
[7,3,2,5,6,1,4,8]=>[1,1,3,3]
[4,7,5,2,6,1,3,8]=>[2,1,2,3]
[4,6,2,8,1,5,3,7]=>[2,2,2,2]
[8,4,1,2,7,5,3,6]=>[1,1,3,1,2]
[4,5,6,2,7,1,3,8]=>[3,2,3]
[8,5,1,2,6,3,4,7]=>[1,1,3,3]
[1,6,2,7,4,8,3,5]=>[2,2,2,2]
[6,2,1,7,8,5,3,4]=>[1,1,3,1,2]
[6,7,3,8,4,1,5,2]=>[2,2,1,2,1]
[2,7,8,4,1,5,6,3]=>[3,1,3,1]
[2,7,1,8,5,6,3,4]=>[2,2,2,2]
[8,2,5,1,6,7,3,4]=>[1,2,3,2]
[8,2,4,5,1,6,7,3]=>[1,3,3,1]
[3,8,4,5,6,1,7,2]=>[2,3,2,1]
[4,5,8,3,6,7,1,2]=>[3,3,2]
[4,5,8,3,7,6,1,2]=>[3,2,1,2]
[4,2,8,3,7,1,6,5]=>[1,2,2,2,1]
[7,2,3,4,8,1,6,5]=>[1,4,2,1]
[7,2,3,4,8,1,5,6]=>[1,4,3]
[7,6,3,4,8,5,1,2]=>[1,1,3,1,2]
[7,6,3,5,8,4,1,2]=>[1,1,3,1,2]
[7,6,3,8,4,5,1,2]=>[1,1,2,2,2]
[7,2,3,8,5,1,4,6]=>[1,3,1,3]
[7,2,3,8,5,1,6,4]=>[1,3,1,2,1]
[2,6,4,8,1,5,7,3]=>[2,2,3,1]
[7,2,3,8,4,1,5,6]=>[1,3,1,3]
[7,2,3,5,8,1,4,6]=>[1,4,3]
[7,8,2,3,6,1,4,5]=>[2,3,3]
[7,8,2,3,6,1,5,4]=>[2,3,2,1]
[4,2,6,3,7,1,5,8]=>[1,2,2,3]
[7,2,3,5,8,1,6,4]=>[1,4,2,1]
[7,2,3,8,4,1,6,5]=>[1,3,1,2,1]
[2,6,4,8,1,3,7,5]=>[2,2,3,1]
[3,6,4,8,1,7,5,2]=>[2,2,2,1,1]
[7,6,5,1,2,3,8,4]=>[1,1,1,4,1]
[7,6,5,1,4,2,8,3]=>[1,1,1,2,2,1]
[2,6,4,5,1,8,7,3]=>[2,2,2,1,1]
[3,5,6,4,1,2,7,8]=>[3,1,4]
[7,8,5,4,1,2,6,3]=>[2,1,1,3,1]
[3,5,6,4,1,2,8,7]=>[3,1,3,1]
[7,6,5,1,4,2,3,8]=>[1,1,1,2,3]
[7,6,5,1,2,4,3,8]=>[1,1,1,3,2]
[7,6,5,1,2,4,8,3]=>[1,1,1,4,1]
[7,6,5,1,3,2,8,4]=>[1,1,1,2,2,1]
[7,6,5,1,3,2,4,8]=>[1,1,1,2,3]
[7,6,5,1,3,4,2,8]=>[1,1,1,3,2]
[7,2,3,4,5,1,8,6]=>[1,4,2,1]
[2,6,4,3,1,5,8,7]=>[2,1,1,3,1]
[2,6,4,3,1,8,5,7]=>[2,1,1,2,2]
[2,6,4,3,1,8,7,5]=>[2,1,1,2,1,1]
[3,5,8,4,1,2,7,6]=>[3,1,3,1]
[3,5,8,4,1,2,6,7]=>[3,1,4]
[3,5,8,4,1,6,2,7]=>[3,1,2,2]
[4,2,8,3,6,1,7,5]=>[1,2,2,2,1]
[3,5,8,4,1,6,7,2]=>[3,1,3,1]
[2,5,8,4,1,7,3,6]=>[3,1,2,2]
[3,6,4,2,1,7,8,5]=>[2,1,1,3,1]
[3,6,4,2,1,7,5,8]=>[2,1,1,2,2]
[3,5,6,4,1,8,7,2]=>[3,1,2,1,1]
[2,6,4,5,1,3,7,8]=>[2,2,4]
[7,6,5,1,4,3,8,2]=>[1,1,1,2,2,1]
[7,6,5,1,2,8,4,3]=>[1,1,1,3,1,1]
[7,6,5,1,2,8,3,4]=>[1,1,1,3,2]
[7,6,5,1,8,2,4,3]=>[1,1,1,2,2,1]
[7,6,5,1,8,2,3,4]=>[1,1,1,2,3]
[7,6,5,1,8,3,2,4]=>[1,1,1,2,1,2]
[7,6,5,1,4,8,2,3]=>[1,1,1,3,2]
[3,6,4,5,1,7,2,8]=>[2,2,2,2]
[2,5,6,4,1,7,8,3]=>[3,1,3,1]
[7,8,5,4,1,6,3,2]=>[2,1,1,2,1,1]
[2,5,6,4,1,7,3,8]=>[3,1,2,2]
[3,6,4,5,1,7,8,2]=>[2,2,3,1]
[7,6,5,1,4,8,3,2]=>[1,1,1,3,1,1]
[7,6,5,1,8,3,4,2]=>[1,1,1,2,2,1]
[7,6,5,1,8,4,2,3]=>[1,1,1,2,1,2]
[4,1,7,6,2,8,5,3]=>[1,2,1,2,1,1]
[7,8,6,2,1,3,5,4]=>[2,1,1,3,1]
[3,7,6,1,2,8,4,5]=>[2,1,3,2]
[2,6,5,3,1,4,8,7]=>[2,1,1,3,1]
[4,6,1,5,3,2,8,7]=>[2,2,1,2,1]
[3,6,1,4,2,5,8,7]=>[2,2,3,1]
[2,6,4,5,7,8,1,3]=>[2,4,2]
[8,7,1,6,5,2,4,3]=>[1,1,2,1,2,1]
[7,2,5,6,8,1,3,4]=>[1,4,3]
[6,1,3,4,2,8,7,5]=>[1,3,2,1,1]
[2,4,5,6,1,8,7,3]=>[4,2,1,1]
[8,4,1,6,5,7,3,2]=>[1,1,2,2,1,1]
[2,8,3,4,7,5,1,6]=>[2,3,1,2]
[6,8,2,7,4,3,5,1]=>[2,2,1,2,1]
[4,7,8,5,1,6,3,2]=>[3,1,2,1,1]
[8,2,6,4,7,3,5,1]=>[1,2,2,2,1]
[4,8,6,1,7,3,2,5]=>[2,1,2,1,2]
[8,7,3,2,1,5,4,6]=>[1,1,1,1,2,2]
[3,8,5,1,7,2,4,6]=>[2,1,2,3]
[6,8,7,1,3,2,4,5]=>[2,1,2,3]
[2,5,1,8,7,4,6,3]=>[2,2,1,2,1]
[3,7,1,8,4,5,6,2]=>[2,2,3,1]
[6,2,3,8,4,7,5,1]=>[1,3,2,1,1]
[8,6,4,3,1,7,2,5]=>[1,1,1,1,2,2]
[8,3,7,4,6,1,2,5]=>[1,2,2,3]
[7,1,3,8,6,4,5,2]=>[1,3,1,2,1]
[2,3,5,8,6,7,4,1]=>[4,2,1,1]
[7,4,2,1,8,6,5,3]=>[1,1,1,2,1,1,1]
[4,6,7,2,5,8,3,1]=>[3,3,1,1]
[7,6,2,5,3,8,1,4]=>[1,1,2,2,2]
[6,2,1,3,4,8,7,5]=>[1,1,4,1,1]
[6,5,4,2,8,3,1,7]=>[1,1,1,2,1,2]
[5,4,3,1,8,7,2,6]=>[1,1,1,2,1,2]
[6,1,4,3,8,5,2,7]=>[1,2,2,1,2]
[4,7,6,2,8,1,5,3]=>[2,1,2,2,1]
[6,4,5,1,7,8,3,2]=>[1,2,3,1,1]
[4,2,3,1,7,8,6,5]=>[1,2,3,1,1]
[3,4,2,1,8,6,7,5]=>[2,1,2,2,1]
[2,7,6,8,1,5,3,4]=>[2,2,2,2]
[6,4,5,8,3,1,2,7]=>[1,3,1,3]
[8,1,3,2,5,6,7,4]=>[1,2,4,1]
[3,6,8,1,5,2,4,7]=>[3,2,3]
[3,2,8,7,4,5,1,6]=>[1,2,1,2,2]
[6,3,8,5,7,4,2,1]=>[1,2,2,1,1,1]
[7,4,6,8,5,1,2,3]=>[1,3,1,3]
[2,1,4,8,7,5,3,6]=>[1,3,1,1,2]
[2,1,6,8,3,7,5,4]=>[1,3,2,1,1]
[3,6,8,2,4,1,5,7]=>[3,2,3]
[6,2,8,1,7,5,4,3]=>[1,2,2,1,1,1]
[2,6,5,4,8,1,3,7]=>[2,1,2,3]
[6,5,3,4,8,1,7,2]=>[1,1,3,2,1]
[8,4,3,2,5,1,7,6]=>[1,1,1,2,2,1]
[4,2,8,1,5,3,6,7]=>[1,2,2,3]
[5,1,8,2,6,4,3,7]=>[1,2,2,1,2]
[7,4,8,6,2,1,3,5]=>[1,2,1,1,3]
[4,6,2,8,3,7,5,1]=>[2,2,2,1,1]
[2,1,5,8,3,6,4,7]=>[1,3,2,2]
[2,8,5,3,6,7,1,4]=>[2,1,3,2]
[7,8,5,6,4,1,3,2]=>[2,2,1,2,1]
[5,8,4,1,6,3,7,2]=>[2,1,2,2,1]
[4,8,1,3,5,7,6,2]=>[2,4,1,1]
[3,8,1,4,5,6,2,7]=>[2,4,2]
[7,6,8,3,5,1,4,2]=>[1,2,2,2,1]
[7,8,6,3,5,1,4,2]=>[2,1,2,2,1]
[5,3,8,7,6,1,4,2]=>[1,2,1,1,2,1]
[6,5,8,4,7,1,3,2]=>[1,2,2,2,1]
[6,7,4,2,5,3,1,8]=>[2,1,2,1,2]
[7,6,4,8,3,1,5,2]=>[1,1,2,1,2,1]
[7,4,8,5,6,1,3,2]=>[1,2,2,2,1]
[7,4,2,5,6,3,1,8]=>[1,1,3,1,2]
[4,2,7,5,6,3,1,8]=>[1,2,2,1,2]
[3,4,7,5,6,2,1,8]=>[3,2,1,2]
[4,7,3,5,6,2,1,8]=>[2,3,1,2]
[3,7,2,5,6,4,1,8]=>[2,3,1,2]
[7,8,3,5,6,1,4,2]=>[2,3,2,1]
[1,6,8,5,2,7,4,3]=>[3,1,2,1,1]
[6,2,8,5,1,7,4,3]=>[1,2,1,2,1,1]
[6,7,4,8,2,1,5,3]=>[2,2,1,2,1]
[3,2,7,8,6,1,5,4]=>[1,3,1,2,1]
[6,8,4,1,2,3,7,5]=>[2,1,4,1]
[4,1,8,5,6,3,2,7]=>[1,2,2,1,2]
[1,8,2,5,6,4,3,7]=>[2,3,1,2]
[6,1,8,5,3,7,4,2]=>[1,2,1,2,1,1]
[3,8,1,5,2,7,6,4]=>[2,2,2,1,1]
[8,2,1,5,3,7,6,4]=>[1,1,2,2,1,1]
[1,5,2,4,6,7,8,3]=>[2,5,1]
[4,1,5,3,6,7,8,2]=>[1,2,4,1]
[8,1,6,5,3,7,2,4]=>[1,2,1,2,2]
[7,1,4,6,3,2,8,5]=>[1,3,1,2,1]
[3,2,6,4,1,7,8,5]=>[1,2,1,3,1]
[7,6,4,3,1,2,8,5]=>[1,1,1,1,3,1]
[8,6,3,5,1,7,2,4]=>[1,1,2,2,2]
[4,5,3,1,6,7,8,2]=>[2,1,4,1]
[3,5,2,1,6,7,8,4]=>[2,1,4,1]
[5,2,3,1,6,7,8,4]=>[1,2,4,1]
[1,5,3,2,6,7,8,4]=>[2,1,4,1]
[8,4,6,5,1,7,2,3]=>[1,2,1,2,2]
[7,5,4,6,1,2,8,3]=>[1,1,2,3,1]
[3,2,5,6,1,7,8,4]=>[1,3,3,1]
[3,2,8,7,6,1,4,5]=>[1,2,1,1,3]
[6,8,4,7,2,1,3,5]=>[2,2,1,3]
[3,8,7,5,6,1,2,4]=>[2,1,2,3]
[8,2,7,5,6,1,3,4]=>[1,2,2,3]
[4,8,6,5,1,7,3,2]=>[2,1,1,2,1,1]
[1,7,4,6,2,3,8,5]=>[2,2,3,1]
[7,6,4,2,1,5,8,3]=>[1,1,1,1,3,1]
[5,7,4,6,1,3,8,2]=>[2,2,3,1]
[8,6,4,7,3,1,2,5]=>[1,1,2,1,3]
[5,2,4,3,7,1,8,6]=>[1,2,2,2,1]
[3,5,4,2,7,1,8,6]=>[2,1,2,2,1]
[8,6,4,1,3,5,2,7]=>[1,1,1,3,2]
[6,7,4,1,5,3,8,2]=>[2,1,2,2,1]
[7,5,4,1,2,6,8,3]=>[1,1,1,4,1]
[1,7,4,2,3,6,8,5]=>[2,1,4,1]
[1,8,2,5,3,7,6,4]=>[2,2,2,1,1]
[6,8,1,5,4,7,3,2]=>[2,2,2,1,1]
[8,2,1,5,6,4,3,7]=>[1,1,3,1,2]
[3,8,1,5,6,4,2,7]=>[2,3,1,2]
[6,8,4,1,2,5,3,7]=>[2,1,3,2]
[3,2,8,1,6,5,4,7]=>[1,2,2,1,2]
[3,2,6,1,5,7,8,4]=>[1,2,4,1]
[7,6,4,1,5,2,8,3]=>[1,1,1,2,2,1]
[8,6,1,5,4,7,2,3]=>[1,1,2,2,2]
[3,5,1,4,6,7,8,2]=>[2,5,1]
[5,2,1,4,6,7,8,3]=>[1,1,5,1]
[5,4,1,3,6,7,8,2]=>[1,1,5,1]
[8,4,1,5,3,7,2,6]=>[1,1,2,2,2]
[7,5,4,1,3,2,8,6]=>[1,1,1,2,2,1]
[3,2,5,1,4,7,8,6]=>[1,2,4,1]
[7,1,4,3,5,2,8,6]=>[1,2,2,2,1]
[8,1,3,5,4,7,2,6]=>[1,3,2,2]
[5,1,3,4,6,7,8,2]=>[1,6,1]
[3,1,8,2,5,7,4,6]=>[1,2,3,2]
[8,3,2,6,1,4,7,5]=>[1,1,2,3,1]
[2,8,1,6,4,3,7,5]=>[2,2,1,2,1]
[2,6,1,3,8,7,5,4]=>[2,3,1,1,1]
[2,5,7,1,3,8,6,4]=>[3,3,1,1]
[2,6,8,1,5,7,4,3]=>[3,3,1,1]
[2,7,1,5,8,4,6,3]=>[2,3,2,1]
[2,7,1,6,4,8,3,5]=>[2,2,2,2]
[2,7,1,6,5,3,8,4]=>[2,2,1,2,1]
[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1]
[8,3,2,7,1,6,5,4]=>[1,1,2,2,1,1]
[4,1,8,7,3,2,6,5]=>[1,2,1,1,2,1]
[4,1,7,2,8,6,5,3]=>[1,2,2,1,1,1]
[3,7,1,8,6,5,4,2]=>[2,2,1,1,1,1]
[3,7,6,1,4,2,5,8]=>[2,1,2,3]
[3,7,5,1,4,6,8,2]=>[2,1,4,1]
[3,6,8,5,1,4,7,2]=>[3,1,3,1]
[7,3,5,8,2,1,4,6]=>[1,3,1,3]
[7,3,6,2,1,4,5,8]=>[1,2,1,4]
[7,3,6,2,1,5,4,8]=>[1,2,1,2,2]
[7,4,2,8,1,6,5,3]=>[1,1,2,2,1,1]
[8,7,5,3,2,1,6,4]=>[1,1,1,1,1,2,1]
[7,5,2,6,3,1,4,8]=>[1,1,2,1,3]
[7,4,6,2,1,8,3,5]=>[1,2,1,2,2]
[6,8,4,5,2,1,7,3]=>[2,2,1,2,1]
[4,6,8,5,1,7,3,2]=>[3,1,2,1,1]
[4,7,5,1,3,8,6,2]=>[2,1,3,1,1]
[4,7,6,1,5,3,2,8]=>[2,1,2,1,2]
[5,1,7,6,3,8,2,4]=>[1,2,1,2,2]
[5,1,7,6,4,2,8,3]=>[1,2,1,1,2,1]
[5,1,8,7,6,4,3,2]=>[1,2,1,1,1,1,1]
[8,5,2,1,7,6,4,3]=>[1,1,1,2,1,1,1]
[8,5,2,1,6,3,7,4]=>[1,1,1,2,2,1]
[5,1,8,6,3,2,7,4]=>[1,2,1,1,2,1]
[3,6,1,7,4,8,2,5]=>[2,2,2,2]
[4,1,8,6,3,7,2,5]=>[1,2,1,2,2]
[8,4,2,5,7,3,1,6]=>[1,1,3,1,2]
[3,4,6,8,5,7,1,2]=>[4,2,2]
[5,4,8,2,7,3,6,1]=>[1,2,2,2,1]
[5,4,8,7,3,6,1,2]=>[1,2,1,2,2]
[8,5,4,7,3,6,2,1]=>[1,1,2,2,1,1]
[6,4,3,8,7,1,2,5]=>[1,1,2,1,3]
[6,3,7,2,4,8,1,5]=>[1,2,3,2]
[5,6,8,4,2,7,3,1]=>[3,1,2,1,1]
[5,7,4,2,8,1,3,6]=>[2,1,2,3]
[6,5,2,7,1,3,8,4]=>[1,1,2,3,1]
[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,2,1]
[6,4,7,3,1,8,2,5]=>[1,2,1,2,2]
[5,7,4,3,8,6,1,2]=>[2,1,2,1,2]
[7,5,8,4,6,3,2,1]=>[1,2,2,1,1,1]
[7,6,4,8,3,5,2,1]=>[1,1,2,2,1,1]
[7,6,5,3,8,2,4,1]=>[1,1,1,2,2,1]
[5,6,3,7,4,2,1,8]=>[2,2,1,1,2]
[7,6,3,8,5,1,4,2]=>[1,1,2,1,2,1]
[6,4,8,1,3,2,5,7]=>[1,2,2,3]
[7,4,8,6,3,1,5,2]=>[1,2,1,1,2,1]
[4,2,7,6,5,3,1,8]=>[1,2,1,1,1,2]
[3,7,2,4,6,5,1,8]=>[2,3,1,2]
[8,1,3,4,5,2,6,7]=>[1,4,3]
[1,6,8,4,2,5,3,7]=>[3,1,2,2]
[6,2,8,4,1,5,7,3]=>[1,2,1,3,1]
[6,7,4,8,5,1,2,3]=>[2,2,1,3]
[3,2,7,8,5,1,6,4]=>[1,3,1,2,1]
[3,2,8,1,5,4,6,7]=>[1,2,2,3]
[6,1,4,8,5,3,7,2]=>[1,3,1,2,1]
[1,4,8,5,2,6,7,3]=>[3,1,3,1]
[6,1,8,4,3,7,2,5]=>[1,2,1,2,2]
[3,7,1,4,2,5,8,6]=>[2,2,3,1]
[7,2,1,4,3,5,6,8]=>[1,1,2,4]
[4,1,5,3,6,8,2,7]=>[1,2,3,2]
[6,1,8,5,3,2,7,4]=>[1,2,1,1,2,1]
[7,1,4,6,3,8,5,2]=>[1,3,2,1,1]
[3,2,6,4,1,8,7,5]=>[1,2,1,2,1,1]
[7,6,4,3,1,8,2,5]=>[1,1,1,1,2,2]
[3,5,2,1,8,7,6,4]=>[2,1,2,1,1,1]
[1,5,3,2,8,6,4,7]=>[2,1,2,1,2]
[5,4,2,1,7,8,6,3]=>[1,1,1,3,1,1]
[8,2,7,6,5,1,3,4]=>[1,2,1,1,3]
[8,6,2,7,1,4,5,3]=>[1,1,2,3,1]
[1,7,3,6,2,8,5,4]=>[2,2,2,1,1]
[7,6,3,2,1,8,5,4]=>[1,1,1,1,2,1,1]
[8,6,3,7,4,1,2,5]=>[1,1,2,1,3]
[5,2,3,4,7,1,8,6]=>[1,4,2,1]
[8,6,3,1,4,5,7,2]=>[1,1,1,4,1]
[6,7,3,1,5,4,2,8]=>[2,1,2,1,2]
[5,8,3,1,2,4,7,6]=>[2,1,4,1]
[8,1,3,2,4,5,6,7]=>[1,2,5]
[8,4,1,7,2,3,6,5]=>[1,1,2,3,1]
[8,2,1,6,5,4,7,3]=>[1,1,2,1,2,1]
[3,8,1,5,6,4,7,2]=>[2,3,2,1]
[6,8,4,1,2,5,7,3]=>[2,1,4,1]
[3,2,8,1,6,5,7,4]=>[1,2,2,2,1]
[7,6,4,1,5,2,3,8]=>[1,1,1,2,3]
[8,6,1,5,4,7,3,2]=>[1,1,2,2,1,1]
[3,5,1,4,6,7,2,8]=>[2,4,2]
[5,2,1,4,7,6,3,8]=>[1,1,3,1,2]
[4,5,8,2,1,3,7,6]=>[3,1,3,1]
[5,8,2,3,1,4,6,7]=>[2,2,4]
[4,2,1,3,5,8,7,6]=>[1,1,4,1,1]
[5,4,1,3,6,2,8,7]=>[1,1,3,2,1]
[8,5,4,1,3,6,2,7]=>[1,1,1,3,2]
[3,2,5,1,4,6,8,7]=>[1,2,4,1]
[8,1,4,3,5,6,7,2]=>[1,2,4,1]
[7,1,3,5,4,6,2,8]=>[1,3,2,2]
[5,1,3,4,6,2,7,8]=>[1,4,3]
[4,1,3,2,5,7,6,8]=>[1,2,3,2]
[6,8,2,4,5,1,3,7]=>[2,3,3]
[3,6,7,2,5,1,4,8]=>[3,2,3]
[4,6,7,3,1,5,2,8]=>[3,1,2,2]
[5,8,1,2,4,7,3,6]=>[2,4,2]
[6,8,1,3,5,2,7,4]=>[2,3,2,1]
[6,8,3,1,4,5,7,2]=>[2,1,4,1]
[7,5,1,8,2,3,6,4]=>[1,1,2,3,1]
[6,1,8,2,3,4,7,5]=>[1,2,4,1]
[5,3,8,4,2,6,7,1]=>[1,2,1,3,1]
[5,1,8,4,6,3,7,2]=>[1,2,2,2,1]
[4,1,8,3,5,7,2,6]=>[1,2,3,2]
[3,4,7,2,6,1,8,5]=>[3,2,2,1]
[4,5,7,3,2,6,8,1]=>[3,1,3,1]
[4,5,7,2,3,6,8,1]=>[3,4,1]
[2,6,3,4,7,5,8,1]=>[2,3,2,1]
[3,6,4,2,7,5,8,1]=>[2,1,2,2,1]
[4,5,2,7,1,6,8,3]=>[2,2,3,1]
[3,4,1,6,5,8,2,7]=>[2,2,2,2]
[4,1,2,8,5,7,3,6]=>[1,3,2,2]
[7,3,1,4,8,5,6,2]=>[1,1,3,2,1]
[5,6,3,1,7,4,2,8]=>[2,1,2,1,2]
[7,3,4,1,8,5,2,6]=>[1,2,2,1,2]
[6,4,2,8,7,1,5,3]=>[1,1,2,1,2,1]
[7,2,4,8,1,5,3,6]=>[1,3,2,2]
[7,1,3,8,5,2,4,6]=>[1,3,1,3]
[3,2,6,7,1,8,4,5]=>[1,3,2,2]
[4,6,3,1,7,8,5,2]=>[2,1,3,1,1]
[5,3,1,6,7,8,4,2]=>[1,1,4,1,1]
[4,1,6,2,7,8,5,3]=>[1,2,3,1,1]
[2,1,3,4,8,7,5,6]=>[1,4,1,2]
[4,8,3,7,6,5,1,2]=>[2,2,1,1,2]
[6,3,8,7,5,4,1,2]=>[1,2,1,1,1,2]
[5,3,8,7,6,4,1,2]=>[1,2,1,1,1,2]
[2,8,7,6,1,5,4,3]=>[2,1,1,2,1,1]
[5,2,8,7,6,1,4,3]=>[1,2,1,1,2,1]
[6,2,8,7,5,1,4,3]=>[1,2,1,1,2,1]
[7,8,2,6,5,1,4,3]=>[2,2,1,2,1]
[6,1,8,7,5,4,3,2]=>[1,2,1,1,1,1,1]
[3,1,8,7,6,5,4,2]=>[1,2,1,1,1,1,1]
[7,8,2,6,1,5,4,3]=>[2,2,2,1,1]
[6,2,8,7,1,5,4,3]=>[1,2,1,2,1,1]
[4,2,8,1,7,6,5,3]=>[1,2,2,1,1,1]
[4,8,2,7,6,1,5,3]=>[2,2,1,2,1]
[3,8,7,2,1,6,5,4]=>[2,1,1,2,1,1]
[6,5,8,7,1,4,3,2]=>[1,2,1,2,1,1]
[4,8,1,7,6,5,3,2]=>[2,2,1,1,1,1]
[5,4,1,8,7,6,3,2]=>[1,1,2,1,1,1,1]
[6,4,8,1,7,5,3,2]=>[1,2,2,1,1,1]
[7,8,4,1,6,5,3,2]=>[2,1,2,1,1,1]
[7,8,3,1,6,5,4,2]=>[2,1,2,1,1,1]
[6,3,8,1,7,5,4,2]=>[1,2,2,1,1,1]
[5,3,1,8,7,6,4,2]=>[1,1,2,1,1,1,1]
[7,8,2,1,6,5,4,3]=>[2,1,2,1,1,1]
[6,5,3,1,8,7,4,2]=>[1,1,1,2,1,1,1]
[6,4,3,1,8,7,5,2]=>[1,1,1,2,1,1,1]
[5,4,3,1,8,7,6,2]=>[1,1,1,2,1,1,1]
[7,5,2,1,8,6,4,3]=>[1,1,1,2,1,1,1]
[5,4,2,1,8,7,6,3]=>[1,1,1,2,1,1,1]
[7,3,2,1,8,6,5,4]=>[1,1,1,2,1,1,1]
[6,3,2,1,8,7,5,4]=>[1,1,1,2,1,1,1]
[6,1,4,2,3,5,8,7]=>[1,2,4,1]
[8,6,1,4,2,3,5,7]=>[1,1,2,4]
[6,8,1,4,2,3,5,7]=>[2,2,4]
[8,1,4,2,3,6,5,7]=>[1,2,3,2]
[4,1,8,2,3,6,5,7]=>[1,2,3,2]
[8,2,3,6,1,4,5,7]=>[1,3,4]
[6,2,3,8,1,4,5,7]=>[1,3,4]
[4,6,2,3,8,1,5,7]=>[2,3,3]
[4,8,2,3,6,1,5,7]=>[2,3,3]
[8,2,3,6,4,1,5,7]=>[1,3,1,3]
[8,4,3,6,2,1,5,7]=>[1,1,2,1,3]
[6,2,3,8,4,1,5,7]=>[1,3,1,3]
[8,4,2,3,6,1,5,7]=>[1,1,3,3]
[6,4,2,3,8,1,5,7]=>[1,1,3,3]
[2,6,4,3,8,1,5,7]=>[2,1,2,3]
[2,8,4,3,6,1,5,7]=>[2,1,2,3]
[2,6,3,8,4,1,5,7]=>[2,2,1,3]
[6,3,8,4,2,1,5,7]=>[1,2,1,1,3]
[2,6,3,8,1,4,5,7]=>[2,2,4]
[2,8,3,6,1,4,5,7]=>[2,2,4]
[8,3,6,4,2,1,5,7]=>[1,2,1,1,3]
[2,8,3,6,4,1,5,7]=>[2,2,1,3]
[8,3,6,2,4,1,5,7]=>[1,2,2,3]
[8,3,6,2,1,4,5,7]=>[1,2,1,4]
[6,2,1,3,8,4,5,7]=>[1,1,3,3]
[8,2,1,3,6,4,5,7]=>[1,1,3,3]
[6,3,8,2,4,1,5,7]=>[1,2,2,3]
[6,2,4,3,8,1,5,7]=>[1,2,2,3]
[3,6,4,7,8,5,1,2]=>[2,3,1,2]
[1,6,4,2,7,5,8,3]=>[2,1,2,2,1]
[3,6,4,2,7,1,5,8]=>[2,1,2,3]
[1,4,7,2,5,6,8,3]=>[3,4,1]
[6,4,8,5,3,7,1,2]=>[1,2,1,2,2]
[1,6,5,4,2,7,8,3]=>[2,1,1,3,1]
[4,2,5,3,6,1,7,8]=>[1,2,2,3]
[7,1,5,3,6,2,8,4]=>[1,2,2,2,1]
[1,6,5,2,4,8,7,3]=>[2,1,3,1,1]
[1,4,6,2,8,5,7,3]=>[3,2,2,1]
[7,8,1,4,2,5,6,3]=>[2,2,3,1]
[3,4,8,5,2,1,6,7]=>[3,1,1,3]
[4,8,5,3,1,6,2,7]=>[2,1,1,2,2]
[6,1,3,5,8,2,7,4]=>[1,4,2,1]
[6,1,8,7,4,2,3,5]=>[1,2,1,1,3]
[1,2,8,5,7,3,6,4]=>[3,2,2,1]
[1,3,6,8,7,5,2,4]=>[4,1,1,2]
[1,8,2,5,4,7,6,3]=>[2,2,2,1,1]
[7,1,2,4,5,8,6,3]=>[1,5,1,1]
[1,2,7,3,5,8,6,4]=>[3,3,1,1]
[6,1,3,2,5,7,8,4]=>[1,2,4,1]
[4,6,2,1,7,5,3,8]=>[2,1,2,1,2]
[1,6,3,7,8,5,2,4]=>[2,3,1,2]
[4,6,2,3,7,8,1,5]=>[2,4,2]
[4,6,3,7,1,2,8,5]=>[2,2,3,1]
[4,2,1,3,5,7,8,6]=>[1,1,5,1]
[7,3,2,4,5,1,8,6]=>[1,1,3,2,1]
[3,8,2,5,4,1,7,6]=>[2,2,1,2,1]
[7,8,4,2,6,3,1,5]=>[2,1,2,1,2]
[4,2,6,3,8,7,1,5]=>[1,2,2,1,2]
[5,8,2,7,4,3,1,6]=>[2,2,1,1,2]
[4,3,8,5,1,7,2,6]=>[1,2,1,2,2]
[4,3,6,8,1,2,7,5]=>[1,3,3,1]
[6,4,3,5,2,8,1,7]=>[1,1,2,2,2]
[6,5,3,8,4,2,1,7]=>[1,1,2,1,1,2]
[3,8,1,7,5,6,4,2]=>[2,2,2,1,1]
[8,2,5,7,3,6,4,1]=>[1,3,2,1,1]
[1,8,6,7,5,3,4,2]=>[2,2,1,2,1]
[8,2,6,7,5,3,4,1]=>[1,3,1,2,1]
[1,5,8,7,2,6,4,3]=>[3,1,2,1,1]
[5,4,8,6,2,3,7,1]=>[1,2,1,3,1]
[2,7,6,1,3,5,4,8]=>[2,1,3,2]
[6,4,1,8,2,5,7,3]=>[1,1,2,3,1]
[2,8,6,1,3,5,4,7]=>[2,1,3,2]
[4,1,3,6,5,8,7,2]=>[1,3,2,1,1]
[2,1,6,3,5,8,7,4]=>[1,2,3,1,1]
[2,4,1,3,8,5,7,6]=>[2,3,2,1]
[2,4,1,3,5,8,7,6]=>[2,4,1,1]
[2,6,1,3,5,8,7,4]=>[2,4,1,1]
[4,6,1,3,5,8,7,2]=>[2,4,1,1]
[6,1,4,3,5,8,7,2]=>[1,2,3,1,1]
[6,4,1,3,5,8,7,2]=>[1,1,4,1,1]
[6,2,1,3,5,8,7,4]=>[1,1,4,1,1]
[4,2,1,3,6,5,7,8]=>[1,1,3,3]
[4,2,1,6,3,5,7,8]=>[1,1,2,4]
[6,2,1,8,3,5,7,4]=>[1,1,2,3,1]
[6,2,1,3,8,5,7,4]=>[1,1,3,2,1]
[6,1,4,3,8,5,7,2]=>[1,2,2,2,1]
[1,6,4,3,8,5,7,2]=>[2,1,2,2,1]
[8,1,4,3,6,5,7,2]=>[1,2,2,2,1]
[8,4,1,3,6,5,7,2]=>[1,1,3,2,1]
[8,2,1,3,6,5,7,4]=>[1,1,3,2,1]
[8,2,1,6,3,5,7,4]=>[1,1,2,3,1]
[8,2,1,4,3,5,7,6]=>[1,1,2,3,1]
[6,2,1,4,3,5,7,8]=>[1,1,2,4]
[8,2,4,1,3,5,7,6]=>[1,2,4,1]
[8,2,6,1,3,5,7,4]=>[1,2,4,1]
[8,4,6,1,3,5,7,2]=>[1,2,4,1]
[8,4,1,6,3,5,7,2]=>[1,1,2,3,1]
[8,1,4,6,3,5,7,2]=>[1,3,3,1]
[1,8,4,6,3,5,7,2]=>[2,2,3,1]
[1,6,4,8,3,5,7,2]=>[2,2,3,1]
[6,4,1,8,3,5,7,2]=>[1,1,2,3,1]
[6,4,8,1,3,5,7,2]=>[1,2,4,1]
[6,2,8,1,3,5,7,4]=>[1,2,4,1]
[4,2,8,1,3,5,7,6]=>[1,2,4,1]
[2,6,8,1,3,5,7,4]=>[3,4,1]
[4,6,8,1,3,5,7,2]=>[3,4,1]
[4,6,1,8,3,5,7,2]=>[2,2,3,1]
[4,1,6,8,3,5,7,2]=>[1,3,3,1]
[1,4,6,3,8,5,7,2]=>[3,2,2,1]
[4,6,1,3,8,5,7,2]=>[2,3,2,1]
[2,4,1,8,3,5,7,6]=>[2,2,3,1]
[2,1,6,8,3,5,7,4]=>[1,3,3,1]
[4,1,3,6,8,5,7,2]=>[1,4,2,1]
[1,4,3,6,8,5,7,2]=>[2,3,2,1]
[4,1,3,8,6,5,7,2]=>[1,3,1,2,1]
[2,1,8,3,6,5,7,4]=>[1,2,2,2,1]
[2,1,6,4,3,5,7,8]=>[1,2,1,4]
[2,6,1,4,3,5,7,8]=>[2,2,4]
[2,8,1,4,3,5,7,6]=>[2,2,3,1]
[2,8,1,6,3,5,7,4]=>[2,2,3,1]
[4,8,1,3,6,5,7,2]=>[2,3,2,1]
[1,4,8,3,6,5,7,2]=>[3,2,2,1]
[1,4,8,6,3,5,7,2]=>[3,1,3,1]
[4,1,8,6,3,5,7,2]=>[1,2,1,3,1]
[4,8,1,6,3,5,7,2]=>[2,2,3,1]
[4,8,6,1,3,5,7,2]=>[2,1,4,1]
[2,8,6,1,3,5,7,4]=>[2,1,4,1]
[2,8,4,1,3,5,7,6]=>[2,1,4,1]
[2,6,4,1,3,5,7,8]=>[2,1,5]
[4,6,2,1,3,5,7,8]=>[2,1,5]
[6,8,1,4,3,5,7,2]=>[2,2,3,1]
[6,1,8,4,3,5,7,2]=>[1,2,1,3,1]
[1,6,8,4,3,5,7,2]=>[3,1,3,1]
[1,8,6,4,3,5,7,2]=>[2,1,1,3,1]
[8,1,6,4,3,5,7,2]=>[1,2,1,3,1]
[8,6,1,4,3,5,7,2]=>[1,1,2,3,1]
[8,6,4,1,3,5,7,2]=>[1,1,1,4,1]
[8,6,2,1,3,5,7,4]=>[1,1,1,4,1]
[8,4,2,1,3,5,7,6]=>[1,1,1,4,1]
[7,8,6,5,2,1,4,3]=>[2,1,1,1,2,1]
[5,7,4,1,8,6,3,2]=>[2,1,2,1,1,1]
[5,6,4,2,8,3,7,1]=>[2,1,2,2,1]
[5,6,4,2,7,3,1,8]=>[2,1,2,1,2]
[5,7,1,4,6,3,2,8]=>[2,3,1,2]
[5,8,1,4,6,3,7,2]=>[2,3,2,1]
[3,6,7,4,5,8,2,1]=>[3,3,1,1]
[3,5,7,4,6,8,2,1]=>[3,3,1,1]
[6,8,4,1,7,2,5,3]=>[2,1,2,2,1]
[5,4,6,1,7,8,3,2]=>[1,2,3,1,1]
[5,6,4,1,8,7,3,2]=>[2,1,2,1,1,1]
[3,5,8,4,6,7,2,1]=>[3,3,1,1]
[3,6,8,4,5,7,2,1]=>[3,3,1,1]
[3,7,8,4,5,6,2,1]=>[3,3,1,1]
[6,8,1,4,5,3,7,2]=>[2,3,2,1]
[6,7,1,4,5,3,2,8]=>[2,3,1,2]
[3,7,1,5,4,6,2,8]=>[2,2,2,2]
[3,8,1,5,4,6,7,2]=>[2,2,3,1]
[3,7,1,5,4,6,8,2]=>[2,2,3,1]
[6,7,1,4,5,3,8,2]=>[2,3,2,1]
[5,7,1,4,6,3,8,2]=>[2,3,2,1]
[5,6,4,2,7,3,8,1]=>[2,1,2,2,1]
[5,4,7,2,8,3,1,6]=>[1,2,2,1,2]
[5,4,7,2,8,3,6,1]=>[1,2,2,2,1]
[5,6,4,2,8,3,1,7]=>[2,1,2,1,2]
[5,8,1,4,6,3,2,7]=>[2,3,1,2]
[3,8,1,5,4,6,2,7]=>[2,2,2,2]
[3,6,1,5,4,2,7,8]=>[2,2,1,3]
[3,6,1,5,4,8,2,7]=>[2,2,2,2]
[6,8,3,1,4,2,5,7]=>[2,1,2,3]
[7,3,8,1,4,2,5,6]=>[1,2,2,3]
[6,7,3,1,4,2,8,5]=>[2,1,2,2,1]
[3,6,1,5,4,7,8,2]=>[2,2,3,1]
[3,4,1,2,7,6,5,8]=>[2,3,1,2]
[3,4,1,2,6,8,7,5]=>[2,4,1,1]
[6,8,3,1,4,7,2,5]=>[2,1,3,2]
[6,4,7,2,8,5,1,3]=>[1,2,2,1,2]
[5,8,1,4,7,3,2,6]=>[2,3,1,2]
[7,8,1,4,5,3,2,6]=>[2,3,1,2]
[3,8,1,5,4,7,2,6]=>[2,2,2,2]
[3,6,1,5,4,8,7,2]=>[2,2,2,1,1]
[3,6,1,5,4,7,2,8]=>[2,2,2,2]
[6,7,3,1,4,2,5,8]=>[2,1,2,3]
[6,8,3,1,4,2,7,5]=>[2,1,2,2,1]
[7,8,3,1,4,6,2,5]=>[2,1,3,2]
[7,8,4,2,6,5,1,3]=>[2,1,2,1,2]
[6,5,8,7,3,4,2,1]=>[1,2,1,2,1,1]
[7,8,3,1,4,6,5,2]=>[2,1,3,1,1]
[6,7,3,1,4,5,2,8]=>[2,1,3,2]
[3,7,1,5,4,2,6,8]=>[2,2,1,3]
[3,8,1,5,4,2,7,6]=>[2,2,1,2,1]
[5,8,1,4,7,3,6,2]=>[2,3,2,1]
[6,8,4,2,7,5,3,1]=>[2,1,2,1,1,1]
[6,4,7,2,8,5,3,1]=>[1,2,2,1,1,1]
[6,3,7,1,4,8,5,2]=>[1,2,3,1,1]
[6,8,3,1,4,7,5,2]=>[2,1,3,1,1]
[3,7,1,5,4,8,6,2]=>[2,2,2,1,1]
[3,4,1,2,8,5,7,6]=>[2,3,2,1]
[3,4,1,2,5,8,7,6]=>[2,4,1,1]
[3,7,1,5,4,2,8,6]=>[2,2,1,2,1]
[6,7,3,1,4,5,8,2]=>[2,1,4,1]
[7,3,8,1,4,5,2,6]=>[1,2,3,2]
[7,3,8,1,4,5,6,2]=>[1,2,4,1]
[6,8,3,1,4,5,2,7]=>[2,1,3,2]
[3,8,1,5,4,2,6,7]=>[2,2,1,3]
[8,7,6,3,5,2,1,4]=>[1,1,1,2,1,2]
[8,7,4,6,3,2,1,5]=>[1,1,2,1,1,2]
[8,5,7,4,3,2,1,6]=>[1,2,1,1,1,2]
[8,7,6,2,5,4,1,3]=>[1,1,1,2,1,2]
[8,5,4,7,3,2,1,6]=>[1,1,2,1,1,2]
[8,7,3,6,5,2,1,4]=>[1,1,2,1,1,2]
[6,5,8,4,3,2,1,7]=>[1,2,1,1,1,2]
[8,4,7,6,3,2,1,5]=>[1,2,1,1,1,2]
[5,8,7,4,3,2,1,6]=>[2,1,1,1,1,2]
[5,8,6,2,3,4,7,1]=>[2,1,4,1]
[4,5,2,7,3,1,8,6]=>[2,2,1,2,1]
[4,8,2,6,3,5,7,1]=>[2,2,3,1]
[4,3,7,8,6,5,1,2]=>[1,3,1,1,2]
[4,1,7,2,5,8,6,3]=>[1,2,3,1,1]
[7,8,2,1,5,6,4,3]=>[2,1,3,1,1]
[1,6,2,5,8,4,3,7]=>[2,3,1,2]
[2,1,8,7,4,5,3,6]=>[1,2,1,2,2]
[7,3,1,6,8,5,2,4]=>[1,1,3,1,2]
[1,5,8,6,2,3,7,4]=>[3,1,3,1]
[2,4,8,3,1,6,5,7]=>[3,1,2,2]
[5,2,7,1,8,6,3,4]=>[1,2,2,1,2]
[2,6,1,3,8,7,4,5]=>[2,3,1,2]
[6,5,2,8,1,7,3,4]=>[1,1,2,2,2]
[2,8,3,5,1,7,4,6]=>[2,2,2,2]
[5,4,3,8,7,1,6,2]=>[1,1,2,1,2,1]
[8,5,4,3,7,2,6,1]=>[1,1,1,2,2,1]
[8,3,7,4,2,6,5,1]=>[1,2,1,2,1,1]
[2,8,6,5,1,7,4,3]=>[2,1,1,2,1,1]
[6,3,2,8,4,1,7,5]=>[1,1,2,1,2,1]
[2,8,3,4,1,7,5,6]=>[2,2,2,2]
[5,4,2,8,3,1,7,6]=>[1,1,2,1,2,1]
[2,8,4,3,1,7,6,5]=>[2,1,1,2,1,1]
[2,8,5,3,1,7,6,4]=>[2,1,1,2,1,1]
[2,8,6,4,1,7,5,3]=>[2,1,1,2,1,1]
[3,8,7,5,1,6,4,2]=>[2,1,1,2,1,1]
[8,3,7,5,2,6,4,1]=>[1,2,1,2,1,1]
[8,4,7,6,2,5,3,1]=>[1,2,1,2,1,1]
[4,8,7,6,1,5,3,2]=>[2,1,1,2,1,1]
[7,4,8,6,2,1,5,3]=>[1,2,1,1,2,1]
[7,3,8,5,2,1,6,4]=>[1,2,1,1,2,1]
[7,3,8,4,2,1,6,5]=>[1,2,1,1,2,1]
[7,5,4,3,8,2,1,6]=>[1,1,1,2,1,2]
[3,7,8,4,1,2,6,5]=>[3,1,3,1]
[3,7,8,5,1,2,6,4]=>[3,1,3,1]
[4,7,8,6,1,2,5,3]=>[3,1,3,1]
[8,7,4,6,3,5,2,1]=>[1,1,2,2,1,1]
[5,7,8,6,1,2,4,3]=>[3,1,3,1]
[6,4,7,8,3,1,2,5]=>[1,3,1,3]
[7,3,4,8,2,1,5,6]=>[1,3,1,3]
[7,6,4,8,3,2,1,5]=>[1,1,2,1,1,2]
[7,5,8,6,2,1,4,3]=>[1,2,1,1,2,1]
[6,5,8,7,3,1,4,2]=>[1,2,1,1,2,1]
[2,4,8,3,1,5,7,6]=>[3,1,3,1]
[6,3,2,4,8,1,5,7]=>[1,1,3,3]
[2,3,8,4,1,6,7,5]=>[3,1,3,1]
[2,3,8,5,1,6,7,4]=>[3,1,3,1]
[6,4,8,7,3,1,5,2]=>[1,2,1,1,2,1]
[8,6,4,7,3,2,5,1]=>[1,1,2,1,2,1]
[8,3,4,7,2,5,6,1]=>[1,3,3,1]
[3,4,8,7,1,5,6,2]=>[3,1,3,1]
[2,4,8,6,1,5,7,3]=>[3,1,3,1]
[2,5,8,6,1,4,7,3]=>[3,1,3,1]
[8,3,5,7,2,4,6,1]=>[1,3,3,1]
[8,4,6,7,2,3,5,1]=>[1,3,3,1]
[4,6,8,7,1,3,5,2]=>[3,1,3,1]
[2,6,8,5,1,3,7,4]=>[3,1,3,1]
[2,6,8,4,1,3,7,5]=>[3,1,3,1]
[2,5,8,3,1,4,7,6]=>[3,1,3,1]
[5,6,8,7,1,3,4,2]=>[3,1,3,1]
[7,4,6,8,2,1,3,5]=>[1,3,1,3]
[2,3,5,4,1,8,6,7]=>[3,1,2,2]
[2,3,6,4,8,1,5,7]=>[3,2,3]
[1,8,4,6,3,5,2,7]=>[2,2,2,2]
[5,4,8,6,2,1,3,7]=>[1,2,1,1,3]
[2,3,6,8,1,5,4,7]=>[4,2,2]
[2,5,6,1,4,7,8,3]=>[3,4,1]
[2,5,6,1,4,7,3,8]=>[3,3,2]
[7,3,5,1,6,8,4,2]=>[1,2,3,1,1]
[2,7,6,1,8,5,4,3]=>[2,1,2,1,1,1]
[2,7,6,8,1,4,5,3]=>[2,2,3,1]
[1,8,7,6,3,2,5,4]=>[2,1,1,1,2,1]
[1,8,7,6,3,2,4,5]=>[2,1,1,1,3]
[5,7,8,6,2,3,4,1]=>[3,1,3,1]
[2,7,6,1,8,5,3,4]=>[2,1,2,1,2]
[6,3,5,1,7,2,4,8]=>[1,2,2,3]
[2,3,4,7,6,1,5,8]=>[4,1,3]
[7,3,5,8,4,1,2,6]=>[1,3,1,3]
[1,8,4,5,2,7,3,6]=>[2,2,2,2]
[1,8,4,5,2,7,6,3]=>[2,2,2,1,1]
[7,3,5,8,4,1,6,2]=>[1,3,1,2,1]
[2,7,6,4,8,5,1,3]=>[2,1,2,1,2]
[7,3,5,4,6,8,1,2]=>[1,2,3,2]
[6,3,5,4,7,1,8,2]=>[1,2,2,2,1]
[6,3,5,4,7,1,2,8]=>[1,2,2,3]
[3,4,1,5,6,8,7,2]=>[2,4,1,1]
[3,7,1,6,8,5,2,4]=>[2,3,1,2]
[2,3,1,8,6,4,7,5]=>[2,2,1,2,1]
[1,8,4,3,6,2,5,7]=>[2,1,2,3]
[2,3,1,8,6,4,5,7]=>[2,2,1,3]
[3,7,1,6,8,5,4,2]=>[2,3,1,1,1]
[6,3,5,4,7,2,1,8]=>[1,2,2,1,2]
[7,3,5,4,6,8,2,1]=>[1,2,3,1,1]
[2,7,6,4,8,5,3,1]=>[2,1,2,1,1,1]
[1,8,4,5,2,6,3,7]=>[2,2,2,2]
[6,4,8,5,3,1,2,7]=>[1,2,1,1,3]
[7,3,5,8,4,6,2,1]=>[1,3,2,1,1]
[2,3,4,6,5,8,1,7]=>[4,2,2]
[2,3,4,7,5,1,8,6]=>[4,1,2,1]
[2,3,4,7,5,1,6,8]=>[4,1,3]
[2,3,4,7,1,6,5,8]=>[4,2,2]
[2,3,4,7,1,6,8,5]=>[4,3,1]
[2,3,4,6,1,8,7,5]=>[4,2,1,1]
[6,3,5,8,4,2,7,1]=>[1,3,1,2,1]
[7,4,8,5,3,2,1,6]=>[1,2,1,1,1,2]
[1,8,4,5,2,3,6,7]=>[2,2,4]
[7,4,8,5,3,2,6,1]=>[1,2,1,1,2,1]
[6,3,5,8,4,2,1,7]=>[1,3,1,1,2]
[5,2,4,6,8,3,7,1]=>[1,4,2,1]
[1,5,7,4,6,3,2,8]=>[3,2,1,2]
[5,2,8,4,6,3,7,1]=>[1,2,2,2,1]
[3,8,5,4,6,7,2,1]=>[2,1,3,1,1]
[6,8,3,4,5,7,2,1]=>[2,4,1,1]
[2,5,7,4,6,3,8,1]=>[3,2,2,1]
[5,4,1,7,8,3,2,6]=>[1,1,3,1,2]
[5,4,2,7,8,3,6,1]=>[1,1,3,2,1]
[5,1,4,6,8,3,2,7]=>[1,4,1,2]
[5,1,8,4,6,3,2,7]=>[1,2,2,1,2]
[8,1,6,4,5,3,2,7]=>[1,2,2,1,2]
[8,1,3,5,4,6,2,7]=>[1,3,2,2]
[8,1,6,2,4,3,5,7]=>[1,2,2,3]
[8,7,1,2,4,3,5,6]=>[1,1,3,3]
[1,7,6,2,4,3,5,8]=>[2,1,2,3]
[8,7,3,2,4,6,5,1]=>[1,1,1,3,1,1]
[8,2,6,3,4,5,7,1]=>[1,2,4,1]
[1,7,6,3,4,5,2,8]=>[2,1,3,2]
[1,7,2,5,4,3,6,8]=>[2,2,1,3]
[8,7,2,4,5,3,6,1]=>[1,1,3,2,1]
[5,8,2,4,7,3,6,1]=>[2,3,2,1]
[6,8,3,2,4,7,5,1]=>[2,1,3,1,1]
[8,7,1,3,4,5,2,6]=>[1,1,4,2]
[8,1,6,3,4,5,2,7]=>[1,2,3,2]
[8,1,2,5,4,3,6,7]=>[1,3,1,3]
[3,4,8,7,5,2,6,1]=>[3,1,1,2,1]
[3,2,8,6,1,5,4,7]=>[1,2,1,2,2]
[8,6,1,2,4,3,5,7]=>[1,1,3,3]
[8,7,3,6,4,2,5,1]=>[1,1,2,1,2,1]
[3,8,7,2,5,4,6,1]=>[2,1,2,2,1]
[8,7,2,4,5,6,3,1]=>[1,1,4,1,1]
[5,3,6,2,4,8,7,1]=>[1,2,3,1,1]
[3,5,2,8,6,1,4,7]=>[2,2,1,3]
[3,7,2,5,1,4,8,6]=>[2,2,3,1]
[5,1,8,6,2,3,4,7]=>[1,2,1,4]
[2,5,4,1,8,6,3,7]=>[2,1,2,1,2]
[3,7,6,1,8,2,5,4]=>[2,1,2,2,1]
[7,6,3,1,8,2,4,5]=>[1,1,1,2,3]
[8,2,3,6,1,4,7,5]=>[1,3,3,1]
[1,8,2,6,3,4,7,5]=>[2,2,3,1]
[8,1,3,6,4,7,2,5]=>[1,3,2,2]
[7,1,3,6,4,8,2,5]=>[1,3,2,2]
[8,2,1,3,5,7,4,6]=>[1,1,4,2]
[8,2,6,3,1,4,7,5]=>[1,2,1,3,1]
[7,5,4,1,3,8,2,6]=>[1,1,1,3,2]
[2,7,5,8,3,4,1,6]=>[2,2,2,2]
[7,3,8,5,4,1,2,6]=>[1,2,1,1,3]
[7,2,3,6,1,4,8,5]=>[1,3,3,1]
[1,3,7,2,5,8,4,6]=>[3,3,2]
[1,7,2,3,5,8,4,6]=>[2,4,2]
[7,4,8,1,3,6,2,5]=>[1,2,3,2]
[8,1,2,3,5,7,4,6]=>[1,5,2]
[7,1,2,3,5,8,4,6]=>[1,5,2]
[8,6,1,4,7,3,2,5]=>[1,1,3,1,2]
[2,6,3,7,1,4,8,5]=>[2,2,3,1]
[2,6,3,8,1,4,7,5]=>[2,2,3,1]
[7,5,4,8,1,3,2,6]=>[1,1,2,2,2]
[8,5,4,7,1,3,2,6]=>[1,1,2,2,2]
[2,3,1,8,5,4,6,7]=>[2,2,1,3]
[8,6,5,1,3,4,2,7]=>[1,1,1,3,2]
[8,5,1,7,6,3,4,2]=>[1,1,2,1,2,1]
[3,4,7,6,1,8,5,2]=>[3,1,2,1,1]
[3,5,2,6,7,1,8,4]=>[2,3,2,1]
[3,2,8,4,7,5,1,6]=>[1,2,2,1,2]
[8,4,7,5,1,3,2,6]=>[1,2,1,2,2]
[3,8,1,6,5,2,7,4]=>[2,2,1,2,1]
[6,1,2,8,3,4,7,5]=>[1,3,3,1]
[6,8,3,1,7,2,4,5]=>[2,1,2,3]
[3,7,2,5,6,1,8,4]=>[2,3,2,1]
[6,8,4,2,5,1,7,3]=>[2,1,2,2,1]
[2,7,5,3,8,4,1,6]=>[2,1,2,1,2]
[8,3,1,4,7,2,6,5]=>[1,1,3,2,1]
[8,3,2,1,5,7,4,6]=>[1,1,1,3,2]
[2,8,3,6,4,7,1,5]=>[2,2,2,2]
[7,3,6,4,8,1,2,5]=>[1,2,2,3]
[8,3,6,4,7,1,2,5]=>[1,2,2,3]
[1,2,8,3,5,7,4,6]=>[3,3,2]
[1,8,3,2,5,7,4,6]=>[2,1,3,2]
[6,5,1,7,4,2,8,3]=>[1,1,2,1,2,1]
[7,3,6,4,8,2,1,5]=>[1,2,2,1,2]
[4,6,1,7,3,5,2,8]=>[2,2,2,2]
[5,6,1,7,3,4,2,8]=>[2,2,2,2]
[6,1,7,3,4,2,8,5]=>[1,2,2,2,1]
[7,3,8,1,6,5,2,4]=>[1,2,2,1,2]
[8,3,7,1,6,5,2,4]=>[1,2,2,1,2]
[5,1,7,4,2,8,6,3]=>[1,2,1,2,1,1]
[2,8,1,7,6,5,3,4]=>[2,2,1,1,2]
[4,2,8,6,5,1,7,3]=>[1,2,1,1,2,1]
[6,4,2,8,5,1,7,3]=>[1,1,2,1,2,1]
[8,6,4,7,1,5,2,3]=>[1,1,2,2,2]
[7,6,4,8,1,5,2,3]=>[1,1,2,2,2]
[5,1,6,4,2,3,8,7]=>[1,2,1,3,1]
[4,2,3,8,7,5,1,6]=>[1,3,1,1,2]
[3,8,7,1,6,5,2,4]=>[2,1,2,1,2]
[2,4,3,8,1,6,7,5]=>[2,2,3,1]
[2,4,3,7,1,6,8,5]=>[2,2,3,1]
[4,2,3,7,8,5,1,6]=>[1,4,1,2]
[5,1,6,4,2,3,7,8]=>[1,2,1,4]
[6,4,7,8,1,5,2,3]=>[1,3,2,2]
[8,7,4,6,1,5,2,3]=>[1,1,2,2,2]
[6,5,7,8,1,4,2,3]=>[1,3,2,2]
[4,7,8,6,1,5,2,3]=>[3,1,2,2]
[3,2,4,7,8,1,5,6]=>[1,4,3]
[3,2,4,8,7,1,5,6]=>[1,3,1,3]
[4,8,7,6,1,5,2,3]=>[2,1,1,2,2]
[5,8,7,6,1,4,2,3]=>[2,1,1,2,2]
[8,6,5,7,1,4,2,3]=>[1,1,2,2,2]
[5,1,6,7,4,2,3,8]=>[1,3,1,3]
[6,7,4,8,1,5,2,3]=>[2,2,2,2]
[8,4,7,6,1,5,2,3]=>[1,2,1,2,2]
[8,3,2,4,7,1,5,6]=>[1,1,3,3]
[7,3,2,4,8,1,5,6]=>[1,1,3,3]
[2,5,3,7,1,6,4,8]=>[2,2,2,2]
[8,4,6,7,1,5,2,3]=>[1,3,2,2]
[7,4,6,8,1,5,2,3]=>[1,3,2,2]
[5,1,6,8,4,2,3,7]=>[1,3,1,3]
[4,2,3,7,5,1,6,8]=>[1,3,1,3]
[3,7,5,8,1,6,2,4]=>[2,2,2,2]
[2,4,3,7,1,6,5,8]=>[2,2,2,2]
[2,4,7,1,5,8,6,3]=>[3,3,1,1]
[3,2,4,7,6,1,5,8]=>[1,3,1,3]
[4,7,6,8,1,5,2,3]=>[2,2,2,2]
[8,5,6,7,1,4,2,3]=>[1,3,2,2]
[8,6,7,5,1,4,2,3]=>[1,2,1,2,2]
[7,6,8,5,1,4,2,3]=>[1,2,1,2,2]
[6,8,7,5,1,4,2,3]=>[2,1,1,2,2]
[5,6,8,7,1,4,2,3]=>[3,1,2,2]
[4,6,8,7,1,5,2,3]=>[3,1,2,2]
[2,4,6,7,1,5,8,3]=>[4,3,1]
[3,2,4,6,1,5,7,8]=>[1,3,4]
[6,7,8,5,1,4,2,3]=>[3,1,2,2]
[7,8,6,5,1,4,2,3]=>[2,1,1,2,2]
[3,1,7,5,4,2,8,6]=>[1,2,1,1,2,1]
[2,1,8,5,4,6,3,7]=>[1,2,1,2,2]
[4,1,8,5,2,3,6,7]=>[1,2,1,4]
[5,4,1,3,6,7,2,8]=>[1,1,4,2]
[8,4,1,2,6,3,7,5]=>[1,1,3,2,1]
[8,2,7,1,5,3,4,6]=>[1,2,2,3]
[3,2,7,1,5,8,4,6]=>[1,2,3,2]
[6,3,7,1,5,4,2,8]=>[1,2,2,1,2]
[7,3,8,1,5,4,2,6]=>[1,2,2,1,2]
[7,1,5,3,8,4,2,6]=>[1,2,2,1,2]
[4,5,1,3,6,8,2,7]=>[2,4,2]
[3,6,8,1,5,4,2,7]=>[3,2,1,2]
[6,8,3,1,5,4,2,7]=>[2,1,2,1,2]
[7,6,3,1,5,4,2,8]=>[1,1,1,2,1,2]
[3,6,2,1,5,8,4,7]=>[2,1,3,2]
[8,6,2,1,5,3,4,7]=>[1,1,1,2,3]
[4,8,2,1,7,5,3,6]=>[2,1,2,1,2]
[2,3,8,1,5,7,4,6]=>[3,3,2]
[7,1,3,2,8,6,4,5]=>[1,2,2,1,2]
[7,1,6,2,8,3,4,5]=>[1,2,2,3]
[4,7,1,2,6,3,8,5]=>[2,3,2,1]
[2,7,8,1,5,3,4,6]=>[3,2,3]
[6,7,2,1,5,3,4,8]=>[2,1,2,3]
[4,7,2,1,8,5,3,6]=>[2,1,2,1,2]
[8,7,2,1,4,5,3,6]=>[1,1,1,3,2]
[8,7,5,6,1,4,3,2]=>[1,1,2,2,1,1]
[5,7,8,6,1,4,3,2]=>[3,1,2,1,1]
[2,7,4,1,6,5,3,8]=>[2,1,2,1,2]
[3,7,1,4,5,6,8,2]=>[2,5,1]
[7,1,6,4,5,8,3,2]=>[1,2,3,1,1]
[3,5,1,4,7,6,8,2]=>[2,3,2,1]
[2,6,4,1,7,5,3,8]=>[2,1,2,1,2]
[5,6,8,7,1,4,3,2]=>[3,1,2,1,1]
[6,8,5,7,1,4,3,2]=>[2,2,2,1,1]
[8,6,5,7,1,4,3,2]=>[1,1,2,2,1,1]
[8,5,7,6,1,4,3,2]=>[1,2,1,2,1,1]
[6,5,7,8,1,4,3,2]=>[1,3,2,1,1]
[7,2,3,1,5,6,4,8]=>[1,2,3,2]
[4,2,8,1,6,5,3,7]=>[1,2,2,1,2]
[6,2,4,1,8,5,3,7]=>[1,2,2,1,2]
[8,3,1,4,5,6,7,2]=>[1,1,5,1]
[5,3,1,4,8,6,7,2]=>[1,1,3,2,1]
[7,5,1,6,3,4,8,2]=>[1,1,2,3,1]
[7,1,5,8,4,3,6,2]=>[1,3,1,2,1]
[5,8,1,6,4,3,7,2]=>[2,2,1,2,1]
[5,3,1,8,4,6,7,2]=>[1,1,2,3,1]
[8,3,1,5,4,6,7,2]=>[1,1,2,3,1]
[8,2,6,1,4,5,3,7]=>[1,2,3,2]
[6,2,8,1,4,5,3,7]=>[1,2,3,2]
[7,2,6,1,5,3,4,8]=>[1,2,2,3]
[2,8,6,1,5,3,4,7]=>[2,1,2,3]
[4,2,1,5,6,3,8,7]=>[1,1,3,2,1]
[7,1,2,5,8,3,4,6]=>[1,4,3]
[7,1,4,5,6,8,3,2]=>[1,5,1,1]
[8,5,6,7,1,4,3,2]=>[1,3,2,1,1]
[7,6,8,5,1,4,3,2]=>[1,2,1,2,1,1]
[6,8,7,5,1,4,3,2]=>[2,1,1,2,1,1]
[2,6,7,1,4,5,3,8]=>[3,3,2]
[3,5,1,7,4,6,8,2]=>[2,2,3,1]
[7,1,5,6,4,8,3,2]=>[1,3,2,1,1]
[7,1,6,5,4,8,3,2]=>[1,2,1,2,1,1]
[2,7,6,1,4,5,3,8]=>[2,1,3,2]
[5,7,6,8,1,4,3,2]=>[2,2,2,1,1]
[7,8,6,5,1,4,3,2]=>[2,1,1,2,1,1]
[4,3,1,6,5,8,7,2]=>[1,1,2,2,1,1]
[5,3,1,2,4,8,7,6]=>[1,1,4,1,1]
[5,3,6,2,1,8,7,4]=>[1,2,1,2,1,1]
[5,3,7,2,1,4,6,8]=>[1,2,1,4]
[5,3,7,2,8,4,1,6]=>[1,2,2,1,2]
[7,2,4,5,8,3,1,6]=>[1,4,1,2]
[7,2,4,5,1,3,6,8]=>[1,3,4]
[6,2,4,5,1,8,7,3]=>[1,3,2,1,1]
[3,1,4,5,2,8,7,6]=>[1,3,2,1,1]
[1,6,4,5,2,8,7,3]=>[2,2,2,1,1]
[3,7,4,5,1,2,6,8]=>[2,2,4]
[3,7,4,5,8,2,1,6]=>[2,3,1,2]
[1,7,4,2,6,3,5,8]=>[2,1,2,3]
[8,7,4,5,2,1,6,3]=>[1,1,2,1,2,1]
[6,3,7,1,8,4,2,5]=>[1,2,2,1,2]
[5,7,4,1,6,3,2,8]=>[2,1,2,1,2]
[1,7,4,8,6,3,2,5]=>[2,2,1,1,2]
[5,7,4,8,6,3,1,2]=>[2,2,1,1,2]
[4,8,3,5,6,7,1,2]=>[2,4,2]
[1,8,3,5,6,7,2,4]=>[2,4,2]
[4,8,1,5,6,7,2,3]=>[2,4,2]
[4,1,3,5,6,7,2,8]=>[1,5,2]
[5,8,4,3,6,1,2,7]=>[2,1,2,3]
[5,3,8,4,1,7,2,6]=>[1,2,1,2,2]
[1,5,8,4,6,7,3,2]=>[3,3,1,1]
[1,4,8,3,6,7,5,2]=>[3,3,1,1]
[4,3,8,2,1,7,5,6]=>[1,2,1,2,2]
[3,8,4,2,6,1,5,7]=>[2,1,2,3]
[1,8,2,5,6,7,4,3]=>[2,4,1,1]
[3,8,1,5,6,7,4,2]=>[2,4,1,1]
[3,8,2,5,6,7,1,4]=>[2,4,2]
[8,2,1,5,6,7,4,3]=>[1,1,4,1,1]
[8,1,3,5,6,7,4,2]=>[1,5,1,1]
[7,1,4,3,6,2,5,8]=>[1,2,2,3]
[7,8,4,3,6,2,1,5]=>[2,1,2,1,2]
[4,3,1,8,5,7,6,2]=>[1,1,2,2,1,1]
[4,3,1,6,8,7,5,2]=>[1,1,3,1,1,1]
[6,3,1,8,2,7,4,5]=>[1,1,2,2,2]
[6,3,5,8,2,7,1,4]=>[1,3,2,2]
[7,5,4,8,6,2,1,3]=>[1,1,2,1,1,2]
[7,1,4,8,6,2,3,5]=>[1,3,1,3]
[7,5,4,1,6,2,3,8]=>[1,1,1,2,3]
[7,6,4,5,8,1,3,2]=>[1,1,3,2,1]
[1,6,4,5,8,2,3,7]=>[2,3,3]
[7,3,6,1,8,2,4,5]=>[1,2,2,3]
[1,7,6,5,8,3,4,2]=>[2,1,2,2,1]
[1,8,5,3,6,7,4,2]=>[2,1,3,1,1]
[8,3,5,2,1,7,4,6]=>[1,2,1,2,2]
[8,4,1,5,6,7,3,2]=>[1,1,4,1,1]
[8,4,2,5,6,7,1,3]=>[1,1,4,2]
[4,1,8,5,6,7,3,2]=>[1,2,3,1,1]
[1,2,8,5,6,7,3,4]=>[3,3,2]
[4,2,1,5,6,7,3,8]=>[1,1,4,2]
[1,5,3,8,6,7,4,2]=>[2,2,2,1,1]
[1,4,5,8,6,7,3,2]=>[4,2,1,1]
[4,3,5,8,1,7,2,6]=>[1,3,2,2]
[3,5,4,8,6,1,2,7]=>[2,2,1,3]
[1,4,8,5,6,7,2,3]=>[3,3,2]
[3,4,8,5,6,7,1,2]=>[3,3,2]
[2,7,1,5,6,3,4,8]=>[2,3,3]
[2,7,1,4,3,6,5,8]=>[2,2,2,2]
[4,3,7,2,5,6,8,1]=>[1,2,4,1]
[2,6,3,1,4,5,8,7]=>[2,1,4,1]
[3,7,1,4,2,6,8,5]=>[2,2,3,1]
[3,7,1,5,6,2,8,4]=>[2,3,2,1]
[4,7,1,5,6,8,2,3]=>[2,4,2]
[8,5,2,6,7,3,1,4]=>[1,1,3,1,2]
[8,4,2,6,3,7,1,5]=>[1,1,2,2,2]
[8,4,2,3,5,7,1,6]=>[1,1,4,2]
[4,7,3,2,5,6,1,8]=>[2,1,3,2]
[5,3,4,6,2,8,1,7]=>[1,3,2,2]
[5,3,7,4,2,8,1,6]=>[1,2,1,2,2]
[6,4,7,2,3,8,1,5]=>[1,2,3,2]
[6,5,7,2,8,3,1,4]=>[1,2,2,1,2]
[5,3,7,2,4,8,6,1]=>[1,2,3,1,1]
[2,6,5,1,8,3,4,7]=>[2,1,2,3]
[8,7,6,1,4,5,2,3]=>[1,1,1,3,2]
[8,7,6,1,3,2,5,4]=>[1,1,1,2,2,1]
[8,7,2,4,3,1,6,5]=>[1,1,2,1,2,1]
[8,7,4,5,1,6,2,3]=>[1,1,2,2,2]
[8,5,6,4,1,7,2,3]=>[1,2,1,2,2]
[8,5,6,3,1,2,7,4]=>[1,2,1,3,1]
[8,4,6,2,3,1,7,5]=>[1,2,2,2,1]
[8,3,5,4,2,1,7,6]=>[1,2,1,1,2,1]
[5,7,3,4,2,1,8,6]=>[2,2,1,2,1]
[6,7,4,2,3,1,8,5]=>[2,1,2,2,1]
[6,7,5,3,1,2,8,4]=>[2,1,1,3,1]
[6,7,5,4,1,8,2,3]=>[2,1,1,2,2]
[6,2,4,3,8,7,5,1]=>[1,2,2,1,1,1]
[7,3,5,4,1,8,6,2]=>[1,2,1,2,1,1]
[5,2,7,1,3,4,8,6]=>[1,2,4,1]
[2,6,5,7,3,1,4,8]=>[2,2,1,3]
[2,6,5,7,3,1,8,4]=>[2,2,1,2,1]
[6,3,1,4,7,8,5,2]=>[1,1,4,1,1]
[6,8,2,1,3,4,5,7]=>[2,1,5]
[3,7,1,8,4,5,2,6]=>[2,2,2,2]
[6,3,2,4,7,5,8,1]=>[1,1,3,2,1]
[6,3,2,4,7,5,1,8]=>[1,1,3,1,2]
[4,2,1,6,3,7,5,8]=>[1,1,2,2,2]
[4,2,1,6,3,7,8,5]=>[1,1,2,3,1]
[7,4,3,5,8,6,1,2]=>[1,1,3,1,2]
[2,7,6,8,3,1,4,5]=>[2,2,1,3]
[7,4,3,5,8,6,2,1]=>[1,1,3,1,1,1]
[4,2,1,7,3,8,6,5]=>[1,1,2,2,1,1]
[4,2,1,3,7,8,6,5]=>[1,1,4,1,1]
[5,8,1,7,4,3,6,2]=>[2,2,1,2,1]
[5,8,1,7,4,3,2,6]=>[2,2,1,1,2]
[3,7,8,6,2,1,4,5]=>[3,1,1,3]
[4,2,1,8,3,5,6,7]=>[1,1,2,4]
[4,2,1,3,6,7,5,8]=>[1,1,4,2]
[4,2,1,3,7,5,6,8]=>[1,1,3,3]
[4,2,1,3,6,8,7,5]=>[1,1,4,1,1]
[7,3,2,4,8,6,5,1]=>[1,1,3,1,1,1]
[4,2,1,6,3,8,7,5]=>[1,1,2,2,1,1]
[4,2,1,7,3,5,6,8]=>[1,1,2,4]
[3,6,7,5,2,1,4,8]=>[3,1,1,3]
[3,6,7,5,2,1,8,4]=>[3,1,1,2,1]
[7,3,4,2,6,8,5,1]=>[1,2,3,1,1]
[4,8,6,2,7,3,5,1]=>[2,1,2,2,1]
[7,3,4,2,6,8,1,5]=>[1,2,3,2]
[3,6,7,5,2,4,8,1]=>[3,1,3,1]
[3,6,7,5,2,4,1,8]=>[3,1,2,2]
[4,2,1,7,3,6,5,8]=>[1,1,2,2,2]
[4,2,1,7,3,6,8,5]=>[1,1,2,3,1]
[3,7,6,8,4,2,5,1]=>[2,2,1,2,1]
[5,8,1,7,4,2,6,3]=>[2,2,1,2,1]
[3,7,8,6,2,4,5,1]=>[3,1,3,1]
[4,2,1,3,8,6,7,5]=>[1,1,3,2,1]
[4,2,1,3,7,6,5,8]=>[1,1,3,1,2]
[4,2,1,3,5,7,6,8]=>[1,1,4,2]
[4,2,1,3,5,8,6,7]=>[1,1,4,2]
[4,8,1,7,3,6,5,2]=>[2,2,2,1,1]
[4,7,8,6,3,5,2,1]=>[3,1,2,1,1]
[4,2,1,8,3,7,6,5]=>[1,1,2,2,1,1]
[4,2,1,3,5,6,8,7]=>[1,1,5,1]
[7,8,2,4,1,3,6,5]=>[2,2,3,1]
[2,6,1,5,4,7,8,3]=>[2,2,3,1]
[4,6,3,5,8,7,1,2]=>[2,3,1,2]
[3,5,6,1,4,8,7,2]=>[3,3,1,1]
[2,3,6,8,4,1,5,7]=>[4,1,3]
[2,7,5,1,8,3,4,6]=>[2,1,2,3]
[4,7,5,2,1,3,6,8]=>[2,1,1,4]
[3,5,6,2,4,1,7,8]=>[3,2,3]
[2,5,6,1,4,8,3,7]=>[3,3,2]
[6,7,8,4,1,5,3,2]=>[3,1,2,1,1]
[7,1,6,8,4,5,3,2]=>[1,3,2,1,1]
[7,4,6,5,2,8,1,3]=>[1,2,1,2,2]
[7,1,5,6,4,2,3,8]=>[1,3,1,3]
[5,7,4,6,8,1,3,2]=>[2,3,2,1]
[5,7,8,1,4,6,3,2]=>[3,3,1,1]
[8,1,5,7,4,6,3,2]=>[1,3,2,1,1]
[1,8,4,6,7,5,3,2]=>[2,3,1,1,1]
[6,1,8,4,7,5,3,2]=>[1,2,2,1,1,1]
[4,5,8,6,1,7,3,2]=>[3,1,2,1,1]
[4,8,5,1,6,7,3,2]=>[2,1,3,1,1]
[8,1,4,5,6,7,3,2]=>[1,5,1,1]
[5,6,7,1,4,2,3,8]=>[3,2,3]
[8,4,2,6,1,5,7,3]=>[1,1,2,3,1]
[4,8,5,2,1,6,7,3]=>[2,1,1,3,1]
[5,1,8,4,2,6,3,7]=>[1,2,1,2,2]
[1,8,4,6,2,5,3,7]=>[2,2,2,2]
[6,1,5,2,3,4,7,8]=>[1,2,5]
[8,3,1,4,6,2,5,7]=>[1,1,3,3]
[3,1,8,2,5,6,4,7]=>[1,2,3,2]
[3,5,1,8,2,6,4,7]=>[2,2,2,2]
[3,5,1,2,8,4,7,6]=>[2,3,2,1]
[2,3,5,8,6,1,7,4]=>[4,1,2,1]
[8,2,4,3,6,7,1,5]=>[1,2,3,2]
[3,2,8,5,7,1,6,4]=>[1,2,2,2,1]
[3,6,2,8,5,1,7,4]=>[2,2,1,2,1]
[6,2,1,8,4,7,5,3]=>[1,1,2,2,1,1]
[2,8,7,1,4,6,5,3]=>[2,1,3,1,1]
[8,2,7,1,5,4,6,3]=>[1,2,2,2,1]
[7,2,5,3,6,8,1,4]=>[1,2,3,2]
[7,3,1,5,6,2,4,8]=>[1,1,3,3]
[3,7,5,1,6,2,4,8]=>[2,1,2,3]
[2,7,3,6,5,8,1,4]=>[2,2,2,2]
[8,7,2,4,1,6,5,3]=>[1,1,2,2,1,1]
[1,8,7,2,3,6,5,4]=>[2,1,3,1,1]
[1,7,8,2,6,4,3,5]=>[3,2,1,2]
[1,7,3,8,2,6,4,5]=>[2,2,2,2]
[1,2,7,3,6,4,5,8]=>[3,2,3]
[7,1,5,8,3,2,4,6]=>[1,3,1,3]
[1,6,2,8,4,3,7,5]=>[2,2,1,2,1]
[1,3,8,7,2,4,6,5]=>[3,1,3,1]
[1,8,3,7,2,5,4,6]=>[2,2,2,2]
[8,1,4,7,3,2,5,6]=>[1,3,1,3]
[4,7,8,1,3,2,5,6]=>[3,2,3]
[7,1,4,2,3,5,6,8]=>[1,2,5]
[8,2,1,4,7,3,5,6]=>[1,1,3,3]
[2,1,3,8,4,6,7,5]=>[1,3,3,1]
[1,2,3,4,8,5,7,6]=>[5,2,1]
[2,4,7,5,6,8,3,1]=>[3,3,1,1]
[2,4,8,7,5,6,3,1]=>[3,1,2,1,1]
[2,5,3,8,4,7,6,1]=>[2,2,2,1,1]
[2,8,5,7,3,6,4,1]=>[2,2,2,1,1]
[3,1,8,5,2,7,6,4]=>[1,2,1,2,1,1]
[8,3,6,1,4,5,7,2]=>[1,2,4,1]
[2,8,6,3,4,5,7,1]=>[2,1,4,1]
[2,6,8,3,4,5,7,1]=>[3,4,1]
[2,5,7,3,4,8,6,1]=>[3,3,1,1]
[2,7,8,5,3,6,4,1]=>[3,1,2,1,1]
[2,7,6,3,4,8,5,1]=>[2,1,3,1,1]
[3,1,8,7,2,6,4,5]=>[1,2,1,2,2]
[8,3,7,6,1,4,5,2]=>[1,2,1,3,1]
[4,8,1,7,2,3,6,5]=>[2,2,3,1]
[4,1,7,2,3,6,5,8]=>[1,2,3,2]
[3,7,1,8,2,6,4,5]=>[2,2,2,2]
[3,1,7,8,2,5,6,4]=>[1,3,3,1]
[3,1,6,5,8,2,7,4]=>[1,2,2,2,1]
[7,3,8,5,1,6,4,2]=>[1,2,1,2,1,1]
[7,3,6,1,4,8,5,2]=>[1,2,3,1,1]
[7,8,3,6,1,4,5,2]=>[2,2,3,1]
[7,4,8,1,2,3,6,5]=>[1,2,4,1]
[7,5,1,2,3,4,8,6]=>[1,1,5,1]
[7,4,6,1,2,8,3,5]=>[1,2,3,2]
[6,4,1,2,8,5,7,3]=>[1,1,3,2,1]
[8,4,6,1,2,3,7,5]=>[1,2,4,1]
[4,8,1,5,2,7,3,6]=>[2,2,2,2]
[4,1,2,5,3,8,7,6]=>[1,3,2,1,1]
[4,3,6,8,7,5,1,2]=>[1,3,1,1,2]
[5,4,1,8,2,7,6,3]=>[1,1,2,2,1,1]
[5,4,1,8,2,7,3,6]=>[1,1,2,2,2]
[8,6,7,4,1,2,5,3]=>[1,2,1,3,1]
[6,4,8,1,2,5,3,7]=>[1,2,3,2]
[6,7,3,1,4,8,5,2]=>[2,1,3,1,1]
[5,6,3,8,7,1,4,2]=>[2,2,1,2,1]
[5,4,1,6,8,2,7,3]=>[1,1,3,2,1]
[5,4,7,1,2,8,6,3]=>[1,2,3,1,1]
[6,7,4,1,2,8,3,5]=>[2,1,3,2]
[6,5,1,2,3,7,8,4]=>[1,1,5,1]
[6,5,1,2,3,4,8,7]=>[1,1,5,1]
[8,6,5,1,2,3,7,4]=>[1,1,1,4,1]
[6,7,4,1,2,5,3,8]=>[2,1,3,2]
[2,4,6,3,5,7,1,8]=>[3,3,2]
[1,4,6,3,7,2,5,8]=>[3,2,3]
[8,6,2,5,3,1,7,4]=>[1,1,2,1,2,1]
[8,2,3,4,5,1,7,6]=>[1,4,2,1]
[1,8,3,4,2,7,5,6]=>[2,2,2,2]
[2,8,3,4,1,6,7,5]=>[2,2,3,1]
[8,7,2,3,1,6,5,4]=>[1,1,2,2,1,1]
[3,8,2,4,6,1,7,5]=>[2,3,2,1]
[7,8,2,4,3,1,6,5]=>[2,2,1,2,1]
[4,5,8,2,3,1,7,6]=>[3,2,2,1]
[5,1,4,3,7,2,6,8]=>[1,2,2,3]
[6,1,3,5,7,2,4,8]=>[1,4,3]
[2,1,4,7,5,3,6,8]=>[1,3,1,3]
[7,1,3,6,2,5,4,8]=>[1,3,2,2]
[8,1,3,6,2,4,7,5]=>[1,3,3,1]
[2,1,8,3,7,5,4,6]=>[1,2,2,1,2]
[7,1,8,2,5,6,3,4]=>[1,2,3,2]
[6,1,5,8,2,7,3,4]=>[1,3,2,2]
[4,5,2,8,1,6,7,3]=>[2,2,3,1]
[6,2,5,8,1,4,7,3]=>[1,3,3,1]
[3,2,8,5,1,6,7,4]=>[1,2,1,3,1]
[8,2,7,1,4,6,5,3]=>[1,2,3,1,1]
[1,3,8,2,5,7,4,6]=>[3,3,2]
[2,8,7,1,6,4,5,3]=>[2,1,2,2,1]
[3,8,7,1,5,6,4,2]=>[2,1,3,1,1]
[3,4,8,5,6,1,7,2]=>[3,2,2,1]
[8,3,7,4,1,6,5,2]=>[1,2,1,2,1,1]
[1,4,8,6,2,7,3,5]=>[3,1,2,2]
[8,4,5,7,1,6,3,2]=>[1,3,2,1,1]
[3,5,6,8,4,1,7,2]=>[4,1,2,1]
[6,2,3,1,5,4,7,8]=>[1,2,2,3]
[7,2,3,1,4,6,5,8]=>[1,2,3,2]
[8,2,3,1,4,5,7,6]=>[1,2,4,1]
[8,5,1,3,2,4,7,6]=>[1,1,2,3,1]
[7,5,1,3,2,6,4,8]=>[1,1,2,2,2]
[2,6,1,4,5,3,7,8]=>[2,3,3]
[3,6,4,1,5,2,7,8]=>[2,1,2,3]
[4,5,6,1,3,2,7,8]=>[3,2,3]
[4,5,7,1,2,6,3,8]=>[3,3,2]
[3,7,4,1,2,6,5,8]=>[2,1,3,2]
[6,7,1,4,2,5,3,8]=>[2,2,2,2]
[2,7,1,3,5,6,4,8]=>[2,4,2]
[8,6,1,2,4,3,7,5]=>[1,1,3,2,1]
[2,8,1,3,4,6,7,5]=>[2,5,1]
[7,8,1,2,5,3,6,4]=>[2,3,2,1]
[3,8,4,1,2,5,7,6]=>[2,1,4,1]
[1,2,6,7,5,3,8,4]=>[4,1,2,1]
[1,7,5,3,2,8,4,6]=>[2,1,1,2,2]
[1,6,7,5,3,8,4,2]=>[3,1,2,1,1]
[1,6,5,7,2,3,8,4]=>[2,2,3,1]
[1,3,8,2,6,5,7,4]=>[3,2,2,1]
[1,2,5,7,6,3,4,8]=>[4,1,3]
[1,3,4,8,2,5,7,6]=>[4,3,1]
[1,5,7,6,2,3,4,8]=>[3,1,4]
[1,5,3,8,2,6,4,7]=>[2,2,2,2]
[1,4,8,3,2,5,7,6]=>[3,1,3,1]
[1,4,8,3,5,7,6,2]=>[3,3,1,1]
[1,2,4,8,3,5,7,6]=>[4,3,1]
[1,3,8,4,2,6,7,5]=>[3,1,3,1]
[1,4,8,2,3,5,7,6]=>[3,4,1]
[6,5,7,3,8,2,4,1]=>[1,2,2,2,1]
[4,2,6,7,5,8,3,1]=>[1,3,2,1,1]
[6,7,5,2,1,8,4,3]=>[2,1,1,2,1,1]
[3,4,8,7,5,2,1,6]=>[3,1,1,1,2]
[1,7,5,2,8,4,6,3]=>[2,1,2,2,1]
[5,6,8,3,1,7,2,4]=>[3,1,2,2]
[6,1,4,8,3,2,7,5]=>[1,3,1,2,1]
[3,4,7,1,8,6,2,5]=>[3,2,1,2]
[3,4,6,8,2,1,5,7]=>[4,1,3]
[3,8,2,5,6,1,4,7]=>[2,3,3]
[3,5,2,8,6,4,1,7]=>[2,2,1,1,2]
[4,2,5,7,3,8,6,1]=>[1,3,2,1,1]
[7,4,2,5,3,8,1,6]=>[1,1,2,2,2]
[3,1,2,8,5,6,4,7]=>[1,3,2,2]
[5,2,1,6,8,3,4,7]=>[1,1,3,3]
[5,2,6,8,4,1,3,7]=>[1,3,1,3]
[1,5,6,8,3,4,2,7]=>[4,2,2]
[4,5,8,1,6,3,2,7]=>[3,2,1,2]
[4,5,1,6,8,3,2,7]=>[2,3,1,2]
[4,5,7,3,8,2,6,1]=>[3,2,2,1]
[6,4,3,7,8,2,5,1]=>[1,1,3,2,1]
[6,4,3,1,7,8,2,5]=>[1,1,1,3,2]
[4,5,3,1,7,8,2,6]=>[2,1,3,2]
[7,1,3,5,4,8,2,6]=>[1,3,2,2]
[7,5,2,8,1,4,3,6]=>[1,1,2,2,2]
[5,7,3,8,4,6,1,2]=>[2,2,2,2]
[1,4,5,7,3,8,6,2]=>[4,2,1,1]
[4,6,3,7,8,5,2,1]=>[2,3,1,1,1]
[5,3,6,7,8,4,2,1]=>[1,4,1,1,1]
[1,5,3,6,7,8,4,2]=>[2,4,1,1]
[4,6,1,7,3,8,5,2]=>[2,2,2,1,1]
[6,3,7,1,8,4,5,2]=>[1,2,2,2,1]
[6,7,2,4,8,1,5,3]=>[2,3,2,1]
[2,6,1,4,7,3,8,5]=>[2,3,2,1]
[3,2,5,6,7,8,1,4]=>[1,5,2]
[5,2,3,6,7,8,4,1]=>[1,5,1,1]
[6,7,1,3,2,8,4,5]=>[2,2,2,2]
[6,2,7,1,3,4,8,5]=>[1,2,4,1]
[5,2,1,7,3,8,4,6]=>[1,1,2,2,2]
[6,4,2,7,1,8,3,5]=>[1,1,2,2,2]
[4,2,6,3,7,8,1,5]=>[1,2,3,2]
[4,2,6,3,7,8,5,1]=>[1,2,3,1,1]
[6,7,3,8,2,4,5,1]=>[2,2,3,1]
[3,6,2,7,4,1,8,5]=>[2,2,1,2,1]
[6,7,3,2,1,4,8,5]=>[2,1,1,3,1]
[7,1,8,3,4,2,5,6]=>[1,2,2,3]
[7,2,4,1,8,3,5,6]=>[1,2,2,3]
[7,2,4,8,6,1,3,5]=>[1,3,1,3]
[7,3,4,8,6,2,1,5]=>[1,3,1,1,2]
[3,5,7,2,1,8,6,4]=>[3,1,2,1,1]
[6,7,8,3,2,5,1,4]=>[3,1,2,2]
[6,3,7,8,2,5,4,1]=>[1,3,2,1,1]
[2,6,7,4,8,5,3,1]=>[3,2,1,1,1]
[6,2,4,7,1,8,5,3]=>[1,3,2,1,1]
[4,6,2,7,1,8,5,3]=>[2,2,2,1,1]
[1,7,4,8,5,2,6,3]=>[2,2,1,2,1]
[1,3,7,8,5,2,6,4]=>[4,1,2,1]
[2,5,7,8,1,6,3,4]=>[4,2,2]
[6,3,7,1,8,2,5,4]=>[1,2,2,2,1]
[1,6,4,7,8,2,5,3]=>[2,3,2,1]
[2,5,6,1,7,8,4,3]=>[3,3,1,1]
[5,6,1,2,7,8,4,3]=>[2,4,1,1]
[6,7,2,1,8,5,3,4]=>[2,1,2,1,2]
[6,7,2,8,5,4,1,3]=>[2,2,1,1,2]
[1,6,7,4,8,5,3,2]=>[3,2,1,1,1]
[1,8,2,4,6,3,5,7]=>[2,3,3]
[1,5,7,4,3,6,2,8]=>[3,1,2,2]
[1,8,4,5,3,6,2,7]=>[2,2,2,2]
[1,8,5,3,4,7,2,6]=>[2,1,3,2]
[1,8,2,4,6,3,7,5]=>[2,3,2,1]
[1,8,2,5,4,6,7,3]=>[2,2,3,1]
[3,6,2,7,1,4,5,8]=>[2,2,4]
[6,3,8,1,2,4,7,5]=>[1,2,4,1]
[1,3,7,4,6,2,8,5]=>[3,2,2,1]
[1,4,7,5,2,6,8,3]=>[3,1,3,1]
[4,5,2,3,6,1,8,7]=>[2,3,2,1]
[4,6,5,3,7,1,8,2]=>[2,1,2,2,1]
[4,2,3,8,6,7,1,5]=>[1,3,2,2]
[6,2,4,8,5,1,7,3]=>[1,3,1,2,1]
[5,2,4,8,1,3,7,6]=>[1,3,3,1]
[6,2,5,4,8,3,7,1]=>[1,2,2,2,1]
[6,4,3,5,8,2,7,1]=>[1,1,3,2,1]
[5,2,3,4,8,1,6,7]=>[1,4,3]
[3,5,2,4,7,1,6,8]=>[2,3,3]
[5,3,4,8,1,6,2,7]=>[1,3,2,2]
[4,5,3,7,1,6,2,8]=>[2,2,2,2]
[6,2,4,8,5,1,3,7]=>[1,3,1,3]
[7,6,3,8,5,1,2,4]=>[1,1,2,1,3]
[1,4,3,7,8,2,5,6]=>[2,3,3]
[4,2,6,7,3,8,1,5]=>[1,3,2,2]
[1,5,7,4,2,8,6,3]=>[3,1,2,1,1]
[1,3,7,2,8,6,4,5]=>[3,2,1,2]
[1,4,3,7,8,6,2,5]=>[2,3,1,2]
[1,5,3,6,8,2,7,4]=>[2,3,2,1]
[4,5,2,7,1,8,6,3]=>[2,2,2,1,1]
[4,3,6,5,7,8,1,2]=>[1,2,3,2]
[4,2,3,5,6,8,1,7]=>[1,5,2]
[5,2,6,4,7,8,3,1]=>[1,2,3,1,1]
[4,2,6,7,3,8,5,1]=>[1,3,2,1,1]
[3,2,5,6,8,1,7,4]=>[1,4,2,1]
[6,4,5,2,3,8,7,1]=>[1,2,3,1,1]
[8,4,6,7,5,2,3,1]=>[1,3,1,2,1]
[4,6,5,2,3,1,8,7]=>[2,1,2,2,1]
[6,4,2,5,3,1,8,7]=>[1,1,2,1,2,1]
[6,4,2,5,3,8,7,1]=>[1,1,2,2,1,1]
[8,6,4,7,5,2,3,1]=>[1,1,2,1,2,1]
[8,6,2,7,4,5,3,1]=>[1,1,2,2,1,1]
[6,4,2,5,8,7,3,1]=>[1,1,3,1,1,1]
[4,6,2,5,3,8,7,1]=>[2,2,2,1,1]
[4,6,5,2,3,8,7,1]=>[2,1,3,1,1]
[6,8,7,4,5,2,3,1]=>[2,1,2,2,1]
[4,8,6,7,5,2,3,1]=>[2,2,1,2,1]
[6,8,4,7,5,2,3,1]=>[2,2,1,2,1]
[6,8,2,7,4,5,3,1]=>[2,2,2,1,1]
[8,6,4,7,2,5,3,1]=>[1,1,2,2,1,1]
[8,6,2,4,7,5,3,1]=>[1,1,3,1,1,1]
[6,8,2,4,7,5,3,1]=>[2,3,1,1,1]
[4,8,2,6,7,5,3,1]=>[2,3,1,1,1]
[2,8,4,6,7,5,3,1]=>[2,3,1,1,1]
[2,8,6,7,4,5,3,1]=>[2,2,2,1,1]
[6,8,7,2,4,5,3,1]=>[2,1,3,1,1]
[2,6,4,5,8,7,3,1]=>[2,3,1,1,1]
[2,6,4,8,7,5,3,1]=>[2,2,1,1,1,1]
[4,6,2,8,7,5,3,1]=>[2,2,1,1,1,1]
[8,2,4,6,7,5,3,1]=>[1,4,1,1,1]
[6,2,4,8,7,5,3,1]=>[1,3,1,1,1,1]
[4,2,6,8,7,5,3,1]=>[1,3,1,1,1,1]
[4,2,6,5,8,7,3,1]=>[1,2,2,1,1,1]
[6,2,4,5,8,7,3,1]=>[1,4,1,1,1]
[8,2,6,7,4,5,3,1]=>[1,3,2,1,1]
[8,6,7,2,4,5,3,1]=>[1,2,3,1,1]
[6,4,5,2,8,7,3,1]=>[1,2,2,1,1,1]
[4,2,3,6,8,7,5,1]=>[1,4,1,1,1]
[6,4,5,8,7,2,3,1]=>[1,3,1,2,1]
[8,6,7,4,2,5,3,1]=>[1,2,1,2,1,1]
[8,4,6,7,2,5,3,1]=>[1,3,2,1,1]
[6,4,8,7,2,5,3,1]=>[1,2,1,2,1,1]
[6,2,8,7,4,5,3,1]=>[1,2,1,2,1,1]
[6,4,8,7,5,2,3,1]=>[1,2,1,1,2,1]
[4,6,8,7,5,2,3,1]=>[3,1,1,2,1]
[4,6,5,8,7,2,3,1]=>[2,2,1,2,1]
[2,1,6,8,7,4,5,3]=>[1,3,1,2,1]
[2,6,8,7,4,5,3,1]=>[3,1,2,1,1]
[2,4,8,6,7,5,3,1]=>[3,2,1,1,1]
[4,2,8,6,7,5,3,1]=>[1,2,2,1,1,1]
[6,2,8,4,7,5,3,1]=>[1,2,2,1,1,1]
[8,2,6,4,7,5,3,1]=>[1,2,2,1,1,1]
[6,4,8,2,7,5,3,1]=>[1,2,2,1,1,1]
[4,6,8,2,7,5,3,1]=>[3,2,1,1,1]
[2,6,8,4,7,5,3,1]=>[3,2,1,1,1]
[4,6,8,7,2,5,3,1]=>[3,1,2,1,1]
[4,6,5,8,2,7,3,1]=>[2,2,2,1,1]
[2,1,6,8,4,7,5,3]=>[1,3,2,1,1]
[2,1,8,6,4,7,5,3]=>[1,2,1,2,1,1]
[6,8,7,4,2,5,3,1]=>[2,1,1,2,1,1]
[2,8,6,4,7,5,3,1]=>[2,1,2,1,1,1]
[4,8,6,2,7,5,3,1]=>[2,1,2,1,1,1]
[4,2,5,6,3,8,1,7]=>[1,3,2,2]
[6,2,5,7,4,8,3,1]=>[1,3,2,1,1]
[8,5,2,1,4,7,6,3]=>[1,1,1,3,1,1]
[6,7,3,2,5,8,4,1]=>[2,1,3,1,1]
[3,2,6,4,8,1,5,7]=>[1,2,2,3]
[2,3,6,4,7,8,5,1]=>[3,3,1,1]
[7,5,1,8,3,4,6,2]=>[1,1,2,3,1]
[5,7,8,2,6,3,4,1]=>[3,2,2,1]
[7,1,6,3,5,8,4,2]=>[1,2,3,1,1]
[6,3,1,7,8,4,5,2]=>[1,1,3,2,1]
[5,3,6,7,4,1,8,2]=>[1,3,1,2,1]
[7,3,1,2,5,8,6,4]=>[1,1,4,1,1]
[1,6,3,5,2,4,8,7]=>[2,2,3,1]
[3,4,8,2,7,5,1,6]=>[3,2,1,2]
[6,3,2,8,5,7,4,1]=>[1,1,2,2,1,1]
[3,8,4,7,2,5,6,1]=>[2,2,3,1]
[2,4,8,1,5,3,7,6]=>[3,2,2,1]
[3,4,8,1,6,2,7,5]=>[3,2,2,1]
[1,8,4,6,7,3,5,2]=>[2,3,2,1]
[8,1,6,3,4,5,7,2]=>[1,2,4,1]
[7,6,5,4,1,2,8,3]=>[1,1,1,1,3,1]
[5,7,6,8,3,4,2,1]=>[2,2,2,1,1]
[2,8,1,6,5,7,4,3]=>[2,2,2,1,1]
[4,6,8,2,5,3,7,1]=>[3,2,2,1]
[5,2,3,7,6,1,8,4]=>[1,3,1,2,1]
[8,1,2,4,6,7,3,5]=>[1,5,2]
[5,2,3,7,4,8,6,1]=>[1,3,2,1,1]
[5,2,6,8,4,3,1,7]=>[1,3,1,1,2]
[7,8,1,5,4,3,6,2]=>[2,2,1,2,1]
[7,2,4,8,5,3,6,1]=>[1,3,1,2,1]
[3,7,5,1,8,4,6,2]=>[2,1,2,2,1]
[2,7,8,5,4,6,1,3]=>[3,1,2,2]
[5,7,4,3,8,6,2,1]=>[2,1,2,1,1,1]
[4,8,1,6,3,5,2,7]=>[2,2,2,2]
[8,3,1,7,4,2,5,6]=>[1,1,2,1,3]
[3,1,8,2,4,5,7,6]=>[1,2,4,1]
[8,1,3,7,6,2,4,5]=>[1,3,1,3]
[2,3,6,8,7,1,4,5]=>[4,1,3]
[4,3,2,8,5,7,1,6]=>[1,1,2,2,2]
[3,6,4,2,8,5,7,1]=>[2,1,2,2,1]
[4,7,3,2,5,1,8,6]=>[2,1,2,2,1]
[3,2,4,7,5,8,6,1]=>[1,3,2,1,1]
[4,2,3,8,6,5,1,7]=>[1,3,1,1,2]
[2,4,3,5,1,8,6,7]=>[2,2,2,2]
[3,2,8,1,4,6,5,7]=>[1,2,3,2]
[3,7,8,5,6,1,2,4]=>[3,2,3]
[3,6,1,8,4,7,2,5]=>[2,2,2,2]
[3,1,6,8,4,7,2,5]=>[1,3,2,2]
[4,1,6,8,3,2,7,5]=>[1,3,1,2,1]
[4,6,1,8,3,2,7,5]=>[2,2,1,2,1]
[4,7,8,1,3,2,6,5]=>[3,2,2,1]
[4,7,8,3,1,2,6,5]=>[3,1,3,1]
[2,7,8,3,4,6,5,1]=>[3,3,1,1]
[4,7,8,2,1,3,6,5]=>[3,1,3,1]
[4,6,1,8,2,3,7,5]=>[2,2,3,1]
[4,1,6,8,2,3,7,5]=>[1,3,3,1]
[4,5,1,2,8,3,7,6]=>[2,3,2,1]
[4,5,2,1,8,3,7,6]=>[2,1,2,2,1]
[4,6,2,8,1,3,7,5]=>[2,2,3,1]
[3,6,2,8,4,7,1,5]=>[2,2,2,2]
[2,3,6,8,4,7,5,1]=>[4,2,1,1]
[3,2,6,8,4,7,1,5]=>[1,3,2,2]
[4,2,6,8,3,1,7,5]=>[1,3,1,2,1]
[4,2,5,1,8,3,7,6]=>[1,2,2,2,1]
[4,1,2,5,8,3,7,6]=>[1,4,2,1]
[5,1,2,4,3,8,7,6]=>[1,3,2,1,1]
[5,2,4,1,3,8,7,6]=>[1,2,3,1,1]
[4,2,5,3,8,1,7,6]=>[1,2,2,2,1]
[3,2,5,4,8,7,1,6]=>[1,2,2,1,2]
[3,5,2,4,8,7,1,6]=>[2,3,1,2]
[5,4,2,1,3,8,7,6]=>[1,1,1,3,1,1]
[5,1,4,2,3,8,7,6]=>[1,2,3,1,1]
[5,4,1,3,2,8,7,6]=>[1,1,2,2,1,1]
[5,4,3,1,2,8,7,6]=>[1,1,1,3,1,1]
[4,5,3,1,8,2,7,6]=>[2,1,2,2,1]
[4,5,1,3,8,2,7,6]=>[2,3,2,1]
[3,1,5,4,8,7,2,6]=>[1,2,2,1,2]
[3,5,1,4,8,7,2,6]=>[2,3,1,2]
[3,5,4,1,8,7,2,6]=>[2,1,2,1,2]
[3,6,5,8,7,1,2,4]=>[2,2,1,3]
[2,5,6,8,7,3,4,1]=>[4,1,2,1]
[3,4,5,1,8,7,2,6]=>[3,2,1,2]
[3,4,1,5,8,7,2,6]=>[2,3,1,2]
[4,1,3,5,8,2,7,6]=>[1,4,2,1]
[4,3,6,8,2,1,7,5]=>[1,3,1,2,1]
[2,4,6,8,3,7,5,1]=>[4,2,1,1]
[3,4,5,2,8,7,1,6]=>[3,2,1,2]
[5,3,1,4,2,8,7,6]=>[1,1,2,2,1,1]
[5,1,3,4,2,8,7,6]=>[1,3,2,1,1]
[5,1,3,2,4,8,7,6]=>[1,2,3,1,1]
[5,3,2,1,4,8,7,6]=>[1,1,1,3,1,1]
[4,3,2,5,8,1,7,6]=>[1,1,3,2,1]
[3,4,2,5,8,7,1,6]=>[2,3,1,2]
[3,2,4,5,8,7,1,6]=>[1,4,1,2]
[4,2,3,5,8,1,7,6]=>[1,4,2,1]
[5,2,3,1,4,8,7,6]=>[1,2,3,1,1]
[5,2,1,3,4,8,7,6]=>[1,1,4,1,1]
[5,1,2,3,4,8,7,6]=>[1,5,1,1]
[8,6,2,5,4,1,3,7]=>[1,1,2,1,3]
[6,5,7,4,2,8,3,1]=>[1,2,1,2,1,1]
[6,7,5,3,8,2,4,1]=>[2,1,2,2,1]
[8,2,1,6,3,4,5,7]=>[1,1,2,4]
[8,3,5,6,2,4,1,7]=>[1,3,2,2]
[8,6,2,1,3,5,4,7]=>[1,1,1,3,2]
[8,1,2,3,4,6,5,7]=>[1,5,2]
[6,2,3,7,8,4,5,1]=>[1,4,2,1]
[7,5,8,2,6,3,4,1]=>[1,2,2,2,1]
[7,3,1,6,5,8,4,2]=>[1,1,2,2,1,1]
[1,5,6,7,3,4,8,2]=>[4,3,1]
[6,7,8,2,1,4,5,3]=>[3,1,3,1]
[8,4,7,6,2,1,3,5]=>[1,2,1,1,3]
[5,3,8,4,7,2,6,1]=>[1,2,2,2,1]
[8,1,3,7,6,4,2,5]=>[1,3,1,1,2]
[5,3,1,7,8,6,2,4]=>[1,1,3,1,2]
[3,5,8,2,7,1,6,4]=>[3,2,2,1]
[6,2,8,5,3,1,7,4]=>[1,2,1,1,2,1]
[8,2,6,4,7,1,3,5]=>[1,2,2,3]
[3,4,2,8,5,1,7,6]=>[2,2,1,2,1]
[3,8,6,5,2,1,7,4]=>[2,1,1,1,2,1]
[8,3,7,4,2,5,6,1]=>[1,2,1,3,1]
[4,8,5,7,2,1,3,6]=>[2,2,1,3]
[3,4,1,8,2,6,7,5]=>[2,2,3,1]
[8,4,6,3,7,1,5,2]=>[1,2,2,2,1]
[6,8,3,4,1,5,7,2]=>[2,2,3,1]
[5,1,7,6,2,8,4,3]=>[1,2,1,2,1,1]
[6,8,2,5,7,4,1,3]=>[2,3,1,2]
[2,8,5,6,7,1,3,4]=>[2,3,3]
[2,5,7,6,3,1,8,4]=>[3,1,1,2,1]
[4,2,8,3,1,5,6,7]=>[1,2,1,4]
[2,5,7,3,8,4,6,1]=>[3,2,2,1]
[4,2,7,1,8,5,3,6]=>[1,2,2,1,2]
[4,2,1,8,7,5,6,3]=>[1,1,2,1,2,1]
[8,3,6,7,1,5,4,2]=>[1,3,2,1,1]
[1,3,7,5,8,6,4,2]=>[3,2,1,1,1]
[5,7,8,4,3,1,6,2]=>[3,1,1,2,1]
[2,7,4,5,8,3,6,1]=>[2,3,2,1]
[3,5,7,1,4,8,6,2]=>[3,3,1,1]
[7,2,8,5,1,4,6,3]=>[1,2,1,3,1]
[1,6,5,3,8,4,2,7]=>[2,1,2,1,2]
[5,7,4,8,3,6,2,1]=>[2,2,2,1,1]
[4,8,6,1,3,5,2,7]=>[2,1,3,2]
[1,8,3,2,4,7,5,6]=>[2,1,3,2]
[8,4,3,2,5,7,1,6]=>[1,1,1,3,2]
[3,6,4,8,2,5,7,1]=>[2,2,3,1]
[4,3,7,2,5,8,1,6]=>[1,2,3,2]
[3,2,4,7,8,5,6,1]=>[1,4,2,1]
[2,6,4,3,8,5,1,7]=>[2,1,2,1,2]
[3,8,2,1,6,4,5,7]=>[2,1,2,3]
[8,2,1,3,4,5,7,6]=>[1,1,5,1]
[4,6,8,3,2,1,5,7]=>[3,1,1,3]
[3,2,6,8,5,4,1,7]=>[1,3,1,1,2]
[7,3,8,2,5,4,1,6]=>[1,2,2,1,2]
[4,2,5,3,8,7,6,1]=>[1,2,2,1,1,1]
[4,8,2,6,5,3,1,7]=>[2,2,1,1,2]
[2,6,8,5,4,1,3,7]=>[3,1,1,3]
[3,1,8,6,5,4,2,7]=>[1,2,1,1,1,2]
[5,4,8,7,3,2,6,1]=>[1,2,1,1,2,1]
[6,4,8,3,7,2,5,1]=>[1,2,2,2,1]
[4,7,3,6,2,1,8,5]=>[2,2,1,2,1]
[5,4,3,7,1,8,2,6]=>[1,1,2,2,2]
[7,3,8,5,1,4,2,6]=>[1,2,1,2,2]
[5,4,8,7,6,2,1,3]=>[1,2,1,1,1,2]
[3,8,1,5,7,4,6,2]=>[2,3,2,1]
[4,8,5,7,3,1,6,2]=>[2,2,1,2,1]
[1,5,4,8,3,7,6,2]=>[2,2,2,1,1]
[4,8,3,6,7,1,5,2]=>[2,3,2,1]
[4,7,8,3,1,6,5,2]=>[3,1,2,1,1]
[8,7,5,3,6,4,2,1]=>[1,1,1,2,1,1,1]
[4,6,1,3,8,7,5,2]=>[2,3,1,1,1]
[6,8,2,1,7,4,5,3]=>[2,1,2,2,1]
[3,7,1,6,4,2,8,5]=>[2,2,1,2,1]
[3,1,2,7,5,6,8,4]=>[1,3,3,1]
[3,6,1,2,7,5,8,4]=>[2,3,2,1]
[3,7,6,2,5,8,1,4]=>[2,1,3,2]
[3,6,2,5,8,7,4,1]=>[2,3,1,1,1]
[8,5,2,3,6,7,4,1]=>[1,1,4,1,1]
[4,7,2,6,3,8,1,5]=>[2,2,2,2]
[6,3,2,4,8,7,5,1]=>[1,1,3,1,1,1]
[3,7,2,4,6,1,8,5]=>[2,3,2,1]
[5,3,7,2,8,1,4,6]=>[1,2,2,3]
[6,3,2,8,7,5,1,4]=>[1,1,2,1,1,2]
[7,3,8,2,6,5,1,4]=>[1,2,2,1,2]
[6,4,8,7,2,5,1,3]=>[1,2,1,2,2]
[2,5,4,8,1,7,6,3]=>[2,2,2,1,1]
[5,2,8,1,7,6,3,4]=>[1,2,2,1,2]
[6,2,1,3,8,7,5,4]=>[1,1,3,1,1,1]
[3,6,1,8,7,5,2,4]=>[2,2,1,1,2]
[5,6,1,2,8,7,4,3]=>[2,3,1,1,1]
[7,5,2,8,1,6,4,3]=>[1,1,2,2,1,1]
[2,7,6,8,1,5,4,3]=>[2,2,2,1,1]
[7,8,5,1,6,2,4,3]=>[2,1,2,2,1]
[7,4,8,6,1,2,5,3]=>[1,2,1,3,1]
[7,2,1,8,3,6,5,4]=>[1,1,2,2,1,1]
[5,8,7,1,6,4,3,2]=>[2,1,2,1,1,1]
[8,5,4,3,7,2,1,6]=>[1,1,1,2,1,2]
[6,5,4,8,3,2,7,1]=>[1,1,2,1,2,1]
[7,6,4,3,2,8,5,1]=>[1,1,1,1,2,1,1]
[7,3,1,4,8,2,5,6]=>[1,1,3,3]
[7,4,1,2,5,8,3,6]=>[1,1,4,2]
[6,7,4,2,5,1,3,8]=>[2,1,2,3]
[5,7,2,4,6,8,1,3]=>[2,4,2]
[4,7,5,1,6,2,8,3]=>[2,1,2,2,1]
[5,7,4,6,3,1,8,2]=>[2,2,1,2,1]
[7,5,1,4,3,2,8,6]=>[1,1,2,1,2,1]
[8,6,4,2,3,7,5,1]=>[1,1,1,3,1,1]
[6,4,7,1,3,8,5,2]=>[1,2,3,1,1]
[5,4,2,7,3,1,6,8]=>[1,1,2,1,3]
[4,5,1,2,7,6,8,3]=>[2,3,2,1]
[5,4,6,8,3,1,2,7]=>[1,3,1,3]
[6,4,8,1,3,7,2,5]=>[1,2,3,2]
[4,6,1,3,8,5,2,7]=>[2,3,1,2]
[1,3,8,4,5,7,2,6]=>[3,3,2]
[2,6,7,4,5,3,1,8]=>[3,2,1,2]
[2,6,8,4,3,5,1,7]=>[3,1,2,2]
[1,3,7,4,2,8,5,6]=>[3,1,2,2]
[4,6,1,3,7,2,5,8]=>[2,3,3]
[7,5,8,6,2,1,3,4]=>[1,2,1,1,3]
[2,8,1,3,6,5,4,7]=>[2,3,1,2]
[2,8,7,3,5,4,1,6]=>[2,1,2,1,2]
[3,4,2,6,8,7,1,5]=>[2,3,1,2]
[7,4,2,3,6,1,8,5]=>[1,1,3,2,1]
[8,4,2,3,6,5,7,1]=>[1,1,3,2,1]
[7,3,8,4,1,2,6,5]=>[1,2,1,3,1]
[6,8,3,2,7,1,5,4]=>[2,1,2,2,1]
[2,8,5,6,3,7,1,4]=>[2,2,2,2]
[7,4,2,5,8,1,6,3]=>[1,1,3,2,1]
[2,7,8,3,4,5,1,6]=>[3,3,2]
[3,7,1,2,4,6,5,8]=>[2,4,2]
[7,5,6,8,2,1,4,3]=>[1,3,1,2,1]
[3,1,6,5,2,7,4,8]=>[1,2,1,2,2]
[2,8,6,5,3,4,1,7]=>[2,1,1,2,2]
[1,7,2,3,5,6,8,4]=>[2,5,1]
[3,7,4,2,1,5,6,8]=>[2,1,1,4]
[3,4,6,2,8,5,7,1]=>[3,2,2,1]
[4,2,1,7,5,8,3,6]=>[1,1,2,2,2]
[4,7,2,6,5,1,3,8]=>[2,2,1,3]
[3,7,4,1,2,5,8,6]=>[2,1,4,1]
[4,7,1,6,5,2,8,3]=>[2,2,1,2,1]
[4,7,3,6,5,1,8,2]=>[2,2,1,2,1]
[4,3,7,1,6,8,5,2]=>[1,2,3,1,1]
[4,2,1,7,5,6,8,3]=>[1,1,2,3,1]
[3,2,4,8,6,7,1,5]=>[1,3,2,2]
[4,2,6,8,7,3,1,5]=>[1,3,1,1,2]
[3,4,6,1,8,5,2,7]=>[3,2,1,2]
[4,1,6,7,5,8,2,3]=>[1,3,2,2]
[4,3,6,7,5,1,2,8]=>[1,3,1,3]
[4,3,7,1,6,8,2,5]=>[1,2,3,2]
[4,3,7,5,6,8,2,1]=>[1,2,3,1,1]
[4,1,7,3,6,5,2,8]=>[1,2,2,1,2]
[2,8,7,4,5,3,1,6]=>[2,1,2,1,2]
[2,8,7,4,3,5,1,6]=>[2,1,1,2,2]
[3,8,1,4,2,6,5,7]=>[2,2,2,2]
[4,1,7,3,6,2,5,8]=>[1,2,2,3]
[5,8,7,6,1,2,4,3]=>[2,1,1,3,1]
[5,8,7,6,2,1,3,4]=>[2,1,1,1,3]
[4,1,7,2,6,8,5,3]=>[1,2,3,1,1]
[4,2,7,3,6,1,8,5]=>[1,2,2,2,1]
[4,2,7,3,6,5,8,1]=>[1,2,2,2,1]
[3,8,2,4,5,6,7,1]=>[2,5,1]
[3,8,2,4,1,6,7,5]=>[2,2,3,1]
[3,8,5,6,2,4,1,7]=>[2,2,2,2]
[2,8,6,5,3,7,1,4]=>[2,1,1,2,2]
[3,8,6,5,1,4,7,2]=>[2,1,1,3,1]
[3,8,2,1,4,6,7,5]=>[2,1,4,1]
[3,8,2,5,4,6,7,1]=>[2,2,3,1]
[4,2,7,5,6,3,8,1]=>[1,2,2,2,1]
[4,2,7,5,6,1,8,3]=>[1,2,2,2,1]
[4,2,6,7,5,3,1,8]=>[1,3,1,1,2]
[3,2,6,1,4,5,8,7]=>[1,2,4,1]
[2,8,7,3,4,5,1,6]=>[2,1,3,2]
[3,8,1,2,4,6,5,7]=>[2,4,2]
[5,8,7,6,1,3,4,2]=>[2,1,1,3,1]
[5,8,7,6,2,3,4,1]=>[2,1,1,3,1]
[4,1,7,5,6,2,3,8]=>[1,2,2,3]
[3,8,1,5,2,6,4,7]=>[2,2,2,2]
[2,8,7,5,3,4,1,6]=>[2,1,1,2,2]
[2,8,7,5,4,3,1,6]=>[2,1,1,1,1,2]
[4,1,7,5,6,3,2,8]=>[1,2,2,1,2]
[5,8,7,6,1,3,2,4]=>[2,1,1,2,2]
[5,8,7,6,4,1,2,3]=>[2,1,1,1,3]
[5,4,2,3,7,6,8,1]=>[1,1,3,2,1]
[7,4,3,5,2,8,1,6]=>[1,1,2,2,2]
[8,4,3,7,5,1,6,2]=>[1,1,2,1,2,1]
[8,4,7,2,5,1,6,3]=>[1,2,2,2,1]
[7,4,6,2,3,5,8,1]=>[1,2,4,1]
[5,1,7,2,4,6,8,3]=>[1,2,4,1]
[4,5,7,1,2,6,8,3]=>[3,4,1]
[5,4,1,7,3,6,8,2]=>[1,1,2,3,1]
[3,6,4,7,5,2,8,1]=>[2,2,1,2,1]
[3,4,7,6,2,5,8,1]=>[3,1,3,1]
[4,7,5,6,1,3,8,2]=>[2,2,3,1]
[5,7,6,4,3,1,8,2]=>[2,1,1,1,2,1]
[5,7,6,3,1,4,8,2]=>[2,1,1,3,1]
[7,5,2,3,4,8,1,6]=>[1,1,4,2]
[8,7,5,3,4,1,6,2]=>[1,1,1,2,2,1]
[6,7,1,3,8,4,2,5]=>[2,3,1,2]
[7,6,1,3,4,8,5,2]=>[1,1,4,1,1]
[3,6,5,2,7,8,1,4]=>[2,1,3,2]
[3,2,8,6,7,1,4,5]=>[1,2,2,3]
[4,8,3,6,5,2,1,7]=>[2,2,1,1,2]
[1,8,6,5,4,2,3,7]=>[2,1,1,1,3]
[1,8,7,2,3,5,4,6]=>[2,1,3,2]
[1,8,7,2,5,3,4,6]=>[2,1,2,3]
[3,6,8,5,1,2,4,7]=>[3,1,4]
[3,7,5,1,8,2,6,4]=>[2,1,2,2,1]
[7,1,2,8,3,5,6,4]=>[1,3,3,1]
[6,1,7,8,2,5,3,4]=>[1,3,2,2]
[6,7,5,2,8,1,4,3]=>[2,1,2,2,1]
[7,1,4,5,8,6,2,3]=>[1,4,1,2]
[5,7,6,4,2,8,1,3]=>[2,1,1,2,2]
[7,5,6,1,2,8,4,3]=>[1,2,3,1,1]
[4,1,3,7,8,6,2,5]=>[1,4,1,2]
[5,1,4,3,6,8,7,2]=>[1,2,3,1,1]
[4,5,7,6,8,2,1,3]=>[3,2,1,2]
[5,7,6,8,4,2,1,3]=>[2,2,1,1,2]
[5,1,6,8,4,2,7,3]=>[1,3,1,2,1]
[7,4,8,2,3,6,5,1]=>[1,2,3,1,1]
[5,6,8,4,7,3,2,1]=>[3,2,1,1,1]
[6,4,7,8,5,2,1,3]=>[1,3,1,1,2]
[3,6,4,8,5,1,2,7]=>[2,2,1,3]
[3,7,4,8,1,2,5,6]=>[2,2,4]
[7,4,3,8,2,6,5,1]=>[1,1,2,2,1,1]
[7,6,8,3,2,5,4,1]=>[1,2,1,2,1,1]
[8,7,1,3,5,4,6,2]=>[1,1,3,2,1]
[7,1,8,3,4,2,6,5]=>[1,2,2,2,1]
[7,6,8,3,1,4,5,2]=>[1,2,1,3,1]
[3,1,4,8,2,5,7,6]=>[1,3,3,1]
[4,8,5,2,1,3,6,7]=>[2,1,1,4]
[5,8,2,6,3,1,4,7]=>[2,2,1,3]
[6,8,2,3,7,4,1,5]=>[2,3,1,2]
[7,8,2,3,4,6,5,1]=>[2,4,1,1]
[8,1,7,2,4,5,3,6]=>[1,2,3,2]
[8,1,3,6,2,5,4,7]=>[1,3,2,2]
[7,2,1,6,3,5,4,8]=>[1,1,2,2,2]
[2,7,1,6,3,5,4,8]=>[2,2,2,2]
[2,7,1,5,4,3,6,8]=>[2,2,1,3]
[7,2,1,5,4,3,6,8]=>[1,1,2,1,3]
[8,1,3,5,4,2,6,7]=>[1,3,1,3]
[8,1,5,3,4,2,6,7]=>[1,2,2,3]
[8,1,5,6,2,3,7,4]=>[1,3,3,1]
[8,1,4,5,3,2,6,7]=>[1,3,1,3]
[8,1,4,3,5,2,6,7]=>[1,2,2,3]
[7,2,1,4,5,3,6,8]=>[1,1,3,3]
[2,7,1,4,5,3,6,8]=>[2,3,3]
[2,6,3,1,5,4,7,8]=>[2,1,2,3]
[6,3,2,1,5,4,7,8]=>[1,1,1,2,3]
[7,3,1,4,5,2,6,8]=>[1,1,3,3]
[7,3,1,5,4,2,6,8]=>[1,1,2,1,3]
[7,3,1,6,2,5,4,8]=>[1,1,2,2,2]
[3,7,1,6,2,5,4,8]=>[2,2,2,2]
[3,7,1,4,5,2,6,8]=>[2,3,3]
[3,6,2,1,5,4,7,8]=>[2,1,2,3]
[2,3,6,1,5,4,7,8]=>[3,2,3]
[3,5,2,4,1,6,7,8]=>[2,2,4]
[6,3,4,1,5,2,7,8]=>[1,2,2,3]
[6,2,4,1,5,3,7,8]=>[1,2,2,3]
[2,6,4,1,5,3,7,8]=>[2,1,2,3]
[2,6,5,1,3,7,4,8]=>[2,1,3,2]
[6,2,5,1,3,7,4,8]=>[1,2,3,2]
[6,5,2,1,3,7,4,8]=>[1,1,1,3,2]
[7,6,1,2,4,5,3,8]=>[1,1,4,2]
[6,7,1,2,8,3,5,4]=>[2,3,2,1]
[6,7,1,2,5,4,3,8]=>[2,3,1,2]
[5,6,2,1,3,7,4,8]=>[2,1,3,2]
[5,2,6,1,3,7,4,8]=>[1,2,3,2]
[2,4,6,1,5,3,7,8]=>[3,2,3]
[4,7,1,3,5,2,6,8]=>[2,3,3]
[4,7,1,5,3,2,6,8]=>[2,2,1,3]
[5,7,1,4,2,6,3,8]=>[2,2,2,2]
[5,7,1,6,2,3,8,4]=>[2,2,3,1]
[5,6,3,1,2,7,4,8]=>[2,1,3,2]
[4,2,5,3,1,6,7,8]=>[1,2,1,4]
[5,3,6,1,2,7,4,8]=>[1,2,3,2]
[3,4,6,1,5,2,7,8]=>[3,2,3]
[6,5,1,8,7,3,4,2]=>[1,1,2,1,2,1]
[8,2,7,5,4,1,3,6]=>[1,2,1,1,3]
[6,8,5,2,3,4,1,7]=>[2,1,3,2]
[2,6,8,7,1,5,3,4]=>[3,1,2,2]
[8,5,6,2,7,1,4,3]=>[1,2,2,2,1]
[6,5,1,2,7,8,4,3]=>[1,1,4,1,1]
[4,7,6,1,5,3,8,2]=>[2,1,2,2,1]
[5,7,6,4,1,3,8,2]=>[2,1,1,3,1]
[7,6,2,4,5,3,8,1]=>[1,1,3,2,1]
[6,1,7,5,3,8,4,2]=>[1,2,1,2,1,1]
[8,6,7,5,3,1,4,2]=>[1,2,1,1,2,1]
[8,5,2,7,1,6,4,3]=>[1,1,2,2,1,1]
[7,6,1,5,3,8,4,2]=>[1,1,2,2,1,1]
[5,6,2,4,7,8,1,3]=>[2,4,2]
[3,4,6,1,7,8,5,2]=>[3,3,1,1]
[3,4,8,6,7,1,5,2]=>[3,2,2,1]
[4,8,5,6,7,2,3,1]=>[2,3,2,1]
[5,8,6,4,1,2,7,3]=>[2,1,1,3,1]
[5,8,6,1,7,2,4,3]=>[2,1,2,2,1]
[5,8,7,3,2,6,4,1]=>[2,1,1,2,1,1]
[5,8,1,7,2,6,4,3]=>[2,2,2,1,1]
[8,1,5,7,2,6,4,3]=>[1,3,2,1,1]
[8,1,7,2,5,6,3,4]=>[1,2,3,2]
[6,8,7,2,5,1,3,4]=>[2,1,2,3]
[5,8,7,2,1,6,3,4]=>[2,1,1,2,2]
[4,8,1,5,2,6,7,3]=>[2,2,3,1]
[3,7,8,5,1,6,2,4]=>[3,1,2,2]
[6,5,2,7,8,1,4,3]=>[1,1,3,2,1]
[7,1,2,8,5,6,3,4]=>[1,3,2,2]
[8,7,2,1,5,6,3,4]=>[1,1,1,3,2]
[8,6,7,1,5,2,3,4]=>[1,2,2,3]
[6,1,7,8,5,2,3,4]=>[1,3,1,3]
[7,5,6,2,1,8,4,3]=>[1,2,1,2,1,1]
[8,7,5,2,1,6,4,3]=>[1,1,1,1,2,1,1]
[7,1,3,5,8,6,2,4]=>[1,4,1,2]
[5,1,3,4,6,8,7,2]=>[1,5,1,1]
[4,5,3,6,8,2,7,1]=>[2,3,2,1]
[5,6,3,4,8,1,7,2]=>[2,3,2,1]
[4,6,7,8,5,1,3,2]=>[4,1,2,1]
[8,4,3,1,2,6,7,5]=>[1,1,1,4,1]
[8,5,1,6,3,4,7,2]=>[1,1,2,3,1]
[5,1,8,6,3,4,7,2]=>[1,2,1,3,1]
[4,6,8,1,5,3,7,2]=>[3,2,2,1]
[6,4,5,8,3,2,7,1]=>[1,3,1,2,1]
[3,6,4,8,7,1,5,2]=>[2,2,1,2,1]
[6,5,8,1,3,4,7,2]=>[1,2,4,1]
[5,6,8,3,1,2,7,4]=>[3,1,3,1]
[6,1,8,3,5,2,7,4]=>[1,2,2,2,1]
[7,6,8,3,5,2,1,4]=>[1,2,2,1,2]
[8,6,1,3,5,2,7,4]=>[1,1,3,2,1]
[8,7,1,3,5,6,2,4]=>[1,1,4,2]
[6,7,8,3,5,1,2,4]=>[3,2,3]
[3,4,8,1,2,6,7,5]=>[3,4,1]
[5,8,2,4,3,6,7,1]=>[2,2,3,1]
[5,8,2,3,1,6,7,4]=>[2,2,3,1]
[6,8,2,3,5,1,7,4]=>[2,3,2,1]
[7,8,2,3,5,6,1,4]=>[2,4,2]
[8,6,5,1,4,3,7,2]=>[1,1,1,2,2,1]
[2,4,8,6,1,3,7,5]=>[3,1,3,1]
[6,7,1,8,4,3,5,2]=>[2,2,1,2,1]
[2,7,8,6,1,4,3,5]=>[3,1,2,2]
[2,7,3,8,1,6,4,5]=>[2,2,2,2]
[7,5,1,8,2,4,6,3]=>[1,1,2,3,1]
[2,7,8,4,1,6,3,5]=>[3,1,2,2]
[2,6,5,4,1,3,8,7]=>[2,1,1,3,1]
[4,1,7,6,3,8,2,5]=>[1,2,1,2,2]
[4,8,2,5,7,6,3,1]=>[2,3,1,1,1]
[3,4,6,5,1,8,2,7]=>[3,1,2,2]
[2,6,5,3,4,1,8,7]=>[2,1,2,2,1]
[4,6,1,5,2,3,8,7]=>[2,2,3,1]
[6,2,3,5,1,4,8,7]=>[1,3,3,1]
[2,6,7,5,1,8,4,3]=>[3,1,2,1,1]
[8,6,1,2,5,3,4,7]=>[1,1,3,3]
[6,2,5,1,8,3,4,7]=>[1,2,2,3]
[7,6,5,2,8,3,4,1]=>[1,1,1,2,2,1]
[2,6,3,5,1,8,7,4]=>[2,2,2,1,1]
[2,4,7,6,5,8,1,3]=>[3,1,2,2]
[2,1,4,8,7,6,3,5]=>[1,3,1,1,2]
[7,4,6,8,5,3,2,1]=>[1,3,1,1,1,1]
[8,1,3,5,7,4,6,2]=>[1,4,2,1]
[3,2,8,7,5,1,6,4]=>[1,2,1,1,2,1]
[4,8,5,1,6,7,2,3]=>[2,1,3,2]
[3,8,5,1,6,7,2,4]=>[2,1,3,2]
[7,8,6,1,3,5,2,4]=>[2,1,3,2]
[5,6,7,2,8,1,3,4]=>[3,2,3]
[2,5,1,8,6,7,4,3]=>[2,2,2,1,1]
[3,5,1,8,6,7,4,2]=>[2,2,2,1,1]
[5,2,3,8,6,7,4,1]=>[1,3,2,1,1]
[8,3,5,4,6,7,1,2]=>[1,2,3,2]
[5,1,3,8,6,7,4,2]=>[1,3,2,1,1]
[3,2,5,8,6,7,4,1]=>[1,3,2,1,1]
[6,2,1,5,3,8,7,4]=>[1,1,2,2,1,1]
[5,6,3,2,8,1,4,7]=>[2,1,2,3]
[8,1,6,3,5,2,7,4]=>[1,2,2,2,1]
[8,7,6,2,5,3,1,4]=>[1,1,1,2,1,2]
[4,7,6,8,3,2,5,1]=>[2,2,1,2,1]
[2,7,5,8,1,3,4,6]=>[2,2,4]
[7,6,2,8,5,1,4,3]=>[1,1,2,1,2,1]
[8,1,3,7,5,2,6,4]=>[1,3,1,2,1]
[3,4,8,7,5,1,6,2]=>[3,1,1,2,1]
[6,3,8,1,4,2,5,7]=>[1,2,2,3]
[6,3,8,5,7,4,1,2]=>[1,2,2,1,2]
[7,4,6,8,5,1,3,2]=>[1,3,1,2,1]
[2,1,4,8,7,5,6,3]=>[1,3,1,2,1]
[7,1,5,8,2,6,4,3]=>[1,3,2,1,1]
[3,6,8,2,4,1,7,5]=>[3,2,2,1]
[4,5,8,2,6,7,3,1]=>[3,3,1,1]
[5,2,8,1,6,7,3,4]=>[1,2,3,2]
[2,5,8,4,6,7,3,1]=>[3,3,1,1]
[5,8,3,4,6,7,2,1]=>[2,4,1,1]
[8,4,3,2,6,7,1,5]=>[1,1,1,3,2]
[4,2,8,1,6,7,3,5]=>[1,2,3,2]
[2,4,8,1,6,7,3,5]=>[3,3,2]
[5,1,8,2,6,7,3,4]=>[1,2,3,2]
[3,4,8,7,2,1,5,6]=>[3,1,1,3]
[7,8,5,3,6,4,2,1]=>[2,1,2,1,1,1]
[2,8,5,7,4,1,3,6]=>[2,2,1,3]
[5,8,4,1,6,7,2,3]=>[2,1,3,2]
[3,8,1,4,6,7,2,5]=>[2,4,2]
[8,2,3,4,6,7,1,5]=>[1,5,2]
[6,2,7,3,8,4,1,5]=>[1,2,2,1,2]
[7,4,3,2,8,5,1,6]=>[1,1,1,2,1,2]
[5,3,2,8,4,6,1,7]=>[1,1,2,2,2]
[8,4,2,6,5,3,1,7]=>[1,1,2,1,1,2]
[7,4,2,5,3,1,6,8]=>[1,1,2,1,3]
[8,3,6,2,5,4,1,7]=>[1,2,2,1,2]
[5,4,8,3,2,6,1,7]=>[1,2,1,2,2]
[3,5,8,2,4,6,1,7]=>[3,3,2]
[6,4,7,8,2,3,1,5]=>[1,3,2,2]
[4,8,6,2,5,3,1,7]=>[2,1,2,1,2]
[1,6,4,3,2,8,7,5]=>[2,1,1,2,1,1]
[1,5,3,2,8,4,7,6]=>[2,1,2,2,1]
[5,7,4,3,1,2,6,8]=>[2,1,1,4]
[2,8,7,3,5,1,4,6]=>[2,1,2,3]
[7,3,8,6,4,1,2,5]=>[1,2,1,1,3]
[6,1,2,7,3,8,5,4]=>[1,3,2,1,1]
[2,1,7,4,3,8,6,5]=>[1,2,1,2,1,1]
[5,1,3,2,8,7,4,6]=>[1,2,2,1,2]
[1,8,4,2,7,6,5,3]=>[2,1,2,1,1,1]
[1,8,3,7,2,6,5,4]=>[2,2,2,1,1]
[5,1,4,8,3,7,2,6]=>[1,3,2,2]
[2,1,6,8,5,4,7,3]=>[1,3,1,2,1]
[6,1,5,7,8,2,4,3]=>[1,4,2,1]
[8,3,1,6,7,2,5,4]=>[1,1,3,2,1]
[7,4,8,6,1,3,2,5]=>[1,2,1,2,2]
[3,7,6,1,5,2,4,8]=>[2,1,2,3]
[1,5,4,8,3,2,7,6]=>[2,2,1,2,1]
[7,3,6,1,2,5,4,8]=>[1,2,3,2]
[5,4,7,1,3,2,6,8]=>[1,2,2,3]
[4,6,8,2,5,1,3,7]=>[3,2,3]
[1,2,6,3,8,5,7,4]=>[3,2,2,1]
[1,5,2,6,8,4,7,3]=>[2,3,2,1]
[5,7,2,3,8,1,4,6]=>[2,3,3]
[6,4,7,5,8,1,2,3]=>[1,2,2,3]
[7,4,8,5,1,6,3,2]=>[1,2,1,2,1,1]
[5,8,3,6,1,7,4,2]=>[2,2,2,1,1]
[8,6,4,2,1,7,5,3]=>[1,1,1,1,2,1,1]
[7,4,2,1,5,8,6,3]=>[1,1,1,3,1,1]
[7,6,4,1,8,5,2,3]=>[1,1,1,2,1,2]
[1,6,4,8,7,5,3,2]=>[2,2,1,1,1,1]
[6,3,1,2,8,4,7,5]=>[1,1,3,2,1]
[7,5,1,3,2,8,6,4]=>[1,1,2,2,1,1]
[4,7,1,2,5,8,6,3]=>[2,4,1,1]
[6,8,4,1,2,7,5,3]=>[2,1,3,1,1]
[7,4,8,1,6,3,5,2]=>[1,2,2,2,1]
[5,8,2,1,7,3,6,4]=>[2,1,2,2,1]
[3,6,1,8,2,4,7,5]=>[2,2,3,1]
[1,3,8,7,6,2,5,4]=>[3,1,1,2,1]
[5,4,1,8,7,3,2,6]=>[1,1,2,1,1,2]
[3,5,1,8,7,2,4,6]=>[2,2,1,3]
[4,6,1,8,3,7,2,5]=>[2,2,2,2]
[4,7,1,2,8,6,3,5]=>[2,3,1,2]
[5,8,4,1,7,6,2,3]=>[2,1,2,1,2]
[7,6,8,1,5,4,2,3]=>[1,2,2,1,2]
[8,6,1,7,5,4,3,2]=>[1,1,2,1,1,1,1]
[7,1,5,8,6,4,3,2]=>[1,3,1,1,1,1]
[5,1,8,7,3,6,4,2]=>[1,2,1,2,1,1]
[4,1,8,7,6,2,5,3]=>[1,2,1,1,2,1]
[3,1,8,7,6,5,2,4]=>[1,2,1,1,1,2]
[1,6,4,5,2,3,7,8]=>[2,2,4]
[1,7,4,5,2,3,6,8]=>[2,2,4]
[1,7,3,5,2,4,6,8]=>[2,2,4]
[1,6,3,5,2,4,7,8]=>[2,2,4]
[1,6,3,4,2,5,7,8]=>[2,2,4]
[1,7,3,4,2,5,6,8]=>[2,2,4]
[1,8,6,7,3,4,2,5]=>[2,2,2,2]
[1,8,5,7,3,4,2,6]=>[2,2,2,2]
[1,7,3,4,2,6,5,8]=>[2,2,2,2]
[1,5,2,8,4,7,3,6]=>[2,2,2,2]
[1,4,2,8,5,7,3,6]=>[2,2,2,2]
[1,7,3,5,2,6,4,8]=>[2,2,2,2]
[1,8,4,7,3,5,2,6]=>[2,2,2,2]
[1,7,3,6,2,5,4,8]=>[2,2,2,2]
[1,7,3,6,2,4,5,8]=>[2,2,4]
[1,7,4,6,2,3,5,8]=>[2,2,4]
[1,8,5,6,2,3,4,7]=>[2,2,4]
[1,8,5,6,2,4,3,7]=>[2,2,2,2]
[1,3,2,8,5,6,4,7]=>[2,2,2,2]
[1,4,2,8,5,6,3,7]=>[2,2,2,2]
[1,5,2,8,4,6,3,7]=>[2,2,2,2]
[1,6,2,8,4,5,3,7]=>[2,2,2,2]
[8,1,2,4,5,3,6,7]=>[1,4,3]
[8,6,4,7,2,1,3,5]=>[1,1,2,1,3]
[1,6,4,7,2,8,3,5]=>[2,2,2,2]
[8,4,6,2,3,5,1,7]=>[1,2,3,2]
[5,4,8,2,3,6,1,7]=>[1,2,3,2]
[3,8,6,2,4,5,1,7]=>[2,1,3,2]
[4,8,6,2,3,5,1,7]=>[2,1,3,2]
[1,7,6,4,8,2,3,5]=>[2,1,2,3]
[5,8,7,4,1,2,3,6]=>[2,1,1,4]
[6,8,5,3,4,1,2,7]=>[2,1,2,3]
[6,8,3,7,2,1,4,5]=>[2,2,1,3]
[8,5,1,6,3,7,2,4]=>[1,1,2,2,2]
[6,1,3,7,4,8,2,5]=>[1,3,2,2]
[4,1,7,3,5,8,2,6]=>[1,2,3,2]
[7,1,6,4,8,2,3,5]=>[1,2,2,3]
[1,8,5,7,2,3,4,6]=>[2,2,4]
[6,1,5,8,2,3,4,7]=>[1,3,4]
[5,1,7,3,8,2,4,6]=>[1,2,2,3]
[6,1,5,7,8,2,3,4]=>[1,4,3]
[7,4,8,6,1,2,3,5]=>[1,2,1,4]
[3,8,7,5,1,2,4,6]=>[2,1,1,4]
[3,7,6,1,2,4,5,8]=>[2,1,5]
[4,7,6,1,2,3,5,8]=>[2,1,5]
[1,6,5,8,2,3,4,7]=>[2,2,4]
[6,5,8,4,1,2,3,7]=>[1,2,1,4]
[8,5,7,4,1,2,3,6]=>[1,2,1,4]
[1,5,7,4,8,2,3,6]=>[3,2,3]
[7,6,4,8,2,1,3,5]=>[1,1,2,1,3]
[7,6,2,3,8,1,4,5]=>[1,1,3,3]
[7,4,8,5,1,6,2,3]=>[1,2,1,2,2]
[8,6,2,3,1,7,4,5]=>[1,1,2,2,2]
[8,6,4,1,2,7,3,5]=>[1,1,1,3,2]
[1,7,2,8,6,3,4,5]=>[2,2,1,3]
[7,6,1,3,8,2,4,5]=>[1,1,3,3]
[7,5,8,1,3,6,2,4]=>[1,2,3,2]
[5,4,1,8,2,3,6,7]=>[1,1,2,4]
[1,4,8,7,2,3,5,6]=>[3,1,4]
[1,5,8,7,2,3,4,6]=>[3,1,4]
[6,5,1,8,2,3,4,7]=>[1,1,2,4]
[5,7,1,3,8,2,4,6]=>[2,3,3]
[7,6,8,1,5,2,3,4]=>[1,2,2,3]
[7,1,5,8,6,2,3,4]=>[1,3,1,3]
[6,1,8,2,7,3,4,5]=>[1,2,2,3]
[4,1,8,7,2,3,5,6]=>[1,2,1,4]
[5,1,8,7,2,3,4,6]=>[1,2,1,4]
[1,8,7,6,4,5,3,2]=>[2,1,1,2,1,1]
[1,8,7,3,6,5,4,2]=>[2,1,2,1,1,1]
[7,1,5,8,3,4,2,6]=>[1,3,2,2]
[7,1,4,3,2,5,6,8]=>[1,2,1,4]
[6,4,2,3,8,5,7,1]=>[1,1,3,2,1]
[6,4,2,7,5,8,3,1]=>[1,1,2,2,1,1]
[2,4,1,7,5,8,3,6]=>[2,2,2,2]
[7,1,4,6,5,2,3,8]=>[1,3,1,3]
[7,1,4,6,5,8,2,3]=>[1,3,2,2]
[7,1,4,6,3,8,2,5]=>[1,3,2,2]
[7,1,4,3,2,5,8,6]=>[1,2,1,3,1]
[7,1,4,6,5,2,8,3]=>[1,3,1,2,1]
[7,1,4,6,5,3,8,2]=>[1,3,1,2,1]
[7,1,4,6,5,3,2,8]=>[1,3,1,1,2]
[6,4,2,7,5,3,8,1]=>[1,1,2,1,2,1]
[3,4,7,2,6,8,5,1]=>[3,3,1,1]
[3,4,7,1,6,8,2,5]=>[3,3,2]
[3,4,7,1,6,8,5,2]=>[3,3,1,1]
[2,4,1,7,5,3,6,8]=>[2,2,1,3]
[3,4,1,7,8,6,2,5]=>[2,3,1,2]
[6,4,2,3,8,5,1,7]=>[1,1,3,1,2]
[6,4,2,7,5,8,1,3]=>[1,1,2,2,2]
[6,4,2,7,5,3,1,8]=>[1,1,2,1,1,2]
[3,4,7,2,6,8,1,5]=>[3,3,2]
[5,4,7,3,6,8,2,1]=>[1,2,3,1,1]
[3,4,7,2,6,5,1,8]=>[3,2,1,2]
[4,8,3,2,5,6,1,7]=>[2,1,3,2]
[4,8,7,3,5,1,2,6]=>[2,1,2,3]
[4,8,7,1,3,5,2,6]=>[2,1,3,2]
[4,8,3,1,2,6,5,7]=>[2,1,3,2]
[3,4,7,1,6,2,5,8]=>[3,2,3]
[3,4,7,1,6,2,8,5]=>[3,2,2,1]
[3,4,7,2,6,5,8,1]=>[3,2,2,1]
[4,8,3,1,2,6,7,5]=>[2,1,4,1]
[5,8,1,6,3,4,2,7]=>[2,2,2,2]
[6,8,5,1,3,7,2,4]=>[2,1,3,2]
[6,8,5,1,3,4,7,2]=>[2,1,4,1]
[5,8,3,4,2,6,7,1]=>[2,2,3,1]
[5,4,7,3,6,2,8,1]=>[1,2,2,2,1]
[5,4,7,2,6,1,8,3]=>[1,2,2,2,1]
[6,4,3,7,5,1,2,8]=>[1,1,2,1,3]
[6,4,3,7,5,1,8,2]=>[1,1,2,1,2,1]
[6,2,4,3,1,5,8,7]=>[1,2,1,3,1]
[3,8,7,4,1,5,2,6]=>[2,1,1,2,2]
[2,4,7,3,6,1,5,8]=>[3,2,3]
[5,8,3,2,1,6,4,7]=>[2,1,1,2,2]
[5,8,7,4,3,1,2,6]=>[2,1,1,1,3]
[5,4,7,3,6,2,1,8]=>[1,2,2,1,2]
[7,3,8,2,1,6,5,4]=>[1,2,1,2,1,1]
[7,4,3,8,5,2,1,6]=>[1,1,2,1,1,2]
[6,5,2,8,4,3,1,7]=>[1,1,2,1,1,2]
[4,3,2,8,6,5,1,7]=>[1,1,2,1,1,2]
[4,3,8,7,5,1,6,2]=>[1,2,1,1,2,1]
[3,2,5,8,6,1,4,7]=>[1,3,1,3]
[8,4,3,7,5,2,6,1]=>[1,1,2,1,2,1]
[4,3,7,8,5,1,2,6]=>[1,3,1,3]
[5,3,7,8,4,1,2,6]=>[1,3,1,3]
[6,2,5,8,3,1,4,7]=>[1,3,1,3]
[6,2,4,8,3,1,5,7]=>[1,3,1,3]
[5,2,3,8,4,1,6,7]=>[1,3,1,3]
[5,3,8,7,4,1,6,2]=>[1,2,1,1,2,1]
[5,3,2,8,6,4,1,7]=>[1,1,2,1,1,2]
[7,5,3,8,4,2,1,6]=>[1,1,2,1,1,2]
[8,7,5,3,6,2,4,1]=>[1,1,1,2,2,1]
[8,6,5,3,7,2,4,1]=>[1,1,1,2,2,1]
[7,5,4,3,8,2,6,1]=>[1,1,1,2,2,1]
[6,4,5,3,8,2,7,1]=>[1,2,2,2,1]
[7,4,6,3,8,2,5,1]=>[1,2,2,2,1]
[7,5,6,3,8,2,4,1]=>[1,2,2,2,1]
[8,5,6,3,7,2,4,1]=>[1,2,2,2,1]
[7,4,6,3,5,2,8,1]=>[1,2,2,2,1]
[8,4,6,3,5,2,7,1]=>[1,2,2,2,1]
[8,4,7,3,5,2,6,1]=>[1,2,2,2,1]
[8,5,7,3,4,2,6,1]=>[1,2,2,2,1]
[7,5,8,4,3,2,6,1]=>[1,2,1,1,2,1]
[6,5,8,4,3,2,7,1]=>[1,2,1,1,2,1]
[6,5,8,3,4,2,7,1]=>[1,2,2,2,1]
[7,5,8,3,4,2,6,1]=>[1,2,2,2,1]
[7,5,8,4,6,2,3,1]=>[1,2,2,2,1]
[7,4,8,3,6,2,5,1]=>[1,2,2,2,1]
[7,4,8,3,5,2,6,1]=>[1,2,2,2,1]
[6,4,8,3,5,2,7,1]=>[1,2,2,2,1]
[6,4,7,3,5,2,8,1]=>[1,2,2,2,1]
[5,4,8,3,7,2,6,1]=>[1,2,2,2,1]
[6,5,8,3,7,2,4,1]=>[1,2,2,2,1]
[6,5,8,4,7,2,3,1]=>[1,2,2,2,1]
[6,5,8,4,7,3,2,1]=>[1,2,2,1,1,1]
[6,4,7,3,8,2,5,1]=>[1,2,2,2,1]
[5,4,7,3,8,2,6,1]=>[1,2,2,2,1]
[5,4,6,3,8,2,7,1]=>[1,2,2,2,1]
[5,3,6,2,4,7,8,1]=>[1,2,4,1]
[5,3,6,1,4,8,7,2]=>[1,2,3,1,1]
[5,3,7,2,4,6,8,1]=>[1,2,4,1]
[4,3,1,5,6,8,7,2]=>[1,1,4,1,1]
[4,2,1,5,8,6,3,7]=>[1,1,3,1,2]
[4,2,1,5,8,6,7,3]=>[1,1,3,2,1]
[4,2,1,5,8,7,6,3]=>[1,1,3,1,1,1]
[4,3,1,5,7,8,6,2]=>[1,1,4,1,1]
[4,3,1,7,5,8,6,2]=>[1,1,2,2,1,1]
[6,7,3,1,4,8,2,5]=>[2,1,3,2]
[5,3,7,1,4,8,2,6]=>[1,2,3,2]
[4,3,1,5,7,8,2,6]=>[1,1,4,2]
[3,2,1,8,5,4,6,7]=>[1,1,2,1,3]
[3,2,1,8,5,7,4,6]=>[1,1,2,2,2]
[3,2,1,8,7,5,4,6]=>[1,1,2,1,1,2]
[5,2,7,1,8,4,3,6]=>[1,2,2,1,2]
[6,7,2,1,8,4,3,5]=>[2,1,2,1,2]
[6,7,2,1,8,4,5,3]=>[2,1,2,2,1]
[3,2,1,8,5,6,4,7]=>[1,1,2,2,2]
[3,2,1,8,6,5,4,7]=>[1,1,2,1,1,2]
[4,3,1,6,7,8,5,2]=>[1,1,4,1,1]
[4,2,1,6,8,7,5,3]=>[1,1,3,1,1,1]
[4,2,1,6,8,5,7,3]=>[1,1,3,2,1]
[4,2,1,6,8,5,3,7]=>[1,1,3,1,2]
[5,2,6,1,8,4,3,7]=>[1,2,2,1,2]
[5,2,6,1,8,7,4,3]=>[1,2,2,1,1,1]
[5,2,6,1,8,7,3,4]=>[1,2,2,1,2]
[5,2,6,1,8,3,4,7]=>[1,2,2,3]
[4,2,1,6,8,3,7,5]=>[1,1,3,2,1]
[4,3,1,6,7,8,2,5]=>[1,1,4,2]
[6,7,3,1,5,8,2,4]=>[2,1,3,2]
[4,2,1,7,8,6,3,5]=>[1,1,3,1,2]
[3,2,1,8,7,6,4,5]=>[1,1,2,1,1,2]
[3,2,1,8,6,4,7,5]=>[1,1,2,1,2,1]
[3,2,1,8,6,4,5,7]=>[1,1,2,1,3]
[3,2,1,8,4,6,5,7]=>[1,1,2,2,2]
[3,2,1,8,4,6,7,5]=>[1,1,2,3,1]
[3,2,1,8,4,7,6,5]=>[1,1,2,2,1,1]
[3,2,1,8,7,4,6,5]=>[1,1,2,1,2,1]
[4,2,1,7,8,3,6,5]=>[1,1,3,2,1]
[5,2,7,1,8,3,6,4]=>[1,2,2,2,1]
[6,7,2,1,8,3,5,4]=>[2,1,2,2,1]
[5,2,7,1,8,3,4,6]=>[1,2,2,3]
[4,2,1,7,8,3,5,6]=>[1,1,3,3]
[3,2,1,8,4,5,7,6]=>[1,1,2,3,1]
[7,5,2,8,6,3,4,1]=>[1,1,2,1,2,1]
[7,4,8,6,2,5,3,1]=>[1,2,1,2,1,1]
[7,3,8,6,2,4,5,1]=>[1,2,1,3,1]
[7,4,3,1,8,2,5,6]=>[1,1,1,2,3]
[7,4,2,8,5,6,1,3]=>[1,1,2,2,2]
[7,3,8,5,2,4,6,1]=>[1,2,1,3,1]
[7,3,8,4,5,6,2,1]=>[1,2,3,1,1]
[6,3,8,2,4,5,1,7]=>[1,2,3,2]
[6,3,8,2,5,7,4,1]=>[1,2,3,1,1]
[6,4,3,8,1,5,2,7]=>[1,1,2,2,2]
[6,3,7,8,2,4,1,5]=>[1,3,2,2]
[5,6,7,3,8,2,4,1]=>[3,2,2,1]
[5,4,7,2,6,8,1,3]=>[1,2,3,2]
[5,3,8,2,4,6,7,1]=>[1,2,4,1]
[6,3,8,2,4,7,5,1]=>[1,2,3,1,1]
[5,7,4,2,6,8,1,3]=>[2,1,3,2]
[6,4,8,2,7,5,1,3]=>[1,2,2,1,2]
[6,5,3,1,4,2,7,8]=>[1,1,1,2,3]
[5,7,4,2,6,1,3,8]=>[2,1,2,3]
[5,6,4,2,3,8,1,7]=>[2,1,3,2]
[5,6,3,7,8,2,4,1]=>[2,3,2,1]
[5,6,3,8,2,4,7,1]=>[2,2,3,1]
[6,3,7,2,4,5,1,8]=>[1,2,3,2]
[6,3,7,2,5,8,4,1]=>[1,2,3,1,1]
[5,3,6,8,2,4,7,1]=>[1,3,3,1]
[5,4,6,2,3,8,1,7]=>[1,2,3,2]
[5,3,6,7,8,2,4,1]=>[1,4,2,1]
[3,6,4,2,1,5,8,7]=>[2,1,1,3,1]
[3,5,8,6,4,2,1,7]=>[3,1,1,1,2]
[5,8,6,3,4,2,1,7]=>[2,1,2,1,2]
[5,6,3,4,2,1,8,7]=>[2,2,1,2,1]
[6,3,4,2,1,5,8,7]=>[1,2,1,3,1]
[5,6,4,2,1,3,8,7]=>[2,1,1,3,1]
[2,5,4,1,7,8,6,3]=>[2,1,3,1,1]
[2,7,8,5,4,1,6,3]=>[3,1,1,2,1]
[2,8,5,4,1,6,3,7]=>[2,1,1,2,2]
[2,6,3,8,5,4,1,7]=>[2,2,1,1,2]
[2,8,6,3,5,4,1,7]=>[2,1,2,1,2]
[5,8,6,4,2,1,3,7]=>[2,1,1,1,3]
[4,2,1,5,7,8,6,3]=>[1,1,4,1,1]
[2,7,8,6,3,5,4,1]=>[3,1,2,1,1]
[4,3,8,5,7,6,2,1]=>[1,2,2,1,1,1]
[7,6,2,1,8,4,3,5]=>[1,1,1,2,1,2]
[2,1,8,5,6,4,3,7]=>[1,2,2,1,2]
[4,2,1,8,5,6,3,7]=>[1,1,2,2,2]
[8,4,2,1,5,6,3,7]=>[1,1,1,3,2]
[2,5,6,3,8,4,1,7]=>[3,2,1,2]
[6,3,4,2,1,8,5,7]=>[1,2,1,2,2]
[3,7,8,5,6,4,2,1]=>[3,2,1,1,1]
[3,8,5,6,4,2,1,7]=>[2,2,1,1,2]
[3,6,4,2,1,8,5,7]=>[2,1,1,2,2]
[3,8,6,4,2,1,5,7]=>[2,1,1,1,3]
[3,7,8,6,4,2,1,5]=>[3,1,1,1,2]
[8,5,3,7,6,2,4,1]=>[1,1,2,1,2,1]
[7,6,2,4,1,8,5,3]=>[1,1,2,2,1,1]
[8,5,4,1,7,6,2,3]=>[1,1,1,2,1,2]
[7,6,2,3,8,5,4,1]=>[1,1,3,1,1,1]
[2,1,7,8,6,4,3,5]=>[1,3,1,1,2]
[2,1,6,4,3,7,8,5]=>[1,2,1,3,1]
[6,4,2,1,3,7,8,5]=>[1,1,1,4,1]
[6,3,7,8,4,2,1,5]=>[1,3,1,1,2]
[7,8,4,2,1,6,3,5]=>[2,1,1,2,2]
[5,7,6,2,3,8,4,1]=>[2,1,3,1,1]
[2,6,1,8,4,3,7,5]=>[2,2,1,2,1]
[2,6,1,7,5,8,4,3]=>[2,2,2,1,1]
[8,4,2,3,7,5,6,1]=>[1,1,3,2,1]
[8,5,7,6,2,1,4,3]=>[1,2,1,1,2,1]
[4,8,5,7,6,2,1,3]=>[2,2,1,1,2]
[4,7,6,2,1,3,8,5]=>[2,1,1,3,1]
[7,5,6,1,8,4,2,3]=>[1,2,2,1,2]
[2,7,5,8,4,3,6,1]=>[2,2,1,2,1]
[2,8,4,3,6,1,7,5]=>[2,1,2,2,1]
[6,4,7,8,3,2,1,5]=>[1,3,1,1,2]
[6,4,3,7,5,2,1,8]=>[1,1,2,1,1,2]
[6,5,3,2,8,4,1,7]=>[1,1,1,2,1,2]
[6,5,2,7,8,4,1,3]=>[1,1,3,1,2]
[6,4,3,2,5,8,1,7]=>[1,1,1,3,2]
[6,3,7,2,5,4,1,8]=>[1,2,2,1,2]
[6,3,2,7,5,4,1,8]=>[1,1,2,1,1,2]
[8,4,2,6,3,1,7,5]=>[1,1,2,1,2,1]
[1,5,3,7,4,2,8,6]=>[2,2,1,2,1]
[1,6,7,3,4,2,8,5]=>[3,2,2,1]
[8,6,5,2,3,1,7,4]=>[1,1,1,2,2,1]
[1,7,6,3,4,2,8,5]=>[2,1,2,2,1]
[1,8,6,3,2,5,7,4]=>[2,1,1,3,1]
[8,7,5,2,1,4,6,3]=>[1,1,1,1,3,1]
[7,8,5,2,1,4,6,3]=>[2,1,1,3,1]
[6,8,5,2,3,1,7,4]=>[2,1,2,2,1]
[5,8,6,2,3,1,7,4]=>[2,1,2,2,1]
[4,8,2,6,3,1,7,5]=>[2,2,1,2,1]
[3,2,8,6,4,1,7,5]=>[1,2,1,1,2,1]
[3,2,1,7,5,4,8,6]=>[1,1,2,1,2,1]
[4,1,3,7,5,2,8,6]=>[1,3,1,2,1]
[5,1,7,3,4,2,8,6]=>[1,2,2,2,1]
[7,1,6,3,2,5,8,4]=>[1,2,1,3,1]
[1,2,7,4,3,6,8,5]=>[3,1,3,1]
[6,1,8,2,4,5,7,3]=>[1,2,4,1]
[5,1,8,3,2,6,7,4]=>[1,2,1,3,1]
[3,2,8,7,1,5,6,4]=>[1,2,1,3,1]
[4,8,2,7,1,5,6,3]=>[2,2,3,1]
[5,8,7,2,1,4,6,3]=>[2,1,1,3,1]
[6,8,7,1,3,4,5,2]=>[2,1,4,1]
[7,8,6,1,3,4,5,2]=>[2,1,4,1]
[1,7,8,2,4,5,6,3]=>[3,4,1]
[8,6,7,1,3,4,5,2]=>[1,2,4,1]
[7,6,8,1,3,4,5,2]=>[1,2,4,1]
[6,5,8,2,3,1,7,4]=>[1,2,2,2,1]
[1,6,8,3,2,5,7,4]=>[3,1,3,1]
[1,5,3,8,2,6,7,4]=>[2,2,3,1]
[8,4,2,7,1,5,6,3]=>[1,1,2,3,1]
[7,4,2,8,1,5,6,3]=>[1,1,2,3,1]
[6,4,2,8,3,1,7,5]=>[1,1,2,1,2,1]
[5,4,2,3,8,1,7,6]=>[1,1,3,2,1]
[4,5,2,3,1,6,8,7]=>[2,2,3,1]
[7,4,2,1,3,6,8,5]=>[1,1,1,4,1]
[8,4,2,1,3,6,7,5]=>[1,1,1,4,1]
[1,5,3,2,4,7,8,6]=>[2,1,4,1]
[8,5,1,3,2,6,7,4]=>[1,1,2,3,1]
[5,6,1,3,4,2,8,7]=>[2,3,2,1]
[4,6,2,1,5,3,8,7]=>[2,1,2,2,1]
[4,7,2,1,3,6,8,5]=>[2,1,4,1]
[5,7,1,3,2,6,8,4]=>[2,2,3,1]
[6,7,1,2,4,5,8,3]=>[2,5,1]
[8,6,1,2,4,5,7,3]=>[1,1,5,1]
[1,8,2,3,5,6,7,4]=>[2,5,1]
[8,7,1,2,4,5,6,3]=>[1,1,5,1]
[7,8,1,2,4,5,6,3]=>[2,5,1]
[5,8,1,3,2,6,7,4]=>[2,2,3,1]
[4,8,2,1,3,6,7,5]=>[2,1,4,1]
[4,1,3,2,5,7,8,6]=>[1,2,4,1]
[5,1,2,4,3,7,8,6]=>[1,3,3,1]
[5,4,8,1,2,3,7,6]=>[1,2,4,1]
[1,4,7,6,3,2,5,8]=>[3,1,1,3]
[4,8,3,2,7,6,1,5]=>[2,1,2,1,2]
[4,3,8,2,7,1,6,5]=>[1,2,2,2,1]
[1,4,7,3,6,2,5,8]=>[3,2,3]
[4,3,2,8,1,7,6,5]=>[1,1,2,2,1,1]
[4,1,8,3,7,2,5,6]=>[1,2,2,3]
[4,1,8,7,3,2,5,6]=>[1,2,1,1,3]
[4,7,8,1,2,5,3,6]=>[3,3,2]
[3,4,7,6,2,1,8,5]=>[3,1,1,2,1]
[3,4,2,7,1,6,8,5]=>[2,2,3,1]
[2,3,6,7,4,1,8,5]=>[4,1,2,1]
[2,6,3,4,7,8,1,5]=>[2,4,2]
[2,6,7,8,3,4,1,5]=>[4,2,2]
[3,1,7,8,4,2,5,6]=>[1,3,1,3]
[4,1,3,2,8,7,5,6]=>[1,2,2,1,2]
[3,7,8,2,6,4,1,5]=>[3,2,1,2]
[4,2,3,8,1,6,7,5]=>[1,3,3,1]
[4,3,1,8,2,5,7,6]=>[1,1,2,3,1]
[1,3,6,7,4,2,5,8]=>[4,1,3]
[3,2,7,8,4,1,6,5]=>[1,3,1,2,1]
[4,2,8,6,3,1,7,5]=>[1,2,1,1,2,1]
[3,7,2,4,8,6,1,5]=>[2,3,1,2]
[3,2,7,4,8,1,6,5]=>[1,2,2,2,1]
[1,3,6,4,7,2,5,8]=>[3,2,3]
[3,2,4,7,1,8,6,5]=>[1,3,2,1,1]
[3,7,4,2,6,8,1,5]=>[2,1,3,2]
[3,7,4,6,2,8,1,5]=>[2,2,2,2]
[4,7,1,5,8,2,3,6]=>[2,3,3]
[3,7,6,4,8,2,1,5]=>[2,1,2,1,2]
[3,1,7,4,8,2,5,6]=>[1,2,2,3]
[2,6,7,3,8,4,1,5]=>[3,2,1,2]
[2,3,6,4,7,1,8,5]=>[3,2,2,1]
[8,7,5,2,6,3,4,1]=>[1,1,1,2,2,1]
[8,6,5,2,7,3,4,1]=>[1,1,1,2,2,1]
[7,4,8,5,6,3,2,1]=>[1,2,2,1,1,1]
[3,4,6,7,8,5,1,2]=>[5,1,2]
[1,2,6,4,7,5,8,3]=>[3,2,2,1]
[3,1,7,5,4,2,6,8]=>[1,2,1,1,3]
[6,3,8,5,4,7,1,2]=>[1,2,1,2,2]
[1,6,2,5,4,7,8,3]=>[2,2,3,1]
[1,8,2,5,6,3,7,4]=>[2,3,2,1]
[1,2,6,4,8,5,7,3]=>[3,2,2,1]
[7,8,3,1,4,2,5,6]=>[2,1,2,3]
[4,8,1,5,2,3,6,7]=>[2,2,4]
[7,4,1,5,2,3,6,8]=>[1,1,2,4]
[5,6,1,8,4,3,2,7]=>[2,2,1,1,2]
[5,1,8,6,4,3,2,7]=>[1,2,1,1,1,2]
[5,1,6,3,8,7,2,4]=>[1,2,2,1,2]
[6,1,2,5,8,3,7,4]=>[1,4,2,1]
[6,1,8,7,4,3,2,5]=>[1,2,1,1,1,2]
[7,1,2,5,4,8,6,3]=>[1,3,2,1,1]
[1,2,7,5,8,3,6,4]=>[3,2,2,1]
[4,1,6,3,7,5,2,8]=>[1,2,2,1,2]
[1,3,6,7,8,5,2,4]=>[5,1,2]
[1,2,6,4,7,8,5,3]=>[3,3,1,1]
[4,1,6,3,7,8,2,5]=>[1,2,3,2]
[3,1,6,4,8,2,7,5]=>[1,2,2,2,1]
[7,8,4,1,6,3,2,5]=>[2,1,2,1,2]
[4,1,6,3,8,7,2,5]=>[1,2,2,1,2]
[7,5,1,8,4,3,2,6]=>[1,1,2,1,1,2]
[6,5,1,7,4,3,2,8]=>[1,1,2,1,1,2]
[4,1,8,5,2,3,7,6]=>[1,2,1,3,1]
[4,1,6,8,3,7,2,5]=>[1,3,2,2]
[5,4,6,1,3,8,2,7]=>[1,2,3,2]
[6,5,8,1,4,3,2,7]=>[1,2,2,1,2]
[1,3,5,7,6,8,2,4]=>[4,2,2]
[1,3,5,7,6,2,8,4]=>[4,1,2,1]
[1,3,5,7,2,6,8,4]=>[4,3,1]
[1,3,5,2,7,6,4,8]=>[3,2,1,2]
[1,3,5,7,6,2,4,8]=>[4,1,3]
[1,3,5,7,4,6,8,2]=>[4,3,1]
[1,3,5,7,4,6,2,8]=>[4,2,2]
[1,3,5,7,4,2,6,8]=>[4,1,3]
[1,3,5,4,7,2,6,8]=>[3,2,3]
[1,3,5,4,7,8,2,6]=>[3,3,2]
[1,3,5,4,7,2,8,6]=>[3,2,2,1]
[1,3,5,7,4,2,8,6]=>[4,1,2,1]
[1,3,5,7,4,8,2,6]=>[4,2,2]
[1,3,5,7,4,8,6,2]=>[4,2,1,1]
[1,3,5,7,8,4,6,2]=>[5,2,1]
[1,3,5,7,8,4,2,6]=>[5,1,2]
[1,3,5,2,7,8,6,4]=>[3,3,1,1]
[1,3,5,7,2,8,6,4]=>[4,2,1,1]
[1,3,5,7,8,2,6,4]=>[5,2,1]
[1,6,3,2,7,4,8,5]=>[2,1,2,2,1]
[3,5,1,6,2,8,7,4]=>[2,2,2,1,1]
[1,3,7,2,5,4,8,6]=>[3,2,2,1]
[2,6,1,7,4,3,8,5]=>[2,2,1,2,1]
[1,4,7,3,5,2,8,6]=>[3,2,2,1]
[1,3,7,5,2,4,8,6]=>[3,1,3,1]
[2,5,7,4,3,8,1,6]=>[3,1,2,2]
[2,5,3,7,4,8,1,6]=>[2,2,2,2]
[1,4,7,2,3,8,6,5]=>[3,3,1,1]
[2,4,7,3,1,8,6,5]=>[3,1,2,1,1]
[1,4,6,3,8,2,7,5]=>[3,2,2,1]
[1,4,7,3,8,2,6,5]=>[3,2,2,1]
[2,5,1,7,8,4,6,3]=>[2,3,2,1]
[3,2,6,7,8,1,5,4]=>[1,4,2,1]
[4,3,6,7,8,2,1,5]=>[1,4,1,2]
[3,5,2,7,8,4,1,6]=>[2,3,1,2]
[1,5,7,4,8,3,2,6]=>[3,2,1,2]
[2,5,1,6,8,4,7,3]=>[2,3,2,1]
[4,6,2,1,7,8,3,5]=>[2,1,3,2]
[5,3,6,4,7,8,2,1]=>[1,2,3,1,1]
[3,5,2,6,8,4,7,1]=>[2,3,2,1]
[2,5,4,6,8,7,1,3]=>[2,3,1,2]
[1,3,6,2,8,7,5,4]=>[3,2,1,1,1]
[1,4,6,3,8,7,2,5]=>[3,2,1,2]
[2,5,7,4,3,8,6,1]=>[3,1,2,1,1]
[1,5,7,2,4,8,6,3]=>[3,3,1,1]
[4,6,3,7,2,8,5,1]=>[2,2,2,1,1]
[1,4,7,3,8,6,2,5]=>[3,2,1,2]
[3,2,6,7,8,5,1,4]=>[1,4,1,2]
[1,3,7,2,8,6,5,4]=>[3,2,1,1,1]
[5,1,6,8,2,4,3,7]=>[1,3,2,2]
[5,3,7,8,2,4,1,6]=>[1,3,2,2]
[8,5,3,7,2,4,1,6]=>[1,1,2,2,2]
[8,2,4,7,3,1,5,6]=>[1,3,1,3]
[2,4,7,8,3,1,5,6]=>[4,1,3]
[6,3,1,5,8,2,4,7]=>[1,1,3,3]
[6,5,3,4,2,8,1,7]=>[1,1,2,2,2]
[5,2,4,3,8,1,6,7]=>[1,2,2,3]
[3,2,4,8,1,5,6,7]=>[1,3,4]
[3,2,4,6,8,1,5,7]=>[1,4,3]
[8,1,5,7,3,2,4,6]=>[1,3,1,3]
[8,4,6,7,2,3,1,5]=>[1,3,2,2]
[4,6,7,8,2,3,1,5]=>[4,2,2]
[7,4,6,8,2,3,1,5]=>[1,3,2,2]
[7,2,4,8,3,1,5,6]=>[1,3,1,3]
[5,3,8,7,2,4,1,6]=>[1,2,1,2,2]
[2,4,8,7,3,1,5,6]=>[3,1,1,3]
[4,6,8,7,2,3,1,5]=>[3,1,2,2]
[8,7,4,6,2,3,1,5]=>[1,1,2,2,2]
[5,6,8,7,2,3,1,4]=>[3,1,2,2]
[6,4,8,7,2,3,1,5]=>[1,2,1,2,2]
[3,1,7,4,2,8,6,5]=>[1,2,1,2,1,1]
[3,2,8,4,1,7,6,5]=>[1,2,1,2,1,1]
[7,6,4,8,2,3,1,5]=>[1,1,2,2,2]
[5,7,6,8,2,3,1,4]=>[2,2,2,2]
[4,7,6,8,2,3,1,5]=>[2,2,2,2]
[8,6,4,7,2,3,1,5]=>[1,1,2,2,2]
[8,2,3,7,4,1,6,5]=>[1,3,1,2,1]
[2,3,7,8,4,1,6,5]=>[4,1,2,1]
[3,7,4,8,2,5,1,6]=>[2,2,2,2]
[2,3,7,4,1,6,8,5]=>[3,1,3,1]
[8,1,6,4,2,3,7,5]=>[1,2,1,3,1]
[4,7,8,6,2,3,1,5]=>[3,1,2,2]
[2,4,7,3,1,5,8,6]=>[3,1,3,1]
[6,3,1,7,4,2,8,5]=>[1,1,2,1,2,1]
[8,5,7,6,2,3,1,4]=>[1,2,1,2,2]
[7,5,8,6,2,3,1,4]=>[1,2,1,2,2]
[7,1,6,4,2,3,8,5]=>[1,2,1,3,1]
[3,1,7,6,4,2,8,5]=>[1,2,1,1,2,1]
[4,8,7,6,2,3,1,5]=>[2,1,1,2,2]
[6,8,7,5,2,3,1,4]=>[2,1,1,2,2]
[4,3,6,1,5,8,7,2]=>[1,2,3,1,1]
[4,3,6,5,1,8,7,2]=>[1,2,1,2,1,1]
[4,6,3,5,1,8,7,2]=>[2,2,2,1,1]
[4,6,3,1,5,8,7,2]=>[2,1,3,1,1]
[4,1,6,5,3,8,7,2]=>[1,2,1,2,1,1]
[4,6,1,5,3,8,7,2]=>[2,2,2,1,1]
[2,6,5,3,1,8,7,4]=>[2,1,1,2,1,1]
[2,6,5,1,8,7,3,4]=>[2,1,2,1,2]
[2,6,5,8,1,7,3,4]=>[2,2,2,2]
[2,6,5,8,1,3,7,4]=>[2,2,3,1]
[2,6,5,8,3,1,7,4]=>[2,2,1,2,1]
[2,6,5,3,8,1,7,4]=>[2,1,2,2,1]
[4,6,1,5,8,3,7,2]=>[2,3,2,1]
[4,1,6,5,8,3,7,2]=>[1,2,2,2,1]
[1,4,6,5,8,3,7,2]=>[3,2,2,1]
[4,1,6,5,8,7,3,2]=>[1,2,2,1,1,1]
[2,6,5,3,8,7,1,4]=>[2,1,2,1,2]
[6,4,3,8,7,1,5,2]=>[1,1,2,1,2,1]
[6,4,8,3,7,1,5,2]=>[1,2,2,2,1]
[2,6,8,5,3,7,1,4]=>[3,1,2,2]
[4,6,8,1,5,7,3,2]=>[3,3,1,1]
[4,6,1,8,5,7,3,2]=>[2,2,2,1,1]
[4,1,6,8,5,7,3,2]=>[1,3,2,1,1]
[1,4,6,8,5,7,3,2]=>[4,2,1,1]
[1,4,6,8,5,3,7,2]=>[4,1,2,1]
[4,6,1,8,5,3,7,2]=>[2,2,1,2,1]
[2,6,8,5,3,1,7,4]=>[3,1,1,2,1]
[2,6,8,5,1,7,3,4]=>[3,1,2,2]
[4,6,8,3,5,1,7,2]=>[3,2,2,1]
[4,6,8,3,1,5,7,2]=>[3,1,3,1]
[4,6,3,1,8,5,7,2]=>[2,1,2,2,1]
[4,6,3,8,1,5,7,2]=>[2,2,3,1]
[4,6,3,8,5,7,1,2]=>[2,2,2,2]
[4,3,6,8,1,5,7,2]=>[1,3,3,1]
[4,3,6,1,8,5,7,2]=>[1,2,2,2,1]
[4,3,1,6,8,5,7,2]=>[1,1,3,2,1]
[4,1,3,6,8,7,5,2]=>[1,4,1,1,1]
[4,3,6,1,8,7,5,2]=>[1,2,2,1,1,1]
[4,3,6,8,1,7,5,2]=>[1,3,2,1,1]
[6,5,2,8,7,3,1,4]=>[1,1,2,1,1,2]
[6,5,2,8,7,1,3,4]=>[1,1,2,1,3]
[6,2,5,8,7,1,3,4]=>[1,3,1,3]
[6,2,5,8,7,3,1,4]=>[1,3,1,1,2]
[4,6,3,8,1,7,5,2]=>[2,2,2,1,1]
[4,6,3,1,8,7,5,2]=>[2,1,2,1,1,1]
[4,1,6,3,8,7,5,2]=>[1,2,2,1,1,1]
[1,4,6,3,8,7,5,2]=>[3,2,1,1,1]
[4,1,6,8,3,7,5,2]=>[1,3,2,1,1]
[4,6,1,8,3,7,5,2]=>[2,2,2,1,1]
[4,6,8,1,3,7,5,2]=>[3,3,1,1]
[6,2,8,5,7,3,1,4]=>[1,2,2,1,2]
[6,2,8,5,7,1,3,4]=>[1,2,2,3]
[2,4,8,7,1,5,3,6]=>[3,1,2,2]
[4,2,8,7,5,3,1,6]=>[1,2,1,1,1,2]
[6,4,1,8,7,5,3,2]=>[1,1,2,1,1,1,1]
[6,1,4,8,7,5,3,2]=>[1,3,1,1,1,1]
[1,6,4,8,7,3,5,2]=>[2,2,1,2,1]
[6,4,1,8,7,3,5,2]=>[1,1,2,1,2,1]
[4,2,8,7,5,1,3,6]=>[1,2,1,1,3]
[2,4,8,7,3,5,1,6]=>[3,1,2,2]
[2,3,4,7,1,8,6,5]=>[4,2,1,1]
[2,3,4,7,8,5,6,1]=>[5,2,1]
[2,3,6,7,4,8,5,1]=>[4,2,1,1]
[2,5,6,3,7,8,1,4]=>[3,3,2]
[2,3,7,1,4,8,6,5]=>[3,3,1,1]
[2,6,1,3,7,8,5,4]=>[2,4,1,1]
[2,5,6,7,4,8,1,3]=>[4,2,2]
[2,3,7,8,4,5,6,1]=>[4,3,1]
[2,6,7,3,4,8,5,1]=>[3,3,1,1]
[1,5,3,2,6,4,7,8]=>[2,1,2,3]
[1,5,3,2,6,7,4,8]=>[2,1,3,2]
[1,7,3,2,8,5,4,6]=>[2,1,2,1,2]
[1,7,3,2,5,8,4,6]=>[2,1,3,2]
[1,3,2,7,5,4,8,6]=>[2,2,1,2,1]
[6,5,2,4,3,7,1,8]=>[1,1,2,2,2]
[6,4,2,5,3,7,1,8]=>[1,1,2,2,2]
[5,4,7,6,2,3,1,8]=>[1,2,1,2,2]
[3,6,4,8,2,1,5,7]=>[2,2,1,3]
[1,6,2,8,5,3,4,7]=>[2,2,1,3]
[4,6,2,3,7,5,1,8]=>[2,3,1,2]
[4,7,2,3,6,5,1,8]=>[2,3,1,2]
[4,7,2,3,5,6,1,8]=>[2,4,2]
[5,3,2,7,4,6,1,8]=>[1,1,2,2,2]
[5,3,2,6,4,7,1,8]=>[1,1,2,2,2]
[4,6,2,3,5,7,1,8]=>[2,4,2]
[3,5,2,1,6,8,4,7]=>[2,1,3,2]
[1,5,2,6,8,4,3,7]=>[2,3,1,2]
[1,5,7,2,8,4,3,6]=>[3,2,1,2]
[3,5,2,1,8,6,4,7]=>[2,1,2,1,2]
[3,6,8,4,2,1,5,7]=>[3,1,1,3]
[4,3,2,6,1,8,5,7]=>[1,1,2,2,2]
[1,5,8,2,7,4,3,6]=>[3,2,1,2]
[1,7,2,3,4,8,6,5]=>[2,4,1,1]
[6,8,2,3,4,1,7,5]=>[2,3,2,1]
[4,1,8,2,3,5,7,6]=>[1,2,4,1]
[2,3,1,8,4,5,7,6]=>[2,2,3,1]
[7,3,2,1,4,5,8,6]=>[1,1,1,4,1]
[7,8,1,4,3,5,2,6]=>[2,2,2,2]
[7,1,2,3,4,6,8,5]=>[1,6,1]
[6,1,2,3,4,8,7,5]=>[1,5,1,1]
[1,8,2,3,4,7,6,5]=>[2,4,1,1]
[8,1,2,3,4,6,7,5]=>[1,6,1]
[2,8,1,3,5,4,7,6]=>[2,3,2,1]
[8,7,1,4,3,5,2,6]=>[1,1,2,2,2]
[8,3,2,1,4,5,7,6]=>[1,1,1,4,1]
[3,8,2,1,5,6,4,7]=>[2,1,3,2]
[3,8,2,1,6,5,4,7]=>[2,1,2,1,2]
[1,7,8,3,5,4,2,6]=>[3,2,1,2]
[7,4,1,8,3,5,2,6]=>[1,1,2,2,2]
[8,4,1,7,3,5,2,6]=>[1,1,2,2,2]
[3,8,4,6,2,1,5,7]=>[2,2,1,3]
[8,4,2,5,3,1,6,7]=>[1,1,2,1,3]
[8,5,2,4,3,1,6,7]=>[1,1,2,1,3]
[8,3,2,5,4,1,6,7]=>[1,1,2,1,3]
[4,3,2,5,1,8,6,7]=>[1,1,2,2,2]
[3,5,2,4,1,8,6,7]=>[2,2,2,2]
[2,4,7,8,1,5,3,6]=>[4,2,2]
[1,8,7,3,5,4,2,6]=>[2,1,2,1,2]
[5,1,8,2,7,4,3,6]=>[1,2,2,1,2]
[5,1,7,2,8,4,3,6]=>[1,2,2,1,2]
[6,1,2,8,5,3,4,7]=>[1,3,1,3]
[6,3,2,1,8,4,5,7]=>[1,1,1,2,3]
[7,3,2,8,4,5,1,6]=>[1,1,2,2,2]
[2,7,8,4,3,5,1,6]=>[3,1,2,2]
[7,1,8,3,5,4,2,6]=>[1,2,2,1,2]
[7,8,2,3,4,6,1,5]=>[2,4,2]
[6,7,1,3,4,8,2,5]=>[2,4,2]
[6,8,1,3,4,7,2,5]=>[2,4,2]
[1,7,2,3,4,6,8,5]=>[2,5,1]
[1,6,2,3,4,8,7,5]=>[2,4,1,1]
[7,6,2,3,4,1,8,5]=>[1,1,3,2,1]
[8,6,2,3,4,1,7,5]=>[1,1,3,2,1]
[8,1,7,3,5,4,2,6]=>[1,2,2,1,2]
[8,3,2,7,4,5,1,6]=>[1,1,2,2,2]
[6,7,2,3,4,1,8,5]=>[2,3,2,1]
[7,6,2,3,4,8,1,5]=>[1,1,4,2]
[8,6,2,3,4,7,1,5]=>[1,1,4,2]
[6,3,4,8,7,5,1,2]=>[1,3,1,1,2]
[4,8,7,3,5,6,1,2]=>[2,1,3,2]
[4,8,7,5,3,6,1,2]=>[2,1,1,2,2]
[5,8,7,3,4,6,1,2]=>[2,1,3,2]
[5,8,4,2,1,6,7,3]=>[2,1,1,3,1]
[5,8,4,1,2,6,7,3]=>[2,1,4,1]
[5,3,7,2,6,1,8,4]=>[1,2,2,2,1]
[5,2,8,1,6,3,7,4]=>[1,2,2,2,1]
[5,8,2,1,4,7,6,3]=>[2,1,3,1,1]
[4,8,2,5,1,7,6,3]=>[2,2,2,1,1]
[7,8,4,1,2,6,5,3]=>[2,1,3,1,1]
[4,8,1,5,2,7,6,3]=>[2,2,2,1,1]
[5,8,1,2,4,7,6,3]=>[2,4,1,1]
[5,2,8,3,6,7,1,4]=>[1,2,3,2]
[3,8,7,6,2,4,1,5]=>[2,1,1,2,2]
[2,8,7,6,4,1,3,5]=>[2,1,1,1,3]
[7,8,2,6,5,1,3,4]=>[2,2,1,3]
[1,8,7,6,4,2,3,5]=>[2,1,1,1,3]
[2,8,7,6,3,1,4,5]=>[2,1,1,1,3]
[1,8,7,6,2,4,3,5]=>[2,1,1,2,2]
[1,8,7,6,3,4,2,5]=>[2,1,1,2,2]
[2,8,1,4,5,6,7,3]=>[2,5,1]
[2,1,7,3,6,5,8,4]=>[1,2,2,2,1]
[3,1,7,2,6,5,8,4]=>[1,2,2,2,1]
[3,2,7,1,6,5,8,4]=>[1,2,2,2,1]
[6,1,2,8,5,7,3,4]=>[1,3,2,2]
[6,2,1,8,5,7,3,4]=>[1,1,2,2,2]
[6,3,1,8,5,7,2,4]=>[1,1,2,2,2]
[6,4,2,1,7,5,8,3]=>[1,1,1,2,2,1]
[6,1,3,8,5,2,7,4]=>[1,3,1,2,1]
[2,3,7,1,6,8,5,4]=>[3,3,1,1]
[1,3,7,2,6,8,5,4]=>[3,3,1,1]
[7,8,2,6,5,3,1,4]=>[2,2,1,1,2]
[3,2,6,7,5,8,1,4]=>[1,3,2,2]
[1,2,7,5,6,3,8,4]=>[3,2,2,1]
[2,8,7,6,4,3,1,5]=>[2,1,1,1,1,2]
[3,8,7,6,1,2,5,4]=>[2,1,1,3,1]
[3,8,7,6,2,1,5,4]=>[2,1,1,1,2,1]
[4,8,7,6,2,1,3,5]=>[2,1,1,1,3]
[4,8,7,6,1,3,2,5]=>[2,1,1,2,2]
[3,8,7,6,4,1,2,5]=>[2,1,1,1,3]
[7,8,3,6,5,1,2,4]=>[2,2,1,3]
[2,3,7,5,6,8,1,4]=>[3,3,2]
[3,8,7,6,4,2,1,5]=>[2,1,1,1,1,2]
[5,1,4,6,8,2,3,7]=>[1,4,3]
[1,7,6,3,5,4,8,2]=>[2,1,2,2,1]
[4,3,7,2,6,5,1,8]=>[1,2,2,1,2]
[3,4,6,1,5,7,2,8]=>[3,3,2]
[1,6,8,5,7,3,4,2]=>[3,2,2,1]
[2,4,1,5,8,6,3,7]=>[2,3,1,2]
[4,6,1,2,5,8,3,7]=>[2,4,2]
[5,6,7,2,1,4,8,3]=>[3,1,3,1]
[7,8,6,5,1,2,4,3]=>[2,1,1,3,1]
[1,3,6,5,7,8,2,4]=>[3,3,2]
[7,4,8,5,3,1,6,2]=>[1,2,1,1,2,1]
[6,8,5,2,4,1,7,3]=>[2,1,2,2,1]
[2,3,1,6,8,5,7,4]=>[2,3,2,1]
[7,3,2,5,1,4,8,6]=>[1,1,2,3,1]
[7,1,4,2,3,6,8,5]=>[1,2,4,1]
[1,5,8,3,4,6,7,2]=>[3,4,1]
[8,3,1,2,4,7,6,5]=>[1,1,4,1,1]
[2,3,8,1,6,5,4,7]=>[3,2,1,2]
[8,1,4,7,2,5,3,6]=>[1,3,2,2]
[3,5,2,4,1,7,8,6]=>[2,2,3,1]
[3,4,7,8,6,2,1,5]=>[4,1,1,2]
[3,4,8,6,2,7,1,5]=>[3,1,2,2]
[5,8,2,1,6,7,3,4]=>[2,1,3,2]
[5,7,2,8,6,4,3,1]=>[2,2,1,1,1,1]
[6,1,2,7,5,3,8,4]=>[1,3,1,2,1]
[7,3,2,8,6,4,1,5]=>[1,1,2,1,1,2]
[2,7,8,4,6,3,1,5]=>[3,2,1,2]
[1,4,5,7,2,6,8,3]=>[4,3,1]
[7,3,5,2,6,1,8,4]=>[1,2,2,2,1]
[8,5,2,3,6,1,7,4]=>[1,1,3,2,1]
[8,1,6,3,5,7,2,4]=>[1,2,3,2]
[2,8,6,4,3,7,1,5]=>[2,1,1,2,2]
[8,3,2,6,4,7,1,5]=>[1,1,2,2,2]
[2,3,8,7,6,5,1,4]=>[3,1,1,1,2]
[1,2,8,7,3,6,5,4]=>[3,1,2,1,1]
[4,2,8,7,3,6,1,5]=>[1,2,1,2,2]
[4,5,8,7,1,2,6,3]=>[3,1,3,1]
[1,5,8,7,3,2,6,4]=>[3,1,1,2,1]
[4,5,8,7,3,2,1,6]=>[3,1,1,1,2]
[2,6,8,1,7,5,4,3]=>[3,2,1,1,1]
[3,6,8,4,7,2,1,5]=>[3,2,1,2]
[2,5,8,3,7,6,1,4]=>[3,2,1,2]
[3,2,8,4,7,6,1,5]=>[1,2,2,1,2]
[1,5,8,3,7,2,6,4]=>[3,2,2,1]
[3,5,8,4,7,2,1,6]=>[3,2,1,2]
[5,6,8,2,3,7,1,4]=>[3,3,2]
[1,6,8,4,2,7,5,3]=>[3,1,2,1,1]
[1,5,8,4,2,7,6,3]=>[3,1,2,1,1]
[1,5,8,2,3,7,6,4]=>[3,3,1,1]
[2,1,8,4,3,7,6,5]=>[1,2,1,2,1,1]
[2,5,8,4,3,7,1,6]=>[3,1,2,2]
[5,6,8,4,1,2,7,3]=>[3,1,3,1]
[5,6,8,1,3,2,7,4]=>[3,2,2,1]
[1,6,8,4,3,2,7,5]=>[3,1,1,2,1]
[5,6,8,4,3,2,1,7]=>[3,1,1,1,2]
[7,1,2,8,6,5,4,3]=>[1,3,1,1,1,1]
[7,1,4,8,6,2,5,3]=>[1,3,1,2,1]
[7,3,1,8,6,2,5,4]=>[1,1,2,1,2,1]
[7,2,4,8,3,6,1,5]=>[1,3,2,2]
[7,1,4,8,3,2,6,5]=>[1,3,1,2,1]
[7,4,5,8,3,2,1,6]=>[1,3,1,1,2]
[1,6,2,8,7,5,4,3]=>[2,2,1,1,1,1]
[1,6,4,8,7,2,5,3]=>[2,2,1,2,1]
[3,6,4,8,7,2,1,5]=>[2,2,1,1,2]
[3,2,5,8,7,6,1,4]=>[1,3,1,1,2]
[3,2,4,8,7,6,1,5]=>[1,3,1,1,2]
[3,1,5,8,7,2,6,4]=>[1,3,1,2,1]
[3,1,4,8,7,2,6,5]=>[1,3,1,2,1]
[1,6,4,8,2,7,5,3]=>[2,2,2,1,1]
[1,4,5,8,2,7,6,3]=>[4,2,1,1]
[2,4,5,8,3,7,1,6]=>[4,2,2]
[4,6,5,8,1,2,7,3]=>[2,2,3,1]
[1,6,4,8,3,2,7,5]=>[2,2,1,2,1]
[1,4,5,8,3,2,7,6]=>[4,1,2,1]
[7,6,1,4,8,2,5,3]=>[1,1,3,2,1]
[7,6,1,3,8,2,5,4]=>[1,1,3,2,1]
[7,6,3,4,8,2,1,5]=>[1,1,3,1,2]
[7,2,5,1,8,6,4,3]=>[1,2,2,1,1,1]
[7,2,5,3,8,6,1,4]=>[1,2,2,1,2]
[7,2,1,4,8,6,5,3]=>[1,1,3,1,1,1]
[7,2,1,3,8,6,5,4]=>[1,1,3,1,1,1]
[7,2,3,4,8,6,1,5]=>[1,4,1,2]
[7,3,5,4,8,2,1,6]=>[1,2,2,1,2]
[2,6,5,1,8,7,4,3]=>[2,1,2,1,1,1]
[2,3,5,4,8,7,1,6]=>[3,2,1,2]
[1,6,5,4,8,2,7,3]=>[2,1,2,2,1]
[1,6,5,3,8,2,7,4]=>[2,1,2,2,1]
[1,6,3,4,8,2,7,5]=>[2,3,2,1]
[1,3,5,4,8,2,7,6]=>[3,2,2,1]
[3,6,5,4,8,2,1,7]=>[2,1,2,1,2]
[7,6,5,2,3,8,1,4]=>[1,1,1,3,2]
[7,6,1,4,2,8,5,3]=>[1,1,2,2,1,1]
[7,6,1,2,3,8,5,4]=>[1,1,4,1,1]
[7,6,2,4,3,8,1,5]=>[1,1,2,2,2]
[7,1,5,4,2,8,6,3]=>[1,2,1,2,1,1]
[7,1,5,2,3,8,6,4]=>[1,2,3,1,1]
[7,1,2,4,3,8,6,5]=>[1,3,2,1,1]
[2,6,5,4,3,8,1,7]=>[2,1,1,2,2]
[7,6,1,4,3,2,8,5]=>[1,1,2,1,2,1]
[7,1,5,4,3,2,8,6]=>[1,2,1,1,2,1]
[3,4,2,6,7,8,1,5]=>[2,4,2]
[3,1,4,2,6,8,7,5]=>[1,2,3,1,1]
[8,3,4,2,6,1,7,5]=>[1,2,2,2,1]
[2,6,7,3,5,4,1,8]=>[3,2,1,2]
[2,7,8,3,5,4,1,6]=>[3,2,1,2]
[2,6,8,3,5,4,1,7]=>[3,2,1,2]
[4,7,1,2,8,5,3,6]=>[2,3,1,2]
[4,8,1,2,7,5,3,6]=>[2,3,1,2]
[2,1,6,3,7,5,4,8]=>[1,2,2,1,2]
[2,7,1,3,6,8,4,5]=>[2,4,2]
[6,7,3,2,8,1,4,5]=>[2,1,2,3]
[7,3,4,2,6,1,8,5]=>[1,2,2,2,1]
[7,4,1,2,8,5,3,6]=>[1,1,3,1,2]
[8,7,4,2,1,5,3,6]=>[1,1,1,1,2,2]
[7,4,1,2,6,5,3,8]=>[1,1,3,1,2]
[7,4,3,1,5,6,8,2]=>[1,1,1,4,1]
[6,7,4,1,5,8,3,2]=>[2,1,3,1,1]
[4,7,5,1,6,8,3,2]=>[2,1,3,1,1]
[4,5,3,1,7,6,8,2]=>[2,1,2,2,1]
[4,6,1,2,7,5,3,8]=>[2,3,1,2]
[2,7,1,3,6,5,4,8]=>[2,3,1,2]
[4,1,8,2,6,5,3,7]=>[1,2,2,1,2]
[4,6,1,2,8,5,3,7]=>[2,3,1,2]
[8,4,3,1,5,6,7,2]=>[1,1,1,4,1]
[4,5,3,1,8,6,7,2]=>[2,1,2,2,1]
[4,8,5,6,3,1,7,2]=>[2,2,1,2,1]
[5,1,3,4,8,6,7,2]=>[1,4,2,1]
[5,4,3,8,1,6,7,2]=>[1,1,2,3,1]
[8,5,3,4,1,6,7,2]=>[1,1,2,3,1]
[6,4,8,2,1,5,3,7]=>[1,2,1,2,2]
[6,7,3,2,5,1,4,8]=>[2,1,2,3]
[6,8,3,2,5,1,4,7]=>[2,1,2,3]
[5,7,1,4,6,8,3,2]=>[2,4,1,1]
[5,1,3,4,7,6,8,2]=>[1,4,2,1]
[6,1,4,2,7,5,3,8]=>[1,2,2,1,2]
[5,4,3,7,1,6,8,2]=>[1,1,2,3,1]
[6,7,5,4,1,8,3,2]=>[2,1,1,2,1,1]
[7,6,4,2,1,5,3,8]=>[1,1,1,1,2,2]
[8,2,7,6,5,4,1,3]=>[1,2,1,1,1,2]
[7,2,8,6,5,4,3,1]=>[1,2,1,1,1,1,1]
[8,7,2,6,5,4,1,3]=>[1,1,2,1,1,2]
[3,2,8,7,6,5,1,4]=>[1,2,1,1,1,2]
[4,8,7,6,5,3,1,2]=>[2,1,1,1,1,2]
[7,8,6,1,5,4,3,2]=>[2,1,2,1,1,1]
[7,3,8,6,5,4,2,1]=>[1,2,1,1,1,1,1]
[4,8,5,7,6,3,2,1]=>[2,2,1,1,1,1]
[3,8,7,4,6,5,2,1]=>[2,1,2,1,1,1]
[8,5,6,1,3,2,4,7]=>[1,2,2,3]
[8,6,1,5,3,2,4,7]=>[1,1,2,1,3]
[7,8,1,5,3,2,4,6]=>[2,2,1,3]
[8,1,7,5,3,2,4,6]=>[1,2,1,1,3]
[8,6,1,4,5,2,3,7]=>[1,1,3,3]
[8,6,3,1,5,2,4,7]=>[1,1,1,2,3]
[8,4,6,1,5,2,3,7]=>[1,2,2,3]
[8,6,2,1,5,4,3,7]=>[1,1,1,2,1,2]
[8,5,2,6,1,4,3,7]=>[1,1,2,2,2]
[8,5,2,1,7,4,3,6]=>[1,1,1,2,1,2]
[7,8,2,1,5,4,3,6]=>[2,1,2,1,2]
[7,8,3,1,5,2,4,6]=>[2,1,2,3]
[8,2,7,5,1,3,4,6]=>[1,2,1,4]
[8,4,1,7,5,2,3,6]=>[1,1,2,1,3]
[8,2,7,1,5,4,3,6]=>[1,2,2,1,2]
[8,2,6,1,7,4,3,5]=>[1,2,2,1,2]
[8,1,7,4,3,2,6,5]=>[1,2,1,1,2,1]
[8,1,5,7,3,2,6,4]=>[1,3,1,2,1]
[5,7,8,1,3,2,6,4]=>[3,2,2,1]
[8,2,6,1,5,7,3,4]=>[1,2,3,2]
[5,8,1,6,7,2,3,4]=>[2,3,3]
[5,7,6,1,8,2,3,4]=>[2,1,2,3]
[6,7,2,5,1,8,3,4]=>[2,2,2,2]
[7,5,1,6,8,2,3,4]=>[1,1,3,3]
[6,5,7,1,8,2,3,4]=>[1,2,2,3]
[6,7,3,8,1,2,4,5]=>[2,2,4]
[7,5,4,1,8,2,3,6]=>[1,1,1,2,3]
[7,6,1,4,8,2,3,5]=>[1,1,3,3]
[8,1,6,4,7,2,3,5]=>[1,2,2,3]
[7,5,8,1,3,2,4,6]=>[1,2,2,3]
[7,8,4,1,3,2,5,6]=>[2,1,2,3]
[8,3,7,4,1,2,5,6]=>[1,2,1,4]
[8,5,1,7,3,2,4,6]=>[1,1,2,1,3]
[6,8,1,7,3,2,4,5]=>[2,2,1,3]
[7,1,8,4,3,6,2,5]=>[1,2,1,2,2]
[7,3,1,8,6,4,2,5]=>[1,1,2,1,1,2]
[8,3,1,7,4,6,2,5]=>[1,1,2,2,2]
[8,4,5,1,7,2,3,6]=>[1,2,2,3]
[5,6,8,1,7,2,3,4]=>[3,2,3]
[6,5,8,1,2,7,3,4]=>[1,2,3,2]
[7,3,1,8,5,6,2,4]=>[1,1,2,2,2]
[6,2,7,8,3,1,5,4]=>[1,3,1,2,1]
[5,8,1,7,3,2,6,4]=>[2,2,1,2,1]
[8,4,1,7,3,2,6,5]=>[1,1,2,1,2,1]
[8,3,4,7,1,2,6,5]=>[1,3,3,1]
[8,2,7,4,1,3,6,5]=>[1,2,1,3,1]
[7,4,8,2,1,3,6,5]=>[1,2,1,3,1]
[7,4,3,8,1,2,6,5]=>[1,1,2,3,1]
[8,2,3,6,7,1,5,4]=>[1,4,2,1]
[2,6,8,7,1,5,4,3]=>[3,1,2,1,1]
[7,8,5,2,3,6,4,1]=>[2,1,3,1,1]
[8,7,5,2,3,1,6,4]=>[1,1,1,2,2,1]
[6,8,5,2,3,4,7,1]=>[2,1,4,1]
[3,5,2,6,8,1,4,7]=>[2,3,3]
[3,5,2,4,6,8,1,7]=>[2,4,2]
[2,4,5,7,3,6,8,1]=>[4,3,1]
[2,4,5,3,6,8,1,7]=>[3,3,2]
[5,2,4,6,8,1,3,7]=>[1,4,3]
[5,1,3,4,6,8,2,7]=>[1,5,2]
[4,3,5,2,6,8,1,7]=>[1,2,3,2]
[4,3,5,7,2,8,1,6]=>[1,3,2,2]
[4,3,5,7,2,6,8,1]=>[1,3,3,1]
[4,6,3,7,2,5,8,1]=>[2,2,3,1]
[4,6,3,1,7,8,2,5]=>[2,1,3,2]
[4,3,5,1,7,8,2,6]=>[1,2,3,2]
[5,7,1,3,4,8,2,6]=>[2,4,2]
[5,7,1,3,4,6,8,2]=>[2,5,1]
[4,5,7,1,3,6,8,2]=>[3,4,1]
[4,3,6,7,1,5,8,2]=>[1,3,3,1]
[4,6,3,5,1,7,8,2]=>[2,2,3,1]
[4,6,3,5,7,2,8,1]=>[2,3,2,1]
[3,5,6,4,1,7,8,2]=>[3,1,3,1]
[3,1,5,6,7,4,8,2]=>[1,4,2,1]
[5,1,6,7,3,4,8,2]=>[1,3,3,1]
[6,4,7,1,3,5,8,2]=>[1,2,4,1]
[1,6,7,3,4,5,8,2]=>[3,4,1]
[2,6,7,4,5,8,1,3]=>[3,3,2]
[2,6,7,4,8,1,3,5]=>[3,2,3]
[5,3,6,1,2,7,8,4]=>[1,2,4,1]
[3,5,2,6,1,7,8,4]=>[2,2,3,1]
[3,5,2,6,7,4,8,1]=>[2,3,2,1]
[5,2,3,6,7,4,8,1]=>[1,4,2,1]
[5,2,3,6,1,7,8,4]=>[1,3,3,1]
[5,2,6,1,3,7,8,4]=>[1,2,4,1]
[4,2,6,7,3,5,8,1]=>[1,3,3,1]
[6,3,7,2,4,5,8,1]=>[1,2,4,1]
[3,5,7,2,8,1,4,6]=>[3,2,3]
[3,7,2,4,8,1,5,6]=>[2,3,3]
[7,2,4,6,8,1,3,5]=>[1,4,3]
[7,1,3,4,6,8,2,5]=>[1,5,2]
[3,7,2,4,6,8,1,5]=>[2,4,2]
[3,5,7,2,6,8,1,4]=>[3,3,2]
[6,3,7,2,5,8,1,4]=>[1,2,3,2]
[6,3,5,7,2,8,1,4]=>[1,3,2,2]
[6,3,5,7,2,4,8,1]=>[1,3,3,1]
[6,2,4,5,7,3,8,1]=>[1,4,2,1]
[6,2,4,5,1,7,8,3]=>[1,3,3,1]
[4,7,1,2,5,6,8,3]=>[2,5,1]
[2,6,7,5,8,1,3,4]=>[3,2,3]
[4,6,7,1,2,5,8,3]=>[3,4,1]
[5,6,2,4,7,3,8,1]=>[2,3,2,1]
[5,4,2,6,7,3,8,1]=>[1,1,3,2,1]
[5,4,2,6,1,7,8,3]=>[1,1,2,3,1]
[1,5,4,6,2,7,8,3]=>[2,2,3,1]
[5,6,4,1,2,7,8,3]=>[2,1,4,1]
[6,4,5,1,2,7,8,3]=>[1,2,4,1]
[6,3,5,1,7,8,2,4]=>[1,2,3,2]
[6,5,7,2,8,1,3,4]=>[1,2,2,3]
[6,5,7,1,3,4,8,2]=>[1,2,4,1]
[5,6,4,7,1,3,8,2]=>[2,2,3,1]
[5,4,6,3,1,7,8,2]=>[1,2,1,3,1]
[7,5,3,2,4,8,1,6]=>[1,1,1,3,2]
[8,4,5,2,6,1,3,7]=>[1,2,2,3]
[8,5,4,2,1,6,3,7]=>[1,1,1,1,2,2]
[8,5,3,4,1,6,2,7]=>[1,1,2,2,2]
[8,4,5,3,1,6,2,7]=>[1,2,1,2,2]
[7,5,4,2,1,8,3,6]=>[1,1,1,1,2,2]
[7,5,4,2,1,6,8,3]=>[1,1,1,1,3,1]
[7,4,5,3,1,6,8,2]=>[1,2,1,3,1]
[7,4,3,5,6,1,8,2]=>[1,1,3,2,1]
[5,6,3,7,4,1,8,2]=>[2,2,1,2,1]
[5,6,7,3,1,4,8,2]=>[3,1,3,1]
[6,7,3,4,1,5,8,2]=>[2,2,3,1]
[6,7,4,2,1,5,8,3]=>[2,1,1,3,1]
[5,6,7,3,1,8,2,4]=>[3,1,2,2]
[5,6,3,7,8,1,2,4]=>[2,3,3]
[5,6,3,7,2,4,8,1]=>[2,2,3,1]
[5,6,7,2,3,8,1,4]=>[3,3,2]
[7,4,5,2,8,1,3,6]=>[1,2,2,3]
[6,7,3,2,4,8,1,5]=>[2,1,3,2]
[7,6,4,2,1,3,8,5]=>[1,1,1,1,3,1]
[7,6,3,4,1,2,8,5]=>[1,1,2,3,1]
[7,6,3,2,4,1,8,5]=>[1,1,1,2,2,1]
[6,7,3,2,5,1,8,4]=>[2,1,2,2,1]
[6,5,3,2,7,8,1,4]=>[1,1,1,3,2]
[6,5,3,2,7,4,8,1]=>[1,1,1,2,2,1]
[6,4,5,2,7,3,8,1]=>[1,2,2,2,1]
[6,4,5,2,7,8,1,3]=>[1,2,3,2]
[7,4,5,2,6,1,8,3]=>[1,2,2,2,1]
[7,4,5,6,1,2,8,3]=>[1,3,3,1]
[7,5,6,2,1,3,8,4]=>[1,2,1,3,1]
[6,7,3,5,1,2,8,4]=>[2,2,3,1]
[5,6,7,4,1,2,8,3]=>[3,1,3,1]
[5,6,7,2,4,1,8,3]=>[3,2,2,1]
[5,6,4,2,7,8,1,3]=>[2,1,3,2]
[6,5,7,2,1,8,3,4]=>[1,2,1,2,2]
[6,5,7,2,1,4,8,3]=>[1,2,1,3,1]
[5,4,6,7,3,1,8,2]=>[1,3,1,2,1]
[5,7,8,3,6,4,1,2]=>[3,2,1,2]
[3,7,8,5,6,4,1,2]=>[3,2,1,2]
[3,7,8,5,6,1,4,2]=>[3,2,2,1]
[1,7,8,5,6,3,4,2]=>[3,2,2,1]
[1,7,5,8,6,3,4,2]=>[2,2,1,2,1]
[3,7,5,8,6,1,4,2]=>[2,2,1,2,1]
[3,7,5,8,6,4,1,2]=>[2,2,1,1,2]
[5,7,3,8,6,4,1,2]=>[2,2,1,1,2]
[7,3,8,5,6,4,1,2]=>[1,2,2,1,2]
[7,3,5,8,6,4,1,2]=>[1,3,1,1,2]
[3,5,7,8,6,4,1,2]=>[4,1,1,2]
[1,5,7,8,6,3,4,2]=>[4,1,2,1]
[1,5,7,8,3,6,4,2]=>[4,2,1,1]
[3,5,7,8,1,6,4,2]=>[4,2,1,1]
[5,3,7,8,1,6,4,2]=>[1,3,2,1,1]
[7,3,5,8,6,1,4,2]=>[1,3,1,2,1]
[7,3,8,5,6,1,4,2]=>[1,2,2,2,1]
[7,8,1,5,6,3,4,2]=>[2,3,2,1]
[7,1,8,5,6,3,4,2]=>[1,2,2,2,1]
[7,1,5,8,6,3,4,2]=>[1,3,1,2,1]
[5,1,7,8,3,6,4,2]=>[1,3,2,1,1]
[3,1,7,8,5,6,4,2]=>[1,3,2,1,1]
[1,3,7,8,5,6,4,2]=>[4,2,1,1]
[3,1,7,5,8,6,4,2]=>[1,2,2,1,1,1]
[5,1,7,3,8,6,4,2]=>[1,2,2,1,1,1]
[7,1,5,3,8,6,4,2]=>[1,2,2,1,1,1]
[7,1,5,8,3,6,4,2]=>[1,3,2,1,1]
[7,8,1,5,3,6,4,2]=>[2,2,2,1,1]
[7,8,3,5,1,6,4,2]=>[2,2,2,1,1]
[7,3,5,8,1,6,4,2]=>[1,3,2,1,1]
[5,3,7,1,8,6,4,2]=>[1,2,2,1,1,1]
[3,5,7,1,8,6,4,2]=>[3,2,1,1,1]
[1,7,5,3,8,6,4,2]=>[2,1,2,1,1,1]
[5,7,3,1,8,6,4,2]=>[2,1,2,1,1,1]
[5,7,3,8,6,1,4,2]=>[2,2,1,2,1]
[3,7,5,8,1,6,4,2]=>[2,2,2,1,1]
[1,7,5,8,3,6,4,2]=>[2,2,2,1,1]
[1,7,8,5,3,6,4,2]=>[3,1,2,1,1]
[3,7,8,5,1,6,4,2]=>[3,1,2,1,1]
[5,7,8,3,6,1,4,2]=>[3,2,2,1]
[5,7,8,6,3,1,4,2]=>[3,1,1,2,1]
[7,5,8,6,1,3,4,2]=>[1,2,1,3,1]
[5,7,8,1,6,3,4,2]=>[3,2,2,1]
[5,7,8,1,3,6,4,2]=>[3,3,1,1]
[3,7,8,1,5,6,4,2]=>[3,3,1,1]
[1,7,8,3,5,6,4,2]=>[3,3,1,1]
[1,7,3,8,5,6,4,2]=>[2,2,2,1,1]
[3,7,1,8,5,6,4,2]=>[2,2,2,1,1]
[5,7,1,8,3,6,4,2]=>[2,2,2,1,1]
[5,7,1,8,6,3,4,2]=>[2,2,1,2,1]
[7,5,1,8,6,3,4,2]=>[1,1,2,1,2,1]
[7,5,8,1,6,3,4,2]=>[1,2,2,2,1]
[7,8,5,1,6,3,4,2]=>[2,1,2,2,1]
[7,8,5,1,3,6,4,2]=>[2,1,3,1,1]
[7,5,8,1,3,6,4,2]=>[1,2,3,1,1]
[7,5,1,8,3,6,4,2]=>[1,1,2,2,1,1]
[7,5,1,3,8,6,4,2]=>[1,1,3,1,1,1]
[5,7,1,3,8,6,4,2]=>[2,3,1,1,1]
[3,7,1,5,8,6,4,2]=>[2,3,1,1,1]
[1,7,3,5,8,6,4,2]=>[2,3,1,1,1]
[1,5,3,7,8,6,4,2]=>[2,3,1,1,1]
[3,5,1,7,8,6,4,2]=>[2,3,1,1,1]
[5,3,1,7,8,6,4,2]=>[1,1,3,1,1,1]
[7,3,1,5,8,6,4,2]=>[1,1,3,1,1,1]
[7,3,1,8,5,6,4,2]=>[1,1,2,2,1,1]
[7,3,8,1,5,6,4,2]=>[1,2,3,1,1]
[7,8,3,1,5,6,4,2]=>[2,1,3,1,1]
[7,8,1,3,5,6,4,2]=>[2,4,1,1]
[7,1,8,3,5,6,4,2]=>[1,2,3,1,1]
[7,1,3,8,5,6,4,2]=>[1,3,2,1,1]
[7,1,3,5,8,6,4,2]=>[1,4,1,1,1]
[3,1,5,7,8,6,4,2]=>[1,4,1,1,1]
[5,7,3,4,6,8,1,2]=>[2,4,2]
[5,7,3,4,8,6,1,2]=>[2,3,1,2]
[5,7,3,4,8,1,6,2]=>[2,3,2,1]
[5,7,3,4,1,8,6,2]=>[2,2,2,1,1]
[5,7,3,4,1,6,8,2]=>[2,2,3,1]
[5,7,3,4,6,1,2,8]=>[2,3,3]
[7,3,5,6,1,2,8,4]=>[1,3,3,1]
[5,7,3,1,4,6,2,8]=>[2,1,3,2]
[5,7,3,1,4,6,8,2]=>[2,1,4,1]
[5,7,3,1,4,8,6,2]=>[2,1,3,1,1]
[5,7,3,1,4,8,2,6]=>[2,1,3,2]
[5,3,7,4,1,2,8,6]=>[1,2,1,3,1]
[5,3,7,4,1,2,6,8]=>[1,2,1,4]
[5,3,7,1,4,2,6,8]=>[1,2,2,3]
[5,3,7,1,4,2,8,6]=>[1,2,2,2,1]
[3,7,5,1,2,8,6,4]=>[2,1,3,1,1]
[7,8,3,5,1,2,6,4]=>[2,2,3,1]
[7,3,8,5,1,2,6,4]=>[1,2,1,3,1]
[7,3,5,8,1,2,6,4]=>[1,3,3,1]
[3,7,5,1,2,6,4,8]=>[2,1,3,2]
[3,7,5,1,2,6,8,4]=>[2,1,4,1]
[6,1,4,3,5,2,8,7]=>[1,2,2,2,1]
[2,5,7,3,8,4,1,6]=>[3,2,1,2]
[5,4,7,8,6,1,3,2]=>[1,3,1,2,1]
[7,5,6,2,8,3,1,4]=>[1,2,2,1,2]
[4,7,2,5,8,3,1,6]=>[2,3,1,2]
[6,2,4,5,1,3,8,7]=>[1,3,3,1]
[5,1,4,6,3,2,8,7]=>[1,3,1,2,1]
[3,5,6,2,4,1,8,7]=>[3,2,2,1]
[3,8,6,7,5,4,1,2]=>[2,2,1,1,2]
[6,2,7,8,3,4,1,5]=>[1,3,2,2]
[2,5,3,4,8,1,7,6]=>[2,3,2,1]
[8,7,1,2,5,3,4,6]=>[1,1,3,3]
[5,1,8,2,3,4,7,6]=>[1,2,4,1]
[5,4,7,6,2,8,1,3]=>[1,2,1,2,2]
[3,7,8,1,5,4,6,2]=>[3,2,2,1]
[7,1,3,4,6,8,5,2]=>[1,5,1,1]
[8,3,6,5,7,1,4,2]=>[1,2,2,2,1]
[5,8,7,1,4,6,2,3]=>[2,1,3,2]
[4,7,6,1,8,3,5,2]=>[2,1,2,2,1]
[4,7,2,6,3,8,5,1]=>[2,2,2,1,1]
[2,1,8,4,6,7,3,5]=>[1,2,3,2]
[4,7,8,6,3,1,2,5]=>[3,1,1,3]
[3,8,1,5,6,7,2,4]=>[2,4,2]
[6,7,2,4,8,5,3,1]=>[2,3,1,1,1]
[2,8,3,6,7,5,1,4]=>[2,3,1,2]
[8,2,1,7,6,3,5,4]=>[1,1,2,1,2,1]
[3,2,4,5,8,1,7,6]=>[1,4,2,1]
[7,4,6,3,2,1,8,5]=>[1,2,1,1,2,1]
[4,7,3,2,1,8,6,5]=>[2,1,1,2,1,1]
[6,4,7,5,2,3,8,1]=>[1,2,1,3,1]
[6,4,8,1,7,3,2,5]=>[1,2,2,1,2]
[4,8,7,2,3,1,5,6]=>[2,1,2,3]
[4,2,3,1,8,7,5,6]=>[1,2,2,1,2]
[7,6,8,1,3,5,2,4]=>[1,2,3,2]
[6,7,5,2,3,1,8,4]=>[2,1,2,2,1]
[4,7,2,6,5,1,8,3]=>[2,2,1,2,1]
[6,4,2,1,8,5,7,3]=>[1,1,1,2,2,1]
[7,2,1,5,6,8,4,3]=>[1,1,4,1,1]
[8,7,2,6,4,1,5,3]=>[1,1,2,1,2,1]
[6,7,8,2,5,3,1,4]=>[3,2,1,2]
[2,1,7,3,6,8,5,4]=>[1,2,3,1,1]
[2,1,5,7,8,4,6,3]=>[1,4,2,1]
[2,5,7,8,3,6,1,4]=>[4,2,2]
[6,4,1,5,7,2,8,3]=>[1,1,3,2,1]
[7,4,8,1,2,5,6,3]=>[1,2,4,1]
[4,2,7,8,6,3,5,1]=>[1,3,1,2,1]
[6,1,7,4,3,2,8,5]=>[1,2,1,1,2,1]
[6,8,3,4,2,1,7,5]=>[2,2,1,2,1]
[4,2,6,1,5,7,8,3]=>[1,2,4,1]
[2,4,6,7,3,5,8,1]=>[4,3,1]
[6,5,8,3,7,4,1,2]=>[1,2,2,1,2]
[7,1,4,8,3,5,6,2]=>[1,3,3,1]
[6,8,7,5,3,4,1,2]=>[2,1,1,2,2]
[4,8,6,3,1,5,7,2]=>[2,1,1,3,1]
[3,4,8,2,5,7,6,1]=>[3,3,1,1]
[3,5,7,2,8,6,1,4]=>[3,2,1,2]
[2,5,7,4,8,6,1,3]=>[3,2,1,2]
[1,6,3,7,5,2,8,4]=>[2,2,1,2,1]
[2,6,3,7,5,1,8,4]=>[2,2,1,2,1]
[2,6,4,8,7,5,1,3]=>[2,2,1,1,2]
[6,3,7,2,8,5,1,4]=>[1,2,2,1,2]
[3,6,2,5,8,7,1,4]=>[2,3,1,2]
[5,2,8,4,7,6,1,3]=>[1,2,2,1,2]
[7,2,4,8,6,5,1,3]=>[1,3,1,1,2]
[6,2,4,8,7,5,1,3]=>[1,3,1,1,2]
[2,4,5,8,7,6,1,3]=>[4,1,1,2]
[1,3,4,6,2,8,7,5]=>[4,2,1,1]
[5,2,3,6,1,8,7,4]=>[1,3,2,1,1]
[4,2,7,3,8,1,6,5]=>[1,2,2,2,1]
[2,5,1,4,7,3,8,6]=>[2,3,2,1]
[6,1,3,8,7,2,5,4]=>[1,3,1,2,1]
[3,1,5,6,2,8,7,4]=>[1,3,2,1,1]
[1,2,4,6,3,8,7,5]=>[4,2,1,1]
[4,1,5,2,8,7,6,3]=>[1,2,2,1,1,1]
[7,1,4,2,8,6,5,3]=>[1,2,2,1,1,1]
[5,1,3,7,2,8,6,4]=>[1,3,2,1,1]
[4,1,5,3,2,8,7,6]=>[1,2,1,2,1,1]
[2,6,1,4,3,8,7,5]=>[2,2,2,1,1]
[7,2,3,5,1,8,6,4]=>[1,3,2,1,1]
[7,3,4,1,8,6,5,2]=>[1,2,2,1,1,1]
[3,4,5,1,8,7,6,2]=>[3,2,1,1,1]
[1,4,5,2,8,7,6,3]=>[3,2,1,1,1]
[1,6,4,2,8,7,5,3]=>[2,1,2,1,1,1]
[5,6,3,1,8,7,4,2]=>[2,1,2,1,1,1]
[7,4,2,5,1,8,6,3]=>[1,1,2,2,1,1]
[5,3,6,2,8,1,7,4]=>[1,2,2,2,1]
[4,6,2,7,5,1,8,3]=>[2,2,1,2,1]
[4,5,2,6,1,8,7,3]=>[2,2,2,1,1]
[1,5,3,6,2,8,7,4]=>[2,2,2,1,1]
[1,5,8,3,2,7,6,4]=>[3,1,2,1,1]
[2,5,8,3,1,7,6,4]=>[3,1,2,1,1]
[4,5,8,2,1,7,6,3]=>[3,1,2,1,1]
[3,6,2,5,1,4,8,7]=>[2,2,3,1]
[5,2,8,4,1,3,7,6]=>[1,2,1,3,1]
[2,4,8,7,1,3,6,5]=>[3,1,3,1]
[2,5,8,1,3,7,6,4]=>[3,3,1,1]
[2,3,8,1,4,7,6,5]=>[3,3,1,1]
[1,3,8,2,4,7,6,5]=>[3,3,1,1]
[3,5,2,1,7,4,8,6]=>[2,1,2,2,1]
[6,3,1,7,2,8,5,4]=>[1,1,2,2,1,1]
[7,5,1,2,8,6,4,3]=>[1,1,3,1,1,1]
[4,6,1,2,8,7,5,3]=>[2,3,1,1,1]
[1,6,2,3,8,7,5,4]=>[2,3,1,1,1]
[1,5,2,3,8,7,6,4]=>[2,3,1,1,1]
[4,5,1,2,8,7,6,3]=>[2,3,1,1,1]
[6,4,1,2,8,7,5,3]=>[1,1,3,1,1,1]
[7,4,1,2,8,6,5,3]=>[1,1,3,1,1,1]
[5,3,1,7,2,8,6,4]=>[1,1,2,2,1,1]
[5,2,8,1,3,7,6,4]=>[1,2,3,1,1]
[4,1,2,8,3,7,6,5]=>[1,3,2,1,1]
[4,7,5,6,8,3,1,2]=>[2,3,1,2]
[8,6,4,7,5,3,1,2]=>[1,1,2,1,1,2]
[1,6,3,7,5,8,4,2]=>[2,2,2,1,1]
[1,3,7,4,5,8,6,2]=>[3,3,1,1]
[7,2,6,3,4,1,5,8]=>[1,2,2,3]
[8,3,7,4,6,5,1,2]=>[1,2,2,1,2]
[6,8,4,7,5,3,1,2]=>[2,2,1,1,2]
[4,8,7,5,6,3,1,2]=>[2,1,2,1,2]
[3,8,7,6,4,5,1,2]=>[2,1,1,2,2]
[1,6,5,2,8,3,7,4]=>[2,1,2,2,1]
[8,6,5,2,1,4,3,7]=>[1,1,1,1,2,2]
[2,7,6,3,1,4,5,8]=>[2,1,1,4]
[6,8,5,3,2,1,4,7]=>[2,1,1,1,3]
[2,7,6,4,5,1,3,8]=>[2,1,2,3]
[5,7,2,6,4,1,3,8]=>[2,2,1,3]
[6,1,3,7,5,8,4,2]=>[1,3,2,1,1]
[4,1,7,3,6,8,5,2]=>[1,2,3,1,1]
[8,1,6,4,3,7,5,2]=>[1,2,1,2,1,1]
[2,1,7,4,8,6,3,5]=>[1,2,2,1,2]
[1,8,6,3,7,5,4,2]=>[2,1,2,1,1,1]
[1,8,2,7,3,6,5,4]=>[2,2,2,1,1]
[2,1,3,8,4,7,5,6]=>[1,3,2,2]
[8,1,2,7,4,3,6,5]=>[1,3,1,2,1]
[5,3,1,6,8,4,7,2]=>[1,1,3,2,1]
[6,2,8,7,1,4,3,5]=>[1,2,1,2,2]
[8,7,2,1,5,4,3,6]=>[1,1,1,2,1,2]
[8,2,3,1,4,6,5,7]=>[1,2,3,2]
[2,4,8,3,1,5,6,7]=>[3,1,4]
[3,4,2,7,1,5,6,8]=>[2,2,4]
[4,7,3,8,2,1,5,6]=>[2,2,1,3]
[5,2,7,3,1,4,6,8]=>[1,2,1,4]
[8,3,7,2,1,5,4,6]=>[1,2,1,2,2]
[1,3,7,2,8,4,6,5]=>[3,2,2,1]
[1,4,2,5,8,6,7,3]=>[2,3,2,1]
[6,5,3,8,2,1,4,7]=>[1,1,2,1,3]
[2,6,4,5,7,1,3,8]=>[2,3,3]
[5,4,6,2,7,1,3,8]=>[1,2,2,3]
[7,6,3,1,8,4,5,2]=>[1,1,1,2,2,1]
[1,7,5,8,6,4,3,2]=>[2,2,1,1,1,1]
[6,5,1,2,8,3,7,4]=>[1,1,3,2,1]
[8,6,1,4,3,7,5,2]=>[1,1,2,2,1,1]
[6,8,4,1,3,7,5,2]=>[2,1,3,1,1]
[6,5,7,1,3,8,4,2]=>[1,2,3,1,1]
[5,8,3,1,7,4,6,2]=>[2,1,2,2,1]
[8,3,1,7,5,4,6,2]=>[1,1,2,1,2,1]
[1,3,8,7,4,6,5,2]=>[3,1,2,1,1]
[1,2,8,7,6,3,5,4]=>[3,1,1,2,1]
[2,3,1,8,7,4,5,6]=>[2,2,1,3]
[2,4,1,8,5,7,3,6]=>[2,2,2,2]
[5,8,2,1,7,6,3,4]=>[2,1,2,1,2]
[6,2,7,1,8,5,3,4]=>[1,2,2,1,2]
[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]
[7,1,8,3,6,5,4,2]=>[1,2,2,1,1,1]
[4,1,8,7,5,6,3,2]=>[1,2,1,2,1,1]
[2,1,7,8,4,6,3,5]=>[1,3,2,2]
[3,5,8,7,2,6,4,1]=>[3,1,2,1,1]
[5,8,2,7,1,6,4,3]=>[2,2,2,1,1]
[2,1,6,4,5,8,3,7]=>[1,2,3,2]
[8,6,3,7,5,2,1,4]=>[1,1,2,1,1,2]
[4,6,3,8,5,2,1,7]=>[2,2,1,1,2]
[4,6,3,7,5,2,8,1]=>[2,2,1,2,1]
[3,5,7,8,2,6,1,4]=>[4,2,2]
[5,6,2,4,1,3,8,7]=>[2,2,3,1]
[7,6,3,8,5,2,4,1]=>[1,1,2,1,2,1]
[8,2,3,4,6,1,5,7]=>[1,4,3]
[7,2,3,4,6,1,8,5]=>[1,4,2,1]
[8,2,3,4,7,5,1,6]=>[1,4,1,2]
[7,2,3,4,6,8,5,1]=>[1,5,1,1]
[4,2,3,6,1,5,8,7]=>[1,3,3,1]
[4,8,3,7,5,1,6,2]=>[2,2,1,2,1]
[5,2,3,4,7,8,6,1]=>[1,5,1,1]
[8,2,3,4,7,1,6,5]=>[1,4,2,1]
[5,2,3,4,8,7,1,6]=>[1,4,1,2]
[5,2,3,4,6,8,1,7]=>[1,5,2]
[4,2,8,5,7,6,1,3]=>[1,2,2,1,2]
[3,7,6,4,5,1,8,2]=>[2,1,2,2,1]
[3,8,6,4,5,1,2,7]=>[2,1,2,3]
[4,7,3,6,5,8,2,1]=>[2,2,2,1,1]
[4,8,3,7,5,2,1,6]=>[2,2,1,1,2]
[8,7,3,6,5,1,2,4]=>[1,1,2,1,3]
[8,2,7,5,1,6,3,4]=>[1,2,1,2,2]
[4,2,7,5,8,6,3,1]=>[1,2,2,1,1,1]
[5,8,1,7,3,6,4,2]=>[2,2,2,1,1]
[5,2,7,8,4,6,3,1]=>[1,3,2,1,1]
[5,2,8,3,7,6,1,4]=>[1,2,2,1,2]
[8,2,7,3,1,6,4,5]=>[1,2,1,2,2]
[6,8,3,2,5,7,1,4]=>[2,1,3,2]
[6,2,3,4,7,5,8,1]=>[1,4,2,1]
[6,2,3,4,8,5,1,7]=>[1,4,1,2]
[8,2,3,4,1,7,5,6]=>[1,3,2,2]
[6,2,3,4,1,8,5,7]=>[1,3,2,2]
[6,2,3,4,8,7,5,1]=>[1,4,1,1,1]
[6,8,3,1,5,7,4,2]=>[2,1,3,1,1]
[7,2,3,4,1,8,6,5]=>[1,3,2,1,1]
[7,2,3,4,1,5,8,6]=>[1,3,3,1]
[1,2,3,4,8,7,5,6]=>[5,1,2]
[1,2,8,5,3,4,6,7]=>[3,1,4]
[1,8,4,2,3,5,6,7]=>[2,1,5]
[8,6,7,4,1,5,3,2]=>[1,2,1,2,1,1]
[4,8,6,7,5,1,3,2]=>[2,2,1,2,1]
[7,1,8,4,6,5,2,3]=>[1,2,2,1,2]
[8,7,1,5,4,6,2,3]=>[1,1,2,2,2]
[8,5,7,1,4,6,3,2]=>[1,2,3,1,1]
[6,4,8,5,1,7,3,2]=>[1,2,1,2,1,1]
[4,8,5,7,1,6,3,2]=>[2,2,2,1,1]
[8,4,7,1,5,6,3,2]=>[1,2,3,1,1]
[8,7,1,4,5,6,3,2]=>[1,1,4,1,1]
[8,7,4,5,6,1,3,2]=>[1,1,3,2,1]
[8,7,5,1,4,6,2,3]=>[1,1,1,3,2]
[8,7,2,5,1,4,6,3]=>[1,1,2,3,1]
[4,8,7,2,5,1,6,3]=>[2,1,2,2,1]
[1,6,4,8,5,2,7,3]=>[2,2,1,2,1]
[8,7,1,4,2,5,6,3]=>[1,1,2,3,1]
[8,7,5,1,2,4,6,3]=>[1,1,1,4,1]
[7,1,8,5,6,2,3,4]=>[1,2,2,3]
[3,8,7,1,2,5,6,4]=>[2,1,4,1]
[3,5,8,7,1,2,6,4]=>[3,1,3,1]
[2,3,8,5,7,1,6,4]=>[3,2,2,1]
[3,8,7,1,5,6,2,4]=>[2,1,3,2]
[3,5,8,7,1,6,2,4]=>[3,1,2,2]
[2,3,8,6,7,5,1,4]=>[3,2,1,2]
[3,2,8,6,7,5,1,4]=>[1,2,2,1,2]
[4,1,8,6,2,7,5,3]=>[1,2,1,2,1,1]
[8,7,4,1,2,6,5,3]=>[1,1,1,3,1,1]
[1,3,8,6,7,5,2,4]=>[3,2,1,2]
[5,7,1,8,2,6,3,4]=>[2,2,2,2]
[2,8,7,1,5,6,3,4]=>[2,1,3,2]
[8,7,1,5,2,4,6,3]=>[1,1,2,3,1]
[7,1,8,2,4,6,5,3]=>[1,2,3,1,1]
[1,6,2,8,4,7,5,3]=>[2,2,2,1,1]
[1,3,8,5,7,2,6,4]=>[3,2,2,1]
[1,8,3,7,2,5,6,4]=>[2,2,3,1]
[2,8,7,1,3,5,6,4]=>[2,1,4,1]
[5,7,1,8,2,3,6,4]=>[2,2,3,1]
[7,1,8,2,3,5,6,4]=>[1,2,4,1]
[8,6,3,7,4,1,5,2]=>[1,1,2,1,2,1]
[4,2,8,6,7,5,1,3]=>[1,2,2,1,2]
[8,4,2,7,5,6,1,3]=>[1,1,2,2,2]
[4,8,3,6,1,7,5,2]=>[2,2,2,1,1]
[8,3,4,7,5,1,6,2]=>[1,3,1,2,1]
[8,3,7,4,5,1,6,2]=>[1,2,2,2,1]
[8,7,4,2,5,6,1,3]=>[1,1,1,3,2]
[8,7,5,1,6,2,3,4]=>[1,1,1,2,3]
[8,7,2,4,1,5,6,3]=>[1,1,2,3,1]
[4,8,6,1,7,2,5,3]=>[2,1,2,2,1]
[4,7,1,8,2,6,5,3]=>[2,2,2,1,1]
[4,2,8,6,7,1,5,3]=>[1,2,2,2,1]
[8,7,4,1,2,5,6,3]=>[1,1,1,4,1]
[8,2,7,1,6,3,4,5]=>[1,2,2,3]
[8,2,7,1,3,6,4,5]=>[1,2,3,2]
[2,8,3,6,7,1,5,4]=>[2,3,2,1]
[8,7,2,1,3,5,6,4]=>[1,1,1,4,1]
[1,8,7,2,3,6,4,5]=>[2,1,3,2]
[1,8,7,2,6,3,4,5]=>[2,1,2,3]
[8,2,7,3,6,1,4,5]=>[1,2,2,3]
[1,8,7,3,6,2,4,5]=>[2,1,2,3]
[1,8,2,7,6,3,4,5]=>[2,2,1,3]
[8,2,7,4,1,5,6,3]=>[1,2,1,3,1]
[8,2,1,7,5,6,3,4]=>[1,1,2,2,2]
[8,7,3,1,5,6,2,4]=>[1,1,1,3,2]
[2,8,7,3,5,6,1,4]=>[2,1,3,2]
[8,3,1,6,7,5,2,4]=>[1,1,3,1,2]
[8,5,2,1,6,7,4,3]=>[1,1,1,3,1,1]
[1,5,2,8,6,7,4,3]=>[2,2,2,1,1]
[1,2,8,6,7,5,3,4]=>[3,2,1,2]
[1,8,3,6,7,5,2,4]=>[2,3,1,2]
[8,2,3,6,7,5,1,4]=>[1,4,1,2]
[8,3,7,2,5,6,1,4]=>[1,2,3,2]
[8,1,3,7,5,6,2,4]=>[1,3,2,2]
[8,4,1,2,7,5,6,3]=>[1,1,3,2,1]
[8,1,4,2,6,7,5,3]=>[1,2,3,1,1]
[1,2,8,6,7,3,5,4]=>[3,2,2,1]
[8,1,2,7,3,6,4,5]=>[1,3,2,2]
[8,1,7,3,6,2,4,5]=>[1,2,2,3]
[8,1,7,2,6,3,4,5]=>[1,2,2,3]
[8,1,7,2,3,6,4,5]=>[1,2,3,2]
[8,1,3,7,2,5,6,4]=>[1,3,3,1]
[1,8,3,6,7,2,5,4]=>[2,3,2,1]
[1,7,8,2,3,6,5,4]=>[3,3,1,1]
[8,3,7,1,2,5,6,4]=>[1,2,4,1]
[8,7,1,2,3,6,4,5]=>[1,1,4,2]
[2,8,5,7,4,6,3,1]=>[2,2,2,1,1]
[3,1,8,5,7,4,2,6]=>[1,2,2,1,2]
[8,3,5,7,4,2,6,1]=>[1,3,1,2,1]
[8,3,6,2,4,5,7,1]=>[1,2,4,1]
[2,8,6,4,3,5,7,1]=>[2,1,1,3,1]
[2,6,8,3,5,4,7,1]=>[3,2,2,1]
[2,7,5,8,4,6,3,1]=>[2,2,2,1,1]
[8,4,2,7,6,1,3,5]=>[1,1,2,1,3]
[4,8,1,7,6,3,2,5]=>[2,2,1,1,2]
[4,1,7,6,2,3,5,8]=>[1,2,1,4]
[3,7,1,8,6,2,5,4]=>[2,2,1,2,1]
[3,1,7,6,4,5,2,8]=>[1,2,1,2,2]
[3,1,7,5,8,4,2,6]=>[1,2,2,1,2]
[3,1,6,8,7,5,2,4]=>[1,3,1,1,2]
[6,3,8,7,5,2,4,1]=>[1,2,1,1,2,1]
[7,3,5,8,4,2,6,1]=>[1,3,1,2,1]
[7,3,6,4,2,8,5,1]=>[1,2,1,2,1,1]
[7,8,3,6,2,5,4,1]=>[2,2,2,1,1]
[7,4,8,2,1,6,3,5]=>[1,2,1,2,2]
[8,7,4,6,3,2,5,1]=>[1,1,2,1,2,1]
[7,8,5,2,1,4,3,6]=>[2,1,1,2,2]
[7,5,2,3,1,4,8,6]=>[1,1,2,3,1]
[7,4,6,2,3,8,1,5]=>[1,2,3,2]
[6,4,2,5,8,3,7,1]=>[1,1,3,2,1]
[4,6,5,8,1,3,2,7]=>[2,2,2,2]
[4,7,1,5,3,8,2,6]=>[2,2,2,2]
[4,7,8,1,3,6,2,5]=>[3,3,2]
[5,7,1,3,4,6,2,8]=>[2,4,2]
[5,7,1,4,2,3,6,8]=>[2,2,4]
[5,8,1,3,2,4,6,7]=>[2,2,4]
[4,8,6,1,3,2,7,5]=>[2,1,2,2,1]
[8,4,6,2,1,3,7,5]=>[1,2,1,3,1]
[5,4,8,7,2,3,6,1]=>[1,2,1,3,1]
[5,4,8,7,3,1,2,6]=>[1,2,1,1,3]
[6,8,3,7,2,5,4,1]=>[2,2,2,1,1]
[5,4,6,8,2,3,7,1]=>[1,3,3,1]
[5,7,4,2,8,3,6,1]=>[2,1,2,2,1]
[6,4,7,2,1,8,3,5]=>[1,2,1,2,2]
[6,5,3,4,1,2,8,7]=>[1,1,2,3,1]
[6,8,5,4,1,3,2,7]=>[2,1,1,2,2]
[6,4,3,7,1,5,2,8]=>[1,1,2,2,2]
[7,4,2,6,1,5,3,8]=>[1,1,2,2,2]
[7,4,2,5,6,1,3,8]=>[1,1,3,3]
[6,4,2,8,1,5,7,3]=>[1,1,2,3,1]
[6,3,7,8,2,5,1,4]=>[1,3,2,2]
[7,3,5,6,4,2,1,8]=>[1,3,1,1,2]
[7,4,3,1,5,6,2,8]=>[1,1,1,3,2]
[7,4,5,2,6,1,3,8]=>[1,2,2,3]
[5,3,7,2,8,6,4,1]=>[1,2,2,1,1,1]
[5,3,8,2,6,7,4,1]=>[1,2,3,1,1]
[6,3,8,2,5,4,7,1]=>[1,2,2,2,1]
[6,4,8,2,1,5,7,3]=>[1,2,1,3,1]
[6,4,3,1,8,2,7,5]=>[1,1,1,2,2,1]
[5,3,7,8,2,6,4,1]=>[1,3,2,1,1]
[4,7,8,5,6,3,2,1]=>[3,2,1,1,1]
[5,3,7,6,8,2,4,1]=>[1,2,2,2,1]
[5,7,8,4,6,2,1,3]=>[3,2,1,2]
[5,8,4,3,6,7,1,2]=>[2,1,3,2]
[5,8,6,4,7,2,1,3]=>[2,1,2,1,2]
[5,3,8,6,2,7,4,1]=>[1,2,1,2,1,1]
[4,7,5,8,6,3,2,1]=>[2,2,1,1,1,1]
[4,8,6,7,5,3,2,1]=>[2,2,1,1,1,1]
[6,3,8,7,2,4,1,5]=>[1,2,1,2,2]
[5,3,8,7,2,6,4,1]=>[1,2,1,2,1,1]
[5,3,8,6,7,2,4,1]=>[1,2,2,2,1]
[5,3,7,8,6,2,4,1]=>[1,3,1,2,1]
[5,7,6,4,8,2,1,3]=>[2,1,2,1,2]
[5,8,4,6,7,2,1,3]=>[2,3,1,2]
[6,4,2,8,1,7,3,5]=>[1,1,2,2,2]
[6,5,2,4,3,7,8,1]=>[1,1,2,3,1]
[5,4,6,2,8,7,1,3]=>[1,2,2,1,2]
[5,6,3,8,7,2,4,1]=>[2,2,1,2,1]
[6,7,4,3,1,8,2,5]=>[2,1,1,2,2]
[5,7,4,3,6,8,1,2]=>[2,1,3,2]
[5,7,3,8,6,2,4,1]=>[2,2,1,2,1]
[4,5,8,6,7,3,2,1]=>[3,2,1,1,1]
[4,6,8,5,7,3,2,1]=>[3,2,1,1,1]
[5,6,8,3,7,2,4,1]=>[3,2,2,1]
[5,4,6,8,2,7,1,3]=>[1,3,2,2]
[3,6,7,8,2,5,1,4]=>[4,2,2]
[5,7,8,2,6,4,1,3]=>[3,2,1,2]
[1,7,4,8,6,2,3,5]=>[2,2,1,3]
[3,6,2,5,7,8,1,4]=>[2,4,2]
[5,2,7,4,6,8,1,3]=>[1,2,3,2]
[5,3,6,7,1,8,4,2]=>[1,3,2,1,1]
[4,2,5,6,7,1,8,3]=>[1,4,2,1]
[7,2,6,3,5,1,8,4]=>[1,2,2,2,1]
[8,1,3,6,7,2,4,5]=>[1,4,3]
[8,1,4,2,5,6,3,7]=>[1,2,3,2]
[8,1,4,2,7,5,3,6]=>[1,2,2,1,2]
[6,1,3,8,2,7,4,5]=>[1,3,2,2]
[3,6,2,4,1,7,8,5]=>[2,2,3,1]
[6,2,7,3,1,5,8,4]=>[1,2,1,3,1]
[6,3,4,1,8,5,7,2]=>[1,2,2,2,1]
[7,3,4,1,5,8,6,2]=>[1,2,3,1,1]
[1,7,5,2,8,6,3,4]=>[2,1,2,1,2]
[3,7,4,1,8,5,6,2]=>[2,1,2,2,1]
[5,6,3,1,7,8,4,2]=>[2,1,3,1,1]
[3,6,4,8,1,5,7,2]=>[2,2,3,1]
[1,5,8,4,2,6,3,7]=>[3,1,2,2]
[3,5,7,4,1,6,8,2]=>[3,1,3,1]
[3,5,7,1,2,6,4,8]=>[3,3,2]
[4,5,1,8,2,3,7,6]=>[2,2,3,1]
[4,7,1,8,2,6,3,5]=>[2,2,2,2]
[6,3,1,8,5,2,4,7]=>[1,1,2,1,3]
[3,5,2,1,8,4,6,7]=>[2,1,2,3]
[7,5,1,2,3,8,6,4]=>[1,1,4,1,1]
[6,4,1,2,7,3,8,5]=>[1,1,3,2,1]
[5,2,6,1,3,4,8,7]=>[1,2,4,1]
[7,8,4,5,1,3,2,6]=>[2,2,2,2]
[6,7,1,3,2,5,4,8]=>[2,2,2,2]
[6,7,1,4,3,5,2,8]=>[2,2,2,2]
[7,8,2,3,1,5,4,6]=>[2,2,2,2]
[7,8,2,4,3,5,1,6]=>[2,2,2,2]
[7,8,2,4,1,5,3,6]=>[2,2,2,2]
[1,4,2,6,5,7,3,8]=>[2,2,2,2]
[5,6,1,4,2,7,3,8]=>[2,2,2,2]
[6,7,2,4,1,5,3,8]=>[2,2,2,2]
[6,7,2,4,3,5,1,8]=>[2,2,2,2]
[6,7,2,3,1,5,4,8]=>[2,2,2,2]
[6,7,3,5,4,8,1,2]=>[2,2,2,2]
[2,4,1,6,5,7,3,8]=>[2,2,2,2]
[1,5,2,6,4,7,3,8]=>[2,2,2,2]
[2,5,1,6,4,7,3,8]=>[2,2,2,2]
[3,6,5,7,4,8,1,2]=>[2,2,2,2]
[5,6,2,4,3,7,1,8]=>[2,2,2,2]
[4,5,2,6,1,7,3,8]=>[2,2,2,2]
[4,5,1,6,3,7,2,8]=>[2,2,2,2]
[4,5,3,6,1,7,2,8]=>[2,2,2,2]
[5,6,3,4,1,7,2,8]=>[2,2,2,2]
[5,6,1,4,3,7,2,8]=>[2,2,2,2]
[5,6,1,3,2,7,4,8]=>[2,2,2,2]
[5,6,4,7,1,3,2,8]=>[2,2,2,2]
[6,7,4,5,1,3,2,8]=>[2,2,2,2]
[6,7,5,8,1,3,2,4]=>[2,2,2,2]
[4,5,1,3,2,7,6,8]=>[2,2,2,2]
[4,6,5,7,1,3,2,8]=>[2,2,2,2]
[4,6,1,3,2,7,5,8]=>[2,2,2,2]
[1,4,3,6,2,7,5,8]=>[2,2,2,2]
[3,4,1,6,5,7,2,8]=>[2,2,2,2]
[4,5,2,3,1,7,6,8]=>[2,2,2,2]
[4,5,3,7,6,8,1,2]=>[2,2,2,2]
[4,6,5,7,3,8,1,2]=>[2,2,2,2]
[4,6,5,7,2,3,1,8]=>[2,2,2,2]
[3,5,4,6,1,7,2,8]=>[2,2,2,2]
[3,5,1,6,4,7,2,8]=>[2,2,2,2]
[1,5,3,6,4,7,2,8]=>[2,2,2,2]
[1,5,3,6,2,7,4,8]=>[2,2,2,2]
[3,5,2,6,1,7,4,8]=>[2,2,2,2]
[3,5,2,6,4,7,1,8]=>[2,2,2,2]
[3,4,2,6,1,7,5,8]=>[2,2,2,2]
[4,6,2,3,1,7,5,8]=>[2,2,2,2]
[2,4,3,6,1,7,5,8]=>[2,2,2,2]
[2,5,3,6,4,7,1,8]=>[2,2,2,2]
[2,5,3,6,1,7,4,8]=>[2,2,2,2]
[4,6,2,7,3,5,8,1]=>[2,2,3,1]
[3,6,2,7,5,4,8,1]=>[2,2,1,2,1]
[4,6,1,7,3,8,2,5]=>[2,2,2,2]
[5,2,6,7,4,3,8,1]=>[1,3,1,2,1]
[3,5,2,7,6,4,8,1]=>[2,2,1,2,1]
[1,5,7,4,3,8,2,6]=>[3,1,2,2]
[2,5,7,3,1,8,6,4]=>[3,1,2,1,1]
[1,5,7,2,8,3,6,4]=>[3,2,2,1]
[2,5,7,3,1,8,4,6]=>[3,1,2,2]
[1,5,7,3,4,8,2,6]=>[3,3,2]
[5,2,6,7,1,8,4,3]=>[1,3,2,1,1]
[1,3,7,2,8,5,6,4]=>[3,2,2,1]
[2,3,1,5,8,4,7,6]=>[2,3,2,1]
[2,1,5,6,8,4,3,7]=>[1,4,1,2]
[2,3,1,5,8,6,4,7]=>[2,3,1,2]
[2,4,7,3,1,8,5,6]=>[3,1,2,2]
[1,3,7,2,8,5,4,6]=>[3,2,1,2]
[2,3,1,6,8,5,4,7]=>[2,3,1,2]
[4,6,2,7,1,8,3,5]=>[2,2,2,2]
[1,5,4,3,6,8,2,7]=>[2,1,3,2]
[1,6,4,5,7,8,3,2]=>[2,4,1,1]
[2,5,1,7,8,6,3,4]=>[2,3,1,2]
[1,3,6,2,8,7,4,5]=>[3,2,1,2]
[2,1,5,6,8,4,7,3]=>[1,4,2,1]
[2,4,1,7,8,5,6,3]=>[2,3,2,1]
[1,3,6,2,8,4,7,5]=>[3,2,2,1]
[2,1,5,6,8,7,3,4]=>[1,4,1,2]
[3,6,5,2,7,8,4,1]=>[2,1,3,1,1]
[6,2,4,7,5,8,3,1]=>[1,3,2,1,1]
[1,5,7,8,4,2,6,3]=>[4,1,2,1]
[3,7,4,1,8,6,2,5]=>[2,1,2,1,2]
[3,4,6,8,5,7,2,1]=>[4,2,1,1]
[4,2,5,7,3,1,8,6]=>[1,3,1,2,1]
[4,5,6,2,8,7,3,1]=>[3,2,1,1,1]
[2,5,6,8,1,7,4,3]=>[4,2,1,1]
[4,5,6,1,8,7,3,2]=>[3,2,1,1,1]
[4,5,6,3,1,8,7,2]=>[3,1,2,1,1]
[4,3,6,2,1,7,5,8]=>[1,2,1,2,2]
[4,6,3,2,1,7,5,8]=>[2,1,1,2,2]
[4,6,3,1,7,5,2,8]=>[2,1,2,1,2]
[4,5,3,7,6,1,8,2]=>[2,2,1,2,1]
[4,5,1,7,3,8,6,2]=>[2,2,2,1,1]
[2,5,7,1,4,3,8,6]=>[3,2,2,1]
[4,3,5,7,6,1,8,2]=>[1,3,1,2,1]
[4,3,6,1,7,5,2,8]=>[1,2,2,1,2]
[4,3,2,6,1,7,5,8]=>[1,1,2,2,2]
[5,3,2,1,6,4,7,8]=>[1,1,1,2,3]
[5,3,1,6,2,7,4,8]=>[1,1,2,2,2]
[5,1,6,3,2,7,4,8]=>[1,2,1,2,2]
[2,6,1,4,7,5,3,8]=>[2,3,1,2]
[3,6,1,7,4,2,5,8]=>[2,2,1,3]
[4,6,1,7,5,3,2,8]=>[2,2,1,1,2]
[5,1,6,3,7,4,2,8]=>[1,2,2,1,2]
[5,3,6,4,2,1,7,8]=>[1,2,1,1,3]
[5,3,2,6,4,1,7,8]=>[1,1,2,1,3]
[5,2,1,6,3,7,4,8]=>[1,1,2,2,2]
[5,2,6,3,1,7,4,8]=>[1,2,1,2,2]
[4,2,6,3,1,7,8,5]=>[1,2,1,3,1]
[3,6,2,1,7,4,5,8]=>[2,1,2,3]
[3,6,2,7,4,1,5,8]=>[2,2,1,3]
[3,5,7,2,8,6,4,1]=>[3,2,1,1,1]
[2,4,7,1,3,6,5,8]=>[3,3,2]
[2,6,1,3,7,5,4,8]=>[2,3,1,2]
[3,6,1,7,5,2,4,8]=>[2,2,1,3]
[5,1,6,2,7,4,3,8]=>[1,2,2,1,2]
[5,2,6,4,3,1,7,8]=>[1,2,1,1,3]
[5,2,1,6,4,3,7,8]=>[1,1,2,1,3]
[5,4,2,1,6,3,7,8]=>[1,1,1,2,3]
[5,4,2,6,3,1,7,8]=>[1,1,2,1,3]
[5,4,1,6,2,7,3,8]=>[1,1,2,2,2]
[5,1,6,4,2,7,3,8]=>[1,2,1,2,2]
[3,6,1,7,5,4,8,2]=>[2,2,1,2,1]
[2,6,1,5,4,3,7,8]=>[2,2,1,3]
[3,1,6,2,5,4,7,8]=>[1,2,2,3]
[5,1,6,4,3,2,7,8]=>[1,2,1,1,3]
[5,4,1,6,3,2,7,8]=>[1,1,2,1,3]
[5,4,3,1,6,2,7,8]=>[1,1,1,2,3]
[7,3,1,6,5,4,8,2]=>[1,1,2,1,2,1]
[7,2,8,1,5,4,3,6]=>[1,2,2,1,2]
[4,2,7,6,5,8,1,3]=>[1,2,1,2,2]
[3,8,2,6,5,4,1,7]=>[2,2,1,1,2]
[7,3,2,1,5,4,6,8]=>[1,1,1,2,3]
[7,2,8,6,1,4,3,5]=>[1,2,1,2,2]
[5,2,7,6,8,4,1,3]=>[1,2,2,1,2]
[3,8,7,2,5,4,1,6]=>[2,1,2,1,2]
[7,5,1,6,8,4,3,2]=>[1,1,3,1,1,1]
[7,4,2,1,5,6,3,8]=>[1,1,1,3,2]
[7,2,8,6,5,1,3,4]=>[1,2,1,1,3]
[5,3,2,6,7,4,1,8]=>[1,1,3,1,2]
[4,3,7,2,5,6,1,8]=>[1,2,3,2]
[6,7,1,4,3,2,5,8]=>[2,2,1,3]
[3,4,2,6,7,1,5,8]=>[2,3,3]
[3,7,1,6,5,2,4,8]=>[2,2,1,3]
[3,5,6,2,4,7,1,8]=>[3,3,2]
[3,5,8,7,2,4,6,1]=>[3,1,3,1]
[1,7,8,2,5,4,3,6]=>[3,2,1,2]
[8,7,2,5,4,3,6,1]=>[1,1,2,1,2,1]
[2,5,6,4,7,1,3,8]=>[3,2,3]
[4,7,1,6,3,5,2,8]=>[2,2,2,2]
[4,5,3,8,7,2,6,1]=>[2,2,1,2,1]
[1,4,5,3,7,8,2,6]=>[3,3,2]
[1,4,8,2,7,6,3,5]=>[3,2,1,2]
[4,7,3,5,1,8,6,2]=>[2,2,2,1,1]
[8,7,3,6,1,5,4,2]=>[1,1,2,2,1,1]
[2,5,8,7,4,6,1,3]=>[3,1,2,2]
[5,4,2,1,7,8,3,6]=>[1,1,1,3,2]
[4,7,8,3,5,2,1,6]=>[3,2,1,2]
[4,7,6,2,1,8,3,5]=>[2,1,1,2,2]
[1,4,6,7,3,5,8,2]=>[4,3,1]
[8,3,6,2,1,7,5,4]=>[1,2,1,2,1,1]
[8,3,7,6,4,2,1,5]=>[1,2,1,1,1,2]
[2,3,1,8,4,7,6,5]=>[2,2,2,1,1]
[2,7,4,8,6,5,1,3]=>[2,2,1,1,2]
[8,6,5,1,4,7,3,2]=>[1,1,1,3,1,1]
[8,5,4,1,7,3,6,2]=>[1,1,1,2,2,1]
[6,3,7,2,8,5,4,1]=>[1,2,2,1,1,1]
[1,6,3,8,2,7,5,4]=>[2,2,2,1,1]
[1,7,5,3,8,2,6,4]=>[2,1,2,2,1]
[6,2,7,4,1,8,5,3]=>[1,2,1,2,1,1]
[8,6,3,2,7,5,1,4]=>[1,1,1,2,1,2]
[2,7,5,1,3,8,6,4]=>[2,1,3,1,1]
[1,7,6,4,3,8,2,5]=>[2,1,1,2,2]
[3,7,2,4,8,6,5,1]=>[2,3,1,1,1]
[3,4,2,8,7,6,1,5]=>[2,2,1,1,2]
[5,1,4,3,2,7,8,6]=>[1,2,1,3,1]
[3,7,8,5,2,4,1,6]=>[3,1,2,2]
[3,7,6,2,4,1,8,5]=>[2,1,2,2,1]
[1,6,8,2,5,7,4,3]=>[3,3,1,1]
[6,7,2,5,8,4,3,1]=>[2,3,1,1,1]
[5,2,7,8,4,3,1,6]=>[1,3,1,1,2]
[5,3,1,7,8,4,2,6]=>[1,1,3,1,2]
[2,7,6,4,1,3,8,5]=>[2,1,1,3,1]
[4,1,7,6,3,2,8,5]=>[1,2,1,1,2,1]
[8,4,2,7,6,3,1,5]=>[1,1,2,1,1,2]
[6,3,1,7,5,2,8,4]=>[1,1,2,1,2,1]
[6,2,7,5,3,1,8,4]=>[1,2,1,1,2,1]
[1,5,8,2,7,4,6,3]=>[3,2,2,1]
[5,7,2,8,4,6,3,1]=>[2,2,2,1,1]
[5,7,3,1,8,4,6,2]=>[2,1,2,2,1]
[8,4,7,3,1,6,5,2]=>[1,2,1,2,1,1]
[2,6,8,5,7,4,1,3]=>[3,2,1,2]
[6,5,2,1,7,4,8,3]=>[1,1,1,2,2,1]
[5,7,4,6,2,1,8,3]=>[2,2,1,2,1]
[5,6,4,8,3,7,2,1]=>[2,2,2,1,1]
[6,7,1,8,3,4,2,5]=>[2,2,2,2]
[7,8,3,5,1,4,2,6]=>[2,2,2,2]
[5,6,2,7,1,8,3,4]=>[2,2,2,2]
[6,7,2,4,3,8,1,5]=>[2,2,2,2]
[2,4,3,8,6,7,1,5]=>[2,2,2,2]
[1,8,2,7,4,5,3,6]=>[2,2,2,2]
[2,5,4,8,3,6,1,7]=>[2,2,2,2]
[2,3,1,8,5,6,4,7]=>[2,2,2,2]
[3,8,5,6,4,7,1,2]=>[2,2,2,2]
[5,7,3,6,4,8,1,2]=>[2,2,2,2]
[5,7,2,3,1,6,4,8]=>[2,2,2,2]
[5,7,2,4,3,6,1,8]=>[2,2,2,2]
[4,6,2,7,1,5,3,8]=>[2,2,2,2]
[4,7,1,6,2,5,3,8]=>[2,2,2,2]
[4,7,1,5,3,6,2,8]=>[2,2,2,2]
[4,6,3,5,1,7,2,8]=>[2,2,2,2]
[6,7,3,5,1,4,2,8]=>[2,2,2,2]
[5,6,3,7,1,4,2,8]=>[2,2,2,2]
[5,7,1,6,3,4,2,8]=>[2,2,2,2]
[1,8,5,6,3,4,2,7]=>[2,2,2,2]
[1,8,5,6,4,7,2,3]=>[2,2,2,2]
[5,7,1,6,4,8,2,3]=>[2,2,2,2]
[4,6,5,8,1,7,2,3]=>[2,2,2,2]
[3,7,1,4,2,8,5,6]=>[2,2,2,2]
[3,5,1,4,2,8,6,7]=>[2,2,2,2]
[4,6,5,8,3,7,1,2]=>[2,2,2,2]
[4,6,5,8,2,3,1,7]=>[2,2,2,2]
[3,4,2,6,5,8,1,7]=>[2,2,2,2]
[3,5,4,6,2,8,1,7]=>[2,2,2,2]
[1,8,3,5,4,7,2,6]=>[2,2,2,2]
[3,4,2,7,1,8,5,6]=>[2,2,2,2]
[4,7,2,3,1,8,5,6]=>[2,2,2,2]
[2,4,3,8,1,7,5,6]=>[2,2,2,2]
[2,5,3,8,4,7,1,6]=>[2,2,2,2]
[2,6,3,8,1,7,4,5]=>[2,2,2,2]
[2,7,1,8,3,6,4,5]=>[2,2,2,2]
[1,2,8,7,4,6,3,5]=>[3,1,2,2]
[4,5,1,8,7,6,2,3]=>[2,2,1,1,2]
[1,5,2,8,7,6,3,4]=>[2,2,1,1,2]
[5,1,2,8,7,6,3,4]=>[1,3,1,1,2]
[4,1,5,8,7,6,2,3]=>[1,3,1,1,2]
[2,3,6,8,7,4,5,1]=>[4,1,2,1]
[2,3,7,8,6,4,5,1]=>[4,1,2,1]
[4,5,7,8,2,6,3,1]=>[4,2,1,1]
[4,5,6,8,2,7,3,1]=>[4,2,1,1]
[5,2,6,8,3,7,4,1]=>[1,3,2,1,1]
[3,1,6,8,7,4,5,2]=>[1,3,1,2,1]
[6,1,4,8,7,2,5,3]=>[1,3,1,2,1]
[6,1,8,4,7,3,5,2]=>[1,2,2,2,1]
[3,1,7,8,6,4,5,2]=>[1,3,1,2,1]
[4,6,7,8,2,5,3,1]=>[4,2,1,1]
[7,4,5,2,8,6,3,1]=>[1,2,2,1,1,1]
[7,5,8,4,2,6,3,1]=>[1,2,1,2,1,1]
[6,8,4,5,2,7,3,1]=>[2,2,2,1,1]
[6,8,2,5,3,7,4,1]=>[2,2,2,1,1]
[6,3,8,4,2,7,5,1]=>[1,2,1,2,1,1]
[7,2,5,3,8,6,4,1]=>[1,2,2,1,1,1]
[3,4,7,5,8,6,2,1]=>[3,2,1,1,1]
[3,6,7,4,8,5,2,1]=>[3,2,1,1,1]
[6,7,4,2,8,5,3,1]=>[2,1,2,1,1,1]
[4,7,5,2,8,6,3,1]=>[2,1,2,1,1,1]
[2,7,5,3,8,6,4,1]=>[2,1,2,1,1,1]
[5,6,2,8,3,7,4,1]=>[2,2,2,1,1]
[5,6,8,3,2,7,4,1]=>[3,1,2,1,1]
[3,6,8,4,2,7,5,1]=>[3,1,2,1,1]
[1,5,8,2,7,3,6,4]=>[3,2,2,1]
[5,8,4,7,2,3,6,1]=>[2,2,3,1]
[6,7,4,8,1,5,3,2]=>[2,2,2,1,1]
[5,7,2,8,3,6,4,1]=>[2,2,2,1,1]
[1,7,4,8,6,2,5,3]=>[2,2,1,2,1]
[6,8,5,3,7,2,4,1]=>[2,1,2,2,1]
[6,8,5,2,3,7,4,1]=>[2,1,3,1,1]
[7,5,3,8,2,6,4,1]=>[1,1,2,2,1,1]
[7,5,2,3,8,6,4,1]=>[1,1,3,1,1,1]
[3,7,4,5,8,6,2,1]=>[2,3,1,1,1]
[6,7,3,4,8,5,2,1]=>[2,3,1,1,1]
[3,6,4,7,8,5,2,1]=>[2,3,1,1,1]
[6,4,2,7,8,5,3,1]=>[1,1,3,1,1,1]
[7,4,2,5,8,6,3,1]=>[1,1,3,1,1,1]
[6,1,8,3,4,7,5,2]=>[1,2,3,1,1]
[6,8,4,2,5,7,3,1]=>[2,1,3,1,1]
[7,5,8,3,4,6,2,1]=>[1,2,3,1,1]
[7,4,5,8,1,6,3,2]=>[1,3,2,1,1]
[6,3,4,7,8,5,2,1]=>[1,4,1,1,1]
[6,1,7,3,4,5,8,2]=>[1,2,4,1]
[5,7,2,3,4,1,8,6]=>[2,3,2,1]
[2,7,1,8,4,5,6,3]=>[2,2,3,1]
[2,6,8,3,4,5,1,7]=>[3,3,2]
[6,1,2,7,4,5,8,3]=>[1,3,3,1]
[4,7,2,3,1,5,8,6]=>[2,2,3,1]
[2,7,1,3,8,5,6,4]=>[2,3,2,1]
[2,6,7,8,4,5,3,1]=>[4,2,1,1]
[2,5,8,3,4,1,6,7]=>[3,2,3]
[5,6,2,7,4,3,8,1]=>[2,2,1,2,1]
[4,6,7,3,2,5,8,1]=>[3,1,3,1]
[2,6,7,3,8,5,4,1]=>[3,2,1,1,1]
[2,6,1,8,4,5,3,7]=>[2,2,2,2]
[2,5,7,8,4,3,6,1]=>[4,1,2,1]
[3,6,8,4,5,7,1,2]=>[3,3,2]
[1,6,8,4,7,2,3,5]=>[3,2,3]
[1,4,5,7,8,2,6,3]=>[5,2,1]
[3,4,5,7,8,6,1,2]=>[5,1,2]
[3,4,5,7,6,8,1,2]=>[4,2,2]
[3,6,7,4,8,5,1,2]=>[3,2,1,2]
[3,4,5,6,8,7,1,2]=>[5,1,2]
[1,4,5,8,7,2,3,6]=>[4,1,3]
[1,2,5,8,3,6,4,7]=>[4,2,2]
[1,4,5,8,6,2,3,7]=>[4,1,3]
[7,8,1,4,6,2,3,5]=>[2,3,3]
[1,6,7,4,8,2,5,3]=>[3,2,2,1]
[1,4,5,6,8,2,7,3]=>[5,2,1]
[1,4,5,8,6,2,7,3]=>[4,1,2,1]
[1,2,5,8,3,4,7,6]=>[4,3,1]
[1,6,7,2,3,5,8,4]=>[3,4,1]
[7,8,1,2,3,5,4,6]=>[2,4,2]
[1,6,7,2,3,5,4,8]=>[3,3,2]
[1,4,5,7,6,2,3,8]=>[4,1,3]
[1,2,5,7,3,6,4,8]=>[4,2,2]
[1,2,5,7,3,6,8,4]=>[4,3,1]
[1,6,8,2,3,5,7,4]=>[3,4,1]
[1,6,8,4,5,2,3,7]=>[3,2,3]
[1,6,8,4,5,2,7,3]=>[3,2,2,1]
[1,6,8,2,3,4,7,5]=>[3,4,1]
[1,6,8,2,3,7,4,5]=>[3,3,2]
[1,4,5,7,6,2,8,3]=>[4,1,2,1]
[7,8,1,4,5,2,6,3]=>[2,3,2,1]
[7,8,1,2,3,4,6,5]=>[2,5,1]
[7,8,1,2,3,6,4,5]=>[2,4,2]
[1,6,7,2,3,8,5,4]=>[3,3,1,1]
[1,2,5,6,3,8,7,4]=>[4,2,1,1]
[4,2,1,6,5,3,8,7]=>[1,1,2,1,2,1]
[8,2,4,3,1,6,5,7]=>[1,2,1,2,2]
[6,2,4,3,1,8,7,5]=>[1,2,1,2,1,1]
[4,2,6,3,5,1,8,7]=>[1,2,2,2,1]
[4,6,2,1,5,8,7,3]=>[2,1,3,1,1]
[4,6,5,2,1,8,7,3]=>[2,1,1,2,1,1]
[2,1,6,4,3,8,7,5]=>[1,2,1,2,1,1]
[4,8,2,1,6,7,3,5]=>[2,1,3,2]
[6,8,2,1,4,3,7,5]=>[2,1,2,2,1]
[8,6,2,4,3,1,5,7]=>[1,1,2,1,3]
[6,8,2,4,3,1,7,5]=>[2,2,1,2,1]
[6,8,7,2,4,3,1,5]=>[2,1,2,1,2]
[2,1,8,4,6,5,3,7]=>[1,2,2,1,2]
[2,1,6,4,8,5,7,3]=>[1,2,2,2,1]
[4,6,5,2,8,3,7,1]=>[2,1,2,2,1]
[2,6,4,5,8,3,7,1]=>[2,3,2,1]
[6,4,2,8,3,5,7,1]=>[1,1,2,3,1]
[8,4,2,6,3,5,1,7]=>[1,1,2,2,2]
[6,2,4,8,5,3,7,1]=>[1,3,1,2,1]
[4,2,6,3,5,8,7,1]=>[1,2,3,1,1]
[4,2,6,3,8,7,5,1]=>[1,2,2,1,1,1]
[6,2,4,3,8,5,7,1]=>[1,2,2,2,1]
[8,2,4,3,6,5,1,7]=>[1,2,2,1,2]
[8,2,1,4,6,5,3,7]=>[1,1,3,1,2]
[6,2,1,4,8,5,7,3]=>[1,1,3,2,1]
[6,2,1,8,7,4,3,5]=>[1,1,2,1,1,2]
[6,2,1,8,4,3,7,5]=>[1,1,2,1,2,1]
[8,4,6,5,2,1,3,7]=>[1,2,1,1,3]
[6,4,8,5,2,1,7,3]=>[1,2,1,1,2,1]
[6,4,8,5,7,2,1,3]=>[1,2,2,1,2]
[4,6,8,7,5,2,1,3]=>[3,1,1,1,2]
[2,1,4,8,6,7,3,5]=>[1,3,2,2]
[2,6,8,7,4,5,1,3]=>[3,1,2,2]
[2,4,8,6,7,5,1,3]=>[3,2,1,2]
[4,2,8,6,5,7,1,3]=>[1,2,1,2,2]
[8,2,6,4,5,1,3,7]=>[1,2,2,3]
[8,4,6,2,1,5,3,7]=>[1,2,1,2,2]
[4,6,8,7,2,1,5,3]=>[3,1,1,2,1]
[4,6,5,8,2,1,7,3]=>[2,2,1,2,1]
[2,1,6,8,4,3,7,5]=>[1,3,1,2,1]
[6,8,7,4,2,1,3,5]=>[2,1,1,1,3]
[2,8,6,4,7,1,3,5]=>[2,1,2,3]
[4,8,6,2,1,7,3,5]=>[2,1,1,2,2]
[2,8,5,3,1,4,6,7]=>[2,1,1,4]
[2,7,4,8,3,5,1,6]=>[2,2,2,2]
[2,7,4,8,3,5,6,1]=>[2,2,3,1]
[7,2,8,4,3,5,1,6]=>[1,2,1,2,2]
[8,4,2,1,5,3,6,7]=>[1,1,1,2,3]
[8,5,1,4,2,3,6,7]=>[1,1,2,4]
[8,4,1,5,3,2,6,7]=>[1,1,2,1,3]
[6,7,3,8,4,2,5,1]=>[2,2,1,2,1]
[6,7,3,8,4,2,1,5]=>[2,2,1,1,2]
[7,1,8,4,3,5,2,6]=>[1,2,1,2,2]
[1,7,8,4,3,5,2,6]=>[3,1,2,2]
[7,1,4,8,3,5,2,6]=>[1,3,2,2]
[7,4,8,1,5,6,2,3]=>[1,2,3,2]
[7,1,8,4,3,5,6,2]=>[1,2,1,3,1]
[6,7,3,1,8,4,5,2]=>[2,1,2,2,1]
[6,7,3,8,4,5,2,1]=>[2,2,2,1,1]
[6,7,1,4,8,3,5,2]=>[2,3,2,1]
[6,7,4,1,3,8,2,5]=>[2,1,3,2]
[1,6,7,8,4,3,2,5]=>[4,1,1,2]
[7,2,1,8,4,5,3,6]=>[1,1,2,2,2]
[6,2,7,1,8,4,3,5]=>[1,2,2,1,2]
[6,2,7,8,4,3,1,5]=>[1,3,1,1,2]
[6,2,7,8,4,3,5,1]=>[1,3,1,2,1]
[2,6,7,4,8,3,5,1]=>[3,2,2,1]
[2,6,7,4,8,3,1,5]=>[3,2,1,2]
[7,8,1,3,6,2,4,5]=>[2,3,3]
[1,2,7,8,6,3,4,5]=>[4,1,3]
[2,6,7,1,8,5,3,4]=>[3,2,1,2]
[2,6,7,8,5,3,1,4]=>[4,1,1,2]
[2,6,7,8,5,3,4,1]=>[4,1,2,1]
[6,2,7,8,4,5,3,1]=>[1,3,2,1,1]
[7,2,1,8,4,5,6,3]=>[1,1,2,3,1]
[1,7,2,8,4,5,6,3]=>[2,2,3,1]
[3,7,8,1,5,6,2,4]=>[3,3,2]
[6,3,7,8,1,5,2,4]=>[1,3,2,2]
[6,7,1,2,8,5,3,4]=>[2,3,1,2]
[1,6,7,8,4,2,5,3]=>[4,1,2,1]
[3,1,2,7,6,5,8,4]=>[1,3,1,2,1]
[6,1,2,4,7,3,8,5]=>[1,4,2,1]
[1,7,5,3,6,4,8,2]=>[2,1,2,2,1]
[5,1,2,6,7,4,8,3]=>[1,4,2,1]
[4,1,5,7,3,2,6,8]=>[1,3,1,3]
[4,6,1,7,3,2,5,8]=>[2,2,1,3]
[4,6,1,8,3,2,5,7]=>[2,2,1,3]
[4,7,1,8,3,5,2,6]=>[2,2,2,2]
[4,1,7,8,6,2,3,5]=>[1,3,1,3]
[1,6,5,7,8,3,4,2]=>[2,3,2,1]
[1,6,5,8,7,3,4,2]=>[2,2,1,2,1]
[4,1,8,7,6,2,3,5]=>[1,2,1,1,3]
[4,8,1,7,3,5,2,6]=>[2,2,2,2]
[4,8,1,6,3,2,5,7]=>[2,2,1,3]
[4,7,1,6,3,2,5,8]=>[2,2,1,3]
[6,1,2,3,7,5,4,8]=>[1,4,1,2]
[6,8,1,5,3,7,2,4]=>[2,2,2,2]
[8,7,5,2,4,1,6,3]=>[1,1,1,2,2,1]
[1,5,7,3,4,8,6,2]=>[3,3,1,1]
[1,5,8,3,4,7,6,2]=>[3,3,1,1]
[7,8,5,2,4,1,6,3]=>[2,1,2,2,1]
[7,1,2,3,5,6,4,8]=>[1,5,2]
[8,1,2,3,5,6,4,7]=>[1,5,2]
[8,1,2,3,5,4,7,6]=>[1,4,2,1]
[7,1,8,4,6,3,2,5]=>[1,2,2,1,2]
[6,8,2,4,3,1,5,7]=>[2,2,1,3]
[6,7,2,4,3,1,5,8]=>[2,2,1,3]
[3,8,1,2,4,5,7,6]=>[2,5,1]
[3,7,1,8,6,4,2,5]=>[2,2,1,1,2]
[1,6,4,3,7,5,8,2]=>[2,1,2,2,1]
[3,1,2,6,7,5,8,4]=>[1,4,2,1]
[3,8,1,7,6,4,2,5]=>[2,2,1,1,2]
[7,6,2,4,3,1,5,8]=>[1,1,2,1,3]
[8,7,2,4,3,5,1,6]=>[1,1,2,2,2]
[8,1,7,4,6,3,2,5]=>[1,2,2,1,2]
[8,1,7,6,5,3,2,4]=>[1,2,1,1,1,2]
[1,5,7,3,4,6,8,2]=>[3,4,1]
[8,7,2,5,3,6,1,4]=>[1,1,2,2,2]
[7,1,2,3,5,4,8,6]=>[1,4,2,1]
[6,1,2,3,5,8,4,7]=>[1,5,2]
[6,1,2,3,5,7,4,8]=>[1,5,2]
[5,1,2,3,7,6,4,8]=>[1,4,1,2]
[5,1,2,3,8,6,4,7]=>[1,4,1,2]
[1,5,6,3,4,7,8,2]=>[3,4,1]
[8,6,5,2,4,7,1,3]=>[1,1,1,3,2]
[7,6,2,5,3,1,8,4]=>[1,1,2,1,2,1]
[7,4,5,2,3,8,6,1]=>[1,2,3,1,1]
[8,2,3,7,4,5,1,6]=>[1,3,2,2]
[8,4,7,3,2,5,1,6]=>[1,2,1,2,2]
[5,4,6,3,1,2,8,7]=>[1,2,1,3,1]
[4,6,2,3,1,5,8,7]=>[2,2,3,1]
[7,2,3,4,5,8,6,1]=>[1,5,1,1]
[8,2,3,4,5,7,1,6]=>[1,5,2]
[7,3,4,6,8,5,1,2]=>[1,4,1,2]
[4,7,3,2,8,6,1,5]=>[2,1,2,1,2]
[3,7,4,5,1,8,6,2]=>[2,2,2,1,1]
[3,8,2,6,7,4,5,1]=>[2,3,2,1]
[4,8,1,5,6,7,3,2]=>[2,4,1,1]
[5,8,2,4,6,7,1,3]=>[2,4,2]
[6,8,1,3,4,2,7,5]=>[2,3,2,1]
[5,8,2,4,3,1,7,6]=>[2,2,1,2,1]
[2,1,7,6,8,5,3,4]=>[1,2,2,1,2]
[3,7,6,1,8,5,2,4]=>[2,1,2,1,2]
[4,7,2,3,8,5,1,6]=>[2,3,1,2]
[7,1,3,6,4,8,5,2]=>[1,3,2,1,1]
[7,6,1,4,8,5,2,3]=>[1,1,3,1,2]
[6,2,3,7,8,5,4,1]=>[1,4,1,1,1]
[6,2,3,8,4,5,1,7]=>[1,3,2,2]
[7,2,3,6,8,4,1,5]=>[1,4,1,2]
[8,2,3,5,7,1,4,6]=>[1,4,3]
[6,4,8,3,5,1,7,2]=>[1,2,2,2,1]
[5,4,8,3,6,7,1,2]=>[1,2,3,2]
[3,5,1,8,4,6,7,2]=>[2,2,3,1]
[3,6,1,8,4,5,2,7]=>[2,2,2,2]
[4,6,8,3,5,2,7,1]=>[3,2,2,1]
[5,7,8,3,2,4,1,6]=>[3,1,2,2]
[4,8,2,3,5,6,1,7]=>[2,4,2]
[6,8,2,3,1,4,5,7]=>[2,2,4]
[5,2,7,4,8,3,1,6]=>[1,2,2,1,2]
[3,7,8,2,1,4,6,5]=>[3,1,3,1]
[3,7,5,2,8,4,1,6]=>[2,1,2,1,2]
[6,3,2,4,1,8,7,5]=>[1,1,2,2,1,1]
[7,2,3,4,8,5,1,6]=>[1,4,1,2]
[5,7,3,1,4,2,6,8]=>[2,1,2,3]
[3,7,4,1,8,2,5,6]=>[2,1,2,3]
[6,3,7,4,8,1,2,5]=>[1,2,2,3]
[8,3,7,4,2,6,1,5]=>[1,2,1,2,2]
[3,7,4,1,5,6,2,8]=>[2,1,3,2]
[1,8,3,2,4,5,7,6]=>[2,1,4,1]
[8,4,1,6,3,7,5,2]=>[1,1,2,2,1,1]
[8,7,4,2,1,6,3,5]=>[1,1,1,1,2,2]
[8,3,5,2,7,4,1,6]=>[1,2,2,1,2]
[1,5,3,8,7,6,4,2]=>[2,2,1,1,1,1]
[7,2,4,8,1,3,6,5]=>[1,3,3,1]
[1,2,8,7,5,6,3,4]=>[3,1,2,2]
[3,1,8,6,7,5,2,4]=>[1,2,2,1,2]
[1,4,8,6,5,7,2,3]=>[3,1,2,2]
[1,6,5,4,8,2,3,7]=>[2,1,2,3]
[5,1,6,8,3,4,2,7]=>[1,3,2,2]
[6,2,5,1,7,4,3,8]=>[1,2,2,1,2]
[5,2,1,8,7,4,3,6]=>[1,1,2,1,1,2]
[5,2,6,3,8,1,4,7]=>[1,2,2,3]
[5,2,8,3,4,6,1,7]=>[1,2,3,2]
[6,2,8,4,3,1,7,5]=>[1,2,1,1,2,1]
[7,2,8,1,3,6,5,4]=>[1,2,3,1,1]
[7,3,8,1,4,6,2,5]=>[1,2,3,2]
[1,7,8,5,4,6,3,2]=>[3,1,2,1,1]
[1,5,8,4,6,3,7,2]=>[3,2,2,1]
[5,3,8,4,1,2,7,6]=>[1,2,1,3,1]
[5,8,4,3,6,2,1,7]=>[2,1,2,1,2]
[1,8,3,6,5,2,7,4]=>[2,2,1,2,1]
[1,8,2,4,7,6,5,3]=>[2,3,1,1,1]
[3,8,1,4,6,7,5,2]=>[2,4,1,1]
[3,8,2,5,1,7,6,4]=>[2,2,2,1,1]
[4,3,8,2,5,1,6,7]=>[1,2,2,3]
[8,2,4,3,5,1,7,6]=>[1,2,2,2,1]
[8,2,1,4,6,5,7,3]=>[1,1,3,2,1]
[8,1,3,4,5,7,6,2]=>[1,5,1,1]
[6,1,5,2,4,7,8,3]=>[1,2,4,1]
[4,1,8,5,2,7,6,3]=>[1,2,1,2,1,1]
[4,8,5,1,3,6,2,7]=>[2,1,3,2]
[3,6,1,5,7,2,8,4]=>[2,3,2,1]
[6,3,1,2,8,5,7,4]=>[1,1,3,2,1]
[4,1,8,2,3,7,5,6]=>[1,2,3,2]
[5,3,8,7,2,1,4,6]=>[1,2,1,1,3]
[6,7,3,5,1,4,8,2]=>[2,2,3,1]
[6,4,7,5,8,2,3,1]=>[1,2,2,2,1]
[5,7,8,4,2,6,3,1]=>[3,1,2,1,1]
[5,7,4,1,6,8,3,2]=>[2,1,3,1,1]
[6,8,4,5,7,1,3,2]=>[2,3,2,1]
[5,8,4,6,1,7,3,2]=>[2,2,2,1,1]
[5,6,1,4,7,8,3,2]=>[2,4,1,1]
[5,6,7,2,4,8,3,1]=>[3,3,1,1]
[5,6,3,7,4,8,2,1]=>[2,2,2,1,1]
[5,3,6,7,4,8,2,1]=>[1,3,2,1,1]
[5,3,2,8,6,7,4,1]=>[1,1,2,2,1,1]
[5,4,8,2,6,7,3,1]=>[1,2,3,1,1]
[5,4,8,6,2,7,3,1]=>[1,2,1,2,1,1]
[7,4,8,5,6,2,1,3]=>[1,2,2,1,2]
[5,6,3,8,4,7,2,1]=>[2,2,2,1,1]
[4,6,3,2,8,7,5,1]=>[2,1,2,1,1,1]
[5,6,3,8,2,7,4,1]=>[2,2,2,1,1]
[3,6,5,8,7,2,4,1]=>[2,2,1,2,1]
[5,3,6,8,2,7,4,1]=>[1,3,2,1,1]
[4,3,7,2,8,6,5,1]=>[1,2,2,1,1,1]
[5,4,7,2,6,8,3,1]=>[1,2,3,1,1]
[6,7,3,8,5,2,4,1]=>[2,2,1,2,1]
[6,3,2,7,5,4,8,1]=>[1,1,2,1,2,1]
[6,4,7,2,5,3,8,1]=>[1,2,2,2,1]
[6,2,7,5,1,4,8,3]=>[1,2,1,3,1]
[2,7,8,5,3,6,1,4]=>[3,1,2,2]
[6,3,7,8,4,2,5,1]=>[1,3,1,2,1]
[3,5,7,8,4,6,2,1]=>[4,2,1,1]
[5,3,7,8,4,6,2,1]=>[1,3,2,1,1]
[5,7,8,2,4,6,3,1]=>[3,3,1,1]
[2,5,8,4,3,7,6,1]=>[3,1,2,1,1]
[2,6,8,4,7,3,5,1]=>[3,2,2,1]
[3,7,4,8,6,2,1,5]=>[2,2,1,1,2]
[3,6,4,8,7,2,5,1]=>[2,2,1,2,1]
[3,5,4,8,2,7,6,1]=>[2,2,2,1,1]
[4,3,7,5,8,6,2,1]=>[1,2,2,1,1,1]
[4,5,7,3,8,6,2,1]=>[3,2,1,1,1]
[3,5,6,8,4,7,2,1]=>[4,2,1,1]
[6,3,1,8,7,5,4,2]=>[1,1,2,1,1,1,1]
[5,4,8,1,7,6,3,2]=>[1,2,2,1,1,1]
[5,8,4,1,7,6,3,2]=>[2,1,2,1,1,1]
[7,5,4,1,8,6,3,2]=>[1,1,1,2,1,1,1]
[8,5,4,1,7,6,3,2]=>[1,1,1,2,1,1,1]
[1,8,2,5,6,3,4,7]=>[2,3,3]
[7,2,8,4,5,1,3,6]=>[1,2,2,3]
[1,3,7,5,6,2,4,8]=>[3,2,3]
[1,6,7,4,3,5,2,8]=>[3,1,2,2]
[1,8,5,2,3,7,4,6]=>[2,1,3,2]
[1,8,2,5,3,6,7,4]=>[2,2,3,1]
[2,6,8,4,3,5,7,1]=>[3,1,3,1]
[7,5,8,3,2,1,6,4]=>[1,2,1,1,2,1]
[7,2,8,4,1,5,6,3]=>[1,2,1,3,1]
[7,5,8,1,2,6,3,4]=>[1,2,3,2]
[1,6,7,4,3,2,8,5]=>[3,1,1,2,1]
[1,5,2,6,4,7,8,3]=>[2,2,3,1]
[1,5,4,6,2,3,7,8]=>[2,2,4]
[6,2,5,7,1,4,8,3]=>[1,3,3,1]
[6,5,4,3,8,1,7,2]=>[1,1,1,2,2,1]
[7,3,6,8,5,2,4,1]=>[1,3,1,2,1]
[2,7,8,3,6,5,1,4]=>[3,2,1,2]
[2,7,8,5,4,6,3,1]=>[3,1,2,1,1]
[2,6,5,8,3,4,1,7]=>[2,2,2,2]
[2,6,5,7,3,4,1,8]=>[2,2,2,2]
[6,2,5,7,4,1,3,8]=>[1,3,1,3]
[6,2,5,8,4,1,3,7]=>[1,3,1,3]
[2,7,8,4,6,1,3,5]=>[3,2,3]
[6,1,2,8,3,7,4,5]=>[1,3,2,2]
[6,1,2,8,5,4,7,3]=>[1,3,1,2,1]
[6,2,5,7,8,1,3,4]=>[1,4,3]
[1,5,4,2,6,7,3,8]=>[2,1,3,2]
[2,6,5,7,3,8,1,4]=>[2,2,2,2]
[1,6,2,7,5,8,4,3]=>[2,2,2,1,1]
[1,3,2,7,8,5,6,4]=>[2,3,2,1]
[1,6,2,4,8,7,3,5]=>[2,3,1,2]
[6,5,2,1,8,7,3,4]=>[1,1,1,2,1,2]
[2,6,5,3,7,8,4,1]=>[2,1,3,1,1]
[6,2,5,3,8,4,7,1]=>[1,2,2,2,1]
[6,5,2,3,8,7,1,4]=>[1,1,3,1,2]
[5,4,1,2,3,8,6,7]=>[1,1,4,2]
[5,1,4,2,3,7,8,6]=>[1,2,4,1]
[1,5,4,2,6,3,8,7]=>[2,1,2,2,1]
[5,1,6,3,8,2,7,4]=>[1,2,2,2,1]
[1,8,7,6,2,5,4,3]=>[2,1,1,2,1,1]
[5,2,7,4,1,6,3,8]=>[1,2,1,2,2]
[4,7,3,1,5,6,2,8]=>[2,1,3,2]
[5,8,3,4,1,6,7,2]=>[2,2,3,1]
[1,7,8,4,5,6,2,3]=>[3,3,2]
[1,5,8,4,2,6,7,3]=>[3,1,3,1]
[1,6,3,8,5,2,7,4]=>[2,2,1,2,1]
[6,2,3,7,5,1,4,8]=>[1,3,1,3]
[1,7,3,4,8,6,2,5]=>[2,3,1,2]
[6,2,3,4,8,1,7,5]=>[1,4,2,1]
[8,7,3,2,1,6,5,4]=>[1,1,1,1,2,1,1]
[8,7,6,3,1,5,2,4]=>[1,1,1,1,2,2]
[8,5,1,7,2,3,4,6]=>[1,1,2,4]
[2,4,8,5,3,7,1,6]=>[3,1,2,2]
[2,4,1,8,5,3,7,6]=>[2,2,1,2,1]
[2,4,8,6,3,1,7,5]=>[3,1,1,2,1]
[3,4,6,8,2,1,7,5]=>[4,1,2,1]
[3,4,1,5,8,2,7,6]=>[2,3,2,1]
[8,1,4,5,3,2,7,6]=>[1,3,1,2,1]
[3,4,1,5,2,8,7,6]=>[2,2,2,1,1]
[3,4,6,2,1,8,7,5]=>[3,1,2,1,1]
[3,5,6,2,1,7,8,4]=>[3,1,3,1]
[3,4,6,2,7,8,1,5]=>[3,3,2]
[8,1,4,6,3,7,2,5]=>[1,3,2,2]
[8,1,4,6,3,7,5,2]=>[1,3,2,1,1]
[3,5,6,2,1,7,4,8]=>[3,1,2,2]
[8,1,5,6,7,3,4,2]=>[1,4,2,1]
[8,1,5,6,7,3,2,4]=>[1,4,1,2]
[3,4,1,6,8,7,2,5]=>[2,3,1,2]
[3,5,6,1,8,7,2,4]=>[3,2,1,2]
[2,1,3,8,6,7,4,5]=>[1,3,2,2]
[8,1,3,2,6,7,5,4]=>[1,2,3,1,1]
[2,3,8,6,7,1,5,4]=>[3,2,2,1]
[2,4,1,8,6,7,5,3]=>[2,2,2,1,1]
[2,5,8,6,1,7,4,3]=>[3,1,2,1,1]
[3,5,6,1,8,7,4,2]=>[3,2,1,1,1]
[3,4,1,6,8,7,5,2]=>[2,3,1,1,1]
[3,4,6,8,7,1,5,2]=>[4,1,2,1]
[8,1,4,6,2,7,5,3]=>[1,3,2,1,1]
[3,5,1,6,7,8,4,2]=>[2,4,1,1]
[4,5,6,1,7,8,3,2]=>[3,3,1,1]
[4,5,6,1,7,3,8,2]=>[3,2,2,1]
[3,5,1,6,7,4,8,2]=>[2,3,2,1]
[8,1,5,6,7,4,2,3]=>[1,4,1,2]
[8,1,5,6,7,4,3,2]=>[1,4,1,1,1]
[3,5,1,6,7,4,2,8]=>[2,3,1,2]
[4,5,6,1,7,3,2,8]=>[3,2,1,2]
[6,5,8,7,4,3,1,2]=>[1,2,1,1,1,2]
[6,4,2,7,8,5,1,3]=>[1,1,3,1,2]
[6,1,4,8,7,5,2,3]=>[1,3,1,1,2]
[1,6,4,8,7,5,2,3]=>[2,2,1,1,2]
[1,8,6,2,4,7,3,5]=>[2,1,3,2]
[8,1,6,2,4,7,3,5]=>[1,2,3,2]
[7,6,2,1,4,8,3,5]=>[1,1,1,3,2]
[6,4,1,7,8,5,2,3]=>[1,1,3,1,2]
[7,6,1,2,4,8,3,5]=>[1,1,4,2]
[7,6,1,3,4,8,2,5]=>[1,1,4,2]
[8,1,6,3,4,7,2,5]=>[1,2,3,2]
[1,8,6,3,4,7,2,5]=>[2,1,3,2]
[1,7,2,5,4,8,3,6]=>[2,2,2,2]
[7,1,2,5,4,8,3,6]=>[1,3,2,2]
[2,7,1,5,4,8,3,6]=>[2,2,2,2]
[2,8,6,3,4,7,1,5]=>[2,1,3,2]
[2,8,6,1,4,7,3,5]=>[2,1,3,2]
[7,2,1,5,4,8,3,6]=>[1,1,2,2,2]
[1,2,7,5,4,8,3,6]=>[3,1,2,2]
[3,2,7,5,4,8,1,6]=>[1,2,1,2,2]
[2,5,8,4,7,3,1,6]=>[3,2,1,2]
[2,3,7,5,4,8,1,6]=>[3,1,2,2]
[6,8,3,2,4,7,1,5]=>[2,1,3,2]
[3,7,2,5,4,8,1,6]=>[2,2,2,2]
[3,1,7,5,4,8,2,6]=>[1,2,1,2,2]
[1,3,7,5,4,8,2,6]=>[3,1,2,2]
[1,5,8,4,7,3,2,6]=>[3,2,1,2]
[5,1,8,4,7,3,2,6]=>[1,2,2,1,2]
[5,8,2,4,7,3,1,6]=>[2,3,1,2]
[6,8,4,3,7,5,1,2]=>[2,1,2,1,2]
[8,7,5,6,2,1,4,3]=>[1,1,2,1,2,1]
[8,5,2,4,7,3,1,6]=>[1,1,3,1,2]
[8,1,5,4,7,3,2,6]=>[1,2,2,1,2]
[1,8,5,4,7,3,2,6]=>[2,1,2,1,2]
[1,7,3,5,4,8,2,6]=>[2,2,2,2]
[8,6,3,1,4,7,2,5]=>[1,1,1,3,2]
[8,6,4,2,7,5,1,3]=>[1,1,1,2,1,2]
[8,6,4,1,7,2,5,3]=>[1,1,1,2,2,1]
[5,3,7,4,6,8,2,1]=>[1,2,3,1,1]
[4,1,3,2,7,8,5,6]=>[1,2,3,2]
[1,4,3,2,7,8,5,6]=>[2,1,3,2]
[2,4,3,1,7,8,5,6]=>[2,1,3,2]
[2,7,3,5,4,8,1,6]=>[2,2,2,2]
[2,8,5,4,7,3,1,6]=>[2,1,2,1,2]
[5,7,3,4,6,8,2,1]=>[2,4,1,1]
[8,2,5,4,7,3,1,6]=>[1,2,2,1,2]
[7,2,3,5,4,8,1,6]=>[1,3,2,2]
[3,2,1,4,7,8,5,6]=>[1,1,4,2]
[8,1,7,6,4,3,5,2]=>[1,2,1,1,2,1]
[8,6,4,5,2,7,1,3]=>[1,1,2,2,2]
[7,1,8,6,4,3,5,2]=>[1,2,1,1,2,1]
[7,4,2,5,1,6,3,8]=>[1,1,2,2,2]
[7,3,6,5,2,1,4,8]=>[1,2,1,1,3]
[8,3,6,5,2,1,7,4]=>[1,2,1,1,2,1]
[7,3,6,5,2,1,8,4]=>[1,2,1,1,2,1]
[7,5,8,6,4,2,1,3]=>[1,2,1,1,1,2]
[5,4,2,8,1,3,7,6]=>[1,1,2,3,1]
[5,8,2,6,4,1,3,7]=>[2,2,1,3]
[6,4,2,5,1,8,3,7]=>[1,1,2,2,2]
[6,3,5,2,1,4,7,8]=>[1,2,1,4]
[2,5,8,6,3,1,4,7]=>[3,1,1,3]
[2,3,5,8,1,4,7,6]=>[4,3,1]
[2,3,6,8,1,5,7,4]=>[4,3,1]
[6,3,8,5,2,7,1,4]=>[1,2,1,2,2]
[6,3,7,5,2,1,4,8]=>[1,2,1,1,3]
[2,5,7,6,3,1,4,8]=>[3,1,1,3]
[2,8,7,6,3,1,5,4]=>[2,1,1,1,2,1]
[2,5,8,7,6,3,1,4]=>[3,1,1,1,2]
[2,4,8,1,6,5,7,3]=>[3,2,2,1]
[2,8,7,3,6,1,4,5]=>[2,1,2,3]
[7,3,5,2,1,4,6,8]=>[1,2,1,4]
[8,4,2,5,1,3,7,6]=>[1,1,2,3,1]
[2,3,6,8,1,4,7,5]=>[4,3,1]
[2,7,8,6,3,1,4,5]=>[3,1,1,3]
[7,3,8,5,2,1,4,6]=>[1,2,1,1,3]
[2,3,6,1,8,4,7,5]=>[3,2,2,1]
[2,8,6,3,1,4,5,7]=>[2,1,1,4]
[8,3,5,2,1,4,6,7]=>[1,2,1,4]
[2,4,8,1,3,7,5,6]=>[3,3,2]
[2,5,8,1,7,3,6,4]=>[3,2,2,1]
[2,8,1,5,7,3,6,4]=>[2,3,2,1]
[8,3,6,1,4,7,5,2]=>[1,2,3,1,1]
[3,8,6,1,4,7,5,2]=>[2,1,3,1,1]
[2,7,1,5,8,3,4,6]=>[2,3,3]
[4,7,6,1,8,5,2,3]=>[2,1,2,1,2]
[3,7,5,8,1,2,6,4]=>[2,2,3,1]
[7,3,6,1,2,8,4,5]=>[1,2,3,2]
[7,4,8,1,6,5,2,3]=>[1,2,2,1,2]
[7,4,6,1,8,2,5,3]=>[1,2,2,2,1]
[7,4,5,8,6,1,2,3]=>[1,3,1,3]
[6,8,4,5,1,7,2,3]=>[2,2,2,2]
[5,1,7,6,2,3,8,4]=>[1,2,1,3,1]
[5,1,8,7,6,2,3,4]=>[1,2,1,1,3]
[8,5,1,7,6,2,3,4]=>[1,1,2,1,3]
[8,5,1,6,2,7,3,4]=>[1,1,2,2,2]
[4,6,1,8,7,5,2,3]=>[2,2,1,1,2]
[8,4,6,1,7,5,2,3]=>[1,2,2,1,2]
[4,8,5,1,7,2,3,6]=>[2,1,2,3]
[4,5,1,8,7,2,3,6]=>[2,2,1,3]
[3,4,8,7,1,2,5,6]=>[3,1,4]
[8,6,4,7,1,2,5,3]=>[1,1,2,3,1]
[6,4,8,7,1,2,5,3]=>[1,2,1,3,1]
[6,5,1,2,7,3,8,4]=>[1,1,3,2,1]
[6,5,1,8,2,7,3,4]=>[1,1,2,2,2]
[8,6,5,1,2,7,3,4]=>[1,1,1,3,2]
[8,6,5,1,7,2,3,4]=>[1,1,1,2,3]
[6,5,1,8,7,2,3,4]=>[1,1,2,1,3]
[6,5,1,7,2,8,3,4]=>[1,1,2,2,2]
[6,5,1,7,2,3,8,4]=>[1,1,2,3,1]
[5,7,4,1,8,2,3,6]=>[2,1,2,3]
[5,6,8,7,4,1,2,3]=>[3,1,1,3]
[6,8,5,7,4,1,2,3]=>[2,2,1,3]
[7,3,8,1,5,2,4,6]=>[1,2,2,3]
[4,1,7,5,3,6,2,8]=>[1,2,1,2,2]
[1,8,4,2,3,6,7,5]=>[2,1,4,1]
[2,5,8,3,4,6,7,1]=>[3,4,1]
[4,1,7,2,3,6,8,5]=>[1,2,4,1]
[4,6,2,1,5,7,8,3]=>[2,1,4,1]
[4,5,2,3,1,7,8,6]=>[2,2,3,1]
[3,2,6,7,4,1,8,5]=>[1,3,1,2,1]
[5,6,2,7,1,4,8,3]=>[2,2,3,1]
[6,2,3,8,1,7,4,5]=>[1,3,2,2]
[2,6,8,3,4,7,1,5]=>[3,3,2]
[4,6,2,7,5,1,3,8]=>[2,2,1,3]
[2,6,3,1,8,4,5,7]=>[2,1,2,3]
[2,4,3,7,8,1,5,6]=>[2,3,3]
[5,3,2,7,4,8,1,6]=>[1,1,2,2,2]
[5,1,2,7,6,8,4,3]=>[1,3,2,1,1]
[2,6,3,1,8,7,4,5]=>[2,1,2,1,2]
[3,5,6,4,7,8,1,2]=>[3,3,2]
[5,3,6,4,2,8,7,1]=>[1,2,1,2,1,1]
[5,4,2,3,7,8,6,1]=>[1,1,4,1,1]
[4,1,8,2,5,7,3,6]=>[1,2,3,2]
[3,1,8,4,7,2,5,6]=>[1,2,2,3]
[6,2,3,8,4,1,7,5]=>[1,3,1,2,1]
[2,6,4,1,5,3,8,7]=>[2,1,2,2,1]
[3,2,7,6,4,1,8,5]=>[1,2,1,1,2,1]
[2,5,4,1,7,6,8,3]=>[2,1,2,2,1]
[6,2,1,4,7,8,3,5]=>[1,1,4,2]
[2,6,5,1,7,8,3,4]=>[2,1,3,2]
[4,7,5,2,1,6,3,8]=>[2,1,1,2,2]
[4,2,3,7,8,1,6,5]=>[1,4,2,1]
[5,8,3,1,7,2,4,6]=>[2,1,2,3]
[6,8,3,1,5,2,4,7]=>[2,1,2,3]
[4,2,7,1,6,3,5,8]=>[1,2,2,3]
[5,1,7,4,2,6,3,8]=>[1,2,1,2,2]
[5,8,2,1,4,7,3,6]=>[2,1,3,2]
[6,8,3,2,5,1,7,4]=>[2,1,2,2,1]
[6,8,4,3,1,5,7,2]=>[2,1,1,3,1]
[6,8,4,2,1,5,7,3]=>[2,1,1,3,1]
[6,8,3,2,1,4,5,7]=>[2,1,1,4]
[5,1,7,3,2,4,6,8]=>[1,2,1,4]
[5,2,1,8,3,6,7,4]=>[1,1,2,3,1]
[4,3,8,1,6,2,7,5]=>[1,2,2,2,1]
[5,4,7,2,1,6,8,3]=>[1,2,1,3,1]
[5,2,1,7,3,4,8,6]=>[1,1,2,3,1]
[6,4,3,1,7,5,8,2]=>[1,1,1,2,2,1]
[5,3,1,7,2,6,8,4]=>[1,1,2,3,1]
[3,2,1,7,6,4,8,5]=>[1,1,2,1,2,1]
[4,2,1,6,5,8,3,7]=>[1,1,2,2,2]
[4,2,1,8,5,7,3,6]=>[1,1,2,2,2]
[7,4,3,1,8,5,6,2]=>[1,1,1,2,2,1]
[6,3,2,1,7,4,5,8]=>[1,1,1,2,3]
[6,4,2,1,7,5,3,8]=>[1,1,1,2,1,2]
[7,5,2,1,8,6,3,4]=>[1,1,1,2,1,2]
[6,1,8,4,2,7,3,5]=>[1,2,1,2,2]
[6,2,1,8,3,7,4,5]=>[1,1,2,2,2]
[5,2,1,7,3,6,4,8]=>[1,1,2,2,2]
[5,3,2,7,6,1,4,8]=>[1,1,2,1,3]
[5,3,2,8,6,1,4,7]=>[1,1,2,1,3]
[6,3,2,8,7,1,4,5]=>[1,1,2,1,3]
[4,2,8,1,7,3,5,6]=>[1,2,2,3]
[4,3,8,7,2,1,5,6]=>[1,2,1,1,3]
[2,1,5,8,4,7,3,6]=>[1,3,2,2]
[4,3,2,5,8,1,6,7]=>[1,1,3,3]
[4,3,2,5,7,1,6,8]=>[1,1,3,3]
[4,3,1,6,2,7,5,8]=>[1,1,2,2,2]
[4,3,1,7,2,8,5,6]=>[1,1,2,2,2]
[5,4,1,7,2,8,6,3]=>[1,1,2,2,1,1]
[6,5,3,1,7,8,4,2]=>[1,1,1,3,1,1]
[6,4,2,1,7,8,3,5]=>[1,1,1,3,2]
[5,3,2,1,6,7,4,8]=>[1,1,1,3,2]
[6,4,2,1,7,8,5,3]=>[1,1,1,3,1,1]
[5,3,2,6,8,1,7,4]=>[1,1,3,2,1]
[3,2,1,4,8,7,5,6]=>[1,1,3,1,2]
[3,2,1,4,6,8,5,7]=>[1,1,4,2]
[4,3,2,6,1,7,8,5]=>[1,1,2,3,1]
[5,3,2,1,6,7,8,4]=>[1,1,1,4,1]
[8,6,1,4,5,7,2,3]=>[1,1,4,2]
[3,8,6,4,5,7,1,2]=>[2,1,3,2]
[5,2,8,3,7,4,6,1]=>[1,2,2,2,1]
[6,2,8,5,4,7,3,1]=>[1,2,1,2,1,1]
[1,8,6,3,7,4,2,5]=>[2,1,2,1,2]
[1,8,6,5,7,2,3,4]=>[2,1,2,3]
[5,2,8,4,3,6,7,1]=>[1,2,1,3,1]
[5,4,2,7,3,6,1,8]=>[1,1,2,2,2]
[5,4,2,8,3,6,1,7]=>[1,1,2,2,2]
[6,5,3,8,4,7,2,1]=>[1,1,2,2,1,1]
[5,2,8,4,3,7,1,6]=>[1,2,1,2,2]
[6,2,8,3,7,4,1,5]=>[1,2,2,1,2]
[5,4,2,7,3,1,8,6]=>[1,1,2,1,2,1]
[6,4,3,7,1,2,8,5]=>[1,1,2,3,1]
[6,4,3,8,1,2,7,5]=>[1,1,2,3,1]
[7,6,3,8,4,2,1,5]=>[1,1,2,1,1,2]
[7,2,8,5,1,6,3,4]=>[1,2,1,2,2]
[7,2,8,4,3,1,5,6]=>[1,2,1,1,3]
[7,5,3,8,4,2,6,1]=>[1,1,2,1,2,1]
[6,4,2,7,3,1,5,8]=>[1,1,2,1,3]
[7,6,4,8,2,3,5,1]=>[1,1,2,3,1]
[7,6,8,1,2,5,3,4]=>[1,2,3,2]
[5,3,1,7,8,4,6,2]=>[1,1,3,2,1]
[5,3,2,7,8,4,6,1]=>[1,1,3,2,1]
[5,4,1,6,3,8,7,2]=>[1,1,2,2,1,1]
[6,5,1,7,8,2,3,4]=>[1,1,3,3]
[6,3,1,7,8,4,2,5]=>[1,1,3,1,2]
[5,4,1,7,3,8,2,6]=>[1,1,2,2,2]
[6,3,2,7,8,4,1,5]=>[1,1,3,1,2]
[6,1,5,4,3,2,8,7]=>[1,2,1,1,2,1]
[8,7,6,1,3,5,2,4]=>[1,1,1,3,2]
[8,1,6,5,7,3,4,2]=>[1,2,2,2,1]
[8,4,1,5,7,6,2,3]=>[1,1,3,1,2]
[7,8,6,2,5,3,1,4]=>[2,1,2,1,2]
[6,1,3,5,2,8,4,7]=>[1,3,2,2]
[8,1,3,7,4,2,5,6]=>[1,3,1,3]
[4,3,8,7,5,2,1,6]=>[1,2,1,1,1,2]
[6,7,1,8,5,3,4,2]=>[2,2,1,2,1]
[2,7,6,4,8,3,5,1]=>[2,1,2,2,1]
[6,5,2,7,1,4,8,3]=>[1,1,2,3,1]
[7,4,6,1,3,2,8,5]=>[1,2,2,2,1]
[7,5,2,1,3,8,4,6]=>[1,1,1,3,2]
[8,4,7,6,3,1,5,2]=>[1,2,1,1,2,1]
[7,4,1,5,6,3,8,2]=>[1,1,3,2,1]
[3,4,7,5,6,1,8,2]=>[3,2,2,1]
[2,4,7,5,6,3,8,1]=>[3,2,2,1]
[5,4,1,7,6,2,8,3]=>[1,1,2,1,2,1]
[3,5,6,7,1,4,8,2]=>[4,3,1]
[2,7,6,1,3,4,8,5]=>[2,1,4,1]
[5,7,2,1,6,3,8,4]=>[2,1,2,2,1]
[4,7,2,5,6,3,8,1]=>[2,3,2,1]
[8,6,2,5,7,1,4,3]=>[1,1,3,2,1]
[2,7,4,5,3,8,1,6]=>[2,2,2,2]
[6,8,7,1,3,2,5,4]=>[2,1,2,2,1]
[2,8,6,5,7,1,4,3]=>[2,1,2,2,1]
[5,8,4,3,2,6,7,1]=>[2,1,1,3,1]
[1,8,5,6,2,4,7,3]=>[2,2,3,1]
[8,1,5,6,2,4,7,3]=>[1,3,3,1]
[6,4,8,1,3,2,7,5]=>[1,2,2,2,1]
[1,4,5,2,8,6,7,3]=>[3,2,2,1]
[2,3,1,7,8,6,4,5]=>[2,3,1,2]
[3,5,7,6,2,8,1,4]=>[3,1,2,2]
[4,5,6,1,2,8,7,3]=>[3,3,1,1]
[5,4,1,2,8,6,7,3]=>[1,1,3,2,1]
[8,4,5,2,1,6,7,3]=>[1,2,1,3,1]
[3,1,2,6,8,4,7,5]=>[1,4,2,1]
[5,1,3,2,7,8,4,6]=>[1,2,3,2]
[1,5,4,2,7,8,3,6]=>[2,1,3,2]
[4,6,7,8,3,1,5,2]=>[4,1,2,1]
[7,6,2,8,4,3,1,5]=>[1,1,2,1,1,2]
[5,2,8,6,3,4,7,1]=>[1,2,1,3,1]
[5,6,8,4,3,2,7,1]=>[3,1,1,2,1]
[5,3,8,1,7,2,4,6]=>[1,2,2,3]
[3,6,7,8,4,2,1,5]=>[4,1,1,2]
[6,5,1,8,4,3,7,2]=>[1,1,2,1,2,1]
[6,3,8,4,2,1,7,5]=>[1,2,1,1,2,1]
[2,5,8,3,1,6,7,4]=>[3,1,3,1]
[3,5,8,1,2,6,7,4]=>[3,4,1]
[3,2,8,1,5,6,7,4]=>[1,2,4,1]
[1,5,8,3,2,6,7,4]=>[3,1,3,1]
[1,3,8,6,2,4,7,5]=>[3,1,3,1]
[3,2,7,8,4,6,1,5]=>[1,3,2,2]
[5,1,8,3,4,6,7,2]=>[1,2,4,1]
[4,8,7,2,1,6,3,5]=>[2,1,1,2,2]
[2,8,1,6,3,4,7,5]=>[2,2,3,1]
[8,3,4,2,1,6,5,7]=>[1,2,1,2,2]
[6,4,7,2,5,8,1,3]=>[1,2,3,2]
[8,4,5,2,6,3,1,7]=>[1,2,2,1,2]
[2,4,5,8,3,6,1,7]=>[4,2,2]
[3,5,8,1,2,6,4,7]=>[3,3,2]
[8,6,1,3,5,2,4,7]=>[1,1,3,3]
[8,5,1,2,6,4,3,7]=>[1,1,3,1,2]
[5,8,6,1,3,4,2,7]=>[2,1,3,2]
[5,8,4,6,1,3,2,7]=>[2,2,2,2]
[7,3,4,5,2,8,1,6]=>[1,3,2,2]
[5,7,4,3,6,1,8,2]=>[2,1,2,2,1]
[2,6,4,3,7,8,5,1]=>[2,1,3,1,1]
[7,4,1,8,3,2,5,6]=>[1,1,2,1,3]
[6,2,1,7,8,4,5,3]=>[1,1,3,2,1]
[7,6,3,1,5,4,8,2]=>[1,1,1,2,2,1]
[2,4,6,5,1,7,8,3]=>[3,1,3,1]
[1,4,7,5,6,8,2,3]=>[3,3,2]
[1,4,7,6,5,8,2,3]=>[3,1,2,2]
[3,7,5,2,4,6,8,1]=>[2,1,4,1]
[5,6,1,7,4,2,8,3]=>[2,2,1,2,1]
[3,7,4,8,1,2,6,5]=>[2,2,3,1]
[6,3,5,7,8,1,4,2]=>[1,4,2,1]
[3,6,5,7,1,8,4,2]=>[2,2,2,1,1]
[6,4,7,8,2,1,3,5]=>[1,3,1,3]
[6,7,3,8,4,1,2,5]=>[2,2,1,3]
[2,7,8,3,4,6,1,5]=>[3,3,2]
[7,5,8,4,1,3,2,6]=>[1,2,1,2,2]
[4,7,5,8,3,1,2,6]=>[2,2,1,3]
[3,6,7,4,8,1,2,5]=>[3,2,3]
[5,7,3,1,6,8,4,2]=>[2,1,3,1,1]
[2,7,3,1,8,6,4,5]=>[2,1,2,1,2]
[2,8,4,3,1,5,7,6]=>[2,1,1,3,1]
[4,8,1,2,3,5,7,6]=>[2,5,1]
[7,6,8,1,2,4,3,5]=>[1,2,3,2]
[7,6,8,5,1,3,2,4]=>[1,2,1,2,2]
[2,8,5,4,6,1,7,3]=>[2,1,2,2,1]
[8,4,5,2,7,6,1,3]=>[1,2,2,1,2]
[8,7,6,4,1,2,5,3]=>[1,1,1,1,3,1]
[6,7,1,3,5,2,8,4]=>[2,3,2,1]
[5,7,2,3,6,8,1,4]=>[2,4,2]
[8,5,3,2,7,6,1,4]=>[1,1,1,2,1,2]
[3,4,6,7,5,8,1,2]=>[4,2,2]
[3,4,5,7,6,1,8,2]=>[4,1,2,1]
[2,6,4,5,7,8,3,1]=>[2,4,1,1]
[3,8,5,1,6,2,7,4]=>[2,1,2,2,1]
[2,5,1,3,6,8,7,4]=>[2,4,1,1]
[5,4,6,1,3,7,8,2]=>[1,2,4,1]
[6,3,5,7,1,4,8,2]=>[1,3,3,1]
[7,3,4,6,8,1,5,2]=>[1,4,2,1]
[7,5,2,8,4,1,3,6]=>[1,1,2,1,3]
[3,7,6,4,1,8,2,5]=>[2,1,1,2,2]
[3,7,8,4,1,5,6,2]=>[3,1,3,1]
[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,2,1]
[3,5,8,6,7,4,2,1]=>[3,2,1,1,1]
[5,8,1,6,7,3,4,2]=>[2,3,2,1]
[6,7,2,5,1,8,4,3]=>[2,2,2,1,1]
[5,8,2,1,6,7,4,3]=>[2,1,3,1,1]
[4,5,2,8,6,3,7,1]=>[2,2,1,2,1]
[3,6,1,2,5,8,4,7]=>[2,4,2]
[1,4,5,8,2,3,7,6]=>[4,3,1]
[1,2,6,4,5,8,3,7]=>[3,3,2]
[1,5,2,4,6,8,3,7]=>[2,4,2]
[3,6,1,5,8,2,4,7]=>[2,3,3]
[2,6,5,1,4,8,3,7]=>[2,1,3,2]
[5,2,6,1,4,8,3,7]=>[1,2,3,2]
[2,5,1,8,4,7,3,6]=>[2,2,2,2]
[2,7,1,4,3,6,8,5]=>[2,2,3,1]
[1,3,7,5,8,2,4,6]=>[3,2,3]
[8,2,1,5,7,3,4,6]=>[1,1,3,3]
[2,5,4,8,1,3,7,6]=>[2,2,3,1]
[2,4,1,3,8,6,7,5]=>[2,3,2,1]
[8,4,3,7,1,2,6,5]=>[1,1,2,3,1]
[1,7,3,5,8,2,6,4]=>[2,3,2,1]
[1,8,4,2,6,7,3,5]=>[2,1,3,2]
[3,1,6,8,7,2,4,5]=>[1,3,1,3]
[7,2,1,6,8,3,4,5]=>[1,1,3,3]
[3,1,7,6,8,2,4,5]=>[1,2,2,3]
[4,1,7,2,6,8,3,5]=>[1,2,3,2]
[5,1,7,2,3,6,8,4]=>[1,2,4,1]
[7,2,1,6,3,5,8,4]=>[1,1,2,3,1]
[2,6,1,7,3,5,8,4]=>[2,2,3,1]
[7,1,2,5,3,6,8,4]=>[1,3,3,1]
[5,4,1,2,7,8,3,6]=>[1,1,4,2]
[8,1,3,2,4,6,7,5]=>[1,2,4,1]
[7,3,1,2,4,6,8,5]=>[1,1,5,1]
[1,8,3,4,7,2,5,6]=>[2,3,3]
[3,5,8,1,2,7,4,6]=>[3,3,2]
[3,6,8,1,2,4,7,5]=>[3,4,1]
[4,1,3,8,7,2,6,5]=>[1,3,1,2,1]
[1,3,7,4,8,2,6,5]=>[3,2,2,1]
[1,4,6,8,2,3,7,5]=>[4,3,1]
[3,5,8,1,7,2,4,6]=>[3,2,3]
[2,6,8,1,7,3,4,5]=>[3,2,3]
[6,1,5,8,2,3,7,4]=>[1,3,3,1]
[1,8,3,2,7,5,6,4]=>[2,1,2,2,1]
[3,1,7,2,8,5,6,4]=>[1,2,2,2,1]
[2,6,7,3,8,1,5,4]=>[3,2,2,1]
[8,4,1,7,3,6,2,5]=>[1,1,2,2,2]
[3,7,2,8,6,1,5,4]=>[2,2,1,2,1]
[6,2,3,8,7,1,5,4]=>[1,3,1,2,1]
[5,1,7,8,4,2,6,3]=>[1,3,1,2,1]
[5,1,8,7,4,2,6,3]=>[1,2,1,1,2,1]
[4,7,2,8,3,6,5,1]=>[2,2,2,1,1]
[4,1,7,8,5,3,6,2]=>[1,3,1,2,1]
[5,1,7,4,8,3,6,2]=>[1,2,2,2,1]
[4,1,8,7,5,3,6,2]=>[1,2,1,1,2,1]
[4,8,2,7,3,6,5,1]=>[2,2,2,1,1]
[4,7,2,6,3,5,8,1]=>[2,2,3,1]
[6,8,2,4,3,7,5,1]=>[2,2,2,1,1]
[6,7,2,4,3,8,5,1]=>[2,2,2,1,1]
[6,8,2,7,3,5,4,1]=>[2,2,2,1,1]
[3,8,7,2,4,1,5,6]=>[2,1,2,3]
[3,7,8,2,4,1,5,6]=>[3,2,3]
[3,6,8,2,4,5,7,1]=>[3,4,1]
[3,6,7,2,4,5,8,1]=>[3,4,1]
[6,5,1,4,2,3,8,7]=>[1,1,2,3,1]
[8,6,1,7,2,5,4,3]=>[1,1,2,2,1,1]
[8,7,6,1,2,3,5,4]=>[1,1,1,4,1]
[5,4,3,1,6,2,8,7]=>[1,1,1,2,2,1]
[8,3,4,7,1,6,2,5]=>[1,3,2,2]
[6,3,4,1,8,5,2,7]=>[1,2,2,1,2]
[3,8,5,2,7,1,6,4]=>[2,1,2,2,1]
[2,8,6,7,5,3,4,1]=>[2,2,1,2,1]
[2,1,8,7,3,6,4,5]=>[1,2,1,2,2]
[3,6,5,8,2,4,7,1]=>[2,2,3,1]
[5,2,1,8,7,3,4,6]=>[1,1,2,1,3]
[6,5,2,7,4,3,8,1]=>[1,1,2,1,2,1]
[4,6,5,2,7,3,8,1]=>[2,1,2,2,1]
[6,2,7,1,8,3,5,4]=>[1,2,2,2,1]
[2,7,5,4,8,3,6,1]=>[2,1,2,2,1]
[8,7,5,1,2,6,4,3]=>[1,1,1,3,1,1]
[8,4,3,2,7,1,6,5]=>[1,1,1,2,2,1]
[7,1,6,2,3,8,5,4]=>[1,2,3,1,1]
[4,8,1,3,2,7,5,6]=>[2,2,2,2]
[3,8,1,4,7,5,2,6]=>[2,3,1,2]
[6,3,8,7,4,5,1,2]=>[1,2,1,2,2]
[6,1,4,8,5,2,3,7]=>[1,3,1,3]
[8,5,7,4,6,2,1,3]=>[1,2,2,1,2]
[4,6,7,8,2,3,5,1]=>[4,3,1]
[8,7,4,6,2,1,5,3]=>[1,1,2,1,2,1]
[7,6,1,3,5,2,8,4]=>[1,1,3,2,1]
[5,8,3,2,4,6,1,7]=>[2,1,3,2]
[8,2,6,5,3,1,7,4]=>[1,2,1,1,2,1]
[4,8,7,6,5,2,3,1]=>[2,1,1,1,2,1]
[2,1,8,6,4,3,7,5]=>[1,2,1,1,2,1]
[2,1,7,6,5,3,8,4]=>[1,2,1,1,2,1]
[2,7,6,1,3,5,8,4]=>[2,1,4,1]
[7,2,5,4,6,1,8,3]=>[1,2,2,2,1]
[4,7,6,1,2,5,8,3]=>[2,1,4,1]
[2,4,1,7,6,8,5,3]=>[2,2,2,1,1]
[3,4,1,7,8,5,6,2]=>[2,3,2,1]
[7,5,4,3,1,8,6,2]=>[1,1,1,1,2,1,1]
[8,5,6,2,7,3,1,4]=>[1,2,2,1,2]
[8,4,2,5,6,1,7,3]=>[1,1,3,2,1]
[6,3,5,4,1,7,8,2]=>[1,2,1,3,1]
[4,1,3,6,7,5,8,2]=>[1,4,2,1]
[1,7,5,3,8,2,4,6]=>[2,1,2,3]
[1,7,2,4,5,8,3,6]=>[2,4,2]
[8,2,5,3,1,6,4,7]=>[1,2,1,2,2]
[1,7,4,5,8,3,2,6]=>[2,3,1,2]
[2,6,4,7,8,3,5,1]=>[2,3,2,1]
[2,6,4,7,8,3,1,5]=>[2,3,1,2]
[1,2,6,4,7,8,3,5]=>[3,3,2]
[2,7,4,5,8,1,3,6]=>[2,3,3]
[2,7,5,3,1,8,4,6]=>[2,1,1,2,2]
[6,1,4,7,8,3,5,2]=>[1,4,2,1]
[3,6,4,7,8,1,5,2]=>[2,3,2,1]
[4,3,6,7,1,8,5,2]=>[1,3,2,1,1]
[4,3,6,7,1,8,2,5]=>[1,3,2,2]
[3,6,4,7,8,1,2,5]=>[2,3,3]
[2,3,6,4,1,7,8,5]=>[3,1,3,1]
[4,7,2,1,5,3,8,6]=>[2,1,2,2,1]
[3,7,4,5,2,1,8,6]=>[2,2,1,2,1]
[1,3,6,4,7,2,8,5]=>[3,2,2,1]
[3,6,4,7,2,8,5,1]=>[2,2,2,1,1]
[5,1,3,4,2,7,8,6]=>[1,3,3,1]
[5,4,2,1,3,7,8,6]=>[1,1,1,4,1]
[6,1,7,3,8,2,5,4]=>[1,2,2,2,1]
[1,6,7,3,8,2,5,4]=>[3,2,2,1]
[6,1,4,7,8,5,2,3]=>[1,4,1,2]
[6,3,2,1,7,8,5,4]=>[1,1,1,3,1,1]
[6,2,7,3,1,8,5,4]=>[1,2,1,2,1,1]
[6,2,4,7,8,1,5,3]=>[1,4,2,1]
[2,6,7,3,1,8,5,4]=>[3,1,2,1,1]
[8,6,5,1,3,2,4,7]=>[1,1,1,2,3]
[6,4,7,8,3,2,5,1]=>[1,3,1,2,1]
[3,8,4,7,1,2,5,6]=>[2,2,4]
[8,6,1,2,5,4,3,7]=>[1,1,3,1,2]
[4,8,6,1,5,3,2,7]=>[2,1,2,1,2]
[5,8,6,4,1,3,2,7]=>[2,1,1,2,2]
[8,3,6,4,5,2,1,7]=>[1,2,2,1,2]
[6,8,5,7,4,2,3,1]=>[2,2,1,2,1]
[2,3,8,7,1,6,4,5]=>[3,1,2,2]
[4,3,7,8,1,6,2,5]=>[1,3,2,2]
[3,5,8,7,4,1,2,6]=>[3,1,1,3]
[7,3,8,4,1,2,5,6]=>[1,2,1,4]
[4,8,1,2,7,3,5,6]=>[2,3,3]
[6,8,1,2,7,4,5,3]=>[2,3,2,1]
[5,6,8,4,1,3,7,2]=>[3,1,3,1]
[8,5,4,7,1,6,3,2]=>[1,1,2,2,1,1]
[2,5,8,7,3,6,4,1]=>[3,1,2,1,1]
[2,4,8,7,5,6,1,3]=>[3,1,2,2]
[3,7,4,8,5,6,2,1]=>[2,2,2,1,1]
[6,4,8,7,5,1,2,3]=>[1,2,1,1,3]
[3,8,5,2,4,6,7,1]=>[2,1,4,1]
[5,7,1,8,4,6,2,3]=>[2,2,2,2]
[6,3,8,7,2,1,4,5]=>[1,2,1,1,3]
[2,3,7,8,5,6,1,4]=>[4,2,2]
[3,7,6,8,5,1,2,4]=>[2,2,1,3]
[2,6,7,8,5,1,3,4]=>[4,1,3]
[2,4,7,8,1,6,3,5]=>[4,2,2]
[5,4,7,8,2,6,3,1]=>[1,3,2,1,1]
[2,8,3,4,1,5,7,6]=>[2,2,3,1]
[6,8,3,4,1,2,7,5]=>[2,2,3,1]
[6,8,7,1,5,2,3,4]=>[2,1,2,3]
[5,8,3,2,7,6,1,4]=>[2,1,2,1,2]
[2,5,3,1,8,6,7,4]=>[2,1,2,2,1]
[4,5,3,2,8,6,7,1]=>[2,1,2,2,1]
[3,5,8,6,1,4,7,2]=>[3,1,3,1]
[2,8,5,6,1,4,7,3]=>[2,2,3,1]
[4,8,6,1,5,2,7,3]=>[2,1,2,2,1]
[5,8,2,3,7,6,1,4]=>[2,3,1,2]
[4,6,8,5,3,2,7,1]=>[3,1,1,2,1]
[2,6,4,8,5,1,7,3]=>[2,2,1,2,1]
[7,6,4,8,5,2,1,3]=>[1,1,2,1,1,2]
[3,4,8,6,5,2,7,1]=>[3,1,1,2,1]
[3,4,8,7,5,6,2,1]=>[3,1,2,1,1]
[7,5,3,2,8,6,1,4]=>[1,1,1,2,1,2]
[2,5,1,3,8,6,7,4]=>[2,3,2,1]
[4,5,1,2,8,6,7,3]=>[2,3,2,1]
[5,4,8,1,3,6,7,2]=>[1,2,4,1]
[8,3,5,4,1,6,7,2]=>[1,2,1,3,1]
[7,3,4,8,5,6,1,2]=>[1,3,2,2]
[6,1,5,7,2,4,8,3]=>[1,3,3,1]
[7,4,5,1,2,3,8,6]=>[1,2,4,1]
[7,4,3,1,2,8,5,6]=>[1,1,1,3,2]
[8,4,7,6,2,1,5,3]=>[1,2,1,1,2,1]
[8,4,6,5,7,1,3,2]=>[1,2,2,2,1]
[7,2,1,4,5,8,3,6]=>[1,1,4,2]
[7,4,1,6,3,5,8,2]=>[1,1,2,3,1]
[3,5,7,6,4,1,8,2]=>[3,1,1,2,1]
[4,7,5,2,1,3,8,6]=>[2,1,1,3,1]
[5,7,2,3,6,4,8,1]=>[2,3,2,1]
[8,6,2,3,7,1,4,5]=>[1,1,3,3]
[5,7,2,4,8,3,6,1]=>[2,3,2,1]
[1,7,2,4,8,6,3,5]=>[2,3,1,2]
[7,6,1,5,4,8,3,2]=>[1,1,2,2,1,1]
[4,7,3,2,1,8,5,6]=>[2,1,1,2,2]
[3,1,7,2,5,8,4,6]=>[1,2,3,2]
[4,8,7,6,1,2,5,3]=>[2,1,1,3,1]
[7,8,6,1,3,2,5,4]=>[2,1,2,2,1]
[2,8,6,7,4,1,3,5]=>[2,2,1,3]
[5,8,6,4,2,3,1,7]=>[2,1,1,2,2]
[2,8,3,1,6,5,4,7]=>[2,1,2,1,2]
[3,8,1,2,5,7,4,6]=>[2,4,2]
[6,8,5,4,2,7,3,1]=>[2,1,1,2,1,1]
[6,8,3,1,2,4,5,7]=>[2,1,5]
[4,6,8,7,3,1,5,2]=>[3,1,1,2,1]
[6,5,3,7,8,4,1,2]=>[1,1,3,1,2]
[4,1,3,8,7,5,6,2]=>[1,3,1,2,1]
[6,2,7,4,8,1,3,5]=>[1,2,2,3]
[8,4,5,2,1,6,3,7]=>[1,2,1,2,2]
[4,3,2,6,8,1,7,5]=>[1,1,3,2,1]
[7,1,5,6,3,8,2,4]=>[1,3,2,2]
[5,1,2,4,7,8,3,6]=>[1,5,2]
[3,5,4,2,8,1,6,7]=>[2,1,2,3]
[5,1,3,8,4,2,7,6]=>[1,3,1,2,1]
[6,2,8,7,3,5,4,1]=>[1,2,1,2,1,1]
[7,1,8,4,3,6,5,2]=>[1,2,1,2,1,1]
[3,6,8,7,4,1,2,5]=>[3,1,1,3]
[5,6,8,1,7,3,2,4]=>[3,2,1,2]
[3,1,6,8,7,4,2,5]=>[1,3,1,1,2]
[7,4,6,8,2,1,5,3]=>[1,3,1,2,1]
[6,5,8,4,3,1,2,7]=>[1,2,1,1,3]
[2,5,8,3,6,7,4,1]=>[3,3,1,1]
[8,5,1,3,7,4,6,2]=>[1,1,3,2,1]
[1,5,8,3,7,4,2,6]=>[3,2,1,2]
[3,8,2,7,1,5,6,4]=>[2,2,3,1]
[5,8,2,3,6,4,1,7]=>[2,3,1,2]
[6,8,2,3,4,7,5,1]=>[2,4,1,1]
[3,5,8,7,4,2,6,1]=>[3,1,1,2,1]
[7,5,1,8,4,2,6,3]=>[1,1,2,1,2,1]
[3,6,8,5,2,7,4,1]=>[3,1,2,1,1]
[2,1,6,5,4,8,3,7]=>[1,2,1,2,2]
[2,1,7,8,4,6,5,3]=>[1,3,2,1,1]
[2,1,7,4,3,5,8,6]=>[1,2,1,3,1]
[3,5,7,8,4,6,1,2]=>[4,2,2]
[7,5,2,8,4,6,3,1]=>[1,1,2,2,1,1]
[7,8,2,4,3,1,5,6]=>[2,2,1,3]
[7,6,3,8,1,5,4,2]=>[1,1,2,2,1,1]
[6,2,7,1,3,5,8,4]=>[1,2,4,1]
[6,1,8,2,3,5,4,7]=>[1,2,3,2]
[7,2,4,1,6,3,8,5]=>[1,2,2,2,1]
[8,4,3,1,7,5,2,6]=>[1,1,1,2,1,2]
[7,3,1,4,6,8,5,2]=>[1,1,4,1,1]
[7,3,8,5,2,6,4,1]=>[1,2,1,2,1,1]
[4,3,8,7,1,6,5,2]=>[1,2,1,2,1,1]
[4,7,1,8,5,2,6,3]=>[2,2,1,2,1]
[5,3,2,4,7,8,6,1]=>[1,1,4,1,1]
[5,2,4,3,6,8,1,7]=>[1,2,3,2]
[3,8,6,5,4,1,2,7]=>[2,1,1,1,3]
[4,7,5,6,3,8,2,1]=>[2,2,2,1,1]
[4,8,5,7,2,3,1,6]=>[2,2,2,2]
[4,2,7,5,8,3,6,1]=>[1,2,2,2,1]
[5,8,2,7,3,4,6,1]=>[2,2,3,1]
[6,8,2,5,4,3,1,7]=>[2,2,1,1,2]
[6,7,2,4,5,3,8,1]=>[2,3,2,1]
[5,7,2,8,3,6,1,4]=>[2,2,2,2]
[6,1,3,4,7,5,8,2]=>[1,4,2,1]
[6,3,2,1,4,8,5,7]=>[1,1,1,3,2]
[6,2,3,1,4,7,8,5]=>[1,2,4,1]
[6,2,1,4,8,7,5,3]=>[1,1,3,1,1,1]
[5,2,1,3,6,4,8,7]=>[1,1,3,2,1]
[7,1,8,3,5,4,6,2]=>[1,2,2,2,1]
[7,1,2,4,8,5,6,3]=>[1,4,2,1]
[7,2,1,3,4,5,8,6]=>[1,1,5,1]
[8,7,3,5,4,2,1,6]=>[1,1,2,1,1,2]
[8,4,6,5,3,2,1,7]=>[1,2,1,1,1,2]
[5,1,6,4,3,2,8,7]=>[1,2,1,1,2,1]
[8,3,7,1,4,6,5,2]=>[1,2,3,1,1]
[2,8,3,6,4,7,5,1]=>[2,2,2,1,1]
[6,2,1,7,5,8,3,4]=>[1,1,2,2,2]
[6,3,8,7,5,2,1,4]=>[1,2,1,1,1,2]
[6,7,2,1,5,8,4,3]=>[2,1,3,1,1]
[7,6,8,1,5,4,3,2]=>[1,2,2,1,1,1]
[5,4,8,7,6,1,3,2]=>[1,2,1,1,2,1]
[7,6,1,8,5,4,3,2]=>[1,1,2,1,1,1,1]
[6,5,8,1,7,4,3,2]=>[1,2,2,1,1,1]
[6,5,8,7,4,1,3,2]=>[1,2,1,1,2,1]
[1,6,4,8,3,2,5,7]=>[2,2,1,3]
[1,8,3,5,6,2,4,7]=>[2,3,3]
[1,4,8,5,6,2,3,7]=>[3,2,3]
[1,2,8,5,3,7,4,6]=>[3,1,2,2]
[6,1,4,8,2,3,5,7]=>[1,3,4]
[8,7,2,5,6,1,4,3]=>[1,1,3,2,1]
[1,8,2,5,4,7,3,6]=>[2,2,2,2]
[5,7,4,1,2,3,8,6]=>[2,1,4,1]
[1,7,4,2,5,3,8,6]=>[2,1,2,2,1]
[6,7,4,2,1,3,8,5]=>[2,1,1,3,1]
[6,4,3,8,5,7,1,2]=>[1,1,2,2,2]
[7,4,3,6,2,1,5,8]=>[1,1,2,1,3]
[7,2,5,3,4,1,6,8]=>[1,2,2,3]
[8,3,7,4,5,6,1,2]=>[1,2,3,2]
[2,7,4,3,1,5,6,8]=>[2,1,1,4]
[6,8,4,2,3,1,5,7]=>[2,1,2,3]
[3,7,5,2,4,1,6,8]=>[2,1,2,3]
[7,1,3,2,8,4,5,6]=>[1,2,2,3]
[2,1,7,4,8,3,5,6]=>[1,2,2,3]
[5,2,8,6,1,3,4,7]=>[1,2,1,4]
[2,8,3,1,4,5,6,7]=>[2,1,5]
[7,4,8,2,3,1,5,6]=>[1,2,2,3]
[4,2,7,3,1,5,6,8]=>[1,2,1,4]
[6,5,2,4,7,1,3,8]=>[1,1,3,3]
[6,5,7,4,1,8,2,3]=>[1,2,1,2,2]
[7,6,4,5,1,8,2,3]=>[1,1,2,2,2]
[8,6,4,1,3,7,2,5]=>[1,1,1,3,2]
[6,4,3,1,8,2,5,7]=>[1,1,1,2,3]
[7,4,1,2,8,3,5,6]=>[1,1,3,3]
[4,8,1,3,5,7,2,6]=>[2,4,2]
[7,8,4,1,3,6,2,5]=>[2,1,3,2]
[6,5,8,1,3,7,2,4]=>[1,2,3,2]
[5,3,6,1,8,2,4,7]=>[1,2,2,3]
[8,3,1,7,2,4,5,6]=>[1,1,2,4]
[3,1,8,5,4,7,6,2]=>[1,2,1,2,1,1]
[4,1,5,8,3,7,6,2]=>[1,3,2,1,1]
[4,1,5,3,8,7,6,2]=>[1,2,2,1,1,1]
[4,5,1,8,2,7,6,3]=>[2,2,2,1,1]
[4,8,5,3,1,7,6,2]=>[2,1,1,2,1,1]
[4,5,2,8,1,7,6,3]=>[2,2,2,1,1]
[4,5,2,1,8,7,6,3]=>[2,1,2,1,1,1]
[5,6,2,7,8,1,4,3]=>[2,3,2,1]
[4,6,2,8,7,1,5,3]=>[2,2,1,2,1]
[4,8,6,3,7,1,5,2]=>[2,1,2,2,1]
[4,8,6,3,7,5,1,2]=>[2,1,2,1,2]
[4,6,8,2,7,5,1,3]=>[3,2,1,2]
[4,6,2,8,7,5,1,3]=>[2,2,1,1,2]
[5,6,2,7,4,1,8,3]=>[2,2,1,2,1]
[5,6,7,2,3,1,8,4]=>[3,2,2,1]
[5,6,7,2,8,3,1,4]=>[3,2,1,2]
[5,6,7,2,1,8,3,4]=>[3,1,2,2]
[5,6,7,2,1,3,8,4]=>[3,1,3,1]
[5,6,1,7,8,2,4,3]=>[2,3,2,1]
[5,6,1,7,2,4,8,3]=>[2,2,3,1]
[5,1,6,7,8,3,4,2]=>[1,4,2,1]
[4,1,6,8,7,3,5,2]=>[1,3,1,2,1]
[3,1,8,6,7,5,4,2]=>[1,2,2,1,1,1]
[4,1,6,8,7,5,3,2]=>[1,3,1,1,1,1]
[5,1,6,7,4,8,3,2]=>[1,3,2,1,1]
[5,6,1,7,8,4,2,3]=>[2,3,1,2]
[4,6,8,1,7,5,2,3]=>[3,2,1,2]
[4,8,6,1,7,5,3,2]=>[2,1,2,1,1,1]
[5,6,7,1,8,3,2,4]=>[3,2,1,2]
[5,6,7,1,3,8,2,4]=>[3,3,2]
[5,6,7,1,3,2,8,4]=>[3,2,2,1]
[5,6,7,3,1,2,8,4]=>[3,1,3,1]
[5,6,7,3,8,1,2,4]=>[3,2,3]
[5,6,8,7,4,2,1,3]=>[3,1,1,1,2]
[5,6,7,3,8,2,1,4]=>[3,2,1,2]
[7,4,6,2,3,5,1,8]=>[1,2,3,2]
[1,4,8,6,3,2,5,7]=>[3,1,1,3]
[7,4,1,6,3,8,5,2]=>[1,1,2,2,1,1]
[7,6,3,1,5,8,4,2]=>[1,1,1,3,1,1]
[6,4,2,5,7,3,1,8]=>[1,1,3,1,2]
[4,2,5,7,6,3,1,8]=>[1,3,1,1,2]
[7,4,5,6,1,8,3,2]=>[1,3,2,1,1]
[4,1,5,8,6,3,2,7]=>[1,3,1,1,2]
[3,2,7,6,1,8,5,4]=>[1,2,1,2,1,1]
[4,7,5,1,6,8,2,3]=>[2,1,3,2]
[8,6,5,1,2,7,4,3]=>[1,1,1,3,1,1]
[3,2,5,1,4,8,7,6]=>[1,2,3,1,1]
[8,5,4,1,3,2,7,6]=>[1,1,1,2,2,1]
[1,4,2,3,6,8,7,5]=>[2,4,1,1]
[5,4,8,3,7,1,6,2]=>[1,2,2,2,1]
[4,7,1,8,2,5,3,6]=>[2,2,2,2]
[6,4,1,8,5,3,7,2]=>[1,1,2,1,2,1]
[8,4,6,1,3,5,2,7]=>[1,2,3,2]
[3,2,5,4,7,8,1,6]=>[1,2,3,2]
[5,2,4,3,7,8,1,6]=>[1,2,3,2]
[8,1,6,7,2,5,3,4]=>[1,3,2,2]
[3,1,7,6,5,8,2,4]=>[1,2,1,2,2]
[1,2,7,5,6,8,3,4]=>[3,3,2]
[6,1,4,7,2,8,3,5]=>[1,3,2,2]
[3,2,1,7,6,8,4,5]=>[1,1,2,2,2]
[3,2,8,6,4,7,1,5]=>[1,2,1,2,2]
[7,8,4,6,3,2,1,5]=>[2,2,1,1,2]
[1,8,6,5,3,7,2,4]=>[2,1,1,2,2]
[8,2,5,3,6,7,1,4]=>[1,2,3,2]
[3,8,5,2,7,6,1,4]=>[2,1,2,1,2]
[4,7,5,3,1,8,6,2]=>[2,1,1,2,1,1]
[4,5,3,6,8,1,7,2]=>[2,3,2,1]
[3,5,2,6,1,8,7,4]=>[2,2,2,1,1]
[1,6,3,5,7,2,8,4]=>[2,3,2,1]
[1,5,4,6,7,8,2,3]=>[2,4,2]
[8,4,6,5,7,2,1,3]=>[1,2,2,1,2]
[7,4,5,2,6,8,1,3]=>[1,2,3,2]
[5,4,2,6,8,7,1,3]=>[1,1,3,1,2]
[7,8,4,3,1,2,6,5]=>[2,1,1,3,1]
[6,5,1,4,3,2,8,7]=>[1,1,2,1,2,1]
[2,6,5,1,4,7,3,8]=>[2,1,3,2]
[3,6,4,5,2,1,8,7]=>[2,2,1,2,1]
[5,7,4,1,3,8,6,2]=>[2,1,3,1,1]
[7,5,4,2,3,8,1,6]=>[1,1,1,3,2]
[5,2,6,7,3,1,4,8]=>[1,3,1,3]
[2,4,3,8,6,1,5,7]=>[2,2,1,3]
[7,8,1,3,5,6,2,4]=>[2,4,2]
[7,8,3,1,5,6,2,4]=>[2,1,3,2]
[7,1,3,8,5,6,2,4]=>[1,3,2,2]
[1,7,8,3,5,6,2,4]=>[3,3,2]
[5,1,7,8,3,4,6,2]=>[1,3,3,1]
[1,5,7,8,3,4,6,2]=>[4,3,1]
[3,7,1,5,8,6,2,4]=>[2,3,1,2]
[1,3,7,8,2,5,6,4]=>[4,3,1]
[3,1,7,8,5,2,6,4]=>[1,3,1,2,1]
[1,3,7,5,8,2,6,4]=>[3,2,2,1]
[3,1,7,5,8,2,6,4]=>[1,2,2,2,1]
[3,5,7,1,8,4,6,2]=>[3,2,2,1]
[3,5,7,8,1,4,6,2]=>[4,3,1]
[5,3,7,8,4,6,1,2]=>[1,3,2,2]
[5,3,7,8,4,1,6,2]=>[1,3,1,2,1]
[5,3,7,8,1,4,6,2]=>[1,3,3,1]
[5,3,7,1,8,4,6,2]=>[1,2,2,2,1]
[1,5,3,7,8,4,2,6]=>[2,3,1,2]
[5,1,3,7,8,4,2,6]=>[1,4,1,2]
[3,6,2,1,4,5,8,7]=>[2,1,4,1]
[4,6,2,5,1,3,8,7]=>[2,2,3,1]
[6,4,2,5,1,3,8,7]=>[1,1,2,3,1]
[8,6,1,7,3,2,4,5]=>[1,1,2,1,3]
[2,5,8,1,7,3,4,6]=>[3,2,3]
[6,8,2,7,3,1,4,5]=>[2,2,1,3]
[6,8,2,3,7,1,4,5]=>[2,3,3]
[8,6,2,7,4,5,1,3]=>[1,1,2,2,2]
[5,2,8,1,7,3,4,6]=>[1,2,2,3]
[4,2,3,8,1,5,6,7]=>[1,3,4]
[5,2,8,3,7,1,4,6]=>[1,2,2,3]
[5,2,8,4,6,1,3,7]=>[1,2,2,3]
[2,1,5,8,4,3,6,7]=>[1,3,1,3]
[5,8,3,2,7,1,4,6]=>[2,1,2,3]
[4,1,3,8,2,5,6,7]=>[1,3,4]
[3,5,8,2,7,1,4,6]=>[3,2,3]
[4,5,8,2,6,1,3,7]=>[3,2,3]
[2,6,8,3,7,1,4,5]=>[3,2,3]
[5,1,8,3,7,2,4,6]=>[1,2,2,3]
[5,1,8,4,6,2,3,7]=>[1,2,2,3]
[5,8,4,1,6,2,3,7]=>[2,1,2,3]
[4,5,8,1,6,2,3,7]=>[3,2,3]
[5,4,8,1,6,2,3,7]=>[1,2,2,3]
[4,8,5,1,6,2,3,7]=>[2,1,2,3]
[2,1,5,4,8,3,6,7]=>[1,2,2,3]
[2,4,3,8,1,5,6,7]=>[2,2,4]
[3,1,8,4,2,5,6,7]=>[1,2,1,4]
[3,8,4,2,1,5,6,7]=>[2,1,1,4]
[2,3,8,4,1,5,6,7]=>[3,1,4]
[3,4,2,8,1,5,6,7]=>[2,2,4]
[3,8,5,2,7,1,4,6]=>[2,1,2,3]
[4,8,5,2,6,1,3,7]=>[2,1,2,3]
[2,1,4,8,5,3,6,7]=>[1,3,1,3]
[3,2,8,4,1,5,6,7]=>[1,2,1,4]
[2,8,4,3,1,5,6,7]=>[2,1,1,4]
[4,1,7,5,6,2,8,3]=>[1,2,2,2,1]
[5,7,4,3,8,1,6,2]=>[2,1,2,2,1]
[5,7,4,3,8,2,6,1]=>[2,1,2,2,1]
[3,8,4,2,6,7,5,1]=>[2,1,3,1,1]
[3,8,4,1,6,7,5,2]=>[2,1,3,1,1]
[6,1,7,5,2,8,4,3]=>[1,2,1,2,1,1]
[5,6,4,3,2,8,1,7]=>[2,1,1,2,2]
[2,6,7,5,3,8,4,1]=>[3,1,2,1,1]
[6,7,4,8,2,5,3,1]=>[2,2,2,1,1]
[2,1,6,7,5,3,8,4]=>[1,3,1,2,1]
[3,8,4,2,1,6,7,5]=>[2,1,1,3,1]
[5,7,4,3,8,2,1,6]=>[2,1,2,1,2]
[6,7,4,8,1,2,5,3]=>[2,2,3,1]
[6,7,5,8,1,2,4,3]=>[2,2,3,1]
[6,7,4,8,3,1,2,5]=>[2,2,1,3]
[3,4,8,1,2,5,7,6]=>[3,4,1]
[6,1,3,4,8,2,5,7]=>[1,4,3]
[6,2,3,4,8,1,5,7]=>[1,4,3]
[3,4,8,2,1,5,7,6]=>[3,1,3,1]
[6,7,5,8,2,4,3,1]=>[2,2,2,1,1]
[6,7,5,8,3,1,4,2]=>[2,2,1,2,1]
[3,4,8,1,5,7,6,2]=>[3,3,1,1]
[2,5,7,6,1,4,8,3]=>[3,1,3,1]
[6,7,4,8,2,3,5,1]=>[2,2,3,1]
[6,7,4,8,1,3,5,2]=>[2,2,3,1]
[2,6,7,5,1,3,8,4]=>[3,1,3,1]
[6,3,1,4,8,2,5,7]=>[1,1,3,3]
[6,7,4,8,1,3,2,5]=>[2,2,2,2]
[6,7,5,8,4,1,3,2]=>[2,2,1,2,1]
[6,7,4,8,2,1,3,5]=>[2,2,1,3]
[6,7,4,8,1,2,3,5]=>[2,2,4]
[1,5,6,3,4,8,2,7]=>[3,3,2]
[1,4,3,6,5,8,2,7]=>[2,2,2,2]
[8,1,3,4,7,2,6,5]=>[1,4,2,1]
[5,1,7,3,4,8,2,6]=>[1,2,3,2]
[6,7,8,2,3,5,4,1]=>[3,3,1,1]
[5,8,6,2,3,7,4,1]=>[2,1,3,1,1]
[2,8,3,4,7,5,6,1]=>[2,3,2,1]
[1,8,3,4,7,6,2,5]=>[2,3,1,2]
[8,7,2,3,6,5,4,1]=>[1,1,3,1,1,1]
[3,8,1,7,5,2,6,4]=>[2,2,1,2,1]
[4,8,1,6,7,2,5,3]=>[2,3,2,1]
[2,1,3,8,4,6,5,7]=>[1,3,2,2]
[8,2,1,7,4,3,6,5]=>[1,1,2,1,2,1]
[1,3,2,8,5,4,6,7]=>[2,2,1,3]
[8,3,1,5,7,2,6,4]=>[1,1,3,2,1]
[8,4,5,1,7,2,6,3]=>[1,2,2,2,1]
[1,5,6,8,7,4,2,3]=>[4,1,1,2]
[8,4,5,7,6,3,2,1]=>[1,3,1,1,1,1]
[1,4,8,5,7,6,2,3]=>[3,2,1,2]
[2,4,8,5,7,3,6,1]=>[3,2,2,1]
[4,3,8,6,5,7,2,1]=>[1,2,1,2,1,1]
[6,7,2,8,5,3,4,1]=>[2,2,1,2,1]
[5,2,7,8,6,3,4,1]=>[1,3,1,2,1]
[4,2,8,6,7,3,5,1]=>[1,2,2,2,1]
[3,2,8,7,5,4,6,1]=>[1,2,1,1,2,1]
[3,1,8,7,5,6,2,4]=>[1,2,1,2,2]
[4,1,8,6,7,5,2,3]=>[1,2,2,1,2]
[5,1,7,8,6,4,2,3]=>[1,3,1,1,2]
[6,7,1,8,5,4,2,3]=>[2,2,1,1,2]
[7,8,3,2,6,1,4,5]=>[2,1,2,3]
[3,4,8,2,6,1,7,5]=>[3,2,2,1]
[7,8,4,1,5,6,3,2]=>[2,1,3,1,1]
[7,8,1,4,5,6,3,2]=>[2,4,1,1]
[7,8,1,2,6,3,4,5]=>[2,3,3]
[7,8,5,1,4,6,3,2]=>[2,1,3,1,1]
[7,8,4,5,1,6,3,2]=>[2,2,2,1,1]
[5,3,8,4,1,6,7,2]=>[1,2,1,3,1]
[6,2,4,8,1,5,3,7]=>[1,3,2,2]
[3,4,8,5,1,6,7,2]=>[3,1,3,1]
[3,5,8,1,4,6,7,2]=>[3,4,1]
[1,4,8,2,6,3,7,5]=>[3,2,2,1]
[5,3,8,1,4,6,7,2]=>[1,2,4,1]
[4,2,6,8,1,5,3,7]=>[1,3,2,2]
[7,4,2,8,1,5,3,6]=>[1,1,2,2,2]
[6,1,7,5,8,4,3,2]=>[1,2,2,1,1,1]
[6,2,1,8,4,5,3,7]=>[1,1,2,2,2]
[1,2,7,8,5,3,4,6]=>[4,1,3]
[6,3,7,8,5,4,1,2]=>[1,3,1,1,2]
[6,1,5,7,8,4,3,2]=>[1,4,1,1,1]
[1,7,5,6,8,4,3,2]=>[2,3,1,1,1]
[3,1,8,4,5,6,7,2]=>[1,2,4,1]
[2,1,4,8,6,5,3,7]=>[1,3,1,1,2]
[2,4,1,8,6,5,3,7]=>[2,2,1,1,2]
[4,2,1,8,6,5,3,7]=>[1,1,2,1,1,2]
[3,2,7,8,5,1,4,6]=>[1,3,1,3]
[2,3,7,8,5,1,4,6]=>[4,1,3]
[2,7,3,8,5,1,4,6]=>[2,2,1,3]
[3,6,2,8,5,1,4,7]=>[2,2,1,3]
[4,1,2,8,7,5,3,6]=>[1,3,1,1,2]
[1,4,2,8,7,5,3,6]=>[2,2,1,1,2]
[7,3,6,8,5,4,1,2]=>[1,3,1,1,2]
[7,2,1,8,5,3,4,6]=>[1,1,2,1,3]
[1,2,6,8,4,5,3,7]=>[4,2,2]
[7,1,6,5,8,4,3,2]=>[1,2,2,1,1,1]
[6,5,7,1,8,4,3,2]=>[1,2,2,1,1,1]
[5,7,6,1,8,4,3,2]=>[2,1,2,1,1,1]
[6,7,1,5,8,4,3,2]=>[2,3,1,1,1]
[6,7,3,8,5,4,1,2]=>[2,2,1,1,2]
[7,1,2,8,4,5,3,6]=>[1,3,2,2]
[7,6,1,5,8,4,3,2]=>[1,1,3,1,1,1]
[7,5,6,1,8,4,3,2]=>[1,2,2,1,1,1]
[7,1,6,5,3,2,4,8]=>[1,2,1,1,3]
[1,8,7,5,3,2,4,6]=>[2,1,1,1,3]
[1,8,7,4,2,5,3,6]=>[2,1,1,2,2]
[8,7,4,2,5,3,6,1]=>[1,1,1,2,2,1]
[7,1,6,4,2,5,3,8]=>[1,2,1,2,2]
[2,6,5,4,7,1,3,8]=>[2,1,2,3]
[7,1,5,3,6,4,2,8]=>[1,2,2,1,2]
[5,3,7,1,6,4,2,8]=>[1,2,2,1,2]
[5,3,6,4,2,7,1,8]=>[1,2,1,2,2]
[1,5,3,8,7,4,2,6]=>[2,2,1,1,2]
[7,4,2,8,6,3,5,1]=>[1,1,2,1,2,1]
[5,3,6,1,8,7,4,2]=>[1,2,2,1,1,1]
[6,1,5,3,8,7,4,2]=>[1,2,2,1,1,1]
[2,8,7,5,4,6,1,3]=>[2,1,1,2,2]
[2,3,1,8,7,5,4,6]=>[2,2,1,1,2]
[5,3,8,7,4,2,1,6]=>[1,2,1,1,1,2]
[7,4,2,1,8,6,3,5]=>[1,1,1,2,1,2]
[8,6,3,5,7,4,2,1]=>[1,1,3,1,1,1]
[1,8,6,3,5,7,4,2]=>[2,1,3,1,1]
[6,3,8,5,2,1,7,4]=>[1,2,1,1,2,1]
[8,6,3,7,4,2,1,5]=>[1,1,2,1,1,2]
[2,8,6,4,7,5,1,3]=>[2,1,2,1,2]
[5,1,8,6,3,7,4,2]=>[1,2,1,2,1,1]
[6,3,7,4,1,8,5,2]=>[1,2,1,2,1,1]
[8,5,2,6,3,7,4,1]=>[1,1,2,2,1,1]
[6,1,8,7,4,2,5,3]=>[1,2,1,1,2,1]
[8,6,3,7,4,2,5,1]=>[1,1,2,1,2,1]
[1,8,6,3,2,4,7,5]=>[2,1,1,3,1]
[8,6,3,2,4,7,5,1]=>[1,1,1,3,1,1]
[7,5,1,8,6,3,2,4]=>[1,1,2,1,1,2]
[6,1,8,7,5,3,2,4]=>[1,2,1,1,1,2]
[4,3,2,8,7,6,1,5]=>[1,1,2,1,1,2]
[2,4,5,1,3,8,7,6]=>[3,3,1,1]
[7,5,8,6,3,2,4,1]=>[1,2,1,1,2,1]
[1,7,5,8,6,3,2,4]=>[2,2,1,1,2]
[1,7,4,2,5,8,6,3]=>[2,1,3,1,1]
[8,6,3,1,7,4,2,5]=>[1,1,1,2,1,2]
[8,7,4,2,5,3,1,6]=>[1,1,1,2,1,2]
[5,3,1,8,7,4,2,6]=>[1,1,2,1,1,2]
[4,1,8,7,5,3,2,6]=>[1,2,1,1,1,2]
[2,8,6,4,1,3,7,5]=>[2,1,1,3,1]
[4,1,8,6,3,2,7,5]=>[1,2,1,1,2,1]
[7,4,2,8,6,3,1,5]=>[1,1,2,1,1,2]
[6,3,1,8,5,2,7,4]=>[1,1,2,1,2,1]
[8,5,2,6,3,1,7,4]=>[1,1,2,1,2,1]
[7,4,8,5,2,6,3,1]=>[1,2,1,2,1,1]
[1,8,5,2,7,4,6,3]=>[2,1,2,2,1]
[8,5,2,7,4,6,3,1]=>[1,1,2,2,1,1]
[7,4,6,3,1,8,5,2]=>[1,2,1,2,1,1]
[6,3,1,7,4,8,5,2]=>[1,1,2,2,1,1]
[8,6,3,1,5,7,4,2]=>[1,1,1,3,1,1]
[4,1,7,5,8,6,3,2]=>[1,2,2,1,1,1]
[2,3,1,7,5,8,6,4]=>[2,2,2,1,1]
[7,4,8,5,2,1,6,3]=>[1,2,1,1,2,1]
[8,5,2,1,7,4,6,3]=>[1,1,1,2,2,1]
[1,7,4,6,3,8,5,2]=>[2,2,2,1,1]
[3,6,5,2,1,4,8,7]=>[2,1,1,3,1]
[3,5,6,2,1,4,8,7]=>[3,1,3,1]
[3,5,7,8,1,4,2,6]=>[4,2,2]
[4,1,8,5,7,3,2,6]=>[1,2,2,1,2]
[4,1,7,5,8,3,2,6]=>[1,2,2,1,2]
[2,1,5,8,7,4,3,6]=>[1,3,1,1,2]
[2,1,5,7,8,4,3,6]=>[1,4,1,2]
[5,1,7,4,8,3,2,6]=>[1,2,2,1,2]
[4,7,2,8,3,6,1,5]=>[2,2,2,2]
[4,6,2,7,3,1,8,5]=>[2,2,1,2,1]
[3,7,8,2,4,1,6,5]=>[3,2,2,1]
[3,8,7,2,4,1,6,5]=>[2,1,2,2,1]
[3,8,6,2,4,1,7,5]=>[2,1,2,2,1]
[6,2,8,4,1,7,3,5]=>[1,2,1,2,2]
[7,3,4,8,1,6,2,5]=>[1,3,2,2]
[6,3,4,8,1,7,2,5]=>[1,3,2,2]
[5,3,4,8,1,2,7,6]=>[1,3,3,1]
[4,3,5,8,1,2,7,6]=>[1,3,3,1]
[1,8,5,4,2,3,7,6]=>[2,1,1,3,1]
[3,5,4,8,1,2,7,6]=>[2,2,3,1]
[4,5,3,8,1,2,7,6]=>[2,2,3,1]
[6,4,3,8,1,7,2,5]=>[1,1,2,2,2]
[7,4,3,8,1,6,2,5]=>[1,1,2,2,2]
[6,5,3,8,7,1,2,4]=>[1,1,2,1,3]
[5,6,3,8,7,1,2,4]=>[2,2,1,3]
[4,6,3,8,1,7,2,5]=>[2,2,2,2]
[2,6,8,4,1,7,3,5]=>[3,1,2,2]
[1,8,7,4,2,6,3,5]=>[2,1,1,2,2]
[5,7,3,8,6,1,2,4]=>[2,2,1,3]
[3,7,5,8,6,1,2,4]=>[2,2,1,3]
[2,7,8,5,6,1,3,4]=>[3,2,3]
[1,8,7,5,6,2,3,4]=>[2,1,2,3]
[2,6,8,5,7,1,3,4]=>[3,2,3]
[5,3,6,8,7,1,2,4]=>[1,3,1,3]
[6,3,5,8,7,1,2,4]=>[1,3,1,3]
[7,2,8,5,6,1,3,4]=>[1,2,2,3]
[5,2,8,6,7,1,3,4]=>[1,2,2,3]
[1,8,3,2,7,6,4,5]=>[2,1,2,1,2]
[5,2,8,7,6,1,3,4]=>[1,2,1,1,3]
[6,2,8,7,5,1,3,4]=>[1,2,1,1,3]
[3,4,7,8,1,6,2,5]=>[4,2,2]
[1,8,5,7,6,2,3,4]=>[2,2,1,3]
[2,5,8,7,6,1,3,4]=>[3,1,1,3]
[7,4,6,5,8,1,2,3]=>[1,2,2,3]
[3,6,7,8,5,1,2,4]=>[4,1,3]
[2,6,8,7,5,1,3,4]=>[3,1,1,3]
[1,8,6,7,5,2,3,4]=>[2,2,1,3]
[2,7,8,6,5,1,3,4]=>[3,1,1,3]
[5,7,6,4,8,1,2,3]=>[2,1,2,3]
[6,3,8,7,5,1,2,4]=>[1,2,1,1,3]
[2,8,7,4,1,3,5,6]=>[2,1,1,4]
[5,4,8,7,1,3,2,6]=>[1,2,1,2,2]
[4,8,6,1,3,2,5,7]=>[2,1,2,3]
[5,4,2,7,6,8,1,3]=>[1,1,2,2,2]
[2,8,7,1,4,5,3,6]=>[2,1,3,2]
[4,2,1,8,7,3,5,6]=>[1,1,2,1,3]
[5,1,6,3,2,8,7,4]=>[1,2,1,2,1,1]
[4,6,1,8,7,3,2,5]=>[2,2,1,1,2]
[8,7,2,3,5,4,1,6]=>[1,1,3,1,2]
[5,3,1,4,8,7,2,6]=>[1,1,3,1,2]
[4,3,5,2,8,7,1,6]=>[1,2,2,1,2]
[3,4,2,8,6,1,5,7]=>[2,2,1,3]
[3,7,6,8,1,5,2,4]=>[2,2,2,2]
[8,1,4,2,3,6,7,5]=>[1,2,4,1]
[3,7,2,1,8,6,4,5]=>[2,1,2,1,2]
[2,8,6,1,7,3,5,4]=>[2,1,2,2,1]
[1,7,6,3,5,8,2,4]=>[2,1,3,2]
[3,7,5,1,6,8,2,4]=>[2,1,3,2]
[3,6,5,8,1,4,7,2]=>[2,2,3,1]
[8,1,5,6,4,7,2,3]=>[1,3,2,2]
[3,6,7,4,1,8,2,5]=>[3,1,2,2]
[1,7,4,6,8,2,5,3]=>[2,3,2,1]
[7,5,8,2,6,3,1,4]=>[1,2,2,1,2]
[2,7,1,6,5,4,8,3]=>[2,2,1,2,1]
[7,3,2,6,1,8,5,4]=>[1,1,2,2,1,1]
[6,4,7,2,3,1,8,5]=>[1,2,2,2,1]
[5,3,1,8,4,6,2,7]=>[1,1,2,2,2]
[3,8,1,6,7,4,2,5]=>[2,3,1,2]
[2,7,4,3,6,8,1,5]=>[2,1,3,2]
[2,8,4,6,1,5,3,7]=>[2,2,2,2]
[8,4,1,6,3,2,5,7]=>[1,1,2,1,3]
[4,7,3,8,5,2,1,6]=>[2,2,1,1,2]
[3,1,7,4,8,5,2,6]=>[1,2,2,1,2]
[7,4,1,6,3,2,8,5]=>[1,1,2,1,2,1]
[3,8,6,2,7,4,1,5]=>[2,1,2,1,2]
[7,3,1,4,5,2,8,6]=>[1,1,3,2,1]
[6,1,4,8,5,3,2,7]=>[1,3,1,1,2]
[8,1,2,4,6,7,5,3]=>[1,5,1,1]
[8,1,3,6,7,5,4,2]=>[1,4,1,1,1]
[7,5,2,3,8,6,1,4]=>[1,1,3,1,2]
[8,6,2,4,1,3,7,5]=>[1,1,2,3,1]
[4,7,5,1,8,6,3,2]=>[2,1,2,1,1,1]
[4,7,3,2,8,5,6,1]=>[2,1,2,2,1]
[8,4,5,7,6,1,3,2]=>[1,3,1,2,1]
[7,5,8,4,2,3,6,1]=>[1,2,1,3,1]
[3,8,4,6,1,7,5,2]=>[2,2,2,1,1]
[3,7,4,6,5,2,8,1]=>[2,2,1,2,1]
[4,2,7,6,1,5,8,3]=>[1,2,1,3,1]
[8,3,1,4,5,7,6,2]=>[1,1,4,1,1]
[3,5,1,6,8,4,7,2]=>[2,3,2,1]
[6,1,5,7,3,8,4,2]=>[1,3,2,1,1]
[5,8,4,7,3,2,6,1]=>[2,2,1,2,1]
[7,2,6,5,8,4,1,3]=>[1,2,2,1,2]
[8,3,2,5,1,6,7,4]=>[1,1,2,3,1]
[2,6,8,3,7,4,1,5]=>[3,2,1,2]
[8,1,5,6,4,7,3,2]=>[1,3,2,1,1]
[2,5,8,1,6,4,7,3]=>[3,2,2,1]
[7,4,1,8,3,2,6,5]=>[1,1,2,1,2,1]
[8,3,7,4,2,1,6,5]=>[1,2,1,1,2,1]
[5,2,6,8,3,1,7,4]=>[1,3,1,2,1]
[3,6,5,8,4,1,7,2]=>[2,2,1,2,1]
[7,3,6,1,8,4,5,2]=>[1,2,2,2,1]
[8,2,7,3,4,6,5,1]=>[1,2,3,1,1]
[7,3,8,2,5,6,4,1]=>[1,2,3,1,1]
[5,7,3,1,6,4,8,2]=>[2,1,2,2,1]
[6,1,3,2,4,8,7,5]=>[1,2,3,1,1]
[8,7,4,2,3,6,1,5]=>[1,1,1,3,2]
[8,7,1,5,4,2,3,6]=>[1,1,2,1,3]
[3,7,1,5,2,8,6,4]=>[2,2,2,1,1]
[8,7,2,5,4,1,3,6]=>[1,1,2,1,3]
[8,7,2,5,3,1,4,6]=>[1,1,2,1,3]
[5,2,8,7,1,4,3,6]=>[1,2,1,2,2]
[7,1,8,6,2,4,3,5]=>[1,2,1,2,2]
[8,1,6,2,7,5,3,4]=>[1,2,2,1,2]
[7,1,6,2,8,5,3,4]=>[1,2,2,1,2]
[6,3,4,1,7,2,8,5]=>[1,2,2,2,1]
[7,2,4,3,5,1,8,6]=>[1,2,2,2,1]
[5,1,7,2,3,8,6,4]=>[1,2,3,1,1]
[8,2,3,5,1,7,6,4]=>[1,3,2,1,1]
[7,6,3,1,4,8,2,5]=>[1,1,1,3,2]
[6,1,8,2,7,5,3,4]=>[1,2,2,1,2]
[7,2,8,1,6,5,3,4]=>[1,2,2,1,2]
[7,2,6,4,3,8,1,5]=>[1,2,1,2,2]
[5,1,7,4,3,8,2,6]=>[1,2,1,2,2]
[5,3,1,7,4,8,2,6]=>[1,1,2,2,2]
[7,4,8,2,1,5,3,6]=>[1,2,1,2,2]
[8,2,4,1,6,3,7,5]=>[1,2,2,2,1]
[8,2,7,5,1,6,4,3]=>[1,2,1,2,1,1]
[6,1,7,3,2,8,5,4]=>[1,2,1,2,1,1]
[4,7,2,1,6,3,8,5]=>[2,1,2,2,1]
[6,2,1,5,3,8,4,7]=>[1,1,2,2,2]
[5,3,1,6,2,8,4,7]=>[1,1,2,2,2]
[6,1,5,2,8,4,3,7]=>[1,2,2,1,2]
[7,4,3,8,1,5,2,6]=>[1,1,2,2,2]
[7,4,8,1,5,3,2,6]=>[1,2,2,1,2]
[6,1,5,3,2,8,4,7]=>[1,2,1,2,2]
[6,3,2,8,4,1,5,7]=>[1,1,2,1,3]
[7,3,4,2,8,5,1,6]=>[1,2,2,1,2]
[7,1,6,3,4,2,8,5]=>[1,2,2,2,1]
[8,5,1,3,7,4,2,6]=>[1,1,3,1,2]
[3,8,6,1,5,2,7,4]=>[2,1,2,2,1]
[8,6,1,3,7,5,2,4]=>[1,1,3,1,2]
[4,8,5,6,1,7,3,2]=>[2,2,2,1,1]
[6,7,1,3,8,5,2,4]=>[2,3,1,2]
[3,6,7,1,5,2,8,4]=>[3,2,2,1]
[7,1,3,8,4,2,6,5]=>[1,3,1,2,1]
[5,6,2,7,1,3,8,4]=>[2,2,3,1]
[5,6,2,8,1,3,7,4]=>[2,2,3,1]
[6,1,8,3,7,5,2,4]=>[1,2,2,1,2]
[7,4,2,1,5,8,3,6]=>[1,1,1,3,2]
[7,4,1,5,8,3,2,6]=>[1,1,3,1,2]
[7,3,2,6,4,8,1,5]=>[1,1,2,2,2]
[6,4,2,7,3,8,1,5]=>[1,1,2,2,2]
[5,1,8,3,7,4,2,6]=>[1,2,2,1,2]
[7,4,8,3,1,5,2,6]=>[1,2,1,2,2]
[5,2,1,7,4,8,3,6]=>[1,1,2,2,2]
[6,1,8,4,5,2,7,3]=>[1,2,2,2,1]
[7,1,6,4,5,2,8,3]=>[1,2,2,2,1]
[3,5,2,7,1,6,8,4]=>[2,2,3,1]
[4,5,7,3,1,6,8,2]=>[3,1,3,1]
[4,5,7,2,8,6,1,3]=>[3,2,1,2]
[3,5,1,7,2,6,8,4]=>[2,2,3,1]
[4,5,7,2,8,1,3,6]=>[3,2,3]
[4,6,7,2,1,5,8,3]=>[3,1,3,1]
[4,6,7,1,3,8,5,2]=>[3,3,1,1]
[3,6,1,5,7,8,4,2]=>[2,4,1,1]
[4,6,7,1,5,8,3,2]=>[3,3,1,1]
[6,1,3,7,4,8,5,2]=>[1,3,2,1,1]
[3,2,1,7,4,8,5,6]=>[1,1,2,2,2]
[4,1,5,2,7,6,3,8]=>[1,2,2,1,2]
[2,5,1,3,7,6,4,8]=>[2,3,1,2]
[2,5,1,4,3,8,6,7]=>[2,2,2,2]
[3,7,2,1,5,8,6,4]=>[2,1,3,1,1]
[6,2,7,1,4,8,5,3]=>[1,2,3,1,1]
[3,7,4,2,1,8,5,6]=>[2,1,1,2,2]
[7,2,5,3,1,8,6,4]=>[1,2,1,2,1,1]
[7,5,1,4,2,8,6,3]=>[1,1,2,2,1,1]
[7,5,4,1,3,8,6,2]=>[1,1,1,3,1,1]
[5,3,2,1,7,6,4,8]=>[1,1,1,2,1,2]
[6,3,2,8,1,5,7,4]=>[1,1,2,3,1]
[7,4,3,2,8,1,6,5]=>[1,1,1,2,2,1]
[7,6,2,4,8,3,5,1]=>[1,1,3,2,1]
[7,3,6,4,8,1,5,2]=>[1,2,2,2,1]
[2,7,5,3,8,1,4,6]=>[2,1,2,3]
[1,8,5,3,6,4,2,7]=>[2,1,2,1,2]
[8,6,2,3,7,5,4,1]=>[1,1,3,1,1,1]
[8,6,3,2,7,5,4,1]=>[1,1,1,2,1,1,1]
[8,3,2,7,1,6,4,5]=>[1,1,2,2,2]
[7,2,6,1,5,4,3,8]=>[1,2,2,1,2]
[8,5,7,4,3,6,2,1]=>[1,2,1,2,1,1]
[8,5,7,2,4,6,3,1]=>[1,2,3,1,1]
[8,4,6,7,1,3,2,5]=>[1,3,2,2]
[2,8,5,6,1,4,3,7]=>[2,2,2,2]
[7,2,6,8,4,1,5,3]=>[1,3,1,2,1]
[7,6,4,8,3,2,5,1]=>[1,1,2,1,2,1]
[6,5,8,1,4,2,7,3]=>[1,2,2,2,1]
[6,5,8,4,1,3,7,2]=>[1,2,1,3,1]
[5,4,8,3,2,1,7,6]=>[1,2,1,1,2,1]
[4,3,7,2,1,6,5,8]=>[1,2,1,2,2]
[2,5,8,1,4,3,7,6]=>[3,2,2,1]
[3,6,8,2,1,5,7,4]=>[3,1,3,1]
[5,7,4,8,1,3,6,2]=>[2,2,3,1]
[5,7,1,4,8,2,6,3]=>[2,3,2,1]
[2,7,4,1,8,3,6,5]=>[2,1,2,2,1]
[3,5,1,8,4,2,7,6]=>[2,2,1,2,1]
[4,1,5,7,3,6,2,8]=>[1,3,2,2]
[4,2,5,8,3,1,7,6]=>[1,3,1,2,1]
[6,1,2,7,8,3,5,4]=>[1,4,2,1]
[5,3,1,8,6,4,2,7]=>[1,1,2,1,1,2]
[3,1,8,4,7,5,2,6]=>[1,2,2,1,2]
[4,2,8,7,3,5,1,6]=>[1,2,1,2,2]
[4,8,1,7,6,2,3,5]=>[2,2,1,3]
[6,8,1,4,7,5,2,3]=>[2,3,1,2]
[7,3,8,1,6,4,2,5]=>[1,2,2,1,2]
[4,7,8,1,5,3,2,6]=>[3,2,1,2]
[7,1,8,6,2,5,3,4]=>[1,2,1,2,2]
[5,8,7,1,3,6,4,2]=>[2,1,3,1,1]
[3,8,7,2,1,6,4,5]=>[2,1,1,2,2]
[2,8,7,1,6,3,5,4]=>[2,1,2,2,1]
[3,7,6,1,5,4,2,8]=>[2,1,2,1,2]
[4,8,7,6,1,3,5,2]=>[2,1,1,3,1]
[5,8,7,2,6,1,4,3]=>[2,1,2,2,1]
[6,8,1,7,5,2,4,3]=>[2,2,1,2,1]
[7,3,8,6,5,1,2,4]=>[1,2,1,1,3]
[5,7,8,4,3,1,2,6]=>[3,1,1,3]
[5,8,6,4,3,2,1,7]=>[2,1,1,1,1,2]
[8,7,3,6,4,2,1,5]=>[1,1,2,1,1,2]
[6,1,4,2,5,3,7,8]=>[1,2,2,3]
[1,3,7,5,4,2,8,6]=>[3,1,1,2,1]
[6,1,3,5,4,2,7,8]=>[1,3,1,3]
[6,1,2,5,4,7,3,8]=>[1,3,2,2]
[5,1,6,3,4,7,8,2]=>[1,2,4,1]
[5,2,6,3,4,7,1,8]=>[1,2,3,2]
[3,4,7,5,8,6,1,2]=>[3,2,1,2]
[2,4,7,1,5,3,8,6]=>[3,2,2,1]
[2,3,6,7,4,8,1,5]=>[4,2,2]
[1,3,6,7,4,8,5,2]=>[4,2,1,1]
[2,7,6,5,3,1,8,4]=>[2,1,1,1,2,1]
[5,2,6,1,4,7,8,3]=>[1,2,4,1]
[4,7,6,5,2,1,8,3]=>[2,1,1,1,2,1]
[5,3,6,2,4,1,7,8]=>[1,2,2,3]
[5,7,4,2,1,3,6,8]=>[2,1,1,4]
[6,3,1,5,4,7,8,2]=>[1,1,2,3,1]
[5,3,6,1,4,2,7,8]=>[1,2,2,3]
[1,7,4,2,6,3,8,5]=>[2,1,2,2,1]
[5,7,4,1,2,3,6,8]=>[2,1,5]
[6,4,1,2,5,3,7,8]=>[1,1,3,3]
[4,7,6,3,8,5,1,2]=>[2,1,2,1,2]
[3,7,6,5,2,8,1,4]=>[2,1,1,2,2]
[3,7,6,5,1,2,8,4]=>[2,1,1,3,1]
[4,7,2,6,1,3,8,5]=>[2,2,3,1]
[2,7,1,6,8,3,5,4]=>[2,3,2,1]
[2,7,6,5,8,1,4,3]=>[2,1,2,2,1]
[5,2,8,7,6,4,3,1]=>[1,2,1,1,1,1,1]
[8,2,7,6,1,5,4,3]=>[1,2,1,2,1,1]
[8,4,1,7,6,5,3,2]=>[1,1,2,1,1,1,1]
[4,5,6,2,3,8,1,7]=>[3,3,2]
[4,5,3,2,7,8,1,6]=>[2,1,3,2]
[6,5,7,3,8,4,2,1]=>[1,2,2,1,1,1]
[6,8,7,2,4,3,5,1]=>[2,1,2,2,1]
[3,2,7,4,5,8,1,6]=>[1,2,3,2]
[6,8,1,5,2,4,3,7]=>[2,2,2,2]
[8,3,4,6,1,5,2,7]=>[1,3,2,2]
[2,3,4,7,5,8,1,6]=>[4,2,2]
[6,3,4,7,8,2,5,1]=>[1,4,2,1]
[5,3,7,4,8,6,1,2]=>[1,2,2,1,2]
[8,3,6,4,1,7,2,5]=>[1,2,1,2,2]
[1,3,7,4,8,6,2,5]=>[3,2,1,2]
[3,7,8,5,4,1,2,6]=>[3,1,1,3]
[5,4,3,1,7,8,2,6]=>[1,1,1,3,2]
[5,7,6,2,8,4,1,3]=>[2,1,2,1,2]
[6,1,7,5,8,3,4,2]=>[1,2,2,2,1]
[7,5,6,4,1,3,8,2]=>[1,2,1,3,1]
[1,5,6,8,4,7,3,2]=>[4,2,1,1]
[4,1,3,7,6,5,8,2]=>[1,3,1,2,1]
[3,4,1,7,5,8,6,2]=>[2,2,2,1,1]
[8,5,7,4,3,1,6,2]=>[1,2,1,1,2,1]
[6,8,5,1,7,2,4,3]=>[2,1,2,2,1]
[8,2,4,1,3,7,6,5]=>[1,2,3,1,1]
[7,8,3,6,2,1,4,5]=>[2,2,1,3]
[8,1,7,4,2,3,6,5]=>[1,2,1,3,1]
[1,8,7,2,3,5,6,4]=>[2,1,4,1]
[2,8,3,1,6,7,5,4]=>[2,1,3,1,1]
[8,2,3,1,5,7,6,4]=>[1,2,3,1,1]
[3,8,4,1,2,7,6,5]=>[2,1,3,1,1]
[5,4,7,2,3,6,8,1]=>[1,2,4,1]
[6,3,2,1,8,4,7,5]=>[1,1,1,2,2,1]
[2,3,7,4,1,8,5,6]=>[3,1,2,2]
[6,4,1,3,2,7,8,5]=>[1,1,2,3,1]
[2,7,8,5,1,3,6,4]=>[3,1,3,1]
[8,2,5,6,7,1,3,4]=>[1,4,3]
[2,8,5,4,7,6,1,3]=>[2,1,2,1,2]
[6,7,1,5,8,2,4,3]=>[2,3,2,1]
[4,8,7,6,2,3,5,1]=>[2,1,1,3,1]
[7,8,1,5,3,2,6,4]=>[2,2,1,2,1]
[6,5,7,3,8,2,1,4]=>[1,2,2,1,2]
[8,1,4,7,2,5,6,3]=>[1,3,3,1]
[7,3,4,6,1,5,8,2]=>[1,3,3,1]
[8,3,4,5,7,1,6,2]=>[1,4,2,1]
[4,2,6,8,3,1,5,7]=>[1,3,1,3]
[3,7,6,2,4,5,1,8]=>[2,1,3,2]
[2,3,6,5,8,1,4,7]=>[3,2,3]
[2,3,5,8,6,1,4,7]=>[4,1,3]
[4,2,3,8,6,1,5,7]=>[1,3,1,3]
[6,4,1,2,8,3,5,7]=>[1,1,3,3]
[1,2,3,7,4,6,8,5]=>[4,3,1]
[3,2,7,1,4,5,8,6]=>[1,2,4,1]
[2,1,5,3,8,7,4,6]=>[1,2,2,1,2]
[5,8,3,2,4,1,6,7]=>[2,1,2,3]
[4,2,7,1,8,3,5,6]=>[1,2,2,3]
[4,1,8,2,7,3,5,6]=>[1,2,2,3]
[1,2,7,5,3,8,4,6]=>[3,1,2,2]
[3,2,7,1,4,8,5,6]=>[1,2,3,2]
[1,2,3,7,6,8,4,5]=>[4,2,2]
[1,2,3,6,8,7,4,5]=>[5,1,2]
[1,2,3,7,8,4,6,5]=>[5,2,1]
[1,2,3,6,8,4,7,5]=>[5,2,1]
[1,2,3,7,8,6,4,5]=>[5,1,2]
[6,2,8,3,7,5,1,4]=>[1,2,2,1,2]
[4,2,8,3,7,5,6,1]=>[1,2,2,2,1]
[7,3,4,8,6,5,1,2]=>[1,3,1,1,2]
[5,3,4,8,7,2,6,1]=>[1,3,1,2,1]
[4,3,5,8,7,2,6,1]=>[1,3,1,2,1]
[4,6,3,8,5,7,2,1]=>[2,2,2,1,1]
[7,5,3,8,6,2,4,1]=>[1,1,2,1,2,1]
[2,6,8,3,7,4,5,1]=>[3,2,2,1]
[1,8,4,3,7,5,6,2]=>[2,1,2,2,1]
[2,5,8,3,7,4,6,1]=>[3,2,2,1]
[7,4,3,8,6,2,5,1]=>[1,1,2,1,2,1]
[3,5,4,8,7,2,6,1]=>[2,2,1,2,1]
[4,5,3,8,6,7,2,1]=>[2,2,2,1,1]
[3,6,7,8,4,5,2,1]=>[4,2,1,1]
[2,6,8,5,4,7,3,1]=>[3,1,2,1,1]
[1,8,5,6,4,7,3,2]=>[2,2,2,1,1]
[2,5,8,6,4,7,3,1]=>[3,1,2,1,1]
[7,4,6,5,8,3,2,1]=>[1,2,2,1,1,1]
[6,3,7,8,4,5,2,1]=>[1,3,2,1,1]
[4,3,7,8,5,6,2,1]=>[1,3,2,1,1]
[5,2,8,6,4,7,3,1]=>[1,2,1,2,1,1]
[4,2,8,6,5,7,3,1]=>[1,2,1,2,1,1]
[3,2,8,6,7,4,5,1]=>[1,2,2,2,1]
[2,3,8,7,5,4,6,1]=>[3,1,1,2,1]
[1,8,2,7,4,5,6,3]=>[2,2,3,1]
[7,2,8,6,3,4,5,1]=>[1,2,1,3,1]
[6,2,8,4,5,7,3,1]=>[1,2,3,1,1]
[5,2,8,4,6,7,3,1]=>[1,2,3,1,1]
[4,2,8,5,6,7,3,1]=>[1,2,3,1,1]
[4,3,6,8,5,7,2,1]=>[1,3,2,1,1]
[3,4,6,8,7,2,5,1]=>[4,1,2,1]
[7,3,5,8,6,2,4,1]=>[1,3,1,2,1]
[1,8,3,5,7,4,6,2]=>[2,3,2,1]
[2,7,8,4,5,6,3,1]=>[3,3,1,1]
[3,7,5,8,4,6,2,1]=>[2,2,2,1,1]
[5,7,4,6,8,3,2,1]=>[2,3,1,1,1]
[3,6,5,8,4,7,2,1]=>[2,2,2,1,1]
[2,6,8,4,5,7,3,1]=>[3,3,1,1]
[4,2,7,1,3,8,5,6]=>[1,2,3,2]
[4,2,5,1,3,8,6,7]=>[1,2,3,2]
[5,3,6,1,7,2,4,8]=>[1,2,2,3]
[3,7,1,2,5,8,6,4]=>[2,4,1,1]
[3,7,4,1,2,8,5,6]=>[2,1,3,2]
[7,5,1,3,4,8,6,2]=>[1,1,4,1,1]
[7,5,1,2,4,8,6,3]=>[1,1,4,1,1]
[6,4,2,3,7,1,5,8]=>[1,1,3,3]
[7,6,3,8,1,2,5,4]=>[1,1,2,3,1]
[7,4,2,3,8,1,6,5]=>[1,1,3,2,1]
[4,7,5,2,8,1,3,6]=>[2,1,2,3]
[8,2,6,3,7,1,4,5]=>[1,2,2,3]
[8,6,1,2,7,4,5,3]=>[1,1,3,2,1]
[8,4,7,1,2,3,6,5]=>[1,2,4,1]
[8,5,7,1,2,4,6,3]=>[1,2,4,1]
[8,5,7,1,3,4,6,2]=>[1,2,4,1]
[8,6,2,7,1,3,5,4]=>[1,1,2,3,1]
[3,8,5,6,1,2,4,7]=>[2,2,4]
[3,7,5,8,1,2,4,6]=>[2,2,4]
[7,6,4,8,1,3,5,2]=>[1,1,2,3,1]
[6,5,8,1,2,4,7,3]=>[1,2,4,1]
[3,6,8,1,2,5,7,4]=>[3,4,1]
[3,7,2,4,8,1,6,5]=>[2,3,2,1]
[4,6,3,8,1,2,5,7]=>[2,2,4]
[4,6,3,7,1,2,5,8]=>[2,2,4]
[4,1,7,8,2,3,6,5]=>[1,3,3,1]
[5,1,2,8,6,3,4,7]=>[1,3,1,3]
[5,3,8,1,6,2,4,7]=>[1,2,2,3]
[6,1,8,5,2,3,4,7]=>[1,2,1,4]
[6,1,7,5,2,3,4,8]=>[1,2,1,4]
[6,8,1,3,7,4,5,2]=>[2,3,2,1]
[7,2,8,1,6,3,4,5]=>[1,2,2,3]
[4,7,8,2,5,1,3,6]=>[3,2,3]
[6,8,2,7,1,4,5,3]=>[2,2,3,1]
[4,8,7,1,3,5,6,2]=>[2,1,4,1]
[3,8,7,1,2,4,6,5]=>[2,1,4,1]
[4,8,7,1,2,3,6,5]=>[2,1,4,1]
[5,8,7,1,2,4,6,3]=>[2,1,4,1]
[5,8,7,1,3,4,6,2]=>[2,1,4,1]
[7,1,8,6,2,3,5,4]=>[1,2,1,3,1]
[5,8,6,4,1,2,3,7]=>[2,1,1,4]
[7,8,4,1,2,5,3,6]=>[2,1,3,2]
[7,8,1,2,6,5,3,4]=>[2,3,1,2]
[1,4,8,2,7,5,3,6]=>[3,2,1,2]
[6,1,3,4,7,2,5,8]=>[1,4,3]
[7,8,2,1,6,3,5,4]=>[2,1,2,2,1]
[6,1,2,7,5,4,3,8]=>[1,3,1,1,2]
[1,2,8,7,5,4,3,6]=>[3,1,1,1,2]
[5,1,7,3,6,4,8,2]=>[1,2,2,2,1]
[6,2,1,5,7,4,3,8]=>[1,1,3,1,2]
[6,2,3,7,4,1,5,8]=>[1,3,1,3]
[3,4,8,7,5,6,1,2]=>[3,1,2,2]
[2,3,8,7,4,1,5,6]=>[3,1,1,3]
[2,7,3,8,6,4,1,5]=>[2,2,1,1,2]
[1,8,3,7,6,4,5,2]=>[2,2,1,2,1]
[5,2,7,1,4,6,8,3]=>[1,2,4,1]
[4,6,7,5,2,1,8,3]=>[3,1,1,2,1]
[6,3,1,4,5,7,8,2]=>[1,1,5,1]
[5,3,1,4,6,2,7,8]=>[1,1,3,3]
[5,1,2,4,7,6,8,3]=>[1,4,2,1]
[5,7,4,1,2,6,3,8]=>[2,1,3,2]
[4,8,1,2,6,7,3,5]=>[2,4,2]
[4,1,7,8,2,6,3,5]=>[1,3,2,2]
[1,2,8,7,6,5,3,4]=>[3,1,1,1,2]
[3,1,2,4,6,8,7,5]=>[1,5,1,1]
[3,1,8,4,5,7,6,2]=>[1,2,3,1,1]
[3,2,8,5,4,7,1,6]=>[1,2,1,2,2]
[4,2,8,1,5,3,7,6]=>[1,2,2,2,1]
[4,3,8,5,7,6,1,2]=>[1,2,2,1,2]
[4,8,2,1,6,3,7,5]=>[2,1,2,2,1]
[3,8,6,5,2,7,1,4]=>[2,1,1,2,2]
[3,8,5,6,1,7,4,2]=>[2,2,2,1,1]
[3,5,7,8,1,2,6,4]=>[4,3,1]
[3,7,8,5,2,1,6,4]=>[3,1,1,2,1]
[3,7,2,8,4,1,6,5]=>[2,2,1,2,1]
[2,8,1,7,4,6,5,3]=>[2,2,2,1,1]
[2,8,7,5,1,6,4,3]=>[2,1,1,2,1,1]
[2,8,6,7,5,1,4,3]=>[2,2,1,2,1]
[5,1,3,4,6,7,2,8]=>[1,5,2]
[1,3,4,8,7,5,2,6]=>[4,1,1,2]
[8,2,4,1,7,3,5,6]=>[1,2,2,3]
[8,6,1,4,2,3,7,5]=>[1,1,2,3,1]
[3,6,1,4,2,8,7,5]=>[2,2,2,1,1]
[1,6,8,4,3,7,2,5]=>[3,1,2,2]
[3,1,4,7,8,5,2,6]=>[1,4,1,2]
[6,1,7,4,3,8,2,5]=>[1,2,1,2,2]
[1,8,7,4,3,6,2,5]=>[2,1,1,2,2]
[7,4,1,3,8,2,6,5]=>[1,1,3,2,1]
[4,8,2,3,1,5,7,6]=>[2,2,3,1]
[4,8,6,2,1,3,7,5]=>[2,1,1,3,1]
[2,7,4,1,8,3,5,6]=>[2,1,2,3]
[1,7,8,4,2,3,6,5]=>[3,1,3,1]
[4,7,1,3,8,2,6,5]=>[2,3,2,1]
[8,7,1,3,4,2,6,5]=>[1,1,3,2,1]
[1,7,4,3,6,2,8,5]=>[2,1,2,2,1]
[3,8,6,4,5,2,1,7]=>[2,1,2,1,2]
[3,8,4,6,5,2,1,7]=>[2,2,1,1,2]
[2,4,3,7,5,8,1,6]=>[2,2,2,2]
[1,4,7,3,6,2,8,5]=>[3,2,2,1]
[1,8,3,4,2,6,7,5]=>[2,2,3,1]
[6,4,1,3,7,2,8,5]=>[1,1,3,2,1]
[8,1,4,3,6,2,7,5]=>[1,2,2,2,1]
[4,2,3,8,5,7,1,6]=>[1,3,2,2]
[2,8,5,7,3,4,1,6]=>[2,2,2,2]
[5,8,2,6,4,3,1,7]=>[2,2,1,1,2]
[7,2,5,8,4,3,1,6]=>[1,3,1,1,2]
[4,2,3,5,8,7,1,6]=>[1,4,1,2]
[8,2,3,5,4,7,1,6]=>[1,3,2,2]
[6,1,8,3,4,2,7,5]=>[1,2,2,2,1]
[1,8,6,4,2,3,7,5]=>[2,1,1,3,1]
[3,8,4,5,6,2,1,7]=>[2,3,1,2]
[2,4,3,5,7,8,1,6]=>[2,4,2]
[3,8,6,5,4,2,1,7]=>[2,1,1,1,1,2]
[6,3,1,4,2,8,7,5]=>[1,1,2,2,1,1]
[7,3,8,1,2,6,4,5]=>[1,2,3,2]
[7,1,4,5,3,2,6,8]=>[1,3,1,3]
[1,8,4,2,6,5,3,7]=>[2,1,2,1,2]
[5,1,4,8,6,3,2,7]=>[1,3,1,1,2]
[5,3,1,8,4,7,2,6]=>[1,1,2,2,2]
[4,3,8,1,5,7,2,6]=>[1,2,3,2]
[6,3,1,2,5,7,4,8]=>[1,1,4,2]
[7,1,4,2,6,5,3,8]=>[1,2,2,1,2]
[3,8,4,1,6,5,2,7]=>[2,1,2,1,2]
[7,5,3,6,4,8,2,1]=>[1,1,2,2,1,1]
[7,3,6,4,5,8,2,1]=>[1,2,3,1,1]
[8,7,2,4,5,1,6,3]=>[1,1,3,2,1]
[7,1,5,4,8,6,3,2]=>[1,2,2,1,1,1]
[2,7,5,4,8,6,3,1]=>[2,1,2,1,1,1]
[2,1,8,7,5,3,6,4]=>[1,2,1,1,2,1]
[5,8,3,7,4,1,6,2]=>[2,2,1,2,1]
[8,1,7,4,2,6,5,3]=>[1,2,1,2,1,1]
[5,6,3,1,8,4,7,2]=>[2,1,2,2,1]
[5,7,1,4,8,6,3,2]=>[2,3,1,1,1]
[3,5,7,4,8,6,2,1]=>[3,2,1,1,1]
[2,6,7,4,5,8,3,1]=>[3,3,1,1]
[6,1,7,4,5,8,3,2]=>[1,2,3,1,1]
[5,3,7,4,8,6,2,1]=>[1,2,2,1,1,1]
[8,5,3,6,1,4,7,2]=>[1,1,2,3,1]
[5,4,3,6,8,2,7,1]=>[1,1,3,2,1]
[6,5,3,7,4,8,2,1]=>[1,1,2,2,1,1]
[7,5,8,4,1,6,3,2]=>[1,2,1,2,1,1]
[2,7,8,4,5,1,6,3]=>[3,2,2,1]
[5,7,3,8,4,1,6,2]=>[2,2,1,2,1]
[5,6,3,8,1,4,7,2]=>[2,2,3,1]
[8,4,1,2,5,6,7,3]=>[1,1,5,1]
[3,7,8,4,1,6,5,2]=>[3,1,2,1,1]
[6,8,3,1,2,5,7,4]=>[2,1,4,1]
[8,5,1,7,2,6,4,3]=>[1,1,2,2,1,1]
[8,7,1,4,5,2,6,3]=>[1,1,3,2,1]
[7,5,1,8,2,6,3,4]=>[1,1,2,2,2]
[8,7,3,1,5,4,2,6]=>[1,1,1,2,1,2]
[3,6,2,1,5,4,8,7]=>[2,1,2,2,1]
[5,4,2,6,1,3,8,7]=>[1,1,2,3,1]
[3,2,6,5,1,4,8,7]=>[1,2,1,3,1]
[2,5,8,1,7,4,3,6]=>[3,2,1,2]
[6,8,2,7,4,3,1,5]=>[2,2,1,1,2]
[6,8,2,3,7,5,1,4]=>[2,3,1,2]
[7,6,2,5,4,8,1,3]=>[1,1,2,2,2]
[2,6,5,1,8,4,3,7]=>[2,1,2,1,2]
[4,2,7,3,1,8,5,6]=>[1,2,1,2,2]
[4,2,3,7,1,5,8,6]=>[1,3,3,1]
[5,2,7,3,8,6,1,4]=>[1,2,2,1,2]
[2,1,5,8,4,3,7,6]=>[1,3,1,2,1]
[5,8,4,2,6,7,1,3]=>[2,1,3,2]
[3,2,4,8,1,5,7,6]=>[1,3,3,1]
[2,4,8,3,1,7,5,6]=>[3,1,2,2]
[4,8,3,2,1,7,6,5]=>[2,1,1,2,1,1]
[4,1,3,7,2,6,8,5]=>[1,3,3,1]
[3,4,8,2,1,6,5,7]=>[3,1,2,2]
[6,8,3,7,2,1,5,4]=>[2,2,1,2,1]
[3,5,8,1,7,2,6,4]=>[3,2,2,1]
[5,1,7,4,6,8,3,2]=>[1,2,3,1,1]
[7,6,4,8,1,5,3,2]=>[1,1,2,2,1,1]
[5,3,7,1,8,2,6,4]=>[1,2,2,2,1]
[2,7,6,3,8,1,4,5]=>[2,1,2,3]
[2,1,7,6,4,8,3,5]=>[1,2,1,2,2]
[2,1,5,4,8,7,3,6]=>[1,2,2,1,2]
[5,4,8,7,2,6,1,3]=>[1,2,1,2,2]
[2,4,3,8,7,1,5,6]=>[2,2,1,3]
[3,4,1,8,6,2,7,5]=>[2,2,1,2,1]
[3,8,5,4,2,1,7,6]=>[2,1,1,1,2,1]
[4,8,6,5,2,7,1,3]=>[2,1,1,2,2]
[3,2,8,7,5,4,1,6]=>[1,2,1,1,1,2]
[2,8,6,5,4,3,1,7]=>[2,1,1,1,1,2]
[5,4,2,6,3,1,8,7]=>[1,1,2,1,2,1]
[6,5,2,1,3,4,8,7]=>[1,1,1,4,1]
[8,5,2,7,3,1,4,6]=>[1,1,2,1,3]
[7,3,6,5,2,8,4,1]=>[1,2,1,2,1,1]
[7,6,2,3,4,8,5,1]=>[1,1,4,1,1]
[8,7,5,3,1,4,2,6]=>[1,1,1,1,2,2]
[7,1,5,3,8,4,6,2]=>[1,2,2,2,1]
[6,7,2,3,5,8,4,1]=>[2,4,1,1]
[3,7,6,4,2,8,5,1]=>[2,1,1,2,1,1]
[2,1,7,6,4,8,5,3]=>[1,2,1,2,1,1]
[2,1,8,7,4,3,5,6]=>[1,2,1,1,3]
[5,8,3,7,2,1,4,6]=>[2,2,1,3]
[3,8,7,4,2,1,5,6]=>[2,1,1,1,3]
[7,8,2,3,5,1,4,6]=>[2,3,3]
[2,8,6,3,1,4,7,5]=>[2,1,1,3,1]
[8,1,6,3,2,4,5,7]=>[1,2,1,4]
[5,7,1,4,8,3,6,2]=>[2,3,2,1]
[6,1,7,5,4,8,3,2]=>[1,2,1,2,1,1]
[6,3,7,5,8,4,2,1]=>[1,2,2,1,1,1]
[7,6,1,5,8,3,4,2]=>[1,1,3,2,1]
[8,6,7,5,1,3,2,4]=>[1,2,1,2,2]
[8,5,2,6,1,7,3,4]=>[1,1,2,2,2]
[5,4,2,6,8,3,7,1]=>[1,1,3,2,1]
[6,5,2,8,1,4,3,7]=>[1,1,2,2,2]
[7,4,2,8,1,3,6,5]=>[1,1,2,3,1]
[2,7,8,4,5,1,3,6]=>[3,2,3]
[5,7,3,8,4,1,2,6]=>[2,2,1,3]
[2,4,8,1,5,6,3,7]=>[3,3,2]
[3,4,8,1,5,2,7,6]=>[3,2,2,1]
[3,6,8,4,1,2,7,5]=>[3,1,3,1]
[4,8,1,2,5,3,6,7]=>[2,3,3]
[8,1,2,4,3,5,6,7]=>[1,3,4]
[5,8,7,4,6,3,2,1]=>[2,1,2,1,1,1]
[4,8,7,6,3,5,2,1]=>[2,1,1,2,1,1]
[3,8,7,6,5,2,4,1]=>[2,1,1,1,2,1]
[5,8,4,7,6,3,2,1]=>[2,2,1,1,1,1]
[6,8,5,4,7,3,2,1]=>[2,1,2,1,1,1]
[3,8,7,6,2,5,4,1]=>[2,1,1,2,1,1]
[4,8,7,6,3,2,5,1]=>[2,1,1,1,2,1]
[3,8,7,6,5,2,1,4]=>[2,1,1,1,1,2]
[7,5,8,4,6,3,1,2]=>[1,2,2,1,2]
[7,6,8,2,5,1,4,3]=>[1,2,2,2,1]
[3,5,2,4,7,6,1,8]=>[2,3,1,2]
[3,5,4,7,2,6,1,8]=>[2,2,2,2]
[3,5,4,7,6,1,2,8]=>[2,2,1,3]
[3,5,4,7,6,1,8,2]=>[2,2,1,2,1]
[3,5,7,4,6,1,8,2]=>[3,2,2,1]
[3,5,7,4,6,1,2,8]=>[3,2,3]
[3,5,7,4,6,2,1,8]=>[3,2,1,2]
[3,2,5,7,4,6,1,8]=>[1,3,2,2]
[3,5,2,7,6,4,1,8]=>[2,2,1,1,2]
[3,5,7,2,6,4,1,8]=>[3,2,1,2]
[5,3,7,6,2,4,1,8]=>[1,2,1,2,2]
[5,3,7,6,1,2,8,4]=>[1,2,1,3,1]
[5,3,7,6,1,4,2,8]=>[1,2,1,2,2]
[5,3,7,6,4,1,2,8]=>[1,2,1,1,3]
[3,5,7,2,6,1,4,8]=>[3,2,3]
[3,5,2,7,6,1,4,8]=>[2,2,1,3]
[5,3,7,6,4,1,8,2]=>[1,2,1,1,2,1]
[3,7,5,4,1,8,2,6]=>[2,1,1,2,2]
[3,7,5,4,1,8,6,2]=>[2,1,1,2,1,1]
[3,7,5,1,4,8,6,2]=>[2,1,3,1,1]
[3,7,5,1,4,8,2,6]=>[2,1,3,2]
[3,5,7,1,2,6,8,4]=>[3,4,1]
[3,5,7,2,1,6,8,4]=>[3,1,3,1]
[3,5,2,7,1,6,4,8]=>[2,2,2,2]
[3,5,7,2,1,6,4,8]=>[3,1,2,2]
[5,3,7,1,6,2,4,8]=>[1,2,2,3]
[3,5,7,1,4,6,8,2]=>[3,4,1]
[3,5,7,1,4,6,2,8]=>[3,3,2]
[3,5,7,1,4,2,6,8]=>[3,2,3]
[3,5,7,2,1,4,6,8]=>[3,1,4]
[3,5,2,7,1,4,6,8]=>[2,2,4]
[3,2,5,7,4,1,6,8]=>[1,3,1,3]
[3,5,2,7,4,1,6,8]=>[2,2,1,3]
[3,5,7,4,2,1,6,8]=>[3,1,1,3]
[3,5,7,4,1,2,6,8]=>[3,1,4]
[3,5,4,7,1,6,8,2]=>[2,2,3,1]
[3,5,4,7,1,2,6,8]=>[2,2,4]
[3,5,4,7,2,1,6,8]=>[2,2,1,3]
[3,5,4,2,7,1,6,8]=>[2,1,2,3]
[3,2,5,4,7,1,6,8]=>[1,2,2,3]
[3,5,4,7,2,1,8,6]=>[2,2,1,2,1]
[3,5,4,7,1,2,8,6]=>[2,2,3,1]
[5,7,6,3,1,8,4,2]=>[2,1,1,2,1,1]
[5,7,6,3,1,8,2,4]=>[2,1,1,2,2]
[3,5,7,4,1,2,8,6]=>[3,1,3,1]
[3,5,7,4,2,1,8,6]=>[3,1,1,2,1]
[3,2,5,7,4,1,8,6]=>[1,3,1,2,1]
[3,2,5,7,1,4,8,6]=>[1,3,3,1]
[3,5,2,7,1,4,8,6]=>[2,2,3,1]
[3,5,7,2,1,4,8,6]=>[3,1,3,1]
[3,5,7,1,4,2,8,6]=>[3,2,2,1]
[3,7,5,2,1,8,6,4]=>[2,1,1,2,1,1]
[3,7,2,5,1,8,6,4]=>[2,2,2,1,1]
[3,2,7,5,1,8,6,4]=>[1,2,1,2,1,1]
[3,2,7,5,1,8,4,6]=>[1,2,1,2,2]
[3,7,2,5,1,8,4,6]=>[2,2,2,2]
[3,7,5,2,1,8,4,6]=>[2,1,1,2,2]
[6,1,2,5,7,4,8,3]=>[1,4,2,1]
[6,3,2,7,4,1,8,5]=>[1,1,2,1,2,1]
[2,1,7,5,8,4,6,3]=>[1,2,2,2,1]
[2,7,3,6,8,4,1,5]=>[2,3,1,2]
[2,1,8,3,4,7,5,6]=>[1,2,3,2]
[5,1,7,2,4,8,3,6]=>[1,2,3,2]
[3,4,2,6,7,1,8,5]=>[2,3,2,1]
[3,5,8,7,2,1,6,4]=>[3,1,1,2,1]
[5,8,3,4,1,7,6,2]=>[2,2,2,1,1]
[5,8,7,2,4,1,6,3]=>[2,1,2,2,1]
[3,8,6,4,1,7,5,2]=>[2,1,1,2,1,1]
[4,3,5,6,8,1,7,2]=>[1,4,2,1]
[3,7,6,4,1,8,5,2]=>[2,1,1,2,1,1]
[3,7,4,1,8,6,5,2]=>[2,1,2,1,1,1]
[3,8,4,1,7,6,5,2]=>[2,1,2,1,1,1]
[3,2,7,6,1,5,4,8]=>[1,2,1,2,2]
[3,2,8,7,6,1,5,4]=>[1,2,1,1,2,1]
[5,7,8,2,4,1,6,3]=>[3,2,2,1]
[4,2,5,8,1,6,7,3]=>[1,3,3,1]
[4,2,5,8,1,7,3,6]=>[1,3,2,2]
[5,8,2,4,1,6,3,7]=>[2,2,2,2]
[8,4,2,6,5,1,3,7]=>[1,1,2,1,3]
[3,2,6,8,1,5,4,7]=>[1,3,2,2]
[8,3,2,5,6,1,4,7]=>[1,1,3,3]
[3,2,8,6,7,1,5,4]=>[1,2,2,2,1]
[3,2,6,8,7,1,5,4]=>[1,3,1,2,1]
[3,2,6,7,1,5,4,8]=>[1,3,2,2]
[8,7,3,2,5,6,1,4]=>[1,1,1,3,2]
[7,2,8,1,5,3,6,4]=>[1,2,2,2,1]
[8,4,2,7,5,1,3,6]=>[1,1,2,1,3]
[7,4,2,8,5,1,3,6]=>[1,1,2,1,3]
[7,2,4,1,8,3,6,5]=>[1,2,2,2,1]
[3,2,8,5,7,1,4,6]=>[1,2,2,3]
[2,6,5,7,1,8,3,4]=>[2,2,2,2]
[2,5,1,8,7,4,3,6]=>[2,2,1,1,2]
[8,1,4,6,3,5,2,7]=>[1,3,2,2]
[8,3,5,4,1,6,2,7]=>[1,2,1,2,2]
[8,6,3,4,1,5,2,7]=>[1,1,2,2,2]
[5,4,7,6,8,2,3,1]=>[1,2,2,2,1]
[4,1,8,2,3,7,6,5]=>[1,2,3,1,1]
[2,1,8,5,3,4,7,6]=>[1,2,1,3,1]
[5,2,4,6,8,7,3,1]=>[1,4,1,1,1]
[1,6,8,3,4,5,7,2]=>[3,4,1]
[5,7,4,8,6,1,3,2]=>[2,2,1,2,1]
[5,4,2,6,7,8,1,3]=>[1,1,4,2]
[6,4,2,7,3,5,8,1]=>[1,1,2,3,1]
[7,4,1,8,3,5,6,2]=>[1,1,2,3,1]
[6,5,4,8,7,3,1,2]=>[1,1,2,1,1,2]
[8,7,4,2,1,3,6,5]=>[1,1,1,1,3,1]
[8,7,1,3,2,5,6,4]=>[1,1,2,3,1]
[6,8,2,3,1,7,5,4]=>[2,2,2,1,1]
[7,4,3,2,6,8,5,1]=>[1,1,1,3,1,1]
[2,7,4,3,8,5,6,1]=>[2,1,2,2,1]
[8,3,7,2,1,5,6,4]=>[1,2,1,3,1]
[5,7,8,2,4,3,1,6]=>[3,2,1,2]
[8,4,7,3,2,6,1,5]=>[1,2,1,2,2]
[8,3,1,6,7,4,2,5]=>[1,1,3,1,2]
[3,2,5,7,4,8,1,6]=>[1,3,2,2]
[8,2,7,3,4,1,5,6]=>[1,2,2,3]
[7,1,6,3,5,8,2,4]=>[1,2,3,2]
[2,8,5,6,7,1,4,3]=>[2,3,2,1]
[1,5,2,7,8,6,4,3]=>[2,3,1,1,1]
[2,6,8,5,1,4,7,3]=>[3,1,3,1]
[1,4,2,8,6,5,7,3]=>[2,2,1,2,1]
[3,5,1,6,8,7,2,4]=>[2,3,1,2]
[5,7,6,2,1,3,8,4]=>[2,1,1,3,1]
[2,5,8,7,4,1,6,3]=>[3,1,1,2,1]
[4,1,7,5,2,6,8,3]=>[1,2,1,3,1]
[7,6,2,4,5,1,8,3]=>[1,1,3,2,1]
[7,3,4,2,5,8,6,1]=>[1,2,3,1,1]
[8,7,4,2,5,1,6,3]=>[1,1,1,2,2,1]
[8,1,4,5,2,6,7,3]=>[1,3,3,1]
[5,2,4,8,6,7,1,3]=>[1,3,2,2]
[8,5,6,2,1,3,7,4]=>[1,2,1,3,1]
[4,2,1,5,6,7,8,3]=>[1,1,5,1]
[3,4,6,5,1,7,8,2]=>[3,1,3,1]
[7,3,5,2,4,6,1,8]=>[1,2,3,2]
[5,3,7,2,4,6,1,8]=>[1,2,3,2]
[3,7,5,2,4,6,1,8]=>[2,1,3,2]
[5,7,3,2,4,6,1,8]=>[2,1,3,2]
[1,5,3,2,4,7,6,8]=>[2,1,3,2]
[1,5,3,2,7,4,6,8]=>[2,1,2,3]
[5,7,3,2,1,4,6,8]=>[2,1,1,4]
[5,7,3,2,4,1,6,8]=>[2,1,2,3]
[3,7,2,5,4,1,6,8]=>[2,2,1,3]
[5,1,3,2,4,7,6,8]=>[1,2,3,2]
[5,1,3,2,7,4,6,8]=>[1,2,2,3]
[7,1,3,2,5,4,6,8]=>[1,2,2,3]
[1,7,3,2,5,4,6,8]=>[2,1,2,3]
[7,1,3,5,2,4,6,8]=>[1,3,4]
[5,1,3,7,2,4,6,8]=>[1,3,4]
[3,2,7,5,1,4,6,8]=>[1,2,1,4]
[3,7,5,1,2,4,6,8]=>[2,1,5]
[5,7,3,1,2,4,6,8]=>[2,1,5]
[1,5,3,7,2,4,6,8]=>[2,2,4]
[5,3,2,7,4,1,6,8]=>[1,1,2,1,3]
[5,3,2,4,7,1,6,8]=>[1,1,3,3]
[5,3,2,1,4,7,6,8]=>[1,1,1,3,2]
[5,3,2,1,7,4,6,8]=>[1,1,1,2,3]
[1,3,2,7,5,4,6,8]=>[2,2,1,3]
[1,3,7,2,5,4,6,8]=>[3,2,3]
[7,3,1,2,5,4,6,8]=>[1,1,3,3]
[5,3,1,2,7,4,6,8]=>[1,1,3,3]
[5,3,1,2,4,7,6,8]=>[1,1,4,2]
[3,2,5,1,4,7,6,8]=>[1,2,3,2]
[7,3,1,5,2,4,6,8]=>[1,1,2,4]
[1,3,7,5,2,4,6,8]=>[3,1,4]
[7,5,1,3,2,4,6,8]=>[1,1,2,4]
[5,7,1,3,2,4,6,8]=>[2,2,4]
[3,7,1,5,2,4,6,8]=>[2,2,4]
[3,7,1,2,5,4,6,8]=>[2,3,3]
[3,7,2,1,5,4,6,8]=>[2,1,2,3]
[3,2,1,7,5,4,6,8]=>[1,1,2,1,3]
[3,1,2,7,5,4,6,8]=>[1,3,1,3]
[3,1,7,2,5,4,6,8]=>[1,2,2,3]
[3,1,7,5,2,4,6,8]=>[1,2,1,4]
[7,1,5,3,2,4,6,8]=>[1,2,1,4]
[1,7,5,3,2,4,6,8]=>[2,1,1,4]
[1,8,7,4,2,6,5,3]=>[2,1,1,2,1,1]
[2,8,5,1,7,6,4,3]=>[2,1,2,1,1,1]
[6,8,5,1,2,7,4,3]=>[2,1,3,1,1]
[2,8,1,4,7,6,5,3]=>[2,3,1,1,1]
[1,8,7,4,3,2,6,5]=>[2,1,1,1,2,1]
[1,8,5,4,2,7,6,3]=>[2,1,1,2,1,1]
[7,5,3,4,2,8,1,6]=>[1,1,2,2,2]
[8,5,3,6,2,4,7,1]=>[1,1,2,3,1]
[8,5,6,3,7,4,2,1]=>[1,2,2,1,1,1]
[8,5,6,2,7,4,3,1]=>[1,2,2,1,1,1]
[8,7,6,3,4,1,5,2]=>[1,1,1,2,2,1]
[1,7,2,3,6,8,5,4]=>[2,4,1,1]
[3,5,6,4,8,2,7,1]=>[3,2,2,1]
[3,5,1,4,8,2,7,6]=>[2,3,2,1]
[1,7,5,4,8,2,6,3]=>[2,1,2,2,1]
[3,7,5,1,6,4,8,2]=>[2,1,2,2,1]
[2,7,5,4,8,1,3,6]=>[2,1,2,3]
[2,7,5,4,8,6,1,3]=>[2,1,2,1,2]
[1,7,5,4,8,6,3,2]=>[2,1,2,1,1,1]
[2,5,1,4,8,7,3,6]=>[2,3,1,2]
[3,6,4,2,8,7,1,5]=>[2,1,2,1,2]
[3,5,2,4,8,1,6,7]=>[2,3,3]
[3,5,6,4,8,1,2,7]=>[3,2,3]
[1,5,6,4,8,7,2,3]=>[3,2,1,2]
[3,6,4,1,8,7,2,5]=>[2,1,2,1,2]
[3,6,4,5,8,7,2,1]=>[2,3,1,1,1]
[1,6,4,3,8,5,2,7]=>[2,1,2,1,2]
[7,1,3,4,5,8,2,6]=>[1,5,2]
[7,6,1,4,5,3,8,2]=>[1,1,3,2,1]
[7,6,1,3,5,4,8,2]=>[1,1,3,2,1]
[7,1,3,2,5,8,4,6]=>[1,2,3,2]
[1,6,4,2,8,5,3,7]=>[2,1,2,1,2]
[7,6,5,8,2,4,3,1]=>[1,1,2,2,1,1]
[7,6,5,8,3,1,4,2]=>[1,1,2,1,2,1]
[2,6,4,3,8,1,7,5]=>[2,1,2,2,1]
[2,6,4,3,8,5,7,1]=>[2,1,2,2,1]
[7,2,3,1,5,8,6,4]=>[1,2,3,1,1]
[7,1,5,6,3,8,4,2]=>[1,3,2,1,1]
[7,3,6,5,1,4,8,2]=>[1,2,1,3,1]
[7,2,6,5,3,8,1,4]=>[1,2,1,2,2]
[7,2,3,1,4,8,6,5]=>[1,2,3,1,1]
[7,2,3,5,4,8,6,1]=>[1,3,2,1,1]
[2,6,4,5,8,1,7,3]=>[2,3,2,1]
[1,5,6,4,8,3,7,2]=>[3,2,2,1]
[2,5,6,4,8,3,1,7]=>[3,2,1,2]
[3,5,6,1,4,7,8,2]=>[3,4,1]
[7,6,1,3,4,5,8,2]=>[1,1,5,1]
[7,1,3,2,4,8,5,6]=>[1,2,3,2]
[7,6,1,5,3,4,8,2]=>[1,1,2,3,1]
[7,6,1,5,4,3,8,2]=>[1,1,2,1,2,1]
[1,6,4,5,8,3,2,7]=>[2,3,1,2]
[7,6,5,8,1,3,2,4]=>[1,1,2,2,2]
[3,4,6,8,7,2,1,5]=>[4,1,1,2]
[3,5,6,8,2,1,7,4]=>[4,1,2,1]
[4,2,1,5,3,7,8,6]=>[1,1,2,3,1]
[4,2,5,6,3,1,8,7]=>[1,3,1,2,1]
[3,5,6,8,1,7,2,4]=>[4,2,2]
[4,1,5,6,3,2,8,7]=>[1,3,1,2,1]
[4,5,3,1,7,2,8,6]=>[2,1,2,2,1]
[4,1,3,5,2,7,8,6]=>[1,3,3,1]
[2,5,4,7,3,8,6,1]=>[2,2,2,1,1]
[3,5,7,1,8,4,2,6]=>[3,2,1,2]
[4,1,5,3,2,7,8,6]=>[1,2,1,3,1]
[4,5,3,7,1,2,8,6]=>[2,2,3,1]
[4,3,6,1,2,7,5,8]=>[1,2,3,2]
[5,1,3,2,4,6,7,8]=>[1,2,5]
[3,6,1,7,4,5,2,8]=>[2,2,2,2]
[5,1,3,4,2,6,7,8]=>[1,3,4]
[5,3,1,4,2,6,7,8]=>[1,1,2,4]
[4,5,2,3,7,1,8,6]=>[2,3,2,1]
[4,2,6,1,3,7,5,8]=>[1,2,3,2]
[4,6,2,1,3,7,5,8]=>[2,1,3,2]
[3,6,2,1,7,4,8,5]=>[2,1,2,2,1]
[3,1,4,7,6,5,2,8]=>[1,3,1,1,2]
[3,6,2,7,1,5,8,4]=>[2,2,3,1]
[4,6,2,7,1,3,5,8]=>[2,2,4]
[3,5,7,1,8,2,6,4]=>[3,2,2,1]
[5,1,4,2,3,6,7,8]=>[1,2,5]
[3,6,1,7,2,5,8,4]=>[2,2,3,1]
[2,6,5,3,4,7,8,1]=>[2,1,4,1]
[3,6,1,7,5,4,2,8]=>[2,2,1,1,2]
[5,1,4,3,2,6,7,8]=>[1,2,1,4]
[5,4,1,3,2,6,7,8]=>[1,1,2,4]
[6,4,2,5,3,8,1,7]=>[1,1,2,2,2]
[4,6,2,3,5,1,8,7]=>[2,3,2,1]
[6,2,4,5,1,8,3,7]=>[1,3,2,2]
[8,2,6,7,1,4,5,3]=>[1,3,3,1]
[8,2,6,7,4,1,5,3]=>[1,3,1,2,1]
[4,6,2,3,5,8,1,7]=>[2,4,2]
[2,6,4,1,5,8,3,7]=>[2,1,3,2]
[2,8,1,6,7,4,5,3]=>[2,3,2,1]
[6,8,4,5,7,2,3,1]=>[2,3,2,1]
[2,8,6,1,4,7,5,3]=>[2,1,3,1,1]
[2,8,1,6,4,7,5,3]=>[2,2,2,1,1]
[2,6,1,4,8,5,3,7]=>[2,3,1,2]
[6,4,5,2,8,3,1,7]=>[1,2,2,1,2]
[4,2,3,6,1,8,5,7]=>[1,3,2,2]
[4,2,3,1,6,8,5,7]=>[1,2,3,2]
[4,2,3,8,6,1,7,5]=>[1,3,1,2,1]
[6,4,5,8,2,3,7,1]=>[1,3,3,1]
[8,6,7,2,4,5,1,3]=>[1,2,3,2]
[6,4,8,5,2,3,7,1]=>[1,2,1,3,1]
[4,2,8,3,1,6,7,5]=>[1,2,1,3,1]
[2,4,8,1,3,6,7,5]=>[3,4,1]
[2,4,1,8,3,6,7,5]=>[2,2,3,1]
[2,1,4,8,6,3,7,5]=>[1,3,1,2,1]
[6,4,8,2,5,3,7,1]=>[1,2,2,2,1]
[8,6,2,4,7,5,1,3]=>[1,1,3,1,2]
[4,6,8,2,3,5,7,1]=>[3,4,1]
[2,6,8,4,1,5,7,3]=>[3,1,3,1]
[2,6,8,1,4,5,7,3]=>[3,4,1]
[2,1,6,8,4,5,7,3]=>[1,3,3,1]
[2,8,1,4,6,7,3,5]=>[2,4,2]
[4,8,6,2,3,7,5,1]=>[2,1,3,1,1]
[8,4,2,6,7,3,1,5]=>[1,1,3,1,2]
[7,6,4,5,1,3,8,2]=>[1,1,2,3,1]
[1,6,7,5,3,4,8,2]=>[3,1,3,1]
[7,6,2,3,8,4,1,5]=>[1,1,3,1,2]
[1,6,7,5,8,2,3,4]=>[3,2,3]
[6,2,5,8,3,4,7,1]=>[1,3,3,1]
[6,2,3,8,7,4,1,5]=>[1,3,1,1,2]
[2,4,7,3,5,8,6,1]=>[3,3,1,1]
[2,5,3,7,1,8,4,6]=>[2,2,2,2]
[5,2,8,3,1,4,6,7]=>[1,2,1,4]
[4,8,2,3,6,5,7,1]=>[2,3,2,1]
[5,8,1,3,6,4,7,2]=>[2,3,2,1]
[5,8,1,4,3,6,2,7]=>[2,2,2,2]
[5,8,4,1,3,7,6,2]=>[2,1,3,1,1]
[6,4,5,3,8,1,7,2]=>[1,2,2,2,1]
[4,6,5,3,7,1,2,8]=>[2,1,2,3]
[4,5,1,3,6,2,8,7]=>[2,3,2,1]
[4,2,6,5,1,7,3,8]=>[1,2,1,2,2]
[4,3,5,7,2,1,6,8]=>[1,3,1,3]
[3,4,7,6,8,1,2,5]=>[3,2,3]
[3,4,6,2,5,8,7,1]=>[3,3,1,1]
[3,5,2,4,6,1,8,7]=>[2,3,2,1]
[4,2,5,1,6,8,3,7]=>[1,2,3,2]
[1,8,2,3,6,5,7,4]=>[2,3,2,1]
[4,2,8,3,5,7,1,6]=>[1,2,3,2]
[4,3,8,6,5,7,1,2]=>[1,2,1,2,2]
[1,3,7,2,6,5,8,4]=>[3,2,2,1]
[1,3,6,4,2,5,8,7]=>[3,1,3,1]
[1,5,4,7,3,6,8,2]=>[2,2,3,1]
[5,2,3,8,4,1,7,6]=>[1,3,1,2,1]
[7,5,3,4,8,2,1,6]=>[1,1,3,1,2]
[7,2,8,3,4,1,5,6]=>[1,2,2,3]
[7,4,3,8,5,2,6,1]=>[1,1,2,1,2,1]
[4,6,2,7,3,1,5,8]=>[2,2,1,3]
[7,6,3,8,2,4,5,1]=>[1,1,2,3,1]
[7,2,8,5,1,3,4,6]=>[1,2,1,4]
[1,5,3,7,6,8,4,2]=>[2,2,2,1,1]
[1,6,3,7,8,2,4,5]=>[2,3,3]
[1,4,3,7,8,5,2,6]=>[2,3,1,2]
[4,2,6,5,7,8,3,1]=>[1,2,3,1,1]
[4,2,6,7,5,8,1,3]=>[1,3,2,2]
[3,2,4,7,8,5,1,6]=>[1,4,1,2]
[3,2,6,7,8,1,4,5]=>[1,4,3]
[5,1,8,3,6,4,7,2]=>[1,2,2,2,1]
[3,6,8,5,7,2,1,4]=>[3,2,1,2]
[5,1,3,8,7,6,4,2]=>[1,3,1,1,1,1]
[3,8,5,6,1,7,2,4]=>[2,2,2,2]
[3,4,8,1,7,6,2,5]=>[3,2,1,2]
[4,7,6,8,5,1,3,2]=>[2,2,1,2,1]
[6,7,4,8,5,1,3,2]=>[2,2,1,2,1]
[5,3,6,8,7,1,4,2]=>[1,3,1,2,1]
[1,8,4,6,7,2,5,3]=>[2,3,2,1]
[5,2,8,3,7,1,6,4]=>[1,2,2,2,1]
[7,4,5,8,6,1,3,2]=>[1,3,1,2,1]
[4,3,6,8,7,1,5,2]=>[1,3,1,2,1]
[6,4,8,3,1,7,5,2]=>[1,2,1,2,1,1]
[3,6,5,8,7,1,4,2]=>[2,2,1,2,1]
[5,7,4,8,2,6,3,1]=>[2,2,2,1,1]
[5,6,4,8,2,7,3,1]=>[2,2,2,1,1]
[4,6,3,8,2,7,5,1]=>[2,2,2,1,1]
[5,3,8,1,7,2,6,4]=>[1,2,2,2,1]
[6,5,3,8,2,7,4,1]=>[1,1,2,2,1,1]
[6,4,8,1,3,7,5,2]=>[1,2,3,1,1]
[6,2,8,3,4,7,5,1]=>[1,2,3,1,1]
[7,6,3,1,4,2,5,8]=>[1,1,1,2,3]
[1,5,4,3,7,8,2,6]=>[2,1,3,2]
[7,8,4,2,5,3,1,6]=>[2,1,2,1,2]
[4,2,7,8,5,3,1,6]=>[1,3,1,1,2]
[4,2,5,3,1,7,8,6]=>[1,2,1,3,1]
[4,2,8,7,6,3,1,5]=>[1,2,1,1,1,2]
[4,2,7,6,3,1,5,8]=>[1,2,1,1,3]
[6,3,1,7,5,2,4,8]=>[1,1,2,1,3]
[6,3,1,8,7,5,2,4]=>[1,1,2,1,1,2]
[8,6,3,1,7,5,2,4]=>[1,1,1,2,1,2]
[4,2,7,6,3,1,8,5]=>[1,2,1,1,2,1]
[7,6,3,1,8,4,2,5]=>[1,1,1,2,1,2]
[7,6,4,2,1,8,3,5]=>[1,1,1,1,2,2]
[1,8,2,7,6,4,3,5]=>[2,2,1,1,2]
[8,3,5,7,6,4,2,1]=>[1,3,1,1,1,1]
[8,4,2,5,7,6,3,1]=>[1,1,3,1,1,1]
[7,5,2,4,8,6,3,1]=>[1,1,3,1,1,1]
[8,7,5,2,4,6,3,1]=>[1,1,1,3,1,1]
[7,5,2,4,6,3,1,8]=>[1,1,3,1,2]
[5,2,8,6,3,7,4,1]=>[1,2,1,2,1,1]
[8,4,7,5,2,6,3,1]=>[1,2,1,2,1,1]
[8,3,6,4,7,5,2,1]=>[1,2,2,1,1,1]
[1,8,2,7,5,3,6,4]=>[2,2,1,2,1]
[7,5,2,1,8,3,6,4]=>[1,1,1,2,2,1]
[7,5,2,6,3,1,8,4]=>[1,1,2,1,2,1]
[5,2,7,4,1,8,6,3]=>[1,2,1,2,1,1]
[5,2,8,7,4,1,6,3]=>[1,2,1,1,2,1]
[8,7,4,1,5,2,6,3]=>[1,1,1,2,2,1]
[7,4,1,5,2,8,6,3]=>[1,1,2,2,1,1]
[7,6,3,1,4,2,8,5]=>[1,1,1,2,2,1]
[7,5,2,8,6,3,1,4]=>[1,1,2,1,1,2]
[8,7,5,2,6,3,1,4]=>[1,1,1,2,1,2]
[7,5,2,1,3,6,4,8]=>[1,1,1,3,2]
[8,7,5,2,1,3,6,4]=>[1,1,1,1,3,1]
[7,5,2,1,3,8,6,4]=>[1,1,1,3,1,1]
[1,3,7,6,5,8,2,4]=>[3,1,2,2]
[8,6,4,7,5,2,1,3]=>[1,1,2,1,1,2]
[6,4,8,7,5,2,1,3]=>[1,2,1,1,1,2]
[6,4,7,5,2,1,3,8]=>[1,2,1,1,3]
[6,3,1,4,7,5,2,8]=>[1,1,3,1,2]
[6,3,1,4,8,7,5,2]=>[1,1,3,1,1,1]
[8,6,3,1,4,7,5,2]=>[1,1,1,3,1,1]
[8,5,7,6,3,1,4,2]=>[1,2,1,1,2,1]
[1,8,2,5,7,6,4,3]=>[2,3,1,1,1]
[1,8,2,6,4,7,5,3]=>[2,2,2,1,1]
[7,5,2,1,6,4,8,3]=>[1,1,1,2,2,1]
[6,3,8,7,4,1,5,2]=>[1,2,1,1,2,1]
[6,3,7,4,1,5,2,8]=>[1,2,1,2,2]
[7,4,1,6,3,5,2,8]=>[1,1,2,2,2]
[7,4,1,8,6,3,5,2]=>[1,1,2,1,2,1]
[8,4,6,3,1,7,5,2]=>[1,2,1,2,1,1]
[6,4,7,5,2,1,8,3]=>[1,2,1,1,2,1]
[1,6,4,7,5,3,8,2]=>[2,2,1,2,1]
[8,6,3,5,2,7,4,1]=>[1,1,2,2,1,1]
[6,3,5,2,8,7,4,1]=>[1,2,2,1,1,1]
[6,3,5,2,7,4,1,8]=>[1,2,2,1,2]
[1,4,7,3,5,2,6,8]=>[3,2,3]
[5,7,4,2,6,3,1,8]=>[2,1,2,1,2]
[4,2,6,3,5,7,1,8]=>[1,2,3,2]
[1,4,5,8,2,7,3,6]=>[4,2,2]
[2,4,5,8,1,6,7,3]=>[4,3,1]
[8,3,4,7,1,6,5,2]=>[1,3,2,1,1]
[4,2,5,7,8,1,6,3]=>[1,4,2,1]
[8,3,4,6,5,1,7,2]=>[1,3,1,2,1]
[6,1,3,7,4,2,5,8]=>[1,3,1,3]
[3,1,6,8,2,7,4,5]=>[1,3,2,2]
[4,8,2,3,1,6,7,5]=>[2,2,3,1]
[3,2,6,8,1,5,7,4]=>[1,3,3,1]
[8,2,6,1,5,4,7,3]=>[1,2,2,2,1]
[8,6,2,7,1,5,4,3]=>[1,1,2,2,1,1]
[7,6,8,3,1,5,4,2]=>[1,2,1,2,1,1]
[6,3,7,2,8,1,5,4]=>[1,2,2,2,1]
[7,5,2,8,6,1,4,3]=>[1,1,2,1,2,1]
[2,7,3,8,1,5,6,4]=>[2,2,3,1]
[1,6,8,5,2,4,3,7]=>[3,1,2,2]
[4,5,7,2,8,1,6,3]=>[3,2,2,1]
[4,5,6,8,3,1,7,2]=>[4,1,2,1]
[8,4,6,5,3,1,7,2]=>[1,2,1,1,2,1]
[5,6,4,8,3,1,7,2]=>[2,2,1,2,1]
[4,8,1,6,2,3,7,5]=>[2,2,3,1]
[4,5,3,1,7,2,6,8]=>[2,1,2,3]
[4,7,3,1,2,6,5,8]=>[2,1,3,2]
[5,2,7,1,3,6,4,8]=>[1,2,3,2]
[7,8,1,2,4,3,6,5]=>[2,3,2,1]
[8,4,1,6,2,3,7,5]=>[1,1,2,3,1]
[4,8,3,1,2,5,7,6]=>[2,1,4,1]
[4,1,3,6,5,7,8,2]=>[1,3,3,1]
[6,1,3,4,2,8,5,7]=>[1,3,2,2]
[8,1,4,2,5,7,6,3]=>[1,2,3,1,1]
[8,1,4,3,5,7,6,2]=>[1,2,3,1,1]
[5,2,4,1,3,7,8,6]=>[1,2,4,1]
[2,6,5,3,1,7,8,4]=>[2,1,1,3,1]
[8,3,2,1,5,7,6,4]=>[1,1,1,3,1,1]
[1,7,4,3,6,8,2,5]=>[2,1,3,2]
[2,7,6,3,1,8,4,5]=>[2,1,1,2,2]
[2,8,4,6,3,7,5,1]=>[2,2,2,1,1]
[8,7,1,3,6,5,4,2]=>[1,1,3,1,1,1]
[1,8,5,7,4,2,6,3]=>[2,2,1,2,1]
[3,8,6,5,7,1,4,2]=>[2,1,2,2,1]
[4,8,6,2,7,1,5,3]=>[2,1,2,2,1]
[4,7,5,3,8,2,1,6]=>[2,1,2,1,2]
[1,6,5,8,3,4,2,7]=>[2,2,2,2]
[6,1,5,3,8,4,2,7]=>[1,2,2,1,2]
[8,1,5,4,7,2,6,3]=>[1,2,2,2,1]
[2,1,4,7,5,8,3,6]=>[1,3,2,2]
[6,3,5,8,7,4,1,2]=>[1,3,1,1,2]
[4,7,2,8,5,6,3,1]=>[2,2,2,1,1]
[1,4,8,7,3,5,6,2]=>[3,1,3,1]
[8,1,7,6,3,5,4,2]=>[1,2,1,2,1,1]
[3,6,8,5,7,4,1,2]=>[3,2,1,2]
[4,7,6,8,5,3,1,2]=>[2,2,1,1,2]
[5,7,2,8,6,4,1,3]=>[2,2,1,1,2]
[3,8,7,5,6,4,2,1]=>[2,1,2,1,1,1]
[2,8,7,6,4,5,3,1]=>[2,1,1,2,1,1]
[1,8,7,6,5,3,4,2]=>[2,1,1,1,2,1]
[4,6,7,2,5,3,1,8]=>[3,2,1,2]
[3,8,5,7,6,1,4,2]=>[2,2,1,2,1]
[1,4,7,8,2,6,5,3]=>[4,2,1,1]
[2,4,7,8,1,6,5,3]=>[4,2,1,1]
[4,2,6,8,7,1,5,3]=>[1,3,1,2,1]
[3,1,7,8,2,6,5,4]=>[1,3,2,1,1]
[6,1,3,8,2,7,5,4]=>[1,3,2,1,1]
[5,1,8,4,2,7,6,3]=>[1,2,1,2,1,1]
[6,8,3,7,1,5,4,2]=>[2,2,2,1,1]
[2,7,3,8,1,6,5,4]=>[2,2,2,1,1]
[1,7,3,8,2,6,5,4]=>[2,2,2,1,1]
[2,6,8,4,1,7,5,3]=>[3,1,2,1,1]
[4,6,7,1,2,8,5,3]=>[3,3,1,1]
[3,6,1,8,2,7,5,4]=>[2,2,2,1,1]
[5,7,4,1,2,8,6,3]=>[2,1,3,1,1]
[6,3,7,1,2,8,5,4]=>[1,2,3,1,1]
[6,2,1,8,3,7,5,4]=>[1,1,2,2,1,1]
[8,1,5,6,3,2,4,7]=>[1,3,1,3]
[1,7,8,3,5,2,4,6]=>[3,2,3]
[8,5,3,7,2,4,6,1]=>[1,1,2,3,1]
[1,7,2,4,8,5,3,6]=>[2,3,1,2]
[1,7,8,5,4,3,2,6]=>[3,1,1,1,2]
[2,6,8,7,4,3,5,1]=>[3,1,1,2,1]
[1,2,6,7,8,4,3,5]=>[5,1,2]
[2,7,5,8,4,1,3,6]=>[2,2,1,3]
[2,1,7,8,4,5,3,6]=>[1,3,2,2]
[3,7,8,2,1,5,4,6]=>[3,1,2,2]
[8,5,1,4,7,3,6,2]=>[1,1,3,2,1]
[8,4,7,5,3,6,1,2]=>[1,2,1,2,2]
[8,1,4,6,7,3,5,2]=>[1,4,2,1]
[3,5,8,6,7,4,1,2]=>[3,2,1,2]
[3,6,8,4,7,1,5,2]=>[3,2,2,1]
[4,7,1,3,6,8,2,5]=>[2,4,2]
[3,7,6,4,8,1,2,5]=>[2,1,2,3]
[3,1,7,5,6,8,2,4]=>[1,2,3,2]
[2,3,6,5,7,1,8,4]=>[3,2,2,1]
[3,7,5,4,2,1,8,6]=>[2,1,1,1,2,1]
[1,3,6,7,4,2,8,5]=>[4,1,2,1]
[3,6,4,8,2,7,5,1]=>[2,2,2,1,1]
[1,4,6,3,2,7,8,5]=>[3,1,3,1]
[8,7,1,5,6,3,2,4]=>[1,1,3,1,2]
[8,1,6,7,5,3,2,4]=>[1,3,1,1,2]
[1,7,8,6,5,3,2,4]=>[3,1,1,1,2]
[8,7,2,4,6,5,3,1]=>[1,1,3,1,1,1]
[1,7,8,2,6,4,5,3]=>[3,2,2,1]
[8,7,2,5,4,6,1,3]=>[1,1,2,2,2]
[8,7,2,5,3,1,6,4]=>[1,1,2,1,2,1]
[8,7,3,2,1,5,6,4]=>[1,1,1,1,3,1]
[8,2,6,7,3,1,5,4]=>[1,3,1,2,1]
[1,7,2,8,5,6,4,3]=>[2,2,2,1,1]
[2,7,1,8,4,6,5,3]=>[2,2,2,1,1]
[3,7,8,2,1,6,5,4]=>[3,1,2,1,1]
[8,7,6,1,4,5,3,2]=>[1,1,1,3,1,1]
[4,8,1,2,3,7,5,6]=>[2,4,2]
[1,8,2,3,6,5,4,7]=>[2,3,1,2]
[3,5,8,4,7,2,6,1]=>[3,2,2,1]
[1,8,5,4,6,2,3,7]=>[2,1,2,3]
[3,8,5,4,6,1,2,7]=>[2,1,2,3]
[3,8,5,1,6,4,2,7]=>[2,1,2,1,2]
[2,8,5,4,6,1,3,7]=>[2,1,2,3]
[2,8,5,4,6,3,1,7]=>[2,1,2,1,2]
[1,8,5,4,6,3,2,7]=>[2,1,2,1,2]
[2,5,8,4,7,3,6,1]=>[3,2,2,1]
[3,6,4,2,7,8,5,1]=>[2,1,3,1,1]
[3,5,4,1,6,2,7,8]=>[2,1,2,3]
[4,5,8,1,7,6,2,3]=>[3,2,1,2]
[3,5,8,4,7,1,6,2]=>[3,2,2,1]
[1,5,8,4,7,3,6,2]=>[3,2,2,1]
[3,6,4,1,7,8,5,2]=>[2,1,3,1,1]
[3,6,4,8,7,5,2,1]=>[2,2,1,1,1,1]
[1,6,4,3,7,8,5,2]=>[2,1,3,1,1]
[7,1,3,4,8,6,5,2]=>[1,4,1,1,1]
[7,6,1,3,8,4,2,5]=>[1,1,3,1,2]
[1,6,4,2,7,8,3,5]=>[2,1,3,2]
[2,6,4,3,7,1,8,5]=>[2,1,2,2,1]
[2,6,4,1,7,8,3,5]=>[2,1,3,2]
[7,2,3,4,8,6,5,1]=>[1,4,1,1,1]
[7,2,3,1,8,6,4,5]=>[1,2,2,1,2]
[7,2,3,4,1,6,8,5]=>[1,3,3,1]
[1,2,4,3,8,5,7,6]=>[3,2,2,1]
[7,3,8,6,1,4,2,5]=>[1,2,1,2,2]
[7,2,8,6,3,4,1,5]=>[1,2,1,2,2]
[7,2,3,1,5,6,8,4]=>[1,2,4,1]
[7,2,3,8,1,6,5,4]=>[1,3,2,1,1]
[7,2,3,8,5,6,4,1]=>[1,3,2,1,1]
[2,6,4,8,7,1,5,3]=>[2,2,1,2,1]
[1,5,8,4,7,6,2,3]=>[3,2,1,2]
[3,5,8,1,6,7,2,4]=>[3,3,2]
[7,6,1,3,5,8,2,4]=>[1,1,4,2]
[7,1,3,2,5,6,8,4]=>[1,2,4,1]
[7,1,3,8,2,6,5,4]=>[1,3,2,1,1]
[7,6,1,8,5,4,2,3]=>[1,1,2,1,1,2]
[4,1,6,5,8,2,7,3]=>[1,2,2,2,1]
[3,1,6,5,8,4,7,2]=>[1,2,2,2,1]
[3,2,6,5,8,4,7,1]=>[1,2,2,2,1]
[4,3,7,1,6,5,8,2]=>[1,2,2,2,1]
[5,2,6,4,8,3,7,1]=>[1,2,2,2,1]
[5,1,6,4,8,3,7,2]=>[1,2,2,2,1]
[5,1,6,4,8,2,7,3]=>[1,2,2,2,1]
[4,3,7,5,8,2,6,1]=>[1,2,2,2,1]
[5,3,7,4,8,2,6,1]=>[1,2,2,2,1]
[5,3,7,4,8,1,6,2]=>[1,2,2,2,1]
[5,4,8,1,6,2,7,3]=>[1,2,2,2,1]
[4,3,7,2,6,1,8,5]=>[1,2,2,2,1]
[4,3,7,1,5,2,8,6]=>[1,2,2,2,1]
[4,3,7,1,6,2,8,5]=>[1,2,2,2,1]
[5,4,8,2,6,3,7,1]=>[1,2,2,2,1]
[5,4,8,1,6,3,7,2]=>[1,2,2,2,1]
[5,1,2,7,6,3,8,4]=>[1,3,1,2,1]
[4,1,7,5,2,3,6,8]=>[1,2,1,4]
[4,7,2,6,3,1,5,8]=>[2,2,1,3]
[4,8,2,7,3,5,1,6]=>[2,2,2,2]
[4,1,8,7,6,3,2,5]=>[1,2,1,1,1,2]
[5,1,8,6,7,3,2,4]=>[1,2,2,1,2]
[4,1,7,8,6,3,2,5]=>[1,3,1,1,2]
[4,7,2,8,3,5,1,6]=>[2,2,2,2]
[1,2,6,8,3,7,4,5]=>[4,2,2]
[6,8,3,2,1,4,7,5]=>[2,1,1,3,1]
[6,7,5,2,1,8,3,4]=>[2,1,1,2,2]
[7,2,4,1,6,5,8,3]=>[1,2,2,2,1]
[8,4,3,1,6,5,7,2]=>[1,1,1,2,2,1]
[7,5,8,4,3,1,6,2]=>[1,2,1,1,2,1]
[6,7,5,2,8,4,1,3]=>[2,1,2,1,2]
[6,8,2,4,1,3,7,5]=>[2,2,3,1]
[8,4,6,5,7,3,2,1]=>[1,2,2,1,1,1]
[5,2,6,7,3,8,4,1]=>[1,3,2,1,1]
[5,2,7,6,3,8,4,1]=>[1,2,1,2,1,1]
[2,8,4,7,6,3,5,1]=>[2,2,1,2,1]
[6,1,2,7,5,8,4,3]=>[1,3,2,1,1]
[3,4,7,5,1,6,8,2]=>[3,1,3,1]
[7,1,2,6,5,8,4,3]=>[1,3,2,1,1]
[8,4,6,5,7,3,1,2]=>[1,2,2,1,2]
[6,2,5,7,3,8,4,1]=>[1,3,2,1,1]
[7,3,4,6,2,8,5,1]=>[1,3,2,1,1]
[4,2,7,3,8,5,6,1]=>[1,2,2,2,1]
[4,5,2,6,8,3,7,1]=>[2,3,2,1]
[4,8,3,2,5,7,6,1]=>[2,1,3,1,1]
[2,6,8,5,3,4,7,1]=>[3,1,3,1]
[7,2,4,3,8,5,6,1]=>[1,2,2,2,1]
[6,8,5,3,4,7,2,1]=>[2,1,3,1,1]
[2,4,7,6,1,5,8,3]=>[3,1,3,1]
[8,2,6,7,5,1,4,3]=>[1,3,1,2,1]
[6,1,7,5,8,4,2,3]=>[1,2,2,1,2]
[3,8,4,5,7,6,2,1]=>[2,3,1,1,1]
[8,4,7,6,2,3,5,1]=>[1,2,1,3,1]
[6,8,4,1,5,3,7,2]=>[2,1,2,2,1]
[6,8,3,4,7,2,5,1]=>[2,3,2,1]
[8,3,4,7,6,2,5,1]=>[1,3,1,2,1]
[4,7,6,2,5,8,3,1]=>[2,1,3,1,1]
[1,8,3,5,2,6,7,4]=>[2,2,3,1]
[8,3,5,1,4,7,6,2]=>[1,2,3,1,1]
[6,8,3,5,1,4,7,2]=>[2,2,3,1]
[6,1,5,8,4,3,7,2]=>[1,3,1,2,1]
[6,8,4,7,2,3,5,1]=>[2,2,3,1]
[1,7,2,6,5,8,4,3]=>[2,2,2,1,1]
[7,1,6,5,8,4,2,3]=>[1,2,2,1,2]
[7,5,3,4,8,2,6,1]=>[1,1,3,2,1]
[5,3,8,2,4,7,6,1]=>[1,2,3,1,1]
[6,7,2,8,5,4,3,1]=>[2,2,1,1,1,1]
[3,7,4,6,2,8,5,1]=>[2,2,2,1,1]
[7,4,2,3,8,5,6,1]=>[1,1,3,2,1]
[6,8,5,4,2,3,7,1]=>[2,1,1,3,1]
[6,8,4,7,1,3,5,2]=>[2,2,3,1]
[5,8,2,4,3,7,6,1]=>[2,2,2,1,1]
[3,4,5,8,2,7,6,1]=>[4,2,1,1]
[6,8,3,4,5,2,7,1]=>[2,3,2,1]
[6,7,1,5,3,8,4,2]=>[2,2,2,1,1]
[7,4,6,3,2,8,5,1]=>[1,2,1,2,1,1]
[8,2,1,3,5,6,4,7]=>[1,1,4,2]
[8,2,1,3,5,4,7,6]=>[1,1,3,2,1]
[8,2,1,3,4,6,7,5]=>[1,1,5,1]
[8,1,3,4,2,6,5,7]=>[1,3,2,2]
[8,1,3,4,2,5,7,6]=>[1,3,3,1]
[8,1,3,2,5,6,4,7]=>[1,2,3,2]
[8,1,2,4,5,3,7,6]=>[1,4,2,1]
[8,1,2,4,3,6,7,5]=>[1,3,3,1]
[6,5,3,8,4,2,7,1]=>[1,1,2,1,2,1]
[7,4,5,1,6,2,8,3]=>[1,2,2,2,1]
[4,7,3,5,6,2,8,1]=>[2,3,2,1]
[6,7,8,4,1,3,5,2]=>[3,1,3,1]
[3,1,6,8,4,7,5,2]=>[1,3,2,1,1]
[8,3,6,1,5,7,4,2]=>[1,2,3,1,1]
[2,7,3,5,8,6,4,1]=>[2,3,1,1,1]
[3,2,7,5,8,6,1,4]=>[1,2,2,1,2]
[2,4,7,5,8,6,1,3]=>[3,2,1,2]
[2,5,4,7,8,1,6,3]=>[2,3,2,1]
[2,4,6,7,8,1,5,3]=>[5,2,1]
[2,4,7,6,1,8,5,3]=>[3,1,2,1,1]
[2,4,6,8,1,7,5,3]=>[4,2,1,1]
[7,3,6,8,2,5,1,4]=>[1,3,2,2]
[5,7,3,8,6,2,1,4]=>[2,2,1,1,2]
[7,4,3,8,6,2,1,5]=>[1,1,2,1,1,2]
[2,4,7,8,3,5,6,1]=>[4,3,1]
[3,4,7,2,8,5,1,6]=>[3,2,1,2]
[3,5,2,7,8,1,4,6]=>[2,3,3]
[3,2,7,6,1,8,4,5]=>[1,2,1,2,2]
[3,2,6,8,1,7,4,5]=>[1,3,2,2]
[3,5,2,8,1,4,7,6]=>[2,2,3,1]
[4,3,6,2,1,8,5,7]=>[1,2,1,2,2]
[3,6,4,2,5,8,1,7]=>[2,1,3,2]
[4,6,2,3,5,8,7,1]=>[2,4,1,1]
[4,6,2,3,7,5,8,1]=>[2,3,2,1]
[3,6,4,2,7,5,1,8]=>[2,1,2,1,2]
[4,3,6,2,7,1,5,8]=>[1,2,2,3]
[3,6,5,2,1,7,4,8]=>[2,1,1,2,2]
[4,8,6,3,2,1,5,7]=>[2,1,1,1,3]
[7,4,6,3,2,1,5,8]=>[1,2,1,1,3]
[5,8,4,2,3,6,7,1]=>[2,1,4,1]
[6,4,8,3,2,1,5,7]=>[1,2,1,1,3]
[8,4,5,3,2,1,7,6]=>[1,2,1,1,2,1]
[5,8,3,4,2,1,7,6]=>[2,2,1,2,1]
[6,8,4,2,3,7,5,1]=>[2,1,3,1,1]
[3,6,4,2,1,8,7,5]=>[2,1,1,2,1,1]
[6,4,8,3,2,7,1,5]=>[1,2,1,2,2]
[5,6,8,3,2,7,1,4]=>[3,1,2,2]
[5,8,3,7,2,1,6,4]=>[2,2,1,2,1]
[2,8,5,7,4,1,6,3]=>[2,2,1,2,1]
[2,8,6,5,4,1,7,3]=>[2,1,1,1,2,1]
[2,5,6,4,1,8,7,3]=>[3,1,2,1,1]
[2,8,6,4,5,7,1,3]=>[2,1,3,2]
[3,8,6,2,5,7,1,4]=>[2,1,3,2]
[2,8,6,5,3,7,4,1]=>[2,1,1,2,1,1]
[2,5,6,4,7,1,8,3]=>[3,2,2,1]
[2,6,5,4,1,7,8,3]=>[2,1,1,3,1]
[2,5,4,8,1,6,7,3]=>[2,2,3,1]
[5,7,6,3,2,8,1,4]=>[2,1,1,2,2]
[6,5,7,3,2,8,1,4]=>[1,2,1,2,2]
[6,4,7,3,8,2,1,5]=>[1,2,2,1,2]
[3,6,4,2,7,1,8,5]=>[2,1,2,2,1]
[7,5,4,2,3,8,6,1]=>[1,1,1,3,1,1]
[6,7,4,3,2,1,8,5]=>[2,1,1,1,2,1]
[8,4,3,6,2,1,7,5]=>[1,1,2,1,2,1]
[8,4,3,7,2,1,5,6]=>[1,1,2,1,3]
[8,4,6,3,2,1,5,7]=>[1,2,1,1,3]
[4,6,3,2,1,5,7,8]=>[2,1,1,4]
[1,2,6,5,8,7,3,4]=>[3,2,1,2]
[1,5,2,8,4,6,7,3]=>[2,2,3,1]
[1,5,2,7,4,6,8,3]=>[2,2,3,1]
[5,1,2,7,3,6,8,4]=>[1,3,3,1]
[5,1,2,8,3,6,7,4]=>[1,3,3,1]
[5,6,3,4,8,7,2,1]=>[2,3,1,1,1]
[6,5,3,4,8,7,2,1]=>[1,1,3,1,1,1]
[4,1,2,8,3,6,7,5]=>[1,3,3,1]
[4,1,2,7,3,6,8,5]=>[1,3,3,1]
[5,1,2,8,3,6,4,7]=>[1,3,2,2]
[7,5,3,8,4,6,2,1]=>[1,1,2,2,1,1]
[8,5,3,7,4,6,2,1]=>[1,1,2,2,1,1]
[4,1,2,7,3,6,5,8]=>[1,3,2,2]
[6,1,7,2,3,5,4,8]=>[1,2,3,2]
[1,6,7,2,4,5,3,8]=>[3,3,2]
[1,6,8,2,4,5,3,7]=>[3,3,2]
[5,8,1,2,3,4,7,6]=>[2,5,1]
[7,1,8,2,3,5,4,6]=>[1,2,3,2]
[7,1,2,8,3,6,4,5]=>[1,3,2,2]
[6,1,8,2,3,5,7,4]=>[1,2,4,1]
[6,1,7,2,3,5,8,4]=>[1,2,4,1]
[1,6,7,2,4,5,8,3]=>[3,4,1]
[1,6,8,2,4,5,7,3]=>[3,4,1]
[4,3,8,7,5,6,2,1]=>[1,2,1,2,1,1]
[1,8,2,7,4,6,5,3]=>[2,2,2,1,1]
[1,8,6,2,4,5,7,3]=>[2,1,4,1]
[1,7,6,2,4,5,8,3]=>[2,1,4,1]
[7,1,6,2,3,5,8,4]=>[1,2,4,1]
[8,1,6,2,3,5,7,4]=>[1,2,4,1]
[8,1,7,2,3,5,6,4]=>[1,2,4,1]
[5,8,3,7,4,6,2,1]=>[2,2,2,1,1]
[6,8,7,3,4,5,2,1]=>[2,1,3,1,1]
[1,8,7,2,4,5,3,6]=>[2,1,3,2]
[8,1,7,2,3,5,4,6]=>[1,2,3,2]
[8,7,1,2,3,4,6,5]=>[1,1,5,1]
[8,6,1,2,3,4,7,5]=>[1,1,5,1]
[8,5,1,2,3,4,7,6]=>[1,1,5,1]
[8,1,6,2,3,5,4,7]=>[1,2,3,2]
[1,8,6,2,4,5,3,7]=>[2,1,3,2]
[1,7,6,2,4,5,3,8]=>[2,1,3,2]
[7,1,6,2,3,5,4,8]=>[1,2,3,2]
[1,8,7,4,6,3,5,2]=>[2,1,2,2,1]
[4,7,2,6,1,8,5,3]=>[2,2,2,1,1]
[6,7,2,5,1,4,8,3]=>[2,2,3,1]
[6,3,7,5,1,4,8,2]=>[1,2,1,3,1]
[4,2,5,8,7,3,6,1]=>[1,3,1,2,1]
[8,1,2,4,7,3,6,5]=>[1,4,2,1]
[1,8,3,5,7,2,6,4]=>[2,3,2,1]
[1,3,4,8,7,5,6,2]=>[4,1,2,1]
[2,3,4,6,8,5,7,1]=>[5,2,1]
[2,3,5,7,4,8,6,1]=>[4,2,1,1]
[2,4,6,3,7,8,5,1]=>[3,3,1,1]
[2,5,7,1,8,6,3,4]=>[3,2,1,2]
[1,5,6,8,3,7,4,2]=>[4,2,1,1]
[8,1,3,5,2,7,4,6]=>[1,3,2,2]
[8,2,4,5,1,3,7,6]=>[1,3,3,1]
[1,3,8,5,2,4,6,7]=>[3,1,4]
[1,4,7,8,3,5,6,2]=>[4,3,1]
[2,6,7,1,8,4,5,3]=>[3,2,2,1]
[4,5,6,1,3,7,8,2]=>[3,4,1]
[3,4,1,8,5,2,6,7]=>[2,2,1,3]
[2,4,8,1,5,3,6,7]=>[3,2,3]
[5,8,3,1,4,2,6,7]=>[2,1,2,3]
[8,2,4,1,5,7,3,6]=>[1,2,3,2]
[3,8,4,2,6,7,1,5]=>[2,1,3,2]
[2,4,1,8,5,6,3,7]=>[2,2,2,2]
[1,6,2,7,8,5,3,4]=>[2,3,1,2]
[3,5,2,6,7,8,4,1]=>[2,4,1,1]
[4,5,1,6,7,3,8,2]=>[2,3,2,1]
[2,8,4,1,7,5,3,6]=>[2,1,2,1,2]
[8,5,3,1,7,4,2,6]=>[1,1,1,2,1,2]
[4,2,8,7,1,5,3,6]=>[1,2,1,2,2]
[5,2,6,8,1,7,4,3]=>[1,3,2,1,1]
[5,2,7,1,6,8,3,4]=>[1,2,3,2]
[5,7,3,2,6,8,1,4]=>[2,1,3,2]
[8,4,7,3,1,6,2,5]=>[1,2,1,2,2]
[5,7,1,2,8,4,6,3]=>[2,3,2,1]
[6,7,1,2,3,5,8,4]=>[2,5,1]
[6,1,7,2,3,8,5,4]=>[1,2,3,1,1]
[3,2,8,6,1,4,5,7]=>[1,2,1,4]
[3,1,6,7,8,4,2,5]=>[1,4,1,2]
[3,1,4,8,5,6,2,7]=>[1,3,2,2]
[5,1,8,2,3,6,4,7]=>[1,2,3,2]
[8,3,1,4,5,7,2,6]=>[1,1,4,2]
[8,6,2,3,5,1,4,7]=>[1,1,3,3]
[8,2,4,5,7,3,1,6]=>[1,4,1,2]
[2,6,3,8,7,5,4,1]=>[2,2,1,1,1,1]
[8,2,3,7,5,4,1,6]=>[1,3,1,1,2]
[8,2,6,3,5,4,1,7]=>[1,2,2,1,2]
[8,6,1,5,2,4,3,7]=>[1,1,2,2,2]
[8,6,2,4,1,5,3,7]=>[1,1,2,2,2]
[8,4,1,6,5,3,2,7]=>[1,1,2,1,1,2]
[8,3,6,1,5,4,2,7]=>[1,2,2,1,2]
[8,3,2,6,5,4,1,7]=>[1,1,2,1,1,2]
[8,3,2,5,7,4,1,6]=>[1,1,3,1,2]
[8,3,1,7,5,4,2,6]=>[1,1,2,1,1,2]
[8,2,7,4,1,5,3,6]=>[1,2,1,2,2]
[6,1,3,8,7,5,4,2]=>[1,3,1,1,1,1]
[3,6,1,8,7,5,4,2]=>[2,2,1,1,1,1]
[3,8,1,5,7,6,4,2]=>[2,3,1,1,1]
[3,5,2,8,7,6,4,1]=>[2,2,1,1,1,1]
[3,4,8,2,7,6,5,1]=>[3,2,1,1,1]
[3,4,8,7,1,6,5,2]=>[3,1,2,1,1]
[8,1,3,5,7,6,4,2]=>[1,4,1,1,1]
[4,1,8,5,7,6,3,2]=>[1,2,2,1,1,1]
[8,2,7,1,4,5,6,3]=>[1,2,4,1]
[8,1,7,3,4,6,2,5]=>[1,2,3,2]
[8,3,1,7,2,6,5,4]=>[1,1,2,2,1,1]
[3,8,2,4,7,6,5,1]=>[2,3,1,1,1]
[2,8,3,7,4,6,5,1]=>[2,2,2,1,1]
[8,2,3,7,1,6,5,4]=>[1,3,2,1,1]
[8,2,7,1,3,6,5,4]=>[1,2,3,1,1]
[8,1,7,2,6,4,3,5]=>[1,2,2,1,2]
[8,1,7,5,2,4,3,6]=>[1,2,1,2,2]
[8,2,3,7,4,6,1,5]=>[1,3,2,2]
[2,4,8,5,7,6,3,1]=>[3,2,1,1,1]
[8,2,4,3,7,6,1,5]=>[1,2,2,1,2]
[8,2,7,3,5,1,4,6]=>[1,2,2,3]
[8,2,7,4,3,1,5,6]=>[1,2,1,1,3]
[8,2,7,3,1,5,6,4]=>[1,2,1,3,1]
[8,2,1,5,7,6,4,3]=>[1,1,3,1,1,1]
[6,2,1,8,7,5,4,3]=>[1,1,2,1,1,1,1]
[6,1,8,2,7,5,4,3]=>[1,2,2,1,1,1]
[8,1,7,3,5,2,6,4]=>[1,2,2,2,1]
[8,1,5,2,7,6,4,3]=>[1,2,2,1,1,1]
[8,1,7,2,4,6,5,3]=>[1,2,3,1,1]
[8,2,4,1,7,6,5,3]=>[1,2,2,1,1,1]
[4,2,8,3,7,6,5,1]=>[1,2,2,1,1,1]
[4,8,2,1,7,6,5,3]=>[2,1,2,1,1,1]
[5,1,8,7,2,6,4,3]=>[1,2,1,2,1,1]
[5,8,1,3,7,6,2,4]=>[2,3,1,2]
[8,2,5,4,1,7,6,3]=>[1,2,1,2,1,1]
[5,1,4,8,7,6,3,2]=>[1,3,1,1,1,1]
[8,1,4,3,7,6,5,2]=>[1,2,2,1,1,1]
[4,8,1,3,7,6,5,2]=>[2,3,1,1,1]
[4,3,8,1,7,6,5,2]=>[1,2,2,1,1,1]
[5,8,6,3,2,1,7,4]=>[2,1,1,1,2,1]
[5,1,7,4,3,2,6,8]=>[1,2,1,1,3]
[5,7,6,3,2,4,1,8]=>[2,1,1,2,2]
[6,5,7,2,4,3,1,8]=>[1,2,2,1,2]
[5,7,1,3,2,8,6,4]=>[2,2,2,1,1]
[5,8,1,3,2,7,4,6]=>[2,2,2,2]
[8,5,1,3,2,4,6,7]=>[1,1,2,4]
[6,5,1,3,7,2,4,8]=>[1,1,3,3]
[7,5,1,3,2,4,8,6]=>[1,1,2,3,1]
[7,5,8,2,1,4,3,6]=>[1,2,1,2,2]
[6,7,1,2,5,4,8,3]=>[2,3,2,1]
[7,4,3,1,2,8,6,5]=>[1,1,1,3,1,1]
[3,2,8,1,4,7,5,6]=>[1,2,3,2]
[8,4,3,1,2,7,5,6]=>[1,1,1,3,2]
[6,8,1,2,5,7,4,3]=>[2,4,1,1]
[7,1,2,3,8,6,4,5]=>[1,4,1,2]
[8,1,6,4,2,3,5,7]=>[1,2,1,4]
[4,1,3,8,2,5,7,6]=>[1,3,3,1]
[6,8,5,3,4,1,7,2]=>[2,1,2,2,1]
[1,5,4,8,2,3,7,6]=>[2,2,3,1]
[1,8,6,5,2,3,7,4]=>[2,1,1,3,1]
[8,5,7,4,1,3,6,2]=>[1,2,1,3,1]
[1,7,8,2,3,5,6,4]=>[3,4,1]
[7,6,8,1,3,4,2,5]=>[1,2,3,2]
[7,5,8,2,3,1,4,6]=>[1,2,2,3]
[7,4,1,2,6,8,3,5]=>[1,1,4,2]
[7,1,3,8,2,5,6,4]=>[1,3,3,1]
[6,2,8,1,5,7,3,4]=>[1,2,3,2]
[7,2,5,4,1,8,6,3]=>[1,2,1,2,1,1]
[7,3,5,4,2,1,8,6]=>[1,2,1,1,2,1]
[7,4,5,2,1,6,8,3]=>[1,2,1,3,1]
[7,4,3,2,6,1,8,5]=>[1,1,1,2,2,1]
[7,3,2,8,5,6,1,4]=>[1,1,2,2,2]
[7,2,5,4,1,6,3,8]=>[1,2,1,2,2]
[1,5,2,4,7,8,3,6]=>[2,4,2]
[3,5,1,2,8,6,7,4]=>[2,3,2,1]
[2,5,3,4,7,8,1,6]=>[2,4,2]
[2,7,4,3,6,8,5,1]=>[2,1,3,1,1]
[1,7,4,3,6,8,5,2]=>[2,1,3,1,1]
[3,7,1,8,2,5,6,4]=>[2,2,3,1]
[4,7,6,3,2,5,8,1]=>[2,1,1,3,1]
[4,7,6,5,2,3,8,1]=>[2,1,1,3,1]
[4,7,6,5,1,3,8,2]=>[2,1,1,3,1]
[1,7,6,5,2,3,8,4]=>[2,1,1,3,1]
[1,7,6,5,8,3,2,4]=>[2,1,2,1,2]
[4,7,6,5,1,3,2,8]=>[2,1,1,2,2]
[4,7,6,5,3,8,1,2]=>[2,1,1,2,2]
[5,7,6,3,2,8,4,1]=>[2,1,1,2,1,1]
[5,4,6,8,7,2,1,3]=>[1,3,1,1,2]
[6,3,4,2,8,1,5,7]=>[1,2,2,3]
[6,7,4,2,1,8,5,3]=>[2,1,1,2,1,1]
[6,7,3,2,1,8,5,4]=>[2,1,1,2,1,1]
[5,7,6,2,1,4,8,3]=>[2,1,1,3,1]
[1,7,6,3,2,8,4,5]=>[2,1,1,2,2]
[5,4,2,1,7,3,6,8]=>[1,1,1,2,3]
[6,5,8,1,7,3,4,2]=>[1,2,2,2,1]
[6,5,8,2,3,7,4,1]=>[1,2,3,1,1]
[6,5,8,3,4,1,7,2]=>[1,2,2,2,1]
[5,7,3,6,8,1,4,2]=>[2,3,2,1]
[5,7,2,6,3,1,4,8]=>[2,2,1,3]
[4,1,2,8,5,6,3,7]=>[1,3,2,2]
[4,1,2,8,5,3,6,7]=>[1,3,1,3]
[2,1,6,3,7,8,5,4]=>[1,2,3,1,1]
[4,7,1,6,8,2,5,3]=>[2,3,2,1]
[3,7,4,1,6,5,2,8]=>[2,1,2,1,2]
[3,7,2,1,4,5,6,8]=>[2,1,5]
[3,5,8,2,6,1,7,4]=>[3,2,2,1]
[4,2,7,8,3,5,1,6]=>[1,3,2,2]
[4,5,1,7,3,6,8,2]=>[2,2,3,1]
[4,3,2,8,5,1,6,7]=>[1,1,2,1,3]
[3,7,6,2,8,4,1,5]=>[2,1,2,1,2]
[3,7,6,1,5,2,8,4]=>[2,1,2,2,1]
[3,7,6,5,8,4,1,2]=>[2,1,2,1,2]
[1,7,6,2,5,8,4,3]=>[2,1,3,1,1]
[1,7,6,5,8,4,2,3]=>[2,1,2,1,2]
[3,7,6,5,8,1,2,4]=>[2,1,2,3]
[3,7,6,2,8,4,5,1]=>[2,1,2,2,1]
[4,3,6,8,5,1,2,7]=>[1,3,1,3]
[3,7,6,1,5,4,8,2]=>[2,1,2,2,1]
[4,7,2,6,8,5,1,3]=>[2,3,1,2]
[2,7,1,5,8,4,3,6]=>[2,3,1,2]
[2,7,6,1,8,4,3,5]=>[2,1,2,1,2]
[7,1,2,6,3,5,4,8]=>[1,3,2,2]
[6,2,7,5,8,4,3,1]=>[1,2,2,1,1,1]
[7,2,5,1,4,6,3,8]=>[1,2,3,2]
[7,1,5,4,3,6,2,8]=>[1,2,1,2,2]
[7,2,6,3,4,5,1,8]=>[1,2,3,2]
[7,4,3,1,5,2,6,8]=>[1,1,1,2,3]
[6,7,8,4,2,5,3,1]=>[3,1,2,1,1]
[6,1,2,5,7,8,4,3]=>[1,5,1,1]
[3,7,8,6,2,5,1,4]=>[3,1,2,2]
[3,6,1,4,8,7,5,2]=>[2,3,1,1,1]
[4,1,2,7,8,5,3,6]=>[1,4,1,2]
[4,7,3,1,6,2,8,5]=>[2,1,2,2,1]
[4,7,3,1,2,6,8,5]=>[2,1,4,1]
[3,6,4,5,8,1,7,2]=>[2,3,2,1]
[3,7,6,1,5,8,2,4]=>[2,1,3,2]
[2,7,6,5,4,1,8,3]=>[2,1,1,1,2,1]
[2,7,1,8,5,3,6,4]=>[2,2,1,2,1]
[3,8,5,4,6,7,1,2]=>[2,1,3,2]
[3,8,5,6,4,2,7,1]=>[2,2,1,2,1]
[1,2,6,4,3,5,8,7]=>[3,1,3,1]
[3,2,6,4,7,8,5,1]=>[1,2,3,1,1]
[4,2,7,5,8,3,1,6]=>[1,2,2,1,2]
[4,2,7,1,3,8,6,5]=>[1,2,3,1,1]
[4,8,1,6,2,7,5,3]=>[2,2,2,1,1]
[5,7,2,3,1,4,6,8]=>[2,2,4]
[6,5,1,3,2,7,4,8]=>[1,1,2,2,2]
[6,5,2,3,1,7,4,8]=>[1,1,2,2,2]
[6,1,8,4,2,7,5,3]=>[1,2,1,2,1,1]
[5,7,2,3,8,4,1,6]=>[2,3,1,2]
[5,2,1,4,7,8,3,6]=>[1,1,4,2]
[5,6,2,7,3,4,8,1]=>[2,2,3,1]
[6,1,3,8,5,4,7,2]=>[1,3,1,2,1]
[3,7,8,6,1,2,4,5]=>[3,1,4]
[2,7,6,8,5,1,3,4]=>[2,2,1,3]
[2,7,8,6,1,5,4,3]=>[3,1,2,1,1]
[2,7,6,8,5,3,1,4]=>[2,2,1,1,2]
[4,7,6,8,2,1,3,5]=>[2,2,1,3]
[4,7,8,6,1,3,2,5]=>[3,1,2,2]
[1,7,8,6,5,2,3,4]=>[3,1,1,3]
[5,7,4,6,3,1,2,8]=>[2,2,1,3]
[5,6,1,8,3,7,4,2]=>[2,2,2,1,1]
[4,7,6,8,1,2,3,5]=>[2,2,4]
[2,8,4,1,5,7,3,6]=>[2,1,3,2]
[1,5,8,6,4,2,3,7]=>[3,1,1,3]
[2,8,5,7,4,3,6,1]=>[2,2,1,2,1]
[2,8,6,4,5,3,1,7]=>[2,1,2,1,2]
[2,8,4,6,3,1,7,5]=>[2,2,1,2,1]
[2,8,6,5,1,4,7,3]=>[2,1,1,3,1]
[2,8,4,3,1,6,7,5]=>[2,1,1,3,1]
[1,2,8,7,4,3,5,6]=>[3,1,1,3]
[1,4,6,2,5,7,8,3]=>[3,4,1]
[2,4,8,6,3,5,7,1]=>[3,1,3,1]
[4,6,8,1,3,2,5,7]=>[3,2,3]
[2,5,8,6,4,1,7,3]=>[3,1,1,2,1]
[2,4,6,1,5,7,3,8]=>[3,3,2]
[2,5,6,8,7,4,1,3]=>[4,1,1,2]
[5,7,2,3,6,1,4,8]=>[2,3,3]
[3,2,7,4,1,8,5,6]=>[1,2,1,2,2]
[1,6,2,3,5,8,7,4]=>[2,4,1,1]
[1,7,2,3,6,5,8,4]=>[2,3,2,1]
[4,7,2,3,5,6,8,1]=>[2,5,1]
[4,7,2,3,1,6,8,5]=>[2,2,3,1]
[4,7,2,3,1,5,6,8]=>[2,2,4]
[6,7,3,1,5,4,8,2]=>[2,1,2,2,1]
[7,4,6,2,8,3,5,1]=>[1,2,2,2,1]
[7,3,5,1,4,8,2,6]=>[1,2,3,2]
[7,2,5,1,4,8,6,3]=>[1,2,3,1,1]
[3,4,6,5,1,2,7,8]=>[3,1,4]
[1,2,7,4,5,8,6,3]=>[3,3,1,1]
[1,5,3,6,8,4,2,7]=>[2,3,1,2]
[7,5,4,3,8,6,2,1]=>[1,1,1,2,1,1,1]
[6,7,5,1,3,4,2,8]=>[2,1,3,2]
[4,3,8,2,6,7,5,1]=>[1,2,3,1,1]
[4,3,8,2,5,7,1,6]=>[1,2,3,2]
[5,7,4,3,6,1,2,8]=>[2,1,2,3]
[1,4,3,8,7,6,2,5]=>[2,2,1,1,2]
[4,1,6,2,5,3,7,8]=>[1,2,2,3]
[5,1,8,6,4,7,2,3]=>[1,2,1,2,2]
[4,1,8,5,6,3,7,2]=>[1,2,2,2,1]
[4,2,6,1,5,3,8,7]=>[1,2,2,2,1]
[6,7,2,3,1,5,8,4]=>[2,2,3,1]
[1,5,2,3,8,6,4,7]=>[2,3,1,2]
[7,5,2,3,8,1,6,4]=>[1,1,3,2,1]
[6,7,2,3,5,1,4,8]=>[2,3,3]
[5,2,7,8,6,1,3,4]=>[1,3,1,3]
[2,1,7,8,6,3,5,4]=>[1,3,1,2,1]
[6,5,2,3,8,1,7,4]=>[1,1,3,2,1]
[7,5,2,3,8,4,1,6]=>[1,1,3,1,2]
[8,7,4,6,2,1,3,5]=>[1,1,2,1,3]
[4,5,1,7,6,3,8,2]=>[2,2,1,2,1]
[7,8,2,4,1,6,3,5]=>[2,2,2,2]
[6,7,1,5,4,8,2,3]=>[2,2,2,2]
[1,8,7,5,2,3,6,4]=>[2,1,1,3,1]
[8,1,7,5,2,3,4,6]=>[1,2,1,4]
[8,6,3,1,4,2,5,7]=>[1,1,1,2,3]
[4,5,1,6,2,8,7,3]=>[2,2,2,1,1]
[4,5,1,3,8,7,6,2]=>[2,3,1,1,1]
[4,8,3,6,1,7,2,5]=>[2,2,2,2]
[6,2,7,8,3,4,5,1]=>[1,3,3,1]
[8,5,6,1,7,4,3,2]=>[1,2,2,1,1,1]
[1,2,4,6,8,5,7,3]=>[5,2,1]
[2,1,7,5,8,6,3,4]=>[1,2,2,1,2]
[4,7,3,8,6,5,2,1]=>[2,2,1,1,1,1]
[3,8,7,4,6,5,1,2]=>[2,1,2,1,2]
[7,3,8,4,6,5,1,2]=>[1,2,2,1,2]
[7,4,3,6,5,8,1,2]=>[1,1,2,2,2]
[4,5,8,7,2,6,1,3]=>[3,1,2,2]
[3,8,6,7,5,1,4,2]=>[2,2,1,2,1]
[4,2,7,6,5,8,3,1]=>[1,2,1,2,1,1]
[4,6,7,8,5,2,3,1]=>[4,1,2,1]
[4,5,3,8,2,7,6,1]=>[2,2,2,1,1]
[3,8,5,4,1,7,6,2]=>[2,1,1,2,1,1]
[6,4,7,2,5,8,3,1]=>[1,2,3,1,1]
[6,3,8,7,5,1,4,2]=>[1,2,1,1,2,1]
[5,3,6,4,1,2,8,7]=>[1,2,1,3,1]
[6,8,4,3,5,7,1,2]=>[2,1,3,2]
[5,2,4,8,7,6,1,3]=>[1,3,1,1,2]
[1,8,3,5,4,2,6,7]=>[2,2,1,3]
[1,8,2,5,4,3,6,7]=>[2,2,1,3]
[3,2,4,5,1,8,6,7]=>[1,3,2,2]
[3,2,4,8,5,1,7,6]=>[1,3,1,2,1]
[5,2,4,1,7,8,3,6]=>[1,2,3,2]
[4,2,5,1,7,8,3,6]=>[1,2,3,2]
[2,5,4,1,3,8,6,7]=>[2,1,3,2]
[2,5,1,4,8,3,6,7]=>[2,3,3]
[1,4,5,3,8,2,6,7]=>[3,2,3]
[5,1,8,2,4,3,6,7]=>[1,2,2,3]
[5,3,2,8,4,1,6,7]=>[1,1,2,1,3]
[4,8,2,1,5,3,6,7]=>[2,1,2,3]
[1,5,4,8,2,3,6,7]=>[2,2,4]
[3,5,1,4,7,8,2,6]=>[2,4,2]
[4,8,3,1,6,7,2,5]=>[2,1,3,2]
[3,4,8,2,6,5,7,1]=>[3,2,2,1]
[1,4,8,2,7,3,6,5]=>[3,2,2,1]
[1,8,7,2,5,3,6,4]=>[2,1,2,2,1]
[7,4,6,5,3,8,2,1]=>[1,2,1,2,1,1]
[3,6,2,4,8,7,1,5]=>[2,3,1,2]
[4,7,3,2,6,8,1,5]=>[2,1,3,2]
[7,3,4,6,8,1,2,5]=>[1,4,3]
[3,6,7,2,5,8,1,4]=>[3,3,2]
[1,5,6,8,3,7,2,4]=>[4,2,2]
[1,6,5,8,3,7,2,4]=>[2,2,2,2]
[8,6,2,7,1,4,3,5]=>[1,1,2,2,2]
[7,8,4,6,3,1,5,2]=>[2,2,1,2,1]
[6,1,5,8,3,4,7,2]=>[1,3,3,1]
[5,6,8,1,3,4,7,2]=>[3,4,1]
[2,8,5,6,3,4,7,1]=>[2,2,3,1]
[6,8,1,3,5,4,7,2]=>[2,3,2,1]
[8,1,6,3,5,4,7,2]=>[1,2,2,2,1]
[1,8,7,3,6,4,5,2]=>[2,1,2,2,1]
[7,4,2,8,3,6,5,1]=>[1,1,2,2,1,1]
[7,1,2,5,8,4,6,3]=>[1,4,2,1]
[2,8,1,4,7,3,6,5]=>[2,3,2,1]
[4,2,8,6,1,5,7,3]=>[1,2,1,3,1]
[6,2,4,8,1,7,3,5]=>[1,3,2,2]
[8,2,6,1,4,5,7,3]=>[1,2,4,1]
[3,1,7,8,5,4,6,2]=>[1,3,1,2,1]
[1,6,2,7,4,8,5,3]=>[2,2,2,1,1]
[2,7,1,8,4,3,5,6]=>[2,2,1,3]
[6,7,1,8,3,2,4,5]=>[2,2,1,3]
[6,2,4,7,3,8,1,5]=>[1,3,2,2]
[8,3,6,7,4,1,5,2]=>[1,3,1,2,1]
[6,8,2,3,7,1,5,4]=>[2,3,2,1]
[6,1,8,3,7,4,2,5]=>[1,2,2,1,2]
[1,5,8,3,6,7,2,4]=>[3,3,2]
[2,7,6,3,5,8,1,4]=>[2,1,3,2]
[2,7,5,6,8,1,3,4]=>[2,3,3]
[1,6,5,7,4,8,2,3]=>[2,2,2,2]
[7,6,2,8,1,5,3,4]=>[1,1,2,2,2]
[6,7,2,8,1,3,4,5]=>[2,2,4]
[5,1,6,8,7,2,3,4]=>[1,3,1,3]
[1,5,7,6,8,2,3,4]=>[3,2,3]
[3,5,6,1,4,2,8,7]=>[3,2,2,1]
[3,7,8,2,4,6,5,1]=>[3,3,1,1]
[7,4,6,8,5,3,1,2]=>[1,3,1,1,2]
[8,4,6,7,3,2,1,5]=>[1,3,1,1,2]
[4,2,7,8,1,5,6,3]=>[1,3,3,1]
[2,1,5,7,8,3,6,4]=>[1,4,2,1]
[2,4,7,8,1,5,6,3]=>[4,3,1]
[2,6,3,5,7,8,4,1]=>[2,4,1,1]
[4,6,2,5,7,1,8,3]=>[2,3,2,1]
[5,1,6,7,3,8,2,4]=>[1,3,2,2]
[3,8,6,7,5,1,2,4]=>[2,2,1,3]
[4,7,5,8,6,3,1,2]=>[2,2,1,1,2]
[4,7,1,8,3,5,6,2]=>[2,2,3,1]
[1,6,8,3,2,5,4,7]=>[3,1,2,2]
[6,1,5,4,7,3,2,8]=>[1,2,2,1,2]
[6,1,5,2,3,7,4,8]=>[1,2,3,2]
[7,8,2,1,3,6,4,5]=>[2,1,3,2]
[7,8,5,1,3,2,6,4]=>[2,1,2,2,1]
[6,1,7,5,4,3,2,8]=>[1,2,1,1,1,2]
[5,1,6,8,2,3,7,4]=>[1,3,3,1]
[2,6,8,1,5,4,7,3]=>[3,2,2,1]
[1,5,4,7,6,2,8,3]=>[2,2,1,2,1]
[2,3,7,6,5,1,8,4]=>[3,1,1,2,1]
[7,5,2,1,6,4,3,8]=>[1,1,1,2,1,2]
[5,7,2,4,3,1,8,6]=>[2,2,1,2,1]
[6,7,1,3,4,2,8,5]=>[2,3,2,1]
[4,3,5,8,6,7,1,2]=>[1,3,2,2]
[6,1,5,8,3,2,7,4]=>[1,3,1,2,1]
[3,1,2,4,8,5,7,6]=>[1,4,2,1]
[2,5,8,4,6,3,1,7]=>[3,2,1,2]
[3,2,5,8,4,1,6,7]=>[1,3,1,3]
[1,4,5,8,7,3,2,6]=>[4,1,1,2]
[7,1,5,4,8,3,2,6]=>[1,2,2,1,2]
[6,4,1,7,5,3,2,8]=>[1,1,2,1,1,2]
[5,2,7,4,6,3,1,8]=>[1,2,2,1,2]
[2,7,1,5,3,8,4,6]=>[2,2,2,2]
[2,7,6,4,8,1,5,3]=>[2,1,2,2,1]
[7,2,5,4,8,1,6,3]=>[1,2,2,2,1]
[1,7,2,5,3,8,6,4]=>[2,2,2,1,1]
[7,2,1,4,3,8,5,6]=>[1,1,2,2,2]
[5,4,2,1,3,8,6,7]=>[1,1,1,3,2]
[6,1,4,2,3,8,7,5]=>[1,2,3,1,1]
[7,1,6,5,3,2,8,4]=>[1,2,1,1,2,1]
[7,2,3,8,6,1,5,4]=>[1,3,1,2,1]
[7,2,3,8,6,1,4,5]=>[1,3,1,3]
[6,2,4,8,1,3,7,5]=>[1,3,3,1]
[7,3,2,8,4,1,6,5]=>[1,1,2,1,2,1]
[7,8,3,2,6,1,5,4]=>[2,1,2,2,1]
[6,3,4,8,1,5,2,7]=>[1,3,2,2]
[6,3,4,8,1,5,7,2]=>[1,3,3,1]
[5,3,8,4,1,2,6,7]=>[1,2,1,4]
[2,4,8,3,7,1,5,6]=>[3,2,3]
[5,2,8,4,1,6,3,7]=>[1,2,1,2,2]
[7,6,5,2,1,8,3,4]=>[1,1,1,1,2,2]
[7,6,5,2,1,8,4,3]=>[1,1,1,1,2,1,1]
[2,7,5,1,8,3,6,4]=>[2,1,2,2,1]
[5,1,8,7,4,3,6,2]=>[1,2,1,1,2,1]
[3,8,7,2,4,6,1,5]=>[2,1,3,2]
[5,7,1,3,2,4,8,6]=>[2,2,3,1]
[4,2,7,6,3,5,8,1]=>[1,2,1,3,1]
[8,4,7,6,3,5,1,2]=>[1,2,1,2,2]
[8,1,7,4,2,3,5,6]=>[1,2,1,4]
[6,5,1,3,8,7,4,2]=>[1,1,3,1,1,1]
[4,7,8,3,2,5,1,6]=>[3,1,2,2]
[6,1,8,5,3,7,2,4]=>[1,2,1,2,2]
[5,1,6,8,3,7,4,2]=>[1,3,2,1,1]
[8,6,5,1,7,4,3,2]=>[1,1,1,2,1,1,1]
[7,6,4,1,3,5,8,2]=>[1,1,1,4,1]
[8,2,3,7,1,4,5,6]=>[1,3,4]
[2,8,3,7,1,4,5,6]=>[2,2,4]
[5,6,2,7,4,3,1,8]=>[2,2,1,1,2]
[8,6,2,7,4,1,3,5]=>[1,1,2,1,3]
[3,4,7,6,2,5,1,8]=>[3,1,2,2]
[3,4,7,5,2,6,1,8]=>[3,1,2,2]
[3,4,7,2,5,6,1,8]=>[3,3,2]
[3,7,8,2,6,1,4,5]=>[3,2,3]
[3,7,8,5,2,1,4,6]=>[3,1,1,3]
[6,8,4,7,3,1,2,5]=>[2,2,1,3]
[3,2,7,8,4,1,5,6]=>[1,3,1,3]
[6,8,4,7,3,1,5,2]=>[2,2,1,2,1]
[3,7,8,2,6,1,5,4]=>[3,2,2,1]
[4,8,6,2,1,7,5,3]=>[2,1,1,2,1,1]
[4,7,6,2,1,5,8,3]=>[2,1,1,3,1]
[4,7,6,2,1,5,3,8]=>[2,1,1,2,2]
[4,8,6,5,1,2,7,3]=>[2,1,1,3,1]
[7,5,4,6,1,8,3,2]=>[1,1,2,2,1,1]
[7,5,4,6,1,8,2,3]=>[1,1,2,2,2]
[4,8,6,5,1,2,3,7]=>[2,1,1,4]
[3,4,5,1,8,6,2,7]=>[3,2,1,2]
[3,4,5,1,7,8,6,2]=>[3,3,1,1]
[3,4,5,1,7,6,8,2]=>[3,2,2,1]
[3,8,7,6,5,1,2,4]=>[2,1,1,1,3]
[8,4,6,7,1,2,5,3]=>[1,3,3,1]
[5,7,2,6,1,8,4,3]=>[2,2,2,1,1]
[5,7,2,6,1,3,8,4]=>[2,2,3,1]
[5,8,2,6,1,4,7,3]=>[2,2,3,1]
[7,4,6,8,1,3,2,5]=>[1,3,2,2]
[7,4,6,8,1,3,5,2]=>[1,3,3,1]
[3,8,7,5,6,1,4,2]=>[2,1,2,2,1]
[6,8,4,7,2,1,5,3]=>[2,2,1,2,1]
[3,2,5,6,1,7,4,8]=>[1,3,2,2]
[8,4,6,5,1,7,3,2]=>[1,2,1,2,1,1]
[3,4,5,1,7,6,2,8]=>[3,2,1,2]
[7,4,6,5,1,3,8,2]=>[1,2,1,3,1]
[8,5,4,6,1,3,2,7]=>[1,1,2,2,2]
[3,2,5,6,1,4,8,7]=>[1,3,3,1]
[8,5,4,6,1,3,7,2]=>[1,1,2,3,1]
[1,7,3,4,5,2,8,6]=>[2,3,2,1]
[4,8,2,1,3,5,6,7]=>[2,1,5]
[1,7,2,5,4,3,8,6]=>[2,2,1,2,1]
[2,6,7,3,4,8,1,5]=>[3,3,2]
[2,1,5,7,4,3,8,6]=>[1,3,1,2,1]
[4,1,8,7,5,6,2,3]=>[1,2,1,2,2]
[1,5,8,7,4,3,6,2]=>[3,1,1,2,1]
[6,4,1,3,8,7,5,2]=>[1,1,3,1,1,1]
[2,1,7,4,6,8,3,5]=>[1,2,3,2]
[1,7,2,4,6,8,3,5]=>[2,4,2]
[8,6,4,2,7,3,5,1]=>[1,1,1,2,2,1]
[7,4,6,1,2,3,8,5]=>[1,2,4,1]
[1,8,6,2,7,3,5,4]=>[2,1,2,2,1]
[1,7,8,6,2,3,5,4]=>[3,1,3,1]
[2,1,8,3,5,7,6,4]=>[1,2,3,1,1]
[3,5,8,1,7,6,2,4]=>[3,2,1,2]
[2,8,1,3,6,7,5,4]=>[2,4,1,1]
[7,2,4,8,6,1,5,3]=>[1,3,1,2,1]
[1,7,5,8,3,6,2,4]=>[2,2,2,2]
[6,4,3,2,8,1,7,5]=>[1,1,1,2,2,1]
[6,2,4,3,8,1,7,5]=>[1,2,2,2,1]
[5,7,4,3,1,6,2,8]=>[2,1,1,2,2]
[5,8,4,3,1,6,7,2]=>[2,1,1,3,1]
[4,2,8,1,5,7,6,3]=>[1,2,3,1,1]
[8,3,5,4,2,6,1,7]=>[1,2,1,2,2]
[6,3,7,2,5,4,8,1]=>[1,2,2,2,1]
[5,4,7,3,2,6,8,1]=>[1,2,1,3,1]
[3,7,6,4,2,5,8,1]=>[2,1,1,3,1]
[5,7,2,6,3,4,8,1]=>[2,2,3,1]
[3,7,5,4,6,2,8,1]=>[2,1,2,2,1]
[2,7,5,4,6,8,3,1]=>[2,1,3,1,1]
[8,2,5,4,6,3,1,7]=>[1,2,2,1,2]
[3,7,5,4,2,8,6,1]=>[2,1,1,2,1,1]
[5,7,2,3,6,8,4,1]=>[2,4,1,1]
[3,7,2,6,5,8,4,1]=>[2,2,2,1,1]
[5,4,2,7,6,8,3,1]=>[1,1,2,2,1,1]
[5,8,1,7,3,4,2,6]=>[2,2,2,2]
[6,8,3,2,1,7,4,5]=>[2,1,1,2,2]
[4,8,5,1,7,3,2,6]=>[2,1,2,1,2]
[4,8,1,7,5,3,2,6]=>[2,2,1,1,2]
[5,4,8,2,6,3,1,7]=>[1,2,2,1,2]
[3,7,6,2,8,1,5,4]=>[2,1,2,2,1]
[7,5,2,8,1,3,6,4]=>[1,1,2,3,1]
[5,4,3,7,2,8,6,1]=>[1,1,2,2,1,1]
[4,3,7,6,2,8,5,1]=>[1,2,1,2,1,1]
[6,3,2,5,8,7,4,1]=>[1,1,3,1,1,1]
[7,3,5,2,8,1,6,4]=>[1,2,2,2,1]
[8,3,5,2,6,4,1,7]=>[1,2,2,1,2]
[8,4,3,2,6,5,1,7]=>[1,1,1,2,1,2]
[3,6,5,2,8,7,4,1]=>[2,1,2,1,1,1]
[3,6,5,7,2,8,4,1]=>[2,2,2,1,1]
[4,6,5,3,8,2,1,7]=>[2,1,2,1,2]
[2,6,5,8,7,3,1,4]=>[2,2,1,1,2]
[2,6,5,8,4,3,7,1]=>[2,2,1,2,1]
[8,2,6,5,3,1,4,7]=>[1,2,1,1,3]
[6,3,8,4,1,7,2,5]=>[1,2,1,2,2]
[7,2,8,1,6,4,3,5]=>[1,2,2,1,2]
[3,2,8,7,6,4,1,5]=>[1,2,1,1,1,2]
[5,4,2,8,7,3,1,6]=>[1,1,2,1,1,2]
[3,6,8,5,1,7,2,4]=>[3,1,2,2]
[8,2,6,4,3,5,1,7]=>[1,2,1,2,2]
[3,7,2,8,5,4,6,1]=>[2,2,1,2,1]
[5,4,2,8,6,3,7,1]=>[1,1,2,1,2,1]
[2,8,7,5,3,1,4,6]=>[2,1,1,1,3]
[2,5,6,3,1,4,8,7]=>[3,1,3,1]
[2,4,7,8,5,3,1,6]=>[4,1,1,2]
[2,4,3,7,8,5,1,6]=>[2,3,1,2]
[6,3,4,5,1,2,8,7]=>[1,3,3,1]
[6,5,3,2,4,1,8,7]=>[1,1,1,2,2,1]
[6,5,8,7,3,2,4,1]=>[1,2,1,1,2,1]
[6,3,2,4,1,7,8,5]=>[1,1,2,3,1]
[2,1,4,7,8,5,3,6]=>[1,4,1,2]
[8,3,6,4,7,5,1,2]=>[1,2,2,1,2]
[8,3,1,6,5,7,4,2]=>[1,1,2,2,1,1]
[8,5,6,7,3,1,4,2]=>[1,3,1,2,1]
[8,7,5,3,2,6,4,1]=>[1,1,1,1,2,1,1]
[4,8,7,5,3,2,6,1]=>[2,1,1,1,2,1]
[4,7,8,5,3,1,6,2]=>[3,1,1,2,1]
[8,5,3,1,4,6,7,2]=>[1,1,1,4,1]
[8,3,4,6,5,7,1,2]=>[1,3,2,2]
[8,5,3,6,4,7,1,2]=>[1,1,2,2,2]
[8,5,1,6,4,3,7,2]=>[1,1,2,1,2,1]
[6,1,4,3,7,8,2,5]=>[1,2,3,2]
[6,3,4,7,8,1,2,5]=>[1,4,3]
[7,3,6,5,8,1,2,4]=>[1,2,2,3]
[6,5,3,2,4,8,7,1]=>[1,1,1,3,1,1]
[2,5,7,1,6,8,3,4]=>[3,3,2]
[6,1,2,7,5,8,3,4]=>[1,3,2,2]
[7,1,2,4,6,8,3,5]=>[1,5,2]
[3,7,1,2,4,6,8,5]=>[2,5,1]
[2,4,1,7,3,6,8,5]=>[2,2,3,1]
[2,4,3,6,1,7,8,5]=>[2,2,3,1]
[2,7,3,1,4,6,8,5]=>[2,1,4,1]
[2,8,3,1,6,5,7,4]=>[2,1,2,2,1]
[2,8,5,6,7,3,1,4]=>[2,3,1,2]
[2,7,8,5,3,1,6,4]=>[3,1,1,2,1]
[8,2,4,6,1,5,7,3]=>[1,3,3,1]
[5,8,1,6,2,4,7,3]=>[2,2,3,1]
[3,8,5,6,7,1,2,4]=>[2,3,3]
[6,5,1,2,8,4,7,3]=>[1,1,3,2,1]
[6,1,2,4,8,5,7,3]=>[1,4,2,1]
[2,5,8,1,4,6,7,3]=>[3,4,1]
[2,4,5,8,7,3,6,1]=>[4,1,2,1]
[7,1,4,2,6,8,5,3]=>[1,2,3,1,1]
[7,1,8,5,2,4,6,3]=>[1,2,1,3,1]
[2,1,8,7,5,4,6,3]=>[1,2,1,1,2,1]
[4,8,1,7,5,3,6,2]=>[2,2,1,2,1]
[8,1,7,5,3,4,6,2]=>[1,2,1,3,1]
[8,1,4,3,6,7,5,2]=>[1,2,3,1,1]
[7,8,3,4,1,6,5,2]=>[2,2,2,1,1]
[8,7,3,4,2,6,5,1]=>[1,1,2,2,1,1]
[8,4,5,2,3,7,1,6]=>[1,2,3,2]
[4,7,2,8,6,3,1,5]=>[2,2,1,1,2]
[4,7,5,2,3,8,1,6]=>[2,1,3,2]
[6,4,7,5,2,8,3,1]=>[1,2,1,2,1,1]
[7,5,1,3,6,4,8,2]=>[1,1,3,2,1]
[6,5,2,3,7,8,4,1]=>[1,1,4,1,1]
[7,2,6,3,1,5,8,4]=>[1,2,1,3,1]
[4,6,3,8,7,5,1,2]=>[2,2,1,1,2]
[2,8,4,1,5,7,6,3]=>[2,1,3,1,1]
[1,8,4,2,5,7,6,3]=>[2,1,3,1,1]
[2,8,5,4,1,7,6,3]=>[2,1,1,2,1,1]
[2,5,8,3,7,1,6,4]=>[3,2,2,1]
[1,8,5,2,4,7,6,3]=>[2,1,3,1,1]
[1,4,6,2,8,7,5,3]=>[3,2,1,1,1]
[7,8,2,4,1,6,5,3]=>[2,2,2,1,1]
[2,4,6,1,8,7,5,3]=>[3,2,1,1,1]
[2,8,4,5,1,7,6,3]=>[2,2,2,1,1]
[3,5,8,2,7,6,1,4]=>[3,2,1,2]
[2,1,6,8,7,5,3,4]=>[1,3,1,1,2]
[1,8,2,4,5,7,6,3]=>[2,4,1,1]
[1,2,8,3,5,7,6,4]=>[3,3,1,1]
[1,3,8,2,5,7,6,4]=>[3,3,1,1]
[2,3,8,1,5,7,6,4]=>[3,3,1,1]
[2,6,1,8,7,5,3,4]=>[2,2,1,1,2]
[1,6,2,8,7,5,3,4]=>[2,2,1,1,2]
[1,6,3,8,7,5,2,4]=>[2,2,1,1,2]
[2,6,3,8,7,5,1,4]=>[2,2,1,1,2]
[3,2,8,1,5,7,6,4]=>[1,2,3,1,1]
[3,1,8,2,5,7,6,4]=>[1,2,3,1,1]
[2,8,1,4,5,7,6,3]=>[2,4,1,1]
[7,8,2,1,4,6,5,3]=>[2,1,3,1,1]
[2,3,6,8,7,5,1,4]=>[4,1,1,2]
[3,1,6,8,7,2,5,4]=>[1,3,1,2,1]
[3,8,4,5,1,6,2,7]=>[2,2,2,2]
[6,1,4,5,7,2,3,8]=>[1,4,3]
[8,1,4,7,6,3,2,5]=>[1,3,1,1,2]
[8,3,1,6,4,7,2,5]=>[1,1,2,2,2]
[5,3,8,6,2,7,1,4]=>[1,2,1,2,2]
[8,3,6,1,5,7,2,4]=>[1,2,3,2]
[8,4,6,3,1,2,5,7]=>[1,2,1,4]
[1,8,5,3,7,2,4,6]=>[2,1,2,3]
[6,8,1,4,5,2,3,7]=>[2,3,3]
[1,5,8,4,6,2,3,7]=>[3,2,3]
[2,1,6,5,3,8,4,7]=>[1,2,1,2,2]
[1,4,6,8,5,2,3,7]=>[4,1,3]
[5,6,8,1,4,2,3,7]=>[3,2,3]
[5,7,4,8,1,2,3,6]=>[2,2,4]
[1,5,4,7,2,3,8,6]=>[2,2,3,1]
[4,7,5,1,8,2,3,6]=>[2,1,2,3]
[5,3,7,1,2,4,8,6]=>[1,2,4,1]
[8,2,1,5,3,7,4,6]=>[1,1,2,2,2]
[4,7,8,1,2,6,3,5]=>[3,3,2]
[8,7,1,5,6,2,3,4]=>[1,1,3,3]
[1,6,5,8,7,2,3,4]=>[2,2,1,3]
[8,6,2,1,3,4,7,5]=>[1,1,1,4,1]
[7,2,1,3,6,4,8,5]=>[1,1,3,2,1]
[3,7,1,6,2,4,8,5]=>[2,2,3,1]
[5,1,2,7,6,8,3,4]=>[1,3,2,2]
[6,1,7,2,5,8,3,4]=>[1,2,3,2]
[1,7,6,5,8,2,3,4]=>[2,1,2,3]
[1,6,8,5,7,2,3,4]=>[3,2,3]
[7,5,1,2,6,8,3,4]=>[1,1,4,2]
[6,1,5,2,7,8,3,4]=>[1,2,3,2]
[1,6,3,8,7,2,4,5]=>[2,2,1,3]
[1,7,3,2,4,6,8,5]=>[2,1,4,1]
[8,3,1,4,2,5,7,6]=>[1,1,2,3,1]
[4,1,8,3,2,7,5,6]=>[1,2,1,2,2]
[3,1,2,7,8,4,6,5]=>[1,4,2,1]
[3,8,1,2,7,6,4,5]=>[2,3,1,2]
[7,1,4,8,2,6,3,5]=>[1,3,2,2]
[5,1,2,6,8,7,3,4]=>[1,4,1,2]
[1,8,6,2,5,7,3,4]=>[2,1,3,2]
[5,7,8,1,2,6,3,4]=>[3,3,2]
[8,1,5,7,6,2,3,4]=>[1,3,1,3]
[7,1,6,8,5,2,3,4]=>[1,3,1,3]
[3,7,1,2,8,4,6,5]=>[2,3,2,1]
[7,2,1,8,3,4,6,5]=>[1,1,2,3,1]
[8,3,1,2,7,6,4,5]=>[1,1,3,1,2]
[1,5,8,7,6,2,3,4]=>[3,1,1,3]
[7,8,6,1,5,2,3,4]=>[2,1,2,3]
[7,8,6,3,1,5,2,4]=>[2,1,1,2,2]
[7,8,1,3,4,5,2,6]=>[2,4,2]
[1,7,4,8,2,5,3,6]=>[2,2,2,2]
[3,8,6,1,4,2,7,5]=>[2,1,2,2,1]
[7,1,8,2,4,6,3,5]=>[1,2,3,2]
[7,6,8,4,1,5,3,2]=>[1,2,1,2,1,1]
[7,3,2,8,1,5,4,6]=>[1,1,2,2,2]
[3,5,4,1,7,2,6,8]=>[2,1,2,3]
[6,4,7,3,2,5,1,8]=>[1,2,1,2,2]
[7,6,5,3,8,4,1,2]=>[1,1,1,2,1,2]
[6,4,5,7,8,1,3,2]=>[1,4,2,1]
[3,7,4,1,6,8,5,2]=>[2,1,3,1,1]
[3,1,2,7,6,8,5,4]=>[1,3,2,1,1]
[6,3,2,8,4,5,1,7]=>[1,1,2,2,2]
[6,1,8,3,5,4,2,7]=>[1,2,2,1,2]
[3,8,5,2,4,6,1,7]=>[2,1,3,2]
[1,6,4,8,3,5,2,7]=>[2,2,2,2]
[1,5,4,8,6,3,7,2]=>[2,2,1,2,1]
[4,8,2,5,3,7,1,6]=>[2,2,2,2]
[3,8,4,5,2,6,7,1]=>[2,2,3,1]
[4,1,8,6,5,3,7,2]=>[1,2,1,1,2,1]
[5,7,8,4,6,3,2,1]=>[3,2,1,1,1]
[5,3,2,8,6,4,7,1]=>[1,1,2,1,2,1]
[6,8,1,2,7,4,3,5]=>[2,3,1,2]
[5,8,7,3,6,2,4,1]=>[2,1,2,2,1]
[7,5,2,3,4,8,6,1]=>[1,1,4,1,1]
[7,3,5,4,2,8,6,1]=>[1,2,1,2,1,1]
[5,6,1,3,2,4,7,8]=>[2,2,4]
[2,5,1,3,7,8,6,4]=>[2,4,1,1]
[4,3,7,2,1,8,6,5]=>[1,2,1,2,1,1]
[4,6,7,2,1,3,5,8]=>[3,1,4]
[4,6,2,3,1,5,7,8]=>[2,2,4]
[3,6,4,2,5,1,7,8]=>[2,1,2,3]
[3,1,6,4,7,5,2,8]=>[1,2,2,1,2]
[3,6,2,7,5,4,1,8]=>[2,2,1,1,2]
[2,4,7,5,3,6,1,8]=>[3,1,2,2]
[2,5,7,3,4,1,6,8]=>[3,2,3]
[2,3,5,8,6,4,7,1]=>[4,1,2,1]
[2,4,7,3,8,6,5,1]=>[3,2,1,1,1]
[3,4,2,7,5,8,6,1]=>[2,2,2,1,1]
[3,1,5,4,7,8,6,2]=>[1,2,3,1,1]
[4,5,7,2,3,1,8,6]=>[3,2,2,1]
[3,7,8,1,4,6,5,2]=>[3,3,1,1]
[2,5,8,7,4,1,3,6]=>[3,1,1,3]
[2,6,4,7,5,3,8,1]=>[2,2,1,2,1]
[6,2,4,7,1,3,8,5]=>[1,3,3,1]
[7,3,5,1,4,2,8,6]=>[1,2,2,2,1]
[5,4,7,1,3,2,8,6]=>[1,2,2,2,1]
[6,1,4,7,5,3,8,2]=>[1,3,1,2,1]
[8,7,4,3,1,5,6,2]=>[1,1,1,1,3,1]
[8,7,1,4,3,5,6,2]=>[1,1,2,3,1]
[6,1,8,4,7,3,2,5]=>[1,2,2,1,2]
[4,7,3,6,1,2,8,5]=>[2,2,3,1]
[5,2,1,7,4,3,8,6]=>[1,1,2,1,2,1]
[4,7,6,2,3,1,8,5]=>[2,1,2,2,1]
[7,6,8,2,5,3,4,1]=>[1,2,2,2,1]
[2,3,6,1,8,7,5,4]=>[3,2,1,1,1]
[2,6,8,7,5,3,1,4]=>[3,1,1,1,2]
[6,4,1,7,5,2,8,3]=>[1,1,2,1,2,1]
[5,7,8,2,3,6,1,4]=>[3,3,2]
[4,8,7,1,2,5,6,3]=>[2,1,4,1]
[2,8,7,4,1,5,6,3]=>[2,1,1,3,1]
[8,6,2,1,5,7,4,3]=>[1,1,1,3,1,1]
[3,8,6,7,5,2,1,4]=>[2,2,1,1,2]
[6,1,3,7,5,8,2,4]=>[1,3,2,2]
[4,7,3,1,8,5,6,2]=>[2,1,2,2,1]
[2,6,7,5,3,4,8,1]=>[3,1,3,1]
[2,6,4,5,7,3,8,1]=>[2,3,2,1]
[6,1,4,5,8,3,7,2]=>[1,4,2,1]
[6,1,8,5,3,4,7,2]=>[1,2,1,3,1]
[4,1,5,6,8,3,7,2]=>[1,4,2,1]
[5,4,7,1,8,6,2,3]=>[1,2,2,1,2]
[6,4,1,8,7,2,5,3]=>[1,1,2,1,2,1]
[4,5,7,2,6,8,1,3]=>[3,3,2]
[2,8,5,4,1,7,3,6]=>[2,1,1,2,2]
[3,2,8,5,1,7,4,6]=>[1,2,1,2,2]
[1,3,8,5,2,7,4,6]=>[3,1,2,2]
[1,3,8,6,7,2,4,5]=>[3,2,3]
[2,8,3,6,7,1,4,5]=>[2,3,3]
[2,8,5,6,1,3,7,4]=>[2,2,3,1]
[2,8,3,7,6,1,4,5]=>[2,2,1,3]
[2,8,7,4,6,1,3,5]=>[2,1,2,3]
[3,7,8,4,6,1,2,5]=>[3,2,3]
[4,7,3,8,6,1,2,5]=>[2,2,1,3]
[4,2,7,8,6,1,3,5]=>[1,3,1,3]
[3,7,8,6,5,1,4,2]=>[3,1,1,2,1]
[6,3,8,5,2,4,7,1]=>[1,2,1,3,1]
[7,3,8,6,5,2,4,1]=>[1,2,1,1,2,1]
[1,3,8,7,6,2,4,5]=>[3,1,1,3]
[1,4,7,8,6,2,3,5]=>[4,1,3]
[1,7,5,6,8,2,3,4]=>[2,3,3]
[7,4,6,8,5,2,3,1]=>[1,3,1,2,1]
[7,4,5,8,2,6,3,1]=>[1,3,2,1,1]
[4,6,5,8,1,3,7,2]=>[2,2,3,1]
[5,7,6,4,8,1,3,2]=>[2,1,2,2,1]
[7,5,3,6,8,2,1,4]=>[1,1,3,1,2]
[5,2,6,7,8,1,3,4]=>[1,4,3]
[4,5,7,8,1,6,2,3]=>[4,2,2]
[4,5,6,8,1,2,7,3]=>[4,3,1]
[3,5,8,6,1,2,7,4]=>[3,1,3,1]
[3,6,8,7,5,1,2,4]=>[3,1,1,3]
[3,6,8,4,7,1,2,5]=>[3,2,3]
[4,2,6,8,7,1,3,5]=>[1,3,1,3]
[1,4,6,8,7,2,3,5]=>[4,1,3]
[4,5,3,8,1,7,2,6]=>[2,2,2,2]
[3,5,8,4,1,7,2,6]=>[3,1,2,2]
[3,4,8,1,5,7,2,6]=>[3,3,2]
[5,3,8,4,2,7,1,6]=>[1,2,1,2,2]
[5,2,4,8,1,7,3,6]=>[1,3,2,2]
[5,3,8,7,2,6,1,4]=>[1,2,1,2,2]
[5,3,8,6,2,1,7,4]=>[1,2,1,1,2,1]
[1,6,5,7,8,2,3,4]=>[2,3,3]
[6,7,3,5,8,2,1,4]=>[2,3,1,2]
[6,7,4,8,5,2,3,1]=>[2,2,1,2,1]
[5,6,4,8,2,3,7,1]=>[2,2,3,1]
[6,5,4,8,1,3,7,2]=>[1,1,2,3,1]
[7,6,4,8,5,1,3,2]=>[1,1,2,1,2,1]
[6,2,7,5,8,1,3,4]=>[1,2,2,3]
[7,2,6,5,8,1,3,4]=>[1,2,2,3]
[7,2,6,4,1,3,5,8]=>[1,2,1,4]
[7,1,3,4,6,2,5,8]=>[1,4,3]
[7,3,6,5,2,4,1,8]=>[1,2,1,2,2]
[6,3,7,5,2,4,8,1]=>[1,2,1,3,1]
[8,1,2,7,4,5,3,6]=>[1,3,2,2]
[2,5,7,4,6,1,3,8]=>[3,2,3]
[8,5,7,4,3,1,2,6]=>[1,2,1,1,3]
[4,6,8,3,1,2,7,5]=>[3,1,3,1]
[6,1,7,4,5,3,8,2]=>[1,2,2,2,1]
[8,5,7,3,2,1,4,6]=>[1,2,1,1,3]
[8,2,7,3,1,5,4,6]=>[1,2,1,2,2]
[8,2,1,7,4,5,3,6]=>[1,1,2,2,2]
[2,6,4,8,3,1,7,5]=>[2,2,1,2,1]
[8,1,3,7,5,6,4,2]=>[1,3,2,1,1]
[3,8,2,6,1,4,7,5]=>[2,2,3,1]
[1,6,4,7,5,8,3,2]=>[2,2,2,1,1]
[1,6,8,5,7,3,2,4]=>[3,2,1,2]
[1,2,5,3,8,6,7,4]=>[3,2,2,1]
[6,3,5,7,8,1,2,4]=>[1,4,3]
[4,1,6,5,7,8,2,3]=>[1,2,3,2]
[3,8,1,2,6,4,7,5]=>[2,3,2,1]
[6,1,3,7,4,2,8,5]=>[1,3,1,2,1]
[6,7,2,4,1,3,8,5]=>[2,2,3,1]
[8,7,1,3,5,4,2,6]=>[1,1,3,1,2]
[7,8,4,6,3,2,5,1]=>[2,2,1,2,1]
[8,7,1,4,6,2,5,3]=>[1,1,3,2,1]
[7,3,8,4,2,6,5,1]=>[1,2,1,2,1,1]
[8,5,3,4,2,7,1,6]=>[1,1,2,2,2]
[8,1,3,4,5,2,7,6]=>[1,4,2,1]
[8,4,3,5,1,7,2,6]=>[1,1,2,2,2]
[8,4,5,2,1,3,7,6]=>[1,2,1,3,1]
[4,8,2,6,1,3,7,5]=>[2,2,3,1]
[3,4,1,6,8,2,7,5]=>[2,3,2,1]
[1,3,8,2,5,6,7,4]=>[3,4,1]
[3,7,8,2,5,6,4,1]=>[3,3,1,1]
[8,1,7,5,2,6,4,3]=>[1,2,1,2,1,1]
[1,8,6,7,2,5,4,3]=>[2,2,2,1,1]
[7,6,8,3,5,4,2,1]=>[1,2,2,1,1,1]
[1,6,7,3,8,5,4,2]=>[3,2,1,1,1]
[7,3,4,8,1,6,5,2]=>[1,3,2,1,1]
[7,8,4,6,2,1,5,3]=>[2,2,1,2,1]
[8,7,6,2,3,1,5,4]=>[1,1,1,2,2,1]
[8,7,2,4,6,1,5,3]=>[1,1,3,2,1]
[2,8,6,7,1,5,4,3]=>[2,2,2,1,1]
[7,8,6,5,2,4,3,1]=>[2,1,1,2,1,1]
[3,6,7,5,2,8,4,1]=>[3,1,2,1,1]
[5,4,6,7,8,1,3,2]=>[1,4,2,1]
[5,3,6,7,8,1,4,2]=>[1,4,2,1]
[5,3,7,6,8,4,1,2]=>[1,2,2,1,2]
[6,3,7,5,4,8,2,1]=>[1,2,1,2,1,1]
[5,3,7,6,4,8,1,2]=>[1,2,1,2,2]
[7,5,3,2,8,6,4,1]=>[1,1,1,2,1,1,1]
[5,4,8,6,7,2,3,1]=>[1,2,2,2,1]
[2,7,8,4,6,3,5,1]=>[3,2,2,1]
[5,4,8,6,3,1,2,7]=>[1,2,1,1,3]
[6,4,3,7,5,2,8,1]=>[1,1,2,1,2,1]
[4,5,7,3,6,2,8,1]=>[3,2,2,1]
[4,5,6,3,8,2,7,1]=>[3,2,2,1]
[8,4,7,1,3,5,2,6]=>[1,2,3,2]
[5,4,8,7,2,1,3,6]=>[1,2,1,1,3]
[2,5,4,7,8,1,3,6]=>[2,3,3]
[7,1,6,3,5,2,8,4]=>[1,2,2,2,1]
[7,1,4,3,6,2,8,5]=>[1,2,2,2,1]
[5,3,6,4,8,2,7,1]=>[1,2,2,2,1]
[5,3,7,4,6,2,8,1]=>[1,2,2,2,1]
[8,2,6,3,7,4,5,1]=>[1,2,2,2,1]
[8,2,4,7,3,5,6,1]=>[1,3,3,1]
[8,2,6,5,7,3,4,1]=>[1,2,2,2,1]
[8,3,4,5,7,2,6,1]=>[1,4,2,1]
[4,5,6,2,7,3,8,1]=>[3,2,2,1]
[5,2,7,1,3,6,8,4]=>[1,2,4,1]
[5,3,1,7,6,2,8,4]=>[1,1,2,1,2,1]
[7,5,1,6,4,2,8,3]=>[1,1,2,1,2,1]
[7,4,6,1,5,2,8,3]=>[1,2,2,2,1]
[5,4,6,2,8,3,7,1]=>[1,2,2,2,1]
[8,4,6,1,7,2,5,3]=>[1,2,2,2,1]
[8,5,1,6,2,7,4,3]=>[1,1,2,2,1,1]
[5,2,1,6,3,8,7,4]=>[1,1,2,2,1,1]
[4,5,6,3,7,1,8,2]=>[3,2,2,1]
[6,3,2,8,5,4,1,7]=>[1,1,2,1,1,2]
[2,7,4,1,5,3,6,8]=>[2,1,2,3]
[3,8,4,2,5,1,6,7]=>[2,1,2,3]
[4,3,1,5,2,8,6,7]=>[1,1,2,2,2]
[8,5,4,1,3,2,6,7]=>[1,1,1,2,3]
[3,8,4,1,5,2,6,7]=>[2,1,2,3]
[2,5,4,3,8,1,6,7]=>[2,1,2,3]
[2,5,7,4,3,1,6,8]=>[3,1,1,3]
[5,3,4,2,7,1,6,8]=>[1,2,2,3]
[3,7,5,4,1,2,6,8]=>[2,1,1,4]
[7,5,1,4,3,2,6,8]=>[1,1,2,1,3]
[4,5,3,1,2,7,6,8]=>[2,1,3,2]
[4,2,5,1,3,8,7,6]=>[1,2,3,1,1]
[4,3,5,1,2,7,6,8]=>[1,2,3,2]
[5,3,4,1,7,2,6,8]=>[1,2,2,3]
[4,1,6,3,5,2,7,8]=>[1,2,2,3]
[4,1,6,5,3,2,7,8]=>[1,2,1,1,3]
[7,1,5,3,2,6,4,8]=>[1,2,1,2,2]
[4,2,1,8,6,3,7,5]=>[1,1,2,1,2,1]
[7,3,6,4,1,2,5,8]=>[1,2,1,4]
[7,1,6,3,5,2,4,8]=>[1,2,2,3]
[3,1,7,2,5,6,4,8]=>[1,2,3,2]
[2,6,5,3,1,4,7,8]=>[2,1,1,4]
[7,6,2,1,5,3,4,8]=>[1,1,1,2,3]
[3,7,5,4,2,1,6,8]=>[2,1,1,1,3]
[3,7,2,4,1,6,5,8]=>[2,2,2,2]
[2,7,6,4,1,3,5,8]=>[2,1,1,4]
[7,3,2,1,6,4,5,8]=>[1,1,1,2,3]
[2,7,3,1,6,4,5,8]=>[2,1,2,3]
[5,8,3,2,7,4,1,6]=>[2,1,2,1,2]
[2,8,6,1,7,4,3,5]=>[2,1,2,1,2]
[7,3,2,6,1,5,4,8]=>[1,1,2,2,2]
[2,7,3,6,1,5,4,8]=>[2,2,2,2]
[2,3,7,6,1,5,4,8]=>[3,1,2,2]
[2,5,4,6,1,3,7,8]=>[2,2,4]
[2,5,6,4,1,3,7,8]=>[3,1,4]
[2,5,4,1,7,3,6,8]=>[2,1,2,3]
[6,4,1,7,2,5,3,8]=>[1,1,2,2,2]
[2,8,5,7,1,3,6,4]=>[2,2,3,1]
[8,5,2,6,1,3,7,4]=>[1,1,2,3,1]
[7,1,5,6,3,2,4,8]=>[1,3,1,3]
[7,1,2,5,4,6,3,8]=>[1,3,2,2]
[2,4,1,6,5,3,7,8]=>[2,2,1,3]
[4,1,2,7,5,6,3,8]=>[1,3,2,2]
[7,1,2,6,5,4,3,8]=>[1,3,1,1,2]
[7,5,1,4,6,2,3,8]=>[1,1,3,3]
[7,1,3,5,6,2,4,8]=>[1,4,3]
[8,2,1,5,6,3,7,4]=>[1,1,3,2,1]
[2,8,5,1,6,4,7,3]=>[2,1,2,2,1]
[6,1,4,5,3,2,7,8]=>[1,3,1,3]
[3,1,6,5,4,2,7,8]=>[1,2,1,1,3]
[3,1,4,6,5,2,7,8]=>[1,3,1,3]
[6,4,1,5,3,2,8,7]=>[1,1,2,1,2,1]
[8,6,1,5,2,3,7,4]=>[1,1,2,3,1]
[5,7,3,1,8,4,2,6]=>[2,1,2,1,2]
[2,1,8,6,3,7,5,4]=>[1,2,1,2,1,1]
[4,8,2,3,7,6,5,1]=>[2,3,1,1,1]
[5,8,3,1,7,6,4,2]=>[2,1,2,1,1,1]
[7,8,5,1,2,6,4,3]=>[2,1,3,1,1]
[6,8,5,7,2,4,3,1]=>[2,2,2,1,1]
[7,4,6,3,1,8,2,5]=>[1,2,1,2,2]
[7,4,1,6,8,3,2,5]=>[1,1,3,1,2]
[7,6,3,2,8,5,1,4]=>[1,1,1,2,1,2]
[7,5,1,8,4,6,2,3]=>[1,1,2,2,2]
[7,6,2,4,1,3,8,5]=>[1,1,2,3,1]
[7,3,8,5,2,6,1,4]=>[1,2,1,2,2]
[5,3,8,4,7,2,1,6]=>[1,2,2,1,2]
[5,6,3,8,7,4,1,2]=>[2,2,1,1,2]
[5,2,6,8,7,4,1,3]=>[1,3,1,1,2]
[6,7,3,8,1,5,4,2]=>[2,2,2,1,1]
[6,3,8,4,1,5,2,7]=>[1,2,1,2,2]
[6,3,8,1,5,4,2,7]=>[1,2,2,1,2]
[6,3,8,1,4,5,2,7]=>[1,2,3,2]
[4,3,8,5,7,2,6,1]=>[1,2,2,2,1]
[6,3,8,5,1,4,2,7]=>[1,2,1,2,2]
[6,3,8,5,4,1,2,7]=>[1,2,1,1,3]
[6,3,8,4,5,1,2,7]=>[1,2,2,3]
[2,6,3,4,8,1,5,7]=>[2,3,3]
[5,6,1,8,7,4,3,2]=>[2,2,1,1,1,1]
[5,2,3,1,4,8,6,7]=>[1,2,3,2]
[5,4,1,3,2,8,6,7]=>[1,1,2,2,2]
[3,7,4,2,8,5,6,1]=>[2,1,2,2,1]
[5,1,4,3,2,8,6,7]=>[1,2,1,2,2]
[5,1,3,4,2,8,6,7]=>[1,3,2,2]
[5,2,1,4,3,8,6,7]=>[1,1,2,2,2]
[5,2,1,3,4,8,6,7]=>[1,1,4,2]
[5,1,2,4,3,8,6,7]=>[1,3,2,2]
[6,7,1,8,3,5,4,2]=>[2,2,2,1,1]
[3,2,6,1,8,4,5,7]=>[1,2,2,3]
[4,2,7,3,8,5,1,6]=>[1,2,2,1,2]
[4,7,3,2,8,5,1,6]=>[2,1,2,1,2]
[2,3,7,4,8,5,1,6]=>[3,2,1,2]
[5,7,6,8,2,4,3,1]=>[2,2,2,1,1]
[4,3,7,2,8,5,6,1]=>[1,2,2,2,1]
[2,3,7,1,8,5,4,6]=>[3,2,1,2]
[5,3,1,2,4,8,6,7]=>[1,1,4,2]
[5,4,3,1,2,8,6,7]=>[1,1,1,3,2]
[5,2,4,1,3,8,6,7]=>[1,2,3,2]
[5,2,4,3,1,8,6,7]=>[1,2,1,2,2]
[3,4,2,7,8,5,6,1]=>[2,3,2,1]
[4,3,1,6,8,2,5,7]=>[1,1,3,3]
[5,3,4,1,2,8,6,7]=>[1,2,3,2]
[5,3,2,4,1,8,6,7]=>[1,1,2,2,2]
[5,2,3,4,1,8,6,7]=>[1,3,2,2]
[2,6,1,7,4,5,8,3]=>[2,2,3,1]
[5,1,7,3,4,6,8,2]=>[1,2,4,1]
[5,8,7,4,3,1,6,2]=>[2,1,1,1,2,1]
[6,8,7,1,4,3,5,2]=>[2,1,2,2,1]
[7,3,1,4,5,8,6,2]=>[1,1,4,1,1]
[6,8,1,3,4,5,7,2]=>[2,5,1]
[5,8,1,3,4,6,7,2]=>[2,5,1]
[5,2,6,3,7,8,1,4]=>[1,2,3,2]
[3,5,2,8,1,6,7,4]=>[2,2,3,1]
[4,5,6,2,8,1,7,3]=>[3,2,2,1]
[2,6,1,4,8,5,7,3]=>[2,3,2,1]
[6,1,8,4,2,5,3,7]=>[1,2,1,2,2]
[8,4,5,1,6,2,3,7]=>[1,2,2,3]
[5,1,6,3,2,8,4,7]=>[1,2,1,2,2]
[3,1,7,8,2,5,4,6]=>[1,3,2,2]
[6,2,8,3,5,7,1,4]=>[1,2,3,2]
[6,2,3,7,4,1,8,5]=>[1,3,1,2,1]
[6,3,7,4,1,2,5,8]=>[1,2,1,4]
[7,2,6,8,4,3,1,5]=>[1,3,1,1,2]
[3,7,2,8,6,5,1,4]=>[2,2,1,1,2]
[5,2,7,3,6,1,8,4]=>[1,2,2,2,1]
[3,6,7,5,1,2,4,8]=>[3,1,4]
[2,7,5,8,1,6,4,3]=>[2,2,2,1,1]
[7,4,5,1,8,2,3,6]=>[1,2,2,3]
[4,7,1,8,2,3,6,5]=>[2,2,3,1]
[7,2,3,1,8,4,5,6]=>[1,2,2,3]
[2,1,4,8,3,7,5,6]=>[1,3,2,2]
[6,2,8,1,7,3,4,5]=>[1,2,2,3]
[4,8,1,6,7,3,2,5]=>[2,3,1,2]
[1,2,7,8,4,3,6,5]=>[4,1,2,1]
[5,8,1,4,3,2,7,6]=>[2,2,1,2,1]
[4,8,1,3,5,6,2,7]=>[2,4,2]
[6,8,1,3,2,4,5,7]=>[2,2,4]
[3,7,4,1,5,6,8,2]=>[2,1,4,1]
[5,3,7,8,4,2,6,1]=>[1,3,1,2,1]
[6,3,7,8,2,4,5,1]=>[1,3,3,1]
[7,3,5,2,4,8,6,1]=>[1,2,3,1,1]
[8,5,2,4,3,1,7,6]=>[1,1,2,1,2,1]
[7,5,4,2,3,1,8,6]=>[1,1,1,2,2,1]
[4,6,5,3,1,8,2,7]=>[2,1,1,2,2]
[5,7,4,1,3,2,8,6]=>[2,1,2,2,1]
[8,6,2,5,1,7,3,4]=>[1,1,2,2,2]
[3,7,6,1,8,4,5,2]=>[2,1,2,2,1]
[7,5,6,2,8,1,3,4]=>[1,2,2,3]
[3,5,6,4,8,1,7,2]=>[3,2,2,1]
[8,4,2,5,3,7,1,6]=>[1,1,2,2,2]
[3,5,4,6,7,1,8,2]=>[2,3,2,1]
[1,4,2,6,5,8,7,3]=>[2,2,2,1,1]
[1,3,2,6,4,8,7,5]=>[2,2,2,1,1]
[1,4,2,5,3,8,7,6]=>[2,2,2,1,1]
[1,4,2,6,3,8,7,5]=>[2,2,2,1,1]
[1,5,2,6,4,8,7,3]=>[2,2,2,1,1]
[1,5,3,6,4,8,7,2]=>[2,2,2,1,1]
[1,6,2,5,3,8,7,4]=>[2,2,2,1,1]
[2,5,1,4,3,8,7,6]=>[2,2,2,1,1]
[1,7,2,5,4,8,6,3]=>[2,2,2,1,1]
[1,7,3,5,4,8,6,2]=>[2,2,2,1,1]
[1,8,2,6,3,7,5,4]=>[2,2,2,1,1]
[1,8,3,6,4,7,5,2]=>[2,2,2,1,1]
[1,7,3,6,4,8,5,2]=>[2,2,2,1,1]
[1,7,2,6,4,8,5,3]=>[2,2,2,1,1]
[1,7,2,6,3,8,5,4]=>[2,2,2,1,1]
[1,5,2,7,4,8,6,3]=>[2,2,2,1,1]
[1,4,3,7,5,8,6,2]=>[2,2,2,1,1]
[1,4,2,8,5,7,6,3]=>[2,2,2,1,1]
[1,3,2,8,4,7,6,5]=>[2,2,2,1,1]
[4,8,1,3,2,6,5,7]=>[2,2,2,2]
[1,5,2,8,4,7,6,3]=>[2,2,2,1,1]
[1,5,3,8,4,7,6,2]=>[2,2,2,1,1]
[1,6,3,8,4,7,5,2]=>[2,2,2,1,1]
[1,6,2,8,3,7,5,4]=>[2,2,2,1,1]
[2,7,3,8,1,5,4,6]=>[2,2,2,2]
[2,8,3,7,1,5,4,6]=>[2,2,2,2]
[1,8,4,7,3,6,5,2]=>[2,2,2,1,1]
[1,7,4,8,3,6,5,2]=>[2,2,2,1,1]
[3,8,2,6,1,5,4,7]=>[2,2,2,2]
[2,6,3,8,1,5,4,7]=>[2,2,2,2]
[8,3,1,4,2,6,5,7]=>[1,1,2,2,2]
[4,8,7,3,5,2,1,6]=>[2,1,2,1,2]
[6,8,7,3,5,2,4,1]=>[2,1,2,2,1]
[8,3,5,1,2,6,4,7]=>[1,2,3,2]
[8,6,3,1,5,4,2,7]=>[1,1,1,2,1,2]
[8,6,4,1,5,3,2,7]=>[1,1,1,2,1,2]
[8,6,5,4,1,3,2,7]=>[1,1,1,1,2,2]
[5,3,8,7,4,6,2,1]=>[1,2,1,2,1,1]
[2,3,8,7,4,6,1,5]=>[3,1,2,2]
[8,3,5,7,4,1,2,6]=>[1,3,1,3]
[4,8,5,3,1,2,7,6]=>[2,1,1,3,1]
[6,8,7,3,1,5,4,2]=>[2,1,1,2,1,1]
[6,8,5,4,1,3,7,2]=>[2,1,1,3,1]
[2,5,8,7,4,6,3,1]=>[3,1,2,1,1]
[4,8,7,6,5,1,3,2]=>[2,1,1,1,2,1]
[3,8,7,5,1,6,2,4]=>[2,1,1,2,2]
[2,3,8,7,5,6,1,4]=>[3,1,2,2]
[2,8,7,1,3,6,4,5]=>[2,1,3,2]
[8,5,4,7,2,1,3,6]=>[1,1,2,1,3]
[6,8,7,3,5,2,1,4]=>[2,1,2,1,2]
[3,5,8,6,4,2,7,1]=>[3,1,1,2,1]
[6,8,4,1,5,2,7,3]=>[2,1,2,2,1]
[6,8,2,1,7,5,3,4]=>[2,1,2,1,2]
[5,8,4,6,1,2,7,3]=>[2,2,3,1]
[2,4,8,6,5,1,7,3]=>[3,1,1,2,1]
[4,8,7,6,5,2,1,3]=>[2,1,1,1,1,2]
[4,8,7,5,1,6,2,3]=>[2,1,1,2,2]
[4,5,2,1,8,6,7,3]=>[2,1,2,2,1]
[4,5,8,3,1,6,7,2]=>[3,1,3,1]
[5,7,2,8,4,6,1,3]=>[2,2,2,2]
[6,7,3,2,4,8,5,1]=>[2,1,3,1,1]
[7,2,8,6,4,5,1,3]=>[1,2,1,2,2]
[8,7,2,6,5,1,3,4]=>[1,1,2,1,3]
[5,2,7,8,4,1,3,6]=>[1,3,1,3]
[2,7,8,6,4,1,3,5]=>[3,1,1,3]
[7,6,3,5,2,8,4,1]=>[1,1,2,2,1,1]
[6,2,7,4,8,5,3,1]=>[1,2,2,1,1,1]
[8,6,5,1,7,2,4,3]=>[1,1,1,2,2,1]
[6,8,5,1,7,3,2,4]=>[2,1,2,1,2]
[1,6,8,3,7,4,2,5]=>[3,2,1,2]
[5,1,6,3,4,8,2,7]=>[1,2,3,2]
[3,5,2,6,4,8,1,7]=>[2,2,2,2]
[3,5,2,4,8,1,7,6]=>[2,3,2,1]
[6,3,8,2,4,1,7,5]=>[1,2,2,2,1]
[4,6,3,8,7,5,2,1]=>[2,2,1,1,1,1]
[6,3,8,7,5,4,2,1]=>[1,2,1,1,1,1,1]
[6,8,4,2,1,7,5,3]=>[2,1,1,2,1,1]
[5,2,6,4,3,8,1,7]=>[1,2,1,2,2]
[6,5,3,1,4,8,2,7]=>[1,1,1,3,2]
[3,1,7,8,6,4,2,5]=>[1,3,1,1,2]
[3,8,1,7,6,2,5,4]=>[2,2,1,2,1]
[8,1,7,6,4,2,5,3]=>[1,2,1,1,2,1]
[7,2,6,3,8,5,4,1]=>[1,2,2,1,1,1]
[7,3,8,6,4,1,5,2]=>[1,2,1,1,2,1]
[1,7,5,8,2,4,3,6]=>[2,2,2,2]
[6,1,5,2,4,8,3,7]=>[1,2,3,2]
[1,5,6,3,8,2,4,7]=>[3,2,3]
[8,7,1,3,6,5,2,4]=>[1,1,3,1,2]
[2,6,7,4,3,8,5,1]=>[3,1,2,1,1]
[5,2,4,7,3,8,6,1]=>[1,3,2,1,1]
[1,5,8,7,2,4,6,3]=>[3,1,3,1]
[1,4,8,7,3,6,5,2]=>[3,1,2,1,1]
[8,3,7,2,5,1,6,4]=>[1,2,2,2,1]
[3,7,2,8,1,5,4,6]=>[2,2,2,2]
[3,2,6,1,5,8,4,7]=>[1,2,3,2]
[7,2,1,5,8,4,3,6]=>[1,1,3,1,2]
[7,2,8,1,4,3,6,5]=>[1,2,2,2,1]
[1,7,8,3,2,6,5,4]=>[3,1,2,1,1]
[1,7,4,8,3,2,6,5]=>[2,2,1,2,1]
[1,7,5,4,8,3,2,6]=>[2,1,2,1,2]
[6,1,5,4,3,8,2,7]=>[1,2,1,2,2]
[1,7,4,5,6,8,2,3]=>[2,4,2]
[1,6,4,2,3,5,7,8]=>[2,1,5]
[1,6,5,2,3,4,7,8]=>[2,1,5]
[1,8,5,2,3,4,6,7]=>[2,1,5]
[1,8,7,2,3,4,5,6]=>[2,1,5]
[1,5,8,6,2,3,4,7]=>[3,1,4]
[1,6,8,5,2,3,4,7]=>[3,1,4]
[1,6,7,5,2,3,4,8]=>[3,1,4]
[1,6,5,7,2,3,4,8]=>[2,2,4]
[1,7,5,6,2,3,4,8]=>[2,2,4]
[1,7,6,5,2,3,4,8]=>[2,1,1,4]
[1,3,2,7,6,4,5,8]=>[2,2,1,3]
[1,2,3,7,6,4,5,8]=>[4,1,3]
[1,5,4,2,3,7,6,8]=>[2,1,3,2]
[1,8,2,3,7,4,5,6]=>[2,3,3]
[1,5,4,2,3,8,6,7]=>[2,1,3,2]
[1,3,2,8,6,4,5,7]=>[2,2,1,3]
[1,8,6,5,2,3,4,7]=>[2,1,1,4]
[1,7,5,8,2,3,4,6]=>[2,2,4]
[1,8,7,5,2,3,4,6]=>[2,1,1,4]
[1,7,4,2,8,3,5,6]=>[2,1,2,3]
[1,7,8,5,2,3,4,6]=>[3,1,4]
[2,1,5,8,6,3,7,4]=>[1,3,1,2,1]
[2,5,8,4,6,1,7,3]=>[3,2,2,1]
[2,5,3,8,6,1,7,4]=>[2,2,1,2,1]
[2,6,3,5,8,1,7,4]=>[2,3,2,1]
[6,3,2,5,8,1,7,4]=>[1,1,3,2,1]
[5,3,2,8,6,1,7,4]=>[1,1,2,1,2,1]
[5,8,4,6,1,3,7,2]=>[2,2,3,1]
[5,3,8,6,1,4,7,2]=>[1,2,1,3,1]
[2,6,5,4,8,1,7,3]=>[2,1,2,2,1]
[8,3,5,7,2,6,4,1]=>[1,3,2,1,1]
[2,4,6,8,5,3,7,1]=>[4,1,2,1]
[2,4,8,1,7,6,5,3]=>[3,2,1,1,1]
[4,3,8,1,5,7,6,2]=>[1,2,3,1,1]
[3,8,4,1,5,7,6,2]=>[2,1,3,1,1]
[4,3,6,8,5,2,7,1]=>[1,3,1,2,1]
[8,5,4,7,2,6,3,1]=>[1,1,2,2,1,1]
[3,6,8,5,4,2,7,1]=>[3,1,1,2,1]
[3,6,4,8,5,2,7,1]=>[2,2,1,2,1]
[3,6,4,1,8,2,7,5]=>[2,1,2,2,1]
[3,6,4,1,5,2,8,7]=>[2,1,2,2,1]
[4,8,6,5,1,3,7,2]=>[2,1,1,3,1]
[2,8,3,5,6,7,1,4]=>[2,4,2]
[5,6,2,4,7,1,8,3]=>[2,3,2,1]
[2,7,5,4,6,1,8,3]=>[2,1,2,2,1]
[2,3,7,4,6,1,8,5]=>[3,2,2,1]
[2,6,7,4,1,3,8,5]=>[3,1,3,1]
[6,5,7,4,1,3,8,2]=>[1,2,1,3,1]
[2,4,6,3,5,7,8,1]=>[3,4,1]
[4,1,6,3,5,7,8,2]=>[1,2,4,1]
[3,6,4,2,5,7,8,1]=>[2,1,4,1]
[2,3,6,1,5,7,8,4]=>[3,4,1]
[4,3,6,2,5,7,8,1]=>[1,2,4,1]
[4,6,1,2,5,7,8,3]=>[2,5,1]
[2,6,4,1,5,7,8,3]=>[2,1,4,1]
[2,4,1,6,5,7,8,3]=>[2,2,3,1]
[8,6,5,3,1,7,4,2]=>[1,1,1,1,2,1,1]
[6,4,7,3,1,8,5,2]=>[1,2,1,2,1,1]
[6,4,7,5,3,1,8,2]=>[1,2,1,1,2,1]
[6,4,2,7,5,1,8,3]=>[1,1,2,1,2,1]
[7,5,4,2,6,3,1,8]=>[1,1,1,2,1,2]
[7,5,4,2,6,1,8,3]=>[1,1,1,2,2,1]
[7,5,4,6,3,1,8,2]=>[1,1,2,1,2,1]
[4,7,3,1,8,6,5,2]=>[2,1,2,1,1,1]
[4,8,6,5,3,1,7,2]=>[2,1,1,1,2,1]
[5,6,4,7,3,1,8,2]=>[2,2,1,2,1]
[5,6,4,2,7,1,8,3]=>[2,1,2,2,1]
[5,3,6,8,2,1,7,4]=>[1,3,1,2,1]
[4,2,7,5,3,1,8,6]=>[1,2,1,1,2,1]
[4,2,8,6,5,3,1,7]=>[1,2,1,1,1,2]
[5,4,2,8,6,3,1,7]=>[1,1,2,1,1,2]
[5,6,3,2,8,4,1,7]=>[2,1,2,1,2]
[5,3,6,4,8,2,1,7]=>[1,2,2,1,2]
[6,8,4,3,2,5,1,7]=>[2,1,1,2,2]
[4,8,3,2,6,5,1,7]=>[2,1,2,1,2]
[7,3,2,5,4,1,8,6]=>[1,1,2,1,2,1]
[7,3,2,5,1,8,6,4]=>[1,1,2,2,1,1]
[4,6,3,8,7,2,1,5]=>[2,2,1,1,2]
[4,7,6,3,2,5,1,8]=>[2,1,1,2,2]
[4,7,6,3,8,2,1,5]=>[2,1,2,1,2]
[4,7,3,8,6,2,1,5]=>[2,2,1,1,2]
[5,4,8,7,2,1,6,3]=>[1,2,1,1,2,1]
[7,5,4,8,2,1,6,3]=>[1,1,2,1,2,1]
[5,7,3,2,6,1,8,4]=>[2,1,2,2,1]
[5,7,3,2,6,4,1,8]=>[2,1,2,1,2]
[6,4,2,7,1,8,5,3]=>[1,1,2,2,1,1]
[6,2,7,5,1,8,4,3]=>[1,2,1,2,1,1]
[2,7,5,1,8,6,4,3]=>[2,1,2,1,1,1]
[2,7,5,3,1,8,6,4]=>[2,1,1,2,1,1]
[2,8,6,5,3,1,7,4]=>[2,1,1,1,2,1]
[3,7,5,4,2,6,1,8]=>[2,1,1,2,2]
[7,5,2,8,4,3,1,6]=>[1,1,2,1,1,2]
[5,2,8,7,4,3,1,6]=>[1,2,1,1,1,2]
[4,2,7,3,1,8,6,5]=>[1,2,1,2,1,1]
[7,3,2,4,1,8,6,5]=>[1,1,2,2,1,1]
[5,3,2,8,7,4,1,6]=>[1,1,2,1,1,2]
[8,4,3,2,7,5,1,6]=>[1,1,1,2,1,2]
[4,3,7,5,8,2,1,6]=>[1,2,2,1,2]
[4,3,7,5,2,6,1,8]=>[1,2,1,2,2]
[4,5,7,3,2,6,1,8]=>[3,1,2,2]
[4,5,7,3,8,2,1,6]=>[3,2,1,2]
[8,4,5,3,7,2,1,6]=>[1,2,2,1,2]
[4,3,5,8,7,2,1,6]=>[1,3,1,1,2]
[3,5,4,8,7,2,1,6]=>[2,2,1,1,2]
[3,6,4,8,2,1,7,5]=>[2,2,1,2,1]
[3,4,2,7,1,8,6,5]=>[2,2,2,1,1]
[3,4,2,7,5,1,8,6]=>[2,2,1,2,1]
[3,4,2,8,6,5,1,7]=>[2,2,1,1,2]
[4,3,5,2,8,6,1,7]=>[1,2,2,1,2]
[4,5,3,6,8,2,1,7]=>[2,3,1,2]
[1,2,8,6,4,5,7,3]=>[3,1,3,1]
[1,8,5,3,4,6,7,2]=>[2,1,4,1]
[7,8,4,1,6,3,5,2]=>[2,1,2,2,1]
[8,7,5,6,1,3,4,2]=>[1,1,2,3,1]
[3,2,6,4,1,8,5,7]=>[1,2,1,2,2]
[2,8,6,5,3,1,4,7]=>[2,1,1,1,3]
[5,4,8,6,2,3,1,7]=>[1,2,1,2,2]
[4,8,7,5,2,3,1,6]=>[2,1,1,2,2]
[5,2,4,7,6,8,3,1]=>[1,3,2,1,1]
[2,5,3,7,6,8,4,1]=>[2,2,2,1,1]
[8,6,5,1,4,2,3,7]=>[1,1,1,2,3]
[4,1,2,8,6,5,3,7]=>[1,3,1,1,2]
[8,5,1,3,2,6,4,7]=>[1,1,2,2,2]
[4,6,1,8,5,2,3,7]=>[2,2,1,3]
[3,4,2,8,7,5,1,6]=>[2,2,1,1,2]
[8,5,7,6,3,2,4,1]=>[1,2,1,1,2,1]
[6,4,1,8,7,3,2,5]=>[1,1,2,1,1,2]
[1,8,5,4,2,7,3,6]=>[2,1,1,2,2]
[3,7,1,2,8,5,4,6]=>[2,3,1,2]
[7,4,6,8,3,1,5,2]=>[1,3,1,2,1]
[3,7,6,1,5,8,4,2]=>[2,1,3,1,1]
[3,6,5,8,2,7,4,1]=>[2,2,2,1,1]
[8,3,2,7,4,6,5,1]=>[1,1,2,2,1,1]
[1,7,6,4,8,3,5,2]=>[2,1,2,2,1]
[7,5,8,4,1,3,6,2]=>[1,2,1,3,1]
[7,1,6,2,3,8,4,5]=>[1,2,3,2]
[6,4,7,1,3,2,8,5]=>[1,2,2,2,1]
[5,1,3,8,7,2,6,4]=>[1,3,1,2,1]
[8,7,1,6,2,5,3,4]=>[1,1,2,2,2]
[3,8,5,2,4,7,6,1]=>[2,1,3,1,1]
[2,8,7,3,5,1,6,4]=>[2,1,2,2,1]
[8,7,5,2,3,6,1,4]=>[1,1,1,3,2]
[3,1,7,4,8,6,2,5]=>[1,2,2,1,2]
[7,1,5,2,4,8,3,6]=>[1,2,3,2]
[3,8,5,1,4,7,2,6]=>[2,1,3,2]
[7,2,5,4,1,3,8,6]=>[1,2,1,3,1]
[6,4,1,8,7,2,3,5]=>[1,1,2,1,3]
[8,7,1,6,3,2,4,5]=>[1,1,2,1,3]
[7,3,2,5,8,4,1,6]=>[1,1,3,1,2]
[4,7,2,3,8,1,6,5]=>[2,3,2,1]
[8,2,3,1,6,7,5,4]=>[1,2,3,1,1]
[7,5,8,1,6,3,2,4]=>[1,2,2,1,2]
[3,7,2,5,6,4,8,1]=>[2,3,2,1]
[6,7,2,4,1,5,8,3]=>[2,2,3,1]
[4,2,7,5,1,6,8,3]=>[1,2,1,3,1]
[5,8,1,6,2,3,7,4]=>[2,2,3,1]
[5,1,2,8,4,7,6,3]=>[1,3,2,1,1]
[8,2,3,7,4,6,5,1]=>[1,3,2,1,1]
[7,1,4,8,5,6,2,3]=>[1,3,2,2]
[8,5,6,1,2,4,7,3]=>[1,2,4,1]
[5,2,6,8,4,7,1,3]=>[1,3,2,2]
[3,6,5,8,2,7,1,4]=>[2,2,2,2]
[7,1,6,3,8,2,5,4]=>[1,2,2,2,1]
[8,1,5,6,4,3,7,2]=>[1,3,1,2,1]
[7,3,8,1,4,6,5,2]=>[1,2,3,1,1]
[7,4,6,1,3,2,5,8]=>[1,2,2,3]
[1,4,5,8,6,3,2,7]=>[4,1,1,2]
[8,4,5,7,2,6,1,3]=>[1,3,2,2]
[7,4,1,5,6,3,2,8]=>[1,1,3,1,2]
[3,7,4,5,6,2,1,8]=>[2,3,1,2]
[4,5,2,6,7,3,1,8]=>[2,3,1,2]
[7,1,2,5,6,3,4,8]=>[1,4,3]
[8,1,7,5,3,6,2,4]=>[1,2,1,2,2]
[1,8,6,3,5,7,2,4]=>[2,1,3,2]
[5,8,6,3,1,7,2,4]=>[2,1,1,2,2]
[4,8,6,3,5,7,2,1]=>[2,1,3,1,1]
[4,7,8,3,2,6,1,5]=>[3,1,2,2]
[5,2,8,3,6,1,4,7]=>[1,2,2,3]
[2,1,6,5,8,3,4,7]=>[1,2,2,3]
[5,2,6,3,1,7,8,4]=>[1,2,1,3,1]
[6,2,5,7,3,4,8,1]=>[1,3,3,1]
[7,2,5,6,3,1,8,4]=>[1,3,1,2,1]
[7,4,3,1,5,2,8,6]=>[1,1,1,2,2,1]
[4,8,6,5,1,7,2,3]=>[2,1,1,2,2]
[4,3,5,1,6,7,8,2]=>[1,2,4,1]
[5,1,4,3,6,7,8,2]=>[1,2,4,1]
[4,6,5,2,3,7,8,1]=>[2,1,4,1]
[5,7,6,1,2,3,8,4]=>[2,1,4,1]
[3,6,7,5,1,2,8,4]=>[3,1,3,1]
[1,7,6,8,5,2,4,3]=>[2,2,1,2,1]
[5,7,6,8,1,2,4,3]=>[2,2,3,1]
[6,1,2,7,5,4,8,3]=>[1,3,1,2,1]
[7,5,4,2,8,6,3,1]=>[1,1,1,2,1,1,1]
[3,1,5,8,7,6,4,2]=>[1,3,1,1,1,1]
[3,4,6,1,5,2,8,7]=>[3,2,2,1]
[5,6,3,7,1,4,8,2]=>[2,2,3,1]
[3,1,2,5,8,6,4,7]=>[1,4,1,2]
[5,3,2,1,8,6,4,7]=>[1,1,1,2,1,2]
[3,8,7,4,5,1,2,6]=>[2,1,2,3]
[7,5,1,4,2,3,8,6]=>[1,1,2,3,1]
[2,6,3,4,1,7,8,5]=>[2,2,3,1]
[1,6,3,4,2,7,8,5]=>[2,2,3,1]
[3,8,6,4,5,7,2,1]=>[2,1,3,1,1]
[7,8,6,1,4,5,2,3]=>[2,1,3,2]
[7,5,1,4,6,2,8,3]=>[1,1,3,2,1]
[7,5,8,1,4,6,2,3]=>[1,2,3,2]
[7,5,1,3,6,8,2,4]=>[1,1,4,2]
[6,5,3,1,7,8,2,4]=>[1,1,1,3,2]
[6,5,8,4,1,7,2,3]=>[1,2,1,2,2]
[1,8,5,4,7,6,2,3]=>[2,1,2,1,2]
[1,8,5,4,6,7,2,3]=>[2,1,3,2]
[6,4,3,7,8,2,1,5]=>[1,1,3,1,2]
[6,5,8,3,7,2,1,4]=>[1,2,2,1,2]
[6,5,3,7,2,1,8,4]=>[1,1,2,1,2,1]
[7,8,5,3,6,2,1,4]=>[2,1,2,1,2]
[7,8,5,3,6,2,4,1]=>[2,1,2,2,1]
[6,4,8,3,2,7,5,1]=>[1,2,1,2,1,1]
[7,8,4,3,2,6,5,1]=>[2,1,1,2,1,1]
[1,8,4,3,2,6,5,7]=>[2,1,1,2,2]
[1,8,4,3,2,6,7,5]=>[2,1,1,3,1]
[7,8,4,3,2,6,1,5]=>[2,1,1,2,2]
[5,4,3,8,2,1,7,6]=>[1,1,2,1,2,1]
[6,4,8,3,2,1,7,5]=>[1,2,1,1,2,1]
[1,8,4,3,2,7,6,5]=>[2,1,1,2,1,1]
[6,5,3,1,2,8,7,4]=>[1,1,1,3,1,1]
[6,5,8,3,1,2,7,4]=>[1,2,1,3,1]
[7,5,8,1,3,2,6,4]=>[1,2,2,2,1]
[7,6,1,3,2,8,5,4]=>[1,1,2,2,1,1]
[1,8,6,7,3,2,5,4]=>[2,2,1,2,1]
[1,8,6,7,3,2,4,5]=>[2,2,1,3]
[7,6,1,3,2,8,4,5]=>[1,1,2,2,2]
[7,8,6,1,3,2,4,5]=>[2,1,2,3]
[6,5,8,3,1,2,4,7]=>[1,2,1,4]
[1,8,4,3,2,7,5,6]=>[2,1,1,2,2]
[5,4,3,8,2,1,6,7]=>[1,1,2,1,3]
[5,4,3,8,2,6,1,7]=>[1,1,2,2,2]
[6,4,8,3,2,5,1,7]=>[1,2,1,2,2]
[1,8,4,3,2,5,7,6]=>[2,1,1,3,1]
[6,4,8,3,2,5,7,1]=>[1,2,1,3,1]
[5,4,3,8,2,6,7,1]=>[1,1,2,3,1]
[6,4,2,3,5,1,8,7]=>[1,1,3,2,1]
[5,2,3,6,1,4,8,7]=>[1,3,3,1]
[5,2,3,8,6,4,7,1]=>[1,3,1,2,1]
[5,2,3,7,4,8,1,6]=>[1,3,2,2]
[8,6,3,2,5,4,7,1]=>[1,1,1,2,2,1]
[7,2,3,4,5,8,1,6]=>[1,5,2]
[7,2,8,1,5,3,4,6]=>[1,2,2,3]
[3,8,6,4,7,2,5,1]=>[2,1,2,2,1]
[2,1,8,6,4,5,7,3]=>[1,2,1,3,1]
[4,8,2,5,7,3,1,6]=>[2,3,1,2]
[5,8,2,3,4,7,1,6]=>[2,4,2]
[6,3,4,7,8,2,1,5]=>[1,4,1,2]
[3,8,5,1,4,7,6,2]=>[2,1,3,1,1]
[4,8,5,1,3,6,7,2]=>[2,1,4,1]
[4,6,8,5,2,7,3,1]=>[3,1,2,1,1]
[3,7,8,5,2,6,4,1]=>[3,1,2,1,1]
[3,8,6,2,7,4,5,1]=>[2,1,2,2,1]
[8,5,4,7,1,3,6,2]=>[1,1,2,3,1]
[7,3,6,2,8,1,5,4]=>[1,2,2,2,1]
[8,1,5,2,3,7,6,4]=>[1,2,3,1,1]
[6,4,2,3,7,8,5,1]=>[1,1,4,1,1]
[8,4,2,3,6,7,1,5]=>[1,1,4,2]
[4,5,8,3,7,2,1,6]=>[3,2,1,2]
[3,7,2,8,4,5,1,6]=>[2,2,2,2]
[3,5,1,8,4,6,2,7]=>[2,2,2,2]
[4,2,1,5,6,8,3,7]=>[1,1,4,2]
[4,1,2,6,5,8,3,7]=>[1,3,2,2]
[4,1,8,3,2,6,7,5]=>[1,2,1,3,1]
[4,2,7,5,8,1,3,6]=>[1,2,2,3]
[4,6,2,7,8,3,1,5]=>[2,3,1,2]
[4,6,1,3,8,2,5,7]=>[2,3,3]
[4,3,6,2,1,8,7,5]=>[1,2,1,2,1,1]
[3,7,4,5,1,6,2,8]=>[2,2,2,2]
[3,6,4,5,8,2,1,7]=>[2,3,1,2]
[6,1,4,5,2,8,7,3]=>[1,3,2,1,1]
[7,2,4,5,1,6,3,8]=>[1,3,2,2]
[7,5,4,1,6,3,2,8]=>[1,1,1,2,1,2]
[1,5,4,8,6,3,2,7]=>[2,2,1,1,2]
[7,5,4,8,6,3,1,2]=>[1,1,2,1,1,2]
[1,8,7,5,3,6,4,2]=>[2,1,1,2,1,1]
[8,3,7,4,1,6,2,5]=>[1,2,1,2,2]
[8,5,4,1,6,3,2,7]=>[1,1,1,2,1,2]
[1,7,4,2,6,5,3,8]=>[2,1,2,1,2]
[8,2,1,5,6,7,3,4]=>[1,1,4,2]
[6,3,1,8,4,7,2,5]=>[1,1,2,2,2]
[7,1,4,8,6,3,2,5]=>[1,3,1,1,2]
[4,1,8,5,6,7,2,3]=>[1,2,3,2]
[5,7,4,8,6,2,1,3]=>[2,2,1,1,2]
[5,3,6,8,2,7,1,4]=>[1,3,2,2]
[6,3,7,4,8,2,1,5]=>[1,2,2,1,2]
[5,3,6,1,4,7,2,8]=>[1,2,3,2]
[4,3,6,8,2,7,1,5]=>[1,3,2,2]
[5,3,7,4,8,2,1,6]=>[1,2,2,1,2]
[5,3,8,4,1,6,2,7]=>[1,2,1,2,2]
[5,3,8,1,4,7,2,6]=>[1,2,3,2]
[5,8,4,1,6,3,2,7]=>[2,1,2,1,2]
[7,3,8,4,1,6,2,5]=>[1,2,1,2,2]
[1,5,8,3,6,7,4,2]=>[3,3,1,1]
[1,8,2,5,6,7,3,4]=>[2,4,2]
[7,8,4,1,6,5,2,3]=>[2,1,2,1,2]
[6,3,8,1,5,7,2,4]=>[1,2,3,2]
[8,3,1,2,5,7,4,6]=>[1,1,4,2]
[8,1,4,2,6,5,3,7]=>[1,2,2,1,2]
[5,1,3,7,4,8,2,6]=>[1,3,2,2]
[5,1,3,4,7,8,2,6]=>[1,5,2]
[2,5,8,7,4,3,6,1]=>[3,1,1,2,1]
[5,4,1,8,3,2,7,6]=>[1,1,2,1,2,1]
[5,1,4,3,8,7,2,6]=>[1,2,2,1,2]
[5,1,7,8,3,4,2,6]=>[1,3,2,2]
[5,4,1,3,8,2,7,6]=>[1,1,3,2,1]
[2,5,4,8,3,7,6,1]=>[2,2,2,1,1]
[5,2,1,4,8,3,6,7]=>[1,1,3,3]
[5,2,1,8,4,3,6,7]=>[1,1,2,1,3]
[5,8,1,2,3,6,4,7]=>[2,4,2]
[5,6,8,2,3,4,1,7]=>[3,3,2]
[2,3,5,7,4,6,8,1]=>[4,3,1]
[4,5,2,3,8,6,1,7]=>[2,3,1,2]
[4,5,2,8,3,6,1,7]=>[2,2,2,2]
[3,7,4,5,8,1,2,6]=>[2,3,3]
[3,7,8,1,4,5,2,6]=>[3,3,2]
[4,8,7,1,5,3,2,6]=>[2,1,2,1,2]
[5,8,2,1,6,3,4,7]=>[2,1,2,3]
[3,7,1,8,5,4,2,6]=>[2,2,1,1,2]
[4,8,1,3,7,5,2,6]=>[2,3,1,2]
[5,4,2,1,3,6,8,7]=>[1,1,1,4,1]
[2,5,3,8,4,6,7,1]=>[2,2,3,1]
[2,4,7,8,5,3,6,1]=>[4,1,2,1]
[4,8,3,1,5,7,2,6]=>[2,1,3,2]
[5,3,1,4,7,2,8,6]=>[1,1,3,2,1]
[5,3,1,7,4,2,8,6]=>[1,1,2,1,2,1]
[4,3,8,5,1,2,7,6]=>[1,2,1,3,1]
[2,4,7,5,8,3,6,1]=>[3,2,2,1]
[4,3,5,8,2,1,7,6]=>[1,3,1,2,1]
[4,8,5,3,7,1,2,6]=>[2,1,2,3]
[4,8,5,7,3,1,2,6]=>[2,2,1,3]
[4,8,7,5,1,3,2,6]=>[2,1,1,2,2]
[4,2,8,5,1,3,6,7]=>[1,2,1,4]
[3,7,8,4,1,5,2,6]=>[3,1,2,2]
[3,4,7,5,8,2,1,6]=>[3,2,1,2]
[3,4,5,7,2,8,1,6]=>[4,2,2]
[1,3,6,8,7,2,4,5]=>[4,1,3]
[1,5,4,8,7,2,3,6]=>[2,2,1,3]
[1,6,3,8,2,5,4,7]=>[2,2,2,2]
[1,8,5,7,2,4,3,6]=>[2,2,2,2]
[1,8,5,4,2,3,6,7]=>[2,1,1,4]
[1,3,6,8,5,4,2,7]=>[4,1,1,2]
[1,6,3,8,4,5,2,7]=>[2,2,2,2]
[1,8,2,6,4,5,3,7]=>[2,2,2,2]
[1,5,2,7,4,8,3,6]=>[2,2,2,2]
[1,6,3,8,2,7,4,5]=>[2,2,2,2]
[1,4,2,7,5,8,3,6]=>[2,2,2,2]
[1,8,2,3,6,7,5,4]=>[2,4,1,1]
[1,3,6,8,2,7,5,4]=>[4,2,1,1]
[1,6,5,4,3,8,2,7]=>[2,1,1,2,2]
[1,8,3,4,5,6,2,7]=>[2,4,2]
[1,8,3,6,2,4,5,7]=>[2,2,4]
[1,8,3,6,2,5,4,7]=>[2,2,2,2]
[1,5,4,8,3,6,2,7]=>[2,2,2,2]
[1,4,5,8,3,6,2,7]=>[4,2,2]
[1,3,6,8,4,5,2,7]=>[4,2,2]
[1,2,7,8,4,5,3,6]=>[4,2,2]
[7,2,8,4,3,6,5,1]=>[1,2,1,2,1,1]
[7,2,8,5,6,3,4,1]=>[1,2,2,2,1]
[7,6,3,8,5,4,2,1]=>[1,1,2,1,1,1,1]
[6,2,8,7,5,4,1,3]=>[1,2,1,1,1,2]
[6,2,8,4,3,7,1,5]=>[1,2,1,2,2]
[5,2,8,4,3,1,7,6]=>[1,2,1,1,2,1]
[1,4,7,3,2,6,8,5]=>[3,1,3,1]
[1,5,7,3,6,2,8,4]=>[3,2,2,1]
[3,6,2,7,1,5,4,8]=>[2,2,2,2]
[1,2,5,4,8,3,7,6]=>[3,2,2,1]
[1,4,3,6,8,7,2,5]=>[2,3,1,2]
[1,5,3,7,6,8,2,4]=>[2,2,2,2]
[4,2,6,5,7,8,1,3]=>[1,2,3,2]
[3,2,5,7,6,8,1,4]=>[1,3,2,2]
[6,3,2,7,4,8,5,1]=>[1,1,2,2,1,1]
[5,3,2,6,8,4,7,1]=>[1,1,3,2,1]
[4,1,8,7,5,2,6,3]=>[1,2,1,1,2,1]
[3,1,8,6,4,7,2,5]=>[1,2,1,2,2]
[3,1,6,8,5,4,2,7]=>[1,3,1,1,2]
[5,3,2,8,7,6,4,1]=>[1,1,2,1,1,1,1]
[2,4,8,1,7,6,3,5]=>[3,2,1,2]
[3,8,1,7,6,5,2,4]=>[2,2,1,1,2]
[4,8,1,5,3,6,2,7]=>[2,2,2,2]
[5,8,1,6,4,2,7,3]=>[2,2,1,2,1]
[5,4,2,6,7,3,1,8]=>[1,1,3,1,2]
[5,4,2,7,6,3,1,8]=>[1,1,2,1,1,2]
[5,3,8,2,7,6,1,4]=>[1,2,2,1,2]
[6,5,4,8,3,7,2,1]=>[1,1,2,2,1,1]
[6,3,5,7,2,4,1,8]=>[1,3,2,2]
[4,8,5,1,3,7,2,6]=>[2,1,3,2]
[4,3,8,7,2,6,5,1]=>[1,2,1,2,1,1]
[4,3,6,8,2,5,7,1]=>[1,3,3,1]
[2,6,5,8,1,4,7,3]=>[2,2,3,1]
[2,7,5,1,8,4,6,3]=>[2,1,2,2,1]
[8,4,6,2,1,7,5,3]=>[1,2,1,2,1,1]
[7,8,5,2,1,6,4,3]=>[2,1,1,2,1,1]
[6,7,3,2,8,1,5,4]=>[2,1,2,2,1]
[7,6,4,8,1,2,5,3]=>[1,1,2,3,1]
[7,5,4,8,3,2,6,1]=>[1,1,2,1,2,1]
[7,8,4,3,1,6,2,5]=>[2,1,1,2,2]
[8,7,5,3,6,2,1,4]=>[1,1,1,2,1,2]
[8,6,4,7,3,2,1,5]=>[1,1,2,1,1,2]
[3,8,5,6,2,7,1,4]=>[2,2,2,2]
[2,4,5,8,7,3,1,6]=>[4,1,1,2]
[2,4,5,8,6,7,1,3]=>[4,2,2]
[4,3,1,5,6,2,8,7]=>[1,1,3,2,1]
[4,1,5,8,6,7,2,3]=>[1,3,2,2]
[4,3,7,6,1,2,8,5]=>[1,2,1,3,1]
[4,7,5,6,1,2,8,3]=>[2,2,3,1]
[4,3,7,5,6,2,8,1]=>[1,2,2,2,1]
[4,5,1,8,6,7,3,2]=>[2,2,2,1,1]
[3,4,5,8,6,7,2,1]=>[4,2,1,1]
[2,1,5,8,6,7,4,3]=>[1,3,2,1,1]
[3,4,5,8,7,1,2,6]=>[4,1,3]
[4,7,1,5,6,2,8,3]=>[2,3,2,1]
[2,6,4,7,1,3,8,5]=>[2,2,3,1]
[5,3,8,6,4,7,2,1]=>[1,2,1,2,1,1]
[6,4,1,5,7,8,3,2]=>[1,1,4,1,1]
[3,6,4,7,2,1,8,5]=>[2,2,1,2,1]
[3,8,4,6,1,7,2,5]=>[2,2,2,2]
[3,8,5,6,4,7,2,1]=>[2,2,2,1,1]
[3,8,4,5,6,7,2,1]=>[2,4,1,1]
[3,8,6,5,2,7,4,1]=>[2,1,1,2,1,1]
[3,8,7,5,2,1,4,6]=>[2,1,1,1,3]
[3,8,6,5,1,7,2,4]=>[2,1,1,2,2]
[6,4,1,7,3,2,8,5]=>[1,1,2,1,2,1]
[5,1,4,6,7,2,8,3]=>[1,4,2,1]
[6,5,4,7,1,3,8,2]=>[1,1,2,3,1]
[2,1,6,5,3,7,8,4]=>[1,2,1,3,1]
[6,1,4,7,2,3,8,5]=>[1,3,3,1]
[1,6,2,5,4,8,3,7]=>[2,2,2,2]
[4,1,2,7,5,8,3,6]=>[1,3,2,2]
[6,1,3,5,8,2,4,7]=>[1,4,3]
[5,6,4,3,1,8,2,7]=>[2,1,1,2,2]
[6,2,3,5,8,1,4,7]=>[1,4,3]
[6,7,2,3,8,4,5,1]=>[2,3,2,1]
[6,7,2,1,3,8,4,5]=>[2,1,3,2]
[5,7,4,1,8,3,2,6]=>[2,1,2,1,2]
[4,1,7,5,8,3,6,2]=>[1,2,2,2,1]
[6,7,1,3,8,4,5,2]=>[2,3,2,1]
[1,6,7,4,3,8,5,2]=>[3,1,2,1,1]
[6,1,7,4,2,8,5,3]=>[1,2,1,2,1,1]
[2,1,6,7,4,3,8,5]=>[1,3,1,2,1]
[6,7,3,2,1,8,4,5]=>[2,1,1,2,2]
[2,5,7,3,1,4,8,6]=>[3,1,3,1]
[6,7,3,2,8,4,5,1]=>[2,1,2,2,1]
[1,2,6,7,4,3,8,5]=>[4,1,2,1]
[2,7,1,8,4,6,3,5]=>[2,2,2,2]
[2,7,5,8,1,6,3,4]=>[2,2,2,2]
[6,7,1,8,4,5,3,2]=>[2,2,2,1,1]
[8,3,7,6,1,2,5,4]=>[1,2,1,3,1]
[8,7,3,4,6,2,5,1]=>[1,1,3,2,1]
[8,2,5,7,1,4,6,3]=>[1,3,3,1]
[8,2,4,7,1,5,6,3]=>[1,3,3,1]
[8,2,3,4,7,1,5,6]=>[1,4,3]
[8,7,3,5,6,2,4,1]=>[1,1,3,2,1]
[8,7,4,6,5,2,3,1]=>[1,1,2,1,2,1]
[8,4,6,7,5,1,2,3]=>[1,3,1,3]
[8,4,6,7,5,1,3,2]=>[1,3,1,2,1]
[8,3,5,7,6,1,4,2]=>[1,3,1,2,1]
[8,7,3,6,2,1,5,4]=>[1,1,2,1,2,1]
[8,7,3,4,6,2,1,5]=>[1,1,3,1,2]
[8,7,4,6,5,2,1,3]=>[1,1,2,1,1,2]
[8,6,5,2,7,4,3,1]=>[1,1,1,2,1,1,1]
[8,4,3,7,6,5,1,2]=>[1,1,2,1,1,2]
[8,5,6,7,4,1,3,2]=>[1,3,1,2,1]
[8,5,7,6,4,1,2,3]=>[1,2,1,1,3]
[8,4,2,7,5,1,6,3]=>[1,1,2,1,2,1]
[8,3,4,2,7,5,6,1]=>[1,2,2,2,1]
[8,4,7,6,5,1,2,3]=>[1,2,1,1,3]
[8,3,5,2,7,4,6,1]=>[1,2,2,2,1]
[8,5,2,6,7,4,1,3]=>[1,1,3,1,2]
[8,5,3,7,6,4,1,2]=>[1,1,2,1,1,2]
[8,6,2,5,7,3,1,4]=>[1,1,3,1,2]
[8,6,2,4,7,3,1,5]=>[1,1,3,1,2]
[8,5,2,3,7,4,1,6]=>[1,1,3,1,2]
[8,5,3,2,7,6,4,1]=>[1,1,1,2,1,1,1]
[8,5,1,7,3,6,2,4]=>[1,1,2,2,2]
[8,6,1,5,4,3,2,7]=>[1,1,2,1,1,2]
[2,4,5,8,3,1,6,7]=>[4,1,3]
[2,7,4,6,1,5,8,3]=>[2,2,3,1]
[2,6,3,7,1,8,5,4]=>[2,2,2,1,1]
[2,5,3,4,8,1,6,7]=>[2,3,3]
[2,4,3,8,5,1,6,7]=>[2,2,1,3]
[2,3,8,4,5,1,6,7]=>[3,2,3]
[6,8,2,4,5,3,1,7]=>[2,3,1,2]
[8,7,3,1,5,4,6,2]=>[1,1,1,2,2,1]
[7,8,3,2,5,4,6,1]=>[2,1,2,2,1]
[7,2,8,3,5,4,6,1]=>[1,2,2,2,1]
[6,2,5,4,8,3,1,7]=>[1,2,2,1,2]
[5,2,6,7,3,8,1,4]=>[1,3,2,2]
[5,4,7,6,3,1,8,2]=>[1,2,1,1,2,1]
[1,5,6,7,3,8,2,4]=>[4,2,2]
[1,6,5,4,8,3,2,7]=>[2,1,2,1,2]
[1,6,4,8,5,3,2,7]=>[2,2,1,1,2]
[8,2,4,3,1,5,6,7]=>[1,2,1,4]
[1,7,3,5,8,4,6,2]=>[2,3,2,1]
[6,3,1,7,4,5,8,2]=>[1,1,2,3,1]
[7,2,1,6,4,8,5,3]=>[1,1,2,2,1,1]
[7,2,3,5,8,4,6,1]=>[1,4,2,1]
[4,8,3,1,2,5,6,7]=>[2,1,5]
[4,8,1,3,2,5,6,7]=>[2,2,4]
[6,5,4,8,2,3,1,7]=>[1,1,2,2,2]
[7,5,8,3,2,4,6,1]=>[1,2,1,3,1]
[8,7,5,1,3,4,6,2]=>[1,1,1,4,1]
[8,7,2,1,4,6,5,3]=>[1,1,1,3,1,1]
[7,1,8,3,4,6,5,2]=>[1,2,3,1,1]
[4,1,5,3,8,6,2,7]=>[1,2,2,1,2]
[3,8,7,2,4,6,5,1]=>[2,1,3,1,1]
[4,6,5,1,8,3,2,7]=>[2,1,2,1,2]
[6,5,7,1,3,2,8,4]=>[1,2,2,2,1]
[2,7,3,6,4,8,5,1]=>[2,2,2,1,1]
[3,7,1,5,8,4,6,2]=>[2,3,2,1]
[3,8,4,1,2,5,6,7]=>[2,1,5]
[3,8,1,4,2,5,6,7]=>[2,2,4]
[2,1,8,4,3,5,6,7]=>[1,2,1,4]
[3,2,7,6,4,8,5,1]=>[1,2,1,2,1,1]
[3,1,6,7,4,5,8,2]=>[1,3,3,1]
[1,3,7,6,4,8,5,2]=>[3,1,2,1,1]
[1,2,7,5,8,4,6,3]=>[3,2,2,1]
[3,1,8,7,6,4,2,5]=>[1,2,1,1,1,2]
[3,1,8,7,5,4,2,6]=>[1,2,1,1,1,2]
[3,1,7,6,5,4,2,8]=>[1,2,1,1,1,2]
[4,7,1,6,5,3,2,8]=>[2,2,1,1,2]
[4,8,1,6,5,3,2,7]=>[2,2,1,1,2]
[8,4,1,7,6,3,2,5]=>[1,1,2,1,1,2]
[5,4,1,8,6,3,2,7]=>[1,1,2,1,1,2]
[5,4,1,7,6,3,2,8]=>[1,1,2,1,1,2]
[6,4,1,8,5,3,2,7]=>[1,1,2,1,1,2]
[8,4,1,7,5,3,2,6]=>[1,1,2,1,1,2]
[7,4,1,6,5,3,2,8]=>[1,1,2,1,1,2]
[7,5,6,1,4,3,2,8]=>[1,2,2,1,2]
[8,5,6,1,4,3,2,7]=>[1,2,2,1,2]
[8,5,7,1,4,3,2,6]=>[1,2,2,1,2]
[5,7,6,1,4,3,2,8]=>[2,1,2,1,2]
[5,8,6,1,4,3,2,7]=>[2,1,2,1,2]
[6,7,5,1,4,3,2,8]=>[2,1,2,1,2]
[8,7,5,1,4,3,2,6]=>[1,1,1,2,1,2]
[8,6,5,1,4,3,2,7]=>[1,1,1,2,1,2]
[3,1,5,2,7,6,4,8]=>[1,2,2,1,2]
[3,1,6,7,8,5,4,2]=>[1,4,1,1,1]
[8,6,1,7,2,5,3,4]=>[1,1,2,2,2]
[1,8,6,3,4,2,5,7]=>[2,1,2,3]
[3,1,6,4,5,8,7,2]=>[1,2,3,1,1]
[3,1,6,4,5,2,7,8]=>[1,2,2,3]
[3,1,6,7,8,5,2,4]=>[1,4,1,2]
[3,1,6,4,5,8,2,7]=>[1,2,3,2]
[3,1,6,4,5,7,2,8]=>[1,2,3,2]
[3,1,6,4,5,7,8,2]=>[1,2,4,1]
[8,1,6,3,4,7,5,2]=>[1,2,3,1,1]
[1,8,6,3,4,2,7,5]=>[2,1,2,2,1]
[4,6,7,3,2,1,8,5]=>[3,1,1,2,1]
[4,6,8,7,2,5,1,3]=>[3,1,2,2]
[4,6,8,3,5,2,1,7]=>[3,2,1,2]
[5,6,3,7,4,2,8,1]=>[2,2,1,2,1]
[6,2,3,7,5,1,8,4]=>[1,3,1,2,1]
[6,2,3,1,7,5,8,4]=>[1,2,2,2,1]
[7,6,3,1,4,8,5,2]=>[1,1,1,3,1,1]
[6,1,7,3,5,2,8,4]=>[1,2,2,2,1]
[7,1,6,3,4,5,2,8]=>[1,2,3,2]
[7,1,6,3,4,5,8,2]=>[1,2,4,1]
[8,6,3,1,4,5,2,7]=>[1,1,1,3,2]
[7,6,3,8,4,5,2,1]=>[1,1,2,2,1,1]
[6,2,7,8,5,4,3,1]=>[1,3,1,1,1,1]
[6,8,1,7,4,5,3,2]=>[2,2,2,1,1]
[5,2,1,4,7,6,8,3]=>[1,1,3,2,1]
[5,2,1,4,7,3,8,6]=>[1,1,3,2,1]
[4,2,5,1,7,6,3,8]=>[1,2,2,1,2]
[8,2,7,6,1,4,3,5]=>[1,2,1,2,2]
[5,2,7,8,1,4,3,6]=>[1,3,2,2]
[5,2,7,6,8,4,3,1]=>[1,2,2,1,1,1]
[5,6,3,8,4,1,2,7]=>[2,2,1,3]
[4,6,7,3,5,1,8,2]=>[3,2,2,1]
[4,6,7,3,5,1,2,8]=>[3,2,3]
[4,7,6,3,1,2,8,5]=>[2,1,1,3,1]
[7,2,3,6,1,5,8,4]=>[1,3,3,1]
[8,2,7,6,1,4,5,3]=>[1,2,1,3,1]
[5,2,3,4,7,1,6,8]=>[1,4,3]
[5,2,3,4,8,1,7,6]=>[1,4,2,1]
[5,2,3,7,1,6,8,4]=>[1,3,3,1]
[5,2,3,4,7,8,1,6]=>[1,5,2]
[8,7,5,3,1,6,4,2]=>[1,1,1,1,2,1,1]
[3,7,4,2,5,1,6,8]=>[2,1,2,3]
[1,4,7,8,5,2,3,6]=>[4,1,3]
[3,2,6,7,4,1,5,8]=>[1,3,1,3]
[6,7,3,5,1,8,4,2]=>[2,2,2,1,1]
[7,6,3,5,2,1,4,8]=>[1,1,2,1,3]
[4,6,3,2,5,8,1,7]=>[2,1,3,2]
[2,6,8,7,4,1,3,5]=>[3,1,1,3]
[5,8,3,7,6,4,1,2]=>[2,2,1,1,2]
[6,5,1,7,2,4,8,3]=>[1,1,2,3,1]
[3,6,7,1,4,2,5,8]=>[3,2,3]
[4,7,5,8,2,1,3,6]=>[2,2,1,3]
[6,1,5,2,7,4,3,8]=>[1,2,2,1,2]
[8,1,2,7,5,4,3,6]=>[1,3,1,1,2]
[6,5,1,8,3,7,2,4]=>[1,1,2,2,2]
[8,1,5,3,2,6,4,7]=>[1,2,1,2,2]
[1,8,3,6,5,4,2,7]=>[2,2,1,1,2]
[7,6,1,5,4,3,2,8]=>[1,1,2,1,1,2]
[4,6,5,2,8,1,3,7]=>[2,1,2,3]
[5,3,1,7,4,6,2,8]=>[1,1,2,2,2]
[1,8,7,5,3,2,6,4]=>[2,1,1,1,2,1]
[5,1,7,6,3,2,8,4]=>[1,2,1,1,2,1]
[4,7,6,2,5,1,3,8]=>[2,1,2,3]
[4,7,3,1,5,6,8,2]=>[2,1,4,1]
[7,8,1,5,4,2,3,6]=>[2,2,1,3]
[2,1,8,4,5,6,3,7]=>[1,2,3,2]
[2,7,5,1,4,6,3,8]=>[2,1,3,2]
[7,2,1,4,5,3,8,6]=>[1,1,3,2,1]
[3,4,6,8,1,5,7,2]=>[4,3,1]
[4,2,5,6,1,3,7,8]=>[1,3,4]
[5,7,6,1,4,3,8,2]=>[2,1,2,2,1]
[6,8,1,7,5,4,2,3]=>[2,2,1,1,2]
[7,6,3,1,2,8,5,4]=>[1,1,1,3,1,1]
[5,6,7,1,4,2,8,3]=>[3,2,2,1]
[6,3,5,7,1,4,2,8]=>[1,3,2,2]
[5,2,6,7,4,8,1,3]=>[1,3,2,2]
[6,7,5,2,4,1,3,8]=>[2,1,2,3]
[5,7,6,1,3,4,8,2]=>[2,1,4,1]
[7,5,6,4,8,1,3,2]=>[1,2,2,2,1]
[1,7,5,2,6,4,8,3]=>[2,1,2,2,1]
[7,1,3,6,8,2,4,5]=>[1,4,3]
[1,2,5,7,8,4,6,3]=>[5,2,1]
[3,1,2,7,5,4,8,6]=>[1,3,1,2,1]
[6,7,4,1,3,2,8,5]=>[2,1,2,2,1]
[1,7,2,8,4,3,5,6]=>[2,2,1,3]
[1,6,3,5,7,8,2,4]=>[2,4,2]
[8,6,1,7,5,2,4,3]=>[1,1,2,1,2,1]
[7,6,4,1,8,3,2,5]=>[1,1,1,2,1,2]
[8,4,1,6,5,2,7,3]=>[1,1,2,1,2,1]
[1,5,3,4,7,8,2,6]=>[2,4,2]
[4,2,1,5,7,8,3,6]=>[1,1,4,2]
[5,4,1,6,7,8,2,3]=>[1,1,4,2]
[5,1,4,6,7,8,2,3]=>[1,5,2]
[4,1,5,3,7,8,2,6]=>[1,2,3,2]
[8,1,4,6,5,2,7,3]=>[1,3,1,2,1]
[7,1,5,4,6,3,2,8]=>[1,2,2,1,2]
[8,2,1,6,7,5,4,3]=>[1,1,3,1,1,1]
[1,2,4,7,6,3,8,5]=>[4,1,2,1]
[6,7,4,1,8,5,2,3]=>[2,1,2,1,2]
[8,6,4,1,5,7,3,2]=>[1,1,1,3,1,1]
[5,2,4,3,7,1,6,8]=>[1,2,2,3]
[6,1,5,4,8,3,2,7]=>[1,2,2,1,2]
[1,2,8,7,4,3,6,5]=>[3,1,1,2,1]
[3,2,1,7,5,8,4,6]=>[1,1,2,2,2]
[1,3,6,4,7,8,2,5]=>[3,3,2]
[4,5,1,3,7,8,2,6]=>[2,4,2]
[5,2,3,1,7,8,4,6]=>[1,2,3,2]
[1,6,4,3,7,8,2,5]=>[2,1,3,2]
[7,6,4,3,1,5,2,8]=>[1,1,1,1,2,2]
[7,5,4,6,1,3,2,8]=>[1,1,2,2,2]
[8,4,6,5,1,2,7,3]=>[1,2,1,3,1]
[1,5,6,3,7,8,2,4]=>[3,3,2]
[6,8,3,5,7,2,4,1]=>[2,3,2,1]
[1,5,2,4,3,8,7,6]=>[2,2,2,1,1]
[8,6,5,7,2,1,4,3]=>[1,1,2,1,2,1]
[8,5,6,1,4,7,3,2]=>[1,2,3,1,1]
[1,6,3,8,4,5,7,2]=>[2,2,3,1]
[7,5,4,2,6,3,8,1]=>[1,1,1,2,2,1]
[7,1,4,3,2,8,6,5]=>[1,2,1,2,1,1]
[2,3,8,4,7,5,6,1]=>[3,2,2,1]
[3,7,2,8,6,4,5,1]=>[2,2,1,2,1]
[3,7,2,4,8,5,6,1]=>[2,3,2,1]
[3,7,4,6,2,5,8,1]=>[2,2,3,1]
[6,2,7,3,1,8,4,5]=>[1,2,1,2,2]
[6,3,7,5,8,2,4,1]=>[1,2,2,2,1]
[4,3,7,8,6,2,5,1]=>[1,3,1,2,1]
[3,8,1,7,5,2,4,6]=>[2,2,1,3]
[8,2,3,4,7,5,6,1]=>[1,4,2,1]
[2,4,7,8,6,1,5,3]=>[4,1,2,1]
[2,6,7,3,8,5,1,4]=>[3,2,1,2]
[2,4,8,5,1,7,3,6]=>[3,1,2,2]
[2,8,3,5,1,6,4,7]=>[2,2,2,2]
[8,2,4,6,3,7,5,1]=>[1,3,2,1,1]
[8,2,4,6,3,5,7,1]=>[1,3,3,1]
[2,8,3,5,1,4,6,7]=>[2,2,4]
[3,4,6,2,5,7,8,1]=>[3,4,1]
[4,5,2,6,1,7,8,3]=>[2,2,3,1]
[3,6,5,7,8,1,2,4]=>[2,3,3]
[4,5,3,8,2,1,7,6]=>[2,2,1,2,1]
[4,8,3,2,5,1,6,7]=>[2,1,2,3]
[2,5,4,8,3,7,1,6]=>[2,2,2,2]
[5,8,3,1,7,4,2,6]=>[2,1,2,1,2]
[5,4,8,6,1,3,2,7]=>[1,2,1,2,2]
[4,7,5,2,6,8,3,1]=>[2,1,3,1,1]
[5,7,4,2,8,6,3,1]=>[2,1,2,1,1,1]
[4,6,2,3,8,5,7,1]=>[2,3,2,1]
[3,7,2,4,5,6,8,1]=>[2,5,1]
[6,2,7,1,4,5,8,3]=>[1,2,4,1]
[5,2,7,1,3,8,6,4]=>[1,2,3,1,1]
[4,3,7,8,2,5,6,1]=>[1,3,3,1]
[6,3,8,5,1,2,4,7]=>[1,2,1,4]
[8,5,3,4,7,2,6,1]=>[1,1,3,2,1]
[5,2,4,7,1,6,8,3]=>[1,3,3,1]
[4,3,5,8,2,7,1,6]=>[1,3,2,2]
[4,3,8,2,5,6,1,7]=>[1,2,3,2]
[3,8,1,2,4,7,5,6]=>[2,4,2]
[1,4,6,2,7,5,3,8]=>[3,2,1,2]
[8,2,7,5,1,4,6,3]=>[1,2,1,3,1]
[1,7,4,6,8,3,5,2]=>[2,3,2,1]
[8,2,1,4,5,6,7,3]=>[1,1,5,1]
[7,3,1,2,5,6,4,8]=>[1,1,4,2]
[7,2,4,1,5,8,6,3]=>[1,2,3,1,1]
[7,8,2,1,5,4,6,3]=>[2,1,2,2,1]
[1,4,2,8,6,5,3,7]=>[2,2,1,1,2]
[1,4,8,5,2,6,3,7]=>[3,1,2,2]
[1,5,2,4,6,3,8,7]=>[2,3,2,1]
[1,8,5,3,2,6,4,7]=>[2,1,1,2,2]
[6,4,1,3,2,5,8,7]=>[1,1,2,3,1]
[5,2,3,7,8,1,6,4]=>[1,4,2,1]
[5,2,8,6,3,1,7,4]=>[1,2,1,1,2,1]
[6,2,3,5,1,8,7,4]=>[1,3,2,1,1]
[7,6,3,4,2,8,1,5]=>[1,1,2,2,2]
[6,2,4,5,7,8,1,3]=>[1,5,2]
[8,6,3,2,5,7,1,4]=>[1,1,1,3,2]
[6,2,5,3,7,1,8,4]=>[1,2,2,2,1]
[8,5,3,6,7,2,1,4]=>[1,1,3,1,2]
[4,5,7,8,6,2,1,3]=>[4,1,1,2]
[1,2,8,4,3,6,7,5]=>[3,1,3,1]
[1,8,3,2,4,6,7,5]=>[2,1,4,1]
[1,2,7,5,3,4,6,8]=>[3,1,4]
[1,2,7,4,5,3,8,6]=>[3,2,2,1]
[1,7,3,2,6,8,4,5]=>[2,1,3,2]
[8,2,7,1,4,3,5,6]=>[1,2,2,3]
[7,2,1,3,6,8,4,5]=>[1,1,4,2]
[6,2,1,7,8,3,4,5]=>[1,1,3,3]
[4,6,5,2,7,1,8,3]=>[2,1,2,2,1]
[6,7,2,5,3,1,8,4]=>[2,2,1,2,1]
[3,7,2,5,4,1,8,6]=>[2,2,1,2,1]
[7,4,2,6,3,1,8,5]=>[1,1,2,1,2,1]
[2,6,4,7,5,1,8,3]=>[2,2,1,2,1]
[3,4,7,6,5,1,8,2]=>[3,1,1,2,1]
[3,4,7,6,2,8,5,1]=>[3,1,2,1,1]
[4,7,8,2,6,5,3,1]=>[3,2,1,1,1]
[4,7,8,1,6,5,3,2]=>[3,2,1,1,1]
[3,6,7,1,5,4,2,8]=>[3,2,1,2]
[3,5,8,6,1,4,2,7]=>[3,1,2,2]
[1,6,4,7,2,8,5,3]=>[2,2,2,1,1]
[1,3,7,5,2,8,4,6]=>[3,1,2,2]
[1,4,7,6,3,8,5,2]=>[3,1,2,1,1]
[1,7,8,2,6,5,4,3]=>[3,2,1,1,1]
[1,3,6,2,7,5,4,8]=>[3,2,1,2]
[1,8,2,6,5,4,3,7]=>[2,2,1,1,2]
[1,3,8,2,7,5,4,6]=>[3,2,1,2]
[1,8,4,2,7,6,3,5]=>[2,1,2,1,2]
[2,6,1,7,5,4,3,8]=>[2,2,1,1,2]
[2,7,1,6,5,4,3,8]=>[2,2,1,1,2]
[8,7,2,6,5,4,3,1]=>[1,1,2,1,1,1,1]
[8,2,1,6,5,4,3,7]=>[1,1,2,1,1,2]
[7,4,2,8,1,6,3,5]=>[1,1,2,2,2]
[5,2,8,6,1,4,3,7]=>[1,2,1,2,2]
[8,3,7,1,5,4,2,6]=>[1,2,2,1,2]
[7,3,8,1,6,5,4,2]=>[1,2,2,1,1,1]
[7,3,8,2,6,5,4,1]=>[1,2,2,1,1,1]
[4,6,5,3,1,7,2,8]=>[2,1,1,2,2]
[5,3,6,1,2,8,7,4]=>[1,2,3,1,1]
[3,5,4,1,2,8,7,6]=>[2,1,3,1,1]
[4,6,5,1,2,8,7,3]=>[2,1,3,1,1]
[6,8,1,2,7,5,3,4]=>[2,3,1,2]
[4,6,2,3,8,7,5,1]=>[2,3,1,1,1]
[3,2,7,4,8,6,5,1]=>[1,2,2,1,1,1]
[8,1,6,2,7,5,4,3]=>[1,2,2,1,1,1]
[5,2,1,7,3,8,6,4]=>[1,1,2,2,1,1]
[6,1,2,8,5,4,3,7]=>[1,3,1,1,2]
[7,1,3,8,6,5,4,2]=>[1,3,1,1,1,1]
[7,2,3,8,6,5,4,1]=>[1,3,1,1,1,1]
[8,1,3,7,6,5,4,2]=>[1,3,1,1,1,1]
[1,3,7,4,8,6,5,2]=>[3,2,1,1,1]
[2,4,1,8,7,3,6,5]=>[2,2,1,2,1]
[2,8,5,1,7,3,6,4]=>[2,1,2,2,1]
[3,5,1,7,2,6,4,8]=>[2,2,2,2]
[2,8,1,5,4,3,7,6]=>[2,2,1,2,1]
[2,8,6,1,5,4,3,7]=>[2,1,2,1,2]
[2,6,1,5,8,4,3,7]=>[2,3,1,2]
[2,8,1,5,4,3,6,7]=>[2,2,1,3]
[7,4,6,1,5,3,2,8]=>[1,2,2,1,2]
[8,4,6,1,5,3,2,7]=>[1,2,2,1,2]
[7,3,8,6,1,5,4,2]=>[1,2,1,2,1,1]
[3,5,1,6,8,4,2,7]=>[2,3,1,2]
[3,5,1,7,8,2,6,4]=>[2,3,2,1]
[3,7,8,6,1,5,4,2]=>[3,1,2,1,1]
[7,8,4,6,1,5,3,2]=>[2,2,2,1,1]
[4,6,1,5,3,2,7,8]=>[2,2,1,3]
[5,4,7,8,2,1,6,3]=>[1,3,1,2,1]
[5,4,6,8,3,2,1,7]=>[1,3,1,1,2]
[6,4,5,8,3,2,1,7]=>[1,3,1,1,2]
[7,4,5,8,2,1,6,3]=>[1,3,1,2,1]
[7,4,6,8,1,5,3,2]=>[1,3,2,1,1]
[5,3,6,1,8,4,2,7]=>[1,2,2,1,2]
[6,3,8,7,1,5,4,2]=>[1,2,1,2,1,1]
[8,6,4,7,1,5,3,2]=>[1,1,2,2,1,1]
[6,4,7,1,5,3,2,8]=>[1,2,2,1,2]
[5,4,7,2,1,6,3,8]=>[1,2,1,2,2]
[8,4,5,7,2,1,6,3]=>[1,3,1,2,1]
[8,5,4,7,2,1,6,3]=>[1,1,2,1,2,1]
[3,4,6,2,1,8,5,7]=>[3,1,2,2]
[4,5,7,2,1,6,3,8]=>[3,1,2,2]
[4,6,7,1,5,3,2,8]=>[3,2,1,2]
[5,6,4,8,3,2,1,7]=>[2,2,1,1,2]
[5,7,4,8,2,1,6,3]=>[2,2,1,2,1]
[4,7,6,8,1,5,3,2]=>[2,2,2,1,1]
[4,7,5,8,2,1,6,3]=>[2,2,1,2,1]
[3,6,1,7,2,8,5,4]=>[2,2,2,1,1]
[5,7,4,2,6,3,8,1]=>[2,1,2,2,1]
[5,7,4,1,6,2,8,3]=>[2,1,2,2,1]
[7,8,3,1,5,2,6,4]=>[2,1,2,2,1]
[8,3,4,1,7,5,2,6]=>[1,2,2,1,2]
[6,8,7,3,1,4,2,5]=>[2,1,1,2,2]
[8,5,6,1,7,3,2,4]=>[1,2,2,1,2]
[4,5,1,6,7,8,3,2]=>[2,4,1,1]
[5,8,2,6,7,4,1,3]=>[2,3,1,2]
[5,6,8,2,1,7,3,4]=>[3,1,2,2]
[6,4,8,7,2,1,3,5]=>[1,2,1,1,3]
[4,5,2,6,1,3,8,7]=>[2,2,3,1]
[5,1,6,8,2,7,3,4]=>[1,3,2,2]
[5,2,6,3,4,7,8,1]=>[1,2,4,1]
[4,6,2,3,5,7,8,1]=>[2,5,1]
[8,3,6,5,7,1,2,4]=>[1,2,2,3]
[8,2,3,7,1,5,4,6]=>[1,3,2,2]
[2,8,6,7,3,1,4,5]=>[2,2,1,3]
[8,4,6,7,2,5,1,3]=>[1,3,2,2]
[3,4,6,7,2,5,8,1]=>[4,3,1]
[7,1,4,6,8,3,5,2]=>[1,4,2,1]
[7,8,2,6,1,4,5,3]=>[2,2,3,1]
[7,5,8,2,1,3,6,4]=>[1,2,1,3,1]
[3,7,1,5,6,8,4,2]=>[2,4,1,1]
[6,7,1,2,4,8,5,3]=>[2,4,1,1]
[1,6,3,4,7,8,5,2]=>[2,4,1,1]
[2,3,6,4,7,5,8,1]=>[3,2,2,1]
[2,5,3,7,4,6,8,1]=>[2,2,3,1]
[7,4,8,1,3,5,6,2]=>[1,2,4,1]
[4,2,7,3,5,6,8,1]=>[1,2,4,1]
[7,8,1,3,4,5,6,2]=>[2,5,1]
[8,7,2,4,5,6,1,3]=>[1,1,4,2]
[1,8,2,6,7,3,4,5]=>[2,3,3]
[4,7,3,2,8,1,5,6]=>[2,1,2,3]
[5,1,4,6,2,3,8,7]=>[1,3,3,1]
[6,1,4,5,2,3,8,7]=>[1,3,3,1]
[7,1,2,5,6,8,3,4]=>[1,5,2]
[7,1,2,6,3,8,5,4]=>[1,3,2,1,1]
[7,8,4,1,2,6,3,5]=>[2,1,3,2]
[8,1,2,6,3,7,5,4]=>[1,3,2,1,1]
[8,1,2,7,6,3,5,4]=>[1,3,1,2,1]
[4,8,6,3,1,2,7,5]=>[2,1,1,3,1]
[4,8,7,3,1,6,2,5]=>[2,1,1,2,2]
[4,7,8,3,1,6,2,5]=>[3,1,2,2]
[7,4,3,1,6,2,8,5]=>[1,1,1,2,2,1]
[8,4,3,1,6,2,7,5]=>[1,1,1,2,2,1]
[7,4,3,1,8,6,2,5]=>[1,1,1,2,1,2]
[3,7,6,2,4,8,1,5]=>[2,1,3,2]
[8,3,5,7,4,2,1,6]=>[1,3,1,1,2]
[4,3,7,2,8,6,1,5]=>[1,2,2,1,2]
[7,1,2,8,6,3,5,4]=>[1,3,1,2,1]
[6,1,2,7,4,3,8,5]=>[1,3,1,2,1]
[5,1,2,6,3,8,7,4]=>[1,3,2,1,1]
[5,1,2,7,3,8,6,4]=>[1,3,2,1,1]
[6,1,2,7,3,5,8,4]=>[1,3,3,1]
[8,3,6,2,1,7,4,5]=>[1,2,1,2,2]
[7,3,6,2,1,8,4,5]=>[1,2,1,2,2]
[6,1,2,8,3,5,7,4]=>[1,3,3,1]
[7,5,3,2,1,8,6,4]=>[1,1,1,1,2,1,1]
[4,2,1,5,3,6,7,8]=>[1,1,2,4]
[6,2,5,4,1,8,7,3]=>[1,2,1,2,1,1]
[4,6,3,2,1,8,7,5]=>[2,1,1,2,1,1]
[6,5,3,2,1,8,7,4]=>[1,1,1,1,2,1,1]
[8,4,3,2,7,6,1,5]=>[1,1,1,2,1,2]
[1,5,8,4,7,6,3,2]=>[3,2,1,1,1]
[3,2,7,4,8,6,1,5]=>[1,2,2,1,2]
[7,4,3,2,8,6,1,5]=>[1,1,1,2,1,2]
[6,8,3,7,5,2,1,4]=>[2,2,1,1,2]
[5,7,8,4,3,2,1,6]=>[3,1,1,1,2]
[6,4,3,8,5,2,1,7]=>[1,1,2,1,1,2]
[8,2,5,4,7,6,1,3]=>[1,2,2,1,2]
[7,2,5,4,8,6,1,3]=>[1,2,2,1,2]
[4,5,3,2,8,6,1,7]=>[2,1,2,1,2]
[3,2,5,4,8,6,1,7]=>[1,2,2,1,2]
[3,2,8,6,5,4,1,7]=>[1,2,1,1,1,2]
[8,4,3,6,5,2,1,7]=>[1,1,2,1,1,2]
[8,4,3,7,5,2,1,6]=>[1,1,2,1,1,2]
[3,2,7,8,5,4,1,6]=>[1,3,1,1,2]
[6,8,7,4,3,2,1,5]=>[2,1,1,1,1,2]
[2,3,1,8,5,7,4,6]=>[2,2,2,2]
[3,6,1,4,8,7,2,5]=>[2,3,1,2]
[5,8,1,3,7,2,6,4]=>[2,3,2,1]
[4,7,5,1,8,2,6,3]=>[2,1,2,2,1]
[6,3,2,1,8,7,4,5]=>[1,1,1,2,1,2]
[6,2,3,1,8,7,4,5]=>[1,2,2,1,2]
[3,4,7,1,8,5,6,2]=>[3,2,2,1]
[3,4,8,1,7,5,6,2]=>[3,2,2,1]
[7,2,5,1,8,3,6,4]=>[1,2,2,2,1]
[7,2,1,5,8,4,6,3]=>[1,1,3,2,1]
[7,1,4,6,8,2,5,3]=>[1,4,2,1]
[8,2,5,1,7,3,6,4]=>[1,2,2,2,1]
[4,2,8,1,7,5,6,3]=>[1,2,2,2,1]
[8,4,6,1,2,7,5,3]=>[1,2,3,1,1]
[8,6,1,5,3,7,4,2]=>[1,1,2,2,1,1]
[8,3,6,4,1,7,5,2]=>[1,2,1,2,1,1]
[5,3,8,6,1,7,4,2]=>[1,2,1,2,1,1]
[7,3,1,5,2,8,6,4]=>[1,1,2,2,1,1]
[7,1,6,4,2,8,5,3]=>[1,2,1,2,1,1]
[3,7,4,1,5,8,6,2]=>[2,1,3,1,1]
[5,8,6,1,2,7,4,3]=>[2,1,3,1,1]
[6,8,1,4,3,7,5,2]=>[2,2,2,1,1]
[6,7,1,4,3,8,5,2]=>[2,2,2,1,1]
[4,7,1,5,3,8,6,2]=>[2,2,2,1,1]
[6,8,1,2,4,7,5,3]=>[2,4,1,1]
[7,1,6,4,8,3,5,2]=>[1,2,2,2,1]
[7,1,6,3,4,8,5,2]=>[1,2,3,1,1]
[8,6,4,1,3,7,5,2]=>[1,1,1,3,1,1]
[8,5,3,6,1,7,4,2]=>[1,1,2,2,1,1]
[8,6,2,1,4,7,5,3]=>[1,1,1,3,1,1]
[7,2,1,4,5,8,6,3]=>[1,1,4,1,1]
[7,1,5,3,6,8,4,2]=>[1,2,3,1,1]
[8,5,6,1,2,7,4,3]=>[1,2,3,1,1]
[8,4,5,6,1,7,3,2]=>[1,3,2,1,1]
[8,6,2,5,4,7,3,1]=>[1,1,2,2,1,1]
[8,2,6,3,5,4,7,1]=>[1,2,2,2,1]
[8,7,2,3,4,6,5,1]=>[1,1,4,1,1]
[8,5,7,3,2,4,6,1]=>[1,2,1,3,1]
[3,6,1,4,5,8,7,2]=>[2,4,1,1]
[4,6,1,3,8,7,2,5]=>[2,3,1,2]
[5,6,8,2,1,7,4,3]=>[3,1,2,1,1]
[7,1,3,8,4,2,5,6]=>[1,3,1,3]
[8,5,2,1,4,3,6,7]=>[1,1,1,2,3]
[2,8,3,5,7,4,1,6]=>[2,3,1,2]
[2,8,4,1,3,6,7,5]=>[2,1,4,1]
[2,7,4,5,8,6,1,3]=>[2,3,1,2]
[1,4,7,2,8,6,5,3]=>[3,2,1,1,1]
[6,4,8,5,1,3,2,7]=>[1,2,1,2,2]
[1,6,7,8,5,2,4,3]=>[4,1,2,1]
[6,2,4,7,5,1,8,3]=>[1,3,1,2,1]
[8,1,2,5,4,7,6,3]=>[1,3,2,1,1]
[8,1,2,4,5,6,7,3]=>[1,6,1]
[8,2,7,3,5,6,1,4]=>[1,2,3,2]
[7,1,3,4,2,8,6,5]=>[1,3,2,1,1]
[6,1,4,3,2,7,8,5]=>[1,2,1,3,1]
[6,1,5,2,3,8,7,4]=>[1,2,3,1,1]
[8,7,5,3,1,6,2,4]=>[1,1,1,1,2,2]
[8,5,6,3,2,1,7,4]=>[1,2,1,1,2,1]
[1,8,3,6,7,2,4,5]=>[2,3,3]
[3,1,8,6,4,2,5,7]=>[1,2,1,1,3]
[1,2,8,3,7,4,6,5]=>[3,2,2,1]
[8,1,3,7,4,5,2,6]=>[1,3,2,2]
[8,2,1,3,7,5,4,6]=>[1,1,3,1,2]
[8,2,7,4,3,5,6,1]=>[1,2,1,3,1]
[8,2,6,5,4,3,1,7]=>[1,2,1,1,1,2]
[8,2,7,6,4,5,3,1]=>[1,2,1,2,1,1]
[8,6,3,5,4,2,1,7]=>[1,1,2,1,1,2]
[8,7,3,5,4,2,6,1]=>[1,1,2,1,2,1]
[4,6,7,2,1,8,3,5]=>[3,1,2,2]
[4,5,8,1,3,6,7,2]=>[3,4,1]
[3,7,1,8,2,5,4,6]=>[2,2,2,2]
[4,5,8,6,1,3,7,2]=>[3,1,3,1]
[4,5,8,6,2,7,3,1]=>[3,1,2,1,1]
[4,6,7,1,5,3,8,2]=>[3,2,2,1]
[4,6,7,2,1,8,5,3]=>[3,1,2,1,1]
[4,2,5,6,7,8,3,1]=>[1,5,1,1]
[4,1,3,5,6,7,8,2]=>[1,6,1]
[3,7,8,4,5,1,6,2]=>[3,2,2,1]
[4,6,8,3,2,7,1,5]=>[3,1,2,2]
[4,6,8,2,3,7,1,5]=>[3,3,2]
[3,8,1,7,4,5,2,6]=>[2,2,2,2]
[4,5,8,3,7,1,2,6]=>[3,2,3]
[4,6,7,1,5,8,2,3]=>[3,3,2]
[3,7,8,4,6,2,5,1]=>[3,2,2,1]
[3,6,1,5,7,8,2,4]=>[2,4,2]
[3,8,2,5,4,7,1,6]=>[2,2,2,2]
[3,8,6,2,5,1,7,4]=>[2,1,2,2,1]
[4,5,8,6,2,1,7,3]=>[3,1,1,2,1]
[4,5,8,6,1,2,7,3]=>[3,1,3,1]
[4,6,8,5,2,7,1,3]=>[3,1,2,2]
[3,7,8,5,2,6,1,4]=>[3,1,2,2]
[3,7,8,5,4,1,6,2]=>[3,1,1,2,1]
[4,6,8,5,3,1,7,2]=>[3,1,1,2,1]
[7,8,2,3,5,4,1,6]=>[2,3,1,2]
[6,3,2,4,7,8,1,5]=>[1,1,4,2]
[2,8,1,5,7,4,6,3]=>[2,3,2,1]
[5,1,3,2,6,7,4,8]=>[1,2,3,2]
[6,7,2,4,8,3,1,5]=>[2,3,1,2]
[6,3,4,5,2,8,1,7]=>[1,3,2,2]
[4,5,6,8,3,7,1,2]=>[4,2,2]
[4,1,3,5,2,6,7,8]=>[1,3,4]
[1,5,7,4,6,3,8,2]=>[3,2,2,1]
[4,3,8,5,7,1,2,6]=>[1,2,2,3]
[1,6,5,3,7,2,8,4]=>[2,1,2,2,1]
[2,5,3,7,8,4,1,6]=>[2,3,1,2]
[5,1,3,7,6,4,8,2]=>[1,3,1,2,1]
[4,6,5,2,7,8,1,3]=>[2,1,3,2]
[4,6,5,1,7,3,2,8]=>[2,1,2,1,2]
[1,6,5,2,3,4,8,7]=>[2,1,4,1]
[1,6,5,3,4,2,8,7]=>[2,1,2,2,1]
[4,6,5,1,7,3,8,2]=>[2,1,2,2,1]
[5,7,3,1,2,4,8,6]=>[2,1,4,1]
[6,3,2,5,1,7,4,8]=>[1,1,2,2,2]
[6,1,2,4,8,5,3,7]=>[1,4,1,2]
[6,7,1,4,8,5,2,3]=>[2,3,1,2]
[5,8,3,2,1,4,6,7]=>[2,1,1,4]
[5,1,3,7,4,8,6,2]=>[1,3,2,1,1]
[6,3,1,7,2,5,8,4]=>[1,1,2,3,1]
[4,2,3,7,1,5,6,8]=>[1,3,4]
[3,4,8,5,1,2,7,6]=>[3,1,3,1]
[3,8,1,6,7,2,5,4]=>[2,3,2,1]
[4,5,7,6,3,8,1,2]=>[3,1,2,2]
[3,7,2,8,5,1,4,6]=>[2,2,1,3]
[1,6,5,3,7,8,2,4]=>[2,1,3,2]
[3,6,5,2,4,7,1,8]=>[2,1,3,2]
[2,6,5,1,4,3,7,8]=>[2,1,2,3]
[3,6,5,8,1,7,2,4]=>[2,2,2,2]
[1,6,5,3,7,8,4,2]=>[2,1,3,1,1]
[2,6,5,8,4,1,7,3]=>[2,2,1,2,1]
[2,3,5,1,8,6,4,7]=>[3,2,1,2]
[2,5,3,8,4,6,1,7]=>[2,2,2,2]
[5,2,7,3,4,6,1,8]=>[1,2,3,2]
[1,4,5,2,8,6,3,7]=>[3,2,1,2]
[1,3,5,8,6,4,7,2]=>[4,1,2,1]
[1,3,5,8,6,7,2,4]=>[4,2,2]
[6,1,7,4,8,5,3,2]=>[1,2,2,1,1,1]
[5,7,4,1,3,6,8,2]=>[2,1,4,1]
[7,4,3,1,6,5,8,2]=>[1,1,1,2,2,1]
[8,6,1,7,5,3,2,4]=>[1,1,2,1,1,2]
[7,8,1,4,6,5,3,2]=>[2,3,1,1,1]
[7,8,6,1,4,5,3,2]=>[2,1,3,1,1]
[7,8,6,4,1,3,5,2]=>[2,1,1,3,1]
[6,2,7,3,8,5,4,1]=>[1,2,2,1,1,1]
[6,7,3,4,8,1,5,2]=>[2,3,2,1]
[1,2,7,5,3,4,8,6]=>[3,1,3,1]
[7,2,8,3,6,4,5,1]=>[1,2,2,2,1]
[6,2,7,8,3,1,4,5]=>[1,3,1,3]
[2,7,3,5,1,8,4,6]=>[2,2,2,2]
[1,7,8,2,5,3,4,6]=>[3,2,3]
[3,7,8,1,2,5,6,4]=>[3,4,1]
[1,2,8,7,3,4,6,5]=>[3,1,3,1]
[8,7,6,2,4,3,5,1]=>[1,1,1,2,2,1]
[8,2,7,4,5,1,6,3]=>[1,2,2,2,1]
[3,8,1,5,7,2,6,4]=>[2,3,2,1]
[7,5,4,8,6,1,2,3]=>[1,1,2,1,3]
[7,1,8,6,4,5,2,3]=>[1,2,1,2,2]
[8,7,5,1,4,3,6,2]=>[1,1,1,2,2,1]
[1,5,7,8,3,4,2,6]=>[4,2,2]
[6,8,4,3,1,7,2,5]=>[2,1,1,2,2]
[8,4,1,3,7,5,6,2]=>[1,1,3,2,1]
[4,8,1,3,7,5,6,2]=>[2,3,2,1]
[5,1,3,4,7,8,6,2]=>[1,5,1,1]
[7,5,4,3,1,2,8,6]=>[1,1,1,1,3,1]
[6,2,5,4,8,1,7,3]=>[1,2,2,2,1]
[1,8,5,7,4,2,3,6]=>[2,2,1,3]
[2,1,6,8,5,3,4,7]=>[1,3,1,3]
[5,4,1,3,8,6,7,2]=>[1,1,3,2,1]
[4,5,1,3,8,6,7,2]=>[2,3,2,1]
[1,2,6,8,5,3,4,7]=>[4,1,3]
[5,6,8,7,3,1,2,4]=>[3,1,1,3]
[6,7,5,3,8,1,2,4]=>[2,1,2,3]
[6,2,3,4,7,1,8,5]=>[1,4,2,1]
[8,5,7,6,3,1,2,4]=>[1,2,1,1,3]
[6,8,5,7,3,1,2,4]=>[2,2,1,3]
[5,7,8,6,3,1,2,4]=>[3,1,1,3]
[5,1,4,2,6,8,7,3]=>[1,2,3,1,1]
[6,3,2,4,7,1,8,5]=>[1,1,3,2,1]
[1,5,6,8,4,2,3,7]=>[4,1,3]
[5,7,8,3,6,1,2,4]=>[3,2,3]
[8,4,1,2,5,7,6,3]=>[1,1,4,1,1]
[4,8,1,2,5,7,6,3]=>[2,4,1,1]
[1,5,8,6,2,4,3,7]=>[3,1,2,2]
[1,5,3,7,2,6,8,4]=>[2,2,3,1]
[5,1,8,6,2,4,3,7]=>[1,2,1,2,2]
[8,5,6,3,7,1,2,4]=>[1,2,2,3]
[5,8,6,3,7,1,2,4]=>[2,1,2,3]
[1,5,2,4,8,6,7,3]=>[2,3,2,1]
[1,5,4,2,6,8,7,3]=>[2,1,3,1,1]
[5,7,6,3,8,1,2,4]=>[2,1,2,3]
[5,7,6,8,3,1,2,4]=>[2,2,1,3]
[6,8,7,5,3,1,2,4]=>[2,1,1,1,3]
[6,5,7,3,8,1,2,4]=>[1,2,2,3]
[2,5,6,3,7,1,8,4]=>[3,2,2,1]
[1,2,5,3,6,8,7,4]=>[3,3,1,1]
[7,1,4,6,2,8,3,5]=>[1,3,2,2]
[6,8,7,2,1,5,3,4]=>[2,1,1,2,2]
[7,3,6,1,4,8,2,5]=>[1,2,3,2]
[7,8,1,6,5,3,4,2]=>[2,2,1,2,1]
[8,7,3,2,1,4,6,5]=>[1,1,1,1,3,1]
[8,3,5,1,7,4,2,6]=>[1,2,2,1,2]
[6,7,5,1,8,4,2,3]=>[2,1,2,1,2]
[8,2,6,1,7,5,3,4]=>[1,2,2,1,2]
[3,8,4,2,6,1,7,5]=>[2,1,2,2,1]
[3,5,6,8,4,2,7,1]=>[4,1,2,1]
[2,5,4,1,6,8,7,3]=>[2,1,3,1,1]
[5,8,2,6,4,3,7,1]=>[2,2,1,2,1]
[2,8,6,3,4,1,7,5]=>[2,1,2,2,1]
[4,3,6,2,8,5,7,1]=>[1,2,2,2,1]
[4,6,8,2,1,3,7,5]=>[3,1,3,1]
[6,8,1,5,3,2,7,4]=>[2,2,1,2,1]
[1,7,2,3,5,8,6,4]=>[2,4,1,1]
[4,6,2,3,5,1,7,8]=>[2,3,3]
[4,2,8,7,5,3,6,1]=>[1,2,1,1,2,1]
[2,8,3,7,5,1,6,4]=>[2,2,1,2,1]
[4,1,8,6,5,2,7,3]=>[1,2,1,1,2,1]
[6,4,8,7,2,1,5,3]=>[1,2,1,1,2,1]
[2,8,5,4,1,6,7,3]=>[2,1,1,3,1]
[4,5,7,3,2,1,6,8]=>[3,1,1,3]
[3,2,8,1,6,7,5,4]=>[1,2,3,1,1]
[1,8,2,3,7,5,6,4]=>[2,3,2,1]
[7,2,4,6,3,8,1,5]=>[1,3,2,2]
[2,8,3,1,4,7,6,5]=>[2,1,3,1,1]
[2,8,4,3,6,7,1,5]=>[2,1,3,2]
[6,4,7,2,8,3,5,1]=>[1,2,2,2,1]
[3,8,1,6,4,7,2,5]=>[2,2,2,2]
[7,3,2,5,6,1,8,4]=>[1,1,3,2,1]
[1,6,7,8,2,4,3,5]=>[4,2,2]
[4,1,2,8,5,3,7,6]=>[1,3,1,2,1]
[3,8,4,2,5,1,7,6]=>[2,1,2,2,1]
[3,8,4,2,7,5,6,1]=>[2,1,2,2,1]
[1,5,6,3,7,4,8,2]=>[3,2,2,1]
[2,6,3,1,4,5,7,8]=>[2,1,5]
[1,8,5,6,4,3,2,7]=>[2,2,1,1,2]
[2,8,3,5,6,4,1,7]=>[2,3,1,2]
[4,1,5,7,6,8,2,3]=>[1,3,2,2]
[7,6,8,3,2,5,1,4]=>[1,2,1,2,2]
[4,6,1,7,5,2,3,8]=>[2,2,1,3]
[3,1,7,2,6,5,4,8]=>[1,2,2,1,2]
[5,6,4,7,2,1,8,3]=>[2,2,1,2,1]
[2,8,7,1,3,6,5,4]=>[2,1,3,1,1]
[5,7,2,8,3,1,6,4]=>[2,2,1,2,1]
[2,7,8,1,6,4,5,3]=>[3,2,2,1]
[7,8,1,3,4,6,5,2]=>[2,4,1,1]
[2,7,1,4,5,3,8,6]=>[2,3,2,1]
[1,5,2,7,4,3,6,8]=>[2,2,1,3]
[5,1,3,8,4,6,2,7]=>[1,3,2,2]
[6,5,8,7,1,3,2,4]=>[1,2,1,2,2]
[2,7,3,5,1,6,8,4]=>[2,2,3,1]
[5,7,6,8,2,1,4,3]=>[2,2,1,2,1]
[1,3,6,5,2,7,4,8]=>[3,1,2,2]
[1,2,6,5,3,4,7,8]=>[3,1,4]
[1,7,2,5,6,8,3,4]=>[2,4,2]
[1,7,2,4,8,3,5,6]=>[2,3,3]
[1,6,2,4,5,3,7,8]=>[2,3,3]
[1,4,8,2,3,7,5,6]=>[3,3,2]
[1,3,2,8,4,5,7,6]=>[2,2,3,1]
[1,6,8,2,4,3,5,7]=>[3,2,3]
[1,6,7,2,5,3,4,8]=>[3,2,3]
[1,5,8,2,6,7,3,4]=>[3,3,2]
[1,8,2,3,6,7,4,5]=>[2,4,2]
[1,2,8,3,6,7,4,5]=>[3,3,2]
[1,3,4,8,2,6,7,5]=>[4,3,1]
[1,7,2,5,3,4,8,6]=>[2,2,3,1]
[1,6,2,3,5,4,7,8]=>[2,3,3]
[7,1,5,6,2,3,8,4]=>[1,3,3,1]
[8,2,1,4,6,7,3,5]=>[1,1,4,2]
[7,2,6,1,3,4,8,5]=>[1,2,4,1]
[4,1,3,7,2,5,8,6]=>[1,3,3,1]
[6,2,7,5,1,3,8,4]=>[1,2,1,3,1]
[1,7,5,6,2,3,8,4]=>[2,2,3,1]
[3,7,6,1,2,4,8,5]=>[2,1,4,1]
[8,6,1,3,5,7,2,4]=>[1,1,4,2]
[1,7,4,3,8,2,5,6]=>[2,1,2,3]
[6,1,5,3,4,8,2,7]=>[1,2,3,2]
[3,6,7,5,2,8,1,4]=>[3,1,2,2]
[7,8,4,1,5,6,2,3]=>[2,1,3,2]
[5,8,1,3,6,7,2,4]=>[2,4,2]
[2,8,4,3,7,1,5,6]=>[2,1,2,3]
[3,8,4,6,7,1,2,5]=>[2,3,3]
[6,3,8,4,7,1,2,5]=>[1,2,2,3]
[1,2,5,4,8,3,6,7]=>[3,2,3]
[7,1,3,8,2,4,5,6]=>[1,3,4]
[8,1,3,7,2,4,5,6]=>[1,3,4]
[3,5,4,7,8,1,2,6]=>[2,3,3]
[8,3,1,4,7,2,5,6]=>[1,1,3,3]
[1,6,4,7,8,2,3,5]=>[2,3,3]
[5,2,3,6,7,8,1,4]=>[1,5,2]
[6,2,7,3,8,5,1,4]=>[1,2,2,1,2]
[1,3,7,8,5,6,2,4]=>[4,2,2]
[8,2,6,7,5,1,3,4]=>[1,3,1,3]
[8,1,7,4,6,2,3,5]=>[1,2,2,3]
[2,5,8,4,7,1,3,6]=>[3,2,3]
[4,5,8,7,1,2,3,6]=>[3,1,4]
[4,1,8,5,7,2,3,6]=>[1,2,2,3]
[1,8,7,4,6,2,3,5]=>[2,1,2,3]
[2,6,5,4,1,8,3,7]=>[2,1,1,2,2]
[6,2,5,1,4,8,3,7]=>[1,2,3,2]
[6,5,4,1,3,8,2,7]=>[1,1,1,3,2]
[6,3,5,4,2,8,1,7]=>[1,2,1,2,2]
[1,3,8,7,4,2,6,5]=>[3,1,1,2,1]
[8,7,4,3,1,5,2,6]=>[1,1,1,1,2,2]
[8,2,5,1,4,6,7,3]=>[1,2,4,1]
[3,8,4,5,1,6,7,2]=>[2,2,3,1]
[8,5,4,1,3,6,7,2]=>[1,1,1,4,1]
[8,3,1,7,5,6,4,2]=>[1,1,2,2,1,1]
[8,4,7,6,5,3,1,2]=>[1,2,1,1,1,2]
[8,1,4,5,7,6,3,2]=>[1,4,1,1,1]
[2,4,1,8,5,7,6,3]=>[2,2,2,1,1]
[8,2,1,4,7,6,3,5]=>[1,1,3,1,2]
[8,3,1,7,4,2,6,5]=>[1,1,2,1,2,1]
[8,2,7,3,1,6,5,4]=>[1,2,1,2,1,1]
[1,8,4,2,3,7,6,5]=>[2,1,3,1,1]
[3,1,2,8,7,4,6,5]=>[1,3,1,2,1]
[8,5,1,2,4,3,7,6]=>[1,1,3,2,1]
[2,8,3,7,4,1,6,5]=>[2,2,1,2,1]
[8,4,5,7,6,2,3,1]=>[1,3,1,2,1]
[2,3,1,8,7,6,4,5]=>[2,2,1,1,2]
[4,2,8,7,3,1,5,6]=>[1,2,1,1,3]
[1,3,4,8,7,2,5,6]=>[4,1,3]
[8,1,3,4,6,7,2,5]=>[1,5,2]
[3,4,8,2,6,7,1,5]=>[3,3,2]
[3,6,8,2,5,1,7,4]=>[3,2,2,1]
[3,8,2,5,7,4,6,1]=>[2,3,2,1]
[8,4,2,1,7,5,6,3]=>[1,1,1,2,2,1]
[8,2,7,5,6,4,1,3]=>[1,2,2,1,2]
[6,2,8,5,4,1,7,3]=>[1,2,1,1,2,1]
[6,8,5,4,1,7,2,3]=>[2,1,1,2,2]
[2,8,1,5,7,6,3,4]=>[2,3,1,2]
[3,1,8,2,7,5,6,4]=>[1,2,2,2,1]
[8,5,7,1,6,4,2,3]=>[1,2,2,1,2]
[2,8,4,7,3,6,5,1]=>[2,2,2,1,1]
[8,4,7,2,1,6,5,3]=>[1,2,1,2,1,1]
[1,8,4,7,6,5,2,3]=>[2,2,1,1,2]
[3,5,8,1,7,4,6,2]=>[3,2,2,1]
[8,4,7,1,3,6,5,2]=>[1,2,3,1,1]
[2,3,4,7,6,8,1,5]=>[4,2,2]
[3,7,1,2,8,6,4,5]=>[2,3,1,2]
[3,8,1,2,5,6,4,7]=>[2,4,2]
[3,7,1,2,5,6,4,8]=>[2,4,2]
[8,5,2,1,4,6,7,3]=>[1,1,1,4,1]
[4,8,1,6,5,2,7,3]=>[2,2,1,2,1]
[2,6,3,1,8,5,7,4]=>[2,1,2,2,1]
[4,2,6,3,8,5,7,1]=>[1,2,2,2,1]
[2,7,3,1,6,5,8,4]=>[2,1,2,2,1]
[7,1,2,4,6,5,8,3]=>[1,4,2,1]
[4,5,2,6,7,1,8,3]=>[2,3,2,1]
[5,7,1,2,6,8,4,3]=>[2,4,1,1]
[5,8,2,6,4,1,7,3]=>[2,2,1,2,1]
[4,2,8,3,5,6,7,1]=>[1,2,4,1]
[8,7,3,4,1,6,2,5]=>[1,1,2,2,2]
[2,7,4,3,8,6,1,5]=>[2,1,2,1,2]
[2,7,6,3,1,5,4,8]=>[2,1,1,2,2]
[2,7,4,1,6,3,5,8]=>[2,1,2,3]
[3,7,4,2,8,1,6,5]=>[2,1,2,2,1]
[8,5,3,4,2,1,7,6]=>[1,1,2,1,2,1]
[7,4,3,5,2,1,8,6]=>[1,1,2,1,2,1]
[8,3,5,4,2,7,1,6]=>[1,2,1,2,2]
[2,8,6,4,7,3,1,5]=>[2,1,2,1,2]
[5,2,7,8,6,1,4,3]=>[1,3,1,2,1]
[5,2,4,6,8,1,7,3]=>[1,4,2,1]
[2,3,8,4,6,1,7,5]=>[3,2,2,1]
[3,1,8,6,5,2,7,4]=>[1,2,1,1,2,1]
[8,3,1,5,2,6,7,4]=>[1,1,2,3,1]
[3,8,2,4,1,5,7,6]=>[2,2,3,1]
[5,8,3,2,4,1,7,6]=>[2,1,2,2,1]
[6,2,8,3,4,5,7,1]=>[1,2,4,1]
[7,2,6,8,4,3,5,1]=>[1,3,1,2,1]
[5,6,3,8,4,2,1,7]=>[2,2,1,1,2]
[6,5,3,2,4,8,1,7]=>[1,1,1,3,2]
[7,2,5,3,4,8,6,1]=>[1,2,3,1,1]
[3,6,2,1,4,5,7,8]=>[2,1,5]
[5,2,4,6,1,3,8,7]=>[1,3,3,1]
[7,2,3,4,6,8,1,5]=>[1,5,2]
[8,3,4,6,7,5,1,2]=>[1,4,1,2]
[6,8,3,4,7,5,2,1]=>[2,3,1,1,1]
[5,8,6,1,3,4,7,2]=>[2,1,4,1]
[4,8,1,5,7,6,3,2]=>[2,3,1,1,1]
[3,7,4,6,8,2,5,1]=>[2,3,2,1]
[4,7,1,6,8,3,2,5]=>[2,3,1,2]
[4,5,2,8,1,7,3,6]=>[2,2,2,2]
[3,7,5,2,8,6,1,4]=>[2,1,2,1,2]
[4,8,5,2,6,7,1,3]=>[2,1,3,2]
[5,4,8,6,1,2,7,3]=>[1,2,1,3,1]
[8,4,6,5,2,7,3,1]=>[1,2,1,2,1,1]
[8,1,6,4,7,5,2,3]=>[1,2,2,1,2]
[5,2,7,6,4,8,1,3]=>[1,2,1,2,2]
[8,6,2,3,5,1,7,4]=>[1,1,3,2,1]
[8,2,5,7,4,1,3,6]=>[1,3,1,3]
[7,2,4,5,6,8,1,3]=>[1,5,2]
[7,1,3,5,6,2,8,4]=>[1,4,2,1]
[7,1,5,8,4,6,3,2]=>[1,3,2,1,1]
[6,3,8,4,7,1,5,2]=>[1,2,2,2,1]
[7,1,4,3,2,8,5,6]=>[1,2,1,2,2]
[5,3,6,1,4,2,8,7]=>[1,2,2,2,1]
[5,7,2,1,4,3,8,6]=>[2,1,2,2,1]
[7,1,8,3,5,2,4,6]=>[1,2,2,3]
[7,2,4,8,1,5,6,3]=>[1,3,3,1]
[7,1,8,4,2,5,6,3]=>[1,2,1,3,1]
[6,4,2,5,8,1,7,3]=>[1,1,3,2,1]
[2,1,7,5,8,3,6,4]=>[1,2,2,2,1]
[7,3,8,5,6,2,1,4]=>[1,2,2,1,2]
[2,7,4,8,1,5,6,3]=>[2,2,3,1]
[7,4,8,3,1,5,6,2]=>[1,2,1,3,1]
[6,1,5,8,3,7,4,2]=>[1,3,2,1,1]
[2,6,3,5,8,7,4,1]=>[2,3,1,1,1]
[8,6,5,3,7,2,1,4]=>[1,1,1,2,1,2]
[4,8,5,3,7,2,1,6]=>[2,1,2,1,2]
[7,4,8,6,5,3,2,1]=>[1,2,1,1,1,1,1]
[7,4,8,5,6,3,1,2]=>[1,2,2,1,2]
[7,8,4,1,3,5,6,2]=>[2,1,4,1]
[7,8,3,4,1,5,6,2]=>[2,2,3,1]
[7,3,1,8,2,5,6,4]=>[1,1,2,3,1]
[7,2,3,8,1,5,6,4]=>[1,3,3,1]
[6,4,8,7,3,2,1,5]=>[1,2,1,1,1,2]
[2,7,4,8,6,3,1,5]=>[2,2,1,1,2]
[6,4,8,2,3,1,7,5]=>[1,2,2,2,1]
[7,2,1,8,3,5,6,4]=>[1,1,2,3,1]
[5,1,6,2,3,8,7,4]=>[1,2,3,1,1]
[5,1,6,3,8,2,4,7]=>[1,2,2,3]
[3,6,5,1,4,8,7,2]=>[2,1,3,1,1]
[7,6,1,3,8,4,5,2]=>[1,1,3,2,1]
[6,7,1,5,8,3,4,2]=>[2,3,2,1]
[6,7,4,1,8,3,5,2]=>[2,1,2,2,1]
[7,3,6,2,8,1,4,5]=>[1,2,2,3]
[1,6,7,3,8,4,5,2]=>[3,2,2,1]
[7,3,6,2,8,4,1,5]=>[1,2,2,1,2]
[7,5,1,8,6,4,2,3]=>[1,1,2,1,1,2]
[6,5,1,8,4,7,2,3]=>[1,1,2,2,2]
[6,5,1,8,4,2,7,3]=>[1,1,2,1,2,1]
[3,4,8,6,1,7,5,2]=>[3,1,2,1,1]
[3,4,8,5,7,1,6,2]=>[3,2,2,1]
[7,5,4,8,1,6,2,3]=>[1,1,2,2,2]
[4,3,5,8,7,1,2,6]=>[1,3,1,3]
[7,5,4,8,1,2,6,3]=>[1,1,2,3,1]
[3,4,8,6,7,5,1,2]=>[3,2,1,2]
[3,5,6,8,1,4,2,7]=>[4,2,2]
[6,1,5,8,7,2,3,4]=>[1,3,1,3]
[5,1,6,2,8,4,3,7]=>[1,2,2,1,2]
[7,3,6,1,8,4,2,5]=>[1,2,2,1,2]
[1,4,5,8,6,3,7,2]=>[4,1,2,1]
[3,5,4,8,6,2,1,7]=>[2,2,1,1,2]
[3,4,8,1,7,6,5,2]=>[3,2,1,1,1]
[3,4,8,1,6,7,5,2]=>[3,3,1,1]
[3,4,8,5,1,7,6,2]=>[3,1,2,1,1]
[3,5,4,8,2,7,1,6]=>[2,2,2,2]
[4,3,5,8,2,1,6,7]=>[1,3,1,3]
[4,3,5,8,2,6,1,7]=>[1,3,2,2]
[3,4,8,1,6,5,7,2]=>[3,2,2,1]
[6,4,7,2,3,1,5,8]=>[1,2,2,3]
[6,2,7,1,5,3,4,8]=>[1,2,2,3]
[6,8,1,5,4,2,7,3]=>[2,2,1,2,1]
[7,8,6,3,1,4,2,5]=>[2,1,1,2,2]
[7,8,6,3,5,1,2,4]=>[2,1,2,3]
[6,2,7,5,4,1,3,8]=>[1,2,1,1,3]
[7,2,8,5,4,6,3,1]=>[1,2,1,2,1,1]
[6,1,8,4,7,2,3,5]=>[1,2,2,3]
[6,1,7,5,4,3,8,2]=>[1,2,1,1,2,1]
[5,6,4,3,7,1,8,2]=>[2,1,2,2,1]
[6,5,3,7,2,4,8,1]=>[1,1,2,3,1]
[6,5,3,8,1,7,4,2]=>[1,1,2,2,1,1]
[5,4,2,3,8,6,7,1]=>[1,1,3,2,1]
[5,6,4,3,8,1,7,2]=>[2,1,2,2,1]
[5,7,6,8,4,3,1,2]=>[2,2,1,1,2]
[6,2,8,7,5,3,4,1]=>[1,2,1,1,2,1]
[6,3,2,8,5,4,7,1]=>[1,1,2,1,2,1]
[5,6,2,8,7,3,1,4]=>[2,2,1,1,2]
[5,6,2,8,4,3,7,1]=>[2,2,1,2,1]
[6,1,8,3,2,5,7,4]=>[1,2,1,3,1]
[6,1,7,8,3,2,4,5]=>[1,3,1,3]
[4,1,2,6,8,3,7,5]=>[1,4,2,1]
[5,1,3,6,2,7,4,8]=>[1,3,2,2]
[5,1,3,6,2,8,7,4]=>[1,3,2,1,1]
[7,1,6,2,5,8,3,4]=>[1,2,3,2]
[6,1,7,4,8,2,5,3]=>[1,2,2,2,1]
[4,3,2,7,8,5,1,6]=>[1,1,3,1,2]
[7,1,3,6,5,8,4,2]=>[1,3,2,1,1]
[5,1,7,4,6,8,2,3]=>[1,2,3,2]
[5,7,4,3,6,8,2,1]=>[2,1,3,1,1]
[5,1,4,3,6,7,2,8]=>[1,2,3,2]
[5,4,2,3,6,8,7,1]=>[1,1,4,1,1]
[7,5,3,6,2,8,4,1]=>[1,1,2,2,1,1]
[4,6,2,7,8,3,5,1]=>[2,3,2,1]
[5,1,2,4,6,7,8,3]=>[1,6,1]
[4,6,3,5,2,8,7,1]=>[2,2,2,1,1]
[5,6,3,4,8,2,7,1]=>[2,3,2,1]
[5,3,6,4,1,7,8,2]=>[1,2,1,3,1]
[5,2,6,4,1,7,8,3]=>[1,2,1,3,1]
[5,4,1,7,6,3,8,2]=>[1,1,2,1,2,1]
[5,8,4,6,3,2,7,1]=>[2,2,1,2,1]
[5,4,3,8,6,2,7,1]=>[1,1,2,1,2,1]
[5,7,8,2,4,3,6,1]=>[3,2,2,1]
[5,6,2,4,8,3,7,1]=>[2,3,2,1]
[6,4,7,8,2,3,5,1]=>[1,3,3,1]
[3,7,5,2,4,8,1,6]=>[2,1,3,2]
[4,7,5,2,3,8,6,1]=>[2,1,3,1,1]
[6,4,7,3,2,5,8,1]=>[1,2,1,3,1]
[5,7,3,2,8,4,6,1]=>[2,1,2,2,1]
[5,3,7,2,8,4,6,1]=>[1,2,2,2,1]
[4,3,7,2,5,8,6,1]=>[1,2,3,1,1]
[4,7,3,2,5,8,6,1]=>[2,1,3,1,1]
[4,8,3,5,1,7,6,2]=>[2,2,2,1,1]
[4,7,3,2,6,8,5,1]=>[2,1,3,1,1]
[7,5,3,2,6,4,8,1]=>[1,1,1,2,2,1]
[8,5,2,6,7,3,4,1]=>[1,1,3,2,1]
[8,4,2,6,3,7,5,1]=>[1,1,2,2,1,1]
[7,4,6,2,3,8,5,1]=>[1,2,3,1,1]
[7,5,6,2,8,3,4,1]=>[1,2,2,2,1]
[5,7,6,2,8,3,4,1]=>[2,1,2,2,1]
[4,7,6,2,3,8,5,1]=>[2,1,3,1,1]
[7,6,3,2,5,8,1,4]=>[1,1,1,3,2]
[7,6,4,2,5,8,3,1]=>[1,1,1,3,1,1]
[6,3,8,5,4,7,2,1]=>[1,2,1,2,1,1]
[7,8,2,5,1,3,6,4]=>[2,2,3,1]
[2,4,6,3,8,7,5,1]=>[3,2,1,1,1]
[2,4,6,1,8,7,3,5]=>[3,2,1,2]
[2,4,3,6,8,7,1,5]=>[2,3,1,2]
[2,4,6,3,8,7,1,5]=>[3,2,1,2]
[2,4,6,5,8,7,1,3]=>[3,2,1,2]
[2,4,6,8,5,7,3,1]=>[4,2,1,1]
[2,4,6,8,5,7,1,3]=>[4,2,2]
[2,4,6,8,3,7,1,5]=>[4,2,2]
[2,4,6,8,1,7,3,5]=>[4,2,2]
[2,4,6,5,1,8,7,3]=>[3,1,2,1,1]
[2,4,6,5,8,3,7,1]=>[3,2,2,1]
[2,4,6,5,8,1,7,3]=>[3,2,2,1]
[2,4,6,8,5,1,7,3]=>[4,1,2,1]
[2,4,6,8,7,3,5,1]=>[4,1,2,1]
[2,4,6,8,7,1,5,3]=>[4,1,2,1]
[2,4,6,8,7,1,3,5]=>[4,1,3]
[2,4,6,8,5,1,3,7]=>[4,1,3]
[2,4,6,5,1,8,3,7]=>[3,1,2,2]
[2,4,6,5,1,3,8,7]=>[3,1,3,1]
[2,4,6,5,3,8,1,7]=>[3,1,2,2]
[2,4,6,5,8,3,1,7]=>[3,2,1,2]
[2,4,6,8,5,3,1,7]=>[4,1,1,2]
[2,4,6,8,7,3,1,5]=>[4,1,1,2]
[2,4,6,8,7,5,1,3]=>[4,1,1,2]
[4,8,7,5,2,1,3,6]=>[2,1,1,1,3]
[6,1,4,7,5,8,2,3]=>[1,3,2,2]
[1,8,6,5,3,2,7,4]=>[2,1,1,1,2,1]
[1,6,3,5,8,2,4,7]=>[2,3,3]
[4,6,1,7,8,5,3,2]=>[2,3,1,1,1]
[6,1,2,7,8,4,5,3]=>[1,4,2,1]
[6,1,3,2,7,8,5,4]=>[1,2,3,1,1]
[5,6,3,1,7,4,8,2]=>[2,1,2,2,1]
[4,8,3,7,1,6,5,2]=>[2,2,2,1,1]
[8,7,2,6,5,1,4,3]=>[1,1,2,1,2,1]
[5,8,3,2,1,7,6,4]=>[2,1,1,2,1,1]
[5,4,3,8,1,7,6,2]=>[1,1,2,2,1,1]
[6,5,3,8,7,1,4,2]=>[1,1,2,1,2,1]
[4,3,8,2,7,6,5,1]=>[1,2,2,1,1,1]
[4,8,2,7,6,5,3,1]=>[2,2,1,1,1,1]
[7,8,2,6,5,4,1,3]=>[2,2,1,1,2]
[3,8,7,6,2,5,1,4]=>[2,1,1,2,2]
[4,8,3,7,2,1,6,5]=>[2,2,1,2,1]
[8,6,3,1,7,5,4,2]=>[1,1,1,2,1,1,1]
[8,6,3,7,1,5,4,2]=>[1,1,2,2,1,1]
[4,8,3,7,6,2,5,1]=>[2,2,1,2,1]
[5,8,2,7,6,4,1,3]=>[2,2,1,1,2]
[8,4,2,1,7,6,5,3]=>[1,1,1,2,1,1,1]
[1,6,4,2,5,3,7,8]=>[2,1,2,3]
[1,8,6,2,7,3,4,5]=>[2,1,2,3]
[1,6,3,2,4,5,7,8]=>[2,1,5]
[1,5,2,6,4,3,7,8]=>[2,2,1,3]
[1,5,2,4,6,3,7,8]=>[2,3,3]
[1,8,6,2,3,7,4,5]=>[2,1,3,2]
[1,5,2,8,6,3,4,7]=>[2,2,1,3]
[1,3,6,8,2,7,4,5]=>[4,2,2]
[1,4,3,8,2,5,6,7]=>[2,2,4]
[1,7,2,3,8,5,4,6]=>[2,3,1,2]
[1,3,8,4,2,5,6,7]=>[3,1,4]
[1,6,2,8,5,4,3,7]=>[2,2,1,1,2]
[1,7,2,3,8,6,4,5]=>[2,3,1,2]
[1,5,3,8,2,7,4,6]=>[2,2,2,2]
[1,4,6,5,2,8,3,7]=>[3,1,2,2]
[1,5,6,4,2,8,3,7]=>[3,1,2,2]
[1,4,8,2,5,6,3,7]=>[3,3,2]
[1,5,7,3,2,8,4,6]=>[3,1,2,2]
[1,2,7,3,6,8,4,5]=>[3,3,2]
[1,7,2,3,6,8,4,5]=>[2,4,2]
[1,4,8,3,2,5,6,7]=>[3,1,4]
[1,7,2,5,8,3,4,6]=>[2,3,3]
[6,2,3,5,8,1,7,4]=>[1,4,2,1]
[5,2,4,8,1,6,7,3]=>[1,3,3,1]
[2,6,4,5,7,3,1,8]=>[2,3,1,2]
[2,5,6,3,4,7,1,8]=>[3,3,2]
[1,3,7,5,6,8,4,2]=>[3,3,1,1]
[1,3,6,7,4,5,8,2]=>[4,3,1]
[1,5,6,3,4,2,7,8]=>[3,2,3]
[1,5,6,3,4,7,2,8]=>[3,3,2]
[1,5,3,6,4,2,7,8]=>[2,2,1,3]
[1,7,5,6,8,3,4,2]=>[2,3,2,1]
[1,7,5,6,3,8,4,2]=>[2,2,2,1,1]
[1,3,7,5,2,8,6,4]=>[3,1,2,1,1]
[1,3,7,2,5,8,6,4]=>[3,3,1,1]
[1,5,3,7,4,6,2,8]=>[2,2,2,2]
[1,5,3,7,6,4,2,8]=>[2,2,1,1,2]
[1,5,3,6,7,4,2,8]=>[2,3,1,2]
[1,5,6,3,7,4,2,8]=>[3,2,1,2]
[1,5,7,6,3,4,8,2]=>[3,1,3,1]
[1,5,7,3,6,4,8,2]=>[3,2,2,1]
[1,3,7,2,5,6,8,4]=>[3,4,1]
[1,3,7,5,6,2,8,4]=>[3,2,2,1]
[4,6,8,3,1,7,2,5]=>[3,1,2,2]
[2,5,7,4,1,3,8,6]=>[3,1,3,1]
[6,7,3,1,8,5,2,4]=>[2,1,2,1,2]
[4,7,3,6,1,8,2,5]=>[2,2,2,2]
[6,3,1,5,8,7,2,4]=>[1,1,3,1,2]
[8,3,5,1,7,6,2,4]=>[1,2,2,1,2]
[6,3,4,7,2,1,8,5]=>[1,3,1,2,1]
[5,3,6,8,7,2,1,4]=>[1,3,1,1,2]
[4,6,3,5,8,2,1,7]=>[2,3,1,2]
[3,6,2,5,8,4,1,7]=>[2,3,1,2]
[7,2,4,8,6,3,1,5]=>[1,3,1,1,2]
[2,3,5,7,4,1,8,6]=>[4,1,2,1]
[2,3,6,4,1,8,7,5]=>[3,1,2,1,1]
[8,2,5,3,1,7,6,4]=>[1,2,1,2,1,1]
[6,2,4,8,3,1,7,5]=>[1,3,1,2,1]
[5,2,6,4,3,1,8,7]=>[1,2,1,1,2,1]
[4,7,3,5,2,1,8,6]=>[2,2,1,2,1]
[8,3,4,6,2,1,7,5]=>[1,3,1,2,1]
[8,4,5,2,1,7,6,3]=>[1,2,1,2,1,1]
[7,4,5,2,1,8,6,3]=>[1,2,1,2,1,1]
[2,5,6,3,1,8,7,4]=>[3,1,2,1,1]
[4,7,5,2,1,8,6,3]=>[2,1,1,2,1,1]
[8,5,3,6,2,1,7,4]=>[1,1,2,1,2,1]
[5,6,4,3,8,2,1,7]=>[2,1,2,1,2]
[4,5,7,3,1,2,8,6]=>[3,1,3,1]
[4,5,1,8,3,2,7,6]=>[2,2,1,2,1]
[5,7,4,6,3,2,1,8]=>[2,2,1,1,2]
[3,6,1,2,4,8,7,5]=>[2,4,1,1]
[2,5,3,8,4,1,7,6]=>[2,2,1,2,1]
[4,5,2,8,3,1,7,6]=>[2,2,1,2,1]
[4,6,3,2,8,5,1,7]=>[2,1,2,1,2]
[7,4,2,8,3,1,6,5]=>[1,1,2,1,2,1]
[8,6,2,3,1,7,5,4]=>[1,1,2,2,1,1]
[6,7,2,3,1,8,5,4]=>[2,2,2,1,1]
[5,7,2,3,1,8,6,4]=>[2,2,2,1,1]
[2,7,3,4,1,8,6,5]=>[2,2,2,1,1]
[2,6,3,4,1,8,7,5]=>[2,2,2,1,1]
[7,5,2,3,1,8,6,4]=>[1,1,2,2,1,1]
[6,3,1,2,4,8,7,5]=>[1,1,4,1,1]
[8,2,3,4,1,7,6,5]=>[1,3,2,1,1]
[6,2,3,4,1,8,7,5]=>[1,3,2,1,1]
[4,7,5,2,3,6,1,8]=>[2,1,3,2]
[3,6,8,4,5,1,2,7]=>[3,2,3]
[5,2,3,7,6,4,1,8]=>[1,3,1,1,2]
[6,2,7,3,5,4,1,8]=>[1,2,2,1,2]
[7,2,6,5,3,4,1,8]=>[1,2,1,2,2]
[8,2,6,5,4,1,3,7]=>[1,2,1,1,3]
[6,2,8,4,5,1,3,7]=>[1,2,2,3]
[2,3,1,7,8,5,6,4]=>[2,3,2,1]
[7,2,8,5,1,4,3,6]=>[1,2,1,2,2]
[8,6,7,1,4,2,3,5]=>[1,2,2,3]
[6,8,7,1,4,3,2,5]=>[2,1,2,1,2]
[6,8,2,5,3,1,4,7]=>[2,2,1,3]
[3,7,8,5,1,4,2,6]=>[3,1,2,2]
[4,8,7,3,1,2,5,6]=>[2,1,1,4]
[4,8,6,2,3,1,5,7]=>[2,1,2,3]
[3,8,5,4,2,1,6,7]=>[2,1,1,1,3]
[4,5,3,8,2,1,6,7]=>[2,2,1,3]
[3,7,4,1,8,2,6,5]=>[2,1,2,2,1]
[3,8,4,1,7,6,2,5]=>[2,1,2,1,2]
[3,7,2,1,8,4,6,5]=>[2,1,2,2,1]
[8,7,1,6,5,2,3,4]=>[1,1,2,1,3]
[8,5,1,2,7,6,3,4]=>[1,1,3,1,2]
[3,8,2,1,7,6,4,5]=>[2,1,2,1,2]
[3,5,7,8,2,4,6,1]=>[4,3,1]
[7,8,2,5,4,3,6,1]=>[2,2,1,2,1]
[4,5,3,7,8,2,6,1]=>[2,3,2,1]
[1,5,4,7,3,6,2,8]=>[2,2,2,2]
[1,7,3,6,8,4,5,2]=>[2,3,2,1]
[4,6,8,2,7,3,5,1]=>[3,2,2,1]
[4,7,6,3,5,1,8,2]=>[2,1,2,2,1]
[7,8,3,6,1,5,4,2]=>[2,2,2,1,1]
[2,5,7,8,4,6,1,3]=>[4,2,2]
[3,7,5,6,2,1,4,8]=>[2,2,1,3]
[6,2,1,7,4,5,3,8]=>[1,1,2,2,2]
[1,2,6,4,7,5,3,8]=>[3,2,1,2]
[7,5,6,3,8,4,2,1]=>[1,2,2,1,1,1]
[8,5,4,2,1,6,7,3]=>[1,1,1,1,3,1]
[2,6,8,4,7,5,1,3]=>[3,2,1,2]
[6,7,5,1,4,8,3,2]=>[2,1,3,1,1]
[7,4,1,6,5,3,8,2]=>[1,1,2,1,2,1]
[5,8,2,7,3,6,4,1]=>[2,2,2,1,1]
[1,6,5,7,3,8,4,2]=>[2,2,2,1,1]
[1,5,6,8,4,2,7,3]=>[4,1,2,1]
[7,5,4,1,8,2,6,3]=>[1,1,1,2,2,1]
[6,4,1,8,2,7,5,3]=>[1,1,2,2,1,1]
[7,8,5,3,2,6,1,4]=>[2,1,1,2,2]
[8,2,5,1,7,6,4,3]=>[1,2,2,1,1,1]
[6,7,4,3,8,2,5,1]=>[2,1,2,2,1]
[3,4,2,7,8,6,1,5]=>[2,3,1,2]
[7,8,6,1,4,3,2,5]=>[2,1,2,1,2]
[2,4,7,8,6,1,3,5]=>[4,1,3]
[3,7,8,6,5,2,4,1]=>[3,1,1,2,1]
[4,5,2,7,8,6,3,1]=>[2,3,1,1,1]
[4,6,2,5,3,1,7,8]=>[2,2,1,3]
[4,1,5,6,3,2,7,8]=>[1,3,1,3]
[2,6,7,5,4,1,3,8]=>[3,1,1,3]
[4,1,6,7,5,3,2,8]=>[1,3,1,1,2]
[6,7,4,3,1,5,2,8]=>[2,1,1,2,2]
[1,7,5,6,4,3,2,8]=>[2,2,1,1,2]
[7,6,5,3,1,8,4,2]=>[1,1,1,1,2,1,1]
[7,8,6,4,3,1,5,2]=>[2,1,1,1,2,1]
[4,1,7,8,6,5,3,2]=>[1,3,1,1,1,1]
[4,5,7,3,8,6,1,2]=>[3,2,1,2]
[6,8,5,3,7,2,1,4]=>[2,1,2,1,2]
[4,6,7,8,5,3,1,2]=>[4,1,1,2]
[3,4,7,5,6,8,1,2]=>[3,3,2]
[4,7,1,5,8,2,6,3]=>[2,3,2,1]
[3,7,6,1,2,8,5,4]=>[2,1,3,1,1]
[3,7,6,2,1,8,4,5]=>[2,1,1,2,2]
[2,7,5,8,3,6,4,1]=>[2,2,2,1,1]
[7,4,8,2,6,5,3,1]=>[1,2,2,1,1,1]
[7,5,4,8,2,6,3,1]=>[1,1,2,2,1,1]
[4,3,8,1,6,5,2,7]=>[1,2,2,1,2]
[2,3,6,5,7,8,1,4]=>[3,3,2]
[8,3,4,1,2,6,7,5]=>[1,2,4,1]
[7,3,4,8,5,2,1,6]=>[1,3,1,1,2]
[7,3,8,4,1,5,6,2]=>[1,2,1,3,1]
[7,2,4,5,1,8,3,6]=>[1,3,2,2]
[3,8,7,5,1,4,2,6]=>[2,1,1,2,2]
[4,3,8,7,1,5,2,6]=>[1,2,1,2,2]
[7,3,1,2,8,5,6,4]=>[1,1,3,2,1]
[4,8,2,3,5,7,6,1]=>[2,4,1,1]
[4,5,2,3,8,6,7,1]=>[2,3,2,1]
[6,7,4,8,5,3,2,1]=>[2,2,1,1,1,1]
[3,7,6,1,4,2,8,5]=>[2,1,2,2,1]
[4,3,5,6,1,7,8,2]=>[1,3,3,1]
[3,5,2,6,4,7,8,1]=>[2,2,3,1]
[5,6,7,2,4,3,8,1]=>[3,2,2,1]
[5,6,1,8,7,3,4,2]=>[2,2,1,2,1]
[4,1,2,8,5,7,6,3]=>[1,3,2,1,1]
[3,1,5,6,4,7,8,2]=>[1,3,3,1]
[3,1,4,6,7,5,8,2]=>[1,4,2,1]
[5,2,1,4,6,8,3,7]=>[1,1,4,2]
[2,6,4,5,8,1,3,7]=>[2,3,3]
[6,4,1,3,5,8,2,7]=>[1,1,4,2]
[5,2,3,6,4,8,1,7]=>[1,3,2,2]
[8,6,5,2,3,7,4,1]=>[1,1,1,3,1,1]
[3,4,1,7,2,6,8,5]=>[2,2,3,1]
[7,3,1,4,5,8,2,6]=>[1,1,4,2]
[2,4,7,5,8,1,3,6]=>[3,2,3]
[6,1,8,7,3,4,5,2]=>[1,2,1,3,1]
[6,8,7,4,1,3,5,2]=>[2,1,1,3,1]
[3,1,6,4,8,7,5,2]=>[1,2,2,1,1,1]
[3,7,1,4,5,8,6,2]=>[2,4,1,1]
[2,5,6,3,8,7,4,1]=>[3,2,1,1,1]
[5,8,7,4,1,3,6,2]=>[2,1,1,3,1]
[8,4,7,5,1,3,6,2]=>[1,2,1,3,1]
[8,7,1,5,3,4,6,2]=>[1,1,2,3,1]
[7,2,6,4,8,1,3,5]=>[1,2,2,3]
[5,7,3,1,2,6,8,4]=>[2,1,4,1]
[3,7,6,2,1,5,8,4]=>[2,1,1,3,1]
[4,2,6,1,3,7,8,5]=>[1,2,4,1]
[8,5,4,2,7,6,3,1]=>[1,1,1,2,1,1,1]
[2,7,4,3,1,6,8,5]=>[2,1,1,3,1]
[2,8,4,6,7,1,3,5]=>[2,3,3]
[1,8,3,4,6,7,2,5]=>[2,4,2]
[8,2,3,6,1,5,7,4]=>[1,3,3,1]
[2,5,3,1,6,8,7,4]=>[2,1,3,1,1]
[2,5,1,6,4,8,7,3]=>[2,2,2,1,1]
[5,8,2,1,4,6,7,3]=>[2,1,4,1]
[8,4,6,1,2,5,7,3]=>[1,2,4,1]
[3,7,8,4,2,6,5,1]=>[3,1,2,1,1]
[8,5,1,4,2,6,7,3]=>[1,1,2,3,1]
[3,5,1,8,6,7,2,4]=>[2,2,2,2]
[5,6,2,8,7,1,3,4]=>[2,2,1,3]
[7,2,4,8,5,6,1,3]=>[1,3,2,2]
[7,1,3,8,4,5,6,2]=>[1,3,3,1]
[7,8,1,4,3,5,6,2]=>[2,2,3,1]
[2,6,7,8,3,5,1,4]=>[4,2,2]
[3,6,7,8,2,1,5,4]=>[4,1,2,1]
[3,6,7,2,8,1,5,4]=>[3,2,2,1]
[2,6,7,1,3,5,8,4]=>[3,4,1]
[3,6,7,1,2,8,5,4]=>[3,3,1,1]
[3,6,7,1,8,2,5,4]=>[3,2,2,1]
[3,4,1,8,7,2,6,5]=>[2,2,1,2,1]
[2,5,1,7,3,6,8,4]=>[2,2,3,1]
[3,1,5,7,2,8,6,4]=>[1,3,2,1,1]
[3,1,5,7,8,2,6,4]=>[1,4,2,1]
[3,8,1,4,7,2,6,5]=>[2,3,2,1]
[4,8,1,3,2,7,6,5]=>[2,2,2,1,1]
[4,1,8,3,2,7,6,5]=>[1,2,1,2,1,1]
[4,1,3,8,2,7,6,5]=>[1,3,2,1,1]
[1,4,2,3,7,6,5,8]=>[2,3,1,2]
[4,3,1,8,2,7,6,5]=>[1,1,2,2,1,1]
[4,3,8,1,2,7,6,5]=>[1,2,3,1,1]
[4,3,8,2,1,7,6,5]=>[1,2,1,2,1,1]
[3,4,2,8,7,1,6,5]=>[2,2,1,2,1]
[3,8,4,2,7,1,6,5]=>[2,1,2,2,1]
[2,8,4,3,7,6,1,5]=>[2,1,2,1,2]
[2,4,3,8,7,6,1,5]=>[2,2,1,1,2]
[2,4,5,7,6,1,8,3]=>[4,1,2,1]
[2,4,5,7,6,8,1,3]=>[4,2,2]
[2,3,5,7,8,6,1,4]=>[5,1,2]
[2,3,8,4,7,6,1,5]=>[3,2,1,2]
[3,8,2,4,7,1,6,5]=>[2,3,2,1]
[3,2,4,8,7,1,6,5]=>[1,3,1,2,1]
[3,2,5,7,1,8,6,4]=>[1,3,2,1,1]
[2,3,5,7,1,6,8,4]=>[4,3,1]
[4,2,3,8,1,7,6,5]=>[1,3,2,1,1]
[4,2,8,3,1,7,6,5]=>[1,2,1,2,1,1]
[4,8,2,3,1,7,6,5]=>[2,2,2,1,1]
[4,8,2,1,3,7,6,5]=>[2,1,3,1,1]
[4,2,8,1,3,7,6,5]=>[1,2,3,1,1]
[3,1,2,4,7,8,6,5]=>[1,5,1,1]
[3,5,4,7,2,8,1,6]=>[2,2,2,2]
[3,6,4,7,8,2,1,5]=>[2,3,1,2]
[2,3,4,6,8,7,1,5]=>[5,1,2]
[5,3,4,6,1,7,8,2]=>[1,3,3,1]
[2,5,7,8,6,1,3,4]=>[4,1,3]
[2,4,7,6,8,1,3,5]=>[3,2,3]
[4,6,5,1,7,2,8,3]=>[2,1,2,2,1]
[5,6,4,7,1,2,8,3]=>[2,2,3,1]
[4,6,7,5,8,2,3,1]=>[3,2,2,1]
[3,5,1,7,6,8,4,2]=>[2,2,2,1,1]
[4,5,7,1,6,8,3,2]=>[3,3,1,1]
[3,2,7,6,8,1,4,5]=>[1,2,2,3]
[6,1,3,5,7,8,4,2]=>[1,5,1,1]
[4,5,1,7,6,8,2,3]=>[2,2,2,2]
[6,2,5,7,1,3,8,4]=>[1,3,3,1]
[7,6,1,5,2,8,4,3]=>[1,1,2,2,1,1]
[4,1,7,8,3,5,2,6]=>[1,3,2,2]
[5,7,2,3,1,8,4,6]=>[2,2,2,2]
[7,2,8,3,1,6,5,4]=>[1,2,1,2,1,1]
[6,7,2,8,3,1,4,5]=>[2,2,1,3]
[3,1,7,6,2,8,4,5]=>[1,2,1,2,2]
[7,6,3,1,2,8,4,5]=>[1,1,1,3,2]
[6,2,7,8,4,1,3,5]=>[1,3,1,3]
[7,2,6,8,3,4,1,5]=>[1,3,2,2]
[7,2,4,1,6,8,3,5]=>[1,2,3,2]
[8,3,6,7,2,4,1,5]=>[1,3,2,2]
[4,1,8,3,6,7,2,5]=>[1,2,3,2]
[6,3,7,8,4,1,2,5]=>[1,3,1,3]
[7,8,5,2,4,1,3,6]=>[2,1,2,3]
[6,2,3,7,8,4,1,5]=>[1,4,1,2]
[7,6,2,3,1,8,4,5]=>[1,1,2,2,2]
[2,6,3,7,8,4,1,5]=>[2,3,1,2]
[2,7,8,5,3,4,1,6]=>[3,1,2,2]
[4,8,5,2,3,1,7,6]=>[2,1,2,2,1]
[4,2,5,1,3,7,8,6]=>[1,2,4,1]
[4,3,5,1,2,7,8,6]=>[1,2,4,1]
[3,5,1,4,2,7,8,6]=>[2,2,3,1]
[3,4,1,7,8,5,2,6]=>[2,3,1,2]
[4,1,3,7,8,5,2,6]=>[1,4,1,2]
[3,1,4,8,5,2,7,6]=>[1,3,1,2,1]
[4,3,1,8,5,2,7,6]=>[1,1,2,1,2,1]
[8,4,7,5,3,6,2,1]=>[1,2,1,2,1,1]
[6,3,8,4,7,5,2,1]=>[1,2,2,1,1,1]
[8,5,3,1,4,2,7,6]=>[1,1,1,2,2,1]
[3,1,8,5,4,2,7,6]=>[1,2,1,1,2,1]
[8,5,4,3,1,2,7,6]=>[1,1,1,1,3,1]
[7,6,3,5,8,4,2,1]=>[1,1,3,1,1,1]
[4,5,1,3,2,7,8,6]=>[2,2,3,1]
[5,1,3,2,4,7,8,6]=>[1,2,4,1]
[8,5,4,2,3,1,7,6]=>[1,1,1,2,2,1]
[2,3,7,8,5,4,1,6]=>[4,1,1,2]
[8,3,5,6,1,7,2,4]=>[1,3,2,2]
[4,5,8,1,2,6,7,3]=>[3,4,1]
[5,3,6,7,8,2,1,4]=>[1,4,1,2]
[1,3,4,8,6,2,7,5]=>[4,1,2,1]
[8,3,7,4,6,2,1,5]=>[1,2,2,1,2]
[4,8,3,5,7,2,1,6]=>[2,3,1,2]
[1,2,4,8,7,3,5,6]=>[4,1,3]
[5,2,7,8,3,1,4,6]=>[1,3,1,3]
[7,2,4,1,3,8,5,6]=>[1,2,3,2]
[3,8,2,5,4,1,6,7]=>[2,2,1,3]
[8,4,5,2,6,1,7,3]=>[1,2,2,2,1]
[4,5,6,2,7,8,1,3]=>[3,3,2]
[2,6,7,3,8,1,4,5]=>[3,2,3]
[2,8,6,3,1,7,4,5]=>[2,1,1,2,2]
[4,7,5,1,2,6,8,3]=>[2,1,4,1]
[5,6,1,4,2,8,7,3]=>[2,2,2,1,1]
[4,5,8,1,3,2,7,6]=>[3,2,2,1]
[4,7,1,2,6,3,5,8]=>[2,3,3]
[4,6,8,2,3,7,5,1]=>[3,3,1,1]
[4,5,7,2,3,6,1,8]=>[3,3,2]
[2,5,7,3,4,6,8,1]=>[3,4,1]
[5,8,2,1,3,7,4,6]=>[2,1,3,2]
[7,4,2,1,6,3,5,8]=>[1,1,1,2,3]
[8,5,2,3,1,7,4,6]=>[1,1,2,2,2]
[6,8,2,3,1,4,7,5]=>[2,2,3,1]
[2,7,3,4,1,5,6,8]=>[2,2,4]
[6,7,2,3,4,8,1,5]=>[2,4,2]
[7,4,2,1,3,5,8,6]=>[1,1,1,4,1]
[3,5,2,4,6,7,8,1]=>[2,5,1]
[4,2,6,3,5,7,8,1]=>[1,2,4,1]
[5,2,3,7,4,6,8,1]=>[1,3,3,1]
[6,2,3,4,8,5,7,1]=>[1,4,2,1]
[2,7,5,8,4,1,6,3]=>[2,2,1,2,1]
[1,7,5,8,4,2,6,3]=>[2,2,1,2,1]
[1,4,8,5,6,2,7,3]=>[3,2,2,1]
[2,4,8,5,6,1,7,3]=>[3,2,2,1]
[6,3,5,8,4,7,1,2]=>[1,3,2,2]
[2,8,7,4,5,1,6,3]=>[2,1,2,2,1]
[1,8,7,4,5,2,6,3]=>[2,1,2,2,1]
[1,3,8,5,2,6,7,4]=>[3,1,3,1]
[7,2,8,4,5,1,6,3]=>[1,2,2,2,1]
[6,2,5,8,4,1,7,3]=>[1,3,1,2,1]
[3,1,8,5,2,6,7,4]=>[1,2,1,3,1]
[1,2,8,5,3,6,7,4]=>[3,1,3,1]
[7,1,3,5,2,6,8,4]=>[1,3,3,1]
[5,4,1,3,2,7,8,6]=>[1,1,2,3,1]
[5,4,8,2,1,6,7,3]=>[1,2,1,3,1]
[6,8,3,2,1,5,7,4]=>[2,1,1,3,1]
[7,8,2,4,1,5,6,3]=>[2,2,3,1]
[6,2,3,5,1,7,8,4]=>[1,3,3,1]
[8,6,2,4,1,5,7,3]=>[1,1,2,3,1]
[1,7,3,5,2,6,8,4]=>[2,2,3,1]
[1,6,4,3,2,7,8,5]=>[2,1,1,3,1]
[8,5,3,2,1,6,7,4]=>[1,1,1,1,3,1]
[2,6,4,3,1,7,8,5]=>[2,1,1,3,1]
[2,7,5,1,3,6,8,4]=>[2,1,4,1]
[1,7,5,2,3,6,8,4]=>[2,1,4,1]
[2,8,1,5,3,6,7,4]=>[2,2,3,1]
[3,8,1,5,2,6,7,4]=>[2,2,3,1]
[4,8,1,5,6,2,7,3]=>[2,3,2,1]
[7,8,4,1,5,2,6,3]=>[2,1,2,2,1]
[5,4,3,1,2,7,8,6]=>[1,1,1,4,1]
[7,3,1,5,2,6,8,4]=>[1,1,2,3,1]
[7,1,5,2,3,6,8,4]=>[1,2,4,1]
[8,1,2,5,3,6,7,4]=>[1,3,3,1]
[8,4,1,6,3,7,2,5]=>[1,1,2,2,2]
[6,3,5,8,1,7,2,4]=>[1,3,2,2]
[6,7,5,3,8,2,1,4]=>[2,1,2,1,2]
[6,5,7,4,2,8,1,3]=>[1,2,1,2,2]
[6,5,2,1,4,8,7,3]=>[1,1,1,3,1,1]
[5,2,6,8,3,7,1,4]=>[1,3,2,2]
[4,2,5,8,6,7,1,3]=>[1,3,2,2]
[5,8,6,3,4,1,7,2]=>[2,1,2,2,1]
[6,3,4,1,5,8,7,2]=>[1,2,3,1,1]
[5,4,6,1,7,2,3,8]=>[1,2,2,3]
[7,5,4,1,8,6,2,3]=>[1,1,1,2,1,2]
[8,7,2,3,5,6,4,1]=>[1,1,4,1,1]
[3,7,2,4,1,8,6,5]=>[2,2,2,1,1]
[3,7,2,4,1,5,8,6]=>[2,2,3,1]
[8,2,7,5,3,4,6,1]=>[1,2,1,3,1]
[2,4,7,8,5,1,3,6]=>[4,1,3]
[7,8,3,4,1,2,6,5]=>[2,2,3,1]
[2,5,3,8,4,1,6,7]=>[2,2,1,3]
[8,2,1,7,4,6,5,3]=>[1,1,2,2,1,1]
[2,7,6,5,3,8,4,1]=>[2,1,1,2,1,1]
[5,7,6,8,1,3,4,2]=>[2,2,3,1]
[3,6,5,1,7,4,8,2]=>[2,1,2,2,1]
[6,1,5,3,7,4,2,8]=>[1,2,2,1,2]
[5,3,7,6,8,4,2,1]=>[1,2,2,1,1,1]
[3,1,7,4,5,6,2,8]=>[1,2,3,2]
[3,6,7,1,2,5,4,8]=>[3,3,2]
[1,7,3,4,8,2,6,5]=>[2,3,2,1]
[8,5,7,4,2,3,1,6]=>[1,2,1,2,2]
[2,6,5,4,8,3,7,1]=>[2,1,2,2,1]
[2,4,8,3,5,7,1,6]=>[3,3,2]
[8,1,7,2,4,3,5,6]=>[1,2,2,3]
[1,3,8,2,4,7,5,6]=>[3,3,2]
[1,3,7,2,4,6,5,8]=>[3,3,2]
[1,7,3,2,4,6,5,8]=>[2,1,3,2]
[1,8,3,7,4,2,5,6]=>[2,2,1,3]
[8,7,3,1,4,2,5,6]=>[1,1,1,2,3]
[2,8,4,3,5,7,1,6]=>[2,1,3,2]
[3,2,8,7,4,1,5,6]=>[1,2,1,1,3]
[3,2,1,7,4,6,5,8]=>[1,1,2,2,2]
[3,2,6,5,1,7,8,4]=>[1,2,1,3,1]
[5,3,2,6,7,1,8,4]=>[1,1,3,2,1]
[3,2,8,6,7,4,1,5]=>[1,2,2,1,2]
[8,4,6,2,7,3,1,5]=>[1,2,2,1,2]
[4,3,8,6,7,2,1,5]=>[1,2,2,1,2]
[4,3,6,2,8,7,1,5]=>[1,2,2,1,2]
[3,8,4,7,6,5,1,2]=>[2,2,1,1,2]
[7,8,4,2,6,3,5,1]=>[2,1,2,2,1]
[3,2,7,8,6,4,5,1]=>[1,3,1,2,1]
[3,2,7,5,6,8,4,1]=>[1,2,3,1,1]
[5,7,8,6,3,2,4,1]=>[3,1,1,2,1]
[6,5,4,2,1,7,8,3]=>[1,1,1,1,3,1]
[5,4,2,1,7,6,3,8]=>[1,1,1,2,1,2]
[4,1,6,5,2,7,8,3]=>[1,2,1,3,1]
[5,4,1,6,7,2,8,3]=>[1,1,3,2,1]
[6,8,5,3,1,7,2,4]=>[2,1,1,2,2]
[5,2,6,3,8,7,1,4]=>[1,2,2,1,2]
[8,6,1,7,3,4,2,5]=>[1,1,2,2,2]
[1,8,3,6,7,4,2,5]=>[2,3,1,2]
[1,6,3,5,2,7,8,4]=>[2,2,3,1]
[1,5,7,3,2,6,4,8]=>[3,1,2,2]
[5,1,3,7,2,6,4,8]=>[1,3,2,2]
[8,1,6,7,2,4,3,5]=>[1,3,2,2]
[6,1,4,8,2,7,3,5]=>[1,3,2,2]
[6,2,4,8,3,7,1,5]=>[1,3,2,2]
[8,7,2,6,3,5,1,4]=>[1,1,2,2,2]
[8,1,7,6,5,2,3,4]=>[1,2,1,1,3]
[7,1,5,6,8,2,4,3]=>[1,4,2,1]
[6,7,1,5,2,4,8,3]=>[2,2,3,1]
[7,6,1,5,2,4,3,8]=>[1,1,2,2,2]
[7,1,6,3,5,4,2,8]=>[1,2,2,1,2]
[1,6,7,3,5,4,8,2]=>[3,2,2,1]
[1,7,3,5,6,8,4,2]=>[2,4,1,1]
[1,7,8,3,6,4,5,2]=>[3,2,2,1]
[1,8,7,6,4,5,2,3]=>[2,1,1,2,2]
[8,2,7,4,6,5,1,3]=>[1,2,2,1,2]
[2,8,5,7,6,4,1,3]=>[2,2,1,1,2]
[7,4,5,1,6,8,3,2]=>[1,2,3,1,1]
[4,1,7,5,6,8,3,2]=>[1,2,3,1,1]
[5,6,7,4,3,1,8,2]=>[3,1,1,2,1]
[6,7,8,5,3,1,4,2]=>[3,1,1,2,1]
[1,4,6,2,5,3,7,8]=>[3,2,3]
[1,6,3,2,5,4,7,8]=>[2,1,2,3]
[1,6,8,2,5,4,7,3]=>[3,2,2,1]
[1,5,4,2,6,3,7,8]=>[2,1,2,3]
[1,2,6,4,3,5,7,8]=>[3,1,4]
[1,6,8,2,7,5,4,3]=>[3,2,1,1,1]
[1,7,4,3,2,6,8,5]=>[2,1,1,3,1]
[1,5,4,7,2,6,8,3]=>[2,2,3,1]
[1,3,7,6,2,8,5,4]=>[3,1,2,1,1]
[1,7,6,2,8,4,3,5]=>[2,1,2,1,2]
[1,5,2,8,4,3,7,6]=>[2,2,1,2,1]
[1,2,8,4,3,6,5,7]=>[3,1,2,2]
[1,2,8,5,6,3,4,7]=>[3,2,3]
[1,7,3,5,2,8,6,4]=>[2,2,2,1,1]
[1,6,7,2,5,8,4,3]=>[3,3,1,1]
[1,5,8,3,2,7,4,6]=>[3,1,2,2]
[1,4,5,8,2,6,3,7]=>[4,2,2]
[1,7,6,4,8,2,5,3]=>[2,1,2,2,1]
[1,4,8,6,5,2,7,3]=>[3,1,1,2,1]
[1,3,8,2,6,5,4,7]=>[3,2,1,2]
[1,7,6,3,8,2,4,5]=>[2,1,2,3]
[1,5,2,7,6,4,8,3]=>[2,2,1,2,1]
[1,2,4,3,8,7,5,6]=>[3,2,1,2]
[1,4,3,8,7,2,5,6]=>[2,2,1,3]
[1,3,8,6,2,4,5,7]=>[3,1,4]
[1,3,8,5,4,2,6,7]=>[3,1,1,3]
[1,7,2,4,8,6,5,3]=>[2,3,1,1,1]
[1,6,5,3,2,8,7,4]=>[2,1,1,2,1,1]
[1,3,2,8,7,5,4,6]=>[2,2,1,1,2]
[1,2,8,6,5,4,3,7]=>[3,1,1,1,2]
[8,1,3,4,6,5,2,7]=>[1,4,1,2]
[8,3,1,4,6,5,2,7]=>[1,1,3,1,2]
[5,8,3,1,2,6,4,7]=>[2,1,3,2]
[4,8,1,7,5,2,3,6]=>[2,2,1,3]
[4,8,1,7,5,2,6,3]=>[2,2,1,2,1]
[8,5,1,4,2,6,3,7]=>[1,1,2,2,2]
[8,4,1,3,5,6,2,7]=>[1,1,4,2]
[8,5,3,2,1,6,4,7]=>[1,1,1,1,2,2]
[8,1,5,4,2,6,3,7]=>[1,2,1,2,2]
[8,5,2,4,1,6,3,7]=>[1,1,2,2,2]
[4,8,7,1,5,2,6,3]=>[2,1,2,2,1]
[4,8,7,1,5,2,3,6]=>[2,1,2,3]
[7,6,8,4,1,3,2,5]=>[1,2,1,2,2]
[7,6,8,4,1,3,5,2]=>[1,2,1,3,1]
[3,8,7,5,4,1,2,6]=>[2,1,1,1,3]
[4,8,2,7,5,1,3,6]=>[2,2,1,3]
[7,6,8,4,1,5,2,3]=>[1,2,1,2,2]
[8,7,6,1,5,2,3,4]=>[1,1,1,2,3]
[7,1,4,8,6,3,5,2]=>[1,3,1,2,1]
[8,1,6,5,3,4,7,2]=>[1,2,1,3,1]
[8,6,2,5,3,4,7,1]=>[1,1,2,3,1]
[8,6,5,1,3,4,7,2]=>[1,1,1,4,1]
[8,7,5,1,3,6,2,4]=>[1,1,1,3,2]
[8,7,1,5,3,6,2,4]=>[1,1,2,2,2]
[8,6,1,3,5,4,7,2]=>[1,1,3,2,1]
[7,1,4,8,3,6,5,2]=>[1,3,2,1,1]
[7,8,5,2,4,3,6,1]=>[2,1,2,2,1]
[7,3,8,2,5,4,6,1]=>[1,2,2,2,1]
[8,4,2,5,3,7,6,1]=>[1,1,2,2,1,1]
[4,8,1,5,3,7,6,2]=>[2,2,2,1,1]
[7,4,8,2,6,3,5,1]=>[1,2,2,2,1]
[7,4,8,2,6,3,1,5]=>[1,2,2,1,2]
[8,7,3,1,6,4,2,5]=>[1,1,1,2,1,2]
[8,7,3,1,6,4,5,2]=>[1,1,1,2,2,1]
[8,7,3,1,4,6,5,2]=>[1,1,1,3,1,1]
[8,4,3,2,7,5,6,1]=>[1,1,1,2,2,1]
[6,4,1,7,8,5,3,2]=>[1,1,3,1,1,1]
[7,6,3,4,1,8,5,2]=>[1,1,2,2,1,1]
[8,7,3,1,6,2,5,4]=>[1,1,1,2,2,1]
[7,8,6,4,2,5,1,3]=>[2,1,1,2,2]
[7,8,2,4,6,5,1,3]=>[2,3,1,2]
[8,1,7,3,5,6,2,4]=>[1,2,3,2]
[8,7,5,2,4,6,1,3]=>[1,1,1,3,2]
[8,1,7,5,4,6,2,3]=>[1,2,1,2,2]
[8,7,3,2,6,1,5,4]=>[1,1,1,2,2,1]
[5,3,1,7,6,4,2,8]=>[1,1,2,1,1,2]
[7,5,3,2,1,6,4,8]=>[1,1,1,1,2,2]
[7,6,5,3,1,4,2,8]=>[1,1,1,1,2,2]
[1,8,6,4,3,2,7,5]=>[2,1,1,1,2,1]
[1,8,7,6,4,2,5,3]=>[2,1,1,1,2,1]
[8,4,6,7,5,3,2,1]=>[1,3,1,1,1,1]
[1,4,8,6,7,5,3,2]=>[3,2,1,1,1]
[7,3,8,5,6,4,2,1]=>[1,2,2,1,1,1]
[7,8,2,5,6,4,3,1]=>[2,3,1,1,1]
[7,6,2,5,8,4,3,1]=>[1,1,3,1,1,1]
[1,7,3,6,8,5,4,2]=>[2,3,1,1,1]
[8,6,2,5,7,4,3,1]=>[1,1,3,1,1,1]
[7,1,3,6,8,5,4,2]=>[1,4,1,1,1]
[1,8,3,6,7,5,4,2]=>[2,3,1,1,1]
[1,8,2,7,5,6,4,3]=>[2,2,2,1,1]
[7,8,1,6,4,5,3,2]=>[2,2,2,1,1]
[7,6,1,8,4,5,3,2]=>[1,1,2,2,1,1]
[8,6,1,7,4,5,3,2]=>[1,1,2,2,1,1]
[7,2,8,6,4,5,3,1]=>[1,2,1,2,1,1]
[8,1,7,6,4,5,3,2]=>[1,2,1,2,1,1]
[7,1,8,6,4,5,3,2]=>[1,2,1,2,1,1]
[1,6,2,5,4,3,7,8]=>[2,2,1,3]
[1,6,2,7,4,5,3,8]=>[2,2,2,2]
[1,7,2,6,4,5,3,8]=>[2,2,2,2]
[1,7,2,8,4,3,6,5]=>[2,2,1,2,1]
[1,8,2,6,4,3,5,7]=>[2,2,1,3]
[1,7,2,6,4,3,5,8]=>[2,2,1,3]
[1,6,2,7,4,3,5,8]=>[2,2,1,3]
[1,7,2,5,4,6,3,8]=>[2,2,2,2]
[1,8,2,5,4,6,3,7]=>[2,2,2,2]
[1,2,8,3,4,7,5,6]=>[3,3,2]
[8,1,2,3,7,6,4,5]=>[1,4,1,2]
[6,5,7,2,3,1,8,4]=>[1,2,2,2,1]
[6,5,7,2,8,3,4,1]=>[1,2,2,2,1]
[6,5,7,2,8,1,4,3]=>[1,2,2,2,1]
[6,2,7,5,8,1,4,3]=>[1,2,2,2,1]
[6,7,2,5,8,1,4,3]=>[2,3,2,1]
[6,7,3,5,8,1,4,2]=>[2,3,2,1]
[7,3,6,8,2,4,1,5]=>[1,3,2,2]
[6,7,3,5,8,2,4,1]=>[2,3,2,1]
[6,3,7,2,4,1,8,5]=>[1,2,2,2,1]
[6,3,7,5,8,1,4,2]=>[1,2,2,2,1]
[6,5,7,3,8,1,4,2]=>[1,2,2,2,1]
[6,3,7,4,8,2,5,1]=>[1,2,2,2,1]
[6,3,7,4,8,1,5,2]=>[1,2,2,2,1]
[6,2,7,4,8,3,5,1]=>[1,2,2,2,1]
[6,2,7,4,8,1,5,3]=>[1,2,2,2,1]
[8,7,6,4,2,5,3,1]=>[1,1,1,1,2,1,1]
[8,7,4,6,2,3,5,1]=>[1,1,2,3,1]
[6,8,4,5,7,3,2,1]=>[2,3,1,1,1]
[4,8,7,1,6,3,5,2]=>[2,1,2,2,1]
[5,6,4,2,1,7,8,3]=>[2,1,1,3,1]
[6,7,5,1,4,3,8,2]=>[2,1,2,2,1]
[6,8,5,1,4,3,7,2]=>[2,1,2,2,1]
[5,6,4,2,1,8,7,3]=>[2,1,1,2,1,1]
[7,8,5,1,4,3,6,2]=>[2,1,2,2,1]
[2,7,6,8,3,5,1,4]=>[2,2,2,2]
[6,1,7,8,4,3,5,2]=>[1,3,1,2,1]
[2,7,8,6,4,5,3,1]=>[3,1,2,1,1]
[4,8,5,6,2,3,1,7]=>[2,2,2,2]
[2,6,8,1,3,5,4,7]=>[3,3,2]
[5,2,1,3,6,8,4,7]=>[1,1,4,2]
[5,2,3,1,8,7,4,6]=>[1,2,2,1,2]
[7,2,1,5,3,8,6,4]=>[1,1,2,2,1,1]
[3,2,7,1,6,8,5,4]=>[1,2,3,1,1]
[5,8,2,7,6,1,3,4]=>[2,2,1,3]
[3,6,8,7,4,5,2,1]=>[3,1,2,1,1]
[8,6,7,1,3,5,2,4]=>[1,2,3,2]
[5,2,1,3,6,7,4,8]=>[1,1,4,2]
[7,2,1,8,6,3,5,4]=>[1,1,2,1,2,1]
[3,2,4,8,1,7,6,5]=>[1,3,2,1,1]
[6,2,7,1,4,8,3,5]=>[1,2,3,2]
[4,3,6,8,7,2,1,5]=>[1,3,1,1,2]
[4,2,3,1,7,5,6,8]=>[1,2,2,3]
[5,1,8,7,3,4,2,6]=>[1,2,1,2,2]
[6,2,8,1,4,7,3,5]=>[1,2,3,2]
[8,2,3,6,7,1,4,5]=>[1,4,3]
[8,2,3,1,4,7,5,6]=>[1,2,3,2]
[4,2,3,1,5,8,6,7]=>[1,2,3,2]
[2,4,8,7,5,3,1,6]=>[3,1,1,1,2]
[2,6,8,7,5,3,4,1]=>[3,1,1,2,1]
[2,6,5,1,4,3,8,7]=>[2,1,2,2,1]
[6,5,1,2,4,3,8,7]=>[1,1,3,2,1]
[4,6,5,3,1,2,8,7]=>[2,1,1,3,1]
[4,8,7,5,3,1,2,6]=>[2,1,1,1,3]
[4,6,8,7,5,3,1,2]=>[3,1,1,1,2]
[6,8,7,5,3,1,4,2]=>[2,1,1,1,2,1]
[8,7,5,6,3,1,4,2]=>[1,1,2,1,2,1]
[8,7,3,4,6,5,1,2]=>[1,1,3,1,2]
[2,1,4,8,7,3,6,5]=>[1,3,1,2,1]
[4,8,7,3,1,2,6,5]=>[2,1,1,3,1]
[8,7,3,4,1,2,6,5]=>[1,1,2,3,1]
[8,7,3,1,6,5,2,4]=>[1,1,1,2,1,2]
[8,7,3,2,6,5,1,4]=>[1,1,1,2,1,2]
[2,8,7,3,4,6,5,1]=>[2,1,3,1,1]
[2,8,7,3,6,5,1,4]=>[2,1,2,1,2]
[2,8,7,1,6,5,3,4]=>[2,1,2,1,2]
[8,7,1,2,6,5,3,4]=>[1,1,3,1,2]
[8,7,1,2,4,3,6,5]=>[1,1,3,2,1]
[2,1,8,7,3,4,6,5]=>[1,2,1,3,1]
[8,7,5,1,2,4,3,6]=>[1,1,1,3,2]
[2,8,7,1,4,3,6,5]=>[2,1,2,2,1]
[2,8,7,3,4,1,6,5]=>[2,1,2,2,1]
[2,8,7,5,6,3,4,1]=>[2,1,2,2,1]
[2,4,8,7,3,1,6,5]=>[3,1,1,2,1]
[2,8,7,3,1,4,6,5]=>[2,1,1,3,1]
[2,4,3,1,8,7,5,6]=>[2,1,2,1,2]
[4,3,1,2,6,8,7,5]=>[1,1,4,1,1]
[2,8,7,5,6,3,1,4]=>[2,1,2,1,2]
[2,8,7,5,3,1,6,4]=>[2,1,1,1,2,1]
[2,8,7,5,3,6,4,1]=>[2,1,1,2,1,1]
[2,8,7,5,6,1,4,3]=>[2,1,2,2,1]
[2,6,8,7,5,1,4,3]=>[3,1,1,2,1]
[6,8,7,5,1,2,4,3]=>[2,1,1,3,1]
[8,7,5,6,1,2,4,3]=>[1,1,2,3,1]
[8,7,1,2,4,6,5,3]=>[1,1,4,1,1]
[2,4,8,7,3,6,5,1]=>[3,1,2,1,1]
[8,7,2,4,3,6,5,1]=>[1,1,2,2,1,1]
[4,8,7,1,2,6,5,3]=>[2,1,3,1,1]
[8,7,5,3,1,2,6,4]=>[1,1,1,1,3,1]
[8,7,5,3,6,4,1,2]=>[1,1,1,2,1,2]
[8,7,1,4,3,6,5,2]=>[1,1,2,2,1,1]
[8,7,3,4,1,6,5,2]=>[1,1,2,2,1,1]
[7,1,2,3,5,4,6,8]=>[1,4,3]
[7,1,2,6,4,5,3,8]=>[1,3,2,2]
[7,1,2,4,3,5,6,8]=>[1,3,4]
[4,7,3,6,5,1,2,8]=>[2,2,1,3]
[5,2,6,3,7,1,4,8]=>[1,2,2,3]
[6,5,4,1,3,8,7,2]=>[1,1,1,3,1,1]
[7,5,4,2,8,3,1,6]=>[1,1,1,2,1,2]
[2,5,8,6,1,4,3,7]=>[3,1,2,2]
[8,3,6,1,5,2,4,7]=>[1,2,2,3]
[3,1,6,8,5,7,2,4]=>[1,3,2,2]
[4,6,1,8,2,5,7,3]=>[2,2,3,1]
[2,5,6,1,8,4,7,3]=>[3,2,2,1]
[2,6,5,1,8,4,7,3]=>[2,1,2,2,1]
[7,5,4,1,2,8,6,3]=>[1,1,1,3,1,1]
[5,7,2,1,8,4,6,3]=>[2,1,2,2,1]
[8,4,2,7,1,5,3,6]=>[1,1,2,2,2]
[7,2,8,6,4,3,1,5]=>[1,2,1,1,1,2]
[6,3,8,7,4,2,1,5]=>[1,2,1,1,1,2]
[7,6,3,2,8,4,1,5]=>[1,1,1,2,1,2]
[7,2,8,5,3,1,4,6]=>[1,2,1,1,3]
[4,7,2,8,3,1,5,6]=>[2,2,1,3]
[8,6,1,3,2,4,5,7]=>[1,1,2,4]
[5,8,3,7,4,2,1,6]=>[2,2,1,1,2]
[4,1,7,3,5,8,6,2]=>[1,2,3,1,1]
[8,4,7,3,5,2,1,6]=>[1,2,2,1,2]
[5,4,8,1,3,2,6,7]=>[1,2,2,3]
[4,5,8,2,1,3,6,7]=>[3,1,4]
[8,1,3,5,2,4,6,7]=>[1,3,4]
[1,8,3,5,7,2,4,6]=>[2,3,3]
[8,1,4,7,3,2,6,5]=>[1,3,1,2,1]
[5,8,1,3,2,7,6,4]=>[2,2,2,1,1]
[5,3,7,1,2,8,6,4]=>[1,2,3,1,1]
[6,5,1,3,8,2,7,4]=>[1,1,3,2,1]
[1,7,3,8,6,2,4,5]=>[2,2,1,3]
[8,6,2,1,3,7,5,4]=>[1,1,1,3,1,1]
[8,1,4,2,7,6,3,5]=>[1,2,2,1,2]
[1,8,7,4,6,2,5,3]=>[2,1,2,2,1]
[1,8,5,7,2,6,4,3]=>[2,2,2,1,1]
[1,5,7,3,6,8,2,4]=>[3,3,2]
[8,4,6,2,5,7,1,3]=>[1,2,3,2]
[1,3,4,7,6,8,2,5]=>[4,2,2]
[8,1,3,6,7,4,2,5]=>[1,4,1,2]
[1,2,4,7,8,5,3,6]=>[5,1,2]
[3,1,4,7,6,8,2,5]=>[1,3,2,2]
[4,1,3,7,6,8,2,5]=>[1,3,2,2]
[5,1,7,3,6,8,2,4]=>[1,2,3,2]
[6,7,8,2,4,5,1,3]=>[3,3,2]
[5,8,6,2,4,7,1,3]=>[2,1,3,2]
[3,8,2,6,5,7,1,4]=>[2,2,2,2]
[2,8,3,6,7,4,1,5]=>[2,3,1,2]
[8,7,2,5,6,3,1,4]=>[1,1,3,1,2]
[8,7,1,6,4,3,2,5]=>[1,1,2,1,1,2]
[1,8,2,7,5,4,3,6]=>[2,2,1,1,2]
[3,8,1,7,5,4,2,6]=>[2,2,1,1,2]
[5,8,6,1,7,3,2,4]=>[2,1,2,1,2]
[6,7,1,2,8,4,3,5]=>[2,3,1,2]
[2,1,3,8,6,5,4,7]=>[1,3,1,1,2]
[8,2,1,7,5,4,3,6]=>[1,1,2,1,1,2]
[1,3,2,8,6,5,4,7]=>[2,2,1,1,2]
[3,4,1,7,6,8,2,5]=>[2,2,2,2]
[2,5,7,1,8,4,3,6]=>[3,2,1,2]
[3,5,7,1,6,8,2,4]=>[3,3,2]
[4,5,7,6,1,8,2,3]=>[3,1,2,2]
[5,4,7,6,8,3,1,2]=>[1,2,2,1,2]
[1,5,7,8,6,3,2,4]=>[4,1,1,2]
[8,4,6,7,5,2,1,3]=>[1,3,1,1,2]
[8,3,7,5,6,2,1,4]=>[1,2,2,1,2]
[1,4,8,6,7,3,2,5]=>[3,2,1,2]
[2,4,8,6,7,3,1,5]=>[3,2,1,2]
[5,2,7,8,6,3,1,4]=>[1,3,1,1,2]
[2,3,8,7,5,4,1,6]=>[3,1,1,1,2]
[1,3,8,7,5,4,2,6]=>[3,1,1,1,2]
[8,2,7,6,4,3,1,5]=>[1,2,1,1,1,2]
[8,1,7,6,4,3,2,5]=>[1,2,1,1,1,2]
[4,1,8,6,7,3,2,5]=>[1,2,2,1,2]
[4,8,7,5,6,2,1,3]=>[2,1,2,1,2]
[5,6,8,1,7,4,3,2]=>[3,2,1,1,1]
[4,1,8,7,3,6,5,2]=>[1,2,1,2,1,1]
[5,6,8,4,1,7,3,2]=>[3,1,2,1,1]
[4,5,8,7,3,1,6,2]=>[3,1,1,2,1]
[3,1,8,4,7,6,5,2]=>[1,2,2,1,1,1]
[1,5,8,4,3,7,6,2]=>[3,1,2,1,1]
[8,1,7,2,5,6,4,3]=>[1,2,3,1,1]
[8,1,3,5,2,7,6,4]=>[1,3,2,1,1]
[2,7,1,5,4,8,6,3]=>[2,2,2,1,1]
[8,6,2,4,3,7,5,1]=>[1,1,2,2,1,1]
[2,4,1,6,7,5,8,3]=>[2,3,2,1]
[8,1,4,5,6,3,7,2]=>[1,4,2,1]
[8,1,4,5,6,2,7,3]=>[1,4,2,1]
[8,1,4,7,6,2,5,3]=>[1,3,1,2,1]
[2,5,1,7,8,6,4,3]=>[2,3,1,1,1]
[3,5,6,2,8,7,4,1]=>[3,2,1,1,1]
[2,4,5,1,7,6,3,8]=>[3,2,1,2]
[7,3,1,5,6,4,2,8]=>[1,1,3,1,2]
[8,3,2,5,6,7,1,4]=>[1,1,4,2]
[8,4,5,3,7,6,2,1]=>[1,2,2,1,1,1]
[3,4,5,6,2,8,1,7]=>[4,2,2]
[3,7,4,2,8,5,1,6]=>[2,1,2,1,2]
[7,3,4,1,6,8,2,5]=>[1,2,3,2]
[2,6,3,1,4,7,5,8]=>[2,1,3,2]
[7,2,1,6,3,4,8,5]=>[1,1,2,3,1]
[7,3,4,1,6,5,8,2]=>[1,2,2,2,1]
[3,7,4,2,5,8,6,1]=>[2,1,3,1,1]
[2,3,5,1,4,8,7,6]=>[3,3,1,1]
[2,7,1,3,6,8,5,4]=>[2,4,1,1]
[2,7,1,3,8,4,6,5]=>[2,3,2,1]
[3,8,7,1,6,2,5,4]=>[2,1,2,2,1]
[3,8,7,1,4,5,2,6]=>[2,1,3,2]
[3,7,4,2,1,8,6,5]=>[2,1,1,2,1,1]
[4,8,5,7,2,6,3,1]=>[2,2,2,1,1]
[8,4,5,7,3,2,6,1]=>[1,3,1,2,1]
[8,3,7,2,4,1,5,6]=>[1,2,2,3]
[8,6,7,2,1,4,3,5]=>[1,2,1,2,2]
[8,3,7,5,1,2,6,4]=>[1,2,1,3,1]
[7,3,4,6,2,1,5,8]=>[1,3,1,3]
[3,7,4,6,1,5,2,8]=>[2,2,2,2]
[3,4,7,6,1,2,8,5]=>[3,1,3,1]
[4,5,8,7,6,1,3,2]=>[3,1,1,2,1]
[8,3,6,7,2,5,1,4]=>[1,3,2,2]
[8,5,7,2,6,4,1,3]=>[1,2,2,1,2]
[8,6,3,7,5,1,4,2]=>[1,1,2,1,2,1]
[7,3,8,2,5,6,1,4]=>[1,2,3,2]
[8,7,3,5,6,1,4,2]=>[1,1,3,2,1]
[7,6,3,8,1,4,5,2]=>[1,1,2,3,1]
[8,5,2,7,6,1,3,4]=>[1,1,2,1,3]
[8,7,3,1,4,5,2,6]=>[1,1,1,3,2]
[6,4,7,2,1,5,8,3]=>[1,2,1,3,1]
[8,4,2,5,1,6,7,3]=>[1,1,2,3,1]
[8,5,3,1,6,4,7,2]=>[1,1,1,2,2,1]
[8,7,3,1,4,5,6,2]=>[1,1,1,4,1]
[8,7,4,1,5,6,2,3]=>[1,1,1,3,2]
[8,6,4,1,7,5,2,3]=>[1,1,1,2,1,2]
[8,6,3,1,7,4,5,2]=>[1,1,1,2,2,1]
[8,5,3,1,6,7,4,2]=>[1,1,1,3,1,1]
[8,5,3,7,1,6,4,2]=>[1,1,2,2,1,1]
[7,6,3,8,1,4,2,5]=>[1,1,2,2,2]
[7,4,8,2,6,1,5,3]=>[1,2,2,2,1]
[6,4,7,3,1,5,2,8]=>[1,2,1,2,2]
[7,4,5,3,1,2,8,6]=>[1,2,1,3,1]
[8,5,3,6,1,2,7,4]=>[1,1,2,3,1]
[5,6,3,2,1,7,4,8]=>[2,1,1,2,2]
[8,5,3,1,6,4,2,7]=>[1,1,1,2,1,2]
[8,7,4,1,5,2,3,6]=>[1,1,1,2,3]
[8,7,5,1,2,6,3,4]=>[1,1,1,3,2]
[8,6,4,1,2,7,5,3]=>[1,1,1,3,1,1]
[8,7,4,1,2,5,3,6]=>[1,1,1,3,2]
[8,7,5,1,2,3,6,4]=>[1,1,1,4,1]
[6,5,3,7,4,2,1,8]=>[1,1,2,1,1,2]
[1,6,3,8,4,2,5,7]=>[2,2,1,3]
[4,7,2,5,3,6,1,8]=>[2,2,2,2]
[1,8,3,4,5,2,6,7]=>[2,3,3]
[1,8,6,4,2,5,3,7]=>[2,1,1,2,2]
[8,2,6,4,1,5,7,3]=>[1,2,1,3,1]
[7,8,3,4,6,1,5,2]=>[2,3,2,1]
[4,8,7,5,3,1,6,2]=>[2,1,1,1,2,1]
[6,1,4,8,3,2,5,7]=>[1,3,1,3]
[4,1,8,5,3,2,6,7]=>[1,2,1,1,3]
[8,1,6,4,2,7,3,5]=>[1,2,1,2,2]
[3,1,7,4,2,5,8,6]=>[1,2,1,3,1]
[1,2,7,4,3,5,6,8]=>[3,1,4]
[6,1,8,5,2,4,3,7]=>[1,2,1,2,2]
[6,8,2,5,1,4,7,3]=>[2,2,3,1]
[4,5,2,1,6,8,7,3]=>[2,1,3,1,1]
[7,2,8,6,5,1,4,3]=>[1,2,1,1,2,1]
[7,4,8,6,1,5,3,2]=>[1,2,1,2,1,1]
[8,7,2,6,1,4,5,3]=>[1,1,2,3,1]
[1,7,8,6,2,4,3,5]=>[3,1,2,2]
[7,6,3,1,2,5,4,8]=>[1,1,1,3,2]
[8,5,3,1,2,4,7,6]=>[1,1,1,4,1]
[8,2,1,6,5,3,4,7]=>[1,1,2,1,3]
[3,8,1,5,6,2,4,7]=>[2,3,3]
[6,8,4,1,5,2,3,7]=>[2,1,2,3]
[3,2,8,1,6,4,5,7]=>[1,2,2,3]
[5,2,1,3,7,6,4,8]=>[1,1,3,1,2]
[5,4,1,2,8,3,7,6]=>[1,1,3,2,1]
[5,8,4,1,2,3,7,6]=>[2,1,4,1]
[7,1,2,5,3,4,6,8]=>[1,3,4]
[1,6,7,3,2,8,4,5]=>[3,1,2,2]
[1,8,6,3,2,7,4,5]=>[2,1,1,2,2]
[1,5,3,7,2,8,4,6]=>[2,2,2,2]
[1,5,7,3,8,2,4,6]=>[3,2,3]
[1,4,6,2,8,5,3,7]=>[3,2,1,2]
[1,8,5,2,6,4,3,7]=>[2,1,2,1,2]
[1,8,6,2,7,4,5,3]=>[2,1,2,2,1]
[1,5,6,2,8,4,3,7]=>[3,2,1,2]
[2,4,6,3,1,7,5,8]=>[3,1,2,2]
[2,3,6,1,8,7,4,5]=>[3,2,1,2]
[3,4,8,6,5,7,2,1]=>[3,1,2,1,1]
[1,2,5,7,4,3,6,8]=>[4,1,3]
[1,2,5,7,4,6,8,3]=>[4,3,1]
[3,5,8,6,1,7,2,4]=>[3,1,2,2]
[2,3,6,8,1,7,4,5]=>[4,2,2]
[2,3,7,1,8,6,4,5]=>[3,2,1,2]
[1,4,3,6,7,8,2,5]=>[2,4,2]
[2,6,1,7,8,5,3,4]=>[2,3,1,2]
[2,4,8,5,6,7,1,3]=>[3,3,2]
[1,4,8,5,6,7,3,2]=>[3,3,1,1]
[3,5,8,6,2,7,4,1]=>[3,1,2,1,1]
[7,8,2,5,1,6,4,3]=>[2,2,2,1,1]
[7,8,1,4,6,3,5,2]=>[2,3,2,1]
[1,2,4,7,3,6,8,5]=>[4,3,1]
[1,2,5,7,4,6,3,8]=>[4,2,2]
[3,2,1,6,8,4,7,5]=>[1,1,3,2,1]
[4,8,3,1,6,5,7,2]=>[2,1,2,2,1]
[6,2,5,8,3,1,7,4]=>[1,3,1,2,1]
[1,6,8,5,4,2,7,3]=>[3,1,1,2,1]
[6,5,8,4,2,1,7,3]=>[1,2,1,1,2,1]
[1,7,8,6,5,4,2,3]=>[3,1,1,1,2]
[6,8,7,4,5,1,3,2]=>[2,1,2,2,1]
[6,1,3,5,4,2,8,7]=>[1,3,1,2,1]
[3,6,4,2,5,1,8,7]=>[2,1,2,2,1]
[2,8,5,7,6,1,4,3]=>[2,2,1,2,1]
[2,1,5,8,6,4,7,3]=>[1,3,1,2,1]
[4,2,8,5,6,3,7,1]=>[1,2,2,2,1]
[5,3,7,2,6,8,4,1]=>[1,2,3,1,1]
[8,7,4,6,1,3,5,2]=>[1,1,2,3,1]
[5,7,2,3,4,6,8,1]=>[2,5,1]
[1,3,8,2,7,5,6,4]=>[3,2,2,1]
[1,8,7,3,2,5,6,4]=>[2,1,1,3,1]
[5,7,1,2,3,8,6,4]=>[2,4,1,1]
[4,7,6,2,1,8,5,3]=>[2,1,1,2,1,1]
[4,2,7,1,6,8,5,3]=>[1,2,3,1,1]
[4,2,1,7,6,8,5,3]=>[1,1,2,2,1,1]
[4,1,2,7,5,8,6,3]=>[1,3,2,1,1]
[6,3,4,7,8,1,5,2]=>[1,4,2,1]
[6,7,8,3,4,1,5,2]=>[3,2,2,1]
[1,7,8,4,2,5,6,3]=>[3,1,3,1]
[1,3,2,8,7,5,6,4]=>[2,2,1,2,1]
[3,1,2,8,5,7,6,4]=>[1,3,2,1,1]
[7,6,8,4,2,1,5,3]=>[1,2,1,1,2,1]
[7,1,8,5,2,3,6,4]=>[1,2,1,3,1]
[6,8,7,4,3,1,5,2]=>[2,1,1,1,2,1]
[7,8,6,2,4,1,5,3]=>[2,1,2,2,1]
[3,6,7,4,2,5,8,1]=>[3,1,3,1]
[7,2,8,4,6,1,5,3]=>[1,2,2,2,1]
[2,8,6,3,1,7,5,4]=>[2,1,1,2,1,1]
[3,6,4,7,2,5,8,1]=>[2,2,3,1]
[3,4,6,2,7,5,8,1]=>[3,2,2,1]
[2,4,7,1,8,6,5,3]=>[3,2,1,1,1]
[7,4,2,6,8,1,5,3]=>[1,1,3,2,1]
[7,4,6,2,8,1,5,3]=>[1,2,2,2,1]
[7,1,5,8,2,3,6,4]=>[1,3,3,1]
[7,6,4,8,2,1,5,3]=>[1,1,2,1,2,1]
[1,7,4,8,2,5,6,3]=>[2,2,3,1]
[7,5,6,1,2,4,3,8]=>[1,2,3,2]
[6,1,8,4,2,3,5,7]=>[1,2,1,4]
[7,1,6,3,8,5,4,2]=>[1,2,2,1,1,1]
[7,3,6,2,1,8,5,4]=>[1,2,1,2,1,1]
[7,4,6,2,1,8,5,3]=>[1,2,1,2,1,1]
[7,2,4,3,1,6,8,5]=>[1,2,1,3,1]
[7,2,3,1,6,4,8,5]=>[1,2,2,2,1]
[6,1,8,2,5,4,3,7]=>[1,2,2,1,2]
[1,5,8,7,3,4,6,2]=>[3,1,3,1]
[6,5,2,3,8,1,4,7]=>[1,1,3,3]
[2,1,8,6,3,4,5,7]=>[1,2,1,4]
[1,8,6,4,2,5,7,3]=>[2,1,1,3,1]
[5,6,2,1,8,4,7,3]=>[2,1,2,2,1]
[2,4,1,8,7,5,3,6]=>[2,2,1,1,2]
[2,8,1,6,5,7,3,4]=>[2,2,2,2]
[2,4,8,1,7,5,6,3]=>[3,2,2,1]
[5,2,1,4,8,3,7,6]=>[1,1,3,2,1]
[5,1,6,4,3,8,7,2]=>[1,2,1,2,1,1]
[6,5,4,7,3,1,8,2]=>[1,1,2,1,2,1]
[6,2,3,1,4,8,5,7]=>[1,2,3,2]
[5,2,1,8,4,7,6,3]=>[1,1,2,2,1,1]
[5,4,6,8,1,3,7,2]=>[1,3,3,1]
[6,7,5,1,3,4,8,2]=>[2,1,4,1]
[6,7,5,3,2,1,8,4]=>[2,1,1,1,2,1]
[3,7,1,6,4,5,8,2]=>[2,2,3,1]
[3,1,6,7,2,5,4,8]=>[1,3,2,2]
[3,5,2,1,4,6,7,8]=>[2,1,5]
[4,8,2,5,3,1,7,6]=>[2,2,1,2,1]
[2,1,3,7,6,4,5,8]=>[1,3,1,3]
[2,8,1,6,7,5,4,3]=>[2,3,1,1,1]
[1,3,8,7,5,4,6,2]=>[3,1,1,2,1]
[4,7,2,6,1,5,8,3]=>[2,2,3,1]
[4,7,8,6,3,1,5,2]=>[3,1,1,2,1]
[2,8,7,3,1,6,4,5]=>[2,1,1,2,2]
[5,3,8,4,6,7,1,2]=>[1,2,3,2]
[3,1,8,4,5,2,6,7]=>[1,2,2,3]
[2,3,8,6,4,7,1,5]=>[3,1,2,2]
[6,3,7,8,4,5,1,2]=>[1,3,2,2]
[6,7,3,4,8,5,1,2]=>[2,3,1,2]
[7,4,1,8,2,5,6,3]=>[1,1,2,3,1]
[3,1,7,2,5,6,8,4]=>[1,2,4,1]
[7,8,3,1,6,2,4,5]=>[2,1,2,3]
[2,3,7,4,5,1,8,6]=>[3,2,2,1]
[2,3,7,1,5,6,8,4]=>[3,4,1]
[7,3,4,8,1,5,6,2]=>[1,3,3,1]
[5,7,2,6,8,1,4,3]=>[2,3,2,1]
[4,1,5,7,3,2,8,6]=>[1,3,1,2,1]
[5,8,6,2,7,3,1,4]=>[2,1,2,1,2]
[6,5,1,7,8,3,4,2]=>[1,1,3,2,1]
[6,4,1,7,2,8,5,3]=>[1,1,2,2,1,1]
[5,4,1,7,3,8,6,2]=>[1,1,2,2,1,1]
[7,3,1,6,2,8,5,4]=>[1,1,2,2,1,1]
[6,4,1,8,2,7,3,5]=>[1,1,2,2,2]
[4,8,2,5,3,1,6,7]=>[2,2,1,3]
[5,4,1,8,3,6,7,2]=>[1,1,2,3,1]
[5,1,3,4,8,2,6,7]=>[1,4,3]
[4,6,2,8,1,7,3,5]=>[2,2,2,2]
[7,2,3,6,1,8,5,4]=>[1,3,2,1,1]
[7,8,2,3,5,1,6,4]=>[2,3,2,1]
[7,8,4,5,1,2,6,3]=>[2,2,3,1]
[6,1,4,5,7,8,2,3]=>[1,5,2]
[6,3,4,7,1,8,5,2]=>[1,3,2,1,1]
[5,1,3,4,7,2,8,6]=>[1,4,2,1]
[7,8,5,1,3,4,6,2]=>[2,1,4,1]
[7,1,3,4,5,6,8,2]=>[1,6,1]
[1,2,4,6,8,7,3,5]=>[5,1,2]
[8,5,2,7,6,3,1,4]=>[1,1,2,1,1,2]
[1,8,3,5,6,2,7,4]=>[2,3,2,1]
[8,3,2,5,6,1,7,4]=>[1,1,3,2,1]
[4,2,5,1,6,8,7,3]=>[1,2,3,1,1]
[8,2,3,5,6,1,7,4]=>[1,4,2,1]
[7,1,2,6,8,3,5,4]=>[1,4,2,1]
[7,2,5,6,1,8,4,3]=>[1,3,2,1,1]
[5,4,2,7,8,6,1,3]=>[1,1,3,1,2]
[7,6,2,3,8,1,5,4]=>[1,1,3,2,1]
[4,7,6,8,1,2,5,3]=>[2,2,3,1]
[6,8,7,2,1,3,4,5]=>[2,1,1,4]
[7,8,6,1,3,4,2,5]=>[2,1,3,2]
[7,1,6,2,3,4,8,5]=>[1,2,4,1]
[7,6,2,1,3,4,8,5]=>[1,1,1,4,1]
[3,7,6,8,5,2,4,1]=>[2,2,1,2,1]
[3,8,5,4,7,6,2,1]=>[2,1,2,1,1,1]
[7,8,6,5,1,3,2,4]=>[2,1,1,2,2]
[1,7,8,5,2,6,3,4]=>[3,1,2,2]
[8,7,1,6,3,2,5,4]=>[1,1,2,1,2,1]
[7,1,8,6,3,2,5,4]=>[1,2,1,1,2,1]
[7,6,1,2,5,3,8,4]=>[1,1,3,2,1]
[7,6,2,5,8,1,4,3]=>[1,1,3,2,1]
[5,8,7,2,6,3,4,1]=>[2,1,2,2,1]
[1,7,6,8,4,2,5,3]=>[2,2,1,2,1]
[7,6,2,4,8,1,5,3]=>[1,1,3,2,1]
[1,5,7,3,8,6,2,4]=>[3,2,1,2]
[5,7,8,2,6,1,3,4]=>[3,2,3]
[3,7,5,6,2,8,4,1]=>[2,2,2,1,1]
[6,7,5,1,8,2,3,4]=>[2,1,2,3]
[6,1,7,3,2,4,8,5]=>[1,2,1,3,1]
[7,6,1,2,4,3,8,5]=>[1,1,3,2,1]
[6,7,3,1,8,2,5,4]=>[2,1,2,2,1]
[6,7,2,1,5,3,8,4]=>[2,1,2,2,1]
[6,7,2,3,1,4,8,5]=>[2,2,3,1]
[4,3,2,8,7,1,6,5]=>[1,1,2,1,2,1]
[4,8,3,2,7,1,6,5]=>[2,1,2,2,1]
[4,8,3,1,7,6,5,2]=>[2,1,2,1,1,1]
[5,3,8,7,1,6,4,2]=>[1,2,1,2,1,1]
[5,8,7,3,1,6,4,2]=>[2,1,1,2,1,1]
[5,3,8,2,1,7,6,4]=>[1,2,1,2,1,1]
[3,8,7,2,6,5,1,4]=>[2,1,2,1,2]
[7,4,1,8,6,5,3,2]=>[1,1,2,1,1,1,1]
[5,4,2,8,1,7,6,3]=>[1,1,2,2,1,1]
[5,8,4,2,1,7,6,3]=>[2,1,1,2,1,1]
[5,8,4,7,1,6,3,2]=>[2,2,2,1,1]
[5,4,8,3,1,7,6,2]=>[1,2,1,2,1,1]
[8,6,1,5,4,3,7,2]=>[1,1,2,1,2,1]
[6,1,8,5,4,3,7,2]=>[1,2,1,1,2,1]
[5,6,1,8,3,4,7,2]=>[2,2,3,1]
[6,5,1,7,3,4,8,2]=>[1,1,2,3,1]
[6,8,1,5,2,4,7,3]=>[2,2,3,1]
[5,1,6,8,2,4,7,3]=>[1,3,3,1]
[6,1,5,8,4,7,2,3]=>[1,3,2,2]
[8,5,6,1,4,7,2,3]=>[1,2,3,2]
[5,8,7,2,3,4,6,1]=>[2,1,4,1]
[7,2,5,6,1,4,8,3]=>[1,3,3,1]
[5,2,6,8,1,4,7,3]=>[1,3,3,1]
[6,7,4,2,5,8,1,3]=>[2,1,3,2]
[6,7,4,1,2,5,8,3]=>[2,1,4,1]
[1,6,8,5,2,4,7,3]=>[3,1,3,1]
[1,6,7,4,2,5,8,3]=>[3,1,3,1]
[3,6,7,5,8,1,2,4]=>[3,2,3]
[1,6,7,5,8,3,2,4]=>[3,2,1,2]
[1,6,8,5,7,4,2,3]=>[3,2,1,2]
[3,8,6,5,7,4,1,2]=>[2,1,2,1,2]
[2,6,7,5,8,3,1,4]=>[3,2,1,2]
[2,6,7,4,1,5,8,3]=>[3,1,3,1]
[6,7,4,1,5,8,2,3]=>[2,1,3,2]
[6,8,1,5,7,4,2,3]=>[2,3,1,2]
[3,8,1,6,5,7,4,2]=>[2,2,2,1,1]
[3,7,4,1,6,5,8,2]=>[2,1,2,2,1]
[5,2,8,7,3,6,4,1]=>[1,2,1,2,1,1]
[8,1,6,5,7,4,3,2]=>[1,2,2,1,1,1]
[6,8,2,1,5,7,4,3]=>[2,1,3,1,1]
[5,2,1,6,8,4,7,3]=>[1,1,3,2,1]
[7,3,1,4,8,6,5,2]=>[1,1,3,1,1,1]
[6,5,2,4,8,7,3,1]=>[1,1,3,1,1,1]
[6,5,8,7,4,2,3,1]=>[1,2,1,1,2,1]
[3,1,8,6,5,7,4,2]=>[1,2,1,2,1,1]
[6,8,5,7,4,2,1,3]=>[2,2,1,1,2]
[3,6,7,5,8,2,1,4]=>[3,2,1,2]
[1,8,6,5,7,4,3,2]=>[2,1,2,1,1,1]
[2,7,8,5,6,3,1,4]=>[3,2,1,2]
[4,7,8,5,6,3,1,2]=>[3,2,1,2]
[4,7,8,5,3,6,1,2]=>[3,1,2,2]
[2,7,8,5,3,4,6,1]=>[3,1,3,1]
[2,7,8,5,3,1,4,6]=>[3,1,1,3]
[4,7,5,3,8,1,2,6]=>[2,1,2,3]
[2,7,5,8,3,1,4,6]=>[2,2,1,3]
[2,7,5,8,3,4,6,1]=>[2,2,3,1]
[2,7,5,6,3,4,8,1]=>[2,2,3,1]
[2,7,5,6,3,1,4,8]=>[2,2,1,3]
[4,7,5,6,3,1,2,8]=>[2,2,1,3]
[4,7,5,3,6,1,2,8]=>[2,1,2,3]
[6,7,5,3,1,4,2,8]=>[2,1,1,2,2]
[4,7,5,3,1,6,2,8]=>[2,1,1,2,2]
[2,7,5,3,1,6,4,8]=>[2,1,1,2,2]
[2,7,5,3,6,1,4,8]=>[2,1,2,3]
[2,7,5,3,6,4,8,1]=>[2,1,2,2,1]
[2,7,5,3,8,4,6,1]=>[2,1,2,2,1]
[4,7,5,3,1,8,2,6]=>[2,1,1,2,2]
[6,7,5,3,1,8,2,4]=>[2,1,1,2,2]
[2,7,5,3,8,1,6,4]=>[2,1,2,2,1]
[2,7,5,3,8,6,1,4]=>[2,1,2,1,2]
[2,7,5,8,3,1,6,4]=>[2,2,1,2,1]
[4,7,5,3,8,1,6,2]=>[2,1,2,2,1]
[6,7,5,3,8,1,4,2]=>[2,1,2,2,1]
[8,7,5,3,6,1,4,2]=>[1,1,1,2,2,1]
[4,7,5,3,8,6,1,2]=>[2,1,2,1,2]
[2,7,5,8,6,3,1,4]=>[2,2,1,1,2]
[2,7,5,8,6,3,4,1]=>[2,2,1,2,1]
[2,7,5,6,8,3,4,1]=>[2,3,2,1]
[2,7,5,6,8,3,1,4]=>[2,3,1,2]
[4,7,5,3,6,8,1,2]=>[2,1,3,2]
[6,7,5,3,4,1,8,2]=>[2,1,2,2,1]
[4,7,5,3,6,1,8,2]=>[2,1,2,2,1]
[2,7,5,6,3,1,8,4]=>[2,2,1,2,1]
[2,7,5,6,3,8,4,1]=>[2,2,2,1,1]
[2,7,5,3,6,8,4,1]=>[2,1,3,1,1]
[2,7,5,3,6,8,1,4]=>[2,1,3,2]
[2,7,5,3,6,1,8,4]=>[2,1,2,2,1]
[2,7,5,3,1,6,8,4]=>[2,1,1,3,1]
[4,7,5,3,1,6,8,2]=>[2,1,1,3,1]
[6,7,5,3,1,4,8,2]=>[2,1,1,3,1]
[8,7,5,3,1,4,6,2]=>[1,1,1,1,3,1]
[2,7,5,3,1,4,8,6]=>[2,1,1,3,1]
[2,7,5,3,4,1,8,6]=>[2,1,2,2,1]
[2,7,5,3,4,8,1,6]=>[2,1,3,2]
[2,7,5,3,4,8,6,1]=>[2,1,3,1,1]
[2,7,5,3,4,6,8,1]=>[2,1,4,1]
[2,7,5,3,4,6,1,8]=>[2,1,3,2]
[2,7,5,3,4,1,6,8]=>[2,1,2,3]
[2,7,5,3,1,4,6,8]=>[2,1,1,4]
[4,7,5,3,1,2,6,8]=>[2,1,1,4]
[5,7,6,2,8,3,1,4]=>[2,1,2,1,2]
[5,1,6,3,2,4,8,7]=>[1,2,1,3,1]
[5,7,6,1,8,3,2,4]=>[2,1,2,1,2]
[3,8,7,1,2,5,4,6]=>[2,1,3,2]
[3,8,7,2,1,5,4,6]=>[2,1,1,2,2]
[3,7,5,2,1,4,8,6]=>[2,1,1,3,1]
[4,6,5,7,8,3,1,2]=>[2,3,1,2]
[5,7,6,3,8,2,1,4]=>[2,1,2,1,2]
[5,7,6,1,8,4,2,3]=>[2,1,2,1,2]
[5,8,6,1,7,4,2,3]=>[2,1,2,1,2]
[6,1,7,2,8,4,3,5]=>[1,2,2,1,2]
[4,8,5,6,7,3,1,2]=>[2,3,1,2]
[6,1,7,2,8,5,3,4]=>[1,2,2,1,2]
[3,7,6,2,8,5,1,4]=>[2,1,2,1,2]
[3,7,6,1,8,4,2,5]=>[2,1,2,1,2]
[2,6,7,1,8,4,3,5]=>[3,2,1,2]
[6,1,7,3,8,5,2,4]=>[1,2,2,1,2]
[7,1,8,3,2,5,4,6]=>[1,2,1,2,2]
[5,1,7,3,2,4,8,6]=>[1,2,1,3,1]
[2,7,8,3,1,5,4,6]=>[3,1,2,2]
[2,5,6,8,7,3,1,4]=>[4,1,1,2]
[4,8,5,6,7,2,1,3]=>[2,3,1,2]
[5,8,7,2,3,4,1,6]=>[2,1,3,2]
[5,8,6,2,7,4,1,3]=>[2,1,2,1,2]
[2,4,6,7,8,5,1,3]=>[5,1,2]
[2,4,6,7,8,3,1,5]=>[5,1,2]
[4,7,6,2,8,3,1,5]=>[2,1,2,1,2]
[4,7,6,2,8,5,1,3]=>[2,1,2,1,2]
[5,8,6,3,7,4,1,2]=>[2,1,2,1,2]
[5,8,7,3,2,4,1,6]=>[2,1,1,2,2]
[4,6,5,8,7,3,1,2]=>[2,2,1,1,2]
[5,8,6,3,7,2,1,4]=>[2,1,2,1,2]
[8,3,1,7,2,6,4,5]=>[1,1,2,2,2]
[4,5,1,2,8,7,3,6]=>[2,3,1,2]
[5,6,1,2,8,3,7,4]=>[2,3,2,1]
[5,8,7,1,6,2,4,3]=>[2,1,2,2,1]
[4,8,5,1,7,6,2,3]=>[2,1,2,1,2]
[8,4,5,1,7,6,2,3]=>[1,2,2,1,2]
[7,3,1,4,8,2,6,5]=>[1,1,3,2,1]
[6,3,1,4,8,2,7,5]=>[1,1,3,2,1]
[8,5,6,1,7,2,4,3]=>[1,2,2,2,1]
[7,5,6,1,3,8,4,2]=>[1,2,3,1,1]
[7,3,1,5,4,8,6,2]=>[1,1,2,2,1,1]
[7,4,6,1,3,8,5,2]=>[1,2,3,1,1]
[6,8,5,1,3,7,4,2]=>[2,1,3,1,1]
[5,7,6,1,3,8,4,2]=>[2,1,3,1,1]
[6,7,1,4,2,8,5,3]=>[2,2,2,1,1]
[5,7,1,4,2,8,6,3]=>[2,2,2,1,1]
[3,4,1,8,6,5,7,2]=>[2,2,1,2,1]
[8,3,1,7,4,5,6,2]=>[1,1,2,3,1]
[5,7,1,2,4,8,6,3]=>[2,4,1,1]
[2,1,6,4,8,3,7,5]=>[1,2,2,2,1]
[7,6,4,1,3,8,5,2]=>[1,1,1,3,1,1]
[1,5,7,8,4,2,3,6]=>[4,1,3]
[1,3,6,4,2,5,7,8]=>[3,1,4]
[1,4,5,7,8,3,6,2]=>[5,2,1]
[1,5,7,8,3,6,2,4]=>[4,2,2]
[1,5,7,8,2,4,3,6]=>[4,2,2]
[6,8,1,7,2,4,5,3]=>[2,2,3,1]
[6,8,4,7,3,2,1,5]=>[2,2,1,1,2]
[3,8,4,2,7,5,1,6]=>[2,1,2,1,2]
[6,8,3,2,1,5,4,7]=>[2,1,1,2,2]
[6,5,8,2,1,3,4,7]=>[1,2,1,4]
[2,8,5,3,6,1,4,7]=>[2,1,2,3]
[2,8,1,4,6,7,5,3]=>[2,4,1,1]
[2,8,4,1,7,6,5,3]=>[2,1,2,1,1,1]
[6,8,5,4,2,7,1,3]=>[2,1,1,2,2]
[1,8,4,6,3,2,7,5]=>[2,2,1,2,1]
[6,4,8,5,3,2,1,7]=>[1,2,1,1,1,2]
[5,4,1,7,3,2,6,8]=>[1,1,2,1,3]
[3,5,6,1,4,2,7,8]=>[3,2,3]
[1,6,3,8,4,2,7,5]=>[2,2,1,2,1]
[5,3,6,8,4,2,7,1]=>[1,3,1,2,1]
[6,5,8,1,2,3,7,4]=>[1,2,4,1]
[5,3,1,4,7,6,8,2]=>[1,1,3,2,1]
[7,1,3,2,4,6,8,5]=>[1,2,4,1]
[6,4,3,2,7,5,8,1]=>[1,1,1,2,2,1]
[7,4,5,6,1,3,8,2]=>[1,3,3,1]
[7,5,4,2,1,3,8,6]=>[1,1,1,1,3,1]
[1,6,7,8,3,5,2,4]=>[4,2,2]
[2,1,4,8,7,3,5,6]=>[1,3,1,3]
[2,6,5,7,8,3,1,4]=>[2,3,1,2]
[3,7,6,8,2,5,4,1]=>[2,2,2,1,1]
[5,4,6,8,7,1,3,2]=>[1,3,1,2,1]
[4,1,8,2,6,7,5,3]=>[1,2,3,1,1]
[3,6,7,8,2,1,4,5]=>[4,1,3]
[2,5,7,1,6,3,4,8]=>[3,2,3]
[4,2,8,3,6,5,1,7]=>[1,2,2,1,2]
[6,3,8,7,2,4,5,1]=>[1,2,1,3,1]
[7,6,1,8,2,4,5,3]=>[1,1,2,3,1]
[2,5,6,3,4,8,1,7]=>[3,3,2]
[5,2,1,4,7,8,6,3]=>[1,1,4,1,1]
[5,2,4,7,8,6,1,3]=>[1,4,1,2]
[3,5,1,2,8,6,4,7]=>[2,3,1,2]
[7,2,1,3,4,8,5,6]=>[1,1,4,2]
[2,4,5,7,1,8,6,3]=>[4,2,1,1]
[2,6,4,7,3,1,5,8]=>[2,2,1,3]
[6,2,4,7,3,8,5,1]=>[1,3,2,1,1]
[7,6,3,1,2,5,8,4]=>[1,1,1,4,1]
[1,5,7,4,3,2,8,6]=>[3,1,1,2,1]
[8,1,6,2,3,4,7,5]=>[1,2,4,1]
[6,1,4,2,5,7,8,3]=>[1,2,4,1]
[3,4,8,6,7,2,5,1]=>[3,2,2,1]
[1,6,7,2,4,3,5,8]=>[3,2,3]
[1,8,7,3,2,6,5,4]=>[2,1,1,2,1,1]
[1,8,3,4,5,2,7,6]=>[2,3,2,1]
[1,8,3,6,4,7,2,5]=>[2,2,2,2]
[1,8,5,3,6,7,2,4]=>[2,1,3,2]
[1,4,7,2,5,6,3,8]=>[3,3,2]
[5,4,1,7,3,6,2,8]=>[1,1,2,2,2]
[7,3,5,8,2,6,1,4]=>[1,3,2,2]
[3,5,8,6,4,7,1,2]=>[3,1,2,2]
[3,4,8,6,7,2,1,5]=>[3,2,1,2]
[3,4,8,2,5,1,7,6]=>[3,2,2,1]
[1,4,6,2,5,8,7,3]=>[3,3,1,1]
[1,4,7,6,3,2,8,5]=>[3,1,1,2,1]
[1,5,6,4,2,3,8,7]=>[3,1,3,1]
[6,3,4,1,8,2,7,5]=>[1,2,2,2,1]
[4,1,6,8,2,5,7,3]=>[1,3,3,1]
[1,6,2,5,8,3,7,4]=>[2,3,2,1]
[1,7,2,5,8,4,3,6]=>[2,3,1,2]
[1,4,6,7,8,3,5,2]=>[5,2,1]
[4,1,5,3,6,8,7,2]=>[1,2,3,1,1]
[3,7,5,1,6,8,4,2]=>[2,1,3,1,1]
[6,1,4,7,8,2,5,3]=>[1,4,2,1]
[5,8,7,4,6,2,3,1]=>[2,1,2,2,1]
[6,8,7,1,5,3,4,2]=>[2,1,2,2,1]
[2,7,8,4,6,5,1,3]=>[3,2,1,2]
[3,7,8,5,4,6,2,1]=>[3,1,2,1,1]
[4,8,7,5,2,6,3,1]=>[2,1,1,2,1,1]
[2,8,7,4,6,1,5,3]=>[2,1,2,2,1]
[4,8,7,2,5,6,3,1]=>[2,1,3,1,1]
[4,7,8,5,3,6,2,1]=>[3,1,2,1,1]
[6,4,8,1,5,7,3,2]=>[1,2,3,1,1]
[1,6,8,3,5,2,7,4]=>[3,2,2,1]
[4,5,8,6,3,7,2,1]=>[3,1,2,1,1]
[2,6,7,8,4,5,1,3]=>[4,2,2]
[6,1,2,8,4,7,5,3]=>[1,3,2,1,1]
[4,7,1,8,5,6,3,2]=>[2,2,2,1,1]
[5,7,1,8,2,6,4,3]=>[2,2,2,1,1]
[7,2,1,8,6,4,5,3]=>[1,1,2,1,2,1]
[5,3,8,4,7,6,2,1]=>[1,2,2,1,1,1]
[2,5,8,1,7,4,6,3]=>[3,2,2,1]
[4,5,8,3,7,6,2,1]=>[3,2,1,1,1]
[1,7,2,8,6,4,5,3]=>[2,2,1,2,1]
[3,5,7,8,1,6,2,4]=>[4,2,2]
[2,4,7,8,5,6,1,3]=>[4,2,2]
[4,1,7,8,5,6,3,2]=>[1,3,2,1,1]
[3,5,8,6,4,7,2,1]=>[3,1,2,1,1]
[2,4,8,5,7,6,1,3]=>[3,2,1,2]
[2,6,3,8,5,1,7,4]=>[2,2,1,2,1]
[4,1,5,8,6,7,3,2]=>[1,3,2,1,1]
[1,4,3,7,2,8,5,6]=>[2,2,2,2]
[4,5,8,2,6,3,1,7]=>[3,2,1,2]
[6,3,5,2,4,7,1,8]=>[1,2,3,2]
[5,2,6,3,4,8,1,7]=>[1,2,3,2]
[5,2,3,8,4,6,1,7]=>[1,3,2,2]
[4,2,3,5,8,6,1,7]=>[1,4,1,2]
[3,8,2,4,6,1,5,7]=>[2,3,3]
[2,3,8,4,6,1,5,7]=>[3,2,3]
[4,3,7,5,2,1,8,6]=>[1,2,1,1,2,1]
[5,3,4,7,6,1,2,8]=>[1,3,1,3]
[6,5,1,3,2,8,4,7]=>[1,1,2,2,2]
[5,1,4,3,2,7,6,8]=>[1,2,1,2,2]
[4,1,3,5,8,7,2,6]=>[1,4,1,2]
[3,1,2,7,4,8,6,5]=>[1,3,2,1,1]
[6,2,1,4,8,3,7,5]=>[1,1,3,2,1]
[3,4,7,2,1,8,5,6]=>[3,1,2,2]
[3,8,2,1,4,7,6,5]=>[2,1,3,1,1]
[3,2,4,7,1,8,5,6]=>[1,3,2,2]
[2,8,5,4,1,3,7,6]=>[2,1,1,3,1]
[4,2,3,5,7,1,8,6]=>[1,4,2,1]
[4,2,8,7,1,3,5,6]=>[1,2,1,4]
[4,8,6,5,3,1,2,7]=>[2,1,1,1,3]
[6,5,4,8,3,1,2,7]=>[1,1,2,1,3]
[5,4,6,3,1,7,2,8]=>[1,2,1,2,2]
[4,3,6,5,1,8,2,7]=>[1,2,1,2,2]
[1,5,6,8,7,3,2,4]=>[4,1,1,2]
[1,4,8,3,6,5,2,7]=>[3,2,1,2]
[4,8,1,3,6,5,2,7]=>[2,3,1,2]
[3,5,4,1,6,7,2,8]=>[2,1,3,2]
[3,4,1,8,6,5,2,7]=>[2,2,1,1,2]
[1,3,8,6,4,7,2,5]=>[3,1,2,2]
[1,2,8,6,4,3,7,5]=>[3,1,1,2,1]
[3,2,1,6,4,8,7,5]=>[1,1,2,2,1,1]
[6,5,1,8,7,3,2,4]=>[1,1,2,1,1,2]
[4,1,7,6,8,3,2,5]=>[1,2,2,1,2]
[3,1,7,6,4,8,2,5]=>[1,2,1,2,2]
[2,1,7,6,4,3,8,5]=>[1,2,1,1,2,1]
[6,3,5,1,2,8,7,4]=>[1,2,3,1,1]
[8,1,4,5,7,3,2,6]=>[1,4,1,2]
[1,8,4,7,6,2,3,5]=>[2,2,1,3]
[5,8,4,7,6,1,3,2]=>[2,2,1,2,1]
[8,3,2,6,1,7,4,5]=>[1,1,2,2,2]
[8,2,4,7,6,1,3,5]=>[1,3,1,3]
[1,6,3,7,4,5,2,8]=>[2,2,2,2]
[2,6,3,7,4,8,5,1]=>[2,2,2,1,1]
[4,6,1,7,8,2,5,3]=>[2,3,2,1]
[7,2,3,8,4,5,6,1]=>[1,3,3,1]
[5,2,6,7,8,3,4,1]=>[1,4,2,1]
[6,5,8,1,2,7,4,3]=>[1,2,3,1,1]
[6,5,1,8,7,2,4,3]=>[1,1,2,1,2,1]
[5,8,4,3,7,2,1,6]=>[2,1,2,1,2]
[6,1,2,8,7,3,4,5]=>[1,3,1,3]
[7,3,2,8,4,6,1,5]=>[1,1,2,2,2]
[4,5,1,7,6,2,8,3]=>[2,2,1,2,1]
[1,5,2,7,6,3,4,8]=>[2,2,1,3]
[7,2,6,8,3,5,4,1]=>[1,3,2,1,1]
[4,8,1,7,6,2,5,3]=>[2,2,1,2,1]
[7,2,8,6,5,3,4,1]=>[1,2,1,1,2,1]
[4,1,8,7,6,5,2,3]=>[1,2,1,1,1,2]
[7,6,5,2,8,4,3,1]=>[1,1,1,2,1,1,1]
[8,6,5,2,7,4,1,3]=>[1,1,1,2,1,2]
[7,8,5,2,6,4,1,3]=>[2,1,2,1,2]
[8,7,5,2,6,1,4,3]=>[1,1,1,2,2,1]
[6,5,1,8,7,4,3,2]=>[1,1,2,1,1,1,1]
[7,5,1,8,6,4,3,2]=>[1,1,2,1,1,1,1]
[8,5,1,7,6,4,3,2]=>[1,1,2,1,1,1,1]
[8,5,3,7,6,1,4,2]=>[1,1,2,1,2,1]
[7,6,8,2,5,4,1,3]=>[1,2,2,1,2]
[7,2,8,6,1,5,4,3]=>[1,2,1,2,1,1]
[7,8,6,2,5,1,4,3]=>[2,1,2,2,1]
[3,8,7,6,1,5,4,2]=>[2,1,1,2,1,1]
[1,6,7,8,4,5,2,3]=>[4,2,2]
[3,6,2,8,4,1,5,7]=>[2,2,1,3]
[8,3,7,5,4,1,6,2]=>[1,2,1,1,2,1]
[8,6,4,5,3,1,7,2]=>[1,1,2,1,2,1]
[3,8,6,5,4,1,7,2]=>[2,1,1,1,2,1]
[1,6,5,8,4,7,2,3]=>[2,2,2,2]
[2,4,5,7,3,1,6,8]=>[4,1,3]
[8,2,6,7,4,5,1,3]=>[1,3,2,2]
[1,2,7,8,4,6,5,3]=>[4,2,1,1]
[6,3,8,4,1,2,5,7]=>[1,2,1,4]
[1,6,3,5,4,8,2,7]=>[2,2,2,2]
[4,5,3,1,8,7,2,6]=>[2,1,2,1,2]
[3,1,5,8,6,4,2,7]=>[1,3,1,1,2]
[3,4,8,1,5,2,6,7]=>[3,2,3]
[4,6,8,1,5,2,3,7]=>[3,2,3]
[5,2,6,7,1,8,3,4]=>[1,3,2,2]
[3,6,8,5,2,7,1,4]=>[3,1,2,2]
[6,1,8,2,7,4,3,5]=>[1,2,2,1,2]
[2,5,6,3,1,7,4,8]=>[3,1,2,2]
[7,5,2,6,1,4,3,8]=>[1,1,2,2,2]
[5,7,6,2,8,1,3,4]=>[2,1,2,3]
[5,2,4,6,8,7,1,3]=>[1,4,1,2]
[8,1,6,5,7,2,3,4]=>[1,2,2,3]
[1,4,6,2,5,7,3,8]=>[3,3,2]
[8,6,5,7,1,3,2,4]=>[1,1,2,2,2]
[7,1,6,5,2,8,4,3]=>[1,2,1,2,1,1]
[1,5,8,6,2,7,4,3]=>[3,1,2,1,1]
[6,4,7,1,3,8,2,5]=>[1,2,3,2]
[8,2,3,6,7,4,1,5]=>[1,4,1,2]
[8,7,5,2,4,3,1,6]=>[1,1,1,2,1,2]
[3,1,8,5,7,2,6,4]=>[1,2,2,2,1]
[6,5,2,1,7,4,3,8]=>[1,1,1,2,1,2]
[6,7,4,2,3,8,1,5]=>[2,1,3,2]
[5,6,4,3,8,1,2,7]=>[2,1,2,3]
[6,8,5,3,4,2,1,7]=>[2,1,2,1,2]
[8,5,2,6,4,3,1,7]=>[1,1,2,1,1,2]
[8,6,4,5,2,1,7,3]=>[1,1,2,1,2,1]
[8,5,2,6,1,4,7,3]=>[1,1,2,3,1]
[8,5,6,4,2,7,1,3]=>[1,2,1,2,2]
[5,7,2,4,8,1,6,3]=>[2,3,2,1]
[2,7,5,8,1,4,6,3]=>[2,2,3,1]
[2,7,3,5,8,1,6,4]=>[2,3,2,1]
[5,2,7,3,8,1,6,4]=>[1,2,2,2,1]
[8,5,6,4,1,3,7,2]=>[1,2,1,3,1]
[8,5,1,6,7,3,2,4]=>[1,1,3,1,2]
[3,7,5,8,2,1,6,4]=>[2,2,1,2,1]
[3,2,6,7,1,8,5,4]=>[1,3,2,1,1]
[6,1,3,7,8,2,5,4]=>[1,4,2,1]
[5,4,7,8,1,2,6,3]=>[1,3,3,1]
[5,7,1,4,3,8,6,2]=>[2,2,2,1,1]
[3,1,6,7,8,2,5,4]=>[1,4,2,1]
[1,3,6,7,8,2,5,4]=>[5,2,1]
[3,4,6,7,8,2,1,5]=>[5,1,2]
[1,6,3,7,8,2,5,4]=>[2,3,2,1]
[3,2,6,7,8,4,1,5]=>[1,4,1,2]
[6,2,7,8,5,3,1,4]=>[1,3,1,1,2]
[6,2,7,4,8,5,1,3]=>[1,2,2,1,2]
[6,2,1,4,7,8,5,3]=>[1,1,4,1,1]
[5,7,2,8,1,4,6,3]=>[2,2,3,1]
[7,8,4,3,1,6,5,2]=>[2,1,1,2,1,1]
[2,6,1,7,8,3,5,4]=>[2,3,2,1]
[2,7,5,8,6,1,3,4]=>[2,2,1,3]
[6,7,1,3,8,5,4,2]=>[2,3,1,1,1]
[6,7,1,8,5,2,4,3]=>[2,2,1,2,1]
[2,6,4,7,8,1,3,5]=>[2,3,3]
[1,2,6,7,8,5,3,4]=>[5,1,2]
[1,6,7,4,8,3,2,5]=>[3,2,1,2]
[1,6,4,7,8,3,2,5]=>[2,3,1,2]
[1,4,6,7,8,3,2,5]=>[5,1,2]
[6,1,2,4,5,3,7,8]=>[1,4,3]
[7,5,1,2,4,6,3,8]=>[1,1,4,2]
[8,1,7,3,2,6,4,5]=>[1,2,1,2,2]
[8,7,2,1,5,4,6,3]=>[1,1,1,2,2,1]
[2,7,4,8,6,5,3,1]=>[2,2,1,1,1,1]
[7,6,5,2,4,1,8,3]=>[1,1,1,2,2,1]
[7,6,4,3,1,5,8,2]=>[1,1,1,1,3,1]
[6,1,8,7,2,3,5,4]=>[1,2,1,3,1]
[8,6,1,2,7,3,4,5]=>[1,1,3,3]
[3,6,8,2,7,1,5,4]=>[3,2,2,1]
[2,8,6,1,4,5,7,3]=>[2,1,4,1]
[6,8,7,2,5,4,1,3]=>[2,1,2,1,2]
[7,8,1,3,4,6,2,5]=>[2,4,2]
[3,2,6,4,8,7,5,1]=>[1,2,2,1,1,1]
[4,7,2,8,6,5,1,3]=>[2,2,1,1,2]
[4,7,1,8,6,5,3,2]=>[2,2,1,1,1,1]
[2,7,4,8,3,6,1,5]=>[2,2,2,2]
[4,7,3,8,6,1,5,2]=>[2,2,1,2,1]
[4,3,6,8,7,2,5,1]=>[1,3,1,2,1]
[4,3,8,2,5,7,6,1]=>[1,2,3,1,1]
[4,1,2,6,8,7,5,3]=>[1,4,1,1,1]
[3,1,6,4,8,7,2,5]=>[1,2,2,1,2]
[4,1,6,8,7,5,2,3]=>[1,3,1,1,2]
[3,8,1,4,5,7,2,6]=>[2,4,2]
[3,8,1,4,2,5,7,6]=>[2,2,3,1]
[4,1,8,3,5,2,7,6]=>[1,2,2,2,1]
[3,8,1,2,5,4,7,6]=>[2,3,2,1]
[4,2,3,6,8,7,1,5]=>[1,4,1,2]
[4,2,8,3,5,1,7,6]=>[1,2,2,2,1]
[4,2,8,3,5,7,6,1]=>[1,2,3,1,1]
[3,8,2,4,5,7,6,1]=>[2,4,1,1]
[3,8,2,5,1,4,7,6]=>[2,2,3,1]
[4,2,8,5,7,1,3,6]=>[1,2,2,3]
[3,8,1,5,2,4,7,6]=>[2,2,3,1]
[7,5,6,4,1,3,2,8]=>[1,2,1,2,2]
[7,8,6,4,1,3,2,5]=>[2,1,1,2,2]
[7,1,4,2,5,6,3,8]=>[1,2,3,2]
[7,3,2,1,4,6,5,8]=>[1,1,1,3,2]
[7,6,1,4,3,2,5,8]=>[1,1,2,1,3]
[7,4,1,3,5,6,2,8]=>[1,1,4,2]
[2,7,1,3,5,6,8,4]=>[2,5,1]
[3,6,2,1,5,8,7,4]=>[2,1,3,1,1]
[2,3,6,1,5,8,7,4]=>[3,3,1,1]
[3,4,7,1,5,6,8,2]=>[3,4,1]
[3,6,7,4,1,2,8,5]=>[3,1,3,1]
[4,3,2,7,1,6,8,5]=>[1,1,2,3,1]
[7,3,2,8,1,6,4,5]=>[1,1,2,2,2]
[7,4,8,1,5,6,3,2]=>[1,2,3,1,1]
[2,6,8,1,5,3,7,4]=>[3,2,2,1]
[6,8,2,1,5,3,7,4]=>[2,1,2,2,1]
[4,8,2,5,3,6,7,1]=>[2,2,3,1]
[4,5,8,2,3,6,7,1]=>[3,4,1]
[2,4,8,5,3,6,7,1]=>[3,1,3,1]
[5,3,2,6,4,8,7,1]=>[1,1,2,2,1,1]
[2,4,5,3,8,6,7,1]=>[3,2,2,1]
[4,3,5,2,8,6,7,1]=>[1,2,2,2,1]
[4,8,5,3,2,6,7,1]=>[2,1,1,3,1]
[3,5,4,2,8,6,7,1]=>[2,1,2,2,1]
[4,1,2,7,5,6,8,3]=>[1,3,3,1]
[5,6,7,4,2,8,3,1]=>[3,1,2,1,1]
[2,5,7,4,6,8,3,1]=>[3,3,1,1]
[7,5,2,4,3,8,6,1]=>[1,1,2,2,1,1]
[6,8,1,2,5,4,7,3]=>[2,3,2,1]
[6,4,1,8,5,2,7,3]=>[1,1,2,1,2,1]
[2,6,1,8,5,4,7,3]=>[2,2,1,2,1]
[7,1,2,8,5,6,4,3]=>[1,3,2,1,1]
[4,3,2,6,8,5,7,1]=>[1,1,3,2,1]
[3,7,6,4,8,5,2,1]=>[2,1,2,1,1,1]
[3,1,6,8,5,4,7,2]=>[1,3,1,2,1]
[2,3,5,8,4,6,7,1]=>[4,3,1]
[3,5,2,8,4,6,7,1]=>[2,2,3,1]
[3,4,5,8,2,6,7,1]=>[4,3,1]
[5,4,2,8,3,6,7,1]=>[1,1,2,3,1]
[5,3,4,8,2,6,7,1]=>[1,3,3,1]
[2,5,4,8,3,6,7,1]=>[2,2,3,1]
[6,3,2,5,8,4,7,1]=>[1,1,3,2,1]
[6,1,8,3,5,4,7,2]=>[1,2,2,2,1]
[5,4,8,3,2,6,7,1]=>[1,2,1,3,1]
[5,8,2,3,4,6,7,1]=>[2,5,1]
[7,2,5,6,4,1,8,3]=>[1,3,1,2,1]
[6,2,1,7,8,5,4,3]=>[1,1,3,1,1,1]
[7,2,5,1,4,6,8,3]=>[1,2,4,1]
[8,2,1,7,4,5,6,3]=>[1,1,2,3,1]
[8,2,5,6,4,1,7,3]=>[1,3,1,2,1]
[8,2,5,6,4,7,1,3]=>[1,3,2,2]
[7,4,6,8,3,2,5,1]=>[1,3,1,2,1]
[7,4,6,8,3,2,1,5]=>[1,3,1,1,2]
[1,5,8,6,3,7,2,4]=>[3,1,2,2]
[6,1,8,7,3,5,2,4]=>[1,2,1,2,2]
[6,1,2,7,3,5,4,8]=>[1,3,2,2]
[3,4,5,2,7,1,6,8]=>[3,2,3]
[1,4,6,7,3,2,5,8]=>[4,1,3]
[3,1,7,8,2,4,6,5]=>[1,3,3,1]
[1,4,6,8,3,2,7,5]=>[4,1,2,1]
[3,4,5,2,7,1,8,6]=>[3,2,2,1]
[3,1,7,6,8,4,2,5]=>[1,2,2,1,2]
[7,5,6,1,2,3,8,4]=>[1,2,4,1]
[1,5,7,6,3,2,8,4]=>[3,1,1,2,1]
[8,4,6,7,3,1,2,5]=>[1,3,1,3]
[8,4,6,7,3,2,5,1]=>[1,3,1,2,1]
[3,8,7,6,2,4,5,1]=>[2,1,1,3,1]
[3,7,5,2,1,6,8,4]=>[2,1,1,3,1]
[3,7,2,4,1,6,8,5]=>[2,2,3,1]
[3,8,2,4,7,6,1,5]=>[2,3,1,2]
[8,4,6,2,3,5,7,1]=>[1,2,4,1]
[8,4,6,2,3,1,5,7]=>[1,2,2,3]
[8,5,2,6,3,4,1,7]=>[1,1,2,2,2]
[7,5,2,1,4,3,8,6]=>[1,1,1,2,2,1]
[3,4,1,7,5,2,8,6]=>[2,2,1,2,1]
[3,1,7,8,5,4,2,6]=>[1,3,1,1,2]
[3,4,5,2,8,6,1,7]=>[3,2,1,2]
[3,4,5,2,8,1,6,7]=>[3,2,3]
[3,4,5,2,8,6,7,1]=>[3,2,2,1]
[3,4,5,2,6,8,1,7]=>[3,3,2]
[3,4,5,2,1,8,6,7]=>[3,1,2,2]
[7,6,4,8,3,1,2,5]=>[1,1,2,1,3]
[7,4,8,5,6,1,2,3]=>[1,2,2,3]
[6,2,8,5,1,3,4,7]=>[1,2,1,4]
[3,2,7,8,6,1,4,5]=>[1,3,1,3]
[6,8,2,5,1,3,7,4]=>[2,2,3,1]
[6,7,4,2,1,5,3,8]=>[2,1,1,2,2]
[5,7,4,1,3,6,2,8]=>[2,1,3,2]
[4,2,7,5,1,8,3,6]=>[1,2,1,2,2]
[4,1,6,5,3,8,2,7]=>[1,2,1,2,2]
[1,5,4,6,3,8,2,7]=>[2,2,2,2]
[1,8,6,4,7,3,2,5]=>[2,1,2,1,2]
[4,7,1,8,6,3,5,2]=>[2,2,1,2,1]
[5,4,8,1,7,3,6,2]=>[1,2,2,2,1]
[4,3,8,6,2,1,7,5]=>[1,2,1,1,2,1]
[8,3,6,2,4,1,7,5]=>[1,2,2,2,1]
[7,8,3,2,4,6,5,1]=>[2,1,3,1,1]
[7,2,8,5,3,1,6,4]=>[1,2,1,1,2,1]
[2,5,4,8,7,3,6,1]=>[2,2,1,2,1]
[6,4,2,8,7,3,1,5]=>[1,1,2,1,1,2]
[3,6,8,1,7,4,2,5]=>[3,2,1,2]
[7,8,6,3,1,4,5,2]=>[2,1,1,3,1]
[3,8,6,1,7,5,2,4]=>[2,1,2,1,2]
[2,7,5,4,8,3,1,6]=>[2,1,2,1,2]
[6,8,7,5,2,1,3,4]=>[2,1,1,1,3]
[7,6,2,8,5,1,3,4]=>[1,1,2,1,3]
[1,5,7,6,2,8,4,3]=>[3,1,2,1,1]
[1,6,5,2,7,8,4,3]=>[2,1,3,1,1]
[4,7,8,5,6,2,3,1]=>[3,2,2,1]
[2,7,8,5,6,1,4,3]=>[3,2,2,1]
[6,7,8,4,2,1,5,3]=>[3,1,1,2,1]
[4,7,8,1,2,5,6,3]=>[3,4,1]
[8,6,4,1,2,5,7,3]=>[1,1,1,4,1]
[6,1,4,7,2,5,8,3]=>[1,3,3,1]
[6,7,8,3,5,4,2,1]=>[3,2,1,1,1]
[2,7,8,3,6,5,4,1]=>[3,2,1,1,1]
[6,7,8,2,1,5,3,4]=>[3,1,2,2]
[8,6,2,1,7,5,4,3]=>[1,1,1,2,1,1,1]
[3,6,1,2,5,7,4,8]=>[2,4,2]
[5,6,3,2,7,4,1,8]=>[2,1,2,1,2]
[2,6,4,3,7,5,8,1]=>[2,1,2,2,1]
[8,2,4,7,1,5,3,6]=>[1,3,2,2]
[5,2,3,7,8,4,1,6]=>[1,4,1,2]
[7,2,3,6,1,8,4,5]=>[1,3,2,2]
[5,2,7,3,6,8,4,1]=>[1,2,3,1,1]
[2,5,6,7,3,8,4,1]=>[4,2,1,1]
[7,5,6,1,2,8,3,4]=>[1,2,3,2]
[4,1,5,8,6,2,7,3]=>[1,3,1,2,1]
[3,4,6,5,7,1,2,8]=>[3,2,3]
[2,4,7,5,6,3,1,8]=>[3,2,1,2]
[7,5,1,6,3,4,2,8]=>[1,1,2,2,2]
[7,6,2,3,5,4,8,1]=>[1,1,3,2,1]
[8,5,2,4,3,6,1,7]=>[1,1,2,2,2]
[8,5,7,2,4,1,6,3]=>[1,2,2,2,1]
[2,6,7,5,8,1,4,3]=>[3,2,2,1]
[2,6,7,5,8,3,4,1]=>[3,2,2,1]
[2,5,8,7,6,3,4,1]=>[3,1,1,2,1]
[4,5,8,7,6,2,3,1]=>[3,1,1,2,1]
[7,4,8,2,1,5,6,3]=>[1,2,1,3,1]
[7,3,2,4,1,6,5,8]=>[1,1,2,2,2]
[8,3,2,7,5,4,6,1]=>[1,1,2,1,2,1]
[5,4,2,7,1,6,3,8]=>[1,1,2,2,2]
[2,3,6,7,8,5,1,4]=>[5,1,2]
[8,3,7,1,6,4,2,5]=>[1,2,2,1,2]
[2,4,7,8,6,3,5,1]=>[4,1,2,1]
[8,2,1,7,6,5,3,4]=>[1,1,2,1,1,2]
[5,7,4,1,6,8,2,3]=>[2,1,3,2]
[1,4,6,8,7,3,2,5]=>[4,1,1,2]
[1,5,8,3,6,2,4,7]=>[3,2,3]
[6,5,1,2,8,3,4,7]=>[1,1,3,3]
[5,6,8,1,3,7,2,4]=>[3,3,2]
[6,4,2,8,3,7,1,5]=>[1,1,2,2,2]
[3,7,4,8,6,1,2,5]=>[2,2,1,3]
[7,8,2,5,6,3,1,4]=>[2,3,1,2]
[6,1,8,5,3,2,4,7]=>[1,2,1,1,3]
[1,6,8,5,3,2,4,7]=>[3,1,1,3]
[5,1,2,8,3,7,4,6]=>[1,3,2,2]
[8,5,2,1,3,7,4,6]=>[1,1,1,3,2]
[5,8,1,6,7,4,2,3]=>[2,3,1,2]
[4,6,7,2,3,1,8,5]=>[3,2,2,1]
[3,6,4,2,8,1,5,7]=>[2,1,2,3]
[7,2,6,5,1,3,8,4]=>[1,2,1,3,1]
[5,2,8,3,1,7,4,6]=>[1,2,1,2,2]
[5,2,1,8,3,7,4,6]=>[1,1,2,2,2]
[1,2,8,4,6,7,3,5]=>[3,3,2]
[7,2,8,4,6,1,3,5]=>[1,2,2,3]
[6,2,7,4,3,8,1,5]=>[1,2,1,2,2]
[8,2,5,7,3,4,1,6]=>[1,3,2,2]
[7,5,2,8,3,1,4,6]=>[1,1,2,1,3]
[1,7,8,4,6,2,3,5]=>[3,2,3]
[7,1,8,4,6,2,3,5]=>[1,2,2,3]
[1,8,6,5,4,7,2,3]=>[2,1,1,2,2]
[5,8,6,1,4,7,2,3]=>[2,1,3,2]
[8,1,6,5,4,7,2,3]=>[1,2,1,2,2]
[4,1,6,8,7,3,2,5]=>[1,3,1,1,2]
[5,1,4,6,7,3,8,2]=>[1,4,2,1]
[4,8,6,1,5,7,2,3]=>[2,1,3,2]
[4,1,6,2,5,7,8,3]=>[1,2,4,1]
[1,5,3,7,2,4,8,6]=>[2,2,3,1]
[5,1,3,7,2,4,8,6]=>[1,3,3,1]
[3,4,8,2,5,7,1,6]=>[3,3,2]
[6,7,3,4,1,2,8,5]=>[2,2,3,1]
[7,1,3,4,6,2,8,5]=>[1,4,2,1]
[1,7,3,4,6,2,8,5]=>[2,3,2,1]
[4,7,2,8,5,3,1,6]=>[2,2,1,1,2]
[2,8,5,1,3,4,7,6]=>[2,1,4,1]
[8,1,6,5,2,4,7,3]=>[1,2,1,3,1]
[8,7,1,4,6,3,2,5]=>[1,1,3,1,2]
[5,7,1,3,6,8,2,4]=>[2,4,2]
[6,5,2,8,4,7,1,3]=>[1,1,2,2,2]
[1,4,7,5,8,6,3,2]=>[3,2,1,1,1]
[8,5,7,2,3,6,1,4]=>[1,2,3,2]
[6,1,8,3,4,7,2,5]=>[1,2,3,2]
[1,7,8,3,4,6,2,5]=>[3,3,2]
[1,8,6,3,5,2,7,4]=>[2,1,2,2,1]
[7,8,1,3,5,4,2,6]=>[2,3,1,2]
[4,7,1,6,8,3,5,2]=>[2,3,2,1]
[3,5,8,2,6,4,1,7]=>[3,2,1,2]
[3,6,5,2,8,4,1,7]=>[2,1,2,1,2]
[4,2,5,8,6,3,7,1]=>[1,3,1,2,1]
[7,2,8,3,5,4,1,6]=>[1,2,2,1,2]
[8,2,5,6,3,1,7,4]=>[1,3,1,2,1]
[4,2,1,5,3,8,7,6]=>[1,1,2,2,1,1]
[6,8,2,4,7,3,1,5]=>[2,3,1,2]
[1,8,2,4,3,5,7,6]=>[2,2,3,1]
[8,7,1,4,2,3,6,5]=>[1,1,2,3,1]
[7,1,8,4,2,5,3,6]=>[1,2,1,2,2]
[1,4,8,7,5,2,6,3]=>[3,1,1,2,1]
[1,4,7,8,5,3,6,2]=>[4,1,2,1]
[4,1,8,6,5,7,3,2]=>[1,2,1,2,1,1]
[5,7,6,4,1,2,3,8]=>[2,1,1,4]
[1,5,6,4,2,3,7,8]=>[3,1,4]
[5,7,3,6,8,4,2,1]=>[2,3,1,1,1]
[7,4,6,2,5,8,1,3]=>[1,2,3,2]
[8,7,3,4,2,6,1,5]=>[1,1,2,2,2]
[6,4,1,2,5,3,8,7]=>[1,1,3,2,1]
[6,2,3,4,7,1,5,8]=>[1,4,3]
[5,8,7,4,2,1,3,6]=>[2,1,1,1,3]
[5,2,1,3,8,6,4,7]=>[1,1,3,1,2]
[3,1,5,2,7,8,6,4]=>[1,2,3,1,1]
[6,3,2,5,1,8,7,4]=>[1,1,2,2,1,1]
[6,2,1,3,8,7,4,5]=>[1,1,3,1,2]
[1,5,8,7,3,4,2,6]=>[3,1,2,2]
[1,8,7,3,2,5,4,6]=>[2,1,1,2,2]
[1,2,5,4,8,7,3,6]=>[3,2,1,2]
[1,2,4,8,6,3,5,7]=>[4,1,3]
[1,5,2,4,7,3,8,6]=>[2,3,2,1]
[2,7,4,1,8,6,3,5]=>[2,1,2,1,2]
[8,6,3,5,7,4,1,2]=>[1,1,3,1,2]
[8,5,3,2,1,4,7,6]=>[1,1,1,1,3,1]
[1,7,6,8,5,3,2,4]=>[2,2,1,1,2]
[1,2,7,6,8,4,3,5]=>[3,2,1,2]
[1,6,3,2,5,7,8,4]=>[2,1,4,1]
[1,7,3,4,2,6,8,5]=>[2,2,3,1]
[7,4,6,8,5,2,1,3]=>[1,3,1,1,2]
[1,6,3,5,8,4,2,7]=>[2,3,1,2]
[1,5,6,3,2,8,4,7]=>[3,1,2,2]
[1,2,5,8,4,6,3,7]=>[4,2,2]
[1,5,3,2,7,8,4,6]=>[2,1,3,2]
[3,1,8,5,2,6,4,7]=>[1,2,1,2,2]
[5,2,1,3,7,4,8,6]=>[1,1,3,2,1]
[4,1,8,6,2,3,7,5]=>[1,2,1,3,1]
[4,8,6,3,2,7,5,1]=>[2,1,1,2,1,1]
[7,5,8,6,2,3,4,1]=>[1,2,1,3,1]
[1,7,6,4,3,8,5,2]=>[2,1,1,2,1,1]
[1,8,5,7,6,3,2,4]=>[2,2,1,1,2]
[1,4,7,3,6,8,5,2]=>[3,3,1,1]
[1,6,3,5,7,8,4,2]=>[2,4,1,1]
[1,5,6,3,2,7,8,4]=>[3,1,3,1]
[1,2,7,6,8,4,5,3]=>[3,2,2,1]
[1,8,4,7,5,3,2,6]=>[2,2,1,1,2]
[6,8,5,2,1,7,4,3]=>[2,1,1,2,1,1]
[2,8,5,6,3,1,7,4]=>[2,2,1,2,1]
[1,2,6,8,4,3,7,5]=>[4,1,2,1]
[5,3,7,2,6,4,1,8]=>[1,2,2,1,2]
[5,3,8,2,6,1,7,4]=>[1,2,2,2,1]
[7,5,2,8,6,1,3,4]=>[1,1,2,1,3]
[7,6,2,5,3,4,1,8]=>[1,1,2,2,2]
[7,6,2,4,5,3,1,8]=>[1,1,3,1,2]
[7,6,2,4,3,5,1,8]=>[1,1,2,2,2]
[7,6,2,3,5,4,1,8]=>[1,1,3,1,2]
[8,4,2,7,1,6,3,5]=>[1,1,2,2,2]
[4,6,3,2,8,1,7,5]=>[2,1,2,2,1]
[8,7,6,1,5,3,2,4]=>[1,1,1,2,1,2]
[7,8,4,3,1,5,6,2]=>[2,1,1,3,1]
[8,7,6,1,4,3,5,2]=>[1,1,1,2,2,1]
[8,7,6,1,3,5,4,2]=>[1,1,1,3,1,1]
[8,7,6,1,5,4,2,3]=>[1,1,1,2,1,2]
[8,6,2,7,1,5,3,4]=>[1,1,2,2,2]
[5,3,7,2,8,1,6,4]=>[1,2,2,2,1]
[8,3,5,4,2,1,6,7]=>[1,2,1,1,3]
[7,8,4,3,1,5,2,6]=>[2,1,1,2,2]
[8,6,3,7,1,5,2,4]=>[1,1,2,2,2]
[8,7,6,1,2,5,3,4]=>[1,1,1,3,2]
[8,7,6,1,2,5,4,3]=>[1,1,1,3,1,1]
[8,7,6,1,4,2,5,3]=>[1,1,1,2,2,1]
[4,7,5,8,6,1,3,2]=>[2,2,1,2,1]
[6,5,7,3,8,4,1,2]=>[1,2,2,1,2]
[8,7,5,4,1,2,6,3]=>[1,1,1,1,3,1]
[8,6,7,1,5,3,2,4]=>[1,2,2,1,2]
[7,5,6,1,3,4,2,8]=>[1,2,3,2]
[5,7,8,1,3,4,2,6]=>[3,3,2]
[7,8,5,1,3,4,2,6]=>[2,1,3,2]
[5,7,8,3,4,6,1,2]=>[3,3,2]
[7,5,1,3,4,2,6,8]=>[1,1,3,3]
[5,7,1,3,4,2,8,6]=>[2,3,2,1]
[7,3,5,6,4,8,1,2]=>[1,3,2,2]
[1,7,3,8,2,5,6,4]=>[2,2,3,1]
[1,5,3,7,8,4,6,2]=>[2,3,2,1]
[1,5,7,3,8,2,6,4]=>[3,2,2,1]
[7,1,5,3,6,2,4,8]=>[1,2,2,3]
[1,7,3,5,8,4,2,6]=>[2,3,1,2]
[1,3,7,5,8,6,2,4]=>[3,2,1,2]
[1,7,8,5,3,6,2,4]=>[3,1,2,2]
[1,7,5,8,3,4,2,6]=>[2,2,2,2]
[7,1,5,6,3,4,2,8]=>[1,3,2,2]
[7,3,5,6,4,1,2,8]=>[1,3,1,3]
[3,7,5,8,4,1,2,6]=>[2,2,1,3]
[7,5,6,8,1,3,4,2]=>[1,3,3,1]
[5,3,4,7,8,1,2,6]=>[1,4,3]
[5,3,7,6,8,1,2,4]=>[1,2,2,3]
[3,7,1,2,5,8,4,6]=>[2,4,2]
[3,1,2,7,5,8,4,6]=>[1,3,2,2]
[3,1,2,5,7,8,6,4]=>[1,5,1,1]
[7,3,1,5,4,6,2,8]=>[1,1,2,2,2]
[7,3,5,1,2,6,4,8]=>[1,2,3,2]
[3,7,1,2,8,5,6,4]=>[2,3,2,1]
[5,3,1,7,4,6,8,2]=>[1,1,2,3,1]
[5,3,7,1,2,6,8,4]=>[1,2,4,1]
[2,5,7,4,6,3,1,8]=>[3,2,1,2]
[7,4,8,3,5,6,1,2]=>[1,2,3,2]
[2,4,7,3,5,6,1,8]=>[3,3,2]
[5,7,6,4,2,3,1,8]=>[2,1,1,2,2]
[7,4,8,2,5,6,1,3]=>[1,2,3,2]
[7,5,8,4,6,2,1,3]=>[1,2,2,1,2]
[5,8,2,4,6,1,3,7]=>[2,3,3]
[6,1,4,8,5,2,7,3]=>[1,3,1,2,1]
[5,8,1,2,3,6,7,4]=>[2,5,1]
[5,6,8,4,7,2,1,3]=>[3,2,1,2]
[4,5,1,8,3,6,7,2]=>[2,2,3,1]
[3,4,5,8,1,6,7,2]=>[4,3,1]
[4,5,1,8,2,6,7,3]=>[2,2,3,1]
[5,8,1,2,4,6,7,3]=>[2,5,1]
[6,8,7,4,2,1,5,3]=>[2,1,1,1,2,1]
[4,3,2,7,8,6,1,5]=>[1,1,3,1,2]
[6,8,7,4,3,1,2,5]=>[2,1,1,1,3]
[5,6,8,4,7,3,1,2]=>[3,2,1,2]
[7,3,5,4,2,8,1,6]=>[1,2,1,2,2]
[7,5,2,4,3,8,1,6]=>[1,1,2,2,2]
[2,8,6,4,3,1,5,7]=>[2,1,1,1,3]
[8,1,7,4,3,2,5,6]=>[1,2,1,1,3]
[3,1,6,8,5,2,7,4]=>[1,3,1,2,1]
[2,3,8,1,5,6,4,7]=>[3,3,2]
[4,8,1,3,2,6,7,5]=>[2,2,3,1]
[5,4,8,1,2,6,7,3]=>[1,2,4,1]
[4,8,1,2,3,6,7,5]=>[2,5,1]
[4,1,5,8,2,6,7,3]=>[1,3,3,1]
[5,1,8,2,4,6,7,3]=>[1,2,4,1]
[3,5,1,8,2,6,7,4]=>[2,2,3,1]
[2,6,1,8,5,3,7,4]=>[2,2,1,2,1]
[3,8,1,2,4,6,7,5]=>[2,5,1]
[4,1,8,2,3,6,7,5]=>[1,2,4,1]
[5,2,3,8,1,7,4,6]=>[1,3,2,2]
[2,3,5,7,1,6,4,8]=>[4,2,2]
[1,5,3,8,2,4,6,7]=>[2,2,4]
[8,6,2,7,5,1,4,3]=>[1,1,2,1,2,1]
[8,6,2,5,3,7,4,1]=>[1,1,2,2,1,1]
[2,7,1,8,6,3,5,4]=>[2,2,1,2,1]
[5,7,6,1,3,2,8,4]=>[2,1,2,2,1]
[5,7,3,2,6,1,4,8]=>[2,1,2,3]
[8,6,5,3,7,4,2,1]=>[1,1,1,2,1,1,1]
[3,5,4,6,1,7,8,2]=>[2,2,3,1]
[8,1,5,4,6,3,7,2]=>[1,2,2,2,1]
[2,7,1,5,6,4,3,8]=>[2,3,1,2]
[4,7,5,1,8,6,2,3]=>[2,1,2,1,2]
[8,4,6,3,1,7,2,5]=>[1,2,1,2,2]
[8,4,2,5,6,3,7,1]=>[1,1,3,2,1]
[8,6,2,7,5,4,3,1]=>[1,1,2,1,1,1,1]
[5,4,7,2,8,6,1,3]=>[1,2,2,1,2]
[3,5,6,4,1,7,2,8]=>[3,1,2,2]
[2,5,6,1,7,4,3,8]=>[3,2,1,2]
[2,7,1,8,6,5,4,3]=>[2,2,1,1,1,1]
[3,7,6,1,8,5,4,2]=>[2,1,2,1,1,1]
[6,2,8,3,1,4,5,7]=>[1,2,1,4]
[2,7,8,3,1,4,5,6]=>[3,1,4]
[1,7,8,5,3,2,6,4]=>[3,1,1,2,1]
[1,5,3,2,8,6,7,4]=>[2,1,2,2,1]
[1,8,5,3,2,6,7,4]=>[2,1,1,3,1]
[1,7,8,5,6,3,2,4]=>[3,2,1,2]
[1,8,5,6,3,2,7,4]=>[2,2,1,2,1]
[1,5,8,6,7,3,2,4]=>[3,2,1,2]
[1,5,6,7,3,2,8,4]=>[4,1,2,1]
[1,7,5,2,3,4,8,6]=>[2,1,4,1]
[1,7,5,2,4,8,6,3]=>[2,1,3,1,1]
[1,7,8,5,2,4,6,3]=>[3,1,3,1]
[1,8,5,2,4,6,7,3]=>[2,1,4,1]
[1,6,7,8,3,2,4,5]=>[4,1,3]
[1,4,8,6,2,3,5,7]=>[3,1,4]
[1,7,8,3,2,4,5,6]=>[3,1,4]
[1,4,5,8,6,7,2,3]=>[4,2,2]
[1,8,4,5,6,7,2,3]=>[2,4,2]
[1,2,8,6,7,4,3,5]=>[3,2,1,2]
[1,2,8,6,3,4,5,7]=>[3,1,4]
[1,2,8,6,3,5,7,4]=>[3,1,3,1]
[1,2,7,4,3,8,5,6]=>[3,1,2,2]
[1,2,7,8,4,3,5,6]=>[4,1,3]
[1,8,6,7,4,2,3,5]=>[2,2,1,3]
[1,6,7,8,4,2,3,5]=>[4,1,3]
[1,6,7,3,5,2,8,4]=>[3,2,2,1]
[1,6,7,8,3,4,2,5]=>[4,2,2]
[1,7,8,5,6,2,3,4]=>[3,2,3]
[1,8,6,2,3,5,7,4]=>[2,1,4,1]
[1,7,4,2,3,8,5,6]=>[2,1,3,2]
[1,7,8,4,2,3,5,6]=>[3,1,4]
[1,7,3,5,6,2,8,4]=>[2,3,2,1]
[1,7,8,3,4,2,5,6]=>[3,2,3]
[1,5,8,6,7,2,3,4]=>[3,2,3]
[1,2,3,7,8,5,4,6]=>[5,1,2]
[1,2,7,4,6,3,8,5]=>[3,2,2,1]
[1,2,8,6,7,3,4,5]=>[3,2,3]
[1,7,4,5,2,3,8,6]=>[2,2,3,1]
[1,7,8,4,5,2,3,6]=>[3,2,3]
[1,7,8,3,4,5,2,6]=>[3,3,2]
[1,2,8,4,5,6,3,7]=>[3,3,2]
[1,8,4,5,6,2,3,7]=>[2,3,3]
[8,2,5,6,3,4,1,7]=>[1,3,2,2]
[5,8,2,7,3,4,1,6]=>[2,2,2,2]
[6,8,7,2,3,4,1,5]=>[2,1,3,2]
[3,8,7,5,2,6,1,4]=>[2,1,1,2,2]
[8,2,3,6,4,5,1,7]=>[1,3,2,2]
[8,2,4,6,3,5,1,7]=>[1,3,2,2]
[3,4,2,7,8,5,1,6]=>[2,3,1,2]
[4,8,7,3,2,5,1,6]=>[2,1,1,2,2]
[5,8,4,2,6,7,3,1]=>[2,1,3,1,1]
[5,3,8,1,6,7,4,2]=>[1,2,3,1,1]
[5,2,8,1,6,4,7,3]=>[1,2,2,2,1]
[5,8,2,1,3,7,6,4]=>[2,1,3,1,1]
[8,3,4,1,2,6,5,7]=>[1,2,3,2]
[1,4,3,2,8,5,7,6]=>[2,1,2,2,1]
[5,1,8,2,6,4,7,3]=>[1,2,2,2,1]
[5,1,8,3,6,7,4,2]=>[1,2,3,1,1]
[5,2,8,3,6,7,4,1]=>[1,2,3,1,1]
[3,1,8,4,6,2,7,5]=>[1,2,2,2,1]
[8,4,1,6,5,2,3,7]=>[1,1,2,1,3]
[1,8,7,6,4,3,5,2]=>[2,1,1,1,2,1]
[3,1,4,7,5,8,2,6]=>[1,3,2,2]
[3,1,7,5,6,8,4,2]=>[1,2,3,1,1]
[6,1,8,7,5,3,4,2]=>[1,2,1,1,2,1]
[6,1,8,7,5,4,2,3]=>[1,2,1,1,1,2]
[8,3,5,6,1,4,2,7]=>[1,3,2,2]
[6,8,7,3,2,4,1,5]=>[2,1,1,2,2]
[2,3,7,5,6,8,4,1]=>[3,3,1,1]
[3,2,4,7,5,8,1,6]=>[1,3,2,2]
[2,8,7,6,5,3,1,4]=>[2,1,1,1,1,2]
[2,8,7,6,4,5,1,3]=>[2,1,1,2,2]
[3,8,7,6,4,1,5,2]=>[2,1,1,1,2,1]
[3,8,7,6,4,2,5,1]=>[2,1,1,1,2,1]
[1,3,4,7,5,2,8,6]=>[4,1,2,1]
[2,3,7,4,6,8,1,5]=>[3,3,2]
[4,8,7,6,2,5,1,3]=>[2,1,1,2,2]
[4,8,7,6,3,1,5,2]=>[2,1,1,1,2,1]
[3,5,2,4,7,6,8,1]=>[2,3,2,1]
[5,3,2,6,4,7,8,1]=>[1,1,2,3,1]
[5,3,2,6,7,4,8,1]=>[1,1,3,2,1]
[5,3,2,7,6,4,8,1]=>[1,1,2,1,2,1]
[7,3,5,2,8,4,6,1]=>[1,2,2,2,1]
[3,5,2,7,4,6,8,1]=>[2,2,3,1]
[3,2,5,7,4,6,8,1]=>[1,3,3,1]
[3,2,7,5,4,8,6,1]=>[1,2,1,2,1,1]
[3,7,5,2,4,8,6,1]=>[2,1,3,1,1]
[2,3,7,5,4,8,6,1]=>[3,1,2,1,1]
[8,3,5,1,6,4,7,2]=>[1,2,2,2,1]
[8,4,5,6,1,3,7,2]=>[1,3,3,1]
[3,4,7,6,8,2,5,1]=>[3,2,2,1]
[5,2,8,4,1,3,6,7]=>[1,2,1,4]
[3,8,5,2,1,4,6,7]=>[2,1,1,4]
[7,6,4,1,8,2,5,3]=>[1,1,1,2,2,1]
[7,5,4,2,1,6,3,8]=>[1,1,1,1,2,2]
[8,1,6,7,3,4,2,5]=>[1,3,2,2]
[8,2,1,6,7,4,3,5]=>[1,1,3,1,2]
[5,2,8,6,3,7,1,4]=>[1,2,1,2,2]
[7,6,8,1,2,5,4,3]=>[1,2,3,1,1]
[2,1,3,4,8,5,7,6]=>[1,4,2,1]
[5,7,1,2,6,8,3,4]=>[2,4,2]
[1,5,2,3,6,8,7,4]=>[2,4,1,1]
[3,7,4,5,2,8,1,6]=>[2,2,2,2]
[2,7,4,3,1,8,5,6]=>[2,1,1,2,2]
[3,5,7,4,1,8,2,6]=>[3,1,2,2]
[2,5,4,6,8,3,1,7]=>[2,3,1,2]
[8,3,6,4,1,2,5,7]=>[1,2,1,4]
[7,4,6,5,8,2,1,3]=>[1,2,2,1,2]
[8,6,4,7,5,1,2,3]=>[1,1,2,1,3]
[1,6,2,5,8,7,4,3]=>[2,3,1,1,1]
[3,7,4,5,6,2,8,1]=>[2,3,2,1]
[7,3,1,8,5,4,6,2]=>[1,1,2,1,2,1]
[8,4,3,1,6,5,2,7]=>[1,1,1,2,1,2]
[2,3,8,5,6,4,1,7]=>[3,2,1,2]
[2,7,4,8,6,1,3,5]=>[2,2,1,3]
[8,6,4,1,2,5,3,7]=>[1,1,1,3,2]
[2,8,4,3,1,6,5,7]=>[2,1,1,2,2]
[6,4,8,2,3,1,5,7]=>[1,2,2,3]
[3,8,4,6,1,5,2,7]=>[2,2,2,2]
[4,5,1,8,2,6,3,7]=>[2,2,2,2]
[6,1,8,4,3,2,7,5]=>[1,2,1,1,2,1]
[8,1,5,6,3,4,7,2]=>[1,3,3,1]
[8,6,2,5,4,7,1,3]=>[1,1,2,2,2]
[2,8,5,7,6,3,1,4]=>[2,2,1,1,2]
[8,5,3,1,7,6,4,2]=>[1,1,1,2,1,1,1]
[8,3,5,6,1,4,7,2]=>[1,3,3,1]
[4,5,8,3,6,2,7,1]=>[3,2,2,1]
[7,2,1,6,5,3,8,4]=>[1,1,2,1,2,1]
[5,6,4,1,7,8,2,3]=>[2,1,3,2]
[5,1,6,4,8,7,3,2]=>[1,2,2,1,1,1]
[2,4,6,7,5,1,8,3]=>[4,1,2,1]
[7,6,4,1,5,3,2,8]=>[1,1,1,2,1,2]
[6,8,7,4,1,5,3,2]=>[2,1,1,2,1,1]
[6,8,7,3,5,4,2,1]=>[2,1,2,1,1,1]
[3,1,2,8,5,7,4,6]=>[1,3,2,2]
[7,3,1,2,5,8,4,6]=>[1,1,4,2]
[8,3,5,7,2,1,4,6]=>[1,3,1,3]
[2,1,3,8,5,7,4,6]=>[1,3,2,2]
[7,3,1,2,8,4,5,6]=>[1,1,3,3]
[2,1,4,7,6,3,5,8]=>[1,3,1,3]
[7,2,4,5,3,8,1,6]=>[1,3,2,2]
[8,4,2,5,6,7,3,1]=>[1,1,4,1,1]
[5,4,1,6,3,7,8,2]=>[1,1,2,3,1]
[4,5,1,3,6,7,8,2]=>[2,5,1]
[5,1,7,6,3,4,8,2]=>[1,2,1,3,1]
[6,1,7,5,4,8,2,3]=>[1,2,1,2,2]
[3,7,2,1,6,8,4,5]=>[2,1,3,2]
[1,5,8,2,4,7,6,3]=>[3,3,1,1]
[5,8,1,6,4,7,3,2]=>[2,2,2,1,1]
[3,8,6,5,7,2,4,1]=>[2,1,2,2,1]
[6,8,1,4,7,3,5,2]=>[2,3,2,1]
[1,6,8,2,7,4,5,3]=>[3,2,2,1]
[5,7,2,1,8,4,3,6]=>[2,1,2,1,2]
[5,7,1,6,8,3,2,4]=>[2,3,1,2]
[5,6,2,1,8,3,4,7]=>[2,1,2,3]
[6,4,1,7,3,8,2,5]=>[1,1,2,2,2]
[8,2,5,6,7,1,4,3]=>[1,4,2,1]
[7,2,4,6,8,3,1,5]=>[1,4,1,2]
[6,2,4,7,8,1,3,5]=>[1,4,3]
[6,1,4,3,2,8,5,7]=>[1,2,1,2,2]
[2,7,4,8,6,1,5,3]=>[2,2,1,2,1]
[2,4,8,6,5,7,3,1]=>[3,1,2,1,1]
[3,7,8,6,4,2,5,1]=>[3,1,1,2,1]
[6,2,8,4,7,5,1,3]=>[1,2,2,1,2]
[4,5,7,3,6,8,1,2]=>[3,3,2]
[3,4,7,8,6,5,1,2]=>[4,1,1,2]
[1,4,7,2,6,8,5,3]=>[3,3,1,1]
[2,3,7,6,5,1,4,8]=>[3,1,1,3]
[3,2,7,6,4,1,5,8]=>[1,2,1,1,3]
[6,2,3,5,7,1,4,8]=>[1,4,3]
[7,8,1,2,5,6,4,3]=>[2,4,1,1]
[7,1,3,6,8,5,2,4]=>[1,4,1,2]
[4,2,8,5,1,6,3,7]=>[1,2,1,2,2]
[6,5,8,1,4,2,3,7]=>[1,2,2,3]
[3,8,2,4,5,1,6,7]=>[2,3,3]
[3,6,2,4,1,5,7,8]=>[2,2,4]
[2,3,8,4,1,6,5,7]=>[3,1,2,2]
[4,5,7,3,1,6,2,8]=>[3,1,2,2]
[2,3,1,4,8,5,7,6]=>[2,3,2,1]
[4,2,6,1,5,8,7,3]=>[1,2,3,1,1]
[7,5,1,8,4,3,6,2]=>[1,1,2,1,2,1]
[3,1,8,5,7,6,4,2]=>[1,2,2,1,1,1]
[5,1,8,7,4,6,3,2]=>[1,2,1,2,1,1]
[3,8,6,2,5,1,4,7]=>[2,1,2,3]
[6,8,7,2,5,1,4,3]=>[2,1,2,2,1]
[5,7,2,8,6,1,4,3]=>[2,2,1,2,1]
[6,4,8,7,5,1,3,2]=>[1,2,1,1,2,1]
[6,2,8,7,4,1,3,5]=>[1,2,1,1,3]
[6,2,5,8,7,1,4,3]=>[1,3,1,2,1]
[2,4,8,6,5,1,3,7]=>[3,1,1,3]
[2,4,8,7,5,1,3,6]=>[3,1,1,3]
[3,5,7,6,1,8,4,2]=>[3,1,2,1,1]
[3,5,7,6,2,8,4,1]=>[3,1,2,1,1]
[2,5,7,6,1,8,3,4]=>[3,1,2,2]
[5,1,4,7,3,8,6,2]=>[1,3,2,1,1]
[1,3,8,7,2,5,4,6]=>[3,1,2,2]
[1,5,6,2,8,7,4,3]=>[3,2,1,1,1]
[2,5,3,8,7,6,4,1]=>[2,2,1,1,1,1]
[1,5,3,2,8,7,6,4]=>[2,1,2,1,1,1]
[6,1,4,3,8,7,5,2]=>[1,2,2,1,1,1]
[6,2,4,1,8,7,5,3]=>[1,2,2,1,1,1]
[3,4,1,8,7,5,2,6]=>[2,2,1,1,2]
[4,5,2,8,7,6,3,1]=>[2,2,1,1,1,1]
[6,4,1,8,7,5,2,3]=>[1,1,2,1,1,2]
[6,3,1,8,7,4,2,5]=>[1,1,2,1,1,2]
[4,2,5,1,8,6,3,7]=>[1,2,2,1,2]
[3,6,2,8,1,7,4,5]=>[2,2,2,2]
[4,2,8,5,1,7,3,6]=>[1,2,1,2,2]
[5,3,6,2,8,7,4,1]=>[1,2,2,1,1,1]
[6,3,5,2,1,8,7,4]=>[1,2,1,2,1,1]
[6,2,5,1,4,8,7,3]=>[1,2,3,1,1]
[2,8,4,1,3,7,6,5]=>[2,1,3,1,1]
[4,8,7,1,3,6,5,2]=>[2,1,3,1,1]
[3,8,1,4,7,6,5,2]=>[2,3,1,1,1]
[4,2,7,3,8,6,5,1]=>[1,2,2,1,1,1]
[3,1,8,6,2,5,4,7]=>[1,2,1,2,2]
[2,7,1,8,3,6,5,4]=>[2,2,2,1,1]
[5,2,1,7,4,8,6,3]=>[1,1,2,2,1,1]
[5,1,2,8,6,4,3,7]=>[1,3,1,1,2]
[6,2,3,8,7,5,4,1]=>[1,3,1,1,1,1]
[5,2,3,8,7,6,4,1]=>[1,3,1,1,1,1]
[2,8,1,3,7,6,4,5]=>[2,3,1,2]
[4,1,3,5,8,7,6,2]=>[1,4,1,1,1]
[3,4,7,5,8,1,2,6]=>[3,2,3]
[2,7,8,3,4,1,5,6]=>[3,2,3]
[2,8,6,7,5,4,3,1]=>[2,2,1,1,1,1]
[7,2,6,8,1,4,3,5]=>[1,3,2,2]
[5,3,6,2,8,4,7,1]=>[1,2,2,2,1]
[8,1,6,3,7,4,5,2]=>[1,2,2,2,1]
[2,4,3,7,1,8,6,5]=>[2,2,2,1,1]
[2,6,5,7,3,8,4,1]=>[2,2,2,1,1]
[6,8,2,7,4,1,5,3]=>[2,2,1,2,1]
[6,1,7,8,5,3,2,4]=>[1,3,1,1,2]
[2,6,5,4,7,1,8,3]=>[2,1,2,2,1]
[5,8,3,4,6,1,7,2]=>[2,3,2,1]
[6,1,7,4,2,5,8,3]=>[1,2,1,3,1]
[6,8,7,1,5,4,2,3]=>[2,1,2,1,2]
[4,8,3,1,5,7,6,2]=>[2,1,3,1,1]
[5,3,8,2,7,1,6,4]=>[1,2,2,2,1]
[8,2,7,1,6,5,3,4]=>[1,2,2,1,2]
[5,3,4,8,2,7,1,6]=>[1,3,2,2]
[8,3,4,5,2,7,1,6]=>[1,3,2,2]
[6,3,4,7,1,5,2,8]=>[1,3,2,2]
[6,7,1,5,3,4,8,2]=>[2,2,3,1]
[6,5,3,4,7,1,8,2]=>[1,1,3,2,1]
[5,3,4,7,1,6,8,2]=>[1,3,3,1]
[7,1,5,3,4,6,8,2]=>[1,2,4,1]
[8,2,6,7,1,5,3,4]=>[1,3,2,2]
[8,3,4,7,1,5,2,6]=>[1,3,2,2]
[7,1,5,2,6,3,4,8]=>[1,2,2,3]
[3,7,1,5,2,6,8,4]=>[2,2,3,1]
[8,3,4,6,7,1,5,2]=>[1,4,2,1]
[7,1,6,8,3,4,5,2]=>[1,3,3,1]
[6,7,1,8,3,4,5,2]=>[2,2,3,1]
[8,7,1,6,3,4,5,2]=>[1,1,2,3,1]
[6,3,4,8,7,1,5,2]=>[1,3,1,2,1]
[3,8,7,1,5,2,6,4]=>[2,1,2,2,1]
[3,4,8,7,1,5,2,6]=>[3,1,2,2]
[3,6,5,2,8,7,1,4]=>[2,1,2,1,2]
[3,6,7,1,8,4,5,2]=>[3,2,2,1]
[3,7,1,6,8,4,5,2]=>[2,3,2,1]
[3,8,4,6,7,1,5,2]=>[2,3,2,1]
[3,8,5,2,6,7,1,4]=>[2,1,3,2]
[3,7,1,4,8,5,2,6]=>[2,3,1,2]
[3,6,5,2,7,1,4,8]=>[2,1,2,3]
[3,7,1,4,6,5,2,8]=>[2,3,1,2]
[3,7,1,8,4,6,5,2]=>[2,2,2,1,1]
[6,8,3,4,7,1,5,2]=>[2,3,2,1]
[3,6,4,7,1,5,2,8]=>[2,2,2,2]
[3,7,1,6,4,5,2,8]=>[2,2,2,2]
[3,8,4,5,2,7,1,6]=>[2,2,2,2]
[3,7,1,6,5,2,8,4]=>[2,2,1,2,1]
[7,1,6,5,2,8,3,4]=>[1,2,1,2,2]
[8,3,5,2,7,1,6,4]=>[1,2,2,2,1]
[7,1,8,4,6,3,5,2]=>[1,2,2,2,1]
[3,4,8,5,2,7,1,6]=>[3,1,2,2]
[3,4,7,1,6,5,2,8]=>[3,2,1,2]
[3,4,6,7,1,5,2,8]=>[4,2,2]
[7,1,5,2,8,6,3,4]=>[1,2,2,1,2]
[8,6,3,4,7,1,5,2]=>[1,1,3,2,1]
[3,7,1,6,4,8,5,2]=>[2,2,2,1,1]
[3,8,6,4,7,1,5,2]=>[2,1,2,2,1]
[3,7,1,4,8,6,5,2]=>[2,3,1,1,1]
[3,7,1,4,5,2,8,6]=>[2,3,2,1]
[3,6,7,1,4,5,2,8]=>[3,3,2]
[3,5,2,6,7,1,4,8]=>[2,3,3]
[3,5,2,8,6,7,1,4]=>[2,2,2,2]
[3,6,8,7,1,4,5,2]=>[3,1,3,1]
[3,5,2,6,8,7,1,4]=>[2,3,1,2]
[2,5,4,6,7,8,1,3]=>[2,4,2]
[2,3,7,6,5,8,1,4]=>[3,1,2,2]
[2,6,5,4,7,8,1,3]=>[2,1,3,2]
[3,5,7,6,8,2,1,4]=>[3,2,1,2]
[4,2,5,3,7,6,1,8]=>[1,2,2,1,2]
[6,2,4,3,7,5,1,8]=>[1,2,2,1,2]
[1,3,6,4,7,5,2,8]=>[3,2,1,2]
[8,2,5,3,6,4,1,7]=>[1,2,2,1,2]
[7,2,5,3,6,4,1,8]=>[1,2,2,1,2]
[6,2,5,3,7,4,1,8]=>[1,2,2,1,2]
[4,2,6,3,7,5,1,8]=>[1,2,2,1,2]
[5,2,7,3,6,4,1,8]=>[1,2,2,1,2]
[7,3,6,2,5,4,1,8]=>[1,2,2,1,2]
[6,3,8,2,5,4,1,7]=>[1,2,2,1,2]
[7,3,1,4,6,5,2,8]=>[1,1,3,1,2]
[8,3,7,2,5,4,1,6]=>[1,2,2,1,2]
[5,2,8,3,6,4,1,7]=>[1,2,2,1,2]
[3,2,8,4,6,5,1,7]=>[1,2,2,1,2]
[1,4,7,3,6,5,2,8]=>[3,2,1,2]
[8,2,5,4,1,6,3,7]=>[1,2,1,2,2]
[8,2,6,4,1,5,3,7]=>[1,2,1,2,2]
[1,4,8,3,7,5,2,6]=>[3,2,1,2]
[6,2,1,4,8,5,3,7]=>[1,1,3,1,2]
[5,2,1,4,8,6,3,7]=>[1,1,3,1,2]
[3,2,1,5,8,6,4,7]=>[1,1,3,1,2]
[4,2,8,3,7,5,1,6]=>[1,2,2,1,2]
[5,2,8,3,7,4,1,6]=>[1,2,2,1,2]
[8,3,7,2,6,4,1,5]=>[1,2,2,1,2]
[7,3,1,4,8,5,2,6]=>[1,1,3,1,2]
[1,3,7,4,8,5,2,6]=>[3,2,1,2]
[8,2,6,3,7,4,1,5]=>[1,2,2,1,2]
[7,2,6,3,8,4,1,5]=>[1,2,2,1,2]
[5,2,7,3,8,4,1,6]=>[1,2,2,1,2]
[3,2,7,4,8,5,1,6]=>[1,2,2,1,2]
[5,2,6,3,8,4,1,7]=>[1,2,2,1,2]
[6,2,5,3,8,4,1,7]=>[1,2,2,1,2]
[7,2,5,3,8,4,1,6]=>[1,2,2,1,2]
[8,2,5,3,7,4,1,6]=>[1,2,2,1,2]
[1,3,6,4,8,5,2,7]=>[3,2,1,2]
[1,3,5,4,8,6,2,7]=>[3,2,1,2]
[8,2,4,3,7,5,1,6]=>[1,2,2,1,2]
[7,2,4,3,8,5,1,6]=>[1,2,2,1,2]
[6,2,4,3,8,5,1,7]=>[1,2,2,1,2]
[5,2,4,3,8,6,1,7]=>[1,2,2,1,2]
[4,2,5,3,8,6,1,7]=>[1,2,2,1,2]
[4,2,5,3,1,7,6,8]=>[1,2,1,2,2]
[6,2,4,3,1,7,5,8]=>[1,2,1,2,2]
[7,2,4,3,1,6,5,8]=>[1,2,1,2,2]
[8,5,1,3,6,4,2,7]=>[1,1,3,1,2]
[8,4,1,3,6,5,2,7]=>[1,1,3,1,2]
[1,5,2,4,7,6,3,8]=>[2,3,1,2]
[7,2,5,3,1,6,4,8]=>[1,2,1,2,2]
[6,2,5,3,1,7,4,8]=>[1,2,1,2,2]
[4,2,6,3,1,7,5,8]=>[1,2,1,2,2]
[3,2,6,4,1,7,5,8]=>[1,2,1,2,2]
[3,2,7,4,1,6,5,8]=>[1,2,1,2,2]
[4,2,7,3,1,6,5,8]=>[1,2,1,2,2]
[5,2,7,3,1,6,4,8]=>[1,2,1,2,2]
[6,2,7,3,1,5,4,8]=>[1,2,1,2,2]
[7,2,6,3,1,5,4,8]=>[1,2,1,2,2]
[1,5,2,4,8,6,3,7]=>[2,3,1,2]
[8,4,1,3,7,5,2,6]=>[1,1,3,1,2]
[6,2,1,5,3,7,4,8]=>[1,1,2,2,2]
[3,2,1,6,4,7,5,8]=>[1,1,2,2,2]
[3,2,8,5,1,6,4,7]=>[1,2,1,2,2]
[6,2,8,4,1,5,3,7]=>[1,2,1,2,2]
[8,3,7,4,1,5,2,6]=>[1,2,1,2,2]
[7,1,3,2,5,6,4,8]=>[1,2,3,2]
[4,2,8,7,5,6,1,3]=>[1,2,1,2,2]
[2,8,1,7,4,5,6,3]=>[2,2,3,1]
[6,3,5,2,4,8,1,7]=>[1,2,3,2]
[1,5,2,8,7,4,3,6]=>[2,2,1,1,2]
[5,7,1,2,6,4,3,8]=>[2,3,1,2]
[1,8,2,5,7,4,3,6]=>[2,3,1,2]
[1,6,4,3,2,5,8,7]=>[2,1,1,3,1]
[2,5,6,7,1,4,3,8]=>[4,2,2]
[5,7,2,8,1,4,3,6]=>[2,2,2,2]
[5,8,2,7,1,4,3,6]=>[2,2,2,2]
[7,5,1,2,6,4,3,8]=>[1,1,3,1,2]
[5,2,1,6,8,4,3,7]=>[1,1,3,1,2]
[6,2,8,5,1,4,3,7]=>[1,2,1,2,2]
[7,8,1,6,3,2,4,5]=>[2,2,1,3]
[7,3,6,4,1,2,8,5]=>[1,2,1,3,1]
[2,3,7,8,4,1,5,6]=>[4,1,3]
[5,4,7,2,3,8,1,6]=>[1,2,3,2]
[4,8,3,1,5,2,7,6]=>[2,1,2,2,1]
[2,3,5,8,7,6,1,4]=>[4,1,1,2]
[7,3,5,1,4,6,2,8]=>[1,2,3,2]
[3,8,5,1,2,6,4,7]=>[2,1,3,2]
[5,2,1,8,6,4,3,7]=>[1,1,2,1,1,2]
[1,2,6,5,8,4,3,7]=>[3,2,1,2]
[5,1,7,2,6,4,3,8]=>[1,2,2,1,2]
[7,1,5,3,2,6,8,4]=>[1,2,1,3,1]
[3,1,5,7,8,6,2,4]=>[1,4,1,2]
[1,8,7,2,6,4,3,5]=>[2,1,2,1,2]
[6,2,3,5,8,7,4,1]=>[1,4,1,1,1]
[8,6,2,3,1,5,7,4]=>[1,1,2,3,1]
[7,3,5,2,1,4,8,6]=>[1,2,1,3,1]
[2,6,3,8,7,4,5,1]=>[2,2,1,2,1]
[6,4,5,8,7,3,2,1]=>[1,3,1,1,1,1]
[1,7,3,6,8,5,2,4]=>[2,3,1,2]
[1,8,5,2,4,7,3,6]=>[2,1,3,2]
[2,5,1,7,4,8,6,3]=>[2,2,2,1,1]
[8,6,7,3,5,2,1,4]=>[1,2,2,1,2]
[1,4,2,7,3,6,8,5]=>[2,2,3,1]
[3,2,1,7,8,5,4,6]=>[1,1,3,1,2]
[7,3,4,2,1,5,8,6]=>[1,2,1,3,1]
[8,6,2,3,7,4,1,5]=>[1,1,3,1,2]
[1,4,3,8,6,5,2,7]=>[2,2,1,1,2]
[1,4,7,5,3,8,6,2]=>[3,1,2,1,1]
[8,6,7,4,1,5,2,3]=>[1,2,1,2,2]
[6,8,5,2,1,3,7,4]=>[2,1,1,3,1]
[1,7,6,3,2,4,8,5]=>[2,1,1,3,1]
[2,7,8,6,4,1,5,3]=>[3,1,1,2,1]
[2,1,6,4,7,8,5,3]=>[1,2,3,1,1]
[1,6,3,2,4,7,8,5]=>[2,1,4,1]
[1,2,3,7,5,8,4,6]=>[4,2,2]
[1,8,5,3,2,4,7,6]=>[2,1,1,3,1]
[6,7,8,2,5,1,4,3]=>[3,2,2,1]
[7,4,8,6,2,3,5,1]=>[1,2,1,3,1]
[6,2,5,7,8,1,4,3]=>[1,4,2,1]
[2,4,5,8,6,1,3,7]=>[4,1,3]
[4,7,8,1,5,6,2,3]=>[3,3,2]
[3,6,7,1,8,4,2,5]=>[3,2,1,2]
[2,3,7,5,1,6,4,8]=>[3,1,2,2]
[2,6,3,5,1,8,4,7]=>[2,2,2,2]
[7,2,4,6,1,8,5,3]=>[1,3,2,1,1]
[1,3,7,6,2,4,5,8]=>[3,1,4]
[1,6,7,2,8,3,5,4]=>[3,2,2,1]
[2,7,3,8,4,5,6,1]=>[2,2,3,1]
[1,4,2,7,5,3,6,8]=>[2,2,1,3]
[1,3,8,2,7,4,5,6]=>[3,2,3]
[7,1,4,3,8,5,6,2]=>[1,2,2,2,1]
[3,4,1,8,5,7,2,6]=>[2,2,2,2]
[3,4,1,5,8,6,2,7]=>[2,3,1,2]
[5,6,2,7,8,3,4,1]=>[2,3,2,1]
[7,4,1,8,5,6,2,3]=>[1,1,2,2,2]
[7,2,5,8,1,6,3,4]=>[1,3,2,2]
[6,4,8,1,5,7,2,3]=>[1,2,3,2]
[5,8,4,2,6,3,7,1]=>[2,1,2,2,1]
[6,2,5,1,4,7,8,3]=>[1,2,4,1]
[2,7,4,1,3,6,8,5]=>[2,1,4,1]
[5,7,1,2,6,4,8,3]=>[2,3,2,1]
[5,1,8,2,3,7,6,4]=>[1,2,3,1,1]
[3,1,8,5,2,4,7,6]=>[1,2,1,3,1]
[5,2,1,8,4,6,7,3]=>[1,1,2,3,1]
[6,2,1,4,7,5,8,3]=>[1,1,3,2,1]
[2,8,1,3,7,4,6,5]=>[2,3,2,1]
[6,2,3,8,4,5,7,1]=>[1,3,3,1]
[2,6,1,3,4,8,7,5]=>[2,4,1,1]
[1,2,6,3,5,7,8,4]=>[3,4,1]
[1,2,8,4,6,3,5,7]=>[3,2,3]
[2,6,1,5,4,7,3,8]=>[2,2,2,2]
[1,2,8,5,4,6,3,7]=>[3,1,2,2]
[1,3,6,8,4,5,7,2]=>[4,3,1]
[1,2,8,4,6,3,7,5]=>[3,2,2,1]
[4,6,3,5,7,8,1,2]=>[2,4,2]
[2,7,6,5,1,4,8,3]=>[2,1,1,3,1]
[2,7,4,8,1,3,6,5]=>[2,2,3,1]
[2,3,6,8,4,1,7,5]=>[4,1,2,1]
[1,2,6,8,4,7,5,3]=>[4,2,1,1]
[1,7,2,8,6,3,5,4]=>[2,2,1,2,1]
[2,3,8,5,4,7,1,6]=>[3,1,2,2]
[1,2,8,4,7,3,5,6]=>[3,2,3]
[2,6,1,4,8,3,7,5]=>[2,3,2,1]
[3,7,6,5,2,1,4,8]=>[2,1,1,1,3]
[2,5,6,1,4,8,7,3]=>[3,3,1,1]
[2,3,5,8,7,1,6,4]=>[4,1,2,1]
[8,4,2,3,7,1,6,5]=>[1,1,3,2,1]
[5,2,4,8,7,3,1,6]=>[1,3,1,1,2]
[3,5,7,6,1,8,2,4]=>[3,1,2,2]
[8,3,2,6,7,4,1,5]=>[1,1,3,1,2]
[6,5,7,3,1,2,8,4]=>[1,2,1,3,1]
[3,8,2,4,1,7,6,5]=>[2,2,2,1,1]
[3,5,8,2,6,7,1,4]=>[3,3,2]
[6,5,7,1,2,8,4,3]=>[1,2,3,1,1]
[3,2,4,6,7,8,1,5]=>[1,5,2]
[3,7,2,4,1,5,6,8]=>[2,2,4]
[3,2,4,6,7,1,5,8]=>[1,4,3]
[5,7,6,1,2,8,4,3]=>[2,1,3,1,1]
[6,5,1,2,7,4,3,8]=>[1,1,3,1,2]
[5,2,6,8,1,3,7,4]=>[1,3,3,1]
[4,8,1,6,3,7,5,2]=>[2,2,2,1,1]
[2,4,7,3,5,1,8,6]=>[3,2,2,1]
[7,1,5,2,6,4,3,8]=>[1,2,2,1,2]
[8,3,5,2,6,1,4,7]=>[1,2,2,3]
[5,6,1,3,8,7,4,2]=>[2,3,1,1,1]
[1,8,5,6,2,7,4,3]=>[2,2,2,1,1]
[8,3,5,2,6,7,1,4]=>[1,2,3,2]
[8,3,2,4,6,7,1,5]=>[1,1,4,2]
[3,7,2,4,6,1,5,8]=>[2,3,3]
[3,2,4,7,1,5,6,8]=>[1,3,4]
[3,8,2,4,1,5,6,7]=>[2,2,4]
[8,3,5,7,2,6,1,4]=>[1,3,2,2]
[4,2,7,6,1,8,5,3]=>[1,2,1,2,1,1]
[7,3,2,1,6,8,5,4]=>[1,1,1,3,1,1]
[7,2,4,8,6,3,5,1]=>[1,3,1,2,1]
[7,3,2,1,8,5,4,6]=>[1,1,1,2,1,2]
[7,3,2,1,6,4,8,5]=>[1,1,1,2,2,1]
[3,5,2,1,8,4,7,6]=>[2,1,2,2,1]
[3,6,5,2,1,8,4,7]=>[2,1,1,2,2]
[6,3,8,4,2,5,1,7]=>[1,2,1,2,2]
[6,7,2,4,3,5,8,1]=>[2,2,3,1]
[3,6,7,4,2,5,1,8]=>[3,1,2,2]
[6,4,7,3,2,1,5,8]=>[1,2,1,1,3]
[5,3,6,2,1,7,4,8]=>[1,2,1,2,2]
[3,2,6,5,1,7,4,8]=>[1,2,1,2,2]
[4,3,2,7,1,6,5,8]=>[1,1,2,2,2]
[4,5,3,7,2,1,6,8]=>[2,2,1,3]
[4,3,8,2,1,5,7,6]=>[1,2,1,3,1]
[4,3,2,8,1,6,7,5]=>[1,1,2,3,1]
[4,5,8,3,2,7,1,6]=>[3,1,2,2]
[5,8,3,4,7,2,1,6]=>[2,3,1,2]
[6,8,5,2,7,3,4,1]=>[2,1,2,2,1]
[2,5,4,6,1,8,7,3]=>[2,2,2,1,1]
[5,3,6,2,1,7,8,4]=>[1,2,1,3,1]
[6,4,7,3,2,8,1,5]=>[1,2,1,2,2]
[3,6,7,4,8,2,1,5]=>[3,2,1,2]
[6,7,2,4,8,3,5,1]=>[2,3,2,1]
[5,4,7,8,2,3,6,1]=>[1,3,3,1]
[4,3,8,2,1,6,7,5]=>[1,2,1,3,1]
[4,3,2,8,1,5,7,6]=>[1,1,2,3,1]
[4,5,3,2,6,8,1,7]=>[2,1,3,2]
[3,6,7,4,5,2,8,1]=>[3,2,2,1]
[3,4,7,5,6,2,8,1]=>[3,2,2,1]
[3,5,7,4,6,2,8,1]=>[3,2,2,1]
[4,5,2,3,7,6,8,1]=>[2,3,2,1]
[6,3,5,1,7,8,4,2]=>[1,2,3,1,1]
[5,3,7,6,2,4,8,1]=>[1,2,1,3,1]
[5,2,7,6,3,4,8,1]=>[1,2,1,3,1]
[5,2,7,6,4,3,8,1]=>[1,2,1,1,2,1]
[4,6,7,2,5,3,8,1]=>[3,2,2,1]
[4,6,7,3,5,2,8,1]=>[3,2,2,1]
[5,3,7,6,4,2,8,1]=>[1,2,1,1,2,1]
[6,4,7,8,3,1,5,2]=>[1,3,1,2,1]
[8,4,7,3,1,5,6,2]=>[1,2,1,3,1]
[7,4,8,6,2,5,1,3]=>[1,2,1,2,2]
[6,4,7,8,1,3,5,2]=>[1,3,3,1]
[6,3,1,5,7,8,4,2]=>[1,1,4,1,1]
[5,6,7,3,8,1,4,2]=>[3,2,2,1]
[8,4,1,7,2,5,6,3]=>[1,1,2,3,1]
[5,8,1,7,6,4,2,3]=>[2,2,1,1,2]
[2,6,7,8,5,4,1,3]=>[4,1,1,2]
[1,6,7,8,5,4,2,3]=>[4,1,1,2]
[5,6,7,1,8,3,4,2]=>[3,2,2,1]
[6,1,7,8,3,4,5,2]=>[1,3,3,1]
[7,1,8,6,2,5,4,3]=>[1,2,1,2,1,1]
[8,2,1,6,4,5,7,3]=>[1,1,2,3,1]
[8,5,1,7,6,4,2,3]=>[1,1,2,1,1,2]
[1,5,8,2,6,4,7,3]=>[3,2,2,1]
[6,1,5,3,7,8,4,2]=>[1,2,3,1,1]
[1,5,7,4,6,8,3,2]=>[3,3,1,1]
[1,4,7,5,6,8,3,2]=>[3,3,1,1]
[1,6,7,4,5,8,3,2]=>[3,3,1,1]
[5,6,7,4,8,1,3,2]=>[3,2,2,1]
[6,4,7,5,8,1,3,2]=>[1,2,2,2,1]
[7,5,2,1,8,4,6,3]=>[1,1,1,2,2,1]
[8,5,2,7,6,4,1,3]=>[1,1,2,1,1,2]
[8,1,2,6,4,5,7,3]=>[1,3,3,1]
[4,8,1,7,2,5,6,3]=>[2,2,3,1]
[2,6,7,1,5,4,8,3]=>[3,2,2,1]
[7,2,1,5,6,4,8,3]=>[1,1,3,2,1]
[2,8,1,6,4,5,7,3]=>[2,2,3,1]
[8,2,7,6,5,3,1,4]=>[1,2,1,1,1,2]
[8,3,7,6,5,1,2,4]=>[1,2,1,1,3]
[1,8,2,6,4,5,7,3]=>[2,2,3,1]
[7,1,2,5,6,4,8,3]=>[1,4,2,1]
[1,6,7,2,5,4,8,3]=>[3,2,2,1]
[3,2,7,6,5,8,1,4]=>[1,2,1,2,2]
[1,3,7,6,5,2,8,4]=>[3,1,1,2,1]
[8,3,7,6,5,2,1,4]=>[1,2,1,1,1,2]
[1,7,3,4,5,8,2,6]=>[2,4,2]
[7,1,8,4,5,6,3,2]=>[1,2,3,1,1]
[1,2,7,4,5,8,3,6]=>[3,3,2]
[6,7,3,2,5,8,1,4]=>[2,1,3,2]
[6,1,8,4,5,3,7,2]=>[1,2,2,2,1]
[4,6,2,5,1,8,7,3]=>[2,2,2,1,1]
[5,1,4,6,2,8,7,3]=>[1,3,2,1,1]
[7,5,2,4,6,8,1,3]=>[1,1,4,2]
[7,3,5,2,1,6,8,4]=>[1,2,1,3,1]
[8,5,1,2,6,3,7,4]=>[1,1,3,2,1]
[2,5,6,3,8,1,7,4]=>[3,2,2,1]
[1,5,6,3,8,7,4,2]=>[3,2,1,1,1]
[6,7,1,3,8,2,5,4]=>[2,3,2,1]
[7,6,5,2,1,4,8,3]=>[1,1,1,1,3,1]
[1,5,8,7,4,6,3,2]=>[3,1,2,1,1]
[5,7,2,1,3,6,8,4]=>[2,1,4,1]
[2,8,7,5,3,6,1,4]=>[2,1,1,2,2]
[2,7,6,3,8,1,5,4]=>[2,1,2,2,1]
[3,4,2,6,1,7,8,5]=>[2,2,3,1]
[3,7,2,6,8,1,5,4]=>[2,3,2,1]
[7,4,8,6,5,1,3,2]=>[1,2,1,1,2,1]
[1,6,5,3,7,4,8,2]=>[2,1,2,2,1]
[2,7,6,8,5,1,4,3]=>[2,2,1,2,1]
[1,6,4,5,7,3,8,2]=>[2,3,2,1]
[1,5,4,7,8,6,2,3]=>[2,3,1,2]
[7,3,1,6,8,2,5,4]=>[1,1,3,2,1]
[7,1,6,8,5,2,4,3]=>[1,3,1,2,1]
[3,5,8,7,6,4,1,2]=>[3,1,1,1,2]
[7,1,5,8,6,2,4,3]=>[1,3,1,2,1]
[1,5,7,8,6,2,4,3]=>[4,1,2,1]
[2,7,5,8,6,1,4,3]=>[2,2,1,2,1]
[4,3,6,2,1,7,8,5]=>[1,2,1,3,1]
[1,6,4,7,3,5,8,2]=>[2,2,3,1]
[4,6,2,3,1,7,8,5]=>[2,2,3,1]
[3,6,2,1,4,7,8,5]=>[2,1,4,1]
[6,8,2,7,5,4,3,1]=>[2,2,1,1,1,1]
[5,8,1,7,6,4,3,2]=>[2,2,1,1,1,1]
[8,6,3,2,1,5,4,7]=>[1,1,1,1,2,2]
[8,5,3,2,4,1,7,6]=>[1,1,1,2,2,1]
[7,5,2,4,3,6,8,1]=>[1,1,2,3,1]
[8,5,1,4,6,3,2,7]=>[1,1,3,1,2]
[8,5,1,6,3,4,2,7]=>[1,1,2,2,2]
[8,4,3,6,1,5,2,7]=>[1,1,2,2,2]
[8,4,3,5,2,1,7,6]=>[1,1,2,1,2,1]
[6,4,3,2,8,7,1,5]=>[1,1,1,2,1,2]
[8,5,1,4,3,7,2,6]=>[1,1,2,2,2]
[8,5,4,2,1,3,7,6]=>[1,1,1,1,3,1]
[4,7,3,6,1,8,5,2]=>[2,2,2,1,1]
[7,6,2,4,1,5,8,3]=>[1,1,2,3,1]
[8,1,6,3,7,4,2,5]=>[1,2,2,1,2]
[5,3,8,2,6,7,1,4]=>[1,2,3,2]
[8,2,5,1,7,6,3,4]=>[1,2,2,1,2]
[8,2,4,6,3,7,1,5]=>[1,3,2,2]
[7,2,6,4,3,5,8,1]=>[1,2,1,3,1]
[7,3,6,2,4,5,8,1]=>[1,2,4,1]
[8,3,7,2,1,4,6,5]=>[1,2,1,3,1]
[7,6,4,1,3,2,8,5]=>[1,1,1,2,2,1]
[7,3,8,2,1,5,6,4]=>[1,2,1,3,1]
[6,2,5,7,4,3,8,1]=>[1,3,1,2,1]
[6,2,5,4,8,7,1,3]=>[1,2,2,1,2]
[7,2,4,8,5,1,6,3]=>[1,3,1,2,1]
[4,2,7,6,8,5,1,3]=>[1,2,2,1,2]
[7,1,6,2,8,5,4,3]=>[1,2,2,1,1,1]
[7,1,6,3,8,5,2,4]=>[1,2,2,1,2]
[7,2,6,8,1,3,5,4]=>[1,3,3,1]
[7,2,8,5,1,3,6,4]=>[1,2,1,3,1]
[7,1,8,5,3,2,6,4]=>[1,2,1,1,2,1]
[7,1,8,2,5,6,4,3]=>[1,2,3,1,1]
[6,1,5,8,7,2,4,3]=>[1,3,1,2,1]
[6,1,5,7,4,8,3,2]=>[1,3,2,1,1]
[6,1,5,7,8,3,4,2]=>[1,4,2,1]
[4,6,7,3,1,8,5,2]=>[3,1,2,1,1]
[4,2,6,3,1,8,7,5]=>[1,2,1,2,1,1]
[6,1,4,2,5,8,7,3]=>[1,2,3,1,1]
[1,5,3,8,4,6,2,7]=>[2,2,2,2]
[7,2,3,5,8,4,1,6]=>[1,4,1,2]
[7,6,4,2,8,5,1,3]=>[1,1,1,2,1,2]
[1,7,6,4,8,5,3,2]=>[2,1,2,1,1,1]
[8,7,4,2,1,5,6,3]=>[1,1,1,1,3,1]
[8,2,3,5,1,4,6,7]=>[1,3,4]
[8,7,4,1,3,2,6,5]=>[1,1,1,2,2,1]
[7,1,4,8,3,6,2,5]=>[1,3,2,2]
[4,1,8,5,7,6,2,3]=>[1,2,2,1,2]
[3,7,5,8,4,2,1,6]=>[2,2,1,1,2]
[6,1,5,8,3,4,2,7]=>[1,3,2,2]
[6,7,5,1,3,2,4,8]=>[2,1,2,3]
[5,2,6,1,7,3,4,8]=>[1,2,2,3]
[4,2,6,8,3,7,1,5]=>[1,3,2,2]
[6,8,5,1,4,2,3,7]=>[2,1,2,3]
[7,8,4,5,1,3,6,2]=>[2,2,3,1]
[1,7,8,5,3,4,6,2]=>[3,1,3,1]
[1,5,8,3,6,4,7,2]=>[3,2,2,1]
[6,3,8,1,4,2,7,5]=>[1,2,2,2,1]
[4,8,1,5,6,3,7,2]=>[2,3,2,1]
[1,8,2,6,5,3,7,4]=>[2,2,1,2,1]
[3,8,1,7,2,6,5,4]=>[2,2,2,1,1]
[7,3,8,1,2,6,5,4]=>[1,2,3,1,1]
[8,1,4,2,3,5,7,6]=>[1,2,4,1]
[8,1,2,4,6,5,7,3]=>[1,4,2,1]
[6,2,8,3,5,4,7,1]=>[1,2,2,2,1]
[5,1,8,3,7,4,6,2]=>[1,2,2,2,1]
[8,3,7,1,5,4,6,2]=>[1,2,2,2,1]
[8,4,7,1,5,3,6,2]=>[1,2,2,2,1]
[8,2,7,3,5,1,6,4]=>[1,2,2,2,1]
[7,2,5,3,4,6,1,8]=>[1,2,3,2]
[7,4,3,1,6,2,5,8]=>[1,1,1,2,3]
[7,6,4,2,5,3,1,8]=>[1,1,1,2,1,2]
[5,8,4,3,6,2,7,1]=>[2,1,2,2,1]
[3,8,4,6,2,5,7,1]=>[2,2,3,1]
[1,7,2,6,3,4,8,5]=>[2,2,3,1]
[7,5,1,6,3,2,4,8]=>[1,1,2,1,3]
[7,1,2,6,3,4,5,8]=>[1,3,4]
[7,2,5,1,6,3,4,8]=>[1,2,2,3]
[7,3,1,4,6,2,5,8]=>[1,1,3,3]
[7,1,6,5,4,2,3,8]=>[1,2,1,1,3]
[5,8,4,3,1,7,2,6]=>[2,1,1,2,2]
[2,1,7,6,3,5,8,4]=>[1,2,1,3,1]
[3,6,8,5,2,4,7,1]=>[3,1,3,1]
[5,7,8,4,3,2,6,1]=>[3,1,1,2,1]
[1,4,8,6,5,7,3,2]=>[3,1,2,1,1]
[1,3,8,4,7,2,6,5]=>[3,2,2,1]
[2,5,8,3,4,7,1,6]=>[3,3,2]
[5,4,2,8,3,7,1,6]=>[1,1,2,2,2]
[5,3,1,7,6,8,4,2]=>[1,1,2,2,1,1]
[4,2,7,1,5,8,6,3]=>[1,2,3,1,1]
[6,1,7,4,3,8,5,2]=>[1,2,1,2,1,1]
[1,3,7,4,8,5,6,2]=>[3,2,2,1]
[3,2,1,4,5,8,6,7]=>[1,1,4,2]
[6,7,1,3,2,8,5,4]=>[2,2,2,1,1]
[1,5,3,2,6,8,4,7]=>[2,1,3,2]
[5,4,3,1,7,2,8,6]=>[1,1,1,2,2,1]
[5,1,4,2,3,6,8,7]=>[1,2,4,1]
[3,7,6,5,8,2,4,1]=>[2,1,2,2,1]
[5,7,4,2,8,6,1,3]=>[2,1,2,1,2]
[5,4,3,7,8,2,6,1]=>[1,1,3,2,1]
[2,3,7,8,6,1,4,5]=>[4,1,3]
[3,8,5,7,6,2,4,1]=>[2,2,1,2,1]
[1,3,6,8,7,2,5,4]=>[4,1,2,1]
[5,4,1,6,8,7,3,2]=>[1,1,3,1,1,1]
[5,7,8,6,2,4,3,1]=>[3,1,2,1,1]
[1,8,7,2,4,3,5,6]=>[2,1,2,3]
[6,2,5,1,4,7,3,8]=>[1,2,3,2]
[5,8,7,1,4,2,3,6]=>[2,1,2,3]
[7,5,2,4,1,8,6,3]=>[1,1,2,2,1,1]
[2,6,3,7,1,4,5,8]=>[2,2,4]
[8,2,3,5,4,1,6,7]=>[1,3,1,3]
[6,5,1,2,4,7,8,3]=>[1,1,5,1]
[6,1,3,7,8,2,4,5]=>[1,4,3]
[1,6,3,8,2,4,5,7]=>[2,2,4]
[7,6,4,3,5,1,8,2]=>[1,1,1,2,2,1]
[7,6,8,4,3,1,5,2]=>[1,2,1,1,2,1]
[3,8,6,1,4,2,5,7]=>[2,1,2,3]
[7,6,5,3,8,1,4,2]=>[1,1,1,2,2,1]
[1,7,6,5,3,2,4,8]=>[2,1,1,1,3]
[2,7,6,5,4,1,3,8]=>[2,1,1,1,3]
[2,8,6,4,5,1,3,7]=>[2,1,2,3]
[7,6,8,5,3,1,4,2]=>[1,2,1,1,2,1]
[8,4,2,1,6,7,3,5]=>[1,1,1,3,2]
[8,1,3,5,4,6,7,2]=>[1,3,3,1]
[3,8,2,5,4,6,1,7]=>[2,2,2,2]
[5,2,3,6,4,1,7,8]=>[1,3,1,3]
[8,1,2,6,7,3,4,5]=>[1,4,3]
[6,2,3,5,8,4,1,7]=>[1,4,1,2]
[3,7,6,8,4,1,5,2]=>[2,2,1,2,1]
[4,7,6,1,5,8,3,2]=>[2,1,3,1,1]
[1,5,6,8,2,4,3,7]=>[4,2,2]
[7,1,6,5,3,8,2,4]=>[1,2,1,2,2]
[1,7,6,4,2,5,8,3]=>[2,1,1,3,1]
[7,6,4,1,5,3,8,2]=>[1,1,1,2,2,1]
[6,8,7,1,5,4,3,2]=>[2,1,2,1,1,1]
[7,8,4,6,5,1,3,2]=>[2,2,1,2,1]
[8,7,4,6,5,1,3,2]=>[1,1,2,1,2,1]
[2,5,3,6,4,8,7,1]=>[2,2,2,1,1]
[2,5,3,7,4,8,6,1]=>[2,2,2,1,1]
[4,6,3,5,7,2,1,8]=>[2,3,1,2]
[4,3,7,2,1,8,5,6]=>[1,2,1,2,2]
[1,7,4,3,2,8,5,6]=>[2,1,1,2,2]
[7,4,6,3,5,8,1,2]=>[1,2,3,2]
[7,2,6,1,5,8,3,4]=>[1,2,3,2]
[7,2,6,1,8,5,4,3]=>[1,2,2,1,1,1]
[4,7,3,8,6,2,5,1]=>[2,2,1,2,1]
[4,7,3,6,8,2,1,5]=>[2,3,1,2]
[5,4,7,3,8,2,1,6]=>[1,2,2,1,2]
[8,3,7,2,4,6,5,1]=>[1,2,3,1,1]
[7,3,6,4,2,5,1,8]=>[1,2,1,2,2]
[8,7,2,4,6,3,5,1]=>[1,1,3,2,1]
[1,3,6,8,5,7,4,2]=>[4,2,1,1]
[6,3,5,8,2,4,1,7]=>[1,3,2,2]
[1,6,4,8,3,7,2,5]=>[2,2,2,2]
[7,3,6,2,8,5,4,1]=>[1,2,2,1,1,1]
[7,4,6,8,3,5,2,1]=>[1,3,2,1,1]
[4,3,5,7,2,6,1,8]=>[1,3,2,2]
[5,4,6,8,3,7,2,1]=>[1,3,2,1,1]
[1,7,2,8,5,4,3,6]=>[2,2,1,1,2]
[5,4,8,3,6,2,1,7]=>[1,2,2,1,2]
[1,3,8,5,7,4,6,2]=>[3,2,2,1]
[6,8,2,5,7,1,4,3]=>[2,3,2,1]
[5,7,2,4,6,1,3,8]=>[2,3,3]
[3,7,5,2,6,4,1,8]=>[2,1,2,1,2]
[3,8,6,2,7,5,1,4]=>[2,1,2,1,2]
[5,8,4,2,7,3,6,1]=>[2,1,2,2,1]
[1,8,6,3,5,2,4,7]=>[2,1,2,3]
[8,4,2,7,3,1,6,5]=>[1,1,2,1,2,1]
[7,4,2,6,3,1,5,8]=>[1,1,2,1,3]
[8,2,7,3,4,5,1,6]=>[1,2,3,2]
[8,1,5,2,4,6,3,7]=>[1,2,3,2]
[6,1,5,7,2,3,8,4]=>[1,3,3,1]
[8,6,1,3,4,5,7,2]=>[1,1,5,1]
[8,5,7,2,4,6,1,3]=>[1,2,3,2]
[6,1,3,7,2,5,8,4]=>[1,3,3,1]
[8,2,5,1,4,7,3,6]=>[1,2,3,2]
[8,1,3,6,4,2,5,7]=>[1,3,1,3]
[8,3,6,7,4,1,2,5]=>[1,3,1,3]
[8,5,1,2,4,6,7,3]=>[1,1,5,1]
[2,6,8,7,3,4,5,1]=>[3,1,3,1]
[1,7,8,3,6,4,2,5]=>[3,2,1,2]
[1,7,8,3,2,4,6,5]=>[3,1,3,1]
[1,7,8,5,6,4,2,3]=>[3,2,1,2]
[8,3,1,2,4,6,7,5]=>[1,1,5,1]
[3,1,7,5,8,2,4,6]=>[1,2,2,3]
[8,1,3,2,4,6,5,7]=>[1,2,3,2]
[3,2,6,5,8,1,4,7]=>[1,2,2,3]
[8,2,3,7,4,1,5,6]=>[1,3,1,3]
[8,1,5,6,4,2,3,7]=>[1,3,1,3]
[3,5,8,1,6,4,2,7]=>[3,2,1,2]
[3,5,8,2,7,4,1,6]=>[3,2,1,2]
[8,3,2,7,4,1,6,5]=>[1,1,2,1,2,1]
[6,5,1,7,3,2,8,4]=>[1,1,2,1,2,1]
[8,3,1,6,4,2,7,5]=>[1,1,2,1,2,1]
[8,2,7,5,4,3,1,6]=>[1,2,1,1,1,2]
[8,1,6,5,4,3,2,7]=>[1,2,1,1,1,2]
[2,6,8,1,5,4,3,7]=>[3,2,1,2]
[5,2,1,7,6,3,8,4]=>[1,1,2,1,2,1]
[3,5,8,2,1,4,7,6]=>[3,1,3,1]
[4,2,8,5,3,7,6,1]=>[1,2,1,2,1,1]
[4,2,7,5,3,8,6,1]=>[1,2,1,2,1,1]
[6,4,5,1,8,3,2,7]=>[1,2,2,1,2]
[5,4,7,8,3,1,2,6]=>[1,3,1,3]
[4,5,8,1,3,7,2,6]=>[3,3,2]
[1,5,3,6,8,7,2,4]=>[2,3,1,2]
[7,6,2,8,1,4,3,5]=>[1,1,2,2,2]
[4,7,2,6,8,3,5,1]=>[2,3,2,1]
[6,3,2,8,7,4,5,1]=>[1,1,2,1,2,1]
[7,4,3,8,5,6,2,1]=>[1,1,2,2,1,1]
[3,1,5,8,7,6,2,4]=>[1,3,1,1,2]
[8,2,1,6,5,7,3,4]=>[1,1,2,2,2]
[3,1,8,6,5,7,2,4]=>[1,2,1,2,2]
[1,2,7,6,4,5,8,3]=>[3,1,3,1]
[7,2,6,5,1,8,3,4]=>[1,2,1,2,2]
[4,2,8,5,6,3,1,7]=>[1,2,2,1,2]
[6,4,2,1,8,7,3,5]=>[1,1,1,2,1,2]
[4,7,3,2,5,1,6,8]=>[2,1,2,3]
[6,2,5,1,7,8,4,3]=>[1,2,3,1,1]
[4,2,5,3,8,7,1,6]=>[1,2,2,1,2]
[6,2,5,8,7,4,1,3]=>[1,3,1,1,2]
[7,2,5,3,8,1,4,6]=>[1,2,2,3]
[7,2,5,3,8,4,6,1]=>[1,2,2,2,1]
[3,7,5,2,6,1,4,8]=>[2,1,2,3]
[3,8,5,6,7,4,2,1]=>[2,3,1,1,1]
[3,8,5,2,6,1,4,7]=>[2,1,2,3]
[3,6,8,1,7,4,5,2]=>[3,2,2,1]
[6,3,4,1,8,7,2,5]=>[1,2,2,1,2]
[4,7,3,2,5,8,1,6]=>[2,1,3,2]
[8,7,3,2,5,4,6,1]=>[1,1,1,2,2,1]
[5,1,7,6,2,4,8,3]=>[1,2,1,3,1]
[5,4,7,3,1,6,8,2]=>[1,2,1,3,1]
[7,5,4,8,3,1,6,2]=>[1,1,2,1,2,1]
[3,4,8,1,6,5,2,7]=>[3,2,1,2]
[7,5,6,1,8,3,2,4]=>[1,2,2,1,2]
[4,5,6,2,7,3,1,8]=>[3,2,1,2]
[5,3,4,7,1,6,2,8]=>[1,3,2,2]
[5,3,7,2,1,6,8,4]=>[1,2,1,3,1]
[3,5,1,4,6,8,2,7]=>[2,4,2]
[4,3,7,1,6,5,2,8]=>[1,2,2,1,2]
[8,5,7,4,2,1,3,6]=>[1,2,1,1,3]
[7,6,3,2,5,4,8,1]=>[1,1,1,2,2,1]
[8,6,3,2,5,4,1,7]=>[1,1,1,2,1,2]
[8,5,3,6,7,4,1,2]=>[1,1,3,1,2]
[6,5,8,4,2,7,1,3]=>[1,2,1,2,2]
[2,3,7,4,1,8,6,5]=>[3,1,2,1,1]
[2,4,5,1,8,6,3,7]=>[3,2,1,2]
[2,4,1,6,7,5,3,8]=>[2,3,1,2]
[6,3,7,1,5,2,4,8]=>[1,2,2,3]
[4,1,3,7,8,2,6,5]=>[1,4,2,1]
[7,1,4,8,6,5,2,3]=>[1,3,1,1,2]
[8,3,4,2,1,7,5,6]=>[1,2,1,2,2]
[1,4,5,3,8,6,7,2]=>[3,2,2,1]
[4,6,2,7,5,8,1,3]=>[2,2,2,2]
[7,3,2,5,1,8,4,6]=>[1,1,2,2,2]
[7,8,1,4,2,3,5,6]=>[2,2,4]
[6,5,2,4,8,7,1,3]=>[1,1,3,1,2]
[8,5,2,4,1,3,7,6]=>[1,1,2,3,1]
[5,1,2,4,3,6,8,7]=>[1,3,3,1]
[5,2,1,4,3,7,6,8]=>[1,1,2,2,2]
[8,6,2,7,5,3,1,4]=>[1,1,2,1,1,2]
[6,2,1,5,8,3,4,7]=>[1,1,3,3]
[2,3,8,7,1,5,4,6]=>[3,1,2,2]
[4,3,8,1,5,2,6,7]=>[1,2,2,3]
[4,1,3,6,7,2,8,5]=>[1,4,2,1]
[7,1,4,5,8,2,6,3]=>[1,4,2,1]
[6,1,3,2,4,5,8,7]=>[1,2,4,1]
[7,8,1,6,5,2,4,3]=>[2,2,1,2,1]
[7,4,8,5,1,3,2,6]=>[1,2,1,2,2]
[7,4,8,6,5,1,2,3]=>[1,2,1,1,3]
[2,8,1,7,6,3,5,4]=>[2,2,1,2,1]
[3,4,8,6,5,1,2,7]=>[3,1,1,3]
[3,7,8,6,5,1,2,4]=>[3,1,1,3]
[5,7,8,2,6,3,1,4]=>[3,2,1,2]
[4,7,8,2,5,3,1,6]=>[3,2,1,2]
[8,4,5,7,2,6,3,1]=>[1,3,2,1,1]
[4,5,8,6,1,3,2,7]=>[3,1,2,2]
[3,6,8,7,1,5,2,4]=>[3,1,2,2]
[4,7,8,2,6,3,1,5]=>[3,2,1,2]
[5,6,8,2,7,3,1,4]=>[3,2,1,2]
[4,5,8,2,7,3,1,6]=>[3,2,1,2]
[4,8,3,1,7,5,2,6]=>[2,1,2,1,2]
[2,8,4,3,7,5,1,6]=>[2,1,2,1,2]
[7,5,4,8,3,2,1,6]=>[1,1,2,1,1,2]
[6,5,8,2,7,3,1,4]=>[1,2,2,1,2]
[6,4,8,2,7,3,1,5]=>[1,2,2,1,2]
[6,8,3,1,7,4,2,5]=>[2,1,2,1,2]
[7,8,3,1,6,4,2,5]=>[2,1,2,1,2]
[2,8,6,3,4,5,1,7]=>[2,1,3,2]
[7,8,1,3,6,4,2,5]=>[2,3,1,2]
[6,8,1,3,7,4,2,5]=>[2,3,1,2]
[5,3,8,6,1,4,2,7]=>[1,2,1,2,2]
[5,8,1,3,7,4,2,6]=>[2,3,1,2]
[5,3,8,2,7,4,1,6]=>[1,2,2,1,2]
[4,3,8,2,7,5,1,6]=>[1,2,2,1,2]
[4,5,7,8,3,2,1,6]=>[4,1,1,2]
[5,7,3,4,2,6,8,1]=>[2,2,3,1]
[5,7,4,2,3,6,8,1]=>[2,1,4,1]
[5,4,7,3,2,8,1,6]=>[1,2,1,2,2]
[6,8,3,2,4,5,1,7]=>[2,1,3,2]
[5,8,3,4,6,1,2,7]=>[2,3,3]
[6,4,3,8,5,1,2,7]=>[1,1,2,1,3]
[6,4,8,2,3,5,1,7]=>[1,2,3,2]
[5,4,6,8,2,3,1,7]=>[1,3,2,2]
[5,6,8,4,1,2,3,7]=>[3,1,4]
[6,4,8,5,1,2,3,7]=>[1,2,1,4]
[7,4,8,3,1,2,5,6]=>[1,2,1,4]
[5,7,8,2,3,1,4,6]=>[3,2,3]
[5,4,7,8,2,1,3,6]=>[1,3,1,3]
[5,8,6,3,1,2,4,7]=>[2,1,1,4]
[6,8,5,2,1,3,4,7]=>[2,1,1,4]
[5,6,1,3,2,4,8,7]=>[2,2,3,1]
[3,5,1,2,7,6,4,8]=>[2,3,1,2]
[4,1,3,7,2,6,5,8]=>[1,3,2,2]
[4,3,6,1,2,5,8,7]=>[1,2,4,1]
[8,1,5,4,6,2,7,3]=>[1,2,2,2,1]
[4,3,8,1,2,5,7,6]=>[1,2,4,1]
[7,4,3,2,5,8,6,1]=>[1,1,1,3,1,1]
[4,6,3,2,8,5,7,1]=>[2,1,2,2,1]
[1,4,3,2,6,8,5,7]=>[2,1,3,2]
[5,3,7,2,1,8,6,4]=>[1,2,1,2,1,1]
[7,4,3,2,5,1,8,6]=>[1,1,1,2,2,1]
[5,4,3,7,2,6,8,1]=>[1,1,2,3,1]
[5,4,8,3,7,2,1,6]=>[1,2,2,1,2]
[3,6,8,5,2,1,7,4]=>[3,1,1,2,1]
[6,1,5,4,7,2,8,3]=>[1,2,2,2,1]
[1,3,6,5,8,2,7,4]=>[3,2,2,1]
[1,4,3,6,2,8,5,7]=>[2,2,2,2]
[4,3,6,8,2,7,5,1]=>[1,3,2,1,1]
[7,6,4,1,2,8,5,3]=>[1,1,1,3,1,1]
[1,6,5,3,2,8,4,7]=>[2,1,1,2,2]
[1,5,3,2,7,8,6,4]=>[2,1,3,1,1]
[5,4,8,3,2,7,1,6]=>[1,2,1,2,2]
[5,4,3,7,2,1,6,8]=>[1,1,2,1,3]
[1,6,5,4,7,2,8,3]=>[2,1,2,2,1]
[3,6,5,7,2,1,8,4]=>[2,2,1,2,1]
[5,4,3,7,8,2,1,6]=>[1,1,3,1,2]
[1,4,8,6,3,2,7,5]=>[3,1,1,2,1]
[2,8,3,6,5,4,1,7]=>[2,2,1,1,2]
[4,1,8,6,2,5,7,3]=>[1,2,1,3,1]
[1,5,3,6,7,4,8,2]=>[2,3,2,1]
[6,7,2,5,3,8,4,1]=>[2,2,2,1,1]
[4,7,6,2,5,1,8,3]=>[2,1,2,2,1]
[4,6,3,1,5,7,8,2]=>[2,1,4,1]
[1,5,7,4,6,2,8,3]=>[3,2,2,1]
[6,3,4,8,1,2,7,5]=>[1,3,3,1]
[1,3,5,2,8,6,4,7]=>[3,2,1,2]
[6,2,8,1,7,4,5,3]=>[1,2,2,2,1]
[1,7,6,3,8,4,2,5]=>[2,1,2,1,2]
[5,2,4,6,8,3,1,7]=>[1,4,1,2]
[6,1,2,3,5,4,8,7]=>[1,4,2,1]
[2,5,4,3,7,8,1,6]=>[2,1,3,2]
[5,4,1,6,8,3,7,2]=>[1,1,3,2,1]
[7,1,6,8,3,5,4,2]=>[1,3,2,1,1]
[2,6,3,1,5,8,7,4]=>[2,1,3,1,1]
[7,2,1,4,8,6,3,5]=>[1,1,3,1,2]
[1,6,2,3,5,4,8,7]=>[2,3,2,1]
[7,2,6,5,3,4,8,1]=>[1,2,1,3,1]
[7,1,3,2,6,5,8,4]=>[1,2,2,2,1]
[7,3,1,2,5,6,8,4]=>[1,1,5,1]
[2,7,1,3,4,6,8,5]=>[2,5,1]
[6,8,5,7,3,4,2,1]=>[2,2,2,1,1]
[5,1,6,8,4,7,3,2]=>[1,3,2,1,1]
[2,4,1,8,7,6,3,5]=>[2,2,1,1,2]
[1,3,5,8,4,7,2,6]=>[4,2,2]
[2,3,8,7,5,1,6,4]=>[3,1,1,2,1]
[5,8,7,2,4,1,3,6]=>[2,1,2,3]
[4,1,3,5,6,2,8,7]=>[1,4,2,1]
[8,2,4,6,1,3,7,5]=>[1,3,3,1]
[6,4,8,7,3,5,2,1]=>[1,2,1,2,1,1]
[8,2,3,5,6,1,4,7]=>[1,4,3]
[8,2,3,4,6,1,7,5]=>[1,4,2,1]
[1,7,4,3,5,2,8,6]=>[2,1,2,2,1]
[3,8,2,7,6,4,1,5]=>[2,2,1,1,2]
[4,3,8,6,2,7,1,5]=>[1,2,1,2,2]
[3,1,6,8,2,7,5,4]=>[1,3,2,1,1]
[5,8,7,2,4,6,1,3]=>[2,1,3,2]
[1,5,2,8,7,6,4,3]=>[2,2,1,1,1,1]
[2,7,1,4,6,5,3,8]=>[2,3,1,2]
[4,7,1,2,6,5,8,3]=>[2,3,2,1]
[6,5,8,3,7,4,2,1]=>[1,2,2,1,1,1]
[8,3,4,5,1,6,7,2]=>[1,3,3,1]
[7,8,1,5,6,3,2,4]=>[2,3,1,2]
[1,7,8,3,2,5,4,6]=>[3,1,2,2]
[7,8,1,3,2,5,6,4]=>[2,2,3,1]
[7,8,1,3,5,4,6,2]=>[2,3,2,1]
[7,8,1,3,5,2,4,6]=>[2,3,3]
[1,3,7,8,5,2,4,6]=>[4,1,3]
[1,7,8,3,5,2,6,4]=>[3,2,2,1]
[1,7,8,3,2,5,6,4]=>[3,1,3,1]
[3,7,8,5,4,6,1,2]=>[3,1,2,2]
[3,5,7,6,4,8,1,2]=>[3,1,2,2]
[1,3,7,8,5,4,6,2]=>[4,1,2,1]
[1,3,7,8,5,4,2,6]=>[4,1,1,2]
[1,3,7,8,2,5,4,6]=>[4,2,2]
[1,3,2,7,8,5,4,6]=>[2,3,1,2]
[1,5,7,6,8,3,2,4]=>[3,2,1,2]
[3,5,4,7,8,6,1,2]=>[2,3,1,2]
[3,5,7,6,8,4,1,2]=>[3,2,1,2]
[1,5,7,6,8,3,4,2]=>[3,2,2,1]
[3,5,7,4,6,8,1,2]=>[3,3,2]
[6,1,4,3,2,5,8,7]=>[1,2,1,3,1]
[7,4,2,1,3,6,5,8]=>[1,1,1,3,2]
[6,5,8,4,3,7,1,2]=>[1,2,1,2,2]
[5,3,6,7,8,4,1,2]=>[1,4,1,2]
[3,7,8,4,6,5,1,2]=>[3,2,1,2]
[5,2,7,6,3,8,1,4]=>[1,2,1,2,2]
[6,2,5,7,1,8,4,3]=>[1,3,2,1,1]
[1,8,3,2,4,6,5,7]=>[2,1,3,2]
[5,8,6,2,3,7,1,4]=>[2,1,3,2]
[1,4,8,3,6,7,2,5]=>[3,3,2]
[6,7,3,1,5,2,4,8]=>[2,1,2,3]
[5,2,4,1,8,3,6,7]=>[1,2,2,3]
[3,5,6,7,2,1,8,4]=>[4,1,2,1]
[6,2,8,5,3,1,4,7]=>[1,2,1,1,3]
[2,1,7,4,3,8,5,6]=>[1,2,1,2,2]
[1,4,2,8,3,6,7,5]=>[2,2,3,1]
[6,5,1,3,4,7,8,2]=>[1,1,5,1]
[7,2,3,8,5,4,1,6]=>[1,3,1,1,2]
[3,4,1,7,8,2,6,5]=>[2,3,2,1]
[7,8,3,1,4,5,6,2]=>[2,1,4,1]
[5,8,1,4,3,7,6,2]=>[2,2,2,1,1]
[3,7,1,5,6,4,8,2]=>[2,3,2,1]
[6,1,8,7,3,2,5,4]=>[1,2,1,1,2,1]
[4,1,5,2,7,8,6,3]=>[1,2,3,1,1]
[7,8,1,5,6,2,4,3]=>[2,3,2,1]
[4,1,5,7,6,3,8,2]=>[1,3,1,2,1]
[1,5,7,4,6,8,2,3]=>[3,3,2]
[1,4,8,2,3,6,5,7]=>[3,3,2]
[1,4,7,3,2,6,5,8]=>[3,1,2,2]
[1,4,6,7,3,5,2,8]=>[4,2,2]
[1,5,3,4,8,2,7,6]=>[2,3,2,1]
[1,4,8,2,6,7,5,3]=>[3,3,1,1]
[1,4,7,8,2,3,6,5]=>[4,3,1]
[2,8,3,5,7,1,4,6]=>[2,3,3]
[1,7,3,2,4,5,6,8]=>[2,1,5]
[7,4,6,2,3,1,5,8]=>[1,2,2,3]
[6,1,4,7,8,3,2,5]=>[1,4,1,2]
[1,7,3,2,4,5,8,6]=>[2,1,4,1]
[1,4,8,7,3,2,6,5]=>[3,1,1,2,1]
[1,6,4,3,2,5,7,8]=>[2,1,1,4]
[4,2,6,5,3,1,7,8]=>[1,2,1,1,3]
[6,5,2,3,4,1,8,7]=>[1,1,3,2,1]
[5,2,1,6,8,7,4,3]=>[1,1,3,1,1,1]
[1,3,5,8,6,2,7,4]=>[4,1,2,1]
[2,3,8,4,1,7,6,5]=>[3,1,2,1,1]
[2,5,1,7,8,4,3,6]=>[2,3,1,2]
[3,7,8,5,4,2,6,1]=>[3,1,1,2,1]
[4,7,5,2,3,1,6,8]=>[2,1,2,3]
[8,3,2,7,5,6,1,4]=>[1,1,2,2,2]
[3,6,7,4,1,5,2,8]=>[3,1,2,2]
[3,5,7,1,6,2,8,4]=>[3,2,2,1]
[1,3,8,5,7,4,2,6]=>[3,2,1,2]
[1,2,3,7,5,4,6,8]=>[4,1,3]
[1,4,2,8,6,3,5,7]=>[2,2,1,3]
[1,7,6,5,3,4,2,8]=>[2,1,1,2,2]
[2,3,8,6,5,4,1,7]=>[3,1,1,1,2]
[2,8,6,3,5,7,4,1]=>[2,1,3,1,1]
[2,6,7,4,3,1,8,5]=>[3,1,1,2,1]
[2,8,6,7,4,1,5,3]=>[2,2,1,2,1]
[6,1,8,2,5,3,4,7]=>[1,2,2,3]
[2,6,1,5,7,3,4,8]=>[2,3,3]
[3,6,1,5,2,7,4,8]=>[2,2,2,2]
[3,8,6,4,2,7,1,5]=>[2,1,1,2,2]
[3,8,6,2,1,7,5,4]=>[2,1,1,2,1,1]
[1,8,2,5,7,4,6,3]=>[2,3,2,1]
[5,2,4,8,3,1,7,6]=>[1,3,1,2,1]
[2,5,8,4,3,1,6,7]=>[3,1,1,3]
[4,1,8,7,2,5,6,3]=>[1,2,1,3,1]
[1,5,4,2,3,6,8,7]=>[2,1,4,1]
[6,1,5,2,3,4,8,7]=>[1,2,4,1]
[4,6,2,8,1,5,7,3]=>[2,2,3,1]
[3,4,1,8,2,5,7,6]=>[2,2,3,1]
[4,2,1,8,5,3,7,6]=>[1,1,2,1,2,1]
[2,5,8,7,6,4,1,3]=>[3,1,1,1,2]
[3,1,8,2,4,6,7,5]=>[1,2,4,1]
[6,5,2,1,7,3,4,8]=>[1,1,1,2,3]
[5,2,6,8,7,3,1,4]=>[1,3,1,1,2]
[2,7,8,6,3,4,1,5]=>[3,1,2,2]
[3,1,2,8,6,7,5,4]=>[1,3,2,1,1]
[3,1,2,4,8,6,7,5]=>[1,4,2,1]
[3,1,2,5,8,7,4,6]=>[1,4,1,2]
[6,5,2,1,8,4,7,3]=>[1,1,1,2,2,1]
[5,6,2,4,3,8,1,7]=>[2,2,2,2]
[3,7,5,2,8,1,4,6]=>[2,1,2,3]
[7,4,1,3,6,2,8,5]=>[1,1,3,2,1]
[5,1,4,7,3,2,8,6]=>[1,3,1,2,1]
[2,3,5,4,8,6,1,7]=>[3,2,1,2]
[2,3,5,7,4,8,1,6]=>[4,2,2]
[3,7,6,1,2,5,8,4]=>[2,1,4,1]
[4,7,1,6,8,5,3,2]=>[2,3,1,1,1]
[4,1,5,8,6,2,3,7]=>[1,3,1,3]
[5,4,8,6,3,7,1,2]=>[1,2,1,2,2]
[5,7,3,4,8,2,6,1]=>[2,3,2,1]
[6,5,2,3,7,4,1,8]=>[1,1,3,1,2]
[6,5,2,3,1,8,7,4]=>[1,1,2,2,1,1]
[6,5,3,7,4,1,2,8]=>[1,1,2,1,3]
[6,4,7,5,3,8,1,2]=>[1,2,1,2,2]
[5,7,6,4,8,3,1,2]=>[2,1,2,1,2]
[5,7,4,8,3,1,6,2]=>[2,2,1,2,1]
[3,1,4,7,5,2,8,6]=>[1,3,1,2,1]
[3,1,4,7,2,8,6,5]=>[1,3,2,1,1]
[3,1,5,4,8,6,2,7]=>[1,2,2,1,2]
[3,1,7,5,4,6,2,8]=>[1,2,1,2,2]
[2,5,6,3,7,4,1,8]=>[3,2,1,2]
[4,3,1,7,5,6,2,8]=>[1,1,2,2,2]
[4,3,1,5,8,6,2,7]=>[1,1,3,1,2]
[4,3,5,1,8,7,2,6]=>[1,2,2,1,2]
[2,5,3,1,6,7,4,8]=>[2,1,3,2]
[2,5,3,6,1,8,4,7]=>[2,2,2,2]
[2,5,6,4,1,8,3,7]=>[3,1,2,2]
[4,6,2,1,5,7,3,8]=>[2,1,3,2]
[4,8,1,5,7,3,2,6]=>[2,3,1,2]
[6,4,2,7,8,3,1,5]=>[1,1,3,1,2]
[2,5,6,7,4,1,8,3]=>[4,1,2,1]
[2,5,6,8,3,1,7,4]=>[4,1,2,1]
[7,1,4,5,3,6,2,8]=>[1,3,2,2]
[1,7,2,4,5,3,6,8]=>[2,3,3]
[1,7,4,5,3,2,6,8]=>[2,2,1,3]
[1,6,4,7,3,5,2,8]=>[2,2,2,2]
[3,5,6,4,8,2,1,7]=>[3,2,1,2]
[1,6,4,7,5,2,3,8]=>[2,2,1,3]
[1,5,2,6,7,4,3,8]=>[2,3,1,2]
[8,5,6,1,4,3,7,2]=>[1,2,2,2,1]
[2,5,4,7,8,3,1,6]=>[2,3,1,2]
[5,6,4,8,2,1,3,7]=>[2,2,1,3]
[6,4,5,8,2,3,1,7]=>[1,3,2,2]
[8,6,1,3,2,5,7,4]=>[1,1,2,3,1]
[7,5,8,1,4,6,3,2]=>[1,2,3,1,1]
[4,2,6,7,8,1,5,3]=>[1,4,2,1]
[4,7,8,2,5,1,6,3]=>[3,2,2,1]
[3,7,8,2,5,1,4,6]=>[3,2,3]
[3,4,6,7,8,1,5,2]=>[5,2,1]
[2,5,3,7,8,1,4,6]=>[2,3,3]
[5,6,3,8,1,2,4,7]=>[2,2,4]
[4,7,3,8,5,1,6,2]=>[2,2,1,2,1]
[4,3,2,7,5,8,1,6]=>[1,1,2,2,2]
[4,8,5,3,2,6,1,7]=>[2,1,1,2,2]
[2,8,4,5,3,6,1,7]=>[2,2,2,2]
[8,1,5,3,2,4,7,6]=>[1,2,1,3,1]
[4,7,3,8,2,1,6,5]=>[2,2,1,2,1]
[7,8,4,1,3,6,5,2]=>[2,1,3,1,1]
[8,6,1,3,2,7,4,5]=>[1,1,2,2,2]
[7,3,8,2,4,1,6,5]=>[1,2,2,2,1]
[6,2,3,7,8,1,5,4]=>[1,4,2,1]
[6,3,7,8,1,5,4,2]=>[1,3,2,1,1]
[2,6,3,7,8,1,5,4]=>[2,3,2,1]
[7,5,8,1,6,4,2,3]=>[1,2,2,1,2]
[1,4,7,3,8,5,2,6]=>[3,2,1,2]
[8,1,4,3,7,5,6,2]=>[1,2,2,2,1]
[1,4,8,5,3,2,6,7]=>[3,1,1,3]
[8,2,7,6,4,1,5,3]=>[1,2,1,1,2,1]
[2,7,4,3,8,5,1,6]=>[2,1,2,1,2]
[5,2,1,7,8,4,3,6]=>[1,1,3,1,2]
[2,7,1,8,6,4,5,3]=>[2,2,1,2,1]
[2,4,7,6,3,8,5,1]=>[3,1,2,1,1]
[7,2,6,1,8,3,5,4]=>[1,2,2,2,1]
[6,3,8,7,1,5,2,4]=>[1,2,1,2,2]
[6,8,2,7,3,1,5,4]=>[2,2,1,2,1]
[6,8,1,4,7,5,3,2]=>[2,3,1,1,1]
[7,6,1,2,8,5,3,4]=>[1,1,3,1,2]
[7,3,1,8,4,6,5,2]=>[1,1,2,2,1,1]
[7,2,4,8,3,6,5,1]=>[1,3,2,1,1]
[8,2,6,3,4,1,7,5]=>[1,2,2,2,1]
[6,1,2,8,5,3,7,4]=>[1,3,1,2,1]
[4,1,8,7,3,5,6,2]=>[1,2,1,3,1]
[4,1,5,8,3,6,7,2]=>[1,3,3,1]
[4,7,2,6,8,3,1,5]=>[2,3,1,2]
[7,5,2,8,1,6,3,4]=>[1,1,2,2,2]
[4,8,5,7,1,3,2,6]=>[2,2,2,2]
[3,4,7,2,1,5,8,6]=>[3,1,3,1]
[4,8,2,7,1,3,6,5]=>[2,2,3,1]
[5,2,1,8,7,4,6,3]=>[1,1,2,1,2,1]
[8,2,1,7,4,6,3,5]=>[1,1,2,2,2]
[4,2,5,8,3,6,7,1]=>[1,3,3,1]
[5,1,6,8,3,2,7,4]=>[1,3,1,2,1]
[4,1,5,6,8,2,7,3]=>[1,4,2,1]
[4,7,8,3,1,2,5,6]=>[3,1,4]
[5,7,8,2,4,1,3,6]=>[3,2,3]
[4,5,2,8,7,3,1,6]=>[2,2,1,1,2]
[5,8,2,3,6,4,7,1]=>[2,3,2,1]
[4,5,7,6,8,2,3,1]=>[3,2,2,1]
[4,8,5,3,1,6,7,2]=>[2,1,1,3,1]
[6,2,3,1,7,8,5,4]=>[1,2,3,1,1]
[5,2,3,8,7,4,6,1]=>[1,3,1,2,1]
[5,2,3,6,8,4,7,1]=>[1,4,2,1]
[8,2,1,7,3,4,6,5]=>[1,1,2,3,1]
[6,2,1,7,8,4,3,5]=>[1,1,3,1,2]
[5,2,1,3,8,4,7,6]=>[1,1,3,2,1]
[5,2,7,8,4,1,6,3]=>[1,3,1,2,1]
[6,2,7,8,3,5,4,1]=>[1,3,2,1,1]
[5,2,8,6,4,1,7,3]=>[1,2,1,1,2,1]
[8,1,7,3,2,4,6,5]=>[1,2,1,3,1]
[5,1,2,8,4,3,7,6]=>[1,3,1,2,1]
[5,7,8,3,4,1,6,2]=>[3,2,2,1]
[6,7,8,3,2,5,4,1]=>[3,1,2,1,1]
[5,7,2,6,4,8,1,3]=>[2,2,2,2]
[6,2,3,4,7,8,5,1]=>[1,5,1,1]
[7,2,1,8,4,3,5,6]=>[1,1,2,1,3]
[6,2,1,3,7,5,8,4]=>[1,1,3,2,1]
[6,8,7,3,4,5,1,2]=>[2,1,3,2]
[6,2,3,7,8,1,4,5]=>[1,4,3]
[7,4,3,2,5,8,1,6]=>[1,1,1,3,2]
[7,2,4,3,5,8,1,6]=>[1,2,3,2]
[1,3,7,4,2,5,6,8]=>[3,1,4]
[1,3,8,6,4,2,7,5]=>[3,1,1,2,1]
[1,3,5,8,4,2,7,6]=>[4,1,2,1]
[1,3,8,4,5,2,7,6]=>[3,2,2,1]
[1,7,6,2,3,5,4,8]=>[2,1,3,2]
[1,7,6,4,2,3,5,8]=>[2,1,1,4]
[1,3,2,5,8,6,4,7]=>[2,3,1,2]
[6,1,4,7,2,8,5,3]=>[1,3,2,1,1]
[1,7,5,8,4,2,3,6]=>[2,2,1,3]
[1,6,7,2,4,8,5,3]=>[3,3,1,1]
[5,7,2,4,3,6,8,1]=>[2,2,3,1]
[5,7,3,4,6,2,8,1]=>[2,3,2,1]
[2,8,3,6,1,7,4,5]=>[2,2,2,2]
[4,3,1,8,5,2,6,7]=>[1,1,2,1,3]
[1,8,4,5,6,2,7,3]=>[2,3,2,1]
[7,3,8,2,1,4,5,6]=>[1,2,1,4]
[8,2,5,3,1,7,4,6]=>[1,2,1,2,2]
[6,3,5,8,1,7,4,2]=>[1,3,2,1,1]
[3,5,4,8,6,1,7,2]=>[2,2,1,2,1]
[7,5,2,3,8,4,6,1]=>[1,1,3,2,1]
[2,7,5,1,4,8,3,6]=>[2,1,3,2]
[5,7,6,1,2,8,3,4]=>[2,1,3,2]
[7,4,6,5,1,8,2,3]=>[1,2,1,2,2]
[2,8,4,1,7,3,6,5]=>[2,1,2,2,1]
[7,1,3,2,6,8,4,5]=>[1,2,3,2]
[4,3,5,2,8,1,6,7]=>[1,2,2,3]
[1,7,3,8,2,4,6,5]=>[2,2,3,1]
[2,7,4,8,5,3,1,6]=>[2,2,1,1,2]
[6,1,3,8,4,2,7,5]=>[1,3,1,2,1]
[5,4,1,8,6,2,7,3]=>[1,1,2,1,2,1]
[5,4,6,8,1,3,2,7]=>[1,3,2,2]
[3,6,1,5,8,4,7,2]=>[2,3,2,1]
[6,4,8,3,5,7,2,1]=>[1,2,3,1,1]
[3,5,8,2,4,1,7,6]=>[3,2,2,1]
[7,2,8,4,1,3,6,5]=>[1,2,1,3,1]
[5,8,1,2,4,3,6,7]=>[2,3,3]
[3,6,5,4,7,1,2,8]=>[2,1,2,3]
[8,4,6,3,5,7,2,1]=>[1,2,3,1,1]
[6,1,7,4,3,2,5,8]=>[1,2,1,1,3]
[2,7,4,6,3,5,1,8]=>[2,2,2,2]
[4,7,2,6,1,5,3,8]=>[2,2,2,2]
[8,3,6,2,7,5,1,4]=>[1,2,2,1,2]
[2,8,4,7,3,1,6,5]=>[2,2,1,2,1]
[2,8,7,3,6,1,5,4]=>[2,1,2,2,1]
[7,1,8,5,4,6,3,2]=>[1,2,1,2,1,1]
[7,6,2,5,1,8,4,3]=>[1,1,2,2,1,1]
[1,8,4,7,5,3,6,2]=>[2,2,1,2,1]
[6,5,2,8,4,1,7,3]=>[1,1,2,1,2,1]
[2,8,5,7,1,4,6,3]=>[2,2,3,1]
[4,1,5,8,3,7,2,6]=>[1,3,2,2]
[2,6,8,5,7,1,4,3]=>[3,2,2,1]
[8,6,3,5,7,2,4,1]=>[1,1,3,2,1]
[1,5,4,6,8,3,7,2]=>[2,3,2,1]
[8,4,3,5,7,2,6,1]=>[1,1,3,2,1]
[4,1,5,2,3,8,7,6]=>[1,2,3,1,1]
[1,7,6,8,3,5,2,4]=>[2,2,2,2]
[1,4,8,3,5,7,2,6]=>[3,3,2]
[7,4,6,3,5,8,2,1]=>[1,2,3,1,1]
[3,7,2,6,1,8,5,4]=>[2,2,2,1,1]
[7,3,6,2,8,5,1,4]=>[1,2,2,1,2]
[6,3,5,8,2,4,7,1]=>[1,3,3,1]
[1,6,8,3,5,7,2,4]=>[3,3,2]
[1,4,8,6,3,7,5,2]=>[3,1,2,1,1]
[4,8,3,7,5,2,6,1]=>[2,2,1,2,1]
[2,8,7,1,4,6,3,5]=>[2,1,3,2]
[6,5,8,2,4,7,1,3]=>[1,2,3,2]
[4,3,8,6,2,7,5,1]=>[1,2,1,2,1,1]
[1,8,5,3,7,4,2,6]=>[2,1,2,1,2]
[6,8,1,3,5,2,4,7]=>[2,3,3]
[7,5,6,2,8,4,3,1]=>[1,2,2,1,1,1]
[8,6,2,1,7,4,3,5]=>[1,1,1,2,1,2]
[8,3,5,1,6,7,4,2]=>[1,2,3,1,1]
[5,7,6,2,8,1,4,3]=>[2,1,2,2,1]
[8,6,7,2,5,4,1,3]=>[1,2,2,1,2]
[4,3,8,7,5,1,2,6]=>[1,2,1,1,3]
[6,3,8,1,2,5,4,7]=>[1,2,3,2]
[8,2,5,1,6,7,4,3]=>[1,2,3,1,1]
[8,1,5,2,6,7,4,3]=>[1,2,3,1,1]
[7,8,2,6,3,4,5,1]=>[2,2,3,1]
[7,6,4,8,5,3,2,1]=>[1,1,2,1,1,1,1]
[7,6,5,3,8,4,2,1]=>[1,1,1,2,1,1,1]
[7,6,5,4,2,8,3,1]=>[1,1,1,1,2,1,1]
[7,5,4,8,6,3,2,1]=>[1,1,2,1,1,1,1]
[7,6,5,3,2,8,4,1]=>[1,1,1,1,2,1,1]
[1,5,7,2,4,3,6,8]=>[3,2,3]
[1,6,5,3,2,4,7,8]=>[2,1,1,4]
[1,7,2,4,6,5,3,8]=>[2,3,1,2]
[1,4,7,2,6,5,3,8]=>[3,2,1,2]
[1,2,6,8,7,4,3,5]=>[4,1,1,2]
[1,2,7,4,3,5,8,6]=>[3,1,3,1]
[1,6,2,8,7,4,3,5]=>[2,2,1,1,2]
[1,7,4,2,3,5,8,6]=>[2,1,4,1]
[1,8,5,2,3,6,4,7]=>[2,1,3,2]
[1,7,4,8,5,2,3,6]=>[2,2,1,3]
[1,4,7,5,2,8,6,3]=>[3,1,2,1,1]
[1,6,3,7,4,2,8,5]=>[2,2,1,2,1]
[1,8,5,2,7,4,3,6]=>[2,1,2,1,2]
[1,4,8,7,5,3,2,6]=>[3,1,1,1,2]
[1,2,5,8,6,3,7,4]=>[4,1,2,1]
[1,2,4,7,5,8,6,3]=>[4,2,1,1]
[1,5,8,7,6,2,4,3]=>[3,1,1,2,1]
[1,3,5,8,7,6,2,4]=>[4,1,1,2]
[1,5,2,4,3,6,8,7]=>[2,2,3,1]
[1,6,8,7,5,3,2,4]=>[3,1,1,1,2]
[1,2,5,7,4,3,8,6]=>[4,1,2,1]
[1,5,3,2,6,8,7,4]=>[2,1,3,1,1]
[1,4,2,6,8,7,5,3]=>[2,3,1,1,1]
[1,5,8,6,3,2,7,4]=>[3,1,1,2,1]
[1,8,5,2,6,3,4,7]=>[2,1,2,3]
[1,7,4,6,3,2,8,5]=>[2,2,1,2,1]
[1,6,3,2,8,5,4,7]=>[2,1,2,1,2]
[1,3,8,6,4,2,5,7]=>[3,1,1,3]
[1,5,7,4,2,3,8,6]=>[3,1,3,1]
[6,3,7,5,4,2,8,1]=>[1,2,1,1,2,1]
[7,5,2,6,3,4,8,1]=>[1,1,2,3,1]
[3,8,2,7,5,4,1,6]=>[2,2,1,1,2]
[5,4,8,6,7,1,2,3]=>[1,2,2,3]
[8,6,2,4,1,7,5,3]=>[1,1,2,2,1,1]
[2,7,3,6,8,5,4,1]=>[2,3,1,1,1]
[3,7,2,8,1,6,4,5]=>[2,2,2,2]
[6,3,1,2,5,8,7,4]=>[1,1,4,1,1]
[8,5,2,4,6,7,3,1]=>[1,1,4,1,1]
[2,5,8,7,1,4,3,6]=>[3,1,2,2]
[6,1,5,8,2,4,3,7]=>[1,3,2,2]
[3,4,6,5,8,2,7,1]=>[3,2,2,1]
[5,2,4,1,6,7,8,3]=>[1,2,4,1]
[4,2,7,1,6,8,3,5]=>[1,2,3,2]
[5,2,8,6,4,7,1,3]=>[1,2,1,2,2]
[4,7,5,1,6,3,8,2]=>[2,1,2,2,1]
[8,5,1,3,6,2,7,4]=>[1,1,3,2,1]
[8,2,1,3,6,7,4,5]=>[1,1,4,2]
[8,5,7,2,3,1,4,6]=>[1,2,2,3]
[6,1,3,4,7,2,8,5]=>[1,4,2,1]
[8,4,7,1,5,3,2,6]=>[1,2,2,1,2]
[8,4,7,2,5,3,1,6]=>[1,2,2,1,2]
[8,3,4,5,2,1,7,6]=>[1,3,1,2,1]
[6,3,4,7,2,1,5,8]=>[1,3,1,3]
[5,3,6,7,2,8,1,4]=>[1,3,2,2]
[3,4,2,6,1,8,7,5]=>[2,2,2,1,1]
[8,6,1,4,7,3,5,2]=>[1,1,3,2,1]
[5,3,6,7,2,8,4,1]=>[1,3,2,1,1]
[5,3,6,7,2,4,8,1]=>[1,3,3,1]
[5,3,6,7,2,4,1,8]=>[1,3,2,2]
[3,8,2,5,6,7,4,1]=>[2,4,1,1]
[3,8,4,1,6,7,2,5]=>[2,1,3,2]
[5,3,6,7,8,1,2,4]=>[1,4,3]
[2,8,3,6,1,4,7,5]=>[2,2,3,1]
[8,6,3,1,7,2,5,4]=>[1,1,1,2,2,1]
[8,6,4,2,7,1,5,3]=>[1,1,1,2,2,1]
[5,6,2,7,1,4,3,8]=>[2,2,2,2]
[5,3,6,7,4,1,2,8]=>[1,3,1,3]
[8,6,3,4,7,5,1,2]=>[1,1,3,1,2]
[8,6,1,4,7,5,2,3]=>[1,1,3,1,2]
[5,1,8,2,6,7,4,3]=>[1,2,3,1,1]
[3,8,5,1,6,7,4,2]=>[2,1,3,1,1]
[4,1,5,6,7,3,8,2]=>[1,4,2,1]
[4,1,5,6,7,3,2,8]=>[1,4,1,2]
[2,8,1,5,6,7,4,3]=>[2,4,1,1]
[1,5,8,2,6,7,4,3]=>[3,3,1,1]
[5,8,6,1,7,4,3,2]=>[2,1,2,1,1,1]
[8,5,2,6,7,4,3,1]=>[1,1,3,1,1,1]
[8,5,3,6,7,4,2,1]=>[1,1,3,1,1,1]
[7,1,3,6,5,2,8,4]=>[1,3,1,2,1]
[8,2,1,4,5,7,6,3]=>[1,1,4,1,1]
[1,4,7,5,2,3,8,6]=>[3,1,3,1]
[6,1,7,5,4,2,8,3]=>[1,2,1,1,2,1]
[2,7,3,6,5,1,8,4]=>[2,2,1,2,1]
[8,6,5,1,3,7,4,2]=>[1,1,1,3,1,1]
[5,7,6,2,4,8,1,3]=>[2,1,3,2]
[3,7,5,6,4,8,1,2]=>[2,2,2,2]
[7,6,8,1,3,5,4,2]=>[1,2,3,1,1]
[2,8,4,6,1,7,5,3]=>[2,2,2,1,1]
[2,8,6,4,7,3,5,1]=>[2,1,2,2,1]
[8,7,1,4,6,5,3,2]=>[1,1,3,1,1,1]
[3,5,8,6,7,1,4,2]=>[3,2,2,1]
[1,2,4,6,8,5,3,7]=>[5,1,2]
[3,1,5,8,6,2,4,7]=>[1,3,1,3]
[2,5,4,6,8,1,3,7]=>[2,3,3]
[6,5,2,4,7,8,1,3]=>[1,1,4,2]
[7,2,5,8,6,4,1,3]=>[1,3,1,1,2]
[5,2,8,3,4,7,6,1]=>[1,2,3,1,1]
[2,4,3,8,7,1,6,5]=>[2,2,1,2,1]
[1,5,8,7,4,2,6,3]=>[3,1,1,2,1]
[6,8,7,5,4,3,1,2]=>[2,1,1,1,1,2]
[5,3,4,8,6,2,7,1]=>[1,3,1,2,1]
[4,5,2,6,3,8,7,1]=>[2,2,2,1,1]
[4,3,5,8,6,2,7,1]=>[1,3,1,2,1]
[3,4,5,8,6,2,7,1]=>[4,1,2,1]
[5,2,6,3,4,8,7,1]=>[1,2,3,1,1]
[7,6,1,5,2,4,8,3]=>[1,1,2,3,1]
[5,4,2,3,6,1,8,7]=>[1,1,3,2,1]
[4,1,7,3,2,6,8,5]=>[1,2,1,3,1]
[6,1,8,5,4,7,2,3]=>[1,2,1,2,2]
[5,1,7,4,3,6,8,2]=>[1,2,1,3,1]
[8,1,5,7,6,4,2,3]=>[1,3,1,1,2]
[4,3,7,6,8,2,1,5]=>[1,2,2,1,2]
[8,1,4,7,2,3,5,6]=>[1,3,4]
[3,2,7,1,5,6,8,4]=>[1,2,4,1]
[6,1,8,5,2,7,3,4]=>[1,2,1,2,2]
[8,7,2,6,3,1,4,5]=>[1,1,2,1,3]
[6,5,2,4,7,1,8,3]=>[1,1,3,2,1]
[5,4,2,3,7,1,8,6]=>[1,1,3,2,1]
[8,7,1,6,4,5,2,3]=>[1,1,2,2,2]
[5,4,1,3,7,2,8,6]=>[1,1,3,2,1]
[6,5,1,4,7,3,8,2]=>[1,1,3,2,1]
[7,6,1,5,8,4,2,3]=>[1,1,3,1,2]
[8,6,3,7,2,5,4,1]=>[1,1,2,2,1,1]
[4,7,8,3,2,6,5,1]=>[3,1,2,1,1]
[8,3,4,7,6,2,1,5]=>[1,3,1,1,2]
[8,4,5,7,1,3,2,6]=>[1,3,2,2]
[3,1,8,7,5,2,4,6]=>[1,2,1,1,3]
[6,5,8,7,2,4,3,1]=>[1,2,1,2,1,1]
[5,4,6,1,8,3,2,7]=>[1,2,2,1,2]
[4,3,6,5,8,2,1,7]=>[1,2,2,1,2]
[7,6,3,2,8,5,4,1]=>[1,1,1,2,1,1,1]
[3,2,6,8,7,1,4,5]=>[1,3,1,3]
[3,8,2,7,6,1,4,5]=>[2,2,1,3]
[2,4,5,1,8,7,3,6]=>[3,2,1,2]
[4,3,7,1,8,5,2,6]=>[1,2,2,1,2]
[3,7,6,8,2,1,4,5]=>[2,2,1,3]
[7,4,2,6,1,8,3,5]=>[1,1,2,2,2]
[7,4,6,1,8,3,2,5]=>[1,2,2,1,2]
[3,6,8,7,2,1,4,5]=>[3,1,1,3]
[3,8,7,2,5,6,1,4]=>[2,1,3,2]
[3,2,8,5,6,7,1,4]=>[1,2,3,2]
[7,3,6,2,5,8,1,4]=>[1,2,3,2]
[8,3,2,1,4,7,5,6]=>[1,1,1,3,2]
[3,7,6,2,8,1,4,5]=>[2,1,2,3]
[7,4,2,1,6,8,3,5]=>[1,1,1,3,2]
[7,3,1,8,5,4,2,6]=>[1,1,2,1,1,2]
[6,8,3,2,7,1,4,5]=>[2,1,2,3]
[4,7,3,1,8,5,2,6]=>[2,1,2,1,2]
[8,3,6,2,5,7,1,4]=>[1,2,3,2]
[3,7,2,5,6,8,1,4]=>[2,4,2]
[4,6,8,2,1,7,3,5]=>[3,1,2,2]
[3,7,8,2,5,6,1,4]=>[3,3,2]
[7,5,1,4,2,3,6,8]=>[1,1,2,4]
[7,8,6,1,2,4,5,3]=>[2,1,4,1]
[1,5,3,4,7,8,6,2]=>[2,4,1,1]
[5,1,2,4,7,8,6,3]=>[1,5,1,1]
[5,1,7,8,6,2,3,4]=>[1,3,1,3]
[8,5,1,6,7,2,3,4]=>[1,1,3,3]
[7,5,1,2,4,6,8,3]=>[1,1,5,1]
[6,1,5,2,7,3,4,8]=>[1,2,2,3]
[7,1,2,6,4,5,8,3]=>[1,3,3,1]
[1,7,3,6,4,5,8,2]=>[2,2,3,1]
[1,8,3,6,4,5,7,2]=>[2,2,3,1]
[8,1,6,2,7,3,4,5]=>[1,2,2,3]
[7,1,6,2,5,3,4,8]=>[1,2,2,3]
[8,1,6,2,5,3,4,7]=>[1,2,2,3]
[8,1,7,2,5,3,4,6]=>[1,2,2,3]
[8,1,2,7,4,5,6,3]=>[1,3,3,1]
[1,8,3,7,4,5,6,2]=>[2,2,3,1]
[8,1,6,7,5,2,3,4]=>[1,3,1,3]
[7,3,1,2,6,4,5,8]=>[1,1,3,3]
[3,1,2,8,5,6,7,4]=>[1,3,3,1]
[6,3,1,2,7,4,5,8]=>[1,1,3,3]
[6,1,7,4,2,3,5,8]=>[1,2,1,4]
[1,7,3,4,6,8,5,2]=>[2,4,1,1]
[1,7,3,8,4,5,6,2]=>[2,2,3,1]
[7,1,8,2,5,3,4,6]=>[1,2,2,3]
[6,1,7,2,5,3,4,8]=>[1,2,2,3]
[5,1,7,2,6,3,4,8]=>[1,2,2,3]
[5,1,8,2,6,3,4,7]=>[1,2,2,3]
[1,6,3,7,4,5,8,2]=>[2,2,3,1]
[2,5,7,3,4,1,8,6]=>[3,2,2,1]
[2,4,7,3,5,1,6,8]=>[3,2,3]
[2,5,8,4,3,6,1,7]=>[3,1,2,2]
[2,4,8,6,3,5,1,7]=>[3,1,2,2]
[2,3,7,5,4,1,6,8]=>[3,1,1,3]
[3,4,6,2,1,5,8,7]=>[3,1,3,1]
[3,4,7,2,1,6,5,8]=>[3,1,2,2]
[3,6,8,5,4,1,2,7]=>[3,1,1,3]
[2,6,8,3,5,1,4,7]=>[3,2,3]
[2,3,6,1,5,8,4,7]=>[3,3,2]
[2,3,7,1,6,5,8,4]=>[3,2,2,1]
[2,4,7,1,3,6,8,5]=>[3,4,1]
[5,4,7,8,1,3,2,6]=>[1,3,2,2]
[4,6,3,8,1,5,2,7]=>[2,2,2,2]
[2,5,7,1,4,6,3,8]=>[3,3,2]
[2,4,7,1,6,3,5,8]=>[3,2,3]
[2,3,7,1,6,5,4,8]=>[3,2,1,2]
[2,5,7,1,4,3,6,8]=>[3,2,3]
[2,5,7,3,1,4,6,8]=>[3,1,4]
[3,4,7,2,1,6,8,5]=>[3,1,3,1]
[4,6,3,7,1,5,2,8]=>[2,2,2,2]
[5,7,3,2,8,1,4,6]=>[2,1,2,3]
[3,6,5,7,1,8,2,4]=>[2,2,2,2]
[2,6,5,7,1,8,4,3]=>[2,2,2,1,1]
[3,6,8,5,4,1,7,2]=>[3,1,1,2,1]
[2,6,8,3,5,1,7,4]=>[3,2,2,1]
[5,4,7,8,1,3,6,2]=>[1,3,3,1]
[2,5,7,1,4,6,8,3]=>[3,4,1]
[2,4,7,1,6,3,8,5]=>[3,2,2,1]
[2,4,7,1,6,8,3,5]=>[3,3,2]
[2,4,8,3,1,7,6,5]=>[3,1,2,1,1]
[5,3,6,4,7,1,2,8]=>[1,2,2,3]
[8,6,5,1,2,4,3,7]=>[1,1,1,3,2]
[7,6,1,4,2,3,5,8]=>[1,1,2,4]
[6,5,1,4,7,2,3,8]=>[1,1,3,3]
[6,5,4,8,1,3,2,7]=>[1,1,2,2,2]
[7,5,4,8,3,1,2,6]=>[1,1,2,1,3]
[2,6,3,5,7,4,8,1]=>[2,3,2,1]
[2,6,3,5,8,4,1,7]=>[2,3,1,2]
[6,5,1,4,8,3,2,7]=>[1,1,3,1,2]
[7,6,5,2,4,8,3,1]=>[1,1,1,3,1,1]
[7,6,5,3,8,2,1,4]=>[1,1,1,2,1,2]
[8,7,6,3,1,2,5,4]=>[1,1,1,1,3,1]
[8,7,1,4,3,2,5,6]=>[1,1,2,1,3]
[2,8,3,7,4,1,5,6]=>[2,2,1,3]
[2,7,3,6,1,5,8,4]=>[2,2,3,1]
[7,6,1,4,2,5,8,3]=>[1,1,2,3,1]
[8,7,5,1,4,2,3,6]=>[1,1,1,2,3]
[6,3,7,4,2,8,1,5]=>[1,2,1,2,2]
[6,3,7,4,1,5,8,2]=>[1,2,1,3,1]
[7,4,1,2,5,3,8,6]=>[1,1,3,2,1]
[2,4,3,7,5,1,8,6]=>[2,2,1,2,1]
[8,4,1,2,5,3,6,7]=>[1,1,3,3]
[7,3,8,4,2,5,1,6]=>[1,2,1,2,2]
[7,3,8,4,2,5,6,1]=>[1,2,1,3,1]
[8,7,5,1,4,2,6,3]=>[1,1,1,2,2,1]
[8,6,1,4,2,5,3,7]=>[1,1,2,2,2]
[8,7,1,4,3,2,6,5]=>[1,1,2,1,2,1]
[8,7,6,3,1,4,5,2]=>[1,1,1,1,3,1]
[8,7,6,3,1,5,4,2]=>[1,1,1,1,2,1,1]
[2,8,3,7,4,5,1,6]=>[2,2,2,2]
[2,8,3,7,4,5,6,1]=>[2,2,3,1]
[8,7,5,2,4,3,6,1]=>[1,1,1,2,2,1]
[4,2,5,7,3,1,6,8]=>[1,3,1,3]
[8,2,4,5,3,1,6,7]=>[1,3,1,3]
[8,4,5,1,3,2,6,7]=>[1,2,2,3]
[4,3,7,5,2,1,6,8]=>[1,2,1,1,3]
[1,6,7,4,3,2,5,8]=>[3,1,1,3]
[1,4,5,7,3,2,6,8]=>[4,1,3]
[3,5,1,4,7,2,6,8]=>[2,3,3]
[2,5,1,4,7,8,3,6]=>[2,4,2]
[4,3,7,1,5,2,6,8]=>[1,2,2,3]
[3,5,1,6,4,2,7,8]=>[2,2,1,3]
[6,4,3,1,7,2,5,8]=>[1,1,1,2,3]
[6,2,7,4,3,1,5,8]=>[1,2,1,1,3]
[2,6,4,1,7,3,5,8]=>[2,1,2,3]
[6,3,2,7,4,5,1,8]=>[1,1,2,2,2]
[7,2,4,1,3,6,8,5]=>[1,2,4,1]
[6,3,2,5,7,1,4,8]=>[1,1,3,3]
[3,2,6,5,7,1,4,8]=>[1,2,2,3]
[1,7,3,2,5,6,4,8]=>[2,1,3,2]
[2,1,7,3,5,6,8,4]=>[1,2,4,1]
[2,1,6,3,5,7,8,4]=>[1,2,4,1]
[1,6,3,2,5,7,4,8]=>[2,1,3,2]
[1,4,6,5,2,7,3,8]=>[3,1,2,2]
[5,6,2,1,4,3,7,8]=>[2,1,2,3]
[2,5,1,6,4,3,7,8]=>[2,2,1,3]
[2,5,4,1,6,3,7,8]=>[2,1,2,3]
[4,6,1,5,2,7,3,8]=>[2,2,2,2]
[1,6,5,3,7,2,4,8]=>[2,1,2,3]
[1,2,4,7,5,3,6,8]=>[4,1,3]
[1,2,5,4,7,3,6,8]=>[3,2,3]
[1,2,5,3,4,8,7,6]=>[3,3,1,1]
[5,4,7,6,1,2,3,8]=>[1,2,1,4]
[4,3,7,6,5,1,2,8]=>[1,2,1,1,3]
[4,8,3,6,5,1,2,7]=>[2,2,1,3]
[5,3,7,6,1,8,2,4]=>[1,2,1,2,2]
[4,2,7,6,5,1,8,3]=>[1,2,1,1,2,1]
[5,2,7,6,1,8,4,3]=>[1,2,1,2,1,1]
[7,8,1,3,6,5,4,2]=>[2,3,1,1,1]
[5,8,2,6,1,7,4,3]=>[2,2,2,1,1]
[1,5,3,7,6,2,8,4]=>[2,2,1,2,1]
[1,6,3,7,2,8,5,4]=>[2,2,2,1,1]
[1,7,8,2,4,6,5,3]=>[3,3,1,1]
[1,5,8,3,6,2,7,4]=>[3,2,2,1]
[6,8,7,1,4,5,2,3]=>[2,1,3,2]
[7,8,1,4,6,5,2,3]=>[2,3,1,2]
[5,8,7,3,1,6,2,4]=>[2,1,1,2,2]
[1,2,6,4,7,3,8,5]=>[3,2,2,1]
[1,2,7,8,3,5,6,4]=>[4,3,1]
[1,6,8,7,2,4,5,3]=>[3,1,3,1]
[6,8,7,1,2,4,5,3]=>[2,1,4,1]
[4,8,7,6,2,1,5,3]=>[2,1,1,1,2,1]
[5,4,2,3,8,6,1,7]=>[1,1,3,1,2]
[2,6,3,4,1,5,8,7]=>[2,2,3,1]
[5,6,2,1,4,3,8,7]=>[2,1,2,2,1]
[5,6,2,3,4,1,8,7]=>[2,3,2,1]
[2,7,4,5,8,1,6,3]=>[2,3,2,1]
[2,6,1,8,5,4,3,7]=>[2,2,1,1,2]
[5,8,6,2,3,4,1,7]=>[2,1,3,2]
[5,8,6,2,1,4,3,7]=>[2,1,1,2,2]
[4,5,8,6,2,1,3,7]=>[3,1,1,3]
[6,4,7,5,8,2,1,3]=>[1,2,2,1,2]
[6,3,7,4,2,5,8,1]=>[1,2,1,3,1]
[4,8,2,1,5,7,6,3]=>[2,1,3,1,1]
[2,1,4,8,5,6,3,7]=>[1,3,2,2]
[4,8,5,6,2,1,3,7]=>[2,2,1,3]
[6,2,1,5,8,4,3,7]=>[1,1,3,1,2]
[7,5,6,2,4,3,8,1]=>[1,2,2,2,1]
[2,8,6,3,4,1,5,7]=>[2,1,2,3]
[2,6,3,4,1,8,5,7]=>[2,2,2,2]
[4,6,2,5,7,3,8,1]=>[2,3,2,1]
[4,2,8,5,3,6,1,7]=>[1,2,1,2,2]
[2,3,6,4,1,8,5,7]=>[3,1,2,2]
[2,3,6,7,8,4,1,5]=>[5,1,2]
[7,8,4,2,5,3,6,1]=>[2,1,2,2,1]
[6,2,4,5,8,1,7,3]=>[1,4,2,1]
[8,1,7,4,5,6,2,3]=>[1,2,3,2]
[2,7,8,3,4,1,6,5]=>[3,2,2,1]
[2,1,7,8,4,3,6,5]=>[1,3,1,2,1]
[4,2,5,7,8,3,6,1]=>[1,4,2,1]
[7,8,3,5,6,2,4,1]=>[2,3,2,1]
[6,2,1,4,5,7,8,3]=>[1,1,5,1]
[2,1,7,8,4,5,6,3]=>[1,3,3,1]
[8,2,1,4,3,7,6,5]=>[1,1,2,2,1,1]
[6,4,2,3,8,1,7,5]=>[1,1,3,2,1]
[6,5,4,2,1,8,3,7]=>[1,1,1,1,2,2]
[5,4,3,1,8,6,2,7]=>[1,1,1,2,1,2]
[7,6,5,3,1,2,8,4]=>[1,1,1,1,3,1]
[6,5,4,1,2,8,7,3]=>[1,1,1,3,1,1]
[6,5,3,2,1,8,4,7]=>[1,1,1,1,2,2]
[5,4,1,6,2,8,3,7]=>[1,1,2,2,2]
[4,3,1,8,6,5,2,7]=>[1,1,2,1,1,2]
[5,4,2,1,8,6,3,7]=>[1,1,1,2,1,2]
[4,1,6,5,2,8,3,7]=>[1,2,1,2,2]
[6,5,3,1,4,7,8,2]=>[1,1,1,4,1]
[6,2,3,1,7,8,4,5]=>[1,2,3,2]
[3,1,8,6,7,2,4,5]=>[1,2,2,3]
[6,5,1,4,2,3,7,8]=>[1,1,2,4]
[5,1,3,2,6,4,7,8]=>[1,2,2,3]
[4,7,8,2,3,6,1,5]=>[3,3,2]
[4,2,5,1,8,6,7,3]=>[1,2,2,2,1]
[7,5,8,1,4,2,6,3]=>[1,2,2,2,1]
[4,5,3,7,1,6,8,2]=>[2,2,3,1]
[4,2,8,5,3,6,7,1]=>[1,2,1,3,1]
[2,7,4,1,8,5,6,3]=>[2,1,2,2,1]
[5,2,8,1,4,7,6,3]=>[1,2,3,1,1]
[2,8,6,3,5,4,7,1]=>[2,1,2,2,1]
[3,5,2,8,6,4,7,1]=>[2,2,1,2,1]
[4,1,3,6,2,8,5,7]=>[1,3,2,2]
[5,2,4,7,6,1,8,3]=>[1,3,1,2,1]
[7,3,5,1,6,4,8,2]=>[1,2,2,2,1]
[7,5,2,3,6,1,4,8]=>[1,1,3,3]
[7,5,1,2,4,8,3,6]=>[1,1,4,2]
[6,2,5,8,4,7,1,3]=>[1,3,2,2]
[5,8,2,3,6,1,4,7]=>[2,3,3]
[5,1,4,7,2,6,8,3]=>[1,3,3,1]
[6,8,2,5,4,1,3,7]=>[2,2,1,3]
[7,1,6,3,2,4,5,8]=>[1,2,1,4]
[4,1,6,8,3,2,5,7]=>[1,3,1,3]
[1,6,5,8,2,3,7,4]=>[2,2,3,1]
[1,6,3,2,4,8,5,7]=>[2,1,3,2]
[2,5,7,1,6,4,8,3]=>[3,2,2,1]
[1,8,2,5,6,4,7,3]=>[2,3,2,1]
[2,4,8,3,7,5,1,6]=>[3,2,1,2]
[4,7,6,1,5,2,3,8]=>[2,1,2,3]
[3,7,4,6,1,8,5,2]=>[2,2,2,1,1]
[5,6,2,3,8,1,4,7]=>[2,3,3]
[5,6,1,2,4,7,3,8]=>[2,4,2]
[4,7,1,3,8,6,2,5]=>[2,3,1,2]
[2,7,1,4,8,5,6,3]=>[2,3,2,1]
[2,5,4,8,1,6,3,7]=>[2,2,2,2]
[1,6,3,4,7,2,8,5]=>[2,3,2,1]
[2,8,4,6,1,3,7,5]=>[2,2,3,1]
[8,4,6,2,5,3,7,1]=>[1,2,2,2,1]
[8,3,7,6,2,1,5,4]=>[1,2,1,1,2,1]
[8,5,2,7,6,1,4,3]=>[1,1,2,1,2,1]
[5,8,2,7,6,1,4,3]=>[2,2,1,2,1]
[8,3,7,6,2,5,1,4]=>[1,2,1,2,2]
[7,3,8,6,5,1,4,2]=>[1,2,1,1,2,1]
[6,2,4,7,5,3,8,1]=>[1,3,1,2,1]
[7,1,3,2,5,8,6,4]=>[1,2,3,1,1]
[2,6,3,7,5,4,8,1]=>[2,2,1,2,1]
[3,7,4,5,2,6,8,1]=>[2,2,3,1]
[7,1,3,4,5,8,6,2]=>[1,5,1,1]
[3,1,4,6,8,7,5,2]=>[1,4,1,1,1]
[2,7,5,1,4,8,6,3]=>[2,1,3,1,1]
[5,4,7,1,3,8,6,2]=>[1,2,3,1,1]
[7,8,4,6,2,1,3,5]=>[2,2,1,3]
[1,8,2,6,4,7,3,5]=>[2,2,2,2]
[2,8,5,1,4,7,3,6]=>[2,1,3,2]
[3,1,7,2,4,8,6,5]=>[1,2,3,1,1]
[1,6,7,5,2,8,4,3]=>[3,1,2,1,1]
[7,6,3,1,8,2,5,4]=>[1,1,1,2,2,1]
[8,1,7,6,3,4,2,5]=>[1,2,1,2,2]
[8,1,4,2,5,7,3,6]=>[1,2,3,2]
[7,2,6,5,8,4,3,1]=>[1,2,2,1,1,1]
[4,3,2,8,5,6,1,7]=>[1,1,2,2,2]
[2,7,3,8,4,5,1,6]=>[2,2,2,2]
[3,5,8,4,6,2,1,7]=>[3,2,1,2]
[8,5,2,3,7,1,4,6]=>[1,1,3,3]
[3,4,8,5,6,2,7,1]=>[3,2,2,1]
[3,2,8,6,4,5,7,1]=>[1,2,1,3,1]
[5,8,2,3,4,6,1,7]=>[2,4,2]
[6,1,3,4,2,5,7,8]=>[1,3,4]
[1,5,6,3,2,4,7,8]=>[3,1,4]
[6,3,5,2,4,1,7,8]=>[1,2,2,3]
[7,8,3,5,2,4,6,1]=>[2,2,3,1]
[2,4,5,7,3,6,1,8]=>[4,2,2]
[2,5,3,1,6,4,7,8]=>[2,1,2,3]
[6,5,1,3,4,2,7,8]=>[1,1,3,3]
[5,7,4,3,2,6,1,8]=>[2,1,1,2,2]
[6,8,7,4,3,5,1,2]=>[2,1,1,2,2]
[2,6,7,8,4,3,5,1]=>[4,1,2,1]
[1,7,8,4,5,3,6,2]=>[3,2,2,1]
[7,1,8,5,3,4,6,2]=>[1,2,1,3,1]
[5,7,4,2,1,6,3,8]=>[2,1,1,2,2]
[5,1,4,7,3,6,2,8]=>[1,3,2,2]
[7,4,8,6,3,5,2,1]=>[1,2,1,2,1,1]
[4,7,6,3,5,2,1,8]=>[2,1,2,1,2]
[1,6,5,8,7,4,2,3]=>[2,2,1,1,2]
[6,1,3,8,7,5,2,4]=>[1,3,1,1,2]
[7,6,2,1,8,3,5,4]=>[1,1,1,2,2,1]
[7,1,3,6,8,2,5,4]=>[1,4,2,1]
[1,7,5,6,8,2,4,3]=>[2,3,2,1]
[3,6,7,5,8,2,4,1]=>[3,2,2,1]
[1,7,4,5,2,8,6,3]=>[2,2,2,1,1]
[7,5,4,2,1,8,6,3]=>[1,1,1,1,2,1,1]
[3,6,7,4,2,8,5,1]=>[3,1,2,1,1]
[4,6,3,2,7,8,5,1]=>[2,1,3,1,1]
[7,6,1,3,4,2,5,8]=>[1,1,3,3]
[7,8,2,6,4,5,3,1]=>[2,2,2,1,1]
[7,2,5,4,6,1,3,8]=>[1,2,2,3]
[7,1,2,4,5,6,3,8]=>[1,5,2]
[7,3,2,1,5,6,4,8]=>[1,1,1,3,2]
[3,6,2,1,7,5,4,8]=>[2,1,2,1,2]
[2,6,7,3,1,5,4,8]=>[3,1,2,2]
[2,1,6,4,7,5,3,8]=>[1,2,2,1,2]
[7,2,8,5,6,4,3,1]=>[1,2,2,1,1,1]
[7,6,8,5,4,1,3,2]=>[1,2,1,1,2,1]
[7,1,8,4,6,5,3,2]=>[1,2,2,1,1,1]
[7,8,6,3,1,5,4,2]=>[2,1,1,2,1,1]
[7,6,1,4,5,3,2,8]=>[1,1,3,1,2]
[7,1,5,6,4,3,2,8]=>[1,3,1,1,2]
[4,1,3,8,6,2,7,5]=>[1,3,1,2,1]
[3,5,8,2,1,6,7,4]=>[3,1,3,1]
[5,1,2,8,4,6,7,3]=>[1,3,3,1]
[5,6,3,2,8,1,7,4]=>[2,1,2,2,1]
[8,2,6,3,1,5,7,4]=>[1,2,1,3,1]
[8,2,5,3,6,1,7,4]=>[1,2,2,2,1]
[5,1,2,4,6,8,7,3]=>[1,5,1,1]
[8,2,5,6,7,4,3,1]=>[1,4,1,1,1]
[5,1,6,4,7,3,2,8]=>[1,2,2,1,2]
[8,2,5,3,4,7,6,1]=>[1,2,3,1,1]
[8,2,5,3,4,7,1,6]=>[1,2,3,2]
[7,5,3,2,4,1,8,6]=>[1,1,1,2,2,1]
[7,1,2,3,6,8,4,5]=>[1,5,2]
[8,2,5,3,4,1,6,7]=>[1,2,2,3]
[5,7,3,6,8,4,1,2]=>[2,3,1,2]
[7,1,6,8,5,3,4,2]=>[1,3,1,2,1]
[6,7,2,8,3,4,5,1]=>[2,2,3,1]
[3,7,8,6,5,4,1,2]=>[3,1,1,1,2]
[3,1,8,4,6,5,2,7]=>[1,2,2,1,2]
[4,1,3,8,6,5,2,7]=>[1,3,1,1,2]
[8,2,4,1,6,5,7,3]=>[1,2,2,2,1]
[3,1,8,4,6,5,7,2]=>[1,2,2,2,1]
[7,6,2,8,3,1,5,4]=>[1,1,2,1,2,1]
[7,1,6,8,5,3,2,4]=>[1,3,1,1,2]
[7,1,6,4,8,3,2,5]=>[1,2,2,1,2]
[6,1,2,3,8,4,7,5]=>[1,4,2,1]
[6,5,2,4,3,1,8,7]=>[1,1,2,1,2,1]
[8,2,5,3,4,6,1,7]=>[1,2,3,2]
[8,2,5,3,4,6,7,1]=>[1,2,4,1]
[6,5,2,4,3,1,7,8]=>[1,1,2,1,3]
[8,1,6,7,4,2,5,3]=>[1,3,1,2,1]
[8,1,6,7,4,2,3,5]=>[1,3,1,3]
[8,1,6,4,5,2,3,7]=>[1,2,2,3]
[8,1,6,4,5,2,7,3]=>[1,2,2,2,1]
[8,6,4,7,2,3,5,1]=>[1,1,2,3,1]
[8,6,4,1,2,3,7,5]=>[1,1,1,4,1]
[8,6,1,4,2,5,7,3]=>[1,1,2,3,1]
[8,6,1,4,5,2,7,3]=>[1,1,3,2,1]
[8,6,7,4,2,5,1,3]=>[1,2,1,2,2]
[8,6,4,2,5,3,7,1]=>[1,1,1,2,2,1]
[8,6,4,2,5,3,1,7]=>[1,1,1,2,1,2]
[8,6,4,2,7,3,1,5]=>[1,1,1,2,1,2]
[8,6,4,1,5,7,2,3]=>[1,1,1,3,2]
[8,6,4,2,1,5,7,3]=>[1,1,1,1,3,1]
[8,6,4,2,1,7,3,5]=>[1,1,1,1,2,2]
[8,6,1,4,7,2,5,3]=>[1,1,3,2,1]
[8,6,4,1,5,2,3,7]=>[1,1,1,2,3]
[8,6,1,4,7,2,3,5]=>[1,1,3,3]
[8,6,7,1,4,5,2,3]=>[1,2,3,2]
[8,6,4,5,2,7,3,1]=>[1,1,2,2,1,1]
[8,6,7,4,2,1,5,3]=>[1,2,1,1,2,1]
[8,6,4,7,2,1,5,3]=>[1,1,2,1,2,1]
[8,6,4,2,5,7,3,1]=>[1,1,1,3,1,1]
[8,6,4,2,5,1,7,3]=>[1,1,1,2,2,1]
[8,6,4,5,1,2,7,3]=>[1,1,2,3,1]
[8,6,4,2,5,7,1,3]=>[1,1,1,3,2]
[3,4,7,5,8,2,6,1]=>[3,2,2,1]
[8,7,1,4,6,5,2,3]=>[1,1,3,1,2]
[8,3,7,6,4,5,1,2]=>[1,2,1,2,2]
[5,3,8,6,4,1,7,2]=>[1,2,1,1,2,1]
[7,4,5,1,2,8,6,3]=>[1,2,3,1,1]
[6,4,7,1,8,5,2,3]=>[1,2,2,1,2]
[5,7,4,2,3,8,6,1]=>[2,1,3,1,1]
[3,8,2,5,1,7,4,6]=>[2,2,2,2]
[5,8,4,2,3,7,1,6]=>[2,1,3,2]
[4,8,5,2,1,7,3,6]=>[2,1,1,2,2]
[8,5,7,6,1,2,4,3]=>[1,2,1,3,1]
[6,8,7,5,2,4,1,3]=>[2,1,1,2,2]
[5,7,6,8,4,1,3,2]=>[2,2,1,2,1]
[7,3,1,6,8,5,4,2]=>[1,1,3,1,1,1]
[5,3,1,7,4,8,6,2]=>[1,1,2,2,1,1]
[7,3,1,8,6,4,5,2]=>[1,1,2,1,2,1]
[8,6,4,1,7,3,2,5]=>[1,1,1,2,1,2]
[4,6,8,3,7,1,2,5]=>[3,2,3]
[3,5,2,8,4,7,1,6]=>[2,2,2,2]
[6,4,8,3,7,2,1,5]=>[1,2,2,1,2]
[3,6,2,8,7,4,1,5]=>[2,2,1,1,2]
[6,8,4,2,7,3,1,5]=>[2,1,2,1,2]
[5,4,8,6,7,3,2,1]=>[1,2,2,1,1,1]
[3,4,7,8,5,1,2,6]=>[4,1,3]
[4,7,3,2,5,6,8,1]=>[2,1,4,1]
[3,2,7,6,4,5,8,1]=>[1,2,1,3,1]
[1,7,3,6,8,4,2,5]=>[2,3,1,2]
[2,3,6,5,1,8,7,4]=>[3,1,2,1,1]
[8,3,1,2,6,4,7,5]=>[1,1,3,2,1]
[1,7,8,2,4,3,5,6]=>[3,2,3]
[3,6,4,7,1,2,8,5]=>[2,2,3,1]
[5,7,4,8,1,3,2,6]=>[2,2,2,2]
[4,3,7,8,1,5,2,6]=>[1,3,2,2]
[8,5,4,2,6,1,7,3]=>[1,1,1,2,2,1]
[3,2,6,8,7,4,1,5]=>[1,3,1,1,2]
[2,3,7,5,1,8,6,4]=>[3,1,2,1,1]
[6,3,1,2,8,7,4,5]=>[1,1,3,1,2]
[5,2,1,3,8,7,6,4]=>[1,1,3,1,1,1]
[7,2,1,5,3,8,4,6]=>[1,1,2,2,2]
[1,5,8,2,4,3,6,7]=>[3,2,3]
[4,3,6,8,1,5,2,7]=>[1,3,2,2]
[5,4,6,8,3,1,7,2]=>[1,3,1,2,1]
[3,6,8,4,5,1,7,2]=>[3,2,2,1]
[8,6,1,7,2,4,3,5]=>[1,1,2,2,2]
[7,3,1,2,8,6,4,5]=>[1,1,3,1,2]
[2,3,7,6,1,8,5,4]=>[3,1,2,1,1]
[3,2,7,8,6,4,1,5]=>[1,3,1,1,2]
[6,2,8,3,1,4,7,5]=>[1,2,1,3,1]
[3,1,2,8,7,4,5,6]=>[1,3,1,3]
[2,1,3,8,7,4,6,5]=>[1,3,1,2,1]
[2,1,3,8,7,4,5,6]=>[1,3,1,3]
[1,6,8,3,2,4,7,5]=>[3,1,3,1]
[8,5,1,7,2,4,3,6]=>[1,1,2,2,2]
[8,4,1,7,3,2,5,6]=>[1,1,2,1,3]
[8,3,1,6,2,7,5,4]=>[1,1,2,2,1,1]
[1,3,2,8,7,6,4,5]=>[2,2,1,1,2]
[2,1,3,8,7,6,4,5]=>[1,3,1,1,2]
[1,7,2,6,3,5,8,4]=>[2,2,3,1]
[1,7,8,2,6,3,5,4]=>[3,2,2,1]
[1,6,3,7,2,5,4,8]=>[2,2,2,2]
[1,7,2,6,8,3,4,5]=>[2,3,3]
[1,7,2,4,6,3,5,8]=>[2,3,3]
[5,7,2,8,4,1,3,6]=>[2,2,1,3]
[2,6,8,3,1,5,4,7]=>[3,1,2,2]
[2,6,8,3,1,4,5,7]=>[3,1,4]
[5,6,2,8,4,1,3,7]=>[2,2,1,3]
[6,3,7,8,2,1,5,4]=>[1,3,1,2,1]
[2,4,8,3,1,6,7,5]=>[3,1,3,1]
[3,4,2,6,1,5,8,7]=>[2,2,3,1]
[2,5,8,3,1,6,4,7]=>[3,1,2,2]
[3,5,8,4,2,1,6,7]=>[3,1,1,3]
[2,5,8,3,1,4,6,7]=>[3,1,4]
[3,4,2,7,1,6,5,8]=>[2,2,2,2]
[2,8,1,3,5,7,4,6]=>[2,4,2]
[1,3,7,6,2,5,4,8]=>[3,1,2,2]
[2,8,7,1,4,3,5,6]=>[2,1,2,3]
[8,7,4,6,1,3,2,5]=>[1,1,2,2,2]
[7,3,8,6,1,4,5,2]=>[1,2,1,3,1]
[5,4,7,8,3,2,6,1]=>[1,3,1,2,1]
[3,2,5,4,6,8,1,7]=>[1,2,3,2]
[7,4,5,8,3,1,6,2]=>[1,3,1,2,1]
[1,5,4,7,3,2,6,8]=>[2,2,1,3]
[8,4,5,7,3,1,2,6]=>[1,3,1,3]
[3,4,8,5,7,1,2,6]=>[3,2,3]
[3,6,8,2,5,1,4,7]=>[3,2,3]
[3,6,8,7,2,5,4,1]=>[3,1,2,1,1]
[3,5,7,2,8,1,6,4]=>[3,2,2,1]
[4,7,6,8,3,5,2,1]=>[2,2,2,1,1]
[3,4,7,5,8,1,6,2]=>[3,2,2,1]
[3,4,6,5,8,2,1,7]=>[3,2,1,2]
[2,4,6,7,8,3,5,1]=>[5,2,1]
[1,4,2,5,7,6,3,8]=>[2,3,1,2]
[1,4,2,6,8,5,3,7]=>[2,3,1,2]
[1,2,6,8,3,5,4,7]=>[4,2,2]
[1,6,8,3,5,4,2,7]=>[3,2,1,2]
[1,5,3,2,4,6,8,7]=>[2,1,4,1]
[1,5,8,7,6,3,2,4]=>[3,1,1,1,2]
[1,5,7,6,3,2,4,8]=>[3,1,1,3]
[1,6,3,2,4,7,5,8]=>[2,1,3,2]
[1,6,3,2,4,8,7,5]=>[2,1,3,1,1]
[1,2,7,6,4,3,5,8]=>[3,1,1,3]
[1,8,7,5,2,4,6,3]=>[2,1,1,3,1]
[1,7,5,2,4,6,3,8]=>[2,1,3,2]
[1,7,4,2,5,3,6,8]=>[2,1,2,3]
[1,8,4,7,5,2,6,3]=>[2,2,1,2,1]
[1,7,5,2,3,6,4,8]=>[2,1,3,2]
[1,7,5,2,6,3,4,8]=>[2,1,2,3]
[1,6,3,7,4,2,5,8]=>[2,2,1,3]
[1,6,3,2,7,5,4,8]=>[2,1,2,1,2]
[1,4,7,5,2,6,3,8]=>[3,1,2,2]
[1,3,6,4,8,7,5,2]=>[3,2,1,1,1]
[1,3,7,6,4,2,5,8]=>[3,1,1,3]
[1,3,2,4,8,5,7,6]=>[2,3,2,1]
[1,3,8,7,5,2,4,6]=>[3,1,1,3]
[1,4,6,3,2,7,5,8]=>[3,1,2,2]
[1,4,6,3,2,8,7,5]=>[3,1,2,1,1]
[1,5,7,6,4,2,3,8]=>[3,1,1,3]
[1,6,3,2,8,4,7,5]=>[2,1,2,2,1]
[1,6,3,5,2,7,4,8]=>[2,2,2,2]
[1,6,3,5,2,8,7,4]=>[2,2,2,1,1]
[1,8,3,7,5,2,4,6]=>[2,2,1,3]
[6,4,7,1,5,3,8,2]=>[1,2,2,2,1]
[5,3,8,2,6,4,7,1]=>[1,2,2,2,1]
[4,3,8,2,6,5,7,1]=>[1,2,2,2,1]
[2,6,1,8,3,4,7,5]=>[2,2,3,1]
[1,6,2,8,3,4,7,5]=>[2,2,3,1]
[5,7,1,4,8,2,3,6]=>[2,3,3]
[6,5,7,1,4,3,8,2]=>[1,2,2,2,1]
[4,8,3,5,7,6,1,2]=>[2,3,1,2]
[5,7,6,1,2,4,8,3]=>[2,1,4,1]
[4,8,3,5,7,6,2,1]=>[2,3,1,1,1]
[1,3,4,2,8,5,7,6]=>[3,2,2,1]
[5,7,6,1,4,8,3,2]=>[2,1,3,1,1]
[5,7,6,2,4,8,3,1]=>[2,1,3,1,1]
[6,7,5,2,3,8,4,1]=>[2,1,3,1,1]
[6,7,5,3,8,4,2,1]=>[2,1,2,1,1,1]
[3,2,1,4,8,5,7,6]=>[1,1,3,2,1]
[7,3,1,4,2,6,5,8]=>[1,1,2,2,2]
[7,6,1,3,2,5,4,8]=>[1,1,2,2,2]
[7,6,1,4,2,5,3,8]=>[1,1,2,2,2]
[7,2,1,5,3,6,4,8]=>[1,1,2,2,2]
[7,4,1,6,2,5,3,8]=>[1,1,2,2,2]
[7,6,2,5,1,4,3,8]=>[1,1,2,2,2]
[5,7,2,6,1,4,3,8]=>[2,2,2,2]
[6,7,2,5,1,4,3,8]=>[2,2,2,2]
[6,3,1,7,2,5,4,8]=>[1,1,2,2,2]
[6,2,1,8,3,5,4,7]=>[1,1,2,2,2]
[6,3,1,8,2,5,4,7]=>[1,1,2,2,2]
[6,4,1,8,2,5,3,7]=>[1,1,2,2,2]
[5,7,1,4,3,8,2,6]=>[2,2,2,2]
[5,4,1,8,2,6,3,7]=>[1,1,2,2,2]
[5,3,1,8,2,6,4,7]=>[1,1,2,2,2]
[5,3,1,7,2,6,4,8]=>[1,1,2,2,2]
[4,7,1,5,2,6,3,8]=>[2,2,2,2]
[6,3,1,5,2,7,4,8]=>[1,1,2,2,2]
[6,5,1,4,2,7,3,8]=>[1,1,2,2,2]
[6,4,1,3,2,7,5,8]=>[1,1,2,2,2]
[6,2,1,4,3,7,5,8]=>[1,1,2,2,2]
[5,6,1,3,2,8,4,7]=>[2,2,2,2]
[5,6,1,4,2,8,3,7]=>[2,2,2,2]
[6,5,1,4,2,8,3,7]=>[1,1,2,2,2]
[4,6,1,5,2,8,3,7]=>[2,2,2,2]
[5,4,1,8,3,7,2,6]=>[1,1,2,2,2]
[5,2,1,8,4,7,3,6]=>[1,1,2,2,2]
[1,8,7,3,4,5,2,6]=>[2,1,3,2]
[1,8,7,4,5,2,3,6]=>[2,1,2,3]
[1,2,6,8,7,3,4,5]=>[4,1,3]
[1,3,7,8,4,5,6,2]=>[4,3,1]
[8,4,2,3,1,6,5,7]=>[1,1,2,2,2]
[8,4,2,3,6,5,1,7]=>[1,1,3,1,2]
[6,4,5,2,1,8,3,7]=>[1,2,1,2,2]
[6,4,5,2,8,1,7,3]=>[1,2,2,2,1]
[4,8,6,2,3,1,7,5]=>[2,1,2,2,1]
[4,6,2,3,1,8,7,5]=>[2,2,2,1,1]
[6,4,2,8,5,3,7,1]=>[1,1,2,1,2,1]
[6,4,2,1,8,5,3,7]=>[1,1,1,2,1,2]
[4,2,6,1,5,8,3,7]=>[1,2,3,2]
[6,4,5,2,8,7,1,3]=>[1,2,2,1,2]
[4,2,3,6,5,8,1,7]=>[1,3,2,2]
[6,4,2,3,5,8,7,1]=>[1,1,4,1,1]
[6,4,2,3,5,8,1,7]=>[1,1,4,2]
[6,4,2,3,1,8,5,7]=>[1,1,2,2,2]
[6,4,2,3,1,5,8,7]=>[1,1,2,3,1]
[8,6,2,1,4,3,7,5]=>[1,1,1,2,2,1]
[2,8,6,4,5,1,7,3]=>[2,1,2,2,1]
[8,6,2,1,4,7,3,5]=>[1,1,1,3,2]
[6,4,2,1,8,3,7,5]=>[1,1,1,2,2,1]
[6,4,8,2,5,7,3,1]=>[1,2,3,1,1]
[8,2,4,6,7,1,5,3]=>[1,4,2,1]
[8,6,7,2,1,4,5,3]=>[1,2,1,3,1]
[2,8,6,1,4,3,7,5]=>[2,1,2,2,1]
[2,8,6,4,3,7,5,1]=>[2,1,1,2,1,1]
[2,6,3,1,7,4,8,5]=>[2,1,2,2,1]
[4,3,2,6,1,8,7,5]=>[1,1,2,2,1,1]
[6,5,1,8,3,2,7,4]=>[1,1,2,1,2,1]
[3,6,1,2,5,8,7,4]=>[2,4,1,1]
[8,1,7,5,4,6,3,2]=>[1,2,1,2,1,1]
[4,1,7,3,8,6,5,2]=>[1,2,2,1,1,1]
[1,4,3,7,2,8,6,5]=>[2,2,2,1,1]
[1,8,7,4,5,3,2,6]=>[2,1,2,1,2]
[2,8,3,1,4,5,7,6]=>[2,1,4,1]
[6,1,7,2,8,4,5,3]=>[1,2,2,2,1]
[6,5,1,3,8,7,2,4]=>[1,1,3,1,2]
[3,2,6,7,8,4,5,1]=>[1,4,2,1]
[1,7,4,6,3,8,2,5]=>[2,2,2,2]
[5,6,4,1,3,8,2,7]=>[2,1,3,2]
[7,2,6,3,5,8,1,4]=>[1,2,3,2]
[4,5,3,1,8,7,6,2]=>[2,1,2,1,1,1]
[6,3,4,2,7,8,5,1]=>[1,2,3,1,1]
[8,7,4,5,1,6,3,2]=>[1,1,2,2,1,1]
[6,2,7,8,1,3,5,4]=>[1,3,3,1]
[4,3,2,8,6,1,7,5]=>[1,1,2,1,2,1]
[5,1,8,4,3,7,2,6]=>[1,2,1,2,2]
[7,2,8,1,3,4,6,5]=>[1,2,4,1]
[1,4,8,3,5,6,7,2]=>[3,4,1]
[7,2,8,1,4,5,6,3]=>[1,2,4,1]
[2,1,8,3,4,5,7,6]=>[1,2,4,1]
[1,4,8,2,5,6,7,3]=>[3,4,1]
[8,1,6,7,2,5,4,3]=>[1,3,2,1,1]
[7,5,2,3,6,8,4,1]=>[1,1,4,1,1]
[2,5,8,3,6,1,4,7]=>[3,2,3]
[8,1,4,6,5,3,2,7]=>[1,3,1,1,2]
[8,1,5,2,3,4,7,6]=>[1,2,4,1]
[8,1,4,7,6,5,2,3]=>[1,3,1,1,2]
[8,1,3,2,6,4,5,7]=>[1,2,2,3]
[8,1,3,7,5,2,4,6]=>[1,3,1,3]
[8,1,3,6,7,5,2,4]=>[1,4,1,2]
[8,1,2,7,6,5,4,3]=>[1,3,1,1,1,1]
[7,2,3,6,8,5,1,4]=>[1,4,1,2]
[7,5,3,2,6,4,1,8]=>[1,1,1,2,1,2]
[4,5,8,1,6,7,2,3]=>[3,3,2]
[3,5,8,2,6,4,7,1]=>[3,2,2,1]
[3,2,8,6,1,5,7,4]=>[1,2,1,3,1]
[3,4,7,2,1,5,6,8]=>[3,1,4]
[3,7,2,5,8,4,6,1]=>[2,3,2,1]
[6,7,8,4,1,5,2,3]=>[3,1,2,2]
[6,2,8,3,5,1,4,7]=>[1,2,2,3]
[6,2,7,4,5,3,1,8]=>[1,2,2,1,2]
[6,8,2,5,3,4,1,7]=>[2,2,2,2]
[6,8,7,5,4,1,2,3]=>[2,1,1,1,3]
[7,4,5,6,1,8,2,3]=>[1,3,2,2]
[7,3,4,6,5,1,2,8]=>[1,3,1,3]
[7,2,4,5,6,1,8,3]=>[1,4,2,1]
[6,3,5,2,8,1,7,4]=>[1,2,2,2,1]
[2,7,3,5,8,1,4,6]=>[2,3,3]
[7,8,6,1,2,5,4,3]=>[2,1,3,1,1]
[6,1,8,7,4,5,2,3]=>[1,2,1,2,2]
[6,1,8,7,3,4,2,5]=>[1,2,1,2,2]
[4,5,3,7,8,2,1,6]=>[2,3,1,2]
[4,1,7,6,3,5,2,8]=>[1,2,1,2,2]
[4,1,6,7,2,5,8,3]=>[1,3,3,1]
[4,7,8,1,6,2,5,3]=>[3,2,2,1]
[4,8,7,1,6,3,2,5]=>[2,1,2,1,2]
[4,8,2,7,5,3,6,1]=>[2,2,1,2,1]
[3,2,8,7,6,4,5,1]=>[1,2,1,1,2,1]
[3,1,2,7,5,6,4,8]=>[1,3,2,2]
[1,3,2,6,8,7,4,5]=>[2,3,1,2]
[1,3,8,2,5,4,6,7]=>[3,2,3]
[1,6,2,5,8,7,3,4]=>[2,3,1,2]
[1,6,8,7,2,3,5,4]=>[3,1,3,1]
[1,6,8,7,2,5,3,4]=>[3,1,2,2]
[1,5,2,4,8,3,6,7]=>[2,3,3]
[1,2,4,5,8,6,3,7]=>[5,1,2]
[1,2,8,3,5,4,7,6]=>[3,2,2,1]
[1,3,8,2,5,4,7,6]=>[3,2,2,1]
[1,6,7,5,2,4,8,3]=>[3,1,3,1]
[1,5,6,4,7,2,3,8]=>[3,2,3]
[1,7,4,2,5,8,3,6]=>[2,1,3,2]
[1,6,4,3,7,5,2,8]=>[2,1,2,1,2]
[1,6,5,4,7,2,3,8]=>[2,1,2,3]
[1,7,3,2,6,4,8,5]=>[2,1,2,2,1]
[1,5,8,2,3,6,7,4]=>[3,4,1]
[1,3,2,6,8,5,4,7]=>[2,3,1,2]
[1,6,3,2,7,4,5,8]=>[2,1,2,3]
[1,7,8,5,4,2,3,6]=>[3,1,1,3]
[1,8,4,2,3,6,5,7]=>[2,1,3,2]
[1,4,2,7,5,3,8,6]=>[2,2,1,2,1]
[1,5,7,6,2,4,3,8]=>[3,1,2,2]
[1,8,4,7,3,2,6,5]=>[2,2,1,2,1]
[1,3,8,4,2,6,5,7]=>[3,1,2,2]
[1,7,4,2,6,5,8,3]=>[2,1,2,2,1]
[1,6,5,8,3,7,4,2]=>[2,2,2,1,1]
[1,7,4,8,3,2,5,6]=>[2,2,1,3]
[1,4,8,3,2,7,5,6]=>[3,1,2,2]
[1,8,3,6,4,5,2,7]=>[2,2,2,2]
[1,6,4,7,3,2,8,5]=>[2,2,1,2,1]
[8,2,3,7,4,5,6,1]=>[1,3,3,1]
[8,5,7,2,3,6,4,1]=>[1,2,3,1,1]
[3,1,5,6,8,4,2,7]=>[1,4,1,2]
[7,5,2,1,6,8,3,4]=>[1,1,1,3,2]
[1,3,6,8,4,2,5,7]=>[4,1,3]
[7,6,1,5,4,8,2,3]=>[1,1,2,2,2]
[7,6,3,2,1,8,4,5]=>[1,1,1,1,2,2]
[2,8,7,3,4,6,1,5]=>[2,1,3,2]
[6,5,1,3,7,2,8,4]=>[1,1,3,2,1]
[8,1,7,3,4,5,2,6]=>[1,2,3,2]
[7,1,8,3,4,5,2,6]=>[1,2,3,2]
[7,4,8,2,5,3,1,6]=>[1,2,2,1,2]
[7,2,1,4,8,5,3,6]=>[1,1,3,1,2]
[6,8,7,3,4,2,1,5]=>[2,1,2,1,2]
[3,8,7,1,2,4,5,6]=>[2,1,5]
[1,8,5,3,4,6,2,7]=>[2,1,3,2]
[5,8,4,3,1,6,2,7]=>[2,1,1,2,2]
[7,1,6,5,4,3,8,2]=>[1,2,1,1,2,1]
[7,1,3,6,4,5,8,2]=>[1,3,3,1]
[7,1,5,3,6,4,8,2]=>[1,2,2,2,1]
[6,1,5,3,7,8,2,4]=>[1,2,3,2]
[5,8,7,1,2,6,3,4]=>[2,1,3,2]
[6,8,2,3,4,7,1,5]=>[2,4,2]
[5,1,7,3,8,6,2,4]=>[1,2,2,1,2]
[6,1,3,2,4,7,8,5]=>[1,2,4,1]
[6,2,1,3,4,7,8,5]=>[1,1,5,1]
[3,2,5,8,7,4,1,6]=>[1,3,1,1,2]
[4,2,5,8,7,3,1,6]=>[1,3,1,1,2]
[8,3,4,1,6,5,2,7]=>[1,2,2,1,2]
[3,4,8,5,7,2,1,6]=>[3,2,1,2]
[3,6,4,8,5,7,2,1]=>[2,2,2,1,1]
[5,8,4,7,3,6,2,1]=>[2,2,2,1,1]
[4,2,8,7,3,1,6,5]=>[1,2,1,1,2,1]
[6,5,8,2,1,7,4,3]=>[1,2,1,2,1,1]
[6,1,4,3,8,7,2,5]=>[1,2,2,1,2]
[5,1,3,2,6,8,7,4]=>[1,2,3,1,1]
[6,1,3,8,7,2,4,5]=>[1,3,1,3]
[1,2,8,4,5,7,3,6]=>[3,3,2]
[4,2,1,8,7,6,3,5]=>[1,1,2,1,1,2]
[3,2,5,8,7,1,4,6]=>[1,3,1,3]
[5,6,3,8,7,2,1,4]=>[2,2,1,1,2]
[2,5,8,4,7,1,6,3]=>[3,2,2,1]
[1,6,2,4,8,5,7,3]=>[2,3,2,1]
[3,1,6,5,8,7,2,4]=>[1,2,2,1,2]
[4,8,5,3,6,7,1,2]=>[2,1,3,2]
[1,8,5,3,4,7,6,2]=>[2,1,3,1,1]
[7,5,2,1,4,3,6,8]=>[1,1,1,2,3]
[3,1,7,6,4,2,5,8]=>[1,2,1,1,3]
[2,3,7,5,6,1,4,8]=>[3,2,3]
[5,1,4,7,6,3,2,8]=>[1,3,1,1,2]
[6,1,7,3,4,5,2,8]=>[1,2,3,2]
[5,7,6,2,4,1,3,8]=>[2,1,2,3]
[2,7,1,3,6,4,5,8]=>[2,3,3]
[8,1,7,3,5,4,6,2]=>[1,2,2,2,1]
[2,8,7,3,5,6,4,1]=>[2,1,3,1,1]
[3,2,7,4,1,8,6,5]=>[1,2,1,2,1,1]
[1,8,6,3,2,5,4,7]=>[2,1,1,2,2]
[3,2,4,8,5,7,1,6]=>[1,3,2,2]
[7,2,5,4,8,1,3,6]=>[1,2,2,3]
[5,1,8,3,2,7,6,4]=>[1,2,1,2,1,1]
[6,8,5,2,3,7,1,4]=>[2,1,3,2]
[8,1,2,4,7,5,6,3]=>[1,4,2,1]
[1,3,4,8,6,7,2,5]=>[4,2,2]
[8,3,1,4,6,7,5,2]=>[1,1,4,1,1]
[6,4,5,8,3,1,7,2]=>[1,3,1,2,1]
[2,7,8,5,6,4,1,3]=>[3,2,1,2]
[8,6,2,1,5,7,3,4]=>[1,1,1,3,2]
[4,6,2,8,5,3,7,1]=>[2,2,1,2,1]
[5,6,2,4,8,3,1,7]=>[2,3,1,2]
[8,7,2,4,1,5,3,6]=>[1,1,2,2,2]
[1,6,8,7,3,5,2,4]=>[3,1,2,2]
[7,1,3,5,4,8,6,2]=>[1,3,2,1,1]
[2,7,3,4,5,8,6,1]=>[2,4,1,1]
[4,1,5,2,8,6,3,7]=>[1,2,2,1,2]
[7,5,3,4,8,6,2,1]=>[1,1,3,1,1,1]
[8,4,3,1,7,2,5,6]=>[1,1,1,2,3]
[2,8,3,1,4,6,7,5]=>[2,1,4,1]
[6,8,3,4,2,5,7,1]=>[2,2,3,1]
[4,2,8,3,5,1,6,7]=>[1,2,2,3]
[5,6,1,2,4,3,7,8]=>[2,3,3]
[8,3,2,7,5,4,1,6]=>[1,1,2,1,1,2]
[3,1,2,6,5,4,7,8]=>[1,3,1,3]
[4,3,6,5,1,2,7,8]=>[1,2,1,4]
[8,2,3,7,5,4,6,1]=>[1,3,1,2,1]
[2,8,3,7,6,4,1,5]=>[2,2,1,1,2]
[2,8,3,7,6,4,5,1]=>[2,2,1,2,1]
[8,1,3,7,5,4,6,2]=>[1,3,1,2,1]
[8,1,3,7,5,4,2,6]=>[1,3,1,1,2]
[1,8,3,7,6,4,2,5]=>[2,2,1,1,2]
[5,8,3,7,6,4,2,1]=>[2,2,1,1,1,1]
[1,3,8,7,6,5,2,4]=>[3,1,1,1,2]
[2,8,1,7,6,4,5,3]=>[2,2,1,2,1]
[8,2,1,7,5,4,6,3]=>[1,1,2,1,2,1]
[8,1,2,7,5,4,6,3]=>[1,3,1,2,1]
[3,8,2,7,6,4,5,1]=>[2,2,1,2,1]
[4,8,7,2,6,3,1,5]=>[2,1,2,1,2]
[1,8,7,2,6,3,5,4]=>[2,1,2,2,1]
[8,7,2,1,4,3,5,6]=>[1,1,1,2,3]
[5,8,7,2,6,3,1,4]=>[2,1,2,1,2]
[2,8,7,1,6,3,4,5]=>[2,1,2,3]
[4,2,8,7,6,5,1,3]=>[1,2,1,1,1,2]
[5,8,7,1,6,3,4,2]=>[2,1,2,2,1]
[5,8,7,1,6,3,2,4]=>[2,1,2,1,2]
[1,4,8,7,6,5,2,3]=>[3,1,1,1,2]
[8,4,2,7,6,5,3,1]=>[1,1,2,1,1,1,1]
[6,8,7,5,2,4,3,1]=>[2,1,1,2,1,1]
[7,6,3,1,4,5,2,8]=>[1,1,1,3,2]
[7,2,3,6,4,5,1,8]=>[1,3,2,2]
[7,2,1,4,6,5,3,8]=>[1,1,3,1,2]
[7,3,6,2,4,5,1,8]=>[1,2,3,2]
[7,2,6,1,4,5,3,8]=>[1,2,3,2]
[6,8,7,2,4,5,1,3]=>[2,1,3,2]
[1,2,5,7,4,8,6,3]=>[4,2,1,1]
[6,2,1,8,7,5,3,4]=>[1,1,2,1,1,2]
[6,3,8,7,4,5,2,1]=>[1,2,1,2,1,1]
[4,2,1,5,3,8,6,7]=>[1,1,2,2,2]
[4,6,5,3,2,8,1,7]=>[2,1,1,2,2]
[2,8,3,4,1,5,6,7]=>[2,2,4]
[2,7,3,5,4,8,6,1]=>[2,2,2,1,1]
[2,6,4,3,5,8,1,7]=>[2,1,3,2]
[4,2,1,7,6,5,8,3]=>[1,1,2,1,2,1]
[4,5,7,3,6,1,8,2]=>[3,2,2,1]
[1,3,7,5,4,8,6,2]=>[3,1,2,1,1]
[3,8,7,5,4,1,6,2]=>[2,1,1,1,2,1]
[4,5,6,3,1,8,2,7]=>[3,1,2,2]
[1,4,6,3,5,8,2,7]=>[3,3,2]
[4,7,5,3,6,2,8,1]=>[2,1,2,2,1]
[5,4,1,3,2,6,8,7]=>[1,1,2,3,1]
[5,2,1,4,3,6,8,7]=>[1,1,2,3,1]
[6,2,4,3,1,8,5,7]=>[1,2,1,2,2]
[1,5,6,3,8,4,2,7]=>[3,2,1,2]
[5,4,6,3,8,1,2,7]=>[1,2,2,3]
[5,8,6,3,1,4,2,7]=>[2,1,1,2,2]
[5,8,7,1,4,3,6,2]=>[2,1,2,2,1]
[2,6,5,3,8,4,1,7]=>[2,1,2,1,2]
[5,7,3,8,4,2,6,1]=>[2,2,1,2,1]
[5,6,8,3,2,4,1,7]=>[3,1,2,2]
[5,3,6,2,8,4,1,7]=>[1,2,2,1,2]
[3,2,6,5,4,8,1,7]=>[1,2,1,2,2]
[2,6,5,4,8,3,1,7]=>[2,1,2,1,2]
[2,3,6,5,4,8,1,7]=>[3,1,2,2]
[3,7,5,4,8,2,6,1]=>[2,1,2,2,1]
[5,3,7,1,2,8,4,6]=>[1,2,3,2]
[1,2,7,6,4,8,3,5]=>[3,1,2,2]
[6,3,8,7,1,2,5,4]=>[1,2,1,3,1]
[2,8,7,6,1,3,5,4]=>[2,1,1,3,1]
[6,3,8,7,1,4,5,2]=>[1,2,1,3,1]
[2,7,5,4,8,1,6,3]=>[2,1,2,2,1]
[7,6,4,8,2,5,3,1]=>[1,1,2,2,1,1]
[6,3,8,7,2,5,4,1]=>[1,2,1,2,1,1]
[2,8,7,6,1,5,3,4]=>[2,1,1,2,2]
[7,6,4,8,1,3,2,5]=>[1,1,2,2,2]
[6,3,8,7,1,4,2,5]=>[1,2,1,2,2]
[6,3,8,7,1,2,4,5]=>[1,2,1,4]
[4,8,1,6,7,5,2,3]=>[2,3,1,2]
[6,8,4,1,7,5,2,3]=>[2,1,2,1,2]
[8,1,4,6,7,5,2,3]=>[1,4,1,2]
[2,6,8,1,7,4,5,3]=>[3,2,2,1]
[2,6,8,1,4,7,5,3]=>[3,3,1,1]
[6,4,8,1,2,7,5,3]=>[1,2,3,1,1]
[8,4,1,6,7,2,5,3]=>[1,1,3,2,1]
[8,1,4,6,7,2,5,3]=>[1,4,2,1]
[8,2,1,6,7,4,5,3]=>[1,1,3,2,1]
[8,2,6,1,7,4,5,3]=>[1,2,2,2,1]
[6,2,8,1,4,7,5,3]=>[1,2,3,1,1]
[4,2,8,1,6,7,5,3]=>[1,2,3,1,1]
[2,4,8,1,6,7,5,3]=>[3,3,1,1]
[4,2,8,6,1,7,5,3]=>[1,2,1,2,1,1]
[8,2,6,4,1,7,5,3]=>[1,2,1,2,1,1]
[8,1,2,6,4,7,5,3]=>[1,3,2,1,1]
[8,4,1,6,2,7,5,3]=>[1,1,2,2,1,1]
[4,8,6,1,2,7,5,3]=>[2,1,3,1,1]
[4,8,1,2,6,7,5,3]=>[2,4,1,1]
[4,8,2,1,6,7,5,3]=>[2,1,3,1,1]
[6,8,2,1,4,7,5,3]=>[2,1,3,1,1]
[8,6,2,1,7,4,5,3]=>[1,1,1,2,2,1]
[8,1,6,2,4,7,5,3]=>[1,2,3,1,1]
[8,6,1,2,4,7,5,3]=>[1,1,4,1,1]
[6,8,2,4,1,7,5,3]=>[2,2,2,1,1]
[4,8,2,6,1,7,5,3]=>[2,2,2,1,1]
[6,4,2,8,1,7,5,3]=>[1,1,2,2,1,1]
[8,4,2,6,1,7,5,3]=>[1,1,2,2,1,1]
[8,2,1,4,6,7,5,3]=>[1,1,4,1,1]
[8,2,4,6,1,7,5,3]=>[1,3,2,1,1]
[5,4,7,6,3,1,2,8]=>[1,2,1,1,3]
[3,6,4,8,1,5,2,7]=>[2,2,2,2]
[3,6,8,4,1,5,2,7]=>[3,1,2,2]
[8,7,1,4,2,3,5,6]=>[1,1,2,4]
[3,8,6,4,1,5,2,7]=>[2,1,1,2,2]
[8,2,6,5,7,1,3,4]=>[1,2,2,3]
[4,6,1,3,2,8,7,5]=>[2,2,2,1,1]
[5,4,6,7,1,3,8,2]=>[1,3,3,1]
[7,1,4,8,2,3,6,5]=>[1,3,3,1]
[3,6,5,4,7,1,8,2]=>[2,1,2,2,1]
[4,5,3,6,7,1,8,2]=>[2,3,2,1]
[1,4,7,8,3,5,2,6]=>[4,2,2]
[4,6,1,3,5,2,8,7]=>[2,3,2,1]
[1,7,6,3,5,8,4,2]=>[2,1,3,1,1]
[2,5,1,4,8,3,7,6]=>[2,3,2,1]
[7,6,2,1,4,5,3,8]=>[1,1,1,3,2]
[4,1,2,8,7,6,3,5]=>[1,3,1,1,2]
[5,1,4,3,8,6,7,2]=>[1,2,2,2,1]
[3,5,1,6,4,8,7,2]=>[2,2,2,1,1]
[2,6,3,5,1,7,4,8]=>[2,2,2,2]
[6,1,2,5,4,8,7,3]=>[1,3,2,1,1]
[8,4,1,7,3,5,6,2]=>[1,1,2,3,1]
[8,4,1,2,5,7,3,6]=>[1,1,4,2]
[1,6,2,8,5,4,7,3]=>[2,2,1,2,1]
[6,1,5,3,2,7,4,8]=>[1,2,1,2,2]
[6,4,7,2,1,8,5,3]=>[1,2,1,2,1,1]
[5,8,4,6,3,1,7,2]=>[2,2,1,2,1]
[2,4,5,6,8,3,1,7]=>[5,1,2]
[3,8,4,2,1,6,5,7]=>[2,1,1,2,2]
[3,4,7,1,2,6,8,5]=>[3,4,1]
[4,1,8,6,5,2,3,7]=>[1,2,1,1,3]
[3,4,5,8,6,2,1,7]=>[4,1,1,2]
[8,6,3,5,4,7,1,2]=>[1,1,2,2,2]
[2,5,3,7,1,8,6,4]=>[2,2,2,1,1]
[4,8,6,2,5,1,7,3]=>[2,1,2,2,1]
[4,5,1,8,6,3,7,2]=>[2,2,1,2,1]
[1,7,2,4,5,3,8,6]=>[2,3,2,1]
[8,5,3,4,6,1,7,2]=>[1,1,3,2,1]
[4,5,3,7,1,8,6,2]=>[2,2,2,1,1]
[1,4,6,2,5,3,8,7]=>[3,2,2,1]
[6,2,8,7,1,3,5,4]=>[1,2,1,3,1]
[4,5,3,6,1,8,7,2]=>[2,2,2,1,1]
[8,3,7,2,1,6,5,4]=>[1,2,1,2,1,1]
[8,4,7,6,2,5,1,3]=>[1,2,1,2,2]
[8,4,7,3,6,2,1,5]=>[1,2,2,1,2]
[3,8,7,5,6,4,1,2]=>[2,1,2,1,2]
[3,8,7,5,6,2,1,4]=>[2,1,2,1,2]
[3,8,7,5,6,2,4,1]=>[2,1,2,2,1]
[2,8,7,5,6,4,1,3]=>[2,1,2,1,2]
[1,5,6,3,8,2,7,4]=>[3,2,2,1]
[2,6,3,8,4,7,1,5]=>[2,2,2,2]
[2,6,3,5,7,8,1,4]=>[2,4,2]
[1,5,6,3,7,2,8,4]=>[3,2,2,1]
[1,7,5,3,6,2,8,4]=>[2,1,2,2,1]
[1,5,7,3,4,2,8,6]=>[3,2,2,1]
[1,5,8,3,4,2,7,6]=>[3,2,2,1]
[1,4,5,3,7,2,8,6]=>[3,2,2,1]
[1,4,5,3,8,2,7,6]=>[3,2,2,1]
[6,5,1,4,2,7,8,3]=>[1,1,2,3,1]
[6,5,1,4,2,8,7,3]=>[1,1,2,2,1,1]
[1,7,5,4,2,8,6,3]=>[2,1,1,2,1,1]
[4,1,2,7,5,3,6,8]=>[1,3,1,3]
[5,1,6,8,3,7,2,4]=>[1,3,2,2]
[6,1,3,7,2,4,5,8]=>[1,3,4]
[4,1,5,6,8,3,2,7]=>[1,4,1,2]
[3,8,5,2,1,4,7,6]=>[2,1,1,3,1]
[3,4,8,2,1,6,7,5]=>[3,1,3,1]
[3,5,4,8,2,6,7,1]=>[2,2,3,1]
[5,4,7,1,8,6,3,2]=>[1,2,2,1,1,1]
[3,1,5,6,8,4,7,2]=>[1,4,2,1]
[3,6,1,8,2,5,4,7]=>[2,2,2,2]
[5,8,3,2,1,7,4,6]=>[2,1,1,2,2]
[1,4,8,2,6,5,3,7]=>[3,2,1,2]
[8,5,1,3,6,2,4,7]=>[1,1,3,3]
[3,8,1,2,6,5,4,7]=>[2,3,1,2]
[1,2,8,5,6,4,3,7]=>[3,2,1,2]
[7,5,1,8,3,4,2,6]=>[1,1,2,2,2]
[5,2,8,1,7,4,3,6]=>[1,2,2,1,2]
[5,4,7,1,2,3,8,6]=>[1,2,4,1]
[1,4,8,2,6,7,3,5]=>[3,3,2]
[1,2,5,6,8,7,3,4]=>[5,1,2]
[1,5,6,8,2,7,4,3]=>[4,2,1,1]
[3,6,1,8,2,7,4,5]=>[2,2,2,2]
[2,6,7,3,4,1,8,5]=>[3,2,2,1]
[1,6,5,7,8,2,4,3]=>[2,3,2,1]
[1,5,6,7,2,8,4,3]=>[4,2,1,1]
[3,6,1,2,8,7,5,4]=>[2,3,1,1,1]
[3,7,6,1,8,2,4,5]=>[2,1,2,3]
[1,3,7,2,6,4,8,5]=>[3,2,2,1]
[1,4,7,2,6,3,8,5]=>[3,2,2,1]
[2,6,8,1,4,7,3,5]=>[3,3,2]
[1,4,6,8,3,7,2,5]=>[4,2,2]
[1,5,8,6,7,3,4,2]=>[3,2,2,1]
[1,6,5,8,7,2,4,3]=>[2,2,1,2,1]
[1,5,7,6,2,8,3,4]=>[3,1,2,2]
[1,2,5,8,6,7,4,3]=>[4,2,1,1]
[1,2,6,5,7,3,8,4]=>[3,2,2,1]
[1,7,5,8,6,4,2,3]=>[2,2,1,1,2]
[7,3,8,6,4,2,1,5]=>[1,2,1,1,1,2]
[2,7,6,3,4,8,1,5]=>[2,1,3,2]
[3,6,5,8,1,2,7,4]=>[2,2,3,1]
[5,4,7,8,1,6,3,2]=>[1,3,2,1,1]
[2,5,6,8,1,3,7,4]=>[4,3,1]
[5,3,6,8,1,2,7,4]=>[1,3,3,1]
[4,6,5,8,3,2,7,1]=>[2,2,1,2,1]
[4,5,6,8,2,3,7,1]=>[4,3,1]
[2,5,8,7,1,6,4,3]=>[3,1,2,1,1]
[4,7,5,8,3,6,2,1]=>[2,2,2,1,1]
[7,3,6,8,5,2,1,4]=>[1,3,1,1,2]
[8,3,6,7,5,2,4,1]=>[1,3,1,2,1]
[8,4,5,7,3,6,2,1]=>[1,3,2,1,1]
[2,4,7,8,5,6,3,1]=>[4,2,1,1]
[3,6,8,7,5,2,4,1]=>[3,1,1,2,1]
[6,4,7,8,5,1,3,2]=>[1,3,1,2,1]
[7,8,4,6,5,3,1,2]=>[2,2,1,1,2]
[6,8,4,7,5,1,3,2]=>[2,2,1,2,1]
[2,7,5,4,3,1,6,8]=>[2,1,1,1,3]
[1,2,6,4,3,8,7,5]=>[3,1,2,1,1]
[6,5,8,3,1,4,2,7]=>[1,2,1,2,2]
[7,6,3,5,4,1,2,8]=>[1,1,2,1,3]
[2,7,4,6,1,5,3,8]=>[2,2,2,2]
[2,7,3,1,6,5,4,8]=>[2,1,2,1,2]
[7,6,1,2,3,5,4,8]=>[1,1,4,2]
[1,8,5,7,2,3,6,4]=>[2,2,3,1]
[2,3,6,8,1,7,5,4]=>[4,2,1,1]
[6,1,3,8,4,2,5,7]=>[1,3,1,3]
[2,8,7,5,1,6,3,4]=>[2,1,1,2,2]
[5,8,1,7,2,3,4,6]=>[2,2,4]
[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,2,1]
[5,8,7,2,3,1,6,4]=>[2,1,2,2,1]
[3,5,8,1,4,7,2,6]=>[3,3,2]
[8,5,3,7,4,6,1,2]=>[1,1,2,2,2]
[3,8,7,5,2,6,4,1]=>[2,1,1,2,1,1]
[4,6,3,1,8,7,2,5]=>[2,1,2,1,2]
[8,3,6,7,1,5,2,4]=>[1,3,2,2]
[3,8,7,5,1,2,6,4]=>[2,1,1,3,1]
[8,1,3,5,6,2,4,7]=>[1,4,3]
[5,8,3,7,1,4,6,2]=>[2,2,3,1]
[3,8,7,4,2,6,5,1]=>[2,1,1,2,1,1]
[5,8,3,2,4,7,6,1]=>[2,1,3,1,1]
[8,4,5,3,7,6,1,2]=>[1,2,2,1,2]
[5,8,2,1,3,4,7,6]=>[2,1,4,1]
[2,5,1,4,3,6,7,8]=>[2,2,4]
[5,3,8,2,4,6,1,7]=>[1,2,3,2]
[4,5,8,3,2,6,1,7]=>[3,1,2,2]
[1,5,3,7,2,8,6,4]=>[2,2,2,1,1]
[3,4,7,1,2,8,6,5]=>[3,3,1,1]
[5,8,2,1,4,6,3,7]=>[2,1,3,2]
[4,1,5,8,3,6,2,7]=>[1,3,2,2]
[4,5,8,3,6,1,2,7]=>[3,2,3]
[6,1,7,8,3,5,2,4]=>[1,3,2,2]
[5,2,7,8,1,3,6,4]=>[1,3,3,1]
[2,6,7,8,3,1,5,4]=>[4,1,2,1]
[3,2,7,1,8,5,4,6]=>[1,2,2,1,2]
[4,7,8,5,2,3,1,6]=>[3,1,2,2]
[6,2,7,8,1,5,3,4]=>[1,3,2,2]
[2,7,1,3,8,5,4,6]=>[2,3,1,2]
[2,6,7,8,4,1,3,5]=>[4,1,3]
[2,6,7,8,4,3,1,5]=>[4,1,1,2]
[7,1,2,6,3,8,4,5]=>[1,3,2,2]
[8,1,2,6,5,3,7,4]=>[1,3,1,2,1]
[8,1,4,6,7,2,3,5]=>[1,4,3]
[8,3,5,6,1,2,7,4]=>[1,3,3,1]
[8,5,1,7,2,6,3,4]=>[1,1,2,2,2]
[8,5,4,6,1,2,7,3]=>[1,1,2,3,1]
[7,3,8,1,2,5,4,6]=>[1,2,3,2]
[7,4,1,8,2,5,3,6]=>[1,1,2,2,2]
[6,4,1,7,2,8,3,5]=>[1,1,2,2,2]
[6,8,1,2,3,5,7,4]=>[2,5,1]
[7,3,4,1,2,8,6,5]=>[1,2,3,1,1]
[7,3,8,1,2,5,6,4]=>[1,2,4,1]
[7,2,1,8,3,6,4,5]=>[1,1,2,2,2]
[7,2,4,5,1,3,8,6]=>[1,3,3,1]
[7,1,8,3,2,4,5,6]=>[1,2,1,4]
[8,1,5,6,3,2,7,4]=>[1,3,1,2,1]
[8,1,2,5,7,6,3,4]=>[1,4,1,2]
[6,8,7,3,1,2,4,5]=>[2,1,1,4]
[7,4,8,3,1,2,6,5]=>[1,2,1,3,1]
[8,4,5,3,1,6,7,2]=>[1,2,1,3,1]
[8,2,3,1,6,7,4,5]=>[1,2,3,2]
[8,2,1,7,4,3,5,6]=>[1,1,2,1,3]
[7,2,6,8,4,1,3,5]=>[1,3,1,3]
[7,2,5,1,6,8,3,4]=>[1,2,3,2]
[8,1,7,3,4,2,5,6]=>[1,2,2,3]
[6,1,8,3,2,7,4,5]=>[1,2,1,2,2]
[7,5,1,6,4,8,2,3]=>[1,1,2,2,2]
[7,2,3,1,8,5,4,6]=>[1,2,2,1,2]
[6,2,1,7,4,8,3,5]=>[1,1,2,2,2]
[1,4,2,5,7,6,8,3]=>[2,3,2,1]
[1,3,4,6,8,5,2,7]=>[5,1,2]
[1,4,6,8,5,2,7,3]=>[4,1,2,1]
[1,3,4,6,8,5,7,2]=>[5,2,1]
[1,4,5,7,2,8,6,3]=>[4,2,1,1]
[1,7,4,3,2,5,6,8]=>[2,1,1,4]
[1,7,4,3,6,2,5,8]=>[2,1,2,3]
[3,7,5,8,2,4,6,1]=>[2,2,3,1]
[5,2,1,6,3,4,8,7]=>[1,1,2,3,1]
[5,1,3,4,6,2,8,7]=>[1,4,2,1]
[3,8,4,5,7,2,6,1]=>[2,3,2,1]
[3,8,4,7,5,6,2,1]=>[2,2,2,1,1]
[4,2,8,6,3,7,5,1]=>[1,2,1,2,1,1]
[4,1,7,6,3,8,5,2]=>[1,2,1,2,1,1]
[7,4,1,8,5,3,6,2]=>[1,1,2,1,2,1]
[3,5,6,8,4,7,1,2]=>[4,2,2]
[5,4,1,8,6,7,2,3]=>[1,1,2,2,2]
[6,2,8,4,5,3,7,1]=>[1,2,2,2,1]
[4,5,2,1,8,7,3,6]=>[2,1,2,1,2]
[4,7,3,8,2,6,5,1]=>[2,2,2,1,1]
[4,7,3,1,8,6,2,5]=>[2,1,2,1,2]
[6,2,1,3,7,4,8,5]=>[1,1,3,2,1]
[6,3,7,1,2,5,8,4]=>[1,2,4,1]
[5,1,4,7,8,2,6,3]=>[1,4,2,1]
[7,2,5,8,1,3,6,4]=>[1,3,3,1]
[8,3,6,7,2,4,5,1]=>[1,3,3,1]
[3,8,7,5,2,1,6,4]=>[2,1,1,1,2,1]
[3,8,5,6,2,7,4,1]=>[2,2,2,1,1]
[3,6,5,8,4,2,7,1]=>[2,2,1,2,1]
[6,8,3,2,5,7,4,1]=>[2,1,3,1,1]
[4,1,5,6,8,7,3,2]=>[1,4,1,1,1]
[8,4,2,3,6,7,5,1]=>[1,1,4,1,1]
[6,1,2,4,5,7,8,3]=>[1,6,1]
[4,5,1,3,7,6,8,2]=>[2,3,2,1]
[3,5,4,8,6,2,7,1]=>[2,2,1,2,1]
[3,6,2,4,5,8,7,1]=>[2,4,1,1]
[8,1,3,7,4,5,6,2]=>[1,3,3,1]
[5,1,2,8,7,4,6,3]=>[1,3,1,2,1]
[7,1,3,4,8,5,6,2]=>[1,4,2,1]
[4,1,7,5,3,8,6,2]=>[1,2,1,2,1,1]
[5,1,2,8,6,7,4,3]=>[1,3,2,1,1]
[3,8,7,4,2,5,6,1]=>[2,1,1,3,1]
[7,6,3,5,1,8,4,2]=>[1,1,2,2,1,1]
[8,1,5,3,4,6,7,2]=>[1,2,4,1]
[8,1,5,3,6,4,7,2]=>[1,2,2,2,1]
[4,5,1,3,7,8,6,2]=>[2,4,1,1]
[2,6,4,8,3,1,5,7]=>[2,2,1,3]
[7,2,3,8,1,4,5,6]=>[1,3,4]
[7,2,3,8,1,4,6,5]=>[1,3,3,1]
[7,6,5,2,3,8,4,1]=>[1,1,1,3,1,1]
[2,6,4,1,5,8,7,3]=>[2,1,3,1,1]
[3,5,1,4,6,2,7,8]=>[2,3,3]
[7,6,5,2,4,3,8,1]=>[1,1,1,2,2,1]
[7,6,5,2,4,3,1,8]=>[1,1,1,2,1,2]
[7,2,3,5,1,4,8,6]=>[1,3,3,1]
[3,6,4,5,2,8,1,7]=>[2,2,2,2]
[7,5,1,8,3,6,2,4]=>[1,1,2,2,2]
[8,1,5,6,3,7,2,4]=>[1,3,2,2]
[8,1,5,6,3,7,4,2]=>[1,3,2,1,1]
[3,6,4,5,2,7,8,1]=>[2,2,3,1]
[7,2,3,5,1,4,6,8]=>[1,3,4]
[8,1,5,4,7,3,6,2]=>[1,2,2,2,1]
[3,5,1,4,6,8,7,2]=>[2,4,1,1]
[7,6,5,4,1,3,8,2]=>[1,1,1,1,3,1]
[7,6,5,3,4,1,8,2]=>[1,1,1,2,2,1]
[7,6,5,2,8,3,1,4]=>[1,1,1,2,1,2]
[7,6,5,4,1,8,2,3]=>[1,1,1,1,2,2]
[3,6,4,1,5,7,2,8]=>[2,1,3,2]
[2,5,1,4,6,7,8,3]=>[2,5,1]
[8,1,5,4,7,6,3,2]=>[1,2,2,1,1,1]
[2,5,1,4,6,7,3,8]=>[2,4,2]
[3,6,4,1,5,7,8,2]=>[2,1,4,1]
[7,6,5,2,8,4,1,3]=>[1,1,1,2,1,2]
[1,4,3,7,5,2,8,6]=>[2,2,1,2,1]
[3,1,6,5,2,8,7,4]=>[1,2,1,2,1,1]
[6,2,7,4,3,1,8,5]=>[1,2,1,1,2,1]
[1,7,2,4,3,5,8,6]=>[2,2,3,1]
[2,7,3,4,5,1,8,6]=>[2,3,2,1]
[3,8,1,7,4,2,6,5]=>[2,2,1,2,1]
[8,1,7,4,3,5,6,2]=>[1,2,1,3,1]
[6,8,2,4,5,3,7,1]=>[2,3,2,1]
[4,8,5,3,6,1,7,2]=>[2,1,2,2,1]
[2,8,3,1,4,7,5,6]=>[2,1,3,2]
[6,4,3,1,8,7,2,5]=>[1,1,1,2,1,2]
[5,7,3,8,6,4,2,1]=>[2,2,1,1,1,1]
[8,6,3,2,7,4,1,5]=>[1,1,1,2,1,2]
[1,4,2,3,8,6,7,5]=>[2,3,2,1]
[2,7,3,1,8,4,5,6]=>[2,1,2,3]
[6,3,1,8,2,5,7,4]=>[1,1,2,3,1]
[3,6,1,8,4,5,7,2]=>[2,2,3,1]
[2,4,8,7,3,6,1,5]=>[3,1,2,2]
[1,6,8,4,5,3,7,2]=>[3,2,2,1]
[1,2,8,3,5,6,4,7]=>[3,3,2]
[3,5,7,4,8,1,6,2]=>[3,2,2,1]
[4,2,8,3,1,5,7,6]=>[1,2,1,3,1]
[2,8,1,3,5,4,6,7]=>[2,3,3]
[1,5,2,8,6,4,3,7]=>[2,2,1,1,2]
[7,4,8,6,3,1,2,5]=>[1,2,1,1,3]
[3,6,8,4,1,2,5,7]=>[3,1,4]
[4,7,8,5,2,1,3,6]=>[3,1,1,3]
[6,1,5,2,8,7,3,4]=>[1,2,2,1,2]
[8,1,3,5,7,4,2,6]=>[1,4,1,2]
[3,1,8,5,4,7,2,6]=>[1,2,1,2,2]
[3,1,6,4,8,5,2,7]=>[1,2,2,1,2]
[5,1,3,4,2,6,8,7]=>[1,3,3,1]
[3,2,6,4,1,5,7,8]=>[1,2,1,4]
[5,4,2,1,8,3,6,7]=>[1,1,1,2,3]
[4,2,5,1,8,7,3,6]=>[1,2,2,1,2]
[6,8,2,7,1,4,3,5]=>[2,2,2,2]
[1,8,4,7,3,2,5,6]=>[2,2,1,3]
[8,6,3,1,5,7,2,4]=>[1,1,1,3,2]
[5,8,3,1,4,7,6,2]=>[2,1,3,1,1]
[1,2,5,4,7,8,3,6]=>[3,3,2]
[1,8,3,2,6,4,7,5]=>[2,1,2,2,1]
[4,7,1,2,5,3,6,8]=>[2,3,3]
[6,8,4,1,3,7,2,5]=>[2,1,3,2]
[3,2,6,1,7,8,5,4]=>[1,2,3,1,1]
[7,6,4,1,8,3,5,2]=>[1,1,1,2,2,1]
[5,4,1,6,7,3,2,8]=>[1,1,3,1,2]
[7,4,1,6,5,8,2,3]=>[1,1,2,2,2]
[8,5,4,1,6,7,3,2]=>[1,1,1,3,1,1]
[6,5,7,3,2,8,4,1]=>[1,2,1,2,1,1]
[6,4,1,2,7,5,3,8]=>[1,1,3,1,2]
[7,4,3,5,2,8,6,1]=>[1,1,2,2,1,1]
[5,2,8,3,6,4,7,1]=>[1,2,2,2,1]
[5,4,6,1,2,7,3,8]=>[1,2,3,2]
[8,5,4,6,2,1,7,3]=>[1,1,2,1,2,1]
[8,5,1,7,2,3,6,4]=>[1,1,2,3,1]
[5,2,6,4,8,1,3,7]=>[1,2,2,3]
[5,2,1,6,4,7,8,3]=>[1,1,2,3,1]
[1,6,2,3,5,7,8,4]=>[2,5,1]
[7,2,5,1,3,4,8,6]=>[1,2,4,1]
[1,3,4,8,5,2,6,7]=>[4,1,3]
[8,2,4,6,1,7,3,5]=>[1,3,2,2]
[6,2,7,5,1,3,4,8]=>[1,2,1,4]
[6,5,7,1,2,3,8,4]=>[1,2,4,1]
[3,2,7,4,1,5,6,8]=>[1,2,1,4]
[4,7,2,1,5,6,8,3]=>[2,1,4,1]
[7,2,3,5,8,6,1,4]=>[1,4,1,2]
[5,8,2,3,6,7,1,4]=>[2,4,2]
[1,5,7,2,3,6,8,4]=>[3,4,1]
[8,4,1,7,2,5,3,6]=>[1,1,2,2,2]
[4,2,7,1,5,3,6,8]=>[1,2,2,3]
[7,3,1,4,2,5,8,6]=>[1,1,2,3,1]
[3,2,5,7,8,4,1,6]=>[1,4,1,2]
[3,4,7,8,2,5,1,6]=>[4,2,2]
[4,2,5,3,7,8,1,6]=>[1,2,3,2]
[4,3,5,1,6,2,7,8]=>[1,2,2,3]
[8,6,3,5,4,1,2,7]=>[1,1,2,1,3]
[8,3,2,6,1,5,4,7]=>[1,1,2,2,2]
[8,5,1,7,4,6,2,3]=>[1,1,2,2,2]
[4,8,1,7,6,3,5,2]=>[2,2,1,2,1]
[8,5,1,7,4,3,6,2]=>[1,1,2,1,2,1]
[8,5,7,6,2,1,3,4]=>[1,2,1,1,3]
[5,4,8,3,1,7,2,6]=>[1,2,1,2,2]
[5,1,4,8,3,2,7,6]=>[1,3,1,2,1]
[4,8,1,7,6,5,2,3]=>[2,2,1,1,2]
[4,3,8,7,2,6,1,5]=>[1,2,1,2,2]
[3,8,7,2,6,4,1,5]=>[2,1,2,1,2]
[8,2,5,7,4,3,6,1]=>[1,3,1,2,1]
[3,8,7,4,6,1,2,5]=>[2,1,2,3]
[8,7,6,3,5,4,1,2]=>[1,1,1,2,1,2]
[2,8,4,7,6,1,5,3]=>[2,2,1,2,1]
[2,5,4,8,3,1,7,6]=>[2,2,1,2,1]
[5,4,8,2,1,3,7,6]=>[1,2,1,3,1]
[3,8,7,2,6,1,5,4]=>[2,1,2,2,1]
[1,8,4,7,6,3,5,2]=>[2,2,1,2,1]
[1,8,3,7,6,5,2,4]=>[2,2,1,1,2]
[1,4,3,8,7,2,6,5]=>[2,2,1,2,1]
[7,1,5,4,6,2,3,8]=>[1,2,2,3]
[7,8,1,5,2,3,6,4]=>[2,2,3,1]
[7,4,1,3,6,2,5,8]=>[1,1,3,3]
[5,6,1,8,4,2,7,3]=>[2,2,1,2,1]
[7,8,6,4,1,5,3,2]=>[2,1,1,2,1,1]
[5,4,3,1,7,6,2,8]=>[1,1,1,2,1,2]
[3,1,6,5,7,4,2,8]=>[1,2,2,1,2]
[4,1,3,7,5,6,2,8]=>[1,3,2,2]
[5,6,1,7,4,2,3,8]=>[2,2,1,3]
[4,2,7,8,5,1,6,3]=>[1,3,1,2,1]
[7,3,8,6,4,5,2,1]=>[1,2,1,2,1,1]
[3,8,6,1,7,4,2,5]=>[2,1,2,1,2]
[2,6,8,3,1,7,4,5]=>[3,1,2,2]
[2,5,4,8,1,7,3,6]=>[2,2,2,2]
[7,5,2,4,8,3,6,1]=>[1,1,3,2,1]
[7,6,2,8,4,3,5,1]=>[1,1,2,1,2,1]
[6,8,1,2,5,7,3,4]=>[2,4,2]
[7,8,2,6,3,5,4,1]=>[2,2,2,1,1]
[3,8,6,4,7,5,2,1]=>[2,1,2,1,1,1]
[7,2,6,5,8,3,4,1]=>[1,2,2,2,1]
[5,6,3,1,4,2,7,8]=>[2,1,2,3]
[2,6,5,3,4,8,7,1]=>[2,1,3,1,1]
[3,1,5,4,2,6,7,8]=>[1,2,1,4]
[2,6,1,5,3,4,7,8]=>[2,2,4]
[5,2,3,6,7,4,1,8]=>[1,4,1,2]
[3,6,2,7,4,5,1,8]=>[2,2,2,2]
[2,3,7,1,6,4,5,8]=>[3,2,3]
[3,4,7,8,5,1,6,2]=>[4,1,2,1]
[3,6,2,4,7,8,5,1]=>[2,4,1,1]
[5,2,3,6,4,8,7,1]=>[1,3,2,1,1]
[8,7,5,4,2,6,3,1]=>[1,1,1,1,2,1,1]
[3,7,6,2,5,4,8,1]=>[2,1,2,2,1]
[5,3,6,4,8,7,2,1]=>[1,2,2,1,1,1]
[1,5,4,8,6,2,7,3]=>[2,2,1,2,1]
[4,5,2,7,6,3,8,1]=>[2,2,1,2,1]
[7,5,1,2,6,4,8,3]=>[1,1,3,2,1]
[5,3,8,1,2,7,6,4]=>[1,2,3,1,1]
[2,1,8,6,5,3,7,4]=>[1,2,1,1,2,1]
[5,8,3,1,2,7,6,4]=>[2,1,3,1,1]
[7,6,2,5,3,8,4,1]=>[1,1,2,2,1,1]
[7,3,4,6,5,8,2,1]=>[1,3,2,1,1]
[6,5,2,4,7,3,8,1]=>[1,1,3,2,1]
[6,1,5,7,4,8,2,3]=>[1,3,2,2]
[8,1,4,3,7,5,2,6]=>[1,2,2,1,2]
[8,4,5,7,2,1,3,6]=>[1,3,1,3]
[8,4,6,1,3,7,2,5]=>[1,2,3,2]
[7,4,6,1,5,8,2,3]=>[1,2,3,2]
[4,8,5,1,2,3,6,7]=>[2,1,5]
[8,6,2,4,5,1,3,7]=>[1,1,3,3]
[4,5,1,3,8,6,2,7]=>[2,3,1,2]
[8,5,1,3,4,7,2,6]=>[1,1,4,2]
[4,2,7,1,3,6,8,5]=>[1,2,4,1]
[8,3,6,5,2,7,4,1]=>[1,2,1,2,1,1]
[8,4,5,6,2,7,3,1]=>[1,3,2,1,1]
[5,8,3,6,4,7,2,1]=>[2,2,2,1,1]
[1,5,8,4,6,2,7,3]=>[3,2,2,1]
[1,7,5,6,2,8,4,3]=>[2,2,2,1,1]
[7,3,6,5,8,4,2,1]=>[1,2,2,1,1,1]
[5,4,6,8,3,2,7,1]=>[1,3,1,2,1]
[7,4,2,3,6,8,5,1]=>[1,1,4,1,1]
[2,7,3,8,5,4,6,1]=>[2,2,1,2,1]
[2,1,6,7,4,8,3,5]=>[1,3,2,2]
[7,4,8,5,1,2,6,3]=>[1,2,1,3,1]
[6,4,5,7,2,8,3,1]=>[1,3,2,1,1]
[1,5,6,4,7,2,8,3]=>[3,2,2,1]
[7,8,1,3,6,4,5,2]=>[2,3,2,1]
[7,2,6,8,4,5,3,1]=>[1,3,2,1,1]
[7,3,6,8,5,1,4,2]=>[1,3,1,2,1]
[7,5,8,1,6,2,4,3]=>[1,2,2,2,1]
[7,5,2,4,8,3,1,6]=>[1,1,3,1,2]
[7,8,3,1,6,2,5,4]=>[2,1,2,2,1]
[6,7,8,4,3,1,5,2]=>[3,1,1,2,1]
[7,3,8,1,6,4,5,2]=>[1,2,2,2,1]
[1,7,5,8,2,4,6,3]=>[2,2,3,1]
[7,5,2,8,1,4,6,3]=>[1,1,2,3,1]
[3,7,8,2,1,6,4,5]=>[3,1,2,2]
[7,8,1,6,3,5,4,2]=>[2,2,2,1,1]
[6,7,8,2,5,4,3,1]=>[3,2,1,1,1]
[6,7,8,3,1,5,4,2]=>[3,1,2,1,1]
[7,8,1,6,2,5,4,3]=>[2,2,2,1,1]
[4,1,8,3,7,6,5,2]=>[1,2,2,1,1,1]
[5,1,6,8,3,4,7,2]=>[1,3,3,1]
[7,1,6,8,5,4,3,2]=>[1,3,1,1,1,1]
[8,7,1,6,5,4,2,3]=>[1,1,2,1,1,2]
[4,7,6,2,5,3,1,8]=>[2,1,2,1,2]
[7,8,1,6,5,4,2,3]=>[2,2,1,1,2]
[3,5,2,8,4,1,7,6]=>[2,2,1,2,1]
[3,6,2,8,5,4,1,7]=>[2,2,1,1,2]
[8,4,6,3,5,2,1,7]=>[1,2,2,1,2]
[4,6,8,2,5,3,1,7]=>[3,2,1,2]
[4,5,8,2,3,6,1,7]=>[3,3,2]
[7,6,8,1,5,3,2,4]=>[1,2,2,1,2]
[8,6,7,4,1,3,2,5]=>[1,2,1,2,2]
[6,8,7,4,1,2,3,5]=>[2,1,1,4]
[5,6,8,1,2,3,7,4]=>[3,4,1]
[5,6,1,8,2,4,7,3]=>[2,2,3,1]
[8,5,7,1,3,6,2,4]=>[1,2,3,2]
[4,8,1,2,7,6,5,3]=>[2,3,1,1,1]
[4,6,1,2,8,5,7,3]=>[2,3,2,1]
[3,6,2,1,8,5,7,4]=>[2,1,2,2,1]
[3,7,2,1,8,6,5,4]=>[2,1,2,1,1,1]
[5,4,7,3,2,6,1,8]=>[1,2,1,2,2]
[6,4,7,3,5,2,1,8]=>[1,2,2,1,2]
[3,8,2,7,5,1,4,6]=>[2,2,1,3]
[3,6,2,8,1,4,7,5]=>[2,2,3,1]
[4,7,8,2,1,6,3,5]=>[3,1,2,2]
[5,7,8,4,2,1,3,6]=>[3,1,1,3]
[7,5,8,4,3,1,2,6]=>[1,2,1,1,3]
[6,4,8,3,1,2,7,5]=>[1,2,1,3,1]
[6,4,8,3,5,2,1,7]=>[1,2,2,1,2]
[3,1,6,2,5,7,8,4]=>[1,2,4,1]
[3,1,6,5,7,8,2,4]=>[1,2,3,2]
[2,1,6,3,5,7,4,8]=>[1,2,3,2]
[1,6,4,5,2,7,3,8]=>[2,2,2,2]
[1,6,5,2,7,3,4,8]=>[2,1,2,3]
[1,4,7,3,2,5,6,8]=>[3,1,4]
[2,1,6,5,7,3,4,8]=>[1,2,2,3]
[2,1,6,7,4,3,5,8]=>[1,3,1,3]
[2,7,4,3,5,1,6,8]=>[2,1,2,3]
[7,1,4,3,5,2,6,8]=>[1,2,2,3]
[3,1,6,7,4,2,5,8]=>[1,3,1,3]
[6,1,7,2,4,3,5,8]=>[1,2,2,3]
[1,3,7,4,5,2,6,8]=>[3,2,3]
[1,5,7,2,6,3,4,8]=>[3,2,3]
[6,2,1,4,5,3,7,8]=>[1,1,3,3]
[6,2,1,5,7,3,4,8]=>[1,1,3,3]
[6,2,4,8,3,5,1,7]=>[1,3,2,2]
[2,7,4,5,3,1,6,8]=>[2,2,1,3]
[5,3,7,4,2,1,6,8]=>[1,2,1,1,3]
[1,2,4,6,8,3,7,5]=>[5,2,1]
[1,3,5,8,2,6,7,4]=>[4,3,1]
[6,1,3,7,2,8,5,4]=>[1,3,2,1,1]
[2,1,8,3,6,5,4,7]=>[1,2,2,1,2]
[2,8,7,3,6,5,4,1]=>[2,1,2,1,1,1]
[6,4,5,8,3,7,1,2]=>[1,3,2,2]
[8,1,4,3,6,7,2,5]=>[1,2,3,2]
[2,6,8,4,3,1,7,5]=>[3,1,1,2,1]
[3,8,5,1,6,2,4,7]=>[2,1,2,3]
[8,1,5,2,6,4,3,7]=>[1,2,2,1,2]
[8,1,6,5,2,4,3,7]=>[1,2,1,2,2]
[3,8,6,5,1,2,4,7]=>[2,1,1,4]
[1,4,5,7,8,3,2,6]=>[5,1,2]
[1,6,7,4,2,8,3,5]=>[3,1,2,2]
[1,7,8,4,3,6,2,5]=>[3,1,2,2]
[5,7,8,1,4,3,2,6]=>[3,2,1,2]
[1,5,8,7,4,3,2,6]=>[3,1,1,1,2]
[5,1,3,7,8,2,4,6]=>[1,4,3]
[1,7,8,4,3,2,6,5]=>[3,1,1,2,1]
[1,4,7,2,3,6,8,5]=>[3,4,1]
[3,1,2,6,7,8,5,4]=>[1,5,1,1]
[2,7,1,4,3,5,8,6]=>[2,2,3,1]
[8,1,5,7,3,4,2,6]=>[1,3,2,2]
[3,8,1,6,4,2,7,5]=>[2,2,1,2,1]
[8,5,1,3,2,7,4,6]=>[1,1,2,2,2]
[2,1,6,3,8,7,5,4]=>[1,2,2,1,1,1]
[1,6,3,4,7,8,2,5]=>[2,4,2]
[3,1,5,7,6,2,8,4]=>[1,3,1,2,1]
[6,3,1,4,2,7,8,5]=>[1,1,2,3,1]
[2,4,3,7,6,1,8,5]=>[2,2,1,2,1]
[3,1,7,6,5,2,8,4]=>[1,2,1,1,2,1]
[1,4,7,6,8,3,2,5]=>[3,2,1,2]
[7,2,1,5,6,3,8,4]=>[1,1,3,2,1]
[4,3,1,8,6,2,7,5]=>[1,1,2,1,2,1]
[3,1,5,2,8,7,6,4]=>[1,2,2,1,1,1]
[1,2,8,4,3,7,6,5]=>[3,1,2,1,1]
[2,6,1,8,7,4,3,5]=>[2,2,1,1,2]
[7,5,1,8,3,2,6,4]=>[1,1,2,1,2,1]
[4,7,6,3,1,8,2,5]=>[2,1,1,2,2]
[5,3,1,8,6,2,4,7]=>[1,1,2,1,3]
[5,1,8,6,3,2,4,7]=>[1,2,1,1,3]
[1,5,4,2,8,6,3,7]=>[2,1,2,1,2]
[1,4,2,8,5,3,7,6]=>[2,2,1,2,1]
[8,3,1,6,4,2,5,7]=>[1,1,2,1,3]
[1,7,4,8,3,5,2,6]=>[2,2,2,2]
[7,3,2,4,8,5,1,6]=>[1,1,3,1,2]
[5,7,8,1,4,2,6,3]=>[3,2,2,1]
[2,6,3,8,1,7,5,4]=>[2,2,2,1,1]
[2,5,1,8,6,3,7,4]=>[2,2,1,2,1]
[2,8,6,4,1,7,3,5]=>[2,1,1,2,2]
[1,8,4,2,7,5,3,6]=>[2,1,2,1,2]
[6,5,1,7,2,8,4,3]=>[1,1,2,2,1,1]
[2,8,1,7,5,3,6,4]=>[2,2,1,2,1]
[1,2,8,7,6,4,3,5]=>[3,1,1,1,2]
[4,1,7,8,6,3,5,2]=>[1,3,1,2,1]
[1,6,5,7,8,4,2,3]=>[2,3,1,2]
[4,1,8,7,6,3,5,2]=>[1,2,1,1,2,1]
[4,8,2,6,3,5,1,7]=>[2,2,2,2]
[4,3,5,7,1,6,2,8]=>[1,3,2,2]
[4,1,8,5,3,6,2,7]=>[1,2,1,2,2]
[6,4,2,5,3,1,7,8]=>[1,1,2,1,3]
[3,1,5,8,2,7,4,6]=>[1,3,2,2]
[6,4,1,5,3,2,7,8]=>[1,1,2,1,3]
[6,2,1,5,4,3,7,8]=>[1,1,2,1,3]
[3,1,8,5,4,6,2,7]=>[1,2,1,2,2]
[6,1,8,4,5,3,2,7]=>[1,2,2,1,2]
[4,5,2,7,1,6,3,8]=>[2,2,2,2]
[4,3,5,7,1,6,8,2]=>[1,3,3,1]
[4,1,8,5,3,6,7,2]=>[1,2,1,3,1]
[6,3,8,4,5,1,7,2]=>[1,2,2,2,1]
[3,1,6,8,5,7,4,2]=>[1,3,2,1,1]
[2,6,1,8,5,7,4,3]=>[2,2,2,1,1]
[6,3,8,4,5,2,1,7]=>[1,2,2,1,2]
[6,5,8,7,2,3,4,1]=>[1,2,1,3,1]
[6,3,8,4,5,2,7,1]=>[1,2,2,2,1]
[2,1,6,8,5,3,7,4]=>[1,3,1,2,1]
[3,2,6,8,5,4,7,1]=>[1,3,1,2,1]
[4,1,8,5,2,6,3,7]=>[1,2,1,2,2]
[3,1,6,8,5,2,4,7]=>[1,3,1,3]
[6,5,8,7,4,1,2,3]=>[1,2,1,1,3]
[6,5,8,7,4,2,1,3]=>[1,2,1,1,1,2]
[6,5,8,7,2,4,1,3]=>[1,2,1,2,2]
[6,2,8,4,5,7,1,3]=>[1,2,3,2]
[6,1,8,4,5,7,3,2]=>[1,2,3,1,1]
[4,2,7,3,5,8,6,1]=>[1,2,3,1,1]
[3,6,2,4,8,5,7,1]=>[2,3,2,1]
[4,7,3,5,2,8,6,1]=>[2,2,2,1,1]
[2,7,5,4,3,8,6,1]=>[2,1,1,2,1,1]
[3,5,1,8,4,7,6,2]=>[2,2,2,1,1]
[3,6,1,8,5,4,7,2]=>[2,2,1,2,1]
[4,7,2,3,8,6,5,1]=>[2,3,1,1,1]
[2,4,8,3,7,6,5,1]=>[3,2,1,1,1]
[3,6,8,2,5,7,4,1]=>[3,3,1,1]
[5,1,7,8,4,6,3,2]=>[1,3,2,1,1]
[5,7,4,8,3,2,6,1]=>[2,2,1,2,1]
[2,6,8,5,4,3,7,1]=>[3,1,1,2,1]
[3,6,8,2,5,4,7,1]=>[3,2,2,1]
[4,6,8,3,2,5,7,1]=>[3,1,3,1]
[4,6,2,8,3,5,7,1]=>[2,2,3,1]
[3,6,1,8,5,7,4,2]=>[2,2,2,1,1]
[5,2,6,8,4,1,7,3]=>[1,3,1,2,1]
[4,6,3,8,7,2,5,1]=>[2,2,1,2,1]
[5,7,2,4,8,6,3,1]=>[2,3,1,1,1]
[3,5,8,2,7,4,6,1]=>[3,2,2,1]
[2,6,7,8,5,1,4,3]=>[4,1,2,1]
[2,6,8,5,7,4,3,1]=>[3,2,1,1,1]
[2,4,8,7,6,3,5,1]=>[3,1,1,2,1]
[6,5,3,1,7,4,8,2]=>[1,1,1,2,2,1]
[6,4,1,7,2,5,8,3]=>[1,1,2,3,1]
[7,5,1,6,3,2,8,4]=>[1,1,2,1,2,1]
[2,7,6,3,4,1,8,5]=>[2,1,2,2,1]
[5,7,6,3,1,2,8,4]=>[2,1,1,3,1]
[7,8,5,4,2,6,3,1]=>[2,1,1,2,1,1]
[4,8,2,1,7,5,6,3]=>[2,1,2,2,1]
[6,3,8,5,7,2,4,1]=>[1,2,2,2,1]
[1,5,4,8,6,2,3,7]=>[2,2,1,3]
[8,2,1,7,5,3,6,4]=>[1,1,2,1,2,1]
[8,3,4,7,1,5,6,2]=>[1,3,3,1]
[5,1,7,4,2,8,3,6]=>[1,2,1,2,2]
[8,2,1,6,7,3,5,4]=>[1,1,3,2,1]
[6,2,8,1,7,5,3,4]=>[1,2,2,1,2]
[4,2,8,7,5,1,6,3]=>[1,2,1,1,2,1]
[8,3,7,6,4,5,2,1]=>[1,2,1,2,1,1]
[5,2,8,7,6,3,1,4]=>[1,2,1,1,1,2]
[3,5,1,8,7,6,2,4]=>[2,2,1,1,2]
[5,6,2,7,8,1,3,4]=>[2,3,3]
[2,7,5,1,3,4,6,8]=>[2,1,5]
[4,7,3,1,2,5,6,8]=>[2,1,5]
[4,7,3,5,6,1,2,8]=>[2,3,3]
[4,7,3,5,6,8,1,2]=>[2,4,2]
[4,7,8,3,5,6,1,2]=>[3,3,2]
[4,7,8,3,5,1,2,6]=>[3,2,3]
[7,8,5,2,6,1,3,4]=>[2,1,2,3]
[3,2,5,1,4,8,6,7]=>[1,2,3,2]
[3,2,5,6,8,4,7,1]=>[1,4,2,1]
[8,4,6,5,2,3,7,1]=>[1,2,1,3,1]
[8,4,5,2,6,3,7,1]=>[1,2,2,2,1]
[2,5,6,4,8,3,7,1]=>[3,2,2,1]
[5,3,2,4,7,8,1,6]=>[1,1,4,2]
[4,2,5,7,3,8,1,6]=>[1,3,2,2]
[4,7,3,1,6,8,2,5]=>[2,1,3,2]
[4,2,3,6,7,1,8,5]=>[1,4,2,1]
[4,2,7,6,8,1,3,5]=>[1,2,2,3]
[1,7,4,6,8,3,2,5]=>[2,3,1,2]
[1,2,5,7,6,3,8,4]=>[4,1,2,1]
[6,4,3,2,7,1,8,5]=>[1,1,1,2,2,1]
[1,3,7,8,6,5,2,4]=>[4,1,1,2]
[1,6,5,7,3,2,8,4]=>[2,2,1,2,1]
[5,2,6,8,1,7,3,4]=>[1,3,2,2]
[5,2,6,7,1,3,8,4]=>[1,3,3,1]
[6,2,4,3,7,1,8,5]=>[1,2,2,2,1]
[5,2,7,6,1,8,3,4]=>[1,2,1,2,2]
[5,6,3,7,1,2,8,4]=>[2,2,3,1]
[4,7,2,5,6,3,1,8]=>[2,3,1,2]
[1,3,2,7,6,4,8,5]=>[2,2,1,2,1]
[6,2,1,7,3,4,5,8]=>[1,1,2,4]
[5,4,1,3,7,8,2,6]=>[1,1,4,2]
[5,1,3,6,7,8,2,4]=>[1,5,2]
[6,1,5,8,3,7,2,4]=>[1,3,2,2]
[4,1,2,7,5,3,8,6]=>[1,3,1,2,1]
[4,1,3,5,7,8,2,6]=>[1,5,2]
[1,2,4,7,5,3,8,6]=>[4,1,2,1]
[6,1,5,8,4,3,2,7]=>[1,3,1,1,2]
[7,2,1,6,8,3,5,4]=>[1,1,3,2,1]
[5,1,4,3,7,8,2,6]=>[1,2,3,2]
[6,1,3,7,2,4,8,5]=>[1,3,3,1]
[5,6,4,1,8,3,2,7]=>[2,1,2,1,2]
[4,5,2,1,7,8,3,6]=>[2,1,3,2]
[7,2,5,6,3,4,1,8]=>[1,3,2,2]
[2,3,7,8,5,1,6,4]=>[4,1,2,1]
[6,2,8,5,7,4,3,1]=>[1,2,2,1,1,1]
[4,1,7,6,2,3,8,5]=>[1,2,1,3,1]
[1,2,6,7,4,3,5,8]=>[4,1,3]
[3,6,7,4,5,1,8,2]=>[3,2,2,1]
[5,8,6,3,4,1,2,7]=>[2,1,2,3]
[6,2,3,1,8,5,4,7]=>[1,2,2,1,2]
[5,1,2,6,4,8,3,7]=>[1,3,2,2]
[8,6,2,3,7,5,1,4]=>[1,1,3,1,2]
[4,5,2,8,6,1,3,7]=>[2,2,1,3]
[3,4,8,2,5,6,1,7]=>[3,3,2]
[8,5,6,3,7,1,4,2]=>[1,2,2,2,1]
[2,8,3,6,7,4,5,1]=>[2,3,2,1]
[2,5,7,8,3,4,6,1]=>[4,3,1]
[8,1,3,6,5,4,7,2]=>[1,3,1,2,1]
[8,1,3,2,5,7,4,6]=>[1,2,3,2]
[6,3,7,8,5,1,4,2]=>[1,3,1,2,1]
[6,8,2,7,5,3,1,4]=>[2,2,1,1,2]
[6,3,2,5,8,4,1,7]=>[1,1,3,1,2]
[5,6,7,2,8,4,1,3]=>[3,2,1,2]
[3,4,1,7,6,2,8,5]=>[2,2,1,2,1]
[6,8,7,1,3,5,2,4]=>[2,1,3,2]
[5,8,3,6,4,1,7,2]=>[2,2,1,2,1]
[7,5,4,6,1,3,8,2]=>[1,1,2,3,1]
[4,3,8,5,2,7,1,6]=>[1,2,1,2,2]
[5,6,8,2,4,3,1,7]=>[3,2,1,2]
[7,5,8,3,2,1,4,6]=>[1,2,1,1,3]
[3,6,4,5,7,2,1,8]=>[2,3,1,2]
[3,6,7,4,5,2,1,8]=>[3,2,1,2]
[4,6,8,5,7,1,3,2]=>[3,2,2,1]
[2,4,7,1,5,8,3,6]=>[3,3,2]
[8,1,4,7,5,3,6,2]=>[1,3,1,2,1]
[3,5,7,1,6,4,8,2]=>[3,2,2,1]
[3,6,5,1,7,4,2,8]=>[2,1,2,1,2]
[2,8,4,5,1,6,3,7]=>[2,2,2,2]
[2,6,7,4,1,5,3,8]=>[3,1,2,2]
[3,2,5,8,4,7,1,6]=>[1,3,2,2]
[8,5,1,2,4,6,3,7]=>[1,1,4,2]
[2,5,8,1,3,4,7,6]=>[3,4,1]
[3,5,1,8,7,4,2,6]=>[2,2,1,1,2]
[1,4,8,7,5,2,3,6]=>[3,1,1,3]
[6,7,1,2,5,3,8,4]=>[2,3,2,1]
[7,8,6,1,2,5,3,4]=>[2,1,3,2]
[4,6,1,3,8,2,7,5]=>[2,3,2,1]
[8,5,1,2,3,7,6,4]=>[1,1,4,1,1]
[6,8,1,2,3,7,5,4]=>[2,4,1,1]
[2,3,7,4,8,6,1,5]=>[3,2,1,2]
[7,3,1,8,4,6,2,5]=>[1,1,2,2,2]
[2,3,7,6,8,1,4,5]=>[3,2,3]
[3,5,1,8,4,7,2,6]=>[2,2,2,2]
[7,6,1,2,3,5,8,4]=>[1,1,5,1]
[8,6,1,2,3,5,7,4]=>[1,1,5,1]
[8,2,6,7,4,3,1,5]=>[1,3,1,1,2]
[7,5,1,2,6,3,8,4]=>[1,1,3,2,1]
[5,1,7,8,3,2,4,6]=>[1,3,1,3]
[3,1,7,6,2,8,5,4]=>[1,2,1,2,1,1]
[5,3,6,7,4,2,8,1]=>[1,3,1,2,1]
[2,4,5,1,8,7,6,3]=>[3,2,1,1,1]
[6,8,7,3,1,5,2,4]=>[2,1,1,2,2]
[5,4,2,8,6,7,3,1]=>[1,1,2,2,1,1]
[6,1,4,2,8,7,3,5]=>[1,2,2,1,2]
[3,2,4,6,8,5,7,1]=>[1,4,2,1]
[3,7,2,6,8,4,5,1]=>[2,3,2,1]
[4,6,5,2,7,8,3,1]=>[2,1,3,1,1]
[5,4,6,2,7,8,3,1]=>[1,2,3,1,1]
[5,1,8,6,4,2,7,3]=>[1,2,1,1,2,1]
[3,7,1,8,2,4,6,5]=>[2,2,3,1]
[7,2,8,3,1,5,6,4]=>[1,2,1,3,1]
[6,2,1,8,5,7,4,3]=>[1,1,2,2,1,1]
[2,6,3,8,5,7,4,1]=>[2,2,2,1,1]
[5,4,7,2,3,8,6,1]=>[1,2,3,1,1]
[5,4,6,2,3,1,8,7]=>[1,2,2,2,1]
[6,5,7,8,1,3,4,2]=>[1,3,3,1]
[2,1,7,6,8,4,5,3]=>[1,2,2,2,1]
[6,5,7,8,1,3,2,4]=>[1,3,2,2]
[6,4,7,2,8,3,1,5]=>[1,2,2,1,2]
[6,3,2,7,8,4,5,1]=>[1,1,3,2,1]
[6,5,7,8,2,4,3,1]=>[1,3,2,1,1]
[6,4,7,1,8,5,3,2]=>[1,2,2,1,1,1]
[1,4,8,2,7,6,5,3]=>[3,2,1,1,1]
[4,7,3,1,5,2,8,6]=>[2,1,2,2,1]
[4,6,3,1,7,5,8,2]=>[2,1,2,2,1]
[5,7,4,3,1,2,8,6]=>[2,1,1,3,1]
[2,1,4,7,5,3,8,6]=>[1,3,1,2,1]
[4,7,3,6,5,2,8,1]=>[2,2,1,2,1]
[4,7,6,3,1,5,8,2]=>[2,1,1,3,1]
[2,4,7,3,8,5,1,6]=>[3,2,1,2]
[2,7,3,1,8,5,4,6]=>[2,1,2,1,2]
[2,5,3,1,7,4,8,6]=>[2,1,2,2,1]
[2,4,3,1,7,5,8,6]=>[2,1,2,2,1]
[2,7,3,8,6,5,1,4]=>[2,2,1,1,2]
[2,8,3,1,7,4,5,6]=>[2,1,2,3]
[6,7,5,2,1,4,8,3]=>[2,1,1,3,1]
[7,8,6,2,1,5,3,4]=>[2,1,1,2,2]
[7,8,6,3,2,5,1,4]=>[2,1,1,2,2]
[7,1,6,3,8,4,2,5]=>[1,2,2,1,2]
[5,8,4,2,6,1,7,3]=>[2,1,2,2,1]
[6,7,4,8,5,3,1,2]=>[2,2,1,1,2]
[7,8,6,3,5,2,1,4]=>[2,1,2,1,2]
[1,6,2,5,7,8,3,4]=>[2,4,2]
[1,7,8,2,5,4,6,3]=>[3,2,2,1]
[1,2,6,8,3,4,7,5]=>[4,3,1]
[1,6,2,5,3,7,8,4]=>[2,2,3,1]
[1,8,2,6,7,3,5,4]=>[2,3,2,1]
[1,3,6,8,4,7,2,5]=>[4,2,2]
[1,5,6,8,3,2,4,7]=>[4,1,3]
[1,7,3,5,4,2,8,6]=>[2,2,1,2,1]
[1,8,2,7,3,5,6,4]=>[2,2,3,1]
[1,8,3,2,7,4,6,5]=>[2,1,2,2,1]
[1,2,8,5,3,4,7,6]=>[3,1,3,1]
[1,7,4,8,6,5,3,2]=>[2,2,1,1,1,1]
[1,6,8,7,2,4,3,5]=>[3,1,2,2]
[1,6,3,7,2,5,8,4]=>[2,2,3,1]
[1,3,6,5,4,8,2,7]=>[3,1,2,2]
[1,6,3,5,7,4,8,2]=>[2,3,2,1]
[1,8,2,3,7,4,6,5]=>[2,3,2,1]
[1,7,2,3,8,4,6,5]=>[2,3,2,1]
[1,5,4,7,2,8,3,6]=>[2,2,2,2]
[8,4,5,6,2,7,1,3]=>[1,3,2,2]
[4,6,7,1,5,2,8,3]=>[3,2,2,1]
[3,8,4,7,5,2,6,1]=>[2,2,1,2,1]
[3,7,5,2,6,1,8,4]=>[2,1,2,2,1]
[3,8,5,2,6,1,7,4]=>[2,1,2,2,1]
[3,7,4,8,5,2,6,1]=>[2,2,1,2,1]
[3,6,1,5,2,8,7,4]=>[2,2,2,1,1]
[8,1,2,6,5,3,4,7]=>[1,3,1,3]
[3,7,4,2,5,6,1,8]=>[2,1,3,2]
[3,4,2,7,5,1,6,8]=>[2,2,1,3]
[6,7,1,3,4,2,5,8]=>[2,3,3]
[6,8,7,1,3,4,2,5]=>[2,1,3,2]
[3,4,2,8,6,7,5,1]=>[2,2,2,1,1]
[3,7,8,6,1,4,2,5]=>[3,1,2,2]
[3,6,1,5,2,7,8,4]=>[2,2,3,1]
[3,8,4,2,5,7,6,1]=>[2,1,3,1,1]
[7,1,6,8,3,4,2,5]=>[1,3,2,2]
[8,1,2,6,3,5,7,4]=>[1,3,3,1]
[7,4,8,1,2,6,3,5]=>[1,2,3,2]
[6,2,8,4,7,1,3,5]=>[1,2,2,3]
[8,3,4,2,5,7,1,6]=>[1,2,3,2]
[3,7,8,4,2,5,6,1]=>[3,1,3,1]
[3,8,4,2,5,6,1,7]=>[2,1,3,2]
[3,6,1,5,2,8,4,7]=>[2,2,2,2]
[7,1,3,4,8,5,2,6]=>[1,4,1,2]
[7,1,3,4,2,5,8,6]=>[1,3,3,1]
[3,4,2,8,5,1,6,7]=>[2,2,1,3]
[3,4,2,6,8,5,1,7]=>[2,3,1,2]
[8,7,1,3,4,2,5,6]=>[1,1,3,3]
[7,1,3,4,2,5,6,8]=>[1,3,4]
[3,6,1,4,2,5,7,8]=>[2,2,4]
[6,8,2,7,5,4,1,3]=>[2,2,1,1,2]
[1,8,4,3,7,6,2,5]=>[2,1,2,1,2]
[4,3,8,7,1,2,6,5]=>[1,2,1,3,1]
[1,8,4,5,7,6,2,3]=>[2,3,1,2]
[4,3,8,5,7,1,6,2]=>[1,2,2,2,1]
[6,3,4,8,7,2,1,5]=>[1,3,1,1,2]
[5,3,8,4,7,1,6,2]=>[1,2,2,2,1]
[5,2,8,7,1,4,6,3]=>[1,2,1,3,1]
[3,2,8,7,1,6,4,5]=>[1,2,1,2,2]
[2,7,8,3,1,6,4,5]=>[3,1,2,2]
[2,7,8,5,1,4,6,3]=>[3,1,3,1]
[3,5,8,7,4,1,6,2]=>[3,1,1,2,1]
[7,4,6,8,3,5,1,2]=>[1,3,2,2]
[2,7,8,1,3,6,4,5]=>[3,3,2]
[2,7,8,1,5,4,6,3]=>[3,2,2,1]
[2,7,8,1,4,5,6,3]=>[3,4,1]
[3,6,7,8,2,4,1,5]=>[4,2,2]
[4,5,7,8,6,3,1,2]=>[4,1,1,2]
[5,4,6,8,7,3,1,2]=>[1,3,1,1,2]
[4,5,8,6,7,1,3,2]=>[3,2,2,1]
[5,7,6,8,2,1,3,4]=>[2,2,1,3]
[3,7,6,8,2,4,1,5]=>[2,2,2,2]
[5,4,7,8,6,3,1,2]=>[1,3,1,1,2]
[4,5,7,8,2,6,1,3]=>[4,2,2]
[4,5,6,8,7,3,1,2]=>[4,1,1,2]
[8,1,7,5,4,3,6,2]=>[1,2,1,1,2,1]
[6,1,3,4,8,5,7,2]=>[1,4,2,1]
[5,7,3,4,2,1,6,8]=>[2,2,1,3]
[8,1,6,5,3,7,4,2]=>[1,2,1,2,1,1]
[7,1,6,4,5,3,8,2]=>[1,2,2,2,1]
[6,1,5,3,8,4,7,2]=>[1,2,2,2,1]
[4,1,8,6,7,2,5,3]=>[1,2,2,2,1]
[1,2,8,3,6,7,5,4]=>[3,3,1,1]
[6,8,5,4,1,2,3,7]=>[2,1,1,4]
[6,4,1,7,3,2,5,8]=>[1,1,2,1,3]
[8,3,6,1,2,5,4,7]=>[1,2,3,2]
[4,6,7,1,2,5,3,8]=>[3,3,2]
[6,1,7,3,2,5,8,4]=>[1,2,1,3,1]
[4,1,7,2,8,6,3,5]=>[1,2,2,1,2]
[7,4,1,8,2,3,6,5]=>[1,1,2,3,1]
[1,4,6,7,8,2,5,3]=>[5,2,1]
[3,7,1,6,2,4,5,8]=>[2,2,4]
[7,1,3,4,8,6,2,5]=>[1,4,1,2]
[5,2,7,4,8,1,3,6]=>[1,2,2,3]
[1,8,6,2,5,4,7,3]=>[2,1,2,2,1]
[8,3,1,2,5,6,4,7]=>[1,1,4,2]
[5,3,4,1,6,7,2,8]=>[1,2,3,2]
[5,2,1,6,4,3,8,7]=>[1,1,2,1,2,1]
[5,2,8,3,4,7,1,6]=>[1,2,3,2]
[3,8,4,1,7,5,2,6]=>[2,1,2,1,2]
[4,7,6,5,1,2,3,8]=>[2,1,1,4]
[6,2,7,4,8,3,1,5]=>[1,2,2,1,2]
[6,4,5,2,8,1,3,7]=>[1,2,2,3]
[2,8,5,1,4,3,7,6]=>[2,1,2,2,1]
[4,8,6,5,2,1,7,3]=>[2,1,1,1,2,1]
[5,6,4,8,7,2,3,1]=>[2,2,1,2,1]
[1,6,8,2,5,7,3,4]=>[3,3,2]
[1,5,4,2,7,6,8,3]=>[2,1,2,2,1]
[8,5,2,3,7,6,1,4]=>[1,1,3,1,2]
[6,8,2,7,5,1,4,3]=>[2,2,1,2,1]
[8,3,4,5,6,1,7,2]=>[1,4,2,1]
[7,4,2,5,6,8,1,3]=>[1,1,4,2]
[5,3,6,4,7,2,1,8]=>[1,2,2,1,2]
[4,2,6,5,7,3,1,8]=>[1,2,2,1,2]
[5,4,6,2,7,3,1,8]=>[1,2,2,1,2]
[3,2,6,5,8,4,1,7]=>[1,2,2,1,2]
[3,2,6,5,8,7,1,4]=>[1,2,2,1,2]
[4,2,6,5,8,7,1,3]=>[1,2,2,1,2]
[5,2,6,4,8,7,1,3]=>[1,2,2,1,2]
[5,4,7,6,8,2,1,3]=>[1,2,2,1,2]
[6,4,7,5,8,3,1,2]=>[1,2,2,1,2]
[4,2,7,5,8,6,1,3]=>[1,2,2,1,2]
[3,2,7,5,8,4,1,6]=>[1,2,2,1,2]
[4,3,7,2,8,5,1,6]=>[1,2,2,1,2]
[4,3,6,2,8,5,1,7]=>[1,2,2,1,2]
[4,3,7,6,8,5,1,2]=>[1,2,2,1,2]
[5,3,7,6,8,2,1,4]=>[1,2,2,1,2]
[5,3,7,2,8,6,1,4]=>[1,2,2,1,2]
[3,2,6,4,8,7,1,5]=>[1,2,2,1,2]
[4,2,7,3,8,6,1,5]=>[1,2,2,1,2]
[5,2,7,6,8,3,1,4]=>[1,2,2,1,2]
[3,2,7,6,8,4,1,5]=>[1,2,2,1,2]
[3,2,7,6,8,5,1,4]=>[1,2,2,1,2]
[6,2,7,5,8,4,1,3]=>[1,2,2,1,2]
[4,8,1,7,3,2,5,6]=>[2,2,1,3]
[3,7,4,8,2,1,5,6]=>[2,2,1,3]
[3,7,8,2,5,4,6,1]=>[3,2,2,1]
[4,7,5,8,3,2,6,1]=>[2,2,1,2,1]
[6,7,1,3,2,5,8,4]=>[2,2,3,1]
[8,7,6,4,1,5,3,2]=>[1,1,1,1,2,1,1]
[3,8,5,2,6,4,7,1]=>[2,1,2,2,1]
[7,2,5,3,4,8,1,6]=>[1,2,3,2]
[7,4,8,3,5,1,6,2]=>[1,2,2,2,1]
[5,4,6,8,7,1,2,3]=>[1,3,1,3]
[6,4,7,8,5,1,2,3]=>[1,3,1,3]
[4,2,5,3,7,8,6,1]=>[1,2,3,1,1]
[5,3,6,2,4,1,8,7]=>[1,2,2,2,1]
[7,8,6,2,3,5,4,1]=>[2,1,3,1,1]
[5,8,2,6,3,7,4,1]=>[2,2,2,1,1]
[4,8,2,3,7,5,6,1]=>[2,3,2,1]
[7,5,6,2,3,8,4,1]=>[1,2,3,1,1]
[2,7,5,6,4,3,8,1]=>[2,2,1,2,1]
[2,8,4,3,7,5,6,1]=>[2,1,2,2,1]
[3,8,5,7,6,4,2,1]=>[2,2,1,1,1,1]
[7,8,6,3,5,4,2,1]=>[2,1,2,1,1,1]
[2,7,6,3,8,5,4,1]=>[2,1,2,1,1,1]
[7,4,2,5,6,3,8,1]=>[1,1,3,2,1]
[6,2,7,5,3,8,4,1]=>[1,2,1,2,1,1]
[2,4,8,3,7,5,6,1]=>[3,2,2,1]
[4,8,3,7,5,6,2,1]=>[2,2,2,1,1]
[6,2,5,8,3,7,4,1]=>[1,3,2,1,1]
[4,7,3,8,2,5,6,1]=>[2,2,3,1]
[8,2,5,6,3,7,4,1]=>[1,3,2,1,1]
[4,5,3,7,1,2,6,8]=>[2,2,4]
[6,4,7,3,1,2,5,8]=>[1,2,1,4]
[6,8,4,1,3,5,2,7]=>[2,1,3,2]
[8,5,3,6,1,4,2,7]=>[1,1,2,2,2]
[5,6,3,7,4,1,2,8]=>[2,2,1,3]
[5,2,6,7,4,1,3,8]=>[1,3,1,3]
[5,6,2,7,4,1,3,8]=>[2,2,1,3]
[8,5,6,4,1,3,2,7]=>[1,2,1,2,2]
[7,8,5,1,4,3,2,6]=>[2,1,2,1,2]
[6,7,2,8,4,3,1,5]=>[2,2,1,1,2]
[6,7,3,2,8,4,1,5]=>[2,1,2,1,2]
[8,5,3,6,2,1,4,7]=>[1,1,2,1,3]
[4,7,8,3,1,5,2,6]=>[3,1,2,2]
[4,5,8,1,3,2,6,7]=>[3,2,3]
[4,7,8,1,6,3,2,5]=>[3,2,1,2]
[5,7,8,1,2,6,4,3]=>[3,3,1,1]
[6,5,4,7,2,8,1,3]=>[1,1,2,2,2]
[6,2,7,3,5,8,1,4]=>[1,2,3,2]
[6,2,7,5,4,8,1,3]=>[1,2,1,2,2]
[4,7,1,3,8,6,5,2]=>[2,3,1,1,1]
[2,6,7,4,3,8,1,5]=>[3,1,2,2]
[3,7,6,4,5,8,1,2]=>[2,1,3,2]
[3,7,6,5,4,8,1,2]=>[2,1,1,2,2]
[5,7,2,8,3,4,6,1]=>[2,2,3,1]
[3,7,2,8,5,6,4,1]=>[2,2,2,1,1]
[3,1,5,8,4,7,6,2]=>[1,3,2,1,1]
[1,5,6,8,4,3,7,2]=>[4,1,2,1]
[3,1,5,8,6,4,7,2]=>[1,3,1,2,1]
[4,7,2,8,5,3,6,1]=>[2,2,1,2,1]
[2,3,8,6,4,5,7,1]=>[3,1,3,1]
[2,3,8,6,4,7,5,1]=>[3,1,2,1,1]
[4,6,1,7,8,3,2,5]=>[2,3,1,2]
[3,6,2,8,7,4,5,1]=>[2,2,1,2,1]
[2,5,6,1,8,7,3,4]=>[3,2,1,2]
[3,6,2,8,4,7,5,1]=>[2,2,2,1,1]
[2,3,8,6,7,4,5,1]=>[3,2,2,1]
[2,3,8,7,4,6,5,1]=>[3,1,2,1,1]
[2,3,8,5,7,4,6,1]=>[3,2,2,1]
[3,5,2,8,7,4,6,1]=>[2,2,1,2,1]
[1,5,6,8,7,3,4,2]=>[4,1,2,1]
[2,3,8,6,7,5,4,1]=>[3,2,1,1,1]
[2,3,8,7,6,4,5,1]=>[3,1,1,2,1]
[8,5,6,3,1,4,2,7]=>[1,2,1,2,2]
[8,5,6,1,3,4,2,7]=>[1,2,3,2]
[8,1,5,6,3,4,2,7]=>[1,3,2,2]
[8,1,5,3,6,4,2,7]=>[1,2,2,1,2]
[8,3,5,6,4,1,2,7]=>[1,3,1,3]
[8,3,5,1,6,4,2,7]=>[1,2,2,1,2]
[1,3,8,5,6,2,4,7]=>[3,2,3]
[3,8,5,6,1,4,2,7]=>[2,2,2,2]
[3,8,5,6,4,1,2,7]=>[2,2,1,3]
[5,7,8,3,4,6,2,1]=>[3,3,1,1]
[3,5,8,6,4,1,2,7]=>[3,1,1,3]
[3,5,1,8,6,4,2,7]=>[2,2,1,1,2]
[1,3,5,8,6,2,4,7]=>[4,1,3]
[7,5,3,8,6,4,2,1]=>[1,1,2,1,1,1,1]
[1,5,3,8,6,4,2,7]=>[2,2,1,1,2]
[5,1,3,8,6,4,2,7]=>[1,3,1,1,2]
[5,3,8,1,6,4,2,7]=>[1,2,2,1,2]
[5,3,8,6,4,1,2,7]=>[1,2,1,1,3]
[5,8,3,1,6,4,2,7]=>[2,1,2,1,2]
[5,8,1,3,6,4,2,7]=>[2,3,1,2]
[5,1,8,3,6,4,2,7]=>[1,2,2,1,2]
[1,5,8,3,6,4,2,7]=>[3,2,1,2]
[7,5,8,3,6,4,2,1]=>[1,2,2,1,1,1]
[1,5,8,6,3,4,2,7]=>[3,1,2,2]
[1,7,8,2,5,6,4,3]=>[3,3,1,1]
[7,1,8,3,6,4,2,5]=>[1,2,2,1,2]
[7,8,3,6,4,1,2,5]=>[2,2,1,3]
[7,1,3,8,6,4,2,5]=>[1,3,1,1,2]
[3,7,5,8,2,6,4,1]=>[2,2,2,1,1]
[3,1,7,8,4,2,6,5]=>[1,3,1,2,1]
[5,7,8,1,4,6,2,3]=>[3,3,2]
[5,7,8,4,6,1,2,3]=>[3,2,3]
[1,3,7,8,4,2,6,5]=>[4,1,2,1]
[6,1,2,5,3,4,7,8]=>[1,3,4]
[5,1,2,4,6,3,7,8]=>[1,4,3]
[7,1,6,5,2,3,4,8]=>[1,2,1,4]
[6,1,2,5,4,3,7,8]=>[1,3,1,3]
[5,1,4,6,7,3,2,8]=>[1,4,1,2]
[1,4,6,5,7,2,3,8]=>[3,2,3]
[6,7,3,5,4,1,2,8]=>[2,2,1,3]
[8,1,6,7,3,5,4,2]=>[1,3,2,1,1]
[7,2,4,1,6,5,3,8]=>[1,2,2,1,2]
[4,2,5,1,3,7,6,8]=>[1,2,3,2]
[1,3,2,6,8,4,7,5]=>[2,3,2,1]
[4,2,6,5,7,1,3,8]=>[1,2,2,3]
[6,2,5,7,3,1,4,8]=>[1,3,1,3]
[8,2,5,6,3,4,7,1]=>[1,3,3,1]
[8,2,5,4,1,6,7,3]=>[1,2,1,3,1]
[2,8,5,1,3,6,7,4]=>[2,1,4,1]
[8,7,4,3,5,1,6,2]=>[1,1,1,2,2,1]
[8,7,3,5,2,6,4,1]=>[1,1,2,2,1,1]
[3,8,5,6,1,2,7,4]=>[2,2,3,1]
[8,1,7,5,4,2,6,3]=>[1,2,1,1,2,1]
[1,2,6,4,7,3,5,8]=>[3,2,3]
[6,3,1,7,2,4,5,8]=>[1,1,2,4]
[1,6,4,3,7,2,5,8]=>[2,1,2,3]
[2,4,5,7,1,6,3,8]=>[4,2,2]
[5,7,8,3,2,6,1,4]=>[3,1,2,2]
[5,6,8,3,2,4,7,1]=>[3,1,3,1]
[4,8,5,2,3,7,6,1]=>[2,1,3,1,1]
[6,8,4,3,7,2,5,1]=>[2,1,2,2,1]
[6,7,4,3,8,2,1,5]=>[2,1,2,1,2]
[7,4,5,1,3,8,2,6]=>[1,2,3,2]
[8,4,5,1,3,7,6,2]=>[1,2,3,1,1]
[8,6,4,3,7,1,5,2]=>[1,1,1,2,2,1]
[8,6,5,7,3,1,4,2]=>[1,1,2,1,2,1]
[8,5,6,7,1,3,4,2]=>[1,3,3,1]
[8,3,1,6,7,4,5,2]=>[1,1,3,2,1]
[7,5,6,8,1,3,2,4]=>[1,3,2,2]
[6,8,5,7,3,2,4,1]=>[2,2,1,2,1]
[4,7,8,2,6,5,1,3]=>[3,2,1,2]
[6,8,7,5,4,2,3,1]=>[2,1,1,1,2,1]
[7,3,1,8,6,5,2,4]=>[1,1,2,1,1,2]
[7,1,3,2,4,6,5,8]=>[1,2,3,2]
[7,2,3,5,1,6,8,4]=>[1,3,3,1]
[7,2,3,1,4,6,8,5]=>[1,2,4,1]
[6,5,2,1,4,8,3,7]=>[1,1,1,3,2]
[2,7,3,1,4,8,6,5]=>[2,1,3,1,1]
[1,4,6,3,7,8,5,2]=>[3,3,1,1]
[3,1,6,5,7,8,4,2]=>[1,2,3,1,1]
[1,2,6,5,8,4,7,3]=>[3,2,2,1]
[4,3,1,5,8,7,6,2]=>[1,1,3,1,1,1]
[4,7,6,8,1,3,5,2]=>[2,2,3,1]
[3,7,2,5,1,6,8,4]=>[2,2,3,1]
[4,7,1,3,2,5,6,8]=>[2,2,4]
[4,1,6,7,3,2,8,5]=>[1,3,1,2,1]
[1,7,2,5,6,8,4,3]=>[2,4,1,1]
[3,2,1,5,8,4,7,6]=>[1,1,3,2,1]
[4,7,6,8,3,1,5,2]=>[2,2,1,2,1]
[2,1,6,5,8,4,3,7]=>[1,2,2,1,2]
[7,4,6,3,5,1,8,2]=>[1,2,2,2,1]
[2,5,4,7,3,1,6,8]=>[2,2,1,3]
[5,4,8,6,1,7,3,2]=>[1,2,1,2,1,1]
[7,4,1,8,5,6,3,2]=>[1,1,2,2,1,1]
[3,6,4,5,7,1,8,2]=>[2,3,2,1]
[3,5,4,7,1,8,6,2]=>[2,2,2,1,1]
[3,8,2,4,5,7,1,6]=>[2,4,2]
[6,3,2,4,1,8,5,7]=>[1,1,2,2,2]
[7,1,5,4,2,3,6,8]=>[1,2,1,4]
[7,1,3,6,4,5,2,8]=>[1,3,2,2]
[6,4,5,1,3,8,2,7]=>[1,2,3,2]
[6,1,3,8,4,5,2,7]=>[1,3,2,2]
[7,4,5,1,3,6,2,8]=>[1,2,3,2]
[7,3,6,4,5,1,2,8]=>[1,2,2,3]
[2,1,8,7,3,6,5,4]=>[1,2,1,2,1,1]
[5,8,6,3,1,2,7,4]=>[2,1,1,3,1]
[5,8,2,7,1,3,6,4]=>[2,2,3,1]
[2,6,5,4,1,3,7,8]=>[2,1,1,4]
[4,1,5,7,6,3,2,8]=>[1,3,1,1,2]
[6,3,4,2,1,8,7,5]=>[1,2,1,2,1,1]
[4,5,1,7,6,3,2,8]=>[2,2,1,1,2]
[2,5,4,1,7,8,3,6]=>[2,1,3,2]
[3,5,4,7,8,2,1,6]=>[2,3,1,2]
[7,3,6,1,4,5,2,8]=>[1,2,3,2]
[7,1,4,5,2,8,3,6]=>[1,3,2,2]
[5,4,2,1,8,7,3,6]=>[1,1,1,2,1,2]
[4,8,6,3,1,5,2,7]=>[2,1,1,2,2]
[6,2,1,5,4,3,8,7]=>[1,1,2,1,2,1]
[5,1,4,8,3,6,2,7]=>[1,3,2,2]
[6,1,4,5,3,8,2,7]=>[1,3,2,2]
[1,7,2,6,8,4,5,3]=>[2,3,2,1]
[1,4,2,6,7,8,5,3]=>[2,4,1,1]
[1,4,2,5,6,8,7,3]=>[2,4,1,1]
[1,4,6,5,7,2,8,3]=>[3,2,2,1]
[2,5,3,6,7,8,4,1]=>[2,4,1,1]
[6,4,2,7,8,3,5,1]=>[1,1,3,2,1]
[5,3,1,6,8,7,2,4]=>[1,1,3,1,2]
[6,2,1,7,4,3,5,8]=>[1,1,2,1,3]
[1,8,6,2,4,3,5,7]=>[2,1,2,3]
[8,3,1,4,2,6,7,5]=>[1,1,2,3,1]
[7,4,2,5,3,8,6,1]=>[1,1,2,2,1,1]
[6,5,8,3,1,7,2,4]=>[1,2,1,2,2]
[3,2,4,5,7,8,1,6]=>[1,5,2]
[2,3,4,7,5,8,6,1]=>[4,2,1,1]
[3,6,2,4,8,5,1,7]=>[2,3,1,2]
[1,8,2,4,7,3,5,6]=>[2,3,3]
[8,1,3,2,7,4,5,6]=>[1,2,2,3]
[6,5,2,8,7,4,3,1]=>[1,1,2,1,1,1,1]
[7,8,5,4,2,1,6,3]=>[2,1,1,1,2,1]
[7,5,2,8,6,4,3,1]=>[1,1,2,1,1,1,1]
[7,8,3,2,6,5,4,1]=>[2,1,2,1,1,1]
[6,5,2,8,1,4,7,3]=>[1,1,2,3,1]
[8,5,2,6,4,1,7,3]=>[1,1,2,1,2,1]
[5,1,8,6,4,3,7,2]=>[1,2,1,1,2,1]
[5,8,6,1,3,2,7,4]=>[2,1,2,2,1]
[1,7,6,3,8,2,5,4]=>[2,1,2,2,1]
[8,2,6,3,7,5,1,4]=>[1,2,2,1,2]
[8,2,6,7,3,4,1,5]=>[1,3,2,2]
[7,2,6,8,3,1,4,5]=>[1,3,1,3]
[6,1,3,7,8,4,5,2]=>[1,4,2,1]
[6,8,7,4,1,3,2,5]=>[2,1,1,2,2]
[8,6,7,2,5,3,1,4]=>[1,2,2,1,2]
[1,6,2,7,8,4,5,3]=>[2,3,2,1]
[8,6,2,7,5,4,1,3]=>[1,1,2,1,1,2]
[1,6,8,2,7,5,3,4]=>[3,2,1,2]
[7,6,3,2,8,1,5,4]=>[1,1,1,2,2,1]
[5,7,3,1,2,8,6,4]=>[2,1,3,1,1]
[5,1,7,4,3,8,6,2]=>[1,2,1,2,1,1]
[6,7,1,4,8,2,5,3]=>[2,3,2,1]
[8,6,3,7,2,4,1,5]=>[1,1,2,2,2]
[1,7,8,6,4,2,3,5]=>[3,1,1,3]
[7,2,8,6,4,1,3,5]=>[1,2,1,1,3]
[7,4,2,6,5,3,1,8]=>[1,1,2,1,1,2]
[1,5,3,7,4,2,6,8]=>[2,2,1,3]
[1,7,6,4,3,2,8,5]=>[2,1,1,1,2,1]
[1,7,6,4,3,2,5,8]=>[2,1,1,1,3]
[7,4,3,6,2,5,1,8]=>[1,1,2,2,2]
[1,7,6,3,4,2,5,8]=>[2,1,2,3]
[1,2,7,4,3,8,6,5]=>[3,1,2,1,1]
[1,7,6,3,5,2,4,8]=>[2,1,2,3]
[1,5,4,7,3,2,8,6]=>[2,2,1,2,1]
[1,7,6,3,5,2,8,4]=>[2,1,2,2,1]
[1,2,7,4,3,6,5,8]=>[3,1,2,2]
[1,5,4,2,3,8,7,6]=>[2,1,3,1,1]
[1,7,6,4,5,2,3,8]=>[2,1,2,3]
[1,5,3,2,4,6,7,8]=>[2,1,5]
[1,5,3,7,6,2,4,8]=>[2,2,1,3]
[1,2,7,5,3,6,8,4]=>[3,1,3,1]
[1,2,7,6,3,5,4,8]=>[3,1,2,2]
[1,5,4,2,3,7,8,6]=>[2,1,4,1]
[1,2,7,6,3,5,8,4]=>[3,1,3,1]
[8,1,3,2,6,5,7,4]=>[1,2,2,2,1]
[4,3,7,2,8,1,6,5]=>[1,2,2,2,1]
[3,2,7,5,6,1,8,4]=>[1,2,2,2,1]
[7,5,6,1,3,2,8,4]=>[1,2,2,2,1]
[7,3,4,1,8,2,6,5]=>[1,2,2,2,1]
[7,4,5,1,6,3,8,2]=>[1,2,2,2,1]
[7,5,6,1,4,3,8,2]=>[1,2,2,2,1]
[4,2,7,6,8,3,5,1]=>[1,2,2,2,1]
[3,2,6,4,8,5,7,1]=>[1,2,2,2,1]
[4,2,8,3,6,5,7,1]=>[1,2,2,2,1]
[8,1,4,3,5,2,7,6]=>[1,2,2,2,1]
[6,2,8,5,7,1,4,3]=>[1,2,2,2,1]
[6,4,8,5,7,1,3,2]=>[1,2,2,2,1]
[5,3,4,1,6,2,8,7]=>[1,2,2,2,1]
[5,2,7,6,8,1,4,3]=>[1,2,2,2,1]
[7,5,6,1,8,2,4,3]=>[1,2,2,2,1]
[7,3,6,1,8,2,5,4]=>[1,2,2,2,1]
[7,2,8,1,6,3,5,4]=>[1,2,2,2,1]
[5,8,4,1,2,6,3,7]=>[2,1,3,2]
[6,4,7,1,2,8,3,5]=>[1,2,3,2]
[3,8,1,7,4,2,5,6]=>[2,2,1,3]
[3,7,4,8,2,5,6,1]=>[2,2,3,1]
[8,3,4,5,1,6,2,7]=>[1,3,2,2]
[8,4,1,2,3,6,5,7]=>[1,1,4,2]
[8,3,6,5,4,1,2,7]=>[1,2,1,1,3]
[8,2,1,5,3,4,6,7]=>[1,1,2,4]
[8,2,5,6,4,1,3,7]=>[1,3,1,3]
[2,7,8,5,4,3,6,1]=>[3,1,1,2,1]
[3,8,2,6,4,7,5,1]=>[2,2,2,1,1]
[1,2,5,7,4,8,3,6]=>[4,2,2]
[4,3,7,5,8,1,2,6]=>[1,2,2,3]
[4,7,1,5,3,6,8,2]=>[2,2,3,1]
[1,7,5,8,4,6,3,2]=>[2,2,2,1,1]
[7,3,6,8,4,1,5,2]=>[1,3,1,2,1]
[8,3,6,7,4,5,2,1]=>[1,3,2,1,1]
[6,8,5,3,1,4,7,2]=>[2,1,1,3,1]
[1,8,3,4,7,5,6,2]=>[2,3,2,1]
[6,1,4,7,3,5,8,2]=>[1,3,3,1]
[5,8,6,2,7,3,4,1]=>[2,1,2,2,1]
[6,5,8,3,2,7,4,1]=>[1,2,1,2,1,1]
[6,5,7,1,2,8,3,4]=>[1,2,3,2]
[7,1,4,2,3,8,6,5]=>[1,2,3,1,1]
[2,3,5,4,8,1,7,6]=>[3,2,2,1]
[6,2,4,7,8,3,5,1]=>[1,4,2,1]
[1,7,2,6,5,3,8,4]=>[2,2,1,2,1]
[4,2,6,7,1,8,5,3]=>[1,3,2,1,1]
[2,7,1,6,3,8,5,4]=>[2,2,2,1,1]
[3,7,5,6,8,1,2,4]=>[2,3,3]
[8,1,2,5,3,7,6,4]=>[1,3,2,1,1]
[1,6,2,4,5,7,8,3]=>[2,5,1]
[8,6,5,2,4,1,7,3]=>[1,1,1,2,2,1]
[7,8,5,1,2,4,6,3]=>[2,1,4,1]
[7,1,6,4,2,5,8,3]=>[1,2,1,3,1]
[1,7,6,5,3,4,8,2]=>[2,1,1,3,1]
[8,1,6,4,5,3,7,2]=>[1,2,2,2,1]
[8,6,7,5,1,3,4,2]=>[1,2,1,3,1]
[7,4,8,5,3,6,2,1]=>[1,2,1,2,1,1]
[6,2,5,7,4,3,1,8]=>[1,3,1,1,2]
[6,2,5,8,1,7,4,3]=>[1,3,2,1,1]
[6,7,5,2,4,3,1,8]=>[2,1,2,1,2]
[4,3,8,6,7,5,2,1]=>[1,2,2,1,1,1]
[3,6,5,2,4,1,7,8]=>[2,1,2,3]
[8,6,5,2,4,3,1,7]=>[1,1,1,2,1,2]
[6,8,5,2,4,3,1,7]=>[2,1,2,1,2]
[6,2,5,8,4,3,1,7]=>[1,3,1,1,2]
[4,7,2,5,6,1,8,3]=>[2,3,2,1]
[3,8,1,6,5,2,4,7]=>[2,2,1,3]
[3,4,2,8,6,7,1,5]=>[2,2,2,2]
[3,7,1,6,2,5,8,4]=>[2,2,3,1]
[3,8,4,1,6,2,5,7]=>[2,1,2,3]
[3,8,5,2,4,1,6,7]=>[2,1,2,3]
[3,4,2,7,6,8,1,5]=>[2,2,2,2]
[7,5,2,4,3,1,8,6]=>[1,1,2,1,2,1]
[3,8,7,5,2,4,1,6]=>[2,1,1,2,2]
[3,8,1,6,2,5,7,4]=>[2,2,3,1]
[3,7,4,1,6,2,5,8]=>[2,1,2,3]
[3,6,2,5,1,8,7,4]=>[2,2,2,1,1]
[3,6,2,5,1,7,4,8]=>[2,2,2,2]
[7,6,1,8,5,2,4,3]=>[1,1,2,1,2,1]
[4,6,7,2,5,1,8,3]=>[3,2,2,1]
[3,6,2,5,1,7,8,4]=>[2,2,3,1]
[3,4,2,7,6,1,5,8]=>[2,2,1,3]
[3,4,2,8,1,5,7,6]=>[2,2,3,1]
[3,4,2,7,8,1,5,6]=>[2,3,3]
[3,4,2,6,1,5,7,8]=>[2,2,4]
[3,6,2,5,1,8,4,7]=>[2,2,2,2]
[8,3,4,7,2,5,1,6]=>[1,3,2,2]
[3,8,5,2,4,7,1,6]=>[2,1,3,2]
[3,4,2,7,1,5,8,6]=>[2,2,3,1]
[3,4,2,8,7,1,5,6]=>[2,2,1,3]
[7,3,4,6,5,8,1,2]=>[1,3,2,2]
[7,3,6,8,1,4,5,2]=>[1,3,3,1]
[6,3,4,1,7,5,2,8]=>[1,2,2,1,2]
[3,4,6,7,2,1,8,5]=>[4,1,2,1]
[5,7,1,8,6,4,3,2]=>[2,2,1,1,1,1]
[5,1,8,6,7,2,4,3]=>[1,2,2,2,1]
[6,1,8,5,2,4,7,3]=>[1,2,1,3,1]
[7,1,4,2,5,8,6,3]=>[1,2,3,1,1]
[7,8,5,1,2,4,3,6]=>[2,1,3,2]
[2,5,3,1,4,8,6,7]=>[2,1,3,2]
[3,6,1,2,5,4,8,7]=>[2,3,2,1]
[5,8,1,4,3,6,7,2]=>[2,2,3,1]
[1,7,3,4,6,8,2,5]=>[2,4,2]
[7,2,3,8,6,4,1,5]=>[1,3,1,1,2]
[5,2,3,8,7,4,1,6]=>[1,3,1,1,2]
[6,5,8,2,1,4,3,7]=>[1,2,1,2,2]
[5,7,6,3,1,2,4,8]=>[2,1,1,4]
[1,4,3,7,2,6,8,5]=>[2,2,3,1]
[5,8,6,3,2,4,1,7]=>[2,1,1,2,2]
[4,6,2,7,8,1,3,5]=>[2,3,3]
[6,2,3,7,1,4,5,8]=>[1,3,4]
[4,6,7,8,2,1,3,5]=>[4,1,3]
[8,6,3,2,1,7,5,4]=>[1,1,1,1,2,1,1]
[5,3,4,1,7,8,2,6]=>[1,2,3,2]
[4,8,6,1,2,3,5,7]=>[2,1,5]
[6,7,3,5,8,4,1,2]=>[2,3,1,2]
[7,5,8,2,3,1,6,4]=>[1,2,2,2,1]
[6,5,1,4,8,2,3,7]=>[1,1,3,3]
[6,8,1,4,3,2,5,7]=>[2,2,1,3]
[6,1,3,4,2,5,8,7]=>[1,3,3,1]
[5,1,3,6,2,4,8,7]=>[1,3,3,1]
[2,6,1,3,5,7,8,4]=>[2,5,1]
[7,8,4,2,3,1,6,5]=>[2,1,2,2,1]
[8,6,3,4,2,1,7,5]=>[1,1,2,1,2,1]
[1,5,7,6,8,2,4,3]=>[3,2,2,1]
[3,7,1,8,5,2,6,4]=>[2,2,1,2,1]
[5,7,1,3,8,4,2,6]=>[2,3,1,2]
[2,6,1,4,3,7,8,5]=>[2,2,3,1]
[1,6,2,4,3,5,8,7]=>[2,2,3,1]
[3,8,5,7,6,4,1,2]=>[2,2,1,1,2]
[1,8,5,7,6,3,4,2]=>[2,2,1,2,1]
[5,8,1,7,6,3,4,2]=>[2,2,1,2,1]
[1,7,6,3,8,5,4,2]=>[2,1,2,1,1,1]
[5,3,7,6,1,8,4,2]=>[1,2,1,2,1,1]
[5,1,7,6,3,8,4,2]=>[1,2,1,2,1,1]
[1,5,6,3,7,8,4,2]=>[3,3,1,1]
[1,5,7,6,3,8,4,2]=>[3,1,2,1,1]
[7,3,5,6,1,8,4,2]=>[1,3,2,1,1]
[7,3,6,1,5,8,4,2]=>[1,2,3,1,1]
[1,6,3,7,8,5,4,2]=>[2,3,1,1,1]
[1,7,8,6,3,5,4,2]=>[3,1,2,1,1]
[3,6,1,7,5,8,4,2]=>[2,2,2,1,1]
[3,7,5,6,1,8,4,2]=>[2,2,2,1,1]
[7,4,5,1,8,3,2,6]=>[1,2,2,1,2]
[7,2,1,8,5,4,3,6]=>[1,1,2,1,1,2]
[2,7,3,4,6,8,1,5]=>[2,4,2]
[5,6,2,8,4,7,3,1]=>[2,2,2,1,1]
[5,6,8,2,3,7,4,1]=>[3,3,1,1]
[3,1,7,6,8,5,2,4]=>[1,2,2,1,2]
[2,7,1,8,6,4,3,5]=>[2,2,1,1,2]
[8,4,5,7,1,2,6,3]=>[1,3,3,1]
[5,6,8,1,7,3,4,2]=>[3,2,2,1]
[8,3,1,5,7,4,6,2]=>[1,1,3,2,1]
[8,1,3,4,7,5,6,2]=>[1,4,2,1]
[1,4,5,7,8,6,2,3]=>[5,1,2]
[2,4,5,8,6,7,3,1]=>[4,2,1,1]
[5,7,6,3,4,8,1,2]=>[2,1,3,2]
[3,7,5,4,6,1,2,8]=>[2,1,2,3]
[5,3,4,7,6,8,1,2]=>[1,3,2,2]
[5,3,7,4,6,1,2,8]=>[1,2,2,3]
[7,3,5,4,6,1,2,8]=>[1,2,2,3]
[7,8,3,5,4,1,2,6]=>[2,2,1,3]
[7,3,5,4,1,2,6,8]=>[1,2,1,4]
[5,7,6,3,4,1,2,8]=>[2,1,2,3]
[3,5,4,1,2,7,6,8]=>[2,1,3,2]
[5,7,6,1,3,2,4,8]=>[2,1,2,3]
[5,3,4,1,2,7,6,8]=>[1,2,3,2]
[7,8,3,1,2,5,4,6]=>[2,1,3,2]
[7,8,5,1,3,2,4,6]=>[2,1,2,3]
[7,5,6,1,3,2,4,8]=>[1,2,2,3]
[7,8,5,1,3,6,2,4]=>[2,1,3,2]
[7,8,3,1,5,4,2,6]=>[2,1,2,1,2]
[3,5,4,1,7,6,2,8]=>[2,1,2,1,2]
[3,5,1,4,7,6,2,8]=>[2,3,1,2]
[7,3,8,5,1,4,6,2]=>[1,2,1,3,1]
[7,5,1,3,8,6,2,4]=>[1,1,3,1,2]
[7,1,3,8,2,5,4,6]=>[1,3,2,2]
[7,5,8,6,1,3,2,4]=>[1,2,1,2,2]
[5,7,6,8,3,1,4,2]=>[2,2,1,2,1]
[3,1,5,4,2,7,6,8]=>[1,2,1,2,2]
[3,1,5,4,7,2,6,8]=>[1,2,2,3]
[5,7,6,1,3,8,2,4]=>[2,1,3,2]
[5,7,6,3,8,1,4,2]=>[2,1,2,2,1]
[3,1,5,7,4,2,6,8]=>[1,3,1,3]
[3,7,5,4,8,6,1,2]=>[2,1,2,1,2]
[5,1,3,7,6,2,4,8]=>[1,3,1,3]
[7,1,6,8,2,3,5,4]=>[1,3,3,1]
[1,6,3,7,2,4,5,8]=>[2,2,4]
[3,8,1,4,7,6,2,5]=>[2,3,1,2]
[1,7,3,4,5,2,6,8]=>[2,3,3]
[1,6,7,5,4,2,3,8]=>[3,1,1,3]
[4,7,8,5,1,3,2,6]=>[3,1,2,2]
[4,2,1,8,7,5,3,6]=>[1,1,2,1,1,2]
[8,2,5,1,7,4,6,3]=>[1,2,2,2,1]
[5,1,4,8,2,3,6,7]=>[1,3,4]
[5,3,2,4,8,1,7,6]=>[1,1,3,2,1]
[8,2,5,7,4,1,6,3]=>[1,3,1,2,1]
[8,7,5,1,6,3,4,2]=>[1,1,1,2,2,1]
[7,4,1,3,6,5,8,2]=>[1,1,3,2,1]
[4,2,8,5,3,1,6,7]=>[1,2,1,1,3]
[6,8,5,3,2,7,1,4]=>[2,1,1,2,2]
[8,3,7,2,6,5,1,4]=>[1,2,2,1,2]
[4,6,2,7,1,3,8,5]=>[2,2,3,1]
[7,2,5,3,6,1,8,4]=>[1,2,2,2,1]
[8,2,4,5,6,7,1,3]=>[1,5,2]
[3,4,6,5,1,8,7,2]=>[3,1,2,1,1]
[3,4,6,5,1,7,2,8]=>[3,1,2,2]
[8,7,1,5,3,2,6,4]=>[1,1,2,1,2,1]
[3,5,1,4,8,6,7,2]=>[2,3,2,1]
[3,5,1,4,7,2,8,6]=>[2,3,2,1]
[4,5,1,8,7,3,2,6]=>[2,2,1,1,2]
[5,1,4,7,3,2,6,8]=>[1,3,1,3]
[5,1,4,8,7,3,2,6]=>[1,3,1,1,2]
[7,2,5,3,1,4,8,6]=>[1,2,1,3,1]
[7,1,4,8,5,3,2,6]=>[1,3,1,1,2]
[3,8,2,6,7,1,5,4]=>[2,3,2,1]
[8,3,2,6,7,1,5,4]=>[1,1,3,2,1]
[5,2,8,7,3,1,4,6]=>[1,2,1,1,3]
[6,7,2,5,3,1,4,8]=>[2,2,1,3]
[6,1,3,4,5,2,8,7]=>[1,4,2,1]
[6,1,3,4,2,7,8,5]=>[1,3,3,1]
[6,5,2,3,1,4,8,7]=>[1,1,2,3,1]
[6,1,3,4,8,2,7,5]=>[1,4,2,1]
[6,5,2,3,7,8,1,4]=>[1,1,4,2]
[8,4,2,7,3,5,1,6]=>[1,1,2,2,2]
[1,5,3,8,4,2,7,6]=>[2,2,1,2,1]
[7,4,2,6,3,8,1,5]=>[1,1,2,2,2]
[8,5,2,7,3,4,1,6]=>[1,1,2,2,2]
[5,4,2,1,8,3,7,6]=>[1,1,1,2,2,1]
[1,5,3,7,8,2,6,4]=>[2,3,2,1]
[3,1,6,4,2,7,8,5]=>[1,2,1,3,1]
[3,1,7,4,2,6,8,5]=>[1,2,1,3,1]
[3,8,1,4,2,6,7,5]=>[2,2,3,1]
[7,4,8,2,3,5,1,6]=>[1,2,3,2]
[8,4,5,2,7,3,1,6]=>[1,2,2,1,2]
[8,4,1,3,2,6,7,5]=>[1,1,2,3,1]
[8,1,7,3,2,5,6,4]=>[1,2,1,3,1]
[8,6,5,2,7,3,1,4]=>[1,1,1,2,1,2]
[6,4,5,2,1,3,8,7]=>[1,2,1,3,1]
[3,4,7,6,2,8,1,5]=>[3,1,2,2]
[3,8,5,1,4,6,7,2]=>[2,1,4,1]
[3,8,1,7,4,5,6,2]=>[2,2,3,1]
[3,1,6,8,4,2,7,5]=>[1,3,1,2,1]
[3,1,8,7,4,2,6,5]=>[1,2,1,1,2,1]
[3,7,5,6,2,8,1,4]=>[2,2,2,2]
[8,4,5,1,3,6,7,2]=>[1,2,4,1]
[8,4,5,7,2,3,1,6]=>[1,3,2,2]
[8,1,6,7,3,4,5,2]=>[1,3,3,1]
[8,1,6,2,4,5,7,3]=>[1,2,4,1]
[1,5,6,8,3,2,7,4]=>[4,1,2,1]
[7,4,5,6,2,8,1,3]=>[1,3,2,2]
[3,1,6,7,2,5,8,4]=>[1,3,3,1]
[1,5,2,8,3,6,7,4]=>[2,2,3,1]
[5,6,2,3,7,4,1,8]=>[2,3,1,2]
[6,2,4,7,3,5,1,8]=>[1,3,2,2]
[1,4,8,5,3,6,7,2]=>[3,1,3,1]
[2,5,6,3,1,8,4,7]=>[3,1,2,2]
[4,5,1,2,7,8,6,3]=>[2,4,1,1]
[4,8,5,1,2,6,7,3]=>[2,1,4,1]
[4,6,7,5,1,2,8,3]=>[3,1,3,1]
[7,2,8,1,4,5,3,6]=>[1,2,3,2]
[6,1,4,7,3,8,2,5]=>[1,3,2,2]
[7,1,6,3,4,8,2,5]=>[1,2,3,2]
[2,8,4,6,3,1,5,7]=>[2,2,1,3]
[8,2,6,3,5,1,4,7]=>[1,2,2,3]
[3,7,4,1,5,8,2,6]=>[2,1,3,2]
[3,8,4,1,7,2,5,6]=>[2,1,2,3]
[6,7,5,1,3,8,2,4]=>[2,1,3,2]
[8,5,1,3,6,7,2,4]=>[1,1,4,2]
[7,8,6,2,4,1,3,5]=>[2,1,2,3]
[8,2,4,1,3,6,7,5]=>[1,2,4,1]
[8,1,3,6,2,5,7,4]=>[1,3,3,1]
[1,5,6,3,8,4,7,2]=>[3,2,2,1]
[5,6,1,3,7,2,8,4]=>[2,3,2,1]
[5,6,1,8,2,3,7,4]=>[2,2,3,1]
[5,6,1,2,8,4,7,3]=>[2,3,2,1]
[3,7,8,6,4,1,2,5]=>[3,1,1,3]
[5,7,8,3,6,4,2,1]=>[3,2,1,1,1]
[5,7,8,1,6,4,2,3]=>[3,2,1,2]
[3,7,8,1,6,4,2,5]=>[3,2,1,2]
[1,7,8,6,3,4,2,5]=>[3,1,2,2]
[3,7,5,8,6,4,2,1]=>[2,2,1,1,1,1]
[1,7,3,8,6,4,2,5]=>[2,2,1,1,2]
[5,7,1,8,6,4,2,3]=>[2,2,1,1,2]
[7,8,1,5,6,4,2,3]=>[2,3,1,2]
[7,8,3,5,6,4,2,1]=>[2,3,1,1,1]
[7,1,8,5,6,4,2,3]=>[1,2,2,1,2]
[7,1,5,8,6,4,2,3]=>[1,3,1,1,2]
[7,3,5,8,6,4,2,1]=>[1,3,1,1,1,1]
[5,3,7,8,6,4,2,1]=>[1,3,1,1,1,1]
[3,1,8,5,6,4,2,7]=>[1,2,2,1,2]
[8,3,1,5,6,4,2,7]=>[1,1,3,1,2]
[8,1,3,5,6,4,2,7]=>[1,4,1,2]
[1,8,3,5,6,4,2,7]=>[2,3,1,2]
[1,3,8,5,6,4,2,7]=>[3,2,1,2]
[1,3,5,8,6,4,2,7]=>[4,1,1,2]
[1,5,7,8,6,4,2,3]=>[4,1,1,2]
[1,8,2,6,5,3,4,7]=>[2,2,1,3]
[8,6,1,5,2,3,4,7]=>[1,1,2,4]
[8,5,1,6,2,3,4,7]=>[1,1,2,4]
[7,6,1,2,3,8,4,5]=>[1,1,4,2]
[2,7,8,4,1,3,5,6]=>[3,1,4]
[6,8,1,2,3,7,4,5]=>[2,4,2]
[8,1,5,4,2,3,7,6]=>[1,2,1,3,1]
[7,5,2,3,1,8,4,6]=>[1,1,2,2,2]
[8,1,3,5,6,7,2,4]=>[1,5,2]
[8,1,2,5,3,4,7,6]=>[1,3,3,1]
[8,1,5,6,4,2,7,3]=>[1,3,1,2,1]
[2,7,3,5,8,4,1,6]=>[2,3,1,2]
[3,7,6,2,5,8,4,1]=>[2,1,3,1,1]
[5,2,7,3,4,8,1,6]=>[1,2,3,2]
[8,6,4,7,3,5,2,1]=>[1,1,2,2,1,1]
[4,7,2,3,5,8,1,6]=>[2,4,2]
[2,5,8,3,6,4,1,7]=>[3,2,1,2]
[7,4,2,1,5,3,8,6]=>[1,1,1,2,2,1]
[7,4,6,8,2,3,5,1]=>[1,3,3,1]
[3,6,8,7,1,2,4,5]=>[3,1,4]
[3,2,7,1,5,6,4,8]=>[1,2,3,2]
[4,8,7,1,6,5,2,3]=>[2,1,2,1,2]
[4,2,1,6,5,7,8,3]=>[1,1,2,3,1]
[4,3,1,5,6,7,2,8]=>[1,1,4,2]
[4,5,8,2,6,3,7,1]=>[3,2,2,1]
[5,2,1,4,7,3,6,8]=>[1,1,3,3]
[2,7,5,4,1,3,6,8]=>[2,1,1,4]
[3,7,4,5,6,1,2,8]=>[2,3,3]
[2,7,4,6,5,1,8,3]=>[2,2,1,2,1]
[2,3,7,4,5,1,6,8]=>[3,2,3]
[6,7,3,1,2,8,5,4]=>[2,1,3,1,1]
[6,8,7,5,2,1,4,3]=>[2,1,1,1,2,1]
[7,8,2,6,3,1,4,5]=>[2,2,1,3]
[2,8,6,3,5,1,4,7]=>[2,1,2,3]
[7,2,6,3,1,4,5,8]=>[1,2,1,4]
[7,8,6,4,1,5,2,3]=>[2,1,1,2,2]
[2,7,6,5,3,4,1,8]=>[2,1,1,2,2]
[8,2,6,4,5,3,1,7]=>[1,2,2,1,2]
[8,7,2,6,4,3,1,5]=>[1,1,2,1,1,2]
[1,2,8,6,4,5,3,7]=>[3,1,2,2]
[1,5,8,7,6,3,4,2]=>[3,1,1,2,1]
[1,4,6,8,5,3,2,7]=>[4,1,1,2]
[1,4,7,8,5,6,3,2]=>[4,2,1,1]
[1,2,5,8,6,4,7,3]=>[4,1,2,1]
[1,8,6,7,2,3,5,4]=>[2,2,3,1]
[1,4,8,5,6,3,2,7]=>[3,2,1,2]
[1,6,4,8,5,7,3,2]=>[2,2,2,1,1]
[1,7,3,2,6,8,5,4]=>[2,1,3,1,1]
[1,7,3,6,4,2,5,8]=>[2,2,1,3]
[1,6,8,5,2,7,3,4]=>[3,1,2,2]
[1,6,8,5,4,2,3,7]=>[3,1,1,3]
[1,6,3,2,4,5,8,7]=>[2,1,4,1]
[1,7,4,5,8,6,2,3]=>[2,3,1,2]
[1,2,8,6,5,3,4,7]=>[3,1,1,3]
[1,3,6,7,2,8,5,4]=>[4,2,1,1]
[1,8,5,2,6,7,3,4]=>[2,1,3,2]
[1,3,4,8,5,2,7,6]=>[4,1,2,1]
[1,3,8,5,2,4,7,6]=>[3,1,3,1]
[3,5,8,7,6,2,4,1]=>[3,1,1,2,1]
[3,1,5,4,6,8,7,2]=>[1,2,3,1,1]
[3,1,6,4,2,5,8,7]=>[1,2,1,3,1]
[3,6,1,4,5,7,8,2]=>[2,5,1]
[5,7,8,2,4,6,1,3]=>[3,3,2]
[5,4,2,3,6,8,1,7]=>[1,1,4,2]
[3,8,1,6,4,2,5,7]=>[2,2,1,3]
[7,3,2,1,8,6,4,5]=>[1,1,1,2,1,2]
[8,7,2,4,1,3,6,5]=>[1,1,2,3,1]
[8,2,6,3,5,7,1,4]=>[1,2,3,2]
[3,1,7,8,6,2,5,4]=>[1,3,1,2,1]
[5,6,1,8,3,7,2,4]=>[2,2,2,2]
[2,8,1,6,5,3,7,4]=>[2,2,1,2,1]
[2,1,5,7,6,3,8,4]=>[1,3,1,2,1]
[4,3,5,1,7,8,6,2]=>[1,2,3,1,1]
[1,8,5,2,3,4,7,6]=>[2,1,4,1]
[1,5,8,2,3,4,7,6]=>[3,4,1]
[1,2,7,8,4,5,6,3]=>[4,3,1]
[4,3,8,7,6,2,5,1]=>[1,2,1,1,2,1]
[5,4,8,2,7,6,3,1]=>[1,2,2,1,1,1]
[2,3,6,4,1,7,5,8]=>[3,1,2,2]
[2,3,6,1,7,5,8,4]=>[3,2,2,1]
[3,6,4,2,1,5,7,8]=>[2,1,1,4]
[4,6,5,2,1,7,8,3]=>[2,1,1,3,1]
[4,6,1,7,5,8,3,2]=>[2,2,2,1,1]
[4,1,5,7,6,8,3,2]=>[1,3,2,1,1]
[3,5,6,2,1,4,7,8]=>[3,1,4]
[4,3,6,5,1,7,8,2]=>[1,2,1,3,1]
[3,6,4,5,2,1,7,8]=>[2,2,1,3]
[3,5,6,4,2,8,1,7]=>[3,1,2,2]
[4,6,5,3,1,7,8,2]=>[2,1,1,3,1]
[5,8,1,4,2,3,6,7]=>[2,2,4]
[4,5,8,2,3,1,6,7]=>[3,2,3]
[3,5,4,8,1,7,2,6]=>[2,2,2,2]
[5,3,6,8,1,4,7,2]=>[1,3,3,1]
[3,5,1,8,6,4,7,2]=>[2,2,1,2,1]
[4,7,2,8,3,1,6,5]=>[2,2,1,2,1]
[1,2,5,6,8,3,7,4]=>[5,2,1]
[5,3,8,4,6,2,7,1]=>[1,2,2,2,1]
[7,4,8,1,5,2,6,3]=>[1,2,2,2,1]
[8,3,2,1,6,5,7,4]=>[1,1,1,2,2,1]
[4,1,5,6,8,7,2,3]=>[1,4,1,2]
[1,2,5,6,8,4,7,3]=>[5,2,1]
[1,5,6,8,4,7,2,3]=>[4,2,2]
[5,6,8,1,2,4,7,3]=>[3,4,1]
[6,8,1,4,5,7,2,3]=>[2,4,2]
[4,3,5,1,8,6,7,2]=>[1,2,2,2,1]
[1,3,5,6,8,4,7,2]=>[5,2,1]
[5,6,8,2,3,4,7,1]=>[3,4,1]
[6,5,1,2,4,8,7,3]=>[1,1,4,1,1]
[5,8,7,2,1,3,6,4]=>[2,1,1,3,1]
[5,1,7,2,8,6,3,4]=>[1,2,2,1,2]
[6,1,5,3,4,8,7,2]=>[1,2,3,1,1]
[5,8,6,3,2,1,4,7]=>[2,1,1,1,3]
[8,7,1,6,3,5,4,2]=>[1,1,2,2,1,1]
[3,2,1,7,8,6,4,5]=>[1,1,3,1,2]
[8,6,7,1,2,5,3,4]=>[1,2,3,2]
[1,5,6,4,2,8,7,3]=>[3,1,2,1,1]
[7,5,1,4,8,2,3,6]=>[1,1,3,3]
[3,2,8,1,7,5,6,4]=>[1,2,2,2,1]
[8,4,3,1,7,5,6,2]=>[1,1,1,2,2,1]
[6,1,7,8,4,2,3,5]=>[1,3,1,3]
[7,4,3,1,8,5,2,6]=>[1,1,1,2,1,2]
[7,8,1,6,3,4,5,2]=>[2,2,3,1]
[6,8,1,7,3,4,2,5]=>[2,2,2,2]
[4,6,5,3,8,2,7,1]=>[2,1,2,2,1]
[4,5,6,3,8,1,7,2]=>[3,2,2,1]
[1,3,7,6,4,5,8,2]=>[3,1,3,1]
[3,2,5,8,4,7,6,1]=>[1,3,2,1,1]
[1,4,5,3,8,6,2,7]=>[3,2,1,2]
[1,3,5,8,4,7,6,2]=>[4,2,1,1]
[1,4,2,6,7,5,8,3]=>[2,3,2,1]
[7,8,3,5,2,1,6,4]=>[2,2,1,2,1]
[7,8,6,3,5,2,4,1]=>[2,1,2,2,1]
[6,3,7,5,2,4,1,8]=>[1,2,1,2,2]
[1,8,2,4,5,7,3,6]=>[2,4,2]
[6,2,4,5,7,3,1,8]=>[1,4,1,2]
[7,8,2,4,6,5,3,1]=>[2,3,1,1,1]
[7,8,1,5,6,4,3,2]=>[2,3,1,1,1]
[6,1,7,4,5,3,2,8]=>[1,2,2,1,2]
[6,3,7,5,1,4,2,8]=>[1,2,1,2,2]
[3,8,5,7,4,2,1,6]=>[2,2,1,1,2]
[2,8,3,7,5,1,4,6]=>[2,2,1,3]
[2,8,5,4,7,3,6,1]=>[2,1,2,2,1]
[5,3,1,2,6,7,4,8]=>[1,1,4,2]
[1,3,8,2,4,6,7,5]=>[3,4,1]
[6,1,7,3,4,2,5,8]=>[1,2,2,3]
[6,4,7,2,1,3,5,8]=>[1,2,1,4]
[4,8,3,6,7,2,1,5]=>[2,3,1,2]
[4,3,7,8,6,2,1,5]=>[1,3,1,1,2]
[3,8,5,4,7,2,6,1]=>[2,1,2,2,1]
[4,8,5,3,7,1,6,2]=>[2,1,2,2,1]
[3,8,2,6,5,7,4,1]=>[2,2,2,1,1]
[3,1,7,2,5,8,6,4]=>[1,2,3,1,1]
[4,3,7,8,1,6,5,2]=>[1,3,2,1,1]
[2,8,7,6,3,5,1,4]=>[2,1,1,2,2]
[2,8,4,7,6,5,1,3]=>[2,2,1,1,2]
[2,8,7,1,5,6,4,3]=>[2,1,3,1,1]
[3,5,6,2,8,1,7,4]=>[3,2,2,1]
[5,3,1,8,6,2,7,4]=>[1,1,2,1,2,1]
[3,1,4,6,8,2,7,5]=>[1,4,2,1]
[4,1,5,7,3,8,2,6]=>[1,3,2,2]
[6,2,5,8,4,7,3,1]=>[1,3,2,1,1]
[7,2,8,5,4,3,6,1]=>[1,2,1,1,2,1]
[7,1,6,8,2,5,3,4]=>[1,3,2,2]
[2,6,5,7,8,4,1,3]=>[2,3,1,2]
[3,6,5,7,4,1,8,2]=>[2,2,1,2,1]
[1,6,5,7,4,2,3,8]=>[2,2,1,3]
[3,4,7,5,2,1,8,6]=>[3,1,1,2,1]
[3,6,7,5,8,4,1,2]=>[3,2,1,2]
[3,4,7,2,5,6,8,1]=>[3,4,1]
[2,5,3,7,8,6,4,1]=>[2,3,1,1,1]
[7,2,8,4,5,6,3,1]=>[1,2,3,1,1]
[6,2,3,8,5,4,7,1]=>[1,3,1,2,1]
[5,1,4,7,8,6,3,2]=>[1,4,1,1,1]
[5,7,8,6,4,1,3,2]=>[3,1,1,2,1]
[6,8,7,3,2,4,5,1]=>[2,1,1,3,1]
[5,1,4,8,6,7,3,2]=>[1,3,2,1,1]
[3,8,6,1,4,5,7,2]=>[2,1,4,1]
[2,7,4,1,3,8,5,6]=>[2,1,3,2]
[6,1,4,8,5,7,2,3]=>[1,3,2,2]
[2,8,5,1,4,6,7,3]=>[2,1,4,1]
[2,3,1,6,5,8,4,7]=>[2,2,2,2]
[7,5,8,6,4,1,3,2]=>[1,2,1,1,2,1]
[2,8,5,6,4,1,3,7]=>[2,2,1,3]
[2,8,5,1,4,6,3,7]=>[2,1,3,2]
[2,7,6,3,8,5,1,4]=>[2,1,2,1,2]
[2,6,3,7,8,5,1,4]=>[2,3,1,2]
[2,3,1,7,8,4,6,5]=>[2,3,2,1]
[2,3,1,8,4,6,5,7]=>[2,2,2,2]
[2,3,1,7,6,8,4,5]=>[2,2,2,2]
[2,3,1,8,4,6,7,5]=>[2,2,3,1]
[2,7,3,6,8,5,1,4]=>[2,3,1,2]
[5,2,3,1,8,4,6,7]=>[1,2,2,3]
[4,2,3,5,1,8,6,7]=>[1,3,2,2]
[5,8,7,2,6,4,1,3]=>[2,1,2,1,2]
[5,8,7,3,6,2,1,4]=>[2,1,2,1,2]
[6,8,5,1,7,4,3,2]=>[2,1,2,1,1,1]
[6,8,5,2,7,4,1,3]=>[2,1,2,1,2]
[6,8,5,3,7,1,4,2]=>[2,1,2,2,1]
[6,8,5,4,1,7,3,2]=>[2,1,1,2,1,1]
[7,3,8,6,5,2,1,4]=>[1,2,1,1,1,2]
[7,4,8,6,3,2,1,5]=>[1,2,1,1,1,2]
[7,5,8,1,6,4,3,2]=>[1,2,2,1,1,1]
[7,5,8,2,6,4,1,3]=>[1,2,2,1,2]
[7,6,2,8,5,4,1,3]=>[1,1,2,1,1,2]
[6,5,4,2,1,8,7,3]=>[1,1,1,1,2,1,1]
[6,5,4,2,8,1,7,3]=>[1,1,1,2,2,1]
[6,3,2,8,1,7,5,4]=>[1,1,2,2,1,1]
[2,6,8,7,1,3,5,4]=>[3,1,3,1]
[5,3,8,7,6,2,1,4]=>[1,2,1,1,1,2]
[3,7,6,1,4,5,2,8]=>[2,1,3,2]
[4,1,6,2,7,5,3,8]=>[1,2,2,1,2]
[7,6,2,5,3,1,4,8]=>[1,1,2,1,3]
[4,3,1,7,6,2,5,8]=>[1,1,2,1,3]
[4,5,3,1,2,8,6,7]=>[2,1,3,2]
[2,4,5,3,1,8,6,7]=>[3,1,2,2]
[5,7,6,2,3,1,4,8]=>[2,1,2,3]
[4,1,3,7,5,2,6,8]=>[1,3,1,3]
[4,1,6,3,2,7,5,8]=>[1,2,1,2,2]
[7,5,4,1,3,2,6,8]=>[1,1,1,2,3]
[2,4,8,5,6,3,1,7]=>[3,2,1,2]
[2,5,7,4,1,3,6,8]=>[3,1,4]
[5,7,4,1,3,2,6,8]=>[2,1,2,3]
[2,6,8,4,5,3,1,7]=>[3,2,1,2]
[5,2,3,7,4,1,6,8]=>[1,3,1,3]
[4,5,1,6,3,2,7,8]=>[2,2,1,3]
[5,1,6,3,2,4,7,8]=>[1,2,1,4]
[4,2,5,1,6,3,7,8]=>[1,2,2,3]
[5,1,6,2,4,3,7,8]=>[1,2,2,3]
[3,5,4,2,1,8,6,7]=>[2,1,1,2,2]
[5,3,4,8,7,6,2,1]=>[1,3,1,1,1,1]
[8,3,1,6,7,5,4,2]=>[1,1,3,1,1,1]
[8,4,6,5,7,2,3,1]=>[1,2,2,2,1]
[1,8,2,6,7,4,5,3]=>[2,3,2,1]
[8,5,7,2,4,3,6,1]=>[1,2,2,2,1]
[8,5,3,6,4,7,2,1]=>[1,1,2,2,1,1]
[8,2,5,3,6,7,4,1]=>[1,2,3,1,1]
[1,2,8,3,4,7,6,5]=>[3,3,1,1]
[6,8,5,2,7,1,3,4]=>[2,1,2,3]
[1,5,7,2,6,8,4,3]=>[3,3,1,1]
[7,6,4,5,2,1,8,3]=>[1,1,2,1,2,1]
[8,2,4,7,6,3,1,5]=>[1,3,1,1,2]
[8,7,5,1,4,6,3,2]=>[1,1,1,3,1,1]
[7,3,8,5,4,2,1,6]=>[1,2,1,1,1,2]
[6,3,4,7,2,8,5,1]=>[1,3,2,1,1]
[8,1,7,3,6,4,2,5]=>[1,2,2,1,2]
[7,1,8,5,3,4,2,6]=>[1,2,1,2,2]
[6,8,4,3,1,5,2,7]=>[2,1,1,2,2]
[5,6,4,1,8,2,3,7]=>[2,1,2,3]
[1,4,5,8,3,2,6,7]=>[4,1,3]
[1,5,2,4,7,8,6,3]=>[2,4,1,1]
[5,2,7,4,3,8,6,1]=>[1,2,1,2,1,1]
[2,7,3,4,8,5,6,1]=>[2,3,2,1]
[2,7,6,8,3,5,4,1]=>[2,2,2,1,1]
[2,7,4,5,3,8,6,1]=>[2,2,2,1,1]
[4,6,7,3,1,2,8,5]=>[3,1,3,1]
[6,2,3,7,4,5,8,1]=>[1,3,3,1]
[1,6,3,2,7,5,8,4]=>[2,1,2,2,1]
[7,3,5,2,6,8,1,4]=>[1,2,3,2]
[6,4,2,7,1,5,8,3]=>[1,1,2,3,1]
[2,5,3,6,4,7,8,1]=>[2,2,3,1]
[4,2,5,3,6,7,8,1]=>[1,2,4,1]
[1,6,5,2,4,7,3,8]=>[2,1,3,2]
[1,8,7,2,4,6,3,5]=>[2,1,3,2]
[1,8,7,2,5,4,3,6]=>[2,1,2,1,2]
[1,5,4,2,7,3,6,8]=>[2,1,2,3]
[1,5,4,2,8,7,3,6]=>[2,1,2,1,2]
[1,6,8,3,5,2,4,7]=>[3,2,3]
[1,7,6,2,3,5,8,4]=>[2,1,4,1]
[1,2,8,3,6,5,4,7]=>[3,2,1,2]
[1,3,8,6,5,2,4,7]=>[3,1,1,3]
[1,4,7,3,2,8,6,5]=>[3,1,2,1,1]
[1,8,6,5,2,4,7,3]=>[2,1,1,3,1]
[1,6,8,4,3,2,5,7]=>[3,1,1,3]
[1,7,5,3,2,6,4,8]=>[2,1,1,2,2]
[1,2,6,5,3,8,4,7]=>[3,1,2,2]
[1,7,3,2,8,4,6,5]=>[2,1,2,2,1]
[1,6,5,2,8,4,7,3]=>[2,1,2,2,1]
[1,8,3,7,2,4,6,5]=>[2,2,3,1]
[5,4,2,8,7,6,1,3]=>[1,1,2,1,1,2]
[8,6,3,2,5,7,4,1]=>[1,1,1,3,1,1]
[7,3,2,1,6,5,8,4]=>[1,1,1,2,2,1]
[7,3,2,6,1,5,8,4]=>[1,1,2,3,1]
[6,8,5,2,7,1,4,3]=>[2,1,2,2,1]
[6,8,2,5,1,7,4,3]=>[2,2,2,1,1]
[6,7,5,2,8,1,3,4]=>[2,1,2,3]
[5,8,1,2,6,7,4,3]=>[2,4,1,1]
[6,8,5,7,2,1,4,3]=>[2,2,1,2,1]
[6,5,8,2,7,4,1,3]=>[1,2,2,1,2]
[6,2,5,7,3,1,8,4]=>[1,3,1,2,1]
[8,4,6,5,3,2,7,1]=>[1,2,1,1,2,1]
[6,2,1,7,5,8,4,3]=>[1,1,2,2,1,1]
[8,6,3,1,5,2,7,4]=>[1,1,1,2,2,1]
[1,6,4,8,5,3,7,2]=>[2,2,1,2,1]
[2,8,1,6,5,4,7,3]=>[2,2,1,2,1]
[3,5,6,2,8,7,1,4]=>[3,2,1,2]
[8,2,7,5,1,3,6,4]=>[1,2,1,3,1]
[5,2,8,6,1,3,7,4]=>[1,2,1,3,1]
[5,2,3,8,6,1,7,4]=>[1,3,1,2,1]
[1,6,5,3,4,7,8,2]=>[2,1,4,1]
[2,5,1,7,6,4,8,3]=>[2,2,1,2,1]
[4,2,6,7,8,1,3,5]=>[1,4,3]
[4,6,5,1,3,7,8,2]=>[2,1,4,1]
[5,1,8,3,6,2,7,4]=>[1,2,2,2,1]
[5,1,7,2,6,4,8,3]=>[1,2,2,2,1]
[7,4,5,2,6,3,8,1]=>[1,2,2,2,1]
[2,5,1,8,7,6,4,3]=>[2,2,1,1,1,1]
[4,7,6,1,3,5,8,2]=>[2,1,4,1]
[4,2,5,7,6,8,1,3]=>[1,3,2,2]
[4,1,7,6,2,5,8,3]=>[1,2,1,3,1]
[4,1,7,6,5,8,2,3]=>[1,2,1,2,2]
[8,2,7,5,6,3,1,4]=>[1,2,2,1,2]
[6,5,4,1,3,7,8,2]=>[1,1,1,4,1]
[5,2,1,7,6,4,8,3]=>[1,1,2,1,2,1]
[4,2,3,6,7,8,1,5]=>[1,5,2]
[4,7,2,1,6,5,8,3]=>[2,1,2,2,1]
[2,7,6,4,1,5,8,3]=>[2,1,1,3,1]
[2,4,3,6,7,8,1,5]=>[2,4,2]
[5,4,1,7,2,8,3,6]=>[1,1,2,2,2]
[6,8,5,2,7,3,1,4]=>[2,1,2,1,2]
[6,7,5,2,8,3,1,4]=>[2,1,2,1,2]
[4,1,7,6,8,2,3,5]=>[1,2,2,3]
[7,5,2,4,1,8,3,6]=>[1,1,2,2,2]
[5,2,1,3,7,8,4,6]=>[1,1,4,2]
[8,4,2,6,1,7,3,5]=>[1,1,2,2,2]
[8,5,1,7,6,2,4,3]=>[1,1,2,1,2,1]
[7,2,1,3,8,4,5,6]=>[1,1,3,3]
[7,1,2,8,5,4,6,3]=>[1,3,1,2,1]
[8,2,1,6,3,7,4,5]=>[1,1,2,2,2]
[7,1,6,8,2,4,3,5]=>[1,3,2,2]
[4,8,1,7,3,2,6,5]=>[2,2,1,2,1]
[4,7,1,8,3,2,6,5]=>[2,2,1,2,1]
[7,8,5,2,6,3,1,4]=>[2,1,2,1,2]
[5,1,8,6,7,4,2,3]=>[1,2,2,1,2]
[5,1,7,2,6,8,3,4]=>[1,2,3,2]
[4,7,1,6,3,8,2,5]=>[2,2,2,2]
[6,5,1,3,7,8,2,4]=>[1,1,4,2]
[7,2,1,4,3,5,8,6]=>[1,1,2,3,1]
[6,1,2,7,4,8,3,5]=>[1,3,2,2]
[7,1,2,5,4,3,8,6]=>[1,3,1,2,1]
[7,2,1,3,5,4,8,6]=>[1,1,3,2,1]
[4,1,2,8,6,5,7,3]=>[1,3,1,2,1]
[4,1,2,6,8,7,3,5]=>[1,4,1,2]
[5,1,2,7,8,6,3,4]=>[1,4,1,2]
[7,6,2,3,5,1,8,4]=>[1,1,3,2,1]
[6,1,2,4,3,7,8,5]=>[1,3,3,1]
[8,1,5,4,2,3,6,7]=>[1,2,1,4]
[7,1,2,4,6,3,8,5]=>[1,4,2,1]
[7,1,2,6,5,3,8,4]=>[1,3,1,2,1]
[7,5,6,1,2,4,8,3]=>[1,2,4,1]
[7,1,4,5,2,3,6,8]=>[1,3,4]
[6,1,4,8,7,2,3,5]=>[1,3,1,3]
[6,1,8,5,7,2,3,4]=>[1,2,2,3]
[1,6,7,5,8,3,4,2]=>[3,2,2,1]
[6,1,7,5,8,2,3,4]=>[1,2,2,3]
[6,1,4,7,8,2,3,5]=>[1,4,3]
[8,1,2,3,7,5,4,6]=>[1,4,1,2]
[5,8,6,1,2,4,7,3]=>[2,1,4,1]
[1,6,8,7,5,3,4,2]=>[3,1,1,2,1]
[6,1,8,7,5,2,3,4]=>[1,2,1,1,3]
[8,3,1,2,4,6,5,7]=>[1,1,4,2]
[8,3,1,2,4,5,7,6]=>[1,1,5,1]
[6,3,1,2,4,7,5,8]=>[1,1,4,2]
[6,7,1,4,2,3,5,8]=>[2,2,4]
[6,1,7,4,8,2,3,5]=>[1,2,2,3]
[6,7,8,5,1,2,4,3]=>[3,1,3,1]
[4,3,8,5,6,2,7,1]=>[1,2,2,2,1]
[4,3,8,6,7,2,5,1]=>[1,2,2,2,1]
[7,6,8,1,5,3,4,2]=>[1,2,2,2,1]
[7,4,6,1,5,3,8,2]=>[1,2,2,2,1]
[6,1,8,3,7,4,5,2]=>[1,2,2,2,1]
[6,3,8,1,7,2,5,4]=>[1,2,2,2,1]
[8,3,4,2,7,1,6,5]=>[1,2,2,2,1]
[7,2,3,1,5,4,8,6]=>[1,2,2,2,1]
[6,1,5,4,8,2,7,3]=>[1,2,2,2,1]
[6,1,8,5,7,3,4,2]=>[1,2,2,2,1]
[6,2,5,4,7,1,8,3]=>[1,2,2,2,1]
[2,6,3,4,8,7,5,1]=>[2,3,1,1,1]
[2,7,4,5,1,8,3,6]=>[2,2,2,2]
[8,4,5,7,6,1,2,3]=>[1,3,1,3]
[8,4,5,7,1,3,6,2]=>[1,3,3,1]
[8,1,3,4,6,7,5,2]=>[1,5,1,1]
[8,7,6,2,3,5,4,1]=>[1,1,1,3,1,1]
[8,3,6,7,5,1,2,4]=>[1,3,1,3]
[8,2,1,6,5,7,4,3]=>[1,1,2,2,1,1]
[2,7,1,8,5,6,4,3]=>[2,2,2,1,1]
[2,7,8,6,1,5,3,4]=>[3,1,2,2]
[4,6,8,2,3,5,1,7]=>[3,3,2]
[6,8,2,1,3,5,4,7]=>[2,1,3,2]
[3,5,1,6,4,8,2,7]=>[2,2,2,2]
[3,5,8,6,2,1,4,7]=>[3,1,1,3]
[2,4,8,5,6,1,3,7]=>[3,2,3]
[4,8,2,5,6,1,3,7]=>[2,3,3]
[5,3,8,4,2,7,6,1]=>[1,2,1,2,1,1]
[2,8,5,3,1,4,7,6]=>[2,1,1,3,1]
[1,7,8,4,6,3,2,5]=>[3,2,1,2]
[8,7,2,4,6,3,1,5]=>[1,1,3,1,2]
[8,7,3,2,1,6,4,5]=>[1,1,1,1,2,2]
[7,8,3,4,6,5,2,1]=>[2,3,1,1,1]
[8,7,3,6,5,2,4,1]=>[1,1,2,1,2,1]
[3,1,2,8,6,5,7,4]=>[1,3,1,2,1]
[3,8,2,7,5,4,6,1]=>[2,2,1,2,1]
[8,7,1,4,5,3,6,2]=>[1,1,3,2,1]
[2,8,7,4,6,3,5,1]=>[2,1,2,2,1]
[2,8,7,4,6,3,1,5]=>[2,1,2,1,2]
[8,3,4,1,2,5,7,6]=>[1,2,4,1]
[8,4,1,3,2,5,7,6]=>[1,1,2,3,1]
[7,3,8,6,2,1,4,5]=>[1,2,1,1,3]
[7,2,8,4,6,5,1,3]=>[1,2,2,1,2]
[5,8,6,4,7,2,3,1]=>[2,1,2,2,1]
[4,7,2,6,5,8,3,1]=>[2,2,2,1,1]
[3,6,8,5,7,4,2,1]=>[3,2,1,1,1]
[6,7,5,2,4,8,3,1]=>[2,1,3,1,1]
[8,1,2,7,5,6,3,4]=>[1,3,2,2]
[8,2,7,3,4,6,1,5]=>[1,2,3,2]
[6,7,5,4,8,1,3,2]=>[2,1,2,2,1]
[8,3,5,6,4,7,2,1]=>[1,3,2,1,1]
[8,5,6,2,4,3,7,1]=>[1,2,2,2,1]
[6,5,8,1,3,4,2,7]=>[1,2,3,2]
[6,8,4,5,1,3,2,7]=>[2,2,2,2]
[6,4,8,7,5,3,2,1]=>[1,2,1,1,1,1,1]
[6,7,1,4,3,2,8,5]=>[2,2,1,2,1]
[7,2,5,1,4,8,3,6]=>[1,2,3,2]
[5,8,1,3,4,2,7,6]=>[2,3,2,1]
[1,5,6,3,2,8,7,4]=>[3,1,2,1,1]
[1,3,7,6,8,4,2,5]=>[3,2,1,2]
[1,6,7,3,2,8,5,4]=>[3,1,2,1,1]
[3,2,7,6,8,4,5,1]=>[1,2,2,2,1]
[1,3,8,5,2,7,6,4]=>[3,1,2,1,1]
[6,4,1,5,2,8,7,3]=>[1,1,2,2,1,1]
[7,6,5,3,1,8,2,4]=>[1,1,1,1,2,2]
[2,5,1,4,7,3,6,8]=>[2,3,3]
[3,1,6,5,7,2,4,8]=>[1,2,2,3]
[2,6,1,5,7,4,8,3]=>[2,3,2,1]
[2,5,7,1,6,3,8,4]=>[3,2,2,1]
[2,6,1,5,7,4,3,8]=>[2,3,1,2]
[3,1,6,5,2,4,7,8]=>[1,2,1,4]
[3,6,5,1,4,2,7,8]=>[2,1,2,3]
[3,6,5,1,7,2,4,8]=>[2,1,2,3]
[3,6,5,2,1,4,7,8]=>[2,1,1,4]
[5,4,3,6,1,7,2,8]=>[1,1,2,2,2]
[4,5,2,7,6,1,3,8]=>[2,2,1,3]
[4,6,5,3,1,2,7,8]=>[2,1,1,4]
[5,4,1,6,3,7,2,8]=>[1,1,2,2,2]
[5,4,2,6,3,7,8,1]=>[1,1,2,3,1]
[3,6,5,7,1,4,2,8]=>[2,2,2,2]
[3,6,5,1,4,7,2,8]=>[2,1,3,2]
[4,3,6,5,7,1,2,8]=>[1,2,2,3]
[4,2,6,5,1,3,7,8]=>[1,2,1,4]
[4,1,6,5,3,7,8,2]=>[1,2,1,3,1]
[4,2,5,7,6,1,3,8]=>[1,3,1,3]
[3,4,7,6,1,2,5,8]=>[3,1,4]
[4,2,5,7,6,3,8,1]=>[1,3,1,2,1]
[4,1,6,5,2,7,3,8]=>[1,2,1,2,2]
[3,6,5,7,2,1,4,8]=>[2,2,1,3]
[3,5,7,6,2,4,1,8]=>[3,1,2,2]
[5,4,2,6,3,7,1,8]=>[1,1,2,2,2]
[4,6,5,2,7,3,1,8]=>[2,1,2,1,2]
[4,6,5,2,1,7,3,8]=>[2,1,1,2,2]
[3,5,8,2,1,4,6,7]=>[3,1,4]
[3,5,8,2,4,6,7,1]=>[3,4,1]
[5,3,8,2,1,4,6,7]=>[1,2,1,4]
[5,3,1,8,2,4,6,7]=>[1,1,2,4]
[5,1,3,8,2,4,6,7]=>[1,3,4]
[1,5,8,4,2,3,6,7]=>[3,1,4]
[5,8,2,1,4,3,6,7]=>[2,1,2,3]
[5,8,2,4,1,6,7,3]=>[2,2,3,1]
[5,8,2,4,6,3,1,7]=>[2,3,1,2]
[5,8,2,4,3,6,1,7]=>[2,2,2,2]
[5,8,1,4,6,2,3,7]=>[2,3,3]
[1,5,8,4,6,7,2,3]=>[3,3,2]
[5,1,8,4,6,7,2,3]=>[1,2,3,2]
[5,8,2,4,6,3,7,1]=>[2,3,2,1]
[3,8,4,6,7,2,1,5]=>[2,3,1,2]
[3,8,4,6,7,2,5,1]=>[2,3,2,1]
[8,4,3,6,7,2,5,1]=>[1,1,3,2,1]
[8,4,3,6,7,2,1,5]=>[1,1,3,1,2]
[8,6,2,4,5,3,7,1]=>[1,1,3,2,1]
[1,8,6,4,5,7,2,3]=>[2,1,3,2]
[8,6,2,4,5,3,1,7]=>[1,1,3,1,2]
[1,8,6,4,2,3,5,7]=>[2,1,1,4]
[3,8,1,6,2,4,5,7]=>[2,2,4]
[3,8,6,2,1,4,5,7]=>[2,1,1,4]
[3,8,6,2,4,1,5,7]=>[2,1,2,3]
[3,8,6,2,4,5,7,1]=>[2,1,4,1]
[8,3,6,2,4,5,1,7]=>[1,2,3,2]
[8,1,3,6,2,4,5,7]=>[1,3,4]
[8,3,6,7,2,1,4,5]=>[1,3,1,3]
[3,8,6,7,2,1,4,5]=>[2,2,1,3]
[8,2,6,4,5,1,7,3]=>[1,2,2,2,1]
[1,8,4,6,7,5,2,3]=>[2,3,1,2]
[8,4,6,2,3,7,5,1]=>[1,2,3,1,1]
[8,4,7,2,1,3,6,5]=>[1,2,1,3,1]
[8,3,1,7,2,4,6,5]=>[1,1,2,3,1]
[2,7,1,6,3,5,8,4]=>[2,2,3,1]
[1,8,4,2,6,3,7,5]=>[2,1,2,2,1]
[8,4,2,1,5,3,7,6]=>[1,1,1,2,2,1]
[8,2,1,4,7,3,6,5]=>[1,1,3,2,1]
[8,4,3,1,5,7,2,6]=>[1,1,1,3,2]
[8,4,2,1,5,7,3,6]=>[1,1,1,3,2]
[1,6,2,5,8,4,7,3]=>[2,3,2,1]
[4,7,2,1,6,8,3,5]=>[2,1,3,2]
[1,7,4,2,6,8,3,5]=>[2,1,3,2]
[3,1,8,4,6,7,2,5]=>[1,2,3,2]
[4,3,1,8,5,6,2,7]=>[1,1,2,2,2]
[3,2,1,7,4,5,8,6]=>[1,1,2,3,1]
[4,2,1,7,5,3,8,6]=>[1,1,2,1,2,1]
[5,2,1,8,6,3,4,7]=>[1,1,2,1,3]
[3,2,7,6,1,4,8,5]=>[1,2,1,3,1]
[3,2,8,6,1,4,7,5]=>[1,2,1,3,1]
[3,8,7,2,1,5,6,4]=>[2,1,1,3,1]
[2,6,8,5,1,7,4,3]=>[3,1,2,1,1]
[3,2,6,8,1,4,7,5]=>[1,3,3,1]
[2,1,5,8,7,3,6,4]=>[1,3,1,2,1]
[4,2,1,6,7,3,8,5]=>[1,1,3,2,1]
[3,2,1,6,7,4,8,5]=>[1,1,3,2,1]
[4,3,1,7,8,5,2,6]=>[1,1,3,1,2]
[3,1,5,2,6,8,7,4]=>[1,2,3,1,1]
[2,6,5,1,7,4,3,8]=>[2,1,2,1,2]
[7,2,3,1,4,8,5,6]=>[1,2,3,2]
[5,6,8,2,4,3,7,1]=>[3,2,2,1]
[6,8,5,1,4,2,7,3]=>[2,1,2,2,1]
[3,5,8,6,4,1,7,2]=>[3,1,1,2,1]
[5,1,7,6,4,2,3,8]=>[1,2,1,1,3]
[1,4,3,6,8,2,7,5]=>[2,3,2,1]
[5,1,8,6,4,2,3,7]=>[1,2,1,1,3]
[2,8,5,3,6,4,7,1]=>[2,1,2,2,1]
[1,2,8,6,4,7,3,5]=>[3,1,2,2]
[4,2,3,6,7,1,5,8]=>[1,4,3]
[5,3,2,7,8,6,4,1]=>[1,1,3,1,1,1]
[4,2,7,8,3,5,6,1]=>[1,3,3,1]
[1,4,8,7,2,5,6,3]=>[3,1,3,1]
[2,8,3,7,1,4,6,5]=>[2,2,3,1]
[2,8,7,1,5,3,6,4]=>[2,1,2,2,1]
[5,4,7,6,1,2,8,3]=>[1,2,1,3,1]
[3,1,7,4,2,5,6,8]=>[1,2,1,4]
[1,7,2,8,3,5,6,4]=>[2,2,3,1]
[2,8,7,3,5,4,6,1]=>[2,1,2,2,1]
[2,8,4,5,6,3,1,7]=>[2,3,1,2]
[7,3,5,6,4,2,8,1]=>[1,3,1,2,1]
[1,4,6,7,8,5,2,3]=>[5,1,2]
[3,8,4,2,7,6,5,1]=>[2,1,2,1,1,1]
[5,1,6,4,3,7,2,8]=>[1,2,1,2,2]
[1,2,8,7,3,6,4,5]=>[3,1,2,2]
[7,3,2,6,4,1,8,5]=>[1,1,2,1,2,1]
[4,8,3,7,1,5,6,2]=>[2,2,3,1]
[4,8,3,2,7,5,6,1]=>[2,1,2,2,1]
[2,4,3,7,1,5,6,8]=>[2,2,4]
[3,2,4,8,7,5,6,1]=>[1,3,1,2,1]
[2,6,8,1,5,3,4,7]=>[3,2,3]
[3,2,5,6,8,1,4,7]=>[1,4,3]
[3,8,1,6,4,5,2,7]=>[2,2,2,2]
[8,1,3,6,5,4,2,7]=>[1,3,1,1,2]
[7,4,3,6,2,1,8,5]=>[1,1,2,1,2,1]
[1,2,4,8,6,3,7,5]=>[4,1,2,1]
[7,2,1,5,3,4,8,6]=>[1,1,2,3,1]
[5,7,2,3,1,4,8,6]=>[2,2,3,1]
[7,1,5,2,4,6,8,3]=>[1,2,4,1]
[8,4,2,7,3,5,6,1]=>[1,1,2,3,1]
[1,8,6,4,7,5,3,2]=>[2,1,2,1,1,1]
[7,4,1,5,8,6,3,2]=>[1,1,3,1,1,1]
[4,5,8,7,3,1,2,6]=>[3,1,1,3]
[1,3,8,7,6,4,2,5]=>[3,1,1,1,2]
[2,8,5,1,7,4,6,3]=>[2,1,2,2,1]
[1,8,6,4,7,5,2,3]=>[2,1,2,1,2]
[2,7,4,6,3,8,5,1]=>[2,2,2,1,1]
[1,2,8,6,4,7,5,3]=>[3,1,2,1,1]
[4,1,8,6,3,7,5,2]=>[1,2,1,2,1,1]
[7,1,8,4,3,2,5,6]=>[1,2,1,1,3]
[1,7,5,4,8,2,3,6]=>[2,1,2,3]
[3,5,1,7,4,2,6,8]=>[2,2,1,3]
[7,4,1,6,3,2,5,8]=>[1,1,2,1,3]
[8,4,3,1,6,2,5,7]=>[1,1,1,2,3]
[1,6,5,4,2,8,3,7]=>[2,1,1,2,2]
[7,5,4,3,8,1,6,2]=>[1,1,1,2,2,1]
[8,5,4,3,7,1,6,2]=>[1,1,1,2,2,1]
[5,7,2,8,6,3,1,4]=>[2,2,1,1,2]
[1,7,2,8,6,4,3,5]=>[2,2,1,1,2]
[5,2,1,7,8,3,6,4]=>[1,1,3,2,1]
[8,4,3,1,5,2,7,6]=>[1,1,1,2,2,1]
[6,5,4,2,7,3,8,1]=>[1,1,1,2,2,1]
[6,5,4,2,7,1,8,3]=>[1,1,1,2,2,1]
[5,3,1,6,2,8,7,4]=>[1,1,2,2,1,1]
[3,5,4,1,7,8,2,6]=>[2,1,3,2]
[7,5,4,3,1,6,8,2]=>[1,1,1,1,3,1]
[6,4,2,1,5,7,3,8]=>[1,1,1,3,2]
[3,1,5,8,7,2,4,6]=>[1,3,1,3]
[3,2,5,7,8,4,6,1]=>[1,4,2,1]
[5,3,7,4,2,6,8,1]=>[1,2,1,3,1]
[5,3,7,4,2,6,1,8]=>[1,2,1,2,2]
[5,3,8,4,2,1,6,7]=>[1,2,1,1,3]
[5,2,8,4,3,1,6,7]=>[1,2,1,1,3]
[5,1,8,4,3,2,6,7]=>[1,2,1,1,3]
[5,2,7,4,3,6,1,8]=>[1,2,1,2,2]
[5,2,7,4,3,6,8,1]=>[1,2,1,3,1]
[5,3,7,4,1,6,8,2]=>[1,2,1,3,1]
[3,1,5,7,8,4,6,2]=>[1,4,2,1]
[3,1,5,7,8,4,2,6]=>[1,4,1,2]
[5,2,7,4,1,3,8,6]=>[1,2,1,3,1]
[6,2,3,7,4,8,5,1]=>[1,3,2,1,1]
[6,2,3,7,4,8,1,5]=>[1,3,2,2]
[6,2,3,7,4,5,1,8]=>[1,3,2,2]
[6,1,3,7,4,5,8,2]=>[1,3,3,1]
[1,2,8,6,4,3,5,7]=>[3,1,1,3]
[6,1,3,7,4,5,2,8]=>[1,3,2,2]
[6,5,8,1,2,4,3,7]=>[1,2,3,2]
[3,5,8,7,2,1,4,6]=>[3,1,1,3]
[1,8,6,3,5,4,2,7]=>[2,1,2,1,2]
[5,6,8,2,1,4,3,7]=>[3,1,2,2]
[2,6,1,8,5,3,4,7]=>[2,2,1,3]
[4,7,2,8,5,1,3,6]=>[2,2,1,3]
[4,5,7,8,1,6,3,2]=>[4,2,1,1]
[2,5,7,8,4,6,3,1]=>[4,2,1,1]
[1,8,6,7,5,2,4,3]=>[2,2,1,2,1]
[1,8,2,7,5,3,4,6]=>[2,2,1,3]
[2,5,4,1,8,6,7,3]=>[2,1,2,2,1]
[7,4,5,8,2,6,1,3]=>[1,3,2,2]
[2,4,1,5,8,6,7,3]=>[2,3,2,1]
[5,4,2,1,8,6,7,3]=>[1,1,1,2,2,1]
[4,7,5,8,1,6,2,3]=>[2,2,2,2]
[5,6,8,3,4,2,7,1]=>[3,2,2,1]
[4,1,5,3,8,6,7,2]=>[1,2,2,2,1]
[2,3,5,1,8,6,7,4]=>[3,2,2,1]
[7,3,4,8,2,6,1,5]=>[1,3,2,2]
[7,4,2,8,3,6,1,5]=>[1,1,2,2,2]
[3,5,2,1,8,6,7,4]=>[2,1,2,2,1]
[7,3,5,1,4,8,6,2]=>[1,2,3,1,1]
[7,1,3,2,4,5,6,8]=>[1,2,5]
[8,5,4,6,1,7,2,3]=>[1,1,2,2,2]
[3,8,7,1,4,2,5,6]=>[2,1,2,3]
[5,1,7,8,2,4,3,6]=>[1,3,2,2]
[8,5,4,6,1,7,3,2]=>[1,1,2,2,1,1]
[5,3,2,8,4,1,7,6]=>[1,1,2,1,2,1]
[5,3,2,1,4,6,8,7]=>[1,1,1,4,1]
[5,3,2,4,8,1,6,7]=>[1,1,3,3]
[5,3,2,4,8,6,1,7]=>[1,1,3,1,2]
[5,3,2,4,7,1,8,6]=>[1,1,3,2,1]
[8,4,3,5,1,7,6,2]=>[1,1,2,2,1,1]
[5,3,2,8,4,6,7,1]=>[1,1,2,3,1]
[4,7,8,6,3,2,5,1]=>[3,1,1,2,1]
[8,4,5,3,7,1,6,2]=>[1,2,2,2,1]
[5,3,1,7,2,4,8,6]=>[1,1,2,3,1]
[8,4,5,3,7,1,2,6]=>[1,2,2,3]
[5,3,2,8,4,7,1,6]=>[1,1,2,2,2]
[4,8,7,1,5,3,6,2]=>[2,1,2,2,1]
[4,8,1,7,3,5,6,2]=>[2,2,3,1]
[5,3,2,4,8,7,1,6]=>[1,1,3,1,2]
[5,3,2,4,6,8,1,7]=>[1,1,4,2]
[5,1,2,8,4,7,3,6]=>[1,3,2,2]
[5,8,1,7,4,6,3,2]=>[2,2,2,1,1]
[2,7,6,3,1,4,8,5]=>[2,1,1,3,1]
[3,7,4,5,6,8,2,1]=>[2,4,1,1]
[8,7,1,4,2,5,3,6]=>[1,1,2,2,2]
[4,6,8,3,7,1,5,2]=>[3,2,2,1]
[4,7,3,5,8,1,6,2]=>[2,3,2,1]
[8,4,3,5,7,1,6,2]=>[1,1,3,2,1]
[1,7,6,4,2,5,3,8]=>[2,1,1,2,2]
[8,7,1,2,5,6,3,4]=>[1,1,4,2]
[8,6,1,5,2,7,3,4]=>[1,1,2,2,2]
[1,2,6,5,7,8,3,4]=>[3,3,2]
[7,6,4,2,8,3,1,5]=>[1,1,1,2,1,2]
[8,5,2,4,3,7,6,1]=>[1,1,2,2,1,1]
[8,5,2,4,3,7,1,6]=>[1,1,2,2,2]
[8,5,1,4,3,7,6,2]=>[1,1,2,2,1,1]
[8,5,1,4,3,2,7,6]=>[1,1,2,1,2,1]
[8,5,1,4,3,2,6,7]=>[1,1,2,1,3]
[8,5,1,4,3,6,2,7]=>[1,1,2,2,2]
[8,5,1,4,3,6,7,2]=>[1,1,2,3,1]
[7,5,4,1,3,6,8,2]=>[1,1,1,4,1]
[7,5,4,1,3,6,2,8]=>[1,1,1,3,2]
[1,2,6,4,8,3,5,7]=>[3,2,3]
[6,5,4,3,1,7,2,8]=>[1,1,1,1,2,2]
[8,5,2,4,3,6,7,1]=>[1,1,2,3,1]
[3,6,7,2,5,1,8,4]=>[3,2,2,1]
[2,6,5,7,1,4,8,3]=>[2,2,3,1]
[3,5,1,7,8,4,6,2]=>[2,3,2,1]
[1,5,2,4,6,8,7,3]=>[2,4,1,1]
[8,1,2,4,7,6,5,3]=>[1,4,1,1,1]
[3,4,1,8,6,7,5,2]=>[2,2,2,1,1]
[4,3,8,5,1,7,6,2]=>[1,2,1,2,1,1]
[6,1,3,2,8,5,7,4]=>[1,2,2,2,1]
[8,5,3,2,4,7,1,6]=>[1,1,1,3,2]
[6,7,4,2,5,8,3,1]=>[2,1,3,1,1]
[8,5,4,2,6,3,1,7]=>[1,1,1,2,1,2]
[8,5,2,1,6,4,3,7]=>[1,1,1,2,1,2]
[8,4,6,5,1,3,2,7]=>[1,2,1,2,2]
[1,3,8,4,7,5,2,6]=>[3,2,1,2]
[5,3,7,1,4,6,8,2]=>[1,2,4,1]
[5,7,2,6,1,4,8,3]=>[2,2,3,1]
[3,8,5,7,6,1,2,4]=>[2,2,1,3]
[8,4,7,5,2,1,3,6]=>[1,2,1,1,3]
[3,8,6,4,7,2,1,5]=>[2,1,2,1,2]
[5,2,7,4,6,8,3,1]=>[1,2,3,1,1]
[4,8,6,3,7,2,1,5]=>[2,1,2,1,2]
[2,8,3,1,7,6,4,5]=>[2,1,2,1,2]
[2,5,6,4,8,1,7,3]=>[3,2,2,1]
[5,7,2,1,6,8,3,4]=>[2,1,3,2]
[4,7,8,5,1,6,2,3]=>[3,1,2,2]
[4,5,2,1,6,7,8,3]=>[2,1,4,1]
[4,5,6,3,1,7,8,2]=>[3,1,3,1]
[3,5,6,7,4,1,8,2]=>[4,1,2,1]
[3,5,1,4,2,8,7,6]=>[2,2,2,1,1]
[3,5,1,4,2,6,8,7]=>[2,2,3,1]
[3,5,1,4,2,6,7,8]=>[2,2,4]
[1,3,8,4,6,2,5,7]=>[3,2,3]
[1,4,7,5,6,2,3,8]=>[3,2,3]
[1,7,3,6,4,5,2,8]=>[2,2,2,2]
[1,8,4,2,3,7,5,6]=>[2,1,3,2]
[1,5,2,3,8,6,7,4]=>[2,3,2,1]
[1,6,5,3,7,4,2,8]=>[2,1,2,1,2]
[1,5,2,7,6,4,3,8]=>[2,2,1,1,2]
[1,4,8,3,2,7,6,5]=>[3,1,2,1,1]
[1,3,7,6,5,2,4,8]=>[3,1,1,3]
[1,5,3,8,4,2,6,7]=>[2,2,1,3]
[1,8,2,4,7,5,3,6]=>[2,3,1,2]
[1,7,5,2,4,3,6,8]=>[2,1,2,3]
[1,8,6,5,2,4,3,7]=>[2,1,1,2,2]
[1,6,5,4,2,7,3,8]=>[2,1,1,2,2]
[1,7,3,2,6,4,5,8]=>[2,1,2,3]
[1,2,8,6,7,5,4,3]=>[3,2,1,1,1]
[1,3,8,6,5,4,2,7]=>[3,1,1,1,2]
[1,7,5,4,3,2,6,8]=>[2,1,1,1,3]
[3,8,5,7,4,6,2,1]=>[2,2,2,1,1]
[8,6,2,4,5,7,1,3]=>[1,1,4,2]
[7,6,3,2,5,1,8,4]=>[1,1,1,2,2,1]
[4,2,7,8,3,6,1,5]=>[1,3,2,2]
[4,6,3,7,5,8,2,1]=>[2,2,2,1,1]
[4,2,5,7,8,6,3,1]=>[1,4,1,1,1]
[8,2,5,7,3,6,1,4]=>[1,3,2,2]
[4,2,5,8,7,6,3,1]=>[1,3,1,1,1,1]
[6,7,2,4,5,1,8,3]=>[2,3,2,1]
[5,2,7,8,3,6,1,4]=>[1,3,2,2]
[7,2,8,3,1,6,4,5]=>[1,2,1,2,2]
[7,1,3,8,6,2,5,4]=>[1,3,1,2,1]
[2,4,7,8,1,3,6,5]=>[4,3,1]
[2,7,3,8,6,1,5,4]=>[2,2,1,2,1]
[8,5,1,2,3,7,4,6]=>[1,1,4,2]
[8,2,3,5,1,4,7,6]=>[1,3,3,1]
[6,2,1,3,8,5,4,7]=>[1,1,3,1,2]
[8,4,2,3,1,7,6,5]=>[1,1,2,2,1,1]
[5,2,8,3,1,4,7,6]=>[1,2,1,3,1]
[8,7,2,5,1,4,3,6]=>[1,1,2,2,2]
[8,5,3,4,1,2,7,6]=>[1,1,2,3,1]
[8,3,5,4,1,2,7,6]=>[1,2,1,3,1]
[8,2,4,3,1,7,6,5]=>[1,2,1,2,1,1]
[8,4,1,3,2,7,6,5]=>[1,1,2,2,1,1]
[6,2,8,4,1,3,7,5]=>[1,2,1,3,1]
[6,3,5,2,8,7,1,4]=>[1,2,2,1,2]
[3,1,6,2,8,5,4,7]=>[1,2,2,1,2]
[8,1,3,5,2,4,7,6]=>[1,3,3,1]
[8,3,5,1,2,4,7,6]=>[1,2,4,1]
[8,6,5,1,7,4,2,3]=>[1,1,1,2,1,2]
[8,7,4,5,1,2,6,3]=>[1,1,2,3,1]
[5,8,3,1,2,7,4,6]=>[2,1,3,2]
[3,8,6,2,7,1,5,4]=>[2,1,2,2,1]
[8,4,3,5,1,2,7,6]=>[1,1,2,3,1]
[3,2,8,5,1,4,7,6]=>[1,2,1,3,1]
[3,4,8,2,1,7,6,5]=>[3,1,2,1,1]
[8,3,4,1,7,2,6,5]=>[1,2,2,2,1]
[8,3,4,2,1,7,6,5]=>[1,2,1,2,1,1]
[3,8,4,2,1,7,6,5]=>[2,1,1,2,1,1]
[8,4,5,2,7,1,6,3]=>[1,2,2,2,1]
[8,3,1,7,5,6,2,4]=>[1,1,2,2,2]
[8,4,1,7,5,2,6,3]=>[1,1,2,1,2,1]
[8,4,2,7,5,3,1,6]=>[1,1,2,1,1,2]
[8,4,3,7,5,1,2,6]=>[1,1,2,1,3]
[8,5,7,6,4,3,1,2]=>[1,2,1,1,1,2]
[8,4,7,6,5,2,1,3]=>[1,2,1,1,1,2]
[8,3,1,4,7,6,2,5]=>[1,1,3,1,2]
[8,3,5,7,6,2,4,1]=>[1,3,1,2,1]
[1,4,6,8,2,5,7,3]=>[4,3,1]
[4,2,6,8,1,5,7,3]=>[1,3,3,1]
[3,6,2,4,8,1,7,5]=>[2,3,2,1]
[7,3,8,2,4,6,1,5]=>[1,2,3,2]
[4,2,5,8,3,6,1,7]=>[1,3,2,2]
[5,2,1,6,8,3,7,4]=>[1,1,3,2,1]
[1,5,2,6,8,3,7,4]=>[2,3,2,1]
[4,5,3,1,8,2,6,7]=>[2,1,2,3]
[3,5,8,1,4,6,2,7]=>[3,3,2]
[5,1,7,8,3,6,2,4]=>[1,3,2,2]
[7,4,8,3,5,2,1,6]=>[1,2,2,1,2]
[1,6,7,3,8,4,2,5]=>[3,2,1,2]
[7,8,3,1,4,5,2,6]=>[2,1,3,2]
[7,2,8,4,1,3,5,6]=>[1,2,1,4]
[6,1,7,3,2,8,4,5]=>[1,2,1,2,2]
[6,2,1,7,3,8,4,5]=>[1,1,2,2,2]
[5,8,2,1,3,4,6,7]=>[2,1,5]
[7,3,1,8,2,4,6,5]=>[1,1,2,3,1]
[4,2,5,1,8,3,6,7]=>[1,2,2,3]
[7,4,2,8,3,1,5,6]=>[1,1,2,1,3]
[7,4,2,8,3,5,1,6]=>[1,1,2,2,2]
[7,3,8,2,1,4,6,5]=>[1,2,1,3,1]
[4,7,8,2,1,5,6,3]=>[3,1,3,1]
[6,7,2,8,5,1,4,3]=>[2,2,1,2,1]
[6,7,8,5,2,1,4,3]=>[3,1,1,2,1]
[4,7,8,2,1,5,3,6]=>[3,1,2,2]
[4,1,7,8,2,5,3,6]=>[1,3,2,2]
[1,6,2,7,8,4,3,5]=>[2,3,1,2]
[6,7,1,8,4,3,2,5]=>[2,2,1,1,2]
[8,2,1,5,6,3,4,7]=>[1,1,3,3]
[7,3,4,1,8,6,2,5]=>[1,2,2,1,2]
[4,7,6,3,5,8,2,1]=>[2,1,3,1,1]
[3,7,6,5,2,4,8,1]=>[2,1,1,3,1]
[1,4,7,8,6,2,5,3]=>[4,1,2,1]
[1,6,7,8,3,2,5,4]=>[4,1,2,1]
[1,3,2,7,8,4,6,5]=>[2,3,2,1]
[2,7,4,8,5,1,3,6]=>[2,2,1,3]
[2,1,5,3,4,8,7,6]=>[1,2,3,1,1]
[6,8,2,3,5,7,4,1]=>[2,4,1,1]
[3,5,4,1,2,6,8,7]=>[2,1,4,1]
[6,2,4,3,8,7,1,5]=>[1,2,2,1,2]
[5,6,1,3,8,7,2,4]=>[2,3,1,2]
[5,7,1,4,6,2,8,3]=>[2,3,2,1]
[8,5,1,4,7,6,2,3]=>[1,1,3,1,2]
[5,6,4,2,7,1,3,8]=>[2,1,2,3]
[4,5,7,1,6,2,3,8]=>[3,2,3]
[7,4,5,2,8,6,1,3]=>[1,2,2,1,2]
[6,3,1,4,7,8,2,5]=>[1,1,4,2]
[8,2,4,1,5,6,3,7]=>[1,2,3,2]
[8,7,1,5,4,6,3,2]=>[1,1,2,2,1,1]
[4,5,7,1,8,6,2,3]=>[3,2,1,2]
[2,5,7,3,8,1,6,4]=>[3,2,2,1]
[4,3,8,6,5,2,7,1]=>[1,2,1,1,2,1]
[2,3,8,6,5,1,7,4]=>[3,1,1,2,1]
[8,4,1,6,5,7,2,3]=>[1,1,2,2,2]
[4,1,8,6,5,7,2,3]=>[1,2,1,2,2]
[8,1,4,7,5,6,2,3]=>[1,3,2,2]
[8,7,4,6,5,1,2,3]=>[1,1,2,1,3]
[2,1,3,6,8,4,7,5]=>[1,4,2,1]
[7,2,3,6,5,8,1,4]=>[1,3,2,2]
[5,2,7,3,1,8,6,4]=>[1,2,1,2,1,1]
[5,4,7,3,1,2,6,8]=>[1,2,1,4]
[3,4,1,6,5,2,7,8]=>[2,2,1,3]
[7,6,2,1,5,4,3,8]=>[1,1,1,2,1,2]
[3,5,2,6,7,4,1,8]=>[2,3,1,2]
[4,5,7,2,6,1,3,8]=>[3,2,3]
[2,7,1,8,5,4,3,6]=>[2,2,1,1,2]
[7,1,2,8,5,4,3,6]=>[1,3,1,1,2]
[8,1,2,7,6,4,3,5]=>[1,3,1,1,2]
[3,1,2,6,5,7,8,4]=>[1,3,3,1]
[7,3,2,6,1,4,8,5]=>[1,1,2,3,1]
[7,3,5,6,2,4,8,1]=>[1,3,3,1]
[8,3,4,6,5,2,1,7]=>[1,3,1,1,2]
[8,1,2,5,7,4,3,6]=>[1,4,1,2]
[3,2,5,6,8,4,1,7]=>[1,4,1,2]
[8,2,6,1,5,4,3,7]=>[1,2,2,1,2]
[6,2,1,8,5,4,3,7]=>[1,1,2,1,1,2]
[7,2,6,8,5,4,3,1]=>[1,3,1,1,1,1]
[7,6,8,2,5,4,3,1]=>[1,2,2,1,1,1]
[3,5,8,6,2,4,1,7]=>[3,1,2,2]
[8,1,5,7,2,4,3,6]=>[1,3,2,2]
[3,7,5,6,2,4,1,8]=>[2,2,2,2]
[4,2,5,1,3,6,8,7]=>[1,2,4,1]
[3,7,1,5,6,2,4,8]=>[2,3,3]
[2,7,1,5,6,8,3,4]=>[2,4,2]
[7,2,5,8,6,3,4,1]=>[1,3,1,2,1]
[5,8,2,6,7,3,4,1]=>[2,3,2,1]
[3,2,6,7,4,5,8,1]=>[1,3,3,1]
[2,3,6,7,8,4,5,1]=>[5,2,1]
[7,2,4,3,8,6,5,1]=>[1,2,2,1,1,1]
[7,3,4,2,8,6,1,5]=>[1,2,2,1,2]
[5,3,4,2,7,1,8,6]=>[1,2,2,2,1]
[2,4,5,3,7,8,1,6]=>[3,3,2]
[3,6,4,8,1,2,7,5]=>[2,2,3,1]
[3,7,1,4,8,2,6,5]=>[2,3,2,1]
[7,6,1,2,8,3,4,5]=>[1,1,3,3]
[5,6,8,2,1,3,4,7]=>[3,1,4]
[6,5,2,1,3,8,4,7]=>[1,1,1,3,2]
[2,4,3,5,6,8,1,7]=>[2,4,2]
[6,3,2,4,8,5,1,7]=>[1,1,3,1,2]
[6,3,1,2,7,8,4,5]=>[1,1,4,2]
[6,3,1,7,4,8,2,5]=>[1,1,2,2,2]
[7,4,6,2,8,1,3,5]=>[1,2,2,3]
[7,4,6,1,3,8,2,5]=>[1,2,3,2]
[8,4,7,1,2,5,3,6]=>[1,2,3,2]
[7,4,6,1,2,8,5,3]=>[1,2,3,1,1]
[7,4,6,1,8,5,2,3]=>[1,2,2,1,2]
[8,5,6,7,2,1,4,3]=>[1,3,1,2,1]
[8,5,6,7,2,4,1,3]=>[1,3,2,2]
[8,5,6,7,1,2,4,3]=>[1,3,3,1]
[5,1,3,7,6,2,8,4]=>[1,3,1,2,1]
[6,1,3,5,7,4,8,2]=>[1,4,2,1]
[7,1,3,6,5,4,8,2]=>[1,3,1,2,1]
[2,5,6,3,8,4,7,1]=>[3,2,2,1]
[4,3,5,1,7,2,6,8]=>[1,2,2,3]
[6,4,8,1,5,3,2,7]=>[1,2,2,1,2]
[4,8,3,1,5,2,6,7]=>[2,1,2,3]
[3,7,6,2,5,1,4,8]=>[2,1,2,3]
[6,5,4,1,2,7,3,8]=>[1,1,1,3,2]
[6,8,4,2,3,1,7,5]=>[2,1,2,2,1]
[1,7,6,2,8,3,5,4]=>[2,1,2,2,1]
[7,2,6,3,1,4,8,5]=>[1,2,1,3,1]
[7,5,1,3,4,8,2,6]=>[1,1,4,2]
[7,1,5,6,3,2,8,4]=>[1,3,1,2,1]
[2,4,1,7,6,5,3,8]=>[2,2,1,1,2]
[4,1,3,8,5,2,7,6]=>[1,3,1,2,1]
[1,8,5,4,7,2,3,6]=>[2,1,2,3]
[8,2,5,6,4,3,1,7]=>[1,3,1,1,2]
[2,4,3,8,6,5,1,7]=>[2,2,1,1,2]
[3,1,4,5,8,6,2,7]=>[1,4,1,2]
[1,8,3,2,5,4,6,7]=>[2,1,2,3]
[5,1,7,3,2,8,4,6]=>[1,2,1,2,2]
[5,7,8,1,3,2,4,6]=>[3,2,3]
[8,2,4,1,6,7,3,5]=>[1,2,3,2]
[4,1,6,7,3,5,8,2]=>[1,3,3,1]
[8,7,3,6,2,4,1,5]=>[1,1,2,2,2]
[1,7,4,8,3,6,2,5]=>[2,2,2,2]
[7,8,6,1,3,5,4,2]=>[2,1,3,1,1]
[1,7,5,8,4,3,2,6]=>[2,2,1,1,2]
[6,3,1,2,7,8,5,4]=>[1,1,4,1,1]
[8,2,7,5,3,4,1,6]=>[1,2,1,2,2]
[6,3,1,2,8,7,5,4]=>[1,1,3,1,1,1]
[8,4,7,2,6,3,1,5]=>[1,2,2,1,2]
[1,2,5,7,8,3,6,4]=>[5,2,1]
[7,6,3,4,2,1,8,5]=>[1,1,2,1,2,1]
[8,4,6,2,3,7,1,5]=>[1,2,3,2]
[2,3,5,8,7,1,4,6]=>[4,1,3]
[3,4,5,8,1,7,2,6]=>[4,2,2]
[1,8,4,5,3,7,2,6]=>[2,2,2,2]
[6,3,4,2,7,8,1,5]=>[1,2,3,2]
[6,3,4,2,7,1,5,8]=>[1,2,2,3]
[5,6,3,7,8,2,1,4]=>[2,3,1,2]
[6,8,3,4,7,2,1,5]=>[2,3,1,2]
[8,6,3,4,7,2,1,5]=>[1,1,3,1,2]
[4,3,8,6,7,5,1,2]=>[1,2,2,1,2]
[4,5,6,2,7,8,3,1]=>[3,3,1,1]
[4,5,6,2,7,1,8,3]=>[3,2,2,1]
[4,5,6,2,1,7,8,3]=>[3,1,3,1]
[4,5,6,2,1,7,3,8]=>[3,1,2,2]
[5,8,6,2,1,7,3,4]=>[2,1,1,2,2]
[8,6,3,4,1,7,2,5]=>[1,1,2,2,2]
[5,6,3,1,7,2,4,8]=>[2,1,2,3]
[8,4,6,7,2,1,3,5]=>[1,3,1,3]
[6,8,7,2,3,1,4,5]=>[2,1,2,3]
[2,5,6,7,4,1,3,8]=>[4,1,3]
[5,3,6,7,1,4,8,2]=>[1,3,3,1]
[4,5,1,6,7,3,2,8]=>[2,3,1,2]
[5,6,1,8,7,4,2,3]=>[2,2,1,1,2]
[6,7,3,1,2,5,4,8]=>[2,1,3,2]
[3,7,4,8,1,5,6,2]=>[2,2,3,1]
[2,5,1,8,3,7,4,6]=>[2,2,2,2]
[2,3,8,6,5,7,1,4]=>[3,1,2,2]
[6,3,8,4,1,5,7,2]=>[1,2,1,3,1]
[6,3,4,1,7,5,8,2]=>[1,2,2,2,1]
[6,7,2,5,8,3,1,4]=>[2,3,1,2]
[5,7,2,1,3,8,4,6]=>[2,1,3,2]
[3,7,5,4,1,6,8,2]=>[2,1,1,3,1]
[3,8,5,4,1,6,7,2]=>[2,1,1,3,1]
[5,2,1,4,6,8,7,3]=>[1,1,4,1,1]
[4,1,7,6,3,2,5,8]=>[1,2,1,1,3]
[4,6,1,3,2,5,8,7]=>[2,2,3,1]
[1,8,6,4,7,3,5,2]=>[2,1,2,2,1]
[7,1,5,4,2,6,3,8]=>[1,2,1,2,2]
[5,6,1,8,3,2,4,7]=>[2,2,1,3]
[8,5,6,3,7,2,1,4]=>[1,2,2,1,2]
[2,5,3,6,7,1,8,4]=>[2,3,2,1]
[2,7,4,5,6,8,1,3]=>[2,4,2]
[2,3,4,6,8,1,7,5]=>[5,2,1]
[2,3,5,8,1,6,7,4]=>[4,3,1]
[2,4,7,5,6,8,1,3]=>[3,3,2]
[7,3,4,6,2,8,1,5]=>[1,3,2,2]
[4,7,6,5,2,8,3,1]=>[2,1,1,2,1,1]
[2,5,4,8,6,7,3,1]=>[2,2,2,1,1]
[7,5,4,1,6,8,2,3]=>[1,1,1,3,2]
[8,5,2,1,7,6,3,4]=>[1,1,1,2,1,2]
[6,5,4,8,2,1,3,7]=>[1,1,2,1,3]
[4,3,6,2,1,5,8,7]=>[1,2,1,3,1]
[5,4,7,3,2,1,8,6]=>[1,2,1,1,2,1]
[2,7,3,6,4,1,8,5]=>[2,2,1,2,1]
[2,6,7,5,3,1,8,4]=>[3,1,1,2,1]
[8,7,3,6,5,4,1,2]=>[1,1,2,1,1,2]
[5,8,4,1,7,3,6,2]=>[2,1,2,2,1]
[5,1,4,6,8,7,3,2]=>[1,4,1,1,1]
[7,2,1,8,5,6,4,3]=>[1,1,2,2,1,1]
[3,6,5,1,4,8,2,7]=>[2,1,3,2]
[6,2,1,5,4,8,3,7]=>[1,1,2,2,2]
[6,3,5,4,8,1,2,7]=>[1,2,2,3]
[4,6,5,2,3,8,1,7]=>[2,1,3,2]
[1,5,4,6,2,3,8,7]=>[2,2,3,1]
[8,5,7,6,3,4,2,1]=>[1,2,1,2,1,1]
[8,2,1,5,7,3,6,4]=>[1,1,3,2,1]
[3,2,8,5,1,7,6,4]=>[1,2,1,2,1,1]
[1,7,8,4,6,3,5,2]=>[3,2,2,1]
[2,5,1,4,6,3,8,7]=>[2,3,2,1]
[3,1,5,6,4,2,8,7]=>[1,3,1,2,1]
[8,5,6,4,3,1,7,2]=>[1,2,1,1,2,1]
[8,3,5,6,7,1,2,4]=>[1,4,3]
[2,1,4,7,3,6,8,5]=>[1,3,3,1]
[5,3,7,6,4,8,2,1]=>[1,2,1,2,1,1]
[3,7,6,4,2,8,1,5]=>[2,1,1,2,2]
[8,6,1,4,3,7,2,5]=>[1,1,2,2,2]
[8,4,7,5,1,6,3,2]=>[1,2,1,2,1,1]
[2,1,5,3,7,8,6,4]=>[1,2,3,1,1]
[5,1,4,7,6,8,2,3]=>[1,3,2,2]
[8,4,1,3,7,6,5,2]=>[1,1,3,1,1,1]
[8,3,4,1,6,7,5,2]=>[1,2,3,1,1]
[8,1,4,2,6,5,7,3]=>[1,2,2,2,1]
[3,7,6,8,1,4,5,2]=>[2,2,3,1]
[3,7,5,8,4,1,6,2]=>[2,2,1,2,1]
[1,6,5,3,8,7,2,4]=>[2,1,2,1,2]
[3,6,5,4,8,7,1,2]=>[2,1,2,1,2]
[3,6,5,4,1,7,8,2]=>[2,1,1,3,1]
[3,6,5,4,7,8,1,2]=>[2,1,3,2]
[4,7,5,1,3,6,2,8]=>[2,1,3,2]
[8,6,5,3,1,7,2,4]=>[1,1,1,1,2,2]
[8,6,4,3,7,2,1,5]=>[1,1,1,2,1,2]
[8,6,4,3,1,2,7,5]=>[1,1,1,1,3,1]
[7,8,1,4,3,2,6,5]=>[2,2,1,2,1]
[5,8,1,4,3,2,6,7]=>[2,2,1,3]
[4,6,5,3,8,1,2,7]=>[2,1,2,3]
[5,6,4,3,8,2,7,1]=>[2,1,2,2,1]
[1,6,4,3,8,2,7,5]=>[2,1,2,2,1]
[5,8,1,6,7,3,2,4]=>[2,3,1,2]
[1,5,4,3,2,8,6,7]=>[2,1,1,2,2]
[6,7,4,1,3,2,5,8]=>[2,1,2,3]
[7,8,1,4,3,2,5,6]=>[2,2,1,3]
[8,7,4,1,3,2,5,6]=>[1,1,1,2,3]
[7,1,8,4,5,3,6,2]=>[1,2,2,2,1]
[4,3,1,8,6,5,7,2]=>[1,1,2,1,2,1]
[4,3,2,7,5,1,8,6]=>[1,1,2,1,2,1]
[5,2,3,7,4,1,8,6]=>[1,3,1,2,1]
[2,1,7,4,3,6,8,5]=>[1,2,1,3,1]
[7,1,2,4,5,6,8,3]=>[1,6,1]
[2,8,7,1,4,5,6,3]=>[2,1,4,1]
[8,7,1,3,4,5,6,2]=>[1,1,5,1]
[5,8,3,1,4,6,7,2]=>[2,1,4,1]
[1,7,2,5,4,6,8,3]=>[2,2,3,1]
[2,5,3,8,1,6,7,4]=>[2,2,3,1]
[1,6,4,2,5,7,8,3]=>[2,1,4,1]
[6,5,3,4,1,7,8,2]=>[1,1,2,3,1]
[5,6,3,4,1,7,8,2]=>[2,2,3,1]
[2,5,3,1,4,7,8,6]=>[2,1,4,1]
[6,8,2,3,1,5,7,4]=>[2,2,3,1]
[4,3,1,5,2,7,8,6]=>[1,1,2,3,1]
[5,2,3,1,4,7,8,6]=>[1,2,4,1]
[7,2,1,3,5,6,8,4]=>[1,1,5,1]
[7,3,6,4,5,8,1,2]=>[1,2,3,2]
[5,2,4,7,8,6,3,1]=>[1,4,1,1,1]
[5,4,8,7,2,3,1,6]=>[1,2,1,2,2]
[8,1,4,5,3,6,2,7]=>[1,3,2,2]
[8,3,5,1,4,6,2,7]=>[1,2,3,2]
[5,8,2,1,7,4,3,6]=>[2,1,2,1,2]
[6,5,7,2,1,8,4,3]=>[1,2,1,2,1,1]
[1,5,4,7,3,8,6,2]=>[2,2,2,1,1]
[7,4,1,3,8,5,6,2]=>[1,1,3,2,1]
[3,6,8,4,1,7,2,5]=>[3,1,2,2]
[2,1,8,4,7,6,3,5]=>[1,2,2,1,2]
[2,7,5,6,8,4,3,1]=>[2,3,1,1,1]
[3,5,2,4,7,8,6,1]=>[2,4,1,1]
[7,5,6,3,8,2,1,4]=>[1,2,2,1,2]
[1,6,2,7,4,5,8,3]=>[2,2,3,1]
[7,4,2,6,1,5,8,3]=>[1,1,2,3,1]
[8,4,1,6,2,5,7,3]=>[1,1,2,3,1]
[7,3,4,5,1,6,8,2]=>[1,3,3,1]
[6,2,3,7,5,4,8,1]=>[1,3,1,2,1]
[7,6,2,4,3,5,8,1]=>[1,1,2,3,1]
[6,3,1,7,5,8,4,2]=>[1,1,2,2,1,1]
[3,5,8,7,1,6,4,2]=>[3,1,2,1,1]
[8,4,2,7,6,1,5,3]=>[1,1,2,1,2,1]
[8,4,7,1,2,6,5,3]=>[1,2,3,1,1]
[8,7,6,2,3,5,1,4]=>[1,1,1,3,2]
[7,6,3,4,8,1,5,2]=>[1,1,3,2,1]
[7,8,4,6,1,2,5,3]=>[2,2,3,1]
[4,1,6,7,5,8,3,2]=>[1,3,2,1,1]
[5,7,2,8,1,6,4,3]=>[2,2,2,1,1]
[8,4,7,1,6,5,2,3]=>[1,2,2,1,2]
[8,4,7,6,1,2,5,3]=>[1,2,1,3,1]
[3,8,7,4,6,1,5,2]=>[2,1,2,2,1]
[8,7,6,2,1,5,3,4]=>[1,1,1,1,2,2]
[5,7,8,1,6,2,4,3]=>[3,2,2,1]
[8,7,6,2,1,3,5,4]=>[1,1,1,1,3,1]
[6,8,4,7,5,2,1,3]=>[2,2,1,1,2]
[6,8,2,7,1,5,4,3]=>[2,2,2,1,1]
[6,8,7,4,2,5,1,3]=>[2,1,1,2,2]
[6,8,4,5,2,1,3,7]=>[2,2,1,3]
[6,8,4,5,7,2,1,3]=>[2,3,1,2]
[6,8,4,2,5,7,1,3]=>[2,1,3,2]
[6,8,4,2,5,1,3,7]=>[2,1,2,3]
[8,1,4,6,2,3,7,5]=>[1,3,3,1]
[4,8,6,2,3,7,1,5]=>[2,1,3,2]
[2,5,3,7,6,4,8,1]=>[2,2,1,2,1]
[3,1,5,7,6,4,2,8]=>[1,3,1,1,2]
[3,1,6,5,4,7,2,8]=>[1,2,1,2,2]
[2,5,6,8,3,4,7,1]=>[4,3,1]
[4,1,3,6,5,2,7,8]=>[1,3,1,3]
[3,6,2,4,5,7,1,8]=>[2,4,2]
[3,6,2,5,4,7,1,8]=>[2,2,2,2]
[3,5,1,7,6,4,2,8]=>[2,2,1,1,2]
[3,6,1,4,5,7,2,8]=>[2,4,2]
[4,3,1,6,5,2,7,8]=>[1,1,2,1,3]
[4,1,2,6,5,3,7,8]=>[1,3,1,3]
[4,6,1,3,5,2,7,8]=>[2,3,3]
[3,6,4,2,5,7,1,8]=>[2,1,3,2]
[4,2,6,3,5,1,7,8]=>[1,2,2,3]
[3,4,7,6,5,1,2,8]=>[3,1,1,3]
[4,5,2,7,1,3,6,8]=>[2,2,4]
[4,6,1,2,5,3,7,8]=>[2,3,3]
[2,5,4,7,3,6,8,1]=>[2,2,3,1]
[2,5,4,8,6,1,7,3]=>[2,2,1,2,1]
[2,4,3,7,5,8,6,1]=>[2,2,2,1,1]
[2,6,5,1,4,8,7,3]=>[2,1,3,1,1]
[2,6,5,1,7,3,8,4]=>[2,1,2,2,1]
[5,8,4,7,1,3,6,2]=>[2,2,3,1]
[6,4,7,1,3,5,2,8]=>[1,2,3,2]
[6,8,1,3,5,7,4,2]=>[2,4,1,1]
[5,8,3,2,7,4,6,1]=>[2,1,2,2,1]
[6,8,3,1,5,4,7,2]=>[2,1,2,2,1]
[6,8,1,2,5,3,7,4]=>[2,3,2,1]
[5,2,8,3,4,6,7,1]=>[1,2,4,1]
[5,2,7,1,6,4,8,3]=>[1,2,2,2,