Identifier
Mp00062:
Permutations
—Lehmer-code to major-code bijection⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00069: Permutations —complement⟶ Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Images
=>
[1]=>[1]=>[1]=>[1]
[1,2]=>[1,2]=>[2,1]=>[1,1]
[2,1]=>[2,1]=>[1,2]=>[2]
[1,2,3]=>[1,2,3]=>[3,2,1]=>[1,1,1]
[1,3,2]=>[3,1,2]=>[1,3,2]=>[2,1]
[2,1,3]=>[2,1,3]=>[2,3,1]=>[2,1]
[2,3,1]=>[1,3,2]=>[3,1,2]=>[1,2]
[3,1,2]=>[2,3,1]=>[2,1,3]=>[1,2]
[3,2,1]=>[3,2,1]=>[1,2,3]=>[3]
[1,2,3,4]=>[1,2,3,4]=>[4,3,2,1]=>[1,1,1,1]
[1,2,4,3]=>[4,1,2,3]=>[1,4,3,2]=>[2,1,1]
[1,3,2,4]=>[3,1,2,4]=>[2,4,3,1]=>[2,1,1]
[1,3,4,2]=>[2,4,1,3]=>[3,1,4,2]=>[1,2,1]
[1,4,2,3]=>[3,4,1,2]=>[2,1,4,3]=>[1,2,1]
[1,4,3,2]=>[4,3,1,2]=>[1,2,4,3]=>[3,1]
[2,1,3,4]=>[2,1,3,4]=>[3,4,2,1]=>[2,1,1]
[2,1,4,3]=>[1,4,2,3]=>[4,1,3,2]=>[1,2,1]
[2,3,1,4]=>[1,3,2,4]=>[4,2,3,1]=>[1,2,1]
[2,3,4,1]=>[1,2,4,3]=>[4,3,1,2]=>[1,1,2]
[2,4,1,3]=>[1,3,4,2]=>[4,2,1,3]=>[1,1,2]
[2,4,3,1]=>[4,1,3,2]=>[1,4,2,3]=>[2,2]
[3,1,2,4]=>[2,3,1,4]=>[3,2,4,1]=>[1,2,1]
[3,1,4,2]=>[4,2,1,3]=>[1,3,4,2]=>[3,1]
[3,2,1,4]=>[3,2,1,4]=>[2,3,4,1]=>[3,1]
[3,2,4,1]=>[2,1,4,3]=>[3,4,1,2]=>[2,2]
[3,4,1,2]=>[3,1,4,2]=>[2,4,1,3]=>[2,2]
[3,4,2,1]=>[1,4,3,2]=>[4,1,2,3]=>[1,3]
[4,1,2,3]=>[2,3,4,1]=>[3,2,1,4]=>[1,1,2]
[4,1,3,2]=>[4,2,3,1]=>[1,3,2,4]=>[2,2]
[4,2,1,3]=>[3,2,4,1]=>[2,3,1,4]=>[2,2]
[4,2,3,1]=>[2,4,3,1]=>[3,1,2,4]=>[1,3]
[4,3,1,2]=>[3,4,2,1]=>[2,1,3,4]=>[1,3]
[4,3,2,1]=>[4,3,2,1]=>[1,2,3,4]=>[4]
[1,2,3,4,5]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,1,1,1,1]
[1,2,3,5,4]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[2,1,1,1]
[1,2,4,3,5]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[2,1,1,1]
[1,2,4,5,3]=>[3,5,1,2,4]=>[3,1,5,4,2]=>[1,2,1,1]
[1,2,5,3,4]=>[4,5,1,2,3]=>[2,1,5,4,3]=>[1,2,1,1]
[1,2,5,4,3]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[3,1,1]
[1,3,2,4,5]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[2,1,1,1]
[1,3,2,5,4]=>[2,5,1,3,4]=>[4,1,5,3,2]=>[1,2,1,1]
[1,3,4,2,5]=>[2,4,1,3,5]=>[4,2,5,3,1]=>[1,2,1,1]
[1,3,4,5,2]=>[2,3,5,1,4]=>[4,3,1,5,2]=>[1,1,2,1]
[1,3,5,2,4]=>[2,4,5,1,3]=>[4,2,1,5,3]=>[1,1,2,1]
[1,3,5,4,2]=>[5,2,4,1,3]=>[1,4,2,5,3]=>[2,2,1]
[1,4,2,3,5]=>[3,4,1,2,5]=>[3,2,5,4,1]=>[1,2,1,1]
[1,4,2,5,3]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[3,1,1]
[1,4,3,2,5]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[3,1,1]
[1,4,3,5,2]=>[3,2,5,1,4]=>[3,4,1,5,2]=>[2,2,1]
[1,4,5,2,3]=>[4,2,5,1,3]=>[2,4,1,5,3]=>[2,2,1]
[1,4,5,3,2]=>[2,5,4,1,3]=>[4,1,2,5,3]=>[1,3,1]
[1,5,2,3,4]=>[3,4,5,1,2]=>[3,2,1,5,4]=>[1,1,2,1]
[1,5,2,4,3]=>[5,3,4,1,2]=>[1,3,2,5,4]=>[2,2,1]
[1,5,3,2,4]=>[4,3,5,1,2]=>[2,3,1,5,4]=>[2,2,1]
[1,5,3,4,2]=>[3,5,4,1,2]=>[3,1,2,5,4]=>[1,3,1]
[1,5,4,2,3]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[1,3,1]
[1,5,4,3,2]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[4,1]
[2,1,3,4,5]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[2,1,1,1]
[2,1,3,5,4]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[1,2,1,1]
[2,1,4,3,5]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[1,2,1,1]
[2,1,4,5,3]=>[1,3,5,2,4]=>[5,3,1,4,2]=>[1,1,2,1]
[2,1,5,3,4]=>[1,4,5,2,3]=>[5,2,1,4,3]=>[1,1,2,1]
[2,1,5,4,3]=>[5,1,4,2,3]=>[1,5,2,4,3]=>[2,2,1]
[2,3,1,4,5]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[1,2,1,1]
[2,3,1,5,4]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[1,1,2,1]
[2,3,4,1,5]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[1,1,2,1]
[2,3,4,5,1]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[1,1,1,2]
[2,3,5,1,4]=>[1,2,4,5,3]=>[5,4,2,1,3]=>[1,1,1,2]
[2,3,5,4,1]=>[5,1,2,4,3]=>[1,5,4,2,3]=>[2,1,2]
[2,4,1,3,5]=>[1,3,4,2,5]=>[5,3,2,4,1]=>[1,1,2,1]
[2,4,1,5,3]=>[5,1,3,2,4]=>[1,5,3,4,2]=>[2,2,1]
[2,4,3,1,5]=>[4,1,3,2,5]=>[2,5,3,4,1]=>[2,2,1]
[2,4,3,5,1]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[2,1,2]
[2,4,5,1,3]=>[4,1,2,5,3]=>[2,5,4,1,3]=>[2,1,2]
[2,4,5,3,1]=>[2,5,1,4,3]=>[4,1,5,2,3]=>[1,2,2]
[2,5,1,3,4]=>[1,3,4,5,2]=>[5,3,2,1,4]=>[1,1,1,2]
[2,5,1,4,3]=>[5,1,3,4,2]=>[1,5,3,2,4]=>[2,1,2]
[2,5,3,1,4]=>[4,1,3,5,2]=>[2,5,3,1,4]=>[2,1,2]
[2,5,3,4,1]=>[3,5,1,4,2]=>[3,1,5,2,4]=>[1,2,2]
[2,5,4,1,3]=>[4,5,1,3,2]=>[2,1,5,3,4]=>[1,2,2]
[2,5,4,3,1]=>[5,4,1,3,2]=>[1,2,5,3,4]=>[3,2]
[3,1,2,4,5]=>[2,3,1,4,5]=>[4,3,5,2,1]=>[1,2,1,1]
[3,1,2,5,4]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[3,1,1]
[3,1,4,2,5]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[3,1,1]
[3,1,4,5,2]=>[3,1,5,2,4]=>[3,5,1,4,2]=>[2,2,1]
[3,1,5,2,4]=>[4,1,5,2,3]=>[2,5,1,4,3]=>[2,2,1]
[3,1,5,4,2]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[1,3,1]
[3,2,1,4,5]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[3,1,1]
[3,2,1,5,4]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[2,2,1]
[3,2,4,1,5]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[2,2,1]
[3,2,4,5,1]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,2]
[3,2,5,1,4]=>[2,1,4,5,3]=>[4,5,2,1,3]=>[2,1,2]
[3,2,5,4,1]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[1,2,2]
[3,4,1,2,5]=>[3,1,4,2,5]=>[3,5,2,4,1]=>[2,2,1]
[3,4,1,5,2]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[1,3,1]
[3,4,2,1,5]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[1,3,1]
[3,4,2,5,1]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[1,2,2]
[3,4,5,1,2]=>[1,4,2,5,3]=>[5,2,4,1,3]=>[1,2,2]
[3,4,5,2,1]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[1,1,3]
[3,5,1,2,4]=>[3,1,4,5,2]=>[3,5,2,1,4]=>[2,1,2]
[3,5,1,4,2]=>[1,5,3,4,2]=>[5,1,3,2,4]=>[1,2,2]
[3,5,2,1,4]=>[1,4,3,5,2]=>[5,2,3,1,4]=>[1,2,2]
[3,5,2,4,1]=>[1,3,5,4,2]=>[5,3,1,2,4]=>[1,1,3]
[3,5,4,1,2]=>[1,4,5,3,2]=>[5,2,1,3,4]=>[1,1,3]
[3,5,4,2,1]=>[5,1,4,3,2]=>[1,5,2,3,4]=>[2,3]
[4,1,2,3,5]=>[2,3,4,1,5]=>[4,3,2,5,1]=>[1,1,2,1]
[4,1,2,5,3]=>[5,2,3,1,4]=>[1,4,3,5,2]=>[2,2,1]
[4,1,3,2,5]=>[4,2,3,1,5]=>[2,4,3,5,1]=>[2,2,1]
[4,1,3,5,2]=>[3,5,2,1,4]=>[3,1,4,5,2]=>[1,3,1]
[4,1,5,2,3]=>[4,5,2,1,3]=>[2,1,4,5,3]=>[1,3,1]
[4,1,5,3,2]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[4,1]
[4,2,1,3,5]=>[3,2,4,1,5]=>[3,4,2,5,1]=>[2,2,1]
[4,2,1,5,3]=>[2,5,3,1,4]=>[4,1,3,5,2]=>[1,3,1]
[4,2,3,1,5]=>[2,4,3,1,5]=>[4,2,3,5,1]=>[1,3,1]
[4,2,3,5,1]=>[2,3,1,5,4]=>[4,3,5,1,2]=>[1,2,2]
[4,2,5,1,3]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[1,2,2]
[4,2,5,3,1]=>[5,2,1,4,3]=>[1,4,5,2,3]=>[3,2]
[4,3,1,2,5]=>[3,4,2,1,5]=>[3,2,4,5,1]=>[1,3,1]
[4,3,1,5,2]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[4,1]
[4,3,2,1,5]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[4,1]
[4,3,2,5,1]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[3,2]
[4,3,5,1,2]=>[4,2,1,5,3]=>[2,4,5,1,3]=>[3,2]
[4,3,5,2,1]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[2,3]
[4,5,1,2,3]=>[3,4,1,5,2]=>[3,2,5,1,4]=>[1,2,2]
[4,5,1,3,2]=>[5,3,1,4,2]=>[1,3,5,2,4]=>[3,2]
[4,5,2,1,3]=>[4,3,1,5,2]=>[2,3,5,1,4]=>[3,2]
[4,5,2,3,1]=>[3,1,5,4,2]=>[3,5,1,2,4]=>[2,3]
[4,5,3,1,2]=>[4,1,5,3,2]=>[2,5,1,3,4]=>[2,3]
[4,5,3,2,1]=>[1,5,4,3,2]=>[5,1,2,3,4]=>[1,4]
[5,1,2,3,4]=>[2,3,4,5,1]=>[4,3,2,1,5]=>[1,1,1,2]
[5,1,2,4,3]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[2,1,2]
[5,1,3,2,4]=>[4,2,3,5,1]=>[2,4,3,1,5]=>[2,1,2]
[5,1,3,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>[1,2,2]
[5,1,4,2,3]=>[4,5,2,3,1]=>[2,1,4,3,5]=>[1,2,2]
[5,1,4,3,2]=>[5,4,2,3,1]=>[1,2,4,3,5]=>[3,2]
[5,2,1,3,4]=>[3,2,4,5,1]=>[3,4,2,1,5]=>[2,1,2]
[5,2,1,4,3]=>[2,5,3,4,1]=>[4,1,3,2,5]=>[1,2,2]
[5,2,3,1,4]=>[2,4,3,5,1]=>[4,2,3,1,5]=>[1,2,2]
[5,2,3,4,1]=>[2,3,5,4,1]=>[4,3,1,2,5]=>[1,1,3]
[5,2,4,1,3]=>[2,4,5,3,1]=>[4,2,1,3,5]=>[1,1,3]
[5,2,4,3,1]=>[5,2,4,3,1]=>[1,4,2,3,5]=>[2,3]
[5,3,1,2,4]=>[3,4,2,5,1]=>[3,2,4,1,5]=>[1,2,2]
[5,3,1,4,2]=>[5,3,2,4,1]=>[1,3,4,2,5]=>[3,2]
[5,3,2,1,4]=>[4,3,2,5,1]=>[2,3,4,1,5]=>[3,2]
[5,3,2,4,1]=>[3,2,5,4,1]=>[3,4,1,2,5]=>[2,3]
[5,3,4,1,2]=>[4,2,5,3,1]=>[2,4,1,3,5]=>[2,3]
[5,3,4,2,1]=>[2,5,4,3,1]=>[4,1,2,3,5]=>[1,4]
[5,4,1,2,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>[1,1,3]
[5,4,1,3,2]=>[5,3,4,2,1]=>[1,3,2,4,5]=>[2,3]
[5,4,2,1,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>[2,3]
[5,4,2,3,1]=>[3,5,4,2,1]=>[3,1,2,4,5]=>[1,4]
[5,4,3,1,2]=>[4,5,3,2,1]=>[2,1,3,4,5]=>[1,4]
[5,4,3,2,1]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,1,1,1,1,1]
[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[2,1,1,1,1]
[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[2,1,1,1,1]
[1,2,3,5,6,4]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>[1,2,1,1,1]
[1,2,3,6,4,5]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>[1,2,1,1,1]
[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[3,1,1,1]
[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[2,1,1,1,1]
[1,2,4,3,6,5]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>[1,2,1,1,1]
[1,2,4,5,3,6]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>[1,2,1,1,1]
[1,2,4,5,6,3]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[1,1,2,1,1]
[1,2,4,6,3,5]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>[1,1,2,1,1]
[1,2,4,6,5,3]=>[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>[2,2,1,1]
[1,2,5,3,4,6]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>[1,2,1,1,1]
[1,2,5,3,6,4]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[3,1,1,1]
[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[3,1,1,1]
[1,2,5,4,6,3]=>[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>[2,2,1,1]
[1,2,5,6,3,4]=>[5,3,6,1,2,4]=>[2,4,1,6,5,3]=>[2,2,1,1]
[1,2,5,6,4,3]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>[1,3,1,1]
[1,2,6,3,4,5]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[1,1,2,1,1]
[1,2,6,3,5,4]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>[2,2,1,1]
[1,2,6,4,3,5]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>[2,2,1,1]
[1,2,6,4,5,3]=>[4,6,5,1,2,3]=>[3,1,2,6,5,4]=>[1,3,1,1]
[1,2,6,5,3,4]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>[1,3,1,1]
[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[4,1,1]
[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[2,1,1,1,1]
[1,3,2,4,6,5]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>[1,2,1,1,1]
[1,3,2,5,4,6]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>[1,2,1,1,1]
[1,3,2,5,6,4]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>[1,1,2,1,1]
[1,3,2,6,4,5]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[1,1,2,1,1]
[1,3,2,6,5,4]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>[2,2,1,1]
[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>[1,2,1,1,1]
[1,3,4,2,6,5]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>[1,1,2,1,1]
[1,3,4,5,2,6]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>[1,1,2,1,1]
[1,3,4,5,6,2]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>[1,1,1,2,1]
[1,3,4,6,2,5]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>[1,1,1,2,1]
[1,3,4,6,5,2]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>[2,1,2,1]
[1,3,5,2,4,6]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>[1,1,2,1,1]
[1,3,5,2,6,4]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>[2,2,1,1]
[1,3,5,4,2,6]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>[2,2,1,1]
[1,3,5,4,6,2]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>[2,1,2,1]
[1,3,5,6,2,4]=>[5,2,3,6,1,4]=>[2,5,4,1,6,3]=>[2,1,2,1]
[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>[1,2,2,1]
[1,3,6,2,4,5]=>[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>[1,1,1,2,1]
[1,3,6,2,5,4]=>[6,2,4,5,1,3]=>[1,5,3,2,6,4]=>[2,1,2,1]
[1,3,6,4,2,5]=>[5,2,4,6,1,3]=>[2,5,3,1,6,4]=>[2,1,2,1]
[1,3,6,4,5,2]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>[1,2,2,1]
[1,3,6,5,2,4]=>[5,6,2,4,1,3]=>[2,1,5,3,6,4]=>[1,2,2,1]
[1,3,6,5,4,2]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>[3,2,1]
[1,4,2,3,5,6]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>[1,2,1,1,1]
[1,4,2,3,6,5]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[3,1,1,1]
[1,4,2,5,3,6]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[3,1,1,1]
[1,4,2,5,6,3]=>[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>[2,2,1,1]
[1,4,2,6,3,5]=>[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>[2,2,1,1]
[1,4,2,6,5,3]=>[2,6,5,1,3,4]=>[5,1,2,6,4,3]=>[1,3,1,1]
[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[3,1,1,1]
[1,4,3,2,6,5]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>[2,2,1,1]
[1,4,3,5,2,6]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>[2,2,1,1]
[1,4,3,5,6,2]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>[2,1,2,1]
[1,4,3,6,2,5]=>[3,2,5,6,1,4]=>[4,5,2,1,6,3]=>[2,1,2,1]
[1,4,3,6,5,2]=>[2,6,3,5,1,4]=>[5,1,4,2,6,3]=>[1,2,2,1]
[1,4,5,2,3,6]=>[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>[2,2,1,1]
[1,4,5,2,6,3]=>[2,6,4,1,3,5]=>[5,1,3,6,4,2]=>[1,3,1,1]
[1,4,5,3,2,6]=>[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>[1,3,1,1]
[1,4,5,3,6,2]=>[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>[1,2,2,1]
[1,4,5,6,2,3]=>[2,5,3,6,1,4]=>[5,2,4,1,6,3]=>[1,2,2,1]
[1,4,5,6,3,2]=>[2,3,6,5,1,4]=>[5,4,1,2,6,3]=>[1,1,3,1]
[1,4,6,2,3,5]=>[4,2,5,6,1,3]=>[3,5,2,1,6,4]=>[2,1,2,1]
[1,4,6,2,5,3]=>[2,6,4,5,1,3]=>[5,1,3,2,6,4]=>[1,2,2,1]
[1,4,6,3,2,5]=>[2,5,4,6,1,3]=>[5,2,3,1,6,4]=>[1,2,2,1]
[1,4,6,3,5,2]=>[2,4,6,5,1,3]=>[5,3,1,2,6,4]=>[1,1,3,1]
[1,4,6,5,2,3]=>[2,5,6,4,1,3]=>[5,2,1,3,6,4]=>[1,1,3,1]
[1,4,6,5,3,2]=>[6,2,5,4,1,3]=>[1,5,2,3,6,4]=>[2,3,1]
[1,5,2,3,4,6]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>[1,1,2,1,1]
[1,5,2,3,6,4]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>[2,2,1,1]
[1,5,2,4,3,6]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>[2,2,1,1]
[1,5,2,4,6,3]=>[4,6,3,1,2,5]=>[3,1,4,6,5,2]=>[1,3,1,1]
[1,5,2,6,3,4]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>[1,3,1,1]
[1,5,2,6,4,3]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[4,1,1]
[1,5,3,2,4,6]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>[2,2,1,1]
[1,5,3,2,6,4]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>[1,3,1,1]
[1,5,3,4,2,6]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>[1,3,1,1]
[1,5,3,4,6,2]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>[1,2,2,1]
[1,5,3,6,2,4]=>[3,5,2,6,1,4]=>[4,2,5,1,6,3]=>[1,2,2,1]
[1,5,3,6,4,2]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>[3,2,1]
[1,5,4,2,3,6]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>[1,3,1,1]
[1,5,4,2,6,3]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[4,1,1]
[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[4,1,1]
[1,5,4,3,6,2]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>[3,2,1]
[1,5,4,6,2,3]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>[3,2,1]
[1,5,4,6,3,2]=>[3,2,6,5,1,4]=>[4,5,1,2,6,3]=>[2,3,1]
[1,5,6,2,3,4]=>[4,5,2,6,1,3]=>[3,2,5,1,6,4]=>[1,2,2,1]
[1,5,6,2,4,3]=>[6,4,2,5,1,3]=>[1,3,5,2,6,4]=>[3,2,1]
[1,5,6,3,2,4]=>[5,4,2,6,1,3]=>[2,3,5,1,6,4]=>[3,2,1]
[1,5,6,3,4,2]=>[4,2,6,5,1,3]=>[3,5,1,2,6,4]=>[2,3,1]
[1,5,6,4,2,3]=>[5,2,6,4,1,3]=>[2,5,1,3,6,4]=>[2,3,1]
[1,5,6,4,3,2]=>[2,6,5,4,1,3]=>[5,1,2,3,6,4]=>[1,4,1]
[1,6,2,3,4,5]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>[1,1,1,2,1]
[1,6,2,3,5,4]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>[2,1,2,1]
[1,6,2,4,3,5]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>[2,1,2,1]
[1,6,2,4,5,3]=>[4,6,3,5,1,2]=>[3,1,4,2,6,5]=>[1,2,2,1]
[1,6,2,5,3,4]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[1,2,2,1]
[1,6,2,5,4,3]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>[3,2,1]
[1,6,3,2,4,5]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>[2,1,2,1]
[1,6,3,2,5,4]=>[3,6,4,5,1,2]=>[4,1,3,2,6,5]=>[1,2,2,1]
[1,6,3,4,2,5]=>[3,5,4,6,1,2]=>[4,2,3,1,6,5]=>[1,2,2,1]
[1,6,3,4,5,2]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>[1,1,3,1]
[1,6,3,5,2,4]=>[3,5,6,4,1,2]=>[4,2,1,3,6,5]=>[1,1,3,1]
[1,6,3,5,4,2]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>[2,3,1]
[1,6,4,2,3,5]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>[1,2,2,1]
[1,6,4,2,5,3]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>[3,2,1]
[1,6,4,3,2,5]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>[3,2,1]
[1,6,4,3,5,2]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>[2,3,1]
[1,6,4,5,2,3]=>[5,3,6,4,1,2]=>[2,4,1,3,6,5]=>[2,3,1]
[1,6,4,5,3,2]=>[3,6,5,4,1,2]=>[4,1,2,3,6,5]=>[1,4,1]
[1,6,5,2,3,4]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>[1,1,3,1]
[1,6,5,2,4,3]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>[2,3,1]
[1,6,5,3,2,4]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>[2,3,1]
[1,6,5,3,4,2]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[1,4,1]
[1,6,5,4,2,3]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[1,4,1]
[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[5,1]
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[2,1,1,1,1]
[2,1,3,4,6,5]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[1,2,1,1,1]
[2,1,3,5,4,6]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[1,2,1,1,1]
[2,1,3,5,6,4]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>[1,1,2,1,1]
[2,1,3,6,4,5]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>[1,1,2,1,1]
[2,1,3,6,5,4]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[2,2,1,1]
[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[1,2,1,1,1]
[2,1,4,3,6,5]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>[1,1,2,1,1]
[2,1,4,5,3,6]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>[1,1,2,1,1]
[2,1,4,5,6,3]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>[1,1,1,2,1]
[2,1,4,6,3,5]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>[1,1,1,2,1]
[2,1,4,6,5,3]=>[6,1,3,5,2,4]=>[1,6,4,2,5,3]=>[2,1,2,1]
[2,1,5,3,4,6]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>[1,1,2,1,1]
[2,1,5,3,6,4]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[2,2,1,1]
[2,1,5,4,3,6]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>[2,2,1,1]
[2,1,5,4,6,3]=>[4,1,3,6,2,5]=>[3,6,4,1,5,2]=>[2,1,2,1]
[2,1,5,6,3,4]=>[5,1,3,6,2,4]=>[2,6,4,1,5,3]=>[2,1,2,1]
[2,1,5,6,4,3]=>[3,6,1,5,2,4]=>[4,1,6,2,5,3]=>[1,2,2,1]
[2,1,6,3,4,5]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>[1,1,1,2,1]
[2,1,6,3,5,4]=>[6,1,4,5,2,3]=>[1,6,3,2,5,4]=>[2,1,2,1]
[2,1,6,4,3,5]=>[5,1,4,6,2,3]=>[2,6,3,1,5,4]=>[2,1,2,1]
[2,1,6,4,5,3]=>[4,6,1,5,2,3]=>[3,1,6,2,5,4]=>[1,2,2,1]
[2,1,6,5,3,4]=>[5,6,1,4,2,3]=>[2,1,6,3,5,4]=>[1,2,2,1]
[2,1,6,5,4,3]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>[3,2,1]
[2,3,1,4,5,6]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[1,2,1,1,1]
[2,3,1,4,6,5]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[1,1,2,1,1]
[2,3,1,5,4,6]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[1,1,2,1,1]
[2,3,1,5,6,4]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>[1,1,1,2,1]
[2,3,1,6,4,5]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>[1,1,1,2,1]
[2,3,1,6,5,4]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[2,1,2,1]
[2,3,4,1,5,6]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,1,2,1,1]
[2,3,4,1,6,5]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[1,1,1,2,1]
[2,3,4,5,1,6]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[1,1,1,2,1]
[2,3,4,5,6,1]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[1,1,1,1,2]
[2,3,4,6,1,5]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>[1,1,1,1,2]
[2,3,4,6,5,1]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>[2,1,1,2]
[2,3,5,1,4,6]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>[1,1,1,2,1]
[2,3,5,1,6,4]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[2,1,2,1]
[2,3,5,4,1,6]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>[2,1,2,1]
[2,3,5,4,6,1]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[2,1,1,2]
[2,3,5,6,1,4]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>[2,1,1,2]
[2,3,5,6,4,1]=>[3,6,1,2,5,4]=>[4,1,6,5,2,3]=>[1,2,1,2]
[2,3,6,1,4,5]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>[1,1,1,1,2]
[2,3,6,1,5,4]=>[6,1,2,4,5,3]=>[1,6,5,3,2,4]=>[2,1,1,2]
[2,3,6,4,1,5]=>[5,1,2,4,6,3]=>[2,6,5,3,1,4]=>[2,1,1,2]
[2,3,6,4,5,1]=>[4,6,1,2,5,3]=>[3,1,6,5,2,4]=>[1,2,1,2]
[2,3,6,5,1,4]=>[5,6,1,2,4,3]=>[2,1,6,5,3,4]=>[1,2,1,2]
[2,3,6,5,4,1]=>[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>[3,1,2]
[2,4,1,3,5,6]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>[1,1,2,1,1]
[2,4,1,3,6,5]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>[2,2,1,1]
[2,4,1,5,3,6]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>[2,2,1,1]
[2,4,1,5,6,3]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>[2,1,2,1]
[2,4,1,6,3,5]=>[5,1,2,6,3,4]=>[2,6,5,1,4,3]=>[2,1,2,1]
[2,4,1,6,5,3]=>[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>[1,2,2,1]
[2,4,3,1,5,6]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[2,2,1,1]
[2,4,3,1,6,5]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[2,1,2,1]
[2,4,3,5,1,6]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[2,1,2,1]
[2,4,3,5,6,1]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[2,1,1,2]
[2,4,3,6,1,5]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>[2,1,1,2]
[2,4,3,6,5,1]=>[2,6,1,3,5,4]=>[5,1,6,4,2,3]=>[1,2,1,2]
[2,4,5,1,3,6]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>[2,1,2,1]
[2,4,5,1,6,3]=>[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>[1,2,2,1]
[2,4,5,3,1,6]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>[1,2,2,1]
[2,4,5,3,6,1]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>[1,2,1,2]
[2,4,5,6,1,3]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>[1,2,1,2]
[2,4,5,6,3,1]=>[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>[1,1,2,2]
[2,4,6,1,3,5]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>[2,1,1,2]
[2,4,6,1,5,3]=>[2,6,1,4,5,3]=>[5,1,6,3,2,4]=>[1,2,1,2]
[2,4,6,3,1,5]=>[2,5,1,4,6,3]=>[5,2,6,3,1,4]=>[1,2,1,2]
[2,4,6,3,5,1]=>[2,4,6,1,5,3]=>[5,3,1,6,2,4]=>[1,1,2,2]
[2,4,6,5,1,3]=>[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>[1,1,2,2]
[2,4,6,5,3,1]=>[6,2,5,1,4,3]=>[1,5,2,6,3,4]=>[2,2,2]
[2,5,1,3,4,6]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[1,1,1,2,1]
[2,5,1,3,6,4]=>[6,1,3,4,2,5]=>[1,6,4,3,5,2]=>[2,1,2,1]
[2,5,1,4,3,6]=>[5,1,3,4,2,6]=>[2,6,4,3,5,1]=>[2,1,2,1]
[2,5,1,4,6,3]=>[4,6,1,3,2,5]=>[3,1,6,4,5,2]=>[1,2,2,1]
[2,5,1,6,3,4]=>[5,6,1,3,2,4]=>[2,1,6,4,5,3]=>[1,2,2,1]
[2,5,1,6,4,3]=>[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>[3,2,1]
[2,5,3,1,4,6]=>[4,1,3,5,2,6]=>[3,6,4,2,5,1]=>[2,1,2,1]
[2,5,3,1,6,4]=>[3,6,1,4,2,5]=>[4,1,6,3,5,2]=>[1,2,2,1]
[2,5,3,4,1,6]=>[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>[1,2,2,1]
[2,5,3,4,6,1]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>[1,2,1,2]
[2,5,3,6,1,4]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>[1,2,1,2]
[2,5,3,6,4,1]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>[3,1,2]
[2,5,4,1,3,6]=>[4,5,1,3,2,6]=>[3,2,6,4,5,1]=>[1,2,2,1]
[2,5,4,1,6,3]=>[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>[3,2,1]
[2,5,4,3,1,6]=>[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>[3,2,1]
[2,5,4,3,6,1]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[3,1,2]
[2,5,4,6,1,3]=>[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>[3,1,2]
[2,5,4,6,3,1]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>[2,2,2]
[2,5,6,1,3,4]=>[4,5,1,2,6,3]=>[3,2,6,5,1,4]=>[1,2,1,2]
[2,5,6,1,4,3]=>[6,4,1,2,5,3]=>[1,3,6,5,2,4]=>[3,1,2]
[2,5,6,3,1,4]=>[5,4,1,2,6,3]=>[2,3,6,5,1,4]=>[3,1,2]
[2,5,6,3,4,1]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>[2,2,2]
[2,5,6,4,1,3]=>[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>[2,2,2]
[2,5,6,4,3,1]=>[2,6,5,1,4,3]=>[5,1,2,6,3,4]=>[1,3,2]
[2,6,1,3,4,5]=>[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>[1,1,1,1,2]
[2,6,1,3,5,4]=>[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>[2,1,1,2]
[2,6,1,4,3,5]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>[2,1,1,2]
[2,6,1,4,5,3]=>[4,6,1,3,5,2]=>[3,1,6,4,2,5]=>[1,2,1,2]
[2,6,1,5,3,4]=>[5,6,1,3,4,2]=>[2,1,6,4,3,5]=>[1,2,1,2]
[2,6,1,5,4,3]=>[6,5,1,3,4,2]=>[1,2,6,4,3,5]=>[3,1,2]
[2,6,3,1,4,5]=>[4,1,3,5,6,2]=>[3,6,4,2,1,5]=>[2,1,1,2]
[2,6,3,1,5,4]=>[3,6,1,4,5,2]=>[4,1,6,3,2,5]=>[1,2,1,2]
[2,6,3,4,1,5]=>[3,5,1,4,6,2]=>[4,2,6,3,1,5]=>[1,2,1,2]
[2,6,3,4,5,1]=>[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>[1,1,2,2]
[2,6,3,5,1,4]=>[3,5,6,1,4,2]=>[4,2,1,6,3,5]=>[1,1,2,2]
[2,6,3,5,4,1]=>[6,3,5,1,4,2]=>[1,4,2,6,3,5]=>[2,2,2]
[2,6,4,1,3,5]=>[4,5,1,3,6,2]=>[3,2,6,4,1,5]=>[1,2,1,2]
[2,6,4,1,5,3]=>[6,4,1,3,5,2]=>[1,3,6,4,2,5]=>[3,1,2]
[2,6,4,3,1,5]=>[5,4,1,3,6,2]=>[2,3,6,4,1,5]=>[3,1,2]
[2,6,4,3,5,1]=>[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>[2,2,2]
[2,6,4,5,1,3]=>[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>[2,2,2]
[2,6,4,5,3,1]=>[3,6,5,1,4,2]=>[4,1,2,6,3,5]=>[1,3,2]
[2,6,5,1,3,4]=>[4,5,6,1,3,2]=>[3,2,1,6,4,5]=>[1,1,2,2]
[2,6,5,1,4,3]=>[6,4,5,1,3,2]=>[1,3,2,6,4,5]=>[2,2,2]
[2,6,5,3,1,4]=>[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>[2,2,2]
[2,6,5,3,4,1]=>[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>[1,3,2]
[2,6,5,4,1,3]=>[5,6,4,1,3,2]=>[2,1,3,6,4,5]=>[1,3,2]
[2,6,5,4,3,1]=>[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>[4,2]
[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>[1,2,1,1,1]
[3,1,2,4,6,5]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[3,1,1,1]
[3,1,2,5,4,6]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[3,1,1,1]
[3,1,2,5,6,4]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>[2,2,1,1]
[3,1,2,6,4,5]=>[5,1,6,2,3,4]=>[2,6,1,5,4,3]=>[2,2,1,1]
[3,1,2,6,5,4]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[1,3,1,1]
[3,1,4,2,5,6]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[3,1,1,1]
[3,1,4,2,6,5]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>[2,2,1,1]
[3,1,4,5,2,6]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>[2,2,1,1]
[3,1,4,5,6,2]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>[2,1,2,1]
[3,1,4,6,2,5]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>[2,1,2,1]
[3,1,4,6,5,2]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>[1,2,2,1]
[3,1,5,2,4,6]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>[2,2,1,1]
[3,1,5,2,6,4]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[1,3,1,1]
[3,1,5,4,2,6]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[1,3,1,1]
[3,1,5,4,6,2]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>[1,2,2,1]
[3,1,5,6,2,4]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>[1,2,2,1]
[3,1,5,6,4,2]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>[1,1,3,1]
[3,1,6,2,4,5]=>[4,1,5,6,2,3]=>[3,6,2,1,5,4]=>[2,1,2,1]
[3,1,6,2,5,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>[1,2,2,1]
[3,1,6,4,2,5]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>[1,2,2,1]
[3,1,6,4,5,2]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>[1,1,3,1]
[3,1,6,5,2,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>[1,1,3,1]
[3,1,6,5,4,2]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>[2,3,1]
[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[3,1,1,1]
[3,2,1,4,6,5]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[2,2,1,1]
[3,2,1,5,4,6]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[2,2,1,1]
[3,2,1,5,6,4]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>[2,1,2,1]
[3,2,1,6,4,5]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>[2,1,2,1]
[3,2,1,6,5,4]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[1,2,2,1]
[3,2,4,1,5,6]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[2,2,1,1]
[3,2,4,1,6,5]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[2,1,2,1]
[3,2,4,5,1,6]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[2,1,2,1]
[3,2,4,5,6,1]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,1,2]
[3,2,4,6,1,5]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>[2,1,1,2]
[3,2,4,6,5,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[1,2,1,2]
[3,2,5,1,4,6]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>[2,1,2,1]
[3,2,5,1,6,4]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[1,2,2,1]
[3,2,5,4,1,6]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[1,2,2,1]
[3,2,5,4,6,1]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[1,2,1,2]
[3,2,5,6,1,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>[1,2,1,2]
[3,2,5,6,4,1]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>[1,1,2,2]
[3,2,6,1,4,5]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>[2,1,1,2]
[3,2,6,1,5,4]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>[1,2,1,2]
[3,2,6,4,1,5]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>[1,2,1,2]
[3,2,6,4,5,1]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>[1,1,2,2]
[3,2,6,5,1,4]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>[1,1,2,2]
[3,2,6,5,4,1]=>[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[2,2,2]
[3,4,1,2,5,6]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>[2,2,1,1]
[3,4,1,2,6,5]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[1,3,1,1]
[3,4,1,5,2,6]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[1,3,1,1]
[3,4,1,5,6,2]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>[1,2,2,1]
[3,4,1,6,2,5]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>[1,2,2,1]
[3,4,1,6,5,2]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[1,1,3,1]
[3,4,2,1,5,6]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[1,3,1,1]
[3,4,2,1,6,5]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[1,2,2,1]
[3,4,2,5,1,6]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,2,2,1]
[3,4,2,5,6,1]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[1,2,1,2]
[3,4,2,6,1,5]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>[1,2,1,2]
[3,4,2,6,5,1]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[1,1,2,2]
[3,4,5,1,2,6]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>[1,2,2,1]
[3,4,5,1,6,2]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[1,1,3,1]
[3,4,5,2,1,6]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[1,1,3,1]
[3,4,5,2,6,1]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[1,1,2,2]
[3,4,5,6,1,2]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>[1,1,2,2]
[3,4,5,6,2,1]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[1,1,1,3]
[3,4,6,1,2,5]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>[1,2,1,2]
[3,4,6,1,5,2]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>[1,1,2,2]
[3,4,6,2,1,5]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>[1,1,2,2]
[3,4,6,2,5,1]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>[1,1,1,3]
[3,4,6,5,1,2]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>[1,1,1,3]
[3,4,6,5,2,1]=>[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>[2,1,3]
[3,5,1,2,4,6]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>[2,1,2,1]
[3,5,1,2,6,4]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>[1,2,2,1]
[3,5,1,4,2,6]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>[1,2,2,1]
[3,5,1,4,6,2]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>[1,1,3,1]
[3,5,1,6,2,4]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>[1,1,3,1]
[3,5,1,6,4,2]=>[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>[2,3,1]
[3,5,2,1,4,6]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[1,2,2,1]
[3,5,2,1,6,4]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>[1,1,3,1]
[3,5,2,4,1,6]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>[1,1,3,1]
[3,5,2,4,6,1]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>[1,1,2,2]
[3,5,2,6,1,4]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>[1,1,2,2]
[3,5,2,6,4,1]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[2,2,2]
[3,5,4,1,2,6]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>[1,1,3,1]
[3,5,4,1,6,2]=>[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>[2,3,1]
[3,5,4,2,1,6]=>[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>[2,3,1]
[3,5,4,2,6,1]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[2,2,2]
[3,5,4,6,1,2]=>[5,1,3,2,6,4]=>[2,6,4,5,1,3]=>[2,2,2]
[3,5,4,6,2,1]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[2,1,3]
[3,5,6,1,2,4]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>[1,1,2,2]
[3,5,6,1,4,2]=>[6,1,4,2,5,3]=>[1,6,3,5,2,4]=>[2,2,2]
[3,5,6,2,1,4]=>[5,1,4,2,6,3]=>[2,6,3,5,1,4]=>[2,2,2]
[3,5,6,2,4,1]=>[4,1,2,6,5,3]=>[3,6,5,1,2,4]=>[2,1,3]
[3,5,6,4,1,2]=>[5,1,2,6,4,3]=>[2,6,5,1,3,4]=>[2,1,3]
[3,5,6,4,2,1]=>[2,6,1,5,4,3]=>[5,1,6,2,3,4]=>[1,2,3]
[3,6,1,2,4,5]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>[2,1,1,2]
[3,6,1,2,5,4]=>[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>[1,2,1,2]
[3,6,1,4,2,5]=>[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>[1,2,1,2]
[3,6,1,4,5,2]=>[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>[1,1,2,2]
[3,6,1,5,2,4]=>[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>[1,1,2,2]
[3,6,1,5,4,2]=>[6,1,5,3,4,2]=>[1,6,2,4,3,5]=>[2,2,2]
[3,6,2,1,4,5]=>[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>[1,2,1,2]
[3,6,2,1,5,4]=>[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>[1,1,2,2]
[3,6,2,4,1,5]=>[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>[1,1,2,2]
[3,6,2,4,5,1]=>[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>[1,1,1,3]
[3,6,2,5,1,4]=>[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>[1,1,1,3]
[3,6,2,5,4,1]=>[6,1,3,5,4,2]=>[1,6,4,2,3,5]=>[2,1,3]
[3,6,4,1,2,5]=>[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>[1,1,2,2]
[3,6,4,1,5,2]=>[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>[2,2,2]
[3,6,4,2,1,5]=>[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>[2,2,2]
[3,6,4,2,5,1]=>[4,1,3,6,5,2]=>[3,6,4,1,2,5]=>[2,1,3]
[3,6,4,5,1,2]=>[5,1,3,6,4,2]=>[2,6,4,1,3,5]=>[2,1,3]
[3,6,4,5,2,1]=>[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>[1,2,3]
[3,6,5,1,2,4]=>[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>[1,1,1,3]
[3,6,5,1,4,2]=>[6,1,4,5,3,2]=>[1,6,3,2,4,5]=>[2,1,3]
[3,6,5,2,1,4]=>[5,1,4,6,3,2]=>[2,6,3,1,4,5]=>[2,1,3]
[3,6,5,2,4,1]=>[4,6,1,5,3,2]=>[3,1,6,2,4,5]=>[1,2,3]
[3,6,5,4,1,2]=>[5,6,1,4,3,2]=>[2,1,6,3,4,5]=>[1,2,3]
[3,6,5,4,2,1]=>[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>[3,3]
[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>[1,1,2,1,1]
[4,1,2,3,6,5]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>[2,2,1,1]
[4,1,2,5,3,6]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>[2,2,1,1]
[4,1,2,5,6,3]=>[4,6,2,1,3,5]=>[3,1,5,6,4,2]=>[1,3,1,1]
[4,1,2,6,3,5]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>[1,3,1,1]
[4,1,2,6,5,3]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[4,1,1]
[4,1,3,2,5,6]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>[2,2,1,1]
[4,1,3,2,6,5]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>[1,3,1,1]
[4,1,3,5,2,6]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>[1,3,1,1]
[4,1,3,5,6,2]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>[1,2,2,1]
[4,1,3,6,2,5]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>[1,2,2,1]
[4,1,3,6,5,2]=>[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>[3,2,1]
[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>[1,3,1,1]
[4,1,5,2,6,3]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[4,1,1]
[4,1,5,3,2,6]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[4,1,1]
[4,1,5,3,6,2]=>[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>[3,2,1]
[4,1,5,6,2,3]=>[5,3,1,6,2,4]=>[2,4,6,1,5,3]=>[3,2,1]
[4,1,5,6,3,2]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>[2,3,1]
[4,1,6,2,3,5]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>[1,2,2,1]
[4,1,6,2,5,3]=>[6,4,1,5,2,3]=>[1,3,6,2,5,4]=>[3,2,1]
[4,1,6,3,2,5]=>[5,4,1,6,2,3]=>[2,3,6,1,5,4]=>[3,2,1]
[4,1,6,3,5,2]=>[4,1,6,5,2,3]=>[3,6,1,2,5,4]=>[2,3,1]
[4,1,6,5,2,3]=>[5,1,6,4,2,3]=>[2,6,1,3,5,4]=>[2,3,1]
[4,1,6,5,3,2]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[1,4,1]
[4,2,1,3,5,6]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>[2,2,1,1]
[4,2,1,3,6,5]=>[2,6,3,1,4,5]=>[5,1,4,6,3,2]=>[1,3,1,1]
[4,2,1,5,3,6]=>[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>[1,3,1,1]
[4,2,1,5,6,3]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>[1,2,2,1]
[4,2,1,6,3,5]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>[1,2,2,1]
[4,2,1,6,5,3]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>[3,2,1]
[4,2,3,1,5,6]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>[1,3,1,1]
[4,2,3,1,6,5]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>[1,2,2,1]
[4,2,3,5,1,6]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>[1,2,2,1]
[4,2,3,5,6,1]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>[1,2,1,2]
[4,2,3,6,1,5]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[1,2,1,2]
[4,2,3,6,5,1]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>[3,1,2]
[4,2,5,1,3,6]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>[1,2,2,1]
[4,2,5,1,6,3]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>[3,2,1]
[4,2,5,3,1,6]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>[3,2,1]
[4,2,5,3,6,1]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[3,1,2]
[4,2,5,6,1,3]=>[5,2,1,3,6,4]=>[2,5,6,4,1,3]=>[3,1,2]
[4,2,5,6,3,1]=>[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>[2,2,2]
[4,2,6,1,3,5]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>[1,2,1,2]
[4,2,6,1,5,3]=>[6,2,1,4,5,3]=>[1,5,6,3,2,4]=>[3,1,2]
[4,2,6,3,1,5]=>[5,2,1,4,6,3]=>[2,5,6,3,1,4]=>[3,1,2]
[4,2,6,3,5,1]=>[4,1,6,2,5,3]=>[3,6,1,5,2,4]=>[2,2,2]
[4,2,6,5,1,3]=>[5,1,6,2,4,3]=>[2,6,1,5,3,4]=>[2,2,2]
[4,2,6,5,3,1]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[1,3,2]
[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>[1,3,1,1]
[4,3,1,2,6,5]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[4,1,1]
[4,3,1,5,2,6]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[4,1,1]
[4,3,1,5,6,2]=>[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>[3,2,1]
[4,3,1,6,2,5]=>[5,2,1,6,3,4]=>[2,5,6,1,4,3]=>[3,2,1]
[4,3,1,6,5,2]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[2,3,1]
[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[4,1,1]
[4,3,2,1,6,5]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[3,2,1]
[4,3,2,5,1,6]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[3,2,1]
[4,3,2,5,6,1]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[3,1,2]
[4,3,2,6,1,5]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>[3,1,2]
[4,3,2,6,5,1]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[2,2,2]
[4,3,5,1,2,6]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>[3,2,1]
[4,3,5,1,6,2]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[2,3,1]
[4,3,5,2,1,6]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[2,3,1]
[4,3,5,2,6,1]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,2,2]
[4,3,5,6,1,2]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>[2,2,2]
[4,3,5,6,2,1]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[2,1,3]
[4,3,6,1,2,5]=>[4,2,1,5,6,3]=>[3,5,6,2,1,4]=>[3,1,2]
[4,3,6,1,5,2]=>[2,1,6,4,5,3]=>[5,6,1,3,2,4]=>[2,2,2]
[4,3,6,2,1,5]=>[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>[2,2,2]
[4,3,6,2,5,1]=>[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>[2,1,3]
[4,3,6,5,1,2]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>[2,1,3]
[4,3,6,5,2,1]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[1,2,3]
[4,5,1,2,3,6]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>[1,2,2,1]
[4,5,1,2,6,3]=>[6,3,1,4,2,5]=>[1,4,6,3,5,2]=>[3,2,1]
[4,5,1,3,2,6]=>[5,3,1,4,2,6]=>[2,4,6,3,5,1]=>[3,2,1]
[4,5,1,3,6,2]=>[4,1,6,3,2,5]=>[3,6,1,4,5,2]=>[2,3,1]
[4,5,1,6,2,3]=>[5,1,6,3,2,4]=>[2,6,1,4,5,3]=>[2,3,1]
[4,5,1,6,3,2]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[1,4,1]
[4,5,2,1,3,6]=>[4,3,1,5,2,6]=>[3,4,6,2,5,1]=>[3,2,1]
[4,5,2,1,6,3]=>[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>[2,3,1]
[4,5,2,3,1,6]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>[2,3,1]
[4,5,2,3,6,1]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>[2,2,2]
[4,5,2,6,1,3]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>[2,2,2]
[4,5,2,6,3,1]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[1,3,2]
[4,5,3,1,2,6]=>[4,1,5,3,2,6]=>[3,6,2,4,5,1]=>[2,3,1]
[4,5,3,1,6,2]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[1,4,1]
[4,5,3,2,1,6]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[1,4,1]
[4,5,3,2,6,1]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[1,3,2]
[4,5,3,6,1,2]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>[1,3,2]
[4,5,3,6,2,1]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[1,2,3]
[4,5,6,1,2,3]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>[2,2,2]
[4,5,6,1,3,2]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>[1,3,2]
[4,5,6,2,1,3]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>[1,3,2]
[4,5,6,2,3,1]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>[1,2,3]
[4,5,6,3,1,2]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>[1,2,3]
[4,5,6,3,2,1]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[1,1,4]
[4,6,1,2,3,5]=>[3,4,1,5,6,2]=>[4,3,6,2,1,5]=>[1,2,1,2]
[4,6,1,2,5,3]=>[6,3,1,4,5,2]=>[1,4,6,3,2,5]=>[3,1,2]
[4,6,1,3,2,5]=>[5,3,1,4,6,2]=>[2,4,6,3,1,5]=>[3,1,2]
[4,6,1,3,5,2]=>[4,1,6,3,5,2]=>[3,6,1,4,2,5]=>[2,2,2]
[4,6,1,5,2,3]=>[5,1,6,3,4,2]=>[2,6,1,4,3,5]=>[2,2,2]
[4,6,1,5,3,2]=>[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>[1,3,2]
[4,6,2,1,3,5]=>[4,3,1,5,6,2]=>[3,4,6,2,1,5]=>[3,1,2]
[4,6,2,1,5,3]=>[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>[2,2,2]
[4,6,2,3,1,5]=>[3,1,5,4,6,2]=>[4,6,2,3,1,5]=>[2,2,2]
[4,6,2,3,5,1]=>[3,1,4,6,5,2]=>[4,6,3,1,2,5]=>[2,1,3]
[4,6,2,5,1,3]=>[3,1,5,6,4,2]=>[4,6,2,1,3,5]=>[2,1,3]
[4,6,2,5,3,1]=>[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>[1,2,3]
[4,6,3,1,2,5]=>[4,1,5,3,6,2]=>[3,6,2,4,1,5]=>[2,2,2]
[4,6,3,1,5,2]=>[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>[1,3,2]
[4,6,3,2,1,5]=>[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>[1,3,2]
[4,6,3,2,5,1]=>[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>[1,2,3]
[4,6,3,5,1,2]=>[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>[1,2,3]
[4,6,3,5,2,1]=>[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>[1,1,4]
[4,6,5,1,2,3]=>[4,1,5,6,3,2]=>[3,6,2,1,4,5]=>[2,1,3]
[4,6,5,1,3,2]=>[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>[1,2,3]
[4,6,5,2,1,3]=>[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>[1,2,3]
[4,6,5,2,3,1]=>[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>[1,1,4]
[4,6,5,3,1,2]=>[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>[1,1,4]
[4,6,5,3,2,1]=>[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[2,4]
[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>[1,1,1,2,1]
[5,1,2,3,6,4]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>[2,1,2,1]
[5,1,2,4,3,6]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>[2,1,2,1]
[5,1,2,4,6,3]=>[4,6,2,3,1,5]=>[3,1,5,4,6,2]=>[1,2,2,1]
[5,1,2,6,3,4]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>[1,2,2,1]
[5,1,2,6,4,3]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>[3,2,1]
[5,1,3,2,4,6]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>[2,1,2,1]
[5,1,3,2,6,4]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>[1,2,2,1]
[5,1,3,4,2,6]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>[1,2,2,1]
[5,1,3,4,6,2]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>[1,1,3,1]
[5,1,3,6,2,4]=>[3,5,6,2,1,4]=>[4,2,1,5,6,3]=>[1,1,3,1]
[5,1,3,6,4,2]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>[2,3,1]
[5,1,4,2,3,6]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>[1,2,2,1]
[5,1,4,2,6,3]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>[3,2,1]
[5,1,4,3,2,6]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>[3,2,1]
[5,1,4,3,6,2]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>[2,3,1]
[5,1,4,6,2,3]=>[5,3,6,2,1,4]=>[2,4,1,5,6,3]=>[2,3,1]
[5,1,4,6,3,2]=>[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>[1,4,1]
[5,1,6,2,3,4]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>[1,1,3,1]
[5,1,6,2,4,3]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>[2,3,1]
[5,1,6,3,2,4]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>[2,3,1]
[5,1,6,3,4,2]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>[1,4,1]
[5,1,6,4,2,3]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[1,4,1]
[5,1,6,4,3,2]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[5,1]
[5,2,1,3,4,6]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>[2,1,2,1]
[5,2,1,3,6,4]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>[1,2,2,1]
[5,2,1,4,3,6]=>[2,5,3,4,1,6]=>[5,2,4,3,6,1]=>[1,2,2,1]
[5,2,1,4,6,3]=>[2,4,6,3,1,5]=>[5,3,1,4,6,2]=>[1,1,3,1]
[5,2,1,6,3,4]=>[2,5,6,3,1,4]=>[5,2,1,4,6,3]=>[1,1,3,1]
[5,2,1,6,4,3]=>[6,2,5,3,1,4]=>[1,5,2,4,6,3]=>[2,3,1]
[5,2,3,1,4,6]=>[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>[1,2,2,1]
[5,2,3,1,6,4]=>[2,3,6,4,1,5]=>[5,4,1,3,6,2]=>[1,1,3,1]
[5,2,3,4,1,6]=>[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>[1,1,3,1]
[5,2,3,4,6,1]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>[1,1,2,2]
[5,2,3,6,1,4]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>[1,1,2,2]
[5,2,3,6,4,1]=>[6,2,3,1,5,4]=>[1,5,4,6,2,3]=>[2,2,2]
[5,2,4,1,3,6]=>[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>[1,1,3,1]
[5,2,4,1,6,3]=>[6,2,4,3,1,5]=>[1,5,3,4,6,2]=>[2,3,1]
[5,2,4,3,1,6]=>[5,2,4,3,1,6]=>[2,5,3,4,6,1]=>[2,3,1]
[5,2,4,3,6,1]=>[4,2,3,1,6,5]=>[3,5,4,6,1,2]=>[2,2,2]
[5,2,4,6,1,3]=>[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>[2,2,2]
[5,2,4,6,3,1]=>[3,6,2,1,5,4]=>[4,1,5,6,2,3]=>[1,3,2]
[5,2,6,1,3,4]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>[1,1,2,2]
[5,2,6,1,4,3]=>[6,2,4,1,5,3]=>[1,5,3,6,2,4]=>[2,2,2]
[5,2,6,3,1,4]=>[5,2,4,1,6,3]=>[2,5,3,6,1,4]=>[2,2,2]
[5,2,6,3,4,1]=>[4,6,2,1,5,3]=>[3,1,5,6,2,4]=>[1,3,2]
[5,2,6,4,1,3]=>[5,6,2,1,4,3]=>[2,1,5,6,3,4]=>[1,3,2]
[5,2,6,4,3,1]=>[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[4,2]
[5,3,1,2,4,6]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>[1,2,2,1]
[5,3,1,2,6,4]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>[3,2,1]
[5,3,1,4,2,6]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>[3,2,1]
[5,3,1,4,6,2]=>[4,2,6,3,1,5]=>[3,5,1,4,6,2]=>[2,3,1]
[5,3,1,6,2,4]=>[5,2,6,3,1,4]=>[2,5,1,4,6,3]=>[2,3,1]
[5,3,1,6,4,2]=>[2,6,5,3,1,4]=>[5,1,2,4,6,3]=>[1,4,1]
[5,3,2,1,4,6]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>[3,2,1]
[5,3,2,1,6,4]=>[3,2,6,4,1,5]=>[4,5,1,3,6,2]=>[2,3,1]
[5,3,2,4,1,6]=>[3,2,5,4,1,6]=>[4,5,2,3,6,1]=>[2,3,1]
[5,3,2,4,6,1]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>[2,2,2]
[5,3,2,6,1,4]=>[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>[2,2,2]
[5,3,2,6,4,1]=>[2,6,3,1,5,4]=>[5,1,4,6,2,3]=>[1,3,2]
[5,3,4,1,2,6]=>[4,2,5,3,1,6]=>[3,5,2,4,6,1]=>[2,3,1]
[5,3,4,1,6,2]=>[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>[1,4,1]
[5,3,4,2,1,6]=>[2,5,4,3,1,6]=>[5,2,3,4,6,1]=>[1,4,1]
[5,3,4,2,6,1]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>[1,3,2]
[5,3,4,6,1,2]=>[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>[1,3,2]
[5,3,4,6,2,1]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>[1,2,3]
[5,3,6,1,2,4]=>[4,2,5,1,6,3]=>[3,5,2,6,1,4]=>[2,2,2]
[5,3,6,1,4,2]=>[2,6,4,1,5,3]=>[5,1,3,6,2,4]=>[1,3,2]
[5,3,6,2,1,4]=>[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>[1,3,2]
[5,3,6,2,4,1]=>[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>[1,2,3]
[5,3,6,4,1,2]=>[2,5,1,6,4,3]=>[5,2,6,1,3,4]=>[1,2,3]
[5,3,6,4,2,1]=>[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>[3,3]
[5,4,1,2,3,6]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>[1,1,3,1]
[5,4,1,2,6,3]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>[2,3,1]
[5,4,1,3,2,6]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>[2,3,1]
[5,4,1,3,6,2]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>[1,4,1]
[5,4,1,6,2,3]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>[1,4,1]
[5,4,1,6,3,2]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[5,1]
[5,4,2,1,3,6]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>[2,3,1]
[5,4,2,1,6,3]=>[3,6,4,2,1,5]=>[4,1,3,5,6,2]=>[1,4,1]
[5,4,2,3,1,6]=>[3,5,4,2,1,6]=>[4,2,3,5,6,1]=>[1,4,1]
[5,4,2,3,6,1]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>[1,3,2]
[5,4,2,6,1,3]=>[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>[1,3,2]
[5,4,2,6,3,1]=>[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>[4,2]
[5,4,3,1,2,6]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>[1,4,1]
[5,4,3,1,6,2]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[5,1]
[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[5,1]
[5,4,3,2,6,1]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[4,2]
[5,4,3,6,1,2]=>[5,3,2,1,6,4]=>[2,4,5,6,1,3]=>[4,2]
[5,4,3,6,2,1]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[3,3]
[5,4,6,1,2,3]=>[4,5,2,1,6,3]=>[3,2,5,6,1,4]=>[1,3,2]
[5,4,6,1,3,2]=>[6,4,2,1,5,3]=>[1,3,5,6,2,4]=>[4,2]
[5,4,6,2,1,3]=>[5,4,2,1,6,3]=>[2,3,5,6,1,4]=>[4,2]
[5,4,6,2,3,1]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>[3,3]
[5,4,6,3,1,2]=>[5,2,1,6,4,3]=>[2,5,6,1,3,4]=>[3,3]
[5,4,6,3,2,1]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[2,4]
[5,6,1,2,3,4]=>[3,4,5,1,6,2]=>[4,3,2,6,1,5]=>[1,1,2,2]
[5,6,1,2,4,3]=>[6,3,4,1,5,2]=>[1,4,3,6,2,5]=>[2,2,2]
[5,6,1,3,2,4]=>[5,3,4,1,6,2]=>[2,4,3,6,1,5]=>[2,2,2]
[5,6,1,3,4,2]=>[4,6,3,1,5,2]=>[3,1,4,6,2,5]=>[1,3,2]
[5,6,1,4,2,3]=>[5,6,3,1,4,2]=>[2,1,4,6,3,5]=>[1,3,2]
[5,6,1,4,3,2]=>[6,5,3,1,4,2]=>[1,2,4,6,3,5]=>[4,2]
[5,6,2,1,3,4]=>[4,3,5,1,6,2]=>[3,4,2,6,1,5]=>[2,2,2]
[5,6,2,1,4,3]=>[3,6,4,1,5,2]=>[4,1,3,6,2,5]=>[1,3,2]
[5,6,2,3,1,4]=>[3,5,4,1,6,2]=>[4,2,3,6,1,5]=>[1,3,2]
[5,6,2,3,4,1]=>[3,4,1,6,5,2]=>[4,3,6,1,2,5]=>[1,2,3]
[5,6,2,4,1,3]=>[3,5,1,6,4,2]=>[4,2,6,1,3,5]=>[1,2,3]
[5,6,2,4,3,1]=>[6,3,1,5,4,2]=>[1,4,6,2,3,5]=>[3,3]
[5,6,3,1,2,4]=>[4,5,3,1,6,2]=>[3,2,4,6,1,5]=>[1,3,2]
[5,6,3,1,4,2]=>[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>[4,2]
[5,6,3,2,1,4]=>[5,4,3,1,6,2]=>[2,3,4,6,1,5]=>[4,2]
[5,6,3,2,4,1]=>[4,3,1,6,5,2]=>[3,4,6,1,2,5]=>[3,3]
[5,6,3,4,1,2]=>[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>[3,3]
[5,6,3,4,2,1]=>[3,1,6,5,4,2]=>[4,6,1,2,3,5]=>[2,4]
[5,6,4,1,2,3]=>[4,5,1,6,3,2]=>[3,2,6,1,4,5]=>[1,2,3]
[5,6,4,1,3,2]=>[6,4,1,5,3,2]=>[1,3,6,2,4,5]=>[3,3]
[5,6,4,2,1,3]=>[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>[3,3]
[5,6,4,2,3,1]=>[4,1,6,5,3,2]=>[3,6,1,2,4,5]=>[2,4]
[5,6,4,3,1,2]=>[5,1,6,4,3,2]=>[2,6,1,3,4,5]=>[2,4]
[5,6,4,3,2,1]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[1,5]
[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[1,1,1,1,2]
[6,1,2,3,5,4]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[2,1,1,2]
[6,1,2,4,3,5]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[2,1,1,2]
[6,1,2,4,5,3]=>[4,6,2,3,5,1]=>[3,1,5,4,2,6]=>[1,2,1,2]
[6,1,2,5,3,4]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>[1,2,1,2]
[6,1,2,5,4,3]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>[3,1,2]
[6,1,3,2,4,5]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>[2,1,1,2]
[6,1,3,2,5,4]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>[1,2,1,2]
[6,1,3,4,2,5]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>[1,2,1,2]
[6,1,3,4,5,2]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>[1,1,2,2]
[6,1,3,5,2,4]=>[3,5,6,2,4,1]=>[4,2,1,5,3,6]=>[1,1,2,2]
[6,1,3,5,4,2]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>[2,2,2]
[6,1,4,2,3,5]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>[1,2,1,2]
[6,1,4,2,5,3]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>[3,1,2]
[6,1,4,3,2,5]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>[3,1,2]
[6,1,4,3,5,2]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>[2,2,2]
[6,1,4,5,2,3]=>[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>[2,2,2]
[6,1,4,5,3,2]=>[3,6,5,2,4,1]=>[4,1,2,5,3,6]=>[1,3,2]
[6,1,5,2,3,4]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>[1,1,2,2]
[6,1,5,2,4,3]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[2,2,2]
[6,1,5,3,2,4]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>[2,2,2]
[6,1,5,3,4,2]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>[1,3,2]
[6,1,5,4,2,3]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>[1,3,2]
[6,1,5,4,3,2]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>[4,2]
[6,2,1,3,4,5]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>[2,1,1,2]
[6,2,1,3,5,4]=>[2,6,3,4,5,1]=>[5,1,4,3,2,6]=>[1,2,1,2]
[6,2,1,4,3,5]=>[2,5,3,4,6,1]=>[5,2,4,3,1,6]=>[1,2,1,2]
[6,2,1,4,5,3]=>[2,4,6,3,5,1]=>[5,3,1,4,2,6]=>[1,1,2,2]
[6,2,1,5,3,4]=>[2,5,6,3,4,1]=>[5,2,1,4,3,6]=>[1,1,2,2]
[6,2,1,5,4,3]=>[6,2,5,3,4,1]=>[1,5,2,4,3,6]=>[2,2,2]
[6,2,3,1,4,5]=>[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>[1,2,1,2]
[6,2,3,1,5,4]=>[2,3,6,4,5,1]=>[5,4,1,3,2,6]=>[1,1,2,2]
[6,2,3,4,1,5]=>[2,3,5,4,6,1]=>[5,4,2,3,1,6]=>[1,1,2,2]
[6,2,3,4,5,1]=>[2,3,4,6,5,1]=>[5,4,3,1,2,6]=>[1,1,1,3]
[6,2,3,5,1,4]=>[2,3,5,6,4,1]=>[5,4,2,1,3,6]=>[1,1,1,3]
[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>[1,5,4,2,3,6]=>[2,1,3]
[6,2,4,1,3,5]=>[2,4,5,3,6,1]=>[5,3,2,4,1,6]=>[1,1,2,2]
[6,2,4,1,5,3]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>[2,2,2]
[6,2,4,3,1,5]=>[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>[2,2,2]
[6,2,4,3,5,1]=>[4,2,3,6,5,1]=>[3,5,4,1,2,6]=>[2,1,3]
[6,2,4,5,1,3]=>[5,2,3,6,4,1]=>[2,5,4,1,3,6]=>[2,1,3]
[6,2,4,5,3,1]=>[3,6,2,5,4,1]=>[4,1,5,2,3,6]=>[1,2,3]
[6,2,5,1,3,4]=>[2,4,5,6,3,1]=>[5,3,2,1,4,6]=>[1,1,1,3]
[6,2,5,1,4,3]=>[6,2,4,5,3,1]=>[1,5,3,2,4,6]=>[2,1,3]
[6,2,5,3,1,4]=>[5,2,4,6,3,1]=>[2,5,3,1,4,6]=>[2,1,3]
[6,2,5,3,4,1]=>[4,6,2,5,3,1]=>[3,1,5,2,4,6]=>[1,2,3]
[6,2,5,4,1,3]=>[5,6,2,4,3,1]=>[2,1,5,3,4,6]=>[1,2,3]
[6,2,5,4,3,1]=>[6,5,2,4,3,1]=>[1,2,5,3,4,6]=>[3,3]
[6,3,1,2,4,5]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>[1,2,1,2]
[6,3,1,2,5,4]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>[3,1,2]
[6,3,1,4,2,5]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>[3,1,2]
[6,3,1,4,5,2]=>[4,2,6,3,5,1]=>[3,5,1,4,2,6]=>[2,2,2]
[6,3,1,5,2,4]=>[5,2,6,3,4,1]=>[2,5,1,4,3,6]=>[2,2,2]
[6,3,1,5,4,2]=>[2,6,5,3,4,1]=>[5,1,2,4,3,6]=>[1,3,2]
[6,3,2,1,4,5]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>[3,1,2]
[6,3,2,1,5,4]=>[3,2,6,4,5,1]=>[4,5,1,3,2,6]=>[2,2,2]
[6,3,2,4,1,5]=>[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>[2,2,2]
[6,3,2,4,5,1]=>[3,2,4,6,5,1]=>[4,5,3,1,2,6]=>[2,1,3]
[6,3,2,5,1,4]=>[3,2,5,6,4,1]=>[4,5,2,1,3,6]=>[2,1,3]
[6,3,2,5,4,1]=>[2,6,3,5,4,1]=>[5,1,4,2,3,6]=>[1,2,3]
[6,3,4,1,2,5]=>[4,2,5,3,6,1]=>[3,5,2,4,1,6]=>[2,2,2]
[6,3,4,1,5,2]=>[2,6,4,3,5,1]=>[5,1,3,4,2,6]=>[1,3,2]
[6,3,4,2,1,5]=>[2,5,4,3,6,1]=>[5,2,3,4,1,6]=>[1,3,2]
[6,3,4,2,5,1]=>[2,4,3,6,5,1]=>[5,3,4,1,2,6]=>[1,2,3]
[6,3,4,5,1,2]=>[2,5,3,6,4,1]=>[5,2,4,1,3,6]=>[1,2,3]
[6,3,4,5,2,1]=>[2,3,6,5,4,1]=>[5,4,1,2,3,6]=>[1,1,4]
[6,3,5,1,2,4]=>[4,2,5,6,3,1]=>[3,5,2,1,4,6]=>[2,1,3]
[6,3,5,1,4,2]=>[2,6,4,5,3,1]=>[5,1,3,2,4,6]=>[1,2,3]
[6,3,5,2,1,4]=>[2,5,4,6,3,1]=>[5,2,3,1,4,6]=>[1,2,3]
[6,3,5,2,4,1]=>[2,4,6,5,3,1]=>[5,3,1,2,4,6]=>[1,1,4]
[6,3,5,4,1,2]=>[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>[1,1,4]
[6,3,5,4,2,1]=>[6,2,5,4,3,1]=>[1,5,2,3,4,6]=>[2,4]
[6,4,1,2,3,5]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[1,1,2,2]
[6,4,1,2,5,3]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>[2,2,2]
[6,4,1,3,2,5]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>[2,2,2]
[6,4,1,3,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>[1,3,2]
[6,4,1,5,2,3]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>[1,3,2]
[6,4,1,5,3,2]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>[4,2]
[6,4,2,1,3,5]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[2,2,2]
[6,4,2,1,5,3]=>[3,6,4,2,5,1]=>[4,1,3,5,2,6]=>[1,3,2]
[6,4,2,3,1,5]=>[3,5,4,2,6,1]=>[4,2,3,5,1,6]=>[1,3,2]
[6,4,2,3,5,1]=>[3,4,2,6,5,1]=>[4,3,5,1,2,6]=>[1,2,3]
[6,4,2,5,1,3]=>[3,5,2,6,4,1]=>[4,2,5,1,3,6]=>[1,2,3]
[6,4,2,5,3,1]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>[3,3]
[6,4,3,1,2,5]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>[1,3,2]
[6,4,3,1,5,2]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>[4,2]
[6,4,3,2,1,5]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[4,2]
[6,4,3,2,5,1]=>[4,3,2,6,5,1]=>[3,4,5,1,2,6]=>[3,3]
[6,4,3,5,1,2]=>[5,3,2,6,4,1]=>[2,4,5,1,3,6]=>[3,3]
[6,4,3,5,2,1]=>[3,2,6,5,4,1]=>[4,5,1,2,3,6]=>[2,4]
[6,4,5,1,2,3]=>[4,5,2,6,3,1]=>[3,2,5,1,4,6]=>[1,2,3]
[6,4,5,1,3,2]=>[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>[3,3]
[6,4,5,2,1,3]=>[5,4,2,6,3,1]=>[2,3,5,1,4,6]=>[3,3]
[6,4,5,2,3,1]=>[4,2,6,5,3,1]=>[3,5,1,2,4,6]=>[2,4]
[6,4,5,3,1,2]=>[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>[2,4]
[6,4,5,3,2,1]=>[2,6,5,4,3,1]=>[5,1,2,3,4,6]=>[1,5]
[6,5,1,2,3,4]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>[1,1,1,3]
[6,5,1,2,4,3]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>[2,1,3]
[6,5,1,3,2,4]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>[2,1,3]
[6,5,1,3,4,2]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>[1,2,3]
[6,5,1,4,2,3]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>[1,2,3]
[6,5,1,4,3,2]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[3,3]
[6,5,2,1,3,4]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>[2,1,3]
[6,5,2,1,4,3]=>[3,6,4,5,2,1]=>[4,1,3,2,5,6]=>[1,2,3]
[6,5,2,3,1,4]=>[3,5,4,6,2,1]=>[4,2,3,1,5,6]=>[1,2,3]
[6,5,2,3,4,1]=>[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>[1,1,4]
[6,5,2,4,1,3]=>[3,5,6,4,2,1]=>[4,2,1,3,5,6]=>[1,1,4]
[6,5,2,4,3,1]=>[6,3,5,4,2,1]=>[1,4,2,3,5,6]=>[2,4]
[6,5,3,1,2,4]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>[1,2,3]
[6,5,3,1,4,2]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>[3,3]
[6,5,3,2,1,4]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>[3,3]
[6,5,3,2,4,1]=>[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>[2,4]
[6,5,3,4,1,2]=>[5,3,6,4,2,1]=>[2,4,1,3,5,6]=>[2,4]
[6,5,3,4,2,1]=>[3,6,5,4,2,1]=>[4,1,2,3,5,6]=>[1,5]
[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>[1,1,4]
[6,5,4,1,3,2]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>[2,4]
[6,5,4,2,1,3]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>[2,4]
[6,5,4,2,3,1]=>[4,6,5,3,2,1]=>[3,1,2,4,5,6]=>[1,5]
[6,5,4,3,1,2]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>[1,5]
[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6]
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]
[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]
[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]
[1,2,3,4,6,7,5]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>[1,2,1,1,1,1]
[1,2,3,4,7,5,6]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>[1,2,1,1,1,1]
[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[3,1,1,1,1]
[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]
[1,2,3,5,4,7,6]=>[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>[1,2,1,1,1,1]
[1,2,3,5,6,4,7]=>[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]=>[1,2,1,1,1,1]
[1,2,3,5,6,7,4]=>[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]=>[1,1,2,1,1,1]
[1,2,3,5,7,4,6]=>[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]=>[1,1,2,1,1,1]
[1,2,3,5,7,6,4]=>[7,4,6,1,2,3,5]=>[1,4,2,7,6,5,3]=>[2,2,1,1,1]
[1,2,3,6,4,5,7]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>[1,2,1,1,1,1]
[1,2,3,6,4,7,5]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[3,1,1,1,1]
[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[3,1,1,1,1]
[1,2,3,6,5,7,4]=>[5,4,7,1,2,3,6]=>[3,4,1,7,6,5,2]=>[2,2,1,1,1]
[1,2,3,6,7,4,5]=>[6,4,7,1,2,3,5]=>[2,4,1,7,6,5,3]=>[2,2,1,1,1]
[1,2,3,6,7,5,4]=>[4,7,6,1,2,3,5]=>[4,1,2,7,6,5,3]=>[1,3,1,1,1]
[1,2,3,7,4,5,6]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>[1,1,2,1,1,1]
[1,2,3,7,4,6,5]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>[2,2,1,1,1]
[1,2,3,7,5,4,6]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>[2,2,1,1,1]
[1,2,3,7,5,6,4]=>[5,7,6,1,2,3,4]=>[3,1,2,7,6,5,4]=>[1,3,1,1,1]
[1,2,3,7,6,4,5]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>[1,3,1,1,1]
[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[4,1,1,1]
[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]
[1,2,4,3,5,7,6]=>[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]=>[1,2,1,1,1,1]
[1,2,4,3,6,5,7]=>[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]=>[1,2,1,1,1,1]
[1,2,4,3,6,7,5]=>[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>[1,1,2,1,1,1]
[1,2,4,3,7,5,6]=>[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]=>[1,1,2,1,1,1]
[1,2,4,3,7,6,5]=>[7,3,6,1,2,4,5]=>[1,5,2,7,6,4,3]=>[2,2,1,1,1]
[1,2,4,5,3,6,7]=>[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]=>[1,2,1,1,1,1]
[1,2,4,5,3,7,6]=>[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]=>[1,1,2,1,1,1]
[1,2,4,5,6,3,7]=>[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]=>[1,1,2,1,1,1]
[1,2,4,5,6,7,3]=>[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>[1,1,1,2,1,1]
[1,2,4,5,7,3,6]=>[3,4,6,7,1,2,5]=>[5,4,2,1,7,6,3]=>[1,1,1,2,1,1]
[1,2,4,5,7,6,3]=>[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>[2,1,2,1,1]
[1,2,4,6,3,5,7]=>[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]=>[1,1,2,1,1,1]
[1,2,4,6,3,7,5]=>[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>[2,2,1,1,1]
[1,2,4,6,5,3,7]=>[6,3,5,1,2,4,7]=>[2,5,3,7,6,4,1]=>[2,2,1,1,1]
[1,2,4,6,5,7,3]=>[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>[2,1,2,1,1]
[1,2,4,6,7,3,5]=>[6,3,4,7,1,2,5]=>[2,5,4,1,7,6,3]=>[2,1,2,1,1]
[1,2,4,6,7,5,3]=>[4,7,3,6,1,2,5]=>[4,1,5,2,7,6,3]=>[1,2,2,1,1]
[1,2,4,7,3,5,6]=>[3,5,6,7,1,2,4]=>[5,3,2,1,7,6,4]=>[1,1,1,2,1,1]
[1,2,4,7,3,6,5]=>[7,3,5,6,1,2,4]=>[1,5,3,2,7,6,4]=>[2,1,2,1,1]
[1,2,4,7,5,3,6]=>[6,3,5,7,1,2,4]=>[2,5,3,1,7,6,4]=>[2,1,2,1,1]
[1,2,4,7,5,6,3]=>[5,7,3,6,1,2,4]=>[3,1,5,2,7,6,4]=>[1,2,2,1,1]
[1,2,4,7,6,3,5]=>[6,7,3,5,1,2,4]=>[2,1,5,3,7,6,4]=>[1,2,2,1,1]
[1,2,4,7,6,5,3]=>[7,6,3,5,1,2,4]=>[1,2,5,3,7,6,4]=>[3,2,1,1]
[1,2,5,3,4,6,7]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>[1,2,1,1,1,1]
[1,2,5,3,4,7,6]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[3,1,1,1,1]
[1,2,5,3,6,4,7]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[3,1,1,1,1]
[1,2,5,3,6,7,4]=>[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>[2,2,1,1,1]
[1,2,5,3,7,4,6]=>[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>[2,2,1,1,1]
[1,2,5,3,7,6,4]=>[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>[1,3,1,1,1]
[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[3,1,1,1,1]
[1,2,5,4,3,7,6]=>[4,3,7,1,2,5,6]=>[4,5,1,7,6,3,2]=>[2,2,1,1,1]
[1,2,5,4,6,3,7]=>[4,3,6,1,2,5,7]=>[4,5,2,7,6,3,1]=>[2,2,1,1,1]
[1,2,5,4,6,7,3]=>[4,3,5,7,1,2,6]=>[4,5,3,1,7,6,2]=>[2,1,2,1,1]
[1,2,5,4,7,3,6]=>[4,3,6,7,1,2,5]=>[4,5,2,1,7,6,3]=>[2,1,2,1,1]
[1,2,5,4,7,6,3]=>[3,7,4,6,1,2,5]=>[5,1,4,2,7,6,3]=>[1,2,2,1,1]
[1,2,5,6,3,4,7]=>[5,3,6,1,2,4,7]=>[3,5,2,7,6,4,1]=>[2,2,1,1,1]
[1,2,5,6,3,7,4]=>[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>[1,3,1,1,1]
[1,2,5,6,4,3,7]=>[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>[1,3,1,1,1]
[1,2,5,6,4,7,3]=>[3,5,4,7,1,2,6]=>[5,3,4,1,7,6,2]=>[1,2,2,1,1]
[1,2,5,6,7,3,4]=>[3,6,4,7,1,2,5]=>[5,2,4,1,7,6,3]=>[1,2,2,1,1]
[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>[1,1,3,1,1]
[1,2,5,7,3,4,6]=>[5,3,6,7,1,2,4]=>[3,5,2,1,7,6,4]=>[2,1,2,1,1]
[1,2,5,7,3,6,4]=>[3,7,5,6,1,2,4]=>[5,1,3,2,7,6,4]=>[1,2,2,1,1]
[1,2,5,7,4,3,6]=>[3,6,5,7,1,2,4]=>[5,2,3,1,7,6,4]=>[1,2,2,1,1]
[1,2,5,7,4,6,3]=>[3,5,7,6,1,2,4]=>[5,3,1,2,7,6,4]=>[1,1,3,1,1]
[1,2,5,7,6,3,4]=>[3,6,7,5,1,2,4]=>[5,2,1,3,7,6,4]=>[1,1,3,1,1]
[1,2,5,7,6,4,3]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>[2,3,1,1]
[1,2,6,3,4,5,7]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>[1,1,2,1,1,1]
[1,2,6,3,4,7,5]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>[2,2,1,1,1]
[1,2,6,3,5,4,7]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>[2,2,1,1,1]
[1,2,6,3,5,7,4]=>[5,7,4,1,2,3,6]=>[3,1,4,7,6,5,2]=>[1,3,1,1,1]
[1,2,6,3,7,4,5]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>[1,3,1,1,1]
[1,2,6,3,7,5,4]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[4,1,1,1]
[1,2,6,4,3,5,7]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>[2,2,1,1,1]
[1,2,6,4,3,7,5]=>[4,7,5,1,2,3,6]=>[4,1,3,7,6,5,2]=>[1,3,1,1,1]
[1,2,6,4,5,3,7]=>[4,6,5,1,2,3,7]=>[4,2,3,7,6,5,1]=>[1,3,1,1,1]
[1,2,6,4,5,7,3]=>[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>[1,2,2,1,1]
[1,2,6,4,7,3,5]=>[4,6,3,7,1,2,5]=>[4,2,5,1,7,6,3]=>[1,2,2,1,1]
[1,2,6,4,7,5,3]=>[7,4,3,6,1,2,5]=>[1,4,5,2,7,6,3]=>[3,2,1,1]
[1,2,6,5,3,4,7]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>[1,3,1,1,1]
[1,2,6,5,3,7,4]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[4,1,1,1]
[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[4,1,1,1]
[1,2,6,5,4,7,3]=>[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>[3,2,1,1]
[1,2,6,5,7,3,4]=>[6,4,3,7,1,2,5]=>[2,4,5,1,7,6,3]=>[3,2,1,1]
[1,2,6,5,7,4,3]=>[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>[2,3,1,1]
[1,2,6,7,3,4,5]=>[5,6,3,7,1,2,4]=>[3,2,5,1,7,6,4]=>[1,2,2,1,1]
[1,2,6,7,3,5,4]=>[7,5,3,6,1,2,4]=>[1,3,5,2,7,6,4]=>[3,2,1,1]
[1,2,6,7,4,3,5]=>[6,5,3,7,1,2,4]=>[2,3,5,1,7,6,4]=>[3,2,1,1]
[1,2,6,7,4,5,3]=>[5,3,7,6,1,2,4]=>[3,5,1,2,7,6,4]=>[2,3,1,1]
[1,2,6,7,5,3,4]=>[6,3,7,5,1,2,4]=>[2,5,1,3,7,6,4]=>[2,3,1,1]
[1,2,6,7,5,4,3]=>[3,7,6,5,1,2,4]=>[5,1,2,3,7,6,4]=>[1,4,1,1]
[1,2,7,3,4,5,6]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>[1,1,1,2,1,1]
[1,2,7,3,4,6,5]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>[2,1,2,1,1]
[1,2,7,3,5,4,6]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>[2,1,2,1,1]
[1,2,7,3,5,6,4]=>[5,7,4,6,1,2,3]=>[3,1,4,2,7,6,5]=>[1,2,2,1,1]
[1,2,7,3,6,4,5]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>[1,2,2,1,1]
[1,2,7,3,6,5,4]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>[3,2,1,1]
[1,2,7,4,3,5,6]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>[2,1,2,1,1]
[1,2,7,4,3,6,5]=>[4,7,5,6,1,2,3]=>[4,1,3,2,7,6,5]=>[1,2,2,1,1]
[1,2,7,4,5,3,6]=>[4,6,5,7,1,2,3]=>[4,2,3,1,7,6,5]=>[1,2,2,1,1]
[1,2,7,4,5,6,3]=>[4,5,7,6,1,2,3]=>[4,3,1,2,7,6,5]=>[1,1,3,1,1]
[1,2,7,4,6,3,5]=>[4,6,7,5,1,2,3]=>[4,2,1,3,7,6,5]=>[1,1,3,1,1]
[1,2,7,4,6,5,3]=>[7,4,6,5,1,2,3]=>[1,4,2,3,7,6,5]=>[2,3,1,1]
[1,2,7,5,3,4,6]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>[1,2,2,1,1]
[1,2,7,5,3,6,4]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>[3,2,1,1]
[1,2,7,5,4,3,6]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>[3,2,1,1]
[1,2,7,5,4,6,3]=>[5,4,7,6,1,2,3]=>[3,4,1,2,7,6,5]=>[2,3,1,1]
[1,2,7,5,6,3,4]=>[6,4,7,5,1,2,3]=>[2,4,1,3,7,6,5]=>[2,3,1,1]
[1,2,7,5,6,4,3]=>[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>[1,4,1,1]
[1,2,7,6,3,4,5]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[1,1,3,1,1]
[1,2,7,6,3,5,4]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>[2,3,1,1]
[1,2,7,6,4,3,5]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>[2,3,1,1]
[1,2,7,6,4,5,3]=>[5,7,6,4,1,2,3]=>[3,1,2,4,7,6,5]=>[1,4,1,1]
[1,2,7,6,5,3,4]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>[1,4,1,1]
[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[5,1,1]
[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]
[1,3,2,4,5,7,6]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>[1,2,1,1,1,1]
[1,3,2,4,6,5,7]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>[1,2,1,1,1,1]
[1,3,2,4,6,7,5]=>[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]=>[1,1,2,1,1,1]
[1,3,2,4,7,5,6]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>[1,1,2,1,1,1]
[1,3,2,4,7,6,5]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>[2,2,1,1,1]
[1,3,2,5,4,6,7]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>[1,2,1,1,1,1]
[1,3,2,5,4,7,6]=>[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]=>[1,1,2,1,1,1]
[1,3,2,5,6,4,7]=>[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]=>[1,1,2,1,1,1]
[1,3,2,5,6,7,4]=>[2,4,5,7,1,3,6]=>[6,4,3,1,7,5,2]=>[1,1,1,2,1,1]
[1,3,2,5,7,4,6]=>[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>[1,1,1,2,1,1]
[1,3,2,5,7,6,4]=>[7,2,4,6,1,3,5]=>[1,6,4,2,7,5,3]=>[2,1,2,1,1]
[1,3,2,6,4,5,7]=>[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]=>[1,1,2,1,1,1]
[1,3,2,6,4,7,5]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>[2,2,1,1,1]
[1,3,2,6,5,4,7]=>[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>[2,2,1,1,1]
[1,3,2,6,5,7,4]=>[5,2,4,7,1,3,6]=>[3,6,4,1,7,5,2]=>[2,1,2,1,1]
[1,3,2,6,7,4,5]=>[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>[2,1,2,1,1]
[1,3,2,6,7,5,4]=>[4,7,2,6,1,3,5]=>[4,1,6,2,7,5,3]=>[1,2,2,1,1]
[1,3,2,7,4,5,6]=>[2,5,6,7,1,3,4]=>[6,3,2,1,7,5,4]=>[1,1,1,2,1,1]
[1,3,2,7,4,6,5]=>[7,2,5,6,1,3,4]=>[1,6,3,2,7,5,4]=>[2,1,2,1,1]
[1,3,2,7,5,4,6]=>[6,2,5,7,1,3,4]=>[2,6,3,1,7,5,4]=>[2,1,2,1,1]
[1,3,2,7,5,6,4]=>[5,7,2,6,1,3,4]=>[3,1,6,2,7,5,4]=>[1,2,2,1,1]
[1,3,2,7,6,4,5]=>[6,7,2,5,1,3,4]=>[2,1,6,3,7,5,4]=>[1,2,2,1,1]
[1,3,2,7,6,5,4]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>[3,2,1,1]
[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>[1,2,1,1,1,1]
[1,3,4,2,5,7,6]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>[1,1,2,1,1,1]
[1,3,4,2,6,5,7]=>[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>[1,1,2,1,1,1]
[1,3,4,2,6,7,5]=>[2,3,5,7,1,4,6]=>[6,5,3,1,7,4,2]=>[1,1,1,2,1,1]
[1,3,4,2,7,5,6]=>[2,3,6,7,1,4,5]=>[6,5,2,1,7,4,3]=>[1,1,1,2,1,1]
[1,3,4,2,7,6,5]=>[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>[2,1,2,1,1]
[1,3,4,5,2,6,7]=>[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>[1,1,2,1,1,1]
[1,3,4,5,2,7,6]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>[1,1,1,2,1,1]
[1,3,4,5,6,2,7]=>[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>[1,1,1,2,1,1]
[1,3,4,5,6,7,2]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>[1,1,1,1,2,1]
[1,3,4,5,7,2,6]=>[2,3,4,6,7,1,5]=>[6,5,4,2,1,7,3]=>[1,1,1,1,2,1]
[1,3,4,5,7,6,2]=>[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>[2,1,1,2,1]
[1,3,4,6,2,5,7]=>[2,3,5,6,1,4,7]=>[6,5,3,2,7,4,1]=>[1,1,1,2,1,1]
[1,3,4,6,2,7,5]=>[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>[2,1,2,1,1]
[1,3,4,6,5,2,7]=>[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>[2,1,2,1,1]
[1,3,4,6,5,7,2]=>[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>[2,1,1,2,1]
[1,3,4,6,7,2,5]=>[6,2,3,4,7,1,5]=>[2,6,5,4,1,7,3]=>[2,1,1,2,1]
[1,3,4,6,7,5,2]=>[4,7,2,3,6,1,5]=>[4,1,6,5,2,7,3]=>[1,2,1,2,1]
[1,3,4,7,2,5,6]=>[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>[1,1,1,1,2,1]
[1,3,4,7,2,6,5]=>[7,2,3,5,6,1,4]=>[1,6,5,3,2,7,4]=>[2,1,1,2,1]
[1,3,4,7,5,2,6]=>[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>[2,1,1,2,1]
[1,3,4,7,5,6,2]=>[5,7,2,3,6,1,4]=>[3,1,6,5,2,7,4]=>[1,2,1,2,1]
[1,3,4,7,6,2,5]=>[6,7,2,3,5,1,4]=>[2,1,6,5,3,7,4]=>[1,2,1,2,1]
[1,3,4,7,6,5,2]=>[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>[3,1,2,1]
[1,3,5,2,4,6,7]=>[2,4,5,1,3,6,7]=>[6,4,3,7,5,2,1]=>[1,1,2,1,1,1]
[1,3,5,2,4,7,6]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>[2,2,1,1,1]
[1,3,5,2,6,4,7]=>[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>[2,2,1,1,1]
[1,3,5,2,6,7,4]=>[5,2,3,7,1,4,6]=>[3,6,5,1,7,4,2]=>[2,1,2,1,1]
[1,3,5,2,7,4,6]=>[6,2,3,7,1,4,5]=>[2,6,5,1,7,4,3]=>[2,1,2,1,1]
[1,3,5,2,7,6,4]=>[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>[1,2,2,1,1]
[1,3,5,4,2,6,7]=>[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>[2,2,1,1,1]
[1,3,5,4,2,7,6]=>[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>[2,1,2,1,1]
[1,3,5,4,6,2,7]=>[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>[2,1,2,1,1]
[1,3,5,4,6,7,2]=>[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>[2,1,1,2,1]
[1,3,5,4,7,2,6]=>[4,2,3,6,7,1,5]=>[4,6,5,2,1,7,3]=>[2,1,1,2,1]
[1,3,5,4,7,6,2]=>[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>[1,2,1,2,1]
[1,3,5,6,2,4,7]=>[5,2,3,6,1,4,7]=>[3,6,5,2,7,4,1]=>[2,1,2,1,1]
[1,3,5,6,2,7,4]=>[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>[1,2,2,1,1]
[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>[1,2,2,1,1]
[1,3,5,6,4,7,2]=>[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>[1,2,1,2,1]
[1,3,5,6,7,2,4]=>[3,6,2,4,7,1,5]=>[5,2,6,4,1,7,3]=>[1,2,1,2,1]
[1,3,5,6,7,4,2]=>[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>[1,1,2,2,1]
[1,3,5,7,2,4,6]=>[5,2,3,6,7,1,4]=>[3,6,5,2,1,7,4]=>[2,1,1,2,1]
[1,3,5,7,2,6,4]=>[3,7,2,5,6,1,4]=>[5,1,6,3,2,7,4]=>[1,2,1,2,1]
[1,3,5,7,4,2,6]=>[3,6,2,5,7,1,4]=>[5,2,6,3,1,7,4]=>[1,2,1,2,1]
[1,3,5,7,4,6,2]=>[3,5,7,2,6,1,4]=>[5,3,1,6,2,7,4]=>[1,1,2,2,1]
[1,3,5,7,6,2,4]=>[3,6,7,2,5,1,4]=>[5,2,1,6,3,7,4]=>[1,1,2,2,1]
[1,3,5,7,6,4,2]=>[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>[2,2,2,1]
[1,3,6,2,4,5,7]=>[2,4,5,6,1,3,7]=>[6,4,3,2,7,5,1]=>[1,1,1,2,1,1]
[1,3,6,2,4,7,5]=>[7,2,4,5,1,3,6]=>[1,6,4,3,7,5,2]=>[2,1,2,1,1]
[1,3,6,2,5,4,7]=>[6,2,4,5,1,3,7]=>[2,6,4,3,7,5,1]=>[2,1,2,1,1]
[1,3,6,2,5,7,4]=>[5,7,2,4,1,3,6]=>[3,1,6,4,7,5,2]=>[1,2,2,1,1]
[1,3,6,2,7,4,5]=>[6,7,2,4,1,3,5]=>[2,1,6,4,7,5,3]=>[1,2,2,1,1]
[1,3,6,2,7,5,4]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>[3,2,1,1]
[1,3,6,4,2,5,7]=>[5,2,4,6,1,3,7]=>[3,6,4,2,7,5,1]=>[2,1,2,1,1]
[1,3,6,4,2,7,5]=>[4,7,2,5,1,3,6]=>[4,1,6,3,7,5,2]=>[1,2,2,1,1]
[1,3,6,4,5,2,7]=>[4,6,2,5,1,3,7]=>[4,2,6,3,7,5,1]=>[1,2,2,1,1]
[1,3,6,4,5,7,2]=>[4,5,2,3,7,1,6]=>[4,3,6,5,1,7,2]=>[1,2,1,2,1]
[1,3,6,4,7,2,5]=>[4,6,2,3,7,1,5]=>[4,2,6,5,1,7,3]=>[1,2,1,2,1]
[1,3,6,4,7,5,2]=>[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>[3,1,2,1]
[1,3,6,5,2,4,7]=>[5,6,2,4,1,3,7]=>[3,2,6,4,7,5,1]=>[1,2,2,1,1]
[1,3,6,5,2,7,4]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>[3,2,1,1]
[1,3,6,5,4,2,7]=>[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>[3,2,1,1]
[1,3,6,5,4,7,2]=>[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>[3,1,2,1]
[1,3,6,5,7,2,4]=>[6,4,2,3,7,1,5]=>[2,4,6,5,1,7,3]=>[3,1,2,1]
[1,3,6,5,7,4,2]=>[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>[2,2,2,1]
[1,3,6,7,2,4,5]=>[5,6,2,3,7,1,4]=>[3,2,6,5,1,7,4]=>[1,2,1,2,1]
[1,3,6,7,2,5,4]=>[7,5,2,3,6,1,4]=>[1,3,6,5,2,7,4]=>[3,1,2,1]
[1,3,6,7,4,2,5]=>[6,5,2,3,7,1,4]=>[2,3,6,5,1,7,4]=>[3,1,2,1]
[1,3,6,7,4,5,2]=>[5,3,7,2,6,1,4]=>[3,5,1,6,2,7,4]=>[2,2,2,1]
[1,3,6,7,5,2,4]=>[6,3,7,2,5,1,4]=>[2,5,1,6,3,7,4]=>[2,2,2,1]
[1,3,6,7,5,4,2]=>[3,7,6,2,5,1,4]=>[5,1,2,6,3,7,4]=>[1,3,2,1]
[1,3,7,2,4,5,6]=>[2,4,5,6,7,1,3]=>[6,4,3,2,1,7,5]=>[1,1,1,1,2,1]
[1,3,7,2,4,6,5]=>[7,2,4,5,6,1,3]=>[1,6,4,3,2,7,5]=>[2,1,1,2,1]
[1,3,7,2,5,4,6]=>[6,2,4,5,7,1,3]=>[2,6,4,3,1,7,5]=>[2,1,1,2,1]
[1,3,7,2,5,6,4]=>[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>[1,2,1,2,1]
[1,3,7,2,6,4,5]=>[6,7,2,4,5,1,3]=>[2,1,6,4,3,7,5]=>[1,2,1,2,1]
[1,3,7,2,6,5,4]=>[7,6,2,4,5,1,3]=>[1,2,6,4,3,7,5]=>[3,1,2,1]
[1,3,7,4,2,5,6]=>[5,2,4,6,7,1,3]=>[3,6,4,2,1,7,5]=>[2,1,1,2,1]
[1,3,7,4,2,6,5]=>[4,7,2,5,6,1,3]=>[4,1,6,3,2,7,5]=>[1,2,1,2,1]
[1,3,7,4,5,2,6]=>[4,6,2,5,7,1,3]=>[4,2,6,3,1,7,5]=>[1,2,1,2,1]
[1,3,7,4,5,6,2]=>[4,5,7,2,6,1,3]=>[4,3,1,6,2,7,5]=>[1,1,2,2,1]
[1,3,7,4,6,2,5]=>[4,6,7,2,5,1,3]=>[4,2,1,6,3,7,5]=>[1,1,2,2,1]
[1,3,7,4,6,5,2]=>[7,4,6,2,5,1,3]=>[1,4,2,6,3,7,5]=>[2,2,2,1]
[1,3,7,5,2,4,6]=>[5,6,2,4,7,1,3]=>[3,2,6,4,1,7,5]=>[1,2,1,2,1]
[1,3,7,5,2,6,4]=>[7,5,2,4,6,1,3]=>[1,3,6,4,2,7,5]=>[3,1,2,1]
[1,3,7,5,4,2,6]=>[6,5,2,4,7,1,3]=>[2,3,6,4,1,7,5]=>[3,1,2,1]
[1,3,7,5,4,6,2]=>[5,4,7,2,6,1,3]=>[3,4,1,6,2,7,5]=>[2,2,2,1]
[1,3,7,5,6,2,4]=>[6,4,7,2,5,1,3]=>[2,4,1,6,3,7,5]=>[2,2,2,1]
[1,3,7,5,6,4,2]=>[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>[1,3,2,1]
[1,3,7,6,2,4,5]=>[5,6,7,2,4,1,3]=>[3,2,1,6,4,7,5]=>[1,1,2,2,1]
[1,3,7,6,2,5,4]=>[7,5,6,2,4,1,3]=>[1,3,2,6,4,7,5]=>[2,2,2,1]
[1,3,7,6,4,2,5]=>[6,5,7,2,4,1,3]=>[2,3,1,6,4,7,5]=>[2,2,2,1]
[1,3,7,6,4,5,2]=>[5,7,6,2,4,1,3]=>[3,1,2,6,4,7,5]=>[1,3,2,1]
[1,3,7,6,5,2,4]=>[6,7,5,2,4,1,3]=>[2,1,3,6,4,7,5]=>[1,3,2,1]
[1,3,7,6,5,4,2]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>[4,2,1]
[1,4,2,3,5,6,7]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>[1,2,1,1,1,1]
[1,4,2,3,5,7,6]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[3,1,1,1,1]
[1,4,2,3,6,5,7]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[3,1,1,1,1]
[1,4,2,3,6,7,5]=>[5,2,7,1,3,4,6]=>[3,6,1,7,5,4,2]=>[2,2,1,1,1]
[1,4,2,3,7,5,6]=>[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>[2,2,1,1,1]
[1,4,2,3,7,6,5]=>[2,7,6,1,3,4,5]=>[6,1,2,7,5,4,3]=>[1,3,1,1,1]
[1,4,2,5,3,6,7]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[3,1,1,1,1]
[1,4,2,5,3,7,6]=>[4,2,7,1,3,5,6]=>[4,6,1,7,5,3,2]=>[2,2,1,1,1]
[1,4,2,5,6,3,7]=>[4,2,6,1,3,5,7]=>[4,6,2,7,5,3,1]=>[2,2,1,1,1]
[1,4,2,5,6,7,3]=>[4,2,5,7,1,3,6]=>[4,6,3,1,7,5,2]=>[2,1,2,1,1]
[1,4,2,5,7,3,6]=>[4,2,6,7,1,3,5]=>[4,6,2,1,7,5,3]=>[2,1,2,1,1]
[1,4,2,5,7,6,3]=>[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]=>[1,2,2,1,1]
[1,4,2,6,3,5,7]=>[5,2,6,1,3,4,7]=>[3,6,2,7,5,4,1]=>[2,2,1,1,1]
[1,4,2,6,3,7,5]=>[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]=>[1,3,1,1,1]
[1,4,2,6,5,3,7]=>[2,6,5,1,3,4,7]=>[6,2,3,7,5,4,1]=>[1,3,1,1,1]
[1,4,2,6,5,7,3]=>[2,5,4,7,1,3,6]=>[6,3,4,1,7,5,2]=>[1,2,2,1,1]
[1,4,2,6,7,3,5]=>[2,6,4,7,1,3,5]=>[6,2,4,1,7,5,3]=>[1,2,2,1,1]
[1,4,2,6,7,5,3]=>[2,4,7,6,1,3,5]=>[6,4,1,2,7,5,3]=>[1,1,3,1,1]
[1,4,2,7,3,5,6]=>[5,2,6,7,1,3,4]=>[3,6,2,1,7,5,4]=>[2,1,2,1,1]
[1,4,2,7,3,6,5]=>[2,7,5,6,1,3,4]=>[6,1,3,2,7,5,4]=>[1,2,2,1,1]
[1,4,2,7,5,3,6]=>[2,6,5,7,1,3,4]=>[6,2,3,1,7,5,4]=>[1,2,2,1,1]
[1,4,2,7,5,6,3]=>[2,5,7,6,1,3,4]=>[6,3,1,2,7,5,4]=>[1,1,3,1,1]
[1,4,2,7,6,3,5]=>[2,6,7,5,1,3,4]=>[6,2,1,3,7,5,4]=>[1,1,3,1,1]
[1,4,2,7,6,5,3]=>[7,2,6,5,1,3,4]=>[1,6,2,3,7,5,4]=>[2,3,1,1]
[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[3,1,1,1,1]
[1,4,3,2,5,7,6]=>[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>[2,2,1,1,1]
[1,4,3,2,6,5,7]=>[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>[2,2,1,1,1]
[1,4,3,2,6,7,5]=>[3,2,5,7,1,4,6]=>[5,6,3,1,7,4,2]=>[2,1,2,1,1]
[1,4,3,2,7,5,6]=>[3,2,6,7,1,4,5]=>[5,6,2,1,7,4,3]=>[2,1,2,1,1]
[1,4,3,2,7,6,5]=>[2,7,3,6,1,4,5]=>[6,1,5,2,7,4,3]=>[1,2,2,1,1]
[1,4,3,5,2,6,7]=>[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>[2,2,1,1,1]
[1,4,3,5,2,7,6]=>[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>[2,1,2,1,1]
[1,4,3,5,6,2,7]=>[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>[2,1,2,1,1]
[1,4,3,5,6,7,2]=>[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>[2,1,1,2,1]
[1,4,3,5,7,2,6]=>[3,2,4,6,7,1,5]=>[5,6,4,2,1,7,3]=>[2,1,1,2,1]
[1,4,3,5,7,6,2]=>[2,7,3,4,6,1,5]=>[6,1,5,4,2,7,3]=>[1,2,1,2,1]
[1,4,3,6,2,5,7]=>[3,2,5,6,1,4,7]=>[5,6,3,2,7,4,1]=>[2,1,2,1,1]
[1,4,3,6,2,7,5]=>[2,7,3,5,1,4,6]=>[6,1,5,3,7,4,2]=>[1,2,2,1,1]
[1,4,3,6,5,2,7]=>[2,6,3,5,1,4,7]=>[6,2,5,3,7,4,1]=>[1,2,2,1,1]
[1,4,3,6,5,7,2]=>[2,5,3,4,7,1,6]=>[6,3,5,4,1,7,2]=>[1,2,1,2,1]
[1,4,3,6,7,2,5]=>[2,6,3,4,7,1,5]=>[6,2,5,4,1,7,3]=>[1,2,1,2,1]
[1,4,3,6,7,5,2]=>[2,4,7,3,6,1,5]=>[6,4,1,5,2,7,3]=>[1,1,2,2,1]
[1,4,3,7,2,5,6]=>[3,2,5,6,7,1,4]=>[5,6,3,2,1,7,4]=>[2,1,1,2,1]
[1,4,3,7,2,6,5]=>[2,7,3,5,6,1,4]=>[6,1,5,3,2,7,4]=>[1,2,1,2,1]
[1,4,3,7,5,2,6]=>[2,6,3,5,7,1,4]=>[6,2,5,3,1,7,4]=>[1,2,1,2,1]
[1,4,3,7,5,6,2]=>[2,5,7,3,6,1,4]=>[6,3,1,5,2,7,4]=>[1,1,2,2,1]
[1,4,3,7,6,2,5]=>[2,6,7,3,5,1,4]=>[6,2,1,5,3,7,4]=>[1,1,2,2,1]
[1,4,3,7,6,5,2]=>[7,2,6,3,5,1,4]=>[1,6,2,5,3,7,4]=>[2,2,2,1]
[1,4,5,2,3,6,7]=>[4,2,5,1,3,6,7]=>[4,6,3,7,5,2,1]=>[2,2,1,1,1]
[1,4,5,2,3,7,6]=>[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]=>[1,3,1,1,1]
[1,4,5,2,6,3,7]=>[2,6,4,1,3,5,7]=>[6,2,4,7,5,3,1]=>[1,3,1,1,1]
[1,4,5,2,6,7,3]=>[2,5,3,7,1,4,6]=>[6,3,5,1,7,4,2]=>[1,2,2,1,1]
[1,4,5,2,7,3,6]=>[2,6,3,7,1,4,5]=>[6,2,5,1,7,4,3]=>[1,2,2,1,1]
[1,4,5,2,7,6,3]=>[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]=>[1,1,3,1,1]
[1,4,5,3,2,6,7]=>[2,5,4,1,3,6,7]=>[6,3,4,7,5,2,1]=>[1,3,1,1,1]
[1,4,5,3,2,7,6]=>[2,4,3,7,1,5,6]=>[6,4,5,1,7,3,2]=>[1,2,2,1,1]
[1,4,5,3,6,2,7]=>[2,4,3,6,1,5,7]=>[6,4,5,2,7,3,1]=>[1,2,2,1,1]
[1,4,5,3,6,7,2]=>[2,4,3,5,7,1,6]=>[6,4,5,3,1,7,2]=>[1,2,1,2,1]
[1,4,5,3,7,2,6]=>[2,4,3,6,7,1,5]=>[6,4,5,2,1,7,3]=>[1,2,1,2,1]
[1,4,5,3,7,6,2]=>[2,3,7,4,6,1,5]=>[6,5,1,4,2,7,3]=>[1,1,2,2,1]
[1,4,5,6,2,3,7]=>[2,5,3,6,1,4,7]=>[6,3,5,2,7,4,1]=>[1,2,2,1,1]
[1,4,5,6,2,7,3]=>[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]=>[1,1,3,1,1]
[1,4,5,6,3,2,7]=>[2,3,6,5,1,4,7]=>[6,5,2,3,7,4,1]=>[1,1,3,1,1]
[1,4,5,6,3,7,2]=>[2,3,5,4,7,1,6]=>[6,5,3,4,1,7,2]=>[1,1,2,2,1]
[1,4,5,6,7,2,3]=>[2,3,6,4,7,1,5]=>[6,5,2,4,1,7,3]=>[1,1,2,2,1]
[1,4,5,6,7,3,2]=>[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]=>[1,1,1,3,1]
[1,4,5,7,2,3,6]=>[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>[1,2,1,2,1]
[1,4,5,7,2,6,3]=>[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]=>[1,1,2,2,1]
[1,4,5,7,3,2,6]=>[2,3,6,5,7,1,4]=>[6,5,2,3,1,7,4]=>[1,1,2,2,1]
[1,4,5,7,3,6,2]=>[2,3,5,7,6,1,4]=>[6,5,3,1,2,7,4]=>[1,1,1,3,1]
[1,4,5,7,6,2,3]=>[2,3,6,7,5,1,4]=>[6,5,2,1,3,7,4]=>[1,1,1,3,1]
[1,4,5,7,6,3,2]=>[7,2,3,6,5,1,4]=>[1,6,5,2,3,7,4]=>[2,1,3,1]
[1,4,6,2,3,5,7]=>[4,2,5,6,1,3,7]=>[4,6,3,2,7,5,1]=>[2,1,2,1,1]
[1,4,6,2,3,7,5]=>[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]=>[1,2,2,1,1]
[1,4,6,2,5,3,7]=>[2,6,4,5,1,3,7]=>[6,2,4,3,7,5,1]=>[1,2,2,1,1]
[1,4,6,2,5,7,3]=>[2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2]=>[1,1,3,1,1]
[1,4,6,2,7,3,5]=>[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>[1,1,3,1,1]
[1,4,6,2,7,5,3]=>[7,2,6,4,1,3,5]=>[1,6,2,4,7,5,3]=>[2,3,1,1]
[1,4,6,3,2,5,7]=>[2,5,4,6,1,3,7]=>[6,3,4,2,7,5,1]=>[1,2,2,1,1]
[1,4,6,3,2,7,5]=>[2,4,7,5,1,3,6]=>[6,4,1,3,7,5,2]=>[1,1,3,1,1]
[1,4,6,3,5,2,7]=>[2,4,6,5,1,3,7]=>[6,4,2,3,7,5,1]=>[1,1,3,1,1]
[1,4,6,3,5,7,2]=>[2,4,5,3,7,1,6]=>[6,4,3,5,1,7,2]=>[1,1,2,2,1]
[1,4,6,3,7,2,5]=>[2,4,6,3,7,1,5]=>[6,4,2,5,1,7,3]=>[1,1,2,2,1]
[1,4,6,3,7,5,2]=>[7,2,4,3,6,1,5]=>[1,6,4,5,2,7,3]=>[2,2,2,1]
[1,4,6,5,2,3,7]=>[2,5,6,4,1,3,7]=>[6,3,2,4,7,5,1]=>[1,1,3,1,1]
[1,4,6,5,2,7,3]=>[7,2,5,4,1,3,6]=>[1,6,3,4,7,5,2]=>[2,3,1,1]
[1,4,6,5,3,2,7]=>[6,2,5,4,1,3,7]=>[2,6,3,4,7,5,1]=>[2,3,1,1]
[1,4,6,5,3,7,2]=>[5,2,4,3,7,1,6]=>[3,6,4,5,1,7,2]=>[2,2,2,1]
[1,4,6,5,7,2,3]=>[6,2,4,3,7,1,5]=>[2,6,4,5,1,7,3]=>[2,2,2,1]
[1,4,6,5,7,3,2]=>[4,2,3,7,6,1,5]=>[4,6,5,1,2,7,3]=>[2,1,3,1]
[1,4,6,7,2,3,5]=>[2,5,6,3,7,1,4]=>[6,3,2,5,1,7,4]=>[1,1,2,2,1]
[1,4,6,7,2,5,3]=>[7,2,5,3,6,1,4]=>[1,6,3,5,2,7,4]=>[2,2,2,1]
[1,4,6,7,3,2,5]=>[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>[2,2,2,1]
[1,4,6,7,3,5,2]=>[5,2,3,7,6,1,4]=>[3,6,5,1,2,7,4]=>[2,1,3,1]
[1,4,6,7,5,2,3]=>[6,2,3,7,5,1,4]=>[2,6,5,1,3,7,4]=>[2,1,3,1]
[1,4,6,7,5,3,2]=>[3,7,2,6,5,1,4]=>[5,1,6,2,3,7,4]=>[1,2,3,1]
[1,4,7,2,3,5,6]=>[4,2,5,6,7,1,3]=>[4,6,3,2,1,7,5]=>[2,1,1,2,1]
[1,4,7,2,3,6,5]=>[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]=>[1,2,1,2,1]
[1,4,7,2,5,3,6]=>[2,6,4,5,7,1,3]=>[6,2,4,3,1,7,5]=>[1,2,1,2,1]
[1,4,7,2,5,6,3]=>[2,5,7,4,6,1,3]=>[6,3,1,4,2,7,5]=>[1,1,2,2,1]
[1,4,7,2,6,3,5]=>[2,6,7,4,5,1,3]=>[6,2,1,4,3,7,5]=>[1,1,2,2,1]
[1,4,7,2,6,5,3]=>[7,2,6,4,5,1,3]=>[1,6,2,4,3,7,5]=>[2,2,2,1]
[1,4,7,3,2,5,6]=>[2,5,4,6,7,1,3]=>[6,3,4,2,1,7,5]=>[1,2,1,2,1]
[1,4,7,3,2,6,5]=>[2,4,7,5,6,1,3]=>[6,4,1,3,2,7,5]=>[1,1,2,2,1]
[1,4,7,3,5,2,6]=>[2,4,6,5,7,1,3]=>[6,4,2,3,1,7,5]=>[1,1,2,2,1]
[1,4,7,3,5,6,2]=>[2,4,5,7,6,1,3]=>[6,4,3,1,2,7,5]=>[1,1,1,3,1]
[1,4,7,3,6,2,5]=>[2,4,6,7,5,1,3]=>[6,4,2,1,3,7,5]=>[1,1,1,3,1]
[1,4,7,3,6,5,2]=>[7,2,4,6,5,1,3]=>[1,6,4,2,3,7,5]=>[2,1,3,1]
[1,4,7,5,2,3,6]=>[2,5,6,4,7,1,3]=>[6,3,2,4,1,7,5]=>[1,1,2,2,1]
[1,4,7,5,2,6,3]=>[7,2,5,4,6,1,3]=>[1,6,3,4,2,7,5]=>[2,2,2,1]
[1,4,7,5,3,2,6]=>[6,2,5,4,7,1,3]=>[2,6,3,4,1,7,5]=>[2,2,2,1]
[1,4,7,5,3,6,2]=>[5,2,4,7,6,1,3]=>[3,6,4,1,2,7,5]=>[2,1,3,1]
[1,4,7,5,6,2,3]=>[6,2,4,7,5,1,3]=>[2,6,4,1,3,7,5]=>[2,1,3,1]
[1,4,7,5,6,3,2]=>[4,7,2,6,5,1,3]=>[4,1,6,2,3,7,5]=>[1,2,3,1]
[1,4,7,6,2,3,5]=>[2,5,6,7,4,1,3]=>[6,3,2,1,4,7,5]=>[1,1,1,3,1]
[1,4,7,6,2,5,3]=>[7,2,5,6,4,1,3]=>[1,6,3,2,4,7,5]=>[2,1,3,1]
[1,4,7,6,3,2,5]=>[6,2,5,7,4,1,3]=>[2,6,3,1,4,7,5]=>[2,1,3,1]
[1,4,7,6,3,5,2]=>[5,7,2,6,4,1,3]=>[3,1,6,2,4,7,5]=>[1,2,3,1]
[1,4,7,6,5,2,3]=>[6,7,2,5,4,1,3]=>[2,1,6,3,4,7,5]=>[1,2,3,1]
[1,4,7,6,5,3,2]=>[7,6,2,5,4,1,3]=>[1,2,6,3,4,7,5]=>[3,3,1]
[1,5,2,3,4,6,7]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>[1,1,2,1,1,1]
[1,5,2,3,4,7,6]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>[2,2,1,1,1]
[1,5,2,3,6,4,7]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>[2,2,1,1,1]
[1,5,2,3,6,7,4]=>[5,7,3,1,2,4,6]=>[3,1,5,7,6,4,2]=>[1,3,1,1,1]
[1,5,2,3,7,4,6]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>[1,3,1,1,1]
[1,5,2,3,7,6,4]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[4,1,1,1]
[1,5,2,4,3,6,7]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>[2,2,1,1,1]
[1,5,2,4,3,7,6]=>[4,7,3,1,2,5,6]=>[4,1,5,7,6,3,2]=>[1,3,1,1,1]
[1,5,2,4,6,3,7]=>[4,6,3,1,2,5,7]=>[4,2,5,7,6,3,1]=>[1,3,1,1,1]
[1,5,2,4,6,7,3]=>[4,5,2,7,1,3,6]=>[4,3,6,1,7,5,2]=>[1,2,2,1,1]
[1,5,2,4,7,3,6]=>[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>[1,2,2,1,1]
[1,5,2,4,7,6,3]=>[7,4,2,6,1,3,5]=>[1,4,6,2,7,5,3]=>[3,2,1,1]
[1,5,2,6,3,4,7]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>[1,3,1,1,1]
[1,5,2,6,3,7,4]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[4,1,1,1]
[1,5,2,6,4,3,7]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[4,1,1,1]
[1,5,2,6,4,7,3]=>[5,4,2,7,1,3,6]=>[3,4,6,1,7,5,2]=>[3,2,1,1]
[1,5,2,6,7,3,4]=>[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>[3,2,1,1]
[1,5,2,6,7,4,3]=>[4,2,7,6,1,3,5]=>[4,6,1,2,7,5,3]=>[2,3,1,1]
[1,5,2,7,3,4,6]=>[5,6,2,7,1,3,4]=>[3,2,6,1,7,5,4]=>[1,2,2,1,1]
[1,5,2,7,3,6,4]=>[7,5,2,6,1,3,4]=>[1,3,6,2,7,5,4]=>[3,2,1,1]
[1,5,2,7,4,3,6]=>[6,5,2,7,1,3,4]=>[2,3,6,1,7,5,4]=>[3,2,1,1]
[1,5,2,7,4,6,3]=>[5,2,7,6,1,3,4]=>[3,6,1,2,7,5,4]=>[2,3,1,1]
[1,5,2,7,6,3,4]=>[6,2,7,5,1,3,4]=>[2,6,1,3,7,5,4]=>[2,3,1,1]
[1,5,2,7,6,4,3]=>[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]=>[1,4,1,1]
[1,5,3,2,4,6,7]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>[2,2,1,1,1]
[1,5,3,2,4,7,6]=>[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>[1,3,1,1,1]
[1,5,3,2,6,4,7]=>[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>[1,3,1,1,1]
[1,5,3,2,6,7,4]=>[3,5,2,7,1,4,6]=>[5,3,6,1,7,4,2]=>[1,2,2,1,1]
[1,5,3,2,7,4,6]=>[3,6,2,7,1,4,5]=>[5,2,6,1,7,4,3]=>[1,2,2,1,1]
[1,5,3,2,7,6,4]=>[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>[3,2,1,1]
[1,5,3,4,2,6,7]=>[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>[1,3,1,1,1]
[1,5,3,4,2,7,6]=>[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>[1,2,2,1,1]
[1,5,3,4,6,2,7]=>[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>[1,2,2,1,1]
[1,5,3,4,6,7,2]=>[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>[1,2,1,2,1]
[1,5,3,4,7,2,6]=>[3,4,2,6,7,1,5]=>[5,4,6,2,1,7,3]=>[1,2,1,2,1]
[1,5,3,4,7,6,2]=>[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>[3,1,2,1]
[1,5,3,6,2,4,7]=>[3,5,2,6,1,4,7]=>[5,3,6,2,7,4,1]=>[1,2,2,1,1]
[1,5,3,6,2,7,4]=>[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>[3,2,1,1]
[1,5,3,6,4,2,7]=>[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>[3,2,1,1]
[1,5,3,6,4,7,2]=>[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>[3,1,2,1]
[1,5,3,6,7,2,4]=>[6,3,2,4,7,1,5]=>[2,5,6,4,1,7,3]=>[3,1,2,1]
[1,5,3,6,7,4,2]=>[4,2,7,3,6,1,5]=>[4,6,1,5,2,7,3]=>[2,2,2,1]
[1,5,3,7,2,4,6]=>[3,5,2,6,7,1,4]=>[5,3,6,2,1,7,4]=>[1,2,1,2,1]
[1,5,3,7,2,6,4]=>[7,3,2,5,6,1,4]=>[1,5,6,3,2,7,4]=>[3,1,2,1]
[1,5,3,7,4,2,6]=>[6,3,2,5,7,1,4]=>[2,5,6,3,1,7,4]=>[3,1,2,1]
[1,5,3,7,4,6,2]=>[5,2,7,3,6,1,4]=>[3,6,1,5,2,7,4]=>[2,2,2,1]
[1,5,3,7,6,2,4]=>[6,2,7,3,5,1,4]=>[2,6,1,5,3,7,4]=>[2,2,2,1]
[1,5,3,7,6,4,2]=>[2,7,6,3,5,1,4]=>[6,1,2,5,3,7,4]=>[1,3,2,1]
[1,5,4,2,3,6,7]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>[1,3,1,1,1]
[1,5,4,2,3,7,6]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[4,1,1,1]
[1,5,4,2,6,3,7]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[4,1,1,1]
[1,5,4,2,6,7,3]=>[5,3,2,7,1,4,6]=>[3,5,6,1,7,4,2]=>[3,2,1,1]
[1,5,4,2,7,3,6]=>[6,3,2,7,1,4,5]=>[2,5,6,1,7,4,3]=>[3,2,1,1]
[1,5,4,2,7,6,3]=>[3,2,7,6,1,4,5]=>[5,6,1,2,7,4,3]=>[2,3,1,1]
[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[4,1,1,1]
[1,5,4,3,2,7,6]=>[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>[3,2,1,1]
[1,5,4,3,6,2,7]=>[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>[3,2,1,1]
[1,5,4,3,6,7,2]=>[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>[3,1,2,1]
[1,5,4,3,7,2,6]=>[4,3,2,6,7,1,5]=>[4,5,6,2,1,7,3]=>[3,1,2,1]
[1,5,4,3,7,6,2]=>[3,2,7,4,6,1,5]=>[5,6,1,4,2,7,3]=>[2,2,2,1]
[1,5,4,6,2,3,7]=>[5,3,2,6,1,4,7]=>[3,5,6,2,7,4,1]=>[3,2,1,1]
[1,5,4,6,2,7,3]=>[3,2,7,5,1,4,6]=>[5,6,1,3,7,4,2]=>[2,3,1,1]
[1,5,4,6,3,2,7]=>[3,2,6,5,1,4,7]=>[5,6,2,3,7,4,1]=>[2,3,1,1]
[1,5,4,6,3,7,2]=>[3,2,5,4,7,1,6]=>[5,6,3,4,1,7,2]=>[2,2,2,1]
[1,5,4,6,7,2,3]=>[3,2,6,4,7,1,5]=>[5,6,2,4,1,7,3]=>[2,2,2,1]
[1,5,4,6,7,3,2]=>[3,2,4,7,6,1,5]=>[5,6,4,1,2,7,3]=>[2,1,3,1]
[1,5,4,7,2,3,6]=>[5,3,2,6,7,1,4]=>[3,5,6,2,1,7,4]=>[3,1,2,1]
[1,5,4,7,2,6,3]=>[3,2,7,5,6,1,4]=>[5,6,1,3,2,7,4]=>[2,2,2,1]
[1,5,4,7,3,2,6]=>[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>[2,2,2,1]
[1,5,4,7,3,6,2]=>[3,2,5,7,6,1,4]=>[5,6,3,1,2,7,4]=>[2,1,3,1]
[1,5,4,7,6,2,3]=>[3,2,6,7,5,1,4]=>[5,6,2,1,3,7,4]=>[2,1,3,1]
[1,5,4,7,6,3,2]=>[2,7,3,6,5,1,4]=>[6,1,5,2,3,7,4]=>[1,2,3,1]
[1,5,6,2,3,4,7]=>[4,5,2,6,1,3,7]=>[4,3,6,2,7,5,1]=>[1,2,2,1,1]
[1,5,6,2,3,7,4]=>[7,4,2,5,1,3,6]=>[1,4,6,3,7,5,2]=>[3,2,1,1]
[1,5,6,2,4,3,7]=>[6,4,2,5,1,3,7]=>[2,4,6,3,7,5,1]=>[3,2,1,1]
[1,5,6,2,4,7,3]=>[5,2,7,4,1,3,6]=>[3,6,1,4,7,5,2]=>[2,3,1,1]
[1,5,6,2,7,3,4]=>[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>[2,3,1,1]
[1,5,6,2,7,4,3]=>[2,7,6,4,1,3,5]=>[6,1,2,4,7,5,3]=>[1,4,1,1]
[1,5,6,3,2,4,7]=>[5,4,2,6,1,3,7]=>[3,4,6,2,7,5,1]=>[3,2,1,1]
[1,5,6,3,2,7,4]=>[4,2,7,5,1,3,6]=>[4,6,1,3,7,5,2]=>[2,3,1,1]
[1,5,6,3,4,2,7]=>[4,2,6,5,1,3,7]=>[4,6,2,3,7,5,1]=>[2,3,1,1]
[1,5,6,3,4,7,2]=>[4,2,5,3,7,1,6]=>[4,6,3,5,1,7,2]=>[2,2,2,1]
[1,5,6,3,7,2,4]=>[4,2,6,3,7,1,5]=>[4,6,2,5,1,7,3]=>[2,2,2,1]
[1,5,6,3,7,4,2]=>[2,7,4,3,6,1,5]=>[6,1,4,5,2,7,3]=>[1,3,2,1]
[1,5,6,4,2,3,7]=>[5,2,6,4,1,3,7]=>[3,6,2,4,7,5,1]=>[2,3,1,1]
[1,5,6,4,2,7,3]=>[2,7,5,4,1,3,6]=>[6,1,3,4,7,5,2]=>[1,4,1,1]
[1,5,6,4,3,2,7]=>[2,6,5,4,1,3,7]=>[6,2,3,4,7,5,1]=>[1,4,1,1]
[1,5,6,4,3,7,2]=>[2,5,4,3,7,1,6]=>[6,3,4,5,1,7,2]=>[1,3,2,1]
[1,5,6,4,7,2,3]=>[2,6,4,3,7,1,5]=>[6,2,4,5,1,7,3]=>[1,3,2,1]
[1,5,6,4,7,3,2]=>[2,4,3,7,6,1,5]=>[6,4,5,1,2,7,3]=>[1,2,3,1]
[1,5,6,7,2,3,4]=>[5,2,6,3,7,1,4]=>[3,6,2,5,1,7,4]=>[2,2,2,1]
[1,5,6,7,2,4,3]=>[2,7,5,3,6,1,4]=>[6,1,3,5,2,7,4]=>[1,3,2,1]
[1,5,6,7,3,2,4]=>[2,6,5,3,7,1,4]=>[6,2,3,5,1,7,4]=>[1,3,2,1]
[1,5,6,7,3,4,2]=>[2,5,3,7,6,1,4]=>[6,3,5,1,2,7,4]=>[1,2,3,1]
[1,5,6,7,4,2,3]=>[2,6,3,7,5,1,4]=>[6,2,5,1,3,7,4]=>[1,2,3,1]
[1,5,6,7,4,3,2]=>[2,3,7,6,5,1,4]=>[6,5,1,2,3,7,4]=>[1,1,4,1]
[1,5,7,2,3,4,6]=>[4,5,2,6,7,1,3]=>[4,3,6,2,1,7,5]=>[1,2,1,2,1]
[1,5,7,2,3,6,4]=>[7,4,2,5,6,1,3]=>[1,4,6,3,2,7,5]=>[3,1,2,1]
[1,5,7,2,4,3,6]=>[6,4,2,5,7,1,3]=>[2,4,6,3,1,7,5]=>[3,1,2,1]
[1,5,7,2,4,6,3]=>[5,2,7,4,6,1,3]=>[3,6,1,4,2,7,5]=>[2,2,2,1]
[1,5,7,2,6,3,4]=>[6,2,7,4,5,1,3]=>[2,6,1,4,3,7,5]=>[2,2,2,1]
[1,5,7,2,6,4,3]=>[2,7,6,4,5,1,3]=>[6,1,2,4,3,7,5]=>[1,3,2,1]
[1,5,7,3,2,4,6]=>[5,4,2,6,7,1,3]=>[3,4,6,2,1,7,5]=>[3,1,2,1]
[1,5,7,3,2,6,4]=>[4,2,7,5,6,1,3]=>[4,6,1,3,2,7,5]=>[2,2,2,1]
[1,5,7,3,4,2,6]=>[4,2,6,5,7,1,3]=>[4,6,2,3,1,7,5]=>[2,2,2,1]
[1,5,7,3,4,6,2]=>[4,2,5,7,6,1,3]=>[4,6,3,1,2,7,5]=>[2,1,3,1]
[1,5,7,3,6,2,4]=>[4,2,6,7,5,1,3]=>[4,6,2,1,3,7,5]=>[2,1,3,1]
[1,5,7,3,6,4,2]=>[2,7,4,6,5,1,3]=>[6,1,4,2,3,7,5]=>[1,2,3,1]
[1,5,7,4,2,3,6]=>[5,2,6,4,7,1,3]=>[3,6,2,4,1,7,5]=>[2,2,2,1]
[1,5,7,4,2,6,3]=>[2,7,5,4,6,1,3]=>[6,1,3,4,2,7,5]=>[1,3,2,1]
[1,5,7,4,3,2,6]=>[2,6,5,4,7,1,3]=>[6,2,3,4,1,7,5]=>[1,3,2,1]
[1,5,7,4,3,6,2]=>[2,5,4,7,6,1,3]=>[6,3,4,1,2,7,5]=>[1,2,3,1]
[1,5,7,4,6,2,3]=>[2,6,4,7,5,1,3]=>[6,2,4,1,3,7,5]=>[1,2,3,1]
[1,5,7,4,6,3,2]=>[2,4,7,6,5,1,3]=>[6,4,1,2,3,7,5]=>[1,1,4,1]
[1,5,7,6,2,3,4]=>[5,2,6,7,4,1,3]=>[3,6,2,1,4,7,5]=>[2,1,3,1]
[1,5,7,6,2,4,3]=>[2,7,5,6,4,1,3]=>[6,1,3,2,4,7,5]=>[1,2,3,1]
[1,5,7,6,3,2,4]=>[2,6,5,7,4,1,3]=>[6,2,3,1,4,7,5]=>[1,2,3,1]
[1,5,7,6,3,4,2]=>[2,5,7,6,4,1,3]=>[6,3,1,2,4,7,5]=>[1,1,4,1]
[1,5,7,6,4,2,3]=>[2,6,7,5,4,1,3]=>[6,2,1,3,4,7,5]=>[1,1,4,1]
[1,5,7,6,4,3,2]=>[7,2,6,5,4,1,3]=>[1,6,2,3,4,7,5]=>[2,4,1]
[1,6,2,3,4,5,7]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>[1,1,1,2,1,1]
[1,6,2,3,4,7,5]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>[2,1,2,1,1]
[1,6,2,3,5,4,7]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>[2,1,2,1,1]
[1,6,2,3,5,7,4]=>[5,7,3,4,1,2,6]=>[3,1,5,4,7,6,2]=>[1,2,2,1,1]
[1,6,2,3,7,4,5]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>[1,2,2,1,1]
[1,6,2,3,7,5,4]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>[3,2,1,1]
[1,6,2,4,3,5,7]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>[2,1,2,1,1]
[1,6,2,4,3,7,5]=>[4,7,3,5,1,2,6]=>[4,1,5,3,7,6,2]=>[1,2,2,1,1]
[1,6,2,4,5,3,7]=>[4,6,3,5,1,2,7]=>[4,2,5,3,7,6,1]=>[1,2,2,1,1]
[1,6,2,4,5,7,3]=>[4,5,7,3,1,2,6]=>[4,3,1,5,7,6,2]=>[1,1,3,1,1]
[1,6,2,4,7,3,5]=>[4,6,7,3,1,2,5]=>[4,2,1,5,7,6,3]=>[1,1,3,1,1]
[1,6,2,4,7,5,3]=>[7,4,6,3,1,2,5]=>[1,4,2,5,7,6,3]=>[2,3,1,1]
[1,6,2,5,3,4,7]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>[1,2,2,1,1]
[1,6,2,5,3,7,4]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>[3,2,1,1]
[1,6,2,5,4,3,7]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>[3,2,1,1]
[1,6,2,5,4,7,3]=>[5,4,7,3,1,2,6]=>[3,4,1,5,7,6,2]=>[2,3,1,1]
[1,6,2,5,7,3,4]=>[6,4,7,3,1,2,5]=>[2,4,1,5,7,6,3]=>[2,3,1,1]
[1,6,2,5,7,4,3]=>[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>[1,4,1,1]
[1,6,2,7,3,4,5]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>[1,1,3,1,1]
[1,6,2,7,3,5,4]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>[2,3,1,1]
[1,6,2,7,4,3,5]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>[2,3,1,1]
[1,6,2,7,4,5,3]=>[5,7,6,3,1,2,4]=>[3,1,2,5,7,6,4]=>[1,4,1,1]
[1,6,2,7,5,3,4]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>[1,4,1,1]
[1,6,2,7,5,4,3]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[5,1,1]
[1,6,3,2,4,5,7]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>[2,1,2,1,1]
[1,6,3,2,4,7,5]=>[3,7,4,5,1,2,6]=>[5,1,4,3,7,6,2]=>[1,2,2,1,1]
[1,6,3,2,5,4,7]=>[3,6,4,5,1,2,7]=>[5,2,4,3,7,6,1]=>[1,2,2,1,1]
[1,6,3,2,5,7,4]=>[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>[1,1,3,1,1]
[1,6,3,2,7,4,5]=>[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>[1,1,3,1,1]
[1,6,3,2,7,5,4]=>[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>[2,3,1,1]
[1,6,3,4,2,5,7]=>[3,5,4,6,1,2,7]=>[5,3,4,2,7,6,1]=>[1,2,2,1,1]
[1,6,3,4,2,7,5]=>[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>[1,1,3,1,1]
[1,6,3,4,5,2,7]=>[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>[1,1,3,1,1]
[1,6,3,4,5,7,2]=>[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>[1,1,2,2,1]
[1,6,3,4,7,2,5]=>[3,4,6,2,7,1,5]=>[5,4,2,6,1,7,3]=>[1,1,2,2,1]
[1,6,3,4,7,5,2]=>[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>[2,2,2,1]
[1,6,3,5,2,4,7]=>[3,5,6,4,1,2,7]=>[5,3,2,4,7,6,1]=>[1,1,3,1,1]
[1,6,3,5,2,7,4]=>[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>[2,3,1,1]
[1,6,3,5,4,2,7]=>[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>[2,3,1,1]
[1,6,3,5,4,7,2]=>[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>[2,2,2,1]
[1,6,3,5,7,2,4]=>[6,3,4,2,7,1,5]=>[2,5,4,6,1,7,3]=>[2,2,2,1]
[1,6,3,5,7,4,2]=>[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>[1,3,2,1]
[1,6,3,7,2,4,5]=>[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>[1,1,2,2,1]
[1,6,3,7,2,5,4]=>[7,3,5,2,6,1,4]=>[1,5,3,6,2,7,4]=>[2,2,2,1]
[1,6,3,7,4,2,5]=>[6,3,5,2,7,1,4]=>[2,5,3,6,1,7,4]=>[2,2,2,1]
[1,6,3,7,4,5,2]=>[5,7,3,2,6,1,4]=>[3,1,5,6,2,7,4]=>[1,3,2,1]
[1,6,3,7,5,2,4]=>[6,7,3,2,5,1,4]=>[2,1,5,6,3,7,4]=>[1,3,2,1]
[1,6,3,7,5,4,2]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>[4,2,1]
[1,6,4,2,3,5,7]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>[1,2,2,1,1]
[1,6,4,2,3,7,5]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>[3,2,1,1]
[1,6,4,2,5,3,7]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>[3,2,1,1]
[1,6,4,2,5,7,3]=>[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>[2,3,1,1]
[1,6,4,2,7,3,5]=>[6,3,7,4,1,2,5]=>[2,5,1,4,7,6,3]=>[2,3,1,1]
[1,6,4,2,7,5,3]=>[3,7,6,4,1,2,5]=>[5,1,2,4,7,6,3]=>[1,4,1,1]
[1,6,4,3,2,5,7]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>[3,2,1,1]
[1,6,4,3,2,7,5]=>[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>[2,3,1,1]
[1,6,4,3,5,2,7]=>[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>[2,3,1,1]
[1,6,4,3,5,7,2]=>[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>[2,2,2,1]
[1,6,4,3,7,2,5]=>[4,3,6,2,7,1,5]=>[4,5,2,6,1,7,3]=>[2,2,2,1]
[1,6,4,3,7,5,2]=>[3,7,4,2,6,1,5]=>[5,1,4,6,2,7,3]=>[1,3,2,1]
[1,6,4,5,2,3,7]=>[5,3,6,4,1,2,7]=>[3,5,2,4,7,6,1]=>[2,3,1,1]
[1,6,4,5,2,7,3]=>[3,7,5,4,1,2,6]=>[5,1,3,4,7,6,2]=>[1,4,1,1]
[1,6,4,5,3,2,7]=>[3,6,5,4,1,2,7]=>[5,2,3,4,7,6,1]=>[1,4,1,1]
[1,6,4,5,3,7,2]=>[3,5,4,2,7,1,6]=>[5,3,4,6,1,7,2]=>[1,3,2,1]
[1,6,4,5,7,2,3]=>[3,6,4,2,7,1,5]=>[5,2,4,6,1,7,3]=>[1,3,2,1]
[1,6,4,5,7,3,2]=>[3,4,2,7,6,1,5]=>[5,4,6,1,2,7,3]=>[1,2,3,1]
[1,6,4,7,2,3,5]=>[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>[2,2,2,1]
[1,6,4,7,2,5,3]=>[3,7,5,2,6,1,4]=>[5,1,3,6,2,7,4]=>[1,3,2,1]
[1,6,4,7,3,2,5]=>[3,6,5,2,7,1,4]=>[5,2,3,6,1,7,4]=>[1,3,2,1]
[1,6,4,7,3,5,2]=>[3,5,2,7,6,1,4]=>[5,3,6,1,2,7,4]=>[1,2,3,1]
[1,6,4,7,5,2,3]=>[3,6,2,7,5,1,4]=>[5,2,6,1,3,7,4]=>[1,2,3,1]
[1,6,4,7,5,3,2]=>[7,3,2,6,5,1,4]=>[1,5,6,2,3,7,4]=>[3,3,1]
[1,6,5,2,3,4,7]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>[1,1,3,1,1]
[1,6,5,2,3,7,4]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>[2,3,1,1]
[1,6,5,2,4,3,7]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>[2,3,1,1]
[1,6,5,2,4,7,3]=>[5,7,4,3,1,2,6]=>[3,1,4,5,7,6,2]=>[1,4,1,1]
[1,6,5,2,7,3,4]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>[1,4,1,1]
[1,6,5,2,7,4,3]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[5,1,1]
[1,6,5,3,2,4,7]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>[2,3,1,1]
[1,6,5,3,2,7,4]=>[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>[1,4,1,1]
[1,6,5,3,4,2,7]=>[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>[1,4,1,1]
[1,6,5,3,4,7,2]=>[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>[1,3,2,1]
[1,6,5,3,7,2,4]=>[4,6,3,2,7,1,5]=>[4,2,5,6,1,7,3]=>[1,3,2,1]
[1,6,5,3,7,4,2]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>[4,2,1]
[1,6,5,4,2,3,7]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>[1,4,1,1]
[1,6,5,4,2,7,3]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[5,1,1]
[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[5,1,1]
[1,6,5,4,3,7,2]=>[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>[4,2,1]
[1,6,5,4,7,2,3]=>[6,4,3,2,7,1,5]=>[2,4,5,6,1,7,3]=>[4,2,1]
[1,6,5,4,7,3,2]=>[4,3,2,7,6,1,5]=>[4,5,6,1,2,7,3]=>[3,3,1]
[1,6,5,7,2,3,4]=>[5,6,3,2,7,1,4]=>[3,2,5,6,1,7,4]=>[1,3,2,1]
[1,6,5,7,2,4,3]=>[7,5,3,2,6,1,4]=>[1,3,5,6,2,7,4]=>[4,2,1]
[1,6,5,7,3,2,4]=>[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>[4,2,1]
[1,6,5,7,3,4,2]=>[5,3,2,7,6,1,4]=>[3,5,6,1,2,7,4]=>[3,3,1]
[1,6,5,7,4,2,3]=>[6,3,2,7,5,1,4]=>[2,5,6,1,3,7,4]=>[3,3,1]
[1,6,5,7,4,3,2]=>[3,2,7,6,5,1,4]=>[5,6,1,2,3,7,4]=>[2,4,1]
[1,6,7,2,3,4,5]=>[4,5,6,2,7,1,3]=>[4,3,2,6,1,7,5]=>[1,1,2,2,1]
[1,6,7,2,3,5,4]=>[7,4,5,2,6,1,3]=>[1,4,3,6,2,7,5]=>[2,2,2,1]
[1,6,7,2,4,3,5]=>[6,4,5,2,7,1,3]=>[2,4,3,6,1,7,5]=>[2,2,2,1]
[1,6,7,2,4,5,3]=>[5,7,4,2,6,1,3]=>[3,1,4,6,2,7,5]=>[1,3,2,1]
[1,6,7,2,5,3,4]=>[6,7,4,2,5,1,3]=>[2,1,4,6,3,7,5]=>[1,3,2,1]
[1,6,7,2,5,4,3]=>[7,6,4,2,5,1,3]=>[1,2,4,6,3,7,5]=>[4,2,1]
[1,6,7,3,2,4,5]=>[5,4,6,2,7,1,3]=>[3,4,2,6,1,7,5]=>[2,2,2,1]
[1,6,7,3,2,5,4]=>[4,7,5,2,6,1,3]=>[4,1,3,6,2,7,5]=>[1,3,2,1]
[1,6,7,3,4,2,5]=>[4,6,5,2,7,1,3]=>[4,2,3,6,1,7,5]=>[1,3,2,1]
[1,6,7,3,4,5,2]=>[4,5,2,7,6,1,3]=>[4,3,6,1,2,7,5]=>[1,2,3,1]
[1,6,7,3,5,2,4]=>[4,6,2,7,5,1,3]=>[4,2,6,1,3,7,5]=>[1,2,3,1]
[1,6,7,3,5,4,2]=>[7,4,2,6,5,1,3]=>[1,4,6,2,3,7,5]=>[3,3,1]
[1,6,7,4,2,3,5]=>[5,6,4,2,7,1,3]=>[3,2,4,6,1,7,5]=>[1,3,2,1]
[1,6,7,4,2,5,3]=>[7,5,4,2,6,1,3]=>[1,3,4,6,2,7,5]=>[4,2,1]
[1,6,7,4,3,2,5]=>[6,5,4,2,7,1,3]=>[2,3,4,6,1,7,5]=>[4,2,1]
[1,6,7,4,3,5,2]=>[5,4,2,7,6,1,3]=>[3,4,6,1,2,7,5]=>[3,3,1]
[1,6,7,4,5,2,3]=>[6,4,2,7,5,1,3]=>[2,4,6,1,3,7,5]=>[3,3,1]
[1,6,7,4,5,3,2]=>[4,2,7,6,5,1,3]=>[4,6,1,2,3,7,5]=>[2,4,1]
[1,6,7,5,2,3,4]=>[5,6,2,7,4,1,3]=>[3,2,6,1,4,7,5]=>[1,2,3,1]
[1,6,7,5,2,4,3]=>[7,5,2,6,4,1,3]=>[1,3,6,2,4,7,5]=>[3,3,1]
[1,6,7,5,3,2,4]=>[6,5,2,7,4,1,3]=>[2,3,6,1,4,7,5]=>[3,3,1]
[1,6,7,5,3,4,2]=>[5,2,7,6,4,1,3]=>[3,6,1,2,4,7,5]=>[2,4,1]
[1,6,7,5,4,2,3]=>[6,2,7,5,4,1,3]=>[2,6,1,3,4,7,5]=>[2,4,1]
[1,6,7,5,4,3,2]=>[2,7,6,5,4,1,3]=>[6,1,2,3,4,7,5]=>[1,5,1]
[1,7,2,3,4,5,6]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>[1,1,1,1,2,1]
[1,7,2,3,4,6,5]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>[2,1,1,2,1]
[1,7,2,3,5,4,6]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>[2,1,1,2,1]
[1,7,2,3,5,6,4]=>[5,7,3,4,6,1,2]=>[3,1,5,4,2,7,6]=>[1,2,1,2,1]
[1,7,2,3,6,4,5]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[1,2,1,2,1]
[1,7,2,3,6,5,4]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>[3,1,2,1]
[1,7,2,4,3,5,6]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>[2,1,1,2,1]
[1,7,2,4,3,6,5]=>[4,7,3,5,6,1,2]=>[4,1,5,3,2,7,6]=>[1,2,1,2,1]
[1,7,2,4,5,3,6]=>[4,6,3,5,7,1,2]=>[4,2,5,3,1,7,6]=>[1,2,1,2,1]
[1,7,2,4,5,6,3]=>[4,5,7,3,6,1,2]=>[4,3,1,5,2,7,6]=>[1,1,2,2,1]
[1,7,2,4,6,3,5]=>[4,6,7,3,5,1,2]=>[4,2,1,5,3,7,6]=>[1,1,2,2,1]
[1,7,2,4,6,5,3]=>[7,4,6,3,5,1,2]=>[1,4,2,5,3,7,6]=>[2,2,2,1]
[1,7,2,5,3,4,6]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>[1,2,1,2,1]
[1,7,2,5,3,6,4]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>[3,1,2,1]
[1,7,2,5,4,3,6]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>[3,1,2,1]
[1,7,2,5,4,6,3]=>[5,4,7,3,6,1,2]=>[3,4,1,5,2,7,6]=>[2,2,2,1]
[1,7,2,5,6,3,4]=>[6,4,7,3,5,1,2]=>[2,4,1,5,3,7,6]=>[2,2,2,1]
[1,7,2,5,6,4,3]=>[4,7,6,3,5,1,2]=>[4,1,2,5,3,7,6]=>[1,3,2,1]
[1,7,2,6,3,4,5]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>[1,1,2,2,1]
[1,7,2,6,3,5,4]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>[2,2,2,1]
[1,7,2,6,4,3,5]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>[2,2,2,1]
[1,7,2,6,4,5,3]=>[5,7,6,3,4,1,2]=>[3,1,2,5,4,7,6]=>[1,3,2,1]
[1,7,2,6,5,3,4]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>[1,3,2,1]
[1,7,2,6,5,4,3]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>[4,2,1]
[1,7,3,2,4,5,6]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>[2,1,1,2,1]
[1,7,3,2,4,6,5]=>[3,7,4,5,6,1,2]=>[5,1,4,3,2,7,6]=>[1,2,1,2,1]
[1,7,3,2,5,4,6]=>[3,6,4,5,7,1,2]=>[5,2,4,3,1,7,6]=>[1,2,1,2,1]
[1,7,3,2,5,6,4]=>[3,5,7,4,6,1,2]=>[5,3,1,4,2,7,6]=>[1,1,2,2,1]
[1,7,3,2,6,4,5]=>[3,6,7,4,5,1,2]=>[5,2,1,4,3,7,6]=>[1,1,2,2,1]
[1,7,3,2,6,5,4]=>[7,3,6,4,5,1,2]=>[1,5,2,4,3,7,6]=>[2,2,2,1]
[1,7,3,4,2,5,6]=>[3,5,4,6,7,1,2]=>[5,3,4,2,1,7,6]=>[1,2,1,2,1]
[1,7,3,4,2,6,5]=>[3,4,7,5,6,1,2]=>[5,4,1,3,2,7,6]=>[1,1,2,2,1]
[1,7,3,4,5,2,6]=>[3,4,6,5,7,1,2]=>[5,4,2,3,1,7,6]=>[1,1,2,2,1]
[1,7,3,4,5,6,2]=>[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>[1,1,1,3,1]
[1,7,3,4,6,2,5]=>[3,4,6,7,5,1,2]=>[5,4,2,1,3,7,6]=>[1,1,1,3,1]
[1,7,3,4,6,5,2]=>[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>[2,1,3,1]
[1,7,3,5,2,4,6]=>[3,5,6,4,7,1,2]=>[5,3,2,4,1,7,6]=>[1,1,2,2,1]
[1,7,3,5,2,6,4]=>[7,3,5,4,6,1,2]=>[1,5,3,4,2,7,6]=>[2,2,2,1]
[1,7,3,5,4,2,6]=>[6,3,5,4,7,1,2]=>[2,5,3,4,1,7,6]=>[2,2,2,1]
[1,7,3,5,4,6,2]=>[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>[2,1,3,1]
[1,7,3,5,6,2,4]=>[6,3,4,7,5,1,2]=>[2,5,4,1,3,7,6]=>[2,1,3,1]
[1,7,3,5,6,4,2]=>[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>[1,2,3,1]
[1,7,3,6,2,4,5]=>[3,5,6,7,4,1,2]=>[5,3,2,1,4,7,6]=>[1,1,1,3,1]
[1,7,3,6,2,5,4]=>[7,3,5,6,4,1,2]=>[1,5,3,2,4,7,6]=>[2,1,3,1]
[1,7,3,6,4,2,5]=>[6,3,5,7,4,1,2]=>[2,5,3,1,4,7,6]=>[2,1,3,1]
[1,7,3,6,4,5,2]=>[5,7,3,6,4,1,2]=>[3,1,5,2,4,7,6]=>[1,2,3,1]
[1,7,3,6,5,2,4]=>[6,7,3,5,4,1,2]=>[2,1,5,3,4,7,6]=>[1,2,3,1]
[1,7,3,6,5,4,2]=>[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>[3,3,1]
[1,7,4,2,3,5,6]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>[1,2,1,2,1]
[1,7,4,2,3,6,5]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>[3,1,2,1]
[1,7,4,2,5,3,6]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>[3,1,2,1]
[1,7,4,2,5,6,3]=>[5,3,7,4,6,1,2]=>[3,5,1,4,2,7,6]=>[2,2,2,1]
[1,7,4,2,6,3,5]=>[6,3,7,4,5,1,2]=>[2,5,1,4,3,7,6]=>[2,2,2,1]
[1,7,4,2,6,5,3]=>[3,7,6,4,5,1,2]=>[5,1,2,4,3,7,6]=>[1,3,2,1]
[1,7,4,3,2,5,6]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>[3,1,2,1]
[1,7,4,3,2,6,5]=>[4,3,7,5,6,1,2]=>[4,5,1,3,2,7,6]=>[2,2,2,1]
[1,7,4,3,5,2,6]=>[4,3,6,5,7,1,2]=>[4,5,2,3,1,7,6]=>[2,2,2,1]
[1,7,4,3,5,6,2]=>[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>[2,1,3,1]
[1,7,4,3,6,2,5]=>[4,3,6,7,5,1,2]=>[4,5,2,1,3,7,6]=>[2,1,3,1]
[1,7,4,3,6,5,2]=>[3,7,4,6,5,1,2]=>[5,1,4,2,3,7,6]=>[1,2,3,1]
[1,7,4,5,2,3,6]=>[5,3,6,4,7,1,2]=>[3,5,2,4,1,7,6]=>[2,2,2,1]
[1,7,4,5,2,6,3]=>[3,7,5,4,6,1,2]=>[5,1,3,4,2,7,6]=>[1,3,2,1]
[1,7,4,5,3,2,6]=>[3,6,5,4,7,1,2]=>[5,2,3,4,1,7,6]=>[1,3,2,1]
[1,7,4,5,3,6,2]=>[3,5,4,7,6,1,2]=>[5,3,4,1,2,7,6]=>[1,2,3,1]
[1,7,4,5,6,2,3]=>[3,6,4,7,5,1,2]=>[5,2,4,1,3,7,6]=>[1,2,3,1]
[1,7,4,5,6,3,2]=>[3,4,7,6,5,1,2]=>[5,4,1,2,3,7,6]=>[1,1,4,1]
[1,7,4,6,2,3,5]=>[5,3,6,7,4,1,2]=>[3,5,2,1,4,7,6]=>[2,1,3,1]
[1,7,4,6,2,5,3]=>[3,7,5,6,4,1,2]=>[5,1,3,2,4,7,6]=>[1,2,3,1]
[1,7,4,6,3,2,5]=>[3,6,5,7,4,1,2]=>[5,2,3,1,4,7,6]=>[1,2,3,1]
[1,7,4,6,3,5,2]=>[3,5,7,6,4,1,2]=>[5,3,1,2,4,7,6]=>[1,1,4,1]
[1,7,4,6,5,2,3]=>[3,6,7,5,4,1,2]=>[5,2,1,3,4,7,6]=>[1,1,4,1]
[1,7,4,6,5,3,2]=>[7,3,6,5,4,1,2]=>[1,5,2,3,4,7,6]=>[2,4,1]
[1,7,5,2,3,4,6]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>[1,1,2,2,1]
[1,7,5,2,3,6,4]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>[2,2,2,1]
[1,7,5,2,4,3,6]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>[2,2,2,1]
[1,7,5,2,4,6,3]=>[5,7,4,3,6,1,2]=>[3,1,4,5,2,7,6]=>[1,3,2,1]
[1,7,5,2,6,3,4]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>[1,3,2,1]
[1,7,5,2,6,4,3]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>[4,2,1]
[1,7,5,3,2,4,6]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>[2,2,2,1]
[1,7,5,3,2,6,4]=>[4,7,5,3,6,1,2]=>[4,1,3,5,2,7,6]=>[1,3,2,1]
[1,7,5,3,4,2,6]=>[4,6,5,3,7,1,2]=>[4,2,3,5,1,7,6]=>[1,3,2,1]
[1,7,5,3,4,6,2]=>[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>[1,2,3,1]
[1,7,5,3,6,2,4]=>[4,6,3,7,5,1,2]=>[4,2,5,1,3,7,6]=>[1,2,3,1]
[1,7,5,3,6,4,2]=>[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>[3,3,1]
[1,7,5,4,2,3,6]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>[1,3,2,1]
[1,7,5,4,2,6,3]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>[4,2,1]
[1,7,5,4,3,2,6]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>[4,2,1]
[1,7,5,4,3,6,2]=>[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>[3,3,1]
[1,7,5,4,6,2,3]=>[6,4,3,7,5,1,2]=>[2,4,5,1,3,7,6]=>[3,3,1]
[1,7,5,4,6,3,2]=>[4,3,7,6,5,1,2]=>[4,5,1,2,3,7,6]=>[2,4,1]
[1,7,5,6,2,3,4]=>[5,6,3,7,4,1,2]=>[3,2,5,1,4,7,6]=>[1,2,3,1]
[1,7,5,6,2,4,3]=>[7,5,3,6,4,1,2]=>[1,3,5,2,4,7,6]=>[3,3,1]
[1,7,5,6,3,2,4]=>[6,5,3,7,4,1,2]=>[2,3,5,1,4,7,6]=>[3,3,1]
[1,7,5,6,3,4,2]=>[5,3,7,6,4,1,2]=>[3,5,1,2,4,7,6]=>[2,4,1]
[1,7,5,6,4,2,3]=>[6,3,7,5,4,1,2]=>[2,5,1,3,4,7,6]=>[2,4,1]
[1,7,5,6,4,3,2]=>[3,7,6,5,4,1,2]=>[5,1,2,3,4,7,6]=>[1,5,1]
[1,7,6,2,3,4,5]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>[1,1,1,3,1]
[1,7,6,2,3,5,4]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>[2,1,3,1]
[1,7,6,2,4,3,5]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>[2,1,3,1]
[1,7,6,2,4,5,3]=>[5,7,4,6,3,1,2]=>[3,1,4,2,5,7,6]=>[1,2,3,1]
[1,7,6,2,5,3,4]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>[1,2,3,1]
[1,7,6,2,5,4,3]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>[3,3,1]
[1,7,6,3,2,4,5]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>[2,1,3,1]
[1,7,6,3,2,5,4]=>[4,7,5,6,3,1,2]=>[4,1,3,2,5,7,6]=>[1,2,3,1]
[1,7,6,3,4,2,5]=>[4,6,5,7,3,1,2]=>[4,2,3,1,5,7,6]=>[1,2,3,1]
[1,7,6,3,4,5,2]=>[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>[1,1,4,1]
[1,7,6,3,5,2,4]=>[4,6,7,5,3,1,2]=>[4,2,1,3,5,7,6]=>[1,1,4,1]
[1,7,6,3,5,4,2]=>[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>[2,4,1]
[1,7,6,4,2,3,5]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>[1,2,3,1]
[1,7,6,4,2,5,3]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>[3,3,1]
[1,7,6,4,3,2,5]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>[3,3,1]
[1,7,6,4,3,5,2]=>[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>[2,4,1]
[1,7,6,4,5,2,3]=>[6,4,7,5,3,1,2]=>[2,4,1,3,5,7,6]=>[2,4,1]
[1,7,6,4,5,3,2]=>[4,7,6,5,3,1,2]=>[4,1,2,3,5,7,6]=>[1,5,1]
[1,7,6,5,2,3,4]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>[1,1,4,1]
[1,7,6,5,2,4,3]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>[2,4,1]
[1,7,6,5,3,2,4]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>[2,4,1]
[1,7,6,5,3,4,2]=>[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>[1,5,1]
[1,7,6,5,4,2,3]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[1,5,1]
[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[6,1]
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]
[2,1,3,4,5,7,6]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[1,2,1,1,1,1]
[2,1,3,4,6,5,7]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[1,2,1,1,1,1]
[2,1,3,4,6,7,5]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>[1,1,2,1,1,1]
[2,1,3,4,7,5,6]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>[1,1,2,1,1,1]
[2,1,3,4,7,6,5]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[2,2,1,1,1]
[2,1,3,5,4,6,7]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[1,2,1,1,1,1]
[2,1,3,5,4,7,6]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>[1,1,2,1,1,1]
[2,1,3,5,6,4,7]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[1,1,2,1,1,1]
[2,1,3,5,6,7,4]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>[1,1,1,2,1,1]
[2,1,3,5,7,4,6]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>[1,1,1,2,1,1]
[2,1,3,5,7,6,4]=>[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>[2,1,2,1,1]
[2,1,3,6,4,5,7]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>[1,1,2,1,1,1]
[2,1,3,6,4,7,5]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[2,2,1,1,1]
[2,1,3,6,5,4,7]=>[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>[2,2,1,1,1]
[2,1,3,6,5,7,4]=>[5,1,4,7,2,3,6]=>[3,7,4,1,6,5,2]=>[2,1,2,1,1]
[2,1,3,6,7,4,5]=>[6,1,4,7,2,3,5]=>[2,7,4,1,6,5,3]=>[2,1,2,1,1]
[2,1,3,6,7,5,4]=>[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>[1,2,2,1,1]
[2,1,3,7,4,5,6]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>[1,1,1,2,1,1]
[2,1,3,7,4,6,5]=>[7,1,5,6,2,3,4]=>[1,7,3,2,6,5,4]=>[2,1,2,1,1]
[2,1,3,7,5,4,6]=>[6,1,5,7,2,3,4]=>[2,7,3,1,6,5,4]=>[2,1,2,1,1]
[2,1,3,7,5,6,4]=>[5,7,1,6,2,3,4]=>[3,1,7,2,6,5,4]=>[1,2,2,1,1]
[2,1,3,7,6,4,5]=>[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]=>[1,2,2,1,1]
[2,1,3,7,6,5,4]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>[3,2,1,1]
[2,1,4,3,5,6,7]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[1,2,1,1,1,1]
[2,1,4,3,5,7,6]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>[1,1,2,1,1,1]
[2,1,4,3,6,5,7]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>[1,1,2,1,1,1]
[2,1,4,3,6,7,5]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>[1,1,1,2,1,1]
[2,1,4,3,7,5,6]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>[1,1,1,2,1,1]
[2,1,4,3,7,6,5]=>[7,1,3,6,2,4,5]=>[1,7,5,2,6,4,3]=>[2,1,2,1,1]
[2,1,4,5,3,6,7]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>[1,1,2,1,1,1]
[2,1,4,5,3,7,6]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>[1,1,1,2,1,1]
[2,1,4,5,6,3,7]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>[1,1,1,2,1,1]
[2,1,4,5,6,7,3]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>[1,1,1,1,2,1]
[2,1,4,5,7,3,6]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>[1,1,1,1,2,1]
[2,1,4,5,7,6,3]=>[7,1,3,4,6,2,5]=>[1,7,5,4,2,6,3]=>[2,1,1,2,1]
[2,1,4,6,3,5,7]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[1,1,1,2,1,1]
[2,1,4,6,3,7,5]=>[7,1,3,5,2,4,6]=>[1,7,5,3,6,4,2]=>[2,1,2,1,1]
[2,1,4,6,5,3,7]=>[6,1,3,5,2,4,7]=>[2,7,5,3,6,4,1]=>[2,1,2,1,1]
[2,1,4,6,5,7,3]=>[5,1,3,4,7,2,6]=>[3,7,5,4,1,6,2]=>[2,1,1,2,1]
[2,1,4,6,7,3,5]=>[6,1,3,4,7,2,5]=>[2,7,5,4,1,6,3]=>[2,1,1,2,1]
[2,1,4,6,7,5,3]=>[4,7,1,3,6,2,5]=>[4,1,7,5,2,6,3]=>[1,2,1,2,1]
[2,1,4,7,3,5,6]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>[1,1,1,1,2,1]
[2,1,4,7,3,6,5]=>[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>[2,1,1,2,1]
[2,1,4,7,5,3,6]=>[6,1,3,5,7,2,4]=>[2,7,5,3,1,6,4]=>[2,1,1,2,1]
[2,1,4,7,5,6,3]=>[5,7,1,3,6,2,4]=>[3,1,7,5,2,6,4]=>[1,2,1,2,1]
[2,1,4,7,6,3,5]=>[6,7,1,3,5,2,4]=>[2,1,7,5,3,6,4]=>[1,2,1,2,1]
[2,1,4,7,6,5,3]=>[7,6,1,3,5,2,4]=>[1,2,7,5,3,6,4]=>[3,1,2,1]
[2,1,5,3,4,6,7]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>[1,1,2,1,1,1]
[2,1,5,3,4,7,6]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[2,2,1,1,1]
[2,1,5,3,6,4,7]=>[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>[2,2,1,1,1]
[2,1,5,3,6,7,4]=>[5,1,3,7,2,4,6]=>[3,7,5,1,6,4,2]=>[2,1,2,1,1]
[2,1,5,3,7,4,6]=>[6,1,3,7,2,4,5]=>[2,7,5,1,6,4,3]=>[2,1,2,1,1]
[2,1,5,3,7,6,4]=>[3,7,1,6,2,4,5]=>[5,1,7,2,6,4,3]=>[1,2,2,1,1]
[2,1,5,4,3,6,7]=>[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>[2,2,1,1,1]
[2,1,5,4,3,7,6]=>[4,1,3,7,2,5,6]=>[4,7,5,1,6,3,2]=>[2,1,2,1,1]
[2,1,5,4,6,3,7]=>[4,1,3,6,2,5,7]=>[4,7,5,2,6,3,1]=>[2,1,2,1,1]
[2,1,5,4,6,7,3]=>[4,1,3,5,7,2,6]=>[4,7,5,3,1,6,2]=>[2,1,1,2,1]
[2,1,5,4,7,3,6]=>[4,1,3,6,7,2,5]=>[4,7,5,2,1,6,3]=>[2,1,1,2,1]
[2,1,5,4,7,6,3]=>[3,7,1,4,6,2,5]=>[5,1,7,4,2,6,3]=>[1,2,1,2,1]
[2,1,5,6,3,4,7]=>[5,1,3,6,2,4,7]=>[3,7,5,2,6,4,1]=>[2,1,2,1,1]
[2,1,5,6,3,7,4]=>[3,7,1,5,2,4,6]=>[5,1,7,3,6,4,2]=>[1,2,2,1,1]
[2,1,5,6,4,3,7]=>[3,6,1,5,2,4,7]=>[5,2,7,3,6,4,1]=>[1,2,2,1,1]
[2,1,5,6,4,7,3]=>[3,5,1,4,7,2,6]=>[5,3,7,4,1,6,2]=>[1,2,1,2,1]
[2,1,5,6,7,3,4]=>[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>[1,2,1,2,1]
[2,1,5,6,7,4,3]=>[3,4,7,1,6,2,5]=>[5,4,1,7,2,6,3]=>[1,1,2,2,1]
[2,1,5,7,3,4,6]=>[5,1,3,6,7,2,4]=>[3,7,5,2,1,6,4]=>[2,1,1,2,1]
[2,1,5,7,3,6,4]=>[3,7,1,5,6,2,4]=>[5,1,7,3,2,6,4]=>[1,2,1,2,1]
[2,1,5,7,4,3,6]=>[3,6,1,5,7,2,4]=>[5,2,7,3,1,6,4]=>[1,2,1,2,1]
[2,1,5,7,4,6,3]=>[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>[1,1,2,2,1]
[2,1,5,7,6,3,4]=>[3,6,7,1,5,2,4]=>[5,2,1,7,3,6,4]=>[1,1,2,2,1]
[2,1,5,7,6,4,3]=>[7,3,6,1,5,2,4]=>[1,5,2,7,3,6,4]=>[2,2,2,1]
[2,1,6,3,4,5,7]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>[1,1,1,2,1,1]
[2,1,6,3,4,7,5]=>[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]=>[2,1,2,1,1]
[2,1,6,3,5,4,7]=>[6,1,4,5,2,3,7]=>[2,7,4,3,6,5,1]=>[2,1,2,1,1]
[2,1,6,3,5,7,4]=>[5,7,1,4,2,3,6]=>[3,1,7,4,6,5,2]=>[1,2,2,1,1]
[2,1,6,3,7,4,5]=>[6,7,1,4,2,3,5]=>[2,1,7,4,6,5,3]=>[1,2,2,1,1]
[2,1,6,3,7,5,4]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>[3,2,1,1]
[2,1,6,4,3,5,7]=>[5,1,4,6,2,3,7]=>[3,7,4,2,6,5,1]=>[2,1,2,1,1]
[2,1,6,4,3,7,5]=>[4,7,1,5,2,3,6]=>[4,1,7,3,6,5,2]=>[1,2,2,1,1]
[2,1,6,4,5,3,7]=>[4,6,1,5,2,3,7]=>[4,2,7,3,6,5,1]=>[1,2,2,1,1]
[2,1,6,4,5,7,3]=>[4,5,1,3,7,2,6]=>[4,3,7,5,1,6,2]=>[1,2,1,2,1]
[2,1,6,4,7,3,5]=>[4,6,1,3,7,2,5]=>[4,2,7,5,1,6,3]=>[1,2,1,2,1]
[2,1,6,4,7,5,3]=>[7,4,1,3,6,2,5]=>[1,4,7,5,2,6,3]=>[3,1,2,1]
[2,1,6,5,3,4,7]=>[5,6,1,4,2,3,7]=>[3,2,7,4,6,5,1]=>[1,2,2,1,1]
[2,1,6,5,3,7,4]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>[3,2,1,1]
[2,1,6,5,4,3,7]=>[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>[3,2,1,1]
[2,1,6,5,4,7,3]=>[5,4,1,3,7,2,6]=>[3,4,7,5,1,6,2]=>[3,1,2,1]
[2,1,6,5,7,3,4]=>[6,4,1,3,7,2,5]=>[2,4,7,5,1,6,3]=>[3,1,2,1]
[2,1,6,5,7,4,3]=>[4,3,7,1,6,2,5]=>[4,5,1,7,2,6,3]=>[2,2,2,1]
[2,1,6,7,3,4,5]=>[5,6,1,3,7,2,4]=>[3,2,7,5,1,6,4]=>[1,2,1,2,1]
[2,1,6,7,3,5,4]=>[7,5,1,3,6,2,4]=>[1,3,7,5,2,6,4]=>[3,1,2,1]
[2,1,6,7,4,3,5]=>[6,5,1,3,7,2,4]=>[2,3,7,5,1,6,4]=>[3,1,2,1]
[2,1,6,7,4,5,3]=>[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>[2,2,2,1]
[2,1,6,7,5,3,4]=>[6,3,7,1,5,2,4]=>[2,5,1,7,3,6,4]=>[2,2,2,1]
[2,1,6,7,5,4,3]=>[3,7,6,1,5,2,4]=>[5,1,2,7,3,6,4]=>[1,3,2,1]
[2,1,7,3,4,5,6]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>[1,1,1,1,2,1]
[2,1,7,3,4,6,5]=>[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]=>[2,1,1,2,1]
[2,1,7,3,5,4,6]=>[6,1,4,5,7,2,3]=>[2,7,4,3,1,6,5]=>[2,1,1,2,1]
[2,1,7,3,5,6,4]=>[5,7,1,4,6,2,3]=>[3,1,7,4,2,6,5]=>[1,2,1,2,1]
[2,1,7,3,6,4,5]=>[6,7,1,4,5,2,3]=>[2,1,7,4,3,6,5]=>[1,2,1,2,1]
[2,1,7,3,6,5,4]=>[7,6,1,4,5,2,3]=>[1,2,7,4,3,6,5]=>[3,1,2,1]
[2,1,7,4,3,5,6]=>[5,1,4,6,7,2,3]=>[3,7,4,2,1,6,5]=>[2,1,1,2,1]
[2,1,7,4,3,6,5]=>[4,7,1,5,6,2,3]=>[4,1,7,3,2,6,5]=>[1,2,1,2,1]
[2,1,7,4,5,3,6]=>[4,6,1,5,7,2,3]=>[4,2,7,3,1,6,5]=>[1,2,1,2,1]
[2,1,7,4,5,6,3]=>[4,5,7,1,6,2,3]=>[4,3,1,7,2,6,5]=>[1,1,2,2,1]
[2,1,7,4,6,3,5]=>[4,6,7,1,5,2,3]=>[4,2,1,7,3,6,5]=>[1,1,2,2,1]
[2,1,7,4,6,5,3]=>[7,4,6,1,5,2,3]=>[1,4,2,7,3,6,5]=>[2,2,2,1]
[2,1,7,5,3,4,6]=>[5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5]=>[1,2,1,2,1]
[2,1,7,5,3,6,4]=>[7,5,1,4,6,2,3]=>[1,3,7,4,2,6,5]=>[3,1,2,1]
[2,1,7,5,4,3,6]=>[6,5,1,4,7,2,3]=>[2,3,7,4,1,6,5]=>[3,1,2,1]
[2,1,7,5,4,6,3]=>[5,4,7,1,6,2,3]=>[3,4,1,7,2,6,5]=>[2,2,2,1]
[2,1,7,5,6,3,4]=>[6,4,7,1,5,2,3]=>[2,4,1,7,3,6,5]=>[2,2,2,1]
[2,1,7,5,6,4,3]=>[4,7,6,1,5,2,3]=>[4,1,2,7,3,6,5]=>[1,3,2,1]
[2,1,7,6,3,4,5]=>[5,6,7,1,4,2,3]=>[3,2,1,7,4,6,5]=>[1,1,2,2,1]
[2,1,7,6,3,5,4]=>[7,5,6,1,4,2,3]=>[1,3,2,7,4,6,5]=>[2,2,2,1]
[2,1,7,6,4,3,5]=>[6,5,7,1,4,2,3]=>[2,3,1,7,4,6,5]=>[2,2,2,1]
[2,1,7,6,4,5,3]=>[5,7,6,1,4,2,3]=>[3,1,2,7,4,6,5]=>[1,3,2,1]
[2,1,7,6,5,3,4]=>[6,7,5,1,4,2,3]=>[2,1,3,7,4,6,5]=>[1,3,2,1]
[2,1,7,6,5,4,3]=>[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>[4,2,1]
[2,3,1,4,5,6,7]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[1,2,1,1,1,1]
[2,3,1,4,5,7,6]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[1,1,2,1,1,1]
[2,3,1,4,6,5,7]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[1,1,2,1,1,1]
[2,3,1,4,6,7,5]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>[1,1,1,2,1,1]
[2,3,1,4,7,5,6]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>[1,1,1,2,1,1]
[2,3,1,4,7,6,5]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[2,1,2,1,1]
[2,3,1,5,4,6,7]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[1,1,2,1,1,1]
[2,3,1,5,4,7,6]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>[1,1,1,2,1,1]
[2,3,1,5,6,4,7]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>[1,1,1,2,1,1]
[2,3,1,5,6,7,4]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>[1,1,1,1,2,1]
[2,3,1,5,7,4,6]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>[1,1,1,1,2,1]
[2,3,1,5,7,6,4]=>[7,1,2,4,6,3,5]=>[1,7,6,4,2,5,3]=>[2,1,1,2,1]
[2,3,1,6,4,5,7]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>[1,1,1,2,1,1]
[2,3,1,6,4,7,5]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[2,1,2,1,1]
[2,3,1,6,5,4,7]=>[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>[2,1,2,1,1]
[2,3,1,6,5,7,4]=>[5,1,2,4,7,3,6]=>[3,7,6,4,1,5,2]=>[2,1,1,2,1]
[2,3,1,6,7,4,5]=>[6,1,2,4,7,3,5]=>[2,7,6,4,1,5,3]=>[2,1,1,2,1]
[2,3,1,6,7,5,4]=>[4,7,1,2,6,3,5]=>[4,1,7,6,2,5,3]=>[1,2,1,2,1]
[2,3,1,7,4,5,6]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>[1,1,1,1,2,1]
[2,3,1,7,4,6,5]=>[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>[2,1,1,2,1]
[2,3,1,7,5,4,6]=>[6,1,2,5,7,3,4]=>[2,7,6,3,1,5,4]=>[2,1,1,2,1]
[2,3,1,7,5,6,4]=>[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]=>[1,2,1,2,1]
[2,3,1,7,6,4,5]=>[6,7,1,2,5,3,4]=>[2,1,7,6,3,5,4]=>[1,2,1,2,1]
[2,3,1,7,6,5,4]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>[3,1,2,1]
[2,3,4,1,5,6,7]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[1,1,2,1,1,1]
[2,3,4,1,5,7,6]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[1,1,1,2,1,1]
[2,3,4,1,6,5,7]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[1,1,1,2,1,1]
[2,3,4,1,6,7,5]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>[1,1,1,1,2,1]
[2,3,4,1,7,5,6]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>[1,1,1,1,2,1]
[2,3,4,1,7,6,5]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[2,1,1,2,1]
[2,3,4,5,1,6,7]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[1,1,1,2,1,1]
[2,3,4,5,1,7,6]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[1,1,1,1,2,1]
[2,3,4,5,6,1,7]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[1,1,1,1,2,1]
[2,3,4,5,6,7,1]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]
[2,3,4,5,7,1,6]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]
[2,3,4,5,7,6,1]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>[2,1,1,1,2]
[2,3,4,6,1,5,7]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>[1,1,1,1,2,1]
[2,3,4,6,1,7,5]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>[2,1,1,2,1]
[2,3,4,6,5,1,7]=>[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>[2,1,1,2,1]
[2,3,4,6,5,7,1]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>[2,1,1,1,2]
[2,3,4,6,7,1,5]=>[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]=>[2,1,1,1,2]
[2,3,4,6,7,5,1]=>[4,7,1,2,3,6,5]=>[4,1,7,6,5,2,3]=>[1,2,1,1,2]
[2,3,4,7,1,5,6]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]
[2,3,4,7,1,6,5]=>[7,1,2,3,5,6,4]=>[1,7,6,5,3,2,4]=>[2,1,1,1,2]
[2,3,4,7,5,1,6]=>[6,1,2,3,5,7,4]=>[2,7,6,5,3,1,4]=>[2,1,1,1,2]
[2,3,4,7,5,6,1]=>[5,7,1,2,3,6,4]=>[3,1,7,6,5,2,4]=>[1,2,1,1,2]
[2,3,4,7,6,1,5]=>[6,7,1,2,3,5,4]=>[2,1,7,6,5,3,4]=>[1,2,1,1,2]
[2,3,4,7,6,5,1]=>[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>[3,1,1,2]
[2,3,5,1,4,6,7]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[1,1,1,2,1,1]
[2,3,5,1,4,7,6]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>[2,1,2,1,1]
[2,3,5,1,6,4,7]=>[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>[2,1,2,1,1]
[2,3,5,1,6,7,4]=>[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]=>[2,1,1,2,1]
[2,3,5,1,7,4,6]=>[6,1,2,3,7,4,5]=>[2,7,6,5,1,4,3]=>[2,1,1,2,1]
[2,3,5,1,7,6,4]=>[3,7,1,2,6,4,5]=>[5,1,7,6,2,4,3]=>[1,2,1,2,1]
[2,3,5,4,1,6,7]=>[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>[2,1,2,1,1]
[2,3,5,4,1,7,6]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>[2,1,1,2,1]
[2,3,5,4,6,1,7]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>[2,1,1,2,1]
[2,3,5,4,6,7,1]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>[2,1,1,1,2]
[2,3,5,4,7,1,6]=>[4,1,2,3,6,7,5]=>[4,7,6,5,2,1,3]=>[2,1,1,1,2]
[2,3,5,4,7,6,1]=>[3,7,1,2,4,6,5]=>[5,1,7,6,4,2,3]=>[1,2,1,1,2]
[2,3,5,6,1,4,7]=>[5,1,2,3,6,4,7]=>[3,7,6,5,2,4,1]=>[2,1,1,2,1]
[2,3,5,6,1,7,4]=>[3,7,1,2,5,4,6]=>[5,1,7,6,3,4,2]=>[1,2,1,2,1]
[2,3,5,6,4,1,7]=>[3,6,1,2,5,4,7]=>[5,2,7,6,3,4,1]=>[1,2,1,2,1]
[2,3,5,6,4,7,1]=>[3,5,1,2,4,7,6]=>[5,3,7,6,4,1,2]=>[1,2,1,1,2]
[2,3,5,6,7,1,4]=>[3,6,1,2,4,7,5]=>[5,2,7,6,4,1,3]=>[1,2,1,1,2]
[2,3,5,6,7,4,1]=>[3,4,7,1,2,6,5]=>[5,4,1,7,6,2,3]=>[1,1,2,1,2]
[2,3,5,7,1,4,6]=>[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]=>[2,1,1,1,2]
[2,3,5,7,1,6,4]=>[3,7,1,2,5,6,4]=>[5,1,7,6,3,2,4]=>[1,2,1,1,2]
[2,3,5,7,4,1,6]=>[3,6,1,2,5,7,4]=>[5,2,7,6,3,1,4]=>[1,2,1,1,2]
[2,3,5,7,4,6,1]=>[3,5,7,1,2,6,4]=>[5,3,1,7,6,2,4]=>[1,1,2,1,2]
[2,3,5,7,6,1,4]=>[3,6,7,1,2,5,4]=>[5,2,1,7,6,3,4]=>[1,1,2,1,2]
[2,3,5,7,6,4,1]=>[7,3,6,1,2,5,4]=>[1,5,2,7,6,3,4]=>[2,2,1,2]
[2,3,6,1,4,5,7]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>[1,1,1,1,2,1]
[2,3,6,1,4,7,5]=>[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>[2,1,1,2,1]
[2,3,6,1,5,4,7]=>[6,1,2,4,5,3,7]=>[2,7,6,4,3,5,1]=>[2,1,1,2,1]
[2,3,6,1,5,7,4]=>[5,7,1,2,4,3,6]=>[3,1,7,6,4,5,2]=>[1,2,1,2,1]
[2,3,6,1,7,4,5]=>[6,7,1,2,4,3,5]=>[2,1,7,6,4,5,3]=>[1,2,1,2,1]
[2,3,6,1,7,5,4]=>[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>[3,1,2,1]
[2,3,6,4,1,5,7]=>[5,1,2,4,6,3,7]=>[3,7,6,4,2,5,1]=>[2,1,1,2,1]
[2,3,6,4,1,7,5]=>[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>[1,2,1,2,1]
[2,3,6,4,5,1,7]=>[4,6,1,2,5,3,7]=>[4,2,7,6,3,5,1]=>[1,2,1,2,1]
[2,3,6,4,5,7,1]=>[4,5,1,2,3,7,6]=>[4,3,7,6,5,1,2]=>[1,2,1,1,2]
[2,3,6,4,7,1,5]=>[4,6,1,2,3,7,5]=>[4,2,7,6,5,1,3]=>[1,2,1,1,2]
[2,3,6,4,7,5,1]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>[3,1,1,2]
[2,3,6,5,1,4,7]=>[5,6,1,2,4,3,7]=>[3,2,7,6,4,5,1]=>[1,2,1,2,1]
[2,3,6,5,1,7,4]=>[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>[3,1,2,1]
[2,3,6,5,4,1,7]=>[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>[3,1,2,1]
[2,3,6,5,4,7,1]=>[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>[3,1,1,2]
[2,3,6,5,7,1,4]=>[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]=>[3,1,1,2]
[2,3,6,5,7,4,1]=>[4,3,7,1,2,6,5]=>[4,5,1,7,6,2,3]=>[2,2,1,2]
[2,3,6,7,1,4,5]=>[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]=>[1,2,1,1,2]
[2,3,6,7,1,5,4]=>[7,5,1,2,3,6,4]=>[1,3,7,6,5,2,4]=>[3,1,1,2]
[2,3,6,7,4,1,5]=>[6,5,1,2,3,7,4]=>[2,3,7,6,5,1,4]=>[3,1,1,2]
[2,3,6,7,4,5,1]=>[5,3,7,1,2,6,4]=>[3,5,1,7,6,2,4]=>[2,2,1,2]
[2,3,6,7,5,1,4]=>[6,3,7,1,2,5,4]=>[2,5,1,7,6,3,4]=>[2,2,1,2]
[2,3,6,7,5,4,1]=>[3,7,6,1,2,5,4]=>[5,1,2,7,6,3,4]=>[1,3,1,2]
[2,3,7,1,4,5,6]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]
[2,3,7,1,4,6,5]=>[7,1,2,4,5,6,3]=>[1,7,6,4,3,2,5]=>[2,1,1,1,2]
[2,3,7,1,5,4,6]=>[6,1,2,4,5,7,3]=>[2,7,6,4,3,1,5]=>[2,1,1,1,2]
[2,3,7,1,5,6,4]=>[5,7,1,2,4,6,3]=>[3,1,7,6,4,2,5]=>[1,2,1,1,2]
[2,3,7,1,6,4,5]=>[6,7,1,2,4,5,3]=>[2,1,7,6,4,3,5]=>[1,2,1,1,2]
[2,3,7,1,6,5,4]=>[7,6,1,2,4,5,3]=>[1,2,7,6,4,3,5]=>[3,1,1,2]
[2,3,7,4,1,5,6]=>[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>[2,1,1,1,2]
[2,3,7,4,1,6,5]=>[4,7,1,2,5,6,3]=>[4,1,7,6,3,2,5]=>[1,2,1,1,2]
[2,3,7,4,5,1,6]=>[4,6,1,2,5,7,3]=>[4,2,7,6,3,1,5]=>[1,2,1,1,2]
[2,3,7,4,5,6,1]=>[4,5,7,1,2,6,3]=>[4,3,1,7,6,2,5]=>[1,1,2,1,2]
[2,3,7,4,6,1,5]=>[4,6,7,1,2,5,3]=>[4,2,1,7,6,3,5]=>[1,1,2,1,2]
[2,3,7,4,6,5,1]=>[7,4,6,1,2,5,3]=>[1,4,2,7,6,3,5]=>[2,2,1,2]
[2,3,7,5,1,4,6]=>[5,6,1,2,4,7,3]=>[3,2,7,6,4,1,5]=>[1,2,1,1,2]
[2,3,7,5,1,6,4]=>[7,5,1,2,4,6,3]=>[1,3,7,6,4,2,5]=>[3,1,1,2]
[2,3,7,5,4,1,6]=>[6,5,1,2,4,7,3]=>[2,3,7,6,4,1,5]=>[3,1,1,2]
[2,3,7,5,4,6,1]=>[5,4,7,1,2,6,3]=>[3,4,1,7,6,2,5]=>[2,2,1,2]
[2,3,7,5,6,1,4]=>[6,4,7,1,2,5,3]=>[2,4,1,7,6,3,5]=>[2,2,1,2]
[2,3,7,5,6,4,1]=>[4,7,6,1,2,5,3]=>[4,1,2,7,6,3,5]=>[1,3,1,2]
[2,3,7,6,1,4,5]=>[5,6,7,1,2,4,3]=>[3,2,1,7,6,4,5]=>[1,1,2,1,2]
[2,3,7,6,1,5,4]=>[7,5,6,1,2,4,3]=>[1,3,2,7,6,4,5]=>[2,2,1,2]
[2,3,7,6,4,1,5]=>[6,5,7,1,2,4,3]=>[2,3,1,7,6,4,5]=>[2,2,1,2]
[2,3,7,6,4,5,1]=>[5,7,6,1,2,4,3]=>[3,1,2,7,6,4,5]=>[1,3,1,2]
[2,3,7,6,5,1,4]=>[6,7,5,1,2,4,3]=>[2,1,3,7,6,4,5]=>[1,3,1,2]
[2,3,7,6,5,4,1]=>[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>[4,1,2]
[2,4,1,3,5,6,7]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>[1,1,2,1,1,1]
[2,4,1,3,5,7,6]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>[2,2,1,1,1]
[2,4,1,3,6,5,7]=>[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>[2,2,1,1,1]
[2,4,1,3,6,7,5]=>[5,1,2,7,3,4,6]=>[3,7,6,1,5,4,2]=>[2,1,2,1,1]
[2,4,1,3,7,5,6]=>[6,1,2,7,3,4,5]=>[2,7,6,1,5,4,3]=>[2,1,2,1,1]
[2,4,1,3,7,6,5]=>[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]=>[1,2,2,1,1]
[2,4,1,5,3,6,7]=>[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>[2,2,1,1,1]
[2,4,1,5,3,7,6]=>[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]=>[2,1,2,1,1]
[2,4,1,5,6,3,7]=>[4,1,2,6,3,5,7]=>[4,7,6,2,5,3,1]=>[2,1,2,1,1]
[2,4,1,5,6,7,3]=>[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]=>[2,1,1,2,1]
[2,4,1,5,7,3,6]=>[4,1,2,6,7,3,5]=>[4,7,6,2,1,5,3]=>[2,1,1,2,1]
[2,4,1,5,7,6,3]=>[2,7,1,4,6,3,5]=>[6,1,7,4,2,5,3]=>[1,2,1,2,1]
[2,4,1,6,3,5,7]=>[5,1,2,6,3,4,7]=>[3,7,6,2,5,4,1]=>[2,1,2,1,1]
[2,4,1,6,3,7,5]=>[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]=>[1,2,2,1,1]
[2,4,1,6,5,3,7]=>[2,6,1,5,3,4,7]=>[6,2,7,3,5,4,1]=>[1,2,2,1,1]
[2,4,1,6,5,7,3]=>[2,5,1,4,7,3,6]=>[6,3,7,4,1,5,2]=>[1,2,1,2,1]
[2,4,1,6,7,3,5]=>[2,6,1,4,7,3,5]=>[6,2,7,4,1,5,3]=>[1,2,1,2,1]
[2,4,1,6,7,5,3]=>[2,4,7,1,6,3,5]=>[6,4,1,7,2,5,3]=>[1,1,2,2,1]
[2,4,1,7,3,5,6]=>[5,1,2,6,7,3,4]=>[3,7,6,2,1,5,4]=>[2,1,1,2,1]
[2,4,1,7,3,6,5]=>[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]=>[1,2,1,2,1]
[2,4,1,7,5,3,6]=>[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>[1,2,1,2,1]
[2,4,1,7,5,6,3]=>[2,5,7,1,6,3,4]=>[6,3,1,7,2,5,4]=>[1,1,2,2,1]
[2,4,1,7,6,3,5]=>[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>[1,1,2,2,1]
[2,4,1,7,6,5,3]=>[7,2,6,1,5,3,4]=>[1,6,2,7,3,5,4]=>[2,2,2,1]
[2,4,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>[2,2,1,1,1]
[2,4,3,1,5,7,6]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>[2,1,2,1,1]
[2,4,3,1,6,5,7]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>[2,1,2,1,1]
[2,4,3,1,6,7,5]=>[3,1,2,5,7,4,6]=>[5,7,6,3,1,4,2]=>[2,1,1,2,1]
[2,4,3,1,7,5,6]=>[3,1,2,6,7,4,5]=>[5,7,6,2,1,4,3]=>[2,1,1,2,1]
[2,4,3,1,7,6,5]=>[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]=>[1,2,1,2,1]
[2,4,3,5,1,6,7]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>[2,1,2,1,1]
[2,4,3,5,1,7,6]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[2,1,1,2,1]
[2,4,3,5,6,1,7]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>[2,1,1,2,1]
[2,4,3,5,6,7,1]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>[2,1,1,1,2]
[2,4,3,5,7,1,6]=>[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>[2,1,1,1,2]
[2,4,3,5,7,6,1]=>[2,7,1,3,4,6,5]=>[6,1,7,5,4,2,3]=>[1,2,1,1,2]
[2,4,3,6,1,5,7]=>[3,1,2,5,6,4,7]=>[5,7,6,3,2,4,1]=>[2,1,1,2,1]
[2,4,3,6,1,7,5]=>[2,7,1,3,5,4,6]=>[6,1,7,5,3,4,2]=>[1,2,1,2,1]
[2,4,3,6,5,1,7]=>[2,6,1,3,5,4,7]=>[6,2,7,5,3,4,1]=>[1,2,1,2,1]
[2,4,3,6,5,7,1]=>[2,5,1,3,4,7,6]=>[6,3,7,5,4,1,2]=>[1,2,1,1,2]
[2,4,3,6,7,1,5]=>[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]=>[1,2,1,1,2]
[2,4,3,6,7,5,1]=>[2,4,7,1,3,6,5]=>[6,4,1,7,5,2,3]=>[1,1,2,1,2]
[2,4,3,7,1,5,6]=>[3,1,2,5,6,7,4]=>[5,7,6,3,2,1,4]=>[2,1,1,1,2]
[2,4,3,7,1,6,5]=>[2,7,1,3,5,6,4]=>[6,1,7,5,3,2,4]=>[1,2,1,1,2]
[2,4,3,7,5,1,6]=>[2,6,1,3,5,7,4]=>[6,2,7,5,3,1,4]=>[1,2,1,1,2]
[2,4,3,7,5,6,1]=>[2,5,7,1,3,6,4]=>[6,3,1,7,5,2,4]=>[1,1,2,1,2]
[2,4,3,7,6,1,5]=>[2,6,7,1,3,5,4]=>[6,2,1,7,5,3,4]=>[1,1,2,1,2]
[2,4,3,7,6,5,1]=>[7,2,6,1,3,5,4]=>[1,6,2,7,5,3,4]=>[2,2,1,2]
[2,4,5,1,3,6,7]=>[4,1,2,5,3,6,7]=>[4,7,6,3,5,2,1]=>[2,1,2,1,1]
[2,4,5,1,3,7,6]=>[2,7,1,4,3,5,6]=>[6,1,7,4,5,3,2]=>[1,2,2,1,1]
[2,4,5,1,6,3,7]=>[2,6,1,4,3,5,7]=>[6,2,7,4,5,3,1]=>[1,2,2,1,1]
[2,4,5,1,6,7,3]=>[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]=>[1,2,1,2,1]
[2,4,5,1,7,3,6]=>[2,6,1,3,7,4,5]=>[6,2,7,5,1,4,3]=>[1,2,1,2,1]
[2,4,5,1,7,6,3]=>[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]=>[1,1,2,2,1]
[2,4,5,3,1,6,7]=>[2,5,1,4,3,6,7]=>[6,3,7,4,5,2,1]=>[1,2,2,1,1]
[2,4,5,3,1,7,6]=>[2,4,1,3,7,5,6]=>[6,4,7,5,1,3,2]=>[1,2,1,2,1]
[2,4,5,3,6,1,7]=>[2,4,1,3,6,5,7]=>[6,4,7,5,2,3,1]=>[1,2,1,2,1]
[2,4,5,3,6,7,1]=>[2,4,1,3,5,7,6]=>[6,4,7,5,3,1,2]=>[1,2,1,1,2]
[2,4,5,3,7,1,6]=>[2,4,1,3,6,7,5]=>[6,4,7,5,2,1,3]=>[1,2,1,1,2]
[2,4,5,3,7,6,1]=>[2,3,7,1,4,6,5]=>[6,5,1,7,4,2,3]=>[1,1,2,1,2]
[2,4,5,6,1,3,7]=>[2,5,1,3,6,4,7]=>[6,3,7,5,2,4,1]=>[1,2,1,2,1]
[2,4,5,6,1,7,3]=>[2,3,7,1,5,4,6]=>[6,5,1,7,3,4,2]=>[1,1,2,2,1]
[2,4,5,6,3,1,7]=>[2,3,6,1,5,4,7]=>[6,5,2,7,3,4,1]=>[1,1,2,2,1]
[2,4,5,6,3,7,1]=>[2,3,5,1,4,7,6]=>[6,5,3,7,4,1,2]=>[1,1,2,1,2]
[2,4,5,6,7,1,3]=>[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]=>[1,1,2,1,2]
[2,4,5,6,7,3,1]=>[2,3,4,7,1,6,5]=>[6,5,4,1,7,2,3]=>[1,1,1,2,2]
[2,4,5,7,1,3,6]=>[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]=>[1,2,1,1,2]
[2,4,5,7,1,6,3]=>[2,3,7,1,5,6,4]=>[6,5,1,7,3,2,4]=>[1,1,2,1,2]
[2,4,5,7,3,1,6]=>[2,3,6,1,5,7,4]=>[6,5,2,7,3,1,4]=>[1,1,2,1,2]
[2,4,5,7,3,6,1]=>[2,3,5,7,1,6,4]=>[6,5,3,1,7,2,4]=>[1,1,1,2,2]
[2,4,5,7,6,1,3]=>[2,3,6,7,1,5,4]=>[6,5,2,1,7,3,4]=>[1,1,1,2,2]
[2,4,5,7,6,3,1]=>[7,2,3,6,1,5,4]=>[1,6,5,2,7,3,4]=>[2,1,2,2]
[2,4,6,1,3,5,7]=>[4,1,2,5,6,3,7]=>[4,7,6,3,2,5,1]=>[2,1,1,2,1]
[2,4,6,1,3,7,5]=>[2,7,1,4,5,3,6]=>[6,1,7,4,3,5,2]=>[1,2,1,2,1]
[2,4,6,1,5,3,7]=>[2,6,1,4,5,3,7]=>[6,2,7,4,3,5,1]=>[1,2,1,2,1]
[2,4,6,1,5,7,3]=>[2,5,7,1,4,3,6]=>[6,3,1,7,4,5,2]=>[1,1,2,2,1]
[2,4,6,1,7,3,5]=>[2,6,7,1,4,3,5]=>[6,2,1,7,4,5,3]=>[1,1,2,2,1]
[2,4,6,1,7,5,3]=>[7,2,6,1,4,3,5]=>[1,6,2,7,4,5,3]=>[2,2,2,1]
[2,4,6,3,1,5,7]=>[2,5,1,4,6,3,7]=>[6,3,7,4,2,5,1]=>[1,2,1,2,1]
[2,4,6,3,1,7,5]=>[2,4,7,1,5,3,6]=>[6,4,1,7,3,5,2]=>[1,1,2,2,1]
[2,4,6,3,5,1,7]=>[2,4,6,1,5,3,7]=>[6,4,2,7,3,5,1]=>[1,1,2,2,1]
[2,4,6,3,5,7,1]=>[2,4,5,1,3,7,6]=>[6,4,3,7,5,1,2]=>[1,1,2,1,2]
[2,4,6,3,7,1,5]=>[2,4,6,1,3,7,5]=>[6,4,2,7,5,1,3]=>[1,1,2,1,2]
[2,4,6,3,7,5,1]=>[7,2,4,1,3,6,5]=>[1,6,4,7,5,2,3]=>[2,2,1,2]
[2,4,6,5,1,3,7]=>[2,5,6,1,4,3,7]=>[6,3,2,7,4,5,1]=>[1,1,2,2,1]
[2,4,6,5,1,7,3]=>[7,2,5,1,4,3,6]=>[1,6,3,7,4,5,2]=>[2,2,2,1]
[2,4,6,5,3,1,7]=>[6,2,5,1,4,3,7]=>[2,6,3,7,4,5,1]=>[2,2,2,1]
[2,4,6,5,3,7,1]=>[5,2,4,1,3,7,6]=>[3,6,4,7,5,1,2]=>[2,2,1,2]
[2,4,6,5,7,1,3]=>[6,2,4,1,3,7,5]=>[2,6,4,7,5,1,3]=>[2,2,1,2]
[2,4,6,5,7,3,1]=>[4,2,3,7,1,6,5]=>[4,6,5,1,7,2,3]=>[2,1,2,2]
[2,4,6,7,1,3,5]=>[2,5,6,1,3,7,4]=>[6,3,2,7,5,1,4]=>[1,1,2,1,2]
[2,4,6,7,1,5,3]=>[7,2,5,1,3,6,4]=>[1,6,3,7,5,2,4]=>[2,2,1,2]
[2,4,6,7,3,1,5]=>[6,2,5,1,3,7,4]=>[2,6,3,7,5,1,4]=>[2,2,1,2]
[2,4,6,7,3,5,1]=>[5,2,3,7,1,6,4]=>[3,6,5,1,7,2,4]=>[2,1,2,2]
[2,4,6,7,5,1,3]=>[6,2,3,7,1,5,4]=>[2,6,5,1,7,3,4]=>[2,1,2,2]
[2,4,6,7,5,3,1]=>[3,7,2,6,1,5,4]=>[5,1,6,2,7,3,4]=>[1,2,2,2]
[2,4,7,1,3,5,6]=>[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]=>[2,1,1,1,2]
[2,4,7,1,3,6,5]=>[2,7,1,4,5,6,3]=>[6,1,7,4,3,2,5]=>[1,2,1,1,2]
[2,4,7,1,5,3,6]=>[2,6,1,4,5,7,3]=>[6,2,7,4,3,1,5]=>[1,2,1,1,2]
[2,4,7,1,5,6,3]=>[2,5,7,1,4,6,3]=>[6,3,1,7,4,2,5]=>[1,1,2,1,2]
[2,4,7,1,6,3,5]=>[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>[1,1,2,1,2]
[2,4,7,1,6,5,3]=>[7,2,6,1,4,5,3]=>[1,6,2,7,4,3,5]=>[2,2,1,2]
[2,4,7,3,1,5,6]=>[2,5,1,4,6,7,3]=>[6,3,7,4,2,1,5]=>[1,2,1,1,2]
[2,4,7,3,1,6,5]=>[2,4,7,1,5,6,3]=>[6,4,1,7,3,2,5]=>[1,1,2,1,2]
[2,4,7,3,5,1,6]=>[2,4,6,1,5,7,3]=>[6,4,2,7,3,1,5]=>[1,1,2,1,2]
[2,4,7,3,5,6,1]=>[2,4,5,7,1,6,3]=>[6,4,3,1,7,2,5]=>[1,1,1,2,2]
[2,4,7,3,6,1,5]=>[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>[1,1,1,2,2]
[2,4,7,3,6,5,1]=>[7,2,4,6,1,5,3]=>[1,6,4,2,7,3,5]=>[2,1,2,2]
[2,4,7,5,1,3,6]=>[2,5,6,1,4,7,3]=>[6,3,2,7,4,1,5]=>[1,1,2,1,2]
[2,4,7,5,1,6,3]=>[7,2,5,1,4,6,3]=>[1,6,3,7,4,2,5]=>[2,2,1,2]
[2,4,7,5,3,1,6]=>[6,2,5,1,4,7,3]=>[2,6,3,7,4,1,5]=>[2,2,1,2]
[2,4,7,5,3,6,1]=>[5,2,4,7,1,6,3]=>[3,6,4,1,7,2,5]=>[2,1,2,2]
[2,4,7,5,6,1,3]=>[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>[2,1,2,2]
[2,4,7,5,6,3,1]=>[4,7,2,6,1,5,3]=>[4,1,6,2,7,3,5]=>[1,2,2,2]
[2,4,7,6,1,3,5]=>[2,5,6,7,1,4,3]=>[6,3,2,1,7,4,5]=>[1,1,1,2,2]
[2,4,7,6,1,5,3]=>[7,2,5,6,1,4,3]=>[1,6,3,2,7,4,5]=>[2,1,2,2]
[2,4,7,6,3,1,5]=>[6,2,5,7,1,4,3]=>[2,6,3,1,7,4,5]=>[2,1,2,2]
[2,4,7,6,3,5,1]=>[5,7,2,6,1,4,3]=>[3,1,6,2,7,4,5]=>[1,2,2,2]
[2,4,7,6,5,1,3]=>[6,7,2,5,1,4,3]=>[2,1,6,3,7,4,5]=>[1,2,2,2]
[2,4,7,6,5,3,1]=>[7,6,2,5,1,4,3]=>[1,2,6,3,7,4,5]=>[3,2,2]
[2,5,1,3,4,6,7]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>[1,1,1,2,1,1]
[2,5,1,3,4,7,6]=>[7,1,3,4,2,5,6]=>[1,7,5,4,6,3,2]=>[2,1,2,1,1]
[2,5,1,3,6,4,7]=>[6,1,3,4,2,5,7]=>[2,7,5,4,6,3,1]=>[2,1,2,1,1]
[2,5,1,3,6,7,4]=>[5,7,1,3,2,4,6]=>[3,1,7,5,6,4,2]=>[1,2,2,1,1]
[2,5,1,3,7,4,6]=>[6,7,1,3,2,4,5]=>[2,1,7,5,6,4,3]=>[1,2,2,1,1]
[2,5,1,3,7,6,4]=>[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>[3,2,1,1]
[2,5,1,4,3,6,7]=>[5,1,3,4,2,6,7]=>[3,7,5,4,6,2,1]=>[2,1,2,1,1]
[2,5,1,4,3,7,6]=>[4,7,1,3,2,5,6]=>[4,1,7,5,6,3,2]=>[1,2,2,1,1]
[2,5,1,4,6,3,7]=>[4,6,1,3,2,5,7]=>[4,2,7,5,6,3,1]=>[1,2,2,1,1]
[2,5,1,4,6,7,3]=>[4,5,1,2,7,3,6]=>[4,3,7,6,1,5,2]=>[1,2,1,2,1]
[2,5,1,4,7,3,6]=>[4,6,1,2,7,3,5]=>[4,2,7,6,1,5,3]=>[1,2,1,2,1]
[2,5,1,4,7,6,3]=>[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>[3,1,2,1]
[2,5,1,6,3,4,7]=>[5,6,1,3,2,4,7]=>[3,2,7,5,6,4,1]=>[1,2,2,1,1]
[2,5,1,6,3,7,4]=>[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>[3,2,1,1]
[2,5,1,6,4,3,7]=>[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>[3,2,1,1]
[2,5,1,6,4,7,3]=>[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]=>[3,1,2,1]
[2,5,1,6,7,3,4]=>[6,4,1,2,7,3,5]=>[2,4,7,6,1,5,3]=>[3,1,2,1]
[2,5,1,6,7,4,3]=>[4,2,7,1,6,3,5]=>[4,6,1,7,2,5,3]=>[2,2,2,1]
[2,5,1,7,3,4,6]=>[5,6,1,2,7,3,4]=>[3,2,7,6,1,5,4]=>[1,2,1,2,1]
[2,5,1,7,3,6,4]=>[7,5,1,2,6,3,4]=>[1,3,7,6,2,5,4]=>[3,1,2,1]
[2,5,1,7,4,3,6]=>[6,5,1,2,7,3,4]=>[2,3,7,6,1,5,4]=>[3,1,2,1]
[2,5,1,7,4,6,3]=>[5,2,7,1,6,3,4]=>[3,6,1,7,2,5,4]=>[2,2,2,1]
[2,5,1,7,6,3,4]=>[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>[2,2,2,1]
[2,5,1,7,6,4,3]=>[2,7,6,1,5,3,4]=>[6,1,2,7,3,5,4]=>[1,3,2,1]
[2,5,3,1,4,6,7]=>[4,1,3,5,2,6,7]=>[4,7,5,3,6,2,1]=>[2,1,2,1,1]
[2,5,3,1,4,7,6]=>[3,7,1,4,2,5,6]=>[5,1,7,4,6,3,2]=>[1,2,2,1,1]
[2,5,3,1,6,4,7]=>[3,6,1,4,2,5,7]=>[5,2,7,4,6,3,1]=>[1,2,2,1,1]
[2,5,3,1,6,7,4]=>[3,5,1,2,7,4,6]=>[5,3,7,6,1,4,2]=>[1,2,1,2,1]
[2,5,3,1,7,4,6]=>[3,6,1,2,7,4,5]=>[5,2,7,6,1,4,3]=>[1,2,1,2,1]
[2,5,3,1,7,6,4]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[3,1,2,1]
[2,5,3,4,1,6,7]=>[3,5,1,4,2,6,7]=>[5,3,7,4,6,2,1]=>[1,2,2,1,1]
[2,5,3,4,1,7,6]=>[3,4,1,2,7,5,6]=>[5,4,7,6,1,3,2]=>[1,2,1,2,1]
[2,5,3,4,6,1,7]=>[3,4,1,2,6,5,7]=>[5,4,7,6,2,3,1]=>[1,2,1,2,1]
[2,5,3,4,6,7,1]=>[3,4,1,2,5,7,6]=>[5,4,7,6,3,1,2]=>[1,2,1,1,2]
[2,5,3,4,7,1,6]=>[3,4,1,2,6,7,5]=>[5,4,7,6,2,1,3]=>[1,2,1,1,2]
[2,5,3,4,7,6,1]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>[3,1,1,2]
[2,5,3,6,1,4,7]=>[3,5,1,2,6,4,7]=>[5,3,7,6,2,4,1]=>[1,2,1,2,1]
[2,5,3,6,1,7,4]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>[3,1,2,1]
[2,5,3,6,4,1,7]=>[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>[3,1,2,1]
[2,5,3,6,4,7,1]=>[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>[3,1,1,2]
[2,5,3,6,7,1,4]=>[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]=>[3,1,1,2]
[2,5,3,6,7,4,1]=>[4,2,7,1,3,6,5]=>[4,6,1,7,5,2,3]=>[2,2,1,2]
[2,5,3,7,1,4,6]=>[3,5,1,2,6,7,4]=>[5,3,7,6,2,1,4]=>[1,2,1,1,2]
[2,5,3,7,1,6,4]=>[7,3,1,2,5,6,4]=>[1,5,7,6,3,2,4]=>[3,1,1,2]
[2,5,3,7,4,1,6]=>[6,3,1,2,5,7,4]=>[2,5,7,6,3,1,4]=>[3,1,1,2]
[2,5,3,7,4,6,1]=>[5,2,7,1,3,6,4]=>[3,6,1,7,5,2,4]=>[2,2,1,2]
[2,5,3,7,6,1,4]=>[6,2,7,1,3,5,4]=>[2,6,1,7,5,3,4]=>[2,2,1,2]
[2,5,3,7,6,4,1]=>[2,7,6,1,3,5,4]=>[6,1,2,7,5,3,4]=>[1,3,1,2]
[2,5,4,1,3,6,7]=>[4,5,1,3,2,6,7]=>[4,3,7,5,6,2,1]=>[1,2,2,1,1]
[2,5,4,1,3,7,6]=>[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>[3,2,1,1]
[2,5,4,1,6,3,7]=>[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>[3,2,1,1]
[2,5,4,1,6,7,3]=>[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]=>[3,1,2,1]
[2,5,4,1,7,3,6]=>[6,3,1,2,7,4,5]=>[2,5,7,6,1,4,3]=>[3,1,2,1]
[2,5,4,1,7,6,3]=>[3,2,7,1,6,4,5]=>[5,6,1,7,2,4,3]=>[2,2,2,1]
[2,5,4,3,1,6,7]=>[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>[3,2,1,1]
[2,5,4,3,1,7,6]=>[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>[3,1,2,1]
[2,5,4,3,6,1,7]=>[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>[3,1,2,1]
[2,5,4,3,6,7,1]=>[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>[3,1,1,2]
[2,5,4,3,7,1,6]=>[4,3,1,2,6,7,5]=>[4,5,7,6,2,1,3]=>[3,1,1,2]
[2,5,4,3,7,6,1]=>[3,2,7,1,4,6,5]=>[5,6,1,7,4,2,3]=>[2,2,1,2]
[2,5,4,6,1,3,7]=>[5,3,1,2,6,4,7]=>[3,5,7,6,2,4,1]=>[3,1,2,1]
[2,5,4,6,1,7,3]=>[3,2,7,1,5,4,6]=>[5,6,1,7,3,4,2]=>[2,2,2,1]
[2,5,4,6,3,1,7]=>[3,2,6,1,5,4,7]=>[5,6,2,7,3,4,1]=>[2,2,2,1]
[2,5,4,6,3,7,1]=>[3,2,5,1,4,7,6]=>[5,6,3,7,4,1,2]=>[2,2,1,2]
[2,5,4,6,7,1,3]=>[3,2,6,1,4,7,5]=>[5,6,2,7,4,1,3]=>[2,2,1,2]
[2,5,4,6,7,3,1]=>[3,2,4,7,1,6,5]=>[5,6,4,1,7,2,3]=>[2,1,2,2]
[2,5,4,7,1,3,6]=>[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]=>[3,1,1,2]
[2,5,4,7,1,6,3]=>[3,2,7,1,5,6,4]=>[5,6,1,7,3,2,4]=>[2,2,1,2]
[2,5,4,7,3,1,6]=>[3,2,6,1,5,7,4]=>[5,6,2,7,3,1,4]=>[2,2,1,2]
[2,5,4,7,3,6,1]=>[3,2,5,7,1,6,4]=>[5,6,3,1,7,2,4]=>[2,1,2,2]
[2,5,4,7,6,1,3]=>[3,2,6,7,1,5,4]=>[5,6,2,1,7,3,4]=>[2,1,2,2]
[2,5,4,7,6,3,1]=>[2,7,3,6,1,5,4]=>[6,1,5,2,7,3,4]=>[1,2,2,2]
[2,5,6,1,3,4,7]=>[4,5,1,2,6,3,7]=>[4,3,7,6,2,5,1]=>[1,2,1,2,1]
[2,5,6,1,3,7,4]=>[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>[3,1,2,1]
[2,5,6,1,4,3,7]=>[6,4,1,2,5,3,7]=>[2,4,7,6,3,5,1]=>[3,1,2,1]
[2,5,6,1,4,7,3]=>[5,2,7,1,4,3,6]=>[3,6,1,7,4,5,2]=>[2,2,2,1]
[2,5,6,1,7,3,4]=>[6,2,7,1,4,3,5]=>[2,6,1,7,4,5,3]=>[2,2,2,1]
[2,5,6,1,7,4,3]=>[2,7,6,1,4,3,5]=>[6,1,2,7,4,5,3]=>[1,3,2,1]
[2,5,6,3,1,4,7]=>[5,4,1,2,6,3,7]=>[3,4,7,6,2,5,1]=>[3,1,2,1]
[2,5,6,3,1,7,4]=>[4,2,7,1,5,3,6]=>[4,6,1,7,3,5,2]=>[2,2,2,1]
[2,5,6,3,4,1,7]=>[4,2,6,1,5,3,7]=>[4,6,2,7,3,5,1]=>[2,2,2,1]
[2,5,6,3,4,7,1]=>[4,2,5,1,3,7,6]=>[4,6,3,7,5,1,2]=>[2,2,1,2]
[2,5,6,3,7,1,4]=>[4,2,6,1,3,7,5]=>[4,6,2,7,5,1,3]=>[2,2,1,2]
[2,5,6,3,7,4,1]=>[2,7,4,1,3,6,5]=>[6,1,4,7,5,2,3]=>[1,3,1,2]
[2,5,6,4,1,3,7]=>[5,2,6,1,4,3,7]=>[3,6,2,7,4,5,1]=>[2,2,2,1]
[2,5,6,4,1,7,3]=>[2,7,5,1,4,3,6]=>[6,1,3,7,4,5,2]=>[1,3,2,1]
[2,5,6,4,3,1,7]=>[2,6,5,1,4,3,7]=>[6,2,3,7,4,5,1]=>[1,3,2,1]
[2,5,6,4,3,7,1]=>[2,5,4,1,3,7,6]=>[6,3,4,7,5,1,2]=>[1,3,1,2]
[2,5,6,4,7,1,3]=>[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]=>[1,3,1,2]
[2,5,6,4,7,3,1]=>[2,4,3,7,1,6,5]=>[6,4,5,1,7,2,3]=>[1,2,2,2]
[2,5,6,7,1,3,4]=>[5,2,6,1,3,7,4]=>[3,6,2,7,5,1,4]=>[2,2,1,2]
[2,5,6,7,1,4,3]=>[2,7,5,1,3,6,4]=>[6,1,3,7,5,2,4]=>[1,3,1,2]
[2,5,6,7,3,1,4]=>[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]=>[1,3,1,2]
[2,5,6,7,3,4,1]=>[2,5,3,7,1,6,4]=>[6,3,5,1,7,2,4]=>[1,2,2,2]
[2,5,6,7,4,1,3]=>[2,6,3,7,1,5,4]=>[6,2,5,1,7,3,4]=>[1,2,2,2]
[2,5,6,7,4,3,1]=>[2,3,7,6,1,5,4]=>[6,5,1,2,7,3,4]=>[1,1,3,2]
[2,5,7,1,3,4,6]=>[4,5,1,2,6,7,3]=>[4,3,7,6,2,1,5]=>[1,2,1,1,2]
[2,5,7,1,3,6,4]=>[7,4,1,2,5,6,3]=>[1,4,7,6,3,2,5]=>[3,1,1,2]
[2,5,7,1,4,3,6]=>[6,4,1,2,5,7,3]=>[2,4,7,6,3,1,5]=>[3,1,1,2]
[2,5,7,1,4,6,3]=>[5,2,7,1,4,6,3]=>[3,6,1,7,4,2,5]=>[2,2,1,2]
[2,5,7,1,6,3,4]=>[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>[2,2,1,2]
[2,5,7,1,6,4,3]=>[2,7,6,1,4,5,3]=>[6,1,2,7,4,3,5]=>[1,3,1,2]
[2,5,7,3,1,4,6]=>[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]=>[3,1,1,2]
[2,5,7,3,1,6,4]=>[4,2,7,1,5,6,3]=>[4,6,1,7,3,2,5]=>[2,2,1,2]
[2,5,7,3,4,1,6]=>[4,2,6,1,5,7,3]=>[4,6,2,7,3,1,5]=>[2,2,1,2]
[2,5,7,3,4,6,1]=>[4,2,5,7,1,6,3]=>[4,6,3,1,7,2,5]=>[2,1,2,2]
[2,5,7,3,6,1,4]=>[4,2,6,7,1,5,3]=>[4,6,2,1,7,3,5]=>[2,1,2,2]
[2,5,7,3,6,4,1]=>[2,7,4,6,1,5,3]=>[6,1,4,2,7,3,5]=>[1,2,2,2]
[2,5,7,4,1,3,6]=>[5,2,6,1,4,7,3]=>[3,6,2,7,4,1,5]=>[2,2,1,2]
[2,5,7,4,1,6,3]=>[2,7,5,1,4,6,3]=>[6,1,3,7,4,2,5]=>[1,3,1,2]
[2,5,7,4,3,1,6]=>[2,6,5,1,4,7,3]=>[6,2,3,7,4,1,5]=>[1,3,1,2]
[2,5,7,4,3,6,1]=>[2,5,4,7,1,6,3]=>[6,3,4,1,7,2,5]=>[1,2,2,2]
[2,5,7,4,6,1,3]=>[2,6,4,7,1,5,3]=>[6,2,4,1,7,3,5]=>[1,2,2,2]
[2,5,7,4,6,3,1]=>[2,4,7,6,1,5,3]=>[6,4,1,2,7,3,5]=>[1,1,3,2]
[2,5,7,6,1,3,4]=>[5,2,6,7,1,4,3]=>[3,6,2,1,7,4,5]=>[2,1,2,2]
[2,5,7,6,1,4,3]=>[2,7,5,6,1,4,3]=>[6,1,3,2,7,4,5]=>[1,2,2,2]
[2,5,7,6,3,1,4]=>[2,6,5,7,1,4,3]=>[6,2,3,1,7,4,5]=>[1,2,2,2]
[2,5,7,6,3,4,1]=>[2,5,7,6,1,4,3]=>[6,3,1,2,7,4,5]=>[1,1,3,2]
[2,5,7,6,4,1,3]=>[2,6,7,5,1,4,3]=>[6,2,1,3,7,4,5]=>[1,1,3,2]
[2,5,7,6,4,3,1]=>[7,2,6,5,1,4,3]=>[1,6,2,3,7,4,5]=>[2,3,2]
[2,6,1,3,4,5,7]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[1,1,1,1,2,1]
[2,6,1,3,4,7,5]=>[7,1,3,4,5,2,6]=>[1,7,5,4,3,6,2]=>[2,1,1,2,1]
[2,6,1,3,5,4,7]=>[6,1,3,4,5,2,7]=>[2,7,5,4,3,6,1]=>[2,1,1,2,1]
[2,6,1,3,5,7,4]=>[5,7,1,3,4,2,6]=>[3,1,7,5,4,6,2]=>[1,2,1,2,1]
[2,6,1,3,7,4,5]=>[6,7,1,3,4,2,5]=>[2,1,7,5,4,6,3]=>[1,2,1,2,1]
[2,6,1,3,7,5,4]=>[7,6,1,3,4,2,5]=>[1,2,7,5,4,6,3]=>[3,1,2,1]
[2,6,1,4,3,5,7]=>[5,1,3,4,6,2,7]=>[3,7,5,4,2,6,1]=>[2,1,1,2,1]
[2,6,1,4,3,7,5]=>[4,7,1,3,5,2,6]=>[4,1,7,5,3,6,2]=>[1,2,1,2,1]
[2,6,1,4,5,3,7]=>[4,6,1,3,5,2,7]=>[4,2,7,5,3,6,1]=>[1,2,1,2,1]
[2,6,1,4,5,7,3]=>[4,5,7,1,3,2,6]=>[4,3,1,7,5,6,2]=>[1,1,2,2,1]
[2,6,1,4,7,3,5]=>[4,6,7,1,3,2,5]=>[4,2,1,7,5,6,3]=>[1,1,2,2,1]
[2,6,1,4,7,5,3]=>[7,4,6,1,3,2,5]=>[1,4,2,7,5,6,3]=>[2,2,2,1]
[2,6,1,5,3,4,7]=>[5,6,1,3,4,2,7]=>[3,2,7,5,4,6,1]=>[1,2,1,2,1]
[2,6,1,5,3,7,4]=>[7,5,1,3,4,2,6]=>[1,3,7,5,4,6,2]=>[3,1,2,1]
[2,6,1,5,4,3,7]=>[6,5,1,3,4,2,7]=>[2,3,7,5,4,6,1]=>[3,1,2,1]
[2,6,1,5,4,7,3]=>[5,4,7,1,3,2,6]=>[3,4,1,7,5,6,2]=>[2,2,2,1]
[2,6,1,5,7,3,4]=>[6,4,7,1,3,2,5]=>[2,4,1,7,5,6,3]=>[2,2,2,1]
[2,6,1,5,7,4,3]=>[4,7,6,1,3,2,5]=>[4,1,2,7,5,6,3]=>[1,3,2,1]
[2,6,1,7,3,4,5]=>[5,6,7,1,3,2,4]=>[3,2,1,7,5,6,4]=>[1,1,2,2,1]
[2,6,1,7,3,5,4]=>[7,5,6,1,3,2,4]=>[1,3,2,7,5,6,4]=>[2,2,2,1]
[2,6,1,7,4,3,5]=>[6,5,7,1,3,2,4]=>[2,3,1,7,5,6,4]=>[2,2,2,1]
[2,6,1,7,4,5,3]=>[5,7,6,1,3,2,4]=>[3,1,2,7,5,6,4]=>[1,3,2,1]
[2,6,1,7,5,3,4]=>[6,7,5,1,3,2,4]=>[2,1,3,7,5,6,4]=>[1,3,2,1]
[2,6,1,7,5,4,3]=>[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>[4,2,1]
[2,6,3,1,4,5,7]=>[4,1,3,5,6,2,7]=>[4,7,5,3,2,6,1]=>[2,1,1,2,1]
[2,6,3,1,4,7,5]=>[3,7,1,4,5,2,6]=>[5,1,7,4,3,6,2]=>[1,2,1,2,1]
[2,6,3,1,5,4,7]=>[3,6,1,4,5,2,7]=>[5,2,7,4,3,6,1]=>[1,2,1,2,1]
[2,6,3,1,5,7,4]=>[3,5,7,1,4,2,6]=>[5,3,1,7,4,6,2]=>[1,1,2,2,1]
[2,6,3,1,7,4,5]=>[3,6,7,1,4,2,5]=>[5,2,1,7,4,6,3]=>[1,1,2,2,1]
[2,6,3,1,7,5,4]=>[7,3,6,1,4,2,5]=>[1,5,2,7,4,6,3]=>[2,2,2,1]
[2,6,3,4,1,5,7]=>[3,5,1,4,6,2,7]=>[5,3,7,4,2,6,1]=>[1,2,1,2,1]
[2,6,3,4,1,7,5]=>[3,4,7,1,5,2,6]=>[5,4,1,7,3,6,2]=>[1,1,2,2,1]
[2,6,3,4,5,1,7]=>[3,4,6,1,5,2,7]=>[5,4,2,7,3,6,1]=>[1,1,2,2,1]
[2,6,3,4,5,7,1]=>[3,4,5,1,2,7,6]=>[5,4,3,7,6,1,2]=>[1,1,2,1,2]
[2,6,3,4,7,1,5]=>[3,4,6,1,2,7,5]=>[5,4,2,7,6,1,3]=>[1,1,2,1,2]
[2,6,3,4,7,5,1]=>[7,3,4,1,2,6,5]=>[1,5,4,7,6,2,3]=>[2,2,1,2]
[2,6,3,5,1,4,7]=>[3,5,6,1,4,2,7]=>[5,3,2,7,4,6,1]=>[1,1,2,2,1]
[2,6,3,5,1,7,4]=>[7,3,5,1,4,2,6]=>[1,5,3,7,4,6,2]=>[2,2,2,1]
[2,6,3,5,4,1,7]=>[6,3,5,1,4,2,7]=>[2,5,3,7,4,6,1]=>[2,2,2,1]
[2,6,3,5,4,7,1]=>[5,3,4,1,2,7,6]=>[3,5,4,7,6,1,2]=>[2,2,1,2]
[2,6,3,5,7,1,4]=>[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]=>[2,2,1,2]
[2,6,3,5,7,4,1]=>[4,7,3,1,2,6,5]=>[4,1,5,7,6,2,3]=>[1,3,1,2]
[2,6,3,7,1,4,5]=>[3,5,6,1,2,7,4]=>[5,3,2,7,6,1,4]=>[1,1,2,1,2]
[2,6,3,7,1,5,4]=>[7,3,5,1,2,6,4]=>[1,5,3,7,6,2,4]=>[2,2,1,2]
[2,6,3,7,4,1,5]=>[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]=>[2,2,1,2]
[2,6,3,7,4,5,1]=>[5,7,3,1,2,6,4]=>[3,1,5,7,6,2,4]=>[1,3,1,2]
[2,6,3,7,5,1,4]=>[6,7,3,1,2,5,4]=>[2,1,5,7,6,3,4]=>[1,3,1,2]
[2,6,3,7,5,4,1]=>[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>[4,1,2]
[2,6,4,1,3,5,7]=>[4,5,1,3,6,2,7]=>[4,3,7,5,2,6,1]=>[1,2,1,2,1]
[2,6,4,1,3,7,5]=>[7,4,1,3,5,2,6]=>[1,4,7,5,3,6,2]=>[3,1,2,1]
[2,6,4,1,5,3,7]=>[6,4,1,3,5,2,7]=>[2,4,7,5,3,6,1]=>[3,1,2,1]
[2,6,4,1,5,7,3]=>[5,3,7,1,4,2,6]=>[3,5,1,7,4,6,2]=>[2,2,2,1]
[2,6,4,1,7,3,5]=>[6,3,7,1,4,2,5]=>[2,5,1,7,4,6,3]=>[2,2,2,1]
[2,6,4,1,7,5,3]=>[3,7,6,1,4,2,5]=>[5,1,2,7,4,6,3]=>[1,3,2,1]
[2,6,4,3,1,5,7]=>[5,4,1,3,6,2,7]=>[3,4,7,5,2,6,1]=>[3,1,2,1]
[2,6,4,3,1,7,5]=>[4,3,7,1,5,2,6]=>[4,5,1,7,3,6,2]=>[2,2,2,1]
[2,6,4,3,5,1,7]=>[4,3,6,1,5,2,7]=>[4,5,2,7,3,6,1]=>[2,2,2,1]
[2,6,4,3,5,7,1]=>[4,3,5,1,2,7,6]=>[4,5,3,7,6,1,2]=>[2,2,1,2]
[2,6,4,3,7,1,5]=>[4,3,6,1,2,7,5]=>[4,5,2,7,6,1,3]=>[2,2,1,2]
[2,6,4,3,7,5,1]=>[3,7,4,1,2,6,5]=>[5,1,4,7,6,2,3]=>[1,3,1,2]
[2,6,4,5,1,3,7]=>[5,3,6,1,4,2,7]=>[3,5,2,7,4,6,1]=>[2,2,2,1]
[2,6,4,5,1,7,3]=>[3,7,5,1,4,2,6]=>[5,1,3,7,4,6,2]=>[1,3,2,1]
[2,6,4,5,3,1,7]=>[3,6,5,1,4,2,7]=>[5,2,3,7,4,6,1]=>[1,3,2,1]
[2,6,4,5,3,7,1]=>[3,5,4,1,2,7,6]=>[5,3,4,7,6,1,2]=>[1,3,1,2]
[2,6,4,5,7,1,3]=>[3,6,4,1,2,7,5]=>[5,2,4,7,6,1,3]=>[1,3,1,2]
[2,6,4,5,7,3,1]=>[3,4,2,7,1,6,5]=>[5,4,6,1,7,2,3]=>[1,2,2,2]
[2,6,4,7,1,3,5]=>[5,3,6,1,2,7,4]=>[3,5,2,7,6,1,4]=>[2,2,1,2]
[2,6,4,7,1,5,3]=>[3,7,5,1,2,6,4]=>[5,1,3,7,6,2,4]=>[1,3,1,2]
[2,6,4,7,3,1,5]=>[3,6,5,1,2,7,4]=>[5,2,3,7,6,1,4]=>[1,3,1,2]
[2,6,4,7,3,5,1]=>[3,5,2,7,1,6,4]=>[5,3,6,1,7,2,4]=>[1,2,2,2]
[2,6,4,7,5,1,3]=>[3,6,2,7,1,5,4]=>[5,2,6,1,7,3,4]=>[1,2,2,2]
[2,6,4,7,5,3,1]=>[7,3,2,6,1,5,4]=>[1,5,6,2,7,3,4]=>[3,2,2]
[2,6,5,1,3,4,7]=>[4,5,6,1,3,2,7]=>[4,3,2,7,5,6,1]=>[1,1,2,2,1]
[2,6,5,1,3,7,4]=>[7,4,5,1,3,2,6]=>[1,4,3,7,5,6,2]=>[2,2,2,1]
[2,6,5,1,4,3,7]=>[6,4,5,1,3,2,7]=>[2,4,3,7,5,6,1]=>[2,2,2,1]
[2,6,5,1,4,7,3]=>[5,7,4,1,3,2,6]=>[3,1,4,7,5,6,2]=>[1,3,2,1]
[2,6,5,1,7,3,4]=>[6,7,4,1,3,2,5]=>[2,1,4,7,5,6,3]=>[1,3,2,1]
[2,6,5,1,7,4,3]=>[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>[4,2,1]
[2,6,5,3,1,4,7]=>[5,4,6,1,3,2,7]=>[3,4,2,7,5,6,1]=>[2,2,2,1]
[2,6,5,3,1,7,4]=>[4,7,5,1,3,2,6]=>[4,1,3,7,5,6,2]=>[1,3,2,1]
[2,6,5,3,4,1,7]=>[4,6,5,1,3,2,7]=>[4,2,3,7,5,6,1]=>[1,3,2,1]
[2,6,5,3,4,7,1]=>[4,5,3,1,2,7,6]=>[4,3,5,7,6,1,2]=>[1,3,1,2]
[2,6,5,3,7,1,4]=>[4,6,3,1,2,7,5]=>[4,2,5,7,6,1,3]=>[1,3,1,2]
[2,6,5,3,7,4,1]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>[4,1,2]
[2,6,5,4,1,3,7]=>[5,6,4,1,3,2,7]=>[3,2,4,7,5,6,1]=>[1,3,2,1]
[2,6,5,4,1,7,3]=>[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>[4,2,1]
[2,6,5,4,3,1,7]=>[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>[4,2,1]
[2,6,5,4,3,7,1]=>[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>[4,1,2]
[2,6,5,4,7,1,3]=>[6,4,3,1,2,7,5]=>[2,4,5,7,6,1,3]=>[4,1,2]
[2,6,5,4,7,3,1]=>[4,3,2,7,1,6,5]=>[4,5,6,1,7,2,3]=>[3,2,2]
[2,6,5,7,1,3,4]=>[5,6,3,1,2,7,4]=>[3,2,5,7,6,1,4]=>[1,3,1,2]
[2,6,5,7,1,4,3]=>[7,5,3,1,2,6,4]=>[1,3,5,7,6,2,4]=>[4,1,2]
[2,6,5,7,3,1,4]=>[6,5,3,1,2,7,4]=>[2,3,5,7,6,1,4]=>[4,1,2]
[2,6,5,7,3,4,1]=>[5,3,2,7,1,6,4]=>[3,5,6,1,7,2,4]=>[3,2,2]
[2,6,5,7,4,1,3]=>[6,3,2,7,1,5,4]=>[2,5,6,1,7,3,4]=>[3,2,2]
[2,6,5,7,4,3,1]=>[3,2,7,6,1,5,4]=>[5,6,1,2,7,3,4]=>[2,3,2]
[2,6,7,1,3,4,5]=>[4,5,6,1,2,7,3]=>[4,3,2,7,6,1,5]=>[1,1,2,1,2]
[2,6,7,1,3,5,4]=>[7,4,5,1,2,6,3]=>[1,4,3,7,6,2,5]=>[2,2,1,2]
[2,6,7,1,4,3,5]=>[6,4,5,1,2,7,3]=>[2,4,3,7,6,1,5]=>[2,2,1,2]
[2,6,7,1,4,5,3]=>[5,7,4,1,2,6,3]=>[3,1,4,7,6,2,5]=>[1,3,1,2]
[2,6,7,1,5,3,4]=>[6,7,4,1,2,5,3]=>[2,1,4,7,6,3,5]=>[1,3,1,2]
[2,6,7,1,5,4,3]=>[7,6,4,1,2,5,3]=>[1,2,4,7,6,3,5]=>[4,1,2]
[2,6,7,3,1,4,5]=>[5,4,6,1,2,7,3]=>[3,4,2,7,6,1,5]=>[2,2,1,2]
[2,6,7,3,1,5,4]=>[4,7,5,1,2,6,3]=>[4,1,3,7,6,2,5]=>[1,3,1,2]
[2,6,7,3,4,1,5]=>[4,6,5,1,2,7,3]=>[4,2,3,7,6,1,5]=>[1,3,1,2]
[2,6,7,3,4,5,1]=>[4,5,2,7,1,6,3]=>[4,3,6,1,7,2,5]=>[1,2,2,2]
[2,6,7,3,5,1,4]=>[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>[1,2,2,2]
[2,6,7,3,5,4,1]=>[7,4,2,6,1,5,3]=>[1,4,6,2,7,3,5]=>[3,2,2]
[2,6,7,4,1,3,5]=>[5,6,4,1,2,7,3]=>[3,2,4,7,6,1,5]=>[1,3,1,2]
[2,6,7,4,1,5,3]=>[7,5,4,1,2,6,3]=>[1,3,4,7,6,2,5]=>[4,1,2]
[2,6,7,4,3,1,5]=>[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]=>[4,1,2]
[2,6,7,4,3,5,1]=>[5,4,2,7,1,6,3]=>[3,4,6,1,7,2,5]=>[3,2,2]
[2,6,7,4,5,1,3]=>[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>[3,2,2]
[2,6,7,4,5,3,1]=>[4,2,7,6,1,5,3]=>[4,6,1,2,7,3,5]=>[2,3,2]
[2,6,7,5,1,3,4]=>[5,6,2,7,1,4,3]=>[3,2,6,1,7,4,5]=>[1,2,2,2]
[2,6,7,5,1,4,3]=>[7,5,2,6,1,4,3]=>[1,3,6,2,7,4,5]=>[3,2,2]
[2,6,7,5,3,1,4]=>[6,5,2,7,1,4,3]=>[2,3,6,1,7,4,5]=>[3,2,2]
[2,6,7,5,3,4,1]=>[5,2,7,6,1,4,3]=>[3,6,1,2,7,4,5]=>[2,3,2]
[2,6,7,5,4,1,3]=>[6,2,7,5,1,4,3]=>[2,6,1,3,7,4,5]=>[2,3,2]
[2,6,7,5,4,3,1]=>[2,7,6,5,1,4,3]=>[6,1,2,3,7,4,5]=>[1,4,2]
[2,7,1,3,4,5,6]=>[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]
[2,7,1,3,4,6,5]=>[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>[2,1,1,1,2]
[2,7,1,3,5,4,6]=>[6,1,3,4,5,7,2]=>[2,7,5,4,3,1,6]=>[2,1,1,1,2]
[2,7,1,3,5,6,4]=>[5,7,1,3,4,6,2]=>[3,1,7,5,4,2,6]=>[1,2,1,1,2]
[2,7,1,3,6,4,5]=>[6,7,1,3,4,5,2]=>[2,1,7,5,4,3,6]=>[1,2,1,1,2]
[2,7,1,3,6,5,4]=>[7,6,1,3,4,5,2]=>[1,2,7,5,4,3,6]=>[3,1,1,2]
[2,7,1,4,3,5,6]=>[5,1,3,4,6,7,2]=>[3,7,5,4,2,1,6]=>[2,1,1,1,2]
[2,7,1,4,3,6,5]=>[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>[1,2,1,1,2]
[2,7,1,4,5,3,6]=>[4,6,1,3,5,7,2]=>[4,2,7,5,3,1,6]=>[1,2,1,1,2]
[2,7,1,4,5,6,3]=>[4,5,7,1,3,6,2]=>[4,3,1,7,5,2,6]=>[1,1,2,1,2]
[2,7,1,4,6,3,5]=>[4,6,7,1,3,5,2]=>[4,2,1,7,5,3,6]=>[1,1,2,1,2]
[2,7,1,4,6,5,3]=>[7,4,6,1,3,5,2]=>[1,4,2,7,5,3,6]=>[2,2,1,2]
[2,7,1,5,3,4,6]=>[5,6,1,3,4,7,2]=>[3,2,7,5,4,1,6]=>[1,2,1,1,2]
[2,7,1,5,3,6,4]=>[7,5,1,3,4,6,2]=>[1,3,7,5,4,2,6]=>[3,1,1,2]
[2,7,1,5,4,3,6]=>[6,5,1,3,4,7,2]=>[2,3,7,5,4,1,6]=>[3,1,1,2]
[2,7,1,5,4,6,3]=>[5,4,7,1,3,6,2]=>[3,4,1,7,5,2,6]=>[2,2,1,2]
[2,7,1,5,6,3,4]=>[6,4,7,1,3,5,2]=>[2,4,1,7,5,3,6]=>[2,2,1,2]
[2,7,1,5,6,4,3]=>[4,7,6,1,3,5,2]=>[4,1,2,7,5,3,6]=>[1,3,1,2]
[2,7,1,6,3,4,5]=>[5,6,7,1,3,4,2]=>[3,2,1,7,5,4,6]=>[1,1,2,1,2]
[2,7,1,6,3,5,4]=>[7,5,6,1,3,4,2]=>[1,3,2,7,5,4,6]=>[2,2,1,2]
[2,7,1,6,4,3,5]=>[6,5,7,1,3,4,2]=>[2,3,1,7,5,4,6]=>[2,2,1,2]
[2,7,1,6,4,5,3]=>[5,7,6,1,3,4,2]=>[3,1,2,7,5,4,6]=>[1,3,1,2]
[2,7,1,6,5,3,4]=>[6,7,5,1,3,4,2]=>[2,1,3,7,5,4,6]=>[1,3,1,2]
[2,7,1,6,5,4,3]=>[7,6,5,1,3,4,2]=>[1,2,3,7,5,4,6]=>[4,1,2]
[2,7,3,1,4,5,6]=>[4,1,3,5,6,7,2]=>[4,7,5,3,2,1,6]=>[2,1,1,1,2]
[2,7,3,1,4,6,5]=>[3,7,1,4,5,6,2]=>[5,1,7,4,3,2,6]=>[1,2,1,1,2]
[2,7,3,1,5,4,6]=>[3,6,1,4,5,7,2]=>[5,2,7,4,3,1,6]=>[1,2,1,1,2]
[2,7,3,1,5,6,4]=>[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>[1,1,2,1,2]
[2,7,3,1,6,4,5]=>[3,6,7,1,4,5,2]=>[5,2,1,7,4,3,6]=>[1,1,2,1,2]
[2,7,3,1,6,5,4]=>[7,3,6,1,4,5,2]=>[1,5,2,7,4,3,6]=>[2,2,1,2]
[2,7,3,4,1,5,6]=>[3,5,1,4,6,7,2]=>[5,3,7,4,2,1,6]=>[1,2,1,1,2]
[2,7,3,4,1,6,5]=>[3,4,7,1,5,6,2]=>[5,4,1,7,3,2,6]=>[1,1,2,1,2]
[2,7,3,4,5,1,6]=>[3,4,6,1,5,7,2]=>[5,4,2,7,3,1,6]=>[1,1,2,1,2]
[2,7,3,4,5,6,1]=>[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>[1,1,1,2,2]
[2,7,3,4,6,1,5]=>[3,4,6,7,1,5,2]=>[5,4,2,1,7,3,6]=>[1,1,1,2,2]
[2,7,3,4,6,5,1]=>[7,3,4,6,1,5,2]=>[1,5,4,2,7,3,6]=>[2,1,2,2]
[2,7,3,5,1,4,6]=>[3,5,6,1,4,7,2]=>[5,3,2,7,4,1,6]=>[1,1,2,1,2]
[2,7,3,5,1,6,4]=>[7,3,5,1,4,6,2]=>[1,5,3,7,4,2,6]=>[2,2,1,2]
[2,7,3,5,4,1,6]=>[6,3,5,1,4,7,2]=>[2,5,3,7,4,1,6]=>[2,2,1,2]
[2,7,3,5,4,6,1]=>[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>[2,1,2,2]
[2,7,3,5,6,1,4]=>[6,3,4,7,1,5,2]=>[2,5,4,1,7,3,6]=>[2,1,2,2]
[2,7,3,5,6,4,1]=>[4,7,3,6,1,5,2]=>[4,1,5,2,7,3,6]=>[1,2,2,2]
[2,7,3,6,1,4,5]=>[3,5,6,7,1,4,2]=>[5,3,2,1,7,4,6]=>[1,1,1,2,2]
[2,7,3,6,1,5,4]=>[7,3,5,6,1,4,2]=>[1,5,3,2,7,4,6]=>[2,1,2,2]
[2,7,3,6,4,1,5]=>[6,3,5,7,1,4,2]=>[2,5,3,1,7,4,6]=>[2,1,2,2]
[2,7,3,6,4,5,1]=>[5,7,3,6,1,4,2]=>[3,1,5,2,7,4,6]=>[1,2,2,2]
[2,7,3,6,5,1,4]=>[6,7,3,5,1,4,2]=>[2,1,5,3,7,4,6]=>[1,2,2,2]
[2,7,3,6,5,4,1]=>[7,6,3,5,1,4,2]=>[1,2,5,3,7,4,6]=>[3,2,2]
[2,7,4,1,3,5,6]=>[4,5,1,3,6,7,2]=>[4,3,7,5,2,1,6]=>[1,2,1,1,2]
[2,7,4,1,3,6,5]=>[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>[3,1,1,2]
[2,7,4,1,5,3,6]=>[6,4,1,3,5,7,2]=>[2,4,7,5,3,1,6]=>[3,1,1,2]
[2,7,4,1,5,6,3]=>[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>[2,2,1,2]
[2,7,4,1,6,3,5]=>[6,3,7,1,4,5,2]=>[2,5,1,7,4,3,6]=>[2,2,1,2]
[2,7,4,1,6,5,3]=>[3,7,6,1,4,5,2]=>[5,1,2,7,4,3,6]=>[1,3,1,2]
[2,7,4,3,1,5,6]=>[5,4,1,3,6,7,2]=>[3,4,7,5,2,1,6]=>[3,1,1,2]
[2,7,4,3,1,6,5]=>[4,3,7,1,5,6,2]=>[4,5,1,7,3,2,6]=>[2,2,1,2]
[2,7,4,3,5,1,6]=>[4,3,6,1,5,7,2]=>[4,5,2,7,3,1,6]=>[2,2,1,2]
[2,7,4,3,5,6,1]=>[4,3,5,7,1,6,2]=>[4,5,3,1,7,2,6]=>[2,1,2,2]
[2,7,4,3,6,1,5]=>[4,3,6,7,1,5,2]=>[4,5,2,1,7,3,6]=>[2,1,2,2]
[2,7,4,3,6,5,1]=>[3,7,4,6,1,5,2]=>[5,1,4,2,7,3,6]=>[1,2,2,2]
[2,7,4,5,1,3,6]=>[5,3,6,1,4,7,2]=>[3,5,2,7,4,1,6]=>[2,2,1,2]
[2,7,4,5,1,6,3]=>[3,7,5,1,4,6,2]=>[5,1,3,7,4,2,6]=>[1,3,1,2]
[2,7,4,5,3,1,6]=>[3,6,5,1,4,7,2]=>[5,2,3,7,4,1,6]=>[1,3,1,2]
[2,7,4,5,3,6,1]=>[3,5,4,7,1,6,2]=>[5,3,4,1,7,2,6]=>[1,2,2,2]
[2,7,4,5,6,1,3]=>[3,6,4,7,1,5,2]=>[5,2,4,1,7,3,6]=>[1,2,2,2]
[2,7,4,5,6,3,1]=>[3,4,7,6,1,5,2]=>[5,4,1,2,7,3,6]=>[1,1,3,2]
[2,7,4,6,1,3,5]=>[5,3,6,7,1,4,2]=>[3,5,2,1,7,4,6]=>[2,1,2,2]
[2,7,4,6,1,5,3]=>[3,7,5,6,1,4,2]=>[5,1,3,2,7,4,6]=>[1,2,2,2]
[2,7,4,6,3,1,5]=>[3,6,5,7,1,4,2]=>[5,2,3,1,7,4,6]=>[1,2,2,2]
[2,7,4,6,3,5,1]=>[3,5,7,6,1,4,2]=>[5,3,1,2,7,4,6]=>[1,1,3,2]
[2,7,4,6,5,1,3]=>[3,6,7,5,1,4,2]=>[5,2,1,3,7,4,6]=>[1,1,3,2]
[2,7,4,6,5,3,1]=>[7,3,6,5,1,4,2]=>[1,5,2,3,7,4,6]=>[2,3,2]
[2,7,5,1,3,4,6]=>[4,5,6,1,3,7,2]=>[4,3,2,7,5,1,6]=>[1,1,2,1,2]
[2,7,5,1,3,6,4]=>[7,4,5,1,3,6,2]=>[1,4,3,7,5,2,6]=>[2,2,1,2]
[2,7,5,1,4,3,6]=>[6,4,5,1,3,7,2]=>[2,4,3,7,5,1,6]=>[2,2,1,2]
[2,7,5,1,4,6,3]=>[5,7,4,1,3,6,2]=>[3,1,4,7,5,2,6]=>[1,3,1,2]
[2,7,5,1,6,3,4]=>[6,7,4,1,3,5,2]=>[2,1,4,7,5,3,6]=>[1,3,1,2]
[2,7,5,1,6,4,3]=>[7,6,4,1,3,5,2]=>[1,2,4,7,5,3,6]=>[4,1,2]
[2,7,5,3,1,4,6]=>[5,4,6,1,3,7,2]=>[3,4,2,7,5,1,6]=>[2,2,1,2]
[2,7,5,3,1,6,4]=>[4,7,5,1,3,6,2]=>[4,1,3,7,5,2,6]=>[1,3,1,2]
[2,7,5,3,4,1,6]=>[4,6,5,1,3,7,2]=>[4,2,3,7,5,1,6]=>[1,3,1,2]
[2,7,5,3,4,6,1]=>[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>[1,2,2,2]
[2,7,5,3,6,1,4]=>[4,6,3,7,1,5,2]=>[4,2,5,1,7,3,6]=>[1,2,2,2]
[2,7,5,3,6,4,1]=>[7,4,3,6,1,5,2]=>[1,4,5,2,7,3,6]=>[3,2,2]
[2,7,5,4,1,3,6]=>[5,6,4,1,3,7,2]=>[3,2,4,7,5,1,6]=>[1,3,1,2]
[2,7,5,4,1,6,3]=>[7,5,4,1,3,6,2]=>[1,3,4,7,5,2,6]=>[4,1,2]
[2,7,5,4,3,1,6]=>[6,5,4,1,3,7,2]=>[2,3,4,7,5,1,6]=>[4,1,2]
[2,7,5,4,3,6,1]=>[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>[3,2,2]
[2,7,5,4,6,1,3]=>[6,4,3,7,1,5,2]=>[2,4,5,1,7,3,6]=>[3,2,2]
[2,7,5,4,6,3,1]=>[4,3,7,6,1,5,2]=>[4,5,1,2,7,3,6]=>[2,3,2]
[2,7,5,6,1,3,4]=>[5,6,3,7,1,4,2]=>[3,2,5,1,7,4,6]=>[1,2,2,2]
[2,7,5,6,1,4,3]=>[7,5,3,6,1,4,2]=>[1,3,5,2,7,4,6]=>[3,2,2]
[2,7,5,6,3,1,4]=>[6,5,3,7,1,4,2]=>[2,3,5,1,7,4,6]=>[3,2,2]
[2,7,5,6,3,4,1]=>[5,3,7,6,1,4,2]=>[3,5,1,2,7,4,6]=>[2,3,2]
[2,7,5,6,4,1,3]=>[6,3,7,5,1,4,2]=>[2,5,1,3,7,4,6]=>[2,3,2]
[2,7,5,6,4,3,1]=>[3,7,6,5,1,4,2]=>[5,1,2,3,7,4,6]=>[1,4,2]
[2,7,6,1,3,4,5]=>[4,5,6,7,1,3,2]=>[4,3,2,1,7,5,6]=>[1,1,1,2,2]
[2,7,6,1,3,5,4]=>[7,4,5,6,1,3,2]=>[1,4,3,2,7,5,6]=>[2,1,2,2]
[2,7,6,1,4,3,5]=>[6,4,5,7,1,3,2]=>[2,4,3,1,7,5,6]=>[2,1,2,2]
[2,7,6,1,4,5,3]=>[5,7,4,6,1,3,2]=>[3,1,4,2,7,5,6]=>[1,2,2,2]
[2,7,6,1,5,3,4]=>[6,7,4,5,1,3,2]=>[2,1,4,3,7,5,6]=>[1,2,2,2]
[2,7,6,1,5,4,3]=>[7,6,4,5,1,3,2]=>[1,2,4,3,7,5,6]=>[3,2,2]
[2,7,6,3,1,4,5]=>[5,4,6,7,1,3,2]=>[3,4,2,1,7,5,6]=>[2,1,2,2]
[2,7,6,3,1,5,4]=>[4,7,5,6,1,3,2]=>[4,1,3,2,7,5,6]=>[1,2,2,2]
[2,7,6,3,4,1,5]=>[4,6,5,7,1,3,2]=>[4,2,3,1,7,5,6]=>[1,2,2,2]
[2,7,6,3,4,5,1]=>[4,5,7,6,1,3,2]=>[4,3,1,2,7,5,6]=>[1,1,3,2]
[2,7,6,3,5,1,4]=>[4,6,7,5,1,3,2]=>[4,2,1,3,7,5,6]=>[1,1,3,2]
[2,7,6,3,5,4,1]=>[7,4,6,5,1,3,2]=>[1,4,2,3,7,5,6]=>[2,3,2]
[2,7,6,4,1,3,5]=>[5,6,4,7,1,3,2]=>[3,2,4,1,7,5,6]=>[1,2,2,2]
[2,7,6,4,1,5,3]=>[7,5,4,6,1,3,2]=>[1,3,4,2,7,5,6]=>[3,2,2]
[2,7,6,4,3,1,5]=>[6,5,4,7,1,3,2]=>[2,3,4,1,7,5,6]=>[3,2,2]
[2,7,6,4,3,5,1]=>[5,4,7,6,1,3,2]=>[3,4,1,2,7,5,6]=>[2,3,2]
[2,7,6,4,5,1,3]=>[6,4,7,5,1,3,2]=>[2,4,1,3,7,5,6]=>[2,3,2]
[2,7,6,4,5,3,1]=>[4,7,6,5,1,3,2]=>[4,1,2,3,7,5,6]=>[1,4,2]
[2,7,6,5,1,3,4]=>[5,6,7,4,1,3,2]=>[3,2,1,4,7,5,6]=>[1,1,3,2]
[2,7,6,5,1,4,3]=>[7,5,6,4,1,3,2]=>[1,3,2,4,7,5,6]=>[2,3,2]
[2,7,6,5,3,1,4]=>[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>[2,3,2]
[2,7,6,5,3,4,1]=>[5,7,6,4,1,3,2]=>[3,1,2,4,7,5,6]=>[1,4,2]
[2,7,6,5,4,1,3]=>[6,7,5,4,1,3,2]=>[2,1,3,4,7,5,6]=>[1,4,2]
[2,7,6,5,4,3,1]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>[5,2]
[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>[1,2,1,1,1,1]
[3,1,2,4,5,7,6]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[3,1,1,1,1]
[3,1,2,4,6,5,7]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[3,1,1,1,1]
[3,1,2,4,6,7,5]=>[5,1,7,2,3,4,6]=>[3,7,1,6,5,4,2]=>[2,2,1,1,1]
[3,1,2,4,7,5,6]=>[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]=>[2,2,1,1,1]
[3,1,2,4,7,6,5]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[1,3,1,1,1]
[3,1,2,5,4,6,7]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[3,1,1,1,1]
[3,1,2,5,4,7,6]=>[4,1,7,2,3,5,6]=>[4,7,1,6,5,3,2]=>[2,2,1,1,1]
[3,1,2,5,6,4,7]=>[4,1,6,2,3,5,7]=>[4,7,2,6,5,3,1]=>[2,2,1,1,1]
[3,1,2,5,6,7,4]=>[4,1,5,7,2,3,6]=>[4,7,3,1,6,5,2]=>[2,1,2,1,1]
[3,1,2,5,7,4,6]=>[4,1,6,7,2,3,5]=>[4,7,2,1,6,5,3]=>[2,1,2,1,1]
[3,1,2,5,7,6,4]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>[1,2,2,1,1]
[3,1,2,6,4,5,7]=>[5,1,6,2,3,4,7]=>[3,7,2,6,5,4,1]=>[2,2,1,1,1]
[3,1,2,6,4,7,5]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[1,3,1,1,1]
[3,1,2,6,5,4,7]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[1,3,1,1,1]
[3,1,2,6,5,7,4]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>[1,2,2,1,1]
[3,1,2,6,7,4,5]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>[1,2,2,1,1]
[3,1,2,6,7,5,4]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>[1,1,3,1,1]
[3,1,2,7,4,5,6]=>[5,1,6,7,2,3,4]=>[3,7,2,1,6,5,4]=>[2,1,2,1,1]
[3,1,2,7,4,6,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>[1,2,2,1,1]
[3,1,2,7,5,4,6]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>[1,2,2,1,1]
[3,1,2,7,5,6,4]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>[1,1,3,1,1]
[3,1,2,7,6,4,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>[1,1,3,1,1]
[3,1,2,7,6,5,4]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[2,3,1,1]
[3,1,4,2,5,6,7]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[3,1,1,1,1]
[3,1,4,2,5,7,6]=>[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]=>[2,2,1,1,1]
[3,1,4,2,6,5,7]=>[3,1,6,2,4,5,7]=>[5,7,2,6,4,3,1]=>[2,2,1,1,1]
[3,1,4,2,6,7,5]=>[3,1,5,7,2,4,6]=>[5,7,3,1,6,4,2]=>[2,1,2,1,1]
[3,1,4,2,7,5,6]=>[3,1,6,7,2,4,5]=>[5,7,2,1,6,4,3]=>[2,1,2,1,1]
[3,1,4,2,7,6,5]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>[1,2,2,1,1]
[3,1,4,5,2,6,7]=>[3,1,5,2,4,6,7]=>[5,7,3,6,4,2,1]=>[2,2,1,1,1]
[3,1,4,5,2,7,6]=>[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]=>[2,1,2,1,1]
[3,1,4,5,6,2,7]=>[3,1,4,6,2,5,7]=>[5,7,4,2,6,3,1]=>[2,1,2,1,1]
[3,1,4,5,6,7,2]=>[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]=>[2,1,1,2,1]
[3,1,4,5,7,2,6]=>[3,1,4,6,7,2,5]=>[5,7,4,2,1,6,3]=>[2,1,1,2,1]
[3,1,4,5,7,6,2]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>[1,2,1,2,1]
[3,1,4,6,2,5,7]=>[3,1,5,6,2,4,7]=>[5,7,3,2,6,4,1]=>[2,1,2,1,1]
[3,1,4,6,2,7,5]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>[1,2,2,1,1]
[3,1,4,6,5,2,7]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>[1,2,2,1,1]
[3,1,4,6,5,7,2]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>[1,2,1,2,1]
[3,1,4,6,7,2,5]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>[1,2,1,2,1]
[3,1,4,6,7,5,2]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>[1,1,2,2,1]
[3,1,4,7,2,5,6]=>[3,1,5,6,7,2,4]=>[5,7,3,2,1,6,4]=>[2,1,1,2,1]
[3,1,4,7,2,6,5]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>[1,2,1,2,1]
[3,1,4,7,5,2,6]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>[1,2,1,2,1]
[3,1,4,7,5,6,2]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>[1,1,2,2,1]
[3,1,4,7,6,2,5]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>[1,1,2,2,1]
[3,1,4,7,6,5,2]=>[7,1,6,3,5,2,4]=>[1,7,2,5,3,6,4]=>[2,2,2,1]
[3,1,5,2,4,6,7]=>[4,1,5,2,3,6,7]=>[4,7,3,6,5,2,1]=>[2,2,1,1,1]
[3,1,5,2,4,7,6]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[1,3,1,1,1]
[3,1,5,2,6,4,7]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[1,3,1,1,1]
[3,1,5,2,6,7,4]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>[1,2,2,1,1]
[3,1,5,2,7,4,6]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>[1,2,2,1,1]
[3,1,5,2,7,6,4]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>[1,1,3,1,1]
[3,1,5,4,2,6,7]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[1,3,1,1,1]
[3,1,5,4,2,7,6]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>[1,2,2,1,1]
[3,1,5,4,6,2,7]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>[1,2,2,1,1]
[3,1,5,4,6,7,2]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>[1,2,1,2,1]
[3,1,5,4,7,2,6]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>[1,2,1,2,1]
[3,1,5,4,7,6,2]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>[1,1,2,2,1]
[3,1,5,6,2,4,7]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[1,2,2,1,1]
[3,1,5,6,2,7,4]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>[1,1,3,1,1]
[3,1,5,6,4,2,7]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>[1,1,3,1,1]
[3,1,5,6,4,7,2]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>[1,1,2,2,1]
[3,1,5,6,7,2,4]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>[1,1,2,2,1]
[3,1,5,6,7,4,2]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>[1,1,1,3,1]
[3,1,5,7,2,4,6]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>[1,2,1,2,1]
[3,1,5,7,2,6,4]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>[1,1,2,2,1]
[3,1,5,7,4,2,6]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>[1,1,2,2,1]
[3,1,5,7,4,6,2]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>[1,1,1,3,1]
[3,1,5,7,6,2,4]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>[1,1,1,3,1]
[3,1,5,7,6,4,2]=>[7,1,3,6,5,2,4]=>[1,7,5,2,3,6,4]=>[2,1,3,1]
[3,1,6,2,4,5,7]=>[4,1,5,6,2,3,7]=>[4,7,3,2,6,5,1]=>[2,1,2,1,1]
[3,1,6,2,4,7,5]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>[1,2,2,1,1]
[3,1,6,2,5,4,7]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>[1,2,2,1,1]
[3,1,6,2,5,7,4]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>[1,1,3,1,1]
[3,1,6,2,7,4,5]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>[1,1,3,1,1]
[3,1,6,2,7,5,4]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[2,3,1,1]
[3,1,6,4,2,5,7]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>[1,2,2,1,1]
[3,1,6,4,2,7,5]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>[1,1,3,1,1]
[3,1,6,4,5,2,7]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>[1,1,3,1,1]
[3,1,6,4,5,7,2]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>[1,1,2,2,1]
[3,1,6,4,7,2,5]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>[1,1,2,2,1]
[3,1,6,4,7,5,2]=>[7,1,4,3,6,2,5]=>[1,7,4,5,2,6,3]=>[2,2,2,1]
[3,1,6,5,2,4,7]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>[1,1,3,1,1]
[3,1,6,5,2,7,4]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>[2,3,1,1]
[3,1,6,5,4,2,7]=>[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>[2,3,1,1]
[3,1,6,5,4,7,2]=>[5,1,4,3,7,2,6]=>[3,7,4,5,1,6,2]=>[2,2,2,1]
[3,1,6,5,7,2,4]=>[6,1,4,3,7,2,5]=>[2,7,4,5,1,6,3]=>[2,2,2,1]
[3,1,6,5,7,4,2]=>[4,1,3,7,6,2,5]=>[4,7,5,1,2,6,3]=>[2,1,3,1]
[3,1,6,7,2,4,5]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>[1,1,2,2,1]
[3,1,6,7,2,5,4]=>[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>[2,2,2,1]
[3,1,6,7,4,2,5]=>[6,1,5,3,7,2,4]=>[2,7,3,5,1,6,4]=>[2,2,2,1]
[3,1,6,7,4,5,2]=>[5,1,3,7,6,2,4]=>[3,7,5,1,2,6,4]=>[2,1,3,1]
[3,1,6,7,5,2,4]=>[6,1,3,7,5,2,4]=>[2,7,5,1,3,6,4]=>[2,1,3,1]
[3,1,6,7,5,4,2]=>[3,7,1,6,5,2,4]=>[5,1,7,2,3,6,4]=>[1,2,3,1]
[3,1,7,2,4,5,6]=>[4,1,5,6,7,2,3]=>[4,7,3,2,1,6,5]=>[2,1,1,2,1]
[3,1,7,2,4,6,5]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>[1,2,1,2,1]
[3,1,7,2,5,4,6]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>[1,2,1,2,1]
[3,1,7,2,5,6,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>[1,1,2,2,1]
[3,1,7,2,6,4,5]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>[1,1,2,2,1]
[3,1,7,2,6,5,4]=>[7,1,6,4,5,2,3]=>[1,7,2,4,3,6,5]=>[2,2,2,1]
[3,1,7,4,2,5,6]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>[1,2,1,2,1]
[3,1,7,4,2,6,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>[1,1,2,2,1]
[3,1,7,4,5,2,6]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>[1,1,2,2,1]
[3,1,7,4,5,6,2]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>[1,1,1,3,1]
[3,1,7,4,6,2,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>[1,1,1,3,1]
[3,1,7,4,6,5,2]=>[7,1,4,6,5,2,3]=>[1,7,4,2,3,6,5]=>[2,1,3,1]
[3,1,7,5,2,4,6]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>[1,1,2,2,1]
[3,1,7,5,2,6,4]=>[7,1,5,4,6,2,3]=>[1,7,3,4,2,6,5]=>[2,2,2,1]
[3,1,7,5,4,2,6]=>[6,1,5,4,7,2,3]=>[2,7,3,4,1,6,5]=>[2,2,2,1]
[3,1,7,5,4,6,2]=>[5,1,4,7,6,2,3]=>[3,7,4,1,2,6,5]=>[2,1,3,1]
[3,1,7,5,6,2,4]=>[6,1,4,7,5,2,3]=>[2,7,4,1,3,6,5]=>[2,1,3,1]
[3,1,7,5,6,4,2]=>[4,7,1,6,5,2,3]=>[4,1,7,2,3,6,5]=>[1,2,3,1]
[3,1,7,6,2,4,5]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>[1,1,1,3,1]
[3,1,7,6,2,5,4]=>[7,1,5,6,4,2,3]=>[1,7,3,2,4,6,5]=>[2,1,3,1]
[3,1,7,6,4,2,5]=>[6,1,5,7,4,2,3]=>[2,7,3,1,4,6,5]=>[2,1,3,1]
[3,1,7,6,4,5,2]=>[5,7,1,6,4,2,3]=>[3,1,7,2,4,6,5]=>[1,2,3,1]
[3,1,7,6,5,2,4]=>[6,7,1,5,4,2,3]=>[2,1,7,3,4,6,5]=>[1,2,3,1]
[3,1,7,6,5,4,2]=>[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>[3,3,1]
[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[3,1,1,1,1]
[3,2,1,4,5,7,6]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>[2,2,1,1,1]
[3,2,1,4,6,5,7]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>[2,2,1,1,1]
[3,2,1,4,6,7,5]=>[2,1,5,7,3,4,6]=>[6,7,3,1,5,4,2]=>[2,1,2,1,1]
[3,2,1,4,7,5,6]=>[2,1,6,7,3,4,5]=>[6,7,2,1,5,4,3]=>[2,1,2,1,1]
[3,2,1,4,7,6,5]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[1,2,2,1,1]
[3,2,1,5,4,6,7]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>[2,2,1,1,1]
[3,2,1,5,4,7,6]=>[2,1,4,7,3,5,6]=>[6,7,4,1,5,3,2]=>[2,1,2,1,1]
[3,2,1,5,6,4,7]=>[2,1,4,6,3,5,7]=>[6,7,4,2,5,3,1]=>[2,1,2,1,1]
[3,2,1,5,6,7,4]=>[2,1,4,5,7,3,6]=>[6,7,4,3,1,5,2]=>[2,1,1,2,1]
[3,2,1,5,7,4,6]=>[2,1,4,6,7,3,5]=>[6,7,4,2,1,5,3]=>[2,1,1,2,1]
[3,2,1,5,7,6,4]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>[1,2,1,2,1]
[3,2,1,6,4,5,7]=>[2,1,5,6,3,4,7]=>[6,7,3,2,5,4,1]=>[2,1,2,1,1]
[3,2,1,6,4,7,5]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[1,2,2,1,1]
[3,2,1,6,5,4,7]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[1,2,2,1,1]
[3,2,1,6,5,7,4]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>[1,2,1,2,1]
[3,2,1,6,7,4,5]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>[1,2,1,2,1]
[3,2,1,6,7,5,4]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>[1,1,2,2,1]
[3,2,1,7,4,5,6]=>[2,1,5,6,7,3,4]=>[6,7,3,2,1,5,4]=>[2,1,1,2,1]
[3,2,1,7,4,6,5]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[1,2,1,2,1]
[3,2,1,7,5,4,6]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>[1,2,1,2,1]
[3,2,1,7,5,6,4]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>[1,1,2,2,1]
[3,2,1,7,6,4,5]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>[1,1,2,2,1]
[3,2,1,7,6,5,4]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[2,2,2,1]
[3,2,4,1,5,6,7]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>[2,2,1,1,1]
[3,2,4,1,5,7,6]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>[2,1,2,1,1]
[3,2,4,1,6,5,7]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>[2,1,2,1,1]
[3,2,4,1,6,7,5]=>[2,1,3,5,7,4,6]=>[6,7,5,3,1,4,2]=>[2,1,1,2,1]
[3,2,4,1,7,5,6]=>[2,1,3,6,7,4,5]=>[6,7,5,2,1,4,3]=>[2,1,1,2,1]
[3,2,4,1,7,6,5]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[1,2,1,2,1]
[3,2,4,5,1,6,7]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>[2,1,2,1,1]
[3,2,4,5,1,7,6]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>[2,1,1,2,1]
[3,2,4,5,6,1,7]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>[2,1,1,2,1]
[3,2,4,5,6,7,1]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,1,1,1,2]
[3,2,4,5,7,1,6]=>[2,1,3,4,6,7,5]=>[6,7,5,4,2,1,3]=>[2,1,1,1,2]
[3,2,4,5,7,6,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[1,2,1,1,2]
[3,2,4,6,1,5,7]=>[2,1,3,5,6,4,7]=>[6,7,5,3,2,4,1]=>[2,1,1,2,1]
[3,2,4,6,1,7,5]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[1,2,1,2,1]
[3,2,4,6,5,1,7]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[1,2,1,2,1]
[3,2,4,6,5,7,1]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[1,2,1,1,2]
[3,2,4,6,7,1,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>[1,2,1,1,2]
[3,2,4,6,7,5,1]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>[1,1,2,1,2]
[3,2,4,7,1,5,6]=>[2,1,3,5,6,7,4]=>[6,7,5,3,2,1,4]=>[2,1,1,1,2]
[3,2,4,7,1,6,5]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>[1,2,1,1,2]
[3,2,4,7,5,1,6]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>[1,2,1,1,2]
[3,2,4,7,5,6,1]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>[1,1,2,1,2]
[3,2,4,7,6,1,5]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>[1,1,2,1,2]
[3,2,4,7,6,5,1]=>[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>[2,2,1,2]
[3,2,5,1,4,6,7]=>[2,1,4,5,3,6,7]=>[6,7,4,3,5,2,1]=>[2,1,2,1,1]
[3,2,5,1,4,7,6]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[1,2,2,1,1]
[3,2,5,1,6,4,7]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[1,2,2,1,1]
[3,2,5,1,6,7,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>[1,2,1,2,1]
[3,2,5,1,7,4,6]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>[1,2,1,2,1]
[3,2,5,1,7,6,4]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>[1,1,2,2,1]
[3,2,5,4,1,6,7]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[1,2,2,1,1]
[3,2,5,4,1,7,6]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[1,2,1,2,1]
[3,2,5,4,6,1,7]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[1,2,1,2,1]
[3,2,5,4,6,7,1]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[1,2,1,1,2]
[3,2,5,4,7,1,6]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>[1,2,1,1,2]
[3,2,5,4,7,6,1]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>[1,1,2,1,2]
[3,2,5,6,1,4,7]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>[1,2,1,2,1]
[3,2,5,6,1,7,4]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>[1,1,2,2,1]
[3,2,5,6,4,1,7]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>[1,1,2,2,1]
[3,2,5,6,4,7,1]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>[1,1,2,1,2]
[3,2,5,6,7,1,4]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>[1,1,2,1,2]
[3,2,5,6,7,4,1]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>[1,1,1,2,2]
[3,2,5,7,1,4,6]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>[1,2,1,1,2]
[3,2,5,7,1,6,4]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>[1,1,2,1,2]
[3,2,5,7,4,1,6]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>[1,1,2,1,2]
[3,2,5,7,4,6,1]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>[1,1,1,2,2]
[3,2,5,7,6,1,4]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>[1,1,1,2,2]
[3,2,5,7,6,4,1]=>[7,1,3,6,2,5,4]=>[1,7,5,2,6,3,4]=>[2,1,2,2]
[3,2,6,1,4,5,7]=>[2,1,4,5,6,3,7]=>[6,7,4,3,2,5,1]=>[2,1,1,2,1]
[3,2,6,1,4,7,5]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>[1,2,1,2,1]
[3,2,6,1,5,4,7]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[1,2,1,2,1]
[3,2,6,1,5,7,4]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>[1,1,2,2,1]
[3,2,6,1,7,4,5]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>[1,1,2,2,1]
[3,2,6,1,7,5,4]=>[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>[2,2,2,1]
[3,2,6,4,1,5,7]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>[1,2,1,2,1]
[3,2,6,4,1,7,5]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>[1,1,2,2,1]
[3,2,6,4,5,1,7]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[1,1,2,2,1]
[3,2,6,4,5,7,1]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>[1,1,2,1,2]
[3,2,6,4,7,1,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>[1,1,2,1,2]
[3,2,6,4,7,5,1]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>[2,2,1,2]
[3,2,6,5,1,4,7]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>[1,1,2,2,1]
[3,2,6,5,1,7,4]=>[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>[2,2,2,1]
[3,2,6,5,4,1,7]=>[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>[2,2,2,1]
[3,2,6,5,4,7,1]=>[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>[2,2,1,2]
[3,2,6,5,7,1,4]=>[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]=>[2,2,1,2]
[3,2,6,5,7,4,1]=>[4,1,3,7,2,6,5]=>[4,7,5,1,6,2,3]=>[2,1,2,2]
[3,2,6,7,1,4,5]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>[1,1,2,1,2]
[3,2,6,7,1,5,4]=>[7,1,5,2,3,6,4]=>[1,7,3,6,5,2,4]=>[2,2,1,2]
[3,2,6,7,4,1,5]=>[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]=>[2,2,1,2]
[3,2,6,7,4,5,1]=>[5,1,3,7,2,6,4]=>[3,7,5,1,6,2,4]=>[2,1,2,2]
[3,2,6,7,5,1,4]=>[6,1,3,7,2,5,4]=>[2,7,5,1,6,3,4]=>[2,1,2,2]
[3,2,6,7,5,4,1]=>[3,7,1,6,2,5,4]=>[5,1,7,2,6,3,4]=>[1,2,2,2]
[3,2,7,1,4,5,6]=>[2,1,4,5,6,7,3]=>[6,7,4,3,2,1,5]=>[2,1,1,1,2]
[3,2,7,1,4,6,5]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>[1,2,1,1,2]
[3,2,7,1,5,4,6]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>[1,2,1,1,2]
[3,2,7,1,5,6,4]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>[1,1,2,1,2]
[3,2,7,1,6,4,5]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>[1,1,2,1,2]
[3,2,7,1,6,5,4]=>[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>[2,2,1,2]
[3,2,7,4,1,5,6]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>[1,2,1,1,2]
[3,2,7,4,1,6,5]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>[1,1,2,1,2]
[3,2,7,4,5,1,6]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>[1,1,2,1,2]
[3,2,7,4,5,6,1]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>[1,1,1,2,2]
[3,2,7,4,6,1,5]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>[1,1,1,2,2]
[3,2,7,4,6,5,1]=>[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>[2,1,2,2]
[3,2,7,5,1,4,6]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>[1,1,2,1,2]
[3,2,7,5,1,6,4]=>[7,1,5,2,4,6,3]=>[1,7,3,6,4,2,5]=>[2,2,1,2]
[3,2,7,5,4,1,6]=>[6,1,5,2,4,7,3]=>[2,7,3,6,4,1,5]=>[2,2,1,2]
[3,2,7,5,4,6,1]=>[5,1,4,7,2,6,3]=>[3,7,4,1,6,2,5]=>[2,1,2,2]
[3,2,7,5,6,1,4]=>[6,1,4,7,2,5,3]=>[2,7,4,1,6,3,5]=>[2,1,2,2]
[3,2,7,5,6,4,1]=>[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>[1,2,2,2]
[3,2,7,6,1,4,5]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>[1,1,1,2,2]
[3,2,7,6,1,5,4]=>[7,1,5,6,2,4,3]=>[1,7,3,2,6,4,5]=>[2,1,2,2]
[3,2,7,6,4,1,5]=>[6,1,5,7,2,4,3]=>[2,7,3,1,6,4,5]=>[2,1,2,2]
[3,2,7,6,4,5,1]=>[5,7,1,6,2,4,3]=>[3,1,7,2,6,4,5]=>[1,2,2,2]
[3,2,7,6,5,1,4]=>[6,7,1,5,2,4,3]=>[2,1,7,3,6,4,5]=>[1,2,2,2]
[3,2,7,6,5,4,1]=>[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>[3,2,2]
[3,4,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[5,7,4,6,3,2,1]=>[2,2,1,1,1]
[3,4,1,2,5,7,6]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[1,3,1,1,1]
[3,4,1,2,6,5,7]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[1,3,1,1,1]
[3,4,1,2,6,7,5]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>[1,2,2,1,1]
[3,4,1,2,7,5,6]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>[1,2,2,1,1]
[3,4,1,2,7,6,5]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[1,1,3,1,1]
[3,4,1,5,2,6,7]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[1,3,1,1,1]
[3,4,1,5,2,7,6]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>[1,2,2,1,1]
[3,4,1,5,6,2,7]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>[1,2,2,1,1]
[3,4,1,5,6,7,2]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>[1,2,1,2,1]
[3,4,1,5,7,2,6]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>[1,2,1,2,1]
[3,4,1,5,7,6,2]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>[1,1,2,2,1]
[3,4,1,6,2,5,7]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>[1,2,2,1,1]
[3,4,1,6,2,7,5]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[1,1,3,1,1]
[3,4,1,6,5,2,7]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[1,1,3,1,1]
[3,4,1,6,5,7,2]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>[1,1,2,2,1]
[3,4,1,6,7,2,5]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>[1,1,2,2,1]
[3,4,1,6,7,5,2]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>[1,1,1,3,1]
[3,4,1,7,2,5,6]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>[1,2,1,2,1]
[3,4,1,7,2,6,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>[1,1,2,2,1]
[3,4,1,7,5,2,6]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>[1,1,2,2,1]
[3,4,1,7,5,6,2]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>[1,1,1,3,1]
[3,4,1,7,6,2,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>[1,1,1,3,1]
[3,4,1,7,6,5,2]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>[2,1,3,1]
[3,4,2,1,5,6,7]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[1,3,1,1,1]
[3,4,2,1,5,7,6]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[1,2,2,1,1]
[3,4,2,1,6,5,7]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[1,2,2,1,1]
[3,4,2,1,6,7,5]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>[1,2,1,2,1]
[3,4,2,1,7,5,6]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>[1,2,1,2,1]
[3,4,2,1,7,6,5]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[1,1,2,2,1]
[3,4,2,5,1,6,7]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[1,2,2,1,1]
[3,4,2,5,1,7,6]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[1,2,1,2,1]
[3,4,2,5,6,1,7]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,2,1,2,1]
[3,4,2,5,6,7,1]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[1,2,1,1,2]
[3,4,2,5,7,1,6]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>[1,2,1,1,2]
[3,4,2,5,7,6,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[1,1,2,1,2]
[3,4,2,6,1,5,7]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>[1,2,1,2,1]
[3,4,2,6,1,7,5]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[1,1,2,2,1]
[3,4,2,6,5,1,7]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[1,1,2,2,1]
[3,4,2,6,5,7,1]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[1,1,2,1,2]
[3,4,2,6,7,1,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>[1,1,2,1,2]
[3,4,2,6,7,5,1]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>[1,1,1,2,2]
[3,4,2,7,1,5,6]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>[1,2,1,1,2]
[3,4,2,7,1,6,5]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>[1,1,2,1,2]
[3,4,2,7,5,1,6]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>[1,1,2,1,2]
[3,4,2,7,5,6,1]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>[1,1,1,2,2]
[3,4,2,7,6,1,5]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>[1,1,1,2,2]
[3,4,2,7,6,5,1]=>[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>[2,1,2,2]
[3,4,5,1,2,6,7]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>[1,2,2,1,1]
[3,4,5,1,2,7,6]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[1,1,3,1,1]
[3,4,5,1,6,2,7]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[1,1,3,1,1]
[3,4,5,1,6,7,2]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>[1,1,2,2,1]
[3,4,5,1,7,2,6]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>[1,1,2,2,1]
[3,4,5,1,7,6,2]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[1,1,1,3,1]
[3,4,5,2,1,6,7]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[1,1,3,1,1]
[3,4,5,2,1,7,6]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[1,1,2,2,1]
[3,4,5,2,6,1,7]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[1,1,2,2,1]
[3,4,5,2,6,7,1]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[1,1,2,1,2]
[3,4,5,2,7,1,6]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>[1,1,2,1,2]
[3,4,5,2,7,6,1]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[1,1,1,2,2]
[3,4,5,6,1,2,7]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>[1,1,2,2,1]
[3,4,5,6,1,7,2]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[1,1,1,3,1]
[3,4,5,6,2,1,7]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[1,1,1,3,1]
[3,4,5,6,2,7,1]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[1,1,1,2,2]
[3,4,5,6,7,1,2]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>[1,1,1,2,2]
[3,4,5,6,7,2,1]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[1,1,1,1,3]
[3,4,5,7,1,2,6]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>[1,1,2,1,2]
[3,4,5,7,1,6,2]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>[1,1,1,2,2]
[3,4,5,7,2,1,6]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>[1,1,1,2,2]
[3,4,5,7,2,6,1]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>[1,1,1,1,3]
[3,4,5,7,6,1,2]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>[1,1,1,1,3]
[3,4,5,7,6,2,1]=>[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>[2,1,1,3]
[3,4,6,1,2,5,7]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>[1,2,1,2,1]
[3,4,6,1,2,7,5]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>[1,1,2,2,1]
[3,4,6,1,5,2,7]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>[1,1,2,2,1]
[3,4,6,1,5,7,2]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>[1,1,1,3,1]
[3,4,6,1,7,2,5]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>[1,1,1,3,1]
[3,4,6,1,7,5,2]=>[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>[2,1,3,1]
[3,4,6,2,1,5,7]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>[1,1,2,2,1]
[3,4,6,2,1,7,5]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>[1,1,1,3,1]
[3,4,6,2,5,1,7]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>[1,1,1,3,1]
[3,4,6,2,5,7,1]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>[1,1,1,2,2]
[3,4,6,2,7,1,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>[1,1,1,2,2]
[3,4,6,2,7,5,1]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>[2,1,2,2]
[3,4,6,5,1,2,7]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>[1,1,1,3,1]
[3,4,6,5,1,7,2]=>[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[2,1,3,1]
[3,4,6,5,2,1,7]=>[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>[2,1,3,1]
[3,4,6,5,2,7,1]=>[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>[2,1,2,2]
[3,4,6,5,7,1,2]=>[6,1,2,4,3,7,5]=>[2,7,6,4,5,1,3]=>[2,1,2,2]
[3,4,6,5,7,2,1]=>[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>[2,1,1,3]
[3,4,6,7,1,2,5]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>[1,1,1,2,2]
[3,4,6,7,1,5,2]=>[7,1,2,5,3,6,4]=>[1,7,6,3,5,2,4]=>[2,1,2,2]
[3,4,6,7,2,1,5]=>[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]=>[2,1,2,2]
[3,4,6,7,2,5,1]=>[5,1,2,3,7,6,4]=>[3,7,6,5,1,2,4]=>[2,1,1,3]
[3,4,6,7,5,1,2]=>[6,1,2,3,7,5,4]=>[2,7,6,5,1,3,4]=>[2,1,1,3]
[3,4,6,7,5,2,1]=>[3,7,1,2,6,5,4]=>[5,1,7,6,2,3,4]=>[1,2,1,3]
[3,4,7,1,2,5,6]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>[1,2,1,1,2]
[3,4,7,1,2,6,5]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>[1,1,2,1,2]
[3,4,7,1,5,2,6]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>[1,1,2,1,2]
[3,4,7,1,5,6,2]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>[1,1,1,2,2]
[3,4,7,1,6,2,5]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>[1,1,1,2,2]
[3,4,7,1,6,5,2]=>[7,1,2,6,4,5,3]=>[1,7,6,2,4,3,5]=>[2,1,2,2]
[3,4,7,2,1,5,6]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>[1,1,2,1,2]
[3,4,7,2,1,6,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>[1,1,1,2,2]
[3,4,7,2,5,1,6]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>[1,1,1,2,2]
[3,4,7,2,5,6,1]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>[1,1,1,1,3]
[3,4,7,2,6,1,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>[1,1,1,1,3]
[3,4,7,2,6,5,1]=>[7,1,2,4,6,5,3]=>[1,7,6,4,2,3,5]=>[2,1,1,3]
[3,4,7,5,1,2,6]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>[1,1,1,2,2]
[3,4,7,5,1,6,2]=>[7,1,2,5,4,6,3]=>[1,7,6,3,4,2,5]=>[2,1,2,2]
[3,4,7,5,2,1,6]=>[6,1,2,5,4,7,3]=>[2,7,6,3,4,1,5]=>[2,1,2,2]
[3,4,7,5,2,6,1]=>[5,1,2,4,7,6,3]=>[3,7,6,4,1,2,5]=>[2,1,1,3]
[3,4,7,5,6,1,2]=>[6,1,2,4,7,5,3]=>[2,7,6,4,1,3,5]=>[2,1,1,3]
[3,4,7,5,6,2,1]=>[4,7,1,2,6,5,3]=>[4,1,7,6,2,3,5]=>[1,2,1,3]
[3,4,7,6,1,2,5]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>[1,1,1,1,3]
[3,4,7,6,1,5,2]=>[7,1,2,5,6,4,3]=>[1,7,6,3,2,4,5]=>[2,1,1,3]
[3,4,7,6,2,1,5]=>[6,1,2,5,7,4,3]=>[2,7,6,3,1,4,5]=>[2,1,1,3]
[3,4,7,6,2,5,1]=>[5,7,1,2,6,4,3]=>[3,1,7,6,2,4,5]=>[1,2,1,3]
[3,4,7,6,5,1,2]=>[6,7,1,2,5,4,3]=>[2,1,7,6,3,4,5]=>[1,2,1,3]
[3,4,7,6,5,2,1]=>[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>[3,1,3]
[3,5,1,2,4,6,7]=>[3,1,4,5,2,6,7]=>[5,7,4,3,6,2,1]=>[2,1,2,1,1]
[3,5,1,2,4,7,6]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>[1,2,2,1,1]
[3,5,1,2,6,4,7]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>[1,2,2,1,1]
[3,5,1,2,6,7,4]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>[1,1,3,1,1]
[3,5,1,2,7,4,6]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>[1,1,3,1,1]
[3,5,1,2,7,6,4]=>[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>[2,3,1,1]
[3,5,1,4,2,6,7]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>[1,2,2,1,1]
[3,5,1,4,2,7,6]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>[1,1,3,1,1]
[3,5,1,4,6,2,7]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>[1,1,3,1,1]
[3,5,1,4,6,7,2]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>[1,1,2,2,1]
[3,5,1,4,7,2,6]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>[1,1,2,2,1]
[3,5,1,4,7,6,2]=>[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>[2,2,2,1]
[3,5,1,6,2,4,7]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>[1,1,3,1,1]
[3,5,1,6,2,7,4]=>[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>[2,3,1,1]
[3,5,1,6,4,2,7]=>[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>[2,3,1,1]
[3,5,1,6,4,7,2]=>[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]=>[2,2,2,1]
[3,5,1,6,7,2,4]=>[6,1,4,2,7,3,5]=>[2,7,4,6,1,5,3]=>[2,2,2,1]
[3,5,1,6,7,4,2]=>[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]=>[2,1,3,1]
[3,5,1,7,2,4,6]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>[1,1,2,2,1]
[3,5,1,7,2,6,4]=>[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]=>[2,2,2,1]
[3,5,1,7,4,2,6]=>[6,1,5,2,7,3,4]=>[2,7,3,6,1,5,4]=>[2,2,2,1]
[3,5,1,7,4,6,2]=>[5,1,2,7,6,3,4]=>[3,7,6,1,2,5,4]=>[2,1,3,1]
[3,5,1,7,6,2,4]=>[6,1,2,7,5,3,4]=>[2,7,6,1,3,5,4]=>[2,1,3,1]
[3,5,1,7,6,4,2]=>[2,7,1,6,5,3,4]=>[6,1,7,2,3,5,4]=>[1,2,3,1]
[3,5,2,1,4,6,7]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>[1,2,2,1,1]
[3,5,2,1,4,7,6]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>[1,1,3,1,1]
[3,5,2,1,6,4,7]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>[1,1,3,1,1]
[3,5,2,1,6,7,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>[1,1,2,2,1]
[3,5,2,1,7,4,6]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>[1,1,2,2,1]
[3,5,2,1,7,6,4]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>[2,2,2,1]
[3,5,2,4,1,6,7]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>[1,1,3,1,1]
[3,5,2,4,1,7,6]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>[1,1,2,2,1]
[3,5,2,4,6,1,7]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>[1,1,2,2,1]
[3,5,2,4,6,7,1]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>[1,1,2,1,2]
[3,5,2,4,7,1,6]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>[1,1,2,1,2]
[3,5,2,4,7,6,1]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[2,2,1,2]
[3,5,2,6,1,4,7]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>[1,1,2,2,1]
[3,5,2,6,1,7,4]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>[2,2,2,1]
[3,5,2,6,4,1,7]=>[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>[2,2,2,1]
[3,5,2,6,4,7,1]=>[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>[2,2,1,2]
[3,5,2,6,7,1,4]=>[6,1,3,2,4,7,5]=>[2,7,5,6,4,1,3]=>[2,2,1,2]
[3,5,2,6,7,4,1]=>[4,1,2,7,3,6,5]=>[4,7,6,1,5,2,3]=>[2,1,2,2]
[3,5,2,7,1,4,6]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>[1,1,2,1,2]
[3,5,2,7,1,6,4]=>[7,1,3,2,5,6,4]=>[1,7,5,6,3,2,4]=>[2,2,1,2]
[3,5,2,7,4,1,6]=>[6,1,3,2,5,7,4]=>[2,7,5,6,3,1,4]=>[2,2,1,2]
[3,5,2,7,4,6,1]=>[5,1,2,7,3,6,4]=>[3,7,6,1,5,2,4]=>[2,1,2,2]
[3,5,2,7,6,1,4]=>[6,1,2,7,3,5,4]=>[2,7,6,1,5,3,4]=>[2,1,2,2]
[3,5,2,7,6,4,1]=>[2,7,1,6,3,5,4]=>[6,1,7,2,5,3,4]=>[1,2,2,2]
[3,5,4,1,2,6,7]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>[1,1,3,1,1]
[3,5,4,1,2,7,6]=>[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>[2,3,1,1]
[3,5,4,1,6,2,7]=>[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>[2,3,1,1]
[3,5,4,1,6,7,2]=>[5,1,3,2,7,4,6]=>[3,7,5,6,1,4,2]=>[2,2,2,1]
[3,5,4,1,7,2,6]=>[6,1,3,2,7,4,5]=>[2,7,5,6,1,4,3]=>[2,2,2,1]
[3,5,4,1,7,6,2]=>[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>[2,1,3,1]
[3,5,4,2,1,6,7]=>[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>[2,3,1,1]
[3,5,4,2,1,7,6]=>[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>[2,2,2,1]
[3,5,4,2,6,1,7]=>[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>[2,2,2,1]
[3,5,4,2,6,7,1]=>[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>[2,2,1,2]
[3,5,4,2,7,1,6]=>[4,1,3,2,6,7,5]=>[4,7,5,6,2,1,3]=>[2,2,1,2]
[3,5,4,2,7,6,1]=>[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>[2,1,2,2]
[3,5,4,6,1,2,7]=>[5,1,3,2,6,4,7]=>[3,7,5,6,2,4,1]=>[2,2,2,1]
[3,5,4,6,1,7,2]=>[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>[2,1,3,1]
[3,5,4,6,2,1,7]=>[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>[2,1,3,1]
[3,5,4,6,2,7,1]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>[2,1,2,2]
[3,5,4,6,7,1,2]=>[3,1,2,6,4,7,5]=>[5,7,6,2,4,1,3]=>[2,1,2,2]
[3,5,4,6,7,2,1]=>[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>[2,1,1,3]
[3,5,4,7,1,2,6]=>[5,1,3,2,6,7,4]=>[3,7,5,6,2,1,4]=>[2,2,1,2]
[3,5,4,7,1,6,2]=>[3,1,2,7,5,6,4]=>[5,7,6,1,3,2,4]=>[2,1,2,2]
[3,5,4,7,2,1,6]=>[3,1,2,6,5,7,4]=>[5,7,6,2,3,1,4]=>[2,1,2,2]
[3,5,4,7,2,6,1]=>[3,1,2,5,7,6,4]=>[5,7,6,3,1,2,4]=>[2,1,1,3]
[3,5,4,7,6,1,2]=>[3,1,2,6,7,5,4]=>[5,7,6,2,1,3,4]=>[2,1,1,3]
[3,5,4,7,6,2,1]=>[2,7,1,3,6,5,4]=>[6,1,7,5,2,3,4]=>[1,2,1,3]
[3,5,6,1,2,4,7]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>[1,1,2,2,1]
[3,5,6,1,2,7,4]=>[7,1,4,2,5,3,6]=>[1,7,4,6,3,5,2]=>[2,2,2,1]
[3,5,6,1,4,2,7]=>[6,1,4,2,5,3,7]=>[2,7,4,6,3,5,1]=>[2,2,2,1]
[3,5,6,1,4,7,2]=>[5,1,2,7,4,3,6]=>[3,7,6,1,4,5,2]=>[2,1,3,1]
[3,5,6,1,7,2,4]=>[6,1,2,7,4,3,5]=>[2,7,6,1,4,5,3]=>[2,1,3,1]
[3,5,6,1,7,4,2]=>[2,7,1,6,4,3,5]=>[6,1,7,2,4,5,3]=>[1,2,3,1]
[3,5,6,2,1,4,7]=>[5,1,4,2,6,3,7]=>[3,7,4,6,2,5,1]=>[2,2,2,1]
[3,5,6,2,1,7,4]=>[4,1,2,7,5,3,6]=>[4,7,6,1,3,5,2]=>[2,1,3,1]
[3,5,6,2,4,1,7]=>[4,1,2,6,5,3,7]=>[4,7,6,2,3,5,1]=>[2,1,3,1]
[3,5,6,2,4,7,1]=>[4,1,2,5,3,7,6]=>[4,7,6,3,5,1,2]=>[2,1,2,2]
[3,5,6,2,7,1,4]=>[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]=>[2,1,2,2]
[3,5,6,2,7,4,1]=>[2,7,1,4,3,6,5]=>[6,1,7,4,5,2,3]=>[1,2,2,2]
[3,5,6,4,1,2,7]=>[5,1,2,6,4,3,7]=>[3,7,6,2,4,5,1]=>[2,1,3,1]
[3,5,6,4,1,7,2]=>[2,7,1,5,4,3,6]=>[6,1,7,3,4,5,2]=>[1,2,3,1]
[3,5,6,4,2,1,7]=>[2,6,1,5,4,3,7]=>[6,2,7,3,4,5,1]=>[1,2,3,1]
[3,5,6,4,2,7,1]=>[2,5,1,4,3,7,6]=>[6,3,7,4,5,1,2]=>[1,2,2,2]
[3,5,6,4,7,1,2]=>[2,6,1,4,3,7,5]=>[6,2,7,4,5,1,3]=>[1,2,2,2]
[3,5,6,4,7,2,1]=>[2,4,1,3,7,6,5]=>[6,4,7,5,1,2,3]=>[1,2,1,3]
[3,5,6,7,1,2,4]=>[5,1,2,6,3,7,4]=>[3,7,6,2,5,1,4]=>[2,1,2,2]
[3,5,6,7,1,4,2]=>[2,7,1,5,3,6,4]=>[6,1,7,3,5,2,4]=>[1,2,2,2]
[3,5,6,7,2,1,4]=>[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]=>[1,2,2,2]
[3,5,6,7,2,4,1]=>[2,5,1,3,7,6,4]=>[6,3,7,5,1,2,4]=>[1,2,1,3]
[3,5,6,7,4,1,2]=>[2,6,1,3,7,5,4]=>[6,2,7,5,1,3,4]=>[1,2,1,3]
[3,5,6,7,4,2,1]=>[2,3,7,1,6,5,4]=>[6,5,1,7,2,3,4]=>[1,1,2,3]
[3,5,7,1,2,4,6]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>[1,1,2,1,2]
[3,5,7,1,2,6,4]=>[7,1,4,2,5,6,3]=>[1,7,4,6,3,2,5]=>[2,2,1,2]
[3,5,7,1,4,2,6]=>[6,1,4,2,5,7,3]=>[2,7,4,6,3,1,5]=>[2,2,1,2]
[3,5,7,1,4,6,2]=>[5,1,2,7,4,6,3]=>[3,7,6,1,4,2,5]=>[2,1,2,2]
[3,5,7,1,6,2,4]=>[6,1,2,7,4,5,3]=>[2,7,6,1,4,3,5]=>[2,1,2,2]
[3,5,7,1,6,4,2]=>[2,7,1,6,4,5,3]=>[6,1,7,2,4,3,5]=>[1,2,2,2]
[3,5,7,2,1,4,6]=>[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]=>[2,2,1,2]
[3,5,7,2,1,6,4]=>[4,1,2,7,5,6,3]=>[4,7,6,1,3,2,5]=>[2,1,2,2]
[3,5,7,2,4,1,6]=>[4,1,2,6,5,7,3]=>[4,7,6,2,3,1,5]=>[2,1,2,2]
[3,5,7,2,4,6,1]=>[4,1,2,5,7,6,3]=>[4,7,6,3,1,2,5]=>[2,1,1,3]
[3,5,7,2,6,1,4]=>[4,1,2,6,7,5,3]=>[4,7,6,2,1,3,5]=>[2,1,1,3]
[3,5,7,2,6,4,1]=>[2,7,1,4,6,5,3]=>[6,1,7,4,2,3,5]=>[1,2,1,3]
[3,5,7,4,1,2,6]=>[5,1,2,6,4,7,3]=>[3,7,6,2,4,1,5]=>[2,1,2,2]
[3,5,7,4,1,6,2]=>[2,7,1,5,4,6,3]=>[6,1,7,3,4,2,5]=>[1,2,2,2]
[3,5,7,4,2,1,6]=>[2,6,1,5,4,7,3]=>[6,2,7,3,4,1,5]=>[1,2,2,2]
[3,5,7,4,2,6,1]=>[2,5,1,4,7,6,3]=>[6,3,7,4,1,2,5]=>[1,2,1,3]
[3,5,7,4,6,1,2]=>[2,6,1,4,7,5,3]=>[6,2,7,4,1,3,5]=>[1,2,1,3]
[3,5,7,4,6,2,1]=>[2,4,7,1,6,5,3]=>[6,4,1,7,2,3,5]=>[1,1,2,3]
[3,5,7,6,1,2,4]=>[5,1,2,6,7,4,3]=>[3,7,6,2,1,4,5]=>[2,1,1,3]
[3,5,7,6,1,4,2]=>[2,7,1,5,6,4,3]=>[6,1,7,3,2,4,5]=>[1,2,1,3]
[3,5,7,6,2,1,4]=>[2,6,1,5,7,4,3]=>[6,2,7,3,1,4,5]=>[1,2,1,3]
[3,5,7,6,2,4,1]=>[2,5,7,1,6,4,3]=>[6,3,1,7,2,4,5]=>[1,1,2,3]
[3,5,7,6,4,1,2]=>[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>[1,1,2,3]
[3,5,7,6,4,2,1]=>[7,2,6,1,5,4,3]=>[1,6,2,7,3,4,5]=>[2,2,3]
[3,6,1,2,4,5,7]=>[3,1,4,5,6,2,7]=>[5,7,4,3,2,6,1]=>[2,1,1,2,1]
[3,6,1,2,4,7,5]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>[1,2,1,2,1]
[3,6,1,2,5,4,7]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>[1,2,1,2,1]
[3,6,1,2,5,7,4]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>[1,1,2,2,1]
[3,6,1,2,7,4,5]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>[1,1,2,2,1]
[3,6,1,2,7,5,4]=>[7,1,6,3,4,2,5]=>[1,7,2,5,4,6,3]=>[2,2,2,1]
[3,6,1,4,2,5,7]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[1,2,1,2,1]
[3,6,1,4,2,7,5]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>[1,1,2,2,1]
[3,6,1,4,5,2,7]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>[1,1,2,2,1]
[3,6,1,4,5,7,2]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>[1,1,1,3,1]
[3,6,1,4,7,2,5]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>[1,1,1,3,1]
[3,6,1,4,7,5,2]=>[7,1,4,6,3,2,5]=>[1,7,4,2,5,6,3]=>[2,1,3,1]
[3,6,1,5,2,4,7]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>[1,1,2,2,1]
[3,6,1,5,2,7,4]=>[7,1,5,3,4,2,6]=>[1,7,3,5,4,6,2]=>[2,2,2,1]
[3,6,1,5,4,2,7]=>[6,1,5,3,4,2,7]=>[2,7,3,5,4,6,1]=>[2,2,2,1]
[3,6,1,5,4,7,2]=>[5,1,4,7,3,2,6]=>[3,7,4,1,5,6,2]=>[2,1,3,1]
[3,6,1,5,7,2,4]=>[6,1,4,7,3,2,5]=>[2,7,4,1,5,6,3]=>[2,1,3,1]
[3,6,1,5,7,4,2]=>[4,7,1,6,3,2,5]=>[4,1,7,2,5,6,3]=>[1,2,3,1]
[3,6,1,7,2,4,5]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>[1,1,1,3,1]
[3,6,1,7,2,5,4]=>[7,1,5,6,3,2,4]=>[1,7,3,2,5,6,4]=>[2,1,3,1]
[3,6,1,7,4,2,5]=>[6,1,5,7,3,2,4]=>[2,7,3,1,5,6,4]=>[2,1,3,1]
[3,6,1,7,4,5,2]=>[5,7,1,6,3,2,4]=>[3,1,7,2,5,6,4]=>[1,2,3,1]
[3,6,1,7,5,2,4]=>[6,7,1,5,3,2,4]=>[2,1,7,3,5,6,4]=>[1,2,3,1]
[3,6,1,7,5,4,2]=>[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>[3,3,1]
[3,6,2,1,4,5,7]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>[1,2,1,2,1]
[3,6,2,1,4,7,5]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>[1,1,2,2,1]
[3,6,2,1,5,4,7]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>[1,1,2,2,1]
[3,6,2,1,5,7,4]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>[1,1,1,3,1]
[3,6,2,1,7,4,5]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>[1,1,1,3,1]
[3,6,2,1,7,5,4]=>[7,1,3,6,4,2,5]=>[1,7,5,2,4,6,3]=>[2,1,3,1]
[3,6,2,4,1,5,7]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>[1,1,2,2,1]
[3,6,2,4,1,7,5]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>[1,1,1,3,1]
[3,6,2,4,5,1,7]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>[1,1,1,3,1]
[3,6,2,4,5,7,1]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>[1,1,1,2,2]
[3,6,2,4,7,1,5]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>[1,1,1,2,2]
[3,6,2,4,7,5,1]=>[7,1,3,4,2,6,5]=>[1,7,5,4,6,2,3]=>[2,1,2,2]
[3,6,2,5,1,4,7]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[1,1,1,3,1]
[3,6,2,5,1,7,4]=>[7,1,3,5,4,2,6]=>[1,7,5,3,4,6,2]=>[2,1,3,1]
[3,6,2,5,4,1,7]=>[6,1,3,5,4,2,7]=>[2,7,5,3,4,6,1]=>[2,1,3,1]
[3,6,2,5,4,7,1]=>[5,1,3,4,2,7,6]=>[3,7,5,4,6,1,2]=>[2,1,2,2]
[3,6,2,5,7,1,4]=>[6,1,3,4,2,7,5]=>[2,7,5,4,6,1,3]=>[2,1,2,2]
[3,6,2,5,7,4,1]=>[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>[1,2,2,2]
[3,6,2,7,1,4,5]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>[1,1,1,2,2]
[3,6,2,7,1,5,4]=>[7,1,3,5,2,6,4]=>[1,7,5,3,6,2,4]=>[2,1,2,2]
[3,6,2,7,4,1,5]=>[6,1,3,5,2,7,4]=>[2,7,5,3,6,1,4]=>[2,1,2,2]
[3,6,2,7,4,5,1]=>[5,7,1,3,2,6,4]=>[3,1,7,5,6,2,4]=>[1,2,2,2]
[3,6,2,7,5,1,4]=>[6,7,1,3,2,5,4]=>[2,1,7,5,6,3,4]=>[1,2,2,2]
[3,6,2,7,5,4,1]=>[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>[3,2,2]
[3,6,4,1,2,5,7]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[1,1,2,2,1]
[3,6,4,1,2,7,5]=>[7,1,4,3,5,2,6]=>[1,7,4,5,3,6,2]=>[2,2,2,1]
[3,6,4,1,5,2,7]=>[6,1,4,3,5,2,7]=>[2,7,4,5,3,6,1]=>[2,2,2,1]
[3,6,4,1,5,7,2]=>[5,1,3,7,4,2,6]=>[3,7,5,1,4,6,2]=>[2,1,3,1]
[3,6,4,1,7,2,5]=>[6,1,3,7,4,2,5]=>[2,7,5,1,4,6,3]=>[2,1,3,1]
[3,6,4,1,7,5,2]=>[3,7,1,6,4,2,5]=>[5,1,7,2,4,6,3]=>[1,2,3,1]
[3,6,4,2,1,5,7]=>[5,1,4,3,6,2,7]=>[3,7,4,5,2,6,1]=>[2,2,2,1]
[3,6,4,2,1,7,5]=>[4,1,3,7,5,2,6]=>[4,7,5,1,3,6,2]=>[2,1,3,1]
[3,6,4,2,5,1,7]=>[4,1,3,6,5,2,7]=>[4,7,5,2,3,6,1]=>[2,1,3,1]
[3,6,4,2,5,7,1]=>[4,1,3,5,2,7,6]=>[4,7,5,3,6,1,2]=>[2,1,2,2]
[3,6,4,2,7,1,5]=>[4,1,3,6,2,7,5]=>[4,7,5,2,6,1,3]=>[2,1,2,2]
[3,6,4,2,7,5,1]=>[3,7,1,4,2,6,5]=>[5,1,7,4,6,2,3]=>[1,2,2,2]
[3,6,4,5,1,2,7]=>[5,1,3,6,4,2,7]=>[3,7,5,2,4,6,1]=>[2,1,3,1]
[3,6,4,5,1,7,2]=>[3,7,1,5,4,2,6]=>[5,1,7,3,4,6,2]=>[1,2,3,1]
[3,6,4,5,2,1,7]=>[3,6,1,5,4,2,7]=>[5,2,7,3,4,6,1]=>[1,2,3,1]
[3,6,4,5,2,7,1]=>[3,5,1,4,2,7,6]=>[5,3,7,4,6,1,2]=>[1,2,2,2]
[3,6,4,5,7,1,2]=>[3,6,1,4,2,7,5]=>[5,2,7,4,6,1,3]=>[1,2,2,2]
[3,6,4,5,7,2,1]=>[3,4,1,2,7,6,5]=>[5,4,7,6,1,2,3]=>[1,2,1,3]
[3,6,4,7,1,2,5]=>[5,1,3,6,2,7,4]=>[3,7,5,2,6,1,4]=>[2,1,2,2]
[3,6,4,7,1,5,2]=>[3,7,1,5,2,6,4]=>[5,1,7,3,6,2,4]=>[1,2,2,2]
[3,6,4,7,2,1,5]=>[3,6,1,5,2,7,4]=>[5,2,7,3,6,1,4]=>[1,2,2,2]
[3,6,4,7,2,5,1]=>[3,5,1,2,7,6,4]=>[5,3,7,6,1,2,4]=>[1,2,1,3]
[3,6,4,7,5,1,2]=>[3,6,1,2,7,5,4]=>[5,2,7,6,1,3,4]=>[1,2,1,3]
[3,6,4,7,5,2,1]=>[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>[3,1,3]
[3,6,5,1,2,4,7]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>[1,1,1,3,1]
[3,6,5,1,2,7,4]=>[7,1,4,5,3,2,6]=>[1,7,4,3,5,6,2]=>[2,1,3,1]
[3,6,5,1,4,2,7]=>[6,1,4,5,3,2,7]=>[2,7,4,3,5,6,1]=>[2,1,3,1]
[3,6,5,1,4,7,2]=>[5,7,1,4,3,2,6]=>[3,1,7,4,5,6,2]=>[1,2,3,1]
[3,6,5,1,7,2,4]=>[6,7,1,4,3,2,5]=>[2,1,7,4,5,6,3]=>[1,2,3,1]
[3,6,5,1,7,4,2]=>[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>[3,3,1]
[3,6,5,2,1,4,7]=>[5,1,4,6,3,2,7]=>[3,7,4,2,5,6,1]=>[2,1,3,1]
[3,6,5,2,1,7,4]=>[4,7,1,5,3,2,6]=>[4,1,7,3,5,6,2]=>[1,2,3,1]
[3,6,5,2,4,1,7]=>[4,6,1,5,3,2,7]=>[4,2,7,3,5,6,1]=>[1,2,3,1]
[3,6,5,2,4,7,1]=>[4,5,1,3,2,7,6]=>[4,3,7,5,6,1,2]=>[1,2,2,2]
[3,6,5,2,7,1,4]=>[4,6,1,3,2,7,5]=>[4,2,7,5,6,1,3]=>[1,2,2,2]
[3,6,5,2,7,4,1]=>[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[3,2,2]
[3,6,5,4,1,2,7]=>[5,6,1,4,3,2,7]=>[3,2,7,4,5,6,1]=>[1,2,3,1]
[3,6,5,4,1,7,2]=>[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>[3,3,1]
[3,6,5,4,2,1,7]=>[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>[3,3,1]
[3,6,5,4,2,7,1]=>[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>[3,2,2]
[3,6,5,4,7,1,2]=>[6,4,1,3,2,7,5]=>[2,4,7,5,6,1,3]=>[3,2,2]
[3,6,5,4,7,2,1]=>[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>[3,1,3]
[3,6,5,7,1,2,4]=>[5,6,1,3,2,7,4]=>[3,2,7,5,6,1,4]=>[1,2,2,2]
[3,6,5,7,1,4,2]=>[7,5,1,3,2,6,4]=>[1,3,7,5,6,2,4]=>[3,2,2]
[3,6,5,7,2,1,4]=>[6,5,1,3,2,7,4]=>[2,3,7,5,6,1,4]=>[3,2,2]
[3,6,5,7,2,4,1]=>[5,3,1,2,7,6,4]=>[3,5,7,6,1,2,4]=>[3,1,3]
[3,6,5,7,4,1,2]=>[6,3,1,2,7,5,4]=>[2,5,7,6,1,3,4]=>[3,1,3]
[3,6,5,7,4,2,1]=>[3,2,7,1,6,5,4]=>[5,6,1,7,2,3,4]=>[2,2,3]
[3,6,7,1,2,4,5]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>[1,1,1,2,2]
[3,6,7,1,2,5,4]=>[7,1,4,5,2,6,3]=>[1,7,4,3,6,2,5]=>[2,1,2,2]
[3,6,7,1,4,2,5]=>[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]=>[2,1,2,2]
[3,6,7,1,4,5,2]=>[5,7,1,4,2,6,3]=>[3,1,7,4,6,2,5]=>[1,2,2,2]
[3,6,7,1,5,2,4]=>[6,7,1,4,2,5,3]=>[2,1,7,4,6,3,5]=>[1,2,2,2]
[3,6,7,1,5,4,2]=>[7,6,1,4,2,5,3]=>[1,2,7,4,6,3,5]=>[3,2,2]
[3,6,7,2,1,4,5]=>[5,1,4,6,2,7,3]=>[3,7,4,2,6,1,5]=>[2,1,2,2]
[3,6,7,2,1,5,4]=>[4,7,1,5,2,6,3]=>[4,1,7,3,6,2,5]=>[1,2,2,2]
[3,6,7,2,4,1,5]=>[4,6,1,5,2,7,3]=>[4,2,7,3,6,1,5]=>[1,2,2,2]
[3,6,7,2,4,5,1]=>[4,5,1,2,7,6,3]=>[4,3,7,6,1,2,5]=>[1,2,1,3]
[3,6,7,2,5,1,4]=>[4,6,1,2,7,5,3]=>[4,2,7,6,1,3,5]=>[1,2,1,3]
[3,6,7,2,5,4,1]=>[7,4,1,2,6,5,3]=>[1,4,7,6,2,3,5]=>[3,1,3]
[3,6,7,4,1,2,5]=>[5,6,1,4,2,7,3]=>[3,2,7,4,6,1,5]=>[1,2,2,2]
[3,6,7,4,1,5,2]=>[7,5,1,4,2,6,3]=>[1,3,7,4,6,2,5]=>[3,2,2]
[3,6,7,4,2,1,5]=>[6,5,1,4,2,7,3]=>[2,3,7,4,6,1,5]=>[3,2,2]
[3,6,7,4,2,5,1]=>[5,4,1,2,7,6,3]=>[3,4,7,6,1,2,5]=>[3,1,3]
[3,6,7,4,5,1,2]=>[6,4,1,2,7,5,3]=>[2,4,7,6,1,3,5]=>[3,1,3]
[3,6,7,4,5,2,1]=>[4,2,7,1,6,5,3]=>[4,6,1,7,2,3,5]=>[2,2,3]
[3,6,7,5,1,2,4]=>[5,6,1,2,7,4,3]=>[3,2,7,6,1,4,5]=>[1,2,1,3]
[3,6,7,5,1,4,2]=>[7,5,1,2,6,4,3]=>[1,3,7,6,2,4,5]=>[3,1,3]
[3,6,7,5,2,1,4]=>[6,5,1,2,7,4,3]=>[2,3,7,6,1,4,5]=>[3,1,3]
[3,6,7,5,2,4,1]=>[5,2,7,1,6,4,3]=>[3,6,1,7,2,4,5]=>[2,2,3]
[3,6,7,5,4,1,2]=>[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>[2,2,3]
[3,6,7,5,4,2,1]=>[2,7,6,1,5,4,3]=>[6,1,2,7,3,4,5]=>[1,3,3]
[3,7,1,2,4,5,6]=>[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]=>[2,1,1,1,2]
[3,7,1,2,4,6,5]=>[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>[1,2,1,1,2]
[3,7,1,2,5,4,6]=>[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>[1,2,1,1,2]
[3,7,1,2,5,6,4]=>[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>[1,1,2,1,2]
[3,7,1,2,6,4,5]=>[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>[1,1,2,1,2]
[3,7,1,2,6,5,4]=>[7,1,6,3,4,5,2]=>[1,7,2,5,4,3,6]=>[2,2,1,2]
[3,7,1,4,2,5,6]=>[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>[1,2,1,1,2]
[3,7,1,4,2,6,5]=>[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>[1,1,2,1,2]
[3,7,1,4,5,2,6]=>[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>[1,1,2,1,2]
[3,7,1,4,5,6,2]=>[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>[1,1,1,2,2]
[3,7,1,4,6,2,5]=>[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>[1,1,1,2,2]
[3,7,1,4,6,5,2]=>[7,1,4,6,3,5,2]=>[1,7,4,2,5,3,6]=>[2,1,2,2]
[3,7,1,5,2,4,6]=>[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>[1,1,2,1,2]
[3,7,1,5,2,6,4]=>[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>[2,2,1,2]
[3,7,1,5,4,2,6]=>[6,1,5,3,4,7,2]=>[2,7,3,5,4,1,6]=>[2,2,1,2]
[3,7,1,5,4,6,2]=>[5,1,4,7,3,6,2]=>[3,7,4,1,5,2,6]=>[2,1,2,2]
[3,7,1,5,6,2,4]=>[6,1,4,7,3,5,2]=>[2,7,4,1,5,3,6]=>[2,1,2,2]
[3,7,1,5,6,4,2]=>[4,7,1,6,3,5,2]=>[4,1,7,2,5,3,6]=>[1,2,2,2]
[3,7,1,6,2,4,5]=>[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>[1,1,1,2,2]
[3,7,1,6,2,5,4]=>[7,1,5,6,3,4,2]=>[1,7,3,2,5,4,6]=>[2,1,2,2]
[3,7,1,6,4,2,5]=>[6,1,5,7,3,4,2]=>[2,7,3,1,5,4,6]=>[2,1,2,2]
[3,7,1,6,4,5,2]=>[5,7,1,6,3,4,2]=>[3,1,7,2,5,4,6]=>[1,2,2,2]
[3,7,1,6,5,2,4]=>[6,7,1,5,3,4,2]=>[2,1,7,3,5,4,6]=>[1,2,2,2]
[3,7,1,6,5,4,2]=>[7,6,1,5,3,4,2]=>[1,2,7,3,5,4,6]=>[3,2,2]
[3,7,2,1,4,5,6]=>[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>[1,2,1,1,2]
[3,7,2,1,4,6,5]=>[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>[1,1,2,1,2]
[3,7,2,1,5,4,6]=>[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>[1,1,2,1,2]
[3,7,2,1,5,6,4]=>[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>[1,1,1,2,2]
[3,7,2,1,6,4,5]=>[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>[1,1,1,2,2]
[3,7,2,1,6,5,4]=>[7,1,3,6,4,5,2]=>[1,7,5,2,4,3,6]=>[2,1,2,2]
[3,7,2,4,1,5,6]=>[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>[1,1,2,1,2]
[3,7,2,4,1,6,5]=>[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>[1,1,1,2,2]
[3,7,2,4,5,1,6]=>[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>[1,1,1,2,2]
[3,7,2,4,5,6,1]=>[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>[1,1,1,1,3]
[3,7,2,4,6,1,5]=>[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>[1,1,1,1,3]
[3,7,2,4,6,5,1]=>[7,1,3,4,6,5,2]=>[1,7,5,4,2,3,6]=>[2,1,1,3]
[3,7,2,5,1,4,6]=>[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>[1,1,1,2,2]
[3,7,2,5,1,6,4]=>[7,1,3,5,4,6,2]=>[1,7,5,3,4,2,6]=>[2,1,2,2]
[3,7,2,5,4,1,6]=>[6,1,3,5,4,7,2]=>[2,7,5,3,4,1,6]=>[2,1,2,2]
[3,7,2,5,4,6,1]=>[5,1,3,4,7,6,2]=>[3,7,5,4,1,2,6]=>[2,1,1,3]
[3,7,2,5,6,1,4]=>[6,1,3,4,7,5,2]=>[2,7,5,4,1,3,6]=>[2,1,1,3]
[3,7,2,5,6,4,1]=>[4,7,1,3,6,5,2]=>[4,1,7,5,2,3,6]=>[1,2,1,3]
[3,7,2,6,1,4,5]=>[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>[1,1,1,1,3]
[3,7,2,6,1,5,4]=>[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>[2,1,1,3]
[3,7,2,6,4,1,5]=>[6,1,3,5,7,4,2]=>[2,7,5,3,1,4,6]=>[2,1,1,3]
[3,7,2,6,4,5,1]=>[5,7,1,3,6,4,2]=>[3,1,7,5,2,4,6]=>[1,2,1,3]
[3,7,2,6,5,1,4]=>[6,7,1,3,5,4,2]=>[2,1,7,5,3,4,6]=>[1,2,1,3]
[3,7,2,6,5,4,1]=>[7,6,1,3,5,4,2]=>[1,2,7,5,3,4,6]=>[3,1,3]
[3,7,4,1,2,5,6]=>[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>[1,1,2,1,2]
[3,7,4,1,2,6,5]=>[7,1,4,3,5,6,2]=>[1,7,4,5,3,2,6]=>[2,2,1,2]
[3,7,4,1,5,2,6]=>[6,1,4,3,5,7,2]=>[2,7,4,5,3,1,6]=>[2,2,1,2]
[3,7,4,1,5,6,2]=>[5,1,3,7,4,6,2]=>[3,7,5,1,4,2,6]=>[2,1,2,2]
[3,7,4,1,6,2,5]=>[6,1,3,7,4,5,2]=>[2,7,5,1,4,3,6]=>[2,1,2,2]
[3,7,4,1,6,5,2]=>[3,7,1,6,4,5,2]=>[5,1,7,2,4,3,6]=>[1,2,2,2]
[3,7,4,2,1,5,6]=>[5,1,4,3,6,7,2]=>[3,7,4,5,2,1,6]=>[2,2,1,2]
[3,7,4,2,1,6,5]=>[4,1,3,7,5,6,2]=>[4,7,5,1,3,2,6]=>[2,1,2,2]
[3,7,4,2,5,1,6]=>[4,1,3,6,5,7,2]=>[4,7,5,2,3,1,6]=>[2,1,2,2]
[3,7,4,2,5,6,1]=>[4,1,3,5,7,6,2]=>[4,7,5,3,1,2,6]=>[2,1,1,3]
[3,7,4,2,6,1,5]=>[4,1,3,6,7,5,2]=>[4,7,5,2,1,3,6]=>[2,1,1,3]
[3,7,4,2,6,5,1]=>[3,7,1,4,6,5,2]=>[5,1,7,4,2,3,6]=>[1,2,1,3]
[3,7,4,5,1,2,6]=>[5,1,3,6,4,7,2]=>[3,7,5,2,4,1,6]=>[2,1,2,2]
[3,7,4,5,1,6,2]=>[3,7,1,5,4,6,2]=>[5,1,7,3,4,2,6]=>[1,2,2,2]
[3,7,4,5,2,1,6]=>[3,6,1,5,4,7,2]=>[5,2,7,3,4,1,6]=>[1,2,2,2]
[3,7,4,5,2,6,1]=>[3,5,1,4,7,6,2]=>[5,3,7,4,1,2,6]=>[1,2,1,3]
[3,7,4,5,6,1,2]=>[3,6,1,4,7,5,2]=>[5,2,7,4,1,3,6]=>[1,2,1,3]
[3,7,4,5,6,2,1]=>[3,4,7,1,6,5,2]=>[5,4,1,7,2,3,6]=>[1,1,2,3]
[3,7,4,6,1,2,5]=>[5,1,3,6,7,4,2]=>[3,7,5,2,1,4,6]=>[2,1,1,3]
[3,7,4,6,1,5,2]=>[3,7,1,5,6,4,2]=>[5,1,7,3,2,4,6]=>[1,2,1,3]
[3,7,4,6,2,1,5]=>[3,6,1,5,7,4,2]=>[5,2,7,3,1,4,6]=>[1,2,1,3]
[3,7,4,6,2,5,1]=>[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>[1,1,2,3]
[3,7,4,6,5,1,2]=>[3,6,7,1,5,4,2]=>[5,2,1,7,3,4,6]=>[1,1,2,3]
[3,7,4,6,5,2,1]=>[7,3,6,1,5,4,2]=>[1,5,2,7,3,4,6]=>[2,2,3]
[3,7,5,1,2,4,6]=>[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>[1,1,1,2,2]
[3,7,5,1,2,6,4]=>[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>[2,1,2,2]
[3,7,5,1,4,2,6]=>[6,1,4,5,3,7,2]=>[2,7,4,3,5,1,6]=>[2,1,2,2]
[3,7,5,1,4,6,2]=>[5,7,1,4,3,6,2]=>[3,1,7,4,5,2,6]=>[1,2,2,2]
[3,7,5,1,6,2,4]=>[6,7,1,4,3,5,2]=>[2,1,7,4,5,3,6]=>[1,2,2,2]
[3,7,5,1,6,4,2]=>[7,6,1,4,3,5,2]=>[1,2,7,4,5,3,6]=>[3,2,2]
[3,7,5,2,1,4,6]=>[5,1,4,6,3,7,2]=>[3,7,4,2,5,1,6]=>[2,1,2,2]
[3,7,5,2,1,6,4]=>[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>[1,2,2,2]
[3,7,5,2,4,1,6]=>[4,6,1,5,3,7,2]=>[4,2,7,3,5,1,6]=>[1,2,2,2]
[3,7,5,2,4,6,1]=>[4,5,1,3,7,6,2]=>[4,3,7,5,1,2,6]=>[1,2,1,3]
[3,7,5,2,6,1,4]=>[4,6,1,3,7,5,2]=>[4,2,7,5,1,3,6]=>[1,2,1,3]
[3,7,5,2,6,4,1]=>[7,4,1,3,6,5,2]=>[1,4,7,5,2,3,6]=>[3,1,3]
[3,7,5,4,1,2,6]=>[5,6,1,4,3,7,2]=>[3,2,7,4,5,1,6]=>[1,2,2,2]
[3,7,5,4,1,6,2]=>[7,5,1,4,3,6,2]=>[1,3,7,4,5,2,6]=>[3,2,2]
[3,7,5,4,2,1,6]=>[6,5,1,4,3,7,2]=>[2,3,7,4,5,1,6]=>[3,2,2]
[3,7,5,4,2,6,1]=>[5,4,1,3,7,6,2]=>[3,4,7,5,1,2,6]=>[3,1,3]
[3,7,5,4,6,1,2]=>[6,4,1,3,7,5,2]=>[2,4,7,5,1,3,6]=>[3,1,3]
[3,7,5,4,6,2,1]=>[4,3,7,1,6,5,2]=>[4,5,1,7,2,3,6]=>[2,2,3]
[3,7,5,6,1,2,4]=>[5,6,1,3,7,4,2]=>[3,2,7,5,1,4,6]=>[1,2,1,3]
[3,7,5,6,1,4,2]=>[7,5,1,3,6,4,2]=>[1,3,7,5,2,4,6]=>[3,1,3]
[3,7,5,6,2,1,4]=>[6,5,1,3,7,4,2]=>[2,3,7,5,1,4,6]=>[3,1,3]
[3,7,5,6,2,4,1]=>[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>[2,2,3]
[3,7,5,6,4,1,2]=>[6,3,7,1,5,4,2]=>[2,5,1,7,3,4,6]=>[2,2,3]
[3,7,5,6,4,2,1]=>[3,7,6,1,5,4,2]=>[5,1,2,7,3,4,6]=>[1,3,3]
[3,7,6,1,2,4,5]=>[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>[1,1,1,1,3]
[3,7,6,1,2,5,4]=>[7,1,4,5,6,3,2]=>[1,7,4,3,2,5,6]=>[2,1,1,3]
[3,7,6,1,4,2,5]=>[6,1,4,5,7,3,2]=>[2,7,4,3,1,5,6]=>[2,1,1,3]
[3,7,6,1,4,5,2]=>[5,7,1,4,6,3,2]=>[3,1,7,4,2,5,6]=>[1,2,1,3]
[3,7,6,1,5,2,4]=>[6,7,1,4,5,3,2]=>[2,1,7,4,3,5,6]=>[1,2,1,3]
[3,7,6,1,5,4,2]=>[7,6,1,4,5,3,2]=>[1,2,7,4,3,5,6]=>[3,1,3]
[3,7,6,2,1,4,5]=>[5,1,4,6,7,3,2]=>[3,7,4,2,1,5,6]=>[2,1,1,3]
[3,7,6,2,1,5,4]=>[4,7,1,5,6,3,2]=>[4,1,7,3,2,5,6]=>[1,2,1,3]
[3,7,6,2,4,1,5]=>[4,6,1,5,7,3,2]=>[4,2,7,3,1,5,6]=>[1,2,1,3]
[3,7,6,2,4,5,1]=>[4,5,7,1,6,3,2]=>[4,3,1,7,2,5,6]=>[1,1,2,3]
[3,7,6,2,5,1,4]=>[4,6,7,1,5,3,2]=>[4,2,1,7,3,5,6]=>[1,1,2,3]
[3,7,6,2,5,4,1]=>[7,4,6,1,5,3,2]=>[1,4,2,7,3,5,6]=>[2,2,3]
[3,7,6,4,1,2,5]=>[5,6,1,4,7,3,2]=>[3,2,7,4,1,5,6]=>[1,2,1,3]
[3,7,6,4,1,5,2]=>[7,5,1,4,6,3,2]=>[1,3,7,4,2,5,6]=>[3,1,3]
[3,7,6,4,2,1,5]=>[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>[3,1,3]
[3,7,6,4,2,5,1]=>[5,4,7,1,6,3,2]=>[3,4,1,7,2,5,6]=>[2,2,3]
[3,7,6,4,5,1,2]=>[6,4,7,1,5,3,2]=>[2,4,1,7,3,5,6]=>[2,2,3]
[3,7,6,4,5,2,1]=>[4,7,6,1,5,3,2]=>[4,1,2,7,3,5,6]=>[1,3,3]
[3,7,6,5,1,2,4]=>[5,6,7,1,4,3,2]=>[3,2,1,7,4,5,6]=>[1,1,2,3]
[3,7,6,5,1,4,2]=>[7,5,6,1,4,3,2]=>[1,3,2,7,4,5,6]=>[2,2,3]
[3,7,6,5,2,1,4]=>[6,5,7,1,4,3,2]=>[2,3,1,7,4,5,6]=>[2,2,3]
[3,7,6,5,2,4,1]=>[5,7,6,1,4,3,2]=>[3,1,2,7,4,5,6]=>[1,3,3]
[3,7,6,5,4,1,2]=>[6,7,5,1,4,3,2]=>[2,1,3,7,4,5,6]=>[1,3,3]
[3,7,6,5,4,2,1]=>[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>[4,3]
[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>[1,1,2,1,1,1]
[4,1,2,3,5,7,6]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>[2,2,1,1,1]
[4,1,2,3,6,5,7]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>[2,2,1,1,1]
[4,1,2,3,6,7,5]=>[5,7,2,1,3,4,6]=>[3,1,6,7,5,4,2]=>[1,3,1,1,1]
[4,1,2,3,7,5,6]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>[1,3,1,1,1]
[4,1,2,3,7,6,5]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[4,1,1,1]
[4,1,2,5,3,6,7]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>[2,2,1,1,1]
[4,1,2,5,3,7,6]=>[4,7,2,1,3,5,6]=>[4,1,6,7,5,3,2]=>[1,3,1,1,1]
[4,1,2,5,6,3,7]=>[4,6,2,1,3,5,7]=>[4,2,6,7,5,3,1]=>[1,3,1,1,1]
[4,1,2,5,6,7,3]=>[4,5,1,7,2,3,6]=>[4,3,7,1,6,5,2]=>[1,2,2,1,1]
[4,1,2,5,7,3,6]=>[4,6,1,7,2,3,5]=>[4,2,7,1,6,5,3]=>[1,2,2,1,1]
[4,1,2,5,7,6,3]=>[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>[3,2,1,1]
[4,1,2,6,3,5,7]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>[1,3,1,1,1]
[4,1,2,6,3,7,5]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[4,1,1,1]
[4,1,2,6,5,3,7]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[4,1,1,1]
[4,1,2,6,5,7,3]=>[5,4,1,7,2,3,6]=>[3,4,7,1,6,5,2]=>[3,2,1,1]
[4,1,2,6,7,3,5]=>[6,4,1,7,2,3,5]=>[2,4,7,1,6,5,3]=>[3,2,1,1]
[4,1,2,6,7,5,3]=>[4,1,7,6,2,3,5]=>[4,7,1,2,6,5,3]=>[2,3,1,1]
[4,1,2,7,3,5,6]=>[5,6,1,7,2,3,4]=>[3,2,7,1,6,5,4]=>[1,2,2,1,1]
[4,1,2,7,3,6,5]=>[7,5,1,6,2,3,4]=>[1,3,7,2,6,5,4]=>[3,2,1,1]
[4,1,2,7,5,3,6]=>[6,5,1,7,2,3,4]=>[2,3,7,1,6,5,4]=>[3,2,1,1]
[4,1,2,7,5,6,3]=>[5,1,7,6,2,3,4]=>[3,7,1,2,6,5,4]=>[2,3,1,1]
[4,1,2,7,6,3,5]=>[6,1,7,5,2,3,4]=>[2,7,1,3,6,5,4]=>[2,3,1,1]
[4,1,2,7,6,5,3]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[1,4,1,1]
[4,1,3,2,5,6,7]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>[2,2,1,1,1]
[4,1,3,2,5,7,6]=>[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>[1,3,1,1,1]
[4,1,3,2,6,5,7]=>[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>[1,3,1,1,1]
[4,1,3,2,6,7,5]=>[3,5,1,7,2,4,6]=>[5,3,7,1,6,4,2]=>[1,2,2,1,1]
[4,1,3,2,7,5,6]=>[3,6,1,7,2,4,5]=>[5,2,7,1,6,4,3]=>[1,2,2,1,1]
[4,1,3,2,7,6,5]=>[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>[3,2,1,1]
[4,1,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>[1,3,1,1,1]
[4,1,3,5,2,7,6]=>[3,4,1,7,2,5,6]=>[5,4,7,1,6,3,2]=>[1,2,2,1,1]
[4,1,3,5,6,2,7]=>[3,4,1,6,2,5,7]=>[5,4,7,2,6,3,1]=>[1,2,2,1,1]
[4,1,3,5,6,7,2]=>[3,4,1,5,7,2,6]=>[5,4,7,3,1,6,2]=>[1,2,1,2,1]
[4,1,3,5,7,2,6]=>[3,4,1,6,7,2,5]=>[5,4,7,2,1,6,3]=>[1,2,1,2,1]
[4,1,3,5,7,6,2]=>[7,3,1,4,6,2,5]=>[1,5,7,4,2,6,3]=>[3,1,2,1]
[4,1,3,6,2,5,7]=>[3,5,1,6,2,4,7]=>[5,3,7,2,6,4,1]=>[1,2,2,1,1]
[4,1,3,6,2,7,5]=>[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>[3,2,1,1]
[4,1,3,6,5,2,7]=>[6,3,1,5,2,4,7]=>[2,5,7,3,6,4,1]=>[3,2,1,1]
[4,1,3,6,5,7,2]=>[5,3,1,4,7,2,6]=>[3,5,7,4,1,6,2]=>[3,1,2,1]
[4,1,3,6,7,2,5]=>[6,3,1,4,7,2,5]=>[2,5,7,4,1,6,3]=>[3,1,2,1]
[4,1,3,6,7,5,2]=>[4,1,7,3,6,2,5]=>[4,7,1,5,2,6,3]=>[2,2,2,1]
[4,1,3,7,2,5,6]=>[3,5,1,6,7,2,4]=>[5,3,7,2,1,6,4]=>[1,2,1,2,1]
[4,1,3,7,2,6,5]=>[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]=>[3,1,2,1]
[4,1,3,7,5,2,6]=>[6,3,1,5,7,2,4]=>[2,5,7,3,1,6,4]=>[3,1,2,1]
[4,1,3,7,5,6,2]=>[5,1,7,3,6,2,4]=>[3,7,1,5,2,6,4]=>[2,2,2,1]
[4,1,3,7,6,2,5]=>[6,1,7,3,5,2,4]=>[2,7,1,5,3,6,4]=>[2,2,2,1]
[4,1,3,7,6,5,2]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>[1,3,2,1]
[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>[1,3,1,1,1]
[4,1,5,2,3,7,6]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[4,1,1,1]
[4,1,5,2,6,3,7]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[4,1,1,1]
[4,1,5,2,6,7,3]=>[5,3,1,7,2,4,6]=>[3,5,7,1,6,4,2]=>[3,2,1,1]
[4,1,5,2,7,3,6]=>[6,3,1,7,2,4,5]=>[2,5,7,1,6,4,3]=>[3,2,1,1]
[4,1,5,2,7,6,3]=>[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]=>[2,3,1,1]
[4,1,5,3,2,6,7]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[4,1,1,1]
[4,1,5,3,2,7,6]=>[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]=>[3,2,1,1]
[4,1,5,3,6,2,7]=>[4,3,1,6,2,5,7]=>[4,5,7,2,6,3,1]=>[3,2,1,1]
[4,1,5,3,6,7,2]=>[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]=>[3,1,2,1]
[4,1,5,3,7,2,6]=>[4,3,1,6,7,2,5]=>[4,5,7,2,1,6,3]=>[3,1,2,1]
[4,1,5,3,7,6,2]=>[3,1,7,4,6,2,5]=>[5,7,1,4,2,6,3]=>[2,2,2,1]
[4,1,5,6,2,3,7]=>[5,3,1,6,2,4,7]=>[3,5,7,2,6,4,1]=>[3,2,1,1]
[4,1,5,6,2,7,3]=>[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]=>[2,3,1,1]
[4,1,5,6,3,2,7]=>[3,1,6,5,2,4,7]=>[5,7,2,3,6,4,1]=>[2,3,1,1]
[4,1,5,6,3,7,2]=>[3,1,5,4,7,2,6]=>[5,7,3,4,1,6,2]=>[2,2,2,1]
[4,1,5,6,7,2,3]=>[3,1,6,4,7,2,5]=>[5,7,2,4,1,6,3]=>[2,2,2,1]
[4,1,5,6,7,3,2]=>[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]=>[2,1,3,1]
[4,1,5,7,2,3,6]=>[5,3,1,6,7,2,4]=>[3,5,7,2,1,6,4]=>[3,1,2,1]
[4,1,5,7,2,6,3]=>[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>[2,2,2,1]
[4,1,5,7,3,2,6]=>[3,1,6,5,7,2,4]=>[5,7,2,3,1,6,4]=>[2,2,2,1]
[4,1,5,7,3,6,2]=>[3,1,5,7,6,2,4]=>[5,7,3,1,2,6,4]=>[2,1,3,1]
[4,1,5,7,6,2,3]=>[3,1,6,7,5,2,4]=>[5,7,2,1,3,6,4]=>[2,1,3,1]
[4,1,5,7,6,3,2]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>[1,2,3,1]
[4,1,6,2,3,5,7]=>[4,5,1,6,2,3,7]=>[4,3,7,2,6,5,1]=>[1,2,2,1,1]
[4,1,6,2,3,7,5]=>[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]=>[3,2,1,1]
[4,1,6,2,5,3,7]=>[6,4,1,5,2,3,7]=>[2,4,7,3,6,5,1]=>[3,2,1,1]
[4,1,6,2,5,7,3]=>[5,1,7,4,2,3,6]=>[3,7,1,4,6,5,2]=>[2,3,1,1]
[4,1,6,2,7,3,5]=>[6,1,7,4,2,3,5]=>[2,7,1,4,6,5,3]=>[2,3,1,1]
[4,1,6,2,7,5,3]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[1,4,1,1]
[4,1,6,3,2,5,7]=>[5,4,1,6,2,3,7]=>[3,4,7,2,6,5,1]=>[3,2,1,1]
[4,1,6,3,2,7,5]=>[4,1,7,5,2,3,6]=>[4,7,1,3,6,5,2]=>[2,3,1,1]
[4,1,6,3,5,2,7]=>[4,1,6,5,2,3,7]=>[4,7,2,3,6,5,1]=>[2,3,1,1]
[4,1,6,3,5,7,2]=>[4,1,5,3,7,2,6]=>[4,7,3,5,1,6,2]=>[2,2,2,1]
[4,1,6,3,7,2,5]=>[4,1,6,3,7,2,5]=>[4,7,2,5,1,6,3]=>[2,2,2,1]
[4,1,6,3,7,5,2]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>[1,3,2,1]
[4,1,6,5,2,3,7]=>[5,1,6,4,2,3,7]=>[3,7,2,4,6,5,1]=>[2,3,1,1]
[4,1,6,5,2,7,3]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[1,4,1,1]
[4,1,6,5,3,2,7]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[1,4,1,1]
[4,1,6,5,3,7,2]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>[1,3,2,1]
[4,1,6,5,7,2,3]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>[1,3,2,1]
[4,1,6,5,7,3,2]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>[1,2,3,1]
[4,1,6,7,2,3,5]=>[5,1,6,3,7,2,4]=>[3,7,2,5,1,6,4]=>[2,2,2,1]
[4,1,6,7,2,5,3]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>[1,3,2,1]
[4,1,6,7,3,2,5]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>[1,3,2,1]
[4,1,6,7,3,5,2]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>[1,2,3,1]
[4,1,6,7,5,2,3]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>[1,2,3,1]
[4,1,6,7,5,3,2]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>[1,1,4,1]
[4,1,7,2,3,5,6]=>[4,5,1,6,7,2,3]=>[4,3,7,2,1,6,5]=>[1,2,1,2,1]
[4,1,7,2,3,6,5]=>[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]=>[3,1,2,1]
[4,1,7,2,5,3,6]=>[6,4,1,5,7,2,3]=>[2,4,7,3,1,6,5]=>[3,1,2,1]
[4,1,7,2,5,6,3]=>[5,1,7,4,6,2,3]=>[3,7,1,4,2,6,5]=>[2,2,2,1]
[4,1,7,2,6,3,5]=>[6,1,7,4,5,2,3]=>[2,7,1,4,3,6,5]=>[2,2,2,1]
[4,1,7,2,6,5,3]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>[1,3,2,1]
[4,1,7,3,2,5,6]=>[5,4,1,6,7,2,3]=>[3,4,7,2,1,6,5]=>[3,1,2,1]
[4,1,7,3,2,6,5]=>[4,1,7,5,6,2,3]=>[4,7,1,3,2,6,5]=>[2,2,2,1]
[4,1,7,3,5,2,6]=>[4,1,6,5,7,2,3]=>[4,7,2,3,1,6,5]=>[2,2,2,1]
[4,1,7,3,5,6,2]=>[4,1,5,7,6,2,3]=>[4,7,3,1,2,6,5]=>[2,1,3,1]
[4,1,7,3,6,2,5]=>[4,1,6,7,5,2,3]=>[4,7,2,1,3,6,5]=>[2,1,3,1]
[4,1,7,3,6,5,2]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>[1,2,3,1]
[4,1,7,5,2,3,6]=>[5,1,6,4,7,2,3]=>[3,7,2,4,1,6,5]=>[2,2,2,1]
[4,1,7,5,2,6,3]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>[1,3,2,1]
[4,1,7,5,3,2,6]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>[1,3,2,1]
[4,1,7,5,3,6,2]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>[1,2,3,1]
[4,1,7,5,6,2,3]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>[1,2,3,1]
[4,1,7,5,6,3,2]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>[1,1,4,1]
[4,1,7,6,2,3,5]=>[5,1,6,7,4,2,3]=>[3,7,2,1,4,6,5]=>[2,1,3,1]
[4,1,7,6,2,5,3]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>[1,2,3,1]
[4,1,7,6,3,2,5]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>[1,2,3,1]
[4,1,7,6,3,5,2]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>[1,1,4,1]
[4,1,7,6,5,2,3]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>[1,1,4,1]
[4,1,7,6,5,3,2]=>[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>[2,4,1]
[4,2,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>[2,2,1,1,1]
[4,2,1,3,5,7,6]=>[2,7,3,1,4,5,6]=>[6,1,5,7,4,3,2]=>[1,3,1,1,1]
[4,2,1,3,6,5,7]=>[2,6,3,1,4,5,7]=>[6,2,5,7,4,3,1]=>[1,3,1,1,1]
[4,2,1,3,6,7,5]=>[2,5,1,7,3,4,6]=>[6,3,7,1,5,4,2]=>[1,2,2,1,1]
[4,2,1,3,7,5,6]=>[2,6,1,7,3,4,5]=>[6,2,7,1,5,4,3]=>[1,2,2,1,1]
[4,2,1,3,7,6,5]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>[3,2,1,1]
[4,2,1,5,3,6,7]=>[2,5,3,1,4,6,7]=>[6,3,5,7,4,2,1]=>[1,3,1,1,1]
[4,2,1,5,3,7,6]=>[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]=>[1,2,2,1,1]
[4,2,1,5,6,3,7]=>[2,4,1,6,3,5,7]=>[6,4,7,2,5,3,1]=>[1,2,2,1,1]
[4,2,1,5,6,7,3]=>[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]=>[1,2,1,2,1]
[4,2,1,5,7,3,6]=>[2,4,1,6,7,3,5]=>[6,4,7,2,1,5,3]=>[1,2,1,2,1]
[4,2,1,5,7,6,3]=>[7,2,1,4,6,3,5]=>[1,6,7,4,2,5,3]=>[3,1,2,1]
[4,2,1,6,3,5,7]=>[2,5,1,6,3,4,7]=>[6,3,7,2,5,4,1]=>[1,2,2,1,1]
[4,2,1,6,3,7,5]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>[3,2,1,1]
[4,2,1,6,5,3,7]=>[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>[3,2,1,1]
[4,2,1,6,5,7,3]=>[5,2,1,4,7,3,6]=>[3,6,7,4,1,5,2]=>[3,1,2,1]
[4,2,1,6,7,3,5]=>[6,2,1,4,7,3,5]=>[2,6,7,4,1,5,3]=>[3,1,2,1]
[4,2,1,6,7,5,3]=>[4,1,7,2,6,3,5]=>[4,7,1,6,2,5,3]=>[2,2,2,1]
[4,2,1,7,3,5,6]=>[2,5,1,6,7,3,4]=>[6,3,7,2,1,5,4]=>[1,2,1,2,1]
[4,2,1,7,3,6,5]=>[7,2,1,5,6,3,4]=>[1,6,7,3,2,5,4]=>[3,1,2,1]
[4,2,1,7,5,3,6]=>[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>[3,1,2,1]
[4,2,1,7,5,6,3]=>[5,1,7,2,6,3,4]=>[3,7,1,6,2,5,4]=>[2,2,2,1]
[4,2,1,7,6,3,5]=>[6,1,7,2,5,3,4]=>[2,7,1,6,3,5,4]=>[2,2,2,1]
[4,2,1,7,6,5,3]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[1,3,2,1]
[4,2,3,1,5,6,7]=>[2,4,3,1,5,6,7]=>[6,4,5,7,3,2,1]=>[1,3,1,1,1]
[4,2,3,1,5,7,6]=>[2,3,1,7,4,5,6]=>[6,5,7,1,4,3,2]=>[1,2,2,1,1]
[4,2,3,1,6,5,7]=>[2,3,1,6,4,5,7]=>[6,5,7,2,4,3,1]=>[1,2,2,1,1]
[4,2,3,1,6,7,5]=>[2,3,1,5,7,4,6]=>[6,5,7,3,1,4,2]=>[1,2,1,2,1]
[4,2,3,1,7,5,6]=>[2,3,1,6,7,4,5]=>[6,5,7,2,1,4,3]=>[1,2,1,2,1]
[4,2,3,1,7,6,5]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>[3,1,2,1]
[4,2,3,5,1,6,7]=>[2,3,1,5,4,6,7]=>[6,5,7,3,4,2,1]=>[1,2,2,1,1]
[4,2,3,5,1,7,6]=>[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>[1,2,1,2,1]
[4,2,3,5,6,1,7]=>[2,3,1,4,6,5,7]=>[6,5,7,4,2,3,1]=>[1,2,1,2,1]
[4,2,3,5,6,7,1]=>[2,3,1,4,5,7,6]=>[6,5,7,4,3,1,2]=>[1,2,1,1,2]
[4,2,3,5,7,1,6]=>[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>[1,2,1,1,2]
[4,2,3,5,7,6,1]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>[3,1,1,2]
[4,2,3,6,1,5,7]=>[2,3,1,5,6,4,7]=>[6,5,7,3,2,4,1]=>[1,2,1,2,1]
[4,2,3,6,1,7,5]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>[3,1,2,1]
[4,2,3,6,5,1,7]=>[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>[3,1,2,1]
[4,2,3,6,5,7,1]=>[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>[3,1,1,2]
[4,2,3,6,7,1,5]=>[6,2,1,3,4,7,5]=>[2,6,7,5,4,1,3]=>[3,1,1,2]
[4,2,3,6,7,5,1]=>[4,1,7,2,3,6,5]=>[4,7,1,6,5,2,3]=>[2,2,1,2]
[4,2,3,7,1,5,6]=>[2,3,1,5,6,7,4]=>[6,5,7,3,2,1,4]=>[1,2,1,1,2]
[4,2,3,7,1,6,5]=>[7,2,1,3,5,6,4]=>[1,6,7,5,3,2,4]=>[3,1,1,2]
[4,2,3,7,5,1,6]=>[6,2,1,3,5,7,4]=>[2,6,7,5,3,1,4]=>[3,1,1,2]
[4,2,3,7,5,6,1]=>[5,1,7,2,3,6,4]=>[3,7,1,6,5,2,4]=>[2,2,1,2]
[4,2,3,7,6,1,5]=>[6,1,7,2,3,5,4]=>[2,7,1,6,5,3,4]=>[2,2,1,2]
[4,2,3,7,6,5,1]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[1,3,1,2]
[4,2,5,1,3,6,7]=>[2,4,1,5,3,6,7]=>[6,4,7,3,5,2,1]=>[1,2,2,1,1]
[4,2,5,1,3,7,6]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>[3,2,1,1]
[4,2,5,1,6,3,7]=>[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>[3,2,1,1]
[4,2,5,1,6,7,3]=>[5,2,1,3,7,4,6]=>[3,6,7,5,1,4,2]=>[3,1,2,1]
[4,2,5,1,7,3,6]=>[6,2,1,3,7,4,5]=>[2,6,7,5,1,4,3]=>[3,1,2,1]
[4,2,5,1,7,6,3]=>[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]=>[2,2,2,1]
[4,2,5,3,1,6,7]=>[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>[3,2,1,1]
[4,2,5,3,1,7,6]=>[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>[3,1,2,1]
[4,2,5,3,6,1,7]=>[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>[3,1,2,1]
[4,2,5,3,6,7,1]=>[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>[3,1,1,2]
[4,2,5,3,7,1,6]=>[4,2,1,3,6,7,5]=>[4,6,7,5,2,1,3]=>[3,1,1,2]
[4,2,5,3,7,6,1]=>[3,1,7,2,4,6,5]=>[5,7,1,6,4,2,3]=>[2,2,1,2]
[4,2,5,6,1,3,7]=>[5,2,1,3,6,4,7]=>[3,6,7,5,2,4,1]=>[3,1,2,1]
[4,2,5,6,1,7,3]=>[3,1,7,2,5,4,6]=>[5,7,1,6,3,4,2]=>[2,2,2,1]
[4,2,5,6,3,1,7]=>[3,1,6,2,5,4,7]=>[5,7,2,6,3,4,1]=>[2,2,2,1]
[4,2,5,6,3,7,1]=>[3,1,5,2,4,7,6]=>[5,7,3,6,4,1,2]=>[2,2,1,2]
[4,2,5,6,7,1,3]=>[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]=>[2,2,1,2]
[4,2,5,6,7,3,1]=>[3,1,4,7,2,6,5]=>[5,7,4,1,6,2,3]=>[2,1,2,2]
[4,2,5,7,1,3,6]=>[5,2,1,3,6,7,4]=>[3,6,7,5,2,1,4]=>[3,1,1,2]
[4,2,5,7,1,6,3]=>[3,1,7,2,5,6,4]=>[5,7,1,6,3,2,4]=>[2,2,1,2]
[4,2,5,7,3,1,6]=>[3,1,6,2,5,7,4]=>[5,7,2,6,3,1,4]=>[2,2,1,2]
[4,2,5,7,3,6,1]=>[3,1,5,7,2,6,4]=>[5,7,3,1,6,2,4]=>[2,1,2,2]
[4,2,5,7,6,1,3]=>[3,1,6,7,2,5,4]=>[5,7,2,1,6,3,4]=>[2,1,2,2]
[4,2,5,7,6,3,1]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>[1,2,2,2]
[4,2,6,1,3,5,7]=>[2,4,1,5,6,3,7]=>[6,4,7,3,2,5,1]=>[1,2,1,2,1]
[4,2,6,1,3,7,5]=>[7,2,1,4,5,3,6]=>[1,6,7,4,3,5,2]=>[3,1,2,1]
[4,2,6,1,5,3,7]=>[6,2,1,4,5,3,7]=>[2,6,7,4,3,5,1]=>[3,1,2,1]
[4,2,6,1,5,7,3]=>[5,1,7,2,4,3,6]=>[3,7,1,6,4,5,2]=>[2,2,2,1]
[4,2,6,1,7,3,5]=>[6,1,7,2,4,3,5]=>[2,7,1,6,4,5,3]=>[2,2,2,1]
[4,2,6,1,7,5,3]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[1,3,2,1]
[4,2,6,3,1,5,7]=>[5,2,1,4,6,3,7]=>[3,6,7,4,2,5,1]=>[3,1,2,1]
[4,2,6,3,1,7,5]=>[4,1,7,2,5,3,6]=>[4,7,1,6,3,5,2]=>[2,2,2,1]
[4,2,6,3,5,1,7]=>[4,1,6,2,5,3,7]=>[4,7,2,6,3,5,1]=>[2,2,2,1]
[4,2,6,3,5,7,1]=>[4,1,5,2,3,7,6]=>[4,7,3,6,5,1,2]=>[2,2,1,2]
[4,2,6,3,7,1,5]=>[4,1,6,2,3,7,5]=>[4,7,2,6,5,1,3]=>[2,2,1,2]
[4,2,6,3,7,5,1]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[1,3,1,2]
[4,2,6,5,1,3,7]=>[5,1,6,2,4,3,7]=>[3,7,2,6,4,5,1]=>[2,2,2,1]
[4,2,6,5,1,7,3]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[1,3,2,1]
[4,2,6,5,3,1,7]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[1,3,2,1]
[4,2,6,5,3,7,1]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[1,3,1,2]
[4,2,6,5,7,1,3]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>[1,3,1,2]
[4,2,6,5,7,3,1]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>[1,2,2,2]
[4,2,6,7,1,3,5]=>[5,1,6,2,3,7,4]=>[3,7,2,6,5,1,4]=>[2,2,1,2]
[4,2,6,7,1,5,3]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>[1,3,1,2]
[4,2,6,7,3,1,5]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>[1,3,1,2]
[4,2,6,7,3,5,1]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[1,2,2,2]
[4,2,6,7,5,1,3]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>[1,2,2,2]
[4,2,6,7,5,3,1]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>[1,1,3,2]
[4,2,7,1,3,5,6]=>[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]=>[1,2,1,1,2]
[4,2,7,1,3,6,5]=>[7,2,1,4,5,6,3]=>[1,6,7,4,3,2,5]=>[3,1,1,2]
[4,2,7,1,5,3,6]=>[6,2,1,4,5,7,3]=>[2,6,7,4,3,1,5]=>[3,1,1,2]
[4,2,7,1,5,6,3]=>[5,1,7,2,4,6,3]=>[3,7,1,6,4,2,5]=>[2,2,1,2]
[4,2,7,1,6,3,5]=>[6,1,7,2,4,5,3]=>[2,7,1,6,4,3,5]=>[2,2,1,2]
[4,2,7,1,6,5,3]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>[1,3,1,2]
[4,2,7,3,1,5,6]=>[5,2,1,4,6,7,3]=>[3,6,7,4,2,1,5]=>[3,1,1,2]
[4,2,7,3,1,6,5]=>[4,1,7,2,5,6,3]=>[4,7,1,6,3,2,5]=>[2,2,1,2]
[4,2,7,3,5,1,6]=>[4,1,6,2,5,7,3]=>[4,7,2,6,3,1,5]=>[2,2,1,2]
[4,2,7,3,5,6,1]=>[4,1,5,7,2,6,3]=>[4,7,3,1,6,2,5]=>[2,1,2,2]
[4,2,7,3,6,1,5]=>[4,1,6,7,2,5,3]=>[4,7,2,1,6,3,5]=>[2,1,2,2]
[4,2,7,3,6,5,1]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>[1,2,2,2]
[4,2,7,5,1,3,6]=>[5,1,6,2,4,7,3]=>[3,7,2,6,4,1,5]=>[2,2,1,2]
[4,2,7,5,1,6,3]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>[1,3,1,2]
[4,2,7,5,3,1,6]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>[1,3,1,2]
[4,2,7,5,3,6,1]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>[1,2,2,2]
[4,2,7,5,6,1,3]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>[1,2,2,2]
[4,2,7,5,6,3,1]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>[1,1,3,2]
[4,2,7,6,1,3,5]=>[5,1,6,7,2,4,3]=>[3,7,2,1,6,4,5]=>[2,1,2,2]
[4,2,7,6,1,5,3]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>[1,2,2,2]
[4,2,7,6,3,1,5]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>[1,2,2,2]
[4,2,7,6,3,5,1]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>[1,1,3,2]
[4,2,7,6,5,1,3]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>[1,1,3,2]
[4,2,7,6,5,3,1]=>[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>[2,3,2]
[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>[1,3,1,1,1]
[4,3,1,2,5,7,6]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[4,1,1,1]
[4,3,1,2,6,5,7]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[4,1,1,1]
[4,3,1,2,6,7,5]=>[5,2,1,7,3,4,6]=>[3,6,7,1,5,4,2]=>[3,2,1,1]
[4,3,1,2,7,5,6]=>[6,2,1,7,3,4,5]=>[2,6,7,1,5,4,3]=>[3,2,1,1]
[4,3,1,2,7,6,5]=>[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>[2,3,1,1]
[4,3,1,5,2,6,7]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[4,1,1,1]
[4,3,1,5,2,7,6]=>[4,2,1,7,3,5,6]=>[4,6,7,1,5,3,2]=>[3,2,1,1]
[4,3,1,5,6,2,7]=>[4,2,1,6,3,5,7]=>[4,6,7,2,5,3,1]=>[3,2,1,1]
[4,3,1,5,6,7,2]=>[4,2,1,5,7,3,6]=>[4,6,7,3,1,5,2]=>[3,1,2,1]
[4,3,1,5,7,2,6]=>[4,2,1,6,7,3,5]=>[4,6,7,2,1,5,3]=>[3,1,2,1]
[4,3,1,5,7,6,2]=>[2,1,7,4,6,3,5]=>[6,7,1,4,2,5,3]=>[2,2,2,1]
[4,3,1,6,2,5,7]=>[5,2,1,6,3,4,7]=>[3,6,7,2,5,4,1]=>[3,2,1,1]
[4,3,1,6,2,7,5]=>[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>[2,3,1,1]
[4,3,1,6,5,2,7]=>[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>[2,3,1,1]
[4,3,1,6,5,7,2]=>[2,1,5,4,7,3,6]=>[6,7,3,4,1,5,2]=>[2,2,2,1]
[4,3,1,6,7,2,5]=>[2,1,6,4,7,3,5]=>[6,7,2,4,1,5,3]=>[2,2,2,1]
[4,3,1,6,7,5,2]=>[2,1,4,7,6,3,5]=>[6,7,4,1,2,5,3]=>[2,1,3,1]
[4,3,1,7,2,5,6]=>[5,2,1,6,7,3,4]=>[3,6,7,2,1,5,4]=>[3,1,2,1]
[4,3,1,7,2,6,5]=>[2,1,7,5,6,3,4]=>[6,7,1,3,2,5,4]=>[2,2,2,1]
[4,3,1,7,5,2,6]=>[2,1,6,5,7,3,4]=>[6,7,2,3,1,5,4]=>[2,2,2,1]
[4,3,1,7,5,6,2]=>[2,1,5,7,6,3,4]=>[6,7,3,1,2,5,4]=>[2,1,3,1]
[4,3,1,7,6,2,5]=>[2,1,6,7,5,3,4]=>[6,7,2,1,3,5,4]=>[2,1,3,1]
[4,3,1,7,6,5,2]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[1,2,3,1]
[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[4,1,1,1]
[4,3,2,1,5,7,6]=>[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>[3,2,1,1]
[4,3,2,1,6,5,7]=>[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>[3,2,1,1]
[4,3,2,1,6,7,5]=>[3,2,1,5,7,4,6]=>[5,6,7,3,1,4,2]=>[3,1,2,1]
[4,3,2,1,7,5,6]=>[3,2,1,6,7,4,5]=>[5,6,7,2,1,4,3]=>[3,1,2,1]
[4,3,2,1,7,6,5]=>[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>[2,2,2,1]
[4,3,2,5,1,6,7]=>[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>[3,2,1,1]
[4,3,2,5,1,7,6]=>[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>[3,1,2,1]
[4,3,2,5,6,1,7]=>[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>[3,1,2,1]
[4,3,2,5,6,7,1]=>[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>[3,1,1,2]
[4,3,2,5,7,1,6]=>[3,2,1,4,6,7,5]=>[5,6,7,4,2,1,3]=>[3,1,1,2]
[4,3,2,5,7,6,1]=>[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>[2,2,1,2]
[4,3,2,6,1,5,7]=>[3,2,1,5,6,4,7]=>[5,6,7,3,2,4,1]=>[3,1,2,1]
[4,3,2,6,1,7,5]=>[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>[2,2,2,1]
[4,3,2,6,5,1,7]=>[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>[2,2,2,1]
[4,3,2,6,5,7,1]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[2,2,1,2]
[4,3,2,6,7,1,5]=>[2,1,6,3,4,7,5]=>[6,7,2,5,4,1,3]=>[2,2,1,2]
[4,3,2,6,7,5,1]=>[2,1,4,7,3,6,5]=>[6,7,4,1,5,2,3]=>[2,1,2,2]
[4,3,2,7,1,5,6]=>[3,2,1,5,6,7,4]=>[5,6,7,3,2,1,4]=>[3,1,1,2]
[4,3,2,7,1,6,5]=>[2,1,7,3,5,6,4]=>[6,7,1,5,3,2,4]=>[2,2,1,2]
[4,3,2,7,5,1,6]=>[2,1,6,3,5,7,4]=>[6,7,2,5,3,1,4]=>[2,2,1,2]
[4,3,2,7,5,6,1]=>[2,1,5,7,3,6,4]=>[6,7,3,1,5,2,4]=>[2,1,2,2]
[4,3,2,7,6,1,5]=>[2,1,6,7,3,5,4]=>[6,7,2,1,5,3,4]=>[2,1,2,2]
[4,3,2,7,6,5,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[1,2,2,2]
[4,3,5,1,2,6,7]=>[4,2,1,5,3,6,7]=>[4,6,7,3,5,2,1]=>[3,2,1,1]
[4,3,5,1,2,7,6]=>[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>[2,3,1,1]
[4,3,5,1,6,2,7]=>[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>[2,3,1,1]
[4,3,5,1,6,7,2]=>[2,1,5,3,7,4,6]=>[6,7,3,5,1,4,2]=>[2,2,2,1]
[4,3,5,1,7,2,6]=>[2,1,6,3,7,4,5]=>[6,7,2,5,1,4,3]=>[2,2,2,1]
[4,3,5,1,7,6,2]=>[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>[2,1,3,1]
[4,3,5,2,1,6,7]=>[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>[2,3,1,1]
[4,3,5,2,1,7,6]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>[2,2,2,1]
[4,3,5,2,6,1,7]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>[2,2,2,1]
[4,3,5,2,6,7,1]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>[2,2,1,2]
[4,3,5,2,7,1,6]=>[2,1,4,3,6,7,5]=>[6,7,4,5,2,1,3]=>[2,2,1,2]
[4,3,5,2,7,6,1]=>[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>[2,1,2,2]
[4,3,5,6,1,2,7]=>[2,1,5,3,6,4,7]=>[6,7,3,5,2,4,1]=>[2,2,2,1]
[4,3,5,6,1,7,2]=>[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>[2,1,3,1]
[4,3,5,6,2,1,7]=>[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>[2,1,3,1]
[4,3,5,6,2,7,1]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>[2,1,2,2]
[4,3,5,6,7,1,2]=>[2,1,3,6,4,7,5]=>[6,7,5,2,4,1,3]=>[2,1,2,2]
[4,3,5,6,7,2,1]=>[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>[2,1,1,3]
[4,3,5,7,1,2,6]=>[2,1,5,3,6,7,4]=>[6,7,3,5,2,1,4]=>[2,2,1,2]
[4,3,5,7,1,6,2]=>[2,1,3,7,5,6,4]=>[6,7,5,1,3,2,4]=>[2,1,2,2]
[4,3,5,7,2,1,6]=>[2,1,3,6,5,7,4]=>[6,7,5,2,3,1,4]=>[2,1,2,2]
[4,3,5,7,2,6,1]=>[2,1,3,5,7,6,4]=>[6,7,5,3,1,2,4]=>[2,1,1,3]
[4,3,5,7,6,1,2]=>[2,1,3,6,7,5,4]=>[6,7,5,2,1,3,4]=>[2,1,1,3]
[4,3,5,7,6,2,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[1,2,1,3]
[4,3,6,1,2,5,7]=>[4,2,1,5,6,3,7]=>[4,6,7,3,2,5,1]=>[3,1,2,1]
[4,3,6,1,2,7,5]=>[2,1,7,4,5,3,6]=>[6,7,1,4,3,5,2]=>[2,2,2,1]
[4,3,6,1,5,2,7]=>[2,1,6,4,5,3,7]=>[6,7,2,4,3,5,1]=>[2,2,2,1]
[4,3,6,1,5,7,2]=>[2,1,5,7,4,3,6]=>[6,7,3,1,4,5,2]=>[2,1,3,1]
[4,3,6,1,7,2,5]=>[2,1,6,7,4,3,5]=>[6,7,2,1,4,5,3]=>[2,1,3,1]
[4,3,6,1,7,5,2]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[1,2,3,1]
[4,3,6,2,1,5,7]=>[2,1,5,4,6,3,7]=>[6,7,3,4,2,5,1]=>[2,2,2,1]
[4,3,6,2,1,7,5]=>[2,1,4,7,5,3,6]=>[6,7,4,1,3,5,2]=>[2,1,3,1]
[4,3,6,2,5,1,7]=>[2,1,4,6,5,3,7]=>[6,7,4,2,3,5,1]=>[2,1,3,1]
[4,3,6,2,5,7,1]=>[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>[2,1,2,2]
[4,3,6,2,7,1,5]=>[2,1,4,6,3,7,5]=>[6,7,4,2,5,1,3]=>[2,1,2,2]
[4,3,6,2,7,5,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[1,2,2,2]
[4,3,6,5,1,2,7]=>[2,1,5,6,4,3,7]=>[6,7,3,2,4,5,1]=>[2,1,3,1]
[4,3,6,5,1,7,2]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[1,2,3,1]
[4,3,6,5,2,1,7]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[1,2,3,1]
[4,3,6,5,2,7,1]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[1,2,2,2]
[4,3,6,5,7,1,2]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>[1,2,2,2]
[4,3,6,5,7,2,1]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[1,2,1,3]
[4,3,6,7,1,2,5]=>[2,1,5,6,3,7,4]=>[6,7,3,2,5,1,4]=>[2,1,2,2]
[4,3,6,7,1,5,2]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>[1,2,2,2]
[4,3,6,7,2,1,5]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>[1,2,2,2]
[4,3,6,7,2,5,1]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>[1,2,1,3]
[4,3,6,7,5,1,2]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>[1,2,1,3]
[4,3,6,7,5,2,1]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>[1,1,2,3]
[4,3,7,1,2,5,6]=>[4,2,1,5,6,7,3]=>[4,6,7,3,2,1,5]=>[3,1,1,2]
[4,3,7,1,2,6,5]=>[2,1,7,4,5,6,3]=>[6,7,1,4,3,2,5]=>[2,2,1,2]
[4,3,7,1,5,2,6]=>[2,1,6,4,5,7,3]=>[6,7,2,4,3,1,5]=>[2,2,1,2]
[4,3,7,1,5,6,2]=>[2,1,5,7,4,6,3]=>[6,7,3,1,4,2,5]=>[2,1,2,2]
[4,3,7,1,6,2,5]=>[2,1,6,7,4,5,3]=>[6,7,2,1,4,3,5]=>[2,1,2,2]
[4,3,7,1,6,5,2]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>[1,2,2,2]
[4,3,7,2,1,5,6]=>[2,1,5,4,6,7,3]=>[6,7,3,4,2,1,5]=>[2,2,1,2]
[4,3,7,2,1,6,5]=>[2,1,4,7,5,6,3]=>[6,7,4,1,3,2,5]=>[2,1,2,2]
[4,3,7,2,5,1,6]=>[2,1,4,6,5,7,3]=>[6,7,4,2,3,1,5]=>[2,1,2,2]
[4,3,7,2,5,6,1]=>[2,1,4,5,7,6,3]=>[6,7,4,3,1,2,5]=>[2,1,1,3]
[4,3,7,2,6,1,5]=>[2,1,4,6,7,5,3]=>[6,7,4,2,1,3,5]=>[2,1,1,3]
[4,3,7,2,6,5,1]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>[1,2,1,3]
[4,3,7,5,1,2,6]=>[2,1,5,6,4,7,3]=>[6,7,3,2,4,1,5]=>[2,1,2,2]
[4,3,7,5,1,6,2]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>[1,2,2,2]
[4,3,7,5,2,1,6]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>[1,2,2,2]
[4,3,7,5,2,6,1]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>[1,2,1,3]
[4,3,7,5,6,1,2]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>[1,2,1,3]
[4,3,7,5,6,2,1]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>[1,1,2,3]
[4,3,7,6,1,2,5]=>[2,1,5,6,7,4,3]=>[6,7,3,2,1,4,5]=>[2,1,1,3]
[4,3,7,6,1,5,2]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>[1,2,1,3]
[4,3,7,6,2,1,5]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>[1,2,1,3]
[4,3,7,6,2,5,1]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>[1,1,2,3]
[4,3,7,6,5,1,2]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>[1,1,2,3]
[4,3,7,6,5,2,1]=>[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[2,2,3]
[4,5,1,2,3,6,7]=>[3,4,1,5,2,6,7]=>[5,4,7,3,6,2,1]=>[1,2,2,1,1]
[4,5,1,2,3,7,6]=>[7,3,1,4,2,5,6]=>[1,5,7,4,6,3,2]=>[3,2,1,1]
[4,5,1,2,6,3,7]=>[6,3,1,4,2,5,7]=>[2,5,7,4,6,3,1]=>[3,2,1,1]
[4,5,1,2,6,7,3]=>[5,1,7,3,2,4,6]=>[3,7,1,5,6,4,2]=>[2,3,1,1]
[4,5,1,2,7,3,6]=>[6,1,7,3,2,4,5]=>[2,7,1,5,6,4,3]=>[2,3,1,1]
[4,5,1,2,7,6,3]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[1,4,1,1]
[4,5,1,3,2,6,7]=>[5,3,1,4,2,6,7]=>[3,5,7,4,6,2,1]=>[3,2,1,1]
[4,5,1,3,2,7,6]=>[4,1,7,3,2,5,6]=>[4,7,1,5,6,3,2]=>[2,3,1,1]
[4,5,1,3,6,2,7]=>[4,1,6,3,2,5,7]=>[4,7,2,5,6,3,1]=>[2,3,1,1]
[4,5,1,3,6,7,2]=>[4,1,5,2,7,3,6]=>[4,7,3,6,1,5,2]=>[2,2,2,1]
[4,5,1,3,7,2,6]=>[4,1,6,2,7,3,5]=>[4,7,2,6,1,5,3]=>[2,2,2,1]
[4,5,1,3,7,6,2]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>[1,3,2,1]
[4,5,1,6,2,3,7]=>[5,1,6,3,2,4,7]=>[3,7,2,5,6,4,1]=>[2,3,1,1]
[4,5,1,6,2,7,3]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[1,4,1,1]
[4,5,1,6,3,2,7]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[1,4,1,1]
[4,5,1,6,3,7,2]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>[1,3,2,1]
[4,5,1,6,7,2,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>[1,3,2,1]
[4,5,1,6,7,3,2]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>[1,2,3,1]
[4,5,1,7,2,3,6]=>[5,1,6,2,7,3,4]=>[3,7,2,6,1,5,4]=>[2,2,2,1]
[4,5,1,7,2,6,3]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>[1,3,2,1]
[4,5,1,7,3,2,6]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>[1,3,2,1]
[4,5,1,7,3,6,2]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>[1,2,3,1]
[4,5,1,7,6,2,3]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>[1,2,3,1]
[4,5,1,7,6,3,2]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[1,1,4,1]
[4,5,2,1,3,6,7]=>[4,3,1,5,2,6,7]=>[4,5,7,3,6,2,1]=>[3,2,1,1]
[4,5,2,1,3,7,6]=>[3,1,7,4,2,5,6]=>[5,7,1,4,6,3,2]=>[2,3,1,1]
[4,5,2,1,6,3,7]=>[3,1,6,4,2,5,7]=>[5,7,2,4,6,3,1]=>[2,3,1,1]
[4,5,2,1,6,7,3]=>[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]=>[2,2,2,1]
[4,5,2,1,7,3,6]=>[3,1,6,2,7,4,5]=>[5,7,2,6,1,4,3]=>[2,2,2,1]
[4,5,2,1,7,6,3]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[1,3,2,1]
[4,5,2,3,1,6,7]=>[3,1,5,4,2,6,7]=>[5,7,3,4,6,2,1]=>[2,3,1,1]
[4,5,2,3,1,7,6]=>[3,1,4,2,7,5,6]=>[5,7,4,6,1,3,2]=>[2,2,2,1]
[4,5,2,3,6,1,7]=>[3,1,4,2,6,5,7]=>[5,7,4,6,2,3,1]=>[2,2,2,1]
[4,5,2,3,6,7,1]=>[3,1,4,2,5,7,6]=>[5,7,4,6,3,1,2]=>[2,2,1,2]
[4,5,2,3,7,1,6]=>[3,1,4,2,6,7,5]=>[5,7,4,6,2,1,3]=>[2,2,1,2]
[4,5,2,3,7,6,1]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[1,3,1,2]
[4,5,2,6,1,3,7]=>[3,1,5,2,6,4,7]=>[5,7,3,6,2,4,1]=>[2,2,2,1]
[4,5,2,6,1,7,3]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[1,3,2,1]
[4,5,2,6,3,1,7]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[1,3,2,1]
[4,5,2,6,3,7,1]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[1,3,1,2]
[4,5,2,6,7,1,3]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>[1,3,1,2]
[4,5,2,6,7,3,1]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>[1,2,2,2]
[4,5,2,7,1,3,6]=>[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]=>[2,2,1,2]
[4,5,2,7,1,6,3]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>[1,3,1,2]
[4,5,2,7,3,1,6]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>[1,3,1,2]
[4,5,2,7,3,6,1]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>[1,2,2,2]
[4,5,2,7,6,1,3]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>[1,2,2,2]
[4,5,2,7,6,3,1]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[1,1,3,2]
[4,5,3,1,2,6,7]=>[4,1,5,3,2,6,7]=>[4,7,3,5,6,2,1]=>[2,3,1,1]
[4,5,3,1,2,7,6]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[1,4,1,1]
[4,5,3,1,6,2,7]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[1,4,1,1]
[4,5,3,1,6,7,2]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>[1,3,2,1]
[4,5,3,1,7,2,6]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>[1,3,2,1]
[4,5,3,1,7,6,2]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[1,2,3,1]
[4,5,3,2,1,6,7]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[1,4,1,1]
[4,5,3,2,1,7,6]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[1,3,2,1]
[4,5,3,2,6,1,7]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[1,3,2,1]
[4,5,3,2,6,7,1]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[1,3,1,2]
[4,5,3,2,7,1,6]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>[1,3,1,2]
[4,5,3,2,7,6,1]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[1,2,2,2]
[4,5,3,6,1,2,7]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>[1,3,2,1]
[4,5,3,6,1,7,2]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[1,2,3,1]
[4,5,3,6,2,1,7]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[1,2,3,1]
[4,5,3,6,2,7,1]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[1,2,2,2]
[4,5,3,6,7,1,2]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>[1,2,2,2]
[4,5,3,6,7,2,1]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[1,2,1,3]
[4,5,3,7,1,2,6]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>[1,3,1,2]
[4,5,3,7,1,6,2]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>[1,2,2,2]
[4,5,3,7,2,1,6]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>[1,2,2,2]
[4,5,3,7,2,6,1]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>[1,2,1,3]
[4,5,3,7,6,1,2]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>[1,2,1,3]
[4,5,3,7,6,2,1]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[1,1,2,3]
[4,5,6,1,2,3,7]=>[4,1,5,2,6,3,7]=>[4,7,3,6,2,5,1]=>[2,2,2,1]
[4,5,6,1,2,7,3]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>[1,3,2,1]
[4,5,6,1,3,2,7]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[1,3,2,1]
[4,5,6,1,3,7,2]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>[1,2,3,1]
[4,5,6,1,7,2,3]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>[1,2,3,1]
[4,5,6,1,7,3,2]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[1,1,4,1]
[4,5,6,2,1,3,7]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>[1,3,2,1]
[4,5,6,2,1,7,3]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>[1,2,3,1]
[4,5,6,2,3,1,7]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>[1,2,3,1]
[4,5,6,2,3,7,1]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>[1,2,2,2]
[4,5,6,2,7,1,3]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>[1,2,2,2]
[4,5,6,2,7,3,1]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[1,1,3,2]
[4,5,6,3,1,2,7]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>[1,2,3,1]
[4,5,6,3,1,7,2]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[1,1,4,1]
[4,5,6,3,2,1,7]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[1,1,4,1]
[4,5,6,3,2,7,1]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[1,1,3,2]
[4,5,6,3,7,1,2]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>[1,1,3,2]
[4,5,6,3,7,2,1]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[1,1,2,3]
[4,5,6,7,1,2,3]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>[1,2,2,2]
[4,5,6,7,1,3,2]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>[1,1,3,2]
[4,5,6,7,2,1,3]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>[1,1,3,2]
[4,5,6,7,2,3,1]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>[1,1,2,3]
[4,5,6,7,3,1,2]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>[1,1,2,3]
[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[1,1,1,4]
[4,5,7,1,2,3,6]=>[4,1,5,2,6,7,3]=>[4,7,3,6,2,1,5]=>[2,2,1,2]
[4,5,7,1,2,6,3]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>[1,3,1,2]
[4,5,7,1,3,2,6]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>[1,3,1,2]
[4,5,7,1,3,6,2]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>[1,2,2,2]
[4,5,7,1,6,2,3]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>[1,2,2,2]
[4,5,7,1,6,3,2]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>[1,1,3,2]
[4,5,7,2,1,3,6]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>[1,3,1,2]
[4,5,7,2,1,6,3]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>[1,2,2,2]
[4,5,7,2,3,1,6]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>[1,2,2,2]
[4,5,7,2,3,6,1]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>[1,2,1,3]
[4,5,7,2,6,1,3]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>[1,2,1,3]
[4,5,7,2,6,3,1]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>[1,1,2,3]
[4,5,7,3,1,2,6]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>[1,2,2,2]
[4,5,7,3,1,6,2]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>[1,1,3,2]
[4,5,7,3,2,1,6]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>[1,1,3,2]
[4,5,7,3,2,6,1]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>[1,1,2,3]
[4,5,7,3,6,1,2]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>[1,1,2,3]
[4,5,7,3,6,2,1]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>[1,1,1,4]
[4,5,7,6,1,2,3]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>[1,2,1,3]
[4,5,7,6,1,3,2]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>[1,1,2,3]
[4,5,7,6,2,1,3]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>[1,1,2,3]
[4,5,7,6,2,3,1]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>[1,1,1,4]
[4,5,7,6,3,1,2]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>[1,1,1,4]
[4,5,7,6,3,2,1]=>[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>[2,1,4]
[4,6,1,2,3,5,7]=>[3,4,1,5,6,2,7]=>[5,4,7,3,2,6,1]=>[1,2,1,2,1]
[4,6,1,2,3,7,5]=>[7,3,1,4,5,2,6]=>[1,5,7,4,3,6,2]=>[3,1,2,1]
[4,6,1,2,5,3,7]=>[6,3,1,4,5,2,7]=>[2,5,7,4,3,6,1]=>[3,1,2,1]
[4,6,1,2,5,7,3]=>[5,1,7,3,4,2,6]=>[3,7,1,5,4,6,2]=>[2,2,2,1]
[4,6,1,2,7,3,5]=>[6,1,7,3,4,2,5]=>[2,7,1,5,4,6,3]=>[2,2,2,1]
[4,6,1,2,7,5,3]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>[1,3,2,1]
[4,6,1,3,2,5,7]=>[5,3,1,4,6,2,7]=>[3,5,7,4,2,6,1]=>[3,1,2,1]
[4,6,1,3,2,7,5]=>[4,1,7,3,5,2,6]=>[4,7,1,5,3,6,2]=>[2,2,2,1]
[4,6,1,3,5,2,7]=>[4,1,6,3,5,2,7]=>[4,7,2,5,3,6,1]=>[2,2,2,1]
[4,6,1,3,5,7,2]=>[4,1,5,7,3,2,6]=>[4,7,3,1,5,6,2]=>[2,1,3,1]
[4,6,1,3,7,2,5]=>[4,1,6,7,3,2,5]=>[4,7,2,1,5,6,3]=>[2,1,3,1]
[4,6,1,3,7,5,2]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>[1,2,3,1]
[4,6,1,5,2,3,7]=>[5,1,6,3,4,2,7]=>[3,7,2,5,4,6,1]=>[2,2,2,1]
[4,6,1,5,2,7,3]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>[1,3,2,1]
[4,6,1,5,3,2,7]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>[1,3,2,1]
[4,6,1,5,3,7,2]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>[1,2,3,1]
[4,6,1,5,7,2,3]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>[1,2,3,1]
[4,6,1,5,7,3,2]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>[1,1,4,1]
[4,6,1,7,2,3,5]=>[5,1,6,7,3,2,4]=>[3,7,2,1,5,6,4]=>[2,1,3,1]
[4,6,1,7,2,5,3]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>[1,2,3,1]
[4,6,1,7,3,2,5]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>[1,2,3,1]
[4,6,1,7,3,5,2]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>[1,1,4,1]
[4,6,1,7,5,2,3]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>[1,1,4,1]
[4,6,1,7,5,3,2]=>[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[2,4,1]
[4,6,2,1,3,5,7]=>[4,3,1,5,6,2,7]=>[4,5,7,3,2,6,1]=>[3,1,2,1]
[4,6,2,1,3,7,5]=>[3,1,7,4,5,2,6]=>[5,7,1,4,3,6,2]=>[2,2,2,1]
[4,6,2,1,5,3,7]=>[3,1,6,4,5,2,7]=>[5,7,2,4,3,6,1]=>[2,2,2,1]
[4,6,2,1,5,7,3]=>[3,1,5,7,4,2,6]=>[5,7,3,1,4,6,2]=>[2,1,3,1]
[4,6,2,1,7,3,5]=>[3,1,6,7,4,2,5]=>[5,7,2,1,4,6,3]=>[2,1,3,1]
[4,6,2,1,7,5,3]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>[1,2,3,1]
[4,6,2,3,1,5,7]=>[3,1,5,4,6,2,7]=>[5,7,3,4,2,6,1]=>[2,2,2,1]
[4,6,2,3,1,7,5]=>[3,1,4,7,5,2,6]=>[5,7,4,1,3,6,2]=>[2,1,3,1]
[4,6,2,3,5,1,7]=>[3,1,4,6,5,2,7]=>[5,7,4,2,3,6,1]=>[2,1,3,1]
[4,6,2,3,5,7,1]=>[3,1,4,5,2,7,6]=>[5,7,4,3,6,1,2]=>[2,1,2,2]
[4,6,2,3,7,1,5]=>[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]=>[2,1,2,2]
[4,6,2,3,7,5,1]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>[1,2,2,2]
[4,6,2,5,1,3,7]=>[3,1,5,6,4,2,7]=>[5,7,3,2,4,6,1]=>[2,1,3,1]
[4,6,2,5,1,7,3]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>[1,2,3,1]
[4,6,2,5,3,1,7]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>[1,2,3,1]
[4,6,2,5,3,7,1]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>[1,2,2,2]
[4,6,2,5,7,1,3]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>[1,2,2,2]
[4,6,2,5,7,3,1]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>[1,1,3,2]
[4,6,2,7,1,3,5]=>[3,1,5,6,2,7,4]=>[5,7,3,2,6,1,4]=>[2,1,2,2]
[4,6,2,7,1,5,3]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>[1,2,2,2]
[4,6,2,7,3,1,5]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>[1,2,2,2]
[4,6,2,7,3,5,1]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>[1,1,3,2]
[4,6,2,7,5,1,3]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>[1,1,3,2]
[4,6,2,7,5,3,1]=>[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>[2,3,2]
[4,6,3,1,2,5,7]=>[4,1,5,3,6,2,7]=>[4,7,3,5,2,6,1]=>[2,2,2,1]
[4,6,3,1,2,7,5]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>[1,3,2,1]
[4,6,3,1,5,2,7]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>[1,3,2,1]
[4,6,3,1,5,7,2]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>[1,2,3,1]
[4,6,3,1,7,2,5]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>[1,2,3,1]
[4,6,3,1,7,5,2]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>[1,1,4,1]
[4,6,3,2,1,5,7]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[1,3,2,1]
[4,6,3,2,1,7,5]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>[1,2,3,1]
[4,6,3,2,5,1,7]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>[1,2,3,1]
[4,6,3,2,5,7,1]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>[1,2,2,2]
[4,6,3,2,7,1,5]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>[1,2,2,2]
[4,6,3,2,7,5,1]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>[1,1,3,2]
[4,6,3,5,1,2,7]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[1,2,3,1]
[4,6,3,5,1,7,2]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>[1,1,4,1]
[4,6,3,5,2,1,7]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>[1,1,4,1]
[4,6,3,5,2,7,1]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>[1,1,3,2]
[4,6,3,5,7,1,2]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>[1,1,3,2]
[4,6,3,5,7,2,1]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>[1,1,2,3]
[4,6,3,7,1,2,5]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>[1,2,2,2]
[4,6,3,7,1,5,2]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>[1,1,3,2]
[4,6,3,7,2,1,5]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>[1,1,3,2]
[4,6,3,7,2,5,1]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>[1,1,2,3]
[4,6,3,7,5,1,2]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>[1,1,2,3]
[4,6,3,7,5,2,1]=>[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>[2,2,3]
[4,6,5,1,2,3,7]=>[4,1,5,6,3,2,7]=>[4,7,3,2,5,6,1]=>[2,1,3,1]
[4,6,5,1,2,7,3]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>[1,2,3,1]
[4,6,5,1,3,2,7]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>[1,2,3,1]
[4,6,5,1,3,7,2]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>[1,1,4,1]
[4,6,5,1,7,2,3]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>[1,1,4,1]
[4,6,5,1,7,3,2]=>[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>[2,4,1]
[4,6,5,2,1,3,7]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>[1,2,3,1]
[4,6,5,2,1,7,3]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>[1,1,4,1]
[4,6,5,2,3,1,7]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[1,1,4,1]
[4,6,5,2,3,7,1]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>[1,1,3,2]
[4,6,5,2,7,1,3]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>[1,1,3,2]
[4,6,5,2,7,3,1]=>[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>[2,3,2]
[4,6,5,3,1,2,7]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>[1,1,4,1]
[4,6,5,3,1,7,2]=>[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>[2,4,1]
[4,6,5,3,2,1,7]=>[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>[2,4,1]
[4,6,5,3,2,7,1]=>[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>[2,3,2]
[4,6,5,3,7,1,2]=>[6,1,4,3,2,7,5]=>[2,7,4,5,6,1,3]=>[2,3,2]
[4,6,5,3,7,2,1]=>[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>[2,2,3]
[4,6,5,7,1,2,3]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>[1,1,3,2]
[4,6,5,7,1,3,2]=>[7,1,5,3,2,6,4]=>[1,7,3,5,6,2,4]=>[2,3,2]
[4,6,5,7,2,1,3]=>[6,1,5,3,2,7,4]=>[2,7,3,5,6,1,4]=>[2,3,2]
[4,6,5,7,2,3,1]=>[5,1,3,2,7,6,4]=>[3,7,5,6,1,2,4]=>[2,2,3]
[4,6,5,7,3,1,2]=>[6,1,3,2,7,5,4]=>[2,7,5,6,1,3,4]=>[2,2,3]
[4,6,5,7,3,2,1]=>[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>[2,1,4]
[4,6,7,1,2,3,5]=>[4,1,5,6,2,7,3]=>[4,7,3,2,6,1,5]=>[2,1,2,2]
[4,6,7,1,2,5,3]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>[1,2,2,2]
[4,6,7,1,3,2,5]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>[1,2,2,2]
[4,6,7,1,3,5,2]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>[1,1,3,2]
[4,6,7,1,5,2,3]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>[1,1,3,2]
[4,6,7,1,5,3,2]=>[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>[2,3,2]
[4,6,7,2,1,3,5]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>[1,2,2,2]
[4,6,7,2,1,5,3]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>[1,1,3,2]
[4,6,7,2,3,1,5]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>[1,1,3,2]
[4,6,7,2,3,5,1]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>[1,1,2,3]
[4,6,7,2,5,1,3]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>[1,1,2,3]
[4,6,7,2,5,3,1]=>[7,1,4,2,6,5,3]=>[1,7,4,6,2,3,5]=>[2,2,3]
[4,6,7,3,1,2,5]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>[1,1,3,2]
[4,6,7,3,1,5,2]=>[7,1,5,4,2,6,3]=>[1,7,3,4,6,2,5]=>[2,3,2]
[4,6,7,3,2,1,5]=>[6,1,5,4,2,7,3]=>[2,7,3,4,6,1,5]=>[2,3,2]
[4,6,7,3,2,5,1]=>[5,1,4,2,7,6,3]=>[3,7,4,6,1,2,5]=>[2,2,3]
[4,6,7,3,5,1,2]=>[6,1,4,2,7,5,3]=>[2,7,4,6,1,3,5]=>[2,2,3]
[4,6,7,3,5,2,1]=>[4,1,2,7,6,5,3]=>[4,7,6,1,2,3,5]=>[2,1,4]
[4,6,7,5,1,2,3]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>[1,1,2,3]
[4,6,7,5,1,3,2]=>[7,1,5,2,6,4,3]=>[1,7,3,6,2,4,5]=>[2,2,3]
[4,6,7,5,2,1,3]=>[6,1,5,2,7,4,3]=>[2,7,3,6,1,4,5]=>[2,2,3]
[4,6,7,5,2,3,1]=>[5,1,2,7,6,4,3]=>[3,7,6,1,2,4,5]=>[2,1,4]
[4,6,7,5,3,1,2]=>[6,1,2,7,5,4,3]=>[2,7,6,1,3,4,5]=>[2,1,4]
[4,6,7,5,3,2,1]=>[2,7,1,6,5,4,3]=>[6,1,7,2,3,4,5]=>[1,2,4]
[4,7,1,2,3,5,6]=>[3,4,1,5,6,7,2]=>[5,4,7,3,2,1,6]=>[1,2,1,1,2]
[4,7,1,2,3,6,5]=>[7,3,1,4,5,6,2]=>[1,5,7,4,3,2,6]=>[3,1,1,2]
[4,7,1,2,5,3,6]=>[6,3,1,4,5,7,2]=>[2,5,7,4,3,1,6]=>[3,1,1,2]
[4,7,1,2,5,6,3]=>[5,1,7,3,4,6,2]=>[3,7,1,5,4,2,6]=>[2,2,1,2]
[4,7,1,2,6,3,5]=>[6,1,7,3,4,5,2]=>[2,7,1,5,4,3,6]=>[2,2,1,2]
[4,7,1,2,6,5,3]=>[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>[1,3,1,2]
[4,7,1,3,2,5,6]=>[5,3,1,4,6,7,2]=>[3,5,7,4,2,1,6]=>[3,1,1,2]
[4,7,1,3,2,6,5]=>[4,1,7,3,5,6,2]=>[4,7,1,5,3,2,6]=>[2,2,1,2]
[4,7,1,3,5,2,6]=>[4,1,6,3,5,7,2]=>[4,7,2,5,3,1,6]=>[2,2,1,2]
[4,7,1,3,5,6,2]=>[4,1,5,7,3,6,2]=>[4,7,3,1,5,2,6]=>[2,1,2,2]
[4,7,1,3,6,2,5]=>[4,1,6,7,3,5,2]=>[4,7,2,1,5,3,6]=>[2,1,2,2]
[4,7,1,3,6,5,2]=>[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>[1,2,2,2]
[4,7,1,5,2,3,6]=>[5,1,6,3,4,7,2]=>[3,7,2,5,4,1,6]=>[2,2,1,2]
[4,7,1,5,2,6,3]=>[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>[1,3,1,2]
[4,7,1,5,3,2,6]=>[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>[1,3,1,2]
[4,7,1,5,3,6,2]=>[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>[1,2,2,2]
[4,7,1,5,6,2,3]=>[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>[1,2,2,2]
[4,7,1,5,6,3,2]=>[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>[1,1,3,2]
[4,7,1,6,2,3,5]=>[5,1,6,7,3,4,2]=>[3,7,2,1,5,4,6]=>[2,1,2,2]
[4,7,1,6,2,5,3]=>[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>[1,2,2,2]
[4,7,1,6,3,2,5]=>[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>[1,2,2,2]
[4,7,1,6,3,5,2]=>[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>[1,1,3,2]
[4,7,1,6,5,2,3]=>[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>[1,1,3,2]
[4,7,1,6,5,3,2]=>[7,1,6,5,3,4,2]=>[1,7,2,3,5,4,6]=>[2,3,2]
[4,7,2,1,3,5,6]=>[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]=>[3,1,1,2]
[4,7,2,1,3,6,5]=>[3,1,7,4,5,6,2]=>[5,7,1,4,3,2,6]=>[2,2,1,2]
[4,7,2,1,5,3,6]=>[3,1,6,4,5,7,2]=>[5,7,2,4,3,1,6]=>[2,2,1,2]
[4,7,2,1,5,6,3]=>[3,1,5,7,4,6,2]=>[5,7,3,1,4,2,6]=>[2,1,2,2]
[4,7,2,1,6,3,5]=>[3,1,6,7,4,5,2]=>[5,7,2,1,4,3,6]=>[2,1,2,2]
[4,7,2,1,6,5,3]=>[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>[1,2,2,2]
[4,7,2,3,1,5,6]=>[3,1,5,4,6,7,2]=>[5,7,3,4,2,1,6]=>[2,2,1,2]
[4,7,2,3,1,6,5]=>[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>[2,1,2,2]
[4,7,2,3,5,1,6]=>[3,1,4,6,5,7,2]=>[5,7,4,2,3,1,6]=>[2,1,2,2]
[4,7,2,3,5,6,1]=>[3,1,4,5,7,6,2]=>[5,7,4,3,1,2,6]=>[2,1,1,3]
[4,7,2,3,6,1,5]=>[3,1,4,6,7,5,2]=>[5,7,4,2,1,3,6]=>[2,1,1,3]
[4,7,2,3,6,5,1]=>[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>[1,2,1,3]
[4,7,2,5,1,3,6]=>[3,1,5,6,4,7,2]=>[5,7,3,2,4,1,6]=>[2,1,2,2]
[4,7,2,5,1,6,3]=>[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>[1,2,2,2]
[4,7,2,5,3,1,6]=>[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>[1,2,2,2]
[4,7,2,5,3,6,1]=>[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>[1,2,1,3]
[4,7,2,5,6,1,3]=>[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>[1,2,1,3]
[4,7,2,5,6,3,1]=>[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>[1,1,2,3]
[4,7,2,6,1,3,5]=>[3,1,5,6,7,4,2]=>[5,7,3,2,1,4,6]=>[2,1,1,3]
[4,7,2,6,1,5,3]=>[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>[1,2,1,3]
[4,7,2,6,3,1,5]=>[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>[1,2,1,3]
[4,7,2,6,3,5,1]=>[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>[1,1,2,3]
[4,7,2,6,5,1,3]=>[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>[1,1,2,3]
[4,7,2,6,5,3,1]=>[7,1,6,3,5,4,2]=>[1,7,2,5,3,4,6]=>[2,2,3]
[4,7,3,1,2,5,6]=>[4,1,5,3,6,7,2]=>[4,7,3,5,2,1,6]=>[2,2,1,2]
[4,7,3,1,2,6,5]=>[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>[1,3,1,2]
[4,7,3,1,5,2,6]=>[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>[1,3,1,2]
[4,7,3,1,5,6,2]=>[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>[1,2,2,2]
[4,7,3,1,6,2,5]=>[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>[1,2,2,2]
[4,7,3,1,6,5,2]=>[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>[1,1,3,2]
[4,7,3,2,1,5,6]=>[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>[1,3,1,2]
[4,7,3,2,1,6,5]=>[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>[1,2,2,2]
[4,7,3,2,5,1,6]=>[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>[1,2,2,2]
[4,7,3,2,5,6,1]=>[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>[1,2,1,3]
[4,7,3,2,6,1,5]=>[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>[1,2,1,3]
[4,7,3,2,6,5,1]=>[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>[1,1,2,3]
[4,7,3,5,1,2,6]=>[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>[1,2,2,2]
[4,7,3,5,1,6,2]=>[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>[1,1,3,2]
[4,7,3,5,2,1,6]=>[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>[1,1,3,2]
[4,7,3,5,2,6,1]=>[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>[1,1,2,3]
[4,7,3,5,6,1,2]=>[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>[1,1,2,3]
[4,7,3,5,6,2,1]=>[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>[1,1,1,4]
[4,7,3,6,1,2,5]=>[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>[1,2,1,3]
[4,7,3,6,1,5,2]=>[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>[1,1,2,3]
[4,7,3,6,2,1,5]=>[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>[1,1,2,3]
[4,7,3,6,2,5,1]=>[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>[1,1,1,4]
[4,7,3,6,5,1,2]=>[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>[1,1,1,4]
[4,7,3,6,5,2,1]=>[7,1,3,6,5,4,2]=>[1,7,5,2,3,4,6]=>[2,1,4]
[4,7,5,1,2,3,6]=>[4,1,5,6,3,7,2]=>[4,7,3,2,5,1,6]=>[2,1,2,2]
[4,7,5,1,2,6,3]=>[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>[1,2,2,2]
[4,7,5,1,3,2,6]=>[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>[1,2,2,2]
[4,7,5,1,3,6,2]=>[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>[1,1,3,2]
[4,7,5,1,6,2,3]=>[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>[1,1,3,2]
[4,7,5,1,6,3,2]=>[7,1,6,4,3,5,2]=>[1,7,2,4,5,3,6]=>[2,3,2]
[4,7,5,2,1,3,6]=>[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>[1,2,2,2]
[4,7,5,2,1,6,3]=>[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>[1,1,3,2]
[4,7,5,2,3,1,6]=>[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>[1,1,3,2]
[4,7,5,2,3,6,1]=>[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>[1,1,2,3]
[4,7,5,2,6,1,3]=>[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>[1,1,2,3]
[4,7,5,2,6,3,1]=>[7,1,4,3,6,5,2]=>[1,7,4,5,2,3,6]=>[2,2,3]
[4,7,5,3,1,2,6]=>[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>[1,1,3,2]
[4,7,5,3,1,6,2]=>[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>[2,3,2]
[4,7,5,3,2,1,6]=>[6,1,5,4,3,7,2]=>[2,7,3,4,5,1,6]=>[2,3,2]
[4,7,5,3,2,6,1]=>[5,1,4,3,7,6,2]=>[3,7,4,5,1,2,6]=>[2,2,3]
[4,7,5,3,6,1,2]=>[6,1,4,3,7,5,2]=>[2,7,4,5,1,3,6]=>[2,2,3]
[4,7,5,3,6,2,1]=>[4,1,3,7,6,5,2]=>[4,7,5,1,2,3,6]=>[2,1,4]
[4,7,5,6,1,2,3]=>[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>[1,1,2,3]
[4,7,5,6,1,3,2]=>[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>[2,2,3]
[4,7,5,6,2,1,3]=>[6,1,5,3,7,4,2]=>[2,7,3,5,1,4,6]=>[2,2,3]
[4,7,5,6,2,3,1]=>[5,1,3,7,6,4,2]=>[3,7,5,1,2,4,6]=>[2,1,4]
[4,7,5,6,3,1,2]=>[6,1,3,7,5,4,2]=>[2,7,5,1,3,4,6]=>[2,1,4]
[4,7,5,6,3,2,1]=>[3,7,1,6,5,4,2]=>[5,1,7,2,3,4,6]=>[1,2,4]
[4,7,6,1,2,3,5]=>[4,1,5,6,7,3,2]=>[4,7,3,2,1,5,6]=>[2,1,1,3]
[4,7,6,1,2,5,3]=>[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>[1,2,1,3]
[4,7,6,1,3,2,5]=>[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>[1,2,1,3]
[4,7,6,1,3,5,2]=>[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>[1,1,2,3]
[4,7,6,1,5,2,3]=>[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>[1,1,2,3]
[4,7,6,1,5,3,2]=>[7,1,6,4,5,3,2]=>[1,7,2,4,3,5,6]=>[2,2,3]
[4,7,6,2,1,3,5]=>[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>[1,2,1,3]
[4,7,6,2,1,5,3]=>[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>[1,1,2,3]
[4,7,6,2,3,1,5]=>[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>[1,1,2,3]
[4,7,6,2,3,5,1]=>[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>[1,1,1,4]
[4,7,6,2,5,1,3]=>[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>[1,1,1,4]
[4,7,6,2,5,3,1]=>[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>[2,1,4]
[4,7,6,3,1,2,5]=>[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>[1,1,2,3]
[4,7,6,3,1,5,2]=>[7,1,5,4,6,3,2]=>[1,7,3,4,2,5,6]=>[2,2,3]
[4,7,6,3,2,1,5]=>[6,1,5,4,7,3,2]=>[2,7,3,4,1,5,6]=>[2,2,3]
[4,7,6,3,2,5,1]=>[5,1,4,7,6,3,2]=>[3,7,4,1,2,5,6]=>[2,1,4]
[4,7,6,3,5,1,2]=>[6,1,4,7,5,3,2]=>[2,7,4,1,3,5,6]=>[2,1,4]
[4,7,6,3,5,2,1]=>[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>[1,2,4]
[4,7,6,5,1,2,3]=>[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>[1,1,1,4]
[4,7,6,5,1,3,2]=>[7,1,5,6,4,3,2]=>[1,7,3,2,4,5,6]=>[2,1,4]
[4,7,6,5,2,1,3]=>[6,1,5,7,4,3,2]=>[2,7,3,1,4,5,6]=>[2,1,4]
[4,7,6,5,2,3,1]=>[5,7,1,6,4,3,2]=>[3,1,7,2,4,5,6]=>[1,2,4]
[4,7,6,5,3,1,2]=>[6,7,1,5,4,3,2]=>[2,1,7,3,4,5,6]=>[1,2,4]
[4,7,6,5,3,2,1]=>[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>[3,4]
[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>[1,1,1,2,1,1]
[5,1,2,3,4,7,6]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>[2,1,2,1,1]
[5,1,2,3,6,4,7]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>[2,1,2,1,1]
[5,1,2,3,6,7,4]=>[5,7,2,3,1,4,6]=>[3,1,6,5,7,4,2]=>[1,2,2,1,1]
[5,1,2,3,7,4,6]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>[1,2,2,1,1]
[5,1,2,3,7,6,4]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>[3,2,1,1]
[5,1,2,4,3,6,7]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>[2,1,2,1,1]
[5,1,2,4,3,7,6]=>[4,7,2,3,1,5,6]=>[4,1,6,5,7,3,2]=>[1,2,2,1,1]
[5,1,2,4,6,3,7]=>[4,6,2,3,1,5,7]=>[4,2,6,5,7,3,1]=>[1,2,2,1,1]
[5,1,2,4,6,7,3]=>[4,5,7,2,1,3,6]=>[4,3,1,6,7,5,2]=>[1,1,3,1,1]
[5,1,2,4,7,3,6]=>[4,6,7,2,1,3,5]=>[4,2,1,6,7,5,3]=>[1,1,3,1,1]
[5,1,2,4,7,6,3]=>[7,4,6,2,1,3,5]=>[1,4,2,6,7,5,3]=>[2,3,1,1]
[5,1,2,6,3,4,7]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>[1,2,2,1,1]
[5,1,2,6,3,7,4]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>[3,2,1,1]
[5,1,2,6,4,3,7]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>[3,2,1,1]
[5,1,2,6,4,7,3]=>[5,4,7,2,1,3,6]=>[3,4,1,6,7,5,2]=>[2,3,1,1]
[5,1,2,6,7,3,4]=>[6,4,7,2,1,3,5]=>[2,4,1,6,7,5,3]=>[2,3,1,1]
[5,1,2,6,7,4,3]=>[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>[1,4,1,1]
[5,1,2,7,3,4,6]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>[1,1,3,1,1]
[5,1,2,7,3,6,4]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>[2,3,1,1]
[5,1,2,7,4,3,6]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>[2,3,1,1]
[5,1,2,7,4,6,3]=>[5,7,6,2,1,3,4]=>[3,1,2,6,7,5,4]=>[1,4,1,1]
[5,1,2,7,6,3,4]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>[1,4,1,1]
[5,1,2,7,6,4,3]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[5,1,1]
[5,1,3,2,4,6,7]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>[2,1,2,1,1]
[5,1,3,2,4,7,6]=>[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>[1,2,2,1,1]
[5,1,3,2,6,4,7]=>[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>[1,2,2,1,1]
[5,1,3,2,6,7,4]=>[3,5,7,2,1,4,6]=>[5,3,1,6,7,4,2]=>[1,1,3,1,1]
[5,1,3,2,7,4,6]=>[3,6,7,2,1,4,5]=>[5,2,1,6,7,4,3]=>[1,1,3,1,1]
[5,1,3,2,7,6,4]=>[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>[2,3,1,1]
[5,1,3,4,2,6,7]=>[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>[1,2,2,1,1]
[5,1,3,4,2,7,6]=>[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>[1,1,3,1,1]
[5,1,3,4,6,2,7]=>[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>[1,1,3,1,1]
[5,1,3,4,6,7,2]=>[3,4,5,1,7,2,6]=>[5,4,3,7,1,6,2]=>[1,1,2,2,1]
[5,1,3,4,7,2,6]=>[3,4,6,1,7,2,5]=>[5,4,2,7,1,6,3]=>[1,1,2,2,1]
[5,1,3,4,7,6,2]=>[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]=>[2,2,2,1]
[5,1,3,6,2,4,7]=>[3,5,6,2,1,4,7]=>[5,3,2,6,7,4,1]=>[1,1,3,1,1]
[5,1,3,6,2,7,4]=>[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>[2,3,1,1]
[5,1,3,6,4,2,7]=>[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>[2,3,1,1]
[5,1,3,6,4,7,2]=>[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]=>[2,2,2,1]
[5,1,3,6,7,2,4]=>[6,3,4,1,7,2,5]=>[2,5,4,7,1,6,3]=>[2,2,2,1]
[5,1,3,6,7,4,2]=>[4,7,3,1,6,2,5]=>[4,1,5,7,2,6,3]=>[1,3,2,1]
[5,1,3,7,2,4,6]=>[3,5,6,1,7,2,4]=>[5,3,2,7,1,6,4]=>[1,1,2,2,1]
[5,1,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]=>[2,2,2,1]
[5,1,3,7,4,2,6]=>[6,3,5,1,7,2,4]=>[2,5,3,7,1,6,4]=>[2,2,2,1]
[5,1,3,7,4,6,2]=>[5,7,3,1,6,2,4]=>[3,1,5,7,2,6,4]=>[1,3,2,1]
[5,1,3,7,6,2,4]=>[6,7,3,1,5,2,4]=>[2,1,5,7,3,6,4]=>[1,3,2,1]
[5,1,3,7,6,4,2]=>[7,6,3,1,5,2,4]=>[1,2,5,7,3,6,4]=>[4,2,1]
[5,1,4,2,3,6,7]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>[1,2,2,1,1]
[5,1,4,2,3,7,6]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>[3,2,1,1]
[5,1,4,2,6,3,7]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>[3,2,1,1]
[5,1,4,2,6,7,3]=>[5,3,7,2,1,4,6]=>[3,5,1,6,7,4,2]=>[2,3,1,1]
[5,1,4,2,7,3,6]=>[6,3,7,2,1,4,5]=>[2,5,1,6,7,4,3]=>[2,3,1,1]
[5,1,4,2,7,6,3]=>[3,7,6,2,1,4,5]=>[5,1,2,6,7,4,3]=>[1,4,1,1]
[5,1,4,3,2,6,7]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>[3,2,1,1]
[5,1,4,3,2,7,6]=>[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>[2,3,1,1]
[5,1,4,3,6,2,7]=>[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>[2,3,1,1]
[5,1,4,3,6,7,2]=>[4,3,5,1,7,2,6]=>[4,5,3,7,1,6,2]=>[2,2,2,1]
[5,1,4,3,7,2,6]=>[4,3,6,1,7,2,5]=>[4,5,2,7,1,6,3]=>[2,2,2,1]
[5,1,4,3,7,6,2]=>[3,7,4,1,6,2,5]=>[5,1,4,7,2,6,3]=>[1,3,2,1]
[5,1,4,6,2,3,7]=>[5,3,6,2,1,4,7]=>[3,5,2,6,7,4,1]=>[2,3,1,1]
[5,1,4,6,2,7,3]=>[3,7,5,2,1,4,6]=>[5,1,3,6,7,4,2]=>[1,4,1,1]
[5,1,4,6,3,2,7]=>[3,6,5,2,1,4,7]=>[5,2,3,6,7,4,1]=>[1,4,1,1]
[5,1,4,6,3,7,2]=>[3,5,4,1,7,2,6]=>[5,3,4,7,1,6,2]=>[1,3,2,1]
[5,1,4,6,7,2,3]=>[3,6,4,1,7,2,5]=>[5,2,4,7,1,6,3]=>[1,3,2,1]
[5,1,4,6,7,3,2]=>[3,4,1,7,6,2,5]=>[5,4,7,1,2,6,3]=>[1,2,3,1]
[5,1,4,7,2,3,6]=>[5,3,6,1,7,2,4]=>[3,5,2,7,1,6,4]=>[2,2,2,1]
[5,1,4,7,2,6,3]=>[3,7,5,1,6,2,4]=>[5,1,3,7,2,6,4]=>[1,3,2,1]
[5,1,4,7,3,2,6]=>[3,6,5,1,7,2,4]=>[5,2,3,7,1,6,4]=>[1,3,2,1]
[5,1,4,7,3,6,2]=>[3,5,1,7,6,2,4]=>[5,3,7,1,2,6,4]=>[1,2,3,1]
[5,1,4,7,6,2,3]=>[3,6,1,7,5,2,4]=>[5,2,7,1,3,6,4]=>[1,2,3,1]
[5,1,4,7,6,3,2]=>[7,3,1,6,5,2,4]=>[1,5,7,2,3,6,4]=>[3,3,1]
[5,1,6,2,3,4,7]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>[1,1,3,1,1]
[5,1,6,2,3,7,4]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>[2,3,1,1]
[5,1,6,2,4,3,7]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>[2,3,1,1]
[5,1,6,2,4,7,3]=>[5,7,4,2,1,3,6]=>[3,1,4,6,7,5,2]=>[1,4,1,1]
[5,1,6,2,7,3,4]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>[1,4,1,1]
[5,1,6,2,7,4,3]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[5,1,1]
[5,1,6,3,2,4,7]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>[2,3,1,1]
[5,1,6,3,2,7,4]=>[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>[1,4,1,1]
[5,1,6,3,4,2,7]=>[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>[1,4,1,1]
[5,1,6,3,4,7,2]=>[4,5,3,1,7,2,6]=>[4,3,5,7,1,6,2]=>[1,3,2,1]
[5,1,6,3,7,2,4]=>[4,6,3,1,7,2,5]=>[4,2,5,7,1,6,3]=>[1,3,2,1]
[5,1,6,3,7,4,2]=>[7,4,3,1,6,2,5]=>[1,4,5,7,2,6,3]=>[4,2,1]
[5,1,6,4,2,3,7]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>[1,4,1,1]
[5,1,6,4,2,7,3]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[5,1,1]
[5,1,6,4,3,2,7]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[5,1,1]
[5,1,6,4,3,7,2]=>[5,4,3,1,7,2,6]=>[3,4,5,7,1,6,2]=>[4,2,1]
[5,1,6,4,7,2,3]=>[6,4,3,1,7,2,5]=>[2,4,5,7,1,6,3]=>[4,2,1]
[5,1,6,4,7,3,2]=>[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]=>[3,3,1]
[5,1,6,7,2,3,4]=>[5,6,3,1,7,2,4]=>[3,2,5,7,1,6,4]=>[1,3,2,1]
[5,1,6,7,2,4,3]=>[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>[4,2,1]
[5,1,6,7,3,2,4]=>[6,5,3,1,7,2,4]=>[2,3,5,7,1,6,4]=>[4,2,1]
[5,1,6,7,3,4,2]=>[5,3,1,7,6,2,4]=>[3,5,7,1,2,6,4]=>[3,3,1]
[5,1,6,7,4,2,3]=>[6,3,1,7,5,2,4]=>[2,5,7,1,3,6,4]=>[3,3,1]
[5,1,6,7,4,3,2]=>[3,1,7,6,5,2,4]=>[5,7,1,2,3,6,4]=>[2,4,1]
[5,1,7,2,3,4,6]=>[4,5,6,1,7,2,3]=>[4,3,2,7,1,6,5]=>[1,1,2,2,1]
[5,1,7,2,3,6,4]=>[7,4,5,1,6,2,3]=>[1,4,3,7,2,6,5]=>[2,2,2,1]
[5,1,7,2,4,3,6]=>[6,4,5,1,7,2,3]=>[2,4,3,7,1,6,5]=>[2,2,2,1]
[5,1,7,2,4,6,3]=>[5,7,4,1,6,2,3]=>[3,1,4,7,2,6,5]=>[1,3,2,1]
[5,1,7,2,6,3,4]=>[6,7,4,1,5,2,3]=>[2,1,4,7,3,6,5]=>[1,3,2,1]
[5,1,7,2,6,4,3]=>[7,6,4,1,5,2,3]=>[1,2,4,7,3,6,5]=>[4,2,1]
[5,1,7,3,2,4,6]=>[5,4,6,1,7,2,3]=>[3,4,2,7,1,6,5]=>[2,2,2,1]
[5,1,7,3,2,6,4]=>[4,7,5,1,6,2,3]=>[4,1,3,7,2,6,5]=>[1,3,2,1]
[5,1,7,3,4,2,6]=>[4,6,5,1,7,2,3]=>[4,2,3,7,1,6,5]=>[1,3,2,1]
[5,1,7,3,4,6,2]=>[4,5,1,7,6,2,3]=>[4,3,7,1,2,6,5]=>[1,2,3,1]
[5,1,7,3,6,2,4]=>[4,6,1,7,5,2,3]=>[4,2,7,1,3,6,5]=>[1,2,3,1]
[5,1,7,3,6,4,2]=>[7,4,1,6,5,2,3]=>[1,4,7,2,3,6,5]=>[3,3,1]
[5,1,7,4,2,3,6]=>[5,6,4,1,7,2,3]=>[3,2,4,7,1,6,5]=>[1,3,2,1]
[5,1,7,4,2,6,3]=>[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]=>[4,2,1]
[5,1,7,4,3,2,6]=>[6,5,4,1,7,2,3]=>[2,3,4,7,1,6,5]=>[4,2,1]
[5,1,7,4,3,6,2]=>[5,4,1,7,6,2,3]=>[3,4,7,1,2,6,5]=>[3,3,1]
[5,1,7,4,6,2,3]=>[6,4,1,7,5,2,3]=>[2,4,7,1,3,6,5]=>[3,3,1]
[5,1,7,4,6,3,2]=>[4,1,7,6,5,2,3]=>[4,7,1,2,3,6,5]=>[2,4,1]
[5,1,7,6,2,3,4]=>[5,6,1,7,4,2,3]=>[3,2,7,1,4,6,5]=>[1,2,3,1]
[5,1,7,6,2,4,3]=>[7,5,1,6,4,2,3]=>[1,3,7,2,4,6,5]=>[3,3,1]
[5,1,7,6,3,2,4]=>[6,5,1,7,4,2,3]=>[2,3,7,1,4,6,5]=>[3,3,1]
[5,1,7,6,3,4,2]=>[5,1,7,6,4,2,3]=>[3,7,1,2,4,6,5]=>[2,4,1]
[5,1,7,6,4,2,3]=>[6,1,7,5,4,2,3]=>[2,7,1,3,4,6,5]=>[2,4,1]
[5,1,7,6,4,3,2]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[1,5,1]
[5,2,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>[2,1,2,1,1]
[5,2,1,3,4,7,6]=>[2,7,3,4,1,5,6]=>[6,1,5,4,7,3,2]=>[1,2,2,1,1]
[5,2,1,3,6,4,7]=>[2,6,3,4,1,5,7]=>[6,2,5,4,7,3,1]=>[1,2,2,1,1]
[5,2,1,3,6,7,4]=>[2,5,7,3,1,4,6]=>[6,3,1,5,7,4,2]=>[1,1,3,1,1]
[5,2,1,3,7,4,6]=>[2,6,7,3,1,4,5]=>[6,2,1,5,7,4,3]=>[1,1,3,1,1]
[5,2,1,3,7,6,4]=>[7,2,6,3,1,4,5]=>[1,6,2,5,7,4,3]=>[2,3,1,1]
[5,2,1,4,3,6,7]=>[2,5,3,4,1,6,7]=>[6,3,5,4,7,2,1]=>[1,2,2,1,1]
[5,2,1,4,3,7,6]=>[2,4,7,3,1,5,6]=>[6,4,1,5,7,3,2]=>[1,1,3,1,1]
[5,2,1,4,6,3,7]=>[2,4,6,3,1,5,7]=>[6,4,2,5,7,3,1]=>[1,1,3,1,1]
[5,2,1,4,6,7,3]=>[2,4,5,1,7,3,6]=>[6,4,3,7,1,5,2]=>[1,1,2,2,1]
[5,2,1,4,7,3,6]=>[2,4,6,1,7,3,5]=>[6,4,2,7,1,5,3]=>[1,1,2,2,1]
[5,2,1,4,7,6,3]=>[7,2,4,1,6,3,5]=>[1,6,4,7,2,5,3]=>[2,2,2,1]
[5,2,1,6,3,4,7]=>[2,5,6,3,1,4,7]=>[6,3,2,5,7,4,1]=>[1,1,3,1,1]
[5,2,1,6,3,7,4]=>[7,2,5,3,1,4,6]=>[1,6,3,5,7,4,2]=>[2,3,1,1]
[5,2,1,6,4,3,7]=>[6,2,5,3,1,4,7]=>[2,6,3,5,7,4,1]=>[2,3,1,1]
[5,2,1,6,4,7,3]=>[5,2,4,1,7,3,6]=>[3,6,4,7,1,5,2]=>[2,2,2,1]
[5,2,1,6,7,3,4]=>[6,2,4,1,7,3,5]=>[2,6,4,7,1,5,3]=>[2,2,2,1]
[5,2,1,6,7,4,3]=>[4,7,2,1,6,3,5]=>[4,1,6,7,2,5,3]=>[1,3,2,1]
[5,2,1,7,3,4,6]=>[2,5,6,1,7,3,4]=>[6,3,2,7,1,5,4]=>[1,1,2,2,1]
[5,2,1,7,3,6,4]=>[7,2,5,1,6,3,4]=>[1,6,3,7,2,5,4]=>[2,2,2,1]
[5,2,1,7,4,3,6]=>[6,2,5,1,7,3,4]=>[2,6,3,7,1,5,4]=>[2,2,2,1]
[5,2,1,7,4,6,3]=>[5,7,2,1,6,3,4]=>[3,1,6,7,2,5,4]=>[1,3,2,1]
[5,2,1,7,6,3,4]=>[6,7,2,1,5,3,4]=>[2,1,6,7,3,5,4]=>[1,3,2,1]
[5,2,1,7,6,4,3]=>[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[4,2,1]
[5,2,3,1,4,6,7]=>[2,4,3,5,1,6,7]=>[6,4,5,3,7,2,1]=>[1,2,2,1,1]
[5,2,3,1,4,7,6]=>[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>[1,1,3,1,1]
[5,2,3,1,6,4,7]=>[2,3,6,4,1,5,7]=>[6,5,2,4,7,3,1]=>[1,1,3,1,1]
[5,2,3,1,6,7,4]=>[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]=>[1,1,2,2,1]
[5,2,3,1,7,4,6]=>[2,3,6,1,7,4,5]=>[6,5,2,7,1,4,3]=>[1,1,2,2,1]
[5,2,3,1,7,6,4]=>[7,2,3,1,6,4,5]=>[1,6,5,7,2,4,3]=>[2,2,2,1]
[5,2,3,4,1,6,7]=>[2,3,5,4,1,6,7]=>[6,5,3,4,7,2,1]=>[1,1,3,1,1]
[5,2,3,4,1,7,6]=>[2,3,4,1,7,5,6]=>[6,5,4,7,1,3,2]=>[1,1,2,2,1]
[5,2,3,4,6,1,7]=>[2,3,4,1,6,5,7]=>[6,5,4,7,2,3,1]=>[1,1,2,2,1]
[5,2,3,4,6,7,1]=>[2,3,4,1,5,7,6]=>[6,5,4,7,3,1,2]=>[1,1,2,1,2]
[5,2,3,4,7,1,6]=>[2,3,4,1,6,7,5]=>[6,5,4,7,2,1,3]=>[1,1,2,1,2]
[5,2,3,4,7,6,1]=>[7,2,3,1,4,6,5]=>[1,6,5,7,4,2,3]=>[2,2,1,2]
[5,2,3,6,1,4,7]=>[2,3,5,1,6,4,7]=>[6,5,3,7,2,4,1]=>[1,1,2,2,1]
[5,2,3,6,1,7,4]=>[7,2,3,1,5,4,6]=>[1,6,5,7,3,4,2]=>[2,2,2,1]
[5,2,3,6,4,1,7]=>[6,2,3,1,5,4,7]=>[2,6,5,7,3,4,1]=>[2,2,2,1]
[5,2,3,6,4,7,1]=>[5,2,3,1,4,7,6]=>[3,6,5,7,4,1,2]=>[2,2,1,2]
[5,2,3,6,7,1,4]=>[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>[2,2,1,2]
[5,2,3,6,7,4,1]=>[4,7,2,1,3,6,5]=>[4,1,6,7,5,2,3]=>[1,3,1,2]
[5,2,3,7,1,4,6]=>[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]=>[1,1,2,1,2]
[5,2,3,7,1,6,4]=>[7,2,3,1,5,6,4]=>[1,6,5,7,3,2,4]=>[2,2,1,2]
[5,2,3,7,4,1,6]=>[6,2,3,1,5,7,4]=>[2,6,5,7,3,1,4]=>[2,2,1,2]
[5,2,3,7,4,6,1]=>[5,7,2,1,3,6,4]=>[3,1,6,7,5,2,4]=>[1,3,1,2]
[5,2,3,7,6,1,4]=>[6,7,2,1,3,5,4]=>[2,1,6,7,5,3,4]=>[1,3,1,2]
[5,2,3,7,6,4,1]=>[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>[4,1,2]
[5,2,4,1,3,6,7]=>[2,4,5,3,1,6,7]=>[6,4,3,5,7,2,1]=>[1,1,3,1,1]
[5,2,4,1,3,7,6]=>[7,2,4,3,1,5,6]=>[1,6,4,5,7,3,2]=>[2,3,1,1]
[5,2,4,1,6,3,7]=>[6,2,4,3,1,5,7]=>[2,6,4,5,7,3,1]=>[2,3,1,1]
[5,2,4,1,6,7,3]=>[5,2,3,1,7,4,6]=>[3,6,5,7,1,4,2]=>[2,2,2,1]
[5,2,4,1,7,3,6]=>[6,2,3,1,7,4,5]=>[2,6,5,7,1,4,3]=>[2,2,2,1]
[5,2,4,1,7,6,3]=>[3,7,2,1,6,4,5]=>[5,1,6,7,2,4,3]=>[1,3,2,1]
[5,2,4,3,1,6,7]=>[5,2,4,3,1,6,7]=>[3,6,4,5,7,2,1]=>[2,3,1,1]
[5,2,4,3,1,7,6]=>[4,2,3,1,7,5,6]=>[4,6,5,7,1,3,2]=>[2,2,2,1]
[5,2,4,3,6,1,7]=>[4,2,3,1,6,5,7]=>[4,6,5,7,2,3,1]=>[2,2,2,1]
[5,2,4,3,6,7,1]=>[4,2,3,1,5,7,6]=>[4,6,5,7,3,1,2]=>[2,2,1,2]
[5,2,4,3,7,1,6]=>[4,2,3,1,6,7,5]=>[4,6,5,7,2,1,3]=>[2,2,1,2]
[5,2,4,3,7,6,1]=>[3,7,2,1,4,6,5]=>[5,1,6,7,4,2,3]=>[1,3,1,2]
[5,2,4,6,1,3,7]=>[5,2,3,1,6,4,7]=>[3,6,5,7,2,4,1]=>[2,2,2,1]
[5,2,4,6,1,7,3]=>[3,7,2,1,5,4,6]=>[5,1,6,7,3,4,2]=>[1,3,2,1]
[5,2,4,6,3,1,7]=>[3,6,2,1,5,4,7]=>[5,2,6,7,3,4,1]=>[1,3,2,1]
[5,2,4,6,3,7,1]=>[3,5,2,1,4,7,6]=>[5,3,6,7,4,1,2]=>[1,3,1,2]
[5,2,4,6,7,1,3]=>[3,6,2,1,4,7,5]=>[5,2,6,7,4,1,3]=>[1,3,1,2]
[5,2,4,6,7,3,1]=>[3,4,1,7,2,6,5]=>[5,4,7,1,6,2,3]=>[1,2,2,2]
[5,2,4,7,1,3,6]=>[5,2,3,1,6,7,4]=>[3,6,5,7,2,1,4]=>[2,2,1,2]
[5,2,4,7,1,6,3]=>[3,7,2,1,5,6,4]=>[5,1,6,7,3,2,4]=>[1,3,1,2]
[5,2,4,7,3,1,6]=>[3,6,2,1,5,7,4]=>[5,2,6,7,3,1,4]=>[1,3,1,2]
[5,2,4,7,3,6,1]=>[3,5,1,7,2,6,4]=>[5,3,7,1,6,2,4]=>[1,2,2,2]
[5,2,4,7,6,1,3]=>[3,6,1,7,2,5,4]=>[5,2,7,1,6,3,4]=>[1,2,2,2]
[5,2,4,7,6,3,1]=>[7,3,1,6,2,5,4]=>[1,5,7,2,6,3,4]=>[3,2,2]
[5,2,6,1,3,4,7]=>[2,4,5,1,6,3,7]=>[6,4,3,7,2,5,1]=>[1,1,2,2,1]
[5,2,6,1,3,7,4]=>[7,2,4,1,5,3,6]=>[1,6,4,7,3,5,2]=>[2,2,2,1]
[5,2,6,1,4,3,7]=>[6,2,4,1,5,3,7]=>[2,6,4,7,3,5,1]=>[2,2,2,1]
[5,2,6,1,4,7,3]=>[5,7,2,1,4,3,6]=>[3,1,6,7,4,5,2]=>[1,3,2,1]
[5,2,6,1,7,3,4]=>[6,7,2,1,4,3,5]=>[2,1,6,7,4,5,3]=>[1,3,2,1]
[5,2,6,1,7,4,3]=>[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>[4,2,1]
[5,2,6,3,1,4,7]=>[5,2,4,1,6,3,7]=>[3,6,4,7,2,5,1]=>[2,2,2,1]
[5,2,6,3,1,7,4]=>[4,7,2,1,5,3,6]=>[4,1,6,7,3,5,2]=>[1,3,2,1]
[5,2,6,3,4,1,7]=>[4,6,2,1,5,3,7]=>[4,2,6,7,3,5,1]=>[1,3,2,1]
[5,2,6,3,4,7,1]=>[4,5,2,1,3,7,6]=>[4,3,6,7,5,1,2]=>[1,3,1,2]
[5,2,6,3,7,1,4]=>[4,6,2,1,3,7,5]=>[4,2,6,7,5,1,3]=>[1,3,1,2]
[5,2,6,3,7,4,1]=>[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>[4,1,2]
[5,2,6,4,1,3,7]=>[5,6,2,1,4,3,7]=>[3,2,6,7,4,5,1]=>[1,3,2,1]
[5,2,6,4,1,7,3]=>[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>[4,2,1]
[5,2,6,4,3,1,7]=>[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>[4,2,1]
[5,2,6,4,3,7,1]=>[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>[4,1,2]
[5,2,6,4,7,1,3]=>[6,4,2,1,3,7,5]=>[2,4,6,7,5,1,3]=>[4,1,2]
[5,2,6,4,7,3,1]=>[4,3,1,7,2,6,5]=>[4,5,7,1,6,2,3]=>[3,2,2]
[5,2,6,7,1,3,4]=>[5,6,2,1,3,7,4]=>[3,2,6,7,5,1,4]=>[1,3,1,2]
[5,2,6,7,1,4,3]=>[7,5,2,1,3,6,4]=>[1,3,6,7,5,2,4]=>[4,1,2]
[5,2,6,7,3,1,4]=>[6,5,2,1,3,7,4]=>[2,3,6,7,5,1,4]=>[4,1,2]
[5,2,6,7,3,4,1]=>[5,3,1,7,2,6,4]=>[3,5,7,1,6,2,4]=>[3,2,2]
[5,2,6,7,4,1,3]=>[6,3,1,7,2,5,4]=>[2,5,7,1,6,3,4]=>[3,2,2]
[5,2,6,7,4,3,1]=>[3,1,7,6,2,5,4]=>[5,7,1,2,6,3,4]=>[2,3,2]
[5,2,7,1,3,4,6]=>[2,4,5,1,6,7,3]=>[6,4,3,7,2,1,5]=>[1,1,2,1,2]
[5,2,7,1,3,6,4]=>[7,2,4,1,5,6,3]=>[1,6,4,7,3,2,5]=>[2,2,1,2]
[5,2,7,1,4,3,6]=>[6,2,4,1,5,7,3]=>[2,6,4,7,3,1,5]=>[2,2,1,2]
[5,2,7,1,4,6,3]=>[5,7,2,1,4,6,3]=>[3,1,6,7,4,2,5]=>[1,3,1,2]
[5,2,7,1,6,3,4]=>[6,7,2,1,4,5,3]=>[2,1,6,7,4,3,5]=>[1,3,1,2]
[5,2,7,1,6,4,3]=>[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>[4,1,2]
[5,2,7,3,1,4,6]=>[5,2,4,1,6,7,3]=>[3,6,4,7,2,1,5]=>[2,2,1,2]
[5,2,7,3,1,6,4]=>[4,7,2,1,5,6,3]=>[4,1,6,7,3,2,5]=>[1,3,1,2]
[5,2,7,3,4,1,6]=>[4,6,2,1,5,7,3]=>[4,2,6,7,3,1,5]=>[1,3,1,2]
[5,2,7,3,4,6,1]=>[4,5,1,7,2,6,3]=>[4,3,7,1,6,2,5]=>[1,2,2,2]
[5,2,7,3,6,1,4]=>[4,6,1,7,2,5,3]=>[4,2,7,1,6,3,5]=>[1,2,2,2]
[5,2,7,3,6,4,1]=>[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>[3,2,2]
[5,2,7,4,1,3,6]=>[5,6,2,1,4,7,3]=>[3,2,6,7,4,1,5]=>[1,3,1,2]
[5,2,7,4,1,6,3]=>[7,5,2,1,4,6,3]=>[1,3,6,7,4,2,5]=>[4,1,2]
[5,2,7,4,3,1,6]=>[6,5,2,1,4,7,3]=>[2,3,6,7,4,1,5]=>[4,1,2]
[5,2,7,4,3,6,1]=>[5,4,1,7,2,6,3]=>[3,4,7,1,6,2,5]=>[3,2,2]
[5,2,7,4,6,1,3]=>[6,4,1,7,2,5,3]=>[2,4,7,1,6,3,5]=>[3,2,2]
[5,2,7,4,6,3,1]=>[4,1,7,6,2,5,3]=>[4,7,1,2,6,3,5]=>[2,3,2]
[5,2,7,6,1,3,4]=>[5,6,1,7,2,4,3]=>[3,2,7,1,6,4,5]=>[1,2,2,2]
[5,2,7,6,1,4,3]=>[7,5,1,6,2,4,3]=>[1,3,7,2,6,4,5]=>[3,2,2]
[5,2,7,6,3,1,4]=>[6,5,1,7,2,4,3]=>[2,3,7,1,6,4,5]=>[3,2,2]
[5,2,7,6,3,4,1]=>[5,1,7,6,2,4,3]=>[3,7,1,2,6,4,5]=>[2,3,2]
[5,2,7,6,4,1,3]=>[6,1,7,5,2,4,3]=>[2,7,1,3,6,4,5]=>[2,3,2]
[5,2,7,6,4,3,1]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[1,4,2]
[5,3,1,2,4,6,7]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>[1,2,2,1,1]
[5,3,1,2,4,7,6]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>[3,2,1,1]
[5,3,1,2,6,4,7]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>[3,2,1,1]
[5,3,1,2,6,7,4]=>[5,2,7,3,1,4,6]=>[3,6,1,5,7,4,2]=>[2,3,1,1]
[5,3,1,2,7,4,6]=>[6,2,7,3,1,4,5]=>[2,6,1,5,7,4,3]=>[2,3,1,1]
[5,3,1,2,7,6,4]=>[2,7,6,3,1,4,5]=>[6,1,2,5,7,4,3]=>[1,4,1,1]
[5,3,1,4,2,6,7]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>[3,2,1,1]
[5,3,1,4,2,7,6]=>[4,2,7,3,1,5,6]=>[4,6,1,5,7,3,2]=>[2,3,1,1]
[5,3,1,4,6,2,7]=>[4,2,6,3,1,5,7]=>[4,6,2,5,7,3,1]=>[2,3,1,1]
[5,3,1,4,6,7,2]=>[4,2,5,1,7,3,6]=>[4,6,3,7,1,5,2]=>[2,2,2,1]
[5,3,1,4,7,2,6]=>[4,2,6,1,7,3,5]=>[4,6,2,7,1,5,3]=>[2,2,2,1]
[5,3,1,4,7,6,2]=>[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]=>[1,3,2,1]
[5,3,1,6,2,4,7]=>[5,2,6,3,1,4,7]=>[3,6,2,5,7,4,1]=>[2,3,1,1]
[5,3,1,6,2,7,4]=>[2,7,5,3,1,4,6]=>[6,1,3,5,7,4,2]=>[1,4,1,1]
[5,3,1,6,4,2,7]=>[2,6,5,3,1,4,7]=>[6,2,3,5,7,4,1]=>[1,4,1,1]
[5,3,1,6,4,7,2]=>[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]=>[1,3,2,1]
[5,3,1,6,7,2,4]=>[2,6,4,1,7,3,5]=>[6,2,4,7,1,5,3]=>[1,3,2,1]
[5,3,1,6,7,4,2]=>[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]=>[1,2,3,1]
[5,3,1,7,2,4,6]=>[5,2,6,1,7,3,4]=>[3,6,2,7,1,5,4]=>[2,2,2,1]
[5,3,1,7,2,6,4]=>[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]=>[1,3,2,1]
[5,3,1,7,4,2,6]=>[2,6,5,1,7,3,4]=>[6,2,3,7,1,5,4]=>[1,3,2,1]
[5,3,1,7,4,6,2]=>[2,5,1,7,6,3,4]=>[6,3,7,1,2,5,4]=>[1,2,3,1]
[5,3,1,7,6,2,4]=>[2,6,1,7,5,3,4]=>[6,2,7,1,3,5,4]=>[1,2,3,1]
[5,3,1,7,6,4,2]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>[3,3,1]
[5,3,2,1,4,6,7]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>[3,2,1,1]
[5,3,2,1,4,7,6]=>[3,2,7,4,1,5,6]=>[5,6,1,4,7,3,2]=>[2,3,1,1]
[5,3,2,1,6,4,7]=>[3,2,6,4,1,5,7]=>[5,6,2,4,7,3,1]=>[2,3,1,1]
[5,3,2,1,6,7,4]=>[3,2,5,1,7,4,6]=>[5,6,3,7,1,4,2]=>[2,2,2,1]
[5,3,2,1,7,4,6]=>[3,2,6,1,7,4,5]=>[5,6,2,7,1,4,3]=>[2,2,2,1]
[5,3,2,1,7,6,4]=>[2,7,3,1,6,4,5]=>[6,1,5,7,2,4,3]=>[1,3,2,1]
[5,3,2,4,1,6,7]=>[3,2,5,4,1,6,7]=>[5,6,3,4,7,2,1]=>[2,3,1,1]
[5,3,2,4,1,7,6]=>[3,2,4,1,7,5,6]=>[5,6,4,7,1,3,2]=>[2,2,2,1]
[5,3,2,4,6,1,7]=>[3,2,4,1,6,5,7]=>[5,6,4,7,2,3,1]=>[2,2,2,1]
[5,3,2,4,6,7,1]=>[3,2,4,1,5,7,6]=>[5,6,4,7,3,1,2]=>[2,2,1,2]
[5,3,2,4,7,1,6]=>[3,2,4,1,6,7,5]=>[5,6,4,7,2,1,3]=>[2,2,1,2]
[5,3,2,4,7,6,1]=>[2,7,3,1,4,6,5]=>[6,1,5,7,4,2,3]=>[1,3,1,2]
[5,3,2,6,1,4,7]=>[3,2,5,1,6,4,7]=>[5,6,3,7,2,4,1]=>[2,2,2,1]
[5,3,2,6,1,7,4]=>[2,7,3,1,5,4,6]=>[6,1,5,7,3,4,2]=>[1,3,2,1]
[5,3,2,6,4,1,7]=>[2,6,3,1,5,4,7]=>[6,2,5,7,3,4,1]=>[1,3,2,1]
[5,3,2,6,4,7,1]=>[2,5,3,1,4,7,6]=>[6,3,5,7,4,1,2]=>[1,3,1,2]
[5,3,2,6,7,1,4]=>[2,6,3,1,4,7,5]=>[6,2,5,7,4,1,3]=>[1,3,1,2]
[5,3,2,6,7,4,1]=>[2,4,1,7,3,6,5]=>[6,4,7,1,5,2,3]=>[1,2,2,2]
[5,3,2,7,1,4,6]=>[3,2,5,1,6,7,4]=>[5,6,3,7,2,1,4]=>[2,2,1,2]
[5,3,2,7,1,6,4]=>[2,7,3,1,5,6,4]=>[6,1,5,7,3,2,4]=>[1,3,1,2]
[5,3,2,7,4,1,6]=>[2,6,3,1,5,7,4]=>[6,2,5,7,3,1,4]=>[1,3,1,2]
[5,3,2,7,4,6,1]=>[2,5,1,7,3,6,4]=>[6,3,7,1,5,2,4]=>[1,2,2,2]
[5,3,2,7,6,1,4]=>[2,6,1,7,3,5,4]=>[6,2,7,1,5,3,4]=>[1,2,2,2]
[5,3,2,7,6,4,1]=>[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>[3,2,2]
[5,3,4,1,2,6,7]=>[4,2,5,3,1,6,7]=>[4,6,3,5,7,2,1]=>[2,3,1,1]
[5,3,4,1,2,7,6]=>[2,7,4,3,1,5,6]=>[6,1,4,5,7,3,2]=>[1,4,1,1]
[5,3,4,1,6,2,7]=>[2,6,4,3,1,5,7]=>[6,2,4,5,7,3,1]=>[1,4,1,1]
[5,3,4,1,6,7,2]=>[2,5,3,1,7,4,6]=>[6,3,5,7,1,4,2]=>[1,3,2,1]
[5,3,4,1,7,2,6]=>[2,6,3,1,7,4,5]=>[6,2,5,7,1,4,3]=>[1,3,2,1]
[5,3,4,1,7,6,2]=>[2,3,1,7,6,4,5]=>[6,5,7,1,2,4,3]=>[1,2,3,1]
[5,3,4,2,1,6,7]=>[2,5,4,3,1,6,7]=>[6,3,4,5,7,2,1]=>[1,4,1,1]
[5,3,4,2,1,7,6]=>[2,4,3,1,7,5,6]=>[6,4,5,7,1,3,2]=>[1,3,2,1]
[5,3,4,2,6,1,7]=>[2,4,3,1,6,5,7]=>[6,4,5,7,2,3,1]=>[1,3,2,1]
[5,3,4,2,6,7,1]=>[2,4,3,1,5,7,6]=>[6,4,5,7,3,1,2]=>[1,3,1,2]
[5,3,4,2,7,1,6]=>[2,4,3,1,6,7,5]=>[6,4,5,7,2,1,3]=>[1,3,1,2]
[5,3,4,2,7,6,1]=>[2,3,1,7,4,6,5]=>[6,5,7,1,4,2,3]=>[1,2,2,2]
[5,3,4,6,1,2,7]=>[2,5,3,1,6,4,7]=>[6,3,5,7,2,4,1]=>[1,3,2,1]
[5,3,4,6,1,7,2]=>[2,3,1,7,5,4,6]=>[6,5,7,1,3,4,2]=>[1,2,3,1]
[5,3,4,6,2,1,7]=>[2,3,1,6,5,4,7]=>[6,5,7,2,3,4,1]=>[1,2,3,1]
[5,3,4,6,2,7,1]=>[2,3,1,5,4,7,6]=>[6,5,7,3,4,1,2]=>[1,2,2,2]
[5,3,4,6,7,1,2]=>[2,3,1,6,4,7,5]=>[6,5,7,2,4,1,3]=>[1,2,2,2]
[5,3,4,6,7,2,1]=>[2,3,1,4,7,6,5]=>[6,5,7,4,1,2,3]=>[1,2,1,3]
[5,3,4,7,1,2,6]=>[2,5,3,1,6,7,4]=>[6,3,5,7,2,1,4]=>[1,3,1,2]
[5,3,4,7,1,6,2]=>[2,3,1,7,5,6,4]=>[6,5,7,1,3,2,4]=>[1,2,2,2]
[5,3,4,7,2,1,6]=>[2,3,1,6,5,7,4]=>[6,5,7,2,3,1,4]=>[1,2,2,2]
[5,3,4,7,2,6,1]=>[2,3,1,5,7,6,4]=>[6,5,7,3,1,2,4]=>[1,2,1,3]
[5,3,4,7,6,1,2]=>[2,3,1,6,7,5,4]=>[6,5,7,2,1,3,4]=>[1,2,1,3]
[5,3,4,7,6,2,1]=>[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>[3,1,3]
[5,3,6,1,2,4,7]=>[4,2,5,1,6,3,7]=>[4,6,3,7,2,5,1]=>[2,2,2,1]
[5,3,6,1,2,7,4]=>[2,7,4,1,5,3,6]=>[6,1,4,7,3,5,2]=>[1,3,2,1]
[5,3,6,1,4,2,7]=>[2,6,4,1,5,3,7]=>[6,2,4,7,3,5,1]=>[1,3,2,1]
[5,3,6,1,4,7,2]=>[2,5,1,7,4,3,6]=>[6,3,7,1,4,5,2]=>[1,2,3,1]
[5,3,6,1,7,2,4]=>[2,6,1,7,4,3,5]=>[6,2,7,1,4,5,3]=>[1,2,3,1]
[5,3,6,1,7,4,2]=>[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>[3,3,1]
[5,3,6,2,1,4,7]=>[2,5,4,1,6,3,7]=>[6,3,4,7,2,5,1]=>[1,3,2,1]
[5,3,6,2,1,7,4]=>[2,4,1,7,5,3,6]=>[6,4,7,1,3,5,2]=>[1,2,3,1]
[5,3,6,2,4,1,7]=>[2,4,1,6,5,3,7]=>[6,4,7,2,3,5,1]=>[1,2,3,1]
[5,3,6,2,4,7,1]=>[2,4,1,5,3,7,6]=>[6,4,7,3,5,1,2]=>[1,2,2,2]
[5,3,6,2,7,1,4]=>[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]=>[1,2,2,2]
[5,3,6,2,7,4,1]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>[3,2,2]
[5,3,6,4,1,2,7]=>[2,5,1,6,4,3,7]=>[6,3,7,2,4,5,1]=>[1,2,3,1]
[5,3,6,4,1,7,2]=>[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>[3,3,1]
[5,3,6,4,2,1,7]=>[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>[3,3,1]
[5,3,6,4,2,7,1]=>[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>[3,2,2]
[5,3,6,4,7,1,2]=>[6,2,1,4,3,7,5]=>[2,6,7,4,5,1,3]=>[3,2,2]
[5,3,6,4,7,2,1]=>[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>[3,1,3]
[5,3,6,7,1,2,4]=>[2,5,1,6,3,7,4]=>[6,3,7,2,5,1,4]=>[1,2,2,2]
[5,3,6,7,1,4,2]=>[7,2,1,5,3,6,4]=>[1,6,7,3,5,2,4]=>[3,2,2]
[5,3,6,7,2,1,4]=>[6,2,1,5,3,7,4]=>[2,6,7,3,5,1,4]=>[3,2,2]
[5,3,6,7,2,4,1]=>[5,2,1,3,7,6,4]=>[3,6,7,5,1,2,4]=>[3,1,3]
[5,3,6,7,4,1,2]=>[6,2,1,3,7,5,4]=>[2,6,7,5,1,3,4]=>[3,1,3]
[5,3,6,7,4,2,1]=>[3,1,7,2,6,5,4]=>[5,7,1,6,2,3,4]=>[2,2,3]
[5,3,7,1,2,4,6]=>[4,2,5,1,6,7,3]=>[4,6,3,7,2,1,5]=>[2,2,1,2]
[5,3,7,1,2,6,4]=>[2,7,4,1,5,6,3]=>[6,1,4,7,3,2,5]=>[1,3,1,2]
[5,3,7,1,4,2,6]=>[2,6,4,1,5,7,3]=>[6,2,4,7,3,1,5]=>[1,3,1,2]
[5,3,7,1,4,6,2]=>[2,5,1,7,4,6,3]=>[6,3,7,1,4,2,5]=>[1,2,2,2]
[5,3,7,1,6,2,4]=>[2,6,1,7,4,5,3]=>[6,2,7,1,4,3,5]=>[1,2,2,2]
[5,3,7,1,6,4,2]=>[7,2,1,6,4,5,3]=>[1,6,7,2,4,3,5]=>[3,2,2]
[5,3,7,2,1,4,6]=>[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]=>[1,3,1,2]
[5,3,7,2,1,6,4]=>[2,4,1,7,5,6,3]=>[6,4,7,1,3,2,5]=>[1,2,2,2]
[5,3,7,2,4,1,6]=>[2,4,1,6,5,7,3]=>[6,4,7,2,3,1,5]=>[1,2,2,2]
[5,3,7,2,4,6,1]=>[2,4,1,5,7,6,3]=>[6,4,7,3,1,2,5]=>[1,2,1,3]
[5,3,7,2,6,1,4]=>[2,4,1,6,7,5,3]=>[6,4,7,2,1,3,5]=>[1,2,1,3]
[5,3,7,2,6,4,1]=>[7,2,1,4,6,5,3]=>[1,6,7,4,2,3,5]=>[3,1,3]
[5,3,7,4,1,2,6]=>[2,5,1,6,4,7,3]=>[6,3,7,2,4,1,5]=>[1,2,2,2]
[5,3,7,4,1,6,2]=>[7,2,1,5,4,6,3]=>[1,6,7,3,4,2,5]=>[3,2,2]
[5,3,7,4,2,1,6]=>[6,2,1,5,4,7,3]=>[2,6,7,3,4,1,5]=>[3,2,2]
[5,3,7,4,2,6,1]=>[5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5]=>[3,1,3]
[5,3,7,4,6,1,2]=>[6,2,1,4,7,5,3]=>[2,6,7,4,1,3,5]=>[3,1,3]
[5,3,7,4,6,2,1]=>[4,1,7,2,6,5,3]=>[4,7,1,6,2,3,5]=>[2,2,3]
[5,3,7,6,1,2,4]=>[2,5,1,6,7,4,3]=>[6,3,7,2,1,4,5]=>[1,2,1,3]
[5,3,7,6,1,4,2]=>[7,2,1,5,6,4,3]=>[1,6,7,3,2,4,5]=>[3,1,3]
[5,3,7,6,2,1,4]=>[6,2,1,5,7,4,3]=>[2,6,7,3,1,4,5]=>[3,1,3]
[5,3,7,6,2,4,1]=>[5,1,7,2,6,4,3]=>[3,7,1,6,2,4,5]=>[2,2,3]
[5,3,7,6,4,1,2]=>[6,1,7,2,5,4,3]=>[2,7,1,6,3,4,5]=>[2,2,3]
[5,3,7,6,4,2,1]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[1,3,3]
[5,4,1,2,3,6,7]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>[1,1,3,1,1]
[5,4,1,2,3,7,6]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>[2,3,1,1]
[5,4,1,2,6,3,7]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>[2,3,1,1]
[5,4,1,2,6,7,3]=>[5,7,3,2,1,4,6]=>[3,1,5,6,7,4,2]=>[1,4,1,1]
[5,4,1,2,7,3,6]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>[1,4,1,1]
[5,4,1,2,7,6,3]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[5,1,1]
[5,4,1,3,2,6,7]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>[2,3,1,1]
[5,4,1,3,2,7,6]=>[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>[1,4,1,1]
[5,4,1,3,6,2,7]=>[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>[1,4,1,1]
[5,4,1,3,6,7,2]=>[4,5,2,1,7,3,6]=>[4,3,6,7,1,5,2]=>[1,3,2,1]
[5,4,1,3,7,2,6]=>[4,6,2,1,7,3,5]=>[4,2,6,7,1,5,3]=>[1,3,2,1]
[5,4,1,3,7,6,2]=>[7,4,2,1,6,3,5]=>[1,4,6,7,2,5,3]=>[4,2,1]
[5,4,1,6,2,3,7]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>[1,4,1,1]
[5,4,1,6,2,7,3]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[5,1,1]
[5,4,1,6,3,2,7]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[5,1,1]
[5,4,1,6,3,7,2]=>[5,4,2,1,7,3,6]=>[3,4,6,7,1,5,2]=>[4,2,1]
[5,4,1,6,7,2,3]=>[6,4,2,1,7,3,5]=>[2,4,6,7,1,5,3]=>[4,2,1]
[5,4,1,6,7,3,2]=>[4,2,1,7,6,3,5]=>[4,6,7,1,2,5,3]=>[3,3,1]
[5,4,1,7,2,3,6]=>[5,6,2,1,7,3,4]=>[3,2,6,7,1,5,4]=>[1,3,2,1]
[5,4,1,7,2,6,3]=>[7,5,2,1,6,3,4]=>[1,3,6,7,2,5,4]=>[4,2,1]
[5,4,1,7,3,2,6]=>[6,5,2,1,7,3,4]=>[2,3,6,7,1,5,4]=>[4,2,1]
[5,4,1,7,3,6,2]=>[5,2,1,7,6,3,4]=>[3,6,7,1,2,5,4]=>[3,3,1]
[5,4,1,7,6,2,3]=>[6,2,1,7,5,3,4]=>[2,6,7,1,3,5,4]=>[3,3,1]
[5,4,1,7,6,3,2]=>[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>[2,4,1]
[5,4,2,1,3,6,7]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>[2,3,1,1]
[5,4,2,1,3,7,6]=>[3,7,4,2,1,5,6]=>[5,1,4,6,7,3,2]=>[1,4,1,1]
[5,4,2,1,6,3,7]=>[3,6,4,2,1,5,7]=>[5,2,4,6,7,3,1]=>[1,4,1,1]
[5,4,2,1,6,7,3]=>[3,5,2,1,7,4,6]=>[5,3,6,7,1,4,2]=>[1,3,2,1]
[5,4,2,1,7,3,6]=>[3,6,2,1,7,4,5]=>[5,2,6,7,1,4,3]=>[1,3,2,1]
[5,4,2,1,7,6,3]=>[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>[4,2,1]
[5,4,2,3,1,6,7]=>[3,5,4,2,1,6,7]=>[5,3,4,6,7,2,1]=>[1,4,1,1]
[5,4,2,3,1,7,6]=>[3,4,2,1,7,5,6]=>[5,4,6,7,1,3,2]=>[1,3,2,1]
[5,4,2,3,6,1,7]=>[3,4,2,1,6,5,7]=>[5,4,6,7,2,3,1]=>[1,3,2,1]
[5,4,2,3,6,7,1]=>[3,4,2,1,5,7,6]=>[5,4,6,7,3,1,2]=>[1,3,1,2]
[5,4,2,3,7,1,6]=>[3,4,2,1,6,7,5]=>[5,4,6,7,2,1,3]=>[1,3,1,2]
[5,4,2,3,7,6,1]=>[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>[4,1,2]
[5,4,2,6,1,3,7]=>[3,5,2,1,6,4,7]=>[5,3,6,7,2,4,1]=>[1,3,2,1]
[5,4,2,6,1,7,3]=>[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>[4,2,1]
[5,4,2,6,3,1,7]=>[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>[4,2,1]
[5,4,2,6,3,7,1]=>[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>[4,1,2]
[5,4,2,6,7,1,3]=>[6,3,2,1,4,7,5]=>[2,5,6,7,4,1,3]=>[4,1,2]
[5,4,2,6,7,3,1]=>[4,2,1,7,3,6,5]=>[4,6,7,1,5,2,3]=>[3,2,2]
[5,4,2,7,1,3,6]=>[3,5,2,1,6,7,4]=>[5,3,6,7,2,1,4]=>[1,3,1,2]
[5,4,2,7,1,6,3]=>[7,3,2,1,5,6,4]=>[1,5,6,7,3,2,4]=>[4,1,2]
[5,4,2,7,3,1,6]=>[6,3,2,1,5,7,4]=>[2,5,6,7,3,1,4]=>[4,1,2]
[5,4,2,7,3,6,1]=>[5,2,1,7,3,6,4]=>[3,6,7,1,5,2,4]=>[3,2,2]
[5,4,2,7,6,1,3]=>[6,2,1,7,3,5,4]=>[2,6,7,1,5,3,4]=>[3,2,2]
[5,4,2,7,6,3,1]=>[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>[2,3,2]
[5,4,3,1,2,6,7]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>[1,4,1,1]
[5,4,3,1,2,7,6]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[5,1,1]
[5,4,3,1,6,2,7]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[5,1,1]
[5,4,3,1,6,7,2]=>[5,3,2,1,7,4,6]=>[3,5,6,7,1,4,2]=>[4,2,1]
[5,4,3,1,7,2,6]=>[6,3,2,1,7,4,5]=>[2,5,6,7,1,4,3]=>[4,2,1]
[5,4,3,1,7,6,2]=>[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>[3,3,1]
[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[5,1,1]
[5,4,3,2,1,7,6]=>[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>[4,2,1]
[5,4,3,2,6,1,7]=>[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>[4,2,1]
[5,4,3,2,6,7,1]=>[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>[4,1,2]
[5,4,3,2,7,1,6]=>[4,3,2,1,6,7,5]=>[4,5,6,7,2,1,3]=>[4,1,2]
[5,4,3,2,7,6,1]=>[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>[3,2,2]
[5,4,3,6,1,2,7]=>[5,3,2,1,6,4,7]=>[3,5,6,7,2,4,1]=>[4,2,1]
[5,4,3,6,1,7,2]=>[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>[3,3,1]
[5,4,3,6,2,1,7]=>[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>[3,3,1]
[5,4,3,6,2,7,1]=>[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>[3,2,2]
[5,4,3,6,7,1,2]=>[3,2,1,6,4,7,5]=>[5,6,7,2,4,1,3]=>[3,2,2]
[5,4,3,6,7,2,1]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[3,1,3]
[5,4,3,7,1,2,6]=>[5,3,2,1,6,7,4]=>[3,5,6,7,2,1,4]=>[4,1,2]
[5,4,3,7,1,6,2]=>[3,2,1,7,5,6,4]=>[5,6,7,1,3,2,4]=>[3,2,2]
[5,4,3,7,2,1,6]=>[3,2,1,6,5,7,4]=>[5,6,7,2,3,1,4]=>[3,2,2]
[5,4,3,7,2,6,1]=>[3,2,1,5,7,6,4]=>[5,6,7,3,1,2,4]=>[3,1,3]
[5,4,3,7,6,1,2]=>[3,2,1,6,7,5,4]=>[5,6,7,2,1,3,4]=>[3,1,3]
[5,4,3,7,6,2,1]=>[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>[2,2,3]
[5,4,6,1,2,3,7]=>[4,5,2,1,6,3,7]=>[4,3,6,7,2,5,1]=>[1,3,2,1]
[5,4,6,1,2,7,3]=>[7,4,2,1,5,3,6]=>[1,4,6,7,3,5,2]=>[4,2,1]
[5,4,6,1,3,2,7]=>[6,4,2,1,5,3,7]=>[2,4,6,7,3,5,1]=>[4,2,1]
[5,4,6,1,3,7,2]=>[5,2,1,7,4,3,6]=>[3,6,7,1,4,5,2]=>[3,3,1]
[5,4,6,1,7,2,3]=>[6,2,1,7,4,3,5]=>[2,6,7,1,4,5,3]=>[3,3,1]
[5,4,6,1,7,3,2]=>[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>[2,4,1]
[5,4,6,2,1,3,7]=>[5,4,2,1,6,3,7]=>[3,4,6,7,2,5,1]=>[4,2,1]
[5,4,6,2,1,7,3]=>[4,2,1,7,5,3,6]=>[4,6,7,1,3,5,2]=>[3,3,1]
[5,4,6,2,3,1,7]=>[4,2,1,6,5,3,7]=>[4,6,7,2,3,5,1]=>[3,3,1]
[5,4,6,2,3,7,1]=>[4,2,1,5,3,7,6]=>[4,6,7,3,5,1,2]=>[3,2,2]
[5,4,6,2,7,1,3]=>[4,2,1,6,3,7,5]=>[4,6,7,2,5,1,3]=>[3,2,2]
[5,4,6,2,7,3,1]=>[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>[2,3,2]
[5,4,6,3,1,2,7]=>[5,2,1,6,4,3,7]=>[3,6,7,2,4,5,1]=>[3,3,1]
[5,4,6,3,1,7,2]=>[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>[2,4,1]
[5,4,6,3,2,1,7]=>[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>[2,4,1]
[5,4,6,3,2,7,1]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,3,2]
[5,4,6,3,7,1,2]=>[2,1,6,4,3,7,5]=>[6,7,2,4,5,1,3]=>[2,3,2]
[5,4,6,3,7,2,1]=>[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>[2,2,3]
[5,4,6,7,1,2,3]=>[5,2,1,6,3,7,4]=>[3,6,7,2,5,1,4]=>[3,2,2]
[5,4,6,7,1,3,2]=>[2,1,7,5,3,6,4]=>[6,7,1,3,5,2,4]=>[2,3,2]
[5,4,6,7,2,1,3]=>[2,1,6,5,3,7,4]=>[6,7,2,3,5,1,4]=>[2,3,2]
[5,4,6,7,2,3,1]=>[2,1,5,3,7,6,4]=>[6,7,3,5,1,2,4]=>[2,2,3]
[5,4,6,7,3,1,2]=>[2,1,6,3,7,5,4]=>[6,7,2,5,1,3,4]=>[2,2,3]
[5,4,6,7,3,2,1]=>[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>[2,1,4]
[5,4,7,1,2,3,6]=>[4,5,2,1,6,7,3]=>[4,3,6,7,2,1,5]=>[1,3,1,2]
[5,4,7,1,2,6,3]=>[7,4,2,1,5,6,3]=>[1,4,6,7,3,2,5]=>[4,1,2]
[5,4,7,1,3,2,6]=>[6,4,2,1,5,7,3]=>[2,4,6,7,3,1,5]=>[4,1,2]
[5,4,7,1,3,6,2]=>[5,2,1,7,4,6,3]=>[3,6,7,1,4,2,5]=>[3,2,2]
[5,4,7,1,6,2,3]=>[6,2,1,7,4,5,3]=>[2,6,7,1,4,3,5]=>[3,2,2]
[5,4,7,1,6,3,2]=>[2,1,7,6,4,5,3]=>[6,7,1,2,4,3,5]=>[2,3,2]
[5,4,7,2,1,3,6]=>[5,4,2,1,6,7,3]=>[3,4,6,7,2,1,5]=>[4,1,2]
[5,4,7,2,1,6,3]=>[4,2,1,7,5,6,3]=>[4,6,7,1,3,2,5]=>[3,2,2]
[5,4,7,2,3,1,6]=>[4,2,1,6,5,7,3]=>[4,6,7,2,3,1,5]=>[3,2,2]
[5,4,7,2,3,6,1]=>[4,2,1,5,7,6,3]=>[4,6,7,3,1,2,5]=>[3,1,3]
[5,4,7,2,6,1,3]=>[4,2,1,6,7,5,3]=>[4,6,7,2,1,3,5]=>[3,1,3]
[5,4,7,2,6,3,1]=>[2,1,7,4,6,5,3]=>[6,7,1,4,2,3,5]=>[2,2,3]
[5,4,7,3,1,2,6]=>[5,2,1,6,4,7,3]=>[3,6,7,2,4,1,5]=>[3,2,2]
[5,4,7,3,1,6,2]=>[2,1,7,5,4,6,3]=>[6,7,1,3,4,2,5]=>[2,3,2]
[5,4,7,3,2,1,6]=>[2,1,6,5,4,7,3]=>[6,7,2,3,4,1,5]=>[2,3,2]
[5,4,7,3,2,6,1]=>[2,1,5,4,7,6,3]=>[6,7,3,4,1,2,5]=>[2,2,3]
[5,4,7,3,6,1,2]=>[2,1,6,4,7,5,3]=>[6,7,2,4,1,3,5]=>[2,2,3]
[5,4,7,3,6,2,1]=>[2,1,4,7,6,5,3]=>[6,7,4,1,2,3,5]=>[2,1,4]
[5,4,7,6,1,2,3]=>[5,2,1,6,7,4,3]=>[3,6,7,2,1,4,5]=>[3,1,3]
[5,4,7,6,1,3,2]=>[2,1,7,5,6,4,3]=>[6,7,1,3,2,4,5]=>[2,2,3]
[5,4,7,6,2,1,3]=>[2,1,6,5,7,4,3]=>[6,7,2,3,1,4,5]=>[2,2,3]
[5,4,7,6,2,3,1]=>[2,1,5,7,6,4,3]=>[6,7,3,1,2,4,5]=>[2,1,4]
[5,4,7,6,3,1,2]=>[2,1,6,7,5,4,3]=>[6,7,2,1,3,4,5]=>[2,1,4]
[5,4,7,6,3,2,1]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[1,2,4]
[5,6,1,2,3,4,7]=>[3,4,5,1,6,2,7]=>[5,4,3,7,2,6,1]=>[1,1,2,2,1]
[5,6,1,2,3,7,4]=>[7,3,4,1,5,2,6]=>[1,5,4,7,3,6,2]=>[2,2,2,1]
[5,6,1,2,4,3,7]=>[6,3,4,1,5,2,7]=>[2,5,4,7,3,6,1]=>[2,2,2,1]
[5,6,1,2,4,7,3]=>[5,7,3,1,4,2,6]=>[3,1,5,7,4,6,2]=>[1,3,2,1]
[5,6,1,2,7,3,4]=>[6,7,3,1,4,2,5]=>[2,1,5,7,4,6,3]=>[1,3,2,1]
[5,6,1,2,7,4,3]=>[7,6,3,1,4,2,5]=>[1,2,5,7,4,6,3]=>[4,2,1]
[5,6,1,3,2,4,7]=>[5,3,4,1,6,2,7]=>[3,5,4,7,2,6,1]=>[2,2,2,1]
[5,6,1,3,2,7,4]=>[4,7,3,1,5,2,6]=>[4,1,5,7,3,6,2]=>[1,3,2,1]
[5,6,1,3,4,2,7]=>[4,6,3,1,5,2,7]=>[4,2,5,7,3,6,1]=>[1,3,2,1]
[5,6,1,3,4,7,2]=>[4,5,1,7,3,2,6]=>[4,3,7,1,5,6,2]=>[1,2,3,1]
[5,6,1,3,7,2,4]=>[4,6,1,7,3,2,5]=>[4,2,7,1,5,6,3]=>[1,2,3,1]
[5,6,1,3,7,4,2]=>[7,4,1,6,3,2,5]=>[1,4,7,2,5,6,3]=>[3,3,1]
[5,6,1,4,2,3,7]=>[5,6,3,1,4,2,7]=>[3,2,5,7,4,6,1]=>[1,3,2,1]
[5,6,1,4,2,7,3]=>[7,5,3,1,4,2,6]=>[1,3,5,7,4,6,2]=>[4,2,1]
[5,6,1,4,3,2,7]=>[6,5,3,1,4,2,7]=>[2,3,5,7,4,6,1]=>[4,2,1]
[5,6,1,4,3,7,2]=>[5,4,1,7,3,2,6]=>[3,4,7,1,5,6,2]=>[3,3,1]
[5,6,1,4,7,2,3]=>[6,4,1,7,3,2,5]=>[2,4,7,1,5,6,3]=>[3,3,1]
[5,6,1,4,7,3,2]=>[4,1,7,6,3,2,5]=>[4,7,1,2,5,6,3]=>[2,4,1]
[5,6,1,7,2,3,4]=>[5,6,1,7,3,2,4]=>[3,2,7,1,5,6,4]=>[1,2,3,1]
[5,6,1,7,2,4,3]=>[7,5,1,6,3,2,4]=>[1,3,7,2,5,6,4]=>[3,3,1]
[5,6,1,7,3,2,4]=>[6,5,1,7,3,2,4]=>[2,3,7,1,5,6,4]=>[3,3,1]
[5,6,1,7,3,4,2]=>[5,1,7,6,3,2,4]=>[3,7,1,2,5,6,4]=>[2,4,1]
[5,6,1,7,4,2,3]=>[6,1,7,5,3,2,4]=>[2,7,1,3,5,6,4]=>[2,4,1]
[5,6,1,7,4,3,2]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[1,5,1]
[5,6,2,1,3,4,7]=>[4,3,5,1,6,2,7]=>[4,5,3,7,2,6,1]=>[2,2,2,1]
[5,6,2,1,3,7,4]=>[3,7,4,1,5,2,6]=>[5,1,4,7,3,6,2]=>[1,3,2,1]
[5,6,2,1,4,3,7]=>[3,6,4,1,5,2,7]=>[5,2,4,7,3,6,1]=>[1,3,2,1]
[5,6,2,1,4,7,3]=>[3,5,1,7,4,2,6]=>[5,3,7,1,4,6,2]=>[1,2,3,1]
[5,6,2,1,7,3,4]=>[3,6,1,7,4,2,5]=>[5,2,7,1,4,6,3]=>[1,2,3,1]
[5,6,2,1,7,4,3]=>[7,3,1,6,4,2,5]=>[1,5,7,2,4,6,3]=>[3,3,1]
[5,6,2,3,1,4,7]=>[3,5,4,1,6,2,7]=>[5,3,4,7,2,6,1]=>[1,3,2,1]
[5,6,2,3,1,7,4]=>[3,4,1,7,5,2,6]=>[5,4,7,1,3,6,2]=>[1,2,3,1]
[5,6,2,3,4,1,7]=>[3,4,1,6,5,2,7]=>[5,4,7,2,3,6,1]=>[1,2,3,1]
[5,6,2,3,4,7,1]=>[3,4,1,5,2,7,6]=>[5,4,7,3,6,1,2]=>[1,2,2,2]
[5,6,2,3,7,1,4]=>[3,4,1,6,2,7,5]=>[5,4,7,2,6,1,3]=>[1,2,2,2]
[5,6,2,3,7,4,1]=>[7,3,1,4,2,6,5]=>[1,5,7,4,6,2,3]=>[3,2,2]
[5,6,2,4,1,3,7]=>[3,5,1,6,4,2,7]=>[5,3,7,2,4,6,1]=>[1,2,3,1]
[5,6,2,4,1,7,3]=>[7,3,1,5,4,2,6]=>[1,5,7,3,4,6,2]=>[3,3,1]
[5,6,2,4,3,1,7]=>[6,3,1,5,4,2,7]=>[2,5,7,3,4,6,1]=>[3,3,1]
[5,6,2,4,3,7,1]=>[5,3,1,4,2,7,6]=>[3,5,7,4,6,1,2]=>[3,2,2]
[5,6,2,4,7,1,3]=>[6,3,1,4,2,7,5]=>[2,5,7,4,6,1,3]=>[3,2,2]
[5,6,2,4,7,3,1]=>[4,1,7,3,2,6,5]=>[4,7,1,5,6,2,3]=>[2,3,2]
[5,6,2,7,1,3,4]=>[3,5,1,6,2,7,4]=>[5,3,7,2,6,1,4]=>[1,2,2,2]
[5,6,2,7,1,4,3]=>[7,3,1,5,2,6,4]=>[1,5,7,3,6,2,4]=>[3,2,2]
[5,6,2,7,3,1,4]=>[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]=>[3,2,2]
[5,6,2,7,3,4,1]=>[5,1,7,3,2,6,4]=>[3,7,1,5,6,2,4]=>[2,3,2]
[5,6,2,7,4,1,3]=>[6,1,7,3,2,5,4]=>[2,7,1,5,6,3,4]=>[2,3,2]
[5,6,2,7,4,3,1]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[1,4,2]
[5,6,3,1,2,4,7]=>[4,5,3,1,6,2,7]=>[4,3,5,7,2,6,1]=>[1,3,2,1]
[5,6,3,1,2,7,4]=>[7,4,3,1,5,2,6]=>[1,4,5,7,3,6,2]=>[4,2,1]
[5,6,3,1,4,2,7]=>[6,4,3,1,5,2,7]=>[2,4,5,7,3,6,1]=>[4,2,1]
[5,6,3,1,4,7,2]=>[5,3,1,7,4,2,6]=>[3,5,7,1,4,6,2]=>[3,3,1]
[5,6,3,1,7,2,4]=>[6,3,1,7,4,2,5]=>[2,5,7,1,4,6,3]=>[3,3,1]
[5,6,3,1,7,4,2]=>[3,1,7,6,4,2,5]=>[5,7,1,2,4,6,3]=>[2,4,1]
[5,6,3,2,1,4,7]=>[5,4,3,1,6,2,7]=>[3,4,5,7,2,6,1]=>[4,2,1]
[5,6,3,2,1,7,4]=>[4,3,1,7,5,2,6]=>[4,5,7,1,3,6,2]=>[3,3,1]
[5,6,3,2,4,1,7]=>[4,3,1,6,5,2,7]=>[4,5,7,2,3,6,1]=>[3,3,1]
[5,6,3,2,4,7,1]=>[4,3,1,5,2,7,6]=>[4,5,7,3,6,1,2]=>[3,2,2]
[5,6,3,2,7,1,4]=>[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]=>[3,2,2]
[5,6,3,2,7,4,1]=>[3,1,7,4,2,6,5]=>[5,7,1,4,6,2,3]=>[2,3,2]
[5,6,3,4,1,2,7]=>[5,3,1,6,4,2,7]=>[3,5,7,2,4,6,1]=>[3,3,1]
[5,6,3,4,1,7,2]=>[3,1,7,5,4,2,6]=>[5,7,1,3,4,6,2]=>[2,4,1]
[5,6,3,4,2,1,7]=>[3,1,6,5,4,2,7]=>[5,7,2,3,4,6,1]=>[2,4,1]
[5,6,3,4,2,7,1]=>[3,1,5,4,2,7,6]=>[5,7,3,4,6,1,2]=>[2,3,2]
[5,6,3,4,7,1,2]=>[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>[2,3,2]
[5,6,3,4,7,2,1]=>[3,1,4,2,7,6,5]=>[5,7,4,6,1,2,3]=>[2,2,3]
[5,6,3,7,1,2,4]=>[5,3,1,6,2,7,4]=>[3,5,7,2,6,1,4]=>[3,2,2]
[5,6,3,7,1,4,2]=>[3,1,7,5,2,6,4]=>[5,7,1,3,6,2,4]=>[2,3,2]
[5,6,3,7,2,1,4]=>[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]=>[2,3,2]
[5,6,3,7,2,4,1]=>[3,1,5,2,7,6,4]=>[5,7,3,6,1,2,4]=>[2,2,3]
[5,6,3,7,4,1,2]=>[3,1,6,2,7,5,4]=>[5,7,2,6,1,3,4]=>[2,2,3]
[5,6,3,7,4,2,1]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[1,3,3]
[5,6,4,1,2,3,7]=>[4,5,1,6,3,2,7]=>[4,3,7,2,5,6,1]=>[1,2,3,1]
[5,6,4,1,2,7,3]=>[7,4,1,5,3,2,6]=>[1,4,7,3,5,6,2]=>[3,3,1]
[5,6,4,1,3,2,7]=>[6,4,1,5,3,2,7]=>[2,4,7,3,5,6,1]=>[3,3,1]
[5,6,4,1,3,7,2]=>[5,1,7,4,3,2,6]=>[3,7,1,4,5,6,2]=>[2,4,1]
[5,6,4,1,7,2,3]=>[6,1,7,4,3,2,5]=>[2,7,1,4,5,6,3]=>[2,4,1]
[5,6,4,1,7,3,2]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[1,5,1]
[5,6,4,2,1,3,7]=>[5,4,1,6,3,2,7]=>[3,4,7,2,5,6,1]=>[3,3,1]
[5,6,4,2,1,7,3]=>[4,1,7,5,3,2,6]=>[4,7,1,3,5,6,2]=>[2,4,1]
[5,6,4,2,3,1,7]=>[4,1,6,5,3,2,7]=>[4,7,2,3,5,6,1]=>[2,4,1]
[5,6,4,2,3,7,1]=>[4,1,5,3,2,7,6]=>[4,7,3,5,6,1,2]=>[2,3,2]
[5,6,4,2,7,1,3]=>[4,1,6,3,2,7,5]=>[4,7,2,5,6,1,3]=>[2,3,2]
[5,6,4,2,7,3,1]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[1,4,2]
[5,6,4,3,1,2,7]=>[5,1,6,4,3,2,7]=>[3,7,2,4,5,6,1]=>[2,4,1]
[5,6,4,3,1,7,2]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[1,5,1]
[5,6,4,3,2,1,7]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[1,5,1]
[5,6,4,3,2,7,1]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[1,4,2]
[5,6,4,3,7,1,2]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>[1,4,2]
[5,6,4,3,7,2,1]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[1,3,3]
[5,6,4,7,1,2,3]=>[5,1,6,3,2,7,4]=>[3,7,2,5,6,1,4]=>[2,3,2]
[5,6,4,7,1,3,2]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>[1,4,2]
[5,6,4,7,2,1,3]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>[1,4,2]
[5,6,4,7,2,3,1]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>[1,3,3]
[5,6,4,7,3,1,2]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>[1,3,3]
[5,6,4,7,3,2,1]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[1,2,4]
[5,6,7,1,2,3,4]=>[4,5,1,6,2,7,3]=>[4,3,7,2,6,1,5]=>[1,2,2,2]
[5,6,7,1,2,4,3]=>[7,4,1,5,2,6,3]=>[1,4,7,3,6,2,5]=>[3,2,2]
[5,6,7,1,3,2,4]=>[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]=>[3,2,2]
[5,6,7,1,3,4,2]=>[5,1,7,4,2,6,3]=>[3,7,1,4,6,2,5]=>[2,3,2]
[5,6,7,1,4,2,3]=>[6,1,7,4,2,5,3]=>[2,7,1,4,6,3,5]=>[2,3,2]
[5,6,7,1,4,3,2]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>[1,4,2]
[5,6,7,2,1,3,4]=>[5,4,1,6,2,7,3]=>[3,4,7,2,6,1,5]=>[3,2,2]
[5,6,7,2,1,4,3]=>[4,1,7,5,2,6,3]=>[4,7,1,3,6,2,5]=>[2,3,2]
[5,6,7,2,3,1,4]=>[4,1,6,5,2,7,3]=>[4,7,2,3,6,1,5]=>[2,3,2]
[5,6,7,2,3,4,1]=>[4,1,5,2,7,6,3]=>[4,7,3,6,1,2,5]=>[2,2,3]
[5,6,7,2,4,1,3]=>[4,1,6,2,7,5,3]=>[4,7,2,6,1,3,5]=>[2,2,3]
[5,6,7,2,4,3,1]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>[1,3,3]
[5,6,7,3,1,2,4]=>[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>[2,3,2]
[5,6,7,3,1,4,2]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>[1,4,2]
[5,6,7,3,2,1,4]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>[1,4,2]
[5,6,7,3,2,4,1]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>[1,3,3]
[5,6,7,3,4,1,2]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>[1,3,3]
[5,6,7,3,4,2,1]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>[1,2,4]
[5,6,7,4,1,2,3]=>[5,1,6,2,7,4,3]=>[3,7,2,6,1,4,5]=>[2,2,3]
[5,6,7,4,1,3,2]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>[1,3,3]
[5,6,7,4,2,1,3]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>[1,3,3]
[5,6,7,4,2,3,1]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>[1,2,4]
[5,6,7,4,3,1,2]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>[1,2,4]
[5,6,7,4,3,2,1]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[1,1,5]
[5,7,1,2,3,4,6]=>[3,4,5,1,6,7,2]=>[5,4,3,7,2,1,6]=>[1,1,2,1,2]
[5,7,1,2,3,6,4]=>[7,3,4,1,5,6,2]=>[1,5,4,7,3,2,6]=>[2,2,1,2]
[5,7,1,2,4,3,6]=>[6,3,4,1,5,7,2]=>[2,5,4,7,3,1,6]=>[2,2,1,2]
[5,7,1,2,4,6,3]=>[5,7,3,1,4,6,2]=>[3,1,5,7,4,2,6]=>[1,3,1,2]
[5,7,1,2,6,3,4]=>[6,7,3,1,4,5,2]=>[2,1,5,7,4,3,6]=>[1,3,1,2]
[5,7,1,2,6,4,3]=>[7,6,3,1,4,5,2]=>[1,2,5,7,4,3,6]=>[4,1,2]
[5,7,1,3,2,4,6]=>[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]=>[2,2,1,2]
[5,7,1,3,2,6,4]=>[4,7,3,1,5,6,2]=>[4,1,5,7,3,2,6]=>[1,3,1,2]
[5,7,1,3,4,2,6]=>[4,6,3,1,5,7,2]=>[4,2,5,7,3,1,6]=>[1,3,1,2]
[5,7,1,3,4,6,2]=>[4,5,1,7,3,6,2]=>[4,3,7,1,5,2,6]=>[1,2,2,2]
[5,7,1,3,6,2,4]=>[4,6,1,7,3,5,2]=>[4,2,7,1,5,3,6]=>[1,2,2,2]
[5,7,1,3,6,4,2]=>[7,4,1,6,3,5,2]=>[1,4,7,2,5,3,6]=>[3,2,2]
[5,7,1,4,2,3,6]=>[5,6,3,1,4,7,2]=>[3,2,5,7,4,1,6]=>[1,3,1,2]
[5,7,1,4,2,6,3]=>[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>[4,1,2]
[5,7,1,4,3,2,6]=>[6,5,3,1,4,7,2]=>[2,3,5,7,4,1,6]=>[4,1,2]
[5,7,1,4,3,6,2]=>[5,4,1,7,3,6,2]=>[3,4,7,1,5,2,6]=>[3,2,2]
[5,7,1,4,6,2,3]=>[6,4,1,7,3,5,2]=>[2,4,7,1,5,3,6]=>[3,2,2]
[5,7,1,4,6,3,2]=>[4,1,7,6,3,5,2]=>[4,7,1,2,5,3,6]=>[2,3,2]
[5,7,1,6,2,3,4]=>[5,6,1,7,3,4,2]=>[3,2,7,1,5,4,6]=>[1,2,2,2]
[5,7,1,6,2,4,3]=>[7,5,1,6,3,4,2]=>[1,3,7,2,5,4,6]=>[3,2,2]
[5,7,1,6,3,2,4]=>[6,5,1,7,3,4,2]=>[2,3,7,1,5,4,6]=>[3,2,2]
[5,7,1,6,3,4,2]=>[5,1,7,6,3,4,2]=>[3,7,1,2,5,4,6]=>[2,3,2]
[5,7,1,6,4,2,3]=>[6,1,7,5,3,4,2]=>[2,7,1,3,5,4,6]=>[2,3,2]
[5,7,1,6,4,3,2]=>[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>[1,4,2]
[5,7,2,1,3,4,6]=>[4,3,5,1,6,7,2]=>[4,5,3,7,2,1,6]=>[2,2,1,2]
[5,7,2,1,3,6,4]=>[3,7,4,1,5,6,2]=>[5,1,4,7,3,2,6]=>[1,3,1,2]
[5,7,2,1,4,3,6]=>[3,6,4,1,5,7,2]=>[5,2,4,7,3,1,6]=>[1,3,1,2]
[5,7,2,1,4,6,3]=>[3,5,1,7,4,6,2]=>[5,3,7,1,4,2,6]=>[1,2,2,2]
[5,7,2,1,6,3,4]=>[3,6,1,7,4,5,2]=>[5,2,7,1,4,3,6]=>[1,2,2,2]
[5,7,2,1,6,4,3]=>[7,3,1,6,4,5,2]=>[1,5,7,2,4,3,6]=>[3,2,2]
[5,7,2,3,1,4,6]=>[3,5,4,1,6,7,2]=>[5,3,4,7,2,1,6]=>[1,3,1,2]
[5,7,2,3,1,6,4]=>[3,4,1,7,5,6,2]=>[5,4,7,1,3,2,6]=>[1,2,2,2]
[5,7,2,3,4,1,6]=>[3,4,1,6,5,7,2]=>[5,4,7,2,3,1,6]=>[1,2,2,2]
[5,7,2,3,4,6,1]=>[3,4,1,5,7,6,2]=>[5,4,7,3,1,2,6]=>[1,2,1,3]
[5,7,2,3,6,1,4]=>[3,4,1,6,7,5,2]=>[5,4,7,2,1,3,6]=>[1,2,1,3]
[5,7,2,3,6,4,1]=>[7,3,1,4,6,5,2]=>[1,5,7,4,2,3,6]=>[3,1,3]
[5,7,2,4,1,3,6]=>[3,5,1,6,4,7,2]=>[5,3,7,2,4,1,6]=>[1,2,2,2]
[5,7,2,4,1,6,3]=>[7,3,1,5,4,6,2]=>[1,5,7,3,4,2,6]=>[3,2,2]
[5,7,2,4,3,1,6]=>[6,3,1,5,4,7,2]=>[2,5,7,3,4,1,6]=>[3,2,2]
[5,7,2,4,3,6,1]=>[5,3,1,4,7,6,2]=>[3,5,7,4,1,2,6]=>[3,1,3]
[5,7,2,4,6,1,3]=>[6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6]=>[3,1,3]
[5,7,2,4,6,3,1]=>[4,1,7,3,6,5,2]=>[4,7,1,5,2,3,6]=>[2,2,3]
[5,7,2,6,1,3,4]=>[3,5,1,6,7,4,2]=>[5,3,7,2,1,4,6]=>[1,2,1,3]
[5,7,2,6,1,4,3]=>[7,3,1,5,6,4,2]=>[1,5,7,3,2,4,6]=>[3,1,3]
[5,7,2,6,3,1,4]=>[6,3,1,5,7,4,2]=>[2,5,7,3,1,4,6]=>[3,1,3]
[5,7,2,6,3,4,1]=>[5,1,7,3,6,4,2]=>[3,7,1,5,2,4,6]=>[2,2,3]
[5,7,2,6,4,1,3]=>[6,1,7,3,5,4,2]=>[2,7,1,5,3,4,6]=>[2,2,3]
[5,7,2,6,4,3,1]=>[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>[1,3,3]
[5,7,3,1,2,4,6]=>[4,5,3,1,6,7,2]=>[4,3,5,7,2,1,6]=>[1,3,1,2]
[5,7,3,1,2,6,4]=>[7,4,3,1,5,6,2]=>[1,4,5,7,3,2,6]=>[4,1,2]
[5,7,3,1,4,2,6]=>[6,4,3,1,5,7,2]=>[2,4,5,7,3,1,6]=>[4,1,2]
[5,7,3,1,4,6,2]=>[5,3,1,7,4,6,2]=>[3,5,7,1,4,2,6]=>[3,2,2]
[5,7,3,1,6,2,4]=>[6,3,1,7,4,5,2]=>[2,5,7,1,4,3,6]=>[3,2,2]
[5,7,3,1,6,4,2]=>[3,1,7,6,4,5,2]=>[5,7,1,2,4,3,6]=>[2,3,2]
[5,7,3,2,1,4,6]=>[5,4,3,1,6,7,2]=>[3,4,5,7,2,1,6]=>[4,1,2]
[5,7,3,2,1,6,4]=>[4,3,1,7,5,6,2]=>[4,5,7,1,3,2,6]=>[3,2,2]
[5,7,3,2,4,1,6]=>[4,3,1,6,5,7,2]=>[4,5,7,2,3,1,6]=>[3,2,2]
[5,7,3,2,4,6,1]=>[4,3,1,5,7,6,2]=>[4,5,7,3,1,2,6]=>[3,1,3]
[5,7,3,2,6,1,4]=>[4,3,1,6,7,5,2]=>[4,5,7,2,1,3,6]=>[3,1,3]
[5,7,3,2,6,4,1]=>[3,1,7,4,6,5,2]=>[5,7,1,4,2,3,6]=>[2,2,3]
[5,7,3,4,1,2,6]=>[5,3,1,6,4,7,2]=>[3,5,7,2,4,1,6]=>[3,2,2]
[5,7,3,4,1,6,2]=>[3,1,7,5,4,6,2]=>[5,7,1,3,4,2,6]=>[2,3,2]
[5,7,3,4,2,1,6]=>[3,1,6,5,4,7,2]=>[5,7,2,3,4,1,6]=>[2,3,2]
[5,7,3,4,2,6,1]=>[3,1,5,4,7,6,2]=>[5,7,3,4,1,2,6]=>[2,2,3]
[5,7,3,4,6,1,2]=>[3,1,6,4,7,5,2]=>[5,7,2,4,1,3,6]=>[2,2,3]
[5,7,3,4,6,2,1]=>[3,1,4,7,6,5,2]=>[5,7,4,1,2,3,6]=>[2,1,4]
[5,7,3,6,1,2,4]=>[5,3,1,6,7,4,2]=>[3,5,7,2,1,4,6]=>[3,1,3]
[5,7,3,6,1,4,2]=>[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>[2,2,3]
[5,7,3,6,2,1,4]=>[3,1,6,5,7,4,2]=>[5,7,2,3,1,4,6]=>[2,2,3]
[5,7,3,6,2,4,1]=>[3,1,5,7,6,4,2]=>[5,7,3,1,2,4,6]=>[2,1,4]
[5,7,3,6,4,1,2]=>[3,1,6,7,5,4,2]=>[5,7,2,1,3,4,6]=>[2,1,4]
[5,7,3,6,4,2,1]=>[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>[1,2,4]
[5,7,4,1,2,3,6]=>[4,5,1,6,3,7,2]=>[4,3,7,2,5,1,6]=>[1,2,2,2]
[5,7,4,1,2,6,3]=>[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>[3,2,2]
[5,7,4,1,3,2,6]=>[6,4,1,5,3,7,2]=>[2,4,7,3,5,1,6]=>[3,2,2]
[5,7,4,1,3,6,2]=>[5,1,7,4,3,6,2]=>[3,7,1,4,5,2,6]=>[2,3,2]
[5,7,4,1,6,2,3]=>[6,1,7,4,3,5,2]=>[2,7,1,4,5,3,6]=>[2,3,2]
[5,7,4,1,6,3,2]=>[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>[1,4,2]
[5,7,4,2,1,3,6]=>[5,4,1,6,3,7,2]=>[3,4,7,2,5,1,6]=>[3,2,2]
[5,7,4,2,1,6,3]=>[4,1,7,5,3,6,2]=>[4,7,1,3,5,2,6]=>[2,3,2]
[5,7,4,2,3,1,6]=>[4,1,6,5,3,7,2]=>[4,7,2,3,5,1,6]=>[2,3,2]
[5,7,4,2,3,6,1]=>[4,1,5,3,7,6,2]=>[4,7,3,5,1,2,6]=>[2,2,3]
[5,7,4,2,6,1,3]=>[4,1,6,3,7,5,2]=>[4,7,2,5,1,3,6]=>[2,2,3]
[5,7,4,2,6,3,1]=>[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>[1,3,3]
[5,7,4,3,1,2,6]=>[5,1,6,4,3,7,2]=>[3,7,2,4,5,1,6]=>[2,3,2]
[5,7,4,3,1,6,2]=>[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>[1,4,2]
[5,7,4,3,2,1,6]=>[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>[1,4,2]
[5,7,4,3,2,6,1]=>[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>[1,3,3]
[5,7,4,3,6,1,2]=>[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>[1,3,3]
[5,7,4,3,6,2,1]=>[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>[1,2,4]
[5,7,4,6,1,2,3]=>[5,1,6,3,7,4,2]=>[3,7,2,5,1,4,6]=>[2,2,3]
[5,7,4,6,1,3,2]=>[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>[1,3,3]
[5,7,4,6,2,1,3]=>[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>[1,3,3]
[5,7,4,6,2,3,1]=>[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>[1,2,4]
[5,7,4,6,3,1,2]=>[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>[1,2,4]
[5,7,4,6,3,2,1]=>[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>[1,1,5]
[5,7,6,1,2,3,4]=>[4,5,1,6,7,3,2]=>[4,3,7,2,1,5,6]=>[1,2,1,3]
[5,7,6,1,2,4,3]=>[7,4,1,5,6,3,2]=>[1,4,7,3,2,5,6]=>[3,1,3]
[5,7,6,1,3,2,4]=>[6,4,1,5,7,3,2]=>[2,4,7,3,1,5,6]=>[3,1,3]
[5,7,6,1,3,4,2]=>[5,1,7,4,6,3,2]=>[3,7,1,4,2,5,6]=>[2,2,3]
[5,7,6,1,4,2,3]=>[6,1,7,4,5,3,2]=>[2,7,1,4,3,5,6]=>[2,2,3]
[5,7,6,1,4,3,2]=>[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>[1,3,3]
[5,7,6,2,1,3,4]=>[5,4,1,6,7,3,2]=>[3,4,7,2,1,5,6]=>[3,1,3]
[5,7,6,2,1,4,3]=>[4,1,7,5,6,3,2]=>[4,7,1,3,2,5,6]=>[2,2,3]
[5,7,6,2,3,1,4]=>[4,1,6,5,7,3,2]=>[4,7,2,3,1,5,6]=>[2,2,3]
[5,7,6,2,3,4,1]=>[4,1,5,7,6,3,2]=>[4,7,3,1,2,5,6]=>[2,1,4]
[5,7,6,2,4,1,3]=>[4,1,6,7,5,3,2]=>[4,7,2,1,3,5,6]=>[2,1,4]
[5,7,6,2,4,3,1]=>[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>[1,2,4]
[5,7,6,3,1,2,4]=>[5,1,6,4,7,3,2]=>[3,7,2,4,1,5,6]=>[2,2,3]
[5,7,6,3,1,4,2]=>[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>[1,3,3]
[5,7,6,3,2,1,4]=>[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>[1,3,3]
[5,7,6,3,2,4,1]=>[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>[1,2,4]
[5,7,6,3,4,1,2]=>[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>[1,2,4]
[5,7,6,3,4,2,1]=>[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>[1,1,5]
[5,7,6,4,1,2,3]=>[5,1,6,7,4,3,2]=>[3,7,2,1,4,5,6]=>[2,1,4]
[5,7,6,4,1,3,2]=>[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>[1,2,4]
[5,7,6,4,2,1,3]=>[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>[1,2,4]
[5,7,6,4,2,3,1]=>[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>[1,1,5]
[5,7,6,4,3,1,2]=>[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>[1,1,5]
[5,7,6,4,3,2,1]=>[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[2,5]
[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>[1,1,1,1,2,1]
[6,1,2,3,4,7,5]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>[2,1,1,2,1]
[6,1,2,3,5,4,7]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>[2,1,1,2,1]
[6,1,2,3,5,7,4]=>[5,7,2,3,4,1,6]=>[3,1,6,5,4,7,2]=>[1,2,1,2,1]
[6,1,2,3,7,4,5]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>[1,2,1,2,1]
[6,1,2,3,7,5,4]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>[3,1,2,1]
[6,1,2,4,3,5,7]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>[2,1,1,2,1]
[6,1,2,4,3,7,5]=>[4,7,2,3,5,1,6]=>[4,1,6,5,3,7,2]=>[1,2,1,2,1]
[6,1,2,4,5,3,7]=>[4,6,2,3,5,1,7]=>[4,2,6,5,3,7,1]=>[1,2,1,2,1]
[6,1,2,4,5,7,3]=>[4,5,7,2,3,1,6]=>[4,3,1,6,5,7,2]=>[1,1,2,2,1]
[6,1,2,4,7,3,5]=>[4,6,7,2,3,1,5]=>[4,2,1,6,5,7,3]=>[1,1,2,2,1]
[6,1,2,4,7,5,3]=>[7,4,6,2,3,1,5]=>[1,4,2,6,5,7,3]=>[2,2,2,1]
[6,1,2,5,3,4,7]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>[1,2,1,2,1]
[6,1,2,5,3,7,4]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>[3,1,2,1]
[6,1,2,5,4,3,7]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>[3,1,2,1]
[6,1,2,5,4,7,3]=>[5,4,7,2,3,1,6]=>[3,4,1,6,5,7,2]=>[2,2,2,1]
[6,1,2,5,7,3,4]=>[6,4,7,2,3,1,5]=>[2,4,1,6,5,7,3]=>[2,2,2,1]
[6,1,2,5,7,4,3]=>[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>[1,3,2,1]
[6,1,2,7,3,4,5]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>[1,1,2,2,1]
[6,1,2,7,3,5,4]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>[2,2,2,1]
[6,1,2,7,4,3,5]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>[2,2,2,1]
[6,1,2,7,4,5,3]=>[5,7,6,2,3,1,4]=>[3,1,2,6,5,7,4]=>[1,3,2,1]
[6,1,2,7,5,3,4]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>[1,3,2,1]
[6,1,2,7,5,4,3]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>[4,2,1]
[6,1,3,2,4,5,7]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>[2,1,1,2,1]
[6,1,3,2,4,7,5]=>[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>[1,2,1,2,1]
[6,1,3,2,5,4,7]=>[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>[1,2,1,2,1]
[6,1,3,2,5,7,4]=>[3,5,7,2,4,1,6]=>[5,3,1,6,4,7,2]=>[1,1,2,2,1]
[6,1,3,2,7,4,5]=>[3,6,7,2,4,1,5]=>[5,2,1,6,4,7,3]=>[1,1,2,2,1]
[6,1,3,2,7,5,4]=>[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>[2,2,2,1]
[6,1,3,4,2,5,7]=>[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>[1,2,1,2,1]
[6,1,3,4,2,7,5]=>[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>[1,1,2,2,1]
[6,1,3,4,5,2,7]=>[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>[1,1,2,2,1]
[6,1,3,4,5,7,2]=>[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>[1,1,1,3,1]
[6,1,3,4,7,2,5]=>[3,4,6,7,2,1,5]=>[5,4,2,1,6,7,3]=>[1,1,1,3,1]
[6,1,3,4,7,5,2]=>[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>[2,1,3,1]
[6,1,3,5,2,4,7]=>[3,5,6,2,4,1,7]=>[5,3,2,6,4,7,1]=>[1,1,2,2,1]
[6,1,3,5,2,7,4]=>[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>[2,2,2,1]
[6,1,3,5,4,2,7]=>[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>[2,2,2,1]
[6,1,3,5,4,7,2]=>[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>[2,1,3,1]
[6,1,3,5,7,2,4]=>[6,3,4,7,2,1,5]=>[2,5,4,1,6,7,3]=>[2,1,3,1]
[6,1,3,5,7,4,2]=>[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>[1,2,3,1]
[6,1,3,7,2,4,5]=>[3,5,6,7,2,1,4]=>[5,3,2,1,6,7,4]=>[1,1,1,3,1]
[6,1,3,7,2,5,4]=>[7,3,5,6,2,1,4]=>[1,5,3,2,6,7,4]=>[2,1,3,1]
[6,1,3,7,4,2,5]=>[6,3,5,7,2,1,4]=>[2,5,3,1,6,7,4]=>[2,1,3,1]
[6,1,3,7,4,5,2]=>[5,7,3,6,2,1,4]=>[3,1,5,2,6,7,4]=>[1,2,3,1]
[6,1,3,7,5,2,4]=>[6,7,3,5,2,1,4]=>[2,1,5,3,6,7,4]=>[1,2,3,1]
[6,1,3,7,5,4,2]=>[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>[3,3,1]
[6,1,4,2,3,5,7]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>[1,2,1,2,1]
[6,1,4,2,3,7,5]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>[3,1,2,1]
[6,1,4,2,5,3,7]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>[3,1,2,1]
[6,1,4,2,5,7,3]=>[5,3,7,2,4,1,6]=>[3,5,1,6,4,7,2]=>[2,2,2,1]
[6,1,4,2,7,3,5]=>[6,3,7,2,4,1,5]=>[2,5,1,6,4,7,3]=>[2,2,2,1]
[6,1,4,2,7,5,3]=>[3,7,6,2,4,1,5]=>[5,1,2,6,4,7,3]=>[1,3,2,1]
[6,1,4,3,2,5,7]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>[3,1,2,1]
[6,1,4,3,2,7,5]=>[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>[2,2,2,1]
[6,1,4,3,5,2,7]=>[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>[2,2,2,1]
[6,1,4,3,5,7,2]=>[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>[2,1,3,1]
[6,1,4,3,7,2,5]=>[4,3,6,7,2,1,5]=>[4,5,2,1,6,7,3]=>[2,1,3,1]
[6,1,4,3,7,5,2]=>[3,7,4,6,2,1,5]=>[5,1,4,2,6,7,3]=>[1,2,3,1]
[6,1,4,5,2,3,7]=>[5,3,6,2,4,1,7]=>[3,5,2,6,4,7,1]=>[2,2,2,1]
[6,1,4,5,2,7,3]=>[3,7,5,2,4,1,6]=>[5,1,3,6,4,7,2]=>[1,3,2,1]
[6,1,4,5,3,2,7]=>[3,6,5,2,4,1,7]=>[5,2,3,6,4,7,1]=>[1,3,2,1]
[6,1,4,5,3,7,2]=>[3,5,4,7,2,1,6]=>[5,3,4,1,6,7,2]=>[1,2,3,1]
[6,1,4,5,7,2,3]=>[3,6,4,7,2,1,5]=>[5,2,4,1,6,7,3]=>[1,2,3,1]
[6,1,4,5,7,3,2]=>[3,4,7,6,2,1,5]=>[5,4,1,2,6,7,3]=>[1,1,4,1]
[6,1,4,7,2,3,5]=>[5,3,6,7,2,1,4]=>[3,5,2,1,6,7,4]=>[2,1,3,1]
[6,1,4,7,2,5,3]=>[3,7,5,6,2,1,4]=>[5,1,3,2,6,7,4]=>[1,2,3,1]
[6,1,4,7,3,2,5]=>[3,6,5,7,2,1,4]=>[5,2,3,1,6,7,4]=>[1,2,3,1]
[6,1,4,7,3,5,2]=>[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>[1,1,4,1]
[6,1,4,7,5,2,3]=>[3,6,7,5,2,1,4]=>[5,2,1,3,6,7,4]=>[1,1,4,1]
[6,1,4,7,5,3,2]=>[7,3,6,5,2,1,4]=>[1,5,2,3,6,7,4]=>[2,4,1]
[6,1,5,2,3,4,7]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>[1,1,2,2,1]
[6,1,5,2,3,7,4]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>[2,2,2,1]
[6,1,5,2,4,3,7]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>[2,2,2,1]
[6,1,5,2,4,7,3]=>[5,7,4,2,3,1,6]=>[3,1,4,6,5,7,2]=>[1,3,2,1]
[6,1,5,2,7,3,4]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>[1,3,2,1]
[6,1,5,2,7,4,3]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>[4,2,1]
[6,1,5,3,2,4,7]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>[2,2,2,1]
[6,1,5,3,2,7,4]=>[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>[1,3,2,1]
[6,1,5,3,4,2,7]=>[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>[1,3,2,1]
[6,1,5,3,4,7,2]=>[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>[1,2,3,1]
[6,1,5,3,7,2,4]=>[4,6,3,7,2,1,5]=>[4,2,5,1,6,7,3]=>[1,2,3,1]
[6,1,5,3,7,4,2]=>[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>[3,3,1]
[6,1,5,4,2,3,7]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>[1,3,2,1]
[6,1,5,4,2,7,3]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>[4,2,1]
[6,1,5,4,3,2,7]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>[4,2,1]
[6,1,5,4,3,7,2]=>[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>[3,3,1]
[6,1,5,4,7,2,3]=>[6,4,3,7,2,1,5]=>[2,4,5,1,6,7,3]=>[3,3,1]
[6,1,5,4,7,3,2]=>[4,3,7,6,2,1,5]=>[4,5,1,2,6,7,3]=>[2,4,1]
[6,1,5,7,2,3,4]=>[5,6,3,7,2,1,4]=>[3,2,5,1,6,7,4]=>[1,2,3,1]
[6,1,5,7,2,4,3]=>[7,5,3,6,2,1,4]=>[1,3,5,2,6,7,4]=>[3,3,1]
[6,1,5,7,3,2,4]=>[6,5,3,7,2,1,4]=>[2,3,5,1,6,7,4]=>[3,3,1]
[6,1,5,7,3,4,2]=>[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>[2,4,1]
[6,1,5,7,4,2,3]=>[6,3,7,5,2,1,4]=>[2,5,1,3,6,7,4]=>[2,4,1]
[6,1,5,7,4,3,2]=>[3,7,6,5,2,1,4]=>[5,1,2,3,6,7,4]=>[1,5,1]
[6,1,7,2,3,4,5]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>[1,1,1,3,1]
[6,1,7,2,3,5,4]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>[2,1,3,1]
[6,1,7,2,4,3,5]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>[2,1,3,1]
[6,1,7,2,4,5,3]=>[5,7,4,6,2,1,3]=>[3,1,4,2,6,7,5]=>[1,2,3,1]
[6,1,7,2,5,3,4]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>[1,2,3,1]
[6,1,7,2,5,4,3]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>[3,3,1]
[6,1,7,3,2,4,5]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>[2,1,3,1]
[6,1,7,3,2,5,4]=>[4,7,5,6,2,1,3]=>[4,1,3,2,6,7,5]=>[1,2,3,1]
[6,1,7,3,4,2,5]=>[4,6,5,7,2,1,3]=>[4,2,3,1,6,7,5]=>[1,2,3,1]
[6,1,7,3,4,5,2]=>[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>[1,1,4,1]
[6,1,7,3,5,2,4]=>[4,6,7,5,2,1,3]=>[4,2,1,3,6,7,5]=>[1,1,4,1]
[6,1,7,3,5,4,2]=>[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>[2,4,1]
[6,1,7,4,2,3,5]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>[1,2,3,1]
[6,1,7,4,2,5,3]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>[3,3,1]
[6,1,7,4,3,2,5]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>[3,3,1]
[6,1,7,4,3,5,2]=>[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>[2,4,1]
[6,1,7,4,5,2,3]=>[6,4,7,5,2,1,3]=>[2,4,1,3,6,7,5]=>[2,4,1]
[6,1,7,4,5,3,2]=>[4,7,6,5,2,1,3]=>[4,1,2,3,6,7,5]=>[1,5,1]
[6,1,7,5,2,3,4]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>[1,1,4,1]
[6,1,7,5,2,4,3]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>[2,4,1]
[6,1,7,5,3,2,4]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>[2,4,1]
[6,1,7,5,3,4,2]=>[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>[1,5,1]
[6,1,7,5,4,2,3]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>[1,5,1]
[6,1,7,5,4,3,2]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[6,1]
[6,2,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>[2,1,1,2,1]
[6,2,1,3,4,7,5]=>[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>[1,2,1,2,1]
[6,2,1,3,5,4,7]=>[2,6,3,4,5,1,7]=>[6,2,5,4,3,7,1]=>[1,2,1,2,1]
[6,2,1,3,5,7,4]=>[2,5,7,3,4,1,6]=>[6,3,1,5,4,7,2]=>[1,1,2,2,1]
[6,2,1,3,7,4,5]=>[2,6,7,3,4,1,5]=>[6,2,1,5,4,7,3]=>[1,1,2,2,1]
[6,2,1,3,7,5,4]=>[7,2,6,3,4,1,5]=>[1,6,2,5,4,7,3]=>[2,2,2,1]
[6,2,1,4,3,5,7]=>[2,5,3,4,6,1,7]=>[6,3,5,4,2,7,1]=>[1,2,1,2,1]
[6,2,1,4,3,7,5]=>[2,4,7,3,5,1,6]=>[6,4,1,5,3,7,2]=>[1,1,2,2,1]
[6,2,1,4,5,3,7]=>[2,4,6,3,5,1,7]=>[6,4,2,5,3,7,1]=>[1,1,2,2,1]
[6,2,1,4,5,7,3]=>[2,4,5,7,3,1,6]=>[6,4,3,1,5,7,2]=>[1,1,1,3,1]
[6,2,1,4,7,3,5]=>[2,4,6,7,3,1,5]=>[6,4,2,1,5,7,3]=>[1,1,1,3,1]
[6,2,1,4,7,5,3]=>[7,2,4,6,3,1,5]=>[1,6,4,2,5,7,3]=>[2,1,3,1]
[6,2,1,5,3,4,7]=>[2,5,6,3,4,1,7]=>[6,3,2,5,4,7,1]=>[1,1,2,2,1]
[6,2,1,5,3,7,4]=>[7,2,5,3,4,1,6]=>[1,6,3,5,4,7,2]=>[2,2,2,1]
[6,2,1,5,4,3,7]=>[6,2,5,3,4,1,7]=>[2,6,3,5,4,7,1]=>[2,2,2,1]
[6,2,1,5,4,7,3]=>[5,2,4,7,3,1,6]=>[3,6,4,1,5,7,2]=>[2,1,3,1]
[6,2,1,5,7,3,4]=>[6,2,4,7,3,1,5]=>[2,6,4,1,5,7,3]=>[2,1,3,1]
[6,2,1,5,7,4,3]=>[4,7,2,6,3,1,5]=>[4,1,6,2,5,7,3]=>[1,2,3,1]
[6,2,1,7,3,4,5]=>[2,5,6,7,3,1,4]=>[6,3,2,1,5,7,4]=>[1,1,1,3,1]
[6,2,1,7,3,5,4]=>[7,2,5,6,3,1,4]=>[1,6,3,2,5,7,4]=>[2,1,3,1]
[6,2,1,7,4,3,5]=>[6,2,5,7,3,1,4]=>[2,6,3,1,5,7,4]=>[2,1,3,1]
[6,2,1,7,4,5,3]=>[5,7,2,6,3,1,4]=>[3,1,6,2,5,7,4]=>[1,2,3,1]
[6,2,1,7,5,3,4]=>[6,7,2,5,3,1,4]=>[2,1,6,3,5,7,4]=>[1,2,3,1]
[6,2,1,7,5,4,3]=>[7,6,2,5,3,1,4]=>[1,2,6,3,5,7,4]=>[3,3,1]
[6,2,3,1,4,5,7]=>[2,4,3,5,6,1,7]=>[6,4,5,3,2,7,1]=>[1,2,1,2,1]
[6,2,3,1,4,7,5]=>[2,3,7,4,5,1,6]=>[6,5,1,4,3,7,2]=>[1,1,2,2,1]
[6,2,3,1,5,4,7]=>[2,3,6,4,5,1,7]=>[6,5,2,4,3,7,1]=>[1,1,2,2,1]
[6,2,3,1,5,7,4]=>[2,3,5,7,4,1,6]=>[6,5,3,1,4,7,2]=>[1,1,1,3,1]
[6,2,3,1,7,4,5]=>[2,3,6,7,4,1,5]=>[6,5,2,1,4,7,3]=>[1,1,1,3,1]
[6,2,3,1,7,5,4]=>[7,2,3,6,4,1,5]=>[1,6,5,2,4,7,3]=>[2,1,3,1]
[6,2,3,4,1,5,7]=>[2,3,5,4,6,1,7]=>[6,5,3,4,2,7,1]=>[1,1,2,2,1]
[6,2,3,4,1,7,5]=>[2,3,4,7,5,1,6]=>[6,5,4,1,3,7,2]=>[1,1,1,3,1]
[6,2,3,4,5,1,7]=>[2,3,4,6,5,1,7]=>[6,5,4,2,3,7,1]=>[1,1,1,3,1]
[6,2,3,4,5,7,1]=>[2,3,4,5,1,7,6]=>[6,5,4,3,7,1,2]=>[1,1,1,2,2]
[6,2,3,4,7,1,5]=>[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]=>[1,1,1,2,2]
[6,2,3,4,7,5,1]=>[7,2,3,4,1,6,5]=>[1,6,5,4,7,2,3]=>[2,1,2,2]
[6,2,3,5,1,4,7]=>[2,3,5,6,4,1,7]=>[6,5,3,2,4,7,1]=>[1,1,1,3,1]
[6,2,3,5,1,7,4]=>[7,2,3,5,4,1,6]=>[1,6,5,3,4,7,2]=>[2,1,3,1]
[6,2,3,5,4,1,7]=>[6,2,3,5,4,1,7]=>[2,6,5,3,4,7,1]=>[2,1,3,1]
[6,2,3,5,4,7,1]=>[5,2,3,4,1,7,6]=>[3,6,5,4,7,1,2]=>[2,1,2,2]
[6,2,3,5,7,1,4]=>[6,2,3,4,1,7,5]=>[2,6,5,4,7,1,3]=>[2,1,2,2]
[6,2,3,5,7,4,1]=>[4,7,2,3,1,6,5]=>[4,1,6,5,7,2,3]=>[1,2,2,2]
[6,2,3,7,1,4,5]=>[2,3,5,6,1,7,4]=>[6,5,3,2,7,1,4]=>[1,1,1,2,2]
[6,2,3,7,1,5,4]=>[7,2,3,5,1,6,4]=>[1,6,5,3,7,2,4]=>[2,1,2,2]
[6,2,3,7,4,1,5]=>[6,2,3,5,1,7,4]=>[2,6,5,3,7,1,4]=>[2,1,2,2]
[6,2,3,7,4,5,1]=>[5,7,2,3,1,6,4]=>[3,1,6,5,7,2,4]=>[1,2,2,2]
[6,2,3,7,5,1,4]=>[6,7,2,3,1,5,4]=>[2,1,6,5,7,3,4]=>[1,2,2,2]
[6,2,3,7,5,4,1]=>[7,6,2,3,1,5,4]=>[1,2,6,5,7,3,4]=>[3,2,2]
[6,2,4,1,3,5,7]=>[2,4,5,3,6,1,7]=>[6,4,3,5,2,7,1]=>[1,1,2,2,1]
[6,2,4,1,3,7,5]=>[7,2,4,3,5,1,6]=>[1,6,4,5,3,7,2]=>[2,2,2,1]
[6,2,4,1,5,3,7]=>[6,2,4,3,5,1,7]=>[2,6,4,5,3,7,1]=>[2,2,2,1]
[6,2,4,1,5,7,3]=>[5,2,3,7,4,1,6]=>[3,6,5,1,4,7,2]=>[2,1,3,1]
[6,2,4,1,7,3,5]=>[6,2,3,7,4,1,5]=>[2,6,5,1,4,7,3]=>[2,1,3,1]
[6,2,4,1,7,5,3]=>[3,7,2,6,4,1,5]=>[5,1,6,2,4,7,3]=>[1,2,3,1]
[6,2,4,3,1,5,7]=>[5,2,4,3,6,1,7]=>[3,6,4,5,2,7,1]=>[2,2,2,1]
[6,2,4,3,1,7,5]=>[4,2,3,7,5,1,6]=>[4,6,5,1,3,7,2]=>[2,1,3,1]
[6,2,4,3,5,1,7]=>[4,2,3,6,5,1,7]=>[4,6,5,2,3,7,1]=>[2,1,3,1]
[6,2,4,3,5,7,1]=>[4,2,3,5,1,7,6]=>[4,6,5,3,7,1,2]=>[2,1,2,2]
[6,2,4,3,7,1,5]=>[4,2,3,6,1,7,5]=>[4,6,5,2,7,1,3]=>[2,1,2,2]
[6,2,4,3,7,5,1]=>[3,7,2,4,1,6,5]=>[5,1,6,4,7,2,3]=>[1,2,2,2]
[6,2,4,5,1,3,7]=>[5,2,3,6,4,1,7]=>[3,6,5,2,4,7,1]=>[2,1,3,1]
[6,2,4,5,1,7,3]=>[3,7,2,5,4,1,6]=>[5,1,6,3,4,7,2]=>[1,2,3,1]
[6,2,4,5,3,1,7]=>[3,6,2,5,4,1,7]=>[5,2,6,3,4,7,1]=>[1,2,3,1]
[6,2,4,5,3,7,1]=>[3,5,2,4,1,7,6]=>[5,3,6,4,7,1,2]=>[1,2,2,2]
[6,2,4,5,7,1,3]=>[3,6,2,4,1,7,5]=>[5,2,6,4,7,1,3]=>[1,2,2,2]
[6,2,4,5,7,3,1]=>[3,4,7,2,1,6,5]=>[5,4,1,6,7,2,3]=>[1,1,3,2]
[6,2,4,7,1,3,5]=>[5,2,3,6,1,7,4]=>[3,6,5,2,7,1,4]=>[2,1,2,2]
[6,2,4,7,1,5,3]=>[3,7,2,5,1,6,4]=>[5,1,6,3,7,2,4]=>[1,2,2,2]
[6,2,4,7,3,1,5]=>[3,6,2,5,1,7,4]=>[5,2,6,3,7,1,4]=>[1,2,2,2]
[6,2,4,7,3,5,1]=>[3,5,7,2,1,6,4]=>[5,3,1,6,7,2,4]=>[1,1,3,2]
[6,2,4,7,5,1,3]=>[3,6,7,2,1,5,4]=>[5,2,1,6,7,3,4]=>[1,1,3,2]
[6,2,4,7,5,3,1]=>[7,3,6,2,1,5,4]=>[1,5,2,6,7,3,4]=>[2,3,2]
[6,2,5,1,3,4,7]=>[2,4,5,6,3,1,7]=>[6,4,3,2,5,7,1]=>[1,1,1,3,1]
[6,2,5,1,3,7,4]=>[7,2,4,5,3,1,6]=>[1,6,4,3,5,7,2]=>[2,1,3,1]
[6,2,5,1,4,3,7]=>[6,2,4,5,3,1,7]=>[2,6,4,3,5,7,1]=>[2,1,3,1]
[6,2,5,1,4,7,3]=>[5,7,2,4,3,1,6]=>[3,1,6,4,5,7,2]=>[1,2,3,1]
[6,2,5,1,7,3,4]=>[6,7,2,4,3,1,5]=>[2,1,6,4,5,7,3]=>[1,2,3,1]
[6,2,5,1,7,4,3]=>[7,6,2,4,3,1,5]=>[1,2,6,4,5,7,3]=>[3,3,1]
[6,2,5,3,1,4,7]=>[5,2,4,6,3,1,7]=>[3,6,4,2,5,7,1]=>[2,1,3,1]
[6,2,5,3,1,7,4]=>[4,7,2,5,3,1,6]=>[4,1,6,3,5,7,2]=>[1,2,3,1]
[6,2,5,3,4,1,7]=>[4,6,2,5,3,1,7]=>[4,2,6,3,5,7,1]=>[1,2,3,1]
[6,2,5,3,4,7,1]=>[4,5,2,3,1,7,6]=>[4,3,6,5,7,1,2]=>[1,2,2,2]
[6,2,5,3,7,1,4]=>[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>[1,2,2,2]
[6,2,5,3,7,4,1]=>[7,4,2,3,1,6,5]=>[1,4,6,5,7,2,3]=>[3,2,2]
[6,2,5,4,1,3,7]=>[5,6,2,4,3,1,7]=>[3,2,6,4,5,7,1]=>[1,2,3,1]
[6,2,5,4,1,7,3]=>[7,5,2,4,3,1,6]=>[1,3,6,4,5,7,2]=>[3,3,1]
[6,2,5,4,3,1,7]=>[6,5,2,4,3,1,7]=>[2,3,6,4,5,7,1]=>[3,3,1]
[6,2,5,4,3,7,1]=>[5,4,2,3,1,7,6]=>[3,4,6,5,7,1,2]=>[3,2,2]
[6,2,5,4,7,1,3]=>[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>[3,2,2]
[6,2,5,4,7,3,1]=>[4,3,7,2,1,6,5]=>[4,5,1,6,7,2,3]=>[2,3,2]
[6,2,5,7,1,3,4]=>[5,6,2,3,1,7,4]=>[3,2,6,5,7,1,4]=>[1,2,2,2]
[6,2,5,7,1,4,3]=>[7,5,2,3,1,6,4]=>[1,3,6,5,7,2,4]=>[3,2,2]
[6,2,5,7,3,1,4]=>[6,5,2,3,1,7,4]=>[2,3,6,5,7,1,4]=>[3,2,2]
[6,2,5,7,3,4,1]=>[5,3,7,2,1,6,4]=>[3,5,1,6,7,2,4]=>[2,3,2]
[6,2,5,7,4,1,3]=>[6,3,7,2,1,5,4]=>[2,5,1,6,7,3,4]=>[2,3,2]
[6,2,5,7,4,3,1]=>[3,7,6,2,1,5,4]=>[5,1,2,6,7,3,4]=>[1,4,2]
[6,2,7,1,3,4,5]=>[2,4,5,6,1,7,3]=>[6,4,3,2,7,1,5]=>[1,1,1,2,2]
[6,2,7,1,3,5,4]=>[7,2,4,5,1,6,3]=>[1,6,4,3,7,2,5]=>[2,1,2,2]
[6,2,7,1,4,3,5]=>[6,2,4,5,1,7,3]=>[2,6,4,3,7,1,5]=>[2,1,2,2]
[6,2,7,1,4,5,3]=>[5,7,2,4,1,6,3]=>[3,1,6,4,7,2,5]=>[1,2,2,2]
[6,2,7,1,5,3,4]=>[6,7,2,4,1,5,3]=>[2,1,6,4,7,3,5]=>[1,2,2,2]
[6,2,7,1,5,4,3]=>[7,6,2,4,1,5,3]=>[1,2,6,4,7,3,5]=>[3,2,2]
[6,2,7,3,1,4,5]=>[5,2,4,6,1,7,3]=>[3,6,4,2,7,1,5]=>[2,1,2,2]
[6,2,7,3,1,5,4]=>[4,7,2,5,1,6,3]=>[4,1,6,3,7,2,5]=>[1,2,2,2]
[6,2,7,3,4,1,5]=>[4,6,2,5,1,7,3]=>[4,2,6,3,7,1,5]=>[1,2,2,2]
[6,2,7,3,4,5,1]=>[4,5,7,2,1,6,3]=>[4,3,1,6,7,2,5]=>[1,1,3,2]
[6,2,7,3,5,1,4]=>[4,6,7,2,1,5,3]=>[4,2,1,6,7,3,5]=>[1,1,3,2]
[6,2,7,3,5,4,1]=>[7,4,6,2,1,5,3]=>[1,4,2,6,7,3,5]=>[2,3,2]
[6,2,7,4,1,3,5]=>[5,6,2,4,1,7,3]=>[3,2,6,4,7,1,5]=>[1,2,2,2]
[6,2,7,4,1,5,3]=>[7,5,2,4,1,6,3]=>[1,3,6,4,7,2,5]=>[3,2,2]
[6,2,7,4,3,1,5]=>[6,5,2,4,1,7,3]=>[2,3,6,4,7,1,5]=>[3,2,2]
[6,2,7,4,3,5,1]=>[5,4,7,2,1,6,3]=>[3,4,1,6,7,2,5]=>[2,3,2]
[6,2,7,4,5,1,3]=>[6,4,7,2,1,5,3]=>[2,4,1,6,7,3,5]=>[2,3,2]
[6,2,7,4,5,3,1]=>[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>[1,4,2]
[6,2,7,5,1,3,4]=>[5,6,7,2,1,4,3]=>[3,2,1,6,7,4,5]=>[1,1,3,2]
[6,2,7,5,1,4,3]=>[7,5,6,2,1,4,3]=>[1,3,2,6,7,4,5]=>[2,3,2]
[6,2,7,5,3,1,4]=>[6,5,7,2,1,4,3]=>[2,3,1,6,7,4,5]=>[2,3,2]
[6,2,7,5,3,4,1]=>[5,7,6,2,1,4,3]=>[3,1,2,6,7,4,5]=>[1,4,2]
[6,2,7,5,4,1,3]=>[6,7,5,2,1,4,3]=>[2,1,3,6,7,4,5]=>[1,4,2]
[6,2,7,5,4,3,1]=>[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>[5,2]
[6,3,1,2,4,5,7]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>[1,2,1,2,1]
[6,3,1,2,4,7,5]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>[3,1,2,1]
[6,3,1,2,5,4,7]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>[3,1,2,1]
[6,3,1,2,5,7,4]=>[5,2,7,3,4,1,6]=>[3,6,1,5,4,7,2]=>[2,2,2,1]
[6,3,1,2,7,4,5]=>[6,2,7,3,4,1,5]=>[2,6,1,5,4,7,3]=>[2,2,2,1]
[6,3,1,2,7,5,4]=>[2,7,6,3,4,1,5]=>[6,1,2,5,4,7,3]=>[1,3,2,1]
[6,3,1,4,2,5,7]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>[3,1,2,1]
[6,3,1,4,2,7,5]=>[4,2,7,3,5,1,6]=>[4,6,1,5,3,7,2]=>[2,2,2,1]
[6,3,1,4,5,2,7]=>[4,2,6,3,5,1,7]=>[4,6,2,5,3,7,1]=>[2,2,2,1]
[6,3,1,4,5,7,2]=>[4,2,5,7,3,1,6]=>[4,6,3,1,5,7,2]=>[2,1,3,1]
[6,3,1,4,7,2,5]=>[4,2,6,7,3,1,5]=>[4,6,2,1,5,7,3]=>[2,1,3,1]
[6,3,1,4,7,5,2]=>[2,7,4,6,3,1,5]=>[6,1,4,2,5,7,3]=>[1,2,3,1]
[6,3,1,5,2,4,7]=>[5,2,6,3,4,1,7]=>[3,6,2,5,4,7,1]=>[2,2,2,1]
[6,3,1,5,2,7,4]=>[2,7,5,3,4,1,6]=>[6,1,3,5,4,7,2]=>[1,3,2,1]
[6,3,1,5,4,2,7]=>[2,6,5,3,4,1,7]=>[6,2,3,5,4,7,1]=>[1,3,2,1]
[6,3,1,5,4,7,2]=>[2,5,4,7,3,1,6]=>[6,3,4,1,5,7,2]=>[1,2,3,1]
[6,3,1,5,7,2,4]=>[2,6,4,7,3,1,5]=>[6,2,4,1,5,7,3]=>[1,2,3,1]
[6,3,1,5,7,4,2]=>[2,4,7,6,3,1,5]=>[6,4,1,2,5,7,3]=>[1,1,4,1]
[6,3,1,7,2,4,5]=>[5,2,6,7,3,1,4]=>[3,6,2,1,5,7,4]=>[2,1,3,1]
[6,3,1,7,2,5,4]=>[2,7,5,6,3,1,4]=>[6,1,3,2,5,7,4]=>[1,2,3,1]
[6,3,1,7,4,2,5]=>[2,6,5,7,3,1,4]=>[6,2,3,1,5,7,4]=>[1,2,3,1]
[6,3,1,7,4,5,2]=>[2,5,7,6,3,1,4]=>[6,3,1,2,5,7,4]=>[1,1,4,1]
[6,3,1,7,5,2,4]=>[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>[1,1,4,1]
[6,3,1,7,5,4,2]=>[7,2,6,5,3,1,4]=>[1,6,2,3,5,7,4]=>[2,4,1]
[6,3,2,1,4,5,7]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>[3,1,2,1]
[6,3,2,1,4,7,5]=>[3,2,7,4,5,1,6]=>[5,6,1,4,3,7,2]=>[2,2,2,1]
[6,3,2,1,5,4,7]=>[3,2,6,4,5,1,7]=>[5,6,2,4,3,7,1]=>[2,2,2,1]
[6,3,2,1,5,7,4]=>[3,2,5,7,4,1,6]=>[5,6,3,1,4,7,2]=>[2,1,3,1]
[6,3,2,1,7,4,5]=>[3,2,6,7,4,1,5]=>[5,6,2,1,4,7,3]=>[2,1,3,1]
[6,3,2,1,7,5,4]=>[2,7,3,6,4,1,5]=>[6,1,5,2,4,7,3]=>[1,2,3,1]
[6,3,2,4,1,5,7]=>[3,2,5,4,6,1,7]=>[5,6,3,4,2,7,1]=>[2,2,2,1]
[6,3,2,4,1,7,5]=>[3,2,4,7,5,1,6]=>[5,6,4,1,3,7,2]=>[2,1,3,1]
[6,3,2,4,5,1,7]=>[3,2,4,6,5,1,7]=>[5,6,4,2,3,7,1]=>[2,1,3,1]
[6,3,2,4,5,7,1]=>[3,2,4,5,1,7,6]=>[5,6,4,3,7,1,2]=>[2,1,2,2]
[6,3,2,4,7,1,5]=>[3,2,4,6,1,7,5]=>[5,6,4,2,7,1,3]=>[2,1,2,2]
[6,3,2,4,7,5,1]=>[2,7,3,4,1,6,5]=>[6,1,5,4,7,2,3]=>[1,2,2,2]
[6,3,2,5,1,4,7]=>[3,2,5,6,4,1,7]=>[5,6,3,2,4,7,1]=>[2,1,3,1]
[6,3,2,5,1,7,4]=>[2,7,3,5,4,1,6]=>[6,1,5,3,4,7,2]=>[1,2,3,1]
[6,3,2,5,4,1,7]=>[2,6,3,5,4,1,7]=>[6,2,5,3,4,7,1]=>[1,2,3,1]
[6,3,2,5,4,7,1]=>[2,5,3,4,1,7,6]=>[6,3,5,4,7,1,2]=>[1,2,2,2]
[6,3,2,5,7,1,4]=>[2,6,3,4,1,7,5]=>[6,2,5,4,7,1,3]=>[1,2,2,2]
[6,3,2,5,7,4,1]=>[2,4,7,3,1,6,5]=>[6,4,1,5,7,2,3]=>[1,1,3,2]
[6,3,2,7,1,4,5]=>[3,2,5,6,1,7,4]=>[5,6,3,2,7,1,4]=>[2,1,2,2]
[6,3,2,7,1,5,4]=>[2,7,3,5,1,6,4]=>[6,1,5,3,7,2,4]=>[1,2,2,2]
[6,3,2,7,4,1,5]=>[2,6,3,5,1,7,4]=>[6,2,5,3,7,1,4]=>[1,2,2,2]
[6,3,2,7,4,5,1]=>[2,5,7,3,1,6,4]=>[6,3,1,5,7,2,4]=>[1,1,3,2]
[6,3,2,7,5,1,4]=>[2,6,7,3,1,5,4]=>[6,2,1,5,7,3,4]=>[1,1,3,2]
[6,3,2,7,5,4,1]=>[7,2,6,3,1,5,4]=>[1,6,2,5,7,3,4]=>[2,3,2]
[6,3,4,1,2,5,7]=>[4,2,5,3,6,1,7]=>[4,6,3,5,2,7,1]=>[2,2,2,1]
[6,3,4,1,2,7,5]=>[2,7,4,3,5,1,6]=>[6,1,4,5,3,7,2]=>[1,3,2,1]
[6,3,4,1,5,2,7]=>[2,6,4,3,5,1,7]=>[6,2,4,5,3,7,1]=>[1,3,2,1]
[6,3,4,1,5,7,2]=>[2,5,3,7,4,1,6]=>[6,3,5,1,4,7,2]=>[1,2,3,1]
[6,3,4,1,7,2,5]=>[2,6,3,7,4,1,5]=>[6,2,5,1,4,7,3]=>[1,2,3,1]
[6,3,4,1,7,5,2]=>[2,3,7,6,4,1,5]=>[6,5,1,2,4,7,3]=>[1,1,4,1]
[6,3,4,2,1,5,7]=>[2,5,4,3,6,1,7]=>[6,3,4,5,2,7,1]=>[1,3,2,1]
[6,3,4,2,1,7,5]=>[2,4,3,7,5,1,6]=>[6,4,5,1,3,7,2]=>[1,2,3,1]
[6,3,4,2,5,1,7]=>[2,4,3,6,5,1,7]=>[6,4,5,2,3,7,1]=>[1,2,3,1]
[6,3,4,2,5,7,1]=>[2,4,3,5,1,7,6]=>[6,4,5,3,7,1,2]=>[1,2,2,2]
[6,3,4,2,7,1,5]=>[2,4,3,6,1,7,5]=>[6,4,5,2,7,1,3]=>[1,2,2,2]
[6,3,4,2,7,5,1]=>[2,3,7,4,1,6,5]=>[6,5,1,4,7,2,3]=>[1,1,3,2]
[6,3,4,5,1,2,7]=>[2,5,3,6,4,1,7]=>[6,3,5,2,4,7,1]=>[1,2,3,1]
[6,3,4,5,1,7,2]=>[2,3,7,5,4,1,6]=>[6,5,1,3,4,7,2]=>[1,1,4,1]
[6,3,4,5,2,1,7]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,7,1]=>[1,1,4,1]
[6,3,4,5,2,7,1]=>[2,3,5,4,1,7,6]=>[6,5,3,4,7,1,2]=>[1,1,3,2]
[6,3,4,5,7,1,2]=>[2,3,6,4,1,7,5]=>[6,5,2,4,7,1,3]=>[1,1,3,2]
[6,3,4,5,7,2,1]=>[2,3,4,1,7,6,5]=>[6,5,4,7,1,2,3]=>[1,1,2,3]
[6,3,4,7,1,2,5]=>[2,5,3,6,1,7,4]=>[6,3,5,2,7,1,4]=>[1,2,2,2]
[6,3,4,7,1,5,2]=>[2,3,7,5,1,6,4]=>[6,5,1,3,7,2,4]=>[1,1,3,2]
[6,3,4,7,2,1,5]=>[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]=>[1,1,3,2]
[6,3,4,7,2,5,1]=>[2,3,5,1,7,6,4]=>[6,5,3,7,1,2,4]=>[1,1,2,3]
[6,3,4,7,5,1,2]=>[2,3,6,1,7,5,4]=>[6,5,2,7,1,3,4]=>[1,1,2,3]
[6,3,4,7,5,2,1]=>[7,2,3,1,6,5,4]=>[1,6,5,7,2,3,4]=>[2,2,3]
[6,3,5,1,2,4,7]=>[4,2,5,6,3,1,7]=>[4,6,3,2,5,7,1]=>[2,1,3,1]
[6,3,5,1,2,7,4]=>[2,7,4,5,3,1,6]=>[6,1,4,3,5,7,2]=>[1,2,3,1]
[6,3,5,1,4,2,7]=>[2,6,4,5,3,1,7]=>[6,2,4,3,5,7,1]=>[1,2,3,1]
[6,3,5,1,4,7,2]=>[2,5,7,4,3,1,6]=>[6,3,1,4,5,7,2]=>[1,1,4,1]
[6,3,5,1,7,2,4]=>[2,6,7,4,3,1,5]=>[6,2,1,4,5,7,3]=>[1,1,4,1]
[6,3,5,1,7,4,2]=>[7,2,6,4,3,1,5]=>[1,6,2,4,5,7,3]=>[2,4,1]
[6,3,5,2,1,4,7]=>[2,5,4,6,3,1,7]=>[6,3,4,2,5,7,1]=>[1,2,3,1]
[6,3,5,2,1,7,4]=>[2,4,7,5,3,1,6]=>[6,4,1,3,5,7,2]=>[1,1,4,1]
[6,3,5,2,4,1,7]=>[2,4,6,5,3,1,7]=>[6,4,2,3,5,7,1]=>[1,1,4,1]
[6,3,5,2,4,7,1]=>[2,4,5,3,1,7,6]=>[6,4,3,5,7,1,2]=>[1,1,3,2]
[6,3,5,2,7,1,4]=>[2,4,6,3,1,7,5]=>[6,4,2,5,7,1,3]=>[1,1,3,2]
[6,3,5,2,7,4,1]=>[7,2,4,3,1,6,5]=>[1,6,4,5,7,2,3]=>[2,3,2]
[6,3,5,4,1,2,7]=>[2,5,6,4,3,1,7]=>[6,3,2,4,5,7,1]=>[1,1,4,1]
[6,3,5,4,1,7,2]=>[7,2,5,4,3,1,6]=>[1,6,3,4,5,7,2]=>[2,4,1]
[6,3,5,4,2,1,7]=>[6,2,5,4,3,1,7]=>[2,6,3,4,5,7,1]=>[2,4,1]
[6,3,5,4,2,7,1]=>[5,2,4,3,1,7,6]=>[3,6,4,5,7,1,2]=>[2,3,2]
[6,3,5,4,7,1,2]=>[6,2,4,3,1,7,5]=>[2,6,4,5,7,1,3]=>[2,3,2]
[6,3,5,4,7,2,1]=>[4,2,3,1,7,6,5]=>[4,6,5,7,1,2,3]=>[2,2,3]
[6,3,5,7,1,2,4]=>[2,5,6,3,1,7,4]=>[6,3,2,5,7,1,4]=>[1,1,3,2]
[6,3,5,7,1,4,2]=>[7,2,5,3,1,6,4]=>[1,6,3,5,7,2,4]=>[2,3,2]
[6,3,5,7,2,1,4]=>[6,2,5,3,1,7,4]=>[2,6,3,5,7,1,4]=>[2,3,2]
[6,3,5,7,2,4,1]=>[5,2,3,1,7,6,4]=>[3,6,5,7,1,2,4]=>[2,2,3]
[6,3,5,7,4,1,2]=>[6,2,3,1,7,5,4]=>[2,6,5,7,1,3,4]=>[2,2,3]
[6,3,5,7,4,2,1]=>[3,7,2,1,6,5,4]=>[5,1,6,7,2,3,4]=>[1,3,3]
[6,3,7,1,2,4,5]=>[4,2,5,6,1,7,3]=>[4,6,3,2,7,1,5]=>[2,1,2,2]
[6,3,7,1,2,5,4]=>[2,7,4,5,1,6,3]=>[6,1,4,3,7,2,5]=>[1,2,2,2]
[6,3,7,1,4,2,5]=>[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]=>[1,2,2,2]
[6,3,7,1,4,5,2]=>[2,5,7,4,1,6,3]=>[6,3,1,4,7,2,5]=>[1,1,3,2]
[6,3,7,1,5,2,4]=>[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>[1,1,3,2]
[6,3,7,1,5,4,2]=>[7,2,6,4,1,5,3]=>[1,6,2,4,7,3,5]=>[2,3,2]
[6,3,7,2,1,4,5]=>[2,5,4,6,1,7,3]=>[6,3,4,2,7,1,5]=>[1,2,2,2]
[6,3,7,2,1,5,4]=>[2,4,7,5,1,6,3]=>[6,4,1,3,7,2,5]=>[1,1,3,2]
[6,3,7,2,4,1,5]=>[2,4,6,5,1,7,3]=>[6,4,2,3,7,1,5]=>[1,1,3,2]
[6,3,7,2,4,5,1]=>[2,4,5,1,7,6,3]=>[6,4,3,7,1,2,5]=>[1,1,2,3]
[6,3,7,2,5,1,4]=>[2,4,6,1,7,5,3]=>[6,4,2,7,1,3,5]=>[1,1,2,3]
[6,3,7,2,5,4,1]=>[7,2,4,1,6,5,3]=>[1,6,4,7,2,3,5]=>[2,2,3]
[6,3,7,4,1,2,5]=>[2,5,6,4,1,7,3]=>[6,3,2,4,7,1,5]=>[1,1,3,2]
[6,3,7,4,1,5,2]=>[7,2,5,4,1,6,3]=>[1,6,3,4,7,2,5]=>[2,3,2]
[6,3,7,4,2,1,5]=>[6,2,5,4,1,7,3]=>[2,6,3,4,7,1,5]=>[2,3,2]
[6,3,7,4,2,5,1]=>[5,2,4,1,7,6,3]=>[3,6,4,7,1,2,5]=>[2,2,3]
[6,3,7,4,5,1,2]=>[6,2,4,1,7,5,3]=>[2,6,4,7,1,3,5]=>[2,2,3]
[6,3,7,4,5,2,1]=>[4,7,2,1,6,5,3]=>[4,1,6,7,2,3,5]=>[1,3,3]
[6,3,7,5,1,2,4]=>[2,5,6,1,7,4,3]=>[6,3,2,7,1,4,5]=>[1,1,2,3]
[6,3,7,5,1,4,2]=>[7,2,5,1,6,4,3]=>[1,6,3,7,2,4,5]=>[2,2,3]
[6,3,7,5,2,1,4]=>[6,2,5,1,7,4,3]=>[2,6,3,7,1,4,5]=>[2,2,3]
[6,3,7,5,2,4,1]=>[5,7,2,1,6,4,3]=>[3,1,6,7,2,4,5]=>[1,3,3]
[6,3,7,5,4,1,2]=>[6,7,2,1,5,4,3]=>[2,1,6,7,3,4,5]=>[1,3,3]
[6,3,7,5,4,2,1]=>[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[4,3]
[6,4,1,2,3,5,7]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>[1,1,2,2,1]
[6,4,1,2,3,7,5]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>[2,2,2,1]
[6,4,1,2,5,3,7]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>[2,2,2,1]
[6,4,1,2,5,7,3]=>[5,7,3,2,4,1,6]=>[3,1,5,6,4,7,2]=>[1,3,2,1]
[6,4,1,2,7,3,5]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>[1,3,2,1]
[6,4,1,2,7,5,3]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>[4,2,1]
[6,4,1,3,2,5,7]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>[2,2,2,1]
[6,4,1,3,2,7,5]=>[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>[1,3,2,1]
[6,4,1,3,5,2,7]=>[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>[1,3,2,1]
[6,4,1,3,5,7,2]=>[4,5,2,7,3,1,6]=>[4,3,6,1,5,7,2]=>[1,2,3,1]
[6,4,1,3,7,2,5]=>[4,6,2,7,3,1,5]=>[4,2,6,1,5,7,3]=>[1,2,3,1]
[6,4,1,3,7,5,2]=>[7,4,2,6,3,1,5]=>[1,4,6,2,5,7,3]=>[3,3,1]
[6,4,1,5,2,3,7]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>[1,3,2,1]
[6,4,1,5,2,7,3]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>[4,2,1]
[6,4,1,5,3,2,7]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>[4,2,1]
[6,4,1,5,3,7,2]=>[5,4,2,7,3,1,6]=>[3,4,6,1,5,7,2]=>[3,3,1]
[6,4,1,5,7,2,3]=>[6,4,2,7,3,1,5]=>[2,4,6,1,5,7,3]=>[3,3,1]
[6,4,1,5,7,3,2]=>[4,2,7,6,3,1,5]=>[4,6,1,2,5,7,3]=>[2,4,1]
[6,4,1,7,2,3,5]=>[5,6,2,7,3,1,4]=>[3,2,6,1,5,7,4]=>[1,2,3,1]
[6,4,1,7,2,5,3]=>[7,5,2,6,3,1,4]=>[1,3,6,2,5,7,4]=>[3,3,1]
[6,4,1,7,3,2,5]=>[6,5,2,7,3,1,4]=>[2,3,6,1,5,7,4]=>[3,3,1]
[6,4,1,7,3,5,2]=>[5,2,7,6,3,1,4]=>[3,6,1,2,5,7,4]=>[2,4,1]
[6,4,1,7,5,2,3]=>[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>[2,4,1]
[6,4,1,7,5,3,2]=>[2,7,6,5,3,1,4]=>[6,1,2,3,5,7,4]=>[1,5,1]
[6,4,2,1,3,5,7]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>[2,2,2,1]
[6,4,2,1,3,7,5]=>[3,7,4,2,5,1,6]=>[5,1,4,6,3,7,2]=>[1,3,2,1]
[6,4,2,1,5,3,7]=>[3,6,4,2,5,1,7]=>[5,2,4,6,3,7,1]=>[1,3,2,1]
[6,4,2,1,5,7,3]=>[3,5,2,7,4,1,6]=>[5,3,6,1,4,7,2]=>[1,2,3,1]
[6,4,2,1,7,3,5]=>[3,6,2,7,4,1,5]=>[5,2,6,1,4,7,3]=>[1,2,3,1]
[6,4,2,1,7,5,3]=>[7,3,2,6,4,1,5]=>[1,5,6,2,4,7,3]=>[3,3,1]
[6,4,2,3,1,5,7]=>[3,5,4,2,6,1,7]=>[5,3,4,6,2,7,1]=>[1,3,2,1]
[6,4,2,3,1,7,5]=>[3,4,2,7,5,1,6]=>[5,4,6,1,3,7,2]=>[1,2,3,1]
[6,4,2,3,5,1,7]=>[3,4,2,6,5,1,7]=>[5,4,6,2,3,7,1]=>[1,2,3,1]
[6,4,2,3,5,7,1]=>[3,4,2,5,1,7,6]=>[5,4,6,3,7,1,2]=>[1,2,2,2]
[6,4,2,3,7,1,5]=>[3,4,2,6,1,7,5]=>[5,4,6,2,7,1,3]=>[1,2,2,2]
[6,4,2,3,7,5,1]=>[7,3,2,4,1,6,5]=>[1,5,6,4,7,2,3]=>[3,2,2]
[6,4,2,5,1,3,7]=>[3,5,2,6,4,1,7]=>[5,3,6,2,4,7,1]=>[1,2,3,1]
[6,4,2,5,1,7,3]=>[7,3,2,5,4,1,6]=>[1,5,6,3,4,7,2]=>[3,3,1]
[6,4,2,5,3,1,7]=>[6,3,2,5,4,1,7]=>[2,5,6,3,4,7,1]=>[3,3,1]
[6,4,2,5,3,7,1]=>[5,3,2,4,1,7,6]=>[3,5,6,4,7,1,2]=>[3,2,2]
[6,4,2,5,7,1,3]=>[6,3,2,4,1,7,5]=>[2,5,6,4,7,1,3]=>[3,2,2]
[6,4,2,5,7,3,1]=>[4,2,7,3,1,6,5]=>[4,6,1,5,7,2,3]=>[2,3,2]
[6,4,2,7,1,3,5]=>[3,5,2,6,1,7,4]=>[5,3,6,2,7,1,4]=>[1,2,2,2]
[6,4,2,7,1,5,3]=>[7,3,2,5,1,6,4]=>[1,5,6,3,7,2,4]=>[3,2,2]
[6,4,2,7,3,1,5]=>[6,3,2,5,1,7,4]=>[2,5,6,3,7,1,4]=>[3,2,2]
[6,4,2,7,3,5,1]=>[5,2,7,3,1,6,4]=>[3,6,1,5,7,2,4]=>[2,3,2]
[6,4,2,7,5,1,3]=>[6,2,7,3,1,5,4]=>[2,6,1,5,7,3,4]=>[2,3,2]
[6,4,2,7,5,3,1]=>[2,7,6,3,1,5,4]=>[6,1,2,5,7,3,4]=>[1,4,2]
[6,4,3,1,2,5,7]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>[1,3,2,1]
[6,4,3,1,2,7,5]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>[4,2,1]
[6,4,3,1,5,2,7]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>[4,2,1]
[6,4,3,1,5,7,2]=>[5,3,2,7,4,1,6]=>[3,5,6,1,4,7,2]=>[3,3,1]
[6,4,3,1,7,2,5]=>[6,3,2,7,4,1,5]=>[2,5,6,1,4,7,3]=>[3,3,1]
[6,4,3,1,7,5,2]=>[3,2,7,6,4,1,5]=>[5,6,1,2,4,7,3]=>[2,4,1]
[6,4,3,2,1,5,7]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>[4,2,1]
[6,4,3,2,1,7,5]=>[4,3,2,7,5,1,6]=>[4,5,6,1,3,7,2]=>[3,3,1]
[6,4,3,2,5,1,7]=>[4,3,2,6,5,1,7]=>[4,5,6,2,3,7,1]=>[3,3,1]
[6,4,3,2,5,7,1]=>[4,3,2,5,1,7,6]=>[4,5,6,3,7,1,2]=>[3,2,2]
[6,4,3,2,7,1,5]=>[4,3,2,6,1,7,5]=>[4,5,6,2,7,1,3]=>[3,2,2]
[6,4,3,2,7,5,1]=>[3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3]=>[2,3,2]
[6,4,3,5,1,2,7]=>[5,3,2,6,4,1,7]=>[3,5,6,2,4,7,1]=>[3,3,1]
[6,4,3,5,1,7,2]=>[3,2,7,5,4,1,6]=>[5,6,1,3,4,7,2]=>[2,4,1]
[6,4,3,5,2,1,7]=>[3,2,6,5,4,1,7]=>[5,6,2,3,4,7,1]=>[2,4,1]
[6,4,3,5,2,7,1]=>[3,2,5,4,1,7,6]=>[5,6,3,4,7,1,2]=>[2,3,2]
[6,4,3,5,7,1,2]=>[3,2,6,4,1,7,5]=>[5,6,2,4,7,1,3]=>[2,3,2]
[6,4,3,5,7,2,1]=>[3,2,4,1,7,6,5]=>[5,6,4,7,1,2,3]=>[2,2,3]
[6,4,3,7,1,2,5]=>[5,3,2,6,1,7,4]=>[3,5,6,2,7,1,4]=>[3,2,2]
[6,4,3,7,1,5,2]=>[3,2,7,5,1,6,4]=>[5,6,1,3,7,2,4]=>[2,3,2]
[6,4,3,7,2,1,5]=>[3,2,6,5,1,7,4]=>[5,6,2,3,7,1,4]=>[2,3,2]
[6,4,3,7,2,5,1]=>[3,2,5,1,7,6,4]=>[5,6,3,7,1,2,4]=>[2,2,3]
[6,4,3,7,5,1,2]=>[3,2,6,1,7,5,4]=>[5,6,2,7,1,3,4]=>[2,2,3]
[6,4,3,7,5,2,1]=>[2,7,3,1,6,5,4]=>[6,1,5,7,2,3,4]=>[1,3,3]
[6,4,5,1,2,3,7]=>[4,5,2,6,3,1,7]=>[4,3,6,2,5,7,1]=>[1,2,3,1]
[6,4,5,1,2,7,3]=>[7,4,2,5,3,1,6]=>[1,4,6,3,5,7,2]=>[3,3,1]
[6,4,5,1,3,2,7]=>[6,4,2,5,3,1,7]=>[2,4,6,3,5,7,1]=>[3,3,1]
[6,4,5,1,3,7,2]=>[5,2,7,4,3,1,6]=>[3,6,1,4,5,7,2]=>[2,4,1]
[6,4,5,1,7,2,3]=>[6,2,7,4,3,1,5]=>[2,6,1,4,5,7,3]=>[2,4,1]
[6,4,5,1,7,3,2]=>[2,7,6,4,3,1,5]=>[6,1,2,4,5,7,3]=>[1,5,1]
[6,4,5,2,1,3,7]=>[5,4,2,6,3,1,7]=>[3,4,6,2,5,7,1]=>[3,3,1]
[6,4,5,2,1,7,3]=>[4,2,7,5,3,1,6]=>[4,6,1,3,5,7,2]=>[2,4,1]
[6,4,5,2,3,1,7]=>[4,2,6,5,3,1,7]=>[4,6,2,3,5,7,1]=>[2,4,1]
[6,4,5,2,3,7,1]=>[4,2,5,3,1,7,6]=>[4,6,3,5,7,1,2]=>[2,3,2]
[6,4,5,2,7,1,3]=>[4,2,6,3,1,7,5]=>[4,6,2,5,7,1,3]=>[2,3,2]
[6,4,5,2,7,3,1]=>[2,7,4,3,1,6,5]=>[6,1,4,5,7,2,3]=>[1,4,2]
[6,4,5,3,1,2,7]=>[5,2,6,4,3,1,7]=>[3,6,2,4,5,7,1]=>[2,4,1]
[6,4,5,3,1,7,2]=>[2,7,5,4,3,1,6]=>[6,1,3,4,5,7,2]=>[1,5,1]
[6,4,5,3,2,1,7]=>[2,6,5,4,3,1,7]=>[6,2,3,4,5,7,1]=>[1,5,1]
[6,4,5,3,2,7,1]=>[2,5,4,3,1,7,6]=>[6,3,4,5,7,1,2]=>[1,4,2]
[6,4,5,3,7,1,2]=>[2,6,4,3,1,7,5]=>[6,2,4,5,7,1,3]=>[1,4,2]
[6,4,5,3,7,2,1]=>[2,4,3,1,7,6,5]=>[6,4,5,7,1,2,3]=>[1,3,3]
[6,4,5,7,1,2,3]=>[5,2,6,3,1,7,4]=>[3,6,2,5,7,1,4]=>[2,3,2]
[6,4,5,7,1,3,2]=>[2,7,5,3,1,6,4]=>[6,1,3,5,7,2,4]=>[1,4,2]
[6,4,5,7,2,1,3]=>[2,6,5,3,1,7,4]=>[6,2,3,5,7,1,4]=>[1,4,2]
[6,4,5,7,2,3,1]=>[2,5,3,1,7,6,4]=>[6,3,5,7,1,2,4]=>[1,3,3]
[6,4,5,7,3,1,2]=>[2,6,3,1,7,5,4]=>[6,2,5,7,1,3,4]=>[1,3,3]
[6,4,5,7,3,2,1]=>[2,3,1,7,6,5,4]=>[6,5,7,1,2,3,4]=>[1,2,4]
[6,4,7,1,2,3,5]=>[4,5,2,6,1,7,3]=>[4,3,6,2,7,1,5]=>[1,2,2,2]
[6,4,7,1,2,5,3]=>[7,4,2,5,1,6,3]=>[1,4,6,3,7,2,5]=>[3,2,2]
[6,4,7,1,3,2,5]=>[6,4,2,5,1,7,3]=>[2,4,6,3,7,1,5]=>[3,2,2]
[6,4,7,1,3,5,2]=>[5,2,7,4,1,6,3]=>[3,6,1,4,7,2,5]=>[2,3,2]
[6,4,7,1,5,2,3]=>[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>[2,3,2]
[6,4,7,1,5,3,2]=>[2,7,6,4,1,5,3]=>[6,1,2,4,7,3,5]=>[1,4,2]
[6,4,7,2,1,3,5]=>[5,4,2,6,1,7,3]=>[3,4,6,2,7,1,5]=>[3,2,2]
[6,4,7,2,1,5,3]=>[4,2,7,5,1,6,3]=>[4,6,1,3,7,2,5]=>[2,3,2]
[6,4,7,2,3,1,5]=>[4,2,6,5,1,7,3]=>[4,6,2,3,7,1,5]=>[2,3,2]
[6,4,7,2,3,5,1]=>[4,2,5,1,7,6,3]=>[4,6,3,7,1,2,5]=>[2,2,3]
[6,4,7,2,5,1,3]=>[4,2,6,1,7,5,3]=>[4,6,2,7,1,3,5]=>[2,2,3]
[6,4,7,2,5,3,1]=>[2,7,4,1,6,5,3]=>[6,1,4,7,2,3,5]=>[1,3,3]
[6,4,7,3,1,2,5]=>[5,2,6,4,1,7,3]=>[3,6,2,4,7,1,5]=>[2,3,2]
[6,4,7,3,1,5,2]=>[2,7,5,4,1,6,3]=>[6,1,3,4,7,2,5]=>[1,4,2]
[6,4,7,3,2,1,5]=>[2,6,5,4,1,7,3]=>[6,2,3,4,7,1,5]=>[1,4,2]
[6,4,7,3,2,5,1]=>[2,5,4,1,7,6,3]=>[6,3,4,7,1,2,5]=>[1,3,3]
[6,4,7,3,5,1,2]=>[2,6,4,1,7,5,3]=>[6,2,4,7,1,3,5]=>[1,3,3]
[6,4,7,3,5,2,1]=>[2,4,1,7,6,5,3]=>[6,4,7,1,2,3,5]=>[1,2,4]
[6,4,7,5,1,2,3]=>[5,2,6,1,7,4,3]=>[3,6,2,7,1,4,5]=>[2,2,3]
[6,4,7,5,1,3,2]=>[2,7,5,1,6,4,3]=>[6,1,3,7,2,4,5]=>[1,3,3]
[6,4,7,5,2,1,3]=>[2,6,5,1,7,4,3]=>[6,2,3,7,1,4,5]=>[1,3,3]
[6,4,7,5,2,3,1]=>[2,5,1,7,6,4,3]=>[6,3,7,1,2,4,5]=>[1,2,4]
[6,4,7,5,3,1,2]=>[2,6,1,7,5,4,3]=>[6,2,7,1,3,4,5]=>[1,2,4]
[6,4,7,5,3,2,1]=>[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>[3,4]
[6,5,1,2,3,4,7]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>[1,1,1,3,1]
[6,5,1,2,3,7,4]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>[2,1,3,1]
[6,5,1,2,4,3,7]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>[2,1,3,1]
[6,5,1,2,4,7,3]=>[5,7,3,4,2,1,6]=>[3,1,5,4,6,7,2]=>[1,2,3,1]
[6,5,1,2,7,3,4]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>[1,2,3,1]
[6,5,1,2,7,4,3]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>[3,3,1]
[6,5,1,3,2,4,7]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>[2,1,3,1]
[6,5,1,3,2,7,4]=>[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>[1,2,3,1]
[6,5,1,3,4,2,7]=>[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>[1,2,3,1]
[6,5,1,3,4,7,2]=>[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>[1,1,4,1]
[6,5,1,3,7,2,4]=>[4,6,7,3,2,1,5]=>[4,2,1,5,6,7,3]=>[1,1,4,1]
[6,5,1,3,7,4,2]=>[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>[2,4,1]
[6,5,1,4,2,3,7]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>[1,2,3,1]
[6,5,1,4,2,7,3]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>[3,3,1]
[6,5,1,4,3,2,7]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>[3,3,1]
[6,5,1,4,3,7,2]=>[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>[2,4,1]
[6,5,1,4,7,2,3]=>[6,4,7,3,2,1,5]=>[2,4,1,5,6,7,3]=>[2,4,1]
[6,5,1,4,7,3,2]=>[4,7,6,3,2,1,5]=>[4,1,2,5,6,7,3]=>[1,5,1]
[6,5,1,7,2,3,4]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>[1,1,4,1]
[6,5,1,7,2,4,3]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>[2,4,1]
[6,5,1,7,3,2,4]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>[2,4,1]
[6,5,1,7,3,4,2]=>[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>[1,5,1]
[6,5,1,7,4,2,3]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>[1,5,1]
[6,5,1,7,4,3,2]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[6,1]
[6,5,2,1,3,4,7]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>[2,1,3,1]
[6,5,2,1,3,7,4]=>[3,7,4,5,2,1,6]=>[5,1,4,3,6,7,2]=>[1,2,3,1]
[6,5,2,1,4,3,7]=>[3,6,4,5,2,1,7]=>[5,2,4,3,6,7,1]=>[1,2,3,1]
[6,5,2,1,4,7,3]=>[3,5,7,4,2,1,6]=>[5,3,1,4,6,7,2]=>[1,1,4,1]
[6,5,2,1,7,3,4]=>[3,6,7,4,2,1,5]=>[5,2,1,4,6,7,3]=>[1,1,4,1]
[6,5,2,1,7,4,3]=>[7,3,6,4,2,1,5]=>[1,5,2,4,6,7,3]=>[2,4,1]
[6,5,2,3,1,4,7]=>[3,5,4,6,2,1,7]=>[5,3,4,2,6,7,1]=>[1,2,3,1]
[6,5,2,3,1,7,4]=>[3,4,7,5,2,1,6]=>[5,4,1,3,6,7,2]=>[1,1,4,1]
[6,5,2,3,4,1,7]=>[3,4,6,5,2,1,7]=>[5,4,2,3,6,7,1]=>[1,1,4,1]
[6,5,2,3,4,7,1]=>[3,4,5,2,1,7,6]=>[5,4,3,6,7,1,2]=>[1,1,3,2]
[6,5,2,3,7,1,4]=>[3,4,6,2,1,7,5]=>[5,4,2,6,7,1,3]=>[1,1,3,2]
[6,5,2,3,7,4,1]=>[7,3,4,2,1,6,5]=>[1,5,4,6,7,2,3]=>[2,3,2]
[6,5,2,4,1,3,7]=>[3,5,6,4,2,1,7]=>[5,3,2,4,6,7,1]=>[1,1,4,1]
[6,5,2,4,1,7,3]=>[7,3,5,4,2,1,6]=>[1,5,3,4,6,7,2]=>[2,4,1]
[6,5,2,4,3,1,7]=>[6,3,5,4,2,1,7]=>[2,5,3,4,6,7,1]=>[2,4,1]
[6,5,2,4,3,7,1]=>[5,3,4,2,1,7,6]=>[3,5,4,6,7,1,2]=>[2,3,2]
[6,5,2,4,7,1,3]=>[6,3,4,2,1,7,5]=>[2,5,4,6,7,1,3]=>[2,3,2]
[6,5,2,4,7,3,1]=>[4,7,3,2,1,6,5]=>[4,1,5,6,7,2,3]=>[1,4,2]
[6,5,2,7,1,3,4]=>[3,5,6,2,1,7,4]=>[5,3,2,6,7,1,4]=>[1,1,3,2]
[6,5,2,7,1,4,3]=>[7,3,5,2,1,6,4]=>[1,5,3,6,7,2,4]=>[2,3,2]
[6,5,2,7,3,1,4]=>[6,3,5,2,1,7,4]=>[2,5,3,6,7,1,4]=>[2,3,2]
[6,5,2,7,3,4,1]=>[5,7,3,2,1,6,4]=>[3,1,5,6,7,2,4]=>[1,4,2]
[6,5,2,7,4,1,3]=>[6,7,3,2,1,5,4]=>[2,1,5,6,7,3,4]=>[1,4,2]
[6,5,2,7,4,3,1]=>[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>[5,2]
[6,5,3,1,2,4,7]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>[1,2,3,1]
[6,5,3,1,2,7,4]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>[3,3,1]
[6,5,3,1,4,2,7]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>[3,3,1]
[6,5,3,1,4,7,2]=>[5,3,7,4,2,1,6]=>[3,5,1,4,6,7,2]=>[2,4,1]
[6,5,3,1,7,2,4]=>[6,3,7,4,2,1,5]=>[2,5,1,4,6,7,3]=>[2,4,1]
[6,5,3,1,7,4,2]=>[3,7,6,4,2,1,5]=>[5,1,2,4,6,7,3]=>[1,5,1]
[6,5,3,2,1,4,7]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>[3,3,1]
[6,5,3,2,1,7,4]=>[4,3,7,5,2,1,6]=>[4,5,1,3,6,7,2]=>[2,4,1]
[6,5,3,2,4,1,7]=>[4,3,6,5,2,1,7]=>[4,5,2,3,6,7,1]=>[2,4,1]
[6,5,3,2,4,7,1]=>[4,3,5,2,1,7,6]=>[4,5,3,6,7,1,2]=>[2,3,2]
[6,5,3,2,7,1,4]=>[4,3,6,2,1,7,5]=>[4,5,2,6,7,1,3]=>[2,3,2]
[6,5,3,2,7,4,1]=>[3,7,4,2,1,6,5]=>[5,1,4,6,7,2,3]=>[1,4,2]
[6,5,3,4,1,2,7]=>[5,3,6,4,2,1,7]=>[3,5,2,4,6,7,1]=>[2,4,1]
[6,5,3,4,1,7,2]=>[3,7,5,4,2,1,6]=>[5,1,3,4,6,7,2]=>[1,5,1]
[6,5,3,4,2,1,7]=>[3,6,5,4,2,1,7]=>[5,2,3,4,6,7,1]=>[1,5,1]
[6,5,3,4,2,7,1]=>[3,5,4,2,1,7,6]=>[5,3,4,6,7,1,2]=>[1,4,2]
[6,5,3,4,7,1,2]=>[3,6,4,2,1,7,5]=>[5,2,4,6,7,1,3]=>[1,4,2]
[6,5,3,4,7,2,1]=>[3,4,2,1,7,6,5]=>[5,4,6,7,1,2,3]=>[1,3,3]
[6,5,3,7,1,2,4]=>[5,3,6,2,1,7,4]=>[3,5,2,6,7,1,4]=>[2,3,2]
[6,5,3,7,1,4,2]=>[3,7,5,2,1,6,4]=>[5,1,3,6,7,2,4]=>[1,4,2]
[6,5,3,7,2,1,4]=>[3,6,5,2,1,7,4]=>[5,2,3,6,7,1,4]=>[1,4,2]
[6,5,3,7,2,4,1]=>[3,5,2,1,7,6,4]=>[5,3,6,7,1,2,4]=>[1,3,3]
[6,5,3,7,4,1,2]=>[3,6,2,1,7,5,4]=>[5,2,6,7,1,3,4]=>[1,3,3]
[6,5,3,7,4,2,1]=>[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>[4,3]
[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>[1,1,4,1]
[6,5,4,1,2,7,3]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>[2,4,1]
[6,5,4,1,3,2,7]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>[2,4,1]
[6,5,4,1,3,7,2]=>[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>[1,5,1]
[6,5,4,1,7,2,3]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>[1,5,1]
[6,5,4,1,7,3,2]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[6,1]
[6,5,4,2,1,3,7]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>[2,4,1]
[6,5,4,2,1,7,3]=>[4,7,5,3,2,1,6]=>[4,1,3,5,6,7,2]=>[1,5,1]
[6,5,4,2,3,1,7]=>[4,6,5,3,2,1,7]=>[4,2,3,5,6,7,1]=>[1,5,1]
[6,5,4,2,3,7,1]=>[4,5,3,2,1,7,6]=>[4,3,5,6,7,1,2]=>[1,4,2]
[6,5,4,2,7,1,3]=>[4,6,3,2,1,7,5]=>[4,2,5,6,7,1,3]=>[1,4,2]
[6,5,4,2,7,3,1]=>[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>[5,2]
[6,5,4,3,1,2,7]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>[1,5,1]
[6,5,4,3,1,7,2]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[6,1]
[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[6,1]
[6,5,4,3,2,7,1]=>[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>[5,2]
[6,5,4,3,7,1,2]=>[6,4,3,2,1,7,5]=>[2,4,5,6,7,1,3]=>[5,2]
[6,5,4,3,7,2,1]=>[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>[4,3]
[6,5,4,7,1,2,3]=>[5,6,3,2,1,7,4]=>[3,2,5,6,7,1,4]=>[1,4,2]
[6,5,4,7,1,3,2]=>[7,5,3,2,1,6,4]=>[1,3,5,6,7,2,4]=>[5,2]
[6,5,4,7,2,1,3]=>[6,5,3,2,1,7,4]=>[2,3,5,6,7,1,4]=>[5,2]
[6,5,4,7,2,3,1]=>[5,3,2,1,7,6,4]=>[3,5,6,7,1,2,4]=>[4,3]
[6,5,4,7,3,1,2]=>[6,3,2,1,7,5,4]=>[2,5,6,7,1,3,4]=>[4,3]
[6,5,4,7,3,2,1]=>[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>[3,4]
[6,5,7,1,2,3,4]=>[4,5,6,2,1,7,3]=>[4,3,2,6,7,1,5]=>[1,1,3,2]
[6,5,7,1,2,4,3]=>[7,4,5,2,1,6,3]=>[1,4,3,6,7,2,5]=>[2,3,2]
[6,5,7,1,3,2,4]=>[6,4,5,2,1,7,3]=>[2,4,3,6,7,1,5]=>[2,3,2]
[6,5,7,1,3,4,2]=>[5,7,4,2,1,6,3]=>[3,1,4,6,7,2,5]=>[1,4,2]
[6,5,7,1,4,2,3]=>[6,7,4,2,1,5,3]=>[2,1,4,6,7,3,5]=>[1,4,2]
[6,5,7,1,4,3,2]=>[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>[5,2]
[6,5,7,2,1,3,4]=>[5,4,6,2,1,7,3]=>[3,4,2,6,7,1,5]=>[2,3,2]
[6,5,7,2,1,4,3]=>[4,7,5,2,1,6,3]=>[4,1,3,6,7,2,5]=>[1,4,2]
[6,5,7,2,3,1,4]=>[4,6,5,2,1,7,3]=>[4,2,3,6,7,1,5]=>[1,4,2]
[6,5,7,2,3,4,1]=>[4,5,2,1,7,6,3]=>[4,3,6,7,1,2,5]=>[1,3,3]
[6,5,7,2,4,1,3]=>[4,6,2,1,7,5,3]=>[4,2,6,7,1,3,5]=>[1,3,3]
[6,5,7,2,4,3,1]=>[7,4,2,1,6,5,3]=>[1,4,6,7,2,3,5]=>[4,3]
[6,5,7,3,1,2,4]=>[5,6,4,2,1,7,3]=>[3,2,4,6,7,1,5]=>[1,4,2]
[6,5,7,3,1,4,2]=>[7,5,4,2,1,6,3]=>[1,3,4,6,7,2,5]=>[5,2]
[6,5,7,3,2,1,4]=>[6,5,4,2,1,7,3]=>[2,3,4,6,7,1,5]=>[5,2]
[6,5,7,3,2,4,1]=>[5,4,2,1,7,6,3]=>[3,4,6,7,1,2,5]=>[4,3]
[6,5,7,3,4,1,2]=>[6,4,2,1,7,5,3]=>[2,4,6,7,1,3,5]=>[4,3]
[6,5,7,3,4,2,1]=>[4,2,1,7,6,5,3]=>[4,6,7,1,2,3,5]=>[3,4]
[6,5,7,4,1,2,3]=>[5,6,2,1,7,4,3]=>[3,2,6,7,1,4,5]=>[1,3,3]
[6,5,7,4,1,3,2]=>[7,5,2,1,6,4,3]=>[1,3,6,7,2,4,5]=>[4,3]
[6,5,7,4,2,1,3]=>[6,5,2,1,7,4,3]=>[2,3,6,7,1,4,5]=>[4,3]
[6,5,7,4,2,3,1]=>[5,2,1,7,6,4,3]=>[3,6,7,1,2,4,5]=>[3,4]
[6,5,7,4,3,1,2]=>[6,2,1,7,5,4,3]=>[2,6,7,1,3,4,5]=>[3,4]
[6,5,7,4,3,2,1]=>[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>[2,5]
[6,7,1,2,3,4,5]=>[3,4,5,6,1,7,2]=>[5,4,3,2,7,1,6]=>[1,1,1,2,2]
[6,7,1,2,3,5,4]=>[7,3,4,5,1,6,2]=>[1,5,4,3,7,2,6]=>[2,1,2,2]
[6,7,1,2,4,3,5]=>[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]=>[2,1,2,2]
[6,7,1,2,4,5,3]=>[5,7,3,4,1,6,2]=>[3,1,5,4,7,2,6]=>[1,2,2,2]
[6,7,1,2,5,3,4]=>[6,7,3,4,1,5,2]=>[2,1,5,4,7,3,6]=>[1,2,2,2]
[6,7,1,2,5,4,3]=>[7,6,3,4,1,5,2]=>[1,2,5,4,7,3,6]=>[3,2,2]
[6,7,1,3,2,4,5]=>[5,3,4,6,1,7,2]=>[3,5,4,2,7,1,6]=>[2,1,2,2]
[6,7,1,3,2,5,4]=>[4,7,3,5,1,6,2]=>[4,1,5,3,7,2,6]=>[1,2,2,2]
[6,7,1,3,4,2,5]=>[4,6,3,5,1,7,2]=>[4,2,5,3,7,1,6]=>[1,2,2,2]
[6,7,1,3,4,5,2]=>[4,5,7,3,1,6,2]=>[4,3,1,5,7,2,6]=>[1,1,3,2]
[6,7,1,3,5,2,4]=>[4,6,7,3,1,5,2]=>[4,2,1,5,7,3,6]=>[1,1,3,2]
[6,7,1,3,5,4,2]=>[7,4,6,3,1,5,2]=>[1,4,2,5,7,3,6]=>[2,3,2]
[6,7,1,4,2,3,5]=>[5,6,3,4,1,7,2]=>[3,2,5,4,7,1,6]=>[1,2,2,2]
[6,7,1,4,2,5,3]=>[7,5,3,4,1,6,2]=>[1,3,5,4,7,2,6]=>[3,2,2]
[6,7,1,4,3,2,5]=>[6,5,3,4,1,7,2]=>[2,3,5,4,7,1,6]=>[3,2,2]
[6,7,1,4,3,5,2]=>[5,4,7,3,1,6,2]=>[3,4,1,5,7,2,6]=>[2,3,2]
[6,7,1,4,5,2,3]=>[6,4,7,3,1,5,2]=>[2,4,1,5,7,3,6]=>[2,3,2]
[6,7,1,4,5,3,2]=>[4,7,6,3,1,5,2]=>[4,1,2,5,7,3,6]=>[1,4,2]
[6,7,1,5,2,3,4]=>[5,6,7,3,1,4,2]=>[3,2,1,5,7,4,6]=>[1,1,3,2]
[6,7,1,5,2,4,3]=>[7,5,6,3,1,4,2]=>[1,3,2,5,7,4,6]=>[2,3,2]
[6,7,1,5,3,2,4]=>[6,5,7,3,1,4,2]=>[2,3,1,5,7,4,6]=>[2,3,2]
[6,7,1,5,3,4,2]=>[5,7,6,3,1,4,2]=>[3,1,2,5,7,4,6]=>[1,4,2]
[6,7,1,5,4,2,3]=>[6,7,5,3,1,4,2]=>[2,1,3,5,7,4,6]=>[1,4,2]
[6,7,1,5,4,3,2]=>[7,6,5,3,1,4,2]=>[1,2,3,5,7,4,6]=>[5,2]
[6,7,2,1,3,4,5]=>[4,3,5,6,1,7,2]=>[4,5,3,2,7,1,6]=>[2,1,2,2]
[6,7,2,1,3,5,4]=>[3,7,4,5,1,6,2]=>[5,1,4,3,7,2,6]=>[1,2,2,2]
[6,7,2,1,4,3,5]=>[3,6,4,5,1,7,2]=>[5,2,4,3,7,1,6]=>[1,2,2,2]
[6,7,2,1,4,5,3]=>[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>[1,1,3,2]
[6,7,2,1,5,3,4]=>[3,6,7,4,1,5,2]=>[5,2,1,4,7,3,6]=>[1,1,3,2]
[6,7,2,1,5,4,3]=>[7,3,6,4,1,5,2]=>[1,5,2,4,7,3,6]=>[2,3,2]
[6,7,2,3,1,4,5]=>[3,5,4,6,1,7,2]=>[5,3,4,2,7,1,6]=>[1,2,2,2]
[6,7,2,3,1,5,4]=>[3,4,7,5,1,6,2]=>[5,4,1,3,7,2,6]=>[1,1,3,2]
[6,7,2,3,4,1,5]=>[3,4,6,5,1,7,2]=>[5,4,2,3,7,1,6]=>[1,1,3,2]
[6,7,2,3,4,5,1]=>[3,4,5,1,7,6,2]=>[5,4,3,7,1,2,6]=>[1,1,2,3]
[6,7,2,3,5,1,4]=>[3,4,6,1,7,5,2]=>[5,4,2,7,1,3,6]=>[1,1,2,3]
[6,7,2,3,5,4,1]=>[7,3,4,1,6,5,2]=>[1,5,4,7,2,3,6]=>[2,2,3]
[6,7,2,4,1,3,5]=>[3,5,6,4,1,7,2]=>[5,3,2,4,7,1,6]=>[1,1,3,2]
[6,7,2,4,1,5,3]=>[7,3,5,4,1,6,2]=>[1,5,3,4,7,2,6]=>[2,3,2]
[6,7,2,4,3,1,5]=>[6,3,5,4,1,7,2]=>[2,5,3,4,7,1,6]=>[2,3,2]
[6,7,2,4,3,5,1]=>[5,3,4,1,7,6,2]=>[3,5,4,7,1,2,6]=>[2,2,3]
[6,7,2,4,5,1,3]=>[6,3,4,1,7,5,2]=>[2,5,4,7,1,3,6]=>[2,2,3]
[6,7,2,4,5,3,1]=>[4,7,3,1,6,5,2]=>[4,1,5,7,2,3,6]=>[1,3,3]
[6,7,2,5,1,3,4]=>[3,5,6,1,7,4,2]=>[5,3,2,7,1,4,6]=>[1,1,2,3]
[6,7,2,5,1,4,3]=>[7,3,5,1,6,4,2]=>[1,5,3,7,2,4,6]=>[2,2,3]
[6,7,2,5,3,1,4]=>[6,3,5,1,7,4,2]=>[2,5,3,7,1,4,6]=>[2,2,3]
[6,7,2,5,3,4,1]=>[5,7,3,1,6,4,2]=>[3,1,5,7,2,4,6]=>[1,3,3]
[6,7,2,5,4,1,3]=>[6,7,3,1,5,4,2]=>[2,1,5,7,3,4,6]=>[1,3,3]
[6,7,2,5,4,3,1]=>[7,6,3,1,5,4,2]=>[1,2,5,7,3,4,6]=>[4,3]
[6,7,3,1,2,4,5]=>[4,5,3,6,1,7,2]=>[4,3,5,2,7,1,6]=>[1,2,2,2]
[6,7,3,1,2,5,4]=>[7,4,3,5,1,6,2]=>[1,4,5,3,7,2,6]=>[3,2,2]
[6,7,3,1,4,2,5]=>[6,4,3,5,1,7,2]=>[2,4,5,3,7,1,6]=>[3,2,2]
[6,7,3,1,4,5,2]=>[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>[2,3,2]
[6,7,3,1,5,2,4]=>[6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6]=>[2,3,2]
[6,7,3,1,5,4,2]=>[3,7,6,4,1,5,2]=>[5,1,2,4,7,3,6]=>[1,4,2]
[6,7,3,2,1,4,5]=>[5,4,3,6,1,7,2]=>[3,4,5,2,7,1,6]=>[3,2,2]
[6,7,3,2,1,5,4]=>[4,3,7,5,1,6,2]=>[4,5,1,3,7,2,6]=>[2,3,2]
[6,7,3,2,4,1,5]=>[4,3,6,5,1,7,2]=>[4,5,2,3,7,1,6]=>[2,3,2]
[6,7,3,2,4,5,1]=>[4,3,5,1,7,6,2]=>[4,5,3,7,1,2,6]=>[2,2,3]
[6,7,3,2,5,1,4]=>[4,3,6,1,7,5,2]=>[4,5,2,7,1,3,6]=>[2,2,3]
[6,7,3,2,5,4,1]=>[3,7,4,1,6,5,2]=>[5,1,4,7,2,3,6]=>[1,3,3]
[6,7,3,4,1,2,5]=>[5,3,6,4,1,7,2]=>[3,5,2,4,7,1,6]=>[2,3,2]
[6,7,3,4,1,5,2]=>[3,7,5,4,1,6,2]=>[5,1,3,4,7,2,6]=>[1,4,2]
[6,7,3,4,2,1,5]=>[3,6,5,4,1,7,2]=>[5,2,3,4,7,1,6]=>[1,4,2]
[6,7,3,4,2,5,1]=>[3,5,4,1,7,6,2]=>[5,3,4,7,1,2,6]=>[1,3,3]
[6,7,3,4,5,1,2]=>[3,6,4,1,7,5,2]=>[5,2,4,7,1,3,6]=>[1,3,3]
[6,7,3,4,5,2,1]=>[3,4,1,7,6,5,2]=>[5,4,7,1,2,3,6]=>[1,2,4]
[6,7,3,5,1,2,4]=>[5,3,6,1,7,4,2]=>[3,5,2,7,1,4,6]=>[2,2,3]
[6,7,3,5,1,4,2]=>[3,7,5,1,6,4,2]=>[5,1,3,7,2,4,6]=>[1,3,3]
[6,7,3,5,2,1,4]=>[3,6,5,1,7,4,2]=>[5,2,3,7,1,4,6]=>[1,3,3]
[6,7,3,5,2,4,1]=>[3,5,1,7,6,4,2]=>[5,3,7,1,2,4,6]=>[1,2,4]
[6,7,3,5,4,1,2]=>[3,6,1,7,5,4,2]=>[5,2,7,1,3,4,6]=>[1,2,4]
[6,7,3,5,4,2,1]=>[7,3,1,6,5,4,2]=>[1,5,7,2,3,4,6]=>[3,4]
[6,7,4,1,2,3,5]=>[4,5,6,3,1,7,2]=>[4,3,2,5,7,1,6]=>[1,1,3,2]
[6,7,4,1,2,5,3]=>[7,4,5,3,1,6,2]=>[1,4,3,5,7,2,6]=>[2,3,2]
[6,7,4,1,3,2,5]=>[6,4,5,3,1,7,2]=>[2,4,3,5,7,1,6]=>[2,3,2]
[6,7,4,1,3,5,2]=>[5,7,4,3,1,6,2]=>[3,1,4,5,7,2,6]=>[1,4,2]
[6,7,4,1,5,2,3]=>[6,7,4,3,1,5,2]=>[2,1,4,5,7,3,6]=>[1,4,2]
[6,7,4,1,5,3,2]=>[7,6,4,3,1,5,2]=>[1,2,4,5,7,3,6]=>[5,2]
[6,7,4,2,1,3,5]=>[5,4,6,3,1,7,2]=>[3,4,2,5,7,1,6]=>[2,3,2]
[6,7,4,2,1,5,3]=>[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>[1,4,2]
[6,7,4,2,3,1,5]=>[4,6,5,3,1,7,2]=>[4,2,3,5,7,1,6]=>[1,4,2]
[6,7,4,2,3,5,1]=>[4,5,3,1,7,6,2]=>[4,3,5,7,1,2,6]=>[1,3,3]
[6,7,4,2,5,1,3]=>[4,6,3,1,7,5,2]=>[4,2,5,7,1,3,6]=>[1,3,3]
[6,7,4,2,5,3,1]=>[7,4,3,1,6,5,2]=>[1,4,5,7,2,3,6]=>[4,3]
[6,7,4,3,1,2,5]=>[5,6,4,3,1,7,2]=>[3,2,4,5,7,1,6]=>[1,4,2]
[6,7,4,3,1,5,2]=>[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>[5,2]
[6,7,4,3,2,1,5]=>[6,5,4,3,1,7,2]=>[2,3,4,5,7,1,6]=>[5,2]
[6,7,4,3,2,5,1]=>[5,4,3,1,7,6,2]=>[3,4,5,7,1,2,6]=>[4,3]
[6,7,4,3,5,1,2]=>[6,4,3,1,7,5,2]=>[2,4,5,7,1,3,6]=>[4,3]
[6,7,4,3,5,2,1]=>[4,3,1,7,6,5,2]=>[4,5,7,1,2,3,6]=>[3,4]
[6,7,4,5,1,2,3]=>[5,6,3,1,7,4,2]=>[3,2,5,7,1,4,6]=>[1,3,3]
[6,7,4,5,1,3,2]=>[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>[4,3]
[6,7,4,5,2,1,3]=>[6,5,3,1,7,4,2]=>[2,3,5,7,1,4,6]=>[4,3]
[6,7,4,5,2,3,1]=>[5,3,1,7,6,4,2]=>[3,5,7,1,2,4,6]=>[3,4]
[6,7,4,5,3,1,2]=>[6,3,1,7,5,4,2]=>[2,5,7,1,3,4,6]=>[3,4]
[6,7,4,5,3,2,1]=>[3,1,7,6,5,4,2]=>[5,7,1,2,3,4,6]=>[2,5]
[6,7,5,1,2,3,4]=>[4,5,6,1,7,3,2]=>[4,3,2,7,1,5,6]=>[1,1,2,3]
[6,7,5,1,2,4,3]=>[7,4,5,1,6,3,2]=>[1,4,3,7,2,5,6]=>[2,2,3]
[6,7,5,1,3,2,4]=>[6,4,5,1,7,3,2]=>[2,4,3,7,1,5,6]=>[2,2,3]
[6,7,5,1,3,4,2]=>[5,7,4,1,6,3,2]=>[3,1,4,7,2,5,6]=>[1,3,3]
[6,7,5,1,4,2,3]=>[6,7,4,1,5,3,2]=>[2,1,4,7,3,5,6]=>[1,3,3]
[6,7,5,1,4,3,2]=>[7,6,4,1,5,3,2]=>[1,2,4,7,3,5,6]=>[4,3]
[6,7,5,2,1,3,4]=>[5,4,6,1,7,3,2]=>[3,4,2,7,1,5,6]=>[2,2,3]
[6,7,5,2,1,4,3]=>[4,7,5,1,6,3,2]=>[4,1,3,7,2,5,6]=>[1,3,3]
[6,7,5,2,3,1,4]=>[4,6,5,1,7,3,2]=>[4,2,3,7,1,5,6]=>[1,3,3]
[6,7,5,2,3,4,1]=>[4,5,1,7,6,3,2]=>[4,3,7,1,2,5,6]=>[1,2,4]
[6,7,5,2,4,1,3]=>[4,6,1,7,5,3,2]=>[4,2,7,1,3,5,6]=>[1,2,4]
[6,7,5,2,4,3,1]=>[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>[3,4]
[6,7,5,3,1,2,4]=>[5,6,4,1,7,3,2]=>[3,2,4,7,1,5,6]=>[1,3,3]
[6,7,5,3,1,4,2]=>[7,5,4,1,6,3,2]=>[1,3,4,7,2,5,6]=>[4,3]
[6,7,5,3,2,1,4]=>[6,5,4,1,7,3,2]=>[2,3,4,7,1,5,6]=>[4,3]
[6,7,5,3,2,4,1]=>[5,4,1,7,6,3,2]=>[3,4,7,1,2,5,6]=>[3,4]
[6,7,5,3,4,1,2]=>[6,4,1,7,5,3,2]=>[2,4,7,1,3,5,6]=>[3,4]
[6,7,5,3,4,2,1]=>[4,1,7,6,5,3,2]=>[4,7,1,2,3,5,6]=>[2,5]
[6,7,5,4,1,2,3]=>[5,6,1,7,4,3,2]=>[3,2,7,1,4,5,6]=>[1,2,4]
[6,7,5,4,1,3,2]=>[7,5,1,6,4,3,2]=>[1,3,7,2,4,5,6]=>[3,4]
[6,7,5,4,2,1,3]=>[6,5,1,7,4,3,2]=>[2,3,7,1,4,5,6]=>[3,4]
[6,7,5,4,2,3,1]=>[5,1,7,6,4,3,2]=>[3,7,1,2,4,5,6]=>[2,5]
[6,7,5,4,3,1,2]=>[6,1,7,5,4,3,2]=>[2,7,1,3,4,5,6]=>[2,5]
[6,7,5,4,3,2,1]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[1,6]
[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]
[7,1,2,3,4,6,5]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[2,1,1,1,2]
[7,1,2,3,5,4,6]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[2,1,1,1,2]
[7,1,2,3,5,6,4]=>[5,7,2,3,4,6,1]=>[3,1,6,5,4,2,7]=>[1,2,1,1,2]
[7,1,2,3,6,4,5]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>[1,2,1,1,2]
[7,1,2,3,6,5,4]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>[3,1,1,2]
[7,1,2,4,3,5,6]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>[2,1,1,1,2]
[7,1,2,4,3,6,5]=>[4,7,2,3,5,6,1]=>[4,1,6,5,3,2,7]=>[1,2,1,1,2]
[7,1,2,4,5,3,6]=>[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>[1,2,1,1,2]
[7,1,2,4,5,6,3]=>[4,5,7,2,3,6,1]=>[4,3,1,6,5,2,7]=>[1,1,2,1,2]
[7,1,2,4,6,3,5]=>[4,6,7,2,3,5,1]=>[4,2,1,6,5,3,7]=>[1,1,2,1,2]
[7,1,2,4,6,5,3]=>[7,4,6,2,3,5,1]=>[1,4,2,6,5,3,7]=>[2,2,1,2]
[7,1,2,5,3,4,6]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>[1,2,1,1,2]
[7,1,2,5,3,6,4]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>[3,1,1,2]
[7,1,2,5,4,3,6]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>[3,1,1,2]
[7,1,2,5,4,6,3]=>[5,4,7,2,3,6,1]=>[3,4,1,6,5,2,7]=>[2,2,1,2]
[7,1,2,5,6,3,4]=>[6,4,7,2,3,5,1]=>[2,4,1,6,5,3,7]=>[2,2,1,2]
[7,1,2,5,6,4,3]=>[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>[1,3,1,2]
[7,1,2,6,3,4,5]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>[1,1,2,1,2]
[7,1,2,6,3,5,4]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>[2,2,1,2]
[7,1,2,6,4,3,5]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>[2,2,1,2]
[7,1,2,6,4,5,3]=>[5,7,6,2,3,4,1]=>[3,1,2,6,5,4,7]=>[1,3,1,2]
[7,1,2,6,5,3,4]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>[1,3,1,2]
[7,1,2,6,5,4,3]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>[4,1,2]
[7,1,3,2,4,5,6]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>[2,1,1,1,2]
[7,1,3,2,4,6,5]=>[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>[1,2,1,1,2]
[7,1,3,2,5,4,6]=>[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>[1,2,1,1,2]
[7,1,3,2,5,6,4]=>[3,5,7,2,4,6,1]=>[5,3,1,6,4,2,7]=>[1,1,2,1,2]
[7,1,3,2,6,4,5]=>[3,6,7,2,4,5,1]=>[5,2,1,6,4,3,7]=>[1,1,2,1,2]
[7,1,3,2,6,5,4]=>[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>[2,2,1,2]
[7,1,3,4,2,5,6]=>[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>[1,2,1,1,2]
[7,1,3,4,2,6,5]=>[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>[1,1,2,1,2]
[7,1,3,4,5,2,6]=>[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>[1,1,2,1,2]
[7,1,3,4,5,6,2]=>[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>[1,1,1,2,2]
[7,1,3,4,6,2,5]=>[3,4,6,7,2,5,1]=>[5,4,2,1,6,3,7]=>[1,1,1,2,2]
[7,1,3,4,6,5,2]=>[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>[2,1,2,2]
[7,1,3,5,2,4,6]=>[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>[1,1,2,1,2]
[7,1,3,5,2,6,4]=>[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>[2,2,1,2]
[7,1,3,5,4,2,6]=>[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>[2,2,1,2]
[7,1,3,5,4,6,2]=>[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>[2,1,2,2]
[7,1,3,5,6,2,4]=>[6,3,4,7,2,5,1]=>[2,5,4,1,6,3,7]=>[2,1,2,2]
[7,1,3,5,6,4,2]=>[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>[1,2,2,2]
[7,1,3,6,2,4,5]=>[3,5,6,7,2,4,1]=>[5,3,2,1,6,4,7]=>[1,1,1,2,2]
[7,1,3,6,2,5,4]=>[7,3,5,6,2,4,1]=>[1,5,3,2,6,4,7]=>[2,1,2,2]
[7,1,3,6,4,2,5]=>[6,3,5,7,2,4,1]=>[2,5,3,1,6,4,7]=>[2,1,2,2]
[7,1,3,6,4,5,2]=>[5,7,3,6,2,4,1]=>[3,1,5,2,6,4,7]=>[1,2,2,2]
[7,1,3,6,5,2,4]=>[6,7,3,5,2,4,1]=>[2,1,5,3,6,4,7]=>[1,2,2,2]
[7,1,3,6,5,4,2]=>[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>[3,2,2]
[7,1,4,2,3,5,6]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>[1,2,1,1,2]
[7,1,4,2,3,6,5]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>[3,1,1,2]
[7,1,4,2,5,3,6]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[3,1,1,2]
[7,1,4,2,5,6,3]=>[5,3,7,2,4,6,1]=>[3,5,1,6,4,2,7]=>[2,2,1,2]
[7,1,4,2,6,3,5]=>[6,3,7,2,4,5,1]=>[2,5,1,6,4,3,7]=>[2,2,1,2]
[7,1,4,2,6,5,3]=>[3,7,6,2,4,5,1]=>[5,1,2,6,4,3,7]=>[1,3,1,2]
[7,1,4,3,2,5,6]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>[3,1,1,2]
[7,1,4,3,2,6,5]=>[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>[2,2,1,2]
[7,1,4,3,5,2,6]=>[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>[2,2,1,2]
[7,1,4,3,5,6,2]=>[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>[2,1,2,2]
[7,1,4,3,6,2,5]=>[4,3,6,7,2,5,1]=>[4,5,2,1,6,3,7]=>[2,1,2,2]
[7,1,4,3,6,5,2]=>[3,7,4,6,2,5,1]=>[5,1,4,2,6,3,7]=>[1,2,2,2]
[7,1,4,5,2,3,6]=>[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>[2,2,1,2]
[7,1,4,5,2,6,3]=>[3,7,5,2,4,6,1]=>[5,1,3,6,4,2,7]=>[1,3,1,2]
[7,1,4,5,3,2,6]=>[3,6,5,2,4,7,1]=>[5,2,3,6,4,1,7]=>[1,3,1,2]
[7,1,4,5,3,6,2]=>[3,5,4,7,2,6,1]=>[5,3,4,1,6,2,7]=>[1,2,2,2]
[7,1,4,5,6,2,3]=>[3,6,4,7,2,5,1]=>[5,2,4,1,6,3,7]=>[1,2,2,2]
[7,1,4,5,6,3,2]=>[3,4,7,6,2,5,1]=>[5,4,1,2,6,3,7]=>[1,1,3,2]
[7,1,4,6,2,3,5]=>[5,3,6,7,2,4,1]=>[3,5,2,1,6,4,7]=>[2,1,2,2]
[7,1,4,6,2,5,3]=>[3,7,5,6,2,4,1]=>[5,1,3,2,6,4,7]=>[1,2,2,2]
[7,1,4,6,3,2,5]=>[3,6,5,7,2,4,1]=>[5,2,3,1,6,4,7]=>[1,2,2,2]
[7,1,4,6,3,5,2]=>[3,5,7,6,2,4,1]=>[5,3,1,2,6,4,7]=>[1,1,3,2]
[7,1,4,6,5,2,3]=>[3,6,7,5,2,4,1]=>[5,2,1,3,6,4,7]=>[1,1,3,2]
[7,1,4,6,5,3,2]=>[7,3,6,5,2,4,1]=>[1,5,2,3,6,4,7]=>[2,3,2]
[7,1,5,2,3,4,6]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>[1,1,2,1,2]
[7,1,5,2,3,6,4]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>[2,2,1,2]
[7,1,5,2,4,3,6]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>[2,2,1,2]
[7,1,5,2,4,6,3]=>[5,7,4,2,3,6,1]=>[3,1,4,6,5,2,7]=>[1,3,1,2]
[7,1,5,2,6,3,4]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>[1,3,1,2]
[7,1,5,2,6,4,3]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>[4,1,2]
[7,1,5,3,2,4,6]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>[2,2,1,2]
[7,1,5,3,2,6,4]=>[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>[1,3,1,2]
[7,1,5,3,4,2,6]=>[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>[1,3,1,2]
[7,1,5,3,4,6,2]=>[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>[1,2,2,2]
[7,1,5,3,6,2,4]=>[4,6,3,7,2,5,1]=>[4,2,5,1,6,3,7]=>[1,2,2,2]
[7,1,5,3,6,4,2]=>[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>[3,2,2]
[7,1,5,4,2,3,6]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>[1,3,1,2]
[7,1,5,4,2,6,3]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>[4,1,2]
[7,1,5,4,3,2,6]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>[4,1,2]
[7,1,5,4,3,6,2]=>[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>[3,2,2]
[7,1,5,4,6,2,3]=>[6,4,3,7,2,5,1]=>[2,4,5,1,6,3,7]=>[3,2,2]
[7,1,5,4,6,3,2]=>[4,3,7,6,2,5,1]=>[4,5,1,2,6,3,7]=>[2,3,2]
[7,1,5,6,2,3,4]=>[5,6,3,7,2,4,1]=>[3,2,5,1,6,4,7]=>[1,2,2,2]
[7,1,5,6,2,4,3]=>[7,5,3,6,2,4,1]=>[1,3,5,2,6,4,7]=>[3,2,2]
[7,1,5,6,3,2,4]=>[6,5,3,7,2,4,1]=>[2,3,5,1,6,4,7]=>[3,2,2]
[7,1,5,6,3,4,2]=>[5,3,7,6,2,4,1]=>[3,5,1,2,6,4,7]=>[2,3,2]
[7,1,5,6,4,2,3]=>[6,3,7,5,2,4,1]=>[2,5,1,3,6,4,7]=>[2,3,2]
[7,1,5,6,4,3,2]=>[3,7,6,5,2,4,1]=>[5,1,2,3,6,4,7]=>[1,4,2]
[7,1,6,2,3,4,5]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>[1,1,1,2,2]
[7,1,6,2,3,5,4]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>[2,1,2,2]
[7,1,6,2,4,3,5]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>[2,1,2,2]
[7,1,6,2,4,5,3]=>[5,7,4,6,2,3,1]=>[3,1,4,2,6,5,7]=>[1,2,2,2]
[7,1,6,2,5,3,4]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>[1,2,2,2]
[7,1,6,2,5,4,3]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>[3,2,2]
[7,1,6,3,2,4,5]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>[2,1,2,2]
[7,1,6,3,2,5,4]=>[4,7,5,6,2,3,1]=>[4,1,3,2,6,5,7]=>[1,2,2,2]
[7,1,6,3,4,2,5]=>[4,6,5,7,2,3,1]=>[4,2,3,1,6,5,7]=>[1,2,2,2]
[7,1,6,3,4,5,2]=>[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>[1,1,3,2]
[7,1,6,3,5,2,4]=>[4,6,7,5,2,3,1]=>[4,2,1,3,6,5,7]=>[1,1,3,2]
[7,1,6,3,5,4,2]=>[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>[2,3,2]
[7,1,6,4,2,3,5]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>[1,2,2,2]
[7,1,6,4,2,5,3]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>[3,2,2]
[7,1,6,4,3,2,5]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>[3,2,2]
[7,1,6,4,3,5,2]=>[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>[2,3,2]
[7,1,6,4,5,2,3]=>[6,4,7,5,2,3,1]=>[2,4,1,3,6,5,7]=>[2,3,2]
[7,1,6,4,5,3,2]=>[4,7,6,5,2,3,1]=>[4,1,2,3,6,5,7]=>[1,4,2]
[7,1,6,5,2,3,4]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>[1,1,3,2]
[7,1,6,5,2,4,3]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[2,3,2]
[7,1,6,5,3,2,4]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>[2,3,2]
[7,1,6,5,3,4,2]=>[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>[1,4,2]
[7,1,6,5,4,2,3]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>[1,4,2]
[7,1,6,5,4,3,2]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>[5,2]
[7,2,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>[2,1,1,1,2]
[7,2,1,3,4,6,5]=>[2,7,3,4,5,6,1]=>[6,1,5,4,3,2,7]=>[1,2,1,1,2]
[7,2,1,3,5,4,6]=>[2,6,3,4,5,7,1]=>[6,2,5,4,3,1,7]=>[1,2,1,1,2]
[7,2,1,3,5,6,4]=>[2,5,7,3,4,6,1]=>[6,3,1,5,4,2,7]=>[1,1,2,1,2]
[7,2,1,3,6,4,5]=>[2,6,7,3,4,5,1]=>[6,2,1,5,4,3,7]=>[1,1,2,1,2]
[7,2,1,3,6,5,4]=>[7,2,6,3,4,5,1]=>[1,6,2,5,4,3,7]=>[2,2,1,2]
[7,2,1,4,3,5,6]=>[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>[1,2,1,1,2]
[7,2,1,4,3,6,5]=>[2,4,7,3,5,6,1]=>[6,4,1,5,3,2,7]=>[1,1,2,1,2]
[7,2,1,4,5,3,6]=>[2,4,6,3,5,7,1]=>[6,4,2,5,3,1,7]=>[1,1,2,1,2]
[7,2,1,4,5,6,3]=>[2,4,5,7,3,6,1]=>[6,4,3,1,5,2,7]=>[1,1,1,2,2]
[7,2,1,4,6,3,5]=>[2,4,6,7,3,5,1]=>[6,4,2,1,5,3,7]=>[1,1,1,2,2]
[7,2,1,4,6,5,3]=>[7,2,4,6,3,5,1]=>[1,6,4,2,5,3,7]=>[2,1,2,2]
[7,2,1,5,3,4,6]=>[2,5,6,3,4,7,1]=>[6,3,2,5,4,1,7]=>[1,1,2,1,2]
[7,2,1,5,3,6,4]=>[7,2,5,3,4,6,1]=>[1,6,3,5,4,2,7]=>[2,2,1,2]
[7,2,1,5,4,3,6]=>[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>[2,2,1,2]
[7,2,1,5,4,6,3]=>[5,2,4,7,3,6,1]=>[3,6,4,1,5,2,7]=>[2,1,2,2]
[7,2,1,5,6,3,4]=>[6,2,4,7,3,5,1]=>[2,6,4,1,5,3,7]=>[2,1,2,2]
[7,2,1,5,6,4,3]=>[4,7,2,6,3,5,1]=>[4,1,6,2,5,3,7]=>[1,2,2,2]
[7,2,1,6,3,4,5]=>[2,5,6,7,3,4,1]=>[6,3,2,1,5,4,7]=>[1,1,1,2,2]
[7,2,1,6,3,5,4]=>[7,2,5,6,3,4,1]=>[1,6,3,2,5,4,7]=>[2,1,2,2]
[7,2,1,6,4,3,5]=>[6,2,5,7,3,4,1]=>[2,6,3,1,5,4,7]=>[2,1,2,2]
[7,2,1,6,4,5,3]=>[5,7,2,6,3,4,1]=>[3,1,6,2,5,4,7]=>[1,2,2,2]
[7,2,1,6,5,3,4]=>[6,7,2,5,3,4,1]=>[2,1,6,3,5,4,7]=>[1,2,2,2]
[7,2,1,6,5,4,3]=>[7,6,2,5,3,4,1]=>[1,2,6,3,5,4,7]=>[3,2,2]
[7,2,3,1,4,5,6]=>[2,4,3,5,6,7,1]=>[6,4,5,3,2,1,7]=>[1,2,1,1,2]
[7,2,3,1,4,6,5]=>[2,3,7,4,5,6,1]=>[6,5,1,4,3,2,7]=>[1,1,2,1,2]
[7,2,3,1,5,4,6]=>[2,3,6,4,5,7,1]=>[6,5,2,4,3,1,7]=>[1,1,2,1,2]
[7,2,3,1,5,6,4]=>[2,3,5,7,4,6,1]=>[6,5,3,1,4,2,7]=>[1,1,1,2,2]
[7,2,3,1,6,4,5]=>[2,3,6,7,4,5,1]=>[6,5,2,1,4,3,7]=>[1,1,1,2,2]
[7,2,3,1,6,5,4]=>[7,2,3,6,4,5,1]=>[1,6,5,2,4,3,7]=>[2,1,2,2]
[7,2,3,4,1,5,6]=>[2,3,5,4,6,7,1]=>[6,5,3,4,2,1,7]=>[1,1,2,1,2]
[7,2,3,4,1,6,5]=>[2,3,4,7,5,6,1]=>[6,5,4,1,3,2,7]=>[1,1,1,2,2]
[7,2,3,4,5,1,6]=>[2,3,4,6,5,7,1]=>[6,5,4,2,3,1,7]=>[1,1,1,2,2]
[7,2,3,4,5,6,1]=>[2,3,4,5,7,6,1]=>[6,5,4,3,1,2,7]=>[1,1,1,1,3]
[7,2,3,4,6,1,5]=>[2,3,4,6,7,5,1]=>[6,5,4,2,1,3,7]=>[1,1,1,1,3]
[7,2,3,4,6,5,1]=>[7,2,3,4,6,5,1]=>[1,6,5,4,2,3,7]=>[2,1,1,3]
[7,2,3,5,1,4,6]=>[2,3,5,6,4,7,1]=>[6,5,3,2,4,1,7]=>[1,1,1,2,2]
[7,2,3,5,1,6,4]=>[7,2,3,5,4,6,1]=>[1,6,5,3,4,2,7]=>[2,1,2,2]
[7,2,3,5,4,1,6]=>[6,2,3,5,4,7,1]=>[2,6,5,3,4,1,7]=>[2,1,2,2]
[7,2,3,5,4,6,1]=>[5,2,3,4,7,6,1]=>[3,6,5,4,1,2,7]=>[2,1,1,3]
[7,2,3,5,6,1,4]=>[6,2,3,4,7,5,1]=>[2,6,5,4,1,3,7]=>[2,1,1,3]
[7,2,3,5,6,4,1]=>[4,7,2,3,6,5,1]=>[4,1,6,5,2,3,7]=>[1,2,1,3]
[7,2,3,6,1,4,5]=>[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>[1,1,1,1,3]
[7,2,3,6,1,5,4]=>[7,2,3,5,6,4,1]=>[1,6,5,3,2,4,7]=>[2,1,1,3]
[7,2,3,6,4,1,5]=>[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>[2,1,1,3]
[7,2,3,6,4,5,1]=>[5,7,2,3,6,4,1]=>[3,1,6,5,2,4,7]=>[1,2,1,3]
[7,2,3,6,5,1,4]=>[6,7,2,3,5,4,1]=>[2,1,6,5,3,4,7]=>[1,2,1,3]
[7,2,3,6,5,4,1]=>[7,6,2,3,5,4,1]=>[1,2,6,5,3,4,7]=>[3,1,3]
[7,2,4,1,3,5,6]=>[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>[1,1,2,1,2]
[7,2,4,1,3,6,5]=>[7,2,4,3,5,6,1]=>[1,6,4,5,3,2,7]=>[2,2,1,2]
[7,2,4,1,5,3,6]=>[6,2,4,3,5,7,1]=>[2,6,4,5,3,1,7]=>[2,2,1,2]
[7,2,4,1,5,6,3]=>[5,2,3,7,4,6,1]=>[3,6,5,1,4,2,7]=>[2,1,2,2]
[7,2,4,1,6,3,5]=>[6,2,3,7,4,5,1]=>[2,6,5,1,4,3,7]=>[2,1,2,2]
[7,2,4,1,6,5,3]=>[3,7,2,6,4,5,1]=>[5,1,6,2,4,3,7]=>[1,2,2,2]
[7,2,4,3,1,5,6]=>[5,2,4,3,6,7,1]=>[3,6,4,5,2,1,7]=>[2,2,1,2]
[7,2,4,3,1,6,5]=>[4,2,3,7,5,6,1]=>[4,6,5,1,3,2,7]=>[2,1,2,2]
[7,2,4,3,5,1,6]=>[4,2,3,6,5,7,1]=>[4,6,5,2,3,1,7]=>[2,1,2,2]
[7,2,4,3,5,6,1]=>[4,2,3,5,7,6,1]=>[4,6,5,3,1,2,7]=>[2,1,1,3]
[7,2,4,3,6,1,5]=>[4,2,3,6,7,5,1]=>[4,6,5,2,1,3,7]=>[2,1,1,3]
[7,2,4,3,6,5,1]=>[3,7,2,4,6,5,1]=>[5,1,6,4,2,3,7]=>[1,2,1,3]
[7,2,4,5,1,3,6]=>[5,2,3,6,4,7,1]=>[3,6,5,2,4,1,7]=>[2,1,2,2]
[7,2,4,5,1,6,3]=>[3,7,2,5,4,6,1]=>[5,1,6,3,4,2,7]=>[1,2,2,2]
[7,2,4,5,3,1,6]=>[3,6,2,5,4,7,1]=>[5,2,6,3,4,1,7]=>[1,2,2,2]
[7,2,4,5,3,6,1]=>[3,5,2,4,7,6,1]=>[5,3,6,4,1,2,7]=>[1,2,1,3]
[7,2,4,5,6,1,3]=>[3,6,2,4,7,5,1]=>[5,2,6,4,1,3,7]=>[1,2,1,3]
[7,2,4,5,6,3,1]=>[3,4,7,2,6,5,1]=>[5,4,1,6,2,3,7]=>[1,1,2,3]
[7,2,4,6,1,3,5]=>[5,2,3,6,7,4,1]=>[3,6,5,2,1,4,7]=>[2,1,1,3]
[7,2,4,6,1,5,3]=>[3,7,2,5,6,4,1]=>[5,1,6,3,2,4,7]=>[1,2,1,3]
[7,2,4,6,3,1,5]=>[3,6,2,5,7,4,1]=>[5,2,6,3,1,4,7]=>[1,2,1,3]
[7,2,4,6,3,5,1]=>[3,5,7,2,6,4,1]=>[5,3,1,6,2,4,7]=>[1,1,2,3]
[7,2,4,6,5,1,3]=>[3,6,7,2,5,4,1]=>[5,2,1,6,3,4,7]=>[1,1,2,3]
[7,2,4,6,5,3,1]=>[7,3,6,2,5,4,1]=>[1,5,2,6,3,4,7]=>[2,2,3]
[7,2,5,1,3,4,6]=>[2,4,5,6,3,7,1]=>[6,4,3,2,5,1,7]=>[1,1,1,2,2]
[7,2,5,1,3,6,4]=>[7,2,4,5,3,6,1]=>[1,6,4,3,5,2,7]=>[2,1,2,2]
[7,2,5,1,4,3,6]=>[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>[2,1,2,2]
[7,2,5,1,4,6,3]=>[5,7,2,4,3,6,1]=>[3,1,6,4,5,2,7]=>[1,2,2,2]
[7,2,5,1,6,3,4]=>[6,7,2,4,3,5,1]=>[2,1,6,4,5,3,7]=>[1,2,2,2]
[7,2,5,1,6,4,3]=>[7,6,2,4,3,5,1]=>[1,2,6,4,5,3,7]=>[3,2,2]
[7,2,5,3,1,4,6]=>[5,2,4,6,3,7,1]=>[3,6,4,2,5,1,7]=>[2,1,2,2]
[7,2,5,3,1,6,4]=>[4,7,2,5,3,6,1]=>[4,1,6,3,5,2,7]=>[1,2,2,2]
[7,2,5,3,4,1,6]=>[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>[1,2,2,2]
[7,2,5,3,4,6,1]=>[4,5,2,3,7,6,1]=>[4,3,6,5,1,2,7]=>[1,2,1,3]
[7,2,5,3,6,1,4]=>[4,6,2,3,7,5,1]=>[4,2,6,5,1,3,7]=>[1,2,1,3]
[7,2,5,3,6,4,1]=>[7,4,2,3,6,5,1]=>[1,4,6,5,2,3,7]=>[3,1,3]
[7,2,5,4,1,3,6]=>[5,6,2,4,3,7,1]=>[3,2,6,4,5,1,7]=>[1,2,2,2]
[7,2,5,4,1,6,3]=>[7,5,2,4,3,6,1]=>[1,3,6,4,5,2,7]=>[3,2,2]
[7,2,5,4,3,1,6]=>[6,5,2,4,3,7,1]=>[2,3,6,4,5,1,7]=>[3,2,2]
[7,2,5,4,3,6,1]=>[5,4,2,3,7,6,1]=>[3,4,6,5,1,2,7]=>[3,1,3]
[7,2,5,4,6,1,3]=>[6,4,2,3,7,5,1]=>[2,4,6,5,1,3,7]=>[3,1,3]
[7,2,5,4,6,3,1]=>[4,3,7,2,6,5,1]=>[4,5,1,6,2,3,7]=>[2,2,3]
[7,2,5,6,1,3,4]=>[5,6,2,3,7,4,1]=>[3,2,6,5,1,4,7]=>[1,2,1,3]
[7,2,5,6,1,4,3]=>[7,5,2,3,6,4,1]=>[1,3,6,5,2,4,7]=>[3,1,3]
[7,2,5,6,3,1,4]=>[6,5,2,3,7,4,1]=>[2,3,6,5,1,4,7]=>[3,1,3]
[7,2,5,6,3,4,1]=>[5,3,7,2,6,4,1]=>[3,5,1,6,2,4,7]=>[2,2,3]
[7,2,5,6,4,1,3]=>[6,3,7,2,5,4,1]=>[2,5,1,6,3,4,7]=>[2,2,3]
[7,2,5,6,4,3,1]=>[3,7,6,2,5,4,1]=>[5,1,2,6,3,4,7]=>[1,3,3]
[7,2,6,1,3,4,5]=>[2,4,5,6,7,3,1]=>[6,4,3,2,1,5,7]=>[1,1,1,1,3]
[7,2,6,1,3,5,4]=>[7,2,4,5,6,3,1]=>[1,6,4,3,2,5,7]=>[2,1,1,3]
[7,2,6,1,4,3,5]=>[6,2,4,5,7,3,1]=>[2,6,4,3,1,5,7]=>[2,1,1,3]
[7,2,6,1,4,5,3]=>[5,7,2,4,6,3,1]=>[3,1,6,4,2,5,7]=>[1,2,1,3]
[7,2,6,1,5,3,4]=>[6,7,2,4,5,3,1]=>[2,1,6,4,3,5,7]=>[1,2,1,3]
[7,2,6,1,5,4,3]=>[7,6,2,4,5,3,1]=>[1,2,6,4,3,5,7]=>[3,1,3]
[7,2,6,3,1,4,5]=>[5,2,4,6,7,3,1]=>[3,6,4,2,1,5,7]=>[2,1,1,3]
[7,2,6,3,1,5,4]=>[4,7,2,5,6,3,1]=>[4,1,6,3,2,5,7]=>[1,2,1,3]
[7,2,6,3,4,1,5]=>[4,6,2,5,7,3,1]=>[4,2,6,3,1,5,7]=>[1,2,1,3]
[7,2,6,3,4,5,1]=>[4,5,7,2,6,3,1]=>[4,3,1,6,2,5,7]=>[1,1,2,3]
[7,2,6,3,5,1,4]=>[4,6,7,2,5,3,1]=>[4,2,1,6,3,5,7]=>[1,1,2,3]
[7,2,6,3,5,4,1]=>[7,4,6,2,5,3,1]=>[1,4,2,6,3,5,7]=>[2,2,3]
[7,2,6,4,1,3,5]=>[5,6,2,4,7,3,1]=>[3,2,6,4,1,5,7]=>[1,2,1,3]
[7,2,6,4,1,5,3]=>[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>[3,1,3]
[7,2,6,4,3,1,5]=>[6,5,2,4,7,3,1]=>[2,3,6,4,1,5,7]=>[3,1,3]
[7,2,6,4,3,5,1]=>[5,4,7,2,6,3,1]=>[3,4,1,6,2,5,7]=>[2,2,3]
[7,2,6,4,5,1,3]=>[6,4,7,2,5,3,1]=>[2,4,1,6,3,5,7]=>[2,2,3]
[7,2,6,4,5,3,1]=>[4,7,6,2,5,3,1]=>[4,1,2,6,3,5,7]=>[1,3,3]
[7,2,6,5,1,3,4]=>[5,6,7,2,4,3,1]=>[3,2,1,6,4,5,7]=>[1,1,2,3]
[7,2,6,5,1,4,3]=>[7,5,6,2,4,3,1]=>[1,3,2,6,4,5,7]=>[2,2,3]
[7,2,6,5,3,1,4]=>[6,5,7,2,4,3,1]=>[2,3,1,6,4,5,7]=>[2,2,3]
[7,2,6,5,3,4,1]=>[5,7,6,2,4,3,1]=>[3,1,2,6,4,5,7]=>[1,3,3]
[7,2,6,5,4,1,3]=>[6,7,5,2,4,3,1]=>[2,1,3,6,4,5,7]=>[1,3,3]
[7,2,6,5,4,3,1]=>[7,6,5,2,4,3,1]=>[1,2,3,6,4,5,7]=>[4,3]
[7,3,1,2,4,5,6]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>[1,2,1,1,2]
[7,3,1,2,4,6,5]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>[3,1,1,2]
[7,3,1,2,5,4,6]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>[3,1,1,2]
[7,3,1,2,5,6,4]=>[5,2,7,3,4,6,1]=>[3,6,1,5,4,2,7]=>[2,2,1,2]
[7,3,1,2,6,4,5]=>[6,2,7,3,4,5,1]=>[2,6,1,5,4,3,7]=>[2,2,1,2]
[7,3,1,2,6,5,4]=>[2,7,6,3,4,5,1]=>[6,1,2,5,4,3,7]=>[1,3,1,2]
[7,3,1,4,2,5,6]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>[3,1,1,2]
[7,3,1,4,2,6,5]=>[4,2,7,3,5,6,1]=>[4,6,1,5,3,2,7]=>[2,2,1,2]
[7,3,1,4,5,2,6]=>[4,2,6,3,5,7,1]=>[4,6,2,5,3,1,7]=>[2,2,1,2]
[7,3,1,4,5,6,2]=>[4,2,5,7,3,6,1]=>[4,6,3,1,5,2,7]=>[2,1,2,2]
[7,3,1,4,6,2,5]=>[4,2,6,7,3,5,1]=>[4,6,2,1,5,3,7]=>[2,1,2,2]
[7,3,1,4,6,5,2]=>[2,7,4,6,3,5,1]=>[6,1,4,2,5,3,7]=>[1,2,2,2]
[7,3,1,5,2,4,6]=>[5,2,6,3,4,7,1]=>[3,6,2,5,4,1,7]=>[2,2,1,2]
[7,3,1,5,2,6,4]=>[2,7,5,3,4,6,1]=>[6,1,3,5,4,2,7]=>[1,3,1,2]
[7,3,1,5,4,2,6]=>[2,6,5,3,4,7,1]=>[6,2,3,5,4,1,7]=>[1,3,1,2]
[7,3,1,5,4,6,2]=>[2,5,4,7,3,6,1]=>[6,3,4,1,5,2,7]=>[1,2,2,2]
[7,3,1,5,6,2,4]=>[2,6,4,7,3,5,1]=>[6,2,4,1,5,3,7]=>[1,2,2,2]
[7,3,1,5,6,4,2]=>[2,4,7,6,3,5,1]=>[6,4,1,2,5,3,7]=>[1,1,3,2]
[7,3,1,6,2,4,5]=>[5,2,6,7,3,4,1]=>[3,6,2,1,5,4,7]=>[2,1,2,2]
[7,3,1,6,2,5,4]=>[2,7,5,6,3,4,1]=>[6,1,3,2,5,4,7]=>[1,2,2,2]
[7,3,1,6,4,2,5]=>[2,6,5,7,3,4,1]=>[6,2,3,1,5,4,7]=>[1,2,2,2]
[7,3,1,6,4,5,2]=>[2,5,7,6,3,4,1]=>[6,3,1,2,5,4,7]=>[1,1,3,2]
[7,3,1,6,5,2,4]=>[2,6,7,5,3,4,1]=>[6,2,1,3,5,4,7]=>[1,1,3,2]
[7,3,1,6,5,4,2]=>[7,2,6,5,3,4,1]=>[1,6,2,3,5,4,7]=>[2,3,2]
[7,3,2,1,4,5,6]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>[3,1,1,2]
[7,3,2,1,4,6,5]=>[3,2,7,4,5,6,1]=>[5,6,1,4,3,2,7]=>[2,2,1,2]
[7,3,2,1,5,4,6]=>[3,2,6,4,5,7,1]=>[5,6,2,4,3,1,7]=>[2,2,1,2]
[7,3,2,1,5,6,4]=>[3,2,5,7,4,6,1]=>[5,6,3,1,4,2,7]=>[2,1,2,2]
[7,3,2,1,6,4,5]=>[3,2,6,7,4,5,1]=>[5,6,2,1,4,3,7]=>[2,1,2,2]
[7,3,2,1,6,5,4]=>[2,7,3,6,4,5,1]=>[6,1,5,2,4,3,7]=>[1,2,2,2]
[7,3,2,4,1,5,6]=>[3,2,5,4,6,7,1]=>[5,6,3,4,2,1,7]=>[2,2,1,2]
[7,3,2,4,1,6,5]=>[3,2,4,7,5,6,1]=>[5,6,4,1,3,2,7]=>[2,1,2,2]
[7,3,2,4,5,1,6]=>[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>[2,1,2,2]
[7,3,2,4,5,6,1]=>[3,2,4,5,7,6,1]=>[5,6,4,3,1,2,7]=>[2,1,1,3]
[7,3,2,4,6,1,5]=>[3,2,4,6,7,5,1]=>[5,6,4,2,1,3,7]=>[2,1,1,3]
[7,3,2,4,6,5,1]=>[2,7,3,4,6,5,1]=>[6,1,5,4,2,3,7]=>[1,2,1,3]
[7,3,2,5,1,4,6]=>[3,2,5,6,4,7,1]=>[5,6,3,2,4,1,7]=>[2,1,2,2]
[7,3,2,5,1,6,4]=>[2,7,3,5,4,6,1]=>[6,1,5,3,4,2,7]=>[1,2,2,2]
[7,3,2,5,4,1,6]=>[2,6,3,5,4,7,1]=>[6,2,5,3,4,1,7]=>[1,2,2,2]
[7,3,2,5,4,6,1]=>[2,5,3,4,7,6,1]=>[6,3,5,4,1,2,7]=>[1,2,1,3]
[7,3,2,5,6,1,4]=>[2,6,3,4,7,5,1]=>[6,2,5,4,1,3,7]=>[1,2,1,3]
[7,3,2,5,6,4,1]=>[2,4,7,3,6,5,1]=>[6,4,1,5,2,3,7]=>[1,1,2,3]
[7,3,2,6,1,4,5]=>[3,2,5,6,7,4,1]=>[5,6,3,2,1,4,7]=>[2,1,1,3]
[7,3,2,6,1,5,4]=>[2,7,3,5,6,4,1]=>[6,1,5,3,2,4,7]=>[1,2,1,3]
[7,3,2,6,4,1,5]=>[2,6,3,5,7,4,1]=>[6,2,5,3,1,4,7]=>[1,2,1,3]
[7,3,2,6,4,5,1]=>[2,5,7,3,6,4,1]=>[6,3,1,5,2,4,7]=>[1,1,2,3]
[7,3,2,6,5,1,4]=>[2,6,7,3,5,4,1]=>[6,2,1,5,3,4,7]=>[1,1,2,3]
[7,3,2,6,5,4,1]=>[7,2,6,3,5,4,1]=>[1,6,2,5,3,4,7]=>[2,2,3]
[7,3,4,1,2,5,6]=>[4,2,5,3,6,7,1]=>[4,6,3,5,2,1,7]=>[2,2,1,2]
[7,3,4,1,2,6,5]=>[2,7,4,3,5,6,1]=>[6,1,4,5,3,2,7]=>[1,3,1,2]
[7,3,4,1,5,2,6]=>[2,6,4,3,5,7,1]=>[6,2,4,5,3,1,7]=>[1,3,1,2]
[7,3,4,1,5,6,2]=>[2,5,3,7,4,6,1]=>[6,3,5,1,4,2,7]=>[1,2,2,2]
[7,3,4,1,6,2,5]=>[2,6,3,7,4,5,1]=>[6,2,5,1,4,3,7]=>[1,2,2,2]
[7,3,4,1,6,5,2]=>[2,3,7,6,4,5,1]=>[6,5,1,2,4,3,7]=>[1,1,3,2]
[7,3,4,2,1,5,6]=>[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>[1,3,1,2]
[7,3,4,2,1,6,5]=>[2,4,3,7,5,6,1]=>[6,4,5,1,3,2,7]=>[1,2,2,2]
[7,3,4,2,5,1,6]=>[2,4,3,6,5,7,1]=>[6,4,5,2,3,1,7]=>[1,2,2,2]
[7,3,4,2,5,6,1]=>[2,4,3,5,7,6,1]=>[6,4,5,3,1,2,7]=>[1,2,1,3]
[7,3,4,2,6,1,5]=>[2,4,3,6,7,5,1]=>[6,4,5,2,1,3,7]=>[1,2,1,3]
[7,3,4,2,6,5,1]=>[2,3,7,4,6,5,1]=>[6,5,1,4,2,3,7]=>[1,1,2,3]
[7,3,4,5,1,2,6]=>[2,5,3,6,4,7,1]=>[6,3,5,2,4,1,7]=>[1,2,2,2]
[7,3,4,5,1,6,2]=>[2,3,7,5,4,6,1]=>[6,5,1,3,4,2,7]=>[1,1,3,2]
[7,3,4,5,2,1,6]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,1,7]=>[1,1,3,2]
[7,3,4,5,2,6,1]=>[2,3,5,4,7,6,1]=>[6,5,3,4,1,2,7]=>[1,1,2,3]
[7,3,4,5,6,1,2]=>[2,3,6,4,7,5,1]=>[6,5,2,4,1,3,7]=>[1,1,2,3]
[7,3,4,5,6,2,1]=>[2,3,4,7,6,5,1]=>[6,5,4,1,2,3,7]=>[1,1,1,4]
[7,3,4,6,1,2,5]=>[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>[1,2,1,3]
[7,3,4,6,1,5,2]=>[2,3,7,5,6,4,1]=>[6,5,1,3,2,4,7]=>[1,1,2,3]
[7,3,4,6,2,1,5]=>[2,3,6,5,7,4,1]=>[6,5,2,3,1,4,7]=>[1,1,2,3]
[7,3,4,6,2,5,1]=>[2,3,5,7,6,4,1]=>[6,5,3,1,2,4,7]=>[1,1,1,4]
[7,3,4,6,5,1,2]=>[2,3,6,7,5,4,1]=>[6,5,2,1,3,4,7]=>[1,1,1,4]
[7,3,4,6,5,2,1]=>[7,2,3,6,5,4,1]=>[1,6,5,2,3,4,7]=>[2,1,4]
[7,3,5,1,2,4,6]=>[4,2,5,6,3,7,1]=>[4,6,3,2,5,1,7]=>[2,1,2,2]
[7,3,5,1,2,6,4]=>[2,7,4,5,3,6,1]=>[6,1,4,3,5,2,7]=>[1,2,2,2]
[7,3,5,1,4,2,6]=>[2,6,4,5,3,7,1]=>[6,2,4,3,5,1,7]=>[1,2,2,2]
[7,3,5,1,4,6,2]=>[2,5,7,4,3,6,1]=>[6,3,1,4,5,2,7]=>[1,1,3,2]
[7,3,5,1,6,2,4]=>[2,6,7,4,3,5,1]=>[6,2,1,4,5,3,7]=>[1,1,3,2]
[7,3,5,1,6,4,2]=>[7,2,6,4,3,5,1]=>[1,6,2,4,5,3,7]=>[2,3,2]
[7,3,5,2,1,4,6]=>[2,5,4,6,3,7,1]=>[6,3,4,2,5,1,7]=>[1,2,2,2]
[7,3,5,2,1,6,4]=>[2,4,7,5,3,6,1]=>[6,4,1,3,5,2,7]=>[1,1,3,2]
[7,3,5,2,4,1,6]=>[2,4,6,5,3,7,1]=>[6,4,2,3,5,1,7]=>[1,1,3,2]
[7,3,5,2,4,6,1]=>[2,4,5,3,7,6,1]=>[6,4,3,5,1,2,7]=>[1,1,2,3]
[7,3,5,2,6,1,4]=>[2,4,6,3,7,5,1]=>[6,4,2,5,1,3,7]=>[1,1,2,3]
[7,3,5,2,6,4,1]=>[7,2,4,3,6,5,1]=>[1,6,4,5,2,3,7]=>[2,2,3]
[7,3,5,4,1,2,6]=>[2,5,6,4,3,7,1]=>[6,3,2,4,5,1,7]=>[1,1,3,2]
[7,3,5,4,1,6,2]=>[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>[2,3,2]
[7,3,5,4,2,1,6]=>[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>[2,3,2]
[7,3,5,4,2,6,1]=>[5,2,4,3,7,6,1]=>[3,6,4,5,1,2,7]=>[2,2,3]
[7,3,5,4,6,1,2]=>[6,2,4,3,7,5,1]=>[2,6,4,5,1,3,7]=>[2,2,3]
[7,3,5,4,6,2,1]=>[4,2,3,7,6,5,1]=>[4,6,5,1,2,3,7]=>[2,1,4]
[7,3,5,6,1,2,4]=>[2,5,6,3,7,4,1]=>[6,3,2,5,1,4,7]=>[1,1,2,3]
[7,3,5,6,1,4,2]=>[7,2,5,3,6,4,1]=>[1,6,3,5,2,4,7]=>[2,2,3]
[7,3,5,6,2,1,4]=>[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>[2,2,3]
[7,3,5,6,2,4,1]=>[5,2,3,7,6,4,1]=>[3,6,5,1,2,4,7]=>[2,1,4]
[7,3,5,6,4,1,2]=>[6,2,3,7,5,4,1]=>[2,6,5,1,3,4,7]=>[2,1,4]
[7,3,5,6,4,2,1]=>[3,7,2,6,5,4,1]=>[5,1,6,2,3,4,7]=>[1,2,4]
[7,3,6,1,2,4,5]=>[4,2,5,6,7,3,1]=>[4,6,3,2,1,5,7]=>[2,1,1,3]
[7,3,6,1,2,5,4]=>[2,7,4,5,6,3,1]=>[6,1,4,3,2,5,7]=>[1,2,1,3]
[7,3,6,1,4,2,5]=>[2,6,4,5,7,3,1]=>[6,2,4,3,1,5,7]=>[1,2,1,3]
[7,3,6,1,4,5,2]=>[2,5,7,4,6,3,1]=>[6,3,1,4,2,5,7]=>[1,1,2,3]
[7,3,6,1,5,2,4]=>[2,6,7,4,5,3,1]=>[6,2,1,4,3,5,7]=>[1,1,2,3]
[7,3,6,1,5,4,2]=>[7,2,6,4,5,3,1]=>[1,6,2,4,3,5,7]=>[2,2,3]
[7,3,6,2,1,4,5]=>[2,5,4,6,7,3,1]=>[6,3,4,2,1,5,7]=>[1,2,1,3]
[7,3,6,2,1,5,4]=>[2,4,7,5,6,3,1]=>[6,4,1,3,2,5,7]=>[1,1,2,3]
[7,3,6,2,4,1,5]=>[2,4,6,5,7,3,1]=>[6,4,2,3,1,5,7]=>[1,1,2,3]
[7,3,6,2,4,5,1]=>[2,4,5,7,6,3,1]=>[6,4,3,1,2,5,7]=>[1,1,1,4]
[7,3,6,2,5,1,4]=>[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>[1,1,1,4]
[7,3,6,2,5,4,1]=>[7,2,4,6,5,3,1]=>[1,6,4,2,3,5,7]=>[2,1,4]
[7,3,6,4,1,2,5]=>[2,5,6,4,7,3,1]=>[6,3,2,4,1,5,7]=>[1,1,2,3]
[7,3,6,4,1,5,2]=>[7,2,5,4,6,3,1]=>[1,6,3,4,2,5,7]=>[2,2,3]
[7,3,6,4,2,1,5]=>[6,2,5,4,7,3,1]=>[2,6,3,4,1,5,7]=>[2,2,3]
[7,3,6,4,2,5,1]=>[5,2,4,7,6,3,1]=>[3,6,4,1,2,5,7]=>[2,1,4]
[7,3,6,4,5,1,2]=>[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>[2,1,4]
[7,3,6,4,5,2,1]=>[4,7,2,6,5,3,1]=>[4,1,6,2,3,5,7]=>[1,2,4]
[7,3,6,5,1,2,4]=>[2,5,6,7,4,3,1]=>[6,3,2,1,4,5,7]=>[1,1,1,4]
[7,3,6,5,1,4,2]=>[7,2,5,6,4,3,1]=>[1,6,3,2,4,5,7]=>[2,1,4]
[7,3,6,5,2,1,4]=>[6,2,5,7,4,3,1]=>[2,6,3,1,4,5,7]=>[2,1,4]
[7,3,6,5,2,4,1]=>[5,7,2,6,4,3,1]=>[3,1,6,2,4,5,7]=>[1,2,4]
[7,3,6,5,4,1,2]=>[6,7,2,5,4,3,1]=>[2,1,6,3,4,5,7]=>[1,2,4]
[7,3,6,5,4,2,1]=>[7,6,2,5,4,3,1]=>[1,2,6,3,4,5,7]=>[3,4]
[7,4,1,2,3,5,6]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>[1,1,2,1,2]
[7,4,1,2,3,6,5]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>[2,2,1,2]
[7,4,1,2,5,3,6]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>[2,2,1,2]
[7,4,1,2,5,6,3]=>[5,7,3,2,4,6,1]=>[3,1,5,6,4,2,7]=>[1,3,1,2]
[7,4,1,2,6,3,5]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>[1,3,1,2]
[7,4,1,2,6,5,3]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>[4,1,2]
[7,4,1,3,2,5,6]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>[2,2,1,2]
[7,4,1,3,2,6,5]=>[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>[1,3,1,2]
[7,4,1,3,5,2,6]=>[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>[1,3,1,2]
[7,4,1,3,5,6,2]=>[4,5,2,7,3,6,1]=>[4,3,6,1,5,2,7]=>[1,2,2,2]
[7,4,1,3,6,2,5]=>[4,6,2,7,3,5,1]=>[4,2,6,1,5,3,7]=>[1,2,2,2]
[7,4,1,3,6,5,2]=>[7,4,2,6,3,5,1]=>[1,4,6,2,5,3,7]=>[3,2,2]
[7,4,1,5,2,3,6]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>[1,3,1,2]
[7,4,1,5,2,6,3]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>[4,1,2]
[7,4,1,5,3,2,6]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[4,1,2]
[7,4,1,5,3,6,2]=>[5,4,2,7,3,6,1]=>[3,4,6,1,5,2,7]=>[3,2,2]
[7,4,1,5,6,2,3]=>[6,4,2,7,3,5,1]=>[2,4,6,1,5,3,7]=>[3,2,2]
[7,4,1,5,6,3,2]=>[4,2,7,6,3,5,1]=>[4,6,1,2,5,3,7]=>[2,3,2]
[7,4,1,6,2,3,5]=>[5,6,2,7,3,4,1]=>[3,2,6,1,5,4,7]=>[1,2,2,2]
[7,4,1,6,2,5,3]=>[7,5,2,6,3,4,1]=>[1,3,6,2,5,4,7]=>[3,2,2]
[7,4,1,6,3,2,5]=>[6,5,2,7,3,4,1]=>[2,3,6,1,5,4,7]=>[3,2,2]
[7,4,1,6,3,5,2]=>[5,2,7,6,3,4,1]=>[3,6,1,2,5,4,7]=>[2,3,2]
[7,4,1,6,5,2,3]=>[6,2,7,5,3,4,1]=>[2,6,1,3,5,4,7]=>[2,3,2]
[7,4,1,6,5,3,2]=>[2,7,6,5,3,4,1]=>[6,1,2,3,5,4,7]=>[1,4,2]
[7,4,2,1,3,5,6]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>[2,2,1,2]
[7,4,2,1,3,6,5]=>[3,7,4,2,5,6,1]=>[5,1,4,6,3,2,7]=>[1,3,1,2]
[7,4,2,1,5,3,6]=>[3,6,4,2,5,7,1]=>[5,2,4,6,3,1,7]=>[1,3,1,2]
[7,4,2,1,5,6,3]=>[3,5,2,7,4,6,1]=>[5,3,6,1,4,2,7]=>[1,2,2,2]
[7,4,2,1,6,3,5]=>[3,6,2,7,4,5,1]=>[5,2,6,1,4,3,7]=>[1,2,2,2]
[7,4,2,1,6,5,3]=>[7,3,2,6,4,5,1]=>[1,5,6,2,4,3,7]=>[3,2,2]
[7,4,2,3,1,5,6]=>[3,5,4,2,6,7,1]=>[5,3,4,6,2,1,7]=>[1,3,1,2]
[7,4,2,3,1,6,5]=>[3,4,2,7,5,6,1]=>[5,4,6,1,3,2,7]=>[1,2,2,2]
[7,4,2,3,5,1,6]=>[3,4,2,6,5,7,1]=>[5,4,6,2,3,1,7]=>[1,2,2,2]
[7,4,2,3,5,6,1]=>[3,4,2,5,7,6,1]=>[5,4,6,3,1,2,7]=>[1,2,1,3]
[7,4,2,3,6,1,5]=>[3,4,2,6,7,5,1]=>[5,4,6,2,1,3,7]=>[1,2,1,3]
[7,4,2,3,6,5,1]=>[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>[3,1,3]
[7,4,2,5,1,3,6]=>[3,5,2,6,4,7,1]=>[5,3,6,2,4,1,7]=>[1,2,2,2]
[7,4,2,5,1,6,3]=>[7,3,2,5,4,6,1]=>[1,5,6,3,4,2,7]=>[3,2,2]
[7,4,2,5,3,1,6]=>[6,3,2,5,4,7,1]=>[2,5,6,3,4,1,7]=>[3,2,2]
[7,4,2,5,3,6,1]=>[5,3,2,4,7,6,1]=>[3,5,6,4,1,2,7]=>[3,1,3]
[7,4,2,5,6,1,3]=>[6,3,2,4,7,5,1]=>[2,5,6,4,1,3,7]=>[3,1,3]
[7,4,2,5,6,3,1]=>[4,2,7,3,6,5,1]=>[4,6,1,5,2,3,7]=>[2,2,3]
[7,4,2,6,1,3,5]=>[3,5,2,6,7,4,1]=>[5,3,6,2,1,4,7]=>[1,2,1,3]
[7,4,2,6,1,5,3]=>[7,3,2,5,6,4,1]=>[1,5,6,3,2,4,7]=>[3,1,3]
[7,4,2,6,3,1,5]=>[6,3,2,5,7,4,1]=>[2,5,6,3,1,4,7]=>[3,1,3]
[7,4,2,6,3,5,1]=>[5,2,7,3,6,4,1]=>[3,6,1,5,2,4,7]=>[2,2,3]
[7,4,2,6,5,1,3]=>[6,2,7,3,5,4,1]=>[2,6,1,5,3,4,7]=>[2,2,3]
[7,4,2,6,5,3,1]=>[2,7,6,3,5,4,1]=>[6,1,2,5,3,4,7]=>[1,3,3]
[7,4,3,1,2,5,6]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>[1,3,1,2]
[7,4,3,1,2,6,5]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>[4,1,2]
[7,4,3,1,5,2,6]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>[4,1,2]
[7,4,3,1,5,6,2]=>[5,3,2,7,4,6,1]=>[3,5,6,1,4,2,7]=>[3,2,2]
[7,4,3,1,6,2,5]=>[6,3,2,7,4,5,1]=>[2,5,6,1,4,3,7]=>[3,2,2]
[7,4,3,1,6,5,2]=>[3,2,7,6,4,5,1]=>[5,6,1,2,4,3,7]=>[2,3,2]
[7,4,3,2,1,5,6]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>[4,1,2]
[7,4,3,2,1,6,5]=>[4,3,2,7,5,6,1]=>[4,5,6,1,3,2,7]=>[3,2,2]
[7,4,3,2,5,1,6]=>[4,3,2,6,5,7,1]=>[4,5,6,2,3,1,7]=>[3,2,2]
[7,4,3,2,5,6,1]=>[4,3,2,5,7,6,1]=>[4,5,6,3,1,2,7]=>[3,1,3]
[7,4,3,2,6,1,5]=>[4,3,2,6,7,5,1]=>[4,5,6,2,1,3,7]=>[3,1,3]
[7,4,3,2,6,5,1]=>[3,2,7,4,6,5,1]=>[5,6,1,4,2,3,7]=>[2,2,3]
[7,4,3,5,1,2,6]=>[5,3,2,6,4,7,1]=>[3,5,6,2,4,1,7]=>[3,2,2]
[7,4,3,5,1,6,2]=>[3,2,7,5,4,6,1]=>[5,6,1,3,4,2,7]=>[2,3,2]
[7,4,3,5,2,1,6]=>[3,2,6,5,4,7,1]=>[5,6,2,3,4,1,7]=>[2,3,2]
[7,4,3,5,2,6,1]=>[3,2,5,4,7,6,1]=>[5,6,3,4,1,2,7]=>[2,2,3]
[7,4,3,5,6,1,2]=>[3,2,6,4,7,5,1]=>[5,6,2,4,1,3,7]=>[2,2,3]
[7,4,3,5,6,2,1]=>[3,2,4,7,6,5,1]=>[5,6,4,1,2,3,7]=>[2,1,4]
[7,4,3,6,1,2,5]=>[5,3,2,6,7,4,1]=>[3,5,6,2,1,4,7]=>[3,1,3]
[7,4,3,6,1,5,2]=>[3,2,7,5,6,4,1]=>[5,6,1,3,2,4,7]=>[2,2,3]
[7,4,3,6,2,1,5]=>[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>[2,2,3]
[7,4,3,6,2,5,1]=>[3,2,5,7,6,4,1]=>[5,6,3,1,2,4,7]=>[2,1,4]
[7,4,3,6,5,1,2]=>[3,2,6,7,5,4,1]=>[5,6,2,1,3,4,7]=>[2,1,4]
[7,4,3,6,5,2,1]=>[2,7,3,6,5,4,1]=>[6,1,5,2,3,4,7]=>[1,2,4]
[7,4,5,1,2,3,6]=>[4,5,2,6,3,7,1]=>[4,3,6,2,5,1,7]=>[1,2,2,2]
[7,4,5,1,2,6,3]=>[7,4,2,5,3,6,1]=>[1,4,6,3,5,2,7]=>[3,2,2]
[7,4,5,1,3,2,6]=>[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>[3,2,2]
[7,4,5,1,3,6,2]=>[5,2,7,4,3,6,1]=>[3,6,1,4,5,2,7]=>[2,3,2]
[7,4,5,1,6,2,3]=>[6,2,7,4,3,5,1]=>[2,6,1,4,5,3,7]=>[2,3,2]
[7,4,5,1,6,3,2]=>[2,7,6,4,3,5,1]=>[6,1,2,4,5,3,7]=>[1,4,2]
[7,4,5,2,1,3,6]=>[5,4,2,6,3,7,1]=>[3,4,6,2,5,1,7]=>[3,2,2]
[7,4,5,2,1,6,3]=>[4,2,7,5,3,6,1]=>[4,6,1,3,5,2,7]=>[2,3,2]
[7,4,5,2,3,1,6]=>[4,2,6,5,3,7,1]=>[4,6,2,3,5,1,7]=>[2,3,2]
[7,4,5,2,3,6,1]=>[4,2,5,3,7,6,1]=>[4,6,3,5,1,2,7]=>[2,2,3]
[7,4,5,2,6,1,3]=>[4,2,6,3,7,5,1]=>[4,6,2,5,1,3,7]=>[2,2,3]
[7,4,5,2,6,3,1]=>[2,7,4,3,6,5,1]=>[6,1,4,5,2,3,7]=>[1,3,3]
[7,4,5,3,1,2,6]=>[5,2,6,4,3,7,1]=>[3,6,2,4,5,1,7]=>[2,3,2]
[7,4,5,3,1,6,2]=>[2,7,5,4,3,6,1]=>[6,1,3,4,5,2,7]=>[1,4,2]
[7,4,5,3,2,1,6]=>[2,6,5,4,3,7,1]=>[6,2,3,4,5,1,7]=>[1,4,2]
[7,4,5,3,2,6,1]=>[2,5,4,3,7,6,1]=>[6,3,4,5,1,2,7]=>[1,3,3]
[7,4,5,3,6,1,2]=>[2,6,4,3,7,5,1]=>[6,2,4,5,1,3,7]=>[1,3,3]
[7,4,5,3,6,2,1]=>[2,4,3,7,6,5,1]=>[6,4,5,1,2,3,7]=>[1,2,4]
[7,4,5,6,1,2,3]=>[5,2,6,3,7,4,1]=>[3,6,2,5,1,4,7]=>[2,2,3]
[7,4,5,6,1,3,2]=>[2,7,5,3,6,4,1]=>[6,1,3,5,2,4,7]=>[1,3,3]
[7,4,5,6,2,1,3]=>[2,6,5,3,7,4,1]=>[6,2,3,5,1,4,7]=>[1,3,3]
[7,4,5,6,2,3,1]=>[2,5,3,7,6,4,1]=>[6,3,5,1,2,4,7]=>[1,2,4]
[7,4,5,6,3,1,2]=>[2,6,3,7,5,4,1]=>[6,2,5,1,3,4,7]=>[1,2,4]
[7,4,5,6,3,2,1]=>[2,3,7,6,5,4,1]=>[6,5,1,2,3,4,7]=>[1,1,5]
[7,4,6,1,2,3,5]=>[4,5,2,6,7,3,1]=>[4,3,6,2,1,5,7]=>[1,2,1,3]
[7,4,6,1,2,5,3]=>[7,4,2,5,6,3,1]=>[1,4,6,3,2,5,7]=>[3,1,3]
[7,4,6,1,3,2,5]=>[6,4,2,5,7,3,1]=>[2,4,6,3,1,5,7]=>[3,1,3]
[7,4,6,1,3,5,2]=>[5,2,7,4,6,3,1]=>[3,6,1,4,2,5,7]=>[2,2,3]
[7,4,6,1,5,2,3]=>[6,2,7,4,5,3,1]=>[2,6,1,4,3,5,7]=>[2,2,3]
[7,4,6,1,5,3,2]=>[2,7,6,4,5,3,1]=>[6,1,2,4,3,5,7]=>[1,3,3]
[7,4,6,2,1,3,5]=>[5,4,2,6,7,3,1]=>[3,4,6,2,1,5,7]=>[3,1,3]
[7,4,6,2,1,5,3]=>[4,2,7,5,6,3,1]=>[4,6,1,3,2,5,7]=>[2,2,3]
[7,4,6,2,3,1,5]=>[4,2,6,5,7,3,1]=>[4,6,2,3,1,5,7]=>[2,2,3]
[7,4,6,2,3,5,1]=>[4,2,5,7,6,3,1]=>[4,6,3,1,2,5,7]=>[2,1,4]
[7,4,6,2,5,1,3]=>[4,2,6,7,5,3,1]=>[4,6,2,1,3,5,7]=>[2,1,4]
[7,4,6,2,5,3,1]=>[2,7,4,6,5,3,1]=>[6,1,4,2,3,5,7]=>[1,2,4]
[7,4,6,3,1,2,5]=>[5,2,6,4,7,3,1]=>[3,6,2,4,1,5,7]=>[2,2,3]
[7,4,6,3,1,5,2]=>[2,7,5,4,6,3,1]=>[6,1,3,4,2,5,7]=>[1,3,3]
[7,4,6,3,2,1,5]=>[2,6,5,4,7,3,1]=>[6,2,3,4,1,5,7]=>[1,3,3]
[7,4,6,3,2,5,1]=>[2,5,4,7,6,3,1]=>[6,3,4,1,2,5,7]=>[1,2,4]
[7,4,6,3,5,1,2]=>[2,6,4,7,5,3,1]=>[6,2,4,1,3,5,7]=>[1,2,4]
[7,4,6,3,5,2,1]=>[2,4,7,6,5,3,1]=>[6,4,1,2,3,5,7]=>[1,1,5]
[7,4,6,5,1,2,3]=>[5,2,6,7,4,3,1]=>[3,6,2,1,4,5,7]=>[2,1,4]
[7,4,6,5,1,3,2]=>[2,7,5,6,4,3,1]=>[6,1,3,2,4,5,7]=>[1,2,4]
[7,4,6,5,2,1,3]=>[2,6,5,7,4,3,1]=>[6,2,3,1,4,5,7]=>[1,2,4]
[7,4,6,5,2,3,1]=>[2,5,7,6,4,3,1]=>[6,3,1,2,4,5,7]=>[1,1,5]
[7,4,6,5,3,1,2]=>[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>[1,1,5]
[7,4,6,5,3,2,1]=>[7,2,6,5,4,3,1]=>[1,6,2,3,4,5,7]=>[2,5]
[7,5,1,2,3,4,6]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[1,1,1,2,2]
[7,5,1,2,3,6,4]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>[2,1,2,2]
[7,5,1,2,4,3,6]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>[2,1,2,2]
[7,5,1,2,4,6,3]=>[5,7,3,4,2,6,1]=>[3,1,5,4,6,2,7]=>[1,2,2,2]
[7,5,1,2,6,3,4]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>[1,2,2,2]
[7,5,1,2,6,4,3]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>[3,2,2]
[7,5,1,3,2,4,6]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[2,1,2,2]
[7,5,1,3,2,6,4]=>[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>[1,2,2,2]
[7,5,1,3,4,2,6]=>[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>[1,2,2,2]
[7,5,1,3,4,6,2]=>[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>[1,1,3,2]
[7,5,1,3,6,2,4]=>[4,6,7,3,2,5,1]=>[4,2,1,5,6,3,7]=>[1,1,3,2]
[7,5,1,3,6,4,2]=>[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>[2,3,2]
[7,5,1,4,2,3,6]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>[1,2,2,2]
[7,5,1,4,2,6,3]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>[3,2,2]
[7,5,1,4,3,2,6]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>[3,2,2]
[7,5,1,4,3,6,2]=>[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>[2,3,2]
[7,5,1,4,6,2,3]=>[6,4,7,3,2,5,1]=>[2,4,1,5,6,3,7]=>[2,3,2]
[7,5,1,4,6,3,2]=>[4,7,6,3,2,5,1]=>[4,1,2,5,6,3,7]=>[1,4,2]
[7,5,1,6,2,3,4]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>[1,1,3,2]
[7,5,1,6,2,4,3]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>[2,3,2]
[7,5,1,6,3,2,4]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>[2,3,2]
[7,5,1,6,3,4,2]=>[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>[1,4,2]
[7,5,1,6,4,2,3]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>[1,4,2]
[7,5,1,6,4,3,2]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>[5,2]
[7,5,2,1,3,4,6]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>[2,1,2,2]
[7,5,2,1,3,6,4]=>[3,7,4,5,2,6,1]=>[5,1,4,3,6,2,7]=>[1,2,2,2]
[7,5,2,1,4,3,6]=>[3,6,4,5,2,7,1]=>[5,2,4,3,6,1,7]=>[1,2,2,2]
[7,5,2,1,4,6,3]=>[3,5,7,4,2,6,1]=>[5,3,1,4,6,2,7]=>[1,1,3,2]
[7,5,2,1,6,3,4]=>[3,6,7,4,2,5,1]=>[5,2,1,4,6,3,7]=>[1,1,3,2]
[7,5,2,1,6,4,3]=>[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>[2,3,2]
[7,5,2,3,1,4,6]=>[3,5,4,6,2,7,1]=>[5,3,4,2,6,1,7]=>[1,2,2,2]
[7,5,2,3,1,6,4]=>[3,4,7,5,2,6,1]=>[5,4,1,3,6,2,7]=>[1,1,3,2]
[7,5,2,3,4,1,6]=>[3,4,6,5,2,7,1]=>[5,4,2,3,6,1,7]=>[1,1,3,2]
[7,5,2,3,4,6,1]=>[3,4,5,2,7,6,1]=>[5,4,3,6,1,2,7]=>[1,1,2,3]
[7,5,2,3,6,1,4]=>[3,4,6,2,7,5,1]=>[5,4,2,6,1,3,7]=>[1,1,2,3]
[7,5,2,3,6,4,1]=>[7,3,4,2,6,5,1]=>[1,5,4,6,2,3,7]=>[2,2,3]
[7,5,2,4,1,3,6]=>[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>[1,1,3,2]
[7,5,2,4,1,6,3]=>[7,3,5,4,2,6,1]=>[1,5,3,4,6,2,7]=>[2,3,2]
[7,5,2,4,3,1,6]=>[6,3,5,4,2,7,1]=>[2,5,3,4,6,1,7]=>[2,3,2]
[7,5,2,4,3,6,1]=>[5,3,4,2,7,6,1]=>[3,5,4,6,1,2,7]=>[2,2,3]
[7,5,2,4,6,1,3]=>[6,3,4,2,7,5,1]=>[2,5,4,6,1,3,7]=>[2,2,3]
[7,5,2,4,6,3,1]=>[4,7,3,2,6,5,1]=>[4,1,5,6,2,3,7]=>[1,3,3]
[7,5,2,6,1,3,4]=>[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>[1,1,2,3]
[7,5,2,6,1,4,3]=>[7,3,5,2,6,4,1]=>[1,5,3,6,2,4,7]=>[2,2,3]
[7,5,2,6,3,1,4]=>[6,3,5,2,7,4,1]=>[2,5,3,6,1,4,7]=>[2,2,3]
[7,5,2,6,3,4,1]=>[5,7,3,2,6,4,1]=>[3,1,5,6,2,4,7]=>[1,3,3]
[7,5,2,6,4,1,3]=>[6,7,3,2,5,4,1]=>[2,1,5,6,3,4,7]=>[1,3,3]
[7,5,2,6,4,3,1]=>[7,6,3,2,5,4,1]=>[1,2,5,6,3,4,7]=>[4,3]
[7,5,3,1,2,4,6]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[1,2,2,2]
[7,5,3,1,2,6,4]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>[3,2,2]
[7,5,3,1,4,2,6]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>[3,2,2]
[7,5,3,1,4,6,2]=>[5,3,7,4,2,6,1]=>[3,5,1,4,6,2,7]=>[2,3,2]
[7,5,3,1,6,2,4]=>[6,3,7,4,2,5,1]=>[2,5,1,4,6,3,7]=>[2,3,2]
[7,5,3,1,6,4,2]=>[3,7,6,4,2,5,1]=>[5,1,2,4,6,3,7]=>[1,4,2]
[7,5,3,2,1,4,6]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[3,2,2]
[7,5,3,2,1,6,4]=>[4,3,7,5,2,6,1]=>[4,5,1,3,6,2,7]=>[2,3,2]
[7,5,3,2,4,1,6]=>[4,3,6,5,2,7,1]=>[4,5,2,3,6,1,7]=>[2,3,2]
[7,5,3,2,4,6,1]=>[4,3,5,2,7,6,1]=>[4,5,3,6,1,2,7]=>[2,2,3]
[7,5,3,2,6,1,4]=>[4,3,6,2,7,5,1]=>[4,5,2,6,1,3,7]=>[2,2,3]
[7,5,3,2,6,4,1]=>[3,7,4,2,6,5,1]=>[5,1,4,6,2,3,7]=>[1,3,3]
[7,5,3,4,1,2,6]=>[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>[2,3,2]
[7,5,3,4,1,6,2]=>[3,7,5,4,2,6,1]=>[5,1,3,4,6,2,7]=>[1,4,2]
[7,5,3,4,2,1,6]=>[3,6,5,4,2,7,1]=>[5,2,3,4,6,1,7]=>[1,4,2]
[7,5,3,4,2,6,1]=>[3,5,4,2,7,6,1]=>[5,3,4,6,1,2,7]=>[1,3,3]
[7,5,3,4,6,1,2]=>[3,6,4,2,7,5,1]=>[5,2,4,6,1,3,7]=>[1,3,3]
[7,5,3,4,6,2,1]=>[3,4,2,7,6,5,1]=>[5,4,6,1,2,3,7]=>[1,2,4]
[7,5,3,6,1,2,4]=>[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>[2,2,3]
[7,5,3,6,1,4,2]=>[3,7,5,2,6,4,1]=>[5,1,3,6,2,4,7]=>[1,3,3]
[7,5,3,6,2,1,4]=>[3,6,5,2,7,4,1]=>[5,2,3,6,1,4,7]=>[1,3,3]
[7,5,3,6,2,4,1]=>[3,5,2,7,6,4,1]=>[5,3,6,1,2,4,7]=>[1,2,4]
[7,5,3,6,4,1,2]=>[3,6,2,7,5,4,1]=>[5,2,6,1,3,4,7]=>[1,2,4]
[7,5,3,6,4,2,1]=>[7,3,2,6,5,4,1]=>[1,5,6,2,3,4,7]=>[3,4]
[7,5,4,1,2,3,6]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>[1,1,3,2]
[7,5,4,1,2,6,3]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>[2,3,2]
[7,5,4,1,3,2,6]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>[2,3,2]
[7,5,4,1,3,6,2]=>[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>[1,4,2]
[7,5,4,1,6,2,3]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>[1,4,2]
[7,5,4,1,6,3,2]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>[5,2]
[7,5,4,2,1,3,6]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>[2,3,2]
[7,5,4,2,1,6,3]=>[4,7,5,3,2,6,1]=>[4,1,3,5,6,2,7]=>[1,4,2]
[7,5,4,2,3,1,6]=>[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>[1,4,2]
[7,5,4,2,3,6,1]=>[4,5,3,2,7,6,1]=>[4,3,5,6,1,2,7]=>[1,3,3]
[7,5,4,2,6,1,3]=>[4,6,3,2,7,5,1]=>[4,2,5,6,1,3,7]=>[1,3,3]
[7,5,4,2,6,3,1]=>[7,4,3,2,6,5,1]=>[1,4,5,6,2,3,7]=>[4,3]
[7,5,4,3,1,2,6]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>[1,4,2]
[7,5,4,3,1,6,2]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>[5,2]
[7,5,4,3,2,1,6]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[5,2]
[7,5,4,3,2,6,1]=>[5,4,3,2,7,6,1]=>[3,4,5,6,1,2,7]=>[4,3]
[7,5,4,3,6,1,2]=>[6,4,3,2,7,5,1]=>[2,4,5,6,1,3,7]=>[4,3]
[7,5,4,3,6,2,1]=>[4,3,2,7,6,5,1]=>[4,5,6,1,2,3,7]=>[3,4]
[7,5,4,6,1,2,3]=>[5,6,3,2,7,4,1]=>[3,2,5,6,1,4,7]=>[1,3,3]
[7,5,4,6,1,3,2]=>[7,5,3,2,6,4,1]=>[1,3,5,6,2,4,7]=>[4,3]
[7,5,4,6,2,1,3]=>[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>[4,3]
[7,5,4,6,2,3,1]=>[5,3,2,7,6,4,1]=>[3,5,6,1,2,4,7]=>[3,4]
[7,5,4,6,3,1,2]=>[6,3,2,7,5,4,1]=>[2,5,6,1,3,4,7]=>[3,4]
[7,5,4,6,3,2,1]=>[3,2,7,6,5,4,1]=>[5,6,1,2,3,4,7]=>[2,5]
[7,5,6,1,2,3,4]=>[4,5,6,2,7,3,1]=>[4,3,2,6,1,5,7]=>[1,1,2,3]
[7,5,6,1,2,4,3]=>[7,4,5,2,6,3,1]=>[1,4,3,6,2,5,7]=>[2,2,3]
[7,5,6,1,3,2,4]=>[6,4,5,2,7,3,1]=>[2,4,3,6,1,5,7]=>[2,2,3]
[7,5,6,1,3,4,2]=>[5,7,4,2,6,3,1]=>[3,1,4,6,2,5,7]=>[1,3,3]
[7,5,6,1,4,2,3]=>[6,7,4,2,5,3,1]=>[2,1,4,6,3,5,7]=>[1,3,3]
[7,5,6,1,4,3,2]=>[7,6,4,2,5,3,1]=>[1,2,4,6,3,5,7]=>[4,3]
[7,5,6,2,1,3,4]=>[5,4,6,2,7,3,1]=>[3,4,2,6,1,5,7]=>[2,2,3]
[7,5,6,2,1,4,3]=>[4,7,5,2,6,3,1]=>[4,1,3,6,2,5,7]=>[1,3,3]
[7,5,6,2,3,1,4]=>[4,6,5,2,7,3,1]=>[4,2,3,6,1,5,7]=>[1,3,3]
[7,5,6,2,3,4,1]=>[4,5,2,7,6,3,1]=>[4,3,6,1,2,5,7]=>[1,2,4]
[7,5,6,2,4,1,3]=>[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>[1,2,4]
[7,5,6,2,4,3,1]=>[7,4,2,6,5,3,1]=>[1,4,6,2,3,5,7]=>[3,4]
[7,5,6,3,1,2,4]=>[5,6,4,2,7,3,1]=>[3,2,4,6,1,5,7]=>[1,3,3]
[7,5,6,3,1,4,2]=>[7,5,4,2,6,3,1]=>[1,3,4,6,2,5,7]=>[4,3]
[7,5,6,3,2,1,4]=>[6,5,4,2,7,3,1]=>[2,3,4,6,1,5,7]=>[4,3]
[7,5,6,3,2,4,1]=>[5,4,2,7,6,3,1]=>[3,4,6,1,2,5,7]=>[3,4]
[7,5,6,3,4,1,2]=>[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>[3,4]
[7,5,6,3,4,2,1]=>[4,2,7,6,5,3,1]=>[4,6,1,2,3,5,7]=>[2,5]
[7,5,6,4,1,2,3]=>[5,6,2,7,4,3,1]=>[3,2,6,1,4,5,7]=>[1,2,4]
[7,5,6,4,1,3,2]=>[7,5,2,6,4,3,1]=>[1,3,6,2,4,5,7]=>[3,4]
[7,5,6,4,2,1,3]=>[6,5,2,7,4,3,1]=>[2,3,6,1,4,5,7]=>[3,4]
[7,5,6,4,2,3,1]=>[5,2,7,6,4,3,1]=>[3,6,1,2,4,5,7]=>[2,5]
[7,5,6,4,3,1,2]=>[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>[2,5]
[7,5,6,4,3,2,1]=>[2,7,6,5,4,3,1]=>[6,1,2,3,4,5,7]=>[1,6]
[7,6,1,2,3,4,5]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>[1,1,1,1,3]
[7,6,1,2,3,5,4]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>[2,1,1,3]
[7,6,1,2,4,3,5]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>[2,1,1,3]
[7,6,1,2,4,5,3]=>[5,7,3,4,6,2,1]=>[3,1,5,4,2,6,7]=>[1,2,1,3]
[7,6,1,2,5,3,4]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>[1,2,1,3]
[7,6,1,2,5,4,3]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[3,1,3]
[7,6,1,3,2,4,5]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>[2,1,1,3]
[7,6,1,3,2,5,4]=>[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>[1,2,1,3]
[7,6,1,3,4,2,5]=>[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>[1,2,1,3]
[7,6,1,3,4,5,2]=>[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>[1,1,2,3]
[7,6,1,3,5,2,4]=>[4,6,7,3,5,2,1]=>[4,2,1,5,3,6,7]=>[1,1,2,3]
[7,6,1,3,5,4,2]=>[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>[2,2,3]
[7,6,1,4,2,3,5]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>[1,2,1,3]
[7,6,1,4,2,5,3]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>[3,1,3]
[7,6,1,4,3,2,5]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>[3,1,3]
[7,6,1,4,3,5,2]=>[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>[2,2,3]
[7,6,1,4,5,2,3]=>[6,4,7,3,5,2,1]=>[2,4,1,5,3,6,7]=>[2,2,3]
[7,6,1,4,5,3,2]=>[4,7,6,3,5,2,1]=>[4,1,2,5,3,6,7]=>[1,3,3]
[7,6,1,5,2,3,4]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>[1,1,2,3]
[7,6,1,5,2,4,3]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>[2,2,3]
[7,6,1,5,3,2,4]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>[2,2,3]
[7,6,1,5,3,4,2]=>[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>[1,3,3]
[7,6,1,5,4,2,3]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>[1,3,3]
[7,6,1,5,4,3,2]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>[4,3]
[7,6,2,1,3,4,5]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>[2,1,1,3]
[7,6,2,1,3,5,4]=>[3,7,4,5,6,2,1]=>[5,1,4,3,2,6,7]=>[1,2,1,3]
[7,6,2,1,4,3,5]=>[3,6,4,5,7,2,1]=>[5,2,4,3,1,6,7]=>[1,2,1,3]
[7,6,2,1,4,5,3]=>[3,5,7,4,6,2,1]=>[5,3,1,4,2,6,7]=>[1,1,2,3]
[7,6,2,1,5,3,4]=>[3,6,7,4,5,2,1]=>[5,2,1,4,3,6,7]=>[1,1,2,3]
[7,6,2,1,5,4,3]=>[7,3,6,4,5,2,1]=>[1,5,2,4,3,6,7]=>[2,2,3]
[7,6,2,3,1,4,5]=>[3,5,4,6,7,2,1]=>[5,3,4,2,1,6,7]=>[1,2,1,3]
[7,6,2,3,1,5,4]=>[3,4,7,5,6,2,1]=>[5,4,1,3,2,6,7]=>[1,1,2,3]
[7,6,2,3,4,1,5]=>[3,4,6,5,7,2,1]=>[5,4,2,3,1,6,7]=>[1,1,2,3]
[7,6,2,3,4,5,1]=>[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>[1,1,1,4]
[7,6,2,3,5,1,4]=>[3,4,6,7,5,2,1]=>[5,4,2,1,3,6,7]=>[1,1,1,4]
[7,6,2,3,5,4,1]=>[7,3,4,6,5,2,1]=>[1,5,4,2,3,6,7]=>[2,1,4]
[7,6,2,4,1,3,5]=>[3,5,6,4,7,2,1]=>[5,3,2,4,1,6,7]=>[1,1,2,3]
[7,6,2,4,1,5,3]=>[7,3,5,4,6,2,1]=>[1,5,3,4,2,6,7]=>[2,2,3]
[7,6,2,4,3,1,5]=>[6,3,5,4,7,2,1]=>[2,5,3,4,1,6,7]=>[2,2,3]
[7,6,2,4,3,5,1]=>[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>[2,1,4]
[7,6,2,4,5,1,3]=>[6,3,4,7,5,2,1]=>[2,5,4,1,3,6,7]=>[2,1,4]
[7,6,2,4,5,3,1]=>[4,7,3,6,5,2,1]=>[4,1,5,2,3,6,7]=>[1,2,4]
[7,6,2,5,1,3,4]=>[3,5,6,7,4,2,1]=>[5,3,2,1,4,6,7]=>[1,1,1,4]
[7,6,2,5,1,4,3]=>[7,3,5,6,4,2,1]=>[1,5,3,2,4,6,7]=>[2,1,4]
[7,6,2,5,3,1,4]=>[6,3,5,7,4,2,1]=>[2,5,3,1,4,6,7]=>[2,1,4]
[7,6,2,5,3,4,1]=>[5,7,3,6,4,2,1]=>[3,1,5,2,4,6,7]=>[1,2,4]
[7,6,2,5,4,1,3]=>[6,7,3,5,4,2,1]=>[2,1,5,3,4,6,7]=>[1,2,4]
[7,6,2,5,4,3,1]=>[7,6,3,5,4,2,1]=>[1,2,5,3,4,6,7]=>[3,4]
[7,6,3,1,2,4,5]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>[1,2,1,3]
[7,6,3,1,2,5,4]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>[3,1,3]
[7,6,3,1,4,2,5]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>[3,1,3]
[7,6,3,1,4,5,2]=>[5,3,7,4,6,2,1]=>[3,5,1,4,2,6,7]=>[2,2,3]
[7,6,3,1,5,2,4]=>[6,3,7,4,5,2,1]=>[2,5,1,4,3,6,7]=>[2,2,3]
[7,6,3,1,5,4,2]=>[3,7,6,4,5,2,1]=>[5,1,2,4,3,6,7]=>[1,3,3]
[7,6,3,2,1,4,5]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>[3,1,3]
[7,6,3,2,1,5,4]=>[4,3,7,5,6,2,1]=>[4,5,1,3,2,6,7]=>[2,2,3]
[7,6,3,2,4,1,5]=>[4,3,6,5,7,2,1]=>[4,5,2,3,1,6,7]=>[2,2,3]
[7,6,3,2,4,5,1]=>[4,3,5,7,6,2,1]=>[4,5,3,1,2,6,7]=>[2,1,4]
[7,6,3,2,5,1,4]=>[4,3,6,7,5,2,1]=>[4,5,2,1,3,6,7]=>[2,1,4]
[7,6,3,2,5,4,1]=>[3,7,4,6,5,2,1]=>[5,1,4,2,3,6,7]=>[1,2,4]
[7,6,3,4,1,2,5]=>[5,3,6,4,7,2,1]=>[3,5,2,4,1,6,7]=>[2,2,3]
[7,6,3,4,1,5,2]=>[3,7,5,4,6,2,1]=>[5,1,3,4,2,6,7]=>[1,3,3]
[7,6,3,4,2,1,5]=>[3,6,5,4,7,2,1]=>[5,2,3,4,1,6,7]=>[1,3,3]
[7,6,3,4,2,5,1]=>[3,5,4,7,6,2,1]=>[5,3,4,1,2,6,7]=>[1,2,4]
[7,6,3,4,5,1,2]=>[3,6,4,7,5,2,1]=>[5,2,4,1,3,6,7]=>[1,2,4]
[7,6,3,4,5,2,1]=>[3,4,7,6,5,2,1]=>[5,4,1,2,3,6,7]=>[1,1,5]
[7,6,3,5,1,2,4]=>[5,3,6,7,4,2,1]=>[3,5,2,1,4,6,7]=>[2,1,4]
[7,6,3,5,1,4,2]=>[3,7,5,6,4,2,1]=>[5,1,3,2,4,6,7]=>[1,2,4]
[7,6,3,5,2,1,4]=>[3,6,5,7,4,2,1]=>[5,2,3,1,4,6,7]=>[1,2,4]
[7,6,3,5,2,4,1]=>[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>[1,1,5]
[7,6,3,5,4,1,2]=>[3,6,7,5,4,2,1]=>[5,2,1,3,4,6,7]=>[1,1,5]
[7,6,3,5,4,2,1]=>[7,3,6,5,4,2,1]=>[1,5,2,3,4,6,7]=>[2,5]
[7,6,4,1,2,3,5]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>[1,1,2,3]
[7,6,4,1,2,5,3]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>[2,2,3]
[7,6,4,1,3,2,5]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>[2,2,3]
[7,6,4,1,3,5,2]=>[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>[1,3,3]
[7,6,4,1,5,2,3]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>[1,3,3]
[7,6,4,1,5,3,2]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>[4,3]
[7,6,4,2,1,3,5]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>[2,2,3]
[7,6,4,2,1,5,3]=>[4,7,5,3,6,2,1]=>[4,1,3,5,2,6,7]=>[1,3,3]
[7,6,4,2,3,1,5]=>[4,6,5,3,7,2,1]=>[4,2,3,5,1,6,7]=>[1,3,3]
[7,6,4,2,3,5,1]=>[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>[1,2,4]
[7,6,4,2,5,1,3]=>[4,6,3,7,5,2,1]=>[4,2,5,1,3,6,7]=>[1,2,4]
[7,6,4,2,5,3,1]=>[7,4,3,6,5,2,1]=>[1,4,5,2,3,6,7]=>[3,4]
[7,6,4,3,1,2,5]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>[1,3,3]
[7,6,4,3,1,5,2]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>[4,3]
[7,6,4,3,2,1,5]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>[4,3]
[7,6,4,3,2,5,1]=>[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>[3,4]
[7,6,4,3,5,1,2]=>[6,4,3,7,5,2,1]=>[2,4,5,1,3,6,7]=>[3,4]
[7,6,4,3,5,2,1]=>[4,3,7,6,5,2,1]=>[4,5,1,2,3,6,7]=>[2,5]
[7,6,4,5,1,2,3]=>[5,6,3,7,4,2,1]=>[3,2,5,1,4,6,7]=>[1,2,4]
[7,6,4,5,1,3,2]=>[7,5,3,6,4,2,1]=>[1,3,5,2,4,6,7]=>[3,4]
[7,6,4,5,2,1,3]=>[6,5,3,7,4,2,1]=>[2,3,5,1,4,6,7]=>[3,4]
[7,6,4,5,2,3,1]=>[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>[2,5]
[7,6,4,5,3,1,2]=>[6,3,7,5,4,2,1]=>[2,5,1,3,4,6,7]=>[2,5]
[7,6,4,5,3,2,1]=>[3,7,6,5,4,2,1]=>[5,1,2,3,4,6,7]=>[1,6]
[7,6,5,1,2,3,4]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>[1,1,1,4]
[7,6,5,1,2,4,3]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>[2,1,4]
[7,6,5,1,3,2,4]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>[2,1,4]
[7,6,5,1,3,4,2]=>[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>[1,2,4]
[7,6,5,1,4,2,3]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>[1,2,4]
[7,6,5,1,4,3,2]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>[3,4]
[7,6,5,2,1,3,4]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>[2,1,4]
[7,6,5,2,1,4,3]=>[4,7,5,6,3,2,1]=>[4,1,3,2,5,6,7]=>[1,2,4]
[7,6,5,2,3,1,4]=>[4,6,5,7,3,2,1]=>[4,2,3,1,5,6,7]=>[1,2,4]
[7,6,5,2,3,4,1]=>[4,5,7,6,3,2,1]=>[4,3,1,2,5,6,7]=>[1,1,5]
[7,6,5,2,4,1,3]=>[4,6,7,5,3,2,1]=>[4,2,1,3,5,6,7]=>[1,1,5]
[7,6,5,2,4,3,1]=>[7,4,6,5,3,2,1]=>[1,4,2,3,5,6,7]=>[2,5]
[7,6,5,3,1,2,4]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>[1,2,4]
[7,6,5,3,1,4,2]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>[3,4]
[7,6,5,3,2,1,4]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>[3,4]
[7,6,5,3,2,4,1]=>[5,4,7,6,3,2,1]=>[3,4,1,2,5,6,7]=>[2,5]
[7,6,5,3,4,1,2]=>[6,4,7,5,3,2,1]=>[2,4,1,3,5,6,7]=>[2,5]
[7,6,5,3,4,2,1]=>[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>[1,6]
[7,6,5,4,1,2,3]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>[1,1,5]
[7,6,5,4,1,3,2]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>[2,5]
[7,6,5,4,2,1,3]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>[2,5]
[7,6,5,4,2,3,1]=>[5,7,6,4,3,2,1]=>[3,1,2,4,5,6,7]=>[1,6]
[7,6,5,4,3,1,2]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>[1,6]
[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7]
[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8]
[7,8,6,5,4,3,2,1]=>[1,8,7,6,5,4,3,2]=>[8,1,2,3,4,5,6,7]=>[1,7]
[8,6,7,5,4,3,2,1]=>[2,8,7,6,5,4,3,1]=>[7,1,2,3,4,5,6,8]=>[1,7]
[7,6,8,5,4,3,2,1]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>[2,6]
[6,7,8,5,4,3,2,1]=>[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>[1,1,6]
[8,7,5,6,4,3,2,1]=>[3,8,7,6,5,4,2,1]=>[6,1,2,3,4,5,7,8]=>[1,7]
[7,8,5,6,4,3,2,1]=>[3,1,8,7,6,5,4,2]=>[6,8,1,2,3,4,5,7]=>[2,6]
[8,6,5,7,4,3,2,1]=>[3,2,8,7,6,5,4,1]=>[6,7,1,2,3,4,5,8]=>[2,6]
[8,5,6,7,4,3,2,1]=>[2,3,8,7,6,5,4,1]=>[7,6,1,2,3,4,5,8]=>[1,1,6]
[7,6,5,8,4,3,2,1]=>[3,2,1,8,7,6,5,4]=>[6,7,8,1,2,3,4,5]=>[3,5]
[6,7,5,8,4,3,2,1]=>[1,3,2,8,7,6,5,4]=>[8,6,7,1,2,3,4,5]=>[1,2,5]
[7,5,6,8,4,3,2,1]=>[2,3,1,8,7,6,5,4]=>[7,6,8,1,2,3,4,5]=>[1,2,5]
[6,5,7,8,4,3,2,1]=>[2,1,3,8,7,6,5,4]=>[7,8,6,1,2,3,4,5]=>[2,1,5]
[5,6,7,8,4,3,2,1]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[1,1,1,5]
[8,7,6,4,5,3,2,1]=>[4,8,7,6,5,3,2,1]=>[5,1,2,3,4,6,7,8]=>[1,7]
[7,8,6,4,5,3,2,1]=>[4,1,8,7,6,5,3,2]=>[5,8,1,2,3,4,6,7]=>[2,6]
[8,6,7,4,5,3,2,1]=>[4,2,8,7,6,5,3,1]=>[5,7,1,2,3,4,6,8]=>[2,6]
[7,6,8,4,5,3,2,1]=>[4,2,1,8,7,6,5,3]=>[5,7,8,1,2,3,4,6]=>[3,5]
[6,7,8,4,5,3,2,1]=>[1,4,2,8,7,6,5,3]=>[8,5,7,1,2,3,4,6]=>[1,2,5]
[8,7,5,4,6,3,2,1]=>[4,3,8,7,6,5,2,1]=>[5,6,1,2,3,4,7,8]=>[2,6]
[8,7,4,5,6,3,2,1]=>[3,4,8,7,6,5,2,1]=>[6,5,1,2,3,4,7,8]=>[1,1,6]
[8,6,5,4,7,3,2,1]=>[4,3,2,8,7,6,5,1]=>[5,6,7,1,2,3,4,8]=>[3,5]
[8,5,6,4,7,3,2,1]=>[2,4,3,8,7,6,5,1]=>[7,5,6,1,2,3,4,8]=>[1,2,5]
[8,6,4,5,7,3,2,1]=>[3,4,2,8,7,6,5,1]=>[6,5,7,1,2,3,4,8]=>[1,2,5]
[8,5,4,6,7,3,2,1]=>[3,2,4,8,7,6,5,1]=>[6,7,5,1,2,3,4,8]=>[2,1,5]
[8,4,5,6,7,3,2,1]=>[2,3,4,8,7,6,5,1]=>[7,6,5,1,2,3,4,8]=>[1,1,1,5]
[7,6,5,4,8,3,2,1]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[4,4]
[6,7,5,4,8,3,2,1]=>[1,4,3,2,8,7,6,5]=>[8,5,6,7,1,2,3,4]=>[1,3,4]
[7,5,6,4,8,3,2,1]=>[2,4,3,1,8,7,6,5]=>[7,5,6,8,1,2,3,4]=>[1,3,4]
[6,5,7,4,8,3,2,1]=>[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>[2,2,4]
[5,6,7,4,8,3,2,1]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[1,1,2,4]
[7,6,4,5,8,3,2,1]=>[3,4,2,1,8,7,6,5]=>[6,5,7,8,1,2,3,4]=>[1,3,4]
[6,7,4,5,8,3,2,1]=>[3,1,4,2,8,7,6,5]=>[6,8,5,7,1,2,3,4]=>[2,2,4]
[7,5,4,6,8,3,2,1]=>[3,2,4,1,8,7,6,5]=>[6,7,5,8,1,2,3,4]=>[2,2,4]
[7,4,5,6,8,3,2,1]=>[2,3,4,1,8,7,6,5]=>[7,6,5,8,1,2,3,4]=>[1,1,2,4]
[6,5,4,7,8,3,2,1]=>[3,2,1,4,8,7,6,5]=>[6,7,8,5,1,2,3,4]=>[3,1,4]
[5,6,4,7,8,3,2,1]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[1,2,1,4]
[6,4,5,7,8,3,2,1]=>[2,3,1,4,8,7,6,5]=>[7,6,8,5,1,2,3,4]=>[1,2,1,4]
[5,4,6,7,8,3,2,1]=>[2,1,3,4,8,7,6,5]=>[7,8,6,5,1,2,3,4]=>[2,1,1,4]
[4,5,6,7,8,3,2,1]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[1,1,1,1,4]
[8,7,6,5,3,4,2,1]=>[5,8,7,6,4,3,2,1]=>[4,1,2,3,5,6,7,8]=>[1,7]
[7,8,6,5,3,4,2,1]=>[5,1,8,7,6,4,3,2]=>[4,8,1,2,3,5,6,7]=>[2,6]
[8,6,7,5,3,4,2,1]=>[5,2,8,7,6,4,3,1]=>[4,7,1,2,3,5,6,8]=>[2,6]
[7,6,8,5,3,4,2,1]=>[5,2,1,8,7,6,4,3]=>[4,7,8,1,2,3,5,6]=>[3,5]
[8,7,5,6,3,4,2,1]=>[5,3,8,7,6,4,2,1]=>[4,6,1,2,3,5,7,8]=>[2,6]
[7,8,5,6,3,4,2,1]=>[5,3,1,8,7,6,4,2]=>[4,6,8,1,2,3,5,7]=>[3,5]
[8,5,6,7,3,4,2,1]=>[2,5,3,8,7,6,4,1]=>[7,4,6,1,2,3,5,8]=>[1,2,5]
[7,6,5,8,3,4,2,1]=>[5,3,2,1,8,7,6,4]=>[4,6,7,8,1,2,3,5]=>[4,4]
[6,7,5,8,3,4,2,1]=>[1,5,3,2,8,7,6,4]=>[8,4,6,7,1,2,3,5]=>[1,3,4]
[6,5,7,8,3,4,2,1]=>[2,1,5,3,8,7,6,4]=>[7,8,4,6,1,2,3,5]=>[2,2,4]
[5,6,7,8,3,4,2,1]=>[1,2,5,3,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[1,1,2,4]
[8,7,6,4,3,5,2,1]=>[5,4,8,7,6,3,2,1]=>[4,5,1,2,3,6,7,8]=>[2,6]
[7,8,6,4,3,5,2,1]=>[5,4,1,8,7,6,3,2]=>[4,5,8,1,2,3,6,7]=>[3,5]
[8,6,7,4,3,5,2,1]=>[5,4,2,8,7,6,3,1]=>[4,5,7,1,2,3,6,8]=>[3,5]
[7,6,8,4,3,5,2,1]=>[5,4,2,1,8,7,6,3]=>[4,5,7,8,1,2,3,6]=>[4,4]
[8,7,6,3,4,5,2,1]=>[4,5,8,7,6,3,2,1]=>[5,4,1,2,3,6,7,8]=>[1,1,6]
[7,8,6,3,4,5,2,1]=>[4,5,1,8,7,6,3,2]=>[5,4,8,1,2,3,6,7]=>[1,2,5]
[8,6,7,3,4,5,2,1]=>[4,5,2,8,7,6,3,1]=>[5,4,7,1,2,3,6,8]=>[1,2,5]
[7,6,8,3,4,5,2,1]=>[4,5,2,1,8,7,6,3]=>[5,4,7,8,1,2,3,6]=>[1,3,4]
[6,7,8,3,4,5,2,1]=>[4,1,5,2,8,7,6,3]=>[5,8,4,7,1,2,3,6]=>[2,2,4]
[8,7,5,4,3,6,2,1]=>[5,4,3,8,7,6,2,1]=>[4,5,6,1,2,3,7,8]=>[3,5]
[7,8,5,4,3,6,2,1]=>[5,4,3,1,8,7,6,2]=>[4,5,6,8,1,2,3,7]=>[4,4]
[8,7,4,5,3,6,2,1]=>[3,5,4,8,7,6,2,1]=>[6,4,5,1,2,3,7,8]=>[1,2,5]
[7,8,5,3,4,6,2,1]=>[4,5,3,1,8,7,6,2]=>[5,4,6,8,1,2,3,7]=>[1,3,4]
[8,7,3,4,5,6,2,1]=>[3,4,5,8,7,6,2,1]=>[6,5,4,1,2,3,7,8]=>[1,1,1,5]
[7,8,3,4,5,6,2,1]=>[3,4,5,1,8,7,6,2]=>[6,5,4,8,1,2,3,7]=>[1,1,2,4]
[8,6,5,4,3,7,2,1]=>[5,4,3,2,8,7,6,1]=>[4,5,6,7,1,2,3,8]=>[4,4]
[8,6,4,5,3,7,2,1]=>[3,5,4,2,8,7,6,1]=>[6,4,5,7,1,2,3,8]=>[1,3,4]
[8,5,4,6,3,7,2,1]=>[3,2,5,4,8,7,6,1]=>[6,7,4,5,1,2,3,8]=>[2,2,4]
[8,6,4,3,5,7,2,1]=>[4,3,5,2,8,7,6,1]=>[5,6,4,7,1,2,3,8]=>[2,2,4]
[8,5,4,3,6,7,2,1]=>[4,3,2,5,8,7,6,1]=>[5,6,7,4,1,2,3,8]=>[3,1,4]
[8,5,3,4,6,7,2,1]=>[3,4,2,5,8,7,6,1]=>[6,5,7,4,1,2,3,8]=>[1,2,1,4]
[8,4,3,5,6,7,2,1]=>[3,2,4,5,8,7,6,1]=>[6,7,5,4,1,2,3,8]=>[2,1,1,4]
[8,3,4,5,6,7,2,1]=>[2,3,4,5,8,7,6,1]=>[7,6,5,4,1,2,3,8]=>[1,1,1,1,4]
[7,6,5,4,3,8,2,1]=>[5,4,3,2,1,8,7,6]=>[4,5,6,7,8,1,2,3]=>[5,3]
[6,7,5,4,3,8,2,1]=>[1,5,4,3,2,8,7,6]=>[8,4,5,6,7,1,2,3]=>[1,4,3]
[7,5,6,4,3,8,2,1]=>[2,5,4,3,1,8,7,6]=>[7,4,5,6,8,1,2,3]=>[1,4,3]
[6,5,7,4,3,8,2,1]=>[2,1,5,4,3,8,7,6]=>[7,8,4,5,6,1,2,3]=>[2,3,3]
[5,6,7,4,3,8,2,1]=>[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>[1,1,3,3]
[7,6,4,5,3,8,2,1]=>[3,5,4,2,1,8,7,6]=>[6,4,5,7,8,1,2,3]=>[1,4,3]
[6,7,4,5,3,8,2,1]=>[3,1,5,4,2,8,7,6]=>[6,8,4,5,7,1,2,3]=>[2,3,3]
[7,5,4,6,3,8,2,1]=>[3,2,5,4,1,8,7,6]=>[6,7,4,5,8,1,2,3]=>[2,3,3]
[7,4,5,6,3,8,2,1]=>[2,3,5,4,1,8,7,6]=>[7,6,4,5,8,1,2,3]=>[1,1,3,3]
[6,5,4,7,3,8,2,1]=>[3,2,1,5,4,8,7,6]=>[6,7,8,4,5,1,2,3]=>[3,2,3]
[5,4,6,7,3,8,2,1]=>[2,1,3,5,4,8,7,6]=>[7,8,6,4,5,1,2,3]=>[2,1,2,3]
[4,5,6,7,3,8,2,1]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[1,1,1,2,3]
[7,6,5,3,4,8,2,1]=>[4,5,3,2,1,8,7,6]=>[5,4,6,7,8,1,2,3]=>[1,4,3]
[7,6,4,3,5,8,2,1]=>[4,3,5,2,1,8,7,6]=>[5,6,4,7,8,1,2,3]=>[2,3,3]
[7,6,3,4,5,8,2,1]=>[3,4,5,2,1,8,7,6]=>[6,5,4,7,8,1,2,3]=>[1,1,3,3]
[7,5,4,3,6,8,2,1]=>[4,3,2,5,1,8,7,6]=>[5,6,7,4,8,1,2,3]=>[3,2,3]
[7,5,3,4,6,8,2,1]=>[3,4,2,5,1,8,7,6]=>[6,5,7,4,8,1,2,3]=>[1,2,2,3]
[7,3,4,5,6,8,2,1]=>[2,3,4,5,1,8,7,6]=>[7,6,5,4,8,1,2,3]=>[1,1,1,2,3]
[6,5,4,3,7,8,2,1]=>[4,3,2,1,5,8,7,6]=>[5,6,7,8,4,1,2,3]=>[4,1,3]
[6,5,3,4,7,8,2,1]=>[3,4,2,1,5,8,7,6]=>[6,5,7,8,4,1,2,3]=>[1,3,1,3]
[6,3,4,5,7,8,2,1]=>[2,3,4,1,5,8,7,6]=>[7,6,5,8,4,1,2,3]=>[1,1,2,1,3]
[5,4,3,6,7,8,2,1]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[3,1,1,3]
[5,3,4,6,7,8,2,1]=>[2,3,1,4,5,8,7,6]=>[7,6,8,5,4,1,2,3]=>[1,2,1,1,3]
[4,3,5,6,7,8,2,1]=>[2,1,3,4,5,8,7,6]=>[7,8,6,5,4,1,2,3]=>[2,1,1,1,3]
[3,4,5,6,7,8,2,1]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[1,1,1,1,1,3]
[8,7,6,5,4,2,3,1]=>[6,8,7,5,4,3,2,1]=>[3,1,2,4,5,6,7,8]=>[1,7]
[7,8,6,5,4,2,3,1]=>[6,1,8,7,5,4,3,2]=>[3,8,1,2,4,5,6,7]=>[2,6]
[8,6,7,5,4,2,3,1]=>[6,2,8,7,5,4,3,1]=>[3,7,1,2,4,5,6,8]=>[2,6]
[7,6,8,5,4,2,3,1]=>[6,2,1,8,7,5,4,3]=>[3,7,8,1,2,4,5,6]=>[3,5]
[8,7,5,6,4,2,3,1]=>[6,3,8,7,5,4,2,1]=>[3,6,1,2,4,5,7,8]=>[2,6]
[8,6,5,7,4,2,3,1]=>[6,3,2,8,7,5,4,1]=>[3,6,7,1,2,4,5,8]=>[3,5]
[8,5,6,7,4,2,3,1]=>[2,6,3,8,7,5,4,1]=>[7,3,6,1,2,4,5,8]=>[1,2,5]
[7,6,5,8,4,2,3,1]=>[6,3,2,1,8,7,5,4]=>[3,6,7,8,1,2,4,5]=>[4,4]
[7,5,6,8,4,2,3,1]=>[2,6,3,1,8,7,5,4]=>[7,3,6,8,1,2,4,5]=>[1,3,4]
[5,6,7,8,4,2,3,1]=>[1,2,6,3,8,7,5,4]=>[8,7,3,6,1,2,4,5]=>[1,1,2,4]
[8,7,6,4,5,2,3,1]=>[6,4,8,7,5,3,2,1]=>[3,5,1,2,4,6,7,8]=>[2,6]
[8,6,7,4,5,2,3,1]=>[6,4,2,8,7,5,3,1]=>[3,5,7,1,2,4,6,8]=>[3,5]
[7,6,8,4,5,2,3,1]=>[6,4,2,1,8,7,5,3]=>[3,5,7,8,1,2,4,6]=>[4,4]
[6,7,8,4,5,2,3,1]=>[1,6,4,2,8,7,5,3]=>[8,3,5,7,1,2,4,6]=>[1,3,4]
[8,7,5,4,6,2,3,1]=>[6,4,3,8,7,5,2,1]=>[3,5,6,1,2,4,7,8]=>[3,5]
[8,7,4,5,6,2,3,1]=>[3,6,4,8,7,5,2,1]=>[6,3,5,1,2,4,7,8]=>[1,2,5]
[8,6,5,4,7,2,3,1]=>[6,4,3,2,8,7,5,1]=>[3,5,6,7,1,2,4,8]=>[4,4]
[8,5,6,4,7,2,3,1]=>[2,6,4,3,8,7,5,1]=>[7,3,5,6,1,2,4,8]=>[1,3,4]
[8,6,4,5,7,2,3,1]=>[3,6,4,2,8,7,5,1]=>[6,3,5,7,1,2,4,8]=>[1,3,4]
[8,4,5,6,7,2,3,1]=>[2,3,6,4,8,7,5,1]=>[7,6,3,5,1,2,4,8]=>[1,1,2,4]
[7,6,5,4,8,2,3,1]=>[6,4,3,2,1,8,7,5]=>[3,5,6,7,8,1,2,4]=>[5,3]
[7,5,6,4,8,2,3,1]=>[2,6,4,3,1,8,7,5]=>[7,3,5,6,8,1,2,4]=>[1,4,3]
[6,5,7,4,8,2,3,1]=>[2,1,6,4,3,8,7,5]=>[7,8,3,5,6,1,2,4]=>[2,3,3]
[7,6,4,5,8,2,3,1]=>[3,6,4,2,1,8,7,5]=>[6,3,5,7,8,1,2,4]=>[1,4,3]
[6,7,4,5,8,2,3,1]=>[3,1,6,4,2,8,7,5]=>[6,8,3,5,7,1,2,4]=>[2,3,3]
[4,5,6,7,8,2,3,1]=>[1,2,3,6,4,8,7,5]=>[8,7,6,3,5,1,2,4]=>[1,1,1,2,3]
[8,7,6,5,3,2,4,1]=>[6,5,8,7,4,3,2,1]=>[3,4,1,2,5,6,7,8]=>[2,6]
[7,8,6,5,3,2,4,1]=>[6,5,1,8,7,4,3,2]=>[3,4,8,1,2,5,6,7]=>[3,5]
[8,6,7,5,3,2,4,1]=>[6,5,2,8,7,4,3,1]=>[3,4,7,1,2,5,6,8]=>[3,5]
[7,6,8,5,3,2,4,1]=>[6,5,2,1,8,7,4,3]=>[3,4,7,8,1,2,5,6]=>[4,4]
[8,7,5,6,3,2,4,1]=>[6,5,3,8,7,4,2,1]=>[3,4,6,1,2,5,7,8]=>[3,5]
[8,6,5,7,3,2,4,1]=>[6,5,3,2,8,7,4,1]=>[3,4,6,7,1,2,5,8]=>[4,4]
[7,6,5,8,3,2,4,1]=>[6,5,3,2,1,8,7,4]=>[3,4,6,7,8,1,2,5]=>[5,3]
[5,6,7,8,3,2,4,1]=>[1,2,6,5,3,8,7,4]=>[8,7,3,4,6,1,2,5]=>[1,1,3,3]
[8,7,6,5,2,3,4,1]=>[5,6,8,7,4,3,2,1]=>[4,3,1,2,5,6,7,8]=>[1,1,6]
[7,6,8,5,2,3,4,1]=>[5,6,2,1,8,7,4,3]=>[4,3,7,8,1,2,5,6]=>[1,3,4]
[6,7,8,5,2,3,4,1]=>[5,1,6,2,8,7,4,3]=>[4,8,3,7,1,2,5,6]=>[2,2,4]
[8,6,5,7,2,3,4,1]=>[5,6,3,2,8,7,4,1]=>[4,3,6,7,1,2,5,8]=>[1,3,4]
[8,5,6,7,2,3,4,1]=>[5,2,6,3,8,7,4,1]=>[4,7,3,6,1,2,5,8]=>[2,2,4]
[7,6,5,8,2,3,4,1]=>[5,6,3,2,1,8,7,4]=>[4,3,6,7,8,1,2,5]=>[1,4,3]
[6,7,5,8,2,3,4,1]=>[5,1,6,3,2,8,7,4]=>[4,8,3,6,7,1,2,5]=>[2,3,3]
[6,5,7,8,2,3,4,1]=>[5,2,1,6,3,8,7,4]=>[4,7,8,3,6,1,2,5]=>[3,2,3]
[5,6,7,8,2,3,4,1]=>[1,5,2,6,3,8,7,4]=>[8,4,7,3,6,1,2,5]=>[1,2,2,3]
[8,7,6,4,3,2,5,1]=>[6,5,4,8,7,3,2,1]=>[3,4,5,1,2,6,7,8]=>[3,5]
[7,8,6,4,3,2,5,1]=>[6,5,4,1,8,7,3,2]=>[3,4,5,8,1,2,6,7]=>[4,4]
[8,6,7,4,3,2,5,1]=>[6,5,4,2,8,7,3,1]=>[3,4,5,7,1,2,6,8]=>[4,4]
[7,6,8,4,3,2,5,1]=>[6,5,4,2,1,8,7,3]=>[3,4,5,7,8,1,2,6]=>[5,3]
[6,7,8,4,3,2,5,1]=>[1,6,5,4,2,8,7,3]=>[8,3,4,5,7,1,2,6]=>[1,4,3]
[8,7,6,3,4,2,5,1]=>[4,6,5,8,7,3,2,1]=>[5,3,4,1,2,6,7,8]=>[1,2,5]
[7,8,6,3,4,2,5,1]=>[4,6,5,1,8,7,3,2]=>[5,3,4,8,1,2,6,7]=>[1,3,4]
[8,6,7,3,4,2,5,1]=>[4,6,5,2,8,7,3,1]=>[5,3,4,7,1,2,6,8]=>[1,3,4]
[7,6,8,3,4,2,5,1]=>[4,6,5,2,1,8,7,3]=>[5,3,4,7,8,1,2,6]=>[1,4,3]
[8,6,7,4,2,3,5,1]=>[5,6,4,2,8,7,3,1]=>[4,3,5,7,1,2,6,8]=>[1,3,4]
[7,6,8,4,2,3,5,1]=>[5,6,4,2,1,8,7,3]=>[4,3,5,7,8,1,2,6]=>[1,4,3]
[6,7,8,4,2,3,5,1]=>[5,1,6,4,2,8,7,3]=>[4,8,3,5,7,1,2,6]=>[2,3,3]
[8,7,6,3,2,4,5,1]=>[5,4,6,8,7,3,2,1]=>[4,5,3,1,2,6,7,8]=>[2,1,5]
[8,6,7,3,2,4,5,1]=>[5,4,6,2,8,7,3,1]=>[4,5,3,7,1,2,6,8]=>[2,2,4]
[6,7,8,3,2,4,5,1]=>[5,4,1,6,2,8,7,3]=>[4,5,8,3,7,1,2,6]=>[3,2,3]
[8,7,6,2,3,4,5,1]=>[4,5,6,8,7,3,2,1]=>[5,4,3,1,2,6,7,8]=>[1,1,1,5]
[7,8,6,2,3,4,5,1]=>[4,5,6,1,8,7,3,2]=>[5,4,3,8,1,2,6,7]=>[1,1,2,4]
[8,6,7,2,3,4,5,1]=>[4,5,6,2,8,7,3,1]=>[5,4,3,7,1,2,6,8]=>[1,1,2,4]
[7,6,8,2,3,4,5,1]=>[4,5,6,2,1,8,7,3]=>[5,4,3,7,8,1,2,6]=>[1,1,3,3]
[6,7,8,2,3,4,5,1]=>[4,5,1,6,2,8,7,3]=>[5,4,8,3,7,1,2,6]=>[1,2,2,3]
[8,7,5,4,3,2,6,1]=>[6,5,4,3,8,7,2,1]=>[3,4,5,6,1,2,7,8]=>[4,4]
[7,8,5,4,3,2,6,1]=>[6,5,4,3,1,8,7,2]=>[3,4,5,6,8,1,2,7]=>[5,3]
[8,7,5,3,4,2,6,1]=>[4,6,5,3,8,7,2,1]=>[5,3,4,6,1,2,7,8]=>[1,3,4]
[7,8,5,3,4,2,6,1]=>[4,6,5,3,1,8,7,2]=>[5,3,4,6,8,1,2,7]=>[1,4,3]
[8,7,4,3,5,2,6,1]=>[4,3,6,5,8,7,2,1]=>[5,6,3,4,1,2,7,8]=>[2,2,4]
[7,8,4,3,5,2,6,1]=>[4,3,6,5,1,8,7,2]=>[5,6,3,4,8,1,2,7]=>[2,3,3]
[8,7,5,3,2,4,6,1]=>[5,4,6,3,8,7,2,1]=>[4,5,3,6,1,2,7,8]=>[2,2,4]
[8,7,4,3,2,5,6,1]=>[5,4,3,6,8,7,2,1]=>[4,5,6,3,1,2,7,8]=>[3,1,4]
[7,8,4,3,2,5,6,1]=>[5,4,3,6,1,8,7,2]=>[4,5,6,3,8,1,2,7]=>[3,2,3]
[7,8,3,4,2,5,6,1]=>[3,5,4,6,1,8,7,2]=>[6,4,5,3,8,1,2,7]=>[1,2,2,3]
[7,8,4,2,3,5,6,1]=>[4,5,3,6,1,8,7,2]=>[5,4,6,3,8,1,2,7]=>[1,2,2,3]
[7,8,3,2,4,5,6,1]=>[4,3,5,6,1,8,7,2]=>[5,6,4,3,8,1,2,7]=>[2,1,2,3]
[8,7,2,3,4,5,6,1]=>[3,4,5,6,8,7,2,1]=>[6,5,4,3,1,2,7,8]=>[1,1,1,1,4]
[7,8,2,3,4,5,6,1]=>[3,4,5,6,1,8,7,2]=>[6,5,4,3,8,1,2,7]=>[1,1,1,2,3]
[8,6,5,4,3,2,7,1]=>[6,5,4,3,2,8,7,1]=>[3,4,5,6,7,1,2,8]=>[5,3]
[8,5,6,4,3,2,7,1]=>[2,6,5,4,3,8,7,1]=>[7,3,4,5,6,1,2,8]=>[1,4,3]
[8,6,4,5,3,2,7,1]=>[3,6,5,4,2,8,7,1]=>[6,3,4,5,7,1,2,8]=>[1,4,3]
[8,5,4,6,3,2,7,1]=>[3,2,6,5,4,8,7,1]=>[6,7,3,4,5,1,2,8]=>[2,3,3]
[8,6,5,3,4,2,7,1]=>[4,6,5,3,2,8,7,1]=>[5,3,4,6,7,1,2,8]=>[1,4,3]
[8,5,6,3,4,2,7,1]=>[4,2,6,5,3,8,7,1]=>[5,7,3,4,6,1,2,8]=>[2,3,3]
[8,6,4,3,5,2,7,1]=>[4,3,6,5,2,8,7,1]=>[5,6,3,4,7,1,2,8]=>[2,3,3]
[8,6,3,4,5,2,7,1]=>[3,4,6,5,2,8,7,1]=>[6,5,3,4,7,1,2,8]=>[1,1,3,3]
[8,5,4,3,6,2,7,1]=>[4,3,2,6,5,8,7,1]=>[5,6,7,3,4,1,2,8]=>[3,2,3]
[8,4,5,3,6,2,7,1]=>[2,4,3,6,5,8,7,1]=>[7,5,6,3,4,1,2,8]=>[1,2,2,3]
[8,4,3,5,6,2,7,1]=>[3,2,4,6,5,8,7,1]=>[6,7,5,3,4,1,2,8]=>[2,1,2,3]
[8,3,4,5,6,2,7,1]=>[2,3,4,6,5,8,7,1]=>[7,6,5,3,4,1,2,8]=>[1,1,1,2,3]
[8,5,6,4,2,3,7,1]=>[5,2,6,4,3,8,7,1]=>[4,7,3,5,6,1,2,8]=>[2,3,3]
[8,6,4,5,2,3,7,1]=>[5,3,6,4,2,8,7,1]=>[4,6,3,5,7,1,2,8]=>[2,3,3]
[8,6,5,3,2,4,7,1]=>[5,4,6,3,2,8,7,1]=>[4,5,3,6,7,1,2,8]=>[2,3,3]
[8,6,4,2,3,5,7,1]=>[4,5,3,6,2,8,7,1]=>[5,4,6,3,7,1,2,8]=>[1,2,2,3]
[8,6,2,3,4,5,7,1]=>[3,4,5,6,2,8,7,1]=>[6,5,4,3,7,1,2,8]=>[1,1,1,2,3]
[8,5,4,3,2,6,7,1]=>[5,4,3,2,6,8,7,1]=>[4,5,6,7,3,1,2,8]=>[4,1,3]
[8,4,5,3,2,6,7,1]=>[2,5,4,3,6,8,7,1]=>[7,4,5,6,3,1,2,8]=>[1,3,1,3]
[8,3,4,5,2,6,7,1]=>[2,3,5,4,6,8,7,1]=>[7,6,4,5,3,1,2,8]=>[1,1,2,1,3]
[8,5,4,2,3,6,7,1]=>[4,5,3,2,6,8,7,1]=>[5,4,6,7,3,1,2,8]=>[1,3,1,3]
[8,4,5,2,3,6,7,1]=>[4,2,5,3,6,8,7,1]=>[5,7,4,6,3,1,2,8]=>[2,2,1,3]
[8,4,3,2,5,6,7,1]=>[4,3,2,5,6,8,7,1]=>[5,6,7,4,3,1,2,8]=>[3,1,1,3]
[8,3,4,2,5,6,7,1]=>[2,4,3,5,6,8,7,1]=>[7,5,6,4,3,1,2,8]=>[1,2,1,1,3]
[8,4,2,3,5,6,7,1]=>[3,4,2,5,6,8,7,1]=>[6,5,7,4,3,1,2,8]=>[1,2,1,1,3]
[8,3,2,4,5,6,7,1]=>[3,2,4,5,6,8,7,1]=>[6,7,5,4,3,1,2,8]=>[2,1,1,1,3]
[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,8,7,1]=>[7,6,5,4,3,1,2,8]=>[1,1,1,1,1,3]
[7,6,5,4,3,2,8,1]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>[6,2]
[6,7,5,4,3,2,8,1]=>[1,6,5,4,3,2,8,7]=>[8,3,4,5,6,7,1,2]=>[1,5,2]
[7,5,6,4,3,2,8,1]=>[2,6,5,4,3,1,8,7]=>[7,3,4,5,6,8,1,2]=>[1,5,2]
[6,5,7,4,3,2,8,1]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[2,4,2]
[5,6,7,4,3,2,8,1]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[1,1,4,2]
[7,6,4,5,3,2,8,1]=>[3,6,5,4,2,1,8,7]=>[6,3,4,5,7,8,1,2]=>[1,5,2]
[7,4,5,6,3,2,8,1]=>[2,3,6,5,4,1,8,7]=>[7,6,3,4,5,8,1,2]=>[1,1,4,2]
[6,5,4,7,3,2,8,1]=>[3,2,1,6,5,4,8,7]=>[6,7,8,3,4,5,1,2]=>[3,3,2]
[6,4,5,7,3,2,8,1]=>[2,3,1,6,5,4,8,7]=>[7,6,8,3,4,5,1,2]=>[1,2,3,2]
[4,5,6,7,3,2,8,1]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[1,1,1,3,2]
[7,6,5,3,4,2,8,1]=>[4,6,5,3,2,1,8,7]=>[5,3,4,6,7,8,1,2]=>[1,5,2]
[7,5,6,3,4,2,8,1]=>[4,2,6,5,3,1,8,7]=>[5,7,3,4,6,8,1,2]=>[2,4,2]
[6,5,7,3,4,2,8,1]=>[4,2,1,6,5,3,8,7]=>[5,7,8,3,4,6,1,2]=>[3,3,2]
[7,6,4,3,5,2,8,1]=>[4,3,6,5,2,1,8,7]=>[5,6,3,4,7,8,1,2]=>[2,4,2]
[7,6,3,4,5,2,8,1]=>[3,4,6,5,2,1,8,7]=>[6,5,3,4,7,8,1,2]=>[1,1,4,2]
[7,5,4,3,6,2,8,1]=>[4,3,2,6,5,1,8,7]=>[5,6,7,3,4,8,1,2]=>[3,3,2]
[7,4,5,3,6,2,8,1]=>[2,4,3,6,5,1,8,7]=>[7,5,6,3,4,8,1,2]=>[1,2,3,2]
[7,5,3,4,6,2,8,1]=>[3,4,2,6,5,1,8,7]=>[6,5,7,3,4,8,1,2]=>[1,2,3,2]
[7,3,4,5,6,2,8,1]=>[2,3,4,6,5,1,8,7]=>[7,6,5,3,4,8,1,2]=>[1,1,1,3,2]
[6,5,4,3,7,2,8,1]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>[4,2,2]
[6,4,5,3,7,2,8,1]=>[2,4,3,1,6,5,8,7]=>[7,5,6,8,3,4,1,2]=>[1,3,2,2]
[5,4,6,3,7,2,8,1]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[2,2,2,2]
[4,5,6,3,7,2,8,1]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[1,1,2,2,2]
[6,5,3,4,7,2,8,1]=>[3,4,2,1,6,5,8,7]=>[6,5,7,8,3,4,1,2]=>[1,3,2,2]
[5,6,3,4,7,2,8,1]=>[3,1,4,2,6,5,8,7]=>[6,8,5,7,3,4,1,2]=>[2,2,2,2]
[6,4,3,5,7,2,8,1]=>[3,2,4,1,6,5,8,7]=>[6,7,5,8,3,4,1,2]=>[2,2,2,2]
[5,4,3,6,7,2,8,1]=>[3,2,1,4,6,5,8,7]=>[6,7,8,5,3,4,1,2]=>[3,1,2,2]
[4,3,5,6,7,2,8,1]=>[2,1,3,4,6,5,8,7]=>[7,8,6,5,3,4,1,2]=>[2,1,1,2,2]
[3,4,5,6,7,2,8,1]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[1,1,1,1,2,2]
[7,6,5,4,2,3,8,1]=>[5,6,4,3,2,1,8,7]=>[4,3,5,6,7,8,1,2]=>[1,5,2]
[6,7,5,4,2,3,8,1]=>[5,1,6,4,3,2,8,7]=>[4,8,3,5,6,7,1,2]=>[2,4,2]
[7,5,6,4,2,3,8,1]=>[5,2,6,4,3,1,8,7]=>[4,7,3,5,6,8,1,2]=>[2,4,2]
[6,5,7,4,2,3,8,1]=>[5,2,1,6,4,3,8,7]=>[4,7,8,3,5,6,1,2]=>[3,3,2]
[7,6,4,5,2,3,8,1]=>[5,3,6,4,2,1,8,7]=>[4,6,3,5,7,8,1,2]=>[2,4,2]
[6,7,4,5,2,3,8,1]=>[5,3,1,6,4,2,8,7]=>[4,6,8,3,5,7,1,2]=>[3,3,2]
[7,5,4,6,2,3,8,1]=>[5,3,2,6,4,1,8,7]=>[4,6,7,3,5,8,1,2]=>[3,3,2]
[7,4,5,6,2,3,8,1]=>[2,5,3,6,4,1,8,7]=>[7,4,6,3,5,8,1,2]=>[1,2,3,2]
[6,5,4,7,2,3,8,1]=>[5,3,2,1,6,4,8,7]=>[4,6,7,8,3,5,1,2]=>[4,2,2]
[5,6,4,7,2,3,8,1]=>[1,5,3,2,6,4,8,7]=>[8,4,6,7,3,5,1,2]=>[1,3,2,2]
[6,4,5,7,2,3,8,1]=>[2,5,3,1,6,4,8,7]=>[7,4,6,8,3,5,1,2]=>[1,3,2,2]
[5,4,6,7,2,3,8,1]=>[2,1,5,3,6,4,8,7]=>[7,8,4,6,3,5,1,2]=>[2,2,2,2]
[4,5,6,7,2,3,8,1]=>[1,2,5,3,6,4,8,7]=>[8,7,4,6,3,5,1,2]=>[1,1,2,2,2]
[7,6,5,3,2,4,8,1]=>[5,4,6,3,2,1,8,7]=>[4,5,3,6,7,8,1,2]=>[2,4,2]
[6,7,5,3,2,4,8,1]=>[5,4,1,6,3,2,8,7]=>[4,5,8,3,6,7,1,2]=>[3,3,2]
[6,5,7,3,2,4,8,1]=>[5,4,2,1,6,3,8,7]=>[4,5,7,8,3,6,1,2]=>[4,2,2]
[7,6,5,2,3,4,8,1]=>[4,5,6,3,2,1,8,7]=>[5,4,3,6,7,8,1,2]=>[1,1,4,2]
[5,6,7,2,3,4,8,1]=>[4,1,5,2,6,3,8,7]=>[5,8,4,7,3,6,1,2]=>[2,2,2,2]
[6,7,4,3,2,5,8,1]=>[5,4,3,1,6,2,8,7]=>[4,5,6,8,3,7,1,2]=>[4,2,2]
[7,6,3,2,4,5,8,1]=>[4,3,5,6,2,1,8,7]=>[5,6,4,3,7,8,1,2]=>[2,1,3,2]
[6,7,3,2,4,5,8,1]=>[4,3,5,1,6,2,8,7]=>[5,6,4,8,3,7,1,2]=>[2,2,2,2]
[7,6,2,3,4,5,8,1]=>[3,4,5,6,2,1,8,7]=>[6,5,4,3,7,8,1,2]=>[1,1,1,3,2]
[6,7,2,3,4,5,8,1]=>[3,4,5,1,6,2,8,7]=>[6,5,4,8,3,7,1,2]=>[1,1,2,2,2]
[7,5,4,3,2,6,8,1]=>[5,4,3,2,6,1,8,7]=>[4,5,6,7,3,8,1,2]=>[4,2,2]
[7,4,3,5,2,6,8,1]=>[3,2,5,4,6,1,8,7]=>[6,7,4,5,3,8,1,2]=>[2,2,2,2]
[7,5,4,2,3,6,8,1]=>[4,5,3,2,6,1,8,7]=>[5,4,6,7,3,8,1,2]=>[1,3,2,2]
[7,4,5,2,3,6,8,1]=>[4,2,5,3,6,1,8,7]=>[5,7,4,6,3,8,1,2]=>[2,2,2,2]
[7,5,3,2,4,6,8,1]=>[4,3,5,2,6,1,8,7]=>[5,6,4,7,3,8,1,2]=>[2,2,2,2]
[7,5,2,3,4,6,8,1]=>[3,4,5,2,6,1,8,7]=>[6,5,4,7,3,8,1,2]=>[1,1,2,2,2]
[7,4,3,2,5,6,8,1]=>[4,3,2,5,6,1,8,7]=>[5,6,7,4,3,8,1,2]=>[3,1,2,2]
[7,4,2,3,5,6,8,1]=>[3,4,2,5,6,1,8,7]=>[6,5,7,4,3,8,1,2]=>[1,2,1,2,2]
[7,3,2,4,5,6,8,1]=>[3,2,4,5,6,1,8,7]=>[6,7,5,4,3,8,1,2]=>[2,1,1,2,2]
[7,2,3,4,5,6,8,1]=>[2,3,4,5,6,1,8,7]=>[7,6,5,4,3,8,1,2]=>[1,1,1,1,2,2]
[6,5,4,3,2,7,8,1]=>[5,4,3,2,1,6,8,7]=>[4,5,6,7,8,3,1,2]=>[5,1,2]
[5,4,6,3,2,7,8,1]=>[2,1,5,4,3,6,8,7]=>[7,8,4,5,6,3,1,2]=>[2,3,1,2]
[4,5,6,3,2,7,8,1]=>[1,2,5,4,3,6,8,7]=>[8,7,4,5,6,3,1,2]=>[1,1,3,1,2]
[6,5,3,4,2,7,8,1]=>[3,5,4,2,1,6,8,7]=>[6,4,5,7,8,3,1,2]=>[1,4,1,2]
[6,3,4,5,2,7,8,1]=>[2,3,5,4,1,6,8,7]=>[7,6,4,5,8,3,1,2]=>[1,1,3,1,2]
[5,4,3,6,2,7,8,1]=>[3,2,1,5,4,6,8,7]=>[6,7,8,4,5,3,1,2]=>[3,2,1,2]
[4,3,5,6,2,7,8,1]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>[2,1,2,1,2]
[3,4,5,6,2,7,8,1]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[1,1,1,2,1,2]
[6,5,4,2,3,7,8,1]=>[4,5,3,2,1,6,8,7]=>[5,4,6,7,8,3,1,2]=>[1,4,1,2]
[6,5,3,2,4,7,8,1]=>[4,3,5,2,1,6,8,7]=>[5,6,4,7,8,3,1,2]=>[2,3,1,2]
[6,5,2,3,4,7,8,1]=>[3,4,5,2,1,6,8,7]=>[6,5,4,7,8,3,1,2]=>[1,1,3,1,2]
[6,2,3,4,5,7,8,1]=>[2,3,4,5,1,6,8,7]=>[7,6,5,4,8,3,1,2]=>[1,1,1,2,1,2]
[5,4,3,2,6,7,8,1]=>[4,3,2,1,5,6,8,7]=>[5,6,7,8,4,3,1,2]=>[4,1,1,2]
[4,5,3,2,6,7,8,1]=>[1,4,3,2,5,6,8,7]=>[8,5,6,7,4,3,1,2]=>[1,3,1,1,2]
[5,3,4,2,6,7,8,1]=>[2,4,3,1,5,6,8,7]=>[7,5,6,8,4,3,1,2]=>[1,3,1,1,2]
[4,3,5,2,6,7,8,1]=>[2,1,4,3,5,6,8,7]=>[7,8,5,6,4,3,1,2]=>[2,2,1,1,2]
[3,4,5,2,6,7,8,1]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[1,1,2,1,1,2]
[5,4,2,3,6,7,8,1]=>[3,4,2,1,5,6,8,7]=>[6,5,7,8,4,3,1,2]=>[1,3,1,1,2]
[5,3,2,4,6,7,8,1]=>[3,2,4,1,5,6,8,7]=>[6,7,5,8,4,3,1,2]=>[2,2,1,1,2]
[5,2,3,4,6,7,8,1]=>[2,3,4,1,5,6,8,7]=>[7,6,5,8,4,3,1,2]=>[1,1,2,1,1,2]
[4,3,2,5,6,7,8,1]=>[3,2,1,4,5,6,8,7]=>[6,7,8,5,4,3,1,2]=>[3,1,1,1,2]
[3,4,2,5,6,7,8,1]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[1,2,1,1,1,2]
[4,2,3,5,6,7,8,1]=>[2,3,1,4,5,6,8,7]=>[7,6,8,5,4,3,1,2]=>[1,2,1,1,1,2]
[3,2,4,5,6,7,8,1]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[2,1,1,1,1,2]
[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,2]
[8,7,6,5,4,3,1,2]=>[7,8,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8]=>[1,7]
[7,8,6,5,4,3,1,2]=>[7,1,8,6,5,4,3,2]=>[2,8,1,3,4,5,6,7]=>[2,6]
[8,6,7,5,4,3,1,2]=>[7,2,8,6,5,4,3,1]=>[2,7,1,3,4,5,6,8]=>[2,6]
[7,6,8,5,4,3,1,2]=>[7,2,1,8,6,5,4,3]=>[2,7,8,1,3,4,5,6]=>[3,5]
[6,7,8,5,4,3,1,2]=>[1,7,2,8,6,5,4,3]=>[8,2,7,1,3,4,5,6]=>[1,2,5]
[8,7,5,6,4,3,1,2]=>[7,3,8,6,5,4,2,1]=>[2,6,1,3,4,5,7,8]=>[2,6]
[7,8,5,6,4,3,1,2]=>[7,3,1,8,6,5,4,2]=>[2,6,8,1,3,4,5,7]=>[3,5]
[8,6,5,7,4,3,1,2]=>[7,3,2,8,6,5,4,1]=>[2,6,7,1,3,4,5,8]=>[3,5]
[7,6,5,8,4,3,1,2]=>[7,3,2,1,8,6,5,4]=>[2,6,7,8,1,3,4,5]=>[4,4]
[6,7,5,8,4,3,1,2]=>[1,7,3,2,8,6,5,4]=>[8,2,6,7,1,3,4,5]=>[1,3,4]
[7,5,6,8,4,3,1,2]=>[2,7,3,1,8,6,5,4]=>[7,2,6,8,1,3,4,5]=>[1,3,4]
[6,5,7,8,4,3,1,2]=>[2,1,7,3,8,6,5,4]=>[7,8,2,6,1,3,4,5]=>[2,2,4]
[5,6,7,8,4,3,1,2]=>[1,2,7,3,8,6,5,4]=>[8,7,2,6,1,3,4,5]=>[1,1,2,4]
[8,7,6,4,5,3,1,2]=>[7,4,8,6,5,3,2,1]=>[2,5,1,3,4,6,7,8]=>[2,6]
[7,8,6,4,5,3,1,2]=>[7,4,1,8,6,5,3,2]=>[2,5,8,1,3,4,6,7]=>[3,5]
[6,7,8,4,5,3,1,2]=>[1,7,4,2,8,6,5,3]=>[8,2,5,7,1,3,4,6]=>[1,3,4]
[8,7,5,4,6,3,1,2]=>[7,4,3,8,6,5,2,1]=>[2,5,6,1,3,4,7,8]=>[3,5]
[7,8,4,5,6,3,1,2]=>[3,7,4,1,8,6,5,2]=>[6,2,5,8,1,3,4,7]=>[1,3,4]
[8,5,6,4,7,3,1,2]=>[2,7,4,3,8,6,5,1]=>[7,2,5,6,1,3,4,8]=>[1,3,4]
[8,5,4,6,7,3,1,2]=>[3,2,7,4,8,6,5,1]=>[6,7,2,5,1,3,4,8]=>[2,2,4]
[7,6,5,4,8,3,1,2]=>[7,4,3,2,1,8,6,5]=>[2,5,6,7,8,1,3,4]=>[5,3]
[7,5,6,4,8,3,1,2]=>[2,7,4,3,1,8,6,5]=>[7,2,5,6,8,1,3,4]=>[1,4,3]
[6,5,7,4,8,3,1,2]=>[2,1,7,4,3,8,6,5]=>[7,8,2,5,6,1,3,4]=>[2,3,3]
[7,6,4,5,8,3,1,2]=>[3,7,4,2,1,8,6,5]=>[6,2,5,7,8,1,3,4]=>[1,4,3]
[6,7,4,5,8,3,1,2]=>[3,1,7,4,2,8,6,5]=>[6,8,2,5,7,1,3,4]=>[2,3,3]
[6,5,4,7,8,3,1,2]=>[3,2,1,7,4,8,6,5]=>[6,7,8,2,5,1,3,4]=>[3,2,3]
[5,6,4,7,8,3,1,2]=>[1,3,2,7,4,8,6,5]=>[8,6,7,2,5,1,3,4]=>[1,2,2,3]
[5,4,6,7,8,3,1,2]=>[2,1,3,7,4,8,6,5]=>[7,8,6,2,5,1,3,4]=>[2,1,2,3]
[4,5,6,7,8,3,1,2]=>[1,2,3,7,4,8,6,5]=>[8,7,6,2,5,1,3,4]=>[1,1,1,2,3]
[8,7,6,5,3,4,1,2]=>[7,5,8,6,4,3,2,1]=>[2,4,1,3,5,6,7,8]=>[2,6]
[7,8,6,5,3,4,1,2]=>[7,5,1,8,6,4,3,2]=>[2,4,8,1,3,5,6,7]=>[3,5]
[7,6,8,5,3,4,1,2]=>[7,5,2,1,8,6,4,3]=>[2,4,7,8,1,3,5,6]=>[4,4]
[6,7,8,5,3,4,1,2]=>[1,7,5,2,8,6,4,3]=>[8,2,4,7,1,3,5,6]=>[1,3,4]
[8,7,5,6,3,4,1,2]=>[7,5,3,8,6,4,2,1]=>[2,4,6,1,3,5,7,8]=>[3,5]
[7,8,5,6,3,4,1,2]=>[7,5,3,1,8,6,4,2]=>[2,4,6,8,1,3,5,7]=>[4,4]
[8,6,5,7,3,4,1,2]=>[7,5,3,2,8,6,4,1]=>[2,4,6,7,1,3,5,8]=>[4,4]
[8,5,6,7,3,4,1,2]=>[2,7,5,3,8,6,4,1]=>[7,2,4,6,1,3,5,8]=>[1,3,4]
[7,6,5,8,3,4,1,2]=>[7,5,3,2,1,8,6,4]=>[2,4,6,7,8,1,3,5]=>[5,3]
[6,7,5,8,3,4,1,2]=>[1,7,5,3,2,8,6,4]=>[8,2,4,6,7,1,3,5]=>[1,4,3]
[7,5,6,8,3,4,1,2]=>[2,7,5,3,1,8,6,4]=>[7,2,4,6,8,1,3,5]=>[1,4,3]
[6,5,7,8,3,4,1,2]=>[2,1,7,5,3,8,6,4]=>[7,8,2,4,6,1,3,5]=>[2,3,3]
[5,6,7,8,3,4,1,2]=>[1,2,7,5,3,8,6,4]=>[8,7,2,4,6,1,3,5]=>[1,1,3,3]
[6,7,8,4,3,5,1,2]=>[1,7,5,4,2,8,6,3]=>[8,2,4,5,7,1,3,6]=>[1,4,3]
[8,7,6,3,4,5,1,2]=>[4,7,5,8,6,3,2,1]=>[5,2,4,1,3,6,7,8]=>[1,2,5]
[7,8,6,3,4,5,1,2]=>[4,7,5,1,8,6,3,2]=>[5,2,4,8,1,3,6,7]=>[1,3,4]
[8,6,7,3,4,5,1,2]=>[4,7,5,2,8,6,3,1]=>[5,2,4,7,1,3,6,8]=>[1,3,4]
[6,7,8,3,4,5,1,2]=>[4,1,7,5,2,8,6,3]=>[5,8,2,4,7,1,3,6]=>[2,3,3]
[7,8,5,4,3,6,1,2]=>[7,5,4,3,1,8,6,2]=>[2,4,5,6,8,1,3,7]=>[5,3]
[8,7,4,5,3,6,1,2]=>[3,7,5,4,8,6,2,1]=>[6,2,4,5,1,3,7,8]=>[1,3,4]
[7,8,4,5,3,6,1,2]=>[3,7,5,4,1,8,6,2]=>[6,2,4,5,8,1,3,7]=>[1,4,3]
[7,8,5,3,4,6,1,2]=>[4,7,5,3,1,8,6,2]=>[5,2,4,6,8,1,3,7]=>[1,4,3]
[8,7,4,3,5,6,1,2]=>[4,3,7,5,8,6,2,1]=>[5,6,2,4,1,3,7,8]=>[2,2,4]
[7,8,4,3,5,6,1,2]=>[4,3,7,5,1,8,6,2]=>[5,6,2,4,8,1,3,7]=>[2,3,3]
[8,7,3,4,5,6,1,2]=>[3,4,7,5,8,6,2,1]=>[6,5,2,4,1,3,7,8]=>[1,1,2,4]
[7,8,3,4,5,6,1,2]=>[3,4,7,5,1,8,6,2]=>[6,5,2,4,8,1,3,7]=>[1,1,3,3]
[8,6,5,4,3,7,1,2]=>[7,5,4,3,2,8,6,1]=>[2,4,5,6,7,1,3,8]=>[5,3]
[8,5,4,6,3,7,1,2]=>[3,2,7,5,4,8,6,1]=>[6,7,2,4,5,1,3,8]=>[2,3,3]
[8,5,3,4,6,7,1,2]=>[3,4,2,7,5,8,6,1]=>[6,5,7,2,4,1,3,8]=>[1,2,2,3]
[8,4,3,5,6,7,1,2]=>[3,2,4,7,5,8,6,1]=>[6,7,5,2,4,1,3,8]=>[2,1,2,3]
[8,3,4,5,6,7,1,2]=>[2,3,4,7,5,8,6,1]=>[7,6,5,2,4,1,3,8]=>[1,1,1,2,3]
[7,6,5,4,3,8,1,2]=>[7,5,4,3,2,1,8,6]=>[2,4,5,6,7,8,1,3]=>[6,2]
[7,5,6,4,3,8,1,2]=>[2,7,5,4,3,1,8,6]=>[7,2,4,5,6,8,1,3]=>[1,5,2]
[6,5,7,4,3,8,1,2]=>[2,1,7,5,4,3,8,6]=>[7,8,2,4,5,6,1,3]=>[2,4,2]
[5,6,7,4,3,8,1,2]=>[1,2,7,5,4,3,8,6]=>[8,7,2,4,5,6,1,3]=>[1,1,4,2]
[6,7,4,5,3,8,1,2]=>[3,1,7,5,4,2,8,6]=>[6,8,2,4,5,7,1,3]=>[2,4,2]
[6,5,4,7,3,8,1,2]=>[3,2,1,7,5,4,8,6]=>[6,7,8,2,4,5,1,3]=>[3,3,2]
[5,6,4,7,3,8,1,2]=>[1,3,2,7,5,4,8,6]=>[8,6,7,2,4,5,1,3]=>[1,2,3,2]
[6,4,5,7,3,8,1,2]=>[2,3,1,7,5,4,8,6]=>[7,6,8,2,4,5,1,3]=>[1,2,3,2]
[5,4,6,7,3,8,1,2]=>[2,1,3,7,5,4,8,6]=>[7,8,6,2,4,5,1,3]=>[2,1,3,2]
[4,5,6,7,3,8,1,2]=>[1,2,3,7,5,4,8,6]=>[8,7,6,2,4,5,1,3]=>[1,1,1,3,2]
[7,6,5,3,4,8,1,2]=>[4,7,5,3,2,1,8,6]=>[5,2,4,6,7,8,1,3]=>[1,5,2]
[7,5,6,3,4,8,1,2]=>[4,2,7,5,3,1,8,6]=>[5,7,2,4,6,8,1,3]=>[2,4,2]
[5,6,7,3,4,8,1,2]=>[1,4,2,7,5,3,8,6]=>[8,5,7,2,4,6,1,3]=>[1,2,3,2]
[7,6,4,3,5,8,1,2]=>[4,3,7,5,2,1,8,6]=>[5,6,2,4,7,8,1,3]=>[2,4,2]
[7,6,3,4,5,8,1,2]=>[3,4,7,5,2,1,8,6]=>[6,5,2,4,7,8,1,3]=>[1,1,4,2]
[7,4,5,3,6,8,1,2]=>[2,4,3,7,5,1,8,6]=>[7,5,6,2,4,8,1,3]=>[1,2,3,2]
[7,5,3,4,6,8,1,2]=>[3,4,2,7,5,1,8,6]=>[6,5,7,2,4,8,1,3]=>[1,2,3,2]
[7,3,4,5,6,8,1,2]=>[2,3,4,7,5,1,8,6]=>[7,6,5,2,4,8,1,3]=>[1,1,1,3,2]
[6,5,4,3,7,8,1,2]=>[4,3,2,1,7,5,8,6]=>[5,6,7,8,2,4,1,3]=>[4,2,2]
[5,6,4,3,7,8,1,2]=>[1,4,3,2,7,5,8,6]=>[8,5,6,7,2,4,1,3]=>[1,3,2,2]
[5,4,6,3,7,8,1,2]=>[2,1,4,3,7,5,8,6]=>[7,8,5,6,2,4,1,3]=>[2,2,2,2]
[4,5,6,3,7,8,1,2]=>[1,2,4,3,7,5,8,6]=>[8,7,5,6,2,4,1,3]=>[1,1,2,2,2]
[6,5,3,4,7,8,1,2]=>[3,4,2,1,7,5,8,6]=>[6,5,7,8,2,4,1,3]=>[1,3,2,2]
[5,6,3,4,7,8,1,2]=>[3,1,4,2,7,5,8,6]=>[6,8,5,7,2,4,1,3]=>[2,2,2,2]
[6,4,3,5,7,8,1,2]=>[3,2,4,1,7,5,8,6]=>[6,7,5,8,2,4,1,3]=>[2,2,2,2]
[6,3,4,5,7,8,1,2]=>[2,3,4,1,7,5,8,6]=>[7,6,5,8,2,4,1,3]=>[1,1,2,2,2]
[5,4,3,6,7,8,1,2]=>[3,2,1,4,7,5,8,6]=>[6,7,8,5,2,4,1,3]=>[3,1,2,2]
[5,3,4,6,7,8,1,2]=>[2,3,1,4,7,5,8,6]=>[7,6,8,5,2,4,1,3]=>[1,2,1,2,2]
[3,4,5,6,7,8,1,2]=>[1,2,3,4,7,5,8,6]=>[8,7,6,5,2,4,1,3]=>[1,1,1,1,2,2]
[8,7,6,5,4,2,1,3]=>[7,6,8,5,4,3,2,1]=>[2,3,1,4,5,6,7,8]=>[2,6]
[7,8,6,5,4,2,1,3]=>[7,6,1,8,5,4,3,2]=>[2,3,8,1,4,5,6,7]=>[3,5]
[8,6,7,5,4,2,1,3]=>[7,6,2,8,5,4,3,1]=>[2,3,7,1,4,5,6,8]=>[3,5]
[7,6,8,5,4,2,1,3]=>[7,6,2,1,8,5,4,3]=>[2,3,7,8,1,4,5,6]=>[4,4]
[6,7,8,5,4,2,1,3]=>[1,7,6,2,8,5,4,3]=>[8,2,3,7,1,4,5,6]=>[1,3,4]
[8,7,5,6,4,2,1,3]=>[7,6,3,8,5,4,2,1]=>[2,3,6,1,4,5,7,8]=>[3,5]
[7,8,5,6,4,2,1,3]=>[7,6,3,1,8,5,4,2]=>[2,3,6,8,1,4,5,7]=>[4,4]
[8,6,5,7,4,2,1,3]=>[7,6,3,2,8,5,4,1]=>[2,3,6,7,1,4,5,8]=>[4,4]
[7,6,5,8,4,2,1,3]=>[7,6,3,2,1,8,5,4]=>[2,3,6,7,8,1,4,5]=>[5,3]
[6,7,5,8,4,2,1,3]=>[1,7,6,3,2,8,5,4]=>[8,2,3,6,7,1,4,5]=>[1,4,3]
[7,5,6,8,4,2,1,3]=>[2,7,6,3,1,8,5,4]=>[7,2,3,6,8,1,4,5]=>[1,4,3]
[6,5,7,8,4,2,1,3]=>[2,1,7,6,3,8,5,4]=>[7,8,2,3,6,1,4,5]=>[2,3,3]
[5,6,7,8,4,2,1,3]=>[1,2,7,6,3,8,5,4]=>[8,7,2,3,6,1,4,5]=>[1,1,3,3]
[8,7,6,4,5,2,1,3]=>[7,6,4,8,5,3,2,1]=>[2,3,5,1,4,6,7,8]=>[3,5]
[8,6,7,4,5,2,1,3]=>[7,6,4,2,8,5,3,1]=>[2,3,5,7,1,4,6,8]=>[4,4]
[7,6,8,4,5,2,1,3]=>[7,6,4,2,1,8,5,3]=>[2,3,5,7,8,1,4,6]=>[5,3]
[8,6,5,4,7,2,1,3]=>[7,6,4,3,2,8,5,1]=>[2,3,5,6,7,1,4,8]=>[5,3]
[8,6,4,5,7,2,1,3]=>[3,7,6,4,2,8,5,1]=>[6,2,3,5,7,1,4,8]=>[1,4,3]
[8,4,5,6,7,2,1,3]=>[2,3,7,6,4,8,5,1]=>[7,6,2,3,5,1,4,8]=>[1,1,3,3]
[7,6,5,4,8,2,1,3]=>[7,6,4,3,2,1,8,5]=>[2,3,5,6,7,8,1,4]=>[6,2]
[6,7,5,4,8,2,1,3]=>[1,7,6,4,3,2,8,5]=>[8,2,3,5,6,7,1,4]=>[1,5,2]
[7,5,6,4,8,2,1,3]=>[2,7,6,4,3,1,8,5]=>[7,2,3,5,6,8,1,4]=>[1,5,2]
[6,5,7,4,8,2,1,3]=>[2,1,7,6,4,3,8,5]=>[7,8,2,3,5,6,1,4]=>[2,4,2]
[7,6,4,5,8,2,1,3]=>[3,7,6,4,2,1,8,5]=>[6,2,3,5,7,8,1,4]=>[1,5,2]
[7,4,5,6,8,2,1,3]=>[2,3,7,6,4,1,8,5]=>[7,6,2,3,5,8,1,4]=>[1,1,4,2]
[5,4,6,7,8,2,1,3]=>[2,1,3,7,6,4,8,5]=>[7,8,6,2,3,5,1,4]=>[2,1,3,2]
[4,5,6,7,8,2,1,3]=>[1,2,3,7,6,4,8,5]=>[8,7,6,2,3,5,1,4]=>[1,1,1,3,2]
[8,7,6,5,4,1,2,3]=>[6,7,8,5,4,3,2,1]=>[3,2,1,4,5,6,7,8]=>[1,1,6]
[7,8,6,5,4,1,2,3]=>[6,7,1,8,5,4,3,2]=>[3,2,8,1,4,5,6,7]=>[1,2,5]
[7,6,8,5,4,1,2,3]=>[6,7,2,1,8,5,4,3]=>[3,2,7,8,1,4,5,6]=>[1,3,4]
[6,7,8,5,4,1,2,3]=>[6,1,7,2,8,5,4,3]=>[3,8,2,7,1,4,5,6]=>[2,2,4]
[7,8,5,6,4,1,2,3]=>[6,7,3,1,8,5,4,2]=>[3,2,6,8,1,4,5,7]=>[1,3,4]
[8,6,5,7,4,1,2,3]=>[6,7,3,2,8,5,4,1]=>[3,2,6,7,1,4,5,8]=>[1,3,4]
[8,5,6,7,4,1,2,3]=>[6,2,7,3,8,5,4,1]=>[3,7,2,6,1,4,5,8]=>[2,2,4]
[7,6,5,8,4,1,2,3]=>[6,7,3,2,1,8,5,4]=>[3,2,6,7,8,1,4,5]=>[1,4,3]
[6,7,5,8,4,1,2,3]=>[6,1,7,3,2,8,5,4]=>[3,8,2,6,7,1,4,5]=>[2,3,3]
[7,5,6,8,4,1,2,3]=>[6,2,7,3,1,8,5,4]=>[3,7,2,6,8,1,4,5]=>[2,3,3]
[6,5,7,8,4,1,2,3]=>[6,2,1,7,3,8,5,4]=>[3,7,8,2,6,1,4,5]=>[3,2,3]
[5,6,7,8,4,1,2,3]=>[1,6,2,7,3,8,5,4]=>[8,3,7,2,6,1,4,5]=>[1,2,2,3]
[8,7,6,4,5,1,2,3]=>[6,7,4,8,5,3,2,1]=>[3,2,5,1,4,6,7,8]=>[1,2,5]
[8,6,7,4,5,1,2,3]=>[6,7,4,2,8,5,3,1]=>[3,2,5,7,1,4,6,8]=>[1,3,4]
[6,7,8,4,5,1,2,3]=>[6,1,7,4,2,8,5,3]=>[3,8,2,5,7,1,4,6]=>[2,3,3]
[8,7,5,4,6,1,2,3]=>[6,7,4,3,8,5,2,1]=>[3,2,5,6,1,4,7,8]=>[1,3,4]
[7,8,5,4,6,1,2,3]=>[6,7,4,3,1,8,5,2]=>[3,2,5,6,8,1,4,7]=>[1,4,3]
[8,7,4,5,6,1,2,3]=>[6,3,7,4,8,5,2,1]=>[3,6,2,5,1,4,7,8]=>[2,2,4]
[7,8,4,5,6,1,2,3]=>[6,3,7,4,1,8,5,2]=>[3,6,2,5,8,1,4,7]=>[2,3,3]
[8,6,5,4,7,1,2,3]=>[6,7,4,3,2,8,5,1]=>[3,2,5,6,7,1,4,8]=>[1,4,3]
[8,5,6,4,7,1,2,3]=>[6,2,7,4,3,8,5,1]=>[3,7,2,5,6,1,4,8]=>[2,3,3]
[8,6,4,5,7,1,2,3]=>[6,3,7,4,2,8,5,1]=>[3,6,2,5,7,1,4,8]=>[2,3,3]
[8,5,4,6,7,1,2,3]=>[6,3,2,7,4,8,5,1]=>[3,6,7,2,5,1,4,8]=>[3,2,3]
[8,4,5,6,7,1,2,3]=>[2,6,3,7,4,8,5,1]=>[7,3,6,2,5,1,4,8]=>[1,2,2,3]
[7,6,5,4,8,1,2,3]=>[6,7,4,3,2,1,8,5]=>[3,2,5,6,7,8,1,4]=>[1,5,2]
[6,7,5,4,8,1,2,3]=>[6,1,7,4,3,2,8,5]=>[3,8,2,5,6,7,1,4]=>[2,4,2]
[7,5,6,4,8,1,2,3]=>[6,2,7,4,3,1,8,5]=>[3,7,2,5,6,8,1,4]=>[2,4,2]
[6,5,7,4,8,1,2,3]=>[6,2,1,7,4,3,8,5]=>[3,7,8,2,5,6,1,4]=>[3,3,2]
[5,6,7,4,8,1,2,3]=>[1,6,2,7,4,3,8,5]=>[8,3,7,2,5,6,1,4]=>[1,2,3,2]
[7,6,4,5,8,1,2,3]=>[6,3,7,4,2,1,8,5]=>[3,6,2,5,7,8,1,4]=>[2,4,2]
[6,7,4,5,8,1,2,3]=>[6,3,1,7,4,2,8,5]=>[3,6,8,2,5,7,1,4]=>[3,3,2]
[7,5,4,6,8,1,2,3]=>[6,3,2,7,4,1,8,5]=>[3,6,7,2,5,8,1,4]=>[3,3,2]
[7,4,5,6,8,1,2,3]=>[2,6,3,7,4,1,8,5]=>[7,3,6,2,5,8,1,4]=>[1,2,3,2]
[6,5,4,7,8,1,2,3]=>[6,3,2,1,7,4,8,5]=>[3,6,7,8,2,5,1,4]=>[4,2,2]
[5,6,4,7,8,1,2,3]=>[1,6,3,2,7,4,8,5]=>[8,3,6,7,2,5,1,4]=>[1,3,2,2]
[6,4,5,7,8,1,2,3]=>[2,6,3,1,7,4,8,5]=>[7,3,6,8,2,5,1,4]=>[1,3,2,2]
[5,4,6,7,8,1,2,3]=>[2,1,6,3,7,4,8,5]=>[7,8,3,6,2,5,1,4]=>[2,2,2,2]
[4,5,6,7,8,1,2,3]=>[1,2,6,3,7,4,8,5]=>[8,7,3,6,2,5,1,4]=>[1,1,2,2,2]
[8,7,6,5,3,2,1,4]=>[7,6,5,8,4,3,2,1]=>[2,3,4,1,5,6,7,8]=>[3,5]
[7,8,6,5,3,2,1,4]=>[7,6,5,1,8,4,3,2]=>[2,3,4,8,1,5,6,7]=>[4,4]
[8,6,7,5,3,2,1,4]=>[7,6,5,2,8,4,3,1]=>[2,3,4,7,1,5,6,8]=>[4,4]
[7,6,8,5,3,2,1,4]=>[7,6,5,2,1,8,4,3]=>[2,3,4,7,8,1,5,6]=>[5,3]
[6,7,8,5,3,2,1,4]=>[1,7,6,5,2,8,4,3]=>[8,2,3,4,7,1,5,6]=>[1,4,3]
[8,7,5,6,3,2,1,4]=>[7,6,5,3,8,4,2,1]=>[2,3,4,6,1,5,7,8]=>[4,4]
[7,8,5,6,3,2,1,4]=>[7,6,5,3,1,8,4,2]=>[2,3,4,6,8,1,5,7]=>[5,3]
[8,6,5,7,3,2,1,4]=>[7,6,5,3,2,8,4,1]=>[2,3,4,6,7,1,5,8]=>[5,3]
[8,5,6,7,3,2,1,4]=>[2,7,6,5,3,8,4,1]=>[7,2,3,4,6,1,5,8]=>[1,4,3]
[7,6,5,8,3,2,1,4]=>[7,6,5,3,2,1,8,4]=>[2,3,4,6,7,8,1,5]=>[6,2]
[6,7,5,8,3,2,1,4]=>[1,7,6,5,3,2,8,4]=>[8,2,3,4,6,7,1,5]=>[1,5,2]
[7,5,6,8,3,2,1,4]=>[2,7,6,5,3,1,8,4]=>[7,2,3,4,6,8,1,5]=>[1,5,2]
[6,5,7,8,3,2,1,4]=>[2,1,7,6,5,3,8,4]=>[7,8,2,3,4,6,1,5]=>[2,4,2]
[5,6,7,8,3,2,1,4]=>[1,2,7,6,5,3,8,4]=>[8,7,2,3,4,6,1,5]=>[1,1,4,2]
[8,7,6,5,2,3,1,4]=>[5,7,6,8,4,3,2,1]=>[4,2,3,1,5,6,7,8]=>[1,2,5]
[7,8,6,5,2,3,1,4]=>[5,7,6,1,8,4,3,2]=>[4,2,3,8,1,5,6,7]=>[1,3,4]
[8,6,7,5,2,3,1,4]=>[5,7,6,2,8,4,3,1]=>[4,2,3,7,1,5,6,8]=>[1,3,4]
[6,7,8,5,2,3,1,4]=>[5,1,7,6,2,8,4,3]=>[4,8,2,3,7,1,5,6]=>[2,3,3]
[7,8,5,6,2,3,1,4]=>[5,7,6,3,1,8,4,2]=>[4,2,3,6,8,1,5,7]=>[1,4,3]
[8,6,5,7,2,3,1,4]=>[5,7,6,3,2,8,4,1]=>[4,2,3,6,7,1,5,8]=>[1,4,3]
[8,5,6,7,2,3,1,4]=>[5,2,7,6,3,8,4,1]=>[4,7,2,3,6,1,5,8]=>[2,3,3]
[7,6,5,8,2,3,1,4]=>[5,7,6,3,2,1,8,4]=>[4,2,3,6,7,8,1,5]=>[1,5,2]
[6,7,5,8,2,3,1,4]=>[5,1,7,6,3,2,8,4]=>[4,8,2,3,6,7,1,5]=>[2,4,2]
[7,5,6,8,2,3,1,4]=>[5,2,7,6,3,1,8,4]=>[4,7,2,3,6,8,1,5]=>[2,4,2]
[6,5,7,8,2,3,1,4]=>[5,2,1,7,6,3,8,4]=>[4,7,8,2,3,6,1,5]=>[3,3,2]
[5,6,7,8,2,3,1,4]=>[1,5,2,7,6,3,8,4]=>[8,4,7,2,3,6,1,5]=>[1,2,3,2]
[8,7,6,5,3,1,2,4]=>[6,7,5,8,4,3,2,1]=>[3,2,4,1,5,6,7,8]=>[1,2,5]
[7,8,6,5,3,1,2,4]=>[6,7,5,1,8,4,3,2]=>[3,2,4,8,1,5,6,7]=>[1,3,4]
[8,6,7,5,3,1,2,4]=>[6,7,5,2,8,4,3,1]=>[3,2,4,7,1,5,6,8]=>[1,3,4]
[7,6,8,5,3,1,2,4]=>[6,7,5,2,1,8,4,3]=>[3,2,4,7,8,1,5,6]=>[1,4,3]
[8,7,5,6,3,1,2,4]=>[6,7,5,3,8,4,2,1]=>[3,2,4,6,1,5,7,8]=>[1,3,4]
[7,8,5,6,3,1,2,4]=>[6,7,5,3,1,8,4,2]=>[3,2,4,6,8,1,5,7]=>[1,4,3]
[8,6,5,7,3,1,2,4]=>[6,7,5,3,2,8,4,1]=>[3,2,4,6,7,1,5,8]=>[1,4,3]
[7,6,5,8,3,1,2,4]=>[6,7,5,3,2,1,8,4]=>[3,2,4,6,7,8,1,5]=>[1,5,2]
[6,7,5,8,3,1,2,4]=>[6,1,7,5,3,2,8,4]=>[3,8,2,4,6,7,1,5]=>[2,4,2]
[7,5,6,8,3,1,2,4]=>[6,2,7,5,3,1,8,4]=>[3,7,2,4,6,8,1,5]=>[2,4,2]
[6,5,7,8,3,1,2,4]=>[6,2,1,7,5,3,8,4]=>[3,7,8,2,4,6,1,5]=>[3,3,2]
[5,6,7,8,3,1,2,4]=>[1,6,2,7,5,3,8,4]=>[8,3,7,2,4,6,1,5]=>[1,2,3,2]
[8,7,6,5,2,1,3,4]=>[6,5,7,8,4,3,2,1]=>[3,4,2,1,5,6,7,8]=>[2,1,5]
[7,8,6,5,2,1,3,4]=>[6,5,7,1,8,4,3,2]=>[3,4,2,8,1,5,6,7]=>[2,2,4]
[7,6,8,5,2,1,3,4]=>[6,5,7,2,1,8,4,3]=>[3,4,2,7,8,1,5,6]=>[2,3,3]
[6,7,8,5,2,1,3,4]=>[6,5,1,7,2,8,4,3]=>[3,4,8,2,7,1,5,6]=>[3,2,3]
[8,7,5,6,2,1,3,4]=>[6,5,7,3,8,4,2,1]=>[3,4,2,6,1,5,7,8]=>[2,2,4]
[7,8,5,6,2,1,3,4]=>[6,5,7,3,1,8,4,2]=>[3,4,2,6,8,1,5,7]=>[2,3,3]
[8,6,5,7,2,1,3,4]=>[6,5,7,3,2,8,4,1]=>[3,4,2,6,7,1,5,8]=>[2,3,3]
[7,6,5,8,2,1,3,4]=>[6,5,7,3,2,1,8,4]=>[3,4,2,6,7,8,1,5]=>[2,4,2]
[6,7,5,8,2,1,3,4]=>[6,5,1,7,3,2,8,4]=>[3,4,8,2,6,7,1,5]=>[3,3,2]
[7,5,6,8,2,1,3,4]=>[6,5,2,7,3,1,8,4]=>[3,4,7,2,6,8,1,5]=>[3,3,2]
[6,5,7,8,2,1,3,4]=>[6,5,2,1,7,3,8,4]=>[3,4,7,8,2,6,1,5]=>[4,2,2]
[5,6,7,8,2,1,3,4]=>[1,6,5,2,7,3,8,4]=>[8,3,4,7,2,6,1,5]=>[1,3,2,2]
[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>[4,3,2,1,5,6,7,8]=>[1,1,1,5]
[7,8,6,5,1,2,3,4]=>[5,6,7,1,8,4,3,2]=>[4,3,2,8,1,5,6,7]=>[1,1,2,4]
[8,6,7,5,1,2,3,4]=>[5,6,7,2,8,4,3,1]=>[4,3,2,7,1,5,6,8]=>[1,1,2,4]
[7,6,8,5,1,2,3,4]=>[5,6,7,2,1,8,4,3]=>[4,3,2,7,8,1,5,6]=>[1,1,3,3]
[6,7,8,5,1,2,3,4]=>[5,6,1,7,2,8,4,3]=>[4,3,8,2,7,1,5,6]=>[1,2,2,3]
[8,7,5,6,1,2,3,4]=>[5,6,7,3,8,4,2,1]=>[4,3,2,6,1,5,7,8]=>[1,1,2,4]
[7,8,5,6,1,2,3,4]=>[5,6,7,3,1,8,4,2]=>[4,3,2,6,8,1,5,7]=>[1,1,3,3]
[8,6,5,7,1,2,3,4]=>[5,6,7,3,2,8,4,1]=>[4,3,2,6,7,1,5,8]=>[1,1,3,3]
[8,5,6,7,1,2,3,4]=>[5,6,2,7,3,8,4,1]=>[4,3,7,2,6,1,5,8]=>[1,2,2,3]
[7,6,5,8,1,2,3,4]=>[5,6,7,3,2,1,8,4]=>[4,3,2,6,7,8,1,5]=>[1,1,4,2]
[6,7,5,8,1,2,3,4]=>[5,6,1,7,3,2,8,4]=>[4,3,8,2,6,7,1,5]=>[1,2,3,2]
[7,5,6,8,1,2,3,4]=>[5,6,2,7,3,1,8,4]=>[4,3,7,2,6,8,1,5]=>[1,2,3,2]
[6,5,7,8,1,2,3,4]=>[5,6,2,1,7,3,8,4]=>[4,3,7,8,2,6,1,5]=>[1,3,2,2]
[5,6,7,8,1,2,3,4]=>[5,1,6,2,7,3,8,4]=>[4,8,3,7,2,6,1,5]=>[2,2,2,2]
[8,7,6,4,3,2,1,5]=>[7,6,5,4,8,3,2,1]=>[2,3,4,5,1,6,7,8]=>[4,4]
[7,8,6,4,3,2,1,5]=>[7,6,5,4,1,8,3,2]=>[2,3,4,5,8,1,6,7]=>[5,3]
[8,6,7,4,3,2,1,5]=>[7,6,5,4,2,8,3,1]=>[2,3,4,5,7,1,6,8]=>[5,3]
[7,6,8,4,3,2,1,5]=>[7,6,5,4,2,1,8,3]=>[2,3,4,5,7,8,1,6]=>[6,2]
[6,7,8,4,3,2,1,5]=>[1,7,6,5,4,2,8,3]=>[8,2,3,4,5,7,1,6]=>[1,5,2]
[8,7,6,3,4,2,1,5]=>[4,7,6,5,8,3,2,1]=>[5,2,3,4,1,6,7,8]=>[1,3,4]
[7,8,6,3,4,2,1,5]=>[4,7,6,5,1,8,3,2]=>[5,2,3,4,8,1,6,7]=>[1,4,3]
[6,7,8,3,4,2,1,5]=>[4,1,7,6,5,2,8,3]=>[5,8,2,3,4,7,1,6]=>[2,4,2]
[8,7,6,4,2,3,1,5]=>[5,7,6,4,8,3,2,1]=>[4,2,3,5,1,6,7,8]=>[1,3,4]
[7,6,8,4,2,3,1,5]=>[5,7,6,4,2,1,8,3]=>[4,2,3,5,7,8,1,6]=>[1,5,2]
[6,7,8,4,2,3,1,5]=>[5,1,7,6,4,2,8,3]=>[4,8,2,3,5,7,1,6]=>[2,4,2]
[8,7,6,3,2,4,1,5]=>[5,4,7,6,8,3,2,1]=>[4,5,2,3,1,6,7,8]=>[2,2,4]
[6,7,8,3,2,4,1,5]=>[5,4,1,7,6,2,8,3]=>[4,5,8,2,3,7,1,6]=>[3,3,2]
[8,7,6,2,3,4,1,5]=>[4,5,7,6,8,3,2,1]=>[5,4,2,3,1,6,7,8]=>[1,1,2,4]
[8,6,7,2,3,4,1,5]=>[4,5,7,6,2,8,3,1]=>[5,4,2,3,7,1,6,8]=>[1,1,3,3]
[7,6,8,2,3,4,1,5]=>[4,5,7,6,2,1,8,3]=>[5,4,2,3,7,8,1,6]=>[1,1,4,2]
[6,7,8,2,3,4,1,5]=>[4,5,1,7,6,2,8,3]=>[5,4,8,2,3,7,1,6]=>[1,2,3,2]
[8,7,6,4,3,1,2,5]=>[6,7,5,4,8,3,2,1]=>[3,2,4,5,1,6,7,8]=>[1,3,4]
[6,7,8,4,3,1,2,5]=>[6,1,7,5,4,2,8,3]=>[3,8,2,4,5,7,1,6]=>[2,4,2]
[8,7,6,3,4,1,2,5]=>[6,4,7,5,8,3,2,1]=>[3,5,2,4,1,6,7,8]=>[2,2,4]
[7,8,6,3,4,1,2,5]=>[6,4,7,5,1,8,3,2]=>[3,5,2,4,8,1,6,7]=>[2,3,3]
[8,6,7,3,4,1,2,5]=>[6,4,7,5,2,8,3,1]=>[3,5,2,4,7,1,6,8]=>[2,3,3]
[6,7,8,3,4,1,2,5]=>[6,4,1,7,5,2,8,3]=>[3,5,8,2,4,7,1,6]=>[3,3,2]
[8,7,6,4,2,1,3,5]=>[6,5,7,4,8,3,2,1]=>[3,4,2,5,1,6,7,8]=>[2,2,4]
[7,8,6,4,2,1,3,5]=>[6,5,7,4,1,8,3,2]=>[3,4,2,5,8,1,6,7]=>[2,3,3]
[8,6,7,4,2,1,3,5]=>[6,5,7,4,2,8,3,1]=>[3,4,2,5,7,1,6,8]=>[2,3,3]
[6,7,8,4,2,1,3,5]=>[6,5,1,7,4,2,8,3]=>[3,4,8,2,5,7,1,6]=>[3,3,2]
[8,7,6,4,1,2,3,5]=>[5,6,7,4,8,3,2,1]=>[4,3,2,5,1,6,7,8]=>[1,1,2,4]
[7,8,6,4,1,2,3,5]=>[5,6,7,4,1,8,3,2]=>[4,3,2,5,8,1,6,7]=>[1,1,3,3]
[7,6,8,4,1,2,3,5]=>[5,6,7,4,2,1,8,3]=>[4,3,2,5,7,8,1,6]=>[1,1,4,2]
[6,7,8,4,1,2,3,5]=>[5,6,1,7,4,2,8,3]=>[4,3,8,2,5,7,1,6]=>[1,2,3,2]
[8,7,6,3,2,1,4,5]=>[6,5,4,7,8,3,2,1]=>[3,4,5,2,1,6,7,8]=>[3,1,4]
[7,8,6,3,2,1,4,5]=>[6,5,4,7,1,8,3,2]=>[3,4,5,2,8,1,6,7]=>[3,2,3]
[8,6,7,3,2,1,4,5]=>[6,5,4,7,2,8,3,1]=>[3,4,5,2,7,1,6,8]=>[3,2,3]
[7,6,8,3,2,1,4,5]=>[6,5,4,7,2,1,8,3]=>[3,4,5,2,7,8,1,6]=>[3,3,2]
[6,7,8,3,2,1,4,5]=>[6,5,4,1,7,2,8,3]=>[3,4,5,8,2,7,1,6]=>[4,2,2]
[8,7,6,2,3,1,4,5]=>[4,6,5,7,8,3,2,1]=>[5,3,4,2,1,6,7,8]=>[1,2,1,4]
[8,6,7,2,3,1,4,5]=>[4,6,5,7,2,8,3,1]=>[5,3,4,2,7,1,6,8]=>[1,2,2,3]
[7,6,8,2,3,1,4,5]=>[4,6,5,7,2,1,8,3]=>[5,3,4,2,7,8,1,6]=>[1,2,3,2]
[6,7,8,2,3,1,4,5]=>[4,6,5,1,7,2,8,3]=>[5,3,4,8,2,7,1,6]=>[1,3,2,2]
[8,7,6,3,1,2,4,5]=>[5,6,4,7,8,3,2,1]=>[4,3,5,2,1,6,7,8]=>[1,2,1,4]
[7,8,6,3,1,2,4,5]=>[5,6,4,7,1,8,3,2]=>[4,3,5,2,8,1,6,7]=>[1,2,2,3]
[8,6,7,3,1,2,4,5]=>[5,6,4,7,2,8,3,1]=>[4,3,5,2,7,1,6,8]=>[1,2,2,3]
[7,6,8,3,1,2,4,5]=>[5,6,4,7,2,1,8,3]=>[4,3,5,2,7,8,1,6]=>[1,2,3,2]
[6,7,8,3,1,2,4,5]=>[5,6,4,1,7,2,8,3]=>[4,3,5,8,2,7,1,6]=>[1,3,2,2]
[8,7,6,2,1,3,4,5]=>[5,4,6,7,8,3,2,1]=>[4,5,3,2,1,6,7,8]=>[2,1,1,4]
[7,8,6,2,1,3,4,5]=>[5,4,6,7,1,8,3,2]=>[4,5,3,2,8,1,6,7]=>[2,1,2,3]
[8,6,7,2,1,3,4,5]=>[5,4,6,7,2,8,3,1]=>[4,5,3,2,7,1,6,8]=>[2,1,2,3]
[6,7,8,2,1,3,4,5]=>[5,4,6,1,7,2,8,3]=>[4,5,3,8,2,7,1,6]=>[2,2,2,2]
[8,7,6,1,2,3,4,5]=>[4,5,6,7,8,3,2,1]=>[5,4,3,2,1,6,7,8]=>[1,1,1,1,4]
[7,8,6,1,2,3,4,5]=>[4,5,6,7,1,8,3,2]=>[5,4,3,2,8,1,6,7]=>[1,1,1,2,3]
[8,6,7,1,2,3,4,5]=>[4,5,6,7,2,8,3,1]=>[5,4,3,2,7,1,6,8]=>[1,1,1,2,3]
[7,6,8,1,2,3,4,5]=>[4,5,6,7,2,1,8,3]=>[5,4,3,2,7,8,1,6]=>[1,1,1,3,2]
[6,7,8,1,2,3,4,5]=>[4,5,6,1,7,2,8,3]=>[5,4,3,8,2,7,1,6]=>[1,1,2,2,2]
[8,7,5,4,3,2,1,6]=>[7,6,5,4,3,8,2,1]=>[2,3,4,5,6,1,7,8]=>[5,3]
[7,8,5,4,3,2,1,6]=>[7,6,5,4,3,1,8,2]=>[2,3,4,5,6,8,1,7]=>[6,2]
[8,7,4,5,3,2,1,6]=>[3,7,6,5,4,8,2,1]=>[6,2,3,4,5,1,7,8]=>[1,4,3]
[7,8,4,5,3,2,1,6]=>[3,7,6,5,4,1,8,2]=>[6,2,3,4,5,8,1,7]=>[1,5,2]
[8,7,5,3,4,2,1,6]=>[4,7,6,5,3,8,2,1]=>[5,2,3,4,6,1,7,8]=>[1,4,3]
[8,7,3,4,5,2,1,6]=>[3,4,7,6,5,8,2,1]=>[6,5,2,3,4,1,7,8]=>[1,1,3,3]
[7,8,3,4,5,2,1,6]=>[3,4,7,6,5,1,8,2]=>[6,5,2,3,4,8,1,7]=>[1,1,4,2]
[8,7,4,5,2,3,1,6]=>[5,3,7,6,4,8,2,1]=>[4,6,2,3,5,1,7,8]=>[2,3,3]
[7,8,4,5,2,3,1,6]=>[5,3,7,6,4,1,8,2]=>[4,6,2,3,5,8,1,7]=>[2,4,2]
[7,8,5,2,3,4,1,6]=>[4,5,7,6,3,1,8,2]=>[5,4,2,3,6,8,1,7]=>[1,1,4,2]
[8,7,4,3,2,5,1,6]=>[5,4,3,7,6,8,2,1]=>[4,5,6,2,3,1,7,8]=>[3,2,3]
[7,8,4,3,2,5,1,6]=>[5,4,3,7,6,1,8,2]=>[4,5,6,2,3,8,1,7]=>[3,3,2]
[8,7,3,4,2,5,1,6]=>[3,5,4,7,6,8,2,1]=>[6,4,5,2,3,1,7,8]=>[1,2,2,3]
[7,8,3,4,2,5,1,6]=>[3,5,4,7,6,1,8,2]=>[6,4,5,2,3,8,1,7]=>[1,2,3,2]
[8,7,2,3,4,5,1,6]=>[3,4,5,7,6,8,2,1]=>[6,5,4,2,3,1,7,8]=>[1,1,1,2,3]
[7,8,2,3,4,5,1,6]=>[3,4,5,7,6,1,8,2]=>[6,5,4,2,3,8,1,7]=>[1,1,1,3,2]
[8,7,5,4,3,1,2,6]=>[6,7,5,4,3,8,2,1]=>[3,2,4,5,6,1,7,8]=>[1,4,3]
[7,8,5,4,3,1,2,6]=>[6,7,5,4,3,1,8,2]=>[3,2,4,5,6,8,1,7]=>[1,5,2]
[7,8,5,3,4,1,2,6]=>[6,4,7,5,3,1,8,2]=>[3,5,2,4,6,8,1,7]=>[2,4,2]
[8,7,3,4,5,1,2,6]=>[3,6,4,7,5,8,2,1]=>[6,3,5,2,4,1,7,8]=>[1,2,2,3]
[7,8,3,4,5,1,2,6]=>[3,6,4,7,5,1,8,2]=>[6,3,5,2,4,8,1,7]=>[1,2,3,2]
[7,8,5,4,2,1,3,6]=>[6,5,7,4,3,1,8,2]=>[3,4,2,5,6,8,1,7]=>[2,4,2]
[8,7,5,4,1,2,3,6]=>[5,6,7,4,3,8,2,1]=>[4,3,2,5,6,1,7,8]=>[1,1,3,3]
[7,8,5,4,1,2,3,6]=>[5,6,7,4,3,1,8,2]=>[4,3,2,5,6,8,1,7]=>[1,1,4,2]
[8,7,4,5,1,2,3,6]=>[5,6,3,7,4,8,2,1]=>[4,3,6,2,5,1,7,8]=>[1,2,2,3]
[7,8,4,5,1,2,3,6]=>[5,6,3,7,4,1,8,2]=>[4,3,6,2,5,8,1,7]=>[1,2,3,2]
[8,7,5,3,2,1,4,6]=>[6,5,4,7,3,8,2,1]=>[3,4,5,2,6,1,7,8]=>[3,2,3]
[7,8,5,3,2,1,4,6]=>[6,5,4,7,3,1,8,2]=>[3,4,5,2,6,8,1,7]=>[3,3,2]
[8,7,5,3,1,2,4,6]=>[5,6,4,7,3,8,2,1]=>[4,3,5,2,6,1,7,8]=>[1,2,2,3]
[7,8,5,3,1,2,4,6]=>[5,6,4,7,3,1,8,2]=>[4,3,5,2,6,8,1,7]=>[1,2,3,2]
[8,7,5,2,1,3,4,6]=>[5,4,6,7,3,8,2,1]=>[4,5,3,2,6,1,7,8]=>[2,1,2,3]
[7,8,5,2,1,3,4,6]=>[5,4,6,7,3,1,8,2]=>[4,5,3,2,6,8,1,7]=>[2,1,3,2]
[8,7,5,1,2,3,4,6]=>[4,5,6,7,3,8,2,1]=>[5,4,3,2,6,1,7,8]=>[1,1,1,2,3]
[7,8,5,1,2,3,4,6]=>[4,5,6,7,3,1,8,2]=>[5,4,3,2,6,8,1,7]=>[1,1,1,3,2]
[8,7,4,3,2,1,5,6]=>[6,5,4,3,7,8,2,1]=>[3,4,5,6,2,1,7,8]=>[4,1,3]
[7,8,4,3,2,1,5,6]=>[6,5,4,3,7,1,8,2]=>[3,4,5,6,2,8,1,7]=>[4,2,2]
[8,7,3,4,2,1,5,6]=>[3,6,5,4,7,8,2,1]=>[6,3,4,5,2,1,7,8]=>[1,3,1,3]
[7,8,3,4,2,1,5,6]=>[3,6,5,4,7,1,8,2]=>[6,3,4,5,2,8,1,7]=>[1,3,2,2]
[7,8,4,2,3,1,5,6]=>[4,6,5,3,7,1,8,2]=>[5,3,4,6,2,8,1,7]=>[1,3,2,2]
[8,7,3,2,4,1,5,6]=>[4,3,6,5,7,8,2,1]=>[5,6,3,4,2,1,7,8]=>[2,2,1,3]
[7,8,3,2,4,1,5,6]=>[4,3,6,5,7,1,8,2]=>[5,6,3,4,2,8,1,7]=>[2,2,2,2]
[8,7,2,3,4,1,5,6]=>[3,4,6,5,7,8,2,1]=>[6,5,3,4,2,1,7,8]=>[1,1,2,1,3]
[7,8,2,3,4,1,5,6]=>[3,4,6,5,7,1,8,2]=>[6,5,3,4,2,8,1,7]=>[1,1,2,2,2]
[7,8,4,3,1,2,5,6]=>[5,6,4,3,7,1,8,2]=>[4,3,5,6,2,8,1,7]=>[1,3,2,2]
[7,8,3,4,1,2,5,6]=>[5,3,6,4,7,1,8,2]=>[4,6,3,5,2,8,1,7]=>[2,2,2,2]
[8,7,4,2,1,3,5,6]=>[5,4,6,3,7,8,2,1]=>[4,5,3,6,2,1,7,8]=>[2,2,1,3]
[7,8,4,2,1,3,5,6]=>[5,4,6,3,7,1,8,2]=>[4,5,3,6,2,8,1,7]=>[2,2,2,2]
[8,7,4,1,2,3,5,6]=>[4,5,6,3,7,8,2,1]=>[5,4,3,6,2,1,7,8]=>[1,1,2,1,3]
[7,8,4,1,2,3,5,6]=>[4,5,6,3,7,1,8,2]=>[5,4,3,6,2,8,1,7]=>[1,1,2,2,2]
[8,7,3,2,1,4,5,6]=>[5,4,3,6,7,8,2,1]=>[4,5,6,3,2,1,7,8]=>[3,1,1,3]
[7,8,3,2,1,4,5,6]=>[5,4,3,6,7,1,8,2]=>[4,5,6,3,2,8,1,7]=>[3,1,2,2]
[8,7,2,3,1,4,5,6]=>[3,5,4,6,7,8,2,1]=>[6,4,5,3,2,1,7,8]=>[1,2,1,1,3]
[7,8,2,3,1,4,5,6]=>[3,5,4,6,7,1,8,2]=>[6,4,5,3,2,8,1,7]=>[1,2,1,2,2]
[8,7,2,1,3,4,5,6]=>[4,3,5,6,7,8,2,1]=>[5,6,4,3,2,1,7,8]=>[2,1,1,1,3]
[7,8,2,1,3,4,5,6]=>[4,3,5,6,7,1,8,2]=>[5,6,4,3,2,8,1,7]=>[2,1,1,2,2]
[8,7,1,2,3,4,5,6]=>[3,4,5,6,7,8,2,1]=>[6,5,4,3,2,1,7,8]=>[1,1,1,1,1,3]
[7,8,1,2,3,4,5,6]=>[3,4,5,6,7,1,8,2]=>[6,5,4,3,2,8,1,7]=>[1,1,1,1,2,2]
[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,2,8,1]=>[2,3,4,5,6,7,1,8]=>[6,2]
[8,5,6,4,3,2,1,7]=>[2,7,6,5,4,3,8,1]=>[7,2,3,4,5,6,1,8]=>[1,5,2]
[8,6,4,5,3,2,1,7]=>[3,7,6,5,4,2,8,1]=>[6,2,3,4,5,7,1,8]=>[1,5,2]
[8,4,5,6,3,2,1,7]=>[2,3,7,6,5,4,8,1]=>[7,6,2,3,4,5,1,8]=>[1,1,4,2]
[8,6,5,3,4,2,1,7]=>[4,7,6,5,3,2,8,1]=>[5,2,3,4,6,7,1,8]=>[1,5,2]
[8,6,4,3,5,2,1,7]=>[4,3,7,6,5,2,8,1]=>[5,6,2,3,4,7,1,8]=>[2,4,2]
[8,4,5,3,6,2,1,7]=>[2,4,3,7,6,5,8,1]=>[7,5,6,2,3,4,1,8]=>[1,2,3,2]
[8,4,3,5,6,2,1,7]=>[3,2,4,7,6,5,8,1]=>[6,7,5,2,3,4,1,8]=>[2,1,3,2]
[8,3,4,5,6,2,1,7]=>[2,3,4,7,6,5,8,1]=>[7,6,5,2,3,4,1,8]=>[1,1,1,3,2]
[8,6,5,4,2,3,1,7]=>[5,7,6,4,3,2,8,1]=>[4,2,3,5,6,7,1,8]=>[1,5,2]
[8,5,6,4,2,3,1,7]=>[5,2,7,6,4,3,8,1]=>[4,7,2,3,5,6,1,8]=>[2,4,2]
[8,6,4,5,2,3,1,7]=>[5,3,7,6,4,2,8,1]=>[4,6,2,3,5,7,1,8]=>[2,4,2]
[8,4,5,6,2,3,1,7]=>[2,5,3,7,6,4,8,1]=>[7,4,6,2,3,5,1,8]=>[1,2,3,2]
[8,6,5,3,2,4,1,7]=>[5,4,7,6,3,2,8,1]=>[4,5,2,3,6,7,1,8]=>[2,4,2]
[8,6,5,2,3,4,1,7]=>[4,5,7,6,3,2,8,1]=>[5,4,2,3,6,7,1,8]=>[1,1,4,2]
[8,6,4,3,2,5,1,7]=>[5,4,3,7,6,2,8,1]=>[4,5,6,2,3,7,1,8]=>[3,3,2]
[8,6,4,2,3,5,1,7]=>[4,5,3,7,6,2,8,1]=>[5,4,6,2,3,7,1,8]=>[1,2,3,2]
[8,5,4,3,2,6,1,7]=>[5,4,3,2,7,6,8,1]=>[4,5,6,7,2,3,1,8]=>[4,2,2]
[8,4,3,5,2,6,1,7]=>[3,2,5,4,7,6,8,1]=>[6,7,4,5,2,3,1,8]=>[2,2,2,2]
[8,5,4,2,3,6,1,7]=>[4,5,3,2,7,6,8,1]=>[5,4,6,7,2,3,1,8]=>[1,3,2,2]
[8,4,5,2,3,6,1,7]=>[4,2,5,3,7,6,8,1]=>[5,7,4,6,2,3,1,8]=>[2,2,2,2]
[8,5,3,2,4,6,1,7]=>[4,3,5,2,7,6,8,1]=>[5,6,4,7,2,3,1,8]=>[2,2,2,2]
[8,5,2,3,4,6,1,7]=>[3,4,5,2,7,6,8,1]=>[6,5,4,7,2,3,1,8]=>[1,1,2,2,2]
[8,3,4,2,5,6,1,7]=>[2,4,3,5,7,6,8,1]=>[7,5,6,4,2,3,1,8]=>[1,2,1,2,2]
[8,3,2,4,5,6,1,7]=>[3,2,4,5,7,6,8,1]=>[6,7,5,4,2,3,1,8]=>[2,1,1,2,2]
[8,2,3,4,5,6,1,7]=>[2,3,4,5,7,6,8,1]=>[7,6,5,4,2,3,1,8]=>[1,1,1,1,2,2]
[8,6,5,4,3,1,2,7]=>[6,7,5,4,3,2,8,1]=>[3,2,4,5,6,7,1,8]=>[1,5,2]
[8,6,4,5,3,1,2,7]=>[6,3,7,5,4,2,8,1]=>[3,6,2,4,5,7,1,8]=>[2,4,2]
[8,5,6,3,4,1,2,7]=>[6,4,2,7,5,3,8,1]=>[3,5,7,2,4,6,1,8]=>[3,3,2]
[8,6,3,4,5,1,2,7]=>[3,6,4,7,5,2,8,1]=>[6,3,5,2,4,7,1,8]=>[1,2,3,2]
[8,5,4,3,6,1,2,7]=>[6,4,3,2,7,5,8,1]=>[3,5,6,7,2,4,1,8]=>[4,2,2]
[8,4,5,3,6,1,2,7]=>[2,6,4,3,7,5,8,1]=>[7,3,5,6,2,4,1,8]=>[1,3,2,2]
[8,5,3,4,6,1,2,7]=>[3,6,4,2,7,5,8,1]=>[6,3,5,7,2,4,1,8]=>[1,3,2,2]
[8,4,3,5,6,1,2,7]=>[3,2,6,4,7,5,8,1]=>[6,7,3,5,2,4,1,8]=>[2,2,2,2]
[8,3,4,5,6,1,2,7]=>[2,3,6,4,7,5,8,1]=>[7,6,3,5,2,4,1,8]=>[1,1,2,2,2]
[8,6,5,4,2,1,3,7]=>[6,5,7,4,3,2,8,1]=>[3,4,2,5,6,7,1,8]=>[2,4,2]
[8,5,6,4,2,1,3,7]=>[6,5,2,7,4,3,8,1]=>[3,4,7,2,5,6,1,8]=>[3,3,2]
[8,6,4,5,2,1,3,7]=>[6,5,3,7,4,2,8,1]=>[3,4,6,2,5,7,1,8]=>[3,3,2]
[8,4,5,6,2,1,3,7]=>[2,6,5,3,7,4,8,1]=>[7,3,4,6,2,5,1,8]=>[1,3,2,2]
[8,6,5,4,1,2,3,7]=>[5,6,7,4,3,2,8,1]=>[4,3,2,5,6,7,1,8]=>[1,1,4,2]
[8,5,6,4,1,2,3,7]=>[5,6,2,7,4,3,8,1]=>[4,3,7,2,5,6,1,8]=>[1,2,3,2]
[8,6,4,5,1,2,3,7]=>[5,6,3,7,4,2,8,1]=>[4,3,6,2,5,7,1,8]=>[1,2,3,2]
[8,4,5,6,1,2,3,7]=>[5,2,6,3,7,4,8,1]=>[4,7,3,6,2,5,1,8]=>[2,2,2,2]
[8,6,5,3,2,1,4,7]=>[6,5,4,7,3,2,8,1]=>[3,4,5,2,6,7,1,8]=>[3,3,2]
[8,6,5,2,3,1,4,7]=>[4,6,5,7,3,2,8,1]=>[5,3,4,2,6,7,1,8]=>[1,2,3,2]
[8,5,6,2,3,1,4,7]=>[4,6,5,2,7,3,8,1]=>[5,3,4,7,2,6,1,8]=>[1,3,2,2]
[8,5,6,3,1,2,4,7]=>[5,6,4,2,7,3,8,1]=>[4,3,5,7,2,6,1,8]=>[1,3,2,2]
[8,6,5,2,1,3,4,7]=>[5,4,6,7,3,2,8,1]=>[4,5,3,2,6,7,1,8]=>[2,1,3,2]
[8,5,6,2,1,3,4,7]=>[5,4,6,2,7,3,8,1]=>[4,5,3,7,2,6,1,8]=>[2,2,2,2]
[8,6,5,1,2,3,4,7]=>[4,5,6,7,3,2,8,1]=>[5,4,3,2,6,7,1,8]=>[1,1,1,3,2]
[8,5,6,1,2,3,4,7]=>[4,5,6,2,7,3,8,1]=>[5,4,3,7,2,6,1,8]=>[1,1,2,2,2]
[8,6,4,3,2,1,5,7]=>[6,5,4,3,7,2,8,1]=>[3,4,5,6,2,7,1,8]=>[4,2,2]
[8,6,3,4,2,1,5,7]=>[3,6,5,4,7,2,8,1]=>[6,3,4,5,2,7,1,8]=>[1,3,2,2]
[8,6,4,2,3,1,5,7]=>[4,6,5,3,7,2,8,1]=>[5,3,4,6,2,7,1,8]=>[1,3,2,2]
[8,6,3,2,4,1,5,7]=>[4,3,6,5,7,2,8,1]=>[5,6,3,4,2,7,1,8]=>[2,2,2,2]
[8,6,4,3,1,2,5,7]=>[5,6,4,3,7,2,8,1]=>[4,3,5,6,2,7,1,8]=>[1,3,2,2]
[8,6,3,4,1,2,5,7]=>[5,3,6,4,7,2,8,1]=>[4,6,3,5,2,7,1,8]=>[2,2,2,2]
[8,6,4,2,1,3,5,7]=>[5,4,6,3,7,2,8,1]=>[4,5,3,6,2,7,1,8]=>[2,2,2,2]
[8,6,4,1,2,3,5,7]=>[4,5,6,3,7,2,8,1]=>[5,4,3,6,2,7,1,8]=>[1,1,2,2,2]
[8,6,1,2,3,4,5,7]=>[3,4,5,6,7,2,8,1]=>[6,5,4,3,2,7,1,8]=>[1,1,1,1,2,2]
[8,5,4,3,2,1,6,7]=>[6,5,4,3,2,7,8,1]=>[3,4,5,6,7,2,1,8]=>[5,1,2]
[8,4,5,3,2,1,6,7]=>[2,6,5,4,3,7,8,1]=>[7,3,4,5,6,2,1,8]=>[1,4,1,2]
[8,3,4,5,2,1,6,7]=>[2,3,6,5,4,7,8,1]=>[7,6,3,4,5,2,1,8]=>[1,1,3,1,2]
[8,4,5,2,3,1,6,7]=>[4,2,6,5,3,7,8,1]=>[5,7,3,4,6,2,1,8]=>[2,3,1,2]
[8,4,2,3,5,1,6,7]=>[3,4,2,6,5,7,8,1]=>[6,5,7,3,4,2,1,8]=>[1,2,2,1,2]
[8,2,3,4,5,1,6,7]=>[2,3,4,6,5,7,8,1]=>[7,6,5,3,4,2,1,8]=>[1,1,1,2,1,2]
[8,5,3,4,1,2,6,7]=>[5,3,6,4,2,7,8,1]=>[4,6,3,5,7,2,1,8]=>[2,3,1,2]
[8,3,4,5,1,2,6,7]=>[2,5,3,6,4,7,8,1]=>[7,4,6,3,5,2,1,8]=>[1,2,2,1,2]
[8,5,4,2,1,3,6,7]=>[5,4,6,3,2,7,8,1]=>[4,5,3,6,7,2,1,8]=>[2,3,1,2]
[8,5,4,1,2,3,6,7]=>[4,5,6,3,2,7,8,1]=>[5,4,3,6,7,2,1,8]=>[1,1,3,1,2]
[8,4,5,1,2,3,6,7]=>[4,5,2,6,3,7,8,1]=>[5,4,7,3,6,2,1,8]=>[1,2,2,1,2]
[8,5,3,2,1,4,6,7]=>[5,4,3,6,2,7,8,1]=>[4,5,6,3,7,2,1,8]=>[3,2,1,2]
[8,5,3,1,2,4,6,7]=>[4,5,3,6,2,7,8,1]=>[5,4,6,3,7,2,1,8]=>[1,2,2,1,2]
[8,5,2,1,3,4,6,7]=>[4,3,5,6,2,7,8,1]=>[5,6,4,3,7,2,1,8]=>[2,1,2,1,2]
[8,5,1,2,3,4,6,7]=>[3,4,5,6,2,7,8,1]=>[6,5,4,3,7,2,1,8]=>[1,1,1,2,1,2]
[8,4,3,2,1,5,6,7]=>[5,4,3,2,6,7,8,1]=>[4,5,6,7,3,2,1,8]=>[4,1,1,2]
[8,3,4,2,1,5,6,7]=>[2,5,4,3,6,7,8,1]=>[7,4,5,6,3,2,1,8]=>[1,3,1,1,2]
[8,2,3,4,1,5,6,7]=>[2,3,5,4,6,7,8,1]=>[7,6,4,5,3,2,1,8]=>[1,1,2,1,1,2]
[8,3,4,1,2,5,6,7]=>[4,2,5,3,6,7,8,1]=>[5,7,4,6,3,2,1,8]=>[2,2,1,1,2]
[8,4,2,1,3,5,6,7]=>[4,3,5,2,6,7,8,1]=>[5,6,4,7,3,2,1,8]=>[2,2,1,1,2]
[8,4,1,2,3,5,6,7]=>[3,4,5,2,6,7,8,1]=>[6,5,4,7,3,2,1,8]=>[1,1,2,1,1,2]
[8,3,2,1,4,5,6,7]=>[4,3,2,5,6,7,8,1]=>[5,6,7,4,3,2,1,8]=>[3,1,1,1,2]
[8,2,3,1,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[7,5,6,4,3,2,1,8]=>[1,2,1,1,1,2]
[8,3,1,2,4,5,6,7]=>[3,4,2,5,6,7,8,1]=>[6,5,7,4,3,2,1,8]=>[1,2,1,1,1,2]
[8,2,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[6,7,5,4,3,2,1,8]=>[2,1,1,1,1,2]
[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,2]
[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[7,1]
[6,7,5,4,3,2,1,8]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>[1,6,1]
[7,5,6,4,3,2,1,8]=>[2,7,6,5,4,3,1,8]=>[7,2,3,4,5,6,8,1]=>[1,6,1]
[6,5,7,4,3,2,1,8]=>[2,1,7,6,5,4,3,8]=>[7,8,2,3,4,5,6,1]=>[2,5,1]
[5,6,7,4,3,2,1,8]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[1,1,5,1]
[7,6,4,5,3,2,1,8]=>[3,7,6,5,4,2,1,8]=>[6,2,3,4,5,7,8,1]=>[1,6,1]
[6,7,4,5,3,2,1,8]=>[3,1,7,6,5,4,2,8]=>[6,8,2,3,4,5,7,1]=>[2,5,1]
[7,4,5,6,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[7,6,2,3,4,5,8,1]=>[1,1,5,1]
[6,5,4,7,3,2,1,8]=>[3,2,1,7,6,5,4,8]=>[6,7,8,2,3,4,5,1]=>[3,4,1]
[5,6,4,7,3,2,1,8]=>[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>[1,2,4,1]
[5,4,6,7,3,2,1,8]=>[2,1,3,7,6,5,4,8]=>[7,8,6,2,3,4,5,1]=>[2,1,4,1]
[4,5,6,7,3,2,1,8]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[1,1,1,4,1]
[7,6,5,3,4,2,1,8]=>[4,7,6,5,3,2,1,8]=>[5,2,3,4,6,7,8,1]=>[1,6,1]
[6,7,5,3,4,2,1,8]=>[4,1,7,6,5,3,2,8]=>[5,8,2,3,4,6,7,1]=>[2,5,1]
[7,5,6,3,4,2,1,8]=>[4,2,7,6,5,3,1,8]=>[5,7,2,3,4,6,8,1]=>[2,5,1]
[6,7,4,3,5,2,1,8]=>[4,3,1,7,6,5,2,8]=>[5,6,8,2,3,4,7,1]=>[3,4,1]
[7,6,3,4,5,2,1,8]=>[3,4,7,6,5,2,1,8]=>[6,5,2,3,4,7,8,1]=>[1,1,5,1]
[7,5,4,3,6,2,1,8]=>[4,3,2,7,6,5,1,8]=>[5,6,7,2,3,4,8,1]=>[3,4,1]
[7,4,5,3,6,2,1,8]=>[2,4,3,7,6,5,1,8]=>[7,5,6,2,3,4,8,1]=>[1,2,4,1]
[7,3,4,5,6,2,1,8]=>[2,3,4,7,6,5,1,8]=>[7,6,5,2,3,4,8,1]=>[1,1,1,4,1]
[6,5,4,3,7,2,1,8]=>[4,3,2,1,7,6,5,8]=>[5,6,7,8,2,3,4,1]=>[4,3,1]
[5,6,4,3,7,2,1,8]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[1,3,3,1]
[5,4,6,3,7,2,1,8]=>[2,1,4,3,7,6,5,8]=>[7,8,5,6,2,3,4,1]=>[2,2,3,1]
[5,4,3,6,7,2,1,8]=>[3,2,1,4,7,6,5,8]=>[6,7,8,5,2,3,4,1]=>[3,1,3,1]
[3,4,5,6,7,2,1,8]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[1,1,1,1,3,1]
[7,6,5,4,2,3,1,8]=>[5,7,6,4,3,2,1,8]=>[4,2,3,5,6,7,8,1]=>[1,6,1]
[6,7,5,4,2,3,1,8]=>[5,1,7,6,4,3,2,8]=>[4,8,2,3,5,6,7,1]=>[2,5,1]
[7,5,6,4,2,3,1,8]=>[5,2,7,6,4,3,1,8]=>[4,7,2,3,5,6,8,1]=>[2,5,1]
[5,6,7,4,2,3,1,8]=>[1,5,2,7,6,4,3,8]=>[8,4,7,2,3,5,6,1]=>[1,2,4,1]
[7,6,4,5,2,3,1,8]=>[5,3,7,6,4,2,1,8]=>[4,6,2,3,5,7,8,1]=>[2,5,1]
[6,7,4,5,2,3,1,8]=>[5,3,1,7,6,4,2,8]=>[4,6,8,2,3,5,7,1]=>[3,4,1]
[7,5,4,6,2,3,1,8]=>[5,3,2,7,6,4,1,8]=>[4,6,7,2,3,5,8,1]=>[3,4,1]
[7,4,5,6,2,3,1,8]=>[2,5,3,7,6,4,1,8]=>[7,4,6,2,3,5,8,1]=>[1,2,4,1]
[6,5,4,7,2,3,1,8]=>[5,3,2,1,7,6,4,8]=>[4,6,7,8,2,3,5,1]=>[4,3,1]
[5,6,4,7,2,3,1,8]=>[1,5,3,2,7,6,4,8]=>[8,4,6,7,2,3,5,1]=>[1,3,3,1]
[5,4,6,7,2,3,1,8]=>[2,1,5,3,7,6,4,8]=>[7,8,4,6,2,3,5,1]=>[2,2,3,1]
[4,5,6,7,2,3,1,8]=>[1,2,5,3,7,6,4,8]=>[8,7,4,6,2,3,5,1]=>[1,1,2,3,1]
[7,6,5,3,2,4,1,8]=>[5,4,7,6,3,2,1,8]=>[4,5,2,3,6,7,8,1]=>[2,5,1]
[6,5,7,3,2,4,1,8]=>[5,4,2,1,7,6,3,8]=>[4,5,7,8,2,3,6,1]=>[4,3,1]
[7,6,5,2,3,4,1,8]=>[4,5,7,6,3,2,1,8]=>[5,4,2,3,6,7,8,1]=>[1,1,5,1]
[6,7,5,2,3,4,1,8]=>[4,5,1,7,6,3,2,8]=>[5,4,8,2,3,6,7,1]=>[1,2,4,1]
[7,5,6,2,3,4,1,8]=>[4,5,2,7,6,3,1,8]=>[5,4,7,2,3,6,8,1]=>[1,2,4,1]
[6,5,7,2,3,4,1,8]=>[4,5,2,1,7,6,3,8]=>[5,4,7,8,2,3,6,1]=>[1,3,3,1]
[5,6,7,2,3,4,1,8]=>[4,1,5,2,7,6,3,8]=>[5,8,4,7,2,3,6,1]=>[2,2,3,1]
[7,6,4,3,2,5,1,8]=>[5,4,3,7,6,2,1,8]=>[4,5,6,2,3,7,8,1]=>[3,4,1]
[6,7,4,3,2,5,1,8]=>[5,4,3,1,7,6,2,8]=>[4,5,6,8,2,3,7,1]=>[4,3,1]
[6,7,3,4,2,5,1,8]=>[3,5,4,1,7,6,2,8]=>[6,4,5,8,2,3,7,1]=>[1,3,3,1]
[7,6,4,2,3,5,1,8]=>[4,5,3,7,6,2,1,8]=>[5,4,6,2,3,7,8,1]=>[1,2,4,1]
[6,7,4,2,3,5,1,8]=>[4,5,3,1,7,6,2,8]=>[5,4,6,8,2,3,7,1]=>[1,3,3,1]
[7,6,3,2,4,5,1,8]=>[4,3,5,7,6,2,1,8]=>[5,6,4,2,3,7,8,1]=>[2,1,4,1]
[6,7,3,2,4,5,1,8]=>[4,3,5,1,7,6,2,8]=>[5,6,4,8,2,3,7,1]=>[2,2,3,1]
[7,6,2,3,4,5,1,8]=>[3,4,5,7,6,2,1,8]=>[6,5,4,2,3,7,8,1]=>[1,1,1,4,1]
[6,7,2,3,4,5,1,8]=>[3,4,5,1,7,6,2,8]=>[6,5,4,8,2,3,7,1]=>[1,1,2,3,1]
[7,5,4,3,2,6,1,8]=>[5,4,3,2,7,6,1,8]=>[4,5,6,7,2,3,8,1]=>[4,3,1]
[7,4,5,3,2,6,1,8]=>[2,5,4,3,7,6,1,8]=>[7,4,5,6,2,3,8,1]=>[1,3,3,1]
[7,5,3,4,2,6,1,8]=>[3,5,4,2,7,6,1,8]=>[6,4,5,7,2,3,8,1]=>[1,3,3,1]
[7,5,4,2,3,6,1,8]=>[4,5,3,2,7,6,1,8]=>[5,4,6,7,2,3,8,1]=>[1,3,3,1]
[7,4,5,2,3,6,1,8]=>[4,2,5,3,7,6,1,8]=>[5,7,4,6,2,3,8,1]=>[2,2,3,1]
[7,5,3,2,4,6,1,8]=>[4,3,5,2,7,6,1,8]=>[5,6,4,7,2,3,8,1]=>[2,2,3,1]
[7,4,2,3,5,6,1,8]=>[3,4,2,5,7,6,1,8]=>[6,5,7,4,2,3,8,1]=>[1,2,1,3,1]
[7,2,3,4,5,6,1,8]=>[2,3,4,5,7,6,1,8]=>[7,6,5,4,2,3,8,1]=>[1,1,1,1,3,1]
[6,5,4,3,2,7,1,8]=>[5,4,3,2,1,7,6,8]=>[4,5,6,7,8,2,3,1]=>[5,2,1]
[5,6,4,3,2,7,1,8]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[1,4,2,1]
[5,4,6,3,2,7,1,8]=>[2,1,5,4,3,7,6,8]=>[7,8,4,5,6,2,3,1]=>[2,3,2,1]
[5,6,3,4,2,7,1,8]=>[3,1,5,4,2,7,6,8]=>[6,8,4,5,7,2,3,1]=>[2,3,2,1]
[6,3,4,5,2,7,1,8]=>[2,3,5,4,1,7,6,8]=>[7,6,4,5,8,2,3,1]=>[1,1,3,2,1]
[5,4,3,6,2,7,1,8]=>[3,2,1,5,4,7,6,8]=>[6,7,8,4,5,2,3,1]=>[3,2,2,1]
[4,5,3,6,2,7,1,8]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[1,2,2,2,1]
[5,3,4,6,2,7,1,8]=>[2,3,1,5,4,7,6,8]=>[7,6,8,4,5,2,3,1]=>[1,2,2,2,1]
[4,3,5,6,2,7,1,8]=>[2,1,3,5,4,7,6,8]=>[7,8,6,4,5,2,3,1]=>[2,1,2,2,1]
[3,4,5,6,2,7,1,8]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[1,1,1,2,2,1]
[6,5,3,2,4,7,1,8]=>[4,3,5,2,1,7,6,8]=>[5,6,4,7,8,2,3,1]=>[2,3,2,1]
[6,4,2,3,5,7,1,8]=>[3,4,2,5,1,7,6,8]=>[6,5,7,4,8,2,3,1]=>[1,2,2,2,1]
[6,3,2,4,5,7,1,8]=>[3,2,4,5,1,7,6,8]=>[6,7,5,4,8,2,3,1]=>[2,1,2,2,1]
[6,2,3,4,5,7,1,8]=>[2,3,4,5,1,7,6,8]=>[7,6,5,4,8,2,3,1]=>[1,1,1,2,2,1]
[5,4,3,2,6,7,1,8]=>[4,3,2,1,5,7,6,8]=>[5,6,7,8,4,2,3,1]=>[4,1,2,1]
[3,4,5,2,6,7,1,8]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[1,1,2,1,2,1]
[5,4,2,3,6,7,1,8]=>[3,4,2,1,5,7,6,8]=>[6,5,7,8,4,2,3,1]=>[1,3,1,2,1]
[4,5,2,3,6,7,1,8]=>[3,1,4,2,5,7,6,8]=>[6,8,5,7,4,2,3,1]=>[2,2,1,2,1]
[5,2,3,4,6,7,1,8]=>[2,3,4,1,5,7,6,8]=>[7,6,5,8,4,2,3,1]=>[1,1,2,1,2,1]
[3,4,2,5,6,7,1,8]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[1,2,1,1,2,1]
[4,2,3,5,6,7,1,8]=>[2,3,1,4,5,7,6,8]=>[7,6,8,5,4,2,3,1]=>[1,2,1,1,2,1]
[3,2,4,5,6,7,1,8]=>[2,1,3,4,5,7,6,8]=>[7,8,6,5,4,2,3,1]=>[2,1,1,1,2,1]
[2,3,4,5,6,7,1,8]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[1,1,1,1,1,2,1]
[7,6,5,4,3,1,2,8]=>[6,7,5,4,3,2,1,8]=>[3,2,4,5,6,7,8,1]=>[1,6,1]
[6,7,5,4,3,1,2,8]=>[6,1,7,5,4,3,2,8]=>[3,8,2,4,5,6,7,1]=>[2,5,1]
[7,5,6,4,3,1,2,8]=>[6,2,7,5,4,3,1,8]=>[3,7,2,4,5,6,8,1]=>[2,5,1]
[7,6,4,5,3,1,2,8]=>[6,3,7,5,4,2,1,8]=>[3,6,2,4,5,7,8,1]=>[2,5,1]
[7,4,5,6,3,1,2,8]=>[2,6,3,7,5,4,1,8]=>[7,3,6,2,4,5,8,1]=>[1,2,4,1]
[5,4,6,7,3,1,2,8]=>[2,1,6,3,7,5,4,8]=>[7,8,3,6,2,4,5,1]=>[2,2,3,1]
[4,5,6,7,3,1,2,8]=>[1,2,6,3,7,5,4,8]=>[8,7,3,6,2,4,5,1]=>[1,1,2,3,1]
[7,6,5,3,4,1,2,8]=>[6,4,7,5,3,2,1,8]=>[3,5,2,4,6,7,8,1]=>[2,5,1]
[7,5,6,3,4,1,2,8]=>[6,4,2,7,5,3,1,8]=>[3,5,7,2,4,6,8,1]=>[3,4,1]
[6,5,7,3,4,1,2,8]=>[6,4,2,1,7,5,3,8]=>[3,5,7,8,2,4,6,1]=>[4,3,1]
[6,7,3,4,5,1,2,8]=>[3,6,4,1,7,5,2,8]=>[6,3,5,8,2,4,7,1]=>[1,3,3,1]
[7,5,3,4,6,1,2,8]=>[3,6,4,2,7,5,1,8]=>[6,3,5,7,2,4,8,1]=>[1,3,3,1]
[6,5,4,3,7,1,2,8]=>[6,4,3,2,1,7,5,8]=>[3,5,6,7,8,2,4,1]=>[5,2,1]
[6,4,5,3,7,1,2,8]=>[2,6,4,3,1,7,5,8]=>[7,3,5,6,8,2,4,1]=>[1,4,2,1]
[5,6,3,4,7,1,2,8]=>[3,1,6,4,2,7,5,8]=>[6,8,3,5,7,2,4,1]=>[2,3,2,1]
[6,4,3,5,7,1,2,8]=>[3,2,6,4,1,7,5,8]=>[6,7,3,5,8,2,4,1]=>[2,3,2,1]
[6,3,4,5,7,1,2,8]=>[2,3,6,4,1,7,5,8]=>[7,6,3,5,8,2,4,1]=>[1,1,3,2,1]
[4,3,5,6,7,1,2,8]=>[2,1,3,6,4,7,5,8]=>[7,8,6,3,5,2,4,1]=>[2,1,2,2,1]
[3,4,5,6,7,1,2,8]=>[1,2,3,6,4,7,5,8]=>[8,7,6,3,5,2,4,1]=>[1,1,1,2,2,1]
[7,6,5,4,2,1,3,8]=>[6,5,7,4,3,2,1,8]=>[3,4,2,5,6,7,8,1]=>[2,5,1]
[6,5,7,4,2,1,3,8]=>[6,5,2,1,7,4,3,8]=>[3,4,7,8,2,5,6,1]=>[4,3,1]
[7,6,4,5,2,1,3,8]=>[6,5,3,7,4,2,1,8]=>[3,4,6,2,5,7,8,1]=>[3,4,1]
[7,5,4,6,2,1,3,8]=>[6,5,3,2,7,4,1,8]=>[3,4,6,7,2,5,8,1]=>[4,3,1]
[7,4,5,6,2,1,3,8]=>[2,6,5,3,7,4,1,8]=>[7,3,4,6,2,5,8,1]=>[1,3,3,1]
[4,5,6,7,2,1,3,8]=>[1,2,6,5,3,7,4,8]=>[8,7,3,4,6,2,5,1]=>[1,1,3,2,1]
[7,6,5,4,1,2,3,8]=>[5,6,7,4,3,2,1,8]=>[4,3,2,5,6,7,8,1]=>[1,1,5,1]
[7,5,6,4,1,2,3,8]=>[5,6,2,7,4,3,1,8]=>[4,3,7,2,5,6,8,1]=>[1,2,4,1]
[5,6,7,4,1,2,3,8]=>[5,1,6,2,7,4,3,8]=>[4,8,3,7,2,5,6,1]=>[2,2,3,1]
[7,6,4,5,1,2,3,8]=>[5,6,3,7,4,2,1,8]=>[4,3,6,2,5,7,8,1]=>[1,2,4,1]
[7,5,4,6,1,2,3,8]=>[5,6,3,2,7,4,1,8]=>[4,3,6,7,2,5,8,1]=>[1,3,3,1]
[7,4,5,6,1,2,3,8]=>[5,2,6,3,7,4,1,8]=>[4,7,3,6,2,5,8,1]=>[2,2,3,1]
[5,6,4,7,1,2,3,8]=>[5,1,6,3,2,7,4,8]=>[4,8,3,6,7,2,5,1]=>[2,3,2,1]
[5,4,6,7,1,2,3,8]=>[5,2,1,6,3,7,4,8]=>[4,7,8,3,6,2,5,1]=>[3,2,2,1]
[4,5,6,7,1,2,3,8]=>[1,5,2,6,3,7,4,8]=>[8,4,7,3,6,2,5,1]=>[1,2,2,2,1]
[7,6,5,3,2,1,4,8]=>[6,5,4,7,3,2,1,8]=>[3,4,5,2,6,7,8,1]=>[3,4,1]
[7,6,5,2,3,1,4,8]=>[4,6,5,7,3,2,1,8]=>[5,3,4,2,6,7,8,1]=>[1,2,4,1]
[6,7,5,2,3,1,4,8]=>[4,6,5,1,7,3,2,8]=>[5,3,4,8,2,6,7,1]=>[1,3,3,1]
[6,5,7,2,3,1,4,8]=>[4,6,5,2,1,7,3,8]=>[5,3,4,7,8,2,6,1]=>[1,4,2,1]
[7,5,6,3,1,2,4,8]=>[5,6,4,2,7,3,1,8]=>[4,3,5,7,2,6,8,1]=>[1,3,3,1]
[5,6,7,3,1,2,4,8]=>[5,1,6,4,2,7,3,8]=>[4,8,3,5,7,2,6,1]=>[2,3,2,1]
[7,6,5,2,1,3,4,8]=>[5,4,6,7,3,2,1,8]=>[4,5,3,2,6,7,8,1]=>[2,1,4,1]
[6,7,5,2,1,3,4,8]=>[5,4,6,1,7,3,2,8]=>[4,5,3,8,2,6,7,1]=>[2,2,3,1]
[5,6,7,2,1,3,4,8]=>[5,4,1,6,2,7,3,8]=>[4,5,8,3,7,2,6,1]=>[3,2,2,1]
[7,6,5,1,2,3,4,8]=>[4,5,6,7,3,2,1,8]=>[5,4,3,2,6,7,8,1]=>[1,1,1,4,1]
[6,7,5,1,2,3,4,8]=>[4,5,6,1,7,3,2,8]=>[5,4,3,8,2,6,7,1]=>[1,1,2,3,1]
[7,5,6,1,2,3,4,8]=>[4,5,6,2,7,3,1,8]=>[5,4,3,7,2,6,8,1]=>[1,1,2,3,1]
[6,5,7,1,2,3,4,8]=>[4,5,6,2,1,7,3,8]=>[5,4,3,7,8,2,6,1]=>[1,1,3,2,1]
[5,6,7,1,2,3,4,8]=>[4,5,1,6,2,7,3,8]=>[5,4,8,3,7,2,6,1]=>[1,2,2,2,1]
[7,6,4,3,2,1,5,8]=>[6,5,4,3,7,2,1,8]=>[3,4,5,6,2,7,8,1]=>[4,3,1]
[6,7,4,3,2,1,5,8]=>[6,5,4,3,1,7,2,8]=>[3,4,5,6,8,2,7,1]=>[5,2,1]
[7,6,3,4,2,1,5,8]=>[3,6,5,4,7,2,1,8]=>[6,3,4,5,2,7,8,1]=>[1,3,3,1]
[6,7,3,4,2,1,5,8]=>[3,6,5,4,1,7,2,8]=>[6,3,4,5,8,2,7,1]=>[1,4,2,1]
[6,7,4,2,3,1,5,8]=>[4,6,5,3,1,7,2,8]=>[5,3,4,6,8,2,7,1]=>[1,4,2,1]
[7,6,3,2,4,1,5,8]=>[4,3,6,5,7,2,1,8]=>[5,6,3,4,2,7,8,1]=>[2,2,3,1]
[6,7,3,2,4,1,5,8]=>[4,3,6,5,1,7,2,8]=>[5,6,3,4,8,2,7,1]=>[2,3,2,1]
[7,6,2,3,4,1,5,8]=>[3,4,6,5,7,2,1,8]=>[6,5,3,4,2,7,8,1]=>[1,1,2,3,1]
[6,7,2,3,4,1,5,8]=>[3,4,6,5,1,7,2,8]=>[6,5,3,4,8,2,7,1]=>[1,1,3,2,1]
[7,6,4,3,1,2,5,8]=>[5,6,4,3,7,2,1,8]=>[4,3,5,6,2,7,8,1]=>[1,3,3,1]
[6,7,3,4,1,2,5,8]=>[5,3,6,4,1,7,2,8]=>[4,6,3,5,8,2,7,1]=>[2,3,2,1]
[7,6,4,2,1,3,5,8]=>[5,4,6,3,7,2,1,8]=>[4,5,3,6,2,7,8,1]=>[2,2,3,1]
[7,6,3,2,1,4,5,8]=>[5,4,3,6,7,2,1,8]=>[4,5,6,3,2,7,8,1]=>[3,1,3,1]
[6,7,3,2,1,4,5,8]=>[5,4,3,6,1,7,2,8]=>[4,5,6,3,8,2,7,1]=>[3,2,2,1]
[7,6,2,3,1,4,5,8]=>[3,5,4,6,7,2,1,8]=>[6,4,5,3,2,7,8,1]=>[1,2,1,3,1]
[6,7,2,3,1,4,5,8]=>[3,5,4,6,1,7,2,8]=>[6,4,5,3,8,2,7,1]=>[1,2,2,2,1]
[6,7,3,1,2,4,5,8]=>[4,5,3,6,1,7,2,8]=>[5,4,6,3,8,2,7,1]=>[1,2,2,2,1]
[7,6,1,2,3,4,5,8]=>[3,4,5,6,7,2,1,8]=>[6,5,4,3,2,7,8,1]=>[1,1,1,1,3,1]
[6,7,1,2,3,4,5,8]=>[3,4,5,6,1,7,2,8]=>[6,5,4,3,8,2,7,1]=>[1,1,1,2,2,1]
[7,5,4,3,2,1,6,8]=>[6,5,4,3,2,7,1,8]=>[3,4,5,6,7,2,8,1]=>[5,2,1]
[7,4,5,3,2,1,6,8]=>[2,6,5,4,3,7,1,8]=>[7,3,4,5,6,2,8,1]=>[1,4,2,1]
[7,3,4,5,2,1,6,8]=>[2,3,6,5,4,7,1,8]=>[7,6,3,4,5,2,8,1]=>[1,1,3,2,1]
[7,5,4,2,3,1,6,8]=>[4,6,5,3,2,7,1,8]=>[5,3,4,6,7,2,8,1]=>[1,4,2,1]
[7,5,3,2,4,1,6,8]=>[4,3,6,5,2,7,1,8]=>[5,6,3,4,7,2,8,1]=>[2,3,2,1]
[7,5,2,3,4,1,6,8]=>[3,4,6,5,2,7,1,8]=>[6,5,3,4,7,2,8,1]=>[1,1,3,2,1]
[7,4,2,3,5,1,6,8]=>[3,4,2,6,5,7,1,8]=>[6,5,7,3,4,2,8,1]=>[1,2,2,2,1]
[7,2,3,4,5,1,6,8]=>[2,3,4,6,5,7,1,8]=>[7,6,5,3,4,2,8,1]=>[1,1,1,2,2,1]
[7,5,3,4,1,2,6,8]=>[5,3,6,4,2,7,1,8]=>[4,6,3,5,7,2,8,1]=>[2,3,2,1]
[7,4,5,2,1,3,6,8]=>[5,4,2,6,3,7,1,8]=>[4,5,7,3,6,2,8,1]=>[3,2,2,1]
[7,4,5,1,2,3,6,8]=>[4,5,2,6,3,7,1,8]=>[5,4,7,3,6,2,8,1]=>[1,2,2,2,1]
[7,5,3,2,1,4,6,8]=>[5,4,3,6,2,7,1,8]=>[4,5,6,3,7,2,8,1]=>[3,2,2,1]
[7,5,2,3,1,4,6,8]=>[3,5,4,6,2,7,1,8]=>[6,4,5,3,7,2,8,1]=>[1,2,2,2,1]
[7,5,3,1,2,4,6,8]=>[4,5,3,6,2,7,1,8]=>[5,4,6,3,7,2,8,1]=>[1,2,2,2,1]
[7,5,1,2,3,4,6,8]=>[3,4,5,6,2,7,1,8]=>[6,5,4,3,7,2,8,1]=>[1,1,1,2,2,1]
[7,4,3,2,1,5,6,8]=>[5,4,3,2,6,7,1,8]=>[4,5,6,7,3,2,8,1]=>[4,1,2,1]
[7,2,3,4,1,5,6,8]=>[2,3,5,4,6,7,1,8]=>[7,6,4,5,3,2,8,1]=>[1,1,2,1,2,1]
[7,4,3,1,2,5,6,8]=>[4,5,3,2,6,7,1,8]=>[5,4,6,7,3,2,8,1]=>[1,3,1,2,1]
[7,3,4,1,2,5,6,8]=>[4,2,5,3,6,7,1,8]=>[5,7,4,6,3,2,8,1]=>[2,2,1,2,1]
[7,4,1,2,3,5,6,8]=>[3,4,5,2,6,7,1,8]=>[6,5,4,7,3,2,8,1]=>[1,1,2,1,2,1]
[7,3,2,1,4,5,6,8]=>[4,3,2,5,6,7,1,8]=>[5,6,7,4,3,2,8,1]=>[3,1,1,2,1]
[7,2,3,1,4,5,6,8]=>[2,4,3,5,6,7,1,8]=>[7,5,6,4,3,2,8,1]=>[1,2,1,1,2,1]
[7,3,1,2,4,5,6,8]=>[3,4,2,5,6,7,1,8]=>[6,5,7,4,3,2,8,1]=>[1,2,1,1,2,1]
[7,2,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[6,7,5,4,3,2,8,1]=>[2,1,1,1,2,1]
[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[7,6,5,4,3,2,8,1]=>[1,1,1,1,1,2,1]
[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>[6,1,1]
[5,6,4,3,2,1,7,8]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[1,5,1,1]
[5,4,6,3,2,1,7,8]=>[2,1,6,5,4,3,7,8]=>[7,8,3,4,5,6,2,1]=>[2,4,1,1]
[4,5,6,3,2,1,7,8]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[1,1,4,1,1]
[6,5,3,4,2,1,7,8]=>[3,6,5,4,2,1,7,8]=>[6,3,4,5,7,8,2,1]=>[1,5,1,1]
[5,6,3,4,2,1,7,8]=>[3,1,6,5,4,2,7,8]=>[6,8,3,4,5,7,2,1]=>[2,4,1,1]
[6,3,4,5,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>[7,6,3,4,5,8,2,1]=>[1,1,4,1,1]
[5,4,3,6,2,1,7,8]=>[3,2,1,6,5,4,7,8]=>[6,7,8,3,4,5,2,1]=>[3,3,1,1]
[3,4,5,6,2,1,7,8]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[1,1,1,3,1,1]
[5,4,6,2,3,1,7,8]=>[4,2,1,6,5,3,7,8]=>[5,7,8,3,4,6,2,1]=>[3,3,1,1]
[6,5,2,3,4,1,7,8]=>[3,4,6,5,2,1,7,8]=>[6,5,3,4,7,8,2,1]=>[1,1,4,1,1]
[5,6,2,3,4,1,7,8]=>[3,4,1,6,5,2,7,8]=>[6,5,8,3,4,7,2,1]=>[1,2,3,1,1]
[6,4,3,2,5,1,7,8]=>[4,3,2,6,5,1,7,8]=>[5,6,7,3,4,8,2,1]=>[3,3,1,1]
[6,2,3,4,5,1,7,8]=>[2,3,4,6,5,1,7,8]=>[7,6,5,3,4,8,2,1]=>[1,1,1,3,1,1]
[5,4,3,2,6,1,7,8]=>[4,3,2,1,6,5,7,8]=>[5,6,7,8,3,4,2,1]=>[4,2,1,1]
[4,5,3,2,6,1,7,8]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[1,3,2,1,1]
[4,3,5,2,6,1,7,8]=>[2,1,4,3,6,5,7,8]=>[7,8,5,6,3,4,2,1]=>[2,2,2,1,1]
[3,4,5,2,6,1,7,8]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[1,1,2,2,1,1]
[5,3,2,4,6,1,7,8]=>[3,2,4,1,6,5,7,8]=>[6,7,5,8,3,4,2,1]=>[2,2,2,1,1]
[5,2,3,4,6,1,7,8]=>[2,3,4,1,6,5,7,8]=>[7,6,5,8,3,4,2,1]=>[1,1,2,2,1,1]
[4,3,2,5,6,1,7,8]=>[3,2,1,4,6,5,7,8]=>[6,7,8,5,3,4,2,1]=>[3,1,2,1,1]
[3,4,2,5,6,1,7,8]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[1,2,1,2,1,1]
[4,2,3,5,6,1,7,8]=>[2,3,1,4,6,5,7,8]=>[7,6,8,5,3,4,2,1]=>[1,2,1,2,1,1]
[3,2,4,5,6,1,7,8]=>[2,1,3,4,6,5,7,8]=>[7,8,6,5,3,4,2,1]=>[2,1,1,2,1,1]
[2,3,4,5,6,1,7,8]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[1,1,1,1,2,1,1]
[6,5,4,3,1,2,7,8]=>[5,6,4,3,2,1,7,8]=>[4,3,5,6,7,8,2,1]=>[1,5,1,1]
[5,6,4,3,1,2,7,8]=>[5,1,6,4,3,2,7,8]=>[4,8,3,5,6,7,2,1]=>[2,4,1,1]
[6,4,5,3,1,2,7,8]=>[5,2,6,4,3,1,7,8]=>[4,7,3,5,6,8,2,1]=>[2,4,1,1]
[5,4,6,3,1,2,7,8]=>[5,2,1,6,4,3,7,8]=>[4,7,8,3,5,6,2,1]=>[3,3,1,1]
[5,6,3,4,1,2,7,8]=>[5,3,1,6,4,2,7,8]=>[4,6,8,3,5,7,2,1]=>[3,3,1,1]
[6,4,3,5,1,2,7,8]=>[5,3,2,6,4,1,7,8]=>[4,6,7,3,5,8,2,1]=>[3,3,1,1]
[5,4,3,6,1,2,7,8]=>[5,3,2,1,6,4,7,8]=>[4,6,7,8,3,5,2,1]=>[4,2,1,1]
[4,3,5,6,1,2,7,8]=>[2,1,5,3,6,4,7,8]=>[7,8,4,6,3,5,2,1]=>[2,2,2,1,1]
[3,4,5,6,1,2,7,8]=>[1,2,5,3,6,4,7,8]=>[8,7,4,6,3,5,2,1]=>[1,1,2,2,1,1]
[6,5,4,2,1,3,7,8]=>[5,4,6,3,2,1,7,8]=>[4,5,3,6,7,8,2,1]=>[2,4,1,1]
[5,6,4,2,1,3,7,8]=>[5,4,1,6,3,2,7,8]=>[4,5,8,3,6,7,2,1]=>[3,3,1,1]
[6,4,5,2,1,3,7,8]=>[5,4,2,6,3,1,7,8]=>[4,5,7,3,6,8,2,1]=>[3,3,1,1]
[5,4,6,2,1,3,7,8]=>[5,4,2,1,6,3,7,8]=>[4,5,7,8,3,6,2,1]=>[4,2,1,1]
[4,5,6,2,1,3,7,8]=>[1,5,4,2,6,3,7,8]=>[8,4,5,7,3,6,2,1]=>[1,3,2,1,1]
[6,5,4,1,2,3,7,8]=>[4,5,6,3,2,1,7,8]=>[5,4,3,6,7,8,2,1]=>[1,1,4,1,1]
[4,5,6,1,2,3,7,8]=>[4,1,5,2,6,3,7,8]=>[5,8,4,7,3,6,2,1]=>[2,2,2,1,1]
[6,5,3,2,1,4,7,8]=>[5,4,3,6,2,1,7,8]=>[4,5,6,3,7,8,2,1]=>[3,3,1,1]
[5,6,3,2,1,4,7,8]=>[5,4,3,1,6,2,7,8]=>[4,5,6,8,3,7,2,1]=>[4,2,1,1]
[5,6,2,1,3,4,7,8]=>[4,3,5,1,6,2,7,8]=>[5,6,4,8,3,7,2,1]=>[2,2,2,1,1]
[6,5,1,2,3,4,7,8]=>[3,4,5,6,2,1,7,8]=>[6,5,4,3,7,8,2,1]=>[1,1,1,3,1,1]
[5,6,1,2,3,4,7,8]=>[3,4,5,1,6,2,7,8]=>[6,5,4,8,3,7,2,1]=>[1,1,2,2,1,1]
[6,4,3,2,1,5,7,8]=>[5,4,3,2,6,1,7,8]=>[4,5,6,7,3,8,2,1]=>[4,2,1,1]
[6,3,4,2,1,5,7,8]=>[2,5,4,3,6,1,7,8]=>[7,4,5,6,3,8,2,1]=>[1,3,2,1,1]
[6,4,3,1,2,5,7,8]=>[4,5,3,2,6,1,7,8]=>[5,4,6,7,3,8,2,1]=>[1,3,2,1,1]
[6,4,2,1,3,5,7,8]=>[4,3,5,2,6,1,7,8]=>[5,6,4,7,3,8,2,1]=>[2,2,2,1,1]
[6,4,1,2,3,5,7,8]=>[3,4,5,2,6,1,7,8]=>[6,5,4,7,3,8,2,1]=>[1,1,2,2,1,1]
[6,3,2,1,4,5,7,8]=>[4,3,2,5,6,1,7,8]=>[5,6,7,4,3,8,2,1]=>[3,1,2,1,1]
[6,2,3,1,4,5,7,8]=>[2,4,3,5,6,1,7,8]=>[7,5,6,4,3,8,2,1]=>[1,2,1,2,1,1]
[6,3,1,2,4,5,7,8]=>[3,4,2,5,6,1,7,8]=>[6,5,7,4,3,8,2,1]=>[1,2,1,2,1,1]
[6,2,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[6,7,5,4,3,8,2,1]=>[2,1,1,2,1,1]
[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[7,6,5,4,3,8,2,1]=>[1,1,1,1,2,1,1]
[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[5,1,1,1]
[4,5,3,2,1,6,7,8]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[1,4,1,1,1]
[5,3,4,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[7,4,5,6,8,3,2,1]=>[1,4,1,1,1]
[4,3,5,2,1,6,7,8]=>[2,1,5,4,3,6,7,8]=>[7,8,4,5,6,3,2,1]=>[2,3,1,1,1]
[3,4,5,2,1,6,7,8]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[1,1,3,1,1,1]
[5,4,2,3,1,6,7,8]=>[3,5,4,2,1,6,7,8]=>[6,4,5,7,8,3,2,1]=>[1,4,1,1,1]
[4,5,2,3,1,6,7,8]=>[3,1,5,4,2,6,7,8]=>[6,8,4,5,7,3,2,1]=>[2,3,1,1,1]
[5,3,2,4,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>[6,7,4,5,8,3,2,1]=>[2,3,1,1,1]
[5,2,3,4,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[7,6,4,5,8,3,2,1]=>[1,1,3,1,1,1]
[4,3,2,5,1,6,7,8]=>[3,2,1,5,4,6,7,8]=>[6,7,8,4,5,3,2,1]=>[3,2,1,1,1]
[3,4,2,5,1,6,7,8]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[1,2,2,1,1,1]
[4,2,3,5,1,6,7,8]=>[2,3,1,5,4,6,7,8]=>[7,6,8,4,5,3,2,1]=>[1,2,2,1,1,1]
[3,2,4,5,1,6,7,8]=>[2,1,3,5,4,6,7,8]=>[7,8,6,4,5,3,2,1]=>[2,1,2,1,1,1]
[2,3,4,5,1,6,7,8]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[1,1,1,2,1,1,1]
[5,4,3,1,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[5,4,6,7,8,3,2,1]=>[1,4,1,1,1]
[5,3,4,1,2,6,7,8]=>[4,2,5,3,1,6,7,8]=>[5,7,4,6,8,3,2,1]=>[2,3,1,1,1]
[4,3,5,1,2,6,7,8]=>[4,2,1,5,3,6,7,8]=>[5,7,8,4,6,3,2,1]=>[3,2,1,1,1]
[3,4,5,1,2,6,7,8]=>[1,4,2,5,3,6,7,8]=>[8,5,7,4,6,3,2,1]=>[1,2,2,1,1,1]
[5,4,2,1,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[5,6,4,7,8,3,2,1]=>[2,3,1,1,1]
[4,5,2,1,3,6,7,8]=>[4,3,1,5,2,6,7,8]=>[5,6,8,4,7,3,2,1]=>[3,2,1,1,1]
[5,4,1,2,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[6,5,4,7,8,3,2,1]=>[1,1,3,1,1,1]
[4,5,1,2,3,6,7,8]=>[3,4,1,5,2,6,7,8]=>[6,5,8,4,7,3,2,1]=>[1,2,2,1,1,1]
[5,3,2,1,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[5,6,7,4,8,3,2,1]=>[3,2,1,1,1]
[5,2,3,1,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[7,5,6,4,8,3,2,1]=>[1,2,2,1,1,1]
[5,3,1,2,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[6,5,7,4,8,3,2,1]=>[1,2,2,1,1,1]
[5,2,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[6,7,5,4,8,3,2,1]=>[2,1,2,1,1,1]
[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[7,6,5,4,8,3,2,1]=>[1,1,1,2,1,1,1]
[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]
[3,4,2,1,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[1,3,1,1,1,1]
[4,2,3,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[7,5,6,8,4,3,2,1]=>[1,3,1,1,1,1]
[3,2,4,1,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[7,8,5,6,4,3,2,1]=>[2,2,1,1,1,1]
[2,3,4,1,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[1,1,2,1,1,1,1]
[4,3,1,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[6,5,7,8,4,3,2,1]=>[1,3,1,1,1,1]
[3,4,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[6,8,5,7,4,3,2,1]=>[2,2,1,1,1,1]
[4,2,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[6,7,5,8,4,3,2,1]=>[2,2,1,1,1,1]
[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[7,6,5,8,4,3,2,1]=>[1,1,2,1,1,1,1]
[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[3,1,1,1,1,1]
[2,3,1,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[7,6,8,5,4,3,2,1]=>[1,2,1,1,1,1,1]
[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1]
[6,8,7,5,4,3,2,1]=>[8,1,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[2,6]
[5,8,7,6,4,3,2,1]=>[8,7,1,6,5,4,3,2]=>[1,2,8,3,4,5,6,7]=>[3,5]
[5,7,8,6,4,3,2,1]=>[2,8,1,7,6,5,4,3]=>[7,1,8,2,3,4,5,6]=>[1,2,5]
[6,5,8,7,4,3,2,1]=>[1,8,2,7,6,5,4,3]=>[8,1,7,2,3,4,5,6]=>[1,2,5]
[5,6,8,7,4,3,2,1]=>[8,1,2,7,6,5,4,3]=>[1,8,7,2,3,4,5,6]=>[2,1,5]
[5,7,6,8,4,3,2,1]=>[3,1,2,8,7,6,5,4]=>[6,8,7,1,2,3,4,5]=>[2,1,5]
[4,8,7,6,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[1,2,3,8,4,5,6,7]=>[4,4]
[4,7,8,6,5,3,2,1]=>[2,8,7,1,6,5,4,3]=>[7,1,2,8,3,4,5,6]=>[1,3,4]
[4,6,8,7,5,3,2,1]=>[8,2,7,1,6,5,4,3]=>[1,7,2,8,3,4,5,6]=>[2,2,4]
[4,7,6,8,5,3,2,1]=>[3,2,8,1,7,6,5,4]=>[6,7,1,8,2,3,4,5]=>[2,2,4]
[4,6,7,8,5,3,2,1]=>[2,3,8,1,7,6,5,4]=>[7,6,1,8,2,3,4,5]=>[1,1,2,4]
[5,4,7,8,6,3,2,1]=>[1,3,8,2,7,6,5,4]=>[8,6,1,7,2,3,4,5]=>[1,1,2,4]
[4,5,8,7,6,3,2,1]=>[8,7,1,2,6,5,4,3]=>[1,2,8,7,3,4,5,6]=>[3,1,4]
[4,5,7,8,6,3,2,1]=>[3,8,1,2,7,6,5,4]=>[6,1,8,7,2,3,4,5]=>[1,2,1,4]
[6,5,4,8,7,3,2,1]=>[2,1,8,3,7,6,5,4]=>[7,8,1,6,2,3,4,5]=>[2,2,4]
[5,6,4,8,7,3,2,1]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[1,1,2,4]
[4,6,5,8,7,3,2,1]=>[2,8,1,3,7,6,5,4]=>[7,1,8,6,2,3,4,5]=>[1,2,1,4]
[4,5,6,8,7,3,2,1]=>[8,1,2,3,7,6,5,4]=>[1,8,7,6,2,3,4,5]=>[2,1,1,4]
[5,7,6,4,8,3,2,1]=>[4,1,3,2,8,7,6,5]=>[5,8,6,7,1,2,3,4]=>[2,2,4]
[4,7,6,5,8,3,2,1]=>[4,3,1,2,8,7,6,5]=>[5,6,8,7,1,2,3,4]=>[3,1,4]
[4,6,7,5,8,3,2,1]=>[2,4,1,3,8,7,6,5]=>[7,5,8,6,1,2,3,4]=>[1,2,1,4]
[5,4,7,6,8,3,2,1]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[1,2,1,4]
[4,5,7,6,8,3,2,1]=>[4,1,2,3,8,7,6,5]=>[5,8,7,6,1,2,3,4]=>[2,1,1,4]
[4,6,5,7,8,3,2,1]=>[3,1,2,4,8,7,6,5]=>[6,8,7,5,1,2,3,4]=>[2,1,1,4]
[3,8,7,6,5,4,2,1]=>[8,7,6,5,1,4,3,2]=>[1,2,3,4,8,5,6,7]=>[5,3]
[3,7,8,6,5,4,2,1]=>[2,8,7,6,1,5,4,3]=>[7,1,2,3,8,4,5,6]=>[1,4,3]
[3,6,8,7,5,4,2,1]=>[8,2,7,6,1,5,4,3]=>[1,7,2,3,8,4,5,6]=>[2,3,3]
[3,7,6,8,5,4,2,1]=>[3,2,8,7,1,6,5,4]=>[6,7,1,2,8,3,4,5]=>[2,3,3]
[3,5,8,7,6,4,2,1]=>[8,7,2,6,1,5,4,3]=>[1,2,7,3,8,4,5,6]=>[3,2,3]
[3,5,7,8,6,4,2,1]=>[3,8,2,7,1,6,5,4]=>[6,1,7,2,8,3,4,5]=>[1,2,2,3]
[3,5,6,8,7,4,2,1]=>[8,2,3,7,1,6,5,4]=>[1,7,6,2,8,3,4,5]=>[2,1,2,3]
[3,7,6,5,8,4,2,1]=>[4,3,2,8,1,7,6,5]=>[5,6,7,1,8,2,3,4]=>[3,2,3]
[3,6,7,5,8,4,2,1]=>[2,4,3,8,1,7,6,5]=>[7,5,6,1,8,2,3,4]=>[1,2,2,3]
[3,5,7,6,8,4,2,1]=>[4,2,3,8,1,7,6,5]=>[5,7,6,1,8,2,3,4]=>[2,1,2,3]
[3,5,6,7,8,4,2,1]=>[2,3,4,8,1,7,6,5]=>[7,6,5,1,8,2,3,4]=>[1,1,1,2,3]
[4,3,8,7,6,5,2,1]=>[8,7,1,6,2,5,4,3]=>[1,2,8,3,7,4,5,6]=>[3,2,3]
[4,3,7,8,6,5,2,1]=>[3,8,1,7,2,6,5,4]=>[6,1,8,2,7,3,4,5]=>[1,2,2,3]
[4,3,6,7,8,5,2,1]=>[1,3,4,8,2,7,6,5]=>[8,6,5,1,7,2,3,4]=>[1,1,1,2,3]
[3,4,8,7,6,5,2,1]=>[8,7,6,1,2,5,4,3]=>[1,2,3,8,7,4,5,6]=>[4,1,3]
[3,4,6,7,8,5,2,1]=>[3,4,8,1,2,7,6,5]=>[6,5,1,8,7,2,3,4]=>[1,1,2,1,3]
[5,4,3,8,7,6,2,1]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[1,2,2,3]
[5,4,3,7,8,6,2,1]=>[2,1,4,8,3,7,6,5]=>[7,8,5,1,6,2,3,4]=>[2,1,2,3]
[4,5,3,7,8,6,2,1]=>[1,2,4,8,3,7,6,5]=>[8,7,5,1,6,2,3,4]=>[1,1,1,2,3]
[3,5,4,7,8,6,2,1]=>[2,4,8,1,3,7,6,5]=>[7,5,1,8,6,2,3,4]=>[1,1,2,1,3]
[4,3,5,7,8,6,2,1]=>[1,4,8,2,3,7,6,5]=>[8,5,1,7,6,2,3,4]=>[1,1,2,1,3]
[3,4,5,8,7,6,2,1]=>[8,7,1,2,3,6,5,4]=>[1,2,8,7,6,3,4,5]=>[3,1,1,3]
[3,4,5,7,8,6,2,1]=>[4,8,1,2,3,7,6,5]=>[5,1,8,7,6,2,3,4]=>[1,2,1,1,3]
[6,5,4,3,8,7,2,1]=>[3,2,1,8,4,7,6,5]=>[6,7,8,1,5,2,3,4]=>[3,2,3]
[5,6,4,3,8,7,2,1]=>[1,3,2,8,4,7,6,5]=>[8,6,7,1,5,2,3,4]=>[1,2,2,3]
[4,5,6,3,8,7,2,1]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[1,1,1,2,3]
[3,6,5,4,8,7,2,1]=>[3,2,8,1,4,7,6,5]=>[6,7,1,8,5,2,3,4]=>[2,2,1,3]
[4,3,6,5,8,7,2,1]=>[1,3,8,2,4,7,6,5]=>[8,6,1,7,5,2,3,4]=>[1,1,2,1,3]
[5,4,3,6,8,7,2,1]=>[2,1,8,3,4,7,6,5]=>[7,8,1,6,5,2,3,4]=>[2,2,1,3]
[4,5,3,6,8,7,2,1]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[1,1,2,1,3]
[4,3,5,6,8,7,2,1]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[1,2,1,1,3]
[3,4,5,6,8,7,2,1]=>[8,1,2,3,4,7,6,5]=>[1,8,7,6,5,2,3,4]=>[2,1,1,1,3]
[5,7,6,4,3,8,2,1]=>[5,1,4,3,2,8,7,6]=>[4,8,5,6,7,1,2,3]=>[2,3,3]
[4,7,6,5,3,8,2,1]=>[5,4,1,3,2,8,7,6]=>[4,5,8,6,7,1,2,3]=>[3,2,3]
[3,7,6,5,4,8,2,1]=>[5,4,3,1,2,8,7,6]=>[4,5,6,8,7,1,2,3]=>[4,1,3]
[3,5,7,6,4,8,2,1]=>[5,2,4,1,3,8,7,6]=>[4,7,5,8,6,1,2,3]=>[2,2,1,3]
[3,5,6,7,4,8,2,1]=>[2,3,5,1,4,8,7,6]=>[7,6,4,8,5,1,2,3]=>[1,1,2,1,3]
[4,3,7,6,5,8,2,1]=>[5,1,4,2,3,8,7,6]=>[4,8,5,7,6,1,2,3]=>[2,2,1,3]
[3,4,7,6,5,8,2,1]=>[5,4,1,2,3,8,7,6]=>[4,5,8,7,6,1,2,3]=>[3,1,1,3]
[3,4,6,7,5,8,2,1]=>[3,5,1,2,4,8,7,6]=>[6,4,8,7,5,1,2,3]=>[1,2,1,1,3]
[4,5,3,7,6,8,2,1]=>[1,2,5,3,4,8,7,6]=>[8,7,4,6,5,1,2,3]=>[1,1,2,1,3]
[3,5,4,7,6,8,2,1]=>[2,5,1,3,4,8,7,6]=>[7,4,8,6,5,1,2,3]=>[1,2,1,1,3]
[4,3,5,7,6,8,2,1]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[1,2,1,1,3]
[3,4,5,7,6,8,2,1]=>[5,1,2,3,4,8,7,6]=>[4,8,7,6,5,1,2,3]=>[2,1,1,1,3]
[3,6,5,4,7,8,2,1]=>[4,3,1,2,5,8,7,6]=>[5,6,8,7,4,1,2,3]=>[3,1,1,3]
[3,5,6,4,7,8,2,1]=>[2,4,1,3,5,8,7,6]=>[7,5,8,6,4,1,2,3]=>[1,2,1,1,3]
[4,3,6,5,7,8,2,1]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[1,2,1,1,3]
[3,4,6,5,7,8,2,1]=>[4,1,2,3,5,8,7,6]=>[5,8,7,6,4,1,2,3]=>[2,1,1,1,3]
[3,5,4,6,7,8,2,1]=>[3,1,2,4,5,8,7,6]=>[6,8,7,5,4,1,2,3]=>[2,1,1,1,3]
[2,8,7,6,5,4,3,1]=>[8,7,6,5,4,1,3,2]=>[1,2,3,4,5,8,6,7]=>[6,2]
[2,7,8,6,5,4,3,1]=>[2,8,7,6,5,1,4,3]=>[7,1,2,3,4,8,5,6]=>[1,5,2]
[2,6,8,7,5,4,3,1]=>[8,2,7,6,5,1,4,3]=>[1,7,2,3,4,8,5,6]=>[2,4,2]
[2,7,6,8,5,4,3,1]=>[3,2,8,7,6,1,5,4]=>[6,7,1,2,3,8,4,5]=>[2,4,2]
[2,6,7,8,5,4,3,1]=>[2,3,8,7,6,1,5,4]=>[7,6,1,2,3,8,4,5]=>[1,1,4,2]
[2,5,8,7,6,4,3,1]=>[8,7,2,6,5,1,4,3]=>[1,2,7,3,4,8,5,6]=>[3,3,2]
[2,6,7,5,8,4,3,1]=>[2,4,3,8,7,1,6,5]=>[7,5,6,1,2,8,3,4]=>[1,2,3,2]
[2,6,5,7,8,4,3,1]=>[3,2,4,8,7,1,6,5]=>[6,7,5,1,2,8,3,4]=>[2,1,3,2]
[2,5,6,7,8,4,3,1]=>[2,3,4,8,7,1,6,5]=>[7,6,5,1,2,8,3,4]=>[1,1,1,3,2]
[2,4,8,7,6,5,3,1]=>[8,7,6,2,5,1,4,3]=>[1,2,3,7,4,8,5,6]=>[4,2,2]
[2,4,7,8,6,5,3,1]=>[3,8,7,2,6,1,5,4]=>[6,1,2,7,3,8,4,5]=>[1,3,2,2]
[2,4,6,8,7,5,3,1]=>[8,3,7,2,6,1,5,4]=>[1,6,2,7,3,8,4,5]=>[2,2,2,2]
[2,4,6,7,8,5,3,1]=>[3,4,8,2,7,1,6,5]=>[6,5,1,7,2,8,3,4]=>[1,1,2,2,2]
[2,5,4,8,7,6,3,1]=>[8,2,7,3,6,1,5,4]=>[1,7,2,6,3,8,4,5]=>[2,2,2,2]
[2,5,4,7,8,6,3,1]=>[2,4,8,3,7,1,6,5]=>[7,5,1,6,2,8,3,4]=>[1,1,2,2,2]
[2,6,5,4,8,7,3,1]=>[3,2,8,4,7,1,6,5]=>[6,7,1,5,2,8,3,4]=>[2,2,2,2]
[2,5,6,4,8,7,3,1]=>[2,3,8,4,7,1,6,5]=>[7,6,1,5,2,8,3,4]=>[1,1,2,2,2]
[2,4,6,5,8,7,3,1]=>[3,8,2,4,7,1,6,5]=>[6,1,7,5,2,8,3,4]=>[1,2,1,2,2]
[2,4,5,6,8,7,3,1]=>[8,2,3,4,7,1,6,5]=>[1,7,6,5,2,8,3,4]=>[2,1,1,2,2]
[2,7,6,5,4,8,3,1]=>[5,4,3,2,8,1,7,6]=>[4,5,6,7,1,8,2,3]=>[4,2,2]
[2,6,7,5,4,8,3,1]=>[2,5,4,3,8,1,7,6]=>[7,4,5,6,1,8,2,3]=>[1,3,2,2]
[2,5,6,7,4,8,3,1]=>[2,3,5,4,8,1,7,6]=>[7,6,4,5,1,8,2,3]=>[1,1,2,2,2]
[2,4,7,6,5,8,3,1]=>[5,4,2,3,8,1,7,6]=>[4,5,7,6,1,8,2,3]=>[3,1,2,2]
[2,4,6,7,5,8,3,1]=>[3,5,2,4,8,1,7,6]=>[6,4,7,5,1,8,2,3]=>[1,2,1,2,2]
[2,5,4,7,6,8,3,1]=>[2,5,3,4,8,1,7,6]=>[7,4,6,5,1,8,2,3]=>[1,2,1,2,2]
[2,6,5,4,7,8,3,1]=>[4,3,2,5,8,1,7,6]=>[5,6,7,4,1,8,2,3]=>[3,1,2,2]
[2,5,6,4,7,8,3,1]=>[2,4,3,5,8,1,7,6]=>[7,5,6,4,1,8,2,3]=>[1,2,1,2,2]
[2,4,6,5,7,8,3,1]=>[4,2,3,5,8,1,7,6]=>[5,7,6,4,1,8,2,3]=>[2,1,1,2,2]
[2,5,4,6,7,8,3,1]=>[3,2,4,5,8,1,7,6]=>[6,7,5,4,1,8,2,3]=>[2,1,1,2,2]
[2,4,5,6,7,8,3,1]=>[2,3,4,5,8,1,7,6]=>[7,6,5,4,1,8,2,3]=>[1,1,1,1,2,2]
[3,2,8,7,6,5,4,1]=>[8,7,6,1,5,2,4,3]=>[1,2,3,8,4,7,5,6]=>[4,2,2]
[3,2,7,8,6,5,4,1]=>[3,8,7,1,6,2,5,4]=>[6,1,2,8,3,7,4,5]=>[1,3,2,2]
[3,2,6,8,7,5,4,1]=>[8,3,7,1,6,2,5,4]=>[1,6,2,8,3,7,4,5]=>[2,2,2,2]
[3,2,5,7,8,6,4,1]=>[4,8,1,3,7,2,6,5]=>[5,1,8,6,2,7,3,4]=>[1,2,1,2,2]
[3,2,6,5,8,7,4,1]=>[3,8,1,4,7,2,6,5]=>[6,1,8,5,2,7,3,4]=>[1,2,1,2,2]
[3,2,6,7,5,8,4,1]=>[3,5,1,4,8,2,7,6]=>[6,4,8,5,1,7,2,3]=>[1,2,1,2,2]
[3,2,5,7,6,8,4,1]=>[5,1,3,4,8,2,7,6]=>[4,8,6,5,1,7,2,3]=>[2,1,1,2,2]
[3,2,5,6,7,8,4,1]=>[1,3,4,5,8,2,7,6]=>[8,6,5,4,1,7,2,3]=>[1,1,1,1,2,2]
[2,3,8,7,6,5,4,1]=>[8,7,6,5,1,2,4,3]=>[1,2,3,4,8,7,5,6]=>[5,1,2]
[2,3,6,7,8,5,4,1]=>[3,4,8,7,1,2,6,5]=>[6,5,1,2,8,7,3,4]=>[1,1,3,1,2]
[2,3,5,8,7,6,4,1]=>[8,7,3,6,1,2,5,4]=>[1,2,6,3,8,7,4,5]=>[3,2,1,2]
[2,3,5,7,8,6,4,1]=>[4,8,3,7,1,2,6,5]=>[5,1,6,2,8,7,3,4]=>[1,2,2,1,2]
[2,3,6,5,8,7,4,1]=>[3,8,4,7,1,2,6,5]=>[6,1,5,2,8,7,3,4]=>[1,2,2,1,2]
[2,3,5,6,8,7,4,1]=>[8,3,4,7,1,2,6,5]=>[1,6,5,2,8,7,3,4]=>[2,1,2,1,2]
[2,3,7,6,5,8,4,1]=>[5,4,3,8,1,2,7,6]=>[4,5,6,1,8,7,2,3]=>[3,2,1,2]
[2,3,5,7,6,8,4,1]=>[5,3,4,8,1,2,7,6]=>[4,6,5,1,8,7,2,3]=>[2,1,2,1,2]
[2,3,5,6,7,8,4,1]=>[3,4,5,8,1,2,7,6]=>[6,5,4,1,8,7,2,3]=>[1,1,1,2,1,2]
[4,3,2,8,7,6,5,1]=>[8,1,7,2,6,3,5,4]=>[1,8,2,7,3,6,4,5]=>[2,2,2,2]
[4,3,2,7,8,6,5,1]=>[1,4,8,2,7,3,6,5]=>[8,5,1,7,2,6,3,4]=>[1,1,2,2,2]
[4,3,2,6,8,7,5,1]=>[1,8,2,4,7,3,6,5]=>[8,1,7,5,2,6,3,4]=>[1,2,1,2,2]
[3,4,2,8,7,6,5,1]=>[8,7,1,2,6,3,5,4]=>[1,2,8,7,3,6,4,5]=>[3,1,2,2]
[2,4,3,8,7,6,5,1]=>[8,7,2,6,1,3,5,4]=>[1,2,7,3,8,6,4,5]=>[3,2,1,2]
[2,4,3,6,8,7,5,1]=>[8,2,4,7,1,3,6,5]=>[1,7,5,2,8,6,3,4]=>[2,1,2,1,2]
[2,4,3,6,7,8,5,1]=>[2,4,5,8,1,3,7,6]=>[7,5,4,1,8,6,2,3]=>[1,1,1,2,1,2]
[3,2,4,8,7,6,5,1]=>[8,7,1,6,2,3,5,4]=>[1,2,8,3,7,6,4,5]=>[3,2,1,2]
[3,2,4,7,8,6,5,1]=>[4,8,1,7,2,3,6,5]=>[5,1,8,2,7,6,3,4]=>[1,2,2,1,2]
[2,3,4,8,7,6,5,1]=>[8,7,6,1,2,3,5,4]=>[1,2,3,8,7,6,4,5]=>[4,1,1,2]
[2,3,4,7,8,6,5,1]=>[4,8,7,1,2,3,6,5]=>[5,1,2,8,7,6,3,4]=>[1,3,1,1,2]
[2,3,4,6,8,7,5,1]=>[8,4,7,1,2,3,6,5]=>[1,5,2,8,7,6,3,4]=>[2,2,1,1,2]
[2,3,4,7,6,8,5,1]=>[5,4,8,1,2,3,7,6]=>[4,5,1,8,7,6,2,3]=>[2,2,1,1,2]
[2,3,4,6,7,8,5,1]=>[4,5,8,1,2,3,7,6]=>[5,4,1,8,7,6,2,3]=>[1,1,2,1,1,2]
[5,4,3,2,8,7,6,1]=>[2,1,8,3,7,4,6,5]=>[7,8,1,6,2,5,3,4]=>[2,2,2,2]
[5,4,3,2,7,8,6,1]=>[3,2,1,5,8,4,7,6]=>[6,7,8,4,1,5,2,3]=>[3,1,2,2]
[4,5,3,2,8,7,6,1]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[1,1,2,2,2]
[3,5,4,2,7,8,6,1]=>[3,1,2,5,8,4,7,6]=>[6,8,7,4,1,5,2,3]=>[2,1,1,2,2]
[3,4,5,2,7,8,6,1]=>[1,2,3,5,8,4,7,6]=>[8,7,6,4,1,5,2,3]=>[1,1,1,1,2,2]
[2,5,4,3,8,7,6,1]=>[2,8,3,7,1,4,6,5]=>[7,1,6,2,8,5,3,4]=>[1,2,2,1,2]
[2,5,4,3,7,8,6,1]=>[3,2,5,8,1,4,7,6]=>[6,7,4,1,8,5,2,3]=>[2,1,2,1,2]
[2,4,5,3,7,8,6,1]=>[2,3,5,8,1,4,7,6]=>[7,6,4,1,8,5,2,3]=>[1,1,1,2,1,2]
[3,2,5,4,7,8,6,1]=>[1,3,5,8,2,4,7,6]=>[8,6,4,1,7,5,2,3]=>[1,1,1,2,1,2]
[2,3,5,4,8,7,6,1]=>[8,3,7,1,2,4,6,5]=>[1,6,2,8,7,5,3,4]=>[2,2,1,1,2]
[2,3,5,4,7,8,6,1]=>[3,5,8,1,2,4,7,6]=>[6,4,1,8,7,5,2,3]=>[1,1,2,1,1,2]
[4,3,2,5,8,7,6,1]=>[1,8,2,7,3,4,6,5]=>[8,1,7,2,6,5,3,4]=>[1,2,2,1,2]
[4,3,2,5,7,8,6,1]=>[2,1,5,8,3,4,7,6]=>[7,8,4,1,6,5,2,3]=>[2,1,2,1,2]
[3,4,2,5,8,7,6,1]=>[8,1,2,7,3,4,6,5]=>[1,8,7,2,6,5,3,4]=>[2,1,2,1,2]
[3,4,2,5,7,8,6,1]=>[1,2,5,8,3,4,7,6]=>[8,7,4,1,6,5,2,3]=>[1,1,1,2,1,2]
[2,4,3,5,8,7,6,1]=>[8,2,7,1,3,4,6,5]=>[1,7,2,8,6,5,3,4]=>[2,2,1,1,2]
[2,3,4,5,8,7,6,1]=>[8,7,1,2,3,4,6,5]=>[1,2,8,7,6,5,3,4]=>[3,1,1,1,2]
[2,3,4,5,7,8,6,1]=>[5,8,1,2,3,4,7,6]=>[4,1,8,7,6,5,2,3]=>[1,2,1,1,1,2]
[6,5,4,3,2,8,7,1]=>[4,3,2,1,8,5,7,6]=>[5,6,7,8,1,4,2,3]=>[4,2,2]
[4,5,6,3,2,8,7,1]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[1,1,2,2,2]
[3,6,5,4,2,8,7,1]=>[4,3,1,2,8,5,7,6]=>[5,6,8,7,1,4,2,3]=>[3,1,2,2]
[3,5,6,4,2,8,7,1]=>[2,4,1,3,8,5,7,6]=>[7,5,8,6,1,4,2,3]=>[1,2,1,2,2]
[4,3,6,5,2,8,7,1]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[1,2,1,2,2]
[5,4,3,6,2,8,7,1]=>[3,2,1,4,8,5,7,6]=>[6,7,8,5,1,4,2,3]=>[3,1,2,2]
[4,5,3,6,2,8,7,1]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[1,2,1,2,2]
[3,5,4,6,2,8,7,1]=>[3,1,2,4,8,5,7,6]=>[6,8,7,5,1,4,2,3]=>[2,1,1,2,2]
[3,4,5,6,2,8,7,1]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[1,1,1,1,2,2]
[2,6,5,4,3,8,7,1]=>[4,3,2,8,1,5,7,6]=>[5,6,7,1,8,4,2,3]=>[3,2,1,2]
[2,4,6,5,3,8,7,1]=>[4,2,3,8,1,5,7,6]=>[5,7,6,1,8,4,2,3]=>[2,1,2,1,2]
[2,4,5,6,3,8,7,1]=>[2,3,4,8,1,5,7,6]=>[7,6,5,1,8,4,2,3]=>[1,1,1,2,1,2]
[3,2,6,5,4,8,7,1]=>[4,1,3,8,2,5,7,6]=>[5,8,6,1,7,4,2,3]=>[2,1,2,1,2]
[2,3,5,6,4,8,7,1]=>[3,4,8,1,2,5,7,6]=>[6,5,1,8,7,4,2,3]=>[1,1,2,1,1,2]
[4,3,2,6,5,8,7,1]=>[2,1,4,8,3,5,7,6]=>[7,8,5,1,6,4,2,3]=>[2,1,2,1,2]
[3,4,2,6,5,8,7,1]=>[1,2,4,8,3,5,7,6]=>[8,7,5,1,6,4,2,3]=>[1,1,1,2,1,2]
[2,4,3,6,5,8,7,1]=>[2,4,8,1,3,5,7,6]=>[7,5,1,8,6,4,2,3]=>[1,1,2,1,1,2]
[3,2,4,6,5,8,7,1]=>[1,4,8,2,3,5,7,6]=>[8,5,1,7,6,4,2,3]=>[1,1,2,1,1,2]
[2,3,4,6,5,8,7,1]=>[4,8,1,2,3,5,7,6]=>[5,1,8,7,6,4,2,3]=>[1,2,1,1,1,2]
[5,4,3,2,6,8,7,1]=>[3,2,1,8,4,5,7,6]=>[6,7,8,1,5,4,2,3]=>[3,2,1,2]
[4,5,3,2,6,8,7,1]=>[1,3,2,8,4,5,7,6]=>[8,6,7,1,5,4,2,3]=>[1,2,2,1,2]
[2,5,4,3,6,8,7,1]=>[3,2,8,1,4,5,7,6]=>[6,7,1,8,5,4,2,3]=>[2,2,1,1,2]
[2,4,5,3,6,8,7,1]=>[2,3,8,1,4,5,7,6]=>[7,6,1,8,5,4,2,3]=>[1,1,2,1,1,2]
[3,2,5,4,6,8,7,1]=>[1,3,8,2,4,5,7,6]=>[8,6,1,7,5,4,2,3]=>[1,1,2,1,1,2]
[4,3,2,5,6,8,7,1]=>[2,1,8,3,4,5,7,6]=>[7,8,1,6,5,4,2,3]=>[2,2,1,1,2]
[3,4,2,5,6,8,7,1]=>[1,2,8,3,4,5,7,6]=>[8,7,1,6,5,4,2,3]=>[1,1,2,1,1,2]
[2,4,3,5,6,8,7,1]=>[2,8,1,3,4,5,7,6]=>[7,1,8,6,5,4,2,3]=>[1,2,1,1,1,2]
[3,2,4,5,6,8,7,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[1,2,1,1,1,2]
[2,3,4,5,6,8,7,1]=>[8,1,2,3,4,5,7,6]=>[1,8,7,6,5,4,2,3]=>[2,1,1,1,1,2]
[5,7,6,4,3,2,8,1]=>[6,1,5,4,3,2,8,7]=>[3,8,4,5,6,7,1,2]=>[2,4,2]
[4,7,6,5,3,2,8,1]=>[6,5,1,4,3,2,8,7]=>[3,4,8,5,6,7,1,2]=>[3,3,2]
[4,6,5,7,3,2,8,1]=>[3,1,2,6,5,4,8,7]=>[6,8,7,3,4,5,1,2]=>[2,1,3,2]
[3,5,7,6,4,2,8,1]=>[6,2,5,1,4,3,8,7]=>[3,7,4,8,5,6,1,2]=>[2,2,2,2]
[3,5,6,7,4,2,8,1]=>[2,3,6,1,5,4,8,7]=>[7,6,3,8,4,5,1,2]=>[1,1,2,2,2]
[4,3,7,6,5,2,8,1]=>[6,1,5,2,4,3,8,7]=>[3,8,4,7,5,6,1,2]=>[2,2,2,2]
[3,4,7,6,5,2,8,1]=>[6,5,1,2,4,3,8,7]=>[3,4,8,7,5,6,1,2]=>[3,1,2,2]
[3,4,6,7,5,2,8,1]=>[3,6,1,2,5,4,8,7]=>[6,3,8,7,4,5,1,2]=>[1,2,1,2,2]
[3,5,4,7,6,2,8,1]=>[2,6,1,3,5,4,8,7]=>[7,3,8,6,4,5,1,2]=>[1,2,1,2,2]
[3,4,5,7,6,2,8,1]=>[6,1,2,3,5,4,8,7]=>[3,8,7,6,4,5,1,2]=>[2,1,1,2,2]
[3,6,5,4,7,2,8,1]=>[4,3,1,2,6,5,8,7]=>[5,6,8,7,3,4,1,2]=>[3,1,2,2]
[3,5,6,4,7,2,8,1]=>[2,4,1,3,6,5,8,7]=>[7,5,8,6,3,4,1,2]=>[1,2,1,2,2]
[4,3,6,5,7,2,8,1]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[1,2,1,2,2]
[3,4,6,5,7,2,8,1]=>[4,1,2,3,6,5,8,7]=>[5,8,7,6,3,4,1,2]=>[2,1,1,2,2]
[3,5,4,6,7,2,8,1]=>[3,1,2,4,6,5,8,7]=>[6,8,7,5,3,4,1,2]=>[2,1,1,2,2]
[2,7,6,5,4,3,8,1]=>[6,5,4,3,1,2,8,7]=>[3,4,5,6,8,7,1,2]=>[5,1,2]
[2,6,5,7,4,3,8,1]=>[3,2,6,5,1,4,8,7]=>[6,7,3,4,8,5,1,2]=>[2,3,1,2]
[2,5,6,7,4,3,8,1]=>[2,3,6,5,1,4,8,7]=>[7,6,3,4,8,5,1,2]=>[1,1,3,1,2]
[2,4,6,7,5,3,8,1]=>[3,6,2,5,1,4,8,7]=>[6,3,7,4,8,5,1,2]=>[1,2,2,1,2]
[2,5,4,7,6,3,8,1]=>[2,6,3,5,1,4,8,7]=>[7,3,6,4,8,5,1,2]=>[1,2,2,1,2]
[2,4,6,5,7,3,8,1]=>[4,2,3,6,1,5,8,7]=>[5,7,6,3,8,4,1,2]=>[2,1,2,1,2]
[2,5,4,6,7,3,8,1]=>[3,2,4,6,1,5,8,7]=>[6,7,5,3,8,4,1,2]=>[2,1,2,1,2]
[2,4,5,6,7,3,8,1]=>[2,3,4,6,1,5,8,7]=>[7,6,5,3,8,4,1,2]=>[1,1,1,2,1,2]
[3,2,7,6,5,4,8,1]=>[6,5,1,4,2,3,8,7]=>[3,4,8,5,7,6,1,2]=>[3,2,1,2]
[3,2,6,7,5,4,8,1]=>[3,6,1,5,2,4,8,7]=>[6,3,8,4,7,5,1,2]=>[1,2,2,1,2]
[3,2,5,7,6,4,8,1]=>[6,1,3,5,2,4,8,7]=>[3,8,6,4,7,5,1,2]=>[2,1,2,1,2]
[3,2,6,5,7,4,8,1]=>[4,1,3,6,2,5,8,7]=>[5,8,6,3,7,4,1,2]=>[2,1,2,1,2]
[2,3,7,6,5,4,8,1]=>[6,5,4,1,2,3,8,7]=>[3,4,5,8,7,6,1,2]=>[4,1,1,2]
[2,3,5,7,6,4,8,1]=>[6,3,5,1,2,4,8,7]=>[3,6,4,8,7,5,1,2]=>[2,2,1,1,2]
[2,3,5,6,7,4,8,1]=>[3,4,6,1,2,5,8,7]=>[6,5,3,8,7,4,1,2]=>[1,1,2,1,1,2]
[4,3,2,7,6,5,8,1]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[1,2,2,1,2]
[4,3,2,6,7,5,8,1]=>[2,1,4,6,3,5,8,7]=>[7,8,5,3,6,4,1,2]=>[2,1,2,1,2]
[3,4,2,7,6,5,8,1]=>[6,1,2,5,3,4,8,7]=>[3,8,7,4,6,5,1,2]=>[2,1,2,1,2]
[3,4,2,6,7,5,8,1]=>[1,2,4,6,3,5,8,7]=>[8,7,5,3,6,4,1,2]=>[1,1,1,2,1,2]
[2,4,3,7,6,5,8,1]=>[6,2,5,1,3,4,8,7]=>[3,7,4,8,6,5,1,2]=>[2,2,1,1,2]
[2,4,3,6,7,5,8,1]=>[2,4,6,1,3,5,8,7]=>[7,5,3,8,6,4,1,2]=>[1,1,2,1,1,2]
[3,2,4,7,6,5,8,1]=>[6,1,5,2,3,4,8,7]=>[3,8,4,7,6,5,1,2]=>[2,2,1,1,2]
[2,3,4,7,6,5,8,1]=>[6,5,1,2,3,4,8,7]=>[3,4,8,7,6,5,1,2]=>[3,1,1,1,2]
[2,3,4,6,7,5,8,1]=>[4,6,1,2,3,5,8,7]=>[5,3,8,7,6,4,1,2]=>[1,2,1,1,1,2]
[5,4,3,2,7,6,8,1]=>[3,2,1,6,4,5,8,7]=>[6,7,8,3,5,4,1,2]=>[3,2,1,2]
[3,5,4,2,7,6,8,1]=>[3,1,2,6,4,5,8,7]=>[6,8,7,3,5,4,1,2]=>[2,1,2,1,2]
[3,4,5,2,7,6,8,1]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[1,1,1,2,1,2]
[2,5,4,3,7,6,8,1]=>[3,2,6,1,4,5,8,7]=>[6,7,3,8,5,4,1,2]=>[2,2,1,1,2]
[2,3,5,4,7,6,8,1]=>[3,6,1,2,4,5,8,7]=>[6,3,8,7,5,4,1,2]=>[1,2,1,1,1,2]
[4,3,2,5,7,6,8,1]=>[2,1,6,3,4,5,8,7]=>[7,8,3,6,5,4,1,2]=>[2,2,1,1,2]
[3,4,2,5,7,6,8,1]=>[1,2,6,3,4,5,8,7]=>[8,7,3,6,5,4,1,2]=>[1,1,2,1,1,2]
[2,4,3,5,7,6,8,1]=>[2,6,1,3,4,5,8,7]=>[7,3,8,6,5,4,1,2]=>[1,2,1,1,1,2]
[3,2,4,5,7,6,8,1]=>[1,6,2,3,4,5,8,7]=>[8,3,7,6,5,4,1,2]=>[1,2,1,1,1,2]
[2,3,4,5,7,6,8,1]=>[6,1,2,3,4,5,8,7]=>[3,8,7,6,5,4,1,2]=>[2,1,1,1,1,2]
[3,4,6,5,2,7,8,1]=>[5,1,2,4,3,6,8,7]=>[4,8,7,5,6,3,1,2]=>[2,1,2,1,2]
[3,5,4,6,2,7,8,1]=>[3,1,2,5,4,6,8,7]=>[6,8,7,4,5,3,1,2]=>[2,1,2,1,2]
[2,6,5,4,3,7,8,1]=>[5,4,3,1,2,6,8,7]=>[4,5,6,8,7,3,1,2]=>[4,1,1,2]
[2,4,6,5,3,7,8,1]=>[5,2,4,1,3,6,8,7]=>[4,7,5,8,6,3,1,2]=>[2,2,1,1,2]
[2,5,4,6,3,7,8,1]=>[3,2,5,1,4,6,8,7]=>[6,7,4,8,5,3,1,2]=>[2,2,1,1,2]
[2,4,5,6,3,7,8,1]=>[2,3,5,1,4,6,8,7]=>[7,6,4,8,5,3,1,2]=>[1,1,2,1,1,2]
[3,2,5,6,4,7,8,1]=>[1,3,5,2,4,6,8,7]=>[8,6,4,7,5,3,1,2]=>[1,1,2,1,1,2]
[2,3,6,5,4,7,8,1]=>[5,4,1,2,3,6,8,7]=>[4,5,8,7,6,3,1,2]=>[3,1,1,1,2]
[2,3,5,6,4,7,8,1]=>[3,5,1,2,4,6,8,7]=>[6,4,8,7,5,3,1,2]=>[1,2,1,1,1,2]
[4,3,2,6,5,7,8,1]=>[2,1,5,3,4,6,8,7]=>[7,8,4,6,5,3,1,2]=>[2,2,1,1,2]
[3,4,2,6,5,7,8,1]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[1,1,2,1,1,2]
[2,4,3,6,5,7,8,1]=>[2,5,1,3,4,6,8,7]=>[7,4,8,6,5,3,1,2]=>[1,2,1,1,1,2]
[2,3,4,6,5,7,8,1]=>[5,1,2,3,4,6,8,7]=>[4,8,7,6,5,3,1,2]=>[2,1,1,1,1,2]
[3,5,4,2,6,7,8,1]=>[4,1,3,2,5,6,8,7]=>[5,8,6,7,4,3,1,2]=>[2,2,1,1,2]
[2,5,4,3,6,7,8,1]=>[4,3,1,2,5,6,8,7]=>[5,6,8,7,4,3,1,2]=>[3,1,1,1,2]
[3,2,5,4,6,7,8,1]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[1,2,1,1,1,2]
[2,3,5,4,6,7,8,1]=>[4,1,2,3,5,6,8,7]=>[5,8,7,6,4,3,1,2]=>[2,1,1,1,1,2]
[2,4,3,5,6,7,8,1]=>[3,1,2,4,5,6,8,7]=>[6,8,7,5,4,3,1,2]=>[2,1,1,1,1,2]
[1,8,7,6,5,4,3,2]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>[7,1]
[1,7,8,6,5,4,3,2]=>[2,8,7,6,5,4,1,3]=>[7,1,2,3,4,5,8,6]=>[1,6,1]
[1,6,8,7,5,4,3,2]=>[8,2,7,6,5,4,1,3]=>[1,7,2,3,4,5,8,6]=>[2,5,1]
[1,7,6,8,5,4,3,2]=>[3,2,8,7,6,5,1,4]=>[6,7,1,2,3,4,8,5]=>[2,5,1]
[1,6,7,8,5,4,3,2]=>[2,3,8,7,6,5,1,4]=>[7,6,1,2,3,4,8,5]=>[1,1,5,1]
[1,5,8,7,6,4,3,2]=>[8,7,2,6,5,4,1,3]=>[1,2,7,3,4,5,8,6]=>[3,4,1]
[1,6,5,8,7,4,3,2]=>[2,8,3,7,6,5,1,4]=>[7,1,6,2,3,4,8,5]=>[1,2,4,1]
[1,7,6,5,8,4,3,2]=>[4,3,2,8,7,6,1,5]=>[5,6,7,1,2,3,8,4]=>[3,4,1]
[1,6,7,5,8,4,3,2]=>[2,4,3,8,7,6,1,5]=>[7,5,6,1,2,3,8,4]=>[1,2,4,1]
[1,5,7,6,8,4,3,2]=>[4,2,3,8,7,6,1,5]=>[5,7,6,1,2,3,8,4]=>[2,1,4,1]
[1,6,5,7,8,4,3,2]=>[3,2,4,8,7,6,1,5]=>[6,7,5,1,2,3,8,4]=>[2,1,4,1]
[1,5,6,7,8,4,3,2]=>[2,3,4,8,7,6,1,5]=>[7,6,5,1,2,3,8,4]=>[1,1,1,4,1]
[1,4,8,7,6,5,3,2]=>[8,7,6,2,5,4,1,3]=>[1,2,3,7,4,5,8,6]=>[4,3,1]
[1,4,7,8,6,5,3,2]=>[3,8,7,2,6,5,1,4]=>[6,1,2,7,3,4,8,5]=>[1,3,3,1]
[1,4,6,8,7,5,3,2]=>[8,3,7,2,6,5,1,4]=>[1,6,2,7,3,4,8,5]=>[2,2,3,1]
[1,4,6,7,8,5,3,2]=>[3,4,8,2,7,6,1,5]=>[6,5,1,7,2,3,8,4]=>[1,1,2,3,1]
[1,5,4,7,8,6,3,2]=>[2,4,8,3,7,6,1,5]=>[7,5,1,6,2,3,8,4]=>[1,1,2,3,1]
[1,4,5,8,7,6,3,2]=>[8,7,2,3,6,5,1,4]=>[1,2,7,6,3,4,8,5]=>[3,1,3,1]
[1,4,5,7,8,6,3,2]=>[4,8,2,3,7,6,1,5]=>[5,1,7,6,2,3,8,4]=>[1,2,1,3,1]
[1,6,5,4,8,7,3,2]=>[3,2,8,4,7,6,1,5]=>[6,7,1,5,2,3,8,4]=>[2,2,3,1]
[1,5,4,6,8,7,3,2]=>[2,8,3,4,7,6,1,5]=>[7,1,6,5,2,3,8,4]=>[1,2,1,3,1]
[1,7,6,5,4,8,3,2]=>[5,4,3,2,8,7,1,6]=>[4,5,6,7,1,2,8,3]=>[4,3,1]
[1,4,7,6,5,8,3,2]=>[5,4,2,3,8,7,1,6]=>[4,5,7,6,1,2,8,3]=>[3,1,3,1]
[1,4,6,7,5,8,3,2]=>[3,5,2,4,8,7,1,6]=>[6,4,7,5,1,2,8,3]=>[1,2,1,3,1]
[1,6,5,4,7,8,3,2]=>[4,3,2,5,8,7,1,6]=>[5,6,7,4,1,2,8,3]=>[3,1,3,1]
[1,5,6,4,7,8,3,2]=>[2,4,3,5,8,7,1,6]=>[7,5,6,4,1,2,8,3]=>[1,2,1,3,1]
[1,5,4,6,7,8,3,2]=>[3,2,4,5,8,7,1,6]=>[6,7,5,4,1,2,8,3]=>[2,1,1,3,1]
[1,4,5,6,7,8,3,2]=>[2,3,4,5,8,7,1,6]=>[7,6,5,4,1,2,8,3]=>[1,1,1,1,3,1]
[1,3,8,7,6,5,4,2]=>[8,7,6,5,2,4,1,3]=>[1,2,3,4,7,5,8,6]=>[5,2,1]
[1,3,7,8,6,5,4,2]=>[3,8,7,6,2,5,1,4]=>[6,1,2,3,7,4,8,5]=>[1,4,2,1]
[1,3,6,8,7,5,4,2]=>[8,3,7,6,2,5,1,4]=>[1,6,2,3,7,4,8,5]=>[2,3,2,1]
[1,3,6,7,8,5,4,2]=>[3,4,8,7,2,6,1,5]=>[6,5,1,2,7,3,8,4]=>[1,1,3,2,1]
[1,3,5,8,7,6,4,2]=>[8,7,3,6,2,5,1,4]=>[1,2,6,3,7,4,8,5]=>[3,2,2,1]
[1,3,5,7,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>[5,1,6,2,7,3,8,4]=>[1,2,2,2,1]
[1,3,5,6,8,7,4,2]=>[8,3,4,7,2,6,1,5]=>[1,6,5,2,7,3,8,4]=>[2,1,2,2,1]
[1,3,6,7,5,8,4,2]=>[3,5,4,8,2,7,1,6]=>[6,4,5,1,7,2,8,3]=>[1,2,2,2,1]
[1,3,5,7,6,8,4,2]=>[5,3,4,8,2,7,1,6]=>[4,6,5,1,7,2,8,3]=>[2,1,2,2,1]
[1,3,6,5,7,8,4,2]=>[4,3,5,8,2,7,1,6]=>[5,6,4,1,7,2,8,3]=>[2,1,2,2,1]
[1,3,5,6,7,8,4,2]=>[3,4,5,8,2,7,1,6]=>[6,5,4,1,7,2,8,3]=>[1,1,1,2,2,1]
[1,4,3,8,7,6,5,2]=>[8,7,2,6,3,5,1,4]=>[1,2,7,3,6,4,8,5]=>[3,2,2,1]
[1,4,3,7,8,6,5,2]=>[4,8,2,7,3,6,1,5]=>[5,1,7,2,6,3,8,4]=>[1,2,2,2,1]
[1,4,3,6,8,7,5,2]=>[8,2,4,7,3,6,1,5]=>[1,7,5,2,6,3,8,4]=>[2,1,2,2,1]
[1,4,3,7,6,8,5,2]=>[5,2,4,8,3,7,1,6]=>[4,7,5,1,6,2,8,3]=>[2,1,2,2,1]
[1,4,3,6,7,8,5,2]=>[2,4,5,8,3,7,1,6]=>[7,5,4,1,6,2,8,3]=>[1,1,1,2,2,1]
[1,3,4,8,7,6,5,2]=>[8,7,6,2,3,5,1,4]=>[1,2,3,7,6,4,8,5]=>[4,1,2,1]
[1,3,4,7,6,8,5,2]=>[5,4,8,2,3,7,1,6]=>[4,5,1,7,6,2,8,3]=>[2,2,1,2,1]
[1,3,4,6,7,8,5,2]=>[4,5,8,2,3,7,1,6]=>[5,4,1,7,6,2,8,3]=>[1,1,2,1,2,1]
[1,5,4,3,8,7,6,2]=>[2,8,3,7,4,6,1,5]=>[7,1,6,2,5,3,8,4]=>[1,2,2,2,1]
[1,4,5,3,8,7,6,2]=>[8,2,3,7,4,6,1,5]=>[1,7,6,2,5,3,8,4]=>[2,1,2,2,1]
[1,4,5,3,7,8,6,2]=>[2,3,5,8,4,7,1,6]=>[7,6,4,1,5,2,8,3]=>[1,1,1,2,2,1]
[1,3,5,4,8,7,6,2]=>[8,3,7,2,4,6,1,5]=>[1,6,2,7,5,3,8,4]=>[2,2,1,2,1]
[1,3,5,4,7,8,6,2]=>[3,5,8,2,4,7,1,6]=>[6,4,1,7,5,2,8,3]=>[1,1,2,1,2,1]
[1,4,3,5,8,7,6,2]=>[8,2,7,3,4,6,1,5]=>[1,7,2,6,5,3,8,4]=>[2,2,1,2,1]
[1,4,3,5,7,8,6,2]=>[2,5,8,3,4,7,1,6]=>[7,4,1,6,5,2,8,3]=>[1,1,2,1,2,1]
[1,3,4,5,8,7,6,2]=>[8,7,2,3,4,6,1,5]=>[1,2,7,6,5,3,8,4]=>[3,1,1,2,1]
[1,3,4,5,7,8,6,2]=>[5,8,2,3,4,7,1,6]=>[4,1,7,6,5,2,8,3]=>[1,2,1,1,2,1]
[1,6,5,4,3,8,7,2]=>[4,3,2,8,5,7,1,6]=>[5,6,7,1,4,2,8,3]=>[3,2,2,1]
[1,4,6,5,3,8,7,2]=>[4,2,3,8,5,7,1,6]=>[5,7,6,1,4,2,8,3]=>[2,1,2,2,1]
[1,4,5,6,3,8,7,2]=>[2,3,4,8,5,7,1,6]=>[7,6,5,1,4,2,8,3]=>[1,1,1,2,2,1]
[1,3,6,5,4,8,7,2]=>[4,3,8,2,5,7,1,6]=>[5,6,1,7,4,2,8,3]=>[2,2,1,2,1]
[1,4,3,6,5,8,7,2]=>[2,4,8,3,5,7,1,6]=>[7,5,1,6,4,2,8,3]=>[1,1,2,1,2,1]
[1,4,5,3,6,8,7,2]=>[2,3,8,4,5,7,1,6]=>[7,6,1,5,4,2,8,3]=>[1,1,2,1,2,1]
[1,3,4,5,6,8,7,2]=>[8,2,3,4,5,7,1,6]=>[1,7,6,5,4,2,8,3]=>[2,1,1,1,2,1]
[1,7,6,5,4,3,8,2]=>[6,5,4,3,2,8,1,7]=>[3,4,5,6,7,1,8,2]=>[5,2,1]
[1,6,7,5,4,3,8,2]=>[2,6,5,4,3,8,1,7]=>[7,3,4,5,6,1,8,2]=>[1,4,2,1]
[1,4,6,7,5,3,8,2]=>[3,6,2,5,4,8,1,7]=>[6,3,7,4,5,1,8,2]=>[1,2,2,2,1]
[1,5,6,4,7,3,8,2]=>[2,4,3,6,5,8,1,7]=>[7,5,6,3,4,1,8,2]=>[1,2,2,2,1]
[1,4,6,5,7,3,8,2]=>[4,2,3,6,5,8,1,7]=>[5,7,6,3,4,1,8,2]=>[2,1,2,2,1]
[1,5,4,6,7,3,8,2]=>[3,2,4,6,5,8,1,7]=>[6,7,5,3,4,1,8,2]=>[2,1,2,2,1]
[1,4,5,6,7,3,8,2]=>[2,3,4,6,5,8,1,7]=>[7,6,5,3,4,1,8,2]=>[1,1,1,2,2,1]
[1,3,5,7,6,4,8,2]=>[6,3,5,2,4,8,1,7]=>[3,6,4,7,5,1,8,2]=>[2,2,1,2,1]
[1,3,6,5,7,4,8,2]=>[4,3,6,2,5,8,1,7]=>[5,6,3,7,4,1,8,2]=>[2,2,1,2,1]
[1,4,3,6,7,5,8,2]=>[2,4,6,3,5,8,1,7]=>[7,5,3,6,4,1,8,2]=>[1,1,2,1,2,1]
[1,3,4,7,6,5,8,2]=>[6,5,2,3,4,8,1,7]=>[3,4,7,6,5,1,8,2]=>[3,1,1,2,1]
[1,3,4,6,7,5,8,2]=>[4,6,2,3,5,8,1,7]=>[5,3,7,6,4,1,8,2]=>[1,2,1,1,2,1]
[1,3,4,5,7,6,8,2]=>[6,2,3,4,5,8,1,7]=>[3,7,6,5,4,1,8,2]=>[2,1,1,1,2,1]
[1,6,5,4,3,7,8,2]=>[5,4,3,2,6,8,1,7]=>[4,5,6,7,3,1,8,2]=>[4,1,2,1]
[1,5,4,6,3,7,8,2]=>[3,2,5,4,6,8,1,7]=>[6,7,4,5,3,1,8,2]=>[2,2,1,2,1]
[1,3,5,6,4,7,8,2]=>[3,5,2,4,6,8,1,7]=>[6,4,7,5,3,1,8,2]=>[1,2,1,1,2,1]
[1,3,4,6,5,7,8,2]=>[5,2,3,4,6,8,1,7]=>[4,7,6,5,3,1,8,2]=>[2,1,1,1,2,1]
[1,5,4,3,6,7,8,2]=>[4,3,2,5,6,8,1,7]=>[5,6,7,4,3,1,8,2]=>[3,1,1,2,1]
[1,4,5,3,6,7,8,2]=>[2,4,3,5,6,8,1,7]=>[7,5,6,4,3,1,8,2]=>[1,2,1,1,2,1]
[1,3,5,4,6,7,8,2]=>[4,2,3,5,6,8,1,7]=>[5,7,6,4,3,1,8,2]=>[2,1,1,1,2,1]
[1,4,3,5,6,7,8,2]=>[3,2,4,5,6,8,1,7]=>[6,7,5,4,3,1,8,2]=>[2,1,1,1,2,1]
[1,3,4,5,6,7,8,2]=>[2,3,4,5,6,8,1,7]=>[7,6,5,4,3,1,8,2]=>[1,1,1,1,1,2,1]
[2,1,8,7,6,5,4,3]=>[8,7,6,5,1,4,2,3]=>[1,2,3,4,8,5,7,6]=>[5,2,1]
[2,1,7,8,6,5,4,3]=>[3,8,7,6,1,5,2,4]=>[6,1,2,3,8,4,7,5]=>[1,4,2,1]
[2,1,6,8,7,5,4,3]=>[8,3,7,6,1,5,2,4]=>[1,6,2,3,8,4,7,5]=>[2,3,2,1]
[2,1,7,6,8,5,4,3]=>[4,3,8,7,1,6,2,5]=>[5,6,1,2,8,3,7,4]=>[2,3,2,1]
[2,1,6,7,8,5,4,3]=>[3,4,8,7,1,6,2,5]=>[6,5,1,2,8,3,7,4]=>[1,1,3,2,1]
[2,1,5,8,7,6,4,3]=>[8,7,3,6,1,5,2,4]=>[1,2,6,3,8,4,7,5]=>[3,2,2,1]
[2,1,5,7,8,6,4,3]=>[4,8,3,7,1,6,2,5]=>[5,1,6,2,8,3,7,4]=>[1,2,2,2,1]
[2,1,6,5,8,7,4,3]=>[3,8,4,7,1,6,2,5]=>[6,1,5,2,8,3,7,4]=>[1,2,2,2,1]
[2,1,5,6,8,7,4,3]=>[8,3,4,7,1,6,2,5]=>[1,6,5,2,8,3,7,4]=>[2,1,2,2,1]
[2,1,6,7,5,8,4,3]=>[3,5,4,8,1,7,2,6]=>[6,4,5,1,8,2,7,3]=>[1,2,2,2,1]
[2,1,6,5,7,8,4,3]=>[4,3,5,8,1,7,2,6]=>[5,6,4,1,8,2,7,3]=>[2,1,2,2,1]
[2,1,5,6,7,8,4,3]=>[3,4,5,8,1,7,2,6]=>[6,5,4,1,8,2,7,3]=>[1,1,1,2,2,1]
[2,1,4,8,7,6,5,3]=>[8,7,6,1,3,5,2,4]=>[1,2,3,8,6,4,7,5]=>[4,1,2,1]
[2,1,4,7,8,6,5,3]=>[4,8,7,1,3,6,2,5]=>[5,1,2,8,6,3,7,4]=>[1,3,1,2,1]
[2,1,4,6,8,7,5,3]=>[8,4,7,1,3,6,2,5]=>[1,5,2,8,6,3,7,4]=>[2,2,1,2,1]
[2,1,4,7,6,8,5,3]=>[5,4,8,1,3,7,2,6]=>[4,5,1,8,6,2,7,3]=>[2,2,1,2,1]
[2,1,4,6,7,8,5,3]=>[4,5,8,1,3,7,2,6]=>[5,4,1,8,6,2,7,3]=>[1,1,2,1,2,1]
[2,1,5,4,8,7,6,3]=>[8,3,7,1,4,6,2,5]=>[1,6,2,8,5,3,7,4]=>[2,2,1,2,1]
[2,1,5,4,7,8,6,3]=>[3,5,8,1,4,7,2,6]=>[6,4,1,8,5,2,7,3]=>[1,1,2,1,2,1]
[2,1,4,5,8,7,6,3]=>[8,7,1,3,4,6,2,5]=>[1,2,8,6,5,3,7,4]=>[3,1,1,2,1]
[2,1,4,5,7,8,6,3]=>[5,8,1,3,4,7,2,6]=>[4,1,8,6,5,2,7,3]=>[1,2,1,1,2,1]
[2,1,6,5,4,8,7,3]=>[4,3,8,1,5,7,2,6]=>[5,6,1,8,4,2,7,3]=>[2,2,1,2,1]
[2,1,5,6,4,8,7,3]=>[3,4,8,1,5,7,2,6]=>[6,5,1,8,4,2,7,3]=>[1,1,2,1,2,1]
[2,1,4,6,5,8,7,3]=>[4,8,1,3,5,7,2,6]=>[5,1,8,6,4,2,7,3]=>[1,2,1,1,2,1]
[2,1,5,4,6,8,7,3]=>[3,8,1,4,5,7,2,6]=>[6,1,8,5,4,2,7,3]=>[1,2,1,1,2,1]
[2,1,7,6,5,4,8,3]=>[6,5,4,1,3,8,2,7]=>[3,4,5,8,6,1,7,2]=>[4,1,2,1]
[2,1,6,7,5,4,8,3]=>[3,6,5,1,4,8,2,7]=>[6,3,4,8,5,1,7,2]=>[1,3,1,2,1]
[2,1,5,7,6,4,8,3]=>[6,3,5,1,4,8,2,7]=>[3,6,4,8,5,1,7,2]=>[2,2,1,2,1]
[2,1,6,5,7,4,8,3]=>[4,3,6,1,5,8,2,7]=>[5,6,3,8,4,1,7,2]=>[2,2,1,2,1]
[2,1,5,6,7,4,8,3]=>[3,4,6,1,5,8,2,7]=>[6,5,3,8,4,1,7,2]=>[1,1,2,1,2,1]
[2,1,4,7,6,5,8,3]=>[6,5,1,3,4,8,2,7]=>[3,4,8,6,5,1,7,2]=>[3,1,1,2,1]
[2,1,4,6,7,5,8,3]=>[4,6,1,3,5,8,2,7]=>[5,3,8,6,4,1,7,2]=>[1,2,1,1,2,1]
[2,1,5,6,4,7,8,3]=>[3,5,1,4,6,8,2,7]=>[6,4,8,5,3,1,7,2]=>[1,2,1,1,2,1]
[2,1,5,4,6,7,8,3]=>[4,1,3,5,6,8,2,7]=>[5,8,6,4,3,1,7,2]=>[2,1,1,1,2,1]
[2,1,4,5,6,7,8,3]=>[1,3,4,5,6,8,2,7]=>[8,6,5,4,3,1,7,2]=>[1,1,1,1,1,2,1]
[1,2,8,7,6,5,4,3]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[6,1,1]
[1,2,7,8,6,5,4,3]=>[3,8,7,6,5,1,2,4]=>[6,1,2,3,4,8,7,5]=>[1,5,1,1]
[1,2,7,6,8,5,4,3]=>[4,3,8,7,6,1,2,5]=>[5,6,1,2,3,8,7,4]=>[2,4,1,1]
[1,2,6,7,8,5,4,3]=>[3,4,8,7,6,1,2,5]=>[6,5,1,2,3,8,7,4]=>[1,1,4,1,1]
[1,2,5,8,7,6,4,3]=>[8,7,3,6,5,1,2,4]=>[1,2,6,3,4,8,7,5]=>[3,3,1,1]
[1,2,6,5,8,7,4,3]=>[3,8,4,7,6,1,2,5]=>[6,1,5,2,3,8,7,4]=>[1,2,3,1,1]
[1,2,5,6,8,7,4,3]=>[8,3,4,7,6,1,2,5]=>[1,6,5,2,3,8,7,4]=>[2,1,3,1,1]
[1,2,7,6,5,8,4,3]=>[5,4,3,8,7,1,2,6]=>[4,5,6,1,2,8,7,3]=>[3,3,1,1]
[1,2,5,7,6,8,4,3]=>[5,3,4,8,7,1,2,6]=>[4,6,5,1,2,8,7,3]=>[2,1,3,1,1]
[1,2,6,5,7,8,4,3]=>[4,3,5,8,7,1,2,6]=>[5,6,4,1,2,8,7,3]=>[2,1,3,1,1]
[1,2,5,6,7,8,4,3]=>[3,4,5,8,7,1,2,6]=>[6,5,4,1,2,8,7,3]=>[1,1,1,3,1,1]
[1,2,4,8,7,6,5,3]=>[8,7,6,3,5,1,2,4]=>[1,2,3,6,4,8,7,5]=>[4,2,1,1]
[1,2,4,7,8,6,5,3]=>[4,8,7,3,6,1,2,5]=>[5,1,2,6,3,8,7,4]=>[1,3,2,1,1]
[1,2,4,6,8,7,5,3]=>[8,4,7,3,6,1,2,5]=>[1,5,2,6,3,8,7,4]=>[2,2,2,1,1]
[1,2,4,7,6,8,5,3]=>[5,4,8,3,7,1,2,6]=>[4,5,1,6,2,8,7,3]=>[2,2,2,1,1]
[1,2,4,6,7,8,5,3]=>[4,5,8,3,7,1,2,6]=>[5,4,1,6,2,8,7,3]=>[1,1,2,2,1,1]
[1,2,5,4,8,7,6,3]=>[8,3,7,4,6,1,2,5]=>[1,6,2,5,3,8,7,4]=>[2,2,2,1,1]
[1,2,5,4,7,8,6,3]=>[3,5,8,4,7,1,2,6]=>[6,4,1,5,2,8,7,3]=>[1,1,2,2,1,1]
[1,2,4,5,8,7,6,3]=>[8,7,3,4,6,1,2,5]=>[1,2,6,5,3,8,7,4]=>[3,1,2,1,1]
[1,2,4,5,7,8,6,3]=>[5,8,3,4,7,1,2,6]=>[4,1,6,5,2,8,7,3]=>[1,2,1,2,1,1]
[1,2,6,5,4,8,7,3]=>[4,3,8,5,7,1,2,6]=>[5,6,1,4,2,8,7,3]=>[2,2,2,1,1]
[1,2,4,6,5,8,7,3]=>[4,8,3,5,7,1,2,6]=>[5,1,6,4,2,8,7,3]=>[1,2,1,2,1,1]
[1,2,5,4,6,8,7,3]=>[3,8,4,5,7,1,2,6]=>[6,1,5,4,2,8,7,3]=>[1,2,1,2,1,1]
[1,2,4,5,6,8,7,3]=>[8,3,4,5,7,1,2,6]=>[1,6,5,4,2,8,7,3]=>[2,1,1,2,1,1]
[1,2,7,6,5,4,8,3]=>[6,5,4,3,8,1,2,7]=>[3,4,5,6,1,8,7,2]=>[4,2,1,1]
[1,2,5,7,6,4,8,3]=>[6,3,5,4,8,1,2,7]=>[3,6,4,5,1,8,7,2]=>[2,2,2,1,1]
[1,2,4,7,6,5,8,3]=>[6,5,3,4,8,1,2,7]=>[3,4,6,5,1,8,7,2]=>[3,1,2,1,1]
[1,2,5,4,7,6,8,3]=>[3,6,4,5,8,1,2,7]=>[6,3,5,4,1,8,7,2]=>[1,2,1,2,1,1]
[1,2,6,5,4,7,8,3]=>[5,4,3,6,8,1,2,7]=>[4,5,6,3,1,8,7,2]=>[3,1,2,1,1]
[1,2,5,6,4,7,8,3]=>[3,5,4,6,8,1,2,7]=>[6,4,5,3,1,8,7,2]=>[1,2,1,2,1,1]
[1,2,4,6,5,7,8,3]=>[5,3,4,6,8,1,2,7]=>[4,6,5,3,1,8,7,2]=>[2,1,1,2,1,1]
[1,2,4,5,6,7,8,3]=>[3,4,5,6,8,1,2,7]=>[6,5,4,3,1,8,7,2]=>[1,1,1,1,2,1,1]
[3,2,1,8,7,6,5,4]=>[8,7,1,6,2,5,3,4]=>[1,2,8,3,7,4,6,5]=>[3,2,2,1]
[3,2,1,7,8,6,5,4]=>[4,8,1,7,2,6,3,5]=>[5,1,8,2,7,3,6,4]=>[1,2,2,2,1]
[3,2,1,6,8,7,5,4]=>[8,1,4,7,2,6,3,5]=>[1,8,5,2,7,3,6,4]=>[2,1,2,2,1]
[3,2,1,7,6,8,5,4]=>[5,1,4,8,2,7,3,6]=>[4,8,5,1,7,2,6,3]=>[2,1,2,2,1]
[3,2,1,6,7,8,5,4]=>[1,4,5,8,2,7,3,6]=>[8,5,4,1,7,2,6,3]=>[1,1,1,2,2,1]
[3,2,1,5,8,7,6,4]=>[8,1,7,2,4,6,3,5]=>[1,8,2,7,5,3,6,4]=>[2,2,1,2,1]
[3,2,1,5,7,8,6,4]=>[1,5,8,2,4,7,3,6]=>[8,4,1,7,5,2,6,3]=>[1,1,2,1,2,1]
[3,2,1,6,5,8,7,4]=>[1,4,8,2,5,7,3,6]=>[8,5,1,7,4,2,6,3]=>[1,1,2,1,2,1]
[3,2,1,5,6,8,7,4]=>[1,8,2,4,5,7,3,6]=>[8,1,7,5,4,2,6,3]=>[1,2,1,1,2,1]
[3,2,1,7,6,5,8,4]=>[6,1,5,2,4,8,3,7]=>[3,8,4,7,5,1,6,2]=>[2,2,1,2,1]
[3,2,1,6,7,5,8,4]=>[1,4,6,2,5,8,3,7]=>[8,5,3,7,4,1,6,2]=>[1,1,2,1,2,1]
[3,2,1,5,7,6,8,4]=>[1,6,2,4,5,8,3,7]=>[8,3,7,5,4,1,6,2]=>[1,2,1,1,2,1]
[3,2,1,6,5,7,8,4]=>[1,5,2,4,6,8,3,7]=>[8,4,7,5,3,1,6,2]=>[1,2,1,1,2,1]
[3,2,1,5,6,7,8,4]=>[2,1,4,5,6,8,3,7]=>[7,8,5,4,3,1,6,2]=>[2,1,1,1,2,1]
[2,3,1,8,7,6,5,4]=>[8,7,6,1,2,5,3,4]=>[1,2,3,8,7,4,6,5]=>[4,1,2,1]
[2,3,1,6,8,7,5,4]=>[8,4,7,1,2,6,3,5]=>[1,5,2,8,7,3,6,4]=>[2,2,1,2,1]
[2,3,1,7,6,8,5,4]=>[5,4,8,1,2,7,3,6]=>[4,5,1,8,7,2,6,3]=>[2,2,1,2,1]
[2,3,1,6,7,8,5,4]=>[4,5,8,1,2,7,3,6]=>[5,4,1,8,7,2,6,3]=>[1,1,2,1,2,1]
[2,3,1,5,7,8,6,4]=>[5,8,1,2,4,7,3,6]=>[4,1,8,7,5,2,6,3]=>[1,2,1,1,2,1]
[2,3,1,6,5,8,7,4]=>[4,8,1,2,5,7,3,6]=>[5,1,8,7,4,2,6,3]=>[1,2,1,1,2,1]
[2,3,1,7,6,5,8,4]=>[6,5,1,2,4,8,3,7]=>[3,4,8,7,5,1,6,2]=>[3,1,1,2,1]
[2,3,1,6,7,5,8,4]=>[4,6,1,2,5,8,3,7]=>[5,3,8,7,4,1,6,2]=>[1,2,1,1,2,1]
[2,3,1,5,7,6,8,4]=>[6,1,2,4,5,8,3,7]=>[3,8,7,5,4,1,6,2]=>[2,1,1,1,2,1]
[2,3,1,5,6,7,8,4]=>[1,2,4,5,6,8,3,7]=>[8,7,5,4,3,1,6,2]=>[1,1,1,1,1,2,1]
[1,3,2,8,7,6,5,4]=>[8,7,6,2,5,1,3,4]=>[1,2,3,7,4,8,6,5]=>[4,2,1,1]
[1,3,2,6,8,7,5,4]=>[8,4,7,2,6,1,3,5]=>[1,5,2,7,3,8,6,4]=>[2,2,2,1,1]
[1,3,2,7,6,8,5,4]=>[5,4,8,2,7,1,3,6]=>[4,5,1,7,2,8,6,3]=>[2,2,2,1,1]
[1,3,2,6,7,8,5,4]=>[4,5,8,2,7,1,3,6]=>[5,4,1,7,2,8,6,3]=>[1,1,2,2,1,1]
[1,3,2,5,7,8,6,4]=>[5,8,2,4,7,1,3,6]=>[4,1,7,5,2,8,6,3]=>[1,2,1,2,1,1]
[1,3,2,6,5,8,7,4]=>[4,8,2,5,7,1,3,6]=>[5,1,7,4,2,8,6,3]=>[1,2,1,2,1,1]
[1,3,2,5,6,8,7,4]=>[8,2,4,5,7,1,3,6]=>[1,7,5,4,2,8,6,3]=>[2,1,1,2,1,1]
[1,3,2,7,6,5,8,4]=>[6,5,2,4,8,1,3,7]=>[3,4,7,5,1,8,6,2]=>[3,1,2,1,1]
[1,3,2,6,7,5,8,4]=>[4,6,2,5,8,1,3,7]=>[5,3,7,4,1,8,6,2]=>[1,2,1,2,1,1]
[1,3,2,5,7,6,8,4]=>[6,2,4,5,8,1,3,7]=>[3,7,5,4,1,8,6,2]=>[2,1,1,2,1,1]
[1,3,2,6,5,7,8,4]=>[5,2,4,6,8,1,3,7]=>[4,7,5,3,1,8,6,2]=>[2,1,1,2,1,1]
[1,3,2,5,6,7,8,4]=>[2,4,5,6,8,1,3,7]=>[7,5,4,3,1,8,6,2]=>[1,1,1,1,2,1,1]
[2,1,3,8,7,6,5,4]=>[8,7,6,1,5,2,3,4]=>[1,2,3,8,4,7,6,5]=>[4,2,1,1]
[2,1,3,7,8,6,5,4]=>[4,8,7,1,6,2,3,5]=>[5,1,2,8,3,7,6,4]=>[1,3,2,1,1]
[2,1,3,6,8,7,5,4]=>[8,4,7,1,6,2,3,5]=>[1,5,2,8,3,7,6,4]=>[2,2,2,1,1]
[2,1,3,6,7,8,5,4]=>[4,5,8,1,7,2,3,6]=>[5,4,1,8,2,7,6,3]=>[1,1,2,2,1,1]
[2,1,3,6,5,8,7,4]=>[4,8,1,5,7,2,3,6]=>[5,1,8,4,2,7,6,3]=>[1,2,1,2,1,1]
[2,1,3,5,7,6,8,4]=>[6,1,4,5,8,2,3,7]=>[3,8,5,4,1,7,6,2]=>[2,1,1,2,1,1]
[2,1,3,5,6,7,8,4]=>[1,4,5,6,8,2,3,7]=>[8,5,4,3,1,7,6,2]=>[1,1,1,1,2,1,1]
[1,2,3,8,7,6,5,4]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[5,1,1,1]
[1,2,3,7,8,6,5,4]=>[4,8,7,6,1,2,3,5]=>[5,1,2,3,8,7,6,4]=>[1,4,1,1,1]
[1,2,3,6,8,7,5,4]=>[8,4,7,6,1,2,3,5]=>[1,5,2,3,8,7,6,4]=>[2,3,1,1,1]
[1,2,3,7,6,8,5,4]=>[5,4,8,7,1,2,3,6]=>[4,5,1,2,8,7,6,3]=>[2,3,1,1,1]
[1,2,3,6,7,8,5,4]=>[4,5,8,7,1,2,3,6]=>[5,4,1,2,8,7,6,3]=>[1,1,3,1,1,1]
[1,2,3,5,8,7,6,4]=>[8,7,4,6,1,2,3,5]=>[1,2,5,3,8,7,6,4]=>[3,2,1,1,1]
[1,2,3,5,7,8,6,4]=>[5,8,4,7,1,2,3,6]=>[4,1,5,2,8,7,6,3]=>[1,2,2,1,1,1]
[1,2,3,6,5,8,7,4]=>[4,8,5,7,1,2,3,6]=>[5,1,4,2,8,7,6,3]=>[1,2,2,1,1,1]
[1,2,3,7,6,5,8,4]=>[6,5,4,8,1,2,3,7]=>[3,4,5,1,8,7,6,2]=>[3,2,1,1,1]
[1,2,3,6,7,5,8,4]=>[4,6,5,8,1,2,3,7]=>[5,3,4,1,8,7,6,2]=>[1,2,2,1,1,1]
[1,2,3,5,7,6,8,4]=>[6,4,5,8,1,2,3,7]=>[3,5,4,1,8,7,6,2]=>[2,1,2,1,1,1]
[1,2,3,6,5,7,8,4]=>[5,4,6,8,1,2,3,7]=>[4,5,3,1,8,7,6,2]=>[2,1,2,1,1,1]
[1,2,3,5,6,7,8,4]=>[4,5,6,8,1,2,3,7]=>[5,4,3,1,8,7,6,2]=>[1,1,1,2,1,1,1]
[4,3,2,1,8,7,6,5]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[1,2,2,2,1]
[4,3,2,1,7,8,6,5]=>[2,1,5,8,3,7,4,6]=>[7,8,4,1,6,2,5,3]=>[2,1,2,2,1]
[4,3,2,1,6,8,7,5]=>[2,1,8,3,5,7,4,6]=>[7,8,1,6,4,2,5,3]=>[2,2,1,2,1]
[4,3,2,1,6,7,8,5]=>[3,2,1,5,6,8,4,7]=>[6,7,8,4,3,1,5,2]=>[3,1,1,2,1]
[3,4,2,1,8,7,6,5]=>[8,1,2,7,3,6,4,5]=>[1,8,7,2,6,3,5,4]=>[2,1,2,2,1]
[3,4,2,1,7,8,6,5]=>[1,2,5,8,3,7,4,6]=>[8,7,4,1,6,2,5,3]=>[1,1,1,2,2,1]
[3,4,2,1,6,8,7,5]=>[1,2,8,3,5,7,4,6]=>[8,7,1,6,4,2,5,3]=>[1,1,2,1,2,1]
[3,4,2,1,6,7,8,5]=>[1,3,2,5,6,8,4,7]=>[8,6,7,4,3,1,5,2]=>[1,2,1,1,2,1]
[2,4,3,1,8,7,6,5]=>[8,2,7,1,3,6,4,5]=>[1,7,2,8,6,3,5,4]=>[2,2,1,2,1]
[2,4,3,1,7,8,6,5]=>[2,5,8,1,3,7,4,6]=>[7,4,1,8,6,2,5,3]=>[1,1,2,1,2,1]
[2,4,3,1,6,8,7,5]=>[2,8,1,3,5,7,4,6]=>[7,1,8,6,4,2,5,3]=>[1,2,1,1,2,1]
[2,4,3,1,7,6,8,5]=>[2,6,1,3,5,8,4,7]=>[7,3,8,6,4,1,5,2]=>[1,2,1,1,2,1]
[2,4,3,1,6,7,8,5]=>[3,1,2,5,6,8,4,7]=>[6,8,7,4,3,1,5,2]=>[2,1,1,1,2,1]
[3,2,4,1,8,7,6,5]=>[8,1,7,2,3,6,4,5]=>[1,8,2,7,6,3,5,4]=>[2,2,1,2,1]
[3,2,4,1,7,8,6,5]=>[1,5,8,2,3,7,4,6]=>[8,4,1,7,6,2,5,3]=>[1,1,2,1,2,1]
[3,2,4,1,6,8,7,5]=>[1,8,2,3,5,7,4,6]=>[8,1,7,6,4,2,5,3]=>[1,2,1,1,2,1]
[3,2,4,1,6,7,8,5]=>[2,1,3,5,6,8,4,7]=>[7,8,6,4,3,1,5,2]=>[2,1,1,1,2,1]
[2,3,4,1,8,7,6,5]=>[8,7,1,2,3,6,4,5]=>[1,2,8,7,6,3,5,4]=>[3,1,1,2,1]
[2,3,4,1,7,8,6,5]=>[5,8,1,2,3,7,4,6]=>[4,1,8,7,6,2,5,3]=>[1,2,1,1,2,1]
[2,3,4,1,6,8,7,5]=>[8,1,2,3,5,7,4,6]=>[1,8,7,6,4,2,5,3]=>[2,1,1,1,2,1]
[2,3,4,1,7,6,8,5]=>[6,1,2,3,5,8,4,7]=>[3,8,7,6,4,1,5,2]=>[2,1,1,1,2,1]
[2,3,4,1,6,7,8,5]=>[1,2,3,5,6,8,4,7]=>[8,7,6,4,3,1,5,2]=>[1,1,1,1,1,2,1]
[1,4,3,2,8,7,6,5]=>[8,2,7,3,6,1,4,5]=>[1,7,2,6,3,8,5,4]=>[2,2,2,1,1]
[1,4,3,2,6,8,7,5]=>[2,8,3,5,7,1,4,6]=>[7,1,6,4,2,8,5,3]=>[1,2,1,2,1,1]
[1,4,3,2,7,6,8,5]=>[2,6,3,5,8,1,4,7]=>[7,3,6,4,1,8,5,2]=>[1,2,1,2,1,1]
[1,4,3,2,6,7,8,5]=>[3,2,5,6,8,1,4,7]=>[6,7,4,3,1,8,5,2]=>[2,1,1,2,1,1]
[1,3,4,2,8,7,6,5]=>[8,7,2,3,6,1,4,5]=>[1,2,7,6,3,8,5,4]=>[3,1,2,1,1]
[1,3,4,2,7,8,6,5]=>[5,8,2,3,7,1,4,6]=>[4,1,7,6,2,8,5,3]=>[1,2,1,2,1,1]
[1,3,4,2,6,8,7,5]=>[8,2,3,5,7,1,4,6]=>[1,7,6,4,2,8,5,3]=>[2,1,1,2,1,1]
[1,3,4,2,7,6,8,5]=>[6,2,3,5,8,1,4,7]=>[3,7,6,4,1,8,5,2]=>[2,1,1,2,1,1]
[1,3,4,2,6,7,8,5]=>[2,3,5,6,8,1,4,7]=>[7,6,4,3,1,8,5,2]=>[1,1,1,1,2,1,1]
[2,1,4,3,8,7,6,5]=>[8,7,1,3,6,2,4,5]=>[1,2,8,6,3,7,5,4]=>[3,1,2,1,1]
[2,1,4,3,7,8,6,5]=>[5,8,1,3,7,2,4,6]=>[4,1,8,6,2,7,5,3]=>[1,2,1,2,1,1]
[2,1,4,3,6,8,7,5]=>[8,1,3,5,7,2,4,6]=>[1,8,6,4,2,7,5,3]=>[2,1,1,2,1,1]
[2,1,4,3,7,6,8,5]=>[6,1,3,5,8,2,4,7]=>[3,8,6,4,1,7,5,2]=>[2,1,1,2,1,1]
[1,2,4,3,8,7,6,5]=>[8,7,3,6,1,2,4,5]=>[1,2,6,3,8,7,5,4]=>[3,2,1,1,1]
[1,2,4,3,7,8,6,5]=>[5,8,3,7,1,2,4,6]=>[4,1,6,2,8,7,5,3]=>[1,2,2,1,1,1]
[1,2,4,3,6,8,7,5]=>[8,3,5,7,1,2,4,6]=>[1,6,4,2,8,7,5,3]=>[2,1,2,1,1,1]
[1,2,4,3,7,6,8,5]=>[6,3,5,8,1,2,4,7]=>[3,6,4,1,8,7,5,2]=>[2,1,2,1,1,1]
[1,2,4,3,6,7,8,5]=>[3,5,6,8,1,2,4,7]=>[6,4,3,1,8,7,5,2]=>[1,1,1,2,1,1,1]
[3,2,1,4,8,7,6,5]=>[8,1,7,2,6,3,4,5]=>[1,8,2,7,3,6,5,4]=>[2,2,2,1,1]
[3,2,1,4,7,8,6,5]=>[1,5,8,2,7,3,4,6]=>[8,4,1,7,2,6,5,3]=>[1,1,2,2,1,1]
[3,2,1,4,6,8,7,5]=>[1,8,2,5,7,3,4,6]=>[8,1,7,4,2,6,5,3]=>[1,2,1,2,1,1]
[3,2,1,4,7,6,8,5]=>[1,6,2,5,8,3,4,7]=>[8,3,7,4,1,6,5,2]=>[1,2,1,2,1,1]
[3,2,1,4,6,7,8,5]=>[2,1,5,6,8,3,4,7]=>[7,8,4,3,1,6,5,2]=>[2,1,1,2,1,1]
[2,3,1,4,8,7,6,5]=>[8,7,1,2,6,3,4,5]=>[1,2,8,7,3,6,5,4]=>[3,1,2,1,1]
[2,3,1,4,7,6,8,5]=>[6,1,2,5,8,3,4,7]=>[3,8,7,4,1,6,5,2]=>[2,1,1,2,1,1]
[1,3,2,4,8,7,6,5]=>[8,7,2,6,1,3,4,5]=>[1,2,7,3,8,6,5,4]=>[3,2,1,1,1]
[1,3,2,4,6,8,7,5]=>[8,2,5,7,1,3,4,6]=>[1,7,4,2,8,6,5,3]=>[2,1,2,1,1,1]
[1,3,2,4,7,6,8,5]=>[6,2,5,8,1,3,4,7]=>[3,7,4,1,8,6,5,2]=>[2,1,2,1,1,1]
[1,3,2,4,6,7,8,5]=>[2,5,6,8,1,3,4,7]=>[7,4,3,1,8,6,5,2]=>[1,1,1,2,1,1,1]
[2,1,3,4,8,7,6,5]=>[8,7,1,6,2,3,4,5]=>[1,2,8,3,7,6,5,4]=>[3,2,1,1,1]
[2,1,3,4,7,8,6,5]=>[5,8,1,7,2,3,4,6]=>[4,1,8,2,7,6,5,3]=>[1,2,2,1,1,1]
[2,1,3,4,7,6,8,5]=>[6,1,5,8,2,3,4,7]=>[3,8,4,1,7,6,5,2]=>[2,1,2,1,1,1]
[2,1,3,4,6,7,8,5]=>[1,5,6,8,2,3,4,7]=>[8,4,3,1,7,6,5,2]=>[1,1,1,2,1,1,1]
[1,2,3,4,8,7,6,5]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]
[1,2,3,4,7,8,6,5]=>[5,8,7,1,2,3,4,6]=>[4,1,2,8,7,6,5,3]=>[1,3,1,1,1,1]
[1,2,3,4,6,8,7,5]=>[8,5,7,1,2,3,4,6]=>[1,4,2,8,7,6,5,3]=>[2,2,1,1,1,1]
[1,2,3,4,7,6,8,5]=>[6,5,8,1,2,3,4,7]=>[3,4,1,8,7,6,5,2]=>[2,2,1,1,1,1]
[1,2,3,4,6,7,8,5]=>[5,6,8,1,2,3,4,7]=>[4,3,1,8,7,6,5,2]=>[1,1,2,1,1,1,1]
[5,4,3,2,1,8,7,6]=>[3,2,1,8,4,7,5,6]=>[6,7,8,1,5,2,4,3]=>[3,2,2,1]
[5,4,3,2,1,7,8,6]=>[4,3,2,1,6,8,5,7]=>[5,6,7,8,3,1,4,2]=>[4,1,2,1]
[4,5,3,2,1,8,7,6]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[1,2,2,2,1]
[3,5,4,2,1,8,7,6]=>[3,1,2,8,4,7,5,6]=>[6,8,7,1,5,2,4,3]=>[2,1,2,2,1]
[3,5,4,2,1,7,8,6]=>[4,1,3,2,6,8,5,7]=>[5,8,6,7,3,1,4,2]=>[2,2,1,2,1]
[3,4,5,2,1,8,7,6]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[1,1,1,2,2,1]
[3,4,5,2,1,7,8,6]=>[1,2,4,3,6,8,5,7]=>[8,7,5,6,3,1,4,2]=>[1,1,2,1,2,1]
[2,5,4,3,1,8,7,6]=>[3,2,8,1,4,7,5,6]=>[6,7,1,8,5,2,4,3]=>[2,2,1,2,1]
[2,5,4,3,1,7,8,6]=>[4,3,1,2,6,8,5,7]=>[5,6,8,7,3,1,4,2]=>[3,1,1,2,1]
[2,4,5,3,1,8,7,6]=>[2,3,8,1,4,7,5,6]=>[7,6,1,8,5,2,4,3]=>[1,1,2,1,2,1]
[2,4,5,3,1,7,8,6]=>[2,4,1,3,6,8,5,7]=>[7,5,8,6,3,1,4,2]=>[1,2,1,1,2,1]
[3,2,5,4,1,8,7,6]=>[1,3,8,2,4,7,5,6]=>[8,6,1,7,5,2,4,3]=>[1,1,2,1,2,1]
[3,2,5,4,1,7,8,6]=>[1,4,2,3,6,8,5,7]=>[8,5,7,6,3,1,4,2]=>[1,2,1,1,2,1]
[4,3,2,5,1,8,7,6]=>[2,1,8,3,4,7,5,6]=>[7,8,1,6,5,2,4,3]=>[2,2,1,2,1]
[4,3,2,5,1,7,8,6]=>[3,2,1,4,6,8,5,7]=>[6,7,8,5,3,1,4,2]=>[3,1,1,2,1]
[3,4,2,5,1,8,7,6]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[1,1,2,1,2,1]
[3,4,2,5,1,7,8,6]=>[1,3,2,4,6,8,5,7]=>[8,6,7,5,3,1,4,2]=>[1,2,1,1,2,1]
[2,4,3,5,1,8,7,6]=>[2,8,1,3,4,7,5,6]=>[7,1,8,6,5,2,4,3]=>[1,2,1,1,2,1]
[2,4,3,5,1,7,8,6]=>[3,1,2,4,6,8,5,7]=>[6,8,7,5,3,1,4,2]=>[2,1,1,1,2,1]
[3,2,4,5,1,8,7,6]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[1,2,1,1,2,1]
[2,3,4,5,1,8,7,6]=>[8,1,2,3,4,7,5,6]=>[1,8,7,6,5,2,4,3]=>[2,1,1,1,2,1]
[2,3,4,5,1,7,8,6]=>[1,2,3,4,6,8,5,7]=>[8,7,6,5,3,1,4,2]=>[1,1,1,1,1,2,1]
[1,4,5,3,2,8,7,6]=>[2,3,8,4,7,1,5,6]=>[7,6,1,5,2,8,4,3]=>[1,1,2,2,1,1]
[1,4,5,3,2,7,8,6]=>[2,4,3,6,8,1,5,7]=>[7,5,6,3,1,8,4,2]=>[1,2,1,2,1,1]
[1,3,5,4,2,7,8,6]=>[4,2,3,6,8,1,5,7]=>[5,7,6,3,1,8,4,2]=>[2,1,1,2,1,1]
[1,4,3,5,2,8,7,6]=>[2,8,3,4,7,1,5,6]=>[7,1,6,5,2,8,4,3]=>[1,2,1,2,1,1]
[1,4,3,5,2,7,8,6]=>[3,2,4,6,8,1,5,7]=>[6,7,5,3,1,8,4,2]=>[2,1,1,2,1,1]
[1,3,4,5,2,8,7,6]=>[8,2,3,4,7,1,5,6]=>[1,7,6,5,2,8,4,3]=>[2,1,1,2,1,1]
[1,3,4,5,2,7,8,6]=>[2,3,4,6,8,1,5,7]=>[7,6,5,3,1,8,4,2]=>[1,1,1,1,2,1,1]
[2,1,5,4,3,8,7,6]=>[3,8,1,4,7,2,5,6]=>[6,1,8,5,2,7,4,3]=>[1,2,1,2,1,1]
[1,2,5,4,3,8,7,6]=>[3,8,4,7,1,2,5,6]=>[6,1,5,2,8,7,4,3]=>[1,2,2,1,1,1]
[1,2,5,4,3,7,8,6]=>[4,3,6,8,1,2,5,7]=>[5,6,3,1,8,7,4,2]=>[2,1,2,1,1,1]
[1,2,4,5,3,8,7,6]=>[8,3,4,7,1,2,5,6]=>[1,6,5,2,8,7,4,3]=>[2,1,2,1,1,1]
[1,2,4,5,3,7,8,6]=>[3,4,6,8,1,2,5,7]=>[6,5,3,1,8,7,4,2]=>[1,1,1,2,1,1,1]
[1,3,2,5,4,8,7,6]=>[8,2,4,7,1,3,5,6]=>[1,7,5,2,8,6,4,3]=>[2,1,2,1,1,1]
[1,3,2,5,4,7,8,6]=>[2,4,6,8,1,3,5,7]=>[7,5,3,1,8,6,4,2]=>[1,1,1,2,1,1,1]
[2,1,3,5,4,8,7,6]=>[8,1,4,7,2,3,5,6]=>[1,8,5,2,7,6,4,3]=>[2,1,2,1,1,1]
[2,1,3,5,4,7,8,6]=>[1,4,6,8,2,3,5,7]=>[8,5,3,1,7,6,4,2]=>[1,1,1,2,1,1,1]
[1,2,3,5,4,8,7,6]=>[8,4,7,1,2,3,5,6]=>[1,5,2,8,7,6,4,3]=>[2,2,1,1,1,1]
[1,2,3,5,4,7,8,6]=>[4,6,8,1,2,3,5,7]=>[5,3,1,8,7,6,4,2]=>[1,1,2,1,1,1,1]
[4,3,2,1,5,8,7,6]=>[2,1,8,3,7,4,5,6]=>[7,8,1,6,2,5,4,3]=>[2,2,2,1,1]
[4,3,2,1,5,7,8,6]=>[3,2,1,6,8,4,5,7]=>[6,7,8,3,1,5,4,2]=>[3,1,2,1,1]
[3,4,2,1,5,8,7,6]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[1,1,2,2,1,1]
[2,4,3,1,5,8,7,6]=>[2,8,1,3,7,4,5,6]=>[7,1,8,6,2,5,4,3]=>[1,2,1,2,1,1]
[3,2,4,1,5,8,7,6]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[1,2,1,2,1,1]
[3,2,4,1,5,7,8,6]=>[2,1,3,6,8,4,5,7]=>[7,8,6,3,1,5,4,2]=>[2,1,1,2,1,1]
[2,3,4,1,5,8,7,6]=>[8,1,2,3,7,4,5,6]=>[1,8,7,6,2,5,4,3]=>[2,1,1,2,1,1]
[2,3,4,1,5,7,8,6]=>[1,2,3,6,8,4,5,7]=>[8,7,6,3,1,5,4,2]=>[1,1,1,1,2,1,1]
[1,4,3,2,5,8,7,6]=>[2,8,3,7,1,4,5,6]=>[7,1,6,2,8,5,4,3]=>[1,2,2,1,1,1]
[1,4,3,2,5,7,8,6]=>[3,2,6,8,1,4,5,7]=>[6,7,3,1,8,5,4,2]=>[2,1,2,1,1,1]
[1,3,4,2,5,8,7,6]=>[8,2,3,7,1,4,5,6]=>[1,7,6,2,8,5,4,3]=>[2,1,2,1,1,1]
[2,1,4,3,5,7,8,6]=>[1,3,6,8,2,4,5,7]=>[8,6,3,1,7,5,4,2]=>[1,1,1,2,1,1,1]
[1,2,4,3,5,8,7,6]=>[8,3,7,1,2,4,5,6]=>[1,6,2,8,7,5,4,3]=>[2,2,1,1,1,1]
[1,2,4,3,5,7,8,6]=>[3,6,8,1,2,4,5,7]=>[6,3,1,8,7,5,4,2]=>[1,1,2,1,1,1,1]
[3,2,1,4,5,8,7,6]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[1,2,2,1,1,1]
[3,2,1,4,5,7,8,6]=>[2,1,6,8,3,4,5,7]=>[7,8,3,1,6,5,4,2]=>[2,1,2,1,1,1]
[2,3,1,4,5,7,8,6]=>[1,2,6,8,3,4,5,7]=>[8,7,3,1,6,5,4,2]=>[1,1,1,2,1,1,1]
[1,3,2,4,5,8,7,6]=>[8,2,7,1,3,4,5,6]=>[1,7,2,8,6,5,4,3]=>[2,2,1,1,1,1]
[1,3,2,4,5,7,8,6]=>[2,6,8,1,3,4,5,7]=>[7,3,1,8,6,5,4,2]=>[1,1,2,1,1,1,1]
[2,1,3,4,5,8,7,6]=>[8,1,7,2,3,4,5,6]=>[1,8,2,7,6,5,4,3]=>[2,2,1,1,1,1]
[2,1,3,4,5,7,8,6]=>[1,6,8,2,3,4,5,7]=>[8,3,1,7,6,5,4,2]=>[1,1,2,1,1,1,1]
[1,2,3,4,5,8,7,6]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>[3,1,1,1,1,1]
[1,2,3,4,5,7,8,6]=>[6,8,1,2,3,4,5,7]=>[3,1,8,7,6,5,4,2]=>[1,2,1,1,1,1,1]
[6,5,4,3,2,1,8,7]=>[5,4,3,2,1,8,6,7]=>[4,5,6,7,8,1,3,2]=>[5,2,1]
[5,6,4,3,2,1,8,7]=>[1,5,4,3,2,8,6,7]=>[8,4,5,6,7,1,3,2]=>[1,4,2,1]
[4,6,5,3,2,1,8,7]=>[5,1,4,3,2,8,6,7]=>[4,8,5,6,7,1,3,2]=>[2,3,2,1]
[5,4,6,3,2,1,8,7]=>[2,1,5,4,3,8,6,7]=>[7,8,4,5,6,1,3,2]=>[2,3,2,1]
[4,5,6,3,2,1,8,7]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[1,1,3,2,1]
[3,6,5,4,2,1,8,7]=>[5,4,1,3,2,8,6,7]=>[4,5,8,6,7,1,3,2]=>[3,2,2,1]
[3,5,6,4,2,1,8,7]=>[2,5,1,4,3,8,6,7]=>[7,4,8,5,6,1,3,2]=>[1,2,2,2,1]
[4,3,6,5,2,1,8,7]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[1,2,2,2,1]
[3,4,6,5,2,1,8,7]=>[5,1,2,4,3,8,6,7]=>[4,8,7,5,6,1,3,2]=>[2,1,2,2,1]
[5,4,3,6,2,1,8,7]=>[3,2,1,5,4,8,6,7]=>[6,7,8,4,5,1,3,2]=>[3,2,2,1]
[4,5,3,6,2,1,8,7]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[1,2,2,2,1]
[3,4,5,6,2,1,8,7]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[1,1,1,2,2,1]
[2,5,6,4,3,1,8,7]=>[2,5,4,1,3,8,6,7]=>[7,4,5,8,6,1,3,2]=>[1,3,1,2,1]
[2,4,6,5,3,1,8,7]=>[5,2,4,1,3,8,6,7]=>[4,7,5,8,6,1,3,2]=>[2,2,1,2,1]
[3,2,6,5,4,1,8,7]=>[5,1,4,2,3,8,6,7]=>[4,8,5,7,6,1,3,2]=>[2,2,1,2,1]
[3,2,5,6,4,1,8,7]=>[1,3,5,2,4,8,6,7]=>[8,6,4,7,5,1,3,2]=>[1,1,2,1,2,1]
[2,3,6,5,4,1,8,7]=>[5,4,1,2,3,8,6,7]=>[4,5,8,7,6,1,3,2]=>[3,1,1,2,1]
[2,3,5,6,4,1,8,7]=>[3,5,1,2,4,8,6,7]=>[6,4,8,7,5,1,3,2]=>[1,2,1,1,2,1]
[4,3,2,6,5,1,8,7]=>[2,1,5,3,4,8,6,7]=>[7,8,4,6,5,1,3,2]=>[2,2,1,2,1]
[3,4,2,6,5,1,8,7]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[1,1,2,1,2,1]
[2,4,3,6,5,1,8,7]=>[2,5,1,3,4,8,6,7]=>[7,4,8,6,5,1,3,2]=>[1,2,1,1,2,1]
[5,4,3,2,6,1,8,7]=>[4,3,2,1,5,8,6,7]=>[5,6,7,8,4,1,3,2]=>[4,1,2,1]
[4,5,3,2,6,1,8,7]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[1,3,1,2,1]
[3,5,4,2,6,1,8,7]=>[4,1,3,2,5,8,6,7]=>[5,8,6,7,4,1,3,2]=>[2,2,1,2,1]
[4,3,5,2,6,1,8,7]=>[2,1,4,3,5,8,6,7]=>[7,8,5,6,4,1,3,2]=>[2,2,1,2,1]
[3,4,5,2,6,1,8,7]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[1,1,2,1,2,1]
[2,4,5,3,6,1,8,7]=>[2,4,1,3,5,8,6,7]=>[7,5,8,6,4,1,3,2]=>[1,2,1,1,2,1]
[3,2,5,4,6,1,8,7]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[1,2,1,1,2,1]
[3,4,2,5,6,1,8,7]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[1,2,1,1,2,1]
[2,3,4,5,6,1,8,7]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[1,1,1,1,1,2,1]
[1,6,5,4,3,2,8,7]=>[5,4,3,2,8,1,6,7]=>[4,5,6,7,1,8,3,2]=>[4,2,1,1]
[1,5,6,4,3,2,8,7]=>[2,5,4,3,8,1,6,7]=>[7,4,5,6,1,8,3,2]=>[1,3,2,1,1]
[1,3,4,5,6,2,8,7]=>[2,3,4,5,8,1,6,7]=>[7,6,5,4,1,8,3,2]=>[1,1,1,1,2,1,1]
[2,1,6,5,4,3,8,7]=>[5,4,1,3,8,2,6,7]=>[4,5,8,6,1,7,3,2]=>[3,1,2,1,1]
[2,1,5,6,4,3,8,7]=>[3,5,1,4,8,2,6,7]=>[6,4,8,5,1,7,3,2]=>[1,2,1,2,1,1]
[2,1,4,6,5,3,8,7]=>[5,1,3,4,8,2,6,7]=>[4,8,6,5,1,7,3,2]=>[2,1,1,2,1,1]
[2,1,4,5,6,3,8,7]=>[1,3,4,5,8,2,6,7]=>[8,6,5,4,1,7,3,2]=>[1,1,1,1,2,1,1]
[1,2,4,5,6,3,8,7]=>[3,4,5,8,1,2,6,7]=>[6,5,4,1,8,7,3,2]=>[1,1,1,2,1,1,1]
[3,2,1,6,5,4,8,7]=>[1,5,2,4,8,3,6,7]=>[8,4,7,5,1,6,3,2]=>[1,2,1,2,1,1]
[2,3,1,6,5,4,8,7]=>[5,1,2,4,8,3,6,7]=>[4,8,7,5,1,6,3,2]=>[2,1,1,2,1,1]
[1,3,2,6,5,4,8,7]=>[5,2,4,8,1,3,6,7]=>[4,7,5,1,8,6,3,2]=>[2,1,2,1,1,1]
[1,3,2,5,6,4,8,7]=>[2,4,5,8,1,3,6,7]=>[7,5,4,1,8,6,3,2]=>[1,1,1,2,1,1,1]
[2,1,3,6,5,4,8,7]=>[5,1,4,8,2,3,6,7]=>[4,8,5,1,7,6,3,2]=>[2,1,2,1,1,1]
[2,1,3,5,6,4,8,7]=>[1,4,5,8,2,3,6,7]=>[8,5,4,1,7,6,3,2]=>[1,1,1,2,1,1,1]
[1,2,3,6,5,4,8,7]=>[5,4,8,1,2,3,6,7]=>[4,5,1,8,7,6,3,2]=>[2,2,1,1,1,1]
[1,2,3,5,6,4,8,7]=>[4,5,8,1,2,3,6,7]=>[5,4,1,8,7,6,3,2]=>[1,1,2,1,1,1,1]
[4,3,2,1,6,5,8,7]=>[3,2,1,5,8,4,6,7]=>[6,7,8,4,1,5,3,2]=>[3,1,2,1,1]
[3,4,2,1,6,5,8,7]=>[1,3,2,5,8,4,6,7]=>[8,6,7,4,1,5,3,2]=>[1,2,1,2,1,1]
[2,4,3,1,6,5,8,7]=>[3,1,2,5,8,4,6,7]=>[6,8,7,4,1,5,3,2]=>[2,1,1,2,1,1]
[3,2,4,1,6,5,8,7]=>[2,1,3,5,8,4,6,7]=>[7,8,6,4,1,5,3,2]=>[2,1,1,2,1,1]
[2,3,4,1,6,5,8,7]=>[1,2,3,5,8,4,6,7]=>[8,7,6,4,1,5,3,2]=>[1,1,1,1,2,1,1]
[1,3,4,2,6,5,8,7]=>[2,3,5,8,1,4,6,7]=>[7,6,4,1,8,5,3,2]=>[1,1,1,2,1,1,1]
[2,1,4,3,6,5,8,7]=>[1,3,5,8,2,4,6,7]=>[8,6,4,1,7,5,3,2]=>[1,1,1,2,1,1,1]
[1,2,4,3,6,5,8,7]=>[3,5,8,1,2,4,6,7]=>[6,4,1,8,7,5,3,2]=>[1,1,2,1,1,1,1]
[2,3,1,4,6,5,8,7]=>[1,2,5,8,3,4,6,7]=>[8,7,4,1,6,5,3,2]=>[1,1,1,2,1,1,1]
[1,3,2,4,6,5,8,7]=>[2,5,8,1,3,4,6,7]=>[7,4,1,8,6,5,3,2]=>[1,1,2,1,1,1,1]
[2,1,3,4,6,5,8,7]=>[1,5,8,2,3,4,6,7]=>[8,4,1,7,6,5,3,2]=>[1,1,2,1,1,1,1]
[1,2,3,4,6,5,8,7]=>[5,8,1,2,3,4,6,7]=>[4,1,8,7,6,5,3,2]=>[1,2,1,1,1,1,1]
[5,4,3,2,1,6,8,7]=>[4,3,2,1,8,5,6,7]=>[5,6,7,8,1,4,3,2]=>[4,2,1,1]
[4,5,3,2,1,6,8,7]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[1,3,2,1,1]
[3,5,4,2,1,6,8,7]=>[4,1,3,2,8,5,6,7]=>[5,8,6,7,1,4,3,2]=>[2,2,2,1,1]
[3,4,5,2,1,6,8,7]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[1,1,2,2,1,1]
[2,5,4,3,1,6,8,7]=>[4,3,1,2,8,5,6,7]=>[5,6,8,7,1,4,3,2]=>[3,1,2,1,1]
[2,4,5,3,1,6,8,7]=>[2,4,1,3,8,5,6,7]=>[7,5,8,6,1,4,3,2]=>[1,2,1,2,1,1]
[3,2,5,4,1,6,8,7]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[1,2,1,2,1,1]
[2,4,3,5,1,6,8,7]=>[3,1,2,4,8,5,6,7]=>[6,8,7,5,1,4,3,2]=>[2,1,1,2,1,1]
[2,3,4,5,1,6,8,7]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[1,1,1,1,2,1,1]
[1,4,5,3,2,6,8,7]=>[2,4,3,8,1,5,6,7]=>[7,5,6,1,8,4,3,2]=>[1,2,2,1,1,1]
[1,3,5,4,2,6,8,7]=>[4,2,3,8,1,5,6,7]=>[5,7,6,1,8,4,3,2]=>[2,1,2,1,1,1]
[1,3,4,5,2,6,8,7]=>[2,3,4,8,1,5,6,7]=>[7,6,5,1,8,4,3,2]=>[1,1,1,2,1,1,1]
[2,1,5,4,3,6,8,7]=>[4,1,3,8,2,5,6,7]=>[5,8,6,1,7,4,3,2]=>[2,1,2,1,1,1]
[2,1,4,5,3,6,8,7]=>[1,3,4,8,2,5,6,7]=>[8,6,5,1,7,4,3,2]=>[1,1,1,2,1,1,1]
[1,2,5,4,3,6,8,7]=>[4,3,8,1,2,5,6,7]=>[5,6,1,8,7,4,3,2]=>[2,2,1,1,1,1]
[2,1,3,5,4,6,8,7]=>[1,4,8,2,3,5,6,7]=>[8,5,1,7,6,4,3,2]=>[1,1,2,1,1,1,1]
[1,2,3,5,4,6,8,7]=>[4,8,1,2,3,5,6,7]=>[5,1,8,7,6,4,3,2]=>[1,2,1,1,1,1,1]
[4,3,2,1,5,6,8,7]=>[3,2,1,8,4,5,6,7]=>[6,7,8,1,5,4,3,2]=>[3,2,1,1,1]
[3,4,2,1,5,6,8,7]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[1,2,2,1,1,1]
[3,2,4,1,5,6,8,7]=>[2,1,3,8,4,5,6,7]=>[7,8,6,1,5,4,3,2]=>[2,1,2,1,1,1]
[2,3,4,1,5,6,8,7]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[1,1,1,2,1,1,1]
[1,4,3,2,5,6,8,7]=>[3,2,8,1,4,5,6,7]=>[6,7,1,8,5,4,3,2]=>[2,2,1,1,1,1]
[1,3,4,2,5,6,8,7]=>[2,3,8,1,4,5,6,7]=>[7,6,1,8,5,4,3,2]=>[1,1,2,1,1,1,1]
[2,1,4,3,5,6,8,7]=>[1,3,8,2,4,5,6,7]=>[8,6,1,7,5,4,3,2]=>[1,1,2,1,1,1,1]
[1,2,4,3,5,6,8,7]=>[3,8,1,2,4,5,6,7]=>[6,1,8,7,5,4,3,2]=>[1,2,1,1,1,1,1]
[3,2,1,4,5,6,8,7]=>[2,1,8,3,4,5,6,7]=>[7,8,1,6,5,4,3,2]=>[2,2,1,1,1,1]
[2,3,1,4,5,6,8,7]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[1,1,2,1,1,1,1]
[1,3,2,4,5,6,8,7]=>[2,8,1,3,4,5,6,7]=>[7,1,8,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[2,1,3,4,5,6,8,7]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[1,2,1,1,1,1,1]
[1,2,3,4,5,6,8,7]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1]
[5,7,6,4,3,2,1,8]=>[7,1,6,5,4,3,2,8]=>[2,8,3,4,5,6,7,1]=>[2,5,1]
[4,7,6,5,3,2,1,8]=>[7,6,1,5,4,3,2,8]=>[2,3,8,4,5,6,7,1]=>[3,4,1]
[4,6,7,5,3,2,1,8]=>[2,7,1,6,5,4,3,8]=>[7,2,8,3,4,5,6,1]=>[1,2,4,1]
[5,4,7,6,3,2,1,8]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[1,2,4,1]
[4,5,7,6,3,2,1,8]=>[7,1,2,6,5,4,3,8]=>[2,8,7,3,4,5,6,1]=>[2,1,4,1]
[4,6,5,7,3,2,1,8]=>[3,1,2,7,6,5,4,8]=>[6,8,7,2,3,4,5,1]=>[2,1,4,1]
[3,5,7,6,4,2,1,8]=>[7,2,6,1,5,4,3,8]=>[2,7,3,8,4,5,6,1]=>[2,2,3,1]
[3,5,6,7,4,2,1,8]=>[2,3,7,1,6,5,4,8]=>[7,6,2,8,3,4,5,1]=>[1,1,2,3,1]
[4,3,7,6,5,2,1,8]=>[7,1,6,2,5,4,3,8]=>[2,8,3,7,4,5,6,1]=>[2,2,3,1]
[3,4,7,6,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>[2,3,8,7,4,5,6,1]=>[3,1,3,1]
[5,4,3,7,6,2,1,8]=>[2,1,7,3,6,5,4,8]=>[7,8,2,6,3,4,5,1]=>[2,2,3,1]
[3,5,4,7,6,2,1,8]=>[2,7,1,3,6,5,4,8]=>[7,2,8,6,3,4,5,1]=>[1,2,1,3,1]
[4,3,5,7,6,2,1,8]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[1,2,1,3,1]
[3,5,6,4,7,2,1,8]=>[2,4,1,3,7,6,5,8]=>[7,5,8,6,2,3,4,1]=>[1,2,1,3,1]
[4,3,6,5,7,2,1,8]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[1,2,1,3,1]
[2,7,6,5,4,3,1,8]=>[7,6,5,4,1,3,2,8]=>[2,3,4,5,8,6,7,1]=>[5,2,1]
[2,6,7,5,4,3,1,8]=>[2,7,6,5,1,4,3,8]=>[7,2,3,4,8,5,6,1]=>[1,4,2,1]
[2,5,7,6,4,3,1,8]=>[7,2,6,5,1,4,3,8]=>[2,7,3,4,8,5,6,1]=>[2,3,2,1]
[2,4,6,7,5,3,1,8]=>[3,7,2,6,1,5,4,8]=>[6,2,7,3,8,4,5,1]=>[1,2,2,2,1]
[2,5,6,4,7,3,1,8]=>[2,4,3,7,1,6,5,8]=>[7,5,6,2,8,3,4,1]=>[1,2,2,2,1]
[2,4,5,6,7,3,1,8]=>[2,3,4,7,1,6,5,8]=>[7,6,5,2,8,3,4,1]=>[1,1,1,2,2,1]
[3,2,7,6,5,4,1,8]=>[7,6,1,5,2,4,3,8]=>[2,3,8,4,7,5,6,1]=>[3,2,2,1]
[3,2,6,7,5,4,1,8]=>[3,7,1,6,2,5,4,8]=>[6,2,8,3,7,4,5,1]=>[1,2,2,2,1]
[3,2,5,7,6,4,1,8]=>[7,1,3,6,2,5,4,8]=>[2,8,6,3,7,4,5,1]=>[2,1,2,2,1]
[3,2,6,5,7,4,1,8]=>[4,1,3,7,2,6,5,8]=>[5,8,6,2,7,3,4,1]=>[2,1,2,2,1]
[3,2,5,6,7,4,1,8]=>[1,3,4,7,2,6,5,8]=>[8,6,5,2,7,3,4,1]=>[1,1,1,2,2,1]
[2,3,7,6,5,4,1,8]=>[7,6,5,1,2,4,3,8]=>[2,3,4,8,7,5,6,1]=>[4,1,2,1]
[2,3,6,7,5,4,1,8]=>[3,7,6,1,2,5,4,8]=>[6,2,3,8,7,4,5,1]=>[1,3,1,2,1]
[2,3,5,7,6,4,1,8]=>[7,3,6,1,2,5,4,8]=>[2,6,3,8,7,4,5,1]=>[2,2,1,2,1]
[3,4,2,6,7,5,1,8]=>[1,2,4,7,3,6,5,8]=>[8,7,5,2,6,3,4,1]=>[1,1,1,2,2,1]
[2,3,4,7,6,5,1,8]=>[7,6,1,2,3,5,4,8]=>[2,3,8,7,6,4,5,1]=>[3,1,1,2,1]
[2,3,4,6,7,5,1,8]=>[4,7,1,2,3,6,5,8]=>[5,2,8,7,6,3,4,1]=>[1,2,1,1,2,1]
[5,4,3,2,7,6,1,8]=>[3,2,1,7,4,6,5,8]=>[6,7,8,2,5,3,4,1]=>[3,2,2,1]
[4,5,3,2,7,6,1,8]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[1,2,2,2,1]
[3,4,5,2,7,6,1,8]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[1,1,1,2,2,1]
[4,3,2,5,7,6,1,8]=>[2,1,7,3,4,6,5,8]=>[7,8,2,6,5,3,4,1]=>[2,2,1,2,1]
[3,4,2,5,7,6,1,8]=>[1,2,7,3,4,6,5,8]=>[8,7,2,6,5,3,4,1]=>[1,1,2,1,2,1]
[2,3,4,5,7,6,1,8]=>[7,1,2,3,4,6,5,8]=>[2,8,7,6,5,3,4,1]=>[2,1,1,1,2,1]
[3,6,5,4,2,7,1,8]=>[5,4,1,3,2,7,6,8]=>[4,5,8,6,7,2,3,1]=>[3,2,2,1]
[3,5,6,4,2,7,1,8]=>[2,5,1,4,3,7,6,8]=>[7,4,8,5,6,2,3,1]=>[1,2,2,2,1]
[3,4,6,5,2,7,1,8]=>[5,1,2,4,3,7,6,8]=>[4,8,7,5,6,2,3,1]=>[2,1,2,2,1]
[3,5,4,6,2,7,1,8]=>[3,1,2,5,4,7,6,8]=>[6,8,7,4,5,2,3,1]=>[2,1,2,2,1]
[2,5,4,6,3,7,1,8]=>[3,2,5,1,4,7,6,8]=>[6,7,4,8,5,2,3,1]=>[2,2,1,2,1]
[2,4,5,6,3,7,1,8]=>[2,3,5,1,4,7,6,8]=>[7,6,4,8,5,2,3,1]=>[1,1,2,1,2,1]
[2,3,5,6,4,7,1,8]=>[3,5,1,2,4,7,6,8]=>[6,4,8,7,5,2,3,1]=>[1,2,1,1,2,1]
[3,4,2,6,5,7,1,8]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[1,1,2,1,2,1]
[2,4,3,6,5,7,1,8]=>[2,5,1,3,4,7,6,8]=>[7,4,8,6,5,2,3,1]=>[1,2,1,1,2,1]
[2,3,4,6,5,7,1,8]=>[5,1,2,3,4,7,6,8]=>[4,8,7,6,5,2,3,1]=>[2,1,1,1,2,1]
[3,5,4,2,6,7,1,8]=>[4,1,3,2,5,7,6,8]=>[5,8,6,7,4,2,3,1]=>[2,2,1,2,1]
[2,5,4,3,6,7,1,8]=>[4,3,1,2,5,7,6,8]=>[5,6,8,7,4,2,3,1]=>[3,1,1,2,1]
[2,3,5,4,6,7,1,8]=>[4,1,2,3,5,7,6,8]=>[5,8,7,6,4,2,3,1]=>[2,1,1,1,2,1]
[2,4,3,5,6,7,1,8]=>[3,1,2,4,5,7,6,8]=>[6,8,7,5,4,2,3,1]=>[2,1,1,1,2,1]
[1,7,6,5,4,3,2,8]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>[6,1,1]
[1,6,7,5,4,3,2,8]=>[2,7,6,5,4,1,3,8]=>[7,2,3,4,5,8,6,1]=>[1,5,1,1]
[1,6,5,7,4,3,2,8]=>[3,2,7,6,5,1,4,8]=>[6,7,2,3,4,8,5,1]=>[2,4,1,1]
[1,5,6,7,4,3,2,8]=>[2,3,7,6,5,1,4,8]=>[7,6,2,3,4,8,5,1]=>[1,1,4,1,1]
[1,5,4,7,6,3,2,8]=>[2,7,3,6,5,1,4,8]=>[7,2,6,3,4,8,5,1]=>[1,2,3,1,1]
[1,5,6,4,7,3,2,8]=>[2,4,3,7,6,1,5,8]=>[7,5,6,2,3,8,4,1]=>[1,2,3,1,1]
[1,4,6,5,7,3,2,8]=>[4,2,3,7,6,1,5,8]=>[5,7,6,2,3,8,4,1]=>[2,1,3,1,1]
[1,5,4,6,7,3,2,8]=>[3,2,4,7,6,1,5,8]=>[6,7,5,2,3,8,4,1]=>[2,1,3,1,1]
[1,4,5,6,7,3,2,8]=>[2,3,4,7,6,1,5,8]=>[7,6,5,2,3,8,4,1]=>[1,1,1,3,1,1]
[1,3,7,6,5,4,2,8]=>[7,6,5,2,4,1,3,8]=>[2,3,4,7,5,8,6,1]=>[4,2,1,1]
[1,3,6,7,5,4,2,8]=>[3,7,6,2,5,1,4,8]=>[6,2,3,7,4,8,5,1]=>[1,3,2,1,1]
[1,3,5,7,6,4,2,8]=>[7,3,6,2,5,1,4,8]=>[2,6,3,7,4,8,5,1]=>[2,2,2,1,1]
[1,3,6,5,7,4,2,8]=>[4,3,7,2,6,1,5,8]=>[5,6,2,7,3,8,4,1]=>[2,2,2,1,1]
[1,3,4,6,7,5,2,8]=>[4,7,2,3,6,1,5,8]=>[5,2,7,6,3,8,4,1]=>[1,2,1,2,1,1]
[1,3,5,4,7,6,2,8]=>[3,7,2,4,6,1,5,8]=>[6,2,7,5,3,8,4,1]=>[1,2,1,2,1,1]
[1,3,4,5,7,6,2,8]=>[7,2,3,4,6,1,5,8]=>[2,7,6,5,3,8,4,1]=>[2,1,1,2,1,1]
[1,5,4,6,3,7,2,8]=>[3,2,5,4,7,1,6,8]=>[6,7,4,5,2,8,3,1]=>[2,2,2,1,1]
[1,4,5,6,3,7,2,8]=>[2,3,5,4,7,1,6,8]=>[7,6,4,5,2,8,3,1]=>[1,1,2,2,1,1]
[1,3,6,5,4,7,2,8]=>[5,4,2,3,7,1,6,8]=>[4,5,7,6,2,8,3,1]=>[3,1,2,1,1]
[1,3,5,6,4,7,2,8]=>[3,5,2,4,7,1,6,8]=>[6,4,7,5,2,8,3,1]=>[1,2,1,2,1,1]
[1,4,3,6,5,7,2,8]=>[2,5,3,4,7,1,6,8]=>[7,4,6,5,2,8,3,1]=>[1,2,1,2,1,1]
[1,3,4,6,5,7,2,8]=>[5,2,3,4,7,1,6,8]=>[4,7,6,5,2,8,3,1]=>[2,1,1,2,1,1]
[1,5,4,3,6,7,2,8]=>[4,3,2,5,7,1,6,8]=>[5,6,7,4,2,8,3,1]=>[3,1,2,1,1]
[1,4,5,3,6,7,2,8]=>[2,4,3,5,7,1,6,8]=>[7,5,6,4,2,8,3,1]=>[1,2,1,2,1,1]
[1,4,3,5,6,7,2,8]=>[3,2,4,5,7,1,6,8]=>[6,7,5,4,2,8,3,1]=>[2,1,1,2,1,1]
[1,3,4,5,6,7,2,8]=>[2,3,4,5,7,1,6,8]=>[7,6,5,4,2,8,3,1]=>[1,1,1,1,2,1,1]
[2,1,7,6,5,4,3,8]=>[7,6,5,1,4,2,3,8]=>[2,3,4,8,5,7,6,1]=>[4,2,1,1]
[2,1,6,7,5,4,3,8]=>[3,7,6,1,5,2,4,8]=>[6,2,3,8,4,7,5,1]=>[1,3,2,1,1]
[2,1,5,6,7,4,3,8]=>[3,4,7,1,6,2,5,8]=>[6,5,2,8,3,7,4,1]=>[1,1,2,2,1,1]
[2,1,4,6,7,5,3,8]=>[4,7,1,3,6,2,5,8]=>[5,2,8,6,3,7,4,1]=>[1,2,1,2,1,1]
[2,1,5,4,6,7,3,8]=>[4,1,3,5,7,2,6,8]=>[5,8,6,4,2,7,3,1]=>[2,1,1,2,1,1]
[2,1,4,5,6,7,3,8]=>[1,3,4,5,7,2,6,8]=>[8,6,5,4,2,7,3,1]=>[1,1,1,1,2,1,1]
[1,2,7,6,5,4,3,8]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>[5,1,1,1]
[1,2,6,7,5,4,3,8]=>[3,7,6,5,1,2,4,8]=>[6,2,3,4,8,7,5,1]=>[1,4,1,1,1]
[1,2,5,7,6,4,3,8]=>[7,3,6,5,1,2,4,8]=>[2,6,3,4,8,7,5,1]=>[2,3,1,1,1]
[1,2,5,6,7,4,3,8]=>[3,4,7,6,1,2,5,8]=>[6,5,2,3,8,7,4,1]=>[1,1,3,1,1,1]
[1,2,4,6,7,5,3,8]=>[4,7,3,6,1,2,5,8]=>[5,2,6,3,8,7,4,1]=>[1,2,2,1,1,1]
[1,2,5,6,4,7,3,8]=>[3,5,4,7,1,2,6,8]=>[6,4,5,2,8,7,3,1]=>[1,2,2,1,1,1]
[1,2,4,6,5,7,3,8]=>[5,3,4,7,1,2,6,8]=>[4,6,5,2,8,7,3,1]=>[2,1,2,1,1,1]
[1,2,4,5,6,7,3,8]=>[3,4,5,7,1,2,6,8]=>[6,5,4,2,8,7,3,1]=>[1,1,1,2,1,1,1]
[3,2,1,7,6,5,4,8]=>[7,1,6,2,5,3,4,8]=>[2,8,3,7,4,6,5,1]=>[2,2,2,1,1]
[3,2,1,6,7,5,4,8]=>[1,4,7,2,6,3,5,8]=>[8,5,2,7,3,6,4,1]=>[1,1,2,2,1,1]
[3,2,1,5,7,6,4,8]=>[1,7,2,4,6,3,5,8]=>[8,2,7,5,3,6,4,1]=>[1,2,1,2,1,1]
[3,2,1,6,5,7,4,8]=>[1,5,2,4,7,3,6,8]=>[8,4,7,5,2,6,3,1]=>[1,2,1,2,1,1]
[2,3,1,6,7,5,4,8]=>[4,7,1,2,6,3,5,8]=>[5,2,8,7,3,6,4,1]=>[1,2,1,2,1,1]
[2,3,1,6,5,7,4,8]=>[5,1,2,4,7,3,6,8]=>[4,8,7,5,2,6,3,1]=>[2,1,1,2,1,1]
[2,3,1,5,6,7,4,8]=>[1,2,4,5,7,3,6,8]=>[8,7,5,4,2,6,3,1]=>[1,1,1,1,2,1,1]
[1,3,2,7,6,5,4,8]=>[7,6,2,5,1,3,4,8]=>[2,3,7,4,8,6,5,1]=>[3,2,1,1,1]
[1,3,2,5,7,6,4,8]=>[7,2,4,6,1,3,5,8]=>[2,7,5,3,8,6,4,1]=>[2,1,2,1,1,1]
[1,3,2,6,5,7,4,8]=>[5,2,4,7,1,3,6,8]=>[4,7,5,2,8,6,3,1]=>[2,1,2,1,1,1]
[1,3,2,5,6,7,4,8]=>[2,4,5,7,1,3,6,8]=>[7,5,4,2,8,6,3,1]=>[1,1,1,2,1,1,1]
[1,2,3,7,6,5,4,8]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]
[1,2,3,6,7,5,4,8]=>[4,7,6,1,2,3,5,8]=>[5,2,3,8,7,6,4,1]=>[1,3,1,1,1,1]
[1,2,3,5,7,6,4,8]=>[7,4,6,1,2,3,5,8]=>[2,5,3,8,7,6,4,1]=>[2,2,1,1,1,1]
[1,2,3,6,5,7,4,8]=>[5,4,7,1,2,3,6,8]=>[4,5,2,8,7,6,3,1]=>[2,2,1,1,1,1]
[1,2,3,5,6,7,4,8]=>[4,5,7,1,2,3,6,8]=>[5,4,2,8,7,6,3,1]=>[1,1,2,1,1,1,1]
[4,3,2,1,7,6,5,8]=>[2,1,7,3,6,4,5,8]=>[7,8,2,6,3,5,4,1]=>[2,2,2,1,1]
[4,3,2,1,6,7,5,8]=>[3,2,1,5,7,4,6,8]=>[6,7,8,4,2,5,3,1]=>[3,1,2,1,1]
[3,2,4,1,7,6,5,8]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[1,2,1,2,1,1]
[3,2,4,1,6,7,5,8]=>[2,1,3,5,7,4,6,8]=>[7,8,6,4,2,5,3,1]=>[2,1,1,2,1,1]
[2,3,4,1,6,7,5,8]=>[1,2,3,5,7,4,6,8]=>[8,7,6,4,2,5,3,1]=>[1,1,1,1,2,1,1]
[1,4,3,2,7,6,5,8]=>[2,7,3,6,1,4,5,8]=>[7,2,6,3,8,5,4,1]=>[1,2,2,1,1,1]
[1,4,3,2,6,7,5,8]=>[3,2,5,7,1,4,6,8]=>[6,7,4,2,8,5,3,1]=>[2,1,2,1,1,1]
[1,3,4,2,6,7,5,8]=>[2,3,5,7,1,4,6,8]=>[7,6,4,2,8,5,3,1]=>[1,1,1,2,1,1,1]
[2,1,4,3,6,7,5,8]=>[1,3,5,7,2,4,6,8]=>[8,6,4,2,7,5,3,1]=>[1,1,1,2,1,1,1]
[1,2,4,3,6,7,5,8]=>[3,5,7,1,2,4,6,8]=>[6,4,2,8,7,5,3,1]=>[1,1,2,1,1,1,1]
[3,2,1,4,7,6,5,8]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[1,2,2,1,1,1]
[2,3,1,4,6,7,5,8]=>[1,2,5,7,3,4,6,8]=>[8,7,4,2,6,5,3,1]=>[1,1,1,2,1,1,1]
[1,3,2,4,6,7,5,8]=>[2,5,7,1,3,4,6,8]=>[7,4,2,8,6,5,3,1]=>[1,1,2,1,1,1,1]
[2,1,3,4,6,7,5,8]=>[1,5,7,2,3,4,6,8]=>[8,4,2,7,6,5,3,1]=>[1,1,2,1,1,1,1]
[1,2,3,4,7,6,5,8]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>[3,1,1,1,1,1]
[1,2,3,4,6,7,5,8]=>[5,7,1,2,3,4,6,8]=>[4,2,8,7,6,5,3,1]=>[1,2,1,1,1,1,1]
[5,4,3,2,1,7,6,8]=>[4,3,2,1,7,5,6,8]=>[5,6,7,8,2,4,3,1]=>[4,2,1,1]
[4,5,3,2,1,7,6,8]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[1,3,2,1,1]
[3,5,4,2,1,7,6,8]=>[4,1,3,2,7,5,6,8]=>[5,8,6,7,2,4,3,1]=>[2,2,2,1,1]
[3,4,5,2,1,7,6,8]=>[1,2,4,3,7,5,6,8]=>[8,7,5,6,2,4,3,1]=>[1,1,2,2,1,1]
[2,5,4,3,1,7,6,8]=>[4,3,1,2,7,5,6,8]=>[5,6,8,7,2,4,3,1]=>[3,1,2,1,1]
[3,2,5,4,1,7,6,8]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[1,2,1,2,1,1]
[2,3,5,4,1,7,6,8]=>[4,1,2,3,7,5,6,8]=>[5,8,7,6,2,4,3,1]=>[2,1,1,2,1,1]
[3,4,2,5,1,7,6,8]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[1,2,1,2,1,1]
[2,4,3,5,1,7,6,8]=>[3,1,2,4,7,5,6,8]=>[6,8,7,5,2,4,3,1]=>[2,1,1,2,1,1]
[2,3,4,5,1,7,6,8]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[1,1,1,1,2,1,1]
[1,5,4,3,2,7,6,8]=>[4,3,2,7,1,5,6,8]=>[5,6,7,2,8,4,3,1]=>[3,2,1,1,1]
[1,4,5,3,2,7,6,8]=>[2,4,3,7,1,5,6,8]=>[7,5,6,2,8,4,3,1]=>[1,2,2,1,1,1]
[1,3,5,4,2,7,6,8]=>[4,2,3,7,1,5,6,8]=>[5,7,6,2,8,4,3,1]=>[2,1,2,1,1,1]
[1,4,3,5,2,7,6,8]=>[3,2,4,7,1,5,6,8]=>[6,7,5,2,8,4,3,1]=>[2,1,2,1,1,1]
[1,3,4,5,2,7,6,8]=>[2,3,4,7,1,5,6,8]=>[7,6,5,2,8,4,3,1]=>[1,1,1,2,1,1,1]
[1,2,4,5,3,7,6,8]=>[3,4,7,1,2,5,6,8]=>[6,5,2,8,7,4,3,1]=>[1,1,2,1,1,1,1]
[3,2,1,5,4,7,6,8]=>[2,1,4,7,3,5,6,8]=>[7,8,5,2,6,4,3,1]=>[2,1,2,1,1,1]
[2,3,1,5,4,7,6,8]=>[1,2,4,7,3,5,6,8]=>[8,7,5,2,6,4,3,1]=>[1,1,1,2,1,1,1]
[1,3,2,5,4,7,6,8]=>[2,4,7,1,3,5,6,8]=>[7,5,2,8,6,4,3,1]=>[1,1,2,1,1,1,1]
[1,2,3,5,4,7,6,8]=>[4,7,1,2,3,5,6,8]=>[5,2,8,7,6,4,3,1]=>[1,2,1,1,1,1,1]
[4,3,2,1,5,7,6,8]=>[3,2,1,7,4,5,6,8]=>[6,7,8,2,5,4,3,1]=>[3,2,1,1,1]
[3,2,4,1,5,7,6,8]=>[2,1,3,7,4,5,6,8]=>[7,8,6,2,5,4,3,1]=>[2,1,2,1,1,1]
[2,3,4,1,5,7,6,8]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[1,1,1,2,1,1,1]
[1,4,3,2,5,7,6,8]=>[3,2,7,1,4,5,6,8]=>[6,7,2,8,5,4,3,1]=>[2,2,1,1,1,1]
[1,3,4,2,5,7,6,8]=>[2,3,7,1,4,5,6,8]=>[7,6,2,8,5,4,3,1]=>[1,1,2,1,1,1,1]
[1,2,4,3,5,7,6,8]=>[3,7,1,2,4,5,6,8]=>[6,2,8,7,5,4,3,1]=>[1,2,1,1,1,1,1]
[3,2,1,4,5,7,6,8]=>[2,1,7,3,4,5,6,8]=>[7,8,2,6,5,4,3,1]=>[2,2,1,1,1,1]
[2,3,1,4,5,7,6,8]=>[1,2,7,3,4,5,6,8]=>[8,7,2,6,5,4,3,1]=>[1,1,2,1,1,1,1]
[1,3,2,4,5,7,6,8]=>[2,7,1,3,4,5,6,8]=>[7,2,8,6,5,4,3,1]=>[1,2,1,1,1,1,1]
[2,1,3,4,5,7,6,8]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[1,2,1,1,1,1,1]
[1,2,3,4,5,7,6,8]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1]
[3,6,5,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>[3,4,8,5,6,7,2,1]=>[3,3,1,1]
[4,3,6,5,2,1,7,8]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[1,2,3,1,1]
[2,4,6,5,3,1,7,8]=>[6,2,5,1,4,3,7,8]=>[3,7,4,8,5,6,2,1]=>[2,2,2,1,1]
[2,4,5,6,3,1,7,8]=>[2,3,6,1,5,4,7,8]=>[7,6,3,8,4,5,2,1]=>[1,1,2,2,1,1]
[2,3,6,5,4,1,7,8]=>[6,5,1,2,4,3,7,8]=>[3,4,8,7,5,6,2,1]=>[3,1,2,1,1]
[2,3,5,6,4,1,7,8]=>[3,6,1,2,5,4,7,8]=>[6,3,8,7,4,5,2,1]=>[1,2,1,2,1,1]
[2,4,3,6,5,1,7,8]=>[2,6,1,3,5,4,7,8]=>[7,3,8,6,4,5,2,1]=>[1,2,1,2,1,1]
[2,3,4,6,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>[3,8,7,6,4,5,2,1]=>[2,1,1,2,1,1]
[3,5,4,2,6,1,7,8]=>[4,1,3,2,6,5,7,8]=>[5,8,6,7,3,4,2,1]=>[2,2,2,1,1]
[2,3,5,4,6,1,7,8]=>[4,1,2,3,6,5,7,8]=>[5,8,7,6,3,4,2,1]=>[2,1,1,2,1,1]
[1,6,5,4,3,2,7,8]=>[6,5,4,3,1,2,7,8]=>[3,4,5,6,8,7,2,1]=>[5,1,1,1]
[1,5,6,4,3,2,7,8]=>[2,6,5,4,1,3,7,8]=>[7,3,4,5,8,6,2,1]=>[1,4,1,1,1]
[1,4,6,5,3,2,7,8]=>[6,2,5,4,1,3,7,8]=>[3,7,4,5,8,6,2,1]=>[2,3,1,1,1]
[1,5,4,6,3,2,7,8]=>[3,2,6,5,1,4,7,8]=>[6,7,3,4,8,5,2,1]=>[2,3,1,1,1]
[1,4,5,6,3,2,7,8]=>[2,3,6,5,1,4,7,8]=>[7,6,3,4,8,5,2,1]=>[1,1,3,1,1,1]
[1,3,5,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>[6,3,7,4,8,5,2,1]=>[1,2,2,1,1,1]
[1,5,4,3,6,2,7,8]=>[4,3,2,6,1,5,7,8]=>[5,6,7,3,8,4,2,1]=>[3,2,1,1,1]
[1,4,5,3,6,2,7,8]=>[2,4,3,6,1,5,7,8]=>[7,5,6,3,8,4,2,1]=>[1,2,2,1,1,1]
[1,3,5,4,6,2,7,8]=>[4,2,3,6,1,5,7,8]=>[5,7,6,3,8,4,2,1]=>[2,1,2,1,1,1]
[1,4,3,5,6,2,7,8]=>[3,2,4,6,1,5,7,8]=>[6,7,5,3,8,4,2,1]=>[2,1,2,1,1,1]
[1,3,4,5,6,2,7,8]=>[2,3,4,6,1,5,7,8]=>[7,6,5,3,8,4,2,1]=>[1,1,1,2,1,1,1]
[2,1,5,6,4,3,7,8]=>[3,6,1,5,2,4,7,8]=>[6,3,8,4,7,5,2,1]=>[1,2,2,1,1,1]
[2,1,4,6,5,3,7,8]=>[6,1,3,5,2,4,7,8]=>[3,8,6,4,7,5,2,1]=>[2,1,2,1,1,1]
[1,2,6,5,4,3,7,8]=>[6,5,4,1,2,3,7,8]=>[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]
[1,2,4,6,5,3,7,8]=>[6,3,5,1,2,4,7,8]=>[3,6,4,8,7,5,2,1]=>[2,2,1,1,1,1]
[3,2,1,6,5,4,7,8]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[1,2,2,1,1,1]
[3,2,1,5,6,4,7,8]=>[2,1,4,6,3,5,7,8]=>[7,8,5,3,6,4,2,1]=>[2,1,2,1,1,1]
[2,3,1,6,5,4,7,8]=>[6,1,2,5,3,4,7,8]=>[3,8,7,4,6,5,2,1]=>[2,1,2,1,1,1]
[2,3,1,5,6,4,7,8]=>[1,2,4,6,3,5,7,8]=>[8,7,5,3,6,4,2,1]=>[1,1,1,2,1,1,1]
[1,3,2,6,5,4,7,8]=>[6,2,5,1,3,4,7,8]=>[3,7,4,8,6,5,2,1]=>[2,2,1,1,1,1]
[1,3,2,5,6,4,7,8]=>[2,4,6,1,3,5,7,8]=>[7,5,3,8,6,4,2,1]=>[1,1,2,1,1,1,1]
[1,2,3,6,5,4,7,8]=>[6,5,1,2,3,4,7,8]=>[3,4,8,7,6,5,2,1]=>[3,1,1,1,1,1]
[1,2,3,5,6,4,7,8]=>[4,6,1,2,3,5,7,8]=>[5,3,8,7,6,4,2,1]=>[1,2,1,1,1,1,1]
[4,3,2,1,6,5,7,8]=>[3,2,1,6,4,5,7,8]=>[6,7,8,3,5,4,2,1]=>[3,2,1,1,1]
[2,4,3,1,6,5,7,8]=>[3,1,2,6,4,5,7,8]=>[6,8,7,3,5,4,2,1]=>[2,1,2,1,1,1]
[3,2,4,1,6,5,7,8]=>[2,1,3,6,4,5,7,8]=>[7,8,6,3,5,4,2,1]=>[2,1,2,1,1,1]
[2,3,4,1,6,5,7,8]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[1,1,1,2,1,1,1]
[2,1,4,3,6,5,7,8]=>[1,3,6,2,4,5,7,8]=>[8,6,3,7,5,4,2,1]=>[1,1,2,1,1,1,1]
[1,2,4,3,6,5,7,8]=>[3,6,1,2,4,5,7,8]=>[6,3,8,7,5,4,2,1]=>[1,2,1,1,1,1,1]
[1,3,2,4,6,5,7,8]=>[2,6,1,3,4,5,7,8]=>[7,3,8,6,5,4,2,1]=>[1,2,1,1,1,1,1]
[2,1,3,4,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[1,2,1,1,1,1,1]
[1,2,3,4,6,5,7,8]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1]
[3,5,4,2,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>[4,8,5,6,7,3,2,1]=>[2,3,1,1,1]
[2,5,4,3,1,6,7,8]=>[5,4,1,3,2,6,7,8]=>[4,5,8,6,7,3,2,1]=>[3,2,1,1,1]
[2,4,5,3,1,6,7,8]=>[2,5,1,4,3,6,7,8]=>[7,4,8,5,6,3,2,1]=>[1,2,2,1,1,1]
[3,2,5,4,1,6,7,8]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[1,2,2,1,1,1]
[2,3,5,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[4,8,7,5,6,3,2,1]=>[2,1,2,1,1,1]
[2,4,3,5,1,6,7,8]=>[3,1,2,5,4,6,7,8]=>[6,8,7,4,5,3,2,1]=>[2,1,2,1,1,1]
[1,5,4,3,2,6,7,8]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]
[1,4,5,3,2,6,7,8]=>[2,5,4,1,3,6,7,8]=>[7,4,5,8,6,3,2,1]=>[1,3,1,1,1,1]
[1,3,5,4,2,6,7,8]=>[5,2,4,1,3,6,7,8]=>[4,7,5,8,6,3,2,1]=>[2,2,1,1,1,1]
[1,4,3,5,2,6,7,8]=>[3,2,5,1,4,6,7,8]=>[6,7,4,8,5,3,2,1]=>[2,2,1,1,1,1]
[1,3,4,5,2,6,7,8]=>[2,3,5,1,4,6,7,8]=>[7,6,4,8,5,3,2,1]=>[1,1,2,1,1,1,1]
[2,1,5,4,3,6,7,8]=>[5,1,4,2,3,6,7,8]=>[4,8,5,7,6,3,2,1]=>[2,2,1,1,1,1]
[2,1,4,5,3,6,7,8]=>[1,3,5,2,4,6,7,8]=>[8,6,4,7,5,3,2,1]=>[1,1,2,1,1,1,1]
[1,2,5,4,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>[3,1,1,1,1,1]
[1,2,4,5,3,6,7,8]=>[3,5,1,2,4,6,7,8]=>[6,4,8,7,5,3,2,1]=>[1,2,1,1,1,1,1]
[3,2,1,5,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>[7,8,4,6,5,3,2,1]=>[2,2,1,1,1,1]
[2,3,1,5,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[1,1,2,1,1,1,1]
[1,3,2,5,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[7,4,8,6,5,3,2,1]=>[1,2,1,1,1,1,1]
[2,1,3,5,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[1,2,1,1,1,1,1]
[1,2,3,5,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1]
[2,4,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[5,8,6,7,4,3,2,1]=>[2,2,1,1,1,1]
[1,4,3,2,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>[3,1,1,1,1,1]
[1,3,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[7,5,8,6,4,3,2,1]=>[1,2,1,1,1,1,1]
[2,1,4,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[1,2,1,1,1,1,1]
[1,2,4,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1]
[1,3,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1]
[1,2,3,4,8,6,7,5]=>[6,8,7,1,2,3,4,5]=>[3,1,2,8,7,6,5,4]=>[1,3,1,1,1,1]
[1,2,3,5,8,6,7,4]=>[6,8,4,7,1,2,3,5]=>[3,1,5,2,8,7,6,4]=>[1,2,2,1,1,1]
[1,2,3,7,5,6,4,8]=>[5,7,6,1,2,3,4,8]=>[4,2,3,8,7,6,5,1]=>[1,3,1,1,1,1]
[1,2,3,7,5,6,8,4]=>[5,6,4,8,1,2,3,7]=>[4,3,5,1,8,7,6,2]=>[1,2,2,1,1,1]
[1,2,3,8,5,6,7,4]=>[5,6,8,7,1,2,3,4]=>[4,3,1,2,8,7,6,5]=>[1,1,3,1,1,1]
[1,2,3,8,5,7,6,4]=>[8,5,7,6,1,2,3,4]=>[1,4,2,3,8,7,6,5]=>[2,3,1,1,1]
[1,2,3,8,6,5,7,4]=>[6,5,8,7,1,2,3,4]=>[3,4,1,2,8,7,6,5]=>[2,3,1,1,1]
[1,2,3,8,6,7,5,4]=>[5,8,7,6,1,2,3,4]=>[4,1,2,3,8,7,6,5]=>[1,4,1,1,1]
[1,2,4,3,8,6,7,5]=>[6,8,3,7,1,2,4,5]=>[3,1,6,2,8,7,5,4]=>[1,2,2,1,1,1]
[1,2,4,5,8,6,7,3]=>[6,8,3,4,7,1,2,5]=>[3,1,6,5,2,8,7,4]=>[1,2,1,2,1,1]
[1,2,4,7,5,6,8,3]=>[5,6,3,4,8,1,2,7]=>[4,3,6,5,1,8,7,2]=>[1,2,1,2,1,1]
[1,2,4,8,5,6,7,3]=>[5,6,8,3,7,1,2,4]=>[4,3,1,6,2,8,7,5]=>[1,1,2,2,1,1]
[1,2,4,8,6,5,7,3]=>[6,5,8,3,7,1,2,4]=>[3,4,1,6,2,8,7,5]=>[2,2,2,1,1]
[1,2,5,4,8,6,7,3]=>[3,6,8,4,7,1,2,5]=>[6,3,1,5,2,8,7,4]=>[1,1,2,2,1,1]
[1,2,6,4,5,3,7,8]=>[4,6,5,1,2,3,7,8]=>[5,3,4,8,7,6,2,1]=>[1,3,1,1,1,1]
[1,2,6,4,5,7,8,3]=>[4,5,3,6,8,1,2,7]=>[5,4,6,3,1,8,7,2]=>[1,2,1,2,1,1]
[1,2,6,4,5,8,7,3]=>[8,4,3,5,7,1,2,6]=>[1,5,6,4,2,8,7,3]=>[3,1,2,1,1]
[1,2,7,4,5,6,8,3]=>[4,5,6,3,8,1,2,7]=>[5,4,3,6,1,8,7,2]=>[1,1,2,2,1,1]
[1,2,8,4,5,6,7,3]=>[4,5,6,8,7,1,2,3]=>[5,4,3,1,2,8,7,6]=>[1,1,1,3,1,1]
[1,2,8,4,6,7,5,3]=>[5,8,4,7,6,1,2,3]=>[4,1,5,2,3,8,7,6]=>[1,2,3,1,1]
[1,2,8,4,7,6,5,3]=>[8,7,4,6,5,1,2,3]=>[1,2,5,3,4,8,7,6]=>[3,3,1,1]
[1,2,7,5,4,6,8,3]=>[5,4,6,3,8,1,2,7]=>[4,5,3,6,1,8,7,2]=>[2,2,2,1,1]
[1,2,8,5,4,6,7,3]=>[5,4,6,8,7,1,2,3]=>[4,5,3,1,2,8,7,6]=>[2,1,3,1,1]
[1,2,8,5,6,4,7,3]=>[4,6,5,8,7,1,2,3]=>[5,3,4,1,2,8,7,6]=>[1,2,3,1,1]
[1,2,8,5,6,7,4,3]=>[4,5,8,7,6,1,2,3]=>[5,4,1,2,3,8,7,6]=>[1,1,4,1,1]
[1,2,8,6,5,4,7,3]=>[6,5,4,8,7,1,2,3]=>[3,4,5,1,2,8,7,6]=>[3,3,1,1]
[1,2,8,6,5,7,4,3]=>[5,4,8,7,6,1,2,3]=>[4,5,1,2,3,8,7,6]=>[2,4,1,1]
[1,2,8,7,5,6,4,3]=>[5,8,7,6,4,1,2,3]=>[4,1,2,3,5,8,7,6]=>[1,5,1,1]
[1,3,2,4,8,6,7,5]=>[6,8,2,7,1,3,4,5]=>[3,1,7,2,8,6,5,4]=>[1,2,2,1,1,1]
[1,3,2,7,5,6,8,4]=>[5,6,2,4,8,1,3,7]=>[4,3,7,5,1,8,6,2]=>[1,2,1,2,1,1]
[1,3,2,8,5,7,6,4]=>[8,5,7,2,6,1,3,4]=>[1,4,2,7,3,8,6,5]=>[2,2,2,1,1]
[1,3,2,8,6,7,5,4]=>[5,8,7,2,6,1,3,4]=>[4,1,2,7,3,8,6,5]=>[1,3,2,1,1]
[1,3,4,2,8,6,7,5]=>[6,8,2,3,7,1,4,5]=>[3,1,7,6,2,8,5,4]=>[1,2,1,2,1,1]
[1,3,4,5,8,6,7,2]=>[6,8,2,3,4,7,1,5]=>[3,1,7,6,5,2,8,4]=>[1,2,1,1,2,1]
[1,3,4,8,5,6,7,2]=>[5,6,8,2,3,7,1,4]=>[4,3,1,7,6,2,8,5]=>[1,1,2,1,2,1]
[1,3,4,8,6,5,7,2]=>[6,5,8,2,3,7,1,4]=>[3,4,1,7,6,2,8,5]=>[2,2,1,2,1]
[1,3,4,8,6,7,5,2]=>[5,8,7,2,3,6,1,4]=>[4,1,2,7,6,3,8,5]=>[1,3,1,2,1]
[1,3,6,4,5,7,8,2]=>[4,5,2,3,6,8,1,7]=>[5,4,7,6,3,1,8,2]=>[1,2,1,1,2,1]
[1,3,6,4,5,8,7,2]=>[8,4,2,3,5,7,1,6]=>[1,5,7,6,4,2,8,3]=>[3,1,1,2,1]
[1,3,7,4,5,6,2,8]=>[4,5,7,2,6,1,3,8]=>[5,4,2,7,3,8,6,1]=>[1,1,2,2,1,1]
[1,3,7,4,5,6,8,2]=>[4,5,6,2,3,8,1,7]=>[5,4,3,7,6,1,8,2]=>[1,1,2,1,2,1]
[1,3,8,4,5,6,7,2]=>[4,5,6,8,2,7,1,3]=>[5,4,3,1,7,2,8,6]=>[1,1,1,2,2,1]
[1,3,8,4,6,5,7,2]=>[6,4,5,8,2,7,1,3]=>[3,5,4,1,7,2,8,6]=>[2,1,2,2,1]
[1,3,8,4,6,7,5,2]=>[5,8,4,7,2,6,1,3]=>[4,1,5,2,7,3,8,6]=>[1,2,2,2,1]
[1,3,8,5,4,6,7,2]=>[5,4,6,8,2,7,1,3]=>[4,5,3,1,7,2,8,6]=>[2,1,2,2,1]
[1,3,8,5,4,7,6,2]=>[4,8,5,7,2,6,1,3]=>[5,1,4,2,7,3,8,6]=>[1,2,2,2,1]
[1,3,8,5,6,7,4,2]=>[4,5,8,7,2,6,1,3]=>[5,4,1,2,7,3,8,6]=>[1,1,3,2,1]
[1,3,8,5,7,6,4,2]=>[8,4,7,6,2,5,1,3]=>[1,5,2,3,7,4,8,6]=>[2,3,2,1]
[1,3,8,6,5,7,4,2]=>[5,4,8,7,2,6,1,3]=>[4,5,1,2,7,3,8,6]=>[2,3,2,1]
[1,3,8,7,5,6,4,2]=>[5,8,7,6,2,4,1,3]=>[4,1,2,3,7,5,8,6]=>[1,4,2,1]
[1,4,3,2,8,6,7,5]=>[2,6,8,3,7,1,4,5]=>[7,3,1,6,2,8,5,4]=>[1,1,2,2,1,1]
[1,4,3,5,8,6,7,2]=>[2,6,8,3,4,7,1,5]=>[7,3,1,6,5,2,8,4]=>[1,1,2,1,2,1]
[1,4,3,8,5,6,7,2]=>[2,5,6,8,3,7,1,4]=>[7,4,3,1,6,2,8,5]=>[1,1,1,2,2,1]
[1,4,3,8,5,7,6,2]=>[8,2,5,7,3,6,1,4]=>[1,7,4,2,6,3,8,5]=>[2,1,2,2,1]
[1,4,3,8,6,5,7,2]=>[6,2,5,8,3,7,1,4]=>[3,7,4,1,6,2,8,5]=>[2,1,2,2,1]
[1,4,3,8,6,7,5,2]=>[5,8,2,7,3,6,1,4]=>[4,1,7,2,6,3,8,5]=>[1,2,2,2,1]
[1,5,3,4,2,6,7,8]=>[3,5,4,1,2,6,7,8]=>[6,4,5,8,7,3,2,1]=>[1,3,1,1,1,1]
[1,5,3,4,2,8,7,6]=>[8,3,2,4,7,1,5,6]=>[1,6,7,5,2,8,4,3]=>[3,1,2,1,1]
[1,5,3,4,6,2,7,8]=>[3,4,2,6,1,5,7,8]=>[6,5,7,3,8,4,2,1]=>[1,2,2,1,1,1]
[1,5,3,4,6,2,8,7]=>[3,4,2,5,8,1,6,7]=>[6,5,7,4,1,8,3,2]=>[1,2,1,2,1,1]
[1,5,3,4,6,7,2,8]=>[3,4,2,5,7,1,6,8]=>[6,5,7,4,2,8,3,1]=>[1,2,1,2,1,1]
[1,5,3,4,6,7,8,2]=>[3,4,2,5,6,8,1,7]=>[6,5,7,4,3,1,8,2]=>[1,2,1,1,2,1]
[1,5,3,4,7,6,2,8]=>[7,3,2,4,6,1,5,8]=>[2,6,7,5,3,8,4,1]=>[3,1,2,1,1]
[1,5,3,4,8,6,7,2]=>[6,2,8,3,4,7,1,5]=>[3,7,1,6,5,2,8,4]=>[2,2,1,2,1]
[1,6,3,4,5,2,7,8]=>[3,4,6,5,1,2,7,8]=>[6,5,3,4,8,7,2,1]=>[1,1,3,1,1,1]
[1,6,3,4,5,8,7,2]=>[8,3,4,2,5,7,1,6]=>[1,6,5,7,4,2,8,3]=>[2,2,1,2,1]
[1,7,3,4,5,6,2,8]=>[3,4,5,7,6,1,2,8]=>[6,5,4,2,3,8,7,1]=>[1,1,1,3,1,1]
[1,7,3,4,5,6,8,2]=>[3,4,5,6,2,8,1,7]=>[6,5,4,3,7,1,8,2]=>[1,1,1,2,2,1]
[1,8,3,4,5,6,7,2]=>[3,4,5,6,8,7,1,2]=>[6,5,4,3,1,2,8,7]=>[1,1,1,1,3,1]
[1,8,3,4,6,7,5,2]=>[5,8,3,4,7,6,1,2]=>[4,1,6,5,2,3,8,7]=>[1,2,1,3,1]
[1,8,3,4,7,6,5,2]=>[8,7,3,4,6,5,1,2]=>[1,2,6,5,3,4,8,7]=>[3,1,3,1]
[1,6,3,5,4,2,7,8]=>[6,3,5,4,1,2,7,8]=>[3,6,4,5,8,7,2,1]=>[2,3,1,1,1]
[1,6,3,5,4,8,7,2]=>[4,8,3,2,5,7,1,6]=>[5,1,6,7,4,2,8,3]=>[1,3,1,2,1]
[1,7,3,5,4,6,2,8]=>[5,3,4,7,6,1,2,8]=>[4,6,5,2,3,8,7,1]=>[2,1,3,1,1]
[1,8,3,5,4,6,7,2]=>[5,3,4,6,8,7,1,2]=>[4,6,5,3,1,2,8,7]=>[2,1,1,3,1]
[1,8,3,5,4,7,6,2]=>[4,8,3,5,7,6,1,2]=>[5,1,6,4,2,3,8,7]=>[1,2,1,3,1]
[1,8,3,5,6,4,7,2]=>[4,6,3,5,8,7,1,2]=>[5,3,6,4,1,2,8,7]=>[1,2,1,3,1]
[1,8,3,5,6,7,4,2]=>[4,5,8,3,7,6,1,2]=>[5,4,1,6,2,3,8,7]=>[1,1,2,3,1]
[1,8,3,5,7,6,4,2]=>[8,4,7,3,6,5,1,2]=>[1,5,2,6,3,4,8,7]=>[2,2,3,1]
[1,7,3,6,5,4,2,8]=>[7,6,3,5,4,1,2,8]=>[2,3,6,4,5,8,7,1]=>[3,3,1,1]
[1,7,3,6,5,4,8,2]=>[6,5,3,4,2,8,1,7]=>[3,4,6,5,7,1,8,2]=>[3,2,2,1]
[1,8,3,6,5,4,7,2]=>[6,5,3,4,8,7,1,2]=>[3,4,6,5,1,2,8,7]=>[3,1,3,1]
[1,8,3,7,5,6,4,2]=>[5,8,7,3,6,4,1,2]=>[4,1,2,6,3,5,8,7]=>[1,3,3,1]
[1,8,3,7,6,5,4,2]=>[8,7,6,3,5,4,1,2]=>[1,2,3,6,4,5,8,7]=>[4,3,1]
[1,6,4,3,5,2,7,8]=>[4,3,6,5,1,2,7,8]=>[5,6,3,4,8,7,2,1]=>[2,3,1,1,1]
[1,6,4,3,5,8,7,2]=>[3,8,4,2,5,7,1,6]=>[6,1,5,7,4,2,8,3]=>[1,3,1,2,1]
[1,8,4,3,5,6,7,2]=>[4,3,5,6,8,7,1,2]=>[5,6,4,3,1,2,8,7]=>[2,1,1,3,1]
[1,8,4,3,5,7,6,2]=>[3,8,4,5,7,6,1,2]=>[6,1,5,4,2,3,8,7]=>[1,2,1,3,1]
[1,7,4,3,6,5,8,2]=>[3,6,4,5,2,8,1,7]=>[6,3,5,4,7,1,8,2]=>[1,2,2,2,1]
[1,8,4,3,6,5,7,2]=>[3,6,4,5,8,7,1,2]=>[6,3,5,4,1,2,8,7]=>[1,2,1,3,1]
[1,8,4,3,6,7,5,2]=>[3,5,8,4,7,6,1,2]=>[6,4,1,5,2,3,8,7]=>[1,1,2,3,1]
[1,6,4,5,3,2,7,8]=>[3,6,5,4,1,2,7,8]=>[6,3,4,5,8,7,2,1]=>[1,4,1,1,1]
[1,6,4,5,3,2,8,7]=>[3,5,4,2,8,1,6,7]=>[6,4,5,7,1,8,3,2]=>[1,3,2,1,1]
[1,6,4,5,3,8,7,2]=>[3,4,2,8,5,7,1,6]=>[6,5,7,1,4,2,8,3]=>[1,2,2,2,1]
[1,7,4,5,3,6,8,2]=>[3,5,4,6,2,8,1,7]=>[6,4,5,3,7,1,8,2]=>[1,2,2,2,1]
[1,8,4,5,3,6,7,2]=>[3,5,4,6,8,7,1,2]=>[6,4,5,3,1,2,8,7]=>[1,2,1,3,1]
[1,7,4,5,6,3,2,8]=>[3,4,7,6,5,1,2,8]=>[6,5,2,3,4,8,7,1]=>[1,1,4,1,1]
[1,7,4,5,6,3,8,2]=>[3,4,6,5,2,8,1,7]=>[6,5,3,4,7,1,8,2]=>[1,1,3,2,1]
[1,8,4,5,6,3,7,2]=>[3,4,6,5,8,7,1,2]=>[6,5,3,4,1,2,8,7]=>[1,1,2,3,1]
[1,8,4,5,6,7,3,2]=>[3,4,5,8,7,6,1,2]=>[6,5,4,1,2,3,8,7]=>[1,1,1,4,1]
[1,8,4,6,5,3,7,2]=>[6,3,5,4,8,7,1,2]=>[3,6,4,5,1,2,8,7]=>[2,2,3,1]
[1,8,4,6,5,7,3,2]=>[5,3,4,8,7,6,1,2]=>[4,6,5,1,2,3,8,7]=>[2,1,4,1]
[1,8,4,7,6,5,3,2]=>[8,7,3,6,5,4,1,2]=>[1,2,6,3,4,5,8,7]=>[3,4,1]
[1,7,5,4,3,6,8,2]=>[5,4,3,6,2,8,1,7]=>[4,5,6,3,7,1,8,2]=>[3,2,2,1]
[1,8,5,4,3,6,7,2]=>[5,4,3,6,8,7,1,2]=>[4,5,6,3,1,2,8,7]=>[3,1,3,1]
[1,8,5,4,3,7,6,2]=>[4,3,8,5,7,6,1,2]=>[5,6,1,4,2,3,8,7]=>[2,2,3,1]
[1,8,5,4,6,3,7,2]=>[4,3,6,5,8,7,1,2]=>[5,6,3,4,1,2,8,7]=>[2,2,3,1]
[1,8,5,4,6,7,3,2]=>[4,3,5,8,7,6,1,2]=>[5,6,4,1,2,3,8,7]=>[2,1,4,1]
[1,8,5,4,7,6,3,2]=>[3,8,4,7,6,5,1,2]=>[6,1,5,2,3,4,8,7]=>[1,2,4,1]
[1,7,6,4,5,3,2,8]=>[4,7,6,5,3,1,2,8]=>[5,2,3,4,6,8,7,1]=>[1,5,1,1]
[1,8,6,4,5,3,7,2]=>[4,6,5,3,8,7,1,2]=>[5,3,4,6,1,2,8,7]=>[1,3,3,1]
[1,8,6,4,5,7,3,2]=>[4,5,3,8,7,6,1,2]=>[5,4,6,1,2,3,8,7]=>[1,2,4,1]
[1,8,7,4,5,6,3,2]=>[4,5,8,7,6,3,1,2]=>[5,4,1,2,3,6,8,7]=>[1,1,5,1]
[1,8,7,4,6,5,3,2]=>[8,4,7,6,5,3,1,2]=>[1,5,2,3,4,6,8,7]=>[2,5,1]
[1,8,6,5,4,3,7,2]=>[6,5,4,3,8,7,1,2]=>[3,4,5,6,1,2,8,7]=>[4,3,1]
[1,8,6,5,4,7,3,2]=>[5,4,3,8,7,6,1,2]=>[4,5,6,1,2,3,8,7]=>[3,4,1]
[1,8,7,5,4,6,3,2]=>[5,4,8,7,6,3,1,2]=>[4,5,1,2,3,6,8,7]=>[2,5,1]
[1,8,7,5,6,4,3,2]=>[4,8,7,6,5,3,1,2]=>[5,1,2,3,4,6,8,7]=>[1,6,1]
[2,1,3,5,8,6,7,4]=>[6,8,1,4,7,2,3,5]=>[3,1,8,5,2,7,6,4]=>[1,2,1,2,1,1]
[2,1,3,8,5,6,7,4]=>[5,6,8,1,7,2,3,4]=>[4,3,1,8,2,7,6,5]=>[1,1,2,2,1,1]
[2,1,3,8,5,7,6,4]=>[8,5,7,1,6,2,3,4]=>[1,4,2,8,3,7,6,5]=>[2,2,2,1,1]
[2,1,3,8,6,7,5,4]=>[5,8,7,1,6,2,3,4]=>[4,1,2,8,3,7,6,5]=>[1,3,2,1,1]
[2,1,4,3,8,6,7,5]=>[6,8,1,3,7,2,4,5]=>[3,1,8,6,2,7,5,4]=>[1,2,1,2,1,1]
[2,1,4,5,8,6,7,3]=>[6,8,1,3,4,7,2,5]=>[3,1,8,6,5,2,7,4]=>[1,2,1,1,2,1]
[2,1,4,8,5,6,7,3]=>[5,6,8,1,3,7,2,4]=>[4,3,1,8,6,2,7,5]=>[1,1,2,1,2,1]
[2,1,4,8,6,5,7,3]=>[6,5,8,1,3,7,2,4]=>[3,4,1,8,6,2,7,5]=>[2,2,1,2,1]
[2,1,4,8,6,7,5,3]=>[5,8,7,1,3,6,2,4]=>[4,1,2,8,6,3,7,5]=>[1,3,1,2,1]
[2,1,5,4,8,6,7,3]=>[3,6,8,1,4,7,2,5]=>[6,3,1,8,5,2,7,4]=>[1,1,2,1,2,1]
[2,1,6,4,5,3,8,7]=>[4,5,1,3,8,2,6,7]=>[5,4,8,6,1,7,3,2]=>[1,2,1,2,1,1]
[2,1,6,4,5,7,8,3]=>[4,5,1,3,6,8,2,7]=>[5,4,8,6,3,1,7,2]=>[1,2,1,1,2,1]
[2,1,8,4,5,6,7,3]=>[4,5,6,8,1,7,2,3]=>[5,4,3,1,8,2,7,6]=>[1,1,1,2,2,1]
[2,1,8,4,5,7,6,3]=>[8,4,5,7,1,6,2,3]=>[1,5,4,2,8,3,7,6]=>[2,1,2,2,1]
[2,1,7,4,6,5,8,3]=>[6,4,5,1,3,8,2,7]=>[3,5,4,8,6,1,7,2]=>[2,2,1,2,1]
[2,1,8,4,6,5,7,3]=>[6,4,5,8,1,7,2,3]=>[3,5,4,1,8,2,7,6]=>[2,1,2,2,1]
[2,1,8,4,6,7,5,3]=>[5,8,4,7,1,6,2,3]=>[4,1,5,2,8,3,7,6]=>[1,2,2,2,1]
[2,1,8,4,7,6,5,3]=>[8,7,4,6,1,5,2,3]=>[1,2,5,3,8,4,7,6]=>[3,2,2,1]
[2,1,7,5,4,6,8,3]=>[5,4,6,1,3,8,2,7]=>[4,5,3,8,6,1,7,2]=>[2,2,1,2,1]
[2,1,8,5,4,6,7,3]=>[5,4,6,8,1,7,2,3]=>[4,5,3,1,8,2,7,6]=>[2,1,2,2,1]
[2,1,8,5,4,7,6,3]=>[4,8,5,7,1,6,2,3]=>[5,1,4,2,8,3,7,6]=>[1,2,2,2,1]
[2,1,8,5,6,4,7,3]=>[4,6,5,8,1,7,2,3]=>[5,3,4,1,8,2,7,6]=>[1,2,2,2,1]
[2,1,8,5,6,7,4,3]=>[4,5,8,7,1,6,2,3]=>[5,4,1,2,8,3,7,6]=>[1,1,3,2,1]
[2,1,8,5,7,6,4,3]=>[8,4,7,6,1,5,2,3]=>[1,5,2,3,8,4,7,6]=>[2,3,2,1]
[2,1,8,6,5,4,7,3]=>[6,5,4,8,1,7,2,3]=>[3,4,5,1,8,2,7,6]=>[3,2,2,1]
[2,1,8,6,5,7,4,3]=>[5,4,8,7,1,6,2,3]=>[4,5,1,2,8,3,7,6]=>[2,3,2,1]
[2,1,8,7,5,6,4,3]=>[5,8,7,6,1,4,2,3]=>[4,1,2,3,8,5,7,6]=>[1,4,2,1]
[2,3,1,5,8,6,7,4]=>[6,8,1,2,4,7,3,5]=>[3,1,8,7,5,2,6,4]=>[1,2,1,1,2,1]
[2,3,1,7,5,6,4,8]=>[5,7,1,2,6,3,4,8]=>[4,2,8,7,3,6,5,1]=>[1,2,1,2,1,1]
[2,3,1,8,5,6,7,4]=>[5,6,8,1,2,7,3,4]=>[4,3,1,8,7,2,6,5]=>[1,1,2,1,2,1]
[2,3,1,8,6,7,5,4]=>[5,8,7,1,2,6,3,4]=>[4,1,2,8,7,3,6,5]=>[1,3,1,2,1]
[2,3,4,1,8,6,7,5]=>[6,8,1,2,3,7,4,5]=>[3,1,8,7,6,2,5,4]=>[1,2,1,1,2,1]
[2,3,4,5,8,6,7,1]=>[6,8,1,2,3,4,7,5]=>[3,1,8,7,6,5,2,4]=>[1,2,1,1,1,2]
[2,3,4,7,5,6,1,8]=>[5,7,1,2,3,6,4,8]=>[4,2,8,7,6,3,5,1]=>[1,2,1,1,2,1]
[2,3,4,7,5,6,8,1]=>[5,6,1,2,3,4,8,7]=>[4,3,8,7,6,5,1,2]=>[1,2,1,1,1,2]
[2,3,4,8,5,6,7,1]=>[5,6,8,1,2,3,7,4]=>[4,3,1,8,7,6,2,5]=>[1,1,2,1,1,2]
[2,3,4,8,5,7,6,1]=>[8,5,7,1,2,3,6,4]=>[1,4,2,8,7,6,3,5]=>[2,2,1,1,2]
[2,3,4,8,6,5,7,1]=>[6,5,8,1,2,3,7,4]=>[3,4,1,8,7,6,2,5]=>[2,2,1,1,2]
[2,3,4,8,6,7,5,1]=>[5,8,7,1,2,3,6,4]=>[4,1,2,8,7,6,3,5]=>[1,3,1,1,2]
[2,3,5,4,8,6,7,1]=>[3,6,8,1,2,4,7,5]=>[6,3,1,8,7,5,2,4]=>[1,1,2,1,1,2]
[2,3,6,4,5,1,7,8]=>[4,6,1,2,5,3,7,8]=>[5,3,8,7,4,6,2,1]=>[1,2,1,2,1,1]
[2,3,6,4,5,1,8,7]=>[4,5,1,2,3,8,6,7]=>[5,4,8,7,6,1,3,2]=>[1,2,1,1,2,1]
[2,3,6,4,5,7,8,1]=>[4,5,1,2,3,6,8,7]=>[5,4,8,7,6,3,1,2]=>[1,2,1,1,1,2]
[2,3,6,4,5,8,7,1]=>[8,4,1,2,3,5,7,6]=>[1,5,8,7,6,4,2,3]=>[3,1,1,1,2]
[2,3,7,4,5,6,8,1]=>[4,5,6,1,2,3,8,7]=>[5,4,3,8,7,6,1,2]=>[1,1,2,1,1,2]
[2,3,8,4,5,6,7,1]=>[4,5,6,8,1,2,7,3]=>[5,4,3,1,8,7,2,6]=>[1,1,1,2,1,2]
[2,3,7,4,6,5,8,1]=>[6,4,5,1,2,3,8,7]=>[3,5,4,8,7,6,1,2]=>[2,2,1,1,2]
[2,3,8,4,6,7,5,1]=>[5,8,4,7,1,2,6,3]=>[4,1,5,2,8,7,3,6]=>[1,2,2,1,2]
[2,3,7,5,4,6,8,1]=>[5,4,6,1,2,3,8,7]=>[4,5,3,8,7,6,1,2]=>[2,2,1,1,2]
[2,3,8,5,4,6,7,1]=>[5,4,6,8,1,2,7,3]=>[4,5,3,1,8,7,2,6]=>[2,1,2,1,2]
[2,3,7,5,6,4,1,8]=>[4,7,6,1,2,5,3,8]=>[5,2,3,8,7,4,6,1]=>[1,3,1,2,1]
[2,3,7,5,6,4,8,1]=>[4,6,5,1,2,3,8,7]=>[5,3,4,8,7,6,1,2]=>[1,3,1,1,2]
[2,3,8,5,6,4,7,1]=>[4,6,5,8,1,2,7,3]=>[5,3,4,1,8,7,2,6]=>[1,2,2,1,2]
[2,3,8,5,6,7,4,1]=>[4,5,8,7,1,2,6,3]=>[5,4,1,2,8,7,3,6]=>[1,1,3,1,2]
[2,3,8,5,7,6,4,1]=>[8,4,7,6,1,2,5,3]=>[1,5,2,3,8,7,4,6]=>[2,3,1,2]
[2,3,8,6,5,4,7,1]=>[6,5,4,8,1,2,7,3]=>[3,4,5,1,8,7,2,6]=>[3,2,1,2]
[2,4,3,1,8,6,7,5]=>[2,6,8,1,3,7,4,5]=>[7,3,1,8,6,2,5,4]=>[1,1,2,1,2,1]
[2,4,3,5,8,6,7,1]=>[2,6,8,1,3,4,7,5]=>[7,3,1,8,6,5,2,4]=>[1,1,2,1,1,2]
[2,4,3,7,5,6,8,1]=>[2,5,6,1,3,4,8,7]=>[7,4,3,8,6,5,1,2]=>[1,1,2,1,1,2]
[2,4,3,8,5,6,7,1]=>[2,5,6,8,1,3,7,4]=>[7,4,3,1,8,6,2,5]=>[1,1,1,2,1,2]
[2,4,3,8,5,7,6,1]=>[8,2,5,7,1,3,6,4]=>[1,7,4,2,8,6,3,5]=>[2,1,2,1,2]
[2,4,3,8,6,5,7,1]=>[6,2,5,8,1,3,7,4]=>[3,7,4,1,8,6,2,5]=>[2,1,2,1,2]
[2,4,3,8,6,7,5,1]=>[5,8,2,7,1,3,6,4]=>[4,1,7,2,8,6,3,5]=>[1,2,2,1,2]
[2,5,3,4,1,8,7,6]=>[8,3,1,2,4,7,5,6]=>[1,6,8,7,5,2,4,3]=>[3,1,1,2,1]
[2,5,3,4,6,7,1,8]=>[3,4,1,2,5,7,6,8]=>[6,5,8,7,4,2,3,1]=>[1,2,1,1,2,1]
[2,5,3,4,6,7,8,1]=>[3,4,1,2,5,6,8,7]=>[6,5,8,7,4,3,1,2]=>[1,2,1,1,1,2]
[2,5,3,4,6,8,7,1]=>[8,3,1,2,4,5,7,6]=>[1,6,8,7,5,4,2,3]=>[3,1,1,1,2]
[2,5,3,4,8,6,7,1]=>[6,2,8,1,3,4,7,5]=>[3,7,1,8,6,5,2,4]=>[2,2,1,1,2]
[2,6,3,4,5,1,7,8]=>[3,4,6,1,5,2,7,8]=>[6,5,3,8,4,7,2,1]=>[1,1,2,2,1,1]
[2,6,3,4,5,7,8,1]=>[3,4,5,1,2,6,8,7]=>[6,5,4,8,7,3,1,2]=>[1,1,2,1,1,2]
[2,6,3,4,5,8,7,1]=>[8,3,4,1,2,5,7,6]=>[1,6,5,8,7,4,2,3]=>[2,2,1,1,2]
[2,7,3,4,5,6,1,8]=>[3,4,5,7,1,6,2,8]=>[6,5,4,2,8,3,7,1]=>[1,1,1,2,2,1]
[2,8,3,4,5,6,7,1]=>[3,4,5,6,8,1,7,2]=>[6,5,4,3,1,8,2,7]=>[1,1,1,1,2,2]
[2,8,3,4,5,7,6,1]=>[8,3,4,5,7,1,6,2]=>[1,6,5,4,2,8,3,7]=>[2,1,1,2,2]
[2,6,3,5,4,1,7,8]=>[6,3,5,1,4,2,7,8]=>[3,6,4,8,5,7,2,1]=>[2,2,2,1,1]
[2,6,3,5,4,1,8,7]=>[5,3,4,1,2,8,6,7]=>[4,6,5,8,7,1,3,2]=>[2,2,1,2,1]
[2,6,3,5,4,7,8,1]=>[5,3,4,1,2,6,8,7]=>[4,6,5,8,7,3,1,2]=>[2,2,1,1,2]
[2,6,3,5,4,8,7,1]=>[4,8,3,1,2,5,7,6]=>[5,1,6,8,7,4,2,3]=>[1,3,1,1,2]
[2,7,3,5,4,6,8,1]=>[5,3,4,6,1,2,8,7]=>[4,6,5,3,8,7,1,2]=>[2,1,2,1,2]
[2,7,3,5,6,4,8,1]=>[4,6,3,5,1,2,8,7]=>[5,3,6,4,8,7,1,2]=>[1,2,2,1,2]
[2,8,3,5,6,7,4,1]=>[4,5,8,3,7,1,6,2]=>[5,4,1,6,2,8,3,7]=>[1,1,2,2,2]
[2,8,3,5,7,6,4,1]=>[8,4,7,3,6,1,5,2]=>[1,5,2,6,3,8,4,7]=>[2,2,2,2]
[2,8,3,7,5,6,4,1]=>[5,8,7,3,6,1,4,2]=>[4,1,2,6,3,8,5,7]=>[1,3,2,2]
[2,8,3,7,6,5,4,1]=>[8,7,6,3,5,1,4,2]=>[1,2,3,6,4,8,5,7]=>[4,2,2]
[2,5,4,3,8,6,7,1]=>[3,2,6,8,1,4,7,5]=>[6,7,3,1,8,5,2,4]=>[2,1,2,1,2]
[2,6,4,3,5,8,7,1]=>[3,8,4,1,2,5,7,6]=>[6,1,5,8,7,4,2,3]=>[1,3,1,1,2]
[2,7,4,3,5,6,8,1]=>[4,3,5,6,1,2,8,7]=>[5,6,4,3,8,7,1,2]=>[2,1,2,1,2]
[2,8,4,3,5,6,7,1]=>[4,3,5,6,8,1,7,2]=>[5,6,4,3,1,8,2,7]=>[2,1,1,2,2]
[2,7,4,3,6,5,8,1]=>[3,6,4,5,1,2,8,7]=>[6,3,5,4,8,7,1,2]=>[1,2,2,1,2]
[2,8,4,3,6,7,5,1]=>[3,5,8,4,7,1,6,2]=>[6,4,1,5,2,8,3,7]=>[1,1,2,2,2]
[2,8,4,3,7,6,5,1]=>[8,3,7,4,6,1,5,2]=>[1,6,2,5,3,8,4,7]=>[2,2,2,2]
[2,6,4,5,3,1,8,7]=>[3,5,4,1,2,8,6,7]=>[6,4,5,8,7,1,3,2]=>[1,3,1,2,1]
[2,6,4,5,3,7,8,1]=>[3,5,4,1,2,6,8,7]=>[6,4,5,8,7,3,1,2]=>[1,3,1,1,2]
[2,7,4,5,6,3,1,8]=>[3,4,7,6,1,5,2,8]=>[6,5,2,3,8,4,7,1]=>[1,1,3,2,1]
[2,7,4,5,6,3,8,1]=>[3,4,6,5,1,2,8,7]=>[6,5,3,4,8,7,1,2]=>[1,1,3,1,2]
[2,8,4,5,6,3,7,1]=>[3,4,6,5,8,1,7,2]=>[6,5,3,4,1,8,2,7]=>[1,1,2,2,2]
[2,8,4,5,6,7,3,1]=>[3,4,5,8,7,1,6,2]=>[6,5,4,1,2,8,3,7]=>[1,1,1,3,2]
[2,7,4,6,5,3,8,1]=>[6,3,5,4,1,2,8,7]=>[3,6,4,5,8,7,1,2]=>[2,3,1,2]
[2,8,4,6,5,3,7,1]=>[6,3,5,4,8,1,7,2]=>[3,6,4,5,1,8,2,7]=>[2,2,2,2]
[2,8,4,7,6,5,3,1]=>[8,7,3,6,5,1,4,2]=>[1,2,6,3,4,8,5,7]=>[3,3,2]
[2,7,5,4,3,6,8,1]=>[5,4,3,6,1,2,8,7]=>[4,5,6,3,8,7,1,2]=>[3,2,1,2]
[2,8,5,4,3,6,7,1]=>[5,4,3,6,8,1,7,2]=>[4,5,6,3,1,8,2,7]=>[3,1,2,2]
[2,8,5,4,3,7,6,1]=>[4,3,8,5,7,1,6,2]=>[5,6,1,4,2,8,3,7]=>[2,2,2,2]
[2,8,5,4,6,7,3,1]=>[4,3,5,8,7,1,6,2]=>[5,6,4,1,2,8,3,7]=>[2,1,3,2]
[2,8,5,4,7,6,3,1]=>[3,8,4,7,6,1,5,2]=>[6,1,5,2,3,8,4,7]=>[1,2,3,2]
[2,7,6,4,5,3,8,1]=>[4,6,5,3,1,2,8,7]=>[5,3,4,6,8,7,1,2]=>[1,4,1,2]
[2,8,7,4,5,6,3,1]=>[4,5,8,7,6,1,3,2]=>[5,4,1,2,3,8,6,7]=>[1,1,4,2]
[2,8,7,4,6,5,3,1]=>[8,4,7,6,5,1,3,2]=>[1,5,2,3,4,8,6,7]=>[2,4,2]
[2,8,7,5,4,6,3,1]=>[5,4,8,7,6,1,3,2]=>[4,5,1,2,3,8,6,7]=>[2,4,2]
[2,8,7,5,6,4,3,1]=>[4,8,7,6,5,1,3,2]=>[5,1,2,3,4,8,6,7]=>[1,5,2]
[3,2,1,4,8,6,7,5]=>[1,6,8,2,7,3,4,5]=>[8,3,1,7,2,6,5,4]=>[1,1,2,2,1,1]
[3,2,1,5,8,6,7,4]=>[1,6,8,2,4,7,3,5]=>[8,3,1,7,5,2,6,4]=>[1,1,2,1,2,1]
[3,2,1,7,5,6,8,4]=>[1,5,6,2,4,8,3,7]=>[8,4,3,7,5,1,6,2]=>[1,1,2,1,2,1]
[3,2,1,8,5,6,7,4]=>[1,5,6,8,2,7,3,4]=>[8,4,3,1,7,2,6,5]=>[1,1,1,2,2,1]
[3,2,1,8,5,7,6,4]=>[8,1,5,7,2,6,3,4]=>[1,8,4,2,7,3,6,5]=>[2,1,2,2,1]
[3,2,1,8,6,5,7,4]=>[6,1,5,8,2,7,3,4]=>[3,8,4,1,7,2,6,5]=>[2,1,2,2,1]
[3,2,1,8,6,7,5,4]=>[5,8,1,7,2,6,3,4]=>[4,1,8,2,7,3,6,5]=>[1,2,2,2,1]
[3,2,4,1,8,6,7,5]=>[1,6,8,2,3,7,4,5]=>[8,3,1,7,6,2,5,4]=>[1,1,2,1,2,1]
[3,2,4,5,8,6,7,1]=>[1,6,8,2,3,4,7,5]=>[8,3,1,7,6,5,2,4]=>[1,1,2,1,1,2]
[3,2,4,7,5,6,8,1]=>[1,5,6,2,3,4,8,7]=>[8,4,3,7,6,5,1,2]=>[1,1,2,1,1,2]
[3,2,4,8,5,6,7,1]=>[1,5,6,8,2,3,7,4]=>[8,4,3,1,7,6,2,5]=>[1,1,1,2,1,2]
[3,2,4,8,6,7,5,1]=>[5,8,1,7,2,3,6,4]=>[4,1,8,2,7,6,3,5]=>[1,2,2,1,2]
[3,2,5,4,8,6,7,1]=>[1,3,6,8,2,4,7,5]=>[8,6,3,1,7,5,2,4]=>[1,1,1,2,1,2]
[3,2,6,4,5,1,7,8]=>[1,4,6,2,5,3,7,8]=>[8,5,3,7,4,6,2,1]=>[1,1,2,2,1,1]
[3,2,7,4,5,6,1,8]=>[1,4,5,7,2,6,3,8]=>[8,5,4,2,7,3,6,1]=>[1,1,1,2,2,1]
[3,2,8,4,5,6,7,1]=>[1,4,5,6,8,2,7,3]=>[8,5,4,3,1,7,2,6]=>[1,1,1,1,2,2]
[3,2,7,4,6,5,1,8]=>[7,1,4,6,2,5,3,8]=>[2,8,5,3,7,4,6,1]=>[2,1,2,2,1]
[3,2,7,4,6,5,8,1]=>[6,1,4,5,2,3,8,7]=>[3,8,5,4,7,6,1,2]=>[2,1,2,1,2]
[3,2,8,4,6,5,7,1]=>[6,1,4,5,8,2,7,3]=>[3,8,5,4,1,7,2,6]=>[2,1,1,2,2]
[3,2,7,5,4,6,1,8]=>[5,1,4,7,2,6,3,8]=>[4,8,5,2,7,3,6,1]=>[2,1,2,2,1]
[3,2,8,5,4,6,7,1]=>[5,1,4,6,8,2,7,3]=>[4,8,5,3,1,7,2,6]=>[2,1,1,2,2]
[3,2,8,5,4,7,6,1]=>[4,8,1,5,7,2,6,3]=>[5,1,8,4,2,7,3,6]=>[1,2,1,2,2]
[3,2,7,5,6,4,1,8]=>[4,7,1,6,2,5,3,8]=>[5,2,8,3,7,4,6,1]=>[1,2,2,2,1]
[3,2,7,5,6,4,8,1]=>[4,6,1,5,2,3,8,7]=>[5,3,8,4,7,6,1,2]=>[1,2,2,1,2]
[3,2,8,5,6,4,7,1]=>[4,6,1,5,8,2,7,3]=>[5,3,8,4,1,7,2,6]=>[1,2,1,2,2]
[3,2,8,5,7,6,4,1]=>[8,4,7,1,6,2,5,3]=>[1,5,2,8,3,7,4,6]=>[2,2,2,2]
[3,2,8,6,5,7,4,1]=>[5,4,8,1,7,2,6,3]=>[4,5,1,8,2,7,3,6]=>[2,2,2,2]
[3,2,8,7,5,6,4,1]=>[5,8,7,1,6,2,4,3]=>[4,1,2,8,3,7,5,6]=>[1,3,2,2]
[4,2,3,1,5,7,6,8]=>[2,3,1,7,4,5,6,8]=>[7,6,8,2,5,4,3,1]=>[1,2,2,1,1,1]
[4,2,3,1,5,7,8,6]=>[2,3,1,6,8,4,5,7]=>[7,6,8,3,1,5,4,2]=>[1,2,1,2,1,1]
[4,2,3,1,5,8,7,6]=>[8,2,1,3,7,4,5,6]=>[1,7,8,6,2,5,4,3]=>[3,1,2,1,1]
[4,2,3,1,6,5,7,8]=>[2,3,1,6,4,5,7,8]=>[7,6,8,3,5,4,2,1]=>[1,2,2,1,1,1]
[4,2,3,1,6,5,8,7]=>[2,3,1,5,8,4,6,7]=>[7,6,8,4,1,5,3,2]=>[1,2,1,2,1,1]
[4,2,3,1,6,7,8,5]=>[2,3,1,5,6,8,4,7]=>[7,6,8,4,3,1,5,2]=>[1,2,1,1,2,1]
[4,2,3,1,6,8,7,5]=>[8,2,1,3,5,7,4,6]=>[1,7,8,6,4,2,5,3]=>[3,1,1,2,1]
[4,2,3,1,7,6,5,8]=>[7,2,1,3,6,4,5,8]=>[2,7,8,6,3,5,4,1]=>[3,1,2,1,1]
[4,2,3,1,7,6,8,5]=>[6,2,1,3,5,8,4,7]=>[3,7,8,6,4,1,5,2]=>[3,1,1,2,1]
[4,2,3,1,8,6,7,5]=>[6,1,8,2,3,7,4,5]=>[3,8,1,7,6,2,5,4]=>[2,2,1,2,1]
[4,2,3,1,8,7,6,5]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[1,3,1,2,1]
[4,2,3,5,1,6,8,7]=>[2,3,1,4,8,5,6,7]=>[7,6,8,5,1,4,3,2]=>[1,2,1,2,1,1]
[4,2,3,5,1,7,8,6]=>[2,3,1,4,6,8,5,7]=>[7,6,8,5,3,1,4,2]=>[1,2,1,1,2,1]
[4,2,3,5,1,8,7,6]=>[8,2,1,3,4,7,5,6]=>[1,7,8,6,5,2,4,3]=>[3,1,1,2,1]
[4,2,3,5,6,1,8,7]=>[2,3,1,4,5,8,6,7]=>[7,6,8,5,4,1,3,2]=>[1,2,1,1,2,1]
[4,2,3,5,6,8,7,1]=>[8,2,1,3,4,5,7,6]=>[1,7,8,6,5,4,2,3]=>[3,1,1,1,2]
[4,2,3,5,7,6,1,8]=>[7,2,1,3,4,6,5,8]=>[2,7,8,6,5,3,4,1]=>[3,1,1,2,1]
[4,2,3,6,5,1,7,8]=>[6,2,1,3,5,4,7,8]=>[3,7,8,6,4,5,2,1]=>[3,1,2,1,1]
[4,2,3,6,5,1,8,7]=>[5,2,1,3,4,8,6,7]=>[4,7,8,6,5,1,3,2]=>[3,1,1,2,1]
[4,2,3,6,5,8,7,1]=>[4,1,8,2,3,5,7,6]=>[5,8,1,7,6,4,2,3]=>[2,2,1,1,2]
[4,2,3,7,5,6,8,1]=>[5,1,6,2,3,4,8,7]=>[4,8,3,7,6,5,1,2]=>[2,2,1,1,2]
[4,2,3,8,5,6,7,1]=>[5,1,6,8,2,3,7,4]=>[4,8,3,1,7,6,2,5]=>[2,1,2,1,2]
[4,2,3,8,5,7,6,1]=>[1,8,5,7,2,3,6,4]=>[8,1,4,2,7,6,3,5]=>[1,2,2,1,2]
[4,2,3,7,6,5,8,1]=>[1,6,5,2,3,4,8,7]=>[8,3,4,7,6,5,1,2]=>[1,3,1,1,2]
[4,2,3,8,6,7,5,1]=>[1,5,8,7,2,3,6,4]=>[8,4,1,2,7,6,3,5]=>[1,1,3,1,2]
[4,2,3,8,7,6,5,1]=>[8,1,7,6,2,3,5,4]=>[1,8,2,3,7,6,4,5]=>[2,3,1,2]
[5,2,3,4,1,6,8,7]=>[2,3,4,1,8,5,6,7]=>[7,6,5,8,1,4,3,2]=>[1,1,2,2,1,1]
[5,2,3,4,1,7,8,6]=>[2,3,4,1,6,8,5,7]=>[7,6,5,8,3,1,4,2]=>[1,1,2,1,2,1]
[5,2,3,4,1,8,7,6]=>[8,2,3,1,4,7,5,6]=>[1,7,6,8,5,2,4,3]=>[2,2,1,2,1]
[5,2,3,4,6,1,8,7]=>[2,3,4,1,5,8,6,7]=>[7,6,5,8,4,1,3,2]=>[1,1,2,1,2,1]
[5,2,3,4,7,6,1,8]=>[7,2,3,1,4,6,5,8]=>[2,7,6,8,5,3,4,1]=>[2,2,1,2,1]
[5,2,3,4,8,6,7,1]=>[6,8,2,1,3,4,7,5]=>[3,1,7,8,6,5,2,4]=>[1,3,1,1,2]
[5,2,3,4,8,7,6,1]=>[8,7,2,1,3,4,6,5]=>[1,2,7,8,6,5,3,4]=>[4,1,1,2]
[6,2,3,4,5,1,8,7]=>[2,3,4,5,1,8,6,7]=>[7,6,5,4,8,1,3,2]=>[1,1,1,2,2,1]
[6,2,3,4,5,8,7,1]=>[8,2,3,4,1,5,7,6]=>[1,7,6,5,8,4,2,3]=>[2,1,2,1,2]
[8,2,3,4,5,7,6,1]=>[8,2,3,4,5,7,6,1]=>[1,7,6,5,4,2,3,8]=>[2,1,1,1,3]
[7,2,3,4,6,5,1,8]=>[7,2,3,4,6,5,1,8]=>[2,7,6,5,3,4,8,1]=>[2,1,1,3,1]
[8,2,3,4,7,6,5,1]=>[8,7,2,3,4,6,5,1]=>[1,2,7,6,5,3,4,8]=>[3,1,1,3]
[6,2,3,5,4,1,7,8]=>[6,2,3,5,4,1,7,8]=>[3,7,6,4,5,8,2,1]=>[2,1,3,1,1]
[6,2,3,5,4,1,8,7]=>[5,2,3,4,1,8,6,7]=>[4,7,6,5,8,1,3,2]=>[2,1,2,2,1]
[6,2,3,5,4,7,1,8]=>[5,2,3,4,1,7,6,8]=>[4,7,6,5,8,2,3,1]=>[2,1,2,2,1]
[7,2,3,5,4,6,1,8]=>[5,2,3,4,7,6,1,8]=>[4,7,6,5,2,3,8,1]=>[2,1,1,3,1]
[8,2,3,5,4,6,7,1]=>[5,2,3,4,6,8,7,1]=>[4,7,6,5,3,1,2,8]=>[2,1,1,1,3]
[8,2,3,5,4,7,6,1]=>[4,8,2,3,5,7,6,1]=>[5,1,7,6,4,2,3,8]=>[1,2,1,1,3]
[7,2,3,5,6,4,1,8]=>[4,7,2,3,6,5,1,8]=>[5,2,7,6,3,4,8,1]=>[1,2,1,3,1]
[8,2,3,5,6,7,4,1]=>[4,5,8,2,3,7,6,1]=>[5,4,1,7,6,2,3,8]=>[1,1,2,1,3]
[8,2,3,5,7,6,4,1]=>[8,4,7,2,3,6,5,1]=>[1,5,2,7,6,3,4,8]=>[2,2,1,3]
[7,2,3,6,5,4,1,8]=>[7,6,2,3,5,4,1,8]=>[2,3,7,6,4,5,8,1]=>[3,1,3,1]
[8,2,3,6,5,4,7,1]=>[6,5,2,3,4,8,7,1]=>[3,4,7,6,5,1,2,8]=>[3,1,1,3]
[8,2,3,7,6,5,4,1]=>[8,7,6,2,3,5,4,1]=>[1,2,3,7,6,4,5,8]=>[4,1,3]
[5,2,4,3,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[4,7,5,6,8,3,2,1]=>[2,3,1,1,1]
[5,2,4,3,1,6,8,7]=>[4,2,3,1,8,5,6,7]=>[5,7,6,8,1,4,3,2]=>[2,2,2,1,1]
[5,2,4,3,1,7,6,8]=>[4,2,3,1,7,5,6,8]=>[5,7,6,8,2,4,3,1]=>[2,2,2,1,1]
[5,2,4,3,1,8,7,6]=>[3,8,2,1,4,7,5,6]=>[6,1,7,8,5,2,4,3]=>[1,3,1,2,1]
[5,2,4,3,6,1,7,8]=>[4,2,3,1,6,5,7,8]=>[5,7,6,8,3,4,2,1]=>[2,2,2,1,1]
[5,2,4,3,6,1,8,7]=>[4,2,3,1,5,8,6,7]=>[5,7,6,8,4,1,3,2]=>[2,2,1,2,1]
[5,2,4,3,6,7,1,8]=>[4,2,3,1,5,7,6,8]=>[5,7,6,8,4,2,3,1]=>[2,2,1,2,1]
[5,2,4,3,7,6,1,8]=>[3,7,2,1,4,6,5,8]=>[6,2,7,8,5,3,4,1]=>[1,3,1,2,1]
[5,2,4,3,7,6,8,1]=>[3,6,2,1,4,5,8,7]=>[6,3,7,8,5,4,1,2]=>[1,3,1,1,2]
[5,2,4,3,8,7,6,1]=>[8,3,1,7,2,4,6,5]=>[1,6,8,2,7,5,3,4]=>[3,2,1,2]
[6,2,4,3,5,1,8,7]=>[4,2,3,5,1,8,6,7]=>[5,7,6,4,8,1,3,2]=>[2,1,2,2,1]
[7,2,4,3,6,5,1,8]=>[3,7,2,4,6,5,1,8]=>[6,2,7,5,3,4,8,1]=>[1,2,1,3,1]
[7,2,4,3,6,5,8,1]=>[3,6,2,4,5,1,8,7]=>[6,3,7,5,4,8,1,2]=>[1,2,1,2,2]
[8,2,4,3,6,5,7,1]=>[3,6,2,4,5,8,7,1]=>[6,3,7,5,4,1,2,8]=>[1,2,1,1,3]
[8,2,4,3,6,7,5,1]=>[3,5,8,2,4,7,6,1]=>[6,4,1,7,5,2,3,8]=>[1,1,2,1,3]
[8,2,4,3,7,6,5,1]=>[8,3,7,2,4,6,5,1]=>[1,6,2,7,5,3,4,8]=>[2,2,1,3]
[6,2,4,5,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>[6,3,7,4,5,8,2,1]=>[1,2,3,1,1]
[6,2,4,5,3,1,8,7]=>[3,5,2,4,1,8,6,7]=>[6,4,7,5,8,1,3,2]=>[1,2,2,2,1]
[6,2,4,5,3,8,7,1]=>[3,4,8,2,1,5,7,6]=>[6,5,1,7,8,4,2,3]=>[1,1,3,1,2]
[7,2,4,5,3,6,1,8]=>[3,5,2,4,7,6,1,8]=>[6,4,7,5,2,3,8,1]=>[1,2,1,3,1]
[7,2,4,5,3,6,8,1]=>[3,5,2,4,6,1,8,7]=>[6,4,7,5,3,8,1,2]=>[1,2,1,2,2]
[8,2,4,5,3,7,6,1]=>[3,4,8,2,5,7,6,1]=>[6,5,1,7,4,2,3,8]=>[1,1,2,1,3]
[8,2,4,5,6,3,7,1]=>[3,4,6,2,5,8,7,1]=>[6,5,3,7,4,1,2,8]=>[1,1,2,1,3]
[8,2,4,5,6,7,3,1]=>[3,4,5,8,2,7,6,1]=>[6,5,4,1,7,2,3,8]=>[1,1,1,2,3]
[8,2,4,5,7,6,3,1]=>[8,3,4,7,2,6,5,1]=>[1,6,5,2,7,3,4,8]=>[2,1,2,3]
[7,2,4,6,5,3,1,8]=>[7,3,6,2,5,4,1,8]=>[2,6,3,7,4,5,8,1]=>[2,2,3,1]
[7,2,4,6,5,3,8,1]=>[6,3,5,2,4,1,8,7]=>[3,6,4,7,5,8,1,2]=>[2,2,2,2]
[8,2,4,7,5,6,3,1]=>[5,8,3,7,2,6,4,1]=>[4,1,6,2,7,3,5,8]=>[1,2,2,3]
[8,2,4,7,6,5,3,1]=>[8,7,3,6,2,5,4,1]=>[1,2,6,3,7,4,5,8]=>[3,2,3]
[6,2,5,4,3,1,7,8]=>[6,5,2,4,3,1,7,8]=>[3,4,7,5,6,8,2,1]=>[3,3,1,1]
[6,2,5,4,3,1,8,7]=>[5,4,2,3,1,8,6,7]=>[4,5,7,6,8,1,3,2]=>[3,2,2,1]
[6,2,5,4,3,7,1,8]=>[5,4,2,3,1,7,6,8]=>[4,5,7,6,8,2,3,1]=>[3,2,2,1]
[6,2,5,4,3,7,8,1]=>[5,4,2,3,1,6,8,7]=>[4,5,7,6,8,3,1,2]=>[3,2,1,2]
[7,2,5,4,3,6,1,8]=>[5,4,2,3,7,6,1,8]=>[4,5,7,6,2,3,8,1]=>[3,1,3,1]
[8,2,5,4,3,7,6,1]=>[4,3,8,2,5,7,6,1]=>[5,6,1,7,4,2,3,8]=>[2,2,1,3]
[7,2,5,4,6,3,8,1]=>[4,3,6,2,5,1,8,7]=>[5,6,3,7,4,8,1,2]=>[2,2,2,2]
[7,2,6,4,5,3,1,8]=>[4,7,6,2,5,3,1,8]=>[5,2,3,7,4,6,8,1]=>[1,3,3,1]
[7,2,6,4,5,3,8,1]=>[4,6,5,2,3,1,8,7]=>[5,3,4,7,6,8,1,2]=>[1,3,2,2]
[8,2,6,4,5,3,7,1]=>[4,6,5,2,3,8,7,1]=>[5,3,4,7,6,1,2,8]=>[1,3,1,3]
[8,2,6,4,5,7,3,1]=>[4,5,3,8,2,7,6,1]=>[5,4,6,1,7,2,3,8]=>[1,2,2,3]
[8,2,7,4,5,6,3,1]=>[4,5,8,7,2,6,3,1]=>[5,4,1,2,7,3,6,8]=>[1,1,3,3]
[8,2,7,4,6,5,3,1]=>[8,4,7,6,2,5,3,1]=>[1,5,2,3,7,4,6,8]=>[2,3,3]
[7,2,6,5,4,3,1,8]=>[7,6,5,2,4,3,1,8]=>[2,3,4,7,5,6,8,1]=>[4,3,1]
[7,2,6,5,4,3,8,1]=>[6,5,4,2,3,1,8,7]=>[3,4,5,7,6,8,1,2]=>[4,2,2]
[8,2,6,5,4,7,3,1]=>[5,4,3,8,2,7,6,1]=>[4,5,6,1,7,2,3,8]=>[3,2,3]
[8,2,7,5,4,6,3,1]=>[5,4,8,7,2,6,3,1]=>[4,5,1,2,7,3,6,8]=>[2,3,3]
[8,2,7,5,6,4,3,1]=>[4,8,7,6,2,5,3,1]=>[5,1,2,3,7,4,6,8]=>[1,4,3]
[8,2,7,6,5,4,3,1]=>[8,7,6,5,2,4,3,1]=>[1,2,3,4,7,5,6,8]=>[5,3]
[4,3,2,1,8,6,7,5]=>[2,1,6,8,3,7,4,5]=>[7,8,3,1,6,2,5,4]=>[2,1,2,2,1]
[4,3,2,7,5,6,8,1]=>[2,1,5,6,3,4,8,7]=>[7,8,4,3,6,5,1,2]=>[2,1,2,1,2]
[4,3,2,8,5,6,7,1]=>[2,1,5,6,8,3,7,4]=>[7,8,4,3,1,6,2,5]=>[2,1,1,2,2]
[4,3,2,8,5,7,6,1]=>[1,8,2,5,7,3,6,4]=>[8,1,7,4,2,6,3,5]=>[1,2,1,2,2]
[4,3,2,8,6,7,5,1]=>[1,5,8,2,7,3,6,4]=>[8,4,1,7,2,6,3,5]=>[1,1,2,2,2]
[5,3,2,4,1,6,8,7]=>[3,2,4,1,8,5,6,7]=>[6,7,5,8,1,4,3,2]=>[2,2,2,1,1]
[5,3,2,4,1,7,6,8]=>[3,2,4,1,7,5,6,8]=>[6,7,5,8,2,4,3,1]=>[2,2,2,1,1]
[5,3,2,4,1,8,7,6]=>[2,8,3,1,4,7,5,6]=>[7,1,6,8,5,2,4,3]=>[1,3,1,2,1]
[5,3,2,4,6,1,8,7]=>[3,2,4,1,5,8,6,7]=>[6,7,5,8,4,1,3,2]=>[2,2,1,2,1]
[5,3,2,4,7,6,1,8]=>[2,7,3,1,4,6,5,8]=>[7,2,6,8,5,3,4,1]=>[1,3,1,2,1]
[8,3,2,4,6,5,7,1]=>[2,6,3,4,5,8,7,1]=>[7,3,6,5,4,1,2,8]=>[1,2,1,1,3]
[8,3,2,4,6,7,5,1]=>[2,5,8,3,4,7,6,1]=>[7,4,1,6,5,2,3,8]=>[1,1,2,1,3]
[8,3,2,4,7,6,5,1]=>[8,2,7,3,4,6,5,1]=>[1,7,2,6,5,3,4,8]=>[2,2,1,3]
[6,3,2,5,4,1,7,8]=>[2,6,3,5,4,1,7,8]=>[7,3,6,4,5,8,2,1]=>[1,2,3,1,1]
[6,3,2,5,4,1,8,7]=>[2,5,3,4,1,8,6,7]=>[7,4,6,5,8,1,3,2]=>[1,2,2,2,1]
[6,3,2,5,4,7,1,8]=>[2,5,3,4,1,7,6,8]=>[7,4,6,5,8,2,3,1]=>[1,2,2,2,1]
[6,3,2,5,4,7,8,1]=>[2,5,3,4,1,6,8,7]=>[7,4,6,5,8,3,1,2]=>[1,2,2,1,2]
[6,3,2,5,4,8,7,1]=>[2,4,8,3,1,5,7,6]=>[7,5,1,6,8,4,2,3]=>[1,1,3,1,2]
[8,3,2,5,4,7,6,1]=>[2,4,8,3,5,7,6,1]=>[7,5,1,6,4,2,3,8]=>[1,1,2,1,3]
[7,3,2,5,6,4,8,1]=>[2,4,6,3,5,1,8,7]=>[7,5,3,6,4,8,1,2]=>[1,1,2,2,2]
[8,3,2,5,6,4,7,1]=>[2,4,6,3,5,8,7,1]=>[7,5,3,6,4,1,2,8]=>[1,1,2,1,3]
[8,3,2,5,6,7,4,1]=>[2,4,5,8,3,7,6,1]=>[7,5,4,1,6,2,3,8]=>[1,1,1,2,3]
[8,3,2,5,7,6,4,1]=>[8,2,4,7,3,6,5,1]=>[1,7,5,2,6,3,4,8]=>[2,1,2,3]
[8,3,2,6,5,7,4,1]=>[5,2,4,8,3,7,6,1]=>[4,7,5,1,6,2,3,8]=>[2,1,2,3]
[8,3,2,7,5,6,4,1]=>[5,8,2,7,3,6,4,1]=>[4,1,7,2,6,3,5,8]=>[1,2,2,3]
[8,3,2,7,6,5,4,1]=>[8,7,2,6,3,5,4,1]=>[1,2,7,3,6,4,5,8]=>[3,2,3]
[5,3,4,2,1,6,8,7]=>[2,4,3,1,8,5,6,7]=>[7,5,6,8,1,4,3,2]=>[1,3,2,1,1]
[5,3,4,2,1,7,8,6]=>[2,4,3,1,6,8,5,7]=>[7,5,6,8,3,1,4,2]=>[1,3,1,2,1]
[5,3,4,2,1,8,7,6]=>[2,3,1,8,4,7,5,6]=>[7,6,8,1,5,2,4,3]=>[1,2,2,2,1]
[5,3,4,2,6,1,8,7]=>[2,4,3,1,5,8,6,7]=>[7,5,6,8,4,1,3,2]=>[1,3,1,2,1]
[5,3,4,2,7,6,1,8]=>[2,3,1,7,4,6,5,8]=>[7,6,8,2,5,3,4,1]=>[1,2,2,2,1]
[5,3,4,2,7,6,8,1]=>[2,3,1,6,4,5,8,7]=>[7,6,8,3,5,4,1,2]=>[1,2,2,1,2]
[5,3,4,2,8,6,7,1]=>[2,3,1,6,8,4,7,5]=>[7,6,8,3,1,5,2,4]=>[1,2,1,2,2]
[6,3,4,2,5,1,8,7]=>[2,4,3,5,1,8,6,7]=>[7,5,6,4,8,1,3,2]=>[1,2,2,2,1]
[7,3,4,2,6,5,8,1]=>[2,3,6,4,5,1,8,7]=>[7,6,3,5,4,8,1,2]=>[1,1,2,2,2]
[8,3,4,2,6,5,7,1]=>[2,3,6,4,5,8,7,1]=>[7,6,3,5,4,1,2,8]=>[1,1,2,1,3]
[6,3,4,5,2,1,8,7]=>[2,3,5,4,1,8,6,7]=>[7,6,4,5,8,1,3,2]=>[1,1,3,2,1]
[8,3,4,5,2,7,6,1]=>[2,3,4,8,5,7,6,1]=>[7,6,5,1,4,2,3,8]=>[1,1,1,2,3]
[8,3,4,5,7,6,2,1]=>[8,2,3,4,7,6,5,1]=>[1,7,6,5,2,3,4,8]=>[2,1,1,4]
[7,3,4,6,5,2,1,8]=>[7,2,3,6,5,4,1,8]=>[2,7,6,3,4,5,8,1]=>[2,1,4,1]
[8,3,4,7,6,5,2,1]=>[8,7,2,3,6,5,4,1]=>[1,2,7,6,3,4,5,8]=>[3,1,4]
[6,3,5,4,2,1,8,7]=>[5,2,4,3,1,8,6,7]=>[4,7,5,6,8,1,3,2]=>[2,3,2,1]
[6,3,5,4,2,7,1,8]=>[5,2,4,3,1,7,6,8]=>[4,7,5,6,8,2,3,1]=>[2,3,2,1]
[6,3,5,4,2,7,8,1]=>[5,2,4,3,1,6,8,7]=>[4,7,5,6,8,3,1,2]=>[2,3,1,2]
[6,3,5,4,2,8,7,1]=>[4,2,3,1,8,5,7,6]=>[5,7,6,8,1,4,2,3]=>[2,2,2,2]
[7,3,5,4,2,6,1,8]=>[5,2,4,3,7,6,1,8]=>[4,7,5,6,2,3,8,1]=>[2,2,3,1]
[8,3,5,4,2,6,7,1]=>[5,2,4,3,6,8,7,1]=>[4,7,5,6,3,1,2,8]=>[2,2,1,3]
[8,3,5,4,2,7,6,1]=>[4,2,3,8,5,7,6,1]=>[5,7,6,1,4,2,3,8]=>[2,1,2,3]
[7,3,5,4,6,2,8,1]=>[4,2,3,6,5,1,8,7]=>[5,7,6,3,4,8,1,2]=>[2,1,3,2]
[8,3,5,4,6,7,2,1]=>[4,2,3,5,8,7,6,1]=>[5,7,6,4,1,2,3,8]=>[2,1,1,4]
[8,3,5,4,7,6,2,1]=>[3,8,2,4,7,6,5,1]=>[6,1,7,5,2,3,4,8]=>[1,2,1,4]
[7,3,6,4,5,2,1,8]=>[4,7,2,6,5,3,1,8]=>[5,2,7,3,4,6,8,1]=>[1,2,4,1]
[7,3,6,4,5,2,8,1]=>[4,6,2,5,3,1,8,7]=>[5,3,7,4,6,8,1,2]=>[1,2,3,2]
[8,3,6,4,5,2,7,1]=>[4,6,2,5,3,8,7,1]=>[5,3,7,4,6,1,2,8]=>[1,2,2,3]
[8,3,6,4,5,7,2,1]=>[4,5,2,3,8,7,6,1]=>[5,4,7,6,1,2,3,8]=>[1,2,1,4]
[8,3,7,4,5,6,2,1]=>[4,5,8,2,7,6,3,1]=>[5,4,1,7,2,3,6,8]=>[1,1,2,4]
[8,3,7,4,6,5,2,1]=>[8,4,7,2,6,5,3,1]=>[1,5,2,7,3,4,6,8]=>[2,2,4]
[7,3,6,5,4,2,1,8]=>[7,6,2,5,4,3,1,8]=>[2,3,7,4,5,6,8,1]=>[3,4,1]
[7,3,6,5,4,2,8,1]=>[6,5,2,4,3,1,8,7]=>[3,4,7,5,6,8,1,2]=>[3,3,2]
[8,3,6,5,4,2,7,1]=>[6,5,2,4,3,8,7,1]=>[3,4,7,5,6,1,2,8]=>[3,2,3]
[8,3,6,5,4,7,2,1]=>[5,4,2,3,8,7,6,1]=>[4,5,7,6,1,2,3,8]=>[3,1,4]
[8,3,7,5,4,6,2,1]=>[5,4,8,2,7,6,3,1]=>[4,5,1,7,2,3,6,8]=>[2,2,4]
[8,3,7,5,6,4,2,1]=>[4,8,7,2,6,5,3,1]=>[5,1,2,7,3,4,6,8]=>[1,3,4]
[8,3,7,6,5,4,2,1]=>[8,7,6,2,5,4,3,1]=>[1,2,3,7,4,5,6,8]=>[4,4]
[6,4,3,2,5,1,8,7]=>[4,3,2,5,1,8,6,7]=>[5,6,7,4,8,1,3,2]=>[3,2,2,1]
[7,4,3,2,6,5,1,8]=>[3,2,7,4,6,5,1,8]=>[6,7,2,5,3,4,8,1]=>[2,2,3,1]
[7,4,3,2,6,5,8,1]=>[3,2,6,4,5,1,8,7]=>[6,7,3,5,4,8,1,2]=>[2,2,2,2]
[8,4,3,2,6,5,7,1]=>[3,2,6,4,5,8,7,1]=>[6,7,3,5,4,1,2,8]=>[2,2,1,3]
[8,4,3,2,6,7,5,1]=>[3,2,5,8,4,7,6,1]=>[6,7,4,1,5,2,3,8]=>[2,1,2,3]
[8,4,3,2,7,6,5,1]=>[2,8,3,7,4,6,5,1]=>[7,1,6,2,5,3,4,8]=>[1,2,2,3]
[6,4,3,5,2,1,8,7]=>[3,2,5,4,1,8,6,7]=>[6,7,4,5,8,1,3,2]=>[2,3,2,1]
[8,4,3,5,7,6,2,1]=>[2,8,3,4,7,6,5,1]=>[7,1,6,5,2,3,4,8]=>[1,2,1,4]
[7,4,3,6,5,2,1,8]=>[2,7,3,6,5,4,1,8]=>[7,2,6,3,4,5,8,1]=>[1,2,4,1]
[7,4,3,6,5,2,8,1]=>[2,6,3,5,4,1,8,7]=>[7,3,6,4,5,8,1,2]=>[1,2,3,2]
[8,4,3,7,5,6,2,1]=>[2,5,8,3,7,6,4,1]=>[7,4,1,6,2,3,5,8]=>[1,1,2,4]
[8,4,3,7,6,5,2,1]=>[8,2,7,3,6,5,4,1]=>[1,7,2,6,3,4,5,8]=>[2,2,4]
[6,5,3,4,2,1,8,7]=>[3,5,4,2,1,8,6,7]=>[6,4,5,7,8,1,3,2]=>[1,4,2,1]
[8,5,3,4,2,7,6,1]=>[3,4,2,8,5,7,6,1]=>[6,5,7,1,4,2,3,8]=>[1,2,2,3]
[8,5,3,4,7,6,2,1]=>[8,3,2,4,7,6,5,1]=>[1,6,7,5,2,3,4,8]=>[3,1,4]
[8,7,3,4,6,5,2,1]=>[8,3,4,7,6,5,2,1]=>[1,6,5,2,3,4,7,8]=>[2,1,5]
[7,6,3,5,4,2,1,8]=>[7,3,6,5,4,2,1,8]=>[2,6,3,4,5,7,8,1]=>[2,5,1]
[8,6,3,5,4,7,2,1]=>[5,3,4,2,8,7,6,1]=>[4,6,5,7,1,2,3,8]=>[2,2,4]
[8,7,3,5,4,6,2,1]=>[5,3,4,8,7,6,2,1]=>[4,6,5,1,2,3,7,8]=>[2,1,5]
[8,7,3,5,6,4,2,1]=>[4,8,3,7,6,5,2,1]=>[5,1,6,2,3,4,7,8]=>[1,2,5]
[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[1,2,6,3,4,5,7,8]=>[3,5]
[8,5,4,3,2,7,6,1]=>[4,3,2,8,5,7,6,1]=>[5,6,7,1,4,2,3,8]=>[3,2,3]
[8,5,4,3,7,6,2,1]=>[3,2,8,4,7,6,5,1]=>[6,7,1,5,2,3,4,8]=>[2,2,4]
[8,7,4,3,6,5,2,1]=>[3,8,4,7,6,5,2,1]=>[6,1,5,2,3,4,7,8]=>[1,2,5]
[8,7,4,6,5,3,2,1]=>[8,3,7,6,5,4,2,1]=>[1,6,2,3,4,5,7,8]=>[2,6]
[2,4,1,3,6,5,8,7]=>[5,1,2,8,3,4,6,7]=>[4,8,7,1,6,5,3,2]=>[2,1,2,1,1,1]
[2,1,4,6,3,5,8,7]=>[8,1,3,5,2,4,6,7]=>[1,8,6,4,7,5,3,2]=>[2,1,2,1,1,1]
[2,4,1,6,3,5,8,7]=>[2,8,1,5,3,4,6,7]=>[7,1,8,4,6,5,3,2]=>[1,2,2,1,1,1]
[2,4,6,1,3,5,8,7]=>[2,8,1,4,5,3,6,7]=>[7,1,8,5,4,6,3,2]=>[1,2,1,2,1,1]
[2,1,4,3,6,8,5,7]=>[1,3,5,7,8,2,4,6]=>[8,6,4,2,1,7,5,3]=>[1,1,1,1,2,1,1]
[2,4,1,3,6,8,5,7]=>[5,1,2,7,8,3,4,6]=>[4,8,7,2,1,6,5,3]=>[2,1,1,2,1,1]
[2,1,4,6,3,8,5,7]=>[7,1,3,4,8,2,5,6]=>[2,8,6,5,1,7,4,3]=>[2,1,1,2,1,1]
[2,4,1,6,3,8,5,7]=>[2,7,1,4,8,3,5,6]=>[7,2,8,5,1,6,4,3]=>[1,2,1,2,1,1]
[2,4,6,1,3,8,5,7]=>[2,7,8,1,4,3,5,6]=>[7,2,1,8,5,6,4,3]=>[1,1,2,2,1,1]
[2,1,4,6,8,3,5,7]=>[6,1,3,4,7,8,2,5]=>[3,8,6,5,2,1,7,4]=>[2,1,1,1,2,1]
[2,4,1,6,8,3,5,7]=>[2,6,1,4,7,8,3,5]=>[7,3,8,5,2,1,6,4]=>[1,2,1,1,2,1]
[2,4,6,1,8,3,5,7]=>[2,6,7,1,3,8,4,5]=>[7,3,2,8,6,1,5,4]=>[1,1,2,1,2,1]
[2,4,6,8,1,3,5,7]=>[2,5,6,1,3,7,8,4]=>[7,4,3,8,6,2,1,5]=>[1,1,2,1,1,2]
[2,4,1,3,6,5,7,8]=>[6,1,3,2,4,5,7,8]=>[3,8,6,7,5,4,2,1]=>[2,2,1,1,1,1]
[2,1,4,6,3,5,7,8]=>[1,3,5,6,2,4,7,8]=>[8,6,4,3,7,5,2,1]=>[1,1,1,2,1,1,1]
[2,4,1,6,3,5,7,8]=>[5,1,2,6,3,4,7,8]=>[4,8,7,3,6,5,2,1]=>[2,1,2,1,1,1]
[2,4,6,1,3,5,7,8]=>[4,1,2,5,6,3,7,8]=>[5,8,7,4,3,6,2,1]=>[2,1,1,2,1,1]
[2,1,4,6,3,7,5,8]=>[7,1,3,5,2,4,6,8]=>[2,8,6,4,7,5,3,1]=>[2,1,2,1,1,1]
[2,4,1,6,3,7,5,8]=>[2,7,1,5,3,4,6,8]=>[7,2,8,4,6,5,3,1]=>[1,2,2,1,1,1]
[2,4,6,1,3,7,5,8]=>[2,7,1,4,5,3,6,8]=>[7,2,8,5,4,6,3,1]=>[1,2,1,2,1,1]
[2,1,4,6,7,3,5,8]=>[6,1,3,4,7,2,5,8]=>[3,8,6,5,2,7,4,1]=>[2,1,1,2,1,1]
[2,4,1,6,7,3,5,8]=>[2,6,1,4,7,3,5,8]=>[7,3,8,5,2,6,4,1]=>[1,2,1,2,1,1]
[2,4,6,7,1,3,5,8]=>[2,5,6,1,3,7,4,8]=>[7,4,3,8,6,2,5,1]=>[1,1,2,1,2,1]
[2,4,1,3,6,7,8,5]=>[5,1,2,6,8,3,4,7]=>[4,8,7,3,1,6,5,2]=>[2,1,1,2,1,1]
[2,1,4,6,3,7,8,5]=>[6,1,3,4,8,2,5,7]=>[3,8,6,5,1,7,4,2]=>[2,1,1,2,1,1]
[2,4,1,6,3,7,8,5]=>[2,6,1,4,8,3,5,7]=>[7,3,8,5,1,6,4,2]=>[1,2,1,2,1,1]
[2,4,6,1,3,7,8,5]=>[2,6,8,1,4,3,5,7]=>[7,3,1,8,5,6,4,2]=>[1,1,2,2,1,1]
[2,1,4,6,7,3,8,5]=>[4,8,1,3,6,2,5,7]=>[5,1,8,6,3,7,4,2]=>[1,2,1,2,1,1]
[2,4,1,6,7,3,8,5]=>[2,4,8,1,6,3,5,7]=>[7,5,1,8,3,6,4,2]=>[1,1,2,2,1,1]
[2,4,6,1,7,3,8,5]=>[8,2,6,1,4,3,5,7]=>[1,7,3,8,5,6,4,2]=>[2,2,2,1,1]
[2,4,6,7,1,3,8,5]=>[8,2,5,1,3,6,4,7]=>[1,7,4,8,6,3,5,2]=>[2,2,1,2,1]
[2,1,4,6,7,8,3,5]=>[4,7,1,3,5,8,2,6]=>[5,2,8,6,4,1,7,3]=>[1,2,1,1,2,1]
[2,4,1,6,7,8,3,5]=>[2,4,7,1,5,8,3,6]=>[7,5,2,8,4,1,6,3]=>[1,1,2,1,2,1]
[2,4,6,1,7,8,3,5]=>[7,2,5,1,3,8,4,6]=>[2,7,4,8,6,1,5,3]=>[2,2,1,2,1]
[2,4,6,7,8,1,3,5]=>[6,2,3,7,1,4,8,5]=>[3,7,6,2,8,5,1,4]=>[2,1,2,1,2]
[2,1,4,3,7,5,8,6]=>[8,1,3,6,2,4,5,7]=>[1,8,6,3,7,5,4,2]=>[2,1,2,1,1,1]
[2,4,1,3,7,5,8,6]=>[2,8,1,6,3,4,5,7]=>[7,1,8,3,6,5,4,2]=>[1,2,2,1,1,1]
[2,4,1,7,3,5,8,6]=>[2,8,1,5,6,3,4,7]=>[7,1,8,4,3,6,5,2]=>[1,2,1,2,1,1]
[2,4,7,1,3,5,8,6]=>[2,8,1,4,5,6,3,7]=>[7,1,8,5,4,3,6,2]=>[1,2,1,1,2,1]
[2,1,4,3,7,8,5,6]=>[7,1,3,5,8,2,4,6]=>[2,8,6,4,1,7,5,3]=>[2,1,1,2,1,1]
[2,4,1,3,7,8,5,6]=>[2,7,1,5,8,3,4,6]=>[7,2,8,4,1,6,5,3]=>[1,2,1,2,1,1]
[2,4,1,7,3,8,5,6]=>[2,7,8,1,5,3,4,6]=>[7,2,1,8,4,6,5,3]=>[1,1,2,2,1,1]
[2,4,7,1,3,8,5,6]=>[2,7,8,1,4,5,3,6]=>[7,2,1,8,5,4,6,3]=>[1,1,2,1,2,1]
[2,1,4,7,8,3,5,6]=>[6,7,1,3,4,8,2,5]=>[3,2,8,6,5,1,7,4]=>[1,2,1,1,2,1]
[2,4,1,7,8,3,5,6]=>[2,6,7,1,4,8,3,5]=>[7,3,2,8,5,1,6,4]=>[1,1,2,1,2,1]
[2,4,7,1,8,3,5,6]=>[2,6,7,8,1,4,3,5]=>[7,3,2,1,8,5,6,4]=>[1,1,1,2,2,1]
[2,4,7,8,1,3,5,6]=>[2,5,6,7,1,3,8,4]=>[7,4,3,2,8,6,1,5]=>[1,1,1,2,1,2]
[2,4,1,5,3,7,6,8]=>[4,1,2,7,3,5,6,8]=>[5,8,7,2,6,4,3,1]=>[2,1,2,1,1,1]
[2,4,5,1,3,7,6,8]=>[2,7,1,4,3,5,6,8]=>[7,2,8,5,6,4,3,1]=>[1,2,2,1,1,1]
[2,4,5,1,7,3,6,8]=>[2,6,1,3,7,4,5,8]=>[7,3,8,6,2,5,4,1]=>[1,2,1,2,1,1]
[2,4,1,3,5,7,8,6]=>[6,1,2,8,3,4,5,7]=>[3,8,7,1,6,5,4,2]=>[2,1,2,1,1,1]
[2,4,1,5,3,7,8,6]=>[4,1,2,6,8,3,5,7]=>[5,8,7,3,1,6,4,2]=>[2,1,1,2,1,1]
[2,4,5,1,3,7,8,6]=>[2,6,1,3,8,4,5,7]=>[7,3,8,6,1,5,4,2]=>[1,2,1,2,1,1]
[2,1,4,5,7,3,8,6]=>[8,1,3,4,6,2,5,7]=>[1,8,6,5,3,7,4,2]=>[2,1,1,2,1,1]
[2,4,1,5,7,3,8,6]=>[2,8,1,4,6,3,5,7]=>[7,1,8,5,3,6,4,2]=>[1,2,1,2,1,1]
[2,1,4,5,7,8,3,6]=>[7,1,3,4,5,8,2,6]=>[2,8,6,5,4,1,7,3]=>[2,1,1,1,2,1]
[2,4,5,1,7,8,3,6]=>[2,3,7,1,5,8,4,6]=>[7,6,2,8,4,1,5,3]=>[1,1,2,1,2,1]
[2,4,5,7,1,8,3,6]=>[2,3,7,8,1,5,4,6]=>[7,6,2,1,8,4,5,3]=>[1,1,1,2,2,1]
[2,4,5,7,8,1,3,6]=>[2,3,6,7,1,4,8,5]=>[7,6,3,2,8,5,1,4]=>[1,1,1,2,1,2]
[2,1,4,3,8,5,6,7]=>[1,3,6,7,8,2,4,5]=>[8,6,3,2,1,7,5,4]=>[1,1,1,1,2,1,1]
[2,4,1,3,8,5,6,7]=>[6,1,2,7,8,3,4,5]=>[3,8,7,2,1,6,5,4]=>[2,1,1,2,1,1]
[2,1,4,8,3,5,6,7]=>[1,3,5,6,7,8,2,4]=>[8,6,4,3,2,1,7,5]=>[1,1,1,1,1,2,1]
[2,4,1,8,3,5,6,7]=>[5,1,2,6,7,8,3,4]=>[4,8,7,3,2,1,6,5]=>[2,1,1,1,2,1]
[2,4,8,1,3,5,6,7]=>[4,1,2,5,6,7,8,3]=>[5,8,7,4,3,2,1,6]=>[2,1,1,1,1,2]
[2,1,4,3,5,8,6,7]=>[1,3,7,8,2,4,5,6]=>[8,6,2,1,7,5,4,3]=>[1,1,1,2,1,1,1]
[2,4,1,5,3,8,6,7]=>[4,1,2,7,8,3,5,6]=>[5,8,7,2,1,6,4,3]=>[2,1,1,2,1,1]
[2,1,4,5,8,3,6,7]=>[1,3,4,6,7,8,2,5]=>[8,6,5,3,2,1,7,4]=>[1,1,1,1,1,2,1]
[2,4,1,5,8,3,6,7]=>[4,1,2,6,7,8,3,5]=>[5,8,7,3,2,1,6,4]=>[2,1,1,1,2,1]
[2,4,5,1,8,3,6,7]=>[2,6,1,3,7,8,4,5]=>[7,3,8,6,2,1,5,4]=>[1,2,1,1,2,1]
[2,4,5,8,1,3,6,7]=>[2,5,1,3,6,7,8,4]=>[7,4,8,6,3,2,1,5]=>[1,2,1,1,1,2]
[2,4,1,5,3,6,8,7]=>[4,1,2,8,3,5,6,7]=>[5,8,7,1,6,4,3,2]=>[2,1,2,1,1,1]
[2,4,1,5,6,3,8,7]=>[4,1,2,5,8,3,6,7]=>[5,8,7,4,1,6,3,2]=>[2,1,1,2,1,1]
[2,4,5,1,6,3,8,7]=>[2,5,1,3,8,4,6,7]=>[7,4,8,6,1,5,3,2]=>[1,2,1,2,1,1]
[2,4,5,6,1,3,8,7]=>[2,3,8,1,5,4,6,7]=>[7,6,1,8,4,5,3,2]=>[1,1,2,2,1,1]
[2,1,4,5,6,8,3,7]=>[1,3,4,5,7,8,2,6]=>[8,6,5,4,2,1,7,3]=>[1,1,1,1,1,2,1]
[2,4,1,5,6,8,3,7]=>[4,1,2,5,7,8,3,6]=>[5,8,7,4,2,1,6,3]=>[2,1,1,1,2,1]
[2,4,5,1,6,8,3,7]=>[2,5,1,3,7,8,4,6]=>[7,4,8,6,2,1,5,3]=>[1,2,1,1,2,1]
[2,4,5,6,1,8,3,7]=>[2,3,7,1,4,8,5,6]=>[7,6,2,8,5,1,4,3]=>[1,1,2,1,2,1]
[2,4,5,6,8,1,3,7]=>[2,3,6,1,4,7,8,5]=>[7,6,3,8,5,2,1,4]=>[1,1,2,1,1,2]
[2,4,1,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[8,6,5,7,4,3,2,1]=>[1,1,2,1,1,1,1]
[2,4,1,5,3,6,7,8]=>[5,1,3,2,4,6,7,8]=>[4,8,6,7,5,3,2,1]=>[2,2,1,1,1,1]
[2,4,5,1,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>[5,8,7,4,6,3,2,1]=>[2,1,2,1,1,1]
[2,4,1,5,6,3,7,8]=>[4,1,2,6,3,5,7,8]=>[5,8,7,3,6,4,2,1]=>[2,1,2,1,1,1]
[2,4,5,1,6,3,7,8]=>[2,6,1,4,3,5,7,8]=>[7,3,8,5,6,4,2,1]=>[1,2,2,1,1,1]
[2,4,5,6,1,3,7,8]=>[2,5,1,3,6,4,7,8]=>[7,4,8,6,3,5,2,1]=>[1,2,1,2,1,1]
[2,4,1,5,6,7,3,8]=>[4,1,2,5,7,3,6,8]=>[5,8,7,4,2,6,3,1]=>[2,1,1,2,1,1]
[2,4,5,1,6,7,3,8]=>[2,5,1,3,7,4,6,8]=>[7,4,8,6,2,5,3,1]=>[1,2,1,2,1,1]
[2,4,5,6,1,7,3,8]=>[2,3,7,1,5,4,6,8]=>[7,6,2,8,4,5,3,1]=>[1,1,2,2,1,1]
[2,4,5,6,7,1,3,8]=>[2,3,6,1,4,7,5,8]=>[7,6,3,8,5,2,4,1]=>[1,1,2,1,2,1]
[2,4,1,5,6,7,8,3]=>[4,1,2,5,6,8,3,7]=>[5,8,7,4,3,1,6,2]=>[2,1,1,1,2,1]
[2,4,5,1,6,7,8,3]=>[2,5,1,3,6,8,4,7]=>[7,4,8,6,3,1,5,2]=>[1,2,1,1,2,1]
[2,4,5,6,1,7,8,3]=>[2,3,6,1,4,8,5,7]=>[7,6,3,8,5,1,4,2]=>[1,1,2,1,2,1]
[2,4,5,6,7,1,8,3]=>[2,3,4,8,1,6,5,7]=>[7,6,5,1,8,3,4,2]=>[1,1,1,2,2,1]
[2,4,5,6,7,8,1,3]=>[2,3,4,7,1,5,8,6]=>[7,6,5,2,8,4,1,3]=>[1,1,1,2,1,2]
[2,1,5,3,6,4,8,7]=>[5,1,3,8,2,4,6,7]=>[4,8,6,1,7,5,3,2]=>[2,1,2,1,1,1]
[2,5,1,3,6,4,8,7]=>[5,8,1,3,2,4,6,7]=>[4,1,8,6,7,5,3,2]=>[1,2,2,1,1,1]
[2,1,5,6,3,4,8,7]=>[3,8,1,5,2,4,6,7]=>[6,1,8,4,7,5,3,2]=>[1,2,2,1,1,1]
[2,5,1,6,3,4,8,7]=>[8,5,1,3,2,4,6,7]=>[1,4,8,6,7,5,3,2]=>[3,2,1,1,1]
[2,5,6,1,3,4,8,7]=>[8,4,1,2,5,3,6,7]=>[1,5,8,7,4,6,3,2]=>[3,1,2,1,1]
[2,1,5,3,6,8,4,7]=>[5,1,3,7,8,2,4,6]=>[4,8,6,2,1,7,5,3]=>[2,1,1,2,1,1]
[2,5,1,3,6,8,4,7]=>[5,7,1,2,8,3,4,6]=>[4,2,8,7,1,6,5,3]=>[1,2,1,2,1,1]
[2,5,1,6,3,8,4,7]=>[7,4,1,2,8,3,5,6]=>[2,5,8,7,1,6,4,3]=>[3,1,2,1,1]
[2,5,6,1,3,8,4,7]=>[7,2,8,1,4,3,5,6]=>[2,7,1,8,5,6,4,3]=>[2,2,2,1,1]
[2,1,5,6,8,3,4,7]=>[3,6,1,4,7,8,2,5]=>[6,3,8,5,2,1,7,4]=>[1,2,1,1,2,1]
[2,5,1,6,8,3,4,7]=>[6,4,1,2,7,8,3,5]=>[3,5,8,7,2,1,6,4]=>[3,1,1,2,1]
[2,5,6,8,1,3,4,7]=>[5,2,6,1,3,7,8,4]=>[4,7,3,8,6,2,1,5]=>[2,2,1,1,2]
[2,5,1,3,6,4,7,8]=>[6,1,3,4,2,5,7,8]=>[3,8,6,5,7,4,2,1]=>[2,1,2,1,1,1]
[2,1,5,6,3,4,7,8]=>[5,1,3,6,2,4,7,8]=>[4,8,6,3,7,5,2,1]=>[2,1,2,1,1,1]
[2,5,1,6,3,4,7,8]=>[5,6,1,3,2,4,7,8]=>[4,3,8,6,7,5,2,1]=>[1,2,2,1,1,1]
[2,1,5,3,6,7,4,8]=>[5,1,3,7,2,4,6,8]=>[4,8,6,2,7,5,3,1]=>[2,1,2,1,1,1]
[2,1,5,6,3,7,4,8]=>[3,7,1,5,2,4,6,8]=>[6,2,8,4,7,5,3,1]=>[1,2,2,1,1,1]
[2,5,1,6,3,7,4,8]=>[7,5,1,3,2,4,6,8]=>[2,4,8,6,7,5,3,1]=>[3,2,1,1,1]
[2,5,6,1,3,7,4,8]=>[7,4,1,2,5,3,6,8]=>[2,5,8,7,4,6,3,1]=>[3,1,2,1,1]
[2,1,5,6,7,3,4,8]=>[3,6,1,4,7,2,5,8]=>[6,3,8,5,2,7,4,1]=>[1,2,1,2,1,1]
[2,5,1,6,7,3,4,8]=>[6,4,1,2,7,3,5,8]=>[3,5,8,7,2,6,4,1]=>[3,1,2,1,1]
[2,5,6,1,7,3,4,8]=>[6,2,7,1,4,3,5,8]=>[3,7,2,8,5,6,4,1]=>[2,2,2,1,1]
[2,5,1,3,6,7,8,4]=>[5,6,1,2,8,3,4,7]=>[4,3,8,7,1,6,5,2]=>[1,2,1,2,1,1]
[2,5,1,6,3,7,8,4]=>[6,4,1,2,8,3,5,7]=>[3,5,8,7,1,6,4,2]=>[3,1,2,1,1]
[2,5,6,1,3,7,8,4]=>[6,2,8,1,4,3,5,7]=>[3,7,1,8,5,6,4,2]=>[2,2,2,1,1]
[2,1,5,6,7,3,8,4]=>[3,4,8,1,6,2,5,7]=>[6,5,1,8,3,7,4,2]=>[1,1,2,2,1,1]
[2,5,1,6,7,3,8,4]=>[4,2,8,1,6,3,5,7]=>[5,7,1,8,3,6,4,2]=>[2,2,2,1,1]
[2,5,6,7,1,3,8,4]=>[2,8,5,1,3,6,4,7]=>[7,1,4,8,6,3,5,2]=>[1,3,1,2,1]
[2,1,5,6,7,8,3,4]=>[3,4,7,1,5,8,2,6]=>[6,5,2,8,4,1,7,3]=>[1,1,2,1,2,1]
[2,5,1,6,7,8,3,4]=>[4,2,7,1,5,8,3,6]=>[5,7,2,8,4,1,6,3]=>[2,2,1,2,1]
[2,5,6,1,7,8,3,4]=>[2,7,5,1,3,8,4,6]=>[7,2,4,8,6,1,5,3]=>[1,3,1,2,1]
[2,5,6,7,1,8,3,4]=>[2,7,3,8,1,5,4,6]=>[7,2,6,1,8,4,5,3]=>[1,2,2,2,1]
[2,5,6,7,8,1,3,4]=>[2,6,3,7,1,4,8,5]=>[7,3,6,2,8,5,1,4]=>[1,2,2,1,2]
[2,1,5,3,7,4,8,6]=>[3,8,1,6,2,4,5,7]=>[6,1,8,3,7,5,4,2]=>[1,2,2,1,1,1]
[2,5,1,7,3,4,8,6]=>[8,5,1,2,6,3,4,7]=>[1,4,8,7,3,6,5,2]=>[3,1,2,1,1]
[2,5,7,1,3,4,8,6]=>[8,4,1,2,5,6,3,7]=>[1,5,8,7,4,3,6,2]=>[3,1,1,2,1]
[2,1,5,3,7,8,4,6]=>[3,7,1,5,8,2,4,6]=>[6,2,8,4,1,7,5,3]=>[1,2,1,2,1,1]
[2,5,1,3,7,8,4,6]=>[7,5,1,2,8,3,4,6]=>[2,4,8,7,1,6,5,3]=>[3,1,2,1,1]
[2,1,5,7,3,8,4,6]=>[3,7,8,1,5,2,4,6]=>[6,2,1,8,4,7,5,3]=>[1,1,2,2,1,1]
[2,5,1,7,3,8,4,6]=>[7,2,8,1,5,3,4,6]=>[2,7,1,8,4,6,5,3]=>[2,2,2,1,1]
[2,5,7,1,3,8,4,6]=>[7,2,8,1,4,5,3,6]=>[2,7,1,8,5,4,6,3]=>[2,2,1,2,1]
[2,1,5,7,8,3,4,6]=>[3,6,7,1,4,8,2,5]=>[6,3,2,8,5,1,7,4]=>[1,1,2,1,2,1]
[2,5,1,7,8,3,4,6]=>[6,2,7,1,4,8,3,5]=>[3,7,2,8,5,1,6,4]=>[2,2,1,2,1]
[2,5,7,1,8,3,4,6]=>[6,2,7,8,1,4,3,5]=>[3,7,2,1,8,5,6,4]=>[2,1,2,2,1]
[2,5,7,8,1,3,4,6]=>[5,2,6,7,1,3,8,4]=>[4,7,3,2,8,6,1,5]=>[2,1,2,1,2]
[2,1,5,7,3,4,6,8]=>[5,1,3,6,7,2,4,8]=>[4,8,6,3,2,7,5,1]=>[2,1,1,2,1,1]
[2,3,5,1,4,7,6,8]=>[7,1,2,4,3,5,6,8]=>[2,8,7,5,6,4,3,1]=>[2,1,2,1,1,1]
[2,3,5,7,1,4,6,8]=>[5,1,2,3,6,7,4,8]=>[4,8,7,6,3,2,5,1]=>[2,1,1,1,2,1]
[2,3,5,7,1,4,8,6]=>[3,8,1,2,5,6,4,7]=>[6,1,8,7,4,3,5,2]=>[1,2,1,1,2,1]
[2,3,1,5,7,8,4,6]=>[7,1,2,4,5,8,3,6]=>[2,8,7,5,4,1,6,3]=>[2,1,1,1,2,1]
[2,3,5,7,1,8,4,6]=>[3,7,8,1,2,5,4,6]=>[6,2,1,8,7,4,5,3]=>[1,1,2,1,2,1]
[2,3,5,7,8,1,4,6]=>[3,6,7,1,2,4,8,5]=>[6,3,2,8,7,5,1,4]=>[1,1,2,1,1,2]
[2,1,5,3,8,4,6,7]=>[6,1,3,7,8,2,4,5]=>[3,8,6,2,1,7,5,4]=>[2,1,1,2,1,1]
[2,5,1,3,8,4,6,7]=>[6,7,1,2,8,3,4,5]=>[3,2,8,7,1,6,5,4]=>[1,2,1,2,1,1]
[2,1,5,8,3,4,6,7]=>[5,1,3,6,7,8,2,4]=>[4,8,6,3,2,1,7,5]=>[2,1,1,1,2,1]
[2,5,1,8,3,4,6,7]=>[5,6,1,2,7,8,3,4]=>[4,3,8,7,2,1,6,5]=>[1,2,1,1,2,1]
[2,5,8,1,3,4,6,7]=>[4,5,1,2,6,7,8,3]=>[5,4,8,7,3,2,1,6]=>[1,2,1,1,1,2]
[2,3,5,1,4,8,6,7]=>[7,1,2,3,8,4,5,6]=>[2,8,7,6,1,5,4,3]=>[2,1,1,2,1,1]
[2,1,3,5,8,4,6,7]=>[1,4,6,7,8,2,3,5]=>[8,5,3,2,1,7,6,4]=>[1,1,1,1,2,1,1]
[2,3,5,1,8,4,6,7]=>[6,1,2,3,7,8,4,5]=>[3,8,7,6,2,1,5,4]=>[2,1,1,1,2,1]
[2,3,5,8,1,4,6,7]=>[5,1,2,3,6,7,8,4]=>[4,8,7,6,3,2,1,5]=>[2,1,1,1,1,2]
[2,3,5,1,6,4,8,7]=>[5,1,2,3,8,4,6,7]=>[4,8,7,6,1,5,3,2]=>[2,1,1,2,1,1]
[2,3,5,6,1,4,8,7]=>[3,8,1,2,5,4,6,7]=>[6,1,8,7,4,5,3,2]=>[1,2,1,2,1,1]
[2,1,3,5,6,8,4,7]=>[1,4,5,7,8,2,3,6]=>[8,5,4,2,1,7,6,3]=>[1,1,1,1,2,1,1]
[2,3,1,5,6,8,4,7]=>[1,2,4,5,7,8,3,6]=>[8,7,5,4,2,1,6,3]=>[1,1,1,1,1,2,1]
[2,3,5,1,6,8,4,7]=>[5,1,2,3,7,8,4,6]=>[4,8,7,6,2,1,5,3]=>[2,1,1,1,2,1]
[2,3,5,6,1,8,4,7]=>[3,7,1,2,4,8,5,6]=>[6,2,8,7,5,1,4,3]=>[1,2,1,1,2,1]
[2,3,5,6,8,1,4,7]=>[3,6,1,2,4,7,8,5]=>[6,3,8,7,5,2,1,4]=>[1,2,1,1,1,2]
[2,1,5,3,4,6,7,8]=>[1,4,5,2,3,6,7,8]=>[8,5,4,7,6,3,2,1]=>[1,1,2,1,1,1,1]
[2,5,1,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>[8,6,5,4,7,3,2,1]=>[1,1,1,2,1,1,1]
[2,3,5,1,4,6,7,8]=>[1,2,4,5,3,6,7,8]=>[8,7,5,4,6,3,2,1]=>[1,1,1,2,1,1,1]
[2,3,5,1,6,4,7,8]=>[6,1,2,4,3,5,7,8]=>[3,8,7,5,6,4,2,1]=>[2,1,2,1,1,1]
[2,3,5,6,1,4,7,8]=>[5,1,2,3,6,4,7,8]=>[4,8,7,6,3,5,2,1]=>[2,1,1,2,1,1]
[2,3,5,6,1,7,4,8]=>[3,7,1,2,5,4,6,8]=>[6,2,8,7,4,5,3,1]=>[1,2,1,2,1,1]
[2,3,5,6,7,1,4,8]=>[3,6,1,2,4,7,5,8]=>[6,3,8,7,5,2,4,1]=>[1,2,1,1,2,1]
[2,3,5,1,6,7,8,4]=>[5,1,2,3,6,8,4,7]=>[4,8,7,6,3,1,5,2]=>[2,1,1,1,2,1]
[2,3,5,6,1,7,8,4]=>[3,6,1,2,4,8,5,7]=>[6,3,8,7,5,1,4,2]=>[1,2,1,1,2,1]
[2,3,5,6,7,1,8,4]=>[3,4,8,1,2,6,5,7]=>[6,5,1,8,7,3,4,2]=>[1,1,2,1,2,1]
[2,3,5,6,7,8,1,4]=>[3,4,7,1,2,5,8,6]=>[6,5,2,8,7,4,1,3]=>[1,1,2,1,1,2]
[2,1,6,3,7,4,8,5]=>[8,6,1,4,2,3,5,7]=>[1,3,8,5,7,6,4,2]=>[3,2,1,1,1]
[2,6,1,3,7,4,8,5]=>[8,6,1,3,4,2,5,7]=>[1,3,8,6,5,7,4,2]=>[3,1,2,1,1]
[2,1,6,7,3,4,8,5]=>[8,5,1,3,6,2,4,7]=>[1,4,8,6,3,7,5,2]=>[3,1,2,1,1]
[2,6,1,7,3,4,8,5]=>[8,5,6,1,3,2,4,7]=>[1,4,3,8,6,7,5,2]=>[2,2,2,1,1]
[2,6,7,1,3,4,8,5]=>[8,4,5,1,2,6,3,7]=>[1,5,4,8,7,3,6,2]=>[2,2,1,2,1]
[2,1,6,3,7,8,4,5]=>[7,5,1,3,8,2,4,6]=>[2,4,8,6,1,7,5,3]=>[3,1,2,1,1]
[2,6,1,3,7,8,4,5]=>[7,5,8,1,3,2,4,6]=>[2,4,1,8,6,7,5,3]=>[2,2,2,1,1]
[2,1,6,7,3,8,4,5]=>[7,3,8,1,5,2,4,6]=>[2,6,1,8,4,7,5,3]=>[2,2,2,1,1]
[2,6,1,7,3,8,4,5]=>[7,8,5,1,3,2,4,6]=>[2,1,4,8,6,7,5,3]=>[1,3,2,1,1]
[2,6,7,1,3,8,4,5]=>[7,8,4,1,2,5,3,6]=>[2,1,5,8,7,4,6,3]=>[1,3,1,2,1]
[2,1,6,7,8,3,4,5]=>[6,3,7,1,4,8,2,5]=>[3,6,2,8,5,1,7,4]=>[2,2,1,2,1]
[2,6,1,7,8,3,4,5]=>[6,7,4,1,2,8,3,5]=>[3,2,5,8,7,1,6,4]=>[1,3,1,2,1]
[2,6,7,1,8,3,4,5]=>[6,7,2,8,1,4,3,5]=>[3,2,7,1,8,5,6,4]=>[1,2,2,2,1]
[2,6,7,8,1,3,4,5]=>[5,6,2,7,1,3,8,4]=>[4,3,7,2,8,6,1,5]=>[1,2,2,1,2]
[2,1,6,3,7,4,5,8]=>[6,7,1,4,2,3,5,8]=>[3,2,8,5,7,6,4,1]=>[1,2,2,1,1,1]
[2,6,1,7,3,4,5,8]=>[5,6,7,1,3,2,4,8]=>[4,3,2,8,6,7,5,1]=>[1,1,2,2,1,1]
[2,6,1,3,4,7,5,8]=>[7,1,3,4,5,2,6,8]=>[2,8,6,5,4,7,3,1]=>[2,1,1,2,1,1]
[2,3,1,6,4,7,5,8]=>[7,1,2,5,3,4,6,8]=>[2,8,7,4,6,5,3,1]=>[2,1,2,1,1,1]
[2,3,6,1,4,7,5,8]=>[7,1,2,4,5,3,6,8]=>[2,8,7,5,4,6,3,1]=>[2,1,1,2,1,1]
[2,3,6,7,1,4,5,8]=>[5,6,1,2,3,7,4,8]=>[4,3,8,7,6,2,5,1]=>[1,2,1,1,2,1]
[2,1,6,3,4,7,8,5]=>[6,8,1,4,2,3,5,7]=>[3,1,8,5,7,6,4,2]=>[1,2,2,1,1,1]
[2,6,1,3,4,7,8,5]=>[6,8,1,3,4,2,5,7]=>[3,1,8,6,5,7,4,2]=>[1,2,1,2,1,1]
[2,3,6,1,4,7,8,5]=>[6,8,1,2,4,3,5,7]=>[3,1,8,7,5,6,4,2]=>[1,2,1,2,1,1]
[2,1,3,6,7,4,8,5]=>[4,8,1,6,2,3,5,7]=>[5,1,8,3,7,6,4,2]=>[1,2,2,1,1,1]
[2,3,6,7,1,4,8,5]=>[8,5,1,2,3,6,4,7]=>[1,4,8,7,6,3,5,2]=>[3,1,1,2,1]
[2,1,3,6,7,8,4,5]=>[4,7,1,5,8,2,3,6]=>[5,2,8,4,1,7,6,3]=>[1,2,1,2,1,1]
[2,3,1,6,7,8,4,5]=>[4,7,1,2,5,8,3,6]=>[5,2,8,7,4,1,6,3]=>[1,2,1,1,2,1]
[2,3,6,1,7,8,4,5]=>[7,5,1,2,3,8,4,6]=>[2,4,8,7,6,1,5,3]=>[3,1,1,2,1]
[2,3,6,7,1,8,4,5]=>[7,3,8,1,2,5,4,6]=>[2,6,1,8,7,4,5,3]=>[2,2,1,2,1]
[2,3,6,7,8,1,4,5]=>[6,3,7,1,2,4,8,5]=>[3,6,2,8,7,5,1,4]=>[2,2,1,1,2]
[2,1,6,3,8,4,5,7]=>[6,7,1,3,8,2,4,5]=>[3,2,8,6,1,7,5,4]=>[1,2,1,2,1,1]
[2,6,1,3,8,4,5,7]=>[6,7,8,1,3,2,4,5]=>[3,2,1,8,6,7,5,4]=>[1,1,2,2,1,1]
[2,1,6,8,3,4,5,7]=>[5,6,1,3,7,8,2,4]=>[4,3,8,6,2,1,7,5]=>[1,2,1,1,2,1]
[2,6,1,8,3,4,5,7]=>[5,6,7,1,2,8,3,4]=>[4,3,2,8,7,1,6,5]=>[1,1,2,1,2,1]
[2,6,8,1,3,4,5,7]=>[4,5,6,1,2,7,8,3]=>[5,4,3,8,7,2,1,6]=>[1,1,2,1,1,2]
[2,1,6,3,4,8,5,7]=>[7,8,1,4,2,3,5,6]=>[2,1,8,5,7,6,4,3]=>[1,2,2,1,1,1]
[2,6,1,3,4,8,5,7]=>[7,8,1,3,4,2,5,6]=>[2,1,8,6,5,7,4,3]=>[1,2,1,2,1,1]
[2,1,3,6,4,8,5,7]=>[7,1,4,8,2,3,5,6]=>[2,8,5,1,7,6,4,3]=>[2,1,2,1,1,1]
[2,3,1,6,4,8,5,7]=>[7,1,2,4,8,3,5,6]=>[2,8,7,5,1,6,4,3]=>[2,1,1,2,1,1]
[2,3,6,1,4,8,5,7]=>[7,8,1,2,4,3,5,6]=>[2,1,8,7,5,6,4,3]=>[1,2,1,2,1,1]
[2,3,1,6,8,4,5,7]=>[6,1,2,4,7,8,3,5]=>[3,8,7,5,2,1,6,4]=>[2,1,1,1,2,1]
[2,3,6,1,8,4,5,7]=>[6,7,1,2,3,8,4,5]=>[3,2,8,7,6,1,5,4]=>[1,2,1,1,2,1]
[2,3,6,8,1,4,5,7]=>[5,6,1,2,3,7,8,4]=>[4,3,8,7,6,2,1,5]=>[1,2,1,1,1,2]
[2,1,6,3,4,5,8,7]=>[8,1,4,5,2,3,6,7]=>[1,8,5,4,7,6,3,2]=>[2,1,2,1,1,1]
[2,6,1,3,4,5,8,7]=>[8,1,3,4,5,2,6,7]=>[1,8,6,5,4,7,3,2]=>[2,1,1,2,1,1]
[2,1,3,6,4,5,8,7]=>[8,1,5,2,3,4,6,7]=>[1,8,4,7,6,5,3,2]=>[2,2,1,1,1,1]
[2,3,6,1,4,5,8,7]=>[8,1,2,4,5,3,6,7]=>[1,8,7,5,4,6,3,2]=>[2,1,1,2,1,1]
[2,3,4,1,6,8,5,7]=>[1,2,3,5,7,8,4,6]=>[8,7,6,4,2,1,5,3]=>[1,1,1,1,1,2,1]
[2,3,4,6,1,8,5,7]=>[7,1,2,3,4,8,5,6]=>[2,8,7,6,5,1,4,3]=>[2,1,1,1,2,1]
[2,3,4,6,8,1,5,7]=>[6,1,2,3,4,7,8,5]=>[3,8,7,6,5,2,1,4]=>[2,1,1,1,1,2]
[2,6,1,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>[8,6,5,4,3,7,2,1]=>[1,1,1,1,2,1,1]
[2,1,3,6,4,5,7,8]=>[1,5,6,2,3,4,7,8]=>[8,4,3,7,6,5,2,1]=>[1,1,2,1,1,1,1]
[2,3,1,6,4,5,7,8]=>[1,2,5,6,3,4,7,8]=>[8,7,4,3,6,5,2,1]=>[1,1,1,2,1,1,1]
[2,3,6,1,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>[8,7,5,4,3,6,2,1]=>[1,1,1,1,2,1,1]
[2,3,4,6,1,5,7,8]=>[1,2,3,5,6,4,7,8]=>[8,7,6,4,3,5,2,1]=>[1,1,1,1,2,1,1]
[2,3,4,6,1,7,5,8]=>[7,1,2,3,5,4,6,8]=>[2,8,7,6,4,5,3,1]=>[2,1,1,2,1,1]
[2,3,4,6,7,1,5,8]=>[6,1,2,3,4,7,5,8]=>[3,8,7,6,5,2,4,1]=>[2,1,1,1,2,1]
[2,3,4,6,1,7,8,5]=>[6,1,2,3,4,8,5,7]=>[3,8,7,6,5,1,4,2]=>[2,1,1,1,2,1]
[2,3,4,6,7,8,1,5]=>[4,7,1,2,3,5,8,6]=>[5,2,8,7,6,4,1,3]=>[1,2,1,1,1,2]
[2,1,7,3,8,4,5,6]=>[6,7,8,1,4,2,3,5]=>[3,2,1,8,5,7,6,4]=>[1,1,2,2,1,1]
[2,7,1,3,8,4,5,6]=>[6,7,8,1,3,4,2,5]=>[3,2,1,8,6,5,7,4]=>[1,1,2,1,2,1]
[2,1,7,8,3,4,5,6]=>[5,6,7,1,3,8,2,4]=>[4,3,2,8,6,1,7,5]=>[1,1,2,1,2,1]
[2,7,1,8,3,4,5,6]=>[5,6,7,8,1,3,2,4]=>[4,3,2,1,8,6,7,5]=>[1,1,1,2,2,1]
[2,7,8,1,3,4,5,6]=>[4,5,6,7,1,2,8,3]=>[5,4,3,2,8,7,1,6]=>[1,1,1,2,1,2]
[2,1,7,3,4,8,5,6]=>[7,8,1,4,5,2,3,6]=>[2,1,8,5,4,7,6,3]=>[1,2,1,2,1,1]
[2,7,1,3,4,8,5,6]=>[7,8,1,3,4,5,2,6]=>[2,1,8,6,5,4,7,3]=>[1,2,1,1,2,1]
[2,1,3,7,4,8,5,6]=>[7,8,1,5,2,3,4,6]=>[2,1,8,4,7,6,5,3]=>[1,2,2,1,1,1]
[2,3,1,7,4,8,5,6]=>[7,8,1,2,5,3,4,6]=>[2,1,8,7,4,6,5,3]=>[1,2,1,2,1,1]
[2,3,7,1,4,8,5,6]=>[7,8,1,2,4,5,3,6]=>[2,1,8,7,5,4,6,3]=>[1,2,1,1,2,1]
[2,1,3,7,8,4,5,6]=>[6,7,1,4,8,2,3,5]=>[3,2,8,5,1,7,6,4]=>[1,2,1,2,1,1]
[2,3,1,7,8,4,5,6]=>[6,7,1,2,4,8,3,5]=>[3,2,8,7,5,1,6,4]=>[1,2,1,1,2,1]
[2,3,7,8,1,4,5,6]=>[5,6,7,1,2,3,8,4]=>[4,3,2,8,7,6,1,5]=>[1,1,2,1,1,2]
[2,1,7,3,4,5,8,6]=>[8,1,4,5,6,2,3,7]=>[1,8,5,4,3,7,6,2]=>[2,1,1,2,1,1]
[2,7,1,3,4,5,8,6]=>[8,1,3,4,5,6,2,7]=>[1,8,6,5,4,3,7,2]=>[2,1,1,1,2,1]
[2,3,1,7,4,5,8,6]=>[8,1,2,5,6,3,4,7]=>[1,8,7,4,3,6,5,2]=>[2,1,1,2,1,1]
[2,3,7,1,4,5,8,6]=>[8,1,2,4,5,6,3,7]=>[1,8,7,5,4,3,6,2]=>[2,1,1,1,2,1]
[2,1,3,4,7,5,8,6]=>[8,1,6,2,3,4,5,7]=>[1,8,3,7,6,5,4,2]=>[2,2,1,1,1,1]
[2,3,4,7,1,5,8,6]=>[8,1,2,3,5,6,4,7]=>[1,8,7,6,4,3,5,2]=>[2,1,1,1,2,1]
[2,1,3,4,7,8,5,6]=>[7,1,5,8,2,3,4,6]=>[2,8,4,1,7,6,5,3]=>[2,1,2,1,1,1]
[2,3,1,4,7,8,5,6]=>[7,1,2,5,8,3,4,6]=>[2,8,7,4,1,6,5,3]=>[2,1,1,2,1,1]
[2,3,4,1,7,8,5,6]=>[7,1,2,3,5,8,4,6]=>[2,8,7,6,4,1,5,3]=>[2,1,1,1,2,1]
[2,3,4,7,1,8,5,6]=>[7,8,1,2,3,5,4,6]=>[2,1,8,7,6,4,5,3]=>[1,2,1,1,2,1]
[2,3,4,7,8,1,5,6]=>[6,7,1,2,3,4,8,5]=>[3,2,8,7,6,5,1,4]=>[1,2,1,1,1,2]
[2,1,7,3,4,5,6,8]=>[1,4,5,6,7,2,3,8]=>[8,5,4,3,2,7,6,1]=>[1,1,1,1,2,1,1]
[2,7,1,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>[8,6,5,4,3,2,7,1]=>[1,1,1,1,1,2,1]
[2,3,7,1,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>[8,7,5,4,3,2,6,1]=>[1,1,1,1,1,2,1]
[2,1,3,4,7,5,6,8]=>[1,6,7,2,3,4,5,8]=>[8,3,2,7,6,5,4,1]=>[1,1,2,1,1,1,1]
[2,3,1,4,7,5,6,8]=>[1,2,6,7,3,4,5,8]=>[8,7,3,2,6,5,4,1]=>[1,1,1,2,1,1,1]
[2,3,4,1,7,5,6,8]=>[1,2,3,6,7,4,5,8]=>[8,7,6,3,2,5,4,1]=>[1,1,1,1,2,1,1]
[2,3,4,7,1,5,6,8]=>[1,2,3,5,6,7,4,8]=>[8,7,6,4,3,2,5,1]=>[1,1,1,1,1,2,1]
[2,3,4,5,7,1,6,8]=>[1,2,3,4,6,7,5,8]=>[8,7,6,5,3,2,4,1]=>[1,1,1,1,1,2,1]
[2,3,4,5,7,1,8,6]=>[8,1,2,3,4,6,5,7]=>[1,8,7,6,5,3,4,2]=>[2,1,1,1,2,1]
[2,3,4,5,7,8,1,6]=>[7,1,2,3,4,5,8,6]=>[2,8,7,6,5,4,1,3]=>[2,1,1,1,1,2]
[2,1,8,3,4,5,6,7]=>[1,4,5,6,7,8,2,3]=>[8,5,4,3,2,1,7,6]=>[1,1,1,1,1,2,1]
[2,8,1,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>[8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,2]
[2,1,3,8,4,5,6,7]=>[1,5,6,7,8,2,3,4]=>[8,4,3,2,1,7,6,5]=>[1,1,1,1,2,1,1]
[2,3,1,8,4,5,6,7]=>[1,2,5,6,7,8,3,4]=>[8,7,4,3,2,1,6,5]=>[1,1,1,1,1,2,1]
[2,3,8,1,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>[8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,2]
[2,1,3,4,8,5,6,7]=>[1,6,7,8,2,3,4,5]=>[8,3,2,1,7,6,5,4]=>[1,1,1,2,1,1,1]
[2,3,1,4,8,5,6,7]=>[1,2,6,7,8,3,4,5]=>[8,7,3,2,1,6,5,4]=>[1,1,1,1,2,1,1]
[2,3,4,1,8,5,6,7]=>[1,2,3,6,7,8,4,5]=>[8,7,6,3,2,1,5,4]=>[1,1,1,1,1,2,1]
[2,3,4,8,1,5,6,7]=>[1,2,3,5,6,7,8,4]=>[8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,2]
[2,1,3,4,5,8,6,7]=>[1,7,8,2,3,4,5,6]=>[8,2,1,7,6,5,4,3]=>[1,1,2,1,1,1,1]
[2,3,1,4,5,8,6,7]=>[1,2,7,8,3,4,5,6]=>[8,7,2,1,6,5,4,3]=>[1,1,1,2,1,1,1]
[2,3,4,5,1,8,6,7]=>[1,2,3,4,7,8,5,6]=>[8,7,6,5,2,1,4,3]=>[1,1,1,1,1,2,1]
[2,3,4,5,8,1,6,7]=>[1,2,3,4,6,7,8,5]=>[8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,2]
[2,3,4,5,6,8,1,7]=>[1,2,3,4,5,7,8,6]=>[8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,2]
[3,1,4,2,6,5,8,7]=>[3,1,5,8,2,4,6,7]=>[6,8,4,1,7,5,3,2]=>[2,1,2,1,1,1]
[3,4,1,2,6,5,8,7]=>[1,5,2,8,3,4,6,7]=>[8,4,7,1,6,5,3,2]=>[1,2,2,1,1,1]
[3,1,4,6,2,5,8,7]=>[1,8,3,5,2,4,6,7]=>[8,1,6,4,7,5,3,2]=>[1,2,2,1,1,1]
[3,4,1,6,2,5,8,7]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[1,1,3,1,1,1]
[3,4,6,1,2,5,8,7]=>[1,2,8,4,5,3,6,7]=>[8,7,1,5,4,6,3,2]=>[1,1,2,2,1,1]
[3,1,4,2,6,8,5,7]=>[3,1,5,7,8,2,4,6]=>[6,8,4,2,1,7,5,3]=>[2,1,1,2,1,1]
[3,4,1,2,6,8,5,7]=>[1,5,2,7,8,3,4,6]=>[8,4,7,2,1,6,5,3]=>[1,2,1,2,1,1]
[3,1,4,6,2,8,5,7]=>[1,7,3,4,8,2,5,6]=>[8,2,6,5,1,7,4,3]=>[1,2,1,2,1,1]
[3,4,1,6,2,8,5,7]=>[1,2,7,4,8,3,5,6]=>[8,7,2,5,1,6,4,3]=>[1,1,2,2,1,1]
[3,1,4,6,8,2,5,7]=>[1,6,3,4,7,8,2,5]=>[8,3,6,5,2,1,7,4]=>[1,2,1,1,2,1]
[3,4,1,6,8,2,5,7]=>[1,2,6,4,7,8,3,5]=>[8,7,3,5,2,1,6,4]=>[1,1,2,1,2,1]
[3,4,6,8,1,2,5,7]=>[1,2,5,6,3,7,8,4]=>[8,7,4,3,6,2,1,5]=>[1,1,1,2,1,2]
[3,1,4,2,6,7,5,8]=>[3,1,5,7,2,4,6,8]=>[6,8,4,2,7,5,3,1]=>[2,1,2,1,1,1]
[3,4,1,2,6,7,5,8]=>[1,5,2,7,3,4,6,8]=>[8,4,7,2,6,5,3,1]=>[1,2,2,1,1,1]
[3,4,1,6,2,7,5,8]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[1,1,3,1,1,1]
[3,4,1,6,7,2,5,8]=>[1,2,6,4,7,3,5,8]=>[8,7,3,5,2,6,4,1]=>[1,1,2,2,1,1]
[3,4,6,7,1,2,5,8]=>[1,2,5,6,3,7,4,8]=>[8,7,4,3,6,2,5,1]=>[1,1,1,2,2,1]
[3,1,4,2,6,7,8,5]=>[3,1,5,6,8,2,4,7]=>[6,8,4,3,1,7,5,2]=>[2,1,1,2,1,1]
[3,4,1,2,6,7,8,5]=>[1,5,2,6,8,3,4,7]=>[8,4,7,3,1,6,5,2]=>[1,2,1,2,1,1]
[3,1,4,6,2,7,8,5]=>[1,6,3,4,8,2,5,7]=>[8,3,6,5,1,7,4,2]=>[1,2,1,2,1,1]
[3,4,1,6,2,7,8,5]=>[1,2,6,4,8,3,5,7]=>[8,7,3,5,1,6,4,2]=>[1,1,2,2,1,1]
[3,4,6,7,1,2,8,5]=>[8,1,2,5,3,6,4,7]=>[1,8,7,4,6,3,5,2]=>[2,1,2,2,1]
[3,1,4,6,7,8,2,5]=>[1,4,7,3,5,8,2,6]=>[8,5,2,6,4,1,7,3]=>[1,1,2,1,2,1]
[3,4,1,6,7,8,2,5]=>[1,2,4,7,5,8,3,6]=>[8,7,5,2,4,1,6,3]=>[1,1,1,2,2,1]
[3,4,6,1,7,8,2,5]=>[7,1,2,5,3,8,4,6]=>[2,8,7,4,6,1,5,3]=>[2,1,2,2,1]
[3,4,6,7,1,8,2,5]=>[7,1,2,3,8,5,4,6]=>[2,8,7,6,1,4,5,3]=>[2,1,1,3,1]
[3,4,6,7,8,1,2,5]=>[6,1,2,3,7,4,8,5]=>[3,8,7,6,2,5,1,4]=>[2,1,1,2,2]
[3,1,4,2,7,5,8,6]=>[1,8,3,6,2,4,5,7]=>[8,1,6,3,7,5,4,2]=>[1,2,2,1,1,1]
[3,4,1,2,7,5,8,6]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[1,1,3,1,1,1]
[3,1,4,7,2,5,8,6]=>[1,8,3,5,6,2,4,7]=>[8,1,6,4,3,7,5,2]=>[1,2,1,2,1,1]
[3,4,1,7,2,5,8,6]=>[1,2,8,5,6,3,4,7]=>[8,7,1,4,3,6,5,2]=>[1,1,2,2,1,1]
[3,1,4,2,7,8,5,6]=>[1,7,3,5,8,2,4,6]=>[8,2,6,4,1,7,5,3]=>[1,2,1,2,1,1]
[3,4,1,2,7,8,5,6]=>[1,2,7,5,8,3,4,6]=>[8,7,2,4,1,6,5,3]=>[1,1,2,2,1,1]
[3,1,4,7,2,8,5,6]=>[1,7,8,3,5,2,4,6]=>[8,2,1,6,4,7,5,3]=>[1,1,2,2,1,1]
[3,4,7,1,8,2,5,6]=>[1,2,6,7,8,4,3,5]=>[8,7,3,2,1,5,6,4]=>[1,1,1,1,3,1]
[3,4,7,8,1,2,5,6]=>[1,2,5,6,7,3,8,4]=>[8,7,4,3,2,6,1,5]=>[1,1,1,1,2,2]
[3,4,1,2,7,5,6,8]=>[1,6,2,7,3,4,5,8]=>[8,3,7,2,6,5,4,1]=>[1,2,2,1,1,1]
[3,4,1,2,5,7,6,8]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[1,3,1,1,1,1]
[3,1,4,5,2,7,6,8]=>[3,1,4,7,2,5,6,8]=>[6,8,5,2,7,4,3,1]=>[2,1,2,1,1,1]
[3,4,1,5,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>[8,5,7,2,6,4,3,1]=>[1,2,2,1,1,1]
[3,4,1,5,7,2,6,8]=>[1,4,2,6,7,3,5,8]=>[8,5,7,3,2,6,4,1]=>[1,2,1,2,1,1]
[3,4,5,1,7,2,6,8]=>[1,2,6,3,7,4,5,8]=>[8,7,3,6,2,5,4,1]=>[1,1,2,2,1,1]
[3,4,5,7,1,2,6,8]=>[1,2,5,3,6,7,4,8]=>[8,7,4,6,3,2,5,1]=>[1,1,2,1,2,1]
[3,4,1,2,5,7,8,6]=>[1,6,2,8,3,4,5,7]=>[8,3,7,1,6,5,4,2]=>[1,2,2,1,1,1]
[3,4,5,1,2,7,8,6]=>[1,2,6,3,8,4,5,7]=>[8,7,3,6,1,5,4,2]=>[1,1,2,2,1,1]
[3,1,4,5,7,2,8,6]=>[1,8,3,4,6,2,5,7]=>[8,1,6,5,3,7,4,2]=>[1,2,1,2,1,1]
[3,4,5,7,1,2,8,6]=>[1,2,3,8,5,6,4,7]=>[8,7,6,1,4,3,5,2]=>[1,1,1,2,2,1]
[3,4,5,7,8,1,2,6]=>[1,2,3,6,7,4,8,5]=>[8,7,6,3,2,5,1,4]=>[1,1,1,1,2,2]
[3,4,1,2,8,5,6,7]=>[1,6,2,7,8,3,4,5]=>[8,3,7,2,1,6,5,4]=>[1,2,1,2,1,1]
[3,1,4,8,2,5,6,7]=>[3,1,5,6,7,8,2,4]=>[6,8,4,3,2,1,7,5]=>[2,1,1,1,2,1]
[3,4,8,1,2,5,6,7]=>[1,4,2,5,6,7,8,3]=>[8,5,7,4,3,2,1,6]=>[1,2,1,1,1,2]
[3,4,1,2,5,8,6,7]=>[1,7,2,8,3,4,5,6]=>[8,2,7,1,6,5,4,3]=>[1,2,2,1,1,1]
[3,4,1,5,2,8,6,7]=>[1,4,2,7,8,3,5,6]=>[8,5,7,2,1,6,4,3]=>[1,2,1,2,1,1]
[3,4,5,1,2,8,6,7]=>[1,2,7,3,8,4,5,6]=>[8,7,2,6,1,5,4,3]=>[1,1,2,2,1,1]
[3,1,4,5,8,2,6,7]=>[3,1,4,6,7,8,2,5]=>[6,8,5,3,2,1,7,4]=>[2,1,1,1,2,1]
[3,4,1,5,8,2,6,7]=>[1,4,2,6,7,8,3,5]=>[8,5,7,3,2,1,6,4]=>[1,2,1,1,2,1]
[3,4,5,8,1,2,6,7]=>[1,2,5,3,6,7,8,4]=>[8,7,4,6,3,2,1,5]=>[1,1,2,1,1,2]
[3,4,1,2,5,6,8,7]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[1,3,1,1,1,1]
[3,4,5,1,2,6,8,7]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[1,1,3,1,1,1]
[3,1,4,5,6,2,8,7]=>[3,1,4,5,8,2,6,7]=>[6,8,5,4,1,7,3,2]=>[2,1,1,2,1,1]
[3,4,1,5,6,2,8,7]=>[1,4,2,5,8,3,6,7]=>[8,5,7,4,1,6,3,2]=>[1,2,1,2,1,1]
[3,4,5,1,6,2,8,7]=>[1,2,5,3,8,4,6,7]=>[8,7,4,6,1,5,3,2]=>[1,1,2,2,1,1]
[3,4,5,6,1,2,8,7]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[1,1,1,3,1,1]
[3,1,4,5,6,8,2,7]=>[3,1,4,5,7,8,2,6]=>[6,8,5,4,2,1,7,3]=>[2,1,1,1,2,1]
[3,4,1,5,6,8,2,7]=>[1,4,2,5,7,8,3,6]=>[8,5,7,4,2,1,6,3]=>[1,2,1,1,2,1]
[3,4,5,6,1,8,2,7]=>[1,2,3,7,4,8,5,6]=>[8,7,6,2,5,1,4,3]=>[1,1,1,2,2,1]
[3,4,5,6,8,1,2,7]=>[1,2,3,6,4,7,8,5]=>[8,7,6,3,5,2,1,4]=>[1,1,1,2,1,2]
[3,1,4,2,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>[3,1,1,1,1,1]
[3,1,4,5,2,6,7,8]=>[3,1,5,2,4,6,7,8]=>[6,8,4,7,5,3,2,1]=>[2,2,1,1,1,1]
[3,4,1,5,2,6,7,8]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[1,3,1,1,1,1]
[3,1,4,5,6,2,7,8]=>[3,1,4,6,2,5,7,8]=>[6,8,5,3,7,4,2,1]=>[2,1,2,1,1,1]
[3,4,1,5,6,2,7,8]=>[1,4,2,6,3,5,7,8]=>[8,5,7,3,6,4,2,1]=>[1,2,2,1,1,1]
[3,4,5,1,6,2,7,8]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[1,1,3,1,1,1]
[3,1,4,5,6,7,2,8]=>[3,1,4,5,7,2,6,8]=>[6,8,5,4,2,7,3,1]=>[2,1,1,2,1,1]
[3,4,1,5,6,7,2,8]=>[1,4,2,5,7,3,6,8]=>[8,5,7,4,2,6,3,1]=>[1,2,1,2,1,1]
[3,4,5,1,6,7,2,8]=>[1,2,5,3,7,4,6,8]=>[8,7,4,6,2,5,3,1]=>[1,1,2,2,1,1]
[3,4,5,6,1,7,2,8]=>[1,2,3,7,5,4,6,8]=>[8,7,6,2,4,5,3,1]=>[1,1,1,3,1,1]
[3,1,4,5,6,7,8,2]=>[3,1,4,5,6,8,2,7]=>[6,8,5,4,3,1,7,2]=>[2,1,1,1,2,1]
[3,4,1,5,6,7,8,2]=>[1,4,2,5,6,8,3,7]=>[8,5,7,4,3,1,6,2]=>[1,2,1,1,2,1]
[3,4,5,1,6,7,8,2]=>[1,2,5,3,6,8,4,7]=>[8,7,4,6,3,1,5,2]=>[1,1,2,1,2,1]
[3,4,5,6,1,7,8,2]=>[1,2,3,6,4,8,5,7]=>[8,7,6,3,5,1,4,2]=>[1,1,1,2,2,1]
[3,4,5,6,7,1,8,2]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[1,1,1,1,3,1]
[3,1,5,2,6,4,8,7]=>[1,5,3,8,2,4,6,7]=>[8,4,6,1,7,5,3,2]=>[1,2,2,1,1,1]
[3,5,1,2,6,4,8,7]=>[1,5,8,3,2,4,6,7]=>[8,4,1,6,7,5,3,2]=>[1,1,3,1,1,1]
[3,1,5,6,2,4,8,7]=>[1,3,8,5,2,4,6,7]=>[8,6,1,4,7,5,3,2]=>[1,1,3,1,1,1]
[3,5,1,6,2,4,8,7]=>[8,1,5,3,2,4,6,7]=>[1,8,4,6,7,5,3,2]=>[2,3,1,1,1]
[3,5,6,1,2,4,8,7]=>[8,1,4,2,5,3,6,7]=>[1,8,5,7,4,6,3,2]=>[2,2,2,1,1]
[3,1,5,2,6,8,4,7]=>[1,5,3,7,8,2,4,6]=>[8,4,6,2,1,7,5,3]=>[1,2,1,2,1,1]
[3,5,1,2,6,8,4,7]=>[1,5,7,2,8,3,4,6]=>[8,4,2,7,1,6,5,3]=>[1,1,2,2,1,1]
[3,1,5,6,2,8,4,7]=>[1,3,7,4,8,2,5,6]=>[8,6,2,5,1,7,4,3]=>[1,1,2,2,1,1]
[3,5,6,1,2,8,4,7]=>[7,1,2,8,4,3,5,6]=>[2,8,7,1,5,6,4,3]=>[2,1,3,1,1]
[3,1,5,6,8,2,4,7]=>[1,3,6,4,7,8,2,5]=>[8,6,3,5,2,1,7,4]=>[1,1,2,1,2,1]
[3,5,1,6,8,2,4,7]=>[6,1,4,2,7,8,3,5]=>[3,8,5,7,2,1,6,4]=>[2,2,1,2,1]
[3,5,6,1,8,2,4,7]=>[6,1,2,7,3,8,4,5]=>[3,8,7,2,6,1,5,4]=>[2,1,2,2,1]
[3,5,6,8,1,2,4,7]=>[5,1,2,6,3,7,8,4]=>[4,8,7,3,6,2,1,5]=>[2,1,2,1,2]
[3,1,5,6,2,4,7,8]=>[1,5,3,6,2,4,7,8]=>[8,4,6,3,7,5,2,1]=>[1,2,2,1,1,1]
[3,5,1,6,2,4,7,8]=>[1,5,6,3,2,4,7,8]=>[8,4,3,6,7,5,2,1]=>[1,1,3,1,1,1]
[3,5,6,1,2,4,7,8]=>[1,4,5,2,6,3,7,8]=>[8,5,4,7,3,6,2,1]=>[1,1,2,2,1,1]
[3,5,1,2,6,7,4,8]=>[1,5,7,3,2,4,6,8]=>[8,4,2,6,7,5,3,1]=>[1,1,3,1,1,1]
[3,5,1,6,2,7,4,8]=>[7,1,5,3,2,4,6,8]=>[2,8,4,6,7,5,3,1]=>[2,3,1,1,1]
[3,5,6,1,2,7,4,8]=>[7,1,4,2,5,3,6,8]=>[2,8,5,7,4,6,3,1]=>[2,2,2,1,1]
[3,5,1,6,7,2,4,8]=>[6,1,4,2,7,3,5,8]=>[3,8,5,7,2,6,4,1]=>[2,2,2,1,1]
[3,5,6,7,1,2,4,8]=>[5,1,2,6,3,7,4,8]=>[4,8,7,3,6,2,5,1]=>[2,1,2,2,1]
[3,1,5,2,6,7,8,4]=>[1,5,3,6,8,2,4,7]=>[8,4,6,3,1,7,5,2]=>[1,2,1,2,1,1]
[3,5,1,2,6,7,8,4]=>[1,5,6,2,8,3,4,7]=>[8,4,3,7,1,6,5,2]=>[1,1,2,2,1,1]
[3,1,5,6,2,7,8,4]=>[1,3,6,4,8,2,5,7]=>[8,6,3,5,1,7,4,2]=>[1,1,2,2,1,1]
[3,5,1,6,2,7,8,4]=>[6,1,4,2,8,3,5,7]=>[3,8,5,7,1,6,4,2]=>[2,2,2,1,1]
[3,5,6,1,2,7,8,4]=>[6,1,2,8,4,3,5,7]=>[3,8,7,1,5,6,4,2]=>[2,1,3,1,1]
[3,1,5,6,7,2,8,4]=>[1,3,4,8,6,2,5,7]=>[8,6,5,1,3,7,4,2]=>[1,1,1,3,1,1]
[3,5,1,6,7,2,8,4]=>[4,1,2,8,6,3,5,7]=>[5,8,7,1,3,6,4,2]=>[2,1,3,1,1]
[3,5,6,1,7,2,8,4]=>[2,8,1,6,4,3,5,7]=>[7,1,8,3,5,6,4,2]=>[1,2,3,1,1]
[3,5,6,7,1,2,8,4]=>[2,8,1,5,3,6,4,7]=>[7,1,8,4,6,3,5,2]=>[1,2,2,2,1]
[3,1,5,6,7,8,2,4]=>[1,3,4,7,5,8,2,6]=>[8,6,5,2,4,1,7,3]=>[1,1,1,2,2,1]
[3,5,1,6,7,8,2,4]=>[4,1,2,7,5,8,3,6]=>[5,8,7,2,4,1,6,3]=>[2,1,2,2,1]
[3,5,6,1,7,8,2,4]=>[2,7,1,5,3,8,4,6]=>[7,2,8,4,6,1,5,3]=>[1,2,2,2,1]
[3,5,6,7,1,8,2,4]=>[2,7,1,3,8,5,4,6]=>[7,2,8,6,1,4,5,3]=>[1,2,1,3,1]
[3,5,6,7,8,1,2,4]=>[2,6,1,3,7,4,8,5]=>[7,3,8,6,2,5,1,4]=>[1,2,1,2,2]
[3,5,1,2,7,4,8,6]=>[8,1,6,3,2,4,5,7]=>[1,8,3,6,7,5,4,2]=>[2,3,1,1,1]
[3,1,5,7,2,4,8,6]=>[1,3,8,5,6,2,4,7]=>[8,6,1,4,3,7,5,2]=>[1,1,2,2,1,1]
[3,5,1,7,2,4,8,6]=>[8,1,5,2,6,3,4,7]=>[1,8,4,7,3,6,5,2]=>[2,2,2,1,1]
[3,5,7,1,2,4,8,6]=>[8,1,4,2,5,6,3,7]=>[1,8,5,7,4,3,6,2]=>[2,2,1,2,1]
[3,1,5,2,7,8,4,6]=>[1,3,7,5,8,2,4,6]=>[8,6,2,4,1,7,5,3]=>[1,1,2,2,1,1]
[3,5,1,2,7,8,4,6]=>[7,1,5,2,8,3,4,6]=>[2,8,4,7,1,6,5,3]=>[2,2,2,1,1]
[3,1,5,7,2,8,4,6]=>[1,3,7,8,5,2,4,6]=>[8,6,2,1,4,7,5,3]=>[1,1,1,3,1,1]
[3,5,1,7,2,8,4,6]=>[7,1,2,8,5,3,4,6]=>[2,8,7,1,4,6,5,3]=>[2,1,3,1,1]
[3,5,7,1,2,8,4,6]=>[7,1,2,8,4,5,3,6]=>[2,8,7,1,5,4,6,3]=>[2,1,2,2,1]
[3,5,1,7,8,2,4,6]=>[6,1,2,7,4,8,3,5]=>[3,8,7,2,5,1,6,4]=>[2,1,2,2,1]
[3,5,7,8,1,2,4,6]=>[5,1,2,6,7,3,8,4]=>[4,8,7,3,2,6,1,5]=>[2,1,1,2,2]
[3,1,5,2,7,4,6,8]=>[1,6,3,7,2,4,5,8]=>[8,3,6,2,7,5,4,1]=>[1,2,2,1,1,1]
[3,5,1,2,7,4,6,8]=>[1,6,7,3,2,4,5,8]=>[8,3,2,6,7,5,4,1]=>[1,1,3,1,1,1]
[3,1,5,7,2,4,6,8]=>[1,5,3,6,7,2,4,8]=>[8,4,6,3,2,7,5,1]=>[1,2,1,2,1,1]
[3,1,5,2,4,7,6,8]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[1,3,1,1,1,1]
[3,5,1,2,4,7,6,8]=>[1,7,3,4,2,5,6,8]=>[8,2,6,5,7,4,3,1]=>[1,2,2,1,1,1]
[3,1,2,5,4,7,6,8]=>[4,1,7,2,3,5,6,8]=>[5,8,2,7,6,4,3,1]=>[2,2,1,1,1,1]
[1,3,5,2,4,7,6,8]=>[7,2,4,1,3,5,6,8]=>[2,7,5,8,6,4,3,1]=>[2,2,1,1,1,1]
[3,1,2,5,7,4,6,8]=>[4,1,6,7,2,3,5,8]=>[5,8,3,2,7,6,4,1]=>[2,1,2,1,1,1]
[1,3,2,5,7,4,6,8]=>[2,4,6,7,1,3,5,8]=>[7,5,3,2,8,6,4,1]=>[1,1,1,2,1,1,1]
[3,5,1,2,4,7,8,6]=>[1,6,8,3,2,4,5,7]=>[8,3,1,6,7,5,4,2]=>[1,1,3,1,1,1]
[1,3,5,2,4,7,8,6]=>[6,2,3,8,1,4,5,7]=>[3,7,6,1,8,5,4,2]=>[2,1,2,1,1,1]
[1,3,2,5,7,4,8,6]=>[8,2,4,6,1,3,5,7]=>[1,7,5,3,8,6,4,2]=>[2,1,2,1,1,1]
[1,3,5,2,7,4,8,6]=>[3,8,2,6,1,4,5,7]=>[6,1,7,3,8,5,4,2]=>[1,2,2,1,1,1]
[1,3,5,7,2,4,8,6]=>[3,8,2,5,6,1,4,7]=>[6,1,7,4,3,8,5,2]=>[1,2,1,2,1,1]
[3,1,2,5,7,8,4,6]=>[1,7,4,5,8,2,3,6]=>[8,2,5,4,1,7,6,3]=>[1,2,1,2,1,1]
[1,3,2,5,7,8,4,6]=>[7,2,4,5,8,1,3,6]=>[2,7,5,4,1,8,6,3]=>[2,1,1,2,1,1]
[1,3,5,2,7,8,4,6]=>[3,7,2,5,8,1,4,6]=>[6,2,7,4,1,8,5,3]=>[1,2,1,2,1,1]
[1,3,5,7,8,2,4,6]=>[3,6,7,2,4,8,1,5]=>[6,3,2,7,5,1,8,4]=>[1,1,2,1,2,1]
[3,1,5,2,8,4,6,7]=>[1,6,3,7,8,2,4,5]=>[8,3,6,2,1,7,5,4]=>[1,2,1,2,1,1]
[3,5,1,2,8,4,6,7]=>[1,6,7,2,8,3,4,5]=>[8,3,2,7,1,6,5,4]=>[1,1,2,2,1,1]
[3,1,5,8,2,4,6,7]=>[1,5,3,6,7,8,2,4]=>[8,4,6,3,2,1,7,5]=>[1,2,1,1,2,1]
[3,5,1,8,2,4,6,7]=>[1,5,6,2,7,8,3,4]=>[8,4,3,7,2,1,6,5]=>[1,1,2,1,2,1]
[3,5,1,2,4,8,6,7]=>[1,7,8,3,2,4,5,6]=>[8,2,1,6,7,5,4,3]=>[1,1,3,1,1,1]
[1,3,2,5,4,8,6,7]=>[2,4,7,8,1,3,5,6]=>[7,5,2,1,8,6,4,3]=>[1,1,1,2,1,1,1]
[1,3,5,2,4,8,6,7]=>[7,2,3,8,1,4,5,6]=>[2,7,6,1,8,5,4,3]=>[2,1,2,1,1,1]
[3,1,2,5,8,4,6,7]=>[4,1,6,7,8,2,3,5]=>[5,8,3,2,1,7,6,4]=>[2,1,1,2,1,1]
[1,3,2,5,8,4,6,7]=>[2,4,6,7,8,1,3,5]=>[7,5,3,2,1,8,6,4]=>[1,1,1,1,2,1,1]
[1,3,5,2,8,4,6,7]=>[6,2,3,7,8,1,4,5]=>[3,7,6,2,1,8,5,4]=>[2,1,1,2,1,1]
[3,1,5,2,4,6,8,7]=>[1,8,4,2,3,5,6,7]=>[8,1,5,7,6,4,3,2]=>[1,3,1,1,1,1]
[3,5,1,2,4,6,8,7]=>[1,8,3,4,2,5,6,7]=>[8,1,6,5,7,4,3,2]=>[1,2,2,1,1,1]
[3,1,2,5,4,6,8,7]=>[4,1,8,2,3,5,6,7]=>[5,8,1,7,6,4,3,2]=>[2,2,1,1,1,1]
[1,3,5,2,4,6,8,7]=>[8,2,4,1,3,5,6,7]=>[1,7,5,8,6,4,3,2]=>[2,2,1,1,1,1]
[1,3,5,6,2,4,8,7]=>[3,8,2,5,1,4,6,7]=>[6,1,7,4,8,5,3,2]=>[1,2,2,1,1,1]
[3,1,2,5,6,8,4,7]=>[4,1,5,7,8,2,3,6]=>[5,8,4,2,1,7,6,3]=>[2,1,1,2,1,1]
[1,3,5,2,6,8,4,7]=>[5,2,3,7,8,1,4,6]=>[4,7,6,2,1,8,5,3]=>[2,1,1,2,1,1]
[1,3,5,6,2,8,4,7]=>[3,7,2,4,8,1,5,6]=>[6,2,7,5,1,8,4,3]=>[1,2,1,2,1,1]
[1,3,5,6,8,2,4,7]=>[3,6,2,4,7,8,1,5]=>[6,3,7,5,2,1,8,4]=>[1,2,1,1,2,1]
[3,1,5,2,4,6,7,8]=>[4,1,5,2,3,6,7,8]=>[5,8,4,7,6,3,2,1]=>[2,2,1,1,1,1]
[3,5,1,2,4,6,7,8]=>[3,1,4,5,2,6,7,8]=>[6,8,5,4,7,3,2,1]=>[2,1,2,1,1,1]
[1,3,5,2,4,6,7,8]=>[2,4,5,1,3,6,7,8]=>[7,5,4,8,6,3,2,1]=>[1,1,2,1,1,1,1]
[3,1,2,5,6,4,7,8]=>[4,1,6,2,3,5,7,8]=>[5,8,3,7,6,4,2,1]=>[2,2,1,1,1,1]
[1,3,5,2,6,4,7,8]=>[6,2,4,1,3,5,7,8]=>[3,7,5,8,6,4,2,1]=>[2,2,1,1,1,1]
[1,3,5,6,2,4,7,8]=>[5,2,3,6,1,4,7,8]=>[4,7,6,3,8,5,2,1]=>[2,1,2,1,1,1]
[3,1,2,5,6,7,4,8]=>[4,1,5,7,2,3,6,8]=>[5,8,4,2,7,6,3,1]=>[2,1,2,1,1,1]
[1,3,5,6,2,7,4,8]=>[3,7,2,5,1,4,6,8]=>[6,2,7,4,8,5,3,1]=>[1,2,2,1,1,1]
[1,3,5,6,7,2,4,8]=>[3,6,2,4,7,1,5,8]=>[6,3,7,5,2,8,4,1]=>[1,2,1,2,1,1]
[3,1,2,5,6,7,8,4]=>[4,1,5,6,8,2,3,7]=>[5,8,4,3,1,7,6,2]=>[2,1,1,2,1,1]
[1,3,5,2,6,7,8,4]=>[5,2,3,6,8,1,4,7]=>[4,7,6,3,1,8,5,2]=>[2,1,1,2,1,1]
[1,3,5,6,2,7,8,4]=>[3,6,2,4,8,1,5,7]=>[6,3,7,5,1,8,4,2]=>[1,2,1,2,1,1]
[1,3,5,6,7,2,8,4]=>[3,4,8,2,6,1,5,7]=>[6,5,1,7,3,8,4,2]=>[1,1,2,2,1,1]
[1,3,5,6,7,8,2,4]=>[3,4,7,2,5,8,1,6]=>[6,5,2,7,4,1,8,3]=>[1,1,2,1,2,1]
[3,1,6,2,7,4,8,5]=>[8,1,6,4,2,3,5,7]=>[1,8,3,5,7,6,4,2]=>[2,3,1,1,1]
[3,6,1,2,7,4,8,5]=>[8,1,6,3,4,2,5,7]=>[1,8,3,6,5,7,4,2]=>[2,2,2,1,1]
[3,6,1,7,2,4,8,5]=>[8,1,5,6,3,2,4,7]=>[1,8,4,3,6,7,5,2]=>[2,1,3,1,1]
[3,6,1,2,7,8,4,5]=>[7,1,5,8,3,2,4,6]=>[2,8,4,1,6,7,5,3]=>[2,1,3,1,1]
[3,1,6,7,2,8,4,5]=>[7,1,3,8,5,2,4,6]=>[2,8,6,1,4,7,5,3]=>[2,1,3,1,1]
[3,6,1,7,2,8,4,5]=>[7,8,1,5,3,2,4,6]=>[2,1,8,4,6,7,5,3]=>[1,2,3,1,1]
[3,6,7,1,2,8,4,5]=>[7,8,1,4,2,5,3,6]=>[2,1,8,5,7,4,6,3]=>[1,2,2,2,1]
[3,6,1,7,8,2,4,5]=>[6,7,1,4,2,8,3,5]=>[3,2,8,5,7,1,6,4]=>[1,2,2,2,1]
[3,6,7,8,1,2,4,5]=>[5,6,1,2,7,3,8,4]=>[4,3,8,7,2,6,1,5]=>[1,2,1,2,2]
[3,1,6,2,7,4,5,8]=>[1,6,7,4,2,3,5,8]=>[8,3,2,5,7,6,4,1]=>[1,1,3,1,1,1]
[3,6,7,1,2,4,5,8]=>[1,4,5,6,2,7,3,8]=>[8,5,4,3,7,2,6,1]=>[1,1,1,2,2,1]
[3,1,6,2,4,7,5,8]=>[1,7,4,5,2,3,6,8]=>[8,2,5,4,7,6,3,1]=>[1,2,2,1,1,1]
[3,6,1,2,4,7,5,8]=>[1,7,3,4,5,2,6,8]=>[8,2,6,5,4,7,3,1]=>[1,2,1,2,1,1]
[3,1,2,6,4,7,5,8]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[1,3,1,1,1,1]
[1,3,2,6,4,7,5,8]=>[7,2,5,1,3,4,6,8]=>[2,7,4,8,6,5,3,1]=>[2,2,1,1,1,1]
[1,3,6,2,4,7,5,8]=>[7,2,4,5,1,3,6,8]=>[2,7,5,4,8,6,3,1]=>[2,1,2,1,1,1]
[1,3,6,2,7,4,5,8]=>[6,7,2,4,1,3,5,8]=>[3,2,7,5,8,6,4,1]=>[1,2,2,1,1,1]
[3,6,1,2,4,7,8,5]=>[1,6,8,3,4,2,5,7]=>[8,3,1,6,5,7,4,2]=>[1,1,2,2,1,1]
[3,1,2,6,4,7,8,5]=>[1,6,4,8,2,3,5,7]=>[8,3,5,1,7,6,4,2]=>[1,2,2,1,1,1]
[1,3,2,6,4,7,8,5]=>[6,2,4,8,1,3,5,7]=>[3,7,5,1,8,6,4,2]=>[2,1,2,1,1,1]
[1,3,6,2,4,7,8,5]=>[6,8,2,4,1,3,5,7]=>[3,1,7,5,8,6,4,2]=>[1,2,2,1,1,1]
[3,1,2,6,7,4,8,5]=>[1,4,8,6,2,3,5,7]=>[8,5,1,3,7,6,4,2]=>[1,1,3,1,1,1]
[1,3,2,6,7,4,8,5]=>[4,8,2,6,1,3,5,7]=>[5,1,7,3,8,6,4,2]=>[1,2,2,1,1,1]
[1,3,6,2,7,4,8,5]=>[8,6,2,4,1,3,5,7]=>[1,3,7,5,8,6,4,2]=>[3,2,1,1,1]
[1,3,6,7,2,4,8,5]=>[8,5,2,3,6,1,4,7]=>[1,4,7,6,3,8,5,2]=>[3,1,2,1,1]
[1,3,2,6,7,8,4,5]=>[4,7,2,5,8,1,3,6]=>[5,2,7,4,1,8,6,3]=>[1,2,1,2,1,1]
[1,3,6,2,7,8,4,5]=>[7,5,2,3,8,1,4,6]=>[2,4,7,6,1,8,5,3]=>[3,1,2,1,1]
[1,3,6,7,8,2,4,5]=>[6,3,7,2,4,8,1,5]=>[3,6,2,7,5,1,8,4]=>[2,2,1,2,1]
[3,1,6,8,2,4,5,7]=>[1,5,6,3,7,8,2,4]=>[8,4,3,6,2,1,7,5]=>[1,1,2,1,2,1]
[3,6,1,8,2,4,5,7]=>[1,5,6,7,2,8,3,4]=>[8,4,3,2,7,1,6,5]=>[1,1,1,2,2,1]
[3,6,8,1,2,4,5,7]=>[1,4,5,6,2,7,8,3]=>[8,5,4,3,7,2,1,6]=>[1,1,1,2,1,2]
[3,1,6,2,4,8,5,7]=>[1,7,8,4,2,3,5,6]=>[8,2,1,5,7,6,4,3]=>[1,1,3,1,1,1]
[3,6,1,2,4,8,5,7]=>[1,7,8,3,4,2,5,6]=>[8,2,1,6,5,7,4,3]=>[1,1,2,2,1,1]
[1,3,2,6,4,8,5,7]=>[7,2,4,8,1,3,5,6]=>[2,7,5,1,8,6,4,3]=>[2,1,2,1,1,1]
[1,3,6,2,4,8,5,7]=>[7,8,2,4,1,3,5,6]=>[2,1,7,5,8,6,4,3]=>[1,2,2,1,1,1]
[1,3,2,6,8,4,5,7]=>[6,2,4,7,8,1,3,5]=>[3,7,5,2,1,8,6,4]=>[2,1,1,2,1,1]
[3,1,6,2,4,5,8,7]=>[1,8,4,5,2,3,6,7]=>[8,1,5,4,7,6,3,2]=>[1,2,2,1,1,1]
[3,1,2,6,4,5,8,7]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[1,3,1,1,1,1]
[1,3,6,2,4,5,8,7]=>[8,2,4,5,1,3,6,7]=>[1,7,5,4,8,6,3,2]=>[2,1,2,1,1,1]
[3,1,2,4,6,5,8,7]=>[5,1,8,2,3,4,6,7]=>[4,8,1,7,6,5,3,2]=>[2,2,1,1,1,1]
[1,3,4,6,2,5,8,7]=>[8,2,3,5,1,4,6,7]=>[1,7,6,4,8,5,3,2]=>[2,1,2,1,1,1]
[3,1,2,4,6,8,5,7]=>[5,1,7,8,2,3,4,6]=>[4,8,2,1,7,6,5,3]=>[2,1,2,1,1,1]
[1,3,2,4,6,8,5,7]=>[2,5,7,8,1,3,4,6]=>[7,4,2,1,8,6,5,3]=>[1,1,1,2,1,1,1]
[1,3,4,6,8,2,5,7]=>[6,2,3,4,7,8,1,5]=>[3,7,6,5,2,1,8,4]=>[2,1,1,1,2,1]
[3,1,6,2,4,5,7,8]=>[4,1,5,6,2,3,7,8]=>[5,8,4,3,7,6,2,1]=>[2,1,2,1,1,1]
[3,6,1,2,4,5,7,8]=>[3,1,4,5,6,2,7,8]=>[6,8,5,4,3,7,2,1]=>[2,1,1,2,1,1]
[1,3,6,2,4,5,7,8]=>[2,4,5,6,1,3,7,8]=>[7,5,4,3,8,6,2,1]=>[1,1,1,2,1,1,1]
[1,3,4,6,2,5,7,8]=>[2,3,5,6,1,4,7,8]=>[7,6,4,3,8,5,2,1]=>[1,1,1,2,1,1,1]
[3,1,2,4,6,7,5,8]=>[5,1,7,2,3,4,6,8]=>[4,8,2,7,6,5,3,1]=>[2,2,1,1,1,1]
[1,3,4,6,2,7,5,8]=>[7,2,3,5,1,4,6,8]=>[2,7,6,4,8,5,3,1]=>[2,1,2,1,1,1]
[3,1,2,4,6,7,8,5]=>[5,1,6,8,2,3,4,7]=>[4,8,3,1,7,6,5,2]=>[2,1,2,1,1,1]
[1,3,4,6,7,2,8,5]=>[4,8,2,3,6,1,5,7]=>[5,1,7,6,3,8,4,2]=>[1,2,1,2,1,1]
[1,3,4,6,7,8,2,5]=>[4,7,2,3,5,8,1,6]=>[5,2,7,6,4,1,8,3]=>[1,2,1,1,2,1]
[3,1,7,2,8,4,5,6]=>[1,6,7,8,4,2,3,5]=>[8,3,2,1,5,7,6,4]=>[1,1,1,3,1,1]
[3,7,1,2,8,4,5,6]=>[1,6,7,8,3,4,2,5]=>[8,3,2,1,6,5,7,4]=>[1,1,1,2,2,1]
[3,7,1,8,2,4,5,6]=>[1,5,6,7,8,3,2,4]=>[8,4,3,2,1,6,7,5]=>[1,1,1,1,3,1]
[3,7,8,1,2,4,5,6]=>[1,4,5,6,7,2,8,3]=>[8,5,4,3,2,7,1,6]=>[1,1,1,1,2,2]
[3,7,1,2,4,8,5,6]=>[1,7,8,3,4,5,2,6]=>[8,2,1,6,5,4,7,3]=>[1,1,2,1,2,1]
[3,1,2,7,4,8,5,6]=>[1,7,8,5,2,3,4,6]=>[8,2,1,4,7,6,5,3]=>[1,1,3,1,1,1]
[1,3,2,7,4,8,5,6]=>[7,8,2,5,1,3,4,6]=>[2,1,7,4,8,6,5,3]=>[1,2,2,1,1,1]
[1,3,7,2,4,8,5,6]=>[7,8,2,4,5,1,3,6]=>[2,1,7,5,4,8,6,3]=>[1,2,1,2,1,1]
[3,1,2,7,8,4,5,6]=>[1,6,7,4,8,2,3,5]=>[8,3,2,5,1,7,6,4]=>[1,1,2,2,1,1]
[1,3,7,2,8,4,5,6]=>[6,7,8,2,4,1,3,5]=>[3,2,1,7,5,8,6,4]=>[1,1,2,2,1,1]
[1,3,7,8,2,4,5,6]=>[5,6,7,2,3,8,1,4]=>[4,3,2,7,6,1,8,5]=>[1,1,2,1,2,1]
[3,1,7,2,4,5,8,6]=>[1,8,4,5,6,2,3,7]=>[8,1,5,4,3,7,6,2]=>[1,2,1,2,1,1]
[3,7,1,2,4,5,8,6]=>[1,8,3,4,5,6,2,7]=>[8,1,6,5,4,3,7,2]=>[1,2,1,1,2,1]
[3,1,2,4,7,5,8,6]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[1,3,1,1,1,1]
[1,3,4,2,7,5,8,6]=>[8,2,3,6,1,4,5,7]=>[1,7,6,3,8,5,4,2]=>[2,1,2,1,1,1]
[1,3,4,7,2,5,8,6]=>[8,2,3,5,6,1,4,7]=>[1,7,6,4,3,8,5,2]=>[2,1,1,2,1,1]
[3,1,2,4,7,8,5,6]=>[1,7,5,8,2,3,4,6]=>[8,2,4,1,7,6,5,3]=>[1,2,2,1,1,1]
[1,3,4,2,7,8,5,6]=>[7,2,3,5,8,1,4,6]=>[2,7,6,4,1,8,5,3]=>[2,1,1,2,1,1]
[1,3,4,7,8,2,5,6]=>[6,7,2,3,4,8,1,5]=>[3,2,7,6,5,1,8,4]=>[1,2,1,1,2,1]
[3,1,7,2,4,5,6,8]=>[4,1,5,6,7,2,3,8]=>[5,8,4,3,2,7,6,1]=>[2,1,1,2,1,1]
[3,7,1,2,4,5,6,8]=>[3,1,4,5,6,7,2,8]=>[6,8,5,4,3,2,7,1]=>[2,1,1,1,2,1]
[3,1,2,7,4,5,6,8]=>[5,1,6,7,2,3,4,8]=>[4,8,3,2,7,6,5,1]=>[2,1,2,1,1,1]
[1,3,7,2,4,5,6,8]=>[2,4,5,6,7,1,3,8]=>[7,5,4,3,2,8,6,1]=>[1,1,1,1,2,1,1]
[3,1,2,4,7,5,6,8]=>[6,1,7,2,3,4,5,8]=>[3,8,2,7,6,5,4,1]=>[2,2,1,1,1,1]
[1,3,4,7,2,5,6,8]=>[2,3,5,6,7,1,4,8]=>[7,6,4,3,2,8,5,1]=>[1,1,1,1,2,1,1]
[3,1,2,4,5,7,6,8]=>[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>[3,1,1,1,1,1]
[1,3,4,5,7,2,6,8]=>[2,3,4,6,7,1,5,8]=>[7,6,5,3,2,8,4,1]=>[1,1,1,1,2,1,1]
[3,1,2,4,5,7,8,6]=>[6,1,8,2,3,4,5,7]=>[3,8,1,7,6,5,4,2]=>[2,2,1,1,1,1]
[1,3,4,5,7,2,8,6]=>[8,2,3,4,6,1,5,7]=>[1,7,6,5,3,8,4,2]=>[2,1,1,2,1,1]
[1,3,4,5,7,8,2,6]=>[7,2,3,4,5,8,1,6]=>[2,7,6,5,4,1,8,3]=>[2,1,1,1,2,1]
[3,1,8,2,4,5,6,7]=>[4,1,5,6,7,8,2,3]=>[5,8,4,3,2,1,7,6]=>[2,1,1,1,2,1]
[3,8,1,2,4,5,6,7]=>[3,1,4,5,6,7,8,2]=>[6,8,5,4,3,2,1,7]=>[2,1,1,1,1,2]
[3,1,2,8,4,5,6,7]=>[5,1,6,7,8,2,3,4]=>[4,8,3,2,1,7,6,5]=>[2,1,1,2,1,1]
[1,3,2,8,4,5,6,7]=>[2,5,6,7,8,1,3,4]=>[7,4,3,2,1,8,6,5]=>[1,1,1,1,2,1,1]
[1,3,8,2,4,5,6,7]=>[2,4,5,6,7,8,1,3]=>[7,5,4,3,2,1,8,6]=>[1,1,1,1,1,2,1]
[3,1,2,4,8,5,6,7]=>[6,1,7,8,2,3,4,5]=>[3,8,2,1,7,6,5,4]=>[2,1,2,1,1,1]
[1,3,2,4,8,5,6,7]=>[2,6,7,8,1,3,4,5]=>[7,3,2,1,8,6,5,4]=>[1,1,1,2,1,1,1]
[1,3,4,2,8,5,6,7]=>[2,3,6,7,8,1,4,5]=>[7,6,3,2,1,8,5,4]=>[1,1,1,1,2,1,1]
[1,3,4,8,2,5,6,7]=>[2,3,5,6,7,8,1,4]=>[7,6,4,3,2,1,8,5]=>[1,1,1,1,1,2,1]
[3,1,2,4,5,8,6,7]=>[7,1,8,2,3,4,5,6]=>[2,8,1,7,6,5,4,3]=>[2,2,1,1,1,1]
[1,3,2,4,5,8,6,7]=>[2,7,8,1,3,4,5,6]=>[7,2,1,8,6,5,4,3]=>[1,1,2,1,1,1,1]
[1,3,4,2,5,8,6,7]=>[2,3,7,8,1,4,5,6]=>[7,6,2,1,8,5,4,3]=>[1,1,1,2,1,1,1]
[1,3,4,5,2,8,6,7]=>[2,3,4,7,8,1,5,6]=>[7,6,5,2,1,8,4,3]=>[1,1,1,1,2,1,1]
[1,3,4,5,8,2,6,7]=>[2,3,4,6,7,8,1,5]=>[7,6,5,3,2,1,8,4]=>[1,1,1,1,1,2,1]
[3,1,2,4,5,6,8,7]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>[3,1,1,1,1,1]
[1,3,4,5,6,8,2,7]=>[2,3,4,5,7,8,1,6]=>[7,6,5,4,2,1,8,3]=>[1,1,1,1,1,2,1]
[4,1,5,2,6,3,8,7]=>[5,3,1,8,2,4,6,7]=>[4,6,8,1,7,5,3,2]=>[3,2,1,1,1]
[4,5,1,2,6,3,8,7]=>[5,1,8,3,2,4,6,7]=>[4,8,1,6,7,5,3,2]=>[2,3,1,1,1]
[4,1,5,6,2,3,8,7]=>[3,1,8,5,2,4,6,7]=>[6,8,1,4,7,5,3,2]=>[2,3,1,1,1]
[4,5,1,6,2,3,8,7]=>[1,8,5,3,2,4,6,7]=>[8,1,4,6,7,5,3,2]=>[1,4,1,1,1]
[4,5,6,1,2,3,8,7]=>[1,8,4,2,5,3,6,7]=>[8,1,5,7,4,6,3,2]=>[1,3,2,1,1]
[4,1,5,2,6,8,3,7]=>[5,3,1,7,8,2,4,6]=>[4,6,8,2,1,7,5,3]=>[3,1,2,1,1]
[4,1,5,6,2,8,3,7]=>[3,1,7,4,8,2,5,6]=>[6,8,2,5,1,7,4,3]=>[2,2,2,1,1]
[4,5,1,6,2,8,3,7]=>[1,7,4,2,8,3,5,6]=>[8,2,5,7,1,6,4,3]=>[1,3,2,1,1]
[4,1,5,6,8,2,3,7]=>[3,1,6,4,7,8,2,5]=>[6,8,3,5,2,1,7,4]=>[2,2,1,2,1]
[4,5,1,6,8,2,3,7]=>[1,6,4,2,7,8,3,5]=>[8,3,5,7,2,1,6,4]=>[1,3,1,2,1]
[4,5,6,1,8,2,3,7]=>[1,6,2,7,3,8,4,5]=>[8,3,7,2,6,1,5,4]=>[1,2,2,2,1]
[4,5,6,8,1,2,3,7]=>[1,5,2,6,3,7,8,4]=>[8,4,7,3,6,2,1,5]=>[1,2,2,1,2]
[4,1,5,2,6,3,7,8]=>[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]
[4,1,5,6,2,3,7,8]=>[5,3,1,6,2,4,7,8]=>[4,6,8,3,7,5,2,1]=>[3,2,1,1,1]
[4,5,1,6,2,3,7,8]=>[5,1,6,3,2,4,7,8]=>[4,8,3,6,7,5,2,1]=>[2,3,1,1,1]
[4,5,1,2,6,7,3,8]=>[5,1,7,3,2,4,6,8]=>[4,8,2,6,7,5,3,1]=>[2,3,1,1,1]
[4,5,1,6,2,7,3,8]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[1,4,1,1,1]
[4,1,5,6,7,2,3,8]=>[3,1,6,4,7,2,5,8]=>[6,8,3,5,2,7,4,1]=>[2,2,2,1,1]
[4,5,1,6,7,2,3,8]=>[1,6,4,2,7,3,5,8]=>[8,3,5,7,2,6,4,1]=>[1,3,2,1,1]
[4,1,5,2,6,7,8,3]=>[5,3,1,6,8,2,4,7]=>[4,6,8,3,1,7,5,2]=>[3,1,2,1,1]
[4,5,1,2,6,7,8,3]=>[5,1,6,2,8,3,4,7]=>[4,8,3,7,1,6,5,2]=>[2,2,2,1,1]
[4,5,6,1,2,7,8,3]=>[1,6,2,8,4,3,5,7]=>[8,3,7,1,5,6,4,2]=>[1,2,3,1,1]
[4,1,5,6,7,2,8,3]=>[3,1,4,8,6,2,5,7]=>[6,8,5,1,3,7,4,2]=>[2,1,3,1,1]
[4,5,6,1,7,2,8,3]=>[1,2,8,6,4,3,5,7]=>[8,7,1,3,5,6,4,2]=>[1,1,4,1,1]
[4,5,6,7,1,2,8,3]=>[1,2,8,5,3,6,4,7]=>[8,7,1,4,6,3,5,2]=>[1,1,3,2,1]
[4,1,5,6,7,8,2,3]=>[3,1,4,7,5,8,2,6]=>[6,8,5,2,4,1,7,3]=>[2,1,2,2,1]
[4,5,1,6,7,8,2,3]=>[1,4,2,7,5,8,3,6]=>[8,5,7,2,4,1,6,3]=>[1,2,2,2,1]
[4,5,6,1,7,8,2,3]=>[1,2,7,5,3,8,4,6]=>[8,7,2,4,6,1,5,3]=>[1,1,3,2,1]
[4,5,6,7,1,8,2,3]=>[1,2,7,3,8,5,4,6]=>[8,7,2,6,1,4,5,3]=>[1,1,2,3,1]
[4,1,5,2,7,3,8,6]=>[3,1,8,6,2,4,5,7]=>[6,8,1,3,7,5,4,2]=>[2,3,1,1,1]
[4,5,1,2,7,3,8,6]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[1,4,1,1,1]
[4,5,1,7,2,3,8,6]=>[1,8,5,2,6,3,4,7]=>[8,1,4,7,3,6,5,2]=>[1,3,2,1,1]
[4,5,7,1,2,3,8,6]=>[1,8,4,2,5,6,3,7]=>[8,1,5,7,4,3,6,2]=>[1,3,1,2,1]
[4,1,5,2,7,8,3,6]=>[3,1,7,5,8,2,4,6]=>[6,8,2,4,1,7,5,3]=>[2,2,2,1,1]
[4,5,1,2,7,8,3,6]=>[1,7,5,2,8,3,4,6]=>[8,2,4,7,1,6,5,3]=>[1,3,2,1,1]
[4,1,5,7,2,8,3,6]=>[3,1,7,8,5,2,4,6]=>[6,8,2,1,4,7,5,3]=>[2,1,3,1,1]
[4,5,1,7,2,8,3,6]=>[1,7,2,8,5,3,4,6]=>[8,2,7,1,4,6,5,3]=>[1,2,3,1,1]
[4,5,7,1,2,8,3,6]=>[1,7,2,8,4,5,3,6]=>[8,2,7,1,5,4,6,3]=>[1,2,2,2,1]
[4,5,1,7,8,2,3,6]=>[1,6,2,7,4,8,3,5]=>[8,3,7,2,5,1,6,4]=>[1,2,2,2,1]
[4,5,7,8,1,2,3,6]=>[1,5,2,6,7,3,8,4]=>[8,4,7,3,2,6,1,5]=>[1,2,1,2,2]
[4,5,1,2,7,3,6,8]=>[6,1,7,3,2,4,5,8]=>[3,8,2,6,7,5,4,1]=>[2,3,1,1,1]
[4,1,5,7,2,3,6,8]=>[5,3,1,6,7,2,4,8]=>[4,6,8,3,2,7,5,1]=>[3,1,2,1,1]
[4,5,1,7,2,3,6,8]=>[5,1,6,2,7,3,4,8]=>[4,8,3,7,2,6,5,1]=>[2,2,2,1,1]
[4,1,5,2,3,7,6,8]=>[7,4,2,1,3,5,6,8]=>[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]
[4,5,1,2,3,7,6,8]=>[7,3,1,4,2,5,6,8]=>[2,6,8,5,7,4,3,1]=>[3,2,1,1,1]
[1,4,2,5,3,7,6,8]=>[4,2,7,1,3,5,6,8]=>[5,7,2,8,6,4,3,1]=>[2,2,1,1,1,1]
[1,4,5,2,3,7,6,8]=>[2,7,4,1,3,5,6,8]=>[7,2,5,8,6,4,3,1]=>[1,3,1,1,1,1]
[4,1,2,5,7,3,6,8]=>[4,6,1,7,2,3,5,8]=>[5,3,8,2,7,6,4,1]=>[1,2,2,1,1,1]
[1,4,2,5,7,3,6,8]=>[4,2,6,7,1,3,5,8]=>[5,7,3,2,8,6,4,1]=>[2,1,2,1,1,1]
[1,4,5,2,7,3,6,8]=>[2,6,3,7,1,4,5,8]=>[7,3,6,2,8,5,4,1]=>[1,2,2,1,1,1]
[1,4,5,7,2,3,6,8]=>[2,5,3,6,7,1,4,8]=>[7,4,6,3,2,8,5,1]=>[1,2,1,2,1,1]
[4,1,5,2,3,7,8,6]=>[6,3,1,8,2,4,5,7]=>[3,6,8,1,7,5,4,2]=>[3,2,1,1,1]
[4,1,2,5,3,7,8,6]=>[4,6,1,8,2,3,5,7]=>[5,3,8,1,7,6,4,2]=>[1,2,2,1,1,1]
[1,4,2,5,3,7,8,6]=>[4,2,6,8,1,3,5,7]=>[5,7,3,1,8,6,4,2]=>[2,1,2,1,1,1]
[1,4,5,2,3,7,8,6]=>[2,6,3,8,1,4,5,7]=>[7,3,6,1,8,5,4,2]=>[1,2,2,1,1,1]
[4,1,2,5,7,3,8,6]=>[8,4,1,6,2,3,5,7]=>[1,5,8,3,7,6,4,2]=>[3,2,1,1,1]
[1,4,2,5,7,3,8,6]=>[2,8,4,6,1,3,5,7]=>[7,1,5,3,8,6,4,2]=>[1,2,2,1,1,1]
[1,4,5,2,7,3,8,6]=>[2,3,8,6,1,4,5,7]=>[7,6,1,3,8,5,4,2]=>[1,1,3,1,1,1]
[1,4,5,7,2,3,8,6]=>[2,3,8,5,6,1,4,7]=>[7,6,1,4,3,8,5,2]=>[1,1,2,2,1,1]
[4,1,2,5,7,8,3,6]=>[7,4,1,5,8,2,3,6]=>[2,5,8,4,1,7,6,3]=>[3,1,2,1,1]
[1,4,2,5,7,8,3,6]=>[2,7,4,5,8,1,3,6]=>[7,2,5,4,1,8,6,3]=>[1,2,1,2,1,1]
[1,4,5,2,7,8,3,6]=>[2,3,7,5,8,1,4,6]=>[7,6,2,4,1,8,5,3]=>[1,1,2,2,1,1]
[1,4,5,7,8,2,3,6]=>[2,3,6,7,4,8,1,5]=>[7,6,3,2,5,1,8,4]=>[1,1,1,2,2,1]
[4,1,5,2,8,3,6,7]=>[6,3,1,7,8,2,4,5]=>[3,6,8,2,1,7,5,4]=>[3,1,2,1,1]
[4,5,1,2,8,3,6,7]=>[6,1,7,2,8,3,4,5]=>[3,8,2,7,1,6,5,4]=>[2,2,2,1,1]
[4,1,5,8,2,3,6,7]=>[5,3,1,6,7,8,2,4]=>[4,6,8,3,2,1,7,5]=>[3,1,1,2,1]
[4,5,1,8,2,3,6,7]=>[5,1,6,2,7,8,3,4]=>[4,8,3,7,2,1,6,5]=>[2,2,1,2,1]
[4,5,8,1,2,3,6,7]=>[4,1,5,2,6,7,8,3]=>[5,8,4,7,3,2,1,6]=>[2,2,1,1,2]
[4,1,5,2,3,8,6,7]=>[7,3,1,8,2,4,5,6]=>[2,6,8,1,7,5,4,3]=>[3,2,1,1,1]
[4,5,1,2,3,8,6,7]=>[7,1,8,3,2,4,5,6]=>[2,8,1,6,7,5,4,3]=>[2,3,1,1,1]
[1,4,5,2,3,8,6,7]=>[2,7,3,8,1,4,5,6]=>[7,2,6,1,8,5,4,3]=>[1,2,2,1,1,1]
[4,1,2,5,8,3,6,7]=>[4,6,1,7,8,2,3,5]=>[5,3,8,2,1,7,6,4]=>[1,2,1,2,1,1]
[1,4,2,5,8,3,6,7]=>[4,2,6,7,8,1,3,5]=>[5,7,3,2,1,8,6,4]=>[2,1,1,2,1,1]
[1,4,5,2,8,3,6,7]=>[2,6,3,7,8,1,4,5]=>[7,3,6,2,1,8,5,4]=>[1,2,1,2,1,1]
[1,4,5,8,2,3,6,7]=>[2,5,3,6,7,8,1,4]=>[7,4,6,3,2,1,8,5]=>[1,2,1,1,2,1]
[4,5,1,2,3,6,8,7]=>[8,3,1,4,2,5,6,7]=>[1,6,8,5,7,4,3,2]=>[3,2,1,1,1]
[1,4,2,5,3,6,8,7]=>[4,2,8,1,3,5,6,7]=>[5,7,1,8,6,4,3,2]=>[2,2,1,1,1,1]
[4,1,2,5,6,3,8,7]=>[4,5,1,8,2,3,6,7]=>[5,4,8,1,7,6,3,2]=>[1,2,2,1,1,1]
[1,4,5,2,6,3,8,7]=>[2,5,3,8,1,4,6,7]=>[7,4,6,1,8,5,3,2]=>[1,2,2,1,1,1]
[4,1,2,5,6,8,3,7]=>[4,5,1,7,8,2,3,6]=>[5,4,8,2,1,7,6,3]=>[1,2,1,2,1,1]
[1,4,2,5,6,8,3,7]=>[4,2,5,7,8,1,3,6]=>[5,7,4,2,1,8,6,3]=>[2,1,1,2,1,1]
[1,4,5,2,6,8,3,7]=>[2,5,3,7,8,1,4,6]=>[7,4,6,2,1,8,5,3]=>[1,2,1,2,1,1]
[1,4,5,6,2,8,3,7]=>[2,3,7,4,8,1,5,6]=>[7,6,2,5,1,8,4,3]=>[1,1,2,2,1,1]
[1,4,5,6,8,2,3,7]=>[2,3,6,4,7,8,1,5]=>[7,6,3,5,2,1,8,4]=>[1,1,2,1,2,1]
[4,1,5,2,3,6,7,8]=>[4,5,2,1,3,6,7,8]=>[5,4,7,8,6,3,2,1]=>[1,3,1,1,1,1]
[4,1,2,5,3,6,7,8]=>[5,2,3,1,4,6,7,8]=>[4,7,6,8,5,3,2,1]=>[2,2,1,1,1,1]
[1,4,2,5,3,6,7,8]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>[3,1,1,1,1,1]
[1,4,5,2,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>[5,7,4,8,6,3,2,1]=>[2,2,1,1,1,1]
[4,1,2,5,6,3,7,8]=>[4,6,2,1,3,5,7,8]=>[5,3,7,8,6,4,2,1]=>[1,3,1,1,1,1]
[1,4,5,2,6,3,7,8]=>[2,6,4,1,3,5,7,8]=>[7,3,5,8,6,4,2,1]=>[1,3,1,1,1,1]
[1,4,5,6,2,3,7,8]=>[2,5,3,6,1,4,7,8]=>[7,4,6,3,8,5,2,1]=>[1,2,2,1,1,1]
[4,1,2,5,6,7,3,8]=>[4,5,1,7,2,3,6,8]=>[5,4,8,2,7,6,3,1]=>[1,2,2,1,1,1]
[1,4,2,5,6,7,3,8]=>[4,2,5,7,1,3,6,8]=>[5,7,4,2,8,6,3,1]=>[2,1,2,1,1,1]
[1,4,5,2,6,7,3,8]=>[2,5,3,7,1,4,6,8]=>[7,4,6,2,8,5,3,1]=>[1,2,2,1,1,1]
[1,4,5,6,7,2,3,8]=>[2,3,6,4,7,1,5,8]=>[7,6,3,5,2,8,4,1]=>[1,1,2,2,1,1]
[4,1,2,5,6,7,8,3]=>[4,5,1,6,8,2,3,7]=>[5,4,8,3,1,7,6,2]=>[1,2,1,2,1,1]
[1,4,2,5,6,7,8,3]=>[4,2,5,6,8,1,3,7]=>[5,7,4,3,1,8,6,2]=>[2,1,1,2,1,1]
[1,4,5,2,6,7,8,3]=>[2,5,3,6,8,1,4,7]=>[7,4,6,3,1,8,5,2]=>[1,2,1,2,1,1]
[1,4,5,6,2,7,8,3]=>[2,3,6,4,8,1,5,7]=>[7,6,3,5,1,8,4,2]=>[1,1,2,2,1,1]
[1,4,5,6,7,2,8,3]=>[2,3,4,8,6,1,5,7]=>[7,6,5,1,3,8,4,2]=>[1,1,1,3,1,1]
[1,4,5,6,7,8,2,3]=>[2,3,4,7,5,8,1,6]=>[7,6,5,2,4,1,8,3]=>[1,1,1,2,2,1]
[4,1,6,2,7,3,8,5]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[1,4,1,1,1]
[4,1,6,7,2,3,8,5]=>[1,8,5,3,6,2,4,7]=>[8,1,4,6,3,7,5,2]=>[1,3,2,1,1]
[4,6,1,7,2,3,8,5]=>[1,8,5,6,3,2,4,7]=>[8,1,4,3,6,7,5,2]=>[1,2,3,1,1]
[4,6,7,1,2,3,8,5]=>[1,8,4,5,2,6,3,7]=>[8,1,5,4,7,3,6,2]=>[1,2,2,2,1]
[4,6,1,2,7,8,3,5]=>[1,7,5,8,3,2,4,6]=>[8,2,4,1,6,7,5,3]=>[1,2,3,1,1]
[4,1,6,7,2,8,3,5]=>[1,7,3,8,5,2,4,6]=>[8,2,6,1,4,7,5,3]=>[1,2,3,1,1]
[4,6,1,7,2,8,3,5]=>[1,7,8,5,3,2,4,6]=>[8,2,1,4,6,7,5,3]=>[1,1,4,1,1]
[4,6,7,1,2,8,3,5]=>[1,7,8,4,2,5,3,6]=>[8,2,1,5,7,4,6,3]=>[1,1,3,2,1]
[4,6,7,1,8,2,3,5]=>[1,6,7,2,8,4,3,5]=>[8,3,2,7,1,5,6,4]=>[1,1,2,3,1]
[4,6,7,8,1,2,3,5]=>[1,5,6,2,7,3,8,4]=>[8,4,3,7,2,6,1,5]=>[1,1,2,2,2]
[4,1,6,2,7,3,5,8]=>[6,1,7,4,2,3,5,8]=>[3,8,2,5,7,6,4,1]=>[2,3,1,1,1]
[4,6,1,2,7,3,5,8]=>[6,1,7,3,4,2,5,8]=>[3,8,2,6,5,7,4,1]=>[2,2,2,1,1]
[4,6,7,1,2,3,5,8]=>[4,1,5,6,2,7,3,8]=>[5,8,4,3,7,2,6,1]=>[2,1,2,2,1]
[4,1,6,2,3,7,5,8]=>[7,4,1,5,2,3,6,8]=>[2,5,8,4,7,6,3,1]=>[3,2,1,1,1]
[4,6,1,2,3,7,5,8]=>[7,3,1,4,5,2,6,8]=>[2,6,8,5,4,7,3,1]=>[3,1,2,1,1]
[4,1,2,6,3,7,5,8]=>[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]
[1,4,2,6,3,7,5,8]=>[2,7,5,1,3,4,6,8]=>[7,2,4,8,6,5,3,1]=>[1,3,1,1,1,1]
[1,4,6,7,2,3,5,8]=>[2,5,6,3,7,1,4,8]=>[7,4,3,6,2,8,5,1]=>[1,1,2,2,1,1]
[4,1,6,2,3,7,8,5]=>[6,1,8,4,2,3,5,7]=>[3,8,1,5,7,6,4,2]=>[2,3,1,1,1]
[4,1,2,6,3,7,8,5]=>[6,4,1,8,2,3,5,7]=>[3,5,8,1,7,6,4,2]=>[3,2,1,1,1]
[1,4,6,2,3,7,8,5]=>[2,6,8,4,1,3,5,7]=>[7,3,1,5,8,6,4,2]=>[1,1,3,1,1,1]
[4,1,2,6,7,3,8,5]=>[4,1,8,6,2,3,5,7]=>[5,8,1,3,7,6,4,2]=>[2,3,1,1,1]
[1,4,6,2,7,3,8,5]=>[8,2,6,4,1,3,5,7]=>[1,7,3,5,8,6,4,2]=>[2,3,1,1,1]
[1,4,6,7,2,3,8,5]=>[8,2,5,3,6,1,4,7]=>[1,7,4,6,3,8,5,2]=>[2,2,2,1,1]
[1,4,2,6,7,8,3,5]=>[2,4,7,5,8,1,3,6]=>[7,5,2,4,1,8,6,3]=>[1,1,2,2,1,1]
[1,4,6,2,7,8,3,5]=>[7,2,5,3,8,1,4,6]=>[2,7,4,6,1,8,5,3]=>[2,2,2,1,1]
[1,4,6,7,2,8,3,5]=>[7,2,3,8,5,1,4,6]=>[2,7,6,1,4,8,5,3]=>[2,1,3,1,1]
[1,4,6,7,8,2,3,5]=>[6,2,3,7,4,8,1,5]=>[3,7,6,2,5,1,8,4]=>[2,1,2,2,1]
[4,6,1,2,8,3,5,7]=>[6,1,7,8,3,2,4,5]=>[3,8,2,1,6,7,5,4]=>[2,1,3,1,1]
[4,1,6,8,2,3,5,7]=>[5,1,6,3,7,8,2,4]=>[4,8,3,6,2,1,7,5]=>[2,2,1,2,1]
[4,6,1,8,2,3,5,7]=>[5,1,6,7,2,8,3,4]=>[4,8,3,2,7,1,6,5]=>[2,1,2,2,1]
[4,6,8,1,2,3,5,7]=>[4,1,5,6,2,7,8,3]=>[5,8,4,3,7,2,1,6]=>[2,1,2,1,2]
[4,1,6,2,3,8,5,7]=>[7,1,8,4,2,3,5,6]=>[2,8,1,5,7,6,4,3]=>[2,3,1,1,1]
[4,6,1,2,3,8,5,7]=>[7,1,8,3,4,2,5,6]=>[2,8,1,6,5,7,4,3]=>[2,2,2,1,1]
[4,1,2,6,3,8,5,7]=>[7,4,1,8,2,3,5,6]=>[2,5,8,1,7,6,4,3]=>[3,2,1,1,1]
[1,4,2,6,3,8,5,7]=>[2,7,4,8,1,3,5,6]=>[7,2,5,1,8,6,4,3]=>[1,2,2,1,1,1]
[1,4,2,6,8,3,5,7]=>[2,6,4,7,8,1,3,5]=>[7,3,5,2,1,8,6,4]=>[1,2,1,2,1,1]
[1,4,6,2,8,3,5,7]=>[2,6,7,3,8,1,4,5]=>[7,3,2,6,1,8,5,4]=>[1,1,2,2,1,1]
[1,4,6,8,2,3,5,7]=>[2,5,6,3,7,8,1,4]=>[7,4,3,6,2,1,8,5]=>[1,1,2,1,2,1]
[4,1,6,2,3,5,8,7]=>[8,4,1,5,2,3,6,7]=>[1,5,8,4,7,6,3,2]=>[3,2,1,1,1]
[4,1,2,6,3,5,8,7]=>[8,5,2,1,3,4,6,7]=>[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]
[1,4,6,2,3,5,8,7]=>[2,8,4,5,1,3,6,7]=>[7,1,5,4,8,6,3,2]=>[1,2,2,1,1,1]
[4,1,2,3,6,5,8,7]=>[5,8,2,1,3,4,6,7]=>[4,1,7,8,6,5,3,2]=>[1,3,1,1,1,1]
[1,4,2,3,6,5,8,7]=>[5,2,8,1,3,4,6,7]=>[4,7,1,8,6,5,3,2]=>[2,2,1,1,1,1]
[1,2,4,6,3,5,8,7]=>[8,3,5,1,2,4,6,7]=>[1,6,4,8,7,5,3,2]=>[2,2,1,1,1,1]
[4,1,2,3,6,8,5,7]=>[5,7,1,8,2,3,4,6]=>[4,2,8,1,7,6,5,3]=>[1,2,2,1,1,1]
[1,2,4,3,6,8,5,7]=>[3,5,7,8,1,2,4,6]=>[6,4,2,1,8,7,5,3]=>[1,1,1,2,1,1,1]
[1,2,4,6,3,8,5,7]=>[7,3,4,8,1,2,5,6]=>[2,6,5,1,8,7,4,3]=>[2,1,2,1,1,1]
[1,2,4,6,8,3,5,7]=>[6,3,4,7,8,1,2,5]=>[3,6,5,2,1,8,7,4]=>[2,1,1,2,1,1]
[4,6,1,2,3,5,7,8]=>[3,4,1,5,6,2,7,8]=>[6,5,8,4,3,7,2,1]=>[1,2,1,2,1,1]
[4,1,2,6,3,5,7,8]=>[5,6,2,1,3,4,7,8]=>[4,3,7,8,6,5,2,1]=>[1,3,1,1,1,1]
[1,4,2,6,3,5,7,8]=>[5,2,6,1,3,4,7,8]=>[4,7,3,8,6,5,2,1]=>[2,2,1,1,1,1]
[1,4,6,2,3,5,7,8]=>[4,2,5,6,1,3,7,8]=>[5,7,4,3,8,6,2,1]=>[2,1,2,1,1,1]
[4,1,2,3,6,5,7,8]=>[6,2,3,1,4,5,7,8]=>[3,7,6,8,5,4,2,1]=>[2,2,1,1,1,1]
[1,4,2,3,6,5,7,8]=>[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>[3,1,1,1,1,1]
[1,2,4,6,3,5,7,8]=>[3,5,6,1,2,4,7,8]=>[6,4,3,8,7,5,2,1]=>[1,1,2,1,1,1,1]
[4,1,2,3,6,7,5,8]=>[5,7,2,1,3,4,6,8]=>[4,2,7,8,6,5,3,1]=>[1,3,1,1,1,1]
[1,2,4,6,3,7,5,8]=>[7,3,5,1,2,4,6,8]=>[2,6,4,8,7,5,3,1]=>[2,2,1,1,1,1]
[1,2,4,6,7,3,5,8]=>[6,3,4,7,1,2,5,8]=>[3,6,5,2,8,7,4,1]=>[2,1,2,1,1,1]
[4,1,2,3,6,7,8,5]=>[5,6,1,8,2,3,4,7]=>[4,3,8,1,7,6,5,2]=>[1,2,2,1,1,1]
[1,4,2,3,6,7,8,5]=>[5,2,6,8,1,3,4,7]=>[4,7,3,1,8,6,5,2]=>[2,1,2,1,1,1]
[1,2,4,6,3,7,8,5]=>[6,3,4,8,1,2,5,7]=>[3,6,5,1,8,7,4,2]=>[2,1,2,1,1,1]
[1,2,4,6,7,8,3,5]=>[4,7,3,5,8,1,2,6]=>[5,2,6,4,1,8,7,3]=>[1,2,1,2,1,1]
[4,1,7,2,8,3,5,6]=>[6,1,7,8,4,2,3,5]=>[3,8,2,1,5,7,6,4]=>[2,1,3,1,1]
[4,1,7,8,2,3,5,6]=>[5,1,6,7,3,8,2,4]=>[4,8,3,2,6,1,7,5]=>[2,1,2,2,1]
[4,7,1,8,2,3,5,6]=>[5,1,6,7,8,3,2,4]=>[4,8,3,2,1,6,7,5]=>[2,1,1,3,1]
[4,7,8,1,2,3,5,6]=>[4,1,5,6,7,2,8,3]=>[5,8,4,3,2,7,1,6]=>[2,1,1,2,2]
[4,1,7,2,3,8,5,6]=>[7,1,8,4,5,2,3,6]=>[2,8,1,5,4,7,6,3]=>[2,2,2,1,1]
[4,7,1,2,3,8,5,6]=>[7,1,8,3,4,5,2,6]=>[2,8,1,6,5,4,7,3]=>[2,2,1,2,1]
[1,4,2,7,3,8,5,6]=>[2,7,8,5,1,3,4,6]=>[7,2,1,4,8,6,5,3]=>[1,1,3,1,1,1]
[1,4,7,2,3,8,5,6]=>[2,7,8,4,5,1,3,6]=>[7,2,1,5,4,8,6,3]=>[1,1,2,2,1,1]
[4,1,2,7,8,3,5,6]=>[6,1,7,4,8,2,3,5]=>[3,8,2,5,1,7,6,4]=>[2,2,2,1,1]
[1,4,2,7,8,3,5,6]=>[2,6,7,4,8,1,3,5]=>[7,3,2,5,1,8,6,4]=>[1,1,2,2,1,1]
[1,4,7,2,8,3,5,6]=>[2,6,7,8,4,1,3,5]=>[7,3,2,1,5,8,6,4]=>[1,1,1,3,1,1]
[1,4,7,8,2,3,5,6]=>[2,5,6,7,3,8,1,4]=>[7,4,3,2,6,1,8,5]=>[1,1,1,2,2,1]
[4,1,7,2,3,5,8,6]=>[8,4,1,5,6,2,3,7]=>[1,5,8,4,3,7,6,2]=>[3,1,2,1,1]
[4,7,1,2,3,5,8,6]=>[8,3,1,4,5,6,2,7]=>[1,6,8,5,4,3,7,2]=>[3,1,1,2,1]
[4,1,2,7,3,5,8,6]=>[8,5,1,6,2,3,4,7]=>[1,4,8,3,7,6,5,2]=>[3,2,1,1,1]
[1,4,2,7,3,5,8,6]=>[2,8,5,6,1,3,4,7]=>[7,1,4,3,8,6,5,2]=>[1,2,2,1,1,1]
[1,4,7,2,3,5,8,6]=>[2,8,4,5,6,1,3,7]=>[7,1,5,4,3,8,6,2]=>[1,2,1,2,1,1]
[4,1,2,3,7,5,8,6]=>[8,6,2,1,3,4,5,7]=>[1,3,7,8,6,5,4,2]=>[4,1,1,1,1]
[1,4,2,3,7,5,8,6]=>[2,8,6,1,3,4,5,7]=>[7,1,3,8,6,5,4,2]=>[1,3,1,1,1,1]
[1,2,4,7,3,5,8,6]=>[8,3,5,6,1,2,4,7]=>[1,6,4,3,8,7,5,2]=>[2,1,2,1,1,1]
[4,1,2,3,7,8,5,6]=>[7,5,1,8,2,3,4,6]=>[2,4,8,1,7,6,5,3]=>[3,2,1,1,1]
[1,4,2,3,7,8,5,6]=>[2,7,5,8,1,3,4,6]=>[7,2,4,1,8,6,5,3]=>[1,2,2,1,1,1]
[1,2,4,3,7,8,5,6]=>[7,3,5,8,1,2,4,6]=>[2,6,4,1,8,7,5,3]=>[2,1,2,1,1,1]
[1,2,4,7,3,8,5,6]=>[7,8,3,5,1,2,4,6]=>[2,1,6,4,8,7,5,3]=>[1,2,2,1,1,1]
[1,2,4,7,8,3,5,6]=>[6,7,3,4,8,1,2,5]=>[3,2,6,5,1,8,7,4]=>[1,2,1,2,1,1]
[4,1,7,2,3,5,6,8]=>[4,5,1,6,7,2,3,8]=>[5,4,8,3,2,7,6,1]=>[1,2,1,2,1,1]
[4,7,1,2,3,5,6,8]=>[3,4,1,5,6,7,2,8]=>[6,5,8,4,3,2,7,1]=>[1,2,1,1,2,1]
[4,1,2,7,3,5,6,8]=>[5,6,1,7,2,3,4,8]=>[4,3,8,2,7,6,5,1]=>[1,2,2,1,1,1]
[1,4,2,7,3,5,6,8]=>[5,2,6,7,1,3,4,8]=>[4,7,3,2,8,6,5,1]=>[2,1,2,1,1,1]
[1,4,7,2,3,5,6,8]=>[4,2,5,6,7,1,3,8]=>[5,7,4,3,2,8,6,1]=>[2,1,1,2,1,1]
[4,1,2,3,7,5,6,8]=>[6,7,2,1,3,4,5,8]=>[3,2,7,8,6,5,4,1]=>[1,3,1,1,1,1]
[1,4,2,3,7,5,6,8]=>[6,2,7,1,3,4,5,8]=>[3,7,2,8,6,5,4,1]=>[2,2,1,1,1,1]
[1,2,4,3,7,5,6,8]=>[3,6,7,1,2,4,5,8]=>[6,3,2,8,7,5,4,1]=>[1,1,2,1,1,1,1]
[1,2,4,7,3,5,6,8]=>[3,5,6,7,1,2,4,8]=>[6,4,3,2,8,7,5,1]=>[1,1,1,2,1,1,1]
[4,1,2,3,5,7,6,8]=>[7,2,3,1,4,5,6,8]=>[2,7,6,8,5,4,3,1]=>[2,2,1,1,1,1]
[1,4,2,3,5,7,6,8]=>[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>[3,1,1,1,1,1]
[1,2,4,5,7,3,6,8]=>[3,4,6,7,1,2,5,8]=>[6,5,3,2,8,7,4,1]=>[1,1,1,2,1,1,1]
[4,1,2,3,5,7,8,6]=>[6,8,2,1,3,4,5,7]=>[3,1,7,8,6,5,4,2]=>[1,3,1,1,1,1]
[1,4,2,3,5,7,8,6]=>[6,2,8,1,3,4,5,7]=>[3,7,1,8,6,5,4,2]=>[2,2,1,1,1,1]
[1,2,4,5,7,3,8,6]=>[8,3,4,6,1,2,5,7]=>[1,6,5,3,8,7,4,2]=>[2,1,2,1,1,1]
[1,2,4,5,7,8,3,6]=>[7,3,4,5,8,1,2,6]=>[2,6,5,4,1,8,7,3]=>[2,1,1,2,1,1]
[4,1,8,2,3,5,6,7]=>[4,5,1,6,7,8,2,3]=>[5,4,8,3,2,1,7,6]=>[1,2,1,1,2,1]
[4,8,1,2,3,5,6,7]=>[3,4,1,5,6,7,8,2]=>[6,5,8,4,3,2,1,7]=>[1,2,1,1,1,2]
[4,1,2,8,3,5,6,7]=>[5,6,1,7,8,2,3,4]=>[4,3,8,2,1,7,6,5]=>[1,2,1,2,1,1]
[1,4,2,8,3,5,6,7]=>[5,2,6,7,8,1,3,4]=>[4,7,3,2,1,8,6,5]=>[2,1,1,2,1,1]
[1,4,8,2,3,5,6,7]=>[4,2,5,6,7,8,1,3]=>[5,7,4,3,2,1,8,6]=>[2,1,1,1,2,1]
[4,1,2,3,8,5,6,7]=>[6,7,1,8,2,3,4,5]=>[3,2,8,1,7,6,5,4]=>[1,2,2,1,1,1]
[1,4,2,3,8,5,6,7]=>[6,2,7,8,1,3,4,5]=>[3,7,2,1,8,6,5,4]=>[2,1,2,1,1,1]
[1,2,4,3,8,5,6,7]=>[3,6,7,8,1,2,4,5]=>[6,3,2,1,8,7,5,4]=>[1,1,1,2,1,1,1]
[1,2,4,8,3,5,6,7]=>[3,5,6,7,8,1,2,4]=>[6,4,3,2,1,8,7,5]=>[1,1,1,1,2,1,1]
[4,1,2,3,5,8,6,7]=>[7,8,2,1,3,4,5,6]=>[2,1,7,8,6,5,4,3]=>[1,3,1,1,1,1]
[1,4,2,3,5,8,6,7]=>[7,2,8,1,3,4,5,6]=>[2,7,1,8,6,5,4,3]=>[2,2,1,1,1,1]
[1,2,4,3,5,8,6,7]=>[3,7,8,1,2,4,5,6]=>[6,2,1,8,7,5,4,3]=>[1,1,2,1,1,1,1]
[1,2,4,5,3,8,6,7]=>[3,4,7,8,1,2,5,6]=>[6,5,2,1,8,7,4,3]=>[1,1,1,2,1,1,1]
[1,2,4,5,8,3,6,7]=>[3,4,6,7,8,1,2,5]=>[6,5,3,2,1,8,7,4]=>[1,1,1,1,2,1,1]
[4,1,2,3,5,6,8,7]=>[8,2,3,1,4,5,6,7]=>[1,7,6,8,5,4,3,2]=>[2,2,1,1,1,1]
[1,4,2,3,5,6,8,7]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>[3,1,1,1,1,1]
[1,2,4,5,6,8,3,7]=>[3,4,5,7,8,1,2,6]=>[6,5,4,2,1,8,7,3]=>[1,1,1,1,2,1,1]
[1,4,2,3,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[6,5,8,7,4,3,2,1]=>[1,2,1,1,1,1,1]
[5,1,6,2,7,3,8,4]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>[5,1,1,1]
[5,6,1,2,7,3,8,4]=>[8,6,3,1,4,2,5,7]=>[1,3,6,8,5,7,4,2]=>[4,2,1,1]
[5,1,6,7,2,3,8,4]=>[8,5,3,1,6,2,4,7]=>[1,4,6,8,3,7,5,2]=>[4,2,1,1]
[5,6,1,7,2,3,8,4]=>[8,5,1,6,3,2,4,7]=>[1,4,8,3,6,7,5,2]=>[3,3,1,1]
[5,6,7,1,2,3,8,4]=>[8,4,1,5,2,6,3,7]=>[1,5,8,4,7,3,6,2]=>[3,2,2,1]
[5,1,6,2,7,8,3,4]=>[7,5,3,1,8,2,4,6]=>[2,4,6,8,1,7,5,3]=>[4,2,1,1]
[5,6,1,2,7,8,3,4]=>[7,5,1,8,3,2,4,6]=>[2,4,8,1,6,7,5,3]=>[3,3,1,1]
[5,1,6,7,2,8,3,4]=>[7,3,1,8,5,2,4,6]=>[2,6,8,1,4,7,5,3]=>[3,3,1,1]
[5,6,1,7,2,8,3,4]=>[7,1,8,5,3,2,4,6]=>[2,8,1,4,6,7,5,3]=>[2,4,1,1]
[5,6,7,1,2,8,3,4]=>[7,1,8,4,2,5,3,6]=>[2,8,1,5,7,4,6,3]=>[2,3,2,1]
[5,1,6,7,8,2,3,4]=>[6,3,1,7,4,8,2,5]=>[3,6,8,2,5,1,7,4]=>[3,2,2,1]
[5,6,1,7,8,2,3,4]=>[6,1,7,4,2,8,3,5]=>[3,8,2,5,7,1,6,4]=>[2,3,2,1]
[5,6,7,1,8,2,3,4]=>[6,1,7,2,8,4,3,5]=>[3,8,2,7,1,5,6,4]=>[2,2,3,1]
[5,1,6,2,7,3,4,8]=>[6,7,4,2,1,3,5,8]=>[3,2,5,7,8,6,4,1]=>[1,4,1,1,1]
[5,6,1,2,7,3,4,8]=>[6,7,3,1,4,2,5,8]=>[3,2,6,8,5,7,4,1]=>[1,3,2,1,1]
[5,6,1,7,2,3,4,8]=>[5,6,1,7,3,2,4,8]=>[4,3,8,2,6,7,5,1]=>[1,2,3,1,1]
[5,1,6,2,3,7,4,8]=>[7,4,5,2,1,3,6,8]=>[2,5,4,7,8,6,3,1]=>[2,3,1,1,1]
[1,5,2,6,3,7,4,8]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]
[5,1,2,6,7,3,4,8]=>[6,4,7,2,1,3,5,8]=>[3,5,2,7,8,6,4,1]=>[2,3,1,1,1]
[1,5,2,6,7,3,4,8]=>[6,4,2,7,1,3,5,8]=>[3,5,7,2,8,6,4,1]=>[3,2,1,1,1]
[1,5,6,2,7,3,4,8]=>[6,2,7,4,1,3,5,8]=>[3,7,2,5,8,6,4,1]=>[2,3,1,1,1]
[1,5,6,7,2,3,4,8]=>[5,2,6,3,7,1,4,8]=>[4,7,3,6,2,8,5,1]=>[2,2,2,1,1]
[5,1,6,2,3,7,8,4]=>[6,8,4,2,1,3,5,7]=>[3,1,5,7,8,6,4,2]=>[1,4,1,1,1]
[5,6,1,2,3,7,8,4]=>[6,8,3,1,4,2,5,7]=>[3,1,6,8,5,7,4,2]=>[1,3,2,1,1]
[5,1,2,6,3,7,8,4]=>[6,4,8,2,1,3,5,7]=>[3,5,1,7,8,6,4,2]=>[2,3,1,1,1]
[1,5,2,6,3,7,8,4]=>[6,4,2,8,1,3,5,7]=>[3,5,7,1,8,6,4,2]=>[3,2,1,1,1]
[1,5,6,2,3,7,8,4]=>[6,2,8,4,1,3,5,7]=>[3,7,1,5,8,6,4,2]=>[2,3,1,1,1]
[5,1,2,6,7,3,8,4]=>[4,8,6,2,1,3,5,7]=>[5,1,3,7,8,6,4,2]=>[1,4,1,1,1]
[1,5,6,7,2,3,8,4]=>[2,8,5,3,6,1,4,7]=>[7,1,4,6,3,8,5,2]=>[1,3,2,1,1]
[5,1,2,6,7,8,3,4]=>[4,7,5,1,8,2,3,6]=>[5,2,4,8,1,7,6,3]=>[1,3,2,1,1]
[1,5,2,6,7,8,3,4]=>[4,2,7,5,8,1,3,6]=>[5,7,2,4,1,8,6,3]=>[2,2,2,1,1]
[1,5,6,2,7,8,3,4]=>[2,7,5,3,8,1,4,6]=>[7,2,4,6,1,8,5,3]=>[1,3,2,1,1]
[1,5,6,7,8,2,3,4]=>[2,6,3,7,4,8,1,5]=>[7,3,6,2,5,1,8,4]=>[1,2,2,2,1]
[5,6,1,2,8,3,4,7]=>[6,7,1,8,3,2,4,5]=>[3,2,8,1,6,7,5,4]=>[1,2,3,1,1]
[5,6,1,8,2,3,4,7]=>[5,6,1,7,2,8,3,4]=>[4,3,8,2,7,1,6,5]=>[1,2,2,2,1]
[5,6,8,1,2,3,4,7]=>[4,5,1,6,2,7,8,3]=>[5,4,8,3,7,2,1,6]=>[1,2,2,1,2]
[5,1,6,2,3,8,4,7]=>[7,8,4,2,1,3,5,6]=>[2,1,5,7,8,6,4,3]=>[1,4,1,1,1]
[5,6,1,2,3,8,4,7]=>[7,8,3,1,4,2,5,6]=>[2,1,6,8,5,7,4,3]=>[1,3,2,1,1]
[5,1,2,6,3,8,4,7]=>[7,4,8,2,1,3,5,6]=>[2,5,1,7,8,6,4,3]=>[2,3,1,1,1]
[1,5,2,6,3,8,4,7]=>[7,4,2,8,1,3,5,6]=>[2,5,7,1,8,6,4,3]=>[3,2,1,1,1]
[1,5,6,2,3,8,4,7]=>[7,2,8,4,1,3,5,6]=>[2,7,1,5,8,6,4,3]=>[2,3,1,1,1]
[5,1,2,6,8,3,4,7]=>[6,4,7,1,8,2,3,5]=>[3,5,2,8,1,7,6,4]=>[2,2,2,1,1]
[1,5,2,6,8,3,4,7]=>[6,4,2,7,8,1,3,5]=>[3,5,7,2,1,8,6,4]=>[3,1,2,1,1]
[1,5,6,2,8,3,4,7]=>[6,2,7,3,8,1,4,5]=>[3,7,2,6,1,8,5,4]=>[2,2,2,1,1]
[1,5,6,8,2,3,4,7]=>[5,2,6,3,7,8,1,4]=>[4,7,3,6,2,1,8,5]=>[2,2,1,2,1]
[5,1,6,2,3,4,8,7]=>[8,4,5,2,1,3,6,7]=>[1,5,4,7,8,6,3,2]=>[2,3,1,1,1]
[5,1,2,6,3,4,8,7]=>[8,5,2,3,1,4,6,7]=>[1,4,7,6,8,5,3,2]=>[3,2,1,1,1]
[1,5,2,6,3,4,8,7]=>[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]
[1,5,6,2,3,4,8,7]=>[8,4,2,5,1,3,6,7]=>[1,5,7,4,8,6,3,2]=>[3,2,1,1,1]
[1,5,2,3,6,4,8,7]=>[5,8,3,1,2,4,6,7]=>[4,1,6,8,7,5,3,2]=>[1,3,1,1,1,1]
[1,2,5,3,6,4,8,7]=>[5,3,8,1,2,4,6,7]=>[4,6,1,8,7,5,3,2]=>[2,2,1,1,1,1]
[1,2,5,6,3,4,8,7]=>[3,8,5,1,2,4,6,7]=>[6,1,4,8,7,5,3,2]=>[1,3,1,1,1,1]
[5,1,2,3,6,8,4,7]=>[5,7,8,2,1,3,4,6]=>[4,2,1,7,8,6,5,3]=>[1,1,3,1,1,1]
[1,5,2,3,6,8,4,7]=>[5,7,2,8,1,3,4,6]=>[4,2,7,1,8,6,5,3]=>[1,2,2,1,1,1]
[1,2,5,6,3,8,4,7]=>[3,7,4,8,1,2,5,6]=>[6,2,5,1,8,7,4,3]=>[1,2,2,1,1,1]
[1,2,5,6,8,3,4,7]=>[3,6,4,7,8,1,2,5]=>[6,3,5,2,1,8,7,4]=>[1,2,1,2,1,1]
[5,1,6,2,3,4,7,8]=>[4,5,6,2,1,3,7,8]=>[5,4,3,7,8,6,2,1]=>[1,1,3,1,1,1]
[5,1,2,6,3,4,7,8]=>[5,6,2,3,1,4,7,8]=>[4,3,7,6,8,5,2,1]=>[1,2,2,1,1,1]
[1,5,2,6,3,4,7,8]=>[5,6,3,1,2,4,7,8]=>[4,3,6,8,7,5,2,1]=>[1,3,1,1,1,1]
[1,5,6,2,3,4,7,8]=>[4,5,2,6,1,3,7,8]=>[5,4,7,3,8,6,2,1]=>[1,2,2,1,1,1]
[5,1,2,3,6,4,7,8]=>[6,2,3,4,1,5,7,8]=>[3,7,6,5,8,4,2,1]=>[2,1,2,1,1,1]
[1,5,2,3,6,4,7,8]=>[6,3,4,1,2,5,7,8]=>[3,6,5,8,7,4,2,1]=>[2,2,1,1,1,1]
[1,2,5,3,6,4,7,8]=>[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>[3,1,1,1,1,1]
[1,2,5,6,3,4,7,8]=>[5,3,6,1,2,4,7,8]=>[4,6,3,8,7,5,2,1]=>[2,2,1,1,1,1]
[5,1,2,3,6,7,4,8]=>[5,7,2,3,1,4,6,8]=>[4,2,7,6,8,5,3,1]=>[1,2,2,1,1,1]
[1,5,2,3,6,7,4,8]=>[5,7,3,1,2,4,6,8]=>[4,2,6,8,7,5,3,1]=>[1,3,1,1,1,1]
[1,2,5,3,6,7,4,8]=>[5,3,7,1,2,4,6,8]=>[4,6,2,8,7,5,3,1]=>[2,2,1,1,1,1]
[1,2,5,6,3,7,4,8]=>[3,7,5,1,2,4,6,8]=>[6,2,4,8,7,5,3,1]=>[1,3,1,1,1,1]
[5,1,2,3,6,7,8,4]=>[5,6,8,2,1,3,4,7]=>[4,3,1,7,8,6,5,2]=>[1,1,3,1,1,1]
[1,5,2,3,6,7,8,4]=>[5,6,2,8,1,3,4,7]=>[4,3,7,1,8,6,5,2]=>[1,2,2,1,1,1]
[1,2,5,3,6,7,8,4]=>[5,3,6,8,1,2,4,7]=>[4,6,3,1,8,7,5,2]=>[2,1,2,1,1,1]
[1,2,5,6,3,7,8,4]=>[3,6,4,8,1,2,5,7]=>[6,3,5,1,8,7,4,2]=>[1,2,2,1,1,1]
[1,2,5,6,7,3,8,4]=>[3,4,8,6,1,2,5,7]=>[6,5,1,3,8,7,4,2]=>[1,1,3,1,1,1]
[5,1,7,2,8,3,4,6]=>[6,7,1,8,4,2,3,5]=>[3,2,8,1,5,7,6,4]=>[1,2,3,1,1]
[5,7,1,2,8,3,4,6]=>[6,7,1,8,3,4,2,5]=>[3,2,8,1,6,5,7,4]=>[1,2,2,2,1]
[5,1,7,8,2,3,4,6]=>[5,6,1,7,3,8,2,4]=>[4,3,8,2,6,1,7,5]=>[1,2,2,2,1]
[5,7,1,8,2,3,4,6]=>[5,6,1,7,8,3,2,4]=>[4,3,8,2,1,6,7,5]=>[1,2,1,3,1]
[5,7,8,1,2,3,4,6]=>[4,5,1,6,7,2,8,3]=>[5,4,8,3,2,7,1,6]=>[1,2,1,2,2]
[5,1,7,2,3,8,4,6]=>[7,8,4,1,5,2,3,6]=>[2,1,5,8,4,7,6,3]=>[1,3,2,1,1]
[5,7,1,2,3,8,4,6]=>[7,8,3,1,4,5,2,6]=>[2,1,6,8,5,4,7,3]=>[1,3,1,2,1]
[5,1,2,7,3,8,4,6]=>[7,8,5,2,1,3,4,6]=>[2,1,4,7,8,6,5,3]=>[1,4,1,1,1]
[1,5,7,2,3,8,4,6]=>[7,2,8,4,5,1,3,6]=>[2,7,1,5,4,8,6,3]=>[2,2,2,1,1]
[5,1,2,7,8,3,4,6]=>[6,7,4,1,8,2,3,5]=>[3,2,5,8,1,7,6,4]=>[1,3,2,1,1]
[1,5,2,7,8,3,4,6]=>[6,2,7,4,8,1,3,5]=>[3,7,2,5,1,8,6,4]=>[2,2,2,1,1]
[1,5,7,2,8,3,4,6]=>[6,2,7,8,4,1,3,5]=>[3,7,2,1,5,8,6,4]=>[2,1,3,1,1]
[5,1,7,2,3,4,8,6]=>[8,4,5,1,6,2,3,7]=>[1,5,4,8,3,7,6,2]=>[2,2,2,1,1]
[5,1,2,7,3,4,8,6]=>[8,5,6,2,1,3,4,7]=>[1,4,3,7,8,6,5,2]=>[2,3,1,1,1]
[1,5,2,7,3,4,8,6]=>[8,5,2,6,1,3,4,7]=>[1,4,7,3,8,6,5,2]=>[3,2,1,1,1]
[1,5,7,2,3,4,8,6]=>[8,4,2,5,6,1,3,7]=>[1,5,7,4,3,8,6,2]=>[3,1,2,1,1]
[5,1,2,3,7,4,8,6]=>[8,6,2,3,1,4,5,7]=>[1,3,7,6,8,5,4,2]=>[3,2,1,1,1]
[1,5,2,3,7,4,8,6]=>[8,6,3,1,2,4,5,7]=>[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]
[1,2,5,3,7,4,8,6]=>[3,8,6,1,2,4,5,7]=>[6,1,3,8,7,5,4,2]=>[1,3,1,1,1,1]
[1,2,5,7,3,4,8,6]=>[3,8,5,6,1,2,4,7]=>[6,1,4,3,8,7,5,2]=>[1,2,2,1,1,1]
[5,1,2,3,7,8,4,6]=>[7,5,8,2,1,3,4,6]=>[2,4,1,7,8,6,5,3]=>[2,3,1,1,1]
[1,5,2,3,7,8,4,6]=>[7,5,2,8,1,3,4,6]=>[2,4,7,1,8,6,5,3]=>[3,2,1,1,1]
[1,2,5,3,7,8,4,6]=>[3,7,5,8,1,2,4,6]=>[6,2,4,1,8,7,5,3]=>[1,2,2,1,1,1]
[1,2,5,7,3,8,4,6]=>[3,7,8,5,1,2,4,6]=>[6,2,1,4,8,7,5,3]=>[1,1,3,1,1,1]
[1,2,5,7,8,3,4,6]=>[3,6,7,4,8,1,2,5]=>[6,3,2,5,1,8,7,4]=>[1,1,2,2,1,1]
[5,1,7,2,3,4,6,8]=>[4,5,6,1,7,2,3,8]=>[5,4,3,8,2,7,6,1]=>[1,1,2,2,1,1]
[5,7,1,2,3,4,6,8]=>[3,4,5,1,6,7,2,8]=>[6,5,4,8,3,2,7,1]=>[1,1,2,1,2,1]
[5,1,2,7,3,4,6,8]=>[5,6,7,2,1,3,4,8]=>[4,3,2,7,8,6,5,1]=>[1,1,3,1,1,1]
[1,5,2,7,3,4,6,8]=>[5,6,2,7,1,3,4,8]=>[4,3,7,2,8,6,5,1]=>[1,2,2,1,1,1]
[1,5,7,2,3,4,6,8]=>[4,5,2,6,7,1,3,8]=>[5,4,7,3,2,8,6,1]=>[1,2,1,2,1,1]
[5,1,2,3,7,4,6,8]=>[6,7,2,3,1,4,5,8]=>[3,2,7,6,8,5,4,1]=>[1,2,2,1,1,1]
[1,5,2,3,7,4,6,8]=>[6,7,3,1,2,4,5,8]=>[3,2,6,8,7,5,4,1]=>[1,3,1,1,1,1]
[1,2,5,3,7,4,6,8]=>[6,3,7,1,2,4,5,8]=>[3,6,2,8,7,5,4,1]=>[2,2,1,1,1,1]
[1,2,5,7,3,4,6,8]=>[5,3,6,7,1,2,4,8]=>[4,6,3,2,8,7,5,1]=>[2,1,2,1,1,1]
[1,5,2,3,4,7,6,8]=>[7,3,4,1,2,5,6,8]=>[2,6,5,8,7,4,3,1]=>[2,2,1,1,1,1]
[1,2,5,3,4,7,6,8]=>[7,4,1,2,3,5,6,8]=>[2,5,8,7,6,4,3,1]=>[3,1,1,1,1,1]
[1,2,3,5,7,4,6,8]=>[4,6,7,1,2,3,5,8]=>[5,3,2,8,7,6,4,1]=>[1,1,2,1,1,1,1]
[5,1,2,3,4,7,8,6]=>[6,8,2,3,1,4,5,7]=>[3,1,7,6,8,5,4,2]=>[1,2,2,1,1,1]
[1,5,2,3,4,7,8,6]=>[6,8,3,1,2,4,5,7]=>[3,1,6,8,7,5,4,2]=>[1,3,1,1,1,1]
[1,2,5,3,4,7,8,6]=>[6,3,8,1,2,4,5,7]=>[3,6,1,8,7,5,4,2]=>[2,2,1,1,1,1]
[1,2,3,5,7,4,8,6]=>[8,4,6,1,2,3,5,7]=>[1,5,3,8,7,6,4,2]=>[2,2,1,1,1,1]
[1,2,3,5,7,8,4,6]=>[7,4,5,8,1,2,3,6]=>[2,5,4,1,8,7,6,3]=>[2,1,2,1,1,1]
[5,1,8,2,3,4,6,7]=>[4,5,6,1,7,8,2,3]=>[5,4,3,8,2,1,7,6]=>[1,1,2,1,2,1]
[5,8,1,2,3,4,6,7]=>[3,4,5,1,6,7,8,2]=>[6,5,4,8,3,2,1,7]=>[1,1,2,1,1,2]
[5,1,2,8,3,4,6,7]=>[5,6,7,1,8,2,3,4]=>[4,3,2,8,1,7,6,5]=>[1,1,2,2,1,1]
[1,5,2,8,3,4,6,7]=>[5,6,2,7,8,1,3,4]=>[4,3,7,2,1,8,6,5]=>[1,2,1,2,1,1]
[1,5,8,2,3,4,6,7]=>[4,5,2,6,7,8,1,3]=>[5,4,7,3,2,1,8,6]=>[1,2,1,1,2,1]
[5,1,2,3,8,4,6,7]=>[6,7,8,2,1,3,4,5]=>[3,2,1,7,8,6,5,4]=>[1,1,3,1,1,1]
[1,5,2,3,8,4,6,7]=>[6,7,2,8,1,3,4,5]=>[3,2,7,1,8,6,5,4]=>[1,2,2,1,1,1]
[1,2,5,8,3,4,6,7]=>[5,3,6,7,8,1,2,4]=>[4,6,3,2,1,8,7,5]=>[2,1,1,2,1,1]
[5,1,2,3,4,8,6,7]=>[7,8,2,3,1,4,5,6]=>[2,1,7,6,8,5,4,3]=>[1,2,2,1,1,1]
[1,5,2,3,4,8,6,7]=>[7,8,3,1,2,4,5,6]=>[2,1,6,8,7,5,4,3]=>[1,3,1,1,1,1]
[1,2,3,5,4,8,6,7]=>[4,7,8,1,2,3,5,6]=>[5,2,1,8,7,6,4,3]=>[1,1,2,1,1,1,1]
[1,2,3,5,8,4,6,7]=>[4,6,7,8,1,2,3,5]=>[5,3,2,1,8,7,6,4]=>[1,1,1,2,1,1,1]
[5,1,2,3,4,6,8,7]=>[8,2,3,4,1,5,6,7]=>[1,7,6,5,8,4,3,2]=>[2,1,2,1,1,1]
[1,5,2,3,4,6,8,7]=>[8,3,4,1,2,5,6,7]=>[1,6,5,8,7,4,3,2]=>[2,2,1,1,1,1]
[1,2,5,3,4,6,8,7]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>[3,1,1,1,1,1]
[1,2,3,5,6,8,4,7]=>[4,5,7,8,1,2,3,6]=>[5,4,2,1,8,7,6,3]=>[1,1,1,2,1,1,1]
[1,5,2,3,4,6,7,8]=>[3,4,5,1,2,6,7,8]=>[6,5,4,8,7,3,2,1]=>[1,1,2,1,1,1,1]
[1,2,5,3,4,6,7,8]=>[4,5,1,2,3,6,7,8]=>[5,4,8,7,6,3,2,1]=>[1,2,1,1,1,1,1]
[6,1,7,2,8,3,4,5]=>[6,7,8,4,2,1,3,5]=>[3,2,1,5,7,8,6,4]=>[1,1,4,1,1]
[6,7,1,2,8,3,4,5]=>[6,7,8,3,1,4,2,5]=>[3,2,1,6,8,5,7,4]=>[1,1,3,2,1]
[6,1,7,8,2,3,4,5]=>[5,6,7,3,1,8,2,4]=>[4,3,2,6,8,1,7,5]=>[1,1,3,2,1]
[6,7,1,8,2,3,4,5]=>[5,6,7,1,8,3,2,4]=>[4,3,2,8,1,6,7,5]=>[1,1,2,3,1]
[6,1,7,2,3,8,4,5]=>[7,8,4,5,2,1,3,6]=>[2,1,5,4,7,8,6,3]=>[1,2,3,1,1]
[6,7,1,2,3,8,4,5]=>[7,8,3,4,1,5,2,6]=>[2,1,6,5,8,4,7,3]=>[1,2,2,2,1]
[6,1,2,7,3,8,4,5]=>[7,8,5,2,3,1,4,6]=>[2,1,4,7,6,8,5,3]=>[1,3,2,1,1]
[1,6,2,7,3,8,4,5]=>[7,8,5,3,1,2,4,6]=>[2,1,4,6,8,7,5,3]=>[1,4,1,1,1]
[1,6,7,2,3,8,4,5]=>[7,8,4,2,5,1,3,6]=>[2,1,5,7,4,8,6,3]=>[1,3,2,1,1]
[6,1,2,7,8,3,4,5]=>[6,7,4,8,2,1,3,5]=>[3,2,5,1,7,8,6,4]=>[1,2,3,1,1]
[1,6,2,7,8,3,4,5]=>[6,7,4,2,8,1,3,5]=>[3,2,5,7,1,8,6,4]=>[1,3,2,1,1]
[1,6,7,2,8,3,4,5]=>[6,7,2,8,4,1,3,5]=>[3,2,7,1,5,8,6,4]=>[1,2,3,1,1]
[1,6,7,8,2,3,4,5]=>[5,6,2,7,3,8,1,4]=>[4,3,7,2,6,1,8,5]=>[1,2,2,2,1]
[6,1,7,2,3,4,8,5]=>[8,4,5,6,2,1,3,7]=>[1,5,4,3,7,8,6,2]=>[2,1,3,1,1]
[6,1,2,7,3,4,8,5]=>[8,5,6,2,3,1,4,7]=>[1,4,3,7,6,8,5,2]=>[2,2,2,1,1]
[1,6,2,7,3,4,8,5]=>[8,5,6,3,1,2,4,7]=>[1,4,3,6,8,7,5,2]=>[2,3,1,1,1]
[1,6,7,2,3,4,8,5]=>[8,4,5,2,6,1,3,7]=>[1,5,4,7,3,8,6,2]=>[2,2,2,1,1]
[6,1,2,3,7,4,8,5]=>[8,6,2,3,4,1,5,7]=>[1,3,7,6,5,8,4,2]=>[3,1,2,1,1]
[1,6,2,3,7,4,8,5]=>[8,6,3,4,1,2,5,7]=>[1,3,6,5,8,7,4,2]=>[3,2,1,1,1]
[1,2,6,3,7,4,8,5]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]
[1,2,6,7,3,4,8,5]=>[8,5,3,6,1,2,4,7]=>[1,4,6,3,8,7,5,2]=>[3,2,1,1,1]
[6,1,2,3,7,8,4,5]=>[7,5,8,2,3,1,4,6]=>[2,4,1,7,6,8,5,3]=>[2,2,2,1,1]
[1,6,2,3,7,8,4,5]=>[7,5,8,3,1,2,4,6]=>[2,4,1,6,8,7,5,3]=>[2,3,1,1,1]
[1,2,6,3,7,8,4,5]=>[7,5,3,8,1,2,4,6]=>[2,4,6,1,8,7,5,3]=>[3,2,1,1,1]
[1,2,6,7,3,8,4,5]=>[7,3,8,5,1,2,4,6]=>[2,6,1,4,8,7,5,3]=>[2,3,1,1,1]
[1,2,6,7,8,3,4,5]=>[6,3,7,4,8,1,2,5]=>[3,6,2,5,1,8,7,4]=>[2,2,2,1,1]
[6,1,7,2,3,4,5,8]=>[4,5,6,7,2,1,3,8]=>[5,4,3,2,7,8,6,1]=>[1,1,1,3,1,1]
[1,6,2,7,3,4,5,8]=>[5,6,7,3,1,2,4,8]=>[4,3,2,6,8,7,5,1]=>[1,1,3,1,1,1]
[1,6,7,2,3,4,5,8]=>[4,5,6,2,7,1,3,8]=>[5,4,3,7,2,8,6,1]=>[1,1,2,2,1,1]
[6,1,2,3,7,4,5,8]=>[6,7,2,3,4,1,5,8]=>[3,2,7,6,5,8,4,1]=>[1,2,1,2,1,1]
[1,6,2,3,7,4,5,8]=>[6,7,3,4,1,2,5,8]=>[3,2,6,5,8,7,4,1]=>[1,2,2,1,1,1]
[1,2,6,3,7,4,5,8]=>[6,7,4,1,2,3,5,8]=>[3,2,5,8,7,6,4,1]=>[1,3,1,1,1,1]
[1,2,6,7,3,4,5,8]=>[5,6,3,7,1,2,4,8]=>[4,3,6,2,8,7,5,1]=>[1,2,2,1,1,1]
[6,1,2,3,4,7,5,8]=>[7,2,3,4,5,1,6,8]=>[2,7,6,5,4,8,3,1]=>[2,1,1,2,1,1]
[1,6,2,3,4,7,5,8]=>[7,3,4,5,1,2,6,8]=>[2,6,5,4,8,7,3,1]=>[2,1,2,1,1,1]
[1,2,6,3,4,7,5,8]=>[7,4,5,1,2,3,6,8]=>[2,5,4,8,7,6,3,1]=>[2,2,1,1,1,1]
[1,2,3,6,4,7,5,8]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>[3,1,1,1,1,1]
[1,2,3,6,7,4,5,8]=>[6,4,7,1,2,3,5,8]=>[3,5,2,8,7,6,4,1]=>[2,2,1,1,1,1]
[6,1,2,3,4,7,8,5]=>[6,8,2,3,4,1,5,7]=>[3,1,7,6,5,8,4,2]=>[1,2,1,2,1,1]
[1,6,2,3,4,7,8,5]=>[6,8,3,4,1,2,5,7]=>[3,1,6,5,8,7,4,2]=>[1,2,2,1,1,1]
[1,2,6,3,4,7,8,5]=>[6,8,4,1,2,3,5,7]=>[3,1,5,8,7,6,4,2]=>[1,3,1,1,1,1]
[1,2,3,6,7,4,8,5]=>[4,8,6,1,2,3,5,7]=>[5,1,3,8,7,6,4,2]=>[1,3,1,1,1,1]
[1,2,3,6,7,8,4,5]=>[4,7,5,8,1,2,3,6]=>[5,2,4,1,8,7,6,3]=>[1,2,2,1,1,1]
[6,1,8,2,3,4,5,7]=>[4,5,6,7,1,8,2,3]=>[5,4,3,2,8,1,7,6]=>[1,1,1,2,2,1]
[6,8,1,2,3,4,5,7]=>[3,4,5,6,1,7,8,2]=>[6,5,4,3,8,2,1,7]=>[1,1,1,2,1,2]
[6,1,2,8,3,4,5,7]=>[5,6,7,8,2,1,3,4]=>[4,3,2,1,7,8,6,5]=>[1,1,1,3,1,1]
[1,6,2,8,3,4,5,7]=>[5,6,7,2,8,1,3,4]=>[4,3,2,7,1,8,6,5]=>[1,1,2,2,1,1]
[1,6,8,2,3,4,5,7]=>[4,5,6,2,7,8,1,3]=>[5,4,3,7,2,1,8,6]=>[1,1,2,1,2,1]
[6,1,2,3,8,4,5,7]=>[6,7,8,2,3,1,4,5]=>[3,2,1,7,6,8,5,4]=>[1,1,2,2,1,1]
[1,6,2,3,8,4,5,7]=>[6,7,8,3,1,2,4,5]=>[3,2,1,6,8,7,5,4]=>[1,1,3,1,1,1]
[1,2,6,3,8,4,5,7]=>[6,7,3,8,1,2,4,5]=>[3,2,6,1,8,7,5,4]=>[1,2,2,1,1,1]
[1,2,6,8,3,4,5,7]=>[5,6,3,7,8,1,2,4]=>[4,3,6,2,1,8,7,5]=>[1,2,1,2,1,1]
[6,1,2,3,4,8,5,7]=>[7,8,2,3,4,1,5,6]=>[2,1,7,6,5,8,4,3]=>[1,2,1,2,1,1]
[1,6,2,3,4,8,5,7]=>[7,8,3,4,1,2,5,6]=>[2,1,6,5,8,7,4,3]=>[1,2,2,1,1,1]
[1,2,6,3,4,8,5,7]=>[7,8,4,1,2,3,5,6]=>[2,1,5,8,7,6,4,3]=>[1,3,1,1,1,1]
[1,2,3,6,4,8,5,7]=>[7,4,8,1,2,3,5,6]=>[2,5,1,8,7,6,4,3]=>[2,2,1,1,1,1]
[1,2,3,6,8,4,5,7]=>[6,4,7,8,1,2,3,5]=>[3,5,2,1,8,7,6,4]=>[2,1,2,1,1,1]
[6,1,2,3,4,5,8,7]=>[8,2,3,4,5,1,6,7]=>[1,7,6,5,4,8,3,2]=>[2,1,1,2,1,1]
[1,6,2,3,4,5,8,7]=>[8,3,4,5,1,2,6,7]=>[1,6,5,4,8,7,3,2]=>[2,1,2,1,1,1]
[1,2,6,3,4,5,8,7]=>[8,4,5,1,2,3,6,7]=>[1,5,4,8,7,6,3,2]=>[2,2,1,1,1,1]
[1,2,3,6,4,5,8,7]=>[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>[3,1,1,1,1,1]
[1,2,3,4,6,8,5,7]=>[5,7,8,1,2,3,4,6]=>[4,2,1,8,7,6,5,3]=>[1,1,2,1,1,1,1]
[1,6,2,3,4,5,7,8]=>[3,4,5,6,1,2,7,8]=>[6,5,4,3,8,7,2,1]=>[1,1,1,2,1,1,1]
[1,2,6,3,4,5,7,8]=>[4,5,6,1,2,3,7,8]=>[5,4,3,8,7,6,2,1]=>[1,1,2,1,1,1,1]
[1,2,3,6,4,5,7,8]=>[5,6,1,2,3,4,7,8]=>[4,3,8,7,6,5,2,1]=>[1,2,1,1,1,1,1]
[7,1,8,2,3,4,5,6]=>[4,5,6,7,8,2,1,3]=>[5,4,3,2,1,7,8,6]=>[1,1,1,1,3,1]
[7,1,2,8,3,4,5,6]=>[5,6,7,8,2,3,1,4]=>[4,3,2,1,7,6,8,5]=>[1,1,1,2,2,1]
[1,7,2,8,3,4,5,6]=>[5,6,7,8,3,1,2,4]=>[4,3,2,1,6,8,7,5]=>[1,1,1,3,1,1]
[1,7,8,2,3,4,5,6]=>[4,5,6,7,2,8,1,3]=>[5,4,3,2,7,1,8,6]=>[1,1,1,2,2,1]
[7,1,2,3,8,4,5,6]=>[6,7,8,2,3,4,1,5]=>[3,2,1,7,6,5,8,4]=>[1,1,2,1,2,1]
[1,7,2,3,8,4,5,6]=>[6,7,8,3,4,1,2,5]=>[3,2,1,6,5,8,7,4]=>[1,1,2,2,1,1]
[1,2,7,3,8,4,5,6]=>[6,7,8,4,1,2,3,5]=>[3,2,1,5,8,7,6,4]=>[1,1,3,1,1,1]
[1,2,7,8,3,4,5,6]=>[5,6,7,3,8,1,2,4]=>[4,3,2,6,1,8,7,5]=>[1,1,2,2,1,1]
[7,1,2,3,4,8,5,6]=>[7,8,2,3,4,5,1,6]=>[2,1,7,6,5,4,8,3]=>[1,2,1,1,2,1]
[1,7,2,3,4,8,5,6]=>[7,8,3,4,5,1,2,6]=>[2,1,6,5,4,8,7,3]=>[1,2,1,2,1,1]
[1,2,7,3,4,8,5,6]=>[7,8,4,5,1,2,3,6]=>[2,1,5,4,8,7,6,3]=>[1,2,2,1,1,1]
[1,2,3,7,4,8,5,6]=>[7,8,5,1,2,3,4,6]=>[2,1,4,8,7,6,5,3]=>[1,3,1,1,1,1]
[1,2,3,7,8,4,5,6]=>[6,7,4,8,1,2,3,5]=>[3,2,5,1,8,7,6,4]=>[1,2,2,1,1,1]
[7,1,2,3,4,5,8,6]=>[8,2,3,4,5,6,1,7]=>[1,7,6,5,4,3,8,2]=>[2,1,1,1,2,1]
[1,7,2,3,4,5,8,6]=>[8,3,4,5,6,1,2,7]=>[1,6,5,4,3,8,7,2]=>[2,1,1,2,1,1]
[1,2,7,3,4,5,8,6]=>[8,4,5,6,1,2,3,7]=>[1,5,4,3,8,7,6,2]=>[2,1,2,1,1,1]
[1,2,3,7,4,5,8,6]=>[8,5,6,1,2,3,4,7]=>[1,4,3,8,7,6,5,2]=>[2,2,1,1,1,1]
[1,2,3,4,7,5,8,6]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>[3,1,1,1,1,1]
[1,2,3,4,7,8,5,6]=>[7,5,8,1,2,3,4,6]=>[2,4,1,8,7,6,5,3]=>[2,2,1,1,1,1]
[1,7,2,3,4,5,6,8]=>[3,4,5,6,7,1,2,8]=>[6,5,4,3,2,8,7,1]=>[1,1,1,1,2,1,1]
[1,2,7,3,4,5,6,8]=>[4,5,6,7,1,2,3,8]=>[5,4,3,2,8,7,6,1]=>[1,1,1,2,1,1,1]
[1,2,3,7,4,5,6,8]=>[5,6,7,1,2,3,4,8]=>[4,3,2,8,7,6,5,1]=>[1,1,2,1,1,1,1]
[1,2,3,4,7,5,6,8]=>[6,7,1,2,3,4,5,8]=>[3,2,8,7,6,5,4,1]=>[1,2,1,1,1,1,1]
[1,8,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,2]=>[6,5,4,3,2,1,8,7]=>[1,1,1,1,1,2,1]
[1,2,8,3,4,5,6,7]=>[4,5,6,7,8,1,2,3]=>[5,4,3,2,1,8,7,6]=>[1,1,1,1,2,1,1]
[1,2,3,8,4,5,6,7]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[1,1,1,2,1,1,1]
[1,2,3,4,8,5,6,7]=>[6,7,8,1,2,3,4,5]=>[3,2,1,8,7,6,5,4]=>[1,1,2,1,1,1,1]
[1,2,3,4,5,8,6,7]=>[7,8,1,2,3,4,5,6]=>[2,1,8,7,6,5,4,3]=>[1,2,1,1,1,1,1]
[5,3,2,6,1,4,8,7]=>[2,8,3,1,5,4,6,7]=>[7,1,6,8,4,5,3,2]=>[1,3,2,1,1]
[7,3,2,5,4,8,1,6]=>[2,5,3,4,7,1,8,6]=>[7,4,6,5,2,8,1,3]=>[1,2,1,2,2]
[8,4,5,2,3,7,6,1]=>[2,8,4,3,5,7,6,1]=>[7,1,5,6,4,2,3,8]=>[1,3,1,3]
[7,4,5,2,3,8,1,6]=>[4,2,5,3,7,1,8,6]=>[5,7,4,6,2,8,1,3]=>[2,2,2,2]
[6,4,5,2,3,1,8,7]=>[4,2,5,3,1,8,6,7]=>[5,7,4,6,8,1,3,2]=>[2,3,2,1]
[5,4,6,2,1,3,8,7]=>[4,2,1,8,5,3,6,7]=>[5,7,8,1,4,6,3,2]=>[3,3,1,1]
[3,6,1,5,4,2,8,7]=>[5,1,4,8,3,2,6,7]=>[4,8,5,1,6,7,3,2]=>[2,1,3,1,1]
[4,6,5,1,3,2,8,7]=>[1,5,8,4,3,2,6,7]=>[8,4,1,5,6,7,3,2]=>[1,1,4,1,1]
[5,6,4,3,1,2,8,7]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[1,5,1,1]
[7,5,4,3,2,8,1,6]=>[5,4,3,2,7,1,8,6]=>[4,5,6,7,2,8,1,3]=>[4,2,2]
[8,6,4,3,7,2,5,1]=>[4,3,6,2,8,7,5,1]=>[5,6,3,7,1,2,4,8]=>[2,2,4]
[7,6,4,3,8,2,1,5]=>[4,3,7,6,2,1,8,5]=>[5,6,2,3,7,8,1,4]=>[2,4,2]
[6,7,4,3,8,1,2,5]=>[6,4,3,1,7,2,8,5]=>[3,5,6,8,2,7,1,4]=>[4,2,2]
[5,7,4,3,1,8,2,6]=>[1,7,4,3,8,5,2,6]=>[8,2,5,6,1,4,7,3]=>[1,3,3,1]
[4,7,5,1,3,8,2,6]=>[1,5,7,3,8,4,2,6]=>[8,4,2,6,1,5,7,3]=>[1,1,2,3,1]
[3,7,1,5,4,8,2,6]=>[5,1,4,7,8,3,2,6]=>[4,8,5,2,1,6,7,3]=>[2,1,1,3,1]
[2,1,7,5,4,8,3,6]=>[5,4,7,1,3,8,2,6]=>[4,5,2,8,6,1,7,3]=>[2,2,1,2,1]
[3,8,1,5,4,7,6,2]=>[4,8,1,5,7,3,6,2]=>[5,1,8,4,2,6,3,7]=>[1,2,1,2,2]
[4,8,5,1,3,7,6,2]=>[8,1,5,3,7,4,6,2]=>[1,8,4,6,2,5,3,7]=>[2,2,2,2]
[5,8,4,3,1,7,6,2]=>[1,4,3,8,7,5,6,2]=>[8,5,6,1,2,4,3,7]=>[1,2,3,2]
[6,8,4,3,7,1,5,2]=>[4,3,1,8,6,7,5,2]=>[5,6,8,1,3,2,4,7]=>[3,2,3]
[7,8,4,3,6,5,1,2]=>[4,3,7,1,8,6,5,2]=>[5,6,2,8,1,3,4,7]=>[2,2,4]
[6,8,5,7,3,1,4,2]=>[1,8,6,5,3,7,4,2]=>[8,1,3,4,6,2,5,7]=>[1,4,3]
[5,8,6,7,1,3,4,2]=>[1,6,8,5,3,7,4,2]=>[8,3,1,4,6,2,5,7]=>[1,1,3,3]
[4,8,6,1,7,3,5,2]=>[6,8,1,7,4,3,5,2]=>[3,1,8,2,5,6,4,7]=>[1,2,3,2]
[3,8,1,6,7,4,5,2]=>[6,4,8,1,7,3,5,2]=>[3,5,1,8,2,6,4,7]=>[2,2,2,2]
[2,1,8,6,7,4,5,3]=>[6,4,8,7,1,5,2,3]=>[3,5,1,2,8,4,7,6]=>[2,3,2,1]
[2,1,7,6,8,4,3,5]=>[7,6,4,1,3,8,2,5]=>[2,3,5,8,6,1,7,4]=>[4,1,2,1]
[3,7,1,6,8,4,2,5]=>[7,6,1,4,8,3,2,5]=>[2,3,8,5,1,6,7,4]=>[3,1,3,1]
[4,7,6,1,8,3,2,5]=>[7,1,6,8,4,3,2,5]=>[2,8,3,1,5,6,7,4]=>[2,1,4,1]
[5,7,6,8,1,3,2,4]=>[1,7,5,6,3,2,8,4]=>[8,2,4,3,6,7,1,5]=>[1,2,3,2]
[5,4,7,2,1,8,3,6]=>[4,2,1,7,8,5,3,6]=>[5,7,8,2,1,4,6,3]=>[3,1,3,1]
[6,4,7,2,8,1,3,5]=>[4,2,6,1,7,3,8,5]=>[5,7,3,8,2,6,1,4]=>[2,2,2,2]
[7,4,6,2,8,3,1,5]=>[2,7,4,6,3,1,8,5]=>[7,2,5,3,6,8,1,4]=>[1,2,3,2]
[8,4,6,2,7,3,5,1]=>[2,6,8,4,3,7,5,1]=>[7,3,1,5,6,2,4,8]=>[1,1,3,3]
[8,3,2,6,7,4,5,1]=>[6,2,4,8,3,7,5,1]=>[3,7,5,1,6,2,4,8]=>[2,1,2,3]
[7,3,2,6,8,4,1,5]=>[7,2,6,3,4,1,8,5]=>[2,7,3,6,5,8,1,4]=>[2,2,2,2]
[6,3,2,7,8,1,4,5]=>[2,6,7,3,1,4,8,5]=>[7,3,2,6,8,5,1,4]=>[1,1,3,1,2]
[5,3,2,7,1,8,4,6]=>[2,7,1,8,3,5,4,6]=>[7,2,8,1,6,4,5,3]=>[1,2,2,2,1]
[4,3,2,1,7,8,5,6]=>[2,1,7,3,5,8,4,6]=>[7,8,2,6,4,1,5,3]=>[2,2,1,2,1]
[3,4,1,2,8,7,6,5]=>[8,1,2,7,6,3,4,5]=>[1,8,7,2,3,6,5,4]=>[2,1,3,1,1]
[5,3,2,8,1,7,6,4]=>[8,2,1,7,3,5,6,4]=>[1,7,8,2,6,4,3,5]=>[3,2,1,2]
[6,3,2,8,7,1,5,4]=>[8,2,6,1,7,3,5,4]=>[1,7,3,8,2,6,4,5]=>[2,2,2,2]
[7,3,2,8,6,5,1,4]=>[7,8,2,6,3,1,5,4]=>[2,1,7,3,6,8,4,5]=>[1,2,3,2]
[8,4,7,2,6,5,3,1]=>[8,2,7,4,6,5,3,1]=>[1,7,2,5,3,4,6,8]=>[2,2,4]
[7,4,8,2,6,5,1,3]=>[2,7,8,4,1,6,5,3]=>[7,2,1,5,8,3,4,6]=>[1,1,3,3]
[6,4,8,2,7,1,5,3]=>[2,8,4,1,6,7,5,3]=>[7,1,5,8,3,2,4,6]=>[1,3,1,3]
[5,4,8,2,1,7,6,3]=>[2,1,8,4,7,5,6,3]=>[7,8,1,5,2,4,3,6]=>[2,2,2,2]
[4,5,8,1,2,7,6,3]=>[1,2,8,7,4,5,6,3]=>[8,7,1,2,5,4,3,6]=>[1,1,3,1,2]
[3,5,1,8,2,7,6,4]=>[2,8,1,7,5,6,3,4]=>[7,1,8,2,4,3,6,5]=>[1,2,2,2,1]
[2,1,5,8,3,7,6,4]=>[8,3,7,1,5,6,2,4]=>[1,6,2,8,4,3,7,5]=>[2,2,1,2,1]
[2,1,6,8,7,3,5,4]=>[3,8,6,7,1,5,2,4]=>[6,1,3,2,8,4,7,5]=>[1,2,2,2,1]
[3,6,1,8,7,2,5,4]=>[8,6,1,2,7,5,3,4]=>[1,3,8,7,2,4,6,5]=>[3,1,3,1]
[4,6,8,1,7,2,5,3]=>[8,1,6,2,7,4,5,3]=>[1,8,3,7,2,5,4,6]=>[2,2,2,2]
[5,6,8,7,1,2,4,3]=>[1,8,5,2,6,7,4,3]=>[8,1,4,7,3,2,5,6]=>[1,3,1,3]
[6,5,8,7,2,1,4,3]=>[5,2,1,8,6,7,4,3]=>[4,7,8,1,3,2,5,6]=>[3,2,3]
[7,5,8,6,2,4,1,3]=>[5,2,7,1,8,6,4,3]=>[4,7,2,8,1,3,5,6]=>[2,2,4]
[8,5,7,6,2,4,3,1]=>[2,8,5,7,6,4,3,1]=>[7,1,4,2,3,5,6,8]=>[1,2,5]
[5,7,8,6,1,4,2,3]=>[1,7,8,5,2,6,4,3]=>[8,2,1,4,7,3,5,6]=>[1,1,3,3]
[4,7,8,1,6,5,2,3]=>[7,8,1,6,4,2,5,3]=>[2,1,8,3,5,7,4,6]=>[1,2,3,2]
[3,7,1,8,6,5,2,4]=>[7,8,6,1,5,3,2,4]=>[2,1,3,8,4,6,7,5]=>[1,3,3,1]
[2,1,7,8,6,5,3,4]=>[7,3,8,6,1,5,2,4]=>[2,6,1,3,8,4,7,5]=>[2,3,2,1]
[3,8,1,7,6,5,4,2]=>[8,7,6,1,5,3,4,2]=>[1,2,3,8,4,6,5,7]=>[4,2,2]
[4,8,7,1,6,5,3,2]=>[8,7,1,6,4,5,3,2]=>[1,2,8,3,5,4,6,7]=>[3,2,3]
[5,8,7,6,1,4,3,2]=>[8,1,7,5,6,4,3,2]=>[1,8,2,4,3,5,6,7]=>[2,2,4]
[6,8,7,5,4,1,3,2]=>[1,8,6,7,5,4,3,2]=>[8,1,3,2,4,5,6,7]=>[1,2,5]
[8,7,6,5,4,3,2,1,10,9]=>[7,6,5,4,3,2,1,10,8,9]=>[4,5,6,7,8,9,10,1,3,2]=>[7,2,1]
[9,7,6,5,4,3,2,10,1,8]=>[7,6,5,4,3,2,9,1,10,8]=>[4,5,6,7,8,9,2,10,1,3]=>[6,2,2]
[10,8,9,6,7,4,5,2,3,1]=>[8,6,4,2,10,9,7,5,3,1]=>[3,5,7,9,1,2,4,6,8,10]=>[4,6]
[6,7,8,9,10,1,2,3,4,5]=>[6,1,7,2,8,3,9,4,10,5]=>[5,10,4,9,3,8,2,7,1,6]=>[2,2,2,2,2]
[4,3,2,1,10,9,8,7,6,5]=>[10,9,1,8,2,7,3,6,4,5]=>[1,2,10,3,9,4,8,5,7,6]=>[3,2,2,2,1]
[2,1,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,1,4,2,3]=>[1,2,3,4,5,6,10,7,9,8]=>[7,2,1]
[9,10,8,7,6,5,4,3,1,2]=>[9,1,10,8,7,6,5,4,3,2]=>[2,10,1,3,4,5,6,7,8,9]=>[2,8]
[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10]
[3,2,5,1,4,6,7,8]=>[2,1,4,5,3,6,7,8]=>[7,8,5,4,6,3,2,1]=>[2,1,2,1,1,1]
[4,2,5,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>[7,5,8,4,6,3,2,1]=>[1,2,2,1,1,1]
[5,2,4,1,3,6,7,8]=>[2,4,5,3,1,6,7,8]=>[7,5,4,6,8,3,2,1]=>[1,1,3,1,1,1]
[3,2,6,1,4,5,7,8]=>[2,1,4,5,6,3,7,8]=>[7,8,5,4,3,6,2,1]=>[2,1,1,2,1,1]
[4,2,6,1,3,5,7,8]=>[2,4,1,5,6,3,7,8]=>[7,5,8,4,3,6,2,1]=>[1,2,1,2,1,1]
[5,3,6,1,2,4,7,8]=>[4,2,5,1,6,3,7,8]=>[5,7,4,8,3,6,2,1]=>[2,2,2,1,1]
[6,2,4,1,3,5,7,8]=>[2,4,5,3,6,1,7,8]=>[7,5,4,6,3,8,2,1]=>[1,1,2,2,1,1]
[6,3,5,1,2,4,7,8]=>[4,2,5,6,3,1,7,8]=>[5,7,4,3,6,8,2,1]=>[2,1,3,1,1]
[5,2,7,1,3,4,6,8]=>[2,4,5,1,6,7,3,8]=>[7,5,4,8,3,2,6,1]=>[1,1,2,1,2,1]
[5,3,7,1,2,4,6,8]=>[4,2,5,1,6,7,3,8]=>[5,7,4,8,3,2,6,1]=>[2,2,1,2,1]
[5,4,7,1,2,3,6,8]=>[4,5,2,1,6,7,3,8]=>[5,4,7,8,3,2,6,1]=>[1,3,1,2,1]
[6,2,7,1,3,4,5,8]=>[2,4,5,6,1,7,3,8]=>[7,5,4,3,8,2,6,1]=>[1,1,1,2,2,1]
[6,3,7,1,2,4,5,8]=>[4,2,5,6,1,7,3,8]=>[5,7,4,3,8,2,6,1]=>[2,1,2,2,1]
[6,4,7,1,2,3,5,8]=>[4,5,2,6,1,7,3,8]=>[5,4,7,3,8,2,6,1]=>[1,2,2,2,1]
[7,3,5,1,2,4,6,8]=>[4,2,5,6,3,7,1,8]=>[5,7,4,3,6,2,8,1]=>[2,1,2,2,1]
[7,4,6,1,2,3,5,8]=>[4,5,2,6,7,3,1,8]=>[5,4,7,3,2,6,8,1]=>[1,2,1,3,1]
[3,2,8,1,4,5,6,7]=>[2,1,4,5,6,7,8,3]=>[7,8,5,4,3,2,1,6]=>[2,1,1,1,1,2]
[4,2,8,1,3,5,6,7]=>[2,4,1,5,6,7,8,3]=>[7,5,8,4,3,2,1,6]=>[1,2,1,1,1,2]
[5,2,8,1,3,4,6,7]=>[2,4,5,1,6,7,8,3]=>[7,5,4,8,3,2,1,6]=>[1,1,2,1,1,2]
[5,4,8,1,2,3,6,7]=>[4,5,2,1,6,7,8,3]=>[5,4,7,8,3,2,1,6]=>[1,3,1,1,2]
[6,2,8,1,3,4,5,7]=>[2,4,5,6,1,7,8,3]=>[7,5,4,3,8,2,1,6]=>[1,1,1,2,1,2]
[6,3,8,1,2,4,5,7]=>[4,2,5,6,1,7,8,3]=>[5,7,4,3,8,2,1,6]=>[2,1,2,1,2]
[6,4,8,1,2,3,5,7]=>[4,5,2,6,1,7,8,3]=>[5,4,7,3,8,2,1,6]=>[1,2,2,1,2]
[6,5,8,1,2,3,4,7]=>[4,5,6,2,1,7,8,3]=>[5,4,3,7,8,2,1,6]=>[1,1,3,1,2]
[7,2,8,1,3,4,5,6]=>[2,4,5,6,7,1,8,3]=>[7,5,4,3,2,8,1,6]=>[1,1,1,1,2,2]
[7,3,8,1,2,4,5,6]=>[4,2,5,6,7,1,8,3]=>[5,7,4,3,2,8,1,6]=>[2,1,1,2,2]
[7,4,8,1,2,3,5,6]=>[4,5,2,6,7,1,8,3]=>[5,4,7,3,2,8,1,6]=>[1,2,1,2,2]
[7,5,8,1,2,3,4,6]=>[4,5,6,2,7,1,8,3]=>[5,4,3,7,2,8,1,6]=>[1,1,2,2,2]
[8,2,4,1,3,5,6,7]=>[2,4,5,3,6,7,8,1]=>[7,5,4,6,3,2,1,8]=>[1,1,2,1,1,2]
[8,3,5,1,2,4,6,7]=>[4,2,5,6,3,7,8,1]=>[5,7,4,3,6,2,1,8]=>[2,1,2,1,2]
[8,3,6,1,2,4,5,7]=>[4,2,5,6,7,3,8,1]=>[5,7,4,3,2,6,1,8]=>[2,1,1,2,2]
[8,4,7,1,2,3,5,6]=>[4,5,2,6,7,8,3,1]=>[5,4,7,3,2,1,6,8]=>[1,2,1,1,3]
[8,5,7,1,2,3,4,6]=>[4,5,6,2,7,8,3,1]=>[5,4,3,7,2,1,6,8]=>[1,1,2,1,3]
[4,2,5,7,1,3,6,8]=>[5,2,1,3,6,7,4,8]=>[4,7,8,6,3,2,5,1]=>[3,1,1,2,1]
[4,3,5,7,1,2,6,8]=>[2,1,5,3,6,7,4,8]=>[7,8,4,6,3,2,5,1]=>[2,2,1,2,1]
[5,2,4,7,1,3,6,8]=>[5,2,3,1,6,7,4,8]=>[4,7,6,8,3,2,5,1]=>[2,2,1,2,1]
[4,2,6,7,1,3,5,8]=>[5,1,6,2,3,7,4,8]=>[4,8,3,7,6,2,5,1]=>[2,2,1,2,1]
[5,2,6,7,1,3,4,8]=>[5,6,2,1,3,7,4,8]=>[4,3,7,8,6,2,5,1]=>[1,3,1,2,1]
[5,3,6,7,1,2,4,8]=>[2,5,1,6,3,7,4,8]=>[7,4,8,3,6,2,5,1]=>[1,2,2,2,1]
[6,2,5,7,1,3,4,8]=>[5,6,2,3,1,7,4,8]=>[4,3,7,6,8,2,5,1]=>[1,2,2,2,1]
[6,3,5,7,1,2,4,8]=>[2,5,6,3,1,7,4,8]=>[7,4,3,6,8,2,5,1]=>[1,1,3,2,1]
[7,2,4,6,1,3,5,8]=>[5,2,3,6,7,4,1,8]=>[4,7,6,3,2,5,8,1]=>[2,1,1,3,1]
[7,3,5,6,1,2,4,8]=>[2,5,6,3,7,4,1,8]=>[7,4,3,6,2,5,8,1]=>[1,1,2,3,1]
[3,2,5,8,1,4,6,7]=>[1,5,2,3,6,7,8,4]=>[8,4,7,6,3,2,1,5]=>[1,2,1,1,1,2]
[4,2,5,8,1,3,6,7]=>[5,2,1,3,6,7,8,4]=>[4,7,8,6,3,2,1,5]=>[3,1,1,1,2]
[4,3,5,8,1,2,6,7]=>[2,1,5,3,6,7,8,4]=>[7,8,4,6,3,2,1,5]=>[2,2,1,1,2]
[5,2,4,8,1,3,6,7]=>[5,2,3,1,6,7,8,4]=>[4,7,6,8,3,2,1,5]=>[2,2,1,1,2]
[3,2,6,8,1,4,5,7]=>[1,5,6,2,3,7,8,4]=>[8,4,3,7,6,2,1,5]=>[1,1,2,1,1,2]
[4,2,6,8,1,3,5,7]=>[5,1,6,2,3,7,8,4]=>[4,8,3,7,6,2,1,5]=>[2,2,1,1,2]
[4,3,6,8,1,2,5,7]=>[2,1,5,6,3,7,8,4]=>[7,8,4,3,6,2,1,5]=>[2,1,2,1,2]
[5,2,6,8,1,3,4,7]=>[5,6,2,1,3,7,8,4]=>[4,3,7,8,6,2,1,5]=>[1,3,1,1,2]
[6,2,4,8,1,3,5,7]=>[5,2,3,6,1,7,8,4]=>[4,7,6,3,8,2,1,5]=>[2,1,2,1,2]
[6,3,4,8,1,2,5,7]=>[2,5,3,6,1,7,8,4]=>[7,4,6,3,8,2,1,5]=>[1,2,2,1,2]
[6,2,5,8,1,3,4,7]=>[5,6,2,3,1,7,8,4]=>[4,3,7,6,8,2,1,5]=>[1,2,2,1,2]
[6,3,5,8,1,2,4,7]=>[2,5,6,3,1,7,8,4]=>[7,4,3,6,8,2,1,5]=>[1,1,3,1,2]
[6,4,5,8,1,2,3,7]=>[5,2,6,3,1,7,8,4]=>[4,7,3,6,8,2,1,5]=>[2,3,1,2]
[3,2,7,8,1,4,5,6]=>[1,5,6,7,2,3,8,4]=>[8,4,3,2,7,6,1,5]=>[1,1,1,2,1,2]
[4,3,7,8,1,2,5,6]=>[2,1,5,6,7,3,8,4]=>[7,8,4,3,2,6,1,5]=>[2,1,1,2,2]
[5,3,7,8,1,2,4,6]=>[2,5,1,6,7,3,8,4]=>[7,4,8,3,2,6,1,5]=>[1,2,1,2,2]
[5,4,7,8,1,2,3,6]=>[5,2,1,6,7,3,8,4]=>[4,7,8,3,2,6,1,5]=>[3,1,2,2]
[6,2,7,8,1,3,4,5]=>[5,6,7,2,1,3,8,4]=>[4,3,2,7,8,6,1,5]=>[1,1,3,1,2]
[6,3,7,8,1,2,4,5]=>[2,5,6,1,7,3,8,4]=>[7,4,3,8,2,6,1,5]=>[1,1,2,2,2]
[6,4,7,8,1,2,3,5]=>[5,2,6,1,7,3,8,4]=>[4,7,3,8,2,6,1,5]=>[2,2,2,2]
[7,2,4,8,1,3,5,6]=>[5,2,3,6,7,1,8,4]=>[4,7,6,3,2,8,1,5]=>[2,1,1,2,2]
[7,3,4,8,1,2,5,6]=>[2,5,3,6,7,1,8,4]=>[7,4,6,3,2,8,1,5]=>[1,2,1,2,2]
[7,4,5,8,1,2,3,6]=>[5,2,6,3,7,1,8,4]=>[4,7,3,6,2,8,1,5]=>[2,2,2,2]
[7,4,6,8,1,2,3,5]=>[5,2,6,7,3,1,8,4]=>[4,7,3,2,6,8,1,5]=>[2,1,3,2]
[8,2,4,6,1,3,5,7]=>[5,2,3,6,7,4,8,1]=>[4,7,6,3,2,5,1,8]=>[2,1,1,2,2]
[8,3,4,6,1,2,5,7]=>[2,5,3,6,7,4,8,1]=>[7,4,6,3,2,5,1,8]=>[1,2,1,2,2]
[8,2,5,6,1,3,4,7]=>[5,6,2,3,7,4,8,1]=>[4,3,7,6,2,5,1,8]=>[1,2,1,2,2]
[8,3,5,6,1,2,4,7]=>[2,5,6,3,7,4,8,1]=>[7,4,3,6,2,5,1,8]=>[1,1,2,2,2]
[8,2,4,7,1,3,5,6]=>[5,2,3,6,7,8,4,1]=>[4,7,6,3,2,1,5,8]=>[2,1,1,1,3]
[8,2,5,7,1,3,4,6]=>[5,6,2,3,7,8,4,1]=>[4,3,7,6,2,1,5,8]=>[1,2,1,1,3]
[8,3,5,7,1,2,4,6]=>[2,5,6,3,7,8,4,1]=>[7,4,3,6,2,1,5,8]=>[1,1,2,1,3]
[8,2,6,7,1,3,4,5]=>[5,6,7,2,3,8,4,1]=>[4,3,2,7,6,1,5,8]=>[1,1,2,1,3]
[3,6,2,5,1,4,7,8]=>[1,3,5,6,4,2,7,8]=>[8,6,4,3,5,7,2,1]=>[1,1,1,3,1,1]
[4,6,3,5,1,2,7,8]=>[1,5,3,6,4,2,7,8]=>[8,4,6,3,5,7,2,1]=>[1,2,3,1,1]
[5,6,2,4,1,3,7,8]=>[3,5,1,6,4,2,7,8]=>[6,4,8,3,5,7,2,1]=>[1,2,3,1,1]
[3,7,2,5,1,4,6,8]=>[1,3,5,6,4,7,2,8]=>[8,6,4,3,5,2,7,1]=>[1,1,1,2,2,1]
[4,7,3,5,1,2,6,8]=>[1,5,3,6,4,7,2,8]=>[8,4,6,3,5,2,7,1]=>[1,2,2,2,1]
[5,7,2,4,1,3,6,8]=>[3,5,1,6,4,7,2,8]=>[6,4,8,3,5,2,7,1]=>[1,2,2,2,1]
[5,7,3,4,1,2,6,8]=>[5,3,1,6,4,7,2,8]=>[4,6,8,3,5,2,7,1]=>[3,2,2,1]
[3,7,2,6,1,4,5,8]=>[1,3,5,6,7,4,2,8]=>[8,6,4,3,2,5,7,1]=>[1,1,1,1,3,1]
[5,7,2,6,1,3,4,8]=>[3,5,1,6,7,4,2,8]=>[6,4,8,3,2,5,7,1]=>[1,2,1,3,1]
[6,7,2,5,1,3,4,8]=>[3,5,6,1,7,4,2,8]=>[6,4,3,8,2,5,7,1]=>[1,1,2,3,1]
[5,8,2,4,1,3,6,7]=>[3,5,1,6,4,7,8,2]=>[6,4,8,3,5,2,1,7]=>[1,2,2,1,2]
[5,8,3,4,1,2,6,7]=>[5,3,1,6,4,7,8,2]=>[4,6,8,3,5,2,1,7]=>[3,2,1,2]
[3,8,2,6,1,4,5,7]=>[1,3,5,6,7,4,8,2]=>[8,6,4,3,2,5,1,7]=>[1,1,1,1,2,2]
[4,8,2,6,1,3,5,7]=>[3,1,5,6,7,4,8,2]=>[6,8,4,3,2,5,1,7]=>[2,1,1,2,2]
[5,8,3,6,1,2,4,7]=>[5,3,1,6,7,4,8,2]=>[4,6,8,3,2,5,1,7]=>[3,1,2,2]
[6,8,2,4,1,3,5,7]=>[3,5,6,4,1,7,8,2]=>[6,4,3,5,8,2,1,7]=>[1,1,3,1,2]
[6,8,3,4,1,2,5,7]=>[5,3,6,4,1,7,8,2]=>[4,6,3,5,8,2,1,7]=>[2,3,1,2]
[6,8,3,5,1,2,4,7]=>[5,3,6,1,7,4,8,2]=>[4,6,3,8,2,5,1,7]=>[2,2,2,2]
[6,8,4,5,1,2,3,7]=>[5,6,3,1,7,4,8,2]=>[4,3,6,8,2,5,1,7]=>[1,3,2,2]
[3,8,2,7,1,4,5,6]=>[1,3,5,6,7,8,4,2]=>[8,6,4,3,2,1,5,7]=>[1,1,1,1,1,3]
[4,8,2,7,1,3,5,6]=>[3,1,5,6,7,8,4,2]=>[6,8,4,3,2,1,5,7]=>[2,1,1,1,3]
[4,8,3,7,1,2,5,6]=>[1,5,3,6,7,8,4,2]=>[8,4,6,3,2,1,5,7]=>[1,2,1,1,3]
[5,8,2,7,1,3,4,6]=>[3,5,1,6,7,8,4,2]=>[6,4,8,3,2,1,5,7]=>[1,2,1,1,3]
[5,8,3,7,1,2,4,6]=>[5,3,1,6,7,8,4,2]=>[4,6,8,3,2,1,5,7]=>[3,1,1,3]
[5,8,4,7,1,2,3,6]=>[5,1,6,3,7,8,4,2]=>[4,8,3,6,2,1,5,7]=>[2,2,1,3]
[6,8,2,7,1,3,4,5]=>[3,5,6,1,7,8,4,2]=>[6,4,3,8,2,1,5,7]=>[1,1,2,1,3]
[6,8,3,7,1,2,4,5]=>[5,3,6,1,7,8,4,2]=>[4,6,3,8,2,1,5,7]=>[2,2,1,3]
[6,8,5,7,1,2,3,4]=>[5,6,1,7,3,8,4,2]=>[4,3,8,2,6,1,5,7]=>[1,2,2,3]
[7,8,2,4,1,3,5,6]=>[3,5,6,4,7,1,8,2]=>[6,4,3,5,2,8,1,7]=>[1,1,2,2,2]
[7,8,2,5,1,3,4,6]=>[3,5,6,7,4,1,8,2]=>[6,4,3,2,5,8,1,7]=>[1,1,1,3,2]
[7,8,3,5,1,2,4,6]=>[5,3,6,7,4,1,8,2]=>[4,6,3,2,5,8,1,7]=>[2,1,3,2]
[7,8,4,6,1,2,3,5]=>[5,6,3,7,1,8,4,2]=>[4,3,6,2,8,1,5,7]=>[1,2,2,3]
[4,3,2,6,1,5,7,8]=>[3,2,1,5,6,4,7,8]=>[6,7,8,4,3,5,2,1]=>[3,1,2,1,1]
[5,3,2,6,1,4,7,8]=>[3,2,5,1,6,4,7,8]=>[6,7,4,8,3,5,2,1]=>[2,2,2,1,1]
[5,4,2,6,1,3,7,8]=>[3,5,2,1,6,4,7,8]=>[6,4,7,8,3,5,2,1]=>[1,3,2,1,1]
[6,4,2,5,1,3,7,8]=>[3,5,2,6,4,1,7,8]=>[6,4,7,3,5,8,2,1]=>[1,2,3,1,1]
[6,5,2,4,1,3,7,8]=>[3,5,6,4,2,1,7,8]=>[6,4,3,5,7,8,2,1]=>[1,1,4,1,1]
[4,3,2,7,1,5,6,8]=>[3,2,1,5,6,7,4,8]=>[6,7,8,4,3,2,5,1]=>[3,1,1,2,1]
[5,3,2,7,1,4,6,8]=>[3,2,5,1,6,7,4,8]=>[6,7,4,8,3,2,5,1]=>[2,2,1,2,1]
[5,4,3,7,1,2,6,8]=>[5,3,2,1,6,7,4,8]=>[4,6,7,8,3,2,5,1]=>[4,1,2,1]
[6,3,2,7,1,4,5,8]=>[3,2,5,6,1,7,4,8]=>[6,7,4,3,8,2,5,1]=>[2,1,2,2,1]
[6,4,2,7,1,3,5,8]=>[3,5,2,6,1,7,4,8]=>[6,4,7,3,8,2,5,1]=>[1,2,2,2,1]
[6,4,3,7,1,2,5,8]=>[5,3,2,6,1,7,4,8]=>[4,6,7,3,8,2,5,1]=>[3,2,2,1]
[6,5,2,7,1,3,4,8]=>[3,5,6,2,1,7,4,8]=>[6,4,3,7,8,2,5,1]=>[1,1,3,2,1]
[6,5,3,7,1,2,4,8]=>[5,3,6,2,1,7,4,8]=>[4,6,3,7,8,2,5,1]=>[2,3,2,1]
[7,3,2,5,1,4,6,8]=>[3,2,5,6,4,7,1,8]=>[6,7,4,3,5,2,8,1]=>[2,1,2,2,1]
[7,4,2,5,1,3,6,8]=>[3,5,2,6,4,7,1,8]=>[6,4,7,3,5,2,8,1]=>[1,2,2,2,1]
[7,3,2,6,1,4,5,8]=>[3,2,5,6,7,4,1,8]=>[6,7,4,3,2,5,8,1]=>[2,1,1,3,1]
[7,4,2,6,1,3,5,8]=>[3,5,2,6,7,4,1,8]=>[6,4,7,3,2,5,8,1]=>[1,2,1,3,1]
[7,4,3,6,1,2,5,8]=>[5,3,2,6,7,4,1,8]=>[4,6,7,3,2,5,8,1]=>[3,1,3,1]
[7,5,2,6,1,3,4,8]=>[3,5,6,2,7,4,1,8]=>[6,4,3,7,2,5,8,1]=>[1,1,2,3,1]
[7,5,3,6,1,2,4,8]=>[5,3,6,2,7,4,1,8]=>[4,6,3,7,2,5,8,1]=>[2,2,3,1]
[4,3,2,8,1,5,6,7]=>[3,2,1,5,6,7,8,4]=>[6,7,8,4,3,2,1,5]=>[3,1,1,1,2]
[5,3,2,8,1,4,6,7]=>[3,2,5,1,6,7,8,4]=>[6,7,4,8,3,2,1,5]=>[2,2,1,1,2]
[5,4,3,8,1,2,6,7]=>[5,3,2,1,6,7,8,4]=>[4,6,7,8,3,2,1,5]=>[4,1,1,2]
[6,3,2,8,1,4,5,7]=>[3,2,5,6,1,7,8,4]=>[6,7,4,3,8,2,1,5]=>[2,1,2,1,2]
[6,4,2,8,1,3,5,7]=>[3,5,2,6,1,7,8,4]=>[6,4,7,3,8,2,1,5]=>[1,2,2,1,2]
[6,4,3,8,1,2,5,7]=>[5,3,2,6,1,7,8,4]=>[4,6,7,3,8,2,1,5]=>[3,2,1,2]
[6,5,2,8,1,3,4,7]=>[3,5,6,2,1,7,8,4]=>[6,4,3,7,8,2,1,5]=>[1,1,3,1,2]
[6,5,3,8,1,2,4,7]=>[5,3,6,2,1,7,8,4]=>[4,6,3,7,8,2,1,5]=>[2,3,1,2]
[6,5,4,8,1,2,3,7]=>[5,6,3,2,1,7,8,4]=>[4,3,6,7,8,2,1,5]=>[1,4,1,2]
[7,3,2,8,1,4,5,6]=>[3,2,5,6,7,1,8,4]=>[6,7,4,3,2,8,1,5]=>[2,1,1,2,2]
[7,4,2,8,1,3,5,6]=>[3,5,2,6,7,1,8,4]=>[6,4,7,3,2,8,1,5]=>[1,2,1,2,2]
[7,4,3,8,1,2,5,6]=>[5,3,2,6,7,1,8,4]=>[4,6,7,3,2,8,1,5]=>[3,1,2,2]
[7,5,3,8,1,2,4,6]=>[5,3,6,2,7,1,8,4]=>[4,6,3,7,2,8,1,5]=>[2,2,2,2]
[7,5,4,8,1,2,3,6]=>[5,6,3,2,7,1,8,4]=>[4,3,6,7,2,8,1,5]=>[1,3,2,2]
[7,6,2,8,1,3,4,5]=>[3,5,6,7,2,1,8,4]=>[6,4,3,2,7,8,1,5]=>[1,1,1,3,2]
[7,6,4,8,1,2,3,5]=>[5,6,3,7,2,1,8,4]=>[4,3,6,2,7,8,1,5]=>[1,2,3,2]
[8,3,2,5,1,4,6,7]=>[3,2,5,6,4,7,8,1]=>[6,7,4,3,5,2,1,8]=>[2,1,2,1,2]
[8,4,2,5,1,3,6,7]=>[3,5,2,6,4,7,8,1]=>[6,4,7,3,5,2,1,8]=>[1,2,2,1,2]
[8,3,2,6,1,4,5,7]=>[3,2,5,6,7,4,8,1]=>[6,7,4,3,2,5,1,8]=>[2,1,1,2,2]
[8,4,2,6,1,3,5,7]=>[3,5,2,6,7,4,8,1]=>[6,4,7,3,2,5,1,8]=>[1,2,1,2,2]
[8,5,3,6,1,2,4,7]=>[5,3,6,2,7,4,8,1]=>[4,6,3,7,2,5,1,8]=>[2,2,2,2]
[8,6,2,4,1,3,5,7]=>[3,5,6,4,7,2,8,1]=>[6,4,3,5,2,7,1,8]=>[1,1,2,2,2]
[8,3,2,7,1,4,5,6]=>[3,2,5,6,7,8,4,1]=>[6,7,4,3,2,1,5,8]=>[2,1,1,1,3]
[8,4,2,7,1,3,5,6]=>[3,5,2,6,7,8,4,1]=>[6,4,7,3,2,1,5,8]=>[1,2,1,1,3]
[8,5,2,7,1,3,4,6]=>[3,5,6,2,7,8,4,1]=>[6,4,3,7,2,1,5,8]=>[1,1,2,1,3]
[8,5,3,7,1,2,4,6]=>[5,3,6,2,7,8,4,1]=>[4,6,3,7,2,1,5,8]=>[2,2,1,3]
[8,5,4,7,1,2,3,6]=>[5,6,3,2,7,8,4,1]=>[4,3,6,7,2,1,5,8]=>[1,3,1,3]
[8,6,3,7,1,2,4,5]=>[5,3,6,7,2,8,4,1]=>[4,6,3,2,7,1,5,8]=>[2,1,2,3]
[8,7,2,4,1,3,5,6]=>[3,5,6,4,7,8,2,1]=>[6,4,3,5,2,1,7,8]=>[1,1,2,1,3]
[8,7,2,5,1,3,4,6]=>[3,5,6,7,4,8,2,1]=>[6,4,3,2,5,1,7,8]=>[1,1,1,2,3]
[8,7,3,5,1,2,4,6]=>[5,3,6,7,4,8,2,1]=>[4,6,3,2,5,1,7,8]=>[2,1,2,3]
[8,7,2,6,1,3,4,5]=>[3,5,6,7,8,4,2,1]=>[6,4,3,2,1,5,7,8]=>[1,1,1,1,4]
[8,7,3,6,1,2,4,5]=>[5,3,6,7,8,4,2,1]=>[4,6,3,2,1,5,7,8]=>[2,1,1,4]
[8,7,4,6,1,2,3,5]=>[5,6,3,7,8,4,2,1]=>[4,3,6,2,1,5,7,8]=>[1,2,1,4]
[3,6,2,5,8,1,4,7]=>[6,1,3,4,2,7,8,5]=>[3,8,6,5,7,2,1,4]=>[2,1,2,1,2]
[4,6,3,5,8,1,2,7]=>[1,3,6,4,2,7,8,5]=>[8,6,3,5,7,2,1,4]=>[1,1,3,1,2]
[5,6,2,4,8,1,3,7]=>[6,3,1,4,2,7,8,5]=>[3,6,8,5,7,2,1,4]=>[3,2,1,2]
[4,7,2,5,8,1,3,6]=>[1,6,3,4,7,2,8,5]=>[8,3,6,5,2,7,1,4]=>[1,2,1,2,2]
[4,7,3,5,8,1,2,6]=>[1,3,6,4,7,2,8,5]=>[8,6,3,5,2,7,1,4]=>[1,1,2,2,2]
[5,7,2,4,8,1,3,6]=>[6,3,1,4,7,2,8,5]=>[3,6,8,5,2,7,1,4]=>[3,1,2,2]
[5,7,3,4,8,1,2,6]=>[3,1,6,4,7,2,8,5]=>[6,8,3,5,2,7,1,4]=>[2,2,2,2]
[4,7,3,6,8,1,2,5]=>[1,3,6,7,4,2,8,5]=>[8,6,3,2,5,7,1,4]=>[1,1,1,3,2]
[5,7,2,6,8,1,3,4]=>[6,1,7,3,4,2,8,5]=>[3,8,2,6,5,7,1,4]=>[2,2,2,2]
[5,7,4,6,8,1,2,3]=>[1,6,3,7,4,2,8,5]=>[8,3,6,2,5,7,1,4]=>[1,2,3,2]
[6,7,3,4,8,1,2,5]=>[3,6,4,1,7,2,8,5]=>[6,3,5,8,2,7,1,4]=>[1,3,2,2]
[6,7,3,5,8,1,2,4]=>[3,6,1,7,4,2,8,5]=>[6,3,8,2,5,7,1,4]=>[1,2,3,2]
[3,8,2,5,7,1,4,6]=>[6,1,3,4,7,8,5,2]=>[3,8,6,5,2,1,4,7]=>[2,1,1,1,3]
[4,8,2,5,7,1,3,6]=>[1,6,3,4,7,8,5,2]=>[8,3,6,5,2,1,4,7]=>[1,2,1,1,3]
[4,8,3,5,7,1,2,6]=>[1,3,6,4,7,8,5,2]=>[8,6,3,5,2,1,4,7]=>[1,1,2,1,3]
[5,8,2,4,7,1,3,6]=>[6,3,1,4,7,8,5,2]=>[3,6,8,5,2,1,4,7]=>[3,1,1,3]
[3,8,2,6,7,1,4,5]=>[6,7,1,3,4,8,5,2]=>[3,2,8,6,5,1,4,7]=>[1,2,1,1,3]
[5,8,2,6,7,1,3,4]=>[6,1,7,3,4,8,5,2]=>[3,8,2,6,5,1,4,7]=>[2,2,1,3]
[5,8,3,6,7,1,2,4]=>[3,1,6,7,4,8,5,2]=>[6,8,3,2,5,1,4,7]=>[2,1,2,3]
[5,8,4,6,7,1,2,3]=>[1,6,3,7,4,8,5,2]=>[8,3,6,2,5,1,4,7]=>[1,2,2,3]
[6,8,2,5,7,1,3,4]=>[6,7,3,1,4,8,5,2]=>[3,2,6,8,5,1,4,7]=>[1,3,1,3]
[6,8,3,5,7,1,2,4]=>[3,6,1,7,4,8,5,2]=>[6,3,8,2,5,1,4,7]=>[1,2,2,3]
[6,8,4,5,7,1,2,3]=>[6,3,1,7,4,8,5,2]=>[3,6,8,2,5,1,4,7]=>[3,2,3]
[7,8,2,4,6,1,3,5]=>[6,3,4,7,1,8,5,2]=>[3,6,5,2,8,1,4,7]=>[2,1,2,3]
[7,8,3,4,6,1,2,5]=>[3,6,4,7,1,8,5,2]=>[6,3,5,2,8,1,4,7]=>[1,2,2,3]
[7,8,2,5,6,1,3,4]=>[6,7,3,4,1,8,5,2]=>[3,2,6,5,8,1,4,7]=>[1,2,2,3]
[7,8,3,5,6,1,2,4]=>[3,6,7,4,1,8,5,2]=>[6,3,2,5,8,1,4,7]=>[1,1,3,3]
[4,3,2,6,8,1,5,7]=>[2,1,6,3,4,7,8,5]=>[7,8,3,6,5,2,1,4]=>[2,2,1,1,2]
[5,3,2,6,8,1,4,7]=>[2,6,3,1,4,7,8,5]=>[7,3,6,8,5,2,1,4]=>[1,3,1,1,2]
[5,4,2,6,8,1,3,7]=>[6,3,2,1,4,7,8,5]=>[3,6,7,8,5,2,1,4]=>[4,1,1,2]
[5,4,3,6,8,1,2,7]=>[3,2,1,6,4,7,8,5]=>[6,7,8,3,5,2,1,4]=>[3,2,1,2]
[6,3,2,5,8,1,4,7]=>[2,6,3,4,1,7,8,5]=>[7,3,6,5,8,2,1,4]=>[1,2,2,1,2]
[6,4,3,5,8,1,2,7]=>[3,2,6,4,1,7,8,5]=>[6,7,3,5,8,2,1,4]=>[2,3,1,2]
[6,5,2,4,8,1,3,7]=>[6,3,4,2,1,7,8,5]=>[3,6,5,7,8,2,1,4]=>[2,3,1,2]
[5,3,2,7,8,1,4,6]=>[2,6,1,7,3,4,8,5]=>[7,3,8,2,6,5,1,4]=>[1,2,2,1,2]
[5,4,3,7,8,1,2,6]=>[3,2,1,6,7,4,8,5]=>[6,7,8,3,2,5,1,4]=>[3,1,2,2]
[6,4,2,7,8,1,3,5]=>[6,2,7,3,1,4,8,5]=>[3,7,2,6,8,5,1,4]=>[2,3,1,2]
[6,4,3,7,8,1,2,5]=>[3,2,6,1,7,4,8,5]=>[6,7,3,8,2,5,1,4]=>[2,2,2,2]
[6,5,2,7,8,1,3,4]=>[6,7,3,2,1,4,8,5]=>[3,2,6,7,8,5,1,4]=>[1,4,1,2]
[7,4,2,5,8,1,3,6]=>[6,3,2,4,7,1,8,5]=>[3,6,7,5,2,8,1,4]=>[3,1,2,2]
[7,4,3,5,8,1,2,6]=>[3,2,6,4,7,1,8,5]=>[6,7,3,5,2,8,1,4]=>[2,2,2,2]
[7,5,3,4,8,1,2,6]=>[3,6,4,2,7,1,8,5]=>[6,3,5,7,2,8,1,4]=>[1,3,2,2]
[7,3,2,6,8,1,4,5]=>[2,6,7,3,4,1,8,5]=>[7,3,2,6,5,8,1,4]=>[1,1,2,2,2]
[7,5,2,6,8,1,3,4]=>[6,7,3,2,4,1,8,5]=>[3,2,6,7,5,8,1,4]=>[1,3,2,2]
[7,5,3,6,8,1,2,4]=>[3,6,2,7,4,1,8,5]=>[6,3,7,2,5,8,1,4]=>[1,2,3,2]
[7,6,2,4,8,1,3,5]=>[6,3,4,7,2,1,8,5]=>[3,6,5,2,7,8,1,4]=>[2,1,3,2]
[7,6,3,5,8,1,2,4]=>[3,6,7,4,2,1,8,5]=>[6,3,2,5,7,8,1,4]=>[1,1,4,2]
[8,3,2,5,7,1,4,6]=>[2,6,3,4,7,8,5,1]=>[7,3,6,5,2,1,4,8]=>[1,2,1,1,3]
[8,4,2,5,7,1,3,6]=>[6,3,2,4,7,8,5,1]=>[3,6,7,5,2,1,4,8]=>[3,1,1,3]
[8,5,2,4,7,1,3,6]=>[6,3,4,2,7,8,5,1]=>[3,6,5,7,2,1,4,8]=>[2,2,1,3]
[8,3,2,6,7,1,4,5]=>[2,6,7,3,4,8,5,1]=>[7,3,2,6,5,1,4,8]=>[1,1,2,1,3]
[8,5,2,6,7,1,3,4]=>[6,7,3,2,4,8,5,1]=>[3,2,6,7,5,1,4,8]=>[1,3,1,3]
[8,5,3,6,7,1,2,4]=>[3,6,2,7,4,8,5,1]=>[6,3,7,2,5,1,4,8]=>[1,2,2,3]
[8,6,2,4,7,1,3,5]=>[6,3,4,7,2,8,5,1]=>[3,6,5,2,7,1,4,8]=>[2,1,2,3]
[8,6,2,5,7,1,3,4]=>[6,7,3,4,2,8,5,1]=>[3,2,6,5,7,1,4,8]=>[1,2,2,3]
[8,6,3,5,7,1,2,4]=>[3,6,7,4,2,8,5,1]=>[6,3,2,5,7,1,4,8]=>[1,1,3,3]
[8,7,2,4,6,1,3,5]=>[6,3,4,7,8,5,2,1]=>[3,6,5,2,1,4,7,8]=>[2,1,1,4]
[8,7,3,4,6,1,2,5]=>[3,6,4,7,8,5,2,1]=>[6,3,5,2,1,4,7,8]=>[1,2,1,4]
[8,7,2,5,6,1,3,4]=>[6,7,3,4,8,5,2,1]=>[3,2,6,5,1,4,7,8]=>[1,2,1,4]
[8,7,3,5,6,1,2,4]=>[3,6,7,4,8,5,2,1]=>[6,3,2,5,1,4,7,8]=>[1,1,2,4]
[5,3,7,2,6,1,4,8]=>[2,4,1,6,7,5,3,8]=>[7,5,8,3,2,4,6,1]=>[1,2,1,3,1]
[5,4,7,2,6,1,3,8]=>[4,2,1,6,7,5,3,8]=>[5,7,8,3,2,4,6,1]=>[3,1,3,1]
[6,3,7,2,5,1,4,8]=>[2,4,6,1,7,5,3,8]=>[7,5,3,8,2,4,6,1]=>[1,1,2,3,1]
[6,4,7,2,5,1,3,8]=>[4,2,6,1,7,5,3,8]=>[5,7,3,8,2,4,6,1]=>[2,2,3,1]
[6,4,7,3,5,1,2,8]=>[2,6,4,1,7,5,3,8]=>[7,3,5,8,2,4,6,1]=>[1,3,3,1]
[7,3,6,2,5,1,4,8]=>[2,4,6,7,5,3,1,8]=>[7,5,3,2,4,6,8,1]=>[1,1,1,4,1]
[4,3,8,2,6,1,5,7]=>[2,1,4,6,7,5,8,3]=>[7,8,5,3,2,4,1,6]=>[2,1,1,2,2]
[5,3,8,2,6,1,4,7]=>[2,4,1,6,7,5,8,3]=>[7,5,8,3,2,4,1,6]=>[1,2,1,2,2]
[5,4,8,2,6,1,3,7]=>[4,2,1,6,7,5,8,3]=>[5,7,8,3,2,4,1,6]=>[3,1,2,2]
[6,3,8,2,5,1,4,7]=>[2,4,6,1,7,5,8,3]=>[7,5,3,8,2,4,1,6]=>[1,1,2,2,2]
[6,4,8,2,5,1,3,7]=>[4,2,6,1,7,5,8,3]=>[5,7,3,8,2,4,1,6]=>[2,2,2,2]
[6,4,8,3,5,1,2,7]=>[2,6,4,1,7,5,8,3]=>[7,3,5,8,2,4,1,6]=>[1,3,2,2]
[6,5,8,2,4,1,3,7]=>[4,6,2,1,7,5,8,3]=>[5,3,7,8,2,4,1,6]=>[1,3,2,2]
[6,5,8,3,4,1,2,7]=>[6,4,2,1,7,5,8,3]=>[3,5,7,8,2,4,1,6]=>[4,2,2]
[4,3,8,2,7,1,5,6]=>[2,1,4,6,7,8,5,3]=>[7,8,5,3,2,1,4,6]=>[2,1,1,1,3]
[5,3,8,2,7,1,4,6]=>[2,4,1,6,7,8,5,3]=>[7,5,8,3,2,1,4,6]=>[1,2,1,1,3]
[5,4,8,2,7,1,3,6]=>[4,2,1,6,7,8,5,3]=>[5,7,8,3,2,1,4,6]=>[3,1,1,3]
[5,4,8,3,7,1,2,6]=>[2,1,6,4,7,8,5,3]=>[7,8,3,5,2,1,4,6]=>[2,2,1,3]
[6,3,8,2,7,1,4,5]=>[2,4,6,1,7,8,5,3]=>[7,5,3,8,2,1,4,6]=>[1,1,2,1,3]
[6,4,8,2,7,1,3,5]=>[4,2,6,1,7,8,5,3]=>[5,7,3,8,2,1,4,6]=>[2,2,1,3]
[6,4,8,3,7,1,2,5]=>[2,6,4,1,7,8,5,3]=>[7,3,5,8,2,1,4,6]=>[1,3,1,3]
[6,5,8,2,7,1,3,4]=>[4,6,2,1,7,8,5,3]=>[5,3,7,8,2,1,4,6]=>[1,3,1,3]
[7,3,8,2,5,1,4,6]=>[2,4,6,7,5,1,8,3]=>[7,5,3,2,4,8,1,6]=>[1,1,1,3,2]
[7,4,8,3,5,1,2,6]=>[2,6,4,7,5,1,8,3]=>[7,3,5,2,4,8,1,6]=>[1,2,3,2]
[7,5,8,2,4,1,3,6]=>[4,6,2,7,5,1,8,3]=>[5,3,7,2,4,8,1,6]=>[1,2,3,2]
[7,5,8,3,4,1,2,6]=>[6,4,2,7,5,1,8,3]=>[3,5,7,2,4,8,1,6]=>[3,3,2]
[7,3,8,2,6,1,4,5]=>[2,4,6,7,1,8,5,3]=>[7,5,3,2,8,1,4,6]=>[1,1,1,2,3]
[7,4,8,2,6,1,3,5]=>[4,2,6,7,1,8,5,3]=>[5,7,3,2,8,1,4,6]=>[2,1,2,3]
[7,5,8,2,6,1,3,4]=>[4,6,2,7,1,8,5,3]=>[5,3,7,2,8,1,4,6]=>[1,2,2,3]
[7,5,8,3,6,1,2,4]=>[6,4,2,7,1,8,5,3]=>[3,5,7,2,8,1,4,6]=>[3,2,3]
[7,5,8,4,6,1,2,3]=>[6,2,7,4,1,8,5,3]=>[3,7,2,5,8,1,4,6]=>[2,3,3]
[7,6,8,2,5,1,3,4]=>[4,6,7,2,1,8,5,3]=>[5,3,2,7,8,1,4,6]=>[1,1,3,3]
[7,6,8,3,5,1,2,4]=>[6,4,7,2,1,8,5,3]=>[3,5,2,7,8,1,4,6]=>[2,3,3]
[8,3,6,2,5,1,4,7]=>[2,4,6,7,5,3,8,1]=>[7,5,3,2,4,6,1,8]=>[1,1,1,3,2]
[8,4,6,2,5,1,3,7]=>[4,2,6,7,5,3,8,1]=>[5,7,3,2,4,6,1,8]=>[2,1,3,2]
[8,5,6,2,4,1,3,7]=>[4,6,2,7,5,3,8,1]=>[5,3,7,2,4,6,1,8]=>[1,2,3,2]
[8,3,7,2,5,1,4,6]=>[2,4,6,7,5,8,3,1]=>[7,5,3,2,4,1,6,8]=>[1,1,1,2,3]
[8,4,7,3,5,1,2,6]=>[2,6,4,7,5,8,3,1]=>[7,3,5,2,4,1,6,8]=>[1,2,2,3]
[8,5,7,2,4,1,3,6]=>[4,6,2,7,5,8,3,1]=>[5,3,7,2,4,1,6,8]=>[1,2,2,3]
[8,3,7,2,6,1,4,5]=>[2,4,6,7,8,5,3,1]=>[7,5,3,2,1,4,6,8]=>[1,1,1,1,4]
[8,4,7,2,6,1,3,5]=>[4,2,6,7,8,5,3,1]=>[5,7,3,2,1,4,6,8]=>[2,1,1,4]
[8,4,7,3,6,1,2,5]=>[2,6,4,7,8,5,3,1]=>[7,3,5,2,1,4,6,8]=>[1,2,1,4]
[8,5,7,2,6,1,3,4]=>[4,6,2,7,8,5,3,1]=>[5,3,7,2,1,4,6,8]=>[1,2,1,4]
[8,6,7,2,4,1,3,5]=>[4,6,7,5,2,8,3,1]=>[5,3,2,4,7,1,6,8]=>[1,1,3,3]
[8,6,7,2,5,1,3,4]=>[4,6,7,2,8,5,3,1]=>[5,3,2,7,1,4,6,8]=>[1,1,2,4]
[8,6,7,3,5,1,2,4]=>[6,4,7,2,8,5,3,1]=>[3,5,2,7,1,4,6,8]=>[2,2,4]
[5,4,3,2,7,1,6,8]=>[4,3,2,1,6,7,5,8]=>[5,6,7,8,3,2,4,1]=>[4,1,2,1]
[6,4,3,2,7,1,5,8]=>[4,3,2,6,1,7,5,8]=>[5,6,7,3,8,2,4,1]=>[3,2,2,1]
[6,5,3,2,7,1,4,8]=>[4,3,6,2,1,7,5,8]=>[5,6,3,7,8,2,4,1]=>[2,3,2,1]
[6,5,4,2,7,1,3,8]=>[4,6,3,2,1,7,5,8]=>[5,3,6,7,8,2,4,1]=>[1,4,2,1]
[7,5,3,2,6,1,4,8]=>[4,3,6,2,7,5,1,8]=>[5,6,3,7,2,4,8,1]=>[2,2,3,1]
[7,5,4,2,6,1,3,8]=>[4,6,3,2,7,5,1,8]=>[5,3,6,7,2,4,8,1]=>[1,3,3,1]
[5,4,3,2,8,1,6,7]=>[4,3,2,1,6,7,8,5]=>[5,6,7,8,3,2,1,4]=>[4,1,1,2]
[6,5,3,2,8,1,4,7]=>[4,3,6,2,1,7,8,5]=>[5,6,3,7,8,2,1,4]=>[2,3,1,2]
[6,5,4,2,8,1,3,7]=>[4,6,3,2,1,7,8,5]=>[5,3,6,7,8,2,1,4]=>[1,4,1,2]
[6,5,4,3,8,1,2,7]=>[6,4,3,2,1,7,8,5]=>[3,5,6,7,8,2,1,4]=>[5,1,2]
[7,5,3,2,8,1,4,6]=>[4,3,6,2,7,1,8,5]=>[5,6,3,7,2,8,1,4]=>[2,2,2,2]
[7,5,4,2,8,1,3,6]=>[4,6,3,2,7,1,8,5]=>[5,3,6,7,2,8,1,4]=>[1,3,2,2]
[7,6,3,2,8,1,4,5]=>[4,3,6,7,2,1,8,5]=>[5,6,3,2,7,8,1,4]=>[2,1,3,2]
[7,6,4,3,8,1,2,5]=>[6,4,3,7,2,1,8,5]=>[3,5,6,2,7,8,1,4]=>[3,3,2]
[7,6,5,2,8,1,3,4]=>[4,6,7,3,2,1,8,5]=>[5,3,2,6,7,8,1,4]=>[1,1,4,2]
[7,6,5,3,8,1,2,4]=>[6,4,7,3,2,1,8,5]=>[3,5,2,6,7,8,1,4]=>[2,4,2]
[8,5,3,2,6,1,4,7]=>[4,3,6,2,7,5,8,1]=>[5,6,3,7,2,4,1,8]=>[2,2,2,2]
[8,5,4,2,6,1,3,7]=>[4,6,3,2,7,5,8,1]=>[5,3,6,7,2,4,1,8]=>[1,3,2,2]
[8,6,3,2,5,1,4,7]=>[4,3,6,7,5,2,8,1]=>[5,6,3,2,4,7,1,8]=>[2,1,3,2]
[8,6,4,2,5,1,3,7]=>[4,6,3,7,5,2,8,1]=>[5,3,6,2,4,7,1,8]=>[1,2,3,2]
[8,6,5,2,4,1,3,7]=>[4,6,7,5,3,2,8,1]=>[5,3,2,4,6,7,1,8]=>[1,1,4,2]
[8,5,3,2,7,1,4,6]=>[4,3,6,2,7,8,5,1]=>[5,6,3,7,2,1,4,8]=>[2,2,1,3]
[8,6,4,2,7,1,3,5]=>[4,6,3,7,2,8,5,1]=>[5,3,6,2,7,1,4,8]=>[1,2,2,3]
[8,6,4,3,7,1,2,5]=>[6,4,3,7,2,8,5,1]=>[3,5,6,2,7,1,4,8]=>[3,2,3]
[8,6,5,3,7,1,2,4]=>[6,4,7,3,2,8,5,1]=>[3,5,2,6,7,1,4,8]=>[2,3,3]
[8,7,3,2,5,1,4,6]=>[4,3,6,7,5,8,2,1]=>[5,6,3,2,4,1,7,8]=>[2,1,2,3]
[8,7,3,2,6,1,4,5]=>[4,3,6,7,8,5,2,1]=>[5,6,3,2,1,4,7,8]=>[2,1,1,4]
[8,7,4,2,6,1,3,5]=>[4,6,3,7,8,5,2,1]=>[5,3,6,2,1,4,7,8]=>[1,2,1,4]
[8,7,4,3,6,1,2,5]=>[6,4,3,7,8,5,2,1]=>[3,5,6,2,1,4,7,8]=>[3,1,4]
[8,7,5,2,6,1,3,4]=>[4,6,7,3,8,5,2,1]=>[5,3,2,6,1,4,7,8]=>[1,1,2,4]
[8,7,5,3,6,1,2,4]=>[6,4,7,3,8,5,2,1]=>[3,5,2,6,1,4,7,8]=>[2,2,4]
[8,7,6,2,4,1,3,5]=>[4,6,7,5,8,3,2,1]=>[5,3,2,4,1,6,7,8]=>[1,1,2,4]
[8,7,6,2,5,1,3,4]=>[4,6,7,8,5,3,2,1]=>[5,3,2,1,4,6,7,8]=>[1,1,1,5]
[8,7,6,3,5,1,2,4]=>[6,4,7,8,5,3,2,1]=>[3,5,2,1,4,6,7,8]=>[2,1,5]
[4,8,3,7,2,6,1,5]=>[1,3,5,7,8,6,4,2]=>[8,6,4,2,1,3,5,7]=>[1,1,1,1,4]
[5,8,3,7,2,6,1,4]=>[3,1,5,7,8,6,4,2]=>[6,8,4,2,1,3,5,7]=>[2,1,1,4]
[5,8,4,7,2,6,1,3]=>[1,5,3,7,8,6,4,2]=>[8,4,6,2,1,3,5,7]=>[1,2,1,4]
[5,8,4,7,3,6,1,2]=>[1,3,7,5,8,6,4,2]=>[8,6,2,4,1,3,5,7]=>[1,1,2,4]
[6,8,3,7,2,5,1,4]=>[3,5,1,7,8,6,4,2]=>[6,4,8,2,1,3,5,7]=>[1,2,1,4]
[6,8,4,7,2,5,1,3]=>[5,3,1,7,8,6,4,2]=>[4,6,8,2,1,3,5,7]=>[3,1,4]
[6,8,4,7,3,5,1,2]=>[3,1,7,5,8,6,4,2]=>[6,8,2,4,1,3,5,7]=>[2,2,4]
[6,8,5,7,2,4,1,3]=>[5,1,7,3,8,6,4,2]=>[4,8,2,6,1,3,5,7]=>[2,2,4]
[6,8,5,7,3,4,1,2]=>[1,7,5,3,8,6,4,2]=>[8,2,4,6,1,3,5,7]=>[1,3,4]
[7,8,3,6,2,5,1,4]=>[3,5,7,1,8,6,4,2]=>[6,4,2,8,1,3,5,7]=>[1,1,2,4]
[7,8,4,6,2,5,1,3]=>[5,3,7,1,8,6,4,2]=>[4,6,2,8,1,3,5,7]=>[2,2,4]
[7,8,4,6,3,5,1,2]=>[3,7,5,1,8,6,4,2]=>[6,2,4,8,1,3,5,7]=>[1,3,4]
[7,8,5,6,2,4,1,3]=>[5,7,3,1,8,6,4,2]=>[4,2,6,8,1,3,5,7]=>[1,3,4]
[5,4,3,8,2,7,1,6]=>[3,2,1,5,7,8,6,4]=>[6,7,8,4,2,1,3,5]=>[3,1,1,3]
[6,4,3,8,2,7,1,5]=>[3,2,5,1,7,8,6,4]=>[6,7,4,8,2,1,3,5]=>[2,2,1,3]
[6,5,3,8,2,7,1,4]=>[3,5,2,1,7,8,6,4]=>[6,4,7,8,2,1,3,5]=>[1,3,1,3]
[6,5,4,8,2,7,1,3]=>[5,3,2,1,7,8,6,4]=>[4,6,7,8,2,1,3,5]=>[4,1,3]
[6,5,4,8,3,7,1,2]=>[3,2,1,7,5,8,6,4]=>[6,7,8,2,4,1,3,5]=>[3,2,3]
[7,4,3,8,2,6,1,5]=>[3,2,5,7,1,8,6,4]=>[6,7,4,2,8,1,3,5]=>[2,1,2,3]
[7,5,3,8,2,6,1,4]=>[3,5,2,7,1,8,6,4]=>[6,4,7,2,8,1,3,5]=>[1,2,2,3]
[7,5,4,8,2,6,1,3]=>[5,3,2,7,1,8,6,4]=>[4,6,7,2,8,1,3,5]=>[3,2,3]
[7,6,3,8,2,5,1,4]=>[3,5,7,2,1,8,6,4]=>[6,4,2,7,8,1,3,5]=>[1,1,3,3]
[7,6,4,8,2,5,1,3]=>[5,3,7,2,1,8,6,4]=>[4,6,2,7,8,1,3,5]=>[2,3,3]
[7,6,5,8,2,4,1,3]=>[5,7,3,2,1,8,6,4]=>[4,2,6,7,8,1,3,5]=>[1,4,3]
[8,5,3,7,2,6,1,4]=>[3,5,2,7,8,6,4,1]=>[6,4,7,2,1,3,5,8]=>[1,2,1,4]
[8,5,4,7,2,6,1,3]=>[5,3,2,7,8,6,4,1]=>[4,6,7,2,1,3,5,8]=>[3,1,4]
[8,5,4,7,3,6,1,2]=>[3,2,7,5,8,6,4,1]=>[6,7,2,4,1,3,5,8]=>[2,2,4]
[8,6,3,7,2,5,1,4]=>[3,5,7,2,8,6,4,1]=>[6,4,2,7,1,3,5,8]=>[1,1,2,4]
[8,6,4,7,2,5,1,3]=>[5,3,7,2,8,6,4,1]=>[4,6,2,7,1,3,5,8]=>[2,2,4]
[8,6,4,7,3,5,1,2]=>[3,7,5,2,8,6,4,1]=>[6,2,4,7,1,3,5,8]=>[1,3,4]
[8,6,5,7,2,4,1,3]=>[5,7,3,2,8,6,4,1]=>[4,2,6,7,1,3,5,8]=>[1,3,4]
[8,7,3,6,2,5,1,4]=>[3,5,7,8,6,4,2,1]=>[6,4,2,1,3,5,7,8]=>[1,1,1,5]
[8,7,4,6,2,5,1,3]=>[5,3,7,8,6,4,2,1]=>[4,6,2,1,3,5,7,8]=>[2,1,5]
[8,7,4,6,3,5,1,2]=>[3,7,5,8,6,4,2,1]=>[6,2,4,1,3,5,7,8]=>[1,2,5]
[8,7,5,6,2,4,1,3]=>[5,7,3,8,6,4,2,1]=>[4,2,6,1,3,5,7,8]=>[1,2,5]
[6,5,4,3,2,8,1,7]=>[5,4,3,2,1,7,8,6]=>[4,5,6,7,8,2,1,3]=>[5,1,2]
[7,6,4,3,2,8,1,5]=>[5,4,3,7,2,1,8,6]=>[4,5,6,2,7,8,1,3]=>[3,3,2]
[7,6,5,4,2,8,1,3]=>[5,7,4,3,2,1,8,6]=>[4,2,5,6,7,8,1,3]=>[1,5,2]
[8,5,4,3,2,7,1,6]=>[5,4,3,2,7,8,6,1]=>[4,5,6,7,2,1,3,8]=>[4,1,3]
[8,6,4,3,2,7,1,5]=>[5,4,3,7,2,8,6,1]=>[4,5,6,2,7,1,3,8]=>[3,2,3]
[8,6,5,3,2,7,1,4]=>[5,4,7,3,2,8,6,1]=>[4,5,2,6,7,1,3,8]=>[2,3,3]
[8,6,5,4,2,7,1,3]=>[5,7,4,3,2,8,6,1]=>[4,2,5,6,7,1,3,8]=>[1,4,3]
[8,7,4,3,2,6,1,5]=>[5,4,3,7,8,6,2,1]=>[4,5,6,2,1,3,7,8]=>[3,1,4]
[8,7,5,3,2,6,1,4]=>[5,4,7,3,8,6,2,1]=>[4,5,2,6,1,3,7,8]=>[2,2,4]
[8,7,5,4,2,6,1,3]=>[5,7,4,3,8,6,2,1]=>[4,2,5,6,1,3,7,8]=>[1,3,4]
[8,7,6,4,2,5,1,3]=>[5,7,4,8,6,3,2,1]=>[4,2,5,1,3,6,7,8]=>[1,2,5]
[8,7,6,5,2,4,1,3]=>[5,7,8,6,4,3,2,1]=>[4,2,1,3,5,6,7,8]=>[1,1,6]
[8,1,2,3,4,7,5,6]=>[7,8,2,3,4,5,6,1]=>[2,1,7,6,5,4,3,8]=>[1,2,1,1,1,2]
[8,1,2,3,6,4,5,7]=>[6,7,2,3,4,5,8,1]=>[3,2,7,6,5,4,1,8]=>[1,2,1,1,1,2]
[8,1,2,3,7,4,5,6]=>[6,7,8,2,3,4,5,1]=>[3,2,1,7,6,5,4,8]=>[1,1,2,1,1,2]
[5,1,2,3,8,7,4,6]=>[7,8,6,2,1,3,4,5]=>[2,1,3,7,8,6,5,4]=>[1,4,1,1,1]
[8,1,2,3,6,7,4,5]=>[7,5,8,2,3,4,6,1]=>[2,4,1,7,6,5,3,8]=>[2,2,1,1,2]
[4,1,2,8,3,7,5,6]=>[7,1,8,5,6,2,3,4]=>[2,8,1,4,3,7,6,5]=>[2,2,2,1,1]
[8,1,2,5,3,4,6,7]=>[5,6,2,3,4,7,8,1]=>[4,3,7,6,5,2,1,8]=>[1,2,1,1,1,2]
[7,1,2,5,3,4,8,6]=>[8,5,2,3,4,6,1,7]=>[1,4,7,6,5,3,8,2]=>[3,1,1,2,1]
[8,1,2,6,3,4,5,7]=>[5,6,7,2,3,4,8,1]=>[4,3,2,7,6,5,1,8]=>[1,1,2,1,1,2]
[6,1,2,5,3,8,4,7]=>[7,4,8,2,3,1,5,6]=>[2,5,1,7,6,8,4,3]=>[2,2,2,1,1]
[8,1,2,6,3,7,4,5]=>[7,8,5,2,3,4,6,1]=>[2,1,4,7,6,5,3,8]=>[1,3,1,1,2]
[6,1,2,5,3,7,8,4]=>[6,4,8,2,3,1,5,7]=>[3,5,1,7,6,8,4,2]=>[2,2,2,1,1]
[4,1,2,8,6,3,5,7]=>[6,1,7,5,8,2,3,4]=>[3,8,2,4,1,7,6,5]=>[2,2,2,1,1]
[4,1,2,8,7,3,5,6]=>[6,1,7,8,5,2,3,4]=>[3,8,2,1,4,7,6,5]=>[2,1,3,1,1]
[8,1,2,5,6,3,4,7]=>[6,4,7,2,3,5,8,1]=>[3,5,2,7,6,4,1,8]=>[2,2,1,1,2]
[8,1,2,7,6,3,4,5]=>[6,7,8,5,2,3,4,1]=>[3,2,1,4,7,6,5,8]=>[1,1,3,1,2]
[7,1,2,5,6,3,8,4]=>[4,8,6,2,3,5,1,7]=>[5,1,3,7,6,4,8,2]=>[1,3,1,2,1]
[4,1,2,5,8,7,3,6]=>[7,1,8,4,6,2,3,5]=>[2,8,1,5,3,7,6,4]=>[2,2,2,1,1]
[4,1,2,8,6,7,3,5]=>[1,7,5,8,6,2,3,4]=>[8,2,4,1,3,7,6,5]=>[1,2,3,1,1]
[3,1,8,2,4,7,5,6]=>[1,7,8,4,5,6,2,3]=>[8,2,1,5,4,3,7,6]=>[1,1,2,1,2,1]
[3,1,8,2,7,4,5,6]=>[1,6,7,8,4,5,2,3]=>[8,3,2,1,5,4,7,6]=>[1,1,1,2,2,1]
[3,1,7,2,6,4,8,5]=>[8,1,6,4,5,2,3,7]=>[1,8,3,5,4,7,6,2]=>[2,2,2,1,1]
[3,1,5,2,8,7,4,6]=>[1,3,7,8,6,2,4,5]=>[8,6,2,1,3,7,5,4]=>[1,1,1,3,1,1]
[3,1,8,2,6,7,4,5]=>[7,1,5,8,4,6,2,3]=>[2,8,4,1,5,3,7,6]=>[2,1,2,2,1]
[8,1,4,2,3,5,6,7]=>[4,5,2,3,6,7,8,1]=>[5,4,7,6,3,2,1,8]=>[1,2,1,1,1,2]
[7,1,4,2,3,5,8,6]=>[8,4,2,3,5,6,1,7]=>[1,5,7,6,4,3,8,2]=>[3,1,1,2,1]
[6,1,4,2,3,8,5,7]=>[7,3,8,2,4,1,5,6]=>[2,6,1,7,5,8,4,3]=>[2,2,2,1,1]
[8,1,4,2,3,7,5,6]=>[7,3,8,2,4,5,6,1]=>[2,6,1,7,5,4,3,8]=>[2,2,1,1,2]
[6,1,4,2,3,7,8,5]=>[6,3,8,2,4,1,5,7]=>[3,6,1,7,5,8,4,2]=>[2,2,2,1,1]
[8,1,5,2,3,4,6,7]=>[4,5,6,2,3,7,8,1]=>[5,4,3,7,6,2,1,8]=>[1,1,2,1,1,2]
[7,1,5,2,3,4,8,6]=>[8,4,5,2,3,6,1,7]=>[1,5,4,7,6,3,8,2]=>[2,2,1,2,1]
[8,1,7,2,3,4,5,6]=>[4,5,6,7,8,2,3,1]=>[5,4,3,2,1,7,6,8]=>[1,1,1,1,2,2]
[6,1,5,2,3,8,4,7]=>[7,8,4,2,3,1,5,6]=>[2,1,5,7,6,8,4,3]=>[1,3,2,1,1]
[6,1,8,2,3,7,4,5]=>[7,8,4,5,1,6,2,3]=>[2,1,5,4,8,3,7,6]=>[1,2,2,2,1]
[6,1,5,2,3,7,8,4]=>[6,8,4,2,3,1,5,7]=>[3,1,5,7,6,8,4,2]=>[1,3,2,1,1]
[5,1,4,2,7,3,8,6]=>[3,8,6,2,1,4,5,7]=>[6,1,3,7,8,5,4,2]=>[1,4,1,1,1]
[8,1,4,2,6,3,5,7]=>[6,3,7,2,4,5,8,1]=>[3,6,2,7,5,4,1,8]=>[2,2,1,1,2]
[8,1,4,2,7,3,5,6]=>[6,3,7,8,2,4,5,1]=>[3,6,2,1,7,5,4,8]=>[2,1,2,1,2]
[8,1,5,2,6,3,4,7]=>[6,7,4,2,3,5,8,1]=>[3,2,5,7,6,4,1,8]=>[1,3,1,1,2]
[8,1,5,2,7,3,4,6]=>[6,7,3,8,2,4,5,1]=>[3,2,6,1,7,5,4,8]=>[1,2,2,1,2]
[7,1,8,2,6,3,4,5]=>[6,7,8,4,5,2,1,3]=>[3,2,1,5,4,7,8,6]=>[1,1,2,3,1]
[7,1,5,2,6,3,8,4]=>[8,6,4,2,3,5,1,7]=>[1,3,5,7,6,4,8,2]=>[4,1,2,1]
[5,1,4,2,6,8,3,7]=>[5,3,7,1,8,2,4,6]=>[4,6,2,8,1,7,5,3]=>[2,2,2,1,1]
[5,1,4,2,8,7,3,6]=>[3,7,1,8,6,2,4,5]=>[6,2,8,1,3,7,5,4]=>[1,2,3,1,1]
[8,1,5,2,6,7,3,4]=>[7,5,3,8,2,4,6,1]=>[2,4,6,1,7,5,3,8]=>[3,2,1,2]
[5,1,4,2,6,7,8,3]=>[5,3,6,1,8,2,4,7]=>[4,6,3,8,1,7,5,2]=>[2,2,2,1,1]
[3,1,8,5,2,4,6,7]=>[1,5,6,4,7,8,2,3]=>[8,4,3,5,2,1,7,6]=>[1,1,2,1,2,1]
[3,1,7,5,2,4,8,6]=>[8,1,5,4,6,2,3,7]=>[1,8,4,5,3,7,6,2]=>[2,2,2,1,1]
[3,1,8,6,2,4,5,7]=>[1,5,6,7,4,8,2,3]=>[8,4,3,2,5,1,7,6]=>[1,1,1,2,2,1]
[3,1,7,6,2,4,8,5]=>[8,1,5,6,4,2,3,7]=>[1,8,4,3,5,7,6,2]=>[2,1,3,1,1]
[3,1,8,5,2,7,4,6]=>[7,1,4,8,5,6,2,3]=>[2,8,5,1,4,3,7,6]=>[2,1,2,2,1]
[3,1,8,6,2,7,4,5]=>[7,8,1,5,4,6,2,3]=>[2,1,8,4,5,3,7,6]=>[1,2,2,2,1]
[3,1,6,5,2,7,8,4]=>[6,1,4,3,8,2,5,7]=>[3,8,5,6,1,7,4,2]=>[2,2,2,1,1]
[8,1,4,5,2,3,6,7]=>[5,3,6,2,4,7,8,1]=>[4,6,3,7,5,2,1,8]=>[2,2,1,1,2]
[7,1,4,5,2,3,8,6]=>[3,8,5,2,4,6,1,7]=>[6,1,4,7,5,3,8,2]=>[1,3,1,2,1]
[8,1,4,6,2,3,5,7]=>[5,3,6,7,2,4,8,1]=>[4,6,3,2,7,5,1,8]=>[2,1,2,1,2]
[7,1,4,6,2,3,8,5]=>[3,8,5,6,2,4,1,7]=>[6,1,4,3,7,5,8,2]=>[1,2,2,2,1]
[8,1,6,5,2,3,4,7]=>[5,6,7,4,2,3,8,1]=>[4,3,2,5,7,6,1,8]=>[1,1,3,1,2]
[7,1,8,5,2,3,4,6]=>[5,6,7,4,8,2,1,3]=>[4,3,2,5,1,7,8,6]=>[1,1,2,3,1]
[7,1,8,6,2,3,4,5]=>[5,6,7,8,4,2,1,3]=>[4,3,2,1,5,7,8,6]=>[1,1,1,4,1]
[7,1,6,5,2,3,8,4]=>[8,5,6,4,2,3,1,7]=>[1,4,3,5,7,6,8,2]=>[2,3,2,1]
[6,1,4,5,2,8,3,7]=>[3,7,4,8,2,1,5,6]=>[6,2,5,1,7,8,4,3]=>[1,2,3,1,1]
[8,1,4,5,2,7,3,6]=>[3,7,4,8,2,5,6,1]=>[6,2,5,1,7,4,3,8]=>[1,2,2,1,2]
[8,1,6,5,2,7,3,4]=>[7,8,5,4,2,3,6,1]=>[2,1,4,5,7,6,3,8]=>[1,4,1,2]
[6,1,4,5,2,7,8,3]=>[3,6,4,8,2,1,5,7]=>[6,3,5,1,7,8,4,2]=>[1,2,3,1,1]
[3,1,4,8,6,2,5,7]=>[1,6,7,3,5,8,2,4]=>[8,3,2,6,4,1,7,5]=>[1,1,2,1,2,1]
[3,1,4,8,7,2,5,6]=>[1,6,7,8,3,5,2,4]=>[8,3,2,1,6,4,7,5]=>[1,1,1,2,2,1]
[3,1,4,7,6,2,8,5]=>[8,1,6,3,5,2,4,7]=>[1,8,3,6,4,7,5,2]=>[2,2,2,1,1]
[3,1,8,5,7,2,4,6]=>[6,1,4,7,8,5,2,3]=>[3,8,5,2,1,4,7,6]=>[2,1,1,3,1]
[3,1,8,7,6,2,4,5]=>[6,7,8,1,5,4,2,3]=>[3,2,1,8,4,5,7,6]=>[1,1,2,3,1]
[3,1,7,5,6,2,8,4]=>[4,8,1,6,5,2,3,7]=>[5,1,8,3,4,7,6,2]=>[1,2,3,1,1]
[8,1,4,5,6,2,3,7]=>[3,6,4,7,2,5,8,1]=>[6,3,5,2,7,4,1,8]=>[1,2,2,1,2]
[8,1,4,5,7,2,3,6]=>[3,6,4,7,8,2,5,1]=>[6,3,5,2,1,7,4,8]=>[1,2,1,2,2]
[8,1,4,7,6,2,3,5]=>[3,6,7,8,5,2,4,1]=>[6,3,2,1,4,7,5,8]=>[1,1,1,3,2]
[8,1,7,5,6,2,3,4]=>[6,7,4,8,5,2,3,1]=>[3,2,5,1,4,7,6,8]=>[1,2,3,2]
[7,1,4,5,6,2,8,3]=>[3,4,8,6,2,5,1,7]=>[6,5,1,3,7,4,8,2]=>[1,1,3,2,1]
[3,1,4,8,6,7,2,5]=>[7,1,5,8,3,6,2,4]=>[2,8,4,1,6,3,7,5]=>[2,1,2,2,1]
[3,1,8,5,6,7,2,4]=>[4,7,1,5,8,6,2,3]=>[5,2,8,4,1,3,7,6]=>[1,2,1,3,1]
[8,1,4,5,6,7,2,3]=>[3,4,7,5,8,2,6,1]=>[6,5,2,4,1,7,3,8]=>[1,1,2,2,2]
[2,8,1,3,4,7,5,6]=>[7,8,1,3,4,5,6,2]=>[2,1,8,6,5,4,3,7]=>[1,2,1,1,1,2]
[2,8,1,3,6,4,5,7]=>[6,7,1,3,4,5,8,2]=>[3,2,8,6,5,4,1,7]=>[1,2,1,1,1,2]
[2,8,1,3,7,4,5,6]=>[6,7,8,1,3,4,5,2]=>[3,2,1,8,6,5,4,7]=>[1,1,2,1,1,2]
[2,5,1,3,8,7,4,6]=>[7,2,8,1,6,3,4,5]=>[2,7,1,8,3,6,5,4]=>[2,2,2,1,1]
[2,8,1,3,6,7,4,5]=>[7,5,8,1,3,4,6,2]=>[2,4,1,8,6,5,3,7]=>[2,2,1,1,2]
[2,4,1,8,3,7,5,6]=>[2,7,8,1,5,6,3,4]=>[7,2,1,8,4,3,6,5]=>[1,1,2,1,2,1]
[2,7,1,5,3,4,8,6]=>[8,5,1,3,4,6,2,7]=>[1,4,8,6,5,3,7,2]=>[3,1,1,2,1]
[2,8,1,6,3,4,5,7]=>[5,6,7,1,3,4,8,2]=>[4,3,2,8,6,5,1,7]=>[1,1,2,1,1,2]
[2,7,1,6,3,4,8,5]=>[8,5,6,1,3,4,2,7]=>[1,4,3,8,6,5,7,2]=>[2,2,1,2,1]
[2,6,1,5,3,8,4,7]=>[7,4,8,1,3,2,5,6]=>[2,5,1,8,6,7,4,3]=>[2,2,2,1,1]
[2,8,1,5,3,7,4,6]=>[7,4,8,1,3,5,6,2]=>[2,5,1,8,6,4,3,7]=>[2,2,1,1,2]
[2,8,1,6,3,7,4,5]=>[7,8,5,1,3,4,6,2]=>[2,1,4,8,6,5,3,7]=>[1,3,1,1,2]
[2,6,1,5,3,7,8,4]=>[6,4,8,1,3,2,5,7]=>[3,5,1,8,6,7,4,2]=>[2,2,2,1,1]
[2,4,1,8,6,3,5,7]=>[2,6,7,1,5,8,3,4]=>[7,3,2,8,4,1,6,5]=>[1,1,2,1,2,1]
[2,4,1,8,7,3,5,6]=>[2,6,7,8,1,5,3,4]=>[7,3,2,1,8,4,6,5]=>[1,1,1,2,2,1]
[2,4,1,7,6,3,8,5]=>[8,2,6,1,5,3,4,7]=>[1,7,3,8,4,6,5,2]=>[2,2,2,1,1]
[2,8,1,5,6,3,4,7]=>[6,4,7,1,3,5,8,2]=>[3,5,2,8,6,4,1,7]=>[2,2,1,1,2]
[2,8,1,5,7,3,4,6]=>[6,4,7,8,1,3,5,2]=>[3,5,2,1,8,6,4,7]=>[2,1,2,1,2]
[2,7,1,5,6,3,8,4]=>[4,8,6,1,3,5,2,7]=>[5,1,3,8,6,4,7,2]=>[1,3,1,2,1]
[2,4,1,5,8,7,3,6]=>[2,7,8,1,4,6,3,5]=>[7,2,1,8,5,3,6,4]=>[1,1,2,1,2,1]
[2,4,1,8,6,7,3,5]=>[7,2,5,8,1,6,3,4]=>[2,7,4,1,8,3,6,5]=>[2,1,2,2,1]
[7,3,1,2,4,5,8,6]=>[8,3,2,4,5,6,1,7]=>[1,6,7,5,4,3,8,2]=>[3,1,1,2,1]
[8,3,1,2,4,7,5,6]=>[7,2,8,3,4,5,6,1]=>[2,7,1,6,5,4,3,8]=>[2,2,1,1,2]
[5,3,1,2,7,4,8,6]=>[2,8,6,3,1,4,5,7]=>[7,1,3,6,8,5,4,2]=>[1,4,1,1,1]
[8,3,1,2,6,4,5,7]=>[6,2,7,3,4,5,8,1]=>[3,7,2,6,5,4,1,8]=>[2,2,1,1,2]
[7,3,1,2,6,4,8,5]=>[2,8,6,3,4,5,1,7]=>[7,1,3,6,5,4,8,2]=>[1,3,1,2,1]
[5,3,1,2,6,8,4,7]=>[5,2,7,1,8,3,4,6]=>[4,7,2,8,1,6,5,3]=>[2,2,2,1,1]
[5,3,1,2,8,7,4,6]=>[2,7,1,8,6,3,4,5]=>[7,2,8,1,3,6,5,4]=>[1,2,3,1,1]
[8,3,1,2,6,7,4,5]=>[2,7,5,8,3,4,6,1]=>[7,2,4,1,6,5,3,8]=>[1,2,2,1,2]
[5,3,1,2,6,7,8,4]=>[5,2,6,1,8,3,4,7]=>[4,7,3,8,1,6,5,2]=>[2,2,2,1,1]
[7,4,1,2,3,5,8,6]=>[8,3,4,2,5,6,1,7]=>[1,6,5,7,4,3,8,2]=>[2,2,1,2,1]
[6,4,1,2,3,8,5,7]=>[7,8,3,2,4,1,5,6]=>[2,1,6,7,5,8,4,3]=>[1,3,2,1,1]
[8,4,1,2,3,7,5,6]=>[7,8,3,2,4,5,6,1]=>[2,1,6,7,5,4,3,8]=>[1,3,1,1,2]
[6,4,1,2,3,7,8,5]=>[6,8,3,2,4,1,5,7]=>[3,1,6,7,5,8,4,2]=>[1,3,2,1,1]
[7,6,1,2,3,4,8,5]=>[8,3,4,5,6,2,1,7]=>[1,6,5,4,3,7,8,2]=>[2,1,1,3,1]
[5,8,1,2,3,7,4,6]=>[7,8,3,1,4,5,6,2]=>[2,1,6,8,5,4,3,7]=>[1,3,1,1,2]
[5,4,1,2,8,3,6,7]=>[6,7,2,1,8,3,4,5]=>[3,2,7,8,1,6,5,4]=>[1,3,2,1,1]
[5,4,1,2,7,3,8,6]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>[5,1,1,1]
[8,4,1,2,6,3,5,7]=>[6,7,3,2,4,5,8,1]=>[3,2,6,7,5,4,1,8]=>[1,3,1,1,2]
[5,8,1,2,6,3,4,7]=>[6,7,3,1,4,5,8,2]=>[3,2,6,8,5,4,1,7]=>[1,3,1,1,2]
[5,8,1,2,7,3,4,6]=>[6,7,1,8,3,4,5,2]=>[3,2,8,1,6,5,4,7]=>[1,2,2,1,2]
[8,7,1,2,6,3,4,5]=>[6,7,8,3,4,5,2,1]=>[3,2,1,6,5,4,7,8]=>[1,1,2,1,3]
[5,7,1,2,6,3,8,4]=>[8,6,3,1,4,5,2,7]=>[1,3,6,8,5,4,7,2]=>[4,1,2,1]
[5,4,1,2,6,8,3,7]=>[5,7,2,1,8,3,4,6]=>[4,2,7,8,1,6,5,3]=>[1,3,2,1,1]
[5,4,1,2,8,7,3,6]=>[7,2,1,8,6,3,4,5]=>[2,7,8,1,3,6,5,4]=>[3,3,1,1]
[8,4,1,2,6,7,3,5]=>[7,5,2,8,3,4,6,1]=>[2,4,7,1,6,5,3,8]=>[3,2,1,2]
[5,8,1,2,6,7,3,4]=>[7,5,1,8,3,4,6,2]=>[2,4,8,1,6,5,3,7]=>[3,2,1,2]
[5,4,1,2,6,7,8,3]=>[5,6,2,1,8,3,4,7]=>[4,3,7,8,1,6,5,2]=>[1,3,2,1,1]
[4,3,1,8,2,5,6,7]=>[5,2,1,6,7,8,3,4]=>[4,7,8,3,2,1,6,5]=>[3,1,1,2,1]
[4,3,1,6,2,8,5,7]=>[2,1,7,4,8,3,5,6]=>[7,8,2,5,1,6,4,3]=>[2,2,2,1,1]
[4,3,1,8,2,7,5,6]=>[2,1,7,8,5,6,3,4]=>[7,8,2,1,4,3,6,5]=>[2,1,2,2,1]
[4,3,1,6,2,7,8,5]=>[2,1,6,4,8,3,5,7]=>[7,8,3,5,1,6,4,2]=>[2,2,2,1,1]
[8,3,1,5,2,4,6,7]=>[5,2,6,3,4,7,8,1]=>[4,7,3,6,5,2,1,8]=>[2,2,1,1,2]
[7,3,1,5,2,4,8,6]=>[2,8,5,3,4,6,1,7]=>[7,1,4,6,5,3,8,2]=>[1,3,1,2,1]
[8,3,1,6,2,4,5,7]=>[5,2,6,7,3,4,8,1]=>[4,7,3,2,6,5,1,8]=>[2,1,2,1,2]
[7,3,1,6,2,4,8,5]=>[2,8,5,6,3,4,1,7]=>[7,1,4,3,6,5,8,2]=>[1,2,2,2,1]
[6,3,1,5,2,8,4,7]=>[2,7,4,8,3,1,5,6]=>[7,2,5,1,6,8,4,3]=>[1,2,3,1,1]
[8,3,1,5,2,7,4,6]=>[2,7,4,8,3,5,6,1]=>[7,2,5,1,6,4,3,8]=>[1,2,2,1,2]
[8,3,1,6,2,7,4,5]=>[2,7,8,5,3,4,6,1]=>[7,2,1,4,6,5,3,8]=>[1,1,3,1,2]
[6,3,1,5,2,7,8,4]=>[2,6,4,8,3,1,5,7]=>[7,3,5,1,6,8,4,2]=>[1,2,3,1,1]
[7,4,1,5,2,3,8,6]=>[8,5,3,2,4,6,1,7]=>[1,4,6,7,5,3,8,2]=>[4,1,2,1]
[8,4,1,6,2,3,5,7]=>[5,6,2,7,3,4,8,1]=>[4,3,7,2,6,5,1,8]=>[1,2,2,1,2]
[7,4,1,6,2,3,8,5]=>[8,5,2,6,3,4,1,7]=>[1,4,7,3,6,5,8,2]=>[3,2,2,1]
[6,8,1,5,2,3,4,7]=>[5,6,7,3,1,4,8,2]=>[4,3,2,6,8,5,1,7]=>[1,1,3,1,2]
[8,7,1,5,2,3,4,6]=>[5,6,7,3,4,8,2,1]=>[4,3,2,6,5,1,7,8]=>[1,1,2,1,3]
[8,7,1,6,2,3,4,5]=>[5,6,7,8,3,4,2,1]=>[4,3,2,1,6,5,7,8]=>[1,1,1,2,3]
[6,7,1,5,2,3,8,4]=>[8,5,6,3,1,4,2,7]=>[1,4,3,6,8,5,7,2]=>[2,3,2,1]
[8,4,1,5,2,7,3,6]=>[7,4,2,8,3,5,6,1]=>[2,5,7,1,6,4,3,8]=>[3,2,1,2]
[8,4,1,6,2,7,3,5]=>[7,2,8,5,3,4,6,1]=>[2,7,1,4,6,5,3,8]=>[2,3,1,2]
[6,8,1,5,2,7,3,4]=>[7,8,5,3,1,4,6,2]=>[2,1,4,6,8,5,3,7]=>[1,4,1,2]
[6,4,1,5,2,7,8,3]=>[6,4,2,8,3,1,5,7]=>[3,5,7,1,6,8,4,2]=>[3,3,1,1]
[4,3,1,5,8,2,6,7]=>[4,2,1,6,7,8,3,5]=>[5,7,8,3,2,1,6,4]=>[3,1,1,2,1]
[4,3,1,5,7,2,8,6]=>[2,1,8,4,6,3,5,7]=>[7,8,1,5,3,6,4,2]=>[2,2,2,1,1]
[4,3,1,8,6,2,5,7]=>[2,1,6,7,5,8,3,4]=>[7,8,3,2,4,1,6,5]=>[2,1,2,2,1]
[4,3,1,8,7,2,5,6]=>[2,1,6,7,8,5,3,4]=>[7,8,3,2,1,4,6,5]=>[2,1,1,3,1]
[8,3,1,5,6,2,4,7]=>[2,6,4,7,3,5,8,1]=>[7,3,5,2,6,4,1,8]=>[1,2,2,1,2]
[8,3,1,5,7,2,4,6]=>[2,6,4,7,8,3,5,1]=>[7,3,5,2,1,6,4,8]=>[1,2,1,2,2]
[8,3,1,7,6,2,4,5]=>[2,6,7,8,5,3,4,1]=>[7,3,2,1,4,6,5,8]=>[1,1,1,3,2]
[7,3,1,5,6,2,8,4]=>[2,4,8,6,3,5,1,7]=>[7,5,1,3,6,4,8,2]=>[1,1,3,2,1]
[8,4,1,5,6,2,3,7]=>[6,4,2,7,3,5,8,1]=>[3,5,7,2,6,4,1,8]=>[3,2,1,2]
[8,4,1,5,7,2,3,6]=>[6,4,2,7,8,3,5,1]=>[3,5,7,2,1,6,4,8]=>[3,1,2,2]
[7,8,1,5,6,2,3,4]=>[6,7,4,8,3,1,5,2]=>[3,2,5,1,6,8,4,7]=>[1,2,3,2]
[7,4,1,5,6,2,8,3]=>[4,2,8,6,3,5,1,7]=>[5,7,1,3,6,4,8,2]=>[2,3,2,1]
[4,3,1,5,6,8,2,7]=>[4,2,1,5,7,8,3,6]=>[5,7,8,4,2,1,6,3]=>[3,1,1,2,1]
[4,3,1,5,8,7,2,6]=>[2,1,7,8,4,6,3,5]=>[7,8,2,1,5,3,6,4]=>[2,1,2,2,1]
[4,3,1,8,6,7,2,5]=>[1,7,2,5,8,6,3,4]=>[8,2,7,4,1,3,6,5]=>[1,2,1,3,1]
[8,4,1,5,6,7,2,3]=>[4,2,7,5,8,3,6,1]=>[5,7,2,4,1,6,3,8]=>[2,2,2,2]
[4,3,1,5,6,7,8,2]=>[4,2,1,5,6,8,3,7]=>[5,7,8,4,3,1,6,2]=>[3,1,1,2,1]
[2,3,8,1,4,7,5,6]=>[7,8,1,2,4,5,6,3]=>[2,1,8,7,5,4,3,6]=>[1,2,1,1,1,2]
[2,3,8,1,6,4,5,7]=>[6,7,1,2,4,5,8,3]=>[3,2,8,7,5,4,1,6]=>[1,2,1,1,1,2]
[2,3,8,1,7,4,5,6]=>[6,7,8,1,2,4,5,3]=>[3,2,1,8,7,5,4,6]=>[1,1,2,1,1,2]
[2,3,7,1,6,4,8,5]=>[8,6,1,2,4,5,3,7]=>[1,3,8,7,5,4,6,2]=>[3,1,1,2,1]
[2,3,5,1,8,7,4,6]=>[3,7,8,1,2,6,4,5]=>[6,2,1,8,7,3,5,4]=>[1,1,2,1,2,1]
[2,3,8,1,6,7,4,5]=>[7,5,8,1,2,4,6,3]=>[2,4,1,8,7,5,3,6]=>[2,2,1,1,2]
[2,8,4,1,3,5,6,7]=>[4,5,1,3,6,7,8,2]=>[5,4,8,6,3,2,1,7]=>[1,2,1,1,1,2]
[2,7,4,1,3,5,8,6]=>[8,4,1,3,5,6,2,7]=>[1,5,8,6,4,3,7,2]=>[3,1,1,2,1]
[2,6,4,1,3,8,5,7]=>[7,3,8,1,4,2,5,6]=>[2,6,1,8,5,7,4,3]=>[2,2,2,1,1]
[2,8,4,1,3,7,5,6]=>[7,3,8,1,4,5,6,2]=>[2,6,1,8,5,4,3,7]=>[2,2,1,1,2]
[2,6,4,1,3,7,8,5]=>[6,3,8,1,4,2,5,7]=>[3,6,1,8,5,7,4,2]=>[2,2,2,1,1]
[2,8,5,1,3,4,6,7]=>[4,5,6,1,3,7,8,2]=>[5,4,3,8,6,2,1,7]=>[1,1,2,1,1,2]
[2,7,5,1,3,4,8,6]=>[8,4,5,1,3,6,2,7]=>[1,5,4,8,6,3,7,2]=>[2,2,1,2,1]
[2,8,7,1,3,4,5,6]=>[4,5,6,7,8,1,3,2]=>[5,4,3,2,1,8,6,7]=>[1,1,1,1,2,2]
[2,6,5,1,3,8,4,7]=>[7,8,4,1,3,2,5,6]=>[2,1,5,8,6,7,4,3]=>[1,3,2,1,1]
[2,8,5,1,3,7,4,6]=>[7,8,4,1,3,5,6,2]=>[2,1,5,8,6,4,3,7]=>[1,3,1,1,2]
[2,6,8,1,3,7,4,5]=>[7,8,4,1,2,5,6,3]=>[2,1,5,8,7,4,3,6]=>[1,3,1,1,2]
[2,6,5,1,3,7,8,4]=>[6,8,4,1,3,2,5,7]=>[3,1,5,8,6,7,4,2]=>[1,3,2,1,1]
[2,5,4,1,8,3,6,7]=>[6,3,1,2,7,8,4,5]=>[3,6,8,7,2,1,5,4]=>[3,1,1,2,1]
[2,5,4,1,7,3,8,6]=>[3,2,8,1,6,4,5,7]=>[6,7,1,8,3,5,4,2]=>[2,2,2,1,1]
[2,8,4,1,6,3,5,7]=>[6,3,7,1,4,5,8,2]=>[3,6,2,8,5,4,1,7]=>[2,2,1,1,2]
[2,8,4,1,7,3,5,6]=>[6,3,7,8,1,4,5,2]=>[3,6,2,1,8,5,4,7]=>[2,1,2,1,2]
[2,7,4,1,6,3,8,5]=>[3,8,6,1,4,5,2,7]=>[6,1,3,8,5,4,7,2]=>[1,3,1,2,1]
[2,8,5,1,7,3,4,6]=>[6,7,3,8,1,4,5,2]=>[3,2,6,1,8,5,4,7]=>[1,2,2,1,2]
[2,7,8,1,6,3,4,5]=>[6,7,8,4,1,2,5,3]=>[3,2,1,5,8,7,4,6]=>[1,1,3,1,2]
[2,7,5,1,6,3,8,4]=>[8,6,4,1,3,5,2,7]=>[1,3,5,8,6,4,7,2]=>[4,1,2,1]
[2,5,4,1,6,8,3,7]=>[5,3,1,2,7,8,4,6]=>[4,6,8,7,2,1,5,3]=>[3,1,1,2,1]
[2,5,4,1,8,7,3,6]=>[3,2,7,8,1,6,4,5]=>[6,7,2,1,8,3,5,4]=>[2,1,2,2,1]
[2,8,4,1,6,7,3,5]=>[3,7,5,8,1,4,6,2]=>[6,2,4,1,8,5,3,7]=>[1,2,2,1,2]
[2,8,5,1,6,7,3,4]=>[7,5,3,8,1,4,6,2]=>[2,4,6,1,8,5,3,7]=>[3,2,1,2]
[2,5,4,1,6,7,8,3]=>[5,3,1,2,6,8,4,7]=>[4,6,8,7,3,1,5,2]=>[3,1,1,2,1]
[7,3,4,1,2,5,8,6]=>[2,8,4,3,5,6,1,7]=>[7,1,5,6,4,3,8,2]=>[1,3,1,2,1]
[6,3,4,1,2,8,5,7]=>[2,7,3,8,4,1,5,6]=>[7,2,6,1,5,8,4,3]=>[1,2,3,1,1]
[8,3,4,1,2,7,5,6]=>[2,7,3,8,4,5,6,1]=>[7,2,6,1,5,4,3,8]=>[1,2,2,1,2]
[6,3,4,1,2,7,8,5]=>[2,6,3,8,4,1,5,7]=>[7,3,6,1,5,8,4,2]=>[1,2,3,1,1]
[7,3,5,1,2,4,8,6]=>[2,8,4,5,3,6,1,7]=>[7,1,5,4,6,3,8,2]=>[1,2,2,2,1]
[6,3,7,1,2,4,8,5]=>[2,8,4,5,1,6,3,7]=>[7,1,5,4,8,3,6,2]=>[1,2,2,2,1]
[6,3,5,1,2,8,4,7]=>[2,7,8,4,3,1,5,6]=>[7,2,1,5,6,8,4,3]=>[1,1,4,1,1]
[8,3,5,1,2,7,4,6]=>[2,7,8,4,3,5,6,1]=>[7,2,1,5,6,4,3,8]=>[1,1,3,1,2]
[6,3,8,1,2,7,4,5]=>[2,7,8,4,1,5,6,3]=>[7,2,1,5,8,4,3,6]=>[1,1,3,1,2]
[6,3,5,1,2,7,8,4]=>[2,6,8,4,3,1,5,7]=>[7,3,1,5,6,8,4,2]=>[1,1,4,1,1]
[7,5,4,1,2,3,8,6]=>[8,4,5,3,2,6,1,7]=>[1,5,4,6,7,3,8,2]=>[2,3,2,1]
[6,7,4,1,2,3,8,5]=>[8,4,5,3,1,6,2,7]=>[1,5,4,6,8,3,7,2]=>[2,3,2,1]
[6,8,5,1,2,3,4,7]=>[4,5,6,1,7,3,8,2]=>[5,4,3,8,2,6,1,7]=>[1,1,2,2,2]
[6,7,5,1,2,3,8,4]=>[8,4,5,1,6,3,2,7]=>[1,5,4,8,3,6,7,2]=>[2,2,3,1]
[6,5,4,1,2,8,3,7]=>[7,8,4,3,2,1,5,6]=>[2,1,5,6,7,8,4,3]=>[1,5,1,1]
[8,5,4,1,2,7,3,6]=>[7,8,4,3,2,5,6,1]=>[2,1,5,6,7,4,3,8]=>[1,4,1,2]
[6,8,4,1,2,7,3,5]=>[7,8,4,3,1,5,6,2]=>[2,1,5,6,8,4,3,7]=>[1,4,1,2]
[6,8,5,1,2,7,3,4]=>[7,8,4,1,5,3,6,2]=>[2,1,5,8,4,6,3,7]=>[1,3,2,2]
[6,5,4,1,2,7,8,3]=>[6,8,4,3,2,1,5,7]=>[3,1,5,6,7,8,4,2]=>[1,5,1,1]
[5,3,4,1,8,2,6,7]=>[2,6,3,1,7,8,4,5]=>[7,3,6,8,2,1,5,4]=>[1,3,1,2,1]
[5,3,4,1,7,2,8,6]=>[2,3,1,8,6,4,5,7]=>[7,6,8,1,3,5,4,2]=>[1,2,3,1,1]
[8,3,4,1,6,2,5,7]=>[2,6,3,7,4,5,8,1]=>[7,3,6,2,5,4,1,8]=>[1,2,2,1,2]
[8,3,4,1,7,2,5,6]=>[2,6,3,7,8,4,5,1]=>[7,3,6,2,1,5,4,8]=>[1,2,1,2,2]
[7,3,4,1,6,2,8,5]=>[2,3,8,6,4,5,1,7]=>[7,6,1,3,5,4,8,2]=>[1,1,3,2,1]
[8,3,5,1,7,2,4,6]=>[2,6,7,3,8,4,5,1]=>[7,3,2,6,1,5,4,8]=>[1,1,2,2,2]
[7,3,5,1,6,2,8,4]=>[8,2,6,4,3,5,1,7]=>[1,7,3,5,6,4,8,2]=>[2,3,2,1]
[8,5,4,1,6,2,3,7]=>[6,7,4,3,2,5,8,1]=>[3,2,5,6,7,4,1,8]=>[1,4,1,2]
[8,5,4,1,7,2,3,6]=>[6,7,3,2,8,4,5,1]=>[3,2,6,7,1,5,4,8]=>[1,3,2,2]
[7,8,4,1,6,2,3,5]=>[6,7,3,8,4,1,5,2]=>[3,2,6,1,5,8,4,7]=>[1,2,3,2]
[7,8,5,1,6,2,3,4]=>[6,7,8,4,3,1,5,2]=>[3,2,1,5,6,8,4,7]=>[1,1,4,2]
[7,5,4,1,6,2,8,3]=>[8,6,4,3,2,5,1,7]=>[1,3,5,6,7,4,8,2]=>[5,2,1]
[5,3,4,1,6,8,2,7]=>[2,5,3,1,7,8,4,6]=>[7,4,6,8,2,1,5,3]=>[1,3,1,2,1]
[5,3,4,1,8,7,2,6]=>[2,3,1,7,8,6,4,5]=>[7,6,8,2,1,3,5,4]=>[1,2,1,3,1]
[8,3,5,1,6,7,2,4]=>[7,2,5,3,8,4,6,1]=>[2,7,4,6,1,5,3,8]=>[2,2,2,2]
[8,5,4,1,6,7,2,3]=>[7,5,3,2,8,4,6,1]=>[2,4,6,7,1,5,3,8]=>[4,2,2]
[5,3,4,1,6,7,8,2]=>[2,5,3,1,6,8,4,7]=>[7,4,6,8,3,1,5,2]=>[1,3,1,2,1]
[2,3,4,8,1,7,5,6]=>[7,8,1,2,3,5,6,4]=>[2,1,8,7,6,4,3,5]=>[1,2,1,1,1,2]
[2,3,8,5,1,4,6,7]=>[5,6,1,2,4,7,8,3]=>[4,3,8,7,5,2,1,6]=>[1,2,1,1,1,2]
[2,3,7,6,1,4,8,5]=>[8,5,6,1,2,4,3,7]=>[1,4,3,8,7,5,6,2]=>[2,2,1,2,1]
[2,3,6,5,1,8,4,7]=>[7,4,1,2,3,8,5,6]=>[2,5,8,7,6,1,4,3]=>[3,1,1,2,1]
[2,3,8,5,1,7,4,6]=>[7,4,8,1,2,5,6,3]=>[2,5,1,8,7,4,3,6]=>[2,2,1,1,2]
[2,3,8,6,1,7,4,5]=>[7,8,5,1,2,4,6,3]=>[2,1,4,8,7,5,3,6]=>[1,3,1,1,2]
[2,3,6,5,1,7,8,4]=>[6,4,1,2,3,8,5,7]=>[3,5,8,7,6,1,4,2]=>[3,1,1,2,1]
[2,8,4,5,1,3,6,7]=>[5,3,6,1,4,7,8,2]=>[4,6,3,8,5,2,1,7]=>[2,2,1,1,2]
[2,7,4,5,1,3,8,6]=>[3,8,5,1,4,6,2,7]=>[6,1,4,8,5,3,7,2]=>[1,3,1,2,1]
[2,8,4,6,1,3,5,7]=>[5,3,6,7,1,4,8,2]=>[4,6,3,2,8,5,1,7]=>[2,1,2,1,2]
[2,7,4,8,1,3,5,6]=>[5,3,6,7,1,2,8,4]=>[4,6,3,2,8,7,1,5]=>[2,1,2,1,2]
[2,7,4,6,1,3,8,5]=>[3,8,5,6,1,4,2,7]=>[6,1,4,3,8,5,7,2]=>[1,2,2,2,1]
[2,7,8,5,1,3,4,6]=>[5,6,7,4,1,2,8,3]=>[4,3,2,5,8,7,1,6]=>[1,1,3,1,2]
[2,7,6,5,1,3,8,4]=>[8,5,6,4,1,3,2,7]=>[1,4,3,5,8,6,7,2]=>[2,3,2,1]
[2,6,4,5,1,8,3,7]=>[3,7,4,1,2,8,5,6]=>[6,2,5,8,7,1,4,3]=>[1,3,1,2,1]
[2,8,4,5,1,7,3,6]=>[3,7,4,8,1,5,6,2]=>[6,2,5,1,8,4,3,7]=>[1,2,2,1,2]
[2,8,4,6,1,7,3,5]=>[3,7,8,5,1,4,6,2]=>[6,2,1,4,8,5,3,7]=>[1,1,3,1,2]
[2,8,6,5,1,7,3,4]=>[7,8,5,4,1,3,6,2]=>[2,1,4,5,8,6,3,7]=>[1,4,1,2]
[7,3,4,5,1,2,8,6]=>[2,3,8,5,4,6,1,7]=>[7,6,1,4,5,3,8,2]=>[1,1,3,2,1]
[7,3,4,6,1,2,8,5]=>[2,3,8,5,6,4,1,7]=>[7,6,1,4,3,5,8,2]=>[1,1,2,3,1]
[8,3,6,5,1,2,4,7]=>[2,5,6,7,4,3,8,1]=>[7,4,3,2,5,6,1,8]=>[1,1,1,3,2]
[7,3,8,5,1,2,4,6]=>[2,5,6,7,4,1,8,3]=>[7,4,3,2,5,8,1,6]=>[1,1,1,3,2]
[7,3,8,6,1,2,4,5]=>[2,5,6,7,1,8,4,3]=>[7,4,3,2,8,1,5,6]=>[1,1,1,2,3]
[7,6,4,5,1,2,8,3]=>[8,5,3,6,4,2,1,7]=>[1,4,6,3,5,7,8,2]=>[3,4,1]
[6,3,4,5,1,8,2,7]=>[2,3,7,4,1,8,5,6]=>[7,6,2,5,8,1,4,3]=>[1,1,3,2,1]
[8,3,4,5,1,7,2,6]=>[2,3,7,4,8,5,6,1]=>[7,6,2,5,1,4,3,8]=>[1,1,2,2,2]
[8,3,4,6,1,7,2,5]=>[2,3,7,8,5,4,6,1]=>[7,6,2,1,4,5,3,8]=>[1,1,1,3,2]
[2,3,4,8,6,1,5,7]=>[6,7,1,2,3,5,8,4]=>[3,2,8,7,6,4,1,5]=>[1,2,1,1,1,2]
[2,3,4,8,7,1,5,6]=>[6,7,8,1,2,3,5,4]=>[3,2,1,8,7,6,4,5]=>[1,1,2,1,1,2]
[2,3,4,7,6,1,8,5]=>[8,6,1,2,3,5,4,7]=>[1,3,8,7,6,4,5,2]=>[3,1,1,2,1]
[2,3,8,5,6,1,4,7]=>[6,4,7,1,2,5,8,3]=>[3,5,2,8,7,4,1,6]=>[2,2,1,1,2]
[2,3,8,7,6,1,4,5]=>[6,7,8,5,1,2,4,3]=>[3,2,1,4,8,7,5,6]=>[1,1,3,1,2]
[2,3,7,5,6,1,8,4]=>[4,8,6,1,2,5,3,7]=>[5,1,3,8,7,4,6,2]=>[1,3,1,2,1]
[2,8,4,5,7,1,3,6]=>[3,6,4,7,8,1,5,2]=>[6,3,5,2,1,8,4,7]=>[1,2,1,2,2]
[2,8,4,7,6,1,3,5]=>[3,6,7,8,5,1,4,2]=>[6,3,2,1,4,8,5,7]=>[1,1,1,3,2]
[2,8,7,5,6,1,3,4]=>[6,7,4,8,5,1,3,2]=>[3,2,5,1,4,8,6,7]=>[1,2,3,2]
[2,7,4,5,6,1,8,3]=>[3,4,8,6,1,5,2,7]=>[6,5,1,3,8,4,7,2]=>[1,1,3,2,1]
[8,3,4,5,7,1,2,6]=>[2,3,6,4,7,8,5,1]=>[7,6,3,5,2,1,4,8]=>[1,1,2,1,3]
[8,3,4,7,6,1,2,5]=>[2,3,6,7,8,5,4,1]=>[7,6,3,2,1,4,5,8]=>[1,1,1,1,4]
[8,3,7,5,6,1,2,4]=>[6,7,2,4,8,5,3,1]=>[3,2,7,5,1,4,6,8]=>[1,2,1,4]
[7,3,4,5,6,1,8,2]=>[2,3,4,8,6,5,1,7]=>[7,6,5,1,3,4,8,2]=>[1,1,1,4,1]
[2,3,4,5,8,7,1,6]=>[7,8,1,2,3,4,6,5]=>[2,1,8,7,6,5,3,4]=>[1,2,1,1,1,2]
[2,3,4,8,6,7,1,5]=>[7,5,8,1,2,3,6,4]=>[2,4,1,8,7,6,3,5]=>[2,2,1,1,2]
[2,8,4,5,6,7,1,3]=>[3,4,7,5,8,1,6,2]=>[6,5,2,4,1,8,3,7]=>[1,1,2,2,2]
[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>[8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,2]
[9,1,2,3,4,5,8,6,7]=>[8,9,2,3,4,5,6,7,1]=>[2,1,8,7,6,5,4,3,9]=>[1,2,1,1,1,1,2]
[9,1,2,3,6,4,5,7,8]=>[6,7,2,3,4,5,8,9,1]=>[4,3,8,7,6,5,2,1,9]=>[1,2,1,1,1,1,2]
[9,1,2,5,3,4,6,7,8]=>[5,6,2,3,4,7,8,9,1]=>[5,4,8,7,6,3,2,1,9]=>[1,2,1,1,1,1,2]
[9,1,2,8,3,4,5,6,7]=>[5,6,7,8,9,2,3,4,1]=>[5,4,3,2,1,8,7,6,9]=>[1,1,1,1,2,1,2]
[9,1,8,2,3,4,5,6,7]=>[4,5,6,7,8,9,2,3,1]=>[6,5,4,3,2,1,8,7,9]=>[1,1,1,1,1,2,2]
[9,1,4,8,2,3,5,6,7]=>[5,3,6,7,8,9,2,4,1]=>[5,7,4,3,2,1,8,6,9]=>[2,1,1,1,2,2]
[2,9,1,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>[9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,2]
[9,3,1,2,4,5,6,7,8]=>[3,4,2,5,6,7,8,9,1]=>[7,6,8,5,4,3,2,1,9]=>[1,2,1,1,1,1,2]
[9,4,1,2,3,5,6,7,8]=>[3,4,5,2,6,7,8,9,1]=>[7,6,5,8,4,3,2,1,9]=>[1,1,2,1,1,1,2]
[5,9,1,2,3,4,6,7,8]=>[3,4,5,1,6,7,8,9,2]=>[7,6,5,9,4,3,2,1,8]=>[1,1,2,1,1,1,2]
[9,6,1,2,3,4,5,7,8]=>[3,4,5,6,7,2,8,9,1]=>[7,6,5,4,3,8,2,1,9]=>[1,1,1,1,2,1,2]
[9,7,1,2,3,4,5,6,8]=>[3,4,5,6,7,8,2,9,1]=>[7,6,5,4,3,2,8,1,9]=>[1,1,1,1,1,2,2]
[8,9,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,1,9,2]=>[7,6,5,4,3,2,9,1,8]=>[1,1,1,1,1,2,2]
[2,3,9,1,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>[9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,2]
[2,9,8,1,3,4,5,6,7]=>[4,5,6,7,8,9,1,3,2]=>[6,5,4,3,2,1,9,7,8]=>[1,1,1,1,1,2,2]
[9,7,8,1,2,3,4,5,6]=>[4,5,6,7,8,2,9,3,1]=>[6,5,4,3,2,8,1,7,9]=>[1,1,1,1,2,3]
[2,3,4,9,1,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>[9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,2]
[2,3,4,5,9,1,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>[9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,2]
[2,3,4,5,6,9,1,7,8]=>[1,2,3,4,5,7,8,9,6]=>[9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,2]
[2,3,4,5,6,7,9,1,8]=>[1,2,3,4,5,6,8,9,7]=>[9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,2]
[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,2]
[]=>[]=>[]=>[]
[3,5,2,6,1,4,8,7]=>[8,1,3,2,5,4,6,7]=>[1,8,6,7,4,5,3,2]=>[2,2,2,1,1]
[3,5,2,6,4,1,8,7]=>[5,1,3,2,4,8,6,7]=>[4,8,6,7,5,1,3,2]=>[2,2,1,2,1]
[3,5,2,7,4,8,1,6]=>[5,1,2,7,3,4,8,6]=>[4,8,7,2,6,5,1,3]=>[2,1,2,1,2]
[3,5,2,7,4,8,6,1]=>[2,8,1,5,3,4,7,6]=>[7,1,8,4,6,5,2,3]=>[1,2,2,1,2]
[4,5,7,2,3,8,6,1]=>[1,2,8,4,5,3,7,6]=>[8,7,1,5,4,6,2,3]=>[1,1,2,2,2]
[4,5,7,2,3,8,1,6]=>[1,4,2,5,7,3,8,6]=>[8,5,7,4,2,6,1,3]=>[1,2,1,2,2]
[4,5,6,2,3,1,8,7]=>[1,4,2,5,3,8,6,7]=>[8,5,7,4,6,1,3,2]=>[1,2,2,2,1]
[4,5,6,2,1,3,8,7]=>[1,4,2,8,5,3,6,7]=>[8,5,7,1,4,6,3,2]=>[1,2,3,1,1]
[3,5,1,6,4,2,8,7]=>[5,1,4,2,8,3,6,7]=>[4,8,5,7,1,6,3,2]=>[2,2,2,1,1]
[4,5,6,1,3,2,8,7]=>[1,5,2,8,4,3,6,7]=>[8,4,7,1,5,6,3,2]=>[1,2,3,1,1]
[4,5,6,3,1,2,8,7]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[1,1,4,1,1]
[4,5,7,3,2,8,1,6]=>[1,2,5,4,7,3,8,6]=>[8,7,4,5,2,6,1,3]=>[1,1,2,2,2]
[4,5,7,3,2,8,6,1]=>[1,2,4,8,5,3,7,6]=>[8,7,5,1,4,6,2,3]=>[1,1,1,3,2]
[4,6,7,3,8,2,5,1]=>[4,1,2,6,3,8,7,5]=>[5,8,7,3,6,1,2,4]=>[2,1,2,3]
[4,6,7,3,8,2,1,5]=>[4,1,2,7,6,3,8,5]=>[5,8,7,2,3,6,1,4]=>[2,1,3,2]
[4,6,7,3,8,1,2,5]=>[6,1,4,2,7,3,8,5]=>[3,8,5,7,2,6,1,4]=>[2,2,2,2]
[4,5,7,3,1,8,2,6]=>[1,2,7,4,8,5,3,6]=>[8,7,2,5,1,4,6,3]=>[1,1,2,3,1]
[4,5,7,1,3,8,2,6]=>[1,5,2,7,8,4,3,6]=>[8,4,7,2,1,5,6,3]=>[1,2,1,3,1]
[3,5,1,7,4,8,2,6]=>[5,1,2,7,4,8,3,6]=>[4,8,7,2,5,1,6,3]=>[2,1,2,2,1]
[2,1,5,7,4,8,3,6]=>[3,5,7,1,4,8,2,6]=>[6,4,2,8,5,1,7,3]=>[1,1,2,1,2,1]
[2,1,5,7,4,8,6,3]=>[8,3,5,1,4,7,2,6]=>[1,6,4,8,5,2,7,3]=>[2,2,1,2,1]
[3,5,1,7,4,8,6,2]=>[2,8,1,5,4,7,3,6]=>[7,1,8,4,5,2,6,3]=>[1,2,2,2,1]
[4,5,7,1,3,8,6,2]=>[1,2,8,5,7,4,3,6]=>[8,7,1,4,2,5,6,3]=>[1,1,2,3,1]
[4,5,7,3,1,8,6,2]=>[1,2,4,8,7,5,3,6]=>[8,7,5,1,2,4,6,3]=>[1,1,1,4,1]
[4,6,7,3,8,1,5,2]=>[4,1,2,8,6,3,7,5]=>[5,8,7,1,3,6,2,4]=>[2,1,3,2]
[4,6,7,3,8,5,1,2]=>[4,1,2,7,3,8,6,5]=>[5,8,7,2,6,1,3,4]=>[2,1,2,3]
[4,6,7,3,8,5,2,1]=>[2,8,1,4,3,7,6,5]=>[7,1,8,5,6,2,3,4]=>[1,2,2,3]
[5,6,7,8,3,1,4,2]=>[1,2,8,6,5,3,7,4]=>[8,7,1,3,4,6,2,5]=>[1,1,4,2]
[5,6,7,8,1,3,4,2]=>[1,6,2,8,5,3,7,4]=>[8,3,7,1,4,6,2,5]=>[1,2,3,2]
[4,6,7,1,8,3,5,2]=>[6,1,2,8,7,4,3,5]=>[3,8,7,1,2,5,6,4]=>[2,1,4,1]
[3,6,1,7,8,4,5,2]=>[6,4,1,2,8,7,3,5]=>[3,5,8,7,1,2,6,4]=>[3,1,3,1]
[2,1,6,7,8,4,5,3]=>[3,6,4,8,1,7,2,5]=>[6,3,5,1,8,2,7,4]=>[1,2,2,2,1]
[2,1,6,7,8,4,3,5]=>[3,7,6,1,4,8,2,5]=>[6,2,3,8,5,1,7,4]=>[1,3,1,2,1]
[3,6,1,7,8,4,2,5]=>[7,6,1,4,2,8,3,5]=>[2,3,8,5,7,1,6,4]=>[3,2,2,1]
[4,6,7,1,8,3,2,5]=>[7,1,6,2,8,4,3,5]=>[2,8,3,7,1,5,6,4]=>[2,2,3,1]
[5,6,7,8,1,3,2,4]=>[1,7,5,2,6,3,8,4]=>[8,2,4,7,3,6,1,5]=>[1,3,2,2]
[4,5,7,2,1,8,3,6]=>[1,4,2,7,8,5,3,6]=>[8,5,7,2,1,4,6,3]=>[1,2,1,3,1]
[4,6,7,2,8,1,3,5]=>[1,4,6,2,7,3,8,5]=>[8,5,3,7,2,6,1,4]=>[1,1,2,2,2]
[4,6,7,2,8,3,1,5]=>[7,1,4,2,6,3,8,5]=>[2,8,5,7,3,6,1,4]=>[2,2,2,2]
[4,6,7,2,8,3,5,1]=>[6,1,2,8,4,3,7,5]=>[3,8,7,1,5,6,2,4]=>[2,1,3,2]
[3,6,2,7,8,4,5,1]=>[6,4,1,2,8,3,7,5]=>[3,5,8,7,1,6,2,4]=>[3,1,2,2]
[3,6,2,7,8,4,1,5]=>[7,6,1,3,2,4,8,5]=>[2,3,8,6,7,5,1,4]=>[3,2,1,2]
[3,6,2,7,8,1,4,5]=>[6,7,1,3,2,4,8,5]=>[3,2,8,6,7,5,1,4]=>[1,2,2,1,2]
[3,5,2,7,1,8,4,6]=>[7,1,2,8,3,5,4,6]=>[2,8,7,1,6,4,5,3]=>[2,1,2,2,1]
[3,4,2,1,7,8,5,6]=>[1,2,7,3,5,8,4,6]=>[8,7,2,6,4,1,5,3]=>[1,1,2,1,2,1]
[3,4,1,2,7,8,6,5]=>[1,2,5,8,7,3,4,6]=>[8,7,4,1,2,6,5,3]=>[1,1,1,3,1,1]
[3,5,2,7,1,8,6,4]=>[2,8,1,7,3,5,4,6]=>[7,1,8,2,6,4,5,3]=>[1,2,2,2,1]
[3,6,2,7,8,1,5,4]=>[8,6,1,3,2,4,7,5]=>[1,3,8,6,7,5,2,4]=>[3,2,1,2]
[3,6,2,7,8,5,1,4]=>[7,4,1,2,8,3,6,5]=>[2,5,8,7,1,6,3,4]=>[3,1,2,2]
[3,6,2,7,8,5,4,1]=>[4,2,8,1,7,3,6,5]=>[5,7,1,8,2,6,3,4]=>[2,2,2,2]
[4,6,7,2,8,5,3,1]=>[2,8,1,7,4,3,6,5]=>[7,1,8,2,5,6,3,4]=>[1,2,3,2]
[4,6,7,2,8,5,1,3]=>[7,1,2,8,4,3,6,5]=>[2,8,7,1,5,6,3,4]=>[2,1,3,2]
[4,6,7,2,8,1,5,3]=>[8,1,4,2,6,3,7,5]=>[1,8,5,7,3,6,2,4]=>[2,2,2,2]
[4,5,7,2,1,8,6,3]=>[1,2,8,4,7,5,3,6]=>[8,7,1,5,2,4,6,3]=>[1,1,2,3,1]
[4,5,7,1,2,8,6,3]=>[1,2,8,7,4,5,3,6]=>[8,7,1,2,5,4,6,3]=>[1,1,3,2,1]
[3,5,1,7,2,8,6,4]=>[2,8,1,7,5,3,4,6]=>[7,1,8,2,4,6,5,3]=>[1,2,3,1,1]
[2,1,5,7,3,8,6,4]=>[8,3,7,1,5,2,4,6]=>[1,6,2,8,4,7,5,3]=>[2,2,2,1,1]
[2,1,6,7,8,3,5,4]=>[3,8,6,1,4,7,2,5]=>[6,1,3,8,5,2,7,4]=>[1,3,1,2,1]
[3,6,1,7,8,2,5,4]=>[8,6,1,4,2,7,3,5]=>[1,3,8,5,7,2,6,4]=>[3,2,2,1]
[4,6,7,1,8,2,5,3]=>[8,1,6,2,7,4,3,5]=>[1,8,3,7,2,5,6,4]=>[2,2,3,1]
[5,6,7,8,1,2,4,3]=>[1,8,5,2,6,3,7,4]=>[8,1,4,7,3,6,2,5]=>[1,3,2,2]
[5,6,7,8,2,1,4,3]=>[1,5,2,8,6,3,7,4]=>[8,4,7,1,3,6,2,5]=>[1,2,3,2]
[5,6,7,8,2,4,1,3]=>[1,5,2,7,3,8,6,4]=>[8,4,7,2,6,1,3,5]=>[1,2,2,3]
[5,6,7,8,2,4,3,1]=>[1,2,8,5,3,7,6,4]=>[8,7,1,4,6,2,3,5]=>[1,1,3,3]
[5,6,7,8,1,4,2,3]=>[1,7,2,8,5,3,6,4]=>[8,2,7,1,4,6,3,5]=>[1,2,3,2]
[4,6,7,1,8,5,2,3]=>[7,1,2,8,6,4,3,5]=>[2,8,7,1,3,5,6,4]=>[2,1,4,1]
[3,6,1,7,8,5,2,4]=>[7,4,1,2,8,6,3,5]=>[2,5,8,7,1,3,6,4]=>[3,1,3,1]
[2,1,6,7,8,5,3,4]=>[3,7,4,8,1,6,2,5]=>[6,2,5,1,8,3,7,4]=>[1,2,2,2,1]
[3,6,1,7,8,5,4,2]=>[4,2,8,1,7,6,3,5]=>[5,7,1,8,2,3,6,4]=>[2,2,3,1]
[4,6,7,1,8,5,3,2]=>[2,8,1,7,6,4,3,5]=>[7,1,8,2,3,5,6,4]=>[1,2,4,1]
[5,6,7,8,1,4,3,2]=>[1,2,8,7,5,3,6,4]=>[8,7,1,2,4,6,3,5]=>[1,1,4,2]
[5,6,7,8,4,1,3,2]=>[1,2,8,6,3,7,5,4]=>[8,7,1,3,6,2,4,5]=>[1,1,3,3]
[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,1,2,3,4,5,6]=>[1,1,1,1,6]
[6,5,8,7,3,4,1,2]=>[2,1,7,5,8,6,4,3]=>[7,8,2,4,1,3,5,6]=>[2,2,4]
[3,6,7,4,5,8,1,2]=>[4,2,7,1,5,3,8,6]=>[5,7,2,8,4,6,1,3]=>[2,2,2,2]
[2,6,7,4,5,1,8,3]=>[4,2,8,6,1,5,3,7]=>[5,7,1,3,8,4,6,2]=>[2,3,2,1]
[1,6,7,4,5,2,3,8]=>[6,4,2,7,5,1,3,8]=>[3,5,7,2,4,8,6,1]=>[3,3,1,1]
[1,5,4,7,6,2,3,8]=>[3,2,6,7,5,1,4,8]=>[6,7,3,2,4,8,5,1]=>[2,1,3,1,1]
[2,5,4,7,6,1,8,3]=>[2,8,3,6,1,5,4,7]=>[7,1,6,3,8,4,5,2]=>[1,2,2,2,1]
[3,5,4,7,6,8,1,2]=>[2,7,1,3,5,4,8,6]=>[7,2,8,6,4,5,1,3]=>[1,2,1,2,2]
[4,5,3,7,8,6,1,2]=>[1,2,7,3,4,8,6,5]=>[8,7,2,6,5,1,3,4]=>[1,1,2,1,3]
[5,4,3,8,7,6,1,2]=>[2,1,7,8,3,6,5,4]=>[7,8,2,1,6,3,4,5]=>[2,1,2,3]
[6,4,8,3,7,5,1,2]=>[2,4,1,7,8,6,5,3]=>[7,5,8,2,1,3,4,6]=>[1,2,1,4]
[6,3,8,4,5,7,1,2]=>[4,7,2,1,5,8,6,3]=>[5,2,7,8,4,1,3,6]=>[1,3,1,3]
[5,3,4,8,6,7,1,2]=>[7,2,1,3,5,8,6,4]=>[2,7,8,6,4,1,3,5]=>[3,1,1,3]
[4,3,5,6,8,7,1,2]=>[2,1,3,4,7,8,6,5]=>[7,8,6,5,2,1,3,4]=>[2,1,1,1,3]
[3,2,5,6,1,8,7,4]=>[1,3,4,8,2,7,5,6]=>[8,6,5,1,7,2,4,3]=>[1,1,1,2,2,1]
[4,2,5,6,8,1,7,3]=>[3,1,4,8,2,6,7,5]=>[6,8,5,1,7,3,2,4]=>[2,1,2,1,2]
[5,2,4,8,6,1,7,3]=>[8,3,1,6,2,5,7,4]=>[1,6,8,3,7,4,2,5]=>[3,2,1,2]
[6,2,8,4,5,1,7,3]=>[4,8,6,2,1,5,7,3]=>[5,1,3,7,8,4,2,6]=>[1,4,1,2]
[7,8,2,4,5,1,6,3]=>[4,8,3,6,5,1,7,2]=>[5,1,6,3,4,8,2,7]=>[1,2,3,2]
[7,8,1,4,5,2,3,6]=>[6,4,7,3,5,1,8,2]=>[3,5,2,6,4,8,1,7]=>[2,2,2,2]
[6,1,8,4,5,2,3,7]=>[6,4,7,5,1,8,2,3]=>[3,5,2,4,8,1,7,6]=>[2,3,2,1]
[5,1,4,8,6,2,3,7]=>[3,6,1,7,5,8,2,4]=>[6,3,8,2,4,1,7,5]=>[1,2,2,2,1]
[4,1,3,2,8,6,5,7]=>[7,3,1,6,8,2,4,5]=>[2,6,8,3,1,7,5,4]=>[3,1,2,1,1]
[5,1,3,8,2,6,4,7]=>[7,3,5,1,6,8,2,4]=>[2,6,4,8,3,1,7,5]=>[2,2,1,2,1]
[6,1,8,3,2,5,4,7]=>[4,7,5,6,1,8,2,3]=>[5,2,4,3,8,1,7,6]=>[1,2,2,2,1]
[7,8,1,3,2,5,4,6]=>[4,7,3,5,6,1,8,2]=>[5,2,6,4,3,8,1,7]=>[1,2,1,2,2]
[7,8,2,3,1,5,6,4]=>[3,4,6,8,5,1,7,2]=>[6,5,3,1,4,8,2,7]=>[1,1,1,3,2]
[6,2,8,3,1,5,7,4]=>[4,6,8,2,1,5,7,3]=>[5,3,1,7,8,4,2,6]=>[1,1,3,1,2]
[5,2,3,8,1,6,7,4]=>[6,8,2,1,3,5,7,4]=>[3,1,7,8,6,4,2,5]=>[1,3,1,1,2]
[6,3,8,2,1,7,5,4]=>[8,2,4,1,7,5,6,3]=>[1,7,5,8,2,4,3,6]=>[2,2,2,2]
[7,8,3,2,1,6,5,4]=>[3,8,4,7,5,1,6,2]=>[6,1,5,2,4,8,3,7]=>[1,2,3,2]
[7,8,4,2,6,1,5,3]=>[8,4,3,6,1,7,5,2]=>[1,5,6,3,8,2,4,7]=>[3,2,3]
[5,4,2,8,7,1,6,3]=>[2,1,8,6,7,3,5,4]=>[7,8,1,3,2,6,4,5]=>[2,2,2,2]
[4,5,2,7,8,1,6,3]=>[1,2,8,6,3,4,7,5]=>[8,7,1,3,6,5,2,4]=>[1,1,3,1,2]
[2,5,3,7,1,6,8,4]=>[6,2,8,1,3,5,4,7]=>[3,7,1,8,6,4,5,2]=>[2,2,1,2,1]
[1,5,3,7,2,6,4,8]=>[7,3,2,5,6,1,4,8]=>[2,6,7,4,3,8,5,1]=>[3,1,2,1,1]
[1,6,7,3,2,5,4,8]=>[4,7,5,2,6,1,3,8]=>[5,2,4,7,3,8,6,1]=>[1,3,2,1,1]
[2,6,7,3,1,5,8,4]=>[4,6,2,8,1,5,3,7]=>[5,3,7,1,8,4,6,2]=>[1,2,2,2,1]
[3,6,7,2,1,8,5,4]=>[8,4,1,2,7,5,3,6]=>[1,5,8,7,2,4,6,3]=>[3,1,3,1]
[7,8,5,6,2,1,4,3]=>[5,8,6,3,1,7,4,2]=>[4,1,3,6,8,2,5,7]=>[1,4,3]
[6,5,8,7,1,2,3,4]=>[5,6,2,1,7,8,4,3]=>[4,3,7,8,2,1,5,6]=>[1,3,1,3]
[5,4,1,8,7,2,3,6]=>[6,2,1,7,8,5,3,4]=>[3,7,8,2,1,4,6,5]=>[3,1,3,1]
[6,4,8,1,7,2,3,5]=>[6,2,7,1,8,4,5,3]=>[3,7,2,8,1,5,4,6]=>[2,2,2,2]
[7,8,3,1,2,6,4,5]=>[7,3,8,4,5,1,6,2]=>[2,6,1,5,4,8,3,7]=>[2,2,2,2]
[5,3,1,8,2,7,4,6]=>[2,7,1,8,5,6,3,4]=>[7,2,8,1,4,3,6,5]=>[1,2,2,2,1]
[4,3,1,2,8,7,5,6]=>[2,1,7,8,6,3,4,5]=>[7,8,2,1,3,6,5,4]=>[2,1,3,1,1]
[4,2,1,3,8,5,7,6]=>[8,2,1,6,7,3,4,5]=>[1,7,8,3,2,6,5,4]=>[3,1,2,1,1]
[5,2,1,8,3,4,7,6]=>[8,2,5,1,6,7,3,4]=>[1,7,4,8,3,2,6,5]=>[2,2,1,2,1]
[6,2,8,1,3,4,7,5]=>[8,2,4,5,1,6,7,3]=>[1,7,5,4,8,3,2,6]=>[2,1,2,1,2]
[7,8,2,1,3,4,6,5]=>[3,8,4,5,6,1,7,2]=>[6,1,5,4,3,8,2,7]=>[1,2,1,2,2]
[4,3,1,2,6,5,8,7]=>[5,2,1,8,3,4,6,7]=>[4,7,8,1,6,5,3,2]=>[3,2,1,1,1]
[6,3,1,5,2,4,8,7]=>[2,8,5,3,4,1,6,7]=>[7,1,4,6,5,8,3,2]=>[1,3,2,1,1]
[8,4,5,1,2,7,3,6]=>[7,2,8,4,3,5,6,1]=>[2,7,1,5,6,4,3,8]=>[2,3,1,2]
[6,4,5,1,2,3,8,7]=>[8,4,2,5,3,1,6,7]=>[1,5,7,4,6,8,3,2]=>[3,3,1,1]
[3,6,1,5,2,4,8,7]=>[8,1,5,3,4,2,6,7]=>[1,8,4,6,5,7,3,2]=>[2,2,2,1,1]
[4,6,5,1,2,3,8,7]=>[1,8,4,5,3,2,6,7]=>[8,1,5,4,6,7,3,2]=>[1,2,3,1,1]
[5,6,4,1,2,3,8,7]=>[8,4,1,5,3,2,6,7]=>[1,5,8,4,6,7,3,2]=>[3,3,1,1]
[6,5,4,1,2,3,8,7]=>[8,4,5,3,2,1,6,7]=>[1,5,4,6,7,8,3,2]=>[2,4,1,1]
[7,5,4,1,2,8,3,6]=>[7,8,4,3,2,5,1,6]=>[2,1,5,6,7,4,8,3]=>[1,4,2,1]
[8,6,4,1,7,2,3,5]=>[6,7,3,8,4,2,5,1]=>[3,2,6,1,5,7,4,8]=>[1,2,3,2]
[7,6,4,1,8,2,3,5]=>[6,7,3,8,4,2,1,5]=>[3,2,6,1,5,7,8,4]=>[1,2,4,1]
[6,7,4,1,8,2,3,5]=>[6,7,3,1,8,4,2,5]=>[3,2,6,8,1,5,7,4]=>[1,3,3,1]
[4,7,5,1,2,8,3,6]=>[1,7,8,4,3,5,2,6]=>[8,2,1,5,6,4,7,3]=>[1,1,3,2,1]
[3,7,1,5,2,8,4,6]=>[7,1,4,8,3,5,2,6]=>[2,8,5,1,6,4,7,3]=>[2,1,2,2,1]
[2,1,7,5,3,8,4,6]=>[7,4,8,1,5,2,3,6]=>[2,5,1,8,4,7,6,3]=>[2,2,2,1,1]
[2,1,8,5,3,7,4,6]=>[7,4,8,1,5,6,2,3]=>[2,5,1,8,4,3,7,6]=>[2,2,1,2,1]
[3,8,1,5,2,7,4,6]=>[7,1,4,8,3,5,6,2]=>[2,8,5,1,6,4,3,7]=>[2,1,2,1,2]
[4,8,5,1,2,7,3,6]=>[1,7,8,4,3,5,6,2]=>[8,2,1,5,6,4,3,7]=>[1,1,3,1,2]
[5,8,4,1,2,7,3,6]=>[7,1,8,4,3,5,6,2]=>[2,8,1,5,6,4,3,7]=>[2,3,1,2]
[6,8,4,1,7,2,3,5]=>[6,7,3,1,8,4,5,2]=>[3,2,6,8,1,5,4,7]=>[1,3,2,2]
[8,7,4,1,6,2,3,5]=>[6,7,3,8,4,5,2,1]=>[3,2,6,1,5,4,7,8]=>[1,2,2,3]
[5,8,6,7,1,2,3,4]=>[5,1,6,7,3,8,4,2]=>[4,8,3,2,6,1,5,7]=>[2,1,2,3]
[4,8,6,1,7,2,3,5]=>[1,6,7,8,4,3,5,2]=>[8,3,2,1,5,6,4,7]=>[1,1,1,3,2]
[3,8,1,6,7,2,4,5]=>[6,7,1,4,8,3,5,2]=>[3,2,8,5,1,6,4,7]=>[1,2,1,2,2]
[2,1,8,6,7,3,4,5]=>[6,7,4,8,1,5,2,3]=>[3,2,5,1,8,4,7,6]=>[1,2,2,2,1]
[2,1,7,6,8,3,4,5]=>[6,7,4,1,3,8,2,5]=>[3,2,5,8,6,1,7,4]=>[1,3,1,2,1]
[3,7,1,6,8,2,4,5]=>[6,7,1,4,8,3,2,5]=>[3,2,8,5,1,6,7,4]=>[1,2,1,3,1]
[5,7,6,8,1,2,3,4]=>[5,1,6,7,3,2,8,4]=>[4,8,3,2,6,7,1,5]=>[2,1,3,2]
[5,4,7,1,2,8,3,6]=>[7,2,1,8,4,5,3,6]=>[2,7,8,1,5,4,6,3]=>[3,2,2,1]
[7,4,6,1,8,2,3,5]=>[6,2,7,8,4,3,1,5]=>[3,7,2,1,5,6,8,4]=>[2,1,4,1]
[8,4,6,1,7,2,3,5]=>[6,2,7,8,4,3,5,1]=>[3,7,2,1,5,6,4,8]=>[2,1,3,2]
[8,3,1,6,7,2,4,5]=>[2,6,7,4,8,3,5,1]=>[7,3,2,5,1,6,4,8]=>[1,1,2,2,2]
[7,3,1,6,8,2,4,5]=>[2,6,7,4,8,3,1,5]=>[7,3,2,5,1,6,8,4]=>[1,1,2,3,1]
[5,3,1,7,2,8,4,6]=>[2,7,1,8,5,3,4,6]=>[7,2,8,1,4,6,5,3]=>[1,2,3,1,1]
[4,3,1,2,7,8,5,6]=>[2,1,7,5,8,3,4,6]=>[7,8,2,4,1,6,5,3]=>[2,2,2,1,1]
[2,1,4,3,8,7,5,6]=>[7,8,1,3,6,2,4,5]=>[2,1,8,6,3,7,5,4]=>[1,2,1,2,1,1]
[7,3,1,8,6,2,4,5]=>[2,6,7,8,5,3,1,4]=>[7,3,2,1,4,6,8,5]=>[1,1,1,4,1]
[8,4,7,1,6,2,3,5]=>[6,2,7,8,4,5,3,1]=>[3,7,2,1,5,4,6,8]=>[2,1,2,3]
[7,4,8,1,6,2,3,5]=>[6,2,7,8,4,1,5,3]=>[3,7,2,1,5,8,4,6]=>[2,1,3,2]
[5,4,8,1,2,7,3,6]=>[7,2,1,8,4,5,6,3]=>[2,7,8,1,5,4,3,6]=>[3,2,1,2]
[4,5,8,1,2,7,3,6]=>[1,7,2,8,4,5,6,3]=>[8,2,7,1,5,4,3,6]=>[1,2,2,1,2]
[3,5,1,8,2,7,4,6]=>[7,1,2,8,5,6,3,4]=>[2,8,7,1,4,3,6,5]=>[2,1,2,2,1]
[2,1,5,8,3,7,4,6]=>[3,7,8,1,5,6,2,4]=>[6,2,1,8,4,3,7,5]=>[1,1,2,1,2,1]
[2,1,6,8,7,3,4,5]=>[6,3,7,8,1,5,2,4]=>[3,6,2,1,8,4,7,5]=>[2,1,2,2,1]
[3,6,1,8,7,2,4,5]=>[6,7,1,2,8,5,3,4]=>[3,2,8,7,1,4,6,5]=>[1,2,1,3,1]
[4,6,8,1,7,2,3,5]=>[1,6,7,2,8,4,5,3]=>[8,3,2,7,1,5,4,6]=>[1,1,2,2,2]
[5,6,8,7,1,2,3,4]=>[5,1,6,2,7,8,4,3]=>[4,8,3,7,2,1,5,6]=>[2,2,1,3]
[7,5,8,6,1,2,3,4]=>[5,6,2,7,1,8,4,3]=>[4,3,7,2,8,1,5,6]=>[1,2,2,3]
[8,5,7,6,1,2,3,4]=>[5,6,2,7,8,4,3,1]=>[4,3,7,2,1,5,6,8]=>[1,2,1,4]
[5,7,8,6,1,2,3,4]=>[5,1,6,7,2,8,4,3]=>[4,8,3,2,7,1,5,6]=>[2,1,2,3]
[4,7,8,1,6,2,3,5]=>[1,6,7,8,4,2,5,3]=>[8,3,2,1,5,7,4,6]=>[1,1,1,3,2]
[3,7,1,8,6,2,4,5]=>[6,7,8,1,5,3,2,4]=>[3,2,1,8,4,6,7,5]=>[1,1,2,3,1]
[2,1,7,8,6,3,4,5]=>[6,7,3,8,1,5,2,4]=>[3,2,6,1,8,4,7,5]=>[1,2,2,2,1]
[2,1,8,7,6,3,4,5]=>[6,7,8,5,1,4,2,3]=>[3,2,1,4,8,5,7,6]=>[1,1,3,2,1]
[3,8,1,7,6,2,4,5]=>[6,7,8,1,5,3,4,2]=>[3,2,1,8,4,6,5,7]=>[1,1,2,2,2]
[4,8,7,1,6,2,3,5]=>[1,6,7,8,4,5,3,2]=>[8,3,2,1,5,4,6,7]=>[1,1,1,2,3]
[5,8,7,6,1,2,3,4]=>[5,1,6,7,8,4,3,2]=>[4,8,3,2,1,5,6,7]=>[2,1,1,4]
[6,8,7,5,1,2,3,4]=>[5,6,1,7,8,4,3,2]=>[4,3,8,2,1,5,6,7]=>[1,2,1,4]
[6,4,7,3,8,5,1,2]=>[2,4,1,7,3,8,6,5]=>[7,5,8,2,6,1,3,4]=>[1,2,2,3]
[6,4,7,3,5,8,1,2]=>[2,4,1,7,5,3,8,6]=>[7,5,8,2,4,6,1,3]=>[1,2,3,2]
[6,4,7,2,5,1,8,3]=>[2,8,4,1,6,5,3,7]=>[7,1,5,8,3,4,6,2]=>[1,3,3,1]
[5,4,2,7,6,1,3,8]=>[6,2,1,7,3,5,4,8]=>[3,7,8,2,6,4,5,1]=>[3,2,2,1]
[5,4,2,7,6,1,8,3]=>[2,1,8,6,3,5,4,7]=>[7,8,1,3,6,4,5,2]=>[2,3,2,1]
[5,4,3,7,6,8,1,2]=>[2,1,7,3,5,4,8,6]=>[7,8,2,6,4,5,1,3]=>[2,2,2,2]
[5,4,3,7,8,6,1,2]=>[2,1,7,3,4,8,6,5]=>[7,8,2,6,5,1,3,4]=>[2,2,1,3]
[6,4,8,3,5,7,1,2]=>[2,4,1,7,5,8,6,3]=>[7,5,8,2,4,1,3,6]=>[1,2,2,3]
[5,4,3,8,6,7,1,2]=>[2,1,7,3,5,8,6,4]=>[7,8,2,6,4,1,3,5]=>[2,2,1,3]
[5,4,3,6,8,7,1,2]=>[3,2,1,4,7,8,6,5]=>[6,7,8,5,2,1,3,4]=>[3,1,1,3]
[5,4,2,6,7,1,8,3]=>[4,2,1,8,3,6,5,7]=>[5,7,8,1,6,3,4,2]=>[3,2,2,1]
[5,4,2,6,7,1,3,8]=>[6,3,2,1,4,7,5,8]=>[3,6,7,8,5,2,4,1]=>[4,1,2,1]
[5,3,2,6,1,7,4,8]=>[2,7,3,1,5,4,6,8]=>[7,2,6,8,4,5,3,1]=>[1,3,2,1,1]
[5,3,2,6,1,7,8,4]=>[2,6,3,1,4,8,5,7]=>[7,3,6,8,5,1,4,2]=>[1,3,1,2,1]
[5,3,2,6,1,8,7,4]=>[2,4,1,8,3,7,5,6]=>[7,5,8,1,6,2,4,3]=>[1,2,2,2,1]
[5,4,2,8,6,1,7,3]=>[2,1,8,6,3,5,7,4]=>[7,8,1,3,6,4,2,5]=>[2,3,1,2]
[6,4,8,2,5,1,7,3]=>[2,8,4,1,6,5,7,3]=>[7,1,5,8,3,4,2,6]=>[1,3,2,2]
[7,8,4,2,5,1,6,3]=>[8,4,3,6,5,1,7,2]=>[1,5,6,3,4,8,2,7]=>[3,3,2]
[7,8,4,2,5,1,3,6]=>[4,6,3,7,5,1,8,2]=>[5,3,6,2,4,8,1,7]=>[1,2,3,2]
[5,4,2,8,6,1,3,7]=>[6,2,1,7,3,5,8,4]=>[3,7,8,2,6,4,1,5]=>[3,2,1,2]
[4,3,2,1,6,8,5,7]=>[3,2,1,5,7,8,4,6]=>[6,7,8,4,2,1,5,3]=>[3,1,1,2,1]
[4,3,2,1,8,6,5,7]=>[2,1,7,3,6,8,4,5]=>[7,8,2,6,3,1,5,4]=>[2,2,1,2,1]
[5,3,2,8,1,6,4,7]=>[2,7,3,1,5,6,8,4]=>[7,2,6,8,4,3,1,5]=>[1,3,1,1,2]
[6,3,8,2,1,5,4,7]=>[2,4,7,5,1,6,8,3]=>[7,5,2,4,8,3,1,6]=>[1,1,3,1,2]
[7,8,3,2,1,5,4,6]=>[4,3,7,5,6,1,8,2]=>[5,6,2,4,3,8,1,7]=>[2,2,2,2]
[7,8,3,2,1,5,6,4]=>[4,3,6,8,5,1,7,2]=>[5,6,3,1,4,8,2,7]=>[2,1,3,2]
[6,3,8,2,1,5,7,4]=>[2,4,6,1,8,5,7,3]=>[7,5,3,8,1,4,2,6]=>[1,1,2,2,2]
[5,3,2,8,1,6,7,4]=>[2,6,1,8,3,5,7,4]=>[7,3,8,1,6,4,2,5]=>[1,2,2,1,2]
[5,4,2,7,8,1,6,3]=>[2,1,8,6,3,4,7,5]=>[7,8,1,3,6,5,2,4]=>[2,3,1,2]
[5,3,2,7,1,8,6,4]=>[8,2,1,7,3,5,4,6]=>[1,7,8,2,6,4,5,3]=>[3,2,2,1]
[5,3,2,7,1,6,8,4]=>[2,6,1,8,3,5,4,7]=>[7,3,8,1,6,4,5,2]=>[1,2,2,2,1]
[5,3,2,7,1,6,4,8]=>[2,7,3,1,5,6,4,8]=>[7,2,6,8,4,3,5,1]=>[1,3,1,2,1]
[6,3,7,2,1,5,4,8]=>[2,4,7,5,1,6,3,8]=>[7,5,2,4,8,3,6,1]=>[1,1,3,2,1]
[6,3,7,2,1,5,8,4]=>[2,4,6,1,8,5,3,7]=>[7,5,3,8,1,4,6,2]=>[1,1,2,3,1]
[6,3,7,2,1,8,5,4]=>[8,2,4,1,7,5,3,6]=>[1,7,5,8,2,4,6,3]=>[2,2,3,1]
[6,4,7,2,8,1,5,3]=>[2,8,4,1,6,3,7,5]=>[7,1,5,8,3,6,2,4]=>[1,3,2,2]
[6,5,7,8,2,1,4,3]=>[5,2,1,8,6,3,7,4]=>[4,7,8,1,3,6,2,5]=>[3,3,2]
[6,5,8,7,2,1,3,4]=>[6,5,2,1,7,8,4,3]=>[3,4,7,8,2,1,5,6]=>[4,1,3]
[6,3,7,2,1,8,4,5]=>[2,4,7,1,8,5,3,6]=>[7,5,2,8,1,4,6,3]=>[1,1,2,3,1]
[6,3,7,2,1,4,8,5]=>[2,4,8,5,1,6,3,7]=>[7,5,1,4,8,3,6,2]=>[1,1,3,2,1]
[6,3,7,2,1,4,5,8]=>[2,5,4,6,1,7,3,8]=>[7,4,5,3,8,2,6,1]=>[1,2,2,2,1]
[5,3,2,7,1,4,8,6]=>[2,8,3,1,5,6,4,7]=>[7,1,6,8,4,3,5,2]=>[1,3,1,2,1]
[5,4,2,8,7,1,3,6]=>[6,2,1,7,8,3,5,4]=>[3,7,8,2,1,6,4,5]=>[3,1,2,2]
[7,8,4,2,6,1,3,5]=>[4,6,3,7,1,8,5,2]=>[5,3,6,2,8,1,4,7]=>[1,2,2,3]
[7,8,3,2,1,6,4,5]=>[4,3,7,8,5,1,6,2]=>[5,6,2,1,4,8,3,7]=>[2,1,3,2]
[6,3,8,2,1,7,4,5]=>[2,4,7,1,8,5,6,3]=>[7,5,2,8,1,4,3,6]=>[1,1,2,2,2]
[5,3,2,8,1,7,4,6]=>[2,7,1,8,3,5,6,4]=>[7,2,8,1,6,4,3,5]=>[1,2,2,1,2]
[4,3,2,1,8,7,5,6]=>[2,1,7,8,3,6,4,5]=>[7,8,2,1,6,3,5,4]=>[2,1,2,2,1]
[4,3,2,1,7,5,8,6]=>[2,1,8,3,6,4,5,7]=>[7,8,1,6,3,5,4,2]=>[2,2,2,1,1]
[4,3,2,1,7,5,6,8]=>[3,2,1,6,7,4,5,8]=>[6,7,8,3,2,5,4,1]=>[3,1,2,1,1]
[4,3,2,1,8,5,7,6]=>[2,1,8,3,6,7,4,5]=>[7,8,1,6,3,2,5,4]=>[2,2,1,2,1]
[5,3,2,8,1,4,7,6]=>[2,8,3,1,5,6,7,4]=>[7,1,6,8,4,3,2,5]=>[1,3,1,1,2]
[6,3,8,2,1,4,7,5]=>[2,4,8,5,1,6,7,3]=>[7,5,1,4,8,3,2,6]=>[1,1,3,1,2]
[6,3,8,2,1,4,5,7]=>[2,5,4,6,1,7,8,3]=>[7,4,5,3,8,2,1,6]=>[1,2,2,1,2]
[4,3,2,1,8,5,6,7]=>[3,2,1,6,7,8,4,5]=>[6,7,8,3,2,1,5,4]=>[3,1,1,2,1]
[4,3,2,1,5,8,6,7]=>[3,2,1,7,8,4,5,6]=>[6,7,8,2,1,5,4,3]=>[3,1,2,1,1]
[7,8,5,6,1,2,4,3]=>[8,5,6,3,1,7,4,2]=>[1,4,3,6,8,2,5,7]=>[2,3,3]
[7,8,4,1,6,2,5,3]=>[8,6,3,7,4,1,5,2]=>[1,3,6,2,5,8,4,7]=>[3,3,2]
[7,8,1,4,6,2,5,3]=>[4,8,6,7,3,1,5,2]=>[5,1,3,2,6,8,4,7]=>[1,2,3,2]
[6,1,8,4,7,2,5,3]=>[4,8,6,1,7,5,2,3]=>[5,1,3,8,2,4,7,6]=>[1,3,3,1]
[1,6,8,4,7,2,5,3]=>[4,2,8,6,7,5,1,3]=>[5,7,1,3,2,4,8,6]=>[2,2,3,1]
[1,6,8,3,2,7,5,4]=>[8,4,2,7,5,6,1,3]=>[1,5,7,2,4,3,8,6]=>[3,2,2,1]
[6,1,8,3,2,7,5,4]=>[8,4,7,5,1,6,2,3]=>[1,5,2,4,8,3,7,6]=>[2,3,2,1]
[7,8,1,3,2,6,5,4]=>[8,4,7,3,5,1,6,2]=>[1,5,2,6,4,8,3,7]=>[2,2,2,2]
[7,8,3,1,2,6,5,4]=>[3,8,7,4,5,1,6,2]=>[6,1,2,5,4,8,3,7]=>[1,3,2,2]
[7,8,3,4,6,5,1,2]=>[3,4,7,1,8,6,5,2]=>[6,5,2,8,1,3,4,7]=>[1,1,2,4]
[7,8,2,4,6,1,5,3]=>[4,8,3,6,1,7,5,2]=>[5,1,6,3,8,2,4,7]=>[1,2,2,3]
[7,8,2,3,1,6,5,4]=>[8,3,4,7,5,1,6,2]=>[1,6,5,2,4,8,3,7]=>[2,1,3,2]
[7,8,2,1,3,6,5,4]=>[8,3,7,4,5,1,6,2]=>[1,6,2,5,4,8,3,7]=>[2,2,2,2]
[7,8,1,2,3,6,5,4]=>[8,7,3,4,5,1,6,2]=>[1,2,6,5,4,8,3,7]=>[3,1,2,2]
[6,1,8,2,3,7,5,4]=>[8,7,4,5,1,6,2,3]=>[1,2,5,4,8,3,7,6]=>[3,2,2,1]
[1,6,8,2,3,7,5,4]=>[8,7,4,2,5,6,1,3]=>[1,2,5,7,4,3,8,6]=>[4,1,2,1]
[1,5,2,8,3,7,6,4]=>[2,8,7,5,6,1,3,4]=>[7,1,2,4,3,8,6,5]=>[1,3,2,1,1]
[5,1,2,8,3,7,6,4]=>[8,7,5,1,6,2,3,4]=>[1,2,4,8,3,7,6,5]=>[4,2,1,1]
[5,2,1,8,3,7,6,4]=>[8,7,2,1,5,6,3,4]=>[1,2,7,8,4,3,6,5]=>[4,1,2,1]
[6,2,8,1,3,7,5,4]=>[8,7,2,4,1,5,6,3]=>[1,2,7,5,8,4,3,6]=>[3,2,1,2]
[6,2,8,3,1,7,5,4]=>[8,4,7,2,1,5,6,3]=>[1,5,2,7,8,4,3,6]=>[2,3,1,2]
[6,2,8,4,7,1,5,3]=>[4,8,6,1,7,2,5,3]=>[5,1,3,8,2,7,4,6]=>[1,3,2,2]
[6,3,8,4,7,5,1,2]=>[4,7,1,8,2,6,5,3]=>[5,2,8,1,7,3,4,6]=>[1,2,2,3]
[3,6,8,4,7,5,1,2]=>[4,2,7,8,1,6,5,3]=>[5,7,2,1,8,3,4,6]=>[2,1,2,3]
[2,6,8,4,7,1,5,3]=>[4,2,8,6,7,1,5,3]=>[5,7,1,3,2,8,4,6]=>[2,2,2,2]
[2,6,8,3,1,7,5,4]=>[8,4,2,7,1,5,6,3]=>[1,5,7,2,8,4,3,6]=>[3,2,1,2]
[2,6,8,1,3,7,5,4]=>[8,7,4,1,2,5,6,3]=>[1,2,5,8,7,4,3,6]=>[4,1,1,2]
[2,5,1,8,3,7,6,4]=>[2,8,7,1,5,6,3,4]=>[7,1,2,8,4,3,6,5]=>[1,3,1,2,1]
[1,2,5,8,3,7,6,4]=>[8,3,7,5,6,1,2,4]=>[1,6,2,4,3,8,7,5]=>[2,2,2,1,1]
[2,4,1,3,8,7,6,5]=>[8,2,7,1,6,3,4,5]=>[1,7,2,8,3,6,5,4]=>[2,2,2,1,1]
[2,5,3,8,1,7,6,4]=>[2,8,7,1,3,5,6,4]=>[7,1,2,8,6,4,3,5]=>[1,3,1,1,2]
[2,5,4,8,7,1,6,3]=>[2,8,3,6,7,1,5,4]=>[7,1,6,3,2,8,4,5]=>[1,2,1,2,2]
[3,5,4,8,7,6,1,2]=>[2,7,8,1,3,6,5,4]=>[7,2,1,8,6,3,4,5]=>[1,1,2,1,3]
[5,3,4,8,7,6,1,2]=>[7,1,8,2,3,6,5,4]=>[2,8,1,7,6,3,4,5]=>[2,2,1,3]
[5,2,4,8,7,1,6,3]=>[8,3,1,6,7,2,5,4]=>[1,6,8,3,2,7,4,5]=>[3,1,2,2]
[5,2,3,8,1,7,6,4]=>[8,7,2,1,3,5,6,4]=>[1,2,7,8,6,4,3,5]=>[4,1,1,2]
[4,2,1,3,8,7,6,5]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[1,3,2,1,1]
[4,1,2,3,8,7,6,5]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[1,4,1,1,1]
[1,4,2,3,8,7,6,5]=>[8,2,7,6,1,3,4,5]=>[1,7,2,3,8,6,5,4]=>[2,3,1,1,1]
[4,1,3,2,8,7,6,5]=>[1,8,7,3,6,2,4,5]=>[8,1,2,6,3,7,5,4]=>[1,3,2,1,1]
[4,3,1,2,8,7,6,5]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[1,2,3,1,1]
[6,3,8,1,2,7,5,4]=>[8,2,7,4,1,5,6,3]=>[1,7,2,5,8,4,3,6]=>[2,3,1,2]
[5,3,1,8,2,7,6,4]=>[8,2,1,7,5,6,3,4]=>[1,7,8,2,4,3,6,5]=>[3,2,2,1]
[5,1,3,8,2,7,6,4]=>[8,7,3,1,5,6,2,4]=>[1,2,6,8,4,3,7,5]=>[4,1,2,1]
[1,5,3,8,2,7,6,4]=>[2,8,7,3,5,6,1,4]=>[7,1,2,6,4,3,8,5]=>[1,3,1,2,1]
[1,5,4,8,7,2,6,3]=>[2,8,3,6,7,5,1,4]=>[7,1,6,3,2,4,8,5]=>[1,2,1,3,1]
[5,1,4,8,7,2,6,3]=>[8,3,1,6,7,5,2,4]=>[1,6,8,3,2,4,7,5]=>[3,1,3,1]
[5,4,1,8,7,2,6,3]=>[2,1,8,6,7,5,3,4]=>[7,8,1,3,2,4,6,5]=>[2,2,3,1]
[6,4,8,1,7,2,5,3]=>[2,8,6,1,7,4,5,3]=>[7,1,3,8,2,5,4,6]=>[1,3,2,2]
[6,5,8,7,1,2,4,3]=>[8,5,2,1,6,7,4,3]=>[1,4,7,8,3,2,5,6]=>[4,1,3]
[5,6,8,7,3,4,1,2]=>[1,2,7,5,8,6,4,3]=>[8,7,2,4,1,3,5,6]=>[1,1,2,4]
[5,6,8,7,2,1,4,3]=>[1,5,2,8,6,7,4,3]=>[8,4,7,1,3,2,5,6]=>[1,2,2,3]
[4,5,1,8,7,2,6,3]=>[1,2,8,6,7,5,3,4]=>[8,7,1,3,2,4,6,5]=>[1,1,2,3,1]
[4,1,5,8,7,2,6,3]=>[1,8,3,6,7,5,2,4]=>[8,1,6,3,2,4,7,5]=>[1,2,1,3,1]
[1,4,5,8,7,2,6,3]=>[8,2,3,6,7,5,1,4]=>[1,7,6,3,2,4,8,5]=>[2,1,1,3,1]
[1,3,5,8,2,7,6,4]=>[8,3,7,2,5,6,1,4]=>[1,6,2,7,4,3,8,5]=>[2,2,1,2,1]
[3,1,5,8,2,7,6,4]=>[8,1,3,7,5,6,2,4]=>[1,8,6,2,4,3,7,5]=>[2,1,2,2,1]
[3,6,8,1,2,7,5,4]=>[8,7,1,4,2,5,6,3]=>[1,2,8,5,7,4,3,6]=>[3,2,1,2]
[3,6,8,2,1,7,5,4]=>[8,4,1,2,7,5,6,3]=>[1,5,8,7,2,4,3,6]=>[3,1,2,2]
[4,6,8,2,7,1,5,3]=>[8,1,4,2,6,7,5,3]=>[1,8,5,7,3,2,4,6]=>[2,2,1,3]
[4,6,8,3,7,5,1,2]=>[4,1,2,7,8,6,5,3]=>[5,8,7,2,1,3,4,6]=>[2,1,1,4]
[4,5,3,8,7,6,1,2]=>[1,2,7,8,3,6,5,4]=>[8,7,2,1,6,3,4,5]=>[1,1,1,2,3]
[4,5,2,8,7,1,6,3]=>[1,2,8,6,7,3,5,4]=>[8,7,1,3,2,6,4,5]=>[1,1,2,2,2]
[3,5,2,8,1,7,6,4]=>[2,8,1,7,3,5,6,4]=>[7,1,8,2,6,4,3,5]=>[1,2,2,1,2]
[3,1,4,2,8,7,6,5]=>[8,1,7,3,6,2,4,5]=>[1,8,2,6,3,7,5,4]=>[2,2,2,1,1]
[3,1,2,4,8,7,6,5]=>[8,1,7,6,2,3,4,5]=>[1,8,2,3,7,6,5,4]=>[2,3,1,1,1]
[3,2,5,8,1,7,6,4]=>[8,1,3,7,2,5,6,4]=>[1,8,6,2,7,4,3,5]=>[2,1,2,1,2]
[4,2,5,8,7,1,6,3]=>[1,8,3,6,7,2,5,4]=>[8,1,6,3,2,7,4,5]=>[1,2,1,2,2]
[4,3,5,8,7,6,1,2]=>[1,7,8,2,3,6,5,4]=>[8,2,1,7,6,3,4,5]=>[1,1,2,1,3]
[3,4,5,8,7,6,1,2]=>[7,8,1,2,3,6,5,4]=>[2,1,8,7,6,3,4,5]=>[1,2,1,1,3]
[2,4,5,8,7,1,6,3]=>[8,2,3,6,7,1,5,4]=>[1,7,6,3,2,8,4,5]=>[2,1,1,2,2]
[2,3,5,8,1,7,6,4]=>[8,3,7,1,2,5,6,4]=>[1,6,2,8,7,4,3,5]=>[2,2,1,1,2]
[4,1,3,2,6,5,8,7]=>[3,5,1,8,2,4,6,7]=>[6,4,8,1,7,5,3,2]=>[1,2,2,1,1,1]
[5,1,3,2,6,4,8,7]=>[3,5,8,2,1,4,6,7]=>[6,4,1,7,8,5,3,2]=>[1,1,3,1,1,1]
[6,1,3,2,5,4,8,7]=>[3,5,8,2,4,1,6,7]=>[6,4,1,7,5,8,3,2]=>[1,1,2,2,1,1]
[8,1,3,2,5,4,7,6]=>[3,5,8,2,4,6,7,1]=>[6,4,1,7,5,3,2,8]=>[1,1,2,1,1,2]
[8,1,4,2,5,3,7,6]=>[5,3,8,2,4,6,7,1]=>[4,6,1,7,5,3,2,8]=>[2,2,1,1,2]
[7,1,4,2,5,3,8,6]=>[5,3,8,2,4,6,1,7]=>[4,6,1,7,5,3,8,2]=>[2,2,1,2,1]
[6,1,4,2,5,3,8,7]=>[5,3,8,2,4,1,6,7]=>[4,6,1,7,5,8,3,2]=>[2,2,2,1,1]
[5,1,4,2,6,3,8,7]=>[5,3,8,2,1,4,6,7]=>[4,6,1,7,8,5,3,2]=>[2,3,1,1,1]
[2,1,6,3,5,4,8,7]=>[5,8,1,4,2,3,6,7]=>[4,1,8,5,7,6,3,2]=>[1,2,2,1,1,1]
[3,1,6,2,5,4,8,7]=>[1,5,8,4,2,3,6,7]=>[8,4,1,5,7,6,3,2]=>[1,1,3,1,1,1]
[4,1,6,2,5,3,8,7]=>[5,1,8,4,2,3,6,7]=>[4,8,1,5,7,6,3,2]=>[2,3,1,1,1]
[6,2,5,1,4,3,8,7]=>[5,8,2,4,3,1,6,7]=>[4,1,7,5,6,8,3,2]=>[1,2,3,1,1]
[5,2,6,1,4,3,8,7]=>[5,8,2,1,4,3,6,7]=>[4,1,7,8,5,6,3,2]=>[1,3,2,1,1]
[5,2,7,1,4,3,8,6]=>[5,8,2,1,4,6,3,7]=>[4,1,7,8,5,3,6,2]=>[1,3,1,2,1]
[5,2,8,1,4,3,7,6]=>[5,8,2,1,4,6,7,3]=>[4,1,7,8,5,3,2,6]=>[1,3,1,1,2]
[6,2,8,1,4,3,7,5]=>[5,8,2,4,1,6,7,3]=>[4,1,7,5,8,3,2,6]=>[1,2,2,1,2]
[6,2,7,1,4,3,8,5]=>[5,8,2,4,1,6,3,7]=>[4,1,7,5,8,3,6,2]=>[1,2,2,2,1]
[7,2,6,1,4,3,8,5]=>[5,8,2,4,6,3,1,7]=>[4,1,7,5,3,6,8,2]=>[1,2,1,3,1]
[4,1,7,2,5,3,8,6]=>[5,1,8,4,6,2,3,7]=>[4,8,1,5,3,7,6,2]=>[2,2,2,1,1]
[3,1,7,2,5,4,8,6]=>[1,5,8,4,6,2,3,7]=>[8,4,1,5,3,7,6,2]=>[1,1,2,2,1,1]
[2,1,7,3,5,4,8,6]=>[5,8,1,4,6,2,3,7]=>[4,1,8,5,3,7,6,2]=>[1,2,1,2,1,1]
[2,1,8,3,5,4,7,6]=>[5,8,1,4,6,7,2,3]=>[4,1,8,5,3,2,7,6]=>[1,2,1,1,2,1]
[8,2,5,1,4,3,7,6]=>[5,8,2,4,3,6,7,1]=>[4,1,7,5,6,3,2,8]=>[1,2,2,1,2]
[8,2,6,1,4,3,7,5]=>[5,8,2,4,6,3,7,1]=>[4,1,7,5,3,6,2,8]=>[1,2,1,2,2]
[7,1,4,3,8,2,6,5]=>[3,8,4,6,7,2,1,5]=>[6,1,5,3,2,7,8,4]=>[1,2,1,3,1]
[8,1,4,3,7,2,6,5]=>[3,8,4,6,7,2,5,1]=>[6,1,5,3,2,7,4,8]=>[1,2,1,2,2]
[7,1,5,3,8,2,6,4]=>[8,4,3,6,7,2,1,5]=>[1,5,6,3,2,7,8,4]=>[3,1,3,1]
[5,1,8,2,6,3,7,4]=>[8,6,4,1,5,7,2,3]=>[1,3,5,8,4,2,7,6]=>[4,1,2,1]
[3,1,8,2,6,4,7,5]=>[8,1,6,4,5,7,2,3]=>[1,8,3,5,4,2,7,6]=>[2,2,1,2,1]
[2,1,8,3,6,4,7,5]=>[8,6,1,4,5,7,2,3]=>[1,3,8,5,4,2,7,6]=>[3,1,1,2,1]
[2,1,7,3,6,4,8,5]=>[8,6,1,4,5,2,3,7]=>[1,3,8,5,4,7,6,2]=>[3,1,2,1,1]
[4,1,7,2,6,3,8,5]=>[1,8,6,4,5,2,3,7]=>[8,1,3,5,4,7,6,2]=>[1,3,2,1,1]
[5,1,7,2,6,3,8,4]=>[8,6,4,1,5,2,3,7]=>[1,3,5,8,4,7,6,2]=>[4,2,1,1]
[7,2,6,1,5,3,8,4]=>[8,6,2,4,5,3,1,7]=>[1,3,7,5,4,6,8,2]=>[3,1,3,1]
[6,2,7,1,5,3,8,4]=>[8,6,2,4,1,5,3,7]=>[1,3,7,5,8,4,6,2]=>[3,2,2,1]
[8,1,5,2,6,3,7,4]=>[8,6,4,2,3,5,7,1]=>[1,3,5,7,6,4,2,8]=>[4,1,1,2]
[6,1,5,2,7,3,8,4]=>[8,6,4,2,3,1,5,7]=>[1,3,5,7,6,8,4,2]=>[4,2,1,1]
[6,1,4,2,7,3,8,5]=>[3,8,6,2,4,1,5,7]=>[6,1,3,7,5,8,4,2]=>[1,3,2,1,1]
[8,1,3,2,6,4,7,5]=>[8,3,6,2,4,5,7,1]=>[1,6,3,7,5,4,2,8]=>[2,2,1,1,2]
[7,1,3,2,6,4,8,5]=>[8,3,6,2,4,5,1,7]=>[1,6,3,7,5,4,8,2]=>[2,2,1,2,1]
[6,1,3,2,7,4,8,5]=>[8,3,6,2,4,1,5,7]=>[1,6,3,7,5,8,4,2]=>[2,2,2,1,1]
[5,1,3,2,7,4,8,6]=>[8,3,6,2,1,4,5,7]=>[1,6,3,7,8,5,4,2]=>[2,3,1,1,1]
[4,1,3,2,7,5,8,6]=>[8,3,1,6,2,4,5,7]=>[1,6,8,3,7,5,4,2]=>[3,2,1,1,1]
[2,1,4,3,8,5,7,6]=>[8,1,3,6,7,2,4,5]=>[1,8,6,3,2,7,5,4]=>[2,1,1,2,1,1]
[3,1,4,2,8,5,7,6]=>[1,8,3,6,7,2,4,5]=>[8,1,6,3,2,7,5,4]=>[1,2,1,2,1,1]
[4,1,3,2,8,5,7,6]=>[8,3,1,6,7,2,4,5]=>[1,6,8,3,2,7,5,4]=>[3,1,2,1,1]
[5,1,3,2,8,4,7,6]=>[8,3,6,1,7,2,4,5]=>[1,6,3,8,2,7,5,4]=>[2,2,2,1,1]
[8,4,7,1,3,2,6,5]=>[5,2,8,4,6,7,3,1]=>[4,7,1,5,3,2,6,8]=>[2,2,1,3]
[7,4,8,1,3,2,6,5]=>[5,2,8,4,6,1,7,3]=>[4,7,1,5,3,8,2,6]=>[2,2,2,2]
[7,3,8,1,4,2,6,5]=>[2,5,8,4,6,1,7,3]=>[7,4,1,5,3,8,2,6]=>[1,1,2,2,2]
[8,3,7,1,4,2,6,5]=>[2,5,8,4,6,7,3,1]=>[7,4,1,5,3,2,6,8]=>[1,1,2,1,3]
[6,1,4,2,8,3,7,5]=>[3,8,6,7,2,1,4,5]=>[6,1,3,2,7,8,5,4]=>[1,2,3,1,1]
[5,1,4,2,8,3,7,6]=>[3,8,6,1,7,2,4,5]=>[6,1,3,8,2,7,5,4]=>[1,3,2,1,1]
[4,1,5,2,8,3,7,6]=>[3,1,8,6,7,2,4,5]=>[6,8,1,3,2,7,5,4]=>[2,2,2,1,1]
[3,1,5,2,8,4,7,6]=>[1,3,8,6,7,2,4,5]=>[8,6,1,3,2,7,5,4]=>[1,1,2,2,1,1]
[2,1,5,3,8,4,7,6]=>[3,8,1,6,7,2,4,5]=>[6,1,8,3,2,7,5,4]=>[1,2,1,2,1,1]
[2,1,6,3,8,4,7,5]=>[8,6,1,3,7,2,4,5]=>[1,3,8,6,2,7,5,4]=>[3,1,2,1,1]
[3,1,6,2,8,4,7,5]=>[8,1,6,3,7,2,4,5]=>[1,8,3,6,2,7,5,4]=>[2,2,2,1,1]
[4,1,6,2,8,3,7,5]=>[1,8,6,3,7,2,4,5]=>[8,1,3,6,2,7,5,4]=>[1,3,2,1,1]
[5,1,6,2,8,3,7,4]=>[8,6,3,1,7,2,4,5]=>[1,3,6,8,2,7,5,4]=>[4,2,1,1]
[6,1,5,2,8,3,7,4]=>[8,6,3,7,2,1,4,5]=>[1,3,6,2,7,8,5,4]=>[3,3,1,1]
[8,3,7,1,5,2,6,4]=>[8,2,6,4,5,7,3,1]=>[1,7,3,5,4,2,6,8]=>[2,2,1,3]
[7,3,8,1,5,2,6,4]=>[8,2,6,4,5,1,7,3]=>[1,7,3,5,4,8,2,6]=>[2,2,2,2]
[6,2,7,3,8,1,5,4]=>[8,4,6,2,1,3,7,5]=>[1,5,3,7,8,6,2,4]=>[2,3,1,2]
[6,2,8,3,7,1,5,4]=>[8,4,6,1,7,2,5,3]=>[1,5,3,8,2,7,4,6]=>[2,2,2,2]
[8,3,7,2,6,1,5,4]=>[8,2,4,6,7,5,3,1]=>[1,7,5,3,2,4,6,8]=>[2,1,1,4]
[5,1,8,3,7,2,6,4]=>[8,4,1,6,7,5,2,3]=>[1,5,8,3,2,4,7,6]=>[3,1,3,1]
[4,1,8,3,7,2,6,5]=>[1,8,4,6,7,5,2,3]=>[8,1,5,3,2,4,7,6]=>[1,2,1,3,1]
[3,1,8,4,7,2,6,5]=>[8,1,4,6,7,5,2,3]=>[1,8,5,3,2,4,7,6]=>[2,1,1,3,1]
[2,1,8,4,7,3,6,5]=>[8,4,6,7,1,5,2,3]=>[1,5,3,2,8,4,7,6]=>[2,1,2,2,1]
[3,1,7,4,8,2,6,5]=>[8,1,4,6,3,7,2,5]=>[1,8,5,3,6,2,7,4]=>[2,1,2,2,1]
[4,1,7,3,8,2,6,5]=>[1,8,4,6,3,7,2,5]=>[8,1,5,3,6,2,7,4]=>[1,2,2,2,1]
[5,1,7,3,8,2,6,4]=>[8,4,1,6,3,7,2,5]=>[1,5,8,3,6,2,7,4]=>[3,2,2,1]
[7,3,8,2,6,1,5,4]=>[8,2,4,6,1,7,5,3]=>[1,7,5,3,8,2,4,6]=>[2,1,2,3]
[8,2,6,3,7,1,5,4]=>[8,4,6,2,3,7,5,1]=>[1,5,3,7,6,2,4,8]=>[2,2,1,3]
[7,2,6,3,8,1,5,4]=>[8,4,6,2,3,1,7,5]=>[1,5,3,7,6,8,2,4]=>[2,2,2,2]
[3,4,2,6,8,1,5,7]=>[1,2,6,3,4,7,8,5]=>[8,7,3,6,5,2,1,4]=>[1,1,2,1,1,2]
[5,3,6,2,8,1,4,7]=>[2,4,1,6,3,7,8,5]=>[7,5,8,3,6,2,1,4]=>[1,2,2,1,2]
[5,3,6,2,4,8,1,7]=>[2,4,1,5,3,7,8,6]=>[7,5,8,4,6,2,1,3]=>[1,2,2,1,2]
[5,7,3,8,2,4,1,6]=>[3,1,5,7,6,2,8,4]=>[6,8,4,2,3,7,1,5]=>[2,1,3,2]
[5,7,3,8,2,4,6,1]=>[3,1,5,6,2,8,7,4]=>[6,8,4,3,7,1,2,5]=>[2,1,2,3]
[7,4,2,5,8,3,6,1]=>[4,2,6,8,3,1,7,5]=>[5,7,3,1,6,8,2,4]=>[2,1,3,2]
[7,4,2,5,8,3,1,6]=>[4,2,7,3,6,1,8,5]=>[5,7,2,6,3,8,1,4]=>[2,2,2,2]
[4,5,2,6,3,8,1,7]=>[1,5,3,2,4,7,8,6]=>[8,4,6,7,5,2,1,3]=>[1,3,1,1,2]
[4,5,2,1,6,8,3,7]=>[3,1,5,2,7,8,4,6]=>[6,8,4,7,2,1,5,3]=>[2,2,1,2,1]
[5,3,1,6,8,2,4,7]=>[2,6,4,1,7,8,3,5]=>[7,3,5,8,2,1,6,4]=>[1,3,1,2,1]
[5,6,2,8,1,3,4,7]=>[3,5,1,6,2,7,8,4]=>[6,4,8,3,7,2,1,5]=>[1,2,2,1,2]
[3,5,6,1,4,8,2,7]=>[5,1,2,7,3,8,4,6]=>[4,8,7,2,6,1,5,3]=>[2,1,2,2,1]
[4,1,5,6,3,8,2,7]=>[3,1,5,4,7,8,2,6]=>[6,8,4,5,2,1,7,3]=>[2,2,1,2,1]
[4,5,1,6,3,8,2,7]=>[1,5,4,2,7,8,3,6]=>[8,4,5,7,2,1,6,3]=>[1,3,1,2,1]
[4,5,6,3,2,8,1,7]=>[1,2,5,4,3,7,8,6]=>[8,7,4,5,6,2,1,3]=>[1,1,3,1,2]
[7,4,5,3,8,2,1,6]=>[2,4,3,7,6,1,8,5]=>[7,5,6,2,3,8,1,4]=>[1,2,3,2]
[7,4,5,3,8,2,6,1]=>[2,4,3,6,1,8,7,5]=>[7,5,6,3,8,1,2,4]=>[1,2,2,3]
[6,7,4,8,3,2,1,5]=>[3,1,7,6,5,2,8,4]=>[6,8,2,3,4,7,1,5]=>[2,4,2]
[6,7,4,1,8,3,2,5]=>[7,6,3,1,8,4,2,5]=>[2,3,6,8,1,5,7,4]=>[4,3,1]
[7,4,5,3,1,8,2,6]=>[2,7,4,3,8,5,1,6]=>[7,2,5,6,1,4,8,3]=>[1,3,3,1]
[4,7,1,5,8,3,2,6]=>[1,4,7,6,8,3,2,5]=>[8,5,2,3,1,6,7,4]=>[1,1,2,3,1]
[7,5,8,2,4,6,1,3]=>[7,4,2,5,1,8,6,3]=>[2,5,7,4,8,1,3,6]=>[3,2,3]
[7,3,5,8,1,4,6,2]=>[6,2,3,8,5,1,7,4]=>[3,7,6,1,4,8,2,5]=>[2,1,3,2]
[4,5,1,7,8,3,6,2]=>[1,2,6,4,8,7,3,5]=>[8,7,3,5,1,2,6,4]=>[1,1,2,3,1]
[7,4,1,5,8,3,6,2]=>[4,2,6,8,7,3,1,5]=>[5,7,3,1,2,6,8,4]=>[2,1,4,1]
[6,7,4,3,8,1,5,2]=>[4,3,1,8,6,2,7,5]=>[5,6,8,1,3,7,2,4]=>[3,3,2]
[6,7,4,8,3,1,5,2]=>[3,1,8,6,5,2,7,4]=>[6,8,1,3,4,7,2,5]=>[2,4,2]
[6,7,4,8,3,5,2,1]=>[3,1,5,2,8,7,6,4]=>[6,8,4,7,1,2,3,5]=>[2,2,4]
[5,6,7,3,8,4,2,1]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[1,1,3,3]
[5,6,7,3,1,8,4,2]=>[1,4,2,8,7,5,3,6]=>[8,5,7,1,2,4,6,3]=>[1,2,4,1]
[5,6,1,7,3,8,4,2]=>[1,8,5,4,2,7,3,6]=>[8,1,4,5,7,2,6,3]=>[1,4,2,1]
[5,1,6,7,3,8,4,2]=>[3,1,8,5,4,7,2,6]=>[6,8,1,4,5,2,7,3]=>[2,3,2,1]
[6,4,7,1,8,3,5,2]=>[2,6,1,8,7,4,3,5]=>[7,3,8,1,2,5,6,4]=>[1,2,4,1]
[6,7,8,3,1,4,5,2]=>[6,4,1,8,5,2,7,3]=>[3,5,8,1,4,7,2,6]=>[3,3,2]
[6,7,2,8,4,5,1,3]=>[7,5,1,8,3,2,6,4]=>[2,4,8,1,6,7,3,5]=>[3,3,2]
[6,7,2,8,4,1,3,5]=>[6,7,3,1,5,2,8,4]=>[3,2,6,8,4,7,1,5]=>[1,3,2,2]
[5,1,6,7,3,2,8,4]=>[5,3,1,8,6,2,4,7]=>[4,6,8,1,3,7,5,2]=>[3,3,1,1]
[5,6,1,7,3,2,8,4]=>[5,1,8,6,3,2,4,7]=>[4,8,1,3,6,7,5,2]=>[2,4,1,1]
[5,6,7,3,2,1,8,4]=>[1,5,4,2,8,6,3,7]=>[8,4,5,7,1,3,6,2]=>[1,3,3,1]
[5,6,2,7,3,8,4,1]=>[1,8,5,3,2,4,7,6]=>[8,1,4,6,7,5,2,3]=>[1,4,1,2]
[5,6,2,7,3,1,8,4]=>[5,1,8,3,2,6,4,7]=>[4,8,1,6,7,3,5,2]=>[2,3,2,1]
[6,1,7,4,2,8,3,5]=>[7,4,8,5,2,1,3,6]=>[2,5,1,4,7,8,6,3]=>[2,4,1,1]
[6,7,2,1,8,3,4,5]=>[3,6,7,1,8,4,2,5]=>[6,3,2,8,1,5,7,4]=>[1,1,2,3,1]
[7,5,8,2,1,3,4,6]=>[5,4,6,2,7,1,8,3]=>[4,5,3,7,2,8,1,6]=>[2,2,2,2]
[5,7,3,1,8,2,4,6]=>[6,3,1,7,8,4,2,5]=>[3,6,8,2,1,5,7,4]=>[3,1,3,1]
[7,4,2,5,1,8,3,6]=>[7,3,2,4,8,5,1,6]=>[2,6,7,5,1,4,8,3]=>[3,1,3,1]
[6,7,4,2,1,8,3,5]=>[4,7,3,1,8,5,2,6]=>[5,2,6,8,1,4,7,3]=>[1,3,3,1]
[6,7,4,2,8,3,5,1]=>[6,3,1,8,4,2,7,5]=>[3,6,8,1,5,7,2,4]=>[3,3,2]
[3,6,7,2,8,4,5,1]=>[6,2,8,1,4,3,7,5]=>[3,7,1,8,5,6,2,4]=>[2,2,2,2]
[3,6,7,2,8,4,1,5]=>[7,4,1,2,6,3,8,5]=>[2,5,8,7,3,6,1,4]=>[3,1,2,2]
[3,6,7,2,1,8,4,5]=>[4,7,1,2,8,5,3,6]=>[5,2,8,7,1,4,6,3]=>[1,2,1,3,1]
[5,7,3,8,2,1,4,6]=>[3,1,6,5,7,2,8,4]=>[6,8,3,4,2,7,1,5]=>[2,2,2,2]
[3,4,7,8,2,1,5,6]=>[6,1,2,5,7,3,8,4]=>[3,8,7,4,2,6,1,5]=>[2,1,1,2,2]
[3,7,8,1,4,6,2,5]=>[5,7,8,1,4,2,6,3]=>[4,2,1,8,5,7,3,6]=>[1,1,2,2,2]
[3,4,7,8,2,6,1,5]=>[5,7,1,2,3,8,6,4]=>[4,2,8,7,6,1,3,5]=>[1,2,1,1,3]
[5,7,3,8,2,6,1,4]=>[3,1,5,7,2,8,6,4]=>[6,8,4,2,7,1,3,5]=>[2,1,2,3]
[3,6,7,2,8,5,1,4]=>[7,2,8,1,4,3,6,5]=>[2,7,1,8,5,6,3,4]=>[2,2,2,2]
[3,6,7,8,5,2,1,4]=>[2,7,6,1,3,8,5,4]=>[7,2,3,8,6,1,4,5]=>[1,3,1,3]
[3,6,7,8,5,2,4,1]=>[2,6,3,8,1,7,5,4]=>[7,3,6,1,8,2,4,5]=>[1,2,2,3]
[6,4,7,8,2,5,3,1]=>[8,2,1,5,3,7,6,4]=>[1,7,8,4,6,2,3,5]=>[3,2,3]
[6,4,7,8,2,1,5,3]=>[2,5,1,8,6,3,7,4]=>[7,4,8,1,3,6,2,5]=>[1,2,3,2]
[4,1,5,7,8,2,6,3]=>[1,8,3,6,4,7,2,5]=>[8,1,6,3,5,2,7,4]=>[1,2,2,2,1]
[5,3,7,8,1,6,2,4]=>[7,1,8,2,5,3,6,4]=>[2,8,1,7,4,6,3,5]=>[2,2,2,2]
[6,7,2,8,5,1,3,4]=>[6,7,1,8,3,2,5,4]=>[3,2,8,1,6,7,4,5]=>[1,2,3,2]
[6,4,1,7,8,2,5,3]=>[2,8,6,4,1,7,3,5]=>[7,1,3,5,8,2,6,4]=>[1,4,2,1]
[5,1,6,2,7,8,4,3]=>[5,3,1,8,7,2,4,6]=>[4,6,8,1,2,7,5,3]=>[3,3,1,1]
[5,6,2,1,7,8,4,3]=>[5,1,8,3,2,7,4,6]=>[4,8,1,6,7,2,5,3]=>[2,3,2,1]
[5,6,2,7,1,8,4,3]=>[1,8,7,3,2,5,4,6]=>[8,1,2,6,7,4,5,3]=>[1,4,2,1]
[5,6,2,7,8,4,3,1]=>[1,4,2,8,7,3,6,5]=>[8,5,7,1,2,6,3,4]=>[1,2,3,2]
[5,6,7,2,8,4,3,1]=>[1,2,8,7,4,3,6,5]=>[8,7,1,2,5,6,3,4]=>[1,1,4,2]
[5,6,7,2,1,8,4,3]=>[1,8,4,2,7,5,3,6]=>[8,1,5,7,2,4,6,3]=>[1,3,3,1]
[5,6,1,7,2,8,4,3]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[1,5,1,1]
[5,1,6,7,2,8,4,3]=>[3,1,8,7,5,2,4,6]=>[6,8,1,2,4,7,5,3]=>[2,4,1,1]
[6,4,7,1,8,2,5,3]=>[2,8,6,1,7,4,3,5]=>[7,1,3,8,2,5,6,4]=>[1,3,3,1]
[6,7,8,5,2,4,1,3]=>[5,1,7,2,8,6,4,3]=>[4,8,2,7,1,3,5,6]=>[2,2,4]
[6,7,8,3,5,1,4,2]=>[4,1,8,6,2,7,5,3]=>[5,8,1,3,7,2,4,6]=>[2,3,3]
[4,6,7,8,1,5,3,2]=>[2,8,1,7,5,3,6,4]=>[7,1,8,2,4,6,3,5]=>[1,2,3,2]
[5,1,6,7,8,4,3,2]=>[3,1,4,8,7,6,2,5]=>[6,8,5,1,2,3,7,4]=>[2,1,4,1]
[5,6,1,7,8,4,3,2]=>[1,4,2,8,7,6,3,5]=>[8,5,7,1,2,3,6,4]=>[1,2,4,1]
[5,6,7,1,8,4,3,2]=>[1,2,8,7,6,4,3,5]=>[8,7,1,2,3,5,6,4]=>[1,1,5,1]
[8,6,1,3,4,2,5,7]=>[4,6,3,5,7,2,8,1]=>[5,3,6,4,2,7,1,8]=>[1,2,1,2,2]
[8,3,2,5,1,6,4,7]=>[2,7,3,5,4,6,8,1]=>[7,2,6,4,5,3,1,8]=>[1,2,2,1,2]
[5,3,2,7,4,1,8,6]=>[2,5,1,8,3,6,4,7]=>[7,4,8,1,6,3,5,2]=>[1,2,2,2,1]
[7,5,3,8,2,4,6,1]=>[3,5,2,6,1,8,7,4]=>[6,4,7,3,8,1,2,5]=>[1,2,2,3]
[7,2,4,5,8,3,6,1]=>[3,4,6,8,2,1,7,5]=>[6,5,3,1,7,8,2,4]=>[1,1,1,3,2]
[8,2,4,5,6,3,1,7]=>[3,4,7,2,6,5,8,1]=>[6,5,2,7,3,4,1,8]=>[1,1,2,2,2]
[8,2,4,5,6,1,3,7]=>[3,6,2,4,7,5,8,1]=>[6,3,7,5,2,4,1,8]=>[1,2,1,2,2]
[8,1,2,4,5,6,3,7]=>[4,5,7,2,3,6,8,1]=>[5,4,2,7,6,3,1,8]=>[1,1,2,1,1,2]
[8,5,3,6,4,1,2,7]=>[3,6,2,7,5,4,8,1]=>[6,3,7,2,4,5,1,8]=>[1,2,3,2]
[8,4,1,5,6,3,2,7]=>[4,2,7,6,3,5,8,1]=>[5,7,2,3,6,4,1,8]=>[2,3,1,2]
[8,1,4,5,6,3,2,7]=>[3,4,7,6,2,5,8,1]=>[6,5,2,3,7,4,1,8]=>[1,1,3,1,2]
[4,5,3,7,2,1,8,6]=>[1,3,2,5,8,6,4,7]=>[8,6,7,4,1,3,5,2]=>[1,2,1,3,1]
[7,4,5,8,3,2,6,1]=>[2,3,6,5,1,8,7,4]=>[7,6,3,4,8,1,2,5]=>[1,1,3,3]
[4,3,6,7,2,8,5,1]=>[1,3,8,2,5,4,7,6]=>[8,6,1,7,4,5,2,3]=>[1,1,2,2,2]
[4,3,6,7,2,8,1,5]=>[1,5,2,3,7,4,8,6]=>[8,4,7,6,2,5,1,3]=>[1,2,1,2,2]
[1,4,3,6,7,2,8,5]=>[2,4,8,3,6,1,5,7]=>[7,5,1,6,3,8,4,2]=>[1,1,2,2,1,1]
[4,5,3,7,1,8,2,6]=>[1,3,2,7,8,5,4,6]=>[8,6,7,2,1,4,5,3]=>[1,2,1,3,1]
[4,1,5,3,7,2,8,6]=>[3,1,8,4,6,2,5,7]=>[6,8,1,5,3,7,4,2]=>[2,2,2,1,1]
[5,3,4,7,1,2,8,6]=>[2,3,1,8,5,6,4,7]=>[7,6,8,1,4,3,5,2]=>[1,2,2,2,1]
[7,5,8,2,1,4,6,3]=>[4,6,2,8,5,1,7,3]=>[5,3,7,1,4,8,2,6]=>[1,2,3,2]
[7,5,3,8,4,1,6,2]=>[8,3,2,6,5,1,7,4]=>[1,6,7,3,4,8,2,5]=>[3,3,2]
[7,4,5,8,3,6,1,2]=>[2,3,7,5,1,8,6,4]=>[7,6,2,4,8,1,3,5]=>[1,1,3,3]
[4,3,6,7,8,1,5,2]=>[1,3,8,2,6,4,7,5]=>[8,6,1,7,3,5,2,4]=>[1,1,2,2,2]
[1,6,4,7,8,3,5,2]=>[6,3,2,4,8,7,1,5]=>[3,6,7,5,1,2,8,4]=>[3,1,3,1]
[3,5,6,7,8,4,1,2]=>[2,3,7,1,4,8,6,5]=>[7,6,2,8,5,1,3,4]=>[1,1,2,1,3]
[3,1,5,6,7,8,4,2]=>[1,3,4,5,8,7,2,6]=>[8,6,5,4,1,2,7,3]=>[1,1,1,1,3,1]
[4,6,1,7,8,3,5,2]=>[6,1,4,2,8,7,3,5]=>[3,8,5,7,1,2,6,4]=>[2,2,3,1]
[3,6,7,1,4,8,5,2]=>[8,5,1,2,7,4,3,6]=>[1,4,8,7,2,5,6,3]=>[3,1,3,1]
[6,2,4,1,7,8,5,3]=>[3,5,8,2,1,7,4,6]=>[6,4,1,7,8,2,5,3]=>[1,1,3,2,1]
[2,6,7,1,4,8,3,5]=>[5,7,2,8,1,4,3,6]=>[4,2,7,1,8,5,6,3]=>[1,2,2,2,1]
[4,3,6,7,8,1,2,5]=>[1,6,2,3,7,4,8,5]=>[8,3,7,6,2,5,1,4]=>[1,2,1,2,2]
[1,5,3,6,7,8,2,4]=>[4,2,7,3,5,8,1,6]=>[5,7,2,6,4,1,8,3]=>[2,2,1,2,1]
[3,5,6,7,8,2,1,4]=>[2,3,7,1,6,4,8,5]=>[7,6,2,8,3,5,1,4]=>[1,1,2,2,2]
[3,5,6,7,8,2,4,1]=>[2,3,6,1,4,8,7,5]=>[7,6,3,8,5,1,2,4]=>[1,1,2,1,3]
[5,2,7,1,3,8,4,6]=>[7,8,2,1,4,5,3,6]=>[2,1,7,8,5,4,6,3]=>[1,3,1,2,1]
[5,3,1,7,8,2,4,6]=>[2,6,1,7,4,8,3,5]=>[7,3,8,2,5,1,6,4]=>[1,2,2,2,1]
[4,5,2,7,8,1,3,6]=>[1,6,2,7,3,4,8,5]=>[8,3,7,2,6,5,1,4]=>[1,2,2,1,2]
[4,2,6,7,8,3,1,5]=>[1,3,7,6,2,4,8,5]=>[8,6,2,3,7,5,1,4]=>[1,1,3,1,2]
[4,2,6,7,8,3,5,1]=>[1,3,6,4,8,2,7,5]=>[8,6,3,5,1,7,2,4]=>[1,1,2,2,2]
[3,6,2,7,4,8,5,1]=>[8,5,1,3,2,4,7,6]=>[1,4,8,6,7,5,2,3]=>[3,2,1,2]
[3,6,2,7,4,8,1,5]=>[5,7,1,3,2,4,8,6]=>[4,2,8,6,7,5,1,3]=>[1,2,2,1,2]
[3,2,1,6,4,7,8,5]=>[1,6,2,4,8,3,5,7]=>[8,3,7,5,1,6,4,2]=>[1,2,1,2,1,1]
[1,7,3,4,2,5,8,6]=>[3,4,8,5,6,1,2,7]=>[6,5,1,4,3,8,7,2]=>[1,1,2,2,1,1]
[7,8,4,2,1,3,6,5]=>[4,8,5,3,6,1,7,2]=>[5,1,4,6,3,8,2,7]=>[1,3,2,2]
[7,8,1,3,4,2,6,5]=>[4,5,8,3,6,1,7,2]=>[5,4,1,6,3,8,2,7]=>[1,1,2,2,2]
[7,8,3,4,2,1,6,5]=>[3,5,4,8,6,1,7,2]=>[6,4,5,1,3,8,2,7]=>[1,2,3,2]
[6,3,2,7,1,8,5,4]=>[8,2,7,3,1,5,4,6]=>[1,7,2,6,8,4,5,3]=>[2,3,2,1]
[3,6,2,7,1,8,5,4]=>[8,7,1,3,2,5,4,6]=>[1,2,8,6,7,4,5,3]=>[3,2,2,1]
[6,7,3,8,2,5,4,1]=>[8,3,1,5,2,7,6,4]=>[1,6,8,4,7,2,3,5]=>[3,2,3]
[6,4,7,8,5,2,3,1]=>[6,2,1,3,8,7,5,4]=>[3,7,8,6,1,2,4,5]=>[3,1,4]
[2,6,4,7,8,1,5,3]=>[8,3,2,6,1,4,7,5]=>[1,6,7,3,8,5,2,4]=>[3,2,1,2]
[4,6,2,7,8,1,5,3]=>[8,1,6,3,2,4,7,5]=>[1,8,3,6,7,5,2,4]=>[2,3,1,2]
[7,4,5,8,6,2,1,3]=>[2,3,7,6,1,8,5,4]=>[7,6,2,3,8,1,4,5]=>[1,1,3,3]
[7,4,1,5,8,6,2,3]=>[4,2,7,8,6,3,1,5]=>[5,7,2,1,3,6,8,4]=>[2,1,4,1]
[7,5,3,8,6,1,2,4]=>[3,6,2,7,1,8,5,4]=>[6,3,7,2,8,1,4,5]=>[1,2,2,3]
[7,5,8,2,1,6,3,4]=>[4,7,2,8,5,1,6,3]=>[5,2,7,1,4,8,3,6]=>[1,2,3,2]
[6,2,7,1,3,8,5,4]=>[8,7,2,4,1,5,3,6]=>[1,2,7,5,8,4,6,3]=>[3,2,2,1]
[6,3,1,7,8,2,5,4]=>[8,2,6,4,1,7,3,5]=>[1,7,3,5,8,2,6,4]=>[2,3,2,1]
[4,6,1,7,8,5,2,3]=>[7,1,4,2,8,6,3,5]=>[2,8,5,7,1,3,6,4]=>[2,2,3,1]
[5,1,2,6,7,8,4,3]=>[4,5,1,8,7,2,3,6]=>[5,4,8,1,2,7,6,3]=>[1,2,3,1,1]
[5,2,6,7,8,4,1,3]=>[3,1,7,4,8,2,6,5]=>[6,8,2,5,1,7,3,4]=>[2,2,2,2]
[5,2,6,7,8,4,3,1]=>[3,1,4,8,7,2,6,5]=>[6,8,5,1,2,7,3,4]=>[2,1,3,2]
[1,5,2,6,7,8,4,3]=>[4,2,5,8,7,1,3,6]=>[5,7,4,1,2,8,6,3]=>[2,1,3,1,1]
[1,6,4,7,8,5,2,3]=>[7,3,2,4,8,6,1,5]=>[2,6,7,5,1,3,8,4]=>[3,1,3,1]
[2,6,7,1,3,8,5,4]=>[8,7,4,1,2,5,3,6]=>[1,2,5,8,7,4,6,3]=>[4,1,2,1]
[6,7,8,2,1,5,4,3]=>[8,4,1,7,5,2,6,3]=>[1,5,8,2,4,7,3,6]=>[3,3,2]
[6,7,3,8,5,1,4,2]=>[8,3,1,6,2,7,5,4]=>[1,6,8,3,7,2,4,5]=>[3,2,3]
[6,4,7,8,5,3,1,2]=>[7,2,1,3,8,6,5,4]=>[2,7,8,6,1,3,4,5]=>[3,1,4]
[4,5,2,3,7,6,1,8]=>[1,7,3,2,4,6,5,8]=>[8,2,6,7,5,3,4,1]=>[1,3,1,2,1]
[6,4,3,7,2,5,1,8]=>[3,2,5,1,7,6,4,8]=>[6,7,4,8,2,3,5,1]=>[2,2,3,1]
[8,4,3,6,5,1,2,7]=>[3,2,6,7,5,4,8,1]=>[6,7,3,2,4,5,1,8]=>[2,1,3,2]
[4,6,2,7,3,5,1,8]=>[1,5,7,3,2,6,4,8]=>[8,4,2,6,7,3,5,1]=>[1,1,3,2,1]
[3,2,6,7,4,5,1,8]=>[5,1,3,7,2,6,4,8]=>[4,8,6,2,7,3,5,1]=>[2,1,2,2,1]
[4,7,2,6,5,3,1,8]=>[7,1,6,3,5,4,2,8]=>[2,8,3,6,4,5,7,1]=>[2,2,3,1]
[5,7,6,2,4,3,1,8]=>[1,7,4,6,5,3,2,8]=>[8,2,5,3,4,6,7,1]=>[1,2,4,1]
[1,7,5,4,8,3,6,2]=>[4,3,6,2,8,7,1,5]=>[5,6,3,7,1,2,8,4]=>[2,2,3,1]
[8,7,5,4,1,3,2,6]=>[7,5,6,4,3,8,2,1]=>[2,4,3,5,6,1,7,8]=>[2,3,3]
[6,8,5,4,2,1,3,7]=>[6,5,1,7,4,3,8,2]=>[3,4,8,2,5,6,1,7]=>[3,3,2]
[5,8,6,2,4,1,3,7]=>[4,1,6,7,5,3,8,2]=>[5,8,3,2,4,6,1,7]=>[2,1,3,2]
[4,8,2,6,5,1,3,7]=>[1,6,7,3,5,4,8,2]=>[8,3,2,6,4,5,1,7]=>[1,1,2,2,2]
[3,2,8,6,5,1,4,7]=>[6,7,1,5,2,4,8,3]=>[3,2,8,4,7,5,1,6]=>[1,2,2,1,2]
[5,1,6,2,4,8,7,3]=>[8,5,3,1,7,2,4,6]=>[1,4,6,8,2,7,5,3]=>[4,2,1,1]
[6,1,5,4,2,8,7,3]=>[4,3,8,7,2,1,5,6]=>[5,6,1,2,7,8,4,3]=>[2,4,1,1]
[7,1,5,4,8,2,6,3]=>[4,3,8,6,7,2,1,5]=>[5,6,1,3,2,7,8,4]=>[2,2,3,1]
[8,1,5,4,7,6,2,3]=>[4,3,7,8,6,2,5,1]=>[5,6,2,1,3,7,4,8]=>[2,1,3,2]
[1,8,6,7,4,5,3,2]=>[5,3,8,7,6,4,1,2]=>[4,6,1,2,3,5,8,7]=>[2,5,1]
[8,1,6,7,4,5,2,3]=>[7,5,3,8,6,2,4,1]=>[2,4,6,1,3,7,5,8]=>[3,3,2]
[7,1,6,8,4,2,5,3]=>[8,6,5,3,7,2,1,4]=>[1,3,4,6,2,7,8,5]=>[4,3,1]
[6,1,7,8,2,4,5,3]=>[6,8,5,3,1,7,2,4]=>[3,1,4,6,8,2,7,5]=>[1,4,2,1]
[5,1,7,2,8,4,6,3]=>[6,1,8,7,4,2,3,5]=>[3,8,1,2,5,7,6,4]=>[2,4,1,1]
[4,1,2,7,8,5,6,3]=>[1,6,4,8,7,2,3,5]=>[8,3,5,1,2,7,6,4]=>[1,2,3,1,1]
[3,2,1,7,8,5,6,4]=>[6,1,4,8,2,7,3,5]=>[3,8,5,1,7,2,6,4]=>[2,1,2,2,1]
[3,2,8,7,1,5,4,6]=>[7,1,5,6,8,2,4,3]=>[2,8,4,3,1,7,5,6]=>[2,1,1,2,2]
[4,8,2,7,1,5,3,6]=>[1,7,3,5,6,8,4,2]=>[8,2,6,4,3,1,5,7]=>[1,2,1,1,3]
[5,8,7,2,1,4,3,6]=>[4,1,7,5,6,8,3,2]=>[5,8,2,4,3,1,6,7]=>[2,2,1,3]
[6,8,7,1,2,4,3,5]=>[7,4,5,1,6,8,3,2]=>[2,5,4,8,3,1,6,7]=>[2,2,1,3]
[7,8,6,1,4,2,3,5]=>[6,7,4,5,1,8,3,2]=>[3,2,5,4,8,1,6,7]=>[1,2,2,3]
[8,7,6,1,4,3,2,5]=>[7,6,4,5,8,3,2,1]=>[2,3,5,4,1,6,7,8]=>[3,1,4]
[1,7,6,8,4,3,5,2]=>[6,5,3,2,8,7,1,4]=>[3,4,6,7,1,2,8,5]=>[4,3,1]
[1,6,7,8,3,4,5,2]=>[5,2,6,3,8,7,1,4]=>[4,7,3,6,1,2,8,5]=>[2,2,3,1]
[8,6,7,1,3,4,2,5]=>[5,7,4,6,2,8,3,1]=>[4,2,5,3,7,1,6,8]=>[1,2,2,3]
[7,6,8,1,3,2,4,5]=>[6,4,5,7,2,1,8,3]=>[3,5,4,2,7,8,1,6]=>[2,1,3,2]
[5,7,8,2,1,3,4,6]=>[5,4,1,6,7,2,8,3]=>[4,5,8,3,2,7,1,6]=>[3,1,2,2]
[4,7,2,8,1,3,5,6]=>[3,1,5,6,7,2,8,4]=>[6,8,4,3,2,7,1,5]=>[2,1,1,2,2]
[3,2,6,8,4,1,5,7]=>[6,1,5,2,3,7,8,4]=>[3,8,4,7,6,2,1,5]=>[2,2,1,1,2]
[4,6,2,8,3,1,5,7]=>[1,6,3,5,2,7,8,4]=>[8,3,6,4,7,2,1,5]=>[1,2,2,1,2]
[5,6,8,2,3,1,4,7]=>[4,1,6,5,2,7,8,3]=>[5,8,3,4,7,2,1,6]=>[2,3,1,2]
[6,5,8,3,2,1,4,7]=>[6,5,4,2,1,7,8,3]=>[3,4,5,7,8,2,1,6]=>[5,1,2]
[7,5,8,3,1,2,4,6]=>[5,6,4,2,7,1,8,3]=>[4,3,5,7,2,8,1,6]=>[1,3,2,2]
[8,5,7,3,1,4,2,6]=>[7,5,4,2,6,8,3,1]=>[2,4,5,7,3,1,6,8]=>[4,1,3]
[1,5,7,3,8,4,6,2]=>[2,6,8,4,3,7,1,5]=>[7,3,1,5,6,2,8,4]=>[1,1,3,2,1]
[1,4,3,7,8,5,6,2]=>[6,2,4,8,3,7,1,5]=>[3,7,5,1,6,2,8,4]=>[2,1,2,2,1]
[8,4,3,7,1,5,2,6]=>[3,2,7,5,6,8,4,1]=>[6,7,2,4,3,1,5,8]=>[2,2,1,3]
[6,4,3,8,2,1,5,7]=>[3,2,6,5,1,7,8,4]=>[6,7,3,4,8,2,1,5]=>[2,3,1,2]
[4,5,2,3,8,1,6,7]=>[3,1,4,2,6,7,8,5]=>[6,8,5,7,3,2,1,4]=>[2,2,1,1,2]
[3,2,5,4,8,1,6,7]=>[1,4,2,3,6,7,8,5]=>[8,5,7,6,3,2,1,4]=>[1,2,1,1,1,2]
[4,5,2,3,1,8,7,6]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[1,3,1,2,1]
[6,4,3,1,2,8,7,5]=>[3,2,8,7,4,1,5,6]=>[6,7,1,2,5,8,4,3]=>[2,4,1,1]
[7,4,3,1,8,2,6,5]=>[3,2,8,6,7,4,1,5]=>[6,7,1,3,2,5,8,4]=>[2,2,3,1]
[1,5,8,3,7,6,4,2]=>[8,2,7,4,6,5,1,3]=>[1,7,2,5,3,4,8,6]=>[2,2,3,1]
[8,5,1,3,7,6,2,4]=>[7,8,4,2,6,3,5,1]=>[2,1,5,7,3,6,4,8]=>[1,3,2,2]
[7,5,1,3,8,2,6,4]=>[8,4,6,2,7,3,1,5]=>[1,5,3,7,2,6,8,4]=>[2,2,3,1]
[6,5,1,3,2,8,7,4]=>[8,4,7,3,2,1,5,6]=>[1,5,2,6,7,8,4,3]=>[2,4,1,1]
[5,6,1,2,3,8,7,4]=>[8,7,3,1,4,2,5,6]=>[1,2,6,8,5,7,4,3]=>[4,2,1,1]
[4,6,2,1,3,8,7,5]=>[1,8,3,7,4,2,5,6]=>[8,1,6,2,5,7,4,3]=>[1,2,3,1,1]
[3,2,6,1,4,8,7,5]=>[8,1,7,2,4,3,5,6]=>[1,8,2,7,5,6,4,3]=>[2,2,2,1,1]
[3,2,7,1,8,4,6,5]=>[8,1,6,7,2,4,3,5]=>[1,8,3,2,7,5,6,4]=>[2,1,2,2,1]
[4,7,2,1,8,3,6,5]=>[1,8,3,6,7,4,2,5]=>[8,1,6,3,2,5,7,4]=>[1,2,1,3,1]
[5,7,1,2,8,3,6,4]=>[8,6,1,7,3,4,2,5]=>[1,3,8,2,6,5,7,4]=>[3,2,2,1]
[6,7,1,8,2,3,5,4]=>[8,5,6,1,7,3,2,4]=>[1,4,3,8,2,6,7,5]=>[2,2,3,1]
[7,6,1,8,3,2,5,4]=>[5,8,6,7,3,2,1,4]=>[4,1,3,2,6,7,8,5]=>[1,2,4,1]
[8,6,1,7,3,5,2,4]=>[5,7,8,6,3,2,4,1]=>[4,2,1,3,6,7,5,8]=>[1,1,4,2]
[1,6,8,7,3,5,4,2]=>[2,8,5,7,6,4,1,3]=>[7,1,4,2,3,5,8,6]=>[1,2,4,1]
[1,7,8,6,5,3,4,2]=>[6,2,8,7,5,4,1,3]=>[3,7,1,2,4,5,8,6]=>[2,5,1]
[8,7,1,6,5,3,2,4]=>[7,6,8,5,3,4,2,1]=>[2,3,1,4,6,5,7,8]=>[2,3,3]
[7,8,1,6,5,2,3,4]=>[6,7,8,5,3,1,4,2]=>[3,2,1,4,6,8,5,7]=>[1,1,4,2]
[6,8,1,7,2,5,3,4]=>[7,8,5,1,6,3,4,2]=>[2,1,4,8,3,6,5,7]=>[1,3,2,2]
[5,8,1,2,7,6,3,4]=>[7,1,8,6,3,4,5,2]=>[2,8,1,3,6,5,4,7]=>[2,3,1,2]
[4,8,2,1,7,6,3,5]=>[1,7,8,3,6,4,5,2]=>[8,2,1,6,3,5,4,7]=>[1,1,2,2,2]
[3,2,8,1,7,6,4,5]=>[7,8,1,6,2,4,5,3]=>[2,1,8,3,7,5,4,6]=>[1,2,2,1,2]
[4,1,2,8,7,6,5,3]=>[8,1,7,6,5,2,3,4]=>[1,8,2,3,4,7,6,5]=>[2,4,1,1]
[5,1,8,2,7,6,4,3]=>[1,8,7,6,4,5,2,3]=>[8,1,2,3,5,4,7,6]=>[1,4,2,1]
[6,1,8,7,2,5,4,3]=>[8,7,5,1,6,4,2,3]=>[1,2,4,8,3,5,7,6]=>[4,3,1]
[7,1,8,6,5,2,4,3]=>[8,6,7,5,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>[2,5,1]
[8,1,7,6,5,4,2,3]=>[7,8,6,5,4,2,3,1]=>[2,1,3,4,5,7,6,8]=>[1,5,2]
[3,1,6,2,4,8,7,5]=>[8,1,7,4,2,3,5,6]=>[1,8,2,5,7,6,4,3]=>[2,3,1,1,1]
[3,1,5,2,4,8,7,6]=>[1,3,8,7,2,4,5,6]=>[8,6,1,2,7,5,4,3]=>[1,1,3,1,1,1]
[4,5,1,2,3,8,7,6]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[1,4,1,1,1]
[4,6,1,2,3,8,7,5]=>[1,8,7,3,4,2,5,6]=>[8,1,2,6,5,7,4,3]=>[1,3,2,1,1]
[1,6,5,3,4,8,7,2]=>[8,4,3,2,5,7,1,6]=>[1,5,6,7,4,2,8,3]=>[4,1,2,1]
[6,1,5,2,4,8,7,3]=>[8,5,3,7,2,1,4,6]=>[1,4,6,2,7,8,5,3]=>[3,3,1,1]
[6,5,1,2,3,8,7,4]=>[8,7,3,4,2,1,5,6]=>[1,2,6,5,7,8,4,3]=>[3,3,1,1]
[6,4,1,2,3,8,7,5]=>[8,7,3,2,4,1,5,6]=>[1,2,6,7,5,8,4,3]=>[4,2,1,1]
[5,4,1,2,3,8,7,6]=>[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>[5,1,1,1]
[6,4,1,7,2,3,5,8]=>[5,6,2,7,3,1,4,8]=>[4,3,7,2,6,8,5,1]=>[1,2,3,1,1]
[6,4,1,8,2,3,5,7]=>[5,6,2,7,1,8,3,4]=>[4,3,7,2,8,1,6,5]=>[1,2,2,2,1]
[7,4,1,2,8,3,6,5]=>[8,6,2,7,3,4,1,5]=>[1,3,7,2,6,5,8,4]=>[3,2,2,1]
[7,5,1,2,8,3,6,4]=>[8,6,7,3,2,4,1,5]=>[1,3,2,6,7,5,8,4]=>[2,3,2,1]
[7,1,5,2,8,4,6,3]=>[6,3,8,7,2,4,1,5]=>[3,6,1,2,7,5,8,4]=>[2,3,2,1]
[1,7,5,3,8,4,6,2]=>[6,3,8,4,2,7,1,5]=>[3,6,1,5,7,2,8,4]=>[2,3,2,1]
[1,8,5,3,7,4,6,2]=>[6,3,8,4,7,5,1,2]=>[3,6,1,5,2,4,8,7]=>[2,2,3,1]
[8,5,1,2,7,3,6,4]=>[8,6,7,3,2,4,5,1]=>[1,3,2,6,7,5,4,8]=>[2,3,1,2]
[8,4,1,2,7,3,6,5]=>[8,6,2,7,3,4,5,1]=>[1,3,7,2,6,5,4,8]=>[3,2,1,2]
[8,4,1,7,2,3,5,6]=>[5,6,2,7,8,3,4,1]=>[4,3,7,2,1,6,5,8]=>[1,2,1,2,2]
[7,4,1,6,2,3,5,8]=>[5,6,2,7,3,4,1,8]=>[4,3,7,2,6,5,8,1]=>[1,2,2,2,1]
[8,6,1,7,2,3,5,4]=>[8,5,6,7,3,2,4,1]=>[1,4,3,2,6,7,5,8]=>[2,1,3,2]
[8,1,6,7,2,4,5,3]=>[6,8,5,3,7,2,4,1]=>[3,1,4,6,2,7,5,8]=>[1,3,2,2]
[1,8,6,7,3,4,5,2]=>[5,6,3,8,7,4,1,2]=>[4,3,6,1,2,5,8,7]=>[1,2,4,1]
[1,7,6,8,3,4,5,2]=>[5,6,3,2,8,7,1,4]=>[4,3,6,7,1,2,8,5]=>[1,3,3,1]
[7,1,6,8,2,4,5,3]=>[6,8,5,3,7,2,1,4]=>[3,1,4,6,2,7,8,5]=>[1,3,3,1]
[7,6,1,8,2,3,5,4]=>[8,5,6,7,3,2,1,4]=>[1,4,3,2,6,7,8,5]=>[2,1,4,1]
[4,7,1,2,8,3,6,5]=>[1,8,6,7,3,4,2,5]=>[8,1,3,2,6,5,7,4]=>[1,2,2,2,1]
[3,1,7,2,8,4,6,5]=>[8,1,6,7,4,2,3,5]=>[1,8,3,2,5,7,6,4]=>[2,1,3,1,1]
[3,1,2,7,8,5,6,4]=>[6,1,4,8,7,2,3,5]=>[3,8,5,1,2,7,6,4]=>[2,1,3,1,1]
[1,4,3,8,7,5,6,2]=>[6,8,2,7,3,5,1,4]=>[3,1,7,2,6,4,8,5]=>[1,2,2,2,1]
[4,1,2,8,7,5,6,3]=>[1,6,8,7,5,2,3,4]=>[8,3,1,2,4,7,6,5]=>[1,1,4,1,1]
[3,1,2,8,7,5,6,4]=>[6,8,1,7,5,2,3,4]=>[3,1,8,2,4,7,6,5]=>[1,2,3,1,1]
[3,1,8,2,7,4,6,5]=>[8,1,6,7,4,5,2,3]=>[1,8,3,2,5,4,7,6]=>[2,1,2,2,1]
[3,1,8,7,2,4,5,6]=>[1,5,6,7,8,4,2,3]=>[8,4,3,2,1,5,7,6]=>[1,1,1,1,3,1]
[3,1,7,6,2,4,5,8]=>[1,5,6,7,4,2,3,8]=>[8,4,3,2,5,7,6,1]=>[1,1,1,3,1,1]
[4,7,1,6,2,3,5,8]=>[5,1,6,7,3,4,2,8]=>[4,8,3,2,6,5,7,1]=>[2,1,2,2,1]
[4,8,1,6,2,3,5,7]=>[5,1,6,7,3,4,8,2]=>[4,8,3,2,6,5,1,7]=>[2,1,2,1,2]
[4,8,1,7,2,3,5,6]=>[5,1,6,7,8,3,4,2]=>[4,8,3,2,1,6,5,7]=>[2,1,1,2,2]
[4,8,1,2,7,3,6,5]=>[1,8,6,7,3,4,5,2]=>[8,1,3,2,6,5,4,7]=>[1,2,2,1,2]
[5,8,1,2,7,3,6,4]=>[8,6,1,7,3,4,5,2]=>[1,3,8,2,6,5,4,7]=>[3,2,1,2]
[5,1,8,2,7,4,6,3]=>[6,1,8,7,4,5,2,3]=>[3,8,1,2,5,4,7,6]=>[2,3,2,1]
[1,5,8,3,7,4,6,2]=>[2,6,8,4,7,5,1,3]=>[7,3,1,5,2,4,8,6]=>[1,1,2,3,1]
[6,1,8,7,2,4,5,3]=>[6,8,5,1,7,4,2,3]=>[3,1,4,8,2,5,7,6]=>[1,3,3,1]
[6,8,1,7,2,3,5,4]=>[8,5,6,1,7,3,4,2]=>[1,4,3,8,2,6,5,7]=>[2,2,2,2]
[6,8,7,1,2,3,4,5]=>[4,5,6,1,7,8,3,2]=>[5,4,3,8,2,1,6,7]=>[1,1,2,1,3]
[5,8,7,1,2,3,4,6]=>[4,5,1,6,7,8,3,2]=>[5,4,8,3,2,1,6,7]=>[1,2,1,1,3]
[5,8,6,1,2,3,4,7]=>[4,5,1,6,7,3,8,2]=>[5,4,8,3,2,6,1,7]=>[1,2,1,2,2]
[5,7,6,1,2,3,4,8]=>[4,5,1,6,7,3,2,8]=>[5,4,8,3,2,6,7,1]=>[1,2,1,3,1]
[7,8,1,6,2,3,5,4]=>[8,5,6,7,3,1,4,2]=>[1,4,3,2,6,8,5,7]=>[2,1,3,2]
[7,1,8,6,2,4,5,3]=>[6,8,5,7,4,2,1,3]=>[3,1,4,2,5,7,8,6]=>[1,2,4,1]
[1,7,8,6,3,4,5,2]=>[5,6,2,8,7,4,1,3]=>[4,3,7,1,2,5,8,6]=>[1,2,4,1]
[1,8,7,6,3,4,5,2]=>[5,6,8,7,4,3,1,2]=>[4,3,1,2,5,6,8,7]=>[1,1,5,1]
[8,1,7,6,2,4,5,3]=>[6,8,5,7,4,2,3,1]=>[3,1,4,2,5,7,6,8]=>[1,2,3,2]
[8,7,1,6,2,3,5,4]=>[8,5,6,7,3,4,2,1]=>[1,4,3,2,6,5,7,8]=>[2,1,2,3]
[3,2,5,1,6,4,8,7]=>[1,5,2,3,8,4,6,7]=>[8,4,7,6,1,5,3,2]=>[1,2,1,2,1,1]
[3,2,5,4,7,1,8,6]=>[1,3,8,2,4,6,5,7]=>[8,6,1,7,5,3,4,2]=>[1,1,2,1,2,1]
[4,2,5,3,7,6,8,1]=>[3,1,6,2,4,5,8,7]=>[6,8,3,7,5,4,1,2]=>[2,2,1,1,2]
[4,2,5,3,6,1,8,7]=>[4,2,1,3,5,8,6,7]=>[5,7,8,6,4,1,3,2]=>[3,1,1,2,1]
[4,2,5,1,6,3,8,7]=>[5,2,1,3,8,4,6,7]=>[4,7,8,6,1,5,3,2]=>[3,1,2,1,1]
[3,1,5,4,6,2,8,7]=>[1,4,3,5,8,2,6,7]=>[8,5,6,4,1,7,3,2]=>[1,2,1,2,1,1]
[4,1,5,3,6,2,8,7]=>[4,3,1,5,8,2,6,7]=>[5,6,8,4,1,7,3,2]=>[3,1,2,1,1]
[4,3,5,1,6,2,8,7]=>[2,1,5,3,8,4,6,7]=>[7,8,4,6,1,5,3,2]=>[2,2,2,1,1]
[4,3,5,2,7,1,8,6]=>[2,1,3,8,4,6,5,7]=>[7,8,6,1,5,3,4,2]=>[2,1,2,2,1]
[4,3,6,2,7,1,8,5]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[1,2,2,2,1]
[4,3,6,1,7,2,8,5]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[1,2,3,1,1]
[4,3,5,1,7,2,8,6]=>[2,1,3,8,6,4,5,7]=>[7,8,6,1,3,5,4,2]=>[2,1,3,1,1]
[3,1,5,4,7,2,8,6]=>[1,3,8,4,6,2,5,7]=>[8,6,1,5,3,7,4,2]=>[1,1,2,2,1,1]
[2,1,5,4,7,3,8,6]=>[3,8,1,4,6,2,5,7]=>[6,1,8,5,3,7,4,2]=>[1,2,1,2,1,1]
[3,1,5,4,7,6,8,2]=>[1,3,6,4,5,8,2,7]=>[8,6,3,5,4,1,7,2]=>[1,1,2,1,2,1]
[4,1,5,3,7,6,8,2]=>[3,1,6,4,5,8,2,7]=>[6,8,3,5,4,1,7,2]=>[2,2,1,2,1]
[4,3,6,1,7,5,8,2]=>[1,6,2,5,3,8,4,7]=>[8,3,7,4,6,1,5,2]=>[1,2,2,2,1]
[4,3,6,5,7,1,8,2]=>[1,4,2,3,8,6,5,7]=>[8,5,7,6,1,3,4,2]=>[1,2,1,3,1]
[5,3,6,4,7,2,8,1]=>[4,2,1,3,6,5,8,7]=>[5,7,8,6,3,4,1,2]=>[3,1,2,2]
[5,3,6,4,7,1,8,2]=>[4,2,1,3,8,6,5,7]=>[5,7,8,6,1,3,4,2]=>[3,1,3,1]
[5,3,6,1,7,4,8,2]=>[6,2,1,5,3,8,4,7]=>[3,7,8,4,6,1,5,2]=>[3,2,2,1]
[5,1,6,3,7,4,8,2]=>[6,4,3,1,5,8,2,7]=>[3,5,6,8,4,1,7,2]=>[4,1,2,1]
[4,1,6,3,7,5,8,2]=>[1,6,4,3,5,8,2,7]=>[8,3,5,6,4,1,7,2]=>[1,3,1,2,1]
[3,1,6,4,7,5,8,2]=>[6,1,4,3,5,8,2,7]=>[3,8,5,6,4,1,7,2]=>[2,2,1,2,1]
[2,1,6,4,7,5,8,3]=>[6,4,1,3,5,8,2,7]=>[3,5,8,6,4,1,7,2]=>[3,1,1,2,1]
[2,1,6,4,7,3,8,5]=>[8,4,1,3,6,2,5,7]=>[1,5,8,6,3,7,4,2]=>[3,1,2,1,1]
[3,1,6,4,7,2,8,5]=>[8,1,4,3,6,2,5,7]=>[1,8,5,6,3,7,4,2]=>[2,2,2,1,1]
[4,1,6,3,7,2,8,5]=>[1,8,4,3,6,2,5,7]=>[8,1,5,6,3,7,4,2]=>[1,3,2,1,1]
[5,1,6,3,7,2,8,4]=>[8,4,3,1,6,2,5,7]=>[1,5,6,8,3,7,4,2]=>[4,2,1,1]
[5,3,6,1,7,2,8,4]=>[8,2,1,6,4,3,5,7]=>[1,7,8,3,5,6,4,2]=>[3,3,1,1]
[5,3,6,2,7,1,8,4]=>[8,2,1,4,3,6,5,7]=>[1,7,8,5,6,3,4,2]=>[3,2,2,1]
[5,3,6,2,7,4,8,1]=>[6,2,1,4,3,5,8,7]=>[3,7,8,5,6,4,1,2]=>[3,2,1,2]
[5,2,6,3,7,4,8,1]=>[6,4,2,1,3,5,8,7]=>[3,5,7,8,6,4,1,2]=>[4,1,1,2]
[5,2,6,3,7,1,8,4]=>[8,4,2,1,3,6,5,7]=>[1,5,7,8,6,3,4,2]=>[4,1,2,1]
[5,2,6,1,7,3,8,4]=>[8,6,2,1,4,3,5,7]=>[1,3,7,8,5,6,4,2]=>[4,2,1,1]
[4,2,5,1,7,3,8,6]=>[3,1,8,2,6,4,5,7]=>[6,8,1,7,3,5,4,2]=>[2,2,2,1,1]
[4,2,6,1,7,3,8,5]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[1,3,2,1,1]
[4,2,6,3,7,5,8,1]=>[1,6,4,2,3,5,8,7]=>[8,3,5,7,6,4,1,2]=>[1,3,1,1,2]
[3,2,6,4,7,5,8,1]=>[6,1,4,2,3,5,8,7]=>[3,8,5,7,6,4,1,2]=>[2,2,1,1,2]
[3,2,6,4,7,1,8,5]=>[8,1,4,2,3,6,5,7]=>[1,8,5,7,6,3,4,2]=>[2,2,1,2,1]
[3,2,6,1,7,4,8,5]=>[8,1,6,2,4,3,5,7]=>[1,8,3,7,5,6,4,2]=>[2,2,2,1,1]
[3,2,5,1,7,4,8,6]=>[1,3,8,2,6,4,5,7]=>[8,6,1,7,3,5,4,2]=>[1,1,2,2,1,1]
[3,2,4,1,7,5,8,6]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[1,2,1,2,1,1]
[3,1,4,2,7,6,8,5]=>[1,6,3,5,8,2,4,7]=>[8,3,6,4,1,7,5,2]=>[1,2,1,2,1,1]
[3,2,5,1,7,6,8,4]=>[1,3,6,2,5,8,4,7]=>[8,6,3,7,4,1,5,2]=>[1,1,2,1,2,1]
[3,2,6,1,7,5,8,4]=>[6,1,5,2,3,8,4,7]=>[3,8,4,7,6,1,5,2]=>[2,2,1,2,1]
[3,2,6,5,7,1,8,4]=>[4,1,3,8,2,6,5,7]=>[5,8,6,1,7,3,4,2]=>[2,1,2,2,1]
[4,2,6,5,7,3,8,1]=>[1,4,3,6,2,5,8,7]=>[8,5,6,3,7,4,1,2]=>[1,2,2,1,2]
[4,2,6,5,7,1,8,3]=>[1,4,3,8,2,6,5,7]=>[8,5,6,1,7,3,4,2]=>[1,2,2,2,1]
[4,2,6,1,7,5,8,3]=>[1,6,5,2,3,8,4,7]=>[8,3,4,7,6,1,5,2]=>[1,3,1,2,1]
[4,2,5,1,7,6,8,3]=>[3,1,6,2,5,8,4,7]=>[6,8,3,7,4,1,5,2]=>[2,2,1,2,1]
[4,1,5,2,7,6,8,3]=>[3,1,6,5,8,2,4,7]=>[6,8,3,4,1,7,5,2]=>[2,2,2,1,1]
[2,1,5,3,7,6,8,4]=>[3,6,1,5,8,2,4,7]=>[6,3,8,4,1,7,5,2]=>[1,2,1,2,1,1]
[2,1,6,3,7,5,8,4]=>[6,5,1,3,8,2,4,7]=>[3,4,8,6,1,7,5,2]=>[3,1,2,1,1]
[3,1,6,2,7,5,8,4]=>[6,1,5,3,8,2,4,7]=>[3,8,4,6,1,7,5,2]=>[2,2,2,1,1]
[5,1,6,2,7,4,8,3]=>[6,5,3,1,8,2,4,7]=>[3,4,6,8,1,7,5,2]=>[4,2,1,1]
[5,2,6,1,7,4,8,3]=>[6,5,2,1,3,8,4,7]=>[3,4,7,8,6,1,5,2]=>[4,1,2,1]
[5,2,6,4,7,1,8,3]=>[4,3,1,8,2,6,5,7]=>[5,6,8,1,7,3,4,2]=>[3,2,2,1]
[5,4,6,2,7,3,8,1]=>[2,1,6,4,3,5,8,7]=>[7,8,3,5,6,4,1,2]=>[2,3,1,2]
[5,4,6,2,7,1,8,3]=>[2,1,8,4,3,6,5,7]=>[7,8,1,5,6,3,4,2]=>[2,3,2,1]
[5,4,6,1,7,2,8,3]=>[2,1,8,6,4,3,5,7]=>[7,8,1,3,5,6,4,2]=>[2,4,1,1]
[2,1,6,5,7,3,8,4]=>[4,3,8,1,6,2,5,7]=>[5,6,1,8,3,7,4,2]=>[2,2,2,1,1]
[3,1,6,5,7,4,8,2]=>[4,1,3,6,5,8,2,7]=>[5,8,6,3,4,1,7,2]=>[2,1,2,2,1]
[4,1,6,5,7,3,8,2]=>[1,4,3,6,5,8,2,7]=>[8,5,6,3,4,1,7,2]=>[1,2,2,2,1]
[5,1,6,4,7,3,8,2]=>[4,3,1,6,5,8,2,7]=>[5,6,8,3,4,1,7,2]=>[3,2,2,1]
[5,4,6,1,7,3,8,2]=>[2,1,6,5,3,8,4,7]=>[7,8,3,4,6,1,5,2]=>[2,3,2,1]
[5,4,6,3,7,1,8,2]=>[2,1,4,3,8,6,5,7]=>[7,8,5,6,1,3,4,2]=>[2,2,3,1]
[8,3,5,2,1,6,4,7]=>[2,4,7,5,3,6,8,1]=>[7,5,2,4,6,3,1,8]=>[1,1,3,1,2]
[8,6,3,5,2,4,1,7]=>[3,5,7,6,4,2,8,1]=>[6,4,2,3,5,7,1,8]=>[1,1,4,2]
[3,7,5,2,4,1,8,6]=>[4,5,1,3,8,6,2,7]=>[5,4,8,6,1,3,7,2]=>[1,2,1,3,1]
[8,3,7,5,2,4,6,1]=>[5,6,2,4,8,7,3,1]=>[4,3,7,5,1,2,6,8]=>[1,2,1,4]
[8,2,4,5,7,3,6,1]=>[3,4,6,8,2,7,5,1]=>[6,5,3,1,7,2,4,8]=>[1,1,1,2,3]
[2,4,5,7,3,1,8,6]=>[2,3,5,8,1,6,4,7]=>[7,6,4,1,8,3,5,2]=>[1,1,1,2,2,1]
[8,2,5,4,6,1,3,7]=>[6,4,2,3,7,5,8,1]=>[3,5,7,6,2,4,1,8]=>[3,1,2,2]
[8,6,1,4,5,3,2,7]=>[4,7,6,3,5,2,8,1]=>[5,2,3,6,4,7,1,8]=>[1,3,2,2]
[5,7,4,3,2,1,8,6]=>[1,5,4,3,8,6,2,7]=>[8,4,5,6,1,3,7,2]=>[1,3,3,1]
[8,5,7,4,3,2,6,1]=>[2,6,5,4,8,7,3,1]=>[7,3,4,5,1,2,6,8]=>[1,3,4]
[4,6,8,3,2,7,5,1]=>[4,1,2,8,5,7,6,3]=>[5,8,7,1,4,2,3,6]=>[2,1,2,3]
[4,7,6,3,2,8,1,5]=>[5,1,4,7,3,2,8,6]=>[4,8,5,2,6,7,1,3]=>[2,1,3,2]
[1,4,6,7,3,2,8,5]=>[5,2,3,8,6,1,4,7]=>[4,7,6,1,3,8,5,2]=>[2,1,3,1,1]
[1,7,4,5,3,2,8,6]=>[3,5,4,8,6,1,2,7]=>[6,4,5,1,3,8,7,2]=>[1,2,3,1,1]
[3,7,5,1,4,2,8,6]=>[5,8,1,4,3,6,2,7]=>[4,1,8,5,6,3,7,2]=>[1,2,2,2,1]
[5,7,4,2,1,3,8,6]=>[4,1,8,5,3,6,2,7]=>[5,8,1,4,6,3,7,2]=>[2,3,2,1]
[8,5,7,4,2,1,6,3]=>[5,2,8,6,4,7,3,1]=>[4,7,1,3,5,2,6,8]=>[2,3,3]
[8,3,7,5,1,4,6,2]=>[6,8,2,5,4,7,3,1]=>[3,1,7,4,5,2,6,8]=>[1,2,2,3]
[8,4,1,7,5,3,6,2]=>[2,6,5,8,7,3,4,1]=>[7,3,4,1,2,6,5,8]=>[1,2,3,2]
[4,6,3,8,7,1,5,2]=>[8,1,3,2,6,7,5,4]=>[1,8,6,7,3,2,4,5]=>[2,2,1,3]
[8,4,7,6,3,5,2,1]=>[5,8,2,7,6,4,3,1]=>[4,1,7,2,3,5,6,8]=>[1,2,5]
[3,6,5,8,7,4,1,2]=>[3,2,7,8,1,6,5,4]=>[6,7,2,1,8,3,4,5]=>[2,1,2,3]
[3,1,5,8,6,7,4,2]=>[5,8,1,3,7,6,2,4]=>[4,1,8,6,2,3,7,5]=>[1,2,1,3,1]
[4,8,1,6,7,3,5,2]=>[6,1,4,8,7,3,5,2]=>[3,8,5,1,2,6,4,7]=>[2,1,3,2]
[3,6,4,1,8,7,5,2]=>[8,3,1,2,7,6,4,5]=>[1,6,8,7,2,3,5,4]=>[3,1,3,1]
[8,2,6,1,4,7,5,3]=>[8,5,7,2,4,3,6,1]=>[1,4,2,7,5,6,3,8]=>[2,2,2,2]
[2,7,6,8,1,4,3,5]=>[7,5,6,3,1,2,8,4]=>[2,4,3,6,8,7,1,5]=>[2,3,1,2]
[3,7,1,6,4,8,2,5]=>[5,7,1,4,8,3,2,6]=>[4,2,8,5,1,6,7,3]=>[1,2,1,3,1]
[1,7,3,5,6,8,2,4]=>[4,7,3,5,2,8,1,6]=>[5,2,6,4,7,1,8,3]=>[1,2,2,2,1]
[1,3,6,7,5,8,2,4]=>[3,7,5,2,4,8,1,6]=>[6,2,4,7,5,1,8,3]=>[1,3,1,2,1]
[3,7,6,5,8,2,1,4]=>[7,6,4,1,3,2,8,5]=>[2,3,5,8,6,7,1,4]=>[4,2,2]
[3,6,8,5,7,2,4,1]=>[2,6,4,8,1,7,5,3]=>[7,3,5,1,8,2,4,6]=>[1,2,2,3]
[2,3,5,7,6,8,1,4]=>[7,3,5,1,2,4,8,6]=>[2,6,4,8,7,5,1,3]=>[2,2,1,1,2]
[2,1,6,5,7,8,3,4]=>[4,3,7,1,5,8,2,6]=>[5,6,2,8,4,1,7,3]=>[2,2,1,2,1]
[4,2,7,6,8,3,1,5]=>[7,1,6,4,2,3,8,5]=>[2,8,3,5,7,6,1,4]=>[2,3,1,2]
[3,8,2,4,6,7,5,1]=>[5,8,1,3,4,7,6,2]=>[4,1,8,6,5,2,3,7]=>[1,2,1,1,3]
[3,7,2,6,4,8,1,5]=>[5,7,1,3,4,2,8,6]=>[4,2,8,6,5,7,1,3]=>[1,2,1,2,2]
[3,2,6,1,4,7,8,5]=>[1,6,8,2,4,3,5,7]=>[8,3,1,7,5,6,4,2]=>[1,1,2,2,1,1]
[5,3,7,2,1,8,4,6]=>[2,4,1,7,8,5,3,6]=>[7,5,8,2,1,4,6,3]=>[1,2,1,3,1]
[4,7,3,2,1,5,8,6]=>[1,4,3,8,5,6,2,7]=>[8,5,6,1,4,3,7,2]=>[1,2,2,2,1]
[8,7,6,1,3,4,2,5]=>[5,7,4,6,8,3,2,1]=>[4,2,5,3,1,6,7,8]=>[1,2,1,4]
[8,3,6,7,2,1,5,4]=>[5,8,2,6,3,7,4,1]=>[4,1,7,3,6,2,5,8]=>[1,2,2,3]
[8,7,6,3,5,2,4,1]=>[4,6,8,7,5,3,2,1]=>[5,3,1,2,4,6,7,8]=>[1,1,6]
[2,7,4,8,1,6,5,3]=>[8,3,7,5,1,2,6,4]=>[1,6,2,4,8,7,3,5]=>[2,3,1,2]
[4,6,8,2,1,7,5,3]=>[8,1,4,2,7,5,6,3]=>[1,8,5,7,2,4,3,6]=>[2,2,2,2]
[8,4,1,5,7,2,6,3]=>[4,2,8,6,7,3,5,1]=>[5,7,1,3,2,6,4,8]=>[2,2,2,2]
[8,5,3,7,1,6,2,4]=>[3,7,2,8,5,6,4,1]=>[6,2,7,1,4,3,5,8]=>[1,2,2,3]
[8,5,7,2,1,3,6,4]=>[4,8,5,2,6,7,3,1]=>[5,1,4,7,3,2,6,8]=>[1,3,1,3]
[8,2,6,7,1,3,5,4]=>[8,5,6,2,3,7,4,1]=>[1,4,3,7,6,2,5,8]=>[2,2,1,3]
[4,6,1,8,7,2,5,3]=>[8,1,6,2,7,5,3,4]=>[1,8,3,7,2,4,6,5]=>[2,2,3,1]
[8,1,2,5,6,7,4,3]=>[4,5,8,7,2,3,6,1]=>[5,4,1,2,7,6,3,8]=>[1,1,3,1,2]
[8,2,6,5,7,4,1,3]=>[7,4,3,8,2,6,5,1]=>[2,5,6,1,7,3,4,8]=>[3,2,3]
[2,1,7,8,5,6,4,3]=>[5,3,8,7,1,6,2,4]=>[4,6,1,2,8,3,7,5]=>[2,3,2,1]
[8,2,5,7,6,4,3,1]=>[8,3,7,6,2,5,4,1]=>[1,6,2,3,7,4,5,8]=>[2,3,3]
[2,7,6,8,5,4,1,3]=>[7,3,2,8,6,1,5,4]=>[2,6,7,1,3,8,4,5]=>[3,3,2]
[1,7,2,5,8,6,4,3]=>[8,4,7,6,3,1,2,5]=>[1,5,2,3,6,8,7,4]=>[2,4,1,1]
[1,7,4,8,2,6,5,3]=>[8,3,7,5,2,6,1,4]=>[1,6,2,4,7,3,8,5]=>[2,3,2,1]
[3,7,8,1,6,5,2,4]=>[7,8,6,1,4,2,5,3]=>[2,1,3,8,5,7,4,6]=>[1,3,2,2]
[2,7,8,6,1,3,5,4]=>[8,5,6,2,7,1,4,3]=>[1,4,3,7,2,8,5,6]=>[2,2,2,2]
[8,7,6,3,5,1,4,2]=>[4,8,6,7,5,3,2,1]=>[5,1,3,2,4,6,7,8]=>[1,2,5]
[8,4,7,6,5,1,3,2]=>[8,2,6,7,5,4,3,1]=>[1,7,3,2,4,5,6,8]=>[2,1,5]
[8,7,1,5,6,4,3,2]=>[4,8,7,6,3,5,2,1]=>[5,1,2,3,6,4,7,8]=>[1,4,3]
[8,1,6,7,5,4,3,2]=>[3,8,7,6,5,2,4,1]=>[6,1,2,3,4,7,5,8]=>[1,5,2]
[6,5,3,1,2,4,8,7]=>[8,4,3,5,2,1,6,7]=>[1,5,6,4,7,8,3,2]=>[3,3,1,1]
[8,5,3,7,2,1,4,6]=>[3,6,5,2,7,8,4,1]=>[6,3,4,7,2,1,5,8]=>[1,3,1,3]
[8,7,2,4,5,1,3,6]=>[6,3,4,7,5,8,2,1]=>[3,6,5,2,4,1,7,8]=>[2,1,2,3]
[3,6,2,4,5,1,8,7]=>[1,3,4,5,2,8,6,7]=>[8,6,5,4,7,1,3,2]=>[1,1,1,2,2,1]
[2,6,1,4,5,3,8,7]=>[4,5,8,1,3,2,6,7]=>[5,4,1,8,6,7,3,2]=>[1,1,2,2,1,1]
[6,1,2,4,5,3,8,7]=>[4,5,8,2,3,1,6,7]=>[5,4,1,7,6,8,3,2]=>[1,1,2,2,1,1]
[5,6,3,2,1,4,8,7]=>[4,3,1,8,5,2,6,7]=>[5,6,8,1,4,7,3,2]=>[3,3,1,1]
[5,4,3,6,1,2,8,7]=>[3,2,1,8,5,4,6,7]=>[6,7,8,1,4,5,3,2]=>[3,3,1,1]
[6,3,1,4,5,2,8,7]=>[4,2,5,8,3,1,6,7]=>[5,7,4,1,6,8,3,2]=>[2,1,3,1,1]
[3,1,6,4,5,2,8,7]=>[1,4,5,3,8,2,6,7]=>[8,5,4,6,1,7,3,2]=>[1,1,2,2,1,1]
[8,3,7,4,5,1,2,6]=>[6,2,4,7,5,8,3,1]=>[3,7,5,2,4,1,6,8]=>[2,1,2,3]
[5,8,7,4,2,6,3,1]=>[8,1,5,4,7,6,3,2]=>[1,8,4,5,2,3,6,7]=>[2,2,4]
[2,8,7,4,1,6,3,5]=>[7,4,8,5,6,1,3,2]=>[2,5,1,4,3,8,6,7]=>[2,2,2,2]
[8,1,7,4,2,6,3,5]=>[7,4,8,5,6,2,3,1]=>[2,5,1,4,3,7,6,8]=>[2,2,2,2]
[3,7,8,4,5,1,2,6]=>[6,4,7,1,5,2,8,3]=>[3,5,2,8,4,7,1,6]=>[2,2,2,2]
[2,1,8,7,5,3,4,6]=>[6,7,5,8,1,4,2,3]=>[3,2,4,1,8,5,7,6]=>[1,2,2,2,1]
[2,1,6,8,5,7,3,4]=>[3,7,5,8,1,6,2,4]=>[6,2,4,1,8,3,7,5]=>[1,2,2,2,1]
[5,6,3,8,1,7,2,4]=>[3,1,7,2,8,5,6,4]=>[6,8,2,7,1,4,3,5]=>[2,2,2,2]
[7,6,1,4,5,8,3,2]=>[4,5,8,7,3,2,1,6]=>[5,4,1,2,6,7,8,3]=>[1,1,5,1]
[3,7,6,4,5,8,2,1]=>[4,5,3,1,2,8,7,6]=>[5,4,6,8,7,1,2,3]=>[1,3,1,3]
[8,5,7,4,1,6,3,2]=>[2,8,7,5,4,6,3,1]=>[7,1,2,4,5,3,6,8]=>[1,4,3]
[5,1,8,4,7,6,2,3]=>[4,1,7,8,6,5,2,3]=>[5,8,2,1,3,4,7,6]=>[2,1,4,1]
[2,5,8,4,7,6,1,3]=>[2,4,7,8,6,1,5,3]=>[7,5,2,1,3,8,4,6]=>[1,1,1,3,2]
[2,4,8,3,5,6,7,1]=>[2,4,5,6,8,1,7,3]=>[7,5,4,3,1,8,2,6]=>[1,1,1,1,2,2]
[3,8,4,2,5,6,7,1]=>[4,1,3,5,6,8,7,2]=>[5,8,6,4,3,1,2,7]=>[2,1,1,1,3]
[7,5,8,4,3,6,1,2]=>[2,7,5,4,1,8,6,3]=>[7,2,4,5,8,1,3,6]=>[1,4,3]
[6,5,3,8,4,1,7,2]=>[8,3,2,1,6,5,7,4]=>[1,6,7,8,3,4,2,5]=>[4,2,2]
[2,1,5,8,4,6,7,3]=>[3,5,6,8,1,7,2,4]=>[6,4,3,1,8,2,7,5]=>[1,1,1,2,2,1]
[2,1,4,8,3,6,7,5]=>[6,8,1,3,5,7,2,4]=>[3,1,8,6,4,2,7,5]=>[1,2,1,1,2,1]
[6,4,3,8,2,1,7,5]=>[3,2,5,1,8,6,7,4]=>[6,7,4,8,1,3,2,5]=>[2,2,2,2]
[7,3,8,4,2,6,1,5]=>[5,2,4,7,1,8,6,3]=>[4,7,5,2,8,1,3,6]=>[2,1,2,3]
[8,3,1,2,5,6,7,4]=>[5,2,6,8,3,4,7,1]=>[4,7,3,1,6,5,2,8]=>[2,1,2,1,2]
[3,1,8,2,5,6,7,4]=>[1,5,6,8,4,7,2,3]=>[8,4,3,1,5,2,7,6]=>[1,1,1,2,2,1]
[2,3,8,1,5,6,7,4]=>[5,6,8,1,2,4,7,3]=>[4,3,1,8,7,5,2,6]=>[1,1,2,1,1,2]
[4,3,8,2,5,6,7,1]=>[2,1,4,5,6,8,7,3]=>[7,8,5,4,3,1,2,6]=>[2,1,1,1,3]
[4,8,2,3,5,6,7,1]=>[3,1,4,5,6,8,7,2]=>[6,8,5,4,3,1,2,7]=>[2,1,1,1,3]
[3,8,2,1,5,6,7,4]=>[1,3,5,6,8,4,7,2]=>[8,6,4,3,1,5,2,7]=>[1,1,1,1,2,2]
[2,8,1,3,5,6,7,4]=>[5,6,8,1,3,4,7,2]=>[4,3,1,8,6,5,2,7]=>[1,1,2,1,1,2]
[8,1,2,3,5,6,7,4]=>[5,6,8,2,3,4,7,1]=>[4,3,1,7,6,5,2,8]=>[1,1,2,1,1,2]
[7,8,2,4,3,6,1,5]=>[5,3,4,7,1,8,6,2]=>[4,6,5,2,8,1,3,7]=>[2,1,2,3]
[6,8,3,2,4,1,7,5]=>[4,3,5,1,8,6,7,2]=>[5,6,4,8,1,3,2,7]=>[2,2,2,2]
[2,1,8,3,4,6,7,5]=>[6,8,1,4,5,7,2,3]=>[3,1,8,5,4,2,7,6]=>[1,2,1,1,2,1]
[2,1,7,8,5,4,3,6]=>[7,6,5,1,3,8,2,4]=>[2,3,4,8,6,1,7,5]=>[4,1,2,1]
[5,7,3,8,1,4,2,6]=>[3,1,7,5,6,2,8,4]=>[6,8,2,4,3,7,1,5]=>[2,2,2,2]
[7,1,8,4,5,3,2,6]=>[4,7,6,5,8,2,1,3]=>[5,2,3,4,1,7,8,6]=>[1,3,3,1]
[2,7,8,4,5,3,1,6]=>[4,7,6,5,1,2,8,3]=>[5,2,3,4,8,7,1,6]=>[1,4,1,2]
[8,7,1,4,3,6,2,5]=>[5,4,7,8,3,6,2,1]=>[4,5,2,1,6,3,7,8]=>[2,1,2,3]
[3,8,7,4,2,6,1,5]=>[5,4,7,8,1,6,3,2]=>[4,5,2,1,8,3,6,7]=>[2,1,2,3]
[5,7,8,4,3,6,2,1]=>[5,1,4,2,8,7,6,3]=>[4,8,5,7,1,2,3,6]=>[2,2,4]
[5,6,3,8,4,2,7,1]=>[1,6,3,2,5,8,7,4]=>[8,3,6,7,4,1,2,5]=>[1,3,1,3]
[4,8,3,6,2,1,7,5]=>[1,3,5,8,6,4,7,2]=>[8,6,4,1,3,5,2,7]=>[1,1,1,3,2]
[7,5,3,8,2,4,1,6]=>[3,5,2,7,6,1,8,4]=>[6,4,7,2,3,8,1,5]=>[1,2,3,2]
[2,4,3,1,8,5,7,6]=>[2,8,1,3,6,7,4,5]=>[7,1,8,6,3,2,5,4]=>[1,2,1,1,2,1]
[4,1,3,2,6,8,7,5]=>[8,3,1,5,7,2,4,6]=>[1,6,8,4,2,7,5,3]=>[3,1,2,1,1]
[7,5,3,6,2,8,1,4]=>[3,5,2,7,4,1,8,6]=>[6,4,7,2,5,8,1,3]=>[1,2,3,2]
[5,8,3,2,6,1,7,4]=>[3,1,8,4,6,5,7,2]=>[6,8,1,5,3,4,2,7]=>[2,2,2,2]
[4,5,3,8,6,2,7,1]=>[1,2,6,3,5,8,7,4]=>[8,7,3,6,4,1,2,5]=>[1,1,2,1,3]
[3,5,8,4,7,6,2,1]=>[8,2,4,7,1,6,5,3]=>[1,7,5,2,8,3,4,6]=>[2,1,2,3]
[5,8,2,4,7,6,1,3]=>[4,1,7,8,3,6,5,2]=>[5,8,2,1,6,3,4,7]=>[2,1,2,3]
[8,7,5,4,1,6,2,3]=>[7,8,5,4,3,6,2,1]=>[2,1,4,5,6,3,7,8]=>[1,4,3]
[2,7,6,4,5,8,1,3]=>[4,7,5,3,1,2,8,6]=>[5,2,4,6,8,7,1,3]=>[1,4,1,2]
[7,1,6,4,5,8,2,3]=>[4,7,5,3,8,2,1,6]=>[5,2,4,6,1,7,8,3]=>[1,3,3,1]
[5,7,3,6,1,8,2,4]=>[3,1,7,8,5,4,2,6]=>[6,8,2,1,4,5,7,3]=>[2,1,4,1]
[2,1,7,6,5,8,3,4]=>[7,5,4,1,3,8,2,6]=>[2,4,5,8,6,1,7,3]=>[4,1,2,1]
[2,1,8,5,3,6,7,4]=>[6,4,8,1,5,7,2,3]=>[3,5,1,8,4,2,7,6]=>[2,2,1,2,1]
[7,8,5,4,2,6,1,3]=>[5,7,4,3,1,8,6,2]=>[4,2,5,6,8,1,3,7]=>[1,4,3]
[8,1,4,2,5,6,7,3]=>[5,3,6,8,2,4,7,1]=>[4,6,3,1,7,5,2,8]=>[2,1,2,1,2]
[3,4,8,1,5,6,7,2]=>[1,2,5,6,8,4,7,3]=>[8,7,4,3,1,5,2,6]=>[1,1,1,1,2,2]
[3,4,2,8,5,6,7,1]=>[1,2,5,6,8,3,7,4]=>[8,7,4,3,1,6,2,5]=>[1,1,1,1,2,2]
[2,4,1,8,5,6,7,3]=>[2,5,6,8,1,7,3,4]=>[7,4,3,1,8,2,6,5]=>[1,1,1,2,2,1]
[4,1,2,8,5,6,7,3]=>[5,1,6,8,7,2,3,4]=>[4,8,3,1,2,7,6,5]=>[2,1,3,1,1]
[8,4,2,1,5,6,7,3]=>[3,5,2,6,8,4,7,1]=>[6,4,7,3,1,5,2,8]=>[1,2,1,2,2]
[7,5,2,4,8,6,1,3]=>[4,7,2,8,3,1,6,5]=>[5,2,7,1,6,8,3,4]=>[1,2,3,2]
[6,5,3,2,8,1,7,4]=>[3,8,4,2,1,6,7,5]=>[6,1,5,7,8,3,2,4]=>[1,4,1,2]
[2,1,5,3,8,6,7,4]=>[3,6,8,1,7,2,4,5]=>[6,3,1,8,2,7,5,4]=>[1,1,2,2,1,1]
[6,4,3,5,8,1,7,2]=>[3,2,4,1,8,6,7,5]=>[6,7,5,8,1,3,2,4]=>[2,2,2,2]
[7,3,5,4,8,6,1,2]=>[4,2,3,7,1,8,6,5]=>[5,7,6,2,8,1,3,4]=>[2,1,2,3]
[8,3,4,1,5,6,7,2]=>[2,5,3,6,8,4,7,1]=>[7,4,6,3,1,5,2,8]=>[1,2,1,2,2]
[4,3,1,8,5,6,7,2]=>[2,1,5,6,8,7,3,4]=>[7,8,4,3,1,2,6,5]=>[2,1,1,3,1]
[3,1,4,8,5,6,7,2]=>[1,5,6,8,3,7,2,4]=>[8,4,3,1,6,2,7,5]=>[1,1,1,2,2,1]
[6,5,3,7,2,8,4,1]=>[8,3,2,1,5,4,7,6]=>[1,6,7,8,4,5,2,3]=>[4,2,2]
[6,3,7,4,5,8,2,1]=>[4,5,2,1,3,8,7,6]=>[5,4,7,8,6,1,2,3]=>[1,3,1,3]
[5,1,7,4,8,6,3,2]=>[1,8,4,3,7,6,2,5]=>[8,1,5,6,2,3,7,4]=>[1,3,3,1]
[2,5,7,4,8,6,3,1]=>[8,2,4,3,7,1,6,5]=>[1,7,5,6,2,8,3,4]=>[2,2,2,2]
[5,6,3,7,1,8,4,2]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[1,3,3,1]
[3,8,7,4,5,2,1,6]=>[4,7,6,1,5,8,3,2]=>[5,2,3,8,4,1,6,7]=>[1,3,1,3]
[3,7,5,4,8,6,2,1]=>[3,8,4,1,2,7,6,5]=>[6,1,5,8,7,2,3,4]=>[1,3,1,3]
[5,6,3,1,8,2,7,4]=>[3,1,8,6,2,7,4,5]=>[6,8,1,3,7,2,5,4]=>[2,3,2,1]
[4,6,3,5,8,2,7,1]=>[1,3,4,2,6,8,7,5]=>[8,6,5,7,3,1,2,4]=>[1,1,2,1,3]
[4,6,3,8,1,2,7,5]=>[1,3,8,5,2,6,7,4]=>[8,6,1,4,7,3,2,5]=>[1,1,3,1,2]
[3,7,8,4,1,6,2,5]=>[7,4,8,1,5,2,6,3]=>[2,5,1,8,4,7,3,6]=>[2,2,2,2]
[3,2,5,1,6,8,4,7]=>[1,5,2,3,7,8,4,6]=>[8,4,7,6,2,1,5,3]=>[1,2,1,1,2,1]
[3,6,2,5,4,8,1,7]=>[5,1,3,4,2,7,8,6]=>[4,8,6,5,7,2,1,3]=>[2,1,2,1,2]
[3,5,2,4,7,1,8,6]=>[8,1,3,2,4,6,5,7]=>[1,8,6,7,5,3,4,2]=>[2,2,1,2,1]
[3,5,8,2,4,7,6,1]=>[2,8,1,4,5,7,6,3]=>[7,1,8,5,4,2,3,6]=>[1,2,1,1,3]
[4,2,5,8,3,7,6,1]=>[1,8,3,5,7,2,6,4]=>[8,1,6,4,2,7,3,5]=>[1,2,1,2,2]
[5,4,2,1,6,8,3,7]=>[3,5,2,1,7,8,4,6]=>[6,4,7,8,2,1,5,3]=>[1,3,1,2,1]
[6,3,5,1,4,8,2,7]=>[2,5,7,3,1,8,4,6]=>[7,4,2,6,8,1,5,3]=>[1,1,3,2,1]
[4,6,1,5,3,8,2,7]=>[1,5,4,7,2,8,3,6]=>[8,4,5,2,7,1,6,3]=>[1,2,2,2,1]
[5,1,6,4,3,8,2,7]=>[5,4,3,1,7,8,2,6]=>[4,5,6,8,2,1,7,3]=>[4,1,2,1]
[5,4,3,2,7,1,8,6]=>[3,2,1,8,4,6,5,7]=>[6,7,8,1,5,3,4,2]=>[3,2,2,1]
[5,4,3,8,2,7,6,1]=>[2,1,8,3,5,7,6,4]=>[7,8,1,6,4,2,3,5]=>[2,2,1,3]
[4,3,6,2,8,7,5,1]=>[1,3,8,2,7,4,6,5]=>[8,6,1,7,2,5,3,4]=>[1,1,2,2,2]
[4,3,7,6,2,1,8,5]=>[1,5,8,2,6,4,3,7]=>[8,4,1,7,3,5,6,2]=>[1,1,2,3,1]
[6,4,3,1,7,2,8,5]=>[3,2,8,6,4,1,5,7]=>[6,7,1,3,5,8,4,2]=>[2,4,1,1]
[7,5,4,3,1,8,2,6]=>[7,4,3,2,8,5,1,6]=>[2,5,6,7,1,4,8,3]=>[4,3,1]
[1,4,7,5,8,3,2,6]=>[4,7,2,6,3,8,1,5]=>[5,2,7,3,6,1,8,4]=>[1,2,2,2,1]
[7,1,3,5,8,4,2,6]=>[4,7,3,6,8,2,1,5]=>[5,2,6,3,1,7,8,4]=>[1,2,1,3,1]
[7,2,5,8,4,1,3,6]=>[6,3,7,2,5,1,8,4]=>[3,6,2,7,4,8,1,5]=>[2,2,2,2]
[2,8,5,7,4,6,1,3]=>[3,7,5,8,6,1,4,2]=>[6,2,4,1,3,8,5,7]=>[1,2,3,2]
[3,5,8,7,1,4,6,2]=>[2,6,8,1,5,7,4,3]=>[7,3,1,8,4,2,5,6]=>[1,1,2,1,3]
[1,4,5,8,7,3,6,2]=>[6,8,2,3,7,5,1,4]=>[3,1,7,6,2,4,8,5]=>[1,2,1,3,1]
[1,5,4,8,7,3,6,2]=>[2,6,8,3,7,5,1,4]=>[7,3,1,6,2,4,8,5]=>[1,1,2,3,1]
[6,4,3,8,1,7,5,2]=>[2,8,3,1,7,5,6,4]=>[7,1,6,8,2,4,3,5]=>[1,3,2,2]
[4,3,7,1,8,6,5,2]=>[8,1,7,2,6,4,3,5]=>[1,8,2,7,3,5,6,4]=>[2,2,3,1]
[4,8,3,7,6,5,2,1]=>[8,7,1,3,6,5,4,2]=>[1,2,8,6,3,4,5,7]=>[3,1,4]
[5,3,8,7,6,4,2,1]=>[8,1,7,6,2,5,4,3]=>[1,8,2,3,7,4,5,6]=>[2,3,3]
[7,5,3,1,8,6,4,2]=>[8,3,2,7,6,4,1,5]=>[1,6,7,2,3,5,8,4]=>[3,4,1]
[1,8,6,5,3,7,4,2]=>[8,5,4,3,7,6,1,2]=>[1,4,5,6,2,3,8,7]=>[4,3,1]
[1,5,8,6,3,7,4,2]=>[8,2,5,4,7,6,1,3]=>[1,7,4,5,2,3,8,6]=>[2,2,3,1]
[4,6,1,8,7,3,5,2]=>[6,1,2,8,7,5,3,4]=>[3,8,7,1,2,4,6,5]=>[2,1,4,1]
[6,8,7,3,1,4,5,2]=>[6,4,1,8,5,7,3,2]=>[3,5,8,1,4,2,6,7]=>[3,2,3]
[6,2,8,7,4,5,1,3]=>[7,5,1,8,6,2,4,3]=>[2,4,8,1,3,7,5,6]=>[3,3,2]
[7,6,2,8,4,1,3,5]=>[6,7,3,5,2,1,8,4]=>[3,2,6,4,7,8,1,5]=>[1,2,3,2]
[7,3,1,6,8,4,2,5]=>[7,2,6,4,8,3,1,5]=>[2,7,3,5,1,6,8,4]=>[2,2,3,1]
[1,7,6,4,8,3,2,5]=>[4,7,6,3,2,8,1,5]=>[5,2,3,6,7,1,8,4]=>[1,4,2,1]
[5,7,1,6,3,2,8,4]=>[5,1,8,6,3,4,2,7]=>[4,8,1,3,6,5,7,2]=>[2,3,2,1]
[6,1,7,5,3,2,8,4]=>[5,8,6,4,2,1,3,7]=>[4,1,3,5,7,8,6,2]=>[1,5,1,1]
[7,6,5,3,2,1,8,4]=>[5,4,8,6,3,2,1,7]=>[4,5,1,3,6,7,8,2]=>[2,5,1]
[6,5,3,2,8,7,4,1]=>[8,3,2,1,7,4,6,5]=>[1,6,7,8,2,5,3,4]=>[4,2,2]
[5,2,6,3,8,7,4,1]=>[3,1,8,7,2,4,6,5]=>[6,8,1,2,7,5,3,4]=>[2,3,1,2]
[5,2,7,6,3,1,8,4]=>[5,1,8,6,2,4,3,7]=>[4,8,1,3,7,5,6,2]=>[2,3,2,1]
[6,5,2,1,7,3,8,4]=>[8,3,6,4,2,1,5,7]=>[1,6,3,5,7,8,4,2]=>[2,4,1,1]
[5,2,7,4,1,8,3,6]=>[7,4,1,8,2,5,3,6]=>[2,5,8,1,7,4,6,3]=>[3,2,2,1]
[4,7,2,6,3,1,8,5]=>[1,5,8,3,6,4,2,7]=>[8,4,1,6,3,5,7,2]=>[1,1,2,3,1]
[2,4,8,6,3,7,5,1]=>[8,5,2,4,7,1,6,3]=>[1,4,7,5,2,8,3,6]=>[3,1,2,2]
[3,8,6,2,4,7,5,1]=>[8,4,5,1,3,7,6,2]=>[1,5,4,8,6,2,3,7]=>[2,2,1,3]
[7,3,6,2,4,1,8,5]=>[2,4,5,8,6,3,1,7]=>[7,5,4,1,3,6,8,2]=>[1,1,1,4,1]
[3,6,7,2,1,4,8,5]=>[4,8,1,5,2,6,3,7]=>[5,1,8,4,7,3,6,2]=>[1,2,2,2,1]
[4,3,7,8,2,1,5,6]=>[1,6,2,5,7,3,8,4]=>[8,3,7,4,2,6,1,5]=>[1,2,1,2,2]
[8,3,7,1,4,6,2,5]=>[2,5,7,8,4,6,3,1]=>[7,4,2,1,5,3,6,8]=>[1,1,1,2,3]
[3,8,2,5,7,1,6,4]=>[4,8,1,3,6,7,5,2]=>[5,1,8,6,3,2,4,7]=>[1,2,1,1,3]
[8,3,6,2,7,1,5,4]=>[8,2,4,6,3,7,5,1]=>[1,7,5,3,6,2,4,8]=>[2,1,2,3]
[7,8,3,6,2,1,5,4]=>[3,5,8,6,1,7,4,2]=>[6,4,1,3,8,2,5,7]=>[1,1,3,3]
[8,7,3,6,2,5,4,1]=>[8,3,5,7,6,4,2,1]=>[1,6,4,2,3,5,7,8]=>[2,1,5]
[4,7,8,2,1,6,5,3]=>[8,1,4,7,5,2,6,3]=>[1,8,5,2,4,7,3,6]=>[2,1,3,2]
[4,2,6,8,1,7,5,3]=>[1,3,8,7,2,5,6,4]=>[8,6,1,2,7,4,3,5]=>[1,1,3,1,2]
[5,4,8,2,7,1,6,3]=>[2,1,8,4,6,7,5,3]=>[7,8,1,5,3,2,4,6]=>[2,2,1,3]
[4,8,1,5,7,2,6,3]=>[1,4,8,6,7,3,5,2]=>[8,5,1,3,2,6,4,7]=>[1,1,2,2,2]
[5,8,3,7,1,6,2,4]=>[3,1,7,8,5,6,4,2]=>[6,8,2,1,4,3,5,7]=>[2,1,2,3]
[5,8,7,2,6,1,3,4]=>[4,1,6,7,8,5,3,2]=>[5,8,3,2,1,4,6,7]=>[2,1,1,4]
[8,6,2,7,5,1,3,4]=>[6,7,8,3,2,5,4,1]=>[3,2,1,6,7,4,5,8]=>[1,1,3,3]
[3,6,8,1,7,5,2,4]=>[7,2,8,1,6,4,5,3]=>[2,7,1,8,3,5,4,6]=>[2,2,2,2]
[5,1,6,8,2,7,4,3]=>[3,1,8,7,5,6,2,4]=>[6,8,1,2,4,3,7,5]=>[2,3,2,1]
[6,5,2,8,1,7,4,3]=>[8,7,3,2,1,5,6,4]=>[1,2,6,7,8,4,3,5]=>[5,1,2]
[5,2,7,1,8,6,4,3]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[1,4,2,1]
[5,8,2,7,6,4,3,1]=>[8,1,7,6,3,5,4,2]=>[1,8,2,3,6,4,5,7]=>[2,3,3]
[6,2,8,7,5,4,3,1]=>[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>[1,5,2]
[7,6,2,1,8,5,4,3]=>[8,7,3,6,4,2,1,5]=>[1,2,6,3,5,7,8,4]=>[3,4,1]
[6,1,7,2,8,5,4,3]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[6,1,1]
[7,5,1,8,2,6,4,3]=>[8,7,5,2,6,3,1,4]=>[1,2,4,7,3,6,8,5]=>[4,3,1]
[4,7,1,8,6,2,5,3]=>[8,1,6,7,5,3,2,4]=>[1,8,3,2,4,6,7,5]=>[2,1,4,1]
[8,7,4,6,1,5,3,2]=>[3,8,7,5,6,4,2,1]=>[6,1,2,4,3,5,7,8]=>[1,3,4]
[8,5,7,1,6,4,3,2]=>[2,8,7,6,4,5,3,1]=>[7,1,2,3,5,4,6,8]=>[1,4,3]
[6,8,1,7,5,4,3,2]=>[1,8,7,6,5,3,4,2]=>[8,1,2,3,4,6,5,7]=>[1,5,2]
[7,1,8,6,5,4,3,2]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[7,1]
[5,4,2,3,7,6,1,8]=>[7,3,2,1,4,6,5,8]=>[2,6,7,8,5,3,4,1]=>[4,1,2,1]
[6,4,2,7,3,5,1,8]=>[5,2,7,3,1,6,4,8]=>[4,7,2,6,8,3,5,1]=>[2,3,2,1]
[7,4,2,6,3,5,1,8]=>[5,2,7,3,6,4,1,8]=>[4,7,2,6,3,5,8,1]=>[2,2,3,1]
[8,4,2,6,3,1,5,7]=>[6,3,2,5,7,4,8,1]=>[3,6,7,4,2,5,1,8]=>[3,1,2,2]
[3,2,7,6,4,5,1,8]=>[5,7,1,6,2,4,3,8]=>[4,2,8,3,7,5,6,1]=>[1,2,2,2,1]
[4,7,2,6,3,5,1,8]=>[1,5,7,3,6,4,2,8]=>[8,4,2,6,3,5,7,1]=>[1,1,2,3,1]
[5,7,6,2,3,4,1,8]=>[4,1,5,7,6,3,2,8]=>[5,8,4,2,3,6,7,1]=>[2,1,4,1]
[1,6,5,2,3,8,4,7]=>[7,8,4,3,1,2,5,6]=>[2,1,5,6,8,7,4,3]=>[1,4,1,1,1]
[1,7,5,2,8,3,4,6]=>[6,7,3,8,4,1,2,5]=>[3,2,6,1,5,8,7,4]=>[1,2,3,1,1]
[6,8,5,2,3,1,4,7]=>[4,6,5,1,7,3,8,2]=>[5,3,4,8,2,6,1,7]=>[1,3,2,2]
[5,8,6,2,3,1,4,7]=>[4,1,6,5,7,3,8,2]=>[5,8,3,4,2,6,1,7]=>[2,2,2,2]
[3,2,8,6,4,1,5,7]=>[6,1,5,7,2,4,8,3]=>[3,8,4,2,7,5,1,6]=>[2,1,2,1,2]
[3,2,1,6,4,8,5,7]=>[1,7,2,4,8,3,5,6]=>[8,2,7,5,1,6,4,3]=>[1,2,1,2,1,1]
[7,1,5,2,8,3,4,6]=>[6,7,3,8,2,4,1,5]=>[3,2,6,1,7,5,8,4]=>[1,2,2,2,1]
[1,8,5,2,7,3,4,6]=>[6,7,3,8,4,5,1,2]=>[3,2,6,1,5,4,8,7]=>[1,2,2,2,1]
[1,8,6,7,2,3,4,5]=>[5,6,7,3,8,4,1,2]=>[4,3,2,6,1,5,8,7]=>[1,1,2,3,1]
[8,1,6,7,2,3,4,5]=>[5,6,7,3,8,2,4,1]=>[4,3,2,6,1,7,5,8]=>[1,1,2,2,2]
[7,1,6,8,2,3,4,5]=>[5,6,7,3,8,2,1,4]=>[4,3,2,6,1,7,8,5]=>[1,1,2,3,1]
[3,2,1,7,8,4,5,6]=>[1,6,7,2,4,8,3,5]=>[8,3,2,7,5,1,6,4]=>[1,1,2,1,2,1]
[3,2,8,7,1,4,5,6]=>[1,5,6,7,8,2,4,3]=>[8,4,3,2,1,7,5,6]=>[1,1,1,1,2,2]
[5,8,7,2,1,3,4,6]=>[5,4,1,6,7,8,3,2]=>[4,5,8,3,2,1,6,7]=>[3,1,1,3]
[1,7,6,8,2,3,4,5]=>[5,6,7,3,2,8,1,4]=>[4,3,2,6,7,1,8,5]=>[1,1,3,2,1]
[6,5,8,2,3,1,4,7]=>[4,6,5,2,1,7,8,3]=>[5,3,4,7,8,2,1,6]=>[1,4,1,2]
[8,5,7,2,1,3,4,6]=>[5,4,6,2,7,8,3,1]=>[4,5,3,7,2,1,6,8]=>[2,2,1,3]
[6,4,2,8,3,1,5,7]=>[6,3,2,5,1,7,8,4]=>[3,6,7,4,8,2,1,5]=>[3,2,1,2]
[5,4,2,3,8,1,6,7]=>[3,4,2,1,6,7,8,5]=>[6,5,7,8,3,2,1,4]=>[1,3,1,1,2]
[3,2,5,4,1,8,6,7]=>[1,4,2,3,7,8,5,6]=>[8,5,7,6,2,1,4,3]=>[1,2,1,1,2,1]
[4,5,2,3,1,8,6,7]=>[3,1,4,2,7,8,5,6]=>[6,8,5,7,2,1,4,3]=>[2,2,1,2,1]
[5,4,2,3,1,8,6,7]=>[3,4,2,1,7,8,5,6]=>[6,5,7,8,2,1,4,3]=>[1,3,1,2,1]
[6,4,2,1,3,8,5,7]=>[3,7,2,8,4,1,5,6]=>[6,2,7,1,5,8,4,3]=>[1,2,3,1,1]
[7,4,2,1,8,3,5,6]=>[3,6,2,7,8,4,1,5]=>[6,3,7,2,1,5,8,4]=>[1,2,1,3,1]
[8,4,2,1,7,3,5,6]=>[3,6,2,7,8,4,5,1]=>[6,3,7,2,1,5,4,8]=>[1,2,1,2,2]
[1,4,2,8,7,3,5,6]=>[2,6,7,8,5,1,3,4]=>[7,3,2,1,4,8,6,5]=>[1,1,1,3,1,1]
[1,5,8,2,7,3,4,6]=>[6,2,7,8,4,5,1,3]=>[3,7,2,1,5,4,8,6]=>[2,1,2,2,1]
[8,5,1,2,7,3,4,6]=>[6,7,8,3,2,4,5,1]=>[3,2,1,6,7,5,4,8]=>[1,1,3,1,2]
[7,5,1,2,8,3,4,6]=>[6,7,8,3,2,4,1,5]=>[3,2,1,6,7,5,8,4]=>[1,1,3,2,1]
[6,5,1,2,3,8,4,7]=>[7,8,3,4,2,1,5,6]=>[2,1,6,5,7,8,4,3]=>[1,2,3,1,1]
[4,6,2,1,3,8,5,7]=>[3,1,7,8,4,2,5,6]=>[6,8,2,1,5,7,4,3]=>[2,1,3,1,1]
[3,2,6,1,4,8,5,7]=>[1,7,8,2,4,3,5,6]=>[8,2,1,7,5,6,4,3]=>[1,1,2,2,1,1]
[4,7,2,1,8,3,5,6]=>[3,1,6,7,8,4,2,5]=>[6,8,3,2,1,5,7,4]=>[2,1,1,3,1]
[7,6,1,8,2,3,4,5]=>[5,6,7,8,3,2,1,4]=>[4,3,2,1,6,7,8,5]=>[1,1,1,4,1]
[8,6,1,7,2,3,4,5]=>[5,6,7,8,3,2,4,1]=>[4,3,2,1,6,7,5,8]=>[1,1,1,3,2]
[1,6,8,7,2,3,4,5]=>[5,6,2,7,8,4,1,3]=>[4,3,7,2,1,5,8,6]=>[1,2,1,3,1]
[1,7,8,6,2,3,4,5]=>[5,6,7,2,8,4,1,3]=>[4,3,2,7,1,5,8,6]=>[1,1,2,3,1]
[7,8,1,6,2,3,4,5]=>[5,6,7,8,3,1,4,2]=>[4,3,2,1,6,8,5,7]=>[1,1,1,3,2]
[6,8,1,7,2,3,4,5]=>[5,6,7,1,8,3,4,2]=>[4,3,2,8,1,6,5,7]=>[1,1,2,2,2]
[4,8,2,1,7,3,5,6]=>[3,1,6,7,8,4,5,2]=>[6,8,3,2,1,5,4,7]=>[2,1,1,2,2]
[3,2,8,1,7,4,5,6]=>[1,6,7,8,2,4,5,3]=>[8,3,2,1,7,5,4,6]=>[1,1,1,2,1,2]
[3,2,1,8,7,4,5,6]=>[1,6,7,8,2,5,3,4]=>[8,3,2,1,7,4,6,5]=>[1,1,1,2,2,1]
[5,1,8,2,7,3,4,6]=>[6,7,1,8,4,5,2,3]=>[3,2,8,1,5,4,7,6]=>[1,2,2,2,1]
[6,1,8,7,2,3,4,5]=>[5,6,7,1,8,4,2,3]=>[4,3,2,8,1,5,7,6]=>[1,1,2,3,1]
[8,1,7,6,2,3,4,5]=>[5,6,7,8,4,2,3,1]=>[4,3,2,1,5,7,6,8]=>[1,1,1,3,2]
[1,8,7,6,2,3,4,5]=>[5,6,7,8,4,3,1,2]=>[4,3,2,1,5,6,8,7]=>[1,1,1,4,1]
[6,3,5,1,2,4,8,7]=>[2,8,4,5,3,1,6,7]=>[7,1,5,4,6,8,3,2]=>[1,2,3,1,1]
[4,3,5,6,1,2,8,7]=>[2,1,3,8,5,4,6,7]=>[7,8,6,1,4,5,3,2]=>[2,1,3,1,1]
[8,3,7,5,2,1,4,6]=>[6,2,5,7,4,8,3,1]=>[3,7,4,2,5,1,6,8]=>[2,1,2,3]
[6,3,7,5,1,8,4,2]=>[8,7,2,1,5,4,3,6]=>[1,2,7,8,4,5,6,3]=>[4,3,1]
[6,5,2,7,1,8,3,4]=>[7,8,3,2,1,5,4,6]=>[2,1,6,7,8,4,5,3]=>[1,4,2,1]
[8,5,2,7,4,1,3,6]=>[6,7,3,2,5,8,4,1]=>[3,2,6,7,4,1,5,8]=>[1,3,1,3]
[2,6,1,5,4,3,8,7]=>[5,4,8,1,3,2,6,7]=>[4,5,1,8,6,7,3,2]=>[2,2,2,1,1]
[5,3,1,4,6,2,8,7]=>[4,2,5,1,8,3,6,7]=>[5,7,4,8,1,6,3,2]=>[2,2,2,1,1]
[3,1,4,6,5,2,8,7]=>[1,5,3,4,8,2,6,7]=>[8,4,6,5,1,7,3,2]=>[1,2,1,2,1,1]
[5,7,4,6,2,8,3,1]=>[1,3,8,5,4,2,7,6]=>[8,6,1,4,5,7,2,3]=>[1,1,4,2]
[8,1,4,7,2,6,3,5]=>[3,7,8,5,6,2,4,1]=>[6,2,1,4,3,7,5,8]=>[1,1,2,2,2]
[3,4,7,8,5,2,1,6]=>[7,6,1,2,5,3,8,4]=>[2,3,8,7,4,6,1,5]=>[3,1,2,2]
[2,1,8,5,7,3,4,6]=>[6,4,7,8,1,5,2,3]=>[3,5,2,1,8,4,7,6]=>[2,1,2,2,1]
[5,8,2,4,6,7,3,1]=>[4,1,5,8,3,7,6,2]=>[5,8,4,1,6,2,3,7]=>[2,1,2,3]
[3,4,8,6,5,7,1,2]=>[7,5,1,2,4,8,6,3]=>[2,4,8,7,5,1,3,6]=>[3,1,1,3]
[7,5,4,8,1,6,3,2]=>[3,2,8,7,5,1,6,4]=>[6,7,1,2,4,8,3,5]=>[2,4,2]
[5,1,4,6,8,2,7,3]=>[3,4,1,8,6,7,2,5]=>[6,5,8,1,3,2,7,4]=>[1,2,2,2,1]
[2,4,6,3,7,5,8,1]=>[6,2,4,1,3,5,8,7]=>[3,7,5,8,6,4,1,2]=>[2,2,1,1,2]
[4,1,6,3,8,5,7,2]=>[1,6,3,8,4,7,2,5]=>[8,3,6,1,5,2,7,4]=>[1,2,2,2,1]
[3,7,4,2,8,6,5,1]=>[8,3,7,1,4,2,6,5]=>[1,6,2,8,5,7,3,4]=>[2,2,2,2]
[7,4,1,3,5,8,6,2]=>[8,4,2,5,7,3,1,6]=>[1,5,7,4,2,6,8,3]=>[3,1,3,1]
[6,5,8,4,1,7,3,2]=>[2,1,8,7,5,4,6,3]=>[7,8,1,2,4,5,3,6]=>[2,4,2]
[8,5,3,7,4,1,6,2]=>[8,3,2,6,5,7,4,1]=>[1,6,7,3,4,2,5,8]=>[3,2,3]
[2,1,4,8,3,7,6,5]=>[8,7,1,3,5,6,2,4]=>[1,2,8,6,4,3,7,5]=>[3,1,1,2,1]
[7,4,3,8,2,1,6,5]=>[3,2,5,8,6,1,7,4]=>[6,7,4,1,3,8,2,5]=>[2,1,3,2]
[6,3,7,4,1,8,2,5]=>[7,2,4,1,8,5,3,6]=>[2,7,5,8,1,4,6,3]=>[2,2,3,1]
[8,3,1,2,5,7,6,4]=>[2,8,5,7,3,4,6,1]=>[7,1,4,2,6,5,3,8]=>[1,2,2,1,2]
[3,1,8,2,7,6,5,4]=>[8,7,1,6,4,5,2,3]=>[1,2,8,3,5,4,7,6]=>[3,2,2,1]
[2,3,8,1,6,7,5,4]=>[5,8,7,1,2,4,6,3]=>[4,1,2,8,7,5,3,6]=>[1,3,1,1,2]
[4,3,7,2,6,8,5,1]=>[1,5,8,2,4,3,7,6]=>[8,4,1,7,5,6,2,3]=>[1,1,2,2,2]
[3,8,2,1,7,5,6,4]=>[6,8,1,3,7,4,5,2]=>[3,1,8,6,2,5,4,7]=>[1,2,1,2,2]
[2,8,1,3,6,5,7,4]=>[6,5,8,1,3,4,7,2]=>[3,4,1,8,6,5,2,7]=>[2,2,1,1,2]
[2,7,8,5,4,3,1,6]=>[7,6,5,4,1,2,8,3]=>[2,3,4,5,8,7,1,6]=>[5,1,2]
[8,7,1,6,3,4,2,5]=>[5,7,6,8,3,4,2,1]=>[4,2,3,1,6,5,7,8]=>[1,2,2,3]
[3,8,6,7,2,4,1,5]=>[5,7,6,1,3,8,4,2]=>[4,2,3,8,6,1,5,7]=>[1,3,1,3]
[5,3,8,7,4,2,6,1]=>[1,6,5,8,2,7,4,3]=>[8,3,4,1,7,2,5,6]=>[1,2,2,3]
[4,3,8,7,2,1,6,5]=>[1,5,8,2,6,7,4,3]=>[8,4,1,7,3,2,5,6]=>[1,1,2,1,3]
[8,3,6,1,4,2,7,5]=>[2,5,8,4,6,3,7,1]=>[7,4,1,5,3,6,2,8]=>[1,1,2,2,2]
[7,3,5,8,2,4,1,6]=>[5,2,3,7,6,1,8,4]=>[4,7,6,2,3,8,1,5]=>[2,1,3,2]
[2,3,4,1,8,5,7,6]=>[8,1,2,3,6,7,4,5]=>[1,8,7,6,3,2,5,4]=>[2,1,1,1,2,1]
[4,1,3,2,6,7,8,5]=>[3,5,1,6,8,2,4,7]=>[6,4,8,3,1,7,5,2]=>[1,2,1,2,1,1]
[8,3,5,6,2,7,1,4]=>[5,2,3,7,4,8,6,1]=>[4,7,6,2,5,1,3,8]=>[2,1,2,3]
[5,3,6,1,8,7,2,4]=>[7,2,1,3,8,6,4,5]=>[2,7,8,6,1,3,5,4]=>[3,1,3,1]
[5,6,2,8,7,4,1,3]=>[1,7,2,8,6,3,5,4]=>[8,2,7,1,3,6,4,5]=>[1,2,3,2]
[7,8,5,6,1,4,2,3]=>[7,8,5,3,1,6,4,2]=>[2,1,4,6,8,3,5,7]=>[1,4,3]
[2,8,6,5,4,7,1,3]=>[7,5,4,3,8,1,6,2]=>[2,4,5,6,1,8,3,7]=>[4,2,2]
[8,1,6,4,5,7,2,3]=>[4,7,5,3,8,2,6,1]=>[5,2,4,6,1,7,3,8]=>[1,3,2,2]
[5,8,3,6,1,7,2,4]=>[3,1,7,8,5,4,6,2]=>[6,8,2,1,4,5,3,7]=>[2,1,3,2]
[2,1,8,6,5,7,3,4]=>[7,5,4,8,1,6,2,3]=>[2,4,5,1,8,3,7,6]=>[3,2,2,1]
[2,1,7,5,3,6,8,4]=>[6,4,8,1,5,2,3,7]=>[3,5,1,8,4,7,6,2]=>[2,2,2,1,1]
[6,7,3,5,2,1,8,4]=>[3,5,1,8,6,4,2,7]=>[6,4,8,1,3,5,7,2]=>[1,2,4,1]
[7,1,4,2,5,6,8,3]=>[5,3,6,8,2,4,1,7]=>[4,6,3,1,7,5,8,2]=>[2,1,2,2,1]
[2,7,4,1,6,5,8,3]=>[3,6,5,8,1,4,2,7]=>[6,3,4,1,8,5,7,2]=>[1,2,2,2,1]
[4,6,1,2,8,7,3,5]=>[1,7,8,6,3,2,4,5]=>[8,2,1,3,6,7,5,4]=>[1,1,4,1,1]
[2,4,1,5,8,7,6,3]=>[8,2,7,1,4,6,3,5]=>[1,7,2,8,5,3,6,4]=>[2,2,1,2,1]
[4,1,2,5,8,6,7,3]=>[6,1,8,4,7,2,3,5]=>[3,8,1,5,2,7,6,4]=>[2,2,2,1,1]
[6,4,2,1,5,8,7,3]=>[8,3,2,5,1,7,4,6]=>[1,6,7,4,8,2,5,3]=>[3,2,2,1]
[8,5,2,4,6,1,7,3]=>[4,8,3,2,6,5,7,1]=>[5,1,6,7,3,4,2,8]=>[1,3,2,2]
[7,5,3,2,6,8,1,4]=>[3,7,4,2,5,1,8,6]=>[6,2,5,7,4,8,1,3]=>[1,3,2,2]
[2,1,5,3,6,8,7,4]=>[3,8,1,5,7,2,4,6]=>[6,1,8,4,2,7,5,3]=>[1,2,1,2,1,1]
[7,3,5,4,6,1,8,2]=>[4,2,3,8,6,5,1,7]=>[5,7,6,1,3,4,8,2]=>[2,1,4,1]
[6,3,4,1,5,7,8,2]=>[2,5,3,6,1,8,4,7]=>[7,4,6,3,8,1,5,2]=>[1,2,2,2,1]
[4,3,1,5,7,6,8,2]=>[2,1,6,4,5,8,3,7]=>[7,8,3,5,4,1,6,2]=>[2,2,1,2,1]
[4,5,2,6,3,1,8,7]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[1,3,1,2,1]
[6,5,2,1,4,3,8,7]=>[3,5,8,4,2,1,6,7]=>[6,4,1,5,7,8,3,2]=>[1,1,4,1,1]
[6,5,2,7,4,8,3,1]=>[5,4,2,1,8,3,7,6]=>[4,5,7,8,1,6,2,3]=>[4,2,2]
[8,5,2,7,4,1,6,3]=>[8,6,3,2,5,7,4,1]=>[1,3,6,7,4,2,5,8]=>[4,1,3]
[6,3,7,5,2,8,4,1]=>[8,5,2,1,4,3,7,6]=>[1,4,7,8,5,6,2,3]=>[4,2,2]
[3,1,6,5,4,2,8,7]=>[5,1,4,3,8,2,6,7]=>[4,8,5,6,1,7,3,2]=>[2,2,2,1,1]
[5,6,3,2,4,1,8,7]=>[4,3,1,5,2,8,6,7]=>[5,6,8,4,7,1,3,2]=>[3,2,2,1]
[3,6,2,4,1,5,8,7]=>[1,3,4,8,5,2,6,7]=>[8,6,5,1,4,7,3,2]=>[1,1,1,3,1,1]
[2,6,1,3,5,4,8,7]=>[5,8,1,3,4,2,6,7]=>[4,1,8,6,5,7,3,2]=>[1,2,1,2,1,1]
[6,7,2,3,4,8,5,1]=>[8,3,4,1,5,2,7,6]=>[1,6,5,8,4,7,2,3]=>[2,2,2,2]
[5,1,7,3,8,4,6,2]=>[6,1,8,4,3,7,2,5]=>[3,8,1,5,6,2,7,4]=>[2,3,2,1]
[2,5,7,3,8,6,4,1]=>[8,2,7,4,1,3,6,5]=>[1,7,2,5,8,6,3,4]=>[2,3,1,2]
[7,6,1,3,5,8,4,2]=>[5,8,4,7,3,2,1,6]=>[4,1,5,2,6,7,8,3]=>[1,2,4,1]
[3,6,7,4,1,8,5,2]=>[4,2,8,1,7,5,3,6]=>[5,7,1,8,2,4,6,3]=>[2,2,3,1]
[5,6,3,7,4,8,1,2]=>[1,7,3,2,5,4,8,6]=>[8,2,6,7,4,5,1,3]=>[1,3,2,2]
[2,1,6,7,4,8,5,3]=>[3,8,5,1,4,7,2,6]=>[6,1,4,8,5,2,7,3]=>[1,3,1,2,1]
[2,1,8,7,4,3,6,5]=>[5,8,6,7,1,4,2,3]=>[4,1,3,2,8,5,7,6]=>[1,2,2,2,1]
[5,8,3,7,4,2,6,1]=>[1,6,3,5,8,7,4,2]=>[8,3,6,4,1,2,5,7]=>[1,2,1,4]
[3,8,7,4,1,2,6,5]=>[8,5,1,4,6,7,3,2]=>[1,4,8,5,3,2,6,7]=>[3,1,1,3]
[7,8,1,3,5,2,6,4]=>[8,4,6,3,5,1,7,2]=>[1,5,3,6,4,8,2,7]=>[2,2,2,2]
[5,8,7,3,2,6,1,4]=>[1,5,4,7,8,6,3,2]=>[8,4,5,2,1,3,6,7]=>[1,2,1,4]
[2,8,6,3,1,5,7,4]=>[4,6,8,5,1,3,7,2]=>[5,3,1,4,8,6,2,7]=>[1,1,3,1,2]
[8,1,6,3,2,5,4,7]=>[4,7,5,6,2,3,8,1]=>[5,2,4,3,7,6,1,8]=>[1,2,2,1,2]
[2,8,4,1,6,3,7,5]=>[3,8,6,1,4,5,7,2]=>[6,1,3,8,5,4,2,7]=>[1,3,1,1,2]
[4,8,1,2,7,6,3,5]=>[1,7,8,6,3,4,5,2]=>[8,2,1,3,6,5,4,7]=>[1,1,3,1,2]
[3,8,4,2,5,7,1,6]=>[4,1,3,5,7,8,6,2]=>[5,8,6,4,2,1,3,7]=>[2,1,1,1,3]
[6,8,3,5,2,7,4,1]=>[8,3,1,5,4,7,6,2]=>[1,6,8,4,5,2,3,7]=>[3,2,3]
[2,1,5,3,8,7,6,4]=>[8,3,7,1,6,2,4,5]=>[1,6,2,8,3,7,5,4]=>[2,2,2,1,1]
[6,5,3,2,8,7,1,4]=>[3,7,2,1,8,4,6,5]=>[6,2,7,8,1,5,3,4]=>[1,3,2,2]
[7,5,2,4,8,1,6,3]=>[4,8,3,2,6,1,7,5]=>[5,1,6,7,3,8,2,4]=>[1,3,2,2]
[3,4,2,8,5,7,6,1]=>[8,1,2,5,7,3,6,4]=>[1,8,7,4,2,6,3,5]=>[2,1,1,2,2]
[2,4,1,8,7,6,5,3]=>[8,7,2,6,1,5,3,4]=>[1,2,7,3,8,4,6,5]=>[3,2,2,1]
[8,4,2,1,7,5,3,6]=>[7,3,2,6,8,4,5,1]=>[2,6,7,3,1,5,4,8]=>[3,1,2,2]
[4,3,1,8,6,7,5,2]=>[1,5,8,2,7,6,3,4]=>[8,4,1,7,2,3,6,5]=>[1,1,2,3,1]
[3,1,4,8,6,5,7,2]=>[6,1,5,8,3,7,2,4]=>[3,8,4,1,6,2,7,5]=>[2,1,2,2,1]
[7,1,6,5,4,8,2,3]=>[7,5,4,3,8,2,1,6]=>[2,4,5,6,1,7,8,3]=>[4,3,1]
[3,7,5,6,8,4,2,1]=>[3,4,2,8,1,7,6,5]=>[6,5,7,1,8,2,3,4]=>[1,2,2,3]
[5,6,2,1,8,7,3,4]=>[7,1,8,3,2,6,4,5]=>[2,8,1,6,7,3,5,4]=>[2,3,2,1]
[4,6,2,5,8,3,7,1]=>[1,4,6,2,8,3,7,5]=>[8,5,3,7,1,6,2,4]=>[1,1,2,2,2]
[7,5,2,6,3,8,1,4]=>[5,7,3,2,4,1,8,6]=>[4,2,6,7,5,8,1,3]=>[1,3,2,2]
[4,1,2,3,6,8,7,5]=>[8,5,1,7,2,3,4,6]=>[1,4,8,2,7,6,5,3]=>[3,2,1,1,1]
[2,4,3,1,8,5,6,7]=>[3,1,2,6,7,8,4,5]=>[6,8,7,3,2,1,5,4]=>[2,1,1,1,2,1]
[7,5,2,8,3,4,6,1]=>[5,6,2,8,3,1,7,4]=>[4,3,7,1,6,8,2,5]=>[1,2,3,2]
[5,6,2,8,4,3,1,7]=>[1,7,6,3,2,5,8,4]=>[8,2,3,6,7,4,1,5]=>[1,4,1,2]
[4,7,2,8,1,5,3,6]=>[1,7,3,5,6,2,8,4]=>[8,2,6,4,3,7,1,5]=>[1,2,1,2,2]
[8,7,2,1,4,5,6,3]=>[3,5,6,8,4,7,2,1]=>[6,4,3,1,5,2,7,8]=>[1,1,1,2,3]
[3,6,8,7,1,5,4,2]=>[2,8,7,1,5,6,4,3]=>[7,1,2,8,4,3,5,6]=>[1,3,1,3]
[5,7,8,6,3,4,1,2]=>[7,1,5,2,8,6,4,3]=>[2,8,4,7,1,3,5,6]=>[2,2,4]
[7,1,8,5,4,3,6,2]=>[6,5,4,8,7,2,1,3]=>[3,4,5,1,2,7,8,6]=>[3,4,1]
[2,7,8,4,5,3,6,1]=>[4,6,5,2,8,1,7,3]=>[5,3,4,7,1,8,2,6]=>[1,3,2,2]
[5,7,3,8,1,4,6,2]=>[3,1,6,8,5,2,7,4]=>[6,8,3,1,4,7,2,5]=>[2,1,3,2]
[2,1,7,8,5,4,6,3]=>[6,5,3,8,1,7,2,4]=>[3,4,6,1,8,2,7,5]=>[3,2,2,1]
[2,1,5,8,4,6,3,7]=>[3,5,7,1,6,8,2,4]=>[6,4,2,8,3,1,7,5]=>[1,1,2,1,2,1]
[6,5,3,8,4,1,2,7]=>[3,6,2,1,7,5,8,4]=>[6,3,7,8,2,4,1,5]=>[1,3,2,2]
[7,5,8,4,3,6,2,1]=>[2,5,4,1,8,7,6,3]=>[7,4,5,8,1,2,3,6]=>[1,3,4]
[2,4,8,3,5,6,1,7]=>[2,4,5,7,1,6,8,3]=>[7,5,4,2,8,3,1,6]=>[1,1,1,2,1,2]
[4,1,8,3,6,5,2,7]=>[1,7,4,6,5,8,2,3]=>[8,2,5,3,4,1,7,6]=>[1,2,2,2,1]
[3,4,8,1,7,2,5,6]=>[1,2,6,7,8,4,5,3]=>[8,7,3,2,1,5,4,6]=>[1,1,1,1,2,2]
[8,4,1,3,7,2,6,5]=>[8,4,2,6,7,3,5,1]=>[1,5,7,3,2,6,4,8]=>[3,1,2,2]
[2,3,8,1,4,6,7,5]=>[6,8,1,2,4,5,7,3]=>[3,1,8,7,5,4,2,6]=>[1,2,1,1,1,2]
[4,3,8,2,5,1,7,6]=>[2,1,4,5,8,6,7,3]=>[7,8,5,4,1,3,2,6]=>[2,1,1,2,2]
[6,3,8,4,2,5,7,1]=>[5,2,4,1,6,8,7,3]=>[4,7,5,8,3,1,2,6]=>[2,2,1,3]
[7,4,3,8,2,5,1,6]=>[3,2,5,7,6,1,8,4]=>[6,7,4,2,3,8,1,5]=>[2,1,3,2]
[2,1,4,8,3,5,7,6]=>[8,1,3,5,6,7,2,4]=>[1,8,6,4,3,2,7,5]=>[2,1,1,1,2,1]
[6,8,2,4,3,5,1,7]=>[5,3,4,1,7,6,8,2]=>[4,6,5,8,2,3,1,7]=>[2,2,2,2]
[4,8,2,3,5,1,6,7]=>[3,1,4,6,5,7,8,2]=>[6,8,5,3,4,2,1,7]=>[2,1,2,1,2]
[2,8,1,3,4,5,7,6]=>[8,1,3,4,5,6,7,2]=>[1,8,6,5,4,3,2,7]=>[2,1,1,1,1,2]
[2,8,4,1,6,5,7,3]=>[3,6,5,8,1,4,7,2]=>[6,3,4,1,8,5,2,7]=>[1,2,2,1,2]
[2,8,7,6,1,4,3,5]=>[7,5,6,8,4,1,3,2]=>[2,4,3,1,5,8,6,7]=>[2,1,3,2]
[2,8,5,6,7,4,3,1]=>[3,4,8,7,6,1,5,2]=>[6,5,1,2,3,8,4,7]=>[1,1,4,2]
[7,5,8,6,1,4,2,3]=>[7,2,8,5,1,6,4,3]=>[2,7,1,4,8,3,5,6]=>[2,3,3]
[3,5,7,6,1,4,2,8]=>[2,7,1,5,6,4,3,8]=>[7,2,8,4,3,5,6,1]=>[1,2,1,3,1]
[3,5,7,2,4,1,6,8]=>[4,1,2,6,5,7,3,8]=>[5,8,7,3,4,2,6,1]=>[2,1,2,2,1]
[7,5,8,2,4,1,6,3]=>[8,4,2,6,5,1,7,3]=>[1,5,7,3,4,8,2,6]=>[3,3,2]
[2,8,5,3,4,7,6,1]=>[8,4,3,5,7,1,6,2]=>[1,5,6,4,2,8,3,7]=>[3,1,2,2]
[2,8,5,3,4,1,7,6]=>[4,5,3,8,1,6,7,2]=>[5,4,6,1,8,3,2,7]=>[1,2,2,1,2]
[2,8,7,6,1,4,5,3]=>[6,8,5,7,4,1,3,2]=>[3,1,4,2,5,8,6,7]=>[1,2,3,2]
[2,8,5,3,6,1,7,4]=>[8,4,3,6,1,5,7,2]=>[1,5,6,3,8,4,2,7]=>[3,2,1,2]
[2,8,5,6,7,4,1,3]=>[3,7,4,8,6,1,5,2]=>[6,2,5,1,3,8,4,7]=>[1,2,3,2]
[2,8,5,3,4,7,1,6]=>[4,5,3,7,8,1,6,2]=>[5,4,6,2,1,8,3,7]=>[1,2,1,2,2]
[2,8,5,3,4,6,1,7]=>[4,5,3,7,1,6,8,2]=>[5,4,6,2,8,3,1,7]=>[1,2,2,1,2]
[2,8,5,3,4,6,7,1]=>[4,5,3,6,8,1,7,2]=>[5,4,6,3,1,8,2,7]=>[1,2,1,2,2]
[6,5,2,7,3,1,4,8]=>[6,3,5,2,1,7,4,8]=>[3,6,4,7,8,2,5,1]=>[2,3,2,1]
[6,5,2,8,3,1,7,4]=>[5,8,3,2,1,6,7,4]=>[4,1,6,7,8,3,2,5]=>[1,4,1,2]
[6,5,2,8,3,1,4,7]=>[6,3,5,2,1,7,8,4]=>[3,6,4,7,8,2,1,5]=>[2,3,1,2]
[7,5,8,2,4,6,3,1]=>[5,2,8,4,1,7,6,3]=>[4,7,1,5,8,2,3,6]=>[2,3,3]
[7,5,8,6,1,4,3,2]=>[2,8,7,5,1,6,4,3]=>[7,1,2,4,8,3,5,6]=>[1,4,3]
[6,5,8,2,1,3,7,4]=>[4,8,5,2,1,6,7,3]=>[5,1,4,7,8,3,2,6]=>[1,4,1,2]
[3,5,6,2,1,8,7,4]=>[2,8,1,4,3,7,5,6]=>[7,1,8,5,6,2,4,3]=>[1,2,2,2,1]
[3,5,7,6,1,4,8,2]=>[2,6,8,1,5,4,3,7]=>[7,3,1,8,4,5,6,2]=>[1,1,2,3,1]
[3,5,7,2,4,1,8,6]=>[4,1,2,5,8,6,3,7]=>[5,8,7,4,1,3,6,2]=>[2,1,1,3,1]
[3,5,7,2,4,6,8,1]=>[4,1,2,5,6,3,8,7]=>[5,8,7,4,3,6,1,2]=>[2,1,1,2,2]
[6,5,2,7,3,1,8,4]=>[5,8,3,2,1,6,4,7]=>[4,1,6,7,8,3,5,2]=>[1,4,2,1]
[4,5,2,6,3,1,7,8]=>[1,6,3,2,5,4,7,8]=>[8,3,6,7,4,5,2,1]=>[1,3,2,1,1]
[4,1,2,3,7,6,8,5]=>[6,5,1,8,2,3,4,7]=>[3,4,8,1,7,6,5,2]=>[3,2,1,1,1]
[6,5,2,7,3,4,8,1]=>[5,6,3,2,1,4,8,7]=>[4,3,6,7,8,5,1,2]=>[1,4,1,2]
[5,1,6,7,4,3,8,2]=>[3,1,6,5,4,8,2,7]=>[6,8,3,4,5,1,7,2]=>[2,3,2,1]
[5,1,2,6,4,8,7,3]=>[4,8,5,1,7,2,3,6]=>[5,1,4,8,2,7,6,3]=>[1,3,2,1,1]
[5,1,2,8,6,4,7,3]=>[6,5,1,8,7,2,3,4]=>[3,4,8,1,2,7,6,5]=>[3,3,1,1]
[5,1,6,8,7,3,4,2]=>[3,1,6,8,7,5,2,4]=>[6,8,3,1,2,4,7,5]=>[2,1,4,1]
[6,5,2,8,3,7,4,1]=>[8,5,2,1,7,3,6,4]=>[1,4,7,8,2,6,3,5]=>[4,2,2]
[4,1,2,3,8,7,5,6]=>[7,1,8,6,2,3,4,5]=>[2,8,1,3,7,6,5,4]=>[2,3,1,1,1]
[4,1,2,3,8,6,5,7]=>[7,6,1,8,2,3,4,5]=>[2,3,8,1,7,6,5,4]=>[3,2,1,1,1]
[4,1,2,3,8,6,7,5]=>[6,1,8,7,2,3,4,5]=>[3,8,1,2,7,6,5,4]=>[2,3,1,1,1]
[4,1,2,3,7,6,5,8]=>[7,6,2,1,3,4,5,8]=>[2,3,7,8,6,5,4,1]=>[4,1,1,1,1]
[4,1,2,3,8,5,7,6]=>[8,6,1,7,2,3,4,5]=>[1,3,8,2,7,6,5,4]=>[3,2,1,1,1]
[7,1,6,8,4,3,5,2]=>[6,5,3,8,7,2,1,4]=>[3,4,6,1,2,7,8,5]=>[3,4,1]
[6,1,2,8,4,5,7,3]=>[5,6,8,7,2,1,3,4]=>[4,3,1,2,7,8,6,5]=>[1,1,4,1,1]
[5,6,8,2,3,1,7,4]=>[4,1,5,2,8,6,7,3]=>[5,8,4,7,1,3,2,6]=>[2,2,2,2]
[6,5,8,2,4,3,1,7]=>[7,4,2,1,6,5,8,3]=>[2,5,7,8,3,4,1,6]=>[4,2,2]
[6,5,8,2,4,3,7,1]=>[6,4,2,1,5,8,7,3]=>[3,5,7,8,4,1,2,6]=>[4,1,3]
[7,5,2,8,3,4,1,6]=>[5,7,3,2,6,1,8,4]=>[4,2,6,7,3,8,1,5]=>[1,3,2,2]
[6,5,2,8,3,7,1,4]=>[5,7,2,1,8,3,6,4]=>[4,2,7,8,1,6,3,5]=>[1,3,2,2]
[6,5,2,7,3,4,1,8]=>[5,7,3,2,1,6,4,8]=>[4,2,6,7,8,3,5,1]=>[1,4,2,1]
[5,1,6,7,4,3,2,8]=>[3,1,7,6,5,2,4,8]=>[6,8,2,3,4,7,5,1]=>[2,4,1,1]
[5,1,6,8,7,3,2,4]=>[3,1,7,6,8,5,2,4]=>[6,8,2,3,1,4,7,5]=>[2,2,3,1]
[7,1,6,8,4,3,2,5]=>[7,6,5,3,8,2,1,4]=>[2,3,4,6,1,7,8,5]=>[4,3,1]
[5,7,8,6,3,4,2,1]=>[5,1,2,8,7,6,4,3]=>[4,8,7,1,2,3,5,6]=>[2,1,5]
[4,1,8,3,6,5,7,2]=>[1,6,4,5,8,7,2,3]=>[8,3,5,4,1,2,7,6]=>[1,2,1,3,1]
[4,1,8,3,6,2,7,5]=>[1,8,4,6,5,7,2,3]=>[8,1,5,3,4,2,7,6]=>[1,2,2,2,1]
[3,1,4,8,6,2,7,5]=>[8,1,6,3,5,7,2,4]=>[1,8,3,6,4,2,7,5]=>[2,2,1,2,1]
[3,1,4,8,6,5,2,7]=>[7,1,6,3,5,8,2,4]=>[2,8,3,6,4,1,7,5]=>[2,2,1,2,1]
[7,1,6,5,8,3,2,4]=>[7,6,4,3,8,2,1,5]=>[2,3,5,6,1,7,8,4]=>[4,3,1]
[4,1,6,7,8,3,2,5]=>[1,3,7,6,4,8,2,5]=>[8,6,2,3,5,1,7,4]=>[1,1,3,2,1]
[4,1,6,5,7,3,2,8]=>[1,4,3,7,6,2,5,8]=>[8,5,6,2,3,7,4,1]=>[1,2,3,1,1]
[4,5,2,6,3,7,1,8]=>[1,5,3,2,4,7,6,8]=>[8,4,6,7,5,2,3,1]=>[1,3,1,2,1]
[4,5,2,7,3,8,1,6]=>[1,5,2,7,3,4,8,6]=>[8,4,7,2,6,5,1,3]=>[1,2,2,1,2]
[3,5,6,2,4,8,7,1]=>[2,8,1,4,3,5,7,6]=>[7,1,8,5,6,4,2,3]=>[1,2,2,1,2]
[3,5,6,2,4,8,1,7]=>[4,1,2,5,3,7,8,6]=>[5,8,7,4,6,2,1,3]=>[2,1,2,1,2]
[3,7,5,6,8,4,1,2]=>[3,7,4,1,2,8,6,5]=>[6,2,5,8,7,1,3,4]=>[1,3,1,3]
[3,6,5,2,8,1,7,4]=>[8,4,1,3,2,6,7,5]=>[1,5,8,6,7,3,2,4]=>[3,2,1,2]
[6,1,2,5,8,4,7,3]=>[4,6,8,7,2,1,3,5]=>[5,3,1,2,7,8,6,4]=>[1,1,4,1,1]
[7,1,6,5,8,3,4,2]=>[6,4,3,8,7,2,1,5]=>[3,5,6,1,2,7,8,4]=>[3,4,1]
[7,5,2,6,3,8,4,1]=>[8,5,3,2,4,1,7,6]=>[1,4,6,7,5,8,2,3]=>[4,2,2]
[4,1,2,3,5,8,7,6]=>[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>[4,1,1,1,1]
[4,1,2,3,7,8,6,5]=>[5,1,8,7,2,3,4,6]=>[4,8,1,2,7,6,5,3]=>[2,3,1,1,1]
[4,5,2,7,3,8,6,1]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[1,1,3,1,2]
[4,1,6,7,8,3,5,2]=>[1,3,6,4,8,7,2,5]=>[8,6,3,5,1,2,7,4]=>[1,1,2,3,1]
[4,1,2,6,8,5,7,3]=>[4,1,6,8,7,2,3,5]=>[5,8,3,1,2,7,6,4]=>[2,1,3,1,1]
[4,1,2,5,6,8,7,3]=>[8,4,1,5,7,2,3,6]=>[1,5,8,4,2,7,6,3]=>[3,1,2,1,1]
[4,5,2,6,3,7,8,1]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[1,3,1,1,2]
[7,8,5,6,1,4,3,2]=>[8,7,5,3,1,6,4,2]=>[1,2,4,6,8,3,5,7]=>[5,3]
[6,4,1,2,5,7,3,8]=>[5,7,3,2,4,1,6,8]=>[4,2,6,7,5,8,3,1]=>[1,3,2,1,1]
[2,4,8,1,5,7,3,6]=>[2,5,7,8,1,4,6,3]=>[7,4,2,1,8,5,3,6]=>[1,1,1,2,1,2]
[4,3,8,1,7,2,5,6]=>[2,1,6,7,8,4,5,3]=>[7,8,3,2,1,5,4,6]=>[2,1,1,2,2]
[6,3,1,4,7,2,5,8]=>[4,2,6,7,3,1,5,8]=>[5,7,3,2,6,8,4,1]=>[2,1,3,1,1]
[7,8,3,4,5,1,6,2]=>[3,4,8,6,5,1,7,2]=>[6,5,1,3,4,8,2,7]=>[1,1,4,2]
[7,8,3,5,4,2,1,6]=>[7,3,6,5,4,1,8,2]=>[2,6,3,4,5,8,1,7]=>[2,4,2]
[7,8,4,1,2,3,6,5]=>[8,4,5,3,6,1,7,2]=>[1,5,4,6,3,8,2,7]=>[2,2,2,2]
[7,8,3,6,5,4,1,2]=>[7,8,3,1,6,5,4,2]=>[2,1,6,8,3,4,5,7]=>[1,3,4]
[7,8,2,1,5,3,4,6]=>[3,6,7,4,5,1,8,2]=>[6,3,2,5,4,8,1,7]=>[1,1,2,2,2]
[7,8,2,6,4,1,3,5]=>[6,7,3,5,1,8,4,2]=>[3,2,6,4,8,1,5,7]=>[1,2,2,3]
[7,8,2,5,6,4,1,3]=>[7,4,8,3,1,6,5,2]=>[2,5,1,6,8,3,4,7]=>[2,3,3]
[7,8,1,6,5,4,3,2]=>[8,7,6,5,3,1,4,2]=>[1,2,3,4,6,8,5,7]=>[6,2]
[2,1,8,7,5,4,3,6]=>[7,6,5,8,1,4,2,3]=>[2,3,4,1,8,5,7,6]=>[3,2,2,1]
[1,3,8,2,6,4,7,5]=>[8,6,2,4,5,7,1,3]=>[1,3,7,5,4,2,8,6]=>[3,1,1,2,1]
[5,3,7,1,6,4,8,2]=>[6,2,1,5,8,4,3,7]=>[3,7,8,4,1,5,6,2]=>[3,1,3,1]
[5,3,6,2,7,4,1,8]=>[7,2,1,4,3,6,5,8]=>[2,7,8,5,6,3,4,1]=>[3,2,2,1]
[6,1,2,5,8,7,4,3]=>[8,4,7,6,2,1,3,5]=>[1,5,2,3,7,8,6,4]=>[2,4,1,1]
[6,3,1,8,4,2,7,5]=>[2,5,8,6,1,7,3,4]=>[7,4,1,3,8,2,6,5]=>[1,1,3,2,1]
[6,4,2,1,5,3,8,7]=>[3,5,2,8,4,1,6,7]=>[6,4,7,1,5,8,3,2]=>[1,2,3,1,1]
[6,4,3,7,5,8,1,2]=>[2,7,3,1,5,4,8,6]=>[7,2,6,8,4,5,1,3]=>[1,3,2,2]
[4,3,8,7,5,6,1,2]=>[7,1,5,8,2,6,4,3]=>[2,8,4,1,7,3,5,6]=>[2,1,2,3]
[2,4,7,1,5,3,6,8]=>[2,6,1,4,5,7,3,8]=>[7,3,8,5,4,2,6,1]=>[1,2,1,1,2,1]
[1,3,7,6,4,2,8,5]=>[5,8,6,2,4,1,3,7]=>[4,1,3,7,5,8,6,2]=>[1,3,2,1,1]
[2,1,7,5,6,8,4,3]=>[4,5,3,8,1,7,2,6]=>[5,4,6,1,8,2,7,3]=>[1,2,2,2,1]
[3,7,2,8,6,4,1,5]=>[7,6,8,1,3,2,5,4]=>[2,3,1,8,6,7,4,5]=>[2,2,2,2]
[3,8,1,7,6,4,5,2]=>[6,8,7,1,5,3,4,2]=>[3,1,2,8,4,6,5,7]=>[1,3,2,2]
[1,8,5,7,3,6,4,2]=>[3,8,5,7,6,4,1,2]=>[6,1,4,2,3,5,8,7]=>[1,2,4,1]
[2,7,5,8,3,6,1,4]=>[5,3,7,2,8,1,6,4]=>[4,6,2,7,1,8,3,5]=>[2,2,2,2]
[1,5,6,8,2,4,7,3]=>[2,6,3,8,5,7,1,4]=>[7,3,6,1,4,2,8,5]=>[1,2,2,2,1]
[2,6,8,5,3,1,4,7]=>[6,5,2,7,1,4,8,3]=>[3,4,7,2,8,5,1,6]=>[3,2,1,2]
[2,6,1,4,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[5,3,2,8,6,7,4,1]=>[1,1,2,2,1,1]
[5,6,7,3,8,4,1,2]=>[1,4,2,7,3,8,6,5]=>[8,5,7,2,6,1,3,4]=>[1,2,2,3]
[5,2,8,1,4,7,3,6]=>[5,7,1,8,2,4,6,3]=>[4,2,8,1,7,5,3,6]=>[1,2,2,1,2]
[4,6,7,5,2,1,3,8]=>[6,1,5,2,7,4,3,8]=>[3,8,4,7,2,5,6,1]=>[2,2,3,1]
[4,5,6,7,2,8,1,3]=>[1,2,5,3,7,4,8,6]=>[8,7,4,6,2,5,1,3]=>[1,1,2,2,2]
[4,5,7,6,1,8,3,2]=>[8,1,2,7,5,4,3,6]=>[1,8,7,2,4,5,6,3]=>[2,1,4,1]
[1,5,8,6,2,7,3,4]=>[2,7,8,5,4,6,1,3]=>[7,2,1,4,5,3,8,6]=>[1,1,3,2,1]
[1,6,5,8,3,2,7,4]=>[5,3,2,8,6,7,1,4]=>[4,6,7,1,3,2,8,5]=>[3,2,2,1]
[4,6,5,7,1,2,8,3]=>[8,1,5,3,2,6,4,7]=>[1,8,4,6,7,3,5,2]=>[2,3,2,1]
[4,7,5,6,3,1,8,2]=>[3,8,1,6,5,4,2,7]=>[6,1,8,3,4,5,7,2]=>[1,2,4,1]
[5,7,1,4,2,3,8,6]=>[8,5,3,1,4,6,2,7]=>[1,4,6,8,5,3,7,2]=>[4,1,2,1]
[5,7,6,4,3,8,1,2]=>[7,1,5,4,3,2,8,6]=>[2,8,4,5,6,7,1,3]=>[2,4,2]
[6,3,4,5,8,7,1,2]=>[2,3,4,1,7,8,6,5]=>[7,6,5,8,2,1,3,4]=>[1,1,2,1,3]
[6,2,4,1,8,3,7,5]=>[3,8,2,6,1,7,4,5]=>[6,1,7,3,8,2,5,4]=>[1,2,2,2,1]
[6,2,3,5,4,8,1,7]=>[5,2,3,4,1,7,8,6]=>[4,7,6,5,8,2,1,3]=>[2,1,2,1,2]
[6,1,3,4,5,8,7,2]=>[8,3,4,5,1,7,2,6]=>[1,6,5,4,8,2,7,3]=>[2,1,2,2,1]
[5,1,4,2,7,6,8,3]=>[3,6,5,1,8,2,4,7]=>[6,3,4,8,1,7,5,2]=>[1,3,2,1,1]
[1,6,2,4,7,8,3,5]=>[7,4,5,2,8,1,3,6]=>[2,5,4,7,1,8,6,3]=>[2,2,2,1,1]
[5,7,2,4,1,6,3,8]=>[7,3,1,5,4,6,2,8]=>[2,6,8,4,5,3,7,1]=>[3,2,2,1]
[6,1,4,2,8,5,3,7]=>[3,7,6,8,2,1,4,5]=>[6,2,3,1,7,8,5,4]=>[1,2,3,1,1]
[6,7,5,8,1,4,3,2]=>[1,8,7,5,3,2,6,4]=>[8,1,2,4,6,7,3,5]=>[1,5,2]
[5,8,7,6,3,4,1,2]=>[7,1,5,8,6,4,3,2]=>[2,8,4,1,3,5,6,7]=>[2,1,5]
[5,8,7,6,2,3,1,4]=>[1,5,7,6,8,4,3,2]=>[8,4,2,3,1,5,6,7]=>[1,1,2,4]
[4,1,7,2,6,5,3,8]=>[1,7,6,4,5,2,3,8]=>[8,2,3,5,4,7,6,1]=>[1,3,2,1,1]
[4,2,7,8,1,6,3,5]=>[1,7,8,5,2,3,6,4]=>[8,2,1,4,7,6,3,5]=>[1,1,3,1,2]
[2,1,8,7,6,5,3,4]=>[7,8,6,5,1,4,2,3]=>[2,1,3,4,8,5,7,6]=>[1,4,2,1]
[3,1,4,7,8,2,6,5]=>[8,1,6,3,4,7,2,5]=>[1,8,3,6,5,2,7,4]=>[2,2,1,2,1]
[4,2,7,1,6,3,8,5]=>[1,8,6,2,4,5,3,7]=>[8,1,3,7,5,4,6,2]=>[1,3,1,2,1]
[4,3,7,5,6,8,1,2]=>[1,4,7,2,5,3,8,6]=>[8,5,2,7,4,6,1,3]=>[1,1,2,2,2]
[4,8,6,3,5,7,1,2]=>[4,7,1,5,3,8,6,2]=>[5,2,8,4,6,1,3,7]=>[1,2,2,3]
[4,8,1,2,5,3,7,6]=>[5,1,8,3,4,6,7,2]=>[4,8,1,6,5,3,2,7]=>[2,2,1,1,2]
[3,8,6,5,2,4,1,7]=>[5,7,6,1,4,3,8,2]=>[4,2,3,8,5,6,1,7]=>[1,3,2,2]
[3,8,5,6,1,4,7,2]=>[6,3,8,1,5,4,7,2]=>[3,6,1,8,4,5,2,7]=>[2,2,2,2]
[5,3,7,8,2,1,6,4]=>[5,1,8,2,6,3,7,4]=>[4,8,1,7,3,6,2,5]=>[2,2,2,2]
[5,2,8,7,1,6,4,3]=>[1,8,7,5,6,2,4,3]=>[8,1,2,4,3,7,5,6]=>[1,3,2,2]
[3,6,7,8,5,1,4,2]=>[2,8,6,1,3,7,5,4]=>[7,1,3,8,6,2,4,5]=>[1,3,1,3]
[3,7,6,8,5,2,1,4]=>[7,6,3,1,2,8,5,4]=>[2,3,6,8,7,1,4,5]=>[4,1,3]
[3,7,8,5,1,2,4,6]=>[5,6,7,1,4,2,8,3]=>[4,3,2,8,5,7,1,6]=>[1,1,2,2,2]
[3,7,1,6,4,2,5,8]=>[6,1,5,7,3,4,2,8]=>[3,8,4,2,6,5,7,1]=>[2,1,2,2,1]
[4,1,8,6,2,3,5,7]=>[5,1,6,7,4,8,2,3]=>[4,8,3,2,5,1,7,6]=>[2,1,2,2,1]
[4,7,8,6,3,5,1,2]=>[7,5,1,2,8,6,4,3]=>[2,4,8,7,1,3,5,6]=>[3,1,4]
[3,8,7,6,5,4,1,2]=>[7,8,6,5,1,4,3,2]=>[2,1,3,4,8,5,6,7]=>[1,4,3]
[2,1,7,6,5,3,4,8]=>[6,7,5,1,4,2,3,8]=>[3,2,4,8,5,7,6,1]=>[1,3,2,1,1]
[2,8,1,6,4,5,3,7]=>[5,7,6,1,3,4,8,2]=>[4,2,3,8,6,5,1,7]=>[1,3,1,1,2]
[2,8,7,5,1,4,3,6]=>[7,5,6,4,8,1,3,2]=>[2,4,3,5,1,8,6,7]=>[2,2,2,2]
[2,8,6,7,5,1,3,4]=>[6,7,3,8,5,1,4,2]=>[3,2,6,1,4,8,5,7]=>[1,2,3,2]
[2,7,8,6,5,4,1,3]=>[7,2,8,6,5,1,4,3]=>[2,7,1,3,4,8,5,6]=>[2,4,2]
[6,3,1,2,7,4,8,5]=>[2,8,6,3,4,1,5,7]=>[7,1,3,6,5,8,4,2]=>[1,3,2,1,1]
[6,4,2,7,1,3,8,5]=>[8,3,2,5,1,6,4,7]=>[1,6,7,4,8,3,5,2]=>[3,2,2,1]
[7,4,2,5,1,3,8,6]=>[8,3,2,5,4,6,1,7]=>[1,6,7,4,5,3,8,2]=>[3,2,2,1]
[7,5,3,6,1,8,2,4]=>[3,7,2,8,5,4,1,6]=>[6,2,7,1,4,5,8,3]=>[1,2,4,1]
[8,3,6,2,4,7,1,5]=>[2,4,5,7,3,8,6,1]=>[7,5,4,2,6,1,3,8]=>[1,1,1,2,3]
[7,3,6,2,4,8,1,5]=>[2,4,5,7,3,1,8,6]=>[7,5,4,2,6,8,1,3]=>[1,1,1,3,2]
[4,3,7,1,2,5,8,6]=>[2,1,8,4,5,6,3,7]=>[7,8,1,5,4,3,6,2]=>[2,2,1,2,1]
[3,6,2,7,1,4,8,5]=>[8,1,3,5,2,6,4,7]=>[1,8,6,4,7,3,5,2]=>[2,1,2,2,1]
[5,3,6,7,1,2,8,4]=>[8,2,1,5,3,6,4,7]=>[1,7,8,4,6,3,5,2]=>[3,2,2,1]
[6,3,7,4,1,2,8,5]=>[8,2,5,4,1,6,3,7]=>[1,7,4,5,8,3,6,2]=>[2,3,2,1]
[4,7,1,5,2,3,8,6]=>[1,8,5,3,4,6,2,7]=>[8,1,4,6,5,3,7,2]=>[1,3,1,2,1]
[3,7,5,1,2,4,8,6]=>[8,1,4,5,3,6,2,7]=>[1,8,5,4,6,3,7,2]=>[2,1,2,2,1]
[7,6,4,2,3,8,1,5]=>[4,5,3,7,2,1,8,6]=>[5,4,6,2,7,8,1,3]=>[1,2,3,2]
[8,6,4,2,3,7,1,5]=>[4,5,3,7,2,8,6,1]=>[5,4,6,2,7,1,3,8]=>[1,2,2,3]
[4,7,6,3,8,1,2,5]=>[6,1,4,7,3,2,8,5]=>[3,8,5,2,6,7,1,4]=>[2,1,3,2]
[5,7,4,2,3,8,1,6]=>[4,1,5,3,7,2,8,6]=>[5,8,4,6,2,7,1,3]=>[2,2,2,2]
[3,7,6,1,4,8,2,5]=>[5,7,8,1,4,3,2,6]=>[4,2,1,8,5,6,7,3]=>[1,1,2,3,1]
[5,7,2,6,1,8,3,4]=>[7,1,8,3,5,4,2,6]=>[2,8,1,6,4,5,7,3]=>[2,2,3,1]
[6,4,7,5,2,8,1,3]=>[2,5,1,7,4,3,8,6]=>[7,4,8,2,5,6,1,3]=>[1,2,3,2]
[7,4,8,5,2,6,1,3]=>[2,5,7,4,1,8,6,3]=>[7,4,2,5,8,1,3,6]=>[1,1,3,3]
[5,8,2,6,3,7,1,4]=>[5,1,7,3,4,8,6,2]=>[4,8,2,6,5,1,3,7]=>[2,2,1,3]
[3,8,6,1,2,7,4,5]=>[7,8,1,4,5,3,6,2]=>[2,1,8,5,4,6,3,7]=>[1,2,1,2,2]
[3,8,6,2,4,7,1,5]=>[4,5,7,1,3,8,6,2]=>[5,4,2,8,6,1,3,7]=>[1,1,2,1,3]
[6,8,4,3,7,1,2,5]=>[6,4,3,1,7,8,5,2]=>[3,5,6,8,2,1,4,7]=>[4,1,3]
[6,8,5,3,7,1,2,4]=>[6,4,1,7,3,8,5,2]=>[3,5,8,2,6,1,4,7]=>[3,2,3]
[3,8,5,7,1,2,4,6]=>[5,6,1,3,7,8,4,2]=>[4,3,8,6,2,1,5,7]=>[1,2,1,1,3]
[2,8,5,7,1,3,4,6]=>[5,6,3,7,8,1,4,2]=>[4,3,6,2,1,8,5,7]=>[1,2,1,2,2]
[4,8,6,2,7,1,3,5]=>[1,4,6,7,3,8,5,2]=>[8,5,3,2,6,1,4,7]=>[1,1,1,2,3]
[7,3,8,5,6,1,2,4]=>[6,7,2,4,1,8,5,3]=>[3,2,7,5,8,1,4,6]=>[1,2,2,3]
[6,3,7,5,8,1,2,4]=>[6,7,2,1,4,3,8,5]=>[3,2,7,8,5,6,1,4]=>[1,3,2,2]
[2,7,6,4,8,1,3,5]=>[6,4,7,3,1,2,8,5]=>[3,5,2,6,8,7,1,4]=>[2,3,1,2]
[2,6,5,8,1,3,4,7]=>[5,6,3,1,2,7,8,4]=>[4,3,6,8,7,2,1,5]=>[1,3,1,1,2]
[3,6,5,8,1,2,4,7]=>[5,6,1,3,2,7,8,4]=>[4,3,8,6,7,2,1,5]=>[1,2,2,1,2]
[2,5,7,4,8,1,3,6]=>[2,6,4,7,1,3,8,5]=>[7,3,5,2,8,6,1,4]=>[1,2,2,1,2]
[5,4,6,7,2,8,1,3]=>[2,1,5,3,7,4,8,6]=>[7,8,4,6,2,5,1,3]=>[2,2,2,2]
[4,6,3,7,1,8,2,5]=>[1,3,7,2,8,5,4,6]=>[8,6,2,7,1,4,5,3]=>[1,1,2,3,1]
[3,5,7,1,4,8,2,6]=>[5,1,2,7,8,4,3,6]=>[4,8,7,2,1,5,6,3]=>[2,1,1,3,1]
[5,3,7,2,4,8,1,6]=>[2,4,1,5,7,3,8,6]=>[7,5,8,4,2,6,1,3]=>[1,2,1,2,2]
[5,4,7,3,8,1,2,6]=>[2,1,6,4,7,3,8,5]=>[7,8,3,5,2,6,1,4]=>[2,2,2,2]
[7,4,6,3,8,1,2,5]=>[2,6,4,7,3,1,8,5]=>[7,3,5,2,6,8,1,4]=>[1,2,3,2]
[8,4,6,3,7,1,2,5]=>[2,6,4,7,3,8,5,1]=>[7,3,5,2,6,1,4,8]=>[1,2,2,3]
[8,4,1,6,7,2,3,5]=>[6,2,7,4,8,3,5,1]=>[3,7,2,5,1,6,4,8]=>[2,2,2,2]
[7,4,1,6,8,2,3,5]=>[6,2,7,4,8,3,1,5]=>[3,7,2,5,1,6,8,4]=>[2,2,3,1]
[5,4,1,7,8,2,3,6]=>[6,2,1,7,4,8,3,5]=>[3,7,8,2,5,1,6,4]=>[3,2,2,1]
[6,5,3,7,1,8,2,4]=>[3,7,2,1,8,5,4,6]=>[6,2,7,8,1,4,5,3]=>[1,3,3,1]
[6,5,1,2,7,8,3,4]=>[7,5,8,3,2,1,4,6]=>[2,4,1,6,7,8,5,3]=>[2,4,1,1]
[5,3,6,4,7,8,1,2]=>[4,2,1,3,7,5,8,6]=>[5,7,8,6,2,4,1,3]=>[3,1,2,2]
[6,3,7,4,8,5,1,2]=>[4,7,2,1,3,8,6,5]=>[5,2,7,8,6,1,3,4]=>[1,3,1,3]
[7,5,1,2,8,6,3,4]=>[7,8,6,3,2,4,1,5]=>[2,1,3,6,7,5,8,4]=>[1,4,2,1]
[7,5,3,8,1,6,2,4]=>[3,7,2,8,5,1,6,4]=>[6,2,7,1,4,8,3,5]=>[1,2,3,2]
[7,4,1,8,6,2,3,5]=>[6,2,7,8,5,3,1,4]=>[3,7,2,1,4,6,8,5]=>[2,1,4,1]
[7,6,1,8,5,2,3,4]=>[6,7,8,5,3,2,1,4]=>[3,2,1,4,6,7,8,5]=>[1,1,5,1]
[8,6,1,7,5,2,3,4]=>[6,7,8,5,3,2,4,1]=>[3,2,1,4,6,7,5,8]=>[1,1,4,2]
[6,4,7,8,2,5,1,3]=>[2,5,1,7,3,8,6,4]=>[7,4,8,2,6,1,3,5]=>[1,2,2,3]
[6,3,7,8,5,1,2,4]=>[6,7,2,1,3,8,5,4]=>[3,2,7,8,6,1,4,5]=>[1,3,1,3]
[3,6,8,2,7,1,4,5]=>[4,6,1,2,7,8,5,3]=>[5,3,8,7,2,1,4,6]=>[1,2,1,1,3]
[2,4,8,7,1,3,5,6]=>[2,5,6,7,8,1,4,3]=>[7,4,3,2,1,8,5,6]=>[1,1,1,1,2,2]
[4,3,8,7,1,2,5,6]=>[2,1,5,6,7,8,4,3]=>[7,8,4,3,2,1,5,6]=>[2,1,1,1,3]
[5,3,8,7,1,2,4,6]=>[2,5,1,6,7,8,4,3]=>[7,4,8,3,2,1,5,6]=>[1,2,1,1,3]
[8,3,7,6,1,2,4,5]=>[2,5,6,7,8,4,3,1]=>[7,4,3,2,1,5,6,8]=>[1,1,1,1,4]
[8,4,7,6,1,2,3,5]=>[5,2,6,7,8,4,3,1]=>[4,7,3,2,1,5,6,8]=>[2,1,1,4]
[5,4,8,7,1,2,3,6]=>[5,2,1,6,7,8,4,3]=>[4,7,8,3,2,1,5,6]=>[3,1,1,3]
[3,5,8,7,1,2,4,6]=>[5,1,2,6,7,8,4,3]=>[4,8,7,3,2,1,5,6]=>[2,1,1,1,3]
[2,5,8,7,1,3,4,6]=>[5,2,6,7,8,1,4,3]=>[4,7,3,2,1,8,5,6]=>[2,1,1,2,2]
[4,6,8,2,7,1,3,5]=>[1,4,6,2,7,8,5,3]=>[8,5,3,7,2,1,4,6]=>[1,1,2,1,3]
[7,5,8,6,4,1,2,3]=>[6,2,7,1,8,5,4,3]=>[3,7,2,8,1,4,5,6]=>[2,2,4]
[6,8,4,7,5,1,2,3]=>[6,3,1,7,8,5,4,2]=>[3,6,8,2,1,4,5,7]=>[3,1,4]
[5,8,7,1,6,2,3,4]=>[6,1,7,8,4,5,3,2]=>[3,8,2,1,5,4,6,7]=>[2,1,2,3]
[2,8,7,6,1,3,4,5]=>[5,6,7,8,4,1,3,2]=>[4,3,2,1,5,8,6,7]=>[1,1,1,3,2]
[3,8,7,6,1,2,4,5]=>[5,6,7,8,1,4,3,2]=>[4,3,2,1,8,5,6,7]=>[1,1,1,2,3]
[4,8,7,6,1,2,3,5]=>[1,5,6,7,8,4,3,2]=>[8,4,3,2,1,5,6,7]=>[1,1,1,1,4]
[5,6,3,1,4,2,8,7]=>[5,3,1,8,4,2,6,7]=>[4,6,8,1,5,7,3,2]=>[3,3,1,1]
[7,5,3,8,2,1,6,4]=>[3,5,2,8,6,1,7,4]=>[6,4,7,1,3,8,2,5]=>[1,2,3,2]
[6,7,1,4,5,8,2,3]=>[4,7,5,1,8,3,2,6]=>[5,2,4,8,1,6,7,3]=>[1,3,3,1]
[2,1,7,8,5,3,6,4]=>[8,6,5,1,3,7,2,4]=>[1,3,4,8,6,2,7,5]=>[4,1,2,1]
[5,7,3,8,1,2,6,4]=>[3,1,8,5,6,2,7,4]=>[6,8,1,4,3,7,2,5]=>[2,2,2,2]
[8,7,1,4,5,3,2,6]=>[4,7,6,3,5,8,2,1]=>[5,2,3,6,4,1,7,8]=>[1,3,1,3]
[2,7,8,4,1,6,5,3]=>[4,8,7,5,1,2,6,3]=>[5,1,2,4,8,7,3,6]=>[1,4,1,2]
[7,1,8,4,2,6,5,3]=>[4,8,7,5,6,2,1,3]=>[5,1,2,4,3,7,8,6]=>[1,3,3,1]
[7,5,1,4,8,6,3,2]=>[8,4,2,7,6,3,1,5]=>[1,5,7,2,3,6,8,4]=>[3,4,1]
[6,5,3,1,8,4,7,2]=>[3,6,2,1,8,7,4,5]=>[6,3,7,8,1,2,5,4]=>[1,3,3,1]
[6,4,3,8,1,5,7,2]=>[3,2,6,1,8,5,7,4]=>[6,7,3,8,1,4,2,5]=>[2,2,2,2]
[8,6,3,1,2,5,7,4]=>[6,3,8,4,5,2,7,1]=>[3,6,1,5,4,7,2,8]=>[2,2,2,2]
[8,7,1,4,2,6,5,3]=>[4,8,7,3,5,6,2,1]=>[5,1,2,6,4,3,7,8]=>[1,3,1,3]
[7,3,8,4,1,6,5,2]=>[4,8,2,7,5,1,6,3]=>[5,1,7,2,4,8,3,6]=>[1,2,3,2]
[2,3,4,5,6,7,8,1,9]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,2,1]
[2,3,4,5,6,8,9,1,7]=>[8,1,2,3,4,5,6,9,7]=>[2,9,8,7,6,5,4,1,3]=>[2,1,1,1,1,1,2]
[2,3,5,6,7,8,9,1,4]=>[3,4,5,8,1,2,6,9,7]=>[7,6,5,2,9,8,4,1,3]=>[1,1,1,2,1,1,2]
[3,4,5,6,7,8,9,1,2]=>[1,2,3,4,5,8,6,9,7]=>[9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,2,2]
[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,2]
[2,3,4,5,6,7,8,9,1,10]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[1,1,1,1,1,1,1,2,1]
[2,3,4,5,6,7,8,10,1,9]=>[1,2,3,4,5,6,7,9,10,8]=>[10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,2]
[2,3,4,5,6,1,9,7,8]=>[1,2,3,4,5,8,9,6,7]=>[9,8,7,6,5,2,1,4,3]=>[1,1,1,1,1,1,2,1]
[2,3,4,5,6,7,9,10,1,8]=>[9,1,2,3,4,5,6,7,10,8]=>[2,10,9,8,7,6,5,4,1,3]=>[2,1,1,1,1,1,1,2]
[3,4,5,6,7,8,9,10,1,2]=>[1,2,3,4,5,6,9,7,10,8]=>[10,9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,2,2]
[3,6,4,5,7,2,8,1]=>[3,4,1,2,6,5,8,7]=>[6,5,8,7,3,4,1,2]=>[1,2,1,2,2]
[5,3,2,7,4,6,8,1]=>[2,5,1,6,3,4,8,7]=>[7,4,8,3,6,5,1,2]=>[1,2,2,1,2]
[7,5,3,6,2,4,8,1]=>[3,5,2,6,4,1,8,7]=>[6,4,7,3,5,8,1,2]=>[1,2,3,2]
[8,5,3,6,2,7,1,4]=>[3,5,2,7,4,8,6,1]=>[6,4,7,2,5,1,3,8]=>[1,2,2,3]
[8,2,6,3,4,7,1,5]=>[4,5,7,2,3,8,6,1]=>[5,4,2,7,6,1,3,8]=>[1,1,2,1,3]
[7,2,6,3,4,5,8,1]=>[4,5,6,2,3,1,8,7]=>[5,4,3,7,6,8,1,2]=>[1,1,2,2,2]
[6,2,7,3,4,5,8,1]=>[4,5,6,2,1,3,8,7]=>[5,4,3,7,8,6,1,2]=>[1,1,3,1,2]
[3,6,2,7,4,5,8,1]=>[5,6,1,3,2,4,8,7]=>[4,3,8,6,7,5,1,2]=>[1,2,2,1,2]
[4,2,5,7,3,6,8,1]=>[3,1,5,6,2,4,8,7]=>[6,8,4,3,7,5,1,2]=>[2,1,2,1,2]
[5,4,7,6,2,3,8,1]=>[2,1,5,6,4,3,8,7]=>[7,8,4,3,5,6,1,2]=>[2,1,3,2]
[6,7,3,5,2,4,8,1]=>[3,5,1,6,4,2,8,7]=>[6,4,8,3,5,7,1,2]=>[1,2,3,2]
[3,7,6,2,4,5,8,1]=>[4,5,6,1,3,2,8,7]=>[5,4,3,8,6,7,1,2]=>[1,1,2,2,2]
[2,7,6,3,4,5,8,1]=>[4,5,6,3,1,2,8,7]=>[5,4,3,6,8,7,1,2]=>[1,1,3,1,2]
[6,5,3,1,2,8,4,7]=>[7,3,8,4,2,1,5,6]=>[2,6,1,5,7,8,4,3]=>[2,4,1,1]
[8,6,5,2,3,7,1,4]=>[4,5,7,3,2,8,6,1]=>[5,4,2,6,7,1,3,8]=>[1,1,3,3]
[8,5,2,1,7,3,4,6]=>[3,6,7,2,8,4,5,1]=>[6,3,2,7,1,5,4,8]=>[1,1,2,2,2]
[7,5,2,1,8,3,4,6]=>[3,6,7,2,8,4,1,5]=>[6,3,2,7,1,5,8,4]=>[1,1,2,3,1]
[1,6,3,2,8,4,5,7]=>[3,6,7,2,8,1,4,5]=>[6,3,2,7,1,8,5,4]=>[1,1,2,2,1,1]
[5,7,3,1,2,8,4,6]=>[7,3,1,8,4,5,2,6]=>[2,6,8,1,5,4,7,3]=>[3,2,2,1]
[5,6,2,3,1,8,4,7]=>[3,4,1,7,2,8,5,6]=>[6,5,8,2,7,1,4,3]=>[1,2,2,2,1]
[4,2,6,5,1,8,3,7]=>[1,7,4,2,3,8,5,6]=>[8,2,5,7,6,1,4,3]=>[1,3,1,2,1]
[5,4,8,6,2,7,1,3]=>[2,1,5,7,4,8,6,3]=>[7,8,4,2,5,1,3,6]=>[2,1,2,3]
[6,8,3,5,2,7,1,4]=>[3,5,1,7,4,8,6,2]=>[6,4,8,2,5,1,3,7]=>[1,2,2,3]
[7,8,5,2,3,6,1,4]=>[4,5,7,3,1,8,6,2]=>[5,4,2,6,8,1,3,7]=>[1,1,3,3]
[1,8,6,3,7,2,4,5]=>[4,6,7,3,8,5,1,2]=>[5,3,2,6,1,4,8,7]=>[1,1,2,3,1]
[1,8,2,7,3,4,5,6]=>[5,6,7,8,3,4,1,2]=>[4,3,2,1,6,5,8,7]=>[1,1,1,2,2,1]
[2,8,1,7,3,4,5,6]=>[5,6,7,8,1,3,4,2]=>[4,3,2,1,8,6,5,7]=>[1,1,1,2,1,2]
[3,8,6,1,7,2,4,5]=>[6,7,8,1,4,3,5,2]=>[3,2,1,8,5,6,4,7]=>[1,1,2,2,2]
[4,8,1,5,7,2,3,6]=>[1,6,4,7,8,3,5,2]=>[8,3,5,2,1,6,4,7]=>[1,2,1,2,2]
[4,2,8,3,7,1,5,6]=>[4,1,6,7,8,2,5,3]=>[5,8,3,2,1,7,4,6]=>[2,1,1,2,2]
[4,1,7,5,8,2,3,6]=>[1,6,4,7,3,8,2,5]=>[8,3,5,2,6,1,7,4]=>[1,2,2,2,1]
[1,7,3,8,2,4,5,6]=>[3,5,6,7,2,8,1,4]=>[6,4,3,2,7,1,8,5]=>[1,1,1,2,2,1]
[8,1,2,7,3,4,5,6]=>[5,6,7,8,2,3,4,1]=>[4,3,2,1,7,6,5,8]=>[1,1,1,2,1,2]
[4,2,5,7,1,8,3,6]=>[3,1,7,8,2,5,4,6]=>[6,8,2,1,7,4,5,3]=>[2,1,2,2,1]
[3,6,2,7,1,8,4,5]=>[7,8,1,3,2,5,4,6]=>[2,1,8,6,7,4,5,3]=>[1,2,2,2,1]
[6,3,7,1,2,8,4,5]=>[2,7,8,4,1,5,3,6]=>[7,2,1,5,8,4,6,3]=>[1,1,3,2,1]
[7,2,6,1,8,3,4,5]=>[6,7,8,2,4,3,1,5]=>[3,2,1,7,5,6,8,4]=>[1,1,2,3,1]
[8,2,6,1,7,3,4,5]=>[6,7,8,2,4,3,5,1]=>[3,2,1,7,5,6,4,8]=>[1,1,2,2,2]
[7,3,1,5,8,2,4,6]=>[2,6,4,7,8,3,1,5]=>[7,3,5,2,1,6,8,4]=>[1,2,1,3,1]
[3,2,1,5,8,4,6,7]=>[2,1,4,6,7,8,3,5]=>[7,8,5,3,2,1,6,4]=>[2,1,1,1,2,1]
[5,4,1,3,6,8,2,7]=>[4,5,2,1,7,8,3,6]=>[5,4,7,8,2,1,6,3]=>[1,3,1,2,1]
[4,3,5,1,6,8,2,7]=>[2,1,5,3,7,8,4,6]=>[7,8,4,6,2,1,5,3]=>[2,2,1,2,1]
[5,4,6,3,8,7,1,2]=>[2,1,4,3,7,8,6,5]=>[7,8,5,6,2,1,3,4]=>[2,2,1,3]
[3,6,4,5,8,7,1,2]=>[3,4,1,2,7,8,6,5]=>[6,5,8,7,2,1,3,4]=>[1,2,1,1,3]
[6,5,3,4,8,7,1,2]=>[3,4,2,1,7,8,6,5]=>[6,5,7,8,2,1,3,4]=>[1,3,1,3]
[5,3,2,8,7,1,4,6]=>[2,6,1,7,8,3,5,4]=>[7,3,8,2,1,6,4,5]=>[1,2,1,2,2]
[5,3,1,8,7,2,4,6]=>[2,6,1,7,8,5,3,4]=>[7,3,8,2,1,4,6,5]=>[1,2,1,3,1]
[8,5,3,7,6,1,2,4]=>[3,6,2,7,8,5,4,1]=>[6,3,7,2,1,4,5,8]=>[1,2,1,4]
[6,1,8,3,7,2,4,5]=>[4,6,7,1,8,5,2,3]=>[5,3,2,8,1,4,7,6]=>[1,1,2,3,1]
[6,3,8,1,7,2,4,5]=>[2,6,7,1,8,4,5,3]=>[7,3,2,8,1,5,4,6]=>[1,1,2,2,2]
[7,6,8,2,3,5,1,4]=>[4,5,7,2,1,8,6,3]=>[5,4,2,7,8,1,3,6]=>[1,1,3,3]
[3,7,8,2,4,6,1,5]=>[4,5,7,1,2,8,6,3]=>[5,4,2,8,7,1,3,6]=>[1,1,2,1,3]
[6,7,3,8,2,5,1,4]=>[3,5,1,7,2,8,6,4]=>[6,4,8,2,7,1,3,5]=>[1,2,2,3]
[5,4,7,8,2,6,1,3]=>[2,1,5,7,3,8,6,4]=>[7,8,4,2,6,1,3,5]=>[2,1,2,3]
[4,2,5,8,7,1,3,6]=>[3,1,6,7,8,2,5,4]=>[6,8,3,2,1,7,4,5]=>[2,1,1,2,2]
[3,6,2,8,7,1,4,5]=>[6,7,1,2,8,3,5,4]=>[3,2,8,7,1,6,4,5]=>[1,2,1,2,2]
[3,7,8,1,6,2,4,5]=>[6,7,8,1,4,2,5,3]=>[3,2,1,8,5,7,4,6]=>[1,1,2,2,2]
[2,3,8,7,1,4,5,6]=>[5,6,7,8,1,2,4,3]=>[4,3,2,1,8,7,5,6]=>[1,1,1,2,1,2]
[7,2,8,6,1,3,4,5]=>[5,6,7,8,2,1,4,3]=>[4,3,2,1,7,8,5,6]=>[1,1,1,3,2]
[2,1,8,7,3,4,5,6]=>[5,6,7,8,1,4,2,3]=>[4,3,2,1,8,5,7,6]=>[1,1,1,2,2,1]
[8,2,7,6,1,3,4,5]=>[5,6,7,8,2,4,3,1]=>[4,3,2,1,7,5,6,8]=>[1,1,1,2,3]
[1,2,8,7,3,4,5,6]=>[5,6,7,8,4,1,2,3]=>[4,3,2,1,5,8,7,6]=>[1,1,1,3,1,1]
[1,3,8,7,2,4,5,6]=>[5,6,7,8,2,4,1,3]=>[4,3,2,1,7,5,8,6]=>[1,1,1,2,2,1]
[1,7,8,3,6,2,4,5]=>[4,6,7,2,8,5,1,3]=>[5,3,2,7,1,4,8,6]=>[1,1,2,3,1]
[4,1,5,8,7,2,3,6]=>[3,1,6,7,8,5,2,4]=>[6,8,3,2,1,4,7,5]=>[2,1,1,3,1]
[5,4,8,7,6,1,2,3]=>[2,1,6,7,8,5,4,3]=>[7,8,3,2,1,4,5,6]=>[2,1,1,4]
[6,8,3,7,5,1,2,4]=>[3,6,1,7,8,5,4,2]=>[6,3,8,2,1,4,5,7]=>[1,2,1,4]
[7,8,6,2,5,1,3,4]=>[4,6,7,1,8,5,3,2]=>[5,3,2,8,1,4,6,7]=>[1,1,2,4]
[8,1,6,7,3,2,4,5]=>[6,5,7,3,8,2,4,1]=>[3,4,2,6,1,7,5,8]=>[2,2,2,2]
[8,1,5,3,7,2,4,6]=>[4,6,3,7,8,2,5,1]=>[5,3,6,2,1,7,4,8]=>[1,2,1,2,2]
[8,1,5,3,6,2,4,7]=>[4,6,3,7,2,5,8,1]=>[5,3,6,2,7,4,1,8]=>[1,2,2,1,2]
[7,5,1,3,6,2,4,8]=>[4,6,7,3,2,5,1,8]=>[5,3,2,6,7,4,8,1]=>[1,1,3,2,1]
[7,5,8,3,6,2,4,1]=>[4,2,6,1,8,7,5,3]=>[5,7,3,8,1,2,4,6]=>[2,2,4]
[7,4,8,3,2,6,5,1]=>[2,4,8,5,1,7,6,3]=>[7,5,1,4,8,2,3,6]=>[1,1,3,3]
[7,4,1,3,2,6,5,8]=>[4,7,3,2,5,6,1,8]=>[5,2,6,7,4,3,8,1]=>[1,3,1,2,1]
[8,1,4,3,2,6,5,7]=>[4,3,7,2,5,6,8,1]=>[5,6,2,7,4,3,1,8]=>[2,2,1,1,2]
[8,1,4,3,2,7,5,6]=>[4,3,7,8,2,5,6,1]=>[5,6,2,1,7,4,3,8]=>[2,1,2,1,2]
[8,1,4,3,2,7,6,5]=>[3,8,4,7,2,5,6,1]=>[6,1,5,2,7,4,3,8]=>[1,2,2,1,2]
[8,1,5,4,6,7,2,3]=>[4,3,7,5,8,2,6,1]=>[5,6,2,4,1,7,3,8]=>[2,2,2,2]
[8,1,5,3,6,2,7,4]=>[8,4,3,6,2,5,7,1]=>[1,5,6,3,7,4,2,8]=>[3,2,1,2]
[8,1,4,3,2,6,7,5]=>[4,3,6,8,2,5,7,1]=>[5,6,3,1,7,4,2,8]=>[2,1,2,1,2]
[8,1,4,3,2,5,7,6]=>[4,3,8,2,5,6,7,1]=>[5,6,1,7,4,3,2,8]=>[2,2,1,1,2]
[8,1,4,3,2,5,6,7]=>[5,4,2,3,6,7,8,1]=>[4,5,7,6,3,2,1,8]=>[3,1,1,1,2]
[7,4,1,3,2,5,6,8]=>[5,3,4,2,6,7,1,8]=>[4,6,5,7,3,2,8,1]=>[2,2,1,2,1]
[7,4,8,3,2,5,6,1]=>[2,5,4,6,1,8,7,3]=>[7,4,5,3,8,1,2,6]=>[1,2,2,3]
[6,4,3,8,2,5,7,1]=>[3,2,5,1,6,8,7,4]=>[6,7,4,8,3,1,2,5]=>[2,2,1,3]
[6,4,3,1,2,5,8,7]=>[8,4,3,2,5,1,6,7]=>[1,5,6,7,4,8,3,2]=>[4,2,1,1]
[7,4,1,3,2,5,8,6]=>[4,8,3,2,5,6,1,7]=>[5,1,6,7,4,3,8,2]=>[1,3,1,2,1]
[7,4,1,3,2,6,8,5]=>[4,6,2,8,3,5,1,7]=>[5,3,7,1,6,4,8,2]=>[1,2,2,2,1]
[7,5,1,3,6,2,8,4]=>[8,4,6,3,2,5,1,7]=>[1,5,3,6,7,4,8,2]=>[2,3,2,1]
[7,5,1,4,6,8,2,3]=>[4,7,5,2,8,3,1,6]=>[5,2,4,7,1,6,8,3]=>[1,3,3,1]
[7,5,8,3,6,2,1,4]=>[4,2,7,6,1,8,5,3]=>[5,7,2,3,8,1,4,6]=>[2,3,3]
[7,4,8,3,2,6,1,5]=>[2,5,4,7,1,8,6,3]=>[7,4,5,2,8,1,3,6]=>[1,2,2,3]
[7,4,8,3,2,5,1,6]=>[2,5,4,7,6,1,8,3]=>[7,4,5,2,3,8,1,6]=>[1,2,3,2]
[6,4,3,8,2,5,1,7]=>[3,2,5,1,7,6,8,4]=>[6,7,4,8,2,3,1,5]=>[2,2,2,2]
[6,4,3,7,2,5,8,1]=>[3,2,5,1,6,4,8,7]=>[6,7,4,8,3,5,1,2]=>[2,2,2,2]
[5,4,3,2,8,6,1,7]=>[3,2,1,7,4,6,8,5]=>[6,7,8,2,5,3,1,4]=>[3,2,1,2]
[5,4,3,2,8,7,1,6]=>[3,2,1,7,8,4,6,5]=>[6,7,8,2,1,5,3,4]=>[3,1,2,2]
[6,5,3,8,7,2,1,4]=>[7,3,2,1,6,8,5,4]=>[2,6,7,8,3,1,4,5]=>[4,1,3]
[6,5,4,8,7,1,2,3]=>[6,3,2,1,7,8,5,4]=>[3,6,7,8,2,1,4,5]=>[4,1,3]
[6,5,4,1,7,8,2,3]=>[7,5,3,2,1,8,4,6]=>[2,4,6,7,8,1,5,3]=>[5,2,1]
[6,5,3,1,7,2,8,4]=>[3,8,6,4,2,1,5,7]=>[6,1,3,5,7,8,4,2]=>[1,5,1,1]
[6,4,3,1,2,7,8,5]=>[6,3,2,8,4,1,5,7]=>[3,6,7,1,5,8,4,2]=>[3,3,1,1]
[5,4,3,2,1,8,6,7]=>[4,3,2,1,7,8,5,6]=>[5,6,7,8,2,1,4,3]=>[4,1,2,1]
[6,5,3,1,8,2,7,4]=>[3,8,6,2,1,7,4,5]=>[6,1,3,7,8,2,5,4]=>[1,4,2,1]
[6,5,4,1,8,7,2,3]=>[7,3,2,1,8,6,4,5]=>[2,6,7,8,1,3,5,4]=>[4,3,1]
[7,5,1,4,8,6,2,3]=>[4,7,2,8,6,3,1,5]=>[5,2,7,1,3,6,8,4]=>[1,2,4,1]
[7,4,1,3,2,8,6,5]=>[8,4,2,7,3,5,1,6]=>[1,5,7,2,6,4,8,3]=>[3,2,2,1]
[7,4,1,3,2,8,5,6]=>[4,7,2,8,3,5,1,6]=>[5,2,7,1,6,4,8,3]=>[1,2,2,2,1]
[6,4,3,1,2,8,5,7]=>[7,3,2,8,4,1,5,6]=>[2,6,7,1,5,8,4,3]=>[3,3,1,1]
[6,4,3,1,2,7,5,8]=>[7,4,3,2,5,1,6,8]=>[2,5,6,7,4,8,3,1]=>[4,2,1,1]
[6,5,3,8,7,2,4,1]=>[6,2,1,8,3,7,5,4]=>[3,7,8,1,6,2,4,5]=>[3,2,3]
[6,5,3,1,7,2,4,8]=>[6,3,7,4,2,1,5,8]=>[3,6,2,5,7,8,4,1]=>[2,4,1,1]
[6,5,3,1,8,2,4,7]=>[6,3,7,2,1,8,4,5]=>[3,6,2,7,8,1,5,4]=>[2,3,2,1]
[7,5,1,3,8,2,4,6]=>[4,6,7,2,8,3,1,5]=>[5,3,2,7,1,6,8,4]=>[1,1,2,3,1]
[7,6,1,8,3,2,4,5]=>[6,5,7,8,3,2,1,4]=>[3,4,2,1,6,7,8,5]=>[2,1,4,1]
[7,6,1,8,4,5,2,3]=>[7,5,8,6,3,2,1,4]=>[2,4,1,3,6,7,8,5]=>[2,5,1]
[7,6,8,1,4,5,2,3]=>[7,5,8,4,2,1,6,3]=>[2,4,1,5,7,8,3,6]=>[2,4,2]
[7,6,8,1,3,2,5,4]=>[5,8,4,6,2,1,7,3]=>[4,1,5,3,7,8,2,6]=>[1,2,3,2]
[6,5,3,7,8,2,4,1]=>[6,3,2,1,4,8,7,5]=>[3,6,7,8,5,1,2,4]=>[4,1,3]
[6,4,3,7,2,1,5,8]=>[3,2,6,5,1,7,4,8]=>[6,7,3,4,8,2,5,1]=>[2,3,2,1]
[7,4,8,3,2,1,5,6]=>[2,6,5,4,7,1,8,3]=>[7,3,4,5,2,8,1,6]=>[1,3,2,2]
[7,4,8,3,2,1,6,5]=>[2,5,4,8,6,1,7,3]=>[7,4,5,1,3,8,2,6]=>[1,2,3,2]
[7,5,8,3,1,2,6,4]=>[8,5,4,2,6,1,7,3]=>[1,4,5,7,3,8,2,6]=>[4,2,2]
[7,5,8,4,1,6,2,3]=>[7,2,8,5,4,1,6,3]=>[2,7,1,4,5,8,3,6]=>[2,4,2]
[6,5,4,8,1,7,2,3]=>[7,3,2,1,8,5,6,4]=>[2,6,7,8,1,4,3,5]=>[4,2,2]
[6,5,3,8,1,2,7,4]=>[3,8,5,2,1,6,7,4]=>[6,1,4,7,8,3,2,5]=>[1,4,1,2]
[5,4,3,2,8,1,7,6]=>[3,2,1,8,4,6,7,5]=>[6,7,8,1,5,3,2,4]=>[3,2,1,2]
[6,4,3,7,2,1,8,5]=>[3,2,5,1,8,6,4,7]=>[6,7,4,8,1,3,5,2]=>[2,2,3,1]
[6,5,3,7,1,2,8,4]=>[3,8,5,2,1,6,4,7]=>[6,1,4,7,8,3,5,2]=>[1,4,2,1]
[6,5,4,7,1,8,2,3]=>[7,3,2,1,8,5,4,6]=>[2,6,7,8,1,4,5,3]=>[4,3,1]
[6,5,3,7,8,2,1,4]=>[7,3,2,1,6,4,8,5]=>[2,6,7,8,3,5,1,4]=>[4,2,2]
[6,4,3,7,2,8,1,5]=>[3,2,5,1,7,4,8,6]=>[6,7,4,8,2,5,1,3]=>[2,2,2,2]
[5,4,3,2,7,8,1,6]=>[3,2,1,7,4,5,8,6]=>[6,7,8,2,5,4,1,3]=>[3,2,1,2]
[5,4,3,2,6,8,1,7]=>[4,3,2,1,5,7,8,6]=>[5,6,7,8,4,2,1,3]=>[4,1,1,2]
[5,6,2,1,3,4,8,7]=>[3,8,4,1,5,2,6,7]=>[6,1,5,8,4,7,3,2]=>[1,3,2,1,1]
[5,8,2,7,4,1,3,6]=>[6,1,7,3,5,8,4,2]=>[3,8,2,6,4,1,5,7]=>[2,2,1,3]
[5,3,7,8,2,1,4,6]=>[6,2,1,5,7,3,8,4]=>[3,7,8,4,2,6,1,5]=>[3,1,2,2]
[7,6,1,2,5,8,3,4]=>[7,5,8,3,4,2,1,6]=>[2,4,1,6,5,7,8,3]=>[2,2,3,1]
[2,1,7,8,4,3,5,6]=>[6,5,7,1,3,8,2,4]=>[3,4,2,8,6,1,7,5]=>[2,2,1,2,1]
[7,8,1,2,5,4,6,3]=>[6,5,8,3,4,1,7,2]=>[3,4,1,6,5,8,2,7]=>[2,2,2,2]
[2,6,8,3,1,4,7,5]=>[4,8,5,1,2,6,7,3]=>[5,1,4,8,7,3,2,6]=>[1,3,1,1,2]
[6,1,8,3,2,4,5,7]=>[5,4,6,7,1,8,2,3]=>[4,5,3,2,8,1,7,6]=>[2,1,2,2,1]
[5,8,7,4,2,1,6,3]=>[1,5,8,6,4,7,3,2]=>[8,4,1,3,5,2,6,7]=>[1,1,3,3]
[7,5,1,6,8,3,4,2]=>[6,4,2,8,7,3,1,5]=>[3,5,7,1,2,6,8,4]=>[3,4,1]
[4,7,2,8,1,3,6,5]=>[1,8,3,5,6,2,7,4]=>[8,1,6,4,3,7,2,5]=>[1,2,1,2,2]
[7,3,8,6,1,2,5,4]=>[8,2,5,6,1,7,4,3]=>[1,7,4,3,8,2,5,6]=>[2,1,2,3]
[3,4,7,1,8,2,6,5]=>[8,1,2,6,7,4,3,5]=>[1,8,7,3,2,5,6,4]=>[2,1,1,3,1]
[1,8,2,4,3,5,6,7]=>[5,3,4,6,7,8,1,2]=>[4,6,5,3,2,1,8,7]=>[2,1,1,1,2,1]
[1,7,2,4,3,5,6,8]=>[5,3,4,6,7,1,2,8]=>[4,6,5,3,2,8,7,1]=>[2,1,1,2,1,1]
[1,6,2,4,3,5,7,8]=>[5,3,4,6,1,2,7,8]=>[4,6,5,3,8,7,2,1]=>[2,1,2,1,1,1]
[1,5,2,4,3,6,7,8]=>[5,3,4,1,2,6,7,8]=>[4,6,5,8,7,3,2,1]=>[2,2,1,1,1,1]
[1,6,2,5,3,4,7,8]=>[5,6,3,4,1,2,7,8]=>[4,3,6,5,8,7,2,1]=>[1,2,2,1,1,1]
[1,7,2,5,3,4,6,8]=>[5,6,3,4,7,1,2,8]=>[4,3,6,5,2,8,7,1]=>[1,2,1,2,1,1]
[1,8,2,5,3,4,6,7]=>[5,6,3,4,7,8,1,2]=>[4,3,6,5,2,1,8,7]=>[1,2,1,1,2,1]
[1,8,2,6,3,4,5,7]=>[5,6,7,3,4,8,1,2]=>[4,3,2,6,5,1,8,7]=>[1,1,2,1,2,1]
[1,7,2,6,3,4,5,8]=>[5,6,7,3,4,1,2,8]=>[4,3,2,6,5,8,7,1]=>[1,1,2,2,1,1]
[1,8,2,7,3,5,4,6]=>[7,5,6,8,3,4,1,2]=>[2,4,3,1,6,5,8,7]=>[2,1,2,2,1]
[1,7,2,8,3,5,4,6]=>[7,5,6,8,3,1,2,4]=>[2,4,3,1,6,8,7,5]=>[2,1,3,1,1]
[1,6,2,8,3,5,4,7]=>[7,5,6,2,8,1,3,4]=>[2,4,3,7,1,8,6,5]=>[2,2,2,1,1]
[1,5,2,8,3,6,4,7]=>[7,5,2,6,8,1,3,4]=>[2,4,7,3,1,8,6,5]=>[3,1,2,1,1]
[1,4,2,8,3,6,5,7]=>[2,7,5,6,8,1,3,4]=>[7,2,4,3,1,8,6,5]=>[1,2,1,2,1,1]
[1,3,2,8,4,6,5,7]=>[7,2,5,6,8,1,3,4]=>[2,7,4,3,1,8,6,5]=>[2,1,1,2,1,1]
[1,2,3,8,4,6,5,7]=>[7,5,6,8,1,2,3,4]=>[2,4,3,1,8,7,6,5]=>[2,1,2,1,1,1]
[1,2,3,7,4,6,5,8]=>[7,5,6,1,2,3,4,8]=>[2,4,3,8,7,6,5,1]=>[2,2,1,1,1,1]
[1,4,2,7,3,6,5,8]=>[2,7,5,6,1,3,4,8]=>[7,2,4,3,8,6,5,1]=>[1,2,2,1,1,1]
[1,5,2,7,3,6,4,8]=>[7,5,2,6,1,3,4,8]=>[2,4,7,3,8,6,5,1]=>[3,2,1,1,1]
[1,6,2,7,3,5,4,8]=>[7,5,6,3,1,2,4,8]=>[2,4,3,6,8,7,5,1]=>[2,3,1,1,1]
[1,7,2,6,3,5,4,8]=>[7,5,6,3,4,1,2,8]=>[2,4,3,6,5,8,7,1]=>[2,2,2,1,1]
[1,8,2,6,3,5,4,7]=>[7,5,6,3,4,8,1,2]=>[2,4,3,6,5,1,8,7]=>[2,2,1,2,1]
[1,8,2,5,3,6,4,7]=>[7,5,3,4,6,8,1,2]=>[2,4,6,5,3,1,8,7]=>[3,1,1,2,1]
[1,7,2,5,3,6,4,8]=>[7,5,3,4,6,1,2,8]=>[2,4,6,5,3,8,7,1]=>[3,1,2,1,1]
[1,6,2,5,3,7,4,8]=>[7,5,3,4,1,2,6,8]=>[2,4,6,5,8,7,3,1]=>[3,2,1,1,1]
[1,5,2,4,3,7,6,8]=>[4,7,3,1,2,5,6,8]=>[5,2,6,8,7,4,3,1]=>[1,3,1,1,1,1]
[1,6,2,4,3,7,5,8]=>[4,7,3,5,1,2,6,8]=>[5,2,6,4,8,7,3,1]=>[1,2,2,1,1,1]
[1,8,2,4,3,6,5,7]=>[4,7,3,5,6,8,1,2]=>[5,2,6,4,3,1,8,7]=>[1,2,1,1,2,1]
[1,8,2,3,4,6,5,7]=>[7,3,4,5,6,8,1,2]=>[2,6,5,4,3,1,8,7]=>[2,1,1,1,2,1]
[1,7,2,3,4,6,5,8]=>[7,3,4,5,6,1,2,8]=>[2,6,5,4,3,8,7,1]=>[2,1,1,2,1,1]
[1,8,2,3,4,7,5,6]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[1,2,1,1,2,1]
[1,8,2,4,3,7,5,6]=>[4,7,8,3,5,6,1,2]=>[5,2,1,6,4,3,8,7]=>[1,1,2,1,2,1]
[1,7,2,4,3,8,5,6]=>[4,7,8,3,5,1,2,6]=>[5,2,1,6,4,8,7,3]=>[1,1,2,2,1,1]
[1,6,2,4,3,8,5,7]=>[4,7,8,3,1,2,5,6]=>[5,2,1,6,8,7,4,3]=>[1,1,3,1,1,1]
[1,5,2,4,3,8,6,7]=>[4,7,2,8,1,3,5,6]=>[5,2,7,1,8,6,4,3]=>[1,2,2,1,1,1]
[1,6,2,5,3,8,4,7]=>[7,4,8,3,1,2,5,6]=>[2,5,1,6,8,7,4,3]=>[2,3,1,1,1]
[1,7,2,5,3,8,4,6]=>[7,4,8,3,5,1,2,6]=>[2,5,1,6,4,8,7,3]=>[2,2,2,1,1]
[1,8,2,5,3,7,4,6]=>[7,4,8,3,5,6,1,2]=>[2,5,1,6,4,3,8,7]=>[2,2,1,2,1]
[1,8,2,6,3,7,4,5]=>[7,8,5,3,4,6,1,2]=>[2,1,4,6,5,3,8,7]=>[1,3,1,2,1]
[1,7,2,6,3,8,4,5]=>[7,8,5,3,4,1,2,6]=>[2,1,4,6,5,8,7,3]=>[1,3,2,1,1]
[1,2,3,8,4,7,5,6]=>[7,8,5,6,1,2,3,4]=>[2,1,4,3,8,7,6,5]=>[1,2,2,1,1,1]
[1,3,2,8,4,7,5,6]=>[7,8,2,5,6,1,3,4]=>[2,1,7,4,3,8,6,5]=>[1,2,1,2,1,1]
[1,4,2,8,3,7,5,6]=>[2,7,8,5,6,1,3,4]=>[7,2,1,4,3,8,6,5]=>[1,1,2,2,1,1]
[1,5,2,8,3,7,4,6]=>[7,2,8,5,6,1,3,4]=>[2,7,1,4,3,8,6,5]=>[2,2,2,1,1]
[1,7,2,8,3,6,4,5]=>[7,8,5,6,3,1,2,4]=>[2,1,4,3,6,8,7,5]=>[1,2,3,1,1]
[1,8,2,7,3,6,4,5]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[1,2,2,2,1]
[4,6,3,7,2,5,1,8]=>[1,3,5,2,7,6,4,8]=>[8,6,4,7,2,3,5,1]=>[1,1,2,3,1]
[4,6,3,7,5,2,1,8]=>[7,1,3,2,6,5,4,8]=>[2,8,6,7,3,4,5,1]=>[2,2,3,1]
[4,6,3,8,5,1,7,2]=>[8,1,3,2,6,5,7,4]=>[1,8,6,7,3,4,2,5]=>[2,2,2,2]
[4,6,3,8,5,1,2,7]=>[1,3,6,2,7,5,8,4]=>[8,6,3,7,2,4,1,5]=>[1,1,2,2,2]
[5,6,8,3,4,1,2,7]=>[1,6,4,2,7,5,8,3]=>[8,3,5,7,2,4,1,6]=>[1,3,2,2]
[5,6,8,3,4,1,7,2]=>[1,4,2,8,6,5,7,3]=>[8,5,7,1,3,4,2,6]=>[1,2,3,2]
[4,6,2,7,5,3,1,8]=>[7,1,6,3,2,5,4,8]=>[2,8,3,6,7,4,5,1]=>[2,3,2,1]
[5,6,7,2,4,3,1,8]=>[1,7,4,2,6,5,3,8]=>[8,2,5,7,3,4,6,1]=>[1,3,3,1]
[5,6,8,4,3,1,7,2]=>[1,2,8,6,5,4,7,3]=>[8,7,1,3,4,5,2,6]=>[1,1,4,2]
[5,7,8,4,1,6,2,3]=>[1,7,8,5,4,2,6,3]=>[8,2,1,4,5,7,3,6]=>[1,1,4,2]
[5,7,8,4,1,6,3,2]=>[8,1,7,5,4,2,6,3]=>[1,8,2,4,5,7,3,6]=>[2,4,2]
[5,7,8,4,1,3,6,2]=>[1,6,8,5,4,2,7,3]=>[8,3,1,4,5,7,2,6]=>[1,1,4,2]
[5,6,8,4,2,1,7,3]=>[1,5,2,8,6,4,7,3]=>[8,4,7,1,3,5,2,6]=>[1,2,3,2]
[5,6,8,2,4,1,7,3]=>[1,8,4,2,6,5,7,3]=>[8,1,5,7,3,4,2,6]=>[1,3,2,2]
[4,6,2,8,5,1,7,3]=>[8,1,6,3,2,5,7,4]=>[1,8,3,6,7,4,2,5]=>[2,3,1,2]
[3,2,6,8,5,1,7,4]=>[3,8,1,6,2,5,7,4]=>[6,1,8,3,7,4,2,5]=>[1,2,2,1,2]
[3,2,6,8,5,1,4,7]=>[6,1,3,7,2,5,8,4]=>[3,8,6,2,7,4,1,5]=>[2,1,2,1,2]
[4,6,2,8,5,1,3,7]=>[1,6,7,3,2,5,8,4]=>[8,3,2,6,7,4,1,5]=>[1,1,3,1,2]
[5,6,8,2,4,1,3,7]=>[4,1,6,2,7,5,8,3]=>[5,8,3,7,2,4,1,6]=>[2,2,2,2]
[5,6,8,4,2,1,3,7]=>[1,6,5,2,7,4,8,3]=>[8,3,4,7,2,5,1,6]=>[1,3,2,2]
[6,7,8,1,5,2,3,4]=>[6,7,1,8,4,2,5,3]=>[3,2,8,1,5,7,4,6]=>[1,2,3,2]
[6,7,8,1,5,2,4,3]=>[8,6,1,7,4,2,5,3]=>[1,3,8,2,5,7,4,6]=>[3,3,2]
[6,7,8,1,5,3,2,4]=>[7,6,1,8,4,2,5,3]=>[2,3,8,1,5,7,4,6]=>[3,3,2]
[6,7,8,1,3,5,2,4]=>[5,7,1,8,4,2,6,3]=>[4,2,8,1,5,7,3,6]=>[1,2,3,2]
[5,7,8,2,1,6,3,4]=>[4,1,7,8,5,2,6,3]=>[5,8,2,1,4,7,3,6]=>[2,1,3,2]
[4,7,2,8,1,6,3,5]=>[1,7,8,3,5,2,6,4]=>[8,2,1,6,4,7,3,5]=>[1,1,2,2,2]
[3,2,7,8,1,6,4,5]=>[7,8,1,5,2,3,6,4]=>[2,1,8,4,7,6,3,5]=>[1,2,2,1,2]
[3,2,7,8,1,6,5,4]=>[8,7,1,5,2,3,6,4]=>[1,2,8,4,7,6,3,5]=>[3,2,1,2]
[4,7,2,8,1,6,5,3]=>[8,1,7,3,5,2,6,4]=>[1,8,2,6,4,7,3,5]=>[2,2,2,2]
[5,7,8,2,1,6,4,3]=>[1,8,4,7,5,2,6,3]=>[8,1,5,2,4,7,3,6]=>[1,2,3,2]
[6,7,8,1,3,5,4,2]=>[8,5,1,7,4,2,6,3]=>[1,4,8,2,5,7,3,6]=>[3,3,2]
[6,7,8,1,5,3,4,2]=>[6,1,8,7,4,2,5,3]=>[3,8,1,2,5,7,4,6]=>[2,4,2]
[6,7,8,1,5,4,3,2]=>[1,8,7,6,4,2,5,3]=>[8,1,2,3,5,7,4,6]=>[1,5,2]
[6,7,8,1,5,4,2,3]=>[7,1,8,6,4,2,5,3]=>[2,8,1,3,5,7,4,6]=>[2,4,2]
[6,7,8,1,4,5,2,3]=>[7,5,1,8,4,2,6,3]=>[2,4,8,1,5,7,3,6]=>[3,3,2]
[6,7,8,1,4,5,3,2]=>[5,1,8,7,4,2,6,3]=>[4,8,1,2,5,7,3,6]=>[2,4,2]
[6,7,8,1,4,3,5,2]=>[6,5,1,8,4,2,7,3]=>[3,4,8,1,5,7,2,6]=>[3,3,2]
[6,7,8,1,3,4,5,2]=>[5,6,1,8,4,2,7,3]=>[4,3,8,1,5,7,2,6]=>[1,2,3,2]
[5,7,8,2,1,4,6,3]=>[4,1,6,8,5,2,7,3]=>[5,8,3,1,4,7,2,6]=>[2,1,3,2]
[4,7,2,8,1,5,6,3]=>[1,6,8,3,5,2,7,4]=>[8,3,1,6,4,7,2,5]=>[1,1,2,2,2]
[3,2,6,8,4,1,7,5]=>[5,1,3,8,2,6,7,4]=>[4,8,6,1,7,3,2,5]=>[2,1,2,1,2]
[4,6,2,8,3,1,7,5]=>[1,5,8,3,2,6,7,4]=>[8,4,1,6,7,3,2,5]=>[1,1,3,1,2]
[5,6,8,3,2,1,7,4]=>[1,5,4,2,8,6,7,3]=>[8,4,5,7,1,3,2,6]=>[1,3,2,2]
[5,7,8,3,1,4,6,2]=>[1,6,4,8,5,2,7,3]=>[8,3,5,1,4,7,2,6]=>[1,2,3,2]
[5,7,8,3,1,6,4,2]=>[1,4,8,7,5,2,6,3]=>[8,5,1,2,4,7,3,6]=>[1,1,4,2]
[5,7,8,3,1,6,2,4]=>[1,7,4,8,5,2,6,3]=>[8,2,5,1,4,7,3,6]=>[1,2,3,2]
[4,7,3,8,1,6,2,5]=>[1,3,7,8,5,2,6,4]=>[8,6,2,1,4,7,3,5]=>[1,1,1,3,2]
[4,7,3,8,1,6,5,2]=>[8,1,3,7,5,2,6,4]=>[1,8,6,2,4,7,3,5]=>[2,1,3,2]
[4,7,3,8,1,5,6,2]=>[1,3,6,8,5,2,7,4]=>[8,6,3,1,4,7,2,5]=>[1,1,1,3,2]
[4,6,3,8,2,1,7,5]=>[1,3,5,2,8,6,7,4]=>[8,6,4,7,1,3,2,5]=>[1,1,2,2,2]
[4,5,3,2,8,1,7,6]=>[1,3,2,8,4,6,7,5]=>[8,6,7,1,5,3,2,4]=>[1,2,2,1,2]
[4,5,2,3,8,1,7,6]=>[1,8,3,2,4,6,7,5]=>[8,1,6,7,5,3,2,4]=>[1,3,1,1,2]
[3,2,5,4,8,1,7,6]=>[1,3,8,2,4,6,7,5]=>[8,6,1,7,5,3,2,4]=>[1,1,2,1,1,2]
[4,5,3,2,8,1,6,7]=>[1,4,3,2,6,7,8,5]=>[8,5,6,7,3,2,1,4]=>[1,3,1,1,2]
[4,6,3,8,2,1,5,7]=>[1,3,6,5,2,7,8,4]=>[8,6,3,4,7,2,1,5]=>[1,1,3,1,2]
[4,7,3,8,1,2,6,5]=>[1,3,8,5,6,2,7,4]=>[8,6,1,4,3,7,2,5]=>[1,1,2,2,2]
[5,7,8,3,1,2,4,6]=>[5,1,6,4,7,2,8,3]=>[4,8,3,5,2,7,1,6]=>[2,2,2,2]
[5,7,8,3,1,2,6,4]=>[1,8,5,4,6,2,7,3]=>[8,1,4,5,3,7,2,6]=>[1,3,2,2]
[5,7,8,3,1,4,2,6]=>[1,7,5,4,6,2,8,3]=>[8,2,4,5,3,7,1,6]=>[1,3,2,2]
[5,6,8,3,2,1,4,7]=>[1,6,5,4,2,7,8,3]=>[8,3,4,5,7,2,1,6]=>[1,4,1,2]
[3,2,7,8,1,5,4,6]=>[7,1,5,6,2,3,8,4]=>[2,8,4,3,7,6,1,5]=>[2,1,2,1,2]
[5,7,8,2,1,4,3,6]=>[4,1,7,5,6,2,8,3]=>[5,8,2,4,3,7,1,6]=>[2,2,2,2]
[6,7,8,1,3,4,2,5]=>[5,7,4,1,6,2,8,3]=>[4,2,5,8,3,7,1,6]=>[1,3,2,2]
[6,7,8,1,4,3,2,5]=>[7,6,4,1,5,2,8,3]=>[2,3,5,8,4,7,1,6]=>[4,2,2]
[6,7,8,1,4,2,5,3]=>[8,6,4,1,5,2,7,3]=>[1,3,5,8,4,7,2,6]=>[4,2,2]
[6,7,8,1,4,2,3,5]=>[6,7,4,1,5,2,8,3]=>[3,2,5,8,4,7,1,6]=>[1,3,2,2]
[6,7,8,1,2,5,3,4]=>[7,8,4,1,5,2,6,3]=>[2,1,5,8,4,7,3,6]=>[1,3,2,2]
[6,7,8,1,2,5,4,3]=>[8,7,4,1,5,2,6,3]=>[1,2,5,8,4,7,3,6]=>[4,2,2]
[6,7,8,1,2,4,5,3]=>[6,8,4,1,5,2,7,3]=>[3,1,5,8,4,7,2,6]=>[1,3,2,2]
[6,7,8,1,3,2,5,4]=>[5,8,4,1,6,2,7,3]=>[4,1,5,8,3,7,2,6]=>[1,3,2,2]
[5,7,8,2,1,3,6,4]=>[4,1,8,5,6,2,7,3]=>[5,8,1,4,3,7,2,6]=>[2,2,2,2]
[3,2,7,8,1,4,6,5]=>[8,1,5,6,2,3,7,4]=>[1,8,4,3,7,6,2,5]=>[2,1,2,1,2]
[6,7,8,1,3,2,4,5]=>[6,4,5,1,7,2,8,3]=>[3,5,4,8,2,7,1,6]=>[2,2,2,2]
[6,7,8,1,2,4,3,5]=>[7,4,5,1,6,2,8,3]=>[2,5,4,8,3,7,1,6]=>[2,2,2,2]
[6,7,8,1,2,3,5,4]=>[8,4,5,1,6,2,7,3]=>[1,5,4,8,3,7,2,6]=>[2,2,2,2]
[7,2,8,5,1,6,4,3]=>[8,7,5,2,4,1,6,3]=>[1,2,4,7,5,8,3,6]=>[4,2,2]
[1,3,7,5,4,2,6,8]=>[6,5,2,4,7,1,3,8]=>[3,4,7,5,2,8,6,1]=>[3,1,2,1,1]
[7,2,8,5,4,1,6,3]=>[8,6,5,2,4,1,7,3]=>[1,3,4,7,5,8,2,6]=>[4,2,2]
[2,8,6,5,7,3,1,4]=>[7,6,4,3,8,1,5,2]=>[2,3,5,6,1,8,4,7]=>[4,2,2]
[2,8,4,5,3,7,1,6]=>[3,5,4,7,8,1,6,2]=>[6,4,5,2,1,8,3,7]=>[1,2,1,2,2]
[2,8,4,3,5,6,1,7]=>[4,3,5,7,1,6,8,2]=>[5,6,4,2,8,3,1,7]=>[2,1,2,1,2]
[7,2,8,4,5,6,1,3]=>[4,7,5,8,2,1,6,3]=>[5,2,4,1,7,8,3,6]=>[1,2,3,2]
[6,2,3,8,5,1,7,4]=>[8,6,2,3,1,5,7,4]=>[1,3,7,6,8,4,2,5]=>[3,2,1,2]
[6,3,2,8,5,1,4,7]=>[2,6,7,3,1,5,8,4]=>[7,3,2,6,8,4,1,5]=>[1,1,3,1,2]
[7,4,8,2,5,6,3,1]=>[2,5,8,4,1,7,6,3]=>[7,4,1,5,8,2,3,6]=>[1,1,3,3]
[6,4,8,5,1,3,7,2]=>[2,6,1,8,5,4,7,3]=>[7,3,8,1,4,5,2,6]=>[1,2,3,2]
[6,3,7,5,2,1,8,4]=>[5,8,2,1,6,4,3,7]=>[4,1,7,8,3,5,6,2]=>[1,3,3,1]
[4,3,7,1,5,6,8,2]=>[2,1,5,6,8,4,3,7]=>[7,8,4,3,1,5,6,2]=>[2,1,1,3,1]
[3,6,1,7,5,2,8,4]=>[8,6,1,5,3,2,4,7]=>[1,3,8,4,6,7,5,2]=>[3,3,1,1]
[3,4,1,2,7,6,8,5]=>[1,2,6,5,8,3,4,7]=>[8,7,3,4,1,6,5,2]=>[1,1,2,2,1,1]
[3,4,2,1,7,5,8,6]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[1,1,2,2,1,1]
[3,6,5,7,1,4,8,2]=>[6,3,1,2,8,5,4,7]=>[3,6,8,7,1,4,5,2]=>[3,1,3,1]
[3,5,2,6,4,8,7,1]=>[4,1,2,8,3,5,7,6]=>[5,8,7,1,6,4,2,3]=>[2,1,2,1,2]
[5,3,1,8,6,4,7,2]=>[6,2,1,5,8,7,3,4]=>[3,7,8,4,1,2,6,5]=>[3,1,3,1]
[5,6,1,8,7,2,4,3]=>[1,8,6,2,7,5,3,4]=>[8,1,3,7,2,4,6,5]=>[1,3,3,1]
[6,3,5,8,2,7,4,1]=>[3,8,2,1,5,7,6,4]=>[6,1,7,8,4,2,3,5]=>[1,3,1,3]
[6,5,8,4,2,3,7,1]=>[5,2,1,6,4,8,7,3]=>[4,7,8,3,5,1,2,6]=>[3,2,3]
[6,2,5,8,3,7,1,4]=>[5,3,7,1,8,2,6,4]=>[4,6,2,8,1,7,3,5]=>[2,2,2,2]
[1,6,5,7,3,4,2,8]=>[5,3,2,7,6,1,4,8]=>[4,6,7,2,3,8,5,1]=>[3,3,1,1]
[1,5,2,7,4,6,3,8]=>[5,2,7,6,1,3,4,8]=>[4,7,2,3,8,6,5,1]=>[2,3,1,1,1]
[5,2,1,8,7,6,3,4]=>[7,1,8,6,2,5,3,4]=>[2,8,1,3,7,4,6,5]=>[2,3,2,1]
[7,1,3,8,4,6,2,5]=>[5,7,8,3,6,2,1,4]=>[4,2,1,6,3,7,8,5]=>[1,1,2,3,1]
[2,3,4,8,6,1,7,5]=>[8,6,1,2,3,5,7,4]=>[1,3,8,7,6,4,2,5]=>[3,1,1,1,2]
[2,3,4,8,6,5,1,7]=>[7,6,1,2,3,5,8,4]=>[2,3,8,7,6,4,1,5]=>[3,1,1,1,2]
[2,7,3,5,8,6,1,4]=>[4,7,8,3,1,2,6,5]=>[5,2,1,6,8,7,3,4]=>[1,1,3,1,2]
[3,2,4,7,8,6,1,5]=>[7,1,4,8,2,3,6,5]=>[2,8,5,1,7,6,3,4]=>[2,1,2,1,2]
[1,5,4,6,2,7,3,8]=>[3,2,7,5,1,4,6,8]=>[6,7,2,4,8,5,3,1]=>[2,3,1,1,1]
[5,2,4,7,1,8,3,6]=>[3,7,1,8,2,5,4,6]=>[6,2,8,1,7,4,5,3]=>[1,2,2,2,1]
[5,3,6,4,1,8,7,2]=>[4,2,1,3,8,7,5,6]=>[5,7,8,6,1,2,4,3]=>[3,1,3,1]
[5,3,6,1,4,8,2,7]=>[2,5,1,7,3,8,4,6]=>[7,4,8,2,6,1,5,3]=>[1,2,2,2,1]
[7,3,5,6,8,4,2,1]=>[3,4,8,2,1,7,6,5]=>[6,5,1,7,8,2,3,4]=>[1,1,3,3]
[6,3,5,1,8,2,7,4]=>[8,2,6,3,1,7,4,5]=>[1,7,3,6,8,2,5,4]=>[2,3,2,1]
[2,6,1,5,8,4,7,3]=>[4,6,2,8,1,7,3,5]=>[5,3,7,1,8,2,6,4]=>[1,2,2,2,1]
[2,7,6,5,8,3,4,1]=>[6,4,3,2,8,1,7,5]=>[3,5,6,7,1,8,2,4]=>[4,2,2]
[5,7,1,6,3,8,4,2]=>[1,8,5,4,7,3,2,6]=>[8,1,4,5,2,6,7,3]=>[1,3,3,1]
[3,2,4,1,7,8,5,6]=>[1,7,2,3,5,8,4,6]=>[8,2,7,6,4,1,5,3]=>[1,2,1,1,2,1]
[3,1,4,2,7,8,6,5]=>[1,5,8,3,7,2,4,6]=>[8,4,1,6,2,7,5,3]=>[1,1,2,2,1,1]
[3,6,4,7,8,2,5,1]=>[6,3,1,2,4,8,7,5]=>[3,6,8,7,5,1,2,4]=>[3,1,1,3]
[6,3,4,5,7,1,8,2]=>[2,3,4,1,8,6,5,7]=>[7,6,5,8,1,3,4,2]=>[1,1,2,3,1]
[2,5,4,6,1,7,8,3]=>[3,2,6,1,4,8,5,7]=>[6,7,3,8,5,1,4,2]=>[2,2,1,2,1]
[7,4,3,2,1,6,5,8]=>[4,3,2,7,5,6,1,8]=>[5,6,7,2,4,3,8,1]=>[3,2,2,1]
[6,7,3,2,5,4,8,1]=>[3,6,4,1,5,2,8,7]=>[6,3,5,8,4,7,1,2]=>[1,3,2,2]
[1,8,3,2,5,4,7,6]=>[3,5,8,4,6,7,1,2]=>[6,4,1,5,3,2,8,7]=>[1,1,2,1,2,1]
[1,8,4,5,2,3,7,6]=>[3,8,5,4,6,7,1,2]=>[6,1,4,5,3,2,8,7]=>[1,3,1,2,1]
[7,3,5,1,6,2,4,8]=>[2,6,7,4,3,5,1,8]=>[7,3,2,5,6,4,8,1]=>[1,1,3,2,1]
[7,2,1,5,6,3,4,8]=>[6,2,4,7,3,5,1,8]=>[3,7,5,2,6,4,8,1]=>[2,1,2,2,1]
[7,2,1,6,5,4,3,8]=>[7,6,2,5,3,4,1,8]=>[2,3,7,4,6,5,8,1]=>[3,2,2,1]
[7,3,6,1,5,4,2,8]=>[7,2,6,4,5,3,1,8]=>[2,7,3,5,4,6,8,1]=>[2,2,3,1]
[7,4,6,5,1,3,2,8]=>[2,7,5,6,4,3,1,8]=>[7,2,4,3,5,6,8,1]=>[1,2,4,1]
[1,8,5,4,3,2,7,6]=>[5,4,3,8,6,7,1,2]=>[4,5,6,1,3,2,8,7]=>[3,2,2,1]
[1,8,6,4,3,7,2,5]=>[5,4,7,3,8,6,1,2]=>[4,5,2,6,1,3,8,7]=>[2,2,3,1]
[6,5,7,4,3,1,8,2]=>[2,1,8,6,5,4,3,7]=>[7,8,1,3,4,5,6,2]=>[2,5,1]
[6,4,7,5,1,3,8,2]=>[2,6,1,8,5,4,3,7]=>[7,3,8,1,4,5,6,2]=>[1,2,4,1]
[6,3,7,1,5,4,8,2]=>[6,2,5,1,8,4,3,7]=>[3,7,4,8,1,5,6,2]=>[2,2,3,1]
[6,2,1,7,5,4,8,3]=>[6,5,2,4,1,8,3,7]=>[3,4,7,5,8,1,6,2]=>[3,2,2,1]
[3,2,1,8,5,4,7,6]=>[1,5,8,2,6,7,3,4]=>[8,4,1,7,3,2,6,5]=>[1,1,2,1,2,1]
[2,3,8,1,5,4,7,6]=>[5,8,1,2,4,6,7,3]=>[4,1,8,7,5,3,2,6]=>[1,2,1,1,1,2]
[2,4,8,5,1,3,7,6]=>[8,2,5,1,4,6,7,3]=>[1,7,4,8,5,3,2,6]=>[2,2,1,1,2]
[2,5,8,4,3,1,7,6]=>[2,5,4,8,1,6,7,3]=>[7,4,5,1,8,3,2,6]=>[1,2,2,1,2]
[2,6,8,4,3,7,1,5]=>[5,4,2,7,8,1,6,3]=>[4,5,7,2,1,8,3,6]=>[3,1,2,2]
[2,7,8,4,3,6,5,1]=>[4,8,5,2,7,1,6,3]=>[5,1,4,7,2,8,3,6]=>[1,3,2,2]
[1,8,7,4,3,6,5,2]=>[4,8,5,7,6,3,1,2]=>[5,1,4,2,3,6,8,7]=>[1,2,4,1]
[1,8,7,5,6,3,4,2]=>[6,4,8,7,5,3,1,2]=>[3,5,1,2,4,6,8,7]=>[2,5,1]
[2,7,8,5,6,3,4,1]=>[6,4,2,8,7,1,5,3]=>[3,5,7,1,2,8,4,6]=>[3,3,2]
[2,5,8,6,7,1,3,4]=>[2,6,7,4,8,1,5,3]=>[7,3,2,5,1,8,4,6]=>[1,1,2,2,2]
[2,4,8,6,1,7,3,5]=>[7,8,2,5,1,4,6,3]=>[2,1,7,4,8,5,3,6]=>[1,2,2,1,2]
[3,2,1,8,6,7,4,5]=>[7,1,5,8,2,6,3,4]=>[2,8,4,1,7,3,6,5]=>[2,1,2,2,1]
[5,2,1,7,6,8,4,3]=>[5,4,1,8,2,7,3,6]=>[4,5,8,1,7,2,6,3]=>[3,2,2,1]
[5,3,7,1,6,8,4,2]=>[5,1,8,2,7,4,3,6]=>[4,8,1,7,2,5,6,3]=>[2,2,3,1]
[5,4,7,6,1,8,3,2]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[1,2,4,1]
[4,5,7,6,8,1,3,2]=>[8,1,2,6,4,3,7,5]=>[1,8,7,3,5,6,2,4]=>[2,1,3,2]
[4,6,7,5,8,3,1,2]=>[2,7,1,4,3,8,6,5]=>[7,2,8,5,6,1,3,4]=>[1,2,2,3]
[1,8,6,5,7,3,2,4]=>[7,6,4,3,8,5,1,2]=>[2,3,5,6,1,4,8,7]=>[4,3,1]
[1,8,5,6,7,2,3,4]=>[6,3,7,4,8,5,1,2]=>[3,6,2,5,1,4,8,7]=>[2,2,3,1]
[4,7,5,6,8,2,3,1]=>[3,6,1,4,2,8,7,5]=>[6,3,8,5,7,1,2,4]=>[1,2,2,3]
[4,6,5,7,8,2,1,3]=>[3,1,2,7,6,4,8,5]=>[6,8,7,2,3,5,1,4]=>[2,1,3,2]
[5,4,6,7,1,8,2,3]=>[2,1,7,3,8,5,4,6]=>[7,8,2,6,1,4,5,3]=>[2,2,3,1]
[5,2,1,6,7,8,3,4]=>[4,7,2,1,5,8,3,6]=>[5,2,7,8,4,1,6,3]=>[1,3,1,2,1]
[6,2,1,5,7,3,8,4]=>[4,8,2,6,3,1,5,7]=>[5,1,7,3,6,8,4,2]=>[1,2,3,1,1]
[6,3,5,1,7,2,8,4]=>[8,2,6,4,3,1,5,7]=>[1,7,3,5,6,8,4,2]=>[2,4,1,1]
[6,4,5,7,1,2,8,3]=>[2,8,5,3,1,6,4,7]=>[7,1,4,6,8,3,5,2]=>[1,4,2,1]
[6,5,4,7,2,1,8,3]=>[5,3,2,1,8,6,4,7]=>[4,6,7,8,1,3,5,2]=>[4,3,1]
[5,6,4,7,2,8,1,3]=>[1,5,3,2,7,4,8,6]=>[8,4,6,7,2,5,1,3]=>[1,3,2,2]
[1,8,3,2,6,7,4,5]=>[7,3,5,8,4,6,1,2]=>[2,6,4,1,5,3,8,7]=>[2,1,2,2,1]
[5,7,3,2,6,8,4,1]=>[3,1,5,8,4,2,7,6]=>[6,8,4,1,5,7,2,3]=>[2,1,3,2]
[5,6,3,2,7,8,1,4]=>[3,1,7,4,2,5,8,6]=>[6,8,2,5,7,4,1,3]=>[2,3,1,2]
[6,5,3,2,7,1,8,4]=>[3,8,4,2,1,6,5,7]=>[6,1,5,7,8,3,4,2]=>[1,4,2,1]
[6,4,3,2,1,7,8,5]=>[4,3,2,6,1,8,5,7]=>[5,6,7,3,8,1,4,2]=>[3,2,2,1]
[6,2,1,4,3,7,8,5]=>[2,4,6,8,3,1,5,7]=>[7,5,3,1,6,8,4,2]=>[1,1,1,3,1,1]
[5,2,1,4,3,8,7,6]=>[8,2,4,1,7,3,5,6]=>[1,7,5,8,2,6,4,3]=>[2,2,2,1,1]
[5,3,4,1,2,8,7,6]=>[2,3,1,8,7,4,5,6]=>[7,6,8,1,2,5,4,3]=>[1,2,3,1,1]
[4,6,3,2,8,7,1,5]=>[1,3,7,2,8,4,6,5]=>[8,6,2,7,1,5,3,4]=>[1,1,2,2,2]
[4,7,3,2,8,6,5,1]=>[8,1,3,7,4,2,6,5]=>[1,8,6,2,5,7,3,4]=>[2,1,3,2]
[1,8,4,7,2,6,5,3]=>[8,3,7,5,6,4,1,2]=>[1,6,2,4,3,5,8,7]=>[2,2,3,1]
[3,7,4,8,2,6,5,1]=>[8,3,5,1,2,7,6,4]=>[1,6,4,8,7,2,3,5]=>[2,2,1,3]
[3,6,4,8,2,7,1,5]=>[3,5,1,2,7,8,6,4]=>[6,4,8,7,2,1,3,5]=>[1,2,1,1,3]
[3,5,4,8,2,1,7,6]=>[3,1,2,5,8,6,7,4]=>[6,8,7,4,1,3,2,5]=>[2,1,1,2,2]
[3,4,5,8,1,2,7,6]=>[1,2,3,8,5,6,7,4]=>[8,7,6,1,4,3,2,5]=>[1,1,1,2,1,2]
[4,3,5,1,8,2,7,6]=>[2,1,3,8,6,7,4,5]=>[7,8,6,1,3,2,5,4]=>[2,1,2,2,1]
[4,2,1,5,8,3,7,6]=>[8,2,1,4,6,7,3,5]=>[1,7,8,5,3,2,6,4]=>[3,1,1,2,1]
[4,2,1,6,8,7,3,5]=>[4,1,7,8,2,6,3,5]=>[5,8,2,1,7,3,6,4]=>[2,1,2,2,1]
[3,4,6,8,1,7,2,5]=>[7,1,2,3,8,5,6,4]=>[2,8,7,6,1,4,3,5]=>[2,1,1,2,2]
[3,5,6,8,7,1,2,4]=>[2,6,1,3,7,8,5,4]=>[7,3,8,6,2,1,4,5]=>[1,2,1,1,3]
[3,6,5,8,7,2,1,4]=>[3,2,7,1,6,8,5,4]=>[6,7,2,8,3,1,4,5]=>[2,2,1,3]
[3,7,5,8,6,2,4,1]=>[3,6,2,8,1,7,5,4]=>[6,3,7,1,8,2,4,5]=>[1,2,2,3]
[1,8,5,7,6,2,4,3]=>[3,8,6,7,5,4,1,2]=>[6,1,3,2,4,5,8,7]=>[1,2,4,1]
[1,8,6,7,5,4,2,3]=>[7,3,8,6,5,4,1,2]=>[2,6,1,3,4,5,8,7]=>[2,5,1]
[3,6,7,8,5,4,1,2]=>[2,7,3,8,1,6,5,4]=>[7,2,6,1,8,3,4,5]=>[1,2,2,3]
[3,5,7,8,6,1,4,2]=>[8,2,6,1,3,7,5,4]=>[1,7,3,8,6,2,4,5]=>[2,2,1,3]
[3,4,7,8,1,6,5,2]=>[8,7,1,2,5,3,6,4]=>[1,2,8,7,4,6,3,5]=>[3,1,2,2]
[4,2,1,7,8,6,5,3]=>[1,4,8,7,2,6,3,5]=>[8,5,1,2,7,3,6,4]=>[1,1,3,2,1]
[2,3,8,1,7,6,5,4]=>[8,7,6,1,2,4,5,3]=>[1,2,3,8,7,5,4,6]=>[4,1,1,2]
[2,4,8,7,1,6,5,3]=>[8,7,2,5,6,1,4,3]=>[1,2,7,4,3,8,5,6]=>[3,1,2,2]
[2,5,8,7,6,1,4,3]=>[8,2,6,7,5,1,4,3]=>[1,7,3,2,4,8,5,6]=>[2,1,3,2]
[2,6,8,7,5,4,1,3]=>[2,7,8,6,5,1,4,3]=>[7,2,1,3,4,8,5,6]=>[1,1,4,2]
[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,12,2,11,3,10,4,9,5,8,6,7]=>[12,1,11,2,10,3,9,4,8,5,7,6]=>[1,2,2,2,2,2,1]
[12,11,10,9,8,7,6,5,4,3,2,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12]
[7,4,6,1,8,3,5,2]=>[2,6,8,7,4,3,1,5]=>[7,3,1,2,5,6,8,4]=>[1,1,5,1]
[8,3,5,1,7,4,6,2]=>[6,2,3,8,7,4,5,1]=>[3,7,6,1,2,5,4,8]=>[2,1,3,2]
[8,3,4,1,7,5,6,2]=>[2,3,6,8,7,4,5,1]=>[7,6,3,1,2,5,4,8]=>[1,1,1,3,2]
[4,8,3,1,7,5,6,2]=>[1,3,6,8,7,4,5,2]=>[8,6,3,1,2,5,4,7]=>[1,1,1,3,2]
[4,6,2,1,7,5,8,3]=>[1,6,3,5,2,8,4,7]=>[8,3,6,4,7,1,5,2]=>[1,2,2,2,1]
[1,4,6,2,7,5,8,3]=>[6,2,5,3,8,1,4,7]=>[3,7,4,6,1,8,5,2]=>[2,2,2,1,1]
[1,7,5,2,6,8,4,3]=>[5,3,8,7,4,1,2,6]=>[4,6,1,2,5,8,7,3]=>[2,4,1,1]
[7,5,2,1,6,8,4,3]=>[5,8,3,2,7,4,1,6]=>[4,1,6,7,2,5,8,3]=>[1,3,3,1]
[6,8,4,3,1,7,5,2]=>[4,3,1,8,7,5,6,2]=>[5,6,8,1,2,4,3,7]=>[3,3,2]
[3,6,8,4,1,7,5,2]=>[4,2,8,1,7,5,6,3]=>[5,7,1,8,2,4,3,6]=>[2,2,2,2]
[3,6,7,5,1,8,4,2]=>[2,8,7,1,5,4,3,6]=>[7,1,2,8,4,5,6,3]=>[1,3,3,1]
[7,5,6,1,8,3,4,2]=>[6,2,8,7,4,3,1,5]=>[3,7,1,2,5,6,8,4]=>[2,5,1]
[3,4,6,5,7,1,8,2]=>[4,1,2,3,8,6,5,7]=>[5,8,7,6,1,3,4,2]=>[2,1,1,3,1]
[4,7,5,6,1,8,3,2]=>[3,8,1,7,5,4,2,6]=>[6,1,8,2,4,5,7,3]=>[1,2,4,1]
[6,7,5,1,8,4,3,2]=>[1,8,7,6,4,3,2,5]=>[8,1,2,3,5,6,7,4]=>[1,6,1]
[6,8,4,1,7,5,3,2]=>[3,1,8,7,6,4,5,2]=>[6,8,1,2,3,5,4,7]=>[2,4,2]
[6,7,5,3,1,8,4,2]=>[4,1,8,7,5,3,2,6]=>[5,8,1,2,4,6,7,3]=>[2,5,1]
[8,4,2,1,6,7,5,3]=>[5,2,8,3,7,4,6,1]=>[4,7,1,6,2,5,3,8]=>[2,2,2,2]
[1,8,4,2,6,7,5,3]=>[3,5,8,7,4,6,1,2]=>[6,4,1,2,5,3,8,7]=>[1,1,3,2,1]
[1,5,3,2,7,6,8,4]=>[6,3,2,5,8,1,4,7]=>[3,6,7,4,1,8,5,2]=>[3,1,2,1,1]
[5,3,2,1,7,6,8,4]=>[2,6,3,1,5,8,4,7]=>[7,3,6,8,4,1,5,2]=>[1,3,1,2,1]
[2,8,4,1,6,7,5,3]=>[3,5,8,7,1,4,6,2]=>[6,4,1,2,8,5,3,7]=>[1,1,3,1,2]
[2,7,5,1,6,8,4,3]=>[5,3,8,7,1,4,2,6]=>[4,6,1,2,8,5,7,3]=>[2,3,2,1]
[4,7,1,6,5,8,2,3]=>[7,1,5,4,8,3,2,6]=>[2,8,4,5,1,6,7,3]=>[2,2,3,1]
[4,8,2,6,5,7,1,3]=>[7,1,5,3,4,8,6,2]=>[2,8,4,6,5,1,3,7]=>[2,2,1,3]
[4,6,1,2,7,5,8,3]=>[1,6,5,8,3,2,4,7]=>[8,3,4,1,6,7,5,2]=>[1,2,3,1,1]
[7,5,1,2,6,8,4,3]=>[5,8,7,3,2,4,1,6]=>[4,1,2,6,7,5,8,3]=>[1,4,2,1]
[5,3,1,2,7,6,8,4]=>[2,6,5,1,8,3,4,7]=>[7,3,4,8,1,6,5,2]=>[1,3,2,1,1]
[4,3,1,2,7,6,8,5]=>[2,1,6,5,8,3,4,7]=>[7,8,3,4,1,6,5,2]=>[2,2,2,1,1]
[3,5,1,2,7,6,8,4]=>[6,1,5,2,8,3,4,7]=>[3,8,4,7,1,6,5,2]=>[2,2,2,1,1]
[6,7,1,5,8,2,3,4]=>[6,7,4,1,8,3,2,5]=>[3,2,5,8,1,6,7,4]=>[1,3,3,1]
[2,7,6,1,5,8,3,4]=>[7,5,8,4,1,3,2,6]=>[2,4,1,5,8,6,7,3]=>[2,3,2,1]
[2,3,5,1,7,6,8,4]=>[3,6,1,2,5,8,4,7]=>[6,3,8,7,4,1,5,2]=>[1,2,1,1,2,1]
[7,6,1,5,8,3,2,4]=>[7,6,4,8,3,2,1,5]=>[2,3,5,1,6,7,8,4]=>[3,4,1]
[3,6,7,1,5,8,2,4]=>[7,5,1,2,8,4,3,6]=>[2,4,8,7,1,5,6,3]=>[3,1,3,1]
[7,1,6,5,8,2,4,3]=>[8,6,4,3,7,2,1,5]=>[1,3,5,6,2,7,8,4]=>[4,3,1]
[7,5,1,6,8,4,2,3]=>[7,4,2,8,6,3,1,5]=>[2,5,7,1,3,6,8,4]=>[3,4,1]
[8,4,1,6,7,5,2,3]=>[2,7,4,8,6,3,5,1]=>[7,2,5,1,3,6,4,8]=>[1,2,3,2]
[5,2,3,1,7,6,8,4]=>[6,2,3,1,5,8,4,7]=>[3,7,6,8,4,1,5,2]=>[2,2,1,2,1]
[1,3,5,2,7,6,8,4]=>[3,6,2,5,8,1,4,7]=>[6,3,7,4,1,8,5,2]=>[1,2,1,2,1,1]
[7,6,2,1,5,8,3,4]=>[7,3,5,8,4,2,1,6]=>[2,6,4,1,5,7,8,3]=>[2,1,4,1]
[8,3,1,5,7,6,2,4]=>[2,4,7,8,6,3,5,1]=>[7,5,2,1,3,6,4,8]=>[1,1,1,3,2]
[6,2,4,1,7,5,8,3]=>[3,6,2,5,1,8,4,7]=>[6,3,7,4,8,1,5,2]=>[1,2,2,2,1]
[6,2,5,1,7,4,8,3]=>[6,5,2,3,1,8,4,7]=>[3,4,7,6,8,1,5,2]=>[3,2,2,1]
[8,2,6,4,7,1,5,3]=>[4,8,6,2,3,7,5,1]=>[5,1,3,7,6,2,4,8]=>[1,3,1,3]
[6,1,5,2,7,4,8,3]=>[6,5,3,8,2,1,4,7]=>[3,4,6,1,7,8,5,2]=>[3,3,1,1]
[7,6,2,5,8,3,1,4]=>[7,6,3,4,2,1,8,5]=>[2,3,6,5,7,8,1,4]=>[3,3,2]
[8,3,5,7,6,2,1,4]=>[3,7,2,6,8,5,4,1]=>[6,2,7,3,1,4,5,8]=>[1,2,1,4]
[1,8,3,5,7,6,2,4]=>[4,7,8,3,6,5,1,2]=>[5,2,1,6,3,4,8,7]=>[1,1,2,3,1]
[1,5,2,3,7,6,8,4]=>[6,5,2,8,1,3,4,7]=>[3,4,7,1,8,6,5,2]=>[3,2,1,1,1]
[5,2,1,3,7,6,8,4]=>[6,2,5,1,8,3,4,7]=>[3,7,4,8,1,6,5,2]=>[2,2,2,1,1]
[7,5,2,6,8,4,1,3]=>[7,4,2,8,3,1,6,5]=>[2,5,7,1,6,8,3,4]=>[3,3,2]
[8,4,2,6,7,5,1,3]=>[2,7,4,8,3,6,5,1]=>[7,2,5,1,6,3,4,8]=>[1,2,2,3]
[8,2,6,5,7,1,4,3]=>[8,6,4,2,3,7,5,1]=>[1,3,5,7,6,2,4,8]=>[4,1,3]
[3,6,8,2,5,7,1,4]=>[7,4,1,2,5,8,6,3]=>[2,5,8,7,4,1,3,6]=>[3,1,1,3]
[5,1,3,2,7,6,8,4]=>[6,3,5,1,8,2,4,7]=>[3,6,4,8,1,7,5,2]=>[2,2,2,1,1]
[4,1,3,2,7,6,8,5]=>[6,3,1,5,8,2,4,7]=>[3,6,8,4,1,7,5,2]=>[3,1,2,1,1]
[4,2,1,3,7,6,8,5]=>[6,2,1,5,8,3,4,7]=>[3,7,8,4,1,6,5,2]=>[3,1,2,1,1]
[1,4,2,3,7,6,8,5]=>[2,6,5,8,1,3,4,7]=>[7,3,4,1,8,6,5,2]=>[1,2,2,1,1,1]
[2,4,1,3,7,6,8,5]=>[2,6,1,5,8,3,4,7]=>[7,3,8,4,1,6,5,2]=>[1,2,1,2,1,1]
[2,5,1,3,7,6,8,4]=>[6,5,1,2,8,3,4,7]=>[3,4,8,7,1,6,5,2]=>[3,1,2,1,1]
[2,8,3,5,7,6,1,4]=>[4,7,8,3,6,1,5,2]=>[5,2,1,6,3,8,4,7]=>[1,1,2,2,2]
[6,8,2,3,5,7,1,4]=>[7,3,4,1,5,8,6,2]=>[2,6,5,8,4,1,3,7]=>[2,2,1,3]
[6,7,1,3,5,8,2,4]=>[7,4,5,1,8,3,2,6]=>[2,5,4,8,1,6,7,3]=>[2,2,3,1]
[8,3,5,7,6,1,2,4]=>[6,2,3,7,8,5,4,1]=>[3,7,6,2,1,4,5,8]=>[2,1,1,4]
[5,1,2,3,7,6,8,4]=>[6,5,8,2,1,3,4,7]=>[3,4,1,7,8,6,5,2]=>[2,3,1,1,1]
[3,1,2,4,7,6,8,5]=>[1,6,5,8,2,3,4,7]=>[8,3,4,1,7,6,5,2]=>[1,2,2,1,1,1]
[10,8,9,5,6,7,1,2,3,4]=>[7,8,4,9,5,2,10,6,3,1]=>[4,3,7,2,6,9,1,5,8,10]=>[1,2,3,4]
[8,1,3,5,6,2,7,4]=>[4,8,3,6,2,5,7,1]=>[5,1,6,3,7,4,2,8]=>[1,2,2,1,2]
[8,1,3,2,4,5,7,6]=>[3,8,2,4,5,6,7,1]=>[6,1,7,5,4,3,2,8]=>[1,2,1,1,1,2]
[2,7,8,3,4,5,6,1]=>[4,5,6,2,8,1,7,3]=>[5,4,3,7,1,8,2,6]=>[1,1,2,2,2]
[2,6,3,8,4,5,7,1]=>[5,6,2,8,1,3,7,4]=>[4,3,7,1,8,6,2,5]=>[1,2,2,1,2]
[6,3,2,1,4,5,8,7]=>[3,2,8,4,5,1,6,7]=>[6,7,1,5,4,8,3,2]=>[2,2,2,1,1]
[7,3,1,4,2,6,8,5]=>[4,2,6,8,3,5,1,7]=>[5,7,3,1,6,4,8,2]=>[2,1,2,2,1]
[7,4,1,5,6,8,2,3]=>[4,2,7,5,8,3,1,6]=>[5,7,2,4,1,6,8,3]=>[2,2,3,1]
[4,7,8,5,6,1,2,3]=>[6,7,1,4,2,8,5,3]=>[3,2,8,5,7,1,4,6]=>[1,2,2,3]
[3,7,8,5,6,2,1,4]=>[7,6,4,1,2,8,5,3]=>[2,3,5,8,7,1,4,6]=>[4,1,3]
[3,7,8,4,2,6,1,5]=>[5,4,7,1,2,8,6,3]=>[4,5,2,8,7,1,3,6]=>[2,2,1,3]
[3,7,8,2,4,5,1,6]=>[4,5,7,1,6,2,8,3]=>[5,4,2,8,3,7,1,6]=>[1,1,2,2,2]
[3,6,2,8,4,5,1,7]=>[5,7,1,3,2,6,8,4]=>[4,2,8,6,7,3,1,5]=>[1,2,2,1,2]
[2,3,6,7,4,5,8,1]=>[5,3,6,1,2,4,8,7]=>[4,6,3,8,7,5,1,2]=>[2,2,1,1,2]
[3,5,2,4,8,6,1,7]=>[7,1,3,2,4,6,8,5]=>[2,8,6,7,5,3,1,4]=>[2,2,1,1,2]
[3,5,4,2,8,7,1,6]=>[3,1,2,7,8,4,6,5]=>[6,8,7,2,1,5,3,4]=>[2,1,1,2,2]
[4,6,5,8,7,1,2,3]=>[6,1,3,2,7,8,5,4]=>[3,8,6,7,2,1,4,5]=>[2,2,1,3]
[6,4,5,1,7,8,2,3]=>[2,7,5,3,1,8,4,6]=>[7,2,4,6,8,1,5,3]=>[1,4,2,1]
[7,4,1,2,3,8,5,6]=>[7,8,3,2,4,5,1,6]=>[2,1,6,7,5,4,8,3]=>[1,3,1,2,1]
[2,6,4,8,3,7,5,1]=>[8,3,2,5,7,1,6,4]=>[1,6,7,4,2,8,3,5]=>[3,1,2,2]
[2,6,5,8,7,3,4,1]=>[3,2,6,8,7,1,5,4]=>[6,7,3,1,2,8,4,5]=>[2,1,3,2]
[6,2,5,1,7,3,4,8]=>[6,7,2,4,3,1,5,8]=>[3,2,7,5,6,8,4,1]=>[1,2,3,1,1]
[6,5,2,1,8,3,4,7]=>[3,6,7,2,1,8,4,5]=>[6,3,2,7,8,1,5,4]=>[1,1,3,2,1]
[2,5,6,7,8,3,4,1]=>[2,3,6,4,8,1,7,5]=>[7,6,3,5,1,8,2,4]=>[1,1,2,2,2]
[2,4,6,7,3,8,5,1]=>[3,8,2,5,1,4,7,6]=>[6,1,7,4,8,5,2,3]=>[1,2,2,1,2]
[4,2,6,7,3,1,5,8]=>[1,6,5,2,3,7,4,8]=>[8,3,4,7,6,2,5,1]=>[1,3,1,2,1]
[4,7,8,2,3,1,5,6]=>[1,4,6,5,7,2,8,3]=>[8,5,3,4,2,7,1,6]=>[1,1,2,2,2]
[4,7,8,3,2,1,6,5]=>[5,1,4,8,6,2,7,3]=>[4,8,5,1,3,7,2,6]=>[2,1,3,2]
[5,6,4,8,1,7,2,3]=>[1,7,3,2,8,5,6,4]=>[8,2,6,7,1,4,3,5]=>[1,3,2,2]
[5,6,3,8,1,2,7,4]=>[3,1,8,5,2,6,7,4]=>[6,8,1,4,7,3,2,5]=>[2,3,1,2]
[4,2,5,3,7,1,6,8]=>[4,2,1,3,6,7,5,8]=>[5,7,8,6,3,2,4,1]=>[3,1,1,2,1]
[3,4,6,7,2,8,1,5]=>[5,1,2,3,7,4,8,6]=>[4,8,7,6,2,5,1,3]=>[2,1,1,2,2]
[3,4,5,2,7,8,1,6]=>[1,2,3,7,4,5,8,6]=>[8,7,6,2,5,4,1,3]=>[1,1,1,2,1,2]
[3,4,2,5,6,8,1,7]=>[1,3,2,4,5,7,8,6]=>[8,6,7,5,4,2,1,3]=>[1,2,1,1,1,2]
[5,2,7,8,6,4,1,3]=>[1,7,3,8,6,2,5,4]=>[8,2,6,1,3,7,4,5]=>[1,2,3,2]
[5,1,2,7,8,6,4,3]=>[4,1,8,7,6,2,3,5]=>[5,8,1,2,3,7,6,4]=>[2,4,1,1]
[4,7,1,8,6,5,2,3]=>[7,8,1,6,5,3,2,4]=>[2,1,8,3,4,6,7,5]=>[1,2,4,1]
[4,7,1,2,8,6,5,3]=>[8,1,7,6,3,4,2,5]=>[1,8,2,3,6,5,7,4]=>[2,3,2,1]
[4,6,8,1,2,7,5,3]=>[8,1,7,4,2,5,6,3]=>[1,8,2,5,7,4,3,6]=>[2,3,1,2]
[6,8,7,3,5,1,2,4]=>[6,4,1,7,8,5,3,2]=>[3,5,8,2,1,4,6,7]=>[3,1,4]
[7,8,1,6,3,5,2,4]=>[5,7,8,6,3,1,4,2]=>[4,2,1,3,6,8,5,7]=>[1,1,4,2]
[7,8,1,3,6,5,2,4]=>[7,8,4,6,3,1,5,2]=>[2,1,5,3,6,8,4,7]=>[1,2,3,2]
[7,8,3,6,5,2,1,4]=>[7,3,6,1,8,5,4,2]=>[2,6,3,8,1,4,5,7]=>[2,2,4]
[4,7,2,8,6,1,5,3]=>[8,1,6,7,3,2,5,4]=>[1,8,3,2,6,7,4,5]=>[2,1,3,2]
[1,7,3,4,8,6,5,2]=>[8,7,3,4,2,6,1,5]=>[1,2,6,5,7,3,8,4]=>[3,2,2,1]
[4,2,7,1,8,6,5,3]=>[8,1,7,6,2,4,3,5]=>[1,8,2,3,7,5,6,4]=>[2,3,2,1]
[7,8,2,3,6,5,1,4]=>[7,8,3,4,1,6,5,2]=>[2,1,6,5,8,3,4,7]=>[1,2,2,3]
[8,5,7,1,6,2,3,4]=>[6,7,2,8,4,5,3,1]=>[3,2,7,1,5,4,6,8]=>[1,2,2,3]
[6,8,2,7,1,3,5,4]=>[8,3,5,1,6,7,4,2]=>[1,6,4,8,3,2,5,7]=>[2,2,1,3]
[6,8,7,2,5,3,1,4]=>[7,4,1,6,8,5,3,2]=>[2,5,8,3,1,4,6,7]=>[3,1,4]
[6,2,4,8,7,1,5,3]=>[8,3,6,1,7,2,5,4]=>[1,6,3,8,2,7,4,5]=>[2,2,2,2]
[1,6,8,3,7,4,5,2]=>[6,2,8,4,7,5,1,3]=>[3,7,1,5,2,4,8,6]=>[2,2,3,1]
[1,6,8,3,4,7,5,2]=>[8,4,2,5,7,6,1,3]=>[1,5,7,4,2,3,8,6]=>[3,1,3,1]
[6,2,4,8,1,7,5,3]=>[8,3,7,2,1,5,6,4]=>[1,6,2,7,8,4,3,5]=>[2,3,1,2]
[6,8,7,2,3,5,1,4]=>[4,5,1,7,8,6,3,2]=>[5,4,8,2,1,3,6,7]=>[1,2,1,4]
[6,8,2,1,7,3,5,4]=>[8,3,6,1,7,4,5,2]=>[1,6,3,8,2,5,4,7]=>[2,2,2,2]
[8,5,7,2,1,6,3,4]=>[4,7,2,8,5,6,3,1]=>[5,2,7,1,4,3,6,8]=>[1,2,2,3]
[8,5,7,1,2,3,6,4]=>[8,4,5,2,6,7,3,1]=>[1,5,4,7,3,2,6,8]=>[2,2,1,3]
[8,7,6,2,1,4,3,5]=>[4,7,5,6,8,3,2,1]=>[5,2,4,3,1,6,7,8]=>[1,2,1,4]
[8,5,7,2,3,1,6,4]=>[4,5,2,8,6,7,3,1]=>[5,4,7,1,3,2,6,8]=>[1,2,2,3]
[5,8,4,2,7,1,6,3]=>[1,8,4,3,6,7,5,2]=>[8,1,5,6,3,2,4,7]=>[1,3,1,3]
[1,8,7,3,5,4,6,2]=>[6,4,5,8,7,3,1,2]=>[3,5,4,1,2,6,8,7]=>[2,1,4,1]
[8,7,6,2,4,3,1,5]=>[7,4,6,5,8,3,2,1]=>[2,5,3,4,1,6,7,8]=>[2,2,4]
[8,7,6,1,2,4,3,5]=>[7,4,5,6,8,3,2,1]=>[2,5,4,3,1,6,7,8]=>[2,1,1,4]
[8,7,6,1,4,2,3,5]=>[6,7,4,5,8,3,2,1]=>[3,2,5,4,1,6,7,8]=>[1,2,1,4]
[8,7,6,4,1,3,2,5]=>[7,5,6,4,8,3,2,1]=>[2,4,3,5,1,6,7,8]=>[2,2,4]
[5,8,4,7,2,1,6,3]=>[1,5,3,8,6,7,4,2]=>[8,4,6,1,3,2,5,7]=>[1,2,2,3]
[1,8,7,5,4,3,6,2]=>[6,5,4,8,7,3,1,2]=>[3,4,5,1,2,6,8,7]=>[3,4,1]
[1,6,8,4,3,7,5,2]=>[4,2,8,5,7,6,1,3]=>[5,7,1,4,2,3,8,6]=>[2,2,3,1]
[6,8,7,3,2,5,1,4]=>[5,4,1,7,8,6,3,2]=>[4,5,8,2,1,3,6,7]=>[3,1,4]
[6,8,1,7,3,2,5,4]=>[5,8,6,1,7,3,4,2]=>[4,1,3,8,2,6,5,7]=>[1,3,2,2]
[8,5,7,3,1,6,2,4]=>[7,4,2,8,5,6,3,1]=>[2,5,7,1,4,3,6,8]=>[3,2,3]
[8,5,7,1,3,2,6,4]=>[5,8,4,2,6,7,3,1]=>[4,1,5,7,3,2,6,8]=>[1,3,1,3]
[8,5,7,3,1,2,6,4]=>[8,5,4,2,6,7,3,1]=>[1,4,5,7,3,2,6,8]=>[4,1,3]
[5,8,4,7,1,2,6,3]=>[1,8,5,3,6,7,4,2]=>[8,1,4,6,3,2,5,7]=>[1,3,1,3]
[5,8,4,1,7,2,6,3]=>[1,8,6,3,7,4,5,2]=>[8,1,3,6,2,5,4,7]=>[1,3,2,2]
[5,8,4,7,1,6,2,3]=>[1,7,3,8,5,6,4,2]=>[8,2,6,1,4,3,5,7]=>[1,2,2,3]
[8,1,2,6,5,7,4,3]=>[5,4,8,7,2,3,6,1]=>[4,5,1,2,7,6,3,8]=>[2,3,1,2]
[8,2,5,6,7,4,1,3]=>[3,7,4,8,2,6,5,1]=>[6,2,5,1,7,3,4,8]=>[1,2,2,3]
[4,8,5,7,1,6,2,3]=>[7,1,3,8,5,6,4,2]=>[2,8,6,1,4,3,5,7]=>[2,1,2,3]
[4,8,5,7,1,2,6,3]=>[8,1,5,3,6,7,4,2]=>[1,8,4,6,3,2,5,7]=>[2,2,1,3]
[4,8,5,1,7,2,6,3]=>[8,1,6,3,7,4,5,2]=>[1,8,3,6,2,5,4,7]=>[2,2,2,2]
[8,5,3,7,1,2,6,4]=>[3,8,5,2,6,7,4,1]=>[6,1,4,7,3,2,5,8]=>[1,3,1,3]
[6,8,1,3,7,2,5,4]=>[8,4,6,1,7,3,5,2]=>[1,5,3,8,2,6,4,7]=>[2,2,2,2]
[4,6,2,8,1,7,5,3]=>[8,1,7,3,2,5,6,4]=>[1,8,2,6,7,4,3,5]=>[2,3,1,2]
[1,6,4,8,3,7,5,2]=>[8,3,2,5,7,6,1,4]=>[1,6,7,4,2,3,8,5]=>[3,1,3,1]
[1,8,7,4,5,3,6,2]=>[4,6,5,8,7,3,1,2]=>[5,3,4,1,2,6,8,7]=>[1,2,4,1]
[4,8,5,7,2,1,6,3]=>[5,1,3,8,6,7,4,2]=>[4,8,6,1,3,2,5,7]=>[2,1,2,3]
[8,7,6,3,1,4,2,5]=>[7,5,4,6,8,3,2,1]=>[2,4,5,3,1,6,7,8]=>[3,1,4]
[8,7,6,1,3,2,4,5]=>[6,4,5,7,8,3,2,1]=>[3,5,4,2,1,6,7,8]=>[2,1,1,4]
[8,5,3,2,7,1,6,4]=>[3,8,4,2,6,7,5,1]=>[6,1,5,7,3,2,4,8]=>[1,3,1,3]
[4,8,5,2,7,1,6,3]=>[8,1,4,3,6,7,5,2]=>[1,8,5,6,3,2,4,7]=>[2,2,1,3]
[1,8,7,4,3,5,6,2]=>[5,4,6,8,7,3,1,2]=>[4,5,3,1,2,6,8,7]=>[2,1,4,1]
[8,2,4,5,7,1,6,3]=>[3,4,8,2,6,7,5,1]=>[6,5,1,7,3,2,4,8]=>[1,1,2,1,3]
[8,5,2,3,7,1,6,4]=>[8,3,4,2,6,7,5,1]=>[1,6,5,7,3,2,4,8]=>[2,2,1,3]
[6,3,1,5,4,2,8,7]=>[2,5,4,8,3,1,6,7]=>[7,4,5,1,6,8,3,2]=>[1,2,3,1,1]
[8,3,1,5,2,7,6,4]=>[2,4,8,7,3,5,6,1]=>[7,5,1,2,6,4,3,8]=>[1,1,3,1,2]
[8,5,4,2,1,7,3,6]=>[4,7,3,2,8,5,6,1]=>[5,2,6,7,1,4,3,8]=>[1,3,2,2]
[8,5,4,2,1,7,6,3]=>[8,4,3,2,7,5,6,1]=>[1,5,6,7,2,4,3,8]=>[4,2,2]
[6,5,4,2,3,1,8,7]=>[4,5,3,2,1,8,6,7]=>[5,4,6,7,8,1,3,2]=>[1,4,2,1]
[6,3,2,5,1,4,8,7]=>[2,8,3,5,4,1,6,7]=>[7,1,6,4,5,8,3,2]=>[1,2,3,1,1]
[6,5,4,3,1,2,8,7]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[6,1,1]
[6,5,4,1,3,2,8,7]=>[5,8,4,3,2,1,6,7]=>[4,1,5,6,7,8,3,2]=>[1,5,1,1]
[8,5,4,1,2,7,6,3]=>[8,7,4,3,2,5,6,1]=>[1,2,5,6,7,4,3,8]=>[5,1,2]
[8,7,4,1,6,3,2,5]=>[7,6,3,8,4,5,2,1]=>[2,3,6,1,5,4,7,8]=>[3,2,3]
[8,7,4,1,6,3,5,2]=>[6,3,8,7,4,5,2,1]=>[3,6,1,2,5,4,7,8]=>[2,3,3]
[8,7,4,1,6,5,3,2]=>[3,8,7,6,4,5,2,1]=>[6,1,2,3,5,4,7,8]=>[1,4,3]
[8,5,4,3,1,7,6,2]=>[4,3,2,8,7,5,6,1]=>[5,6,7,1,2,4,3,8]=>[3,3,2]
[8,3,2,5,1,7,6,4]=>[2,4,8,3,7,5,6,1]=>[7,5,1,6,2,4,3,8]=>[1,1,2,2,2]
[2,1,8,5,3,7,6,4]=>[4,8,7,1,5,6,2,3]=>[5,1,2,8,4,3,7,6]=>[1,3,1,2,1]
[8,3,2,5,1,7,4,6]=>[2,7,3,4,8,5,6,1]=>[7,2,6,5,1,4,3,8]=>[1,2,1,2,2]
[8,5,4,3,1,7,2,6]=>[7,4,3,2,8,5,6,1]=>[2,5,6,7,1,4,3,8]=>[4,2,2]
[8,7,4,1,6,5,2,3]=>[7,3,8,6,4,5,2,1]=>[2,6,1,3,5,4,7,8]=>[2,3,3]
[8,7,4,1,6,2,5,3]=>[8,6,3,7,4,5,2,1]=>[1,3,6,2,5,4,7,8]=>[3,2,3]
[8,7,6,5,2,1,4,3]=>[5,8,6,7,4,3,2,1]=>[4,1,3,2,5,6,7,8]=>[1,2,5]
[8,7,4,3,6,2,1,5]=>[4,3,7,6,8,5,2,1]=>[5,6,2,3,1,4,7,8]=>[2,2,4]
[8,3,2,7,6,4,1,5]=>[7,2,6,8,3,5,4,1]=>[2,7,3,1,6,4,5,8]=>[2,1,2,3]
[2,1,8,7,6,4,3,5]=>[7,6,8,5,1,4,2,3]=>[2,3,1,4,8,5,7,6]=>[2,3,2,1]
[2,1,8,7,6,4,5,3]=>[6,8,7,5,1,4,2,3]=>[3,1,2,4,8,5,7,6]=>[1,4,2,1]
[8,3,2,7,6,4,5,1]=>[6,8,2,7,3,5,4,1]=>[3,1,7,2,6,4,5,8]=>[1,2,2,3]
[8,7,4,3,6,2,5,1]=>[4,3,6,8,7,5,2,1]=>[5,6,3,1,2,4,7,8]=>[2,1,5]
[8,7,6,5,2,4,3,1]=>[8,5,7,6,4,3,2,1]=>[1,4,2,3,5,6,7,8]=>[2,6]
[8,5,4,2,3,7,6,1]=>[8,4,3,2,5,7,6,1]=>[1,5,6,7,4,2,3,8]=>[4,1,3]
[8,7,4,2,6,5,3,1]=>[3,8,7,4,6,5,2,1]=>[6,1,2,5,3,4,7,8]=>[1,3,4]
[8,7,4,2,6,3,5,1]=>[6,3,8,4,7,5,2,1]=>[3,6,1,5,2,4,7,8]=>[2,2,4]
[8,7,4,2,6,3,1,5]=>[7,4,3,6,8,5,2,1]=>[2,5,6,3,1,4,7,8]=>[3,1,4]
[8,3,1,7,6,4,2,5]=>[7,2,6,8,5,3,4,1]=>[2,7,3,1,4,6,5,8]=>[2,1,3,2]
[8,3,1,7,6,5,4,2]=>[8,7,2,6,5,3,4,1]=>[1,2,7,3,4,6,5,8]=>[3,3,2]
[8,3,1,5,4,7,6,2]=>[2,4,8,5,7,3,6,1]=>[7,5,1,4,2,6,3,8]=>[1,1,2,2,2]
[8,3,1,7,6,5,2,4]=>[7,8,2,6,5,3,4,1]=>[2,1,7,3,4,6,5,8]=>[1,2,3,2]
[8,3,1,7,6,2,5,4]=>[8,2,6,7,5,3,4,1]=>[1,7,3,2,4,6,5,8]=>[2,1,3,2]
[8,7,4,2,6,1,5,3]=>[8,4,3,6,7,5,2,1]=>[1,5,6,3,2,4,7,8]=>[3,1,4]
[8,7,4,2,6,5,1,3]=>[7,3,8,4,6,5,2,1]=>[2,6,1,5,3,4,7,8]=>[2,2,4]
[8,5,4,2,3,7,1,6]=>[4,5,3,2,7,8,6,1]=>[5,4,6,7,2,1,3,8]=>[1,3,1,3]
[2,1,8,5,4,7,3,6]=>[5,4,7,8,1,6,2,3]=>[4,5,2,1,8,3,7,6]=>[2,1,2,2,1]
[8,7,6,5,3,1,4,2]=>[8,6,5,7,4,3,2,1]=>[1,3,4,2,5,6,7,8]=>[3,5]
[8,7,6,5,1,3,2,4]=>[7,5,6,8,4,3,2,1]=>[2,4,3,1,5,6,7,8]=>[2,1,5]
[8,7,6,5,1,3,4,2]=>[6,8,5,7,4,3,2,1]=>[3,1,4,2,5,6,7,8]=>[1,2,5]
[8,7,6,5,1,4,3,2]=>[8,7,5,6,4,3,2,1]=>[1,2,4,3,5,6,7,8]=>[3,5]
[8,7,6,5,4,1,3,2]=>[8,6,7,5,4,3,2,1]=>[1,3,2,4,5,6,7,8]=>[2,6]
[8,7,4,3,6,1,5,2]=>[4,3,8,6,7,5,2,1]=>[5,6,1,3,2,4,7,8]=>[2,2,4]
[8,3,2,7,6,1,5,4]=>[8,2,6,7,3,5,4,1]=>[1,7,3,2,6,4,5,8]=>[2,1,2,3]
[2,1,8,7,6,3,5,4]=>[8,6,7,5,1,4,2,3]=>[1,3,2,4,8,5,7,6]=>[2,3,2,1]
[8,3,2,7,6,1,4,5]=>[2,6,7,8,3,5,4,1]=>[7,3,2,1,6,4,5,8]=>[1,1,1,2,3]
[8,7,6,5,1,4,2,3]=>[7,8,5,6,4,3,2,1]=>[2,1,4,3,5,6,7,8]=>[1,2,5]
[8,7,6,5,1,2,4,3]=>[8,5,6,7,4,3,2,1]=>[1,4,3,2,5,6,7,8]=>[2,1,5]
[7,3,5,1,8,4,6,2]=>[6,2,3,8,7,4,1,5]=>[3,7,6,1,2,5,8,4]=>[2,1,4,1]
[7,3,4,1,8,5,6,2]=>[2,3,6,8,7,4,1,5]=>[7,6,3,1,2,5,8,4]=>[1,1,1,4,1]
[4,5,6,2,1,8,7,3]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[1,1,3,2,1]
[1,6,5,2,7,4,3,8]=>[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>[5,1,1,1]
[7,4,3,1,8,6,5,2]=>[2,8,3,7,6,4,1,5]=>[7,1,6,2,3,5,8,4]=>[1,2,4,1]
[7,6,5,1,8,4,3,2]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[7,1]
[7,6,4,1,8,5,3,2]=>[3,8,7,6,4,2,1,5]=>[6,1,2,3,5,7,8,4]=>[1,6,1]
[6,4,2,1,8,7,5,3]=>[2,8,7,3,1,6,4,5]=>[7,1,2,6,8,3,5,4]=>[1,4,2,1]
[1,6,4,2,7,5,3,8]=>[3,7,6,4,1,2,5,8]=>[6,2,3,5,8,7,4,1]=>[1,4,1,1,1]
[1,5,3,2,7,6,4,8]=>[7,3,2,6,1,4,5,8]=>[2,6,7,3,8,5,4,1]=>[3,2,1,1,1]
[5,3,2,1,8,7,6,4]=>[8,2,1,7,3,6,4,5]=>[1,7,8,2,6,3,5,4]=>[3,2,2,1]
[2,5,3,1,7,8,6,4]=>[5,2,8,1,3,7,4,6]=>[4,7,1,8,6,2,5,3]=>[2,2,1,2,1]
[2,6,4,1,7,8,5,3]=>[3,5,2,8,1,7,4,6]=>[6,4,7,1,8,2,5,3]=>[1,2,2,2,1]
[2,6,5,1,7,8,4,3]=>[5,3,2,8,1,7,4,6]=>[4,6,7,1,8,2,5,3]=>[3,2,2,1]
[4,5,7,1,6,8,2,3]=>[1,2,7,5,8,4,3,6]=>[8,7,2,4,1,5,6,3]=>[1,1,2,3,1]
[6,5,1,2,8,4,3,7]=>[7,6,8,3,2,1,4,5]=>[2,3,1,6,7,8,5,4]=>[2,4,1,1]
[6,4,1,2,8,5,3,7]=>[7,6,2,8,3,1,4,5]=>[2,3,7,1,6,8,5,4]=>[3,3,1,1]
[5,3,1,2,8,6,4,7]=>[2,7,6,1,8,3,4,5]=>[7,2,3,8,1,6,5,4]=>[1,3,2,1,1]
[4,3,1,2,8,6,5,7]=>[2,1,7,6,8,3,4,5]=>[7,8,2,3,1,6,5,4]=>[2,2,2,1,1]
[6,1,2,5,8,3,4,7]=>[6,4,7,8,2,1,3,5]=>[3,5,2,1,7,8,6,4]=>[2,1,3,1,1]
[7,1,3,4,8,2,5,6]=>[3,4,6,7,8,2,1,5]=>[6,5,3,2,1,7,8,4]=>[1,1,1,1,3,1]
[7,1,5,6,8,2,3,4]=>[6,3,7,4,8,2,1,5]=>[3,6,2,5,1,7,8,4]=>[2,2,3,1]
[2,6,1,5,7,8,3,4]=>[4,7,5,1,2,8,3,6]=>[5,2,4,8,7,1,6,3]=>[1,3,1,2,1]
[7,4,1,6,8,5,2,3]=>[2,7,4,8,6,3,1,5]=>[7,2,5,1,3,6,8,4]=>[1,2,4,1]
[5,2,3,1,8,6,7,4]=>[6,8,2,1,3,7,4,5]=>[3,1,7,8,6,2,5,4]=>[1,3,1,2,1]
[3,5,2,1,6,8,7,4]=>[8,1,3,2,5,7,4,6]=>[1,8,6,7,4,2,5,3]=>[2,2,1,2,1]
[1,6,2,5,7,3,4,8]=>[6,4,7,3,1,2,5,8]=>[3,5,2,6,8,7,4,1]=>[2,3,1,1,1]
[6,2,1,5,8,7,3,4]=>[4,7,8,2,1,6,3,5]=>[5,2,1,7,8,3,6,4]=>[1,1,3,2,1]
[7,3,1,5,8,6,2,4]=>[2,4,7,8,6,3,1,5]=>[7,5,2,1,3,6,8,4]=>[1,1,1,4,1]
[6,2,4,1,8,5,7,3]=>[3,6,8,2,1,7,4,5]=>[6,3,1,7,8,2,5,4]=>[1,1,3,2,1]
[6,2,5,1,8,4,7,3]=>[6,3,8,2,1,7,4,5]=>[3,6,1,7,8,2,5,4]=>[2,3,2,1]
[7,3,1,4,8,6,2,5]=>[2,7,8,4,6,3,1,5]=>[7,2,1,5,3,6,8,4]=>[1,1,2,3,1]
[6,2,1,4,8,7,3,5]=>[7,8,2,4,1,6,3,5]=>[2,1,7,5,8,3,6,4]=>[1,2,2,2,1]
[1,6,2,4,7,3,5,8]=>[4,6,7,3,1,2,5,8]=>[5,3,2,6,8,7,4,1]=>[1,1,3,1,1,1]
[5,2,1,3,8,7,4,6]=>[7,8,2,1,6,3,4,5]=>[2,1,7,8,3,6,5,4]=>[1,3,2,1,1]
[7,5,1,3,8,4,2,6]=>[7,4,6,2,8,3,1,5]=>[2,5,3,7,1,6,8,4]=>[2,2,3,1]
[7,6,1,4,8,3,2,5]=>[4,7,6,8,3,2,1,5]=>[5,2,3,1,6,7,8,4]=>[1,2,4,1]
[2,6,1,4,7,8,3,5]=>[7,4,5,1,2,8,3,6]=>[2,5,4,8,7,1,6,3]=>[2,2,1,2,1]
[7,1,4,6,8,2,3,5]=>[3,6,7,4,8,2,1,5]=>[6,3,2,5,1,7,8,4]=>[1,1,2,3,1]
[7,1,3,5,8,2,4,6]=>[6,3,4,7,8,2,1,5]=>[3,6,5,2,1,7,8,4]=>[2,1,1,3,1]
[6,1,2,4,8,3,5,7]=>[4,6,7,8,2,1,3,5]=>[5,3,2,1,7,8,6,4]=>[1,1,1,3,1,1]
[5,2,3,1,6,4,8,7]=>[2,3,5,1,8,4,6,7]=>[7,6,4,8,1,5,3,2]=>[1,1,2,2,1,1]
[7,4,5,2,3,1,8,6]=>[4,2,5,3,8,6,1,7]=>[5,7,4,6,1,3,8,2]=>[2,2,3,1]
[8,6,7,3,5,2,4,1]=>[4,6,2,8,7,5,3,1]=>[5,3,7,1,2,4,6,8]=>[1,2,5]
[7,3,5,2,4,1,8,6]=>[2,4,5,3,8,6,1,7]=>[7,5,4,6,1,3,8,2]=>[1,1,2,3,1]
[6,3,5,2,4,1,8,7]=>[2,4,5,3,1,8,6,7]=>[7,5,4,6,8,1,3,2]=>[1,1,3,2,1]
[5,2,4,1,6,3,8,7]=>[5,2,3,1,8,4,6,7]=>[4,7,6,8,1,5,3,2]=>[2,2,2,1,1]
[4,1,6,3,5,2,8,7]=>[4,1,5,3,8,2,6,7]=>[5,8,4,6,1,7,3,2]=>[2,2,2,1,1]
[5,2,6,3,4,1,8,7]=>[4,5,2,1,3,8,6,7]=>[5,4,7,8,6,1,3,2]=>[1,3,1,2,1]
[5,2,7,3,4,1,8,6]=>[4,5,1,8,2,6,3,7]=>[5,4,8,1,7,3,6,2]=>[1,2,2,2,1]
[5,2,8,6,7,3,4,1]=>[1,6,4,8,7,2,5,3]=>[8,3,5,1,2,7,4,6]=>[1,2,3,2]
[6,2,8,5,7,3,4,1]=>[6,4,1,8,7,2,5,3]=>[3,5,8,1,2,7,4,6]=>[3,3,2]
[7,3,4,1,5,2,8,6]=>[2,5,3,8,4,6,1,7]=>[7,4,6,1,5,3,8,2]=>[1,2,2,2,1]
[4,1,7,3,5,2,8,6]=>[4,1,5,8,6,2,3,7]=>[5,8,4,1,3,7,6,2]=>[2,1,3,1,1]
[3,1,7,4,5,2,8,6]=>[1,4,5,8,6,2,3,7]=>[8,5,4,1,3,7,6,2]=>[1,1,1,3,1,1]
[2,1,7,4,5,3,8,6]=>[4,5,8,1,6,2,3,7]=>[5,4,1,8,3,7,6,2]=>[1,1,2,2,1,1]
[3,1,8,6,7,4,5,2]=>[6,4,8,1,7,5,2,3]=>[3,5,1,8,2,4,7,6]=>[2,2,3,1]
[4,1,8,6,7,3,5,2]=>[6,1,4,8,7,5,2,3]=>[3,8,5,1,2,4,7,6]=>[2,1,4,1]
[8,5,7,3,4,1,6,2]=>[4,2,8,6,5,7,3,1]=>[5,7,1,3,4,2,6,8]=>[2,3,3]
[8,5,6,2,7,3,4,1]=>[6,2,8,4,3,7,5,1]=>[3,7,1,5,6,2,4,8]=>[2,3,3]
[8,4,7,3,5,1,6,2]=>[2,4,8,6,5,7,3,1]=>[7,5,1,3,4,2,6,8]=>[1,1,3,3]
[5,1,8,4,7,3,6,2]=>[4,1,6,8,7,5,2,3]=>[5,8,3,1,2,4,7,6]=>[2,1,4,1]
[4,1,8,5,7,3,6,2]=>[1,4,6,8,7,5,2,3]=>[8,5,3,1,2,4,7,6]=>[1,1,1,4,1]
[3,1,8,5,7,4,6,2]=>[4,6,8,1,7,5,2,3]=>[5,3,1,8,2,4,7,6]=>[1,1,2,3,1]
[2,1,8,5,7,4,6,3]=>[4,6,8,7,1,5,2,3]=>[5,3,1,2,8,4,7,6]=>[1,1,3,2,1]
[2,1,7,4,6,3,8,5]=>[8,4,6,1,5,2,3,7]=>[1,5,3,8,4,7,6,2]=>[2,2,2,1,1]
[3,1,7,4,6,2,8,5]=>[8,1,4,6,5,2,3,7]=>[1,8,5,3,4,7,6,2]=>[2,1,3,1,1]
[5,1,7,3,6,2,8,4]=>[8,4,1,6,5,2,3,7]=>[1,5,8,3,4,7,6,2]=>[3,3,1,1]
[6,2,7,3,5,1,8,4]=>[8,4,6,2,1,5,3,7]=>[1,5,3,7,8,4,6,2]=>[2,3,2,1]
[6,2,8,4,7,3,5,1]=>[4,6,1,8,7,2,5,3]=>[5,3,8,1,2,7,4,6]=>[1,2,3,2]
[8,4,7,3,6,2,5,1]=>[2,4,6,8,7,5,3,1]=>[7,5,3,1,2,4,6,8]=>[1,1,1,5]
[7,3,6,2,5,1,8,4]=>[8,2,4,6,5,3,1,7]=>[1,7,5,3,4,6,8,2]=>[2,1,4,1]
[6,2,5,1,7,3,8,4]=>[8,6,2,4,3,1,5,7]=>[1,3,7,5,6,8,4,2]=>[3,3,1,1]
[5,2,4,1,7,3,8,6]=>[3,8,2,1,6,4,5,7]=>[6,1,7,8,3,5,4,2]=>[1,3,2,1,1]
[6,2,4,1,7,3,8,5]=>[3,8,2,6,4,1,5,7]=>[6,1,7,3,5,8,4,2]=>[1,2,3,1,1]
[8,5,7,3,6,2,4,1]=>[4,2,6,8,7,5,3,1]=>[5,7,3,1,2,4,6,8]=>[2,1,5]
[8,5,7,4,6,2,3,1]=>[2,6,4,8,7,5,3,1]=>[7,3,5,1,2,4,6,8]=>[1,2,5]
[7,4,6,2,3,1,8,5]=>[4,2,5,8,6,3,1,7]=>[5,7,4,1,3,6,8,2]=>[2,1,4,1]
[6,2,3,1,7,4,8,5]=>[8,2,3,6,4,1,5,7]=>[1,7,6,3,5,8,4,2]=>[2,1,3,1,1]
[5,2,3,1,7,4,8,6]=>[8,2,3,1,6,4,5,7]=>[1,7,6,8,3,5,4,2]=>[2,2,2,1,1]
[4,2,3,1,7,5,8,6]=>[8,2,1,3,6,4,5,7]=>[1,7,8,6,3,5,4,2]=>[3,1,2,1,1]
[3,1,4,2,8,6,7,5]=>[1,6,8,3,7,2,4,5]=>[8,3,1,6,2,7,5,4]=>[1,1,2,2,1,1]
[6,2,3,1,8,5,7,4]=>[6,8,2,3,1,7,4,5]=>[3,1,7,6,8,2,5,4]=>[1,2,2,2,1]
[8,5,6,2,3,1,7,4]=>[4,5,2,8,6,3,7,1]=>[5,4,7,1,3,6,2,8]=>[1,2,3,2]
[7,4,8,5,6,2,3,1]=>[6,2,4,1,8,7,5,3]=>[3,7,5,8,1,2,4,6]=>[2,2,4]
[7,3,8,5,6,2,4,1]=>[6,4,8,2,1,7,5,3]=>[3,5,1,7,8,2,4,6]=>[2,3,3]
[5,2,4,1,8,6,7,3]=>[3,6,1,8,2,7,4,5]=>[6,3,8,1,7,2,5,4]=>[1,2,2,2,1]
[4,1,5,2,8,6,7,3]=>[3,1,6,8,7,2,4,5]=>[6,8,3,1,2,7,5,4]=>[2,1,3,1,1]
[3,1,5,2,8,6,7,4]=>[1,3,6,8,7,2,4,5]=>[8,6,3,1,2,7,5,4]=>[1,1,1,3,1,1]
[2,1,6,3,8,5,7,4]=>[6,3,8,1,7,2,4,5]=>[3,6,1,8,2,7,5,4]=>[2,2,2,1,1]
[3,1,6,2,8,5,7,4]=>[6,1,3,8,7,2,4,5]=>[3,8,6,1,2,7,5,4]=>[2,1,3,1,1]
[4,1,6,2,8,5,7,3]=>[1,6,3,8,7,2,4,5]=>[8,3,6,1,2,7,5,4]=>[1,2,3,1,1]
[5,1,6,2,8,4,7,3]=>[6,3,1,8,7,2,4,5]=>[3,6,8,1,2,7,5,4]=>[3,3,1,1]
[7,3,8,4,6,2,5,1]=>[4,6,8,2,1,7,5,3]=>[5,3,1,7,8,2,4,6]=>[1,1,3,3]
[6,2,7,3,8,4,5,1]=>[6,8,4,2,1,3,7,5]=>[3,1,5,7,8,6,2,4]=>[1,4,1,2]
[8,4,5,1,6,2,7,3]=>[2,8,6,4,3,5,7,1]=>[7,1,3,5,6,4,2,8]=>[1,4,1,2]
[5,1,8,4,6,2,7,3]=>[4,1,8,6,5,7,2,3]=>[5,8,1,3,4,2,7,6]=>[2,3,2,1]
[4,1,8,5,6,2,7,3]=>[1,4,8,6,5,7,2,3]=>[8,5,1,3,4,2,7,6]=>[1,1,3,2,1]
[3,1,8,5,6,2,7,4]=>[4,8,1,6,5,7,2,3]=>[5,1,8,3,4,2,7,6]=>[1,2,2,2,1]
[2,1,8,5,6,3,7,4]=>[4,8,6,1,5,7,2,3]=>[5,1,3,8,4,2,7,6]=>[1,3,1,2,1]
[2,1,7,4,8,5,6,3]=>[6,8,4,1,3,7,2,5]=>[3,1,5,8,6,2,7,4]=>[1,3,1,2,1]
[3,1,7,4,8,5,6,2]=>[6,8,1,4,3,7,2,5]=>[3,1,8,5,6,2,7,4]=>[1,2,2,2,1]
[4,1,7,3,8,5,6,2]=>[1,6,8,4,3,7,2,5]=>[8,3,1,5,6,2,7,4]=>[1,1,3,2,1]
[7,3,8,4,5,1,6,2]=>[4,8,2,6,5,1,7,3]=>[5,1,7,3,4,8,2,6]=>[1,2,3,2]
[8,4,5,1,7,3,6,2]=>[2,6,3,8,7,4,5,1]=>[7,3,6,1,2,5,4,8]=>[1,2,3,2]
[7,3,6,2,8,4,5,1]=>[6,8,2,4,3,1,7,5]=>[3,1,7,5,6,8,2,4]=>[1,2,3,2]
[7,8,5,6,1,3,4,2]=>[6,8,5,3,1,7,4,2]=>[3,1,4,6,8,2,5,7]=>[1,4,3]
[7,8,1,3,6,2,5,4]=>[8,4,6,7,3,1,5,2]=>[1,5,3,2,6,8,4,7]=>[2,1,3,2]
[1,3,8,4,7,2,5,6]=>[4,6,7,8,2,5,1,3]=>[5,3,2,1,7,4,8,6]=>[1,1,1,2,2,1]
[1,4,8,2,5,7,3,6]=>[2,5,7,8,4,6,1,3]=>[7,4,2,1,5,3,8,6]=>[1,1,1,2,2,1]
[7,8,2,4,5,6,1,3]=>[4,7,3,5,1,8,6,2]=>[5,2,6,4,8,1,3,7]=>[1,2,2,3]
[7,8,1,5,4,6,3,2]=>[5,4,8,7,3,1,6,2]=>[4,5,1,2,6,8,3,7]=>[2,4,2]
[7,8,2,1,6,3,4,5]=>[3,6,7,8,4,1,5,2]=>[6,3,2,1,5,8,4,7]=>[1,1,1,3,2]
[7,8,3,5,6,4,1,2]=>[7,3,4,1,8,6,5,2]=>[2,6,5,8,1,3,4,7]=>[2,2,4]
[7,8,1,4,2,3,6,5]=>[8,5,3,4,6,1,7,2]=>[1,4,6,5,3,8,2,7]=>[3,1,2,2]
[7,8,5,1,4,2,6,3]=>[8,6,4,5,3,1,7,2]=>[1,3,5,4,6,8,2,7]=>[3,3,2]
[7,8,4,5,3,1,6,2]=>[3,8,6,5,4,1,7,2]=>[6,1,3,4,5,8,2,7]=>[1,5,2]
[5,6,1,4,3,2,7,8]=>[6,5,3,1,4,2,7,8]=>[3,4,6,8,5,7,2,1]=>[4,2,1,1]
[2,6,4,8,3,7,1,5]=>[3,5,2,7,8,1,6,4]=>[6,4,7,2,1,8,3,5]=>[1,2,1,2,2]
[1,4,6,8,3,7,5,2]=>[3,8,2,5,7,6,1,4]=>[6,1,7,4,2,3,8,5]=>[1,2,1,3,1]
[2,4,8,5,3,1,6,7]=>[6,2,5,1,4,7,8,3]=>[3,7,4,8,5,2,1,6]=>[2,2,1,1,2]
[2,5,8,1,4,7,6,3]=>[2,8,5,7,1,4,6,3]=>[7,1,4,2,8,5,3,6]=>[1,2,2,1,2]
[3,5,8,4,7,6,1,2]=>[2,4,7,8,1,6,5,3]=>[7,5,2,1,8,3,4,6]=>[1,1,1,2,3]
[1,6,2,4,7,3,8,5]=>[8,4,6,3,1,2,5,7]=>[1,5,3,6,8,7,4,2]=>[2,3,1,1,1]
[5,6,2,1,4,7,8,3]=>[3,5,1,6,2,8,4,7]=>[6,4,8,3,7,1,5,2]=>[1,2,2,2,1]
[4,6,2,5,3,1,8,7]=>[1,5,3,4,2,8,6,7]=>[8,4,6,5,7,1,3,2]=>[1,2,2,2,1]
[7,5,3,6,2,4,1,8]=>[3,5,2,7,6,4,1,8]=>[6,4,7,2,3,5,8,1]=>[1,2,4,1]
[5,7,3,6,1,4,8,2]=>[3,1,6,8,5,4,2,7]=>[6,8,3,1,4,5,7,2]=>[2,1,4,1]
[6,1,7,5,2,4,8,3]=>[6,8,5,4,2,1,3,7]=>[3,1,4,5,7,8,6,2]=>[1,5,1,1]
[1,4,7,2,5,3,8,6]=>[2,5,8,4,6,1,3,7]=>[7,4,1,5,3,8,6,2]=>[1,1,2,2,1,1]
[4,6,7,8,3,5,1,2]=>[2,7,1,5,3,8,6,4]=>[7,2,8,4,6,1,3,5]=>[1,2,2,3]
[3,6,1,8,4,2,5,7]=>[6,1,5,7,2,8,3,4]=>[3,8,4,2,7,1,6,5]=>[2,1,2,2,1]
[1,6,7,5,8,2,4,3]=>[2,8,6,4,3,7,1,5]=>[7,1,3,5,6,2,8,4]=>[1,4,2,1]
[3,5,6,7,8,1,4,2]=>[2,3,8,1,6,4,7,5]=>[7,6,1,8,3,5,2,4]=>[1,1,2,2,2]
[3,6,5,7,8,2,1,4]=>[3,2,7,1,6,4,8,5]=>[6,7,2,8,3,5,1,4]=>[2,2,2,2]
[5,2,7,6,1,4,3,8]=>[7,5,1,6,2,4,3,8]=>[2,4,8,3,7,5,6,1]=>[3,2,2,1]
[2,5,7,6,8,1,3,4]=>[2,6,7,4,1,3,8,5]=>[7,3,2,5,8,6,1,4]=>[1,1,3,1,2]
[2,7,5,6,8,4,1,3]=>[3,7,4,2,8,1,6,5]=>[6,2,5,7,1,8,3,4]=>[1,3,2,2]
[2,1,6,8,4,5,3,7]=>[5,3,7,1,6,8,2,4]=>[4,6,2,8,3,1,7,5]=>[2,2,1,2,1]
[2,7,1,8,5,3,4,6]=>[6,7,5,8,1,3,2,4]=>[3,2,4,1,8,6,7,5]=>[1,2,2,2,1]
[3,7,6,8,5,4,1,2]=>[7,3,2,8,1,6,5,4]=>[2,6,7,1,8,3,4,5]=>[3,2,3]
[4,3,8,5,6,7,1,2]=>[1,4,7,2,5,8,6,3]=>[8,5,2,7,4,1,3,6]=>[1,1,2,1,3]
[4,2,8,1,6,3,7,5]=>[1,8,6,2,4,5,7,3]=>[8,1,3,7,5,4,2,6]=>[1,3,1,1,2]
[3,1,8,5,4,6,7,2]=>[5,1,4,6,8,7,2,3]=>[4,8,5,3,1,2,7,6]=>[2,1,1,3,1]
[3,2,8,4,5,6,1,7]=>[1,4,5,7,2,6,8,3]=>[8,5,4,2,7,3,1,6]=>[1,1,1,2,1,2]
[3,4,2,8,6,1,7,5]=>[8,1,2,6,3,5,7,4]=>[1,8,7,3,6,4,2,5]=>[2,1,2,1,2]
[3,4,7,1,5,2,6,8]=>[1,2,6,4,5,7,3,8]=>[8,7,3,5,4,2,6,1]=>[1,1,2,1,2,1]
[4,3,7,8,1,2,6,5]=>[1,8,2,5,6,3,7,4]=>[8,1,7,4,3,6,2,5]=>[1,2,1,2,2]
[1,7,3,8,5,2,6,4]=>[8,6,3,5,2,7,1,4]=>[1,3,6,4,7,2,8,5]=>[3,2,2,1]
[4,1,8,3,6,2,5,7]=>[4,1,6,7,5,8,2,3]=>[5,8,3,2,4,1,7,6]=>[2,1,2,2,1]
[5,7,8,6,3,2,1,4]=>[7,1,6,5,2,8,4,3]=>[2,8,3,4,7,1,5,6]=>[2,3,3]
[5,7,8,6,1,3,4,2]=>[1,6,8,5,2,7,4,3]=>[8,3,1,4,7,2,5,6]=>[1,1,3,3]
[7,6,5,8,1,3,4,2]=>[6,8,5,3,2,1,7,4]=>[3,1,4,6,7,8,2,5]=>[1,5,2]
[1,6,4,3,8,2,5,7]=>[4,3,6,2,7,8,1,5]=>[5,6,3,7,2,1,8,4]=>[2,2,1,2,1]
[3,6,5,4,1,2,7,8]=>[5,6,1,4,3,2,7,8]=>[4,3,8,5,6,7,2,1]=>[1,2,3,1,1]
[2,4,5,1,7,8,6,3]=>[2,3,5,8,1,7,4,6]=>[7,6,4,1,8,2,5,3]=>[1,1,1,2,2,1]
[2,6,3,4,5,8,1,7]=>[3,4,5,1,2,7,8,6]=>[6,5,4,8,7,2,1,3]=>[1,1,2,1,1,2]
[2,6,4,1,8,3,7,5]=>[3,8,6,1,2,7,4,5]=>[6,1,3,8,7,2,5,4]=>[1,3,1,2,1]
[7,3,6,4,8,5,1,2]=>[4,7,2,3,1,8,6,5]=>[5,2,7,6,8,1,3,4]=>[1,2,2,3]
[7,2,1,4,8,3,5,6]=>[2,4,6,7,8,3,1,5]=>[7,5,3,2,1,6,8,4]=>[1,1,1,1,3,1]
[7,1,6,5,3,8,4,2]=>[8,5,4,3,7,2,1,6]=>[1,4,5,6,2,7,8,3]=>[4,3,1]
[7,2,5,6,3,8,1,4]=>[5,3,7,2,4,1,8,6]=>[4,6,2,7,5,8,1,3]=>[2,2,2,2]
[6,5,2,7,1,8,4,3]=>[8,7,3,2,1,5,4,6]=>[1,2,6,7,8,4,5,3]=>[5,2,1]
[5,6,2,7,3,1,4,8]=>[6,3,1,5,2,7,4,8]=>[3,6,8,4,7,2,5,1]=>[3,2,2,1]
[5,6,7,4,2,8,1,3]=>[1,5,2,7,4,3,8,6]=>[8,4,7,2,5,6,1,3]=>[1,2,3,2]
[5,7,6,4,1,8,3,2]=>[8,1,7,5,4,3,2,6]=>[1,8,2,4,5,6,7,3]=>[2,5,1]
[6,7,1,5,2,8,3,4]=>[7,8,5,3,1,4,2,6]=>[2,1,4,6,8,5,7,3]=>[1,4,2,1]
[1,7,5,2,4,8,3,6]=>[5,7,3,8,4,1,2,6]=>[4,2,6,1,5,8,7,3]=>[1,2,3,1,1]
[6,1,5,2,8,3,4,7]=>[6,7,3,8,2,1,4,5]=>[3,2,6,1,7,8,5,4]=>[1,2,3,1,1]
[6,7,5,3,8,4,1,2]=>[4,1,7,3,2,8,6,5]=>[5,8,2,6,7,1,3,4]=>[2,3,3]
[7,1,5,3,4,2,8,6]=>[4,5,3,8,2,6,1,7]=>[5,4,6,1,7,3,8,2]=>[1,2,2,2,1]
[7,6,1,5,3,2,8,4]=>[5,8,6,3,4,2,1,7]=>[4,1,3,6,5,7,8,2]=>[1,3,3,1]
[7,5,6,4,1,2,8,3]=>[8,5,2,6,4,3,1,7]=>[1,4,7,3,5,6,8,2]=>[3,4,1]
[6,7,5,4,3,1,8,2]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[1,6,1]
[7,5,2,4,3,1,6,8]=>[6,3,5,4,2,7,1,8]=>[3,6,4,5,7,2,8,1]=>[2,3,2,1]
[7,4,6,1,2,5,3,8]=>[7,4,2,5,6,3,1,8]=>[2,5,7,4,3,6,8,1]=>[3,1,3,1]
[7,1,4,2,5,3,6,8]=>[6,4,2,3,5,7,1,8]=>[3,5,7,6,4,2,8,1]=>[3,1,1,2,1]
[6,8,1,4,2,5,7,3]=>[6,4,8,3,1,5,7,2]=>[3,5,1,6,8,4,2,7]=>[2,3,1,2]
[1,6,4,2,5,7,3,8]=>[5,3,7,4,1,2,6,8]=>[4,6,2,5,8,7,3,1]=>[2,3,1,1,1]
[1,6,3,7,5,4,2,8]=>[7,6,3,2,5,1,4,8]=>[2,3,6,7,4,8,5,1]=>[4,2,1,1]
[6,8,1,3,7,5,4,2]=>[8,7,4,1,6,3,5,2]=>[1,2,5,8,3,6,4,7]=>[4,2,2]
[7,1,3,5,6,4,2,8]=>[4,7,3,6,2,5,1,8]=>[5,2,6,3,7,4,8,1]=>[1,2,2,2,1]
[7,4,6,3,1,5,2,8]=>[2,7,5,4,6,3,1,8]=>[7,2,4,5,3,6,8,1]=>[1,3,3,1]
[7,2,4,1,5,3,6,8]=>[6,2,4,3,5,7,1,8]=>[3,7,5,6,4,2,8,1]=>[2,2,1,2,1]
[7,2,3,5,4,1,6,8]=>[6,2,3,5,4,7,1,8]=>[3,7,6,4,5,2,8,1]=>[2,1,2,2,1]
[6,8,1,2,3,4,7,5]=>[8,3,4,5,1,6,7,2]=>[1,6,5,4,8,3,2,7]=>[2,1,2,1,2]
[1,5,7,2,3,8,6,4]=>[2,8,7,4,5,1,3,6]=>[7,1,2,5,4,8,6,3]=>[1,3,2,1,1]
[5,1,8,2,3,6,7,4]=>[6,8,4,1,5,7,2,3]=>[3,1,5,8,4,2,7,6]=>[1,3,1,2,1]
[5,8,2,3,7,6,4,1]=>[1,8,7,3,4,6,5,2]=>[8,1,2,6,5,3,4,7]=>[1,3,1,3]
[6,2,8,1,3,7,4,5]=>[7,8,2,4,1,5,6,3]=>[2,1,7,5,8,4,3,6]=>[1,2,2,1,2]
[6,8,2,3,5,4,7,1]=>[6,3,4,1,5,8,7,2]=>[3,6,5,8,4,1,2,7]=>[2,2,1,3]
[6,8,2,4,1,5,7,3]=>[6,3,4,1,8,5,7,2]=>[3,6,5,8,1,4,2,7]=>[2,2,2,2]
[6,8,3,1,2,4,7,5]=>[8,4,3,5,1,6,7,2]=>[1,5,6,4,8,3,2,7]=>[3,2,1,2]
[2,6,4,1,5,7,3,8]=>[5,3,7,1,4,2,6,8]=>[4,6,2,8,5,7,3,1]=>[2,2,2,1,1]
[2,6,3,5,7,1,4,8]=>[6,3,4,1,2,7,5,8]=>[3,6,5,8,7,2,4,1]=>[2,2,1,2,1]
[2,5,1,7,8,3,6,4]=>[2,8,6,1,4,7,3,5]=>[7,1,3,8,5,2,6,4]=>[1,3,1,2,1]
[2,5,3,6,8,4,7,1]=>[4,2,6,8,1,3,7,5]=>[5,7,3,1,8,6,2,4]=>[2,1,2,1,2]
[2,4,7,6,8,5,1,3]=>[7,4,2,3,8,1,6,5]=>[2,5,7,6,1,8,3,4]=>[3,1,2,2]
[2,5,3,7,6,1,8,4]=>[2,8,6,1,3,5,4,7]=>[7,1,3,8,6,4,5,2]=>[1,3,1,2,1]
[2,5,7,8,1,4,6,3]=>[2,6,8,5,1,3,7,4]=>[7,3,1,4,8,6,2,5]=>[1,1,3,1,2]
[3,5,7,4,1,6,2,8]=>[2,7,1,5,4,6,3,8]=>[7,2,8,4,5,3,6,1]=>[1,2,2,2,1]
[5,3,4,1,8,6,7,2]=>[2,3,1,6,8,7,4,5]=>[7,6,8,3,1,2,5,4]=>[1,2,1,3,1]
[5,2,8,4,6,1,7,3]=>[4,1,8,6,2,5,7,3]=>[5,8,1,3,7,4,2,6]=>[2,3,1,2]
[5,2,1,8,6,3,7,4]=>[8,6,2,1,5,7,3,4]=>[1,3,7,8,4,2,6,5]=>[4,1,2,1]
[4,2,8,5,7,6,3,1]=>[8,1,4,7,6,2,5,3]=>[1,8,5,2,3,7,4,6]=>[2,1,3,2]
[1,4,2,7,5,8,6,3]=>[8,2,5,4,7,1,3,6]=>[1,7,4,5,2,8,6,3]=>[2,2,2,1,1]
[4,1,8,6,7,5,3,2]=>[4,8,1,7,6,5,2,3]=>[5,1,8,2,3,4,7,6]=>[1,2,4,1]
[5,3,8,7,6,2,4,1]=>[1,6,8,7,2,5,4,3]=>[8,3,1,2,7,4,5,6]=>[1,1,3,3]
[5,8,4,7,6,2,1,3]=>[1,3,7,6,8,5,4,2]=>[8,6,2,3,1,4,5,7]=>[1,1,2,4]
[5,8,7,4,3,6,1,2]=>[7,1,5,4,8,6,3,2]=>[2,8,4,5,1,3,6,7]=>[2,2,4]
[6,4,8,3,1,7,2,5]=>[2,7,4,1,8,5,6,3]=>[7,2,5,8,1,4,3,6]=>[1,3,2,2]
[6,4,2,8,7,1,3,5]=>[6,2,7,1,8,3,5,4]=>[3,7,2,8,1,6,4,5]=>[2,2,2,2]
[6,3,8,7,2,5,1,4]=>[5,7,1,8,2,6,4,3]=>[4,2,8,1,7,3,5,6]=>[1,2,2,3]
[5,8,3,7,1,6,4,2]=>[1,8,3,7,5,6,4,2]=>[8,1,6,2,4,3,5,7]=>[1,2,2,3]
[5,1,3,8,6,7,2,4]=>[7,5,1,8,3,6,2,4]=>[2,4,8,1,6,3,7,5]=>[3,2,2,1]
[5,8,7,4,1,6,2,3]=>[1,7,8,5,4,6,3,2]=>[8,2,1,4,5,3,6,7]=>[1,1,3,3]
[6,4,8,1,2,7,3,5]=>[7,2,8,4,1,5,6,3]=>[2,7,1,5,8,4,3,6]=>[2,3,1,2]
[6,8,5,1,2,3,7,4]=>[8,4,5,1,6,3,7,2]=>[1,5,4,8,3,6,2,7]=>[2,2,2,2]
[6,8,5,2,4,3,7,1]=>[6,4,1,5,3,8,7,2]=>[3,5,8,4,6,1,2,7]=>[3,2,3]
[6,8,5,3,1,2,7,4]=>[8,5,4,1,6,3,7,2]=>[1,4,5,8,3,6,2,7]=>[4,2,2]
[4,5,1,2,7,6,3,8]=>[1,7,6,3,2,4,5,8]=>[8,2,3,6,7,5,4,1]=>[1,4,1,1,1]
[4,5,1,2,6,8,7,3]=>[1,8,5,2,7,3,4,6]=>[8,1,4,7,2,6,5,3]=>[1,3,2,1,1]
[3,5,6,1,8,4,7,2]=>[2,6,1,3,8,7,4,5]=>[7,3,8,6,1,2,5,4]=>[1,2,1,3,1]
[3,5,7,1,2,8,6,4]=>[2,8,1,7,4,5,3,6]=>[7,1,8,2,5,4,6,3]=>[1,2,2,2,1]
[3,6,2,7,5,1,4,8]=>[6,7,1,3,2,5,4,8]=>[3,2,8,6,7,4,5,1]=>[1,2,2,2,1]
[4,5,3,1,7,6,2,8]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[1,2,3,1,1]
[4,2,5,7,1,6,3,8]=>[3,1,7,2,5,6,4,8]=>[6,8,2,7,4,3,5,1]=>[2,2,1,2,1]
[3,5,2,7,8,1,6,4]=>[2,8,1,6,3,4,7,5]=>[7,1,8,3,6,5,2,4]=>[1,2,2,1,2]
[3,1,4,7,5,6,2,8]=>[1,5,7,3,6,2,4,8]=>[8,4,2,6,3,7,5,1]=>[1,1,2,2,1,1]
[3,4,6,5,8,7,1,2]=>[4,1,2,3,7,8,6,5]=>[5,8,7,6,2,1,3,4]=>[2,1,1,1,3]
[3,1,4,5,8,6,7,2]=>[1,6,8,3,4,7,2,5]=>[8,3,1,6,5,2,7,4]=>[1,1,2,1,2,1]
[3,4,6,8,5,2,7,1]=>[3,6,1,2,5,8,7,4]=>[6,3,8,7,4,1,2,5]=>[1,2,1,1,3]
[3,5,6,2,8,4,7,1]=>[2,6,1,3,8,4,7,5]=>[7,3,8,6,1,5,2,4]=>[1,2,1,2,2]
[4,2,5,6,1,8,7,3]=>[3,1,4,8,2,7,5,6]=>[6,8,5,1,7,2,4,3]=>[2,1,2,2,1]
[4,5,3,1,6,8,7,2]=>[1,3,2,8,5,7,4,6]=>[8,6,7,1,4,2,5,3]=>[1,2,2,2,1]
[2,1,7,5,8,6,4,3]=>[8,4,3,7,1,6,2,5]=>[1,5,6,2,8,3,7,4]=>[3,2,2,1]
[1,2,7,5,3,8,6,4]=>[4,8,7,5,1,2,3,6]=>[5,1,2,4,8,7,6,3]=>[1,4,1,1,1]
[4,1,2,7,3,8,6,5]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[1,4,1,1,1]
[6,1,3,7,5,2,4,8]=>[6,7,3,5,2,1,4,8]=>[3,2,6,4,7,8,5,1]=>[1,2,3,1,1]
[3,1,2,6,8,5,4,7]=>[1,4,7,6,8,2,3,5]=>[8,5,2,3,1,7,6,4]=>[1,1,2,2,1,1]
[3,7,1,2,5,4,8,6]=>[1,5,8,3,4,6,2,7]=>[8,4,1,6,5,3,7,2]=>[1,1,2,1,2,1]
[1,3,7,2,4,8,6,5]=>[8,7,2,4,5,1,3,6]=>[1,2,7,5,4,8,6,3]=>[3,1,2,1,1]
[2,4,1,7,8,6,5,3]=>[4,8,2,7,1,6,3,5]=>[5,1,7,2,8,3,6,4]=>[1,2,2,2,1]
[3,4,7,5,1,8,6,2]=>[4,8,1,2,7,5,3,6]=>[5,1,8,7,2,4,6,3]=>[1,2,1,3,1]
[2,7,4,1,5,8,6,3]=>[3,8,5,7,1,4,2,6]=>[6,1,4,2,8,5,7,3]=>[1,2,2,2,1]
[5,2,8,1,3,7,4,6]=>[7,8,2,1,4,5,6,3]=>[2,1,7,8,5,4,3,6]=>[1,3,1,1,2]
[2,1,6,8,3,4,7,5]=>[8,5,1,3,6,7,2,4]=>[1,4,8,6,3,2,7,5]=>[3,1,1,2,1]
[2,8,6,4,1,5,7,3]=>[6,4,8,5,1,3,7,2]=>[3,5,1,4,8,6,2,7]=>[2,3,1,2]
[3,6,4,8,5,1,7,2]=>[8,3,1,2,6,5,7,4]=>[1,6,8,7,3,4,2,5]=>[3,1,2,2]
[6,3,7,4,5,1,8,2]=>[4,8,2,1,6,5,3,7]=>[5,1,7,8,3,4,6,2]=>[1,3,3,1]
[2,6,3,7,5,8,1,4]=>[7,5,3,1,2,4,8,6]=>[2,4,6,8,7,5,1,3]=>[4,1,1,2]
[5,2,1,7,8,3,4,6]=>[6,7,2,1,4,8,3,5]=>[3,2,7,8,5,1,6,4]=>[1,3,1,2,1]
[4,7,2,3,6,8,1,5]=>[1,7,3,4,5,2,8,6]=>[8,2,6,5,4,7,1,3]=>[1,2,1,2,2]
[5,2,7,3,6,8,1,4]=>[7,4,1,5,2,3,8,6]=>[2,5,8,4,7,6,1,3]=>[3,2,1,2]
[5,7,4,6,2,8,1,3]=>[1,5,3,7,4,2,8,6]=>[8,4,6,2,5,7,1,3]=>[1,2,3,2]
[5,7,3,4,6,1,8,2]=>[3,1,4,8,6,5,2,7]=>[6,8,5,1,3,4,7,2]=>[2,1,4,1]
[5,3,8,4,6,1,7,2]=>[4,1,8,2,6,5,7,3]=>[5,8,1,7,3,4,2,6]=>[2,2,2,2]
[8,5,2,4,1,6,7,3]=>[6,3,4,2,8,5,7,1]=>[3,6,5,7,1,4,2,8]=>[2,2,2,2]
[8,2,3,5,1,6,7,4]=>[6,2,3,4,8,5,7,1]=>[3,7,6,5,1,4,2,8]=>[2,1,1,2,2]
[4,2,8,3,6,7,1,5]=>[1,7,4,5,8,2,6,3]=>[8,2,5,4,1,7,3,6]=>[1,2,1,2,2]
[2,4,8,1,7,3,5,6]=>[2,6,7,8,1,4,5,3]=>[7,3,2,1,8,5,4,6]=>[1,1,1,2,1,2]
[8,4,1,3,6,2,5,7]=>[4,6,2,7,3,5,8,1]=>[5,3,7,2,6,4,1,8]=>[1,2,2,1,2]
[4,8,3,1,7,2,5,6]=>[1,6,3,7,8,4,5,2]=>[8,3,6,2,1,5,4,7]=>[1,2,1,2,2]
[5,2,8,4,7,1,6,3]=>[4,1,8,6,7,2,5,3]=>[5,8,1,3,2,7,4,6]=>[2,2,2,2]
[5,8,4,7,3,1,6,2]=>[1,3,8,6,5,7,4,2]=>[8,6,1,3,4,2,5,7]=>[1,1,3,3]
[4,6,8,3,1,7,5,2]=>[4,1,2,8,7,5,6,3]=>[5,8,7,1,2,4,3,6]=>[2,1,3,2]
[6,3,1,8,2,4,7,5]=>[2,8,5,6,1,7,3,4]=>[7,1,4,3,8,2,6,5]=>[1,2,2,2,1]
[5,3,8,1,2,6,4,7]=>[2,7,4,1,5,6,8,3]=>[7,2,5,8,4,3,1,6]=>[1,3,1,1,2]
[8,5,4,1,2,6,3,7]=>[7,4,5,3,2,6,8,1]=>[2,5,4,6,7,3,1,8]=>[2,3,1,2]
[5,1,8,4,2,7,3,6]=>[7,4,1,8,5,6,2,3]=>[2,5,8,1,4,3,7,6]=>[3,2,2,1]
[6,8,5,3,1,7,4,2]=>[4,1,8,7,5,3,6,2]=>[5,8,1,2,4,6,3,7]=>[2,4,2]
[8,4,5,1,2,6,3,7]=>[7,4,2,5,3,6,8,1]=>[2,5,7,4,6,3,1,8]=>[3,2,1,2]
[5,6,3,7,1,2,4,8]=>[5,3,1,6,2,7,4,8]=>[4,6,8,3,7,2,5,1]=>[3,2,2,1]
[1,6,3,7,2,8,4,5]=>[7,8,3,2,5,1,4,6]=>[2,1,6,7,4,8,5,3]=>[1,3,2,1,1]
[6,3,2,7,8,5,1,4]=>[7,2,4,1,8,3,6,5]=>[2,7,5,8,1,6,3,4]=>[2,2,2,2]
[4,7,2,5,8,1,6,3]=>[1,4,8,3,6,2,7,5]=>[8,5,1,6,3,7,2,4]=>[1,1,2,2,2]
[8,1,3,4,6,2,5,7]=>[3,4,6,7,2,5,8,1]=>[6,5,3,2,7,4,1,8]=>[1,1,1,2,1,2]
[3,8,2,4,6,7,1,5]=>[7,1,3,4,5,8,6,2]=>[2,8,6,5,4,1,3,7]=>[2,1,1,1,3]
[3,5,6,8,2,7,1,4]=>[2,5,1,3,7,8,6,4]=>[7,4,8,6,2,1,3,5]=>[1,2,1,1,3]
[2,4,5,6,8,1,7,3]=>[2,3,4,8,1,6,7,5]=>[7,6,5,1,8,3,2,4]=>[1,1,1,2,1,2]
[4,8,3,5,6,1,7,2]=>[1,3,4,8,6,5,7,2]=>[8,6,5,1,3,4,2,7]=>[1,1,1,3,2]
[5,6,2,3,7,8,1,4]=>[7,3,1,4,2,5,8,6]=>[2,6,8,5,7,4,1,3]=>[3,2,1,2]
[5,8,7,3,4,1,2,6]=>[1,6,4,7,5,8,3,2]=>[8,3,5,2,4,1,6,7]=>[1,2,2,3]
[6,8,7,3,4,1,2,5]=>[6,4,1,7,5,8,3,2]=>[3,5,8,2,4,1,6,7]=>[3,2,3]
[6,8,4,7,1,5,3,2]=>[3,1,8,7,5,6,4,2]=>[6,8,1,2,4,3,5,7]=>[2,3,3]
[6,8,4,7,2,5,3,1]=>[3,1,8,5,7,6,4,2]=>[6,8,1,4,2,3,5,7]=>[2,2,4]
[5,4,8,7,2,6,3,1]=>[1,8,2,5,7,6,4,3]=>[8,1,7,4,2,3,5,6]=>[1,2,1,4]
[5,4,8,7,1,6,3,2]=>[1,8,2,7,5,6,4,3]=>[8,1,7,2,4,3,5,6]=>[1,2,2,3]
[5,3,8,7,6,1,2,4]=>[6,1,7,8,2,5,4,3]=>[3,8,2,1,7,4,5,6]=>[2,1,2,3]
[4,3,8,7,6,1,2,5]=>[1,6,7,8,2,5,4,3]=>[8,3,2,1,7,4,5,6]=>[1,1,1,2,3]
[4,8,3,7,5,1,2,6]=>[1,3,6,7,5,8,4,2]=>[8,6,3,2,4,1,5,7]=>[1,1,1,2,3]
[8,3,4,6,5,1,2,7]=>[2,3,6,7,5,4,8,1]=>[7,6,3,2,4,5,1,8]=>[1,1,1,3,2]
[3,8,4,7,5,1,2,6]=>[3,6,7,1,5,8,4,2]=>[6,3,2,8,4,1,5,7]=>[1,1,2,1,3]
[3,4,8,7,6,1,2,5]=>[6,7,8,1,2,5,4,3]=>[3,2,1,8,7,4,5,6]=>[1,1,2,1,3]
[3,5,8,7,6,1,2,4]=>[2,6,7,8,1,5,4,3]=>[7,3,2,1,8,4,5,6]=>[1,1,1,2,3]
[4,5,8,7,6,1,2,3]=>[1,2,6,7,8,5,4,3]=>[8,7,3,2,1,4,5,6]=>[1,1,1,1,4]
[4,5,8,7,1,6,3,2]=>[8,1,2,7,5,6,4,3]=>[1,8,7,2,4,3,5,6]=>[2,1,2,3]
[4,5,8,7,2,6,3,1]=>[8,1,2,5,7,6,4,3]=>[1,8,7,4,2,3,5,6]=>[2,1,1,4]
[3,5,8,2,7,6,4,1]=>[8,2,7,1,4,6,5,3]=>[1,7,2,8,5,3,4,6]=>[2,2,1,3]
[3,5,8,1,7,6,4,2]=>[8,2,7,1,6,4,5,3]=>[1,7,2,8,3,5,4,6]=>[2,2,2,2]
[2,5,8,1,7,6,4,3]=>[8,2,7,6,1,4,5,3]=>[1,7,2,3,8,5,4,6]=>[2,3,1,2]
[2,5,8,7,1,6,3,4]=>[2,7,8,5,6,1,4,3]=>[7,2,1,4,3,8,5,6]=>[1,1,2,2,2]
[2,4,8,7,1,6,3,5]=>[7,8,2,5,6,1,4,3]=>[2,1,7,4,3,8,5,6]=>[1,2,1,2,2]
[2,8,4,7,1,5,3,6]=>[3,7,5,6,8,1,4,2]=>[6,2,4,3,1,8,5,7]=>[1,2,1,2,2]
[8,2,4,6,1,5,3,7]=>[3,7,2,5,6,4,8,1]=>[6,2,7,4,3,5,1,8]=>[1,2,1,2,2]
[8,1,4,6,2,5,3,7]=>[3,7,5,6,2,4,8,1]=>[6,2,4,3,7,5,1,8]=>[1,2,2,1,2]
[1,8,4,7,2,5,3,6]=>[3,7,5,6,8,4,1,2]=>[6,2,4,3,1,5,8,7]=>[1,2,1,3,1]
[1,4,8,7,2,6,3,5]=>[7,8,2,5,6,4,1,3]=>[2,1,7,4,3,5,8,6]=>[1,2,1,3,1]
[1,5,8,7,2,6,3,4]=>[2,7,8,5,6,4,1,3]=>[7,2,1,4,3,5,8,6]=>[1,1,2,3,1]
[1,5,8,2,7,6,4,3]=>[8,2,7,6,4,5,1,3]=>[1,7,2,3,5,4,8,6]=>[2,3,2,1]
[2,5,8,3,7,6,4,1]=>[8,2,7,4,6,1,5,3]=>[1,7,2,5,3,8,4,6]=>[2,2,2,2]
[1,4,2,8,7,6,5,3]=>[8,7,2,6,5,1,3,4]=>[1,2,7,3,4,8,6,5]=>[3,3,1,1]
[1,3,8,2,7,6,4,5]=>[7,8,6,2,4,5,1,3]=>[2,1,3,7,5,4,8,6]=>[1,3,1,2,1]
[1,8,3,2,7,5,4,6]=>[7,3,6,8,4,5,1,2]=>[2,6,3,1,5,4,8,7]=>[2,1,2,2,1]
[8,1,3,2,6,5,4,7]=>[7,3,6,2,4,5,8,1]=>[2,6,3,7,5,4,1,8]=>[2,2,1,1,2]
[8,2,3,1,6,5,4,7]=>[7,2,3,6,4,5,8,1]=>[2,7,6,3,5,4,1,8]=>[2,1,2,1,2]
[2,8,3,1,7,5,4,6]=>[7,3,6,8,1,4,5,2]=>[2,6,3,1,8,5,4,7]=>[2,1,2,1,2]
[2,3,8,1,7,6,4,5]=>[7,8,6,1,2,4,5,3]=>[2,1,3,8,7,5,4,6]=>[1,3,1,1,2]
[3,4,1,8,7,6,5,2]=>[8,7,1,2,6,5,3,4]=>[1,2,8,7,3,4,6,5]=>[3,1,3,1]
[4,3,1,8,7,6,5,2]=>[8,1,7,2,6,5,3,4]=>[1,8,2,7,3,4,6,5]=>[2,2,3,1]
[4,2,1,8,7,6,5,3]=>[8,1,7,6,2,5,3,4]=>[1,8,2,3,7,4,6,5]=>[2,3,2,1]
[3,8,2,1,7,5,4,6]=>[7,1,3,6,8,4,5,2]=>[2,8,6,3,1,5,4,7]=>[2,1,1,2,2]
[8,3,2,1,6,5,4,7]=>[2,7,3,6,4,5,8,1]=>[7,2,6,3,5,4,1,8]=>[1,2,2,1,2]
[4,2,8,7,1,6,3,5]=>[1,7,8,5,6,2,4,3]=>[8,2,1,4,3,7,5,6]=>[1,1,2,2,2]
[5,2,8,7,1,6,3,4]=>[7,1,8,5,6,2,4,3]=>[2,8,1,4,3,7,5,6]=>[2,2,2,2]
[5,2,8,1,7,6,4,3]=>[1,8,7,6,2,4,5,3]=>[8,1,2,3,7,5,4,6]=>[1,4,1,2]
[5,3,8,1,7,6,4,2]=>[1,8,7,2,6,4,5,3]=>[8,1,2,7,3,5,4,6]=>[1,3,2,2]
[5,3,8,2,7,6,4,1]=>[1,8,7,2,4,6,5,3]=>[8,1,2,7,5,3,4,6]=>[1,3,1,3]
[6,8,3,2,7,5,4,1]=>[8,3,1,7,4,6,5,2]=>[1,6,8,2,5,3,4,7]=>[3,2,3]
[6,8,3,1,7,5,4,2]=>[8,3,1,7,6,4,5,2]=>[1,6,8,2,3,5,4,7]=>[3,3,2]
[6,8,2,1,7,5,4,3]=>[8,7,3,1,6,4,5,2]=>[1,2,6,8,3,5,4,7]=>[4,2,2]
[6,8,2,7,1,5,3,4]=>[7,8,3,1,5,6,4,2]=>[2,1,6,8,4,3,5,7]=>[1,3,1,3]
[6,8,7,2,1,4,3,5]=>[4,7,5,1,6,8,3,2]=>[5,2,4,8,3,1,6,7]=>[1,3,1,3]
[8,5,6,1,2,4,3,7]=>[7,4,5,2,6,3,8,1]=>[2,5,4,7,3,6,1,8]=>[2,2,2,2]
[5,8,7,1,2,4,3,6]=>[7,4,1,5,6,8,3,2]=>[2,5,8,4,3,1,6,7]=>[3,1,1,3]
[6,8,1,2,7,5,4,3]=>[8,7,6,3,1,4,5,2]=>[1,2,3,6,8,5,4,7]=>[5,1,2]
[6,8,2,3,7,5,4,1]=>[8,7,3,1,4,6,5,2]=>[1,2,6,8,5,3,4,7]=>[4,1,3]
[5,2,8,3,7,6,4,1]=>[1,8,7,4,6,2,5,3]=>[8,1,2,5,3,7,4,6]=>[1,3,2,2]
[5,1,8,3,7,6,4,2]=>[1,8,7,4,6,5,2,3]=>[8,1,2,5,3,4,7,6]=>[1,3,3,1]
[5,1,8,7,2,6,3,4]=>[7,1,8,5,6,4,2,3]=>[2,8,1,4,3,5,7,6]=>[2,2,3,1]
[4,1,8,7,2,6,3,5]=>[1,7,8,5,6,4,2,3]=>[8,2,1,4,3,5,7,6]=>[1,1,2,3,1]
[4,8,1,7,2,5,3,6]=>[1,7,5,6,8,3,4,2]=>[8,2,4,3,1,6,5,7]=>[1,2,1,2,2]
[8,4,1,6,2,5,3,7]=>[7,5,2,6,3,4,8,1]=>[2,4,7,3,6,5,1,8]=>[3,2,1,2]
[8,3,1,2,6,5,4,7]=>[2,7,6,3,4,5,8,1]=>[7,2,3,6,5,4,1,8]=>[1,3,1,1,2]
[3,8,1,2,7,5,4,6]=>[7,1,6,8,3,4,5,2]=>[2,8,3,1,6,5,4,7]=>[2,1,2,1,2]
[3,1,8,2,7,6,4,5]=>[7,8,1,6,4,5,2,3]=>[2,1,8,3,5,4,7,6]=>[1,2,2,2,1]
[3,1,2,8,7,6,5,4]=>[8,7,1,6,5,2,3,4]=>[1,2,8,3,4,7,6,5]=>[3,3,1,1]
[4,1,3,8,7,6,5,2]=>[8,1,7,6,3,5,2,4]=>[1,8,2,3,6,4,7,5]=>[2,3,2,1]
[3,1,4,8,7,6,5,2]=>[8,7,1,6,3,5,2,4]=>[1,2,8,3,6,4,7,5]=>[3,2,2,1]
[2,1,8,3,7,6,4,5]=>[7,8,6,1,4,5,2,3]=>[2,1,3,8,5,4,7,6]=>[1,3,1,2,1]
[2,8,1,3,7,5,4,6]=>[7,6,8,1,3,4,5,2]=>[2,3,1,8,6,5,4,7]=>[2,2,1,1,2]
[8,2,1,3,6,5,4,7]=>[7,2,6,3,4,5,8,1]=>[2,7,3,6,5,4,1,8]=>[2,2,1,1,2]
[8,1,2,3,6,5,4,7]=>[7,6,2,3,4,5,8,1]=>[2,3,7,6,5,4,1,8]=>[3,1,1,1,2]
[1,8,2,3,7,5,4,6]=>[7,6,8,3,4,5,1,2]=>[2,3,1,6,5,4,8,7]=>[2,2,1,2,1]
[1,2,8,3,7,6,4,5]=>[7,8,6,4,5,1,2,3]=>[2,1,3,5,4,8,7,6]=>[1,3,2,1,1]
[1,4,3,6,8,2,5,7]=>[2,6,3,4,7,8,1,5]=>[7,3,6,5,2,1,8,4]=>[1,2,1,1,2,1]
[3,1,6,2,5,8,4,7]=>[1,5,7,3,8,2,4,6]=>[8,4,2,6,1,7,5,3]=>[1,1,2,2,1,1]
[3,5,1,8,2,4,7,6]=>[8,1,5,2,6,7,3,4]=>[1,8,4,7,3,2,6,5]=>[2,2,1,2,1]
[1,4,5,2,8,3,7,6]=>[2,3,8,6,7,1,4,5]=>[7,6,1,3,2,8,5,4]=>[1,1,2,2,1,1]
[1,4,2,6,5,8,3,7]=>[2,5,4,7,8,1,3,6]=>[7,4,5,2,1,8,6,3]=>[1,2,1,2,1,1]
[1,5,4,2,6,8,3,7]=>[5,3,2,7,8,1,4,6]=>[4,6,7,2,1,8,5,3]=>[3,1,2,1,1]
[1,6,4,2,5,8,3,7]=>[5,3,7,2,8,1,4,6]=>[4,6,2,7,1,8,5,3]=>[2,2,2,1,1]
[1,5,2,6,4,8,3,7]=>[5,4,2,7,8,1,3,6]=>[4,5,7,2,1,8,6,3]=>[3,1,2,1,1]
[1,2,6,5,4,8,3,7]=>[5,4,3,7,8,1,2,6]=>[4,5,6,2,1,8,7,3]=>[3,1,2,1,1]
[1,2,5,4,7,3,8,6]=>[3,8,4,6,1,2,5,7]=>[6,1,5,3,8,7,4,2]=>[1,2,2,1,1,1]
[4,1,2,6,3,8,7,5]=>[4,1,8,7,2,3,5,6]=>[5,8,1,2,7,6,4,3]=>[2,3,1,1,1]
[7,1,5,4,2,8,3,6]=>[7,4,3,8,2,5,1,6]=>[2,5,6,1,7,4,8,3]=>[3,2,2,1]
[1,4,7,5,2,8,3,6]=>[7,2,4,8,5,1,3,6]=>[2,7,5,1,4,8,6,3]=>[2,1,3,1,1]
[7,1,3,5,2,8,4,6]=>[7,3,4,8,2,5,1,6]=>[2,6,5,1,7,4,8,3]=>[2,1,2,2,1]
[7,2,5,1,8,3,4,6]=>[6,7,2,3,8,4,1,5]=>[3,2,7,6,1,5,8,4]=>[1,2,1,3,1]
[1,4,5,2,8,7,3,6]=>[2,3,7,8,6,1,4,5]=>[7,6,2,1,3,8,5,4]=>[1,1,1,3,1,1]
[1,6,4,2,8,3,7,5]=>[3,8,6,2,7,1,4,5]=>[6,1,3,7,2,8,5,4]=>[1,3,2,1,1]
[1,4,2,8,3,7,6,5]=>[8,2,7,5,6,1,3,4]=>[1,7,2,4,3,8,6,5]=>[2,2,2,1,1]
[1,2,5,3,8,7,6,4]=>[8,3,7,6,1,2,4,5]=>[1,6,2,3,8,7,5,4]=>[2,3,1,1,1]
[1,2,8,6,5,3,7,4]=>[8,6,5,4,7,1,2,3]=>[1,3,4,5,2,8,7,6]=>[4,2,1,1]
[1,5,2,8,6,3,7,4]=>[2,8,6,5,7,1,3,4]=>[7,1,3,4,2,8,6,5]=>[1,3,2,1,1]
[1,6,4,2,8,7,3,5]=>[3,7,2,8,6,1,4,5]=>[6,2,7,1,3,8,5,4]=>[1,2,3,1,1]
[7,6,2,1,8,3,4,5]=>[3,6,7,8,4,2,1,5]=>[6,3,2,1,5,7,8,4]=>[1,1,1,4,1]
[1,7,5,2,6,3,8,4]=>[8,6,4,3,5,1,2,7]=>[1,3,5,6,4,8,7,2]=>[4,2,1,1]
[1,6,2,7,5,3,8,4]=>[8,6,5,3,1,2,4,7]=>[1,3,4,6,8,7,5,2]=>[5,1,1,1]
[1,2,7,6,5,3,8,4]=>[8,6,5,4,1,2,3,7]=>[1,3,4,5,8,7,6,2]=>[5,1,1,1]
[1,2,6,5,3,8,7,4]=>[4,3,8,7,1,2,5,6]=>[5,6,1,2,8,7,4,3]=>[2,3,1,1,1]
[1,5,2,6,3,8,7,4]=>[4,2,8,7,1,3,5,6]=>[5,7,1,2,8,6,4,3]=>[2,3,1,1,1]
[1,5,2,7,6,3,8,4]=>[2,8,6,5,1,3,4,7]=>[7,1,3,4,8,6,5,2]=>[1,4,1,1,1]
[1,6,5,2,7,3,8,4]=>[8,6,4,3,1,2,5,7]=>[1,3,5,6,8,7,4,2]=>[5,1,1,1]
[1,5,7,4,2,8,3,6]=>[2,7,4,8,5,1,3,6]=>[7,2,5,1,4,8,6,3]=>[1,2,3,1,1]
[4,1,2,8,6,3,7,5]=>[1,8,6,5,7,2,3,4]=>[8,1,3,4,2,7,6,5]=>[1,3,2,1,1]
[3,1,8,6,2,4,7,5]=>[8,1,5,6,4,7,2,3]=>[1,8,4,3,5,2,7,6]=>[2,1,2,2,1]
[4,3,7,1,8,2,5,6]=>[2,1,6,7,8,4,3,5]=>[7,8,3,2,1,5,6,4]=>[2,1,1,3,1]
[7,1,8,3,2,4,6,5]=>[4,8,5,6,7,2,1,3]=>[5,1,4,3,2,7,8,6]=>[1,2,1,3,1]
[1,8,7,3,2,4,6,5]=>[4,8,5,6,7,3,1,2]=>[5,1,4,3,2,6,8,7]=>[1,2,1,3,1]
[1,4,2,8,7,3,6,5]=>[8,2,6,7,5,1,3,4]=>[1,7,3,2,4,8,6,5]=>[2,1,3,1,1]
[1,7,4,2,8,3,6,5]=>[3,8,6,7,4,1,2,5]=>[6,1,3,2,5,8,7,4]=>[1,2,3,1,1]
[8,1,5,4,2,7,3,6]=>[7,4,3,8,2,5,6,1]=>[2,5,6,1,7,4,3,8]=>[3,2,1,2]
[1,4,8,5,2,7,3,6]=>[7,2,4,8,5,6,1,3]=>[2,7,5,1,4,3,8,6]=>[2,1,2,2,1]
[8,5,3,1,7,2,4,6]=>[6,3,7,2,8,4,5,1]=>[3,6,2,7,1,5,4,8]=>[2,2,2,2]
[8,6,2,1,7,3,4,5]=>[3,6,7,8,4,2,5,1]=>[6,3,2,1,5,7,4,8]=>[1,1,1,3,2]
[1,8,6,4,2,7,3,5]=>[7,4,8,5,3,6,1,2]=>[2,5,1,4,6,3,8,7]=>[2,3,2,1]
[1,8,5,2,6,3,7,4]=>[8,6,4,3,5,7,1,2]=>[1,3,5,6,4,2,8,7]=>[4,1,2,1]
[1,5,2,7,3,8,6,4]=>[2,8,7,5,1,3,4,6]=>[7,1,2,4,8,6,5,3]=>[1,4,1,1,1]
[1,2,8,5,3,7,6,4]=>[4,8,7,5,6,1,2,3]=>[5,1,2,4,3,8,7,6]=>[1,3,2,1,1]
[1,2,6,3,8,7,5,4]=>[3,8,7,6,1,2,4,5]=>[6,1,2,3,8,7,5,4]=>[1,4,1,1,1]
[1,2,7,6,3,8,5,4]=>[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>[5,1,1,1]
[1,6,2,7,3,8,5,4]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>[5,1,1,1]
[1,7,2,8,5,3,6,4]=>[8,6,5,7,3,1,2,4]=>[1,3,4,2,6,8,7,5]=>[3,3,1,1]
[1,7,4,2,8,6,3,5]=>[3,7,8,6,4,1,2,5]=>[6,2,1,3,5,8,7,4]=>[1,1,4,1,1]
[7,1,8,3,2,6,4,5]=>[4,7,8,5,6,2,1,3]=>[5,2,1,4,3,7,8,6]=>[1,1,2,3,1]
[7,2,1,8,6,3,4,5]=>[6,7,8,2,5,3,1,4]=>[3,2,1,7,4,6,8,5]=>[1,1,2,3,1]
[1,8,7,3,2,6,4,5]=>[4,7,8,5,6,3,1,2]=>[5,2,1,4,3,6,8,7]=>[1,1,2,3,1]
[1,4,2,8,7,6,3,5]=>[7,8,2,6,5,1,3,4]=>[2,1,7,3,4,8,6,5]=>[1,2,3,1,1]
[1,2,8,7,5,3,6,4]=>[8,6,5,7,4,1,2,3]=>[1,3,4,2,5,8,7,6]=>[3,3,1,1]
[1,2,8,6,3,7,5,4]=>[8,7,5,4,6,1,2,3]=>[1,2,4,5,3,8,7,6]=>[4,2,1,1]
[1,2,7,3,8,6,5,4]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>[5,1,1,1]
[5,1,8,7,6,2,4,3]=>[1,8,6,7,5,4,2,3]=>[8,1,3,2,4,5,7,6]=>[1,2,4,1]
[8,1,7,6,3,4,5,2]=>[5,6,8,7,4,2,3,1]=>[4,3,1,2,5,7,6,8]=>[1,1,4,2]
[5,7,8,6,2,4,1,3]=>[1,5,7,2,8,6,4,3]=>[8,4,2,7,1,3,5,6]=>[1,1,2,4]
[5,7,1,6,2,4,3,8]=>[7,5,1,6,3,4,2,8]=>[2,4,8,3,6,5,7,1]=>[3,2,2,1]
[6,4,1,5,2,7,3,8]=>[7,5,3,2,4,1,6,8]=>[2,4,6,7,5,8,3,1]=>[4,2,1,1]
[8,1,4,5,3,7,6,2]=>[3,4,8,5,7,2,6,1]=>[6,5,1,4,2,7,3,8]=>[1,1,2,2,2]
[6,1,4,5,3,7,8,2]=>[3,5,4,6,1,8,2,7]=>[6,4,5,3,8,1,7,2]=>[1,2,2,2,1]
[5,1,7,8,6,2,4,3]=>[1,8,6,3,7,5,2,4]=>[8,1,3,6,2,4,7,5]=>[1,3,3,1]
[6,1,4,8,3,5,7,2]=>[3,5,6,1,8,7,2,4]=>[6,4,3,8,1,2,7,5]=>[1,1,2,3,1]
[7,1,8,6,3,4,5,2]=>[5,6,8,7,4,2,1,3]=>[4,3,1,2,5,7,8,6]=>[1,1,5,1]
[7,1,4,5,3,8,6,2]=>[3,4,8,5,7,2,1,6]=>[6,5,1,4,2,7,8,3]=>[1,1,2,3,1]
[7,1,4,5,3,6,8,2]=>[3,5,4,6,8,2,1,7]=>[6,4,5,3,1,7,8,2]=>[1,2,1,3,1]
[8,1,4,5,3,6,7,2]=>[3,5,4,6,8,2,7,1]=>[6,4,5,3,1,7,2,8]=>[1,2,1,2,2]
[7,4,1,5,2,6,3,8]=>[7,5,3,2,4,6,1,8]=>[2,4,6,7,5,3,8,1]=>[4,1,2,1]
[6,3,5,7,2,1,4,8]=>[6,2,5,3,1,7,4,8]=>[3,7,4,6,8,2,5,1]=>[2,3,2,1]
[6,3,5,8,2,1,7,4]=>[5,2,3,1,8,6,7,4]=>[4,7,6,8,1,3,2,5]=>[2,2,2,2]
[6,3,5,7,2,1,8,4]=>[5,2,3,1,8,6,4,7]=>[4,7,6,8,1,3,5,2]=>[2,2,3,1]
[6,4,5,8,3,7,2,1]=>[2,3,1,5,8,7,6,4]=>[7,6,8,4,1,2,3,5]=>[1,2,1,4]
[5,8,7,6,2,4,1,3]=>[1,5,7,8,6,4,3,2]=>[8,4,2,1,3,5,6,7]=>[1,1,1,5]
[5,4,8,6,3,1,7,2]=>[1,8,2,6,5,4,7,3]=>[8,1,7,3,4,5,2,6]=>[1,2,3,2]
[5,4,1,8,2,3,7,6]=>[8,5,2,1,6,7,3,4]=>[1,4,7,8,3,2,6,5]=>[4,1,2,1]
[5,8,1,6,2,4,3,7]=>[7,5,1,6,3,4,8,2]=>[2,4,8,3,6,5,1,7]=>[3,2,1,2]
[8,4,1,5,2,6,3,7]=>[7,5,3,2,4,6,8,1]=>[2,4,6,7,5,3,1,8]=>[4,1,1,2]
[6,3,5,8,2,1,4,7]=>[6,2,5,3,1,7,8,4]=>[3,7,4,6,8,2,1,5]=>[2,3,1,2]
[2,3,4,1,8,6,5,7]=>[7,1,2,3,6,8,4,5]=>[2,8,7,6,3,1,5,4]=>[2,1,1,1,2,1]
[2,3,8,5,1,4,7,6]=>[8,5,1,2,4,6,7,3]=>[1,4,8,7,5,3,2,6]=>[3,1,1,1,2]
[2,8,6,7,1,3,5,4]=>[8,5,6,3,7,1,4,2]=>[1,4,3,6,2,8,5,7]=>[2,2,2,2]
[8,3,5,7,2,1,6,4]=>[5,2,3,8,6,7,4,1]=>[4,7,6,1,3,2,5,8]=>[2,1,2,3]
[7,4,5,6,3,1,8,2]=>[2,3,8,6,5,4,1,7]=>[7,6,1,3,4,5,8,2]=>[1,1,5,1]
[7,3,5,6,2,8,1,4]=>[5,2,3,7,4,1,8,6]=>[4,7,6,2,5,8,1,3]=>[2,1,3,2]
[7,3,5,6,2,1,4,8]=>[6,2,5,3,7,4,1,8]=>[3,7,4,6,2,5,8,1]=>[2,2,3,1]
[2,7,6,8,1,3,5,4]=>[8,5,6,3,1,2,7,4]=>[1,4,3,6,8,7,2,5]=>[2,3,1,2]
[2,7,6,5,8,3,1,4]=>[7,6,4,3,1,2,8,5]=>[2,3,5,6,8,7,1,4]=>[5,1,2]
[8,7,5,6,1,4,2,3]=>[7,8,5,3,6,4,2,1]=>[2,1,4,6,3,5,7,8]=>[1,3,4]
[2,6,4,1,8,5,7,3]=>[3,6,2,8,1,7,4,5]=>[6,3,7,1,8,2,5,4]=>[1,2,2,2,1]
[2,6,1,3,8,5,7,4]=>[6,8,7,1,3,2,4,5]=>[3,1,2,8,6,7,5,4]=>[1,3,2,1,1]
[2,7,1,3,6,5,8,4]=>[6,5,8,1,3,4,2,7]=>[3,4,1,8,6,5,7,2]=>[2,2,1,2,1]
[2,7,6,8,4,3,1,5]=>[7,6,5,3,1,2,8,4]=>[2,3,4,6,8,7,1,5]=>[5,1,2]
[2,7,6,1,8,3,4,5]=>[6,7,8,4,1,3,2,5]=>[3,2,1,5,8,6,7,4]=>[1,1,3,2,1]
[2,7,6,1,4,3,5,8]=>[6,4,5,7,1,3,2,8]=>[3,5,4,2,8,6,7,1]=>[2,1,2,2,1]
[7,3,5,1,2,8,4,6]=>[2,7,8,4,3,5,1,6]=>[7,2,1,5,6,4,8,3]=>[1,1,3,2,1]
[8,4,1,5,2,3,7,6]=>[8,5,3,2,4,6,7,1]=>[1,4,6,7,5,3,2,8]=>[4,1,1,2]
[7,8,1,6,3,4,2,5]=>[5,7,6,8,3,1,4,2]=>[4,2,3,1,6,8,5,7]=>[1,2,3,2]
[6,4,1,8,3,2,7,5]=>[5,2,8,6,1,7,3,4]=>[4,7,1,3,8,2,6,5]=>[2,3,2,1]
[2,3,8,6,4,1,7,5]=>[5,8,6,1,2,4,7,3]=>[4,1,3,8,7,5,2,6]=>[1,3,1,1,2]
[2,8,6,7,4,3,1,5]=>[7,6,5,3,8,1,4,2]=>[2,3,4,6,1,8,5,7]=>[4,2,2]
[8,3,5,7,2,4,1,6]=>[5,2,3,7,6,8,4,1]=>[4,7,6,2,3,1,5,8]=>[2,1,2,3]
[2,3,4,1,8,7,5,6]=>[7,8,1,2,3,6,4,5]=>[2,1,8,7,6,3,5,4]=>[1,2,1,1,2,1]
[2,8,6,1,7,3,4,5]=>[6,7,8,4,1,3,5,2]=>[3,2,1,5,8,6,4,7]=>[1,1,3,1,2]
[2,3,8,1,6,4,7,5]=>[8,6,1,2,4,5,7,3]=>[1,3,8,7,5,4,2,6]=>[3,1,1,1,2]
[2,3,8,1,4,5,7,6]=>[8,1,2,4,5,6,7,3]=>[1,8,7,5,4,3,2,6]=>[2,1,1,1,1,2]
[2,8,6,1,4,3,5,7]=>[6,4,5,7,1,3,8,2]=>[3,5,4,2,8,6,1,7]=>[2,1,2,1,2]
[1,2,3,4,5,6,7,9,8]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,10,9]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9,11,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[2,1,1,1,1,1,1,1,1,1]
[1,8,2,3,4,5,6,9,7]=>[9,3,4,5,6,7,1,2,8]=>[1,7,6,5,4,3,9,8,2]=>[2,1,1,1,2,1,1]
[2,1,9,3,4,5,6,7,8]=>[1,4,5,6,7,8,9,2,3]=>[9,6,5,4,3,2,1,8,7]=>[1,1,1,1,1,1,2,1]
[2,8,1,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>[9,7,6,5,4,3,2,8,1]=>[1,1,1,1,1,1,2,1]
[2,10,1,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>[10,8,7,6,5,4,3,2,1,9]=>[1,1,1,1,1,1,1,1,2]
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1,1]
[8,4,3,6,5,1,7,2]=>[2,8,3,6,5,4,7,1]=>[7,1,6,3,4,5,2,8]=>[1,2,3,2]
[8,5,6,3,4,1,7,2]=>[4,2,8,6,5,3,7,1]=>[5,7,1,3,4,6,2,8]=>[2,4,2]
[8,6,5,4,3,1,7,2]=>[8,6,5,4,3,2,7,1]=>[1,3,4,5,6,7,2,8]=>[6,2]
[1,7,6,5,4,2,3,8]=>[6,7,5,4,3,1,2,8]=>[3,2,4,5,6,8,7,1]=>[1,5,1,1]
[1,8,6,5,2,7,3,4]=>[7,8,5,4,3,6,1,2]=>[2,1,4,5,6,3,8,7]=>[1,4,2,1]
[8,7,5,4,1,6,3,2]=>[8,7,5,4,3,6,2,1]=>[1,2,4,5,6,3,7,8]=>[5,3]
[7,8,5,4,1,3,6,2]=>[6,8,5,4,3,1,7,2]=>[3,1,4,5,6,8,2,7]=>[1,5,2]
[6,8,5,4,2,1,7,3]=>[5,1,8,6,4,3,7,2]=>[4,8,1,3,5,6,2,7]=>[2,4,2]
[5,8,6,2,4,1,7,3]=>[1,8,4,6,5,3,7,2]=>[8,1,5,3,4,6,2,7]=>[1,2,3,2]
[4,8,2,6,5,1,7,3]=>[8,1,6,3,5,4,7,2]=>[1,8,3,6,4,5,2,7]=>[2,2,2,2]
[3,2,8,6,5,1,7,4]=>[8,6,1,5,2,4,7,3]=>[1,3,8,4,7,5,2,6]=>[3,2,1,2]
[3,2,1,7,6,4,5,8]=>[1,6,7,2,5,3,4,8]=>[8,3,2,7,4,6,5,1]=>[1,1,2,2,1,1]
[4,1,3,7,6,2,5,8]=>[6,1,7,3,5,2,4,8]=>[3,8,2,6,4,7,5,1]=>[2,2,2,1,1]
[5,1,7,3,6,2,4,8]=>[4,6,1,7,5,2,3,8]=>[5,3,8,2,4,7,6,1]=>[1,2,3,1,1]
[6,1,7,5,3,2,4,8]=>[6,5,7,4,2,1,3,8]=>[3,4,2,5,7,8,6,1]=>[2,4,1,1]
[7,1,6,5,2,4,3,8]=>[7,5,6,4,2,3,1,8]=>[2,4,3,5,7,6,8,1]=>[2,3,2,1]
[8,1,6,5,2,3,7,4]=>[8,5,6,4,2,3,7,1]=>[1,4,3,5,7,6,2,8]=>[2,3,1,2]
[1,2,7,6,3,4,5,8]=>[5,6,7,4,1,2,3,8]=>[4,3,2,5,8,7,6,1]=>[1,1,3,1,1,1]
[1,2,8,3,7,4,5,6]=>[6,7,8,4,5,1,2,3]=>[3,2,1,5,4,8,7,6]=>[1,1,2,2,1,1]
[8,1,7,2,6,3,5,4]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[2,2,2,2]
[7,1,8,2,6,4,3,5]=>[7,6,8,4,5,2,1,3]=>[2,3,1,5,4,7,8,6]=>[2,2,3,1]
[6,1,8,2,4,7,3,5]=>[5,7,8,4,1,6,2,3]=>[4,2,1,5,8,3,7,6]=>[1,1,3,2,1]
[5,1,8,3,2,7,4,6]=>[4,7,1,8,5,6,2,3]=>[5,2,8,1,4,3,7,6]=>[1,2,2,2,1]
[4,1,3,8,2,7,5,6]=>[7,1,8,3,5,6,2,4]=>[2,8,1,6,4,3,7,5]=>[2,2,1,2,1]
[3,2,1,8,4,7,5,6]=>[1,7,8,2,5,6,3,4]=>[8,2,1,7,4,3,6,5]=>[1,1,2,1,2,1]
[3,2,8,7,1,6,5,4]=>[8,7,1,5,6,2,4,3]=>[1,2,8,4,3,7,5,6]=>[3,1,2,2]
[4,8,2,7,1,6,5,3]=>[8,1,7,3,5,6,4,2]=>[1,8,2,6,4,3,5,7]=>[2,2,1,3]
[5,8,7,2,1,6,4,3]=>[1,8,4,7,5,6,3,2]=>[8,1,5,2,4,3,6,7]=>[1,2,2,3]
[6,8,7,1,3,5,4,2]=>[8,5,1,7,4,6,3,2]=>[1,4,8,2,5,3,6,7]=>[3,2,3]
[7,8,6,1,5,3,4,2]=>[6,8,7,4,1,5,3,2]=>[3,1,2,5,8,4,6,7]=>[1,4,3]
[8,7,6,1,5,4,3,2]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[4,4]
[1,8,7,2,6,5,3,4]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>[1,3,3,1]
[1,7,8,2,5,6,3,4]=>[7,5,8,4,2,6,1,3]=>[2,4,1,5,7,3,8,6]=>[2,3,2,1]
[8,6,7,1,4,5,3,2]=>[5,8,7,4,2,6,3,1]=>[4,1,2,5,7,3,6,8]=>[1,4,3]
[7,6,8,1,4,3,5,2]=>[6,5,8,4,2,1,7,3]=>[3,4,1,5,7,8,2,6]=>[2,4,2]
[7,5,8,3,1,4,6,2]=>[6,4,2,8,5,1,7,3]=>[3,5,7,1,4,8,2,6]=>[3,3,2]
[1,6,8,4,2,7,3,5]=>[7,4,2,8,5,6,1,3]=>[2,5,7,1,4,3,8,6]=>[3,2,2,1]
[1,5,4,8,2,7,3,6]=>[3,2,7,8,5,6,1,4]=>[6,7,2,1,4,3,8,5]=>[2,1,2,2,1]
[7,4,3,8,1,5,6,2]=>[3,2,6,8,5,1,7,4]=>[6,7,3,1,4,8,2,5]=>[2,1,3,2]
[6,4,3,1,5,2,7,8]=>[6,4,3,2,5,1,7,8]=>[3,5,6,7,4,8,2,1]=>[4,2,1,1]
[7,4,3,1,2,6,5,8]=>[7,4,3,2,5,6,1,8]=>[2,5,6,7,4,3,8,1]=>[4,1,2,1]
[8,4,3,1,2,5,7,6]=>[8,4,3,2,5,6,7,1]=>[1,5,6,7,4,3,2,8]=>[4,1,1,2]
[1,5,4,2,3,6,7,8]=>[4,5,3,1,2,6,7,8]=>[5,4,6,8,7,3,2,1]=>[1,3,1,1,1,1]
[8,5,1,4,2,3,7,6]=>[8,5,3,4,2,6,7,1]=>[1,4,6,5,7,3,2,8]=>[3,2,1,2]
[7,5,1,4,2,6,3,8]=>[7,5,3,4,2,6,1,8]=>[2,4,6,5,7,3,8,1]=>[3,2,2,1]
[6,5,1,4,3,2,7,8]=>[6,5,3,4,2,1,7,8]=>[3,4,6,5,7,8,2,1]=>[3,3,1,1]
[5,6,1,3,4,2,7,8]=>[4,6,3,1,5,2,7,8]=>[5,3,6,8,4,7,2,1]=>[1,3,2,1,1]
[4,6,2,1,5,3,7,8]=>[3,1,6,4,5,2,7,8]=>[6,8,3,5,4,7,2,1]=>[2,2,2,1,1]
[3,2,6,1,5,4,7,8]=>[1,6,2,4,5,3,7,8]=>[8,3,7,5,4,6,2,1]=>[1,2,1,2,1,1]
[3,2,7,1,4,6,5,8]=>[1,7,2,4,5,6,3,8]=>[8,2,7,5,4,3,6,1]=>[1,2,1,1,2,1]
[5,7,1,3,2,6,4,8]=>[4,7,3,1,5,6,2,8]=>[5,2,6,8,4,3,7,1]=>[1,3,1,2,1]
[6,7,1,2,4,5,3,8]=>[5,7,3,4,1,6,2,8]=>[4,2,6,5,8,3,7,1]=>[1,2,2,2,1]
[7,6,1,2,5,4,3,8]=>[7,6,3,4,5,2,1,8]=>[2,3,6,5,4,7,8,1]=>[3,1,3,1]
[8,6,1,2,5,3,7,4]=>[8,6,3,4,5,2,7,1]=>[1,3,6,5,4,7,2,8]=>[3,1,2,2]
[1,7,2,3,6,4,5,8]=>[6,7,3,4,5,1,2,8]=>[3,2,6,5,4,8,7,1]=>[1,2,1,2,1,1]
[8,7,1,2,3,6,5,4]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>[3,1,1,3]
[7,8,1,2,3,5,6,4]=>[6,8,3,4,5,1,7,2]=>[3,1,6,5,4,8,2,7]=>[1,2,1,2,2]
[6,8,1,2,4,3,7,5]=>[5,8,3,4,1,6,7,2]=>[4,1,6,5,8,3,2,7]=>[1,2,2,1,2]
[5,8,1,3,2,4,7,6]=>[4,8,3,1,5,6,7,2]=>[5,1,6,8,4,3,2,7]=>[1,3,1,1,2]
[3,2,8,1,4,5,7,6]=>[1,8,2,4,5,6,7,3]=>[8,1,7,5,4,3,2,6]=>[1,2,1,1,1,2]
[4,1,3,2,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[5,7,6,8,4,3,2,1]=>[2,2,1,1,1,1]
[5,1,2,4,3,6,7,8]=>[5,2,3,4,1,6,7,8]=>[4,7,6,5,8,3,2,1]=>[2,1,2,1,1,1]
[6,1,2,3,5,4,7,8]=>[6,2,3,4,5,1,7,8]=>[3,7,6,5,4,8,2,1]=>[2,1,1,2,1,1]
[7,1,2,3,4,6,5,8]=>[7,2,3,4,5,6,1,8]=>[2,7,6,5,4,3,8,1]=>[2,1,1,1,2,1]
[8,1,2,3,4,5,7,6]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>[2,1,1,1,1,2]
[6,7,3,8,5,1,2,4]=>[3,6,1,7,2,8,5,4]=>[6,3,8,2,7,1,4,5]=>[1,2,2,3]
[6,7,4,5,1,8,3,2]=>[3,1,8,7,5,4,2,6]=>[6,8,1,2,4,5,7,3]=>[2,5,1]
[5,4,7,6,8,1,2,3]=>[2,1,6,7,4,3,8,5]=>[7,8,3,2,5,6,1,4]=>[2,1,3,2]
[5,3,7,8,6,1,2,4]=>[6,1,7,2,3,8,5,4]=>[3,8,2,7,6,1,4,5]=>[2,2,1,3]
[3,8,4,5,7,1,2,6]=>[3,6,1,4,7,8,5,2]=>[6,3,8,5,2,1,4,7]=>[1,2,1,1,3]
[3,4,8,6,7,1,2,5]=>[6,7,1,2,4,8,5,3]=>[3,2,8,7,5,1,4,6]=>[1,2,1,1,3]
[4,5,6,7,1,8,3,2]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[1,1,1,4,1]
[3,5,6,2,7,4,8,1]=>[2,6,1,4,3,5,8,7]=>[7,3,8,5,6,4,1,2]=>[1,2,2,1,2]
[3,5,6,1,7,8,4,2]=>[2,5,1,3,8,7,4,6]=>[7,4,8,6,1,2,5,3]=>[1,2,1,3,1]
[2,5,6,1,8,7,4,3]=>[2,3,8,7,1,6,4,5]=>[7,6,1,2,8,3,5,4]=>[1,1,3,2,1]
[2,5,6,8,1,7,3,4]=>[2,7,3,8,1,5,6,4]=>[7,2,6,1,8,4,3,5]=>[1,2,2,1,2]
[8,2,4,5,1,6,3,7]=>[3,7,2,5,4,6,8,1]=>[6,2,7,4,5,3,1,8]=>[1,2,2,1,2]
[1,4,8,6,2,3,7,5]=>[8,2,5,6,4,7,1,3]=>[1,7,4,3,5,2,8,6]=>[2,1,2,2,1]
[1,5,6,8,2,3,7,4]=>[2,8,5,3,6,7,1,4]=>[7,1,4,6,3,2,8,5]=>[1,3,1,2,1]
[2,5,6,3,4,7,8,1]=>[4,2,5,1,3,6,8,7]=>[5,7,4,8,6,3,1,2]=>[2,2,1,1,2]
[1,4,2,6,8,5,7,3]=>[2,4,6,8,7,1,3,5]=>[7,5,3,1,2,8,6,4]=>[1,1,1,3,1,1]
[8,1,3,2,5,4,6,7]=>[3,6,2,4,5,7,8,1]=>[6,3,7,5,4,2,1,8]=>[1,2,1,1,1,2]
[8,2,3,1,5,6,4,7]=>[2,3,5,7,4,6,8,1]=>[7,6,4,2,5,3,1,8]=>[1,1,1,2,1,2]
[2,8,3,1,5,7,4,6]=>[3,5,7,8,1,4,6,2]=>[6,4,2,1,8,5,3,7]=>[1,1,1,2,1,2]
[3,4,1,6,7,8,5,2]=>[1,2,4,5,8,7,3,6]=>[8,7,5,4,1,2,6,3]=>[1,1,1,1,3,1]
[4,3,1,7,6,8,5,2]=>[1,5,2,4,8,7,3,6]=>[8,4,7,5,1,2,6,3]=>[1,2,1,3,1]
[5,2,7,8,1,6,3,4]=>[7,1,8,5,2,3,6,4]=>[2,8,1,4,7,6,3,5]=>[2,3,1,2]
[5,3,7,2,6,4,8,1]=>[6,2,1,4,5,3,8,7]=>[3,7,8,5,4,6,1,2]=>[3,1,2,2]
[6,7,3,1,5,8,4,2]=>[3,5,1,8,7,4,2,6]=>[6,4,8,1,2,5,7,3]=>[1,2,4,1]
[6,7,2,8,1,5,3,4]=>[7,8,3,1,5,2,6,4]=>[2,1,6,8,4,7,3,5]=>[1,3,2,2]
[6,7,8,2,1,4,3,5]=>[4,7,5,1,6,2,8,3]=>[5,2,4,8,3,7,1,6]=>[1,3,2,2]
[6,7,1,2,8,4,5,3]=>[6,8,7,3,1,4,2,5]=>[3,1,2,6,8,5,7,4]=>[1,4,2,1]
[6,7,1,3,4,8,5,2]=>[8,4,5,1,7,3,2,6]=>[1,5,4,8,2,6,7,3]=>[2,2,3,1]
[5,2,7,3,4,6,8,1]=>[4,5,1,6,2,3,8,7]=>[5,4,8,3,7,6,1,2]=>[1,2,2,1,2]
[5,1,7,3,4,8,6,2]=>[8,4,1,5,3,7,2,6]=>[1,5,8,4,6,2,7,3]=>[3,2,2,1]
[5,1,7,8,2,3,6,4]=>[8,5,1,6,3,7,2,4]=>[1,4,8,3,6,2,7,5]=>[3,2,2,1]
[4,1,8,7,2,3,6,5]=>[1,8,5,6,7,4,2,3]=>[8,1,4,3,2,5,7,6]=>[1,2,1,3,1]
[3,8,1,2,7,4,5,6]=>[1,6,7,8,3,4,5,2]=>[8,3,2,1,6,5,4,7]=>[1,1,1,2,1,2]
[4,1,3,7,5,8,6,2]=>[1,8,5,3,4,7,2,6]=>[8,1,4,6,5,2,7,3]=>[1,3,1,2,1]
[3,1,4,5,7,8,6,2]=>[1,5,8,3,4,7,2,6]=>[8,4,1,6,5,2,7,3]=>[1,1,2,1,2,1]
[8,2,1,3,4,6,5,7]=>[2,7,3,4,5,6,8,1]=>[7,2,6,5,4,3,1,8]=>[1,2,1,1,1,2]
[1,8,2,3,4,5,7,6]=>[8,3,4,5,6,7,1,2]=>[1,6,5,4,3,2,8,7]=>[2,1,1,1,2,1]
[4,2,1,6,5,8,7,3]=>[4,1,8,2,5,7,3,6]=>[5,8,1,7,4,2,6,3]=>[2,2,1,2,1]
[5,2,6,1,4,8,7,3]=>[8,5,2,1,3,7,4,6]=>[1,4,7,8,6,2,5,3]=>[4,1,2,1]
[5,2,7,4,8,1,6,3]=>[4,1,8,6,2,3,7,5]=>[5,8,1,3,7,6,2,4]=>[2,3,1,2]
[5,2,7,4,8,6,1,3]=>[4,1,7,3,8,2,6,5]=>[5,8,2,6,1,7,3,4]=>[2,2,2,2]
[5,7,2,3,8,6,1,4]=>[7,1,8,3,4,2,6,5]=>[2,8,1,6,5,7,3,4]=>[2,2,2,2]
[5,7,2,3,8,1,6,4]=>[8,3,1,4,6,2,7,5]=>[1,6,8,5,3,7,2,4]=>[3,1,2,2]
[5,6,2,1,3,8,7,4]=>[8,3,1,7,4,2,5,6]=>[1,6,8,2,5,7,4,3]=>[3,3,1,1]
[5,1,6,4,2,8,7,3]=>[4,3,1,8,7,2,5,6]=>[5,6,8,1,2,7,4,3]=>[3,3,1,1]
[5,6,1,3,2,8,7,4]=>[8,4,1,7,3,2,5,6]=>[1,5,8,2,6,7,4,3]=>[3,3,1,1]
[5,6,3,1,2,8,7,4]=>[3,1,8,7,4,2,5,6]=>[6,8,1,2,5,7,4,3]=>[2,4,1,1]
[5,7,3,2,8,1,6,4]=>[3,1,8,4,6,2,7,5]=>[6,8,1,5,3,7,2,4]=>[2,2,2,2]
[5,7,3,2,8,6,1,4]=>[3,1,7,8,4,2,6,5]=>[6,8,2,1,5,7,3,4]=>[2,1,3,2]
[6,7,3,8,2,1,5,4]=>[3,5,1,8,6,2,7,4]=>[6,4,8,1,3,7,2,5]=>[1,2,3,2]
[6,7,3,8,1,2,5,4]=>[3,8,5,1,6,2,7,4]=>[6,1,4,8,3,7,2,5]=>[1,3,2,2]
[5,7,3,1,8,2,6,4]=>[3,1,8,6,7,4,2,5]=>[6,8,1,3,2,5,7,4]=>[2,2,3,1]
[5,7,1,3,8,2,6,4]=>[8,4,1,6,7,3,2,5]=>[1,5,8,3,2,6,7,4]=>[3,1,3,1]
[5,1,7,4,8,2,6,3]=>[4,1,8,6,3,7,2,5]=>[5,8,1,3,6,2,7,4]=>[2,3,2,1]
[1,5,7,4,8,3,6,2]=>[2,4,6,3,8,7,1,5]=>[7,5,3,6,1,2,8,4]=>[1,1,2,3,1]
[1,5,7,4,8,6,3,2]=>[8,2,4,3,7,6,1,5]=>[1,7,5,6,2,3,8,4]=>[2,2,3,1]
[5,1,7,4,8,6,2,3]=>[4,1,7,3,8,6,2,5]=>[5,8,2,6,1,3,7,4]=>[2,2,3,1]
[5,7,1,3,8,6,2,4]=>[7,1,8,4,6,3,2,5]=>[2,8,1,5,3,6,7,4]=>[2,2,3,1]
[5,7,3,1,8,6,2,4]=>[3,1,7,8,6,4,2,5]=>[6,8,2,1,3,5,7,4]=>[2,1,4,1]
[6,7,3,8,1,5,2,4]=>[3,7,1,8,5,2,6,4]=>[6,2,8,1,4,7,3,5]=>[1,2,3,2]
[6,7,3,8,5,2,1,4]=>[7,3,1,6,2,8,5,4]=>[2,6,8,3,7,1,4,5]=>[3,2,3]
[6,7,8,3,1,4,2,5]=>[7,5,4,1,6,2,8,3]=>[2,4,5,8,3,7,1,6]=>[4,2,2]
[6,7,1,8,3,5,2,4]=>[5,7,1,8,6,3,2,4]=>[4,2,8,1,3,6,7,5]=>[1,2,4,1]
[6,1,7,8,4,5,2,3]=>[7,5,3,1,8,6,2,4]=>[2,4,6,8,1,3,7,5]=>[4,3,1]
[1,6,7,8,4,5,3,2]=>[2,5,3,8,7,6,1,4]=>[7,4,6,1,2,3,8,5]=>[1,2,4,1]
[1,6,7,8,4,3,5,2]=>[2,6,5,3,8,7,1,4]=>[7,3,4,6,1,2,8,5]=>[1,3,3,1]
[6,1,7,8,4,2,5,3]=>[8,6,5,3,1,7,2,4]=>[1,3,4,6,8,2,7,5]=>[5,2,1]
[6,7,1,8,3,2,5,4]=>[5,8,6,1,7,3,2,4]=>[4,1,3,8,2,6,7,5]=>[1,3,3,1]
[5,7,2,1,8,3,6,4]=>[8,3,1,6,7,4,2,5]=>[1,6,8,3,2,5,7,4]=>[3,1,3,1]
[6,7,2,8,1,3,5,4]=>[8,3,5,1,6,2,7,4]=>[1,6,4,8,3,7,2,5]=>[2,2,2,2]
[6,7,2,8,3,1,5,4]=>[5,8,3,1,6,2,7,4]=>[4,1,6,8,3,7,2,5]=>[1,3,2,2]
[6,7,2,8,3,5,1,4]=>[5,7,1,8,3,2,6,4]=>[4,2,8,1,6,7,3,5]=>[1,2,3,2]
[6,2,7,8,4,5,1,3]=>[7,5,3,1,8,2,6,4]=>[2,4,6,8,1,7,3,5]=>[4,2,2]
[6,2,7,8,4,1,5,3]=>[8,6,5,2,1,3,7,4]=>[1,3,4,7,8,6,2,5]=>[5,1,2]
[5,2,7,1,8,4,6,3]=>[6,1,8,7,2,4,3,5]=>[3,8,1,2,7,5,6,4]=>[2,3,2,1]
[4,2,1,7,8,5,6,3]=>[1,6,4,8,2,7,3,5]=>[8,3,5,1,7,2,6,4]=>[1,2,2,2,1]
[4,1,2,7,8,6,5,3]=>[1,4,8,7,6,2,3,5]=>[8,5,1,2,3,7,6,4]=>[1,1,4,1,1]
[6,2,7,8,1,5,4,3]=>[8,7,5,2,1,3,6,4]=>[1,2,4,7,8,6,3,5]=>[5,1,2]
[6,2,7,8,5,1,4,3]=>[8,6,3,1,7,2,5,4]=>[1,3,6,8,2,7,4,5]=>[4,2,2]
[6,2,7,8,5,4,1,3]=>[7,3,1,8,6,2,5,4]=>[2,6,8,1,3,7,4,5]=>[3,3,2]
[6,7,2,8,5,3,1,4]=>[7,6,1,8,3,2,5,4]=>[2,3,8,1,6,7,4,5]=>[3,3,2]
[5,7,2,1,8,6,3,4]=>[7,1,8,3,6,4,2,5]=>[2,8,1,6,3,5,7,4]=>[2,2,3,1]
[5,7,1,2,8,6,3,4]=>[7,1,8,6,3,4,2,5]=>[2,8,1,3,6,5,7,4]=>[2,3,2,1]
[5,1,7,2,8,6,4,3]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[1,5,1,1]
[1,6,7,8,3,5,4,2]=>[2,8,5,3,7,6,1,4]=>[7,1,4,6,2,3,8,5]=>[1,3,3,1]
[6,1,7,8,2,5,4,3]=>[8,7,5,3,1,6,2,4]=>[1,2,4,6,8,3,7,5]=>[5,2,1]
[6,7,1,8,2,5,3,4]=>[7,8,5,1,6,3,2,4]=>[2,1,4,8,3,6,7,5]=>[1,3,3,1]
[6,7,8,2,4,1,3,5]=>[4,6,1,7,5,2,8,3]=>[5,3,8,2,4,7,1,6]=>[1,2,3,2]
[6,7,8,2,4,3,1,5]=>[7,4,1,6,5,2,8,3]=>[2,5,8,3,4,7,1,6]=>[3,3,2]
[6,7,1,8,5,2,3,4]=>[6,7,1,8,5,3,2,4]=>[3,2,8,1,4,6,7,5]=>[1,2,4,1]
[6,1,7,8,5,2,4,3]=>[8,6,3,1,7,5,2,4]=>[1,3,6,8,2,4,7,5]=>[4,3,1]
[1,6,7,8,5,3,4,2]=>[2,6,3,8,7,5,1,4]=>[7,3,6,1,2,4,8,5]=>[1,2,4,1]
[6,1,7,8,5,4,2,3]=>[7,3,1,8,6,5,2,4]=>[2,6,8,1,3,4,7,5]=>[3,4,1]
[6,7,1,8,5,3,2,4]=>[7,6,1,8,5,3,2,4]=>[2,3,8,1,4,6,7,5]=>[3,4,1]
[6,7,8,4,1,3,2,5]=>[7,5,1,6,4,2,8,3]=>[2,4,8,3,5,7,1,6]=>[3,3,2]
[6,3,8,5,2,7,4,1]=>[8,5,2,1,4,7,6,3]=>[1,4,7,8,5,2,3,6]=>[4,1,3]
[6,5,2,8,4,7,3,1]=>[5,2,1,8,7,3,6,4]=>[4,7,8,1,2,6,3,5]=>[3,3,2]
[6,3,4,5,8,7,2,1]=>[8,2,3,1,4,7,6,5]=>[1,7,6,8,5,2,3,4]=>[2,2,1,3]
[3,8,4,7,5,2,1,6]=>[7,3,6,1,5,8,4,2]=>[2,6,3,8,4,1,5,7]=>[2,2,1,3]
[5,8,1,4,7,2,3,6]=>[6,4,1,7,8,3,5,2]=>[3,5,8,2,1,6,4,7]=>[3,1,2,2]
[5,6,1,4,8,7,3,2]=>[1,8,4,2,7,6,3,5]=>[8,1,5,7,2,3,6,4]=>[1,3,3,1]
[3,6,4,8,5,7,1,2]=>[7,3,1,2,5,8,6,4]=>[2,6,8,7,4,1,3,5]=>[3,1,1,3]
[5,1,4,8,6,3,7,2]=>[6,3,1,5,8,7,2,4]=>[3,6,8,4,1,2,7,5]=>[3,1,3,1]
[3,4,7,1,8,6,5,2]=>[8,7,1,2,6,4,3,5]=>[1,2,8,7,3,5,6,4]=>[3,1,3,1]
[6,3,8,4,2,7,1,5]=>[5,2,4,1,7,8,6,3]=>[4,7,5,8,2,1,3,6]=>[2,2,1,3]
[3,6,8,7,1,4,2,5]=>[7,5,1,2,6,8,4,3]=>[2,4,8,7,3,1,5,6]=>[3,1,1,3]
[5,3,7,1,6,8,2,4]=>[7,2,1,5,8,4,3,6]=>[2,7,8,4,1,5,6,3]=>[3,1,3,1]
[4,3,8,5,6,7,2,1]=>[1,4,5,8,2,7,6,3]=>[8,5,4,1,7,2,3,6]=>[1,1,1,2,3]
[5,8,1,7,6,2,4,3]=>[1,8,6,7,5,3,4,2]=>[8,1,3,2,4,6,5,7]=>[1,2,3,2]
[4,6,1,2,7,8,5,3]=>[1,5,8,7,3,2,4,6]=>[8,4,1,2,6,7,5,3]=>[1,1,4,1,1]
[3,6,4,2,8,7,5,1]=>[8,3,1,2,7,4,6,5]=>[1,6,8,7,2,5,3,4]=>[3,1,2,2]
[6,3,7,5,2,8,1,4]=>[5,7,2,1,4,3,8,6]=>[4,2,7,8,5,6,1,3]=>[1,3,2,2]
[6,5,2,7,4,8,1,3]=>[7,5,3,2,1,4,8,6]=>[2,4,6,7,8,5,1,3]=>[5,1,2]
[5,7,1,4,8,3,2,6]=>[4,1,7,6,8,3,2,5]=>[5,8,2,3,1,6,7,4]=>[2,2,3,1]
[7,8,3,5,1,4,6,2]=>[3,6,8,5,4,1,7,2]=>[6,3,1,4,5,8,2,7]=>[1,1,4,2]
[5,8,1,4,6,7,2,3]=>[4,1,7,5,8,3,6,2]=>[5,8,2,4,1,6,3,7]=>[2,2,2,2]
[6,5,8,4,3,7,2,1]=>[2,1,5,4,8,7,6,3]=>[7,8,4,5,1,2,3,6]=>[2,2,4]
[8,7,1,6,2,4,5,3]=>[6,8,5,7,3,4,2,1]=>[3,1,4,2,6,5,7,8]=>[1,2,2,3]
[3,8,6,7,1,4,5,2]=>[6,8,5,1,3,7,4,2]=>[3,1,4,8,6,2,5,7]=>[1,3,1,3]
[4,3,8,7,1,5,6,2]=>[1,6,8,2,5,7,4,3]=>[8,3,1,7,4,2,5,6]=>[1,1,2,1,3]
[8,3,6,1,2,5,7,4]=>[2,6,8,4,5,3,7,1]=>[7,3,1,5,4,6,2,8]=>[1,1,2,2,2]
[5,4,2,7,3,6,8,1]=>[5,2,1,6,3,4,8,7]=>[4,7,8,3,6,5,1,2]=>[3,2,1,2]
[7,5,3,6,4,2,8,1]=>[6,3,2,5,4,1,8,7]=>[3,6,7,4,5,8,1,2]=>[3,3,2]
[6,4,1,5,3,8,2,7]=>[5,4,2,7,1,8,3,6]=>[4,5,7,2,8,1,6,3]=>[3,2,2,1]
[8,5,2,6,4,7,3,1]=>[5,4,2,8,3,7,6,1]=>[4,5,7,1,6,2,3,8]=>[3,2,3]
[8,2,6,3,4,7,5,1]=>[8,4,5,2,3,7,6,1]=>[1,5,4,7,6,2,3,8]=>[2,2,1,3]
[7,2,6,3,5,4,8,1]=>[6,4,5,2,3,1,8,7]=>[3,5,4,7,6,8,1,2]=>[2,2,2,2]
[6,2,7,4,3,5,8,1]=>[5,4,6,2,1,3,8,7]=>[4,5,3,7,8,6,1,2]=>[2,3,1,2]
[3,7,6,4,5,2,8,1]=>[4,6,5,1,3,2,8,7]=>[5,3,4,8,6,7,1,2]=>[1,3,2,2]
[2,7,6,5,3,4,8,1]=>[5,6,4,3,1,2,8,7]=>[4,3,5,6,8,7,1,2]=>[1,4,1,2]
[6,5,4,3,1,8,2,7]=>[7,4,3,2,1,8,5,6]=>[2,5,6,7,8,1,4,3]=>[5,2,1]
[8,6,5,4,2,7,3,1]=>[8,5,4,3,2,7,6,1]=>[1,4,5,6,7,2,3,8]=>[5,3]
[8,5,4,1,7,2,6,3]=>[8,6,3,2,7,4,5,1]=>[1,3,6,7,2,5,4,8]=>[4,2,2]
[7,5,4,1,8,3,2,6]=>[7,6,3,2,8,4,1,5]=>[2,3,6,7,1,5,8,4]=>[4,3,1]
[1,6,5,2,8,3,4,7]=>[6,7,3,2,8,1,4,5]=>[3,2,6,7,1,8,5,4]=>[1,3,2,1,1]
[5,7,4,2,1,8,3,6]=>[4,1,7,3,8,5,2,6]=>[5,8,2,6,1,4,7,3]=>[2,2,3,1]
[1,6,5,3,4,8,2,7]=>[4,5,3,2,7,8,1,6]=>[5,4,6,7,2,1,8,3]=>[1,3,1,2,1]
[5,4,6,3,1,8,2,7]=>[2,1,7,4,3,8,5,6]=>[7,8,2,5,6,1,4,3]=>[2,3,2,1]
[6,5,8,4,2,7,3,1]=>[2,1,8,5,4,7,6,3]=>[7,8,1,4,5,2,3,6]=>[2,3,3]
[5,8,2,6,4,7,3,1]=>[1,5,4,8,3,7,6,2]=>[8,4,5,1,6,2,3,7]=>[1,2,2,3]
[3,8,6,2,5,7,4,1]=>[5,8,4,1,3,7,6,2]=>[4,1,5,8,6,2,3,7]=>[1,3,1,3]
[7,8,5,3,2,6,4,1]=>[4,8,5,3,1,7,6,2]=>[5,1,4,6,8,2,3,7]=>[1,4,3]
[1,8,6,3,7,5,2,4]=>[7,8,4,3,6,5,1,2]=>[2,1,5,6,3,4,8,7]=>[1,3,3,1]
[8,7,5,2,6,4,3,1]=>[8,7,4,3,6,5,2,1]=>[1,2,5,6,3,4,7,8]=>[4,4]
[8,7,1,6,2,5,4,3]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[3,2,3]
[7,8,1,6,3,2,5,4]=>[5,8,6,7,3,1,4,2]=>[4,1,3,2,6,8,5,7]=>[1,2,3,2]
[2,8,1,7,3,5,6,4]=>[6,8,5,7,1,3,4,2]=>[3,1,4,2,8,6,5,7]=>[1,2,2,1,2]
[3,8,6,1,7,4,5,2]=>[6,8,7,1,4,3,5,2]=>[3,1,2,8,5,6,4,7]=>[1,3,2,2]
[4,8,1,3,7,2,6,5]=>[1,8,4,6,7,3,5,2]=>[8,1,5,3,2,6,4,7]=>[1,2,1,2,2]
[5,1,7,6,8,3,2,4]=>[1,7,6,4,3,8,2,5]=>[8,2,3,5,6,1,7,4]=>[1,4,2,1]
[3,7,1,5,8,4,2,6]=>[4,7,1,6,8,3,2,5]=>[5,2,8,3,1,6,7,4]=>[1,2,1,3,1]
[6,7,3,1,8,4,2,5]=>[3,7,6,1,8,4,2,5]=>[6,2,3,8,1,5,7,4]=>[1,3,3,1]
[1,7,3,8,4,5,2,6]=>[5,7,3,6,2,8,1,4]=>[4,2,6,3,7,1,8,5]=>[1,2,2,2,1]
[1,7,2,8,5,3,4,6]=>[6,7,5,8,3,1,2,4]=>[3,2,4,1,6,8,7,5]=>[1,2,3,1,1]
[7,6,1,8,4,3,2,5]=>[7,6,5,8,3,2,1,4]=>[2,3,4,1,6,7,8,5]=>[3,4,1]
[8,6,1,7,4,2,5,3]=>[8,6,5,7,3,2,4,1]=>[1,3,4,2,6,7,5,8]=>[3,3,2]
[8,1,2,7,3,4,6,5]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[2,1,2,1,2]
[7,1,2,8,3,5,4,6]=>[7,5,6,8,2,3,1,4]=>[2,4,3,1,7,6,8,5]=>[2,1,2,2,1]
[7,2,6,1,8,4,3,5]=>[7,6,8,2,4,3,1,5]=>[2,3,1,7,5,6,8,4]=>[2,2,3,1]
[8,2,6,1,7,3,5,4]=>[8,6,7,2,4,3,5,1]=>[1,3,2,7,5,6,4,8]=>[2,2,2,2]
[8,3,1,4,7,5,6,2]=>[2,6,8,4,7,3,5,1]=>[7,3,1,5,2,6,4,8]=>[1,1,2,2,2]
[7,3,1,5,8,4,2,6]=>[2,4,7,6,8,3,1,5]=>[7,5,2,3,1,6,8,4]=>[1,1,2,3,1]
[4,2,1,5,8,3,6,7]=>[2,4,1,6,7,8,3,5]=>[7,5,8,3,2,1,6,4]=>[1,2,1,1,2,1]
[5,4,2,7,1,8,3,6]=>[7,2,1,8,3,5,4,6]=>[2,7,8,1,6,4,5,3]=>[3,2,2,1]
[5,4,3,1,6,8,2,7]=>[5,3,2,1,7,8,4,6]=>[4,6,7,8,2,1,5,3]=>[4,1,2,1]
[4,7,5,6,8,3,2,1]=>[3,4,1,2,8,7,6,5]=>[6,5,8,7,1,2,3,4]=>[1,2,1,4]
[6,5,4,8,2,7,3,1]=>[3,2,1,8,5,7,6,4]=>[6,7,8,1,4,2,3,5]=>[3,2,3]
[6,5,1,8,7,4,2,3]=>[7,2,1,8,6,5,3,4]=>[2,7,8,1,3,4,6,5]=>[3,4,1]
[8,6,4,7,5,3,2,1]=>[8,3,2,7,6,5,4,1]=>[1,6,7,2,3,4,5,8]=>[3,5]
[5,1,8,3,7,6,2,4]=>[7,1,8,4,6,5,2,3]=>[2,8,1,5,3,4,7,6]=>[2,2,3,1]
[5,4,8,1,7,2,6,3]=>[2,1,8,6,7,4,5,3]=>[7,8,1,3,2,5,4,6]=>[2,2,2,2]
[7,5,8,3,2,6,4,1]=>[4,2,8,5,1,7,6,3]=>[5,7,1,4,8,2,3,6]=>[2,3,3]
[3,6,8,2,4,7,5,1]=>[8,4,1,2,5,7,6,3]=>[1,5,8,7,4,2,3,6]=>[3,1,1,3]
[5,7,3,8,2,6,4,1]=>[1,8,3,5,2,7,6,4]=>[8,1,6,4,7,2,3,5]=>[1,2,2,3]
[5,4,6,8,2,7,3,1]=>[2,1,3,8,5,7,6,4]=>[7,8,6,1,4,2,3,5]=>[2,1,2,3]
[5,2,6,8,7,3,4,1]=>[3,1,6,8,7,2,5,4]=>[6,8,3,1,2,7,4,5]=>[2,1,3,2]
[4,7,2,8,6,3,5,1]=>[6,8,1,7,3,2,5,4]=>[3,1,8,2,6,7,4,5]=>[1,2,3,2]
[3,6,8,1,7,2,5,4]=>[8,6,1,2,7,4,5,3]=>[1,3,8,7,2,5,4,6]=>[3,1,2,2]
[2,3,8,7,4,5,6,1]=>[5,6,8,7,1,2,4,3]=>[4,3,1,2,8,7,5,6]=>[1,1,3,1,2]
[7,2,8,6,4,3,5,1]=>[6,5,8,7,2,1,4,3]=>[3,4,1,2,7,8,5,6]=>[2,4,2]
[2,1,8,7,5,6,3,4]=>[7,5,8,6,1,4,2,3]=>[2,4,1,3,8,5,7,6]=>[2,3,2,1]
[8,2,7,6,3,5,4,1]=>[8,5,7,6,2,4,3,1]=>[1,4,2,3,7,5,6,8]=>[2,3,3]
[8,1,7,6,5,2,4,3]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[2,4,2]
[7,1,8,6,5,3,2,4]=>[7,6,8,5,4,2,1,3]=>[2,3,1,4,5,7,8,6]=>[2,5,1]
[1,2,8,7,6,3,4,5]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[1,1,4,1,1]
[1,3,8,7,4,6,2,5]=>[5,7,8,6,2,4,1,3]=>[4,2,1,3,7,5,8,6]=>[1,1,3,2,1]
[1,5,8,3,7,6,2,4]=>[2,7,8,4,6,5,1,3]=>[7,2,1,5,3,4,8,6]=>[1,1,2,3,1]
[5,1,6,8,7,4,2,3]=>[3,1,7,8,6,5,2,4]=>[6,8,2,1,3,4,7,5]=>[2,1,4,1]
[6,8,4,7,5,3,2,1]=>[1,8,3,7,6,5,4,2]=>[8,1,6,2,3,4,5,7]=>[1,2,5]
[6,8,7,2,5,4,3,1]=>[1,8,7,4,6,5,3,2]=>[8,1,2,5,3,4,6,7]=>[1,3,4]
[3,8,7,6,4,5,2,1]=>[5,8,7,6,1,4,3,2]=>[4,1,2,3,8,5,6,7]=>[1,4,3]
[2,8,7,6,5,3,4,1]=>[6,8,7,5,4,1,3,2]=>[3,1,2,4,5,8,6,7]=>[1,5,2]
[1,8,7,6,5,4,2,3]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[1,6,1]
[5,8,6,7,3,4,1,2]=>[7,1,5,3,8,6,4,2]=>[2,8,4,6,1,3,5,7]=>[2,2,4]
[4,8,6,7,3,5,1,2]=>[7,5,1,3,8,6,4,2]=>[2,4,8,6,1,3,5,7]=>[3,1,4]
[3,8,6,7,4,5,1,2]=>[7,5,3,8,1,6,4,2]=>[2,4,6,1,8,3,5,7]=>[3,2,3]
[2,8,6,7,4,5,1,3]=>[7,5,3,8,6,1,4,2]=>[2,4,6,1,3,8,5,7]=>[3,3,2]
[1,8,6,7,4,5,2,3]=>[7,5,3,8,6,4,1,2]=>[2,4,6,1,3,5,8,7]=>[3,4,1]
[1,8,5,7,4,6,2,3]=>[3,7,5,8,6,4,1,2]=>[6,2,4,1,3,5,8,7]=>[1,2,4,1]
[3,8,5,7,4,6,1,2]=>[3,7,5,8,1,6,4,2]=>[6,2,4,1,8,3,5,7]=>[1,2,2,3]
[4,8,5,7,3,6,1,2]=>[3,7,1,5,8,6,4,2]=>[6,2,8,4,1,3,5,7]=>[1,2,1,4]
[7,8,3,6,4,5,1,2]=>[7,3,5,1,8,6,4,2]=>[2,6,4,8,1,3,5,7]=>[2,2,4]
[6,8,3,7,4,5,1,2]=>[7,3,1,5,8,6,4,2]=>[2,6,8,4,1,3,5,7]=>[3,1,4]
[5,8,3,7,4,6,1,2]=>[1,7,3,5,8,6,4,2]=>[8,2,6,4,1,3,5,7]=>[1,2,1,4]
[3,7,4,8,5,6,1,2]=>[7,3,5,1,2,8,6,4]=>[2,6,4,8,7,1,3,5]=>[2,2,1,3]
[4,7,3,8,5,6,1,2]=>[7,1,3,5,2,8,6,4]=>[2,8,6,4,7,1,3,5]=>[2,1,2,3]
[4,7,2,8,5,6,1,3]=>[7,1,5,8,3,2,6,4]=>[2,8,4,1,6,7,3,5]=>[2,1,3,2]
[4,7,1,8,5,6,2,3]=>[7,1,5,8,6,3,2,4]=>[2,8,4,1,3,6,7,5]=>[2,1,4,1]
[3,7,1,8,5,6,2,4]=>[7,5,8,1,6,3,2,4]=>[2,4,1,8,3,6,7,5]=>[2,2,3,1]
[3,7,2,8,5,6,1,4]=>[7,5,8,1,3,2,6,4]=>[2,4,1,8,6,7,3,5]=>[2,2,2,2]
[2,7,3,8,5,6,1,4]=>[7,5,8,3,1,2,6,4]=>[2,4,1,6,8,7,3,5]=>[2,3,1,2]
[2,7,4,8,5,6,1,3]=>[7,3,5,2,8,1,6,4]=>[2,6,4,7,1,8,3,5]=>[2,2,2,2]
[5,8,2,7,4,6,1,3]=>[1,7,5,8,3,6,4,2]=>[8,2,4,1,6,3,5,7]=>[1,2,2,3]
[6,8,2,7,4,5,1,3]=>[7,5,1,8,3,6,4,2]=>[2,4,8,1,6,3,5,7]=>[3,2,3]
[7,8,2,6,4,5,1,3]=>[7,5,8,3,1,6,4,2]=>[2,4,1,6,8,3,5,7]=>[2,3,3]
[7,8,1,6,4,5,2,3]=>[7,5,8,6,3,1,4,2]=>[2,4,1,3,6,8,5,7]=>[2,4,2]
[6,8,1,7,4,5,2,3]=>[7,5,1,8,6,3,4,2]=>[2,4,8,1,3,6,5,7]=>[3,3,2]
[5,8,1,7,4,6,2,3]=>[1,7,5,8,6,3,4,2]=>[8,2,4,1,3,6,5,7]=>[1,2,3,2]
[1,7,4,8,5,6,2,3]=>[7,3,5,2,8,6,1,4]=>[2,6,4,7,1,3,8,5]=>[2,2,3,1]
[1,7,3,8,5,6,2,4]=>[7,5,8,3,2,6,1,4]=>[2,4,1,6,7,3,8,5]=>[2,3,2,1]
[2,8,5,6,1,7,3,4]=>[7,3,8,5,1,4,6,2]=>[2,6,1,4,8,5,3,7]=>[2,3,1,2]
[1,8,5,6,2,7,3,4]=>[7,3,8,5,4,6,1,2]=>[2,6,1,4,5,3,8,7]=>[2,3,2,1]
[1,7,3,8,4,6,2,5]=>[5,7,8,3,2,6,1,4]=>[4,2,1,6,7,3,8,5]=>[1,1,3,2,1]
[4,8,1,7,3,6,2,5]=>[1,5,7,8,6,3,4,2]=>[8,4,2,1,3,6,5,7]=>[1,1,1,3,2]
[5,8,1,7,3,6,2,4]=>[5,1,7,8,6,3,4,2]=>[4,8,2,1,3,6,5,7]=>[2,1,3,2]
[6,8,1,7,3,5,2,4]=>[5,7,1,8,6,3,4,2]=>[4,2,8,1,3,6,5,7]=>[1,2,3,2]
[7,8,2,6,3,5,1,4]=>[5,7,8,3,1,6,4,2]=>[4,2,1,6,8,3,5,7]=>[1,1,3,3]
[6,8,2,7,3,5,1,4]=>[5,7,1,8,3,6,4,2]=>[4,2,8,1,6,3,5,7]=>[1,2,2,3]
[5,8,2,7,3,6,1,4]=>[5,1,7,8,3,6,4,2]=>[4,8,2,1,6,3,5,7]=>[2,1,2,3]
[4,8,2,7,3,6,1,5]=>[1,5,7,8,3,6,4,2]=>[8,4,2,1,6,3,5,7]=>[1,1,1,2,3]
[2,7,3,8,4,6,1,5]=>[5,7,8,3,1,2,6,4]=>[4,2,1,6,8,7,3,5]=>[1,1,3,1,2]
[3,7,2,8,4,6,1,5]=>[5,7,8,1,3,2,6,4]=>[4,2,1,8,6,7,3,5]=>[1,1,2,2,2]
[3,7,1,8,4,6,2,5]=>[5,7,8,1,6,3,2,4]=>[4,2,1,8,3,6,7,5]=>[1,1,2,3,1]
[1,8,4,7,3,6,2,5]=>[3,5,7,8,6,4,1,2]=>[6,4,2,1,3,5,8,7]=>[1,1,1,4,1]
[2,8,4,7,3,6,1,5]=>[3,5,7,8,6,1,4,2]=>[6,4,2,1,3,8,5,7]=>[1,1,1,3,2]
[3,8,4,7,2,6,1,5]=>[3,5,7,8,1,6,4,2]=>[6,4,2,1,8,3,5,7]=>[1,1,1,2,3]
[4,8,5,7,2,6,1,3]=>[5,1,3,7,8,6,4,2]=>[4,8,6,2,1,3,5,7]=>[2,1,1,4]
[3,8,5,7,2,6,1,4]=>[5,3,7,8,1,6,4,2]=>[4,6,2,1,8,3,5,7]=>[2,1,2,3]
[2,8,5,7,3,6,1,4]=>[5,3,7,8,6,1,4,2]=>[4,6,2,1,3,8,5,7]=>[2,1,3,2]
[1,8,5,7,3,6,2,4]=>[5,3,7,8,6,4,1,2]=>[4,6,2,1,3,5,8,7]=>[2,1,4,1]
[1,8,6,7,3,5,2,4]=>[5,7,3,8,6,4,1,2]=>[4,2,6,1,3,5,8,7]=>[1,2,4,1]
[2,8,6,7,3,5,1,4]=>[5,7,3,8,6,1,4,2]=>[4,2,6,1,3,8,5,7]=>[1,2,3,2]
[3,8,6,7,2,5,1,4]=>[5,7,3,8,1,6,4,2]=>[4,2,6,1,8,3,5,7]=>[1,2,2,3]
[4,8,6,7,2,5,1,3]=>[5,7,1,3,8,6,4,2]=>[4,2,8,6,1,3,5,7]=>[1,2,1,4]
[5,8,6,7,2,4,1,3]=>[1,5,7,3,8,6,4,2]=>[8,4,2,6,1,3,5,7]=>[1,1,2,4]
[6,8,5,7,1,4,2,3]=>[7,1,8,5,3,6,4,2]=>[2,8,1,4,6,3,5,7]=>[2,3,3]
[5,8,6,7,1,4,2,3]=>[1,7,8,5,3,6,4,2]=>[8,2,1,4,6,3,5,7]=>[1,1,3,3]
[4,8,6,7,1,5,2,3]=>[7,8,1,5,3,6,4,2]=>[2,1,8,4,6,3,5,7]=>[1,2,2,3]
[3,8,6,7,1,5,2,4]=>[7,8,5,1,3,6,4,2]=>[2,1,4,8,6,3,5,7]=>[1,3,1,3]
[1,5,2,8,6,7,3,4]=>[2,7,5,8,6,1,3,4]=>[7,2,4,1,3,8,6,5]=>[1,2,3,1,1]
[2,5,1,8,6,7,3,4]=>[2,7,5,8,1,6,3,4]=>[7,2,4,1,8,3,6,5]=>[1,2,2,2,1]
[2,6,1,8,5,7,3,4]=>[7,5,2,8,1,6,3,4]=>[2,4,7,1,8,3,6,5]=>[3,2,2,1]
[3,8,5,7,1,6,2,4]=>[7,3,8,1,5,6,4,2]=>[2,6,1,8,4,3,5,7]=>[2,2,1,3]
[6,8,4,7,1,5,2,3]=>[7,3,1,8,5,6,4,2]=>[2,6,8,1,4,3,5,7]=>[3,2,3]
[7,8,4,6,1,5,2,3]=>[7,3,8,5,1,6,4,2]=>[2,6,1,4,8,3,5,7]=>[2,3,3]
[7,8,3,6,1,5,2,4]=>[3,7,8,5,1,6,4,2]=>[6,2,1,4,8,3,5,7]=>[1,1,3,3]
[6,8,3,7,1,5,2,4]=>[3,7,1,8,5,6,4,2]=>[6,2,8,1,4,3,5,7]=>[1,2,2,3]
[4,8,3,7,1,6,2,5]=>[1,3,7,8,5,6,4,2]=>[8,6,2,1,4,3,5,7]=>[1,1,1,2,3]
[3,8,4,7,1,6,2,5]=>[3,7,8,1,5,6,4,2]=>[6,2,1,8,4,3,5,7]=>[1,1,2,1,3]
[1,6,2,8,4,7,3,5]=>[5,7,2,8,6,1,3,4]=>[4,2,7,1,3,8,6,5]=>[1,2,3,1,1]
[2,6,1,8,4,7,3,5]=>[5,7,2,8,1,6,3,4]=>[4,2,7,1,8,3,6,5]=>[1,2,2,2,1]
[3,7,2,6,1,8,4,5]=>[7,8,1,3,5,4,2,6]=>[2,1,8,6,4,5,7,3]=>[1,2,1,3,1]
[3,7,1,6,2,8,4,5]=>[7,8,1,5,3,4,2,6]=>[2,1,8,4,6,5,7,3]=>[1,2,2,2,1]
[4,8,1,6,2,7,3,5]=>[1,7,8,5,3,4,6,2]=>[8,2,1,4,6,5,3,7]=>[1,1,3,1,2]
[7,8,1,5,2,6,3,4]=>[7,8,5,3,4,1,6,2]=>[2,1,4,6,5,8,3,7]=>[1,3,2,2]
[7,8,2,5,1,6,3,4]=>[7,8,3,5,4,1,6,2]=>[2,1,6,4,5,8,3,7]=>[1,2,3,2]
[6,8,2,5,1,7,3,4]=>[7,8,3,1,5,4,6,2]=>[2,1,6,8,4,5,3,7]=>[1,3,2,2]
[5,8,2,6,1,7,3,4]=>[7,1,8,3,5,4,6,2]=>[2,8,1,6,4,5,3,7]=>[2,2,2,2]
[4,8,2,6,1,7,3,5]=>[1,7,8,3,5,4,6,2]=>[8,2,1,6,4,5,3,7]=>[1,1,2,2,2]
[1,7,3,6,2,8,4,5]=>[7,8,3,5,4,1,2,6]=>[2,1,6,4,5,8,7,3]=>[1,2,3,1,1]
[2,7,3,6,1,8,4,5]=>[7,8,3,5,1,4,2,6]=>[2,1,6,4,8,5,7,3]=>[1,2,2,2,1]
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,9,7]=>[7,9,1,2,3,4,5,6,8]=>[3,1,9,8,7,6,5,4,2]=>[1,2,1,1,1,1,1,1]
[1,3,4,5,6,7,8,9,2]=>[2,3,4,5,6,7,9,1,8]=>[8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,2,1]
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,9,8,7]=>[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1]
[1,2,3,4,5,6,7,9,10,8]=>[8,10,1,2,3,4,5,6,7,9]=>[3,1,10,9,8,7,6,5,4,2]=>[1,2,1,1,1,1,1,1,1]
[1,2,3,4,6,7,8,9,10,5]=>[5,6,7,8,10,1,2,3,4,9]=>[6,5,4,3,1,10,9,8,7,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,4,5,6,7,8,9,10,3]=>[3,4,5,6,7,8,10,1,2,9]=>[8,7,6,5,4,3,1,10,9,2]=>[1,1,1,1,1,1,2,1,1]
[3,2,4,5,6,7,8,9,1]=>[2,1,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,2]
[1,3,4,5,6,7,8,9,10,2]=>[2,3,4,5,6,7,8,10,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>[1,1,1,1,1,1,1,2,1]
[6,7,4,8,3,5,1,2]=>[3,1,7,5,2,8,6,4]=>[6,8,2,4,7,1,3,5]=>[2,3,3]
[6,7,4,5,2,8,1,3]=>[5,3,1,7,4,2,8,6]=>[4,6,8,2,5,7,1,3]=>[3,3,2]
[5,7,4,6,2,3,1,8]=>[1,5,3,7,6,4,2,8]=>[8,4,6,2,3,5,7,1]=>[1,2,4,1]
[5,7,4,6,3,8,1,2]=>[1,3,7,5,4,2,8,6]=>[8,6,2,4,5,7,1,3]=>[1,1,4,2]
[5,7,4,8,3,6,1,2]=>[1,3,7,5,2,8,6,4]=>[8,6,2,4,7,1,3,5]=>[1,1,3,3]
[6,8,4,5,3,7,1,2]=>[3,1,7,5,4,8,6,2]=>[6,8,2,4,5,1,3,7]=>[2,3,3]
[5,8,4,6,3,7,1,2]=>[1,3,7,5,4,8,6,2]=>[8,6,2,4,5,1,3,7]=>[1,1,3,3]
[5,6,4,8,3,7,1,2]=>[1,3,2,7,5,8,6,4]=>[8,6,7,2,4,1,3,5]=>[1,2,2,3]
[5,6,3,7,2,4,1,8]=>[3,1,5,2,7,6,4,8]=>[6,8,4,7,2,3,5,1]=>[2,2,3,1]
[5,6,3,7,2,8,1,4]=>[3,1,5,2,7,4,8,6]=>[6,8,4,7,2,5,1,3]=>[2,2,2,2]
[5,6,3,8,2,7,1,4]=>[3,1,5,2,7,8,6,4]=>[6,8,4,7,2,1,3,5]=>[2,2,1,3]
[5,6,4,8,2,7,1,3]=>[1,5,3,2,7,8,6,4]=>[8,4,6,7,2,1,3,5]=>[1,3,1,3]
[5,8,4,6,2,7,1,3]=>[1,5,3,7,4,8,6,2]=>[8,4,6,2,5,1,3,7]=>[1,2,2,3]
[6,8,4,5,2,7,1,3]=>[5,3,1,7,4,8,6,2]=>[4,6,8,2,5,1,3,7]=>[3,2,3]
[7,8,4,5,2,6,1,3]=>[5,3,7,4,1,8,6,2]=>[4,6,2,5,8,1,3,7]=>[2,3,3]
[6,8,4,5,2,3,1,7]=>[5,3,1,7,6,4,8,2]=>[4,6,8,2,3,5,1,7]=>[3,3,2]
[5,8,4,6,2,3,1,7]=>[1,5,3,7,6,4,8,2]=>[8,4,6,2,3,5,1,7]=>[1,2,3,2]
[5,6,4,8,2,3,1,7]=>[1,5,3,2,7,6,8,4]=>[8,4,6,7,2,3,1,5]=>[1,3,2,2]
[5,6,3,8,2,4,1,7]=>[3,1,5,2,7,6,8,4]=>[6,8,4,7,2,3,1,5]=>[2,2,2,2]
[5,6,3,4,2,8,1,7]=>[3,1,5,4,2,7,8,6]=>[6,8,4,5,7,2,1,3]=>[2,3,1,2]
[4,6,3,5,2,7,1,8]=>[1,3,5,4,2,7,6,8]=>[8,6,4,5,7,2,3,1]=>[1,1,3,2,1]
[4,6,3,5,2,8,1,7]=>[1,3,5,4,2,7,8,6]=>[8,6,4,5,7,2,1,3]=>[1,1,3,1,2]
[4,6,3,8,2,5,1,7]=>[1,3,5,2,7,6,8,4]=>[8,6,4,7,2,3,1,5]=>[1,1,2,2,2]
[4,8,3,6,2,5,1,7]=>[1,3,5,7,6,4,8,2]=>[8,6,4,2,3,5,1,7]=>[1,1,1,3,2]
[5,8,3,6,2,4,1,7]=>[3,1,5,7,6,4,8,2]=>[6,8,4,2,3,5,1,7]=>[2,1,3,2]
[6,8,3,5,2,4,1,7]=>[3,5,1,7,6,4,8,2]=>[6,4,8,2,3,5,1,7]=>[1,2,3,2]
[7,8,3,5,2,4,1,6]=>[3,5,7,6,4,1,8,2]=>[6,4,2,3,5,8,1,7]=>[1,1,4,2]
[7,8,3,5,2,6,1,4]=>[3,5,7,4,1,8,6,2]=>[6,4,2,5,8,1,3,7]=>[1,1,3,3]
[5,8,3,6,2,7,1,4]=>[3,1,5,7,4,8,6,2]=>[6,8,4,2,5,1,3,7]=>[2,1,2,3]
[4,8,3,6,2,7,1,5]=>[1,3,5,7,4,8,6,2]=>[8,6,4,2,5,1,3,7]=>[1,1,1,2,3]
[4,6,3,8,2,7,1,5]=>[1,3,5,2,7,8,6,4]=>[8,6,4,7,2,1,3,5]=>[1,1,2,1,3]
[4,6,3,7,2,8,1,5]=>[1,3,5,2,7,4,8,6]=>[8,6,4,7,2,5,1,3]=>[1,1,2,2,2]
[4,7,3,6,2,5,1,8]=>[1,3,5,7,6,4,2,8]=>[8,6,4,2,3,5,7,1]=>[1,1,1,4,1]
[4,7,3,6,2,8,1,5]=>[1,3,5,7,4,2,8,6]=>[8,6,4,2,5,7,1,3]=>[1,1,1,3,2]
[4,7,3,8,2,6,1,5]=>[1,3,5,7,2,8,6,4]=>[8,6,4,2,7,1,3,5]=>[1,1,1,2,3]
[5,7,4,8,2,6,1,3]=>[1,5,3,7,2,8,6,4]=>[8,4,6,2,7,1,3,5]=>[1,2,2,3]
[5,7,3,6,2,8,1,4]=>[3,1,5,7,4,2,8,6]=>[6,8,4,2,5,7,1,3]=>[2,1,3,2]
[5,7,3,6,2,4,1,8]=>[3,1,5,7,6,4,2,8]=>[6,8,4,2,3,5,7,1]=>[2,1,4,1]
[6,7,3,5,2,4,1,8]=>[3,5,1,7,6,4,2,8]=>[6,4,8,2,3,5,7,1]=>[1,2,4,1]
[6,7,3,5,2,8,1,4]=>[3,5,1,7,4,2,8,6]=>[6,4,8,2,5,7,1,3]=>[1,2,3,2]
[6,7,4,8,2,5,1,3]=>[5,3,1,7,2,8,6,4]=>[4,6,8,2,7,1,3,5]=>[3,2,3]
[6,7,5,8,2,4,1,3]=>[5,1,7,3,2,8,6,4]=>[4,8,2,6,7,1,3,5]=>[2,3,3]
[6,8,5,7,2,3,1,4]=>[5,1,7,6,3,8,4,2]=>[4,8,2,3,6,1,5,7]=>[2,3,3]
[6,7,4,8,2,3,1,5]=>[5,3,1,7,6,2,8,4]=>[4,6,8,2,3,7,1,5]=>[3,3,2]
[6,7,3,8,2,4,1,5]=>[3,5,1,7,6,2,8,4]=>[6,4,8,2,3,7,1,5]=>[1,2,3,2]
[6,7,3,4,2,8,1,5]=>[3,5,4,1,7,2,8,6]=>[6,4,5,8,2,7,1,3]=>[1,3,2,2]
[5,7,3,4,2,6,1,8]=>[3,1,5,4,7,6,2,8]=>[6,8,4,5,2,3,7,1]=>[2,2,3,1]
[5,7,3,4,2,8,1,6]=>[3,1,5,4,7,2,8,6]=>[6,8,4,5,2,7,1,3]=>[2,2,2,2]
[5,7,4,8,2,3,1,6]=>[1,5,3,7,6,2,8,4]=>[8,4,6,2,3,7,1,5]=>[1,2,3,2]
[5,8,4,7,2,3,1,6]=>[1,5,3,7,6,8,4,2]=>[8,4,6,2,3,1,5,7]=>[1,2,2,3]
[6,8,4,7,2,3,1,5]=>[5,3,1,7,6,8,4,2]=>[4,6,8,2,3,1,5,7]=>[3,2,3]
[7,8,4,6,2,3,1,5]=>[5,3,7,6,1,8,4,2]=>[4,6,2,3,8,1,5,7]=>[2,3,3]
[7,8,3,6,2,4,1,5]=>[3,5,7,6,1,8,4,2]=>[6,4,2,3,8,1,5,7]=>[1,1,3,3]
[6,8,3,7,2,4,1,5]=>[3,5,1,7,6,8,4,2]=>[6,4,8,2,3,1,5,7]=>[1,2,2,3]
[5,8,3,7,2,4,1,6]=>[3,1,5,7,6,8,4,2]=>[6,8,4,2,3,1,5,7]=>[2,1,2,3]
[4,8,3,7,2,5,1,6]=>[1,3,5,7,6,8,4,2]=>[8,6,4,2,3,1,5,7]=>[1,1,1,2,3]
[4,7,3,8,2,5,1,6]=>[1,3,5,7,6,2,8,4]=>[8,6,4,2,3,7,1,5]=>[1,1,1,3,2]
[4,7,3,5,2,8,1,6]=>[1,3,5,4,7,2,8,6]=>[8,6,4,5,2,7,1,3]=>[1,1,2,2,2]
[4,7,3,5,2,6,1,8]=>[1,3,5,4,7,6,2,8]=>[8,6,4,5,2,3,7,1]=>[1,1,2,3,1]
[4,5,3,7,2,6,1,8]=>[1,3,2,5,7,6,4,8]=>[8,6,7,4,2,3,5,1]=>[1,2,1,3,1]
[4,5,3,7,2,8,1,6]=>[1,3,2,5,7,4,8,6]=>[8,6,7,4,2,5,1,3]=>[1,2,1,2,2]
[4,5,3,8,2,7,1,6]=>[1,3,2,5,7,8,6,4]=>[8,6,7,4,2,1,3,5]=>[1,2,1,1,3]
[4,8,3,5,2,7,1,6]=>[1,3,5,4,7,8,6,2]=>[8,6,4,5,2,1,3,7]=>[1,1,2,1,3]
[5,8,3,4,2,7,1,6]=>[3,1,5,4,7,8,6,2]=>[6,8,4,5,2,1,3,7]=>[2,2,1,3]
[6,8,3,4,2,7,1,5]=>[3,5,4,1,7,8,6,2]=>[6,4,5,8,2,1,3,7]=>[1,3,1,3]
[7,8,3,4,2,6,1,5]=>[3,5,4,7,1,8,6,2]=>[6,4,5,2,8,1,3,7]=>[1,2,2,3]
[6,8,3,4,2,5,1,7]=>[3,5,4,1,7,6,8,2]=>[6,4,5,8,2,3,1,7]=>[1,3,2,2]
[5,8,3,4,2,6,1,7]=>[3,1,5,4,7,6,8,2]=>[6,8,4,5,2,3,1,7]=>[2,2,2,2]
[4,8,3,5,2,6,1,7]=>[1,3,5,4,7,6,8,2]=>[8,6,4,5,2,3,1,7]=>[1,1,2,2,2]
[4,5,3,8,2,6,1,7]=>[1,3,2,5,7,6,8,4]=>[8,6,7,4,2,3,1,5]=>[1,2,1,2,2]
[4,5,3,6,2,8,1,7]=>[1,3,2,5,4,7,8,6]=>[8,6,7,4,5,2,1,3]=>[1,2,2,1,2]
[4,7,5,2,1,8,3,6]=>[1,4,7,3,8,5,2,6]=>[8,5,2,6,1,4,7,3]=>[1,1,2,3,1]
[4,8,5,2,1,7,6,3]=>[8,1,4,3,7,5,6,2]=>[1,8,5,6,2,4,3,7]=>[2,2,2,2]
[4,6,5,2,1,3,8,7]=>[1,4,8,5,3,2,6,7]=>[8,5,1,4,6,7,3,2]=>[1,1,4,1,1]
[6,4,5,3,1,2,8,7]=>[2,8,5,4,3,1,6,7]=>[7,1,4,5,6,8,3,2]=>[1,5,1,1]
[4,6,8,1,7,3,2,5]=>[7,1,6,2,8,4,5,3]=>[2,8,3,7,1,5,4,6]=>[2,2,2,2]
[4,7,8,1,6,3,5,2]=>[6,8,1,7,4,2,5,3]=>[3,1,8,2,5,7,4,6]=>[1,2,3,2]
[7,4,8,1,6,5,3,2]=>[8,2,7,6,4,1,5,3]=>[1,7,2,3,5,8,4,6]=>[2,4,2]
[5,4,8,1,3,7,6,2]=>[2,1,8,5,7,4,6,3]=>[7,8,1,4,2,5,3,6]=>[2,2,2,2]
[8,4,5,3,1,7,6,2]=>[2,4,3,8,7,5,6,1]=>[7,5,6,1,2,4,3,8]=>[1,2,3,2]
[5,4,7,1,3,8,2,6]=>[5,2,1,7,8,4,3,6]=>[4,7,8,2,1,5,6,3]=>[3,1,3,1]
[6,4,8,1,7,5,2,3]=>[2,7,1,8,6,4,5,3]=>[7,2,8,1,3,5,4,6]=>[1,2,3,2]
[8,5,7,6,4,2,1,3]=>[2,7,6,8,5,4,3,1]=>[7,2,3,1,4,5,6,8]=>[1,2,5]
[8,4,6,3,7,2,1,5]=>[2,4,7,6,3,8,5,1]=>[7,5,2,3,6,1,4,8]=>[1,1,3,3]
[6,3,2,8,7,4,1,5]=>[7,2,6,1,8,3,5,4]=>[2,7,3,8,1,6,4,5]=>[2,2,2,2]
[2,1,6,8,7,4,3,5]=>[3,7,6,8,1,5,2,4]=>[6,2,3,1,8,4,7,5]=>[1,2,2,2,1]
[7,3,2,8,6,4,5,1]=>[6,8,2,7,3,1,5,4]=>[3,1,7,2,6,8,4,5]=>[1,2,3,2]
[7,6,8,5,2,4,3,1]=>[8,5,2,1,7,6,4,3]=>[1,4,7,8,2,3,5,6]=>[4,4]
[5,7,8,6,2,3,1,4]=>[1,5,7,6,2,8,4,3]=>[8,4,2,3,7,1,5,6]=>[1,1,3,3]
[5,8,7,6,3,2,1,4]=>[7,1,6,5,8,4,3,2]=>[2,8,3,4,1,5,6,7]=>[2,2,4]
[6,8,7,5,3,2,4,1]=>[1,6,5,8,7,4,3,2]=>[8,3,4,1,2,5,6,7]=>[1,2,5]
[5,8,4,2,3,7,6,1]=>[1,8,4,3,5,7,6,2]=>[8,1,5,6,4,2,3,7]=>[1,3,1,3]
[7,8,4,2,6,5,3,1]=>[3,8,7,4,1,6,5,2]=>[6,1,2,5,8,3,4,7]=>[1,4,3]
[4,8,7,2,6,3,5,1]=>[6,8,1,4,7,5,3,2]=>[3,1,8,5,2,4,6,7]=>[1,2,1,4]
[4,8,6,2,7,3,1,5]=>[7,1,4,6,3,8,5,2]=>[2,8,5,3,6,1,4,7]=>[2,1,2,3]
[3,6,1,8,7,4,2,5]=>[7,6,1,2,8,5,3,4]=>[2,3,8,7,1,4,6,5]=>[3,1,3,1]
[3,7,1,8,6,4,5,2]=>[6,8,7,1,5,3,2,4]=>[3,1,2,8,4,6,7,5]=>[1,3,3,1]
[3,8,1,6,7,5,2,4]=>[7,4,8,1,6,3,5,2]=>[2,5,1,8,3,6,4,7]=>[2,2,2,2]
[3,7,1,6,8,2,5,4]=>[8,6,1,4,7,3,2,5]=>[1,3,8,5,2,6,7,4]=>[3,1,3,1]
[4,7,6,2,8,1,3,5]=>[1,4,6,7,3,2,8,5]=>[8,5,3,2,6,7,1,4]=>[1,1,1,3,2]
[6,7,4,2,8,1,5,3]=>[8,4,3,1,6,2,7,5]=>[1,5,6,8,3,7,2,4]=>[4,2,2]
[6,8,4,2,7,5,1,3]=>[7,3,1,8,4,6,5,2]=>[2,6,8,1,5,3,4,7]=>[3,2,3]
[2,1,8,6,7,5,3,4]=>[7,4,8,6,1,5,2,3]=>[2,5,1,3,8,4,7,6]=>[2,3,2,1]
[8,6,4,3,7,5,1,2]=>[4,3,7,2,8,6,5,1]=>[5,6,2,7,1,3,4,8]=>[2,2,4]
[5,8,6,7,3,1,2,4]=>[1,6,7,5,3,8,4,2]=>[8,3,2,4,6,1,5,7]=>[1,1,3,3]
[6,7,5,8,1,3,4,2]=>[6,1,8,5,3,2,7,4]=>[3,8,1,4,6,7,2,5]=>[2,4,2]
[7,6,5,8,1,4,3,2]=>[8,7,5,3,2,1,6,4]=>[1,2,4,6,7,8,3,5]=>[6,2]
[8,6,5,7,4,1,3,2]=>[8,6,3,2,7,5,4,1]=>[1,3,6,7,2,4,5,8]=>[4,4]
[7,6,4,3,8,1,5,2]=>[4,3,8,6,2,1,7,5]=>[5,6,1,3,7,8,2,4]=>[2,4,2]
[7,3,2,6,8,1,5,4]=>[8,2,6,3,4,1,7,5]=>[1,7,3,6,5,8,2,4]=>[2,2,2,2]
[2,1,7,6,8,3,5,4]=>[8,6,4,1,3,7,2,5]=>[1,3,5,8,6,2,7,4]=>[4,1,2,1]
[7,5,6,8,1,4,2,3]=>[7,2,8,5,3,1,6,4]=>[2,7,1,4,6,8,3,5]=>[2,4,2]
[6,5,7,8,1,2,4,3]=>[8,5,2,1,6,3,7,4]=>[1,4,7,8,3,6,2,5]=>[4,2,2]
[8,1,3,7,4,6,5,2]=>[8,5,7,3,6,2,4,1]=>[1,4,2,6,3,7,5,8]=>[2,2,2,2]
[5,2,8,7,4,6,1,3]=>[1,7,5,8,6,2,4,3]=>[8,2,4,1,3,7,5,6]=>[1,2,3,2]
[1,6,2,5,4,7,3,8]=>[5,4,7,3,1,2,6,8]=>[4,5,2,6,8,7,3,1]=>[2,3,1,1,1]
[6,2,7,5,4,8,3,1]=>[5,4,3,1,8,2,7,6]=>[4,5,6,8,1,7,2,3]=>[4,2,2]
[8,1,3,5,4,7,6,2]=>[4,8,3,5,7,2,6,1]=>[5,1,6,4,2,7,3,8]=>[1,2,1,2,2]
[6,1,5,4,3,8,7,2]=>[4,3,8,5,1,7,2,6]=>[5,6,1,4,8,2,7,3]=>[2,3,2,1]
[6,1,8,3,4,5,7,2]=>[4,5,6,1,8,7,2,3]=>[5,4,3,8,1,2,7,6]=>[1,1,2,3,1]
[7,1,4,3,5,6,8,2]=>[4,3,5,6,8,2,1,7]=>[5,6,4,3,1,7,8,2]=>[2,1,1,3,1]
[8,1,3,4,5,6,7,2]=>[3,4,5,6,8,2,7,1]=>[6,5,4,3,1,7,2,8]=>[1,1,1,1,2,2]
[1,7,2,4,5,6,3,8]=>[4,5,7,3,6,1,2,8]=>[5,4,2,6,3,8,7,1]=>[1,1,2,2,1,1]
[6,3,2,7,5,1,8,4]=>[8,2,6,3,1,5,4,7]=>[1,7,3,6,8,4,5,2]=>[2,3,2,1]
[8,4,7,2,5,6,1,3]=>[2,7,4,5,8,6,3,1]=>[7,2,5,4,1,3,6,8]=>[1,2,1,4]
[6,5,8,2,4,7,3,1]=>[5,2,1,8,4,7,6,3]=>[4,7,8,1,5,2,3,6]=>[3,2,3]
[6,5,2,8,4,1,3,7]=>[6,7,3,2,1,5,8,4]=>[3,2,6,7,8,4,1,5]=>[1,4,1,2]
[5,6,2,1,4,8,3,7]=>[3,5,1,7,2,8,4,6]=>[6,4,8,2,7,1,5,3]=>[1,2,2,2,1]
[3,6,1,8,5,2,4,7]=>[6,7,1,5,2,8,3,4]=>[3,2,8,4,7,1,6,5]=>[1,2,2,2,1]
[1,2,6,3,5,4,7,8]=>[6,4,5,1,2,3,7,8]=>[3,5,4,8,7,6,2,1]=>[2,2,1,1,1,1]
[3,4,1,2,8,6,5,7]=>[1,2,7,6,8,3,4,5]=>[8,7,2,3,1,6,5,4]=>[1,1,2,2,1,1]
[4,3,1,2,6,8,5,7]=>[5,2,1,7,8,3,4,6]=>[4,7,8,2,1,6,5,3]=>[3,1,2,1,1]
[6,3,8,5,2,1,4,7]=>[6,2,5,1,7,4,8,3]=>[3,7,4,8,2,5,1,6]=>[2,2,2,2]
[8,3,1,5,2,4,7,6]=>[2,8,5,3,4,6,7,1]=>[7,1,4,6,5,3,2,8]=>[1,3,1,1,2]
[3,8,6,7,2,1,5,4]=>[5,8,6,1,3,7,4,2]=>[4,1,3,8,6,2,5,7]=>[1,3,1,3]
[8,5,6,4,2,1,7,3]=>[5,2,8,6,4,3,7,1]=>[4,7,1,3,5,6,2,8]=>[2,4,2]
[7,2,5,8,3,1,6,4]=>[5,3,8,2,6,1,7,4]=>[4,6,1,7,3,8,2,5]=>[2,2,2,2]
[1,7,5,6,3,2,4,8]=>[6,5,3,7,4,1,2,8]=>[3,4,6,2,5,8,7,1]=>[3,3,1,1]
[6,1,2,3,8,5,7,4]=>[6,8,7,2,3,1,4,5]=>[3,1,2,7,6,8,5,4]=>[1,3,2,1,1]
[7,1,2,3,6,5,8,4]=>[6,5,8,2,3,4,1,7]=>[3,4,1,7,6,5,8,2]=>[2,2,1,2,1]
[7,2,1,3,8,6,4,5]=>[7,8,2,6,3,4,1,5]=>[2,1,7,3,6,5,8,4]=>[1,2,2,2,1]
[1,5,7,3,2,4,6,8]=>[5,4,2,6,7,1,3,8]=>[4,5,7,3,2,8,6,1]=>[3,1,2,1,1]
[5,2,7,3,1,8,4,6]=>[4,7,1,8,2,5,3,6]=>[5,2,8,1,7,4,6,3]=>[1,2,2,2,1]
[5,8,2,4,1,3,7,6]=>[8,3,1,5,4,6,7,2]=>[1,6,8,4,5,3,2,7]=>[3,2,1,2]
[8,7,2,6,3,4,1,5]=>[5,7,3,6,8,4,2,1]=>[4,2,6,3,1,5,7,8]=>[1,2,1,4]
[4,8,1,6,3,2,7,5]=>[1,5,8,6,3,4,7,2]=>[8,4,1,3,6,5,2,7]=>[1,1,3,1,2]
[3,1,8,6,4,2,7,5]=>[5,8,1,6,4,7,2,3]=>[4,1,8,3,5,2,7,6]=>[1,2,2,2,1]
[8,1,6,7,4,3,2,5]=>[7,6,5,3,8,2,4,1]=>[2,3,4,6,1,7,5,8]=>[4,2,2]
[3,5,8,7,2,4,1,6]=>[2,5,7,1,6,8,4,3]=>[7,4,2,8,3,1,5,6]=>[1,1,2,1,3]
[4,2,1,3,7,8,5,6]=>[7,2,1,5,8,3,4,6]=>[2,7,8,4,1,6,5,3]=>[3,1,2,1,1]
[2,4,1,3,8,7,5,6]=>[2,7,8,1,6,3,4,5]=>[7,2,1,8,3,6,5,4]=>[1,1,2,2,1,1]
[2,5,8,3,1,7,4,6]=>[4,2,7,8,1,5,6,3]=>[5,7,2,1,8,4,3,6]=>[2,1,2,1,2]
[8,6,1,3,7,2,4,5]=>[4,6,7,8,3,2,5,1]=>[5,3,2,1,6,7,4,8]=>[1,1,1,3,2]
[2,8,1,3,6,4,7,5]=>[8,6,1,3,4,5,7,2]=>[1,3,8,6,5,4,2,7]=>[3,1,1,1,2]
[6,8,2,3,4,1,5,7]=>[3,4,6,5,1,7,8,2]=>[6,5,3,4,8,2,1,7]=>[1,1,3,1,2]
[5,1,8,3,2,4,6,7]=>[5,4,6,1,7,8,2,3]=>[4,5,3,8,2,1,7,6]=>[2,2,1,2,1]
[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[9]
[8,9,7,6,5,4,3,2,1]=>[1,9,8,7,6,5,4,3,2]=>[9,1,2,3,4,5,6,7,8]=>[1,8]
[8,7,9,6,5,4,3,2,1]=>[2,1,9,8,7,6,5,4,3]=>[8,9,1,2,3,4,5,6,7]=>[2,7]
[8,7,6,9,5,4,3,2,1]=>[3,2,1,9,8,7,6,5,4]=>[7,8,9,1,2,3,4,5,6]=>[3,6]
[8,7,6,5,9,4,3,2,1]=>[4,3,2,1,9,8,7,6,5]=>[6,7,8,9,1,2,3,4,5]=>[4,5]
[8,7,6,5,4,9,3,2,1]=>[5,4,3,2,1,9,8,7,6]=>[5,6,7,8,9,1,2,3,4]=>[5,4]
[8,7,6,5,4,3,9,2,1]=>[6,5,4,3,2,1,9,8,7]=>[4,5,6,7,8,9,1,2,3]=>[6,3]
[8,7,6,5,4,3,2,9,1]=>[7,6,5,4,3,2,1,9,8]=>[3,4,5,6,7,8,9,1,2]=>[7,2]
[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>[8,1]
[9,10,8,7,6,5,4,3,2,1]=>[1,10,9,8,7,6,5,4,3,2]=>[10,1,2,3,4,5,6,7,8,9]=>[1,9]
[7,8,9,6,5,4,3,2,1]=>[1,2,9,8,7,6,5,4,3]=>[9,8,1,2,3,4,5,6,7]=>[1,1,7]
[9,8,10,7,6,5,4,3,2,1]=>[2,1,10,9,8,7,6,5,4,3]=>[9,10,1,2,3,4,5,6,7,8]=>[2,8]
[8,6,7,9,5,4,3,2,1]=>[2,3,1,9,8,7,6,5,4]=>[8,7,9,1,2,3,4,5,6]=>[1,2,6]
[9,8,7,10,6,5,4,3,2,1]=>[3,2,1,10,9,8,7,6,5,4]=>[8,9,10,1,2,3,4,5,6,7]=>[3,7]
[8,7,5,6,9,4,3,2,1]=>[3,4,2,1,9,8,7,6,5]=>[7,6,8,9,1,2,3,4,5]=>[1,3,5]
[9,8,7,6,10,5,4,3,2,1]=>[4,3,2,1,10,9,8,7,6,5]=>[7,8,9,10,1,2,3,4,5,6]=>[4,6]
[9,8,7,6,5,10,4,3,2,1]=>[5,4,3,2,1,10,9,8,7,6]=>[6,7,8,9,10,1,2,3,4,5]=>[5,5]
[9,8,7,6,5,4,10,3,2,1]=>[6,5,4,3,2,1,10,9,8,7]=>[5,6,7,8,9,10,1,2,3,4]=>[6,4]
[9,8,7,6,5,4,3,10,2,1]=>[7,6,5,4,3,2,1,10,9,8]=>[4,5,6,7,8,9,10,1,2,3]=>[7,3]
[8,7,6,5,4,3,1,2,9]=>[7,8,6,5,4,3,2,1,9]=>[3,2,4,5,6,7,8,9,1]=>[1,7,1]
[9,8,7,6,5,4,3,2,10,1]=>[8,7,6,5,4,3,2,1,10,9]=>[3,4,5,6,7,8,9,10,1,2]=>[8,2]
[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>[9,1]
[1,4,2,7,8,6,3,5]=>[7,2,4,8,6,1,3,5]=>[2,7,5,1,3,8,6,4]=>[2,1,3,1,1]
[1,6,2,4,8,5,3,7]=>[7,4,6,2,8,1,3,5]=>[2,5,3,7,1,8,6,4]=>[2,2,2,1,1]
[1,6,2,4,7,5,3,8]=>[7,4,6,3,1,2,5,8]=>[2,5,3,6,8,7,4,1]=>[2,3,1,1,1]
[1,7,3,8,5,2,4,6]=>[6,7,3,5,2,8,1,4]=>[3,2,6,4,7,1,8,5]=>[1,2,2,2,1]
[1,7,3,2,8,6,4,5]=>[7,8,3,6,4,1,2,5]=>[2,1,6,3,5,8,7,4]=>[1,2,3,1,1]
[7,2,3,1,8,5,6,4]=>[6,8,2,3,7,4,1,5]=>[3,1,7,6,2,5,8,4]=>[1,2,1,3,1]
[8,2,5,1,7,3,4,6]=>[6,7,2,3,8,4,5,1]=>[3,2,7,6,1,5,4,8]=>[1,2,1,2,2]
[6,2,8,3,5,1,7,4]=>[8,4,6,2,1,5,7,3]=>[1,5,3,7,8,4,2,6]=>[2,3,1,2]
[6,2,4,8,5,7,1,3]=>[7,3,5,1,8,2,6,4]=>[2,6,4,8,1,7,3,5]=>[2,2,2,2]
[1,3,6,4,8,5,7,2]=>[6,3,8,2,4,7,1,5]=>[3,6,1,7,5,2,8,4]=>[2,2,1,2,1]
[1,3,6,4,7,5,8,2]=>[6,4,2,3,5,8,1,7]=>[3,5,7,6,4,1,8,2]=>[3,1,1,2,1]
[6,2,4,7,5,8,1,3]=>[7,3,5,2,1,4,8,6]=>[2,6,4,7,8,5,1,3]=>[2,3,1,2]
[6,2,1,3,7,8,4,5]=>[7,2,5,8,3,1,4,6]=>[2,7,4,1,6,8,5,3]=>[2,1,3,1,1]
[7,8,2,1,4,3,5,6]=>[3,6,4,5,7,1,8,2]=>[6,3,5,4,2,8,1,7]=>[1,2,1,2,2]
[7,6,4,2,3,1,8,5]=>[4,5,3,8,6,2,1,7]=>[5,4,6,1,3,7,8,2]=>[1,2,4,1]
[5,7,2,3,1,6,8,4]=>[3,4,1,6,8,5,2,7]=>[6,5,8,3,1,4,7,2]=>[1,2,1,3,1]
[7,5,4,2,6,8,1,3]=>[7,4,3,2,5,1,8,6]=>[2,5,6,7,4,8,1,3]=>[4,2,2]
[1,7,5,3,4,6,8,2]=>[4,5,3,6,2,8,1,7]=>[5,4,6,3,7,1,8,2]=>[1,2,2,2,1]
[8,2,5,4,6,7,1,3]=>[4,3,7,2,5,8,6,1]=>[5,6,2,7,4,1,3,8]=>[2,2,1,3]
[5,2,6,3,1,8,7,4]=>[8,4,2,1,3,7,5,6]=>[1,5,7,8,6,2,4,3]=>[4,1,2,1]
[8,2,6,4,3,1,7,5]=>[5,4,8,2,6,3,7,1]=>[4,5,1,7,3,6,2,8]=>[2,2,2,2]
[8,2,7,4,1,3,5,6]=>[5,6,2,4,7,8,3,1]=>[4,3,7,5,2,1,6,8]=>[1,2,1,1,3]
[1,2,8,4,3,5,6,7]=>[5,4,6,7,8,1,2,3]=>[4,5,3,2,1,8,7,6]=>[2,1,1,2,1,1]
[1,7,4,2,3,5,6,8]=>[4,5,3,6,7,1,2,8]=>[5,4,6,3,2,8,7,1]=>[1,2,1,2,1,1]
[6,8,4,1,3,2,5,7]=>[6,4,5,3,1,7,8,2]=>[3,5,4,6,8,2,1,7]=>[2,3,1,2]
[1,8,7,4,3,2,5,6]=>[6,5,4,7,8,3,1,2]=>[3,4,5,2,1,6,8,7]=>[3,1,3,1]
[1,6,3,8,2,4,7,5]=>[8,3,5,2,6,7,1,4]=>[1,6,4,7,3,2,8,5]=>[2,2,1,2,1]
[5,3,8,1,2,7,4,6]=>[2,7,1,8,4,5,6,3]=>[7,2,8,1,5,4,3,6]=>[1,2,2,1,2]
[5,1,8,3,2,6,4,7]=>[4,7,5,1,6,8,2,3]=>[5,2,4,8,3,1,7,6]=>[1,3,1,2,1]
[5,7,3,1,2,6,4,8]=>[7,4,3,1,5,6,2,8]=>[2,5,6,8,4,3,7,1]=>[4,1,2,1]
[1,7,5,4,2,6,3,8]=>[7,5,4,3,6,1,2,8]=>[2,4,5,6,3,8,7,1]=>[4,2,1,1]
[1,5,8,2,4,6,3,7]=>[5,2,7,4,6,8,1,3]=>[4,7,2,5,3,1,8,6]=>[2,2,1,2,1]
[1,5,8,4,2,7,3,6]=>[2,7,4,8,5,6,1,3]=>[7,2,5,1,4,3,8,6]=>[1,2,2,2,1]
[1,4,6,2,8,3,7,5]=>[8,2,6,3,7,1,4,5]=>[1,7,3,6,2,8,5,4]=>[2,2,2,1,1]
[5,3,6,1,2,8,4,7]=>[2,7,1,8,4,3,5,6]=>[7,2,8,1,5,6,4,3]=>[1,2,3,1,1]
[1,6,3,2,7,8,4,5]=>[7,3,5,2,8,1,4,6]=>[2,6,4,7,1,8,5,3]=>[2,2,2,1,1]
[1,7,4,5,3,8,6,2]=>[3,4,8,5,2,7,1,6]=>[6,5,1,4,7,2,8,3]=>[1,1,3,2,1]
[6,3,4,1,2,5,8,7]=>[2,8,4,3,5,1,6,7]=>[7,1,5,6,4,8,3,2]=>[1,3,2,1,1]
[1,8,3,2,4,5,6,7]=>[4,3,5,6,7,8,1,2]=>[5,6,4,3,2,1,8,7]=>[2,1,1,1,2,1]
[8,5,3,2,6,7,1,4]=>[3,7,4,2,5,8,6,1]=>[6,2,5,7,4,1,3,8]=>[1,3,1,3]
[4,5,2,6,8,1,7,3]=>[1,4,2,8,3,6,7,5]=>[8,5,7,1,6,3,2,4]=>[1,2,2,1,2]
[4,2,5,6,7,8,1,3]=>[3,1,4,7,2,5,8,6]=>[6,8,5,2,7,4,1,3]=>[2,1,2,1,2]
[5,2,3,6,7,1,8,4]=>[4,8,2,1,3,6,5,7]=>[5,1,7,8,6,3,4,2]=>[1,3,1,2,1]
[6,2,3,4,1,7,8,5]=>[2,3,4,6,1,8,5,7]=>[7,6,5,3,8,1,4,2]=>[1,1,1,2,2,1]
[7,2,3,1,4,5,8,6]=>[2,3,8,4,5,6,1,7]=>[7,6,1,5,4,3,8,2]=>[1,1,2,1,2,1]
[8,6,1,4,3,2,5,7]=>[6,5,3,4,7,2,8,1]=>[3,4,6,5,2,7,1,8]=>[3,1,2,2]
[3,7,5,1,8,2,4,6]=>[6,7,1,3,8,4,2,5]=>[3,2,8,6,1,5,7,4]=>[1,2,1,3,1]
[4,1,5,2,8,7,3,6]=>[3,1,7,8,6,2,4,5]=>[6,8,2,1,3,7,5,4]=>[2,1,3,1,1]
[8,1,2,4,6,5,3,7]=>[7,4,6,2,3,5,8,1]=>[2,5,3,7,6,4,1,8]=>[2,2,1,1,2]
[8,1,2,5,4,6,3,7]=>[5,4,7,2,3,6,8,1]=>[4,5,2,7,6,3,1,8]=>[2,2,1,1,2]
[8,2,6,5,1,3,4,7]=>[5,6,7,2,4,3,8,1]=>[4,3,2,7,5,6,1,8]=>[1,1,2,2,2]
[8,3,1,6,2,5,4,7]=>[2,7,5,6,3,4,8,1]=>[7,2,4,3,6,5,1,8]=>[1,2,2,1,2]
[8,1,2,6,4,5,3,7]=>[5,7,6,2,3,4,8,1]=>[4,2,3,7,6,5,1,8]=>[1,3,1,1,2]
[8,1,2,5,6,4,3,7]=>[4,7,6,2,3,5,8,1]=>[5,2,3,7,6,4,1,8]=>[1,3,1,1,2]
[8,1,2,6,5,4,3,7]=>[7,6,5,2,3,4,8,1]=>[2,3,4,7,6,5,1,8]=>[4,1,1,2]
[1,7,5,4,2,8,3,6]=>[7,4,3,8,5,1,2,6]=>[2,5,6,1,4,8,7,3]=>[3,3,1,1]
[5,1,4,8,2,7,3,6]=>[3,7,1,8,5,6,2,4]=>[6,2,8,1,4,3,7,5]=>[1,2,2,2,1]
[1,4,6,8,2,7,3,5]=>[7,2,3,8,5,6,1,4]=>[2,7,6,1,4,3,8,5]=>[2,1,2,2,1]
[1,4,7,6,2,8,3,5]=>[7,8,2,5,4,1,3,6]=>[2,1,7,4,5,8,6,3]=>[1,2,3,1,1]
[5,1,4,7,2,8,3,6]=>[3,7,1,8,5,2,4,6]=>[6,2,8,1,4,7,5,3]=>[1,2,3,1,1]
[1,7,4,5,2,8,3,6]=>[3,7,4,8,5,1,2,6]=>[6,2,5,1,4,8,7,3]=>[1,2,3,1,1]
[3,7,5,1,2,8,4,6]=>[7,8,1,4,3,5,2,6]=>[2,1,8,5,6,4,7,3]=>[1,2,2,2,1]
[5,7,2,8,1,3,4,6]=>[3,5,1,6,7,2,8,4]=>[6,4,8,3,2,7,1,5]=>[1,2,1,2,2]
[5,2,8,7,1,3,4,6]=>[5,6,1,7,8,2,4,3]=>[4,3,8,2,1,7,5,6]=>[1,2,1,2,2]
[4,1,5,8,2,7,3,6]=>[3,1,7,8,5,6,2,4]=>[6,8,2,1,4,3,7,5]=>[2,1,2,2,1]
[1,4,6,2,8,7,3,5]=>[7,2,3,8,6,1,4,5]=>[2,7,6,1,3,8,5,4]=>[2,1,3,1,1]
[3,1,2,6,4,8,7,5]=>[1,4,8,7,2,3,5,6]=>[8,5,1,2,7,6,4,3]=>[1,1,3,1,1,1]
[2,1,7,6,3,4,8,5]=>[8,5,6,1,4,2,3,7]=>[1,4,3,8,5,7,6,2]=>[2,2,2,1,1]
[3,1,2,7,4,6,8,5]=>[1,6,8,5,2,3,4,7]=>[8,3,1,4,7,6,5,2]=>[1,1,3,1,1,1]
[1,4,7,2,6,8,3,5]=>[7,2,5,8,4,1,3,6]=>[2,7,4,1,5,8,6,3]=>[2,1,3,1,1]
[5,1,4,2,7,8,3,6]=>[3,7,5,1,8,2,4,6]=>[6,2,4,8,1,7,5,3]=>[1,3,2,1,1]
[1,4,2,7,6,8,3,5]=>[7,2,5,4,8,1,3,6]=>[2,7,4,5,1,8,6,3]=>[2,2,2,1,1]
[1,4,2,6,8,7,3,5]=>[2,4,7,8,6,1,3,5]=>[7,5,2,1,3,8,6,4]=>[1,1,1,3,1,1]
[3,1,2,8,4,6,7,5]=>[1,6,8,5,7,2,3,4]=>[8,3,1,4,2,7,6,5]=>[1,1,2,2,1,1]
[3,1,2,7,6,4,8,5]=>[8,1,6,5,2,3,4,7]=>[1,8,3,4,7,6,5,2]=>[2,3,1,1,1]
[5,3,7,1,8,2,4,6]=>[2,6,1,7,8,4,3,5]=>[7,3,8,2,1,5,6,4]=>[1,2,1,3,1]
[1,7,4,3,2,5,8,6]=>[4,3,8,5,6,1,2,7]=>[5,6,1,4,3,8,7,2]=>[2,2,2,1,1]
[4,8,7,2,1,3,5,6]=>[1,5,4,6,7,8,3,2]=>[8,4,5,3,2,1,6,7]=>[1,2,1,1,3]
[1,8,7,3,4,2,5,6]=>[4,6,5,7,8,3,1,2]=>[5,3,4,2,1,6,8,7]=>[1,2,1,3,1]
[3,1,7,8,2,6,4,5]=>[7,8,1,5,3,6,2,4]=>[2,1,8,4,6,3,7,5]=>[1,2,2,2,1]
[1,4,2,7,8,3,6,5]=>[8,2,6,4,7,1,3,5]=>[1,7,3,5,2,8,6,4]=>[2,2,2,1,1]
[5,2,8,1,3,4,7,6]=>[8,2,4,1,5,6,7,3]=>[1,7,5,8,4,3,2,6]=>[2,2,1,1,2]
[1,4,2,6,8,3,7,5]=>[2,4,8,6,7,1,3,5]=>[7,5,1,3,2,8,6,4]=>[1,1,2,2,1,1]
[1,2,3,7,5,8,6,4]=>[8,5,4,7,1,2,3,6]=>[1,4,5,2,8,7,6,3]=>[3,2,1,1,1]
[1,4,2,7,3,8,6,5]=>[8,2,7,5,1,3,4,6]=>[1,7,2,4,8,6,5,3]=>[2,3,1,1,1]
[3,1,7,2,8,6,4,5]=>[7,8,1,6,4,2,3,5]=>[2,1,8,3,5,7,6,4]=>[1,2,3,1,1]
[1,2,3,8,7,5,6,4]=>[6,8,7,5,1,2,3,4]=>[3,1,2,4,8,7,6,5]=>[1,4,1,1,1]
[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,2]
[10,1,2,3,9,4,5,6,7,8]=>[6,7,8,9,10,2,3,4,5,1]=>[5,4,3,2,1,9,8,7,6,10]=>[1,1,1,1,2,1,1,2]
[10,1,2,9,3,4,5,6,7,8]=>[5,6,7,8,9,10,2,3,4,1]=>[6,5,4,3,2,1,9,8,7,10]=>[1,1,1,1,1,2,1,2]
[9,1,10,2,3,4,5,6,7,8]=>[4,5,6,7,8,9,10,2,1,3]=>[7,6,5,4,3,2,1,9,10,8]=>[1,1,1,1,1,1,3,1]
[10,9,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,10,2,1]=>[8,7,6,5,4,3,2,1,9,10]=>[1,1,1,1,1,1,1,3]
[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,2]
[11,10,1,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,11,2,1]=>[9,8,7,6,5,4,3,2,1,10,11]=>[1,1,1,1,1,1,1,1,3]
[4,7,8,5,6,2,1,3]=>[7,6,1,4,2,8,5,3]=>[2,3,8,5,7,1,4,6]=>[3,2,3]
[5,7,8,4,2,6,1,3]=>[1,5,7,4,2,8,6,3]=>[8,4,2,5,7,1,3,6]=>[1,1,3,3]
[6,7,8,4,2,5,1,3]=>[5,1,7,4,2,8,6,3]=>[4,8,2,5,7,1,3,6]=>[2,3,3]
[8,6,3,7,2,1,5,4]=>[3,5,8,6,2,7,4,1]=>[6,4,1,3,7,2,5,8]=>[1,1,3,3]
[7,6,3,8,2,1,5,4]=>[3,5,8,6,2,1,7,4]=>[6,4,1,3,7,8,2,5]=>[1,1,4,2]
[6,7,8,3,2,1,5,4]=>[5,4,1,8,6,2,7,3]=>[4,5,8,1,3,7,2,6]=>[3,3,2]
[2,7,8,4,3,5,6,1]=>[5,4,6,2,8,1,7,3]=>[4,5,3,7,1,8,2,6]=>[2,2,2,2]
[3,7,8,4,2,5,1,6]=>[5,4,7,1,6,2,8,3]=>[4,5,2,8,3,7,1,6]=>[2,2,2,2]
[4,7,8,3,2,1,5,6]=>[6,1,5,4,7,2,8,3]=>[3,8,4,5,2,7,1,6]=>[2,2,2,2]
[5,7,8,3,2,1,4,6]=>[1,6,5,4,7,2,8,3]=>[8,3,4,5,2,7,1,6]=>[1,3,2,2]
[7,6,3,8,2,1,4,5]=>[3,6,5,7,2,1,8,4]=>[6,3,4,2,7,8,1,5]=>[1,2,3,2]
[8,6,3,7,2,1,4,5]=>[3,6,5,7,2,8,4,1]=>[6,3,4,2,7,1,5,8]=>[1,2,2,3]
[5,6,3,8,2,1,4,7]=>[3,1,6,5,2,7,8,4]=>[6,8,3,4,7,2,1,5]=>[2,3,1,2]
[3,6,4,8,2,5,1,7]=>[3,5,1,2,7,6,8,4]=>[6,4,8,7,2,3,1,5]=>[1,2,1,2,2]
[2,6,4,8,3,5,7,1]=>[3,5,2,6,8,1,7,4]=>[6,4,7,3,1,8,2,5]=>[1,2,1,2,2]
[2,6,4,7,3,5,8,1]=>[3,5,2,6,1,4,8,7]=>[6,4,7,3,8,5,1,2]=>[1,2,2,1,2]
[3,6,4,7,2,5,1,8]=>[3,5,1,2,7,6,4,8]=>[6,4,8,7,2,3,5,1]=>[1,2,1,3,1]
[4,6,3,7,2,1,5,8]=>[1,3,6,5,2,7,4,8]=>[8,6,3,4,7,2,5,1]=>[1,1,3,2,1]
[5,6,3,7,2,1,4,8]=>[3,1,6,5,2,7,4,8]=>[6,8,3,4,7,2,5,1]=>[2,3,2,1]
[8,4,3,2,1,6,5,7]=>[4,3,2,7,5,6,8,1]=>[5,6,7,2,4,3,1,8]=>[3,2,1,2]
[6,4,3,2,1,7,5,8]=>[4,3,2,7,5,1,6,8]=>[5,6,7,2,4,8,3,1]=>[3,3,1,1]
[4,5,3,2,7,1,6,8]=>[1,4,3,2,6,7,5,8]=>[8,5,6,7,3,2,4,1]=>[1,3,1,2,1]
[3,5,4,2,8,6,1,7]=>[3,1,2,7,4,6,8,5]=>[6,8,7,2,5,3,1,4]=>[2,1,2,1,2]
[6,4,3,2,1,8,5,7]=>[4,3,2,7,1,8,5,6]=>[5,6,7,2,8,1,4,3]=>[3,2,2,1]
[7,4,3,2,1,8,5,6]=>[4,3,2,7,8,5,1,6]=>[5,6,7,2,1,4,8,3]=>[3,1,3,1]
[8,4,3,2,1,7,6,5]=>[3,2,8,4,7,5,6,1]=>[6,7,1,5,2,4,3,8]=>[2,2,2,2]
[7,4,3,2,1,8,6,5]=>[3,2,8,4,7,5,1,6]=>[6,7,1,5,2,4,8,3]=>[2,2,3,1]
[6,4,3,2,1,8,7,5]=>[3,2,8,4,1,7,5,6]=>[6,7,1,5,8,2,4,3]=>[2,3,2,1]
[5,6,3,8,2,1,7,4]=>[3,1,5,2,8,6,7,4]=>[6,8,4,7,1,3,2,5]=>[2,2,2,2]
[7,5,3,2,8,1,6,4]=>[3,8,4,2,6,1,7,5]=>[6,1,5,7,3,8,2,4]=>[1,3,2,2]
[7,5,4,2,8,6,1,3]=>[7,3,2,8,4,1,6,5]=>[2,6,7,1,5,8,3,4]=>[3,3,2]
[6,5,4,2,8,7,1,3]=>[7,3,2,1,8,4,6,5]=>[2,6,7,8,1,5,3,4]=>[4,2,2]
[4,6,5,8,7,2,1,3]=>[3,1,2,7,6,8,5,4]=>[6,8,7,2,3,1,4,5]=>[2,1,2,3]
[2,6,5,7,8,3,4,1]=>[3,2,6,4,8,1,7,5]=>[6,7,3,5,1,8,2,4]=>[2,2,2,2]
[6,5,4,2,7,8,1,3]=>[7,4,3,2,1,5,8,6]=>[2,5,6,7,8,4,1,3]=>[5,1,2]
[8,5,4,2,6,7,1,3]=>[7,4,3,2,5,8,6,1]=>[2,5,6,7,4,1,3,8]=>[4,1,3]
[8,5,3,2,6,1,7,4]=>[3,8,4,2,6,5,7,1]=>[6,1,5,7,3,4,2,8]=>[1,3,2,2]
[7,5,3,2,6,1,8,4]=>[3,8,4,2,6,5,1,7]=>[6,1,5,7,3,4,8,2]=>[1,3,3,1]
[5,6,3,7,2,1,8,4]=>[3,1,5,2,8,6,4,7]=>[6,8,4,7,1,3,5,2]=>[2,2,3,1]
[4,6,3,7,2,1,8,5]=>[1,3,5,2,8,6,4,7]=>[8,6,4,7,1,3,5,2]=>[1,1,2,3,1]
[3,6,4,7,2,8,1,5]=>[3,5,1,2,7,4,8,6]=>[6,4,8,7,2,5,1,3]=>[1,2,1,2,2]
[2,6,4,7,3,8,5,1]=>[8,3,2,5,1,4,7,6]=>[1,6,7,4,8,5,2,3]=>[3,2,1,2]
[3,5,4,2,7,8,1,6]=>[3,1,2,7,4,5,8,6]=>[6,8,7,2,5,4,1,3]=>[2,1,2,1,2]
[4,5,3,2,7,1,8,6]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[1,2,2,2,1]
[7,4,3,2,1,6,8,5]=>[4,3,2,6,8,5,1,7]=>[5,6,7,3,1,4,8,2]=>[3,1,3,1]
[8,4,3,2,1,6,7,5]=>[4,3,2,6,8,5,7,1]=>[5,6,7,3,1,4,2,8]=>[3,1,2,2]
[8,4,3,2,1,5,7,6]=>[4,3,2,8,5,6,7,1]=>[5,6,7,1,4,3,2,8]=>[3,2,1,2]
[6,4,3,2,1,5,8,7]=>[4,3,2,8,5,1,6,7]=>[5,6,7,1,4,8,3,2]=>[3,3,1,1]
[3,5,4,2,6,8,1,7]=>[4,1,3,2,5,7,8,6]=>[5,8,6,7,4,2,1,3]=>[2,2,1,1,2]
[5,6,3,4,1,2,8,7]=>[3,1,8,5,4,2,6,7]=>[6,8,1,4,5,7,3,2]=>[2,4,1,1]
[8,5,3,7,2,6,4,1]=>[8,3,2,5,7,6,4,1]=>[1,6,7,4,2,3,5,8]=>[3,1,4]
[8,5,7,4,2,6,3,1]=>[2,8,5,4,7,6,3,1]=>[7,1,4,5,2,3,6,8]=>[1,3,4]
[7,5,8,4,2,6,1,3]=>[5,2,7,4,1,8,6,3]=>[4,7,2,5,8,1,3,6]=>[2,3,3]
[2,1,7,8,5,6,3,4]=>[7,5,3,8,1,6,2,4]=>[2,4,6,1,8,3,7,5]=>[3,2,2,1]
[6,8,3,7,5,1,4,2]=>[8,3,1,6,7,5,4,2]=>[1,6,8,3,2,4,5,7]=>[3,1,4]
[5,7,3,8,1,6,2,4]=>[3,1,7,8,5,2,6,4]=>[6,8,2,1,4,7,3,5]=>[2,1,3,2]
[3,2,6,4,8,5,1,7]=>[7,1,4,2,3,6,8,5]=>[2,8,5,7,6,3,1,4]=>[2,2,1,1,2]
[3,2,5,8,4,6,1,7]=>[1,3,5,7,2,6,8,4]=>[8,6,4,2,7,3,1,5]=>[1,1,1,2,1,2]
[3,5,2,4,1,7,6,8]=>[1,3,4,2,7,5,6,8]=>[8,6,5,7,2,4,3,1]=>[1,1,2,2,1,1]
[4,2,1,5,7,3,6,8]=>[2,4,1,6,7,3,5,8]=>[7,5,8,3,2,6,4,1]=>[1,2,1,2,1,1]
[4,5,2,3,7,1,6,8]=>[3,1,4,2,6,7,5,8]=>[6,8,5,7,3,2,4,1]=>[2,2,1,2,1]
[4,2,5,3,8,1,6,7]=>[4,2,1,3,6,7,8,5]=>[5,7,8,6,3,2,1,4]=>[3,1,1,1,2]
[4,2,5,8,3,1,6,7]=>[3,1,6,2,5,7,8,4]=>[6,8,3,7,4,2,1,5]=>[2,2,1,1,2]
[4,1,5,3,8,2,6,7]=>[4,3,1,6,7,8,2,5]=>[5,6,8,3,2,1,7,4]=>[3,1,1,2,1]
[4,1,5,8,3,2,6,7]=>[3,1,6,5,7,8,2,4]=>[6,8,3,4,2,1,7,5]=>[2,2,1,2,1]
[4,3,8,5,2,1,6,7]=>[1,6,2,5,4,7,8,3]=>[8,3,7,4,5,2,1,6]=>[1,2,2,1,2]
[4,7,3,5,2,1,6,8]=>[1,3,6,5,4,7,2,8]=>[8,6,3,4,5,2,7,1]=>[1,1,3,2,1]
[4,3,6,2,5,1,7,8]=>[2,1,4,6,5,3,7,8]=>[7,8,5,3,4,6,2,1]=>[2,1,3,1,1]
[4,6,3,2,5,1,7,8]=>[1,4,3,6,5,2,7,8]=>[8,5,6,3,4,7,2,1]=>[1,2,3,1,1]
[4,5,1,7,3,2,6,8]=>[1,6,5,2,7,3,4,8]=>[8,3,4,7,2,6,5,1]=>[1,3,2,1,1]
[4,5,1,3,7,2,6,8]=>[4,1,6,2,7,3,5,8]=>[5,8,3,7,2,6,4,1]=>[2,2,2,1,1]
[3,5,1,4,2,7,6,8]=>[1,4,7,3,2,5,6,8]=>[8,5,2,6,7,4,3,1]=>[1,1,3,1,1,1]
[2,5,1,4,3,7,8,6]=>[4,6,1,2,8,3,5,7]=>[5,3,8,7,1,6,4,2]=>[1,2,1,2,1,1]
[5,2,1,4,3,7,8,6]=>[2,4,6,1,8,3,5,7]=>[7,5,3,8,1,6,4,2]=>[1,1,2,2,1,1]
[4,3,1,7,5,2,6,8]=>[2,1,6,5,7,3,4,8]=>[7,8,3,4,2,6,5,1]=>[2,2,2,1,1]
[4,3,6,1,5,2,7,8]=>[2,1,6,4,5,3,7,8]=>[7,8,3,5,4,6,2,1]=>[2,2,2,1,1]
[4,6,3,1,5,2,7,8]=>[1,6,4,3,5,2,7,8]=>[8,3,5,6,4,7,2,1]=>[1,3,2,1,1]
[5,3,6,4,1,2,7,8]=>[2,5,1,6,4,3,7,8]=>[7,4,8,3,5,6,2,1]=>[1,2,3,1,1]
[6,3,4,1,2,7,5,8]=>[2,7,4,3,5,1,6,8]=>[7,2,5,6,4,8,3,1]=>[1,3,2,1,1]
[6,2,4,1,3,7,8,5]=>[6,2,3,8,4,1,5,7]=>[3,7,6,1,5,8,4,2]=>[2,1,3,1,1]
[5,3,6,2,1,4,7,8]=>[2,5,4,1,6,3,7,8]=>[7,4,5,8,3,6,2,1]=>[1,3,2,1,1]
[5,6,2,7,1,3,4,8]=>[3,5,1,6,2,7,4,8]=>[6,4,8,3,7,2,5,1]=>[1,2,2,2,1]
[4,6,7,2,3,1,5,8]=>[1,4,6,5,2,7,3,8]=>[8,5,3,4,7,2,6,1]=>[1,1,3,2,1]
[4,6,2,1,7,3,5,8]=>[3,1,6,7,4,2,5,8]=>[6,8,3,2,5,7,4,1]=>[2,1,3,1,1]
[3,2,6,1,4,7,5,8]=>[1,7,2,4,5,3,6,8]=>[8,2,7,5,4,6,3,1]=>[1,2,1,2,1,1]
[3,6,2,1,4,7,5,8]=>[1,3,7,4,5,2,6,8]=>[8,6,2,5,4,7,3,1]=>[1,1,2,2,1,1]
[3,6,7,2,4,5,1,8]=>[4,5,1,2,7,6,3,8]=>[5,4,8,7,2,3,6,1]=>[1,2,1,3,1]
[3,5,2,7,4,6,1,8]=>[5,1,2,7,3,6,4,8]=>[4,8,7,2,6,3,5,1]=>[2,1,2,2,1]
[3,7,2,4,8,5,1,6]=>[7,1,3,4,6,2,8,5]=>[2,8,6,5,3,7,1,4]=>[2,1,1,2,2]
[7,2,1,4,6,3,8,5]=>[8,2,4,6,3,5,1,7]=>[1,7,5,3,6,4,8,2]=>[2,1,2,2,1]
[7,3,1,4,6,8,2,5]=>[2,7,4,5,8,3,1,6]=>[7,2,5,4,1,6,8,3]=>[1,2,1,3,1]
[3,6,2,1,5,7,4,8]=>[1,3,5,7,4,2,6,8]=>[8,6,4,2,5,7,3,1]=>[1,1,1,3,1,1]
[6,3,2,1,5,7,4,8]=>[3,2,5,7,4,1,6,8]=>[6,7,4,2,5,8,3,1]=>[2,1,3,1,1]
[6,4,2,1,5,3,7,8]=>[3,6,4,2,5,1,7,8]=>[6,3,5,7,4,8,2,1]=>[1,3,2,1,1]
[4,2,6,1,5,3,7,8]=>[6,2,1,4,5,3,7,8]=>[3,7,8,5,4,6,2,1]=>[3,1,2,1,1]
[4,2,1,7,5,3,6,8]=>[6,2,1,5,7,3,4,8]=>[3,7,8,4,2,6,5,1]=>[3,1,2,1,1]
[7,4,1,5,6,2,3,8]=>[6,4,2,7,3,5,1,8]=>[3,5,7,2,6,4,8,1]=>[3,2,2,1]
[7,3,1,5,2,6,4,8]=>[2,7,5,3,4,6,1,8]=>[7,2,4,6,5,3,8,1]=>[1,3,1,2,1]
[7,2,1,5,3,6,8,4]=>[6,2,4,8,3,5,1,7]=>[3,7,5,1,6,4,8,2]=>[2,1,2,2,1]
[6,2,5,1,3,7,8,4]=>[6,8,2,4,3,1,5,7]=>[3,1,7,5,6,8,4,2]=>[1,2,3,1,1]
[6,3,5,1,2,7,4,8]=>[2,7,4,5,3,1,6,8]=>[7,2,5,4,6,8,3,1]=>[1,2,3,1,1]
[5,2,6,4,1,3,7,8]=>[5,6,2,1,4,3,7,8]=>[4,3,7,8,5,6,2,1]=>[1,3,2,1,1]
[4,6,5,1,7,2,3,8]=>[1,6,7,4,3,2,5,8]=>[8,3,2,5,6,7,4,1]=>[1,1,4,1,1]
[3,6,5,1,2,7,4,8]=>[7,1,4,5,3,2,6,8]=>[2,8,5,4,6,7,3,1]=>[2,1,3,1,1]
[6,5,2,1,4,7,8,3]=>[3,5,6,2,1,8,4,7]=>[6,4,3,7,8,1,5,2]=>[1,1,3,2,1]
[2,3,1,8,5,4,7,6]=>[5,8,1,2,6,7,3,4]=>[4,1,8,7,3,2,6,5]=>[1,2,1,1,2,1]
[2,4,1,5,8,3,7,6]=>[2,8,1,4,6,7,3,5]=>[7,1,8,5,3,2,6,4]=>[1,2,1,1,2,1]
[2,4,1,5,3,8,7,6]=>[2,8,1,4,7,3,5,6]=>[7,1,8,5,2,6,4,3]=>[1,2,1,2,1,1]
[3,4,5,1,2,8,7,6]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[1,1,1,3,1,1]
[3,4,5,1,8,2,7,6]=>[1,2,3,8,6,7,4,5]=>[8,7,6,1,3,2,5,4]=>[1,1,1,2,2,1]
[1,8,4,5,3,2,7,6]=>[3,5,4,8,6,7,1,2]=>[6,4,5,1,3,2,8,7]=>[1,2,2,2,1]
[3,4,5,8,2,1,7,6]=>[1,2,3,5,8,6,7,4]=>[8,7,6,4,1,3,2,5]=>[1,1,1,1,2,2]
[3,4,5,2,8,1,7,6]=>[1,2,3,8,4,6,7,5]=>[8,7,6,1,5,3,2,4]=>[1,1,1,2,1,2]
[3,4,6,2,1,7,8,5]=>[1,2,4,6,3,8,5,7]=>[8,7,5,3,6,1,4,2]=>[1,1,1,2,2,1]
[3,4,6,2,1,7,5,8]=>[1,2,4,7,5,3,6,8]=>[8,7,5,2,4,6,3,1]=>[1,1,1,3,1,1]
[3,5,6,2,7,1,4,8]=>[4,1,2,6,3,7,5,8]=>[5,8,7,3,6,2,4,1]=>[2,1,2,2,1]
[3,5,6,2,7,1,8,4]=>[2,8,1,4,3,6,5,7]=>[7,1,8,5,6,3,4,2]=>[1,2,2,2,1]
[3,5,6,2,7,8,1,4]=>[2,7,1,4,3,5,8,6]=>[7,2,8,5,6,4,1,3]=>[1,2,2,1,2]
[3,4,6,2,8,7,1,5]=>[7,1,2,3,8,4,6,5]=>[2,8,7,6,1,5,3,4]=>[2,1,1,2,2]
[3,4,6,8,2,7,1,5]=>[5,1,2,3,7,8,6,4]=>[4,8,7,6,2,1,3,5]=>[2,1,1,1,3]
[2,4,8,6,3,7,1,5]=>[5,7,2,4,8,1,6,3]=>[4,2,7,5,1,8,3,6]=>[1,2,1,2,2]
[1,8,4,6,3,7,2,5]=>[3,5,7,4,8,6,1,2]=>[6,4,2,5,1,3,8,7]=>[1,1,2,3,1]
[3,4,6,8,2,7,5,1]=>[3,8,1,2,5,7,6,4]=>[6,1,8,7,4,2,3,5]=>[1,2,1,1,3]
[3,4,6,2,8,7,5,1]=>[3,8,1,2,7,4,6,5]=>[6,1,8,7,2,5,3,4]=>[1,2,1,2,2]
[3,5,6,2,7,8,4,1]=>[2,5,1,3,8,4,7,6]=>[7,4,8,6,1,5,2,3]=>[1,2,1,2,2]
[3,5,6,2,7,4,1,8]=>[2,7,1,4,3,6,5,8]=>[7,2,8,5,6,3,4,1]=>[1,2,2,2,1]
[4,5,6,7,2,8,3,1]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[1,1,1,3,2]
[3,5,6,8,7,2,4,1]=>[2,3,6,8,1,7,5,4]=>[7,6,3,1,8,2,4,5]=>[1,1,1,2,3]
[2,5,8,6,7,3,4,1]=>[6,2,4,8,7,1,5,3]=>[3,7,5,1,2,8,4,6]=>[2,1,3,2]
[1,8,5,6,7,3,4,2]=>[3,6,4,8,7,5,1,2]=>[6,3,5,1,2,4,8,7]=>[1,2,4,1]
[1,8,5,6,7,3,2,4]=>[3,7,6,4,8,5,1,2]=>[6,2,3,5,1,4,8,7]=>[1,3,3,1]
[2,5,8,6,7,3,1,4]=>[7,2,6,4,8,1,5,3]=>[2,7,3,5,1,8,4,6]=>[2,2,2,2]
[3,5,6,8,7,2,1,4]=>[2,3,7,1,6,8,5,4]=>[7,6,2,8,3,1,4,5]=>[1,1,2,1,3]
[4,5,6,7,2,1,8,3]=>[1,2,5,3,8,6,4,7]=>[8,7,4,6,1,3,5,2]=>[1,1,2,3,1]
[3,4,6,1,8,7,2,5]=>[7,1,2,3,8,6,4,5]=>[2,8,7,6,1,3,5,4]=>[2,1,1,3,1]
[2,4,1,6,8,7,3,5]=>[2,4,7,8,1,6,3,5]=>[7,5,2,1,8,3,6,4]=>[1,1,1,2,2,1]
[2,3,1,8,6,7,4,5]=>[7,5,8,1,2,6,3,4]=>[2,4,1,8,7,3,6,5]=>[2,2,1,2,1]
[1,8,3,2,6,7,5,4]=>[5,8,3,7,4,6,1,2]=>[4,1,6,2,5,3,8,7]=>[1,2,2,2,1]
[2,5,1,6,7,8,4,3]=>[4,2,5,8,1,7,3,6]=>[5,7,4,1,8,2,6,3]=>[2,1,2,2,1]
[2,5,1,6,7,4,8,3]=>[4,2,6,1,5,8,3,7]=>[5,7,3,8,4,1,6,2]=>[2,2,1,2,1]
[2,5,1,6,7,4,3,8]=>[4,2,7,1,6,3,5,8]=>[5,7,2,8,3,6,4,1]=>[2,2,2,1,1]
[3,5,6,1,7,4,2,8]=>[2,7,1,6,4,3,5,8]=>[7,2,8,3,5,6,4,1]=>[1,2,3,1,1]
[3,5,6,1,7,4,8,2]=>[2,6,1,5,3,8,4,7]=>[7,3,8,4,6,1,5,2]=>[1,2,2,2,1]
[3,4,6,1,8,7,5,2]=>[3,8,1,2,7,6,4,5]=>[6,1,8,7,2,3,5,4]=>[1,2,1,3,1]
[2,4,8,6,1,7,5,3]=>[8,7,2,5,1,4,6,3]=>[1,2,7,4,8,5,3,6]=>[3,2,1,2]
[1,8,4,6,2,7,5,3]=>[8,3,7,5,4,6,1,2]=>[1,6,2,4,5,3,8,7]=>[2,3,2,1]
[1,8,5,6,7,2,4,3]=>[3,8,6,4,7,5,1,2]=>[6,1,3,5,2,4,8,7]=>[1,3,3,1]
[2,5,8,6,7,1,4,3]=>[8,2,6,4,7,1,5,3]=>[1,7,3,5,2,8,4,6]=>[2,2,2,2]
[3,5,6,8,7,1,4,2]=>[2,3,8,1,6,7,5,4]=>[7,6,1,8,3,2,4,5]=>[1,1,2,1,3]
[4,5,6,7,8,1,3,2]=>[1,2,3,8,6,4,7,5]=>[8,7,6,1,3,5,2,4]=>[1,1,1,3,2]
[4,5,6,7,1,3,8,2]=>[1,2,6,3,8,5,4,7]=>[8,7,3,6,1,4,5,2]=>[1,1,2,3,1]
[4,5,6,7,1,3,2,8]=>[1,2,7,5,3,6,4,8]=>[8,7,2,4,6,3,5,1]=>[1,1,3,2,1]
[4,5,6,7,3,1,8,2]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[1,1,1,4,1]
[3,5,6,8,7,4,1,2]=>[2,3,7,8,1,6,5,4]=>[7,6,2,1,8,3,4,5]=>[1,1,1,2,3]
[2,5,8,6,7,4,1,3]=>[7,2,4,8,6,1,5,3]=>[2,7,5,1,3,8,4,6]=>[2,1,3,2]
[1,8,5,6,7,4,2,3]=>[3,7,4,8,6,5,1,2]=>[6,2,5,1,3,4,8,7]=>[1,2,4,1]
[1,8,5,6,7,4,3,2]=>[3,4,8,7,6,5,1,2]=>[6,5,1,2,3,4,8,7]=>[1,1,5,1]
[2,5,8,6,7,4,3,1]=>[4,8,2,7,6,1,5,3]=>[5,1,7,2,3,8,4,6]=>[1,2,3,2]
[8,2,5,3,7,1,6,4]=>[8,4,2,3,6,7,5,1]=>[1,5,7,6,3,2,4,8]=>[3,1,1,3]
[8,2,4,3,7,1,6,5]=>[3,8,2,4,6,7,5,1]=>[6,1,7,5,3,2,4,8]=>[1,2,1,1,3]
[5,8,2,4,3,7,1,6]=>[5,3,1,4,7,8,6,2]=>[4,6,8,5,2,1,3,7]=>[3,1,1,3]
[4,2,5,6,1,8,3,7]=>[3,1,7,2,4,8,5,6]=>[6,8,2,7,5,1,4,3]=>[2,2,1,2,1]
[4,2,5,6,1,7,3,8]=>[3,1,7,2,5,4,6,8]=>[6,8,2,7,4,5,3,1]=>[2,2,2,1,1]
[6,1,5,7,3,2,4,8]=>[6,5,3,7,2,1,4,8]=>[3,4,6,2,7,8,5,1]=>[3,3,1,1]
[6,1,5,8,3,2,4,7]=>[6,5,3,7,1,8,2,4]=>[3,4,6,2,8,1,7,5]=>[3,2,2,1]
[3,8,2,4,7,1,5,6]=>[1,3,4,6,7,8,5,2]=>[8,6,5,3,2,1,4,7]=>[1,1,1,1,1,3]
[3,6,8,2,4,7,1,5]=>[4,5,1,2,7,8,6,3]=>[5,4,8,7,2,1,3,6]=>[1,2,1,1,3]
[4,3,5,6,7,1,8,2]=>[2,1,3,4,8,6,5,7]=>[7,8,6,5,1,3,4,2]=>[2,1,1,3,1]
[3,7,1,5,6,8,2,4]=>[4,7,1,5,8,3,2,6]=>[5,2,8,4,1,6,7,3]=>[1,2,1,3,1]
[3,7,1,5,8,2,4,6]=>[6,1,4,7,8,3,2,5]=>[3,8,5,2,1,6,7,4]=>[2,1,1,3,1]
[7,3,2,4,6,1,5,8]=>[3,2,4,6,7,5,1,8]=>[6,7,5,3,2,4,8,1]=>[2,1,1,3,1]
[3,2,5,1,7,4,6,8]=>[1,6,2,3,7,4,5,8]=>[8,3,7,6,2,5,4,1]=>[1,2,1,2,1,1]
[3,2,5,1,8,4,6,7]=>[1,6,2,3,7,8,4,5]=>[8,3,7,6,2,1,5,4]=>[1,2,1,1,2,1]
[3,2,5,1,7,8,4,6]=>[1,3,7,2,5,8,4,6]=>[8,6,2,7,4,1,5,3]=>[1,1,2,1,2,1]
[6,1,5,7,8,3,2,4]=>[3,7,6,4,1,8,2,5]=>[6,2,3,5,8,1,7,4]=>[1,4,2,1]
[4,2,5,6,1,7,8,3]=>[3,1,6,2,4,8,5,7]=>[6,8,3,7,5,1,4,2]=>[2,2,1,2,1]
[5,7,6,1,8,3,4,2]=>[1,6,8,7,4,3,2,5]=>[8,3,1,2,5,6,7,4]=>[1,1,5,1]
[5,8,6,1,7,3,4,2]=>[1,6,8,7,4,3,5,2]=>[8,3,1,2,5,6,4,7]=>[1,1,4,2]
[6,1,5,8,7,3,2,4]=>[3,7,6,1,8,5,2,4]=>[6,2,3,8,1,4,7,5]=>[1,3,3,1]
[8,7,3,2,4,6,1,5]=>[4,3,5,7,8,6,2,1]=>[5,6,4,2,1,3,7,8]=>[2,1,1,4]
[3,2,5,1,8,7,4,6]=>[1,3,7,8,2,6,4,5]=>[8,6,2,1,7,3,5,4]=>[1,1,1,2,2,1]
[3,2,5,1,6,4,7,8]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[1,2,2,1,1,1]
[3,2,4,1,8,7,5,6]=>[1,7,8,2,3,6,4,5]=>[8,2,1,7,6,3,5,4]=>[1,1,2,1,2,1]
[3,2,5,1,6,8,7,4]=>[1,3,8,2,5,7,4,6]=>[8,6,1,7,4,2,5,3]=>[1,1,2,1,2,1]
[3,7,6,5,1,8,4,2]=>[8,7,5,1,4,3,2,6]=>[1,2,4,8,5,6,7,3]=>[4,3,1]
[6,5,1,7,8,4,2,3]=>[7,4,2,1,8,6,3,5]=>[2,5,7,8,1,3,6,4]=>[4,3,1]
[3,2,5,1,6,7,8,4]=>[1,5,2,3,6,8,4,7]=>[8,4,7,6,3,1,5,2]=>[1,2,1,1,2,1]
[3,2,4,1,8,5,6,7]=>[2,1,3,6,7,8,4,5]=>[7,8,6,3,2,1,5,4]=>[2,1,1,1,2,1]
[3,2,4,1,7,5,6,8]=>[2,1,3,6,7,4,5,8]=>[7,8,6,3,2,5,4,1]=>[2,1,1,2,1,1]
[3,2,4,1,8,5,7,6]=>[1,8,2,3,6,7,4,5]=>[8,1,7,6,3,2,5,4]=>[1,2,1,1,2,1]
[8,3,2,4,7,6,1,5]=>[2,7,8,3,4,6,5,1]=>[7,2,1,6,5,3,4,8]=>[1,1,2,1,3]
[3,2,5,1,6,7,4,8]=>[1,5,2,3,7,4,6,8]=>[8,4,7,6,2,5,3,1]=>[1,2,1,2,1,1]
[6,5,1,7,4,2,3,8]=>[6,7,5,3,2,1,4,8]=>[3,2,4,6,7,8,5,1]=>[1,5,1,1]
[6,5,1,8,4,2,3,7]=>[6,7,5,2,1,8,3,4]=>[3,2,4,7,8,1,6,5]=>[1,4,2,1]
[4,2,6,1,8,3,7,5]=>[1,8,6,2,3,7,4,5]=>[8,1,3,7,6,2,5,4]=>[1,3,1,2,1]
[8,4,6,1,7,3,5,2]=>[2,6,8,7,4,3,5,1]=>[7,3,1,2,5,6,4,8]=>[1,1,4,2]
[5,2,6,1,8,4,7,3]=>[6,3,1,8,2,7,4,5]=>[3,6,8,1,7,2,5,4]=>[3,2,2,1]
[7,4,2,3,8,5,1,6]=>[7,3,2,4,6,1,8,5]=>[2,6,7,5,3,8,1,4]=>[3,1,2,2]
[8,5,1,6,4,2,3,7]=>[6,7,5,3,2,4,8,1]=>[3,2,4,6,7,5,1,8]=>[1,4,1,2]
[7,5,1,6,4,2,3,8]=>[6,7,5,3,2,4,1,8]=>[3,2,4,6,7,5,8,1]=>[1,4,2,1]
[3,2,5,1,8,6,4,7]=>[1,3,7,2,6,8,4,5]=>[8,6,2,7,3,1,5,4]=>[1,1,2,1,2,1]
[8,6,1,5,7,3,2,4]=>[7,6,4,8,3,2,5,1]=>[2,3,5,1,6,7,4,8]=>[3,3,2]
[8,5,6,1,7,3,4,2]=>[6,2,8,7,4,3,5,1]=>[3,7,1,2,5,6,4,8]=>[2,4,2]
[3,6,8,5,1,7,4,2]=>[2,8,7,1,5,4,6,3]=>[7,1,2,8,4,5,3,6]=>[1,3,2,2]
[8,5,1,6,7,4,2,3]=>[7,4,2,8,6,3,5,1]=>[2,5,7,1,3,6,4,8]=>[3,3,2]
[3,2,5,1,8,6,7,4]=>[1,3,6,8,2,7,4,5]=>[8,6,3,1,7,2,5,4]=>[1,1,1,2,2,1]
[3,2,4,1,5,8,6,7]=>[2,1,3,7,8,4,5,6]=>[7,8,6,2,1,5,4,3]=>[2,1,1,2,1,1]
[3,2,5,1,7,8,6,4]=>[1,3,5,8,2,7,4,6]=>[8,6,4,1,7,2,5,3]=>[1,1,1,2,2,1]
[3,8,5,1,7,6,4,2]=>[3,8,7,1,6,4,5,2]=>[6,1,2,8,3,5,4,7]=>[1,3,2,2]
[3,7,5,1,8,6,4,2]=>[3,8,7,1,6,4,2,5]=>[6,1,2,8,3,5,7,4]=>[1,3,3,1]
[8,7,5,1,6,4,2,3]=>[7,8,6,4,3,5,2,1]=>[2,1,3,5,6,4,7,8]=>[1,4,3]
[3,2,5,1,8,7,6,4]=>[8,1,3,7,2,6,4,5]=>[1,8,6,2,7,3,5,4]=>[2,1,2,2,1]
[6,5,7,3,1,8,4,2]=>[4,2,1,8,7,5,3,6]=>[5,7,8,1,2,4,6,3]=>[3,4,1]
[4,6,3,7,1,8,5,2]=>[8,1,3,2,7,5,4,6]=>[1,8,6,7,2,4,5,3]=>[2,2,3,1]
[4,6,3,7,5,1,8,2]=>[8,1,3,2,6,5,4,7]=>[1,8,6,7,3,4,5,2]=>[2,2,3,1]
[4,2,6,1,7,5,3,8]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[1,3,2,1,1]
[2,5,7,4,1,6,3,8]=>[2,7,5,1,4,6,3,8]=>[7,2,4,8,5,3,6,1]=>[1,3,1,2,1]
[2,5,7,4,1,6,8,3]=>[2,6,4,8,1,5,3,7]=>[7,3,5,1,8,4,6,2]=>[1,2,2,2,1]
[5,4,7,3,6,1,8,2]=>[2,1,4,8,6,5,3,7]=>[7,8,5,1,3,4,6,2]=>[2,1,4,1]
[5,4,7,8,3,1,6,2]=>[1,8,2,6,5,3,7,4]=>[8,1,7,3,4,6,2,5]=>[1,2,3,2]
[4,3,7,5,1,8,6,2]=>[1,4,8,2,7,5,3,6]=>[8,5,1,7,2,4,6,3]=>[1,1,2,3,1]
[6,4,3,8,5,1,7,2]=>[2,8,3,1,6,5,7,4]=>[7,1,6,8,3,4,2,5]=>[1,3,2,2]
[5,8,4,3,6,1,7,2]=>[1,4,3,8,6,5,7,2]=>[8,5,6,1,3,4,2,7]=>[1,2,3,2]
[5,4,8,3,6,1,7,2]=>[2,1,4,8,6,5,7,3]=>[7,8,5,1,3,4,2,6]=>[2,1,3,2]
[2,5,4,6,1,7,3,8]=>[3,2,7,1,5,4,6,8]=>[6,7,2,8,4,5,3,1]=>[2,2,2,1,1]
[3,2,5,8,1,6,7,4]=>[1,3,6,8,2,5,7,4]=>[8,6,3,1,7,4,2,5]=>[1,1,1,2,1,2]
[2,5,4,6,8,1,7,3]=>[3,2,4,8,1,6,7,5]=>[6,7,5,1,8,3,2,4]=>[2,1,2,1,2]
[5,2,8,4,1,6,7,3]=>[6,4,1,8,2,5,7,3]=>[3,5,8,1,7,4,2,6]=>[3,2,1,2]
[4,6,2,1,8,5,7,3]=>[1,6,8,3,2,7,4,5]=>[8,3,1,6,7,2,5,4]=>[1,1,3,2,1]
[2,4,1,7,5,8,6,3]=>[8,2,5,1,4,7,3,6]=>[1,7,4,8,5,2,6,3]=>[2,2,1,2,1]
[2,4,1,7,5,3,8,6]=>[2,5,8,1,6,3,4,7]=>[7,4,1,8,3,6,5,2]=>[1,1,2,2,1,1]
[2,6,4,1,8,5,3,7]=>[3,7,6,1,2,8,4,5]=>[6,2,3,8,7,1,5,4]=>[1,3,1,2,1]
[5,4,8,2,1,6,3,7]=>[4,2,1,7,5,6,8,3]=>[5,7,8,2,4,3,1,6]=>[3,2,1,2]
[2,5,8,4,1,6,3,7]=>[2,7,5,1,4,6,8,3]=>[7,2,4,8,5,3,1,6]=>[1,3,1,1,2]
[3,2,5,6,1,8,4,7]=>[1,3,7,2,4,8,5,6]=>[8,6,2,7,5,1,4,3]=>[1,1,2,1,2,1]
[3,5,2,8,1,6,4,7]=>[7,1,3,2,5,6,8,4]=>[2,8,6,7,4,3,1,5]=>[2,2,1,1,2]
[3,2,1,6,8,5,4,7]=>[1,4,7,2,6,8,3,5]=>[8,5,2,7,3,1,6,4]=>[1,1,2,1,2,1]
[3,2,7,1,5,4,8,6]=>[1,5,8,2,4,6,3,7]=>[8,4,1,7,5,3,6,2]=>[1,1,2,1,2,1]
[3,2,7,1,5,8,6,4]=>[8,1,5,7,2,4,3,6]=>[1,8,4,2,7,5,6,3]=>[2,1,2,2,1]
[3,8,2,5,1,6,7,4]=>[6,1,3,4,8,5,7,2]=>[3,8,6,5,1,4,2,7]=>[2,1,1,2,2]
[4,8,3,2,6,7,1,5]=>[1,3,7,4,5,8,6,2]=>[8,6,2,5,4,1,3,7]=>[1,1,2,1,3]
[4,3,8,2,6,7,1,5]=>[1,7,2,4,5,8,6,3]=>[8,2,7,5,4,1,3,6]=>[1,2,1,1,3]
[4,3,2,6,7,8,1,5]=>[2,1,4,7,3,5,8,6]=>[7,8,5,2,6,4,1,3]=>[2,1,2,1,2]
[4,3,7,2,6,8,1,5]=>[1,7,2,4,5,3,8,6]=>[8,2,7,5,4,6,1,3]=>[1,2,1,2,2]
[4,3,7,8,2,6,1,5]=>[1,5,7,2,3,8,6,4]=>[8,4,2,7,6,1,3,5]=>[1,1,2,1,3]
[2,5,7,4,8,1,6,3]=>[2,4,8,6,1,3,7,5]=>[7,5,1,3,8,6,2,4]=>[1,1,3,1,2]
[3,2,5,7,8,1,6,4]=>[8,1,3,6,2,4,7,5]=>[1,8,6,3,7,5,2,4]=>[2,1,2,1,2]
[3,2,5,7,1,6,8,4]=>[1,3,6,8,2,5,4,7]=>[8,6,3,1,7,4,5,2]=>[1,1,1,2,2,1]
[6,3,2,7,1,5,4,8]=>[2,7,3,5,1,6,4,8]=>[7,2,6,4,8,3,5,1]=>[1,2,2,2,1]
[6,3,2,7,1,5,8,4]=>[2,6,8,3,1,5,4,7]=>[7,3,1,6,8,4,5,2]=>[1,1,3,2,1]
[6,3,2,7,8,1,5,4]=>[8,2,6,3,1,4,7,5]=>[1,7,3,6,8,5,2,4]=>[2,3,1,2]
[4,2,6,1,7,8,5,3]=>[1,5,3,8,2,7,4,6]=>[8,4,6,1,7,2,5,3]=>[1,2,2,2,1]
[6,5,2,1,7,8,4,3]=>[5,8,3,2,1,7,4,6]=>[4,1,6,7,8,2,5,3]=>[1,4,2,1]
[2,1,7,5,3,8,6,4]=>[4,8,7,1,5,2,3,6]=>[5,1,2,8,4,7,6,3]=>[1,3,2,1,1]
[6,2,1,8,5,3,7,4]=>[8,6,2,5,1,7,3,4]=>[1,3,7,4,8,2,6,5]=>[3,2,2,1]
[6,3,2,7,1,4,8,5]=>[2,8,3,5,1,6,4,7]=>[7,1,6,4,8,3,5,2]=>[1,2,2,2,1]
[6,3,2,1,4,7,8,5]=>[3,2,6,8,4,1,5,7]=>[6,7,3,1,5,8,4,2]=>[2,1,3,1,1]
[3,5,2,1,7,4,6,8]=>[1,3,6,2,7,4,5,8]=>[8,6,3,7,2,5,4,1]=>[1,1,2,2,1,1]
[3,5,2,1,7,8,4,6]=>[7,1,3,2,5,8,4,6]=>[2,8,6,7,4,1,5,3]=>[2,2,1,2,1]
[5,8,4,2,1,7,3,6]=>[4,1,7,3,8,5,6,2]=>[5,8,2,6,1,4,3,7]=>[2,2,2,2]
[4,6,2,1,8,3,7,5]=>[1,8,3,6,2,7,4,5]=>[8,1,6,3,7,2,5,4]=>[1,2,2,2,1]
[2,4,1,7,3,8,6,5]=>[8,2,7,1,5,3,4,6]=>[1,7,2,8,4,6,5,3]=>[2,2,2,1,1]
[3,2,7,1,4,8,6,5]=>[8,1,7,2,4,5,3,6]=>[1,8,2,7,5,4,6,3]=>[2,2,1,2,1]
[3,5,8,2,1,7,4,6]=>[4,1,2,7,8,5,6,3]=>[5,8,7,2,1,4,3,6]=>[2,1,1,2,2]
[4,8,3,7,2,1,5,6]=>[1,3,6,5,7,8,4,2]=>[8,6,3,4,2,1,5,7]=>[1,1,2,1,3]
[4,3,7,2,8,1,5,6]=>[2,1,4,6,7,3,8,5]=>[7,8,5,3,2,6,1,4]=>[2,1,1,2,2]
[4,8,3,2,7,1,5,6]=>[1,4,3,6,7,8,5,2]=>[8,5,6,3,2,1,4,7]=>[1,2,1,1,3]
[3,5,2,8,1,7,4,6]=>[7,1,2,8,3,5,6,4]=>[2,8,7,1,6,4,3,5]=>[2,1,2,1,2]
[6,3,2,8,1,4,7,5]=>[2,8,3,5,1,6,7,4]=>[7,1,6,4,8,3,2,5]=>[1,2,2,1,2]
[3,2,1,4,7,5,8,6]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[1,2,2,1,1,1]
[5,3,2,1,8,4,6,7]=>[3,2,6,1,7,8,4,5]=>[6,7,3,8,2,1,5,4]=>[2,2,1,2,1]
[4,8,3,2,1,5,6,7]=>[1,5,4,3,6,7,8,2]=>[8,4,5,6,3,2,1,7]=>[1,3,1,1,2]
[4,3,8,2,1,5,6,7]=>[2,1,5,4,6,7,8,3]=>[7,8,4,5,3,2,1,6]=>[2,2,1,1,2]
[1,9,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>[8,1]
[1,10,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>[9,1]
[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>[10,1]
[1,11,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,11,10]=>[10,1]
[6,2,3,1,5,4,8,7]=>[2,3,5,8,4,1,6,7]=>[7,6,4,1,5,8,3,2]=>[1,1,1,3,1,1]
[8,6,7,2,5,3,4,1]=>[6,8,4,2,7,5,3,1]=>[3,1,5,7,2,4,6,8]=>[1,3,4]
[8,2,5,3,4,1,7,6]=>[4,5,2,3,8,6,7,1]=>[5,4,7,6,1,3,2,8]=>[1,2,1,2,2]
[6,2,5,3,4,1,8,7]=>[4,5,2,3,1,8,6,7]=>[5,4,7,6,8,1,3,2]=>[1,2,2,2,1]
[6,1,5,2,4,3,8,7]=>[5,8,4,2,3,1,6,7]=>[4,1,5,7,6,8,3,2]=>[1,3,2,1,1]
[6,1,5,3,4,2,8,7]=>[4,5,3,8,2,1,6,7]=>[5,4,6,1,7,8,3,2]=>[1,2,3,1,1]
[6,3,5,1,4,2,8,7]=>[2,5,8,4,3,1,6,7]=>[7,4,1,5,6,8,3,2]=>[1,1,4,1,1]
[8,3,5,2,4,1,7,6]=>[2,4,5,3,8,6,7,1]=>[7,5,4,6,1,3,2,8]=>[1,1,2,2,2]
[8,3,7,5,6,2,4,1]=>[6,4,8,2,7,5,3,1]=>[3,5,1,7,2,4,6,8]=>[2,2,4]
[8,3,7,2,4,1,6,5]=>[2,4,5,8,6,7,3,1]=>[7,5,4,1,3,2,6,8]=>[1,1,1,2,3]
[8,3,5,1,4,2,7,6]=>[2,5,8,4,3,6,7,1]=>[7,4,1,5,6,3,2,8]=>[1,1,3,1,2]
[8,4,5,1,3,2,7,6]=>[5,2,8,4,3,6,7,1]=>[4,7,1,5,6,3,2,8]=>[2,3,1,2]
[2,1,8,4,5,3,7,6]=>[4,5,8,1,6,7,2,3]=>[5,4,1,8,3,2,7,6]=>[1,1,2,1,2,1]
[8,6,7,4,5,1,3,2]=>[8,6,4,2,7,5,3,1]=>[1,3,5,7,2,4,6,8]=>[4,4]
[8,6,7,1,5,3,4,2]=>[6,8,7,4,2,5,3,1]=>[3,1,2,5,7,4,6,8]=>[1,4,3]
[8,6,7,3,5,1,4,2]=>[4,8,6,2,7,5,3,1]=>[5,1,3,7,2,4,6,8]=>[1,3,4]
[8,3,7,5,6,1,4,2]=>[8,6,2,4,7,5,3,1]=>[1,3,7,5,2,4,6,8]=>[3,1,4]
[8,5,7,3,6,1,4,2]=>[4,2,8,6,7,5,3,1]=>[5,7,1,3,2,4,6,8]=>[2,2,4]
[8,3,7,4,6,2,5,1]=>[4,6,8,2,7,5,3,1]=>[5,3,1,7,2,4,6,8]=>[1,1,2,4]
[8,3,7,4,6,1,5,2]=>[4,8,2,6,7,5,3,1]=>[5,1,7,3,2,4,6,8]=>[1,2,1,4]
[8,3,7,1,6,4,5,2]=>[6,8,2,7,4,5,3,1]=>[3,1,7,2,5,4,6,8]=>[1,2,2,3]
[8,1,7,3,6,4,5,2]=>[6,8,4,7,5,2,3,1]=>[3,1,5,2,4,7,6,8]=>[1,2,3,2]
[8,1,7,5,6,3,4,2]=>[6,4,8,7,5,2,3,1]=>[3,5,1,2,4,7,6,8]=>[2,4,2]
[8,4,7,5,6,1,3,2]=>[8,2,6,4,7,5,3,1]=>[1,7,3,5,2,4,6,8]=>[2,2,4]
[2,1,8,4,7,5,6,3]=>[6,8,4,7,1,5,2,3]=>[3,1,5,2,8,4,7,6]=>[1,2,2,2,1]
[8,1,7,3,4,2,6,5]=>[4,5,8,6,7,2,3,1]=>[5,4,1,3,2,7,6,8]=>[1,1,2,2,2]
[8,1,7,3,6,2,5,4]=>[8,4,6,7,5,2,3,1]=>[1,5,3,2,4,7,6,8]=>[2,1,3,2]
[8,3,7,1,6,2,5,4]=>[8,2,6,7,4,5,3,1]=>[1,7,3,2,5,4,6,8]=>[2,1,2,3]
[8,3,7,2,6,4,5,1]=>[6,8,2,4,7,5,3,1]=>[3,1,7,5,2,4,6,8]=>[1,2,1,4]
[8,2,7,3,6,4,5,1]=>[6,8,4,7,2,5,3,1]=>[3,1,5,2,7,4,6,8]=>[1,2,2,3]
[8,2,7,3,6,1,5,4]=>[8,4,6,7,2,5,3,1]=>[1,5,3,2,7,4,6,8]=>[2,1,2,3]
[8,2,7,1,6,3,5,4]=>[8,6,7,2,4,5,3,1]=>[1,3,2,7,5,4,6,8]=>[2,2,1,3]
[8,1,7,2,4,3,6,5]=>[5,8,4,6,7,2,3,1]=>[4,1,5,3,2,7,6,8]=>[1,2,1,2,2]
[8,1,3,2,7,4,6,5]=>[8,3,6,7,2,4,5,1]=>[1,6,3,2,7,5,4,8]=>[2,1,2,1,2]
[2,1,8,3,7,4,6,5]=>[8,6,7,1,4,5,2,3]=>[1,3,2,8,5,4,7,6]=>[2,2,1,2,1]
[8,1,5,2,4,3,7,6]=>[5,8,4,2,3,6,7,1]=>[4,1,5,7,6,3,2,8]=>[1,3,1,1,2]
[8,2,7,1,4,3,6,5]=>[5,8,2,4,6,7,3,1]=>[4,1,7,5,3,2,6,8]=>[1,2,1,1,3]
[8,2,7,3,4,1,6,5]=>[4,5,8,2,6,7,3,1]=>[5,4,1,7,3,2,6,8]=>[1,1,2,1,3]
[8,2,7,5,6,3,4,1]=>[6,4,8,7,2,5,3,1]=>[3,5,1,2,7,4,6,8]=>[2,3,3]
[8,4,7,5,6,2,3,1]=>[6,2,4,8,7,5,3,1]=>[3,7,5,1,2,4,6,8]=>[2,1,5]
[8,4,7,2,3,1,6,5]=>[4,2,5,8,6,7,3,1]=>[5,7,4,1,3,2,6,8]=>[2,1,2,3]
[8,2,3,1,7,4,6,5]=>[8,2,3,6,7,4,5,1]=>[1,7,6,3,2,5,4,8]=>[2,1,1,2,2]
[8,2,3,1,5,4,7,6]=>[2,3,5,8,4,6,7,1]=>[7,6,4,1,5,3,2,8]=>[1,1,1,2,1,2]
[4,2,3,1,8,5,7,6]=>[8,2,1,3,6,7,4,5]=>[1,7,8,6,3,2,5,4]=>[3,1,1,2,1]
[4,1,3,2,8,6,7,5]=>[6,1,8,3,7,2,4,5]=>[3,8,1,6,2,7,5,4]=>[2,2,2,1,1]
[8,6,7,2,3,1,5,4]=>[4,5,8,6,2,7,3,1]=>[5,4,1,3,7,2,6,8]=>[1,1,3,3]
[8,5,7,2,6,3,4,1]=>[6,2,8,4,7,5,3,1]=>[3,7,1,5,2,4,6,8]=>[2,2,4]
[8,5,7,2,6,1,4,3]=>[8,4,2,6,7,5,3,1]=>[1,5,7,3,2,4,6,8]=>[3,1,4]
[8,2,7,5,6,1,4,3]=>[8,6,4,7,2,5,3,1]=>[1,3,5,2,7,4,6,8]=>[3,2,3]
[8,6,7,2,5,1,4,3]=>[8,4,6,2,7,5,3,1]=>[1,5,3,7,2,4,6,8]=>[2,2,4]
[8,6,7,1,5,2,4,3]=>[8,6,7,4,2,5,3,1]=>[1,3,2,5,7,4,6,8]=>[2,3,3]
[2,1,8,6,7,3,5,4]=>[8,6,4,7,1,5,2,3]=>[1,3,5,2,8,4,7,6]=>[3,2,2,1]
[2,1,8,3,7,5,6,4]=>[6,8,7,1,4,5,2,3]=>[3,1,2,8,5,4,7,6]=>[1,3,1,2,1]
[8,1,7,5,6,2,4,3]=>[8,6,4,7,5,2,3,1]=>[1,3,5,2,4,7,6,8]=>[3,3,2]
[8,1,7,2,6,4,5,3]=>[6,8,7,4,5,2,3,1]=>[3,1,2,5,4,7,6,8]=>[1,3,2,2]
[8,2,7,1,6,4,5,3]=>[6,8,7,2,4,5,3,1]=>[3,1,2,7,5,4,6,8]=>[1,3,1,3]
[8,2,7,4,6,1,5,3]=>[4,8,6,7,2,5,3,1]=>[5,1,3,2,7,4,6,8]=>[1,2,2,3]
[8,2,7,4,6,3,5,1]=>[4,6,8,7,2,5,3,1]=>[5,3,1,2,7,4,6,8]=>[1,1,3,3]
[8,4,7,2,6,3,5,1]=>[2,6,8,4,7,5,3,1]=>[7,3,1,5,2,4,6,8]=>[1,1,2,4]
[8,4,7,2,6,1,5,3]=>[2,8,4,6,7,5,3,1]=>[7,1,5,3,2,4,6,8]=>[1,2,1,4]
[8,4,7,1,6,2,5,3]=>[2,8,6,7,4,5,3,1]=>[7,1,3,2,5,4,6,8]=>[1,2,2,3]
[8,1,7,4,6,2,5,3]=>[4,8,6,7,5,2,3,1]=>[5,1,3,2,4,7,6,8]=>[1,2,3,2]
[8,5,7,1,6,2,4,3]=>[8,6,2,7,4,5,3,1]=>[1,3,7,2,5,4,6,8]=>[3,2,3]
[2,1,8,5,7,3,6,4]=>[4,8,6,7,1,5,2,3]=>[5,1,3,2,8,4,7,6]=>[1,2,2,2,1]
[8,5,7,4,6,1,3,2]=>[2,8,6,4,7,5,3,1]=>[7,1,3,5,2,4,6,8]=>[1,3,4]
[8,5,7,1,6,3,4,2]=>[6,2,8,7,4,5,3,1]=>[3,7,1,2,5,4,6,8]=>[2,3,3]
[8,1,7,4,6,3,5,2]=>[4,6,8,7,5,2,3,1]=>[5,3,1,2,4,7,6,8]=>[1,1,4,2]
[8,4,7,1,6,3,5,2]=>[2,6,8,7,4,5,3,1]=>[7,3,1,2,5,4,6,8]=>[1,1,3,3]
[8,4,7,3,6,1,5,2]=>[2,4,8,6,7,5,3,1]=>[7,5,1,3,2,4,6,8]=>[1,1,2,4]
[2,4,8,3,6,1,7,5]=>[8,2,4,6,1,5,7,3]=>[1,7,5,3,8,4,2,6]=>[2,1,2,1,2]
[6,5,8,1,3,2,7,4]=>[5,8,4,2,1,6,7,3]=>[4,1,5,7,8,3,2,6]=>[1,4,1,2]
[4,5,8,6,3,2,7,1]=>[6,1,2,5,4,8,7,3]=>[3,8,7,4,5,1,2,6]=>[2,1,2,3]
[6,5,8,7,3,1,2,4]=>[6,2,1,7,5,8,4,3]=>[3,7,8,2,4,1,5,6]=>[3,2,3]
[1,5,8,7,3,6,2,4]=>[2,5,7,8,6,4,1,3]=>[7,4,2,1,3,5,8,6]=>[1,1,1,4,1]
[1,7,2,8,4,6,5,3]=>[8,5,7,6,3,1,2,4]=>[1,4,2,3,6,8,7,5]=>[2,4,1,1]
[6,7,2,8,4,1,5,3]=>[8,6,3,1,5,2,7,4]=>[1,3,6,8,4,7,2,5]=>[4,2,2]
[3,6,2,8,4,5,7,1]=>[5,6,1,2,8,3,7,4]=>[4,3,8,7,1,6,2,5]=>[1,2,1,2,2]
[2,8,4,6,1,5,7,3]=>[3,6,8,5,1,4,7,2]=>[6,3,1,4,8,5,2,7]=>[1,1,3,1,2]
[6,3,1,8,4,5,7,2]=>[2,5,6,1,8,7,3,4]=>[7,4,3,8,1,2,6,5]=>[1,1,2,3,1]
[3,1,6,8,4,5,7,2]=>[5,1,3,6,8,7,2,4]=>[4,8,6,3,1,2,7,5]=>[2,1,1,3,1]
[2,3,6,8,4,5,7,1]=>[5,3,6,8,1,2,7,4]=>[4,6,3,1,8,7,2,5]=>[2,1,2,1,2]
[6,3,7,8,4,1,5,2]=>[8,6,2,1,5,3,7,4]=>[1,3,7,8,4,6,2,5]=>[4,2,2]
[1,3,7,8,4,6,5,2]=>[8,5,3,7,2,6,1,4]=>[1,4,6,2,7,3,8,5]=>[3,2,2,1]
[1,5,7,8,2,4,6,3]=>[2,6,8,5,3,7,1,4]=>[7,3,1,4,6,2,8,5]=>[1,1,3,2,1]
[5,1,7,8,2,4,6,3]=>[6,1,8,5,3,7,2,4]=>[3,8,1,4,6,2,7,5]=>[2,3,2,1]
[3,6,7,8,4,2,5,1]=>[2,6,5,1,3,8,7,4]=>[7,3,4,8,6,1,2,5]=>[1,3,1,3]
[7,6,1,8,4,2,5,3]=>[8,6,5,7,3,2,1,4]=>[1,3,4,2,6,7,8,5]=>[3,4,1]
[5,6,8,7,3,2,1,4]=>[1,2,7,6,5,8,4,3]=>[8,7,2,3,4,1,5,6]=>[1,1,3,3]
[2,8,3,7,1,6,5,4]=>[8,7,3,5,6,1,4,2]=>[1,2,6,4,3,8,5,7]=>[3,1,2,2]
[5,2,8,7,3,6,1,4]=>[5,1,7,8,6,2,4,3]=>[4,8,2,1,3,7,5,6]=>[2,1,3,2]
[7,2,1,8,4,6,5,3]=>[8,5,7,2,6,3,1,4]=>[1,4,2,7,3,6,8,5]=>[2,2,3,1]
[3,2,7,8,4,6,5,1]=>[8,5,1,3,7,2,6,4]=>[1,4,8,6,2,7,3,5]=>[3,1,2,2]
[5,2,7,8,1,4,6,3]=>[6,1,8,5,2,3,7,4]=>[3,8,1,4,7,6,2,5]=>[2,3,1,2]
[1,2,7,8,5,4,6,3]=>[6,5,3,8,7,1,2,4]=>[3,4,6,1,2,8,7,5]=>[3,3,1,1]
[4,2,1,3,8,5,6,7]=>[2,6,1,7,8,3,4,5]=>[7,3,8,2,1,6,5,4]=>[1,2,1,2,1,1]
[7,2,5,8,3,4,6,1]=>[5,3,6,8,2,1,7,4]=>[4,6,3,1,7,8,2,5]=>[2,1,3,2]
[6,2,8,5,4,3,1,7]=>[7,6,5,2,1,4,8,3]=>[2,3,4,7,8,5,1,6]=>[5,1,2]
[2,8,3,5,4,1,6,7]=>[6,3,5,1,4,7,8,2]=>[3,6,4,8,5,2,1,7]=>[2,2,1,1,2]
[2,8,4,5,3,1,6,7]=>[3,6,5,1,4,7,8,2]=>[6,3,4,8,5,2,1,7]=>[1,3,1,1,2]
[6,4,8,5,2,3,1,7]=>[2,5,1,7,6,4,8,3]=>[7,4,8,2,3,5,1,6]=>[1,2,3,2]
[7,3,5,8,2,4,6,1]=>[5,2,3,6,1,8,7,4]=>[4,7,6,3,8,1,2,5]=>[2,1,2,3]
[4,3,1,2,8,5,6,7]=>[6,2,1,7,8,3,4,5]=>[3,7,8,2,1,6,5,4]=>[3,1,2,1,1]
[3,4,2,1,8,5,6,7]=>[1,3,2,6,7,8,4,5]=>[8,6,7,3,2,1,5,4]=>[1,2,1,1,2,1]
[2,7,6,8,4,3,5,1]=>[6,5,3,2,8,1,7,4]=>[3,4,6,7,1,8,2,5]=>[4,2,2]
[5,7,1,8,3,4,6,2]=>[5,1,6,8,7,3,2,4]=>[4,8,3,1,2,6,7,5]=>[2,1,4,1]
[3,7,5,8,1,4,6,2]=>[6,3,8,1,5,2,7,4]=>[3,6,1,8,4,7,2,5]=>[2,2,2,2]
[1,7,5,8,3,4,6,2]=>[5,3,6,2,8,7,1,4]=>[4,6,3,7,1,2,8,5]=>[2,2,3,1]
[1,6,8,5,4,3,2,7]=>[2,7,6,5,4,8,1,3]=>[7,2,3,4,5,1,8,6]=>[1,4,2,1]
[4,6,8,5,1,3,2,7]=>[7,1,5,2,6,4,8,3]=>[2,8,4,7,3,5,1,6]=>[2,2,2,2]
[7,5,8,6,3,4,2,1]=>[2,5,1,8,7,6,4,3]=>[7,4,8,1,2,3,5,6]=>[1,2,5]
[2,4,8,3,6,5,1,7]=>[7,2,4,6,1,5,8,3]=>[2,7,5,3,8,4,1,6]=>[2,1,2,1,2]
[2,8,4,1,5,6,3,7]=>[5,3,7,1,4,6,8,2]=>[4,6,2,8,5,3,1,7]=>[2,2,1,1,2]
[4,1,8,3,5,6,2,7]=>[4,1,5,7,6,8,2,3]=>[5,8,4,2,3,1,7,6]=>[2,1,2,2,1]
[4,6,8,1,5,3,2,7]=>[7,1,6,4,2,5,8,3]=>[2,8,3,5,7,4,1,6]=>[2,3,1,2]
[1,6,8,4,5,3,2,7]=>[4,2,7,6,5,8,1,3]=>[5,7,2,3,4,1,8,6]=>[2,3,2,1]
[1,7,3,8,5,4,6,2]=>[6,5,8,3,2,7,1,4]=>[3,4,1,6,7,2,8,5]=>[2,3,2,1]
[3,7,1,8,5,4,6,2]=>[6,5,8,1,7,3,2,4]=>[3,4,1,8,2,6,7,5]=>[2,2,3,1]
[2,7,3,8,4,6,5,1]=>[8,5,7,3,1,2,6,4]=>[1,4,2,6,8,7,3,5]=>[2,3,1,2]
[7,1,3,8,4,6,5,2]=>[8,5,7,3,6,2,1,4]=>[1,4,2,6,3,7,8,5]=>[2,2,3,1]
[5,7,8,4,3,6,1,2]=>[7,1,5,4,2,8,6,3]=>[2,8,4,5,7,1,3,6]=>[2,3,3]
[2,8,7,4,1,6,5,3]=>[4,8,7,5,6,1,3,2]=>[5,1,2,4,3,8,6,7]=>[1,3,2,2]
[2,8,5,4,3,1,6,7]=>[6,5,4,1,3,7,8,2]=>[3,4,5,8,6,2,1,7]=>[4,1,1,2]
[4,1,3,2,8,5,6,7]=>[3,6,1,7,8,2,4,5]=>[6,3,8,2,1,7,5,4]=>[1,2,1,2,1,1]
[1,4,3,2,8,5,6,7]=>[3,2,6,7,8,1,4,5]=>[6,7,3,2,1,8,5,4]=>[2,1,1,2,1,1]
[6,4,8,2,5,3,1,7]=>[2,7,4,1,6,5,8,3]=>[7,2,5,8,3,4,1,6]=>[1,3,2,2]
[2,8,4,3,5,1,6,7]=>[4,3,6,1,5,7,8,2]=>[5,6,3,8,4,2,1,7]=>[2,2,1,1,2]
[2,8,3,4,5,1,6,7]=>[3,4,6,1,5,7,8,2]=>[6,5,3,8,4,2,1,7]=>[1,1,2,1,1,2]
[6,2,8,4,5,3,1,7]=>[4,7,6,2,1,5,8,3]=>[5,2,3,7,8,4,1,6]=>[1,4,1,2]
[7,2,3,8,5,4,6,1]=>[6,5,8,2,3,1,7,4]=>[3,4,1,7,6,8,2,5]=>[2,2,2,2]
[4,2,3,1,8,5,6,7]=>[2,3,1,6,7,8,4,5]=>[7,6,8,3,2,1,5,4]=>[1,2,1,1,2,1]
[3,2,1,4,8,5,6,7]=>[2,1,6,7,8,3,4,5]=>[7,8,3,2,1,6,5,4]=>[2,1,1,2,1,1]
[5,1,3,2,4,8,6,7]=>[3,7,8,2,1,4,5,6]=>[6,2,1,7,8,5,4,3]=>[1,1,3,1,1,1]
[1,2,8,4,5,3,7,6]=>[4,5,8,6,7,1,2,3]=>[5,4,1,3,2,8,7,6]=>[1,1,2,2,1,1]
[1,8,4,2,5,3,6,7]=>[6,4,3,5,7,8,1,2]=>[3,5,6,4,2,1,8,7]=>[3,1,1,2,1]
[8,1,5,3,2,4,6,7]=>[5,4,6,2,3,7,8,1]=>[4,5,3,7,6,2,1,8]=>[2,2,1,1,2]
[3,8,1,5,2,4,6,7]=>[1,5,6,3,4,7,8,2]=>[8,4,3,6,5,2,1,7]=>[1,1,2,1,1,2]
[3,5,1,4,8,2,6,7]=>[1,4,6,2,7,8,3,5]=>[8,5,3,7,2,1,6,4]=>[1,1,2,1,2,1]
[1,5,2,8,4,3,6,7]=>[6,5,2,7,8,1,3,4]=>[3,4,7,2,1,8,6,5]=>[3,1,2,1,1]
[1,2,8,5,4,3,6,7]=>[6,5,4,7,8,1,2,3]=>[3,4,5,2,1,8,7,6]=>[3,1,2,1,1]
[1,2,5,4,3,8,6,7]=>[4,3,7,8,1,2,5,6]=>[5,6,2,1,8,7,4,3]=>[2,1,2,1,1,1]
[1,2,4,8,5,3,7,6]=>[5,8,3,6,7,1,2,4]=>[4,1,6,3,2,8,7,5]=>[1,2,1,2,1,1]
[1,2,7,4,8,5,3,6]=>[7,4,6,3,8,1,2,5]=>[2,5,3,6,1,8,7,4]=>[2,2,2,1,1]
[1,5,2,7,8,4,3,6]=>[2,7,6,4,8,1,3,5]=>[7,2,3,5,1,8,6,4]=>[1,3,2,1,1]
[5,1,2,7,4,8,3,6]=>[5,7,4,1,8,2,3,6]=>[4,2,5,8,1,7,6,3]=>[1,3,2,1,1]
[8,3,5,1,4,7,2,6]=>[2,5,7,3,8,4,6,1]=>[7,4,2,6,1,5,3,8]=>[1,1,2,2,2]
[1,2,8,5,7,4,3,6]=>[4,7,6,8,5,1,2,3]=>[5,2,3,1,4,8,7,6]=>[1,2,3,1,1]
[1,2,4,8,7,5,3,6]=>[7,6,8,3,5,1,2,4]=>[2,3,1,6,4,8,7,5]=>[2,2,2,1,1]
[2,8,1,4,3,7,6,5]=>[8,4,7,1,3,5,6,2]=>[1,5,2,8,6,4,3,7]=>[2,2,1,1,2]
[6,1,2,8,7,4,3,5]=>[7,6,8,5,2,1,3,4]=>[2,3,1,4,7,8,6,5]=>[2,4,1,1]
[6,4,1,2,8,7,3,5]=>[7,2,8,6,3,1,4,5]=>[2,7,1,3,6,8,5,4]=>[2,4,1,1]
[3,6,4,8,1,7,2,5]=>[3,7,1,2,8,5,6,4]=>[6,2,8,7,1,4,3,5]=>[1,2,1,2,2]
[7,1,6,2,8,4,3,5]=>[7,6,8,4,2,3,1,5]=>[2,3,1,5,7,6,8,4]=>[2,3,2,1]
[1,6,7,2,8,4,3,5]=>[7,6,2,8,4,1,3,5]=>[2,3,7,1,5,8,6,4]=>[3,3,1,1]
[6,7,1,4,2,8,3,5]=>[7,4,8,3,1,5,2,6]=>[2,5,1,6,8,4,7,3]=>[2,3,2,1]
[6,3,7,1,4,8,2,5]=>[2,5,7,1,8,4,3,6]=>[7,4,2,8,1,5,6,3]=>[1,1,2,3,1]
[3,7,8,1,5,2,4,6]=>[6,7,1,4,5,2,8,3]=>[3,2,8,5,4,7,1,6]=>[1,2,1,2,2]
[7,1,2,8,5,3,4,6]=>[6,7,5,8,2,3,1,4]=>[3,2,4,1,7,6,8,5]=>[1,2,2,2,1]
[1,7,2,8,4,5,3,6]=>[5,7,6,8,3,1,2,4]=>[4,2,3,1,6,8,7,5]=>[1,2,3,1,1]
[1,4,2,7,8,5,3,6]=>[7,2,6,4,8,1,3,5]=>[2,7,3,5,1,8,6,4]=>[2,2,2,1,1]
[6,4,1,2,8,3,7,5]=>[8,6,2,7,3,1,4,5]=>[1,3,7,2,6,8,5,4]=>[3,3,1,1]
[7,6,1,3,2,4,8,5]=>[4,8,3,5,6,2,1,7]=>[5,1,6,4,3,7,8,2]=>[1,2,1,3,1]
[6,7,1,3,2,4,8,5]=>[4,8,3,5,1,6,2,7]=>[5,1,6,4,8,3,7,2]=>[1,2,2,2,1]
[1,2,7,3,5,8,4,6]=>[5,7,8,4,1,2,3,6]=>[4,2,1,5,8,7,6,3]=>[1,1,3,1,1,1]
[1,2,7,5,8,3,4,6]=>[6,4,7,3,8,1,2,5]=>[3,5,2,6,1,8,7,4]=>[2,2,2,1,1]
[5,8,1,3,7,2,4,6]=>[4,6,1,7,8,3,5,2]=>[5,3,8,2,1,6,4,7]=>[1,2,1,2,2]
[1,2,5,8,7,3,4,6]=>[3,6,7,8,5,1,2,4]=>[6,3,2,1,4,8,7,5]=>[1,1,1,3,1,1]
[1,2,5,8,3,7,4,6]=>[3,7,8,5,6,1,2,4]=>[6,2,1,4,3,8,7,5]=>[1,1,2,2,1,1]
[2,8,1,7,3,5,4,6]=>[7,5,6,8,1,3,4,2]=>[2,4,3,1,8,6,5,7]=>[2,1,2,1,2]
[8,6,1,3,2,4,7,5]=>[4,8,3,5,6,2,7,1]=>[5,1,6,4,3,7,2,8]=>[1,2,1,2,2]
[4,2,8,1,7,3,6,5]=>[1,8,6,7,2,4,5,3]=>[8,1,3,2,7,5,4,6]=>[1,2,2,1,2]
[2,8,1,7,4,3,6,5]=>[5,8,6,7,1,3,4,2]=>[4,1,3,2,8,6,5,7]=>[1,2,2,1,2]
[7,1,2,8,4,3,6,5]=>[5,8,6,7,2,3,1,4]=>[4,1,3,2,7,6,8,5]=>[1,2,2,2,1]
[1,2,8,4,7,5,3,6]=>[7,4,6,8,5,1,2,3]=>[2,5,3,1,4,8,7,6]=>[2,1,3,1,1]
[1,2,8,7,4,5,3,6]=>[5,7,6,8,4,1,2,3]=>[4,2,3,1,5,8,7,6]=>[1,2,3,1,1]
[2,8,1,7,5,3,4,6]=>[6,7,5,8,1,3,4,2]=>[3,2,4,1,8,6,5,7]=>[1,2,2,1,2]
[8,3,7,1,5,2,4,6]=>[2,6,7,4,5,8,3,1]=>[7,3,2,5,4,1,6,8]=>[1,1,2,1,3]
[3,8,6,1,4,7,2,5]=>[5,7,8,1,4,3,6,2]=>[4,2,1,8,5,6,3,7]=>[1,1,2,2,2]
[8,6,1,4,2,7,3,5]=>[7,4,8,3,5,2,6,1]=>[2,5,1,6,4,7,3,8]=>[2,2,2,2]
[7,1,2,8,6,4,3,5]=>[7,6,8,5,2,3,1,4]=>[2,3,1,4,7,6,8,5]=>[2,3,2,1]
[7,4,1,2,8,6,3,5]=>[7,2,8,6,3,4,1,5]=>[2,7,1,3,6,5,8,4]=>[2,3,2,1]
[3,7,4,8,1,6,2,5]=>[3,7,8,1,5,2,6,4]=>[6,2,1,8,4,7,3,5]=>[1,1,2,2,2]
[3,4,8,7,1,6,2,5]=>[7,8,1,2,5,6,4,3]=>[2,1,8,7,4,3,5,6]=>[1,2,1,1,3]
[4,2,8,1,7,6,3,5]=>[1,7,8,6,2,4,5,3]=>[8,2,1,3,7,5,4,6]=>[1,1,3,1,2]
[2,8,1,7,6,4,3,5]=>[7,6,8,5,1,3,4,2]=>[2,3,1,4,8,6,5,7]=>[2,3,1,2]
[7,8,3,4,1,5,2,6]=>[3,7,5,4,6,1,8,2]=>[6,2,4,5,3,8,1,7]=>[1,3,2,2]
[7,8,3,4,1,6,2,5]=>[3,7,4,8,5,1,6,2]=>[6,2,5,1,4,8,3,7]=>[1,2,3,2]
[6,8,3,4,1,7,2,5]=>[3,7,4,1,8,5,6,2]=>[6,2,5,8,1,4,3,7]=>[1,3,2,2]
[6,7,3,4,1,8,2,5]=>[3,7,4,1,8,5,2,6]=>[6,2,5,8,1,4,7,3]=>[1,3,3,1]
[5,7,3,4,1,8,2,6]=>[3,1,7,4,8,5,2,6]=>[6,8,2,5,1,4,7,3]=>[2,2,3,1]
[5,8,3,4,1,7,2,6]=>[3,1,7,4,8,5,6,2]=>[6,8,2,5,1,4,3,7]=>[2,2,2,2]
[5,8,3,4,1,6,2,7]=>[3,1,7,5,4,6,8,2]=>[6,8,2,4,5,3,1,7]=>[2,3,1,2]
[6,8,3,4,1,5,2,7]=>[3,7,5,4,1,6,8,2]=>[6,2,4,5,8,3,1,7]=>[1,4,1,2]
[6,7,3,4,1,5,2,8]=>[3,7,5,4,1,6,2,8]=>[6,2,4,5,8,3,7,1]=>[1,4,2,1]
[5,7,3,4,1,6,2,8]=>[3,1,7,5,4,6,2,8]=>[6,8,2,4,5,3,7,1]=>[2,3,2,1]
[5,6,2,8,3,4,1,7]=>[5,1,7,3,2,6,8,4]=>[4,8,2,6,7,3,1,5]=>[2,3,1,2]
[4,6,2,8,3,5,1,7]=>[1,5,7,3,2,6,8,4]=>[8,4,2,6,7,3,1,5]=>[1,1,3,1,2]
[4,7,3,5,1,6,2,8]=>[1,3,7,5,4,6,2,8]=>[8,6,2,4,5,3,7,1]=>[1,1,3,2,1]
[4,8,3,5,1,6,2,7]=>[1,3,7,5,4,6,8,2]=>[8,6,2,4,5,3,1,7]=>[1,1,3,1,2]
[4,8,3,5,1,7,2,6]=>[1,3,7,4,8,5,6,2]=>[8,6,2,5,1,4,3,7]=>[1,1,2,2,2]
[5,6,2,3,1,7,4,8]=>[3,4,1,7,5,2,6,8]=>[6,5,8,2,4,7,3,1]=>[1,2,3,1,1]
[5,6,2,4,1,8,3,7]=>[7,3,1,4,2,8,5,6]=>[2,6,8,5,7,1,4,3]=>[3,2,2,1]
[5,6,2,4,1,7,3,8]=>[7,3,1,5,4,2,6,8]=>[2,6,8,4,5,7,3,1]=>[3,3,1,1]
[4,6,2,5,1,7,3,8]=>[1,7,3,5,4,2,6,8]=>[8,2,6,4,5,7,3,1]=>[1,2,3,1,1]
[4,6,2,5,1,8,3,7]=>[1,7,3,4,2,8,5,6]=>[8,2,6,5,7,1,4,3]=>[1,2,2,2,1]
[4,5,1,8,3,7,2,6]=>[1,5,2,7,8,6,3,4]=>[8,4,7,2,1,3,6,5]=>[1,2,1,3,1]
[4,5,1,7,3,8,2,6]=>[1,5,2,7,4,8,3,6]=>[8,4,7,2,5,1,6,3]=>[1,2,2,2,1]
[4,6,2,7,3,8,1,5]=>[1,5,7,3,2,4,8,6]=>[8,4,2,6,7,5,1,3]=>[1,1,3,1,2]
[5,6,2,7,3,8,1,4]=>[5,1,7,3,2,4,8,6]=>[4,8,2,6,7,5,1,3]=>[2,3,1,2]
[5,6,2,7,4,8,1,3]=>[1,7,5,3,2,4,8,6]=>[8,2,4,6,7,5,1,3]=>[1,4,1,2]
[5,6,3,8,4,7,1,2]=>[1,7,3,2,5,8,6,4]=>[8,2,6,7,4,1,3,5]=>[1,3,1,3]
[5,6,2,8,3,7,1,4]=>[5,1,7,2,8,3,6,4]=>[4,8,2,7,1,6,3,5]=>[2,2,2,2]
[4,6,2,8,3,7,1,5]=>[1,5,7,2,8,3,6,4]=>[8,4,2,7,1,6,3,5]=>[1,1,2,2,2]
[4,5,1,7,3,6,2,8]=>[1,5,2,7,6,3,4,8]=>[8,4,7,2,3,6,5,1]=>[1,2,3,1,1]
[4,5,1,8,3,6,2,7]=>[1,5,2,7,6,8,3,4]=>[8,4,7,2,3,1,6,5]=>[1,2,2,2,1]
[9,2,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[7,8,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,2]
[10,2,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[8,9,7,6,5,4,3,2,1,10]=>[2,1,1,1,1,1,1,2]
[9,2,3,1,4,5,6,7,8]=>[2,4,3,5,6,7,8,9,1]=>[8,6,7,5,4,3,2,1,9]=>[1,2,1,1,1,1,2]
[4,2,3,5,6,7,8,9,1]=>[2,3,1,4,5,6,7,9,8]=>[8,7,9,6,5,4,3,1,2]=>[1,2,1,1,1,1,2]
[3,4,2,5,6,7,8,9,1]=>[1,3,2,4,5,6,7,9,8]=>[9,7,8,6,5,4,3,1,2]=>[1,2,1,1,1,1,2]
[3,2,4,5,6,7,8,9,10,1]=>[2,1,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,1,1,1,1,1,2]
[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,2]
[6,5,3,2,1,4,8,7]=>[4,3,8,5,2,1,6,7]=>[5,6,1,4,7,8,3,2]=>[2,4,1,1]
[4,6,3,5,2,1,8,7]=>[1,3,5,4,2,8,6,7]=>[8,6,4,5,7,1,3,2]=>[1,1,3,2,1]
[8,7,3,5,2,4,1,6]=>[3,5,7,6,4,8,2,1]=>[6,4,2,3,5,1,7,8]=>[1,1,3,3]
[6,8,2,4,5,7,3,1]=>[4,5,1,8,3,7,6,2]=>[5,4,8,1,6,2,3,7]=>[1,2,2,3]
[8,7,2,4,5,3,1,6]=>[4,7,3,6,5,8,2,1]=>[5,2,6,3,4,1,7,8]=>[1,2,2,3]
[3,6,1,4,5,2,8,7]=>[1,4,5,8,3,2,6,7]=>[8,5,4,1,6,7,3,2]=>[1,1,1,3,1,1]
[6,3,8,4,5,7,2,1]=>[4,5,1,8,2,7,6,3]=>[5,4,8,1,7,2,3,6]=>[1,2,2,3]
[5,8,7,4,3,6,2,1]=>[5,1,4,8,7,6,3,2]=>[4,8,5,1,2,3,6,7]=>[2,1,5]
[2,8,7,4,3,6,1,5]=>[5,4,7,8,6,1,3,2]=>[4,5,2,1,3,8,6,7]=>[2,1,3,2]
[8,1,7,4,3,6,2,5]=>[5,4,7,8,6,2,3,1]=>[4,5,2,1,3,7,6,8]=>[2,1,3,2]
[2,1,6,8,5,7,4,3]=>[3,5,8,7,1,6,2,4]=>[6,4,1,2,8,3,7,5]=>[1,1,3,2,1]
[6,8,3,5,1,7,4,2]=>[8,3,1,7,5,4,6,2]=>[1,6,8,2,4,5,3,7]=>[3,3,2]
[5,1,8,4,7,6,3,2]=>[1,8,4,7,6,5,2,3]=>[8,1,5,2,3,4,7,6]=>[1,2,4,1]
[2,5,8,4,7,6,3,1]=>[8,2,4,7,6,1,5,3]=>[1,7,5,2,3,8,4,6]=>[2,1,3,2]
[4,3,8,1,5,6,7,2]=>[2,1,5,6,8,4,7,3]=>[7,8,4,3,1,5,2,6]=>[2,1,1,2,2]
[4,8,1,3,5,6,7,2]=>[4,1,5,6,8,3,7,2]=>[5,8,4,3,1,6,2,7]=>[2,1,1,2,2]
[5,8,7,4,1,6,3,2]=>[8,1,7,5,4,6,3,2]=>[1,8,2,4,5,3,6,7]=>[2,3,3]
[5,8,3,6,1,4,7,2]=>[3,1,6,8,5,4,7,2]=>[6,8,3,1,4,5,2,7]=>[2,1,3,2]
[4,8,3,6,1,2,7,5]=>[1,3,8,5,6,4,7,2]=>[8,6,1,4,3,5,2,7]=>[1,1,2,2,2]
[3,8,1,2,5,6,7,4]=>[1,5,6,8,3,4,7,2]=>[8,4,3,1,6,5,2,7]=>[1,1,1,2,1,2]
[8,7,1,4,2,6,3,5]=>[7,4,8,3,5,6,2,1]=>[2,5,1,6,4,3,7,8]=>[2,2,1,3]
[8,6,3,1,2,4,7,5]=>[8,4,3,5,6,2,7,1]=>[1,5,6,4,3,7,2,8]=>[3,1,2,2]
[8,1,7,4,5,2,3,6]=>[6,4,7,5,8,2,3,1]=>[3,5,2,4,1,7,6,8]=>[2,2,2,2]
[2,8,7,4,5,1,3,6]=>[6,4,7,5,8,1,3,2]=>[3,5,2,4,1,8,6,7]=>[2,2,2,2]
[8,7,2,4,1,6,3,5]=>[7,3,4,8,5,6,2,1]=>[2,6,5,1,4,3,7,8]=>[2,1,2,3]
[5,8,3,6,2,4,7,1]=>[3,1,5,6,4,8,7,2]=>[6,8,4,3,5,1,2,7]=>[2,1,2,3]
[8,6,3,2,1,4,7,5]=>[4,3,8,5,6,2,7,1]=>[5,6,1,4,3,7,2,8]=>[2,2,2,2]
[8,7,3,5,2,1,4,6]=>[3,6,5,7,4,8,2,1]=>[6,3,4,2,5,1,7,8]=>[1,2,2,3]
[5,8,3,6,2,1,7,4]=>[3,1,5,8,6,4,7,2]=>[6,8,4,1,3,5,2,7]=>[2,1,3,2]
[5,8,7,4,2,6,1,3]=>[1,5,7,4,8,6,3,2]=>[8,4,2,5,1,3,6,7]=>[1,1,2,4]
[2,6,8,4,5,7,1,3]=>[4,2,7,5,8,1,6,3]=>[5,7,2,4,1,8,3,6]=>[2,2,2,2]
[6,1,8,4,5,7,2,3]=>[4,7,5,1,8,6,2,3]=>[5,2,4,8,1,3,7,6]=>[1,3,3,1]
[6,8,3,5,1,7,2,4]=>[3,7,1,8,5,4,6,2]=>[6,2,8,1,4,5,3,7]=>[1,2,3,2]
[2,1,5,8,3,6,7,4]=>[3,6,8,1,5,7,2,4]=>[6,3,1,8,4,2,7,5]=>[1,1,2,1,2,1]
[5,8,3,6,1,2,7,4]=>[3,1,8,5,6,4,7,2]=>[6,8,1,4,3,5,2,7]=>[2,2,2,2]
[4,1,8,2,5,6,7,3]=>[5,1,6,8,4,7,2,3]=>[4,8,3,1,5,2,7,6]=>[2,1,2,2,1]
[2,4,8,1,5,6,7,3]=>[2,5,6,8,1,4,7,3]=>[7,4,3,1,8,5,2,6]=>[1,1,1,2,1,2]
[4,8,2,1,5,6,7,3]=>[3,1,5,6,8,4,7,2]=>[6,8,4,3,1,5,2,7]=>[2,1,1,2,2]
[3,4,8,2,5,6,7,1]=>[1,2,4,5,6,8,7,3]=>[8,7,5,4,3,1,2,6]=>[1,1,1,1,1,3]
[5,8,1,4,7,6,2,3]=>[4,1,7,8,6,3,5,2]=>[5,8,2,1,3,6,4,7]=>[2,1,3,2]
[4,5,3,8,6,1,7,2]=>[1,2,8,3,6,5,7,4]=>[8,7,1,6,3,4,2,5]=>[1,1,2,2,2]
[3,4,1,8,5,6,7,2]=>[1,2,5,6,8,7,3,4]=>[8,7,4,3,1,2,6,5]=>[1,1,1,1,3,1]
[3,4,8,9,10,1,2,5,6,7]=>[6,7,8,1,2,3,9,4,10,5]=>[5,4,3,10,9,8,2,7,1,6]=>[1,1,2,1,1,2,2]
[4,7,8,9,10,1,2,3,5,6]=>[6,7,1,2,8,3,9,4,10,5]=>[5,4,10,9,3,8,2,7,1,6]=>[1,2,1,2,2,2]
[4,5,9,10,11,12,1,2,3,6,7,8]=>[7,8,9,1,2,3,10,4,11,5,12,6]=>[6,5,4,12,11,10,3,9,2,8,1,7]=>[1,1,2,1,1,2,2,2]
[5,8,9,10,11,12,1,2,3,4,6,7]=>[7,8,1,2,9,3,10,4,11,5,12,6]=>[6,5,12,11,4,10,3,9,2,8,1,7]=>[1,2,1,2,2,2,2]
[7,8,9,10,11,12,1,2,3,4,5,6]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[6,12,5,11,4,10,3,9,2,8,1,7]=>[2,2,2,2,2,2]
[4,5,7,6,2,3,8,1]=>[1,2,5,6,4,3,8,7]=>[8,7,4,3,5,6,1,2]=>[1,1,1,3,2]
[3,5,7,2,6,4,8,1]=>[2,6,1,4,5,3,8,7]=>[7,3,8,5,4,6,1,2]=>[1,2,1,2,2]
[2,5,7,3,6,4,8,1]=>[2,6,4,5,1,3,8,7]=>[7,3,5,4,8,6,1,2]=>[1,2,2,1,2]
[1,5,7,3,6,8,4,2]=>[2,5,8,4,3,7,1,6]=>[7,4,1,5,6,2,8,3]=>[1,1,3,2,1]
[8,4,3,7,6,1,5,2]=>[2,8,3,6,7,5,4,1]=>[7,1,6,3,2,4,5,8]=>[1,2,1,4]
[6,7,2,3,5,4,8,1]=>[6,3,4,1,5,2,8,7]=>[3,6,5,8,4,7,1,2]=>[2,2,2,2]
[5,2,7,3,6,4,8,1]=>[6,4,1,5,2,3,8,7]=>[3,5,8,4,7,6,1,2]=>[3,2,1,2]
[8,3,4,7,6,1,5,2]=>[8,2,3,6,7,5,4,1]=>[1,7,6,3,2,4,5,8]=>[2,1,1,4]
[8,2,4,7,1,6,5,3]=>[8,3,7,2,5,6,4,1]=>[1,6,2,7,4,3,5,8]=>[2,2,1,3]
[3,1,4,7,6,8,5,2]=>[5,1,4,8,3,7,2,6]=>[4,8,5,1,6,2,7,3]=>[2,1,2,2,1]
[4,1,3,7,6,8,5,2]=>[1,5,4,8,3,7,2,6]=>[8,4,5,1,6,2,7,3]=>[1,2,2,2,1]
[5,1,7,3,6,8,4,2]=>[5,1,8,4,3,7,2,6]=>[4,8,1,5,6,2,7,3]=>[2,3,2,1]
[6,7,1,3,5,8,4,2]=>[5,8,4,1,7,3,2,6]=>[4,1,5,8,2,6,7,3]=>[1,3,3,1]
[5,8,7,3,6,1,4,2]=>[1,4,8,6,7,5,3,2]=>[8,5,1,3,2,4,6,7]=>[1,1,2,4]
[4,8,3,7,6,1,5,2]=>[8,1,3,6,7,5,4,2]=>[1,8,6,3,2,4,5,7]=>[2,1,1,4]
[3,8,4,7,6,1,5,2]=>[8,3,6,7,1,5,4,2]=>[1,6,3,2,8,4,5,7]=>[2,1,2,3]
[2,8,4,7,1,6,5,3]=>[8,3,7,5,6,1,4,2]=>[1,6,2,4,3,8,5,7]=>[2,2,2,2]
[8,1,4,7,2,6,5,3]=>[8,3,7,5,6,2,4,1]=>[1,6,2,4,3,7,5,8]=>[2,2,2,2]
[8,1,3,2,7,6,5,4]=>[8,7,3,6,2,4,5,1]=>[1,2,6,3,7,5,4,8]=>[3,2,1,2]
[2,8,3,1,7,6,5,4]=>[8,7,3,6,1,4,5,2]=>[1,2,6,3,8,5,4,7]=>[3,2,1,2]
[6,7,1,2,8,5,4,3]=>[8,7,6,3,1,4,2,5]=>[1,2,3,6,8,5,7,4]=>[5,2,1]
[8,2,3,1,7,6,5,4]=>[8,7,2,3,6,4,5,1]=>[1,2,7,6,3,5,4,8]=>[3,1,2,2]
[8,3,2,1,7,6,5,4]=>[8,2,7,3,6,4,5,1]=>[1,7,2,6,3,5,4,8]=>[2,2,2,2]
[3,4,1,7,6,8,5,2]=>[5,1,2,4,8,7,3,6]=>[4,8,7,5,1,2,6,3]=>[2,1,1,3,1]
[1,4,2,7,8,6,5,3]=>[4,8,2,7,6,1,3,5]=>[5,1,7,2,3,8,6,4]=>[1,2,3,1,1]
[8,4,2,7,1,6,5,3]=>[2,8,7,3,5,6,4,1]=>[7,1,2,6,4,3,5,8]=>[1,3,1,3]
[8,5,7,2,1,6,4,3]=>[8,4,2,7,5,6,3,1]=>[1,5,7,2,4,3,6,8]=>[3,2,3]
[1,5,7,2,8,6,4,3]=>[8,2,7,6,4,1,3,5]=>[1,7,2,3,5,8,6,4]=>[2,4,1,1]
[2,5,7,1,8,6,4,3]=>[8,2,7,6,1,4,3,5]=>[1,7,2,3,8,5,6,4]=>[2,3,2,1]
[3,5,7,1,6,8,4,2]=>[2,5,8,1,7,4,3,6]=>[7,4,1,8,2,5,6,3]=>[1,1,2,3,1]
[6,7,4,5,8,1,3,2]=>[3,1,8,6,4,2,7,5]=>[6,8,1,3,5,7,2,4]=>[2,4,2]
[5,4,7,6,8,1,3,2]=>[1,8,2,6,4,3,7,5]=>[8,1,7,3,5,6,2,4]=>[1,2,3,2]
[2,5,7,8,1,6,4,3]=>[8,2,7,5,1,3,6,4]=>[1,7,2,4,8,6,3,5]=>[2,3,1,2]
[8,5,7,1,2,6,4,3]=>[8,7,4,2,5,6,3,1]=>[1,2,5,7,4,3,6,8]=>[4,1,3]
[8,4,1,7,2,6,5,3]=>[2,8,7,5,6,3,4,1]=>[7,1,2,4,3,6,5,8]=>[1,3,2,2]
[1,4,8,7,2,6,5,3]=>[8,7,2,5,6,4,1,3]=>[1,2,7,4,3,5,8,6]=>[3,1,3,1]
[3,4,8,7,6,1,5,2]=>[8,6,7,1,2,5,4,3]=>[1,3,2,8,7,4,5,6]=>[2,2,1,3]
[4,3,8,7,6,1,5,2]=>[8,1,6,7,2,5,4,3]=>[1,8,3,2,7,4,5,6]=>[2,1,2,3]
[5,3,7,8,6,1,4,2]=>[1,8,6,2,3,7,5,4]=>[8,1,3,7,6,2,4,5]=>[1,3,1,3]
[6,7,2,8,1,5,4,3]=>[8,7,3,1,5,2,6,4]=>[1,2,6,8,4,7,3,5]=>[4,2,2]
[5,2,7,8,1,6,4,3]=>[1,8,7,5,2,3,6,4]=>[8,1,2,4,7,6,3,5]=>[1,4,1,2]
[4,2,8,7,1,6,5,3]=>[8,1,7,5,6,2,4,3]=>[1,8,2,4,3,7,5,6]=>[2,2,2,2]
[3,2,8,1,7,6,5,4]=>[8,7,1,6,2,4,5,3]=>[1,2,8,3,7,5,4,6]=>[3,2,1,2]
[1,3,8,2,7,6,5,4]=>[8,7,6,2,4,5,1,3]=>[1,2,3,7,5,4,8,6]=>[4,1,2,1]
[1,2,8,3,7,6,5,4]=>[8,7,6,4,5,1,2,3]=>[1,2,3,5,4,8,7,6]=>[4,2,1,1]
[2,1,8,3,7,6,5,4]=>[8,7,6,1,4,5,2,3]=>[1,2,3,8,5,4,7,6]=>[4,1,2,1]
[4,1,8,7,2,6,5,3]=>[8,1,7,5,6,4,2,3]=>[1,8,2,4,3,5,7,6]=>[2,2,3,1]
[5,1,7,8,2,6,4,3]=>[1,8,7,5,3,6,2,4]=>[8,1,2,4,6,3,7,5]=>[1,4,2,1]
[6,7,1,8,2,5,4,3]=>[8,7,5,1,6,3,2,4]=>[1,2,4,8,3,6,7,5]=>[4,3,1]
[5,8,7,1,2,6,4,3]=>[1,8,7,4,5,6,3,2]=>[8,1,2,5,4,3,6,7]=>[1,3,1,3]
[4,8,1,7,2,6,5,3]=>[8,1,7,5,6,3,4,2]=>[1,8,2,4,3,6,5,7]=>[2,2,2,2]
[3,8,1,2,7,6,5,4]=>[8,7,1,6,3,4,5,2]=>[1,2,8,3,6,5,4,7]=>[3,2,1,2]
[2,8,1,3,7,6,5,4]=>[8,7,6,1,3,4,5,2]=>[1,2,3,8,6,5,4,7]=>[4,1,1,2]
[1,8,2,3,7,6,5,4]=>[8,7,6,3,4,5,1,2]=>[1,2,3,6,5,4,8,7]=>[4,1,2,1]
[8,1,2,3,7,6,5,4]=>[8,7,6,2,3,4,5,1]=>[1,2,3,7,6,5,4,8]=>[4,1,1,2]
[2,3,4,5,6,7,8,9,10,12,1,11]=>[1,2,3,4,5,6,7,8,9,11,12,10]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[1,1,1,1,1,1,1,1,1,1,2]
[6,7,1,8,4,5,2,3]=>[7,5,1,8,6,3,2,4]=>[2,4,8,1,3,6,7,5]=>[3,4,1]
[3,7,1,5,8,2,6,4]=>[4,8,1,6,7,3,2,5]=>[5,1,8,3,2,6,7,4]=>[1,2,1,3,1]
[2,7,1,5,8,3,6,4]=>[4,8,6,7,1,3,2,5]=>[5,1,3,2,8,6,7,4]=>[1,2,2,2,1]
[2,6,5,1,8,3,7,4]=>[8,6,3,1,2,7,4,5]=>[1,3,6,8,7,2,5,4]=>[4,1,2,1]
[3,6,5,1,8,2,7,4]=>[8,6,1,3,2,7,4,5]=>[1,3,8,6,7,2,5,4]=>[3,2,2,1]
[4,6,5,1,8,7,2,3]=>[7,1,3,2,8,6,4,5]=>[2,8,6,7,1,3,5,4]=>[2,2,3,1]
[5,6,4,1,8,7,2,3]=>[1,7,3,2,8,6,4,5]=>[8,2,6,7,1,3,5,4]=>[1,3,3,1]
[8,1,4,5,7,6,2,3]=>[3,4,7,8,6,2,5,1]=>[6,5,2,1,3,7,4,8]=>[1,1,1,3,2]
[6,4,5,1,8,7,2,3]=>[2,7,3,1,8,6,4,5]=>[7,2,6,8,1,3,5,4]=>[1,3,3,1]
[4,5,6,1,8,7,2,3]=>[1,2,7,3,8,6,4,5]=>[8,7,2,6,1,3,5,4]=>[1,1,2,3,1]
[3,5,6,1,8,2,7,4]=>[2,8,1,6,3,7,4,5]=>[7,1,8,3,6,2,5,4]=>[1,2,2,2,1]
[2,5,6,1,8,3,7,4]=>[2,8,6,1,3,7,4,5]=>[7,1,3,8,6,2,5,4]=>[1,3,1,2,1]
[2,4,6,1,3,8,7,5]=>[8,2,7,1,4,3,5,6]=>[1,7,2,8,5,6,4,3]=>[2,2,2,1,1]
[3,4,6,1,2,8,7,5]=>[8,1,2,7,4,3,5,6]=>[1,8,7,2,5,6,4,3]=>[2,1,3,1,1]
[4,3,6,1,2,8,7,5]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[1,2,3,1,1]
[5,3,6,1,8,2,7,4]=>[8,2,1,6,3,7,4,5]=>[1,7,8,3,6,2,5,4]=>[3,2,2,1]
[7,3,1,5,8,2,6,4]=>[2,4,8,6,7,3,1,5]=>[7,5,1,3,2,6,8,4]=>[1,1,2,3,1]
[8,1,3,5,7,2,6,4]=>[4,8,3,6,7,2,5,1]=>[5,1,6,3,2,7,4,8]=>[1,2,1,2,2]
[7,2,1,5,8,3,6,4]=>[4,8,2,6,7,3,1,5]=>[5,1,7,3,2,6,8,4]=>[1,2,1,3,1]
[6,2,5,1,8,3,7,4]=>[8,6,2,3,1,7,4,5]=>[1,3,7,6,8,2,5,4]=>[3,2,2,1]
[2,3,6,1,4,8,7,5]=>[8,7,1,2,4,3,5,6]=>[1,2,8,7,5,6,4,3]=>[3,1,2,1,1]
[4,2,5,3,1,8,7,6]=>[3,1,8,2,4,7,5,6]=>[6,8,1,7,5,2,4,3]=>[2,2,1,2,1]
[6,2,4,1,3,8,7,5]=>[3,8,2,7,4,1,5,6]=>[6,1,7,2,5,8,4,3]=>[1,2,3,1,1]
[7,2,1,4,3,8,6,5]=>[8,2,4,7,3,5,1,6]=>[1,7,5,2,6,4,8,3]=>[2,1,2,2,1]
[8,1,2,4,3,7,6,5]=>[8,4,7,2,3,5,6,1]=>[1,5,2,7,6,4,3,8]=>[2,2,1,1,2]
[8,1,3,4,2,7,6,5]=>[8,3,4,7,2,5,6,1]=>[1,6,5,2,7,4,3,8]=>[2,1,2,1,2]
[4,6,3,1,2,8,7,5]=>[1,3,8,7,4,2,5,6]=>[8,6,1,2,5,7,4,3]=>[1,1,4,1,1]
[3,6,4,1,2,8,7,5]=>[3,8,1,7,4,2,5,6]=>[6,1,8,2,5,7,4,3]=>[1,2,3,1,1]
[2,7,1,4,3,8,6,5]=>[8,4,7,1,3,5,2,6]=>[1,5,2,8,6,4,7,3]=>[2,2,1,2,1]
[3,7,1,4,2,8,6,5]=>[8,1,4,7,3,5,2,6]=>[1,8,5,2,6,4,7,3]=>[2,1,2,2,1]
[4,7,1,3,2,8,6,5]=>[1,8,4,7,3,5,2,6]=>[8,1,5,2,6,4,7,3]=>[1,2,2,2,1]
[8,1,6,7,2,3,5,4]=>[8,5,6,3,7,2,4,1]=>[1,4,3,6,2,7,5,8]=>[2,2,2,2]
[4,7,1,2,3,8,6,5]=>[1,8,7,3,4,5,2,6]=>[8,1,2,6,5,4,7,3]=>[1,3,1,2,1]
[2,7,1,3,4,8,6,5]=>[8,7,1,3,4,5,2,6]=>[1,2,8,6,5,4,7,3]=>[3,1,1,2,1]
[2,6,3,1,4,8,7,5]=>[8,3,7,1,4,2,5,6]=>[1,6,2,8,5,7,4,3]=>[2,2,2,1,1]
[3,6,2,1,4,8,7,5]=>[8,1,3,7,4,2,5,6]=>[1,8,6,2,5,7,4,3]=>[2,1,3,1,1]
[5,6,2,1,8,3,7,4]=>[8,3,1,6,2,7,4,5]=>[1,6,8,3,7,2,5,4]=>[3,2,2,1]
[6,5,2,1,8,3,7,4]=>[8,3,6,2,1,7,4,5]=>[1,6,3,7,8,2,5,4]=>[2,3,2,1]
[8,1,5,2,7,3,6,4]=>[8,6,3,7,2,4,5,1]=>[1,3,6,2,7,5,4,8]=>[3,2,1,2]
[8,1,4,2,3,7,6,5]=>[3,8,7,2,4,5,6,1]=>[6,1,2,7,5,4,3,8]=>[1,3,1,1,2]
[7,4,1,2,3,8,6,5]=>[8,7,3,2,4,5,1,6]=>[1,2,6,7,5,4,8,3]=>[4,1,2,1]
[6,4,2,1,3,8,7,5]=>[8,3,2,7,4,1,5,6]=>[1,6,7,2,5,8,4,3]=>[3,3,1,1]
[5,4,2,3,1,8,7,6]=>[8,3,2,1,4,7,5,6]=>[1,6,7,8,5,2,4,3]=>[4,1,2,1]
[3,5,2,4,1,8,7,6]=>[8,1,3,2,4,7,5,6]=>[1,8,6,7,5,2,4,3]=>[2,2,1,2,1]
[6,3,2,1,4,8,7,5]=>[2,8,3,7,4,1,5,6]=>[7,1,6,2,5,8,4,3]=>[1,2,3,1,1]
[8,1,3,2,4,7,6,5]=>[8,3,7,2,4,5,6,1]=>[1,6,2,7,5,4,3,8]=>[2,2,1,1,2]
[8,1,2,3,4,7,6,5]=>[8,7,2,3,4,5,6,1]=>[1,2,7,6,5,4,3,8]=>[3,1,1,1,2]
[6,2,3,1,4,8,7,5]=>[8,2,3,7,4,1,5,6]=>[1,7,6,2,5,8,4,3]=>[2,1,3,1,1]
[2,4,3,6,1,5,8,7]=>[2,8,1,3,5,4,6,7]=>[7,1,8,6,4,5,3,2]=>[1,2,1,2,1,1]
[2,4,3,6,5,8,1,7]=>[2,5,1,3,4,7,8,6]=>[7,4,8,6,5,2,1,3]=>[1,2,1,1,1,2]
[2,4,6,3,5,8,7,1]=>[8,2,4,1,3,5,7,6]=>[1,7,5,8,6,4,2,3]=>[2,2,1,1,2]
[2,4,6,3,5,8,1,7]=>[2,4,5,1,3,7,8,6]=>[7,5,4,8,6,2,1,3]=>[1,1,2,1,1,2]
[2,4,6,3,5,1,8,7]=>[2,4,5,1,3,8,6,7]=>[7,5,4,8,6,1,3,2]=>[1,1,2,1,2,1]
[2,4,6,3,1,5,8,7]=>[2,4,8,1,5,3,6,7]=>[7,5,1,8,4,6,3,2]=>[1,1,2,2,1,1]
[2,4,1,6,5,3,8,7]=>[2,5,1,4,8,3,6,7]=>[7,4,8,5,1,6,3,2]=>[1,2,1,2,1,1]
[2,4,6,1,5,3,8,7]=>[2,5,8,1,4,3,6,7]=>[7,4,1,8,5,6,3,2]=>[1,1,2,2,1,1]
[4,2,6,5,3,1,8,7]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[1,3,1,2,1]
[4,2,6,5,1,3,8,7]=>[1,8,5,2,4,3,6,7]=>[8,1,4,7,5,6,3,2]=>[1,3,2,1,1]
[4,2,6,5,1,8,7,3]=>[1,4,3,8,2,7,5,6]=>[8,5,6,1,7,2,4,3]=>[1,2,2,2,1]
[4,2,6,5,8,1,7,3]=>[1,4,3,8,2,6,7,5]=>[8,5,6,1,7,3,2,4]=>[1,2,2,1,2]
[4,2,6,5,8,1,3,7]=>[1,6,4,2,3,7,8,5]=>[8,3,5,7,6,2,1,4]=>[1,3,1,1,2]
[4,2,6,5,8,3,1,7]=>[1,4,3,7,2,6,8,5]=>[8,5,6,2,7,3,1,4]=>[1,2,2,1,2]
[2,4,1,6,5,8,3,7]=>[2,5,1,4,7,8,3,6]=>[7,4,8,5,2,1,6,3]=>[1,2,1,1,2,1]
[2,1,4,6,5,8,3,7]=>[5,1,3,4,7,8,2,6]=>[4,8,6,5,2,1,7,3]=>[2,1,1,1,2,1]
[2,4,1,6,5,8,7,3]=>[2,4,8,1,5,7,3,6]=>[7,5,1,8,4,2,6,3]=>[1,1,2,1,2,1]
[2,4,6,1,5,8,7,3]=>[8,2,5,1,3,7,4,6]=>[1,7,4,8,6,2,5,3]=>[2,2,1,2,1]
[4,2,6,5,3,8,7,1]=>[1,4,3,8,2,5,7,6]=>[8,5,6,1,7,4,2,3]=>[1,2,2,1,2]
[2,6,4,3,8,7,1,5]=>[3,7,2,8,1,4,6,5]=>[6,2,7,1,8,5,3,4]=>[1,2,2,1,2]
[2,6,4,3,8,7,5,1]=>[8,3,2,7,1,4,6,5]=>[1,6,7,2,8,5,3,4]=>[3,2,1,2]
[4,2,6,8,5,3,7,1]=>[1,3,6,5,8,2,7,4]=>[8,6,3,4,1,7,2,5]=>[1,1,2,2,2]
[2,4,6,8,1,5,7,3]=>[6,2,3,8,1,5,7,4]=>[3,7,6,1,8,4,2,5]=>[2,1,2,1,2]
[2,4,6,1,8,5,7,3]=>[6,2,3,8,1,7,4,5]=>[3,7,6,1,8,2,5,4]=>[2,1,2,2,1]
[2,4,1,6,8,5,7,3]=>[2,4,6,8,1,7,3,5]=>[7,5,3,1,8,2,6,4]=>[1,1,1,2,2,1]
[2,1,4,6,8,5,7,3]=>[4,6,8,1,3,7,2,5]=>[5,3,1,8,6,2,7,4]=>[1,1,2,1,2,1]
[2,1,4,6,8,5,3,7]=>[4,7,1,3,6,8,2,5]=>[5,2,8,6,3,1,7,4]=>[1,2,1,1,2,1]
[2,4,1,6,8,5,3,7]=>[2,4,7,1,6,8,3,5]=>[7,5,2,8,3,1,6,4]=>[1,1,2,1,2,1]
[2,4,6,1,8,5,3,7]=>[7,2,6,1,3,8,4,5]=>[2,7,3,8,6,1,5,4]=>[2,2,1,2,1]
[2,4,6,8,1,5,3,7]=>[7,2,5,1,3,6,8,4]=>[2,7,4,8,6,3,1,5]=>[2,2,1,1,2]
[4,2,6,8,5,3,1,7]=>[1,3,7,6,2,5,8,4]=>[8,6,2,3,7,4,1,5]=>[1,1,3,1,2]
[4,2,6,8,5,1,7,3]=>[1,3,8,6,2,5,7,4]=>[8,6,1,3,7,4,2,5]=>[1,1,3,1,2]
[2,4,6,8,3,5,7,1]=>[5,2,3,6,8,1,7,4]=>[4,7,6,3,1,8,2,5]=>[2,1,1,2,2]
[2,4,6,8,3,5,1,7]=>[5,2,3,7,1,6,8,4]=>[4,7,6,2,8,3,1,5]=>[2,1,2,1,2]
[2,4,6,8,3,1,5,7]=>[6,2,5,1,3,7,8,4]=>[3,7,4,8,6,2,1,5]=>[2,2,1,1,2]
[2,4,6,3,1,8,5,7]=>[2,4,7,1,3,8,5,6]=>[7,5,2,8,6,1,4,3]=>[1,1,2,1,2,1]
[2,4,6,3,8,1,5,7]=>[2,4,6,1,3,7,8,5]=>[7,5,3,8,6,2,1,4]=>[1,1,2,1,1,2]
[2,4,6,3,8,5,1,7]=>[7,2,4,1,3,6,8,5]=>[2,7,5,8,6,3,1,4]=>[2,2,1,1,2]
[2,4,6,3,8,5,7,1]=>[6,2,3,8,1,4,7,5]=>[3,7,6,1,8,5,2,4]=>[2,1,2,1,2]
[2,4,3,6,8,5,7,1]=>[2,4,6,8,1,3,7,5]=>[7,5,3,1,8,6,2,4]=>[1,1,1,2,1,2]
[2,4,3,6,8,5,1,7]=>[2,4,7,1,3,6,8,5]=>[7,5,2,8,6,3,1,4]=>[1,1,2,1,1,2]
[2,4,3,6,8,1,5,7]=>[2,6,1,3,4,7,8,5]=>[7,3,8,6,5,2,1,4]=>[1,2,1,1,1,2]
[2,4,3,6,1,8,5,7]=>[2,7,1,3,4,8,5,6]=>[7,2,8,6,5,1,4,3]=>[1,2,1,1,2,1]
[2,4,3,1,6,8,5,7]=>[3,1,2,5,7,8,4,6]=>[6,8,7,4,2,1,5,3]=>[2,1,1,1,2,1]
[2,4,1,3,6,8,7,5]=>[2,8,1,5,7,3,4,6]=>[7,1,8,4,2,6,5,3]=>[1,2,1,2,1,1]
[2,4,3,6,1,8,7,5]=>[2,4,8,1,3,7,5,6]=>[7,5,1,8,6,2,4,3]=>[1,1,2,1,2,1]
[2,4,3,6,8,1,7,5]=>[2,4,8,1,3,6,7,5]=>[7,5,1,8,6,3,2,4]=>[1,1,2,1,1,2]
[4,6,5,2,8,7,3,1]=>[3,1,2,8,7,4,6,5]=>[6,8,7,1,2,5,3,4]=>[2,1,3,2]
[4,6,5,2,8,7,1,3]=>[7,1,3,2,8,4,6,5]=>[2,8,6,7,1,5,3,4]=>[2,2,2,2]
[4,6,2,5,8,7,1,3]=>[1,4,7,2,8,3,6,5]=>[8,5,2,7,1,6,3,4]=>[1,1,2,2,2]
[4,6,2,5,8,7,3,1]=>[8,1,4,2,7,3,6,5]=>[1,8,5,7,2,6,3,4]=>[2,2,2,2]
[2,4,6,3,8,1,7,5]=>[8,2,4,1,3,6,7,5]=>[1,7,5,8,6,3,2,4]=>[2,2,1,1,2]
[2,4,6,3,1,8,7,5]=>[8,2,4,1,3,7,5,6]=>[1,7,5,8,6,2,4,3]=>[2,2,1,2,1]
[2,4,1,6,3,8,7,5]=>[2,4,8,1,7,3,5,6]=>[7,5,1,8,2,6,4,3]=>[1,1,2,2,1,1]
[2,1,4,6,3,8,7,5]=>[4,8,1,3,7,2,5,6]=>[5,1,8,6,2,7,4,3]=>[1,2,1,2,1,1]
[2,1,4,6,8,3,7,5]=>[4,8,1,3,6,7,2,5]=>[5,1,8,6,3,2,7,4]=>[1,2,1,1,2,1]
[2,4,1,6,8,3,7,5]=>[2,4,8,1,6,7,3,5]=>[7,5,1,8,3,2,6,4]=>[1,1,2,1,2,1]
[2,4,6,1,8,3,7,5]=>[8,2,6,1,3,7,4,5]=>[1,7,3,8,6,2,5,4]=>[2,2,1,2,1]
[2,4,6,8,1,3,7,5]=>[8,2,5,1,3,6,7,4]=>[1,7,4,8,6,3,2,5]=>[2,2,1,1,2]
[2,4,6,8,3,1,7,5]=>[5,2,3,8,1,6,7,4]=>[4,7,6,1,8,3,2,5]=>[2,1,2,1,2]
[4,6,2,8,5,7,3,1]=>[5,1,2,8,7,3,6,4]=>[4,8,7,1,2,6,3,5]=>[2,1,3,2]
[4,6,2,8,5,7,1,3]=>[7,1,5,2,8,3,6,4]=>[2,8,4,7,1,6,3,5]=>[2,2,2,2]
[6,2,4,8,7,1,3,5]=>[3,6,7,1,8,2,5,4]=>[6,3,2,8,1,7,4,5]=>[1,1,2,2,2]
[6,4,2,8,7,5,3,1]=>[8,2,1,7,6,3,5,4]=>[1,7,8,2,3,6,4,5]=>[3,3,2]
[2,6,4,8,1,7,5,3]=>[8,3,2,7,1,5,6,4]=>[1,6,7,2,8,4,3,5]=>[3,2,1,2]
[2,6,4,1,8,7,5,3]=>[8,3,2,7,1,6,4,5]=>[1,6,7,2,8,3,5,4]=>[3,2,2,1]
[2,6,1,4,8,7,5,3]=>[8,7,4,1,2,6,3,5]=>[1,2,5,8,7,3,6,4]=>[4,1,2,1]
[2,1,6,4,8,7,5,3]=>[3,8,7,1,4,6,2,5]=>[6,1,2,8,5,3,7,4]=>[1,3,1,2,1]
[2,1,6,4,8,7,3,5]=>[7,3,8,1,4,6,2,5]=>[2,6,1,8,5,3,7,4]=>[2,2,1,2,1]
[2,6,1,4,8,7,3,5]=>[7,8,4,1,2,6,3,5]=>[2,1,5,8,7,3,6,4]=>[1,3,1,2,1]
[2,6,4,1,8,7,3,5]=>[3,7,2,8,1,6,4,5]=>[6,2,7,1,8,3,5,4]=>[1,2,2,2,1]
[2,6,4,8,1,7,3,5]=>[3,7,2,8,1,5,6,4]=>[6,2,7,1,8,4,3,5]=>[1,2,2,1,2]
[6,4,2,8,7,5,1,3]=>[2,7,1,8,6,3,5,4]=>[7,2,8,1,3,6,4,5]=>[1,2,3,2]
[6,2,4,8,7,3,5,1]=>[6,8,3,1,7,2,5,4]=>[3,1,6,8,2,7,4,5]=>[1,3,2,2]
[6,2,4,8,7,3,1,5]=>[7,3,6,1,8,2,5,4]=>[2,6,3,8,1,7,4,5]=>[2,2,2,2]
[1,6,4,7,3,8,2,5]=>[3,5,2,7,4,8,1,6]=>[6,4,7,2,5,1,8,3]=>[1,2,2,2,1]
[1,3,7,4,5,8,2,6]=>[4,5,7,2,3,8,1,6]=>[5,4,2,7,6,1,8,3]=>[1,1,2,1,2,1]
[5,2,4,7,3,6,8,1]=>[3,5,1,6,2,4,8,7]=>[6,4,8,3,7,5,1,2]=>[1,2,2,1,2]
[1,7,6,3,4,8,2,5]=>[4,5,7,3,2,8,1,6]=>[5,4,2,6,7,1,8,3]=>[1,1,3,2,1]
[8,1,6,3,7,2,4,5]=>[4,6,7,3,8,2,5,1]=>[5,3,2,6,1,7,4,8]=>[1,1,2,2,2]
[7,1,6,3,8,2,4,5]=>[4,6,7,3,8,2,1,5]=>[5,3,2,6,1,7,8,4]=>[1,1,2,3,1]
[1,2,7,4,8,3,5,6]=>[4,6,7,3,8,1,2,5]=>[5,3,2,6,1,8,7,4]=>[1,1,2,2,1,1]
[6,1,7,3,4,8,2,5]=>[4,5,7,3,1,8,2,6]=>[5,4,2,6,8,1,7,3]=>[1,1,3,2,1]
[2,1,7,4,5,8,3,6]=>[4,5,7,1,3,8,2,6]=>[5,4,2,8,6,1,7,3]=>[1,1,2,1,2,1]
[4,3,1,7,5,8,2,6]=>[2,1,5,7,4,8,3,6]=>[7,8,4,2,5,1,6,3]=>[2,1,2,2,1]
[2,8,6,3,7,1,4,5]=>[4,6,7,3,8,1,5,2]=>[5,3,2,6,1,8,4,7]=>[1,1,2,2,2]
[6,8,1,3,7,2,4,5]=>[4,6,7,1,8,3,5,2]=>[5,3,2,8,1,6,4,7]=>[1,1,2,2,2]
[5,8,2,1,7,3,4,6]=>[3,6,1,7,8,4,5,2]=>[6,3,8,2,1,5,4,7]=>[1,2,1,2,2]
[5,7,2,1,8,3,4,6]=>[3,6,1,7,8,4,2,5]=>[6,3,8,2,1,5,7,4]=>[1,2,1,3,1]
[4,3,6,1,5,8,2,7]=>[2,1,5,7,3,8,4,6]=>[7,8,4,2,6,1,5,3]=>[2,1,2,2,1]
[2,6,1,4,5,8,3,7]=>[4,5,7,1,2,8,3,6]=>[5,4,2,8,7,1,6,3]=>[1,1,2,1,2,1]
[6,5,1,3,4,8,2,7]=>[4,5,7,2,1,8,3,6]=>[5,4,2,7,8,1,6,3]=>[1,1,3,2,1]
[1,6,2,4,8,3,5,7]=>[4,6,7,2,8,1,3,5]=>[5,3,2,7,1,8,6,4]=>[1,1,2,2,1,1]
[6,4,2,1,5,8,3,7]=>[3,5,2,7,1,8,4,6]=>[6,4,7,2,8,1,5,3]=>[1,2,2,2,1]
[2,5,3,4,1,8,6,7]=>[3,4,1,2,7,8,5,6]=>[6,5,8,7,2,1,4,3]=>[1,2,1,1,2,1]
[4,3,5,2,1,8,6,7]=>[2,1,4,3,7,8,5,6]=>[7,8,5,6,2,1,4,3]=>[2,2,1,2,1]
[1,6,4,8,7,2,3,5]=>[3,6,2,7,8,5,1,4]=>[6,3,7,2,1,4,8,5]=>[1,2,1,3,1]
[2,7,8,3,6,1,4,5]=>[4,6,7,2,8,1,5,3]=>[5,3,2,7,1,8,4,6]=>[1,1,2,2,2]
[4,8,2,5,1,3,7,6]=>[1,8,3,5,4,6,7,2]=>[8,1,6,4,5,3,2,7]=>[1,2,2,1,2]
[4,7,2,5,1,3,8,6]=>[1,8,3,5,4,6,2,7]=>[8,1,6,4,5,3,7,2]=>[1,2,2,2,1]
[3,8,2,1,5,4,7,6]=>[1,3,5,8,4,6,7,2]=>[8,6,4,1,5,3,2,7]=>[1,1,1,2,1,2]
[8,3,2,1,5,4,6,7]=>[3,2,6,4,5,7,8,1]=>[6,7,3,5,4,2,1,8]=>[2,2,1,1,2]
[8,3,2,1,6,4,5,7]=>[3,2,6,7,4,5,8,1]=>[6,7,3,2,5,4,1,8]=>[2,1,2,1,2]
[8,4,2,5,1,6,3,7]=>[7,3,2,5,4,6,8,1]=>[2,6,7,4,5,3,1,8]=>[3,2,1,2]
[8,3,2,1,5,6,4,7]=>[3,2,5,7,4,6,8,1]=>[6,7,4,2,5,3,1,8]=>[2,1,2,1,2]
[3,8,2,1,4,5,7,6]=>[1,3,8,4,5,6,7,2]=>[8,6,1,5,4,3,2,7]=>[1,1,2,1,1,2]
[3,7,2,1,4,5,8,6]=>[1,3,8,4,5,6,2,7]=>[8,6,1,5,4,3,7,2]=>[1,1,2,1,2,1]
[3,2,7,1,4,6,8,5]=>[1,6,8,2,4,5,3,7]=>[8,3,1,7,5,4,6,2]=>[1,1,2,1,2,1]
[3,2,8,1,4,6,7,5]=>[1,6,8,2,4,5,7,3]=>[8,3,1,7,5,4,2,6]=>[1,1,2,1,1,2]
[3,2,8,1,4,7,6,5]=>[8,1,7,2,4,5,6,3]=>[1,8,2,7,5,4,3,6]=>[2,2,1,1,2]
[3,8,2,1,4,7,5,6]=>[1,3,7,8,4,5,6,2]=>[8,6,2,1,5,4,3,7]=>[1,1,1,2,1,2]
[3,8,2,1,5,7,4,6]=>[1,3,5,7,8,4,6,2]=>[8,6,4,2,1,5,3,7]=>[1,1,1,1,2,2]
[4,8,2,5,1,7,3,6]=>[1,7,3,4,8,5,6,2]=>[8,2,6,5,1,4,3,7]=>[1,2,1,2,2]
[4,7,2,5,1,8,3,6]=>[1,7,3,4,8,5,2,6]=>[8,2,6,5,1,4,7,3]=>[1,2,1,3,1]
[3,7,2,1,5,8,4,6]=>[1,3,5,7,8,4,2,6]=>[8,6,4,2,1,5,7,3]=>[1,1,1,1,3,1]
[3,7,2,1,4,8,5,6]=>[1,3,7,8,4,5,2,6]=>[8,6,2,1,5,4,7,3]=>[1,1,1,2,2,1]
[3,2,1,7,5,8,6,4]=>[8,1,5,2,4,7,3,6]=>[1,8,4,7,5,2,6,3]=>[2,2,1,2,1]
[3,2,7,1,6,8,4,5]=>[7,1,5,8,2,4,3,6]=>[2,8,4,1,7,5,6,3]=>[2,1,2,2,1]
[4,3,7,6,8,1,2,5]=>[1,6,7,2,4,3,8,5]=>[8,3,2,7,5,6,1,4]=>[1,1,2,2,2]
[3,2,8,1,6,7,4,5]=>[7,1,5,8,2,4,6,3]=>[2,8,4,1,7,5,3,6]=>[2,1,2,1,2]
[3,2,1,8,7,5,6,4]=>[6,8,1,7,2,5,3,4]=>[3,1,8,2,7,4,6,5]=>[1,2,2,2,1]
[3,8,2,1,7,4,5,6]=>[1,3,6,7,8,4,5,2]=>[8,6,3,2,1,5,4,7]=>[1,1,1,1,2,2]
[3,2,8,1,7,4,6,5]=>[8,1,6,7,2,4,5,3]=>[1,8,3,2,7,5,4,6]=>[2,1,2,1,2]
[3,2,8,1,6,4,7,5]=>[8,1,6,2,4,5,7,3]=>[1,8,3,7,5,4,2,6]=>[2,2,1,1,2]
[3,2,7,1,6,4,8,5]=>[8,1,6,2,4,5,3,7]=>[1,8,3,7,5,4,6,2]=>[2,2,1,2,1]
[4,2,7,6,1,3,8,5]=>[1,8,5,6,2,4,3,7]=>[8,1,4,3,7,5,6,2]=>[1,2,2,2,1]
[4,2,8,6,1,3,7,5]=>[1,8,5,6,2,4,7,3]=>[8,1,4,3,7,5,2,6]=>[1,2,2,1,2]
[4,2,8,7,1,3,6,5]=>[1,8,5,6,7,2,4,3]=>[8,1,4,3,2,7,5,6]=>[1,2,1,2,2]
[5,7,8,3,4,1,2,6]=>[1,6,4,7,5,2,8,3]=>[8,3,5,2,4,7,1,6]=>[1,2,3,2]
[4,2,6,8,1,3,7,5]=>[1,8,5,2,3,6,7,4]=>[8,1,4,7,6,3,2,5]=>[1,3,1,1,2]
[3,2,6,1,8,4,7,5]=>[8,1,6,2,3,7,4,5]=>[1,8,3,7,6,2,5,4]=>[2,2,1,2,1]
[3,7,2,1,8,5,4,6]=>[7,1,3,6,8,4,2,5]=>[2,8,6,3,1,5,7,4]=>[2,1,1,3,1]
[4,7,3,8,5,1,2,6]=>[1,3,6,7,5,2,8,4]=>[8,6,3,2,4,7,1,5]=>[1,1,1,3,2]
[4,3,7,8,6,1,2,5]=>[1,6,7,2,3,8,5,4]=>[8,3,2,7,6,1,4,5]=>[1,1,2,1,3]
[3,2,7,1,8,6,4,5]=>[7,8,1,6,2,4,3,5]=>[2,1,8,3,7,5,6,4]=>[1,2,2,2,1]
[3,2,1,6,8,5,7,4]=>[1,4,6,8,2,7,3,5]=>[8,5,3,1,7,2,6,4]=>[1,1,1,2,2,1]
[3,2,6,1,8,7,4,5]=>[7,1,3,8,2,6,4,5]=>[2,8,6,1,7,3,5,4]=>[2,1,2,2,1]
[4,2,6,8,1,7,3,5]=>[1,7,3,8,2,5,6,4]=>[8,2,6,1,7,4,3,5]=>[1,2,2,1,2]
[4,3,6,8,7,1,2,5]=>[1,6,2,3,7,8,5,4]=>[8,3,7,6,2,1,4,5]=>[1,2,1,1,3]
[4,2,6,7,1,8,3,5]=>[1,7,3,8,2,5,4,6]=>[8,2,6,1,7,4,5,3]=>[1,2,2,2,1]
[3,2,6,1,7,8,4,5]=>[7,1,5,2,3,8,4,6]=>[2,8,4,7,6,1,5,3]=>[2,2,1,2,1]
[3,4,6,8,7,5,1,2]=>[3,7,8,1,2,6,5,4]=>[6,2,1,8,7,3,4,5]=>[1,1,2,1,3]
[5,3,6,4,8,7,1,2]=>[4,2,1,3,7,8,6,5]=>[5,7,8,6,2,1,3,4]=>[3,1,1,3]
[1,2,7,5,4,8,6,3]=>[4,8,5,3,7,1,2,6]=>[5,1,4,6,2,8,7,3]=>[1,3,2,1,1]
[6,3,7,5,4,8,1,2]=>[7,5,2,1,4,3,8,6]=>[2,4,7,8,5,6,1,3]=>[4,2,2]
[7,3,8,5,4,6,1,2]=>[7,5,2,4,1,8,6,3]=>[2,4,7,5,8,1,3,6]=>[3,2,3]
[3,8,7,5,4,6,1,2]=>[7,5,4,8,1,6,3,2]=>[2,4,5,1,8,3,6,7]=>[3,2,3]
[4,3,6,7,8,5,1,2]=>[1,3,7,2,4,8,6,5]=>[8,6,2,7,5,1,3,4]=>[1,1,2,1,3]
[4,5,6,3,8,7,1,2]=>[1,2,4,3,7,8,6,5]=>[8,7,5,6,2,1,3,4]=>[1,1,2,1,3]
[3,6,8,5,4,7,1,2]=>[2,7,5,1,4,8,6,3]=>[7,2,4,8,5,1,3,6]=>[1,3,1,3]
[7,6,3,5,4,8,1,2]=>[7,3,5,4,2,1,8,6]=>[2,6,4,5,7,8,1,3]=>[2,4,2]
[1,6,2,5,4,8,7,3]=>[4,8,5,2,7,1,3,6]=>[5,1,4,7,2,8,6,3]=>[1,3,2,1,1]
[7,1,2,5,8,3,6,4]=>[4,8,6,7,2,3,1,5]=>[5,1,3,2,7,6,8,4]=>[1,2,2,2,1]
[1,8,2,5,7,3,6,4]=>[4,8,6,7,3,5,1,2]=>[5,1,3,2,6,4,8,7]=>[1,2,2,2,1]
[6,2,1,5,4,8,7,3]=>[4,8,2,5,1,7,3,6]=>[5,1,7,4,8,2,6,3]=>[1,2,2,2,1]
[4,1,6,2,8,7,5,3]=>[1,3,8,7,6,2,4,5]=>[8,6,1,2,3,7,5,4]=>[1,1,4,1,1]
[7,8,1,2,4,6,5,3]=>[8,5,7,3,4,1,6,2]=>[1,4,2,6,5,8,3,7]=>[2,2,2,2]
[7,8,3,1,4,2,6,5]=>[5,3,8,4,6,1,7,2]=>[4,6,1,5,3,8,2,7]=>[2,2,2,2]
[4,3,6,1,8,2,7,5]=>[1,8,2,6,3,7,4,5]=>[8,1,7,3,6,2,5,4]=>[1,2,2,2,1]
[2,3,8,5,4,1,6,7]=>[6,5,1,2,4,7,8,3]=>[3,4,8,7,5,2,1,6]=>[3,1,1,1,2]
[4,8,1,5,2,3,7,6]=>[1,8,5,3,4,6,7,2]=>[8,1,4,6,5,3,2,7]=>[1,3,1,1,2]
[7,5,1,6,4,3,2,8]=>[7,6,5,3,2,4,1,8]=>[2,3,4,6,7,5,8,1]=>[5,2,1]
[6,1,5,7,4,3,2,8]=>[3,7,6,5,2,1,4,8]=>[6,2,3,4,7,8,5,1]=>[1,5,1,1]
[1,5,8,6,4,3,2,7]=>[7,2,6,5,4,8,1,3]=>[2,7,3,4,5,1,8,6]=>[2,3,2,1]
[3,4,6,1,5,8,2,7]=>[1,2,5,7,3,8,4,6]=>[8,7,4,2,6,1,5,3]=>[1,1,1,2,2,1]
[7,8,5,1,6,3,2,4]=>[7,6,8,4,3,1,5,2]=>[2,3,1,5,6,8,4,7]=>[2,4,2]
[2,6,1,5,7,3,8,4]=>[4,8,6,1,3,2,5,7]=>[5,1,3,8,6,7,4,2]=>[1,3,2,1,1]
[1,6,8,7,4,3,2,5]=>[2,7,6,5,8,4,1,3]=>[7,2,3,4,1,5,8,6]=>[1,3,3,1]
[6,8,1,7,4,3,2,5]=>[7,6,5,1,8,3,4,2]=>[2,3,4,8,1,6,5,7]=>[4,2,2]
[5,6,1,7,4,3,2,8]=>[1,7,6,5,3,2,4,8]=>[8,2,3,4,6,7,5,1]=>[1,5,1,1]
[5,1,7,6,4,3,2,8]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[1,5,1,1]
[6,1,7,8,4,3,2,5]=>[7,6,5,3,1,8,2,4]=>[2,3,4,6,8,1,7,5]=>[5,2,1]
[7,1,8,6,4,3,2,5]=>[7,6,5,8,4,2,1,3]=>[2,3,4,1,5,7,8,6]=>[3,4,1]
[1,8,7,6,4,3,2,5]=>[7,6,5,8,4,3,1,2]=>[2,3,4,1,5,6,8,7]=>[3,4,1]
[2,1,7,5,6,3,8,4]=>[4,8,6,1,5,2,3,7]=>[5,1,3,8,4,7,6,2]=>[1,3,2,1,1]
[3,1,6,7,5,8,2,4]=>[3,7,1,5,4,8,2,6]=>[6,2,8,4,5,1,7,3]=>[1,2,2,2,1]
[7,8,1,6,5,3,2,4]=>[7,6,8,5,3,1,4,2]=>[2,3,1,4,6,8,5,7]=>[2,4,2]
[7,8,2,1,4,5,6,3]=>[3,5,6,8,4,1,7,2]=>[6,4,3,1,5,8,2,7]=>[1,1,1,3,2]
[7,2,1,5,4,6,8,3]=>[5,2,4,6,8,3,1,7]=>[4,7,5,3,1,6,8,2]=>[2,1,1,3,1]
[1,2,8,5,6,3,7,4]=>[4,8,6,5,7,1,2,3]=>[5,1,3,4,2,8,7,6]=>[1,3,2,1,1]
[6,1,2,5,7,3,8,4]=>[4,8,6,2,3,1,5,7]=>[5,1,3,7,6,8,4,2]=>[1,3,2,1,1]
[4,2,1,5,6,3,7,8]=>[2,4,1,6,3,5,7,8]=>[7,5,8,3,6,4,2,1]=>[1,2,2,1,1,1]
[1,3,6,8,5,7,2,4]=>[3,7,5,8,2,6,1,4]=>[6,2,4,1,7,3,8,5]=>[1,2,2,2,1]
[2,4,6,3,7,1,8,5]=>[8,2,4,1,3,6,5,7]=>[1,7,5,8,6,3,4,2]=>[2,2,1,2,1]
[1,3,6,4,8,7,2,5]=>[7,3,8,2,4,6,1,5]=>[2,6,1,7,5,3,8,4]=>[2,2,1,2,1]
[4,1,6,7,3,8,2,5]=>[1,5,3,7,4,8,2,6]=>[8,4,6,2,5,1,7,3]=>[1,2,2,2,1]
[6,4,1,5,2,3,7,8]=>[5,6,3,2,4,1,7,8]=>[4,3,6,7,5,8,2,1]=>[1,3,2,1,1]
[4,1,7,5,2,3,8,6]=>[1,8,5,4,6,2,3,7]=>[8,1,4,5,3,7,6,2]=>[1,3,2,1,1]
[1,2,4,5,8,3,7,6]=>[8,3,4,6,7,1,2,5]=>[1,6,5,3,2,8,7,4]=>[2,1,1,2,1,1]
[7,2,3,5,4,1,8,6]=>[5,2,3,4,8,6,1,7]=>[4,7,6,5,1,3,8,2]=>[2,1,1,3,1]
[2,8,3,5,4,1,7,6]=>[5,3,4,8,1,6,7,2]=>[4,6,5,1,8,3,2,7]=>[2,1,2,1,2]
[4,2,6,3,8,1,7,5]=>[1,8,4,2,3,6,7,5]=>[8,1,5,7,6,3,2,4]=>[1,3,1,1,2]
[7,8,2,3,4,1,6,5]=>[3,4,5,8,6,1,7,2]=>[6,5,4,1,3,8,2,7]=>[1,1,1,3,2]
[7,8,1,4,6,3,2,5]=>[4,7,6,8,3,1,5,2]=>[5,2,3,1,6,8,4,7]=>[1,2,3,2]
[3,1,6,4,7,8,2,5]=>[7,1,4,3,5,8,2,6]=>[2,8,5,6,4,1,7,3]=>[2,2,1,2,1]
[1,8,5,7,4,3,2,6]=>[3,7,6,5,8,4,1,2]=>[6,2,3,4,1,5,8,7]=>[1,3,3,1]
[7,1,5,8,4,3,2,6]=>[3,7,6,5,8,2,1,4]=>[6,2,3,4,1,7,8,5]=>[1,3,3,1]
[5,1,8,7,4,3,2,6]=>[1,7,6,5,8,4,2,3]=>[8,2,3,4,1,5,7,6]=>[1,3,3,1]
[6,5,1,8,4,3,2,7]=>[7,6,5,2,1,8,3,4]=>[2,3,4,7,8,1,6,5]=>[5,2,1]
[6,5,7,1,4,3,2,8]=>[7,6,4,2,1,5,3,8]=>[2,3,5,7,8,4,6,1]=>[5,2,1]
[7,5,8,1,4,3,2,6]=>[7,6,4,2,5,1,8,3]=>[2,3,5,7,4,8,1,6]=>[4,2,2]
[5,8,7,1,4,3,2,6]=>[1,7,6,4,5,8,3,2]=>[8,2,3,5,4,1,6,7]=>[1,3,1,3]
[2,4,7,5,1,3,8,6]=>[8,2,5,1,4,6,3,7]=>[1,7,4,8,5,3,6,2]=>[2,2,1,2,1]
[7,8,4,6,1,3,2,5]=>[7,5,3,6,1,8,4,2]=>[2,4,6,3,8,1,5,7]=>[3,2,3]
[7,8,5,4,1,3,2,6]=>[7,5,6,4,3,1,8,2]=>[2,4,3,5,6,8,1,7]=>[2,4,2]
[3,5,6,4,1,8,2,7]=>[2,7,1,4,3,8,5,6]=>[7,2,8,5,6,1,4,3]=>[1,2,2,2,1]
[1,6,5,8,4,3,2,7]=>[3,2,7,6,5,8,1,4]=>[6,7,2,3,4,1,8,5]=>[2,3,2,1]
[7,6,5,1,4,3,2,8]=>[7,6,4,5,3,2,1,8]=>[2,3,5,4,6,7,8,1]=>[3,4,1]
[1,2,3,4,5,6,9,7,8]=>[8,9,1,2,3,4,5,6,7]=>[2,1,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1]
[1,2,3,4,5,8,6,9,7]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>[3,1,1,1,1,1,1]
[9,8,1,2,3,4,5,6,7]=>[3,4,5,6,7,8,9,2,1]=>[7,6,5,4,3,2,1,8,9]=>[1,1,1,1,1,1,3]
[7,8,9,1,2,3,4,5,6]=>[4,5,6,7,1,8,2,9,3]=>[6,5,4,3,9,2,8,1,7]=>[1,1,1,2,2,2]
[9,8,7,1,2,3,4,5,6]=>[4,5,6,7,8,9,3,2,1]=>[6,5,4,3,2,1,7,8,9]=>[1,1,1,1,1,4]
[6,7,8,9,1,2,3,4,5]=>[5,6,1,7,2,8,3,9,4]=>[5,4,9,3,8,2,7,1,6]=>[1,2,2,2,2]
[9,8,7,6,1,2,3,4,5]=>[5,6,7,8,9,4,3,2,1]=>[5,4,3,2,1,6,7,8,9]=>[1,1,1,1,5]
[9,5,6,7,8,1,2,3,4]=>[6,2,7,3,8,4,9,5,1]=>[4,8,3,7,2,6,1,5,9]=>[2,2,2,3]
[9,8,7,6,5,1,2,3,4]=>[6,7,8,9,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9]=>[1,1,1,6]
[7,8,9,4,5,6,1,2,3]=>[7,4,1,8,5,2,9,6,3]=>[3,6,9,2,5,8,1,4,7]=>[3,3,3]
[9,8,7,6,5,4,1,2,3]=>[7,8,9,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9]=>[1,1,7]
[9,7,8,5,6,3,4,1,2]=>[8,6,4,2,9,7,5,3,1]=>[2,4,6,8,1,3,5,7,9]=>[4,5]
[9,8,7,5,6,3,4,1,2]=>[8,6,4,9,7,5,3,2,1]=>[2,4,6,1,3,5,7,8,9]=>[3,6]
[9,8,7,6,5,3,4,1,2]=>[8,6,9,7,5,4,3,2,1]=>[2,4,1,3,5,6,7,8,9]=>[2,7]
[9,8,7,6,5,4,3,1,2]=>[8,9,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9]=>[1,8]
[9,10,1,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,1,10,2]=>[8,7,6,5,4,3,2,10,1,9]=>[1,1,1,1,1,1,2,2]
[10,9,8,1,2,3,4,5,6,7]=>[4,5,6,7,8,9,10,3,2,1]=>[7,6,5,4,3,2,1,8,9,10]=>[1,1,1,1,1,1,4]
[7,8,9,10,1,2,3,4,5,6]=>[5,6,7,1,8,2,9,3,10,4]=>[6,5,4,10,3,9,2,8,1,7]=>[1,1,2,2,2,2]
[9,10,7,8,1,2,3,4,5,6]=>[5,6,7,8,9,3,1,10,4,2]=>[6,5,4,3,2,8,10,1,7,9]=>[1,1,1,1,3,3]
[10,9,8,7,1,2,3,4,5,6]=>[5,6,7,8,9,10,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10]=>[1,1,1,1,1,5]
[10,9,8,7,6,1,2,3,4,5]=>[6,7,8,9,10,5,4,3,2,1]=>[5,4,3,2,1,6,7,8,9,10]=>[1,1,1,1,6]
[9,10,5,6,7,8,1,2,3,4]=>[7,3,8,4,9,5,1,10,6,2]=>[4,8,3,7,2,6,10,1,5,9]=>[2,2,3,3]
[9,10,7,8,5,6,1,2,3,4]=>[7,8,9,5,3,1,10,6,4,2]=>[4,3,2,6,8,10,1,5,7,9]=>[1,1,4,4]
[10,9,8,7,6,5,1,2,3,4]=>[7,8,9,10,6,5,4,3,2,1]=>[4,3,2,1,5,6,7,8,9,10]=>[1,1,1,7]
[10,7,8,9,4,5,6,1,2,3]=>[8,5,2,9,6,3,10,7,4,1]=>[3,6,9,2,5,8,1,4,7,10]=>[3,3,4]
[9,10,7,8,4,5,6,1,2,3]=>[8,5,9,6,3,1,10,7,4,2]=>[3,6,2,5,8,10,1,4,7,9]=>[2,4,4]
[10,9,8,7,6,5,4,1,2,3]=>[8,9,10,7,6,5,4,3,2,1]=>[3,2,1,4,5,6,7,8,9,10]=>[1,1,8]
[9,10,7,8,5,6,3,4,1,2]=>[9,7,5,3,1,10,8,6,4,2]=>[2,4,6,8,10,1,3,5,7,9]=>[5,5]
[10,9,7,8,5,6,3,4,1,2]=>[9,7,5,3,10,8,6,4,2,1]=>[2,4,6,8,1,3,5,7,9,10]=>[4,6]
[10,9,8,7,5,6,3,4,1,2]=>[9,7,5,10,8,6,4,3,2,1]=>[2,4,6,1,3,5,7,8,9,10]=>[3,7]
[10,9,8,7,6,5,3,4,1,2]=>[9,7,10,8,6,5,4,3,2,1]=>[2,4,1,3,5,6,7,8,9,10]=>[2,8]
[10,9,8,7,6,5,4,3,1,2]=>[9,10,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10]=>[1,9]
[3,4,6,2,7,1,5,8]=>[1,2,4,6,3,7,5,8]=>[8,7,5,3,6,2,4,1]=>[1,1,1,2,2,1]
[3,6,2,5,4,1,7,8]=>[6,1,3,5,4,2,7,8]=>[3,8,6,4,5,7,2,1]=>[2,1,3,1,1]
[3,2,7,5,4,1,6,8]=>[6,1,5,2,4,7,3,8]=>[3,8,4,7,5,2,6,1]=>[2,2,1,2,1]
[4,3,6,2,8,1,5,7]=>[2,1,4,6,3,7,8,5]=>[7,8,5,3,6,2,1,4]=>[2,1,2,1,2]
[6,2,4,5,1,3,7,8]=>[5,2,3,6,4,1,7,8]=>[4,7,6,3,5,8,2,1]=>[2,1,3,1,1]
[4,3,6,8,1,7,2,5]=>[1,7,2,3,8,5,6,4]=>[8,2,7,6,1,4,3,5]=>[1,2,1,2,2]
[5,3,6,4,1,7,2,8]=>[7,2,1,5,4,3,6,8]=>[2,7,8,4,5,6,3,1]=>[3,3,1,1]
[6,2,1,5,8,3,7,4]=>[4,8,2,6,1,7,3,5]=>[5,1,7,3,8,2,6,4]=>[1,2,2,2,1]
[1,6,7,4,8,3,5,2]=>[4,2,6,3,8,7,1,5]=>[5,7,3,6,1,2,8,4]=>[2,2,3,1]
[1,4,6,3,7,5,8,2]=>[6,2,4,3,5,8,1,7]=>[3,7,5,6,4,1,8,2]=>[2,2,1,2,1]
[4,6,7,2,5,8,1,3]=>[7,1,4,2,5,3,8,6]=>[2,8,5,7,4,6,1,3]=>[2,2,2,2]
[2,4,6,1,7,5,3,8]=>[7,2,6,1,4,3,5,8]=>[2,7,3,8,5,6,4,1]=>[2,2,2,1,1]
[7,5,4,6,2,8,1,3]=>[5,3,2,7,4,1,8,6]=>[4,6,7,2,5,8,1,3]=>[3,3,2]
[1,7,5,4,3,8,6,2]=>[4,3,8,5,2,7,1,6]=>[5,6,1,4,7,2,8,3]=>[2,3,2,1]
[1,4,6,3,5,8,7,2]=>[8,2,4,3,5,7,1,6]=>[1,7,5,6,4,2,8,3]=>[2,2,1,2,1]
[1,5,8,4,3,6,7,2]=>[2,5,4,6,8,7,1,3]=>[7,4,5,3,1,2,8,6]=>[1,2,1,3,1]
[5,4,6,2,7,8,1,3]=>[2,1,7,4,3,5,8,6]=>[7,8,2,5,6,4,1,3]=>[2,3,1,2]
[2,5,4,1,6,7,3,8]=>[5,3,1,2,7,4,6,8]=>[4,6,8,7,2,5,3,1]=>[3,1,2,1,1]
[5,6,3,2,7,1,4,8]=>[4,3,1,6,2,7,5,8]=>[5,6,8,3,7,2,4,1]=>[3,2,2,1]
[8,5,6,3,2,7,1,4]=>[5,4,2,7,3,8,6,1]=>[4,5,7,2,6,1,3,8]=>[3,2,3]
[5,4,6,2,8,1,7,3]=>[2,1,8,4,3,6,7,5]=>[7,8,1,5,6,3,2,4]=>[2,3,1,2]
[2,4,1,7,8,5,3,6]=>[7,2,6,1,4,8,3,5]=>[2,7,3,8,5,1,6,4]=>[2,2,1,2,1]
[2,5,4,1,6,3,8,7]=>[5,3,1,2,8,4,6,7]=>[4,6,8,7,1,5,3,2]=>[3,1,2,1,1]
[3,5,2,1,6,4,7,8]=>[1,3,6,4,2,5,7,8]=>[8,6,3,5,7,4,2,1]=>[1,1,3,1,1,1]
[6,8,4,3,2,1,5,7]=>[6,5,4,3,1,7,8,2]=>[3,4,5,6,8,2,1,7]=>[5,1,2]
[5,3,8,2,1,6,4,7]=>[2,4,1,7,5,6,8,3]=>[7,5,8,2,4,3,1,6]=>[1,2,2,1,2]
[3,7,5,8,2,1,4,6]=>[6,5,1,3,7,2,8,4]=>[3,4,8,6,2,7,1,5]=>[3,1,2,2]
[7,3,2,8,5,1,6,4]=>[8,2,6,3,5,1,7,4]=>[1,7,3,6,4,8,2,5]=>[2,2,2,2]
[8,4,6,3,2,1,7,5]=>[2,5,4,8,6,3,7,1]=>[7,4,5,1,3,6,2,8]=>[1,2,3,2]
[7,6,4,3,2,1,8,5]=>[5,4,3,8,6,2,1,7]=>[4,5,6,1,3,7,8,2]=>[3,4,1]
[7,8,4,3,2,1,6,5]=>[5,4,3,8,6,1,7,2]=>[4,5,6,1,3,8,2,7]=>[3,3,2]
[5,4,7,2,1,8,6,3]=>[2,1,8,4,7,5,3,6]=>[7,8,1,5,2,4,6,3]=>[2,2,3,1]
[7,5,8,3,2,6,1,4]=>[5,4,2,7,1,8,6,3]=>[4,5,7,2,8,1,3,6]=>[3,2,3]
[5,7,3,2,1,6,8,4]=>[4,3,1,6,8,5,2,7]=>[5,6,8,3,1,4,7,2]=>[3,1,3,1]
[5,7,3,2,1,6,4,8]=>[4,3,1,7,5,6,2,8]=>[5,6,8,2,4,3,7,1]=>[3,2,2,1]
[6,3,7,2,5,1,8,4]=>[8,2,4,1,6,5,3,7]=>[1,7,5,8,3,4,6,2]=>[2,2,3,1]
[6,7,8,3,5,2,1,4]=>[4,1,7,6,2,8,5,3]=>[5,8,2,3,7,1,4,6]=>[2,3,3]
[6,2,5,7,8,4,1,3]=>[3,7,4,1,8,2,6,5]=>[6,2,5,8,1,7,3,4]=>[1,3,2,2]
[2,1,5,7,8,6,3,4]=>[7,3,4,8,1,6,2,5]=>[2,6,5,1,8,3,7,4]=>[2,1,2,2,1]
[3,6,7,2,8,1,4,5]=>[4,6,1,2,7,3,8,5]=>[5,3,8,7,2,6,1,4]=>[1,2,1,2,2]
[6,3,7,2,8,1,4,5]=>[2,4,6,1,7,3,8,5]=>[7,5,3,8,2,6,1,4]=>[1,1,2,2,2]
[3,2,6,1,7,4,5,8]=>[1,6,7,2,4,3,5,8]=>[8,3,2,7,5,6,4,1]=>[1,1,2,2,1,1]
[3,5,2,1,4,7,6,8]=>[1,3,7,4,2,5,6,8]=>[8,6,2,5,7,4,3,1]=>[1,1,3,1,1,1]
[7,3,5,2,1,8,4,6]=>[2,4,7,3,8,5,1,6]=>[7,5,2,6,1,4,8,3]=>[1,1,2,3,1]
[2,5,4,1,3,7,8,6]=>[6,3,1,2,8,4,5,7]=>[3,6,8,7,1,5,4,2]=>[3,1,2,1,1]
[2,5,8,4,1,3,7,6]=>[2,8,5,1,4,6,7,3]=>[7,1,4,8,5,3,2,6]=>[1,3,1,1,2]
[2,4,1,7,8,3,6,5]=>[8,2,6,1,4,7,3,5]=>[1,7,3,8,5,2,6,4]=>[2,2,1,2,1]
[3,7,2,8,6,1,4,5]=>[6,7,8,1,3,2,5,4]=>[3,2,1,8,6,7,4,5]=>[1,1,2,2,2]
[3,6,8,2,1,7,4,5]=>[4,7,1,2,8,5,6,3]=>[5,2,8,7,1,4,3,6]=>[1,2,1,2,2]
[5,3,8,2,1,4,7,6]=>[2,4,1,8,5,6,7,3]=>[7,5,8,1,4,3,2,6]=>[1,2,2,1,2]
[4,8,7,3,2,1,5,6]=>[6,1,5,4,7,8,3,2]=>[3,8,4,5,2,1,6,7]=>[2,2,1,3]
[8,4,7,3,2,1,5,6]=>[2,6,5,4,7,8,3,1]=>[7,3,4,5,2,1,6,8]=>[1,3,1,3]
[8,3,5,2,1,4,7,6]=>[2,4,8,5,3,6,7,1]=>[7,5,1,4,6,3,2,8]=>[1,1,3,1,2]
[7,3,2,8,6,1,4,5]=>[2,6,7,8,3,1,5,4]=>[7,3,2,1,6,8,4,5]=>[1,1,1,3,2]
[3,5,2,1,4,6,8,7]=>[1,3,8,4,2,5,6,7]=>[8,6,1,5,7,4,3,2]=>[1,1,3,1,1,1]
[7,8,6,5,4,3,2,1,9]=>[1,8,7,6,5,4,3,2,9]=>[9,2,3,4,5,6,7,8,1]=>[1,7,1]
[1,8,9,7,6,5,4,3,2]=>[2,9,8,7,6,5,4,1,3]=>[8,1,2,3,4,5,6,9,7]=>[1,7,1]
[8,9,7,6,5,4,3,2,1,10]=>[1,9,8,7,6,5,4,3,2,10]=>[10,2,3,4,5,6,7,8,9,1]=>[1,8,1]
[7,6,8,5,4,3,2,1,9]=>[2,1,8,7,6,5,4,3,9]=>[8,9,2,3,4,5,6,7,1]=>[2,6,1]
[6,8,7,5,4,3,2,1,9]=>[8,1,7,6,5,4,3,2,9]=>[2,9,3,4,5,6,7,8,1]=>[2,6,1]
[1,8,7,9,6,5,4,3,2]=>[3,2,9,8,7,6,5,1,4]=>[7,8,1,2,3,4,5,9,6]=>[2,6,1]
[1,7,9,8,6,5,4,3,2]=>[9,2,8,7,6,5,4,1,3]=>[1,8,2,3,4,5,6,9,7]=>[2,6,1]
[1,9,10,8,7,6,5,4,3,2]=>[2,10,9,8,7,6,5,4,1,3]=>[9,1,2,3,4,5,6,7,10,8]=>[1,8,1]
[7,8,3,5,4,6,1,2]=>[7,3,5,4,1,8,6,2]=>[2,6,4,5,8,1,3,7]=>[2,3,3]
[8,6,3,7,5,2,4,1]=>[6,8,3,2,7,5,4,1]=>[3,1,6,7,2,4,5,8]=>[1,3,4]
[5,4,1,6,3,2,8,7]=>[5,4,2,1,8,3,6,7]=>[4,5,7,8,1,6,3,2]=>[4,2,1,1]
[5,4,1,6,2,3,8,7]=>[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>[5,1,1,1]
[5,7,1,6,2,8,3,4]=>[7,1,8,5,3,4,2,6]=>[2,8,1,4,6,5,7,3]=>[2,3,2,1]
[5,7,1,6,2,8,4,3]=>[1,8,7,5,3,4,2,6]=>[8,1,2,4,6,5,7,3]=>[1,4,2,1]
[2,7,6,5,1,8,3,4]=>[7,8,5,4,1,3,2,6]=>[2,1,4,5,8,6,7,3]=>[1,4,2,1]
[2,7,6,5,1,8,4,3]=>[8,7,5,4,1,3,2,6]=>[1,2,4,5,8,6,7,3]=>[5,2,1]
[2,3,6,5,1,4,8,7]=>[8,5,1,2,4,3,6,7]=>[1,4,8,7,5,6,3,2]=>[3,1,2,1,1]
[2,3,6,4,1,5,8,7]=>[4,8,1,2,5,3,6,7]=>[5,1,8,7,4,6,3,2]=>[1,2,1,2,1,1]
[2,3,6,1,5,4,8,7]=>[5,8,1,2,4,3,6,7]=>[4,1,8,7,5,6,3,2]=>[1,2,1,2,1,1]
[2,7,6,1,4,8,5,3]=>[8,5,7,4,1,3,2,6]=>[1,4,2,5,8,6,7,3]=>[2,3,2,1]
[2,7,6,1,4,8,3,5]=>[5,7,8,4,1,3,2,6]=>[4,2,1,5,8,6,7,3]=>[1,1,3,2,1]
[7,3,5,1,8,4,2,6]=>[7,2,6,3,8,4,1,5]=>[2,7,3,6,1,5,8,4]=>[2,2,3,1]
[7,3,5,1,8,6,4,2]=>[3,8,2,7,6,4,1,5]=>[6,1,7,2,3,5,8,4]=>[1,2,4,1]
[2,7,6,1,5,8,4,3]=>[5,8,7,4,1,3,2,6]=>[4,1,2,5,8,6,7,3]=>[1,4,2,1]
[2,7,6,4,1,8,5,3]=>[4,8,7,5,1,3,2,6]=>[5,1,2,4,8,6,7,3]=>[1,4,2,1]
[2,1,7,6,3,8,5,4]=>[8,7,5,1,4,2,3,6]=>[1,2,4,8,5,7,6,3]=>[4,2,1,1]
[2,1,7,6,3,8,4,5]=>[7,8,5,1,4,2,3,6]=>[2,1,4,8,5,7,6,3]=>[1,3,2,1,1]
[5,7,3,6,2,8,4,1]=>[1,8,3,5,4,2,7,6]=>[8,1,6,4,5,7,2,3]=>[1,2,3,2]
[2,7,6,4,1,8,3,5]=>[7,4,8,5,1,3,2,6]=>[2,5,1,4,8,6,7,3]=>[2,3,2,1]
[7,3,5,1,8,6,2,4]=>[7,2,3,8,6,4,1,5]=>[2,7,6,1,3,5,8,4]=>[2,1,4,1]
[6,3,5,1,8,2,4,7]=>[2,6,7,3,1,8,4,5]=>[7,3,2,6,8,1,5,4]=>[1,1,3,2,1]
[2,3,4,8,7,6,1,5]=>[7,8,6,1,2,3,5,4]=>[2,1,3,8,7,6,4,5]=>[1,3,1,1,2]
[2,3,4,8,5,7,1,6]=>[5,7,8,1,2,3,6,4]=>[4,2,1,8,7,6,3,5]=>[1,1,2,1,1,2]
[7,3,5,4,8,1,2,6]=>[6,2,4,3,7,1,8,5]=>[3,7,5,6,2,8,1,4]=>[2,2,2,2]
[6,4,3,5,8,7,2,1]=>[2,8,3,1,4,7,6,5]=>[7,1,6,8,5,2,3,4]=>[1,3,1,3]
[2,1,4,5,8,7,3,6]=>[7,8,1,3,4,6,2,5]=>[2,1,8,6,5,3,7,4]=>[1,2,1,1,2,1]
[6,4,3,5,8,7,1,2]=>[3,2,4,1,7,8,6,5]=>[6,7,5,8,2,1,3,4]=>[2,2,1,3]
[7,3,5,4,8,1,6,2]=>[4,2,3,8,6,1,7,5]=>[5,7,6,1,3,8,2,4]=>[2,1,3,2]
[2,3,4,8,7,5,6,1]=>[6,8,7,1,2,3,5,4]=>[3,1,2,8,7,6,4,5]=>[1,3,1,1,2]
[2,3,4,8,7,5,1,6]=>[7,6,8,1,2,3,5,4]=>[2,3,1,8,7,6,4,5]=>[2,2,1,1,2]
[2,7,6,5,4,8,1,3]=>[7,5,4,3,1,2,8,6]=>[2,4,5,6,8,7,1,3]=>[5,1,2]
[7,3,5,6,8,4,1,2]=>[3,7,2,4,1,8,6,5]=>[6,2,7,5,8,1,3,4]=>[1,2,2,3]
[7,3,5,6,8,1,4,2]=>[3,8,2,6,4,1,7,5]=>[6,1,7,3,5,8,2,4]=>[1,2,3,2]
[7,3,5,6,8,1,2,4]=>[6,2,3,7,4,1,8,5]=>[3,7,6,2,5,8,1,4]=>[2,1,3,2]
[6,4,1,5,8,7,2,3]=>[4,2,7,1,8,6,3,5]=>[5,7,2,8,1,3,6,4]=>[2,2,3,1]
[6,4,1,5,8,7,3,2]=>[2,8,4,1,7,6,3,5]=>[7,1,5,8,2,3,6,4]=>[1,3,3,1]
[6,4,1,5,8,3,7,2]=>[4,2,6,1,8,7,3,5]=>[5,7,3,8,1,2,6,4]=>[2,2,3,1]
[5,7,1,6,3,8,2,4]=>[5,1,7,4,8,3,2,6]=>[4,8,2,5,1,6,7,3]=>[2,2,3,1]
[6,4,1,5,8,3,2,7]=>[4,2,7,6,1,8,3,5]=>[5,7,2,3,8,1,6,4]=>[2,3,2,1]
[7,4,1,5,8,2,3,6]=>[6,4,2,7,8,3,1,5]=>[3,5,7,2,1,6,8,4]=>[3,1,3,1]
[7,4,1,5,8,2,6,3]=>[4,2,8,6,7,3,1,5]=>[5,7,1,3,2,6,8,4]=>[2,2,3,1]
[6,3,5,7,8,2,4,1]=>[3,6,2,1,4,8,7,5]=>[6,3,7,8,5,1,2,4]=>[1,3,1,3]
[2,7,6,4,5,8,3,1]=>[4,5,3,2,8,1,7,6]=>[5,4,6,7,1,8,2,3]=>[1,3,2,2]
[5,7,3,6,1,8,4,2]=>[1,8,3,7,5,4,2,6]=>[8,1,6,2,4,5,7,3]=>[1,2,4,1]
[2,1,4,5,8,6,3,7]=>[7,1,3,4,6,8,2,5]=>[2,8,6,5,3,1,7,4]=>[2,1,1,1,2,1]
[7,3,5,4,8,6,2,1]=>[3,8,2,4,1,7,6,5]=>[6,1,7,5,8,2,3,4]=>[1,2,2,3]
[2,3,4,8,5,6,1,7]=>[5,7,1,2,3,6,8,4]=>[4,2,8,7,6,3,1,5]=>[1,2,1,1,1,2]
[2,3,4,8,7,1,6,5]=>[8,6,7,1,2,3,5,4]=>[1,3,2,8,7,6,4,5]=>[2,2,1,1,2]
[2,3,4,8,1,7,6,5]=>[8,7,1,2,3,5,6,4]=>[1,2,8,7,6,4,3,5]=>[3,1,1,1,2]
[2,3,4,8,1,6,7,5]=>[6,8,1,2,3,5,7,4]=>[3,1,8,7,6,4,2,5]=>[1,2,1,1,1,2]
[2,3,4,8,5,1,7,6]=>[5,8,1,2,3,6,7,4]=>[4,1,8,7,6,3,2,5]=>[1,2,1,1,1,2]
[6,3,5,4,8,2,7,1]=>[4,2,3,1,6,8,7,5]=>[5,7,6,8,3,1,2,4]=>[2,2,1,3]
[2,1,4,5,8,3,7,6]=>[8,1,3,4,6,7,2,5]=>[1,8,6,5,3,2,7,4]=>[2,1,1,1,2,1]
[7,4,3,5,8,2,6,1]=>[3,2,4,6,1,8,7,5]=>[6,7,5,3,8,1,2,4]=>[2,1,2,3]
[6,3,5,4,8,2,1,7]=>[4,2,3,1,7,6,8,5]=>[5,7,6,8,2,3,1,4]=>[2,2,2,2]
[2,3,4,8,5,1,6,7]=>[6,1,2,3,5,7,8,4]=>[3,8,7,6,4,2,1,5]=>[2,1,1,1,1,2]
[2,3,4,8,1,6,5,7]=>[7,1,2,3,5,6,8,4]=>[2,8,7,6,4,3,1,5]=>[2,1,1,1,1,2]
[2,3,4,8,1,5,7,6]=>[8,1,2,3,5,6,7,4]=>[1,8,7,6,4,3,2,5]=>[2,1,1,1,1,2]
[7,8,2,6,1,5,3,4]=>[7,8,3,5,1,6,4,2]=>[2,1,6,4,8,3,5,7]=>[1,2,2,3]
[7,8,1,6,2,5,3,4]=>[7,8,5,6,3,1,4,2]=>[2,1,4,3,6,8,5,7]=>[1,2,3,2]
[1,8,6,7,2,5,3,4]=>[7,8,5,3,6,4,1,2]=>[2,1,4,6,3,5,8,7]=>[1,3,3,1]
[1,8,5,7,2,6,3,4]=>[7,3,8,5,6,4,1,2]=>[2,6,1,4,3,5,8,7]=>[2,2,3,1]
[5,8,1,7,2,6,3,4]=>[7,1,8,5,6,3,4,2]=>[2,8,1,4,3,6,5,7]=>[2,2,2,2]
[5,8,2,7,1,6,3,4]=>[7,1,8,3,5,6,4,2]=>[2,8,1,6,4,3,5,7]=>[2,2,1,3]
[2,8,6,7,1,5,3,4]=>[7,8,5,3,6,1,4,2]=>[2,1,4,6,3,8,5,7]=>[1,3,2,2]
[2,8,5,7,1,6,3,4]=>[7,3,8,5,6,1,4,2]=>[2,6,1,4,3,8,5,7]=>[2,2,2,2]
[2,8,1,7,5,6,3,4]=>[7,5,8,6,1,3,4,2]=>[2,4,1,3,8,6,5,7]=>[2,3,1,2]
[1,8,2,7,5,6,3,4]=>[7,5,8,6,3,4,1,2]=>[2,4,1,3,6,5,8,7]=>[2,3,2,1]
[1,8,2,7,4,6,3,5]=>[5,7,8,6,3,4,1,2]=>[4,2,1,3,6,5,8,7]=>[1,1,3,2,1]
[2,8,1,7,4,6,3,5]=>[5,7,8,6,1,3,4,2]=>[4,2,1,3,8,6,5,7]=>[1,1,3,1,2]
[2,8,4,7,1,6,3,5]=>[3,7,8,5,6,1,4,2]=>[6,2,1,4,3,8,5,7]=>[1,1,2,2,2]
[4,8,2,7,1,6,3,5]=>[1,7,8,3,5,6,4,2]=>[8,2,1,6,4,3,5,7]=>[1,1,2,1,3]
[4,8,1,7,2,6,3,5]=>[1,7,8,5,6,3,4,2]=>[8,2,1,4,3,6,5,7]=>[1,1,2,2,2]
[1,8,4,7,2,6,3,5]=>[3,7,8,5,6,4,1,2]=>[6,2,1,4,3,5,8,7]=>[1,1,2,3,1]
[4,8,1,7,5,6,2,3]=>[7,1,5,8,6,3,4,2]=>[2,8,4,1,3,6,5,7]=>[2,1,3,2]
[1,8,4,7,5,6,2,3]=>[7,3,5,8,6,4,1,2]=>[2,6,4,1,3,5,8,7]=>[2,1,4,1]
[1,8,3,7,5,6,2,4]=>[7,5,8,3,6,4,1,2]=>[2,4,1,6,3,5,8,7]=>[2,2,3,1]
[3,8,1,7,5,6,2,4]=>[7,5,8,1,6,3,4,2]=>[2,4,1,8,3,6,5,7]=>[2,2,2,2]
[3,8,1,7,4,6,2,5]=>[5,7,8,1,6,3,4,2]=>[4,2,1,8,3,6,5,7]=>[1,1,2,2,2]
[1,8,3,7,4,6,2,5]=>[5,7,8,3,6,4,1,2]=>[4,2,1,6,3,5,8,7]=>[1,1,2,3,1]
[1,8,3,7,2,6,4,5]=>[7,8,3,5,6,4,1,2]=>[2,1,6,4,3,5,8,7]=>[1,2,1,3,1]
[3,8,1,7,2,6,4,5]=>[7,8,1,5,6,3,4,2]=>[2,1,8,4,3,6,5,7]=>[1,2,1,2,2]
[3,8,2,7,1,6,4,5]=>[7,8,1,3,5,6,4,2]=>[2,1,8,6,4,3,5,7]=>[1,2,1,1,3]
[3,8,2,7,4,6,1,5]=>[5,7,8,1,3,6,4,2]=>[4,2,1,8,6,3,5,7]=>[1,1,2,1,3]
[3,8,2,7,5,6,1,4]=>[7,5,8,1,3,6,4,2]=>[2,4,1,8,6,3,5,7]=>[2,2,1,3]
[4,8,2,7,5,6,1,3]=>[7,1,5,8,3,6,4,2]=>[2,8,4,1,6,3,5,7]=>[2,1,2,3]
[4,8,3,7,5,6,1,2]=>[7,1,3,5,8,6,4,2]=>[2,8,6,4,1,3,5,7]=>[2,1,1,4]
[3,8,4,7,5,6,1,2]=>[7,3,5,8,1,6,4,2]=>[2,6,4,1,8,3,5,7]=>[2,1,2,3]
[2,8,4,7,5,6,1,3]=>[7,3,5,8,6,1,4,2]=>[2,6,4,1,3,8,5,7]=>[2,1,3,2]
[2,8,3,7,5,6,1,4]=>[7,5,8,3,6,1,4,2]=>[2,4,1,6,3,8,5,7]=>[2,2,2,2]
[2,8,3,7,4,6,1,5]=>[5,7,8,3,6,1,4,2]=>[4,2,1,6,3,8,5,7]=>[1,1,2,2,2]
[2,8,3,7,1,6,4,5]=>[7,8,3,5,6,1,4,2]=>[2,1,6,4,3,8,5,7]=>[1,2,1,2,2]
[2,8,1,7,3,6,4,5]=>[7,8,5,6,1,3,4,2]=>[2,1,4,3,8,6,5,7]=>[1,2,2,1,2]
[7,5,2,8,6,4,1,3]=>[7,2,8,6,3,1,5,4]=>[2,7,1,3,6,8,4,5]=>[2,4,2]
[7,5,1,8,6,2,3,4]=>[6,7,2,8,5,3,1,4]=>[3,2,7,1,4,6,8,5]=>[1,2,4,1]
[7,4,8,6,1,5,2,3]=>[2,7,8,5,1,6,4,3]=>[7,2,1,4,8,3,5,6]=>[1,1,3,3]
[7,1,8,4,5,2,6,3]=>[4,8,6,5,7,2,1,3]=>[5,1,3,4,2,7,8,6]=>[1,3,3,1]
[6,8,1,7,4,2,5,3]=>[8,6,5,1,7,3,4,2]=>[1,3,4,8,2,6,5,7]=>[4,2,2]
[1,6,7,4,2,8,5,3]=>[4,2,8,7,5,1,3,6]=>[5,7,1,2,4,8,6,3]=>[2,4,1,1]
[1,6,7,3,8,5,2,4]=>[7,2,8,4,3,6,1,5]=>[2,7,1,5,6,3,8,4]=>[2,3,2,1]
[7,1,8,3,5,6,2,4]=>[7,4,5,8,6,2,1,3]=>[2,5,4,1,3,7,8,6]=>[2,1,4,1]
[7,3,8,6,2,5,1,4]=>[5,7,8,2,1,6,4,3]=>[4,2,1,7,8,3,5,6]=>[1,1,3,3]
[7,4,2,8,6,1,3,5]=>[6,2,7,8,3,1,5,4]=>[3,7,2,1,6,8,4,5]=>[2,1,3,2]
[7,2,8,4,1,5,3,6]=>[7,5,2,4,6,1,8,3]=>[2,4,7,5,3,8,1,6]=>[3,1,2,2]
[7,2,8,3,5,1,6,4]=>[8,4,6,2,5,1,7,3]=>[1,5,3,7,4,8,2,6]=>[2,2,2,2]
[7,2,8,3,4,6,1,5]=>[4,5,7,8,2,1,6,3]=>[5,4,2,1,7,8,3,6]=>[1,1,1,3,2]
[1,5,7,8,2,6,3,4]=>[2,7,8,5,3,6,1,4]=>[7,2,1,4,6,3,8,5]=>[1,1,3,2,1]
[6,2,3,8,5,7,4,1]=>[5,8,7,2,1,3,6,4]=>[4,1,2,7,8,6,3,5]=>[1,4,1,2]
[6,2,4,8,5,3,1,7]=>[7,3,6,2,1,5,8,4]=>[2,6,3,7,8,4,1,5]=>[2,3,1,2]
[6,3,1,4,8,5,2,7]=>[2,7,4,6,1,8,3,5]=>[7,2,5,3,8,1,6,4]=>[1,2,2,2,1]
[2,6,3,7,8,5,4,1]=>[4,2,8,7,1,3,6,5]=>[5,7,1,2,8,6,3,4]=>[2,3,1,2]
[2,6,3,7,8,4,5,1]=>[6,4,2,8,1,3,7,5]=>[3,5,7,1,8,6,2,4]=>[3,2,1,2]
[2,4,7,3,5,6,8,1]=>[2,4,5,6,1,3,8,7]=>[7,5,4,3,8,6,1,2]=>[1,1,1,2,1,2]
[2,4,7,3,6,8,5,1]=>[5,8,2,4,1,3,7,6]=>[4,1,7,5,8,6,2,3]=>[1,2,2,1,2]
[2,5,3,7,8,1,6,4]=>[2,8,6,1,3,4,7,5]=>[7,1,3,8,6,5,2,4]=>[1,3,1,1,2]
[3,1,5,4,7,8,2,6]=>[1,3,7,4,5,8,2,6]=>[8,6,2,5,4,1,7,3]=>[1,1,2,1,2,1]
[5,3,1,4,8,2,6,7]=>[4,2,6,1,7,8,3,5]=>[5,7,3,8,2,1,6,4]=>[2,2,1,2,1]
[5,2,4,8,6,1,3,7]=>[3,6,1,7,2,5,8,4]=>[6,3,8,2,7,4,1,5]=>[1,2,2,1,2]
[4,8,2,3,5,7,1,6]=>[3,1,4,5,7,8,6,2]=>[6,8,5,4,2,1,3,7]=>[2,1,1,1,3]
[1,4,7,8,3,6,2,5]=>[5,7,2,3,8,6,1,4]=>[4,2,7,6,1,3,8,5]=>[1,2,1,3,1]
[4,8,1,3,6,7,2,5]=>[1,7,4,5,8,3,6,2]=>[8,2,5,4,1,6,3,7]=>[1,2,1,2,2]
[5,3,8,2,4,7,1,6]=>[2,4,1,5,7,8,6,3]=>[7,5,8,4,2,1,3,6]=>[1,2,1,1,3]
[5,4,3,8,1,2,7,6]=>[3,2,1,8,5,6,7,4]=>[6,7,8,1,4,3,2,5]=>[3,2,1,2]
[6,4,2,8,1,3,7,5]=>[8,3,2,5,1,6,7,4]=>[1,6,7,4,8,3,2,5]=>[3,2,1,2]
[6,3,8,2,5,1,7,4]=>[8,2,4,1,6,5,7,3]=>[1,7,5,8,3,4,2,6]=>[2,2,2,2]
[6,3,8,1,4,7,2,5]=>[2,5,7,1,8,4,6,3]=>[7,4,2,8,1,5,3,6]=>[1,1,2,2,2]
[5,8,1,3,6,2,7,4]=>[8,4,1,6,3,5,7,2]=>[1,5,8,3,6,4,2,7]=>[3,2,1,2]
[1,5,7,4,2,6,8,3]=>[2,6,4,8,5,1,3,7]=>[7,3,5,1,4,8,6,2]=>[1,2,3,1,1]
[5,8,1,4,2,6,3,7]=>[7,5,3,1,4,6,8,2]=>[2,4,6,8,5,3,1,7]=>[4,1,1,2]
[5,8,4,1,2,7,6,3]=>[1,8,7,4,3,5,6,2]=>[8,1,2,5,6,4,3,7]=>[1,4,1,2]
[6,5,1,2,8,7,3,4]=>[7,8,6,3,2,1,4,5]=>[2,1,3,6,7,8,5,4]=>[1,5,1,1]
[5,2,6,4,1,7,3,8]=>[7,5,2,1,4,3,6,8]=>[2,4,7,8,5,6,3,1]=>[4,2,1,1]
[4,6,1,7,5,2,8,3]=>[8,1,6,5,3,2,4,7]=>[1,8,3,4,6,7,5,2]=>[2,4,1,1]
[4,5,1,7,2,6,3,8]=>[1,7,5,2,6,3,4,8]=>[8,2,4,7,3,6,5,1]=>[1,3,2,1,1]
[3,5,6,1,2,8,7,4]=>[2,8,1,7,4,3,5,6]=>[7,1,8,2,5,6,4,3]=>[1,2,3,1,1]
[3,5,7,1,8,6,2,4]=>[2,7,8,1,6,4,3,5]=>[7,2,1,8,3,5,6,4]=>[1,1,2,3,1]
[3,6,2,7,5,1,8,4]=>[8,6,1,3,2,5,4,7]=>[1,3,8,6,7,4,5,2]=>[3,2,2,1]
[4,2,5,7,1,8,6,3]=>[1,8,3,7,2,5,4,6]=>[8,1,6,2,7,4,5,3]=>[1,2,2,2,1]
[3,4,7,2,8,6,1,5]=>[7,8,1,2,4,3,6,5]=>[2,1,8,7,5,6,3,4]=>[1,2,1,2,2]
[3,4,5,8,2,7,1,6]=>[1,2,3,5,7,8,6,4]=>[8,7,6,4,2,1,3,5]=>[1,1,1,1,1,3]
[3,4,6,2,8,1,5,7]=>[1,2,4,6,3,7,8,5]=>[8,7,5,3,6,2,1,4]=>[1,1,1,2,1,2]
[3,5,2,6,8,1,7,4]=>[4,1,2,8,3,6,7,5]=>[5,8,7,1,6,3,2,4]=>[2,1,2,1,2]
[4,2,5,6,1,3,8,7]=>[3,1,8,2,5,4,6,7]=>[6,8,1,7,4,5,3,2]=>[2,2,2,1,1]
[4,3,1,2,5,6,8,7]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]
[5,3,6,8,4,7,2,1]=>[3,1,5,8,2,7,6,4]=>[6,8,4,1,7,2,3,5]=>[2,1,2,3]
[3,7,2,5,4,8,6,1]=>[4,8,1,3,5,2,7,6]=>[5,1,8,6,4,7,2,3]=>[1,2,1,2,2]
[8,4,2,5,7,3,6,1]=>[4,2,6,8,3,7,5,1]=>[5,7,3,1,6,2,4,8]=>[2,1,2,3]
[4,7,2,5,8,3,6,1]=>[1,4,6,8,3,2,7,5]=>[8,5,3,1,6,7,2,4]=>[1,1,1,3,2]
[5,2,6,8,4,3,7,1]=>[3,1,6,5,8,2,7,4]=>[6,8,3,4,1,7,2,5]=>[2,2,2,2]
[3,1,6,5,4,8,2,7]=>[5,1,4,3,7,8,2,6]=>[4,8,5,6,2,1,7,3]=>[2,2,1,2,1]
[4,1,6,5,8,3,2,7]=>[1,4,3,7,6,8,2,5]=>[8,5,6,2,3,1,7,4]=>[1,2,2,2,1]
[5,1,6,8,4,3,2,7]=>[3,1,7,6,5,8,2,4]=>[6,8,2,3,4,1,7,5]=>[2,3,2,1]
[8,5,4,7,6,3,2,1]=>[2,8,3,7,6,5,4,1]=>[7,1,6,2,3,4,5,8]=>[1,2,5]
[5,7,1,8,4,3,2,6]=>[1,7,6,5,8,3,2,4]=>[8,2,3,4,1,6,7,5]=>[1,3,3,1]
[2,7,1,5,4,3,8,6]=>[5,4,8,1,3,6,2,7]=>[4,5,1,8,6,3,7,2]=>[2,2,1,2,1]
[8,4,1,5,7,3,2,6]=>[4,2,7,6,8,3,5,1]=>[5,7,2,3,1,6,4,8]=>[2,2,2,2]
[8,5,6,7,1,3,2,4]=>[7,5,2,6,3,8,4,1]=>[2,4,7,3,6,1,5,8]=>[3,2,3]
[8,4,6,1,7,3,2,5]=>[2,7,6,8,4,3,5,1]=>[7,2,3,1,5,6,4,8]=>[1,2,3,2]
[8,3,6,1,4,7,2,5]=>[2,5,7,8,4,3,6,1]=>[7,4,2,1,5,6,3,8]=>[1,1,1,3,2]
[2,7,6,1,4,3,8,5]=>[5,8,4,6,1,3,2,7]=>[4,1,5,3,8,6,7,2]=>[1,2,2,2,1]
[6,7,8,5,1,3,2,4]=>[7,5,1,6,2,8,4,3]=>[2,4,8,3,7,1,5,6]=>[3,2,3]
[5,7,6,8,2,3,4,1]=>[1,5,6,3,2,8,7,4]=>[8,4,3,6,7,1,2,5]=>[1,1,3,3]
[5,7,2,8,4,3,6,1]=>[1,6,5,8,3,2,7,4]=>[8,3,4,1,6,7,2,5]=>[1,2,3,2]
[6,7,8,2,4,3,5,1]=>[6,4,1,5,2,8,7,3]=>[3,5,8,4,7,1,2,6]=>[3,2,3]
[4,7,6,2,8,3,5,1]=>[6,8,1,4,3,2,7,5]=>[3,1,8,5,6,7,2,4]=>[1,2,3,2]
[8,3,6,2,4,7,5,1]=>[8,2,4,5,3,7,6,1]=>[1,7,5,4,6,2,3,8]=>[2,1,2,3]
[3,7,6,2,4,8,5,1]=>[8,4,5,1,3,2,7,6]=>[1,5,4,8,6,7,2,3]=>[2,2,2,2]
[5,7,3,8,4,6,2,1]=>[1,5,8,3,2,7,6,4]=>[8,4,1,6,7,2,3,5]=>[1,1,3,3]
[4,7,3,5,8,6,2,1]=>[8,1,3,4,2,7,6,5]=>[1,8,6,5,7,2,3,4]=>[2,1,2,3]
[8,7,2,1,4,3,6,5]=>[3,5,8,4,6,7,2,1]=>[6,4,1,5,3,2,7,8]=>[1,1,2,1,3]
[8,7,3,1,4,6,2,5]=>[5,3,7,8,4,6,2,1]=>[4,6,2,1,5,3,7,8]=>[2,1,2,3]
[8,7,6,3,2,5,4,1]=>[4,8,5,7,6,3,2,1]=>[5,1,4,2,3,6,7,8]=>[1,2,5]
[8,7,3,5,1,6,2,4]=>[3,7,8,5,4,6,2,1]=>[6,2,1,4,5,3,7,8]=>[1,1,3,3]
[8,7,2,5,1,3,6,4]=>[8,3,5,6,4,7,2,1]=>[1,6,4,3,5,2,7,8]=>[2,1,2,3]
[8,2,6,5,1,3,7,4]=>[8,5,6,2,4,3,7,1]=>[1,4,3,7,5,6,2,8]=>[2,2,2,2]
[8,4,6,5,7,1,2,3]=>[2,6,7,4,3,8,5,1]=>[7,3,2,5,6,1,4,8]=>[1,1,3,3]
[5,7,6,8,4,1,2,3]=>[1,6,7,3,2,8,5,4]=>[8,3,2,6,7,1,4,5]=>[1,1,3,3]
[4,7,6,5,8,1,2,3]=>[6,7,1,4,3,2,8,5]=>[3,2,8,5,6,7,1,4]=>[1,2,3,2]
[3,7,6,5,1,8,2,4]=>[7,8,5,1,4,3,2,6]=>[2,1,4,8,5,6,7,3]=>[1,3,3,1]
[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[8,7,6,5,4,3,2,9,1]=>[1,1,1,1,1,1,2,1]
[1,9,2,3,4,5,6,7,8]=>[3,4,5,6,7,8,9,1,2]=>[7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,2,1]
[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[9,8,7,6,5,4,3,2,10,1]=>[1,1,1,1,1,1,1,2,1]
[7,8,1,2,3,4,5,6,9]=>[3,4,5,6,7,1,8,2,9]=>[7,6,5,4,3,9,2,8,1]=>[1,1,1,1,2,2,1]
[1,8,9,2,3,4,5,6,7]=>[4,5,6,7,8,2,9,1,3]=>[6,5,4,3,2,8,1,9,7]=>[1,1,1,1,2,2,1]
[1,10,2,3,4,5,6,7,8,9]=>[3,4,5,6,7,8,9,10,1,2]=>[8,7,6,5,4,3,2,1,10,9]=>[1,1,1,1,1,1,1,2,1]
[10,1,2,3,4,5,6,7,8,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,9,8,7,6,5,4,3,2,11,1]=>[1,1,1,1,1,1,1,1,2,1]
[1,9,10,2,3,4,5,6,7,8]=>[4,5,6,7,8,9,2,10,1,3]=>[7,6,5,4,3,2,9,1,10,8]=>[1,1,1,1,1,2,2,1]
[1,11,2,3,4,5,6,7,8,9,10]=>[3,4,5,6,7,8,9,10,11,1,2]=>[9,8,7,6,5,4,3,2,1,11,10]=>[1,1,1,1,1,1,1,1,2,1]
[3,6,4,8,7,5,1,2]=>[7,2,8,1,3,6,5,4]=>[2,7,1,8,6,3,4,5]=>[2,2,1,3]
[5,6,4,3,8,7,1,2]=>[1,4,3,2,7,8,6,5]=>[8,5,6,7,2,1,3,4]=>[1,3,1,3]
[1,6,2,4,7,8,5,3]=>[5,8,4,2,7,1,3,6]=>[4,1,5,7,2,8,6,3]=>[1,3,2,1,1]
[3,6,2,4,8,1,5,7]=>[1,3,4,6,2,7,8,5]=>[8,6,5,3,7,2,1,4]=>[1,1,1,2,1,2]
[1,4,7,2,5,8,6,3]=>[8,2,5,7,4,1,3,6]=>[1,7,4,2,5,8,6,3]=>[2,1,3,1,1]
[7,3,8,4,5,6,1,2]=>[4,7,2,5,1,8,6,3]=>[5,2,7,4,8,1,3,6]=>[1,2,2,3]
[3,5,6,4,8,7,1,2]=>[2,4,1,3,7,8,6,5]=>[7,5,8,6,2,1,3,4]=>[1,2,1,1,3]
[4,6,8,5,3,7,1,2]=>[2,7,1,5,4,8,6,3]=>[7,2,8,4,5,1,3,6]=>[1,2,2,3]
[6,8,5,3,4,7,1,2]=>[4,1,7,5,3,8,6,2]=>[5,8,2,4,6,1,3,7]=>[2,3,3]
[1,6,5,4,2,8,7,3]=>[4,3,2,8,7,1,5,6]=>[5,6,7,1,2,8,4,3]=>[3,3,1,1]
[1,8,5,2,7,3,6,4]=>[8,6,3,7,4,5,1,2]=>[1,3,6,2,5,4,8,7]=>[3,2,2,1]
[4,2,7,5,1,8,6,3]=>[1,4,8,7,2,5,3,6]=>[8,5,1,2,7,4,6,3]=>[1,1,3,2,1]
[7,8,1,4,2,6,5,3]=>[4,8,7,3,5,1,6,2]=>[5,1,2,6,4,8,3,7]=>[1,3,2,2]
[1,3,6,4,8,2,5,7]=>[4,6,2,3,7,8,1,5]=>[5,3,7,6,2,1,8,4]=>[1,2,1,1,2,1]
[4,1,7,5,3,2,6,8]=>[1,6,5,4,7,2,3,8]=>[8,3,4,5,2,7,6,1]=>[1,3,2,1,1]
[6,5,1,3,4,2,8,7]=>[4,5,8,3,2,1,6,7]=>[5,4,1,6,7,8,3,2]=>[1,1,4,1,1]
[4,8,5,3,1,7,2,6]=>[7,1,4,3,8,5,6,2]=>[2,8,5,6,1,4,3,7]=>[2,2,2,2]
[7,4,5,3,2,8,1,6]=>[2,5,4,3,7,1,8,6]=>[7,4,5,6,2,8,1,3]=>[1,3,2,2]
[5,8,3,6,1,4,2,7]=>[3,1,7,5,6,4,8,2]=>[6,8,2,4,3,5,1,7]=>[2,2,2,2]
[2,5,8,6,4,1,3,7]=>[2,6,7,5,1,4,8,3]=>[7,3,2,4,8,5,1,6]=>[1,1,3,1,2]
[3,6,2,5,8,1,7,4]=>[4,8,1,3,2,6,7,5]=>[5,1,8,6,7,3,2,4]=>[1,2,2,1,2]
[1,6,8,7,4,2,3,5]=>[6,2,7,5,8,4,1,3]=>[3,7,2,4,1,5,8,6]=>[2,2,3,1]
[6,1,7,8,2,4,3,5]=>[7,5,6,3,1,8,2,4]=>[2,4,3,6,8,1,7,5]=>[2,3,2,1]
[7,1,8,6,3,4,2,5]=>[5,7,6,8,4,2,1,3]=>[4,2,3,1,5,7,8,6]=>[1,2,4,1]
[7,2,1,4,5,6,8,3]=>[2,4,5,6,8,3,1,7]=>[7,5,4,3,1,6,8,2]=>[1,1,1,1,3,1]
[1,2,8,3,6,5,7,4]=>[6,5,8,4,7,1,2,3]=>[3,4,1,5,2,8,7,6]=>[2,2,2,1,1]
[6,1,3,2,7,5,8,4]=>[6,3,5,8,2,1,4,7]=>[3,6,4,1,7,8,5,2]=>[2,1,3,1,1]
[1,6,3,8,5,7,2,4]=>[7,5,2,8,3,6,1,4]=>[2,4,7,1,6,3,8,5]=>[3,2,2,1]
[2,6,4,1,7,5,8,3]=>[3,6,5,1,2,8,4,7]=>[6,3,4,8,7,1,5,2]=>[1,3,1,2,1]
[7,6,5,8,1,4,2,3]=>[7,8,5,3,2,1,6,4]=>[2,1,4,6,7,8,3,5]=>[1,5,2]
[5,8,6,7,3,2,1,4]=>[7,1,6,5,3,8,4,2]=>[2,8,3,4,6,1,5,7]=>[2,3,3]
[1,6,4,3,7,2,8,5]=>[3,8,4,2,6,1,5,7]=>[6,1,5,7,3,8,4,2]=>[1,3,2,1,1]
[2,6,3,4,8,7,1,5]=>[7,8,3,1,2,4,6,5]=>[2,1,6,8,7,5,3,4]=>[1,3,1,1,2]
[1,8,3,5,4,2,7,6]=>[5,3,4,8,6,7,1,2]=>[4,6,5,1,3,2,8,7]=>[2,1,2,2,1]
[4,1,6,3,8,2,7,5]=>[1,8,4,3,6,7,2,5]=>[8,1,5,6,3,2,7,4]=>[1,3,1,2,1]
[7,8,2,4,6,3,1,5]=>[4,7,3,6,1,8,5,2]=>[5,2,6,3,8,1,4,7]=>[1,2,2,3]
[3,2,6,4,7,8,1,5]=>[7,1,4,2,3,5,8,6]=>[2,8,5,7,6,4,1,3]=>[2,2,1,1,2]
[2,8,5,7,4,3,1,6]=>[3,7,6,5,8,1,4,2]=>[6,2,3,4,1,8,5,7]=>[1,3,2,2]
[7,2,5,8,3,4,1,6]=>[5,3,7,2,6,1,8,4]=>[4,6,2,7,3,8,1,5]=>[2,2,2,2]
[5,3,8,7,1,2,6,4]=>[8,2,1,5,6,7,4,3]=>[1,7,8,4,3,2,5,6]=>[3,1,1,3]
[6,5,3,8,2,1,7,4]=>[3,5,2,1,8,6,7,4]=>[6,4,7,8,1,3,2,5]=>[1,3,2,2]
[7,5,8,4,1,2,3,6]=>[5,6,2,7,4,1,8,3]=>[4,3,7,2,5,8,1,6]=>[1,2,3,2]
[3,5,7,8,4,1,2,6]=>[2,6,7,1,5,3,8,4]=>[7,3,2,8,4,6,1,5]=>[1,1,2,2,2]
[2,4,6,7,3,1,8,5]=>[5,2,3,8,1,6,4,7]=>[4,7,6,1,8,3,5,2]=>[2,1,2,2,1]
[7,8,4,6,3,1,2,5]=>[6,3,7,5,1,8,4,2]=>[3,6,2,4,8,1,5,7]=>[2,3,3]
[2,6,4,5,3,8,1,7]=>[3,5,4,1,2,7,8,6]=>[6,4,5,8,7,2,1,3]=>[1,3,1,1,2]
[3,6,5,8,4,2,1,7]=>[3,2,7,1,6,5,8,4]=>[6,7,2,8,3,4,1,5]=>[2,2,2,2]
[5,6,8,4,2,3,1,7]=>[1,5,2,7,6,4,8,3]=>[8,4,7,2,3,5,1,6]=>[1,2,3,2]
[6,8,5,4,3,1,2,7]=>[6,1,7,5,4,3,8,2]=>[3,8,2,4,5,6,1,7]=>[2,4,2]
[6,1,4,2,8,5,7,3]=>[3,6,8,7,2,1,4,5]=>[6,3,1,2,7,8,5,4]=>[1,1,4,1,1]
[4,8,6,5,3,2,7,1]=>[6,5,1,4,3,8,7,2]=>[3,4,8,5,6,1,2,7]=>[3,2,3]
[8,6,5,1,2,4,7,3]=>[6,8,4,5,3,2,7,1]=>[3,1,5,4,6,7,2,8]=>[1,2,3,2]
[6,7,5,8,2,1,4,3]=>[5,1,8,6,3,2,7,4]=>[4,8,1,3,6,7,2,5]=>[2,4,2]
[1,7,5,8,2,6,4,3]=>[3,8,7,5,2,6,1,4]=>[6,1,2,4,7,3,8,5]=>[1,4,2,1]
[1,3,8,5,7,6,2,4]=>[4,7,8,6,2,5,1,3]=>[5,2,1,3,7,4,8,6]=>[1,1,3,2,1]
[6,3,8,5,7,1,2,4]=>[6,7,2,1,4,8,5,3]=>[3,2,7,8,5,1,4,6]=>[1,3,1,3]
[8,3,1,5,6,2,7,4]=>[2,4,8,6,3,5,7,1]=>[7,5,1,3,6,4,2,8]=>[1,1,3,1,2]
[6,8,5,2,1,4,7,3]=>[4,6,1,8,5,3,7,2]=>[5,3,8,1,4,6,2,7]=>[1,2,3,2]
[3,8,2,5,6,1,7,4]=>[4,8,1,3,6,5,7,2]=>[5,1,8,6,3,4,2,7]=>[1,2,1,2,2]
[2,8,1,5,6,3,7,4]=>[4,8,6,1,3,5,7,2]=>[5,1,3,8,6,4,2,7]=>[1,3,1,1,2]
[1,8,2,5,7,6,3,4]=>[4,7,8,6,3,5,1,2]=>[5,2,1,3,6,4,8,7]=>[1,1,3,2,1]
[2,5,8,6,1,7,3,4]=>[2,7,8,5,1,4,6,3]=>[7,2,1,4,8,5,3,6]=>[1,1,3,1,2]
[8,6,1,5,7,2,3,4]=>[6,7,4,8,3,2,5,1]=>[3,2,5,1,6,7,4,8]=>[1,2,3,2]
[3,8,6,5,7,1,2,4]=>[6,7,4,1,3,8,5,2]=>[3,2,5,8,6,1,4,7]=>[1,3,1,3]
[7,6,5,8,1,2,4,3]=>[8,5,6,3,2,1,7,4]=>[1,4,3,6,7,8,2,5]=>[2,4,2]
[5,1,7,6,8,4,2,3]=>[1,7,4,3,8,6,2,5]=>[8,2,5,6,1,3,7,4]=>[1,3,3,1]
[7,2,5,8,1,6,4,3]=>[3,8,7,2,5,1,6,4]=>[6,1,2,7,4,8,3,5]=>[1,3,2,2]
[3,2,8,5,7,6,1,4]=>[4,7,8,1,6,2,5,3]=>[5,2,1,8,3,7,4,6]=>[1,1,2,2,2]
[8,2,1,5,7,6,3,4]=>[4,7,8,2,6,3,5,1]=>[5,2,1,7,3,6,4,8]=>[1,1,2,2,2]
[1,2,8,6,5,7,3,4]=>[7,5,4,8,6,1,2,3]=>[2,4,5,1,3,8,7,6]=>[3,3,1,1]
[4,2,1,3,6,7,8,5]=>[2,5,1,6,8,3,4,7]=>[7,4,8,3,1,6,5,2]=>[1,2,1,2,1,1]
[8,2,5,6,3,7,1,4]=>[5,3,7,2,4,8,6,1]=>[4,6,2,7,5,1,3,8]=>[2,2,1,3]
[7,2,6,5,4,1,8,3]=>[8,6,5,2,4,3,1,7]=>[1,3,4,7,5,6,8,2]=>[4,3,1]
[6,1,3,5,4,7,8,2]=>[5,3,4,6,1,8,2,7]=>[4,6,5,3,8,1,7,2]=>[2,1,2,2,1]
[6,1,5,3,4,7,8,2]=>[4,5,3,6,1,8,2,7]=>[5,4,6,3,8,1,7,2]=>[1,2,2,2,1]
[7,5,6,2,4,1,8,3]=>[8,4,2,6,5,3,1,7]=>[1,5,7,3,4,6,8,2]=>[3,4,1]
[8,5,2,6,3,7,1,4]=>[5,7,3,2,4,8,6,1]=>[4,2,6,7,5,1,3,8]=>[1,3,1,3]
[4,3,1,2,6,7,8,5]=>[5,2,1,6,8,3,4,7]=>[4,7,8,3,1,6,5,2]=>[3,1,2,1,1]
[8,1,6,5,7,3,2,4]=>[7,6,4,3,8,2,5,1]=>[2,3,5,6,1,7,4,8]=>[4,2,2]
[3,5,8,6,2,7,1,4]=>[2,5,7,1,4,8,6,3]=>[7,4,2,8,5,1,3,6]=>[1,1,2,1,3]
[5,8,1,6,3,7,2,4]=>[5,1,7,4,8,3,6,2]=>[4,8,2,5,1,6,3,7]=>[2,2,2,2]
[1,8,5,6,3,7,2,4]=>[5,3,7,4,8,6,1,2]=>[4,6,2,5,1,3,8,7]=>[2,2,3,1]
[1,7,6,5,4,2,8,3]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>[6,1,1]
[5,7,6,1,4,2,8,3]=>[1,8,6,4,5,3,2,7]=>[8,1,3,5,4,6,7,2]=>[1,3,3,1]
[7,1,4,2,6,5,8,3]=>[3,6,5,8,2,4,1,7]=>[6,3,4,1,7,5,8,2]=>[1,2,2,2,1]
[4,1,7,3,5,6,8,2]=>[4,1,5,6,3,8,2,7]=>[5,8,4,3,6,1,7,2]=>[2,1,2,2,1]
[2,7,4,1,5,6,8,3]=>[5,3,6,8,1,4,2,7]=>[4,6,3,1,8,5,7,2]=>[2,1,2,2,1]
[5,7,6,4,1,2,8,3]=>[1,8,5,6,4,3,2,7]=>[8,1,4,3,5,6,7,2]=>[1,2,4,1]
[4,7,6,1,5,2,8,3]=>[8,1,6,4,5,3,2,7]=>[1,8,3,5,4,6,7,2]=>[2,2,3,1]
[1,7,6,4,5,2,8,3]=>[4,8,6,5,3,1,2,7]=>[5,1,3,4,6,8,7,2]=>[1,5,1,1]
[1,8,3,6,5,7,2,4]=>[7,5,3,4,8,6,1,2]=>[2,4,6,5,1,3,8,7]=>[3,1,3,1]
[3,8,1,6,5,7,2,4]=>[7,5,1,4,8,3,6,2]=>[2,4,8,5,1,6,3,7]=>[3,1,2,2]
[8,1,3,5,7,6,2,4]=>[4,7,8,3,6,2,5,1]=>[5,2,1,6,3,7,4,8]=>[1,1,2,2,2]
[7,8,5,4,1,6,2,3]=>[7,8,5,4,3,1,6,2]=>[2,1,4,5,6,8,3,7]=>[1,5,2]
[6,1,5,4,3,7,8,2]=>[5,4,3,6,1,8,2,7]=>[4,5,6,3,8,1,7,2]=>[3,2,2,1]
[7,5,6,4,2,1,8,3]=>[5,2,8,6,4,3,1,7]=>[4,7,1,3,5,6,8,2]=>[2,5,1]
[7,4,6,2,5,1,8,3]=>[2,8,4,6,5,3,1,7]=>[7,1,5,3,4,6,8,2]=>[1,2,4,1]
[6,1,4,3,5,7,8,2]=>[4,3,5,6,1,8,2,7]=>[5,6,4,3,8,1,7,2]=>[2,1,2,2,1]
[6,1,3,4,5,7,8,2]=>[3,4,5,6,1,8,2,7]=>[6,5,4,3,8,1,7,2]=>[1,1,1,2,2,1]
[3,4,7,8,5,6,1,2]=>[7,5,1,2,3,8,6,4]=>[2,4,8,7,6,1,3,5]=>[3,1,1,3]
[3,4,7,2,5,1,6,8]=>[1,2,4,6,5,7,3,8]=>[8,7,5,3,4,2,6,1]=>[1,1,1,2,2,1]
[1,4,7,2,5,8,3,6]=>[2,5,7,8,4,1,3,6]=>[7,4,2,1,5,8,6,3]=>[1,1,1,3,1,1]
[3,6,2,4,7,1,5,8]=>[1,3,4,6,2,7,5,8]=>[8,6,5,3,7,2,4,1]=>[1,1,1,2,2,1]
[6,8,3,4,5,7,1,2]=>[3,4,1,7,5,8,6,2]=>[6,5,8,2,4,1,3,7]=>[1,2,2,3]
[4,3,6,7,5,8,1,2]=>[1,3,7,2,5,4,8,6]=>[8,6,2,7,4,5,1,3]=>[1,1,2,2,2]
[6,3,7,5,8,4,1,2]=>[7,4,2,1,3,8,6,5]=>[2,5,7,8,6,1,3,4]=>[4,1,3]
[7,3,8,6,4,5,1,2]=>[7,5,8,2,1,6,4,3]=>[2,4,1,7,8,3,5,6]=>[2,3,3]
[3,2,7,6,5,1,4,8]=>[6,7,1,5,2,4,3,8]=>[3,2,8,4,7,5,6,1]=>[1,2,2,2,1]
[1,2,7,6,5,8,3,4]=>[7,5,4,3,8,1,2,6]=>[2,4,5,6,1,8,7,3]=>[4,2,1,1]
[4,8,2,6,1,5,3,7]=>[1,7,3,5,6,4,8,2]=>[8,2,6,4,3,5,1,7]=>[1,2,1,2,2]
[2,3,8,6,4,1,5,7]=>[6,5,7,1,2,4,8,3]=>[3,4,2,8,7,5,1,6]=>[2,2,1,1,2]
[7,8,1,2,5,6,3,4]=>[7,5,8,3,4,1,6,2]=>[2,4,1,6,5,8,3,7]=>[2,2,2,2]
[4,1,6,2,5,7,3,8]=>[5,1,7,4,2,3,6,8]=>[4,8,2,5,7,6,3,1]=>[2,3,1,1,1]
[6,1,2,5,8,7,3,4]=>[4,7,8,6,2,1,3,5]=>[5,2,1,3,7,8,6,4]=>[1,1,4,1,1]
[2,1,8,6,4,7,3,5]=>[5,7,4,8,1,6,2,3]=>[4,2,5,1,8,3,7,6]=>[1,2,2,2,1]
[7,1,3,6,8,4,2,5]=>[7,6,3,4,8,2,1,5]=>[2,3,6,5,1,7,8,4]=>[3,1,3,1]
[1,8,3,6,7,4,5,2]=>[6,4,8,3,7,5,1,2]=>[3,5,1,6,2,4,8,7]=>[2,2,3,1]
[7,1,5,8,3,6,2,4]=>[5,3,7,8,6,2,1,4]=>[4,6,2,1,3,7,8,5]=>[2,1,4,1]
[5,1,8,7,2,3,6,4]=>[8,5,1,6,7,4,2,3]=>[1,4,8,3,2,5,7,6]=>[3,1,3,1]
[3,1,6,4,7,2,5,8]=>[1,4,6,3,7,2,5,8]=>[8,5,3,6,2,7,4,1]=>[1,1,2,2,1,1]
[2,4,7,5,1,8,3,6]=>[7,2,4,8,1,5,3,6]=>[2,7,5,1,8,4,6,3]=>[2,1,2,2,1]
[6,5,7,1,4,2,3,8]=>[6,7,4,2,1,5,3,8]=>[3,2,5,7,8,4,6,1]=>[1,4,2,1]
[5,6,8,1,3,2,4,7]=>[6,4,1,5,2,7,8,3]=>[3,5,8,4,7,2,1,6]=>[3,2,1,2]
[6,8,5,1,3,4,2,7]=>[5,7,4,1,6,3,8,2]=>[4,2,5,8,3,6,1,7]=>[1,3,2,2]
[6,2,4,3,1,5,7,8]=>[5,2,4,3,6,1,7,8]=>[4,7,5,6,3,8,2,1]=>[2,2,2,1,1]
[4,2,8,3,1,7,5,6]=>[4,1,7,8,2,5,6,3]=>[5,8,2,1,7,4,3,6]=>[2,1,2,1,2]
[1,3,7,4,8,2,5,6]=>[4,6,7,2,3,8,1,5]=>[5,3,2,7,6,1,8,4]=>[1,1,2,1,2,1]
[5,3,7,4,1,6,2,8]=>[7,2,1,5,4,6,3,8]=>[2,7,8,4,5,3,6,1]=>[3,2,2,1]
[2,4,7,3,6,1,8,5]=>[8,2,4,6,1,5,3,7]=>[1,7,5,3,8,4,6,2]=>[2,1,2,2,1]
[5,8,7,6,3,1,2,4]=>[1,6,7,5,8,4,3,2]=>[8,3,2,4,1,5,6,7]=>[1,1,2,4]
[7,5,6,8,1,4,3,2]=>[2,8,7,5,3,1,6,4]=>[7,1,2,4,6,8,3,5]=>[1,5,2]
[2,4,7,1,6,5,3,8]=>[7,2,6,1,4,5,3,8]=>[2,7,3,8,5,4,6,1]=>[2,2,1,2,1]
[1,2,7,8,5,4,3,6]=>[7,6,5,3,8,1,2,4]=>[2,3,4,6,1,8,7,5]=>[4,2,1,1]
[4,2,1,3,6,5,8,7]=>[2,5,1,8,3,4,6,7]=>[7,4,8,1,6,5,3,2]=>[1,2,2,1,1,1]
[2,8,1,4,5,6,3,7]=>[4,5,7,1,3,6,8,2]=>[5,4,2,8,6,3,1,7]=>[1,1,2,1,1,2]
[7,2,1,5,4,6,3,8]=>[5,2,4,7,3,6,1,8]=>[4,7,5,2,6,3,8,1]=>[2,1,2,2,1]
[7,8,2,1,4,5,3,6]=>[3,5,7,4,6,1,8,2]=>[6,4,2,5,3,8,1,7]=>[1,1,2,2,2]
[7,8,4,1,5,3,6,2]=>[6,5,3,8,4,1,7,2]=>[3,4,6,1,5,8,2,7]=>[3,3,2]
[3,4,6,1,5,8,7,2]=>[8,1,2,5,3,7,4,6]=>[1,8,7,4,6,2,5,3]=>[2,1,2,2,1]
[7,5,1,6,4,3,8,2]=>[6,5,4,2,8,3,1,7]=>[3,4,5,7,1,6,8,2]=>[4,3,1]
[5,8,1,6,3,4,7,2]=>[5,1,6,4,8,3,7,2]=>[4,8,3,5,1,6,2,7]=>[2,2,2,2]
[6,5,1,8,2,7,4,3]=>[8,7,5,2,1,6,3,4]=>[1,2,4,7,8,3,6,5]=>[5,2,1]
[6,8,1,7,5,2,3,4]=>[6,7,1,8,5,3,4,2]=>[3,2,8,1,4,6,5,7]=>[1,2,3,2]
[7,6,1,8,5,3,2,4]=>[7,6,8,5,3,2,1,4]=>[2,3,1,4,6,7,8,5]=>[2,5,1]
[5,6,1,7,4,8,2,3]=>[1,7,5,4,2,8,3,6]=>[8,2,4,5,7,1,6,3]=>[1,4,2,1]
[3,6,1,5,7,4,2,8]=>[4,7,1,6,3,2,5,8]=>[5,2,8,3,6,7,4,1]=>[1,2,3,1,1]
[2,5,6,1,7,4,8,3]=>[2,6,5,1,3,8,4,7]=>[7,3,4,8,6,1,5,2]=>[1,3,1,2,1]
[3,1,7,5,6,4,8,2]=>[4,6,1,5,3,8,2,7]=>[5,3,8,4,6,1,7,2]=>[1,2,2,2,1]
[6,1,7,8,5,3,4,2]=>[6,3,1,8,7,5,2,4]=>[3,6,8,1,2,4,7,5]=>[3,4,1]
[7,1,8,6,5,4,2,3]=>[7,8,6,5,4,2,1,3]=>[2,1,3,4,5,7,8,6]=>[1,6,1]
[2,6,5,7,3,4,8,1]=>[5,3,2,6,1,4,8,7]=>[4,6,7,3,8,5,1,2]=>[3,2,1,2]
[1,6,4,7,5,8,2,3]=>[7,3,2,5,4,8,1,6]=>[2,6,7,4,5,1,8,3]=>[3,2,2,1]
[1,3,7,4,6,8,2,5]=>[7,4,5,2,3,8,1,6]=>[2,5,4,7,6,1,8,3]=>[2,2,1,2,1]
[4,7,5,6,3,2,8,1]=>[3,6,1,5,4,2,8,7]=>[6,3,8,4,5,7,1,2]=>[1,2,3,2]
[8,1,6,5,7,2,4,3]=>[8,6,4,3,7,2,5,1]=>[1,3,5,6,2,7,4,8]=>[4,2,2]
[1,2,7,6,8,3,4,5]=>[6,7,4,3,8,1,2,5]=>[3,2,5,6,1,8,7,4]=>[1,3,2,1,1]
[3,8,6,4,2,7,5,1]=>[4,8,5,1,3,7,6,2]=>[5,1,4,8,6,2,3,7]=>[1,3,1,3]
[7,8,1,6,2,4,5,3]=>[6,8,5,7,3,1,4,2]=>[3,1,4,2,6,8,5,7]=>[1,2,3,2]
[3,8,4,1,7,2,6,5]=>[3,8,1,6,7,4,5,2]=>[6,1,8,3,2,5,4,7]=>[1,2,1,2,2]
[5,4,7,1,8,3,2,6]=>[2,1,7,6,8,4,3,5]=>[7,8,2,3,1,5,6,4]=>[2,2,3,1]
[3,7,4,1,8,5,2,6]=>[3,7,1,6,8,4,2,5]=>[6,2,8,3,1,5,7,4]=>[1,2,1,3,1]
[6,7,1,4,8,3,2,5]=>[4,7,6,1,8,3,2,5]=>[5,2,3,8,1,6,7,4]=>[1,3,3,1]
[2,7,1,8,4,5,3,6]=>[5,7,6,8,1,3,2,4]=>[4,2,3,1,8,6,7,5]=>[1,2,2,2,1]
[8,4,2,1,7,3,6,5]=>[8,3,2,6,7,4,5,1]=>[1,6,7,3,2,5,4,8]=>[3,1,2,2]
[7,4,2,1,8,5,3,6]=>[7,3,2,6,8,4,1,5]=>[2,6,7,3,1,5,8,4]=>[3,1,3,1]
[1,5,4,2,8,3,6,7]=>[6,3,2,7,8,1,4,5]=>[3,6,7,2,1,8,5,4]=>[3,1,2,1,1]
[6,4,3,1,5,8,2,7]=>[5,3,2,7,1,8,4,6]=>[4,6,7,2,8,1,5,3]=>[3,2,2,1]
[3,7,6,8,4,5,2,1]=>[5,3,2,8,1,7,6,4]=>[4,6,7,1,8,2,3,5]=>[3,2,3]
[1,7,6,8,5,4,2,3]=>[7,3,2,8,6,5,1,4]=>[2,6,7,1,3,4,8,5]=>[3,4,1]
[2,4,8,6,7,3,5,1]=>[6,4,8,2,7,1,5,3]=>[3,5,1,7,2,8,4,6]=>[2,2,2,2]
[3,4,8,5,6,7,2,1]=>[4,5,8,1,2,7,6,3]=>[5,4,1,8,7,2,3,6]=>[1,1,2,1,3]
[6,3,5,8,4,7,2,1]=>[3,5,1,8,2,7,6,4]=>[6,4,8,1,7,2,3,5]=>[1,2,2,3]
[5,4,3,8,6,7,2,1]=>[2,1,5,8,3,7,6,4]=>[7,8,4,1,6,2,3,5]=>[2,1,2,3]
[6,2,5,8,7,3,4,1]=>[3,6,1,8,7,2,5,4]=>[6,3,8,1,2,7,4,5]=>[1,2,3,2]
[3,2,8,5,7,4,6,1]=>[4,6,8,1,7,2,5,3]=>[5,3,1,8,2,7,4,6]=>[1,1,2,2,2]
[2,1,8,7,4,6,3,5]=>[5,7,8,6,1,4,2,3]=>[4,2,1,3,8,5,7,6]=>[1,1,3,2,1]
[3,1,8,5,7,6,2,4]=>[4,7,8,1,6,5,2,3]=>[5,2,1,8,3,4,7,6]=>[1,1,2,3,1]
[6,1,5,8,7,4,2,3]=>[3,7,1,8,6,5,2,4]=>[6,2,8,1,3,4,7,5]=>[1,2,4,1]
[5,8,6,7,4,3,2,1]=>[3,8,1,7,6,5,4,2]=>[6,1,8,2,3,4,5,7]=>[1,2,5]
[4,8,7,5,6,3,2,1]=>[4,8,7,1,6,5,3,2]=>[5,1,2,8,3,4,6,7]=>[1,3,4]
[6,2,1,4,3,8,5,7]=>[2,4,7,8,3,1,5,6]=>[7,5,2,1,6,8,4,3]=>[1,1,1,3,1,1]
[8,2,1,4,3,6,5,7]=>[2,4,7,3,5,6,8,1]=>[7,5,2,6,4,3,1,8]=>[1,1,2,1,1,2]
[6,2,4,1,3,8,5,7]=>[7,2,3,8,4,1,5,6]=>[2,7,6,1,5,8,4,3]=>[2,1,3,1,1]
[6,2,4,1,3,5,8,7]=>[8,2,4,3,5,1,6,7]=>[1,7,5,6,4,8,3,2]=>[2,2,2,1,1]
[4,2,6,1,3,5,8,7]=>[8,2,1,4,5,3,6,7]=>[1,7,8,5,4,6,3,2]=>[3,1,2,1,1]
[2,1,6,4,3,5,8,7]=>[4,8,1,5,2,3,6,7]=>[5,1,8,4,7,6,3,2]=>[1,2,2,1,1,1]
[4,6,2,1,3,5,8,7]=>[3,1,8,4,5,2,6,7]=>[6,8,1,5,4,7,3,2]=>[2,2,2,1,1]
[6,4,2,1,3,5,8,7]=>[3,8,4,2,5,1,6,7]=>[6,1,5,7,4,8,3,2]=>[1,3,2,1,1]
[8,4,2,1,3,6,5,7]=>[3,7,4,2,5,6,8,1]=>[6,2,5,7,4,3,1,8]=>[1,3,1,1,2]
[8,4,2,1,6,3,5,7]=>[3,6,2,7,4,5,8,1]=>[6,3,7,2,5,4,1,8]=>[1,2,2,1,2]
[6,4,2,1,8,3,5,7]=>[3,6,2,7,1,8,4,5]=>[6,3,7,2,8,1,5,4]=>[1,2,2,2,1]
[4,6,2,1,8,3,5,7]=>[3,1,6,7,2,8,4,5]=>[6,8,3,2,7,1,5,4]=>[2,1,2,2,1]
[2,6,1,4,3,8,5,7]=>[4,7,8,1,3,2,5,6]=>[5,2,1,8,6,7,4,3]=>[1,1,2,2,1,1]
[2,1,6,4,3,8,5,7]=>[4,7,1,3,8,2,5,6]=>[5,2,8,6,1,7,4,3]=>[1,2,1,2,1,1]
[2,1,8,4,3,6,5,7]=>[4,7,1,5,6,8,2,3]=>[5,2,8,4,3,1,7,6]=>[1,2,1,1,2,1]
[2,8,1,4,3,6,5,7]=>[4,7,1,3,5,6,8,2]=>[5,2,8,6,4,3,1,7]=>[1,2,1,1,1,2]
[2,8,4,1,3,6,5,7]=>[7,4,1,3,5,6,8,2]=>[2,5,8,6,4,3,1,7]=>[3,1,1,1,2]
[4,8,2,1,3,6,5,7]=>[3,1,7,4,5,6,8,2]=>[6,8,2,5,4,3,1,7]=>[2,2,1,1,2]
[6,8,2,1,4,3,5,7]=>[3,6,4,5,1,7,8,2]=>[6,3,5,4,8,2,1,7]=>[1,2,2,1,2]
[8,6,2,1,4,3,5,7]=>[3,6,4,5,7,2,8,1]=>[6,3,5,4,2,7,1,8]=>[1,2,1,2,2]
[2,8,1,4,6,3,5,7]=>[4,6,7,1,3,5,8,2]=>[5,3,2,8,6,4,1,7]=>[1,1,2,1,1,2]
[2,1,8,4,6,3,5,7]=>[4,6,7,1,5,8,2,3]=>[5,3,2,8,4,1,7,6]=>[1,1,2,1,2,1]
[2,1,6,4,8,3,5,7]=>[4,6,1,3,7,8,2,5]=>[5,3,8,6,2,1,7,4]=>[1,2,1,1,2,1]
[2,6,1,4,8,3,5,7]=>[4,6,7,1,2,8,3,5]=>[5,3,2,8,7,1,6,4]=>[1,1,2,1,2,1]
[2,6,4,1,8,3,5,7]=>[6,3,7,1,2,8,4,5]=>[3,6,2,8,7,1,5,4]=>[2,2,1,2,1]
[2,6,4,8,1,3,5,7]=>[5,3,6,1,2,7,8,4]=>[4,6,3,8,7,2,1,5]=>[2,2,1,1,2]
[4,6,2,8,1,3,5,7]=>[3,1,5,6,2,7,8,4]=>[6,8,4,3,7,2,1,5]=>[2,1,2,1,2]
[4,2,6,1,3,8,5,7]=>[7,1,8,2,4,3,5,6]=>[2,8,1,7,5,6,4,3]=>[2,2,2,1,1]
[4,2,6,1,8,3,5,7]=>[6,1,7,2,3,8,4,5]=>[3,8,2,7,6,1,5,4]=>[2,2,1,2,1]
[6,2,4,1,8,3,5,7]=>[6,2,3,7,1,8,4,5]=>[3,7,6,2,8,1,5,4]=>[2,1,2,2,1]
[8,2,4,1,6,3,5,7]=>[6,2,3,7,4,5,8,1]=>[3,7,6,2,5,4,1,8]=>[2,1,2,1,2]
[8,2,1,4,6,3,5,7]=>[2,4,6,7,3,5,8,1]=>[7,5,3,2,6,4,1,8]=>[1,1,1,2,1,2]
[6,2,1,4,8,3,5,7]=>[2,4,6,7,1,8,3,5]=>[7,5,3,2,8,1,6,4]=>[1,1,1,2,2,1]
[4,2,1,6,8,3,5,7]=>[6,2,1,4,7,8,3,5]=>[3,7,8,5,2,1,6,4]=>[3,1,1,2,1]
[4,2,1,6,3,8,5,7]=>[7,2,1,4,8,3,5,6]=>[2,7,8,5,1,6,4,3]=>[3,1,2,1,1]
[2,1,4,3,8,6,5,7]=>[7,1,3,6,8,2,4,5]=>[2,8,6,3,1,7,5,4]=>[2,1,1,2,1,1]
[2,4,1,3,8,6,5,7]=>[2,7,1,6,8,3,4,5]=>[7,2,8,3,1,6,5,4]=>[1,2,1,2,1,1]
[4,2,1,3,8,6,5,7]=>[7,2,1,6,8,3,4,5]=>[2,7,8,3,1,6,5,4]=>[3,1,2,1,1]
[4,2,1,8,6,3,5,7]=>[6,1,7,2,5,8,3,4]=>[3,8,2,7,4,1,6,5]=>[2,2,1,2,1]
[6,2,1,8,4,3,5,7]=>[6,2,5,7,1,8,3,4]=>[3,7,4,2,8,1,6,5]=>[2,1,2,2,1]
[8,2,1,6,4,3,5,7]=>[6,2,5,7,3,4,8,1]=>[3,7,4,2,6,5,1,8]=>[2,1,2,1,2]
[8,2,6,1,4,3,5,7]=>[6,2,4,5,7,3,8,1]=>[3,7,5,4,2,6,1,8]=>[2,1,1,2,2]
[6,2,8,1,4,3,5,7]=>[6,2,4,5,1,7,8,3]=>[3,7,5,4,8,2,1,6]=>[2,1,2,1,2]
[4,2,8,1,6,3,5,7]=>[6,1,7,2,4,5,8,3]=>[3,8,2,7,5,4,1,6]=>[2,2,1,1,2]
[4,2,8,1,3,6,5,7]=>[7,2,1,4,5,6,8,3]=>[2,7,8,5,4,3,1,6]=>[3,1,1,1,2]
[2,4,8,1,3,6,5,7]=>[2,7,1,4,5,6,8,3]=>[7,2,8,5,4,3,1,6]=>[1,2,1,1,1,2]
[2,4,1,8,3,6,5,7]=>[2,7,1,5,6,8,3,4]=>[7,2,8,4,3,1,6,5]=>[1,2,1,1,2,1]
[2,1,4,8,3,6,5,7]=>[7,1,3,5,6,8,2,4]=>[2,8,6,4,3,1,7,5]=>[2,1,1,1,2,1]
[2,1,4,8,6,3,5,7]=>[6,7,1,3,5,8,2,4]=>[3,2,8,6,4,1,7,5]=>[1,2,1,1,2,1]
[2,4,8,1,6,3,5,7]=>[2,6,7,1,4,5,8,3]=>[7,3,2,8,5,4,1,6]=>[1,1,2,1,1,2]
[2,4,8,6,1,3,5,7]=>[2,5,6,7,1,4,8,3]=>[7,4,3,2,8,5,1,6]=>[1,1,1,2,1,2]
[6,2,8,4,1,3,5,7]=>[5,6,2,4,1,7,8,3]=>[4,3,7,5,8,2,1,6]=>[1,2,2,1,2]
[8,2,6,4,1,3,5,7]=>[5,6,2,4,7,3,8,1]=>[4,3,7,5,2,6,1,8]=>[1,2,1,2,2]
[8,4,6,2,1,3,5,7]=>[5,4,2,6,7,3,8,1]=>[4,5,7,3,2,6,1,8]=>[3,1,2,2]
[6,4,8,2,1,3,5,7]=>[5,4,2,6,1,7,8,3]=>[4,5,7,3,8,2,1,6]=>[3,2,1,2]
[4,6,8,2,1,3,5,7]=>[1,5,4,6,2,7,8,3]=>[8,4,5,3,7,2,1,6]=>[1,2,2,1,2]
[2,6,8,4,1,3,5,7]=>[5,6,4,1,2,7,8,3]=>[4,3,5,8,7,2,1,6]=>[1,3,1,1,2]
[2,6,8,1,4,3,5,7]=>[6,4,5,1,2,7,8,3]=>[3,5,4,8,7,2,1,6]=>[2,2,1,1,2]
[2,6,1,8,4,3,5,7]=>[6,5,7,1,2,8,3,4]=>[3,4,2,8,7,1,6,5]=>[2,2,1,2,1]
[2,1,6,8,4,3,5,7]=>[6,5,1,3,7,8,2,4]=>[3,4,8,6,2,1,7,5]=>[3,1,1,2,1]
[2,1,8,6,4,3,5,7]=>[6,5,7,1,4,8,2,3]=>[3,4,2,8,5,1,7,6]=>[2,2,1,2,1]
[2,8,1,6,4,3,5,7]=>[6,5,7,1,3,4,8,2]=>[3,4,2,8,6,5,1,7]=>[2,2,1,1,2]
[2,8,6,4,1,3,5,7]=>[5,6,4,7,1,3,8,2]=>[4,3,5,2,8,6,1,7]=>[1,2,2,1,2]
[4,8,6,2,1,3,5,7]=>[1,5,4,6,7,3,8,2]=>[8,4,5,3,2,6,1,7]=>[1,2,1,2,2]
[6,8,4,2,1,3,5,7]=>[5,4,6,3,1,7,8,2]=>[4,5,3,6,8,2,1,7]=>[2,3,1,2]
[5,2,4,3,8,1,7,6]=>[3,8,2,1,4,6,7,5]=>[6,1,7,8,5,3,2,4]=>[1,3,1,1,2]
[6,2,4,1,5,3,8,7]=>[5,2,3,8,4,1,6,7]=>[4,7,6,1,5,8,3,2]=>[2,1,3,1,1]
[4,3,6,1,5,2,8,7]=>[2,1,5,8,4,3,6,7]=>[7,8,4,1,5,6,3,2]=>[2,1,3,1,1]
[4,3,5,2,8,1,7,6]=>[2,1,3,8,4,6,7,5]=>[7,8,6,1,5,3,2,4]=>[2,1,2,1,2]
[4,3,8,1,7,2,6,5]=>[1,8,2,6,7,4,5,3]=>[8,1,7,3,2,5,4,6]=>[1,2,1,2,2]
[4,3,8,1,5,2,7,6]=>[2,1,5,8,4,6,7,3]=>[7,8,4,1,5,3,2,6]=>[2,1,2,1,2]
[5,1,8,3,4,2,7,6]=>[4,5,1,8,6,7,2,3]=>[5,4,8,1,3,2,7,6]=>[1,2,2,2,1]
[5,4,8,1,3,2,7,6]=>[5,2,1,8,4,6,7,3]=>[4,7,8,1,5,3,2,6]=>[3,2,1,2]
[2,1,5,4,8,3,7,6]=>[3,8,1,4,6,7,2,5]=>[6,1,8,5,3,2,7,4]=>[1,2,1,1,2,1]
[5,1,7,6,8,3,4,2]=>[1,6,4,3,8,7,2,5]=>[8,3,5,6,1,2,7,4]=>[1,3,3,1]
[4,3,7,6,8,1,5,2]=>[8,1,6,2,4,3,7,5]=>[1,8,3,7,5,6,2,4]=>[2,2,2,2]
[4,3,6,5,8,1,7,2]=>[1,4,2,3,8,6,7,5]=>[8,5,7,6,1,3,2,4]=>[1,2,1,2,2]
[6,3,5,4,7,2,8,1]=>[4,2,3,1,6,5,8,7]=>[5,7,6,8,3,4,1,2]=>[2,2,2,2]
[6,3,5,4,8,1,7,2]=>[4,2,3,1,8,6,7,5]=>[5,7,6,8,1,3,2,4]=>[2,2,2,2]
[7,1,6,3,8,4,5,2]=>[6,8,4,3,7,2,1,5]=>[3,1,5,6,2,7,8,4]=>[1,3,3,1]
[7,4,6,5,8,1,3,2]=>[8,2,6,4,3,1,7,5]=>[1,7,3,5,6,8,2,4]=>[2,4,2]
[2,1,8,4,6,3,7,5]=>[8,4,6,1,5,7,2,3]=>[1,5,3,8,4,2,7,6]=>[2,2,1,2,1]
[8,4,6,1,3,2,7,5]=>[5,2,8,4,6,3,7,1]=>[4,7,1,5,3,6,2,8]=>[2,2,2,2]
[8,1,6,3,4,2,7,5]=>[4,5,8,6,2,3,7,1]=>[5,4,1,3,7,6,2,8]=>[1,1,3,1,2]
[8,1,6,3,7,2,5,4]=>[8,4,6,3,7,2,5,1]=>[1,5,3,6,2,7,4,8]=>[2,2,2,2]
[8,3,5,1,7,2,6,4]=>[8,2,6,3,7,4,5,1]=>[1,7,3,6,2,5,4,8]=>[2,2,2,2]
[8,3,5,2,6,1,7,4]=>[8,2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2,8]=>[2,2,2,2]
[7,3,5,2,6,4,8,1]=>[6,2,4,3,5,1,8,7]=>[3,7,5,6,4,8,1,2]=>[2,2,2,2]
[8,2,6,3,5,1,7,4]=>[8,4,6,2,5,3,7,1]=>[1,5,3,7,4,6,2,8]=>[2,2,2,2]
[8,2,7,1,5,3,6,4]=>[8,6,2,4,5,7,3,1]=>[1,3,7,5,4,2,6,8]=>[3,1,1,3]
[8,2,4,1,5,3,7,6]=>[5,2,3,8,4,6,7,1]=>[4,7,6,1,5,3,2,8]=>[2,1,2,1,2]
[8,2,4,1,7,3,6,5]=>[3,8,2,6,7,4,5,1]=>[6,1,7,3,2,5,4,8]=>[1,2,1,2,2]
[3,2,8,4,6,1,7,5]=>[8,1,4,6,2,5,7,3]=>[1,8,5,3,7,4,2,6]=>[2,1,2,1,2]
[3,2,8,1,5,4,7,6]=>[1,5,8,2,4,6,7,3]=>[8,4,1,7,5,3,2,6]=>[1,1,2,1,1,2]
[3,2,7,6,8,1,5,4]=>[8,6,1,4,2,3,7,5]=>[1,3,8,5,7,6,2,4]=>[3,2,1,2]
[3,2,7,1,8,5,6,4]=>[6,8,1,7,2,4,3,5]=>[3,1,8,2,7,5,6,4]=>[1,2,2,2,1]
[3,2,6,5,8,1,7,4]=>[4,1,3,8,2,6,7,5]=>[5,8,6,1,7,3,2,4]=>[2,1,2,1,2]
[6,5,7,2,4,3,8,1]=>[6,4,2,1,5,3,8,7]=>[3,5,7,8,4,6,1,2]=>[4,2,2]
[6,5,8,2,4,1,7,3]=>[8,4,2,1,6,5,7,3]=>[1,5,7,8,3,4,2,6]=>[4,2,2]
[7,2,4,1,8,5,6,3]=>[3,6,8,2,7,4,1,5]=>[6,3,1,7,2,5,8,4]=>[1,1,2,3,1]
[7,6,8,2,4,1,5,3]=>[8,4,6,5,2,1,7,3]=>[1,5,3,4,7,8,2,6]=>[2,4,2]
[7,6,8,1,5,2,4,3]=>[8,6,7,4,2,1,5,3]=>[1,3,2,5,7,8,4,6]=>[2,4,2]
[2,1,7,3,8,5,6,4]=>[6,8,7,1,4,2,3,5]=>[3,1,2,8,5,7,6,4]=>[1,3,2,1,1]
[7,1,3,2,8,5,6,4]=>[6,8,3,7,2,4,1,5]=>[3,1,6,2,7,5,8,4]=>[1,2,2,2,1]
[7,1,8,5,6,2,4,3]=>[8,6,4,7,5,2,1,3]=>[1,3,5,2,4,7,8,6]=>[3,4,1]
[7,2,8,1,5,4,6,3]=>[6,5,8,2,4,1,7,3]=>[3,4,1,7,5,8,2,6]=>[2,2,2,2]
[6,2,7,4,5,3,8,1]=>[4,6,5,2,1,3,8,7]=>[5,3,4,7,8,6,1,2]=>[1,4,1,2]
[5,4,7,2,6,3,8,1]=>[2,1,6,4,5,3,8,7]=>[7,8,3,5,4,6,1,2]=>[2,2,2,2]
[6,5,8,1,7,2,4,3]=>[8,6,2,1,7,4,5,3]=>[1,3,7,8,2,5,4,6]=>[4,2,2]
[6,5,7,4,8,1,3,2]=>[2,1,8,6,4,3,7,5]=>[7,8,1,3,5,6,2,4]=>[2,4,2]
[6,5,7,1,8,3,4,2]=>[6,2,1,8,7,4,3,5]=>[3,7,8,1,2,5,6,4]=>[3,4,1]
[6,1,7,4,8,3,5,2]=>[4,6,3,1,8,7,2,5]=>[5,3,6,8,1,2,7,4]=>[1,3,3,1]
[5,4,7,1,8,3,6,2]=>[2,1,6,8,7,4,3,5]=>[7,8,3,1,2,5,6,4]=>[2,1,4,1]
[5,4,6,3,8,1,7,2]=>[2,1,4,3,8,6,7,5]=>[7,8,5,6,1,3,2,4]=>[2,2,2,2]
[2,5,3,4,7,1,8,6]=>[8,3,1,2,4,6,5,7]=>[1,6,8,7,5,3,4,2]=>[3,1,1,2,1]
[2,4,8,3,5,7,6,1]=>[8,2,4,5,7,1,6,3]=>[1,7,5,4,2,8,3,6]=>[2,1,1,2,2]
[4,2,5,3,1,8,6,7]=>[4,2,1,3,7,8,5,6]=>[5,7,8,6,2,1,4,3]=>[3,1,1,2,1]
[4,2,1,8,5,3,6,7]=>[6,2,1,5,7,8,3,4]=>[3,7,8,4,2,1,6,5]=>[3,1,1,2,1]
[5,4,1,3,8,2,6,7]=>[4,6,2,1,7,8,3,5]=>[5,3,7,8,2,1,6,4]=>[1,3,1,2,1]
[5,1,4,8,3,2,6,7]=>[3,6,5,1,7,8,2,4]=>[6,3,4,8,2,1,7,5]=>[1,3,1,2,1]
[1,5,8,4,3,2,6,7]=>[2,6,5,4,7,8,1,3]=>[7,3,4,5,2,1,8,6]=>[1,3,1,2,1]
[1,8,5,4,3,2,6,7]=>[6,5,4,3,7,8,1,2]=>[3,4,5,6,2,1,8,7]=>[4,1,2,1]
[1,7,4,3,8,5,2,6]=>[3,7,4,6,2,8,1,5]=>[6,2,5,3,7,1,8,4]=>[1,2,2,2,1]
[1,5,7,3,8,4,2,6]=>[2,7,4,6,3,8,1,5]=>[7,2,5,3,6,1,8,4]=>[1,2,2,2,1]
[5,1,4,7,8,3,2,6]=>[7,3,1,6,4,8,2,5]=>[2,6,8,3,5,1,7,4]=>[3,2,2,1]
[4,8,1,5,7,3,6,2]=>[1,4,6,8,7,3,5,2]=>[8,5,3,1,2,6,4,7]=>[1,1,1,3,2]
[8,1,5,3,7,4,6,2]=>[6,3,8,4,7,2,5,1]=>[3,6,1,5,2,7,4,8]=>[2,2,2,2]
[3,8,4,7,6,5,2,1]=>[8,7,3,6,1,5,4,2]=>[1,2,6,3,8,4,5,7]=>[3,2,3]
[1,6,8,5,3,7,4,2]=>[2,8,5,4,7,6,1,3]=>[7,1,4,5,2,3,8,6]=>[1,3,3,1]
[6,8,1,7,4,3,5,2]=>[6,5,1,8,7,3,4,2]=>[3,4,8,1,2,6,5,7]=>[3,3,2]
[6,4,8,1,7,3,5,2]=>[2,6,1,8,7,4,5,3]=>[7,3,8,1,2,5,4,6]=>[1,2,3,2]
[7,6,4,1,3,8,2,5]=>[5,7,3,8,4,2,1,6]=>[4,2,6,1,5,7,8,3]=>[1,2,4,1]
[1,7,5,6,3,2,8,4]=>[5,3,8,6,4,1,2,7]=>[4,6,1,3,5,8,7,2]=>[2,4,1,1]
[2,7,4,6,3,1,8,5]=>[3,5,8,6,1,4,2,7]=>[6,4,1,3,8,5,7,2]=>[1,1,3,2,1]
[2,6,8,4,3,7,5,1]=>[4,2,8,5,7,1,6,3]=>[5,7,1,4,2,8,3,6]=>[2,2,2,2]
[6,2,4,8,3,7,5,1]=>[8,3,5,1,7,2,6,4]=>[1,6,4,8,2,7,3,5]=>[2,2,2,2]
[7,2,6,3,4,1,8,5]=>[4,5,8,2,6,3,1,7]=>[5,4,1,7,3,6,8,2]=>[1,1,2,3,1]
[2,6,7,3,1,4,8,5]=>[4,8,5,1,2,6,3,7]=>[5,1,4,8,7,3,6,2]=>[1,3,1,2,1]
[2,7,1,8,3,5,4,6]=>[7,5,6,8,1,3,2,4]=>[2,4,3,1,8,6,7,5]=>[2,1,2,2,1]
[2,1,7,3,5,8,4,6]=>[5,7,8,1,4,2,3,6]=>[4,2,1,8,5,7,6,3]=>[1,1,2,2,1,1]
[8,7,1,3,6,2,4,5]=>[4,6,7,8,3,5,2,1]=>[5,3,2,1,6,4,7,8]=>[1,1,1,2,3]
[8,2,1,7,3,5,6,4]=>[6,8,2,5,7,3,4,1]=>[3,1,7,4,2,6,5,8]=>[1,2,1,2,2]
[8,7,2,6,3,5,4,1]=>[8,5,7,3,6,4,2,1]=>[1,4,2,6,3,5,7,8]=>[2,2,4]
[1,2,8,7,4,5,6,3]=>[5,6,8,7,4,1,2,3]=>[4,3,1,2,5,8,7,6]=>[1,1,4,1,1]
[8,3,7,1,5,6,2,4]=>[7,2,5,8,4,6,3,1]=>[2,7,4,1,5,3,6,8]=>[2,1,2,3]
[8,6,1,2,7,5,3,4]=>[7,8,6,3,4,2,5,1]=>[2,1,3,6,5,7,4,8]=>[1,3,2,2]
[8,1,6,2,7,4,5,3]=>[6,8,7,4,2,3,5,1]=>[3,1,2,5,7,6,4,8]=>[1,4,1,2]
[1,8,5,2,6,7,4,3]=>[5,3,8,7,4,6,1,2]=>[4,6,1,2,5,3,8,7]=>[2,3,2,1]
[5,2,1,8,6,7,4,3]=>[5,1,8,7,2,6,3,4]=>[4,8,1,2,7,3,6,5]=>[2,3,2,1]
[2,8,5,7,6,4,3,1]=>[8,3,7,6,5,1,4,2]=>[1,6,2,3,4,8,5,7]=>[2,4,2]
[1,7,8,5,2,6,4,3]=>[8,7,5,4,2,6,1,3]=>[1,2,4,5,7,3,8,6]=>[5,2,1]
[7,8,1,6,4,2,5,3]=>[8,6,5,7,3,1,4,2]=>[1,3,4,2,6,8,5,7]=>[3,3,2]
[7,8,6,1,5,3,2,4]=>[7,6,8,4,1,5,3,2]=>[2,3,1,5,8,4,6,7]=>[2,3,3]
[7,3,8,6,1,5,2,4]=>[7,8,2,5,1,6,4,3]=>[2,1,7,4,8,3,5,6]=>[1,2,2,3]
[8,7,6,1,5,3,4,2]=>[6,8,7,4,5,3,2,1]=>[3,1,2,5,4,6,7,8]=>[1,3,4]
[8,7,1,6,4,5,3,2]=>[5,8,7,6,3,4,2,1]=>[4,1,2,3,6,5,7,8]=>[1,4,3]
[8,1,7,5,6,4,3,2]=>[4,8,7,6,5,2,3,1]=>[5,1,2,3,4,7,6,8]=>[1,5,2]
[1,8,6,7,5,4,3,2]=>[3,8,7,6,5,4,1,2]=>[6,1,2,3,4,5,8,7]=>[1,6,1]
[6,3,5,7,2,8,4,1]=>[3,8,2,1,5,4,7,6]=>[6,1,7,8,4,5,2,3]=>[1,3,2,2]
[4,5,3,6,1,2,8,7]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[1,2,3,1,1]
[3,5,1,4,6,2,8,7]=>[1,4,5,2,8,3,6,7]=>[8,5,4,7,1,6,3,2]=>[1,1,2,2,1,1]
[8,3,4,5,7,2,1,6]=>[2,3,4,7,6,8,5,1]=>[7,6,5,2,3,1,4,8]=>[1,1,1,2,3]
[5,7,4,6,3,8,2,1]=>[1,3,5,4,2,8,7,6]=>[8,6,4,5,7,1,2,3]=>[1,1,3,3]
[2,8,4,6,3,7,1,5]=>[3,5,7,4,8,1,6,2]=>[6,4,2,5,1,8,3,7]=>[1,1,2,2,2]
[8,1,4,7,3,6,2,5]=>[3,5,7,8,6,2,4,1]=>[6,4,2,1,3,7,5,8]=>[1,1,1,3,2]
[8,3,4,7,5,1,2,6]=>[2,3,6,7,5,8,4,1]=>[7,6,3,2,4,1,5,8]=>[1,1,1,2,3]
[8,5,3,7,1,4,2,6]=>[3,7,5,2,6,8,4,1]=>[6,2,4,7,3,1,5,8]=>[1,3,1,3]
[6,5,3,7,1,8,4,2]=>[8,3,2,1,7,5,4,6]=>[1,6,7,8,2,4,5,3]=>[4,3,1]
[6,5,1,4,7,8,3,2]=>[4,5,2,1,8,7,3,6]=>[5,4,7,8,1,2,6,3]=>[1,3,3,1]
[5,1,4,6,8,3,7,2]=>[3,4,1,6,8,7,2,5]=>[6,5,8,3,1,2,7,4]=>[1,2,1,3,1]
[4,7,1,3,5,8,6,2]=>[1,8,4,5,7,3,2,6]=>[8,1,5,4,2,6,7,3]=>[1,2,1,3,1]
[4,8,3,7,1,2,6,5]=>[1,3,8,5,6,7,4,2]=>[8,6,1,4,3,2,5,7]=>[1,1,2,1,3]
[3,8,6,4,1,7,2,5]=>[7,4,8,1,5,3,6,2]=>[2,5,1,8,4,6,3,7]=>[2,2,2,2]
[3,8,1,2,5,7,6,4]=>[8,1,5,7,3,4,6,2]=>[1,8,4,2,6,5,3,7]=>[2,1,2,1,2]
[2,8,7,5,4,1,3,6]=>[6,7,5,4,8,1,3,2]=>[3,2,4,5,1,8,6,7]=>[1,3,2,2]
[8,7,2,6,4,1,3,5]=>[6,7,3,5,8,4,2,1]=>[3,2,6,4,1,5,7,8]=>[1,2,1,4]
[3,8,6,7,4,2,1,5]=>[7,6,5,1,3,8,4,2]=>[2,3,4,8,6,1,5,7]=>[4,1,3]
[5,3,7,8,2,4,6,1]=>[5,1,6,2,3,8,7,4]=>[4,8,3,7,6,1,2,5]=>[2,2,1,3]
[5,3,7,6,2,1,8,4]=>[5,1,8,2,6,4,3,7]=>[4,8,1,7,3,5,6,2]=>[2,2,3,1]
[5,3,6,2,8,7,1,4]=>[7,2,1,3,8,4,6,5]=>[2,7,8,6,1,5,3,4]=>[3,1,2,2]
[5,7,8,6,4,2,1,3]=>[7,1,6,2,8,5,4,3]=>[2,8,3,7,1,4,5,6]=>[2,2,4]
[6,1,7,4,5,8,2,3]=>[4,7,5,3,1,8,2,6]=>[5,2,4,6,8,1,7,3]=>[1,4,2,1]
[6,7,3,5,1,8,2,4]=>[3,7,1,8,5,4,2,6]=>[6,2,8,1,4,5,7,3]=>[1,2,4,1]
[2,1,6,7,5,8,3,4]=>[3,7,5,1,4,8,2,6]=>[6,2,4,8,5,1,7,3]=>[1,3,1,2,1]
[2,1,5,7,3,6,8,4]=>[3,6,8,1,5,2,4,7]=>[6,3,1,8,4,7,5,2]=>[1,1,2,2,1,1]
[5,7,3,6,1,2,8,4]=>[3,1,8,5,6,4,2,7]=>[6,8,1,4,3,5,7,2]=>[2,2,3,1]
[4,1,7,2,5,6,8,3]=>[5,1,6,8,4,2,3,7]=>[4,8,3,1,5,7,6,2]=>[2,1,3,1,1]
[2,4,7,1,6,5,8,3]=>[6,2,5,8,1,4,3,7]=>[3,7,4,1,8,5,6,2]=>[2,1,2,2,1]
[4,6,2,1,8,7,5,3]=>[8,1,7,3,2,6,4,5]=>[1,8,2,6,7,3,5,4]=>[2,3,2,1]
[3,4,6,2,7,8,5,1]=>[5,1,2,3,8,4,7,6]=>[4,8,7,6,1,5,2,3]=>[2,1,1,2,2]
[4,6,1,2,5,8,7,3]=>[1,8,5,7,3,2,4,6]=>[8,1,4,2,6,7,5,3]=>[1,2,3,1,1]
[5,6,1,4,8,2,7,3]=>[4,1,8,6,2,7,3,5]=>[5,8,1,3,7,2,6,4]=>[2,3,2,1]
[5,6,3,1,8,7,2,4]=>[3,1,7,2,8,6,4,5]=>[6,8,2,7,1,3,5,4]=>[2,2,3,1]
[3,5,6,4,7,1,8,2]=>[2,4,1,3,8,6,5,7]=>[7,5,8,6,1,3,4,2]=>[1,2,1,3,1]
[3,4,6,1,5,7,8,2]=>[1,2,5,6,3,8,4,7]=>[8,7,4,3,6,1,5,2]=>[1,1,1,2,2,1]
[3,4,1,5,7,6,8,2]=>[1,2,6,4,5,8,3,7]=>[8,7,3,5,4,1,6,2]=>[1,1,2,1,2,1]
[3,8,2,7,1,6,5,4]=>[8,7,1,3,5,6,4,2]=>[1,2,8,6,4,3,5,7]=>[3,1,1,3]
[3,8,2,7,6,1,5,4]=>[8,6,7,1,3,5,4,2]=>[1,3,2,8,6,4,5,7]=>[2,2,1,3]
[3,8,2,7,6,5,1,4]=>[7,8,6,1,3,5,4,2]=>[2,1,3,8,6,4,5,7]=>[1,3,1,3]
[3,8,2,7,6,5,4,1]=>[8,7,6,1,3,5,4,2]=>[1,2,3,8,6,4,5,7]=>[4,1,3]
[4,8,7,2,6,5,3,1]=>[8,7,1,4,6,5,3,2]=>[1,2,8,5,3,4,6,7]=>[3,1,4]
[4,8,7,2,6,5,1,3]=>[7,8,1,4,6,5,3,2]=>[2,1,8,5,3,4,6,7]=>[1,2,1,4]
[4,8,7,2,6,1,5,3]=>[8,1,4,6,7,5,3,2]=>[1,8,5,3,2,4,6,7]=>[2,1,1,4]
[4,8,7,3,1,6,5,2]=>[4,8,1,7,5,6,3,2]=>[5,1,8,2,4,3,6,7]=>[1,2,2,3]
[4,8,7,3,2,1,6,5]=>[5,1,4,8,6,7,3,2]=>[4,8,5,1,3,2,6,7]=>[2,1,2,3]
[4,8,7,3,2,6,1,5]=>[5,1,4,7,8,6,3,2]=>[4,8,5,2,1,3,6,7]=>[2,1,1,4]
[4,8,7,3,2,6,5,1]=>[4,8,1,5,7,6,3,2]=>[5,1,8,4,2,3,6,7]=>[1,2,1,4]
[4,8,7,3,6,2,5,1]=>[4,6,8,1,7,5,3,2]=>[5,3,1,8,2,4,6,7]=>[1,1,2,4]
[4,8,7,3,6,2,1,5]=>[4,7,1,6,8,5,3,2]=>[5,2,8,3,1,4,6,7]=>[1,2,1,4]
[4,8,7,3,6,1,5,2]=>[4,8,1,6,7,5,3,2]=>[5,1,8,3,2,4,6,7]=>[1,2,1,4]
[4,8,7,3,6,5,1,2]=>[4,7,8,1,6,5,3,2]=>[5,2,1,8,3,4,6,7]=>[1,1,2,4]
[4,8,7,3,6,5,2,1]=>[8,4,7,1,6,5,3,2]=>[1,5,2,8,3,4,6,7]=>[2,2,4]
[5,8,7,6,3,4,2,1]=>[5,8,1,7,6,4,3,2]=>[4,1,8,2,3,5,6,7]=>[1,2,5]
[5,8,7,6,3,1,4,2]=>[8,1,6,5,7,4,3,2]=>[1,8,3,4,2,5,6,7]=>[2,2,4]
[5,8,7,6,3,2,4,1]=>[6,1,5,8,7,4,3,2]=>[3,8,4,1,2,5,6,7]=>[2,1,5]
[5,8,7,6,2,4,3,1]=>[8,1,5,7,6,4,3,2]=>[1,8,4,2,3,5,6,7]=>[2,1,5]
[5,8,7,6,2,1,4,3]=>[1,5,8,6,7,4,3,2]=>[8,4,1,3,2,5,6,7]=>[1,1,2,4]
[5,8,7,6,4,2,3,1]=>[6,8,1,7,5,4,3,2]=>[3,1,8,2,4,5,6,7]=>[1,2,5]
[5,8,7,6,4,2,1,3]=>[7,1,6,8,5,4,3,2]=>[2,8,3,1,4,5,6,7]=>[2,1,5]
[5,8,7,6,4,1,3,2]=>[8,1,6,7,5,4,3,2]=>[1,8,3,2,4,5,6,7]=>[2,1,5]
[5,8,7,6,4,3,1,2]=>[7,8,1,6,5,4,3,2]=>[2,1,8,3,4,5,6,7]=>[1,2,5]
[7,3,4,2,1,6,5,8]=>[2,4,3,7,5,6,1,8]=>[7,5,6,2,4,3,8,1]=>[1,2,2,2,1]
[7,3,5,2,6,1,4,8]=>[2,4,6,3,7,5,1,8]=>[7,5,3,6,2,4,8,1]=>[1,1,2,3,1]
[7,3,5,2,6,4,1,8]=>[7,2,4,3,6,5,1,8]=>[2,7,5,6,3,4,8,1]=>[2,2,3,1]
[6,3,5,2,7,4,8,1]=>[6,2,4,3,1,5,8,7]=>[3,7,5,6,8,4,1,2]=>[2,3,1,2]
[7,2,1,5,6,4,3,8]=>[4,7,2,6,3,5,1,8]=>[5,2,7,3,6,4,8,1]=>[1,2,2,2,1]
[7,3,5,1,6,4,2,8]=>[7,2,6,4,3,5,1,8]=>[2,7,3,5,6,4,8,1]=>[2,3,2,1]
[7,4,5,6,1,3,2,8]=>[2,7,5,3,6,4,1,8]=>[7,2,4,6,3,5,8,1]=>[1,3,3,1]
[1,4,5,7,3,2,8,6]=>[2,3,5,8,6,1,4,7]=>[7,6,4,1,3,8,5,2]=>[1,1,1,3,1,1]
[1,4,6,7,3,8,2,5]=>[5,2,3,7,4,8,1,6]=>[4,7,6,2,5,1,8,3]=>[2,1,2,2,1]
[6,4,5,7,3,1,8,2]=>[2,3,1,8,6,5,4,7]=>[7,6,8,1,3,4,5,2]=>[1,2,4,1]
[6,4,5,7,1,3,8,2]=>[2,6,3,1,8,5,4,7]=>[7,3,6,8,1,4,5,2]=>[1,3,3,1]
[6,3,5,1,7,4,8,2]=>[6,2,5,3,1,8,4,7]=>[3,7,4,6,8,1,5,2]=>[2,3,2,1]
[6,2,1,5,7,4,8,3]=>[4,6,2,5,1,8,3,7]=>[5,3,7,4,8,1,6,2]=>[1,2,2,2,1]
[2,4,6,7,3,8,1,5]=>[5,2,3,7,1,4,8,6]=>[4,7,6,2,8,5,1,3]=>[2,1,2,1,2]
[1,4,6,7,3,8,5,2]=>[3,8,2,5,4,7,1,6]=>[6,1,7,4,5,2,8,3]=>[1,2,2,2,1]
[1,5,6,7,8,3,4,2]=>[2,3,6,4,8,7,1,5]=>[7,6,3,5,1,2,8,4]=>[1,1,2,3,1]
[2,5,6,7,8,3,1,4]=>[2,3,7,6,1,4,8,5]=>[7,6,2,3,8,5,1,4]=>[1,1,3,1,2]
[3,2,1,6,7,8,4,5]=>[1,4,7,2,5,8,3,6]=>[8,5,2,7,4,1,6,3]=>[1,1,2,1,2,1]
[5,2,1,6,7,8,4,3]=>[4,5,1,8,2,7,3,6]=>[5,4,8,1,7,2,6,3]=>[1,2,2,2,1]
[5,3,6,1,7,8,4,2]=>[5,2,1,3,8,7,4,6]=>[4,7,8,6,1,2,5,3]=>[3,1,3,1]
[5,4,6,7,1,8,3,2]=>[2,1,3,8,7,5,4,6]=>[7,8,6,1,2,4,5,3]=>[2,1,4,1]
[1,5,6,7,8,3,2,4]=>[2,3,7,6,4,8,1,5]=>[7,6,2,3,5,1,8,4]=>[1,1,3,2,1]
[6,4,5,7,2,1,8,3]=>[2,5,3,1,8,6,4,7]=>[7,4,6,8,1,3,5,2]=>[1,3,3,1]
[5,4,6,7,2,8,3,1]=>[2,1,3,8,5,4,7,6]=>[7,8,6,1,4,5,2,3]=>[2,1,3,2]
[5,3,6,2,7,8,4,1]=>[5,2,1,3,8,4,7,6]=>[4,7,8,6,1,5,2,3]=>[3,1,2,2]
[5,3,6,2,7,8,1,4]=>[7,2,1,4,3,5,8,6]=>[2,7,8,5,6,4,1,3]=>[3,2,1,2]
[6,3,5,2,7,1,8,4]=>[8,2,4,3,1,6,5,7]=>[1,7,5,6,8,3,4,2]=>[2,3,2,1]
[6,3,4,2,1,7,8,5]=>[2,4,3,6,1,8,5,7]=>[7,5,6,3,8,1,4,2]=>[1,2,2,2,1]
[5,3,4,1,2,7,8,6]=>[2,6,3,1,8,4,5,7]=>[7,3,6,8,1,5,4,2]=>[1,3,2,1,1]
[4,3,6,2,7,8,1,5]=>[1,7,2,4,3,5,8,6]=>[8,2,7,5,6,4,1,3]=>[1,2,2,1,2]
[4,3,6,2,7,8,5,1]=>[1,5,2,3,8,4,7,6]=>[8,4,7,6,1,5,2,3]=>[1,2,1,2,2]
[1,3,6,2,7,8,5,4]=>[5,3,8,2,7,1,4,6]=>[4,6,1,7,2,8,5,3]=>[2,2,2,1,1]
[1,4,6,7,2,8,5,3]=>[3,8,2,7,5,1,4,6]=>[6,1,7,2,4,8,5,3]=>[1,2,3,1,1]
[3,4,6,7,2,8,5,1]=>[3,8,1,2,5,4,7,6]=>[6,1,8,7,4,5,2,3]=>[1,2,1,2,2]
[3,4,5,7,2,1,8,6]=>[1,2,3,5,8,6,4,7]=>[8,7,6,4,1,3,5,2]=>[1,1,1,1,3,1]
[4,2,1,5,7,3,8,6]=>[8,2,1,4,6,3,5,7]=>[1,7,8,5,3,6,4,2]=>[3,1,2,1,1]
[4,2,1,6,7,8,3,5]=>[4,1,7,2,5,8,3,6]=>[5,8,2,7,4,1,6,3]=>[2,2,1,2,1]
[4,3,6,1,7,8,2,5]=>[1,7,2,5,3,8,4,6]=>[8,2,7,4,6,1,5,3]=>[1,2,2,2,1]
[1,5,6,7,8,2,4,3]=>[2,3,8,6,4,7,1,5]=>[7,6,1,3,5,2,8,4]=>[1,1,3,2,1]
[3,4,6,7,1,8,5,2]=>[3,8,1,2,7,5,4,6]=>[6,1,8,7,2,4,5,3]=>[1,2,1,3,1]
[4,3,6,1,7,8,5,2]=>[1,5,2,3,8,7,4,6]=>[8,4,7,6,1,2,5,3]=>[1,2,1,3,1]
[4,2,1,6,7,8,5,3]=>[4,1,5,8,2,7,3,6]=>[5,8,4,1,7,2,6,3]=>[2,1,2,2,1]
[2,3,6,1,7,8,5,4]=>[5,3,8,1,2,7,4,6]=>[4,6,1,8,7,2,5,3]=>[2,2,1,2,1]
[2,4,6,7,1,8,5,3]=>[3,8,2,7,1,5,4,6]=>[6,1,7,2,8,4,5,3]=>[1,2,2,2,1]
[2,5,6,7,8,1,4,3]=>[2,3,8,6,1,4,7,5]=>[7,6,1,3,8,5,2,4]=>[1,1,3,1,2]
[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[8,7,6,5,4,3,9,2,1]=>[1,1,1,1,1,2,1,1]
[1,4,3,6,2,5,7,8]=>[3,2,5,6,1,4,7,8]=>[6,7,4,3,8,5,2,1]=>[2,1,2,1,1,1]
[1,4,3,7,6,8,2,5]=>[7,2,5,3,4,8,1,6]=>[2,7,4,6,5,1,8,3]=>[2,2,1,2,1]
[1,4,3,7,2,6,5,8]=>[2,7,3,5,6,1,4,8]=>[7,2,6,4,3,8,5,1]=>[1,2,1,2,1,1]
[1,5,3,7,4,8,2,6]=>[5,2,7,3,4,8,1,6]=>[4,7,2,6,5,1,8,3]=>[2,2,1,2,1]
[1,3,2,6,5,8,4,7]=>[5,2,4,7,8,1,3,6]=>[4,7,5,2,1,8,6,3]=>[2,1,1,2,1,1]
[1,5,4,8,3,7,2,6]=>[3,2,5,7,8,6,1,4]=>[6,7,4,2,1,3,8,5]=>[2,1,1,3,1]
[1,2,3,6,5,8,4,7]=>[5,4,7,8,1,2,3,6]=>[4,5,2,1,8,7,6,3]=>[2,1,2,1,1,1]
[6,8,2,4,5,7,1,3]=>[4,7,3,1,5,8,6,2]=>[5,2,6,8,4,1,3,7]=>[1,3,1,3]
[3,7,8,4,5,2,6,1]=>[4,6,5,1,2,8,7,3]=>[5,3,4,8,7,1,2,6]=>[1,3,1,3]
[7,8,1,4,5,3,6,2]=>[4,6,5,8,3,1,7,2]=>[5,3,4,1,6,8,2,7]=>[1,2,3,2]
[3,8,7,4,1,6,5,2]=>[4,8,7,1,5,6,3,2]=>[5,1,2,8,4,3,6,7]=>[1,3,1,3]
[4,8,3,6,1,5,7,2]=>[1,3,6,8,5,4,7,2]=>[8,6,3,1,4,5,2,7]=>[1,1,1,3,2]
[5,8,3,1,6,4,7,2]=>[3,1,6,5,8,4,7,2]=>[6,8,3,4,1,5,2,7]=>[2,2,2,2]
[7,4,1,8,2,6,3,5]=>[7,2,8,5,6,3,1,4]=>[2,7,1,4,3,6,8,5]=>[2,2,3,1]
[7,1,8,4,2,6,3,5]=>[7,4,8,5,6,2,1,3]=>[2,5,1,4,3,7,8,6]=>[2,2,3,1]
[1,6,3,8,5,2,4,7]=>[6,7,3,2,5,8,1,4]=>[3,2,6,7,4,1,8,5]=>[1,3,1,2,1]
[6,1,3,8,5,2,4,7]=>[6,7,3,5,1,8,2,4]=>[3,2,6,4,8,1,7,5]=>[1,2,2,2,1]
[7,1,8,3,6,2,5,4]=>[8,4,6,7,5,2,1,3]=>[1,5,3,2,4,7,8,6]=>[2,1,4,1]
[7,3,1,8,4,2,6,5]=>[2,5,8,6,7,3,1,4]=>[7,4,1,3,2,6,8,5]=>[1,1,2,3,1]
[7,2,8,4,1,6,5,3]=>[4,8,7,2,5,1,6,3]=>[5,1,2,7,4,8,3,6]=>[1,3,2,2]
[7,2,8,3,6,5,1,4]=>[7,8,4,6,2,1,5,3]=>[2,1,5,3,7,8,4,6]=>[1,2,3,2]
[7,2,8,3,6,1,5,4]=>[8,4,6,7,2,1,5,3]=>[1,5,3,2,7,8,4,6]=>[2,1,3,2]
[7,1,8,2,3,6,5,4]=>[8,7,4,5,6,2,1,3]=>[1,2,5,4,3,7,8,6]=>[3,1,3,1]
[6,1,2,8,3,5,4,7]=>[7,5,6,8,2,1,3,4]=>[2,4,3,1,7,8,6,5]=>[2,1,3,1,1]
[1,5,2,3,8,4,7,6]=>[8,6,2,7,1,3,4,5]=>[1,3,7,2,8,6,5,4]=>[3,2,1,1,1]
[5,1,2,3,8,4,7,6]=>[8,6,7,2,1,3,4,5]=>[1,3,2,7,8,6,5,4]=>[2,3,1,1,1]
[5,2,3,8,1,4,7,6]=>[8,2,3,1,5,6,7,4]=>[1,7,6,8,4,3,2,5]=>[2,2,1,1,2]
[6,2,8,1,3,5,4,7]=>[7,2,4,5,1,6,8,3]=>[2,7,5,4,8,3,1,6]=>[2,1,2,1,2]
[6,2,4,1,8,7,3,5]=>[3,7,8,2,1,6,4,5]=>[6,2,1,7,8,3,5,4]=>[1,1,3,2,1]
[6,3,1,4,2,8,5,7]=>[4,2,7,8,3,1,5,6]=>[5,7,2,1,6,8,4,3]=>[2,1,3,1,1]
[2,6,3,8,7,1,5,4]=>[8,6,2,7,1,3,5,4]=>[1,3,7,2,8,6,4,5]=>[3,2,1,2]
[2,6,3,8,5,1,4,7]=>[6,7,3,1,2,5,8,4]=>[3,2,6,8,7,4,1,5]=>[1,3,1,1,2]
[2,5,1,8,3,4,7,6]=>[8,5,1,2,6,7,3,4]=>[1,4,8,7,3,2,6,5]=>[3,1,1,2,1]
[1,2,5,3,8,4,7,6]=>[3,8,6,7,1,2,4,5]=>[6,1,3,2,8,7,5,4]=>[1,2,2,1,1,1]
[1,2,4,8,3,7,6,5]=>[8,7,3,5,6,1,2,4]=>[1,2,6,4,3,8,7,5]=>[3,1,2,1,1]
[2,4,8,1,3,7,6,5]=>[8,2,7,1,4,5,6,3]=>[1,7,2,8,5,4,3,6]=>[2,2,1,1,2]
[2,4,8,3,7,1,6,5]=>[8,2,4,6,7,1,5,3]=>[1,7,5,3,2,8,4,6]=>[2,1,1,2,2]
[2,4,8,3,7,6,1,5]=>[7,8,2,4,6,1,5,3]=>[2,1,7,5,3,8,4,6]=>[1,2,1,2,2]
[2,5,3,8,1,7,4,6]=>[7,2,8,1,3,5,6,4]=>[2,7,1,8,6,4,3,5]=>[2,2,1,1,2]
[2,5,4,1,3,8,7,6]=>[3,2,8,1,7,4,5,6]=>[6,7,1,8,2,5,4,3]=>[2,2,2,1,1]
[5,3,1,4,8,2,7,6]=>[2,8,4,1,6,7,3,5]=>[7,1,5,8,3,2,6,4]=>[1,3,1,2,1]
[5,2,3,8,4,7,1,6]=>[5,7,1,8,2,3,6,4]=>[4,2,8,1,7,6,3,5]=>[1,2,2,1,2]
[4,8,2,3,7,6,1,5]=>[1,7,8,3,4,6,5,2]=>[8,2,1,6,5,3,4,7]=>[1,1,2,1,3]
[4,8,2,3,7,1,6,5]=>[1,8,3,4,6,7,5,2]=>[8,1,6,5,3,2,4,7]=>[1,2,1,1,3]
[4,8,1,2,3,7,6,5]=>[1,8,7,3,4,5,6,2]=>[8,1,2,6,5,4,3,7]=>[1,3,1,1,2]
[1,4,8,2,3,7,6,5]=>[8,2,7,4,5,6,1,3]=>[1,7,2,5,4,3,8,6]=>[2,2,1,2,1]
[1,4,8,3,7,2,6,5]=>[8,2,4,6,7,5,1,3]=>[1,7,5,3,2,4,8,6]=>[2,1,1,3,1]
[6,3,8,1,5,2,4,7]=>[2,6,7,4,1,5,8,3]=>[7,3,2,5,8,4,1,6]=>[1,1,3,1,2]
[5,3,8,1,2,4,7,6]=>[2,8,4,1,5,6,7,3]=>[7,1,5,8,4,3,2,6]=>[1,3,1,1,2]
[5,1,3,8,2,4,7,6]=>[8,3,5,1,6,7,2,4]=>[1,6,4,8,3,2,7,5]=>[2,2,1,2,1]
[1,5,3,8,2,4,7,6]=>[8,3,2,5,6,7,1,4]=>[1,6,7,4,3,2,8,5]=>[3,1,1,2,1]
[1,5,4,8,2,7,6,3]=>[2,8,3,7,5,6,1,4]=>[7,1,6,2,4,3,8,5]=>[1,2,2,2,1]
[5,1,4,8,2,7,6,3]=>[8,3,1,7,5,6,2,4]=>[1,6,8,2,4,3,7,5]=>[3,2,2,1]
[5,4,8,1,2,7,6,3]=>[2,1,8,7,4,5,6,3]=>[7,8,1,2,5,4,3,6]=>[2,3,1,2]
[6,5,1,2,8,7,4,3]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>[6,1,1]
[5,3,1,6,4,2,8,7]=>[2,5,4,1,8,3,6,7]=>[7,4,5,8,1,6,3,2]=>[1,3,2,1,1]
[5,1,6,2,8,7,4,3]=>[3,1,8,7,6,2,4,5]=>[6,8,1,2,3,7,5,4]=>[2,4,1,1]
[4,1,5,8,2,7,6,3]=>[1,8,3,7,5,6,2,4]=>[8,1,6,2,4,3,7,5]=>[1,2,2,2,1]
[4,1,2,5,8,7,6,3]=>[1,8,7,4,6,2,3,5]=>[8,1,2,5,3,7,6,4]=>[1,3,2,1,1]
[1,4,2,5,8,7,6,3]=>[8,2,7,4,6,1,3,5]=>[1,7,2,5,3,8,6,4]=>[2,2,2,1,1]
[1,3,5,2,8,7,4,6]=>[3,7,8,2,6,1,4,5]=>[6,2,1,7,3,8,5,4]=>[1,1,2,2,1,1]
[3,5,1,2,8,7,4,6]=>[7,1,2,8,6,3,4,5]=>[2,8,7,1,3,6,5,4]=>[2,1,3,1,1]
[3,6,2,8,7,5,1,4]=>[7,2,8,1,6,3,5,4]=>[2,7,1,8,3,6,4,5]=>[2,2,2,2]
[4,2,6,1,8,7,3,5]=>[1,7,3,8,2,6,4,5]=>[8,2,6,1,7,3,5,4]=>[1,2,2,2,1]
[4,3,1,5,8,2,7,6]=>[2,1,8,4,6,7,3,5]=>[7,8,1,5,3,2,6,4]=>[2,2,1,2,1]
[3,5,2,8,7,1,4,6]=>[6,1,2,7,8,3,5,4]=>[3,8,7,2,1,6,4,5]=>[2,1,1,2,2]
[3,4,8,7,2,6,1,5]=>[5,7,8,1,2,6,4,3]=>[4,2,1,8,7,3,5,6]=>[1,1,2,1,3]
[3,4,8,7,1,2,6,5]=>[8,1,2,5,6,7,4,3]=>[1,8,7,4,3,2,5,6]=>[2,1,1,1,3]
[3,4,8,1,7,2,6,5]=>[8,1,2,6,7,4,5,3]=>[1,8,7,3,2,5,4,6]=>[2,1,1,2,2]
[1,3,4,8,7,2,6,5]=>[8,6,7,2,3,5,1,4]=>[1,3,2,7,6,4,8,5]=>[2,2,1,2,1]
[1,3,4,8,2,7,6,5]=>[8,7,2,3,5,6,1,4]=>[1,2,7,6,4,3,8,5]=>[3,1,1,2,1]
[3,4,8,1,2,7,6,5]=>[8,1,2,7,4,5,6,3]=>[1,8,7,2,5,4,3,6]=>[2,1,2,1,2]
[3,4,8,2,7,1,6,5]=>[8,1,2,4,6,7,5,3]=>[1,8,7,5,3,2,4,6]=>[2,1,1,1,3]
[3,4,8,2,7,6,1,5]=>[7,8,1,2,4,6,5,3]=>[2,1,8,7,5,3,4,6]=>[1,2,1,1,3]
[4,2,5,8,1,7,6,3]=>[1,8,3,7,2,5,6,4]=>[8,1,6,2,7,4,3,5]=>[1,2,2,1,2]
[4,3,1,2,5,8,7,6]=>[2,1,8,7,3,4,5,6]=>[7,8,1,2,6,5,4,3]=>[2,3,1,1,1]
[3,1,4,2,5,8,7,6]=>[1,8,3,7,2,4,5,6]=>[8,1,6,2,7,5,4,3]=>[1,2,2,1,1,1]
[2,3,5,1,8,7,6,4]=>[8,3,7,1,2,6,4,5]=>[1,6,2,8,7,3,5,4]=>[2,2,1,2,1]
[7,8,2,1,5,3,6,4]=>[8,3,6,4,5,1,7,2]=>[1,6,3,5,4,8,2,7]=>[2,2,2,2]
[6,4,1,2,7,3,5,8]=>[6,7,3,2,4,1,5,8]=>[3,2,6,7,5,8,4,1]=>[1,3,2,1,1]
[2,3,7,5,4,1,8,6]=>[5,4,8,1,2,6,3,7]=>[4,5,1,8,7,3,6,2]=>[2,2,1,2,1]
[6,3,1,5,4,2,7,8]=>[2,6,5,3,4,1,7,8]=>[7,3,4,6,5,8,2,1]=>[1,3,2,1,1]
[7,8,1,5,4,2,6,3]=>[8,6,5,3,4,1,7,2]=>[1,3,4,6,5,8,2,7]=>[4,2,2]
[7,8,3,5,4,1,6,2]=>[8,3,6,5,4,1,7,2]=>[1,6,3,4,5,8,2,7]=>[2,4,2]
[7,8,2,5,4,1,3,6]=>[6,7,3,5,4,1,8,2]=>[3,2,6,4,5,8,1,7]=>[1,2,3,2]
[7,8,2,5,4,6,1,3]=>[7,5,3,4,1,8,6,2]=>[2,4,6,5,8,1,3,7]=>[3,2,3]
[6,2,1,5,4,7,3,8]=>[5,2,4,7,3,1,6,8]=>[4,7,5,2,6,8,3,1]=>[2,1,3,1,1]
[5,3,6,1,4,7,8,2]=>[2,5,1,6,3,8,4,7]=>[7,4,8,3,6,1,5,2]=>[1,2,2,2,1]
[5,3,6,2,4,7,1,8]=>[2,4,1,5,3,7,6,8]=>[7,5,8,4,6,2,3,1]=>[1,2,2,2,1]
[6,4,2,1,7,3,8,5]=>[8,3,2,6,4,1,5,7]=>[1,6,7,3,5,8,4,2]=>[3,3,1,1]
[4,3,7,5,8,6,1,2]=>[1,4,7,2,3,8,6,5]=>[8,5,2,7,6,1,3,4]=>[1,1,2,1,3]
[4,2,7,1,8,3,6,5]=>[1,8,6,7,2,4,3,5]=>[8,1,3,2,7,5,6,4]=>[1,2,2,2,1]
[3,2,6,7,4,8,1,5]=>[5,1,3,7,2,4,8,6]=>[4,8,6,2,7,5,1,3]=>[2,1,2,1,2]
[3,1,6,7,4,8,5,2]=>[3,8,1,5,4,7,2,6]=>[6,1,8,4,5,2,7,3]=>[1,2,2,2,1]
[1,7,6,5,3,8,4,2]=>[8,5,4,3,2,7,1,6]=>[1,4,5,6,7,2,8,3]=>[5,2,1]
[2,7,6,5,3,8,1,4]=>[5,7,4,3,1,2,8,6]=>[4,2,5,6,8,7,1,3]=>[1,4,1,2]
[1,7,6,5,2,4,8,3]=>[6,8,5,4,3,1,2,7]=>[3,1,4,5,6,8,7,2]=>[1,5,1,1]
[2,7,6,5,3,1,4,8]=>[6,5,7,4,1,3,2,8]=>[3,4,2,5,8,6,7,1]=>[2,3,2,1]
[2,7,1,4,8,3,5,6]=>[4,6,7,8,1,3,2,5]=>[5,3,2,1,8,6,7,4]=>[1,1,1,2,2,1]
[3,7,6,4,8,5,1,2]=>[4,7,3,1,2,8,6,5]=>[5,2,6,8,7,1,3,4]=>[1,3,1,3]
[5,7,6,3,8,4,1,2]=>[1,4,7,3,2,8,6,5]=>[8,5,2,6,7,1,3,4]=>[1,1,3,3]
[5,1,6,2,4,8,3,7]=>[5,7,3,1,8,2,4,6]=>[4,2,6,8,1,7,5,3]=>[1,3,2,1,1]
[4,7,6,5,2,1,3,8]=>[6,1,5,7,4,3,2,8]=>[3,8,4,2,5,6,7,1]=>[2,1,4,1]
[4,7,6,5,2,8,1,3]=>[5,7,1,4,3,2,8,6]=>[4,2,8,5,6,7,1,3]=>[1,2,3,2]
[4,7,6,5,1,8,3,2]=>[8,7,1,5,4,3,2,6]=>[1,2,8,4,5,6,7,3]=>[3,4,1]
[1,7,6,5,2,8,3,4]=>[7,8,5,4,3,1,2,6]=>[2,1,4,5,6,8,7,3]=>[1,5,1,1]
[1,7,6,5,3,2,8,4]=>[5,8,6,4,3,1,2,7]=>[4,1,3,5,6,8,7,2]=>[1,5,1,1]
[4,7,6,5,1,2,8,3]=>[8,1,5,6,4,3,2,7]=>[1,8,4,3,5,6,7,2]=>[2,1,4,1]
[4,7,6,5,3,1,8,2]=>[8,6,1,5,4,3,2,7]=>[1,3,8,4,5,6,7,2]=>[3,4,1]
[6,1,3,5,4,8,7,2]=>[4,8,3,5,1,7,2,6]=>[5,1,6,4,8,2,7,3]=>[1,2,2,2,1]
[5,2,6,3,4,1,7,8]=>[4,6,2,1,5,3,7,8]=>[5,3,7,8,4,6,2,1]=>[1,3,2,1,1]
[5,1,6,2,4,7,8,3]=>[5,6,3,1,8,2,4,7]=>[4,3,6,8,1,7,5,2]=>[1,3,2,1,1]
[1,2,6,3,4,8,7,5]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]
[1,7,2,4,8,3,6,5]=>[8,4,6,7,3,1,2,5]=>[1,5,3,2,6,8,7,4]=>[2,1,3,1,1]
[6,1,4,2,8,3,5,7]=>[6,3,7,8,2,1,4,5]=>[3,6,2,1,7,8,5,4]=>[2,1,3,1,1]
[4,1,8,2,6,3,5,7]=>[6,1,7,4,5,8,2,3]=>[3,8,2,5,4,1,7,6]=>[2,2,1,2,1]
[4,7,1,6,2,3,8,5]=>[1,8,5,6,3,4,2,7]=>[8,1,4,3,6,5,7,2]=>[1,2,2,2,1]
[1,7,2,6,8,3,5,4]=>[8,6,4,7,3,1,2,5]=>[1,3,5,2,6,8,7,4]=>[3,3,1,1]
[1,2,6,7,4,8,5,3]=>[3,8,5,4,7,1,2,6]=>[6,1,4,5,2,8,7,3]=>[1,3,2,1,1]
[3,1,6,7,4,2,8,5]=>[5,1,3,8,6,2,4,7]=>[4,8,6,1,3,7,5,2]=>[2,1,3,1,1]
[3,2,8,5,4,6,1,7]=>[5,1,4,7,2,6,8,3]=>[4,8,5,2,7,3,1,6]=>[2,1,2,1,2]
[4,7,6,3,5,8,1,2]=>[4,7,1,5,3,2,8,6]=>[5,2,8,4,6,7,1,3]=>[1,2,3,2]
[3,7,6,5,2,4,1,8]=>[5,7,6,1,4,3,2,8]=>[4,2,3,8,5,6,7,1]=>[1,3,3,1]
[3,7,6,5,1,4,8,2]=>[6,8,5,1,4,3,2,7]=>[3,1,4,8,5,6,7,2]=>[1,3,3,1]
[3,7,6,5,2,1,8,4]=>[5,8,6,1,4,3,2,7]=>[4,1,3,8,5,6,7,2]=>[1,3,3,1]
[1,7,6,5,8,2,4,3]=>[8,6,4,3,2,7,1,5]=>[1,3,5,6,7,2,8,4]=>[5,2,1]
[3,7,6,5,8,1,4,2]=>[8,6,4,1,3,2,7,5]=>[1,3,5,8,6,7,2,4]=>[4,2,2]
[3,7,6,5,1,2,4,8]=>[5,6,7,1,4,3,2,8]=>[4,3,2,8,5,6,7,1]=>[1,1,2,3,1]
[4,7,6,8,3,5,1,2]=>[7,5,1,3,2,8,6,4]=>[2,4,8,6,7,1,3,5]=>[3,2,3]
[2,7,6,5,1,4,3,8]=>[7,5,6,4,1,3,2,8]=>[2,4,3,5,8,6,7,1]=>[2,3,2,1]
[2,7,6,5,8,1,3,4]=>[6,7,4,3,1,2,8,5]=>[3,2,5,6,8,7,1,4]=>[1,4,1,2]
[2,7,6,5,8,4,1,3]=>[7,4,3,2,8,1,6,5]=>[2,5,6,7,1,8,3,4]=>[4,2,2]
[6,3,2,1,7,4,8,5]=>[2,8,3,6,4,1,5,7]=>[7,1,6,3,5,8,4,2]=>[1,2,3,1,1]
[4,2,1,7,3,5,8,6]=>[8,2,1,5,6,3,4,7]=>[1,7,8,4,3,6,5,2]=>[3,1,2,1,1]
[7,3,1,5,4,2,8,6]=>[2,5,4,8,3,6,1,7]=>[7,4,5,1,6,3,8,2]=>[1,2,2,2,1]
[8,4,1,5,2,7,6,3]=>[4,2,8,7,3,5,6,1]=>[5,7,1,2,6,4,3,8]=>[2,3,1,2]
[8,2,5,1,3,7,6,4]=>[8,7,2,4,3,5,6,1]=>[1,2,7,5,6,4,3,8]=>[3,2,1,2]
[4,3,7,2,1,5,8,6]=>[2,1,4,8,5,6,3,7]=>[7,8,5,1,4,3,6,2]=>[2,1,2,2,1]
[6,3,7,4,2,1,8,5]=>[5,2,4,1,8,6,3,7]=>[4,7,5,8,1,3,6,2]=>[2,2,3,1]
[4,7,2,5,3,1,8,6]=>[1,5,3,4,8,6,2,7]=>[8,4,6,5,1,3,7,2]=>[1,2,1,3,1]
[2,7,5,4,1,3,8,6]=>[8,5,4,1,3,6,2,7]=>[1,4,5,8,6,3,7,2]=>[4,1,2,1]
[7,5,4,3,2,1,8,6]=>[5,4,3,2,8,6,1,7]=>[4,5,6,7,1,3,8,2]=>[4,3,1]
[8,5,3,2,1,7,6,4]=>[3,8,4,2,7,5,6,1]=>[6,1,5,7,2,4,3,8]=>[1,3,2,2]
[6,5,2,1,8,4,3,7]=>[7,3,6,2,1,8,4,5]=>[2,6,3,7,8,1,5,4]=>[2,3,2,1]
[4,6,3,2,8,1,5,7]=>[1,4,3,6,2,7,8,5]=>[8,5,6,3,7,2,1,4]=>[1,2,2,1,2]
[5,7,4,3,2,8,1,6]=>[1,5,4,3,7,2,8,6]=>[8,4,5,6,2,7,1,3]=>[1,3,2,2]
[1,7,6,2,4,8,3,5]=>[5,7,8,4,3,1,2,6]=>[4,2,1,5,6,8,7,3]=>[1,1,4,1,1]
[2,7,3,6,4,8,1,5]=>[5,7,3,4,1,2,8,6]=>[4,2,6,5,8,7,1,3]=>[1,2,2,1,2]
[6,2,7,5,3,8,1,4]=>[5,7,4,2,1,3,8,6]=>[4,2,5,7,8,6,1,3]=>[1,4,1,2]
[7,1,8,5,3,6,4,2]=>[8,5,4,7,6,2,1,3]=>[1,4,5,2,3,7,8,6]=>[3,4,1]
[5,8,1,6,2,7,4,3]=>[1,8,7,5,3,4,6,2]=>[8,1,2,4,6,5,3,7]=>[1,4,1,2]
[1,8,6,2,3,7,5,4]=>[8,7,4,5,3,6,1,2]=>[1,2,5,4,6,3,8,7]=>[3,2,2,1]
[1,8,6,3,2,7,5,4]=>[8,4,7,5,3,6,1,2]=>[1,5,2,4,6,3,8,7]=>[2,3,2,1]
[5,8,3,2,7,1,6,4]=>[3,1,8,4,6,7,5,2]=>[6,8,1,5,3,2,4,7]=>[2,2,1,3]
[8,7,3,1,6,5,4,2]=>[8,3,7,6,4,5,2,1]=>[1,6,2,3,5,4,7,8]=>[2,3,3]
[8,7,2,6,1,5,4,3]=>[8,7,3,5,6,4,2,1]=>[1,2,6,4,3,5,7,8]=>[3,1,4]
[1,8,5,7,4,3,6,2]=>[3,6,5,8,7,4,1,2]=>[6,3,4,1,2,5,8,7]=>[1,2,4,1]
[1,8,5,7,2,4,6,3]=>[6,3,8,5,7,4,1,2]=>[3,6,1,4,2,5,8,7]=>[2,2,3,1]
[3,8,6,1,7,2,5,4]=>[8,6,7,1,4,3,5,2]=>[1,3,2,8,5,6,4,7]=>[2,2,2,2]
[5,8,4,6,7,1,3,2]=>[1,3,8,6,4,7,5,2]=>[8,6,1,3,5,2,4,7]=>[1,1,3,3]
[7,2,8,5,6,1,4,3]=>[8,6,4,7,2,1,5,3]=>[1,3,5,2,7,8,4,6]=>[3,3,2]
[6,3,7,5,8,2,1,4]=>[7,6,2,1,4,3,8,5]=>[2,3,7,8,5,6,1,4]=>[4,2,2]
[3,7,2,6,8,4,1,5]=>[7,6,1,3,4,2,8,5]=>[2,3,8,6,5,7,1,4]=>[3,1,2,2]
[3,6,5,8,1,4,2,7]=>[7,5,1,3,2,6,8,4]=>[2,4,8,6,7,3,1,5]=>[3,2,1,2]
[2,6,5,8,4,1,3,7]=>[6,3,2,7,1,5,8,4]=>[3,6,7,2,8,4,1,5]=>[3,2,1,2]
[6,5,4,8,3,2,1,7]=>[3,2,1,7,6,5,8,4]=>[6,7,8,2,3,4,1,5]=>[3,3,2]
[8,4,3,7,2,1,6,5]=>[3,2,5,8,6,7,4,1]=>[6,7,4,1,3,2,5,8]=>[2,1,2,3]
[8,2,4,7,1,3,6,5]=>[3,8,2,5,6,7,4,1]=>[6,1,7,4,3,2,5,8]=>[1,2,1,1,3]
[6,2,5,8,1,4,3,7]=>[7,5,2,3,1,6,8,4]=>[2,4,7,6,8,3,1,5]=>[3,2,1,2]
[4,3,6,8,2,1,5,7]=>[1,6,2,5,3,7,8,4]=>[8,3,7,4,6,2,1,5]=>[1,2,2,1,2]
[8,4,1,5,7,3,6,2]=>[4,2,6,8,7,3,5,1]=>[5,7,3,1,2,6,4,8]=>[2,1,3,2]
[5,4,1,6,8,2,3,7]=>[6,4,2,1,7,8,3,5]=>[3,5,7,8,2,1,6,4]=>[4,1,2,1]
[6,5,2,1,7,8,3,4]=>[7,3,5,2,1,8,4,6]=>[2,6,4,7,8,1,5,3]=>[2,3,2,1]
[6,3,7,4,8,5,2,1]=>[8,4,2,1,3,7,6,5]=>[1,5,7,8,6,2,3,4]=>[4,1,3]
[4,7,2,5,8,6,3,1]=>[8,1,4,7,3,2,6,5]=>[1,8,5,2,6,7,3,4]=>[2,1,3,2]
[6,4,2,8,7,3,5,1]=>[2,6,1,8,7,3,5,4]=>[7,3,8,1,2,6,4,5]=>[1,2,3,2]
[6,5,3,8,7,4,1,2]=>[7,2,1,8,3,6,5,4]=>[2,7,8,1,6,3,4,5]=>[3,2,3]
[8,5,3,7,6,4,2,1]=>[2,8,7,3,6,5,4,1]=>[7,1,2,6,3,4,5,8]=>[1,3,4]
[5,4,8,1,7,6,2,3]=>[2,1,7,8,6,4,5,3]=>[7,8,2,1,3,5,4,6]=>[2,1,3,2]
[5,2,8,1,7,3,6,4]=>[8,6,1,7,2,4,5,3]=>[1,3,8,2,7,5,4,6]=>[3,2,1,2]
[6,4,8,2,1,7,5,3]=>[2,8,4,1,7,5,6,3]=>[7,1,5,8,2,4,3,6]=>[1,3,2,2]
[3,6,8,1,4,7,5,2]=>[8,5,1,2,7,4,6,3]=>[1,4,8,7,2,5,3,6]=>[3,1,2,2]
[5,7,3,8,1,6,4,2]=>[1,8,3,7,5,2,6,4]=>[8,1,6,2,4,7,3,5]=>[1,2,3,2]
[6,4,7,8,1,5,3,2]=>[8,2,1,7,5,3,6,4]=>[1,7,8,2,4,6,3,5]=>[3,3,2]
[6,3,7,8,5,2,4,1]=>[6,3,1,8,2,7,5,4]=>[3,6,8,1,7,2,4,5]=>[3,2,3]
[2,5,8,7,1,3,6,4]=>[2,8,5,6,7,1,4,3]=>[7,1,4,3,2,8,5,6]=>[1,2,1,2,2]
[5,3,8,7,2,1,6,4]=>[5,1,8,2,6,7,4,3]=>[4,8,1,7,3,2,5,6]=>[2,2,1,3]
[8,3,7,6,1,5,4,2]=>[8,7,2,5,6,4,3,1]=>[1,2,7,4,3,5,6,8]=>[3,1,4]
[8,2,7,6,5,1,4,3]=>[8,6,7,5,2,4,3,1]=>[1,3,2,4,7,5,6,8]=>[2,3,3]
[4,3,8,7,6,2,1,5]=>[7,1,6,8,2,5,4,3]=>[2,8,3,1,7,4,5,6]=>[2,1,2,3]
[2,4,8,7,6,1,3,5]=>[6,7,8,2,5,1,4,3]=>[3,2,1,7,4,8,5,6]=>[1,1,2,2,2]
[3,5,8,7,2,6,1,4]=>[2,5,7,8,1,6,4,3]=>[7,4,2,1,8,3,5,6]=>[1,1,1,2,3]
[4,7,3,8,6,5,1,2]=>[7,8,1,3,2,6,5,4]=>[2,1,8,6,7,3,4,5]=>[1,2,2,3]
[7,5,8,6,4,3,2,1]=>[8,2,1,7,6,5,4,3]=>[1,7,8,2,3,4,5,6]=>[3,5]
[5,8,7,3,6,4,2,1]=>[8,1,4,7,6,5,3,2]=>[1,8,5,2,3,4,6,7]=>[2,1,5]
[4,8,7,6,2,5,3,1]=>[8,5,7,1,6,4,3,2]=>[1,4,2,8,3,5,6,7]=>[2,2,4]
[3,8,7,6,5,1,4,2]=>[8,6,7,5,1,4,3,2]=>[1,3,2,4,8,5,6,7]=>[2,3,3]
[2,8,7,6,5,4,1,3]=>[7,8,6,5,4,1,3,2]=>[2,1,3,4,5,8,6,7]=>[1,5,2]
[3,4,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>[7,9,6,8,5,4,3,2,1]=>[2,2,1,1,1,1,1]
[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>[3,1,1,1,1,1,1]
[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>[4,1,1,1,1,1]
[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>[5,1,1,1,1]
[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>[6,1,1,1]
[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>[7,1,1]
[8,6,9,4,7,2,5,1,3]=>[6,4,2,8,1,9,7,5,3]=>[4,6,8,2,9,1,3,5,7]=>[3,2,4]
[8,6,5,4,3,2,9,1,7]=>[6,5,4,3,2,8,1,9,7]=>[4,5,6,7,8,2,9,1,3]=>[5,2,2]
[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>[3,1,1,1,1,1,1,1]
[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>[4,1,1,1,1,1,1]
[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>[5,1,1,1,1,1]
[6,4,3,2,7,1,5,8,9,10]=>[4,3,2,6,1,7,5,8,9,10]=>[7,8,9,5,10,4,6,3,2,1]=>[3,2,2,1,1,1]
[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>[6,1,1,1,1]
[7,5,3,8,2,6,1,4,9,10]=>[3,5,2,7,1,8,6,4,9,10]=>[8,6,9,4,10,3,5,7,2,1]=>[1,2,2,3,1,1]
[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>[7,1,1,1]
[8,6,9,4,7,2,5,1,3,10]=>[6,4,2,8,1,9,7,5,3,10]=>[5,7,9,3,10,2,4,6,8,1]=>[3,2,4,1]
[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>[8,1,1]
[3,6,5,1,2,4,8,7]=>[8,1,4,5,3,2,6,7]=>[1,8,5,4,6,7,3,2]=>[2,1,3,1,1]
[3,7,5,8,2,4,1,6]=>[5,3,7,1,6,2,8,4]=>[4,6,2,8,3,7,1,5]=>[2,2,2,2]
[3,8,5,7,2,4,1,6]=>[5,3,7,1,6,8,4,2]=>[4,6,2,8,3,1,5,7]=>[2,2,1,3]
[5,1,7,8,4,3,2,6]=>[1,7,6,5,3,8,2,4]=>[8,2,3,4,6,1,7,5]=>[1,4,2,1]
[5,1,2,6,4,3,8,7]=>[5,4,8,2,1,3,6,7]=>[4,5,1,7,8,6,3,2]=>[2,3,1,1,1]
[6,1,2,5,4,3,8,7]=>[5,4,8,2,3,1,6,7]=>[4,5,1,7,6,8,3,2]=>[2,2,2,1,1]
[5,1,2,4,6,3,8,7]=>[4,5,8,2,1,3,6,7]=>[5,4,1,7,8,6,3,2]=>[1,1,3,1,1,1]
[4,1,2,6,5,3,8,7]=>[5,4,1,8,2,3,6,7]=>[4,5,8,1,7,6,3,2]=>[3,2,1,1,1]
[4,1,5,7,8,3,2,6]=>[1,7,3,6,4,8,2,5]=>[8,2,6,3,5,1,7,4]=>[1,2,2,2,1]
[4,1,5,8,7,3,2,6]=>[1,7,3,6,8,5,2,4]=>[8,2,6,3,1,4,7,5]=>[1,2,1,3,1]
[4,7,1,8,3,6,2,5]=>[1,5,7,8,6,3,2,4]=>[8,4,2,1,3,6,7,5]=>[1,1,1,4,1]
[4,1,7,8,5,2,3,6]=>[1,6,7,5,3,8,2,4]=>[8,3,2,4,6,1,7,5]=>[1,1,3,2,1]
[5,1,7,4,8,2,3,6]=>[6,4,1,7,3,8,2,5]=>[3,5,8,2,6,1,7,4]=>[3,2,2,1]
[7,5,3,8,1,4,2,6]=>[3,7,5,2,6,1,8,4]=>[6,2,4,7,3,8,1,5]=>[1,3,2,2]
[2,1,5,8,7,3,4,6]=>[3,6,7,8,1,5,2,4]=>[6,3,2,1,8,4,7,5]=>[1,1,1,2,2,1]
[5,1,8,4,7,2,3,6]=>[6,4,1,7,8,5,2,3]=>[3,5,8,2,1,4,7,6]=>[3,1,3,1]
[4,7,1,6,3,2,8,5]=>[1,5,8,6,3,4,2,7]=>[8,4,1,3,6,5,7,2]=>[1,1,3,2,1]
[6,1,2,3,7,5,8,4]=>[6,5,8,2,3,1,4,7]=>[3,4,1,7,6,8,5,2]=>[2,2,2,1,1]
[7,1,2,3,8,6,5,4]=>[8,7,6,2,3,4,1,5]=>[1,2,3,7,6,5,8,4]=>[4,1,2,1]
[7,1,2,3,5,8,6,4]=>[8,5,7,2,3,4,1,6]=>[1,4,2,7,6,5,8,3]=>[2,2,1,2,1]
[6,8,1,4,3,7,2,5]=>[5,4,7,1,8,3,6,2]=>[4,5,2,8,1,6,3,7]=>[2,2,2,2]
[8,7,3,2,4,1,6,5]=>[4,3,5,8,6,7,2,1]=>[5,6,4,1,3,2,7,8]=>[2,1,2,3]
[2,1,7,3,4,8,6,5]=>[8,7,1,4,5,2,3,6]=>[1,2,8,5,4,7,6,3]=>[3,1,2,1,1]
[7,8,3,2,4,1,6,5]=>[4,3,5,8,6,1,7,2]=>[5,6,4,1,3,8,2,7]=>[2,1,3,2]
[6,7,1,4,3,8,2,5]=>[5,4,7,1,8,3,2,6]=>[4,5,2,8,1,6,7,3]=>[2,2,3,1]
[8,1,2,3,5,7,6,4]=>[8,5,7,2,3,4,6,1]=>[1,4,2,7,6,5,3,8]=>[2,2,1,1,2]
[7,1,2,3,6,8,5,4]=>[5,8,7,2,3,4,1,6]=>[4,1,2,7,6,5,8,3]=>[1,3,1,2,1]
[7,1,2,3,8,5,6,4]=>[6,8,7,2,3,4,1,5]=>[3,1,2,7,6,5,8,4]=>[1,3,1,2,1]
[8,1,2,3,7,5,6,4]=>[6,8,7,2,3,4,5,1]=>[3,1,2,7,6,5,4,8]=>[1,3,1,1,2]
[7,1,8,5,4,3,2,6]=>[7,6,5,4,8,2,1,3]=>[2,3,4,5,1,7,8,6]=>[4,3,1]
[7,8,2,6,3,4,1,5]=>[5,7,3,6,1,8,4,2]=>[4,2,6,3,8,1,5,7]=>[1,2,2,3]
[6,8,2,7,3,4,1,5]=>[5,7,3,1,6,8,4,2]=>[4,2,6,8,3,1,5,7]=>[1,3,1,3]
[6,7,2,8,3,4,1,5]=>[5,7,3,1,6,2,8,4]=>[4,2,6,8,3,7,1,5]=>[1,3,2,2]
[3,8,7,1,4,2,6,5]=>[5,8,1,4,6,7,3,2]=>[4,1,8,5,3,2,6,7]=>[1,2,1,1,3]
[3,7,8,1,4,2,6,5]=>[5,8,1,4,6,2,7,3]=>[4,1,8,5,3,7,2,6]=>[1,2,1,2,2]
[3,6,8,1,4,2,7,5]=>[5,8,1,4,2,6,7,3]=>[4,1,8,5,7,3,2,6]=>[1,2,2,1,2]
[3,5,7,8,2,4,1,6]=>[2,5,7,1,6,3,8,4]=>[7,4,2,8,3,6,1,5]=>[1,1,2,2,2]
[3,6,7,1,4,2,8,5]=>[5,8,1,4,2,6,3,7]=>[4,1,8,5,7,3,6,2]=>[1,2,2,2,1]
[7,6,2,8,3,1,4,5]=>[6,3,5,7,2,1,8,4]=>[3,6,4,2,7,8,1,5]=>[2,1,3,2]
[8,6,2,7,3,1,4,5]=>[6,3,5,7,2,8,4,1]=>[3,6,4,2,7,1,5,8]=>[2,1,2,3]
[8,1,7,5,4,3,2,6]=>[7,6,5,4,8,2,3,1]=>[2,3,4,5,1,7,6,8]=>[4,2,2]
[8,1,7,4,5,3,2,6]=>[4,7,6,5,8,2,3,1]=>[5,2,3,4,1,7,6,8]=>[1,3,2,2]
[5,8,3,7,1,4,2,6]=>[3,1,7,5,6,8,4,2]=>[6,8,2,4,3,1,5,7]=>[2,2,1,3]
[2,1,7,3,4,6,8,5]=>[6,8,1,4,5,2,3,7]=>[3,1,8,5,4,7,6,2]=>[1,2,1,2,1,1]
[8,7,2,4,3,6,1,5]=>[5,3,4,7,8,6,2,1]=>[4,6,5,2,1,3,7,8]=>[2,1,1,4]
[7,1,2,3,5,6,8,4]=>[5,6,8,2,3,4,1,7]=>[4,3,1,7,6,5,8,2]=>[1,1,2,1,2,1]
[6,1,2,3,8,7,4,5]=>[7,8,6,2,3,1,4,5]=>[2,1,3,7,6,8,5,4]=>[1,3,2,1,1]
[5,1,2,3,7,8,6,4]=>[5,8,7,2,1,3,4,6]=>[4,1,2,7,8,6,5,3]=>[1,4,1,1,1]
[5,1,2,3,8,7,6,4]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[5,1,1,1]
[6,1,2,3,5,8,7,4]=>[8,5,7,2,3,1,4,6]=>[1,4,2,7,6,8,5,3]=>[2,2,2,1,1]
[7,6,3,2,4,8,1,5]=>[4,3,5,7,2,1,8,6]=>[5,6,4,2,7,8,1,3]=>[2,1,3,2]
[2,1,6,3,4,8,7,5]=>[8,7,1,4,2,3,5,6]=>[1,2,8,5,7,6,4,3]=>[3,2,1,1,1]
[8,6,3,2,4,7,1,5]=>[4,3,5,7,2,8,6,1]=>[5,6,4,2,7,1,3,8]=>[2,1,2,3]
[7,6,2,4,3,1,8,5]=>[5,3,4,8,6,2,1,7]=>[4,6,5,1,3,7,8,2]=>[2,1,4,1]
[6,1,2,3,5,7,8,4]=>[5,6,8,2,3,1,4,7]=>[4,3,1,7,6,8,5,2]=>[1,1,2,2,1,1]
[5,1,2,3,6,8,7,4]=>[8,5,7,2,1,3,4,6]=>[1,4,2,7,8,6,5,3]=>[2,3,1,1,1]
[7,8,1,2,6,3,5,4]=>[8,6,7,3,4,1,5,2]=>[1,3,2,6,5,8,4,7]=>[2,2,2,2]
[1,4,8,2,7,3,5,6]=>[2,6,7,8,4,5,1,3]=>[7,3,2,1,5,4,8,6]=>[1,1,1,2,2,1]
[1,2,8,5,4,7,3,6]=>[5,4,7,8,6,1,2,3]=>[4,5,2,1,3,8,7,6]=>[2,1,3,1,1]
[1,3,8,5,4,2,7,6]=>[5,4,8,2,6,7,1,3]=>[4,5,1,7,3,2,8,6]=>[2,2,1,2,1]
[1,3,6,8,4,7,5,2]=>[3,8,5,7,2,6,1,4]=>[6,1,4,2,7,3,8,5]=>[1,2,2,2,1]
[2,4,8,1,7,3,6,5]=>[8,2,6,7,1,4,5,3]=>[1,7,3,2,8,5,4,6]=>[2,1,2,1,2]
[3,4,8,5,7,6,1,2]=>[4,7,8,1,2,6,5,3]=>[5,2,1,8,7,3,4,6]=>[1,1,2,1,3]
[1,2,6,8,4,5,7,3]=>[5,3,6,8,7,1,2,4]=>[4,6,3,1,2,8,7,5]=>[2,1,3,1,1]
[7,5,1,2,4,3,6,8]=>[6,3,4,5,2,7,1,8]=>[3,6,5,4,7,2,8,1]=>[2,1,2,2,1]
[7,4,6,1,5,2,3,8]=>[6,2,7,4,5,3,1,8]=>[3,7,2,5,4,6,8,1]=>[2,2,3,1]
[7,1,4,2,6,3,5,8]=>[6,3,7,2,4,5,1,8]=>[3,6,2,7,5,4,8,1]=>[2,2,1,2,1]
[6,8,1,4,7,2,3,5]=>[6,4,7,1,8,3,5,2]=>[3,5,2,8,1,6,4,7]=>[2,2,2,2]
[1,6,4,2,8,3,5,7]=>[6,3,7,2,8,1,4,5]=>[3,6,2,7,1,8,5,4]=>[2,2,2,1,1]
[1,6,3,8,5,4,2,7]=>[7,6,3,2,5,8,1,4]=>[2,3,6,7,4,1,8,5]=>[4,1,2,1]
[6,8,1,7,3,5,4,2]=>[8,5,1,7,6,3,4,2]=>[1,4,8,2,3,6,5,7]=>[3,3,2]
[7,1,3,6,5,4,2,8]=>[7,6,3,5,2,4,1,8]=>[2,3,6,4,7,5,8,1]=>[3,2,2,1]
[7,2,1,4,6,3,5,8]=>[2,4,6,7,3,5,1,8]=>[7,5,3,2,6,4,8,1]=>[1,1,1,2,2,1]
[7,2,3,6,5,1,4,8]=>[6,7,2,3,5,4,1,8]=>[3,2,7,6,4,5,8,1]=>[1,2,1,3,1]
[7,1,2,3,6,5,4,8]=>[7,6,2,3,4,5,1,8]=>[2,3,7,6,5,4,8,1]=>[3,1,1,2,1]
[6,8,1,2,7,3,5,4]=>[8,6,7,3,1,4,5,2]=>[1,3,2,6,8,5,4,7]=>[2,3,1,2]
[1,6,2,3,8,5,4,7]=>[7,6,8,3,1,2,4,5]=>[2,3,1,6,8,7,5,4]=>[2,3,1,1,1]
[1,5,8,2,7,6,3,4]=>[2,7,8,6,4,5,1,3]=>[7,2,1,3,5,4,8,6]=>[1,1,3,2,1]
[5,1,8,2,7,6,3,4]=>[7,1,8,6,4,5,2,3]=>[2,8,1,3,5,4,7,6]=>[2,3,2,1]
[5,8,2,7,6,3,4,1]=>[1,6,8,7,3,5,4,2]=>[8,3,1,2,6,4,5,7]=>[1,1,3,3]
[6,2,8,1,7,3,5,4]=>[8,6,7,2,1,4,5,3]=>[1,3,2,7,8,5,4,6]=>[2,3,1,2]
[6,8,2,1,7,4,3,5]=>[7,3,6,1,8,4,5,2]=>[2,6,3,8,1,5,4,7]=>[2,2,2,2]
[3,6,4,1,2,8,5,7]=>[7,1,3,8,4,2,5,6]=>[2,8,6,1,5,7,4,3]=>[2,1,3,1,1]
[2,1,6,3,8,5,4,7]=>[7,6,1,3,8,2,4,5]=>[2,3,8,6,1,7,5,4]=>[3,1,2,1,1]
[2,5,1,8,7,6,3,4]=>[2,7,8,6,1,5,3,4]=>[7,2,1,3,8,4,6,5]=>[1,1,3,2,1]
[2,5,3,8,7,4,6,1]=>[2,6,8,7,1,3,5,4]=>[7,3,1,2,8,6,4,5]=>[1,1,3,1,2]
[1,2,5,3,8,7,4,6]=>[3,7,8,6,1,2,4,5]=>[6,2,1,3,8,7,5,4]=>[1,1,3,1,1,1]
[2,4,8,7,6,5,1,3]=>[7,8,6,2,5,1,4,3]=>[2,1,3,7,4,8,5,6]=>[1,3,2,2]
[2,5,3,8,7,1,6,4]=>[2,8,6,7,1,3,5,4]=>[7,1,3,2,8,6,4,5]=>[1,2,2,1,2]
[3,5,8,7,1,4,2,6]=>[2,7,1,5,6,8,4,3]=>[7,2,8,4,3,1,5,6]=>[1,2,1,1,3]
[5,3,8,4,1,7,6,2]=>[4,1,8,2,7,5,6,3]=>[5,8,1,7,2,4,3,6]=>[2,2,2,2]
[4,2,8,7,6,3,5,1]=>[6,8,1,7,5,2,4,3]=>[3,1,8,2,4,7,5,6]=>[1,2,3,2]
[4,2,8,7,6,5,3,1]=>[8,7,1,6,5,2,4,3]=>[1,2,8,3,4,7,5,6]=>[3,3,2]
[4,1,8,7,6,5,3,2]=>[8,7,1,6,5,4,2,3]=>[1,2,8,3,4,5,7,6]=>[3,4,1]
[4,3,8,7,6,5,1,2]=>[7,8,1,6,2,5,4,3]=>[2,1,8,3,7,4,5,6]=>[1,2,2,3]
[6,3,1,8,7,2,5,4]=>[8,2,6,1,7,5,3,4]=>[1,7,3,8,2,4,6,5]=>[2,2,3,1]
[5,8,3,7,6,1,4,2]=>[1,8,3,6,7,5,4,2]=>[8,1,6,3,2,4,5,7]=>[1,2,1,4]
[5,1,3,8,7,6,2,4]=>[7,1,8,6,3,5,2,4]=>[2,8,1,3,6,4,7,5]=>[2,3,2,1]
[1,5,3,8,7,6,2,4]=>[2,7,8,6,3,5,1,4]=>[7,2,1,3,6,4,8,5]=>[1,1,3,2,1]
[1,5,8,4,7,2,6,3]=>[2,4,8,6,7,5,1,3]=>[7,5,1,3,2,4,8,6]=>[1,1,2,3,1]
[5,1,8,4,7,2,6,3]=>[4,1,8,6,7,5,2,3]=>[5,8,1,3,2,4,7,6]=>[2,2,3,1]
[5,8,7,4,6,1,2,3]=>[1,6,7,4,8,5,3,2]=>[8,3,2,5,1,4,6,7]=>[1,1,2,4]
[6,8,5,1,2,4,7,3]=>[6,8,4,1,5,3,7,2]=>[3,1,5,8,4,6,2,7]=>[1,3,2,2]
[5,6,3,1,2,4,8,7]=>[8,4,3,1,5,2,6,7]=>[1,5,6,8,4,7,3,2]=>[4,2,1,1]
[5,6,2,4,3,1,8,7]=>[5,3,1,4,2,8,6,7]=>[4,6,8,5,7,1,3,2]=>[3,2,2,1]
[5,6,1,2,4,3,8,7]=>[5,8,3,1,4,2,6,7]=>[4,1,6,8,5,7,3,2]=>[1,3,2,1,1]
[4,5,8,1,7,2,3,6]=>[1,6,2,7,8,4,5,3]=>[8,3,7,2,1,5,4,6]=>[1,2,1,2,2]
[4,5,8,1,7,2,6,3]=>[1,2,8,6,7,4,5,3]=>[8,7,1,3,2,5,4,6]=>[1,1,2,2,2]
[1,3,2,5,8,7,4,6]=>[7,8,2,4,6,1,3,5]=>[2,1,7,5,3,8,6,4]=>[1,2,1,2,1,1]
[3,5,1,8,7,4,6,2]=>[2,6,8,1,7,5,3,4]=>[7,3,1,8,2,4,6,5]=>[1,1,2,3,1]
[3,5,1,8,7,2,6,4]=>[2,8,1,6,7,5,3,4]=>[7,1,8,3,2,4,6,5]=>[1,2,1,3,1]
[4,3,6,1,2,8,5,7]=>[2,1,7,8,4,3,5,6]=>[7,8,2,1,5,6,4,3]=>[2,1,3,1,1]
[4,5,8,3,1,7,2,6]=>[1,2,7,4,8,5,6,3]=>[8,7,2,5,1,4,3,6]=>[1,1,2,2,2]
[3,2,5,8,7,1,6,4]=>[8,1,3,6,7,2,5,4]=>[1,8,6,3,2,7,4,5]=>[2,1,1,2,2]
[3,4,8,7,6,2,1,5]=>[7,6,8,1,2,5,4,3]=>[2,3,1,8,7,4,5,6]=>[2,2,1,3]
[3,1,4,8,7,6,2,5]=>[7,8,1,6,3,5,2,4]=>[2,1,8,3,6,4,7,5]=>[1,2,2,2,1]
[3,4,8,7,6,5,1,2]=>[7,8,6,1,2,5,4,3]=>[2,1,3,8,7,4,5,6]=>[1,3,1,3]
[3,4,8,7,6,2,5,1]=>[6,8,7,1,2,5,4,3]=>[3,1,2,8,7,4,5,6]=>[1,3,1,3]
[3,2,5,8,7,4,6,1]=>[6,8,1,3,7,2,5,4]=>[3,1,8,6,2,7,4,5]=>[1,2,1,2,2]
[4,5,8,3,1,7,6,2]=>[1,2,4,8,7,5,6,3]=>[8,7,5,1,2,4,3,6]=>[1,1,1,3,2]
[2,1,3,5,8,7,4,6]=>[7,8,1,4,6,2,3,5]=>[2,1,8,5,3,7,6,4]=>[1,2,1,2,1,1]
[1,2,7,5,8,6,4,3]=>[8,4,3,7,6,1,2,5]=>[1,5,6,2,3,8,7,4]=>[3,3,1,1]
[7,1,4,8,2,6,5,3]=>[8,3,7,5,6,2,1,4]=>[1,6,2,4,3,7,8,5]=>[2,2,3,1]
[6,8,1,3,7,5,2,4]=>[7,8,4,1,6,3,5,2]=>[2,1,5,8,3,6,4,7]=>[1,3,2,2]
[3,7,8,1,2,6,5,4]=>[8,7,1,4,5,2,6,3]=>[1,2,8,5,4,7,3,6]=>[3,1,2,2]
[1,3,7,8,2,6,5,4]=>[8,7,5,2,3,6,1,4]=>[1,2,4,7,6,3,8,5]=>[4,1,2,1]
[2,3,7,8,1,6,5,4]=>[8,7,5,1,2,3,6,4]=>[1,2,4,8,7,6,3,5]=>[4,1,1,2]
[2,7,8,1,3,6,5,4]=>[8,7,4,5,1,2,6,3]=>[1,2,5,4,8,7,3,6]=>[3,2,1,2]
[8,1,2,6,7,3,5,4]=>[8,6,4,7,2,3,5,1]=>[1,3,5,2,7,6,4,8]=>[3,2,1,2]
[8,1,2,6,7,5,3,4]=>[7,4,8,6,2,3,5,1]=>[2,5,1,3,7,6,4,8]=>[2,3,1,2]
[8,2,5,7,1,3,6,4]=>[8,5,2,3,6,7,4,1]=>[1,4,7,6,3,2,5,8]=>[3,1,1,3]
[2,8,1,6,7,3,5,4]=>[8,6,4,7,1,3,5,2]=>[1,3,5,2,8,6,4,7]=>[3,2,1,2]
[2,6,8,3,7,1,5,4]=>[8,4,2,6,7,1,5,3]=>[1,5,7,3,2,8,4,6]=>[3,1,2,2]
[2,8,6,4,7,1,5,3]=>[4,8,6,3,7,1,5,2]=>[5,1,3,6,2,8,4,7]=>[1,3,2,2]
[6,8,3,4,1,7,5,2]=>[3,4,1,8,7,5,6,2]=>[6,5,8,1,2,4,3,7]=>[1,2,3,2]
[6,8,3,7,4,1,5,2]=>[8,3,1,6,5,7,4,2]=>[1,6,8,3,4,2,5,7]=>[3,2,3]
[2,6,8,3,7,5,1,4]=>[7,2,8,4,6,1,5,3]=>[2,7,1,5,3,8,4,6]=>[2,2,2,2]
[8,2,5,7,1,6,3,4]=>[7,3,8,2,5,6,4,1]=>[2,6,1,7,4,3,5,8]=>[2,2,1,3]
[8,4,7,2,3,6,1,5]=>[4,2,5,7,8,6,3,1]=>[5,7,4,2,1,3,6,8]=>[2,1,1,4]
[8,5,7,4,2,6,1,3]=>[5,2,7,4,8,6,3,1]=>[4,7,2,5,1,3,6,8]=>[2,2,4]
[8,3,5,7,4,1,6,2]=>[3,8,2,6,5,7,4,1]=>[6,1,7,3,4,2,5,8]=>[1,2,2,3]
[8,5,2,4,7,1,6,3]=>[4,8,3,2,6,7,5,1]=>[5,1,6,7,3,2,4,8]=>[1,3,1,3]
[8,2,3,5,7,1,6,4]=>[4,8,2,3,6,7,5,1]=>[5,1,7,6,3,2,4,8]=>[1,2,1,1,3]
[8,2,4,7,3,6,1,5]=>[3,5,7,8,2,6,4,1]=>[6,4,2,1,7,3,5,8]=>[1,1,1,2,3]
[8,2,7,1,4,6,3,5]=>[5,7,8,2,4,6,3,1]=>[4,2,1,7,5,3,6,8]=>[1,1,2,1,3]
[8,7,1,2,4,6,3,5]=>[5,7,8,3,4,6,2,1]=>[4,2,1,6,5,3,7,8]=>[1,1,2,1,3]
[8,7,1,4,6,2,3,5]=>[6,4,7,8,3,5,2,1]=>[3,5,2,1,6,4,7,8]=>[2,1,2,3]
[8,4,7,1,3,6,2,5]=>[5,2,7,8,4,6,3,1]=>[4,7,2,1,5,3,6,8]=>[2,1,2,3]
[1,6,8,3,7,2,5,4]=>[8,4,2,6,7,5,1,3]=>[1,5,7,3,2,4,8,6]=>[3,1,3,1]
[5,8,7,1,3,6,2,4]=>[5,1,7,8,4,6,3,2]=>[4,8,2,1,5,3,6,7]=>[2,1,2,3]
[8,5,4,7,1,6,2,3]=>[7,3,2,8,5,6,4,1]=>[2,6,7,1,4,3,5,8]=>[3,2,3]
[8,5,4,7,1,2,6,3]=>[8,5,3,2,6,7,4,1]=>[1,4,6,7,3,2,5,8]=>[4,1,3]
[8,5,1,4,7,2,6,3]=>[4,8,6,2,7,3,5,1]=>[5,1,3,7,2,6,4,8]=>[1,3,2,2]
[1,4,6,8,2,7,5,3]=>[3,8,2,7,5,6,1,4]=>[6,1,7,2,4,3,8,5]=>[1,2,2,2,1]
[5,8,7,3,6,1,2,4]=>[1,6,4,7,8,5,3,2]=>[8,3,5,2,1,4,6,7]=>[1,2,1,4]
[8,3,5,7,1,6,2,4]=>[7,2,3,8,5,6,4,1]=>[2,7,6,1,4,3,5,8]=>[2,1,2,3]
[1,6,8,3,7,5,2,4]=>[7,2,8,4,6,5,1,3]=>[2,7,1,5,3,4,8,6]=>[2,2,3,1]
[6,3,8,2,7,5,1,4]=>[7,8,2,1,4,6,5,3]=>[2,1,7,8,5,3,4,6]=>[1,3,1,3]
[6,8,4,2,7,1,5,3]=>[8,4,3,1,6,7,5,2]=>[1,5,6,8,3,2,4,7]=>[4,1,3]
[8,6,4,7,3,1,5,2]=>[3,8,6,5,2,7,4,1]=>[6,1,3,4,7,2,5,8]=>[1,4,3]
[8,4,5,7,3,1,6,2]=>[2,3,8,6,5,7,4,1]=>[7,6,1,3,4,2,5,8]=>[1,1,3,3]
[8,3,4,7,2,6,1,5]=>[2,3,5,7,8,6,4,1]=>[7,6,4,2,1,3,5,8]=>[1,1,1,1,4]
[8,7,1,3,4,6,2,5]=>[4,5,7,8,3,6,2,1]=>[5,4,2,1,6,3,7,8]=>[1,1,1,2,3]
[2,8,4,5,7,1,6,3]=>[3,4,8,6,7,1,5,2]=>[6,5,1,3,2,8,4,7]=>[1,1,2,2,2]
[8,7,3,4,5,1,6,2]=>[3,4,8,6,5,7,2,1]=>[6,5,1,3,4,2,7,8]=>[1,1,3,3]
[8,7,4,5,2,6,1,3]=>[5,3,7,4,8,6,2,1]=>[4,6,2,5,1,3,7,8]=>[2,2,4]
[5,8,7,2,3,6,1,4]=>[4,1,5,7,8,6,3,2]=>[5,8,4,2,1,3,6,7]=>[2,1,1,4]
[8,7,2,3,4,6,1,5]=>[3,4,5,7,8,6,2,1]=>[6,5,4,2,1,3,7,8]=>[1,1,1,1,4]
[8,7,2,3,6,1,4,5]=>[3,4,6,7,8,5,2,1]=>[6,5,3,2,1,4,7,8]=>[1,1,1,1,4]
[1,3,2,8,5,4,7,6]=>[5,8,2,6,7,1,3,4]=>[4,1,7,3,2,8,6,5]=>[1,2,1,2,1,1]
[4,2,8,5,3,7,1,6]=>[1,5,4,7,8,2,6,3]=>[8,4,5,2,1,7,3,6]=>[1,2,1,2,2]
[5,2,1,8,4,3,7,6]=>[5,8,2,1,6,7,3,4]=>[4,1,7,8,3,2,6,5]=>[1,3,1,2,1]
[6,2,8,4,3,7,5,1]=>[4,8,5,1,7,2,6,3]=>[5,1,4,8,2,7,3,6]=>[1,3,2,2]
[7,2,8,4,3,1,6,5]=>[5,4,8,2,6,1,7,3]=>[4,5,1,7,3,8,2,6]=>[2,2,2,2]
[7,3,4,8,2,1,6,5]=>[2,3,5,8,6,1,7,4]=>[7,6,4,1,3,8,2,5]=>[1,1,1,3,2]
[6,3,4,8,2,7,5,1]=>[8,2,3,1,5,7,6,4]=>[1,7,6,8,4,2,3,5]=>[2,2,1,3]
[5,3,4,1,8,2,7,6]=>[2,3,1,8,6,7,4,5]=>[7,6,8,1,3,2,5,4]=>[1,2,2,2,1]
[8,1,4,5,2,3,7,6]=>[3,8,5,2,4,6,7,1]=>[6,1,4,7,5,3,2,8]=>[1,3,1,1,2]
[8,1,5,4,3,2,7,6]=>[5,4,3,8,2,6,7,1]=>[4,5,6,1,7,3,2,8]=>[3,2,1,2]
[3,5,4,2,8,1,7,6]=>[3,1,2,8,4,6,7,5]=>[6,8,7,1,5,3,2,4]=>[2,1,2,1,2]
[6,4,3,2,8,7,5,1]=>[2,8,3,1,7,4,6,5]=>[7,1,6,8,2,5,3,4]=>[1,3,2,2]
[6,5,3,2,1,7,8,4]=>[4,3,6,2,1,8,5,7]=>[5,6,3,7,8,1,4,2]=>[2,3,2,1]
[5,6,3,2,7,8,4,1]=>[3,1,5,2,8,4,7,6]=>[6,8,4,7,1,5,2,3]=>[2,2,2,2]
[4,1,6,3,2,7,8,5]=>[4,1,6,3,8,2,5,7]=>[5,8,3,6,1,7,4,2]=>[2,2,2,1,1]
[3,6,4,2,7,8,1,5]=>[3,7,1,4,2,5,8,6]=>[6,2,8,5,7,4,1,3]=>[1,2,2,1,2]
[8,1,6,4,3,7,2,5]=>[5,4,7,3,8,2,6,1]=>[4,5,2,6,1,7,3,8]=>[2,2,2,2]
[2,7,4,1,3,6,5,8]=>[7,4,1,3,5,6,2,8]=>[2,5,8,6,4,3,7,1]=>[3,1,1,2,1]
[3,7,4,2,6,1,5,8]=>[4,1,3,6,7,5,2,8]=>[5,8,6,3,2,4,7,1]=>[2,1,1,3,1]
[4,1,7,3,2,6,5,8]=>[4,1,7,5,6,2,3,8]=>[5,8,2,4,3,7,6,1]=>[2,2,2,1,1]
[5,7,3,2,6,4,8,1]=>[3,1,6,4,5,2,8,7]=>[6,8,3,5,4,7,1,2]=>[2,2,2,2]
[6,7,3,2,5,4,1,8]=>[3,7,4,1,6,5,2,8]=>[6,2,5,8,3,4,7,1]=>[1,3,3,1]
[4,7,5,6,2,3,8,1]=>[5,1,3,6,4,2,8,7]=>[4,8,6,3,5,7,1,2]=>[2,1,3,2]
[3,1,7,5,6,2,4,8]=>[6,1,4,7,5,2,3,8]=>[3,8,5,2,4,7,6,1]=>[2,1,3,1,1]
[2,7,5,6,1,3,4,8]=>[5,6,3,7,1,4,2,8]=>[4,3,6,2,8,5,7,1]=>[1,2,2,2,1]
[2,6,5,7,1,3,8,4]=>[8,5,3,1,2,6,4,7]=>[1,4,6,8,7,3,5,2]=>[4,1,2,1]
[4,6,5,7,2,8,1,3]=>[5,1,3,2,7,4,8,6]=>[4,8,6,7,2,5,1,3]=>[2,2,2,2]
[5,6,4,7,2,8,3,1]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[1,2,3,2]
[6,5,4,1,7,2,8,3]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>[6,1,1]
[7,5,4,6,2,1,8,3]=>[5,3,2,8,6,4,1,7]=>[4,6,7,1,3,5,8,2]=>[3,4,1]
[5,4,6,1,7,8,2,3]=>[2,1,7,5,3,8,4,6]=>[7,8,2,4,6,1,5,3]=>[2,3,2,1]
[8,1,5,6,7,2,3,4]=>[6,3,7,4,8,2,5,1]=>[3,6,2,5,1,7,4,8]=>[2,2,2,2]
[2,1,4,6,8,7,3,5]=>[4,7,8,1,3,6,2,5]=>[5,2,1,8,6,3,7,4]=>[1,1,2,1,2,1]
[3,4,6,8,7,1,2,5]=>[6,1,2,3,7,8,5,4]=>[3,8,7,6,2,1,4,5]=>[2,1,1,1,3]
[5,3,6,8,7,2,4,1]=>[3,1,6,8,2,7,5,4]=>[6,8,3,1,7,2,4,5]=>[2,1,2,3]
[6,3,5,1,8,7,2,4]=>[7,2,3,1,8,6,4,5]=>[2,7,6,8,1,3,5,4]=>[2,2,3,1]
[7,3,5,8,6,2,1,4]=>[3,7,2,6,1,8,5,4]=>[6,2,7,3,8,1,4,5]=>[1,2,2,3]
[7,2,8,5,6,3,1,4]=>[7,6,4,8,2,1,5,3]=>[2,3,5,1,7,8,4,6]=>[3,3,2]
[6,2,8,5,1,7,3,4]=>[7,8,5,2,1,4,6,3]=>[2,1,4,7,8,5,3,6]=>[1,4,1,2]
[4,2,1,8,6,7,3,5]=>[1,7,5,8,2,6,3,4]=>[8,2,4,1,7,3,6,5]=>[1,2,2,2,1]
[1,3,2,8,6,7,4,5]=>[7,5,8,2,6,1,3,4]=>[2,4,1,7,3,8,6,5]=>[2,2,2,1,1]
[2,3,8,6,7,1,4,5]=>[6,7,4,8,1,2,5,3]=>[3,2,5,1,8,7,4,6]=>[1,2,2,1,2]
[8,1,3,2,6,7,4,5]=>[7,3,5,8,2,4,6,1]=>[2,6,4,1,7,5,3,8]=>[2,1,2,1,2]
[2,3,8,7,1,6,5,4]=>[8,7,5,6,1,2,4,3]=>[1,2,4,3,8,7,5,6]=>[3,2,1,2]
[4,2,8,7,6,1,5,3]=>[8,1,6,7,5,2,4,3]=>[1,8,3,2,4,7,5,6]=>[2,1,3,2]
[5,2,8,7,6,4,1,3]=>[1,7,8,6,5,2,4,3]=>[8,2,1,3,4,7,5,6]=>[1,1,4,2]
[7,2,1,8,6,5,4,3]=>[8,7,6,2,5,3,1,4]=>[1,2,3,7,4,6,8,5]=>[4,3,1]
[6,3,7,8,5,4,2,1]=>[3,1,8,7,2,6,5,4]=>[6,8,1,2,7,3,4,5]=>[2,3,3]
[5,3,7,8,6,4,1,2]=>[1,7,3,8,2,6,5,4]=>[8,2,6,1,7,3,4,5]=>[1,2,2,3]
[4,3,1,7,8,6,5,2]=>[1,4,8,2,7,6,3,5]=>[8,5,1,7,2,3,6,4]=>[1,1,2,3,1]
[3,4,7,8,6,1,5,2]=>[8,6,1,2,3,7,5,4]=>[1,3,8,7,6,2,4,5]=>[3,1,1,3]
[3,5,7,6,8,1,4,2]=>[8,2,6,1,4,3,7,5]=>[1,7,3,8,5,6,2,4]=>[2,2,2,2]
[4,5,7,6,8,3,1,2]=>[7,1,2,4,3,8,6,5]=>[2,8,7,5,6,1,3,4]=>[2,1,2,3]
[5,4,1,7,6,8,3,2]=>[2,1,5,4,8,7,3,6]=>[7,8,4,5,1,2,6,3]=>[2,2,3,1]
[6,4,7,5,8,3,2,1]=>[4,2,1,3,8,7,6,5]=>[5,7,8,6,1,2,3,4]=>[3,1,4]
[7,4,6,5,1,8,3,2]=>[8,2,7,5,4,3,1,6]=>[1,7,2,4,5,6,8,3]=>[2,5,1]
[7,5,6,4,3,1,8,2]=>[2,8,6,5,4,3,1,7]=>[7,1,3,4,5,6,8,2]=>[1,6,1]
[6,5,1,7,4,3,8,2]=>[6,5,4,2,1,8,3,7]=>[3,4,5,7,8,1,6,2]=>[5,2,1]
[4,6,7,5,3,8,1,2]=>[2,7,1,5,4,3,8,6]=>[7,2,8,4,5,6,1,3]=>[1,2,3,2]
[3,6,7,5,1,4,8,2]=>[6,2,8,1,5,4,3,7]=>[3,7,1,8,4,5,6,2]=>[2,2,3,1]
[8,1,6,7,5,4,2,3]=>[7,3,8,6,5,2,4,1]=>[2,6,1,3,4,7,5,8]=>[2,4,2]
[8,1,7,6,5,4,3,2]=>[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>[6,2]
[2,7,6,1,5,4,3,8]=>[7,6,4,5,1,3,2,8]=>[2,3,5,4,8,6,7,1]=>[3,2,2,1]
[3,7,6,5,1,4,2,8]=>[7,5,6,1,4,3,2,8]=>[2,4,3,8,5,6,7,1]=>[2,2,3,1]
[4,7,6,5,3,1,2,8]=>[6,7,1,5,4,3,2,8]=>[3,2,8,4,5,6,7,1]=>[1,2,4,1]
[8,6,4,1,5,2,7,3]=>[8,6,4,3,5,2,7,1]=>[1,3,5,6,4,7,2,8]=>[4,2,2]
[8,6,5,1,3,2,7,4]=>[5,8,4,6,3,2,7,1]=>[4,1,5,3,6,7,2,8]=>[1,2,3,2]
[8,7,3,1,5,2,4,6]=>[6,3,7,4,5,8,2,1]=>[3,6,2,5,4,1,7,8]=>[2,2,1,3]
[5,3,1,7,2,4,6,8]=>[5,2,6,1,7,3,4,8]=>[4,7,3,8,2,6,5,1]=>[2,2,2,1,1]
[8,7,1,2,4,5,3,6]=>[5,7,3,4,6,8,2,1]=>[4,2,6,5,3,1,7,8]=>[1,2,1,1,3]
[8,6,1,2,4,7,3,5]=>[5,7,8,3,4,2,6,1]=>[4,2,1,6,5,7,3,8]=>[1,1,2,2,2]
[8,5,1,2,6,7,3,4]=>[7,5,8,3,2,4,6,1]=>[2,4,1,6,7,5,3,8]=>[2,3,1,2]
[8,5,1,6,4,2,7,3]=>[8,6,5,3,2,4,7,1]=>[1,3,4,6,7,5,2,8]=>[5,1,2]
[8,5,1,3,6,4,7,2]=>[6,4,5,2,8,3,7,1]=>[3,5,4,7,1,6,2,8]=>[2,2,2,2]
[8,6,1,5,3,4,7,2]=>[5,6,4,8,3,2,7,1]=>[4,3,5,1,6,7,2,8]=>[1,2,3,2]
[8,6,1,2,5,7,3,4]=>[7,5,8,3,4,2,6,1]=>[2,4,1,6,5,7,3,8]=>[2,2,2,2]
[8,6,1,2,7,4,3,5]=>[7,6,8,3,4,2,5,1]=>[2,3,1,6,5,7,4,8]=>[2,2,2,2]
[8,7,1,2,5,4,3,6]=>[7,6,3,4,5,8,2,1]=>[2,3,6,5,4,1,7,8]=>[3,1,1,3]
[5,1,4,2,7,3,6,8]=>[6,3,7,2,1,4,5,8]=>[3,6,2,7,8,5,4,1]=>[2,3,1,1,1]
[7,1,5,8,2,6,3,4]=>[7,3,8,5,6,2,1,4]=>[2,6,1,4,3,7,8,5]=>[2,2,3,1]
[5,7,8,1,2,4,6,3]=>[6,1,8,4,5,2,7,3]=>[3,8,1,5,4,7,2,6]=>[2,2,2,2]
[5,7,8,1,3,4,6,2]=>[5,1,6,8,4,2,7,3]=>[4,8,3,1,5,7,2,6]=>[2,1,3,2]
[5,8,1,7,3,4,6,2]=>[5,1,6,8,7,3,4,2]=>[4,8,3,1,2,6,5,7]=>[2,1,3,2]
[8,1,5,7,2,4,6,3]=>[6,3,8,5,7,2,4,1]=>[3,6,1,4,2,7,5,8]=>[2,2,2,2]
[8,4,1,2,7,6,3,5]=>[7,2,8,6,3,4,5,1]=>[2,7,1,3,6,5,4,8]=>[2,3,1,2]
[1,4,2,3,8,7,5,6]=>[2,7,8,6,1,3,4,5]=>[7,2,1,3,8,6,5,4]=>[1,1,3,1,1,1]
[1,4,2,7,6,3,5,8]=>[2,6,7,5,1,3,4,8]=>[7,3,2,4,8,6,5,1]=>[1,1,3,1,1,1]
[6,1,2,8,7,5,3,4]=>[7,8,6,5,2,1,3,4]=>[2,1,3,4,7,8,6,5]=>[1,5,1,1]
[6,1,2,4,8,7,5,3]=>[8,7,4,6,2,1,3,5]=>[1,2,5,3,7,8,6,4]=>[3,3,1,1]
[3,1,8,4,6,7,5,2]=>[5,8,1,4,7,6,2,3]=>[4,1,8,5,2,3,7,6]=>[1,2,1,3,1]
[3,1,7,6,4,8,5,2]=>[8,5,1,4,3,7,2,6]=>[1,4,8,5,6,2,7,3]=>[3,2,2,1]
[7,1,2,4,6,8,5,3]=>[5,8,4,7,2,3,1,6]=>[4,1,5,2,7,6,8,3]=>[1,2,2,2,1]
[7,1,2,6,8,5,3,4]=>[7,4,8,6,2,3,1,5]=>[2,5,1,3,7,6,8,4]=>[2,3,2,1]
[6,1,2,7,8,5,3,4]=>[7,4,8,6,2,1,3,5]=>[2,5,1,3,7,8,6,4]=>[2,4,1,1]
[3,1,6,4,7,8,5,2]=>[5,1,3,8,4,7,2,6]=>[4,8,6,1,5,2,7,3]=>[2,1,2,2,1]
[5,7,1,3,8,4,6,2]=>[6,1,8,4,7,3,2,5]=>[3,8,1,5,2,6,7,4]=>[2,2,3,1]
[5,7,1,8,4,2,6,3]=>[1,8,6,5,7,3,2,4]=>[8,1,3,4,2,6,7,5]=>[1,3,3,1]
[7,1,5,3,2,8,6,4]=>[8,4,3,7,2,5,1,6]=>[1,5,6,2,7,4,8,3]=>[3,2,2,1]
[7,1,4,5,2,8,6,3]=>[3,4,8,7,2,5,1,6]=>[6,5,1,2,7,4,8,3]=>[1,1,3,2,1]
[4,7,3,1,5,8,6,2]=>[1,3,8,5,7,4,2,6]=>[8,6,1,4,2,5,7,3]=>[1,1,2,3,1]
[4,8,7,3,1,5,6,2]=>[6,1,4,8,5,7,3,2]=>[3,8,5,1,4,2,6,7]=>[2,1,2,3]
[8,1,7,4,5,2,6,3]=>[4,8,6,5,7,2,3,1]=>[5,1,3,4,2,7,6,8]=>[1,3,2,2]
[8,1,7,5,3,2,6,4]=>[5,8,6,4,7,2,3,1]=>[4,1,3,5,2,7,6,8]=>[1,3,2,2]
[8,3,7,1,2,6,4,5]=>[2,7,8,4,5,6,3,1]=>[7,2,1,5,4,3,6,8]=>[1,1,2,1,3]
[3,1,2,8,4,7,5,6]=>[1,7,8,5,6,2,3,4]=>[8,2,1,4,3,7,6,5]=>[1,1,2,2,1,1]
[3,1,7,2,6,4,5,8]=>[1,6,7,4,5,2,3,8]=>[8,3,2,5,4,7,6,1]=>[1,1,2,2,1,1]
[1,4,2,3,8,6,5,7]=>[2,7,6,8,1,3,4,5]=>[7,2,3,1,8,6,5,4]=>[1,2,2,1,1,1]
[1,4,2,3,8,5,7,6]=>[2,8,6,7,1,3,4,5]=>[7,1,3,2,8,6,5,4]=>[1,2,2,1,1,1]
[5,8,1,7,2,4,6,3]=>[6,1,8,5,7,3,4,2]=>[3,8,1,4,2,6,5,7]=>[2,2,2,2]
[5,8,1,3,4,7,6,2]=>[8,4,1,5,7,3,6,2]=>[1,5,8,4,2,6,3,7]=>[3,1,2,2]
[3,1,8,6,4,7,5,2]=>[8,5,1,4,7,6,2,3]=>[1,4,8,5,2,3,7,6]=>[3,1,3,1]
[8,1,2,6,7,4,5,3]=>[6,4,8,7,2,3,5,1]=>[3,5,1,2,7,6,4,8]=>[2,3,1,2]
[6,1,2,8,7,3,5,4]=>[8,6,7,5,2,1,3,4]=>[1,3,2,4,7,8,6,5]=>[2,4,1,1]
[1,2,3,5,8,4,7,6]=>[8,4,6,7,1,2,3,5]=>[1,5,3,2,8,7,6,4]=>[2,1,2,1,1,1]
[1,2,3,5,8,6,4,7]=>[7,4,6,8,1,2,3,5]=>[2,5,3,1,8,7,6,4]=>[2,1,2,1,1,1]
[7,1,2,8,3,6,5,4]=>[8,7,5,6,2,3,1,4]=>[1,2,4,3,7,6,8,5]=>[3,2,2,1]
[7,1,2,8,6,4,5,3]=>[6,8,7,5,2,3,1,4]=>[3,1,2,4,7,6,8,5]=>[1,4,2,1]
[3,1,7,8,4,6,5,2]=>[8,5,1,3,7,6,2,4]=>[1,4,8,6,2,3,7,5]=>[3,1,3,1]
[3,1,8,7,6,4,5,2]=>[6,8,7,1,5,4,2,3]=>[3,1,2,8,4,5,7,6]=>[1,3,3,1]
[8,1,2,7,4,6,5,3]=>[8,5,7,6,2,3,4,1]=>[1,4,2,3,7,6,5,8]=>[2,3,1,2]
[8,1,2,7,3,6,5,4]=>[8,7,5,6,2,3,4,1]=>[1,2,4,3,7,6,5,8]=>[3,2,1,2]
[1,2,3,5,8,7,4,6]=>[7,8,4,6,1,2,3,5]=>[2,1,5,3,8,7,6,4]=>[1,2,2,1,1,1]
[1,2,3,6,8,5,4,7]=>[4,7,6,8,1,2,3,5]=>[5,2,3,1,8,7,6,4]=>[1,2,2,1,1,1]
[7,8,5,6,3,1,4,2]=>[8,6,5,3,1,7,4,2]=>[1,3,4,6,8,2,5,7]=>[5,3]
[7,8,5,3,6,1,2,4]=>[6,4,7,3,1,8,5,2]=>[3,5,2,6,8,1,4,7]=>[2,3,3]
[7,5,6,3,1,4,2,8]=>[7,5,4,2,6,3,1,8]=>[2,4,5,7,3,6,8,1]=>[4,3,1]
[7,5,8,3,1,4,2,6]=>[7,5,4,2,6,1,8,3]=>[2,4,5,7,3,8,1,6]=>[4,2,2]
[7,8,5,3,1,4,2,6]=>[7,5,4,6,3,1,8,2]=>[2,4,5,3,6,8,1,7]=>[3,3,2]
[7,8,5,3,1,6,2,4]=>[7,4,8,5,3,1,6,2]=>[2,5,1,4,6,8,3,7]=>[2,4,2]
[7,8,5,3,1,6,4,2]=>[4,8,7,5,3,1,6,2]=>[5,1,2,4,6,8,3,7]=>[1,5,2]
[7,8,5,3,6,1,4,2]=>[4,8,6,3,1,7,5,2]=>[5,1,3,6,8,2,4,7]=>[1,4,3]
[7,8,5,3,6,4,1,2]=>[4,7,3,1,8,6,5,2]=>[5,2,6,8,1,3,4,7]=>[1,3,4]
[7,8,5,3,4,1,6,2]=>[4,8,6,5,3,1,7,2]=>[5,1,3,4,6,8,2,7]=>[1,5,2]
[7,8,5,3,1,4,6,2]=>[6,4,8,5,3,1,7,2]=>[3,5,1,4,6,8,2,7]=>[2,4,2]
[7,8,5,3,1,2,6,4]=>[8,5,4,6,3,1,7,2]=>[1,4,5,3,6,8,2,7]=>[3,3,2]
[7,5,3,8,1,2,6,4]=>[3,8,5,2,6,1,7,4]=>[6,1,4,7,3,8,2,5]=>[1,3,2,2]
[7,5,8,3,4,1,6,2]=>[4,2,8,6,5,1,7,3]=>[5,7,1,3,4,8,2,6]=>[2,4,2]
[7,5,8,3,4,6,1,2]=>[4,2,7,5,1,8,6,3]=>[5,7,2,4,8,1,3,6]=>[2,3,3]
[7,5,6,3,4,1,8,2]=>[4,2,8,6,5,3,1,7]=>[5,7,1,3,4,6,8,2]=>[2,5,1]
[7,5,6,3,1,4,8,2]=>[6,4,2,8,5,3,1,7]=>[3,5,7,1,4,6,8,2]=>[3,4,1]
[7,5,6,3,1,2,8,4]=>[8,5,4,2,6,3,1,7]=>[1,4,5,7,3,6,8,2]=>[4,3,1]
[7,5,3,6,1,2,8,4]=>[3,8,5,2,6,4,1,7]=>[6,1,4,7,3,5,8,2]=>[1,3,3,1]
[7,5,3,1,4,2,6,8]=>[6,4,3,5,2,7,1,8]=>[3,5,6,4,7,2,8,1]=>[3,2,2,1]
[7,5,3,1,6,2,8,4]=>[3,8,6,4,2,5,1,7]=>[6,1,3,5,7,4,8,2]=>[1,4,2,1]
[7,5,3,6,4,1,8,2]=>[8,3,2,6,5,4,1,7]=>[1,6,7,3,4,5,8,2]=>[3,4,1]
[7,5,3,6,4,8,1,2]=>[7,3,2,5,4,1,8,6]=>[2,6,7,4,5,8,1,3]=>[3,3,2]
[7,5,3,8,4,6,1,2]=>[7,3,2,5,1,8,6,4]=>[2,6,7,4,8,1,3,5]=>[3,2,3]
[7,5,3,8,1,4,6,2]=>[3,6,2,8,5,1,7,4]=>[6,3,7,1,4,8,2,5]=>[1,2,3,2]
[7,5,3,1,8,4,6,2]=>[3,6,2,8,7,4,1,5]=>[6,3,7,1,2,5,8,4]=>[1,2,4,1]
[7,5,3,1,8,2,6,4]=>[3,8,6,2,7,4,1,5]=>[6,1,3,7,2,5,8,4]=>[1,3,3,1]
[7,5,3,1,8,2,4,6]=>[6,3,7,2,8,4,1,5]=>[3,6,2,7,1,5,8,4]=>[2,2,3,1]
[7,5,3,1,6,2,4,8]=>[6,3,7,4,2,5,1,8]=>[3,6,2,5,7,4,8,1]=>[2,3,2,1]
[7,5,3,1,6,4,2,8]=>[3,7,6,4,2,5,1,8]=>[6,2,3,5,7,4,8,1]=>[1,4,2,1]
[7,5,3,1,8,6,2,4]=>[3,7,2,8,6,4,1,5]=>[6,2,7,1,3,5,8,4]=>[1,2,4,1]
[7,5,3,8,1,6,4,2]=>[8,3,2,7,5,1,6,4]=>[1,6,7,2,4,8,3,5]=>[3,3,2]
[7,5,3,8,6,4,1,2]=>[7,2,8,3,1,6,5,4]=>[2,7,1,6,8,3,4,5]=>[2,3,3]
[7,5,8,3,6,4,1,2]=>[4,2,7,1,8,6,5,3]=>[5,7,2,8,1,3,4,6]=>[2,2,4]
[7,5,8,3,6,1,4,2]=>[4,2,8,6,1,7,5,3]=>[5,7,1,3,8,2,4,6]=>[2,3,3]
[7,5,8,3,1,6,4,2]=>[4,2,8,7,5,1,6,3]=>[5,7,1,2,4,8,3,6]=>[2,4,2]
[7,5,3,6,4,1,2,8]=>[3,6,2,7,5,4,1,8]=>[6,3,7,2,4,5,8,1]=>[1,2,4,1]
[7,5,3,8,4,1,2,6]=>[3,6,2,7,5,1,8,4]=>[6,3,7,2,4,8,1,5]=>[1,2,3,2]
[7,5,8,6,3,1,2,4]=>[6,2,7,5,1,8,4,3]=>[3,7,2,4,8,1,5,6]=>[2,3,3]
[7,5,8,6,3,1,4,2]=>[2,8,6,5,1,7,4,3]=>[7,1,3,4,8,2,5,6]=>[1,4,3]
[7,5,8,6,3,4,1,2]=>[2,7,5,1,8,6,4,3]=>[7,2,4,8,1,3,5,6]=>[1,3,4]
[7,5,6,8,3,1,4,2]=>[2,8,6,5,3,1,7,4]=>[7,1,3,4,6,8,2,5]=>[1,5,2]
[7,5,6,3,8,1,2,4]=>[6,4,2,7,3,1,8,5]=>[3,5,7,2,6,8,1,4]=>[3,3,2]
[7,5,3,4,1,6,2,8]=>[3,7,5,4,2,6,1,8]=>[6,2,4,5,7,3,8,1]=>[1,4,2,1]
[7,5,3,4,1,8,2,6]=>[3,7,4,2,8,5,1,6]=>[6,2,5,7,1,4,8,3]=>[1,3,3,1]
[7,5,6,3,1,8,2,4]=>[7,4,2,8,5,3,1,6]=>[2,5,7,1,4,6,8,3]=>[3,4,1]
[7,5,6,3,1,8,4,2]=>[4,2,8,7,5,3,1,6]=>[5,7,1,2,4,6,8,3]=>[2,5,1]
[7,5,6,3,8,1,4,2]=>[4,2,8,6,3,1,7,5]=>[5,7,1,3,6,8,2,4]=>[2,4,2]
[7,5,6,3,8,4,1,2]=>[4,2,7,3,1,8,6,5]=>[5,7,2,6,8,1,3,4]=>[2,3,3]
[7,5,3,6,8,4,1,2]=>[7,3,2,4,1,8,6,5]=>[2,6,7,5,8,1,3,4]=>[3,2,3]
[7,5,3,6,8,1,4,2]=>[8,3,2,6,4,1,7,5]=>[1,6,7,3,5,8,2,4]=>[3,3,2]
[7,5,3,1,6,8,4,2]=>[3,5,2,8,7,4,1,6]=>[6,4,7,1,2,5,8,3]=>[1,2,4,1]
[7,5,3,1,6,8,2,4]=>[3,7,5,2,8,4,1,6]=>[6,2,4,7,1,5,8,3]=>[1,3,3,1]
[7,5,3,1,4,8,2,6]=>[5,3,7,2,8,4,1,6]=>[4,6,2,7,1,5,8,3]=>[2,2,3,1]
[7,5,3,1,4,6,2,8]=>[5,3,7,4,2,6,1,8]=>[4,6,2,5,7,3,8,1]=>[2,3,2,1]
[7,5,3,1,2,6,4,8]=>[7,4,3,5,2,6,1,8]=>[2,5,6,4,7,3,8,1]=>[3,2,2,1]
[7,5,3,1,2,8,4,6]=>[7,3,8,4,2,5,1,6]=>[2,6,1,5,7,4,8,3]=>[2,3,2,1]
[7,5,3,1,2,8,6,4]=>[3,8,7,4,2,5,1,6]=>[6,1,2,5,7,4,8,3]=>[1,4,2,1]
[7,5,3,1,4,8,6,2]=>[3,8,5,2,7,4,1,6]=>[6,1,4,7,2,5,8,3]=>[1,3,3,1]
[7,5,3,4,1,8,6,2]=>[3,4,2,8,7,5,1,6]=>[6,5,7,1,2,4,8,3]=>[1,2,4,1]
[7,5,3,4,8,6,1,2]=>[3,4,2,7,1,8,6,5]=>[6,5,7,2,8,1,3,4]=>[1,2,2,3]
[7,5,3,4,6,1,8,2]=>[3,4,2,8,6,5,1,7]=>[6,5,7,1,3,4,8,2]=>[1,2,4,1]
[7,5,3,4,1,6,8,2]=>[3,6,4,2,8,5,1,7]=>[6,3,5,7,1,4,8,2]=>[1,3,3,1]
[7,5,3,1,2,6,8,4]=>[6,3,8,4,2,5,1,7]=>[3,6,1,5,7,4,8,2]=>[2,3,2,1]
[7,5,3,1,2,4,8,6]=>[8,4,3,5,2,6,1,7]=>[1,5,6,4,7,3,8,2]=>[3,2,2,1]
[3,6,2,5,4,1,8,7]=>[5,1,3,4,2,8,6,7]=>[4,8,6,5,7,1,3,2]=>[2,1,2,2,1]
[3,5,2,8,4,7,6,1]=>[2,8,1,5,7,3,6,4]=>[7,1,8,4,2,6,3,5]=>[1,2,1,2,2]
[5,4,7,3,2,8,6,1]=>[2,1,4,8,5,3,7,6]=>[7,8,5,1,4,6,2,3]=>[2,1,3,2]
[5,4,8,3,2,7,6,1]=>[2,1,4,8,5,7,6,3]=>[7,8,5,1,4,2,3,6]=>[2,1,2,3]
[6,4,5,3,2,1,8,7]=>[2,5,4,3,1,8,6,7]=>[7,4,5,6,8,1,3,2]=>[1,4,2,1]
[5,3,2,6,4,1,8,7]=>[2,5,3,1,4,8,6,7]=>[7,4,6,8,5,1,3,2]=>[1,3,1,2,1]
[4,5,8,3,2,7,6,1]=>[1,2,4,8,5,7,6,3]=>[8,7,5,1,4,2,3,6]=>[1,1,1,2,3]
[4,7,6,3,8,5,2,1]=>[8,4,1,3,2,7,6,5]=>[1,5,8,6,7,2,3,4]=>[3,2,3]
[4,8,6,3,7,5,2,1]=>[8,4,1,3,7,6,5,2]=>[1,5,8,6,2,3,4,7]=>[3,1,4]
[4,8,5,3,2,7,6,1]=>[4,1,3,8,5,7,6,2]=>[5,8,6,1,4,2,3,7]=>[2,1,2,3]
[5,8,4,3,2,7,6,1]=>[1,4,3,8,5,7,6,2]=>[8,5,6,1,4,2,3,7]=>[1,2,2,3]
[5,3,2,8,4,7,6,1]=>[8,2,1,5,7,3,6,4]=>[1,7,8,4,2,6,3,5]=>[3,1,2,2]
[2,1,5,8,4,7,6,3]=>[8,3,5,7,1,6,2,4]=>[1,6,4,2,8,3,7,5]=>[2,1,2,2,1]
[5,3,2,7,4,8,6,1]=>[8,2,1,5,3,4,7,6]=>[1,7,8,4,6,5,2,3]=>[3,2,1,2]
[5,7,4,3,2,8,6,1]=>[1,4,3,8,5,2,7,6]=>[8,5,6,1,4,7,2,3]=>[1,2,3,2]
[4,7,5,3,2,8,6,1]=>[4,1,3,8,5,2,7,6]=>[5,8,6,1,4,7,2,3]=>[2,1,3,2]
[4,7,8,3,6,5,2,1]=>[8,4,1,2,7,6,5,3]=>[1,5,8,7,2,3,4,6]=>[3,1,4]
[4,6,8,3,7,5,2,1]=>[2,8,1,4,7,6,5,3]=>[7,1,8,5,2,3,4,6]=>[1,2,1,4]
[7,6,4,3,8,5,2,1]=>[3,8,4,2,1,7,6,5]=>[6,1,5,7,8,2,3,4]=>[1,4,3]
[7,3,2,6,8,5,4,1]=>[4,8,2,7,3,1,6,5]=>[5,1,7,2,6,8,3,4]=>[1,2,3,2]
[2,1,8,6,7,5,4,3]=>[4,8,7,6,1,5,2,3]=>[5,1,2,3,8,4,7,6]=>[1,4,2,1]
[8,3,2,6,7,5,4,1]=>[4,8,2,7,3,6,5,1]=>[5,1,7,2,6,3,4,8]=>[1,2,2,3]
[8,6,4,3,7,5,2,1]=>[3,8,4,2,7,6,5,1]=>[6,1,5,7,2,3,4,8]=>[1,3,4]
[8,5,7,6,4,3,2,1]=>[8,2,7,6,5,4,3,1]=>[1,7,2,3,4,5,6,8]=>[2,6]
[8,4,5,3,2,7,6,1]=>[2,4,3,8,5,7,6,1]=>[7,5,6,1,4,2,3,8]=>[1,2,2,3]
[8,4,7,3,6,5,2,1]=>[8,2,4,7,6,5,3,1]=>[1,7,5,2,3,4,6,8]=>[2,1,5]
[8,4,6,3,7,5,2,1]=>[8,2,4,3,7,6,5,1]=>[1,7,5,6,2,3,4,8]=>[2,2,4]
[7,4,6,3,8,5,2,1]=>[8,2,4,3,1,7,6,5]=>[1,7,5,6,8,2,3,4]=>[2,3,3]
[3,7,2,6,8,5,4,1]=>[4,8,7,1,3,2,6,5]=>[5,1,2,8,6,7,3,4]=>[1,3,2,2]
[3,8,2,6,7,5,4,1]=>[4,8,7,1,3,6,5,2]=>[5,1,2,8,6,3,4,7]=>[1,3,1,3]
[3,8,2,5,4,7,6,1]=>[4,8,1,3,5,7,6,2]=>[5,1,8,6,4,2,3,7]=>[1,2,1,1,3]
[3,7,2,8,6,5,4,1]=>[8,7,6,1,3,2,5,4]=>[1,2,3,8,6,7,4,5]=>[4,2,2]
[3,6,2,8,7,5,4,1]=>[2,8,7,1,6,3,5,4]=>[7,1,2,8,3,6,4,5]=>[1,3,2,2]
[6,4,7,3,8,5,2,1]=>[8,2,1,4,3,7,6,5]=>[1,7,8,5,6,2,3,4]=>[3,2,3]
[6,4,8,3,7,5,2,1]=>[8,2,1,4,7,6,5,3]=>[1,7,8,5,2,3,4,6]=>[3,1,4]
[7,4,8,3,6,5,2,1]=>[8,2,4,1,7,6,5,3]=>[1,7,5,8,2,3,4,6]=>[2,2,4]
[7,4,5,3,2,8,6,1]=>[2,4,3,8,5,1,7,6]=>[7,5,6,1,4,8,2,3]=>[1,2,3,2]
[7,5,4,3,2,8,6,1]=>[4,3,2,8,5,1,7,6]=>[5,6,7,1,4,8,2,3]=>[3,3,2]
[7,3,2,5,4,8,6,1]=>[2,4,8,3,5,1,7,6]=>[7,5,1,6,4,8,2,3]=>[1,1,2,2,2]
[7,3,2,8,6,5,4,1]=>[8,7,2,6,3,1,5,4]=>[1,2,7,3,6,8,4,5]=>[3,3,2]
[7,8,4,3,6,5,2,1]=>[3,8,4,1,7,6,5,2]=>[6,1,5,8,2,3,4,7]=>[1,3,4]
[6,8,5,7,4,3,2,1]=>[1,3,8,7,6,5,4,2]=>[8,6,1,2,3,4,5,7]=>[1,1,6]
[6,8,4,3,7,5,2,1]=>[3,1,8,4,7,6,5,2]=>[6,8,1,5,2,3,4,7]=>[2,2,4]
[6,3,2,8,7,5,4,1]=>[8,7,2,1,6,3,5,4]=>[1,2,7,8,3,6,4,5]=>[4,2,2]
[6,7,4,3,8,5,2,1]=>[3,1,8,4,2,7,6,5]=>[6,8,1,5,7,2,3,4]=>[2,3,3]
[2,3,1,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]
[2,3,4,5,1,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[1,1,1,2,1,1,1,1]
[2,3,4,5,6,1,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[1,1,1,1,2,1,1,1]
[2,3,1,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]
[2,4,3,1,5,6,7,8,9]=>[4,1,3,2,5,6,7,8,9]=>[6,9,7,8,5,4,3,2,1]=>[2,2,1,1,1,1,1]
[2,3,5,4,1,6,7,8,9]=>[5,1,2,4,3,6,7,8,9]=>[5,9,8,6,7,4,3,2,1]=>[2,1,2,1,1,1,1]
[2,3,4,5,1,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[1,1,1,2,1,1,1,1,1]
[2,3,4,6,5,1,7,8,9]=>[6,1,2,3,5,4,7,8,9]=>[4,9,8,7,5,6,3,2,1]=>[2,1,1,2,1,1,1]
[2,3,4,5,6,1,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[1,1,1,1,2,1,1,1,1]
[2,3,4,5,7,6,1,8,9]=>[7,1,2,3,4,6,5,8,9]=>[3,9,8,7,6,4,5,2,1]=>[2,1,1,1,2,1,1]
[2,3,4,5,6,8,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>[2,9,8,7,6,5,3,4,1]=>[2,1,1,1,1,2,1]
[2,3,4,5,6,7,9,8,1]=>[9,1,2,3,4,5,6,8,7]=>[1,9,8,7,6,5,4,2,3]=>[2,1,1,1,1,1,2]
[4,6,8,3,5,7,1,2]=>[4,1,2,7,5,8,6,3]=>[5,8,7,2,4,1,3,6]=>[2,1,2,3]
[6,8,1,2,4,5,7,3]=>[5,6,8,3,1,4,7,2]=>[4,3,1,6,8,5,2,7]=>[1,1,3,1,2]
[3,5,8,2,4,7,1,6]=>[4,1,2,5,7,8,6,3]=>[5,8,7,4,2,1,3,6]=>[2,1,1,1,3]
[4,5,2,8,3,1,6,7]=>[1,6,3,2,5,7,8,4]=>[8,3,6,7,4,2,1,5]=>[1,3,1,1,2]
[4,2,5,8,3,7,1,6]=>[3,1,5,7,8,2,6,4]=>[6,8,4,2,1,7,3,5]=>[2,1,1,2,2]
[2,1,6,8,4,7,3,5]=>[5,3,7,8,1,6,2,4]=>[4,6,2,1,8,3,7,5]=>[2,1,2,2,1]
[1,2,5,8,3,6,7,4]=>[3,6,8,5,7,1,2,4]=>[6,3,1,4,2,8,7,5]=>[1,1,2,2,1,1]
[5,3,6,8,4,7,1,2]=>[3,1,7,2,5,8,6,4]=>[6,8,2,7,4,1,3,5]=>[2,2,1,3]
[1,6,5,8,2,4,7,3]=>[6,3,2,8,5,7,1,4]=>[3,6,7,1,4,2,8,5]=>[3,2,2,1]
[5,4,8,3,2,1,6,7]=>[2,1,6,5,4,7,8,3]=>[7,8,3,4,5,2,1,6]=>[2,3,1,2]
[5,4,3,7,2,6,1,8]=>[3,2,1,5,7,6,4,8]=>[6,7,8,4,2,3,5,1]=>[3,1,3,1]
[4,3,6,2,7,5,1,8]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[1,2,2,2,1]
[4,6,3,2,1,8,5,7]=>[1,4,3,7,2,8,5,6]=>[8,5,6,2,7,1,4,3]=>[1,2,2,2,1]
[4,1,7,3,2,5,8,6]=>[4,1,8,5,6,2,3,7]=>[5,8,1,4,3,7,6,2]=>[2,2,2,1,1]
[4,3,1,7,8,2,6,5]=>[1,8,2,6,4,7,3,5]=>[8,1,7,3,5,2,6,4]=>[1,2,2,2,1]
[3,5,1,2,7,8,6,4]=>[5,1,2,8,7,3,4,6]=>[4,8,7,1,2,6,5,3]=>[2,1,3,1,1]
[7,5,1,4,8,2,6,3]=>[4,8,6,2,7,3,1,5]=>[5,1,3,7,2,6,8,4]=>[1,3,3,1]
[5,4,7,3,8,6,1,2]=>[2,1,4,7,3,8,6,5]=>[7,8,5,2,6,1,3,4]=>[2,1,2,3]
[5,8,7,1,4,2,6,3]=>[1,8,6,4,5,7,3,2]=>[8,1,3,5,4,2,6,7]=>[1,3,1,3]
[8,3,5,1,2,7,6,4]=>[8,2,7,4,3,5,6,1]=>[1,7,2,5,6,4,3,8]=>[2,3,1,2]
[4,6,3,1,5,2,8,7]=>[1,5,3,8,4,2,6,7]=>[8,4,6,1,5,7,3,2]=>[1,2,3,1,1]
[4,7,3,6,5,2,1,8]=>[7,1,3,6,5,4,2,8]=>[2,8,6,3,4,5,7,1]=>[2,1,4,1]
[5,3,7,6,4,2,1,8]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[1,3,3,1]
[1,6,3,4,2,8,7,5]=>[8,3,4,2,7,1,5,6]=>[1,6,5,7,2,8,4,3]=>[2,2,2,1,1]
[6,4,8,7,5,3,1,2]=>[7,1,8,2,6,5,4,3]=>[2,8,1,7,3,4,5,6]=>[2,2,4]
[7,6,4,3,8,5,1,2]=>[4,3,7,2,1,8,6,5]=>[5,6,2,7,8,1,3,4]=>[2,3,3]
[1,7,6,2,8,4,5,3]=>[6,8,7,4,3,1,2,5]=>[3,1,2,5,6,8,7,4]=>[1,5,1,1]
[7,1,3,2,6,8,5,4]=>[5,8,3,7,2,4,1,6]=>[4,1,6,2,7,5,8,3]=>[1,2,2,2,1]
[1,5,3,2,7,4,8,6]=>[8,3,2,6,1,4,5,7]=>[1,6,7,3,8,5,4,2]=>[3,2,1,1,1]
[6,3,2,1,8,5,4,7]=>[2,7,3,6,1,8,4,5]=>[7,2,6,3,8,1,5,4]=>[1,2,2,2,1]
[5,2,6,3,7,4,1,8]=>[7,4,2,1,3,6,5,8]=>[2,5,7,8,6,3,4,1]=>[4,1,2,1]
[2,8,5,3,1,6,4,7]=>[4,7,5,1,3,6,8,2]=>[5,2,4,8,6,3,1,7]=>[1,3,1,1,2]
[2,1,7,3,8,5,4,6]=>[7,6,8,1,4,2,3,5]=>[2,3,1,8,5,7,6,4]=>[2,2,2,1,1]
[1,6,2,3,7,8,5,4]=>[5,8,7,3,1,2,4,6]=>[4,1,2,6,8,7,5,3]=>[1,4,1,1,1]
[1,6,7,2,8,4,5,3]=>[6,2,8,7,4,1,3,5]=>[3,7,1,2,5,8,6,4]=>[2,4,1,1]
[5,7,1,8,2,4,6,3]=>[6,1,8,5,7,3,2,4]=>[3,8,1,4,2,6,7,5]=>[2,2,3,1]
[5,1,2,7,8,3,6,4]=>[8,6,4,1,7,2,3,5]=>[1,3,5,8,2,7,6,4]=>[4,2,1,1]
[2,4,1,7,8,6,3,5]=>[7,2,4,8,1,6,3,5]=>[2,7,5,1,8,3,6,4]=>[2,1,2,2,1]
[4,2,1,7,3,8,5,6]=>[7,1,8,2,5,3,4,6]=>[2,8,1,7,4,6,5,3]=>[2,2,2,1,1]
[6,2,8,4,3,1,5,7]=>[6,5,2,4,1,7,8,3]=>[3,4,7,5,8,2,1,6]=>[3,2,1,2]
[7,3,2,1,8,4,5,6]=>[3,2,6,7,8,4,1,5]=>[6,7,3,2,1,5,8,4]=>[2,1,1,3,1]
[7,8,3,2,5,6,1,4]=>[3,7,4,5,1,8,6,2]=>[6,2,5,4,8,1,3,7]=>[1,2,2,3]
[7,1,8,2,4,5,6,3]=>[5,6,8,4,7,2,1,3]=>[4,3,1,5,2,7,8,6]=>[1,1,2,3,1]
[8,7,6,1,2,4,5,3]=>[6,8,4,5,7,3,2,1]=>[3,1,5,4,2,6,7,8]=>[1,2,1,4]
[8,3,7,6,2,1,4,5]=>[6,2,5,7,8,4,3,1]=>[3,7,4,2,1,5,6,8]=>[2,1,1,4]
[3,2,8,7,5,1,4,6]=>[6,7,1,5,8,2,4,3]=>[3,2,8,4,1,7,5,6]=>[1,2,1,2,2]
[8,3,6,5,2,1,4,7]=>[6,2,5,7,4,3,8,1]=>[3,7,4,2,5,6,1,8]=>[2,1,3,2]
[7,6,3,5,2,4,1,8]=>[3,5,7,6,4,2,1,8]=>[6,4,2,3,5,7,8,1]=>[1,1,5,1]
[8,2,4,1,6,5,3,7]=>[3,7,2,6,4,5,8,1]=>[6,2,7,3,5,4,1,8]=>[1,2,2,1,2]
[8,7,1,5,6,2,4,3]=>[8,6,4,7,3,5,2,1]=>[1,3,5,2,6,4,7,8]=>[3,2,3]
[8,5,7,3,6,4,1,2]=>[4,2,7,8,6,5,3,1]=>[5,7,2,1,3,4,6,8]=>[2,1,5]
[6,8,3,7,5,4,1,2]=>[7,1,8,3,6,5,4,2]=>[2,8,1,6,3,4,5,7]=>[2,2,4]
[8,1,6,7,5,2,4,3]=>[8,6,3,7,5,2,4,1]=>[1,3,6,2,4,7,5,8]=>[3,3,2]
[8,1,2,6,4,3,7,5]=>[5,8,6,2,3,4,7,1]=>[4,1,3,7,6,5,2,8]=>[1,3,1,1,2]
[2,8,1,7,5,4,3,6]=>[7,6,5,8,1,3,4,2]=>[2,3,4,1,8,6,5,7]=>[3,2,1,2]
[2,5,1,8,6,4,3,7]=>[2,7,6,1,5,8,3,4]=>[7,2,3,8,4,1,6,5]=>[1,3,1,2,1]
[6,2,7,5,4,3,1,8]=>[7,6,5,2,1,4,3,8]=>[2,3,4,7,8,5,6,1]=>[5,2,1]
[2,1,8,6,5,4,3,7]=>[7,6,5,1,4,8,2,3]=>[2,3,4,8,5,1,7,6]=>[4,1,2,1]
[1,2,7,5,4,3,8,6]=>[5,4,8,6,1,2,3,7]=>[4,5,1,3,8,7,6,2]=>[2,3,1,1,1]
[1,7,2,4,3,8,6,5]=>[8,4,7,3,5,1,2,6]=>[1,5,2,6,4,8,7,3]=>[2,2,2,1,1]
[1,7,2,8,3,6,5,4]=>[8,7,5,6,3,1,2,4]=>[1,2,4,3,6,8,7,5]=>[3,3,1,1]
[1,7,8,6,5,2,4,3]=>[8,6,2,7,5,4,1,3]=>[1,3,7,2,4,5,8,6]=>[3,4,1]
[7,3,8,6,5,4,1,2]=>[7,8,6,2,1,5,4,3]=>[2,1,3,7,8,4,5,6]=>[1,4,3]
[1,8,7,6,5,2,4,3]=>[8,6,7,5,4,3,1,2]=>[1,3,2,4,5,6,8,7]=>[2,5,1]
[8,1,7,3,2,6,5,4]=>[8,4,7,5,6,2,3,1]=>[1,5,2,4,3,7,6,8]=>[2,2,2,2]
[5,1,4,3,2,8,7,6]=>[3,8,4,1,7,2,5,6]=>[6,1,5,8,2,7,4,3]=>[1,3,2,1,1]
[8,6,3,2,1,7,4,5]=>[4,3,7,8,5,2,6,1]=>[5,6,2,1,4,7,3,8]=>[2,1,3,2]
[8,6,5,4,1,7,2,3]=>[7,8,5,4,3,2,6,1]=>[2,1,4,5,6,7,3,8]=>[1,5,2]
[8,6,5,1,7,3,2,4]=>[7,6,8,4,3,2,5,1]=>[2,3,1,5,6,7,4,8]=>[2,4,2]
[8,6,1,7,4,3,2,5]=>[7,6,5,8,3,2,4,1]=>[2,3,4,1,6,7,5,8]=>[3,3,2]
[4,6,3,2,7,5,1,8]=>[1,3,7,4,2,6,5,8]=>[8,6,2,5,7,3,4,1]=>[1,1,3,2,1]
[1,4,3,7,2,5,8,6]=>[2,8,3,5,6,1,4,7]=>[7,1,6,4,3,8,5,2]=>[1,2,1,2,1,1]
[7,4,8,3,1,6,2,5]=>[2,7,4,8,5,1,6,3]=>[7,2,5,1,4,8,3,6]=>[1,2,3,2]
[7,1,5,8,3,2,6,4]=>[5,3,8,6,7,2,1,4]=>[4,6,1,3,2,7,8,5]=>[2,2,3,1]
[5,7,4,1,8,2,6,3]=>[1,8,6,3,7,4,2,5]=>[8,1,3,6,2,5,7,4]=>[1,3,3,1]
[5,7,4,3,1,8,6,2]=>[1,4,3,8,7,5,2,6]=>[8,5,6,1,2,4,7,3]=>[1,2,4,1]
[1,8,7,2,5,4,6,3]=>[6,5,8,4,7,3,1,2]=>[3,4,1,5,2,6,8,7]=>[2,2,3,1]
[1,4,8,6,3,5,2,7]=>[5,7,2,6,4,8,1,3]=>[4,2,7,3,5,1,8,6]=>[1,2,2,2,1]
[7,4,6,3,5,2,1,8]=>[2,4,7,6,5,3,1,8]=>[7,5,2,3,4,6,8,1]=>[1,1,5,1]
[1,3,5,6,8,4,2,7]=>[3,4,7,2,6,8,1,5]=>[6,5,2,7,3,1,8,4]=>[1,1,2,1,2,1]
[3,5,4,8,7,1,2,6]=>[3,1,2,6,7,8,5,4]=>[6,8,7,3,2,1,4,5]=>[2,1,1,1,3]
[3,1,4,6,8,7,2,5]=>[1,4,7,8,3,6,2,5]=>[8,5,2,1,6,3,7,4]=>[1,1,1,2,2,1]
[1,6,3,8,7,2,5,4]=>[8,6,2,7,3,5,1,4]=>[1,3,7,2,6,4,8,5]=>[3,2,2,1]
[1,6,2,4,8,7,5,3]=>[8,7,4,2,6,1,3,5]=>[1,2,5,7,3,8,6,4]=>[4,2,1,1]
[7,1,6,4,8,5,2,3]=>[4,7,3,8,6,2,1,5]=>[5,2,6,1,3,7,8,4]=>[1,2,4,1]
[7,3,6,8,5,1,2,4]=>[6,7,2,3,1,8,5,4]=>[3,2,7,6,8,1,4,5]=>[1,2,2,3]
[1,3,7,2,6,8,4,5]=>[7,5,8,2,4,1,3,6]=>[2,4,1,7,5,8,6,3]=>[2,2,2,1,1]
[4,2,6,3,8,1,5,7]=>[4,1,6,2,3,7,8,5]=>[5,8,3,7,6,2,1,4]=>[2,2,1,1,2]
[4,2,6,7,3,5,1,8]=>[1,5,3,7,2,6,4,8]=>[8,4,6,2,7,3,5,1]=>[1,2,2,2,1]
[3,6,2,4,7,5,1,8]=>[7,1,3,4,2,6,5,8]=>[2,8,6,5,7,3,4,1]=>[2,1,2,2,1]
[3,6,2,4,1,8,5,7]=>[1,3,4,7,2,8,5,6]=>[8,6,5,2,7,1,4,3]=>[1,1,1,2,2,1]
[7,3,8,2,1,6,4,5]=>[2,4,7,8,5,1,6,3]=>[7,5,2,1,4,8,3,6]=>[1,1,1,3,2]
[8,7,6,4,3,1,5,2]=>[8,6,5,4,7,3,2,1]=>[1,3,4,5,2,6,7,8]=>[4,4]
[8,7,6,4,1,5,2,3]=>[7,8,5,4,6,3,2,1]=>[2,1,4,5,3,6,7,8]=>[1,3,4]
[3,8,7,2,1,4,6,5]=>[4,8,1,5,6,7,3,2]=>[5,1,8,4,3,2,6,7]=>[1,2,1,1,3]
[3,8,2,7,1,5,4,6]=>[7,1,3,5,6,8,4,2]=>[2,8,6,4,3,1,5,7]=>[2,1,1,1,3]
[3,6,8,2,1,5,4,7]=>[4,7,1,5,2,6,8,3]=>[5,2,8,4,7,3,1,6]=>[1,2,2,1,2]
[2,4,8,1,6,5,3,7]=>[7,2,6,1,4,5,8,3]=>[2,7,3,8,5,4,1,6]=>[2,2,1,1,2]
[4,2,8,1,5,7,3,6]=>[5,1,7,8,2,4,6,3]=>[4,8,2,1,7,5,3,6]=>[2,1,2,1,2]
[8,6,1,7,3,5,4,2]=>[8,5,7,6,3,2,4,1]=>[1,4,2,3,6,7,5,8]=>[2,4,2]
[8,6,1,7,5,4,2,3]=>[7,8,6,5,3,2,4,1]=>[2,1,3,4,6,7,5,8]=>[1,5,2]
[1,6,2,8,7,3,5,4]=>[8,6,2,7,5,1,3,4]=>[1,3,7,2,4,8,6,5]=>[3,3,1,1]
[1,8,2,4,6,7,3,5]=>[7,4,5,8,3,6,1,2]=>[2,5,4,1,6,3,8,7]=>[2,1,2,2,1]
[2,8,5,4,7,1,3,6]=>[6,4,3,7,8,1,5,2]=>[3,5,6,2,1,8,4,7]=>[3,1,2,2]
[2,1,5,8,6,4,3,7]=>[7,3,6,1,5,8,2,4]=>[2,6,3,8,4,1,7,5]=>[2,2,1,2,1]
[7,2,5,6,4,3,1,8]=>[3,7,6,2,5,4,1,8]=>[6,2,3,7,4,5,8,1]=>[1,3,3,1]
[1,2,5,7,8,4,3,6]=>[7,3,6,4,8,1,2,5]=>[2,6,3,5,1,8,7,4]=>[2,2,2,1,1]
[1,2,7,4,8,6,3,5]=>[7,8,4,3,6,1,2,5]=>[2,1,5,6,3,8,7,4]=>[1,3,2,1,1]
[1,2,7,8,3,6,5,4]=>[8,7,5,3,6,1,2,4]=>[1,2,4,6,3,8,7,5]=>[4,2,1,1]
[7,1,8,6,3,5,4,2]=>[8,5,7,6,4,2,1,3]=>[1,4,2,3,5,7,8,6]=>[2,5,1]
[1,8,7,6,3,5,2,4]=>[5,7,8,6,4,3,1,2]=>[4,2,1,3,5,6,8,7]=>[1,1,5,1]
[1,8,7,4,6,3,2,5]=>[4,7,6,8,5,3,1,2]=>[5,2,3,1,4,6,8,7]=>[1,2,4,1]
[7,1,5,8,3,4,6,2]=>[5,3,6,8,7,2,1,4]=>[4,6,3,1,2,7,8,5]=>[2,1,4,1]
[7,1,6,4,2,3,5,8]=>[5,6,4,7,2,3,1,8]=>[4,3,5,2,7,6,8,1]=>[1,2,2,2,1]
[8,6,2,4,7,3,5,1]=>[4,6,8,3,2,7,5,1]=>[5,3,1,6,7,2,4,8]=>[1,1,3,3]
[8,6,2,4,5,7,3,1]=>[4,5,8,3,2,7,6,1]=>[5,4,1,6,7,2,3,8]=>[1,1,3,3]
[2,7,1,4,5,8,3,6]=>[4,5,7,8,1,3,2,6]=>[5,4,2,1,8,6,7,3]=>[1,1,1,2,2,1]
[7,1,6,4,5,2,3,8]=>[6,4,7,5,2,3,1,8]=>[3,5,2,4,7,6,8,1]=>[2,3,2,1]
[7,1,4,5,6,8,2,3]=>[3,4,7,5,8,2,1,6]=>[6,5,2,4,1,7,8,3]=>[1,1,2,3,1]
[7,1,2,3,8,5,4,6]=>[7,6,8,2,3,4,1,5]=>[2,3,1,7,6,5,8,4]=>[2,2,1,2,1]
[7,1,5,4,3,8,2,6]=>[5,4,3,7,8,2,1,6]=>[4,5,6,2,1,7,8,3]=>[3,1,3,1]
[7,1,3,4,2,6,8,5]=>[3,4,6,8,2,5,1,7]=>[6,5,3,1,7,4,8,2]=>[1,1,1,2,2,1]
[7,1,5,4,6,2,8,3]=>[4,3,8,6,2,5,1,7]=>[5,6,1,3,7,4,8,2]=>[2,3,2,1]
[7,1,5,6,4,3,8,2]=>[3,6,5,4,8,2,1,7]=>[6,3,4,5,1,7,8,2]=>[1,3,3,1]
[7,1,6,5,4,3,2,8]=>[7,6,5,4,2,3,1,8]=>[2,3,4,5,7,6,8,1]=>[5,2,1]
[8,6,2,5,4,3,7,1]=>[6,5,3,4,2,8,7,1]=>[3,4,6,5,7,1,2,8]=>[3,2,3]
[2,5,1,4,7,8,6,3]=>[5,2,8,1,4,7,3,6]=>[4,7,1,8,5,2,6,3]=>[2,2,1,2,1]
[3,6,2,4,7,8,1,5]=>[7,1,3,4,2,5,8,6]=>[2,8,6,5,7,4,1,3]=>[2,1,2,1,2]
[5,6,2,4,8,7,1,3]=>[4,1,7,2,8,3,6,5]=>[5,8,2,7,1,6,3,4]=>[2,2,2,2]
[6,3,8,2,4,7,1,5]=>[2,4,5,1,7,8,6,3]=>[7,5,4,8,2,1,3,6]=>[1,1,2,1,3]
[6,5,8,7,2,3,1,4]=>[5,2,1,7,6,8,4,3]=>[4,7,8,2,3,1,5,6]=>[3,2,3]
[6,5,7,8,2,4,1,3]=>[5,2,1,7,3,8,6,4]=>[4,7,8,2,6,1,3,5]=>[3,2,3]
[6,3,4,2,8,5,1,7]=>[2,3,7,4,1,6,8,5]=>[7,6,2,5,8,3,1,4]=>[1,1,3,1,2]
[3,4,7,2,5,8,1,6]=>[1,2,4,5,7,3,8,6]=>[8,7,5,4,2,6,1,3]=>[1,1,1,1,2,2]
[4,6,8,1,3,5,2,7]=>[1,5,7,4,2,6,8,3]=>[8,4,2,5,7,3,1,6]=>[1,1,3,1,2]
[4,3,8,1,2,7,5,6]=>[2,1,7,8,4,5,6,3]=>[7,8,2,1,5,4,3,6]=>[2,1,2,1,2]
[3,6,4,1,7,2,5,8]=>[6,1,3,7,4,2,5,8]=>[3,8,6,2,5,7,4,1]=>[2,1,3,1,1]
[2,8,3,1,5,6,4,7]=>[3,5,7,1,4,6,8,2]=>[6,4,2,8,5,3,1,7]=>[1,1,2,1,1,2]
[3,8,7,1,5,4,2,6]=>[7,6,1,4,5,8,3,2]=>[2,3,8,5,4,1,6,7]=>[3,1,1,3]
[4,3,1,7,6,8,2,5]=>[1,7,2,5,4,8,3,6]=>[8,2,7,4,5,1,6,3]=>[1,2,2,2,1]
[3,4,1,7,5,6,8,2]=>[1,2,5,6,4,8,3,7]=>[8,7,4,3,5,1,6,2]=>[1,1,1,2,2,1]
[3,4,1,5,7,6,2,8]=>[1,2,7,4,6,3,5,8]=>[8,7,2,5,3,6,4,1]=>[1,1,2,2,1,1]
[3,7,4,1,6,2,8,5]=>[3,8,1,6,4,5,2,7]=>[6,1,8,3,5,4,7,2]=>[1,2,2,2,1]
[8,4,7,2,5,3,6,1]=>[2,6,4,5,8,7,3,1]=>[7,3,5,4,1,2,6,8]=>[1,2,1,4]
[4,7,8,1,2,3,6,5]=>[1,8,4,5,6,2,7,3]=>[8,1,5,4,3,7,2,6]=>[1,2,1,2,2]
[2,8,6,1,5,3,7,4]=>[8,6,4,5,1,3,7,2]=>[1,3,5,4,8,6,2,7]=>[3,2,1,2]
[7,6,5,1,3,8,2,4]=>[5,7,8,4,3,2,1,6]=>[4,2,1,5,6,7,8,3]=>[1,1,5,1]
[7,6,5,1,3,4,8,2]=>[5,6,8,4,3,2,1,7]=>[4,3,1,5,6,7,8,2]=>[1,1,5,1]
[7,2,6,4,1,3,8,5]=>[8,5,2,4,6,3,1,7]=>[1,4,7,5,3,6,8,2]=>[3,1,3,1]
[8,4,5,3,7,2,6,1]=>[2,4,3,6,8,7,5,1]=>[7,5,6,3,1,2,4,8]=>[1,2,1,4]
[4,7,5,2,8,1,6,3]=>[8,1,4,3,6,2,7,5]=>[1,8,5,6,3,7,2,4]=>[2,2,2,2]
[2,6,4,3,1,5,7,8]=>[5,4,1,3,6,2,7,8]=>[4,5,8,6,3,7,2,1]=>[3,1,2,1,1]
[7,3,8,4,1,5,2,6]=>[7,2,5,4,6,1,8,3]=>[2,7,4,5,3,8,1,6]=>[2,2,2,2]
[7,2,3,4,1,6,5,8]=>[2,3,4,7,5,6,1,8]=>[7,6,5,2,4,3,8,1]=>[1,1,1,2,2,1]
[4,2,8,3,6,1,5,7]=>[4,1,6,7,2,5,8,3]=>[5,8,3,2,7,4,1,6]=>[2,1,2,1,2]
[4,8,5,2,7,1,3,6]=>[1,4,6,3,7,8,5,2]=>[8,5,3,6,2,1,4,7]=>[1,1,2,1,3]
[6,8,5,3,1,4,2,7]=>[7,5,4,1,6,3,8,2]=>[2,4,5,8,3,6,1,7]=>[4,2,2]
[1,6,4,7,2,5,3,8]=>[3,7,5,2,6,1,4,8]=>[6,2,4,7,3,8,5,1]=>[1,3,2,1,1]
[1,6,4,8,2,5,3,7]=>[3,7,5,2,6,8,1,4]=>[6,2,4,7,3,1,8,5]=>[1,3,1,2,1]
[1,6,5,8,2,4,3,7]=>[7,5,3,2,6,8,1,4]=>[2,4,6,7,3,1,8,5]=>[4,1,2,1]
[1,6,8,2,4,3,7,5]=>[5,8,4,2,6,7,1,3]=>[4,1,5,7,3,2,8,6]=>[1,3,1,2,1]
[1,5,6,2,4,7,3,8]=>[5,2,7,4,1,3,6,8]=>[4,7,2,5,8,6,3,1]=>[2,3,1,1,1]
[1,5,6,2,4,7,8,3]=>[5,2,6,3,8,1,4,7]=>[4,7,3,6,1,8,5,2]=>[2,2,2,1,1]
[1,5,8,2,4,7,3,6]=>[5,2,7,8,4,6,1,3]=>[4,7,2,1,5,3,8,6]=>[2,1,2,2,1]
[1,5,7,2,4,8,3,6]=>[5,2,7,8,4,1,3,6]=>[4,7,2,1,5,8,6,3]=>[2,1,3,1,1]
[1,6,5,7,2,4,3,8]=>[7,5,3,2,6,1,4,8]=>[2,4,6,7,3,8,5,1]=>[4,2,1,1]
[1,6,7,2,4,3,8,5]=>[5,8,4,2,6,1,3,7]=>[4,1,5,7,3,8,6,2]=>[1,3,2,1,1]
[1,5,6,7,2,4,8,3]=>[2,6,3,8,5,1,4,7]=>[7,3,6,1,4,8,5,2]=>[1,2,3,1,1]
[1,5,8,2,4,6,7,3]=>[5,2,6,8,4,7,1,3]=>[4,7,3,1,5,2,8,6]=>[2,1,2,2,1]
[1,5,7,2,4,6,8,3]=>[5,2,6,8,4,1,3,7]=>[4,7,3,1,5,8,6,2]=>[2,1,3,1,1]
[1,5,7,8,3,2,4,6]=>[2,6,5,7,3,8,1,4]=>[7,3,4,2,6,1,8,5]=>[1,2,2,2,1]
[1,5,8,3,2,4,6,7]=>[5,4,2,6,7,8,1,3]=>[4,5,7,3,2,1,8,6]=>[3,1,1,2,1]
[1,5,6,2,4,8,3,7]=>[5,2,7,3,8,1,4,6]=>[4,7,2,6,1,8,5,3]=>[2,2,2,1,1]
[1,7,6,2,8,3,4,5]=>[6,7,8,4,3,1,2,5]=>[3,2,1,5,6,8,7,4]=>[1,1,4,1,1]
[1,7,3,4,2,8,6,5]=>[8,3,4,7,5,1,2,6]=>[1,6,5,2,4,8,7,3]=>[2,1,3,1,1]
[1,6,2,4,3,8,7,5]=>[8,4,7,3,1,2,5,6]=>[1,5,2,6,8,7,4,3]=>[2,3,1,1,1]
[1,5,6,2,4,8,7,3]=>[2,8,5,3,7,1,4,6]=>[7,1,4,6,2,8,5,3]=>[1,3,2,1,1]
[1,5,8,7,3,2,4,6]=>[2,6,5,7,8,4,1,3]=>[7,3,4,2,1,5,8,6]=>[1,2,1,3,1]
[1,4,2,3,5,8,7,6]=>[2,8,7,1,3,4,5,6]=>[7,1,2,8,6,5,4,3]=>[1,3,1,1,1,1]
[1,5,2,3,4,8,7,6]=>[8,7,3,1,2,4,5,6]=>[1,2,6,8,7,5,4,3]=>[4,1,1,1,1]
[1,6,5,2,3,8,7,4]=>[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>[5,1,1,1]
[1,7,4,2,8,6,5,3]=>[8,3,7,6,4,1,2,5]=>[1,6,2,3,5,8,7,4]=>[2,4,1,1]
[1,7,6,5,2,8,4,3]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>[6,1,1]
[1,6,7,5,2,3,8,4]=>[8,5,2,6,4,1,3,7]=>[1,4,7,3,5,8,6,2]=>[3,3,1,1]
[1,7,5,2,8,4,3,6]=>[7,6,3,8,4,1,2,5]=>[2,3,6,1,5,8,7,4]=>[3,3,1,1]
[1,7,5,6,2,8,3,4]=>[7,3,8,5,4,1,2,6]=>[2,6,1,4,5,8,7,3]=>[2,4,1,1]
[1,5,7,6,2,4,8,3]=>[2,6,8,5,4,1,3,7]=>[7,3,1,4,5,8,6,2]=>[1,1,4,1,1]
[1,5,8,3,2,4,7,6]=>[4,2,8,5,6,7,1,3]=>[5,7,1,4,3,2,8,6]=>[2,2,1,2,1]
[1,6,8,4,2,3,7,5]=>[8,5,4,2,6,7,1,3]=>[1,4,5,7,3,2,8,6]=>[4,1,2,1]
[1,7,4,6,2,8,3,5]=>[3,7,8,5,4,1,2,6]=>[6,2,1,4,5,8,7,3]=>[1,1,4,1,1]
[1,7,3,5,2,8,4,6]=>[7,3,4,8,5,1,2,6]=>[2,6,5,1,4,8,7,3]=>[2,1,3,1,1]
[1,6,8,5,2,3,7,4]=>[8,5,2,6,4,7,1,3]=>[1,4,7,3,5,2,8,6]=>[3,2,2,1]
[1,6,4,2,3,7,8,5]=>[6,3,8,4,1,2,5,7]=>[3,6,1,5,8,7,4,2]=>[2,3,1,1,1]
[1,6,4,2,3,7,5,8]=>[7,4,3,5,1,2,6,8]=>[2,5,6,4,8,7,3,1]=>[3,2,1,1,1]
[1,5,8,6,2,4,7,3]=>[2,6,8,5,4,7,1,3]=>[7,3,1,4,5,2,8,6]=>[1,1,3,2,1]
[1,5,7,3,2,4,8,6]=>[4,2,8,5,6,1,3,7]=>[5,7,1,4,3,8,6,2]=>[2,2,2,1,1]
[1,7,3,4,2,8,5,6]=>[3,4,7,8,5,1,2,6]=>[6,5,2,1,4,8,7,3]=>[1,1,1,3,1,1]
[1,6,7,4,2,3,8,5]=>[8,5,4,2,6,1,3,7]=>[1,4,5,7,3,8,6,2]=>[4,2,1,1]
[1,6,4,2,3,8,5,7]=>[7,3,8,4,1,2,5,6]=>[2,6,1,5,8,7,4,3]=>[2,3,1,1,1]
[1,7,6,4,2,8,5,3]=>[4,8,7,5,3,1,2,6]=>[5,1,2,4,6,8,7,3]=>[1,5,1,1]
[1,7,5,2,8,6,4,3]=>[3,8,7,6,4,1,2,5]=>[6,1,2,3,5,8,7,4]=>[1,5,1,1]
[1,6,4,2,3,8,7,5]=>[3,8,7,4,1,2,5,6]=>[6,1,2,5,8,7,4,3]=>[1,4,1,1,1]
[7,3,5,6,1,4,8,2]=>[6,2,3,8,5,4,1,7]=>[3,7,6,1,4,5,8,2]=>[2,1,4,1]
[3,7,5,6,1,4,8,2]=>[6,3,8,1,5,4,2,7]=>[3,6,1,8,4,5,7,2]=>[2,2,3,1]
[8,2,4,1,6,7,5,3]=>[3,5,8,2,7,4,6,1]=>[6,4,1,7,2,5,3,8]=>[1,1,2,2,2]
[8,6,1,4,2,7,5,3]=>[4,8,7,3,5,2,6,1]=>[5,1,2,6,4,7,3,8]=>[1,3,2,2]
[3,6,1,4,2,8,5,7]=>[1,4,7,8,3,2,5,6]=>[8,5,2,1,6,7,4,3]=>[1,1,1,3,1,1]
[1,6,7,4,3,5,8,2]=>[5,4,2,6,3,8,1,7]=>[4,5,7,3,6,1,8,2]=>[3,2,2,1]
[7,6,1,4,3,5,8,2]=>[5,4,6,8,3,2,1,7]=>[4,5,3,1,6,7,8,2]=>[2,1,4,1]
[3,5,4,1,6,7,8,2]=>[5,1,3,2,6,8,4,7]=>[4,8,6,7,3,1,5,2]=>[2,2,1,2,1]
[4,7,1,6,3,5,8,2]=>[1,5,6,4,8,3,2,7]=>[8,4,3,5,1,6,7,2]=>[1,1,2,3,1]
[3,1,4,7,6,5,8,2]=>[6,1,5,3,4,8,2,7]=>[3,8,4,6,5,1,7,2]=>[2,2,1,2,1]
[6,1,7,4,3,5,8,2]=>[5,4,6,3,1,8,2,7]=>[4,5,3,6,8,1,7,2]=>[2,3,2,1]
[7,1,6,4,3,5,8,2]=>[5,4,6,3,8,2,1,7]=>[4,5,3,6,1,7,8,2]=>[2,2,3,1]
[1,7,6,4,3,5,8,2]=>[5,4,6,3,2,8,1,7]=>[4,5,3,6,7,1,8,2]=>[2,3,2,1]
[8,4,1,3,7,2,5,6]=>[4,6,2,7,8,3,5,1]=>[5,3,7,2,1,6,4,8]=>[1,2,1,2,2]
[4,7,1,3,8,2,5,6]=>[4,1,6,7,8,3,2,5]=>[5,8,3,2,1,6,7,4]=>[2,1,1,3,1]
[7,4,1,3,8,2,5,6]=>[4,6,2,7,8,3,1,5]=>[5,3,7,2,1,6,8,4]=>[1,2,1,3,1]
[1,3,6,4,2,8,5,7]=>[4,7,2,3,8,1,5,6]=>[5,2,7,6,1,8,4,3]=>[1,2,1,2,1,1]
[4,7,3,1,2,8,5,6]=>[1,7,3,8,4,5,2,6]=>[8,2,6,1,5,4,7,3]=>[1,2,2,2,1]
[4,7,8,1,2,6,5,3]=>[8,1,7,4,5,2,6,3]=>[1,8,2,5,4,7,3,6]=>[2,2,2,2]
[6,8,1,4,2,7,5,3]=>[4,8,7,3,1,5,6,2]=>[5,1,2,6,8,4,3,7]=>[1,4,1,2]
[1,8,6,4,2,7,5,3]=>[4,8,7,5,3,6,1,2]=>[5,1,2,4,6,3,8,7]=>[1,4,2,1]
[4,8,1,3,7,2,5,6]=>[4,1,6,7,8,3,5,2]=>[5,8,3,2,1,6,4,7]=>[2,1,1,2,2]
[8,7,1,3,6,2,5,4]=>[8,4,6,7,3,5,2,1]=>[1,5,3,2,6,4,7,8]=>[2,1,2,3]
[6,8,5,7,3,2,1,4]=>[1,7,6,5,3,8,4,2]=>[8,2,3,4,6,1,5,7]=>[1,4,3]
[1,8,4,3,7,2,5,6]=>[4,3,6,7,8,5,1,2]=>[5,6,3,2,1,4,8,7]=>[2,1,1,3,1]
[2,8,3,4,7,6,1,5]=>[7,8,3,4,6,1,5,2]=>[2,1,6,5,3,8,4,7]=>[1,2,1,2,2]
[3,7,8,4,6,2,1,5]=>[4,7,6,1,2,8,5,3]=>[5,2,3,8,7,1,4,6]=>[1,3,1,3]
[2,4,3,7,8,6,1,5]=>[7,2,4,8,1,3,6,5]=>[2,7,5,1,8,6,3,4]=>[2,1,2,1,2]
[1,4,7,3,8,2,5,6]=>[2,4,6,7,3,8,1,5]=>[7,5,3,2,6,1,8,4]=>[1,1,1,2,2,1]
[5,7,6,8,3,2,1,4]=>[7,1,6,5,3,2,8,4]=>[2,8,3,4,6,7,1,5]=>[2,4,2]
[2,5,3,4,8,6,1,7]=>[7,3,1,2,4,6,8,5]=>[2,6,8,7,5,3,1,4]=>[3,1,1,1,2]
[3,7,5,4,8,2,1,6]=>[4,3,7,1,6,2,8,5]=>[5,6,2,8,3,7,1,4]=>[2,2,2,2]
[7,1,3,4,2,8,5,6]=>[3,4,7,8,2,5,1,6]=>[6,5,2,1,7,4,8,3]=>[1,1,1,2,2,1]
[6,1,4,3,8,2,5,7]=>[4,3,6,7,1,8,2,5]=>[5,6,3,2,8,1,7,4]=>[2,1,2,2,1]
[4,1,7,3,8,2,5,6]=>[4,1,6,7,3,8,2,5]=>[5,8,3,2,6,1,7,4]=>[2,1,2,2,1]
[8,1,4,3,7,2,5,6]=>[4,3,6,7,8,2,5,1]=>[5,6,3,2,1,7,4,8]=>[2,1,1,2,2]
[8,2,3,4,7,6,1,5]=>[7,8,2,3,4,6,5,1]=>[2,1,7,6,5,3,4,8]=>[1,2,1,1,3]
[4,2,3,7,8,6,1,5]=>[1,7,4,8,2,3,6,5]=>[8,2,5,1,7,6,3,4]=>[1,2,2,1,2]
[5,2,3,4,8,6,1,7]=>[7,2,3,1,4,6,8,5]=>[2,7,6,8,5,3,1,4]=>[2,2,1,1,2]
[2,7,5,6,3,8,1,4]=>[5,3,7,4,1,2,8,6]=>[4,6,2,5,8,7,1,3]=>[2,3,1,2]
[5,7,2,6,3,8,1,4]=>[5,1,7,3,4,2,8,6]=>[4,8,2,6,5,7,1,3]=>[2,2,2,2]
[5,7,2,6,8,4,1,3]=>[1,7,4,8,3,2,6,5]=>[8,2,5,1,6,7,3,4]=>[1,2,3,2]
[7,2,5,6,8,4,1,3]=>[3,7,4,8,2,1,6,5]=>[6,2,5,1,7,8,3,4]=>[1,2,3,2]
[4,2,3,8,5,6,1,7]=>[5,1,7,2,3,6,8,4]=>[4,8,2,7,6,3,1,5]=>[2,2,1,1,2]
[5,2,3,8,7,6,1,4]=>[7,1,8,6,2,3,5,4]=>[2,8,1,3,7,6,4,5]=>[2,3,1,2]
[6,1,8,3,7,2,5,4]=>[8,4,6,1,7,5,2,3]=>[1,5,3,8,2,4,7,6]=>[2,2,3,1]
[1,7,8,4,2,6,5,3]=>[4,8,7,5,2,6,1,3]=>[5,1,2,4,7,3,8,6]=>[1,4,2,1]
[4,7,1,8,2,5,6,3]=>[1,6,8,5,7,3,2,4]=>[8,3,1,4,2,6,7,5]=>[1,1,2,3,1]
[3,7,4,8,5,2,1,6]=>[7,3,6,1,5,2,8,4]=>[2,6,3,8,4,7,1,5]=>[2,2,2,2]
[2,4,3,8,5,6,1,7]=>[2,5,7,1,3,6,8,4]=>[7,4,2,8,6,3,1,5]=>[1,1,2,1,1,2]
[1,4,8,3,6,2,5,7]=>[2,4,6,7,5,8,1,3]=>[7,5,3,2,4,1,8,6]=>[1,1,1,2,2,1]
[7,5,8,6,3,2,1,4]=>[2,7,6,5,1,8,4,3]=>[7,2,3,4,8,1,5,6]=>[1,4,3]
[6,5,8,7,3,2,1,4]=>[2,1,7,6,5,8,4,3]=>[7,8,2,3,4,1,5,6]=>[2,3,3]
[8,5,7,6,3,2,1,4]=>[2,7,6,5,8,4,3,1]=>[7,2,3,4,1,5,6,8]=>[1,3,4]
[2,5,3,8,7,6,1,4]=>[2,7,8,6,1,3,5,4]=>[7,2,1,3,8,6,4,5]=>[1,1,3,1,2]
[3,7,5,8,6,2,1,4]=>[3,7,6,1,2,8,5,4]=>[6,2,3,8,7,1,4,5]=>[1,3,1,3]
[3,7,8,6,5,2,1,4]=>[7,6,2,8,1,5,4,3]=>[2,3,7,1,8,4,5,6]=>[3,2,3]
[6,8,7,5,3,2,1,4]=>[1,7,6,5,8,4,3,2]=>[8,2,3,4,1,5,6,7]=>[1,3,4]
[5,7,6,8,3,4,1,2]=>[7,1,5,3,2,8,6,4]=>[2,8,4,6,7,1,3,5]=>[2,3,3]
[3,7,6,8,4,5,1,2]=>[7,5,3,1,2,8,6,4]=>[2,4,6,8,7,1,3,5]=>[4,1,3]
[1,5,4,7,6,8,2,3]=>[2,7,3,5,4,8,1,6]=>[7,2,6,4,5,1,8,3]=>[1,2,2,2,1]
[1,7,4,6,5,8,2,3]=>[7,3,5,4,2,8,1,6]=>[2,6,4,5,7,1,8,3]=>[2,3,2,1]
[3,7,4,6,5,8,1,2]=>[7,3,5,1,4,2,8,6]=>[2,6,4,8,5,7,1,3]=>[2,2,2,2]
[3,5,4,8,6,7,1,2]=>[2,7,1,3,5,8,6,4]=>[7,2,8,6,4,1,3,5]=>[1,2,1,1,3]
[3,6,4,7,5,8,1,2]=>[7,3,1,2,5,4,8,6]=>[2,6,8,7,4,5,1,3]=>[3,1,2,2]
[1,6,2,7,5,8,3,4]=>[7,5,4,2,8,1,3,6]=>[2,4,5,7,1,8,6,3]=>[4,2,1,1]
[1,6,4,8,5,7,2,3]=>[7,3,2,5,8,6,1,4]=>[2,6,7,4,1,3,8,5]=>[3,1,3,1]
[1,8,4,6,5,7,2,3]=>[7,3,5,4,8,6,1,2]=>[2,6,4,5,1,3,8,7]=>[2,2,3,1]
[1,5,4,8,6,7,2,3]=>[2,7,3,5,8,6,1,4]=>[7,2,6,4,1,3,8,5]=>[1,2,1,3,1]
[7,8,1,5,4,6,2,3]=>[7,5,4,8,3,1,6,2]=>[2,4,5,1,6,8,3,7]=>[3,3,2]
[7,8,1,5,2,4,3,6]=>[7,5,6,3,4,1,8,2]=>[2,4,3,6,5,8,1,7]=>[2,2,2,2]
[1,8,2,6,5,7,3,4]=>[7,5,4,8,3,6,1,2]=>[2,4,5,1,6,3,8,7]=>[3,2,2,1]
[1,7,2,8,5,6,3,4]=>[7,5,8,6,3,1,2,4]=>[2,4,1,3,6,8,7,5]=>[2,4,1,1]
[1,7,2,6,5,8,3,4]=>[7,5,4,8,3,1,2,6]=>[2,4,5,1,6,8,7,3]=>[3,3,1,1]
[1,5,2,7,6,8,3,4]=>[2,7,5,4,8,1,3,6]=>[7,2,4,5,1,8,6,3]=>[1,3,2,1,1]
[1,7,6,8,2,5,3,4]=>[7,8,5,3,2,6,1,4]=>[2,1,4,6,7,3,8,5]=>[1,4,2,1]
[1,7,6,8,4,5,2,3]=>[7,5,3,2,8,6,1,4]=>[2,4,6,7,1,3,8,5]=>[4,3,1]
[5,7,6,8,1,4,2,3]=>[1,7,8,5,3,2,6,4]=>[8,2,1,4,6,7,3,5]=>[1,1,4,2]
[7,8,5,6,1,3,2,4]=>[7,5,6,3,1,8,4,2]=>[2,4,3,6,8,1,5,7]=>[2,3,3]
[5,8,6,7,1,3,2,4]=>[1,7,5,6,3,8,4,2]=>[8,2,4,3,6,1,5,7]=>[1,2,2,3]
[1,3,2,7,6,8,4,5]=>[7,5,2,4,8,1,3,6]=>[2,4,7,5,1,8,6,3]=>[3,1,2,1,1]
[7,8,1,6,2,4,3,5]=>[7,5,6,8,3,1,4,2]=>[2,4,3,1,6,8,5,7]=>[2,1,3,2]
[1,8,6,7,2,4,3,5]=>[7,5,6,3,8,4,1,2]=>[2,4,3,6,1,5,8,7]=>[2,2,3,1]
[7,8,1,4,2,6,3,5]=>[7,4,8,3,5,1,6,2]=>[2,5,1,6,4,8,3,7]=>[2,2,2,2]
[7,8,1,4,2,5,3,6]=>[7,5,3,4,6,1,8,2]=>[2,4,6,5,3,8,1,7]=>[3,1,2,2]
[7,8,2,1,4,3,6,5]=>[3,5,8,4,6,1,7,2]=>[6,4,1,5,3,8,2,7]=>[1,1,2,2,2]
[7,8,1,2,4,3,5,6]=>[6,3,4,5,7,1,8,2]=>[3,6,5,4,2,8,1,7]=>[2,1,1,2,2]
[4,3,6,5,8,7,1,2]=>[1,4,2,3,7,8,6,5]=>[8,5,7,6,2,1,3,4]=>[1,2,1,1,3]
[3,4,6,5,7,8,1,2]=>[4,1,2,3,7,5,8,6]=>[5,8,7,6,2,4,1,3]=>[2,1,1,2,2]
[3,4,5,6,7,8,1,9,2]=>[1,2,3,4,5,9,7,6,8]=>[9,8,7,6,5,1,3,4,2]=>[1,1,1,1,1,3,1]
[3,4,5,6,7,1,2,9,8]=>[1,2,3,4,9,6,5,7,8]=>[9,8,7,6,1,4,5,3,2]=>[1,1,1,1,3,1,1]
[1,6,2,3,8,7,4,5]=>[7,8,6,3,1,2,4,5]=>[2,1,3,6,8,7,5,4]=>[1,4,1,1,1]
[1,7,4,3,2,8,6,5]=>[3,8,4,7,5,1,2,6]=>[6,1,5,2,4,8,7,3]=>[1,2,3,1,1]
[1,2,6,5,3,7,8,4]=>[6,4,3,8,1,2,5,7]=>[3,5,6,1,8,7,4,2]=>[3,2,1,1,1]
[1,3,7,5,2,6,8,4]=>[6,4,8,2,5,1,3,7]=>[3,5,1,7,4,8,6,2]=>[2,2,2,1,1]
[1,3,7,4,2,6,8,5]=>[4,6,8,2,5,1,3,7]=>[5,3,1,7,4,8,6,2]=>[1,1,2,2,1,1]
[1,2,6,4,3,7,8,5]=>[4,6,3,8,1,2,5,7]=>[5,3,6,1,8,7,4,2]=>[1,2,2,1,1,1]
[1,4,3,2,5,8,6,7]=>[3,2,7,8,1,4,5,6]=>[6,7,2,1,8,5,4,3]=>[2,1,2,1,1,1]
[1,5,3,2,4,8,6,7]=>[3,7,2,8,1,4,5,6]=>[6,2,7,1,8,5,4,3]=>[1,2,2,1,1,1]
[1,7,5,3,2,8,6,4]=>[8,4,3,7,5,1,2,6]=>[1,5,6,2,4,8,7,3]=>[3,3,1,1]
[1,5,3,2,4,8,7,6]=>[8,3,2,7,1,4,5,6]=>[1,6,7,2,8,5,4,3]=>[3,2,1,1,1]
[7,6,5,4,3,1,8,2]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>[7,1]
[6,8,5,4,3,2,1,7]=>[1,7,6,5,4,3,8,2]=>[8,2,3,4,5,6,1,7]=>[1,5,2]
[8,7,6,5,4,3,1,9,2]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>[8,1]
[7,9,6,5,4,3,2,1,8]=>[1,8,7,6,5,4,3,9,2]=>[9,2,3,4,5,6,7,1,8]=>[1,6,2]
[9,8,7,6,5,4,3,1,10,2]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>[9,1]
[3,6,5,4,8,1,7,2]=>[4,3,1,2,8,6,7,5]=>[5,6,8,7,1,3,2,4]=>[3,1,2,2]
[6,8,1,4,3,2,7,5]=>[5,4,8,3,1,6,7,2]=>[4,5,1,6,8,3,2,7]=>[2,3,1,2]
[2,8,5,4,3,7,1,6]=>[5,4,3,7,8,1,6,2]=>[4,5,6,2,1,8,3,7]=>[3,1,2,2]
[8,10,7,6,5,4,3,2,1,9]=>[1,9,8,7,6,5,4,3,10,2]=>[10,2,3,4,5,6,7,8,1,9]=>[1,7,2]
[10,9,8,7,6,5,4,3,1,11,2]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[10,1]
[7,6,1,4,3,8,5,2]=>[4,8,5,7,3,2,1,6]=>[5,1,4,2,6,7,8,3]=>[1,2,4,1]
[4,6,5,8,3,1,7,2]=>[3,1,2,8,6,5,7,4]=>[6,8,7,1,3,4,2,5]=>[2,1,3,2]
[6,8,5,1,3,2,7,4]=>[5,8,4,1,6,3,7,2]=>[4,1,5,8,3,6,2,7]=>[1,3,2,2]
[3,8,5,4,7,2,1,6]=>[4,3,7,1,6,8,5,2]=>[5,6,2,8,3,1,4,7]=>[2,2,1,3]
[9,11,8,7,6,5,4,3,2,1,10]=>[1,10,9,8,7,6,5,4,3,11,2]=>[11,2,3,4,5,6,7,8,9,1,10]=>[1,8,2]
[11,10,9,8,7,6,5,4,3,1,12,2]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[11,1]
[4,7,6,5,9,3,1,8,2]=>[4,3,1,2,9,7,6,8,5]=>[6,7,9,8,1,3,4,2,5]=>[3,1,3,2]
[7,6,5,1,3,8,4,2]=>[8,5,7,4,3,2,1,6]=>[1,4,2,5,6,7,8,3]=>[2,5,1]
[1,6,3,4,8,7,5,2]=>[8,7,3,2,4,6,1,5]=>[1,2,6,7,5,3,8,4]=>[4,1,2,1]
[1,4,5,8,3,7,6,2]=>[8,2,3,5,7,6,1,4]=>[1,7,6,4,2,3,8,5]=>[2,1,1,3,1]
[6,8,5,4,1,2,7,3]=>[8,5,1,6,4,3,7,2]=>[1,4,8,3,5,6,2,7]=>[3,3,2]
[1,8,5,2,3,7,6,4]=>[8,7,4,3,5,6,1,2]=>[1,2,5,6,4,3,8,7]=>[4,1,2,1]
[6,8,2,4,3,7,1,5]=>[5,3,4,1,7,8,6,2]=>[4,6,5,8,2,1,3,7]=>[2,2,1,3]
[1,8,3,4,7,2,6,5]=>[8,3,4,6,7,5,1,2]=>[1,6,5,3,2,4,8,7]=>[2,1,1,3,1]
[7,5,8,4,3,2,1,6]=>[2,7,6,5,4,1,8,3]=>[7,2,3,4,5,8,1,6]=>[1,5,2]
[10,12,9,8,7,6,5,4,3,2,1,11]=>[1,11,10,9,8,7,6,5,4,3,12,2]=>[12,2,3,4,5,6,7,8,9,10,1,11]=>[1,9,2]
[6,4,8,5,2,7,1,3]=>[2,5,1,7,4,8,6,3]=>[7,4,8,2,5,1,3,6]=>[1,2,2,3]
[5,1,8,6,7,4,3,2]=>[1,4,8,7,6,5,2,3]=>[8,5,1,2,3,4,7,6]=>[1,1,5,1]
[8,4,7,5,2,6,1,3]=>[2,5,7,4,8,6,3,1]=>[7,4,2,5,1,3,6,8]=>[1,1,2,4]
[5,4,6,8,2,1,7,3]=>[2,1,5,3,8,6,7,4]=>[7,8,4,6,1,3,2,5]=>[2,2,2,2]
[8,4,6,5,2,1,7,3]=>[2,5,8,6,4,3,7,1]=>[7,4,1,3,5,6,2,8]=>[1,1,4,2]
[4,8,7,5,6,1,3,2]=>[8,6,1,4,7,5,3,2]=>[1,3,8,5,2,4,6,7]=>[3,1,4]
[2,7,5,1,8,4,3,6]=>[7,6,3,8,1,4,2,5]=>[2,3,6,1,8,5,7,4]=>[3,2,2,1]
[5,1,8,7,4,2,3,6]=>[6,1,7,5,8,4,2,3]=>[3,8,2,4,1,5,7,6]=>[2,2,3,1]
[5,2,3,6,4,1,8,7]=>[5,2,3,1,4,8,6,7]=>[4,7,6,8,5,1,3,2]=>[2,2,1,2,1]
[6,1,4,5,3,2,8,7]=>[3,5,4,8,2,1,6,7]=>[6,4,5,1,7,8,3,2]=>[1,2,3,1,1]
[3,8,7,1,4,6,5,2]=>[8,5,7,1,4,6,3,2]=>[1,4,2,8,5,3,6,7]=>[2,2,1,3]
[5,7,1,2,4,3,8,6]=>[5,8,3,1,4,6,2,7]=>[4,1,6,8,5,3,7,2]=>[1,3,1,2,1]
[4,3,7,6,8,2,5,1]=>[6,1,4,2,3,8,7,5]=>[3,8,5,7,6,1,2,4]=>[2,2,1,3]
[5,3,6,8,1,7,2,4]=>[7,2,1,3,8,5,6,4]=>[2,7,8,6,1,4,3,5]=>[3,1,2,2]
[3,2,6,8,5,7,1,4]=>[3,7,1,5,8,2,6,4]=>[6,2,8,4,1,7,3,5]=>[1,2,1,2,2]
[6,3,7,2,4,8,5,1]=>[8,2,4,1,5,3,7,6]=>[1,7,5,8,4,6,2,3]=>[2,2,2,2]
[7,4,8,6,5,2,1,3]=>[7,2,6,1,8,5,4,3]=>[2,7,3,8,1,4,5,6]=>[2,2,4]
[7,1,8,2,5,4,3,6]=>[7,6,4,5,8,2,1,3]=>[2,3,5,4,1,7,8,6]=>[3,1,3,1]
[2,5,3,7,4,1,8,6]=>[5,2,8,1,3,6,4,7]=>[4,7,1,8,6,3,5,2]=>[2,2,1,2,1]
[3,6,4,7,5,1,8,2]=>[8,3,1,2,6,5,4,7]=>[1,6,8,7,3,4,5,2]=>[3,1,3,1]
[8,4,7,6,2,3,1,5]=>[2,5,7,6,8,4,3,1]=>[7,4,2,3,1,5,6,8]=>[1,1,2,4]
[8,4,7,1,2,5,6,3]=>[6,2,8,4,5,7,3,1]=>[3,7,1,5,4,2,6,8]=>[2,2,1,3]
[4,2,8,7,3,5,6,1]=>[1,5,6,8,7,2,4,3]=>[8,4,3,1,2,7,5,6]=>[1,1,1,3,2]
[8,1,7,4,2,5,6,3]=>[6,4,8,5,7,2,3,1]=>[3,5,1,4,2,7,6,8]=>[2,2,2,2]
[7,4,3,8,2,5,6,1]=>[3,2,5,6,1,8,7,4]=>[6,7,4,3,8,1,2,5]=>[2,1,2,3]
[6,4,1,5,8,2,7,3]=>[4,2,8,6,1,7,3,5]=>[5,7,1,3,8,2,6,4]=>[2,3,2,1]
[2,5,8,7,3,6,1,4]=>[2,5,7,8,6,1,4,3]=>[7,4,2,1,3,8,5,6]=>[1,1,1,3,2]
[2,1,5,8,7,4,6,3]=>[6,8,3,7,1,5,2,4]=>[3,1,6,2,8,4,7,5]=>[1,2,2,2,1]
[8,3,5,6,7,4,1,2]=>[3,7,2,4,8,6,5,1]=>[6,2,7,5,1,3,4,8]=>[1,2,1,4]
[7,4,3,2,8,5,6,1]=>[3,2,6,8,4,1,7,5]=>[6,7,3,1,5,8,2,4]=>[2,1,3,2]
[4,1,7,2,8,5,6,3]=>[1,6,8,7,4,2,3,5]=>[8,3,1,2,5,7,6,4]=>[1,1,4,1,1]
[2,4,8,7,3,5,6,1]=>[5,6,8,2,7,1,4,3]=>[4,3,1,7,2,8,5,6]=>[1,1,2,2,2]
[4,7,8,3,1,5,6,2]=>[6,1,4,8,5,2,7,3]=>[3,8,5,1,4,7,2,6]=>[2,1,3,2]
[3,4,7,2,8,5,6,1]=>[6,8,1,2,4,3,7,5]=>[3,1,8,7,5,6,2,4]=>[1,2,1,2,2]
[3,7,1,4,8,5,6,2]=>[6,8,1,4,7,3,2,5]=>[3,1,8,5,2,6,7,4]=>[1,2,1,3,1]
[7,2,3,4,8,5,6,1]=>[6,8,2,3,4,1,7,5]=>[3,1,7,6,5,8,2,4]=>[1,2,1,2,2]
[6,1,8,5,2,7,4,3]=>[8,7,5,4,1,6,2,3]=>[1,2,4,5,8,3,7,6]=>[5,2,1]
[2,1,7,4,5,8,6,3]=>[8,4,5,1,3,7,2,6]=>[1,5,4,8,6,2,7,3]=>[2,2,1,2,1]
[2,1,8,3,6,7,5,4]=>[5,8,7,1,4,6,2,3]=>[4,1,2,8,5,3,7,6]=>[1,3,1,2,1]
[8,2,1,6,4,7,5,3]=>[8,5,2,4,7,3,6,1]=>[1,4,7,5,2,6,3,8]=>[3,1,2,2]
[7,8,2,6,4,1,5,3]=>[8,6,3,5,1,7,4,2]=>[1,3,6,4,8,2,5,7]=>[3,2,3]
[2,6,3,5,8,7,1,4]=>[4,7,2,8,1,3,6,5]=>[5,2,7,1,8,6,3,4]=>[1,2,2,1,2]
[7,6,2,1,5,8,4,3]=>[5,8,3,7,4,2,1,6]=>[4,1,6,2,5,7,8,3]=>[1,2,4,1]
[4,5,2,7,6,1,8,3]=>[1,2,8,6,3,5,4,7]=>[8,7,1,3,6,4,5,2]=>[1,1,3,2,1]
[5,1,6,8,4,7,2,3]=>[3,1,7,5,8,6,2,4]=>[6,8,2,4,1,3,7,5]=>[2,2,3,1]
[3,6,8,7,5,2,1,4]=>[2,7,6,8,1,5,4,3]=>[7,2,3,1,8,4,5,6]=>[1,2,2,3]
[7,4,8,6,5,2,3,1]=>[6,8,2,1,7,5,4,3]=>[3,1,7,8,2,4,5,6]=>[1,3,4]
[8,1,6,4,7,3,2,5]=>[4,7,6,3,8,2,5,1]=>[5,2,3,6,1,7,4,8]=>[1,3,2,2]
[7,6,4,1,2,3,8,5]=>[8,4,5,3,6,2,1,7]=>[1,5,4,6,3,7,8,2]=>[2,2,3,1]
[2,6,4,8,5,3,7,1]=>[6,3,2,5,8,1,7,4]=>[3,6,7,4,1,8,2,5]=>[3,1,2,2]
[3,2,5,8,4,1,7,6]=>[1,3,5,8,2,6,7,4]=>[8,6,4,1,7,3,2,5]=>[1,1,1,2,1,2]
[8,4,7,1,5,2,3,6]=>[6,2,7,4,5,8,3,1]=>[3,7,2,5,4,1,6,8]=>[2,2,1,3]
[4,8,7,5,6,1,2,3]=>[6,7,1,4,8,5,3,2]=>[3,2,8,5,1,4,6,7]=>[1,2,1,4]
[6,1,4,8,7,3,5,2]=>[6,8,3,1,7,5,2,4]=>[3,1,6,8,2,4,7,5]=>[1,3,3,1]
[7,2,8,4,3,5,6,1]=>[5,4,6,8,2,1,7,3]=>[4,5,3,1,7,8,2,6]=>[2,1,3,2]
[4,7,8,1,3,5,6,2]=>[1,5,6,8,4,2,7,3]=>[8,4,3,1,5,7,2,6]=>[1,1,1,3,2]
[8,7,3,4,1,5,6,2]=>[3,6,4,8,5,7,2,1]=>[6,3,5,1,4,2,7,8]=>[1,2,2,3]
[4,8,2,7,3,5,6,1]=>[1,5,6,8,3,7,4,2]=>[8,4,3,1,6,2,5,7]=>[1,1,1,2,3]
[8,2,3,7,1,5,6,4]=>[6,8,2,3,5,7,4,1]=>[3,1,7,6,4,2,5,8]=>[1,2,1,1,3]
[6,4,8,7,1,3,2,5]=>[2,7,5,1,6,8,4,3]=>[7,2,4,8,3,1,5,6]=>[1,3,1,3]
[2,8,4,6,7,3,1,5]=>[7,3,6,4,8,1,5,2]=>[2,6,3,5,1,8,4,7]=>[2,2,2,2]
[4,3,8,2,7,6,1,5]=>[1,7,8,2,4,6,5,3]=>[8,2,1,7,5,3,4,6]=>[1,1,2,1,3]
[6,8,4,2,1,3,7,5]=>[4,8,5,3,1,6,7,2]=>[5,1,4,6,8,3,2,7]=>[1,4,1,2]
[7,8,2,4,3,5,6,1]=>[5,3,4,6,1,8,7,2]=>[4,6,5,3,8,1,2,7]=>[2,1,2,3]
[2,8,3,7,1,5,6,4]=>[6,8,3,5,7,1,4,2]=>[3,1,6,4,2,8,5,7]=>[1,2,1,2,2]
[8,1,2,7,3,5,6,4]=>[6,8,5,7,2,3,4,1]=>[3,1,4,2,7,6,5,8]=>[1,2,2,1,2]
[5,3,8,6,2,1,4,7]=>[6,2,1,5,7,4,8,3]=>[3,7,8,4,2,5,1,6]=>[3,1,2,2]
[4,6,5,2,8,3,1,7]=>[7,1,4,3,2,6,8,5]=>[2,8,5,6,7,3,1,4]=>[2,3,1,2]
[4,3,7,5,1,8,2,6]=>[1,7,2,4,8,5,3,6]=>[8,2,7,5,1,4,6,3]=>[1,2,1,3,1]
[6,8,5,2,7,4,3,1]=>[1,8,7,4,3,6,5,2]=>[8,1,2,5,6,3,4,7]=>[1,4,3]
[7,2,5,4,3,8,1,6]=>[5,4,2,3,7,1,8,6]=>[4,5,7,6,2,8,1,3]=>[3,1,2,2]
[6,8,1,2,4,5,3,7]=>[5,7,3,4,1,6,8,2]=>[4,2,6,5,8,3,1,7]=>[1,2,2,1,2]
[8,1,6,2,4,5,3,7]=>[5,7,4,6,2,3,8,1]=>[4,2,5,3,7,6,1,8]=>[1,2,2,1,2]
[3,8,6,1,2,5,4,7]=>[7,1,4,5,6,3,8,2]=>[2,8,5,4,3,6,1,7]=>[2,1,1,2,2]
[4,1,6,5,8,2,3,7]=>[1,6,4,3,7,8,2,5]=>[8,3,5,6,2,1,7,4]=>[1,3,1,2,1]
[4,3,8,6,2,5,1,7]=>[1,5,7,2,6,4,8,3]=>[8,4,2,7,3,5,1,6]=>[1,1,2,2,2]
[8,3,6,1,4,5,2,7]=>[2,5,7,4,6,3,8,1]=>[7,4,2,5,3,6,1,8]=>[1,1,2,2,2]
[2,7,5,4,3,8,1,6]=>[5,4,3,7,1,2,8,6]=>[4,5,6,2,8,7,1,3]=>[3,2,1,2]
[6,3,8,7,4,2,5,1]=>[6,5,1,8,2,7,4,3]=>[3,4,8,1,7,2,5,6]=>[3,2,3]
[5,8,4,3,7,6,1,2]=>[1,4,3,7,8,6,5,2]=>[8,5,6,2,1,3,4,7]=>[1,2,1,4]
[8,7,4,3,1,6,2,5]=>[7,4,3,8,5,6,2,1]=>[2,5,6,1,4,3,7,8]=>[3,2,3]
[1,7,4,3,8,6,2,5]=>[3,7,8,4,2,6,1,5]=>[6,2,1,5,7,3,8,4]=>[1,1,3,2,1]
[2,8,6,1,7,4,5,3]=>[6,8,7,4,1,3,5,2]=>[3,1,2,5,8,6,4,7]=>[1,4,1,2]
[4,8,6,5,7,2,1,3]=>[7,6,1,4,3,8,5,2]=>[2,3,8,5,6,1,4,7]=>[3,2,3]
[4,7,6,8,2,1,5,3]=>[5,8,1,6,3,2,7,4]=>[4,1,8,3,6,7,2,5]=>[1,2,3,2]
[6,1,8,7,4,3,5,2]=>[6,5,1,8,7,4,2,3]=>[3,4,8,1,2,5,7,6]=>[3,4,1]
[4,1,3,8,5,6,7,2]=>[5,1,6,8,3,7,2,4]=>[4,8,3,1,6,2,7,5]=>[2,1,2,2,1]
[6,5,8,4,3,1,7,2]=>[2,1,8,6,5,4,7,3]=>[7,8,1,3,4,5,2,6]=>[2,4,2]
[4,6,5,2,8,1,7,3]=>[8,1,4,3,2,6,7,5]=>[1,8,5,6,7,3,2,4]=>[2,3,1,2]
[7,2,8,1,3,6,4,5]=>[7,8,2,4,5,1,6,3]=>[2,1,7,5,4,8,3,6]=>[1,2,1,2,2]
[1,8,5,2,3,6,7,4]=>[6,8,4,3,5,7,1,2]=>[3,1,5,6,4,2,8,7]=>[1,3,1,2,1]
[1,8,3,2,5,6,7,4]=>[3,5,6,8,4,7,1,2]=>[6,4,3,1,5,2,8,7]=>[1,1,1,2,2,1]
[2,8,3,1,5,6,7,4]=>[3,5,6,8,1,4,7,2]=>[6,4,3,1,8,5,2,7]=>[1,1,1,2,1,2]
[8,2,3,1,5,6,7,4]=>[2,3,5,6,8,4,7,1]=>[7,6,4,3,1,5,2,8]=>[1,1,1,1,2,2]
[2,1,8,3,5,6,7,4]=>[5,6,8,1,4,7,2,3]=>[4,3,1,8,5,2,7,6]=>[1,1,2,1,2,1]
[1,4,8,2,3,6,7,5]=>[2,6,8,4,5,7,1,3]=>[7,3,1,5,4,2,8,6]=>[1,1,2,1,2,1]
[3,1,2,7,8,6,4,5]=>[7,1,4,8,6,2,3,5]=>[2,8,5,1,3,7,6,4]=>[2,1,3,1,1]
[7,5,1,8,2,4,3,6]=>[7,5,6,2,8,3,1,4]=>[2,4,3,7,1,6,8,5]=>[2,2,3,1]
[3,5,8,1,2,4,7,6]=>[8,1,4,2,5,6,7,3]=>[1,8,5,7,4,3,2,6]=>[2,2,1,1,2]
[4,5,8,1,2,3,7,6]=>[1,8,4,2,5,6,7,3]=>[8,1,5,7,4,3,2,6]=>[1,3,1,1,2]
[5,4,8,2,3,6,7,1]=>[4,2,1,5,6,8,7,3]=>[5,7,8,4,3,1,2,6]=>[3,1,1,3]
[5,8,3,6,7,4,1,2]=>[1,7,3,4,8,6,5,2]=>[8,2,6,5,1,3,4,7]=>[1,2,1,4]
[2,3,1,6,8,4,7,5]=>[4,8,1,2,6,7,3,5]=>[5,1,8,7,3,2,6,4]=>[1,2,1,1,2,1]
[2,4,3,7,1,8,5,6]=>[2,7,8,1,3,5,4,6]=>[7,2,1,8,6,4,5,3]=>[1,1,2,1,2,1]
[2,4,1,8,6,3,7,5]=>[8,2,6,1,5,7,3,4]=>[1,7,3,8,4,2,6,5]=>[2,2,1,2,1]
[8,4,1,3,6,2,7,5]=>[8,4,2,6,3,5,7,1]=>[1,5,7,3,6,4,2,8]=>[3,2,1,2]
[6,8,5,1,7,2,3,4]=>[6,7,1,8,4,3,5,2]=>[3,2,8,1,5,6,4,7]=>[1,2,3,2]
[7,3,6,5,8,2,1,4]=>[7,6,2,4,3,1,8,5]=>[2,3,7,5,6,8,1,4]=>[3,3,2]
[7,6,3,5,8,2,1,4]=>[7,3,6,4,2,1,8,5]=>[2,6,3,5,7,8,1,4]=>[2,4,2]
[4,5,8,7,3,6,1,2]=>[7,1,2,5,8,6,4,3]=>[2,8,7,4,1,3,5,6]=>[2,1,1,4]
[3,5,2,8,6,1,7,4]=>[2,8,1,6,3,5,7,4]=>[7,1,8,3,6,4,2,5]=>[1,2,2,1,2]
[8,2,5,6,1,4,7,3]=>[6,3,8,2,5,4,7,1]=>[3,6,1,7,4,5,2,8]=>[2,2,2,2]
[2,6,1,8,3,7,5,4]=>[8,7,5,1,2,6,3,4]=>[1,2,4,8,7,3,6,5]=>[4,1,2,1]
[6,1,5,3,8,7,2,4]=>[7,3,8,4,1,6,2,5]=>[2,6,1,5,8,3,7,4]=>[2,3,2,1]
[2,8,6,3,7,1,5,4]=>[8,4,6,3,7,1,5,2]=>[1,5,3,6,2,8,4,7]=>[2,2,2,2]
[7,6,1,5,8,2,3,4]=>[6,7,4,8,3,2,1,5]=>[3,2,5,1,6,7,8,4]=>[1,2,4,1]
[3,6,8,5,1,2,7,4]=>[8,5,1,2,6,4,7,3]=>[1,4,8,7,3,5,2,6]=>[3,1,2,2]
[6,5,2,4,8,1,7,3]=>[4,8,3,2,1,6,7,5]=>[5,1,6,7,8,3,2,4]=>[1,4,1,2]
[5,1,4,8,2,6,7,3]=>[3,6,1,8,5,7,2,4]=>[6,3,8,1,4,2,7,5]=>[1,2,2,2,1]
[3,4,8,5,2,6,7,1]=>[5,1,2,4,6,8,7,3]=>[4,8,7,5,3,1,2,6]=>[2,1,1,1,3]
[4,2,1,8,5,6,7,3]=>[5,1,6,8,2,7,3,4]=>[4,8,3,1,7,2,6,5]=>[2,1,2,2,1]
[1,5,4,8,2,6,7,3]=>[3,2,6,8,5,7,1,4]=>[6,7,3,1,4,2,8,5]=>[2,1,2,2,1]
[2,8,4,5,1,6,7,3]=>[3,6,4,8,1,5,7,2]=>[6,3,5,1,8,4,2,7]=>[1,2,2,1,2]
[5,4,8,3,7,6,1,2]=>[2,1,4,7,8,6,5,3]=>[7,8,5,2,1,3,4,6]=>[2,1,1,4]
[3,1,5,8,6,2,7,4]=>[8,1,3,6,5,7,2,4]=>[1,8,6,3,4,2,7,5]=>[2,1,2,2,1]
[6,3,4,8,5,1,7,2]=>[8,2,3,1,6,5,7,4]=>[1,7,6,8,3,4,2,5]=>[2,2,2,2]
[5,3,4,8,1,6,7,2]=>[2,3,1,6,8,5,7,4]=>[7,6,8,3,1,4,2,5]=>[1,2,1,2,2]
[7,6,1,2,8,3,5,4]=>[8,6,7,3,4,2,1,5]=>[1,3,2,6,5,7,8,4]=>[2,2,3,1]
[7,5,8,4,6,1,3,2]=>[2,8,6,4,1,7,5,3]=>[7,1,3,5,8,2,4,6]=>[1,4,3]
[6,5,4,8,7,1,3,2]=>[3,2,1,8,6,7,5,4]=>[6,7,8,1,3,2,4,5]=>[3,2,3]
[6,5,4,8,1,2,7,3]=>[8,5,3,2,1,6,7,4]=>[1,4,6,7,8,3,2,5]=>[5,1,2]
[7,5,1,6,2,3,8,4]=>[8,5,6,3,2,4,1,7]=>[1,4,3,6,7,5,8,2]=>[2,3,2,1]
[7,5,1,6,8,2,4,3]=>[8,6,4,2,7,3,1,5]=>[1,3,5,7,2,6,8,4]=>[4,3,1]
[6,5,4,1,8,2,7,3]=>[8,6,3,2,1,7,4,5]=>[1,3,6,7,8,2,5,4]=>[5,2,1]
[6,5,4,7,1,2,8,3]=>[8,5,3,2,1,6,4,7]=>[1,4,6,7,8,3,5,2]=>[5,2,1]
[6,5,4,7,8,1,3,2]=>[3,2,1,8,6,4,7,5]=>[6,7,8,1,3,5,2,4]=>[3,3,2]
[6,5,3,7,1,4,2,8]=>[3,7,5,2,1,6,4,8]=>[6,2,4,7,8,3,5,1]=>[1,4,2,1]
[6,5,3,1,8,4,2,7]=>[3,7,6,2,1,8,4,5]=>[6,2,3,7,8,1,5,4]=>[1,4,2,1]
[7,5,1,4,8,3,2,6]=>[4,7,6,2,8,3,1,5]=>[5,2,3,7,1,6,8,4]=>[1,3,3,1]
[8,1,6,4,7,3,5,2]=>[4,6,3,8,7,2,5,1]=>[5,3,6,1,2,7,4,8]=>[1,2,3,2]
[7,5,1,4,8,3,6,2]=>[4,6,2,8,7,3,1,5]=>[5,3,7,1,2,6,8,4]=>[1,2,4,1]
[6,5,3,7,1,4,8,2]=>[3,6,2,1,8,5,4,7]=>[6,3,7,8,1,4,5,2]=>[1,3,3,1]
[6,4,3,1,5,8,7,2]=>[3,2,8,5,1,7,4,6]=>[6,7,1,4,8,2,5,3]=>[2,3,2,1]
[8,1,5,4,3,7,6,2]=>[4,3,8,5,7,2,6,1]=>[5,6,1,4,2,7,3,8]=>[2,2,2,2]
[8,1,5,4,3,7,2,6]=>[5,4,3,7,8,2,6,1]=>[4,5,6,2,1,7,3,8]=>[3,1,2,2]
[7,4,1,5,3,8,2,6]=>[5,4,2,7,8,3,1,6]=>[4,5,7,2,1,6,8,3]=>[3,1,3,1]
[7,4,1,5,3,2,6,8]=>[6,5,3,2,4,7,1,8]=>[3,4,6,7,5,2,8,1]=>[4,1,2,1]
[6,5,3,1,2,7,4,8]=>[7,4,3,5,2,1,6,8]=>[2,5,6,4,7,8,3,1]=>[3,3,1,1]
[7,6,8,1,4,3,2,5]=>[7,6,4,5,2,1,8,3]=>[2,3,5,4,7,8,1,6]=>[3,3,2]
[8,1,7,2,5,4,3,6]=>[7,6,4,5,8,2,3,1]=>[2,3,5,4,1,7,6,8]=>[3,1,2,2]
[8,1,7,2,5,4,6,3]=>[6,5,8,4,7,2,3,1]=>[3,4,1,5,2,7,6,8]=>[2,2,2,2]
[7,6,1,2,5,4,8,3]=>[6,5,8,3,4,2,1,7]=>[3,4,1,6,5,7,8,2]=>[2,2,3,1]
[6,5,3,1,2,7,8,4]=>[6,3,8,4,2,1,5,7]=>[3,6,1,5,7,8,4,2]=>[2,4,1,1]
[7,5,1,4,2,6,8,3]=>[6,4,8,3,2,5,1,7]=>[3,5,1,6,7,4,8,2]=>[2,3,2,1]
[8,1,6,4,2,5,7,3]=>[6,4,8,5,2,3,7,1]=>[3,5,1,4,7,6,2,8]=>[2,3,1,2]
[7,4,1,5,3,2,8,6]=>[5,4,2,8,3,6,1,7]=>[4,5,7,1,6,3,8,2]=>[3,2,2,1]
[6,4,3,1,5,2,8,7]=>[5,3,2,8,4,1,6,7]=>[4,6,7,1,5,8,3,2]=>[3,3,1,1]
[6,4,3,1,5,7,2,8]=>[5,3,2,7,4,1,6,8]=>[4,6,7,2,5,8,3,1]=>[3,3,1,1]
[7,4,1,5,3,6,2,8]=>[5,4,2,7,3,6,1,8]=>[4,5,7,2,6,3,8,1]=>[3,2,2,1]
[8,1,5,4,3,6,2,7]=>[5,4,3,7,2,6,8,1]=>[4,5,6,2,7,3,1,8]=>[3,2,1,2]
[8,1,5,4,3,6,7,2]=>[5,4,3,6,8,2,7,1]=>[4,5,6,3,1,7,2,8]=>[3,1,2,2]
[7,4,1,5,3,6,8,2]=>[5,4,2,6,8,3,1,7]=>[4,5,7,3,1,6,8,2]=>[3,1,3,1]
[6,4,3,1,5,7,8,2]=>[5,3,2,6,1,8,4,7]=>[4,6,7,3,8,1,5,2]=>[3,2,2,1]
[6,7,3,8,4,5,1,2]=>[7,3,1,5,2,8,6,4]=>[2,6,8,4,7,1,3,5]=>[3,2,3]
[6,7,4,5,1,8,2,3]=>[7,3,1,8,5,4,2,6]=>[2,6,8,1,4,5,7,3]=>[3,4,1]
[4,7,5,6,2,3,1,8]=>[5,1,3,7,6,4,2,8]=>[4,8,6,2,3,5,7,1]=>[2,1,4,1]
[4,7,5,6,1,8,2,3]=>[7,1,3,8,5,4,2,6]=>[2,8,6,1,4,5,7,3]=>[2,1,4,1]
[4,7,5,6,3,8,1,2]=>[3,7,1,5,4,2,8,6]=>[6,2,8,4,5,7,1,3]=>[1,2,3,2]
[3,7,5,8,4,6,1,2]=>[3,7,5,1,2,8,6,4]=>[6,2,4,8,7,1,3,5]=>[1,3,1,3]
[4,5,3,8,6,7,1,2]=>[1,2,7,3,5,8,6,4]=>[8,7,2,6,4,1,3,5]=>[1,1,2,1,3]
[4,8,3,6,5,7,1,2]=>[7,1,3,5,4,8,6,2]=>[2,8,6,4,5,1,3,7]=>[2,1,2,3]
[5,6,4,7,1,8,2,3]=>[1,7,3,2,8,5,4,6]=>[8,2,6,7,1,4,5,3]=>[1,3,3,1]
[5,6,1,7,3,8,2,4]=>[5,1,7,4,2,8,3,6]=>[4,8,2,5,7,1,6,3]=>[2,3,2,1]
[5,6,1,8,2,7,3,4]=>[7,1,8,5,2,6,3,4]=>[2,8,1,4,7,3,6,5]=>[2,3,2,1]
[5,6,1,8,4,7,2,3]=>[1,7,5,2,8,6,3,4]=>[8,2,4,7,1,3,6,5]=>[1,3,3,1]
[4,8,1,6,5,7,2,3]=>[7,1,5,4,8,3,6,2]=>[2,8,4,5,1,6,3,7]=>[2,2,2,2]
[4,5,1,8,6,7,2,3]=>[1,2,7,5,8,6,3,4]=>[8,7,2,4,1,3,6,5]=>[1,1,2,3,1]
[7,8,4,5,1,6,2,3]=>[7,3,8,5,4,1,6,2]=>[2,6,1,4,5,8,3,7]=>[2,4,2]
[4,8,2,3,1,6,5,7]=>[3,1,4,7,5,6,8,2]=>[6,8,5,2,4,3,1,7]=>[2,1,2,1,2]
[5,6,2,8,1,4,3,7]=>[7,3,1,5,2,6,8,4]=>[2,6,8,4,7,3,1,5]=>[3,2,1,2]
[5,6,3,4,1,8,2,7]=>[3,1,7,4,2,8,5,6]=>[6,8,2,5,7,1,4,3]=>[2,3,2,1]
[3,6,4,5,1,8,2,7]=>[3,7,1,4,2,8,5,6]=>[6,2,8,5,7,1,4,3]=>[1,2,2,2,1]
[2,6,4,8,1,5,3,7]=>[3,7,5,1,2,6,8,4]=>[6,2,4,8,7,3,1,5]=>[1,3,1,1,2]
[2,8,3,6,1,5,4,7]=>[7,3,5,6,1,4,8,2]=>[2,6,4,3,8,5,1,7]=>[2,1,2,1,2]
[2,8,3,4,1,6,5,7]=>[3,4,7,1,5,6,8,2]=>[6,5,2,8,4,3,1,7]=>[1,1,2,1,1,2]
[7,8,2,5,3,4,1,6]=>[5,7,3,6,4,1,8,2]=>[4,2,6,3,5,8,1,7]=>[1,2,3,2]
[7,8,1,5,3,6,2,4]=>[5,7,4,8,3,1,6,2]=>[4,2,5,1,6,8,3,7]=>[1,2,3,2]
[1,5,3,8,6,7,2,4]=>[2,7,5,8,3,6,1,4]=>[7,2,4,1,6,3,8,5]=>[1,2,2,2,1]
[1,8,3,6,2,7,4,5]=>[7,8,3,5,4,6,1,2]=>[2,1,6,4,5,3,8,7]=>[1,2,2,2,1]
[1,6,4,8,2,7,3,5]=>[3,7,2,8,5,6,1,4]=>[6,2,7,1,4,3,8,5]=>[1,2,2,2,1]
[2,6,4,7,3,5,1,8]=>[3,5,2,7,1,6,4,8]=>[6,4,7,2,8,3,5,1]=>[1,2,2,2,1]
[2,7,3,6,4,5,1,8]=>[5,7,3,6,1,4,2,8]=>[4,2,6,3,8,5,7,1]=>[1,2,2,2,1]
[1,7,3,6,4,8,2,5]=>[5,7,3,4,2,8,1,6]=>[4,2,6,5,7,1,8,3]=>[1,2,2,2,1]
[1,7,2,8,4,6,3,5]=>[5,7,8,6,3,1,2,4]=>[4,2,1,3,6,8,7,5]=>[1,1,4,1,1]
[1,7,5,8,4,6,2,3]=>[3,7,5,2,8,6,1,4]=>[6,2,4,7,1,3,8,5]=>[1,3,3,1]
[1,7,5,8,2,6,3,4]=>[7,3,8,5,2,6,1,4]=>[2,6,1,4,7,3,8,5]=>[2,3,2,1]
[1,7,5,6,3,8,2,4]=>[5,3,7,4,2,8,1,6]=>[4,6,2,5,7,1,8,3]=>[2,3,2,1]
[2,7,5,6,3,4,1,8]=>[5,3,7,6,1,4,2,8]=>[4,6,2,3,8,5,7,1]=>[2,3,2,1]
[6,7,1,5,3,8,2,4]=>[5,7,4,1,8,3,2,6]=>[4,2,5,8,1,6,7,3]=>[1,3,3,1]
[6,7,5,8,1,4,2,3]=>[7,1,8,5,3,2,6,4]=>[2,8,1,4,6,7,3,5]=>[2,4,2]
[5,8,6,7,2,3,1,4]=>[1,5,7,6,3,8,4,2]=>[8,4,2,3,6,1,5,7]=>[1,1,3,3]
[6,7,2,3,1,8,4,5]=>[3,4,7,1,8,5,2,6]=>[6,5,2,8,1,4,7,3]=>[1,1,2,3,1]
[6,7,2,8,1,4,3,5]=>[7,3,5,1,6,2,8,4]=>[2,6,4,8,3,7,1,5]=>[2,2,2,2]
[3,4,2,7,5,6,1,8]=>[1,2,5,7,3,6,4,8]=>[8,7,4,2,6,3,5,1]=>[1,1,1,2,2,1]
[3,4,1,7,5,8,2,6]=>[1,2,5,7,4,8,3,6]=>[8,7,4,2,5,1,6,3]=>[1,1,1,2,2,1]
[2,7,5,8,1,4,3,6]=>[7,5,3,6,1,2,8,4]=>[2,4,6,3,8,7,1,5]=>[3,2,1,2]
[2,3,1,7,5,8,4,6]=>[5,7,1,2,4,8,3,6]=>[4,2,8,7,5,1,6,3]=>[1,2,1,1,2,1]
[2,3,1,8,4,7,5,6]=>[7,8,1,2,5,6,3,4]=>[2,1,8,7,4,3,6,5]=>[1,2,1,1,2,1]
[7,8,2,3,1,6,4,5]=>[3,4,7,8,5,1,6,2]=>[6,5,2,1,4,8,3,7]=>[1,1,1,3,2]
[7,8,2,6,1,4,3,5]=>[7,3,5,6,1,8,4,2]=>[2,6,4,3,8,1,5,7]=>[2,1,2,3]
[2,8,6,7,1,4,3,5]=>[7,5,6,3,8,1,4,2]=>[2,4,3,6,1,8,5,7]=>[2,2,2,2]
[2,8,1,4,3,7,5,6]=>[4,7,8,1,3,5,6,2]=>[5,2,1,8,6,4,3,7]=>[1,1,2,1,1,2]
[3,7,2,5,4,6,1,8]=>[5,1,3,4,7,6,2,8]=>[4,8,6,5,2,3,7,1]=>[2,1,1,3,1]
[4,5,2,7,3,6,1,8]=>[1,5,2,7,3,6,4,8]=>[8,4,7,2,6,3,5,1]=>[1,2,2,2,1]
[4,5,1,8,2,7,3,6]=>[1,7,2,8,5,6,3,4]=>[8,2,7,1,4,3,6,5]=>[1,2,2,2,1]
[3,4,1,8,2,7,5,6]=>[1,2,7,8,5,6,3,4]=>[8,7,2,1,4,3,6,5]=>[1,1,1,2,2,1]
[3,4,1,8,6,7,2,5]=>[7,1,2,5,8,6,3,4]=>[2,8,7,4,1,3,6,5]=>[2,1,1,3,1]
[3,4,2,5,1,8,6,7]=>[1,3,2,4,7,8,5,6]=>[8,6,7,5,2,1,4,3]=>[1,2,1,1,2,1]
[3,4,2,8,1,6,5,7]=>[1,2,7,3,5,6,8,4]=>[8,7,2,6,4,3,1,5]=>[1,1,2,1,1,2]
[3,8,2,5,1,6,4,7]=>[7,1,3,5,4,6,8,2]=>[2,8,6,4,5,3,1,7]=>[2,1,2,1,2]
[4,5,2,8,1,6,3,7]=>[1,7,3,2,5,6,8,4]=>[8,2,6,7,4,3,1,5]=>[1,3,1,1,2]
[4,5,3,6,1,8,2,7]=>[1,3,2,7,4,8,5,6]=>[8,6,7,2,5,1,4,3]=>[1,2,2,2,1]
[7,1,5,8,4,6,2,3]=>[3,7,5,8,6,2,1,4]=>[6,2,4,1,3,7,8,5]=>[1,2,4,1]
[8,6,7,1,4,2,5,3]=>[8,6,4,5,2,7,3,1]=>[1,3,5,4,7,2,6,8]=>[3,2,3]
[8,6,3,7,5,1,2,4]=>[3,6,7,2,8,5,4,1]=>[6,3,2,7,1,4,5,8]=>[1,1,2,4]
[7,6,1,8,3,5,2,4]=>[5,7,8,6,3,2,1,4]=>[4,2,1,3,6,7,8,5]=>[1,1,5,1]
[7,6,1,3,8,5,2,4]=>[7,8,4,6,3,2,1,5]=>[2,1,5,3,6,7,8,4]=>[1,2,4,1]
[7,6,8,2,4,5,1,3]=>[7,4,5,2,1,8,6,3]=>[2,5,4,7,8,1,3,6]=>[2,3,3]
[7,6,2,8,3,5,1,4]=>[5,7,8,3,2,1,6,4]=>[4,2,1,6,7,8,3,5]=>[1,1,4,2]
[7,6,2,3,8,5,1,4]=>[7,8,3,4,2,1,6,5]=>[2,1,6,5,7,8,3,4]=>[1,2,3,2]
[8,7,1,5,2,6,3,4]=>[7,8,5,3,4,6,2,1]=>[2,1,4,6,5,3,7,8]=>[1,3,1,3]
[8,7,1,5,2,3,6,4]=>[8,5,6,3,4,7,2,1]=>[1,4,3,6,5,2,7,8]=>[2,2,1,3]
[8,5,2,3,1,7,6,4]=>[8,3,4,2,7,5,6,1]=>[1,6,5,7,2,4,3,8]=>[2,2,2,2]
[8,6,2,3,7,1,5,4]=>[8,3,4,6,2,7,5,1]=>[1,6,5,3,7,2,4,8]=>[2,1,2,3]
[8,6,2,7,3,1,5,4]=>[5,8,3,6,2,7,4,1]=>[4,1,6,3,7,2,5,8]=>[1,2,2,3]
[8,6,7,2,4,1,5,3]=>[8,4,6,5,2,7,3,1]=>[1,5,3,4,7,2,6,8]=>[2,3,3]
[6,8,7,3,4,1,5,2]=>[4,1,8,6,5,7,3,2]=>[5,8,1,3,4,2,6,7]=>[2,3,3]
[8,7,2,5,1,6,3,4]=>[7,8,3,5,4,6,2,1]=>[2,1,6,4,5,3,7,8]=>[1,2,2,3]
[8,7,2,1,4,6,3,5]=>[3,5,7,8,4,6,2,1]=>[6,4,2,1,5,3,7,8]=>[1,1,1,2,3]
[8,4,2,1,7,6,3,5]=>[7,2,8,3,6,4,5,1]=>[2,7,1,6,3,5,4,8]=>[2,2,2,2]
[8,5,2,7,1,6,3,4]=>[7,8,3,2,5,6,4,1]=>[2,1,6,7,4,3,5,8]=>[1,3,1,3]
[8,5,7,2,1,4,3,6]=>[4,7,5,2,6,8,3,1]=>[5,2,4,7,3,1,6,8]=>[1,3,1,3]
[5,8,7,3,1,4,2,6]=>[1,7,5,4,6,8,3,2]=>[8,2,4,5,3,1,6,7]=>[1,3,1,3]
[8,5,7,2,1,4,6,3]=>[4,6,2,8,5,7,3,1]=>[5,3,7,1,4,2,6,8]=>[1,2,2,3]
[8,4,2,1,3,7,6,5]=>[8,3,2,7,4,5,6,1]=>[1,6,7,2,5,4,3,8]=>[3,2,1,2]
[8,7,4,1,2,3,6,5]=>[8,4,5,3,6,7,2,1]=>[1,5,4,6,3,2,7,8]=>[2,2,1,3]
[8,7,4,1,2,6,3,5]=>[7,8,4,3,5,6,2,1]=>[2,1,5,6,4,3,7,8]=>[1,3,1,3]
[8,4,3,1,7,2,6,5]=>[3,2,8,6,7,4,5,1]=>[6,7,1,3,2,5,4,8]=>[2,2,2,2]
[8,4,3,1,2,7,6,5]=>[3,2,8,7,4,5,6,1]=>[6,7,1,2,5,4,3,8]=>[2,3,1,2]
[8,6,1,3,7,2,5,4]=>[8,4,6,7,3,2,5,1]=>[1,5,3,2,6,7,4,8]=>[2,1,3,2]
[8,5,1,3,2,7,6,4]=>[8,4,7,3,2,5,6,1]=>[1,5,2,6,7,4,3,8]=>[2,3,1,2]
[8,5,7,4,1,6,2,3]=>[7,2,8,5,4,6,3,1]=>[2,7,1,4,5,3,6,8]=>[2,3,3]
[8,5,7,4,1,2,6,3]=>[8,5,2,6,4,7,3,1]=>[1,4,7,3,5,2,6,8]=>[3,2,3]
[8,1,6,4,7,2,5,3]=>[4,8,6,3,7,2,5,1]=>[5,1,3,6,2,7,4,8]=>[1,3,2,2]
[6,1,5,8,4,2,7,3]=>[3,8,6,5,1,7,2,4]=>[6,1,3,4,8,2,7,5]=>[1,4,2,1]
[5,8,3,6,4,1,2,7]=>[3,1,6,7,5,4,8,2]=>[6,8,3,2,4,5,1,7]=>[2,1,3,2]
[5,2,8,6,4,1,3,7]=>[6,1,7,5,2,4,8,3]=>[3,8,2,4,7,5,1,6]=>[2,3,1,2]
[8,4,7,5,1,6,2,3]=>[2,7,8,5,4,6,3,1]=>[7,2,1,4,5,3,6,8]=>[1,1,3,3]
[8,4,7,5,1,2,6,3]=>[2,8,5,6,4,7,3,1]=>[7,1,4,3,5,2,6,8]=>[1,2,2,3]
[8,4,7,5,1,2,3,6]=>[5,2,6,7,4,8,3,1]=>[4,7,3,2,5,1,6,8]=>[2,1,2,3]
[8,7,3,5,1,2,6,4]=>[3,8,5,6,4,7,2,1]=>[6,1,4,3,5,2,7,8]=>[1,2,2,3]
[4,8,6,3,5,1,2,7]=>[6,1,4,7,5,3,8,2]=>[3,8,5,2,4,6,1,7]=>[2,1,3,2]
[4,8,7,3,1,5,2,6]=>[7,1,5,4,6,8,3,2]=>[2,8,4,5,3,1,6,7]=>[2,2,1,3]
[8,3,2,1,7,6,4,5]=>[2,7,8,3,6,4,5,1]=>[7,2,1,6,3,5,4,8]=>[1,1,2,2,2]
[8,7,3,1,4,2,6,5]=>[5,3,8,4,6,7,2,1]=>[4,6,1,5,3,2,7,8]=>[2,2,1,3]
[8,7,3,1,6,2,4,5]=>[6,3,7,8,4,5,2,1]=>[3,6,2,1,5,4,7,8]=>[2,1,2,3]
[8,7,3,1,2,6,4,5]=>[7,3,8,4,5,6,2,1]=>[2,6,1,5,4,3,7,8]=>[2,2,1,3]
[8,7,3,1,2,4,6,5]=>[8,4,3,5,6,7,2,1]=>[1,5,6,4,3,2,7,8]=>[3,1,1,3]
[8,3,2,1,4,7,6,5]=>[2,8,3,7,4,5,6,1]=>[7,1,6,2,5,4,3,8]=>[1,2,2,1,2]
[8,3,2,1,7,4,6,5]=>[2,8,3,6,7,4,5,1]=>[7,1,6,3,2,5,4,8]=>[1,2,1,2,2]
[8,4,7,2,1,5,6,3]=>[4,2,6,8,5,7,3,1]=>[5,7,3,1,4,2,6,8]=>[2,1,2,3]
[3,8,7,4,1,2,5,6]=>[5,6,1,4,7,8,3,2]=>[4,3,8,5,2,1,6,7]=>[1,2,1,1,3]
[8,7,2,1,6,3,4,5]=>[3,6,7,8,4,5,2,1]=>[6,3,2,1,5,4,7,8]=>[1,1,1,2,3]
[8,7,2,1,3,6,4,5]=>[3,7,8,4,5,6,2,1]=>[6,2,1,5,4,3,7,8]=>[1,1,2,1,3]
[3,6,5,4,1,2,8,7]=>[8,5,1,4,3,2,6,7]=>[1,4,8,5,6,7,3,2]=>[3,3,1,1]
[3,8,5,6,7,4,1,2]=>[3,7,4,8,1,6,5,2]=>[6,2,5,1,8,3,4,7]=>[1,2,2,3]
[4,7,5,8,6,2,1,3]=>[3,7,1,6,2,8,5,4]=>[6,2,8,3,7,1,4,5]=>[1,2,2,3]
[2,5,7,8,6,3,4,1]=>[6,2,3,8,7,1,5,4]=>[3,7,6,1,2,8,4,5]=>[2,1,3,2]
[4,8,5,7,6,3,1,2]=>[3,7,8,1,6,5,4,2]=>[6,2,1,8,3,4,5,7]=>[1,1,2,4]
[4,6,3,2,1,5,8,7]=>[1,4,3,8,5,2,6,7]=>[8,5,6,1,4,7,3,2]=>[1,2,3,1,1]
[6,2,1,5,3,4,8,7]=>[8,2,5,3,4,1,6,7]=>[1,7,4,6,5,8,3,2]=>[2,2,2,1,1]
[5,8,1,3,7,6,4,2]=>[1,8,7,4,6,3,5,2]=>[8,1,2,5,3,6,4,7]=>[1,3,2,2]
[4,7,2,3,6,1,8,5]=>[1,8,3,4,6,5,2,7]=>[8,1,6,5,3,4,7,2]=>[1,2,1,3,1]
[3,7,4,2,8,1,5,6]=>[4,1,3,6,7,2,8,5]=>[5,8,6,3,2,7,1,4]=>[2,1,1,2,2]
[4,2,6,8,5,7,3,1]=>[1,3,5,8,7,2,6,4]=>[8,6,4,1,2,7,3,5]=>[1,1,1,3,2]
[8,1,6,7,5,3,4,2]=>[6,3,8,7,5,2,4,1]=>[3,6,1,2,4,7,5,8]=>[2,4,2]
[2,1,5,8,7,6,3,4]=>[7,8,3,6,1,5,2,4]=>[2,1,6,3,8,4,7,5]=>[1,2,2,2,1]
[2,1,4,7,6,3,8,5]=>[8,6,1,3,5,2,4,7]=>[1,3,8,6,4,7,5,2]=>[3,1,2,1,1]
[6,4,7,8,5,3,2,1]=>[3,1,8,2,7,6,5,4]=>[6,8,1,7,2,3,4,5]=>[2,2,4]
[4,1,3,7,6,2,8,5]=>[1,8,6,3,5,2,4,7]=>[8,1,3,6,4,7,5,2]=>[1,3,2,1,1]
[8,5,1,6,3,2,7,4]=>[5,8,6,3,2,4,7,1]=>[4,1,3,6,7,5,2,8]=>[1,4,1,2]
[6,3,7,1,5,2,8,4]=>[8,2,6,4,1,5,3,7]=>[1,7,3,5,8,4,6,2]=>[2,3,2,1]
[3,2,6,8,4,7,5,1]=>[3,8,1,5,7,2,6,4]=>[6,1,8,4,2,7,3,5]=>[1,2,1,2,2]
[8,4,6,1,3,2,5,7]=>[6,4,2,5,7,3,8,1]=>[3,5,7,4,2,6,1,8]=>[3,1,2,2]
[4,2,8,6,7,3,1,5]=>[7,1,6,4,8,2,5,3]=>[2,8,3,5,1,7,4,6]=>[2,2,2,2]
[7,4,3,8,2,1,5,6]=>[3,2,6,5,7,1,8,4]=>[6,7,3,4,2,8,1,5]=>[2,2,2,2]
[4,7,5,8,1,6,3,2]=>[3,8,1,7,5,2,6,4]=>[6,1,8,2,4,7,3,5]=>[1,2,3,2]
[6,4,3,2,7,8,1,5]=>[3,2,7,4,1,5,8,6]=>[6,7,2,5,8,4,1,3]=>[2,3,1,2]
[4,2,5,1,6,7,8,3]=>[5,2,1,3,6,8,4,7]=>[4,7,8,6,3,1,5,2]=>[3,1,1,2,1]
[2,4,8,5,7,1,3,6]=>[6,2,4,7,8,1,5,3]=>[3,7,5,2,1,8,4,6]=>[2,1,1,2,2]
[3,7,1,4,6,8,5,2]=>[5,8,1,4,7,3,2,6]=>[4,1,8,5,2,6,7,3]=>[1,2,1,3,1]
[7,8,2,5,6,1,4,3]=>[8,6,3,4,1,7,5,2]=>[1,3,6,5,8,2,4,7]=>[3,2,3]
[2,4,3,8,7,5,6,1]=>[6,8,2,7,1,3,5,4]=>[3,1,7,2,8,6,4,5]=>[1,2,2,1,2]
[2,6,7,3,5,1,8,4]=>[8,4,2,6,1,5,3,7]=>[1,5,7,3,8,4,6,2]=>[3,2,2,1]
[7,6,8,4,2,5,3,1]=>[8,5,4,2,1,7,6,3]=>[1,4,5,7,8,2,3,6]=>[5,3]
[6,5,7,2,8,4,3,1]=>[2,1,8,7,4,3,6,5]=>[7,8,1,2,5,6,3,4]=>[2,4,2]
[3,4,8,6,5,2,1,7]=>[7,6,1,2,5,4,8,3]=>[2,3,8,7,4,5,1,6]=>[3,1,2,2]
[2,7,6,1,4,5,8,3]=>[5,6,8,4,1,3,2,7]=>[4,3,1,5,8,6,7,2]=>[1,1,3,2,1]
[6,5,8,2,1,7,3,4]=>[4,7,2,1,8,5,6,3]=>[5,2,7,8,1,4,3,6]=>[1,3,2,2]
[7,4,3,5,1,6,8,2]=>[3,2,6,4,8,5,1,7]=>[6,7,3,5,1,4,8,2]=>[2,2,3,1]
[4,1,6,3,5,8,7,2]=>[1,8,4,3,5,7,2,6]=>[8,1,5,6,4,2,7,3]=>[1,3,1,2,1]
[6,2,5,8,4,3,7,1]=>[3,6,5,1,8,2,7,4]=>[6,3,4,8,1,7,2,5]=>[1,3,2,2]
[8,6,7,1,5,4,3,2]=>[8,7,6,4,2,5,3,1]=>[1,2,3,5,7,4,6,8]=>[5,3]
[2,1,6,5,8,4,7,3]=>[4,3,6,8,1,7,2,5]=>[5,6,3,1,8,2,7,4]=>[2,1,2,2,1]
[2,1,6,8,5,4,3,7]=>[3,7,6,1,5,8,2,4]=>[6,2,3,8,4,1,7,5]=>[1,3,1,2,1]
[4,1,8,5,6,2,3,7]=>[1,6,4,7,5,8,2,3]=>[8,3,5,2,4,1,7,6]=>[1,2,2,2,1]
[2,6,4,8,7,3,5,1]=>[6,2,8,3,7,1,5,4]=>[3,7,1,6,2,8,4,5]=>[2,2,2,2]
[6,2,8,4,3,5,1,7]=>[5,4,7,2,1,6,8,3]=>[4,5,2,7,8,3,1,6]=>[2,3,1,2]
[4,8,2,7,6,1,3,5]=>[1,6,7,8,3,5,4,2]=>[8,3,2,1,6,4,5,7]=>[1,1,1,2,3]
[3,1,8,2,7,5,4,6]=>[7,1,6,8,4,5,2,3]=>[2,8,3,1,5,4,7,6]=>[2,1,2,2,1]
[3,8,1,2,6,7,4,5]=>[7,1,5,8,3,4,6,2]=>[2,8,4,1,6,5,3,7]=>[2,1,2,1,2]
[5,8,4,3,2,7,1,6]=>[1,5,4,3,7,8,6,2]=>[8,4,5,6,2,1,3,7]=>[1,3,1,3]
[7,4,8,6,3,2,5,1]=>[6,2,5,1,8,7,4,3]=>[3,7,4,8,1,2,5,6]=>[2,2,4]
[5,8,4,7,2,1,3,6]=>[1,6,5,3,7,8,4,2]=>[8,3,4,6,2,1,5,7]=>[1,3,1,3]
[2,1,8,4,3,7,5,6]=>[4,7,8,1,5,6,2,3]=>[5,2,1,8,4,3,7,6]=>[1,1,2,1,2,1]
[6,3,8,2,4,5,7,1]=>[2,4,5,1,6,8,7,3]=>[7,5,4,8,3,1,2,6]=>[1,1,2,1,3]
[5,8,4,2,3,6,1,7]=>[4,1,5,3,7,6,8,2]=>[5,8,4,6,2,3,1,7]=>[2,2,2,2]
[2,8,3,1,6,4,5,7]=>[3,6,7,1,4,5,8,2]=>[6,3,2,8,5,4,1,7]=>[1,1,2,1,1,2]
[8,2,1,3,4,7,5,6]=>[2,7,8,3,4,5,6,1]=>[7,2,1,6,5,4,3,8]=>[1,1,2,1,1,2]
[1,4,8,2,6,3,5,7]=>[2,6,7,4,5,8,1,3]=>[7,3,2,5,4,1,8,6]=>[1,1,2,1,2,1]
[1,2,7,3,5,4,8,6]=>[5,8,4,6,1,2,3,7]=>[4,1,5,3,8,7,6,2]=>[1,2,2,1,1,1]
[1,2,3,8,4,5,7,6]=>[8,5,6,7,1,2,3,4]=>[1,4,3,2,8,7,6,5]=>[2,1,2,1,1,1]
[1,2,8,3,4,5,7,6]=>[8,4,5,6,7,1,2,3]=>[1,5,4,3,2,8,7,6]=>[2,1,1,2,1,1]
[1,5,7,2,3,6,4,8]=>[7,4,2,5,6,1,3,8]=>[2,5,7,4,3,8,6,1]=>[3,1,2,1,1]
[1,7,2,3,5,4,8,6]=>[5,8,3,4,6,1,2,7]=>[4,1,6,5,3,8,7,2]=>[1,2,1,2,1,1]
[1,3,8,2,4,5,7,6]=>[8,2,4,5,6,7,1,3]=>[1,7,5,4,3,2,8,6]=>[2,1,1,1,2,1]
[1,2,3,8,4,6,7,5]=>[6,8,5,7,1,2,3,4]=>[3,1,4,2,8,7,6,5]=>[1,2,2,1,1,1]
[1,8,2,3,5,4,6,7]=>[6,3,4,5,7,8,1,2]=>[3,6,5,4,2,1,8,7]=>[2,1,1,1,2,1]
[1,7,8,2,3,6,4,5]=>[7,8,4,5,2,6,1,3]=>[2,1,5,4,7,3,8,6]=>[1,2,2,2,1]
[1,6,7,8,2,3,5,4]=>[8,5,2,6,3,7,1,4]=>[1,4,7,3,6,2,8,5]=>[3,2,2,1]
[1,7,8,2,5,3,6,4]=>[8,6,4,5,2,7,1,3]=>[1,3,5,4,7,2,8,6]=>[3,2,2,1]
[1,7,8,2,4,5,3,6]=>[5,7,4,6,2,8,1,3]=>[4,2,5,3,7,1,8,6]=>[1,2,2,2,1]
[1,2,8,3,6,4,5,7]=>[6,7,4,5,8,1,2,3]=>[3,2,5,4,1,8,7,6]=>[1,2,1,2,1,1]
[1,8,2,3,6,4,5,7]=>[6,7,3,4,5,8,1,2]=>[3,2,6,5,4,1,8,7]=>[1,2,1,1,2,1]
[1,2,8,3,5,4,6,7]=>[6,4,5,7,8,1,2,3]=>[3,5,4,2,1,8,7,6]=>[2,1,1,2,1,1]
[1,2,7,8,3,6,4,5]=>[7,8,5,3,6,1,2,4]=>[2,1,4,6,3,8,7,5]=>[1,3,2,1,1]
[1,5,2,7,8,3,6,4]=>[2,8,6,4,7,1,3,5]=>[7,1,3,5,2,8,6,4]=>[1,3,2,1,1]
[1,3,2,8,4,6,7,5]=>[6,8,2,5,7,1,3,4]=>[3,1,7,4,2,8,6,5]=>[1,2,1,2,1,1]
[1,8,2,3,4,6,7,5]=>[6,8,3,4,5,7,1,2]=>[3,1,6,5,4,2,8,7]=>[1,2,1,1,2,1]
[1,7,8,2,4,3,6,5]=>[5,8,4,6,2,7,1,3]=>[4,1,5,3,7,2,8,6]=>[1,2,2,2,1]
[6,8,3,1,5,2,7,4]=>[3,8,6,4,1,5,7,2]=>[6,1,3,5,8,4,2,7]=>[1,4,1,2]
[6,8,4,5,1,2,7,3]=>[8,5,3,1,6,4,7,2]=>[1,4,6,8,3,5,2,7]=>[4,2,2]
[6,7,4,5,1,2,8,3]=>[8,5,3,1,6,4,2,7]=>[1,4,6,8,3,5,7,2]=>[4,3,1]
[7,2,1,6,5,3,4,8]=>[6,7,2,5,3,4,1,8]=>[3,2,7,4,6,5,8,1]=>[1,2,2,2,1]
[7,3,6,1,5,2,4,8]=>[2,6,7,4,5,3,1,8]=>[7,3,2,5,4,6,8,1]=>[1,1,2,3,1]
[7,4,6,5,1,2,3,8]=>[5,2,6,7,4,3,1,8]=>[4,7,3,2,5,6,8,1]=>[2,1,4,1]
[6,7,5,4,1,2,8,3]=>[8,5,1,6,4,3,2,7]=>[1,4,8,3,5,6,7,2]=>[3,4,1]
[5,8,6,4,1,7,2,3]=>[1,7,8,5,4,3,6,2]=>[8,2,1,4,5,6,3,7]=>[1,1,4,2]
[5,7,6,4,1,8,2,3]=>[1,7,8,5,4,3,2,6]=>[8,2,1,4,5,6,7,3]=>[1,1,5,1]
[5,6,7,4,1,8,2,3]=>[1,7,2,8,5,4,3,6]=>[8,2,7,1,4,5,6,3]=>[1,2,4,1]
[6,5,7,4,1,2,8,3]=>[8,5,2,1,6,4,3,7]=>[1,4,7,8,3,5,6,2]=>[4,3,1]
[6,4,7,5,1,2,8,3]=>[2,8,5,1,6,4,3,7]=>[7,1,4,8,3,5,6,2]=>[1,3,3,1]
[6,2,1,7,5,3,8,4]=>[8,6,2,5,3,1,4,7]=>[1,3,7,4,6,8,5,2]=>[3,3,1,1]
[6,3,8,1,5,2,7,4]=>[8,2,6,4,1,5,7,3]=>[1,7,3,5,8,4,2,6]=>[2,3,1,2]
[6,4,8,5,1,2,7,3]=>[2,8,5,1,6,4,7,3]=>[7,1,4,8,3,5,2,6]=>[1,3,2,2]
[6,5,8,4,1,2,7,3]=>[8,5,2,1,6,4,7,3]=>[1,4,7,8,3,5,2,6]=>[4,2,2]
[5,6,8,4,1,7,2,3]=>[1,7,2,8,5,4,6,3]=>[8,2,7,1,4,5,3,6]=>[1,2,3,2]
[4,6,8,5,7,1,2,3]=>[6,1,2,7,4,8,5,3]=>[3,8,7,2,5,1,4,6]=>[2,1,2,3]
[5,4,8,6,1,7,2,3]=>[2,1,7,8,5,4,6,3]=>[7,8,2,1,4,5,3,6]=>[2,1,3,2]
[5,3,8,1,6,7,2,4]=>[7,2,1,5,8,4,6,3]=>[2,7,8,4,1,5,3,6]=>[3,1,2,2]
[5,2,1,8,6,7,3,4]=>[7,5,1,8,2,6,3,4]=>[2,4,8,1,7,3,6,5]=>[3,2,2,1]
[5,2,1,7,6,8,3,4]=>[7,5,2,1,4,8,3,6]=>[2,4,7,8,5,1,6,3]=>[4,1,2,1]
[5,4,7,6,1,8,2,3]=>[2,1,7,8,5,4,3,6]=>[7,8,2,1,4,5,6,3]=>[2,1,4,1]
[4,5,7,6,8,1,2,3]=>[1,2,6,7,4,3,8,5]=>[8,7,3,2,5,6,1,4]=>[1,1,1,3,2]
[4,6,7,5,8,1,2,3]=>[6,1,2,7,4,3,8,5]=>[3,8,7,2,5,6,1,4]=>[2,1,3,2]
[4,8,6,5,7,1,2,3]=>[6,7,1,4,3,8,5,2]=>[3,2,8,5,6,1,4,7]=>[1,2,2,3]
[4,8,5,6,7,1,2,3]=>[6,1,3,7,4,8,5,2]=>[3,8,6,2,5,1,4,7]=>[2,1,2,3]
[4,7,5,6,8,1,2,3]=>[6,1,3,7,4,2,8,5]=>[3,8,6,2,5,7,1,4]=>[2,1,3,2]
[4,6,5,7,8,1,2,3]=>[6,1,3,2,7,4,8,5]=>[3,8,6,7,2,5,1,4]=>[2,2,2,2]
[5,7,4,6,1,8,2,3]=>[1,7,3,8,5,4,2,6]=>[8,2,6,1,4,5,7,3]=>[1,2,4,1]
[5,8,4,6,1,7,2,3]=>[1,7,3,8,5,4,6,2]=>[8,2,6,1,4,5,3,7]=>[1,2,3,2]
[5,8,3,1,6,7,2,4]=>[3,1,7,5,8,4,6,2]=>[6,8,2,4,1,5,3,7]=>[2,2,2,2]
[5,7,3,1,6,8,2,4]=>[3,1,7,5,8,4,2,6]=>[6,8,2,4,1,5,7,3]=>[2,2,3,1]
[5,6,3,1,7,8,2,4]=>[3,1,7,5,2,8,4,6]=>[6,8,2,4,7,1,5,3]=>[2,3,2,1]
[6,2,1,4,3,8,7,5]=>[8,2,4,7,3,1,5,6]=>[1,7,5,2,6,8,4,3]=>[2,1,3,1,1]
[5,8,3,1,7,6,2,4]=>[3,1,7,8,6,4,5,2]=>[6,8,2,1,3,5,4,7]=>[2,1,3,2]
[5,7,4,8,1,6,2,3]=>[1,7,3,8,5,2,6,4]=>[8,2,6,1,4,7,3,5]=>[1,2,3,2]
[5,2,1,6,8,7,3,4]=>[4,7,1,8,2,6,3,5]=>[5,2,8,1,7,3,6,4]=>[1,2,2,2,1]
[5,4,6,8,1,7,2,3]=>[2,1,7,3,8,5,6,4]=>[7,8,2,6,1,4,3,5]=>[2,2,2,2]
[4,5,6,8,7,1,2,3]=>[1,2,6,3,7,8,5,4]=>[8,7,3,6,2,1,4,5]=>[1,1,2,1,3]
[4,8,5,7,6,1,2,3]=>[6,1,3,7,8,5,4,2]=>[3,8,6,2,1,4,5,7]=>[2,1,1,4]
[4,8,6,7,5,1,2,3]=>[6,7,1,3,8,5,4,2]=>[3,2,8,6,1,4,5,7]=>[1,2,1,4]
[4,7,6,8,5,1,2,3]=>[6,7,1,3,2,8,5,4]=>[3,2,8,6,7,1,4,5]=>[1,2,2,3]
[4,6,7,8,5,1,2,3]=>[6,1,2,7,3,8,5,4]=>[3,8,7,2,6,1,4,5]=>[2,1,2,3]
[4,5,7,8,6,1,2,3]=>[1,2,6,7,3,8,5,4]=>[8,7,3,2,6,1,4,5]=>[1,1,1,2,3]
[5,4,7,8,1,6,2,3]=>[2,1,7,8,5,3,6,4]=>[7,8,2,1,4,6,3,5]=>[2,1,3,2]
[5,3,7,1,8,6,2,4]=>[7,1,8,2,6,4,3,5]=>[2,8,1,7,3,5,6,4]=>[2,2,3,1]
[5,2,1,7,8,6,3,4]=>[7,4,1,8,2,6,3,5]=>[2,5,8,1,7,3,6,4]=>[3,2,2,1]
[5,3,8,1,7,6,2,4]=>[7,1,8,2,6,4,5,3]=>[2,8,1,7,3,5,4,6]=>[2,2,2,2]
[5,4,8,7,1,6,2,3]=>[2,1,7,8,5,6,4,3]=>[7,8,2,1,4,3,5,6]=>[2,1,2,3]
[4,6,8,7,5,1,2,3]=>[6,1,2,7,8,5,4,3]=>[3,8,7,2,1,4,5,6]=>[2,1,1,4]
[4,7,8,6,5,1,2,3]=>[6,7,1,2,8,5,4,3]=>[3,2,8,7,1,4,5,6]=>[1,2,1,4]
[4,8,7,6,5,1,2,3]=>[6,7,8,1,5,4,3,2]=>[3,2,1,8,4,5,6,7]=>[1,1,2,4]
[2,5,4,7,3,6,1,8]=>[3,2,5,7,1,6,4,8]=>[6,7,4,2,8,3,5,1]=>[2,1,2,2,1]
[2,4,6,3,7,5,1,8]=>[7,2,4,1,3,6,5,8]=>[2,7,5,8,6,3,4,1]=>[2,2,1,2,1]
[4,2,6,3,1,5,8,7]=>[4,1,8,2,5,3,6,7]=>[5,8,1,7,4,6,3,2]=>[2,2,2,1,1]
[2,5,3,1,6,4,8,7]=>[3,5,1,2,8,4,6,7]=>[6,4,8,7,1,5,3,2]=>[1,2,1,2,1,1]
[2,5,3,7,6,4,1,8]=>[2,7,6,1,3,5,4,8]=>[7,2,3,8,6,4,5,1]=>[1,3,1,2,1]
[2,6,5,3,7,4,1,8]=>[7,4,3,1,2,6,5,8]=>[2,5,6,8,7,3,4,1]=>[4,1,2,1]
[4,2,7,6,3,5,1,8]=>[1,5,7,6,2,4,3,8]=>[8,4,2,3,7,5,6,1]=>[1,1,3,2,1]
[2,7,5,3,6,4,1,8]=>[7,4,3,6,1,5,2,8]=>[2,5,6,3,8,4,7,1]=>[3,2,2,1]
[2,6,3,7,5,4,1,8]=>[7,6,3,1,2,5,4,8]=>[2,3,6,8,7,4,5,1]=>[4,1,2,1]
[1,7,5,2,3,8,4,6]=>[7,8,4,3,5,1,2,6]=>[2,1,5,6,4,8,7,3]=>[1,3,2,1,1]
[2,1,3,7,5,4,8,6]=>[5,8,1,6,2,3,4,7]=>[4,1,8,3,7,6,5,2]=>[1,2,2,1,1,1]
[2,3,1,8,6,5,4,7]=>[7,6,1,2,5,8,3,4]=>[2,3,8,7,4,1,6,5]=>[3,1,1,2,1]
[4,2,8,3,1,6,5,7]=>[4,1,7,2,5,6,8,3]=>[5,8,2,7,4,3,1,6]=>[2,2,1,1,2]
[8,3,2,6,4,1,5,7]=>[2,6,3,5,7,4,8,1]=>[7,3,6,4,2,5,1,8]=>[1,2,1,2,2]
[3,6,8,2,1,4,5,7]=>[5,1,4,6,2,7,8,3]=>[4,8,5,3,7,2,1,6]=>[2,1,2,1,2]
[1,5,2,8,3,4,7,6]=>[8,5,2,6,7,1,3,4]=>[1,4,7,3,2,8,6,5]=>[3,1,2,1,1]
[1,2,6,3,8,7,4,5]=>[7,3,8,6,1,2,4,5]=>[2,6,1,3,8,7,5,4]=>[2,3,1,1,1]
[1,2,8,3,6,4,7,5]=>[8,6,4,5,7,1,2,3]=>[1,3,5,4,2,8,7,6]=>[3,1,2,1,1]
[1,2,7,6,3,4,8,5]=>[8,5,6,4,1,2,3,7]=>[1,4,3,5,8,7,6,2]=>[2,3,1,1,1]
[2,1,3,8,7,5,4,6]=>[7,6,8,1,5,2,3,4]=>[2,3,1,8,4,7,6,5]=>[2,2,2,1,1]
[1,2,3,8,6,4,7,5]=>[8,6,5,7,1,2,3,4]=>[1,3,4,2,8,7,6,5]=>[3,2,1,1,1]
[1,2,3,7,4,8,6,5]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]
[1,2,7,6,3,8,4,5]=>[7,8,5,4,1,2,3,6]=>[2,1,4,5,8,7,6,3]=>[1,4,1,1,1]
[1,2,3,6,4,8,7,5]=>[4,8,7,1,2,3,5,6]=>[5,1,2,8,7,6,4,3]=>[1,3,1,1,1,1]
[1,2,3,7,6,4,8,5]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]
[2,6,3,1,8,5,4,7]=>[7,3,6,1,2,8,4,5]=>[2,6,3,8,7,1,5,4]=>[2,2,1,2,1]
[2,1,3,8,5,4,7,6]=>[5,8,1,6,7,2,3,4]=>[4,1,8,3,2,7,6,5]=>[1,2,1,2,1,1]
[7,1,8,4,2,3,5,6]=>[5,6,4,7,8,2,1,3]=>[4,3,5,2,1,7,8,6]=>[1,2,1,3,1]
[2,1,8,4,3,5,7,6]=>[4,8,1,5,6,7,2,3]=>[5,1,8,4,3,2,7,6]=>[1,2,1,1,2,1]
[4,2,6,3,1,8,5,7]=>[4,1,7,2,3,8,5,6]=>[5,8,2,7,6,1,4,3]=>[2,2,1,2,1]
[5,4,2,8,3,1,6,7]=>[6,3,2,1,5,7,8,4]=>[3,6,7,8,4,2,1,5]=>[4,1,1,2]
[2,5,4,8,3,1,6,7]=>[3,2,6,1,5,7,8,4]=>[6,7,3,8,4,2,1,5]=>[2,2,1,1,2]
[4,2,1,8,3,5,7,6]=>[8,2,1,5,6,7,3,4]=>[1,7,8,4,3,2,6,5]=>[3,1,1,2,1]
[1,8,7,4,2,3,5,6]=>[5,6,4,7,8,3,1,2]=>[4,3,5,2,1,6,8,7]=>[1,2,1,3,1]
[1,5,2,8,7,3,4,6]=>[6,2,7,8,5,1,3,4]=>[3,7,2,1,4,8,6,5]=>[2,1,3,1,1]
[1,2,7,3,6,4,8,5]=>[8,6,4,5,1,2,3,7]=>[1,3,5,4,8,7,6,2]=>[3,2,1,1,1]
[1,2,8,6,3,7,4,5]=>[7,8,5,4,6,1,2,3]=>[2,1,4,5,3,8,7,6]=>[1,3,2,1,1]
[1,2,7,3,8,6,4,5]=>[7,8,6,4,1,2,3,5]=>[2,1,3,5,8,7,6,4]=>[1,4,1,1,1]
[1,2,3,8,4,7,6,5]=>[8,7,5,6,1,2,3,4]=>[1,2,4,3,8,7,6,5]=>[3,2,1,1,1]
[1,2,7,3,4,8,6,5]=>[8,7,4,5,1,2,3,6]=>[1,2,5,4,8,7,6,3]=>[3,2,1,1,1]
[1,2,6,3,8,4,7,5]=>[8,6,3,7,1,2,4,5]=>[1,3,6,2,8,7,5,4]=>[3,2,1,1,1]
[1,5,2,3,8,7,4,6]=>[7,2,8,6,1,3,4,5]=>[2,7,1,3,8,6,5,4]=>[2,3,1,1,1]
[4,2,1,8,3,7,5,6]=>[7,1,8,2,5,6,3,4]=>[2,8,1,7,4,3,6,5]=>[2,2,1,2,1]
[1,8,4,2,7,3,5,6]=>[6,3,7,8,4,5,1,2]=>[3,6,2,1,5,4,8,7]=>[2,1,2,2,1]
[1,2,8,6,3,4,7,5]=>[8,5,6,4,7,1,2,3]=>[1,4,3,5,2,8,7,6]=>[2,2,2,1,1]
[1,2,7,3,8,4,6,5]=>[8,6,7,4,1,2,3,5]=>[1,3,2,5,8,7,6,4]=>[2,3,1,1,1]
[1,2,3,8,7,4,6,5]=>[8,6,7,5,1,2,3,4]=>[1,3,2,4,8,7,6,5]=>[2,3,1,1,1]
[1,2,3,8,7,6,4,5]=>[7,8,6,5,1,2,3,4]=>[2,1,3,4,8,7,6,5]=>[1,4,1,1,1]
[2,5,3,8,1,6,4,7]=>[7,3,1,2,5,6,8,4]=>[2,6,8,7,4,3,1,5]=>[3,1,1,1,2]
[2,6,4,7,1,5,3,8]=>[3,7,5,1,2,6,4,8]=>[6,2,4,8,7,3,5,1]=>[1,3,1,2,1]
[2,6,5,7,1,4,3,8]=>[7,5,3,1,2,6,4,8]=>[2,4,6,8,7,3,5,1]=>[4,1,2,1]
[3,8,5,7,1,2,6,4]=>[8,5,1,3,6,7,4,2]=>[1,4,8,6,3,2,5,7]=>[3,1,1,3]
[3,8,5,7,2,6,4,1]=>[3,8,5,7,1,6,4,2]=>[6,1,4,2,8,3,5,7]=>[1,2,2,3]
[3,4,8,6,2,5,7,1]=>[5,6,1,2,4,8,7,3]=>[4,3,8,7,5,1,2,6]=>[1,2,1,1,3]
[3,4,8,6,1,2,5,7]=>[1,2,5,6,7,4,8,3]=>[8,7,4,3,2,5,1,6]=>[1,1,1,1,2,2]
[2,5,7,1,4,8,6,3]=>[2,8,5,7,1,4,3,6]=>[7,1,4,2,8,5,6,3]=>[1,2,2,2,1]
[2,4,8,1,5,7,6,3]=>[8,2,5,7,1,4,6,3]=>[1,7,4,2,8,5,3,6]=>[2,1,2,1,2]
[2,4,3,8,1,6,5,7]=>[2,7,1,3,5,6,8,4]=>[7,2,8,6,4,3,1,5]=>[1,2,1,1,1,2]
[2,8,1,7,5,6,4,3]=>[5,8,7,6,1,3,4,2]=>[4,1,2,3,8,6,5,7]=>[1,4,1,2]
[2,3,8,1,6,5,7,4]=>[6,5,8,1,2,4,7,3]=>[3,4,1,8,7,5,2,6]=>[2,2,1,1,2]
[2,4,8,1,3,5,7,6]=>[2,8,1,4,5,6,7,3]=>[7,1,8,5,4,3,2,6]=>[1,2,1,1,1,2]
[3,5,7,6,1,2,4,8]=>[5,1,2,6,7,4,3,8]=>[4,8,7,3,2,5,6,1]=>[2,1,1,3,1]
[3,5,7,6,2,4,8,1]=>[2,5,6,1,4,3,8,7]=>[7,4,3,8,5,6,1,2]=>[1,1,2,2,2]
[4,8,6,7,2,3,5,1]=>[5,6,1,3,8,7,4,2]=>[4,3,8,6,1,2,5,7]=>[1,2,1,4]
[4,8,6,7,1,3,5,2]=>[6,8,1,5,3,7,4,2]=>[3,1,8,4,6,2,5,7]=>[1,2,2,3]
[3,8,5,7,1,6,4,2]=>[3,8,7,1,5,6,4,2]=>[6,1,2,8,4,3,5,7]=>[1,3,1,3]
[3,2,8,5,6,1,7,4]=>[4,8,1,6,2,5,7,3]=>[5,1,8,3,7,4,2,6]=>[1,2,2,1,2]
[3,8,5,7,2,1,6,4]=>[5,3,8,1,6,7,4,2]=>[4,6,1,8,3,2,5,7]=>[2,2,1,3]
[3,5,7,6,2,1,4,8]=>[2,6,1,5,7,4,3,8]=>[7,3,8,4,2,5,6,1]=>[1,2,1,3,1]
[4,8,6,7,2,1,3,5]=>[6,1,5,7,3,8,4,2]=>[3,8,4,2,6,1,5,7]=>[2,1,2,3]
[4,8,6,7,3,5,2,1]=>[5,3,8,1,7,6,4,2]=>[4,6,1,8,2,3,5,7]=>[2,2,4]
[5,8,6,7,3,4,2,1]=>[5,1,3,8,7,6,4,2]=>[4,8,6,1,2,3,5,7]=>[2,1,5]
[5,8,6,7,2,1,4,3]=>[1,5,8,6,3,7,4,2]=>[8,4,1,3,6,2,5,7]=>[1,1,3,3]
[4,8,6,7,2,1,5,3]=>[5,8,1,6,3,7,4,2]=>[4,1,8,3,6,2,5,7]=>[1,2,2,3]
[4,3,1,7,5,2,8,6]=>[2,1,5,8,6,3,4,7]=>[7,8,4,1,3,6,5,2]=>[2,1,3,1,1]
[4,3,2,8,5,1,7,6]=>[2,1,5,8,3,6,7,4]=>[7,8,4,1,6,3,2,5]=>[2,1,2,1,2]
[4,3,8,5,1,6,7,2]=>[1,6,2,4,8,5,7,3]=>[8,3,7,5,1,4,2,6]=>[1,2,1,2,2]
[4,8,6,7,1,5,3,2]=>[8,7,1,5,3,6,4,2]=>[1,2,8,4,6,3,5,7]=>[3,2,3]
[5,8,6,7,1,4,3,2]=>[8,1,7,5,3,6,4,2]=>[1,8,2,4,6,3,5,7]=>[2,3,3]
[5,8,6,7,2,4,3,1]=>[8,1,5,3,7,6,4,2]=>[1,8,4,6,2,3,5,7]=>[2,2,4]
[5,8,6,7,1,2,4,3]=>[1,8,5,6,3,7,4,2]=>[8,1,4,3,6,2,5,7]=>[1,2,2,3]
[4,2,3,8,5,1,6,7]=>[6,2,1,3,5,7,8,4]=>[3,7,8,6,4,2,1,5]=>[3,1,1,1,2]
[4,2,8,5,1,7,6,3]=>[1,4,8,7,2,5,6,3]=>[8,5,1,2,7,4,3,6]=>[1,1,3,1,2]
[3,4,2,8,5,6,1,7]=>[1,2,5,7,3,6,8,4]=>[8,7,4,2,6,3,1,5]=>[1,1,1,2,1,2]
[3,2,4,8,6,1,5,7]=>[1,6,7,2,3,5,8,4]=>[8,3,2,7,6,4,1,5]=>[1,1,2,1,1,2]
[3,2,5,7,6,1,4,8]=>[1,3,6,7,2,5,4,8]=>[8,6,3,2,7,4,5,1]=>[1,1,1,2,2,1]
[4,8,6,7,1,3,2,5]=>[7,1,5,6,3,8,4,2]=>[2,8,4,3,6,1,5,7]=>[2,1,2,3]
[4,8,6,7,1,2,5,3]=>[8,1,5,6,3,7,4,2]=>[1,8,4,3,6,2,5,7]=>[2,1,2,3]
[4,8,6,7,2,5,3,1]=>[8,5,1,3,7,6,4,2]=>[1,4,8,6,2,3,5,7]=>[3,1,4]
[4,3,8,5,1,2,6,7]=>[2,1,5,6,4,7,8,3]=>[7,8,4,3,5,2,1,6]=>[2,1,2,1,2]
[4,2,6,7,5,1,3,8]=>[1,6,3,7,2,5,4,8]=>[8,3,6,2,7,4,5,1]=>[1,2,2,2,1]
[3,8,5,7,1,4,2,6]=>[7,5,1,3,6,8,4,2]=>[2,4,8,6,3,1,5,7]=>[3,1,1,3]
[3,8,4,7,1,5,2,6]=>[3,7,1,5,6,8,4,2]=>[6,2,8,4,3,1,5,7]=>[1,2,1,1,3]
[3,5,2,8,4,6,1,7]=>[5,1,2,7,3,6,8,4]=>[4,8,7,2,6,3,1,5]=>[2,1,2,1,2]
[3,8,4,7,2,5,1,6]=>[3,5,7,1,6,8,4,2]=>[6,4,2,8,3,1,5,7]=>[1,1,2,1,3]
[4,1,2,6,7,5,3,8]=>[4,1,7,6,2,3,5,8]=>[5,8,2,3,7,6,4,1]=>[2,3,1,1,1]
[4,2,6,7,5,3,8,1]=>[1,3,6,5,2,4,8,7]=>[8,6,3,4,7,5,1,2]=>[1,1,3,1,2]
[4,8,6,7,3,2,5,1]=>[6,5,1,3,8,7,4,2]=>[3,4,8,6,1,2,5,7]=>[3,1,4]
[3,1,5,7,6,2,4,8]=>[1,3,6,7,5,2,4,8]=>[8,6,3,2,4,7,5,1]=>[1,1,1,3,1,1]
[3,4,1,7,5,6,2,8]=>[1,2,5,7,6,3,4,8]=>[8,7,4,2,3,6,5,1]=>[1,1,1,3,1,1]
[4,1,6,7,5,2,3,8]=>[1,6,3,7,5,2,4,8]=>[8,3,6,2,4,7,5,1]=>[1,2,3,1,1]
[4,8,6,7,2,3,1,5]=>[5,7,1,6,3,8,4,2]=>[4,2,8,3,6,1,5,7]=>[1,2,2,3]
[5,8,6,7,3,2,4,1]=>[6,1,5,3,8,7,4,2]=>[3,8,4,6,1,2,5,7]=>[2,2,4]
[5,8,6,7,4,2,3,1]=>[6,1,3,8,7,5,4,2]=>[3,8,6,1,2,4,5,7]=>[2,1,5]
[5,8,6,7,4,1,2,3]=>[1,6,7,3,8,5,4,2]=>[8,3,2,6,1,4,5,7]=>[1,1,2,4]
[5,8,6,7,4,1,3,2]=>[8,1,6,3,7,5,4,2]=>[1,8,3,6,2,4,5,7]=>[2,2,4]
[4,8,6,7,3,1,5,2]=>[8,6,1,5,3,7,4,2]=>[1,3,8,4,6,2,5,7]=>[3,2,3]
[4,1,6,7,5,3,8,2]=>[1,3,6,5,4,8,2,7]=>[8,6,3,4,5,1,7,2]=>[1,1,3,2,1]
[4,1,7,5,3,2,8,6]=>[1,5,4,8,6,2,3,7]=>[8,4,5,1,3,7,6,2]=>[1,2,3,1,1]
[4,2,8,5,3,1,7,6]=>[1,5,4,8,2,6,7,3]=>[8,4,5,1,7,3,2,6]=>[1,2,2,1,2]
[4,2,1,6,7,5,3,8]=>[4,1,7,2,6,3,5,8]=>[5,8,2,7,3,6,4,1]=>[2,2,2,1,1]
[4,8,6,7,3,2,1,5]=>[7,6,1,5,3,8,4,2]=>[2,3,8,4,6,1,5,7]=>[3,2,3]
[5,8,6,7,4,2,1,3]=>[7,1,6,3,8,5,4,2]=>[2,8,3,6,1,4,5,7]=>[2,2,4]
[5,8,6,7,4,3,1,2]=>[7,1,3,8,6,5,4,2]=>[2,8,6,1,3,4,5,7]=>[2,1,5]
[7,3,5,8,1,4,2,6]=>[7,2,5,3,6,1,8,4]=>[2,7,4,6,3,8,1,5]=>[2,2,2,2]
[3,8,7,6,1,4,2,5]=>[7,5,6,8,1,4,3,2]=>[2,4,3,1,8,5,6,7]=>[2,1,2,3]
[5,1,8,3,6,7,2,4]=>[7,4,1,5,8,6,2,3]=>[2,5,8,4,1,3,7,6]=>[3,1,3,1]
[1,4,7,8,5,6,2,3]=>[7,5,2,3,8,6,1,4]=>[2,4,7,6,1,3,8,5]=>[3,1,3,1]
[3,4,7,1,5,8,6,2]=>[8,1,2,5,7,4,3,6]=>[1,8,7,4,2,5,6,3]=>[2,1,1,3,1]
[3,6,1,4,7,8,5,2]=>[5,8,1,4,2,7,3,6]=>[4,1,8,5,7,2,6,3]=>[1,2,2,2,1]
[1,6,8,4,7,5,2,3]=>[4,2,7,8,6,5,1,3]=>[5,7,2,1,3,4,8,6]=>[2,1,4,1]
[6,8,1,3,5,7,2,4]=>[7,4,5,1,8,3,6,2]=>[2,5,4,8,1,6,3,7]=>[2,2,2,2]
[7,6,1,4,3,8,2,5]=>[5,4,7,8,3,2,1,6]=>[4,5,2,1,6,7,8,3]=>[2,1,4,1]
[3,8,1,6,5,4,2,7]=>[7,6,1,5,3,4,8,2]=>[2,3,8,4,6,5,1,7]=>[3,2,1,2]
[4,1,3,7,5,8,2,6]=>[5,1,7,3,4,8,2,6]=>[4,8,2,6,5,1,7,3]=>[2,2,1,2,1]
[6,1,7,3,8,4,2,5]=>[7,4,6,3,1,8,2,5]=>[2,5,3,6,8,1,7,4]=>[2,3,2,1]
[7,1,8,6,3,5,2,4]=>[5,7,8,6,4,2,1,3]=>[4,2,1,3,5,7,8,6]=>[1,1,5,1]
[3,1,7,6,5,8,4,2]=>[5,4,1,3,8,7,2,6]=>[4,5,8,6,1,2,7,3]=>[3,1,3,1]
[8,2,7,6,5,3,4,1]=>[6,8,7,5,2,4,3,1]=>[3,1,2,4,7,5,6,8]=>[1,4,3]
[8,4,2,6,7,5,3,1]=>[2,4,8,7,3,6,5,1]=>[7,5,1,2,6,3,4,8]=>[1,1,3,3]
[4,8,1,6,7,5,3,2]=>[4,8,1,7,6,3,5,2]=>[5,1,8,2,3,6,4,7]=>[1,2,3,2]
[7,4,1,6,8,2,5,3]=>[2,8,6,4,7,3,1,5]=>[7,1,3,5,2,6,8,4]=>[1,3,3,1]
[1,3,8,6,2,7,5,4]=>[8,7,5,2,4,6,1,3]=>[1,2,4,7,5,3,8,6]=>[4,1,2,1]
[6,1,3,2,7,8,4,5]=>[7,3,5,8,2,1,4,6]=>[2,6,4,1,7,8,5,3]=>[2,1,3,1,1]
[1,8,6,2,5,3,4,7]=>[6,7,4,5,3,8,1,2]=>[3,2,5,4,6,1,8,7]=>[1,2,2,2,1]
[4,7,2,6,8,1,5,3]=>[8,1,6,3,4,2,7,5]=>[1,8,3,6,5,7,2,4]=>[2,2,2,2]
[8,7,3,6,4,5,2,1]=>[5,8,3,7,6,4,2,1]=>[4,1,6,2,3,5,7,8]=>[1,2,5]
[5,7,8,6,2,1,4,3]=>[1,5,8,6,2,7,4,3]=>[8,4,1,3,7,2,5,6]=>[1,1,3,3]
[2,7,4,1,6,8,3,5]=>[3,7,5,8,1,4,2,6]=>[6,2,4,1,8,5,7,3]=>[1,2,2,2,1]
[3,7,2,4,5,1,6,8]=>[1,3,4,6,5,7,2,8]=>[8,6,5,3,4,2,7,1]=>[1,1,1,2,2,1]
[1,8,6,4,5,2,3,7]=>[6,4,7,5,3,8,1,2]=>[3,5,2,4,6,1,8,7]=>[2,3,2,1]
[2,8,4,6,5,1,3,7]=>[3,6,7,5,1,4,8,2]=>[6,3,2,4,8,5,1,7]=>[1,1,3,1,2]
[3,4,1,7,5,2,6,8]=>[1,2,6,5,7,3,4,8]=>[8,7,3,4,2,6,5,1]=>[1,1,2,2,1,1]
[5,6,8,7,3,1,4,2]=>[1,2,8,6,5,7,4,3]=>[8,7,1,3,4,2,5,6]=>[1,1,3,3]
[2,5,4,3,6,8,1,7]=>[4,3,1,2,5,7,8,6]=>[5,6,8,7,4,2,1,3]=>[3,1,1,1,2]
[3,8,5,4,6,2,1,7]=>[4,3,7,1,6,5,8,2]=>[5,6,2,8,3,4,1,7]=>[2,2,2,2]
[4,8,2,1,3,7,5,6]=>[3,1,7,8,4,5,6,2]=>[6,8,2,1,5,4,3,7]=>[2,1,2,1,2]
[6,4,1,2,7,5,8,3]=>[6,5,2,8,3,1,4,7]=>[3,4,7,1,6,8,5,2]=>[3,3,1,1]
[4,1,8,3,6,7,5,2]=>[1,5,8,4,7,6,2,3]=>[8,4,1,5,2,3,7,6]=>[1,1,2,3,1]
[8,3,7,4,5,2,6,1]=>[4,6,2,5,8,7,3,1]=>[5,3,7,4,1,2,6,8]=>[1,2,1,4]
[4,3,7,8,5,1,6,2]=>[8,1,6,2,5,3,7,4]=>[1,8,3,7,4,6,2,5]=>[2,2,2,2]
[5,4,8,2,7,6,1,3]=>[2,1,7,8,4,6,5,3]=>[7,8,2,1,5,3,4,6]=>[2,1,2,3]
[1,2,7,3,6,5,8,4]=>[6,5,8,4,1,2,3,7]=>[3,4,1,5,8,7,6,2]=>[2,3,1,1,1]
[2,8,7,6,3,4,1,5]=>[5,7,6,8,4,1,3,2]=>[4,2,3,1,5,8,6,7]=>[1,2,3,2]
[5,8,2,6,3,4,1,7]=>[5,1,7,3,6,4,8,2]=>[4,8,2,6,3,5,1,7]=>[2,2,2,2]
[4,1,7,5,8,6,2,3]=>[1,4,7,3,8,6,2,5]=>[8,5,2,6,1,3,7,4]=>[1,1,2,3,1]
[8,2,7,5,4,3,6,1]=>[6,5,4,8,2,7,3,1]=>[3,4,5,1,7,2,6,8]=>[3,2,3]
[6,3,8,1,4,7,5,2]=>[8,2,5,1,7,4,6,3]=>[1,7,4,8,2,5,3,6]=>[2,2,2,2]
[1,4,3,5,7,8,2,6]=>[2,7,3,4,5,8,1,6]=>[7,2,6,5,4,1,8,3]=>[1,2,1,1,2,1]
[3,6,7,2,4,8,1,5]=>[4,5,1,2,7,3,8,6]=>[5,4,8,7,2,6,1,3]=>[1,2,1,2,2]
[1,5,2,7,4,3,8,6]=>[5,2,8,6,1,3,4,7]=>[4,7,1,3,8,6,5,2]=>[2,3,1,1,1]
[2,8,5,6,4,3,1,7]=>[3,7,6,5,1,4,8,2]=>[6,2,3,4,8,5,1,7]=>[1,4,1,2]
[1,8,6,5,4,3,2,7]=>[7,6,5,4,3,8,1,2]=>[2,3,4,5,6,1,8,7]=>[5,2,1]
[6,1,5,2,8,4,7,3]=>[6,3,8,7,2,1,4,5]=>[3,6,1,2,7,8,5,4]=>[2,4,1,1]
[4,6,1,8,5,7,2,3]=>[7,1,5,2,8,6,3,4]=>[2,8,4,7,1,3,6,5]=>[2,2,3,1]
[1,4,7,2,8,5,6,3]=>[6,8,2,7,4,1,3,5]=>[3,1,7,2,5,8,6,4]=>[1,2,3,1,1]
[7,3,5,8,6,1,2,4]=>[6,2,3,7,1,8,5,4]=>[3,7,6,2,8,1,4,5]=>[2,1,2,3]
[3,6,8,1,5,7,2,4]=>[7,5,1,2,8,4,6,3]=>[2,4,8,7,1,5,3,6]=>[3,1,2,2]
[3,4,6,5,8,1,7,2]=>[4,1,2,3,8,6,7,5]=>[5,8,7,6,1,3,2,4]=>[2,1,1,2,2]
[7,1,2,5,8,6,3,4]=>[4,7,8,6,2,3,1,5]=>[5,2,1,3,7,6,8,4]=>[1,1,3,2,1]
[1,7,2,5,8,6,3,4]=>[4,7,8,6,3,1,2,5]=>[5,2,1,3,6,8,7,4]=>[1,1,4,1,1]
[1,7,6,8,2,3,5,4]=>[8,5,6,3,2,7,1,4]=>[1,4,3,6,7,2,8,5]=>[2,3,2,1]
[7,6,8,1,2,3,5,4]=>[8,4,5,6,2,1,7,3]=>[1,5,4,3,7,8,2,6]=>[2,1,3,2]
[2,4,7,1,8,5,6,3]=>[6,8,2,7,1,4,3,5]=>[3,1,7,2,8,5,6,4]=>[1,2,2,2,1]
[4,7,5,8,3,1,6,2]=>[3,8,1,6,5,2,7,4]=>[6,1,8,3,4,7,2,5]=>[1,2,3,2]
[4,7,2,1,8,5,6,3]=>[1,6,8,3,7,4,2,5]=>[8,3,1,6,2,5,7,4]=>[1,1,2,3,1]
[7,6,8,2,1,3,5,4]=>[4,8,5,6,2,1,7,3]=>[5,1,4,3,7,8,2,6]=>[1,2,3,2]
[1,2,7,6,8,3,5,4]=>[8,6,4,3,7,1,2,5]=>[1,3,5,6,2,8,7,4]=>[4,2,1,1]
[7,4,2,1,6,8,5,3]=>[5,2,8,3,7,4,1,6]=>[4,7,1,6,2,5,8,3]=>[2,2,3,1]
[6,7,4,1,8,5,3,2]=>[3,1,8,7,6,4,2,5]=>[6,8,1,2,3,5,7,4]=>[2,5,1]
[6,7,4,3,1,8,5,2]=>[4,3,1,8,7,5,2,6]=>[5,6,8,1,2,4,7,3]=>[3,4,1]
[2,7,4,1,6,8,5,3]=>[3,5,8,7,1,4,2,6]=>[6,4,1,2,8,5,7,3]=>[1,1,3,2,1]
[2,3,7,6,8,1,5,4]=>[8,6,4,1,2,3,7,5]=>[1,3,5,8,7,6,2,4]=>[4,1,1,2]
[7,4,2,6,8,5,1,3]=>[2,7,4,8,3,1,6,5]=>[7,2,5,1,6,8,3,4]=>[1,2,3,2]
[7,3,2,5,8,6,1,4]=>[2,4,7,8,3,1,6,5]=>[7,5,2,1,6,8,3,4]=>[1,1,1,3,2]
[3,1,7,6,8,2,5,4]=>[8,6,1,4,3,7,2,5]=>[1,3,8,5,6,2,7,4]=>[3,2,2,1]
[1,3,7,6,8,2,5,4]=>[8,6,4,2,3,7,1,5]=>[1,3,5,7,6,2,8,4]=>[4,1,2,1]
[1,7,4,2,6,8,5,3]=>[3,5,8,7,4,1,2,6]=>[6,4,1,2,5,8,7,3]=>[1,1,4,1,1]
[7,4,1,2,6,8,5,3]=>[5,2,8,7,3,4,1,6]=>[4,7,1,2,6,5,8,3]=>[2,3,2,1]
[7,1,4,2,8,5,6,3]=>[3,6,8,7,2,4,1,5]=>[6,3,1,2,7,5,8,4]=>[1,1,3,2,1]
[7,1,8,2,5,4,6,3]=>[6,5,8,4,7,2,1,3]=>[3,4,1,5,2,7,8,6]=>[2,2,3,1]
[7,3,8,4,6,1,5,2]=>[4,8,2,6,1,7,5,3]=>[5,1,7,3,8,2,4,6]=>[1,2,2,3]
[7,2,8,1,6,4,5,3]=>[6,8,7,2,4,1,5,3]=>[3,1,2,7,5,8,4,6]=>[1,3,2,2]
[7,1,6,8,5,4,2,3]=>[7,3,8,6,5,2,1,4]=>[2,6,1,3,4,7,8,5]=>[2,5,1]
[7,1,2,6,8,5,4,3]=>[4,8,7,6,2,3,1,5]=>[5,1,2,3,7,6,8,4]=>[1,4,2,1]
[1,7,2,6,8,5,4,3]=>[4,8,7,6,3,1,2,5]=>[5,1,2,3,6,8,7,4]=>[1,5,1,1]
[1,7,6,8,3,2,5,4]=>[5,8,6,3,2,7,1,4]=>[4,1,3,6,7,2,8,5]=>[1,4,2,1]
[7,6,8,3,1,2,5,4]=>[8,5,4,6,2,1,7,3]=>[1,4,5,3,7,8,2,6]=>[3,3,2]
[7,1,5,8,6,3,2,4]=>[3,7,6,8,5,2,1,4]=>[6,2,3,1,4,7,8,5]=>[1,2,4,1]
[7,2,5,8,6,3,1,4]=>[3,7,6,8,2,1,5,4]=>[6,2,3,1,7,8,4,5]=>[1,2,3,2]
[3,6,7,1,8,5,4,2]=>[2,8,7,1,6,4,3,5]=>[7,1,2,8,3,5,6,4]=>[1,3,3,1]
[7,2,6,8,5,4,1,3]=>[7,3,8,6,2,1,5,4]=>[2,6,1,3,7,8,4,5]=>[2,4,2]
[7,6,8,2,3,1,5,4]=>[4,5,8,6,2,1,7,3]=>[5,4,1,3,7,8,2,6]=>[1,1,4,2]
[2,7,1,6,8,5,4,3]=>[4,8,7,6,1,3,2,5]=>[5,1,2,3,8,6,7,4]=>[1,4,2,1]
[6,7,3,1,8,5,4,2]=>[8,3,1,7,6,4,2,5]=>[1,6,8,2,3,5,7,4]=>[3,4,1]
[6,7,1,8,5,4,3,2]=>[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>[1,6,1]
[7,2,1,6,8,5,4,3]=>[4,8,7,2,6,3,1,5]=>[5,1,2,7,3,6,8,4]=>[1,3,3,1]
[7,6,8,3,2,1,5,4]=>[5,4,8,6,2,1,7,3]=>[4,5,1,3,7,8,2,6]=>[2,4,2]
[4,6,5,8,7,1,3,2]=>[3,1,2,8,6,7,5,4]=>[6,8,7,1,3,2,4,5]=>[2,1,2,3]
[5,6,4,8,1,2,7,3]=>[1,8,5,3,2,6,7,4]=>[8,1,4,6,7,3,2,5]=>[1,4,1,2]
[6,4,5,1,8,2,7,3]=>[2,8,6,3,1,7,4,5]=>[7,1,3,6,8,2,5,4]=>[1,4,2,1]
[5,4,6,7,1,2,8,3]=>[2,1,8,5,3,6,4,7]=>[7,8,1,4,6,3,5,2]=>[2,3,2,1]
[4,3,6,7,2,1,5,8]=>[1,6,2,5,3,7,4,8]=>[8,3,7,4,6,2,5,1]=>[1,2,2,2,1]
[5,3,6,7,1,4,2,8]=>[7,2,1,5,3,6,4,8]=>[2,7,8,4,6,3,5,1]=>[3,2,2,1]
[8,1,4,6,7,3,2,5]=>[7,3,6,4,8,2,5,1]=>[2,6,3,5,1,7,4,8]=>[2,2,2,2]
[8,1,3,6,7,4,5,2]=>[6,4,8,3,7,2,5,1]=>[3,5,1,6,2,7,4,8]=>[2,2,2,2]
[7,2,1,6,8,4,5,3]=>[6,4,8,2,7,3,1,5]=>[3,5,1,7,2,6,8,4]=>[2,2,3,1]
[5,2,6,7,1,4,8,3]=>[6,3,1,8,2,5,4,7]=>[3,6,8,1,7,4,5,2]=>[3,2,2,1]
[4,2,6,7,3,1,8,5]=>[1,5,3,8,2,6,4,7]=>[8,4,6,1,7,3,5,2]=>[1,2,2,2,1]
[6,2,4,1,5,8,7,3]=>[3,8,2,5,1,7,4,6]=>[6,1,7,4,8,2,5,3]=>[1,2,2,2,1]
[7,2,1,5,4,8,6,3]=>[4,8,2,5,7,3,1,6]=>[5,1,7,4,2,6,8,3]=>[1,2,1,3,1]
[7,3,1,5,4,8,2,6]=>[2,5,4,7,8,3,1,6]=>[7,4,5,2,1,6,8,3]=>[1,2,1,3,1]
[6,3,4,1,5,8,2,7]=>[2,5,3,7,1,8,4,6]=>[7,4,6,2,8,1,5,3]=>[1,2,2,2,1]
[5,3,4,2,1,8,6,7]=>[2,4,3,1,7,8,5,6]=>[7,5,6,8,2,1,4,3]=>[1,3,1,2,1]
[4,3,5,2,7,1,6,8]=>[2,1,4,3,6,7,5,8]=>[7,8,5,6,3,2,4,1]=>[2,2,1,2,1]
[5,6,3,8,1,4,2,7]=>[3,1,7,5,2,6,8,4]=>[6,8,2,4,7,3,1,5]=>[2,3,1,2]
[8,1,7,2,4,5,6,3]=>[5,6,8,4,7,2,3,1]=>[4,3,1,5,2,7,6,8]=>[1,1,2,2,2]
[7,6,1,2,4,5,8,3]=>[5,6,8,3,4,2,1,7]=>[4,3,1,6,5,7,8,2]=>[1,1,2,3,1]
[4,7,8,2,3,1,6,5]=>[1,4,5,8,6,2,7,3]=>[8,5,4,1,3,7,2,6]=>[1,1,1,3,2]
[5,6,2,8,1,4,7,3]=>[6,1,8,3,2,5,7,4]=>[3,8,1,6,7,4,2,5]=>[2,3,1,2]
[6,5,2,1,3,7,8,4]=>[3,6,8,4,2,1,5,7]=>[6,3,1,5,7,8,4,2]=>[1,1,4,1,1]
[7,5,1,3,2,6,8,4]=>[4,6,8,3,2,5,1,7]=>[5,3,1,6,7,4,8,2]=>[1,1,3,2,1]
[8,1,6,3,2,5,7,4]=>[4,6,8,5,2,3,7,1]=>[5,3,1,4,7,6,2,8]=>[1,1,3,1,2]
[5,4,2,3,1,6,8,7]=>[3,4,2,1,8,5,6,7]=>[6,5,7,8,1,4,3,2]=>[1,3,2,1,1]
[7,3,1,4,5,6,2,8]=>[4,2,5,7,3,6,1,8]=>[5,7,4,2,6,3,8,1]=>[2,1,2,2,1]
[8,1,4,3,5,6,2,7]=>[4,3,5,7,2,6,8,1]=>[5,6,4,2,7,3,1,8]=>[2,1,2,1,2]
[6,2,3,1,5,7,8,4]=>[2,3,5,6,1,8,4,7]=>[7,6,4,3,8,1,5,2]=>[1,1,1,2,2,1]
[7,8,4,2,1,6,5,3]=>[8,4,3,7,5,1,6,2]=>[1,5,6,2,4,8,3,7]=>[3,3,2]
[7,8,4,2,1,5,6,3]=>[4,6,3,8,5,1,7,2]=>[5,3,6,1,4,8,2,7]=>[1,2,3,2]
[6,2,3,4,8,7,1,5]=>[7,8,2,3,1,4,6,5]=>[2,1,7,6,8,5,3,4]=>[1,2,2,1,2]
[6,2,3,4,7,8,1,5]=>[7,2,3,4,1,5,8,6]=>[2,7,6,5,8,4,1,3]=>[2,1,2,1,2]
[7,8,3,4,6,2,1,5]=>[3,4,7,6,1,8,5,2]=>[6,5,2,3,8,1,4,7]=>[1,1,3,3]
[7,8,3,6,4,2,1,5]=>[7,3,6,5,1,8,4,2]=>[2,6,3,4,8,1,5,7]=>[2,3,3]
[6,2,3,8,7,5,1,4]=>[7,8,6,2,1,3,5,4]=>[2,1,3,7,8,6,4,5]=>[1,4,1,2]
[6,2,3,7,8,5,1,4]=>[7,4,8,2,1,3,6,5]=>[2,5,1,7,8,6,3,4]=>[2,3,1,2]
[5,2,6,3,8,1,7,4]=>[8,4,2,1,3,6,7,5]=>[1,5,7,8,6,3,2,4]=>[4,1,1,2]
[6,3,2,5,8,7,1,4]=>[2,4,7,1,8,3,6,5]=>[7,5,2,8,1,6,3,4]=>[1,1,2,2,2]
[6,3,2,8,4,7,1,5]=>[2,5,7,1,8,3,6,4]=>[7,4,2,8,1,6,3,5]=>[1,1,2,2,2]
[6,4,3,8,7,5,1,2]=>[2,7,1,8,3,6,5,4]=>[7,2,8,1,6,3,4,5]=>[1,2,2,3]
[6,4,3,7,8,5,1,2]=>[2,7,3,1,4,8,6,5]=>[7,2,6,8,5,1,3,4]=>[1,3,1,3]
[6,2,4,1,7,3,5,8]=>[6,2,3,7,4,1,5,8]=>[3,7,6,2,5,8,4,1]=>[2,1,3,1,1]
[6,3,2,7,4,8,1,5]=>[2,5,7,3,1,4,8,6]=>[7,4,2,6,8,5,1,3]=>[1,1,3,1,2]
[6,3,2,5,7,8,1,4]=>[2,4,7,3,1,5,8,6]=>[7,5,2,6,8,4,1,3]=>[1,1,3,1,2]
[5,7,2,3,6,1,8,4]=>[8,3,1,4,6,5,2,7]=>[1,6,8,5,3,4,7,2]=>[3,1,3,1]
[4,7,5,8,3,2,1,6]=>[3,7,1,6,5,2,8,4]=>[6,2,8,3,4,7,1,5]=>[1,2,3,2]
[4,5,6,8,3,2,1,7]=>[1,2,3,7,6,5,8,4]=>[8,7,6,2,3,4,1,5]=>[1,1,1,3,2]
[4,6,8,5,3,2,1,7]=>[2,7,1,6,5,4,8,3]=>[7,2,8,3,4,5,1,6]=>[1,2,3,2]
[5,6,1,4,2,3,7,8]=>[5,6,3,1,4,2,7,8]=>[4,3,6,8,5,7,2,1]=>[1,3,2,1,1]
[5,6,8,4,3,7,1,2]=>[1,2,7,5,4,8,6,3]=>[8,7,2,4,5,1,3,6]=>[1,1,3,3]
[5,6,1,4,2,3,8,7]=>[8,5,3,1,4,2,6,7]=>[1,4,6,8,5,7,3,2]=>[4,2,1,1]
[4,5,8,6,3,2,1,7]=>[7,1,2,6,5,4,8,3]=>[2,8,7,3,4,5,1,6]=>[2,1,3,2]
[4,6,5,8,3,2,1,7]=>[3,1,2,7,6,5,8,4]=>[6,8,7,2,3,4,1,5]=>[2,1,3,2]
[4,7,5,6,3,2,1,8]=>[3,7,1,6,5,4,2,8]=>[6,2,8,3,4,5,7,1]=>[1,2,4,1]
[6,2,3,4,5,8,1,7]=>[2,3,4,5,1,7,8,6]=>[7,6,5,4,8,2,1,3]=>[1,1,1,2,1,2]
[5,1,4,3,7,2,8,6]=>[3,8,4,1,6,2,5,7]=>[6,1,5,8,3,7,4,2]=>[1,3,2,1,1]
[5,1,4,3,8,2,7,6]=>[3,8,4,1,6,7,2,5]=>[6,1,5,8,3,2,7,4]=>[1,3,1,2,1]
[5,6,2,4,1,8,7,3]=>[4,1,8,3,2,7,5,6]=>[5,8,1,6,7,2,4,3]=>[2,3,2,1]
[5,7,2,4,1,8,6,3]=>[4,1,8,3,7,5,2,6]=>[5,8,1,6,2,4,7,3]=>[2,2,3,1]
[6,1,4,2,8,7,5,3]=>[8,3,7,6,2,1,4,5]=>[1,6,2,3,7,8,5,4]=>[2,4,1,1]
[6,1,4,2,7,8,5,3]=>[3,5,8,7,2,1,4,6]=>[6,4,1,2,7,8,5,3]=>[1,1,4,1,1]
[5,8,2,4,1,7,6,3]=>[4,1,8,3,7,5,6,2]=>[5,8,1,6,2,4,3,7]=>[2,2,2,2]
[5,2,7,4,1,6,8,3]=>[6,4,1,8,2,5,3,7]=>[3,5,8,1,7,4,6,2]=>[3,2,2,1]
[5,4,1,3,7,2,6,8]=>[4,6,2,1,7,3,5,8]=>[5,3,7,8,2,6,4,1]=>[1,3,2,1,1]
[5,1,4,3,6,2,7,8]=>[4,3,6,2,1,5,7,8]=>[5,6,3,7,8,4,2,1]=>[2,3,1,1,1]
[5,8,6,4,3,7,1,2]=>[7,1,5,4,3,8,6,2]=>[2,8,4,5,6,1,3,7]=>[2,3,3]
[5,8,1,4,2,3,7,6]=>[8,5,3,1,4,6,7,2]=>[1,4,6,8,5,3,2,7]=>[4,1,1,2]
[5,1,6,3,4,2,7,8]=>[4,6,5,2,1,3,7,8]=>[5,3,4,7,8,6,2,1]=>[1,4,1,1,1]
[4,8,6,5,3,2,1,7]=>[7,6,1,5,4,3,8,2]=>[2,3,8,4,5,6,1,7]=>[3,3,2]
[4,8,5,6,3,2,1,7]=>[3,7,1,6,5,4,8,2]=>[6,2,8,3,4,5,1,7]=>[1,2,3,2]
[5,4,7,8,3,2,1,6]=>[1,7,2,6,5,3,8,4]=>[8,2,7,3,4,6,1,5]=>[1,2,3,2]
[5,4,8,7,3,2,1,6]=>[1,7,2,6,5,8,4,3]=>[8,2,7,3,4,1,5,6]=>[1,2,2,3]
[4,6,8,7,3,2,1,5]=>[2,7,1,6,5,8,4,3]=>[7,2,8,3,4,1,5,6]=>[1,2,2,3]
[4,6,7,8,3,2,1,5]=>[2,7,1,6,5,3,8,4]=>[7,2,8,3,4,6,1,5]=>[1,2,3,2]
[4,7,6,8,3,2,1,5]=>[7,6,1,5,3,2,8,4]=>[2,3,8,4,6,7,1,5]=>[3,3,2]
[4,7,8,5,3,2,1,6]=>[7,6,1,5,4,2,8,3]=>[2,3,8,4,5,7,1,6]=>[3,3,2]
[5,7,1,3,4,2,6,8]=>[4,6,3,1,5,7,2,8]=>[5,3,6,8,4,2,7,1]=>[1,3,1,2,1]
[5,1,8,4,2,3,6,7]=>[5,6,4,1,7,8,2,3]=>[4,3,5,8,2,1,7,6]=>[1,3,1,2,1]
[4,8,7,5,3,2,1,6]=>[7,6,1,5,4,8,3,2]=>[2,3,8,4,5,1,6,7]=>[3,2,3]
[4,7,8,6,3,2,1,5]=>[7,6,1,5,2,8,4,3]=>[2,3,8,4,7,1,5,6]=>[3,2,3]
[4,8,7,6,3,2,1,5]=>[7,6,1,5,8,4,3,2]=>[2,3,8,4,1,5,6,7]=>[3,1,4]
[4,8,2,3,6,7,5,1]=>[1,5,8,3,4,7,6,2]=>[8,4,1,6,5,2,3,7]=>[1,1,2,1,3]
[4,8,3,1,6,7,5,2]=>[1,3,5,8,7,4,6,2]=>[8,6,4,1,2,5,3,7]=>[1,1,1,3,2]
[4,3,8,1,6,2,5,7]=>[2,1,6,7,4,5,8,3]=>[7,8,3,2,5,4,1,6]=>[2,1,2,1,2]
[1,4,8,7,3,5,2,6]=>[5,7,2,6,8,4,1,3]=>[4,2,7,3,1,5,8,6]=>[1,2,1,3,1]
[5,8,4,3,7,1,6,2]=>[1,4,3,8,6,7,5,2]=>[8,5,6,1,3,2,4,7]=>[1,2,2,3]
[5,8,1,4,7,2,6,3]=>[4,1,8,6,7,3,5,2]=>[5,8,1,3,2,6,4,7]=>[2,2,2,2]
[5,8,1,7,4,2,3,6]=>[6,1,7,5,8,3,4,2]=>[3,8,2,4,1,6,5,7]=>[2,2,2,2]
[6,8,1,2,4,3,5,7]=>[6,3,4,5,1,7,8,2]=>[3,6,5,4,8,2,1,7]=>[2,1,2,1,2]
[5,8,7,1,3,4,2,6]=>[5,1,7,4,6,8,3,2]=>[4,8,2,5,3,1,6,7]=>[2,2,1,3]
[4,8,7,6,3,1,2,5]=>[6,7,1,5,8,4,3,2]=>[3,2,8,4,1,5,6,7]=>[1,2,1,4]
[5,8,4,7,3,1,2,6]=>[1,6,3,7,5,8,4,2]=>[8,3,6,2,4,1,5,7]=>[1,2,2,3]
[1,4,8,3,7,5,6,2]=>[6,8,2,4,7,5,1,3]=>[3,1,7,5,2,4,8,6]=>[1,2,1,3,1]
[1,4,3,8,2,6,5,7]=>[2,7,3,5,6,8,1,4]=>[7,2,6,4,3,1,8,5]=>[1,2,1,1,2,1]
[4,1,3,8,2,6,5,7]=>[7,3,1,5,6,8,2,4]=>[2,6,8,4,3,1,7,5]=>[3,1,1,2,1]
[4,1,8,3,7,5,6,2]=>[1,6,8,4,7,5,2,3]=>[8,3,1,5,2,4,7,6]=>[1,1,2,3,1]
[4,1,8,7,3,5,2,6]=>[1,5,7,6,8,4,2,3]=>[8,4,2,3,1,5,7,6]=>[1,1,2,3,1]
[3,7,8,1,5,4,2,6]=>[7,6,1,4,5,2,8,3]=>[2,3,8,5,4,7,1,6]=>[3,1,2,2]
[7,3,8,1,5,4,6,2]=>[6,2,5,8,4,1,7,3]=>[3,7,4,1,5,8,2,6]=>[2,1,3,2]
[3,4,8,1,6,2,5,7]=>[1,2,6,7,4,5,8,3]=>[8,7,3,2,5,4,1,6]=>[1,1,1,2,1,2]
[3,4,8,7,2,5,1,6]=>[5,7,1,2,6,8,4,3]=>[4,2,8,7,3,1,5,6]=>[1,2,1,1,3]
[3,4,8,2,7,5,6,1]=>[6,8,1,2,4,7,5,3]=>[3,1,8,7,5,2,4,6]=>[1,2,1,1,3]
[1,2,4,8,3,6,5,7]=>[7,3,5,6,8,1,2,4]=>[2,6,4,3,1,8,7,5]=>[2,1,1,2,1,1]
[1,2,4,3,8,6,5,7]=>[7,3,6,8,1,2,4,5]=>[2,6,3,1,8,7,5,4]=>[2,1,2,1,1,1]
[3,4,1,8,2,6,5,7]=>[1,2,7,5,6,8,3,4]=>[8,7,2,4,3,1,6,5]=>[1,1,2,1,2,1]
[3,6,7,8,4,1,2,5]=>[6,2,7,1,5,3,8,4]=>[3,7,2,8,4,6,1,5]=>[2,2,2,2]
[4,1,7,8,5,3,2,6]=>[7,1,6,5,3,8,2,4]=>[2,8,3,4,6,1,7,5]=>[2,3,2,1]
[4,1,2,8,3,6,5,7]=>[7,5,1,6,8,2,3,4]=>[2,4,8,3,1,7,6,5]=>[3,1,2,1,1]
[1,4,3,2,8,6,5,7]=>[2,7,3,6,8,1,4,5]=>[7,2,6,3,1,8,5,4]=>[1,2,1,2,1,1]
[4,2,3,1,8,6,5,7]=>[7,2,1,3,6,8,4,5]=>[2,7,8,6,3,1,5,4]=>[3,1,1,2,1]
[3,7,6,8,4,2,1,5]=>[7,6,5,1,3,2,8,4]=>[2,3,4,8,6,7,1,5]=>[4,2,2]
[4,7,1,8,5,2,3,6]=>[1,6,7,5,8,3,2,4]=>[8,3,2,4,1,6,7,5]=>[1,1,2,3,1]
[3,7,8,2,6,4,5,1]=>[6,8,4,1,2,7,5,3]=>[3,1,5,8,7,2,4,6]=>[1,3,1,3]
[4,2,3,8,1,6,5,7]=>[7,2,1,3,5,6,8,4]=>[2,7,8,6,4,3,1,5]=>[3,1,1,1,2]
[4,3,1,8,2,6,5,7]=>[2,1,7,5,6,8,3,4]=>[7,8,2,4,3,1,6,5]=>[2,2,1,2,1]
[1,4,7,8,5,3,2,6]=>[7,6,2,5,3,8,1,4]=>[2,3,7,4,6,1,8,5]=>[3,2,2,1]
[4,3,7,8,5,2,1,6]=>[7,1,6,2,5,3,8,4]=>[2,8,3,7,4,6,1,5]=>[2,2,2,2]
[3,7,2,8,4,6,5,1]=>[8,5,7,1,3,2,6,4]=>[1,4,2,8,6,7,3,5]=>[2,2,2,2]
[2,4,8,6,3,1,5,7]=>[6,2,5,7,1,4,8,3]=>[3,7,4,2,8,5,1,6]=>[2,1,2,1,2]
[7,3,6,8,4,2,1,5]=>[7,6,2,5,3,1,8,4]=>[2,3,7,4,6,8,1,5]=>[3,3,2]
[7,6,2,8,3,5,4,1]=>[8,5,7,3,2,1,6,4]=>[1,4,2,6,7,8,3,5]=>[2,4,2]
[1,7,3,8,4,6,5,2]=>[8,5,7,3,2,6,1,4]=>[1,4,2,6,7,3,8,5]=>[2,3,2,1]
[3,2,4,8,1,6,5,7]=>[1,7,2,3,5,6,8,4]=>[8,2,7,6,4,3,1,5]=>[1,2,1,1,1,2]
[7,3,8,2,6,4,5,1]=>[6,8,2,4,1,7,5,3]=>[3,1,7,5,8,2,4,6]=>[1,2,2,3]
[2,4,8,3,6,1,5,7]=>[2,4,6,7,1,5,8,3]=>[7,5,3,2,8,4,1,6]=>[1,1,1,2,1,2]
[7,4,1,8,5,2,6,3]=>[2,8,6,5,7,3,1,4]=>[7,1,3,4,2,6,8,5]=>[1,3,3,1]
[7,3,2,8,4,6,5,1]=>[8,2,5,7,3,1,6,4]=>[1,7,4,2,6,8,3,5]=>[2,1,3,2]
[2,4,3,1,8,6,5,7]=>[2,7,1,3,6,8,4,5]=>[7,2,8,6,3,1,5,4]=>[1,2,1,1,2,1]
[1,3,2,4,8,6,5,7]=>[7,2,6,8,1,3,4,5]=>[2,7,3,1,8,6,5,4]=>[2,1,2,1,1,1]
[3,2,1,4,8,6,5,7]=>[1,7,2,6,8,3,4,5]=>[8,2,7,3,1,6,5,4]=>[1,2,1,2,1,1]
[3,1,2,4,8,6,5,7]=>[1,7,6,8,2,3,4,5]=>[8,2,3,1,7,6,5,4]=>[1,2,2,1,1,1]
[3,1,4,8,2,6,5,7]=>[1,7,3,5,6,8,2,4]=>[8,2,6,4,3,1,7,5]=>[1,2,1,1,2,1]
[7,3,4,8,5,1,6,2]=>[8,2,3,6,5,1,7,4]=>[1,7,6,3,4,8,2,5]=>[2,1,3,2]
[3,7,4,8,5,1,2,6]=>[3,6,7,1,5,2,8,4]=>[6,3,2,8,4,7,1,5]=>[1,1,2,2,2]
[6,7,2,8,3,5,4,1]=>[8,5,1,7,3,2,6,4]=>[1,4,8,2,6,7,3,5]=>[3,3,2]
[2,3,1,4,8,6,5,7]=>[7,1,2,6,8,3,4,5]=>[2,8,7,3,1,6,5,4]=>[2,1,1,2,1,1]
[2,1,3,4,8,6,5,7]=>[7,1,6,8,2,3,4,5]=>[2,8,3,1,7,6,5,4]=>[2,1,2,1,1,1]
[1,2,3,4,8,6,5,7]=>[7,6,8,1,2,3,4,5]=>[2,3,1,8,7,6,5,4]=>[2,2,1,1,1,1]
[4,8,3,6,2,1,5,7]=>[1,3,6,5,7,4,8,2]=>[8,6,3,4,2,5,1,7]=>[1,1,2,2,2]
[3,5,8,2,6,1,4,7]=>[4,1,2,6,7,5,8,3]=>[5,8,7,3,2,4,1,6]=>[2,1,1,2,2]
[3,6,5,8,2,4,1,7]=>[5,3,1,2,7,6,8,4]=>[4,6,8,7,2,3,1,5]=>[3,1,2,2]
[5,3,8,7,2,4,6,1]=>[5,1,6,8,2,7,4,3]=>[4,8,3,1,7,2,5,6]=>[2,1,2,3]
[2,8,4,5,7,3,6,1]=>[3,4,6,8,7,1,5,2]=>[6,5,3,1,2,8,4,7]=>[1,1,1,3,2]
[2,4,5,7,3,8,1,6]=>[2,3,5,7,1,4,8,6]=>[7,6,4,2,8,5,1,3]=>[1,1,1,2,1,2]
[4,8,1,2,5,6,3,7]=>[5,1,7,3,4,6,8,2]=>[4,8,2,6,5,3,1,7]=>[2,2,1,1,2]
[8,1,3,5,2,6,4,7]=>[7,3,5,2,4,6,8,1]=>[2,6,4,7,5,3,1,8]=>[2,2,1,1,2]
[5,2,1,6,3,8,4,7]=>[7,2,4,1,8,3,5,6]=>[2,7,5,8,1,6,4,3]=>[2,2,2,1,1]
[6,2,5,1,8,4,3,7]=>[7,6,2,3,1,8,4,5]=>[2,3,7,6,8,1,5,4]=>[3,2,2,1]
[3,6,1,5,8,4,2,7]=>[4,7,1,6,2,8,3,5]=>[5,2,8,3,7,1,6,4]=>[1,2,2,2,1]
[6,1,4,5,8,3,2,7]=>[3,4,7,6,1,8,2,5]=>[6,5,2,3,8,1,7,4]=>[1,1,3,2,1]
[5,6,4,8,1,3,2,7]=>[1,7,5,3,2,6,8,4]=>[8,2,4,6,7,3,1,5]=>[1,4,1,2]
[6,5,4,3,8,2,1,7]=>[4,3,2,1,7,6,8,5]=>[5,6,7,8,2,3,1,4]=>[4,2,2]
[5,4,3,7,2,8,1,6]=>[3,2,1,5,7,4,8,6]=>[6,7,8,4,2,5,1,3]=>[3,1,2,2]
[5,8,4,3,7,2,6,1]=>[1,4,3,6,8,7,5,2]=>[8,5,6,3,1,2,4,7]=>[1,2,1,4]
[4,6,8,3,7,2,5,1]=>[4,1,2,6,8,7,5,3]=>[5,8,7,3,1,2,4,6]=>[2,1,1,4]
[7,4,6,3,2,8,1,5]=>[2,5,4,7,3,1,8,6]=>[7,4,5,2,6,8,1,3]=>[1,2,3,2]
[1,4,3,6,2,7,8,5]=>[2,6,3,4,8,1,5,7]=>[7,3,6,5,1,8,4,2]=>[1,2,1,2,1,1]
[1,5,4,3,7,2,8,6]=>[3,2,8,4,6,1,5,7]=>[6,7,1,5,3,8,4,2]=>[2,2,2,1,1]
[4,7,8,5,3,1,2,6]=>[6,7,1,5,4,2,8,3]=>[3,2,8,4,5,7,1,6]=>[1,2,3,2]
[5,7,3,4,1,2,8,6]=>[3,1,8,5,4,6,2,7]=>[6,8,1,4,5,3,7,2]=>[2,3,2,1]
[8,5,4,7,6,2,1,3]=>[3,2,7,6,8,5,4,1]=>[6,7,2,3,1,4,5,8]=>[2,2,4]
[8,5,7,4,3,6,1,2]=>[2,7,5,4,8,6,3,1]=>[7,2,4,5,1,3,6,8]=>[1,3,4]
[4,3,8,1,6,7,5,2]=>[1,5,8,2,7,4,6,3]=>[8,4,1,7,2,5,3,6]=>[1,1,2,2,2]
[4,7,8,3,6,1,5,2]=>[4,8,1,6,2,7,5,3]=>[5,1,8,3,7,2,4,6]=>[1,2,2,3]
[5,3,8,6,7,4,1,2]=>[1,7,4,8,2,6,5,3]=>[8,2,5,1,7,3,4,6]=>[1,2,2,3]
[1,3,8,6,4,7,5,2]=>[8,5,4,7,2,6,1,3]=>[1,4,5,2,7,3,8,6]=>[3,2,2,1]
[8,6,2,7,4,1,5,3]=>[8,6,3,5,2,7,4,1]=>[1,3,6,4,7,2,5,8]=>[3,2,3]
[7,6,1,3,4,2,8,5]=>[4,5,8,3,6,2,1,7]=>[5,4,1,6,3,7,8,2]=>[1,1,2,3,1]
[1,5,7,3,2,6,8,4]=>[4,2,6,8,5,1,3,7]=>[5,7,3,1,4,8,6,2]=>[2,1,3,1,1]
[1,6,7,3,2,5,8,4]=>[4,6,2,8,5,1,3,7]=>[5,3,7,1,4,8,6,2]=>[1,2,3,1,1]
[3,2,6,8,5,7,4,1]=>[3,5,8,1,7,2,6,4]=>[6,4,1,8,2,7,3,5]=>[1,1,2,2,2]
[5,8,2,3,6,7,4,1]=>[5,1,8,3,4,7,6,2]=>[4,8,1,6,5,2,3,7]=>[2,2,1,3]
[7,5,2,3,1,6,8,4]=>[3,4,6,2,8,5,1,7]=>[6,5,3,7,1,4,8,2]=>[1,1,2,3,1]
[3,1,7,5,2,8,4,6]=>[7,1,4,8,5,2,3,6]=>[2,8,5,1,4,7,6,3]=>[2,1,3,1,1]
[2,5,7,4,1,8,3,6]=>[2,7,4,8,1,5,3,6]=>[7,2,5,1,8,4,6,3]=>[1,2,2,2,1]
[4,2,6,1,7,8,3,5]=>[1,7,5,2,3,8,4,6]=>[8,2,4,7,6,1,5,3]=>[1,3,1,2,1]
[6,4,8,7,2,3,5,1]=>[2,5,1,6,8,7,4,3]=>[7,4,8,3,1,2,5,6]=>[1,2,1,4]
[3,2,6,8,7,4,5,1]=>[3,6,8,1,7,2,5,4]=>[6,3,1,8,2,7,4,5]=>[1,1,2,2,2]
[6,3,2,1,7,8,4,5]=>[2,7,3,5,1,8,4,6]=>[7,2,6,4,8,1,5,3]=>[1,2,2,2,1]
[3,7,1,8,4,2,5,6]=>[6,1,5,7,8,3,2,4]=>[3,8,4,2,1,6,7,5]=>[2,1,1,3,1]
[4,2,1,3,7,5,8,6]=>[8,2,1,6,3,4,5,7]=>[1,7,8,3,6,5,4,2]=>[3,2,1,1,1]
[8,1,3,7,4,2,6,5]=>[5,8,3,6,7,2,4,1]=>[4,1,6,3,2,7,5,8]=>[1,2,1,2,2]
[8,4,3,7,6,2,1,5]=>[2,7,3,6,8,5,4,1]=>[7,2,6,3,1,4,5,8]=>[1,2,1,4]
[8,3,5,2,7,6,1,4]=>[7,2,3,8,4,6,5,1]=>[2,7,6,1,5,3,4,8]=>[2,1,2,3]
[3,8,7,2,6,5,4,1]=>[8,7,4,6,1,5,3,2]=>[1,2,5,3,8,4,6,7]=>[3,2,3]
[4,2,7,8,6,1,5,3]=>[8,1,6,3,7,2,5,4]=>[1,8,3,6,2,7,4,5]=>[2,2,2,2]
[6,8,2,4,7,1,5,3]=>[4,8,3,1,6,7,5,2]=>[5,1,6,8,3,2,4,7]=>[1,3,1,3]
[5,2,1,8,7,3,6,4]=>[8,6,1,7,2,5,3,4]=>[1,3,8,2,7,4,6,5]=>[3,2,2,1]
[8,2,1,6,3,7,5,4]=>[8,7,2,5,3,4,6,1]=>[1,2,7,4,6,5,3,8]=>[3,2,1,2]
[6,8,3,1,7,5,2,4]=>[3,7,1,8,6,4,5,2]=>[6,2,8,1,3,5,4,7]=>[1,2,3,2]
[5,8,1,6,7,2,4,3]=>[1,8,6,4,7,3,5,2]=>[8,1,3,5,2,6,4,7]=>[1,3,2,2]
[6,2,8,1,5,7,4,3]=>[5,8,7,2,1,4,6,3]=>[4,1,2,7,8,5,3,6]=>[1,4,1,2]
[5,7,8,2,6,1,4,3]=>[1,8,4,6,2,7,5,3]=>[8,1,5,3,7,2,4,6]=>[1,2,2,3]
[8,7,2,5,6,4,3,1]=>[4,8,7,3,6,5,2,1]=>[5,1,2,6,3,4,7,8]=>[1,3,4]
[8,6,7,5,2,4,3,1]=>[8,5,2,7,6,4,3,1]=>[1,4,7,2,3,5,6,8]=>[3,5]
[1,2,7,8,5,6,4,3]=>[5,3,8,7,6,1,2,4]=>[4,6,1,2,3,8,7,5]=>[2,4,1,1]
[7,4,8,1,6,2,5,3]=>[2,8,6,7,4,1,5,3]=>[7,1,3,2,5,8,4,6]=>[1,2,3,2]
[3,7,1,8,2,6,5,4]=>[8,7,1,5,6,3,2,4]=>[1,2,8,4,3,6,7,5]=>[3,1,3,1]
[2,1,7,3,8,6,5,4]=>[8,7,6,1,4,2,3,5]=>[1,2,3,8,5,7,6,4]=>[4,2,1,1]
[8,2,1,7,6,5,4,3]=>[8,7,6,2,5,3,4,1]=>[1,2,3,7,4,6,5,8]=>[4,2,2]
[8,1,4,7,6,5,3,2]=>[8,7,3,6,5,2,4,1]=>[1,2,6,3,4,7,5,8]=>[3,3,2]
[8,6,7,5,1,4,3,2]=>[8,7,5,2,6,4,3,1]=>[1,2,4,7,3,5,6,8]=>[4,4]
[7,8,6,5,4,1,3,2]=>[8,6,1,7,5,4,3,2]=>[1,3,8,2,4,5,6,7]=>[3,5]
[5,8,4,3,2,1,6,7]=>[1,6,5,4,3,7,8,2]=>[8,3,4,5,6,2,1,7]=>[1,4,1,2]
[6,4,7,3,2,1,8,5]=>[2,5,4,1,8,6,3,7]=>[7,4,5,8,1,3,6,2]=>[1,3,3,1]
[5,4,7,3,2,1,6,8]=>[2,1,6,5,4,7,3,8]=>[7,8,3,4,5,2,6,1]=>[2,3,2,1]
[6,5,3,7,2,1,4,8]=>[3,6,5,2,1,7,4,8]=>[6,3,4,7,8,2,5,1]=>[1,4,2,1]
[5,8,3,6,2,1,4,7]=>[3,1,6,5,7,4,8,2]=>[6,8,3,4,2,5,1,7]=>[2,2,2,2]
[6,3,7,8,2,1,4,5]=>[6,2,5,1,7,3,8,4]=>[3,7,4,8,2,6,1,5]=>[2,2,2,2]
[5,3,7,6,2,1,4,8]=>[6,2,1,5,7,4,3,8]=>[3,7,8,4,2,5,6,1]=>[3,1,3,1]
[3,8,7,6,2,1,4,5]=>[6,5,7,8,1,4,3,2]=>[3,4,2,1,8,5,6,7]=>[2,1,2,3]
[5,8,4,2,6,1,3,7]=>[4,1,6,3,7,5,8,2]=>[5,8,3,6,2,4,1,7]=>[2,2,2,2]
[4,8,7,2,5,1,3,6]=>[1,4,6,7,5,8,3,2]=>[8,5,3,2,4,1,6,7]=>[1,1,1,2,3]
[5,8,3,2,6,1,4,7]=>[4,3,1,6,7,5,8,2]=>[5,6,8,3,2,4,1,7]=>[3,1,2,2]
[4,8,3,2,5,1,7,6]=>[1,4,3,5,8,6,7,2]=>[8,5,6,4,1,3,2,7]=>[1,2,1,2,2]
[4,3,7,2,5,1,8,6]=>[2,1,4,5,8,6,3,7]=>[7,8,5,4,1,3,6,2]=>[2,1,1,3,1]
[3,8,7,2,5,1,4,6]=>[4,6,7,1,5,8,3,2]=>[5,3,2,8,4,1,6,7]=>[1,1,2,1,3]
[6,4,2,7,5,1,3,8]=>[6,2,7,3,1,5,4,8]=>[3,7,2,6,8,4,5,1]=>[2,3,2,1]
[6,3,2,7,5,1,4,8]=>[2,6,7,3,1,5,4,8]=>[7,3,2,6,8,4,5,1]=>[1,1,3,2,1]
[5,3,2,6,7,1,4,8]=>[2,6,3,1,4,7,5,8]=>[7,3,6,8,5,2,4,1]=>[1,3,1,2,1]
[3,8,2,6,5,1,4,7]=>[6,7,1,3,5,4,8,2]=>[3,2,8,6,4,5,1,7]=>[1,2,1,2,2]
[6,2,7,8,5,1,3,4]=>[6,7,3,1,8,2,5,4]=>[3,2,6,8,1,7,4,5]=>[1,3,2,2]
[5,2,7,6,8,1,3,4]=>[6,1,7,4,2,3,8,5]=>[3,8,2,5,7,6,1,4]=>[2,3,1,2]
[4,2,7,6,5,1,3,8]=>[1,6,7,5,2,4,3,8]=>[8,3,2,4,7,5,6,1]=>[1,1,3,2,1]
[2,8,7,6,5,1,3,4]=>[6,7,8,5,4,1,3,2]=>[3,2,1,4,5,8,6,7]=>[1,1,4,2]
[6,5,4,3,1,7,8,2]=>[6,4,3,2,1,8,5,7]=>[3,5,6,7,8,1,4,2]=>[5,2,1]
[6,4,7,3,1,5,8,2]=>[2,6,4,1,8,5,3,7]=>[7,3,5,8,1,4,6,2]=>[1,3,3,1]
[5,4,7,3,1,8,6,2]=>[2,1,4,8,7,5,3,6]=>[7,8,5,1,2,4,6,3]=>[2,1,4,1]
[6,4,3,7,1,5,8,2]=>[3,2,6,1,8,5,4,7]=>[6,7,3,8,1,4,5,2]=>[2,2,3,1]
[5,4,3,6,1,8,7,2]=>[3,2,1,4,8,7,5,6]=>[6,7,8,5,1,2,4,3]=>[3,1,3,1]
[6,3,7,8,1,4,5,2]=>[6,8,2,1,5,3,7,4]=>[3,1,7,8,4,6,2,5]=>[1,3,2,2]
[5,3,7,6,1,4,8,2]=>[6,1,8,2,5,4,3,7]=>[3,8,1,7,4,5,6,2]=>[2,2,3,1]
[4,3,7,6,1,5,8,2]=>[1,6,8,2,5,4,3,7]=>[8,3,1,7,4,5,6,2]=>[1,1,2,3,1]
[3,8,7,6,1,4,5,2]=>[6,8,5,7,1,4,3,2]=>[3,1,4,2,8,5,6,7]=>[1,2,2,3]
[6,4,7,2,1,5,3,8]=>[4,2,7,5,1,6,3,8]=>[5,7,2,4,8,3,6,1]=>[2,3,2,1]
[4,8,7,2,1,5,3,6]=>[1,4,7,5,6,8,3,2]=>[8,5,2,4,3,1,6,7]=>[1,1,2,1,3]
[5,8,3,2,1,4,7,6]=>[4,3,1,8,5,6,7,2]=>[5,6,8,1,4,3,2,7]=>[3,2,1,2]
[4,8,3,2,1,5,7,6]=>[1,4,3,8,5,6,7,2]=>[8,5,6,1,4,3,2,7]=>[1,2,2,1,2]
[5,3,7,2,1,4,8,6]=>[2,4,1,8,5,6,3,7]=>[7,5,8,1,4,3,6,2]=>[1,2,2,2,1]
[3,8,7,2,1,4,5,6]=>[5,1,4,6,7,8,3,2]=>[4,8,5,3,2,1,6,7]=>[2,1,1,1,3]
[6,5,2,7,1,4,3,8]=>[7,3,5,2,1,6,4,8]=>[2,6,4,7,8,3,5,1]=>[2,3,2,1]
[5,8,2,6,1,4,3,7]=>[7,3,1,5,6,4,8,2]=>[2,6,8,4,3,5,1,7]=>[3,1,2,2]
[6,4,2,7,1,5,3,8]=>[7,3,2,5,1,6,4,8]=>[2,6,7,4,8,3,5,1]=>[3,2,2,1]
[5,4,2,6,1,8,3,7]=>[7,3,2,1,4,8,5,6]=>[2,6,7,8,5,1,4,3]=>[4,1,2,1]
[4,3,2,6,1,5,8,7]=>[2,1,8,3,5,4,6,7]=>[7,8,1,6,4,5,3,2]=>[2,2,2,1,1]
[6,2,7,8,1,4,3,5]=>[7,5,6,2,1,3,8,4]=>[2,4,3,7,8,6,1,5]=>[2,3,1,2]
[4,2,7,6,1,5,3,8]=>[1,7,5,6,2,4,3,8]=>[8,2,4,3,7,5,6,1]=>[1,2,2,2,1]
[3,2,7,6,1,4,5,8]=>[1,5,6,7,2,4,3,8]=>[8,4,3,2,7,5,6,1]=>[1,1,1,2,2,1]
[6,5,4,1,8,7,3,2]=>[3,2,1,8,7,6,4,5]=>[6,7,8,1,2,3,5,4]=>[3,4,1]
[6,4,7,1,5,8,3,2]=>[2,5,1,8,7,4,3,6]=>[7,4,8,1,2,5,6,3]=>[1,2,4,1]
[5,4,7,1,6,8,3,2]=>[2,1,5,8,7,4,3,6]=>[7,8,4,1,2,5,6,3]=>[2,1,4,1]
[5,4,3,1,6,8,7,2]=>[3,2,1,8,5,7,4,6]=>[6,7,8,1,4,2,5,3]=>[3,2,2,1]
[3,8,7,1,5,4,6,2]=>[6,5,8,1,4,7,3,2]=>[3,4,1,8,5,2,6,7]=>[2,2,1,3]
[5,8,2,1,6,4,3,7]=>[7,3,1,6,4,5,8,2]=>[2,6,8,3,5,4,1,7]=>[3,2,1,2]
[6,3,2,1,5,4,8,7]=>[3,2,5,8,4,1,6,7]=>[6,7,4,1,5,8,3,2]=>[2,1,3,1,1]
[5,3,2,1,6,4,8,7]=>[3,2,5,1,8,4,6,7]=>[6,7,4,8,1,5,3,2]=>[2,2,2,1,1]
[3,8,2,1,5,4,6,7]=>[1,3,6,4,5,7,8,2]=>[8,6,3,5,4,2,1,7]=>[1,1,2,1,1,2]
[6,2,7,1,5,4,3,8]=>[7,6,2,4,1,5,3,8]=>[2,3,7,5,8,4,6,1]=>[3,2,2,1]
[5,2,7,1,6,4,3,8]=>[7,6,2,1,4,5,3,8]=>[2,3,7,8,5,4,6,1]=>[4,1,2,1]
[4,2,7,1,5,6,3,8]=>[5,1,7,2,4,6,3,8]=>[4,8,2,7,5,3,6,1]=>[2,2,1,2,1]
[3,2,7,1,5,4,6,8]=>[1,6,2,4,5,7,3,8]=>[8,3,7,5,4,2,6,1]=>[1,2,1,1,2,1]
[2,8,7,1,5,4,3,6]=>[7,6,4,5,8,1,3,2]=>[2,3,5,4,1,8,6,7]=>[3,1,2,2]
[6,5,1,7,8,4,3,2]=>[4,2,1,8,7,6,3,5]=>[5,7,8,1,2,3,6,4]=>[3,4,1]
[6,4,1,7,5,8,3,2]=>[2,5,4,1,8,7,3,6]=>[7,4,5,8,1,2,6,3]=>[1,3,3,1]
[5,4,1,6,7,8,3,2]=>[4,2,1,5,8,7,3,6]=>[5,7,8,4,1,2,6,3]=>[3,1,3,1]
[4,8,1,6,5,7,3,2]=>[5,1,4,8,7,3,6,2]=>[4,8,5,1,2,6,3,7]=>[2,1,3,2]
[6,3,1,7,5,4,8,2]=>[6,2,5,4,1,8,3,7]=>[3,7,4,5,8,1,6,2]=>[2,3,2,1]
[5,3,1,6,7,4,8,2]=>[2,4,1,6,5,8,3,7]=>[7,5,8,3,4,1,6,2]=>[1,2,2,2,1]
[4,3,1,6,5,7,8,2]=>[2,1,5,4,6,8,3,7]=>[7,8,4,5,3,1,6,2]=>[2,2,1,2,1]
[3,8,1,6,5,4,7,2]=>[6,5,1,4,8,3,7,2]=>[3,4,8,5,1,6,2,7]=>[3,1,2,2]
[2,8,1,6,5,4,3,7]=>[7,6,5,1,3,4,8,2]=>[2,3,4,8,6,5,1,7]=>[4,1,1,2]
[6,1,7,8,5,4,3,2]=>[3,1,8,7,6,5,2,4]=>[6,8,1,2,3,4,7,5]=>[2,5,1]
[4,1,7,6,5,8,3,2]=>[5,1,4,3,8,7,2,6]=>[4,8,5,6,1,2,7,3]=>[2,2,3,1]
[3,1,7,6,5,4,8,2]=>[6,5,1,4,3,8,2,7]=>[3,4,8,5,6,1,7,2]=>[3,2,2,1]
[8,1,3,5,7,2,4,6]=>[6,3,4,7,8,2,5,1]=>[3,6,5,2,1,7,4,8]=>[2,1,1,2,2]
[3,6,8,1,7,2,4,5]=>[6,7,1,2,8,4,5,3]=>[3,2,8,7,1,5,4,6]=>[1,2,1,2,2]
[3,4,5,6,8,1,7,2]=>[1,2,3,4,8,6,7,5]=>[8,7,6,5,1,3,2,4]=>[1,1,1,1,2,2]
[4,5,8,2,6,7,1,3]=>[1,2,7,4,5,8,6,3]=>[8,7,2,5,4,1,3,6]=>[1,1,2,1,3]
[1,7,2,3,5,4,6,8]=>[6,3,4,5,7,1,2,8]=>[3,6,5,4,2,8,7,1]=>[2,1,1,2,1,1]
[8,1,2,3,5,4,6,7]=>[6,2,3,4,5,7,8,1]=>[3,7,6,5,4,2,1,8]=>[2,1,1,1,1,2]
[2,7,8,1,3,5,4,6]=>[7,4,5,6,1,2,8,3]=>[2,5,4,3,8,7,1,6]=>[2,1,2,1,2]
[2,7,8,3,5,6,1,4]=>[7,4,5,2,8,1,6,3]=>[2,5,4,7,1,8,3,6]=>[2,2,2,2]
[2,4,5,7,8,1,6,3]=>[8,2,3,6,1,4,7,5]=>[1,7,6,3,8,5,2,4]=>[2,1,2,1,2]
[4,5,8,1,7,6,3,2]=>[8,1,2,7,6,4,5,3]=>[1,8,7,2,3,5,4,6]=>[2,1,3,2]
[4,5,8,7,2,1,6,3]=>[1,2,5,8,6,7,4,3]=>[8,7,4,1,3,2,5,6]=>[1,1,1,2,3]
[8,7,2,1,3,5,4,6]=>[3,7,4,5,6,8,2,1]=>[6,2,5,4,3,1,7,8]=>[1,2,1,1,3]
[3,6,8,7,2,1,5,4]=>[5,2,8,1,6,7,4,3]=>[4,7,1,8,3,2,5,6]=>[2,2,1,3]
[8,6,4,1,7,5,3,2]=>[3,8,7,6,4,2,5,1]=>[6,1,2,3,5,7,4,8]=>[1,5,2]
[7,6,4,3,1,8,5,2]=>[4,3,8,7,5,2,1,6]=>[5,6,1,2,4,7,8,3]=>[2,5,1]
[2,3,6,7,8,1,5,4]=>[3,8,6,1,2,4,7,5]=>[6,1,3,8,7,5,2,4]=>[1,3,1,1,2]
[3,6,8,1,2,5,4,7]=>[7,1,4,5,2,6,8,3]=>[2,8,5,4,7,3,1,6]=>[2,1,2,1,2]
[1,3,6,7,2,5,4,8]=>[7,5,2,3,6,1,4,8]=>[2,4,7,6,3,8,5,1]=>[3,1,2,1,1]
[7,4,1,8,5,2,3,6]=>[6,2,7,5,8,3,1,4]=>[3,7,2,4,1,6,8,5]=>[2,2,3,1]
[7,1,4,2,8,3,6,5]=>[3,8,6,7,2,4,1,5]=>[6,1,3,2,7,5,8,4]=>[1,2,2,2,1]
[7,1,8,2,5,3,6,4]=>[8,6,4,5,7,2,1,3]=>[1,3,5,4,2,7,8,6]=>[3,1,3,1]
[8,1,7,5,4,2,3,6]=>[6,7,5,4,8,2,3,1]=>[3,2,4,5,1,7,6,8]=>[1,3,2,2]
[1,7,2,6,5,4,3,8]=>[7,6,5,3,4,1,2,8]=>[2,3,4,6,5,8,7,1]=>[4,2,1,1]
[8,1,7,6,3,2,4,5]=>[6,5,7,8,4,2,3,1]=>[3,4,2,1,5,7,6,8]=>[2,1,3,2]
[8,2,5,7,6,3,1,4]=>[3,7,6,8,2,5,4,1]=>[6,2,3,1,7,4,5,8]=>[1,2,2,3]
[3,6,8,1,7,5,4,2]=>[2,8,7,1,6,4,5,3]=>[7,1,2,8,3,5,4,6]=>[1,3,2,2]
[8,2,6,7,5,4,1,3]=>[7,3,8,6,2,5,4,1]=>[2,6,1,3,7,4,5,8]=>[2,3,3]
[2,7,8,1,6,5,4,3]=>[8,7,6,4,1,2,5,3]=>[1,2,3,5,8,7,4,6]=>[5,1,2]
[8,7,2,1,6,5,4,3]=>[8,7,3,6,4,5,2,1]=>[1,2,6,3,5,4,7,8]=>[3,2,3]
[8,7,6,3,2,1,5,4]=>[5,4,8,6,7,3,2,1]=>[4,5,1,3,2,6,7,8]=>[2,2,4]
[2,1,8,6,3,7,4,5]=>[7,8,5,1,4,6,2,3]=>[2,1,4,8,5,3,7,6]=>[1,3,1,2,1]
[8,6,1,5,2,7,4,3]=>[8,7,5,3,4,2,6,1]=>[1,2,4,6,5,7,3,8]=>[4,2,2]
[2,1,7,5,4,3,8,6]=>[5,4,8,1,6,2,3,7]=>[4,5,1,8,3,7,6,2]=>[2,2,2,1,1]
[2,1,7,8,3,6,5,4]=>[8,7,5,1,3,6,2,4]=>[1,2,4,8,6,3,7,5]=>[4,1,2,1]
[2,1,8,5,7,6,3,4]=>[4,7,8,6,1,5,2,3]=>[5,2,1,3,8,4,7,6]=>[1,1,3,2,1]
[2,1,4,8,5,7,3,6]=>[5,7,8,1,3,6,2,4]=>[4,2,1,8,6,3,7,5]=>[1,1,2,1,2,1]
[2,1,5,4,6,8,3,7]=>[4,1,3,5,7,8,2,6]=>[5,8,6,4,2,1,7,3]=>[2,1,1,1,2,1]
[6,4,1,5,2,3,8,7]=>[8,5,3,2,4,1,6,7]=>[1,4,6,7,5,8,3,2]=>[4,2,1,1]
[5,3,7,4,6,8,1,2]=>[4,1,7,2,5,3,8,6]=>[5,8,2,7,4,6,1,3]=>[2,2,2,2]
[5,8,3,7,6,2,1,4]=>[1,7,3,6,8,5,4,2]=>[8,2,6,3,1,4,5,7]=>[1,2,1,4]
[5,2,4,8,6,3,1,7]=>[7,3,1,6,2,5,8,4]=>[2,6,8,3,7,4,1,5]=>[3,2,1,2]
[4,2,6,3,8,5,1,7]=>[1,7,4,2,3,6,8,5]=>[8,2,5,7,6,3,1,4]=>[1,3,1,1,2]
[4,6,3,2,7,8,1,5]=>[1,3,7,4,2,5,8,6]=>[8,6,2,5,7,4,1,3]=>[1,1,3,1,2]
[3,8,2,4,7,5,1,6]=>[7,1,3,4,6,8,5,2]=>[2,8,6,5,3,1,4,7]=>[2,1,1,1,3]
[3,6,8,7,5,4,1,2]=>[2,7,8,6,1,5,4,3]=>[7,2,1,3,8,4,5,6]=>[1,1,3,3]
[8,5,2,7,4,6,1,3]=>[7,5,2,8,3,6,4,1]=>[2,4,7,1,6,3,5,8]=>[3,2,3]
[5,8,2,1,7,6,4,3]=>[1,8,7,3,6,4,5,2]=>[8,1,2,6,3,5,4,7]=>[1,3,2,2]
[6,3,8,1,5,7,4,2]=>[5,8,2,1,7,4,6,3]=>[4,1,7,8,2,5,3,6]=>[1,3,2,2]
[8,3,2,4,1,7,5,6]=>[3,2,4,7,8,5,6,1]=>[6,7,5,2,1,4,3,8]=>[2,1,1,2,2]
[7,2,4,3,1,5,8,6]=>[4,2,3,8,5,6,1,7]=>[5,7,6,1,4,3,8,2]=>[2,1,2,2,1]
[7,8,3,1,5,4,6,2]=>[3,6,5,8,4,1,7,2]=>[6,3,4,1,5,8,2,7]=>[1,2,3,2]
[7,2,8,1,4,6,5,3]=>[8,5,7,2,4,1,6,3]=>[1,4,2,7,5,8,3,6]=>[2,2,2,2]
[6,2,3,1,4,5,8,7]=>[2,3,8,4,5,1,6,7]=>[7,6,1,5,4,8,3,2]=>[1,1,2,2,1,1]
[5,6,1,4,3,2,8,7]=>[5,4,1,8,3,2,6,7]=>[4,5,8,1,6,7,3,2]=>[3,3,1,1]
[5,7,1,8,3,6,2,4]=>[5,1,7,8,6,3,2,4]=>[4,8,2,1,3,6,7,5]=>[2,1,4,1]
[6,8,1,4,5,3,2,7]=>[4,7,6,3,1,5,8,2]=>[5,2,3,6,8,4,1,7]=>[1,4,1,2]
[6,7,1,5,4,3,8,2]=>[6,5,4,1,8,3,2,7]=>[3,4,5,8,1,6,7,2]=>[4,3,1]
[8,7,5,1,3,4,2,6]=>[5,7,4,6,3,8,2,1]=>[4,2,5,3,6,1,7,8]=>[1,2,2,3]
[6,5,7,1,3,8,2,4]=>[5,7,2,1,8,4,3,6]=>[4,2,7,8,1,5,6,3]=>[1,3,3,1]
[7,5,4,8,2,1,3,6]=>[6,5,3,2,7,1,8,4]=>[3,4,6,7,2,8,1,5]=>[4,2,2]
[8,3,6,4,5,1,2,7]=>[6,2,4,7,5,3,8,1]=>[3,7,5,2,4,6,1,8]=>[2,1,3,2]
[7,3,5,8,1,6,2,4]=>[7,2,3,8,5,1,6,4]=>[2,7,6,1,4,8,3,5]=>[2,1,3,2]
[6,3,5,4,1,2,8,7]=>[8,2,5,4,3,1,6,7]=>[1,7,4,5,6,8,3,2]=>[2,4,1,1]
[2,6,3,5,1,4,8,7]=>[8,3,5,1,4,2,6,7]=>[1,6,4,8,5,7,3,2]=>[2,2,2,1,1]
[2,7,8,5,1,6,4,3]=>[8,7,5,4,1,2,6,3]=>[1,2,4,5,8,7,3,6]=>[5,1,2]
[8,7,3,6,5,1,4,2]=>[8,3,6,7,5,4,2,1]=>[1,6,3,2,4,5,7,8]=>[2,1,5]
[2,8,3,4,6,1,5,7]=>[3,4,6,7,1,5,8,2]=>[6,5,3,2,8,4,1,7]=>[1,1,1,2,1,2]
[2,7,4,3,6,1,8,5]=>[3,8,4,6,1,5,2,7]=>[6,1,5,3,8,4,7,2]=>[1,2,2,2,1]
[3,4,7,2,8,1,5,6]=>[1,2,4,6,7,3,8,5]=>[8,7,5,3,2,6,1,4]=>[1,1,1,1,2,2]
[4,3,2,5,7,1,8,6]=>[2,1,8,3,4,6,5,7]=>[7,8,1,6,5,3,4,2]=>[2,2,1,2,1]
[4,2,3,5,8,1,6,7]=>[2,3,1,4,6,7,8,5]=>[7,6,8,5,3,2,1,4]=>[1,2,1,1,1,2]
[3,2,8,4,7,1,6,5]=>[8,1,4,6,7,2,5,3]=>[1,8,5,3,2,7,4,6]=>[2,1,1,2,2]
[8,2,4,7,5,1,6,3]=>[8,3,6,2,5,7,4,1]=>[1,6,3,7,4,2,5,8]=>[2,2,1,3]
[3,2,4,6,1,5,8,7]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[1,2,1,2,1,1]
[8,3,4,5,7,6,1,2]=>[2,3,4,7,8,6,5,1]=>[7,6,5,2,1,3,4,8]=>[1,1,1,1,4]
[2,8,4,6,5,7,1,3]=>[7,3,5,4,8,1,6,2]=>[2,6,4,5,1,8,3,7]=>[2,2,2,2]
[2,3,8,4,6,7,1,5]=>[7,4,5,8,1,2,6,3]=>[2,5,4,1,8,7,3,6]=>[2,1,2,1,2]
[3,2,4,5,6,8,1,7]=>[2,1,3,4,5,7,8,6]=>[7,8,6,5,4,2,1,3]=>[2,1,1,1,1,2]
[5,6,8,1,4,2,7,3]=>[1,8,6,4,2,5,7,3]=>[8,1,3,5,7,4,2,6]=>[1,4,1,2]
[1,5,7,8,4,6,2,3]=>[7,2,5,3,8,6,1,4]=>[2,7,4,6,1,3,8,5]=>[2,2,3,1]
[1,3,5,7,8,6,2,4]=>[7,3,4,8,2,6,1,5]=>[2,6,5,1,7,3,8,4]=>[2,1,2,2,1]
[3,5,7,8,6,1,2,4]=>[2,6,7,1,3,8,5,4]=>[7,3,2,8,6,1,4,5]=>[1,1,2,1,3]
[3,1,5,6,8,2,7,4]=>[1,3,4,8,6,7,2,5]=>[8,6,5,1,3,2,7,4]=>[1,1,1,2,2,1]
[2,3,5,6,8,1,7,4]=>[3,4,8,1,2,6,7,5]=>[6,5,1,8,7,3,2,4]=>[1,1,2,1,1,2]
[5,6,4,8,2,1,7,3]=>[1,5,3,2,8,6,7,4]=>[8,4,6,7,1,3,2,5]=>[1,3,2,2]
[5,1,6,3,8,4,7,2]=>[6,3,1,8,4,7,2,5]=>[3,6,8,1,5,2,7,4]=>[3,2,2,1]
[2,5,1,6,8,3,7,4]=>[4,2,8,1,6,7,3,5]=>[5,7,1,8,3,2,6,4]=>[2,2,1,2,1]
[5,1,2,6,8,3,7,4]=>[4,8,6,1,7,2,3,5]=>[5,1,3,8,2,7,6,4]=>[1,3,2,1,1]
[5,7,1,8,6,2,3,4]=>[6,1,7,8,5,3,2,4]=>[3,8,2,1,4,6,7,5]=>[2,1,4,1]
[1,5,2,7,8,6,3,4]=>[2,7,4,8,6,1,3,5]=>[7,2,5,1,3,8,6,4]=>[1,2,3,1,1]
[6,1,7,5,2,8,3,4]=>[7,8,5,4,2,1,3,6]=>[2,1,4,5,7,8,6,3]=>[1,5,1,1]
[2,6,7,5,1,8,3,4]=>[7,2,8,5,1,4,3,6]=>[2,7,1,4,8,5,6,3]=>[2,3,2,1]
[5,1,7,8,6,3,4,2]=>[1,6,3,8,7,5,2,4]=>[8,3,6,1,2,4,7,5]=>[1,2,4,1]
[5,1,3,7,8,6,4,2]=>[4,1,8,7,3,6,2,5]=>[5,8,1,2,6,3,7,4]=>[2,3,2,1]
[5,2,7,8,4,6,1,3]=>[1,7,5,3,8,2,6,4]=>[8,2,4,6,1,7,3,5]=>[1,3,2,2]
[3,2,5,7,8,6,1,4]=>[7,1,3,4,8,2,6,5]=>[2,8,6,5,1,7,3,4]=>[2,1,1,2,2]
[6,2,7,5,1,8,3,4]=>[7,8,5,2,1,4,3,6]=>[2,1,4,7,8,5,6,3]=>[1,4,2,1]
[1,2,6,7,5,8,3,4]=>[3,7,5,4,8,1,2,6]=>[6,2,4,5,1,8,7,3]=>[1,3,2,1,1]
[6,2,7,5,4,1,8,3]=>[8,6,5,2,1,4,3,7]=>[1,3,4,7,8,5,6,2]=>[5,2,1]
[6,7,5,2,4,1,8,3]=>[8,4,1,6,5,3,2,7]=>[1,5,8,3,4,6,7,2]=>[3,4,1]
[6,7,2,5,3,8,1,4]=>[5,7,3,1,4,2,8,6]=>[4,2,6,8,5,7,1,3]=>[1,3,2,2]
[6,7,4,5,2,1,8,3]=>[5,3,1,8,6,4,2,7]=>[4,6,8,1,3,5,7,2]=>[3,4,1]
[5,1,7,8,6,4,3,2]=>[1,3,8,7,6,5,2,4]=>[8,6,1,2,3,4,7,5]=>[1,1,5,1]
[2,5,7,8,6,3,1,4]=>[7,2,6,3,8,1,5,4]=>[2,7,3,6,1,8,4,5]=>[2,2,2,2]
[5,1,7,8,6,3,2,4]=>[1,7,6,3,8,5,2,4]=>[8,2,3,6,1,4,7,5]=>[1,3,3,1]
[6,3,7,5,1,8,2,4]=>[7,8,2,1,5,4,3,6]=>[2,1,7,8,4,5,6,3]=>[1,3,3,1]
[1,6,7,5,3,8,2,4]=>[5,2,7,4,3,8,1,6]=>[4,7,2,5,6,1,8,3]=>[2,3,2,1]
[1,6,7,5,4,2,8,3]=>[2,8,6,5,4,1,3,7]=>[7,1,3,4,5,8,6,2]=>[1,5,1,1]
[6,7,5,1,4,2,8,3]=>[8,6,4,1,5,3,2,7]=>[1,3,5,8,4,6,7,2]=>[4,3,1]
[5,7,8,6,4,1,2,3]=>[1,6,7,2,8,5,4,3]=>[8,3,2,7,1,4,5,6]=>[1,1,2,4]
[4,1,7,2,6,5,8,3]=>[1,6,5,8,4,2,3,7]=>[8,3,4,1,5,7,6,2]=>[1,2,3,1,1]
[2,4,7,1,5,6,8,3]=>[2,5,6,8,1,4,3,7]=>[7,4,3,1,8,5,6,2]=>[1,1,1,2,2,1]
[6,7,4,1,5,2,8,3]=>[8,6,4,3,1,5,2,7]=>[1,3,5,6,8,4,7,2]=>[5,2,1]
[1,6,7,4,5,2,8,3]=>[4,2,8,6,5,1,3,7]=>[5,7,1,3,4,8,6,2]=>[2,4,1,1]
[1,6,3,7,5,8,2,4]=>[7,5,3,2,4,8,1,6]=>[2,4,6,7,5,1,8,3]=>[4,1,2,1]
[6,3,1,7,5,8,2,4]=>[7,2,5,4,1,8,3,6]=>[2,7,4,5,8,1,6,3]=>[2,3,2,1]
[6,7,5,4,2,1,8,3]=>[5,1,8,6,4,3,2,7]=>[4,8,1,3,5,6,7,2]=>[2,5,1]
[6,7,4,2,5,1,8,3]=>[8,4,3,1,6,5,2,7]=>[1,5,6,8,3,4,7,2]=>[4,3,1]
[6,2,7,4,5,1,8,3]=>[4,8,6,2,1,5,3,7]=>[5,1,3,7,8,4,6,2]=>[1,4,2,1]
[6,2,3,7,5,8,1,4]=>[7,5,2,3,1,4,8,6]=>[2,4,7,6,8,5,1,3]=>[3,2,1,2]
[4,5,1,6,3,2,8,7]=>[1,5,4,2,8,3,6,7]=>[8,4,5,7,1,6,3,2]=>[1,3,2,1,1]
[7,5,1,6,3,8,2,4]=>[5,7,4,2,8,3,1,6]=>[4,2,5,7,1,6,8,3]=>[1,3,3,1]
[7,5,1,6,3,8,4,2]=>[8,5,4,2,7,3,1,6]=>[1,4,5,7,2,6,8,3]=>[4,3,1]
[2,7,6,1,3,8,4,5]=>[7,8,4,5,1,3,2,6]=>[2,1,5,4,8,6,7,3]=>[1,2,2,2,1]
[2,7,6,1,3,8,5,4]=>[8,7,4,5,1,3,2,6]=>[1,2,5,4,8,6,7,3]=>[3,2,2,1]
[7,3,5,1,8,2,4,6]=>[2,6,7,3,8,4,1,5]=>[7,3,2,6,1,5,8,4]=>[1,1,2,3,1]
[3,7,5,1,8,6,2,4]=>[7,3,8,1,6,4,2,5]=>[2,6,1,8,3,5,7,4]=>[2,2,3,1]
[2,6,7,1,5,8,3,4]=>[7,5,2,8,1,4,3,6]=>[2,4,7,1,8,5,6,3]=>[3,2,2,1]
[2,1,6,7,3,8,5,4]=>[3,8,7,1,5,2,4,6]=>[6,1,2,8,4,7,5,3]=>[1,3,2,1,1]
[2,6,7,4,1,8,5,3]=>[4,2,8,7,1,5,3,6]=>[5,7,1,2,8,4,6,3]=>[2,3,2,1]
[2,6,7,1,5,8,4,3]=>[5,2,8,7,1,4,3,6]=>[4,7,1,2,8,5,6,3]=>[2,3,2,1]
[3,6,5,1,8,4,7,2]=>[6,3,1,2,8,7,4,5]=>[3,6,8,7,1,2,5,4]=>[3,1,3,1]
[3,6,5,1,8,4,2,7]=>[7,6,1,3,2,8,4,5]=>[2,3,8,6,7,1,5,4]=>[3,2,2,1]
[3,7,5,4,8,1,6,2]=>[4,3,8,1,6,2,7,5]=>[5,6,1,8,3,7,2,4]=>[2,2,2,2]
[3,7,5,4,8,1,2,6]=>[6,4,1,3,7,2,8,5]=>[3,5,8,6,2,7,1,4]=>[3,1,2,2]
[4,6,1,5,8,7,3,2]=>[8,1,4,2,7,6,3,5]=>[1,8,5,7,2,3,6,4]=>[2,2,3,1]
[4,6,1,5,8,7,2,3]=>[1,4,7,2,8,6,3,5]=>[8,5,2,7,1,3,6,4]=>[1,1,2,3,1]
[4,6,1,5,8,2,7,3]=>[1,4,8,6,2,7,3,5]=>[8,5,1,3,7,2,6,4]=>[1,1,3,2,1]
[7,5,1,6,2,8,3,4]=>[7,8,5,3,2,4,1,6]=>[2,1,4,6,7,5,8,3]=>[1,4,2,1]
[7,5,1,6,2,8,4,3]=>[8,7,5,3,2,4,1,6]=>[1,2,4,6,7,5,8,3]=>[5,2,1]
[4,6,1,5,8,2,3,7]=>[1,6,4,7,2,8,3,5]=>[8,3,5,2,7,1,6,4]=>[1,2,2,2,1]
[4,7,1,5,8,3,6,2]=>[1,4,6,8,7,3,2,5]=>[8,5,3,1,2,6,7,4]=>[1,1,1,4,1]
[2,3,4,7,8,1,6,5]=>[8,6,1,2,3,4,7,5]=>[1,3,8,7,6,5,2,4]=>[3,1,1,1,2]
[6,8,5,4,3,2,7,1]=>[1,6,5,4,3,8,7,2]=>[8,3,4,5,6,1,2,7]=>[1,4,3]
[10,11,9,8,7,6,5,4,3,2,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,10]
[7,9,6,5,4,3,2,8,1]=>[1,7,6,5,4,3,9,8,2]=>[9,3,4,5,6,7,1,2,8]=>[1,5,3]
[8,9,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,1,9,2]=>[2,3,4,5,6,7,9,1,8]=>[7,2]
[6,8,5,4,3,7,2,1]=>[1,5,4,3,8,7,6,2]=>[8,4,5,6,1,2,3,7]=>[1,3,4]
[6,5,4,3,1,8,7,2]=>[4,3,2,1,8,7,5,6]=>[5,6,7,8,1,2,4,3]=>[4,3,1]
[8,7,6,5,4,3,9,1,2]=>[8,6,5,4,3,2,1,9,7]=>[2,4,5,6,7,8,9,1,3]=>[7,2]
[8,7,5,4,3,1,6,2]=>[8,6,5,4,3,7,2,1]=>[1,3,4,5,6,2,7,8]=>[5,3]
[9,7,6,5,4,3,1,8,2]=>[9,7,6,5,4,3,2,8,1]=>[1,3,4,5,6,7,8,2,9]=>[7,2]
[11,10,9,8,7,6,5,4,3,1,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,1,3,4,5,6,7,8,9,10,11]=>[1,10]
[3,5,6,2,1,8,4,7]=>[4,1,2,7,3,8,5,6]=>[5,8,7,2,6,1,4,3]=>[2,1,2,2,1]
[3,5,2,6,8,4,1,7]=>[4,1,2,7,3,6,8,5]=>[5,8,7,2,6,3,1,4]=>[2,1,2,1,2]
[4,2,5,6,8,3,1,7]=>[3,1,4,7,2,6,8,5]=>[6,8,5,2,7,3,1,4]=>[2,1,2,1,2]
[4,2,8,1,5,6,3,7]=>[5,1,7,2,4,6,8,3]=>[4,8,2,7,5,3,1,6]=>[2,2,1,1,2]
[2,5,6,1,8,4,3,7]=>[2,7,6,1,3,8,4,5]=>[7,2,3,8,6,1,5,4]=>[1,3,1,2,1]
[5,3,6,8,1,4,2,7]=>[7,2,1,5,3,6,8,4]=>[2,7,8,4,6,3,1,5]=>[3,2,1,2]
[4,5,6,8,1,3,2,7]=>[1,2,7,5,3,6,8,4]=>[8,7,2,4,6,3,1,5]=>[1,1,3,1,2]
[4,5,6,3,8,2,1,7]=>[1,2,4,3,7,6,8,5]=>[8,7,5,6,2,3,1,4]=>[1,1,2,2,2]
[4,5,3,7,2,8,6,1]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[1,1,2,2,2]
[6,4,7,3,2,8,5,1]=>[2,4,1,8,5,3,7,6]=>[7,5,8,1,4,6,2,3]=>[1,2,3,2]
[6,1,4,7,3,2,8,5]=>[3,5,8,6,2,1,4,7]=>[6,4,1,3,7,8,5,2]=>[1,1,4,1,1]
[1,7,8,4,5,3,2,6]=>[4,7,6,5,2,8,1,3]=>[5,2,3,4,7,1,8,6]=>[1,4,2,1]
[5,1,7,3,8,4,2,6]=>[7,4,1,6,3,8,2,5]=>[2,5,8,3,6,1,7,4]=>[3,2,2,1]
[2,5,7,4,1,8,6,3]=>[2,4,8,7,1,5,3,6]=>[7,5,1,2,8,4,6,3]=>[1,1,3,2,1]
[5,3,7,1,4,8,6,2]=>[8,2,1,5,7,4,3,6]=>[1,7,8,4,2,5,6,3]=>[3,1,3,1]
[6,4,3,1,7,8,5,2]=>[3,2,5,1,8,7,4,6]=>[6,7,4,8,1,2,5,3]=>[2,2,3,1]
[6,4,1,7,3,8,5,2]=>[2,8,5,4,1,7,3,6]=>[7,1,4,5,8,2,6,3]=>[1,4,2,1]
[5,6,3,7,8,4,2,1]=>[1,4,2,8,3,7,6,5]=>[8,5,7,1,6,2,3,4]=>[1,2,2,3]
[5,1,6,3,7,8,4,2]=>[5,3,1,8,4,7,2,6]=>[4,6,8,1,5,2,7,3]=>[3,2,2,1]
[5,6,1,3,7,8,4,2]=>[5,1,8,4,2,7,3,6]=>[4,8,1,5,7,2,6,3]=>[2,3,2,1]
[5,6,1,7,8,3,4,2]=>[1,6,4,2,8,7,3,5]=>[8,3,5,7,1,2,6,4]=>[1,3,3,1]
[6,7,2,4,1,8,5,3]=>[4,8,3,1,7,5,2,6]=>[5,1,6,8,2,4,7,3]=>[1,3,3,1]
[6,7,2,1,4,3,8,5]=>[3,5,8,4,1,6,2,7]=>[6,4,1,5,8,3,7,2]=>[1,1,3,2,1]
[6,4,7,3,1,2,8,5]=>[2,8,5,4,1,6,3,7]=>[7,1,4,5,8,3,6,2]=>[1,4,2,1]
[5,6,3,1,2,7,8,4]=>[6,3,1,8,4,2,5,7]=>[3,6,8,1,5,7,4,2]=>[3,3,1,1]
[5,6,1,3,2,7,8,4]=>[4,6,1,8,3,2,5,7]=>[5,3,8,1,6,7,4,2]=>[1,2,3,1,1]
[2,5,6,3,7,8,4,1]=>[2,5,3,8,1,4,7,6]=>[7,4,6,1,8,5,2,3]=>[1,2,2,1,2]
[2,5,6,3,1,7,8,4]=>[4,2,6,1,3,8,5,7]=>[5,7,3,8,6,1,4,2]=>[2,2,1,2,1]
[2,6,4,7,3,1,8,5]=>[3,5,2,8,1,6,4,7]=>[6,4,7,1,8,3,5,2]=>[1,2,2,2,1]
[6,3,7,2,8,4,5,1]=>[6,8,2,1,4,3,7,5]=>[3,1,7,8,5,6,2,4]=>[1,3,2,2]
[6,3,7,2,8,4,1,5]=>[7,2,4,1,6,3,8,5]=>[2,7,5,8,3,6,1,4]=>[2,2,2,2]
[6,3,2,7,1,8,4,5]=>[2,7,8,3,1,5,4,6]=>[7,2,1,6,8,4,5,3]=>[1,1,3,2,1]
[7,5,3,2,1,8,4,6]=>[4,3,7,2,8,5,1,6]=>[5,6,2,7,1,4,8,3]=>[2,2,3,1]
[7,3,8,4,2,1,5,6]=>[6,2,5,4,7,1,8,3]=>[3,7,4,5,2,8,1,6]=>[2,2,2,2]
[4,7,2,1,3,8,6,5]=>[1,8,3,7,4,5,2,6]=>[8,1,6,2,5,4,7,3]=>[1,2,2,2,1]
[1,3,7,8,6,4,2,5]=>[7,6,3,8,2,5,1,4]=>[2,3,6,1,7,4,8,5]=>[3,2,2,1]
[5,7,3,8,2,1,6,4]=>[3,1,5,8,6,2,7,4]=>[6,8,4,1,3,7,2,5]=>[2,1,3,2]
[6,3,7,8,5,2,1,4]=>[7,6,2,1,3,8,5,4]=>[2,3,7,8,6,1,4,5]=>[4,1,3]
[4,6,2,7,8,5,3,1]=>[4,1,2,8,7,3,6,5]=>[5,8,7,1,2,6,3,4]=>[2,1,3,2]
[4,6,2,1,7,8,5,3]=>[1,5,8,3,2,7,4,6]=>[8,4,1,6,7,2,5,3]=>[1,1,3,2,1]
[7,4,5,8,1,2,6,3]=>[2,8,5,3,6,1,7,4]=>[7,1,4,6,3,8,2,5]=>[1,3,2,2]
[2,5,1,7,3,8,6,4]=>[2,8,7,1,5,3,4,6]=>[7,1,2,8,4,6,5,3]=>[1,3,2,1,1]
[6,7,2,1,3,8,5,4]=>[8,3,7,4,1,5,2,6]=>[1,6,2,5,8,4,7,3]=>[2,3,2,1]
[5,1,6,7,8,2,4,3]=>[3,1,8,6,4,7,2,5]=>[6,8,1,3,5,2,7,4]=>[2,3,2,1]
[6,3,7,1,8,5,2,4]=>[7,8,2,1,6,4,3,5]=>[2,1,7,8,3,5,6,4]=>[1,3,3,1]
[6,2,1,7,3,8,5,4]=>[8,7,2,5,3,1,4,6]=>[1,2,7,4,6,8,5,3]=>[3,3,1,1]
[6,2,7,1,8,5,4,3]=>[8,7,6,2,1,4,3,5]=>[1,2,3,7,8,5,6,4]=>[5,2,1]
[6,3,1,7,8,5,4,2]=>[4,8,2,1,7,6,3,5]=>[5,1,7,8,2,3,6,4]=>[1,3,3,1]
[4,1,3,6,8,2,5,7]=>[6,3,1,4,7,8,2,5]=>[3,6,8,5,2,1,7,4]=>[3,1,1,2,1]
[4,2,3,6,8,1,5,7]=>[6,2,1,3,4,7,8,5]=>[3,7,8,6,5,2,1,4]=>[3,1,1,1,2]
[5,3,2,1,8,4,7,6]=>[2,8,3,1,6,7,4,5]=>[7,1,6,8,3,2,5,4]=>[1,3,1,2,1]
[3,6,5,8,2,1,7,4]=>[5,3,1,2,8,6,7,4]=>[4,6,8,7,1,3,2,5]=>[3,1,2,2]
[4,5,2,1,3,8,7,6]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[1,3,2,1,1]
[3,2,6,4,5,8,1,7]=>[1,4,5,2,3,7,8,6]=>[8,5,4,7,6,2,1,3]=>[1,1,2,1,1,2]
[2,4,6,5,8,1,3,7]=>[6,2,4,1,3,7,8,5]=>[3,7,5,8,6,2,1,4]=>[2,2,1,1,2]
[1,6,2,4,5,8,3,7]=>[4,5,7,2,8,1,3,6]=>[5,4,2,7,1,8,6,3]=>[1,1,2,2,1,1]
[5,3,2,1,6,8,4,7]=>[3,2,5,1,7,8,4,6]=>[6,7,4,8,2,1,5,3]=>[2,2,1,2,1]
[6,2,4,5,8,1,3,7]=>[3,6,2,4,1,7,8,5]=>[6,3,7,5,8,2,1,4]=>[1,2,2,1,2]
[1,3,4,6,5,8,2,7]=>[5,2,3,4,7,8,1,6]=>[4,7,6,5,2,1,8,3]=>[2,1,1,1,2,1]
[1,6,3,4,5,8,2,7]=>[3,4,5,2,7,8,1,6]=>[6,5,4,7,2,1,8,3]=>[1,1,2,1,2,1]
[3,4,1,8,5,2,7,6]=>[1,2,5,8,6,7,3,4]=>[8,7,4,1,3,2,6,5]=>[1,1,1,2,2,1]
[2,8,4,1,7,6,3,5]=>[3,7,8,6,1,4,5,2]=>[6,2,1,3,8,5,4,7]=>[1,1,3,1,2]
[1,5,3,2,8,7,4,6]=>[7,2,8,3,6,1,4,5]=>[2,7,1,6,3,8,5,4]=>[2,2,2,1,1]
[8,2,1,7,5,3,4,6]=>[6,7,2,5,8,3,4,1]=>[3,2,7,4,1,6,5,8]=>[1,2,1,2,2]
[1,7,6,4,5,8,3,2]=>[4,5,3,2,8,7,1,6]=>[5,4,6,7,1,2,8,3]=>[1,3,3,1]
[5,8,7,4,1,2,6,3]=>[1,8,5,6,4,7,3,2]=>[8,1,4,3,5,2,6,7]=>[1,2,2,3]
[5,8,7,4,6,2,1,3]=>[7,1,6,4,8,5,3,2]=>[2,8,3,5,1,4,6,7]=>[2,2,4]
[3,4,2,5,8,6,7,1]=>[1,2,6,8,3,4,7,5]=>[8,7,3,1,6,5,2,4]=>[1,1,1,2,1,2]
[4,1,3,5,6,8,7,2]=>[8,3,1,4,5,7,2,6]=>[1,6,8,5,4,2,7,3]=>[3,1,1,2,1]
[2,4,8,6,7,1,3,5]=>[6,7,2,4,8,1,5,3]=>[3,2,7,5,1,8,4,6]=>[1,2,1,2,2]
[2,3,5,8,6,7,1,4]=>[7,3,5,8,1,2,6,4]=>[2,6,4,1,8,7,3,5]=>[2,1,2,1,2]
[4,2,3,7,1,8,6,5]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[1,3,1,2,1]
[3,2,6,4,8,1,7,5]=>[8,1,4,2,3,6,7,5]=>[1,8,5,7,6,3,2,4]=>[2,2,1,1,2]
[8,2,1,6,7,3,4,5]=>[6,7,2,4,8,3,5,1]=>[3,2,7,5,1,6,4,8]=>[1,2,1,2,2]
[2,7,8,5,4,1,3,6]=>[6,7,5,4,1,2,8,3]=>[3,2,4,5,8,7,1,6]=>[1,4,1,2]
[1,7,5,3,8,4,2,6]=>[7,4,3,6,2,8,1,5]=>[2,5,6,3,7,1,8,4]=>[3,2,2,1]
[4,7,5,3,1,2,8,6]=>[8,1,5,4,3,6,2,7]=>[1,8,4,5,6,3,7,2]=>[2,3,2,1]
[7,2,4,8,5,3,1,6]=>[7,3,6,2,5,1,8,4]=>[2,6,3,7,4,8,1,5]=>[2,2,2,2]
[4,8,3,1,2,7,6,5]=>[1,3,8,7,4,5,6,2]=>[8,6,1,2,5,4,3,7]=>[1,1,3,1,2]
[3,5,2,7,4,1,8,6]=>[5,1,2,8,3,6,4,7]=>[4,8,7,1,6,3,5,2]=>[2,1,2,2,1]
[2,8,4,7,1,3,5,6]=>[5,3,6,7,8,1,4,2]=>[4,6,3,2,1,8,5,7]=>[2,1,1,2,2]
[8,2,4,6,7,1,3,5]=>[3,6,7,2,4,8,5,1]=>[6,3,2,7,5,1,4,8]=>[1,1,2,1,3]
[4,8,2,3,6,7,1,5]=>[1,7,3,4,5,8,6,2]=>[8,2,6,5,4,1,3,7]=>[1,2,1,1,3]
[3,5,2,7,6,1,8,4]=>[2,8,1,6,3,5,4,7]=>[7,1,8,3,6,4,5,2]=>[1,2,2,2,1]
[1,6,3,2,5,8,7,4]=>[8,3,5,2,7,1,4,6]=>[1,6,4,7,2,8,5,3]=>[2,2,2,1,1]
[5,8,3,2,1,6,7,4]=>[4,3,1,6,8,5,7,2]=>[5,6,8,3,1,4,2,7]=>[3,1,2,2]
[5,8,7,3,4,6,2,1]=>[1,4,5,8,7,6,3,2]=>[8,5,4,1,2,3,6,7]=>[1,1,1,5]
[5,8,2,7,4,1,6,3]=>[1,8,6,3,5,7,4,2]=>[8,1,3,6,4,2,5,7]=>[1,3,1,3]
[5,1,4,2,8,7,6,3]=>[8,3,1,7,6,2,4,5]=>[1,6,8,2,3,7,5,4]=>[3,3,1,1]
[4,7,6,5,8,2,1,3]=>[7,6,1,4,3,2,8,5]=>[2,3,8,5,6,7,1,4]=>[3,3,2]
[5,2,6,8,7,1,3,4]=>[6,3,1,7,8,2,5,4]=>[3,6,8,2,1,7,4,5]=>[3,1,2,2]
[6,3,2,1,8,5,7,4]=>[2,6,8,3,1,7,4,5]=>[7,3,1,6,8,2,5,4]=>[1,1,3,2,1]
[2,7,5,4,1,8,6,3]=>[4,3,8,7,1,5,2,6]=>[5,6,1,2,8,4,7,3]=>[2,3,2,1]
[1,8,4,2,5,6,7,3]=>[5,3,6,8,4,7,1,2]=>[4,6,3,1,5,2,8,7]=>[2,1,2,2,1]
[3,8,4,1,5,6,7,2]=>[5,1,3,6,8,4,7,2]=>[4,8,6,3,1,5,2,7]=>[2,1,1,2,2]
[4,2,8,5,6,7,1,3]=>[1,4,7,5,8,2,6,3]=>[8,5,2,4,1,7,3,6]=>[1,1,2,2,2]
[5,2,4,7,1,8,6,3]=>[8,3,1,7,2,5,4,6]=>[1,6,8,2,7,4,5,3]=>[3,2,2,1]
[5,3,4,7,1,8,6,2]=>[8,2,1,3,7,5,4,6]=>[1,7,8,6,2,4,5,3]=>[3,1,3,1]
[8,6,4,1,3,2,5,7]=>[6,4,5,3,7,2,8,1]=>[3,5,4,6,2,7,1,8]=>[2,2,2,2]
[8,1,3,6,5,2,4,7]=>[6,7,3,5,2,4,8,1]=>[3,2,6,4,7,5,1,8]=>[1,2,2,1,2]
[8,1,4,3,6,5,2,7]=>[3,7,4,6,2,5,8,1]=>[6,2,5,3,7,4,1,8]=>[1,2,2,1,2]
[8,3,2,4,6,5,1,7]=>[2,7,3,4,6,5,8,1]=>[7,2,6,5,3,4,1,8]=>[1,2,1,2,2]
[8,4,2,1,6,5,3,7]=>[7,3,2,6,4,5,8,1]=>[2,6,7,3,5,4,1,8]=>[3,2,1,2]
[8,4,1,2,6,5,3,7]=>[7,6,3,2,4,5,8,1]=>[2,3,6,7,5,4,1,8]=>[4,1,1,2]
[8,3,6,4,1,5,2,7]=>[7,2,5,4,6,3,8,1]=>[2,7,4,5,3,6,1,8]=>[2,2,2,2]
[8,2,6,3,4,5,1,7]=>[4,5,7,2,6,3,8,1]=>[5,4,2,7,3,6,1,8]=>[1,1,2,2,2]
[1,3,4,8,5,7,2,6]=>[5,7,8,2,3,6,1,4]=>[4,2,1,7,6,3,8,5]=>[1,1,2,1,2,1]
[1,3,4,7,5,8,2,6]=>[5,7,2,3,4,8,1,6]=>[4,2,7,6,5,1,8,3]=>[1,2,1,1,2,1]
[1,3,5,2,4,8,7,6]=>[3,8,2,7,1,4,5,6]=>[6,1,7,2,8,5,4,3]=>[1,2,2,1,1,1]
[2,6,5,1,3,8,7,4]=>[8,7,4,1,3,2,5,6]=>[1,2,5,8,6,7,4,3]=>[4,2,1,1]
[4,7,1,6,5,8,3,2]=>[5,1,4,8,7,3,2,6]=>[4,8,5,1,2,6,7,3]=>[2,1,4,1]
[5,4,8,7,6,3,1,2]=>[1,7,8,2,6,5,4,3]=>[8,2,1,7,3,4,5,6]=>[1,1,2,4]
[2,8,5,1,4,7,6,3]=>[8,5,3,7,1,4,6,2]=>[1,4,6,2,8,5,3,7]=>[3,2,1,2]
[4,3,1,5,8,6,7,2]=>[2,1,6,8,4,7,3,5]=>[7,8,3,1,5,2,6,4]=>[2,1,2,2,1]
[4,1,3,5,8,6,7,2]=>[6,1,8,3,4,7,2,5]=>[3,8,1,6,5,2,7,4]=>[2,2,1,2,1]
[6,5,3,8,4,7,1,2]=>[7,3,2,1,5,8,6,4]=>[2,6,7,8,4,1,3,5]=>[4,1,3]
[5,4,2,1,6,8,7,3]=>[8,3,2,1,5,7,4,6]=>[1,6,7,8,4,2,5,3]=>[4,1,2,1]
[5,1,3,2,8,6,7,4]=>[6,8,3,1,7,2,4,5]=>[3,1,6,8,2,7,5,4]=>[1,3,2,1,1]
[5,3,1,2,8,6,7,4]=>[2,6,1,8,7,3,4,5]=>[7,3,8,1,2,6,5,4]=>[1,2,3,1,1]
[5,2,3,1,6,8,7,4]=>[8,2,3,1,5,7,4,6]=>[1,7,6,8,4,2,5,3]=>[2,2,1,2,1]
[5,3,2,1,8,6,7,4]=>[2,6,1,8,3,7,4,5]=>[7,3,8,1,6,2,5,4]=>[1,2,2,2,1]
[5,2,1,3,6,8,7,4]=>[8,2,5,1,7,3,4,6]=>[1,7,4,8,2,6,5,3]=>[2,2,2,1,1]
[2,4,7,3,8,1,6,5]=>[8,2,4,6,1,3,7,5]=>[1,7,5,3,8,6,2,4]=>[2,1,2,1,2]
[6,3,8,2,7,4,1,5]=>[7,2,4,1,6,8,5,3]=>[2,7,5,8,3,1,4,6]=>[2,2,1,3]
[8,2,1,3,6,4,7,5]=>[8,2,6,3,4,5,7,1]=>[1,7,3,6,5,4,2,8]=>[2,2,1,1,2]
[3,5,1,7,8,4,2,6]=>[2,7,1,6,4,8,3,5]=>[7,2,8,3,5,1,6,4]=>[1,2,2,2,1]
[2,7,4,5,8,3,1,6]=>[3,4,7,6,1,2,8,5]=>[6,5,2,3,8,7,1,4]=>[1,1,3,1,2]
[5,4,7,8,3,6,2,1]=>[1,5,2,3,8,7,6,4]=>[8,4,7,6,1,2,3,5]=>[1,2,1,4]
[6,4,3,8,7,2,1,5]=>[2,7,3,1,6,8,5,4]=>[7,2,6,8,3,1,4,5]=>[1,3,1,3]
[6,3,8,7,4,1,2,5]=>[6,7,2,1,5,8,4,3]=>[3,2,7,8,4,1,5,6]=>[1,3,1,3]
[3,5,7,2,4,8,1,6]=>[4,1,2,5,7,3,8,6]=>[5,8,7,4,2,6,1,3]=>[2,1,1,2,2]
[8,4,7,2,3,1,5,6]=>[4,2,6,5,7,8,3,1]=>[5,7,3,4,2,1,6,8]=>[2,2,1,3]
[8,4,7,1,3,2,5,6]=>[6,4,2,5,7,8,3,1]=>[3,5,7,4,2,1,6,8]=>[3,1,1,3]
[8,4,7,2,1,3,5,6]=>[5,4,2,6,7,8,3,1]=>[4,5,7,3,2,1,6,8]=>[3,1,1,3]
[8,6,4,2,1,3,7,5]=>[4,8,5,3,6,2,7,1]=>[5,1,4,6,3,7,2,8]=>[1,3,2,2]
[8,6,4,2,3,1,7,5]=>[4,5,3,8,6,2,7,1]=>[5,4,6,1,3,7,2,8]=>[1,2,3,2]
[3,5,7,2,6,1,8,4]=>[2,8,1,4,6,5,3,7]=>[7,1,8,5,3,4,6,2]=>[1,2,1,3,1]
[6,1,3,8,5,7,2,4]=>[7,5,8,3,1,6,2,4]=>[2,4,1,6,8,3,7,5]=>[2,3,2,1]
[5,8,3,2,6,7,1,4]=>[3,1,7,4,5,8,6,2]=>[6,8,2,5,4,1,3,7]=>[2,2,1,3]
[4,8,5,3,6,2,7,1]=>[4,1,3,6,5,8,7,2]=>[5,8,6,3,4,1,2,7]=>[2,1,2,3]
[1,5,8,7,4,6,2,3]=>[7,2,5,8,6,4,1,3]=>[2,7,4,1,3,5,8,6]=>[2,1,4,1]
[2,1,7,6,4,5,8,3]=>[5,6,4,1,3,8,2,7]=>[4,3,5,8,6,1,7,2]=>[1,3,1,2,1]
[1,7,2,4,6,5,8,3]=>[6,4,5,8,3,1,2,7]=>[3,5,4,1,6,8,7,2]=>[2,1,3,1,1]
[3,5,1,7,6,8,2,4]=>[2,7,1,5,4,8,3,6]=>[7,2,8,4,5,1,6,3]=>[1,2,2,2,1]
[5,8,2,6,1,3,7,4]=>[8,3,1,5,6,4,7,2]=>[1,6,8,4,3,5,2,7]=>[3,1,2,2]
[6,3,5,8,7,2,1,4]=>[3,7,2,1,6,8,5,4]=>[6,2,7,8,3,1,4,5]=>[1,3,1,3]
[2,5,7,8,4,1,6,3]=>[8,2,6,5,1,3,7,4]=>[1,7,3,4,8,6,2,5]=>[2,3,1,2]
[4,2,8,1,5,6,7,3]=>[5,1,6,8,2,4,7,3]=>[4,8,3,1,7,5,2,6]=>[2,1,2,1,2]
[4,1,5,2,6,8,7,3]=>[3,1,8,5,7,2,4,6]=>[6,8,1,4,2,7,5,3]=>[2,2,2,1,1]
[3,4,5,1,6,8,7,2]=>[1,2,3,8,5,7,4,6]=>[8,7,6,1,4,2,5,3]=>[1,1,1,2,2,1]
[4,2,8,5,1,6,7,3]=>[1,6,4,8,2,5,7,3]=>[8,3,5,1,7,4,2,6]=>[1,2,2,1,2]
[4,1,8,5,2,6,7,3]=>[1,6,4,8,5,7,2,3]=>[8,3,5,1,4,2,7,6]=>[1,2,2,2,1]
[2,7,1,8,5,4,6,3]=>[6,5,8,7,1,3,2,4]=>[3,4,1,2,8,6,7,5]=>[2,3,2,1]
[5,8,6,2,1,3,7,4]=>[4,1,8,5,6,3,7,2]=>[5,8,1,4,3,6,2,7]=>[2,2,2,2]
[8,2,4,1,5,6,7,3]=>[5,2,3,6,8,4,7,1]=>[4,7,6,3,1,5,2,8]=>[2,1,1,2,2]
[4,6,3,5,8,1,7,2]=>[1,3,4,2,8,6,7,5]=>[8,6,5,7,1,3,2,4]=>[1,1,2,2,2]
[1,7,8,3,5,4,6,2]=>[6,4,5,2,8,7,1,3]=>[3,5,4,7,1,2,8,6]=>[2,2,3,1]
[3,4,5,1,8,6,7,2]=>[1,2,3,6,8,7,4,5]=>[8,7,6,3,1,2,5,4]=>[1,1,1,1,3,1]
[3,4,5,6,8,2,1,7]=>[1,2,3,4,7,6,8,5]=>[8,7,6,5,2,3,1,4]=>[1,1,1,1,2,2]
[3,4,5,7,1,8,6,2]=>[8,1,2,3,7,5,4,6]=>[1,8,7,6,2,4,5,3]=>[2,1,1,3,1]
[3,4,5,7,8,2,6,1]=>[6,1,2,3,4,8,7,5]=>[3,8,7,6,5,1,2,4]=>[2,1,1,1,3]
[3,4,6,2,8,5,1,7]=>[7,1,2,4,3,6,8,5]=>[2,8,7,5,6,3,1,4]=>[2,1,2,1,2]
[3,4,6,8,1,5,2,7]=>[7,1,2,5,3,6,8,4]=>[2,8,7,4,6,3,1,5]=>[2,1,2,1,2]
[3,4,7,2,1,8,6,5]=>[8,1,2,4,7,5,3,6]=>[1,8,7,5,2,4,6,3]=>[2,1,1,3,1]
[3,4,7,8,1,5,6,2]=>[6,8,1,2,5,3,7,4]=>[3,1,8,7,4,6,2,5]=>[1,2,1,2,2]
[3,4,8,2,1,5,6,7]=>[1,2,5,4,6,7,8,3]=>[8,7,4,5,3,2,1,6]=>[1,1,2,1,1,2]
[3,5,2,6,7,8,1,4]=>[4,1,2,7,3,5,8,6]=>[5,8,7,2,6,4,1,3]=>[2,1,2,1,2]
[3,5,2,7,8,4,6,1]=>[2,6,1,4,8,3,7,5]=>[7,3,8,5,1,6,2,4]=>[1,2,1,2,2]
[3,5,2,8,4,1,6,7]=>[6,1,3,2,5,7,8,4]=>[3,8,6,7,4,2,1,5]=>[2,2,1,1,2]
[3,5,6,2,8,4,1,7]=>[2,7,1,4,3,6,8,5]=>[7,2,8,5,6,3,1,4]=>[1,2,2,1,2]
[3,5,6,8,4,1,2,7]=>[2,6,1,3,7,5,8,4]=>[7,3,8,6,2,4,1,5]=>[1,2,1,2,2]
[3,5,7,2,4,8,6,1]=>[2,8,1,4,5,3,7,6]=>[7,1,8,5,4,6,2,3]=>[1,2,1,2,2]
[3,5,7,2,8,4,6,1]=>[2,6,8,1,4,3,7,5]=>[7,3,1,8,5,6,2,4]=>[1,1,2,2,2]
[3,5,7,8,4,1,6,2]=>[8,2,6,1,5,3,7,4]=>[1,7,3,8,4,6,2,5]=>[2,2,2,2]
[3,6,2,1,7,8,5,4]=>[5,8,1,3,2,7,4,6]=>[4,1,8,6,7,2,5,3]=>[1,2,2,2,1]
[3,6,2,1,8,5,4,7]=>[7,1,3,6,2,8,4,5]=>[2,8,6,3,7,1,5,4]=>[2,1,2,2,1]
[3,6,7,2,4,8,5,1]=>[8,4,1,2,5,3,7,6]=>[1,5,8,7,4,6,2,3]=>[3,1,2,2]
[3,6,7,2,8,5,4,1]=>[2,8,7,1,4,3,6,5]=>[7,1,2,8,5,6,3,4]=>[1,3,2,2]
[3,6,7,8,4,5,1,2]=>[2,7,5,1,3,8,6,4]=>[7,2,4,8,6,1,3,5]=>[1,3,1,3]
[3,6,8,2,4,5,1,7]=>[4,5,1,2,7,6,8,3]=>[5,4,8,7,2,3,1,6]=>[1,2,1,2,2]
[3,7,2,1,4,8,6,5]=>[8,1,3,7,4,5,2,6]=>[1,8,6,2,5,4,7,3]=>[2,1,2,2,1]
[3,7,2,1,8,5,6,4]=>[6,8,1,3,7,4,2,5]=>[3,1,8,6,2,5,7,4]=>[1,2,1,3,1]
[3,7,2,8,4,5,6,1]=>[5,6,8,1,3,2,7,4]=>[4,3,1,8,6,7,2,5]=>[1,1,2,2,2]
[3,7,8,2,4,5,6,1]=>[4,5,6,1,2,8,7,3]=>[5,4,3,8,7,1,2,6]=>[1,1,2,1,3]
[3,8,2,1,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>[8,5,6,4,3,2,1,7]=>[1,2,1,1,1,2]
[4,1,5,6,7,8,3,2]=>[3,1,4,5,8,7,2,6]=>[6,8,5,4,1,2,7,3]=>[2,1,1,3,1]
[4,1,5,7,3,8,6,2]=>[1,8,3,5,4,7,2,6]=>[8,1,6,4,5,2,7,3]=>[1,2,2,2,1]
[4,1,6,3,8,5,2,7]=>[1,7,4,3,6,8,2,5]=>[8,2,5,6,3,1,7,4]=>[1,3,1,2,1]
[4,1,6,7,3,8,5,2]=>[1,3,8,5,4,7,2,6]=>[8,6,1,4,5,2,7,3]=>[1,1,3,2,1]
[4,1,6,7,8,5,2,3]=>[1,3,7,4,8,6,2,5]=>[8,6,2,5,1,3,7,4]=>[1,1,2,3,1]
[4,1,6,8,3,5,2,7]=>[1,5,3,7,6,8,2,4]=>[8,4,6,2,3,1,7,5]=>[1,2,2,2,1]
[4,1,8,3,2,5,6,7]=>[5,4,1,6,7,8,2,3]=>[4,5,8,3,2,1,7,6]=>[3,1,1,2,1]
[4,5,2,6,7,8,3,1]=>[1,4,2,5,8,3,7,6]=>[8,5,7,4,1,6,2,3]=>[1,2,1,2,2]
[4,5,2,6,8,1,3,7]=>[1,6,3,2,4,7,8,5]=>[8,3,6,7,5,2,1,4]=>[1,3,1,1,2]
[4,5,6,3,8,1,2,7]=>[1,2,6,4,3,7,8,5]=>[8,7,3,5,6,2,1,4]=>[1,1,3,1,2]
[4,5,6,8,3,1,2,7]=>[1,2,6,3,7,5,8,4]=>[8,7,3,6,2,4,1,5]=>[1,1,2,2,2]
[4,5,7,3,8,1,6,2]=>[1,2,4,8,6,3,7,5]=>[8,7,5,1,3,6,2,4]=>[1,1,1,3,2]
[4,5,8,3,2,1,6,7]=>[1,2,6,5,4,7,8,3]=>[8,7,3,4,5,2,1,6]=>[1,1,3,1,2]
[4,6,2,3,7,8,5,1]=>[1,5,8,3,2,4,7,6]=>[8,4,1,6,7,5,2,3]=>[1,1,3,1,2]
[4,6,2,3,8,5,1,7]=>[1,7,3,4,2,6,8,5]=>[8,2,6,5,7,3,1,4]=>[1,2,2,1,2]
[4,6,2,7,3,8,5,1]=>[8,1,5,3,2,4,7,6]=>[1,8,4,6,7,5,2,3]=>[2,3,1,2]
[4,6,2,7,8,5,1,3]=>[7,1,4,2,8,3,6,5]=>[2,8,5,7,1,6,3,4]=>[2,2,2,2]
[4,6,7,3,2,8,5,1]=>[4,1,2,8,5,3,7,6]=>[5,8,7,1,4,6,2,3]=>[2,1,3,2]
[4,6,8,3,2,5,1,7]=>[5,1,4,2,7,6,8,3]=>[4,8,5,7,2,3,1,6]=>[2,2,2,2]
[4,7,2,3,1,8,6,5]=>[1,8,3,4,7,5,2,6]=>[8,1,6,5,2,4,7,3]=>[1,2,1,3,1]
[4,7,2,8,3,5,6,1]=>[1,5,6,8,3,2,7,4]=>[8,4,3,1,6,7,2,5]=>[1,1,1,3,2]
[4,7,8,3,2,5,6,1]=>[5,1,4,6,2,8,7,3]=>[4,8,5,3,7,1,2,6]=>[2,1,2,3]
[4,8,2,3,1,5,6,7]=>[3,1,5,4,6,7,8,2]=>[6,8,4,5,3,2,1,7]=>[2,2,1,1,2]
[5,1,2,6,8,4,3,7]=>[4,7,6,1,8,2,3,5]=>[5,2,3,8,1,7,6,4]=>[1,3,2,1,1]
[5,1,2,7,4,8,6,3]=>[8,5,4,1,7,2,3,6]=>[1,4,5,8,2,7,6,3]=>[4,2,1,1]
[5,1,2,7,8,4,6,3]=>[6,4,1,8,7,2,3,5]=>[3,5,8,1,2,7,6,4]=>[3,3,1,1]
[5,1,2,8,4,3,6,7]=>[6,5,7,1,8,2,3,4]=>[3,4,2,8,1,7,6,5]=>[2,2,2,1,1]
[5,1,6,3,8,4,2,7]=>[7,4,3,1,6,8,2,5]=>[2,5,6,8,3,1,7,4]=>[4,1,2,1]
[5,1,6,7,4,8,2,3]=>[3,1,7,5,4,8,2,6]=>[6,8,2,4,5,1,7,3]=>[2,3,2,1]
[5,1,6,7,8,4,2,3]=>[3,1,7,4,8,6,2,5]=>[6,8,2,5,1,3,7,4]=>[2,2,3,1]
[5,1,8,3,4,2,6,7]=>[4,6,5,1,7,8,2,3]=>[5,3,4,8,2,1,7,6]=>[1,3,1,2,1]
[5,6,2,3,8,4,1,7]=>[7,3,1,4,2,6,8,5]=>[2,6,8,5,7,3,1,4]=>[3,2,1,2]
[5,6,2,7,8,4,1,3]=>[1,7,4,2,8,3,6,5]=>[8,2,5,7,1,6,3,4]=>[1,3,2,2]
[5,7,2,3,4,8,6,1]=>[8,3,1,4,5,2,7,6]=>[1,6,8,5,4,7,2,3]=>[3,1,2,2]
[5,7,2,3,8,4,6,1]=>[6,1,8,3,4,2,7,5]=>[3,8,1,6,5,7,2,4]=>[2,2,2,2]
[5,7,8,3,4,2,6,1]=>[1,4,6,5,2,8,7,3]=>[8,5,3,4,7,1,2,6]=>[1,1,3,3]
[5,8,2,3,4,1,6,7]=>[3,4,1,6,5,7,8,2]=>[6,5,8,3,4,2,1,7]=>[1,2,2,1,2]
[6,1,2,3,7,8,5,4]=>[5,8,7,2,3,1,4,6]=>[4,1,2,7,6,8,5,3]=>[1,3,2,1,1]
[6,1,2,3,8,5,4,7]=>[7,6,8,2,3,1,4,5]=>[2,3,1,7,6,8,5,4]=>[2,2,2,1,1]
[6,1,2,7,8,5,4,3]=>[4,8,7,6,2,1,3,5]=>[5,1,2,3,7,8,6,4]=>[1,5,1,1]
[6,1,2,8,4,5,3,7]=>[5,7,6,8,2,1,3,4]=>[4,2,3,1,7,8,6,5]=>[1,2,3,1,1]
[6,1,7,3,8,5,4,2]=>[8,7,4,3,1,6,2,5]=>[1,2,5,6,8,3,7,4]=>[5,2,1]
[6,1,8,3,4,5,2,7]=>[4,5,7,6,1,8,2,3]=>[5,4,2,3,8,1,7,6]=>[1,1,3,2,1]
[6,7,2,3,8,5,4,1]=>[8,7,3,1,4,2,6,5]=>[1,2,6,8,5,7,3,4]=>[4,2,2]
[6,7,2,8,4,5,3,1]=>[5,1,8,7,3,2,6,4]=>[4,8,1,2,6,7,3,5]=>[2,4,2]
[6,8,2,3,4,5,1,7]=>[3,4,5,1,7,6,8,2]=>[6,5,4,8,2,3,1,7]=>[1,1,2,2,2]
[7,1,2,3,4,8,6,5]=>[8,7,2,3,4,5,1,6]=>[1,2,7,6,5,4,8,3]=>[3,1,1,2,1]
[7,1,2,8,4,5,6,3]=>[5,6,8,7,2,3,1,4]=>[4,3,1,2,7,6,8,5]=>[1,1,3,2,1]
[7,1,8,3,4,5,6,2]=>[4,5,6,8,7,2,1,3]=>[5,4,3,1,2,7,8,6]=>[1,1,1,4,1]
[6,4,1,8,2,3,7,5]=>[8,5,2,6,1,7,3,4]=>[1,4,7,3,8,2,6,5]=>[3,2,2,1]
[1,3,5,7,2,6,4,8]=>[3,7,2,5,6,1,4,8]=>[6,2,7,4,3,8,5,1]=>[1,2,1,2,1,1]
[3,5,8,6,1,2,4,7]=>[5,1,2,6,7,4,8,3]=>[4,8,7,3,2,5,1,6]=>[2,1,1,2,2]
[3,1,6,8,2,4,7,5]=>[8,1,5,3,6,7,2,4]=>[1,8,4,6,3,2,7,5]=>[2,2,1,2,1]
[3,6,2,8,1,5,7,4]=>[6,8,1,3,2,5,7,4]=>[3,1,8,6,7,4,2,5]=>[1,2,2,1,2]
[2,6,1,3,8,4,7,5]=>[8,6,7,1,3,2,4,5]=>[1,3,2,8,6,7,5,4]=>[2,2,2,1,1]
[1,7,5,2,3,4,6,8]=>[4,5,6,3,7,1,2,8]=>[5,4,3,6,2,8,7,1]=>[1,1,2,2,1,1]
[2,7,5,1,3,8,4,6]=>[7,8,4,1,3,5,2,6]=>[2,1,5,8,6,4,7,3]=>[1,3,1,2,1]
[8,2,5,7,4,6,1,3]=>[3,7,5,8,2,6,4,1]=>[6,2,4,1,7,3,5,8]=>[1,2,2,3]
[8,2,5,1,3,7,4,6]=>[7,8,2,4,3,5,6,1]=>[2,1,7,5,6,4,3,8]=>[1,2,2,1,2]
[8,2,7,5,3,1,6,4]=>[5,8,6,2,4,7,3,1]=>[4,1,3,7,5,2,6,8]=>[1,3,1,3]
[8,2,6,5,4,7,1,3]=>[7,5,4,2,3,8,6,1]=>[2,4,5,7,6,1,3,8]=>[4,1,3]
[7,6,5,2,4,8,1,3]=>[7,4,5,3,2,1,8,6]=>[2,5,4,6,7,8,1,3]=>[2,4,2]
[7,8,2,5,3,1,6,4]=>[5,8,3,6,4,1,7,2]=>[4,1,6,3,5,8,2,7]=>[1,2,3,2]
[6,8,1,5,3,2,4,7]=>[6,5,7,3,1,4,8,2]=>[3,4,2,6,8,5,1,7]=>[2,3,1,2]
[1,6,7,5,3,2,4,8]=>[6,5,2,7,4,1,3,8]=>[3,4,7,2,5,8,6,1]=>[3,3,1,1]
[6,5,1,2,4,8,3,7]=>[5,7,8,3,2,1,4,6]=>[4,2,1,6,7,8,5,3]=>[1,1,4,1,1]
[7,8,1,6,4,2,3,5]=>[6,7,5,8,3,1,4,2]=>[3,2,4,1,6,8,5,7]=>[1,2,3,2]
[8,4,1,2,5,6,3,7]=>[5,7,3,2,4,6,8,1]=>[4,2,6,7,5,3,1,8]=>[1,3,1,1,2]
[8,1,3,7,2,6,4,5]=>[7,8,3,5,6,2,4,1]=>[2,1,6,4,3,7,5,8]=>[1,2,1,2,2]
[7,3,2,6,5,1,8,4]=>[8,2,6,3,5,4,1,7]=>[1,7,3,6,4,5,8,2]=>[2,2,3,1]
[7,8,4,2,5,6,1,3]=>[7,4,3,5,1,8,6,2]=>[2,5,6,4,8,1,3,7]=>[3,2,3]
[7,9,8,6,5,4,3,2,1]=>[9,1,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[2,7]
[6,9,8,7,5,4,3,2,1]=>[9,8,1,7,6,5,4,3,2]=>[1,2,9,3,4,5,6,7,8]=>[3,6]
[5,9,8,7,6,4,3,2,1]=>[9,8,7,1,6,5,4,3,2]=>[1,2,3,9,4,5,6,7,8]=>[4,5]
[4,9,8,7,6,5,3,2,1]=>[9,8,7,6,1,5,4,3,2]=>[1,2,3,4,9,5,6,7,8]=>[5,4]
[3,9,8,7,6,5,4,2,1]=>[9,8,7,6,5,1,4,3,2]=>[1,2,3,4,5,9,6,7,8]=>[6,3]
[2,9,8,7,6,5,4,3,1]=>[9,8,7,6,5,4,1,3,2]=>[1,2,3,4,5,6,9,7,8]=>[7,2]
[8,10,9,7,6,5,4,3,2,1]=>[10,1,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[2,8]
[6,9,7,8,5,4,3,2,1]=>[3,9,1,8,7,6,5,4,2]=>[7,1,9,2,3,4,5,6,8]=>[1,2,6]
[7,10,9,8,6,5,4,3,2,1]=>[10,9,1,8,7,6,5,4,3,2]=>[1,2,10,3,4,5,6,7,8,9]=>[3,7]
[4,8,6,5,7,3,2,1]=>[4,3,8,1,7,6,5,2]=>[5,6,1,8,2,3,4,7]=>[2,2,4]
[6,10,9,8,7,5,4,3,2,1]=>[10,9,8,1,7,6,5,4,3,2]=>[1,2,3,10,4,5,6,7,8,9]=>[4,6]
[3,8,7,5,4,6,2,1]=>[5,4,8,7,1,6,3,2]=>[4,5,1,2,8,3,6,7]=>[2,3,3]
[4,8,5,6,7,3,2,1]=>[3,4,8,1,7,6,5,2]=>[6,5,1,8,2,3,4,7]=>[1,1,2,4]
[5,10,9,8,7,6,4,3,2,1]=>[10,9,8,7,1,6,5,4,3,2]=>[1,2,3,4,10,5,6,7,8,9]=>[5,5]
[2,8,7,6,4,3,5,1]=>[6,5,8,7,4,1,3,2]=>[3,4,1,2,5,8,6,7]=>[2,4,2]
[3,8,7,4,5,6,2,1]=>[4,5,8,7,1,6,3,2]=>[5,4,1,2,8,3,6,7]=>[1,1,3,3]
[4,10,9,8,7,6,5,3,2,1]=>[10,9,8,7,6,1,5,4,3,2]=>[1,2,3,4,5,10,6,7,8,9]=>[6,4]
[1,8,7,6,5,3,2,4]=>[7,6,8,5,4,3,1,2]=>[2,3,1,4,5,6,8,7]=>[2,5,1]
[3,10,9,8,7,6,5,4,2,1]=>[10,9,8,7,6,5,1,4,3,2]=>[1,2,3,4,5,6,10,7,8,9]=>[7,3]
[1,8,7,6,5,2,3,4]=>[6,7,8,5,4,3,1,2]=>[3,2,1,4,5,6,8,7]=>[1,1,5,1]
[1,9,8,7,6,5,4,2,3]=>[8,9,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,9,8]=>[1,7,1]
[2,10,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,4,1,3,2]=>[1,2,3,4,5,6,7,10,8,9]=>[8,2]
[7,2,8,6,5,4,1,3]=>[7,8,6,5,2,1,4,3]=>[2,1,3,4,7,8,5,6]=>[1,5,2]
[7,2,8,5,4,6,1,3]=>[7,5,4,8,2,1,6,3]=>[2,4,5,1,7,8,3,6]=>[3,3,2]
[6,3,2,8,5,1,7,4]=>[8,2,6,3,1,5,7,4]=>[1,7,3,6,8,4,2,5]=>[2,3,1,2]
[8,4,7,2,5,6,3,1]=>[2,5,8,4,7,6,3,1]=>[7,4,1,5,2,3,6,8]=>[1,1,2,4]
[3,6,1,8,5,2,7,4]=>[8,6,1,5,2,7,3,4]=>[1,3,8,4,7,2,6,5]=>[3,2,2,1]
[7,2,5,8,3,6,1,4]=>[5,3,7,8,2,1,6,4]=>[4,6,2,1,7,8,3,5]=>[2,1,3,2]
[1,7,5,6,3,4,2,8]=>[5,3,7,6,4,1,2,8]=>[4,6,2,3,5,8,7,1]=>[2,4,1,1]
[7,2,6,8,5,3,1,4]=>[7,6,3,8,2,1,5,4]=>[2,3,6,1,7,8,4,5]=>[3,3,2]
[7,6,3,8,5,2,1,4]=>[7,3,6,2,1,8,5,4]=>[2,6,3,7,8,1,4,5]=>[2,3,3]
[1,5,7,4,2,6,3,8]=>[2,7,5,4,6,1,3,8]=>[7,2,4,5,3,8,6,1]=>[1,3,2,1,1]
[4,2,3,1,7,8,5,6]=>[7,2,1,3,5,8,4,6]=>[2,7,8,6,4,1,5,3]=>[3,1,1,2,1]
[5,2,8,4,1,7,6,3]=>[4,1,8,7,2,5,6,3]=>[5,8,1,2,7,4,3,6]=>[2,3,1,2]
[8,6,3,4,7,2,5,1]=>[3,4,6,2,8,7,5,1]=>[6,5,3,7,1,2,4,8]=>[1,1,2,4]
[6,8,3,4,5,1,7,2]=>[3,4,1,8,6,5,7,2]=>[6,5,8,1,3,4,2,7]=>[1,2,3,2]
[1,6,3,2,5,8,4,7]=>[3,5,7,2,8,1,4,6]=>[6,4,2,7,1,8,5,3]=>[1,1,2,2,1,1]
[6,3,7,1,5,8,4,2]=>[5,8,2,1,7,4,3,6]=>[4,1,7,8,2,5,6,3]=>[1,3,3,1]
[2,5,1,8,4,3,7,6]=>[5,2,8,1,6,7,3,4]=>[4,7,1,8,3,2,6,5]=>[2,2,1,2,1]
[6,2,5,4,8,1,3,7]=>[6,4,2,3,1,7,8,5]=>[3,5,7,6,8,2,1,4]=>[3,2,1,2]
[6,1,3,4,5,8,2,7]=>[3,4,5,7,1,8,2,6]=>[6,5,4,2,8,1,7,3]=>[1,1,1,2,2,1]
[8,3,4,1,5,2,7,6]=>[2,5,3,8,4,6,7,1]=>[7,4,6,1,5,3,2,8]=>[1,2,2,1,2]
[7,5,4,2,6,8,3,1]=>[5,3,2,8,4,1,7,6]=>[4,6,7,1,5,8,2,3]=>[3,3,2]
[7,3,8,4,5,2,1,6]=>[4,7,2,6,5,1,8,3]=>[5,2,7,3,4,8,1,6]=>[1,2,3,2]
[1,7,3,2,5,4,8,6]=>[3,5,8,4,6,1,2,7]=>[6,4,1,5,3,8,7,2]=>[1,1,2,2,1,1]
[8,7,2,1,5,3,4,6]=>[3,6,7,4,5,8,2,1]=>[6,3,2,5,4,1,7,8]=>[1,1,2,1,3]
[3,6,1,5,8,7,4,2]=>[8,4,1,2,7,6,3,5]=>[1,5,8,7,2,3,6,4]=>[3,1,3,1]
[5,4,6,8,1,2,7,3]=>[2,1,8,5,3,6,7,4]=>[7,8,1,4,6,3,2,5]=>[2,3,1,2]
[6,4,7,2,3,5,8,1]=>[4,2,5,1,6,3,8,7]=>[5,7,4,8,3,6,1,2]=>[2,2,2,2]
[6,8,4,1,3,5,7,2]=>[5,6,3,1,8,4,7,2]=>[4,3,6,8,1,5,2,7]=>[1,3,2,2]
[3,4,7,8,6,2,5,1]=>[6,3,8,1,2,7,5,4]=>[3,6,1,8,7,2,4,5]=>[2,2,1,3]
[4,1,3,5,7,8,6,2]=>[5,1,8,3,4,7,2,6]=>[4,8,1,6,5,2,7,3]=>[2,2,1,2,1]
[6,5,1,8,4,7,3,2]=>[5,2,1,8,7,6,3,4]=>[4,7,8,1,2,3,6,5]=>[3,4,1]
[5,3,1,8,4,7,6,2]=>[8,2,1,5,7,6,3,4]=>[1,7,8,4,2,3,6,5]=>[3,1,3,1]
[8,2,7,4,6,1,3,5]=>[6,4,7,8,2,5,3,1]=>[3,5,2,1,7,4,6,8]=>[2,1,2,3]
[4,7,3,2,8,1,6,5]=>[1,3,8,4,6,2,7,5]=>[8,6,1,5,3,7,2,4]=>[1,1,2,2,2]
[6,3,1,4,7,2,8,5]=>[2,8,4,6,3,1,5,7]=>[7,1,5,3,6,8,4,2]=>[1,2,3,1,1]
[8,7,3,6,1,5,2,4]=>[3,7,8,5,6,4,2,1]=>[6,2,1,4,3,5,7,8]=>[1,1,2,4]
[7,4,3,6,8,2,5,1]=>[2,6,3,4,1,8,7,5]=>[7,3,6,5,8,1,2,4]=>[1,2,2,3]
[2,4,7,3,8,5,6,1]=>[6,8,2,4,1,3,7,5]=>[3,1,7,5,8,6,2,4]=>[1,2,2,1,2]
[2,8,6,1,5,7,3,4]=>[7,5,8,4,1,3,6,2]=>[2,4,1,5,8,6,3,7]=>[2,3,1,2]
[8,5,3,7,4,2,6,1]=>[6,3,2,5,8,7,4,1]=>[3,6,7,4,1,2,5,8]=>[3,1,4]
[5,7,3,2,4,1,8,6]=>[4,3,1,5,8,6,2,7]=>[5,6,8,4,1,3,7,2]=>[3,1,3,1]
[2,8,3,4,7,1,5,6]=>[3,4,6,7,8,1,5,2]=>[6,5,3,2,1,8,4,7]=>[1,1,1,1,2,2]
[4,1,3,6,7,8,2,5]=>[4,1,7,3,5,8,2,6]=>[5,8,2,6,4,1,7,3]=>[2,2,1,2,1]
[1,7,6,3,2,5,8,4]=>[4,6,8,5,3,1,2,7]=>[5,3,1,4,6,8,7,2]=>[1,1,4,1,1]
[3,8,1,5,6,2,7,4]=>[4,8,1,6,3,5,7,2]=>[5,1,8,3,6,4,2,7]=>[1,2,2,1,2]
[8,2,5,6,1,7,4,3]=>[3,8,7,2,5,4,6,1]=>[6,1,2,7,4,5,3,8]=>[1,3,2,2]
[7,1,5,2,8,6,4,3]=>[3,8,7,6,2,4,1,5]=>[6,1,2,3,7,5,8,4]=>[1,4,2,1]
[6,5,4,8,7,2,1,3]=>[3,2,1,7,6,8,5,4]=>[6,7,8,2,3,1,4,5]=>[3,2,3]
[1,8,6,4,5,2,7,3]=>[4,8,6,5,3,7,1,2]=>[5,1,3,4,6,2,8,7]=>[1,4,2,1]
[1,8,5,3,6,2,7,4]=>[8,4,3,6,5,7,1,2]=>[1,5,6,3,4,2,8,7]=>[3,2,2,1]
[3,6,2,1,7,5,8,4]=>[6,1,3,5,2,8,4,7]=>[3,8,6,4,7,1,5,2]=>[2,1,2,2,1]
[2,5,4,1,8,7,6,3]=>[2,8,3,7,1,6,4,5]=>[7,1,6,2,8,3,5,4]=>[1,2,2,2,1]
[6,3,4,7,1,8,2,5]=>[2,3,7,1,8,5,4,6]=>[7,6,2,8,1,4,5,3]=>[1,1,2,3,1]
[3,4,7,8,2,5,6,1]=>[5,6,1,2,3,8,7,4]=>[4,3,8,7,6,1,2,5]=>[1,2,1,1,3]
[1,8,2,4,5,6,7,3]=>[4,5,6,8,3,7,1,2]=>[5,4,3,1,6,2,8,7]=>[1,1,1,2,2,1]
[5,2,4,1,6,8,7,3]=>[3,8,2,1,5,7,4,6]=>[6,1,7,8,4,2,5,3]=>[1,3,1,2,1]
[3,2,5,7,6,1,8,4]=>[8,1,3,6,2,5,4,7]=>[1,8,6,3,7,4,5,2]=>[2,1,2,2,1]
[4,3,5,6,1,8,7,2]=>[2,1,3,4,8,7,5,6]=>[7,8,6,5,1,2,4,3]=>[2,1,1,3,1]
[5,3,4,1,7,6,8,2]=>[2,3,1,6,5,8,4,7]=>[7,6,8,3,4,1,5,2]=>[1,2,2,2,1]
[3,1,4,6,5,7,8,2]=>[1,5,3,4,6,8,2,7]=>[8,4,6,5,3,1,7,2]=>[1,2,1,1,2,1]
[1,4,7,3,5,6,8,2]=>[2,4,5,6,3,8,1,7]=>[7,5,4,3,6,1,8,2]=>[1,1,1,2,2,1]
[5,1,3,6,4,8,7,2]=>[4,8,3,1,5,7,2,6]=>[5,1,6,8,4,2,7,3]=>[1,3,1,2,1]
[1,3,2,7,5,8,6,4]=>[8,5,2,4,7,1,3,6]=>[1,4,7,5,2,8,6,3]=>[3,1,2,1,1]
[1,4,2,5,8,3,7,6]=>[2,8,4,6,7,1,3,5]=>[7,1,5,3,2,8,6,4]=>[1,2,1,2,1,1]
[1,4,2,7,8,5,6,3]=>[6,2,4,8,7,1,3,5]=>[3,7,5,1,2,8,6,4]=>[2,1,3,1,1]
[5,1,2,6,8,4,7,3]=>[4,6,1,8,7,2,3,5]=>[5,3,8,1,2,7,6,4]=>[1,2,3,1,1]
[3,1,2,6,5,8,4,7]=>[1,5,4,7,8,2,3,6]=>[8,4,5,2,1,7,6,3]=>[1,2,1,2,1,1]
[4,1,2,6,8,5,3,7]=>[4,1,7,6,8,2,3,5]=>[5,8,2,3,1,7,6,4]=>[2,2,2,1,1]
[1,5,2,4,8,7,6,3]=>[2,8,7,4,6,1,3,5]=>[7,1,2,5,3,8,6,4]=>[1,3,2,1,1]
[1,2,6,4,8,7,5,3]=>[3,8,7,4,6,1,2,5]=>[6,1,2,5,3,8,7,4]=>[1,3,2,1,1]
[1,2,7,4,8,6,5,3]=>[8,7,4,3,6,1,2,5]=>[1,2,5,6,3,8,7,4]=>[4,2,1,1]
[1,3,2,7,5,8,4,6]=>[5,7,2,4,8,1,3,6]=>[4,2,7,5,1,8,6,3]=>[1,2,1,2,1,1]
[2,3,1,7,5,4,8,6]=>[5,8,1,2,6,3,4,7]=>[4,1,8,7,3,6,5,2]=>[1,2,1,2,1,1]
[1,3,2,8,5,7,4,6]=>[5,7,8,2,6,1,3,4]=>[4,2,1,7,3,8,6,5]=>[1,1,2,2,1,1]
[1,4,2,5,8,7,3,6]=>[2,7,8,4,6,1,3,5]=>[7,2,1,5,3,8,6,4]=>[1,1,2,2,1,1]
[1,5,2,4,8,7,3,6]=>[7,2,8,4,6,1,3,5]=>[2,7,1,5,3,8,6,4]=>[2,2,2,1,1]
[1,2,7,8,5,6,3,4]=>[7,5,3,8,6,1,2,4]=>[2,4,6,1,3,8,7,5]=>[3,3,1,1]
[1,2,6,8,5,7,3,4]=>[3,7,5,8,6,1,2,4]=>[6,2,4,1,3,8,7,5]=>[1,2,3,1,1]
[1,5,6,8,2,7,3,4]=>[2,7,3,8,5,6,1,4]=>[7,2,6,1,4,3,8,5]=>[1,2,2,2,1]
[1,3,8,2,6,7,4,5]=>[7,5,8,2,4,6,1,3]=>[2,4,1,7,5,3,8,6]=>[2,2,1,2,1]
[1,4,7,2,8,6,3,5]=>[7,8,2,6,4,1,3,5]=>[2,1,7,3,5,8,6,4]=>[1,2,3,1,1]
[1,6,7,8,2,5,3,4]=>[7,2,8,5,3,6,1,4]=>[2,7,1,4,6,3,8,5]=>[2,3,2,1]
[1,2,6,8,3,7,5,4]=>[3,8,7,5,6,1,2,4]=>[6,1,2,4,3,8,7,5]=>[1,3,2,1,1]
[1,5,7,8,2,3,6,4]=>[2,8,5,6,3,7,1,4]=>[7,1,4,3,6,2,8,5]=>[1,2,2,2,1]
[1,5,2,7,8,4,6,3]=>[2,6,4,8,7,1,3,5]=>[7,3,5,1,2,8,6,4]=>[1,2,3,1,1]
[1,3,6,2,4,8,7,5]=>[8,7,2,4,1,3,5,6]=>[1,2,7,5,8,6,4,3]=>[3,2,1,1,1]
[1,6,7,3,4,8,5,2]=>[8,4,2,5,3,7,1,6]=>[1,5,7,4,6,2,8,3]=>[3,2,2,1]
[1,5,3,7,4,8,6,2]=>[2,8,5,3,4,7,1,6]=>[7,1,4,6,5,2,8,3]=>[1,3,1,2,1]
[2,8,4,1,5,3,7,6]=>[5,3,8,1,4,6,7,2]=>[4,6,1,8,5,3,2,7]=>[2,2,1,1,2]
[1,3,6,4,2,8,7,5]=>[8,4,2,3,7,1,5,6]=>[1,5,7,6,2,8,4,3]=>[3,1,2,1,1]
[1,3,7,4,2,8,6,5]=>[8,4,7,2,5,1,3,6]=>[1,5,2,7,4,8,6,3]=>[2,2,2,1,1]
[1,3,8,4,2,7,6,5]=>[8,4,7,2,5,6,1,3]=>[1,5,2,7,4,3,8,6]=>[2,2,1,2,1]
[1,2,8,4,7,3,6,5]=>[8,4,6,7,5,1,2,3]=>[1,5,3,2,4,8,7,6]=>[2,1,3,1,1]
[1,2,7,4,8,3,6,5]=>[8,4,6,3,7,1,2,5]=>[1,5,3,6,2,8,7,4]=>[2,2,2,1,1]
[1,2,6,4,8,3,7,5]=>[8,4,3,6,7,1,2,5]=>[1,5,6,3,2,8,7,4]=>[3,1,2,1,1]
[1,5,2,4,8,3,7,6]=>[8,4,2,6,7,1,3,5]=>[1,5,7,3,2,8,6,4]=>[3,1,2,1,1]
[1,8,4,5,7,2,3,6]=>[3,6,4,7,8,5,1,2]=>[6,3,5,2,1,4,8,7]=>[1,2,1,3,1]
[1,8,3,5,2,7,4,6]=>[7,3,4,8,5,6,1,2]=>[2,6,5,1,4,3,8,7]=>[2,1,2,2,1]
[2,8,3,5,1,4,7,6]=>[8,3,5,1,4,6,7,2]=>[1,6,4,8,5,3,2,7]=>[2,2,1,1,2]
[1,3,8,6,2,7,4,5]=>[7,8,5,2,4,6,1,3]=>[2,1,4,7,5,3,8,6]=>[1,3,1,2,1]
[1,5,6,8,7,2,3,4]=>[2,6,3,7,8,5,1,4]=>[7,3,6,2,1,4,8,5]=>[1,2,1,3,1]
[1,2,6,8,5,3,7,4]=>[3,8,6,5,7,1,2,4]=>[6,1,3,4,2,8,7,5]=>[1,3,2,1,1]
[1,2,7,8,5,3,6,4]=>[8,6,5,3,7,1,2,4]=>[1,3,4,6,2,8,7,5]=>[4,2,1,1]
[1,2,5,8,7,3,6,4]=>[8,3,6,7,5,1,2,4]=>[1,6,3,2,4,8,7,5]=>[2,1,3,1,1]
[1,2,6,8,7,3,5,4]=>[3,8,6,7,5,1,2,4]=>[6,1,3,2,4,8,7,5]=>[1,2,3,1,1]
[1,2,7,8,6,3,5,4]=>[8,6,3,7,5,1,2,4]=>[1,3,6,2,4,8,7,5]=>[3,3,1,1]
[1,5,7,8,6,2,3,4]=>[2,6,7,3,8,5,1,4]=>[7,3,2,6,1,4,8,5]=>[1,1,2,3,1]
[1,4,7,6,8,2,3,5]=>[6,7,2,4,3,8,1,5]=>[3,2,7,5,6,1,8,4]=>[1,2,2,2,1]
[1,3,7,6,2,8,4,5]=>[7,8,5,2,4,1,3,6]=>[2,1,4,7,5,8,6,3]=>[1,3,2,1,1]
[2,3,8,7,4,1,6,5]=>[5,8,6,7,1,2,4,3]=>[4,1,3,2,8,7,5,6]=>[1,2,2,1,2]
[1,2,8,4,7,6,3,5]=>[7,8,4,6,5,1,2,3]=>[2,1,5,3,4,8,7,6]=>[1,2,3,1,1]
[1,2,5,8,7,6,3,4]=>[7,8,3,6,5,1,2,4]=>[2,1,6,3,4,8,7,5]=>[1,2,3,1,1]
[1,2,6,8,7,5,3,4]=>[3,7,8,6,5,1,2,4]=>[6,2,1,3,4,8,7,5]=>[1,1,4,1,1]
[1,2,7,8,6,5,3,4]=>[7,3,8,6,5,1,2,4]=>[2,6,1,3,4,8,7,5]=>[2,4,1,1]
[5,6,2,1,7,8,3,4]=>[7,3,1,5,2,8,4,6]=>[2,6,8,4,7,1,5,3]=>[3,2,2,1]
[2,3,7,6,4,5,8,1]=>[5,6,4,1,2,3,8,7]=>[4,3,5,8,7,6,1,2]=>[1,3,1,1,2]
[2,6,1,7,4,8,3,5]=>[5,7,4,1,2,8,3,6]=>[4,2,5,8,7,1,6,3]=>[1,3,1,2,1]
[3,6,4,1,7,8,2,5]=>[3,7,1,5,2,8,4,6]=>[6,2,8,4,7,1,5,3]=>[1,2,2,2,1]
[3,6,4,1,5,8,7,2]=>[3,8,1,5,2,7,4,6]=>[6,1,8,4,7,2,5,3]=>[1,2,2,2,1]
[2,6,1,4,7,8,5,3]=>[5,8,4,1,2,7,3,6]=>[4,1,5,8,7,2,6,3]=>[1,3,1,2,1]
[1,2,3,8,5,4,7,6]=>[5,8,6,7,1,2,3,4]=>[4,1,3,2,8,7,6,5]=>[1,2,2,1,1,1]
[4,3,1,2,8,5,7,6]=>[2,1,8,6,7,3,4,5]=>[7,8,1,3,2,6,5,4]=>[2,2,2,1,1]
[2,1,5,3,8,6,4,7]=>[3,7,1,6,8,2,4,5]=>[6,2,8,3,1,7,5,4]=>[1,2,1,2,1,1]
[1,2,3,8,5,6,4,7]=>[5,7,6,8,1,2,3,4]=>[4,2,3,1,8,7,6,5]=>[1,2,2,1,1,1]
[1,2,3,8,6,4,5,7]=>[6,7,5,8,1,2,3,4]=>[3,2,4,1,8,7,6,5]=>[1,2,2,1,1,1]
[1,2,3,8,6,5,4,7]=>[7,6,5,8,1,2,3,4]=>[2,3,4,1,8,7,6,5]=>[3,2,1,1,1]
[1,2,3,8,5,4,6,7]=>[6,5,7,8,1,2,3,4]=>[3,4,2,1,8,7,6,5]=>[2,1,2,1,1,1]
[2,6,1,5,4,8,3,7]=>[5,4,7,1,2,8,3,6]=>[4,5,2,8,7,1,6,3]=>[2,2,1,2,1]
[5,1,2,4,8,3,7,6]=>[8,4,6,1,7,2,3,5]=>[1,5,3,8,2,7,6,4]=>[2,2,2,1,1]
[5,6,3,1,4,8,2,7]=>[5,3,1,7,2,8,4,6]=>[4,6,8,2,7,1,5,3]=>[3,2,2,1]
[2,5,4,3,1,8,6,7]=>[4,3,1,2,7,8,5,6]=>[5,6,8,7,2,1,4,3]=>[3,1,1,2,1]
[3,6,4,5,1,8,7,2]=>[3,4,1,2,8,7,5,6]=>[6,5,8,7,1,2,4,3]=>[1,2,1,3,1]
[3,6,5,4,1,8,7,2]=>[4,3,1,2,8,7,5,6]=>[5,6,8,7,1,2,4,3]=>[3,1,3,1]
[5,2,6,1,7,8,4,3]=>[5,3,1,8,2,7,4,6]=>[4,6,8,1,7,2,5,3]=>[3,2,2,1]
[5,1,6,2,8,7,3,4]=>[7,3,1,8,6,2,4,5]=>[2,6,8,1,3,7,5,4]=>[3,3,1,1]
[2,1,3,7,8,6,4,5]=>[7,4,8,1,6,2,3,5]=>[2,5,1,8,3,7,6,4]=>[2,2,2,1,1]
[5,2,4,1,7,8,6,3]=>[3,5,1,8,2,7,4,6]=>[6,4,8,1,7,2,5,3]=>[1,2,2,2,1]
[4,3,1,2,8,6,7,5]=>[2,1,6,8,7,3,4,5]=>[7,8,3,1,2,6,5,4]=>[2,1,3,1,1]
[2,1,3,6,8,5,7,4]=>[4,6,8,1,7,2,3,5]=>[5,3,1,8,2,7,6,4]=>[1,1,2,2,1,1]
[1,2,3,8,6,7,4,5]=>[7,5,8,6,1,2,3,4]=>[2,4,1,3,8,7,6,5]=>[2,3,1,1,1]
[1,2,3,8,7,5,4,6]=>[7,6,8,5,1,2,3,4]=>[2,3,1,4,8,7,6,5]=>[2,3,1,1,1]
[1,2,3,8,7,4,5,6]=>[6,7,8,5,1,2,3,4]=>[3,2,1,4,8,7,6,5]=>[1,1,3,1,1,1]
[1,2,3,8,5,7,4,6]=>[5,7,8,6,1,2,3,4]=>[4,2,1,3,8,7,6,5]=>[1,1,3,1,1,1]
[5,4,1,2,8,7,6,3]=>[2,1,8,7,6,3,4,5]=>[7,8,1,2,3,6,5,4]=>[2,4,1,1]
[3,1,6,2,8,7,5,4]=>[3,8,1,7,6,2,4,5]=>[6,1,8,2,3,7,5,4]=>[1,2,3,1,1]
[1,2,3,4,5,9,6,7,8]=>[7,8,9,1,2,3,4,5,6]=>[3,2,1,9,8,7,6,5,4]=>[1,1,2,1,1,1,1,1]
[1,2,3,4,9,5,6,7,8]=>[6,7,8,9,1,2,3,4,5]=>[4,3,2,1,9,8,7,6,5]=>[1,1,1,2,1,1,1,1]
[1,2,3,9,4,5,6,7,8]=>[5,6,7,8,9,1,2,3,4]=>[5,4,3,2,1,9,8,7,6]=>[1,1,1,1,2,1,1,1]
[1,2,9,3,4,5,6,7,8]=>[4,5,6,7,8,9,1,2,3]=>[6,5,4,3,2,1,9,8,7]=>[1,1,1,1,1,2,1,1]
[1,2,3,4,5,6,7,10,8,9]=>[9,10,1,2,3,4,5,6,7,8]=>[2,1,10,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1,1]
[1,2,3,4,5,9,7,6,8]=>[8,7,9,1,2,3,4,5,6]=>[2,3,1,9,8,7,6,5,4]=>[2,2,1,1,1,1,1]
[1,2,3,4,5,6,10,7,8,9]=>[8,9,10,1,2,3,4,5,6,7]=>[3,2,1,10,9,8,7,6,5,4]=>[1,1,2,1,1,1,1,1,1]
[1,2,3,4,9,6,5,7,8]=>[7,6,8,9,1,2,3,4,5]=>[3,4,2,1,9,8,7,6,5]=>[2,1,2,1,1,1,1]
[1,2,3,4,5,10,6,7,8,9]=>[7,8,9,10,1,2,3,4,5,6]=>[4,3,2,1,10,9,8,7,6,5]=>[1,1,1,2,1,1,1,1,1]
[1,2,8,4,5,3,6,7]=>[4,6,5,7,8,1,2,3]=>[5,3,4,2,1,8,7,6]=>[1,2,1,2,1,1]
[1,2,3,9,5,4,6,7,8]=>[6,5,7,8,9,1,2,3,4]=>[4,5,3,2,1,9,8,7,6]=>[2,1,1,2,1,1,1]
[1,2,3,4,10,5,6,7,8,9]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[1,1,1,1,2,1,1,1,1]
[1,8,3,4,2,5,6,7]=>[3,5,4,6,7,8,1,2]=>[6,4,5,3,2,1,8,7]=>[1,2,1,1,2,1]
[1,2,9,4,3,5,6,7,8]=>[5,4,6,7,8,9,1,2,3]=>[5,6,4,3,2,1,9,8,7]=>[2,1,1,1,2,1,1]
[1,2,3,10,4,5,6,7,8,9]=>[5,6,7,8,9,10,1,2,3,4]=>[6,5,4,3,2,1,10,9,8,7]=>[1,1,1,1,1,2,1,1,1]
[1,8,4,3,2,5,6,7]=>[5,4,3,6,7,8,1,2]=>[4,5,6,3,2,1,8,7]=>[3,1,1,2,1]
[1,9,3,2,4,5,6,7,8]=>[4,3,5,6,7,8,9,1,2]=>[6,7,5,4,3,2,1,9,8]=>[2,1,1,1,1,2,1]
[1,2,10,3,4,5,6,7,8,9]=>[4,5,6,7,8,9,10,1,2,3]=>[7,6,5,4,3,2,1,10,9,8]=>[1,1,1,1,1,1,2,1,1]
[8,4,7,6,5,3,2,1]=>[8,7,2,6,5,4,3,1]=>[1,2,7,3,4,5,6,8]=>[3,5]
[8,4,7,5,6,3,2,1]=>[4,8,2,7,6,5,3,1]=>[5,1,7,2,3,4,6,8]=>[1,2,5]
[8,5,7,4,6,3,2,1]=>[2,4,8,7,6,5,3,1]=>[7,5,1,2,3,4,6,8]=>[1,1,6]
[8,7,6,3,5,4,2,1]=>[8,4,7,6,5,3,2,1]=>[1,5,2,3,4,6,7,8]=>[2,6]
[8,6,7,3,5,4,2,1]=>[8,4,2,7,6,5,3,1]=>[1,5,7,2,3,4,6,8]=>[3,5]
[8,5,7,3,6,4,2,1]=>[2,8,4,7,6,5,3,1]=>[7,1,5,2,3,4,6,8]=>[1,2,5]
[8,1,7,4,6,5,3,2]=>[8,4,7,6,5,2,3,1]=>[1,5,2,3,4,7,6,8]=>[2,4,2]
[8,1,7,3,6,5,4,2]=>[8,7,4,6,5,2,3,1]=>[1,2,5,3,4,7,6,8]=>[3,3,2]
[8,2,7,3,6,5,4,1]=>[8,7,4,6,2,5,3,1]=>[1,2,5,3,7,4,6,8]=>[3,2,3]
[8,3,7,2,6,5,4,1]=>[8,7,2,4,6,5,3,1]=>[1,2,7,5,3,4,6,8]=>[3,1,4]
[8,5,7,2,6,4,3,1]=>[2,8,7,4,6,5,3,1]=>[7,1,2,5,3,4,6,8]=>[1,3,4]
[8,6,7,2,5,4,3,1]=>[8,7,4,2,6,5,3,1]=>[1,2,5,7,3,4,6,8]=>[4,4]
[8,7,6,2,5,4,3,1]=>[8,7,4,6,5,3,2,1]=>[1,2,5,3,4,6,7,8]=>[3,5]
[8,4,7,1,6,5,3,2]=>[8,2,7,6,4,5,3,1]=>[1,7,2,3,5,4,6,8]=>[2,3,3]
[8,3,7,1,6,5,4,2]=>[8,7,2,6,4,5,3,1]=>[1,2,7,3,5,4,6,8]=>[3,2,3]
[8,2,7,1,6,5,4,3]=>[8,7,6,2,4,5,3,1]=>[1,2,3,7,5,4,6,8]=>[4,1,3]
[8,1,7,2,6,5,4,3]=>[8,7,6,4,5,2,3,1]=>[1,2,3,5,4,7,6,8]=>[4,2,2]
[8,7,6,2,5,3,4,1]=>[6,8,4,7,5,3,2,1]=>[3,1,5,2,4,6,7,8]=>[1,2,5]
[8,1,7,6,5,3,4,2]=>[6,8,7,5,4,2,3,1]=>[3,1,2,4,5,7,6,8]=>[1,5,2]
[8,3,7,6,5,2,4,1]=>[6,8,7,2,5,4,3,1]=>[3,1,2,7,4,5,6,8]=>[1,3,4]
[8,4,7,6,5,2,3,1]=>[6,8,2,7,5,4,3,1]=>[3,1,7,2,4,5,6,8]=>[1,2,5]
[8,5,7,6,4,2,3,1]=>[2,6,8,7,5,4,3,1]=>[7,3,1,2,4,5,6,8]=>[1,1,6]
[8,6,7,5,4,1,3,2]=>[8,6,2,7,5,4,3,1]=>[1,3,7,2,4,5,6,8]=>[3,5]
[8,5,7,6,4,1,3,2]=>[2,8,6,7,5,4,3,1]=>[7,1,3,2,4,5,6,8]=>[1,2,5]
[8,3,7,6,5,1,4,2]=>[8,6,7,2,5,4,3,1]=>[1,3,2,7,4,5,6,8]=>[2,2,4]
[8,7,6,4,5,1,3,2]=>[8,6,4,7,5,3,2,1]=>[1,3,5,2,4,6,7,8]=>[3,5]
[8,7,6,2,5,1,4,3]=>[8,4,6,7,5,3,2,1]=>[1,5,3,2,4,6,7,8]=>[2,1,5]
[8,7,6,1,5,2,4,3]=>[8,6,7,4,5,3,2,1]=>[1,3,2,5,4,6,7,8]=>[2,2,4]
[6,8,1,3,2,5,4,7]=>[4,7,3,5,1,6,8,2]=>[5,2,6,4,8,3,1,7]=>[1,2,2,1,2]
[6,8,1,4,2,5,3,7]=>[7,5,3,4,1,6,8,2]=>[2,4,6,5,8,3,1,7]=>[3,2,1,2]
[7,8,3,6,1,4,2,5]=>[3,7,5,6,1,8,4,2]=>[6,2,4,3,8,1,5,7]=>[1,2,2,3]
[7,8,2,5,3,6,1,4]=>[5,7,3,4,1,8,6,2]=>[4,2,6,5,8,1,3,7]=>[1,2,2,3]
[7,8,2,5,1,4,3,6]=>[7,3,5,6,4,1,8,2]=>[2,6,4,3,5,8,1,7]=>[2,1,3,2]
[7,8,1,4,3,6,2,5]=>[5,4,7,8,3,1,6,2]=>[4,5,2,1,6,8,3,7]=>[2,1,3,2]
[6,8,2,5,1,4,3,7]=>[7,3,5,1,6,4,8,2]=>[2,6,4,8,3,5,1,7]=>[2,2,2,2]
[6,8,2,5,3,7,1,4]=>[5,7,3,1,4,8,6,2]=>[4,2,6,8,5,1,3,7]=>[1,3,1,3]
[6,8,2,5,4,7,1,3]=>[7,5,3,1,4,8,6,2]=>[2,4,6,8,5,1,3,7]=>[4,1,3]
[2,5,4,7,6,8,1,3]=>[2,7,3,5,1,4,8,6]=>[7,2,6,4,8,5,1,3]=>[1,2,2,1,2]
[2,5,3,7,6,8,1,4]=>[2,7,5,1,3,4,8,6]=>[7,2,4,8,6,5,1,3]=>[1,3,1,1,2]
[2,6,1,4,3,7,5,8]=>[4,7,1,3,5,2,6,8]=>[5,2,8,6,4,7,3,1]=>[1,2,1,2,1,1]
[2,6,5,8,1,4,3,7]=>[7,5,3,1,2,6,8,4]=>[2,4,6,8,7,3,1,5]=>[4,1,1,2]
[2,6,1,5,3,7,4,8]=>[7,5,1,3,4,2,6,8]=>[2,4,8,6,5,7,3,1]=>[3,1,2,1,1]
[2,6,4,7,5,8,1,3]=>[7,3,2,5,1,4,8,6]=>[2,6,7,4,8,5,1,3]=>[3,2,1,2]
[5,8,3,6,4,7,1,2]=>[1,7,3,5,4,8,6,2]=>[8,2,6,4,5,1,3,7]=>[1,2,2,3]
[4,8,2,6,3,7,1,5]=>[1,5,7,3,4,8,6,2]=>[8,4,2,6,5,1,3,7]=>[1,1,2,1,3]
[4,8,1,5,3,7,2,6]=>[1,5,4,7,8,3,6,2]=>[8,4,5,2,1,6,3,7]=>[1,2,1,2,2]
[4,8,1,5,2,6,3,7]=>[1,7,5,3,4,6,8,2]=>[8,2,4,6,5,3,1,7]=>[1,3,1,1,2]
[4,8,3,7,1,5,2,6]=>[1,3,7,5,6,8,4,2]=>[8,6,2,4,3,1,5,7]=>[1,1,2,1,3]
[6,8,3,7,1,4,2,5]=>[3,7,5,1,6,8,4,2]=>[6,2,4,8,3,1,5,7]=>[1,3,1,3]
[5,8,1,3,2,6,4,7]=>[4,7,3,1,5,6,8,2]=>[5,2,6,8,4,3,1,7]=>[1,3,1,1,2]
[5,8,4,7,1,3,2,6]=>[1,7,5,3,6,8,4,2]=>[8,2,4,6,3,1,5,7]=>[1,3,1,3]
[6,8,4,7,1,3,2,5]=>[7,5,3,1,6,8,4,2]=>[2,4,6,8,3,1,5,7]=>[4,1,3]
[6,8,5,7,1,3,2,4]=>[7,5,1,6,3,8,4,2]=>[2,4,8,3,6,1,5,7]=>[3,2,3]
[5,7,6,8,2,4,1,3]=>[1,5,7,3,2,8,6,4]=>[8,4,2,6,7,1,3,5]=>[1,1,3,3]
[4,7,6,8,1,3,2,5]=>[7,1,5,6,3,2,8,4]=>[2,8,4,3,6,7,1,5]=>[2,1,3,2]
[4,7,5,8,1,3,2,6]=>[7,1,5,3,6,2,8,4]=>[2,8,4,6,3,7,1,5]=>[2,2,2,2]
[4,7,1,3,2,6,5,8]=>[4,1,7,3,5,6,2,8]=>[5,8,2,6,4,3,7,1]=>[2,2,1,2,1]
[3,7,5,8,1,4,2,6]=>[7,5,1,3,6,2,8,4]=>[2,4,8,6,3,7,1,5]=>[3,1,2,2]
[3,7,6,8,1,4,2,5]=>[7,5,6,1,3,2,8,4]=>[2,4,3,8,6,7,1,5]=>[2,2,2,2]
[3,7,6,8,2,5,1,4]=>[5,7,3,1,2,8,6,4]=>[4,2,6,8,7,1,3,5]=>[1,3,1,3]
[4,7,6,8,2,5,1,3]=>[5,7,1,3,2,8,6,4]=>[4,2,8,6,7,1,3,5]=>[1,2,2,3]
[4,7,5,8,3,6,1,2]=>[3,7,1,5,2,8,6,4]=>[6,2,8,4,7,1,3,5]=>[1,2,2,3]
[4,7,5,8,2,6,1,3]=>[5,1,3,7,2,8,6,4]=>[4,8,6,2,7,1,3,5]=>[2,1,2,3]
[3,7,5,8,2,6,1,4]=>[5,3,7,1,2,8,6,4]=>[4,6,2,8,7,1,3,5]=>[2,2,1,3]
[3,7,4,8,2,6,1,5]=>[3,5,7,1,2,8,6,4]=>[6,4,2,8,7,1,3,5]=>[1,1,2,1,3]
[3,7,4,8,1,5,2,6]=>[3,7,1,5,6,2,8,4]=>[6,2,8,4,3,7,1,5]=>[1,2,1,2,2]
[3,7,1,5,2,6,4,8]=>[7,1,5,3,4,6,2,8]=>[2,8,4,6,5,3,7,1]=>[2,2,1,2,1]
[3,7,2,6,1,5,4,8]=>[7,1,3,5,6,4,2,8]=>[2,8,6,4,3,5,7,1]=>[2,1,1,3,1]
[3,7,2,6,5,8,1,4]=>[7,5,1,3,4,2,8,6]=>[2,4,8,6,5,7,1,3]=>[3,1,2,2]
[4,7,3,6,5,8,1,2]=>[7,1,3,5,4,2,8,6]=>[2,8,6,4,5,7,1,3]=>[2,1,3,2]
[3,6,5,8,4,7,1,2]=>[3,2,7,1,5,8,6,4]=>[6,7,2,8,4,1,3,5]=>[2,2,1,3]
[2,6,5,8,3,7,1,4]=>[5,3,2,7,8,1,6,4]=>[4,6,7,2,1,8,3,5]=>[3,1,2,2]
[2,6,3,7,1,5,4,8]=>[7,3,5,1,2,6,4,8]=>[2,6,4,8,7,3,5,1]=>[2,2,1,2,1]
[7,6,4,2,8,5,3,1]=>[3,8,7,4,2,1,6,5]=>[6,1,2,5,7,8,3,4]=>[1,5,2]
[7,6,4,3,8,2,5,1]=>[4,3,6,2,1,8,7,5]=>[5,6,3,7,8,1,2,4]=>[2,3,3]
[7,6,4,8,5,2,3,1]=>[3,6,2,1,8,7,5,4]=>[6,3,7,8,1,2,4,5]=>[1,3,4]
[6,8,4,3,7,2,1,5]=>[4,3,1,7,6,8,5,2]=>[5,6,8,2,3,1,4,7]=>[3,2,3]
[6,7,4,3,5,1,8,2]=>[4,3,1,8,6,5,2,7]=>[5,6,8,1,3,4,7,2]=>[3,4,1]
[6,7,3,5,4,8,2,1]=>[5,3,1,4,2,8,7,6]=>[4,6,8,5,7,1,2,3]=>[3,2,3]
[6,8,3,7,5,2,4,1]=>[6,1,8,3,7,5,4,2]=>[3,8,1,6,2,4,5,7]=>[2,2,4]
[7,6,8,3,5,2,4,1]=>[4,6,2,1,8,7,5,3]=>[5,3,7,8,1,2,4,6]=>[1,3,4]
[7,6,3,5,8,2,4,1]=>[6,3,4,2,1,8,7,5]=>[3,6,5,7,8,1,2,4]=>[2,3,3]
[7,6,3,5,2,4,8,1]=>[3,5,6,4,2,1,8,7]=>[6,4,3,5,7,8,1,2]=>[1,1,4,2]
[7,6,4,2,5,1,8,3]=>[8,4,3,6,5,2,1,7]=>[1,5,6,3,4,7,8,2]=>[3,4,1]
[7,6,2,8,4,1,5,3]=>[8,6,3,5,2,1,7,4]=>[1,3,6,4,7,8,2,5]=>[3,3,2]
[7,6,3,4,8,2,5,1]=>[3,4,6,2,1,8,7,5]=>[6,5,3,7,8,1,2,4]=>[1,1,3,3]
[6,8,3,7,4,5,2,1]=>[5,1,8,3,7,6,4,2]=>[4,8,1,6,2,3,5,7]=>[2,2,4]
[6,7,3,5,8,4,2,1]=>[4,1,8,3,2,7,6,5]=>[5,8,1,6,7,2,3,4]=>[2,3,3]
[5,7,8,3,6,2,1,4]=>[1,4,7,6,2,8,5,3]=>[8,5,2,3,7,1,4,6]=>[1,1,3,3]
[5,8,3,6,7,2,1,4]=>[1,7,3,6,4,8,5,2]=>[8,2,6,3,5,1,4,7]=>[1,2,2,3]
[6,3,4,8,7,2,5,1]=>[6,8,2,1,3,7,5,4]=>[3,1,7,8,6,2,4,5]=>[1,3,1,3]
[6,3,8,4,7,2,1,5]=>[4,7,2,1,6,8,5,3]=>[5,2,7,8,3,1,4,6]=>[1,3,1,3]
[6,2,8,4,1,7,5,3]=>[4,8,7,2,1,5,6,3]=>[5,1,2,7,8,4,3,6]=>[1,4,1,2]
[6,2,7,4,1,5,3,8]=>[7,5,2,4,1,6,3,8]=>[2,4,7,5,8,3,6,1]=>[3,2,2,1]
[6,3,4,7,5,8,2,1]=>[5,2,3,1,4,8,7,6]=>[4,7,6,8,5,1,2,3]=>[2,2,1,3]
[5,7,3,6,8,2,1,4]=>[1,7,3,6,4,2,8,5]=>[8,2,6,3,5,7,1,4]=>[1,2,3,2]
[5,6,8,3,7,2,1,4]=>[1,4,2,7,6,8,5,3]=>[8,5,7,2,3,1,4,6]=>[1,2,2,3]
[5,6,7,3,4,1,8,2]=>[1,4,2,8,6,5,3,7]=>[8,5,7,1,3,4,6,2]=>[1,2,4,1]
[4,6,7,8,3,5,2,1]=>[2,5,1,3,8,7,6,4]=>[7,4,8,6,1,2,3,5]=>[1,2,1,4]
[4,6,8,3,5,7,2,1]=>[4,1,2,5,8,7,6,3]=>[5,8,7,4,1,2,3,6]=>[2,1,1,4]
[4,7,3,5,6,8,2,1]=>[1,3,4,5,2,8,7,6]=>[8,6,5,4,7,1,2,3]=>[1,1,1,2,3]
[4,7,3,5,8,2,6,1]=>[1,3,4,6,2,8,7,5]=>[8,6,5,3,7,1,2,4]=>[1,1,1,2,3]
[5,3,4,7,8,2,1,6]=>[7,2,1,3,6,4,8,5]=>[2,7,8,6,3,5,1,4]=>[3,1,2,2]
[5,3,8,2,4,1,6,7]=>[2,4,1,6,5,7,8,3]=>[7,5,8,3,4,2,1,6]=>[1,2,2,1,2]
[5,3,4,8,2,6,1,7]=>[2,3,1,5,7,6,8,4]=>[7,6,8,4,2,3,1,5]=>[1,2,1,2,2]
[4,8,3,6,2,5,7,1]=>[1,3,5,6,4,8,7,2]=>[8,6,4,3,5,1,2,7]=>[1,1,1,2,3]
[4,8,3,5,7,2,6,1]=>[1,3,4,6,8,7,5,2]=>[8,6,5,3,1,2,4,7]=>[1,1,1,1,4]
[4,8,3,5,6,7,2,1]=>[1,3,4,5,8,7,6,2]=>[8,6,5,4,1,2,3,7]=>[1,1,1,1,4]
[4,7,8,3,5,6,2,1]=>[4,5,1,2,8,7,6,3]=>[5,4,8,7,1,2,3,6]=>[1,2,1,4]
[4,7,8,3,6,2,5,1]=>[4,6,1,2,8,7,5,3]=>[5,3,8,7,1,2,4,6]=>[1,2,1,4]
[4,8,3,6,7,2,5,1]=>[6,1,3,4,8,7,5,2]=>[3,8,6,5,1,2,4,7]=>[2,1,1,4]
[4,8,3,7,2,5,6,1]=>[1,3,5,6,8,7,4,2]=>[8,6,4,3,1,2,5,7]=>[1,1,1,1,4]
[5,3,4,8,2,7,6,1]=>[8,2,1,3,5,7,6,4]=>[1,7,8,6,4,2,3,5]=>[3,1,1,3]
[5,3,8,2,4,1,7,6]=>[2,4,1,5,8,6,7,3]=>[7,5,8,4,1,3,2,6]=>[1,2,1,2,2]
[5,2,8,4,1,7,3,6]=>[7,4,1,8,2,5,6,3]=>[2,5,8,1,7,4,3,6]=>[3,2,1,2]
[6,4,2,5,1,8,7,3]=>[4,2,8,3,1,7,5,6]=>[5,7,1,6,8,2,4,3]=>[2,3,2,1]
[6,4,3,5,8,2,1,7]=>[3,2,4,1,7,6,8,5]=>[6,7,5,8,2,3,1,4]=>[2,2,2,2]
[6,3,5,8,7,2,4,1]=>[3,6,1,8,2,7,5,4]=>[6,3,8,1,7,2,4,5]=>[1,2,2,3]
[5,8,3,7,2,6,4,1]=>[1,8,3,5,7,6,4,2]=>[8,1,6,4,2,3,5,7]=>[1,2,1,4]
[5,7,3,4,8,2,1,6]=>[3,1,4,7,6,2,8,5]=>[6,8,5,2,3,7,1,4]=>[2,1,3,2]
[5,8,4,2,3,1,6,7]=>[4,1,6,5,3,7,8,2]=>[5,8,3,4,6,2,1,7]=>[2,3,1,2]
[5,8,4,2,3,1,7,6]=>[4,1,5,3,8,6,7,2]=>[5,8,4,6,1,3,2,7]=>[2,2,2,2]
[6,4,5,3,8,2,1,7]=>[2,4,3,1,7,6,8,5]=>[7,5,6,8,2,3,1,4]=>[1,3,2,2]
[6,4,3,8,5,7,2,1]=>[2,5,1,8,3,7,6,4]=>[7,4,8,1,6,2,3,5]=>[1,2,2,3]
[6,4,2,8,5,3,1,7]=>[2,7,6,3,1,5,8,4]=>[7,2,3,6,8,4,1,5]=>[1,4,1,2]
[6,4,2,7,3,1,8,5]=>[5,2,8,3,1,6,4,7]=>[4,7,1,6,8,3,5,2]=>[2,3,2,1]
[6,4,3,7,8,5,2,1]=>[2,4,1,8,3,7,6,5]=>[7,5,8,1,6,2,3,4]=>[1,2,2,3]
[6,4,5,3,7,1,8,2]=>[2,4,3,1,8,6,5,7]=>[7,5,6,8,1,3,4,2]=>[1,3,3,1]
[5,7,4,2,3,1,6,8]=>[4,1,6,5,3,7,2,8]=>[5,8,3,4,6,2,7,1]=>[2,3,2,1]
[5,6,3,7,1,8,2,4]=>[3,1,7,2,8,5,4,6]=>[6,8,2,7,1,4,5,3]=>[2,2,3,1]
[5,6,3,4,7,1,8,2]=>[3,1,4,2,8,6,5,7]=>[6,8,5,7,1,3,4,2]=>[2,2,3,1]
[5,6,3,4,8,2,1,7]=>[3,1,4,2,7,6,8,5]=>[6,8,5,7,2,3,1,4]=>[2,2,2,2]
[6,3,5,7,4,8,2,1]=>[3,5,2,1,4,8,7,6]=>[6,4,7,8,5,1,2,3]=>[1,3,1,3]
[6,3,5,4,7,8,2,1]=>[4,2,3,1,5,8,7,6]=>[5,7,6,8,4,1,2,3]=>[2,2,1,3]
[6,4,3,5,7,1,8,2]=>[3,2,4,1,8,6,5,7]=>[6,7,5,8,1,3,4,2]=>[2,2,3,1]
[6,4,2,5,1,7,3,8]=>[7,3,2,5,4,1,6,8]=>[2,6,7,4,5,8,3,1]=>[3,3,1,1]
[5,3,7,2,4,1,6,8]=>[2,4,1,6,5,7,3,8]=>[7,5,8,3,4,2,6,1]=>[1,2,2,2,1]
[5,3,4,7,2,6,1,8]=>[2,3,1,5,7,6,4,8]=>[7,6,8,4,2,3,5,1]=>[1,2,1,3,1]
[4,7,3,6,2,5,8,1]=>[1,3,5,6,4,2,8,7]=>[8,6,4,3,5,7,1,2]=>[1,1,1,3,2]
[4,7,3,6,8,2,5,1]=>[6,1,3,4,2,8,7,5]=>[3,8,6,5,7,1,2,4]=>[2,1,2,3]
[4,6,7,3,5,8,2,1]=>[4,1,2,5,3,8,7,6]=>[5,8,7,4,6,1,2,3]=>[2,1,2,3]
[4,5,7,8,3,6,2,1]=>[5,1,2,3,8,7,6,4]=>[4,8,7,6,1,2,3,5]=>[2,1,1,4]
[4,5,8,3,6,7,2,1]=>[1,2,4,5,8,7,6,3]=>[8,7,5,4,1,2,3,6]=>[1,1,1,1,4]
[4,5,8,3,7,2,6,1]=>[1,2,4,6,8,7,5,3]=>[8,7,5,3,1,2,4,6]=>[1,1,1,1,4]
[5,3,4,6,8,2,1,7]=>[2,3,1,4,7,6,8,5]=>[7,6,8,5,2,3,1,4]=>[1,2,1,2,2]
[5,3,6,8,2,1,4,7]=>[6,2,1,5,3,7,8,4]=>[3,7,8,4,6,2,1,5]=>[3,2,1,2]
[5,3,4,6,7,1,8,2]=>[2,3,1,4,8,6,5,7]=>[7,6,8,5,1,3,4,2]=>[1,2,1,3,1]
[4,6,3,5,7,8,2,1]=>[1,3,4,2,5,8,7,6]=>[8,6,5,7,4,1,2,3]=>[1,1,2,1,3]
[4,5,7,3,6,8,2,1]=>[1,2,4,5,3,8,7,6]=>[8,7,5,4,6,1,2,3]=>[1,1,1,2,3]
[4,5,6,8,3,7,2,1]=>[1,2,3,5,8,7,6,4]=>[8,7,6,4,1,2,3,5]=>[1,1,1,1,4]
[5,7,4,8,6,3,2,1]=>[8,1,3,2,7,6,5,4]=>[1,8,6,7,2,3,4,5]=>[2,2,4]
[3,2,6,5,1,8,7,4]=>[4,1,3,8,2,7,5,6]=>[5,8,6,1,7,2,4,3]=>[2,1,2,2,1]
[3,5,6,7,2,8,4,1]=>[2,3,8,1,5,4,7,6]=>[7,6,1,8,4,5,2,3]=>[1,1,2,2,2]
[7,6,9,8,5,4,3,2,1]=>[1,9,2,8,7,6,5,4,3]=>[9,1,8,2,3,4,5,6,7]=>[1,2,6]
[6,5,4,9,8,7,3,2,1]=>[1,9,2,8,3,7,6,5,4]=>[9,1,8,2,7,3,4,5,6]=>[1,2,2,4]
[6,7,8,9,5,4,3,2,1]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[1,1,1,6]
[5,4,3,2,9,8,7,6,1]=>[1,9,2,8,3,7,4,6,5]=>[9,1,8,2,7,3,6,4,5]=>[1,2,2,2,2]
[5,6,7,8,9,4,3,2,1]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[1,1,1,1,5]
[4,5,6,7,8,9,3,2,1]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,4]
[3,4,5,6,7,8,9,2,1]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,3]
[8,7,10,9,6,5,4,3,2,1]=>[1,10,2,9,8,7,6,5,4,3]=>[10,1,9,2,3,4,5,6,7,8]=>[1,2,7]
[8,9,10,7,6,5,4,3,2,1]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,1,2,3,4,5,6,7,8]=>[1,1,8]
[7,6,5,10,9,8,4,3,2,1]=>[1,10,2,9,3,8,7,6,5,4]=>[10,1,9,2,8,3,4,5,6,7]=>[1,2,2,5]
[7,8,9,10,6,5,4,3,2,1]=>[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,1,2,3,4,5,6,7]=>[1,1,1,7]
[6,5,4,3,10,9,8,7,2,1]=>[1,10,2,9,3,8,4,7,6,5]=>[10,1,9,2,8,3,7,4,5,6]=>[1,2,2,2,3]
[5,4,3,2,1,10,9,8,7,6]=>[1,10,2,9,3,8,4,7,5,6]=>[10,1,9,2,8,3,7,4,6,5]=>[1,2,2,2,2,1]
[5,6,7,8,9,10,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,6,1,2,3,4,5]=>[1,1,1,1,1,5]
[4,5,6,7,8,9,10,3,2,1]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,7,6,5,1,2,3,4]=>[1,1,1,1,1,1,4]
[3,4,5,6,7,8,9,10,2,1]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,8,7,6,5,4,1,2,3]=>[1,1,1,1,1,1,1,3]
[1,6,2,5,3,4,8,7]=>[8,5,3,4,1,2,6,7]=>[1,4,6,5,8,7,3,2]=>[3,2,1,1,1]
[1,7,2,3,6,4,8,5]=>[8,6,3,4,5,1,2,7]=>[1,3,6,5,4,8,7,2]=>[3,1,2,1,1]
[1,6,8,2,5,3,7,4]=>[8,6,4,2,5,7,1,3]=>[1,3,5,7,4,2,8,6]=>[4,1,2,1]
[1,8,2,3,6,4,7,5]=>[8,6,3,4,5,7,1,2]=>[1,3,6,5,4,2,8,7]=>[3,1,1,2,1]
[1,3,5,2,8,4,7,6]=>[3,8,2,6,7,1,4,5]=>[6,1,7,3,2,8,5,4]=>[1,2,1,2,1,1]
[1,8,2,7,3,4,6,5]=>[8,5,6,7,3,4,1,2]=>[1,4,3,2,6,5,8,7]=>[2,1,2,2,1]
[1,5,8,2,3,7,4,6]=>[7,2,8,4,5,6,1,3]=>[2,7,1,5,4,3,8,6]=>[2,2,1,2,1]
[1,6,8,2,3,5,4,7]=>[7,4,5,2,6,8,1,3]=>[2,5,4,7,3,1,8,6]=>[2,2,1,2,1]
[5,3,6,1,2,4,8,7]=>[2,8,4,1,5,3,6,7]=>[7,1,5,8,4,6,3,2]=>[1,3,2,1,1]
[7,1,5,8,4,2,3,6]=>[6,3,7,5,8,2,1,4]=>[3,6,2,4,1,7,8,5]=>[2,2,3,1]
[7,1,4,5,8,2,3,6]=>[3,6,4,7,8,2,1,5]=>[6,3,5,2,1,7,8,4]=>[1,2,1,3,1]
[7,4,1,6,2,8,3,5]=>[7,2,8,5,3,4,1,6]=>[2,7,1,4,6,5,8,3]=>[2,3,2,1]
[8,4,1,7,2,6,3,5]=>[7,2,8,5,6,3,4,1]=>[2,7,1,4,3,6,5,8]=>[2,2,2,2]
[8,1,4,7,5,2,3,6]=>[3,6,7,5,8,2,4,1]=>[6,3,2,4,1,7,5,8]=>[1,1,2,2,2]
[8,1,5,4,7,2,3,6]=>[6,4,3,7,8,2,5,1]=>[3,5,6,2,1,7,4,8]=>[3,1,2,2]
[2,1,7,5,8,3,4,6]=>[6,4,7,1,3,8,2,5]=>[3,5,2,8,6,1,7,4]=>[2,2,1,2,1]
[7,1,5,4,8,2,3,6]=>[6,4,3,7,8,2,1,5]=>[3,5,6,2,1,7,8,4]=>[3,1,3,1]
[7,1,4,8,5,2,3,6]=>[3,6,7,5,8,2,1,4]=>[6,3,2,4,1,7,8,5]=>[1,1,2,3,1]
[6,4,1,7,2,3,8,5]=>[8,5,2,6,3,1,4,7]=>[1,4,7,3,6,8,5,2]=>[3,3,1,1]
[7,8,3,1,2,4,6,5]=>[8,4,3,5,6,1,7,2]=>[1,5,6,4,3,8,2,7]=>[3,1,2,2]
[8,7,1,6,4,2,3,5]=>[6,7,5,8,3,4,2,1]=>[3,2,4,1,6,5,7,8]=>[1,2,2,3]
[8,6,1,7,4,2,3,5]=>[6,7,5,8,3,2,4,1]=>[3,2,4,1,6,7,5,8]=>[1,2,3,2]
[7,6,1,8,4,2,3,5]=>[6,7,5,8,3,2,1,4]=>[3,2,4,1,6,7,8,5]=>[1,2,4,1]
[7,3,8,1,2,4,6,5]=>[2,8,4,5,6,1,7,3]=>[7,1,5,4,3,8,2,6]=>[1,2,1,2,2]
[8,3,6,1,2,4,7,5]=>[2,8,4,5,6,3,7,1]=>[7,1,5,4,3,6,2,8]=>[1,2,1,2,2]
[8,3,7,5,1,2,4,6]=>[2,5,6,7,4,8,3,1]=>[7,4,3,2,5,1,6,8]=>[1,1,1,2,3]
[6,8,1,7,4,2,3,5]=>[6,7,5,1,8,3,4,2]=>[3,2,4,8,1,6,5,7]=>[1,3,2,2]
[7,1,8,5,4,2,3,6]=>[6,7,5,4,8,2,1,3]=>[3,2,4,5,1,7,8,6]=>[1,3,3,1]
[7,1,8,4,5,2,3,6]=>[6,4,7,5,8,2,1,3]=>[3,5,2,4,1,7,8,6]=>[2,2,3,1]
[2,1,7,8,5,3,4,6]=>[6,7,5,1,3,8,2,4]=>[3,2,4,8,6,1,7,5]=>[1,3,1,2,1]
[6,1,2,3,8,7,5,4]=>[8,7,6,2,3,1,4,5]=>[1,2,3,7,6,8,5,4]=>[4,2,1,1]
[6,8,1,4,2,3,7,5]=>[8,5,3,4,1,6,7,2]=>[1,4,6,5,8,3,2,7]=>[3,2,1,2]
[6,8,3,1,2,7,4,5]=>[7,3,8,4,1,5,6,2]=>[2,6,1,5,8,4,3,7]=>[2,3,1,2]
[6,7,3,1,2,8,4,5]=>[7,3,8,4,1,5,2,6]=>[2,6,1,5,8,4,7,3]=>[2,3,2,1]
[6,7,1,4,2,3,8,5]=>[8,5,3,4,1,6,2,7]=>[1,4,6,5,8,3,7,2]=>[3,2,2,1]
[4,3,6,8,5,7,1,2]=>[1,3,7,2,5,8,6,4]=>[8,6,2,7,4,1,3,5]=>[1,1,2,1,3]
[6,1,2,5,4,8,3,7]=>[5,4,7,8,2,1,3,6]=>[4,5,2,1,7,8,6,3]=>[2,1,3,1,1]
[3,2,8,5,4,1,7,6]=>[5,1,4,8,2,6,7,3]=>[4,8,5,1,7,3,2,6]=>[2,1,2,1,2]
[7,8,2,1,4,6,3,5]=>[3,5,7,8,4,1,6,2]=>[6,4,2,1,5,8,3,7]=>[1,1,1,3,2]
[7,2,1,5,8,3,4,6]=>[6,2,4,7,8,3,1,5]=>[3,7,5,2,1,6,8,4]=>[2,1,1,3,1]
[2,4,8,5,1,3,6,7]=>[2,5,6,1,4,7,8,3]=>[7,4,3,8,5,2,1,6]=>[1,1,2,1,1,2]
[3,5,6,1,8,4,2,7]=>[2,7,1,6,3,8,4,5]=>[7,2,8,3,6,1,5,4]=>[1,2,2,2,1]
[1,3,6,8,7,4,2,5]=>[3,7,6,8,2,5,1,4]=>[6,2,3,1,7,4,8,5]=>[1,2,2,2,1]
[2,6,1,5,8,3,4,7]=>[6,4,7,1,2,8,3,5]=>[3,5,2,8,7,1,6,4]=>[2,2,1,2,1]
[5,7,1,6,8,4,3,2]=>[1,4,8,7,6,3,2,5]=>[8,5,1,2,3,6,7,4]=>[1,1,5,1]
[8,4,6,2,5,7,3,1]=>[2,5,8,4,3,7,6,1]=>[7,4,1,5,6,2,3,8]=>[1,1,3,3]
[8,3,6,4,7,2,5,1]=>[4,6,2,3,8,7,5,1]=>[5,3,7,6,1,2,4,8]=>[1,2,1,4]
[3,8,1,4,7,2,5,6]=>[1,4,6,7,8,3,5,2]=>[8,5,3,2,1,6,4,7]=>[1,1,1,1,2,2]
[1,7,8,4,6,2,5,3]=>[4,8,6,2,7,5,1,3]=>[5,1,3,7,2,4,8,6]=>[1,3,3,1]
[3,7,4,8,5,1,6,2]=>[8,3,6,1,5,2,7,4]=>[1,6,3,8,4,7,2,5]=>[2,2,2,2]
[3,7,1,6,5,4,8,2]=>[6,5,1,4,8,3,2,7]=>[3,4,8,5,1,6,7,2]=>[3,1,3,1]
[2,7,3,1,5,8,4,6]=>[3,5,7,8,1,4,2,6]=>[6,4,2,1,8,5,7,3]=>[1,1,1,2,2,1]
[2,7,4,6,8,1,3,5]=>[3,6,7,4,1,2,8,5]=>[6,3,2,5,8,7,1,4]=>[1,1,3,1,2]
[2,7,5,8,6,4,1,3]=>[3,7,2,8,6,1,5,4]=>[6,2,7,1,3,8,4,5]=>[1,2,3,2]
[8,2,6,7,5,4,3,1]=>[3,8,7,6,2,5,4,1]=>[6,1,2,3,7,4,5,8]=>[1,4,3]
[3,8,7,1,6,4,5,2]=>[6,8,7,1,4,5,3,2]=>[3,1,2,8,5,4,6,7]=>[1,3,1,3]
[3,6,8,2,7,4,1,5]=>[7,4,1,2,6,8,5,3]=>[2,5,8,7,3,1,4,6]=>[3,1,1,3]
[1,5,2,8,7,4,6,3]=>[2,6,8,7,5,1,3,4]=>[7,3,1,2,4,8,6,5]=>[1,1,4,1,1]
[4,1,3,7,5,6,8,2]=>[5,1,6,3,4,8,2,7]=>[4,8,3,6,5,1,7,2]=>[2,2,1,2,1]
[6,3,8,1,7,4,2,5]=>[7,2,6,1,8,4,5,3]=>[2,7,3,8,1,5,4,6]=>[2,2,2,2]
[4,1,7,3,8,5,2,6]=>[1,7,4,6,3,8,2,5]=>[8,2,5,3,6,1,7,4]=>[1,2,2,2,1]
[3,6,1,4,5,8,2,7]=>[1,4,5,7,2,8,3,6]=>[8,5,4,2,7,1,6,3]=>[1,1,1,2,2,1]
[1,6,7,4,5,3,8,2]=>[4,2,6,5,3,8,1,7]=>[5,7,3,4,6,1,8,2]=>[2,3,2,1]
[6,1,7,3,5,4,8,2]=>[6,4,5,3,1,8,2,7]=>[3,5,4,6,8,1,7,2]=>[2,3,2,1]
[1,4,7,2,8,5,3,6]=>[7,2,6,8,4,1,3,5]=>[2,7,3,1,5,8,6,4]=>[2,1,3,1,1]
[5,6,8,7,2,4,1,3]=>[1,5,2,7,8,6,4,3]=>[8,4,7,2,1,3,5,6]=>[1,2,1,4]
[6,8,5,7,1,2,4,3]=>[8,5,1,6,3,7,4,2]=>[1,4,8,3,6,2,5,7]=>[3,2,3]
[2,8,4,1,7,5,6,3]=>[3,6,8,7,1,4,5,2]=>[6,3,1,2,8,5,4,7]=>[1,1,3,1,2]
[8,2,4,3,7,5,6,1]=>[3,6,8,2,4,7,5,1]=>[6,3,1,7,5,2,4,8]=>[1,1,2,1,3]
[6,8,2,1,5,7,3,4]=>[7,3,5,1,8,4,6,2]=>[2,6,4,8,1,5,3,7]=>[2,2,2,2]
[1,2,4,8,6,5,3,7]=>[7,6,3,5,8,1,2,4]=>[2,3,6,4,1,8,7,5]=>[3,1,2,1,1]
[7,1,5,6,8,4,3,2]=>[3,4,8,7,6,2,1,5]=>[6,5,1,2,3,7,8,4]=>[1,1,5,1]
[2,7,8,1,4,6,3,5]=>[5,7,8,4,1,2,6,3]=>[4,2,1,5,8,7,3,6]=>[1,1,3,1,2]
[4,8,2,5,7,1,6,3]=>[1,4,8,3,6,7,5,2]=>[8,5,1,6,3,2,4,7]=>[1,1,2,1,3]
[4,1,6,8,5,3,7,2]=>[1,3,6,5,8,7,2,4]=>[8,6,3,4,1,2,7,5]=>[1,1,2,3,1]
[5,2,6,4,8,3,1,7]=>[4,3,1,7,2,6,8,5]=>[5,6,8,2,7,3,1,4]=>[3,2,1,2]
[6,7,1,3,4,5,8,2]=>[4,5,6,1,8,3,2,7]=>[5,4,3,8,1,6,7,2]=>[1,1,2,3,1]
[1,7,3,2,4,8,5,6]=>[3,7,8,4,5,1,2,6]=>[6,2,1,5,4,8,7,3]=>[1,1,2,2,1,1]
[7,1,6,5,3,4,8,2]=>[5,6,4,3,8,2,1,7]=>[4,3,5,6,1,7,8,2]=>[1,3,3,1]
[6,3,4,2,8,7,5,1]=>[8,2,3,1,7,4,6,5]=>[1,7,6,8,2,5,3,4]=>[2,2,2,2]
[4,3,8,7,5,2,6,1]=>[6,1,5,8,2,7,4,3]=>[3,8,4,1,7,2,5,6]=>[2,1,2,3]
[6,8,7,4,2,3,5,1]=>[5,1,6,4,8,7,3,2]=>[4,8,3,5,1,2,6,7]=>[2,2,4]
[3,6,4,5,2,8,7,1]=>[3,4,1,2,8,5,7,6]=>[6,5,8,7,1,4,2,3]=>[1,2,1,2,2]
[8,6,1,3,5,4,2,7]=>[7,4,6,3,5,2,8,1]=>[2,5,3,6,4,7,1,8]=>[2,2,2,2]
[5,3,8,6,1,2,4,7]=>[2,5,1,6,7,4,8,3]=>[7,4,8,3,2,5,1,6]=>[1,2,1,2,2]
[2,5,6,3,4,8,7,1]=>[2,8,4,1,3,5,7,6]=>[7,1,5,8,6,4,2,3]=>[1,3,1,1,2]
[2,5,3,6,8,7,4,1]=>[2,8,4,7,1,3,6,5]=>[7,1,5,2,8,6,3,4]=>[1,2,2,1,2]
[4,8,7,3,5,2,6,1]=>[4,6,1,5,8,7,3,2]=>[5,3,8,4,1,2,6,7]=>[1,2,1,4]
[3,8,7,2,6,4,5,1]=>[6,8,4,7,1,5,3,2]=>[3,1,5,2,8,4,6,7]=>[1,2,2,3]
[6,3,5,4,8,7,2,1]=>[3,8,2,1,4,7,6,5]=>[6,1,7,8,5,2,3,4]=>[1,3,1,3]
[4,3,8,6,1,5,2,7]=>[1,7,2,5,6,4,8,3]=>[8,2,7,4,3,5,1,6]=>[1,2,1,2,2]
[4,7,6,2,5,3,8,1]=>[6,1,4,5,3,2,8,7]=>[3,8,5,4,6,7,1,2]=>[2,1,3,2]
[7,5,2,6,8,1,4,3]=>[8,6,3,2,4,1,7,5]=>[1,3,6,7,5,8,2,4]=>[4,2,2]
[8,5,2,7,1,4,3,6]=>[7,3,5,2,6,8,4,1]=>[2,6,4,7,3,1,5,8]=>[2,2,1,3]
[1,8,5,3,6,2,4,7]=>[4,6,3,7,5,8,1,2]=>[5,3,6,2,4,1,8,7]=>[1,2,2,2,1]
[5,1,7,2,4,3,8,6]=>[5,8,4,1,6,2,3,7]=>[4,1,5,8,3,7,6,2]=>[1,3,2,1,1]
[1,5,3,4,8,6,2,7]=>[7,3,2,4,6,8,1,5]=>[2,6,7,5,3,1,8,4]=>[3,1,1,2,1]
[5,4,1,3,8,6,2,7]=>[7,4,2,1,6,8,3,5]=>[2,5,7,8,3,1,6,4]=>[4,1,2,1]
[4,5,2,8,3,7,6,1]=>[1,2,8,5,7,3,6,4]=>[8,7,1,4,2,6,3,5]=>[1,1,2,2,2]
[8,2,3,7,6,4,5,1]=>[6,8,7,2,3,5,4,1]=>[3,1,2,7,6,4,5,8]=>[1,3,1,3]
[5,8,2,4,7,6,3,1]=>[1,8,4,7,3,6,5,2]=>[8,1,5,2,6,3,4,7]=>[1,2,2,3]
[6,8,2,5,3,4,7,1]=>[5,6,3,1,4,8,7,2]=>[4,3,6,8,5,1,2,7]=>[1,3,1,3]
[7,2,5,6,4,8,1,3]=>[3,7,5,2,4,1,8,6]=>[6,2,4,7,5,8,1,3]=>[1,3,2,2]
[1,6,7,4,8,2,3,5]=>[6,4,2,7,3,8,1,5]=>[3,5,7,2,6,1,8,4]=>[3,2,2,1]
[8,2,1,3,5,6,7,4]=>[2,5,6,8,3,4,7,1]=>[7,4,3,1,6,5,2,8]=>[1,1,1,2,1,2]
[6,3,1,4,7,5,8,2]=>[2,6,4,5,1,8,3,7]=>[7,3,5,4,8,1,6,2]=>[1,2,2,2,1]
[4,1,3,8,2,6,7,5]=>[6,1,8,3,5,7,2,4]=>[3,8,1,6,4,2,7,5]=>[2,2,1,2,1]
[2,8,3,6,7,5,4,1]=>[4,8,7,3,6,1,5,2]=>[5,1,2,6,3,8,4,7]=>[1,3,2,2]
[3,6,1,4,7,2,8,5]=>[8,1,4,6,3,2,5,7]=>[1,8,5,3,6,7,4,2]=>[2,1,3,1,1]
[1,5,8,4,7,2,3,6]=>[2,6,4,7,8,5,1,3]=>[7,3,5,2,1,4,8,6]=>[1,2,1,3,1]
[7,1,3,6,2,8,4,5]=>[7,8,3,5,2,4,1,6]=>[2,1,6,4,7,5,8,3]=>[1,2,2,2,1]
[6,2,7,4,5,8,1,3]=>[4,7,5,2,1,3,8,6]=>[5,2,4,7,8,6,1,3]=>[1,4,1,2]
[2,1,8,4,5,7,3,6]=>[4,5,7,8,1,6,2,3]=>[5,4,2,1,8,3,7,6]=>[1,1,1,2,2,1]
[1,8,5,7,3,2,4,6]=>[6,5,3,7,8,4,1,2]=>[3,4,6,2,1,5,8,7]=>[3,1,3,1]
[2,1,8,5,4,3,6,7]=>[6,5,1,4,7,8,2,3]=>[3,4,8,5,2,1,7,6]=>[3,1,1,2,1]
[2,7,4,1,5,3,8,6]=>[5,3,8,1,4,6,2,7]=>[4,6,1,8,5,3,7,2]=>[2,2,1,2,1]
[2,7,1,4,6,3,8,5]=>[8,4,6,1,3,5,2,7]=>[1,5,3,8,6,4,7,2]=>[2,2,1,2,1]
[7,1,3,2,8,5,4,6]=>[7,3,6,8,2,4,1,5]=>[2,6,3,1,7,5,8,4]=>[2,1,2,2,1]
[2,8,5,4,1,3,6,7]=>[5,6,4,1,3,7,8,2]=>[4,3,5,8,6,2,1,7]=>[1,3,1,1,2]
[5,1,7,4,2,3,8,6]=>[8,5,4,1,6,2,3,7]=>[1,4,5,8,3,7,6,2]=>[4,2,1,1]
[3,8,6,5,1,4,2,7]=>[7,5,6,1,4,3,8,2]=>[2,4,3,8,5,6,1,7]=>[2,2,2,2]
[4,1,8,6,5,3,2,7]=>[7,1,6,5,4,8,2,3]=>[2,8,3,4,5,1,7,6]=>[2,3,2,1]
[4,8,5,2,7,3,6,1]=>[6,1,3,8,4,7,5,2]=>[3,8,6,1,5,2,4,7]=>[2,1,2,3]
[7,2,8,5,3,6,4,1]=>[8,5,4,7,2,1,6,3]=>[1,4,5,2,7,8,3,6]=>[3,3,2]
[5,2,8,4,3,7,6,1]=>[4,1,8,5,7,2,6,3]=>[5,8,1,4,2,7,3,6]=>[2,2,2,2]
[8,4,7,5,2,3,6,1]=>[2,5,6,4,8,7,3,1]=>[7,4,3,5,1,2,6,8]=>[1,1,2,4]
[7,5,2,8,4,6,1,3]=>[7,5,2,8,3,1,6,4]=>[2,4,7,1,6,8,3,5]=>[3,3,2]
[5,7,4,3,6,2,8,1]=>[1,4,3,6,5,2,8,7]=>[8,5,6,3,4,7,1,2]=>[1,2,3,2]
[6,7,5,1,2,8,3,4]=>[7,8,4,1,5,3,2,6]=>[2,1,5,8,4,6,7,3]=>[1,3,3,1]
[5,2,6,8,3,4,7,1]=>[5,3,1,6,8,2,7,4]=>[4,6,8,3,1,7,2,5]=>[3,1,2,2]
[7,6,2,4,5,8,3,1]=>[4,5,8,3,2,1,7,6]=>[5,4,1,6,7,8,2,3]=>[1,1,4,2]
[3,6,8,4,7,2,5,1]=>[4,2,6,8,1,7,5,3]=>[5,7,3,1,8,2,4,6]=>[2,1,2,3]
[7,6,3,8,4,2,5,1]=>[6,3,5,2,1,8,7,4]=>[3,6,4,7,8,1,2,5]=>[2,3,3]
[2,6,3,8,4,7,5,1]=>[8,5,2,7,1,3,6,4]=>[1,4,7,2,8,6,3,5]=>[3,2,1,2]
[7,2,3,6,5,8,4,1]=>[5,4,8,2,3,1,7,6]=>[4,5,1,7,6,8,2,3]=>[2,2,2,2]
[6,2,7,5,8,3,1,4]=>[7,6,4,2,1,3,8,5]=>[2,3,5,7,8,6,1,4]=>[5,1,2]
[2,8,3,6,4,5,7,1]=>[5,6,3,4,8,1,7,2]=>[4,3,6,5,1,8,2,7]=>[1,2,1,2,2]
[2,1,5,6,8,3,7,4]=>[3,4,8,1,6,7,2,5]=>[6,5,1,8,3,2,7,4]=>[1,1,2,1,2,1]
[5,8,1,2,6,4,7,3]=>[6,5,1,8,3,4,7,2]=>[3,4,8,1,6,5,2,7]=>[3,2,1,2]
[1,6,8,3,2,7,4,5]=>[4,7,2,8,5,6,1,3]=>[5,2,7,1,4,3,8,6]=>[1,2,2,2,1]
[6,5,7,2,8,4,1,3]=>[7,2,1,8,4,3,6,5]=>[2,7,8,1,5,6,3,4]=>[3,3,2]
[7,5,1,2,8,4,6,3]=>[6,8,7,3,2,4,1,5]=>[3,1,2,6,7,5,8,4]=>[1,4,2,1]
[5,4,8,3,6,2,7,1]=>[2,1,4,6,5,8,7,3]=>[7,8,5,3,4,1,2,6]=>[2,1,2,3]
[5,8,2,7,4,3,6,1]=>[1,6,5,8,3,7,4,2]=>[8,3,4,1,6,2,5,7]=>[1,2,2,3]
[6,4,5,8,2,7,3,1]=>[2,3,1,8,5,7,6,4]=>[7,6,8,1,4,2,3,5]=>[1,2,2,3]
[5,7,3,6,4,8,2,1]=>[1,5,3,4,2,8,7,6]=>[8,4,6,5,7,1,2,3]=>[1,2,2,3]
[1,5,6,4,8,2,7,3]=>[2,4,3,8,6,7,1,5]=>[7,5,6,1,3,2,8,4]=>[1,2,2,2,1]
[3,1,5,6,4,8,7,2]=>[1,3,4,8,5,7,2,6]=>[8,6,5,1,4,2,7,3]=>[1,1,1,2,2,1]
[1,3,6,2,5,7,8,4]=>[5,6,2,3,8,1,4,7]=>[4,3,7,6,1,8,5,2]=>[1,2,1,2,1,1]
[1,4,6,3,5,7,8,2]=>[2,4,5,3,6,8,1,7]=>[7,5,4,6,3,1,8,2]=>[1,1,2,1,2,1]
[3,5,1,6,4,7,8,2]=>[5,1,4,2,6,8,3,7]=>[4,8,5,7,3,1,6,2]=>[2,2,1,2,1]
[3,6,1,4,2,7,8,5]=>[1,4,6,8,3,2,5,7]=>[8,5,3,1,6,7,4,2]=>[1,1,1,3,1,1]
[2,4,6,3,1,7,8,5]=>[2,4,6,1,3,8,5,7]=>[7,5,3,8,6,1,4,2]=>[1,1,2,1,2,1]
[1,3,6,5,2,7,8,4]=>[6,4,2,3,8,1,5,7]=>[3,5,7,6,1,8,4,2]=>[3,1,2,1,1]
[1,2,6,4,3,8,5,7]=>[4,7,3,8,1,2,5,6]=>[5,2,6,1,8,7,4,3]=>[1,2,2,1,1,1]
[1,2,6,3,5,8,7,4]=>[8,5,3,7,1,2,4,6]=>[1,4,6,2,8,7,5,3]=>[3,2,1,1,1]
[2,3,5,1,8,4,7,6]=>[3,8,1,2,6,7,4,5]=>[6,1,8,7,3,2,5,4]=>[1,2,1,1,2,1]
[1,2,7,4,6,8,3,5]=>[7,4,5,3,8,1,2,6]=>[2,5,4,6,1,8,7,3]=>[2,2,2,1,1]
[2,3,7,5,1,8,4,6]=>[7,4,8,1,2,5,3,6]=>[2,5,1,8,7,4,6,3]=>[2,2,1,2,1]
[3,1,7,5,4,8,6,2]=>[4,8,1,5,3,7,2,6]=>[5,1,8,4,6,2,7,3]=>[1,2,2,2,1]
[1,2,7,6,4,8,5,3]=>[8,5,4,3,7,1,2,6]=>[1,4,5,6,2,8,7,3]=>[4,2,1,1]
[1,2,7,3,6,8,5,4]=>[5,8,7,4,1,2,3,6]=>[4,1,2,5,8,7,6,3]=>[1,4,1,1,1]
[2,3,6,1,8,5,7,4]=>[6,3,8,1,2,7,4,5]=>[3,6,1,8,7,2,5,4]=>[2,2,1,2,1]
[3,1,5,4,8,7,6,2]=>[8,1,3,7,4,6,2,5]=>[1,8,6,2,5,3,7,4]=>[2,1,2,2,1]
[1,2,5,8,4,7,3,6]=>[3,5,7,8,6,1,2,4]=>[6,4,2,1,3,8,7,5]=>[1,1,1,3,1,1]
[1,2,6,8,5,4,7,3]=>[3,6,5,8,7,1,2,4]=>[6,3,4,1,2,8,7,5]=>[1,2,3,1,1]
[1,3,6,8,5,2,7,4]=>[3,8,6,2,5,7,1,4]=>[6,1,3,7,4,2,8,5]=>[1,3,1,2,1]
[3,5,7,4,8,2,1,6]=>[2,4,7,1,6,3,8,5]=>[7,5,2,8,3,6,1,4]=>[1,1,2,2,2]
[2,4,7,6,8,3,1,5]=>[7,6,2,4,1,3,8,5]=>[2,3,7,5,8,6,1,4]=>[3,2,1,2]
[1,4,6,8,3,5,2,7]=>[5,2,3,7,6,8,1,4]=>[4,7,6,2,3,1,8,5]=>[2,1,2,2,1]
[1,3,6,8,5,2,4,7]=>[6,3,7,2,5,8,1,4]=>[3,6,2,7,4,1,8,5]=>[2,2,1,2,1]
[1,2,6,8,5,4,3,7]=>[3,7,6,5,8,1,2,4]=>[6,2,3,4,1,8,7,5]=>[1,3,2,1,1]
[1,2,5,8,4,3,7,6]=>[3,5,8,6,7,1,2,4]=>[6,4,1,3,2,8,7,5]=>[1,1,2,2,1,1]
[1,3,5,8,2,4,7,6]=>[3,8,2,5,6,7,1,4]=>[6,1,7,4,3,2,8,5]=>[1,2,1,1,2,1]
[1,3,6,8,2,5,4,7]=>[7,5,2,3,6,8,1,4]=>[2,4,7,6,3,1,8,5]=>[3,1,1,2,1]
[1,4,6,8,3,2,5,7]=>[6,2,5,3,7,8,1,4]=>[3,7,4,6,2,1,8,5]=>[2,2,1,2,1]
[3,5,7,4,8,1,2,6]=>[2,6,1,4,7,3,8,5]=>[7,3,8,5,2,6,1,4]=>[1,2,1,2,2]
[4,6,1,7,5,8,2,3]=>[7,1,5,4,2,8,3,6]=>[2,8,4,5,7,1,6,3]=>[2,3,2,1]
[2,3,6,7,5,8,1,4]=>[3,7,5,1,2,4,8,6]=>[6,2,4,8,7,5,1,3]=>[1,3,1,1,2]
[1,3,7,5,6,8,2,4]=>[4,7,5,2,3,8,1,6]=>[5,2,4,7,6,1,8,3]=>[1,3,1,2,1]
[2,3,6,5,8,1,7,4]=>[4,3,8,1,2,6,7,5]=>[5,6,1,8,7,3,2,4]=>[2,2,1,1,2]
[3,5,4,6,8,2,1,7]=>[3,1,2,4,7,6,8,5]=>[6,8,7,5,2,3,1,4]=>[2,1,1,2,2]
[3,5,4,6,8,1,2,7]=>[3,1,2,6,4,7,8,5]=>[6,8,7,3,5,2,1,4]=>[2,1,2,1,2]
[1,2,4,7,5,8,3,6]=>[5,7,3,4,8,1,2,6]=>[4,2,6,5,1,8,7,3]=>[1,2,1,2,1,1]
[1,2,6,7,4,8,3,5]=>[5,3,7,4,8,1,2,6]=>[4,6,2,5,1,8,7,3]=>[2,2,2,1,1]
[3,6,4,7,1,8,5,2]=>[8,3,1,2,7,5,4,6]=>[1,6,8,7,2,4,5,3]=>[3,1,3,1]
[1,2,6,7,3,8,5,4]=>[3,8,7,5,1,2,4,6]=>[6,1,2,4,8,7,5,3]=>[1,4,1,1,1]
[1,2,5,7,3,8,6,4]=>[8,3,7,5,1,2,4,6]=>[1,6,2,4,8,7,5,3]=>[2,3,1,1,1]
[3,1,5,7,6,8,4,2]=>[5,1,3,4,8,7,2,6]=>[4,8,6,5,1,2,7,3]=>[2,1,1,3,1]
[3,5,4,6,8,2,7,1]=>[3,1,2,4,6,8,7,5]=>[6,8,7,5,3,1,2,4]=>[2,1,1,1,3]
[4,2,6,1,8,7,5,3]=>[1,3,8,7,2,6,4,5]=>[8,6,1,2,7,3,5,4]=>[1,1,3,2,1]
[2,3,6,5,8,7,1,4]=>[4,3,7,8,1,2,6,5]=>[5,6,2,1,8,7,3,4]=>[2,1,2,1,2]
[1,2,7,4,6,8,5,3]=>[5,8,4,3,7,1,2,6]=>[4,1,5,6,2,8,7,3]=>[1,3,2,1,1]
[1,2,7,5,6,8,4,3]=>[4,5,3,8,7,1,2,6]=>[5,4,6,1,2,8,7,3]=>[1,2,3,1,1]
[3,1,6,7,5,8,4,2]=>[3,5,1,4,8,7,2,6]=>[6,4,8,5,1,2,7,3]=>[1,2,1,3,1]
[4,6,2,7,5,8,3,1]=>[5,1,4,2,8,3,7,6]=>[4,8,5,7,1,6,2,3]=>[2,2,2,2]
[3,5,7,4,8,2,6,1]=>[2,4,6,1,3,8,7,5]=>[7,5,3,8,6,1,2,4]=>[1,1,2,1,3]
[2,4,7,6,8,3,5,1]=>[6,4,2,3,8,1,7,5]=>[3,5,7,6,1,8,2,4]=>[3,1,2,2]
[1,4,6,8,3,5,7,2]=>[5,2,3,6,8,7,1,4]=>[4,7,6,3,1,2,8,5]=>[2,1,1,3,1]
[1,3,5,8,2,7,4,6]=>[3,7,8,2,5,6,1,4]=>[6,2,1,7,4,3,8,5]=>[1,1,2,1,2,1]
[1,2,5,8,4,7,6,3]=>[8,3,5,7,6,1,2,4]=>[1,6,4,2,3,8,7,5]=>[2,1,3,1,1]
[1,2,4,8,7,3,6,5]=>[8,6,7,3,5,1,2,4]=>[1,3,2,6,4,8,7,5]=>[2,2,2,1,1]
[1,2,5,8,7,4,3,6]=>[7,3,6,8,5,1,2,4]=>[2,6,3,1,4,8,7,5]=>[2,1,3,1,1]
[1,3,5,8,7,2,4,6]=>[3,6,7,8,2,5,1,4]=>[6,3,2,1,7,4,8,5]=>[1,1,1,2,2,1]
[2,3,7,6,8,5,1,4]=>[7,4,3,8,1,2,6,5]=>[2,5,6,1,8,7,3,4]=>[3,2,1,2]
[5,7,1,2,8,6,4,3]=>[1,8,7,6,3,4,2,5]=>[8,1,2,3,6,5,7,4]=>[1,4,2,1]
[3,1,7,6,8,5,4,2]=>[4,3,8,1,7,6,2,5]=>[5,6,1,8,2,3,7,4]=>[2,2,3,1]
[1,2,6,8,5,7,4,3]=>[3,5,8,7,6,1,2,4]=>[6,4,1,2,3,8,7,5]=>[1,1,4,1,1]
[1,2,5,8,7,4,6,3]=>[6,8,3,7,5,1,2,4]=>[3,1,6,2,4,8,7,5]=>[1,2,3,1,1]
[1,2,4,8,7,6,3,5]=>[7,8,6,3,5,1,2,4]=>[2,1,3,6,4,8,7,5]=>[1,3,2,1,1]
[6,4,5,7,2,8,1,3]=>[2,5,3,1,7,4,8,6]=>[7,4,6,8,2,5,1,3]=>[1,3,2,2]
[5,3,4,7,2,8,1,6]=>[2,3,1,5,7,4,8,6]=>[7,6,8,4,2,5,1,3]=>[1,2,1,2,2]
[3,2,7,4,6,8,1,5]=>[7,1,4,5,2,3,8,6]=>[2,8,5,4,7,6,1,3]=>[2,1,2,1,2]
[5,3,6,2,7,1,4,8]=>[2,4,1,6,3,7,5,8]=>[7,5,8,3,6,2,4,1]=>[1,2,2,2,1]
[2,6,3,4,7,1,5,8]=>[3,4,6,1,2,7,5,8]=>[6,5,3,8,7,2,4,1]=>[1,1,2,1,2,1]
[2,7,3,4,5,8,1,6]=>[3,4,5,7,1,2,8,6]=>[6,5,4,2,8,7,1,3]=>[1,1,1,2,1,2]
[3,7,4,5,6,8,1,2]=>[3,4,7,1,5,2,8,6]=>[6,5,2,8,4,7,1,3]=>[1,1,2,2,2]
[2,5,7,3,6,8,1,4]=>[2,7,4,5,1,3,8,6]=>[7,2,5,4,8,6,1,3]=>[1,2,2,1,2]
[4,7,6,2,3,8,1,5]=>[1,4,5,7,3,2,8,6]=>[8,5,4,2,6,7,1,3]=>[1,1,1,3,2]
[7,3,5,2,4,8,1,6]=>[2,4,5,3,7,1,8,6]=>[7,5,4,6,2,8,1,3]=>[1,1,2,2,2]
[6,5,2,3,4,8,1,7]=>[3,4,5,2,1,7,8,6]=>[6,5,4,7,8,2,1,3]=>[1,1,3,1,2]
[5,3,1,2,8,4,7,6]=>[2,8,6,1,7,3,4,5]=>[7,1,3,8,2,6,5,4]=>[1,3,2,1,1]
[6,5,2,3,7,1,4,8]=>[3,4,6,2,1,7,5,8]=>[6,5,3,7,8,2,4,1]=>[1,1,3,2,1]
[5,2,1,7,3,4,6,8]=>[2,5,6,1,7,3,4,8]=>[7,4,3,8,2,6,5,1]=>[1,1,2,2,1,1]
[5,2,1,8,3,4,6,7]=>[2,5,6,1,7,8,3,4]=>[7,4,3,8,2,1,6,5]=>[1,1,2,1,2,1]
[6,3,2,8,4,5,7,1]=>[2,5,6,1,8,3,7,4]=>[7,4,3,8,1,6,2,5]=>[1,1,2,2,2]
[7,3,1,2,8,4,6,5]=>[2,8,6,7,3,4,1,5]=>[7,1,3,2,6,5,8,4]=>[1,2,2,2,1]
[6,4,1,3,8,5,7,2]=>[6,2,8,4,1,7,3,5]=>[3,7,1,5,8,2,6,4]=>[2,3,2,1]
[6,2,3,1,8,4,7,5]=>[8,2,3,6,1,7,4,5]=>[1,7,6,3,8,2,5,4]=>[2,1,2,2,1]
[8,3,5,2,7,1,4,6]=>[2,4,6,3,7,8,5,1]=>[7,5,3,6,2,1,4,8]=>[1,1,2,1,3]
[8,6,2,4,7,1,5,3]=>[4,8,3,6,2,7,5,1]=>[5,1,6,3,7,2,4,8]=>[1,2,2,3]
[8,5,2,3,6,1,4,7]=>[3,4,6,2,7,5,8,1]=>[6,5,3,7,2,4,1,8]=>[1,1,2,2,2]
[8,2,1,7,3,4,5,6]=>[2,5,6,7,8,3,4,1]=>[7,4,3,2,1,6,5,8]=>[1,1,1,1,2,2]
[8,6,3,7,2,4,5,1]=>[3,5,6,2,8,7,4,1]=>[6,4,3,7,1,2,5,8]=>[1,1,2,4]
[7,1,6,2,3,4,5,8]=>[4,5,6,7,2,3,1,8]=>[5,4,3,2,7,6,8,1]=>[1,1,1,2,2,1]
[8,2,7,3,4,5,6,1]=>[4,5,6,8,2,7,3,1]=>[5,4,3,1,7,2,6,8]=>[1,1,1,2,3]
[8,1,6,2,3,4,5,7]=>[4,5,6,7,2,3,8,1]=>[5,4,3,2,7,6,1,8]=>[1,1,1,2,1,2]
[8,1,7,3,4,5,6,2]=>[4,5,6,8,7,2,3,1]=>[5,4,3,1,2,7,6,8]=>[1,1,1,3,2]
[8,6,1,7,2,4,5,3]=>[6,8,5,7,3,2,4,1]=>[3,1,4,2,6,7,5,8]=>[1,2,3,2]
[8,1,5,7,2,3,6,4]=>[8,5,3,6,7,2,4,1]=>[1,4,6,3,2,7,5,8]=>[3,1,2,2]
[1,7,5,8,2,3,6,4]=>[8,5,3,6,2,7,1,4]=>[1,4,6,3,7,2,8,5]=>[3,2,2,1]
[7,2,1,8,3,4,5,6]=>[2,5,6,7,8,3,1,4]=>[7,4,3,2,1,6,8,5]=>[1,1,1,1,3,1]
[7,3,8,2,4,5,6,1]=>[2,4,5,6,1,8,7,3]=>[7,5,4,3,8,1,2,6]=>[1,1,1,2,3]
[7,2,8,3,4,5,6,1]=>[4,5,6,8,2,1,7,3]=>[5,4,3,1,7,8,2,6]=>[1,1,1,3,2]
[1,4,5,8,3,6,7,2]=>[2,3,5,6,8,7,1,4]=>[7,6,4,3,1,2,8,5]=>[1,1,1,1,3,1]
[2,5,7,1,8,3,6,4]=>[2,8,6,7,1,4,3,5]=>[7,1,3,2,8,5,6,4]=>[1,2,2,2,1]
[6,2,7,1,8,4,5,3]=>[6,8,7,2,1,4,3,5]=>[3,1,2,7,8,5,6,4]=>[1,4,2,1]
[4,7,1,3,8,5,6,2]=>[1,6,8,4,7,3,2,5]=>[8,3,1,5,2,6,7,4]=>[1,1,2,3,1]
[1,6,2,8,4,5,7,3]=>[5,6,2,8,7,1,3,4]=>[4,3,7,1,2,8,6,5]=>[1,2,3,1,1]
[4,1,3,6,8,2,7,5]=>[4,1,8,3,6,7,2,5]=>[5,8,1,6,3,2,7,4]=>[2,2,1,2,1]
[5,3,4,6,8,2,7,1]=>[2,3,1,4,6,8,7,5]=>[7,6,8,5,3,1,2,4]=>[1,2,1,1,3]
[4,6,3,8,7,1,2,5]=>[1,3,6,2,7,8,5,4]=>[8,6,3,7,2,1,4,5]=>[1,1,2,1,3]
[5,3,4,8,7,1,2,6]=>[2,3,1,6,7,8,5,4]=>[7,6,8,3,2,1,4,5]=>[1,2,1,1,3]
[3,2,8,7,1,4,6,5]=>[8,1,5,6,7,2,4,3]=>[1,8,4,3,2,7,5,6]=>[2,1,1,2,2]
[3,1,8,7,2,4,6,5]=>[8,1,5,6,7,4,2,3]=>[1,8,4,3,2,5,7,6]=>[2,1,1,3,1]
[5,3,7,6,1,2,4,8]=>[2,5,1,6,7,4,3,8]=>[7,4,8,3,2,5,6,1]=>[1,2,1,3,1]
[1,8,3,7,2,4,5,6]=>[3,5,6,7,8,4,1,2]=>[6,4,3,2,1,5,8,7]=>[1,1,1,1,3,1]
[3,8,1,7,2,4,5,6]=>[1,5,6,7,8,3,4,2]=>[8,4,3,2,1,6,5,7]=>[1,1,1,1,2,2]
[4,7,8,2,6,1,3,5]=>[1,4,6,7,2,8,5,3]=>[8,5,3,2,7,1,4,6]=>[1,1,1,2,3]
[6,2,8,7,1,4,5,3]=>[6,8,5,1,7,2,4,3]=>[3,1,4,8,2,7,5,6]=>[1,3,2,2]
[3,8,7,1,4,5,6,2]=>[5,6,8,1,4,7,3,2]=>[4,3,1,8,5,2,6,7]=>[1,1,2,1,3]
[2,8,6,1,3,4,5,7]=>[4,5,6,7,1,3,8,2]=>[5,4,3,2,8,6,1,7]=>[1,1,1,2,1,2]
[2,7,6,1,3,4,5,8]=>[4,5,6,7,1,3,2,8]=>[5,4,3,2,8,6,7,1]=>[1,1,1,2,2,1]
[1,7,6,2,3,4,5,8]=>[4,5,6,7,3,1,2,8]=>[5,4,3,2,6,8,7,1]=>[1,1,1,3,1,1]
[1,8,6,2,3,4,5,7]=>[4,5,6,7,3,8,1,2]=>[5,4,3,2,6,1,8,7]=>[1,1,1,2,2,1]
[2,8,7,3,4,5,6,1]=>[4,5,6,8,7,1,3,2]=>[5,4,3,1,2,8,6,7]=>[1,1,1,3,2]
[3,8,7,2,4,5,6,1]=>[4,5,6,8,1,7,3,2]=>[5,4,3,1,8,2,6,7]=>[1,1,1,2,3]
[7,8,3,6,2,4,5,1]=>[3,5,6,1,8,7,4,2]=>[6,4,3,8,1,2,5,7]=>[1,1,2,4]
[1,5,8,7,2,3,6,4]=>[2,8,5,6,7,4,1,3]=>[7,1,4,3,2,5,8,6]=>[1,2,1,3,1]
[8,7,6,1,3,4,5,2]=>[5,6,8,4,7,3,2,1]=>[4,3,1,5,2,6,7,8]=>[1,1,2,4]
[3,6,2,4,7,1,8,5]=>[8,1,3,4,2,6,5,7]=>[1,8,6,5,7,3,4,2]=>[2,1,2,2,1]
[4,1,8,5,3,2,7,6]=>[1,5,4,8,6,7,2,3]=>[8,4,5,1,3,2,7,6]=>[1,2,2,2,1]
[3,6,2,5,7,1,4,8]=>[6,1,3,4,2,7,5,8]=>[3,8,6,5,7,2,4,1]=>[2,1,2,2,1]
[6,1,3,2,8,5,4,7]=>[7,3,6,8,2,1,4,5]=>[2,6,3,1,7,8,5,4]=>[2,1,3,1,1]
[5,6,1,2,8,4,3,7]=>[7,6,1,8,3,2,4,5]=>[2,3,8,1,6,7,5,4]=>[3,3,1,1]
[1,6,3,8,7,4,2,5]=>[7,6,2,8,3,5,1,4]=>[2,3,7,1,6,4,8,5]=>[3,2,2,1]
[4,3,8,1,2,6,7,5]=>[2,1,6,8,4,5,7,3]=>[7,8,3,1,5,4,2,6]=>[2,1,2,1,2]
[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[5,1,1,1,1,1]
[11,12,9,10,7,8,5,6,3,4,1,2]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[6,6]
[1,2,3,4,5,6,12,11,10,9,8,7]=>[12,11,10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,12,11,10,9,8,7,6]=>[6,1,1,1,1,1,1]
[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[8,7,9,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]
[2,3,5,1,4,6,7,8,9]=>[1,2,4,5,3,6,7,8,9]=>[9,8,6,5,7,4,3,2,1]=>[1,1,1,2,1,1,1,1]
[2,3,4,6,1,5,7,8,9]=>[1,2,3,5,6,4,7,8,9]=>[9,8,7,5,4,6,3,2,1]=>[1,1,1,1,2,1,1,1]
[2,3,4,5,6,8,1,7,9]=>[1,2,3,4,5,7,8,6,9]=>[9,8,7,6,5,3,2,4,1]=>[1,1,1,1,1,1,2,1]
[6,2,8,5,4,7,1,3]=>[7,5,4,1,8,2,6,3]=>[2,4,5,8,1,7,3,6]=>[4,2,2]
[6,5,7,2,4,8,1,3]=>[7,4,2,1,5,3,8,6]=>[2,5,7,8,4,6,1,3]=>[4,2,2]
[3,4,1,6,5,8,7,2]=>[1,2,4,8,5,7,3,6]=>[8,7,5,1,4,2,6,3]=>[1,1,1,2,2,1]
[3,5,1,2,4,8,7,6]=>[8,1,7,3,2,4,5,6]=>[1,8,2,6,7,5,4,3]=>[2,3,1,1,1]
[3,7,5,2,1,4,6,8]=>[5,1,4,6,3,7,2,8]=>[4,8,5,3,6,2,7,1]=>[2,1,2,2,1]
[3,8,5,2,7,4,1,6]=>[7,4,1,3,6,8,5,2]=>[2,5,8,6,3,1,4,7]=>[3,1,1,3]
[5,2,7,4,1,3,6,8]=>[5,6,2,1,4,7,3,8]=>[4,3,7,8,5,2,6,1]=>[1,3,1,2,1]
[4,3,5,1,2,8,7,6]=>[2,1,3,8,7,4,5,6]=>[7,8,6,1,2,5,4,3]=>[2,1,3,1,1]
[3,1,4,6,2,8,7,5]=>[1,4,8,3,7,2,5,6]=>[8,5,1,6,2,7,4,3]=>[1,1,2,2,1,1]
[3,4,5,6,1,8,7,2]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[1,1,1,1,3,1]
[3,4,5,8,7,2,1,6]=>[7,1,2,3,6,8,5,4]=>[2,8,7,6,3,1,4,5]=>[2,1,1,1,3]
[1,4,7,2,6,3,5,8]=>[2,6,7,4,5,1,3,8]=>[7,3,2,5,4,8,6,1]=>[1,1,2,2,1,1]
[8,4,7,5,2,1,6,3]=>[2,5,8,6,4,7,3,1]=>[7,4,1,3,5,2,6,8]=>[1,1,3,3]
[1,8,5,7,3,4,6,2]=>[5,3,6,8,7,4,1,2]=>[4,6,3,1,2,5,8,7]=>[2,1,4,1]
[6,1,4,8,7,3,2,5]=>[7,3,6,1,8,5,2,4]=>[2,6,3,8,1,4,7,5]=>[2,2,3,1]
[6,4,8,5,7,1,2,3]=>[2,6,1,7,4,8,5,3]=>[7,3,8,2,5,1,4,6]=>[1,2,2,3]
[5,4,8,1,6,3,2,7]=>[2,1,7,6,4,5,8,3]=>[7,8,2,3,5,4,1,6]=>[2,3,1,2]
[1,4,8,6,3,7,2,5]=>[5,7,2,4,8,6,1,3]=>[4,2,7,5,1,3,8,6]=>[1,2,1,3,1]
[5,4,7,6,3,8,1,2]=>[1,7,2,5,4,3,8,6]=>[8,2,7,4,5,6,1,3]=>[1,2,3,2]
[4,6,3,7,5,8,1,2]=>[7,1,3,2,5,4,8,6]=>[2,8,6,7,4,5,1,3]=>[2,2,2,2]
[4,1,3,5,8,6,2,7]=>[7,3,1,4,6,8,2,5]=>[2,6,8,5,3,1,7,4]=>[3,1,1,2,1]
[5,7,4,3,8,1,2,6]=>[1,6,4,3,7,2,8,5]=>[8,3,5,6,2,7,1,4]=>[1,3,2,2]
[1,4,8,3,7,6,5,2]=>[8,7,2,4,6,5,1,3]=>[1,2,7,5,3,4,8,6]=>[3,1,3,1]
[3,8,4,2,7,1,5,6]=>[4,1,3,6,7,8,5,2]=>[5,8,6,3,2,1,4,7]=>[2,1,1,1,3]
[3,1,2,5,7,6,4,8]=>[1,7,4,6,2,3,5,8]=>[8,2,5,3,7,6,4,1]=>[1,2,2,1,1,1]
[1,8,2,7,6,5,4,3]=>[8,7,6,5,3,4,1,2]=>[1,2,3,4,6,5,8,7]=>[5,2,1]
[3,8,1,6,7,5,4,2]=>[4,8,7,1,6,3,5,2]=>[5,1,2,8,3,6,4,7]=>[1,3,2,2]
[3,7,2,6,8,5,1,4]=>[7,4,8,1,3,2,6,5]=>[2,5,1,8,6,7,3,4]=>[2,2,2,2]
[7,2,3,8,5,6,1,4]=>[7,5,8,2,3,1,6,4]=>[2,4,1,7,6,8,3,5]=>[2,2,2,2]
[8,2,1,7,5,6,4,3]=>[5,8,7,2,6,3,4,1]=>[4,1,2,7,3,6,5,8]=>[1,3,2,2]
[8,1,3,6,5,7,4,2]=>[5,4,8,3,7,2,6,1]=>[4,5,1,6,2,7,3,8]=>[2,2,2,2]
[8,2,4,3,6,1,5,7]=>[4,2,3,6,7,5,8,1]=>[5,7,6,3,2,4,1,8]=>[2,1,1,2,2]
[1,7,8,5,4,3,6,2]=>[6,5,4,2,8,7,1,3]=>[3,4,5,7,1,2,8,6]=>[4,3,1]
[1,8,4,5,3,2,6,7]=>[3,6,5,4,7,8,1,2]=>[6,3,4,5,2,1,8,7]=>[1,3,1,2,1]
[7,8,5,4,3,1,6,2]=>[8,6,5,4,3,1,7,2]=>[1,3,4,5,6,8,2,7]=>[6,2]
[7,1,6,3,4,2,5,8]=>[4,6,5,7,2,3,1,8]=>[5,3,4,2,7,6,8,1]=>[1,2,2,2,1]
[6,8,7,1,4,2,5,3]=>[8,6,4,1,5,7,3,2]=>[1,3,5,8,4,2,6,7]=>[4,1,3]
[3,4,1,8,5,7,6,2]=>[8,1,2,5,7,6,3,4]=>[1,8,7,4,2,3,6,5]=>[2,1,1,3,1]
[3,6,5,1,2,8,4,7]=>[7,8,1,4,3,2,5,6]=>[2,1,8,5,6,7,4,3]=>[1,2,3,1,1]
[3,8,5,6,7,2,1,4]=>[3,7,6,1,4,8,5,2]=>[6,2,3,8,5,1,4,7]=>[1,3,1,3]
[8,1,7,6,2,4,3,5]=>[7,5,6,8,4,2,3,1]=>[2,4,3,1,5,7,6,8]=>[2,1,3,2]
[8,5,6,1,4,2,3,7]=>[6,7,4,2,5,3,8,1]=>[3,2,5,7,4,6,1,8]=>[1,3,2,2]
[8,6,5,4,7,1,3,2]=>[8,6,4,3,2,7,5,1]=>[1,3,5,6,7,2,4,8]=>[5,3]
[1,6,4,5,7,2,3,8]=>[3,6,4,2,7,1,5,8]=>[6,3,5,7,2,8,4,1]=>[1,3,2,1,1]
[8,3,6,1,7,2,4,5]=>[2,6,7,8,4,3,5,1]=>[7,3,2,1,5,6,4,8]=>[1,1,1,3,2]
[1,8,6,5,7,3,4,2]=>[6,4,3,8,7,5,1,2]=>[3,5,6,1,2,4,8,7]=>[3,4,1]
[1,7,5,3,6,8,4,2]=>[5,3,8,4,2,7,1,6]=>[4,6,1,5,7,2,8,3]=>[2,3,2,1]
[7,4,1,6,5,8,3,2]=>[2,5,4,8,7,3,1,6]=>[7,4,5,1,2,6,8,3]=>[1,2,4,1]
[4,1,5,8,7,6,3,2]=>[8,1,7,3,6,5,2,4]=>[1,8,2,6,3,4,7,5]=>[2,2,3,1]
[1,2,5,8,6,7,3,4]=>[7,3,5,8,6,1,2,4]=>[2,6,4,1,3,8,7,5]=>[2,1,3,1,1]
[4,2,1,5,8,7,3,6]=>[7,1,8,2,4,6,3,5]=>[2,8,1,7,5,3,6,4]=>[2,2,1,2,1]
[5,2,4,6,1,7,3,8]=>[3,7,2,1,5,4,6,8]=>[6,2,7,8,4,5,3,1]=>[1,3,2,1,1]
[1,5,3,6,8,7,4,2]=>[2,8,4,7,3,6,1,5]=>[7,1,5,2,6,3,8,4]=>[1,2,2,2,1]
[3,5,4,6,1,8,2,7]=>[3,1,2,7,4,8,5,6]=>[6,8,7,2,5,1,4,3]=>[2,1,2,2,1]
[3,1,5,7,6,8,2,4]=>[7,1,3,5,4,8,2,6]=>[2,8,6,4,5,1,7,3]=>[2,1,2,2,1]
[1,4,5,6,8,7,2,3]=>[2,3,4,7,8,6,1,5]=>[7,6,5,2,1,3,8,4]=>[1,1,1,1,3,1]
[1,4,6,3,7,2,8,5]=>[8,2,4,3,6,1,5,7]=>[1,7,5,6,3,8,4,2]=>[2,2,2,1,1]
[1,7,3,6,5,2,8,4]=>[8,6,3,5,4,1,2,7]=>[1,3,6,4,5,8,7,2]=>[3,3,1,1]
[8,6,2,5,4,1,7,3]=>[8,6,3,5,4,2,7,1]=>[1,3,6,4,5,7,2,8]=>[3,3,2]
[3,7,2,6,5,4,1,8]=>[7,6,1,3,5,4,2,8]=>[2,3,8,6,4,5,7,1]=>[3,1,3,1]
[7,6,2,5,4,3,1,8]=>[7,6,3,5,4,2,1,8]=>[2,3,6,4,5,7,8,1]=>[3,4,1]
[4,7,5,2,6,3,1,8]=>[7,1,4,3,6,5,2,8]=>[2,8,5,6,3,4,7,1]=>[2,2,3,1]
[3,2,6,4,7,5,1,8]=>[7,1,4,2,3,6,5,8]=>[2,8,5,7,6,3,4,1]=>[2,2,1,2,1]
[1,3,4,7,6,2,8,5]=>[8,6,2,3,5,1,4,7]=>[1,3,7,6,4,8,5,2]=>[3,1,2,1,1]
[2,8,3,6,1,7,5,4]=>[8,7,3,5,1,4,6,2]=>[1,2,6,4,8,5,3,7]=>[3,2,1,2]
[8,7,2,5,1,6,4,3]=>[8,7,3,5,4,6,2,1]=>[1,2,6,4,5,3,7,8]=>[3,2,3]
[7,8,2,5,4,1,6,3]=>[8,6,3,5,4,1,7,2]=>[1,3,6,4,5,8,2,7]=>[3,3,2]
[4,8,5,2,6,1,7,3]=>[8,1,4,3,6,5,7,2]=>[1,8,5,6,3,4,2,7]=>[2,2,2,2]
[4,5,1,3,7,2,8,6]=>[1,8,4,2,6,3,5,7]=>[8,1,5,7,3,6,4,2]=>[1,3,2,1,1]
[7,1,3,6,2,8,5,4]=>[8,7,3,5,2,4,1,6]=>[1,2,6,4,7,5,8,3]=>[3,2,2,1]
[8,1,3,6,2,7,5,4]=>[8,7,3,5,2,4,6,1]=>[1,2,6,4,7,5,3,8]=>[3,2,1,2]
[1,2,4,7,3,8,6,5]=>[8,7,3,5,1,2,4,6]=>[1,2,6,4,8,7,5,3]=>[3,2,1,1,1]
[7,1,8,2,6,5,4,3]=>[8,7,6,4,5,2,1,3]=>[1,2,3,5,4,7,8,6]=>[4,3,1]
[3,1,8,6,2,7,5,4]=>[8,7,1,5,4,6,2,3]=>[1,2,8,4,5,3,7,6]=>[3,2,2,1]
[4,1,7,8,2,6,5,3]=>[8,1,7,5,3,6,2,4]=>[1,8,2,4,6,3,7,5]=>[2,3,2,1]
[5,6,1,8,2,7,4,3]=>[1,8,7,5,2,6,3,4]=>[8,1,2,4,7,3,6,5]=>[1,4,2,1]
[4,2,7,8,1,6,5,3]=>[8,1,7,5,2,3,6,4]=>[1,8,2,4,7,6,3,5]=>[2,3,1,2]
[3,2,8,6,1,7,5,4]=>[8,7,1,5,2,4,6,3]=>[1,2,8,4,7,5,3,6]=>[3,2,1,2]
[7,2,8,1,6,5,4,3]=>[8,7,6,2,4,1,5,3]=>[1,2,3,7,5,8,4,6]=>[4,2,2]
[1,8,7,2,6,5,4,3]=>[8,7,6,4,5,3,1,2]=>[1,2,3,5,4,6,8,7]=>[4,3,1]
[2,8,7,1,6,5,4,3]=>[8,7,6,4,5,1,3,2]=>[1,2,3,5,4,8,6,7]=>[4,2,2]
[3,8,7,1,6,5,4,2]=>[8,7,6,1,4,5,3,2]=>[1,2,3,8,5,4,6,7]=>[4,1,3]
[4,8,7,5,1,6,3,2]=>[8,7,1,5,4,6,3,2]=>[1,2,8,4,5,3,6,7]=>[3,2,3]
[6,7,8,5,1,4,3,2]=>[1,8,7,5,2,6,4,3]=>[8,1,2,4,7,3,5,6]=>[1,4,3]
[5,6,3,8,4,1,7,2]=>[1,8,3,2,6,5,7,4]=>[8,1,6,7,3,4,2,5]=>[1,3,2,2]
[7,3,8,5,4,1,6,2]=>[8,6,2,5,4,1,7,3]=>[1,3,7,4,5,8,2,6]=>[3,3,2]
[3,4,8,6,5,1,7,2]=>[8,6,1,2,5,4,7,3]=>[1,3,8,7,4,5,2,6]=>[3,1,2,2]
[8,3,7,5,1,6,4,2]=>[8,7,2,5,4,6,3,1]=>[1,2,7,4,5,3,6,8]=>[3,2,3]
[1,4,8,6,2,7,5,3]=>[8,7,2,5,4,6,1,3]=>[1,2,7,4,5,3,8,6]=>[3,2,2,1]
[8,4,6,7,1,5,3,2]=>[8,2,7,5,3,6,4,1]=>[1,7,2,4,6,3,5,8]=>[2,3,3]
[5,6,4,7,8,1,3,2]=>[1,3,2,8,6,4,7,5]=>[8,6,7,1,3,5,2,4]=>[1,2,3,2]
[3,4,6,5,1,2,8,7]=>[8,1,2,5,4,3,6,7]=>[1,8,7,4,5,6,3,2]=>[2,1,3,1,1]
[7,3,5,1,2,8,6,4]=>[8,2,7,4,3,5,1,6]=>[1,7,2,5,6,4,8,3]=>[2,3,2,1]
[1,4,6,2,3,8,7,5]=>[8,2,7,4,1,3,5,6]=>[1,7,2,5,8,6,4,3]=>[2,3,1,1,1]
[1,3,2,7,4,8,6,5]=>[8,7,2,5,1,3,4,6]=>[1,2,7,4,8,6,5,3]=>[3,2,1,1,1]
[7,2,1,6,3,8,5,4]=>[8,7,2,5,3,4,1,6]=>[1,2,7,4,6,5,8,3]=>[3,2,2,1]
[2,3,1,7,6,4,8,5]=>[8,6,1,2,5,3,4,7]=>[1,3,8,7,4,6,5,2]=>[3,1,2,1,1]
[4,5,2,1,7,3,8,6]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[1,3,2,1,1]
[5,6,7,1,2,8,4,3]=>[1,8,7,4,2,5,3,6]=>[8,1,2,5,7,4,6,3]=>[1,4,2,1]
[4,7,5,1,2,8,6,3]=>[8,1,7,4,3,5,2,6]=>[1,8,2,5,6,4,7,3]=>[2,3,2,1]
[7,6,1,2,8,5,4,3]=>[8,7,6,3,4,2,1,5]=>[1,2,3,6,5,7,8,4]=>[4,3,1]
[2,7,1,3,8,6,5,4]=>[8,7,6,1,3,4,2,5]=>[1,2,3,8,6,5,7,4]=>[4,1,2,1]
[8,6,1,2,7,5,4,3]=>[8,7,6,3,4,2,5,1]=>[1,2,3,6,5,7,4,8]=>[4,2,2]
[1,7,2,3,8,6,5,4]=>[8,7,6,3,4,1,2,5]=>[1,2,3,6,5,8,7,4]=>[4,2,1,1]
[8,7,1,2,6,5,4,3]=>[8,7,6,3,4,5,2,1]=>[1,2,3,6,5,4,7,8]=>[4,1,3]
[7,8,1,2,6,5,4,3]=>[8,7,6,3,4,1,5,2]=>[1,2,3,6,5,8,4,7]=>[4,2,2]
[4,8,5,1,2,7,6,3]=>[8,1,7,4,3,5,6,2]=>[1,8,2,5,6,4,3,7]=>[2,3,1,2]
[5,6,8,1,2,7,4,3]=>[1,8,7,4,2,5,6,3]=>[8,1,2,5,7,4,3,6]=>[1,4,1,2]
[2,1,3,7,4,8,6,5]=>[8,7,1,5,2,3,4,6]=>[1,2,8,4,7,6,5,3]=>[3,2,1,1,1]
[4,2,7,3,6,8,1,5]=>[1,7,4,5,2,3,8,6]=>[8,2,5,4,7,6,1,3]=>[1,2,2,1,2]
[5,3,6,4,2,8,1,7]=>[5,2,1,4,3,7,8,6]=>[4,7,8,5,6,2,1,3]=>[3,2,1,2]
[4,1,5,3,8,2,7,6]=>[3,1,8,4,6,7,2,5]=>[6,8,1,5,3,2,7,4]=>[2,2,1,2,1]
[2,6,3,4,7,5,1,8]=>[7,3,4,1,2,6,5,8]=>[2,6,5,8,7,3,4,1]=>[2,2,1,2,1]
[2,6,3,5,4,8,1,7]=>[5,3,4,1,2,7,8,6]=>[4,6,5,8,7,2,1,3]=>[2,2,1,1,2]
[2,7,4,3,5,8,1,6]=>[4,3,5,7,1,2,8,6]=>[5,6,4,2,8,7,1,3]=>[2,1,2,1,2]
[7,6,4,5,2,8,1,3]=>[5,3,7,4,2,1,8,6]=>[4,6,2,5,7,8,1,3]=>[2,4,2]
[5,4,3,1,8,2,7,6]=>[3,2,1,8,6,7,4,5]=>[6,7,8,1,3,2,5,4]=>[3,2,2,1]
[6,5,4,2,7,3,1,8]=>[7,4,3,2,1,6,5,8]=>[2,5,6,7,8,3,4,1]=>[5,2,1]
[5,4,1,7,2,6,3,8]=>[7,5,2,1,6,3,4,8]=>[2,4,7,8,3,6,5,1]=>[4,2,1,1]
[5,4,1,8,3,2,6,7]=>[6,5,2,1,7,8,3,4]=>[3,4,7,8,2,1,6,5]=>[4,1,2,1]
[6,5,2,8,3,4,7,1]=>[5,6,2,1,8,3,7,4]=>[4,3,7,8,1,6,2,5]=>[1,3,2,2]
[7,4,2,1,8,3,6,5]=>[8,3,2,6,7,4,1,5]=>[1,6,7,3,2,5,8,4]=>[3,1,3,1]
[6,5,3,4,8,2,7,1]=>[3,4,2,1,6,8,7,5]=>[6,5,7,8,3,1,2,4]=>[1,3,1,3]
[6,1,5,3,8,2,7,4]=>[8,4,3,6,1,7,2,5]=>[1,5,6,3,8,2,7,4]=>[3,2,2,1]
[4,6,3,1,8,2,7,5]=>[1,3,8,6,2,7,4,5]=>[8,6,1,3,7,2,5,4]=>[1,1,3,2,1]
[5,8,4,2,7,3,1,6]=>[1,7,4,3,6,8,5,2]=>[8,2,5,6,3,1,4,7]=>[1,3,1,3]
[8,2,6,4,7,3,1,5]=>[4,7,6,2,3,8,5,1]=>[5,2,3,7,6,1,4,8]=>[1,3,1,3]
[8,6,2,5,7,4,1,3]=>[7,4,8,3,2,6,5,1]=>[2,5,1,6,7,3,4,8]=>[2,3,3]
[8,3,1,7,2,5,4,6]=>[2,7,5,6,8,3,4,1]=>[7,2,4,3,1,6,5,8]=>[1,2,1,2,2]
[7,5,2,6,4,3,1,8]=>[7,6,3,2,5,4,1,8]=>[2,3,6,7,4,5,8,1]=>[4,3,1]
[7,1,6,2,5,4,3,8]=>[7,6,4,5,2,3,1,8]=>[2,3,5,4,7,6,8,1]=>[3,2,2,1]
[8,1,7,3,5,6,4,2]=>[5,8,4,7,6,2,3,1]=>[4,1,5,2,3,7,6,8]=>[1,2,3,2]
[8,6,1,7,4,5,2,3]=>[7,5,8,6,3,2,4,1]=>[2,4,1,3,6,7,5,8]=>[2,4,2]
[8,1,3,7,2,6,5,4]=>[8,7,3,5,6,2,4,1]=>[1,2,6,4,3,7,5,8]=>[3,1,2,2]
[1,7,6,8,3,2,4,5]=>[6,5,7,3,2,8,1,4]=>[3,4,2,6,7,1,8,5]=>[2,3,2,1]
[7,1,5,8,4,2,6,3]=>[3,8,6,5,7,2,1,4]=>[6,1,3,4,2,7,8,5]=>[1,3,3,1]
[7,2,8,5,3,4,6,1]=>[5,6,4,8,2,1,7,3]=>[4,3,5,1,7,8,2,6]=>[1,2,3,2]
[6,1,8,4,3,2,5,7]=>[6,5,4,7,1,8,2,3]=>[3,4,5,2,8,1,7,6]=>[3,2,2,1]
[6,1,7,4,2,5,3,8]=>[7,5,4,6,2,1,3,8]=>[2,4,5,3,7,8,6,1]=>[3,3,1,1]
[1,2,7,3,4,6,5,8]=>[7,4,5,6,1,2,3,8]=>[2,5,4,3,8,7,6,1]=>[2,1,2,1,1,1]
[1,7,8,4,3,5,6,2]=>[5,4,6,2,8,7,1,3]=>[4,5,3,7,1,2,8,6]=>[2,2,3,1]
[1,6,2,8,3,5,7,4]=>[6,8,5,2,7,1,3,4]=>[3,1,4,7,2,8,6,5]=>[1,3,2,1,1]
[2,6,1,7,3,5,4,8]=>[7,5,6,1,3,2,4,8]=>[2,4,3,8,6,7,5,1]=>[2,2,2,1,1]
[3,1,5,8,4,2,6,7]=>[1,3,6,5,7,8,2,4]=>[8,6,3,4,2,1,7,5]=>[1,1,2,1,2,1]
[4,3,1,6,8,2,7,5]=>[2,1,4,8,6,7,3,5]=>[7,8,5,1,3,2,6,4]=>[2,1,2,2,1]
[5,7,4,8,3,2,1,6]=>[1,3,7,6,5,2,8,4]=>[8,6,2,3,4,7,1,5]=>[1,1,4,2]
[6,4,7,5,3,2,1,8]=>[7,2,1,6,5,4,3,8]=>[2,7,8,3,4,5,6,1]=>[3,4,1]
[1,8,3,7,6,2,4,5]=>[6,7,8,3,5,4,1,2]=>[3,2,1,6,4,5,8,7]=>[1,1,2,3,1]
[5,8,3,2,6,4,1,7]=>[3,1,7,4,6,5,8,2]=>[6,8,2,5,3,4,1,7]=>[2,2,2,2]
[7,3,8,2,6,4,1,5]=>[7,2,4,6,1,8,5,3]=>[2,7,5,3,8,1,4,6]=>[2,1,2,3]
[4,6,8,2,7,3,1,5]=>[7,1,4,2,6,8,5,3]=>[2,8,5,7,3,1,4,6]=>[2,2,1,3]
[2,6,8,7,3,4,1,5]=>[5,2,7,6,8,1,4,3]=>[4,7,2,3,1,8,5,6]=>[2,2,2,2]
[7,2,8,6,3,5,1,4]=>[5,7,8,6,2,1,4,3]=>[4,2,1,3,7,8,5,6]=>[1,1,4,2]
[6,8,1,7,2,5,4,3]=>[8,7,5,1,6,3,4,2]=>[1,2,4,8,3,6,5,7]=>[4,2,2]
[3,8,7,4,5,6,1,2]=>[4,7,5,8,1,6,3,2]=>[5,2,4,1,8,3,6,7]=>[1,2,2,3]
[2,8,6,4,3,5,1,7]=>[5,4,7,6,1,3,8,2]=>[4,5,2,3,8,6,1,7]=>[2,3,1,2]
[2,7,6,3,5,4,1,8]=>[7,4,6,5,1,3,2,8]=>[2,5,3,4,8,6,7,1]=>[2,3,2,1]
[1,7,6,5,2,4,3,8]=>[7,5,6,4,3,1,2,8]=>[2,4,3,5,6,8,7,1]=>[2,4,1,1]
[1,8,6,5,3,2,4,7]=>[6,5,7,4,3,8,1,2]=>[3,4,2,5,6,1,8,7]=>[2,3,2,1]
[3,8,7,4,6,2,5,1]=>[4,6,8,7,1,5,3,2]=>[5,3,1,2,8,4,6,7]=>[1,1,3,3]
[5,8,3,7,6,2,4,1]=>[1,6,8,3,7,5,4,2]=>[8,3,1,6,2,4,5,7]=>[1,1,2,4]
[7,1,8,6,5,2,3,4]=>[6,7,8,5,4,2,1,3]=>[3,2,1,4,5,7,8,6]=>[1,1,5,1]
[8,7,2,5,4,3,1,6]=>[7,6,3,5,4,8,2,1]=>[2,3,6,4,5,1,7,8]=>[3,2,3]
[6,8,3,2,5,4,7,1]=>[3,6,4,1,5,8,7,2]=>[6,3,5,8,4,1,2,7]=>[1,3,1,3]
[6,8,4,5,2,3,7,1]=>[5,3,1,6,4,8,7,2]=>[4,6,8,3,5,1,2,7]=>[3,2,3]
[6,3,8,1,5,4,7,2]=>[6,2,5,1,8,4,7,3]=>[3,7,4,8,1,5,2,6]=>[2,2,2,2]
[6,2,1,8,5,4,7,3]=>[6,5,8,2,1,7,3,4]=>[3,4,1,7,8,2,6,5]=>[2,3,2,1]
[2,6,3,1,7,5,4,8]=>[7,3,6,1,4,2,5,8]=>[2,6,3,8,5,7,4,1]=>[2,2,2,1,1]
[2,6,5,7,4,1,3,8]=>[6,3,2,7,1,5,4,8]=>[3,6,7,2,8,4,5,1]=>[3,2,2,1]
[2,5,6,8,4,3,7,1]=>[2,3,6,5,8,1,7,4]=>[7,6,3,4,1,8,2,5]=>[1,1,2,2,2]
[2,4,7,5,8,1,6,3]=>[4,8,2,6,1,3,7,5]=>[5,1,7,3,8,6,2,4]=>[1,2,2,1,2]
[2,5,4,7,1,8,6,3]=>[2,8,3,7,1,5,4,6]=>[7,1,6,2,8,4,5,3]=>[1,2,2,2,1]
[5,2,1,8,7,6,4,3]=>[1,8,7,6,2,5,3,4]=>[8,1,2,3,7,4,6,5]=>[1,4,2,1]
[4,8,5,7,6,1,3,2]=>[3,8,1,6,7,5,4,2]=>[6,1,8,3,2,4,5,7]=>[1,2,1,4]
[4,8,6,7,5,3,1,2]=>[7,3,8,1,6,5,4,2]=>[2,6,1,8,3,4,5,7]=>[2,2,4]
[4,8,7,5,6,2,3,1]=>[6,4,8,1,7,5,3,2]=>[3,5,1,8,2,4,6,7]=>[2,2,4]
[6,5,4,8,2,1,7,3]=>[5,3,2,1,8,6,7,4]=>[4,6,7,8,1,3,2,5]=>[4,2,2]
[5,8,4,7,2,6,3,1]=>[1,3,8,5,7,6,4,2]=>[8,6,1,4,2,3,5,7]=>[1,1,2,4]
[1,5,7,4,8,2,6,3]=>[2,4,8,6,3,7,1,5]=>[7,5,1,3,6,2,8,4]=>[1,1,3,2,1]
[1,5,7,3,2,8,6,4]=>[2,8,4,7,5,1,3,6]=>[7,1,5,2,4,8,6,3]=>[1,2,3,1,1]
[5,8,3,2,7,6,4,1]=>[1,8,3,7,4,6,5,2]=>[8,1,6,2,5,3,4,7]=>[1,2,2,3]
[5,2,1,4,3,6,7,8]=>[2,5,3,4,1,6,7,8]=>[7,4,6,5,8,3,2,1]=>[1,2,2,1,1,1]
[3,5,7,4,2,6,1,8]=>[2,5,1,4,7,6,3,8]=>[7,4,8,5,2,3,6,1]=>[1,2,1,3,1]
[3,6,4,5,1,2,7,8]=>[5,1,3,6,4,2,7,8]=>[4,8,6,3,5,7,2,1]=>[2,1,3,1,1]
[4,2,1,6,5,3,7,8]=>[6,2,1,5,3,4,7,8]=>[3,7,8,4,6,5,2,1]=>[3,2,1,1,1]
[4,2,1,5,7,6,3,8]=>[7,2,1,4,6,3,5,8]=>[2,7,8,5,3,6,4,1]=>[3,1,2,1,1]
[4,3,5,1,7,6,2,8]=>[2,1,3,7,6,4,5,8]=>[7,8,6,2,3,5,4,1]=>[2,1,3,1,1]
[3,5,4,7,1,6,2,8]=>[3,1,2,7,5,6,4,8]=>[6,8,7,2,4,3,5,1]=>[2,1,2,2,1]
[3,4,5,8,6,7,1,2]=>[7,1,2,3,5,8,6,4]=>[2,8,7,6,4,1,3,5]=>[2,1,1,1,3]
[3,5,4,6,1,8,7,2]=>[3,1,2,4,8,7,5,6]=>[6,8,7,5,1,2,4,3]=>[2,1,1,3,1]
[4,3,5,1,6,8,7,2]=>[2,1,3,8,5,7,4,6]=>[7,8,6,1,4,2,5,3]=>[2,1,2,2,1]
[4,2,1,5,6,8,7,3]=>[8,2,1,4,5,7,3,6]=>[1,7,8,5,4,2,6,3]=>[3,1,1,2,1]
[10,3,2,1,9,5,4,8,6,7]=>[2,6,9,10,3,7,8,4,5,1]=>[9,5,2,1,8,4,3,7,6,10]=>[1,1,1,2,1,2,2]
[12,11,10,9,8,7,1,2,3,4,5,6]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>[6,5,4,3,2,1,7,8,9,10,11,12]=>[1,1,1,1,1,7]
[7,6,5,4,3,2,9,1,8]=>[6,5,4,3,2,1,8,9,7]=>[4,5,6,7,8,9,2,1,3]=>[6,1,2]
[8,7,6,5,4,3,2,10,1,9]=>[7,6,5,4,3,2,1,9,10,8]=>[4,5,6,7,8,9,10,2,1,3]=>[7,1,2]
[5,10,4,9,3,8,2,7,1,6]=>[1,3,5,7,9,10,8,6,4,2]=>[10,8,6,4,2,1,3,5,7,9]=>[1,1,1,1,1,5]
[2,1,7,3,8,4,6,5]=>[8,6,7,1,4,2,3,5]=>[1,3,2,8,5,7,6,4]=>[2,2,2,1,1]
[4,1,8,2,7,3,6,5]=>[1,8,6,7,4,5,2,3]=>[8,1,3,2,5,4,7,6]=>[1,2,2,2,1]
[7,1,3,2,8,4,6,5]=>[8,3,6,7,2,4,1,5]=>[1,6,3,2,7,5,8,4]=>[2,1,2,2,1]
[7,1,8,2,4,3,6,5]=>[5,8,4,6,7,2,1,3]=>[4,1,5,3,2,7,8,6]=>[1,2,1,3,1]
[8,1,7,2,5,3,6,4]=>[8,6,4,5,7,2,3,1]=>[1,3,5,4,2,7,6,8]=>[3,1,2,2]
[7,1,5,2,8,3,6,4]=>[8,6,3,7,2,4,1,5]=>[1,3,6,2,7,5,8,4]=>[3,2,2,1]
[5,1,7,2,8,3,6,4]=>[8,6,1,7,4,2,3,5]=>[1,3,8,2,5,7,6,4]=>[3,3,1,1]
[5,1,8,2,7,3,6,4]=>[8,6,1,7,4,5,2,3]=>[1,3,8,2,5,4,7,6]=>[3,2,2,1]
[5,1,8,2,4,3,7,6]=>[5,8,4,1,6,7,2,3]=>[4,1,5,8,3,2,7,6]=>[1,3,1,2,1]
[8,1,6,2,4,3,7,5]=>[5,8,4,6,2,3,7,1]=>[4,1,5,3,7,6,2,8]=>[1,2,2,1,2]
[6,1,8,2,4,3,7,5]=>[5,8,4,6,1,7,2,3]=>[4,1,5,3,8,2,7,6]=>[1,2,2,2,1]
[6,1,8,2,5,3,7,4]=>[8,6,4,5,1,7,2,3]=>[1,3,5,4,8,2,7,6]=>[3,2,2,1]
[8,1,6,2,5,3,7,4]=>[8,6,4,5,2,3,7,1]=>[1,3,5,4,7,6,2,8]=>[3,2,1,2]
[8,1,6,2,7,3,5,4]=>[8,6,7,4,2,3,5,1]=>[1,3,2,5,7,6,4,8]=>[2,3,1,2]
[6,1,8,2,7,3,5,4]=>[8,6,7,4,1,5,2,3]=>[1,3,2,5,8,4,7,6]=>[2,3,2,1]
[6,1,7,2,8,3,5,4]=>[8,6,7,4,2,1,3,5]=>[1,3,2,5,7,8,6,4]=>[2,4,1,1]
[6,1,7,2,5,3,8,4]=>[8,6,4,5,2,1,3,7]=>[1,3,5,4,7,8,6,2]=>[3,3,1,1]
[5,1,6,2,4,3,8,7]=>[5,8,4,2,1,3,6,7]=>[4,1,5,7,8,6,3,2]=>[1,4,1,1,1]
[7,1,5,2,4,3,8,6]=>[5,8,4,2,3,6,1,7]=>[4,1,5,7,6,3,8,2]=>[1,3,1,2,1]
[7,1,6,2,4,3,8,5]=>[5,8,4,6,2,3,1,7]=>[4,1,5,3,7,6,8,2]=>[1,2,2,2,1]
[7,1,6,2,5,3,8,4]=>[8,6,4,5,2,3,1,7]=>[1,3,5,4,7,6,8,2]=>[3,2,2,1]
[7,1,6,2,8,3,5,4]=>[8,6,7,4,2,3,1,5]=>[1,3,2,5,7,6,8,4]=>[2,3,2,1]
[7,1,8,2,6,3,5,4]=>[8,6,7,4,5,2,1,3]=>[1,3,2,5,4,7,8,6]=>[2,2,3,1]
[1,8,2,7,5,4,6,3]=>[6,5,8,7,3,4,1,2]=>[3,4,1,2,6,5,8,7]=>[2,3,2,1]
[1,8,2,7,4,3,5,6]=>[6,5,7,8,3,4,1,2]=>[3,4,2,1,6,5,8,7]=>[2,1,2,2,1]
[1,8,6,4,7,2,3,5]=>[6,4,7,3,8,5,1,2]=>[3,5,2,6,1,4,8,7]=>[2,2,3,1]
[1,8,4,2,6,3,5,7]=>[6,3,7,4,5,8,1,2]=>[3,6,2,5,4,1,8,7]=>[2,2,1,2,1]
[7,4,8,1,5,2,3,6]=>[6,2,7,4,5,1,8,3]=>[3,7,2,5,4,8,1,6]=>[2,2,2,2]
[4,1,7,2,6,3,5,8]=>[6,1,7,4,5,2,3,8]=>[3,8,2,5,4,7,6,1]=>[2,2,2,1,1]
[5,1,7,4,3,6,2,8]=>[5,4,1,7,6,2,3,8]=>[4,5,8,2,3,7,6,1]=>[3,3,1,1]
[7,5,8,3,2,4,1,6]=>[5,4,2,7,6,1,8,3]=>[4,5,7,2,3,8,1,6]=>[3,3,2]
[1,8,5,4,3,6,2,7]=>[5,4,3,7,6,8,1,2]=>[4,5,6,2,3,1,8,7]=>[3,2,2,1]
[1,8,5,4,3,7,2,6]=>[5,4,3,7,8,6,1,2]=>[4,5,6,2,1,3,8,7]=>[3,1,3,1]
[1,8,5,4,7,2,6,3]=>[4,3,8,6,7,5,1,2]=>[5,6,1,3,2,4,8,7]=>[2,2,3,1]
[1,8,4,2,5,3,7,6]=>[5,3,8,4,6,7,1,2]=>[4,6,1,5,3,2,8,7]=>[2,2,1,2,1]
[1,8,5,4,2,6,7,3]=>[6,4,3,8,5,7,1,2]=>[3,5,6,1,4,2,8,7]=>[3,2,2,1]
[7,4,8,2,1,3,5,6]=>[5,4,2,6,7,1,8,3]=>[4,5,7,3,2,8,1,6]=>[3,1,2,2]
[4,1,7,3,2,5,6,8]=>[5,4,1,6,7,2,3,8]=>[4,5,8,3,2,7,6,1]=>[3,1,2,1,1]
[7,5,4,8,2,3,6,1]=>[5,3,2,6,1,8,7,4]=>[4,6,7,3,8,1,2,5]=>[3,2,3]
[6,4,8,2,1,3,7,5]=>[4,2,8,5,1,6,7,3]=>[5,7,1,4,8,3,2,6]=>[2,3,1,2]
[3,1,7,2,6,8,4,5]=>[7,1,5,8,4,2,3,6]=>[2,8,4,1,5,7,6,3]=>[2,1,3,1,1]
[4,1,6,3,2,5,8,7]=>[4,1,8,5,2,3,6,7]=>[5,8,1,4,7,6,3,2]=>[2,3,1,1,1]
[5,4,3,7,1,2,8,6]=>[3,2,1,8,5,6,4,7]=>[6,7,8,1,4,3,5,2]=>[3,2,2,1]
[4,3,1,6,2,5,7,8]=>[5,2,1,6,3,4,7,8]=>[4,7,8,3,6,5,2,1]=>[3,2,1,1,1]
[6,5,4,3,7,1,8,2]=>[4,3,2,1,8,6,5,7]=>[5,6,7,8,1,3,4,2]=>[4,3,1]
[6,5,1,7,3,8,2,4]=>[5,7,4,2,1,8,3,6]=>[4,2,5,7,8,1,6,3]=>[1,4,2,1]
[6,3,2,8,5,7,1,4]=>[7,2,5,1,8,3,6,4]=>[2,7,4,8,1,6,3,5]=>[2,2,2,2]
[6,5,4,2,8,3,7,1]=>[6,3,2,1,8,4,7,5]=>[3,6,7,8,1,5,2,4]=>[4,2,2]
[6,5,4,3,8,2,7,1]=>[4,3,2,1,6,8,7,5]=>[5,6,7,8,3,1,2,4]=>[4,1,3]
[6,5,4,3,8,7,1,2]=>[4,3,2,1,7,8,6,5]=>[5,6,7,8,2,1,3,4]=>[4,1,3]
[7,5,4,8,6,1,3,2]=>[3,2,8,6,1,7,5,4]=>[6,7,1,3,8,2,4,5]=>[2,3,3]
[7,6,3,8,5,4,1,2]=>[7,8,3,2,1,6,5,4]=>[2,1,6,7,8,3,4,5]=>[1,4,3]
[6,3,8,1,7,5,2,4]=>[7,8,2,1,6,4,5,3]=>[2,1,7,8,3,5,4,6]=>[1,3,2,2]
[6,5,8,3,1,7,4,2]=>[4,2,1,8,7,5,6,3]=>[5,7,8,1,2,4,3,6]=>[3,3,2]
[5,4,8,2,1,7,3,6]=>[4,2,1,7,8,5,6,3]=>[5,7,8,2,1,4,3,6]=>[3,1,2,2]
[5,4,3,8,1,6,2,7]=>[3,2,1,7,5,6,8,4]=>[6,7,8,2,4,3,1,5]=>[3,2,1,2]
[5,4,3,7,1,6,2,8]=>[3,2,1,7,5,6,4,8]=>[6,7,8,2,4,3,5,1]=>[3,2,2,1]
[6,4,2,8,5,1,3,7]=>[6,2,7,3,1,5,8,4]=>[3,7,2,6,8,4,1,5]=>[2,3,1,2]
[7,6,4,8,5,1,2,3]=>[6,3,7,2,1,8,5,4]=>[3,6,2,7,8,1,4,5]=>[2,3,3]
[7,2,8,6,3,1,4,5]=>[6,5,7,8,2,1,4,3]=>[3,4,2,1,7,8,5,6]=>[2,1,3,2]
[7,2,8,6,1,5,3,4]=>[7,8,5,6,2,1,4,3]=>[2,1,4,3,7,8,5,6]=>[1,2,3,2]
[2,1,7,8,3,6,4,5]=>[7,8,5,1,3,6,2,4]=>[2,1,4,8,6,3,7,5]=>[1,3,1,2,1]
[4,2,1,6,7,3,5,8]=>[6,2,1,4,7,3,5,8]=>[3,7,8,5,2,6,4,1]=>[3,1,2,1,1]
[4,3,1,5,2,7,6,8]=>[4,2,1,7,3,5,6,8]=>[5,7,8,2,6,4,3,1]=>[3,2,1,1,1]
[5,4,2,7,3,8,1,6]=>[5,2,1,7,3,4,8,6]=>[4,7,8,2,6,5,1,3]=>[3,2,1,2]
[4,1,5,3,2,8,6,7]=>[4,3,1,7,8,2,5,6]=>[5,6,8,2,1,7,4,3]=>[3,1,2,1,1]
[3,1,6,2,8,7,4,5]=>[7,1,3,8,6,2,4,5]=>[2,8,6,1,3,7,5,4]=>[2,1,3,1,1]
[6,3,1,7,8,5,2,4]=>[7,2,4,1,8,6,3,5]=>[2,7,5,8,1,3,6,4]=>[2,2,3,1]
[5,4,1,7,8,2,6,3]=>[2,1,8,6,4,7,3,5]=>[7,8,1,3,5,2,6,4]=>[2,3,2,1]
[5,4,2,6,1,8,7,3]=>[4,2,1,8,3,7,5,6]=>[5,7,8,1,6,2,4,3]=>[3,2,2,1]
[6,5,4,1,7,8,3,2]=>[5,3,2,1,8,7,4,6]=>[4,6,7,8,1,2,5,3]=>[4,3,1]
[5,4,3,1,6,7,2,8]=>[5,3,2,1,7,4,6,8]=>[4,6,7,8,2,5,3,1]=>[4,2,1,1]
[6,5,4,2,7,8,3,1]=>[5,3,2,1,8,4,7,6]=>[4,6,7,8,1,5,2,3]=>[4,2,2]
[5,4,2,6,3,8,7,1]=>[4,2,1,8,3,5,7,6]=>[5,7,8,1,6,4,2,3]=>[3,2,1,2]
[4,3,1,5,2,6,8,7]=>[4,2,1,8,3,5,6,7]=>[5,7,8,1,6,4,3,2]=>[3,2,1,1,1]
[5,4,2,1,6,7,8,3]=>[3,5,2,1,6,8,4,7]=>[6,4,7,8,3,1,5,2]=>[1,3,1,2,1]
[5,4,3,1,6,7,8,2]=>[5,3,2,1,6,8,4,7]=>[4,6,7,8,3,1,5,2]=>[4,1,2,1]
[6,3,8,1,2,5,7,4]=>[2,6,8,4,1,5,7,3]=>[7,3,1,5,8,4,2,6]=>[1,1,3,1,2]
[3,6,7,1,2,5,8,4]=>[6,8,1,4,2,5,3,7]=>[3,1,8,5,7,4,6,2]=>[1,2,2,2,1]
[7,8,3,1,2,5,6,4]=>[6,3,8,4,5,1,7,2]=>[3,6,1,5,4,8,2,7]=>[2,2,2,2]
[7,8,1,3,2,4,6,5]=>[4,8,3,5,6,1,7,2]=>[5,1,6,4,3,8,2,7]=>[1,2,1,2,2]
[5,2,3,7,1,8,6,4]=>[8,7,2,1,3,5,4,6]=>[1,2,7,8,6,4,5,3]=>[4,1,2,1]
[2,5,3,6,1,8,7,4]=>[4,2,8,1,3,7,5,6]=>[5,7,1,8,6,2,4,3]=>[2,2,1,2,1]
[2,6,7,3,1,8,4,5]=>[4,7,2,8,1,5,3,6]=>[5,2,7,1,8,4,6,3]=>[1,2,2,2,1]
[2,6,7,1,3,5,4,8]=>[7,4,5,1,2,6,3,8]=>[2,5,4,8,7,3,6,1]=>[2,2,1,2,1]
[6,2,8,3,1,7,4,5]=>[4,7,8,2,1,5,6,3]=>[5,2,1,7,8,4,3,6]=>[1,1,3,1,2]
[3,2,5,7,1,8,4,6]=>[1,3,7,8,2,5,4,6]=>[8,6,2,1,7,4,5,3]=>[1,1,1,2,2,1]
[4,3,1,2,7,8,6,5]=>[2,1,5,8,7,3,4,6]=>[7,8,4,1,2,6,5,3]=>[2,1,3,1,1]
[5,1,2,7,3,6,4,8]=>[7,5,6,2,1,3,4,8]=>[2,4,3,7,8,6,5,1]=>[2,3,1,1,1]
[5,1,4,7,8,2,3,6]=>[3,6,1,7,4,8,2,5]=>[6,3,8,2,5,1,7,4]=>[1,2,2,2,1]
[5,3,4,7,8,6,1,2]=>[7,2,1,3,4,8,6,5]=>[2,7,8,6,5,1,3,4]=>[3,1,1,3]
[3,5,4,6,8,7,1,2]=>[3,1,2,4,7,8,6,5]=>[6,8,7,5,2,1,3,4]=>[2,1,1,1,3]
[1,5,4,6,8,2,3,7]=>[3,2,6,4,7,8,1,5]=>[6,7,3,5,2,1,8,4]=>[2,2,1,2,1]
[1,6,7,3,2,4,8,5]=>[4,8,5,2,6,1,3,7]=>[5,1,4,7,3,8,6,2]=>[1,3,2,1,1]
[1,5,3,6,2,7,8,4]=>[6,3,2,4,8,1,5,7]=>[3,6,7,5,1,8,4,2]=>[3,1,2,1,1]
[5,1,3,7,2,6,8,4]=>[6,8,3,1,5,2,4,7]=>[3,1,6,8,4,7,5,2]=>[1,3,2,1,1]
[5,2,4,7,8,1,6,3]=>[8,3,1,6,2,4,7,5]=>[1,6,8,3,7,5,2,4]=>[3,2,1,2]
[4,2,5,7,6,1,8,3]=>[1,8,3,6,2,5,4,7]=>[8,1,6,3,7,4,5,2]=>[1,2,2,2,1]
[5,3,1,8,2,6,7,4]=>[2,6,1,8,5,7,3,4]=>[7,3,8,1,4,2,6,5]=>[1,2,2,2,1]
[6,1,8,3,2,4,7,5]=>[4,8,5,6,1,7,2,3]=>[5,1,4,3,8,2,7,6]=>[1,2,2,2,1]
[4,3,5,7,6,8,1,2]=>[1,7,2,3,5,4,8,6]=>[8,2,7,6,4,5,1,3]=>[1,2,1,2,2]
[4,1,5,7,6,2,3,8]=>[3,1,6,7,5,2,4,8]=>[6,8,3,2,4,7,5,1]=>[2,1,3,1,1]
[4,5,1,8,6,2,3,7]=>[1,6,2,7,5,8,3,4]=>[8,3,7,2,4,1,6,5]=>[1,2,2,2,1]
[5,2,1,8,3,6,4,7]=>[7,2,5,1,6,8,3,4]=>[2,7,4,8,3,1,6,5]=>[2,2,1,2,1]
[3,4,2,1,8,7,5,6]=>[1,2,7,8,3,6,4,5]=>[8,7,2,1,6,3,5,4]=>[1,1,1,2,2,1]
[7,6,5,4,2,1,8,3]=>[5,8,6,4,3,2,1,7]=>[4,1,3,5,6,7,8,2]=>[1,6,1]
[7,6,5,4,8,1,3,2]=>[8,6,4,3,2,1,7,5]=>[1,3,5,6,7,8,2,4]=>[6,2]
[7,6,5,8,2,1,4,3]=>[5,8,6,3,2,1,7,4]=>[4,1,3,6,7,8,2,5]=>[1,5,2]
[8,5,4,3,2,1,7,6]=>[5,4,3,2,8,6,7,1]=>[4,5,6,7,1,3,2,8]=>[4,2,2]
[8,6,5,4,3,2,1,9,7]=>[6,5,4,3,2,9,7,1,8]=>[4,5,6,7,8,1,3,9,2]=>[5,3,1]
[7,6,5,4,3,2,1,9,8]=>[6,5,4,3,2,1,9,7,8]=>[4,5,6,7,8,9,1,3,2]=>[6,2,1]
[7,6,5,4,1,8,3,2]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>[7,1]
[8,7,6,5,4,9,1,3,2]=>[9,7,5,4,3,2,1,8,6]=>[1,3,5,6,7,8,9,2,4]=>[7,2]
[7,6,5,2,8,1,4,3]=>[8,4,6,3,2,1,7,5]=>[1,5,3,6,7,8,2,4]=>[2,4,2]
[7,6,5,8,4,1,3,2]=>[8,6,3,2,1,7,5,4]=>[1,3,6,7,8,2,4,5]=>[5,3]
[7,6,8,5,2,1,4,3]=>[5,8,6,2,1,7,4,3]=>[4,1,3,7,8,2,5,6]=>[1,4,3]
[7,8,6,3,2,1,5,4]=>[5,4,8,6,1,7,3,2]=>[4,5,1,3,8,2,6,7]=>[2,3,3]
[8,7,4,3,2,1,6,5]=>[5,4,3,8,6,7,2,1]=>[4,5,6,1,3,2,7,8]=>[3,2,3]
[7,8,9,10,4,5,6,2,3,1]=>[1,5,2,8,6,3,10,9,7,4]=>[10,6,9,3,5,8,1,2,4,7]=>[1,2,3,4]
[7,8,2,4,5,1,3,6]=>[6,3,4,7,5,1,8,2]=>[3,6,5,2,4,8,1,7]=>[2,1,3,2]
[4,6,7,2,5,1,3,8]=>[1,4,6,2,7,5,3,8]=>[8,5,3,7,2,4,6,1]=>[1,1,2,3,1]
[7,8,1,3,2,4,5,6]=>[5,3,4,6,7,1,8,2]=>[4,6,5,3,2,8,1,7]=>[2,1,1,2,2]
[5,2,3,6,1,4,7,8]=>[2,3,5,1,6,4,7,8]=>[7,6,4,8,3,5,2,1]=>[1,1,2,2,1,1]
[2,5,3,6,1,4,7,8]=>[3,5,1,2,6,4,7,8]=>[6,4,8,7,3,5,2,1]=>[1,2,1,2,1,1]
[2,6,7,3,1,4,5,8]=>[5,4,6,1,2,7,3,8]=>[4,5,3,8,7,2,6,1]=>[2,2,1,2,1]
[4,6,7,3,5,8,1,2]=>[4,1,2,7,5,3,8,6]=>[5,8,7,2,4,6,1,3]=>[2,1,3,2]
[6,4,7,1,5,2,3,8]=>[6,2,7,4,1,5,3,8]=>[3,7,2,5,8,4,6,1]=>[2,3,2,1]
[6,2,7,3,1,4,5,8]=>[5,2,4,6,1,7,3,8]=>[4,7,5,3,8,2,6,1]=>[2,1,2,2,1]
[3,2,5,6,1,4,7,8]=>[1,5,2,3,6,4,7,8]=>[8,4,7,6,3,5,2,1]=>[1,2,1,2,1,1]
[3,5,2,6,1,4,7,8]=>[1,3,5,2,6,4,7,8]=>[8,6,4,7,3,5,2,1]=>[1,1,2,2,1,1]
[5,1,4,6,7,2,3,8]=>[3,6,4,1,7,2,5,8]=>[6,3,5,8,2,7,4,1]=>[1,3,2,1,1]
[3,5,4,6,7,8,1,2]=>[3,1,2,4,7,5,8,6]=>[6,8,7,5,2,4,1,3]=>[2,1,1,2,2]
[1,6,7,3,2,4,5,8]=>[5,4,6,2,7,1,3,8]=>[4,5,3,7,2,8,6,1]=>[2,2,2,1,1]
[1,5,3,6,2,4,7,8]=>[3,5,2,6,1,4,7,8]=>[6,4,7,3,8,5,2,1]=>[1,2,2,1,1,1]
[5,1,3,6,2,4,7,8]=>[3,5,6,2,1,4,7,8]=>[6,4,3,7,8,5,2,1]=>[1,1,3,1,1,1]
[2,5,4,6,7,1,3,8]=>[3,2,6,1,4,7,5,8]=>[6,7,3,8,5,2,4,1]=>[2,2,1,2,1]
[2,6,7,4,5,1,3,8]=>[6,4,2,7,1,5,3,8]=>[3,5,7,2,8,4,6,1]=>[3,2,2,1]
[6,2,7,4,5,1,3,8]=>[6,4,7,2,1,5,3,8]=>[3,5,2,7,8,4,6,1]=>[2,3,2,1]
[4,2,5,6,7,1,3,8]=>[3,1,6,2,4,7,5,8]=>[6,8,3,7,5,2,4,1]=>[2,2,1,2,1]
[4,5,2,6,7,1,3,8]=>[1,6,3,2,4,7,5,8]=>[8,3,6,7,5,2,4,1]=>[1,3,1,2,1]
[6,1,7,3,2,4,5,8]=>[5,4,6,7,2,1,3,8]=>[4,5,3,2,7,8,6,1]=>[2,1,3,1,1]
[6,1,7,4,5,2,3,8]=>[6,4,7,5,2,1,3,8]=>[3,5,2,4,7,8,6,1]=>[2,4,1,1]
[6,3,7,4,5,8,1,2]=>[4,7,2,1,5,3,8,6]=>[5,2,7,8,4,6,1,3]=>[1,3,2,2]
[5,4,1,6,7,2,3,8]=>[6,4,2,1,7,3,5,8]=>[3,5,7,8,2,6,4,1]=>[4,2,1,1]
[5,2,1,6,3,4,7,8]=>[2,5,6,3,1,4,7,8]=>[7,4,3,6,8,5,2,1]=>[1,1,3,1,1,1]
[7,3,2,5,4,1,6,8]=>[2,6,3,5,4,7,1,8]=>[7,3,6,4,5,2,8,1]=>[1,2,2,2,1]
[7,3,5,4,2,1,6,8]=>[6,2,5,4,3,7,1,8]=>[3,7,4,5,6,2,8,1]=>[2,3,2,1]
[7,3,5,2,4,1,6,8]=>[2,4,6,5,3,7,1,8]=>[7,5,3,4,6,2,8,1]=>[1,1,3,2,1]
[7,6,5,2,1,4,3,8]=>[4,7,5,6,3,2,1,8]=>[5,2,4,3,6,7,8,1]=>[1,2,4,1]
[1,3,6,7,5,2,8,4]=>[3,8,6,2,5,1,4,7]=>[6,1,3,7,4,8,5,2]=>[1,3,2,1,1]
[7,3,4,1,6,2,5,8]=>[2,6,3,7,4,5,1,8]=>[7,3,6,2,5,4,8,1]=>[1,2,2,2,1]
[7,3,4,1,5,6,2,8]=>[2,5,3,7,4,6,1,8]=>[7,4,6,2,5,3,8,1]=>[1,2,2,2,1]
[7,6,5,4,1,3,2,8]=>[7,5,6,4,3,2,1,8]=>[2,4,3,5,6,7,8,1]=>[2,5,1]
[7,3,4,1,5,2,6,8]=>[2,6,4,3,5,7,1,8]=>[7,3,5,6,4,2,8,1]=>[1,3,1,2,1]
[1,7,4,6,2,8,5,3]=>[8,3,7,5,4,1,2,6]=>[1,6,2,4,5,8,7,3]=>[2,4,1,1]
[4,3,1,7,2,6,8,5]=>[2,1,6,8,5,3,4,7]=>[7,8,3,1,4,6,5,2]=>[2,1,3,1,1]
[5,3,2,1,7,4,8,6]=>[2,8,3,1,6,4,5,7]=>[7,1,6,8,3,5,4,2]=>[1,3,2,1,1]
[1,3,4,5,8,7,2,6]=>[7,8,2,3,4,6,1,5]=>[2,1,7,6,5,3,8,4]=>[1,2,1,1,2,1]
[6,3,4,5,8,1,7,2]=>[2,3,4,1,8,6,7,5]=>[7,6,5,8,1,3,2,4]=>[1,1,2,2,2]
[2,4,5,1,6,8,7,3]=>[2,3,8,1,5,7,4,6]=>[7,6,1,8,4,2,5,3]=>[1,1,2,1,2,1]
[4,3,2,5,6,8,1,7]=>[3,2,1,4,5,7,8,6]=>[6,7,8,5,4,2,1,3]=>[3,1,1,1,2]
[3,7,5,4,6,8,1,2]=>[4,3,7,1,5,2,8,6]=>[5,6,2,8,4,7,1,3]=>[2,2,2,2]
[3,1,4,6,5,8,2,7]=>[1,5,3,4,7,8,2,6]=>[8,4,6,5,2,1,7,3]=>[1,2,1,1,2,1]
[2,3,4,5,8,6,1,7]=>[7,1,2,3,4,6,8,5]=>[2,8,7,6,5,3,1,4]=>[2,1,1,1,1,2]
[2,3,4,5,8,1,7,6]=>[8,1,2,3,4,6,7,5]=>[1,8,7,6,5,3,2,4]=>[2,1,1,1,1,2]
[3,1,4,6,5,8,7,2]=>[1,4,8,3,5,7,2,6]=>[8,5,1,6,4,2,7,3]=>[1,1,2,1,2,1]
[3,7,5,4,6,8,2,1]=>[4,3,5,1,2,8,7,6]=>[5,6,4,8,7,1,2,3]=>[2,2,1,3]
[5,6,1,4,7,2,8,3]=>[4,1,8,6,3,2,5,7]=>[5,8,1,3,6,7,4,2]=>[2,4,1,1]
[4,3,1,7,5,6,8,2]=>[2,1,5,6,4,8,3,7]=>[7,8,4,3,5,1,6,2]=>[2,1,2,2,1]
[4,3,1,7,6,5,8,2]=>[1,6,2,5,4,8,3,7]=>[8,3,7,4,5,1,6,2]=>[1,2,2,2,1]
[3,1,4,6,7,8,5,2]=>[1,4,5,8,3,7,2,6]=>[8,5,4,1,6,2,7,3]=>[1,1,1,2,2,1]
[1,4,5,2,6,8,7,3]=>[2,3,8,5,7,1,4,6]=>[7,6,1,4,2,8,5,3]=>[1,1,2,2,1,1]
[3,7,5,2,6,8,1,4]=>[7,4,1,3,5,2,8,6]=>[2,5,8,6,4,7,1,3]=>[3,1,2,2]
[3,7,5,2,6,8,4,1]=>[5,3,8,1,4,2,7,6]=>[4,6,1,8,5,7,2,3]=>[2,2,2,2]
[5,6,1,2,7,4,8,3]=>[6,5,1,8,3,2,4,7]=>[3,4,8,1,6,7,5,2]=>[3,3,1,1]
[6,3,5,2,4,7,8,1]=>[2,4,5,3,1,6,8,7]=>[7,5,4,6,8,3,1,2]=>[1,1,3,1,2]
[5,3,2,1,4,7,8,6]=>[3,2,6,1,8,4,5,7]=>[6,7,3,8,1,5,4,2]=>[2,2,2,1,1]
[5,3,1,4,2,7,8,6]=>[4,2,6,1,8,3,5,7]=>[5,7,3,8,1,6,4,2]=>[2,2,2,1,1]
[5,3,1,2,4,7,8,6]=>[6,2,8,3,1,4,5,7]=>[3,7,1,6,8,5,4,2]=>[2,3,1,1,1]
[7,1,5,2,6,8,4,3]=>[5,3,8,7,2,4,1,6]=>[4,6,1,2,7,5,8,3]=>[2,3,2,1]
[7,1,5,2,6,8,3,4]=>[7,5,3,8,2,4,1,6]=>[2,4,6,1,7,5,8,3]=>[3,2,2,1]
[1,7,4,6,5,8,3,2]=>[5,3,4,2,8,7,1,6]=>[4,6,5,7,1,2,8,3]=>[2,2,3,1]
[2,7,4,6,1,8,3,5]=>[3,7,8,5,1,4,2,6]=>[6,2,1,4,8,5,7,3]=>[1,1,3,2,1]
[2,7,4,6,1,8,5,3]=>[8,3,7,5,1,4,2,6]=>[1,6,2,4,8,5,7,3]=>[2,3,2,1]
[2,3,6,7,1,5,8,4]=>[6,3,8,1,2,5,4,7]=>[3,6,1,8,7,4,5,2]=>[2,2,1,2,1]
[2,3,6,7,5,1,8,4]=>[3,8,6,1,2,5,4,7]=>[6,1,3,8,7,4,5,2]=>[1,3,1,2,1]
[4,3,2,6,7,1,8,5]=>[2,1,4,8,3,6,5,7]=>[7,8,5,1,6,3,4,2]=>[2,1,2,2,1]
[7,1,5,4,6,8,2,3]=>[4,3,7,5,8,2,1,6]=>[5,6,2,4,1,7,8,3]=>[2,2,3,1]
[2,7,4,6,5,8,1,3]=>[7,3,5,4,1,2,8,6]=>[2,6,4,5,8,7,1,3]=>[2,3,1,2]
[7,3,4,5,8,6,1,2]=>[2,3,4,7,1,8,6,5]=>[7,6,5,2,8,1,3,4]=>[1,1,1,2,3]
[7,3,4,5,8,1,6,2]=>[2,3,4,8,6,1,7,5]=>[7,6,5,1,3,8,2,4]=>[1,1,1,3,2]
[1,3,4,5,8,6,2,7]=>[7,2,3,4,6,8,1,5]=>[2,7,6,5,3,1,8,4]=>[2,1,1,1,2,1]
[1,3,4,5,8,2,7,6]=>[8,2,3,4,6,7,1,5]=>[1,7,6,5,3,2,8,4]=>[2,1,1,1,2,1]
[6,3,4,5,8,2,1,7]=>[2,3,4,1,7,6,8,5]=>[7,6,5,8,2,3,1,4]=>[1,1,2,2,2]
[6,3,4,5,8,2,7,1]=>[2,3,4,1,6,8,7,5]=>[7,6,5,8,3,1,2,4]=>[1,1,2,1,3]
[7,3,4,5,8,6,2,1]=>[8,2,3,4,1,7,6,5]=>[1,7,6,5,8,2,3,4]=>[2,1,2,3]
[2,7,4,6,5,8,3,1]=>[5,3,4,2,8,1,7,6]=>[4,6,5,7,1,8,2,3]=>[2,2,2,2]
[7,1,5,4,6,8,3,2]=>[4,3,5,8,7,2,1,6]=>[5,6,4,1,2,7,8,3]=>[2,1,4,1]
[7,3,2,5,6,8,4,1]=>[2,4,5,8,3,1,7,6]=>[7,5,4,1,6,8,2,3]=>[1,1,1,3,2]
[5,7,4,6,1,8,3,2]=>[1,3,8,7,5,4,2,6]=>[8,6,1,2,4,5,7,3]=>[1,1,5,1]
[6,3,4,5,8,1,2,7]=>[2,3,6,4,1,7,8,5]=>[7,6,3,5,8,2,1,4]=>[1,1,3,1,2]
[7,3,4,5,8,2,1,6]=>[2,3,4,7,6,1,8,5]=>[7,6,5,2,3,8,1,4]=>[1,1,1,3,2]
[7,3,4,5,8,2,6,1]=>[2,3,4,6,1,8,7,5]=>[7,6,5,3,8,1,2,4]=>[1,1,1,2,3]
[4,7,6,1,8,2,5,3]=>[8,1,6,7,4,3,2,5]=>[1,8,3,2,5,6,7,4]=>[2,1,4,1]
[4,7,8,2,6,1,5,3]=>[8,1,4,6,2,7,5,3]=>[1,8,5,3,7,2,4,6]=>[2,1,2,3]
[7,6,4,2,8,3,5,1]=>[6,3,8,4,2,1,7,5]=>[3,6,1,5,7,8,2,4]=>[2,4,2]
[8,4,7,3,6,5,1,2]=>[2,4,7,8,6,5,3,1]=>[7,5,2,1,3,4,6,8]=>[1,1,1,5]
[8,4,6,1,7,5,3,2]=>[8,2,7,6,4,3,5,1]=>[1,7,2,3,5,6,4,8]=>[2,4,2]
[6,4,7,1,8,3,2,5]=>[2,7,6,1,8,4,3,5]=>[7,2,3,8,1,5,6,4]=>[1,3,3,1]
[7,4,8,3,6,1,5,2]=>[2,4,8,6,1,7,5,3]=>[7,5,1,3,8,2,4,6]=>[1,1,3,3]
[7,8,4,3,6,2,5,1]=>[4,3,6,1,8,7,5,2]=>[5,6,3,8,1,2,4,7]=>[2,2,4]
[9,10,7,8,5,6,2,4,1,3]=>[7,9,5,3,1,10,8,6,4,2]=>[4,2,6,8,10,1,3,5,7,9]=>[1,4,5]
[9,10,7,8,4,6,2,5,1,3]=>[7,5,9,3,1,10,8,6,4,2]=>[4,6,2,8,10,1,3,5,7,9]=>[2,3,5]
[9,10,6,8,4,7,2,5,1,3]=>[7,5,3,9,1,10,8,6,4,2]=>[4,6,8,2,10,1,3,5,7,9]=>[3,2,5]
[8,10,6,9,4,7,2,5,1,3]=>[7,5,3,1,9,10,8,6,4,2]=>[4,6,8,10,2,1,3,5,7,9]=>[4,1,5]
[6,12,5,11,4,10,3,9,2,8,1,7]=>[1,3,5,7,9,11,12,10,8,6,4,2]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[1,1,1,1,1,1,6]
[6,2,1,7,3,5,4,8]=>[7,2,5,6,3,1,4,8]=>[2,7,4,3,6,8,5,1]=>[2,1,3,1,1]
[2,1,8,6,3,5,4,7]=>[7,5,6,1,4,8,2,3]=>[2,4,3,8,5,1,7,6]=>[2,2,1,2,1]
[2,1,7,3,5,8,6,4]=>[8,5,7,1,4,2,3,6]=>[1,4,2,8,5,7,6,3]=>[2,2,2,1,1]
[2,7,3,1,5,4,6,8]=>[3,6,1,4,5,7,2,8]=>[6,3,8,5,4,2,7,1]=>[1,2,1,1,2,1]
[2,6,3,1,4,8,5,7]=>[3,7,8,1,4,2,5,6]=>[6,2,1,8,5,7,4,3]=>[1,1,2,2,1,1]
[4,2,1,8,3,6,7,5]=>[6,1,8,2,5,7,3,4]=>[3,8,1,7,4,2,6,5]=>[2,2,1,2,1]
[2,1,8,6,3,5,7,4]=>[6,8,5,1,4,7,2,3]=>[3,1,4,8,5,2,7,6]=>[1,3,1,2,1]
[2,7,3,1,4,8,5,6]=>[3,7,8,1,4,5,2,6]=>[6,2,1,8,5,4,7,3]=>[1,1,2,1,2,1]
[3,2,1,6,4,5,7,8]=>[2,1,5,6,3,4,7,8]=>[7,8,4,3,6,5,2,1]=>[2,1,2,1,1,1]
[3,2,1,5,7,8,4,6]=>[1,7,2,4,5,8,3,6]=>[8,2,7,5,4,1,6,3]=>[1,2,1,1,2,1]
[2,1,7,3,6,8,4,5]=>[7,5,8,1,4,2,3,6]=>[2,4,1,8,5,7,6,3]=>[2,2,2,1,1]
[2,7,3,1,5,6,8,4]=>[3,5,6,8,1,4,2,7]=>[6,4,3,1,8,5,7,2]=>[1,1,1,2,2,1]
[2,4,7,5,1,6,8,3]=>[6,2,4,8,1,5,3,7]=>[3,7,5,1,8,4,6,2]=>[2,1,2,2,1]
[4,3,7,5,6,1,8,2]=>[1,4,8,2,6,5,3,7]=>[8,5,1,7,3,4,6,2]=>[1,1,2,3,1]
[4,3,6,8,5,1,7,2]=>[1,3,8,2,6,5,7,4]=>[8,6,1,7,3,4,2,5]=>[1,1,2,2,2]
[2,6,1,8,3,5,7,4]=>[6,8,5,1,2,7,3,4]=>[3,1,4,8,7,2,6,5]=>[1,3,1,2,1]
[2,1,6,8,3,7,4,5]=>[7,3,8,1,5,6,2,4]=>[2,6,1,8,4,3,7,5]=>[2,2,1,2,1]
[2,1,8,3,5,7,4,6]=>[5,7,8,1,4,6,2,3]=>[4,2,1,8,5,3,7,6]=>[1,1,2,1,2,1]
[3,2,1,5,6,8,4,7]=>[2,1,4,5,7,8,3,6]=>[7,8,5,4,2,1,6,3]=>[2,1,1,1,2,1]
[3,2,1,5,7,4,6,8]=>[2,1,4,6,7,3,5,8]=>[7,8,5,3,2,6,4,1]=>[2,1,1,2,1,1]
[2,1,7,3,6,4,5,8]=>[6,7,1,4,5,2,3,8]=>[3,2,8,5,4,7,6,1]=>[1,2,1,2,1,1]
[2,1,6,3,5,8,4,7]=>[5,7,1,3,8,2,4,6]=>[4,2,8,6,1,7,5,3]=>[1,2,1,2,1,1]
[8,2,4,1,7,5,6,3]=>[3,6,8,2,7,4,5,1]=>[6,3,1,7,2,5,4,8]=>[1,1,2,2,2]
[3,8,4,7,5,1,6,2]=>[8,3,6,1,5,7,4,2]=>[1,6,3,8,4,2,5,7]=>[2,2,1,3]
[8,4,3,6,1,7,5,2]=>[2,8,3,7,5,4,6,1]=>[7,1,6,2,4,5,3,8]=>[1,2,3,2]
[2,6,1,8,3,5,4,7]=>[7,5,6,1,2,8,3,4]=>[2,4,3,8,7,1,6,5]=>[2,2,1,2,1]
[2,7,3,1,5,6,4,8]=>[3,5,7,1,4,6,2,8]=>[6,4,2,8,5,3,7,1]=>[1,1,2,1,2,1]
[2,4,7,5,1,6,3,8]=>[7,2,5,1,4,6,3,8]=>[2,7,4,8,5,3,6,1]=>[2,2,1,2,1]
[8,2,4,1,7,5,3,6]=>[3,7,2,6,8,4,5,1]=>[6,2,7,3,1,5,4,8]=>[1,2,1,2,2]
[5,8,6,3,1,7,4,2]=>[1,4,8,7,5,3,6,2]=>[8,5,1,2,4,6,3,7]=>[1,1,4,2]
[2,4,7,1,8,5,3,6]=>[7,2,6,8,1,4,3,5]=>[2,7,3,1,8,5,6,4]=>[2,1,2,2,1]
[2,4,8,5,1,6,3,7]=>[7,2,5,1,4,6,8,3]=>[2,7,4,8,5,3,1,6]=>[2,2,1,1,2]
[6,2,1,7,3,4,8,5]=>[8,2,5,6,3,1,4,7]=>[1,7,4,3,6,8,5,2]=>[2,1,3,1,1]
[6,2,1,7,8,3,5,4]=>[8,6,2,4,1,7,3,5]=>[1,3,7,5,8,2,6,4]=>[3,2,2,1]
[2,7,1,8,3,5,6,4]=>[6,8,5,7,1,3,2,4]=>[3,1,4,2,8,6,7,5]=>[1,2,2,2,1]
[2,1,8,3,6,4,5,7]=>[6,7,1,4,5,8,2,3]=>[3,2,8,5,4,1,7,6]=>[1,2,1,1,2,1]
[3,2,1,6,7,4,5,8]=>[1,6,2,4,7,3,5,8]=>[8,3,7,5,2,6,4,1]=>[1,2,1,2,1,1]
[3,2,1,7,4,5,6,8]=>[2,1,5,6,7,3,4,8]=>[7,8,4,3,2,6,5,1]=>[2,1,1,2,1,1]
[3,2,1,6,8,4,5,7]=>[1,6,2,4,7,8,3,5]=>[8,3,7,5,2,1,6,4]=>[1,2,1,1,2,1]
[2,1,8,3,7,4,5,6]=>[6,7,8,1,4,5,2,3]=>[3,2,1,8,5,4,7,6]=>[1,1,2,1,2,1]
[2,1,8,3,6,7,4,5]=>[7,5,8,1,4,6,2,3]=>[2,4,1,8,5,3,7,6]=>[2,2,1,2,1]
[2,4,8,5,1,6,7,3]=>[6,2,4,8,1,5,7,3]=>[3,7,5,1,8,4,2,6]=>[2,1,2,1,2]
[3,2,1,8,4,5,6,7]=>[2,1,5,6,7,8,3,4]=>[7,8,4,3,2,1,6,5]=>[2,1,1,1,2,1]
[1,6,8,3,7,2,4,5]=>[4,6,2,7,8,5,1,3]=>[5,3,7,2,1,4,8,6]=>[1,2,1,3,1]
[3,8,1,5,7,2,4,6]=>[6,1,4,7,8,3,5,2]=>[3,8,5,2,1,6,4,7]=>[2,1,1,2,2]
[6,1,5,8,2,4,7,3]=>[6,3,8,5,1,7,2,4]=>[3,6,1,4,8,2,7,5]=>[2,3,2,1]
[1,2,4,8,3,6,7,5]=>[6,8,3,5,7,1,2,4]=>[3,1,6,4,2,8,7,5]=>[1,2,1,2,1,1]
[4,1,2,7,8,3,6,5]=>[1,8,6,4,7,2,3,5]=>[8,1,3,5,2,7,6,4]=>[1,3,2,1,1]
[3,5,7,4,8,6,1,2]=>[2,4,7,1,3,8,6,5]=>[7,5,2,8,6,1,3,4]=>[1,1,2,1,3]
[5,3,8,4,7,6,1,2]=>[4,1,7,8,2,6,5,3]=>[5,8,2,1,7,3,4,6]=>[2,1,2,3]
[8,7,1,2,5,4,6,3]=>[6,5,8,3,4,7,2,1]=>[3,4,1,6,5,2,7,8]=>[2,2,1,3]
[5,8,1,2,3,7,6,4]=>[8,7,3,1,4,5,6,2]=>[1,2,6,8,5,4,3,7]=>[4,1,1,2]
[1,2,8,4,3,5,7,6]=>[4,8,5,6,7,1,2,3]=>[5,1,4,3,2,8,7,6]=>[1,2,1,2,1,1]
[1,2,5,3,7,6,4,8]=>[3,7,6,1,2,4,5,8]=>[6,2,3,8,7,5,4,1]=>[1,3,1,1,1,1]
[6,1,2,8,7,4,5,3]=>[6,8,7,5,2,1,3,4]=>[3,1,2,4,7,8,6,5]=>[1,5,1,1]
[7,1,6,2,8,4,5,3]=>[6,8,7,4,2,3,1,5]=>[3,1,2,5,7,6,8,4]=>[1,4,2,1]
[1,2,6,3,8,5,4,7]=>[7,6,3,8,1,2,4,5]=>[2,3,6,1,8,7,5,4]=>[3,2,1,1,1]
[1,2,8,5,3,6,4,7]=>[7,5,4,6,8,1,2,3]=>[2,4,5,3,1,8,7,6]=>[3,1,2,1,1]
[1,2,7,3,8,5,4,6]=>[7,6,8,4,1,2,3,5]=>[2,3,1,5,8,7,6,4]=>[2,3,1,1,1]
[4,1,2,7,8,6,3,5]=>[1,7,4,8,6,2,3,5]=>[8,2,5,1,3,7,6,4]=>[1,2,3,1,1]
[1,6,2,8,4,3,5,7]=>[6,5,7,2,8,1,3,4]=>[3,4,2,7,1,8,6,5]=>[2,2,2,1,1]
[1,6,4,2,7,3,5,8]=>[6,3,7,4,1,2,5,8]=>[3,6,2,5,8,7,4,1]=>[2,3,1,1,1]
[1,8,6,3,2,4,5,7]=>[5,4,6,7,3,8,1,2]=>[4,5,3,2,6,1,8,7]=>[2,1,2,2,1]
[3,1,7,8,6,2,4,5]=>[6,7,1,3,8,5,2,4]=>[3,2,8,6,1,4,7,5]=>[1,2,1,3,1]
[1,8,7,2,4,5,6,3]=>[5,6,8,4,7,3,1,2]=>[4,3,1,5,2,6,8,7]=>[1,1,2,3,1]
[1,3,2,8,7,4,5,6]=>[6,7,8,2,5,1,3,4]=>[3,2,1,7,4,8,6,5]=>[1,1,2,2,1,1]
[1,8,3,2,6,4,5,7]=>[3,6,7,4,5,8,1,2]=>[6,3,2,5,4,1,8,7]=>[1,1,2,1,2,1]
[1,7,6,3,2,4,5,8]=>[5,4,6,7,3,1,2,8]=>[4,5,3,2,6,8,7,1]=>[2,1,3,1,1]
[1,2,8,4,3,7,5,6]=>[4,7,8,5,6,1,2,3]=>[5,2,1,4,3,8,7,6]=>[1,1,2,2,1,1]
[8,5,1,7,2,4,6,3]=>[6,8,5,2,7,3,4,1]=>[3,1,4,7,2,6,5,8]=>[1,3,2,2]
[5,3,8,7,4,6,1,2]=>[1,7,5,8,2,6,4,3]=>[8,2,4,1,7,3,5,6]=>[1,2,2,3]
[3,8,6,4,7,5,1,2]=>[4,7,3,8,1,6,5,2]=>[5,2,6,1,8,3,4,7]=>[1,2,2,3]
[1,2,7,5,3,6,4,8]=>[7,5,4,6,1,2,3,8]=>[2,4,5,3,8,7,6,1]=>[3,2,1,1,1]
[1,2,3,7,5,4,8,6]=>[5,8,6,1,2,3,4,7]=>[4,1,3,8,7,6,5,2]=>[1,3,1,1,1,1]
[3,7,4,8,6,5,1,2]=>[7,8,3,1,2,6,5,4]=>[2,1,6,8,7,3,4,5]=>[1,3,1,3]
[1,8,2,7,6,4,5,3]=>[6,8,7,5,3,4,1,2]=>[3,1,2,4,6,5,8,7]=>[1,4,2,1]
[2,9,8,7,6,5,4,1,3]=>[8,9,7,6,5,4,1,3,2]=>[2,1,3,4,5,6,9,7,8]=>[1,6,2]
[2,8,7,6,5,1,4,3]=>[8,6,7,5,4,1,3,2]=>[1,3,2,4,5,8,6,7]=>[2,4,2]
[7,1,6,3,2,5,4,8]=>[4,7,5,6,2,3,1,8]=>[5,2,4,3,7,6,8,1]=>[1,2,2,2,1]
[2,7,6,3,1,5,8,4]=>[4,6,8,5,1,3,2,7]=>[5,3,1,4,8,6,7,2]=>[1,1,3,2,1]
[1,8,4,3,6,5,2,7]=>[3,7,4,6,5,8,1,2]=>[6,2,5,3,4,1,8,7]=>[1,2,2,2,1]
[1,8,4,6,5,3,2,7]=>[7,3,6,5,4,8,1,2]=>[2,6,3,4,5,1,8,7]=>[2,3,2,1]
[7,6,1,4,3,5,2,8]=>[5,4,7,3,6,2,1,8]=>[4,5,2,6,3,7,8,1]=>[2,2,3,1]
[7,4,1,3,5,2,6,8]=>[4,6,3,2,5,7,1,8]=>[5,3,6,7,4,2,8,1]=>[1,3,1,2,1]
[1,8,6,3,4,5,2,7]=>[4,5,7,6,3,8,1,2]=>[5,4,2,3,6,1,8,7]=>[1,1,3,2,1]
[1,8,6,7,4,2,5,3]=>[8,6,5,3,7,4,1,2]=>[1,3,4,6,2,5,8,7]=>[4,3,1]
[3,6,2,1,4,8,5,7]=>[1,3,7,8,4,2,5,6]=>[8,6,2,1,5,7,4,3]=>[1,1,1,3,1,1]
[3,1,7,2,4,6,8,5]=>[1,6,8,4,5,2,3,7]=>[8,3,1,5,4,7,6,2]=>[1,1,2,2,1,1]
[3,4,7,1,5,2,8,6]=>[1,2,5,8,4,6,3,7]=>[8,7,4,1,5,3,6,2]=>[1,1,1,2,2,1]
[3,6,7,4,1,5,8,2]=>[6,4,1,2,8,5,3,7]=>[3,5,8,7,1,4,6,2]=>[3,1,3,1]
[3,1,2,8,6,5,4,7]=>[7,1,6,5,8,2,3,4]=>[2,8,3,4,1,7,6,5]=>[2,2,2,1,1]
[5,4,8,6,1,2,3,7]=>[5,2,1,6,7,4,8,3]=>[4,7,8,3,2,5,1,6]=>[3,1,2,2]
[5,6,8,7,4,3,1,2]=>[1,2,7,8,6,5,4,3]=>[8,7,2,1,3,4,5,6]=>[1,1,1,5]
[1,8,2,7,4,3,6,5]=>[5,8,6,7,3,4,1,2]=>[4,1,3,2,6,5,8,7]=>[1,2,2,2,1]
[6,5,8,2,3,7,1,4]=>[4,5,2,1,7,8,6,3]=>[5,4,7,8,2,1,3,6]=>[1,3,1,3]
[6,4,8,5,3,1,7,2]=>[8,2,1,6,5,4,7,3]=>[1,7,8,3,4,5,2,6]=>[3,3,2]
[5,7,8,6,1,3,2,4]=>[1,7,5,6,2,8,4,3]=>[8,2,4,3,7,1,5,6]=>[1,2,2,3]
[2,4,8,1,6,3,7,5]=>[8,2,6,1,4,5,7,3]=>[1,7,3,8,5,4,2,6]=>[2,2,1,1,2]
[3,1,2,8,6,4,7,5]=>[8,1,6,5,7,2,3,4]=>[1,8,3,4,2,7,6,5]=>[2,2,2,1,1]
[5,3,2,6,4,8,1,7]=>[2,5,3,1,4,7,8,6]=>[7,4,6,8,5,2,1,3]=>[1,3,1,1,2]
[4,1,6,3,5,8,2,7]=>[4,1,5,3,7,8,2,6]=>[5,8,4,6,2,1,7,3]=>[2,2,1,2,1]
[2,4,5,3,8,6,1,7]=>[2,3,7,1,4,6,8,5]=>[7,6,2,8,5,3,1,4]=>[1,1,2,1,1,2]
[1,8,5,3,2,7,6,4]=>[8,4,3,7,5,6,1,2]=>[1,5,6,2,4,3,8,7]=>[3,2,2,1]
[1,8,4,5,2,6,7,3]=>[3,6,4,8,5,7,1,2]=>[6,3,5,1,4,2,8,7]=>[1,2,2,2,1]
[4,1,2,7,6,5,8,3]=>[1,6,5,4,8,2,3,7]=>[8,3,4,5,1,7,6,2]=>[1,3,2,1,1]
[2,4,1,6,7,8,5,3]=>[2,4,5,8,1,7,3,6]=>[7,5,4,1,8,2,6,3]=>[1,1,1,2,2,1]
[1,8,4,3,6,2,7,5]=>[3,8,4,6,5,7,1,2]=>[6,1,5,3,4,2,8,7]=>[1,2,2,2,1]
[5,6,7,3,2,8,1,4]=>[1,5,4,2,7,3,8,6]=>[8,4,5,7,2,6,1,3]=>[1,3,2,2]
[2,5,7,3,6,8,4,1]=>[2,5,8,4,1,3,7,6]=>[7,4,1,5,8,6,2,3]=>[1,1,3,1,2]
[5,3,2,1,4,8,6,7]=>[3,2,7,1,8,4,5,6]=>[6,7,2,8,1,5,4,3]=>[2,2,2,1,1]
[5,3,1,4,2,8,6,7]=>[4,2,7,1,8,3,5,6]=>[5,7,2,8,1,6,4,3]=>[2,2,2,1,1]
[7,6,1,3,8,5,4,2]=>[8,7,4,6,3,2,1,5]=>[1,2,5,3,6,7,8,4]=>[3,4,1]
[3,4,7,8,1,2,6,5]=>[8,1,2,5,6,3,7,4]=>[1,8,7,4,3,6,2,5]=>[2,1,1,2,2]
[3,6,7,8,1,4,5,2]=>[6,2,8,1,5,3,7,4]=>[3,7,1,8,4,6,2,5]=>[2,2,2,2]
[3,6,2,8,1,5,4,7]=>[7,1,3,5,2,6,8,4]=>[2,8,6,4,7,3,1,5]=>[2,1,2,1,2]
[2,3,6,8,5,1,4,7]=>[6,3,7,1,2,5,8,4]=>[3,6,2,8,7,4,1,5]=>[2,2,1,1,2]
[3,1,6,4,8,2,5,7]=>[1,4,6,3,7,8,2,5]=>[8,5,3,6,2,1,7,4]=>[1,1,2,1,2,1]
[7,3,2,6,8,5,1,4]=>[7,2,4,8,3,1,6,5]=>[2,7,5,1,6,8,3,4]=>[2,1,3,2]
[7,3,5,8,4,6,1,2]=>[3,7,2,5,1,8,6,4]=>[6,2,7,4,8,1,3,5]=>[1,2,2,3]
[7,5,2,8,4,1,6,3]=>[8,6,3,2,5,1,7,4]=>[1,3,6,7,4,8,2,5]=>[4,2,2]
[7,4,5,8,2,1,3,6]=>[2,6,5,3,7,1,8,4]=>[7,3,4,6,2,8,1,5]=>[1,3,2,2]
[1,8,5,2,4,6,3,7]=>[5,7,4,3,6,8,1,2]=>[4,2,5,6,3,1,8,7]=>[1,3,1,2,1]
[1,8,4,2,3,5,7,6]=>[8,4,3,5,6,7,1,2]=>[1,5,6,4,3,2,8,7]=>[3,1,1,2,1]
[6,4,2,8,3,5,1,7]=>[5,2,7,3,1,6,8,4]=>[4,7,2,6,8,3,1,5]=>[2,3,1,2]
[6,3,4,8,2,5,7,1]=>[2,3,5,1,6,8,7,4]=>[7,6,4,8,3,1,2,5]=>[1,1,2,1,3]
[7,5,4,8,3,6,2,1]=>[3,2,5,1,8,7,6,4]=>[6,7,4,8,1,2,3,5]=>[2,2,4]
[2,7,4,8,5,3,6,1]=>[6,3,5,2,8,1,7,4]=>[3,6,4,7,1,8,2,5]=>[2,2,2,2]
[7,1,5,4,8,3,6,2]=>[4,3,6,8,7,2,1,5]=>[5,6,3,1,2,7,8,4]=>[2,1,4,1]
[7,3,2,5,8,4,6,1]=>[2,4,6,8,3,1,7,5]=>[7,5,3,1,6,8,2,4]=>[1,1,1,3,2]
[8,4,6,3,7,2,5,1]=>[2,4,6,3,8,7,5,1]=>[7,5,3,6,1,2,4,8]=>[1,1,2,4]
[7,4,6,3,8,5,1,2]=>[2,4,7,3,1,8,6,5]=>[7,5,2,6,8,1,3,4]=>[1,1,3,3]
[2,5,6,8,3,4,1,7]=>[2,5,3,7,1,6,8,4]=>[7,4,6,2,8,3,1,5]=>[1,2,2,1,2]
[8,4,6,2,7,5,3,1]=>[8,2,7,4,3,6,5,1]=>[1,7,2,5,6,3,4,8]=>[2,3,3]
[8,5,6,7,2,4,3,1]=>[2,8,5,3,7,6,4,1]=>[7,1,4,6,2,3,5,8]=>[1,3,4]
[2,5,6,8,4,3,1,7]=>[2,3,7,6,1,5,8,4]=>[7,6,2,3,8,4,1,5]=>[1,1,3,1,2]
[2,5,7,8,4,1,3,6]=>[2,6,7,5,1,3,8,4]=>[7,3,2,4,8,6,1,5]=>[1,1,3,1,2]
[6,5,7,8,4,1,3,2]=>[2,1,8,6,3,7,5,4]=>[7,8,1,3,6,2,4,5]=>[2,3,3]
[7,5,6,8,2,4,1,3]=>[5,2,7,3,1,8,6,4]=>[4,7,2,6,8,1,3,5]=>[2,3,3]
[4,3,2,6,8,5,1,7]=>[2,1,4,7,3,6,8,5]=>[7,8,5,2,6,3,1,4]=>[2,1,2,1,2]
[3,5,6,8,2,4,1,7]=>[2,5,1,3,7,6,8,4]=>[7,4,8,6,2,3,1,5]=>[1,2,1,2,2]
[2,6,7,8,1,4,5,3]=>[6,2,8,5,1,3,7,4]=>[3,7,1,4,8,6,2,5]=>[2,3,1,2]
[3,6,7,8,1,4,2,5]=>[7,5,1,2,6,3,8,4]=>[2,4,8,7,3,6,1,5]=>[3,1,2,2]
[3,5,7,8,2,1,4,6]=>[2,6,1,5,7,3,8,4]=>[7,3,8,4,2,6,1,5]=>[1,2,1,2,2]
[6,5,7,8,3,1,4,2]=>[2,1,8,6,5,3,7,4]=>[7,8,1,3,4,6,2,5]=>[2,4,2]
[2,5,7,8,3,1,4,6]=>[2,6,5,7,1,3,8,4]=>[7,3,4,2,8,6,1,5]=>[1,2,2,1,2]
[2,4,7,3,8,1,5,6]=>[2,4,6,7,1,3,8,5]=>[7,5,3,2,8,6,1,4]=>[1,1,1,2,1,2]
[6,4,7,3,8,1,5,2]=>[2,4,1,8,6,3,7,5]=>[7,5,8,1,3,6,2,4]=>[1,2,3,2]
[6,4,7,3,8,1,2,5]=>[2,6,4,1,7,3,8,5]=>[7,3,5,8,2,6,1,4]=>[1,3,2,2]
[7,4,6,3,8,2,1,5]=>[2,4,7,6,3,1,8,5]=>[7,5,2,3,6,8,1,4]=>[1,1,4,2]
[6,3,2,5,4,8,1,7]=>[2,5,3,4,1,7,8,6]=>[7,4,6,5,8,2,1,3]=>[1,2,2,1,2]
[6,4,5,2,3,8,1,7]=>[4,2,5,3,1,7,8,6]=>[5,7,4,6,8,2,1,3]=>[2,3,1,2]
[6,4,5,3,2,8,1,7]=>[2,5,4,3,1,7,8,6]=>[7,4,5,6,8,2,1,3]=>[1,4,1,2]
[5,4,6,3,8,2,1,7]=>[2,1,4,3,7,6,8,5]=>[7,8,5,6,2,3,1,4]=>[2,2,2,2]
[5,4,7,3,8,1,6,2]=>[2,1,4,8,6,3,7,5]=>[7,8,5,1,3,6,2,4]=>[2,1,3,2]
[2,5,7,8,3,1,6,4]=>[2,5,8,6,1,3,7,4]=>[7,4,1,3,8,6,2,5]=>[1,1,3,1,2]
[4,5,7,8,3,1,2,6]=>[1,2,6,7,5,3,8,4]=>[8,7,3,2,4,6,1,5]=>[1,1,1,3,2]
[4,5,6,8,2,3,1,7]=>[1,2,5,3,7,6,8,4]=>[8,7,4,6,2,3,1,5]=>[1,1,2,2,2]
[5,4,6,2,8,3,1,7]=>[2,1,7,4,3,6,8,5]=>[7,8,2,5,6,3,1,4]=>[2,3,1,2]
[5,3,2,6,8,4,1,7]=>[2,4,1,7,3,6,8,5]=>[7,5,8,2,6,3,1,4]=>[1,2,2,1,2]
[5,4,7,2,8,1,3,6]=>[4,2,1,6,7,3,8,5]=>[5,7,8,3,2,6,1,4]=>[3,1,2,2]
[4,5,7,8,2,1,3,6]=>[1,2,6,5,7,3,8,4]=>[8,7,3,4,2,6,1,5]=>[1,1,2,2,2]
[4,6,7,8,1,3,2,5]=>[7,1,5,2,6,3,8,4]=>[2,8,4,7,3,6,1,5]=>[2,2,2,2]
[4,6,7,8,1,3,5,2]=>[6,1,2,8,5,3,7,4]=>[3,8,7,1,4,6,2,5]=>[2,1,3,2]
[2,6,7,8,1,3,5,4]=>[8,5,2,6,1,3,7,4]=>[1,4,7,3,8,6,2,5]=>[3,2,1,2]
[4,6,7,8,1,5,2,3]=>[7,1,2,8,5,3,6,4]=>[2,8,7,1,4,6,3,5]=>[2,1,3,2]
[4,6,7,8,1,2,5,3]=>[8,1,5,2,6,3,7,4]=>[1,8,4,7,3,6,2,5]=>[2,2,2,2]
[4,5,7,8,2,1,6,3]=>[1,2,5,8,6,3,7,4]=>[8,7,4,1,3,6,2,5]=>[1,1,1,3,2]
[5,4,7,2,8,1,6,3]=>[2,1,8,4,6,3,7,5]=>[7,8,1,5,3,6,2,4]=>[2,2,2,2]
[5,3,2,7,8,1,6,4]=>[8,2,1,6,3,4,7,5]=>[1,7,8,3,6,5,2,4]=>[3,2,1,2]
[4,3,2,7,8,1,6,5]=>[1,8,2,6,3,4,7,5]=>[8,1,7,3,6,5,2,4]=>[1,2,2,1,2]
[3,5,7,8,2,1,6,4]=>[2,5,8,1,6,3,7,4]=>[7,4,1,8,3,6,2,5]=>[1,1,2,2,2]
[3,6,7,8,1,2,5,4]=>[8,5,1,2,6,3,7,4]=>[1,4,8,7,3,6,2,5]=>[3,1,2,2]
[3,6,7,8,1,5,2,4]=>[7,2,8,1,5,3,6,4]=>[2,7,1,8,4,6,3,5]=>[2,2,2,2]
[3,6,7,8,1,5,4,2]=>[2,8,7,1,5,3,6,4]=>[7,1,2,8,4,6,3,5]=>[1,3,2,2]
[2,6,7,8,1,5,4,3]=>[2,8,7,5,1,3,6,4]=>[7,1,2,4,8,6,3,5]=>[1,4,1,2]
[3,4,5,6,7,8,9,1,2,10]=>[1,2,3,4,5,8,6,9,7,10]=>[10,9,8,7,6,3,5,2,4,1]=>[1,1,1,1,1,2,2,1]
[1,3,4,5,6,7,8,9,10,11,2]=>[2,3,4,5,6,7,8,9,11,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>[1,1,1,1,1,1,1,1,2,1]
[4,2,7,1,5,3,8,6]=>[5,1,8,2,4,6,3,7]=>[4,8,1,7,5,3,6,2]=>[2,2,1,2,1]
[4,2,8,6,1,5,3,7]=>[1,7,5,6,2,4,8,3]=>[8,2,4,3,7,5,1,6]=>[1,2,2,1,2]
[3,2,6,7,5,1,4,8]=>[6,1,3,7,2,5,4,8]=>[3,8,6,2,7,4,5,1]=>[2,1,2,2,1]
[2,7,1,3,5,4,8,6]=>[5,8,1,3,4,6,2,7]=>[4,1,8,6,5,3,7,2]=>[1,2,1,1,2,1]
[4,7,2,1,5,8,6,3]=>[1,8,3,5,7,4,2,6]=>[8,1,6,4,2,5,7,3]=>[1,2,1,3,1]
[7,2,1,3,5,8,6,4]=>[8,2,5,7,3,4,1,6]=>[1,7,4,2,6,5,8,3]=>[2,1,2,2,1]
[2,3,6,4,7,1,5,8]=>[4,6,1,2,3,7,5,8]=>[5,3,8,7,6,2,4,1]=>[1,2,1,1,2,1]
[1,3,4,8,2,7,5,6]=>[7,8,2,3,5,6,1,4]=>[2,1,7,6,4,3,8,5]=>[1,2,1,1,2,1]
[3,1,4,8,2,6,7,5]=>[1,6,8,3,5,7,2,4]=>[8,3,1,6,4,2,7,5]=>[1,1,2,1,2,1]
[8,3,1,6,2,5,7,4]=>[2,6,8,5,3,4,7,1]=>[7,3,1,4,6,5,2,8]=>[1,1,3,1,2]
[4,8,6,2,1,5,7,3]=>[1,4,6,8,5,3,7,2]=>[8,5,3,1,4,6,2,7]=>[1,1,1,3,2]
[4,8,3,6,5,1,7,2]=>[8,1,3,6,5,4,7,2]=>[1,8,6,3,4,5,2,7]=>[2,1,3,2]
[6,4,7,5,1,8,2,3]=>[2,7,1,8,5,4,3,6]=>[7,2,8,1,4,5,6,3]=>[1,2,4,1]
[3,6,1,7,5,8,2,4]=>[7,5,1,4,2,8,3,6]=>[2,4,8,5,7,1,6,3]=>[3,2,2,1]
[7,3,5,1,6,8,2,4]=>[7,2,5,3,8,4,1,6]=>[2,7,4,6,1,5,8,3]=>[2,2,3,1]
[4,7,3,5,6,1,8,2]=>[1,3,4,8,6,5,2,7]=>[8,6,5,1,3,4,7,2]=>[1,1,1,4,1]
[3,4,6,8,5,1,7,2]=>[3,8,1,2,6,5,7,4]=>[6,1,8,7,3,4,2,5]=>[1,2,1,2,2]
[4,6,8,2,1,5,7,3]=>[1,4,6,2,8,5,7,3]=>[8,5,3,7,1,4,2,6]=>[1,1,2,2,2]
[6,8,2,1,3,5,7,4]=>[3,6,8,4,1,5,7,2]=>[6,3,1,5,8,4,2,7]=>[1,1,3,1,2]
[1,8,2,3,5,7,4,6]=>[5,7,8,3,4,6,1,2]=>[4,2,1,6,5,3,8,7]=>[1,1,2,1,2,1]
[2,6,1,3,5,8,4,7]=>[5,7,8,1,3,2,4,6]=>[4,2,1,8,6,7,5,3]=>[1,1,2,2,1,1]
[7,3,2,5,6,1,4,8]=>[2,6,3,4,7,5,1,8]=>[7,3,6,5,2,4,8,1]=>[1,2,1,3,1]
[4,7,5,2,6,1,3,8]=>[1,4,6,3,7,5,2,8]=>[8,5,3,6,2,4,7,1]=>[1,1,2,3,1]
[4,6,2,8,1,5,3,7]=>[1,7,3,5,2,6,8,4]=>[8,2,6,4,7,3,1,5]=>[1,2,2,1,2]
[8,4,1,2,7,5,3,6]=>[7,6,2,8,3,4,5,1]=>[2,3,7,1,6,5,4,8]=>[3,2,1,2]
[4,5,6,2,7,1,3,8]=>[1,4,2,6,3,7,5,8]=>[8,5,7,3,6,2,4,1]=>[1,2,2,2,1]
[8,5,1,2,6,3,4,7]=>[6,7,3,4,2,5,8,1]=>[3,2,6,5,7,4,1,8]=>[1,2,2,1,2]
[1,6,2,7,4,8,3,5]=>[5,7,4,2,8,1,3,6]=>[4,2,5,7,1,8,6,3]=>[1,3,2,1,1]
[6,2,1,7,8,5,3,4]=>[7,4,8,2,1,6,3,5]=>[2,5,1,7,8,3,6,4]=>[2,3,2,1]
[2,7,8,4,1,5,6,3]=>[6,4,8,5,1,2,7,3]=>[3,5,1,4,8,7,2,6]=>[2,3,1,2]
[2,7,1,8,5,6,3,4]=>[7,5,8,6,1,3,2,4]=>[2,4,1,3,8,6,7,5]=>[2,3,2,1]
[8,2,4,5,1,6,7,3]=>[3,6,2,4,8,5,7,1]=>[6,3,7,5,1,4,2,8]=>[1,2,1,2,2]
[4,5,8,3,6,7,1,2]=>[1,2,4,7,5,8,6,3]=>[8,7,5,2,4,1,3,6]=>[1,1,1,2,3]
[4,5,8,3,7,6,1,2]=>[1,2,4,7,8,6,5,3]=>[8,7,5,2,1,3,4,6]=>[1,1,1,1,4]
[4,2,8,3,7,1,6,5]=>[1,8,4,6,7,2,5,3]=>[8,1,5,3,2,7,4,6]=>[1,2,1,2,2]
[7,2,3,4,8,1,6,5]=>[8,2,3,4,6,1,7,5]=>[1,7,6,5,3,8,2,4]=>[2,1,1,2,2]
[7,2,3,4,8,1,5,6]=>[2,3,4,6,7,1,8,5]=>[7,6,5,3,2,8,1,4]=>[1,1,1,1,2,2]
[7,6,3,4,8,5,1,2]=>[3,4,7,2,1,8,6,5]=>[6,5,2,7,8,1,3,4]=>[1,1,3,3]
[7,6,3,8,4,5,1,2]=>[7,3,5,2,1,8,6,4]=>[2,6,4,7,8,1,3,5]=>[2,3,3]
[7,2,3,8,5,1,6,4]=>[8,6,2,3,5,1,7,4]=>[1,3,7,6,4,8,2,5]=>[3,1,2,2]
[2,6,4,8,1,5,7,3]=>[3,6,2,8,1,5,7,4]=>[6,3,7,1,8,4,2,5]=>[1,2,2,1,2]
[7,2,3,8,4,1,5,6]=>[6,2,3,5,7,1,8,4]=>[3,7,6,4,2,8,1,5]=>[2,1,1,2,2]
[7,2,3,5,8,1,4,6]=>[6,2,3,4,7,1,8,5]=>[3,7,6,5,2,8,1,4]=>[2,1,1,2,2]
[7,8,2,3,6,1,4,5]=>[3,4,6,7,1,8,5,2]=>[6,5,3,2,8,1,4,7]=>[1,1,1,2,3]
[7,8,2,3,6,1,5,4]=>[8,3,4,6,1,7,5,2]=>[1,6,5,3,8,2,4,7]=>[2,1,2,3]
[4,2,6,3,7,1,5,8]=>[4,1,6,2,3,7,5,8]=>[5,8,3,7,6,2,4,1]=>[2,2,1,2,1]
[7,2,3,5,8,1,6,4]=>[4,8,2,3,6,1,7,5]=>[5,1,7,6,3,8,2,4]=>[1,2,1,2,2]
[7,2,3,8,4,1,6,5]=>[5,8,2,3,6,1,7,4]=>[4,1,7,6,3,8,2,5]=>[1,2,1,2,2]
[2,6,4,8,1,3,7,5]=>[3,8,5,1,2,6,7,4]=>[6,1,4,8,7,3,2,5]=>[1,3,1,1,2]
[3,6,4,8,1,7,5,2]=>[8,3,1,2,7,5,6,4]=>[1,6,8,7,2,4,3,5]=>[3,1,2,2]
[7,6,5,1,2,3,8,4]=>[8,4,5,6,3,2,1,7]=>[1,5,4,3,6,7,8,2]=>[2,1,4,1]
[7,6,5,1,4,2,8,3]=>[8,6,4,5,3,2,1,7]=>[1,3,5,4,6,7,8,2]=>[3,4,1]
[3,5,6,4,1,2,7,8]=>[5,1,2,6,4,3,7,8]=>[4,8,7,3,5,6,2,1]=>[2,1,3,1,1]
[7,8,5,4,1,2,6,3]=>[8,5,6,4,3,1,7,2]=>[1,4,3,5,6,8,2,7]=>[2,4,2]
[3,5,6,4,1,2,8,7]=>[2,8,1,5,4,3,6,7]=>[7,1,8,4,5,6,3,2]=>[1,2,3,1,1]
[7,6,5,1,4,2,3,8]=>[6,7,4,5,3,2,1,8]=>[3,2,5,4,6,7,8,1]=>[1,2,4,1]
[7,6,5,1,2,4,3,8]=>[7,4,5,6,3,2,1,8]=>[2,5,4,3,6,7,8,1]=>[2,1,4,1]
[7,6,5,1,2,4,8,3]=>[6,8,4,5,3,2,1,7]=>[3,1,5,4,6,7,8,2]=>[1,2,4,1]
[7,6,5,1,3,2,8,4]=>[5,8,4,6,3,2,1,7]=>[4,1,5,3,6,7,8,2]=>[1,2,4,1]
[7,6,5,1,3,2,4,8]=>[6,4,5,7,3,2,1,8]=>[3,5,4,2,6,7,8,1]=>[2,1,4,1]
[7,6,5,1,3,4,2,8]=>[5,7,4,6,3,2,1,8]=>[4,2,5,3,6,7,8,1]=>[1,2,4,1]
[7,2,3,4,5,1,8,6]=>[2,3,4,5,8,6,1,7]=>[7,6,5,4,1,3,8,2]=>[1,1,1,1,3,1]
[2,6,4,3,1,8,7,5]=>[3,8,4,1,2,7,5,6]=>[6,1,5,8,7,2,4,3]=>[1,3,1,2,1]
[3,5,8,4,1,2,7,6]=>[2,8,1,5,4,6,7,3]=>[7,1,8,4,5,3,2,6]=>[1,2,2,1,2]
[3,5,8,4,1,2,6,7]=>[5,1,2,6,4,7,8,3]=>[4,8,7,3,5,2,1,6]=>[2,1,2,1,2]
[3,5,8,4,1,6,7,2]=>[2,6,1,4,8,5,7,3]=>[7,3,8,5,1,4,2,6]=>[1,2,1,2,2]
[2,5,8,4,1,7,3,6]=>[2,7,4,8,1,5,6,3]=>[7,2,5,1,8,4,3,6]=>[1,2,2,1,2]
[3,6,4,2,1,7,5,8]=>[4,1,3,7,5,2,6,8]=>[5,8,6,2,4,7,3,1]=>[2,1,3,1,1]
[3,5,6,4,1,8,7,2]=>[2,4,1,3,8,7,5,6]=>[7,5,8,6,1,2,4,3]=>[1,2,1,3,1]
[2,6,4,5,1,3,7,8]=>[5,3,6,1,4,2,7,8]=>[4,6,3,8,5,7,2,1]=>[2,2,2,1,1]
[7,6,5,1,4,3,8,2]=>[6,5,8,4,3,2,1,7]=>[3,4,1,5,6,7,8,2]=>[2,5,1]
[7,6,5,1,2,8,4,3]=>[8,7,4,5,3,2,1,6]=>[1,2,5,4,6,7,8,3]=>[3,4,1]
[7,6,5,1,2,8,3,4]=>[7,8,4,5,3,2,1,6]=>[2,1,5,4,6,7,8,3]=>[1,2,4,1]
[7,6,5,1,8,2,4,3]=>[8,6,7,4,3,2,1,5]=>[1,3,2,5,6,7,8,4]=>[2,5,1]
[7,6,5,1,8,2,3,4]=>[6,7,8,4,3,2,1,5]=>[3,2,1,5,6,7,8,4]=>[1,1,5,1]
[7,6,5,1,8,3,2,4]=>[7,6,8,4,3,2,1,5]=>[2,3,1,5,6,7,8,4]=>[2,5,1]
[7,6,5,1,4,8,2,3]=>[7,5,8,4,3,2,1,6]=>[2,4,1,5,6,7,8,3]=>[2,5,1]
[3,6,4,5,1,7,2,8]=>[3,7,1,5,4,2,6,8]=>[6,2,8,4,5,7,3,1]=>[1,2,3,1,1]
[2,5,6,4,1,7,8,3]=>[2,6,4,1,3,8,5,7]=>[7,3,5,8,6,1,4,2]=>[1,3,1,2,1]
[7,8,5,4,1,6,3,2]=>[8,7,5,4,3,1,6,2]=>[1,2,4,5,6,8,3,7]=>[6,2]
[2,5,6,4,1,7,3,8]=>[2,7,5,1,4,3,6,8]=>[7,2,4,8,5,6,3,1]=>[1,3,2,1,1]
[3,6,4,5,1,7,8,2]=>[3,6,1,4,2,8,5,7]=>[6,3,8,5,7,1,4,2]=>[1,2,2,2,1]
[7,6,5,1,4,8,3,2]=>[5,8,7,4,3,2,1,6]=>[4,1,2,5,6,7,8,3]=>[1,6,1]
[7,6,5,1,8,3,4,2]=>[6,8,7,4,3,2,1,5]=>[3,1,2,5,6,7,8,4]=>[1,6,1]
[7,6,5,1,8,4,2,3]=>[7,8,6,4,3,2,1,5]=>[2,1,3,5,6,7,8,4]=>[1,6,1]
[4,1,7,6,2,8,5,3]=>[8,1,7,5,4,2,3,6]=>[1,8,2,4,5,7,6,3]=>[2,4,1,1]
[7,8,6,2,1,3,5,4]=>[4,8,5,6,1,7,3,2]=>[5,1,4,3,8,2,6,7]=>[1,2,2,3]
[3,7,6,1,2,8,4,5]=>[7,8,1,4,5,3,2,6]=>[2,1,8,5,4,6,7,3]=>[1,2,1,3,1]
[2,6,5,3,1,4,8,7]=>[4,8,5,1,3,2,6,7]=>[5,1,4,8,6,7,3,2]=>[1,3,2,1,1]
[4,6,1,5,3,2,8,7]=>[1,5,4,8,3,2,6,7]=>[8,4,5,1,6,7,3,2]=>[1,2,3,1,1]
[3,6,1,4,2,5,8,7]=>[1,4,8,3,5,2,6,7]=>[8,5,1,6,4,7,3,2]=>[1,1,2,2,1,1]
[2,6,4,5,7,8,1,3]=>[3,4,2,7,1,5,8,6]=>[6,5,7,2,8,4,1,3]=>[1,2,2,1,2]
[8,7,1,6,5,2,4,3]=>[8,6,7,5,3,4,2,1]=>[1,3,2,4,6,5,7,8]=>[2,3,3]
[7,2,5,6,8,1,3,4]=>[6,3,7,2,4,1,8,5]=>[3,6,2,7,5,8,1,4]=>[2,2,2,2]
[2,4,5,6,1,8,7,3]=>[2,3,4,8,1,7,5,6]=>[7,6,5,1,8,2,4,3]=>[1,1,1,2,2,1]
[8,4,1,6,5,7,3,2]=>[2,5,4,8,7,3,6,1]=>[7,4,5,1,2,6,3,8]=>[1,2,3,2]
[2,8,3,4,7,5,1,6]=>[7,3,4,6,8,1,5,2]=>[2,6,5,3,1,8,4,7]=>[2,1,1,2,2]
[6,8,2,7,4,3,5,1]=>[6,5,1,8,3,7,4,2]=>[3,4,8,1,6,2,5,7]=>[3,2,3]
[4,7,8,5,1,6,3,2]=>[8,7,1,5,4,2,6,3]=>[1,2,8,4,5,7,3,6]=>[3,3,2]
[8,2,6,4,7,3,5,1]=>[4,6,3,8,2,7,5,1]=>[5,3,6,1,7,2,4,8]=>[1,2,2,3]
[4,8,6,1,7,3,2,5]=>[7,1,6,8,4,3,5,2]=>[2,8,3,1,5,6,4,7]=>[2,1,3,2]
[3,8,5,1,7,2,4,6]=>[6,7,1,3,8,4,5,2]=>[3,2,8,6,1,5,4,7]=>[1,2,1,2,2]
[6,8,7,1,3,2,4,5]=>[6,4,5,1,7,8,3,2]=>[3,5,4,8,2,1,6,7]=>[2,2,1,3]
[2,5,1,8,7,4,6,3]=>[2,6,8,7,1,5,3,4]=>[7,3,1,2,8,4,6,5]=>[1,1,3,2,1]
[3,7,1,8,4,5,6,2]=>[5,6,8,1,7,3,2,4]=>[4,3,1,8,2,6,7,5]=>[1,1,2,3,1]
[6,2,3,8,4,7,5,1]=>[8,5,7,2,1,3,6,4]=>[1,4,2,7,8,6,3,5]=>[2,3,1,2]
[8,6,4,3,1,7,2,5]=>[7,4,3,8,5,2,6,1]=>[2,5,6,1,4,7,3,8]=>[3,3,2]
[8,3,7,4,6,1,2,5]=>[6,2,4,7,8,5,3,1]=>[3,7,5,2,1,4,6,8]=>[2,1,1,4]
[7,1,3,8,6,4,5,2]=>[6,8,7,3,5,2,1,4]=>[3,1,2,6,4,7,8,5]=>[1,3,3,1]
[7,4,2,1,8,6,5,3]=>[2,8,7,3,6,4,1,5]=>[7,1,2,6,3,5,8,4]=>[1,3,3,1]
[4,6,7,2,5,8,3,1]=>[5,1,2,8,4,3,7,6]=>[4,8,7,1,5,6,2,3]=>[2,1,3,2]
[7,6,2,5,3,8,1,4]=>[5,7,3,4,2,1,8,6]=>[4,2,6,5,7,8,1,3]=>[1,2,3,2]
[6,2,1,3,4,8,7,5]=>[8,2,7,3,4,1,5,6]=>[1,7,2,6,5,8,4,3]=>[2,2,2,1,1]
[6,5,4,2,8,3,1,7]=>[7,4,3,2,1,6,8,5]=>[2,5,6,7,8,3,1,4]=>[5,1,2]
[6,1,4,3,8,5,2,7]=>[3,7,4,6,1,8,2,5]=>[6,2,5,3,8,1,7,4]=>[1,2,2,2,1]
[4,7,6,2,8,1,5,3]=>[8,1,4,6,3,2,7,5]=>[1,8,5,3,6,7,2,4]=>[2,1,3,2]
[6,4,5,1,7,8,3,2]=>[2,5,3,1,8,7,4,6]=>[7,4,6,8,1,2,5,3]=>[1,3,3,1]
[4,2,3,1,7,8,6,5]=>[5,1,8,2,3,7,4,6]=>[4,8,1,7,6,2,5,3]=>[2,2,1,2,1]
[3,4,2,1,8,6,7,5]=>[1,2,6,8,3,7,4,5]=>[8,7,3,1,6,2,5,4]=>[1,1,1,2,2,1]
[2,7,6,8,1,5,3,4]=>[7,8,5,3,1,2,6,4]=>[2,1,4,6,8,7,3,5]=>[1,4,1,2]
[6,4,5,8,3,1,2,7]=>[2,6,3,1,7,5,8,4]=>[7,3,6,8,2,4,1,5]=>[1,3,2,2]
[3,6,8,1,5,2,4,7]=>[6,7,1,4,2,5,8,3]=>[3,2,8,5,7,4,1,6]=>[1,2,2,1,2]
[3,2,8,7,4,5,1,6]=>[5,7,1,6,8,2,4,3]=>[4,2,8,3,1,7,5,6]=>[1,2,1,2,2]
[7,4,6,8,5,1,2,3]=>[2,6,7,3,1,8,5,4]=>[7,3,2,6,8,1,4,5]=>[1,1,3,3]
[2,1,4,8,7,5,3,6]=>[7,6,8,1,3,5,2,4]=>[2,3,1,8,6,4,7,5]=>[2,2,1,2,1]
[2,1,6,8,3,7,5,4]=>[3,8,7,1,5,6,2,4]=>[6,1,2,8,4,3,7,5]=>[1,3,1,2,1]
[3,6,8,2,4,1,5,7]=>[4,6,1,5,2,7,8,3]=>[5,3,8,4,7,2,1,6]=>[1,2,2,1,2]
[6,2,8,1,7,5,4,3]=>[8,7,6,2,1,4,5,3]=>[1,2,3,7,8,5,4,6]=>[5,1,2]
[2,6,5,4,8,1,3,7]=>[6,4,3,1,2,7,8,5]=>[3,5,6,8,7,2,1,4]=>[4,1,1,2]
[6,5,3,4,8,1,7,2]=>[3,4,2,1,8,6,7,5]=>[6,5,7,8,1,3,2,4]=>[1,3,2,2]
[8,4,3,2,5,1,7,6]=>[4,3,2,5,8,6,7,1]=>[5,6,7,4,1,3,2,8]=>[3,1,2,2]
[4,2,8,1,5,3,6,7]=>[6,2,1,4,5,7,8,3]=>[3,7,8,5,4,2,1,6]=>[3,1,1,1,2]
[5,1,8,2,6,4,3,7]=>[7,6,4,1,5,8,2,3]=>[2,3,5,8,4,1,7,6]=>[4,1,2,1]
[4,6,2,8,3,7,5,1]=>[8,1,5,2,7,3,6,4]=>[1,8,4,7,2,6,3,5]=>[2,2,2,2]
[2,1,5,8,3,6,4,7]=>[3,7,1,5,6,8,2,4]=>[6,2,8,4,3,1,7,5]=>[1,2,1,1,2,1]
[2,8,5,3,6,7,1,4]=>[7,4,3,5,8,1,6,2]=>[2,5,6,4,1,8,3,7]=>[3,1,2,2]
[7,8,5,6,4,1,3,2]=>[8,6,3,1,7,5,4,2]=>[1,3,6,8,2,4,5,7]=>[4,4]
[5,8,4,1,6,3,7,2]=>[1,6,5,3,8,4,7,2]=>[8,3,4,6,1,5,2,7]=>[1,3,2,2]
[4,8,1,3,5,7,6,2]=>[1,8,4,5,7,3,6,2]=>[8,1,5,4,2,6,3,7]=>[1,2,1,2,2]
[3,8,1,4,5,6,2,7]=>[1,4,5,7,3,6,8,2]=>[8,5,4,2,6,3,1,7]=>[1,1,1,2,1,2]
[7,6,8,3,5,1,4,2]=>[4,8,6,2,1,7,5,3]=>[5,1,3,7,8,2,4,6]=>[1,4,3]
[8,9,6,7,4,5,1,3,2]=>[9,7,5,3,1,8,6,4,2]=>[1,3,5,7,9,2,4,6,8]=>[5,4]
[8,9,6,7,4,5,2,3,1]=>[7,5,3,1,9,8,6,4,2]=>[3,5,7,9,1,2,4,6,8]=>[4,5]
[7,8,6,3,5,1,4,2]=>[4,8,6,1,7,5,3,2]=>[5,1,3,8,2,4,6,7]=>[1,3,4]
[5,3,8,7,6,1,4,2]=>[1,8,6,7,2,5,4,3]=>[8,1,3,2,7,4,5,6]=>[1,2,2,3]
[6,5,8,4,7,1,3,2]=>[2,1,8,6,4,7,5,3]=>[7,8,1,3,5,2,4,6]=>[2,3,3]
[10,8,9,6,7,4,5,1,3,2]=>[10,8,6,4,2,9,7,5,3,1]=>[1,3,5,7,9,2,4,6,8,10]=>[5,5]
[6,7,4,2,5,3,1,8]=>[7,4,3,1,6,5,2,8]=>[2,5,6,8,3,4,7,1]=>[4,3,1]
[7,6,4,8,3,1,5,2]=>[3,8,6,5,2,1,7,4]=>[6,1,3,4,7,8,2,5]=>[1,5,2]
[7,4,2,5,6,3,1,8]=>[4,2,7,3,6,5,1,8]=>[5,7,2,6,3,4,8,1]=>[2,2,3,1]
[4,2,7,5,6,3,1,8]=>[1,4,7,6,2,5,3,8]=>[8,5,2,3,7,4,6,1]=>[1,1,3,2,1]
[3,7,2,5,6,4,1,8]=>[4,7,1,3,6,5,2,8]=>[5,2,8,6,3,4,7,1]=>[1,2,1,3,1]
[7,8,3,5,6,1,4,2]=>[8,3,6,4,1,7,5,2]=>[1,6,3,5,8,2,4,7]=>[2,3,3]
[1,6,8,5,2,7,4,3]=>[2,8,7,5,4,6,1,3]=>[7,1,2,4,5,3,8,6]=>[1,4,2,1]
[6,2,8,5,1,7,4,3]=>[8,7,5,2,1,4,6,3]=>[1,2,4,7,8,5,3,6]=>[5,1,2]
[3,2,7,8,6,1,5,4]=>[8,6,1,3,7,2,5,4]=>[1,3,8,6,2,7,4,5]=>[3,1,2,2]
[4,1,8,5,6,3,2,7]=>[1,4,7,6,5,8,2,3]=>[8,5,2,3,4,1,7,6]=>[1,1,3,2,1]
[1,8,2,5,6,4,3,7]=>[4,7,6,3,5,8,1,2]=>[5,2,3,6,4,1,8,7]=>[1,3,1,2,1]
[6,1,8,5,3,7,4,2]=>[8,5,4,1,7,6,2,3]=>[1,4,5,8,2,3,7,6]=>[4,3,1]
[3,8,1,5,2,7,6,4]=>[4,8,1,7,3,5,6,2]=>[5,1,8,2,6,4,3,7]=>[1,2,2,1,2]
[8,2,1,5,3,7,6,4]=>[4,8,2,7,3,5,6,1]=>[5,1,7,2,6,4,3,8]=>[1,2,2,1,2]
[1,5,2,4,6,7,8,3]=>[4,5,2,6,8,1,3,7]=>[5,4,7,3,1,8,6,2]=>[1,2,1,2,1,1]
[4,1,5,3,6,7,8,2]=>[4,3,1,5,6,8,2,7]=>[5,6,8,4,3,1,7,2]=>[3,1,1,2,1]
[8,1,6,5,3,7,2,4]=>[5,7,4,3,8,2,6,1]=>[4,2,5,6,1,7,3,8]=>[1,3,2,2]
[7,1,4,6,3,2,8,5]=>[3,5,8,6,2,4,1,7]=>[6,4,1,3,7,5,8,2]=>[1,1,3,2,1]
[3,2,6,4,1,7,8,5]=>[1,4,6,2,3,8,5,7]=>[8,5,3,7,6,1,4,2]=>[1,1,2,1,2,1]
[7,6,4,3,1,2,8,5]=>[8,5,4,3,6,2,1,7]=>[1,4,5,6,3,7,8,2]=>[4,3,1]
[4,5,3,1,6,7,8,2]=>[1,5,3,2,6,8,4,7]=>[8,4,6,7,3,1,5,2]=>[1,3,1,2,1]
[3,5,2,1,6,7,8,4]=>[1,3,5,2,6,8,4,7]=>[8,6,4,7,3,1,5,2]=>[1,1,2,1,2,1]
[5,2,3,1,6,7,8,4]=>[2,3,5,1,6,8,4,7]=>[7,6,4,8,3,1,5,2]=>[1,1,2,1,2,1]
[1,5,3,2,6,7,8,4]=>[3,5,2,6,8,1,4,7]=>[6,4,7,3,1,8,5,2]=>[1,2,1,2,1,1]
[8,4,6,5,1,7,2,3]=>[2,7,8,5,4,3,6,1]=>[7,2,1,4,5,6,3,8]=>[1,1,4,2]
[7,5,4,6,1,2,8,3]=>[8,5,3,2,6,4,1,7]=>[1,4,6,7,3,5,8,2]=>[4,3,1]
[3,2,5,6,1,7,8,4]=>[1,3,6,2,4,8,5,7]=>[8,6,3,7,5,1,4,2]=>[1,1,2,1,2,1]
[3,2,8,7,6,1,4,5]=>[6,7,8,1,5,2,4,3]=>[3,2,1,8,4,7,5,6]=>[1,1,2,2,2]
[6,8,4,7,2,1,3,5]=>[6,5,3,1,7,8,4,2]=>[3,4,6,8,2,1,5,7]=>[4,1,3]
[3,8,7,5,6,1,2,4]=>[6,7,4,8,1,5,3,2]=>[3,2,5,1,8,4,6,7]=>[1,2,2,3]
[8,2,7,5,6,1,3,4]=>[6,7,4,8,2,5,3,1]=>[3,2,5,1,7,4,6,8]=>[1,2,2,3]
[4,8,6,5,1,7,3,2]=>[8,7,1,5,4,3,6,2]=>[1,2,8,4,5,6,3,7]=>[3,3,2]
[1,7,4,6,2,3,8,5]=>[3,8,5,6,4,1,2,7]=>[6,1,4,3,5,8,7,2]=>[1,2,3,1,1]
[7,6,4,2,1,5,8,3]=>[4,6,3,8,5,2,1,7]=>[5,3,6,1,4,7,8,2]=>[1,2,4,1]
[5,7,4,6,1,3,8,2]=>[1,6,3,8,5,4,2,7]=>[8,3,6,1,4,5,7,2]=>[1,2,4,1]
[8,6,4,7,3,1,2,5]=>[6,3,7,5,2,8,4,1]=>[3,6,2,4,7,1,5,8]=>[2,3,3]
[5,2,4,3,7,1,8,6]=>[3,8,2,1,4,6,5,7]=>[6,1,7,8,5,3,4,2]=>[1,3,1,2,1]
[3,5,4,2,7,1,8,6]=>[3,1,2,8,4,6,5,7]=>[6,8,7,1,5,3,4,2]=>[2,1,2,2,1]
[8,6,4,1,3,5,2,7]=>[5,7,4,3,6,2,8,1]=>[4,2,5,6,3,7,1,8]=>[1,3,2,2]
[6,7,4,1,5,3,8,2]=>[6,5,3,1,8,4,2,7]=>[3,4,6,8,1,5,7,2]=>[4,3,1]
[7,5,4,1,2,6,8,3]=>[6,8,4,3,2,5,1,7]=>[3,1,5,6,7,4,8,2]=>[1,4,2,1]
[1,7,4,2,3,6,8,5]=>[6,3,8,4,5,1,2,7]=>[3,6,1,5,4,8,7,2]=>[2,2,2,1,1]
[1,8,2,5,3,7,6,4]=>[4,8,7,3,5,6,1,2]=>[5,1,2,6,4,3,8,7]=>[1,3,1,2,1]
[6,8,1,5,4,7,3,2]=>[5,4,1,8,7,3,6,2]=>[4,5,8,1,2,6,3,7]=>[3,3,2]
[8,2,1,5,6,4,3,7]=>[4,7,2,6,3,5,8,1]=>[5,2,7,3,6,4,1,8]=>[1,2,2,1,2]
[3,8,1,5,6,4,2,7]=>[4,7,1,6,3,5,8,2]=>[5,2,8,3,6,4,1,7]=>[1,2,2,1,2]
[6,8,4,1,2,5,3,7]=>[7,4,5,3,1,6,8,2]=>[2,5,4,6,8,3,1,7]=>[2,3,1,2]
[3,2,8,1,6,5,4,7]=>[7,1,6,2,4,5,8,3]=>[2,8,3,7,5,4,1,6]=>[2,2,1,1,2]
[3,2,6,1,5,7,8,4]=>[1,5,6,2,3,8,4,7]=>[8,4,3,7,6,1,5,2]=>[1,1,2,1,2,1]
[7,6,4,1,5,2,8,3]=>[8,6,4,3,5,2,1,7]=>[1,3,5,6,4,7,8,2]=>[4,3,1]
[8,6,1,5,4,7,2,3]=>[7,5,4,8,3,2,6,1]=>[2,4,5,1,6,7,3,8]=>[3,3,2]
[3,5,1,4,6,7,8,2]=>[1,4,5,2,6,8,3,7]=>[8,5,4,7,3,1,6,2]=>[1,1,2,1,2,1]
[5,2,1,4,6,7,8,3]=>[2,4,5,1,6,8,3,7]=>[7,5,4,8,3,1,6,2]=>[1,1,2,1,2,1]
[5,4,1,3,6,7,8,2]=>[4,5,2,1,6,8,3,7]=>[5,4,7,8,3,1,6,2]=>[1,3,1,2,1]
[8,4,1,5,3,7,2,6]=>[5,4,2,7,8,3,6,1]=>[4,5,7,2,1,6,3,8]=>[3,1,2,2]
[7,5,4,1,3,2,8,6]=>[5,8,4,3,2,6,1,7]=>[4,1,5,6,7,3,8,2]=>[1,4,2,1]
[3,2,5,1,4,7,8,6]=>[1,6,2,3,8,4,5,7]=>[8,3,7,6,1,5,4,2]=>[1,2,1,2,1,1]
[7,1,4,3,5,2,8,6]=>[4,3,5,8,2,6,1,7]=>[5,6,4,1,7,3,8,2]=>[2,1,2,2,1]
[8,1,3,5,4,7,2,6]=>[5,3,4,7,8,2,6,1]=>[4,6,5,2,1,7,3,8]=>[2,1,1,2,2]
[5,1,3,4,6,7,8,2]=>[3,4,5,1,6,8,2,7]=>[6,5,4,8,3,1,7,2]=>[1,1,2,1,2,1]
[3,1,8,2,5,7,4,6]=>[1,5,7,8,4,6,2,3]=>[8,4,2,1,5,3,7,6]=>[1,1,1,2,2,1]
[2,8,1,6,4,3,7,5]=>[5,8,6,1,3,4,7,2]=>[4,1,3,8,6,5,2,7]=>[1,3,1,1,2]
[2,6,1,3,8,7,5,4]=>[8,7,6,1,3,2,4,5]=>[1,2,3,8,6,7,5,4]=>[4,2,1,1]
[2,5,7,1,3,8,6,4]=>[2,8,7,1,4,5,3,6]=>[7,1,2,8,5,4,6,3]=>[1,3,1,2,1]
[2,6,8,1,5,7,4,3]=>[5,2,8,7,1,4,6,3]=>[4,7,1,2,8,5,3,6]=>[2,3,1,2]
[2,7,1,5,8,4,6,3]=>[4,6,8,7,1,3,2,5]=>[5,3,1,2,8,6,7,4]=>[1,1,3,2,1]
[2,7,1,6,4,8,3,5]=>[5,7,4,8,1,3,2,6]=>[4,2,5,1,8,6,7,3]=>[1,2,2,2,1]
[2,7,1,6,5,3,8,4]=>[8,6,5,1,3,4,2,7]=>[1,3,4,8,6,5,7,2]=>[4,1,2,1]
[2,8,1,7,6,5,4,3]=>[8,7,6,5,1,3,4,2]=>[1,2,3,4,8,6,5,7]=>[5,1,2]
[8,3,2,7,1,6,5,4]=>[8,2,7,3,5,6,4,1]=>[1,7,2,6,4,3,5,8]=>[2,2,1,3]
[4,1,8,7,3,2,6,5]=>[1,5,8,6,7,4,2,3]=>[8,4,1,3,2,5,7,6]=>[1,1,2,3,1]
[4,1,7,2,8,6,5,3]=>[8,1,7,6,4,2,3,5]=>[1,8,2,3,5,7,6,4]=>[2,4,1,1]
[3,7,1,8,6,5,4,2]=>[8,7,6,1,5,3,2,4]=>[1,2,3,8,4,6,7,5]=>[4,3,1]
[3,7,6,1,4,2,5,8]=>[6,1,4,5,7,3,2,8]=>[3,8,5,4,2,6,7,1]=>[2,1,1,3,1]
[3,7,5,1,4,6,8,2]=>[5,6,1,3,8,4,2,7]=>[4,3,8,6,1,5,7,2]=>[1,2,1,3,1]
[3,6,8,5,1,4,7,2]=>[6,2,8,1,5,4,7,3]=>[3,7,1,8,4,5,2,6]=>[2,2,2,2]
[7,3,5,8,2,1,4,6]=>[6,2,5,3,7,1,8,4]=>[3,7,4,6,2,8,1,5]=>[2,2,2,2]
[7,3,6,2,1,4,5,8]=>[2,5,4,6,7,3,1,8]=>[7,4,5,3,2,6,8,1]=>[1,2,1,3,1]
[7,3,6,2,1,5,4,8]=>[2,4,7,5,6,3,1,8]=>[7,5,2,4,3,6,8,1]=>[1,1,2,3,1]
[7,4,2,8,1,6,5,3]=>[2,8,7,3,5,1,6,4]=>[7,1,2,6,4,8,3,5]=>[1,3,2,2]
[8,7,5,3,2,1,6,4]=>[5,4,8,6,3,7,2,1]=>[4,5,1,3,6,2,7,8]=>[2,3,3]
[7,5,2,6,3,1,4,8]=>[6,3,5,2,7,4,1,8]=>[3,6,4,7,2,5,8,1]=>[2,2,3,1]
[7,4,6,2,1,8,3,5]=>[4,2,7,8,5,3,1,6]=>[5,7,2,1,4,6,8,3]=>[2,1,4,1]
[6,8,4,5,2,1,7,3]=>[5,3,1,8,6,4,7,2]=>[4,6,8,1,3,5,2,7]=>[3,3,2]
[4,6,8,5,1,7,3,2]=>[2,8,1,7,5,4,6,3]=>[7,1,8,2,4,5,3,6]=>[1,2,3,2]
[4,7,6,1,5,3,2,8]=>[7,1,6,4,5,3,2,8]=>[2,8,3,5,4,6,7,1]=>[2,2,3,1]
[5,1,7,6,3,8,2,4]=>[5,1,7,4,3,8,2,6]=>[4,8,2,5,6,1,7,3]=>[2,3,2,1]
[5,1,7,6,4,2,8,3]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[1,5,1,1]
[5,1,8,7,6,4,3,2]=>[8,1,7,6,5,4,2,3]=>[1,8,2,3,4,5,7,6]=>[2,5,1]
[8,5,2,1,7,6,4,3]=>[8,7,3,2,6,4,5,1]=>[1,2,6,7,3,5,4,8]=>[4,2,2]
[5,1,8,6,3,2,7,4]=>[5,1,8,6,4,7,2,3]=>[4,8,1,3,5,2,7,6]=>[2,3,2,1]
[3,6,1,7,4,8,2,5]=>[5,7,1,4,2,8,3,6]=>[4,2,8,5,7,1,6,3]=>[1,2,2,2,1]
[4,1,8,6,3,7,2,5]=>[1,5,7,4,8,6,2,3]=>[8,4,2,5,1,3,7,6]=>[1,1,2,3,1]
[8,4,2,5,7,3,1,6]=>[4,2,7,3,6,8,5,1]=>[5,7,2,6,3,1,4,8]=>[2,2,1,3]
[3,4,6,8,5,7,1,2]=>[3,7,1,2,5,8,6,4]=>[6,2,8,7,4,1,3,5]=>[1,2,1,1,3]
[5,4,8,2,7,3,6,1]=>[2,1,6,8,4,7,5,3]=>[7,8,3,1,5,2,4,6]=>[2,1,2,3]
[5,4,8,7,3,6,1,2]=>[1,7,2,5,8,6,4,3]=>[8,2,7,4,1,3,5,6]=>[1,2,1,4]
[6,4,3,8,7,1,2,5]=>[3,2,6,1,7,8,5,4]=>[6,7,3,8,2,1,4,5]=>[2,2,1,3]
[6,3,7,2,4,8,1,5]=>[2,4,5,1,7,3,8,6]=>[7,5,4,8,2,6,1,3]=>[1,1,2,2,2]
[5,6,8,4,2,7,3,1]=>[1,2,8,5,4,7,6,3]=>[8,7,1,4,5,2,3,6]=>[1,1,3,3]
[5,7,4,2,8,1,3,6]=>[4,1,6,3,7,2,8,5]=>[5,8,3,6,2,7,1,4]=>[2,2,2,2]
[6,5,2,7,1,3,8,4]=>[8,3,5,2,1,6,4,7]=>[1,6,4,7,8,3,5,2]=>[2,3,2,1]
[8,6,5,4,2,1,7,3]=>[5,8,6,4,3,2,7,1]=>[4,1,3,5,6,7,2,8]=>[1,5,2]
[6,4,7,3,1,8,2,5]=>[2,7,4,1,8,5,3,6]=>[7,2,5,8,1,4,6,3]=>[1,3,3,1]
[5,7,4,3,8,6,1,2]=>[1,4,3,7,2,8,6,5]=>[8,5,6,2,7,1,3,4]=>[1,2,2,3]
[7,5,8,4,6,3,2,1]=>[2,4,1,8,7,6,5,3]=>[7,5,8,1,2,3,4,6]=>[1,2,5]
[7,6,4,8,3,5,2,1]=>[3,5,2,1,8,7,6,4]=>[6,4,7,8,1,2,3,5]=>[1,3,4]
[7,6,5,3,8,2,4,1]=>[4,6,3,2,1,8,7,5]=>[5,3,6,7,8,1,2,4]=>[1,4,3]
[7,6,3,8,5,1,4,2]=>[8,3,6,2,1,7,5,4]=>[1,6,3,7,8,2,4,5]=>[2,3,3]
[6,4,8,1,3,2,5,7]=>[6,4,2,5,1,7,8,3]=>[3,5,7,4,8,2,1,6]=>[3,2,1,2]
[7,4,8,6,3,1,5,2]=>[8,2,6,5,1,7,4,3]=>[1,7,3,4,8,2,5,6]=>[2,3,3]
[4,2,7,6,5,3,1,8]=>[7,1,6,5,2,4,3,8]=>[2,8,3,4,7,5,6,1]=>[2,3,2,1]
[8,1,3,4,5,2,6,7]=>[3,4,6,2,5,7,8,1]=>[6,5,3,7,4,2,1,8]=>[1,1,2,1,1,2]
[1,6,8,4,2,5,3,7]=>[7,5,4,2,6,8,1,3]=>[2,4,5,7,3,1,8,6]=>[4,1,2,1]
[6,2,8,4,1,5,7,3]=>[6,4,8,2,1,5,7,3]=>[3,5,1,7,8,4,2,6]=>[2,3,1,2]
[6,7,4,8,5,1,2,3]=>[6,3,1,7,2,8,5,4]=>[3,6,8,2,7,1,4,5]=>[3,2,3]
[3,2,7,8,5,1,6,4]=>[8,6,1,5,2,3,7,4]=>[1,3,8,4,7,6,2,5]=>[3,2,1,2]
[6,1,4,8,5,3,7,2]=>[6,3,5,1,8,7,2,4]=>[3,6,4,8,1,2,7,5]=>[2,2,3,1]
[1,4,8,5,2,6,7,3]=>[6,2,4,8,5,7,1,3]=>[3,7,5,1,4,2,8,6]=>[2,1,2,2,1]
[6,1,8,4,3,7,2,5]=>[5,4,7,1,8,6,2,3]=>[4,5,2,8,1,3,7,6]=>[2,2,3,1]
[3,7,1,4,2,5,8,6]=>[1,4,8,3,5,6,2,7]=>[8,5,1,6,4,3,7,2]=>[1,1,2,1,2,1]
[7,2,1,4,3,5,6,8]=>[2,5,3,4,6,7,1,8]=>[7,4,6,5,3,2,8,1]=>[1,2,1,1,2,1]
[4,1,5,3,6,8,2,7]=>[4,3,1,5,7,8,2,6]=>[5,6,8,4,2,1,7,3]=>[3,1,1,2,1]
[6,1,8,5,3,2,7,4]=>[5,8,6,4,1,7,2,3]=>[4,1,3,5,8,2,7,6]=>[1,4,2,1]
[3,2,6,4,1,8,7,5]=>[8,1,4,2,3,7,5,6]=>[1,8,5,7,6,2,4,3]=>[2,2,1,2,1]
[7,6,4,3,1,8,2,5]=>[7,4,3,8,5,2,1,6]=>[2,5,6,1,4,7,8,3]=>[3,4,1]
[3,5,2,1,8,7,6,4]=>[2,8,1,7,3,6,4,5]=>[7,1,8,2,6,3,5,4]=>[1,2,2,2,1]
[1,5,3,2,8,6,4,7]=>[7,3,2,6,8,1,4,5]=>[2,6,7,3,1,8,5,4]=>[3,1,2,1,1]
[5,4,2,1,7,8,6,3]=>[5,2,1,8,3,7,4,6]=>[4,7,8,1,6,2,5,3]=>[3,2,2,1]
[8,6,2,7,1,4,5,3]=>[6,8,3,5,2,7,4,1]=>[3,1,6,4,7,2,5,8]=>[1,2,2,3]
[1,7,3,6,2,8,5,4]=>[8,7,3,5,4,1,2,6]=>[1,2,6,4,5,8,7,3]=>[3,3,1,1]
[8,6,3,7,4,1,2,5]=>[3,6,7,5,2,8,4,1]=>[6,3,2,4,7,1,5,8]=>[1,1,3,3]
[5,2,3,4,7,1,8,6]=>[8,2,3,1,4,6,5,7]=>[1,7,6,8,5,3,4,2]=>[2,2,1,2,1]
[6,7,3,1,5,4,2,8]=>[3,7,6,4,1,5,2,8]=>[6,2,3,5,8,4,7,1]=>[1,4,2,1]
[5,8,3,1,2,4,7,6]=>[8,4,3,1,5,6,7,2]=>[1,5,6,8,4,3,2,7]=>[4,1,1,2]
[8,1,3,2,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[5,7,6,4,3,2,1,8]=>[2,1,1,1,1,2]
[8,4,1,7,2,3,6,5]=>[8,5,2,6,7,3,4,1]=>[1,4,7,3,2,6,5,8]=>[3,1,2,2]
[3,8,1,5,6,4,7,2]=>[4,6,1,5,8,3,7,2]=>[5,3,8,4,1,6,2,7]=>[1,2,1,2,2]
[6,8,4,1,2,5,7,3]=>[6,8,4,3,1,5,7,2]=>[3,1,5,6,8,4,2,7]=>[1,4,1,2]
[3,2,8,1,6,5,7,4]=>[6,1,5,8,2,4,7,3]=>[3,8,4,1,7,5,2,6]=>[2,1,2,1,2]
[7,6,4,1,5,2,3,8]=>[6,7,4,3,5,2,1,8]=>[3,2,5,6,4,7,8,1]=>[1,3,3,1]
[8,6,1,5,4,7,3,2]=>[5,4,8,7,3,2,6,1]=>[4,5,1,2,6,7,3,8]=>[2,4,2]
[3,5,1,4,6,7,2,8]=>[1,4,5,2,7,3,6,8]=>[8,5,4,7,2,6,3,1]=>[1,1,2,2,1,1]
[5,2,1,4,7,6,3,8]=>[7,2,4,1,6,3,5,8]=>[2,7,5,8,3,6,4,1]=>[2,2,2,1,1]
[4,5,8,2,1,3,7,6]=>[1,4,2,8,5,6,7,3]=>[8,5,7,1,4,3,2,6]=>[1,2,2,1,2]
[5,8,2,3,1,4,6,7]=>[3,5,4,1,6,7,8,2]=>[6,4,5,8,3,2,1,7]=>[1,3,1,1,2]
[4,2,1,3,5,8,7,6]=>[8,2,1,7,3,4,5,6]=>[1,7,8,2,6,5,4,3]=>[3,2,1,1,1]
[5,4,1,3,6,2,8,7]=>[4,5,2,1,8,3,6,7]=>[5,4,7,8,1,6,3,2]=>[1,3,2,1,1]
[3,2,5,1,4,6,8,7]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[1,2,2,1,1,1]
[8,1,4,3,5,6,7,2]=>[4,3,5,6,8,2,7,1]=>[5,6,4,3,1,7,2,8]=>[2,1,1,2,2]
[7,1,3,5,4,6,2,8]=>[5,3,4,7,2,6,1,8]=>[4,6,5,2,7,3,8,1]=>[2,1,2,2,1]
[4,1,3,2,5,7,6,8]=>[3,7,2,1,4,5,6,8]=>[6,2,7,8,5,4,3,1]=>[1,3,1,1,1,1]
[6,8,2,4,5,1,3,7]=>[6,3,4,1,7,5,8,2]=>[3,6,5,8,2,4,1,7]=>[2,2,2,2]
[3,6,7,2,5,1,4,8]=>[4,6,1,2,7,5,3,8]=>[5,3,8,7,2,4,6,1]=>[1,2,1,3,1]
[4,6,7,3,1,5,2,8]=>[7,1,5,4,2,6,3,8]=>[2,8,4,5,7,3,6,1]=>[2,3,2,1]
[5,8,1,2,4,7,3,6]=>[5,7,1,8,3,4,6,2]=>[4,2,8,1,6,5,3,7]=>[1,2,2,1,2]
[6,8,1,3,5,2,7,4]=>[8,4,6,3,1,5,7,2]=>[1,5,3,6,8,4,2,7]=>[2,3,1,2]
[6,8,3,1,4,5,7,2]=>[5,3,6,1,8,4,7,2]=>[4,6,3,8,1,5,2,7]=>[2,2,2,2]
[7,5,1,8,2,3,6,4]=>[8,5,6,2,7,3,1,4]=>[1,4,3,7,2,6,8,5]=>[2,2,3,1]
[6,1,8,2,3,4,7,5]=>[8,4,5,6,1,7,2,3]=>[1,5,4,3,8,2,7,6]=>[2,1,2,2,1]
[5,3,8,4,2,6,7,1]=>[5,2,1,4,6,8,7,3]=>[4,7,8,5,3,1,2,6]=>[3,1,1,3]
[5,1,8,4,6,3,7,2]=>[4,1,6,5,8,7,2,3]=>[5,8,3,4,1,2,7,6]=>[2,2,3,1]
[4,1,8,3,5,7,2,6]=>[4,1,5,7,8,6,2,3]=>[5,8,4,2,1,3,7,6]=>[2,1,1,3,1]
[3,4,7,2,6,1,8,5]=>[8,1,2,4,6,5,3,7]=>[1,8,7,5,3,4,6,2]=>[2,1,1,3,1]
[4,5,7,3,2,6,8,1]=>[1,2,5,4,6,3,8,7]=>[8,7,4,5,3,6,1,2]=>[1,1,2,2,2]
[4,5,7,2,3,6,8,1]=>[1,4,2,5,6,3,8,7]=>[8,5,7,4,3,6,1,2]=>[1,2,1,2,2]
[2,6,3,4,7,5,8,1]=>[6,3,4,1,2,5,8,7]=>[3,6,5,8,7,4,1,2]=>[2,2,1,1,2]
[3,6,4,2,7,5,8,1]=>[3,6,1,4,2,5,8,7]=>[6,3,8,5,7,4,1,2]=>[1,2,2,1,2]
[4,5,2,7,1,6,8,3]=>[1,6,2,8,3,5,4,7]=>[8,3,7,1,6,4,5,2]=>[1,2,2,2,1]
[3,4,1,6,5,8,2,7]=>[1,2,5,4,7,8,3,6]=>[8,7,4,5,2,1,6,3]=>[1,1,2,1,2,1]
[4,1,2,8,5,7,3,6]=>[5,1,7,8,6,2,3,4]=>[4,8,2,1,3,7,6,5]=>[2,1,3,1,1]
[5,1,4,8,6,2,7,3]=>[8,3,1,6,5,7,2,4]=>[1,6,8,3,4,2,7,5]=>[3,2,2,1]
[7,3,1,4,8,5,6,2]=>[2,6,8,4,7,3,1,5]=>[7,3,1,5,2,6,8,4]=>[1,1,2,3,1]
[5,6,3,1,7,4,2,8]=>[3,1,7,6,4,2,5,8]=>[6,8,2,3,5,7,4,1]=>[2,4,1,1]
[7,3,4,1,8,5,2,6]=>[2,3,7,6,8,4,1,5]=>[7,6,2,3,1,5,8,4]=>[1,1,2,3,1]
[6,4,2,8,7,1,5,3]=>[2,8,6,1,7,3,5,4]=>[7,1,3,8,2,6,4,5]=>[1,3,2,2]
[7,2,4,8,1,5,3,6]=>[3,7,2,5,6,1,8,4]=>[6,2,7,4,3,8,1,5]=>[1,2,1,2,2]
[2,6,3,7,5,1,4,8]=>[6,7,3,1,2,5,4,8]=>[3,2,6,8,7,4,5,1]=>[1,3,1,2,1]
[7,1,3,8,5,2,4,6]=>[6,7,3,5,8,2,1,4]=>[3,2,6,4,1,7,8,5]=>[1,2,1,3,1]
[3,2,6,7,1,8,4,5]=>[7,1,3,8,2,5,4,6]=>[2,8,6,1,7,4,5,3]=>[2,1,2,2,1]
[4,6,3,1,7,8,5,2]=>[1,3,5,2,8,7,4,6]=>[8,6,4,7,1,2,5,3]=>[1,1,2,3,1]
[5,3,1,6,7,8,4,2]=>[2,4,1,5,8,7,3,6]=>[7,5,8,4,1,2,6,3]=>[1,2,1,3,1]
[4,1,6,2,7,8,5,3]=>[1,5,3,8,7,2,4,6]=>[8,4,6,1,2,7,5,3]=>[1,2,3,1,1]
[2,1,3,4,8,7,5,6]=>[7,8,1,6,2,3,4,5]=>[2,1,8,3,7,6,5,4]=>[1,2,2,1,1,1]
[4,5,6,7,8,9,1,2,3]=>[1,2,3,7,4,8,5,9,6]=>[9,8,7,3,6,2,5,1,4]=>[1,1,1,2,2,2]
[5,6,7,8,9,1,2,3,4]=>[1,6,2,7,3,8,4,9,5]=>[9,4,8,3,7,2,6,1,5]=>[1,2,2,2,2]
[5,6,7,8,9,3,4,1,2]=>[1,2,3,8,6,4,9,7,5]=>[9,8,7,2,4,6,1,3,5]=>[1,1,1,3,3]
[6,7,8,9,4,5,2,3,1]=>[1,2,7,5,3,9,8,6,4]=>[9,8,3,5,7,1,2,4,6]=>[1,1,3,4]
[7,8,9,5,6,3,4,1,2]=>[1,8,6,4,2,9,7,5,3]=>[9,2,4,6,8,1,3,5,7]=>[1,4,4]
[8,9,6,7,4,5,3,2,1]=>[5,3,1,9,8,7,6,4,2]=>[5,7,9,1,2,3,4,6,8]=>[3,6]
[8,9,6,7,5,4,3,2,1]=>[3,1,9,8,7,6,5,4,2]=>[7,9,1,2,3,4,5,6,8]=>[2,7]
[4,5,6,7,8,9,10,1,2,3]=>[1,2,3,4,8,5,9,6,10,7]=>[10,9,8,7,3,6,2,5,1,4]=>[1,1,1,1,2,2,2]
[5,6,7,8,9,10,1,2,3,4]=>[1,2,7,3,8,4,9,5,10,6]=>[10,9,4,8,3,7,2,6,1,5]=>[1,1,2,2,2,2]
[5,6,7,8,9,10,3,4,1,2]=>[1,2,3,4,9,7,5,10,8,6]=>[10,9,8,7,2,4,6,1,3,5]=>[1,1,1,1,3,3]
[7,8,9,10,3,4,5,6,1,2]=>[5,1,6,2,9,7,3,10,8,4]=>[6,10,5,9,2,4,8,1,3,7]=>[2,2,3,3]
[7,8,9,10,4,5,6,1,2,3]=>[1,8,5,2,9,6,3,10,7,4]=>[10,3,6,9,2,5,8,1,4,7]=>[1,3,3,3]
[7,8,9,10,5,6,3,4,1,2]=>[1,2,9,7,5,3,10,8,6,4]=>[10,9,2,4,6,8,1,3,5,7]=>[1,1,4,4]
[8,9,10,6,7,4,5,2,3,1]=>[1,8,6,4,2,10,9,7,5,3]=>[10,3,5,7,9,1,2,4,6,8]=>[1,4,5]
[9,10,7,8,5,6,4,3,2,1]=>[5,3,1,10,9,8,7,6,4,2]=>[6,8,10,1,2,3,4,5,7,9]=>[3,7]
[9,10,7,8,6,5,4,3,2,1]=>[3,1,10,9,8,7,6,5,4,2]=>[8,10,1,2,3,4,5,6,7,9]=>[2,8]
[4,8,3,7,6,5,1,2]=>[7,8,1,3,6,5,4,2]=>[2,1,8,6,3,4,5,7]=>[1,2,1,4]
[6,3,8,7,5,4,1,2]=>[7,1,8,6,2,5,4,3]=>[2,8,1,3,7,4,5,6]=>[2,3,3]
[5,3,8,7,6,4,1,2]=>[1,7,8,6,2,5,4,3]=>[8,2,1,3,7,4,5,6]=>[1,1,3,3]
[2,8,7,6,1,5,4,3]=>[8,7,5,6,4,1,3,2]=>[1,2,4,3,5,8,6,7]=>[3,3,2]
[6,2,8,7,5,1,4,3]=>[8,6,1,7,5,2,4,3]=>[1,3,8,2,4,7,5,6]=>[3,3,2]
[7,8,2,6,5,1,4,3]=>[8,6,7,3,1,5,4,2]=>[1,3,2,6,8,4,5,7]=>[2,3,3]
[6,1,8,7,5,4,3,2]=>[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>[1,6,1]
[3,1,8,7,6,5,4,2]=>[8,7,6,1,5,4,2,3]=>[1,2,3,8,4,5,7,6]=>[4,3,1]
[7,8,2,6,1,5,4,3]=>[8,7,3,5,1,6,4,2]=>[1,2,6,4,8,3,5,7]=>[3,2,3]
[6,2,8,7,1,5,4,3]=>[8,7,5,1,6,2,4,3]=>[1,2,4,8,3,7,5,6]=>[4,2,2]
[4,2,8,1,7,6,5,3]=>[8,1,7,6,2,4,5,3]=>[1,8,2,3,7,5,4,6]=>[2,3,1,2]
[4,8,2,7,6,1,5,3]=>[8,1,6,7,3,5,4,2]=>[1,8,3,2,6,4,5,7]=>[2,1,2,3]
[3,8,7,2,1,6,5,4]=>[8,4,7,1,5,6,3,2]=>[1,5,2,8,4,3,6,7]=>[2,2,1,3]
[6,5,8,7,1,4,3,2]=>[2,1,8,7,5,6,4,3]=>[7,8,1,2,4,3,5,6]=>[2,3,3]
[4,8,1,7,6,5,3,2]=>[8,7,1,6,5,3,4,2]=>[1,2,8,3,4,6,5,7]=>[3,3,2]
[5,4,1,8,7,6,3,2]=>[1,8,2,7,6,5,3,4]=>[8,1,7,2,3,4,6,5]=>[1,2,4,1]
[7,8,4,1,6,5,3,2]=>[3,8,7,6,4,1,5,2]=>[6,1,2,3,5,8,4,7]=>[1,5,2]
[7,8,3,1,6,5,4,2]=>[8,3,7,6,4,1,5,2]=>[1,6,2,3,5,8,4,7]=>[2,4,2]
[6,3,8,1,7,5,4,2]=>[8,7,2,1,6,4,5,3]=>[1,2,7,8,3,5,4,6]=>[4,2,2]
[5,3,1,8,7,6,4,2]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[1,3,3,1]
[6,5,3,1,8,7,4,2]=>[8,3,2,1,7,6,4,5]=>[1,6,7,8,2,3,5,4]=>[4,3,1]
[6,4,3,1,8,7,5,2]=>[2,8,3,1,7,6,4,5]=>[7,1,6,8,2,3,5,4]=>[1,3,3,1]
[5,4,3,1,8,7,6,2]=>[2,1,8,3,7,6,4,5]=>[7,8,1,6,2,3,5,4]=>[2,2,3,1]
[5,4,2,1,8,7,6,3]=>[2,1,8,7,3,6,4,5]=>[7,8,1,2,6,3,5,4]=>[2,3,2,1]
[7,3,2,1,8,6,5,4]=>[8,2,7,3,6,4,1,5]=>[1,7,2,6,3,5,8,4]=>[2,2,3,1]
[6,3,2,1,8,7,5,4]=>[8,2,7,3,1,6,4,5]=>[1,7,2,6,8,3,5,4]=>[2,3,2,1]
[9,4,3,2,1,10,8,7,6,5]=>[10,2,9,3,8,4,7,5,1,6]=>[1,9,2,8,3,7,4,6,10,5]=>[2,2,2,3,1]
[8,4,3,2,1,10,9,7,6,5]=>[10,2,9,3,8,4,1,7,5,6]=>[1,9,2,8,3,7,10,4,6,5]=>[2,2,3,2,1]
[7,4,3,2,1,10,9,8,6,5]=>[10,2,9,3,1,8,4,7,5,6]=>[1,9,2,8,10,3,7,4,6,5]=>[2,3,2,2,1]
[6,4,3,2,1,10,9,8,7,5]=>[10,2,1,9,3,8,4,7,5,6]=>[1,9,10,2,8,3,7,4,6,5]=>[3,2,2,2,1]
[8,6,1,4,2,3,5,7]=>[5,6,3,4,7,2,8,1]=>[4,3,6,5,2,7,1,8]=>[1,2,1,2,2]
[6,8,1,4,2,3,5,7]=>[5,6,3,4,1,7,8,2]=>[4,3,6,5,8,2,1,7]=>[1,2,2,1,2]
[8,1,4,2,3,6,5,7]=>[7,4,2,3,5,6,8,1]=>[2,5,7,6,4,3,1,8]=>[3,1,1,1,2]
[4,1,8,2,3,6,5,7]=>[7,4,1,5,6,8,2,3]=>[2,5,8,4,3,1,7,6]=>[3,1,1,2,1]
[8,2,3,6,1,4,5,7]=>[2,3,5,6,7,4,8,1]=>[7,6,4,3,2,5,1,8]=>[1,1,1,1,2,2]
[6,2,3,8,1,4,5,7]=>[2,3,5,6,1,7,8,4]=>[7,6,4,3,8,2,1,5]=>[1,1,1,2,1,2]
[4,6,2,3,8,1,5,7]=>[3,1,4,6,2,7,8,5]=>[6,8,5,3,7,2,1,4]=>[2,1,2,1,2]
[4,8,2,3,6,1,5,7]=>[3,1,4,6,7,5,8,2]=>[6,8,5,3,2,4,1,7]=>[2,1,1,2,2]
[8,4,3,6,2,1,5,7]=>[3,2,6,5,7,4,8,1]=>[6,7,3,4,2,5,1,8]=>[2,2,2,2]
[6,2,3,8,4,1,5,7]=>[6,2,3,5,1,7,8,4]=>[3,7,6,4,8,2,1,5]=>[2,1,2,1,2]
[8,4,2,3,6,1,5,7]=>[3,4,2,6,7,5,8,1]=>[6,5,7,3,2,4,1,8]=>[1,2,1,2,2]
[6,4,2,3,8,1,5,7]=>[3,4,2,6,1,7,8,5]=>[6,5,7,3,8,2,1,4]=>[1,2,2,1,2]
[2,6,4,3,8,1,5,7]=>[4,3,6,1,2,7,8,5]=>[5,6,3,8,7,2,1,4]=>[2,2,1,1,2]
[2,8,4,3,6,1,5,7]=>[4,3,6,7,1,5,8,2]=>[5,6,3,2,8,4,1,7]=>[2,1,2,1,2]
[2,6,3,8,4,1,5,7]=>[6,3,5,1,2,7,8,4]=>[3,6,4,8,7,2,1,5]=>[2,2,1,1,2]
[6,3,8,4,2,1,5,7]=>[6,2,5,4,1,7,8,3]=>[3,7,4,5,8,2,1,6]=>[2,3,1,2]
[2,6,3,8,1,4,5,7]=>[3,5,6,1,2,7,8,4]=>[6,4,3,8,7,2,1,5]=>[1,1,2,1,1,2]
[2,8,3,6,1,4,5,7]=>[3,5,6,7,1,4,8,2]=>[6,4,3,2,8,5,1,7]=>[1,1,1,2,1,2]
[2,8,3,6,4,1,5,7]=>[6,3,5,7,1,4,8,2]=>[3,6,4,2,8,5,1,7]=>[2,1,2,1,2]
[8,3,6,2,4,1,5,7]=>[2,4,6,5,7,3,8,1]=>[7,5,3,4,2,6,1,8]=>[1,1,2,2,2]
[8,3,6,2,1,4,5,7]=>[2,5,4,6,7,3,8,1]=>[7,4,5,3,2,6,1,8]=>[1,2,1,2,2]
[6,2,1,3,8,4,5,7]=>[2,6,7,8,3,1,4,5]=>[7,3,2,1,6,8,5,4]=>[1,1,1,3,1,1]
[6,3,8,2,4,1,5,7]=>[2,4,6,5,1,7,8,3]=>[7,5,3,4,8,2,1,6]=>[1,1,3,1,2]
[3,6,4,7,8,5,1,2]=>[7,3,1,2,4,8,6,5]=>[2,6,8,7,5,1,3,4]=>[3,1,1,3]
[1,6,4,2,7,5,8,3]=>[3,6,5,2,8,1,4,7]=>[6,3,4,7,1,8,5,2]=>[1,3,2,1,1]
[1,4,7,2,5,6,8,3]=>[2,5,6,8,4,1,3,7]=>[7,4,3,1,5,8,6,2]=>[1,1,1,3,1,1]
[6,4,8,5,3,7,1,2]=>[7,2,1,5,4,8,6,3]=>[2,7,8,4,5,1,3,6]=>[3,2,3]
[1,6,5,4,2,7,8,3]=>[6,4,3,2,8,1,5,7]=>[3,5,6,7,1,8,4,2]=>[4,2,1,1]
[4,2,5,3,6,1,7,8]=>[4,2,1,3,6,5,7,8]=>[5,7,8,6,3,4,2,1]=>[3,1,2,1,1]
[7,1,5,3,6,2,8,4]=>[8,4,3,6,2,5,1,7]=>[1,5,6,3,7,4,8,2]=>[3,2,2,1]
[1,6,5,2,4,8,7,3]=>[8,5,3,2,7,1,4,6]=>[1,4,6,7,2,8,5,3]=>[4,2,1,1]
[1,4,6,2,8,5,7,3]=>[6,2,3,8,7,1,4,5]=>[3,7,6,1,2,8,5,4]=>[2,1,3,1,1]
[7,8,1,4,2,5,6,3]=>[6,4,8,3,5,1,7,2]=>[3,5,1,6,4,8,2,7]=>[2,2,2,2]
[3,4,8,5,2,1,6,7]=>[6,1,2,5,4,7,8,3]=>[3,8,7,4,5,2,1,6]=>[2,1,2,1,2]
[4,8,5,3,1,6,2,7]=>[7,1,5,4,3,6,8,2]=>[2,8,4,5,6,3,1,7]=>[2,3,1,2]
[6,1,3,5,8,2,7,4]=>[4,8,3,6,1,7,2,5]=>[5,1,6,3,8,2,7,4]=>[1,2,2,2,1]
[6,1,8,7,4,2,3,5]=>[6,7,5,1,8,4,2,3]=>[3,2,4,8,1,5,7,6]=>[1,3,3,1]
[1,2,8,5,7,3,6,4]=>[4,8,6,7,5,1,2,3]=>[5,1,3,2,4,8,7,6]=>[1,2,3,1,1]
[1,3,6,8,7,5,2,4]=>[3,7,8,6,2,5,1,4]=>[6,2,1,3,7,4,8,5]=>[1,1,3,2,1]
[1,8,2,5,4,7,6,3]=>[4,8,5,7,3,6,1,2]=>[5,1,4,2,6,3,8,7]=>[1,2,2,2,1]
[7,1,2,4,5,8,6,3]=>[8,4,5,7,2,3,1,6]=>[1,5,4,2,7,6,8,3]=>[2,1,2,2,1]
[1,2,7,3,5,8,6,4]=>[8,5,7,4,1,2,3,6]=>[1,4,2,5,8,7,6,3]=>[2,3,1,1,1]
[6,1,3,2,5,7,8,4]=>[3,5,6,8,2,1,4,7]=>[6,4,3,1,7,8,5,2]=>[1,1,1,3,1,1]
[4,6,2,1,7,5,3,8]=>[1,7,3,6,4,2,5,8]=>[8,2,6,3,5,7,4,1]=>[1,2,3,1,1]
[1,6,3,7,8,5,2,4]=>[7,4,2,8,3,6,1,5]=>[2,5,7,1,6,3,8,4]=>[3,2,2,1]
[4,6,2,3,7,8,1,5]=>[1,7,3,4,2,5,8,6]=>[8,2,6,5,7,4,1,3]=>[1,2,2,1,2]
[4,6,3,7,1,2,8,5]=>[1,3,8,5,2,6,4,7]=>[8,6,1,4,7,3,5,2]=>[1,1,3,2,1]
[4,2,1,3,5,7,8,6]=>[2,6,1,8,3,4,5,7]=>[7,3,8,1,6,5,4,2]=>[1,2,2,1,1,1]
[7,8,4,2,6,3,1,5]=>[7,4,3,6,1,8,5,2]=>[2,5,6,3,8,1,4,7]=>[3,2,3]
[4,2,6,3,8,7,1,5]=>[1,7,3,8,2,4,6,5]=>[8,2,6,1,7,5,3,4]=>[1,2,2,1,2]
[5,8,2,7,4,3,1,6]=>[1,7,6,3,5,8,4,2]=>[8,2,3,6,4,1,5,7]=>[1,3,1,3]
[4,3,6,8,1,2,7,5]=>[1,8,2,5,3,6,7,4]=>[8,1,7,4,6,3,2,5]=>[1,2,2,1,2]
[6,4,3,5,2,8,1,7]=>[3,2,5,4,1,7,8,6]=>[6,7,4,5,8,2,1,3]=>[2,3,1,2]
[6,5,3,8,4,2,1,7]=>[7,3,2,1,6,5,8,4]=>[2,6,7,8,3,4,1,5]=>[4,2,2]
[6,1,7,2,8,3,9,4,10,5]=>[10,8,6,4,2,1,3,5,7,9]=>[1,3,5,7,9,10,8,6,4,2]=>[6,1,1,1,1]
[7,1,8,2,9,3,10,4,11,5,12,6]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[1,3,5,7,9,11,12,10,8,6,4,2]=>[7,1,1,1,1,1]
[3,8,1,7,5,6,4,2]=>[5,8,7,1,6,3,4,2]=>[4,1,2,8,3,6,5,7]=>[1,3,2,2]
[8,2,5,7,3,6,4,1]=>[3,8,5,7,2,6,4,1]=>[6,1,4,2,7,3,5,8]=>[1,2,2,3]
[1,8,6,7,5,3,4,2]=>[6,3,8,7,5,4,1,2]=>[3,6,1,2,4,5,8,7]=>[2,5,1]
[8,2,6,7,5,3,4,1]=>[6,3,8,7,2,5,4,1]=>[3,6,1,2,7,4,5,8]=>[2,3,3]
[1,5,8,7,2,6,4,3]=>[8,2,7,5,6,4,1,3]=>[1,7,2,4,3,5,8,6]=>[2,2,3,1]
[5,4,8,6,2,3,7,1]=>[2,1,5,6,4,8,7,3]=>[7,8,4,3,5,1,2,6]=>[2,1,2,3]
[2,7,6,1,3,5,4,8]=>[7,4,5,6,1,3,2,8]=>[2,5,4,3,8,6,7,1]=>[2,1,2,2,1]
[6,4,1,8,2,5,7,3]=>[6,2,8,5,1,7,3,4]=>[3,7,1,4,8,2,6,5]=>[2,3,2,1]
[2,8,6,1,3,5,4,7]=>[7,4,5,6,1,3,8,2]=>[2,5,4,3,8,6,1,7]=>[2,1,2,1,2]
[4,1,3,6,5,8,7,2]=>[4,1,8,3,5,7,2,6]=>[5,8,1,6,4,2,7,3]=>[2,2,1,2,1]
[2,1,6,3,5,8,7,4]=>[8,5,1,3,7,2,4,6]=>[1,4,8,6,2,7,5,3]=>[3,1,2,1,1]
[2,4,1,3,8,5,7,6]=>[2,8,1,6,7,3,4,5]=>[7,1,8,3,2,6,5,4]=>[1,2,1,2,1,1]
[2,4,1,3,5,8,7,6]=>[2,8,1,7,3,4,5,6]=>[7,1,8,2,6,5,4,3]=>[1,2,2,1,1,1]
[4,6,1,3,5,8,7,2]=>[1,8,4,5,2,7,3,6]=>[8,1,5,4,7,2,6,3]=>[1,2,2,2,1]
[6,1,4,3,5,8,7,2]=>[3,8,4,5,1,7,2,6]=>[6,1,5,4,8,2,7,3]=>[1,2,2,2,1]
[6,2,1,3,5,8,7,4]=>[8,2,5,7,3,1,4,6]=>[1,7,4,2,6,8,5,3]=>[2,1,3,1,1]
[4,2,1,6,3,5,7,8]=>[2,5,1,6,3,4,7,8]=>[7,4,8,3,6,5,2,1]=>[1,2,2,1,1,1]
[6,2,1,8,3,5,7,4]=>[6,8,2,5,1,7,3,4]=>[3,1,7,4,8,2,6,5]=>[1,2,2,2,1]
[6,2,1,3,8,5,7,4]=>[6,8,2,7,3,1,4,5]=>[3,1,7,2,6,8,5,4]=>[1,2,3,1,1]
[6,1,4,3,8,5,7,2]=>[3,6,8,4,1,7,2,5]=>[6,3,1,5,8,2,7,4]=>[1,1,3,2,1]
[1,6,4,3,8,5,7,2]=>[3,6,2,8,4,7,1,5]=>[6,3,7,1,5,2,8,4]=>[1,2,2,2,1]
[8,1,4,3,6,5,7,2]=>[3,6,4,5,8,2,7,1]=>[6,3,5,4,1,7,2,8]=>[1,2,1,2,2]
[8,4,1,3,6,5,7,2]=>[6,4,2,5,8,3,7,1]=>[3,5,7,4,1,6,2,8]=>[3,1,2,2]
[8,2,1,3,6,5,7,4]=>[6,2,5,8,3,4,7,1]=>[3,7,4,1,6,5,2,8]=>[2,1,2,1,2]
[8,2,1,6,3,5,7,4]=>[6,8,2,5,3,4,7,1]=>[3,1,7,4,6,5,2,8]=>[1,2,2,1,2]
[8,2,1,4,3,5,7,6]=>[2,4,8,3,5,6,7,1]=>[7,5,1,6,4,3,2,8]=>[1,1,2,1,1,2]
[6,2,1,4,3,5,7,8]=>[2,5,3,4,6,1,7,8]=>[7,4,6,5,3,8,2,1]=>[1,2,1,2,1,1]
[8,2,4,1,3,5,7,6]=>[8,2,4,3,5,6,7,1]=>[1,7,5,6,4,3,2,8]=>[2,2,1,1,2]
[8,2,6,1,3,5,7,4]=>[6,8,2,4,5,3,7,1]=>[3,1,7,5,4,6,2,8]=>[1,2,1,2,2]
[8,4,6,1,3,5,7,2]=>[5,2,6,8,4,3,7,1]=>[4,7,3,1,5,6,2,8]=>[2,1,3,2]
[8,4,1,6,3,5,7,2]=>[5,2,6,4,8,3,7,1]=>[4,7,3,5,1,6,2,8]=>[2,2,2,2]
[8,1,4,6,3,5,7,2]=>[3,5,6,4,8,2,7,1]=>[6,4,3,5,1,7,2,8]=>[1,1,2,2,2]
[1,8,4,6,3,5,7,2]=>[3,5,6,4,8,7,1,2]=>[6,4,3,5,1,2,8,7]=>[1,1,2,3,1]
[1,6,4,8,3,5,7,2]=>[3,5,2,6,8,7,1,4]=>[6,4,7,3,1,2,8,5]=>[1,2,1,3,1]
[6,4,1,8,3,5,7,2]=>[5,2,6,1,8,7,3,4]=>[4,7,3,8,1,2,6,5]=>[2,2,3,1]
[6,4,8,1,3,5,7,2]=>[5,2,6,1,8,4,7,3]=>[4,7,3,8,1,5,2,6]=>[2,2,2,2]
[6,2,8,1,3,5,7,4]=>[6,8,2,4,1,5,7,3]=>[3,1,7,5,8,4,2,6]=>[1,2,2,1,2]
[4,2,8,1,3,5,7,6]=>[8,2,1,4,5,6,7,3]=>[1,7,8,5,4,3,2,6]=>[3,1,1,1,2]
[2,6,8,1,3,5,7,4]=>[6,8,4,1,2,5,7,3]=>[3,1,5,8,7,4,2,6]=>[1,3,1,1,2]
[4,6,8,1,3,5,7,2]=>[1,5,6,2,8,4,7,3]=>[8,4,3,7,1,5,2,6]=>[1,1,2,2,2]
[4,6,1,8,3,5,7,2]=>[1,5,6,2,8,7,3,4]=>[8,4,3,7,1,2,6,5]=>[1,1,2,3,1]
[4,1,6,8,3,5,7,2]=>[1,5,3,6,8,7,2,4]=>[8,4,6,3,1,2,7,5]=>[1,2,1,3,1]
[1,4,6,3,8,5,7,2]=>[6,2,3,8,4,7,1,5]=>[3,7,6,1,5,2,8,4]=>[2,1,2,2,1]
[4,6,1,3,8,5,7,2]=>[1,6,8,4,2,7,3,5]=>[8,3,1,5,7,2,6,4]=>[1,1,3,2,1]
[2,4,1,8,3,5,7,6]=>[2,8,1,5,6,7,3,4]=>[7,1,8,4,3,2,6,5]=>[1,2,1,1,2,1]
[2,1,6,8,3,5,7,4]=>[6,3,8,1,5,7,2,4]=>[3,6,1,8,4,2,7,5]=>[2,2,1,2,1]
[4,1,3,6,8,5,7,2]=>[4,1,6,8,3,7,2,5]=>[5,8,3,1,6,2,7,4]=>[2,1,2,2,1]
[1,4,3,6,8,5,7,2]=>[2,4,6,8,3,7,1,5]=>[7,5,3,1,6,2,8,4]=>[1,1,1,2,2,1]
[4,1,3,8,6,5,7,2]=>[1,6,5,8,3,7,2,4]=>[8,3,4,1,6,2,7,5]=>[1,2,2,2,1]
[2,1,8,3,6,5,7,4]=>[6,5,8,1,4,7,2,3]=>[3,4,1,8,5,2,7,6]=>[2,2,1,2,1]
[2,6,1,4,3,5,7,8]=>[5,1,3,4,6,2,7,8]=>[4,8,6,5,3,7,2,1]=>[2,1,1,2,1,1]
[2,8,1,4,3,5,7,6]=>[4,8,1,3,5,6,7,2]=>[5,1,8,6,4,3,2,7]=>[1,2,1,1,1,2]
[2,8,1,6,3,5,7,4]=>[6,8,5,1,3,4,7,2]=>[3,1,4,8,6,5,2,7]=>[1,3,1,1,2]
[4,8,1,3,6,5,7,2]=>[1,6,4,5,8,3,7,2]=>[8,3,5,4,1,6,2,7]=>[1,2,1,2,2]
[1,4,8,6,3,5,7,2]=>[5,6,2,4,8,7,1,3]=>[4,3,7,5,1,2,8,6]=>[1,2,1,3,1]
[4,1,8,6,3,5,7,2]=>[1,5,6,4,8,7,2,3]=>[8,4,3,5,1,2,7,6]=>[1,1,2,3,1]
[4,8,6,1,3,5,7,2]=>[1,5,6,8,4,3,7,2]=>[8,4,3,1,5,6,2,7]=>[1,1,1,3,2]
[2,8,6,1,3,5,7,4]=>[6,8,4,5,1,3,7,2]=>[3,1,5,4,8,6,2,7]=>[1,2,2,1,2]
[2,8,4,1,3,5,7,6]=>[8,4,1,3,5,6,7,2]=>[1,5,8,6,4,3,2,7]=>[3,1,1,1,2]
[2,6,4,1,3,5,7,8]=>[4,5,1,3,6,2,7,8]=>[5,4,8,6,3,7,2,1]=>[1,2,1,2,1,1]
[4,6,2,1,3,5,7,8]=>[4,3,1,5,6,2,7,8]=>[5,6,8,4,3,7,2,1]=>[3,1,2,1,1]
[6,8,1,4,3,5,7,2]=>[5,4,6,1,8,3,7,2]=>[4,5,3,8,1,6,2,7]=>[2,2,2,2]
[6,1,8,4,3,5,7,2]=>[5,4,6,1,8,7,2,3]=>[4,5,3,8,1,2,7,6]=>[2,2,3,1]
[1,6,8,4,3,5,7,2]=>[5,4,2,6,8,7,1,3]=>[4,5,7,3,1,2,8,6]=>[3,1,3,1]
[1,8,6,4,3,5,7,2]=>[5,4,6,3,8,7,1,2]=>[4,5,3,6,1,2,8,7]=>[2,2,3,1]
[8,1,6,4,3,5,7,2]=>[5,4,6,3,8,2,7,1]=>[4,5,3,6,1,7,2,8]=>[2,2,2,2]
[8,6,4,1,3,5,7,2]=>[5,6,3,8,4,2,7,1]=>[4,3,6,1,5,7,2,8]=>[1,2,3,2]
[8,6,2,1,3,5,7,4]=>[3,6,8,4,5,2,7,1]=>[6,3,1,5,4,7,2,8]=>[1,1,2,2,2]
[8,4,2,1,3,5,7,6]=>[3,8,4,2,5,6,7,1]=>[6,1,5,7,4,3,2,8]=>[1,3,1,1,2]
[7,8,6,5,2,1,4,3]=>[5,8,6,1,7,4,3,2]=>[4,1,3,8,2,5,6,7]=>[1,3,4]
[5,7,4,1,8,6,3,2]=>[1,3,8,7,6,4,2,5]=>[8,6,1,2,3,5,7,4]=>[1,1,5,1]
[5,6,4,2,8,3,7,1]=>[1,6,3,2,8,4,7,5]=>[8,3,6,7,1,5,2,4]=>[1,3,2,2]
[5,7,1,4,6,3,2,8]=>[4,1,7,6,3,5,2,8]=>[5,8,2,3,6,4,7,1]=>[2,3,2,1]
[5,8,1,4,6,3,7,2]=>[4,1,6,5,8,3,7,2]=>[5,8,3,4,1,6,2,7]=>[2,2,2,2]
[3,5,7,4,6,8,2,1]=>[2,4,5,1,3,8,7,6]=>[7,5,4,8,6,1,2,3]=>[1,1,2,1,3]
[6,8,4,1,7,2,5,3]=>[8,6,3,1,7,4,5,2]=>[1,3,6,8,2,5,4,7]=>[4,2,2]
[5,4,6,1,7,8,3,2]=>[2,1,5,3,8,7,4,6]=>[7,8,4,6,1,2,5,3]=>[2,2,3,1]
[5,6,4,1,8,7,3,2]=>[1,3,2,8,7,6,4,5]=>[8,6,7,1,2,3,5,4]=>[1,2,4,1]
[3,5,8,4,6,7,2,1]=>[2,4,5,8,1,7,6,3]=>[7,5,4,1,8,2,3,6]=>[1,1,1,2,3]
[3,6,8,4,5,7,2,1]=>[4,2,5,8,1,7,6,3]=>[5,7,4,1,8,2,3,6]=>[2,1,2,3]
[3,7,8,4,5,6,2,1]=>[4,5,2,8,1,7,6,3]=>[5,4,7,1,8,2,3,6]=>[1,2,2,3]
[6,8,1,4,5,3,7,2]=>[4,6,5,1,8,3,7,2]=>[5,3,4,8,1,6,2,7]=>[1,3,2,2]
[6,7,1,4,5,3,2,8]=>[4,7,6,3,1,5,2,8]=>[5,2,3,6,8,4,7,1]=>[1,4,2,1]
[3,7,1,5,4,6,2,8]=>[5,1,4,7,3,6,2,8]=>[4,8,5,2,6,3,7,1]=>[2,1,2,2,1]
[3,8,1,5,4,6,7,2]=>[5,1,4,6,8,3,7,2]=>[4,8,5,3,1,6,2,7]=>[2,1,1,2,2]
[3,7,1,5,4,6,8,2]=>[5,1,4,6,8,3,2,7]=>[4,8,5,3,1,6,7,2]=>[2,1,1,3,1]
[6,7,1,4,5,3,8,2]=>[4,6,5,1,8,3,2,7]=>[5,3,4,8,1,6,7,2]=>[1,3,3,1]
[5,7,1,4,6,3,8,2]=>[4,1,6,5,8,3,2,7]=>[5,8,3,4,1,6,7,2]=>[2,2,3,1]
[5,6,4,2,7,3,8,1]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[1,4,1,2]
[5,4,7,2,8,3,1,6]=>[2,1,7,4,6,3,8,5]=>[7,8,2,5,3,6,1,4]=>[2,2,2,2]
[5,4,7,2,8,3,6,1]=>[2,1,6,8,4,3,7,5]=>[7,8,3,1,5,6,2,4]=>[2,1,3,2]
[5,6,4,2,8,3,1,7]=>[1,7,4,3,2,6,8,5]=>[8,2,5,6,7,3,1,4]=>[1,4,1,2]
[5,8,1,4,6,3,2,7]=>[4,1,7,6,3,5,8,2]=>[5,8,2,3,6,4,1,7]=>[2,3,1,2]
[3,6,1,5,4,2,7,8]=>[6,1,5,3,4,2,7,8]=>[3,8,4,6,5,7,2,1]=>[2,2,2,1,1]
[3,6,1,5,4,8,2,7]=>[5,1,4,7,2,8,3,6]=>[4,8,5,2,7,1,6,3]=>[2,1,2,2,1]
[6,8,3,1,4,2,5,7]=>[6,4,3,5,1,7,8,2]=>[3,5,6,4,8,2,1,7]=>[3,2,1,2]
[7,3,8,1,4,2,5,6]=>[2,6,4,5,7,1,8,3]=>[7,3,5,4,2,8,1,6]=>[1,2,1,2,2]
[6,7,3,1,4,2,8,5]=>[5,3,8,4,1,6,2,7]=>[4,6,1,5,8,3,7,2]=>[2,3,2,1]
[3,6,1,5,4,7,8,2]=>[5,1,4,6,2,8,3,7]=>[4,8,5,3,7,1,6,2]=>[2,1,2,2,1]
[3,4,1,2,7,6,5,8]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[1,1,3,1,1,1]
[3,4,1,2,6,8,7,5]=>[1,2,8,5,7,3,4,6]=>[8,7,1,4,2,6,5,3]=>[1,1,2,2,1,1]
[6,8,3,1,4,7,2,5]=>[5,3,7,1,8,4,6,2]=>[4,6,2,8,1,5,3,7]=>[2,2,2,2]
[5,8,1,4,7,3,2,6]=>[4,1,7,6,8,3,5,2]=>[5,8,2,3,1,6,4,7]=>[2,2,2,2]
[7,8,1,4,5,3,2,6]=>[4,7,6,3,5,1,8,2]=>[5,2,3,6,4,8,1,7]=>[1,3,2,2]
[3,6,1,5,4,8,7,2]=>[4,8,1,5,2,7,3,6]=>[5,1,8,4,7,2,6,3]=>[1,2,2,2,1]
[3,6,1,5,4,7,2,8]=>[5,1,4,7,3,2,6,8]=>[4,8,5,2,6,7,3,1]=>[2,1,3,1,1]
[6,7,3,1,4,2,5,8]=>[6,4,3,5,1,7,2,8]=>[3,5,6,4,8,2,7,1]=>[3,2,2,1]
[7,8,3,1,4,6,2,5]=>[5,3,7,8,4,1,6,2]=>[4,6,2,1,5,8,3,7]=>[2,1,3,2]
[7,8,4,2,6,5,1,3]=>[7,3,8,4,1,6,5,2]=>[2,6,1,5,8,3,4,7]=>[2,3,3]
[6,5,8,7,3,4,2,1]=>[2,1,5,8,7,6,4,3]=>[7,8,4,1,2,3,5,6]=>[2,1,5]
[6,7,3,1,4,5,2,8]=>[5,3,7,4,1,6,2,8]=>[4,6,2,5,8,3,7,1]=>[2,3,2,1]
[3,7,1,5,4,2,6,8]=>[6,1,5,3,4,7,2,8]=>[3,8,4,6,5,2,7,1]=>[2,2,1,2,1]
[5,8,1,4,7,3,6,2]=>[4,1,6,8,7,3,5,2]=>[5,8,3,1,2,6,4,7]=>[2,1,3,2]
[6,4,7,2,8,5,3,1]=>[8,2,1,7,4,3,6,5]=>[1,7,8,2,5,6,3,4]=>[3,3,2]
[6,3,7,1,4,8,5,2]=>[8,2,5,1,7,4,3,6]=>[1,7,4,8,2,5,6,3]=>[2,2,3,1]
[6,8,3,1,4,7,5,2]=>[3,8,5,1,7,4,6,2]=>[6,1,4,8,2,5,3,7]=>[1,3,2,2]
[3,4,1,2,8,5,7,6]=>[1,2,8,6,7,3,4,5]=>[8,7,1,3,2,6,5,4]=>[1,1,2,2,1,1]
[3,4,1,2,5,8,7,6]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[1,1,3,1,1,1]
[3,7,1,5,4,2,8,6]=>[5,1,4,8,3,6,2,7]=>[4,8,5,1,6,3,7,2]=>[2,1,2,2,1]
[6,7,3,1,4,5,8,2]=>[5,3,6,1,8,4,2,7]=>[4,6,3,8,1,5,7,2]=>[2,2,3,1]
[7,3,8,1,4,5,2,6]=>[2,5,7,4,6,1,8,3]=>[7,4,2,5,3,8,1,6]=>[1,1,2,2,2]
[7,3,8,1,4,5,6,2]=>[2,5,6,8,4,1,7,3]=>[7,4,3,1,5,8,2,6]=>[1,1,1,3,2]
[3,8,1,5,4,2,6,7]=>[6,1,5,3,4,7,8,2]=>[3,8,4,6,5,2,1,7]=>[2,2,1,1,2]
[9,8,7,6,5,4,2,1,3]=>[8,7,9,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9]=>[2,7]
[9,8,7,6,5,3,2,1,4]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9]=>[3,6]
[8,7,6,3,5,2,1,4]=>[4,7,6,8,5,3,2,1]=>[5,2,3,1,4,6,7,8]=>[1,2,5]
[9,8,7,6,4,3,2,1,5]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,5,1,6,7,8,9]=>[4,5]
[8,7,4,6,3,2,1,5]=>[3,7,6,5,8,4,2,1]=>[6,2,3,4,1,5,7,8]=>[1,3,4]
[9,8,7,5,4,3,2,1,6]=>[8,7,6,5,4,9,3,2,1]=>[2,3,4,5,6,1,7,8,9]=>[5,4]
[8,5,7,4,3,2,1,6]=>[2,7,6,5,4,8,3,1]=>[7,2,3,4,5,1,6,8]=>[1,4,3]
[9,8,6,5,4,3,2,1,7]=>[8,7,6,5,4,3,9,2,1]=>[2,3,4,5,6,7,1,8,9]=>[6,3]
[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,2,9,1]=>[2,3,4,5,6,7,8,1,9]=>[7,2]
[9,8,7,6,5,4,1,3,2]=>[9,7,8,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9]=>[2,7]
[10,9,8,7,6,5,4,2,1,3]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,1,4,5,6,7,8,9,10]=>[2,8]
[10,9,8,7,6,5,3,2,1,4]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,1,5,6,7,8,9,10]=>[3,7]
[10,9,8,7,6,4,3,2,1,5]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,1,6,7,8,9,10]=>[4,6]
[8,7,6,2,5,4,1,3]=>[7,8,4,6,5,3,2,1]=>[2,1,5,3,4,6,7,8]=>[1,2,5]
[10,9,8,7,5,4,3,2,1,6]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,5,6,1,7,8,9,10]=>[5,5]
[8,5,4,7,3,2,1,6]=>[3,2,7,6,5,8,4,1]=>[6,7,2,3,4,1,5,8]=>[2,3,3]
[8,7,3,6,5,2,1,4]=>[7,3,6,8,5,4,2,1]=>[2,6,3,1,4,5,7,8]=>[2,1,5]
[10,9,8,6,5,4,3,2,1,7]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,4,5,6,7,1,8,9,10]=>[6,4]
[6,5,8,4,3,2,1,7]=>[2,1,7,6,5,4,8,3]=>[7,8,2,3,4,5,1,6]=>[2,4,2]
[8,4,7,6,3,2,1,5]=>[7,2,6,5,8,4,3,1]=>[2,7,3,4,1,5,6,8]=>[2,2,4]
[10,9,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,10,2,1]=>[2,3,4,5,6,7,8,1,9,10]=>[7,3]
[5,8,7,4,3,2,1,6]=>[7,1,6,5,4,8,3,2]=>[2,8,3,4,5,1,6,7]=>[2,3,3]
[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,2,10,1]=>[2,3,4,5,6,7,8,9,1,10]=>[8,2]
[5,8,6,2,3,4,7,1]=>[4,1,5,6,3,8,7,2]=>[5,8,4,3,6,1,2,7]=>[2,1,2,3]
[4,5,2,7,3,1,8,6]=>[1,5,2,8,3,6,4,7]=>[8,4,7,1,6,3,5,2]=>[1,2,2,2,1]
[4,8,2,6,3,5,7,1]=>[1,5,6,3,4,8,7,2]=>[8,4,3,6,5,1,2,7]=>[1,1,2,1,3]
[4,3,7,8,6,5,1,2]=>[7,1,3,8,2,6,5,4]=>[2,8,6,1,7,3,4,5]=>[2,1,2,3]
[4,1,7,2,5,8,6,3]=>[1,8,5,7,4,2,3,6]=>[8,1,4,2,5,7,6,3]=>[1,2,3,1,1]
[7,8,2,1,5,6,4,3]=>[5,8,3,7,4,1,6,2]=>[4,1,6,2,5,8,3,7]=>[1,2,3,2]
[1,6,2,5,8,4,3,7]=>[4,7,6,2,8,1,3,5]=>[5,2,3,7,1,8,6,4]=>[1,3,2,1,1]
[2,1,8,7,4,5,3,6]=>[5,7,6,8,1,4,2,3]=>[4,2,3,1,8,5,7,6]=>[1,2,2,2,1]
[7,3,1,6,8,5,2,4]=>[7,2,4,8,6,3,1,5]=>[2,7,5,1,3,6,8,4]=>[2,1,4,1]
[1,5,8,6,2,3,7,4]=>[2,8,5,6,4,7,1,3]=>[7,1,4,3,5,2,8,6]=>[1,2,2,2,1]
[2,4,8,3,1,6,5,7]=>[2,4,7,1,5,6,8,3]=>[7,5,2,8,4,3,1,6]=>[1,1,2,1,1,2]
[5,2,7,1,8,6,3,4]=>[7,1,8,6,2,4,3,5]=>[2,8,1,3,7,5,6,4]=>[2,3,2,1]
[2,6,1,3,8,7,4,5]=>[7,8,6,1,3,2,4,5]=>[2,1,3,8,6,7,5,4]=>[1,3,2,1,1]
[6,5,2,8,1,7,3,4]=>[7,8,3,2,1,5,6,4]=>[2,1,6,7,8,4,3,5]=>[1,4,1,2]
[2,8,3,5,1,7,4,6]=>[7,3,4,8,1,5,6,2]=>[2,6,5,1,8,4,3,7]=>[2,1,2,1,2]
[5,4,3,8,7,1,6,2]=>[2,1,8,3,6,7,5,4]=>[7,8,1,6,3,2,4,5]=>[2,2,1,3]
[8,5,4,3,7,2,6,1]=>[4,3,2,6,8,7,5,1]=>[5,6,7,3,1,2,4,8]=>[3,1,4]
[8,3,7,4,2,6,5,1]=>[4,8,2,5,7,6,3,1]=>[5,1,7,4,2,3,6,8]=>[1,2,1,4]
[2,8,6,5,1,7,4,3]=>[8,7,5,4,1,3,6,2]=>[1,2,4,5,8,6,3,7]=>[5,1,2]
[6,3,2,8,4,1,7,5]=>[2,5,8,3,1,6,7,4]=>[7,4,1,6,8,3,2,5]=>[1,1,3,1,2]
[5,4,2,8,3,1,7,6]=>[5,2,1,8,3,6,7,4]=>[4,7,8,1,6,3,2,5]=>[3,2,1,2]
[2,8,4,3,1,7,6,5]=>[3,8,4,7,1,5,6,2]=>[6,1,5,2,8,4,3,7]=>[1,2,2,1,2]
[2,8,5,3,1,7,6,4]=>[8,4,3,7,1,5,6,2]=>[1,5,6,2,8,4,3,7]=>[3,2,1,2]
[2,8,6,4,1,7,5,3]=>[4,8,7,5,1,3,6,2]=>[5,1,2,4,8,6,3,7]=>[1,4,1,2]
[8,3,7,5,2,6,4,1]=>[8,5,2,4,7,6,3,1]=>[1,4,7,5,2,3,6,8]=>[3,1,4]
[8,4,7,6,2,5,3,1]=>[8,2,5,7,6,4,3,1]=>[1,7,4,2,3,5,6,8]=>[2,1,5]
[4,8,7,6,1,5,3,2]=>[8,7,1,5,6,4,3,2]=>[1,2,8,4,3,5,6,7]=>[3,1,4]
[7,4,8,6,2,1,5,3]=>[2,5,8,6,1,7,4,3]=>[7,4,1,3,8,2,5,6]=>[1,1,3,3]
[7,3,8,5,2,1,6,4]=>[5,8,2,6,4,1,7,3]=>[4,1,7,3,5,8,2,6]=>[1,2,3,2]
[7,3,8,4,2,1,6,5]=>[5,2,4,8,6,1,7,3]=>[4,7,5,1,3,8,2,6]=>[2,1,3,2]
[7,5,4,3,8,2,1,6]=>[4,3,2,7,6,1,8,5]=>[5,6,7,2,3,8,1,4]=>[3,3,2]
[3,7,8,5,1,2,6,4]=>[8,5,6,1,4,2,7,3]=>[1,4,3,8,5,7,2,6]=>[2,2,2,2]
[4,7,8,6,1,2,5,3]=>[8,1,5,6,2,7,4,3]=>[1,8,4,3,7,2,5,6]=>[2,1,2,3]
[8,7,4,6,3,5,2,1]=>[3,5,8,7,6,4,2,1]=>[6,4,1,2,3,5,7,8]=>[1,1,6]
[5,7,8,6,1,2,4,3]=>[1,8,5,6,2,7,4,3]=>[8,1,4,3,7,2,5,6]=>[1,2,2,3]
[6,4,7,8,3,1,2,5]=>[2,6,1,7,5,3,8,4]=>[7,3,8,2,4,6,1,5]=>[1,2,3,2]
[7,3,4,8,2,1,5,6]=>[2,3,6,5,7,1,8,4]=>[7,6,3,4,2,8,1,5]=>[1,1,2,2,2]
[7,6,4,8,3,2,1,5]=>[3,7,6,5,2,1,8,4]=>[6,2,3,4,7,8,1,5]=>[1,5,2]
[7,5,8,6,2,1,4,3]=>[5,2,8,6,1,7,4,3]=>[4,7,1,3,8,2,5,6]=>[2,3,3]
[6,5,8,7,3,1,4,2]=>[2,1,8,6,5,7,4,3]=>[7,8,1,3,4,2,5,6]=>[2,3,3]
[2,4,8,3,1,5,7,6]=>[2,4,8,1,5,6,7,3]=>[7,5,1,8,4,3,2,6]=>[1,1,2,1,1,2]
[6,3,2,4,8,1,5,7]=>[3,2,4,6,1,7,8,5]=>[6,7,5,3,8,2,1,4]=>[2,1,2,1,2]
[2,3,8,4,1,6,7,5]=>[4,6,8,1,2,5,7,3]=>[5,3,1,8,7,4,2,6]=>[1,1,2,1,1,2]
[2,3,8,5,1,6,7,4]=>[6,4,8,1,2,5,7,3]=>[3,5,1,8,7,4,2,6]=>[2,2,1,1,2]
[6,4,8,7,3,1,5,2]=>[8,2,1,6,5,7,4,3]=>[1,7,8,3,4,2,5,6]=>[3,2,3]
[8,6,4,7,3,2,5,1]=>[3,6,5,2,8,7,4,1]=>[6,3,4,7,1,2,5,8]=>[1,3,4]
[8,3,4,7,2,5,6,1]=>[2,3,5,6,8,7,4,1]=>[7,6,4,3,1,2,5,8]=>[1,1,1,1,4]
[3,4,8,7,1,5,6,2]=>[6,8,1,2,5,7,4,3]=>[3,1,8,7,4,2,5,6]=>[1,2,1,1,3]
[2,4,8,6,1,5,7,3]=>[6,8,2,5,1,4,7,3]=>[3,1,7,4,8,5,2,6]=>[1,2,2,1,2]
[2,5,8,6,1,4,7,3]=>[2,6,8,5,1,4,7,3]=>[7,3,1,4,8,5,2,6]=>[1,1,3,1,2]
[4,6,8,7,1,3,5,2]=>[6,1,2,8,5,7,4,3]=>[3,8,7,1,4,2,5,6]=>[2,1,2,3]
[2,6,8,5,1,3,7,4]=>[8,5,2,6,1,4,7,3]=>[1,4,7,3,8,5,2,6]=>[3,2,1,2]
[2,6,8,4,1,3,7,5]=>[8,5,4,1,2,6,7,3]=>[1,4,5,8,7,3,2,6]=>[4,1,1,2]
[2,5,8,3,1,4,7,6]=>[4,2,8,1,5,6,7,3]=>[5,7,1,8,4,3,2,6]=>[2,2,1,1,2]
[7,4,6,8,2,1,3,5]=>[2,6,5,7,3,1,8,4]=>[7,3,4,2,6,8,1,5]=>[1,2,3,2]
[2,3,5,4,1,8,6,7]=>[4,1,2,3,7,8,5,6]=>[5,8,7,6,2,1,4,3]=>[2,1,1,1,2,1]
[2,3,6,4,8,1,5,7]=>[4,6,1,2,3,7,8,5]=>[5,3,8,7,6,2,1,4]=>[1,2,1,1,1,2]
[1,8,4,6,3,5,2,7]=>[3,5,7,6,4,8,1,2]=>[6,4,2,3,5,1,8,7]=>[1,1,3,2,1]
[5,4,8,6,2,1,3,7]=>[2,1,6,5,7,4,8,3]=>[7,8,3,4,2,5,1,6]=>[2,2,2,2]
[2,3,6,8,1,5,4,7]=>[7,5,1,2,3,6,8,4]=>[2,4,8,7,6,3,1,5]=>[3,1,1,1,2]
[2,5,6,1,4,7,8,3]=>[5,2,6,1,3,8,4,7]=>[4,7,3,8,6,1,5,2]=>[2,2,1,2,1]
[2,5,6,1,4,7,3,8]=>[5,2,7,1,4,3,6,8]=>[4,7,2,8,5,6,3,1]=>[2,2,2,1,1]
[7,3,5,1,6,8,4,2]=>[5,2,3,8,7,4,1,6]=>[4,7,6,1,2,5,8,3]=>[2,1,4,1]
[2,7,6,1,8,5,4,3]=>[8,7,6,4,1,3,2,5]=>[1,2,3,5,8,6,7,4]=>[5,2,1]
[2,7,6,8,1,4,5,3]=>[6,8,5,3,1,2,7,4]=>[3,1,4,6,8,7,2,5]=>[1,4,1,2]
[1,8,7,6,3,2,5,4]=>[5,8,6,7,4,3,1,2]=>[4,1,3,2,5,6,8,7]=>[1,2,4,1]
[1,8,7,6,3,2,4,5]=>[6,5,7,8,4,3,1,2]=>[3,4,2,1,5,6,8,7]=>[2,1,4,1]
[5,7,8,6,2,3,4,1]=>[1,5,6,2,8,7,4,3]=>[8,4,3,7,1,2,5,6]=>[1,1,2,4]
[2,7,6,1,8,5,3,4]=>[7,8,6,4,1,3,2,5]=>[2,1,3,5,8,6,7,4]=>[1,4,2,1]
[6,3,5,1,7,2,4,8]=>[2,6,7,4,3,1,5,8]=>[7,3,2,5,6,8,4,1]=>[1,1,4,1,1]
[2,3,4,7,6,1,5,8]=>[6,7,1,2,3,5,4,8]=>[3,2,8,7,6,4,5,1]=>[1,2,1,1,2,1]
[7,3,5,8,4,1,2,6]=>[6,2,3,7,5,1,8,4]=>[3,7,6,2,4,8,1,5]=>[2,1,3,2]
[1,8,4,5,2,7,3,6]=>[3,7,4,8,5,6,1,2]=>[6,2,5,1,4,3,8,7]=>[1,2,2,2,1]
[1,8,4,5,2,7,6,3]=>[3,4,8,7,5,6,1,2]=>[6,5,1,2,4,3,8,7]=>[1,1,3,2,1]
[7,3,5,8,4,1,6,2]=>[3,8,2,6,5,1,7,4]=>[6,1,7,3,4,8,2,5]=>[1,2,3,2]
[2,7,6,4,8,5,1,3]=>[4,7,3,2,8,1,6,5]=>[5,2,6,7,1,8,3,4]=>[1,3,2,2]
[7,3,5,4,6,8,1,2]=>[4,2,3,7,5,1,8,6]=>[5,7,6,2,4,8,1,3]=>[2,1,3,2]
[6,3,5,4,7,1,8,2]=>[4,2,3,1,8,6,5,7]=>[5,7,6,8,1,3,4,2]=>[2,2,3,1]
[6,3,5,4,7,1,2,8]=>[6,2,4,3,1,7,5,8]=>[3,7,5,6,8,2,4,1]=>[2,3,2,1]
[2,3,1,8,6,4,7,5]=>[8,6,1,2,5,7,3,4]=>[1,3,8,7,4,2,6,5]=>[3,1,1,2,1]
[1,8,4,3,6,2,5,7]=>[4,3,6,7,5,8,1,2]=>[5,6,3,2,4,1,8,7]=>[2,1,2,2,1]
[3,7,1,6,8,5,4,2]=>[4,8,7,1,6,3,2,5]=>[5,1,2,8,3,6,7,4]=>[1,3,3,1]
[6,3,5,4,7,2,1,8]=>[4,2,3,1,7,6,5,8]=>[5,7,6,8,2,3,4,1]=>[2,2,3,1]
[7,3,5,4,6,8,2,1]=>[4,2,3,5,1,8,7,6]=>[5,7,6,4,8,1,2,3]=>[2,1,2,3]
[2,7,6,4,8,5,3,1]=>[8,4,3,2,7,1,6,5]=>[1,5,6,7,2,8,3,4]=>[4,2,2]
[1,8,4,5,2,6,3,7]=>[3,7,5,4,6,8,1,2]=>[6,2,4,5,3,1,8,7]=>[1,3,1,2,1]
[6,4,8,5,3,1,2,7]=>[2,6,1,7,5,4,8,3]=>[7,3,8,2,4,5,1,6]=>[1,2,3,2]
[7,3,5,8,4,6,2,1]=>[3,5,8,2,1,7,6,4]=>[6,4,1,7,8,2,3,5]=>[1,1,3,3]
[2,3,4,6,5,8,1,7]=>[5,1,2,3,4,7,8,6]=>[4,8,7,6,5,2,1,3]=>[2,1,1,1,1,2]
[2,3,4,7,5,1,8,6]=>[5,8,1,2,3,6,4,7]=>[4,1,8,7,6,3,5,2]=>[1,2,1,1,2,1]
[2,3,4,7,5,1,6,8]=>[6,1,2,3,5,7,4,8]=>[3,8,7,6,4,2,5,1]=>[2,1,1,1,2,1]
[2,3,4,7,1,6,5,8]=>[7,1,2,3,5,6,4,8]=>[2,8,7,6,4,3,5,1]=>[2,1,1,1,2,1]
[2,3,4,7,1,6,8,5]=>[6,8,1,2,3,5,4,7]=>[3,1,8,7,6,4,5,2]=>[1,2,1,1,2,1]
[2,3,4,6,1,8,7,5]=>[4,8,1,2,3,7,5,6]=>[5,1,8,7,6,2,4,3]=>[1,2,1,1,2,1]
[6,3,5,8,4,2,7,1]=>[3,6,2,1,5,8,7,4]=>[6,3,7,8,4,1,2,5]=>[1,3,1,3]
[7,4,8,5,3,2,1,6]=>[7,2,6,5,4,1,8,3]=>[2,7,3,4,5,8,1,6]=>[2,4,2]
[1,8,4,5,2,3,6,7]=>[5,3,6,4,7,8,1,2]=>[4,6,3,5,2,1,8,7]=>[2,2,1,2,1]
[7,4,8,5,3,2,6,1]=>[6,2,5,4,1,8,7,3]=>[3,7,4,5,8,1,2,6]=>[2,3,3]
[6,3,5,8,4,2,1,7]=>[3,7,2,1,6,5,8,4]=>[6,2,7,8,3,4,1,5]=>[1,3,2,2]
[5,2,4,6,8,3,7,1]=>[3,4,1,6,8,2,7,5]=>[6,5,8,3,1,7,2,4]=>[1,2,1,2,2]
[1,5,7,4,6,3,2,8]=>[2,4,7,6,5,1,3,8]=>[7,5,2,3,4,8,6,1]=>[1,1,4,1,1]
[5,2,8,4,6,3,7,1]=>[4,1,6,5,8,2,7,3]=>[5,8,3,4,1,7,2,6]=>[2,2,2,2]
[3,8,5,4,6,7,2,1]=>[4,3,5,8,1,7,6,2]=>[5,6,4,1,8,2,3,7]=>[2,1,2,3]
[6,8,3,4,5,7,2,1]=>[3,4,1,5,8,7,6,2]=>[6,5,8,4,1,2,3,7]=>[1,2,1,4]
[2,5,7,4,6,3,8,1]=>[2,4,6,5,1,3,8,7]=>[7,5,3,4,8,6,1,2]=>[1,1,3,1,2]
[5,4,1,7,8,3,2,6]=>[2,1,7,6,4,8,3,5]=>[7,8,2,3,5,1,6,4]=>[2,3,2,1]
[5,1,4,6,8,3,2,7]=>[3,4,1,7,6,8,2,5]=>[6,5,8,2,3,1,7,4]=>[1,2,2,2,1]
[8,1,6,4,5,3,2,7]=>[4,7,6,5,2,3,8,1]=>[5,2,3,4,7,6,1,8]=>[1,4,1,2]
[8,1,3,5,4,6,2,7]=>[5,3,4,7,2,6,8,1]=>[4,6,5,2,7,3,1,8]=>[2,1,2,1,2]
[8,1,6,2,4,3,5,7]=>[6,4,5,7,2,3,8,1]=>[3,5,4,2,7,6,1,8]=>[2,1,2,1,2]
[8,7,1,2,4,3,5,6]=>[6,3,4,5,7,8,2,1]=>[3,6,5,4,2,1,7,8]=>[2,1,1,1,3]
[1,7,6,2,4,3,5,8]=>[6,4,5,7,3,1,2,8]=>[3,5,4,2,6,8,7,1]=>[2,1,3,1,1]
[8,2,6,3,4,5,7,1]=>[4,5,6,2,3,8,7,1]=>[5,4,3,7,6,1,2,8]=>[1,1,2,1,3]
[1,7,6,3,4,5,2,8]=>[4,5,7,6,3,1,2,8]=>[5,4,2,3,6,8,7,1]=>[1,1,4,1,1]
[8,7,2,4,5,3,6,1]=>[4,6,3,5,8,7,2,1]=>[5,3,6,4,1,2,7,8]=>[1,2,1,4]
[5,8,2,4,7,3,6,1]=>[4,1,6,8,3,7,5,2]=>[5,8,3,1,6,2,4,7]=>[2,1,2,3]
[6,8,3,2,4,7,5,1]=>[3,8,4,1,5,7,6,2]=>[6,1,5,8,4,2,3,7]=>[1,3,1,3]
[8,7,1,3,4,5,2,6]=>[4,5,7,3,6,8,2,1]=>[5,4,2,6,3,1,7,8]=>[1,1,2,1,3]
[8,1,6,3,4,5,2,7]=>[4,5,7,6,2,3,8,1]=>[5,4,2,3,7,6,1,8]=>[1,1,3,1,2]
[8,1,2,5,4,3,6,7]=>[6,5,2,3,4,7,8,1]=>[3,4,7,6,5,2,1,8]=>[3,1,1,1,2]
[3,4,8,7,5,2,6,1]=>[6,5,8,1,2,7,4,3]=>[3,4,1,8,7,2,5,6]=>[2,2,1,3]
[3,2,8,6,1,5,4,7]=>[7,1,5,6,2,4,8,3]=>[2,8,4,3,7,5,1,6]=>[2,1,2,1,2]
[8,6,1,2,4,3,5,7]=>[6,3,4,5,7,2,8,1]=>[3,6,5,4,2,7,1,8]=>[2,1,1,2,2]
[8,7,3,6,4,2,5,1]=>[6,3,5,8,7,4,2,1]=>[3,6,4,1,2,5,7,8]=>[2,1,5]
[3,8,7,2,5,4,6,1]=>[6,4,5,8,1,7,3,2]=>[3,5,4,1,8,2,6,7]=>[2,1,2,3]
[8,7,2,4,5,6,3,1]=>[4,5,8,3,7,6,2,1]=>[5,4,1,6,2,3,7,8]=>[1,1,2,4]
[5,3,6,2,4,8,7,1]=>[8,2,1,4,3,5,7,6]=>[1,7,8,5,6,4,2,3]=>[3,2,1,2]
[3,5,2,8,6,1,4,7]=>[6,1,2,7,3,5,8,4]=>[3,8,7,2,6,4,1,5]=>[2,1,2,1,2]
[3,7,2,5,1,4,8,6]=>[8,1,3,5,4,6,2,7]=>[1,8,6,4,5,3,7,2]=>[2,1,2,2,1]
[5,1,8,6,2,3,4,7]=>[5,6,1,7,4,8,2,3]=>[4,3,8,2,5,1,7,6]=>[1,2,2,2,1]
[2,5,4,1,8,6,3,7]=>[3,2,7,1,6,8,4,5]=>[6,7,2,8,3,1,5,4]=>[2,2,1,2,1]
[3,7,6,1,8,2,5,4]=>[8,6,7,1,4,3,2,5]=>[1,3,2,8,5,6,7,4]=>[2,2,3,1]
[7,6,3,1,8,2,4,5]=>[6,3,7,8,4,2,1,5]=>[3,6,2,1,5,7,8,4]=>[2,1,4,1]
[8,1,3,6,4,7,2,5]=>[5,7,3,4,8,2,6,1]=>[4,2,6,5,1,7,3,8]=>[1,2,1,2,2]
[8,2,1,3,5,7,4,6]=>[2,5,7,8,3,4,6,1]=>[7,4,2,1,6,5,3,8]=>[1,1,1,2,1,2]
[8,2,6,3,1,4,7,5]=>[4,8,2,5,6,3,7,1]=>[5,1,7,4,3,6,2,8]=>[1,2,1,2,2]
[7,5,4,1,3,8,2,6]=>[5,7,3,2,8,4,1,6]=>[4,2,6,7,1,5,8,3]=>[1,3,3,1]
[2,7,5,8,3,4,1,6]=>[5,3,7,6,1,2,8,4]=>[4,6,2,3,8,7,1,5]=>[2,3,1,2]
[7,3,8,5,4,1,2,6]=>[6,7,2,5,4,1,8,3]=>[3,2,7,4,5,8,1,6]=>[1,2,3,2]
[7,2,3,6,1,4,8,5]=>[8,2,3,5,6,4,1,7]=>[1,7,6,4,3,5,8,2]=>[2,1,1,3,1]
[1,3,7,2,5,8,4,6]=>[5,7,8,2,4,1,3,6]=>[4,2,1,7,5,8,6,3]=>[1,1,2,2,1,1]
[1,7,2,3,5,8,4,6]=>[5,7,8,3,4,1,2,6]=>[4,2,1,6,5,8,7,3]=>[1,1,2,2,1,1]
[7,4,8,1,3,6,2,5]=>[5,2,7,8,4,1,6,3]=>[4,7,2,1,5,8,3,6]=>[2,1,3,2]
[8,1,2,3,5,7,4,6]=>[5,7,8,2,3,4,6,1]=>[4,2,1,7,6,5,3,8]=>[1,1,2,1,1,2]
[7,1,2,3,5,8,4,6]=>[5,7,8,2,3,4,1,6]=>[4,2,1,7,6,5,8,3]=>[1,1,2,1,2,1]
[8,6,1,4,7,3,2,5]=>[4,7,6,8,3,2,5,1]=>[5,2,3,1,6,7,4,8]=>[1,2,3,2]
[2,6,3,7,1,4,8,5]=>[8,3,5,1,2,6,4,7]=>[1,6,4,8,7,3,5,2]=>[2,2,1,2,1]
[2,6,3,8,1,4,7,5]=>[8,3,5,1,2,6,7,4]=>[1,6,4,8,7,3,2,5]=>[2,2,1,1,2]
[7,5,4,8,1,3,2,6]=>[7,5,3,2,6,1,8,4]=>[2,4,6,7,3,8,1,5]=>[4,2,2]
[8,6,5,1,3,4,2,7]=>[5,7,4,6,3,2,8,1]=>[4,2,5,3,6,7,1,8]=>[1,2,3,2]
[8,5,1,7,6,3,4,2]=>[6,2,8,7,5,3,4,1]=>[3,7,1,2,4,6,5,8]=>[2,4,2]
[3,4,7,6,1,8,5,2]=>[8,7,1,2,5,4,3,6]=>[1,2,8,7,4,5,6,3]=>[3,1,3,1]
[3,5,2,6,7,1,8,4]=>[4,1,2,8,3,6,5,7]=>[5,8,7,1,6,3,4,2]=>[2,1,2,2,1]
[3,2,8,4,7,5,1,6]=>[7,1,4,6,8,2,5,3]=>[2,8,5,3,1,7,4,6]=>[2,1,1,2,2]
[3,8,1,6,5,2,7,4]=>[8,6,1,5,3,4,7,2]=>[1,3,8,4,6,5,2,7]=>[3,2,1,2]
[6,1,2,8,3,4,7,5]=>[8,5,6,7,2,1,3,4]=>[1,4,3,2,7,8,6,5]=>[2,1,3,1,1]
[6,8,3,1,7,2,4,5]=>[6,3,7,1,8,4,5,2]=>[3,6,2,8,1,5,4,7]=>[2,2,2,2]
[3,7,2,5,6,1,8,4]=>[4,8,1,3,6,5,2,7]=>[5,1,8,6,3,4,7,2]=>[1,2,1,3,1]
[6,8,4,2,5,1,7,3]=>[8,4,3,1,6,5,7,2]=>[1,5,6,8,3,4,2,7]=>[4,2,2]
[2,7,5,3,8,4,1,6]=>[7,4,3,6,1,2,8,5]=>[2,5,6,3,8,7,1,4]=>[3,2,1,2]
[8,3,1,4,7,2,6,5]=>[2,8,4,6,7,3,5,1]=>[7,1,5,3,2,6,4,8]=>[1,2,1,2,2]
[8,3,2,1,5,7,4,6]=>[3,2,5,7,8,4,6,1]=>[6,7,4,2,1,5,3,8]=>[2,1,1,2,2]
[2,8,3,6,4,7,1,5]=>[5,7,3,4,8,1,6,2]=>[4,2,6,5,1,8,3,7]=>[1,2,1,2,2]
[7,3,6,4,8,1,2,5]=>[6,2,4,7,3,1,8,5]=>[3,7,5,2,6,8,1,4]=>[2,1,3,2]
[8,3,6,4,7,1,2,5]=>[6,2,4,7,3,8,5,1]=>[3,7,5,2,6,1,4,8]=>[2,1,2,3]
[1,2,8,3,5,7,4,6]=>[5,7,8,4,6,1,2,3]=>[4,2,1,5,3,8,7,6]=>[1,1,2,2,1,1]
[1,8,3,2,5,7,4,6]=>[3,5,7,8,4,6,1,2]=>[6,4,2,1,5,3,8,7]=>[1,1,1,2,2,1]
[6,5,1,7,4,2,8,3]=>[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>[6,1,1]
[7,3,6,4,8,2,1,5]=>[4,7,2,6,3,1,8,5]=>[5,2,7,3,6,8,1,4]=>[1,2,3,2]
[4,6,1,7,3,5,2,8]=>[1,5,7,6,3,2,4,8]=>[8,4,2,3,6,7,5,1]=>[1,1,4,1,1]
[5,6,1,7,3,4,2,8]=>[5,1,7,6,3,2,4,8]=>[4,8,2,3,6,7,5,1]=>[2,4,1,1]
[7,3,8,1,6,5,2,4]=>[7,8,2,6,4,1,5,3]=>[2,1,7,3,5,8,4,6]=>[1,2,3,2]
[5,1,7,4,2,8,6,3]=>[4,1,8,7,5,2,3,6]=>[5,8,1,2,4,7,6,3]=>[2,4,1,1]
[2,8,1,7,6,5,3,4]=>[7,8,6,5,1,3,4,2]=>[2,1,3,4,8,6,5,7]=>[1,4,1,2]
[4,2,8,6,5,1,7,3]=>[8,1,6,5,2,4,7,3]=>[1,8,3,4,7,5,2,6]=>[2,3,1,2]
[6,4,2,8,5,1,7,3]=>[2,8,6,3,1,5,7,4]=>[7,1,3,6,8,4,2,5]=>[1,4,1,2]
[8,6,4,7,1,5,2,3]=>[7,3,8,5,2,6,4,1]=>[2,6,1,4,7,3,5,8]=>[2,3,3]
[7,6,4,8,1,5,2,3]=>[7,3,8,5,2,1,6,4]=>[2,6,1,4,7,8,3,5]=>[2,4,2]
[5,1,6,4,2,3,8,7]=>[8,5,4,2,1,3,6,7]=>[1,4,5,7,8,6,3,2]=>[5,1,1,1]
[4,2,3,8,7,5,1,6]=>[1,7,6,8,2,3,5,4]=>[8,2,3,1,7,6,4,5]=>[1,2,2,1,2]
[3,8,7,1,6,5,2,4]=>[7,8,6,1,4,5,3,2]=>[2,1,3,8,5,4,6,7]=>[1,3,1,3]
[2,4,3,8,1,6,7,5]=>[2,6,8,1,3,5,7,4]=>[7,3,1,8,6,4,2,5]=>[1,1,2,1,1,2]
[2,4,3,7,1,6,8,5]=>[2,6,8,1,3,5,4,7]=>[7,3,1,8,6,4,5,2]=>[1,1,2,1,2,1]
[5,1,6,4,2,3,7,8]=>[5,6,4,2,1,3,7,8]=>[4,3,5,7,8,6,2,1]=>[1,4,1,1,1]
[6,4,7,8,1,5,2,3]=>[2,7,1,8,5,3,6,4]=>[7,2,8,1,4,6,3,5]=>[1,2,3,2]
[8,7,4,6,1,5,2,3]=>[7,3,8,5,6,4,2,1]=>[2,6,1,4,3,5,7,8]=>[2,2,4]
[6,5,7,8,1,4,2,3]=>[7,2,1,8,5,3,6,4]=>[2,7,8,1,4,6,3,5]=>[3,3,2]
[3,2,4,7,8,1,5,6]=>[1,6,7,2,3,4,8,5]=>[8,3,2,7,6,5,1,4]=>[1,1,2,1,1,2]
[3,2,4,8,7,1,5,6]=>[1,6,7,8,2,3,5,4]=>[8,3,2,1,7,6,4,5]=>[1,1,1,2,1,2]
[4,8,7,6,1,5,2,3]=>[7,8,1,5,6,4,3,2]=>[2,1,8,4,3,5,6,7]=>[1,2,1,4]
[5,8,7,6,1,4,2,3]=>[1,7,8,5,6,4,3,2]=>[8,2,1,4,3,5,6,7]=>[1,1,2,4]
[5,1,6,7,4,2,3,8]=>[6,3,1,7,5,2,4,8]=>[3,6,8,2,4,7,5,1]=>[3,3,1,1]
[6,7,4,8,1,5,2,3]=>[7,3,1,8,5,2,6,4]=>[2,6,8,1,4,7,3,5]=>[3,3,2]
[8,4,7,6,1,5,2,3]=>[2,7,8,5,6,4,3,1]=>[7,2,1,4,3,5,6,8]=>[1,1,2,4]
[8,3,2,4,7,1,5,6]=>[3,2,4,6,7,8,5,1]=>[6,7,5,3,2,1,4,8]=>[2,1,1,1,3]
[7,3,2,4,8,1,5,6]=>[3,2,4,6,7,1,8,5]=>[6,7,5,3,2,8,1,4]=>[2,1,1,2,2]
[2,5,3,7,1,6,4,8]=>[7,3,1,2,5,6,4,8]=>[2,6,8,7,4,3,5,1]=>[3,1,1,2,1]
[8,4,6,7,1,5,2,3]=>[2,7,8,5,3,6,4,1]=>[7,2,1,4,6,3,5,8]=>[1,1,3,3]
[5,1,6,8,4,2,3,7]=>[6,3,1,7,5,8,2,4]=>[3,6,8,2,4,1,7,5]=>[3,2,2,1]
[4,2,3,7,5,1,6,8]=>[6,2,1,3,5,7,4,8]=>[3,7,8,6,4,2,5,1]=>[3,1,1,2,1]
[3,7,5,8,1,6,2,4]=>[7,3,8,1,5,2,6,4]=>[2,6,1,8,4,7,3,5]=>[2,2,2,2]
[2,4,3,7,1,6,5,8]=>[2,7,1,3,5,6,4,8]=>[7,2,8,6,4,3,5,1]=>[1,2,1,1,2,1]
[2,4,7,1,5,8,6,3]=>[8,2,5,7,1,4,3,6]=>[1,7,4,2,8,5,6,3]=>[2,1,2,2,1]
[3,2,4,7,6,1,5,8]=>[1,6,7,2,3,5,4,8]=>[8,3,2,7,6,4,5,1]=>[1,1,2,1,2,1]
[4,7,6,8,1,5,2,3]=>[7,8,1,5,3,2,6,4]=>[2,1,8,4,6,7,3,5]=>[1,2,3,2]
[8,5,6,7,1,4,2,3]=>[7,2,8,5,3,6,4,1]=>[2,7,1,4,6,3,5,8]=>[2,3,3]
[8,6,7,5,1,4,2,3]=>[7,8,5,2,6,4,3,1]=>[2,1,4,7,3,5,6,8]=>[1,3,4]
[7,6,8,5,1,4,2,3]=>[7,8,5,2,1,6,4,3]=>[2,1,4,7,8,3,5,6]=>[1,4,3]
[5,6,8,7,1,4,2,3]=>[1,7,2,8,5,6,4,3]=>[8,2,7,1,4,3,5,6]=>[1,2,2,3]
[4,6,8,7,1,5,2,3]=>[7,1,2,8,5,6,4,3]=>[2,8,7,1,4,3,5,6]=>[2,1,2,3]
[2,4,6,7,1,5,8,3]=>[6,2,3,8,1,5,4,7]=>[3,7,6,1,8,4,5,2]=>[2,1,2,2,1]
[3,2,4,6,1,5,7,8]=>[2,1,3,5,6,4,7,8]=>[7,8,6,4,3,5,2,1]=>[2,1,1,2,1,1]
[7,8,6,5,1,4,2,3]=>[7,8,5,1,6,4,3,2]=>[2,1,4,8,3,5,6,7]=>[1,3,4]
[3,1,7,5,4,2,8,6]=>[5,1,4,8,6,2,3,7]=>[4,8,5,1,3,7,6,2]=>[2,1,3,1,1]
[2,1,8,5,4,6,3,7]=>[5,4,7,1,6,8,2,3]=>[4,5,2,8,3,1,7,6]=>[2,2,1,2,1]
[5,4,1,3,6,7,2,8]=>[4,5,2,1,7,3,6,8]=>[5,4,7,8,2,6,3,1]=>[1,3,2,1,1]
[8,2,7,1,5,3,4,6]=>[6,7,2,4,5,8,3,1]=>[3,2,7,5,4,1,6,8]=>[1,2,1,1,3]
[3,2,7,1,5,8,4,6]=>[1,5,7,8,2,4,3,6]=>[8,4,2,1,7,5,6,3]=>[1,1,1,2,2,1]
[6,3,7,1,5,4,2,8]=>[7,2,6,4,1,5,3,8]=>[2,7,3,5,8,4,6,1]=>[2,3,2,1]
[7,3,8,1,5,4,2,6]=>[7,2,6,4,5,1,8,3]=>[2,7,3,5,4,8,1,6]=>[2,2,2,2]
[7,1,5,3,8,4,2,6]=>[7,4,3,6,8,2,1,5]=>[2,5,6,3,1,7,8,4]=>[3,1,3,1]
[4,5,1,3,6,8,2,7]=>[4,1,5,2,7,8,3,6]=>[5,8,4,7,2,1,6,3]=>[2,2,1,2,1]
[3,6,8,1,5,4,2,7]=>[7,6,1,4,2,5,8,3]=>[2,3,8,5,7,4,1,6]=>[3,2,1,2]
[6,8,3,1,5,4,2,7]=>[3,7,6,4,1,5,8,2]=>[6,2,3,5,8,4,1,7]=>[1,4,1,2]
[7,6,3,1,5,4,2,8]=>[3,7,6,4,5,2,1,8]=>[6,2,3,5,4,7,8,1]=>[1,3,3,1]
[3,6,2,1,5,8,4,7]=>[1,3,5,7,2,8,4,6]=>[8,6,4,2,7,1,5,3]=>[1,1,1,2,2,1]
[8,6,2,1,5,3,4,7]=>[3,6,7,4,5,2,8,1]=>[6,3,2,5,4,7,1,8]=>[1,1,2,2,2]
[4,8,2,1,7,5,3,6]=>[1,7,3,6,8,4,5,2]=>[8,2,6,3,1,5,4,7]=>[1,2,1,2,2]
[2,3,8,1,5,7,4,6]=>[5,7,8,1,2,4,6,3]=>[4,2,1,8,7,5,3,6]=>[1,1,2,1,1,2]
[7,1,3,2,8,6,4,5]=>[7,8,3,6,2,4,1,5]=>[2,1,6,3,7,5,8,4]=>[1,2,2,2,1]
[7,1,6,2,8,3,4,5]=>[6,7,8,4,2,3,1,5]=>[3,2,1,5,7,6,8,4]=>[1,1,3,2,1]
[4,7,1,2,6,3,8,5]=>[1,8,6,3,4,5,2,7]=>[8,1,3,6,5,4,7,2]=>[1,3,1,2,1]
[2,7,8,1,5,3,4,6]=>[6,7,4,5,1,2,8,3]=>[3,2,5,4,8,7,1,6]=>[1,2,2,1,2]
[6,7,2,1,5,3,4,8]=>[3,6,7,4,1,5,2,8]=>[6,3,2,5,8,4,7,1]=>[1,1,3,2,1]
[4,7,2,1,8,5,3,6]=>[1,7,3,6,8,4,2,5]=>[8,2,6,3,1,5,7,4]=>[1,2,1,3,1]
[8,7,2,1,4,5,3,6]=>[3,5,7,4,6,8,2,1]=>[6,4,2,5,3,1,7,8]=>[1,1,2,1,3]
[8,7,5,6,1,4,3,2]=>[8,7,5,3,6,4,2,1]=>[1,2,4,6,3,5,7,8]=>[4,4]
[5,7,8,6,1,4,3,2]=>[8,1,7,5,2,6,4,3]=>[1,8,2,4,7,3,5,6]=>[2,3,3]
[2,7,4,1,6,5,3,8]=>[3,7,6,1,4,5,2,8]=>[6,2,3,8,5,4,7,1]=>[1,3,1,2,1]
[3,7,1,4,5,6,8,2]=>[1,4,5,6,8,3,2,7]=>[8,5,4,3,1,6,7,2]=>[1,1,1,1,3,1]
[7,1,6,4,5,8,3,2]=>[4,5,3,8,7,2,1,6]=>[5,4,6,1,2,7,8,3]=>[1,2,4,1]
[2,6,4,1,7,5,3,8]=>[3,7,6,1,4,2,5,8]=>[6,2,3,8,5,7,4,1]=>[1,3,2,1,1]
[5,6,8,7,1,4,3,2]=>[1,2,8,7,5,6,4,3]=>[8,7,1,2,4,3,5,6]=>[1,1,3,3]
[6,8,5,7,1,4,3,2]=>[1,8,7,5,3,6,4,2]=>[8,1,2,4,6,3,5,7]=>[1,4,3]
[8,6,5,7,1,4,3,2]=>[8,7,5,3,2,6,4,1]=>[1,2,4,6,7,3,5,8]=>[5,3]
[8,5,7,6,1,4,3,2]=>[2,8,7,5,6,4,3,1]=>[7,1,2,4,3,5,6,8]=>[1,3,4]
[6,5,7,8,1,4,3,2]=>[2,1,8,7,5,3,6,4]=>[7,8,1,2,4,6,3,5]=>[2,4,2]
[7,2,3,1,5,6,4,8]=>[2,3,5,7,4,6,1,8]=>[7,6,4,2,5,3,8,1]=>[1,1,1,2,2,1]
[4,2,8,1,6,5,3,7]=>[1,7,6,2,4,5,8,3]=>[8,2,3,7,5,4,1,6]=>[1,3,1,1,2]
[6,2,4,1,8,5,3,7]=>[3,7,2,6,1,8,4,5]=>[6,2,7,3,8,1,5,4]=>[1,2,2,2,1]
[8,3,1,4,5,6,7,2]=>[4,2,5,6,8,3,7,1]=>[5,7,4,3,1,6,2,8]=>[2,1,1,2,2]
[5,3,1,4,8,6,7,2]=>[2,6,1,8,4,7,3,5]=>[7,3,8,1,5,2,6,4]=>[1,2,2,2,1]
[7,5,1,6,3,4,8,2]=>[5,6,4,2,8,3,1,7]=>[4,3,5,7,1,6,8,2]=>[1,3,3,1]
[7,1,5,8,4,3,6,2]=>[3,6,5,8,7,2,1,4]=>[6,3,4,1,2,7,8,5]=>[1,2,4,1]
[5,8,1,6,4,3,7,2]=>[1,6,5,4,8,3,7,2]=>[8,3,4,5,1,6,2,7]=>[1,3,2,2]
[5,3,1,8,4,6,7,2]=>[2,5,1,6,8,7,3,4]=>[7,4,8,3,1,2,6,5]=>[1,2,1,3,1]
[8,2,6,1,4,5,3,7]=>[5,7,2,4,6,3,8,1]=>[4,2,7,5,3,6,1,8]=>[1,2,1,2,2]
[6,2,8,1,4,5,3,7]=>[5,7,2,4,1,6,8,3]=>[4,2,7,5,8,3,1,6]=>[1,2,2,1,2]
[2,8,6,1,5,3,4,7]=>[6,7,4,5,1,3,8,2]=>[3,2,5,4,8,6,1,7]=>[1,2,2,1,2]
[4,2,1,5,6,3,8,7]=>[2,4,1,5,8,3,6,7]=>[7,5,8,4,1,6,3,2]=>[1,2,1,2,1,1]
[7,1,2,5,8,3,4,6]=>[6,4,7,8,2,3,1,5]=>[3,5,2,1,7,6,8,4]=>[2,1,2,2,1]
[7,1,4,5,6,8,3,2]=>[3,4,5,8,7,2,1,6]=>[6,5,4,1,2,7,8,3]=>[1,1,1,4,1]
[8,5,6,7,1,4,3,2]=>[2,8,7,5,3,6,4,1]=>[7,1,2,4,6,3,5,8]=>[1,4,3]
[7,6,8,5,1,4,3,2]=>[8,7,5,2,1,6,4,3]=>[1,2,4,7,8,3,5,6]=>[5,3]
[6,8,7,5,1,4,3,2]=>[1,8,7,5,6,4,3,2]=>[8,1,2,4,3,5,6,7]=>[1,3,4]
[2,6,7,1,4,5,3,8]=>[5,7,4,1,2,6,3,8]=>[4,2,5,8,7,3,6,1]=>[1,3,1,2,1]
[3,5,1,7,4,6,8,2]=>[5,1,2,6,4,8,3,7]=>[4,8,7,3,5,1,6,2]=>[2,1,2,2,1]
[7,1,5,6,4,8,3,2]=>[3,5,4,8,7,2,1,6]=>[6,4,5,1,2,7,8,3]=>[1,2,4,1]
[7,1,6,5,4,8,3,2]=>[5,4,3,8,7,2,1,6]=>[4,5,6,1,2,7,8,3]=>[3,4,1]
[2,7,6,1,4,5,3,8]=>[5,7,4,6,1,3,2,8]=>[4,2,5,3,8,6,7,1]=>[1,2,2,2,1]
[5,7,6,8,1,4,3,2]=>[8,1,7,5,3,2,6,4]=>[1,8,2,4,6,7,3,5]=>[2,4,2]
[7,8,6,5,1,4,3,2]=>[8,7,5,1,6,4,3,2]=>[1,2,4,8,3,5,6,7]=>[4,4]
[4,3,1,6,5,8,7,2]=>[2,1,4,8,5,7,3,6]=>[7,8,5,1,4,2,6,3]=>[2,1,2,2,1]
[5,3,1,2,4,8,7,6]=>[2,8,7,3,1,4,5,6]=>[7,1,2,6,8,5,4,3]=>[1,4,1,1,1]
[5,3,7,2,1,4,6,8]=>[2,5,4,1,6,7,3,8]=>[7,4,5,8,3,2,6,1]=>[1,3,1,2,1]
[5,3,7,2,8,4,1,6]=>[7,2,1,4,6,3,8,5]=>[2,7,8,5,3,6,1,4]=>[3,1,2,2]
[7,2,4,5,1,3,6,8]=>[5,2,3,6,4,7,1,8]=>[4,7,6,3,5,2,8,1]=>[2,1,2,2,1]
[3,1,4,5,2,8,7,6]=>[1,8,3,4,7,2,5,6]=>[8,1,6,5,2,7,4,3]=>[1,2,1,2,1,1]
[1,6,4,5,2,8,7,3]=>[3,4,2,8,7,1,5,6]=>[6,5,7,1,2,8,4,3]=>[1,2,3,1,1]
[3,7,4,5,8,2,1,6]=>[3,4,7,1,6,2,8,5]=>[6,5,2,8,3,7,1,4]=>[1,1,2,2,2]
[1,7,4,2,6,3,5,8]=>[6,3,7,4,5,1,2,8]=>[3,6,2,5,4,8,7,1]=>[2,2,2,1,1]
[8,7,4,5,2,1,6,3]=>[5,3,8,6,4,7,2,1]=>[4,6,1,3,5,2,7,8]=>[2,3,3]
[6,3,7,1,8,4,2,5]=>[7,2,6,1,8,4,3,5]=>[2,7,3,8,1,5,6,4]=>[2,2,3,1]
[5,7,4,1,6,3,2,8]=>[1,7,6,4,3,5,2,8]=>[8,2,3,5,6,4,7,1]=>[1,4,2,1]
[1,7,4,8,6,3,2,5]=>[7,3,6,2,8,5,1,4]=>[2,6,3,7,1,4,8,5]=>[2,2,3,1]
[5,7,4,8,6,3,1,2]=>[1,3,7,2,8,6,5,4]=>[8,6,2,7,1,3,4,5]=>[1,1,2,4]
[4,8,3,5,6,7,1,2]=>[1,3,4,7,5,8,6,2]=>[8,6,5,2,4,1,3,7]=>[1,1,1,2,3]
[1,8,3,5,6,7,2,4]=>[4,7,3,5,8,6,1,2]=>[5,2,6,4,1,3,8,7]=>[1,2,1,3,1]
[4,8,1,5,6,7,2,3]=>[1,4,7,5,8,3,6,2]=>[8,5,2,4,1,6,3,7]=>[1,1,2,2,2]
[4,1,3,5,6,7,2,8]=>[3,4,1,5,7,2,6,8]=>[6,5,8,4,2,7,3,1]=>[1,2,1,2,1,1]
[5,8,4,3,6,1,2,7]=>[1,6,4,3,7,5,8,2]=>[8,3,5,6,2,4,1,7]=>[1,3,2,2]
[1,5,8,4,6,7,3,2]=>[2,4,5,8,7,6,1,3]=>[7,5,4,1,2,3,8,6]=>[1,1,1,4,1]
[1,4,8,3,6,7,5,2]=>[5,8,2,4,7,6,1,3]=>[4,1,7,5,2,3,8,6]=>[1,2,1,3,1]
[4,3,8,2,1,7,5,6]=>[2,1,4,7,8,5,6,3]=>[7,8,5,2,1,4,3,6]=>[2,1,1,2,2]
[3,8,4,2,6,1,5,7]=>[4,1,3,6,7,5,8,2]=>[5,8,6,3,2,4,1,7]=>[2,1,1,2,2]
[1,8,2,5,6,7,4,3]=>[4,5,8,7,3,6,1,2]=>[5,4,1,2,6,3,8,7]=>[1,1,3,2,1]
[3,8,1,5,6,7,4,2]=>[4,5,8,1,7,3,6,2]=>[5,4,1,8,2,6,3,7]=>[1,1,2,2,2]
[3,8,2,5,6,7,1,4]=>[4,7,1,3,5,8,6,2]=>[5,2,8,6,4,1,3,7]=>[1,2,1,1,3]
[8,2,1,5,6,7,4,3]=>[4,5,8,2,7,3,6,1]=>[5,4,1,7,2,6,3,8]=>[1,1,2,2,2]
[8,1,3,5,6,7,4,2]=>[4,5,8,3,7,2,6,1]=>[5,4,1,6,2,7,3,8]=>[1,1,2,2,2]
[7,8,4,3,6,2,1,5]=>[4,3,7,6,1,8,5,2]=>[5,6,2,3,8,1,4,7]=>[2,3,3]
[4,3,1,8,5,7,6,2]=>[1,8,2,5,7,6,3,4]=>[8,1,7,4,2,3,6,5]=>[1,2,1,3,1]
[4,3,1,6,8,7,5,2]=>[1,8,2,4,7,6,3,5]=>[8,1,7,5,2,3,6,4]=>[1,2,1,3,1]
[6,3,5,8,2,7,1,4]=>[5,2,3,1,7,8,6,4]=>[4,7,6,8,2,1,3,5]=>[2,2,1,3]
[7,5,4,8,6,2,1,3]=>[3,2,7,6,1,8,5,4]=>[6,7,2,3,8,1,4,5]=>[2,3,3]
[7,1,4,8,6,2,3,5]=>[3,6,7,8,5,2,1,4]=>[6,3,2,1,4,7,8,5]=>[1,1,1,4,1]
[7,5,4,1,6,2,3,8]=>[6,7,4,3,2,5,1,8]=>[3,2,5,6,7,4,8,1]=>[1,4,2,1]
[7,6,4,5,8,1,3,2]=>[3,8,6,4,2,1,7,5]=>[6,1,3,5,7,8,2,4]=>[1,5,2]
[1,6,4,5,8,2,3,7]=>[3,6,4,2,7,8,1,5]=>[6,3,5,7,2,1,8,4]=>[1,3,1,2,1]
[1,7,6,5,8,3,4,2]=>[6,4,3,2,8,7,1,5]=>[3,5,6,7,1,2,8,4]=>[4,3,1]
[1,8,5,3,6,7,4,2]=>[5,3,8,4,7,6,1,2]=>[4,6,1,5,2,3,8,7]=>[2,2,3,1]
[8,3,5,2,1,7,4,6]=>[2,4,7,3,8,5,6,1]=>[7,5,2,6,1,4,3,8]=>[1,1,2,2,2]
[8,4,1,5,6,7,3,2]=>[4,2,5,8,7,3,6,1]=>[5,7,4,1,2,6,3,8]=>[2,1,3,2]
[8,4,2,5,6,7,1,3]=>[4,2,7,3,5,8,6,1]=>[5,7,2,6,4,1,3,8]=>[2,2,1,3]
[4,1,8,5,6,7,3,2]=>[1,4,5,8,7,6,2,3]=>[8,5,4,1,2,3,7,6]=>[1,1,1,4,1]
[1,2,8,5,6,7,3,4]=>[4,7,5,8,6,1,2,3]=>[5,2,4,1,3,8,7,6]=>[1,2,3,1,1]
[4,2,1,5,6,7,3,8]=>[2,4,1,5,7,3,6,8]=>[7,5,8,4,2,6,3,1]=>[1,2,1,2,1,1]
[1,5,3,8,6,7,4,2]=>[2,5,8,7,3,6,1,4]=>[7,4,1,2,6,3,8,5]=>[1,1,3,2,1]
[1,4,5,8,6,7,3,2]=>[5,8,2,3,7,6,1,4]=>[4,1,7,6,2,3,8,5]=>[1,2,1,3,1]
[4,3,5,8,1,7,2,6]=>[2,1,3,7,8,5,6,4]=>[7,8,6,2,1,4,3,5]=>[2,1,1,2,2]
[3,5,4,8,6,1,2,7]=>[3,1,2,6,7,5,8,4]=>[6,8,7,3,2,4,1,5]=>[2,1,1,2,2]
[1,4,8,5,6,7,2,3]=>[4,7,2,5,8,6,1,3]=>[5,2,7,4,1,3,8,6]=>[1,2,1,3,1]
[2,7,1,5,6,3,4,8]=>[6,4,7,1,3,5,2,8]=>[3,5,2,8,6,4,7,1]=>[2,2,1,2,1]
[4,3,7,2,5,6,8,1]=>[2,1,4,5,6,3,8,7]=>[7,8,5,4,3,6,1,2]=>[2,1,1,2,2]
[2,6,3,1,4,5,8,7]=>[3,8,1,4,5,2,6,7]=>[6,1,8,5,4,7,3,2]=>[1,2,1,2,1,1]
[3,7,1,4,2,6,8,5]=>[1,4,6,8,3,5,2,7]=>[8,5,3,1,6,4,7,2]=>[1,1,1,2,2,1]
[3,7,1,5,6,2,8,4]=>[4,8,1,6,3,5,2,7]=>[5,1,8,3,6,4,7,2]=>[1,2,2,2,1]
[4,7,1,5,6,8,2,3]=>[1,4,7,5,8,3,2,6]=>[8,5,2,4,1,6,7,3]=>[1,1,2,3,1]
[8,4,2,6,3,7,1,5]=>[5,2,7,3,4,8,6,1]=>[4,7,2,6,5,1,3,8]=>[2,2,1,3]
[8,4,2,3,5,7,1,6]=>[3,4,2,5,7,8,6,1]=>[6,5,7,4,2,1,3,8]=>[1,2,1,1,3]
[4,7,3,2,5,6,1,8]=>[1,4,3,5,7,6,2,8]=>[8,5,6,4,2,3,7,1]=>[1,2,1,3,1]
[5,3,4,6,2,8,1,7]=>[2,3,1,5,4,7,8,6]=>[7,6,8,4,5,2,1,3]=>[1,2,2,1,2]
[6,4,7,2,3,8,1,5]=>[4,2,5,1,7,3,8,6]=>[5,7,4,8,2,6,1,3]=>[2,2,2,2]
[6,5,7,2,8,3,1,4]=>[7,4,2,1,6,3,8,5]=>[2,5,7,8,3,6,1,4]=>[4,2,2]
[5,3,7,2,4,8,6,1]=>[8,2,1,4,5,3,7,6]=>[1,7,8,5,4,6,2,3]=>[3,1,2,2]
[2,6,5,1,8,3,4,7]=>[6,7,3,1,2,8,4,5]=>[3,2,6,8,7,1,5,4]=>[1,3,1,2,1]
[8,7,6,1,4,5,2,3]=>[7,5,8,4,6,3,2,1]=>[2,4,1,5,3,6,7,8]=>[2,2,4]
[8,7,6,1,3,2,5,4]=>[5,8,4,6,7,3,2,1]=>[4,1,5,3,2,6,7,8]=>[1,2,1,4]
[8,7,4,5,1,6,2,3]=>[7,3,8,5,4,6,2,1]=>[2,6,1,4,5,3,7,8]=>[2,3,3]
[8,5,6,4,1,7,2,3]=>[7,2,8,5,4,3,6,1]=>[2,7,1,4,5,6,3,8]=>[2,4,2]
[8,4,6,2,3,1,7,5]=>[4,2,5,8,6,3,7,1]=>[5,7,4,1,3,6,2,8]=>[2,1,3,2]
[5,7,3,4,2,1,8,6]=>[3,1,5,4,8,6,2,7]=>[6,8,4,5,1,3,7,2]=>[2,2,3,1]
[6,7,4,2,3,1,8,5]=>[4,5,3,1,8,6,2,7]=>[5,4,6,8,1,3,7,2]=>[1,3,3,1]
[6,7,5,3,1,2,8,4]=>[8,5,4,1,6,3,2,7]=>[1,4,5,8,3,6,7,2]=>[4,3,1]
[6,7,5,4,1,8,2,3]=>[7,1,8,5,4,3,2,6]=>[2,8,1,4,5,6,7,3]=>[2,5,1]
[10,3,1,2,4,5,6,7,8,9]=>[3,4,2,5,6,7,8,9,10,1]=>[8,7,9,6,5,4,3,2,1,10]=>[1,2,1,1,1,1,1,2]
[10,4,1,2,3,5,6,7,8,9]=>[3,4,5,2,6,7,8,9,10,1]=>[8,7,6,9,5,4,3,2,1,10]=>[1,1,2,1,1,1,1,2]
[5,10,1,2,3,4,6,7,8,9]=>[3,4,5,1,6,7,8,9,10,2]=>[8,7,6,10,5,4,3,2,1,9]=>[1,1,2,1,1,1,1,2]
[10,6,1,2,3,4,5,7,8,9]=>[3,4,5,6,7,2,8,9,10,1]=>[8,7,6,5,4,9,3,2,1,10]=>[1,1,1,1,2,1,1,2]
[10,7,1,2,3,4,5,6,8,9]=>[3,4,5,6,7,8,2,9,10,1]=>[8,7,6,5,4,3,9,2,1,10]=>[1,1,1,1,1,2,1,2]
[8,10,1,2,3,4,5,6,7,9]=>[3,4,5,6,7,8,1,9,10,2]=>[8,7,6,5,4,3,10,2,1,9]=>[1,1,1,1,1,2,1,2]
[2,11,1,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,1,1,1,1,1,1,1,1,2]
[2,3,10,1,4,5,6,7,8,9]=>[1,2,4,5,6,7,8,9,10,3]=>[10,9,7,6,5,4,3,2,1,8]=>[1,1,1,1,1,1,1,1,2]
[11,3,1,2,4,5,6,7,8,9,10]=>[3,4,2,5,6,7,8,9,10,11,1]=>[9,8,10,7,6,5,4,3,2,1,11]=>[1,2,1,1,1,1,1,1,2]
[11,4,1,2,3,5,6,7,8,9,10]=>[3,4,5,2,6,7,8,9,10,11,1]=>[9,8,7,10,6,5,4,3,2,1,11]=>[1,1,2,1,1,1,1,1,2]
[11,6,1,2,3,4,5,7,8,9,10]=>[3,4,5,6,7,2,8,9,10,11,1]=>[9,8,7,6,5,10,4,3,2,1,11]=>[1,1,1,1,2,1,1,1,2]
[11,7,1,2,3,4,5,6,8,9,10]=>[3,4,5,6,7,8,2,9,10,11,1]=>[9,8,7,6,5,4,10,3,2,1,11]=>[1,1,1,1,1,2,1,1,2]
[11,9,1,2,3,4,5,6,7,8,10]=>[3,4,5,6,7,8,9,10,2,11,1]=>[9,8,7,6,5,4,3,2,10,1,11]=>[1,1,1,1,1,1,1,2,2]
[6,2,4,3,8,7,5,1]=>[8,3,7,2,1,4,6,5]=>[1,6,2,7,8,5,3,4]=>[2,3,1,2]
[7,3,5,4,1,8,6,2]=>[4,2,3,8,7,5,1,6]=>[5,7,6,1,2,4,8,3]=>[2,1,4,1]
[5,2,7,1,3,4,8,6]=>[8,2,4,1,5,6,3,7]=>[1,7,5,8,4,3,6,2]=>[2,2,1,2,1]
[2,6,5,7,3,1,4,8]=>[6,5,3,1,2,7,4,8]=>[3,4,6,8,7,2,5,1]=>[4,1,2,1]
[2,6,5,7,3,1,8,4]=>[5,3,2,8,1,6,4,7]=>[4,6,7,1,8,3,5,2]=>[3,2,2,1]
[6,3,1,4,7,8,5,2]=>[2,5,8,4,1,7,3,6]=>[7,4,1,5,8,2,6,3]=>[1,1,3,2,1]
[6,8,2,1,3,4,5,7]=>[4,3,5,6,1,7,8,2]=>[5,6,4,3,8,2,1,7]=>[2,1,2,1,2]
[3,7,1,8,4,5,2,6]=>[5,7,1,6,8,3,2,4]=>[4,2,8,3,1,6,7,5]=>[1,2,1,3,1]
[6,3,2,4,7,5,1,8]=>[2,7,3,4,1,6,5,8]=>[7,2,6,5,8,3,4,1]=>[1,2,2,2,1]
[4,2,1,6,3,7,8,5]=>[6,2,1,4,8,3,5,7]=>[3,7,8,5,1,6,4,2]=>[3,1,2,1,1]
[7,4,3,5,8,6,1,2]=>[3,2,4,7,1,8,6,5]=>[6,7,5,2,8,1,3,4]=>[2,1,2,3]
[2,7,6,8,3,1,4,5]=>[6,5,7,3,1,2,8,4]=>[3,4,2,6,8,7,1,5]=>[2,3,1,2]
[4,2,1,7,3,8,6,5]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[1,3,2,1,1]
[4,2,1,3,7,8,6,5]=>[5,1,8,2,7,3,4,6]=>[4,8,1,7,2,6,5,3]=>[2,2,2,1,1]
[5,8,1,7,4,3,6,2]=>[1,6,5,8,7,3,4,2]=>[8,3,4,1,2,6,5,7]=>[1,2,3,2]
[5,8,1,7,4,3,2,6]=>[1,7,6,5,8,3,4,2]=>[8,2,3,4,1,6,5,7]=>[1,3,2,2]
[3,7,8,6,2,1,4,5]=>[6,5,7,1,2,8,4,3]=>[3,4,2,8,7,1,5,6]=>[2,2,1,3]
[4,2,1,8,3,5,6,7]=>[2,5,1,6,7,8,3,4]=>[7,4,8,3,2,1,6,5]=>[1,2,1,1,2,1]
[4,2,1,3,6,7,5,8]=>[2,5,1,7,3,4,6,8]=>[7,4,8,2,6,5,3,1]=>[1,2,2,1,1,1]
[4,2,1,3,7,5,6,8]=>[2,6,1,7,3,4,5,8]=>[7,3,8,2,6,5,4,1]=>[1,2,2,1,1,1]
[4,2,1,3,6,8,7,5]=>[8,2,1,5,7,3,4,6]=>[1,7,8,4,2,6,5,3]=>[3,1,2,1,1]
[7,3,2,4,8,6,5,1]=>[8,2,7,3,4,1,6,5]=>[1,7,2,6,5,8,3,4]=>[2,2,2,2]
[4,2,1,6,3,8,7,5]=>[4,1,8,2,7,3,5,6]=>[5,8,1,7,2,6,4,3]=>[2,2,2,1,1]
[4,2,1,7,3,5,6,8]=>[2,5,1,6,7,3,4,8]=>[7,4,8,3,2,6,5,1]=>[1,2,1,2,1,1]
[3,6,7,5,2,1,8,4]=>[5,2,8,1,6,4,3,7]=>[4,7,1,8,3,5,6,2]=>[2,2,3,1]
[7,3,4,2,6,8,5,1]=>[2,3,5,8,4,1,7,6]=>[7,6,4,1,5,8,2,3]=>[1,1,1,3,2]
[4,8,6,2,7,3,5,1]=>[6,8,1,4,3,7,5,2]=>[3,1,8,5,6,2,4,7]=>[1,2,2,3]
[7,3,4,2,6,8,1,5]=>[2,3,7,4,5,1,8,6]=>[7,6,2,5,4,8,1,3]=>[1,1,2,2,2]
[3,6,7,5,2,4,8,1]=>[5,2,6,1,4,3,8,7]=>[4,7,3,8,5,6,1,2]=>[2,2,2,2]
[3,6,7,5,2,4,1,8]=>[5,2,7,1,6,4,3,8]=>[4,7,2,8,3,5,6,1]=>[2,2,3,1]
[4,2,1,7,3,6,5,8]=>[7,2,1,5,6,3,4,8]=>[2,7,8,4,3,6,5,1]=>[3,1,2,1,1]
[4,2,1,7,3,6,8,5]=>[6,1,8,2,5,3,4,7]=>[3,8,1,7,4,6,5,2]=>[2,2,2,1,1]
[3,7,6,8,4,2,5,1]=>[6,5,3,1,2,8,7,4]=>[3,4,6,8,7,1,2,5]=>[4,1,3]
[5,8,1,7,4,2,6,3]=>[1,8,6,5,7,3,4,2]=>[8,1,3,4,2,6,5,7]=>[1,3,2,2]
[3,7,8,6,2,4,5,1]=>[5,6,2,8,1,7,4,3]=>[4,3,7,1,8,2,5,6]=>[1,2,2,3]
[4,2,1,3,8,6,7,5]=>[6,1,8,2,7,3,4,5]=>[3,8,1,7,2,6,5,4]=>[2,2,2,1,1]
[4,2,1,3,7,6,5,8]=>[7,2,1,6,3,4,5,8]=>[2,7,8,3,6,5,4,1]=>[3,2,1,1,1]
[4,2,1,3,5,7,6,8]=>[2,7,3,1,4,5,6,8]=>[7,2,6,8,5,4,3,1]=>[1,3,1,1,1,1]
[4,2,1,3,5,8,6,7]=>[2,7,1,8,3,4,5,6]=>[7,2,8,1,6,5,4,3]=>[1,2,2,1,1,1]
[4,8,1,7,3,6,5,2]=>[8,1,5,7,6,3,4,2]=>[1,8,4,2,3,6,5,7]=>[2,1,3,2]
[4,7,8,6,3,5,2,1]=>[5,2,8,1,7,6,4,3]=>[4,7,1,8,2,3,5,6]=>[2,2,4]
[4,2,1,8,3,7,6,5]=>[1,8,7,2,5,6,3,4]=>[8,1,2,7,4,3,6,5]=>[1,3,1,2,1]
[4,2,1,3,5,6,8,7]=>[2,8,3,1,4,5,6,7]=>[7,1,6,8,5,4,3,2]=>[1,3,1,1,1,1]
[4,6,3,5,8,7,1,2]=>[1,3,4,2,7,8,6,5]=>[8,6,5,7,2,1,3,4]=>[1,1,2,1,3]
[2,3,6,8,4,1,5,7]=>[6,5,1,2,3,7,8,4]=>[3,4,8,7,6,2,1,5]=>[3,1,1,1,2]
[4,7,5,2,1,3,6,8]=>[1,5,4,6,3,7,2,8]=>[8,4,5,3,6,2,7,1]=>[1,2,2,2,1]
[3,5,6,2,4,1,7,8]=>[4,1,2,6,5,3,7,8]=>[5,8,7,3,4,6,2,1]=>[2,1,3,1,1]
[2,5,6,1,4,8,3,7]=>[5,2,7,1,3,8,4,6]=>[4,7,2,8,6,1,5,3]=>[2,2,1,2,1]
[7,1,6,8,4,5,3,2]=>[5,3,8,7,6,2,1,4]=>[4,6,1,2,3,7,8,5]=>[2,5,1]
[7,4,6,5,2,8,1,3]=>[2,5,7,4,3,1,8,6]=>[7,4,2,5,6,8,1,3]=>[1,1,4,2]
[7,1,5,6,4,2,3,8]=>[6,3,7,5,2,4,1,8]=>[3,6,2,4,7,5,8,1]=>[2,3,2,1]
[5,7,4,6,8,1,3,2]=>[1,3,8,6,4,2,7,5]=>[8,6,1,3,5,7,2,4]=>[1,1,4,2]
[5,7,8,1,4,6,3,2]=>[1,5,8,7,4,2,6,3]=>[8,4,1,2,5,7,3,6]=>[1,1,4,2]
[1,8,4,6,7,5,3,2]=>[4,8,3,7,6,5,1,2]=>[5,1,6,2,3,4,8,7]=>[1,2,4,1]
[6,1,8,4,7,5,3,2]=>[8,4,1,7,6,5,2,3]=>[1,5,8,2,3,4,7,6]=>[3,4,1]
[4,5,8,6,1,7,3,2]=>[8,1,2,7,5,4,6,3]=>[1,8,7,2,4,5,3,6]=>[2,1,3,2]
[4,8,5,1,6,7,3,2]=>[5,1,3,8,7,4,6,2]=>[4,8,6,1,2,5,3,7]=>[2,1,3,2]
[8,1,4,5,6,7,3,2]=>[3,4,5,8,7,2,6,1]=>[6,5,4,1,2,7,3,8]=>[1,1,1,3,2]
[5,6,7,1,4,2,3,8]=>[6,1,7,4,2,5,3,8]=>[3,8,2,5,7,4,6,1]=>[2,3,2,1]
[8,4,2,6,1,5,7,3]=>[6,2,8,3,5,4,7,1]=>[3,7,1,6,4,5,2,8]=>[2,2,2,2]
[4,8,5,2,1,6,7,3]=>[1,4,6,3,8,5,7,2]=>[8,5,3,6,1,4,2,7]=>[1,1,2,2,2]
[5,1,8,4,2,6,3,7]=>[7,5,4,1,6,8,2,3]=>[2,4,5,8,3,1,7,6]=>[4,1,2,1]
[1,8,4,6,2,5,3,7]=>[3,7,5,6,4,8,1,2]=>[6,2,4,3,5,1,8,7]=>[1,2,2,2,1]
[6,1,5,2,3,4,7,8]=>[4,5,6,2,3,1,7,8]=>[5,4,3,7,6,8,2,1]=>[1,1,2,2,1,1]
[8,3,1,4,6,2,5,7]=>[4,2,6,7,3,5,8,1]=>[5,7,3,2,6,4,1,8]=>[2,1,2,1,2]
[3,5,1,8,2,6,4,7]=>[7,1,5,2,6,8,3,4]=>[2,8,4,7,3,1,6,5]=>[2,2,1,2,1]
[3,5,1,2,8,4,7,6]=>[8,1,6,2,7,3,4,5]=>[1,8,3,7,2,6,5,4]=>[2,2,2,1,1]
[2,3,5,8,6,1,7,4]=>[8,3,6,1,2,5,7,4]=>[1,6,3,8,7,4,2,5]=>[2,2,1,1,2]
[8,2,4,3,6,7,1,5]=>[3,7,2,4,5,8,6,1]=>[6,2,7,5,4,1,3,8]=>[1,2,1,1,3]
[3,2,8,5,7,1,6,4]=>[4,8,1,6,7,2,5,3]=>[5,1,8,3,2,7,4,6]=>[1,2,1,2,2]
[6,2,1,8,4,7,5,3]=>[8,5,7,2,1,6,3,4]=>[1,4,2,7,8,3,6,5]=>[2,3,2,1]
[2,8,7,1,4,6,5,3]=>[8,5,7,4,6,1,3,2]=>[1,4,2,5,3,8,6,7]=>[2,2,2,2]
[8,2,7,1,5,4,6,3]=>[6,5,8,2,4,7,3,1]=>[3,4,1,7,5,2,6,8]=>[2,2,1,3]
[7,2,5,3,6,8,1,4]=>[7,4,2,3,5,1,8,6]=>[2,5,7,6,4,8,1,3]=>[3,1,2,2]
[7,3,1,5,6,2,4,8]=>[2,6,4,7,3,5,1,8]=>[7,3,5,2,6,4,8,1]=>[1,2,2,2,1]
[3,7,5,1,6,2,4,8]=>[6,7,1,4,3,5,2,8]=>[3,2,8,5,6,4,7,1]=>[1,2,2,2,1]
[2,7,3,6,5,8,1,4]=>[7,5,3,4,1,2,8,6]=>[2,4,6,5,8,7,1,3]=>[3,2,1,2]
[8,7,2,4,1,6,5,3]=>[4,8,3,7,5,6,2,1]=>[5,1,6,2,4,3,7,8]=>[1,2,2,3]
[1,8,7,2,3,6,5,4]=>[8,7,4,5,6,3,1,2]=>[1,2,5,4,3,6,8,7]=>[3,1,3,1]
[1,7,3,8,2,6,4,5]=>[7,8,3,5,2,6,1,4]=>[2,1,6,4,7,3,8,5]=>[1,2,2,2,1]
[7,1,5,8,3,2,4,6]=>[6,5,3,7,8,2,1,4]=>[3,4,6,2,1,7,8,5]=>[3,1,3,1]
[1,6,2,8,4,3,7,5]=>[5,8,6,2,7,1,3,4]=>[4,1,3,7,2,8,6,5]=>[1,3,2,1,1]
[1,3,8,7,2,4,6,5]=>[8,5,6,7,2,4,1,3]=>[1,4,3,2,7,5,8,6]=>[2,1,2,2,1]
[1,8,3,7,2,5,4,6]=>[7,3,5,6,8,4,1,2]=>[2,6,4,3,1,5,8,7]=>[2,1,1,3,1]
[4,7,8,1,3,2,5,6]=>[1,6,4,5,7,2,8,3]=>[8,3,5,4,2,7,1,6]=>[1,2,1,2,2]
[7,1,4,2,3,5,6,8]=>[4,5,2,3,6,7,1,8]=>[5,4,7,6,3,2,8,1]=>[1,2,1,1,2,1]
[8,2,1,4,7,3,5,6]=>[2,4,6,7,8,3,5,1]=>[7,5,3,2,1,6,4,8]=>[1,1,1,1,2,2]
[2,1,3,8,4,6,7,5]=>[6,8,1,5,7,2,3,4]=>[3,1,8,4,2,7,6,5]=>[1,2,1,2,1,1]
[1,2,3,4,8,5,7,6]=>[8,6,7,1,2,3,4,5]=>[1,3,2,8,7,6,5,4]=>[2,2,1,1,1,1]
[2,4,7,5,6,8,3,1]=>[4,5,2,3,8,1,7,6]=>[5,4,7,6,1,8,2,3]=>[1,2,1,2,2]
[2,4,8,7,5,6,3,1]=>[5,8,7,2,6,1,4,3]=>[4,1,2,7,3,8,5,6]=>[1,3,2,2]
[2,5,3,8,4,7,6,1]=>[2,8,5,7,1,3,6,4]=>[7,1,4,2,8,6,3,5]=>[1,2,2,1,2]
[2,8,5,7,3,6,4,1]=>[3,8,5,7,6,1,4,2]=>[6,1,4,2,3,8,5,7]=>[1,2,3,2]
[3,1,8,5,2,7,6,4]=>[4,8,1,7,5,6,2,3]=>[5,1,8,2,4,3,7,6]=>[1,2,2,2,1]
[8,3,6,1,4,5,7,2]=>[2,5,6,8,4,3,7,1]=>[7,4,3,1,5,6,2,8]=>[1,1,1,3,2]
[2,8,6,3,4,5,7,1]=>[4,5,6,3,8,1,7,2]=>[5,4,3,6,1,8,2,7]=>[1,1,2,2,2]
[2,6,8,3,4,5,7,1]=>[4,5,2,6,8,1,7,3]=>[5,4,7,3,1,8,2,6]=>[1,2,1,2,2]
[2,7,8,5,3,6,4,1]=>[8,5,4,2,7,1,6,3]=>[1,4,5,7,2,8,3,6]=>[4,2,2]
[3,1,8,7,2,6,4,5]=>[7,8,1,5,6,4,2,3]=>[2,1,8,4,3,5,7,6]=>[1,2,1,3,1]
[8,3,7,6,1,4,5,2]=>[6,8,2,5,7,4,3,1]=>[3,1,7,4,2,5,6,8]=>[1,2,1,4]
[4,8,1,7,2,3,6,5]=>[1,8,5,6,7,3,4,2]=>[8,1,4,3,2,6,5,7]=>[1,2,1,2,2]
[4,1,7,2,3,6,5,8]=>[7,4,1,5,6,2,3,8]=>[2,5,8,4,3,7,6,1]=>[3,1,2,1,1]
[3,1,7,8,2,5,6,4]=>[6,8,1,5,3,7,2,4]=>[3,1,8,4,6,2,7,5]=>[1,2,2,2,1]
[3,1,6,5,8,2,7,4]=>[4,1,3,8,6,7,2,5]=>[5,8,6,1,3,2,7,4]=>[2,1,2,2,1]
[6,3,5,8,7,1,4,2]=>[3,8,2,1,6,7,5,4]=>[6,1,7,8,3,2,4,5]=>[1,3,1,3]
[7,3,8,5,1,6,4,2]=>[8,7,2,5,4,1,6,3]=>[1,2,7,4,5,8,3,6]=>[3,3,2]
[7,8,3,6,1,4,5,2]=>[3,6,8,5,1,7,4,2]=>[6,3,1,4,8,2,5,7]=>[1,1,3,3]
[7,4,8,1,2,3,6,5]=>[8,4,2,5,6,1,7,3]=>[1,5,7,4,3,8,2,6]=>[3,1,2,2]
[8,7,4,6,1,2,5,3]=>[8,5,3,6,7,4,2,1]=>[1,4,6,3,2,5,7,8]=>[3,1,4]
[7,5,1,2,3,4,8,6]=>[8,3,4,5,2,6,1,7]=>[1,6,5,4,7,3,8,2]=>[2,1,2,2,1]
[5,7,1,2,3,6,4,8]=>[7,3,4,1,5,6,2,8]=>[2,6,5,8,4,3,7,1]=>[2,2,1,2,1]
[3,6,8,1,2,7,4,5]=>[7,8,1,4,2,5,6,3]=>[2,1,8,5,7,4,3,6]=>[1,2,2,1,2]
[4,8,6,1,2,3,7,5]=>[1,8,4,5,6,3,7,2]=>[8,1,5,4,3,6,2,7]=>[1,2,1,2,2]
[8,4,6,1,2,3,7,5]=>[8,4,2,5,6,3,7,1]=>[1,5,7,4,3,6,2,8]=>[3,1,2,2]
[4,1,2,5,3,8,7,6]=>[8,4,1,7,2,3,5,6]=>[1,5,8,2,7,6,4,3]=>[3,2,1,1,1]
[3,1,4,8,7,5,2,6]=>[7,1,6,8,3,5,2,4]=>[2,8,3,1,6,4,7,5]=>[2,1,2,2,1]
[4,3,6,8,7,5,1,2]=>[1,3,7,8,2,6,5,4]=>[8,6,2,1,7,3,4,5]=>[1,1,1,2,3]
[5,4,1,8,2,7,6,3]=>[2,1,8,7,5,6,3,4]=>[7,8,1,2,4,3,6,5]=>[2,3,2,1]
[8,6,7,4,1,2,5,3]=>[8,5,6,4,2,7,3,1]=>[1,4,3,5,7,2,6,8]=>[2,3,3]
[6,4,8,1,2,5,3,7]=>[7,4,2,5,1,6,8,3]=>[2,5,7,4,8,3,1,6]=>[3,2,1,2]
[6,7,3,1,4,8,5,2]=>[3,8,5,1,7,4,2,6]=>[6,1,4,8,2,5,7,3]=>[1,3,3,1]
[5,6,3,8,7,1,4,2]=>[1,8,3,2,6,7,5,4]=>[8,1,6,7,3,2,4,5]=>[1,3,1,3]
[5,4,1,6,8,2,7,3]=>[4,2,1,8,6,7,3,5]=>[5,7,8,1,3,2,6,4]=>[3,2,2,1]
[5,4,7,1,2,8,6,3]=>[2,1,8,7,4,5,3,6]=>[7,8,1,2,5,4,6,3]=>[2,3,2,1]
[6,7,4,1,2,8,3,5]=>[7,8,4,3,1,5,2,6]=>[2,1,5,6,8,4,7,3]=>[1,4,2,1]
[6,5,1,2,3,7,8,4]=>[6,8,3,4,2,1,5,7]=>[3,1,6,5,7,8,4,2]=>[1,2,3,1,1]
[6,5,1,2,3,4,8,7]=>[8,3,4,5,2,1,6,7]=>[1,6,5,4,7,8,3,2]=>[2,1,3,1,1]
[8,6,5,1,2,3,7,4]=>[8,4,5,6,3,2,7,1]=>[1,5,4,3,6,7,2,8]=>[2,1,3,2]
[6,5,1,2,3,7,4,8]=>[7,3,4,5,2,1,6,8]=>[2,6,5,4,7,8,3,1]=>[2,1,3,1,1]
[6,7,4,1,2,5,3,8]=>[7,4,5,3,1,6,2,8]=>[2,5,4,6,8,3,7,1]=>[2,3,2,1]
[7,8,6,4,1,2,5,3]=>[8,5,6,4,1,7,3,2]=>[1,4,3,5,8,2,6,7]=>[2,3,3]
[1,4,6,3,7,2,5,8]=>[2,4,6,3,7,1,5,8]=>[7,5,3,6,2,8,4,1]=>[1,1,2,2,1,1]
[8,2,3,4,5,1,7,6]=>[2,3,4,5,8,6,7,1]=>[7,6,5,4,1,3,2,8]=>[1,1,1,1,2,2]
[1,8,3,4,2,7,5,6]=>[3,4,7,8,5,6,1,2]=>[6,5,2,1,4,3,8,7]=>[1,1,1,2,2,1]
[2,8,3,4,1,6,7,5]=>[3,4,6,8,1,5,7,2]=>[6,5,3,1,8,4,2,7]=>[1,1,1,2,1,2]
[8,7,2,3,1,6,5,4]=>[8,3,4,7,5,6,2,1]=>[1,6,5,2,4,3,7,8]=>[2,1,2,3]
[5,1,4,3,7,2,6,8]=>[4,3,6,1,7,2,5,8]=>[5,6,3,8,2,7,4,1]=>[2,2,2,1,1]
[6,1,3,5,7,2,4,8]=>[6,3,4,7,2,1,5,8]=>[3,6,5,2,7,8,4,1]=>[2,1,3,1,1]
[2,1,4,7,5,3,6,8]=>[6,1,3,5,7,2,4,8]=>[3,8,6,4,2,7,5,1]=>[2,1,1,2,1,1]
[7,1,3,6,2,5,4,8]=>[7,3,5,6,2,4,1,8]=>[2,6,4,3,7,5,8,1]=>[2,1,2,2,1]
[8,1,3,6,2,4,7,5]=>[8,3,5,6,2,4,7,1]=>[1,6,4,3,7,5,2,8]=>[2,1,2,1,2]
[2,1,8,3,7,5,4,6]=>[7,6,8,1,4,5,2,3]=>[2,3,1,8,5,4,7,6]=>[2,2,1,2,1]
[7,1,8,2,5,6,3,4]=>[7,5,8,4,6,2,1,3]=>[2,4,1,5,3,7,8,6]=>[2,2,3,1]
[6,1,5,8,2,7,3,4]=>[7,3,8,5,1,6,2,4]=>[2,6,1,4,8,3,7,5]=>[2,3,2,1]
[4,5,2,8,1,6,7,3]=>[1,6,2,8,3,5,7,4]=>[8,3,7,1,6,4,2,5]=>[1,2,2,1,2]
[6,2,5,8,1,4,7,3]=>[6,3,8,2,1,5,7,4]=>[3,6,1,7,8,4,2,5]=>[2,3,1,2]
[8,2,7,1,4,6,5,3]=>[8,5,7,2,4,6,3,1]=>[1,4,2,7,5,3,6,8]=>[2,2,1,3]
[1,3,8,2,5,7,4,6]=>[5,7,8,2,4,6,1,3]=>[4,2,1,7,5,3,8,6]=>[1,1,2,1,2,1]
[3,8,7,1,5,6,4,2]=>[5,8,7,1,4,6,3,2]=>[4,1,2,8,5,3,6,7]=>[1,3,1,3]
[3,4,8,5,6,1,7,2]=>[4,8,1,2,6,5,7,3]=>[5,1,8,7,3,4,2,6]=>[1,2,1,2,2]
[8,3,7,4,1,6,5,2]=>[4,8,2,7,5,6,3,1]=>[5,1,7,2,4,3,6,8]=>[1,2,2,3]
[1,4,8,6,2,7,3,5]=>[7,8,2,5,4,6,1,3]=>[2,1,7,4,5,3,8,6]=>[1,2,2,2,1]
[8,4,5,7,1,6,3,2]=>[2,3,8,7,5,6,4,1]=>[7,6,1,2,4,3,5,8]=>[1,1,3,3]
[3,5,6,8,4,1,7,2]=>[2,3,8,1,6,5,7,4]=>[7,6,1,8,3,4,2,5]=>[1,1,2,2,2]
[6,2,3,1,5,4,7,8]=>[2,3,6,4,5,1,7,8]=>[7,6,3,5,4,8,2,1]=>[1,1,2,2,1,1]
[7,2,3,1,4,6,5,8]=>[2,3,7,4,5,6,1,8]=>[7,6,2,5,4,3,8,1]=>[1,1,2,1,2,1]
[8,2,3,1,4,5,7,6]=>[2,3,8,4,5,6,7,1]=>[7,6,1,5,4,3,2,8]=>[1,1,2,1,1,2]
[8,5,1,3,2,4,7,6]=>[4,8,3,5,2,6,7,1]=>[5,1,6,4,7,3,2,8]=>[1,2,2,1,2]
[7,5,1,3,2,6,4,8]=>[4,7,3,5,2,6,1,8]=>[5,2,6,4,7,3,8,1]=>[1,2,2,2,1]
[2,6,1,4,5,3,7,8]=>[4,6,1,3,5,2,7,8]=>[5,3,8,6,4,7,2,1]=>[1,2,1,2,1,1]
[3,6,4,1,5,2,7,8]=>[6,1,4,3,5,2,7,8]=>[3,8,5,6,4,7,2,1]=>[2,2,2,1,1]
[4,5,6,1,3,2,7,8]=>[1,6,4,2,5,3,7,8]=>[8,3,5,7,4,6,2,1]=>[1,3,2,1,1]
[4,5,7,1,2,6,3,8]=>[1,7,4,2,5,6,3,8]=>[8,2,5,7,4,3,6,1]=>[1,3,1,2,1]
[6,7,1,4,2,5,3,8]=>[7,5,3,4,1,6,2,8]=>[2,4,6,5,8,3,7,1]=>[3,2,2,1]
[2,7,1,3,5,6,4,8]=>[5,7,1,3,4,6,2,8]=>[4,2,8,6,5,3,7,1]=>[1,2,1,1,2,1]
[2,8,1,3,4,6,7,5]=>[6,8,1,3,4,5,7,2]=>[3,1,8,6,5,4,2,7]=>[1,2,1,1,1,2]
[7,8,1,2,5,3,6,4]=>[8,6,3,4,5,1,7,2]=>[1,3,6,5,4,8,2,7]=>[3,1,2,2]
[3,8,4,1,2,5,7,6]=>[8,1,4,3,5,6,7,2]=>[1,8,5,6,4,3,2,7]=>[2,2,1,1,2]
[1,2,6,7,5,3,8,4]=>[3,8,6,5,1,2,4,7]=>[6,1,3,4,8,7,5,2]=>[1,4,1,1,1]
[1,7,5,3,2,8,4,6]=>[4,7,3,8,5,1,2,6]=>[5,2,6,1,4,8,7,3]=>[1,2,3,1,1]
[1,6,7,5,3,8,4,2]=>[2,8,5,4,3,7,1,6]=>[7,1,4,5,6,2,8,3]=>[1,4,2,1]
[1,6,5,7,2,3,8,4]=>[8,5,3,2,6,1,4,7]=>[1,4,6,7,3,8,5,2]=>[4,2,1,1]
[1,3,8,2,6,5,7,4]=>[6,5,8,2,4,7,1,3]=>[3,4,1,7,5,2,8,6]=>[2,2,1,2,1]
[1,2,5,7,6,3,4,8]=>[3,6,7,5,1,2,4,8]=>[6,3,2,4,8,7,5,1]=>[1,1,3,1,1,1]
[1,3,4,8,2,5,7,6]=>[8,2,3,5,6,7,1,4]=>[1,7,6,4,3,2,8,5]=>[2,1,1,1,2,1]
[1,5,7,6,2,3,4,8]=>[5,2,6,7,4,1,3,8]=>[4,7,3,2,5,8,6,1]=>[2,1,3,1,1]
[1,5,3,8,2,6,4,7]=>[7,3,2,5,6,8,1,4]=>[2,6,7,4,3,1,8,5]=>[3,1,1,2,1]
[1,4,8,3,2,5,7,6]=>[2,4,8,5,6,7,1,3]=>[7,5,1,4,3,2,8,6]=>[1,1,2,1,2,1]
[1,4,8,3,5,7,6,2]=>[8,2,4,5,7,6,1,3]=>[1,7,5,4,2,3,8,6]=>[2,1,1,3,1]
[1,2,4,8,3,5,7,6]=>[8,3,5,6,7,1,2,4]=>[1,6,4,3,2,8,7,5]=>[2,1,1,2,1,1]
[1,3,8,4,2,6,7,5]=>[4,6,8,2,5,7,1,3]=>[5,3,1,7,4,2,8,6]=>[1,1,2,1,2,1]
[1,4,8,2,3,5,7,6]=>[2,8,4,5,6,7,1,3]=>[7,1,5,4,3,2,8,6]=>[1,2,1,1,2,1]
[6,5,7,3,8,2,4,1]=>[4,2,1,6,3,8,7,5]=>[5,7,8,3,6,1,2,4]=>[3,2,3]
[4,2,6,7,5,8,3,1]=>[1,3,5,4,8,2,7,6]=>[8,6,4,5,1,7,2,3]=>[1,1,2,2,2]
[6,7,5,2,1,8,4,3]=>[8,4,1,7,5,3,2,6]=>[1,5,8,2,4,6,7,3]=>[3,4,1]
[3,4,8,7,5,2,1,6]=>[7,6,1,2,5,8,4,3]=>[2,3,8,7,4,1,5,6]=>[3,1,1,3]
[1,7,5,2,8,4,6,3]=>[6,3,8,7,4,1,2,5]=>[3,6,1,2,5,8,7,4]=>[2,4,1,1]
[3,4,6,8,2,1,5,7]=>[6,1,2,5,3,7,8,4]=>[3,8,7,4,6,2,1,5]=>[2,1,2,1,2]
[3,8,2,5,6,1,4,7]=>[6,1,3,4,7,5,8,2]=>[3,8,6,5,2,4,1,7]=>[2,1,1,2,2]
[3,5,2,8,6,4,1,7]=>[2,7,1,6,3,5,8,4]=>[7,2,8,3,6,4,1,5]=>[1,2,2,1,2]
[4,2,5,7,3,8,6,1]=>[1,8,3,5,2,4,7,6]=>[8,1,6,4,7,5,2,3]=>[1,2,2,1,2]
[3,1,2,8,5,6,4,7]=>[1,5,7,6,8,2,3,4]=>[8,4,2,3,1,7,6,5]=>[1,1,2,2,1,1]
[5,2,1,6,8,3,4,7]=>[6,2,4,1,7,8,3,5]=>[3,7,5,8,2,1,6,4]=>[2,2,1,2,1]
[5,2,6,8,4,1,3,7]=>[6,3,1,7,2,5,8,4]=>[3,6,8,2,7,4,1,5]=>[3,2,1,2]
[1,5,6,8,3,4,2,7]=>[2,5,3,7,6,8,1,4]=>[7,4,6,2,3,1,8,5]=>[1,2,2,2,1]
[4,5,8,1,6,3,2,7]=>[1,2,7,6,4,5,8,3]=>[8,7,2,3,5,4,1,6]=>[1,1,3,1,2]
[4,5,1,6,8,3,2,7]=>[1,4,2,7,6,8,3,5]=>[8,5,7,2,3,1,6,4]=>[1,2,2,2,1]
[4,5,7,3,8,2,6,1]=>[1,2,4,6,3,8,7,5]=>[8,7,5,3,6,1,2,4]=>[1,1,1,2,3]
[6,4,3,7,8,2,5,1]=>[2,6,3,1,4,8,7,5]=>[7,3,6,8,5,1,2,4]=>[1,3,1,3]
[6,4,3,1,7,8,2,5]=>[3,2,7,5,1,8,4,6]=>[6,7,2,4,8,1,5,3]=>[2,3,2,1]
[4,5,3,1,7,8,2,6]=>[1,3,2,7,5,8,4,6]=>[8,6,7,2,4,1,5,3]=>[1,2,2,2,1]
[7,1,3,5,4,8,2,6]=>[5,3,4,7,8,2,1,6]=>[4,6,5,2,1,7,8,3]=>[2,1,1,3,1]
[7,5,2,8,1,4,3,6]=>[7,3,5,2,6,1,8,4]=>[2,6,4,7,3,8,1,5]=>[2,2,2,2]
[5,7,3,8,4,6,1,2]=>[1,7,3,5,2,8,6,4]=>[8,2,6,4,7,1,3,5]=>[1,2,2,3]
[1,4,5,7,3,8,6,2]=>[8,2,3,5,4,7,1,6]=>[1,7,6,4,5,2,8,3]=>[2,1,2,2,1]
[4,6,3,7,8,5,2,1]=>[4,1,2,8,3,7,6,5]=>[5,8,7,1,6,2,3,4]=>[2,1,2,3]
[5,3,6,7,8,4,2,1]=>[3,1,4,8,2,7,6,5]=>[6,8,5,1,7,2,3,4]=>[2,1,2,3]
[1,5,3,6,7,8,4,2]=>[4,2,5,8,3,7,1,6]=>[5,7,4,1,6,2,8,3]=>[2,1,2,2,1]
[4,6,1,7,3,8,5,2]=>[8,1,5,4,2,7,3,6]=>[1,8,4,5,7,2,6,3]=>[2,3,2,1]
[6,3,7,1,8,4,5,2]=>[6,8,2,1,7,4,3,5]=>[3,1,7,8,2,5,6,4]=>[1,3,3,1]
[6,7,2,4,8,1,5,3]=>[4,8,3,1,6,2,7,5]=>[5,1,6,8,3,7,2,4]=>[1,3,2,2]
[2,6,1,4,7,3,8,5]=>[8,4,6,1,3,2,5,7]=>[1,5,3,8,6,7,4,2]=>[2,2,2,1,1]
[3,2,5,6,7,8,1,4]=>[1,3,4,7,2,5,8,6]=>[8,6,5,2,7,4,1,3]=>[1,1,1,2,1,2]
[5,2,3,6,7,8,4,1]=>[4,5,1,8,2,3,7,6]=>[5,4,8,1,7,6,2,3]=>[1,2,2,1,2]
[6,7,1,3,2,8,4,5]=>[4,7,8,3,1,5,2,6]=>[5,2,1,6,8,4,7,3]=>[1,1,3,2,1]
[6,2,7,1,3,4,8,5]=>[8,2,4,5,1,6,3,7]=>[1,7,5,4,8,3,6,2]=>[2,1,2,2,1]
[5,2,1,7,3,8,4,6]=>[7,8,2,1,5,3,4,6]=>[2,1,7,8,4,6,5,3]=>[1,3,2,1,1]
[6,4,2,7,1,8,3,5]=>[7,2,8,3,1,5,4,6]=>[2,7,1,6,8,4,5,3]=>[2,3,2,1]
[4,2,6,3,7,8,5,1]=>[1,5,3,8,2,4,7,6]=>[8,4,6,1,7,5,2,3]=>[1,2,2,1,2]
[6,7,3,8,2,4,5,1]=>[3,5,1,6,2,8,7,4]=>[6,4,8,3,7,1,2,5]=>[1,2,2,3]
[3,6,2,7,4,1,8,5]=>[5,8,1,3,2,6,4,7]=>[4,1,8,6,7,3,5,2]=>[1,2,2,2,1]
[6,7,3,2,1,4,8,5]=>[4,3,8,5,1,6,2,7]=>[5,6,1,4,8,3,7,2]=>[2,3,2,1]
[7,1,8,3,4,2,5,6]=>[4,6,5,7,8,2,1,3]=>[5,3,4,2,1,7,8,6]=>[1,2,1,3,1]
[7,2,4,1,8,3,5,6]=>[6,2,3,7,8,4,1,5]=>[3,7,6,2,1,5,8,4]=>[2,1,1,3,1]
[7,2,4,8,6,1,3,5]=>[3,6,7,8,2,1,5,4]=>[6,3,2,1,7,8,4,5]=>[1,1,1,3,2]
[7,3,4,8,6,2,1,5]=>[7,2,3,6,1,8,5,4]=>[2,7,6,3,8,1,4,5]=>[2,1,2,3]
[3,5,7,2,1,8,6,4]=>[2,8,1,4,7,5,3,6]=>[7,1,8,5,2,4,6,3]=>[1,2,1,3,1]
[6,3,7,8,2,5,4,1]=>[8,5,2,1,3,7,6,4]=>[1,4,7,8,6,2,3,5]=>[4,1,3]
[2,6,7,4,8,5,3,1]=>[2,8,4,3,7,1,6,5]=>[7,1,5,6,2,8,3,4]=>[1,3,2,2]
[6,2,4,7,1,8,5,3]=>[8,3,7,2,1,5,4,6]=>[1,6,2,7,8,4,5,3]=>[2,3,2,1]
[4,6,2,7,1,8,5,3]=>[8,1,7,3,2,5,4,6]=>[1,8,2,6,7,4,5,3]=>[2,3,2,1]
[1,3,7,8,5,2,6,4]=>[8,6,5,2,3,7,1,4]=>[1,3,4,7,6,2,8,5]=>[4,1,2,1]
[2,5,7,8,1,6,3,4]=>[2,7,8,5,1,3,6,4]=>[7,2,1,4,8,6,3,5]=>[1,1,3,1,2]
[6,3,7,1,8,2,5,4]=>[8,2,6,1,7,4,3,5]=>[1,7,3,8,2,5,6,4]=>[2,2,3,1]
[1,6,4,7,8,2,5,3]=>[8,3,2,6,4,7,1,5]=>[1,6,7,3,5,2,8,4]=>[3,2,2,1]
[2,5,6,1,7,8,4,3]=>[2,5,3,8,1,7,4,6]=>[7,4,6,1,8,2,5,3]=>[1,2,2,2,1]
[5,6,1,2,7,8,4,3]=>[5,1,8,7,3,2,4,6]=>[4,8,1,2,6,7,5,3]=>[2,4,1,1]
[6,7,2,1,8,5,3,4]=>[7,8,3,1,6,4,2,5]=>[2,1,6,8,3,5,7,4]=>[1,3,3,1]
[6,7,2,8,5,4,1,3]=>[7,1,8,6,3,2,5,4]=>[2,8,1,3,6,7,4,5]=>[2,4,2]
[1,6,7,4,8,5,3,2]=>[2,8,4,3,7,6,1,5]=>[7,1,5,6,2,3,8,4]=>[1,3,3,1]
[1,8,2,4,6,3,5,7]=>[4,6,7,3,5,8,1,2]=>[5,3,2,6,4,1,8,7]=>[1,1,2,1,2,1]
[7,2,8,3,5,1,4,6]=>[4,6,7,2,5,1,8,3]=>[5,3,2,7,4,8,1,6]=>[1,1,2,2,2]
[1,3,7,4,6,2,5,8]=>[4,6,7,2,5,1,3,8]=>[5,3,2,7,4,8,6,1]=>[1,1,2,2,1,1]
[1,5,7,4,3,6,2,8]=>[2,5,4,7,6,1,3,8]=>[7,4,5,2,3,8,6,1]=>[1,2,3,1,1]
[1,8,4,5,3,6,2,7]=>[3,5,4,7,6,8,1,2]=>[6,4,5,2,3,1,8,7]=>[1,2,2,2,1]
[1,8,5,3,4,7,2,6]=>[4,5,3,7,8,6,1,2]=>[5,4,6,2,1,3,8,7]=>[1,2,1,3,1]
[1,8,2,5,4,6,7,3]=>[5,4,6,8,3,7,1,2]=>[4,5,3,1,6,2,8,7]=>[2,1,2,2,1]
[3,6,2,7,1,4,5,8]=>[1,3,5,6,2,7,4,8]=>[8,6,4,3,7,2,5,1]=>[1,1,1,2,2,1]
[6,3,8,1,2,4,7,5]=>[2,8,4,5,1,6,7,3]=>[7,1,5,4,8,3,2,6]=>[1,2,2,1,2]
[1,3,7,4,6,2,8,5]=>[8,4,6,2,5,1,3,7]=>[1,5,3,7,4,8,6,2]=>[2,2,2,1,1]
[1,4,7,5,2,6,8,3]=>[6,2,4,8,5,1,3,7]=>[3,7,5,1,4,8,6,2]=>[2,1,3,1,1]
[4,6,5,3,7,1,8,2]=>[4,1,3,2,8,6,5,7]=>[5,8,6,7,1,3,4,2]=>[2,2,3,1]
[2,5,4,7,1,6,8,3]=>[3,2,6,8,1,5,4,7]=>[6,7,3,1,8,4,5,2]=>[2,1,2,2,1]
[4,2,3,8,6,7,1,5]=>[1,7,5,8,2,3,6,4]=>[8,2,4,1,7,6,3,5]=>[1,2,2,1,2]
[6,2,4,8,5,1,7,3]=>[8,3,6,2,1,5,7,4]=>[1,6,3,7,8,4,2,5]=>[2,3,1,2]
[5,2,4,8,1,3,7,6]=>[3,8,2,1,5,6,7,4]=>[6,1,7,8,4,3,2,5]=>[1,3,1,1,2]
[6,2,5,4,8,3,7,1]=>[4,3,6,1,8,2,7,5]=>[5,6,3,8,1,7,2,4]=>[2,2,2,2]
[6,4,3,5,8,2,7,1]=>[3,2,4,1,6,8,7,5]=>[6,7,5,8,3,1,2,4]=>[2,2,1,3]
[5,2,3,4,8,1,6,7]=>[2,3,4,1,6,7,8,5]=>[7,6,5,8,3,2,1,4]=>[1,1,2,1,1,2]
[3,5,2,4,7,1,6,8]=>[1,3,4,2,6,7,5,8]=>[8,6,5,7,3,2,4,1]=>[1,1,2,1,2,1]
[4,5,3,7,1,6,2,8]=>[1,3,2,7,5,6,4,8]=>[8,6,7,2,4,3,5,1]=>[1,2,2,2,1]
[6,2,4,8,5,1,3,7]=>[3,6,7,2,1,5,8,4]=>[6,3,2,7,8,4,1,5]=>[1,1,3,1,2]
[7,6,3,8,5,1,2,4]=>[3,6,7,2,1,8,5,4]=>[6,3,2,7,8,1,4,5]=>[1,1,3,3]
[1,4,3,7,8,2,5,6]=>[2,6,7,3,4,8,1,5]=>[7,3,2,6,5,1,8,4]=>[1,1,2,1,2,1]
[1,5,7,4,2,8,6,3]=>[2,4,8,7,5,1,3,6]=>[7,5,1,2,4,8,6,3]=>[1,1,4,1,1]
[1,3,7,2,8,6,4,5]=>[7,8,6,2,4,1,3,5]=>[2,1,3,7,5,8,6,4]=>[1,3,2,1,1]
[1,4,3,7,8,6,2,5]=>[7,2,4,8,3,6,1,5]=>[2,7,5,1,6,3,8,4]=>[2,1,2,2,1]
[1,5,3,6,8,2,7,4]=>[4,2,8,3,6,7,1,5]=>[5,7,1,6,3,2,8,4]=>[2,2,1,2,1]
[4,3,6,5,7,8,1,2]=>[1,4,2,3,7,5,8,6]=>[8,5,7,6,2,4,1,3]=>[1,2,1,2,2]
[4,2,3,5,6,8,1,7]=>[2,3,1,4,5,7,8,6]=>[7,6,8,5,4,2,1,3]=>[1,2,1,1,1,2]
[5,2,6,4,7,8,3,1]=>[4,3,1,5,8,2,7,6]=>[5,6,8,4,1,7,2,3]=>[3,1,2,2]
[4,2,6,7,3,8,5,1]=>[1,3,8,5,2,4,7,6]=>[8,6,1,4,7,5,2,3]=>[1,1,3,1,2]
[3,2,5,6,8,1,7,4]=>[1,3,4,8,2,6,7,5]=>[8,6,5,1,7,3,2,4]=>[1,1,1,2,1,2]
[6,4,5,2,3,8,7,1]=>[2,8,4,3,1,5,7,6]=>[7,1,5,6,8,4,2,3]=>[1,4,1,2]
[8,4,6,7,5,2,3,1]=>[6,2,3,8,7,5,4,1]=>[3,7,6,1,2,4,5,8]=>[2,1,5]
[6,4,2,5,3,8,7,1]=>[4,2,8,3,1,5,7,6]=>[5,7,1,6,8,4,2,3]=>[2,3,1,2]
[8,6,4,7,5,2,3,1]=>[3,6,2,8,7,5,4,1]=>[6,3,7,1,2,4,5,8]=>[1,2,5]
[8,6,2,7,4,5,3,1]=>[5,8,7,3,2,6,4,1]=>[4,1,2,6,7,3,5,8]=>[1,4,3]
[6,4,2,5,8,7,3,1]=>[2,8,4,1,7,3,6,5]=>[7,1,5,8,2,6,3,4]=>[1,3,2,2]
[4,6,2,5,3,8,7,1]=>[1,4,8,3,2,5,7,6]=>[8,5,1,6,7,4,2,3]=>[1,1,3,1,2]
[4,6,5,2,3,8,7,1]=>[8,1,4,3,2,5,7,6]=>[1,8,5,6,7,4,2,3]=>[2,3,1,2]
[6,8,7,4,5,2,3,1]=>[1,6,4,8,7,5,3,2]=>[8,3,5,1,2,4,6,7]=>[1,2,5]
[4,8,6,7,5,2,3,1]=>[6,3,8,1,7,5,4,2]=>[3,6,1,8,2,4,5,7]=>[2,2,4]
[6,8,4,7,5,2,3,1]=>[3,1,6,8,7,5,4,2]=>[6,8,3,1,2,4,5,7]=>[2,1,5]
[6,8,2,7,4,5,3,1]=>[5,1,8,7,3,6,4,2]=>[4,8,1,2,6,3,5,7]=>[2,3,3]
[8,6,2,4,7,5,3,1]=>[8,4,7,3,2,6,5,1]=>[1,5,2,6,7,3,4,8]=>[2,3,3]
[6,8,2,4,7,5,3,1]=>[8,4,1,7,3,6,5,2]=>[1,5,8,2,6,3,4,7]=>[3,2,3]
[4,8,2,6,7,5,3,1]=>[4,8,1,7,3,6,5,2]=>[5,1,8,2,6,3,4,7]=>[1,2,2,3]
[2,8,4,6,7,5,3,1]=>[4,8,3,7,6,1,5,2]=>[5,1,6,2,3,8,4,7]=>[1,2,3,2]
[2,8,6,7,4,5,3,1]=>[5,3,8,7,6,1,4,2]=>[4,6,1,2,3,8,5,7]=>[2,4,2]
[6,8,7,2,4,5,3,1]=>[5,1,8,4,7,6,3,2]=>[4,8,1,5,2,3,6,7]=>[2,2,4]
[2,6,4,5,8,7,3,1]=>[8,3,2,4,7,1,6,5]=>[1,6,7,5,2,8,3,4]=>[3,1,2,2]
[2,6,4,8,7,5,3,1]=>[2,8,7,3,6,1,5,4]=>[7,1,2,6,3,8,4,5]=>[1,3,2,2]
[4,6,2,8,7,5,3,1]=>[2,8,1,7,6,3,5,4]=>[7,1,8,2,3,6,4,5]=>[1,2,3,2]
[8,2,4,6,7,5,3,1]=>[4,8,3,7,2,6,5,1]=>[5,1,6,2,7,3,4,8]=>[1,2,2,3]
[6,2,4,8,7,5,3,1]=>[8,7,3,1,6,2,5,4]=>[1,2,6,8,3,7,4,5]=>[4,2,2]
[4,2,6,8,7,5,3,1]=>[8,1,3,7,6,2,5,4]=>[1,8,6,2,3,7,4,5]=>[2,1,3,2]
[4,2,6,5,8,7,3,1]=>[1,3,8,4,7,2,6,5]=>[8,6,1,5,2,7,3,4]=>[1,1,2,2,2]
[6,2,4,5,8,7,3,1]=>[8,3,4,1,7,2,6,5]=>[1,6,5,8,2,7,3,4]=>[2,2,2,2]
[8,2,6,7,4,5,3,1]=>[5,3,8,7,2,6,4,1]=>[4,6,1,2,7,3,5,8]=>[2,3,3]
[8,6,7,2,4,5,3,1]=>[5,8,4,2,7,6,3,1]=>[4,1,5,7,2,3,6,8]=>[1,3,4]
[6,4,5,2,8,7,3,1]=>[2,3,1,8,7,4,6,5]=>[7,6,8,1,2,5,3,4]=>[1,2,3,2]
[6,4,5,8,7,2,3,1]=>[2,3,1,6,8,7,5,4]=>[7,6,8,3,1,2,4,5]=>[1,2,1,4]
[8,6,7,4,2,5,3,1]=>[8,5,4,2,7,6,3,1]=>[1,4,5,7,2,3,6,8]=>[4,4]
[8,4,6,7,2,5,3,1]=>[8,2,5,3,7,6,4,1]=>[1,7,4,6,2,3,5,8]=>[2,2,4]
[6,4,8,7,2,5,3,1]=>[8,2,1,5,7,6,4,3]=>[1,7,8,4,2,3,5,6]=>[3,1,4]
[6,2,8,7,4,5,3,1]=>[5,1,8,7,6,2,4,3]=>[4,8,1,2,3,7,5,6]=>[2,4,2]
[6,4,8,7,5,2,3,1]=>[6,1,8,2,7,5,4,3]=>[3,8,1,7,2,4,5,6]=>[2,2,4]
[4,6,8,7,5,2,3,1]=>[2,6,8,1,7,5,4,3]=>[7,3,1,8,2,4,5,6]=>[1,1,2,4]
[4,6,5,8,7,2,3,1]=>[3,1,2,6,8,7,5,4]=>[6,8,7,3,1,2,4,5]=>[2,1,1,4]
[2,1,6,8,7,4,5,3]=>[3,6,8,7,1,5,2,4]=>[6,3,1,2,8,4,7,5]=>[1,1,3,2,1]
[2,6,8,7,4,5,3,1]=>[2,5,8,7,6,1,4,3]=>[7,4,1,2,3,8,5,6]=>[1,1,4,2]
[2,4,8,6,7,5,3,1]=>[4,8,7,2,6,1,5,3]=>[5,1,2,7,3,8,4,6]=>[1,3,2,2]
[6,2,8,4,7,5,3,1]=>[8,4,1,7,6,2,5,3]=>[1,5,8,2,3,7,4,6]=>[3,3,2]
[8,2,6,4,7,5,3,1]=>[8,4,3,7,2,6,5,1]=>[1,5,6,2,7,3,4,8]=>[3,2,3]
[6,4,8,2,7,5,3,1]=>[8,2,1,7,4,6,5,3]=>[1,7,8,2,5,3,4,6]=>[3,2,3]
[4,6,8,2,7,5,3,1]=>[2,8,1,7,4,6,5,3]=>[7,1,8,2,5,3,4,6]=>[1,2,2,3]
[4,6,8,7,2,5,3,1]=>[2,8,1,5,7,6,4,3]=>[7,1,8,4,2,3,5,6]=>[1,2,1,4]
[4,6,5,8,2,7,3,1]=>[3,1,2,8,5,7,6,4]=>[6,8,7,1,4,2,3,5]=>[2,1,2,3]
[2,1,6,8,4,7,5,3]=>[3,8,5,7,1,6,2,4]=>[6,1,4,2,8,3,7,5]=>[1,2,2,2,1]
[2,1,8,6,4,7,5,3]=>[8,5,4,7,1,6,2,3]=>[1,4,5,2,8,3,7,6]=>[3,2,2,1]
[6,8,7,4,2,5,3,1]=>[1,8,5,4,7,6,3,2]=>[8,1,4,5,2,3,6,7]=>[1,3,4]
[2,8,6,4,7,5,3,1]=>[8,4,3,7,6,1,5,2]=>[1,5,6,2,3,8,4,7]=>[3,3,2]
[4,8,6,2,7,5,3,1]=>[8,7,1,4,3,6,5,2]=>[1,2,8,5,6,3,4,7]=>[3,2,3]
[9,4,8,3,7,2,6,1,5]=>[2,4,6,8,9,7,5,3,1]=>[8,6,4,2,1,3,5,7,9]=>[1,1,1,1,5]
[7,9,1,2,3,4,5,6,8]=>[3,4,5,6,7,1,8,9,2]=>[7,6,5,4,3,9,2,1,8]=>[1,1,1,1,2,1,2]
[4,2,5,6,3,8,1,7]=>[3,1,5,2,4,7,8,6]=>[6,8,4,7,5,2,1,3]=>[2,2,1,1,2]
[6,2,5,7,4,8,3,1]=>[3,5,4,1,8,2,7,6]=>[6,4,5,8,1,7,2,3]=>[1,3,2,2]
[8,5,2,1,4,7,6,3]=>[8,3,5,2,7,4,6,1]=>[1,6,4,7,2,5,3,8]=>[2,2,2,2]
[6,7,3,2,5,8,4,1]=>[3,5,1,8,4,2,7,6]=>[6,4,8,1,5,7,2,3]=>[1,2,3,2]
[3,2,6,4,8,1,5,7]=>[1,4,6,2,3,7,8,5]=>[8,5,3,7,6,2,1,4]=>[1,1,2,1,1,2]
[2,3,6,4,7,8,5,1]=>[5,3,8,1,2,4,7,6]=>[4,6,1,8,7,5,2,3]=>[2,2,1,1,2]
[7,5,1,8,3,4,6,2]=>[5,6,2,8,7,3,1,4]=>[4,3,7,1,2,6,8,5]=>[1,2,4,1]
[5,7,8,2,6,3,4,1]=>[1,6,8,4,2,7,5,3]=>[8,3,1,5,7,2,4,6]=>[1,1,3,3]
[6,3,1,7,8,4,5,2]=>[6,2,4,1,8,7,3,5]=>[3,7,5,8,1,2,6,4]=>[2,2,3,1]
[5,3,6,7,4,1,8,2]=>[3,1,8,2,6,5,4,7]=>[6,8,1,7,3,4,5,2]=>[2,2,3,1]
[7,3,1,2,5,8,6,4]=>[2,8,5,7,3,4,1,6]=>[7,1,4,2,6,5,8,3]=>[1,2,2,2,1]
[1,6,3,5,2,4,8,7]=>[8,3,5,4,1,2,6,7]=>[1,6,4,5,8,7,3,2]=>[2,3,1,1,1]
[3,4,8,2,7,5,1,6]=>[7,1,2,4,6,8,5,3]=>[2,8,7,5,3,1,4,6]=>[2,1,1,1,3]
[6,3,2,8,5,7,4,1]=>[5,8,2,1,7,3,6,4]=>[4,1,7,8,2,6,3,5]=>[1,3,2,2]
[3,8,4,7,2,5,6,1]=>[3,5,6,8,1,7,4,2]=>[6,4,3,1,8,2,5,7]=>[1,1,1,2,3]
[3,4,8,1,6,2,7,5]=>[8,1,2,6,4,5,7,3]=>[1,8,7,3,5,4,2,6]=>[2,1,2,1,2]
[1,8,4,6,7,3,5,2]=>[6,3,4,8,7,5,1,2]=>[3,6,5,1,2,4,8,7]=>[2,1,4,1]
[8,1,6,3,4,5,7,2]=>[4,5,6,3,8,2,7,1]=>[5,4,3,6,1,7,2,8]=>[1,1,2,2,2]
[7,6,5,4,1,2,8,3]=>[8,5,6,4,3,2,1,7]=>[1,4,3,5,6,7,8,2]=>[2,5,1]
[5,7,6,8,3,4,2,1]=>[5,1,3,2,8,7,6,4]=>[4,8,6,7,1,2,3,5]=>[2,2,4]
[5,2,3,7,6,1,8,4]=>[8,6,2,1,3,5,4,7]=>[1,3,7,8,6,4,5,2]=>[4,1,2,1]
[8,1,2,4,6,7,3,5]=>[7,4,5,8,2,3,6,1]=>[2,5,4,1,7,6,3,8]=>[2,1,2,1,2]
[5,2,6,8,4,3,1,7]=>[3,1,7,6,2,5,8,4]=>[6,8,2,3,7,4,1,5]=>[2,3,1,2]
[7,8,1,5,4,3,6,2]=>[6,5,4,8,3,1,7,2]=>[3,4,5,1,6,8,2,7]=>[3,3,2]
[7,2,4,8,5,3,6,1]=>[6,3,5,8,2,1,7,4]=>[3,6,4,1,7,8,2,5]=>[2,1,3,2]
[3,7,5,1,8,4,6,2]=>[6,3,8,1,7,4,2,5]=>[3,6,1,8,2,5,7,4]=>[2,2,3,1]
[2,7,8,5,4,6,1,3]=>[7,5,4,2,8,1,6,3]=>[2,4,5,7,1,8,3,6]=>[4,2,2]
[5,7,4,3,8,6,2,1]=>[1,3,8,4,2,7,6,5]=>[8,6,1,5,7,2,3,4]=>[1,1,3,3]
[4,8,1,6,3,5,2,7]=>[1,5,7,6,3,4,8,2]=>[8,4,2,3,6,5,1,7]=>[1,1,3,1,2]
[8,3,1,7,4,2,5,6]=>[2,6,5,7,8,3,4,1]=>[7,3,4,2,1,6,5,8]=>[1,2,1,2,2]
[3,1,8,2,4,5,7,6]=>[1,8,4,5,6,7,2,3]=>[8,1,5,4,3,2,7,6]=>[1,2,1,1,2,1]
[8,1,3,7,6,2,4,5]=>[6,7,8,3,5,2,4,1]=>[3,2,1,6,4,7,5,8]=>[1,1,2,2,2]
[2,3,6,8,7,1,4,5]=>[6,3,7,8,1,2,5,4]=>[3,6,2,1,8,7,4,5]=>[2,1,2,1,2]
[4,3,2,8,5,7,1,6]=>[2,1,5,7,8,3,6,4]=>[7,8,4,2,1,6,3,5]=>[2,1,1,2,2]
[3,6,4,2,8,5,7,1]=>[3,6,1,2,8,4,7,5]=>[6,3,8,7,1,5,2,4]=>[1,2,1,2,2]
[4,7,3,2,5,1,8,6]=>[1,4,3,5,8,6,2,7]=>[8,5,6,4,1,3,7,2]=>[1,2,1,3,1]
[3,2,4,7,5,8,6,1]=>[8,1,5,2,3,4,7,6]=>[1,8,4,7,6,5,2,3]=>[2,2,1,1,2]
[2,4,3,5,1,8,6,7]=>[3,1,2,4,7,8,5,6]=>[6,8,7,5,2,1,4,3]=>[2,1,1,1,2,1]
[3,2,8,1,4,6,5,7]=>[1,7,2,4,5,6,8,3]=>[8,2,7,5,4,3,1,6]=>[1,2,1,1,1,2]
[3,7,8,5,6,1,2,4]=>[6,7,4,1,2,8,5,3]=>[3,2,5,8,7,1,4,6]=>[1,3,1,3]
[3,6,1,8,4,7,2,5]=>[5,7,1,2,8,6,3,4]=>[4,2,8,7,1,3,6,5]=>[1,2,1,3,1]
[3,1,6,8,4,7,2,5]=>[5,1,3,7,8,6,2,4]=>[4,8,6,2,1,3,7,5]=>[2,1,1,3,1]
[4,1,6,8,3,2,7,5]=>[1,5,3,8,6,7,2,4]=>[8,4,6,1,3,2,7,5]=>[1,2,2,2,1]
[4,6,1,8,3,2,7,5]=>[1,5,8,6,2,7,3,4]=>[8,4,1,3,7,2,6,5]=>[1,1,3,2,1]
[4,7,8,1,3,2,6,5]=>[1,5,8,4,6,2,7,3]=>[8,4,1,5,3,7,2,6]=>[1,1,2,2,2]
[4,7,8,3,1,2,6,5]=>[8,1,5,4,6,2,7,3]=>[1,8,4,5,3,7,2,6]=>[2,2,2,2]
[4,7,8,2,1,3,6,5]=>[1,4,8,5,6,2,7,3]=>[8,5,1,4,3,7,2,6]=>[1,1,2,2,2]
[4,6,1,8,2,3,7,5]=>[1,8,5,6,2,7,3,4]=>[8,1,4,3,7,2,6,5]=>[1,2,2,2,1]
[4,5,1,2,8,3,7,6]=>[1,8,6,2,7,3,4,5]=>[8,1,3,7,2,6,5,4]=>[1,3,2,1,1]
[4,5,2,1,8,3,7,6]=>[1,8,3,2,6,7,4,5]=>[8,1,6,7,3,2,5,4]=>[1,3,1,2,1]
[4,6,2,8,1,3,7,5]=>[1,8,3,5,2,6,7,4]=>[8,1,6,4,7,3,2,5]=>[1,2,2,1,2]
[3,6,2,8,4,7,1,5]=>[5,7,1,2,8,3,6,4]=>[4,2,8,7,1,6,3,5]=>[1,2,1,2,2]
[2,3,6,8,4,7,5,1]=>[3,8,5,7,1,2,6,4]=>[6,1,4,2,8,7,3,5]=>[1,2,2,1,2]
[3,2,6,8,4,7,1,5]=>[5,1,3,7,8,2,6,4]=>[4,8,6,2,1,7,3,5]=>[2,1,1,2,2]
[4,2,6,8,3,1,7,5]=>[1,5,3,8,2,6,7,4]=>[8,4,6,1,7,3,2,5]=>[1,2,2,1,2]
[4,2,5,1,8,3,7,6]=>[3,1,8,2,6,7,4,5]=>[6,8,1,7,3,2,5,4]=>[2,2,1,2,1]
[4,1,2,5,8,3,7,6]=>[8,4,1,6,7,2,3,5]=>[1,5,8,3,2,7,6,4]=>[3,1,2,1,1]
[5,1,2,4,3,8,7,6]=>[8,4,7,2,1,3,5,6]=>[1,5,2,7,8,6,4,3]=>[2,3,1,1,1]
[5,2,4,1,3,8,7,6]=>[3,8,2,1,7,4,5,6]=>[6,1,7,8,2,5,4,3]=>[1,3,2,1,1]
[3,5,2,4,8,7,1,6]=>[7,1,2,8,3,4,6,5]=>[2,8,7,1,6,5,3,4]=>[2,1,2,1,2]
[5,4,2,1,3,8,7,6]=>[8,3,2,1,7,4,5,6]=>[1,6,7,8,2,5,4,3]=>[4,2,1,1]
[5,1,4,2,3,8,7,6]=>[3,8,7,2,1,4,5,6]=>[6,1,2,7,8,5,4,3]=>[1,4,1,1,1]
[5,4,1,3,2,8,7,6]=>[8,4,2,1,7,3,5,6]=>[1,5,7,8,2,6,4,3]=>[4,2,1,1]
[5,4,3,1,2,8,7,6]=>[3,2,1,8,7,4,5,6]=>[6,7,8,1,2,5,4,3]=>[3,3,1,1]
[4,5,3,1,8,2,7,6]=>[1,3,2,8,6,7,4,5]=>[8,6,7,1,3,2,5,4]=>[1,2,2,2,1]
[4,5,1,3,8,2,7,6]=>[1,8,4,2,6,7,3,5]=>[8,1,5,7,3,2,6,4]=>[1,3,1,2,1]
[3,1,5,4,8,7,2,6]=>[1,3,7,8,4,6,2,5]=>[8,6,2,1,5,3,7,4]=>[1,1,1,2,2,1]
[3,5,1,4,8,7,2,6]=>[7,1,2,8,4,6,3,5]=>[2,8,7,1,5,3,6,4]=>[2,1,2,2,1]
[3,5,4,1,8,7,2,6]=>[3,1,2,7,8,6,4,5]=>[6,8,7,2,1,3,5,4]=>[2,1,1,3,1]
[3,6,5,8,7,1,2,4]=>[6,3,1,2,7,8,5,4]=>[3,6,8,7,2,1,4,5]=>[3,1,1,3]
[2,5,6,8,7,3,4,1]=>[2,3,6,8,7,1,5,4]=>[7,6,3,1,2,8,4,5]=>[1,1,1,3,2]
[3,4,5,1,8,7,2,6]=>[1,2,3,7,8,6,4,5]=>[8,7,6,2,1,3,5,4]=>[1,1,1,1,3,1]
[3,4,1,5,8,7,2,6]=>[1,2,7,8,4,6,3,5]=>[8,7,2,1,5,3,6,4]=>[1,1,1,2,2,1]
[4,1,3,5,8,2,7,6]=>[8,3,1,4,6,7,2,5]=>[1,6,8,5,3,2,7,4]=>[3,1,1,2,1]
[4,3,6,8,2,1,7,5]=>[1,5,2,3,8,6,7,4]=>[8,4,7,6,1,3,2,5]=>[1,2,1,2,2]
[2,4,6,8,3,7,5,1]=>[3,8,2,5,7,1,6,4]=>[6,1,7,4,2,8,3,5]=>[1,2,1,2,2]
[3,4,5,2,8,7,1,6]=>[1,2,3,7,8,4,6,5]=>[8,7,6,2,1,5,3,4]=>[1,1,1,1,2,2]
[5,3,1,4,2,8,7,6]=>[2,8,4,1,7,3,5,6]=>[7,1,5,8,2,6,4,3]=>[1,3,2,1,1]
[5,1,3,4,2,8,7,6]=>[8,3,4,1,7,2,5,6]=>[1,6,5,8,2,7,4,3]=>[2,2,2,1,1]
[5,1,3,2,4,8,7,6]=>[8,3,7,2,1,4,5,6]=>[1,6,2,7,8,5,4,3]=>[2,3,1,1,1]
[5,3,2,1,4,8,7,6]=>[2,8,3,1,7,4,5,6]=>[7,1,6,8,2,5,4,3]=>[1,3,2,1,1]
[4,3,2,5,8,1,7,6]=>[2,1,8,3,4,6,7,5]=>[7,8,1,6,5,3,2,4]=>[2,2,1,1,2]
[3,2,4,5,8,7,1,6]=>[1,7,8,2,3,4,6,5]=>[8,2,1,7,6,5,3,4]=>[1,1,2,1,1,2]
[4,2,3,5,8,1,7,6]=>[8,2,1,3,4,6,7,5]=>[1,7,8,6,5,3,2,4]=>[3,1,1,1,2]
[5,2,3,1,4,8,7,6]=>[8,2,3,1,7,4,5,6]=>[1,7,6,8,2,5,4,3]=>[2,2,2,1,1]
[5,1,2,3,4,8,7,6]=>[8,7,2,3,1,4,5,6]=>[1,2,7,6,8,5,4,3]=>[3,2,1,1,1]
[8,6,2,5,4,1,3,7]=>[6,7,3,5,4,2,8,1]=>[3,2,6,4,5,7,1,8]=>[1,2,3,2]
[6,5,7,4,2,8,3,1]=>[2,1,8,5,4,3,7,6]=>[7,8,1,4,5,6,2,3]=>[2,4,2]
[6,7,5,3,8,2,4,1]=>[4,1,6,3,2,8,7,5]=>[5,8,3,6,7,1,2,4]=>[2,3,3]
[8,6,2,1,3,5,4,7]=>[3,7,4,5,6,2,8,1]=>[6,2,5,4,3,7,1,8]=>[1,2,1,2,2]
[8,1,2,3,4,6,5,7]=>[7,2,3,4,5,6,8,1]=>[2,7,6,5,4,3,1,8]=>[2,1,1,1,1,2]
[6,2,3,7,8,4,5,1]=>[6,4,8,2,1,3,7,5]=>[3,5,1,7,8,6,2,4]=>[2,3,1,2]
[7,5,8,2,6,3,4,1]=>[6,2,8,4,1,7,5,3]=>[3,7,1,5,8,2,4,6]=>[2,3,3]
[7,3,1,6,5,8,4,2]=>[5,2,4,8,7,3,1,6]=>[4,7,5,1,2,6,8,3]=>[2,1,4,1]
[1,5,6,7,3,4,8,2]=>[2,5,3,6,4,8,1,7]=>[7,4,6,3,5,1,8,2]=>[1,2,2,2,1]
[6,7,8,2,1,4,5,3]=>[4,6,1,8,5,2,7,3]=>[5,3,8,1,4,7,2,6]=>[1,2,3,2]
[8,4,7,6,2,1,3,5]=>[2,6,5,7,8,4,3,1]=>[7,3,4,2,1,5,6,8]=>[1,2,1,4]
[5,3,8,4,7,2,6,1]=>[4,1,6,8,2,7,5,3]=>[5,8,3,1,7,2,4,6]=>[2,1,2,3]
[8,1,3,7,6,4,2,5]=>[7,6,8,3,5,2,4,1]=>[2,3,1,6,4,7,5,8]=>[2,2,2,2]
[5,3,1,7,8,6,2,4]=>[7,2,1,4,8,6,3,5]=>[2,7,8,5,1,3,6,4]=>[3,1,3,1]
[3,5,8,2,7,1,6,4]=>[2,8,1,4,6,7,5,3]=>[7,1,8,5,3,2,4,6]=>[1,2,1,1,3]
[6,2,8,5,3,1,7,4]=>[5,8,6,2,1,4,7,3]=>[4,1,3,7,8,5,2,6]=>[1,4,1,2]
[8,2,6,4,7,1,3,5]=>[6,4,7,2,3,8,5,1]=>[3,5,2,7,6,1,4,8]=>[2,2,1,3]
[3,4,2,8,5,1,7,6]=>[1,2,5,8,3,6,7,4]=>[8,7,4,1,6,3,2,5]=>[1,1,1,2,1,2]
[3,8,6,5,2,1,7,4]=>[5,8,6,1,4,3,7,2]=>[4,1,3,8,5,6,2,7]=>[1,3,2,2]
[8,3,7,4,2,5,6,1]=>[5,2,4,6,8,7,3,1]=>[4,7,5,3,1,2,6,8]=>[2,1,1,4]
[4,8,5,7,2,1,3,6]=>[6,1,5,3,7,8,4,2]=>[3,8,4,6,2,1,5,7]=>[2,2,1,3]
[3,4,1,8,2,6,7,5]=>[1,2,6,8,5,7,3,4]=>[8,7,3,1,4,2,6,5]=>[1,1,1,2,2,1]
[8,4,6,3,7,1,5,2]=>[2,4,8,6,3,7,5,1]=>[7,5,1,3,6,2,4,8]=>[1,1,3,3]
[2,8,5,6,7,1,3,4]=>[6,3,7,4,8,1,5,2]=>[3,6,2,5,1,8,4,7]=>[2,2,2,2]
[2,5,7,6,3,1,8,4]=>[2,5,8,6,1,4,3,7]=>[7,4,1,3,8,5,6,2]=>[1,1,3,2,1]
[4,2,8,3,1,5,6,7]=>[5,2,1,4,6,7,8,3]=>[4,7,8,5,3,2,1,6]=>[3,1,1,1,2]
[2,5,7,3,8,4,6,1]=>[2,6,8,4,1,3,7,5]=>[7,3,1,5,8,6,2,4]=>[1,1,3,1,2]
[4,2,7,1,8,5,3,6]=>[1,7,6,8,2,4,3,5]=>[8,2,3,1,7,5,6,4]=>[1,2,2,2,1]
[1,3,7,5,8,6,4,2]=>[8,4,3,7,2,6,1,5]=>[1,5,6,2,7,3,8,4]=>[3,2,2,1]
[5,7,8,4,3,1,6,2]=>[8,1,6,5,4,2,7,3]=>[1,8,3,4,5,7,2,6]=>[2,4,2]
[2,7,4,5,8,3,6,1]=>[3,4,6,2,8,1,7,5]=>[6,5,3,7,1,8,2,4]=>[1,1,2,2,2]
[7,2,8,5,1,4,6,3]=>[6,8,5,2,4,1,7,3]=>[3,1,4,7,5,8,2,6]=>[1,3,2,2]
[1,6,5,3,8,4,2,7]=>[7,4,3,2,6,8,1,5]=>[2,5,6,7,3,1,8,4]=>[4,1,2,1]
[5,7,4,8,3,6,2,1]=>[1,3,5,2,8,7,6,4]=>[8,6,4,7,1,2,3,5]=>[1,1,2,4]
[1,8,3,2,4,7,5,6]=>[3,7,8,4,5,6,1,2]=>[6,2,1,5,4,3,8,7]=>[1,1,2,1,2,1]
[8,4,3,2,5,7,1,6]=>[4,3,2,5,7,8,6,1]=>[5,6,7,4,2,1,3,8]=>[3,1,1,3]
[3,6,4,8,2,5,7,1]=>[3,5,1,2,6,8,7,4]=>[6,4,8,7,3,1,2,5]=>[1,2,1,1,3]
[4,3,7,2,5,8,1,6]=>[2,1,4,5,7,3,8,6]=>[7,8,5,4,2,6,1,3]=>[2,1,1,2,2]
[3,2,4,7,8,5,6,1]=>[6,1,4,8,2,3,7,5]=>[3,8,5,1,7,6,2,4]=>[2,1,2,1,2]
[2,6,4,3,8,5,1,7]=>[3,7,4,1,2,6,8,5]=>[6,2,5,8,7,3,1,4]=>[1,3,1,1,2]
[3,8,2,1,6,4,5,7]=>[1,3,6,7,4,5,8,2]=>[8,6,3,2,5,4,1,7]=>[1,1,1,2,1,2]
[8,2,1,3,4,5,7,6]=>[2,8,3,4,5,6,7,1]=>[7,1,6,5,4,3,2,8]=>[1,2,1,1,1,2]
[4,6,8,3,2,1,5,7]=>[6,1,5,4,2,7,8,3]=>[3,8,4,5,7,2,1,6]=>[2,3,1,2]
[3,2,6,8,5,4,1,7]=>[3,7,1,6,2,5,8,4]=>[6,2,8,3,7,4,1,5]=>[1,2,2,1,2]
[7,3,8,2,5,4,1,6]=>[7,2,4,6,5,1,8,3]=>[2,7,5,3,4,8,1,6]=>[2,1,3,2]
[4,2,5,3,8,7,6,1]=>[1,8,3,7,2,4,6,5]=>[8,1,6,2,7,5,3,4]=>[1,2,2,1,2]
[2,6,8,5,4,1,3,7]=>[6,2,7,5,1,4,8,3]=>[3,7,2,4,8,5,1,6]=>[2,3,1,2]
[3,1,8,6,5,4,2,7]=>[7,6,1,5,4,8,2,3]=>[2,3,8,4,5,1,7,6]=>[3,2,2,1]
[5,4,8,7,3,2,6,1]=>[1,6,2,5,8,7,4,3]=>[8,3,7,4,1,2,5,6]=>[1,2,1,4]
[6,4,8,3,7,2,5,1]=>[2,4,1,6,8,7,5,3]=>[7,5,8,3,1,2,4,6]=>[1,2,1,4]
[4,7,3,6,2,1,8,5]=>[1,3,5,8,6,4,2,7]=>[8,6,4,1,3,5,7,2]=>[1,1,1,4,1]
[5,4,3,7,1,8,2,6]=>[3,2,1,7,8,5,4,6]=>[6,7,8,2,1,4,5,3]=>[3,1,3,1]
[7,3,8,5,1,4,2,6]=>[7,2,5,6,4,1,8,3]=>[2,7,4,3,5,8,1,6]=>[2,1,3,2]
[5,4,8,7,6,2,1,3]=>[1,7,2,6,8,5,4,3]=>[8,2,7,3,1,4,5,6]=>[1,2,1,4]
[3,8,1,5,7,4,6,2]=>[4,6,8,1,7,3,5,2]=>[5,3,1,8,2,6,4,7]=>[1,1,2,2,2]
[4,8,5,7,3,1,6,2]=>[3,8,1,6,5,7,4,2]=>[6,1,8,3,4,2,5,7]=>[1,2,2,3]
[1,5,4,8,3,7,6,2]=>[2,8,3,5,7,6,1,4]=>[7,1,6,4,2,3,8,5]=>[1,2,1,3,1]
[4,8,3,6,7,1,5,2]=>[8,1,3,6,4,7,5,2]=>[1,8,6,3,5,2,4,7]=>[2,1,2,3]
[4,7,8,3,1,6,5,2]=>[4,8,1,7,5,2,6,3]=>[5,1,8,2,4,7,3,6]=>[1,2,3,2]
[8,7,5,3,6,4,2,1]=>[8,4,3,7,6,5,2,1]=>[1,5,6,2,3,4,7,8]=>[3,5]
[4,6,1,3,8,7,5,2]=>[8,1,7,4,2,6,3,5]=>[1,8,2,5,7,3,6,4]=>[2,3,2,1]
[3,7,1,6,4,2,8,5]=>[5,8,1,6,3,4,2,7]=>[4,1,8,3,6,5,7,2]=>[1,2,2,2,1]
[3,1,2,7,5,6,8,4]=>[1,5,6,4,8,2,3,7]=>[8,4,3,5,1,7,6,2]=>[1,1,2,2,1,1]
[3,6,1,2,7,5,8,4]=>[6,1,5,8,3,2,4,7]=>[3,8,4,1,6,7,5,2]=>[2,1,3,1,1]
[3,6,2,5,8,7,4,1]=>[8,4,1,2,7,3,6,5]=>[1,5,8,7,2,6,3,4]=>[3,1,2,2]
[8,5,2,3,6,7,4,1]=>[5,8,3,2,4,7,6,1]=>[4,1,6,7,5,2,3,8]=>[1,3,1,3]
[4,7,2,6,3,8,1,5]=>[1,5,7,3,4,2,8,6]=>[8,4,2,6,5,7,1,3]=>[1,1,2,2,2]
[6,3,2,4,8,7,5,1]=>[8,2,7,3,1,4,6,5]=>[1,7,2,6,8,5,3,4]=>[2,3,1,2]
[5,3,7,2,8,1,4,6]=>[2,4,1,6,7,3,8,5]=>[7,5,8,3,2,6,1,4]=>[1,2,1,2,2]
[6,3,2,8,7,5,1,4]=>[7,8,2,1,6,3,5,4]=>[2,1,7,8,3,6,4,5]=>[1,3,2,2]
[7,3,8,2,6,5,1,4]=>[7,8,2,4,1,6,5,3]=>[2,1,7,5,8,3,4,6]=>[1,2,2,3]
[6,4,8,7,2,5,1,3]=>[2,5,1,7,8,6,4,3]=>[7,4,8,2,1,3,5,6]=>[1,2,1,4]
[2,5,4,8,1,7,6,3]=>[2,8,3,7,1,5,6,4]=>[7,1,6,2,8,4,3,5]=>[1,2,2,1,2]
[5,2,8,1,7,6,3,4]=>[7,1,8,6,2,4,5,3]=>[2,8,1,3,7,5,4,6]=>[2,3,1,2]
[6,2,1,3,8,7,5,4]=>[8,7,2,6,3,1,4,5]=>[1,2,7,3,6,8,5,4]=>[3,3,1,1]
[3,6,1,8,7,5,2,4]=>[7,2,8,1,6,5,3,4]=>[2,7,1,8,3,4,6,5]=>[2,2,3,1]
[5,6,1,2,8,7,4,3]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[1,5,1,1]
[7,5,2,8,1,6,4,3]=>[8,7,3,2,5,1,6,4]=>[1,2,6,7,4,8,3,5]=>[4,2,2]
[2,7,6,8,1,5,4,3]=>[8,7,5,3,1,2,6,4]=>[1,2,4,6,8,7,3,5]=>[5,1,2]
[7,8,5,1,6,2,4,3]=>[8,6,7,4,3,1,5,2]=>[1,3,2,5,6,8,4,7]=>[2,4,2]
[7,2,1,8,3,6,5,4]=>[8,7,2,5,6,3,1,4]=>[1,2,7,4,3,6,8,5]=>[3,1,3,1]
[5,8,7,1,6,4,3,2]=>[8,1,7,6,4,5,3,2]=>[1,8,2,3,5,4,6,7]=>[2,3,3]
[11,9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[2,3,4,5,6,7,8,9,10,1,11]=>[9,2]
[9,6,5,4,3,2,8,1,7]=>[6,5,4,3,2,8,9,7,1]=>[4,5,6,7,8,2,1,3,9]=>[5,1,3]
[8,5,4,3,7,2,1,6]=>[4,3,2,7,6,8,5,1]=>[5,6,7,2,3,1,4,8]=>[3,2,3]
[6,5,4,8,3,2,7,1]=>[3,2,1,6,5,8,7,4]=>[6,7,8,3,4,1,2,5]=>[3,2,3]
[7,6,5,4,3,9,2,8,1]=>[5,4,3,2,1,7,9,8,6]=>[5,6,7,8,9,3,1,2,4]=>[5,1,3]
[10,9,8,7,6,5,4,3,2,11,1]=>[9,8,7,6,5,4,3,2,1,11,10]=>[3,4,5,6,7,8,9,10,11,1,2]=>[9,2]
[7,3,1,4,8,2,5,6]=>[4,2,6,7,8,3,1,5]=>[5,7,3,2,1,6,8,4]=>[2,1,1,3,1]
[7,4,1,2,5,8,3,6]=>[5,7,2,8,3,4,1,6]=>[4,2,7,1,6,5,8,3]=>[1,2,2,2,1]
[6,7,4,2,5,1,3,8]=>[4,6,3,1,7,5,2,8]=>[5,3,6,8,2,4,7,1]=>[1,3,3,1]
[5,7,2,4,6,8,1,3]=>[4,1,7,3,5,2,8,6]=>[5,8,2,6,4,7,1,3]=>[2,2,2,2]
[4,7,5,1,6,2,8,3]=>[8,1,6,4,3,5,2,7]=>[1,8,3,5,6,4,7,2]=>[2,3,2,1]
[5,7,4,6,3,1,8,2]=>[1,3,8,6,5,4,2,7]=>[8,6,1,3,4,5,7,2]=>[1,1,5,1]
[7,5,1,4,3,2,8,6]=>[5,4,8,3,2,6,1,7]=>[4,5,1,6,7,3,8,2]=>[2,3,2,1]
[8,6,4,2,3,7,5,1]=>[8,4,3,5,2,7,6,1]=>[1,5,6,4,7,2,3,8]=>[3,2,3]
[5,4,2,7,3,1,6,8]=>[6,3,2,1,5,7,4,8]=>[3,6,7,8,4,2,5,1]=>[4,1,2,1]
[4,5,1,2,7,6,8,3]=>[1,6,5,2,8,3,4,7]=>[8,3,4,7,1,6,5,2]=>[1,3,2,1,1]
[5,4,6,8,3,1,2,7]=>[2,1,6,3,7,5,8,4]=>[7,8,3,6,2,4,1,5]=>[2,2,2,2]
[6,4,8,1,3,7,2,5]=>[5,2,7,1,8,4,6,3]=>[4,7,2,8,1,5,3,6]=>[2,2,2,2]
[4,6,1,3,8,5,2,7]=>[1,7,4,6,2,8,3,5]=>[8,2,5,3,7,1,6,4]=>[1,2,2,2,1]
[1,3,8,4,5,7,2,6]=>[4,5,7,8,2,6,1,3]=>[5,4,2,1,7,3,8,6]=>[1,1,1,2,2,1]
[2,6,7,4,5,3,1,8]=>[4,2,7,6,1,5,3,8]=>[5,7,2,3,8,4,6,1]=>[2,3,2,1]
[2,6,8,4,3,5,1,7]=>[5,4,2,7,1,6,8,3]=>[4,5,7,2,8,3,1,6]=>[3,2,1,2]
[1,3,7,4,2,8,5,6]=>[4,7,8,2,5,1,3,6]=>[5,2,1,7,4,8,6,3]=>[1,1,2,2,1,1]
[4,6,1,3,7,2,5,8]=>[4,1,6,7,3,2,5,8]=>[5,8,3,2,6,7,4,1]=>[2,1,3,1,1]
[7,5,8,6,2,1,3,4]=>[6,5,2,7,1,8,4,3]=>[3,4,7,2,8,1,5,6]=>[3,2,3]
[2,8,1,3,6,5,4,7]=>[7,6,1,3,4,5,8,2]=>[2,3,8,6,5,4,1,7]=>[3,1,1,1,2]
[2,8,7,3,5,4,1,6]=>[7,4,6,5,8,1,3,2]=>[2,5,3,4,1,8,6,7]=>[2,2,2,2]
[7,4,2,3,6,1,8,5]=>[8,3,2,4,6,5,1,7]=>[1,6,7,5,3,4,8,2]=>[3,1,3,1]
[7,3,8,4,1,2,6,5]=>[8,2,5,4,6,1,7,3]=>[1,7,4,5,3,8,2,6]=>[2,2,2,2]
[6,8,3,2,7,1,5,4]=>[3,8,4,1,6,7,5,2]=>[6,1,5,8,3,2,4,7]=>[1,3,1,3]
[2,8,5,6,3,7,1,4]=>[5,3,7,4,8,1,6,2]=>[4,6,2,5,1,8,3,7]=>[2,2,2,2]
[7,4,2,5,8,1,6,3]=>[4,2,8,3,6,1,7,5]=>[5,7,1,6,3,8,2,4]=>[2,2,2,2]
[2,7,8,3,4,5,1,6]=>[4,5,7,6,1,2,8,3]=>[5,4,2,3,8,7,1,6]=>[1,1,3,1,2]
[3,7,1,2,4,6,5,8]=>[1,7,3,4,5,6,2,8]=>[8,2,6,5,4,3,7,1]=>[1,2,1,1,2,1]
[7,5,6,8,2,1,4,3]=>[5,2,8,6,3,1,7,4]=>[4,7,1,3,6,8,2,5]=>[2,4,2]
[2,8,6,5,3,4,1,7]=>[5,7,6,4,1,3,8,2]=>[4,2,3,5,8,6,1,7]=>[1,4,1,2]
[1,7,2,3,5,6,8,4]=>[5,6,8,3,4,1,2,7]=>[4,3,1,6,5,8,7,2]=>[1,1,2,2,1,1]
[3,7,4,2,1,5,6,8]=>[5,1,4,3,6,7,2,8]=>[4,8,5,6,3,2,7,1]=>[2,2,1,2,1]
[3,4,6,2,8,5,7,1]=>[6,1,2,3,8,4,7,5]=>[3,8,7,6,1,5,2,4]=>[2,1,1,2,2]
[4,2,1,7,5,8,3,6]=>[5,1,7,2,4,8,3,6]=>[4,8,2,7,5,1,6,3]=>[2,2,1,2,1]
[3,7,4,1,2,5,8,6]=>[8,1,4,3,5,6,2,7]=>[1,8,5,6,4,3,7,2]=>[2,2,1,2,1]
[4,7,1,6,5,2,8,3]=>[8,1,6,5,3,4,2,7]=>[1,8,3,4,6,5,7,2]=>[2,3,2,1]
[4,7,3,6,5,1,8,2]=>[8,1,3,6,5,4,2,7]=>[1,8,6,3,4,5,7,2]=>[2,1,4,1]
[4,3,7,1,6,8,5,2]=>[1,5,8,2,7,4,3,6]=>[8,4,1,7,2,5,6,3]=>[1,1,2,3,1]
[4,2,1,7,5,6,8,3]=>[5,1,6,2,4,8,3,7]=>[4,8,3,7,5,1,6,2]=>[2,2,1,2,1]
[3,2,4,8,6,7,1,5]=>[7,1,5,8,2,3,6,4]=>[2,8,4,1,7,6,3,5]=>[2,1,2,1,2]
[4,2,6,8,7,3,1,5]=>[1,3,7,6,8,2,5,4]=>[8,6,2,3,1,7,4,5]=>[1,1,2,2,2]
[3,4,6,1,8,5,2,7]=>[7,1,2,6,3,8,4,5]=>[2,8,7,3,6,1,5,4]=>[2,1,2,2,1]
[4,1,6,7,5,8,2,3]=>[1,3,7,5,4,8,2,6]=>[8,6,2,4,5,1,7,3]=>[1,1,3,2,1]
[4,3,6,7,5,1,2,8]=>[1,6,2,3,7,5,4,8]=>[8,3,7,6,2,4,5,1]=>[1,2,1,3,1]
[4,3,7,1,6,8,2,5]=>[1,7,2,5,8,4,3,6]=>[8,2,7,4,1,5,6,3]=>[1,2,1,3,1]
[4,1,7,3,6,5,2,8]=>[1,7,4,6,5,2,3,8]=>[8,2,5,3,4,7,6,1]=>[1,2,3,1,1]
[2,8,7,4,5,3,1,6]=>[4,7,6,5,8,1,3,2]=>[5,2,3,4,1,8,6,7]=>[1,3,2,2]
[2,8,7,4,3,5,1,6]=>[5,4,7,6,8,1,3,2]=>[4,5,2,3,1,8,6,7]=>[2,2,2,2]
[3,8,1,4,2,6,5,7]=>[1,4,7,3,5,6,8,2]=>[8,5,2,6,4,3,1,7]=>[1,1,2,1,1,2]
[4,1,7,3,6,2,5,8]=>[4,1,6,7,5,2,3,8]=>[5,8,3,2,4,7,6,1]=>[2,1,3,1,1]
[5,8,7,6,1,2,4,3]=>[1,8,5,6,7,4,3,2]=>[8,1,4,3,2,5,6,7]=>[1,2,1,4]
[5,8,7,6,2,1,3,4]=>[1,6,5,7,8,4,3,2]=>[8,3,4,2,1,5,6,7]=>[1,2,1,4]
[4,1,7,2,6,8,5,3]=>[1,5,8,7,4,2,3,6]=>[8,4,1,2,5,7,6,3]=>[1,1,4,1,1]
[4,2,7,3,6,1,8,5]=>[1,8,4,6,2,5,3,7]=>[8,1,5,3,7,4,6,2]=>[1,2,2,2,1]
[4,2,7,3,6,5,8,1]=>[1,6,4,5,2,3,8,7]=>[8,3,5,4,7,6,1,2]=>[1,2,2,1,2]
[3,8,2,4,5,6,7,1]=>[1,3,4,5,6,8,7,2]=>[8,6,5,4,3,1,2,7]=>[1,1,1,1,1,3]
[3,8,5,6,2,4,1,7]=>[5,3,7,1,6,4,8,2]=>[4,6,2,8,3,5,1,7]=>[2,2,2,2]
[2,8,6,5,3,7,1,4]=>[5,7,4,3,8,1,6,2]=>[4,2,5,6,1,8,3,7]=>[1,3,2,2]
[3,8,6,5,1,4,7,2]=>[6,8,5,1,4,3,7,2]=>[3,1,4,8,5,6,2,7]=>[1,3,2,2]
[3,8,2,1,4,6,7,5]=>[1,3,6,8,4,5,7,2]=>[8,6,3,1,5,4,2,7]=>[1,1,1,2,1,2]
[3,8,2,5,4,6,7,1]=>[5,1,3,4,6,8,7,2]=>[4,8,6,5,3,1,2,7]=>[2,1,1,1,3]
[4,2,7,5,6,3,8,1]=>[1,4,6,5,2,3,8,7]=>[8,5,3,4,7,6,1,2]=>[1,1,3,1,2]
[4,2,7,5,6,1,8,3]=>[1,4,8,6,2,5,3,7]=>[8,5,1,3,7,4,6,2]=>[1,1,3,2,1]
[3,2,6,1,4,5,8,7]=>[1,8,2,4,5,3,6,7]=>[8,1,7,5,4,6,3,2]=>[1,2,1,2,1,1]
[2,8,7,3,4,5,1,6]=>[4,5,7,6,8,1,3,2]=>[5,4,2,3,1,8,6,7]=>[1,1,2,2,2]
[3,8,1,2,4,6,5,7]=>[1,7,3,4,5,6,8,2]=>[8,2,6,5,4,3,1,7]=>[1,2,1,1,1,2]
[5,8,7,6,1,3,4,2]=>[1,6,8,5,7,4,3,2]=>[8,3,1,4,2,5,6,7]=>[1,1,2,4]
[5,8,7,6,2,3,4,1]=>[1,5,6,8,7,4,3,2]=>[8,4,3,1,2,5,6,7]=>[1,1,1,5]
[2,8,7,5,3,4,1,6]=>[5,7,6,4,8,1,3,2]=>[4,2,3,5,1,8,6,7]=>[1,3,2,2]
[2,8,7,5,4,3,1,6]=>[7,6,5,4,8,1,3,2]=>[2,3,4,5,1,8,6,7]=>[4,2,2]
[4,1,7,5,6,3,2,8]=>[1,4,7,6,5,2,3,8]=>[8,5,2,3,4,7,6,1]=>[1,1,4,1,1]
[5,8,7,6,1,3,2,4]=>[1,7,5,6,8,4,3,2]=>[8,2,4,3,1,5,6,7]=>[1,2,1,4]
[5,8,7,6,4,1,2,3]=>[1,6,7,8,5,4,3,2]=>[8,3,2,1,4,5,6,7]=>[1,1,1,5]
[5,4,2,3,7,6,8,1]=>[6,3,2,1,4,5,8,7]=>[3,6,7,8,5,4,1,2]=>[4,1,1,2]
[7,4,3,5,2,8,1,6]=>[3,2,5,4,7,1,8,6]=>[6,7,4,5,2,8,1,3]=>[2,2,2,2]
[7,4,6,2,3,5,8,1]=>[4,2,5,6,3,1,8,7]=>[5,7,4,3,6,8,1,2]=>[2,1,3,2]
[5,1,7,2,4,6,8,3]=>[5,6,1,8,4,2,3,7]=>[4,3,8,1,5,7,6,2]=>[1,2,3,1,1]
[4,5,7,1,2,6,8,3]=>[1,6,2,8,4,5,3,7]=>[8,3,7,1,5,4,6,2]=>[1,2,2,2,1]
[5,4,1,7,3,6,8,2]=>[5,2,1,6,4,8,3,7]=>[4,7,8,3,5,1,6,2]=>[3,2,2,1]
[3,6,4,7,5,2,8,1]=>[6,3,1,2,5,4,8,7]=>[3,6,8,7,4,5,1,2]=>[3,1,2,2]
[3,4,7,6,2,5,8,1]=>[5,6,1,2,4,3,8,7]=>[4,3,8,7,5,6,1,2]=>[1,2,1,2,2]
[4,7,5,6,1,3,8,2]=>[6,1,3,8,5,4,2,7]=>[3,8,6,1,4,5,7,2]=>[2,1,4,1]
[5,7,6,4,3,1,8,2]=>[8,1,6,5,4,3,2,7]=>[1,8,3,4,5,6,7,2]=>[2,5,1]
[5,7,6,3,1,4,8,2]=>[1,6,4,8,5,3,2,7]=>[8,3,5,1,4,6,7,2]=>[1,2,4,1]
[7,5,2,3,4,8,1,6]=>[3,4,5,2,7,1,8,6]=>[6,5,4,7,2,8,1,3]=>[1,1,2,2,2]
[8,7,5,3,4,1,6,2]=>[4,8,6,5,3,7,2,1]=>[5,1,3,4,6,2,7,8]=>[1,4,3]
[6,7,1,3,8,4,2,5]=>[7,4,6,1,8,3,2,5]=>[2,5,3,8,1,6,7,4]=>[2,2,3,1]
[3,6,5,2,7,8,1,4]=>[7,4,1,3,2,5,8,6]=>[2,5,8,6,7,4,1,3]=>[3,2,1,2]
[3,2,8,6,7,1,4,5]=>[6,7,1,4,8,2,5,3]=>[3,2,8,5,1,7,4,6]=>[1,2,1,2,2]
[4,8,3,6,5,2,1,7]=>[7,1,3,6,5,4,8,2]=>[2,8,6,3,4,5,1,7]=>[2,1,3,2]
[1,8,7,2,3,5,4,6]=>[7,4,5,6,8,3,1,2]=>[2,5,4,3,1,6,8,7]=>[2,1,1,3,1]
[1,8,7,2,5,3,4,6]=>[6,7,4,5,8,3,1,2]=>[3,2,5,4,1,6,8,7]=>[1,2,1,3,1]
[3,6,8,5,1,2,4,7]=>[5,6,1,2,7,4,8,3]=>[4,3,8,7,2,5,1,6]=>[1,2,1,2,2]
[7,1,2,8,3,5,6,4]=>[6,8,5,7,2,3,1,4]=>[3,1,4,2,7,6,8,5]=>[1,2,2,2,1]
[6,1,7,8,2,5,3,4]=>[7,8,5,3,1,6,2,4]=>[2,1,4,6,8,3,7,5]=>[1,4,2,1]
[6,7,5,2,8,1,4,3]=>[8,4,1,6,3,2,7,5]=>[1,5,8,3,6,7,2,4]=>[3,3,2]
[7,1,4,5,8,6,2,3]=>[3,4,7,8,6,2,1,5]=>[6,5,2,1,3,7,8,4]=>[1,1,1,4,1]
[5,7,6,4,2,8,1,3]=>[1,5,7,4,3,2,8,6]=>[8,4,2,5,6,7,1,3]=>[1,1,4,2]
[7,5,6,1,2,8,4,3]=>[8,7,4,2,5,3,1,6]=>[1,2,5,7,4,6,8,3]=>[4,3,1]
[5,1,4,3,6,8,7,2]=>[3,8,4,1,5,7,2,6]=>[6,1,5,8,4,2,7,3]=>[1,3,1,2,1]
[4,5,7,6,8,2,1,3]=>[7,1,2,6,4,3,8,5]=>[2,8,7,3,5,6,1,4]=>[2,1,3,2]
[5,7,6,8,4,2,1,3]=>[7,1,6,3,2,8,5,4]=>[2,8,3,6,7,1,4,5]=>[2,3,3]
[5,1,6,8,4,2,7,3]=>[3,1,8,6,5,7,2,4]=>[6,8,1,3,4,2,7,5]=>[2,3,2,1]
[7,4,8,2,3,6,5,1]=>[2,8,4,5,1,7,6,3]=>[7,1,5,4,8,2,3,6]=>[1,2,2,3]
[5,6,8,4,7,3,2,1]=>[1,2,4,8,7,6,5,3]=>[8,7,5,1,2,3,4,6]=>[1,1,1,5]
[6,4,7,8,5,2,1,3]=>[7,2,1,6,3,8,5,4]=>[2,7,8,3,6,1,4,5]=>[3,2,3]
[3,6,4,8,5,1,2,7]=>[3,6,1,2,7,5,8,4]=>[6,3,8,7,2,4,1,5]=>[1,2,1,2,2]
[3,7,4,8,1,2,5,6]=>[5,1,3,6,7,2,8,4]=>[4,8,6,3,2,7,1,5]=>[2,1,1,2,2]
[7,4,3,8,2,6,5,1]=>[2,8,3,5,1,7,6,4]=>[7,1,6,4,8,2,3,5]=>[1,2,2,3]
[7,6,8,3,2,5,4,1]=>[4,8,5,2,1,7,6,3]=>[5,1,4,7,8,2,3,6]=>[1,4,3]
[8,7,1,3,5,4,6,2]=>[6,4,5,8,3,7,2,1]=>[3,5,4,1,6,2,7,8]=>[2,1,2,3]
[7,1,8,3,4,2,6,5]=>[4,5,8,6,7,2,1,3]=>[5,4,1,3,2,7,8,6]=>[1,1,2,3,1]
[7,6,8,3,1,4,5,2]=>[6,4,8,5,2,1,7,3]=>[3,5,1,4,7,8,2,6]=>[2,4,2]
[3,1,4,8,2,5,7,6]=>[1,8,3,5,6,7,2,4]=>[8,1,6,4,3,2,7,5]=>[1,2,1,1,2,1]
[4,8,5,2,1,3,6,7]=>[1,5,4,6,3,7,8,2]=>[8,4,5,3,6,2,1,7]=>[1,2,2,1,2]
[5,8,2,6,3,1,4,7]=>[6,3,1,5,7,4,8,2]=>[3,6,8,4,2,5,1,7]=>[3,1,2,2]
[6,8,2,3,7,4,1,5]=>[7,3,4,1,6,8,5,2]=>[2,6,5,8,3,1,4,7]=>[2,2,1,3]
[7,8,2,3,4,6,5,1]=>[8,3,4,5,1,7,6,2]=>[1,6,5,4,8,2,3,7]=>[2,1,2,3]
[8,1,7,2,4,5,3,6]=>[5,7,4,6,8,2,3,1]=>[4,2,5,3,1,7,6,8]=>[1,2,1,2,2]
[8,1,3,6,2,5,4,7]=>[7,3,5,6,2,4,8,1]=>[2,6,4,3,7,5,1,8]=>[2,1,2,1,2]
[7,2,1,6,3,5,4,8]=>[7,2,5,6,3,4,1,8]=>[2,7,4,3,6,5,8,1]=>[2,1,2,2,1]
[2,7,1,6,3,5,4,8]=>[7,5,6,1,3,4,2,8]=>[2,4,3,8,6,5,7,1]=>[2,2,1,2,1]
[2,7,1,5,4,3,6,8]=>[6,5,1,3,4,7,2,8]=>[3,4,8,6,5,2,7,1]=>[3,1,1,2,1]
[7,2,1,5,4,3,6,8]=>[6,2,5,3,4,7,1,8]=>[3,7,4,6,5,2,8,1]=>[2,2,1,2,1]
[8,1,3,5,4,2,6,7]=>[6,3,5,2,4,7,8,1]=>[3,6,4,7,5,2,1,8]=>[2,2,1,1,2]
[8,1,5,3,4,2,6,7]=>[4,6,5,2,3,7,8,1]=>[5,3,4,7,6,2,1,8]=>[1,3,1,1,2]
[8,1,5,6,2,3,7,4]=>[8,5,3,6,2,4,7,1]=>[1,4,6,3,7,5,2,8]=>[3,2,1,2]
[8,1,4,3,5,2,6,7]=>[4,3,6,2,5,7,8,1]=>[5,6,3,7,4,2,1,8]=>[2,2,1,1,2]
[7,2,1,4,5,3,6,8]=>[2,4,6,3,5,7,1,8]=>[7,5,3,6,4,2,8,1]=>[1,1,2,1,2,1]
[2,7,1,4,5,3,6,8]=>[4,6,1,3,5,7,2,8]=>[5,3,8,6,4,2,7,1]=>[1,2,1,1,2,1]
[2,6,3,1,5,4,7,8]=>[3,6,1,4,5,2,7,8]=>[6,3,8,5,4,7,2,1]=>[1,2,1,2,1,1]
[6,3,2,1,5,4,7,8]=>[3,2,6,4,5,1,7,8]=>[6,7,3,5,4,8,2,1]=>[2,2,2,1,1]
[7,3,1,4,5,2,6,8]=>[4,2,6,3,5,7,1,8]=>[5,7,3,6,4,2,8,1]=>[2,2,1,2,1]
[7,3,1,5,4,2,6,8]=>[2,6,5,3,4,7,1,8]=>[7,3,4,6,5,2,8,1]=>[1,3,1,2,1]
[7,3,1,6,2,5,4,8]=>[2,7,5,6,3,4,1,8]=>[7,2,4,3,6,5,8,1]=>[1,2,2,2,1]
[3,7,1,6,2,5,4,8]=>[7,1,5,6,3,4,2,8]=>[2,8,4,3,6,5,7,1]=>[2,1,2,2,1]
[3,7,1,4,5,2,6,8]=>[1,4,6,3,5,7,2,8]=>[8,5,3,6,4,2,7,1]=>[1,1,2,1,2,1]
[3,6,2,1,5,4,7,8]=>[1,3,6,4,5,2,7,8]=>[8,6,3,5,4,7,2,1]=>[1,1,2,2,1,1]
[2,3,6,1,5,4,7,8]=>[6,1,2,4,5,3,7,8]=>[3,8,7,5,4,6,2,1]=>[2,1,1,2,1,1]
[3,5,2,4,1,6,7,8]=>[1,3,5,4,2,6,7,8]=>[8,6,4,5,7,3,2,1]=>[1,1,3,1,1,1]
[6,2,4,1,5,3,7,8]=>[6,2,4,3,5,1,7,8]=>[3,7,5,6,4,8,2,1]=>[2,2,2,1,1]
[2,6,4,1,5,3,7,8]=>[6,4,1,3,5,2,7,8]=>[3,5,8,6,4,7,2,1]=>[3,1,2,1,1]
[2,6,5,1,3,7,4,8]=>[7,4,5,1,3,2,6,8]=>[2,5,4,8,6,7,3,1]=>[2,2,2,1,1]
[6,2,5,1,3,7,4,8]=>[7,2,4,5,3,1,6,8]=>[2,7,5,4,6,8,3,1]=>[2,1,3,1,1]
[7,6,1,2,4,5,3,8]=>[5,7,3,4,6,2,1,8]=>[4,2,6,5,3,7,8,1]=>[1,2,1,3,1]
[5,6,2,1,3,7,4,8]=>[3,7,4,1,5,2,6,8]=>[6,2,5,8,4,7,3,1]=>[1,3,2,1,1]
[5,2,6,1,3,7,4,8]=>[7,2,4,1,5,3,6,8]=>[2,7,5,8,4,6,3,1]=>[2,2,2,1,1]
[2,4,6,1,5,3,7,8]=>[2,6,1,4,5,3,7,8]=>[7,3,8,5,4,6,2,1]=>[1,2,1,2,1,1]
[4,7,1,5,3,2,6,8]=>[1,6,5,3,4,7,2,8]=>[8,3,4,6,5,2,7,1]=>[1,3,1,2,1]
[5,7,1,4,2,6,3,8]=>[7,5,3,1,4,6,2,8]=>[2,4,6,8,5,3,7,1]=>[4,1,2,1]
[5,7,1,6,2,3,8,4]=>[8,5,1,6,3,4,2,7]=>[1,4,8,3,6,5,7,2]=>[3,2,2,1]
[4,2,5,3,1,6,7,8]=>[5,2,1,4,3,6,7,8]=>[4,7,8,5,6,3,2,1]=>[3,2,1,1,1]
[5,3,6,1,2,7,4,8]=>[2,7,4,1,5,3,6,8]=>[7,2,5,8,4,6,3,1]=>[1,3,2,1,1]
[3,4,6,1,5,2,7,8]=>[1,2,6,4,5,3,7,8]=>[8,7,3,5,4,6,2,1]=>[1,1,2,2,1,1]
[6,5,1,8,7,3,4,2]=>[6,2,1,8,7,5,3,4]=>[3,7,8,1,2,4,6,5]=>[3,4,1]
[6,8,5,2,3,4,1,7]=>[4,5,1,7,6,3,8,2]=>[5,4,8,2,3,6,1,7]=>[1,2,3,2]
[2,6,8,7,1,5,3,4]=>[7,2,8,5,6,1,4,3]=>[2,7,1,4,3,8,5,6]=>[2,2,2,2]
[8,5,6,2,7,1,4,3]=>[8,4,2,6,3,7,5,1]=>[1,5,7,3,6,2,4,8]=>[3,2,3]
[6,5,1,2,7,8,4,3]=>[5,8,7,3,2,1,4,6]=>[4,1,2,6,7,8,5,3]=>[1,5,1,1]
[4,7,6,1,5,3,8,2]=>[6,1,5,8,4,3,2,7]=>[3,8,4,1,5,6,7,2]=>[2,1,4,1]
[5,7,6,4,1,3,8,2]=>[1,6,8,5,4,3,2,7]=>[8,3,1,4,5,6,7,2]=>[1,1,5,1]
[7,6,2,4,5,3,8,1]=>[4,6,3,5,2,1,8,7]=>[5,3,6,4,7,8,1,2]=>[1,2,3,2]
[6,1,7,5,3,8,4,2]=>[8,5,4,3,1,7,2,6]=>[1,4,5,6,8,2,7,3]=>[5,2,1]
[8,6,7,5,3,1,4,2]=>[8,6,5,2,7,4,3,1]=>[1,3,4,7,2,5,6,8]=>[4,4]
[8,5,2,7,1,6,4,3]=>[8,7,3,2,5,6,4,1]=>[1,2,6,7,4,3,5,8]=>[4,1,3]
[7,6,1,5,3,8,4,2]=>[8,5,4,7,3,2,1,6]=>[1,4,5,2,6,7,8,3]=>[3,4,1]
[5,6,2,4,7,8,1,3]=>[4,1,7,3,2,5,8,6]=>[5,8,2,6,7,4,1,3]=>[2,3,1,2]
[3,4,6,1,7,8,5,2]=>[5,1,2,3,8,7,4,6]=>[4,8,7,6,1,2,5,3]=>[2,1,1,3,1]
[3,4,8,6,7,1,5,2]=>[8,6,1,2,4,7,5,3]=>[1,3,8,7,5,2,4,6]=>[3,1,1,3]
[4,8,5,6,7,2,3,1]=>[3,6,1,4,8,7,5,2]=>[6,3,8,5,1,2,4,7]=>[1,2,1,4]
[5,8,6,4,1,2,7,3]=>[1,8,5,6,4,3,7,2]=>[8,1,4,3,5,6,2,7]=>[1,2,3,2]
[5,8,6,1,7,2,4,3]=>[1,8,6,7,4,3,5,2]=>[8,1,3,2,5,6,4,7]=>[1,2,3,2]
[5,8,7,3,2,6,4,1]=>[1,4,8,5,7,6,3,2]=>[8,5,1,4,2,3,6,7]=>[1,1,2,4]
[5,8,1,7,2,6,4,3]=>[1,8,7,5,6,3,4,2]=>[8,1,2,4,3,6,5,7]=>[1,3,2,2]
[8,1,5,7,2,6,4,3]=>[3,8,7,5,6,2,4,1]=>[6,1,2,4,3,7,5,8]=>[1,3,2,2]
[8,1,7,2,5,6,3,4]=>[7,5,8,4,6,2,3,1]=>[2,4,1,5,3,7,6,8]=>[2,2,2,2]
[6,8,7,2,5,1,3,4]=>[4,6,1,7,8,5,3,2]=>[5,3,8,2,1,4,6,7]=>[1,2,1,4]
[5,8,7,2,1,6,3,4]=>[4,1,7,8,5,6,3,2]=>[5,8,2,1,4,3,6,7]=>[2,1,2,3]
[4,8,1,5,2,6,7,3]=>[1,6,4,8,3,5,7,2]=>[8,3,5,1,6,4,2,7]=>[1,2,2,1,2]
[3,7,8,5,1,6,2,4]=>[7,8,5,1,4,2,6,3]=>[2,1,4,8,5,7,3,6]=>[1,3,2,2]
[6,5,2,7,8,1,4,3]=>[8,6,3,2,1,4,7,5]=>[1,3,6,7,8,5,2,4]=>[5,1,2]
[7,1,2,8,5,6,3,4]=>[7,5,8,6,2,3,1,4]=>[2,4,1,3,7,6,8,5]=>[2,3,2,1]
[8,7,2,1,5,6,3,4]=>[7,3,5,8,4,6,2,1]=>[2,6,4,1,5,3,7,8]=>[2,1,2,3]
[8,6,7,1,5,2,3,4]=>[6,7,8,4,2,5,3,1]=>[3,2,1,5,7,4,6,8]=>[1,1,3,3]
[6,1,7,8,5,2,3,4]=>[6,7,3,1,8,5,2,4]=>[3,2,6,8,1,4,7,5]=>[1,3,3,1]
[7,5,6,2,1,8,4,3]=>[8,4,2,7,5,3,1,6]=>[1,5,7,2,4,6,8,3]=>[3,4,1]
[8,7,5,2,1,6,4,3]=>[8,4,7,5,3,6,2,1]=>[1,5,2,4,6,3,7,8]=>[2,3,3]
[4,5,3,6,8,2,7,1]=>[1,3,2,4,6,8,7,5]=>[8,6,7,5,3,1,2,4]=>[1,2,1,1,3]
[5,6,3,4,8,1,7,2]=>[3,1,4,2,8,6,7,5]=>[6,8,5,7,1,3,2,4]=>[2,2,2,2]
[8,4,3,1,2,6,7,5]=>[6,3,2,8,4,5,7,1]=>[3,6,7,1,5,4,2,8]=>[3,2,1,2]
[8,5,1,6,3,4,7,2]=>[5,6,4,2,8,3,7,1]=>[4,3,5,7,1,6,2,8]=>[1,3,2,2]
[5,1,8,6,3,4,7,2]=>[5,1,6,4,8,7,2,3]=>[4,8,3,5,1,2,7,6]=>[2,2,3,1]
[4,6,8,1,5,3,7,2]=>[6,1,5,2,8,4,7,3]=>[3,8,4,7,1,5,2,6]=>[2,2,2,2]
[6,4,5,8,3,2,7,1]=>[2,3,1,6,5,8,7,4]=>[7,6,8,3,4,1,2,5]=>[1,2,2,3]
[3,6,4,8,7,1,5,2]=>[8,3,1,2,6,7,5,4]=>[1,6,8,7,3,2,4,5]=>[3,1,1,3]
[6,5,8,1,3,4,7,2]=>[5,6,2,1,8,4,7,3]=>[4,3,7,8,1,5,2,6]=>[1,3,2,2]
[5,6,8,3,1,2,7,4]=>[1,8,5,4,2,6,7,3]=>[8,1,4,5,7,3,2,6]=>[1,4,1,2]
[6,1,8,3,5,2,7,4]=>[8,4,6,5,1,7,2,3]=>[1,5,3,4,8,2,7,6]=>[2,3,2,1]
[8,6,1,3,5,2,7,4]=>[8,4,6,3,5,2,7,1]=>[1,5,3,6,4,7,2,8]=>[2,2,2,2]
[8,7,1,3,5,6,2,4]=>[7,4,5,8,3,6,2,1]=>[2,5,4,1,6,3,7,8]=>[2,1,2,3]
[6,7,8,3,5,1,2,4]=>[6,4,1,7,2,8,5,3]=>[3,5,8,2,7,1,4,6]=>[3,2,3]
[3,4,8,1,2,6,7,5]=>[1,2,6,8,4,5,7,3]=>[8,7,3,1,5,4,2,6]=>[1,1,1,2,1,2]
[5,8,2,4,3,6,7,1]=>[5,3,1,4,6,8,7,2]=>[4,6,8,5,3,1,2,7]=>[3,1,1,3]
[5,8,2,3,1,6,7,4]=>[3,4,1,6,8,5,7,2]=>[6,5,8,3,1,4,2,7]=>[1,2,1,2,2]
[6,8,2,3,5,1,7,4]=>[8,3,4,1,6,5,7,2]=>[1,6,5,8,3,4,2,7]=>[2,2,2,2]
[7,8,2,3,5,6,1,4]=>[7,3,4,5,1,8,6,2]=>[2,6,5,4,8,1,3,7]=>[2,1,2,3]
[8,6,5,1,4,3,7,2]=>[6,5,8,4,3,2,7,1]=>[3,4,1,5,6,7,2,8]=>[2,4,2]
[2,4,8,6,1,3,7,5]=>[8,2,5,6,1,4,7,3]=>[1,7,4,3,8,5,2,6]=>[2,1,2,1,2]
[6,7,1,8,4,3,5,2]=>[6,5,1,8,7,3,2,4]=>[3,4,8,1,2,6,7,5]=>[3,4,1]
[2,7,8,6,1,4,3,5]=>[7,5,6,2,8,1,4,3]=>[2,4,3,7,1,8,5,6]=>[2,2,2,2]
[2,7,3,8,1,6,4,5]=>[7,8,3,5,1,2,6,4]=>[2,1,6,4,8,7,3,5]=>[1,2,2,1,2]
[2,7,8,4,1,6,3,5]=>[7,4,8,5,1,2,6,3]=>[2,5,1,4,8,7,3,6]=>[2,3,1,2]
[2,6,5,4,1,3,8,7]=>[8,5,4,1,3,2,6,7]=>[1,4,5,8,6,7,3,2]=>[4,2,1,1]
[4,1,7,6,3,8,2,5]=>[1,5,7,4,3,8,2,6]=>[8,4,2,5,6,1,7,3]=>[1,1,3,2,1]
[4,8,2,5,7,6,3,1]=>[8,1,4,7,3,6,5,2]=>[1,8,5,2,6,3,4,7]=>[2,1,2,3]
[3,4,6,5,1,8,2,7]=>[7,1,2,4,3,8,5,6]=>[2,8,7,5,6,1,4,3]=>[2,1,2,2,1]
[2,6,5,3,4,1,8,7]=>[4,5,3,1,2,8,6,7]=>[5,4,6,8,7,1,3,2]=>[1,3,1,2,1]
[4,6,1,5,2,3,8,7]=>[1,8,5,3,4,2,6,7]=>[8,1,4,6,5,7,3,2]=>[1,3,2,1,1]
[6,2,3,5,1,4,8,7]=>[8,2,3,5,4,1,6,7]=>[1,7,6,4,5,8,3,2]=>[2,1,3,1,1]
[2,6,7,5,1,8,4,3]=>[2,8,7,5,1,4,3,6]=>[7,1,2,4,8,5,6,3]=>[1,4,2,1]
[8,6,1,2,5,3,4,7]=>[6,7,3,4,5,2,8,1]=>[3,2,6,5,4,7,1,8]=>[1,2,1,2,2]
[6,2,5,1,8,3,4,7]=>[6,7,2,3,1,8,4,5]=>[3,2,7,6,8,1,5,4]=>[1,2,2,2,1]
[7,6,5,2,8,3,4,1]=>[6,8,4,3,2,1,7,5]=>[3,1,5,6,7,8,2,4]=>[1,5,2]
[2,6,3,5,1,8,7,4]=>[4,8,3,1,2,7,5,6]=>[5,1,6,8,7,2,4,3]=>[1,3,1,2,1]
[2,4,7,6,5,8,1,3]=>[7,5,2,4,1,3,8,6]=>[2,4,7,5,8,6,1,3]=>[3,2,1,2]
[2,1,4,8,7,6,3,5]=>[7,8,6,1,3,5,2,4]=>[2,1,3,8,6,4,7,5]=>[1,3,1,2,1]
[7,4,6,8,5,3,2,1]=>[3,8,2,1,7,6,5,4]=>[6,1,7,8,2,3,4,5]=>[1,3,4]
[8,1,3,5,7,4,6,2]=>[4,6,8,3,7,2,5,1]=>[5,3,1,6,2,7,4,8]=>[1,1,2,2,2]
[3,2,8,7,5,1,6,4]=>[8,6,1,5,7,2,4,3]=>[1,3,8,4,2,7,5,6]=>[3,1,2,2]
[4,8,5,1,6,7,2,3]=>[7,1,5,3,8,4,6,2]=>[2,8,4,6,1,5,3,7]=>[2,2,2,2]
[3,8,5,1,6,7,2,4]=>[7,5,1,3,8,4,6,2]=>[2,4,8,6,1,5,3,7]=>[3,1,2,2]
[7,8,6,1,3,5,2,4]=>[5,7,8,4,1,6,3,2]=>[4,2,1,5,8,3,6,7]=>[1,1,3,3]
[5,6,7,2,8,1,3,4]=>[4,1,6,2,7,3,8,5]=>[5,8,3,7,2,6,1,4]=>[2,2,2,2]
[2,5,1,8,6,7,4,3]=>[2,5,8,7,1,6,3,4]=>[7,4,1,2,8,3,6,5]=>[1,1,3,2,1]
[3,5,1,8,6,7,4,2]=>[2,5,8,1,7,6,3,4]=>[7,4,1,8,2,3,6,5]=>[1,1,2,3,1]
[5,2,3,8,6,7,4,1]=>[5,1,8,7,2,3,6,4]=>[4,8,1,2,7,6,3,5]=>[2,3,1,2]
[8,3,5,4,6,7,1,2]=>[4,2,3,7,5,8,6,1]=>[5,7,6,2,4,1,3,8]=>[2,1,2,3]
[5,1,3,8,6,7,4,2]=>[5,1,8,7,3,6,2,4]=>[4,8,1,2,6,3,7,5]=>[2,3,2,1]
[3,2,5,8,6,7,4,1]=>[5,8,1,3,7,2,6,4]=>[4,1,8,6,2,7,3,5]=>[1,2,1,2,2]
[6,2,1,5,3,8,7,4]=>[4,8,2,7,3,1,5,6]=>[5,1,7,2,6,8,4,3]=>[1,2,3,1,1]
[5,6,3,2,8,1,4,7]=>[4,3,1,6,2,7,8,5]=>[5,6,8,3,7,2,1,4]=>[3,2,1,2]
[8,1,6,3,5,2,7,4]=>[8,4,6,5,2,3,7,1]=>[1,5,3,4,7,6,2,8]=>[2,3,1,2]
[8,7,6,2,5,3,1,4]=>[7,4,6,8,5,3,2,1]=>[2,5,3,1,4,6,7,8]=>[2,1,5]
[4,7,6,8,3,2,5,1]=>[6,5,1,3,2,8,7,4]=>[3,4,8,6,7,1,2,5]=>[3,2,3]
[2,7,5,8,1,3,4,6]=>[5,6,3,7,1,2,8,4]=>[4,3,6,2,8,7,1,5]=>[1,2,2,1,2]
[7,6,2,8,5,1,4,3]=>[8,6,7,3,2,1,5,4]=>[1,3,2,6,7,8,4,5]=>[2,4,2]
[8,1,3,7,5,2,6,4]=>[8,6,3,5,7,2,4,1]=>[1,3,6,4,2,7,5,8]=>[3,1,2,2]
[6,3,8,1,4,2,5,7]=>[2,6,4,5,1,7,8,3]=>[7,3,5,4,8,2,1,6]=>[1,2,2,1,2]
[6,3,8,5,7,4,1,2]=>[7,4,1,8,2,6,5,3]=>[2,5,8,1,7,3,4,6]=>[3,2,3]
[2,1,4,8,7,5,6,3]=>[6,8,7,1,3,5,2,4]=>[3,1,2,8,6,4,7,5]=>[1,3,1,2,1]
[7,1,5,8,2,6,4,3]=>[3,8,7,5,6,2,1,4]=>[6,1,2,4,3,7,8,5]=>[1,3,3,1]
[3,6,8,2,4,1,7,5]=>[4,5,1,2,8,6,7,3]=>[5,4,8,7,1,3,2,6]=>[1,2,1,2,2]
[4,5,8,2,6,7,3,1]=>[1,2,5,8,4,7,6,3]=>[8,7,4,1,5,2,3,6]=>[1,1,1,2,3]
[2,5,8,4,6,7,3,1]=>[2,4,5,8,7,1,6,3]=>[7,5,4,1,2,8,3,6]=>[1,1,1,3,2]
[5,8,3,4,6,7,2,1]=>[3,1,4,5,8,7,6,2]=>[6,8,5,4,1,2,3,7]=>[2,1,1,4]
[2,4,8,1,6,7,3,5]=>[7,2,5,8,1,4,6,3]=>[2,7,4,1,8,5,3,6]=>[2,1,2,1,2]
[5,1,8,2,6,7,3,4]=>[7,5,1,8,4,6,2,3]=>[2,4,8,1,5,3,7,6]=>[3,2,2,1]
[3,4,8,7,2,1,5,6]=>[6,1,2,5,7,8,4,3]=>[3,8,7,4,2,1,5,6]=>[2,1,1,1,3]
[7,8,5,3,6,4,2,1]=>[8,4,3,1,7,6,5,2]=>[1,5,6,8,2,3,4,7]=>[4,4]
[2,8,5,7,4,1,3,6]=>[6,3,7,5,8,1,4,2]=>[3,6,2,4,1,8,5,7]=>[2,2,2,2]
[5,8,4,1,6,7,2,3]=>[1,7,5,3,8,4,6,2]=>[8,2,4,6,1,5,3,7]=>[1,3,2,2]
[3,8,1,4,6,7,2,5]=>[7,1,4,5,8,3,6,2]=>[2,8,5,4,1,6,3,7]=>[2,1,1,2,2]
[8,2,3,4,6,7,1,5]=>[7,2,3,4,5,8,6,1]=>[2,7,6,5,4,1,3,8]=>[2,1,1,1,3]
[6,2,7,3,8,4,1,5]=>[7,4,6,2,1,3,8,5]=>[2,5,3,7,8,6,1,4]=>[2,3,1,2]
[7,4,3,2,8,5,1,6]=>[3,2,7,4,6,1,8,5]=>[6,7,2,5,3,8,1,4]=>[2,2,2,2]
[5,3,2,8,4,6,1,7]=>[2,5,1,7,3,6,8,4]=>[7,4,8,2,6,3,1,5]=>[1,2,2,1,2]
[8,4,2,6,5,3,1,7]=>[2,7,6,3,5,4,8,1]=>[7,2,3,6,4,5,1,8]=>[1,3,2,2]
[7,4,2,5,3,1,6,8]=>[6,3,2,5,4,7,1,8]=>[3,6,7,4,5,2,8,1]=>[3,2,2,1]
[8,3,6,2,5,4,1,7]=>[7,2,4,6,5,3,8,1]=>[2,7,5,3,4,6,1,8]=>[2,1,3,2]
[5,4,8,3,2,6,1,7]=>[2,1,5,4,7,6,8,3]=>[7,8,4,5,2,3,1,6]=>[2,2,2,2]
[3,5,8,2,4,6,1,7]=>[4,1,2,5,7,6,8,3]=>[5,8,7,4,2,3,1,6]=>[2,1,1,2,2]
[6,4,7,8,2,3,1,5]=>[2,5,1,7,6,3,8,4]=>[7,4,8,2,3,6,1,5]=>[1,2,3,2]
[5,8,3,6,4,2,1,7]=>[1,7,3,6,5,4,8,2]=>[8,2,6,3,4,5,1,7]=>[1,2,3,2]
[4,8,6,2,5,3,1,7]=>[7,1,4,6,5,3,8,2]=>[2,8,5,3,4,6,1,7]=>[2,1,3,2]
[1,6,4,3,2,8,7,5]=>[3,8,4,2,7,1,5,6]=>[6,1,5,7,2,8,4,3]=>[1,3,2,1,1]
[1,5,3,2,8,4,7,6]=>[8,3,2,6,7,1,4,5]=>[1,6,7,3,2,8,5,4]=>[3,1,2,1,1]
[5,7,4,3,1,2,6,8]=>[5,1,6,4,3,7,2,8]=>[4,8,3,5,6,2,7,1]=>[2,3,2,1]
[2,8,7,3,5,1,4,6]=>[4,6,7,5,8,1,3,2]=>[5,3,2,4,1,8,6,7]=>[1,1,2,2,2]
[7,3,8,6,4,1,2,5]=>[6,7,2,5,1,8,4,3]=>[3,2,7,4,8,1,5,6]=>[1,2,2,3]
[6,1,2,7,3,8,5,4]=>[8,7,5,2,3,1,4,6]=>[1,2,4,7,6,8,5,3]=>[4,2,1,1]
[2,1,7,4,3,8,6,5]=>[8,4,7,1,5,2,3,6]=>[1,5,2,8,4,7,6,3]=>[2,2,2,1,1]
[6,1,4,3,8,2,7,5]=>[3,8,4,6,1,7,2,5]=>[6,1,5,3,8,2,7,4]=>[1,2,2,2,1]
[5,1,3,2,8,7,4,6]=>[7,8,3,1,6,2,4,5]=>[2,1,6,8,3,7,5,4]=>[1,3,2,1,1]
[1,8,4,2,7,6,5,3]=>[8,3,7,6,4,5,1,2]=>[1,6,2,3,5,4,8,7]=>[2,3,2,1]
[1,8,3,7,2,6,5,4]=>[8,7,3,5,6,4,1,2]=>[1,2,6,4,3,5,8,7]=>[3,1,3,1]
[2,1,6,8,5,4,7,3]=>[3,6,5,8,1,7,2,4]=>[6,3,4,1,8,2,7,5]=>[1,2,2,2,1]
[6,1,5,7,8,2,4,3]=>[3,8,6,4,1,7,2,5]=>[6,1,3,5,8,2,7,4]=>[1,4,2,1]
[8,3,1,6,7,2,5,4]=>[8,2,6,4,7,3,5,1]=>[1,7,3,5,2,6,4,8]=>[2,2,2,2]
[7,4,8,6,1,3,2,5]=>[2,7,5,6,1,8,4,3]=>[7,2,4,3,8,1,5,6]=>[1,2,2,3]
[4,7,6,1,2,5,3,8]=>[1,7,4,5,6,3,2,8]=>[8,2,5,4,3,6,7,1]=>[1,2,1,3,1]
[3,7,6,1,5,2,4,8]=>[6,7,1,4,5,3,2,8]=>[3,2,8,5,4,6,7,1]=>[1,2,1,3,1]
[1,5,4,8,3,2,7,6]=>[3,2,5,8,6,7,1,4]=>[6,7,4,1,3,2,8,5]=>[2,1,2,2,1]
[7,3,6,1,2,5,4,8]=>[2,7,4,5,6,3,1,8]=>[7,2,5,4,3,6,8,1]=>[1,2,1,3,1]
[5,4,7,1,3,2,6,8]=>[6,4,2,1,5,7,3,8]=>[3,5,7,8,4,2,6,1]=>[4,1,2,1]
[4,6,8,2,5,1,3,7]=>[1,4,6,2,7,5,8,3]=>[8,5,3,7,2,4,1,6]=>[1,1,2,2,2]
[7,4,6,2,1,5,3,8]=>[4,2,7,5,6,3,1,8]=>[5,7,2,4,3,6,8,1]=>[2,2,3,1]
[1,2,6,3,8,5,7,4]=>[6,3,8,7,1,2,4,5]=>[3,6,1,2,8,7,5,4]=>[2,3,1,1,1]
[1,5,2,6,8,4,7,3]=>[4,2,6,8,7,1,3,5]=>[5,7,3,1,2,8,6,4]=>[2,1,3,1,1]
[5,7,2,3,8,1,4,6]=>[3,4,1,6,7,2,8,5]=>[6,5,8,3,2,7,1,4]=>[1,2,1,2,2]
[6,4,7,5,8,1,2,3]=>[2,6,1,7,4,3,8,5]=>[7,3,8,2,5,6,1,4]=>[1,2,3,2]
[7,4,8,5,1,6,3,2]=>[8,2,7,5,4,1,6,3]=>[1,7,2,4,5,8,3,6]=>[2,4,2]
[5,8,3,6,1,7,4,2]=>[1,8,3,7,5,4,6,2]=>[8,1,6,2,4,5,3,7]=>[1,2,3,2]
[8,6,4,2,1,7,5,3]=>[8,4,3,7,5,2,6,1]=>[1,5,6,2,4,7,3,8]=>[3,3,2]
[7,4,2,1,5,8,6,3]=>[8,3,2,5,7,4,1,6]=>[1,6,7,4,2,5,8,3]=>[3,1,3,1]
[7,6,4,1,8,5,2,3]=>[7,3,8,6,4,2,1,5]=>[2,6,1,3,5,7,8,4]=>[2,5,1]
[1,6,4,8,7,5,3,2]=>[2,8,7,3,6,5,1,4]=>[7,1,2,6,3,4,8,5]=>[1,3,3,1]
[6,3,1,2,8,4,7,5]=>[2,8,6,7,3,1,4,5]=>[7,1,3,2,6,8,5,4]=>[1,2,3,1,1]
[7,5,1,3,2,8,6,4]=>[8,4,7,3,2,5,1,6]=>[1,5,2,6,7,4,8,3]=>[2,3,2,1]
[4,7,1,2,5,8,6,3]=>[1,8,5,7,3,4,2,6]=>[8,1,4,2,6,5,7,3]=>[1,2,2,2,1]
[7,5,8,1,2,6,4,3]=>[8,7,4,2,5,1,6,3]=>[1,2,5,7,4,8,3,6]=>[4,2,2]
[7,4,8,1,6,3,5,2]=>[2,6,8,7,4,1,5,3]=>[7,3,1,2,5,8,4,6]=>[1,1,4,2]
[5,8,2,1,7,3,6,4]=>[8,3,1,6,7,4,5,2]=>[1,6,8,3,2,5,4,7]=>[3,1,2,2]
[3,6,1,8,2,4,7,5]=>[8,1,5,6,2,7,3,4]=>[1,8,4,3,7,2,6,5]=>[2,1,2,2,1]
[1,3,8,7,6,2,5,4]=>[8,6,7,5,2,4,1,3]=>[1,3,2,4,7,5,8,6]=>[2,3,2,1]
[5,4,1,8,7,3,2,6]=>[2,1,7,6,8,5,3,4]=>[7,8,2,3,1,4,6,5]=>[2,2,3,1]
[3,5,1,8,7,2,4,6]=>[6,1,2,7,8,5,3,4]=>[3,8,7,2,1,4,6,5]=>[2,1,1,3,1]
[4,6,1,8,3,7,2,5]=>[1,5,7,2,8,6,3,4]=>[8,4,2,7,1,3,6,5]=>[1,1,2,3,1]
[4,7,1,2,8,6,3,5]=>[1,7,8,6,3,4,2,5]=>[8,2,1,3,6,5,7,4]=>[1,1,3,2,1]
[5,8,4,1,7,6,2,3]=>[1,7,3,8,6,4,5,2]=>[8,2,6,1,3,5,4,7]=>[1,2,3,2]
[7,6,8,1,5,4,2,3]=>[7,8,6,4,2,1,5,3]=>[2,1,3,5,7,8,4,6]=>[1,5,2]
[8,6,1,7,5,4,3,2]=>[8,7,6,5,3,2,4,1]=>[1,2,3,4,6,7,5,8]=>[6,2]
[7,1,5,8,6,4,3,2]=>[8,3,7,6,5,2,1,4]=>[1,6,2,3,4,7,8,5]=>[2,5,1]
[5,1,8,7,3,6,4,2]=>[1,8,5,7,6,4,2,3]=>[8,1,4,2,3,5,7,6]=>[1,2,4,1]
[4,1,8,7,6,2,5,3]=>[8,1,6,7,5,4,2,3]=>[1,8,3,2,4,5,7,6]=>[2,1,4,1]
[3,1,8,7,6,5,2,4]=>[7,8,6,1,5,4,2,3]=>[2,1,3,8,4,5,7,6]=>[1,3,3,1]
[1,7,4,5,2,3,6,8]=>[5,3,6,4,7,1,2,8]=>[4,6,3,5,2,8,7,1]=>[2,2,2,1,1]
[1,7,3,5,2,4,6,8]=>[3,5,6,4,7,1,2,8]=>[6,4,3,5,2,8,7,1]=>[1,1,2,2,1,1]
[1,6,3,5,2,4,7,8]=>[3,5,6,4,1,2,7,8]=>[6,4,3,5,8,7,2,1]=>[1,1,3,1,1,1]
[1,7,3,4,2,5,6,8]=>[3,5,4,6,7,1,2,8]=>[6,4,5,3,2,8,7,1]=>[1,2,1,2,1,1]
[1,8,6,7,3,4,2,5]=>[5,7,6,3,8,4,1,2]=>[4,2,3,6,1,5,8,7]=>[1,3,3,1]
[1,8,5,7,3,4,2,6]=>[5,3,7,6,8,4,1,2]=>[4,6,2,3,1,5,8,7]=>[2,2,3,1]
[1,7,3,4,2,6,5,8]=>[3,4,7,5,6,1,2,8]=>[6,5,2,4,3,8,7,1]=>[1,1,2,2,1,1]
[1,5,2,8,4,7,3,6]=>[5,2,7,8,6,1,3,4]=>[4,7,2,1,3,8,6,5]=>[2,1,3,1,1]
[1,4,2,8,5,7,3,6]=>[2,5,7,8,6,1,3,4]=>[7,4,2,1,3,8,6,5]=>[1,1,1,3,1,1]
[1,7,3,5,2,6,4,8]=>[7,3,5,4,6,1,2,8]=>[2,6,4,5,3,8,7,1]=>[2,2,2,1,1]
[1,8,4,7,3,5,2,6]=>[3,5,7,6,8,4,1,2]=>[6,4,2,3,1,5,8,7]=>[1,1,2,3,1]
[1,7,3,6,2,5,4,8]=>[7,3,5,6,4,1,2,8]=>[2,6,4,3,5,8,7,1]=>[2,1,3,1,1]
[1,7,3,6,2,4,5,8]=>[3,5,6,7,4,1,2,8]=>[6,4,3,2,5,8,7,1]=>[1,1,1,3,1,1]
[1,7,4,6,2,3,5,8]=>[5,3,6,7,4,1,2,8]=>[4,6,3,2,5,8,7,1]=>[2,1,3,1,1]
[1,8,5,6,2,3,4,7]=>[5,6,3,7,4,8,1,2]=>[4,3,6,2,5,1,8,7]=>[1,2,2,2,1]
[1,8,5,6,2,4,3,7]=>[7,5,3,6,4,8,1,2]=>[2,4,6,3,5,1,8,7]=>[3,2,2,1]
[1,3,2,8,5,6,4,7]=>[5,7,2,6,8,1,3,4]=>[4,2,7,3,1,8,6,5]=>[1,2,1,2,1,1]
[1,5,2,8,4,6,3,7]=>[5,2,7,6,8,1,3,4]=>[4,7,2,3,1,8,6,5]=>[2,2,2,1,1]
[1,6,2,8,4,5,3,7]=>[5,7,6,2,8,1,3,4]=>[4,2,3,7,1,8,6,5]=>[1,3,2,1,1]
[9,1,2,3,5,4,6,7,8]=>[6,2,3,4,5,7,8,9,1]=>[4,8,7,6,5,3,2,1,9]=>[2,1,1,1,1,1,2]
[8,1,2,4,5,3,6,7]=>[4,6,2,3,5,7,8,1]=>[5,3,7,6,4,2,1,8]=>[1,2,1,1,1,2]
[2,3,4,6,5,7,8,9,1]=>[5,1,2,3,4,6,7,9,8]=>[5,9,8,7,6,4,3,1,2]=>[2,1,1,1,1,1,2]
[10,1,2,3,4,6,5,7,8,9]=>[7,2,3,4,5,6,8,9,10,1]=>[4,9,8,7,6,5,3,2,1,10]=>[2,1,1,1,1,1,1,2]
[2,3,4,7,5,6,8,9,1]=>[5,6,1,2,3,4,7,9,8]=>[5,4,9,8,7,6,3,1,2]=>[1,2,1,1,1,1,2]
[2,3,4,5,7,6,8,9,10,1]=>[6,1,2,3,4,5,7,8,10,9]=>[5,10,9,8,7,6,4,3,1,2]=>[2,1,1,1,1,1,1,2]
[9,10,5,6,7,8,3,4,1,2]=>[3,4,9,7,5,1,10,8,6,2]=>[8,7,2,4,6,10,1,3,5,9]=>[1,1,4,4]
[9,10,7,8,3,4,5,6,1,2]=>[5,6,9,7,3,1,10,8,4,2]=>[6,5,2,4,8,10,1,3,7,9]=>[1,1,4,4]
[9,10,3,4,5,6,7,8,1,2]=>[3,4,5,6,9,7,1,10,8,2]=>[8,7,6,5,2,4,10,1,3,9]=>[1,1,1,1,3,3]
[7,8,9,10,5,6,1,2,3,4]=>[7,1,8,2,9,5,3,10,6,4]=>[4,10,3,9,2,6,8,1,5,7]=>[2,2,3,3]
[5,8,9,6,7,10,1,2,3,4]=>[7,8,1,4,2,9,5,3,10,6]=>[4,3,10,7,9,2,6,8,1,5]=>[1,2,2,3,2]
[9,10,11,12,7,8,5,6,3,4,1,2]=>[1,2,11,9,7,5,3,12,10,8,6,4]=>[12,11,2,4,6,8,10,1,3,5,7,9]=>[1,1,5,5]
[11,12,7,8,9,10,5,6,3,4,1,2]=>[3,4,11,9,7,5,1,12,10,8,6,2]=>[10,9,2,4,6,8,12,1,3,5,7,11]=>[1,1,5,5]
[7,8,9,10,11,12,5,6,3,4,1,2]=>[1,2,3,4,11,9,7,5,12,10,8,6]=>[12,11,10,9,2,4,6,8,1,3,5,7]=>[1,1,1,1,4,4]
[11,12,9,10,5,6,7,8,3,4,1,2]=>[5,6,11,9,7,3,1,12,10,8,4,2]=>[8,7,2,4,6,10,12,1,3,5,9,11]=>[1,1,5,5]
[9,10,11,12,5,6,7,8,3,4,1,2]=>[5,1,6,2,11,9,7,3,12,10,8,4]=>[8,12,7,11,2,4,6,10,1,3,5,9]=>[2,2,4,4]
[11,12,5,6,7,8,9,10,3,4,1,2]=>[3,4,5,6,11,9,7,1,12,10,8,2]=>[10,9,8,7,2,4,6,12,1,3,5,11]=>[1,1,1,1,4,4]
[5,6,7,8,9,10,11,12,3,4,1,2]=>[1,2,3,4,5,6,11,9,7,12,10,8]=>[12,11,10,9,8,7,2,4,6,1,3,5]=>[1,1,1,1,1,1,3,3]
[11,12,9,10,7,8,3,4,5,6,1,2]=>[7,8,11,9,5,3,1,12,10,6,4,2]=>[6,5,2,4,8,10,12,1,3,7,9,11]=>[1,1,5,5]
[9,10,11,12,7,8,3,4,5,6,1,2]=>[7,1,8,2,11,9,5,3,12,10,6,4]=>[6,12,5,11,2,4,8,10,1,3,7,9]=>[2,2,4,4]
[11,12,7,8,9,10,3,4,5,6,1,2]=>[7,3,8,4,11,9,5,1,12,10,6,2]=>[6,10,5,9,2,4,8,12,1,3,7,11]=>[2,2,4,4]
[7,10,11,8,9,12,3,4,5,6,1,2]=>[7,8,1,4,2,11,9,5,3,12,10,6]=>[6,5,12,9,11,2,4,8,10,1,3,7]=>[1,2,2,4,3]
[7,8,9,10,11,12,3,4,5,6,1,2]=>[1,2,7,3,8,4,11,9,5,12,10,6]=>[12,11,6,10,5,9,2,4,8,1,3,7]=>[1,1,2,2,3,3]
[11,12,9,10,3,4,5,6,7,8,1,2]=>[5,6,7,8,11,9,3,1,12,10,4,2]=>[8,7,6,5,2,4,10,12,1,3,9,11]=>[1,1,1,1,4,4]
[9,10,11,12,3,4,5,6,7,8,1,2]=>[5,6,7,1,8,2,11,9,3,12,10,4]=>[8,7,6,12,5,11,2,4,10,1,3,9]=>[1,1,2,2,3,3]
[11,12,3,4,5,6,7,8,9,10,1,2]=>[3,4,5,6,7,8,11,9,1,12,10,2]=>[10,9,8,7,6,5,2,4,12,1,3,11]=>[1,1,1,1,1,1,3,3]
[3,4,5,6,7,8,9,10,11,12,1,2]=>[1,2,3,4,5,6,7,8,11,9,12,10]=>[12,11,10,9,8,7,6,5,2,4,1,3]=>[1,1,1,1,1,1,1,1,2,2]
[11,12,9,10,7,8,5,6,1,2,3,4]=>[9,10,11,7,5,3,1,12,8,6,4,2]=>[4,3,2,6,8,10,12,1,5,7,9,11]=>[1,1,5,5]
[9,10,11,12,7,8,5,6,1,2,3,4]=>[9,1,10,2,11,7,5,3,12,8,6,4]=>[4,12,3,11,2,6,8,10,1,5,7,9]=>[2,2,4,4]
[11,12,7,8,9,10,5,6,1,2,3,4]=>[9,3,10,4,11,7,5,1,12,8,6,2]=>[4,10,3,9,2,6,8,12,1,5,7,11]=>[2,2,4,4]
[7,10,11,8,9,12,5,6,1,2,3,4]=>[9,10,1,4,2,11,7,5,3,12,8,6]=>[4,3,12,9,11,2,6,8,10,1,5,7]=>[1,2,2,4,3]
[7,8,9,10,11,12,5,6,1,2,3,4]=>[1,2,9,3,10,4,11,7,5,12,8,6]=>[12,11,4,10,3,9,2,6,8,1,5,7]=>[1,1,2,2,3,3]
[11,12,9,10,5,6,7,8,1,2,3,4]=>[9,5,10,6,11,7,3,1,12,8,4,2]=>[4,8,3,7,2,6,10,12,1,5,9,11]=>[2,2,4,4]
[9,10,11,12,5,6,7,8,1,2,3,4]=>[9,5,1,10,6,2,11,7,3,12,8,4]=>[4,8,12,3,7,11,2,6,10,1,5,9]=>[3,3,3,3]
[11,12,5,8,9,6,7,10,1,2,3,4]=>[9,10,3,6,4,11,7,5,1,12,8,2]=>[4,3,10,7,9,2,6,8,12,1,5,11]=>[1,2,2,4,3]
[5,10,11,8,9,6,7,12,1,2,3,4]=>[9,10,6,4,1,2,11,7,5,3,12,8]=>[4,3,7,9,12,11,2,6,8,10,1,5]=>[1,4,1,4,2]
[11,12,5,6,7,8,9,10,1,2,3,4]=>[3,4,9,5,10,6,11,7,1,12,8,2]=>[10,9,4,8,3,7,2,6,12,1,5,11]=>[1,1,2,2,3,3]
[5,6,9,10,7,8,11,12,1,2,3,4]=>[9,5,1,2,3,10,6,4,11,7,12,8]=>[4,8,12,11,10,3,7,9,2,6,1,5]=>[3,1,1,3,2,2]
[5,6,7,8,9,10,11,12,1,2,3,4]=>[1,2,3,4,9,5,10,6,11,7,12,8]=>[12,11,10,9,4,8,3,7,2,6,1,5]=>[1,1,1,1,2,2,2,2]
[11,12,9,10,7,8,1,2,3,4,5,6]=>[7,8,9,10,11,5,3,1,12,6,4,2]=>[6,5,4,3,2,8,10,12,1,7,9,11]=>[1,1,1,1,4,4]
[9,10,11,12,7,8,1,2,3,4,5,6]=>[7,8,9,1,10,2,11,5,3,12,6,4]=>[6,5,4,12,3,11,2,8,10,1,7,9]=>[1,1,2,2,3,3]
[11,12,7,8,9,10,1,2,3,4,5,6]=>[7,8,9,3,10,4,11,5,1,12,6,2]=>[6,5,4,10,3,9,2,8,12,1,7,11]=>[1,1,2,2,3,3]
[7,10,11,8,9,12,1,2,3,4,5,6]=>[7,1,8,9,10,4,2,11,5,3,12,6]=>[6,12,5,4,3,9,11,2,8,10,1,7]=>[2,1,1,3,3,2]
[11,12,9,10,1,2,3,4,5,6,7,8]=>[5,6,7,8,9,10,11,3,1,12,4,2]=>[8,7,6,5,4,3,2,10,12,1,9,11]=>[1,1,1,1,1,1,3,3]
[9,10,11,12,1,2,3,4,5,6,7,8]=>[5,6,7,8,9,1,10,2,11,3,12,4]=>[8,7,6,5,4,12,3,11,2,10,1,9]=>[1,1,1,1,2,2,2,2]
[11,12,1,2,3,4,5,6,7,8,9,10]=>[3,4,5,6,7,8,9,10,11,1,12,2]=>[10,9,8,7,6,5,4,3,2,12,1,11]=>[1,1,1,1,1,1,1,1,2,2]
[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1,1]
[8,6,4,7,2,1,3,5]=>[6,5,3,7,2,8,4,1]=>[3,4,6,2,7,1,5,8]=>[3,2,3]
[1,6,4,7,2,8,3,5]=>[3,7,2,8,5,1,4,6]=>[6,2,7,1,4,8,5,3]=>[1,2,3,1,1]
[1,4,7,3,5,8,2,6]=>[2,4,5,7,3,8,1,6]=>[7,5,4,2,6,1,8,3]=>[1,1,1,2,2,1]
[5,4,8,2,3,6,1,7]=>[4,2,1,5,7,6,8,3]=>[5,7,8,4,2,3,1,6]=>[3,1,2,2]
[3,8,6,2,4,5,1,7]=>[4,5,7,1,6,3,8,2]=>[5,4,2,8,3,6,1,7]=>[1,1,2,2,2]
[4,8,6,2,3,5,1,7]=>[1,4,5,7,6,3,8,2]=>[8,5,4,2,3,6,1,7]=>[1,1,1,3,2]
[1,7,5,3,4,8,2,6]=>[4,5,3,7,2,8,1,6]=>[5,4,6,2,7,1,8,3]=>[1,2,2,2,1]
[5,8,7,4,1,2,3,6]=>[5,1,6,7,4,8,3,2]=>[4,8,3,2,5,1,6,7]=>[2,1,2,3]
[6,8,5,3,4,1,2,7]=>[6,4,1,7,5,3,8,2]=>[3,5,8,2,4,6,1,7]=>[3,3,2]
[6,8,3,7,2,1,4,5]=>[3,6,5,1,7,8,4,2]=>[6,3,4,8,2,1,5,7]=>[1,3,1,3]
[8,5,1,6,3,7,2,4]=>[5,7,4,2,8,3,6,1]=>[4,2,5,7,1,6,3,8]=>[1,3,2,2]
[6,1,3,7,4,8,2,5]=>[5,7,3,4,1,8,2,6]=>[4,2,6,5,8,1,7,3]=>[1,2,2,2,1]
[4,1,7,3,5,8,2,6]=>[4,1,5,7,3,8,2,6]=>[5,8,4,2,6,1,7,3]=>[2,1,2,2,1]
[7,1,6,4,8,2,3,5]=>[6,4,7,3,8,2,1,5]=>[3,5,2,6,1,7,8,4]=>[2,2,3,1]
[1,8,5,7,2,3,4,6]=>[5,6,3,7,8,4,1,2]=>[4,3,6,2,1,5,8,7]=>[1,2,1,3,1]
[6,1,5,8,2,3,4,7]=>[5,6,3,7,1,8,2,4]=>[4,3,6,2,8,1,7,5]=>[1,2,2,2,1]
[5,1,7,3,8,2,4,6]=>[4,6,1,7,3,8,2,5]=>[5,3,8,2,6,1,7,4]=>[1,2,2,2,1]
[6,1,5,7,8,2,3,4]=>[6,3,7,4,1,8,2,5]=>[3,6,2,5,8,1,7,4]=>[2,3,2,1]
[7,4,8,6,1,2,3,5]=>[5,2,6,7,1,8,4,3]=>[4,7,3,2,8,1,5,6]=>[2,1,2,3]
[3,8,7,5,1,2,4,6]=>[5,6,7,1,4,8,3,2]=>[4,3,2,8,5,1,6,7]=>[1,1,2,1,3]
[3,7,6,1,2,4,5,8]=>[1,4,5,6,7,3,2,8]=>[8,5,4,3,2,6,7,1]=>[1,1,1,1,3,1]
[4,7,6,1,2,3,5,8]=>[4,1,5,6,7,3,2,8]=>[5,8,4,3,2,6,7,1]=>[2,1,1,3,1]
[1,6,5,8,2,3,4,7]=>[5,6,3,2,7,8,1,4]=>[4,3,6,7,2,1,8,5]=>[1,3,1,2,1]
[6,5,8,4,1,2,3,7]=>[5,6,2,1,7,4,8,3]=>[4,3,7,8,2,5,1,6]=>[1,3,2,2]
[8,5,7,4,1,2,3,6]=>[5,6,2,7,4,8,3,1]=>[4,3,7,2,5,1,6,8]=>[1,2,2,3]
[1,5,7,4,8,2,3,6]=>[2,6,4,7,3,8,1,5]=>[7,3,5,2,6,1,8,4]=>[1,2,2,2,1]
[7,6,4,8,2,1,3,5]=>[6,5,3,7,2,1,8,4]=>[3,4,6,2,7,8,1,5]=>[3,3,2]
[7,6,2,3,8,1,4,5]=>[3,4,6,7,2,1,8,5]=>[6,5,3,2,7,8,1,4]=>[1,1,1,3,2]
[7,4,8,5,1,6,2,3]=>[2,7,8,5,4,1,6,3]=>[7,2,1,4,5,8,3,6]=>[1,1,4,2]
[8,6,2,3,1,7,4,5]=>[3,4,7,8,5,2,6,1]=>[6,5,2,1,4,7,3,8]=>[1,1,1,3,2]
[1,7,2,8,6,3,4,5]=>[6,7,8,5,3,1,2,4]=>[3,2,1,4,6,8,7,5]=>[1,1,4,1,1]
[7,6,1,3,8,2,4,5]=>[4,6,7,8,3,2,1,5]=>[5,3,2,1,6,7,8,4]=>[1,1,1,4,1]
[7,5,8,1,3,6,2,4]=>[5,7,2,8,4,1,6,3]=>[4,2,7,1,5,8,3,6]=>[1,2,3,2]
[5,4,1,8,2,3,6,7]=>[5,6,2,1,7,8,3,4]=>[4,3,7,8,2,1,6,5]=>[1,3,1,2,1]
[1,4,8,7,2,3,5,6]=>[2,5,6,7,8,4,1,3]=>[7,4,3,2,1,5,8,6]=>[1,1,1,1,3,1]
[1,5,8,7,2,3,4,6]=>[5,2,6,7,8,4,1,3]=>[4,7,3,2,1,5,8,6]=>[2,1,1,3,1]
[6,5,1,8,2,3,4,7]=>[5,6,7,2,1,8,3,4]=>[4,3,2,7,8,1,6,5]=>[1,1,3,2,1]
[7,6,8,1,5,2,3,4]=>[6,7,8,4,2,1,5,3]=>[3,2,1,5,7,8,4,6]=>[1,1,4,2]
[7,1,5,8,6,2,3,4]=>[6,3,7,8,5,2,1,4]=>[3,6,2,1,4,7,8,5]=>[2,1,4,1]
[6,1,8,2,7,3,4,5]=>[6,7,8,4,1,5,2,3]=>[3,2,1,5,8,4,7,6]=>[1,1,3,2,1]
[4,1,8,7,2,3,5,6]=>[5,1,6,7,8,4,2,3]=>[4,8,3,2,1,5,7,6]=>[2,1,1,3,1]
[5,1,8,7,2,3,4,6]=>[5,6,1,7,8,4,2,3]=>[4,3,8,2,1,5,7,6]=>[1,2,1,3,1]
[1,8,7,6,4,5,3,2]=>[5,8,7,6,4,3,1,2]=>[4,1,2,3,5,6,8,7]=>[1,6,1]
[9,8,7,6,4,5,3,2,1,10]=>[5,9,8,7,6,4,3,2,1,10]=>[6,2,3,4,5,7,8,9,10,1]=>[1,8,1]
[1,8,7,3,6,5,4,2]=>[8,7,4,6,5,3,1,2]=>[1,2,5,3,4,6,8,7]=>[3,4,1]
[7,1,5,8,3,4,2,6]=>[5,3,7,6,8,2,1,4]=>[4,6,2,3,1,7,8,5]=>[2,2,3,1]
[7,1,4,3,2,5,6,8]=>[5,4,2,3,6,7,1,8]=>[4,5,7,6,3,2,8,1]=>[3,1,1,2,1]
[6,4,2,3,8,5,7,1]=>[6,2,8,3,1,4,7,5]=>[3,7,1,6,8,5,2,4]=>[2,3,1,2]
[6,4,2,7,5,8,3,1]=>[2,5,4,1,8,3,7,6]=>[7,4,5,8,1,6,2,3]=>[1,3,2,2]
[2,4,1,7,5,8,3,6]=>[2,5,7,1,4,8,3,6]=>[7,4,2,8,5,1,6,3]=>[1,1,2,1,2,1]
[7,1,4,6,5,2,3,8]=>[3,6,7,5,2,4,1,8]=>[6,3,2,4,7,5,8,1]=>[1,1,3,2,1]
[7,1,4,6,5,8,2,3]=>[7,3,5,4,8,2,1,6]=>[2,6,4,5,1,7,8,3]=>[2,2,3,1]
[7,1,4,6,3,8,2,5]=>[3,5,7,4,8,2,1,6]=>[6,4,2,5,1,7,8,3]=>[1,1,2,3,1]
[7,1,4,3,2,5,8,6]=>[4,3,8,2,5,6,1,7]=>[5,6,1,7,4,3,8,2]=>[2,2,1,2,1]
[7,1,4,6,5,3,8,2]=>[6,3,5,4,8,2,1,7]=>[3,6,4,5,1,7,8,2]=>[2,2,3,1]
[7,1,4,6,5,3,2,8]=>[7,3,6,5,2,4,1,8]=>[2,6,3,4,7,5,8,1]=>[2,3,2,1]
[6,4,2,7,5,3,8,1]=>[2,6,5,3,1,4,8,7]=>[7,3,4,6,8,5,1,2]=>[1,4,1,2]
[3,4,7,2,6,8,5,1]=>[5,8,1,2,4,3,7,6]=>[4,1,8,7,5,6,2,3]=>[1,2,1,2,2]
[3,4,7,1,6,8,2,5]=>[7,1,2,5,8,4,3,6]=>[2,8,7,4,1,5,6,3]=>[2,1,1,3,1]
[3,4,7,1,6,8,5,2]=>[5,8,1,2,7,4,3,6]=>[4,1,8,7,2,5,6,3]=>[1,2,1,3,1]
[2,4,1,7,5,3,6,8]=>[2,6,1,5,7,3,4,8]=>[7,3,8,4,2,6,5,1]=>[1,2,1,2,1,1]
[6,4,2,7,5,3,1,8]=>[2,7,6,3,1,5,4,8]=>[7,2,3,6,8,4,5,1]=>[1,4,2,1]
[3,4,7,2,6,8,1,5]=>[7,1,2,4,5,3,8,6]=>[2,8,7,5,4,6,1,3]=>[2,1,1,2,2]
[5,4,7,3,6,8,2,1]=>[2,1,4,5,3,8,7,6]=>[7,8,5,4,6,1,2,3]=>[2,1,2,3]
[4,8,3,2,5,6,1,7]=>[1,4,3,5,7,6,8,2]=>[8,5,6,4,2,3,1,7]=>[1,2,1,2,2]
[4,8,7,3,5,1,2,6]=>[6,1,4,7,5,8,3,2]=>[3,8,5,2,4,1,6,7]=>[2,1,2,3]
[4,8,7,1,3,5,2,6]=>[1,5,7,4,6,8,3,2]=>[8,4,2,5,3,1,6,7]=>[1,1,2,1,3]
[4,8,3,1,2,6,5,7]=>[1,7,4,3,5,6,8,2]=>[8,2,5,6,4,3,1,7]=>[1,3,1,1,2]
[3,4,7,1,6,2,5,8]=>[1,2,6,7,4,5,3,8]=>[8,7,3,2,5,4,6,1]=>[1,1,1,2,2,1]
[3,4,7,1,6,2,8,5]=>[8,1,2,6,4,5,3,7]=>[1,8,7,3,5,4,6,2]=>[2,1,2,2,1]
[3,4,7,2,6,5,8,1]=>[6,1,2,4,5,3,8,7]=>[3,8,7,5,4,6,1,2]=>[2,1,1,2,2]
[4,8,3,1,2,6,7,5]=>[1,6,3,8,4,5,7,2]=>[8,3,6,1,5,4,2,7]=>[1,2,2,1,2]
[5,8,1,6,3,4,2,7]=>[5,1,7,6,3,4,8,2]=>[4,8,2,3,6,5,1,7]=>[2,3,1,2]
[6,8,5,1,3,7,2,4]=>[5,7,1,8,4,3,6,2]=>[4,2,8,1,5,6,3,7]=>[1,2,3,2]
[6,8,5,1,3,4,7,2]=>[5,6,1,8,4,3,7,2]=>[4,3,8,1,5,6,2,7]=>[1,2,3,2]
[5,4,7,3,6,2,8,1]=>[2,1,4,6,5,3,8,7]=>[7,8,5,3,4,6,1,2]=>[2,1,3,2]
[5,4,7,2,6,1,8,3]=>[2,1,8,4,6,5,3,7]=>[7,8,1,5,3,4,6,2]=>[2,2,3,1]
[6,4,3,7,5,1,2,8]=>[3,2,6,1,7,5,4,8]=>[6,7,3,8,2,4,5,1]=>[2,2,3,1]
[6,4,3,7,5,1,8,2]=>[2,8,3,1,6,5,4,7]=>[7,1,6,8,3,4,5,2]=>[1,3,3,1]
[6,2,4,3,1,5,8,7]=>[4,2,3,8,5,1,6,7]=>[5,7,6,1,4,8,3,2]=>[2,1,3,1,1]
[3,8,7,4,1,5,2,6]=>[7,5,1,4,6,8,3,2]=>[2,4,8,5,3,1,6,7]=>[3,1,1,3]
[2,4,7,3,6,1,5,8]=>[2,4,6,7,1,5,3,8]=>[7,5,3,2,8,4,6,1]=>[1,1,1,2,2,1]
[5,8,3,2,1,6,4,7]=>[4,3,1,7,5,6,8,2]=>[5,6,8,2,4,3,1,7]=>[3,2,1,2]
[5,4,7,3,6,2,1,8]=>[2,1,4,7,6,5,3,8]=>[7,8,5,2,3,4,6,1]=>[2,1,4,1]
[7,3,8,2,1,6,5,4]=>[8,2,4,7,5,1,6,3]=>[1,7,5,2,4,8,3,6]=>[2,1,3,2]
[7,4,3,8,5,2,1,6]=>[2,7,3,6,5,1,8,4]=>[7,2,6,3,4,8,1,5]=>[1,2,3,2]
[6,5,2,8,4,3,1,7]=>[7,6,3,2,1,5,8,4]=>[2,3,6,7,8,4,1,5]=>[5,1,2]
[4,3,2,8,6,5,1,7]=>[1,7,2,6,3,5,8,4]=>[8,2,7,3,6,4,1,5]=>[1,2,2,1,2]
[4,3,8,7,5,1,6,2]=>[8,1,6,2,5,7,4,3]=>[1,8,3,7,4,2,5,6]=>[2,2,1,3]
[3,2,5,8,6,1,4,7]=>[1,3,6,7,2,5,8,4]=>[8,6,3,2,7,4,1,5]=>[1,1,1,2,1,2]
[8,4,3,7,5,2,6,1]=>[2,6,3,5,8,7,4,1]=>[7,3,6,4,1,2,5,8]=>[1,2,1,4]
[5,3,7,8,4,1,2,6]=>[6,1,7,2,5,3,8,4]=>[3,8,2,7,4,6,1,5]=>[2,2,2,2]
[6,2,5,8,3,1,4,7]=>[6,5,2,3,1,7,8,4]=>[3,4,7,6,8,2,1,5]=>[3,2,1,2]
[6,2,4,8,3,1,5,7]=>[3,6,2,5,1,7,8,4]=>[6,3,7,4,8,2,1,5]=>[1,2,2,1,2]
[5,2,3,8,4,1,6,7]=>[6,2,3,1,5,7,8,4]=>[3,7,6,8,4,2,1,5]=>[2,2,1,1,2]
[5,3,8,7,4,1,6,2]=>[1,8,6,2,5,7,4,3]=>[8,1,3,7,4,2,5,6]=>[1,3,1,3]
[5,3,2,8,6,4,1,7]=>[7,2,1,6,3,5,8,4]=>[2,7,8,3,6,4,1,5]=>[3,2,1,2]
[7,5,3,8,4,2,1,6]=>[7,3,2,6,5,1,8,4]=>[2,6,7,3,4,8,1,5]=>[3,3,2]
[8,7,5,3,6,2,4,1]=>[4,6,3,8,7,5,2,1]=>[5,3,6,1,2,4,7,8]=>[1,2,5]
[8,6,5,3,7,2,4,1]=>[4,6,3,2,8,7,5,1]=>[5,3,6,7,1,2,4,8]=>[1,3,4]
[7,5,4,3,8,2,6,1]=>[4,3,2,6,1,8,7,5]=>[5,6,7,3,8,1,2,4]=>[3,2,3]
[6,4,5,3,8,2,7,1]=>[2,4,3,1,6,8,7,5]=>[7,5,6,8,3,1,2,4]=>[1,3,1,3]
[7,4,6,3,8,2,5,1]=>[2,4,6,3,1,8,7,5]=>[7,5,3,6,8,1,2,4]=>[1,1,3,3]
[7,5,6,3,8,2,4,1]=>[4,2,6,3,1,8,7,5]=>[5,7,3,6,8,1,2,4]=>[2,3,3]
[8,5,6,3,7,2,4,1]=>[4,2,6,3,8,7,5,1]=>[5,7,3,6,1,2,4,8]=>[2,2,4]
[7,4,6,3,5,2,8,1]=>[2,4,6,5,3,1,8,7]=>[7,5,3,4,6,8,1,2]=>[1,1,4,2]
[8,4,6,3,5,2,7,1]=>[2,4,6,5,3,8,7,1]=>[7,5,3,4,6,1,2,8]=>[1,1,3,3]
[8,4,7,3,5,2,6,1]=>[2,4,6,5,8,7,3,1]=>[7,5,3,4,1,2,6,8]=>[1,1,2,4]
[8,5,7,3,4,2,6,1]=>[4,2,6,5,8,7,3,1]=>[5,7,3,4,1,2,6,8]=>[2,2,4]
[7,5,8,4,3,2,6,1]=>[2,6,5,4,1,8,7,3]=>[7,3,4,5,8,1,2,6]=>[1,4,3]
[6,5,8,4,3,2,7,1]=>[2,1,6,5,4,8,7,3]=>[7,8,3,4,5,1,2,6]=>[2,3,3]
[6,5,8,3,4,2,7,1]=>[4,2,1,6,5,8,7,3]=>[5,7,8,3,4,1,2,6]=>[3,2,3]
[7,5,8,3,4,2,6,1]=>[4,2,6,5,1,8,7,3]=>[5,7,3,4,8,1,2,6]=>[2,3,3]
[7,5,8,4,6,2,3,1]=>[2,6,4,1,8,7,5,3]=>[7,3,5,8,1,2,4,6]=>[1,3,4]
[7,4,8,3,6,2,5,1]=>[2,4,6,1,8,7,5,3]=>[7,5,3,8,1,2,4,6]=>[1,1,2,4]
[7,4,8,3,5,2,6,1]=>[2,4,6,5,1,8,7,3]=>[7,5,3,4,8,1,2,6]=>[1,1,3,3]
[6,4,8,3,5,2,7,1]=>[2,4,1,6,5,8,7,3]=>[7,5,8,3,4,1,2,6]=>[1,2,2,3]
[6,4,7,3,5,2,8,1]=>[2,4,1,6,5,3,8,7]=>[7,5,8,3,4,6,1,2]=>[1,2,3,2]
[5,4,8,3,7,2,6,1]=>[2,1,4,6,8,7,5,3]=>[7,8,5,3,1,2,4,6]=>[2,1,1,4]
[6,5,8,3,7,2,4,1]=>[4,2,1,6,8,7,5,3]=>[5,7,8,3,1,2,4,6]=>[3,1,4]
[6,5,8,4,7,2,3,1]=>[2,1,6,4,8,7,5,3]=>[7,8,3,5,1,2,4,6]=>[2,2,4]
[6,5,8,4,7,3,2,1]=>[2,1,4,8,7,6,5,3]=>[7,8,5,1,2,3,4,6]=>[2,1,5]
[6,4,7,3,8,2,5,1]=>[2,4,1,6,3,8,7,5]=>[7,5,8,3,6,1,2,4]=>[1,2,2,3]
[5,4,7,3,8,2,6,1]=>[2,1,4,6,3,8,7,5]=>[7,8,5,3,6,1,2,4]=>[2,1,2,3]
[5,4,6,3,8,2,7,1]=>[2,1,4,3,6,8,7,5]=>[7,8,5,6,3,1,2,4]=>[2,2,1,3]
[5,3,6,2,4,7,8,1]=>[2,4,1,5,3,6,8,7]=>[7,5,8,4,6,3,1,2]=>[1,2,2,1,2]
[5,3,6,1,4,8,7,2]=>[8,2,1,5,3,7,4,6]=>[1,7,8,4,6,2,5,3]=>[3,2,2,1]
[5,3,7,2,4,6,8,1]=>[2,4,1,5,6,3,8,7]=>[7,5,8,4,3,6,1,2]=>[1,2,1,2,2]
[4,3,1,5,6,8,7,2]=>[2,1,8,4,5,7,3,6]=>[7,8,1,5,4,2,6,3]=>[2,2,1,2,1]
[4,2,1,5,8,6,3,7]=>[7,2,1,4,6,8,3,5]=>[2,7,8,5,3,1,6,4]=>[3,1,1,2,1]
[4,2,1,5,8,6,7,3]=>[6,1,8,2,4,7,3,5]=>[3,8,1,7,5,2,6,4]=>[2,2,1,2,1]
[4,3,1,5,7,8,6,2]=>[2,1,5,8,4,7,3,6]=>[7,8,4,1,5,2,6,3]=>[2,1,2,2,1]
[4,3,1,7,5,8,6,2]=>[1,8,2,5,4,7,3,6]=>[8,1,7,4,5,2,6,3]=>[1,2,2,2,1]
[6,7,3,1,4,8,2,5]=>[5,3,7,1,8,4,2,6]=>[4,6,2,8,1,5,7,3]=>[2,2,3,1]
[5,3,7,1,4,8,2,6]=>[2,5,1,7,8,4,3,6]=>[7,4,8,2,1,5,6,3]=>[1,2,1,3,1]
[4,3,1,5,7,8,2,6]=>[2,1,7,4,5,8,3,6]=>[7,8,2,5,4,1,6,3]=>[2,2,1,2,1]
[3,2,1,8,5,4,6,7]=>[1,6,2,5,7,8,3,4]=>[8,3,7,4,2,1,6,5]=>[1,2,1,1,2,1]
[3,2,1,8,5,7,4,6]=>[1,5,7,8,2,6,3,4]=>[8,4,2,1,7,3,6,5]=>[1,1,1,2,2,1]
[3,2,1,8,7,5,4,6]=>[7,1,6,8,2,5,3,4]=>[2,8,3,1,7,4,6,5]=>[2,1,2,2,1]
[5,2,7,1,8,4,3,6]=>[7,6,1,8,2,4,3,5]=>[2,3,8,1,7,5,6,4]=>[3,2,2,1]
[6,7,2,1,8,4,3,5]=>[7,3,6,1,8,4,2,5]=>[2,6,3,8,1,5,7,4]=>[2,2,3,1]
[3,2,1,8,5,6,4,7]=>[1,5,7,2,6,8,3,4]=>[8,4,2,7,3,1,6,5]=>[1,1,2,1,2,1]
[3,2,1,8,6,5,4,7]=>[7,1,6,2,5,8,3,4]=>[2,8,3,7,4,1,6,5]=>[2,2,1,2,1]
[4,3,1,6,7,8,5,2]=>[2,1,4,5,8,7,3,6]=>[7,8,5,4,1,2,6,3]=>[2,1,1,3,1]
[4,2,1,6,8,7,5,3]=>[1,8,4,7,2,6,3,5]=>[8,1,5,2,7,3,6,4]=>[1,2,2,2,1]
[4,2,1,6,8,5,7,3]=>[4,1,6,8,2,7,3,5]=>[5,8,3,1,7,2,6,4]=>[2,1,2,2,1]
[4,2,1,6,8,5,3,7]=>[4,1,7,2,6,8,3,5]=>[5,8,2,7,3,1,6,4]=>[2,2,1,2,1]
[5,2,6,1,8,7,4,3]=>[3,1,8,7,2,6,4,5]=>[6,8,1,2,7,3,5,4]=>[2,3,2,1]
[5,2,6,1,8,7,3,4]=>[7,3,1,8,2,6,4,5]=>[2,6,8,1,7,3,5,4]=>[3,2,2,1]
[5,2,6,1,8,3,4,7]=>[6,7,2,1,3,8,4,5]=>[3,2,7,8,6,1,5,4]=>[1,3,1,2,1]
[4,2,1,6,8,3,7,5]=>[4,1,8,2,6,7,3,5]=>[5,8,1,7,3,2,6,4]=>[2,2,1,2,1]
[4,3,1,6,7,8,2,5]=>[2,1,4,7,5,8,3,6]=>[7,8,5,2,4,1,6,3]=>[2,1,2,2,1]
[6,7,3,1,5,8,2,4]=>[3,7,5,1,8,4,2,6]=>[6,2,4,8,1,5,7,3]=>[1,3,3,1]
[4,2,1,7,8,6,3,5]=>[1,7,4,8,2,6,3,5]=>[8,2,5,1,7,3,6,4]=>[1,2,2,2,1]
[3,2,1,8,7,6,4,5]=>[7,8,1,6,2,5,3,4]=>[2,1,8,3,7,4,6,5]=>[1,2,2,2,1]
[3,2,1,8,6,4,7,5]=>[8,1,6,2,5,7,3,4]=>[1,8,3,7,4,2,6,5]=>[2,2,1,2,1]
[3,2,1,8,6,4,5,7]=>[1,6,7,2,5,8,3,4]=>[8,3,2,7,4,1,6,5]=>[1,1,2,1,2,1]
[3,2,1,8,4,6,7,5]=>[1,6,8,2,5,7,3,4]=>[8,3,1,7,4,2,6,5]=>[1,1,2,1,2,1]
[3,2,1,8,4,7,6,5]=>[8,1,7,2,5,6,3,4]=>[1,8,2,7,4,3,6,5]=>[2,2,1,2,1]
[3,2,1,8,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[1,8,3,2,7,4,6,5]=>[2,1,2,2,1]
[4,2,1,7,8,3,6,5]=>[1,8,6,2,4,7,3,5]=>[8,1,3,7,5,2,6,4]=>[1,3,1,2,1]
[5,2,7,1,8,3,6,4]=>[8,6,1,7,2,4,3,5]=>[1,3,8,2,7,5,6,4]=>[3,2,2,1]
[5,2,7,1,8,3,4,6]=>[6,7,1,8,2,4,3,5]=>[3,2,8,1,7,5,6,4]=>[1,2,2,2,1]
[3,2,1,8,4,5,7,6]=>[1,8,2,5,6,7,3,4]=>[8,1,7,4,3,2,6,5]=>[1,2,1,1,2,1]
[7,5,2,8,6,3,4,1]=>[6,2,8,7,3,1,5,4]=>[3,7,1,2,6,8,4,5]=>[2,4,2]
[7,3,8,6,2,4,5,1]=>[5,6,8,2,1,7,4,3]=>[4,3,1,7,8,2,5,6]=>[1,1,3,3]
[7,4,3,1,8,2,5,6]=>[6,3,2,7,8,4,1,5]=>[3,6,7,2,1,5,8,4]=>[3,1,3,1]
[7,4,2,8,5,6,1,3]=>[2,7,5,8,3,1,6,4]=>[7,2,4,1,6,8,3,5]=>[1,2,3,2]
[7,3,8,5,2,4,6,1]=>[5,6,2,4,1,8,7,3]=>[4,3,7,5,8,1,2,6]=>[1,2,2,3]
[7,3,8,4,5,6,2,1]=>[4,5,8,2,1,7,6,3]=>[5,4,1,7,8,2,3,6]=>[1,1,3,3]
[6,3,8,2,5,7,4,1]=>[5,8,2,1,4,7,6,3]=>[4,1,7,8,5,2,3,6]=>[1,3,1,3]
[6,4,3,8,1,5,2,7]=>[3,2,7,5,1,6,8,4]=>[6,7,2,4,8,3,1,5]=>[2,3,1,2]
[6,3,7,8,2,4,1,5]=>[5,7,2,1,6,3,8,4]=>[4,2,7,8,3,6,1,5]=>[1,3,2,2]
[5,4,7,2,6,8,1,3]=>[2,1,7,4,5,3,8,6]=>[7,8,2,5,4,6,1,3]=>[2,2,2,2]
[5,3,8,2,4,6,7,1]=>[2,4,1,5,6,8,7,3]=>[7,5,8,4,3,1,2,6]=>[1,2,1,1,3]
[6,3,8,2,4,7,5,1]=>[8,2,4,1,5,7,6,3]=>[1,7,5,8,4,2,3,6]=>[2,2,1,3]
[5,7,4,2,6,8,1,3]=>[1,7,4,3,5,2,8,6]=>[8,2,5,6,4,7,1,3]=>[1,3,2,2]
[6,4,8,2,7,5,1,3]=>[2,7,1,8,4,6,5,3]=>[7,2,8,1,5,3,4,6]=>[1,2,2,3]
[6,5,3,1,4,2,7,8]=>[6,4,3,5,2,1,7,8]=>[3,5,6,4,7,8,2,1]=>[3,3,1,1]
[5,7,4,2,6,1,3,8]=>[4,1,6,3,7,5,2,8]=>[5,8,3,6,2,4,7,1]=>[2,2,3,1]
[5,6,4,2,3,8,1,7]=>[4,1,5,3,2,7,8,6]=>[5,8,4,6,7,2,1,3]=>[2,3,1,2]
[5,6,3,7,8,2,4,1]=>[1,6,3,2,4,8,7,5]=>[8,3,6,7,5,1,2,4]=>[1,3,1,3]
[5,6,3,8,2,4,7,1]=>[3,1,5,2,6,8,7,4]=>[6,8,4,7,3,1,2,5]=>[2,2,1,3]
[6,3,7,2,4,5,1,8]=>[2,4,5,1,7,6,3,8]=>[7,5,4,8,2,3,6,1]=>[1,1,2,3,1]
[5,3,6,8,2,4,7,1]=>[5,2,1,3,6,8,7,4]=>[4,7,8,6,3,1,2,5]=>[3,1,1,3]
[5,4,6,2,3,8,1,7]=>[4,2,1,5,3,7,8,6]=>[5,7,8,4,6,2,1,3]=>[3,2,1,2]
[5,3,6,7,8,2,4,1]=>[3,1,6,2,4,8,7,5]=>[6,8,3,7,5,1,2,4]=>[2,2,1,3]
[3,5,8,6,4,2,1,7]=>[7,2,6,1,5,4,8,3]=>[2,7,3,8,4,5,1,6]=>[2,2,2,2]
[5,8,6,3,4,2,1,7]=>[1,4,7,6,5,3,8,2]=>[8,5,2,3,4,6,1,7]=>[1,1,4,2]
[5,6,3,4,2,1,8,7]=>[3,1,5,4,2,8,6,7]=>[6,8,4,5,7,1,3,2]=>[2,3,2,1]
[2,5,4,1,7,8,6,3]=>[3,2,5,8,1,7,4,6]=>[6,7,4,1,8,2,5,3]=>[2,1,2,2,1]
[2,7,8,5,4,1,6,3]=>[8,6,5,4,1,2,7,3]=>[1,3,4,5,8,7,2,6]=>[5,1,2]
[2,8,5,4,1,6,3,7]=>[7,5,4,1,3,6,8,2]=>[2,4,5,8,6,3,1,7]=>[4,1,1,2]
[2,6,3,8,5,4,1,7]=>[7,6,3,1,2,5,8,4]=>[2,3,6,8,7,4,1,5]=>[4,1,1,2]
[2,8,6,3,5,4,1,7]=>[7,4,6,5,1,3,8,2]=>[2,5,3,4,8,6,1,7]=>[2,3,1,2]
[5,8,6,4,2,1,3,7]=>[1,6,5,7,4,3,8,2]=>[8,3,4,2,5,6,1,7]=>[1,2,3,2]
[4,2,1,5,7,8,6,3]=>[5,1,8,2,4,7,3,6]=>[4,8,1,7,5,2,6,3]=>[2,2,1,2,1]
[2,7,8,6,3,5,4,1]=>[8,5,2,7,6,1,4,3]=>[1,4,7,2,3,8,5,6]=>[3,3,2]
[4,3,8,5,7,6,2,1]=>[8,1,4,7,2,6,5,3]=>[1,8,5,2,7,3,4,6]=>[2,1,2,3]
[7,6,2,1,8,4,3,5]=>[7,3,6,8,4,2,1,5]=>[2,6,3,1,5,7,8,4]=>[2,1,4,1]
[2,1,8,5,6,4,3,7]=>[4,7,6,1,5,8,2,3]=>[5,2,3,8,4,1,7,6]=>[1,3,1,2,1]
[8,4,2,1,5,6,3,7]=>[3,5,2,7,4,6,8,1]=>[6,4,7,2,5,3,1,8]=>[1,2,2,1,2]
[2,5,6,3,8,4,1,7]=>[2,7,4,1,3,6,8,5]=>[7,2,5,8,6,3,1,4]=>[1,3,1,1,2]
[6,3,4,2,1,8,5,7]=>[2,4,3,7,1,8,5,6]=>[7,5,6,2,8,1,4,3]=>[1,2,2,2,1]
[3,7,8,5,6,4,2,1]=>[4,2,8,7,1,6,5,3]=>[5,7,1,2,8,3,4,6]=>[2,3,3]
[3,8,5,6,4,2,1,7]=>[3,7,6,1,5,4,8,2]=>[6,2,3,8,4,5,1,7]=>[1,3,2,2]
[3,7,8,6,4,2,1,5]=>[7,6,5,1,2,8,4,3]=>[2,3,4,8,7,1,5,6]=>[4,1,3]
[8,5,3,7,6,2,4,1]=>[6,2,8,3,7,5,4,1]=>[3,7,1,6,2,4,5,8]=>[2,2,4]
[7,6,2,4,1,8,5,3]=>[4,8,3,7,5,2,1,6]=>[5,1,6,2,4,7,8,3]=>[1,2,4,1]
[8,5,4,1,7,6,2,3]=>[7,3,2,8,6,4,5,1]=>[2,6,7,1,3,5,4,8]=>[3,3,2]
[7,6,2,3,8,5,4,1]=>[8,7,3,4,2,1,6,5]=>[1,2,6,5,7,8,3,4]=>[3,3,2]
[2,1,7,8,6,4,3,5]=>[7,6,3,8,1,5,2,4]=>[2,3,6,1,8,4,7,5]=>[3,2,2,1]
[2,1,6,4,3,7,8,5]=>[4,6,1,3,8,2,5,7]=>[5,3,8,6,1,7,4,2]=>[1,2,1,2,1,1]
[6,4,2,1,3,7,8,5]=>[3,6,2,8,4,1,5,7]=>[6,3,7,1,5,8,4,2]=>[1,2,3,1,1]
[6,3,7,8,4,2,1,5]=>[7,6,2,1,5,3,8,4]=>[2,3,7,8,4,6,1,5]=>[4,2,2]
[7,8,4,2,1,6,3,5]=>[4,7,3,8,5,1,6,2]=>[5,2,6,1,4,8,3,7]=>[1,2,3,2]
[5,7,6,2,3,8,4,1]=>[1,8,4,5,3,2,7,6]=>[8,1,5,4,6,7,2,3]=>[1,2,3,2]
[2,6,1,7,5,8,4,3]=>[5,4,2,8,1,7,3,6]=>[4,5,7,1,8,2,6,3]=>[3,2,2,1]
[8,4,2,3,7,5,6,1]=>[6,2,8,3,4,7,5,1]=>[3,7,1,6,5,2,4,8]=>[2,2,1,3]
[8,5,7,6,2,1,4,3]=>[5,2,8,6,7,4,3,1]=>[4,7,1,3,2,5,6,8]=>[2,2,4]
[4,8,5,7,6,2,1,3]=>[3,7,1,6,8,5,4,2]=>[6,2,8,3,1,4,5,7]=>[1,2,1,4]
[4,7,6,2,1,3,8,5]=>[1,4,8,5,6,3,2,7]=>[8,5,1,4,3,6,7,2]=>[1,1,2,3,1]
[7,5,6,1,8,4,2,3]=>[7,2,8,6,4,3,1,5]=>[2,7,1,3,5,6,8,4]=>[2,5,1]
[2,7,5,8,4,3,6,1]=>[3,6,5,2,8,1,7,4]=>[6,3,4,7,1,8,2,5]=>[1,3,2,2]
[2,8,4,3,6,1,7,5]=>[3,8,4,6,1,5,7,2]=>[6,1,5,3,8,4,2,7]=>[1,2,2,1,2]
[6,4,7,8,3,2,1,5]=>[7,2,1,6,5,3,8,4]=>[2,7,8,3,4,6,1,5]=>[3,3,2]
[7,6,5,8,4,3,2,1,9]=>[3,2,1,8,7,6,5,4,9]=>[7,8,9,2,3,4,5,6,1]=>[3,5,1]
[7,6,5,4,9,3,2,1,8]=>[4,3,2,1,8,7,6,9,5]=>[6,7,8,9,2,3,4,1,5]=>[4,3,2]
[7,6,5,4,3,8,2,1,9]=>[5,4,3,2,1,8,7,6,9]=>[5,6,7,8,9,2,3,4,1]=>[5,3,1]
[7,6,5,4,3,2,8,1,9]=>[6,5,4,3,2,1,8,7,9]=>[4,5,6,7,8,9,2,3,1]=>[6,2,1]
[6,9,8,5,4,3,2,1,7]=>[8,1,7,6,5,4,9,3,2]=>[2,9,3,4,5,6,1,7,8]=>[2,4,3]
[8,7,9,6,5,4,3,2,1,10]=>[2,1,9,8,7,6,5,4,3,10]=>[9,10,2,3,4,5,6,7,8,1]=>[2,7,1]
[8,7,6,9,5,4,3,2,1,10]=>[3,2,1,9,8,7,6,5,4,10]=>[8,9,10,2,3,4,5,6,7,1]=>[3,6,1]
[6,4,3,7,5,2,1,8]=>[2,7,3,1,6,5,4,8]=>[7,2,6,8,3,4,5,1]=>[1,3,3,1]
[8,7,6,5,10,4,3,2,1,9]=>[4,3,2,1,9,8,7,6,10,5]=>[7,8,9,10,2,3,4,5,1,6]=>[4,4,2]
[6,5,3,2,8,4,1,7]=>[3,7,4,2,1,6,8,5]=>[6,2,5,7,8,3,1,4]=>[1,4,1,2]
[8,7,6,5,4,9,3,2,1,10]=>[5,4,3,2,1,9,8,7,6,10]=>[6,7,8,9,10,2,3,4,5,1]=>[5,4,1]
[6,5,2,7,8,4,1,3]=>[7,4,2,1,8,3,6,5]=>[2,5,7,8,1,6,3,4]=>[4,2,2]
[8,7,6,5,4,3,9,2,1,10]=>[6,5,4,3,2,1,9,8,7,10]=>[5,6,7,8,9,10,2,3,4,1]=>[6,3,1]
[7,6,5,4,3,1,8,9,2]=>[7,5,4,3,2,1,9,6,8]=>[3,5,6,7,8,9,1,4,2]=>[6,2,1]
[9,8,10,7,6,5,4,3,2,1,11]=>[2,1,10,9,8,7,6,5,4,3,11]=>[10,11,2,3,4,5,6,7,8,9,1]=>[2,8,1]
[9,8,7,10,6,5,4,3,2,1,11]=>[3,2,1,10,9,8,7,6,5,4,11]=>[9,10,11,2,3,4,5,6,7,8,1]=>[3,7,1]
[9,8,7,6,11,5,4,3,2,1,10]=>[4,3,2,1,10,9,8,7,6,11,5]=>[8,9,10,11,2,3,4,5,6,1,7]=>[4,5,2]
[6,4,3,2,5,8,1,7]=>[4,3,2,5,1,7,8,6]=>[5,6,7,4,8,2,1,3]=>[3,2,1,2]
[9,8,7,6,5,10,4,3,2,1,11]=>[5,4,3,2,1,10,9,8,7,6,11]=>[7,8,9,10,11,2,3,4,5,6,1]=>[5,5,1]
[6,3,7,2,5,4,1,8]=>[7,2,4,1,6,5,3,8]=>[2,7,5,8,3,4,6,1]=>[2,2,3,1]
[9,8,7,6,5,4,10,3,2,1,11]=>[6,5,4,3,2,1,10,9,8,7,11]=>[6,7,8,9,10,11,2,3,4,5,1]=>[6,4,1]
[9,8,7,6,5,4,3,11,2,1,10]=>[7,6,5,4,3,2,1,10,9,11,8]=>[5,6,7,8,9,10,11,2,3,1,4]=>[7,2,2]
[9,8,7,6,5,4,3,2,10,1,11]=>[8,7,6,5,4,3,2,1,10,9,11]=>[4,5,6,7,8,9,10,11,2,3,1]=>[8,2,1]
[9,8,7,6,5,4,3,2,1,10,11]=>[9,8,7,6,5,4,3,2,1,10,11]=>[3,4,5,6,7,8,9,10,11,2,1]=>[9,1,1]
[8,4,2,6,3,1,7,5]=>[5,2,8,3,6,4,7,1]=>[4,7,1,6,3,5,2,8]=>[2,2,2,2]
[1,6,7,3,4,2,8,5]=>[4,5,2,8,6,1,3,7]=>[5,4,7,1,3,8,6,2]=>[1,2,3,1,1]
[8,6,5,2,3,1,7,4]=>[4,5,8,6,3,2,7,1]=>[5,4,1,3,6,7,2,8]=>[1,1,4,2]
[1,7,6,3,4,2,8,5]=>[4,5,8,6,3,1,2,7]=>[5,4,1,3,6,8,7,2]=>[1,1,4,1,1]
[1,8,6,3,2,5,7,4]=>[4,6,8,5,3,7,1,2]=>[5,3,1,4,6,2,8,7]=>[1,1,3,2,1]
[8,7,5,2,1,4,6,3]=>[4,6,8,5,3,7,2,1]=>[5,3,1,4,6,2,7,8]=>[1,1,3,3]
[7,8,5,2,1,4,6,3]=>[4,6,8,5,3,1,7,2]=>[5,3,1,4,6,8,2,7]=>[1,1,4,2]
[6,8,5,2,3,1,7,4]=>[4,5,1,8,6,3,7,2]=>[5,4,8,1,3,6,2,7]=>[1,2,3,2]
[5,8,6,2,3,1,7,4]=>[4,1,5,8,6,3,7,2]=>[5,8,4,1,3,6,2,7]=>[2,1,3,2]
[4,8,2,6,3,1,7,5]=>[1,5,8,3,6,4,7,2]=>[8,4,1,6,3,5,2,7]=>[1,1,2,2,2]
[3,2,8,6,4,1,7,5]=>[5,8,1,6,2,4,7,3]=>[4,1,8,3,7,5,2,6]=>[1,2,2,1,2]
[3,2,1,7,5,4,8,6]=>[1,5,8,2,6,3,4,7]=>[8,4,1,7,3,6,5,2]=>[1,1,2,2,1,1]
[4,1,3,7,5,2,8,6]=>[5,1,8,3,6,2,4,7]=>[4,8,1,6,3,7,5,2]=>[2,2,2,1,1]
[5,1,7,3,4,2,8,6]=>[4,5,1,8,6,2,3,7]=>[5,4,8,1,3,7,6,2]=>[1,2,3,1,1]
[7,1,6,3,2,5,8,4]=>[4,6,8,5,2,3,1,7]=>[5,3,1,4,7,6,8,2]=>[1,1,3,2,1]
[6,1,8,2,4,5,7,3]=>[5,6,8,4,1,7,2,3]=>[4,3,1,5,8,2,7,6]=>[1,1,3,2,1]
[5,1,8,3,2,6,7,4]=>[4,6,1,8,5,7,2,3]=>[5,3,8,1,4,2,7,6]=>[1,2,2,2,1]
[3,2,8,7,1,5,6,4]=>[6,8,1,5,7,2,4,3]=>[3,1,8,4,2,7,5,6]=>[1,2,1,2,2]
[4,8,2,7,1,5,6,3]=>[1,6,8,3,5,7,4,2]=>[8,3,1,6,4,2,5,7]=>[1,1,2,1,3]
[5,8,7,2,1,4,6,3]=>[4,1,6,8,5,7,3,2]=>[5,8,3,1,4,2,6,7]=>[2,1,2,3]
[6,8,7,1,3,4,5,2]=>[5,6,1,8,4,7,3,2]=>[4,3,8,1,5,2,6,7]=>[1,2,2,3]
[7,8,6,1,3,4,5,2]=>[5,6,8,4,1,7,3,2]=>[4,3,1,5,8,2,6,7]=>[1,1,3,3]
[1,7,8,2,4,5,6,3]=>[5,6,8,4,2,7,1,3]=>[4,3,1,5,7,2,8,6]=>[1,1,3,2,1]
[8,6,7,1,3,4,5,2]=>[5,6,8,4,2,7,3,1]=>[4,3,1,5,7,2,6,8]=>[1,1,3,3]
[7,6,8,1,3,4,5,2]=>[5,6,8,4,2,1,7,3]=>[4,3,1,5,7,8,2,6]=>[1,1,4,2]
[6,5,8,2,3,1,7,4]=>[4,5,2,1,8,6,7,3]=>[5,4,7,8,1,3,2,6]=>[1,3,2,2]
[1,6,8,3,2,5,7,4]=>[4,6,2,8,5,7,1,3]=>[5,3,7,1,4,2,8,6]=>[1,2,2,2,1]
[1,5,3,8,2,6,7,4]=>[6,2,8,3,5,7,1,4]=>[3,7,1,6,4,2,8,5]=>[2,2,1,2,1]
[8,4,2,7,1,5,6,3]=>[6,2,8,3,5,7,4,1]=>[3,7,1,6,4,2,5,8]=>[2,2,1,3]
[7,4,2,8,1,5,6,3]=>[6,2,8,3,5,1,7,4]=>[3,7,1,6,4,8,2,5]=>[2,2,2,2]
[6,4,2,8,3,1,7,5]=>[5,2,8,3,1,6,7,4]=>[4,7,1,6,8,3,2,5]=>[2,3,1,2]
[4,5,2,3,1,6,8,7]=>[3,1,4,2,8,5,6,7]=>[6,8,5,7,1,4,3,2]=>[2,2,2,1,1]
[7,4,2,1,3,6,8,5]=>[3,6,2,8,4,5,1,7]=>[6,3,7,1,5,4,8,2]=>[1,2,2,2,1]
[8,4,2,1,3,6,7,5]=>[3,6,2,8,4,5,7,1]=>[6,3,7,1,5,4,2,8]=>[1,2,2,1,2]
[1,5,3,2,4,7,8,6]=>[3,6,2,8,1,4,5,7]=>[6,3,7,1,8,5,4,2]=>[1,2,2,1,1,1]
[4,6,2,1,5,3,8,7]=>[3,1,5,8,4,2,6,7]=>[6,8,4,1,5,7,3,2]=>[2,1,3,1,1]
[4,7,2,1,3,6,8,5]=>[3,1,6,8,4,5,2,7]=>[6,8,3,1,5,4,7,2]=>[2,1,2,2,1]
[5,7,1,3,2,6,8,4]=>[4,6,1,8,3,5,2,7]=>[5,3,8,1,6,4,7,2]=>[1,2,2,2,1]
[6,7,1,2,4,5,8,3]=>[5,6,8,3,1,4,2,7]=>[4,3,1,6,8,5,7,2]=>[1,1,3,2,1]
[8,6,1,2,4,5,7,3]=>[5,6,8,3,4,2,7,1]=>[4,3,1,6,5,7,2,8]=>[1,1,2,2,2]
[1,8,2,3,5,6,7,4]=>[5,6,8,3,4,7,1,2]=>[4,3,1,6,5,2,8,7]=>[1,1,2,1,2,1]
[8,7,1,2,4,5,6,3]=>[5,6,8,3,4,7,2,1]=>[4,3,1,6,5,2,7,8]=>[1,1,2,1,3]
[7,8,1,2,4,5,6,3]=>[5,6,8,3,4,1,7,2]=>[4,3,1,6,5,8,2,7]=>[1,1,2,2,2]
[5,8,1,3,2,6,7,4]=>[4,6,1,8,3,5,7,2]=>[5,3,8,1,6,4,2,7]=>[1,2,2,1,2]
[4,8,2,1,3,6,7,5]=>[3,1,6,8,4,5,7,2]=>[6,8,3,1,5,4,2,7]=>[2,1,2,1,2]
[4,1,3,2,5,7,8,6]=>[3,6,1,8,2,4,5,7]=>[6,3,8,1,7,5,4,2]=>[1,2,2,1,1,1]
[5,1,2,4,3,7,8,6]=>[4,6,8,2,1,3,5,7]=>[5,3,1,7,8,6,4,2]=>[1,1,3,1,1,1]
[5,4,8,1,2,3,7,6]=>[8,4,2,1,5,6,7,3]=>[1,5,7,8,4,3,2,6]=>[4,1,1,2]
[1,4,7,6,3,2,5,8]=>[6,2,5,7,4,1,3,8]=>[3,7,4,2,5,8,6,1]=>[2,1,3,1,1]
[4,8,3,2,7,6,1,5]=>[1,3,7,8,4,6,5,2]=>[8,6,2,1,5,3,4,7]=>[1,1,1,2,3]
[4,3,8,2,7,1,6,5]=>[1,8,2,4,6,7,5,3]=>[8,1,7,5,3,2,4,6]=>[1,2,1,1,3]
[4,3,2,8,1,7,6,5]=>[1,8,2,7,3,5,6,4]=>[8,1,7,2,6,4,3,5]=>[1,2,2,1,2]
[4,1,8,3,7,2,5,6]=>[4,1,6,7,8,5,2,3]=>[5,8,3,2,1,4,7,6]=>[2,1,1,3,1]
[4,1,8,7,3,2,5,6]=>[1,6,5,7,8,4,2,3]=>[8,3,4,2,1,5,7,6]=>[1,2,1,3,1]
[4,7,8,1,2,5,3,6]=>[1,7,4,5,6,2,8,3]=>[8,2,5,4,3,7,1,6]=>[1,2,1,2,2]
[3,4,7,6,2,1,8,5]=>[5,8,1,2,6,4,3,7]=>[4,1,8,7,3,5,6,2]=>[1,2,1,3,1]
[3,4,2,7,1,6,8,5]=>[1,2,6,8,3,5,4,7]=>[8,7,3,1,6,4,5,2]=>[1,1,1,2,2,1]
[2,3,6,7,4,1,8,5]=>[5,3,8,1,2,6,4,7]=>[4,6,1,8,7,3,5,2]=>[2,2,1,2,1]
[2,6,3,4,7,8,1,5]=>[7,3,4,1,2,5,8,6]=>[2,6,5,8,7,4,1,3]=>[2,2,1,1,2]
[3,1,7,8,4,2,5,6]=>[6,1,5,7,3,8,2,4]=>[3,8,4,2,6,1,7,5]=>[2,1,2,2,1]
[4,1,3,2,8,7,5,6]=>[7,1,8,3,6,2,4,5]=>[2,8,1,6,3,7,5,4]=>[2,2,2,1,1]
[3,7,8,2,6,4,1,5]=>[7,4,6,1,2,8,5,3]=>[2,5,3,8,7,1,4,6]=>[2,2,1,3]
[4,2,3,8,1,6,7,5]=>[6,1,8,2,3,5,7,4]=>[3,8,1,7,6,4,2,5]=>[2,2,1,1,2]
[4,3,1,8,2,5,7,6]=>[2,1,8,5,6,7,3,4]=>[7,8,1,4,3,2,6,5]=>[2,2,1,2,1]
[1,3,6,7,4,2,5,8]=>[6,5,2,3,7,1,4,8]=>[3,4,7,6,2,8,5,1]=>[3,1,2,1,1]
[4,2,8,6,3,1,7,5]=>[1,5,8,6,2,4,7,3]=>[8,4,1,3,7,5,2,6]=>[1,1,3,1,2]
[3,7,2,4,8,6,1,5]=>[7,8,1,3,4,2,6,5]=>[2,1,8,6,5,7,3,4]=>[1,2,1,2,2]
[3,2,7,4,8,1,6,5]=>[8,1,4,6,2,3,7,5]=>[1,8,5,3,7,6,2,4]=>[2,1,2,1,2]
[3,2,4,7,1,8,6,5]=>[8,1,7,2,3,5,4,6]=>[1,8,2,7,6,4,5,3]=>[2,2,1,2,1]
[3,7,4,2,6,8,1,5]=>[3,7,1,4,5,2,8,6]=>[6,2,8,5,4,7,1,3]=>[1,2,1,2,2]
[3,7,4,6,2,8,1,5]=>[3,5,7,1,4,2,8,6]=>[6,4,2,8,5,7,1,3]=>[1,1,2,2,2]
[4,7,1,5,8,2,3,6]=>[1,6,4,7,8,3,2,5]=>[8,3,5,2,1,6,7,4]=>[1,2,1,3,1]
[3,1,7,4,8,2,5,6]=>[1,4,6,7,3,8,2,5]=>[8,5,3,2,6,1,7,4]=>[1,1,1,2,2,1]
[2,6,7,3,8,4,1,5]=>[7,4,2,6,1,3,8,5]=>[2,5,7,3,8,6,1,4]=>[3,2,1,2]
[2,3,6,4,7,1,8,5]=>[8,4,1,2,3,6,5,7]=>[1,5,8,7,6,3,4,2]=>[3,1,1,2,1]
[8,7,5,2,6,3,4,1]=>[6,8,4,3,7,5,2,1]=>[3,1,5,6,2,4,7,8]=>[1,3,4]
[8,6,5,2,7,3,4,1]=>[6,8,4,3,2,7,5,1]=>[3,1,5,6,7,2,4,8]=>[1,4,3]
[7,4,8,5,6,3,2,1]=>[4,8,2,1,7,6,5,3]=>[5,1,7,8,2,3,4,6]=>[1,3,4]
[3,4,6,7,8,5,1,2]=>[3,7,1,2,4,8,6,5]=>[6,2,8,7,5,1,3,4]=>[1,2,1,1,3]
[1,2,6,4,7,5,8,3]=>[6,4,3,5,8,1,2,7]=>[3,5,6,4,1,8,7,2]=>[3,1,2,1,1]
[6,3,8,5,4,7,1,2]=>[7,5,2,1,4,8,6,3]=>[2,4,7,8,5,1,3,6]=>[4,1,3]
[1,6,2,5,4,7,8,3]=>[5,4,6,2,8,1,3,7]=>[4,5,3,7,1,8,6,2]=>[2,2,2,1,1]
[1,2,6,4,8,5,7,3]=>[6,3,8,4,7,1,2,5]=>[3,6,1,5,2,8,7,4]=>[2,2,2,1,1]
[7,8,3,1,4,2,5,6]=>[6,4,3,5,7,1,8,2]=>[3,5,6,4,2,8,1,7]=>[3,1,2,2]
[4,8,1,5,2,3,6,7]=>[5,1,6,3,4,7,8,2]=>[4,8,3,6,5,2,1,7]=>[2,2,1,1,2]
[7,4,1,5,2,3,6,8]=>[5,6,3,2,4,7,1,8]=>[4,3,6,7,5,2,8,1]=>[1,3,1,2,1]
[5,6,1,8,4,3,2,7]=>[1,7,6,5,2,8,3,4]=>[8,2,3,4,7,1,6,5]=>[1,4,2,1]
[5,1,8,6,4,3,2,7]=>[1,7,6,5,4,8,2,3]=>[8,2,3,4,5,1,7,6]=>[1,4,2,1]
[5,1,6,3,8,7,2,4]=>[7,3,1,8,4,6,2,5]=>[2,6,8,1,5,3,7,4]=>[3,2,2,1]
[6,1,2,5,8,3,7,4]=>[4,8,6,7,2,1,3,5]=>[5,1,3,2,7,8,6,4]=>[1,2,3,1,1]
[6,1,8,7,4,3,2,5]=>[7,6,5,1,8,4,2,3]=>[2,3,4,8,1,5,7,6]=>[4,3,1]
[7,1,2,5,4,8,6,3]=>[4,8,5,7,2,3,1,6]=>[5,1,4,2,7,6,8,3]=>[1,2,2,2,1]
[1,2,7,5,8,3,6,4]=>[4,8,6,3,7,1,2,5]=>[5,1,3,6,2,8,7,4]=>[1,3,2,1,1]
[4,1,6,3,7,5,2,8]=>[1,7,4,3,6,2,5,8]=>[8,2,5,6,3,7,4,1]=>[1,3,2,1,1]
[1,3,6,7,8,5,2,4]=>[3,7,4,8,2,6,1,5]=>[6,2,5,1,7,3,8,4]=>[1,2,2,2,1]
[1,2,6,4,7,8,5,3]=>[5,3,8,4,7,1,2,6]=>[4,6,1,5,2,8,7,3]=>[2,2,2,1,1]
[4,1,6,3,7,8,2,5]=>[1,7,4,3,5,8,2,6]=>[8,2,5,6,4,1,7,3]=>[1,3,1,2,1]
[3,1,6,4,8,2,7,5]=>[8,1,4,3,6,7,2,5]=>[1,8,5,6,3,2,7,4]=>[2,2,1,2,1]
[7,8,4,1,6,3,2,5]=>[7,6,3,8,4,1,5,2]=>[2,3,6,1,5,8,4,7]=>[3,3,2]
[4,1,6,3,8,7,2,5]=>[1,7,3,8,4,6,2,5]=>[8,2,6,1,5,3,7,4]=>[1,2,2,2,1]
[7,5,1,8,4,3,2,6]=>[7,6,5,2,8,3,1,4]=>[2,3,4,7,1,6,8,5]=>[4,3,1]
[6,5,1,7,4,3,2,8]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[6,1,1]
[4,1,8,5,2,3,7,6]=>[1,8,5,4,6,7,2,3]=>[8,1,4,5,3,2,7,6]=>[1,3,1,2,1]
[4,1,6,8,3,7,2,5]=>[1,5,3,7,8,6,2,4]=>[8,4,6,2,1,3,7,5]=>[1,2,1,3,1]
[5,4,6,1,3,8,2,7]=>[5,2,1,7,3,8,4,6]=>[4,7,8,2,6,1,5,3]=>[3,2,2,1]
[6,5,8,1,4,3,2,7]=>[7,6,4,2,1,5,8,3]=>[2,3,5,7,8,4,1,6]=>[5,1,2]
[1,3,5,7,6,8,2,4]=>[7,3,5,2,4,8,1,6]=>[2,6,4,7,5,1,8,3]=>[2,2,1,2,1]
[1,3,5,7,6,2,8,4]=>[8,3,6,2,5,1,4,7]=>[1,6,3,7,4,8,5,2]=>[2,2,2,1,1]
[1,3,5,7,2,6,8,4]=>[3,6,8,2,5,1,4,7]=>[6,3,1,7,4,8,5,2]=>[1,1,2,2,1,1]
[1,3,5,2,7,6,4,8]=>[3,7,2,6,1,4,5,8]=>[6,2,7,3,8,5,4,1]=>[1,2,2,1,1,1]
[1,3,5,7,6,2,4,8]=>[3,6,7,2,5,1,4,8]=>[6,3,2,7,4,8,5,1]=>[1,1,2,2,1,1]
[1,3,5,7,4,6,8,2]=>[3,5,6,2,4,8,1,7]=>[6,4,3,7,5,1,8,2]=>[1,1,2,1,2,1]
[1,3,5,7,4,6,2,8]=>[3,5,7,2,6,1,4,8]=>[6,4,2,7,3,8,5,1]=>[1,1,2,2,1,1]
[1,3,5,7,4,2,6,8]=>[3,6,2,5,7,1,4,8]=>[6,3,7,4,2,8,5,1]=>[1,2,1,2,1,1]
[1,3,5,4,7,2,6,8]=>[4,2,3,6,7,1,5,8]=>[5,7,6,3,2,8,4,1]=>[2,1,1,2,1,1]
[1,3,5,4,7,8,2,6]=>[3,7,2,4,5,8,1,6]=>[6,2,7,5,4,1,8,3]=>[1,2,1,1,2,1]
[1,3,5,4,7,2,8,6]=>[3,8,2,4,6,1,5,7]=>[6,1,7,5,3,8,4,2]=>[1,2,1,2,1,1]
[1,3,5,7,4,2,8,6]=>[3,5,8,2,6,1,4,7]=>[6,4,1,7,3,8,5,2]=>[1,1,2,2,1,1]
[1,3,5,7,4,8,2,6]=>[3,5,7,2,4,8,1,6]=>[6,4,2,7,5,1,8,3]=>[1,1,2,1,2,1]
[1,3,5,7,8,4,6,2]=>[6,3,4,8,2,7,1,5]=>[3,6,5,1,7,2,8,4]=>[2,1,2,2,1]
[1,3,5,7,8,4,2,6]=>[7,3,6,2,4,8,1,5]=>[2,6,3,7,5,1,8,4]=>[2,2,1,2,1]
[1,3,5,2,7,8,6,4]=>[3,5,8,2,7,1,4,6]=>[6,4,1,7,2,8,5,3]=>[1,1,2,2,1,1]
[1,3,5,7,2,8,6,4]=>[8,3,7,2,5,1,4,6]=>[1,6,2,7,4,8,5,3]=>[2,2,2,1,1]
[1,3,5,7,8,2,6,4]=>[8,3,6,2,4,7,1,5]=>[1,6,3,7,5,2,8,4]=>[2,2,1,2,1]
[1,6,3,2,7,4,8,5]=>[8,3,6,4,1,2,5,7]=>[1,6,3,5,8,7,4,2]=>[2,3,1,1,1]
[3,5,1,6,2,8,7,4]=>[4,1,2,8,7,3,5,6]=>[5,8,7,1,2,6,4,3]=>[2,1,3,1,1]
[1,3,7,2,5,4,8,6]=>[5,8,2,4,6,1,3,7]=>[4,1,7,5,3,8,6,2]=>[1,2,1,2,1,1]
[2,6,1,7,4,3,8,5]=>[5,8,6,1,3,2,4,7]=>[4,1,3,8,6,7,5,2]=>[1,3,2,1,1]
[1,4,7,3,5,2,8,6]=>[2,4,5,8,6,1,3,7]=>[7,5,4,1,3,8,6,2]=>[1,1,1,3,1,1]
[1,3,7,5,2,4,8,6]=>[8,5,2,4,6,1,3,7]=>[1,4,7,5,3,8,6,2]=>[3,1,2,1,1]
[2,5,7,4,3,8,1,6]=>[2,5,4,7,1,3,8,6]=>[7,4,5,2,8,6,1,3]=>[1,2,2,1,2]
[2,5,3,7,4,8,1,6]=>[5,2,7,1,3,4,8,6]=>[4,7,2,8,6,5,1,3]=>[2,2,1,1,2]
[1,4,7,2,3,8,6,5]=>[8,2,7,4,5,1,3,6]=>[1,7,2,5,4,8,6,3]=>[2,2,2,1,1]
[2,4,7,3,1,8,6,5]=>[8,2,4,7,1,5,3,6]=>[1,7,5,2,8,4,6,3]=>[2,1,2,2,1]
[1,4,6,3,8,2,7,5]=>[8,2,4,3,6,7,1,5]=>[1,7,5,6,3,2,8,4]=>[2,2,1,2,1]
[1,3,5,2,8,7,6,4]=>[8,3,7,2,6,1,4,5]=>[1,6,2,7,3,8,5,4]=>[2,2,2,1,1]
[1,4,7,3,8,2,6,5]=>[8,2,4,6,3,7,1,5]=>[1,7,5,3,6,2,8,4]=>[2,1,2,2,1]
[2,5,1,7,8,4,6,3]=>[2,6,4,8,1,7,3,5]=>[7,3,5,1,8,2,6,4]=>[1,2,2,2,1]
[3,2,6,7,8,1,5,4]=>[3,8,1,6,2,4,7,5]=>[6,1,8,3,7,5,2,4]=>[1,2,2,1,2]
[4,3,6,7,8,2,1,5]=>[1,3,7,2,6,4,8,5]=>[8,6,2,7,3,5,1,4]=>[1,1,2,2,2]
[3,5,2,7,8,4,1,6]=>[2,7,1,6,3,4,8,5]=>[7,2,8,3,6,5,1,4]=>[1,2,2,1,2]
[1,5,7,4,8,3,2,6]=>[2,4,7,6,3,8,1,5]=>[7,5,2,3,6,1,8,4]=>[1,1,3,2,1]
[2,5,1,6,8,4,7,3]=>[4,2,6,8,1,7,3,5]=>[5,7,3,1,8,2,6,4]=>[2,1,2,2,1]
[4,6,2,1,7,8,3,5]=>[1,7,3,5,2,8,4,6]=>[8,2,6,4,7,1,5,3]=>[1,2,2,2,1]
[5,3,6,4,7,8,2,1]=>[4,2,1,3,5,8,7,6]=>[5,7,8,6,4,1,2,3]=>[3,1,1,3]
[3,5,2,6,8,4,7,1]=>[4,1,2,6,8,3,7,5]=>[5,8,7,3,1,6,2,4]=>[2,1,1,2,2]
[2,5,4,6,8,7,1,3]=>[3,2,4,7,8,1,6,5]=>[6,7,5,2,1,8,3,4]=>[2,1,1,2,2]
[1,3,6,2,8,7,5,4]=>[3,8,7,2,6,1,4,5]=>[6,1,2,7,3,8,5,4]=>[1,3,2,1,1]
[1,4,6,3,8,7,2,5]=>[7,2,3,8,4,6,1,5]=>[2,7,6,1,5,3,8,4]=>[2,1,2,2,1]
[2,5,7,4,3,8,6,1]=>[2,4,8,5,1,3,7,6]=>[7,5,1,4,8,6,2,3]=>[1,1,3,1,2]
[1,5,7,2,4,8,6,3]=>[2,8,5,7,4,1,3,6]=>[7,1,4,2,5,8,6,3]=>[1,2,3,1,1]
[4,6,3,7,2,8,5,1]=>[8,1,3,2,5,4,7,6]=>[1,8,6,7,4,5,2,3]=>[2,2,2,2]
[4,3,6,7,8,2,5,1]=>[1,3,6,2,4,8,7,5]=>[8,6,3,7,5,1,2,4]=>[1,1,2,1,3]
[1,4,7,3,8,6,2,5]=>[7,8,2,4,3,6,1,5]=>[2,1,7,5,6,3,8,4]=>[1,2,2,2,1]
[2,5,4,7,8,6,1,3]=>[2,7,3,4,8,1,6,5]=>[7,2,6,5,1,8,3,4]=>[1,2,1,2,2]
[3,2,6,7,8,5,1,4]=>[3,7,1,4,8,2,6,5]=>[6,2,8,5,1,7,3,4]=>[1,2,1,2,2]
[1,3,7,2,8,6,5,4]=>[8,7,6,2,4,1,3,5]=>[1,2,3,7,5,8,6,4]=>[4,2,1,1]
[5,1,6,8,2,4,3,7]=>[7,5,3,1,6,8,2,4]=>[2,4,6,8,3,1,7,5]=>[4,1,2,1]
[5,3,7,8,2,4,1,6]=>[5,1,7,2,6,3,8,4]=>[4,8,2,7,3,6,1,5]=>[2,2,2,2]
[8,5,3,7,2,4,1,6]=>[3,5,2,7,6,8,4,1]=>[6,4,7,2,3,1,5,8]=>[1,2,2,3]
[8,2,4,7,3,1,5,6]=>[3,6,2,5,7,8,4,1]=>[6,3,7,4,2,1,5,8]=>[1,2,1,1,3]
[6,3,1,5,8,2,4,7]=>[2,6,4,7,1,8,3,5]=>[7,3,5,2,8,1,6,4]=>[1,2,2,2,1]
[5,2,4,3,8,1,6,7]=>[4,2,3,1,6,7,8,5]=>[5,7,6,8,3,2,1,4]=>[2,2,1,1,2]
[3,2,4,8,1,5,6,7]=>[2,1,3,5,6,7,8,4]=>[7,8,6,4,3,2,1,5]=>[2,1,1,1,1,2]
[3,2,4,6,8,1,5,7]=>[1,6,2,3,4,7,8,5]=>[8,3,7,6,5,2,1,4]=>[1,2,1,1,1,2]
[8,1,5,7,3,2,4,6]=>[6,5,3,7,8,2,4,1]=>[3,4,6,2,1,7,5,8]=>[3,1,2,2]
[7,4,6,8,2,3,1,5]=>[2,5,7,6,3,1,8,4]=>[7,4,2,3,6,8,1,5]=>[1,1,4,2]
[7,2,4,8,3,1,5,6]=>[3,6,2,5,7,1,8,4]=>[6,3,7,4,2,8,1,5]=>[1,2,1,2,2]
[2,4,8,7,3,1,5,6]=>[6,2,5,7,8,1,4,3]=>[3,7,4,2,1,8,5,6]=>[2,1,1,2,2]
[4,6,8,7,2,3,1,5]=>[5,1,2,7,6,8,4,3]=>[4,8,7,2,3,1,5,6]=>[2,1,2,3]
[8,7,4,6,2,3,1,5]=>[5,3,7,6,8,4,2,1]=>[4,6,2,3,1,5,7,8]=>[2,2,4]
[5,6,8,7,2,3,1,4]=>[1,5,2,7,6,8,4,3]=>[8,4,7,2,3,1,5,6]=>[1,2,2,3]
[6,4,8,7,2,3,1,5]=>[2,5,1,7,6,8,4,3]=>[7,4,8,2,3,1,5,6]=>[1,2,2,3]
[3,1,7,4,2,8,6,5]=>[8,1,4,7,5,2,3,6]=>[1,8,5,2,4,7,6,3]=>[2,1,3,1,1]
[3,2,8,4,1,7,6,5]=>[8,1,4,7,2,5,6,3]=>[1,8,5,2,7,4,3,6]=>[2,1,2,1,2]
[7,6,4,8,2,3,1,5]=>[5,3,7,6,2,1,8,4]=>[4,6,2,3,7,8,1,5]=>[2,4,2]
[5,7,6,8,2,3,1,4]=>[1,5,7,6,3,2,8,4]=>[8,4,2,3,6,7,1,5]=>[1,1,4,2]
[4,7,6,8,2,3,1,5]=>[5,7,1,6,3,2,8,4]=>[4,2,8,3,6,7,1,5]=>[1,2,3,2]
[8,2,3,7,4,1,6,5]=>[5,8,2,3,6,7,4,1]=>[4,1,7,6,3,2,5,8]=>[1,2,1,1,3]
[3,7,4,8,2,5,1,6]=>[3,5,7,1,6,2,8,4]=>[6,4,2,8,3,7,1,5]=>[1,1,2,2,2]
[2,3,7,4,1,6,8,5]=>[4,6,8,1,2,5,3,7]=>[5,3,1,8,7,4,6,2]=>[1,1,2,1,2,1]
[8,1,6,4,2,3,7,5]=>[8,5,4,6,2,3,7,1]=>[1,4,5,3,7,6,2,8]=>[3,2,1,2]
[4,7,8,6,2,3,1,5]=>[5,7,1,6,2,8,4,3]=>[4,2,8,3,7,1,5,6]=>[1,2,2,3]
[2,4,7,3,1,5,8,6]=>[2,4,8,1,5,6,3,7]=>[7,5,1,8,4,3,6,2]=>[1,1,2,1,2,1]
[6,3,1,7,4,2,8,5]=>[2,5,8,6,3,1,4,7]=>[7,4,1,3,6,8,5,2]=>[1,1,4,1,1]
[8,5,7,6,2,3,1,4]=>[5,2,7,6,8,4,3,1]=>[4,7,2,3,1,5,6,8]=>[2,2,4]
[3,1,7,6,4,2,8,5]=>[5,8,1,6,4,2,3,7]=>[4,1,8,3,5,7,6,2]=>[1,2,3,1,1]
[4,8,7,6,2,3,1,5]=>[5,7,1,6,8,4,3,2]=>[4,2,8,3,1,5,6,7]=>[1,2,1,4]
[6,8,7,5,2,3,1,4]=>[5,1,7,6,8,4,3,2]=>[4,8,2,3,1,5,6,7]=>[2,2,4]
[4,3,6,1,5,8,7,2]=>[1,8,2,5,3,7,4,6]=>[8,1,7,4,6,2,5,3]=>[1,2,2,2,1]
[4,3,6,5,1,8,7,2]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[1,2,1,3,1]
[4,6,3,1,5,8,7,2]=>[1,3,8,5,2,7,4,6]=>[8,6,1,4,7,2,5,3]=>[1,1,3,2,1]
[4,1,6,5,3,8,7,2]=>[1,4,3,8,5,7,2,6]=>[8,5,6,1,4,2,7,3]=>[1,2,2,2,1]
[4,6,1,5,3,8,7,2]=>[1,4,8,5,2,7,3,6]=>[8,5,1,4,7,2,6,3]=>[1,1,3,2,1]
[2,6,5,8,1,7,3,4]=>[7,3,2,8,1,5,6,4]=>[2,6,7,1,8,4,3,5]=>[3,2,1,2]
[2,6,5,8,1,3,7,4]=>[8,5,3,1,2,6,7,4]=>[1,4,6,8,7,3,2,5]=>[4,1,1,2]
[2,6,5,8,3,1,7,4]=>[5,3,2,8,1,6,7,4]=>[4,6,7,1,8,3,2,5]=>[3,2,1,2]
[2,6,5,3,8,1,7,4]=>[8,4,3,1,2,6,7,5]=>[1,5,6,8,7,3,2,4]=>[4,1,1,2]
[4,6,1,5,8,3,7,2]=>[1,4,6,2,8,7,3,5]=>[8,5,3,7,1,2,6,4]=>[1,1,2,3,1]
[4,1,6,5,8,3,7,2]=>[1,4,3,6,8,7,2,5]=>[8,5,6,3,1,2,7,4]=>[1,2,1,3,1]
[1,4,6,5,8,3,7,2]=>[4,2,3,6,8,7,1,5]=>[5,7,6,3,1,2,8,4]=>[2,1,1,3,1]
[4,1,6,5,8,7,3,2]=>[1,3,8,4,7,6,2,5]=>[8,6,1,5,2,3,7,4]=>[1,1,2,3,1]
[2,6,5,3,8,7,1,4]=>[7,3,2,8,1,4,6,5]=>[2,6,7,1,8,5,3,4]=>[3,2,1,2]
[6,4,3,8,7,1,5,2]=>[2,8,3,1,6,7,5,4]=>[7,1,6,8,3,2,4,5]=>[1,3,1,3]
[6,4,8,3,7,1,5,2]=>[2,4,1,8,6,7,5,3]=>[7,5,8,1,3,2,4,6]=>[1,2,2,3]
[2,6,8,5,3,7,1,4]=>[5,2,7,4,8,1,6,3]=>[4,7,2,5,1,8,3,6]=>[2,2,2,2]
[4,6,8,1,5,7,3,2]=>[5,1,2,8,7,4,6,3]=>[4,8,7,1,2,5,3,6]=>[2,1,3,2]
[4,6,1,8,5,7,3,2]=>[5,1,2,8,7,6,3,4]=>[4,8,7,1,2,3,6,5]=>[2,1,4,1]
[4,1,6,8,5,7,3,2]=>[1,3,5,8,7,6,2,4]=>[8,6,4,1,2,3,7,5]=>[1,1,1,4,1]
[1,4,6,8,5,7,3,2]=>[3,5,8,2,7,6,1,4]=>[6,4,1,7,2,3,8,5]=>[1,1,2,3,1]
[1,4,6,8,5,3,7,2]=>[3,6,2,5,8,7,1,4]=>[6,3,7,4,1,2,8,5]=>[1,2,1,3,1]
[2,6,8,5,3,1,7,4]=>[5,2,8,6,1,4,7,3]=>[4,7,1,3,8,5,2,6]=>[2,3,1,2]
[2,6,8,5,1,7,3,4]=>[7,2,8,5,1,4,6,3]=>[2,7,1,4,8,5,3,6]=>[2,3,1,2]
[4,6,8,3,5,1,7,2]=>[4,1,2,8,6,5,7,3]=>[5,8,7,1,3,4,2,6]=>[2,1,3,2]
[4,6,8,3,1,5,7,2]=>[6,1,4,2,8,5,7,3]=>[3,8,5,7,1,4,2,6]=>[2,2,2,2]
[4,6,3,8,1,5,7,2]=>[1,3,6,2,8,5,7,4]=>[8,6,3,7,1,4,2,5]=>[1,1,2,2,2]
[4,6,3,8,5,7,1,2]=>[7,1,3,2,5,8,6,4]=>[2,8,6,7,4,1,3,5]=>[2,2,1,3]
[4,3,6,1,8,5,7,2]=>[1,6,2,3,8,7,4,5]=>[8,3,7,6,1,2,5,4]=>[1,2,1,3,1]
[4,3,1,6,8,5,7,2]=>[2,1,4,6,8,7,3,5]=>[7,8,5,3,1,2,6,4]=>[2,1,1,3,1]
[4,1,3,6,8,7,5,2]=>[1,8,4,7,3,6,2,5]=>[8,1,5,2,6,3,7,4]=>[1,2,2,2,1]
[4,3,6,1,8,7,5,2]=>[1,3,8,2,7,6,4,5]=>[8,6,1,7,2,3,5,4]=>[1,1,2,3,1]
[4,3,6,8,1,7,5,2]=>[1,3,8,2,7,5,6,4]=>[8,6,1,7,2,4,3,5]=>[1,1,2,2,2]
[6,5,2,8,7,3,1,4]=>[7,6,2,1,8,3,5,4]=>[2,3,7,8,1,6,4,5]=>[4,2,2]
[6,5,2,8,7,1,3,4]=>[6,7,2,1,8,3,5,4]=>[3,2,7,8,1,6,4,5]=>[1,3,2,2]
[6,2,5,8,7,1,3,4]=>[6,3,7,1,8,2,5,4]=>[3,6,2,8,1,7,4,5]=>[2,2,2,2]
[6,2,5,8,7,3,1,4]=>[3,7,6,1,8,2,5,4]=>[6,2,3,8,1,7,4,5]=>[1,3,2,2]
[4,6,3,8,1,7,5,2]=>[8,1,3,2,7,5,6,4]=>[1,8,6,7,2,4,3,5]=>[2,2,2,2]
[4,6,3,1,8,7,5,2]=>[8,1,3,2,7,6,4,5]=>[1,8,6,7,2,3,5,4]=>[2,2,3,1]
[4,1,6,3,8,7,5,2]=>[1,3,8,7,4,6,2,5]=>[8,6,1,2,5,3,7,4]=>[1,1,3,2,1]
[1,4,6,3,8,7,5,2]=>[3,8,2,7,4,6,1,5]=>[6,1,7,2,5,3,8,4]=>[1,2,2,2,1]
[4,1,6,8,3,7,5,2]=>[1,3,8,5,7,6,2,4]=>[8,6,1,4,2,3,7,5]=>[1,1,2,3,1]
[4,6,8,1,3,7,5,2]=>[8,1,5,2,7,4,6,3]=>[1,8,4,7,2,5,3,6]=>[2,2,2,2]
[6,2,8,5,7,3,1,4]=>[7,6,4,1,8,2,5,3]=>[2,3,5,8,1,7,4,6]=>[4,2,2]
[2,4,8,7,1,5,3,6]=>[7,2,5,6,8,1,4,3]=>[2,7,4,3,1,8,5,6]=>[2,1,1,2,2]
[4,2,8,7,5,3,1,6]=>[7,1,6,5,8,2,4,3]=>[2,8,3,4,1,7,5,6]=>[2,2,2,2]
[6,4,1,8,7,5,3,2]=>[8,2,1,7,6,5,3,4]=>[1,7,8,2,3,4,6,5]=>[3,4,1]
[6,1,4,8,7,5,3,2]=>[8,7,3,1,6,5,2,4]=>[1,2,6,8,3,4,7,5]=>[4,3,1]
[1,6,4,8,7,3,5,2]=>[6,2,8,3,7,5,1,4]=>[3,7,1,6,2,4,8,5]=>[2,2,3,1]
[6,4,1,8,7,3,5,2]=>[2,6,1,8,7,5,3,4]=>[7,3,8,1,2,4,6,5]=>[1,2,4,1]
[4,2,8,7,5,1,3,6]=>[1,6,7,5,8,2,4,3]=>[8,3,2,4,1,7,5,6]=>[1,1,2,2,2]
[2,4,8,7,3,5,1,6]=>[5,7,2,6,8,1,4,3]=>[4,2,7,3,1,8,5,6]=>[1,2,1,2,2]
[2,3,4,7,1,8,6,5]=>[8,7,1,2,3,5,4,6]=>[1,2,8,7,6,4,5,3]=>[3,1,1,2,1]
[2,3,4,7,8,5,6,1]=>[6,4,8,1,2,3,7,5]=>[3,5,1,8,7,6,2,4]=>[2,2,1,1,2]
[2,3,6,7,4,8,5,1]=>[3,8,5,1,2,4,7,6]=>[6,1,4,8,7,5,2,3]=>[1,3,1,1,2]
[2,5,6,3,7,8,1,4]=>[2,7,4,1,3,5,8,6]=>[7,2,5,8,6,4,1,3]=>[1,3,1,1,2]
[2,3,7,1,4,8,6,5]=>[8,7,1,2,4,5,3,6]=>[1,2,8,7,5,4,6,3]=>[3,1,1,2,1]
[2,3,4,5,6,7,10,1,8,9]=>[1,2,3,4,5,6,8,9,10,7]=>[10,9,8,7,6,5,3,2,1,4]=>[1,1,1,1,1,1,1,1,2]
[2,5,6,7,4,8,1,3]=>[2,3,7,5,1,4,8,6]=>[7,6,2,4,8,5,1,3]=>[1,1,3,1,2]
[2,3,7,8,4,5,6,1]=>[5,6,3,8,1,2,7,4]=>[4,3,6,1,8,7,2,5]=>[1,2,2,1,2]
[2,6,7,3,4,8,5,1]=>[8,4,2,5,1,3,7,6]=>[1,5,7,4,8,6,2,3]=>[3,2,1,2]
[1,5,3,2,6,7,4,8]=>[3,5,2,7,1,4,6,8]=>[6,4,7,2,8,5,3,1]=>[1,2,2,1,1,1]
[1,7,3,2,8,5,4,6]=>[7,3,6,8,4,1,2,5]=>[2,6,3,1,5,8,7,4]=>[2,1,3,1,1]
[1,7,3,2,5,8,4,6]=>[3,5,7,8,4,1,2,6]=>[6,4,2,1,5,8,7,3]=>[1,1,1,3,1,1]
[1,3,2,7,5,4,8,6]=>[5,8,2,6,1,3,4,7]=>[4,1,7,3,8,6,5,2]=>[1,2,2,1,1,1]
[6,5,2,4,3,7,1,8]=>[5,3,4,2,1,7,6,8]=>[4,6,5,7,8,2,3,1]=>[2,3,2,1]
[6,4,2,5,3,7,1,8]=>[5,3,2,4,1,7,6,8]=>[4,6,7,5,8,2,3,1]=>[3,2,2,1]
[5,4,7,6,2,3,1,8]=>[2,1,5,7,6,4,3,8]=>[7,8,4,2,3,5,6,1]=>[2,1,4,1]
[3,6,4,8,2,1,5,7]=>[3,6,1,5,2,7,8,4]=>[6,3,8,4,7,2,1,5]=>[1,2,2,1,2]
[1,6,2,8,5,3,4,7]=>[6,7,5,2,8,1,3,4]=>[3,2,4,7,1,8,6,5]=>[1,3,2,1,1]
[4,6,2,3,7,5,1,8]=>[1,7,3,4,2,6,5,8]=>[8,2,6,5,7,3,4,1]=>[1,2,2,2,1]
[4,7,2,3,5,6,1,8]=>[3,1,4,5,7,6,2,8]=>[6,8,5,4,2,3,7,1]=>[2,1,1,3,1]
[5,3,2,7,4,6,1,8]=>[2,5,1,7,3,6,4,8]=>[7,4,8,2,6,3,5,1]=>[1,2,2,2,1]
[5,3,2,6,4,7,1,8]=>[2,5,3,1,4,7,6,8]=>[7,4,6,8,5,2,3,1]=>[1,3,1,2,1]
[4,6,2,3,5,7,1,8]=>[3,1,4,5,2,7,6,8]=>[6,8,5,4,7,2,3,1]=>[2,1,2,2,1]
[3,5,2,1,6,8,4,7]=>[1,3,5,2,7,8,4,6]=>[8,6,4,7,2,1,5,3]=>[1,1,2,1,2,1]
[1,5,2,6,8,4,3,7]=>[4,2,7,6,8,1,3,5]=>[5,7,2,3,1,8,6,4]=>[2,2,2,1,1]
[1,5,7,2,8,4,3,6]=>[2,7,6,8,4,1,3,5]=>[7,2,3,1,5,8,6,4]=>[1,2,3,1,1]
[3,6,8,4,2,1,5,7]=>[6,5,1,4,2,7,8,3]=>[3,4,8,5,7,2,1,6]=>[3,2,1,2]
[4,3,2,6,1,8,5,7]=>[2,1,7,3,4,8,5,6]=>[7,8,2,6,5,1,4,3]=>[2,2,1,2,1]
[1,5,8,2,7,4,3,6]=>[2,7,6,8,4,5,1,3]=>[7,2,3,1,5,4,8,6]=>[1,2,2,2,1]
[1,7,2,3,4,8,6,5]=>[8,7,3,4,5,1,2,6]=>[1,2,6,5,4,8,7,3]=>[3,1,2,1,1]
[6,8,2,3,4,1,7,5]=>[3,4,5,1,8,6,7,2]=>[6,5,4,8,1,3,2,7]=>[1,1,2,2,2]
[4,1,8,2,3,5,7,6]=>[8,4,1,5,6,7,2,3]=>[1,5,8,4,3,2,7,6]=>[3,1,1,2,1]
[2,3,1,8,4,5,7,6]=>[8,1,2,5,6,7,3,4]=>[1,8,7,4,3,2,6,5]=>[2,1,1,1,2,1]
[7,3,2,1,4,5,8,6]=>[3,2,8,4,5,6,1,7]=>[6,7,1,5,4,3,8,2]=>[2,2,1,2,1]
[7,8,1,4,3,5,2,6]=>[5,4,7,3,6,1,8,2]=>[4,5,2,6,3,8,1,7]=>[2,2,2,2]
[7,1,2,3,4,6,8,5]=>[6,8,2,3,4,5,1,7]=>[3,1,7,6,5,4,8,2]=>[1,2,1,1,2,1]
[6,1,2,3,4,8,7,5]=>[8,7,2,3,4,1,5,6]=>[1,2,7,6,5,8,4,3]=>[3,1,2,1,1]
[1,8,2,3,4,7,6,5]=>[8,7,3,4,5,6,1,2]=>[1,2,6,5,4,3,8,7]=>[3,1,1,2,1]
[8,1,2,3,4,6,7,5]=>[6,8,2,3,4,5,7,1]=>[3,1,7,6,5,4,2,8]=>[1,2,1,1,1,2]
[2,8,1,3,5,4,7,6]=>[5,8,1,3,4,6,7,2]=>[4,1,8,6,5,3,2,7]=>[1,2,1,1,1,2]
[8,7,1,4,3,5,2,6]=>[5,4,7,3,6,8,2,1]=>[4,5,2,6,3,1,7,8]=>[2,2,1,3]
[8,3,2,1,4,5,7,6]=>[3,2,8,4,5,6,7,1]=>[6,7,1,5,4,3,2,8]=>[2,2,1,1,2]
[3,8,2,1,5,6,4,7]=>[1,3,5,7,4,6,8,2]=>[8,6,4,2,5,3,1,7]=>[1,1,1,2,1,2]
[3,8,2,1,6,5,4,7]=>[7,1,3,6,4,5,8,2]=>[2,8,6,3,5,4,1,7]=>[2,1,2,1,2]
[1,7,8,3,5,4,2,6]=>[7,4,6,5,2,8,1,3]=>[2,5,3,4,7,1,8,6]=>[2,3,2,1]
[7,4,1,8,3,5,2,6]=>[5,2,7,6,8,3,1,4]=>[4,7,2,3,1,6,8,5]=>[2,2,3,1]
[3,8,4,6,2,1,5,7]=>[3,6,1,5,7,4,8,2]=>[6,3,8,4,2,5,1,7]=>[1,2,1,2,2]
[8,4,2,5,3,1,6,7]=>[6,3,2,5,4,7,8,1]=>[3,6,7,4,5,2,1,8]=>[3,2,1,2]
[8,5,2,4,3,1,6,7]=>[6,3,5,4,2,7,8,1]=>[3,6,4,5,7,2,1,8]=>[2,3,1,2]
[8,3,2,5,4,1,6,7]=>[2,6,3,5,4,7,8,1]=>[7,3,6,4,5,2,1,8]=>[1,2,2,1,2]
[4,3,2,5,1,8,6,7]=>[3,2,1,4,7,8,5,6]=>[6,7,8,5,2,1,4,3]=>[3,1,1,2,1]
[3,5,2,4,1,8,6,7]=>[1,3,4,2,7,8,5,6]=>[8,6,5,7,2,1,4,3]=>[1,1,2,1,2,1]
[2,4,7,8,1,5,3,6]=>[7,2,5,6,1,3,8,4]=>[2,7,4,3,8,6,1,5]=>[2,1,2,1,2]
[5,1,8,2,7,4,3,6]=>[7,6,1,8,4,5,2,3]=>[2,3,8,1,5,4,7,6]=>[3,2,2,1]
[5,1,7,2,8,4,3,6]=>[7,6,1,8,4,2,3,5]=>[2,3,8,1,5,7,6,4]=>[3,3,1,1]
[6,1,2,8,5,3,4,7]=>[6,7,5,8,2,1,3,4]=>[3,2,4,1,7,8,6,5]=>[1,2,3,1,1]
[6,3,2,1,8,4,5,7]=>[3,2,6,7,1,8,4,5]=>[6,7,3,2,8,1,5,4]=>[2,1,2,2,1]
[7,3,2,8,4,5,1,6]=>[2,5,7,3,6,1,8,4]=>[7,4,2,6,3,8,1,5]=>[1,1,2,2,2]
[2,7,8,4,3,5,1,6]=>[5,4,7,6,1,2,8,3]=>[4,5,2,3,8,7,1,6]=>[2,3,1,2]
[7,1,8,3,5,4,2,6]=>[7,4,6,5,8,2,1,3]=>[2,5,3,4,1,7,8,6]=>[2,2,3,1]
[7,8,2,3,4,6,1,5]=>[3,4,5,7,1,8,6,2]=>[6,5,4,2,8,1,3,7]=>[1,1,1,2,3]
[6,7,1,3,4,8,2,5]=>[4,5,7,1,8,3,2,6]=>[5,4,2,8,1,6,7,3]=>[1,1,2,3,1]
[6,8,1,3,4,7,2,5]=>[4,5,7,1,8,3,6,2]=>[5,4,2,8,1,6,3,7]=>[1,1,2,2,2]
[1,6,2,3,4,8,7,5]=>[8,7,3,4,1,2,5,6]=>[1,2,6,5,8,7,4,3]=>[3,2,1,1,1]
[7,6,2,3,4,1,8,5]=>[3,4,5,8,6,2,1,7]=>[6,5,4,1,3,7,8,2]=>[1,1,1,4,1]
[8,1,7,3,5,4,2,6]=>[7,4,6,5,8,2,3,1]=>[2,5,3,4,1,7,6,8]=>[2,2,2,2]
[8,3,2,7,4,5,1,6]=>[2,5,7,3,6,8,4,1]=>[7,4,2,6,3,1,5,8]=>[1,1,2,1,3]
[6,7,2,3,4,1,8,5]=>[3,4,5,1,8,6,2,7]=>[6,5,4,8,1,3,7,2]=>[1,1,2,3,1]
[7,6,2,3,4,8,1,5]=>[3,4,5,7,2,1,8,6]=>[6,5,4,2,7,8,1,3]=>[1,1,1,3,2]
[8,6,2,3,4,7,1,5]=>[3,4,5,7,2,8,6,1]=>[6,5,4,2,7,1,3,8]=>[1,1,1,2,3]
[6,3,4,8,7,5,1,2]=>[7,8,2,1,3,6,5,4]=>[2,1,7,8,6,3,4,5]=>[1,3,1,3]
[4,8,7,3,5,6,1,2]=>[4,7,1,5,8,6,3,2]=>[5,2,8,4,1,3,6,7]=>[1,2,1,4]
[4,8,7,5,3,6,1,2]=>[7,5,1,4,8,6,3,2]=>[2,4,8,5,1,3,6,7]=>[3,1,4]
[5,8,7,3,4,6,1,2]=>[1,4,7,5,8,6,3,2]=>[8,5,2,4,1,3,6,7]=>[1,1,2,4]
[5,8,4,2,1,6,7,3]=>[4,1,6,3,8,5,7,2]=>[5,8,3,6,1,4,2,7]=>[2,2,2,2]
[5,8,4,1,2,6,7,3]=>[6,1,8,4,3,5,7,2]=>[3,8,1,5,6,4,2,7]=>[2,3,1,2]
[5,3,7,2,6,1,8,4]=>[8,2,1,4,6,5,3,7]=>[1,7,8,5,3,4,6,2]=>[3,1,3,1]
[5,2,8,1,6,3,7,4]=>[8,6,2,1,4,5,7,3]=>[1,3,7,8,5,4,2,6]=>[4,1,1,2]
[5,8,2,1,4,7,6,3]=>[8,3,1,5,7,4,6,2]=>[1,6,8,4,2,5,3,7]=>[3,1,2,2]
[7,8,4,1,2,6,5,3]=>[8,7,4,3,5,1,6,2]=>[1,2,5,6,4,8,3,7]=>[4,2,2]
[4,8,1,5,2,7,6,3]=>[1,4,8,7,3,5,6,2]=>[8,5,1,2,6,4,3,7]=>[1,1,3,1,2]
[5,8,1,2,4,7,6,3]=>[8,5,1,7,3,4,6,2]=>[1,4,8,2,6,5,3,7]=>[3,2,1,2]
[5,2,8,3,6,7,1,4]=>[7,4,1,5,8,2,6,3]=>[2,5,8,4,1,7,3,6]=>[3,1,2,2]
[3,8,7,6,2,4,1,5]=>[5,7,6,8,1,4,3,2]=>[4,2,3,1,8,5,6,7]=>[1,2,2,3]
[2,8,7,6,4,1,3,5]=>[6,7,5,8,4,1,3,2]=>[3,2,4,1,5,8,6,7]=>[1,2,3,2]
[7,8,2,6,5,1,3,4]=>[6,7,8,3,1,5,4,2]=>[3,2,1,6,8,4,5,7]=>[1,1,3,3]
[1,8,7,6,4,2,3,5]=>[6,7,5,8,4,3,1,2]=>[3,2,4,1,5,6,8,7]=>[1,2,4,1]
[2,8,7,6,3,1,4,5]=>[6,5,7,8,4,1,3,2]=>[3,4,2,1,5,8,6,7]=>[2,1,3,2]
[1,8,7,6,2,4,3,5]=>[7,5,6,8,4,3,1,2]=>[2,4,3,1,5,6,8,7]=>[2,1,4,1]
[1,8,7,6,3,4,2,5]=>[5,7,6,8,4,3,1,2]=>[4,2,3,1,5,6,8,7]=>[1,2,4,1]
[2,8,1,4,5,6,7,3]=>[4,5,6,8,1,3,7,2]=>[5,4,3,1,8,6,2,7]=>[1,1,1,2,1,2]
[2,1,7,3,6,5,8,4]=>[6,5,8,1,4,2,3,7]=>[3,4,1,8,5,7,6,2]=>[2,2,2,1,1]
[3,1,7,2,6,5,8,4]=>[6,1,5,8,4,2,3,7]=>[3,8,4,1,5,7,6,2]=>[2,1,3,1,1]
[3,2,7,1,6,5,8,4]=>[6,1,5,8,2,4,3,7]=>[3,8,4,1,7,5,6,2]=>[2,1,2,2,1]
[6,1,2,8,5,7,3,4]=>[7,5,8,6,2,1,3,4]=>[2,4,1,3,7,8,6,5]=>[2,4,1,1]
[6,2,1,8,5,7,3,4]=>[7,5,8,2,1,6,3,4]=>[2,4,1,7,8,3,6,5]=>[2,3,2,1]
[6,3,1,8,5,7,2,4]=>[7,2,5,1,8,6,3,4]=>[2,7,4,8,1,3,6,5]=>[2,2,3,1]
[6,1,3,8,5,2,7,4]=>[8,6,3,5,1,7,2,4]=>[1,3,6,4,8,2,7,5]=>[3,2,2,1]
[2,3,7,1,6,8,5,4]=>[5,8,7,1,2,4,3,6]=>[4,1,2,8,7,5,6,3]=>[1,3,1,2,1]
[1,3,7,2,6,8,5,4]=>[5,8,7,2,4,1,3,6]=>[4,1,2,7,5,8,6,3]=>[1,3,2,1,1]
[7,8,2,6,5,3,1,4]=>[7,6,8,3,1,5,4,2]=>[2,3,1,6,8,4,5,7]=>[2,3,3]
[3,2,6,7,5,8,1,4]=>[3,7,1,5,2,4,8,6]=>[6,2,8,4,7,5,1,3]=>[1,2,2,1,2]
[1,2,7,5,6,3,8,4]=>[4,8,6,5,1,2,3,7]=>[5,1,3,4,8,7,6,2]=>[1,4,1,1,1]
[2,8,7,6,4,3,1,5]=>[7,6,5,8,4,1,3,2]=>[2,3,4,1,5,8,6,7]=>[3,3,2]
[3,8,7,6,1,2,5,4]=>[8,5,6,7,1,4,3,2]=>[1,4,3,2,8,5,6,7]=>[2,1,2,3]
[3,8,7,6,2,1,5,4]=>[5,8,6,7,1,4,3,2]=>[4,1,3,2,8,5,6,7]=>[1,2,2,3]
[4,8,7,6,2,1,3,5]=>[6,1,5,7,8,4,3,2]=>[3,8,4,2,1,5,6,7]=>[2,1,1,4]
[4,8,7,6,1,3,2,5]=>[7,1,5,6,8,4,3,2]=>[2,8,4,3,1,5,6,7]=>[2,1,1,4]
[3,8,7,6,4,1,2,5]=>[6,7,5,8,1,4,3,2]=>[3,2,4,1,8,5,6,7]=>[1,2,2,3]
[7,8,3,6,5,1,2,4]=>[3,6,7,1,8,5,4,2]=>[6,3,2,8,1,4,5,7]=>[1,1,2,4]
[2,3,7,5,6,8,1,4]=>[4,7,5,1,2,3,8,6]=>[5,2,4,8,7,6,1,3]=>[1,3,1,1,2]
[3,8,7,6,4,2,1,5]=>[7,6,5,8,1,4,3,2]=>[2,3,4,1,8,5,6,7]=>[3,2,3]
[5,1,4,6,8,2,3,7]=>[3,6,4,1,7,8,2,5]=>[6,3,5,8,2,1,7,4]=>[1,3,1,2,1]
[1,7,6,3,5,4,8,2]=>[6,4,5,3,2,8,1,7]=>[3,5,4,6,7,1,8,2]=>[2,3,2,1]
[4,3,7,2,6,5,1,8]=>[1,7,2,4,6,5,3,8]=>[8,2,7,5,3,4,6,1]=>[1,2,1,3,1]
[1,6,8,5,7,3,4,2]=>[2,6,4,8,7,5,1,3]=>[7,3,5,1,2,4,8,6]=>[1,2,4,1]
[2,4,1,5,8,6,3,7]=>[2,7,1,4,6,8,3,5]=>[7,2,8,5,3,1,6,4]=>[1,2,1,1,2,1]
[4,6,1,2,5,8,3,7]=>[5,1,7,8,3,2,4,6]=>[4,8,2,1,6,7,5,3]=>[2,1,3,1,1]
[5,6,7,2,1,4,8,3]=>[4,1,6,2,8,5,3,7]=>[5,8,3,7,1,4,6,2]=>[2,2,3,1]
[7,8,6,5,1,2,4,3]=>[8,5,6,1,7,4,3,2]=>[1,4,3,8,2,5,6,7]=>[2,2,4]
[1,3,6,5,7,8,2,4]=>[4,3,7,2,5,8,1,6]=>[5,6,2,7,4,1,8,3]=>[2,2,1,2,1]
[7,4,8,5,3,1,6,2]=>[8,2,6,5,4,1,7,3]=>[1,7,3,4,5,8,2,6]=>[2,4,2]
[6,8,5,2,4,1,7,3]=>[8,4,1,6,5,3,7,2]=>[1,5,8,3,4,6,2,7]=>[3,3,2]
[7,3,2,5,1,4,8,6]=>[2,8,3,5,4,6,1,7]=>[7,1,6,4,5,3,8,2]=>[1,2,2,2,1]
[7,1,4,2,3,6,8,5]=>[6,3,8,2,4,5,1,7]=>[3,6,1,7,5,4,8,2]=>[2,2,1,2,1]
[1,5,8,3,4,6,7,2]=>[4,2,5,6,8,7,1,3]=>[5,7,4,3,1,2,8,6]=>[2,1,1,3,1]
[8,3,1,2,4,7,6,5]=>[2,8,7,3,4,5,6,1]=>[7,1,2,6,5,4,3,8]=>[1,3,1,1,2]
[2,3,8,1,6,5,4,7]=>[7,6,1,2,4,5,8,3]=>[2,3,8,7,5,4,1,6]=>[3,1,1,1,2]
[8,1,4,7,2,5,3,6]=>[3,7,5,6,8,2,4,1]=>[6,2,4,3,1,7,5,8]=>[1,2,1,2,2]
[3,5,2,4,1,7,8,6]=>[1,3,4,2,6,8,5,7]=>[8,6,5,7,3,1,4,2]=>[1,1,2,1,2,1]
[3,4,7,8,6,2,1,5]=>[7,6,1,2,3,8,5,4]=>[2,3,8,7,6,1,4,5]=>[3,1,1,3]
[3,4,8,6,2,7,1,5]=>[5,7,1,2,4,8,6,3]=>[4,2,8,7,5,1,3,6]=>[1,2,1,1,3]
[5,7,2,8,6,4,3,1]=>[8,1,7,6,3,2,5,4]=>[1,8,2,3,6,7,4,5]=>[2,4,2]
[6,1,2,7,5,3,8,4]=>[8,6,5,2,3,1,4,7]=>[1,3,4,7,6,8,5,2]=>[4,2,1,1]
[7,3,2,8,6,4,1,5]=>[7,2,6,8,3,1,5,4]=>[2,7,3,1,6,8,4,5]=>[2,1,3,2]
[2,7,8,4,6,3,1,5]=>[4,7,6,2,8,1,5,3]=>[5,2,3,7,1,8,4,6]=>[1,3,2,2]
[1,4,5,7,2,6,8,3]=>[2,3,6,8,5,1,4,7]=>[7,6,3,1,4,8,5,2]=>[1,1,1,3,1,1]
[7,3,5,2,6,1,8,4]=>[8,2,4,3,6,5,1,7]=>[1,7,5,6,3,4,8,2]=>[2,2,3,1]
[8,5,2,3,6,1,7,4]=>[8,3,4,2,6,5,7,1]=>[1,6,5,7,3,4,2,8]=>[2,2,2,2]
[8,1,6,3,5,7,2,4]=>[7,4,5,3,8,2,6,1]=>[2,5,4,6,1,7,3,8]=>[2,2,2,2]
[2,8,6,4,3,7,1,5]=>[5,4,7,3,8,1,6,2]=>[4,5,2,6,1,8,3,7]=>[2,2,2,2]
[8,3,2,6,4,7,1,5]=>[2,5,7,3,4,8,6,1]=>[7,4,2,6,5,1,3,8]=>[1,1,2,1,3]
[2,3,8,7,6,5,1,4]=>[7,8,6,5,1,2,4,3]=>[2,1,3,4,8,7,5,6]=>[1,4,1,2]
[1,2,8,7,3,6,5,4]=>[8,7,5,6,4,1,2,3]=>[1,2,4,3,5,8,7,6]=>[3,3,1,1]
[4,2,8,7,3,6,1,5]=>[1,5,7,8,6,2,4,3]=>[8,4,2,1,3,7,5,6]=>[1,1,1,3,2]
[4,5,8,7,1,2,6,3]=>[1,2,8,5,6,7,4,3]=>[8,7,1,4,3,2,5,6]=>[1,1,2,1,3]
[1,5,8,7,3,2,6,4]=>[2,5,8,6,7,4,1,3]=>[7,4,1,3,2,5,8,6]=>[1,1,2,3,1]
[4,5,8,7,3,2,1,6]=>[7,1,2,6,5,8,4,3]=>[2,8,7,3,4,1,5,6]=>[2,1,2,3]
[2,6,8,1,7,5,4,3]=>[2,8,7,6,1,4,5,3]=>[7,1,2,3,8,5,4,6]=>[1,4,1,2]
[3,6,8,4,7,2,1,5]=>[4,2,7,1,6,8,5,3]=>[5,7,2,8,3,1,4,6]=>[2,2,1,3]
[2,5,8,3,7,6,1,4]=>[2,7,8,4,6,1,5,3]=>[7,2,1,5,3,8,4,6]=>[1,1,2,2,2]
[3,2,8,4,7,6,1,5]=>[7,8,1,4,6,2,5,3]=>[2,1,8,5,3,7,4,6]=>[1,2,1,2,2]
[1,5,8,3,7,2,6,4]=>[2,8,4,6,7,5,1,3]=>[7,1,5,3,2,4,8,6]=>[1,2,1,3,1]
[3,5,8,4,7,2,1,6]=>[2,4,7,1,6,8,5,3]=>[7,5,2,8,3,1,4,6]=>[1,1,2,1,3]
[5,6,8,2,3,7,1,4]=>[4,1,5,2,7,8,6,3]=>[5,8,4,7,2,1,3,6]=>[2,2,1,3]
[1,6,8,4,2,7,5,3]=>[4,2,8,7,5,6,1,3]=>[5,7,1,2,4,3,8,6]=>[2,3,2,1]
[1,5,8,4,2,7,6,3]=>[2,4,8,7,5,6,1,3]=>[7,5,1,2,4,3,8,6]=>[1,1,3,2,1]
[1,5,8,2,3,7,6,4]=>[2,8,7,4,5,6,1,3]=>[7,1,2,5,4,3,8,6]=>[1,3,1,2,1]
[2,1,8,4,3,7,6,5]=>[8,4,7,1,5,6,2,3]=>[1,5,2,8,4,3,7,6]=>[2,2,1,2,1]
[2,5,8,4,3,7,1,6]=>[2,5,4,7,8,1,6,3]=>[7,4,5,2,1,8,3,6]=>[1,2,1,2,2]
[5,6,8,4,1,2,7,3]=>[1,8,5,2,6,4,7,3]=>[8,1,4,7,3,5,2,6]=>[1,3,2,2]
[5,6,8,1,3,2,7,4]=>[5,1,8,4,2,6,7,3]=>[4,8,1,5,7,3,2,6]=>[2,3,1,2]
[1,6,8,4,3,2,7,5]=>[5,4,2,8,6,7,1,3]=>[4,5,7,1,3,2,8,6]=>[3,2,2,1]
[5,6,8,4,3,2,1,7]=>[1,2,7,6,5,4,8,3]=>[8,7,2,3,4,5,1,6]=>[1,1,4,2]
[7,1,2,8,6,5,4,3]=>[8,7,6,5,2,3,1,4]=>[1,2,3,4,7,6,8,5]=>[5,2,1]
[7,1,4,8,6,2,5,3]=>[8,3,6,7,5,2,1,4]=>[1,6,3,2,4,7,8,5]=>[2,1,4,1]
[7,3,1,8,6,2,5,4]=>[8,2,6,7,5,3,1,4]=>[1,7,3,2,4,6,8,5]=>[2,1,4,1]
[7,2,4,8,3,6,1,5]=>[3,5,7,8,2,1,6,4]=>[6,4,2,1,7,8,3,5]=>[1,1,1,3,2]
[7,1,4,8,3,2,6,5]=>[3,5,8,6,7,2,1,4]=>[6,4,1,3,2,7,8,5]=>[1,1,2,3,1]
[7,4,5,8,3,2,1,6]=>[2,3,7,6,5,1,8,4]=>[7,6,2,3,4,8,1,5]=>[1,1,4,2]
[1,6,2,8,7,5,4,3]=>[2,8,7,6,5,1,3,4]=>[7,1,2,3,4,8,6,5]=>[1,5,1,1]
[1,6,4,8,7,2,5,3]=>[8,3,2,6,7,5,1,4]=>[1,6,7,3,2,4,8,5]=>[3,1,3,1]
[3,6,4,8,7,2,1,5]=>[7,3,1,2,6,8,5,4]=>[2,6,8,7,3,1,4,5]=>[3,1,1,3]
[3,2,5,8,7,6,1,4]=>[7,8,1,3,6,2,5,4]=>[2,1,8,6,3,7,4,5]=>[1,2,1,2,2]
[3,2,4,8,7,6,1,5]=>[7,8,1,6,2,3,5,4]=>[2,1,8,3,7,6,4,5]=>[1,2,2,1,2]
[3,1,5,8,7,2,6,4]=>[8,1,3,6,7,5,2,4]=>[1,8,6,3,2,4,7,5]=>[2,1,1,3,1]
[3,1,4,8,7,2,6,5]=>[8,1,6,7,3,5,2,4]=>[1,8,3,2,6,4,7,5]=>[2,1,2,2,1]
[1,6,4,8,2,7,5,3]=>[8,3,2,7,5,6,1,4]=>[1,6,7,2,4,3,8,5]=>[3,2,2,1]
[1,4,5,8,2,7,6,3]=>[8,2,3,7,5,6,1,4]=>[1,7,6,2,4,3,8,5]=>[2,1,2,2,1]
[2,4,5,8,3,7,1,6]=>[2,3,5,7,8,1,6,4]=>[7,6,4,2,1,8,3,5]=>[1,1,1,1,2,2]
[1,6,4,8,3,2,7,5]=>[3,5,2,8,6,7,1,4]=>[6,4,7,1,3,2,8,5]=>[1,2,2,2,1]
[1,4,5,8,3,2,7,6]=>[2,3,5,8,6,7,1,4]=>[7,6,4,1,3,2,8,5]=>[1,1,1,2,2,1]
[7,6,1,4,8,2,5,3]=>[4,8,6,7,3,2,1,5]=>[5,1,3,2,6,7,8,4]=>[1,2,4,1]
[7,6,1,3,8,2,5,4]=>[8,4,6,7,3,2,1,5]=>[1,5,3,2,6,7,8,4]=>[2,1,4,1]
[7,6,3,4,8,2,1,5]=>[3,4,7,6,2,1,8,5]=>[6,5,2,3,7,8,1,4]=>[1,1,4,2]
[7,2,5,1,8,6,4,3]=>[3,8,7,2,6,4,1,5]=>[6,1,2,7,3,5,8,4]=>[1,3,3,1]
[7,2,5,3,8,6,1,4]=>[7,3,8,2,4,1,6,5]=>[2,6,1,7,5,8,3,4]=>[2,2,2,2]
[7,2,1,4,8,6,5,3]=>[8,7,2,4,6,3,1,5]=>[1,2,7,5,3,6,8,4]=>[3,1,3,1]
[7,2,1,3,8,6,5,4]=>[8,7,2,6,3,4,1,5]=>[1,2,7,3,6,5,8,4]=>[3,2,2,1]
[7,2,3,4,8,6,1,5]=>[7,8,2,3,4,1,6,5]=>[2,1,7,6,5,8,3,4]=>[1,2,1,2,2]
[7,3,5,4,8,2,1,6]=>[4,2,3,7,6,1,8,5]=>[5,7,6,2,3,8,1,4]=>[2,1,3,2]
[2,6,5,1,8,7,4,3]=>[3,2,8,7,1,6,4,5]=>[6,7,1,2,8,3,5,4]=>[2,3,2,1]
[2,3,5,4,8,7,1,6]=>[3,7,8,1,2,4,6,5]=>[6,2,1,8,7,5,3,4]=>[1,1,2,1,1,2]
[1,6,5,4,8,2,7,3]=>[4,3,2,8,6,7,1,5]=>[5,6,7,1,3,2,8,4]=>[3,2,2,1]
[1,6,5,3,8,2,7,4]=>[8,4,3,2,6,7,1,5]=>[1,5,6,7,3,2,8,4]=>[4,1,2,1]
[1,6,3,4,8,2,7,5]=>[8,3,4,2,6,7,1,5]=>[1,6,5,7,3,2,8,4]=>[2,2,1,2,1]
[1,3,5,4,8,2,7,6]=>[3,8,2,4,6,7,1,5]=>[6,1,7,5,3,2,8,4]=>[1,2,1,1,2,1]
[3,6,5,4,8,2,1,7]=>[4,3,1,2,7,6,8,5]=>[5,6,8,7,2,3,1,4]=>[3,1,2,2]
[7,6,5,2,3,8,1,4]=>[4,5,7,3,2,1,8,6]=>[5,4,2,6,7,8,1,3]=>[1,1,4,2]
[7,6,1,4,2,8,5,3]=>[4,8,7,3,5,2,1,6]=>[5,1,2,6,4,7,8,3]=>[1,3,3,1]
[7,6,1,2,3,8,5,4]=>[8,7,3,4,5,2,1,6]=>[1,2,6,5,4,7,8,3]=>[3,1,3,1]
[7,6,2,4,3,8,1,5]=>[5,3,4,7,2,1,8,6]=>[4,6,5,2,7,8,1,3]=>[2,1,3,2]
[7,1,5,4,2,8,6,3]=>[4,3,8,7,2,5,1,6]=>[5,6,1,2,7,4,8,3]=>[2,3,2,1]
[7,1,5,2,3,8,6,4]=>[8,7,4,2,3,5,1,6]=>[1,2,5,7,6,4,8,3]=>[4,1,2,1]
[7,1,2,4,3,8,6,5]=>[8,4,7,2,3,5,1,6]=>[1,5,2,7,6,4,8,3]=>[2,2,1,2,1]
[2,6,5,4,3,8,1,7]=>[5,4,3,1,2,7,8,6]=>[4,5,6,8,7,2,1,3]=>[4,1,1,2]
[7,1,5,4,3,2,8,6]=>[5,4,3,8,2,6,1,7]=>[4,5,6,1,7,3,8,2]=>[3,2,2,1]
[3,4,2,6,7,8,1,5]=>[1,2,4,7,3,5,8,6]=>[8,7,5,2,6,4,1,3]=>[1,1,1,2,1,2]
[3,1,4,2,6,8,7,5]=>[1,8,3,5,7,2,4,6]=>[8,1,6,4,2,7,5,3]=>[1,2,1,2,1,1]
[8,3,4,2,6,1,7,5]=>[2,3,8,4,6,5,7,1]=>[7,6,1,5,3,4,2,8]=>[1,1,2,2,2]
[2,6,7,3,5,4,1,8]=>[7,4,2,6,1,5,3,8]=>[2,5,7,3,8,4,6,1]=>[3,2,2,1]
[2,7,8,3,5,4,1,6]=>[7,4,6,5,1,2,8,3]=>[2,5,3,4,8,7,1,6]=>[2,3,1,2]
[2,6,8,3,5,4,1,7]=>[7,4,2,6,1,5,8,3]=>[2,5,7,3,8,4,1,6]=>[3,2,1,2]
[4,7,1,2,8,5,3,6]=>[1,7,6,8,3,4,2,5]=>[8,2,3,1,6,5,7,4]=>[1,2,2,2,1]
[4,8,1,2,7,5,3,6]=>[1,7,6,8,3,4,5,2]=>[8,2,3,1,6,5,4,7]=>[1,2,2,1,2]
[2,1,6,3,7,5,4,8]=>[7,6,1,4,2,3,5,8]=>[2,3,8,5,7,6,4,1]=>[3,2,1,1,1]
[2,7,1,3,6,8,4,5]=>[7,5,8,1,3,4,2,6]=>[2,4,1,8,6,5,7,3]=>[2,2,1,2,1]
[6,7,3,2,8,1,4,5]=>[4,3,6,1,7,2,8,5]=>[5,6,3,8,2,7,1,4]=>[2,2,2,2]
[7,3,4,2,6,1,8,5]=>[2,3,8,4,6,5,1,7]=>[7,6,1,5,3,4,8,2]=>[1,1,2,3,1]
[7,4,1,2,8,5,3,6]=>[7,6,2,8,3,4,1,5]=>[2,3,7,1,6,5,8,4]=>[3,2,2,1]
[8,7,4,2,1,5,3,6]=>[4,7,5,3,6,8,2,1]=>[5,2,4,6,3,1,7,8]=>[1,3,1,3]
[7,4,1,2,6,5,3,8]=>[7,6,3,2,4,5,1,8]=>[2,3,6,7,5,4,8,1]=>[4,1,2,1]
[7,4,3,1,5,6,8,2]=>[5,3,2,6,8,4,1,7]=>[4,6,7,3,1,5,8,2]=>[3,1,3,1]
[6,7,4,1,5,8,3,2]=>[5,3,1,8,7,4,2,6]=>[4,6,8,1,2,5,7,3]=>[3,4,1]
[4,7,5,1,6,8,3,2]=>[5,1,3,8,7,4,2,6]=>[4,8,6,1,2,5,7,3]=>[2,1,4,1]
[4,5,3,1,7,6,8,2]=>[1,3,2,6,5,8,4,7]=>[8,6,7,3,4,1,5,2]=>[1,2,2,2,1]
[4,6,1,2,7,5,3,8]=>[1,7,6,3,4,2,5,8]=>[8,2,3,6,5,7,4,1]=>[1,3,2,1,1]
[4,1,8,2,6,5,3,7]=>[1,7,6,4,5,8,2,3]=>[8,2,3,5,4,1,7,6]=>[1,3,1,2,1]
[4,6,1,2,8,5,3,7]=>[1,7,6,8,3,2,4,5]=>[8,2,3,1,6,7,5,4]=>[1,2,3,1,1]
[8,4,3,1,5,6,7,2]=>[5,3,2,6,8,4,7,1]=>[4,6,7,3,1,5,2,8]=>[3,1,2,2]
[4,8,5,6,3,1,7,2]=>[3,8,1,6,5,4,7,2]=>[6,1,8,3,4,5,2,7]=>[1,2,3,2]
[5,1,3,4,8,6,7,2]=>[6,8,3,1,4,7,2,5]=>[3,1,6,8,5,2,7,4]=>[1,3,1,2,1]
[5,4,3,8,1,6,7,2]=>[3,2,1,6,8,5,7,4]=>[6,7,8,3,1,4,2,5]=>[3,1,2,2]
[8,5,3,4,1,6,7,2]=>[3,6,4,2,8,5,7,1]=>[6,3,5,7,1,4,2,8]=>[1,3,2,2]
[6,7,3,2,5,1,4,8]=>[4,3,6,1,7,5,2,8]=>[5,6,3,8,2,4,7,1]=>[2,2,3,1]
[6,8,3,2,5,1,4,7]=>[4,3,6,1,7,5,8,2]=>[5,6,3,8,2,4,1,7]=>[2,2,2,2]
[5,7,1,4,6,8,3,2]=>[4,1,5,8,7,3,2,6]=>[5,8,4,1,2,6,7,3]=>[2,1,4,1]
[5,1,3,4,7,6,8,2]=>[6,3,4,1,5,8,2,7]=>[3,6,5,8,4,1,7,2]=>[2,2,1,2,1]
[5,4,3,7,1,6,8,2]=>[3,2,1,6,8,5,4,7]=>[6,7,8,3,1,4,5,2]=>[3,1,3,1]
[6,7,5,4,1,8,3,2]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[1,6,1]
[8,2,7,6,5,4,1,3]=>[7,8,6,5,2,4,3,1]=>[2,1,3,4,7,5,6,8]=>[1,4,3]
[7,2,8,6,5,4,3,1]=>[8,7,6,5,2,1,4,3]=>[1,2,3,4,7,8,5,6]=>[6,2]
[8,1,9,7,6,5,4,3,2]=>[9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,8,9,7]=>[8,1]
[2,10,9,8,7,6,5,4,1,3]=>[9,10,8,7,6,5,4,1,3,2]=>[2,1,3,4,5,6,7,10,8,9]=>[1,7,2]
[9,2,8,7,6,5,4,1,3]=>[8,9,7,6,5,2,4,3,1]=>[2,1,3,4,5,8,6,7,9]=>[1,5,3]
[3,9,8,7,6,5,4,1,2]=>[8,9,7,6,5,1,4,3,2]=>[2,1,3,4,5,9,6,7,8]=>[1,5,3]
[8,7,2,6,5,4,1,3]=>[7,8,6,3,5,4,2,1]=>[2,1,3,6,4,5,7,8]=>[1,3,4]
[3,2,8,7,6,5,1,4]=>[7,8,6,1,5,2,4,3]=>[2,1,3,8,4,7,5,6]=>[1,3,2,2]
[4,8,7,6,5,3,1,2]=>[7,8,6,1,5,4,3,2]=>[2,1,3,8,4,5,6,7]=>[1,3,4]
[7,8,6,1,5,4,3,2]=>[8,7,6,4,1,5,3,2]=>[1,2,3,5,8,4,6,7]=>[5,3]
[8,9,1,7,6,5,4,3,2]=>[9,8,7,6,5,3,1,4,2]=>[1,2,3,4,5,7,9,6,8]=>[7,2]
[7,3,8,6,5,4,2,1]=>[8,7,6,2,1,5,4,3]=>[1,2,3,7,8,4,5,6]=>[5,3]
[8,2,9,7,6,5,4,3,1]=>[9,8,7,6,5,2,1,4,3]=>[1,2,3,4,5,8,9,6,7]=>[7,2]
[9,1,10,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,9,10,8]=>[9,1]
[4,8,5,7,6,3,2,1]=>[8,3,7,1,6,5,4,2]=>[1,6,2,8,3,4,5,7]=>[2,2,4]
[3,8,7,4,6,5,2,1]=>[8,4,7,6,1,5,3,2]=>[1,5,2,3,8,4,6,7]=>[2,3,3]
[2,8,7,6,3,5,4,1]=>[8,5,7,6,4,1,3,2]=>[1,4,2,3,5,8,6,7]=>[2,4,2]
[8,5,6,1,3,2,4,7]=>[6,4,5,2,7,3,8,1]=>[3,5,4,7,2,6,1,8]=>[2,2,2,2]
[8,6,1,5,3,2,4,7]=>[6,5,7,3,4,2,8,1]=>[3,4,2,6,5,7,1,8]=>[2,2,2,2]
[7,8,1,5,3,2,4,6]=>[6,5,7,3,4,1,8,2]=>[3,4,2,6,5,8,1,7]=>[2,2,2,2]
[8,1,7,5,3,2,4,6]=>[6,5,7,4,8,2,3,1]=>[3,4,2,5,1,7,6,8]=>[2,2,2,2]
[8,6,1,4,5,2,3,7]=>[6,4,7,3,5,2,8,1]=>[3,5,2,6,4,7,1,8]=>[2,2,2,2]
[8,6,3,1,5,2,4,7]=>[6,3,7,4,5,2,8,1]=>[3,6,2,5,4,7,1,8]=>[2,2,2,2]
[8,4,6,1,5,2,3,7]=>[6,2,7,4,5,3,8,1]=>[3,7,2,5,4,6,1,8]=>[2,2,2,2]
[8,5,2,6,1,4,3,7]=>[7,3,5,2,6,4,8,1]=>[2,6,4,7,3,5,1,8]=>[2,2,2,2]
[8,5,2,1,7,4,3,6]=>[7,3,6,2,8,4,5,1]=>[2,6,3,7,1,5,4,8]=>[2,2,2,2]
[7,8,2,1,5,4,3,6]=>[7,3,6,4,5,1,8,2]=>[2,6,3,5,4,8,1,7]=>[2,2,2,2]
[7,8,3,1,5,2,4,6]=>[6,3,7,4,5,1,8,2]=>[3,6,2,5,4,8,1,7]=>[2,2,2,2]
[8,2,7,5,1,3,4,6]=>[5,6,7,2,4,8,3,1]=>[4,3,2,7,5,1,6,8]=>[1,1,2,1,3]
[8,4,1,7,5,2,3,6]=>[6,2,7,5,8,3,4,1]=>[3,7,2,4,1,6,5,8]=>[2,2,2,2]
[8,2,7,1,5,4,3,6]=>[7,6,2,4,5,8,3,1]=>[2,3,7,5,4,1,6,8]=>[3,1,1,3]
[8,2,6,1,7,4,3,5]=>[7,6,8,2,4,3,5,1]=>[2,3,1,7,5,6,4,8]=>[2,2,2,2]
[8,1,7,4,3,2,6,5]=>[5,4,8,6,7,2,3,1]=>[4,5,1,3,2,7,6,8]=>[2,2,2,2]
[8,1,5,7,3,2,6,4]=>[5,3,8,6,7,2,4,1]=>[4,6,1,3,2,7,5,8]=>[2,2,2,2]
[5,7,8,1,3,2,6,4]=>[5,1,8,4,6,2,7,3]=>[4,8,1,5,3,7,2,6]=>[2,2,2,2]
[8,2,6,1,5,7,3,4]=>[7,5,8,2,4,3,6,1]=>[2,4,1,7,5,6,3,8]=>[2,2,2,2]
[5,8,1,6,7,2,3,4]=>[6,1,7,4,8,3,5,2]=>[3,8,2,5,1,6,4,7]=>[2,2,2,2]
[5,7,6,1,8,2,3,4]=>[6,1,7,8,4,3,2,5]=>[3,8,2,1,5,6,7,4]=>[2,1,4,1]
[6,7,2,5,1,8,3,4]=>[7,8,3,1,5,4,2,6]=>[2,1,6,8,4,5,7,3]=>[1,3,3,1]
[7,5,1,6,8,2,3,4]=>[6,7,4,2,8,3,1,5]=>[3,2,5,7,1,6,8,4]=>[1,3,3,1]
[6,5,7,1,8,2,3,4]=>[6,7,2,1,8,4,3,5]=>[3,2,7,8,1,5,6,4]=>[1,3,3,1]
[6,7,3,8,1,2,4,5]=>[5,3,6,1,7,2,8,4]=>[4,6,3,8,2,7,1,5]=>[2,2,2,2]
[7,6,1,4,8,2,3,5]=>[6,4,7,8,3,2,1,5]=>[3,5,2,1,6,7,8,4]=>[2,1,4,1]
[8,1,6,4,7,2,3,5]=>[6,4,7,3,8,2,5,1]=>[3,5,2,6,1,7,4,8]=>[2,2,2,2]
[7,5,8,1,3,2,4,6]=>[6,4,5,2,7,1,8,3]=>[3,5,4,7,2,8,1,6]=>[2,2,2,2]
[7,8,4,1,3,2,5,6]=>[6,4,5,3,7,1,8,2]=>[3,5,4,6,2,8,1,7]=>[2,2,2,2]
[8,3,7,4,1,2,5,6]=>[2,5,6,4,7,8,3,1]=>[7,4,3,5,2,1,6,8]=>[1,1,2,1,3]
[8,5,1,7,3,2,4,6]=>[6,5,7,2,8,3,4,1]=>[3,4,2,7,1,6,5,8]=>[2,2,2,2]
[6,8,1,7,3,2,4,5]=>[6,5,7,1,8,3,4,2]=>[3,4,2,8,1,6,5,7]=>[2,2,2,2]
[7,3,1,8,6,4,2,5]=>[7,2,6,8,5,3,1,4]=>[2,7,3,1,4,6,8,5]=>[2,1,4,1]
[8,3,1,7,4,6,2,5]=>[2,5,7,8,6,3,4,1]=>[7,4,2,1,3,6,5,8]=>[1,1,1,3,2]
[8,4,5,1,7,2,3,6]=>[6,2,7,3,8,4,5,1]=>[3,7,2,6,1,5,4,8]=>[2,2,2,2]
[5,6,8,1,7,2,3,4]=>[6,1,7,2,8,4,5,3]=>[3,8,2,7,1,5,4,6]=>[2,2,2,2]
[6,5,8,1,2,7,3,4]=>[7,8,4,2,1,5,6,3]=>[2,1,5,7,8,4,3,6]=>[1,4,1,2]
[7,3,1,8,5,6,2,4]=>[7,2,5,8,6,3,1,4]=>[2,7,4,1,3,6,8,5]=>[2,1,4,1]
[6,2,7,8,3,1,5,4]=>[5,8,6,2,1,3,7,4]=>[4,1,3,7,8,6,2,5]=>[1,4,1,2]
[5,8,1,7,3,2,6,4]=>[5,1,8,6,7,3,4,2]=>[4,8,1,3,2,6,5,7]=>[2,2,2,2]
[8,4,1,7,3,2,6,5]=>[5,2,8,6,7,3,4,1]=>[4,7,1,3,2,6,5,8]=>[2,2,2,2]
[8,3,4,7,1,2,6,5]=>[2,3,8,5,6,7,4,1]=>[7,6,1,4,3,2,5,8]=>[1,1,2,1,3]
[8,2,7,4,1,3,6,5]=>[8,5,2,4,6,7,3,1]=>[1,4,7,5,3,2,6,8]=>[3,1,1,3]
[7,4,8,2,1,3,6,5]=>[4,2,8,5,6,1,7,3]=>[5,7,1,4,3,8,2,6]=>[2,2,2,2]
[7,4,3,8,1,2,6,5]=>[3,2,8,5,6,1,7,4]=>[6,7,1,4,3,8,2,5]=>[2,2,2,2]
[8,2,3,6,7,1,5,4]=>[8,6,2,3,4,7,5,1]=>[1,3,7,6,5,2,4,8]=>[3,1,1,3]
[7,8,5,2,3,6,4,1]=>[8,4,5,3,1,7,6,2]=>[1,5,4,6,8,2,3,7]=>[2,3,3]
[8,7,5,2,3,1,6,4]=>[4,5,8,6,3,7,2,1]=>[5,4,1,3,6,2,7,8]=>[1,1,3,3]
[6,8,5,2,3,4,7,1]=>[4,5,1,6,3,8,7,2]=>[5,4,8,3,6,1,2,7]=>[1,2,2,3]
[3,5,2,6,8,1,4,7]=>[6,1,3,2,4,7,8,5]=>[3,8,6,7,5,2,1,4]=>[2,2,1,1,2]
[3,5,2,4,6,8,1,7]=>[1,3,4,2,5,7,8,6]=>[8,6,5,7,4,2,1,3]=>[1,1,2,1,1,2]
[2,4,5,7,3,6,8,1]=>[2,3,5,6,1,4,8,7]=>[7,6,4,3,8,5,1,2]=>[1,1,1,2,1,2]
[2,4,5,3,6,8,1,7]=>[2,4,1,3,5,7,8,6]=>[7,5,8,6,4,2,1,3]=>[1,2,1,1,1,2]
[5,2,4,6,8,1,3,7]=>[3,6,2,1,4,7,8,5]=>[6,3,7,8,5,2,1,4]=>[1,3,1,1,2]
[5,1,3,4,6,8,2,7]=>[3,4,5,1,7,8,2,6]=>[6,5,4,8,2,1,7,3]=>[1,1,2,1,2,1]
[4,3,5,2,6,8,1,7]=>[2,1,4,3,5,7,8,6]=>[7,8,5,6,4,2,1,3]=>[2,2,1,1,2]
[4,3,5,7,2,8,1,6]=>[2,1,3,5,7,4,8,6]=>[7,8,6,4,2,5,1,3]=>[2,1,1,2,2]
[4,3,5,7,2,6,8,1]=>[2,1,3,5,6,4,8,7]=>[7,8,6,4,3,5,1,2]=>[2,1,1,2,2]
[4,6,3,7,2,5,8,1]=>[1,3,5,2,6,4,8,7]=>[8,6,4,7,3,5,1,2]=>[1,1,2,2,2]
[4,6,3,1,7,8,2,5]=>[1,3,7,5,2,8,4,6]=>[8,6,2,4,7,1,5,3]=>[1,1,3,2,1]
[4,3,5,1,7,8,2,6]=>[2,1,3,7,5,8,4,6]=>[7,8,6,2,4,1,5,3]=>[2,1,2,2,1]
[5,7,1,3,4,8,2,6]=>[4,5,1,7,8,3,2,6]=>[5,4,8,2,1,6,7,3]=>[1,2,1,3,1]
[5,7,1,3,4,6,8,2]=>[4,5,1,6,8,3,2,7]=>[5,4,8,3,1,6,7,2]=>[1,2,1,3,1]
[4,5,7,1,3,6,8,2]=>[1,5,2,6,8,4,3,7]=>[8,4,7,3,1,5,6,2]=>[1,2,1,3,1]
[4,3,6,7,1,5,8,2]=>[1,6,2,3,8,5,4,7]=>[8,3,7,6,1,4,5,2]=>[1,2,1,3,1]
[4,6,3,5,7,2,8,1]=>[1,3,4,2,6,5,8,7]=>[8,6,5,7,3,4,1,2]=>[1,1,2,2,2]
[3,5,6,4,1,7,8,2]=>[2,6,1,4,3,8,5,7]=>[7,3,8,5,6,1,4,2]=>[1,2,2,2,1]
[3,1,5,6,7,4,8,2]=>[1,3,4,6,5,8,2,7]=>[8,6,5,3,4,1,7,2]=>[1,1,1,2,2,1]
[5,1,6,7,3,4,8,2]=>[5,3,1,6,4,8,2,7]=>[4,6,8,3,5,1,7,2]=>[3,2,2,1]
[1,6,7,3,4,5,8,2]=>[4,5,2,6,3,8,1,7]=>[5,4,7,3,6,1,8,2]=>[1,2,2,2,1]
[2,6,7,4,5,8,1,3]=>[4,2,7,5,1,3,8,6]=>[5,7,2,4,8,6,1,3]=>[2,3,1,2]
[2,6,7,4,8,1,3,5]=>[6,4,2,7,1,3,8,5]=>[3,5,7,2,8,6,1,4]=>[3,2,1,2]
[5,3,6,1,2,7,8,4]=>[2,6,1,8,4,3,5,7]=>[7,3,8,1,5,6,4,2]=>[1,2,3,1,1]
[3,5,2,6,1,7,8,4]=>[6,1,3,2,4,8,5,7]=>[3,8,6,7,5,1,4,2]=>[2,2,1,2,1]
[3,5,2,6,7,4,8,1]=>[4,1,2,6,3,5,8,7]=>[5,8,7,3,6,4,1,2]=>[2,1,2,1,2]
[5,2,3,6,7,4,8,1]=>[4,6,2,1,3,5,8,7]=>[5,3,7,8,6,4,1,2]=>[1,3,1,1,2]
[5,2,3,6,1,7,8,4]=>[6,2,3,1,4,8,5,7]=>[3,7,6,8,5,1,4,2]=>[2,2,1,2,1]
[5,2,6,1,3,7,8,4]=>[6,8,2,1,4,3,5,7]=>[3,1,7,8,5,6,4,2]=>[1,3,2,1,1]
[4,2,6,7,3,5,8,1]=>[1,5,3,6,2,4,8,7]=>[8,4,6,3,7,5,1,2]=>[1,2,2,1,2]
[6,3,7,2,4,5,8,1]=>[2,4,5,1,6,3,8,7]=>[7,5,4,8,3,6,1,2]=>[1,1,2,2,2]
[3,5,7,2,8,1,4,6]=>[4,1,2,6,7,3,8,5]=>[5,8,7,3,2,6,1,4]=>[2,1,1,2,2]
[3,7,2,4,8,1,5,6]=>[1,3,4,6,7,2,8,5]=>[8,6,5,3,2,7,1,4]=>[1,1,1,1,2,2]
[7,2,4,6,8,1,3,5]=>[3,6,7,2,4,1,8,5]=>[6,3,2,7,5,8,1,4]=>[1,1,2,2,2]
[7,1,3,4,6,8,2,5]=>[7,3,4,5,8,2,1,6]=>[2,6,5,4,1,7,8,3]=>[2,1,1,3,1]
[3,7,2,4,6,8,1,5]=>[7,1,3,4,5,2,8,6]=>[2,8,6,5,4,7,1,3]=>[2,1,1,2,2]
[3,5,7,2,6,8,1,4]=>[2,7,1,4,5,3,8,6]=>[7,2,8,5,4,6,1,3]=>[1,2,1,2,2]
[6,3,5,7,2,8,1,4]=>[5,2,3,1,7,4,8,6]=>[4,7,6,8,2,5,1,3]=>[2,2,2,2]
[6,3,5,7,2,4,8,1]=>[5,2,3,1,6,4,8,7]=>[4,7,6,8,3,5,1,2]=>[2,2,2,2]
[6,2,4,5,7,3,8,1]=>[3,4,6,2,1,5,8,7]=>[6,5,3,7,8,4,1,2]=>[1,1,3,1,2]
[6,2,4,5,1,7,8,3]=>[3,6,2,4,1,8,5,7]=>[6,3,7,5,8,1,4,2]=>[1,2,2,2,1]
[4,7,1,2,5,6,8,3]=>[5,1,6,8,3,4,2,7]=>[4,8,3,1,6,5,7,2]=>[2,1,2,2,1]
[4,6,7,1,2,5,8,3]=>[1,6,8,4,2,5,3,7]=>[8,3,1,5,7,4,6,2]=>[1,1,3,2,1]
[5,6,2,4,7,3,8,1]=>[4,1,6,3,2,5,8,7]=>[5,8,3,6,7,4,1,2]=>[2,3,1,2]
[5,4,2,6,7,3,8,1]=>[4,2,1,6,3,5,8,7]=>[5,7,8,3,6,4,1,2]=>[3,2,1,2]
[5,4,2,6,1,7,8,3]=>[6,3,2,1,4,8,5,7]=>[3,6,7,8,5,1,4,2]=>[4,1,2,1]
[1,5,4,6,2,7,8,3]=>[3,2,6,4,8,1,5,7]=>[6,7,3,5,1,8,4,2]=>[2,2,2,1,1]
[5,6,4,1,2,7,8,3]=>[6,1,8,4,3,2,5,7]=>[3,8,1,5,6,7,4,2]=>[2,4,1,1]
[6,4,5,1,2,7,8,3]=>[6,2,8,4,3,1,5,7]=>[3,7,1,5,6,8,4,2]=>[2,4,1,1]
[6,3,5,1,7,8,2,4]=>[7,2,5,3,1,8,4,6]=>[2,7,4,6,8,1,5,3]=>[2,3,2,1]
[6,5,7,2,8,1,3,4]=>[4,6,2,1,7,3,8,5]=>[5,3,7,8,2,6,1,4]=>[1,3,2,2]
[6,5,7,1,3,4,8,2]=>[5,6,2,1,8,4,3,7]=>[4,3,7,8,1,5,6,2]=>[1,3,3,1]
[5,6,4,7,1,3,8,2]=>[1,6,3,2,8,5,4,7]=>[8,3,6,7,1,4,5,2]=>[1,3,3,1]
[5,4,6,3,1,7,8,2]=>[2,1,6,4,3,8,5,7]=>[7,8,3,5,6,1,4,2]=>[2,3,2,1]
[7,5,3,2,4,8,1,6]=>[4,3,5,2,7,1,8,6]=>[5,6,4,7,2,8,1,3]=>[2,2,2,2]
[8,4,5,2,6,1,3,7]=>[4,2,6,3,7,5,8,1]=>[5,7,3,6,2,4,1,8]=>[2,2,2,2]
[8,5,4,2,1,6,3,7]=>[4,7,5,3,2,6,8,1]=>[5,2,4,6,7,3,1,8]=>[1,4,1,2]
[8,5,3,4,1,6,2,7]=>[3,7,5,4,2,6,8,1]=>[6,2,4,5,7,3,1,8]=>[1,4,1,2]
[8,4,5,3,1,6,2,7]=>[2,7,5,4,3,6,8,1]=>[7,2,4,5,6,3,1,8]=>[1,4,1,2]
[7,5,4,2,1,8,3,6]=>[4,7,3,2,8,5,1,6]=>[5,2,6,7,1,4,8,3]=>[1,3,3,1]
[7,5,4,2,1,6,8,3]=>[4,6,3,2,8,5,1,7]=>[5,3,6,7,1,4,8,2]=>[1,3,3,1]
[7,4,5,3,1,6,8,2]=>[2,6,4,3,8,5,1,7]=>[7,3,5,6,1,4,8,2]=>[1,3,3,1]
[7,4,3,5,6,1,8,2]=>[3,2,4,8,6,5,1,7]=>[6,7,5,1,3,4,8,2]=>[2,1,4,1]
[5,6,3,7,4,1,8,2]=>[1,8,3,2,6,5,4,7]=>[8,1,6,7,3,4,5,2]=>[1,3,3,1]
[6,7,4,2,1,5,8,3]=>[4,6,3,1,8,5,2,7]=>[5,3,6,8,1,4,7,2]=>[1,3,3,1]
[5,6,7,3,1,8,2,4]=>[1,7,4,2,8,5,3,6]=>[8,2,5,7,1,4,6,3]=>[1,3,3,1]
[5,6,3,7,8,1,2,4]=>[3,1,6,2,7,4,8,5]=>[6,8,3,7,2,5,1,4]=>[2,2,2,2]
[5,6,3,7,2,4,8,1]=>[3,1,5,2,6,4,8,7]=>[6,8,4,7,3,5,1,2]=>[2,2,2,2]
[5,6,7,2,3,8,1,4]=>[4,1,5,2,7,3,8,6]=>[5,8,4,7,2,6,1,3]=>[2,2,2,2]
[7,4,5,2,8,1,3,6]=>[4,2,6,3,7,1,8,5]=>[5,7,3,6,2,8,1,4]=>[2,2,2,2]
[6,7,3,2,4,8,1,5]=>[4,3,5,1,7,2,8,6]=>[5,6,4,8,2,7,1,3]=>[2,2,2,2]
[7,6,4,2,1,3,8,5]=>[4,8,5,3,6,2,1,7]=>[5,1,4,6,3,7,8,2]=>[1,3,3,1]
[7,6,3,4,1,2,8,5]=>[3,8,5,4,6,2,1,7]=>[6,1,4,5,3,7,8,2]=>[1,3,3,1]
[6,7,3,2,5,1,8,4]=>[3,8,4,1,6,5,2,7]=>[6,1,5,8,3,4,7,2]=>[1,3,3,1]
[6,5,3,2,7,8,1,4]=>[3,7,4,2,1,5,8,6]=>[6,2,5,7,8,4,1,3]=>[1,4,1,2]
[6,5,3,2,7,4,8,1]=>[3,6,4,2,1,5,8,7]=>[6,3,5,7,8,4,1,2]=>[1,4,1,2]
[6,4,5,2,7,3,8,1]=>[2,6,4,3,1,5,8,7]=>[7,3,5,6,8,4,1,2]=>[1,4,1,2]
[6,4,5,2,7,8,1,3]=>[2,7,4,3,1,5,8,6]=>[7,2,5,6,8,4,1,3]=>[1,4,1,2]
[7,4,5,2,6,1,8,3]=>[2,8,4,3,6,5,1,7]=>[7,1,5,6,3,4,8,2]=>[1,3,3,1]
[7,4,5,6,1,2,8,3]=>[2,8,5,3,6,4,1,7]=>[7,1,4,6,3,5,8,2]=>[1,3,3,1]
[6,7,3,5,1,2,8,4]=>[3,8,5,1,6,4,2,7]=>[6,1,4,8,3,5,7,2]=>[1,3,3,1]
[5,6,7,4,1,2,8,3]=>[1,8,5,2,6,4,3,7]=>[8,1,4,7,3,5,6,2]=>[1,3,3,1]
[5,6,7,2,4,1,8,3]=>[1,8,4,2,6,5,3,7]=>[8,1,5,7,3,4,6,2]=>[1,3,3,1]
[5,6,4,2,7,8,1,3]=>[1,7,4,3,2,5,8,6]=>[8,2,5,6,7,4,1,3]=>[1,4,1,2]
[6,5,7,2,1,8,3,4]=>[4,7,2,1,8,5,3,6]=>[5,2,7,8,1,4,6,3]=>[1,3,3,1]
[6,5,7,2,1,4,8,3]=>[4,6,2,1,8,5,3,7]=>[5,3,7,8,1,4,6,2]=>[1,3,3,1]
[5,4,6,7,3,1,8,2]=>[2,1,3,8,6,5,4,7]=>[7,8,6,1,3,4,5,2]=>[2,1,4,1]
[5,7,8,3,6,4,1,2]=>[1,4,7,2,8,6,5,3]=>[8,5,2,7,1,3,4,6]=>[1,1,2,4]
[3,7,8,5,6,4,1,2]=>[7,4,2,8,1,6,5,3]=>[2,5,7,1,8,3,4,6]=>[3,2,3]
[3,7,8,5,6,1,4,2]=>[8,6,4,1,2,7,5,3]=>[1,3,5,8,7,2,4,6]=>[4,1,3]
[1,7,8,5,6,3,4,2]=>[6,4,2,8,7,5,1,3]=>[3,5,7,1,2,4,8,6]=>[3,4,1]
[1,7,5,8,6,3,4,2]=>[3,6,2,8,7,5,1,4]=>[6,3,7,1,2,4,8,5]=>[1,2,4,1]
[3,7,5,8,6,1,4,2]=>[3,8,6,1,2,7,5,4]=>[6,1,3,8,7,2,4,5]=>[1,3,1,3]
[3,7,5,8,6,4,1,2]=>[3,7,2,8,1,6,5,4]=>[6,2,7,1,8,3,4,5]=>[1,2,2,3]
[5,7,3,8,6,4,1,2]=>[1,7,8,3,2,6,5,4]=>[8,2,1,6,7,3,4,5]=>[1,1,3,3]
[7,3,8,5,6,4,1,2]=>[7,4,8,2,1,6,5,3]=>[2,5,1,7,8,3,4,6]=>[2,3,3]
[7,3,5,8,6,4,1,2]=>[3,7,8,2,1,6,5,4]=>[6,2,1,7,8,3,4,5]=>[1,1,3,3]
[3,5,7,8,6,4,1,2]=>[7,2,3,8,1,6,5,4]=>[2,7,6,1,8,3,4,5]=>[2,1,2,3]
[1,5,7,8,6,3,4,2]=>[6,2,3,8,7,5,1,4]=>[3,7,6,1,2,4,8,5]=>[2,1,4,1]
[1,5,7,8,3,6,4,2]=>[8,2,5,3,7,6,1,4]=>[1,7,4,6,2,3,8,5]=>[2,2,3,1]
[3,5,7,8,1,6,4,2]=>[8,2,7,1,5,3,6,4]=>[1,7,2,8,4,6,3,5]=>[2,2,2,2]
[7,3,5,8,6,1,4,2]=>[3,8,2,6,1,7,5,4]=>[6,1,7,3,8,2,4,5]=>[1,2,2,3]
[7,3,8,5,6,1,4,2]=>[8,6,2,4,1,7,5,3]=>[1,3,7,5,8,2,4,6]=>[3,2,3]
[7,8,1,5,6,3,4,2]=>[6,4,8,7,3,1,5,2]=>[3,5,1,2,6,8,4,7]=>[2,4,2]
[7,1,8,5,6,3,4,2]=>[6,4,8,7,5,2,1,3]=>[3,5,1,2,4,7,8,6]=>[2,5,1]
[7,1,5,8,6,3,4,2]=>[3,6,8,7,5,2,1,4]=>[6,3,1,2,4,7,8,5]=>[1,1,5,1]
[5,1,7,8,3,6,4,2]=>[1,8,5,3,7,6,2,4]=>[8,1,4,6,2,3,7,5]=>[1,3,3,1]
[3,1,7,8,5,6,4,2]=>[5,3,8,1,7,6,2,4]=>[4,6,1,8,2,3,7,5]=>[2,2,3,1]
[1,3,7,8,5,6,4,2]=>[5,3,8,7,2,6,1,4]=>[4,6,1,2,7,3,8,5]=>[2,3,2,1]
[3,1,7,5,8,6,4,2]=>[8,4,1,3,7,6,2,5]=>[1,5,8,6,2,3,7,4]=>[3,1,3,1]
[5,1,7,3,8,6,4,2]=>[1,8,7,4,3,6,2,5]=>[8,1,2,5,6,3,7,4]=>[1,4,2,1]
[7,1,5,3,8,6,4,2]=>[3,8,7,4,6,2,1,5]=>[6,1,2,5,3,7,8,4]=>[1,3,3,1]
[7,1,5,8,3,6,4,2]=>[3,8,5,7,6,2,1,4]=>[6,1,4,2,3,7,8,5]=>[1,2,4,1]
[7,8,1,5,3,6,4,2]=>[8,5,4,7,3,1,6,2]=>[1,4,5,2,6,8,3,7]=>[3,3,2]
[7,8,3,5,1,6,4,2]=>[8,3,7,5,4,1,6,2]=>[1,6,2,4,5,8,3,7]=>[2,4,2]
[5,3,7,1,8,6,4,2]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[1,3,3,1]
[3,5,7,1,8,6,4,2]=>[8,2,7,1,6,4,3,5]=>[1,7,2,8,3,5,6,4]=>[2,2,3,1]
[1,7,5,3,8,6,4,2]=>[3,8,7,4,2,6,1,5]=>[6,1,2,5,7,3,8,4]=>[1,4,2,1]
[5,7,3,1,8,6,4,2]=>[1,8,3,7,6,4,2,5]=>[8,1,6,2,3,5,7,4]=>[1,2,4,1]
[5,7,3,8,6,1,4,2]=>[1,8,3,6,2,7,5,4]=>[8,1,6,3,7,2,4,5]=>[1,2,2,3]
[1,7,5,8,3,6,4,2]=>[3,8,5,2,7,6,1,4]=>[6,1,4,7,2,3,8,5]=>[1,3,3,1]
[1,7,8,5,3,6,4,2]=>[8,5,4,2,7,6,1,3]=>[1,4,5,7,2,3,8,6]=>[4,3,1]
[3,7,8,5,1,6,4,2]=>[8,7,5,1,4,2,6,3]=>[1,2,4,8,5,7,3,6]=>[4,2,2]
[5,7,8,3,6,1,4,2]=>[1,4,8,6,2,7,5,3]=>[8,5,1,3,7,2,4,6]=>[1,1,3,3]
[5,7,8,6,3,1,4,2]=>[8,1,6,5,2,7,4,3]=>[1,8,3,4,7,2,5,6]=>[2,3,3]
[7,5,8,6,1,3,4,2]=>[6,2,8,5,1,7,4,3]=>[3,7,1,4,8,2,5,6]=>[2,3,3]
[5,7,8,1,6,3,4,2]=>[1,6,8,7,4,2,5,3]=>[8,3,1,2,5,7,4,6]=>[1,1,4,2]
[5,7,8,1,3,6,4,2]=>[1,8,5,7,4,2,6,3]=>[8,1,4,2,5,7,3,6]=>[1,2,3,2]
[3,7,8,1,5,6,4,2]=>[5,8,7,1,4,2,6,3]=>[4,1,2,8,5,7,3,6]=>[1,3,2,2]
[1,7,8,3,5,6,4,2]=>[5,8,4,2,7,6,1,3]=>[4,1,5,7,2,3,8,6]=>[1,3,3,1]
[1,7,3,8,5,6,4,2]=>[5,8,7,3,2,6,1,4]=>[4,1,2,6,7,3,8,5]=>[1,4,2,1]
[3,7,1,8,5,6,4,2]=>[5,8,7,1,6,3,2,4]=>[4,1,2,8,3,6,7,5]=>[1,3,3,1]
[5,7,1,8,3,6,4,2]=>[1,8,5,7,6,3,2,4]=>[8,1,4,2,3,6,7,5]=>[1,2,4,1]
[5,7,1,8,6,3,4,2]=>[1,6,8,7,5,3,2,4]=>[8,3,1,2,4,6,7,5]=>[1,1,5,1]
[7,5,1,8,6,3,4,2]=>[6,2,8,7,5,3,1,4]=>[3,7,1,2,4,6,8,5]=>[2,5,1]
[7,5,8,1,6,3,4,2]=>[6,2,8,7,4,1,5,3]=>[3,7,1,2,5,8,4,6]=>[2,4,2]
[7,8,5,1,6,3,4,2]=>[6,8,7,4,3,1,5,2]=>[3,1,2,5,6,8,4,7]=>[1,5,2]
[7,8,5,1,3,6,4,2]=>[8,5,7,4,3,1,6,2]=>[1,4,2,5,6,8,3,7]=>[2,4,2]
[7,5,8,1,3,6,4,2]=>[8,5,2,7,4,1,6,3]=>[1,4,7,2,5,8,3,6]=>[3,3,2]
[7,5,1,8,3,6,4,2]=>[8,5,2,7,6,3,1,4]=>[1,4,7,2,3,6,8,5]=>[3,4,1]
[7,5,1,3,8,6,4,2]=>[8,7,4,2,6,3,1,5]=>[1,2,5,7,3,6,8,4]=>[4,3,1]
[5,7,1,3,8,6,4,2]=>[1,8,7,4,6,3,2,5]=>[8,1,2,5,3,6,7,4]=>[1,3,3,1]
[3,7,1,5,8,6,4,2]=>[8,4,7,1,6,3,2,5]=>[1,5,2,8,3,6,7,4]=>[2,2,3,1]
[1,7,3,5,8,6,4,2]=>[8,4,7,3,2,6,1,5]=>[1,5,2,6,7,3,8,4]=>[2,3,2,1]
[1,5,3,7,8,6,4,2]=>[2,4,8,7,3,6,1,5]=>[7,5,1,2,6,3,8,4]=>[1,1,3,2,1]
[3,5,1,7,8,6,4,2]=>[2,4,8,1,7,6,3,5]=>[7,5,1,8,2,3,6,4]=>[1,1,2,3,1]
[5,3,1,7,8,6,4,2]=>[4,1,8,2,7,6,3,5]=>[5,8,1,7,2,3,6,4]=>[2,2,3,1]
[7,3,1,5,8,6,4,2]=>[8,2,4,7,6,3,1,5]=>[1,7,5,2,3,6,8,4]=>[2,1,4,1]
[7,3,1,8,5,6,4,2]=>[5,8,2,7,6,3,1,4]=>[4,1,7,2,3,6,8,5]=>[1,2,4,1]
[7,3,8,1,5,6,4,2]=>[5,8,2,7,4,1,6,3]=>[4,1,7,2,5,8,3,6]=>[1,2,3,2]
[7,8,3,1,5,6,4,2]=>[3,5,8,7,4,1,6,2]=>[6,4,1,2,5,8,3,7]=>[1,1,4,2]
[7,8,1,3,5,6,4,2]=>[5,8,4,7,3,1,6,2]=>[4,1,5,2,6,8,3,7]=>[1,2,3,2]
[7,1,8,3,5,6,4,2]=>[5,8,4,7,6,2,1,3]=>[4,1,5,2,3,7,8,6]=>[1,2,4,1]
[7,1,3,8,5,6,4,2]=>[5,8,7,3,6,2,1,4]=>[4,1,2,6,3,7,8,5]=>[1,3,3,1]
[7,1,3,5,8,6,4,2]=>[8,4,7,3,6,2,1,5]=>[1,5,2,6,3,7,8,4]=>[2,2,3,1]
[5,7,3,4,6,8,1,2]=>[3,1,4,7,5,2,8,6]=>[6,8,5,2,4,7,1,3]=>[2,1,3,2]
[5,7,3,4,8,1,6,2]=>[3,1,4,8,6,2,7,5]=>[6,8,5,1,3,7,2,4]=>[2,1,3,2]
[5,7,3,4,1,8,6,2]=>[3,1,4,8,7,5,2,6]=>[6,8,5,1,2,4,7,3]=>[2,1,4,1]
[5,7,3,4,1,6,8,2]=>[3,1,6,4,8,5,2,7]=>[6,8,3,5,1,4,7,2]=>[2,2,3,1]
[5,7,3,4,6,1,2,8]=>[3,1,6,4,7,5,2,8]=>[6,8,3,5,2,4,7,1]=>[2,2,3,1]
[7,3,5,6,1,2,8,4]=>[8,2,5,3,6,4,1,7]=>[1,7,4,6,3,5,8,2]=>[2,2,3,1]
[5,7,3,1,4,6,2,8]=>[5,3,1,7,4,6,2,8]=>[4,6,8,2,5,3,7,1]=>[3,2,2,1]
[5,7,3,1,4,6,8,2]=>[5,3,1,6,8,4,2,7]=>[4,6,8,3,1,5,7,2]=>[3,1,3,1]
[5,7,3,1,4,8,6,2]=>[3,1,8,5,7,4,2,6]=>[6,8,1,4,2,5,7,3]=>[2,2,3,1]
[5,7,3,1,4,8,2,6]=>[5,3,1,7,8,4,2,6]=>[4,6,8,2,1,5,7,3]=>[3,1,3,1]
[5,3,7,4,1,2,8,6]=>[8,2,1,5,4,6,3,7]=>[1,7,8,4,5,3,6,2]=>[3,2,2,1]
[5,3,7,4,1,2,6,8]=>[2,5,1,6,4,7,3,8]=>[7,4,8,3,5,2,6,1]=>[1,2,2,2,1]
[5,3,7,1,4,2,6,8]=>[2,6,4,1,5,7,3,8]=>[7,3,5,8,4,2,6,1]=>[1,3,1,2,1]
[5,3,7,1,4,2,8,6]=>[2,5,1,8,4,6,3,7]=>[7,4,8,1,5,3,6,2]=>[1,2,2,2,1]
[3,7,5,1,2,8,6,4]=>[8,7,1,4,3,5,2,6]=>[1,2,8,5,6,4,7,3]=>[3,2,2,1]
[7,8,3,5,1,2,6,4]=>[3,8,5,6,4,1,7,2]=>[6,1,4,3,5,8,2,7]=>[1,2,3,2]
[7,3,8,5,1,2,6,4]=>[8,2,5,6,4,1,7,3]=>[1,7,4,3,5,8,2,6]=>[2,1,3,2]
[7,3,5,8,1,2,6,4]=>[8,2,5,3,6,1,7,4]=>[1,7,4,6,3,8,2,5]=>[2,2,2,2]
[3,7,5,1,2,6,4,8]=>[7,1,4,5,3,6,2,8]=>[2,8,5,4,6,3,7,1]=>[2,1,2,2,1]
[3,7,5,1,2,6,8,4]=>[6,8,1,4,3,5,2,7]=>[3,1,8,5,6,4,7,2]=>[1,2,2,2,1]
[2,5,7,3,8,4,1,6]=>[2,7,4,6,1,3,8,5]=>[7,2,5,3,8,6,1,4]=>[1,2,2,1,2]
[5,4,7,8,6,1,3,2]=>[1,8,2,6,3,7,5,4]=>[8,1,7,3,6,2,4,5]=>[1,2,2,3]
[7,5,6,2,8,3,1,4]=>[7,4,2,6,3,1,8,5]=>[2,5,7,3,6,8,1,4]=>[3,3,2]
[4,7,2,5,8,3,1,6]=>[1,4,7,3,6,2,8,5]=>[8,5,2,6,3,7,1,4]=>[1,1,2,2,2]
[6,2,4,5,1,3,8,7]=>[3,8,2,5,4,1,6,7]=>[6,1,7,4,5,8,3,2]=>[1,2,3,1,1]
[3,5,6,2,4,1,8,7]=>[4,1,2,5,3,8,6,7]=>[5,8,7,4,6,1,3,2]=>[2,1,2,2,1]
[3,8,6,7,5,4,1,2]=>[7,3,8,6,1,5,4,2]=>[2,6,1,3,8,4,5,7]=>[2,3,3]
[6,2,7,8,3,4,1,5]=>[5,7,6,2,1,3,8,4]=>[4,2,3,7,8,6,1,5]=>[1,4,1,2]
[2,5,3,4,8,1,7,6]=>[8,3,1,2,4,6,7,5]=>[1,6,8,7,5,3,2,4]=>[3,1,1,1,2]
[5,1,8,2,3,4,7,6]=>[8,4,5,1,6,7,2,3]=>[1,5,4,8,3,2,7,6]=>[2,2,1,2,1]
[5,4,7,6,2,8,1,3]=>[2,1,5,7,4,3,8,6]=>[7,8,4,2,5,6,1,3]=>[2,1,3,2]
[3,7,8,1,5,4,6,2]=>[6,5,8,1,4,2,7,3]=>[3,4,1,8,5,7,2,6]=>[2,2,2,2]
[7,1,3,4,6,8,5,2]=>[5,8,3,4,7,2,1,6]=>[4,1,6,5,2,7,8,3]=>[1,2,1,3,1]
[8,3,6,5,7,1,4,2]=>[8,6,2,4,3,7,5,1]=>[1,3,7,5,6,2,4,8]=>[3,2,3]
[4,7,6,1,8,3,5,2]=>[6,8,1,7,4,3,2,5]=>[3,1,8,2,5,6,7,4]=>[1,2,4,1]
[4,7,2,6,3,8,5,1]=>[8,1,5,3,4,2,7,6]=>[1,8,4,6,5,7,2,3]=>[2,2,2,2]
[2,1,8,4,6,7,3,5]=>[7,4,5,8,1,6,2,3]=>[2,5,4,1,8,3,7,6]=>[2,1,2,2,1]
[3,8,1,5,6,7,2,4]=>[4,7,1,5,8,3,6,2]=>[5,2,8,4,1,6,3,7]=>[1,2,1,2,2]
[6,7,2,4,8,5,3,1]=>[8,4,1,7,3,2,6,5]=>[1,5,8,2,6,7,3,4]=>[3,3,2]
[2,8,3,6,7,5,1,4]=>[7,4,8,3,6,1,5,2]=>[2,5,1,6,3,8,4,7]=>[2,2,2,2]
[8,2,1,7,6,3,5,4]=>[8,6,7,2,5,3,4,1]=>[1,3,2,7,4,6,5,8]=>[2,2,2,2]
[3,2,4,5,8,1,7,6]=>[1,8,2,3,4,6,7,5]=>[8,1,7,6,5,3,2,4]=>[1,2,1,1,1,2]
[7,4,6,3,2,1,8,5]=>[2,5,4,8,6,3,1,7]=>[7,4,5,1,3,6,8,2]=>[1,2,4,1]
[4,7,3,2,1,8,6,5]=>[1,3,8,4,7,5,2,6]=>[8,6,1,5,2,4,7,3]=>[1,1,2,3,1]
[6,4,7,5,2,3,8,1]=>[2,5,1,6,4,3,8,7]=>[7,4,8,3,5,6,1,2]=>[1,2,3,2]
[4,2,3,1,8,7,5,6]=>[7,1,8,2,3,6,4,5]=>[2,8,1,7,6,3,5,4]=>[2,2,1,2,1]
[7,6,8,1,3,5,2,4]=>[5,7,8,4,2,1,6,3]=>[4,2,1,5,7,8,3,6]=>[1,1,4,2]
[6,7,5,2,3,1,8,4]=>[4,5,1,8,6,3,2,7]=>[5,4,8,1,3,6,7,2]=>[1,2,4,1]
[4,7,2,6,5,1,8,3]=>[8,1,6,3,5,4,2,7]=>[1,8,3,6,4,5,7,2]=>[2,2,3,1]
[6,4,2,1,8,5,7,3]=>[6,2,8,3,1,7,4,5]=>[3,7,1,6,8,2,5,4]=>[2,3,2,1]
[8,7,2,6,4,1,5,3]=>[8,6,3,5,7,4,2,1]=>[1,3,6,4,2,5,7,8]=>[3,1,4]
[6,7,8,2,5,3,1,4]=>[7,4,1,6,2,8,5,3]=>[2,5,8,3,7,1,4,6]=>[3,2,3]
[2,1,7,3,6,8,5,4]=>[5,8,7,1,4,2,3,6]=>[4,1,2,8,5,7,6,3]=>[1,3,2,1,1]
[2,1,5,7,8,4,6,3]=>[6,3,4,8,1,7,2,5]=>[3,6,5,1,8,2,7,4]=>[2,1,2,2,1]
[2,5,7,8,3,6,1,4]=>[2,5,7,3,8,1,6,4]=>[7,4,2,6,1,8,3,5]=>[1,1,2,2,2]
[6,4,1,5,7,2,8,3]=>[4,2,8,6,3,1,5,7]=>[5,7,1,3,6,8,4,2]=>[2,4,1,1]
[7,4,8,1,2,5,6,3]=>[6,2,8,4,5,1,7,3]=>[3,7,1,5,4,8,2,6]=>[2,2,2,2]
[4,2,7,8,6,3,5,1]=>[6,1,3,8,7,2,5,4]=>[3,8,6,1,2,7,4,5]=>[2,1,3,2]
[6,1,7,4,3,2,8,5]=>[5,4,8,6,2,1,3,7]=>[4,5,1,3,7,8,6,2]=>[2,4,1,1]
[4,2,6,1,5,7,8,3]=>[5,1,6,2,3,8,4,7]=>[4,8,3,7,6,1,5,2]=>[2,2,1,2,1]
[2,4,6,7,3,5,8,1]=>[5,2,3,6,1,4,8,7]=>[4,7,6,3,8,5,1,2]=>[2,1,2,1,2]
[6,5,8,3,7,4,1,2]=>[4,2,1,7,8,6,5,3]=>[5,7,8,2,1,3,4,6]=>[3,1,4]
[7,1,4,8,3,5,6,2]=>[3,5,6,8,7,2,1,4]=>[6,4,3,1,2,7,8,5]=>[1,1,1,4,1]
[6,8,7,5,3,4,1,2]=>[1,7,5,8,6,4,3,2]=>[8,2,4,1,3,5,6,7]=>[1,2,5]
[4,8,6,3,1,5,7,2]=>[6,1,4,8,5,3,7,2]=>[3,8,5,1,4,6,2,7]=>[2,1,3,2]
[3,4,8,2,5,7,6,1]=>[8,1,2,4,5,7,6,3]=>[1,8,7,5,4,2,3,6]=>[2,1,1,1,3]
[3,6,8,7,2,5,1,4]=>[5,2,7,8,1,6,4,3]=>[4,7,2,1,8,3,5,6]=>[2,1,2,3]
[2,5,7,4,8,6,1,3]=>[2,4,7,3,8,1,6,5]=>[7,5,2,6,1,8,3,4]=>[1,1,2,2,2]
[1,6,3,7,5,2,8,4]=>[8,6,3,2,5,1,4,7]=>[1,3,6,7,4,8,5,2]=>[4,2,1,1]
[2,6,3,7,5,1,8,4]=>[8,6,3,1,2,5,4,7]=>[1,3,6,8,7,4,5,2]=>[4,1,2,1]
[6,3,7,2,8,5,1,4]=>[7,8,2,1,4,3,6,5]=>[2,1,7,8,5,6,3,4]=>[1,3,2,2]
[3,6,2,5,8,7,1,4]=>[4,7,1,2,8,3,6,5]=>[5,2,8,7,1,6,3,4]=>[1,2,1,2,2]
[5,2,8,4,7,6,1,3]=>[4,1,7,8,6,2,5,3]=>[5,8,2,1,3,7,4,6]=>[2,1,3,2]
[7,2,4,8,6,5,1,3]=>[7,8,3,6,2,1,5,4]=>[2,1,6,3,7,8,4,5]=>[1,2,3,2]
[6,2,4,8,7,5,1,3]=>[7,8,3,1,6,2,5,4]=>[2,1,6,8,3,7,4,5]=>[1,3,2,2]
[2,4,5,8,7,6,1,3]=>[7,8,2,3,6,1,5,4]=>[2,1,7,6,3,8,4,5]=>[1,2,1,2,2]
[2,3,5,7,6,1,8,4]=>[8,3,6,1,2,5,4,7]=>[1,6,3,8,7,4,5,2]=>[2,2,1,2,1]
[1,3,4,6,2,8,7,5]=>[4,8,2,3,7,1,5,6]=>[5,1,7,6,2,8,4,3]=>[1,2,1,2,1,1]
[5,2,3,6,1,8,7,4]=>[4,8,2,1,3,7,5,6]=>[5,1,7,8,6,2,4,3]=>[1,3,1,2,1]
[4,2,7,3,8,1,6,5]=>[1,8,4,6,2,3,7,5]=>[8,1,5,3,7,6,2,4]=>[1,2,2,1,2]
[2,5,1,4,7,3,8,6]=>[8,4,1,2,6,3,5,7]=>[1,5,8,7,3,6,4,2]=>[3,1,2,1,1]
[6,1,3,8,7,2,5,4]=>[8,6,7,3,1,5,2,4]=>[1,3,2,6,8,4,7,5]=>[2,3,2,1]
[3,1,5,6,2,8,7,4]=>[1,3,4,8,7,2,5,6]=>[8,6,5,1,2,7,4,3]=>[1,1,1,3,1,1]
[1,2,4,6,3,8,7,5]=>[4,8,3,7,1,2,5,6]=>[5,1,6,2,8,7,4,3]=>[1,2,2,1,1,1]
[4,1,5,2,8,7,6,3]=>[1,8,3,7,6,2,4,5]=>[8,1,6,2,3,7,5,4]=>[1,2,3,1,1]
[7,1,4,2,8,6,5,3]=>[8,3,7,6,2,4,1,5]=>[1,6,2,3,7,5,8,4]=>[2,3,2,1]
[5,1,3,7,2,8,6,4]=>[8,7,3,1,5,2,4,6]=>[1,2,6,8,4,7,5,3]=>[4,2,1,1]
[4,1,5,3,2,8,7,6]=>[3,1,8,4,7,2,5,6]=>[6,8,1,5,2,7,4,3]=>[2,2,2,1,1]
[2,6,1,4,3,8,7,5]=>[8,4,7,1,3,2,5,6]=>[1,5,2,8,6,7,4,3]=>[2,2,2,1,1]
[3,6,2,4,1,8,7,5]=>[8,1,3,4,2,7,5,6]=>[1,8,6,5,7,2,4,3]=>[2,1,2,2,1]
[7,2,3,5,1,8,6,4]=>[4,8,2,3,7,5,1,6]=>[5,1,7,6,2,4,8,3]=>[1,2,1,3,1]
[7,3,4,1,8,6,5,2]=>[8,2,3,7,6,4,1,5]=>[1,7,6,2,3,5,8,4]=>[2,1,4,1]
[6,3,4,1,8,7,5,2]=>[8,2,3,1,7,6,4,5]=>[1,7,6,8,2,3,5,4]=>[2,2,3,1]
[3,4,5,1,8,7,6,2]=>[8,1,2,3,7,6,4,5]=>[1,8,7,6,2,3,5,4]=>[2,1,1,3,1]
[1,4,5,2,8,7,6,3]=>[8,2,3,7,6,1,4,5]=>[1,7,6,2,3,8,5,4]=>[2,1,3,1,1]
[1,6,4,2,8,7,5,3]=>[8,3,2,7,6,1,4,5]=>[1,6,7,2,3,8,5,4]=>[3,3,1,1]
[5,6,3,1,8,7,4,2]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[1,3,3,1]
[7,4,2,5,1,8,6,3]=>[4,2,8,3,7,5,1,6]=>[5,7,1,6,2,4,8,3]=>[2,2,3,1]
[5,3,6,2,8,1,7,4]=>[8,2,1,4,3,6,7,5]=>[1,7,8,5,6,3,2,4]=>[3,2,1,2]
[4,6,2,7,5,1,8,3]=>[8,1,6,3,2,5,4,7]=>[1,8,3,6,7,4,5,2]=>[2,3,2,1]
[4,5,2,6,1,8,7,3]=>[1,4,2,8,3,7,5,6]=>[8,5,7,1,6,2,4,3]=>[1,2,2,2,1]
[1,5,3,6,2,8,7,4]=>[4,2,8,3,7,1,5,6]=>[5,7,1,6,2,8,4,3]=>[2,2,2,1,1]
[1,5,8,3,2,7,6,4]=>[2,8,4,7,5,6,1,3]=>[7,1,5,2,4,3,8,6]=>[1,2,2,2,1]
[2,5,8,3,1,7,6,4]=>[2,8,4,7,1,5,6,3]=>[7,1,5,2,8,4,3,6]=>[1,2,2,1,2]
[3,6,2,5,1,4,8,7]=>[8,1,3,5,4,2,6,7]=>[1,8,6,4,5,7,3,2]=>[2,1,3,1,1]
[5,2,8,4,1,3,7,6]=>[8,5,2,1,4,6,7,3]=>[1,4,7,8,5,3,2,6]=>[4,1,1,2]
[2,4,8,7,1,3,6,5]=>[8,2,5,6,7,1,4,3]=>[1,7,4,3,2,8,5,6]=>[2,1,1,2,2]
[2,5,8,1,3,7,6,4]=>[2,8,7,1,4,5,6,3]=>[7,1,2,8,5,4,3,6]=>[1,3,1,1,2]
[2,3,8,1,4,7,6,5]=>[8,7,1,2,4,5,6,3]=>[1,2,8,7,5,4,3,6]=>[3,1,1,1,2]
[1,3,8,2,4,7,6,5]=>[8,7,2,4,5,6,1,3]=>[1,2,7,5,4,3,8,6]=>[3,1,1,2,1]
[7,5,1,2,8,6,4,3]=>[8,7,6,3,2,4,1,5]=>[1,2,3,6,7,5,8,4]=>[5,2,1]
[4,6,1,2,8,7,5,3]=>[8,1,7,6,3,2,4,5]=>[1,8,2,3,6,7,5,4]=>[2,4,1,1]
[1,6,2,3,8,7,5,4]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>[5,1,1,1]
[1,5,2,3,8,7,6,4]=>[2,8,7,6,1,3,4,5]=>[7,1,2,3,8,6,5,4]=>[1,4,1,1,1]
[4,5,1,2,8,7,6,3]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[1,1,4,1,1]
[6,4,1,2,8,7,5,3]=>[2,8,7,6,3,1,4,5]=>[7,1,2,3,6,8,5,4]=>[1,5,1,1]
[7,4,1,2,8,6,5,3]=>[2,8,7,6,3,4,1,5]=>[7,1,2,3,6,5,8,4]=>[1,4,2,1]
[5,3,1,7,2,8,6,4]=>[8,2,1,7,5,3,4,6]=>[1,7,8,2,4,6,5,3]=>[3,3,1,1]
[5,2,8,1,3,7,6,4]=>[8,7,2,1,4,5,6,3]=>[1,2,7,8,5,4,3,6]=>[4,1,1,2]
[4,1,2,8,3,7,6,5]=>[1,8,7,5,6,2,3,4]=>[8,1,2,4,3,7,6,5]=>[1,3,2,1,1]
[4,7,5,6,8,3,1,2]=>[3,7,1,4,2,8,6,5]=>[6,2,8,5,7,1,3,4]=>[1,2,2,3]
[8,6,4,7,5,3,1,2]=>[3,7,2,8,6,5,4,1]=>[6,2,7,1,3,4,5,8]=>[1,2,5]
[7,5,2,6,4,1,3,8]=>[6,7,3,2,5,4,1,8]=>[3,2,6,7,4,5,8,1]=>[1,3,3,1]
[1,6,3,7,5,8,4,2]=>[5,4,2,8,3,7,1,6]=>[4,5,7,1,6,2,8,3]=>[3,2,2,1]
[1,3,7,4,5,8,6,2]=>[8,4,5,2,3,7,1,6]=>[1,5,4,7,6,2,8,3]=>[2,2,1,2,1]
[7,2,6,3,4,1,5,8]=>[4,6,2,5,7,3,1,8]=>[5,3,7,4,2,6,8,1]=>[1,2,1,3,1]
[8,3,7,4,6,5,1,2]=>[4,7,8,2,6,5,3,1]=>[5,2,1,7,3,4,6,8]=>[1,1,2,4]
[6,8,4,7,5,3,1,2]=>[3,1,7,8,6,5,4,2]=>[6,8,2,1,3,4,5,7]=>[2,1,5]
[4,8,7,5,6,3,1,2]=>[7,4,8,1,6,5,3,2]=>[2,5,1,8,3,4,6,7]=>[2,2,4]
[3,8,7,6,4,5,1,2]=>[7,5,8,6,1,4,3,2]=>[2,4,1,3,8,5,6,7]=>[2,3,3]
[1,6,5,2,8,3,7,4]=>[8,6,3,2,7,1,4,5]=>[1,3,6,7,2,8,5,4]=>[4,2,1,1]
[8,6,5,2,1,4,3,7]=>[4,7,5,6,3,2,8,1]=>[5,2,4,3,6,7,1,8]=>[1,2,3,2]
[2,7,6,3,1,4,5,8]=>[5,4,6,7,1,3,2,8]=>[4,5,3,2,8,6,7,1]=>[2,1,2,2,1]
[6,1,3,7,5,8,4,2]=>[5,4,8,3,1,7,2,6]=>[4,5,1,6,8,2,7,3]=>[2,3,2,1]
[2,1,7,4,8,6,3,5]=>[7,8,4,1,3,6,2,5]=>[2,1,5,8,6,3,7,4]=>[1,3,1,2,1]
[1,8,6,3,7,5,4,2]=>[8,7,4,3,6,5,1,2]=>[1,2,5,6,3,4,8,7]=>[4,3,1]
[1,8,2,7,3,6,5,4]=>[8,7,5,6,3,4,1,2]=>[1,2,4,3,6,5,8,7]=>[3,2,2,1]
[2,1,3,8,4,7,5,6]=>[7,8,1,5,6,2,3,4]=>[2,1,8,4,3,7,6,5]=>[1,2,1,2,1,1]
[5,3,1,6,8,4,7,2]=>[2,4,1,6,8,7,3,5]=>[7,5,8,3,1,2,6,4]=>[1,2,1,3,1]
[6,2,8,7,1,4,3,5]=>[7,5,6,1,8,2,4,3]=>[2,4,3,8,1,7,5,6]=>[2,2,2,2]
[8,7,2,1,5,4,3,6]=>[7,3,6,4,5,8,2,1]=>[2,6,3,5,4,1,7,8]=>[2,2,1,3]
[8,2,3,1,4,6,5,7]=>[2,3,7,4,5,6,8,1]=>[7,6,2,5,4,3,1,8]=>[1,1,2,1,1,2]
[2,4,8,3,1,5,6,7]=>[2,5,1,4,6,7,8,3]=>[7,4,8,5,3,2,1,6]=>[1,2,1,1,1,2]
[3,4,2,7,1,5,6,8]=>[1,3,2,5,6,7,4,8]=>[8,6,7,4,3,2,5,1]=>[1,2,1,1,2,1]
[5,2,7,3,1,4,6,8]=>[5,2,4,1,6,7,3,8]=>[4,7,5,8,3,2,6,1]=>[2,2,1,2,1]
[8,3,7,2,1,5,4,6]=>[2,4,7,5,6,8,3,1]=>[7,5,2,4,3,1,6,8]=>[1,1,2,1,3]
[1,3,7,2,8,4,6,5]=>[8,6,7,2,4,1,3,5]=>[1,3,2,7,5,8,6,4]=>[2,2,2,1,1]
[1,4,2,5,8,6,7,3]=>[2,6,8,4,7,1,3,5]=>[7,3,1,5,2,8,6,4]=>[1,1,2,2,1,1]
[6,5,3,8,2,1,4,7]=>[3,6,5,2,1,7,8,4]=>[6,3,4,7,8,2,1,5]=>[1,4,1,2]
[2,6,4,5,7,1,3,8]=>[3,6,4,1,2,7,5,8]=>[6,3,5,8,7,2,4,1]=>[1,3,1,2,1]
[5,4,6,2,7,1,3,8]=>[4,2,1,6,3,7,5,8]=>[5,7,8,3,6,2,4,1]=>[3,2,2,1]
[7,6,2,1,8,5,3,4]=>[7,8,3,6,4,2,1,5]=>[2,1,6,3,5,7,8,4]=>[1,2,4,1]
[1,7,5,8,6,4,3,2]=>[8,3,2,7,6,5,1,4]=>[1,6,7,2,3,4,8,5]=>[3,4,1]
[6,5,1,2,8,3,7,4]=>[8,6,7,3,2,1,4,5]=>[1,3,2,6,7,8,5,4]=>[2,4,1,1]
[6,5,7,1,3,8,4,2]=>[8,5,2,1,7,4,3,6]=>[1,4,7,8,2,5,6,3]=>[4,3,1]
[5,8,3,1,7,4,6,2]=>[3,1,6,8,7,4,5,2]=>[6,8,3,1,2,5,4,7]=>[2,1,3,2]
[8,3,1,7,5,4,6,2]=>[6,2,5,8,7,3,4,1]=>[3,7,4,1,2,6,5,8]=>[2,1,3,2]
[1,3,8,7,4,6,5,2]=>[8,5,7,6,2,4,1,3]=>[1,4,2,3,7,5,8,6]=>[2,3,2,1]
[1,2,8,7,6,3,5,4]=>[8,6,7,5,4,1,2,3]=>[1,3,2,4,5,8,7,6]=>[2,4,1,1]
[8,2,1,7,6,4,3,5]=>[7,6,8,2,5,3,4,1]=>[2,3,1,7,4,6,5,8]=>[2,2,2,2]
[2,3,1,8,7,4,5,6]=>[6,7,8,1,2,5,3,4]=>[3,2,1,8,7,4,6,5]=>[1,1,2,1,2,1]
[2,4,1,8,5,7,3,6]=>[2,5,7,8,1,6,3,4]=>[7,4,2,1,8,3,6,5]=>[1,1,1,2,2,1]
[6,2,7,1,8,5,3,4]=>[7,8,6,2,1,4,3,5]=>[2,1,3,7,8,5,6,4]=>[1,4,2,1]
[8,7,1,6,5,4,3,2]=>[8,7,6,5,3,4,2,1]=>[1,2,3,4,6,5,7,8]=>[5,3]
[7,1,8,3,6,5,4,2]=>[8,7,4,6,5,2,1,3]=>[1,2,5,3,4,7,8,6]=>[3,4,1]
[4,1,8,7,5,6,3,2]=>[5,8,1,7,6,4,2,3]=>[4,1,8,2,3,5,7,6]=>[1,2,4,1]
[8,1,9,2,3,4,5,6,7]=>[4,5,6,7,8,9,2,1,3]=>[6,5,4,3,2,1,8,9,7]=>[1,1,1,1,1,3,1]
[2,1,7,8,4,6,3,5]=>[5,7,3,8,1,6,2,4]=>[4,2,6,1,8,3,7,5]=>[1,2,2,2,1]
[3,5,8,7,2,6,4,1]=>[8,2,5,7,1,6,4,3]=>[1,7,4,2,8,3,5,6]=>[2,1,2,3]
[8,6,3,7,5,2,1,4]=>[7,3,6,2,8,5,4,1]=>[2,6,3,7,1,4,5,8]=>[2,2,4]
[4,6,3,7,5,2,8,1]=>[6,1,3,2,5,4,8,7]=>[3,8,6,7,4,5,1,2]=>[2,2,2,2]
[3,5,7,8,2,6,1,4]=>[2,5,7,1,3,8,6,4]=>[7,4,2,8,6,1,3,5]=>[1,1,2,1,3]
[7,6,3,8,5,2,4,1]=>[6,8,3,2,1,7,5,4]=>[3,1,6,7,8,2,4,5]=>[1,4,3]
[8,2,3,4,6,1,5,7]=>[2,3,4,6,7,5,8,1]=>[7,6,5,3,2,4,1,8]=>[1,1,1,1,2,2]
[7,2,3,4,6,1,8,5]=>[8,2,3,4,6,5,1,7]=>[1,7,6,5,3,4,8,2]=>[2,1,1,3,1]
[8,2,3,4,7,5,1,6]=>[7,2,3,4,6,8,5,1]=>[2,7,6,5,3,1,4,8]=>[2,1,1,1,3]
[7,2,3,4,6,8,5,1]=>[5,8,2,3,4,1,7,6]=>[4,1,7,6,5,8,2,3]=>[1,2,1,2,2]
[4,2,3,6,1,5,8,7]=>[8,2,1,3,5,4,6,7]=>[1,7,8,6,4,5,3,2]=>[3,1,2,1,1]
[4,8,3,7,5,1,6,2]=>[8,1,3,6,5,7,4,2]=>[1,8,6,3,4,2,5,7]=>[2,1,2,3]
[5,2,3,4,7,8,6,1]=>[5,8,2,1,3,4,7,6]=>[4,1,7,8,6,5,2,3]=>[1,3,1,1,2]
[8,2,3,4,7,1,6,5]=>[8,2,3,4,6,7,5,1]=>[1,7,6,5,3,2,4,8]=>[2,1,1,1,3]
[5,2,3,4,8,7,1,6]=>[7,8,2,1,3,4,6,5]=>[2,1,7,8,6,5,3,4]=>[1,3,1,1,2]
[5,2,3,4,6,8,1,7]=>[2,3,4,1,5,7,8,6]=>[7,6,5,8,4,2,1,3]=>[1,1,2,1,1,2]
[4,2,8,5,7,6,1,3]=>[1,4,7,8,6,2,5,3]=>[8,5,2,1,3,7,4,6]=>[1,1,1,3,2]
[3,7,6,4,5,1,8,2]=>[4,8,6,1,5,3,2,7]=>[5,1,3,8,4,6,7,2]=>[1,3,3,1]
[3,8,6,4,5,1,2,7]=>[6,4,7,1,5,3,8,2]=>[3,5,2,8,4,6,1,7]=>[2,2,2,2]
[4,7,3,6,5,8,2,1]=>[5,1,3,4,2,8,7,6]=>[4,8,6,5,7,1,2,3]=>[2,1,2,3]
[4,8,3,7,5,2,1,6]=>[7,1,3,6,5,8,4,2]=>[2,8,6,3,4,1,5,7]=>[2,1,2,3]
[8,7,3,6,5,1,2,4]=>[3,6,7,8,5,4,2,1]=>[6,3,2,1,4,5,7,8]=>[1,1,1,5]
[8,2,7,5,1,6,3,4]=>[7,8,5,2,4,6,3,1]=>[2,1,4,7,5,3,6,8]=>[1,3,1,3]
[4,2,7,5,8,6,3,1]=>[8,1,4,3,7,2,6,5]=>[1,8,5,6,2,7,3,4]=>[2,2,2,2]
[5,8,1,7,3,6,4,2]=>[1,8,5,7,6,3,4,2]=>[8,1,4,2,3,6,5,7]=>[1,2,3,2]
[5,2,7,8,4,6,3,1]=>[1,5,3,8,7,2,6,4]=>[8,4,6,1,2,7,3,5]=>[1,2,3,2]
[5,2,8,3,7,6,1,4]=>[7,1,8,4,6,2,5,3]=>[2,8,1,5,3,7,4,6]=>[2,2,2,2]
[6,8,3,2,5,7,1,4]=>[3,7,4,1,5,8,6,2]=>[6,2,5,8,4,1,3,7]=>[1,3,1,3]
[6,7,3,8,5,4,2,1]=>[1,8,7,3,2,6,5,4]=>[8,1,2,6,7,3,4,5]=>[1,4,3]
[6,2,3,4,7,5,8,1]=>[6,2,3,4,1,5,8,7]=>[3,7,6,5,8,4,1,2]=>[2,1,2,1,2]
[6,2,3,4,8,5,1,7]=>[7,2,3,4,1,6,8,5]=>[2,7,6,5,8,3,1,4]=>[2,1,2,1,2]
[8,2,3,4,1,7,5,6]=>[2,3,4,7,8,5,6,1]=>[7,6,5,2,1,4,3,8]=>[1,1,1,1,2,2]
[6,2,3,4,1,8,5,7]=>[2,3,4,7,1,8,5,6]=>[7,6,5,2,8,1,4,3]=>[1,1,1,2,2,1]
[6,2,3,4,8,7,5,1]=>[8,7,2,3,1,4,6,5]=>[1,2,7,6,8,5,3,4]=>[3,2,1,2]
[6,8,3,1,5,7,4,2]=>[3,5,1,8,7,4,6,2]=>[6,4,8,1,2,5,3,7]=>[1,2,3,2]
[7,2,3,4,1,8,6,5]=>[8,2,3,4,7,5,1,6]=>[1,7,6,5,2,4,8,3]=>[2,1,1,3,1]
[7,2,3,4,1,5,8,6]=>[2,3,4,8,5,6,1,7]=>[7,6,5,1,4,3,8,2]=>[1,1,1,2,2,1]
[1,2,3,4,8,7,5,6]=>[7,8,6,1,2,3,4,5]=>[2,1,3,8,7,6,5,4]=>[1,3,1,1,1,1]
[1,2,8,5,3,4,6,7]=>[5,6,4,7,8,1,2,3]=>[4,3,5,2,1,8,7,6]=>[1,2,1,2,1,1]
[1,8,4,2,3,5,6,7]=>[4,5,3,6,7,8,1,2]=>[5,4,6,3,2,1,8,7]=>[1,2,1,1,2,1]
[8,6,7,4,1,5,3,2]=>[8,7,5,4,2,6,3,1]=>[1,2,4,5,7,3,6,8]=>[5,3]
[4,8,6,7,5,1,3,2]=>[8,6,1,3,7,5,4,2]=>[1,3,8,6,2,4,5,7]=>[3,1,4]
[8,7,1,5,4,6,2,3]=>[7,5,4,8,3,6,2,1]=>[2,4,5,1,6,3,7,8]=>[3,2,3]
[8,5,7,1,4,6,3,2]=>[5,2,8,7,4,6,3,1]=>[4,7,1,2,5,3,6,8]=>[2,3,3]
[6,4,8,5,1,7,3,2]=>[8,2,1,7,5,4,6,3]=>[1,7,8,2,4,5,3,6]=>[3,3,2]
[4,8,5,7,1,6,3,2]=>[3,8,1,7,5,6,4,2]=>[6,1,8,2,4,3,5,7]=>[1,2,2,3]
[8,4,7,1,5,6,3,2]=>[2,5,8,7,4,6,3,1]=>[7,4,1,2,5,3,6,8]=>[1,1,3,3]
[8,7,4,5,6,1,3,2]=>[3,8,6,4,7,5,2,1]=>[6,1,3,5,2,4,7,8]=>[1,3,4]
[8,7,5,1,4,6,2,3]=>[7,5,8,4,3,6,2,1]=>[2,4,1,5,6,3,7,8]=>[2,3,3]
[8,7,2,5,1,4,6,3]=>[6,8,3,5,4,7,2,1]=>[3,1,6,4,5,2,7,8]=>[1,2,2,3]
[4,8,7,2,5,1,6,3]=>[8,1,4,6,5,7,3,2]=>[1,8,5,3,4,2,6,7]=>[2,1,2,3]
[1,6,4,8,5,2,7,3]=>[8,3,2,6,5,7,1,4]=>[1,6,7,3,4,2,8,5]=>[3,2,2,1]
[8,7,1,4,2,5,6,3]=>[6,4,8,3,5,7,2,1]=>[3,5,1,6,4,2,7,8]=>[2,2,1,3]
[8,7,5,1,2,4,6,3]=>[6,8,4,5,3,7,2,1]=>[3,1,5,4,6,2,7,8]=>[1,2,2,3]
[7,1,8,5,6,2,3,4]=>[6,7,4,8,5,2,1,3]=>[3,2,5,1,4,7,8,6]=>[1,2,4,1]
[3,8,7,1,2,5,6,4]=>[6,8,1,4,5,7,3,2]=>[3,1,8,5,4,2,6,7]=>[1,2,1,1,3]
[3,5,8,7,1,2,6,4]=>[2,8,1,5,6,7,4,3]=>[7,1,8,4,3,2,5,6]=>[1,2,1,1,3]
[2,3,8,5,7,1,6,4]=>[4,8,6,7,1,2,5,3]=>[5,1,3,2,8,7,4,6]=>[1,2,2,1,2]
[3,8,7,1,5,6,2,4]=>[7,5,8,1,4,6,3,2]=>[2,4,1,8,5,3,6,7]=>[2,2,1,3]
[3,5,8,7,1,6,2,4]=>[2,7,8,1,5,6,4,3]=>[7,2,1,8,4,3,5,6]=>[1,1,2,1,3]
[2,3,8,6,7,5,1,4]=>[7,4,8,6,1,2,5,3]=>[2,5,1,3,8,7,4,6]=>[2,3,1,2]
[3,2,8,6,7,5,1,4]=>[7,4,8,1,6,2,5,3]=>[2,5,1,8,3,7,4,6]=>[2,2,2,2]
[4,1,8,6,2,7,5,3]=>[8,1,7,5,4,6,2,3]=>[1,8,2,4,5,3,7,6]=>[2,3,2,1]
[8,7,4,1,2,6,5,3]=>[8,7,4,3,5,6,2,1]=>[1,2,5,6,4,3,7,8]=>[4,1,3]
[1,3,8,6,7,5,2,4]=>[7,4,8,6,2,5,1,3]=>[2,5,1,3,7,4,8,6]=>[2,3,2,1]
[2,8,7,1,5,6,3,4]=>[7,5,8,4,6,1,3,2]=>[2,4,1,5,3,8,6,7]=>[2,2,2,2]
[8,7,1,5,2,4,6,3]=>[6,8,5,3,4,7,2,1]=>[3,1,4,6,5,2,7,8]=>[1,3,1,3]
[7,1,8,2,4,6,5,3]=>[8,5,7,4,6,2,1,3]=>[1,4,2,5,3,7,8,6]=>[2,2,3,1]
[1,6,2,8,4,7,5,3]=>[8,5,2,7,6,1,3,4]=>[1,4,7,2,3,8,6,5]=>[3,3,1,1]
[1,3,8,5,7,2,6,4]=>[4,8,6,7,2,5,1,3]=>[5,1,3,2,7,4,8,6]=>[1,2,2,2,1]
[1,8,3,7,2,5,6,4]=>[6,8,3,5,7,4,1,2]=>[3,1,6,4,2,5,8,7]=>[1,2,1,3,1]
[2,8,7,1,3,5,6,4]=>[6,8,4,5,7,1,3,2]=>[3,1,5,4,2,8,6,7]=>[1,2,1,2,2]
[5,7,1,8,2,3,6,4]=>[8,5,1,6,7,3,2,4]=>[1,4,8,3,2,6,7,5]=>[3,1,3,1]
[7,1,8,2,3,5,6,4]=>[6,8,4,5,7,2,1,3]=>[3,1,5,4,2,7,8,6]=>[1,2,1,3,1]
[4,2,8,6,7,5,1,3]=>[7,1,4,8,6,2,5,3]=>[2,8,5,1,3,7,4,6]=>[2,1,3,2]
[8,4,2,7,5,6,1,3]=>[2,7,5,8,3,6,4,1]=>[7,2,4,1,6,3,5,8]=>[1,2,2,3]
[4,8,3,6,1,7,5,2]=>[8,1,3,7,5,4,6,2]=>[1,8,6,2,4,5,3,7]=>[2,1,3,2]
[8,3,4,7,5,1,6,2]=>[8,2,3,6,5,7,4,1]=>[1,7,6,3,4,2,5,8]=>[2,1,2,3]
[8,3,7,4,5,1,6,2]=>[4,8,2,6,5,7,3,1]=>[5,1,7,3,4,2,6,8]=>[1,2,2,3]
[8,7,4,2,5,6,1,3]=>[7,4,3,5,8,6,2,1]=>[2,5,6,4,1,3,7,8]=>[3,1,4]
[8,7,5,1,6,2,3,4]=>[6,7,8,4,3,5,2,1]=>[3,2,1,5,6,4,7,8]=>[1,1,3,3]
[8,7,2,4,1,5,6,3]=>[6,3,4,8,5,7,2,1]=>[3,6,5,1,4,2,7,8]=>[2,1,2,3]
[4,8,6,1,7,2,5,3]=>[8,1,6,7,4,3,5,2]=>[1,8,3,2,5,6,4,7]=>[2,1,3,2]
[4,2,8,6,7,1,5,3]=>[8,1,6,4,7,2,5,3]=>[1,8,3,5,2,7,4,6]=>[2,2,2,2]
[8,7,4,1,2,5,6,3]=>[6,8,4,3,5,7,2,1]=>[3,1,5,6,4,2,7,8]=>[1,3,1,3]
[8,2,7,1,6,3,4,5]=>[6,7,8,2,4,5,3,1]=>[3,2,1,7,5,4,6,8]=>[1,1,2,1,3]
[2,8,3,6,7,1,5,4]=>[8,6,3,4,7,1,5,2]=>[1,3,6,5,2,8,4,7]=>[3,1,2,2]
[8,7,2,1,3,5,6,4]=>[3,6,8,4,5,7,2,1]=>[6,3,1,5,4,2,7,8]=>[1,1,2,1,3]
[1,8,7,2,3,6,4,5]=>[7,8,4,5,6,3,1,2]=>[2,1,5,4,3,6,8,7]=>[1,2,1,3,1]
[1,8,7,2,6,3,4,5]=>[6,7,8,4,5,3,1,2]=>[3,2,1,5,4,6,8,7]=>[1,1,2,3,1]
[8,2,7,3,6,1,4,5]=>[4,6,7,8,2,5,3,1]=>[5,3,2,1,7,4,6,8]=>[1,1,1,2,3]
[1,8,7,3,6,2,4,5]=>[4,6,7,8,5,3,1,2]=>[5,3,2,1,4,6,8,7]=>[1,1,1,4,1]
[1,8,2,7,6,3,4,5]=>[6,7,8,5,3,4,1,2]=>[3,2,1,4,6,5,8,7]=>[1,1,3,2,1]
[8,2,7,4,1,5,6,3]=>[6,4,8,2,5,7,3,1]=>[3,5,1,7,4,2,6,8]=>[2,2,1,3]
[8,2,1,7,5,6,3,4]=>[7,5,8,2,6,3,4,1]=>[2,4,1,7,3,6,5,8]=>[2,2,2,2]
[8,7,3,1,5,6,2,4]=>[3,7,5,8,4,6,2,1]=>[6,2,4,1,5,3,7,8]=>[1,2,2,3]
[2,8,7,3,5,6,1,4]=>[7,4,5,8,6,1,3,2]=>[2,5,4,1,3,8,6,7]=>[2,1,3,2]
[8,3,1,6,7,5,2,4]=>[7,2,4,8,6,3,5,1]=>[2,7,5,1,3,6,4,8]=>[2,1,3,2]
[8,5,2,1,6,7,4,3]=>[5,8,3,2,7,4,6,1]=>[4,1,6,7,2,5,3,8]=>[1,3,2,2]
[1,5,2,8,6,7,4,3]=>[2,5,8,7,6,1,3,4]=>[7,4,1,2,3,8,6,5]=>[1,1,4,1,1]
[1,2,8,6,7,5,3,4]=>[7,4,8,6,5,1,2,3]=>[2,5,1,3,4,8,7,6]=>[2,4,1,1]
[1,8,3,6,7,5,2,4]=>[7,4,8,3,6,5,1,2]=>[2,5,1,6,3,4,8,7]=>[2,2,3,1]
[8,2,3,6,7,5,1,4]=>[7,4,8,2,3,6,5,1]=>[2,5,1,7,6,3,4,8]=>[2,2,1,3]
[8,3,7,2,5,6,1,4]=>[7,2,4,5,8,6,3,1]=>[2,7,5,4,1,3,6,8]=>[2,1,1,4]
[8,1,3,7,5,6,2,4]=>[7,5,8,3,6,2,4,1]=>[2,4,1,6,3,7,5,8]=>[2,2,2,2]
[8,1,4,2,6,7,5,3]=>[3,5,8,7,2,4,6,1]=>[6,4,1,2,7,5,3,8]=>[1,1,3,1,2]
[1,2,8,6,7,3,5,4]=>[8,6,4,7,5,1,2,3]=>[1,3,5,2,4,8,7,6]=>[3,3,1,1]
[8,1,7,3,6,2,4,5]=>[4,6,7,8,5,2,3,1]=>[5,3,2,1,4,7,6,8]=>[1,1,1,3,2]
[8,1,7,2,6,3,4,5]=>[6,7,8,4,5,2,3,1]=>[3,2,1,5,4,7,6,8]=>[1,1,2,2,2]
[8,1,7,2,3,6,4,5]=>[7,8,4,5,6,2,3,1]=>[2,1,5,4,3,7,6,8]=>[1,2,1,2,2]
[8,1,3,7,2,5,6,4]=>[6,8,3,5,7,2,4,1]=>[3,1,6,4,2,7,5,8]=>[1,2,1,2,2]
[1,8,3,6,7,2,5,4]=>[8,6,3,4,7,5,1,2]=>[1,3,6,5,2,4,8,7]=>[3,1,3,1]
[1,7,8,2,3,6,5,4]=>[8,7,4,5,2,6,1,3]=>[1,2,5,4,7,3,8,6]=>[3,2,2,1]
[8,3,7,1,2,5,6,4]=>[2,6,8,4,5,7,3,1]=>[7,3,1,5,4,2,6,8]=>[1,1,2,1,3]
[2,8,5,7,4,6,3,1]=>[3,5,8,7,6,1,4,2]=>[6,4,1,2,3,8,5,7]=>[1,1,4,2]
[3,1,8,5,7,4,2,6]=>[4,7,1,6,8,5,2,3]=>[5,2,8,3,1,4,7,6]=>[1,2,1,3,1]
[8,3,5,7,4,2,6,1]=>[3,6,2,5,8,7,4,1]=>[6,3,7,4,1,2,5,8]=>[1,2,1,4]
[8,3,6,2,4,5,7,1]=>[2,4,5,6,3,8,7,1]=>[7,5,4,3,6,1,2,8]=>[1,1,1,2,3]
[2,8,6,4,3,5,7,1]=>[5,4,6,3,8,1,7,2]=>[4,5,3,6,1,8,2,7]=>[2,2,2,2]
[2,6,8,3,5,4,7,1]=>[6,4,2,5,8,1,7,3]=>[3,5,7,4,1,8,2,6]=>[3,1,2,2]
[2,7,5,8,4,6,3,1]=>[3,5,2,8,7,1,6,4]=>[6,4,7,1,2,8,3,5]=>[1,2,3,2]
[4,8,1,7,6,3,2,5]=>[7,1,6,8,5,3,4,2]=>[2,8,3,1,4,6,5,7]=>[2,1,3,2]
[4,1,7,6,2,3,5,8]=>[5,1,6,7,4,2,3,8]=>[4,8,3,2,5,7,6,1]=>[2,1,3,1,1]
[3,7,1,8,6,2,5,4]=>[8,6,7,1,5,3,2,4]=>[1,3,2,8,4,6,7,5]=>[2,2,3,1]
[3,1,7,6,4,5,2,8]=>[5,7,1,6,4,2,3,8]=>[4,2,8,3,5,7,6,1]=>[1,2,3,1,1]
[3,1,7,5,8,4,2,6]=>[4,7,1,6,3,8,2,5]=>[5,2,8,3,6,1,7,4]=>[1,2,2,2,1]
[3,1,6,8,7,5,2,4]=>[3,7,8,1,6,5,2,4]=>[6,2,1,8,3,4,7,5]=>[1,1,2,3,1]
[6,3,8,7,5,2,4,1]=>[6,1,8,7,2,5,4,3]=>[3,8,1,2,7,4,5,6]=>[2,3,3]
[7,3,5,8,4,2,6,1]=>[3,6,2,5,1,8,7,4]=>[6,3,7,4,8,1,2,5]=>[1,2,2,3]
[7,3,6,4,2,8,5,1]=>[4,8,2,5,3,1,7,6]=>[5,1,7,4,6,8,2,3]=>[1,2,3,2]
[7,8,3,6,2,5,4,1]=>[8,3,5,1,7,6,4,2]=>[1,6,4,8,2,3,5,7]=>[2,2,4]
[7,4,8,2,1,6,3,5]=>[4,2,7,8,5,1,6,3]=>[5,7,2,1,4,8,3,6]=>[2,1,3,2]
[7,8,5,2,1,4,3,6]=>[4,7,5,6,3,1,8,2]=>[5,2,4,3,6,8,1,7]=>[1,2,3,2]
[7,5,2,3,1,4,8,6]=>[3,4,8,5,2,6,1,7]=>[6,5,1,4,7,3,8,2]=>[1,1,3,2,1]
[7,4,6,2,3,8,1,5]=>[4,2,5,7,3,1,8,6]=>[5,7,4,2,6,8,1,3]=>[2,1,3,2]
[6,4,2,5,8,3,7,1]=>[4,2,6,1,8,3,7,5]=>[5,7,3,8,1,6,2,4]=>[2,2,2,2]
[4,6,5,8,1,3,2,7]=>[7,1,5,3,2,6,8,4]=>[2,8,4,6,7,3,1,5]=>[2,3,1,2]
[4,7,1,5,3,8,2,6]=>[1,5,4,7,8,3,2,6]=>[8,4,5,2,1,6,7,3]=>[1,2,1,3,1]
[4,7,8,1,3,6,2,5]=>[1,5,7,8,4,2,6,3]=>[8,4,2,1,5,7,3,6]=>[1,1,1,3,2]
[5,7,1,3,4,6,2,8]=>[4,5,1,7,3,6,2,8]=>[5,4,8,2,6,3,7,1]=>[1,2,2,2,1]
[5,7,1,4,2,3,6,8]=>[5,6,3,1,4,7,2,8]=>[4,3,6,8,5,2,7,1]=>[1,3,1,2,1]
[5,8,1,3,2,4,6,7]=>[5,3,4,1,6,7,8,2]=>[4,6,5,8,3,2,1,7]=>[2,2,1,1,2]
[4,8,6,1,3,2,7,5]=>[1,5,8,4,6,3,7,2]=>[8,4,1,5,3,6,2,7]=>[1,1,2,2,2]
[8,4,6,2,1,3,7,5]=>[4,2,8,5,6,3,7,1]=>[5,7,1,4,3,6,2,8]=>[2,2,2,2]
[5,4,8,7,2,3,6,1]=>[2,1,5,6,8,7,4,3]=>[7,8,4,3,1,2,5,6]=>[2,1,1,4]
[5,4,8,7,3,1,2,6]=>[2,1,6,7,5,8,4,3]=>[7,8,3,2,4,1,5,6]=>[2,1,2,3]
[6,8,3,7,2,5,4,1]=>[8,3,1,5,7,6,4,2]=>[1,6,8,4,2,3,5,7]=>[3,1,4]
[5,4,6,8,2,3,7,1]=>[2,1,5,3,6,8,7,4]=>[7,8,4,6,3,1,2,5]=>[2,2,1,3]
[5,7,4,2,8,3,6,1]=>[1,6,3,8,4,2,7,5]=>[8,3,6,1,5,7,2,4]=>[1,2,3,2]
[6,4,7,2,1,8,3,5]=>[4,2,7,1,8,5,3,6]=>[5,7,2,8,1,4,6,3]=>[2,2,3,1]
[6,8,5,4,1,3,2,7]=>[7,5,1,6,4,3,8,2]=>[2,4,8,3,5,6,1,7]=>[3,3,2]
[6,4,3,7,1,5,2,8]=>[3,2,7,5,1,6,4,8]=>[6,7,2,4,8,3,5,1]=>[2,3,2,1]
[9,8,7,6,5,2,3,1,4]=>[6,8,7,9,5,4,3,2,1]=>[4,2,3,1,5,6,7,8,9]=>[1,2,6]
[9,8,7,6,3,4,2,1,5]=>[5,8,7,6,9,4,3,2,1]=>[5,2,3,4,1,6,7,8,9]=>[1,3,5]
[9,8,7,4,5,3,2,1,6]=>[4,8,7,6,5,9,3,2,1]=>[6,2,3,4,5,1,7,8,9]=>[1,4,4]
[9,8,5,6,4,3,2,1,7]=>[3,8,7,6,5,4,9,2,1]=>[7,2,3,4,5,6,1,8,9]=>[1,5,3]
[9,6,7,5,4,3,2,1,8]=>[2,8,7,6,5,4,3,9,1]=>[8,2,3,4,5,6,7,1,9]=>[1,6,2]
[7,4,2,5,6,1,3,8]=>[6,3,2,4,7,5,1,8]=>[3,6,7,5,2,4,8,1]=>[3,1,3,1]
[6,4,2,8,1,5,7,3]=>[6,2,8,3,1,5,7,4]=>[3,7,1,6,8,4,2,5]=>[2,3,1,2]
[6,3,7,8,2,5,1,4]=>[5,7,2,1,3,8,6,4]=>[4,2,7,8,6,1,3,5]=>[1,3,1,3]
[7,3,5,6,4,2,1,8]=>[3,7,2,6,5,4,1,8]=>[6,2,7,3,4,5,8,1]=>[1,2,4,1]
[7,4,3,1,5,6,2,8]=>[5,3,2,7,4,6,1,8]=>[4,6,7,2,5,3,8,1]=>[3,2,2,1]
[7,4,5,2,6,1,3,8]=>[4,2,6,3,7,5,1,8]=>[5,7,3,6,2,4,8,1]=>[2,2,3,1]
[5,3,7,2,8,6,4,1]=>[1,8,7,2,4,3,6,5]=>[8,1,2,7,5,6,3,4]=>[1,3,2,2]
[5,3,8,2,6,7,4,1]=>[5,1,8,2,4,7,6,3]=>[4,8,1,7,5,2,3,6]=>[2,2,1,3]
[6,3,8,2,5,4,7,1]=>[6,2,4,1,5,8,7,3]=>[3,7,5,8,4,1,2,6]=>[2,2,1,3]
[6,4,8,2,1,5,7,3]=>[4,2,6,1,8,5,7,3]=>[5,7,3,8,1,4,2,6]=>[2,2,2,2]
[6,4,3,1,8,2,7,5]=>[3,2,8,6,1,7,4,5]=>[6,7,1,3,8,2,5,4]=>[2,3,2,1]
[5,3,7,8,2,6,4,1]=>[1,8,5,2,3,7,6,4]=>[8,1,4,7,6,2,3,5]=>[1,3,1,3]
[4,7,8,5,6,3,2,1]=>[4,2,8,1,7,6,5,3]=>[5,7,1,8,2,3,4,6]=>[2,2,4]
[5,3,7,6,8,2,4,1]=>[1,6,4,2,3,8,7,5]=>[8,3,5,7,6,1,2,4]=>[1,3,1,3]
[5,7,8,4,6,2,1,3]=>[7,1,6,4,2,8,5,3]=>[2,8,3,5,7,1,4,6]=>[2,3,3]
[5,8,4,3,6,7,1,2]=>[1,4,3,7,5,8,6,2]=>[8,5,6,2,4,1,3,7]=>[1,2,2,3]
[5,8,6,4,7,2,1,3]=>[7,1,6,4,3,8,5,2]=>[2,8,3,5,6,1,4,7]=>[2,3,3]
[5,3,8,6,2,7,4,1]=>[1,8,5,2,4,7,6,3]=>[8,1,4,7,5,2,3,6]=>[1,3,1,3]
[4,7,5,8,6,3,2,1]=>[8,3,1,2,7,6,5,4]=>[1,6,8,7,2,3,4,5]=>[3,1,4]
[4,8,6,7,5,3,2,1]=>[3,8,7,1,6,5,4,2]=>[6,1,2,8,3,4,5,7]=>[1,3,4]
[5,3,8,7,2,6,4,1]=>[1,8,5,7,2,6,4,3]=>[8,1,4,2,7,3,5,6]=>[1,2,2,3]
[5,3,8,6,7,2,4,1]=>[1,6,4,8,2,7,5,3]=>[8,3,5,1,7,2,4,6]=>[1,2,2,3]
[5,3,7,8,6,2,4,1]=>[1,6,3,8,2,7,5,4]=>[8,3,6,1,7,2,4,5]=>[1,2,2,3]
[5,7,6,4,8,2,1,3]=>[7,1,6,4,3,2,8,5]=>[2,8,3,5,6,7,1,4]=>[2,4,2]
[5,8,4,6,7,2,1,3]=>[1,3,7,6,4,8,5,2]=>[8,6,2,3,5,1,4,7]=>[1,1,3,3]
[6,4,2,8,1,7,3,5]=>[7,2,8,3,1,5,6,4]=>[2,7,1,6,8,4,3,5]=>[2,3,1,2]
[6,5,2,4,3,7,8,1]=>[5,3,4,2,1,6,8,7]=>[4,6,5,7,8,3,1,2]=>[2,3,1,2]
[5,4,6,2,8,7,1,3]=>[2,1,7,3,8,4,6,5]=>[7,8,2,6,1,5,3,4]=>[2,2,2,2]
[5,6,3,8,7,2,4,1]=>[1,6,2,8,3,7,5,4]=>[8,3,7,1,6,2,4,5]=>[1,2,2,3]
[6,7,4,3,1,8,2,5]=>[7,4,3,1,8,5,2,6]=>[2,5,6,8,1,4,7,3]=>[4,3,1]
[5,7,4,3,6,8,1,2]=>[1,4,3,7,5,2,8,6]=>[8,5,6,2,4,7,1,3]=>[1,2,3,2]
[5,7,3,8,6,2,4,1]=>[1,6,8,3,2,7,5,4]=>[8,3,1,6,7,2,4,5]=>[1,1,3,3]
[4,5,8,6,7,3,2,1]=>[4,8,1,2,7,6,5,3]=>[5,1,8,7,2,3,4,6]=>[1,2,1,4]
[4,6,8,5,7,3,2,1]=>[2,4,8,1,7,6,5,3]=>[7,5,1,8,2,3,4,6]=>[1,1,2,4]
[5,6,8,3,7,2,4,1]=>[1,4,2,6,8,7,5,3]=>[8,5,7,3,1,2,4,6]=>[1,2,1,4]
[5,4,6,8,2,7,1,3]=>[2,1,5,3,7,8,6,4]=>[7,8,4,6,2,1,3,5]=>[2,2,1,3]
[3,6,7,8,2,5,1,4]=>[5,2,7,1,3,8,6,4]=>[4,7,2,8,6,1,3,5]=>[2,2,1,3]
[5,7,8,2,6,4,1,3]=>[1,7,8,4,2,6,5,3]=>[8,2,1,5,7,3,4,6]=>[1,1,3,3]
[3,6,8,5,7,1,4,2]=>[2,8,6,1,4,7,5,3]=>[7,1,3,8,5,2,4,6]=>[1,3,1,3]
[1,7,4,8,6,2,3,5]=>[3,6,7,2,8,5,1,4]=>[6,3,2,7,1,4,8,5]=>[1,1,2,3,1]
[3,6,2,5,7,8,1,4]=>[4,7,1,3,2,5,8,6]=>[5,2,8,6,7,4,1,3]=>[1,2,2,1,2]
[5,2,7,4,6,8,1,3]=>[4,1,7,5,2,3,8,6]=>[5,8,2,4,7,6,1,3]=>[2,3,1,2]
[7,2,4,5,8,6,1,3]=>[3,4,7,8,2,1,6,5]=>[6,5,2,1,7,8,3,4]=>[1,1,1,3,2]
[5,3,6,7,1,8,4,2]=>[3,1,8,2,7,5,4,6]=>[6,8,1,7,2,4,5,3]=>[2,2,3,1]
[4,2,5,6,7,1,8,3]=>[3,1,4,8,2,6,5,7]=>[6,8,5,1,7,3,4,2]=>[2,1,2,2,1]
[8,2,3,7,5,1,6,4]=>[8,6,2,3,5,7,4,1]=>[1,3,7,6,4,2,5,8]=>[3,1,1,3]
[8,1,3,6,7,2,4,5]=>[6,7,3,4,8,2,5,1]=>[3,2,6,5,1,7,4,8]=>[1,2,1,2,2]
[8,1,4,2,5,6,3,7]=>[5,3,7,2,4,6,8,1]=>[4,6,2,7,5,3,1,8]=>[2,2,1,1,2]
[6,1,3,8,2,7,4,5]=>[7,8,3,5,1,6,2,4]=>[2,1,6,4,8,3,7,5]=>[1,2,2,2,1]
[3,6,2,4,1,7,8,5]=>[1,3,4,6,2,8,5,7]=>[8,6,5,3,7,1,4,2]=>[1,1,1,2,2,1]
[6,2,7,3,1,5,8,4]=>[4,6,8,2,1,5,3,7]=>[5,3,1,7,8,4,6,2]=>[1,1,3,2,1]
[6,3,4,1,8,5,7,2]=>[2,3,6,1,8,7,4,5]=>[7,6,3,8,1,2,5,4]=>[1,1,2,3,1]
[7,3,4,1,5,8,6,2]=>[2,3,8,5,7,4,1,6]=>[7,6,1,4,2,5,8,3]=>[1,1,2,3,1]
[1,7,5,2,8,6,3,4]=>[7,3,8,6,4,1,2,5]=>[2,6,1,3,5,8,7,4]=>[2,4,1,1]
[3,7,4,1,8,5,6,2]=>[3,6,8,1,7,4,2,5]=>[6,3,1,8,2,5,7,4]=>[1,1,2,3,1]
[3,6,4,8,1,5,7,2]=>[3,6,1,2,8,5,7,4]=>[6,3,8,7,1,4,2,5]=>[1,2,1,2,2]
[3,5,7,4,1,6,8,2]=>[2,6,1,4,8,5,3,7]=>[7,3,8,5,1,4,6,2]=>[1,2,1,3,1]
[3,5,7,1,2,6,4,8]=>[7,1,4,2,5,6,3,8]=>[2,8,5,7,4,3,6,1]=>[2,2,1,2,1]
[4,5,1,8,2,3,7,6]=>[1,8,5,2,6,7,3,4]=>[8,1,4,7,3,2,6,5]=>[1,3,1,2,1]
[4,7,1,8,2,6,3,5]=>[1,7,8,5,6,3,2,4]=>[8,2,1,4,3,6,7,5]=>[1,1,2,3,1]
[6,3,1,8,5,2,4,7]=>[2,6,7,5,1,8,3,4]=>[7,3,2,4,8,1,6,5]=>[1,1,3,2,1]
[3,5,2,1,8,4,6,7]=>[1,3,6,2,7,8,4,5]=>[8,6,3,7,2,1,5,4]=>[1,1,2,1,2,1]
[7,5,1,2,3,8,6,4]=>[8,7,3,4,2,5,1,6]=>[1,2,6,5,7,4,8,3]=>[3,2,2,1]
[6,4,1,2,7,3,8,5]=>[8,6,3,2,4,1,5,7]=>[1,3,6,7,5,8,4,2]=>[4,2,1,1]
[5,2,6,1,3,4,8,7]=>[8,2,4,1,5,3,6,7]=>[1,7,5,8,4,6,3,2]=>[2,2,2,1,1]
[7,8,4,5,1,3,2,6]=>[7,5,3,6,4,1,8,2]=>[2,4,6,3,5,8,1,7]=>[3,3,2]
[6,7,1,3,2,5,4,8]=>[4,7,3,5,1,6,2,8]=>[5,2,6,4,8,3,7,1]=>[1,2,2,2,1]
[6,7,1,4,3,5,2,8]=>[5,4,7,3,1,6,2,8]=>[4,5,2,6,8,3,7,1]=>[2,3,2,1]
[7,8,2,3,1,5,4,6]=>[3,4,7,5,6,1,8,2]=>[6,5,2,4,3,8,1,7]=>[1,1,2,2,2]
[7,8,2,4,3,5,1,6]=>[5,3,4,7,6,1,8,2]=>[4,6,5,2,3,8,1,7]=>[2,1,3,2]
[7,8,2,4,1,5,3,6]=>[7,3,5,4,6,1,8,2]=>[2,6,4,5,3,8,1,7]=>[2,2,2,2]
[1,4,2,6,5,7,3,8]=>[2,5,4,7,1,3,6,8]=>[7,4,5,2,8,6,3,1]=>[1,2,2,1,1,1]
[5,6,1,4,2,7,3,8]=>[7,5,3,1,4,2,6,8]=>[2,4,6,8,5,7,3,1]=>[4,2,1,1]
[6,7,2,4,1,5,3,8]=>[7,3,5,4,1,6,2,8]=>[2,6,4,5,8,3,7,1]=>[2,3,2,1]
[6,7,2,4,3,5,1,8]=>[5,3,4,1,7,6,2,8]=>[4,6,5,8,2,3,7,1]=>[2,2,3,1]
[6,7,3,5,4,8,1,2]=>[7,3,1,5,4,2,8,6]=>[2,6,8,4,5,7,1,3]=>[3,3,2]
[2,4,1,6,5,7,3,8]=>[2,5,1,4,7,3,6,8]=>[7,4,8,5,2,6,3,1]=>[1,2,1,2,1,1]
[1,5,2,6,4,7,3,8]=>[5,4,2,7,1,3,6,8]=>[4,5,7,2,8,6,3,1]=>[3,2,1,1,1]
[2,5,1,6,4,7,3,8]=>[5,4,1,2,7,3,6,8]=>[4,5,8,7,2,6,3,1]=>[3,1,2,1,1]
[3,6,5,7,4,8,1,2]=>[3,2,7,1,5,4,8,6]=>[6,7,2,8,4,5,1,3]=>[2,2,2,2]
[4,5,2,6,1,7,3,8]=>[1,7,3,2,5,4,6,8]=>[8,2,6,7,4,5,3,1]=>[1,3,2,1,1]
[4,5,1,6,3,7,2,8]=>[1,5,4,2,7,3,6,8]=>[8,4,5,7,2,6,3,1]=>[1,3,2,1,1]
[4,5,3,6,1,7,2,8]=>[1,3,2,7,5,4,6,8]=>[8,6,7,2,4,5,3,1]=>[1,2,3,1,1]
[5,6,3,4,1,7,2,8]=>[3,1,7,5,4,2,6,8]=>[6,8,2,4,5,7,3,1]=>[2,4,1,1]
[5,6,1,4,3,7,2,8]=>[5,4,1,7,3,2,6,8]=>[4,5,8,2,6,7,3,1]=>[3,3,1,1]
[5,6,1,3,2,7,4,8]=>[4,7,3,1,5,2,6,8]=>[5,2,6,8,4,7,3,1]=>[1,3,2,1,1]
[6,7,4,5,1,3,2,8]=>[7,5,3,1,6,4,2,8]=>[2,4,6,8,3,5,7,1]=>[4,3,1]
[6,7,5,8,1,3,2,4]=>[7,5,1,6,3,2,8,4]=>[2,4,8,3,6,7,1,5]=>[3,3,2]
[4,5,1,3,2,7,6,8]=>[4,1,7,3,2,5,6,8]=>[5,8,2,6,7,4,3,1]=>[2,3,1,1,1]
[4,6,5,7,1,3,2,8]=>[7,1,5,3,2,6,4,8]=>[2,8,4,6,7,3,5,1]=>[2,3,2,1]
[4,6,1,3,2,7,5,8]=>[4,1,7,3,5,2,6,8]=>[5,8,2,6,4,7,3,1]=>[2,2,2,1,1]
[1,4,3,6,2,7,5,8]=>[2,7,3,5,1,4,6,8]=>[7,2,6,4,8,5,3,1]=>[1,2,2,1,1,1]
[4,5,2,3,1,7,6,8]=>[3,1,4,2,7,5,6,8]=>[6,8,5,7,2,4,3,1]=>[2,2,2,1,1]
[4,5,3,7,6,8,1,2]=>[1,2,7,3,5,4,8,6]=>[8,7,2,6,4,5,1,3]=>[1,1,2,2,2]
[4,6,5,7,3,8,1,2]=>[3,1,2,7,5,4,8,6]=>[6,8,7,2,4,5,1,3]=>[2,1,3,2]
[4,6,5,7,2,3,1,8]=>[5,1,3,2,7,6,4,8]=>[4,8,6,7,2,3,5,1]=>[2,2,3,1]
[3,5,4,6,1,7,2,8]=>[3,1,2,7,5,4,6,8]=>[6,8,7,2,4,5,3,1]=>[2,1,3,1,1]
[3,5,1,6,4,7,2,8]=>[5,1,4,2,7,3,6,8]=>[4,8,5,7,2,6,3,1]=>[2,2,2,1,1]
[1,5,3,6,4,7,2,8]=>[5,3,2,4,7,1,6,8]=>[4,6,7,5,2,8,3,1]=>[3,1,2,1,1]
[1,5,3,6,2,7,4,8]=>[7,3,2,5,1,4,6,8]=>[2,6,7,4,8,5,3,1]=>[3,2,1,1,1]
[3,5,2,6,1,7,4,8]=>[7,1,3,2,5,4,6,8]=>[2,8,6,7,4,5,3,1]=>[2,2,2,1,1]
[3,5,2,6,4,7,1,8]=>[5,1,3,2,4,7,6,8]=>[4,8,6,7,5,2,3,1]=>[2,2,1,2,1]
[3,4,2,6,1,7,5,8]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[1,1,2,2,1,1]
[2,4,3,6,1,7,5,8]=>[2,7,1,3,5,4,6,8]=>[7,2,8,6,4,5,3,1]=>[1,2,1,2,1,1]
[2,5,3,6,4,7,1,8]=>[5,3,1,2,4,7,6,8]=>[4,6,8,7,5,2,3,1]=>[3,1,1,2,1]
[2,5,3,6,1,7,4,8]=>[7,3,1,2,5,4,6,8]=>[2,6,8,7,4,5,3,1]=>[3,1,2,1,1]
[3,6,2,7,5,4,8,1]=>[6,5,1,3,2,4,8,7]=>[3,4,8,6,7,5,1,2]=>[3,2,1,2]
[4,6,1,7,3,8,2,5]=>[1,5,7,4,2,8,3,6]=>[8,4,2,5,7,1,6,3]=>[1,1,3,2,1]
[2,4,7,1,3,8,6,5]=>[8,2,7,1,4,5,3,6]=>[1,7,2,8,5,4,6,3]=>[2,2,1,2,1]
[5,2,6,7,4,3,8,1]=>[3,1,6,5,2,4,8,7]=>[6,8,3,4,7,5,1,2]=>[2,3,1,2]
[3,5,2,7,6,4,8,1]=>[2,6,1,5,3,4,8,7]=>[7,3,8,4,6,5,1,2]=>[1,2,2,1,2]
[1,5,7,4,3,8,2,6]=>[2,5,4,7,3,8,1,6]=>[7,4,5,2,6,1,8,3]=>[1,2,2,2,1]
[2,5,7,3,1,8,6,4]=>[2,8,4,7,1,5,3,6]=>[7,1,5,2,8,4,6,3]=>[1,2,2,2,1]
[1,5,7,2,8,3,6,4]=>[2,8,6,7,4,1,3,5]=>[7,1,3,2,5,8,6,4]=>[1,2,3,1,1]
[2,5,7,3,1,8,4,6]=>[4,2,7,8,1,5,3,6]=>[5,7,2,1,8,4,6,3]=>[2,1,2,2,1]
[1,5,7,3,4,8,2,6]=>[4,2,5,7,3,8,1,6]=>[5,7,4,2,6,1,8,3]=>[2,1,2,2,1]
[5,2,6,7,1,8,4,3]=>[3,1,8,7,2,5,4,6]=>[6,8,1,2,7,4,5,3]=>[2,3,2,1]
[1,3,7,2,8,5,6,4]=>[6,8,7,2,4,1,3,5]=>[3,1,2,7,5,8,6,4]=>[1,3,2,1,1]
[2,3,1,5,8,4,7,6]=>[8,1,2,4,6,7,3,5]=>[1,8,7,5,3,2,6,4]=>[2,1,1,1,2,1]
[2,1,5,6,8,4,3,7]=>[3,4,7,1,6,8,2,5]=>[6,5,2,8,3,1,7,4]=>[1,1,2,1,2,1]
[2,3,1,5,8,6,4,7]=>[7,1,2,4,6,8,3,5]=>[2,8,7,5,3,1,6,4]=>[2,1,1,1,2,1]
[2,4,7,3,1,8,5,6]=>[2,4,7,8,1,5,3,6]=>[7,5,2,1,8,4,6,3]=>[1,1,1,2,2,1]
[1,3,7,2,8,5,4,6]=>[7,6,8,2,4,1,3,5]=>[2,3,1,7,5,8,6,4]=>[2,2,2,1,1]
[2,3,1,6,8,5,4,7]=>[4,7,1,2,6,8,3,5]=>[5,2,8,7,3,1,6,4]=>[1,2,1,1,2,1]
[4,6,2,7,1,8,3,5]=>[1,7,8,3,2,5,4,6]=>[8,2,1,6,7,4,5,3]=>[1,1,3,2,1]
[1,5,4,3,6,8,2,7]=>[4,3,2,5,7,8,1,6]=>[5,6,7,4,2,1,8,3]=>[3,1,1,2,1]
[1,6,4,5,7,8,3,2]=>[3,4,2,5,8,7,1,6]=>[6,5,7,4,1,2,8,3]=>[1,2,1,3,1]
[2,5,1,7,8,6,3,4]=>[2,7,4,8,1,6,3,5]=>[7,2,5,1,8,3,6,4]=>[1,2,2,2,1]
[1,3,6,2,8,7,4,5]=>[7,3,8,2,6,1,4,5]=>[2,6,1,7,3,8,5,4]=>[2,2,2,1,1]
[2,1,5,6,8,4,7,3]=>[3,4,6,8,1,7,2,5]=>[6,5,3,1,8,2,7,4]=>[1,1,1,2,2,1]
[2,4,1,7,8,5,6,3]=>[6,2,4,8,1,7,3,5]=>[3,7,5,1,8,2,6,4]=>[2,1,2,2,1]
[1,3,6,2,8,4,7,5]=>[8,6,2,3,7,1,4,5]=>[1,3,7,6,2,8,5,4]=>[3,1,2,1,1]
[2,1,5,6,8,7,3,4]=>[3,4,7,8,1,6,2,5]=>[6,5,2,1,8,3,7,4]=>[1,1,1,2,2,1]
[3,6,5,2,7,8,4,1]=>[5,3,1,2,8,4,7,6]=>[4,6,8,7,1,5,2,3]=>[3,1,2,2]
[6,2,4,7,5,8,3,1]=>[5,3,4,1,8,2,7,6]=>[4,6,5,8,1,7,2,3]=>[2,2,2,2]
[1,5,7,8,4,2,6,3]=>[8,2,6,5,3,7,1,4]=>[1,7,3,4,6,2,8,5]=>[2,3,2,1]
[3,7,4,1,8,6,2,5]=>[3,7,8,1,6,4,2,5]=>[6,2,1,8,3,5,7,4]=>[1,1,2,3,1]
[3,4,6,8,5,7,2,1]=>[3,5,8,1,2,7,6,4]=>[6,4,1,8,7,2,3,5]=>[1,1,2,1,3]
[4,2,5,7,3,1,8,6]=>[3,1,5,8,2,6,4,7]=>[6,8,4,1,7,3,5,2]=>[2,1,2,2,1]
[4,5,6,2,8,7,3,1]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[1,1,1,3,2]
[4,5,6,1,8,7,3,2]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[1,1,1,4,1]
[4,5,6,3,1,8,7,2]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[1,1,2,3,1]
[4,3,6,2,1,7,5,8]=>[2,1,4,7,5,3,6,8]=>[7,8,5,2,4,6,3,1]=>[2,1,3,1,1]
[4,6,3,2,1,7,5,8]=>[1,4,3,7,5,2,6,8]=>[8,5,6,2,4,7,3,1]=>[1,2,3,1,1]
[4,6,3,1,7,5,2,8]=>[1,3,7,6,4,2,5,8]=>[8,6,2,3,5,7,4,1]=>[1,1,4,1,1]
[4,5,3,7,6,1,8,2]=>[1,2,8,3,6,5,4,7]=>[8,7,1,6,3,4,5,2]=>[1,1,2,3,1]
[4,5,1,7,3,8,6,2]=>[1,2,8,5,4,7,3,6]=>[8,7,1,4,5,2,6,3]=>[1,1,3,2,1]
[4,3,5,7,6,1,8,2]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[1,2,1,3,1]
[4,3,2,6,1,7,5,8]=>[2,1,7,3,5,4,6,8]=>[7,8,2,6,4,5,3,1]=>[2,2,2,1,1]
[5,3,2,1,6,4,7,8]=>[3,2,6,4,1,5,7,8]=>[6,7,3,5,8,4,2,1]=>[2,3,1,1,1]
[5,1,6,3,2,7,4,8]=>[4,7,5,2,1,3,6,8]=>[5,2,4,7,8,6,3,1]=>[1,4,1,1,1]
[2,6,1,4,7,5,3,8]=>[7,4,6,1,3,2,5,8]=>[2,5,3,8,6,7,4,1]=>[2,2,2,1,1]
[3,6,1,7,4,2,5,8]=>[6,1,5,7,3,2,4,8]=>[3,8,4,2,6,7,5,1]=>[2,1,3,1,1]
[4,6,1,7,5,3,2,8]=>[7,1,6,5,3,2,4,8]=>[2,8,3,4,6,7,5,1]=>[2,4,1,1]
[5,1,6,3,7,4,2,8]=>[7,4,3,1,6,2,5,8]=>[2,5,6,8,3,7,4,1]=>[4,2,1,1]
[5,3,6,4,2,1,7,8]=>[6,2,1,5,4,3,7,8]=>[3,7,8,4,5,6,2,1]=>[3,3,1,1]
[5,3,2,6,4,1,7,8]=>[2,6,3,1,5,4,7,8]=>[7,3,6,8,4,5,2,1]=>[1,3,2,1,1]
[5,2,1,6,3,7,4,8]=>[7,2,5,3,1,4,6,8]=>[2,7,4,6,8,5,3,1]=>[2,3,1,1,1]
[5,2,6,3,1,7,4,8]=>[4,7,2,1,5,3,6,8]=>[5,2,7,8,4,6,3,1]=>[1,3,2,1,1]
[4,2,6,3,1,7,8,5]=>[4,1,6,2,3,8,5,7]=>[5,8,3,7,6,1,4,2]=>[2,2,1,2,1]
[3,6,2,1,7,4,5,8]=>[1,3,6,7,4,2,5,8]=>[8,6,3,2,5,7,4,1]=>[1,1,1,3,1,1]
[3,5,7,2,8,6,4,1]=>[8,2,7,1,4,3,6,5]=>[1,7,2,8,5,6,3,4]=>[2,2,2,2]
[2,4,7,1,3,6,5,8]=>[2,7,1,4,5,6,3,8]=>[7,2,8,5,4,3,6,1]=>[1,2,1,1,2,1]
[2,6,1,3,7,5,4,8]=>[7,6,1,3,4,2,5,8]=>[2,3,8,6,5,7,4,1]=>[3,1,2,1,1]
[5,1,6,2,7,4,3,8]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>[5,1,1,1]
[5,2,1,6,4,3,7,8]=>[6,2,5,3,1,4,7,8]=>[3,7,4,6,8,5,2,1]=>[2,3,1,1,1]
[5,4,2,6,3,1,7,8]=>[6,3,2,1,5,4,7,8]=>[3,6,7,8,4,5,2,1]=>[4,2,1,1]
[5,4,1,6,2,7,3,8]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>[5,1,1,1]
[5,1,6,4,2,7,3,8]=>[7,5,4,2,1,3,6,8]=>[2,4,5,7,8,6,3,1]=>[5,1,1,1]
[3,6,1,7,5,4,8,2]=>[6,5,1,4,2,8,3,7]=>[3,4,8,5,7,1,6,2]=>[3,2,2,1]
[2,6,1,5,4,3,7,8]=>[6,5,1,3,4,2,7,8]=>[3,4,8,6,5,7,2,1]=>[3,1,2,1,1]
[3,1,6,2,5,4,7,8]=>[1,6,4,5,2,3,7,8]=>[8,3,5,4,7,6,2,1]=>[1,2,2,1,1,1]
[5,1,6,4,3,2,7,8]=>[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>[5,1,1,1]
[5,4,1,6,3,2,7,8]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>[5,1,1,1]
[5,4,3,1,6,2,7,8]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>[5,1,1,1]
[7,3,1,6,5,4,8,2]=>[6,2,5,4,8,3,1,7]=>[3,7,4,5,1,6,8,2]=>[2,2,3,1]
[7,2,8,1,5,4,3,6]=>[7,6,2,4,5,1,8,3]=>[2,3,7,5,4,8,1,6]=>[3,1,2,2]
[4,2,7,6,5,8,1,3]=>[7,1,5,4,2,3,8,6]=>[2,8,4,5,7,6,1,3]=>[2,3,1,2]
[3,8,2,6,5,4,1,7]=>[7,6,1,3,5,4,8,2]=>[2,3,8,6,4,5,1,7]=>[3,1,2,2]
[10,1,11,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,8,10,11,9]=>[10,1]
[7,3,2,1,5,4,6,8]=>[3,2,6,4,5,7,1,8]=>[6,7,3,5,4,2,8,1]=>[2,2,1,2,1]
[7,2,8,6,1,4,3,5]=>[7,5,6,8,2,1,4,3]=>[2,4,3,1,7,8,5,6]=>[2,1,3,2]
[5,2,7,6,8,4,1,3]=>[1,7,4,3,8,2,6,5]=>[8,2,5,6,1,7,3,4]=>[1,3,2,2]
[3,8,7,2,5,4,1,6]=>[7,4,6,1,5,8,3,2]=>[2,5,3,8,4,1,6,7]=>[2,2,1,3]
[11,1,12,10,9,8,7,6,5,4,3,2]=>[12,11,10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,8,9,11,12,10]=>[11,1]
[7,5,1,6,8,4,3,2]=>[4,2,8,7,6,3,1,5]=>[5,7,1,2,3,6,8,4]=>[2,5,1]
[7,4,2,1,5,6,3,8]=>[3,5,2,7,4,6,1,8]=>[6,4,7,2,5,3,8,1]=>[1,2,2,2,1]
[7,2,8,6,5,1,3,4]=>[6,7,8,5,2,1,4,3]=>[3,2,1,4,7,8,5,6]=>[1,1,4,2]
[5,3,2,6,7,4,1,8]=>[2,4,1,7,3,6,5,8]=>[7,5,8,2,6,3,4,1]=>[1,2,2,2,1]
[4,3,7,2,5,6,1,8]=>[2,1,4,5,7,6,3,8]=>[7,8,5,4,2,3,6,1]=>[2,1,1,3,1]
[6,7,1,4,3,2,5,8]=>[6,5,3,4,1,7,2,8]=>[3,4,6,5,8,2,7,1]=>[3,2,2,1]
[3,4,2,6,7,1,5,8]=>[1,2,6,3,4,7,5,8]=>[8,7,3,6,5,2,4,1]=>[1,1,2,1,2,1]
[3,7,1,6,5,2,4,8]=>[6,7,1,5,3,4,2,8]=>[3,2,8,4,6,5,7,1]=>[1,2,2,2,1]
[3,5,6,2,4,7,1,8]=>[4,1,2,5,3,7,6,8]=>[5,8,7,4,6,2,3,1]=>[2,1,2,2,1]
[3,5,8,7,2,4,6,1]=>[2,5,6,8,1,7,4,3]=>[7,4,3,1,8,2,5,6]=>[1,1,1,2,3]
[1,7,8,2,5,4,3,6]=>[7,6,4,5,2,8,1,3]=>[2,3,5,4,7,1,8,6]=>[3,2,2,1]
[8,7,2,5,4,3,6,1]=>[6,5,3,4,8,7,2,1]=>[3,4,6,5,1,2,7,8]=>[3,1,4]
[2,5,6,4,7,1,3,8]=>[2,6,4,1,3,7,5,8]=>[7,3,5,8,6,2,4,1]=>[1,3,1,2,1]
[4,7,1,6,3,5,2,8]=>[1,5,7,6,3,4,2,8]=>[8,4,2,3,6,5,7,1]=>[1,1,3,2,1]
[4,5,3,8,7,2,6,1]=>[1,2,6,8,3,7,5,4]=>[8,7,3,1,6,2,4,5]=>[1,1,1,2,3]
[1,4,5,3,7,8,2,6]=>[2,3,7,4,5,8,1,6]=>[7,6,2,5,4,1,8,3]=>[1,1,2,1,2,1]
[1,4,8,2,7,6,3,5]=>[7,8,2,6,4,5,1,3]=>[2,1,7,3,5,4,8,6]=>[1,2,2,2,1]
[4,7,3,5,1,8,6,2]=>[1,3,4,8,7,5,2,6]=>[8,6,5,1,2,4,7,3]=>[1,1,1,4,1]
[8,7,3,6,1,5,4,2]=>[8,3,7,5,6,4,2,1]=>[1,6,2,4,3,5,7,8]=>[2,2,4]
[2,5,8,7,4,6,1,3]=>[7,2,5,8,6,1,4,3]=>[2,7,4,1,3,8,5,6]=>[2,1,3,2]
[5,4,2,1,7,8,3,6]=>[7,3,2,1,5,8,4,6]=>[2,6,7,8,4,1,5,3]=>[4,1,2,1]
[4,7,8,3,5,2,1,6]=>[4,7,1,6,5,2,8,3]=>[5,2,8,3,4,7,1,6]=>[1,2,3,2]
[4,7,6,2,1,8,3,5]=>[1,4,7,8,5,3,2,6]=>[8,5,2,1,4,6,7,3]=>[1,1,1,4,1]
[1,4,6,7,3,5,8,2]=>[5,2,3,6,4,8,1,7]=>[4,7,6,3,5,1,8,2]=>[2,1,2,2,1]
[8,3,6,2,1,7,5,4]=>[8,2,4,7,5,3,6,1]=>[1,7,5,2,4,6,3,8]=>[2,1,3,2]
[8,3,7,6,4,2,1,5]=>[7,6,2,5,8,4,3,1]=>[2,3,7,4,1,5,6,8]=>[3,1,4]
[2,3,1,8,4,7,6,5]=>[8,7,1,2,5,6,3,4]=>[1,2,8,7,4,3,6,5]=>[3,1,1,2,1]
[2,7,4,8,6,5,1,3]=>[7,8,3,2,6,1,5,4]=>[2,1,6,7,3,8,4,5]=>[1,3,2,2]
[8,6,5,1,4,7,3,2]=>[5,8,7,4,3,2,6,1]=>[4,1,2,5,6,7,3,8]=>[1,5,2]
[8,5,4,1,7,3,6,2]=>[6,3,2,8,7,4,5,1]=>[3,6,7,1,2,5,4,8]=>[3,3,2]
[6,3,7,2,8,5,4,1]=>[8,7,2,1,4,3,6,5]=>[1,2,7,8,5,6,3,4]=>[4,2,2]
[1,6,3,8,2,7,5,4]=>[8,7,3,2,5,6,1,4]=>[1,2,6,7,4,3,8,5]=>[4,1,2,1]
[1,7,5,3,8,2,6,4]=>[8,4,3,6,2,7,1,5]=>[1,5,6,3,7,2,8,4]=>[3,2,2,1]
[6,2,7,4,1,8,5,3]=>[4,8,7,2,1,5,3,6]=>[5,1,2,7,8,4,6,3]=>[1,4,2,1]
[8,6,3,2,7,5,1,4]=>[3,7,8,4,2,6,5,1]=>[6,2,1,5,7,3,4,8]=>[1,1,3,3]
[2,7,5,1,3,8,6,4]=>[8,7,4,1,3,5,2,6]=>[1,2,5,8,6,4,7,3]=>[4,1,2,1]
[1,7,6,4,3,8,2,5]=>[5,4,7,3,2,8,1,6]=>[4,5,2,6,7,1,8,3]=>[2,3,2,1]
[3,7,2,4,8,6,5,1]=>[8,7,1,3,4,2,6,5]=>[1,2,8,6,5,7,3,4]=>[3,1,2,2]
[3,4,2,8,7,6,1,5]=>[7,8,1,2,6,3,5,4]=>[2,1,8,7,3,6,4,5]=>[1,2,1,2,2]
[5,1,4,3,2,7,8,6]=>[4,3,6,1,8,2,5,7]=>[5,6,3,8,1,7,4,2]=>[2,2,2,1,1]
[3,7,8,5,2,4,1,6]=>[5,7,6,1,4,2,8,3]=>[4,2,3,8,5,7,1,6]=>[1,3,2,2]
[3,7,6,2,4,1,8,5]=>[4,5,8,1,6,3,2,7]=>[5,4,1,8,3,6,7,2]=>[1,1,2,3,1]
[1,6,8,2,5,7,4,3]=>[5,2,8,7,4,6,1,3]=>[4,7,1,2,5,3,8,6]=>[2,3,2,1]
[5,2,7,8,4,3,1,6]=>[1,7,6,5,2,3,8,4]=>[8,2,3,4,7,6,1,5]=>[1,4,1,2]
[5,3,1,7,8,4,2,6]=>[7,2,1,6,4,8,3,5]=>[2,7,8,3,5,1,6,4]=>[3,2,2,1]
[2,7,6,4,1,3,8,5]=>[8,5,4,6,1,3,2,7]=>[1,4,5,3,8,6,7,2]=>[3,2,2,1]
[4,1,7,6,3,2,8,5]=>[1,5,8,6,4,2,3,7]=>[8,4,1,3,5,7,6,2]=>[1,1,4,1,1]
[6,3,1,7,5,2,8,4]=>[8,2,6,5,3,1,4,7]=>[1,7,3,4,6,8,5,2]=>[2,4,1,1]
[1,5,8,2,7,4,6,3]=>[2,6,8,7,4,5,1,3]=>[7,3,1,2,5,4,8,6]=>[1,1,3,2,1]
[5,7,2,8,4,6,3,1]=>[1,5,8,7,3,2,6,4]=>[8,4,1,2,6,7,3,5]=>[1,1,4,2]
[5,7,3,1,8,4,6,2]=>[3,1,6,8,7,4,2,5]=>[6,8,3,1,2,5,7,4]=>[2,1,4,1]
[8,4,7,3,1,6,5,2]=>[2,4,8,7,5,6,3,1]=>[7,5,1,2,4,3,6,8]=>[1,1,3,3]
[6,5,2,1,7,4,8,3]=>[6,3,5,2,1,8,4,7]=>[3,6,4,7,8,1,5,2]=>[2,3,2,1]
[5,7,4,6,2,1,8,3]=>[1,5,3,8,6,4,2,7]=>[8,4,6,1,3,5,7,2]=>[1,2,4,1]
[5,6,4,8,3,7,2,1]=>[1,3,2,5,8,7,6,4]=>[8,6,7,4,1,2,3,5]=>[1,2,1,4]
[6,7,1,8,3,4,2,5]=>[5,7,6,1,8,3,2,4]=>[4,2,3,8,1,6,7,5]=>[1,3,3,1]
[7,8,3,5,1,4,2,6]=>[3,7,5,6,4,1,8,2]=>[6,2,4,3,5,8,1,7]=>[1,2,3,2]
[5,6,2,7,1,8,3,4]=>[7,1,8,3,2,5,4,6]=>[2,8,1,6,7,4,5,3]=>[2,3,2,1]
[6,7,2,4,3,8,1,5]=>[5,3,4,1,7,2,8,6]=>[4,6,5,8,2,7,1,3]=>[2,2,2,2]
[2,4,3,8,6,7,1,5]=>[7,2,5,8,1,3,6,4]=>[2,7,4,1,8,6,3,5]=>[2,1,2,1,2]
[1,8,2,7,4,5,3,6]=>[5,7,6,8,3,4,1,2]=>[4,2,3,1,6,5,8,7]=>[1,2,2,2,1]
[2,5,4,8,3,6,1,7]=>[3,2,5,7,1,6,8,4]=>[6,7,4,2,8,3,1,5]=>[2,1,2,1,2]
[2,3,1,8,5,6,4,7]=>[5,7,1,2,6,8,3,4]=>[4,2,8,7,3,1,6,5]=>[1,2,1,1,2,1]
[3,8,5,6,4,7,1,2]=>[3,7,5,1,4,8,6,2]=>[6,2,4,8,5,1,3,7]=>[1,3,1,3]
[5,7,2,3,1,6,4,8]=>[3,4,1,7,5,6,2,8]=>[6,5,8,2,4,3,7,1]=>[1,2,2,2,1]
[4,6,2,7,1,5,3,8]=>[1,7,3,5,2,6,4,8]=>[8,2,6,4,7,3,5,1]=>[1,2,2,2,1]
[4,7,1,6,2,5,3,8]=>[1,7,5,6,3,4,2,8]=>[8,2,4,3,6,5,7,1]=>[1,2,2,2,1]
[4,7,1,5,3,6,2,8]=>[1,5,4,7,3,6,2,8]=>[8,4,5,2,6,3,7,1]=>[1,2,2,2,1]
[4,6,3,5,1,7,2,8]=>[1,3,7,5,4,2,6,8]=>[8,6,2,4,5,7,3,1]=>[1,1,4,1,1]
[6,7,3,5,1,4,2,8]=>[3,7,5,1,6,4,2,8]=>[6,2,4,8,3,5,7,1]=>[1,3,3,1]
[5,6,3,7,1,4,2,8]=>[3,1,7,5,2,6,4,8]=>[6,8,2,4,7,3,5,1]=>[2,3,2,1]
[5,7,1,6,3,4,2,8]=>[5,1,7,6,3,4,2,8]=>[4,8,2,3,6,5,7,1]=>[2,3,2,1]
[1,8,5,6,3,4,2,7]=>[5,3,7,6,4,8,1,2]=>[4,6,2,3,5,1,8,7]=>[2,3,2,1]
[1,8,5,6,4,7,2,3]=>[3,7,5,4,8,6,1,2]=>[6,2,4,5,1,3,8,7]=>[1,3,3,1]
[5,7,1,6,4,8,2,3]=>[1,7,5,4,8,3,2,6]=>[8,2,4,5,1,6,7,3]=>[1,3,3,1]
[4,6,5,8,1,7,2,3]=>[7,1,3,2,8,5,6,4]=>[2,8,6,7,1,4,3,5]=>[2,2,2,2]
[3,7,1,4,2,8,5,6]=>[1,4,7,8,3,5,2,6]=>[8,5,2,1,6,4,7,3]=>[1,1,1,2,2,1]
[3,5,1,4,2,8,6,7]=>[1,4,7,2,8,3,5,6]=>[8,5,2,7,1,6,4,3]=>[1,1,2,2,1,1]
[4,6,5,8,3,7,1,2]=>[3,1,2,7,5,8,6,4]=>[6,8,7,2,4,1,3,5]=>[2,1,2,3]
[4,6,5,8,2,3,1,7]=>[5,1,3,2,7,6,8,4]=>[4,8,6,7,2,3,1,5]=>[2,2,2,2]
[3,4,2,6,5,8,1,7]=>[1,2,5,3,4,7,8,6]=>[8,7,4,6,5,2,1,3]=>[1,1,2,1,1,2]
[3,5,4,6,2,8,1,7]=>[3,1,2,5,4,7,8,6]=>[6,8,7,4,5,2,1,3]=>[2,1,2,1,2]
[1,8,3,5,4,7,2,6]=>[5,3,4,7,8,6,1,2]=>[4,6,5,2,1,3,8,7]=>[2,1,1,3,1]
[3,4,2,7,1,8,5,6]=>[1,2,7,8,3,5,4,6]=>[8,7,2,1,6,4,5,3]=>[1,1,1,2,2,1]
[4,7,2,3,1,8,5,6]=>[3,1,4,7,8,5,2,6]=>[6,8,5,2,1,4,7,3]=>[2,1,1,3,1]
[2,6,3,8,1,7,4,5]=>[7,8,3,1,2,5,6,4]=>[2,1,6,8,7,4,3,5]=>[1,3,1,1,2]
[2,7,1,8,3,6,4,5]=>[7,8,5,6,1,3,2,4]=>[2,1,4,3,8,6,7,5]=>[1,2,2,2,1]
[1,2,8,7,4,6,3,5]=>[5,7,8,6,4,1,2,3]=>[4,2,1,3,5,8,7,6]=>[1,1,4,1,1]
[3,7,4,8,6,1,5,2]=>[8,3,6,1,2,7,5,4]=>[1,6,3,8,7,2,4,5]=>[2,2,1,3]
[4,5,1,8,7,6,2,3]=>[1,2,7,8,6,5,3,4]=>[8,7,2,1,3,4,6,5]=>[1,1,1,4,1]
[1,5,2,8,7,6,3,4]=>[2,7,8,6,5,1,3,4]=>[7,2,1,3,4,8,6,5]=>[1,1,4,1,1]
[5,1,2,8,7,6,3,4]=>[7,1,8,6,5,2,3,4]=>[2,8,1,3,4,7,6,5]=>[2,4,1,1]
[2,3,6,8,7,4,5,1]=>[3,6,8,7,1,2,5,4]=>[6,3,1,2,8,7,4,5]=>[1,1,3,1,2]
[4,5,7,8,2,6,3,1]=>[8,1,2,5,3,7,6,4]=>[1,8,7,4,6,2,3,5]=>[2,1,2,3]
[4,5,6,8,2,7,3,1]=>[1,2,3,8,5,7,6,4]=>[8,7,6,1,4,2,3,5]=>[1,1,1,2,3]
[5,2,6,8,3,7,4,1]=>[3,1,8,5,7,2,6,4]=>[6,8,1,4,2,7,3,5]=>[2,2,2,2]
[3,1,6,8,7,4,5,2]=>[3,6,8,1,7,5,2,4]=>[6,3,1,8,2,4,7,5]=>[1,1,2,3,1]
[6,1,4,8,7,2,5,3]=>[8,3,6,1,7,5,2,4]=>[1,6,3,8,2,4,7,5]=>[2,2,3,1]
[6,1,8,4,7,3,5,2]=>[4,6,1,8,7,5,2,3]=>[5,3,8,1,2,4,7,6]=>[1,2,4,1]
[6,8,3,5,7,1,4,2]=>[8,3,1,6,4,7,5,2]=>[1,6,8,3,5,2,4,7]=>[3,2,3]
[3,1,7,8,6,4,5,2]=>[6,3,8,1,7,5,2,4]=>[3,6,1,8,2,4,7,5]=>[2,2,3,1]
[5,2,7,8,3,6,4,1]=>[1,8,5,3,7,2,6,4]=>[8,1,4,6,2,7,3,5]=>[1,3,2,2]
[4,6,7,8,2,5,3,1]=>[2,8,1,5,3,7,6,4]=>[7,1,8,4,6,2,3,5]=>[1,2,2,3]
[7,4,5,2,8,6,3,1]=>[2,3,8,7,4,1,6,5]=>[7,6,1,2,5,8,3,4]=>[1,1,4,2]
[7,5,8,4,2,6,3,1]=>[2,8,5,4,1,7,6,3]=>[7,1,4,5,8,2,3,6]=>[1,4,3]
[6,8,2,5,3,7,4,1]=>[8,5,3,1,4,7,6,2]=>[1,4,6,8,5,2,3,7]=>[4,1,3]
[6,3,8,4,2,7,5,1]=>[4,8,2,1,5,7,6,3]=>[5,1,7,8,4,2,3,6]=>[1,3,1,3]
[7,2,5,3,8,6,4,1]=>[3,8,7,2,4,1,6,5]=>[6,1,2,7,5,8,3,4]=>[1,3,2,2]
[3,4,7,5,8,6,2,1]=>[8,4,1,2,3,7,6,5]=>[1,5,8,7,6,2,3,4]=>[3,1,1,3]
[3,6,7,4,8,5,2,1]=>[2,8,4,1,3,7,6,5]=>[7,1,5,8,6,2,3,4]=>[1,3,1,3]
[6,7,4,2,8,5,3,1]=>[3,1,8,7,4,2,6,5]=>[6,8,1,2,5,7,3,4]=>[2,4,2]
[2,7,5,3,8,6,4,1]=>[3,8,7,4,1,2,6,5]=>[6,1,2,5,8,7,3,4]=>[1,4,1,2]
[5,6,2,8,3,7,4,1]=>[1,8,5,2,7,3,6,4]=>[8,1,4,7,2,6,3,5]=>[1,3,2,2]
[5,6,8,3,2,7,4,1]=>[1,4,2,8,5,7,6,3]=>[8,5,7,1,4,2,3,6]=>[1,2,2,3]
[1,5,8,2,7,3,6,4]=>[2,8,6,7,4,5,1,3]=>[7,1,3,2,5,4,8,6]=>[1,2,2,2,1]
[5,8,4,7,2,3,6,1]=>[1,5,3,6,8,7,4,2]=>[8,4,6,3,1,2,5,7]=>[1,2,1,4]
[5,6,8,1,3,7,4,2]=>[1,8,5,2,7,4,6,3]=>[8,1,4,7,2,5,3,6]=>[1,3,2,2]
[6,7,4,8,1,5,3,2]=>[3,1,8,7,5,2,6,4]=>[6,8,1,2,4,7,3,5]=>[2,4,2]
[5,7,2,8,3,6,4,1]=>[1,8,5,7,3,2,6,4]=>[8,1,4,2,6,7,3,5]=>[1,2,3,2]
[1,7,4,8,6,2,5,3]=>[8,3,6,2,7,5,1,4]=>[1,6,3,7,2,4,8,5]=>[2,2,3,1]
[7,4,2,8,6,1,5,3]=>[2,8,6,7,3,1,5,4]=>[7,1,3,2,6,8,4,5]=>[1,2,3,2]
[6,8,5,3,7,2,4,1]=>[4,1,6,3,8,7,5,2]=>[5,8,3,6,1,2,4,7]=>[2,2,4]
[6,8,5,2,3,7,4,1]=>[8,4,1,5,3,7,6,2]=>[1,5,8,4,6,2,3,7]=>[3,2,3]
[7,5,3,8,2,6,4,1]=>[8,3,2,5,1,7,6,4]=>[1,6,7,4,8,2,3,5]=>[3,2,3]
[7,5,2,3,8,6,4,1]=>[8,7,3,2,4,1,6,5]=>[1,2,6,7,5,8,3,4]=>[4,2,2]
[3,7,4,5,8,6,2,1]=>[8,3,4,1,2,7,6,5]=>[1,6,5,8,7,2,3,4]=>[2,2,1,3]
[6,7,3,4,8,5,2,1]=>[8,3,1,4,2,7,6,5]=>[1,6,8,5,7,2,3,4]=>[3,2,3]
[3,6,4,7,8,5,2,1]=>[4,2,8,1,3,7,6,5]=>[5,7,1,8,6,2,3,4]=>[2,2,1,3]
[6,4,2,7,8,5,3,1]=>[2,4,1,8,7,3,6,5]=>[7,5,8,1,2,6,3,4]=>[1,2,3,2]
[7,4,2,5,8,6,3,1]=>[2,8,4,7,3,1,6,5]=>[7,1,5,2,6,8,3,4]=>[1,2,3,2]
[6,1,8,3,4,7,5,2]=>[8,4,5,1,7,6,2,3]=>[1,5,4,8,2,3,7,6]=>[2,2,3,1]
[6,8,4,2,5,7,3,1]=>[5,3,1,8,4,7,6,2]=>[4,6,8,1,5,2,3,7]=>[3,2,3]
[7,5,8,3,4,6,2,1]=>[4,2,5,1,8,7,6,3]=>[5,7,4,8,1,2,3,6]=>[2,2,4]
[7,4,5,8,1,6,3,2]=>[2,3,8,7,5,1,6,4]=>[7,6,1,2,4,8,3,5]=>[1,1,4,2]
[6,3,4,7,8,5,2,1]=>[4,8,2,1,3,7,6,5]=>[5,1,7,8,6,2,3,4]=>[1,3,1,3]
[6,1,7,3,4,5,8,2]=>[4,5,6,3,1,8,2,7]=>[5,4,3,6,8,1,7,2]=>[1,1,3,2,1]
[5,7,2,3,4,1,8,6]=>[3,4,1,5,8,6,2,7]=>[6,5,8,4,1,3,7,2]=>[1,2,1,3,1]
[2,7,1,8,4,5,6,3]=>[5,6,8,7,1,3,2,4]=>[4,3,1,2,8,6,7,5]=>[1,1,3,2,1]
[2,6,8,3,4,5,1,7]=>[4,5,2,7,1,6,8,3]=>[5,4,7,2,8,3,1,6]=>[1,2,2,1,2]
[6,1,2,7,4,5,8,3]=>[5,6,4,8,2,1,3,7]=>[4,3,5,1,7,8,6,2]=>[1,2,3,1,1]
[4,7,2,3,1,5,8,6]=>[3,1,4,8,5,6,2,7]=>[6,8,5,1,4,3,7,2]=>[2,1,2,2,1]
[2,7,1,3,8,5,6,4]=>[6,8,7,1,3,4,2,5]=>[3,1,2,8,6,5,7,4]=>[1,3,1,2,1]
[2,6,7,8,4,5,3,1]=>[2,5,3,8,7,1,6,4]=>[7,4,6,1,2,8,3,5]=>[1,2,3,2]
[2,5,8,3,4,1,6,7]=>[4,2,6,1,5,7,8,3]=>[5,7,3,8,4,2,1,6]=>[2,2,1,1,2]
[5,6,2,7,4,3,8,1]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[1,4,1,2]
[4,6,7,3,2,5,8,1]=>[5,1,4,2,6,3,8,7]=>[4,8,5,7,3,6,1,2]=>[2,2,2,2]
[2,6,7,3,8,5,4,1]=>[2,8,7,4,1,3,6,5]=>[7,1,2,5,8,6,3,4]=>[1,4,1,2]
[2,12,1,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,1,1,1,1,1,1,1,1,1,2]
[3,6,8,4,5,7,1,2]=>[4,2,7,1,5,8,6,3]=>[5,7,2,8,4,1,3,6]=>[2,2,1,3]
[1,6,8,4,7,2,3,5]=>[6,4,2,7,8,5,1,3]=>[3,5,7,2,1,4,8,6]=>[3,1,3,1]
[1,4,5,7,8,2,6,3]=>[8,2,3,6,4,7,1,5]=>[1,7,6,3,5,2,8,4]=>[2,1,2,2,1]
[3,4,5,7,8,6,1,2]=>[7,1,2,3,4,8,6,5]=>[2,8,7,6,5,1,3,4]=>[2,1,1,1,3]
[3,4,5,7,6,8,1,2]=>[7,1,2,3,5,4,8,6]=>[2,8,7,6,4,5,1,3]=>[2,1,1,2,2]
[3,6,7,4,8,5,1,2]=>[4,2,7,1,3,8,6,5]=>[5,7,2,8,6,1,3,4]=>[2,2,1,3]
[3,4,5,6,8,7,1,2]=>[1,2,3,4,7,8,6,5]=>[8,7,6,5,2,1,3,4]=>[1,1,1,1,1,3]
[1,4,5,8,7,2,3,6]=>[2,3,6,7,8,5,1,4]=>[7,6,3,2,1,4,8,5]=>[1,1,1,1,3,1]
[1,2,5,8,3,6,4,7]=>[3,7,5,6,8,1,2,4]=>[6,2,4,3,1,8,7,5]=>[1,2,1,2,1,1]
[1,4,5,8,6,2,3,7]=>[2,3,6,7,5,8,1,4]=>[7,6,3,2,4,1,8,5]=>[1,1,1,2,2,1]
[7,8,1,4,6,2,3,5]=>[6,4,7,8,3,1,5,2]=>[3,5,2,1,6,8,4,7]=>[2,1,3,2]
[1,6,7,4,8,2,5,3]=>[4,2,8,6,3,7,1,5]=>[5,7,1,3,6,2,8,4]=>[2,3,2,1]
[1,4,5,6,8,2,7,3]=>[2,3,4,8,6,7,1,5]=>[7,6,5,1,3,2,8,4]=>[1,1,1,2,2,1]
[1,4,5,8,6,2,7,3]=>[8,2,3,6,5,7,1,4]=>[1,7,6,3,4,2,8,5]=>[2,1,2,2,1]
[1,2,5,8,3,4,7,6]=>[3,8,5,6,7,1,2,4]=>[6,1,4,3,2,8,7,5]=>[1,2,1,2,1,1]
[1,6,7,2,3,5,8,4]=>[6,8,4,2,5,1,3,7]=>[3,1,5,7,4,8,6,2]=>[1,3,2,1,1]
[7,8,1,2,3,5,4,6]=>[7,3,4,5,6,1,8,2]=>[2,6,5,4,3,8,1,7]=>[2,1,1,2,2]
[1,6,7,2,3,5,4,8]=>[7,4,5,2,6,1,3,8]=>[2,5,4,7,3,8,6,1]=>[2,2,2,1,1]
[1,2,5,7,3,6,4,8]=>[3,7,5,6,1,2,4,8]=>[6,2,4,3,8,7,5,1]=>[1,2,2,1,1,1]
[1,2,5,7,3,6,8,4]=>[3,6,8,5,1,2,4,7]=>[6,3,1,4,8,7,5,2]=>[1,1,3,1,1,1]
[1,6,8,2,3,5,7,4]=>[6,8,4,2,5,7,1,3]=>[3,1,5,7,4,2,8,6]=>[1,3,1,2,1]
[1,6,8,4,5,2,3,7]=>[6,4,2,7,5,8,1,3]=>[3,5,7,2,4,1,8,6]=>[3,2,2,1]
[1,6,8,4,5,2,7,3]=>[4,2,8,6,5,7,1,3]=>[5,7,1,3,4,2,8,6]=>[2,3,2,1]
[1,6,8,2,3,4,7,5]=>[8,4,5,2,6,7,1,3]=>[1,5,4,7,3,2,8,6]=>[2,2,1,2,1]
[1,6,8,2,3,7,4,5]=>[7,8,4,2,5,6,1,3]=>[2,1,5,7,4,3,8,6]=>[1,3,1,2,1]
[7,8,1,2,3,4,6,5]=>[8,3,4,5,6,1,7,2]=>[1,6,5,4,3,8,2,7]=>[2,1,1,2,2]
[7,8,1,2,3,6,4,5]=>[7,8,3,4,5,1,6,2]=>[2,1,6,5,4,8,3,7]=>[1,2,1,2,2]
[1,6,7,2,3,8,5,4]=>[8,7,4,2,5,1,3,6]=>[1,2,5,7,4,8,6,3]=>[4,2,1,1]
[1,2,5,6,3,8,7,4]=>[3,4,8,7,1,2,5,6]=>[6,5,1,2,8,7,4,3]=>[1,1,3,1,1,1]
[4,2,1,6,5,3,8,7]=>[5,2,1,4,8,3,6,7]=>[4,7,8,5,1,6,3,2]=>[3,1,2,1,1]
[8,2,4,3,1,6,5,7]=>[4,2,3,7,5,6,8,1]=>[5,7,6,2,4,3,1,8]=>[2,1,2,1,2]
[4,2,6,3,5,1,8,7]=>[4,1,5,2,3,8,6,7]=>[5,8,4,7,6,1,3,2]=>[2,2,1,2,1]
[4,6,2,1,5,8,7,3]=>[1,8,3,5,2,7,4,6]=>[8,1,6,4,7,2,5,3]=>[1,2,2,2,1]
[4,6,5,2,1,8,7,3]=>[8,1,4,3,2,7,5,6]=>[1,8,5,6,7,2,4,3]=>[2,3,2,1]
[2,1,6,4,3,8,7,5]=>[8,4,1,3,7,2,5,6]=>[1,5,8,6,2,7,4,3]=>[3,1,2,1,1]
[4,8,2,1,6,7,3,5]=>[1,7,3,5,8,4,6,2]=>[8,2,6,4,1,5,3,7]=>[1,2,1,2,2]
[6,8,2,1,4,3,7,5]=>[3,5,8,4,1,6,7,2]=>[6,4,1,5,8,3,2,7]=>[1,1,3,1,2]
[8,6,2,4,3,1,5,7]=>[6,3,5,4,7,2,8,1]=>[3,6,4,5,2,7,1,8]=>[2,2,2,2]
[6,8,2,4,3,1,7,5]=>[5,3,4,1,8,6,7,2]=>[4,6,5,8,1,3,2,7]=>[2,2,2,2]
[6,8,7,2,4,3,1,5]=>[7,4,1,6,5,8,3,2]=>[2,5,8,3,4,1,6,7]=>[3,2,3]
[2,1,8,4,6,5,3,7]=>[7,4,6,1,5,8,2,3]=>[2,5,3,8,4,1,7,6]=>[2,2,1,2,1]
[2,1,6,4,8,5,7,3]=>[6,3,8,1,4,7,2,5]=>[3,6,1,8,5,2,7,4]=>[2,2,1,2,1]
[4,6,5,2,8,3,7,1]=>[6,1,3,2,8,4,7,5]=>[3,8,6,7,1,5,2,4]=>[2,2,2,2]
[2,6,4,5,8,3,7,1]=>[3,4,2,6,8,1,7,5]=>[6,5,7,3,1,8,2,4]=>[1,2,1,2,2]
[6,4,2,8,3,5,7,1]=>[5,2,6,1,8,3,7,4]=>[4,7,3,8,1,6,2,5]=>[2,2,2,2]
[8,4,2,6,3,5,1,7]=>[5,2,7,3,6,4,8,1]=>[4,7,2,6,3,5,1,8]=>[2,2,2,2]
[6,2,4,8,5,3,7,1]=>[6,3,5,1,8,2,7,4]=>[3,6,4,8,1,7,2,5]=>[2,2,2,2]
[4,2,6,3,5,8,7,1]=>[1,8,4,2,3,5,7,6]=>[8,1,5,7,6,4,2,3]=>[1,3,1,1,2]
[4,2,6,3,8,7,5,1]=>[1,3,8,7,2,4,6,5]=>[8,6,1,2,7,5,3,4]=>[1,1,3,1,2]
[6,2,4,3,8,5,7,1]=>[3,6,8,2,1,4,7,5]=>[6,3,1,7,8,5,2,4]=>[1,1,3,1,2]
[8,2,1,4,6,5,3,7]=>[7,2,4,6,3,5,8,1]=>[2,7,5,3,6,4,1,8]=>[2,1,2,1,2]
[6,2,1,4,8,5,7,3]=>[6,8,2,4,1,7,3,5]=>[3,1,7,5,8,2,6,4]=>[1,2,2,2,1]
[6,2,1,8,7,4,3,5]=>[7,6,8,2,1,5,3,4]=>[2,3,1,7,8,4,6,5]=>[2,3,2,1]
[6,2,1,8,4,3,7,5]=>[5,8,2,6,1,7,3,4]=>[4,1,7,3,8,2,6,5]=>[1,2,2,2,1]
[6,4,8,5,2,1,7,3]=>[2,5,1,8,6,4,7,3]=>[7,4,8,1,3,5,2,6]=>[1,2,3,2]
[6,4,8,5,7,2,1,3]=>[7,2,1,6,4,8,5,3]=>[2,7,8,3,5,1,4,6]=>[3,2,3]
[4,6,8,7,5,2,1,3]=>[2,7,1,6,8,5,4,3]=>[7,2,8,3,1,4,5,6]=>[1,2,1,4]
[2,1,4,8,6,7,3,5]=>[7,5,8,1,3,6,2,4]=>[2,4,1,8,6,3,7,5]=>[2,2,1,2,1]
[2,6,8,7,4,5,1,3]=>[2,7,5,8,6,1,4,3]=>[7,2,4,1,3,8,5,6]=>[1,2,3,2]
[2,4,8,6,7,5,1,3]=>[7,4,8,2,6,1,5,3]=>[2,5,1,7,3,8,4,6]=>[2,2,2,2]
[4,2,8,6,5,7,1,3]=>[7,1,5,4,8,2,6,3]=>[2,8,4,5,1,7,3,6]=>[2,2,2,2]
[8,2,6,4,5,1,3,7]=>[6,4,7,2,5,3,8,1]=>[3,5,2,7,4,6,1,8]=>[2,2,2,2]
[8,4,6,2,1,5,3,7]=>[4,2,7,5,6,3,8,1]=>[5,7,2,4,3,6,1,8]=>[2,2,2,2]
[4,6,5,8,2,1,7,3]=>[5,1,3,2,8,6,7,4]=>[4,8,6,7,1,3,2,5]=>[2,2,2,2]
[2,1,6,8,4,3,7,5]=>[5,3,8,1,6,7,2,4]=>[4,6,1,8,3,2,7,5]=>[2,2,1,2,1]
[2,8,6,4,7,1,3,5]=>[6,4,7,3,8,1,5,2]=>[3,5,2,6,1,8,4,7]=>[2,2,2,2]
[2,8,5,3,1,4,6,7]=>[5,4,6,1,3,7,8,2]=>[4,5,3,8,6,2,1,7]=>[2,2,1,1,2]
[2,7,4,8,3,5,1,6]=>[3,5,7,6,1,2,8,4]=>[6,4,2,3,8,7,1,5]=>[1,1,3,1,2]
[2,7,4,8,3,5,6,1]=>[3,5,6,2,8,1,7,4]=>[6,4,3,7,1,8,2,5]=>[1,1,2,2,2]
[7,2,8,4,3,5,1,6]=>[5,4,7,2,6,1,8,3]=>[4,5,2,7,3,8,1,6]=>[2,2,2,2]
[8,5,1,4,2,3,6,7]=>[5,6,3,4,2,7,8,1]=>[4,3,6,5,7,2,1,8]=>[1,2,2,1,2]
[6,7,3,8,4,2,5,1]=>[6,3,1,5,2,8,7,4]=>[3,6,8,4,7,1,2,5]=>[3,2,3]
[6,7,3,8,4,2,1,5]=>[7,3,1,6,5,2,8,4]=>[2,6,8,3,4,7,1,5]=>[3,3,2]
[7,1,8,4,3,5,2,6]=>[5,4,7,6,8,2,1,3]=>[4,5,2,3,1,7,8,6]=>[2,2,3,1]
[1,7,8,4,3,5,2,6]=>[5,4,7,6,2,8,1,3]=>[4,5,2,3,7,1,8,6]=>[2,3,2,1]
[7,1,4,8,3,5,2,6]=>[3,5,7,6,8,2,1,4]=>[6,4,2,3,1,7,8,5]=>[1,1,2,3,1]
[6,7,3,1,8,4,5,2]=>[3,6,1,8,7,4,2,5]=>[6,3,8,1,2,5,7,4]=>[1,2,4,1]
[6,7,3,8,4,5,2,1]=>[5,1,8,3,2,7,6,4]=>[4,8,1,6,7,2,3,5]=>[2,3,3]
[6,7,1,4,8,3,5,2]=>[4,6,1,8,7,3,2,5]=>[5,3,8,1,2,6,7,4]=>[1,2,4,1]
[6,7,4,1,3,8,2,5]=>[5,7,3,1,8,4,2,6]=>[4,2,6,8,1,5,7,3]=>[1,3,3,1]
[1,6,7,8,4,3,2,5]=>[2,7,6,5,3,8,1,4]=>[7,2,3,4,6,1,8,5]=>[1,4,2,1]
[7,2,1,8,4,5,3,6]=>[5,7,2,6,8,3,1,4]=>[4,2,7,3,1,6,8,5]=>[1,2,1,3,1]
[6,2,7,1,8,4,3,5]=>[7,6,8,2,1,4,3,5]=>[2,3,1,7,8,5,6,4]=>[2,3,2,1]
[6,2,7,8,4,3,1,5]=>[7,6,5,2,1,3,8,4]=>[2,3,4,7,8,6,1,5]=>[5,1,2]
[6,2,7,8,4,3,5,1]=>[6,5,3,1,8,2,7,4]=>[3,4,6,8,1,7,2,5]=>[4,2,2]
[2,6,7,4,8,3,5,1]=>[4,2,6,3,8,1,7,5]=>[5,7,3,6,1,8,2,4]=>[2,2,2,2]
[2,6,7,4,8,3,1,5]=>[4,2,7,6,1,3,8,5]=>[5,7,2,3,8,6,1,4]=>[2,3,1,2]
[7,8,1,3,6,2,4,5]=>[4,6,7,8,3,1,5,2]=>[5,3,2,1,6,8,4,7]=>[1,1,1,3,2]
[1,2,7,8,6,3,4,5]=>[6,7,3,8,5,1,2,4]=>[3,2,6,1,4,8,7,5]=>[1,2,3,1,1]
[2,6,7,1,8,5,3,4]=>[7,2,8,6,1,4,3,5]=>[2,7,1,3,8,5,6,4]=>[2,3,2,1]
[2,6,7,8,5,3,1,4]=>[2,7,6,3,8,1,5,4]=>[7,2,3,6,1,8,4,5]=>[1,3,2,2]
[2,6,7,8,5,3,4,1]=>[2,6,3,8,7,1,5,4]=>[7,3,6,1,2,8,4,5]=>[1,2,3,2]
[7,2,1,8,4,5,6,3]=>[5,6,8,2,7,3,1,4]=>[4,3,1,7,2,6,8,5]=>[1,1,2,3,1]
[1,7,2,8,4,5,6,3]=>[5,6,8,7,3,1,2,4]=>[4,3,1,2,6,8,7,5]=>[1,1,4,1,1]
[3,7,8,1,5,6,2,4]=>[7,5,8,1,4,2,6,3]=>[2,4,1,8,5,7,3,6]=>[2,2,2,2]
[6,3,7,8,1,5,2,4]=>[7,8,2,1,5,3,6,4]=>[2,1,7,8,4,6,3,5]=>[1,3,2,2]
[6,7,1,2,8,5,3,4]=>[7,8,6,3,1,4,2,5]=>[2,1,3,6,8,5,7,4]=>[1,4,2,1]
[1,6,7,8,4,2,5,3]=>[2,8,6,5,3,7,1,4]=>[7,1,3,4,6,2,8,5]=>[1,4,2,1]
[6,1,2,4,7,3,8,5]=>[8,4,6,2,3,1,5,7]=>[1,5,3,7,6,8,4,2]=>[2,2,2,1,1]
[1,7,5,3,6,4,8,2]=>[6,4,3,5,2,8,1,7]=>[3,5,6,4,7,1,8,2]=>[3,2,2,1]
[4,6,1,7,3,2,5,8]=>[1,6,5,7,3,2,4,8]=>[8,3,4,2,6,7,5,1]=>[1,2,3,1,1]
[4,6,1,8,3,2,5,7]=>[1,6,5,7,2,8,3,4]=>[8,3,4,2,7,1,6,5]=>[1,2,2,2,1]
[4,7,1,8,3,5,2,6]=>[1,5,7,6,8,3,2,4]=>[8,4,2,3,1,6,7,5]=>[1,1,2,3,1]
[4,1,7,8,6,2,3,5]=>[1,6,7,3,8,5,2,4]=>[8,3,2,6,1,4,7,5]=>[1,1,2,3,1]
[1,6,5,7,8,3,4,2]=>[3,2,6,4,8,7,1,5]=>[6,7,3,5,1,2,8,4]=>[2,2,3,1]
[1,6,5,8,7,3,4,2]=>[3,2,6,8,7,5,1,4]=>[6,7,3,1,2,4,8,5]=>[2,1,4,1]
[4,1,8,7,6,2,3,5]=>[1,6,7,8,5,4,2,3]=>[8,3,2,1,4,5,7,6]=>[1,1,1,4,1]
[4,8,1,7,3,5,2,6]=>[1,5,7,6,8,3,4,2]=>[8,4,2,3,1,6,5,7]=>[1,1,2,2,2]
[4,7,1,6,3,2,5,8]=>[1,6,5,7,3,4,2,8]=>[8,3,4,2,6,5,7,1]=>[1,2,2,2,1]
[6,1,2,3,7,5,4,8]=>[7,6,2,3,4,1,5,8]=>[2,3,7,6,5,8,4,1]=>[3,1,2,1,1]
[6,8,1,5,3,7,2,4]=>[5,7,4,1,8,3,6,2]=>[4,2,5,8,1,6,3,7]=>[1,3,2,2]
[8,7,5,2,4,1,6,3]=>[8,4,6,5,3,7,2,1]=>[1,5,3,4,6,2,7,8]=>[2,3,3]
[1,5,7,3,4,8,6,2]=>[2,8,4,5,3,7,1,6]=>[7,1,5,4,6,2,8,3]=>[1,2,2,2,1]
[1,5,8,3,4,7,6,2]=>[2,8,4,5,7,6,1,3]=>[7,1,5,4,2,3,8,6]=>[1,2,1,3,1]
[7,8,5,2,4,1,6,3]=>[8,4,6,5,3,1,7,2]=>[1,5,3,4,6,8,2,7]=>[2,4,2]
[8,1,2,3,5,6,4,7]=>[5,7,2,3,4,6,8,1]=>[4,2,7,6,5,3,1,8]=>[1,2,1,1,1,2]
[8,1,2,3,5,4,7,6]=>[5,8,2,3,4,6,7,1]=>[4,1,7,6,5,3,2,8]=>[1,2,1,1,1,2]
[7,1,8,4,6,3,2,5]=>[4,7,6,8,5,2,1,3]=>[5,2,3,1,4,7,8,6]=>[1,2,4,1]
[6,8,2,4,3,1,5,7]=>[6,3,5,4,1,7,8,2]=>[3,6,4,5,8,2,1,7]=>[2,3,1,2]
[3,8,1,2,4,5,7,6]=>[1,8,3,4,5,6,7,2]=>[8,1,6,5,4,3,2,7]=>[1,2,1,1,1,2]
[3,7,1,8,6,4,2,5]=>[7,6,8,1,5,3,2,4]=>[2,3,1,8,4,6,7,5]=>[2,2,3,1]
[1,6,4,3,7,5,8,2]=>[3,6,4,2,5,8,1,7]=>[6,3,5,7,4,1,8,2]=>[1,3,1,2,1]
[3,1,2,6,7,5,8,4]=>[1,4,6,5,8,2,3,7]=>[8,5,3,4,1,7,6,2]=>[1,1,2,2,1,1]
[3,8,1,7,6,4,2,5]=>[7,6,8,1,5,3,4,2]=>[2,3,1,8,4,6,5,7]=>[2,2,2,2]
[7,6,2,4,3,1,5,8]=>[6,3,5,4,7,2,1,8]=>[3,6,4,5,2,7,8,1]=>[2,2,3,1]
[8,7,2,4,3,5,1,6]=>[5,3,4,7,6,8,2,1]=>[4,6,5,2,3,1,7,8]=>[2,1,2,3]
[8,1,7,4,6,3,2,5]=>[4,7,6,8,5,2,3,1]=>[5,2,3,1,4,7,6,8]=>[1,2,3,2]
[8,1,7,6,5,3,2,4]=>[7,6,8,5,4,2,3,1]=>[2,3,1,4,5,7,6,8]=>[2,4,2]
[1,5,7,3,4,6,8,2]=>[4,2,5,6,3,8,1,7]=>[5,7,4,3,6,1,8,2]=>[2,1,2,2,1]
[8,7,2,5,3,6,1,4]=>[5,7,3,4,8,6,2,1]=>[4,2,6,5,1,3,7,8]=>[1,2,1,4]
[6,1,2,3,5,8,4,7]=>[5,7,8,2,3,1,4,6]=>[4,2,1,7,6,8,5,3]=>[1,1,2,2,1,1]
[6,1,2,3,5,7,4,8]=>[5,7,2,3,4,1,6,8]=>[4,2,7,6,5,8,3,1]=>[1,2,1,2,1,1]
[5,1,2,3,7,6,4,8]=>[7,6,2,3,1,4,5,8]=>[2,3,7,6,8,5,4,1]=>[3,2,1,1,1]
[5,1,2,3,8,6,4,7]=>[7,6,8,2,1,3,4,5]=>[2,3,1,7,8,6,5,4]=>[2,3,1,1,1]
[1,5,6,3,4,7,8,2]=>[4,2,5,3,6,8,1,7]=>[5,7,4,6,3,1,8,2]=>[2,2,1,2,1]
[8,6,5,2,4,7,1,3]=>[7,4,5,3,2,8,6,1]=>[2,5,4,6,7,1,3,8]=>[2,3,3]
[7,6,2,5,3,1,8,4]=>[5,8,3,6,4,2,1,7]=>[4,1,6,3,5,7,8,2]=>[1,2,4,1]
[7,4,5,2,3,8,6,1]=>[2,8,4,3,5,1,7,6]=>[7,1,5,6,4,8,2,3]=>[1,3,2,2]
[8,2,3,7,4,5,1,6]=>[5,7,2,3,6,8,4,1]=>[4,2,7,6,3,1,5,8]=>[1,2,1,1,3]
[8,4,7,3,2,5,1,6]=>[2,5,4,7,6,8,3,1]=>[7,4,5,2,3,1,6,8]=>[1,2,2,3]
[5,4,6,3,1,2,8,7]=>[2,1,8,5,4,3,6,7]=>[7,8,1,4,5,6,3,2]=>[2,4,1,1]
[4,6,2,3,1,5,8,7]=>[3,1,4,8,5,2,6,7]=>[6,8,5,1,4,7,3,2]=>[2,1,3,1,1]
[7,2,3,4,5,8,6,1]=>[8,2,3,4,5,1,7,6]=>[1,7,6,5,4,8,2,3]=>[2,1,1,2,2]
[8,2,3,4,5,7,1,6]=>[2,3,4,5,7,8,6,1]=>[7,6,5,4,2,1,3,8]=>[1,1,1,1,1,3]
[7,3,4,6,8,5,1,2]=>[7,2,3,4,1,8,6,5]=>[2,7,6,5,8,1,3,4]=>[2,1,2,3]
[4,7,3,2,8,6,1,5]=>[1,3,7,8,4,2,6,5]=>[8,6,2,1,5,7,3,4]=>[1,1,1,3,2]
[3,7,4,5,1,8,6,2]=>[3,4,8,1,7,5,2,6]=>[6,5,1,8,2,4,7,3]=>[1,1,2,3,1]
[3,8,2,6,7,4,5,1]=>[6,4,8,1,3,7,5,2]=>[3,5,1,8,6,2,4,7]=>[2,2,1,3]
[4,8,1,5,6,7,3,2]=>[1,4,5,8,7,3,6,2]=>[8,5,4,1,2,6,3,7]=>[1,1,1,3,2]
[5,8,2,4,6,7,1,3]=>[4,1,7,3,5,8,6,2]=>[5,8,2,6,4,1,3,7]=>[2,2,1,3]
[6,8,1,3,4,2,7,5]=>[4,5,8,3,1,6,7,2]=>[5,4,1,6,8,3,2,7]=>[1,1,3,1,2]
[5,8,2,4,3,1,7,6]=>[5,3,1,4,8,6,7,2]=>[4,6,8,5,1,3,2,7]=>[3,1,2,2]
[2,1,7,6,8,5,3,4]=>[7,4,3,8,1,6,2,5]=>[2,5,6,1,8,3,7,4]=>[3,2,2,1]
[3,7,6,1,8,5,2,4]=>[7,8,6,1,4,3,2,5]=>[2,1,3,8,5,6,7,4]=>[1,3,3,1]
[4,7,2,3,8,5,1,6]=>[1,7,3,4,6,2,8,5]=>[8,2,6,5,3,7,1,4]=>[1,2,1,2,2]
[7,6,1,4,8,5,2,3]=>[4,7,8,6,3,2,1,5]=>[5,2,1,3,6,7,8,4]=>[1,1,5,1]
[6,2,3,7,8,5,4,1]=>[4,8,7,2,1,3,6,5]=>[5,1,2,7,8,6,3,4]=>[1,4,1,2]
[6,2,3,8,4,5,1,7]=>[5,7,2,3,1,6,8,4]=>[4,2,7,6,8,3,1,5]=>[1,2,2,1,2]
[7,2,3,6,8,4,1,5]=>[7,6,2,3,4,1,8,5]=>[2,3,7,6,5,8,1,4]=>[3,1,2,2]
[8,2,3,5,7,1,4,6]=>[6,2,3,4,7,8,5,1]=>[3,7,6,5,2,1,4,8]=>[2,1,1,1,3]
[6,4,8,3,5,1,7,2]=>[2,4,1,8,6,5,7,3]=>[7,5,8,1,3,4,2,6]=>[1,2,3,2]
[5,4,8,3,6,7,1,2]=>[2,1,4,7,5,8,6,3]=>[7,8,5,2,4,1,3,6]=>[2,1,2,3]
[3,5,1,8,4,6,7,2]=>[5,1,2,6,8,7,3,4]=>[4,8,7,3,1,2,6,5]=>[2,1,1,3,1]
[3,6,1,8,4,5,2,7]=>[5,7,1,6,2,8,3,4]=>[4,2,8,3,7,1,6,5]=>[1,2,2,2,1]
[4,6,8,3,5,2,7,1]=>[4,1,2,6,5,8,7,3]=>[5,8,7,3,4,1,2,6]=>[2,1,2,3]
[5,7,8,3,2,4,1,6]=>[1,5,4,7,6,2,8,3]=>[8,4,5,2,3,7,1,6]=>[1,2,3,2]
[4,8,2,3,5,6,1,7]=>[3,1,4,5,7,6,8,2]=>[6,8,5,4,2,3,1,7]=>[2,1,1,2,2]
[6,8,2,3,1,4,5,7]=>[3,5,4,6,1,7,8,2]=>[6,4,5,3,8,2,1,7]=>[1,2,2,1,2]
[5,2,7,4,8,3,1,6]=>[4,1,7,6,2,3,8,5]=>[5,8,2,3,7,6,1,4]=>[2,3,1,2]
[3,7,8,2,1,4,6,5]=>[4,8,1,5,6,2,7,3]=>[5,1,8,4,3,7,2,6]=>[1,2,1,2,2]
[6,3,2,4,1,8,7,5]=>[2,8,3,4,1,7,5,6]=>[7,1,6,5,8,2,4,3]=>[1,2,2,2,1]
[7,2,3,4,8,5,1,6]=>[7,2,3,4,6,1,8,5]=>[2,7,6,5,3,8,1,4]=>[2,1,1,2,2]
[5,7,3,1,4,2,6,8]=>[6,4,3,1,5,7,2,8]=>[3,5,6,8,4,2,7,1]=>[4,1,2,1]
[6,3,7,4,8,1,2,5]=>[6,2,4,1,7,3,8,5]=>[3,7,5,8,2,6,1,4]=>[2,2,2,2]
[8,3,7,4,2,6,1,5]=>[5,2,4,7,8,6,3,1]=>[4,7,5,2,1,3,6,8]=>[2,1,1,4]
[1,8,3,2,4,5,7,6]=>[3,8,4,5,6,7,1,2]=>[6,1,5,4,3,2,8,7]=>[1,2,1,1,2,1]
[8,7,4,2,1,6,3,5]=>[4,7,3,8,5,6,2,1]=>[5,2,6,1,4,3,7,8]=>[1,2,2,3]
[8,3,5,2,7,4,1,6]=>[7,2,4,3,6,8,5,1]=>[2,7,5,6,3,1,4,8]=>[2,2,1,3]
[1,5,3,8,7,6,4,2]=>[8,2,7,6,3,5,1,4]=>[1,7,2,3,6,4,8,5]=>[2,3,2,1]
[7,2,4,8,1,3,6,5]=>[3,8,2,5,6,1,7,4]=>[6,1,7,4,3,8,2,5]=>[1,2,1,2,2]
[1,2,8,7,5,6,3,4]=>[7,5,8,6,4,1,2,3]=>[2,4,1,3,5,8,7,6]=>[2,4,1,1]
[3,1,8,6,7,5,2,4]=>[7,4,8,1,6,5,2,3]=>[2,5,1,8,3,4,7,6]=>[2,2,3,1]
[1,4,8,6,5,7,2,3]=>[7,5,2,4,8,6,1,3]=>[2,4,7,5,1,3,8,6]=>[3,1,3,1]
[1,6,5,4,8,2,3,7]=>[6,4,3,2,7,8,1,5]=>[3,5,6,7,2,1,8,4]=>[4,1,2,1]
[5,1,6,8,3,4,2,7]=>[5,3,1,7,6,8,2,4]=>[4,6,8,2,3,1,7,5]=>[3,2,2,1]
[6,2,5,1,7,4,3,8]=>[7,6,2,4,3,1,5,8]=>[2,3,7,5,6,8,4,1]=>[3,3,1,1]
[5,2,8,3,4,6,1,7]=>[4,5,1,7,2,6,8,3]=>[5,4,8,2,7,3,1,6]=>[1,2,2,1,2]
[6,2,8,4,3,1,7,5]=>[5,4,8,2,1,6,7,3]=>[4,5,1,7,8,3,2,6]=>[2,3,1,2]
[7,2,8,1,3,6,5,4]=>[8,7,2,4,5,1,6,3]=>[1,2,7,5,4,8,3,6]=>[3,1,2,2]
[7,3,8,1,4,6,2,5]=>[2,5,7,8,4,1,6,3]=>[7,4,2,1,5,8,3,6]=>[1,1,1,3,2]
[1,7,8,5,4,6,3,2]=>[5,4,2,8,7,6,1,3]=>[4,5,7,1,2,3,8,6]=>[3,4,1]
[1,5,8,4,6,3,7,2]=>[2,4,6,5,8,7,1,3]=>[7,5,3,4,1,2,8,6]=>[1,1,2,3,1]
[5,3,8,4,1,2,7,6]=>[8,2,1,5,4,6,7,3]=>[1,7,8,4,5,3,2,6]=>[3,2,1,2]
[5,8,4,3,6,2,1,7]=>[1,4,3,7,6,5,8,2]=>[8,5,6,2,3,4,1,7]=>[1,2,3,2]
[1,8,3,6,5,2,7,4]=>[8,6,3,5,4,7,1,2]=>[1,3,6,4,5,2,8,7]=>[3,2,2,1]
[1,8,2,4,7,6,5,3]=>[8,7,4,6,3,5,1,2]=>[1,2,5,3,6,4,8,7]=>[3,2,2,1]
[3,8,1,4,6,7,5,2]=>[5,8,1,4,7,3,6,2]=>[4,1,8,5,2,6,3,7]=>[1,2,1,2,2]
[3,8,2,5,1,7,6,4]=>[4,8,1,3,7,5,6,2]=>[5,1,8,6,2,4,3,7]=>[1,2,1,2,2]
[8,1,3,4,5,7,6,2]=>[8,3,4,5,7,2,6,1]=>[1,6,5,4,2,7,3,8]=>[2,1,1,2,2]
[6,1,5,2,4,7,8,3]=>[5,6,3,8,2,1,4,7]=>[4,3,6,1,7,8,5,2]=>[1,2,3,1,1]
[4,1,8,5,2,7,6,3]=>[1,4,8,7,5,6,2,3]=>[8,5,1,2,4,3,7,6]=>[1,1,3,2,1]
[3,6,1,5,7,2,8,4]=>[4,8,1,6,3,2,5,7]=>[5,1,8,3,6,7,4,2]=>[1,2,3,1,1]
[6,3,1,2,8,5,7,4]=>[2,6,8,7,3,1,4,5]=>[7,3,1,2,6,8,5,4]=>[1,1,4,1,1]
[4,1,8,2,3,7,5,6]=>[7,1,8,4,5,6,2,3]=>[2,8,1,5,4,3,7,6]=>[2,2,1,2,1]
[5,3,8,7,2,1,4,6]=>[6,2,1,5,7,8,4,3]=>[3,7,8,4,2,1,5,6]=>[3,1,1,3]
[6,7,3,5,1,4,8,2]=>[3,6,1,8,5,4,2,7]=>[6,3,8,1,4,5,7,2]=>[1,2,4,1]
[6,4,7,5,8,2,3,1]=>[6,2,1,4,3,8,7,5]=>[3,7,8,5,6,1,2,4]=>[3,2,3]
[5,7,8,4,2,6,3,1]=>[8,1,5,4,2,7,6,3]=>[1,8,4,5,7,2,3,6]=>[2,3,3]
[5,4,7,6,2,8,3,1]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[1,2,3,2]
[5,7,4,1,6,8,3,2]=>[1,5,3,8,7,4,2,6]=>[8,4,6,1,2,5,7,3]=>[1,2,4,1]
[6,8,4,5,7,1,3,2]=>[3,1,8,6,4,7,5,2]=>[6,8,1,3,5,2,4,7]=>[2,3,3]
[5,8,4,6,1,7,3,2]=>[1,3,8,7,5,4,6,2]=>[8,6,1,2,4,5,3,7]=>[1,1,4,2]
[5,6,1,4,7,8,3,2]=>[4,1,5,2,8,7,3,6]=>[5,8,4,7,1,2,6,3]=>[2,2,3,1]
[5,6,3,7,4,8,2,1]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[1,3,1,3]
[5,3,6,7,4,8,2,1]=>[3,1,5,2,4,8,7,6]=>[6,8,4,7,5,1,2,3]=>[2,2,1,3]
[5,3,2,8,6,7,4,1]=>[5,1,8,2,7,3,6,4]=>[4,8,1,7,2,6,3,5]=>[2,2,2,2]
[5,4,8,2,6,7,3,1]=>[2,1,5,8,4,7,6,3]=>[7,8,4,1,5,2,3,6]=>[2,1,2,3]
[5,4,8,6,2,7,3,1]=>[1,8,2,5,4,7,6,3]=>[8,1,7,4,5,2,3,6]=>[1,2,2,3]
[6,4,8,5,7,2,3,1]=>[6,2,1,4,8,7,5,3]=>[3,7,8,5,1,2,4,6]=>[3,1,4]
[7,4,8,5,6,2,1,3]=>[7,2,6,4,1,8,5,3]=>[2,7,3,5,8,1,4,6]=>[2,3,3]
[4,6,8,5,7,2,3,1]=>[2,6,1,4,8,7,5,3]=>[7,3,8,5,1,2,4,6]=>[1,2,1,4]
[5,6,8,2,4,7,3,1]=>[1,5,2,8,4,7,6,3]=>[8,4,7,1,5,2,3,6]=>[1,2,2,3]
[5,6,3,8,4,7,2,1]=>[1,5,2,8,3,7,6,4]=>[8,4,7,1,6,2,3,5]=>[1,2,2,3]
[4,6,3,5,8,7,2,1]=>[8,1,3,2,4,7,6,5]=>[1,8,6,7,5,2,3,4]=>[2,2,1,3]
[4,6,3,2,8,7,5,1]=>[8,1,3,2,7,4,6,5]=>[1,8,6,7,2,5,3,4]=>[2,2,2,2]
[5,6,3,8,2,7,4,1]=>[1,8,3,2,5,7,6,4]=>[8,1,6,7,4,2,3,5]=>[1,3,1,3]
[3,6,5,8,7,2,4,1]=>[3,2,6,8,1,7,5,4]=>[6,7,3,1,8,2,4,5]=>[2,1,2,3]
[5,3,6,8,2,7,4,1]=>[3,1,8,2,5,7,6,4]=>[6,8,1,7,4,2,3,5]=>[2,2,1,3]
[4,3,7,2,8,6,5,1]=>[8,1,7,2,4,3,6,5]=>[1,8,2,7,5,6,3,4]=>[2,2,2,2]
[5,4,7,2,6,8,3,1]=>[2,1,5,8,4,3,7,6]=>[7,8,4,1,5,6,2,3]=>[2,1,3,2]
[5,3,2,7,6,8,4,1]=>[5,2,1,4,8,3,7,6]=>[4,7,8,5,1,6,2,3]=>[3,1,2,2]
[6,7,3,8,5,2,4,1]=>[6,1,8,3,2,7,5,4]=>[3,8,1,6,7,2,4,5]=>[2,3,3]
[6,4,7,2,5,3,8,1]=>[2,6,4,1,5,3,8,7]=>[7,3,5,8,4,6,1,2]=>[1,3,2,2]
[6,3,7,8,4,2,5,1]=>[6,5,2,1,3,8,7,4]=>[3,4,7,8,6,1,2,5]=>[4,1,3]
[3,5,7,8,4,6,2,1]=>[5,2,3,8,1,7,6,4]=>[4,7,6,1,8,2,3,5]=>[2,1,2,3]
[5,3,7,8,4,6,2,1]=>[1,5,3,8,2,7,6,4]=>[8,4,6,1,7,2,3,5]=>[1,2,2,3]
[5,7,8,2,4,6,3,1]=>[1,5,8,4,2,7,6,3]=>[8,4,1,5,7,2,3,6]=>[1,1,3,3]
[2,5,8,4,3,7,6,1]=>[2,4,8,5,7,1,6,3]=>[7,5,1,4,2,8,3,6]=>[1,1,2,2,2]
[3,7,4,8,6,2,1,5]=>[7,3,6,1,2,8,5,4]=>[2,6,3,8,7,1,4,5]=>[2,2,1,3]
[3,6,4,8,7,2,5,1]=>[6,2,8,1,3,7,5,4]=>[3,7,1,8,6,2,4,5]=>[2,2,1,3]
[3,5,4,8,2,7,6,1]=>[2,8,1,3,5,7,6,4]=>[7,1,8,6,4,2,3,5]=>[1,2,1,1,3]
[4,3,7,5,8,6,2,1]=>[8,1,4,2,3,7,6,5]=>[1,8,5,7,6,2,3,4]=>[2,2,1,3]
[4,5,7,3,8,6,2,1]=>[8,1,2,4,3,7,6,5]=>[1,8,7,5,6,2,3,4]=>[2,1,2,3]
[3,5,6,8,4,7,2,1]=>[2,3,5,8,1,7,6,4]=>[7,6,4,1,8,2,3,5]=>[1,1,1,2,3]
[6,3,1,8,7,5,4,2]=>[8,7,2,1,6,5,3,4]=>[1,2,7,8,3,4,6,5]=>[4,3,1]
[5,4,8,1,7,6,3,2]=>[1,8,2,7,6,4,5,3]=>[8,1,7,2,3,5,4,6]=>[1,2,3,2]
[5,8,4,1,7,6,3,2]=>[1,3,8,7,6,4,5,2]=>[8,6,1,2,3,5,4,7]=>[1,1,4,2]
[7,5,4,1,8,6,3,2]=>[3,2,8,7,6,4,1,5]=>[6,7,1,2,3,5,8,4]=>[2,5,1]
[1,8,2,5,6,3,4,7]=>[6,4,7,3,5,8,1,2]=>[3,5,2,6,4,1,8,7]=>[2,2,1,2,1]
[7,2,8,4,5,1,3,6]=>[6,4,7,2,5,1,8,3]=>[3,5,2,7,4,8,1,6]=>[2,2,2,2]
[1,3,7,5,6,2,4,8]=>[6,4,7,2,5,1,3,8]=>[3,5,2,7,4,8,6,1]=>[2,2,2,1,1]
[1,8,5,2,3,7,4,6]=>[7,8,4,3,5,6,1,2]=>[2,1,5,6,4,3,8,7]=>[1,3,1,2,1]
[7,5,8,3,2,1,6,4]=>[5,4,2,8,6,1,7,3]=>[4,5,7,1,3,8,2,6]=>[3,3,2]
[7,5,8,1,2,6,3,4]=>[7,8,4,2,5,1,6,3]=>[2,1,5,7,4,8,3,6]=>[1,3,2,2]
[1,5,4,6,2,3,7,8]=>[5,3,2,6,1,4,7,8]=>[4,6,7,3,8,5,2,1]=>[3,2,1,1,1]
[6,5,4,3,8,1,7,2]=>[4,3,2,1,8,6,7,5]=>[5,6,7,8,1,3,2,4]=>[4,2,2]
[7,3,6,8,5,2,4,1]=>[6,3,8,2,1,7,5,4]=>[3,6,1,7,8,2,4,5]=>[2,3,3]
[2,7,8,5,4,6,3,1]=>[5,4,2,8,7,1,6,3]=>[4,5,7,1,2,8,3,6]=>[3,3,2]
[6,1,2,8,3,7,4,5]=>[7,8,5,6,2,1,3,4]=>[2,1,4,3,7,8,6,5]=>[1,2,3,1,1]
[2,6,5,7,3,8,1,4]=>[5,3,2,7,1,4,8,6]=>[4,6,7,2,8,5,1,3]=>[3,2,1,2]
[1,3,2,7,8,5,6,4]=>[6,4,8,2,7,1,3,5]=>[3,5,1,7,2,8,6,4]=>[2,2,2,1,1]
[6,5,2,1,8,7,3,4]=>[7,8,3,2,1,6,4,5]=>[2,1,6,7,8,3,5,4]=>[1,4,2,1]
[2,6,5,3,7,8,4,1]=>[5,3,2,8,1,4,7,6]=>[4,6,7,1,8,5,2,3]=>[3,2,1,2]
[6,5,2,3,8,7,1,4]=>[7,8,3,2,1,4,6,5]=>[2,1,6,7,8,5,3,4]=>[1,4,1,2]
[5,4,1,2,3,8,6,7]=>[7,8,3,2,1,4,5,6]=>[2,1,6,7,8,5,4,3]=>[1,4,1,1,1]
[5,1,4,2,3,7,8,6]=>[6,3,8,2,1,4,5,7]=>[3,6,1,7,8,5,4,2]=>[2,3,1,1,1]
[1,5,4,2,6,3,8,7]=>[5,3,2,8,1,4,6,7]=>[4,6,7,1,8,5,3,2]=>[3,2,1,1,1]
[5,1,6,3,8,2,7,4]=>[8,4,3,1,6,7,2,5]=>[1,5,6,8,3,2,7,4]=>[4,1,2,1]
[9,8,7,6,5,4,3,1,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>[3,2,4,5,6,7,8,9,10,1]=>[1,8,1]
[8,7,6,5,4,2,1,3,9]=>[7,6,8,5,4,3,2,1,9]=>[3,4,2,5,6,7,8,9,1]=>[2,6,1]
[8,7,6,5,4,1,3,2,9]=>[8,6,7,5,4,3,2,1,9]=>[2,4,3,5,6,7,8,9,1]=>[2,6,1]
[1,9,8,7,6,5,3,2,4]=>[8,7,9,6,5,4,3,1,2]=>[2,3,1,4,5,6,7,9,8]=>[2,6,1]
[1,8,7,6,2,5,4,3]=>[8,7,5,6,4,3,1,2]=>[1,2,4,3,5,6,8,7]=>[3,4,1]
[1,9,8,7,6,5,2,4,3]=>[9,7,8,6,5,4,3,1,2]=>[1,3,2,4,5,6,7,9,8]=>[2,6,1]
[1,10,9,8,7,6,5,4,2,3]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,10,9]=>[1,8,1]
[2,1,9,8,7,6,5,4,3]=>[9,8,7,6,5,1,4,2,3]=>[1,2,3,4,5,9,6,8,7]=>[6,2,1]
[1,2,9,8,7,6,5,4,3]=>[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>[7,1,1]
[3,2,1,9,8,7,6,5,4]=>[9,8,7,1,6,2,5,3,4]=>[1,2,3,9,4,8,5,7,6]=>[4,2,2,1]
[1,2,3,9,8,7,6,5,4]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>[6,1,1,1]
[4,3,2,1,9,8,7,6,5]=>[9,1,8,2,7,3,6,4,5]=>[1,9,2,8,3,7,4,6,5]=>[2,2,2,2,1]
[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[5,1,1,1,1]
[1,2,3,4,5,9,8,7,6]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[4,1,1,1,1,1]
[1,2,3,4,5,7,6,9,8]=>[6,9,1,2,3,4,5,7,8]=>[4,1,9,8,7,6,5,3,2]=>[1,2,1,1,1,1,1,1]
[1,2,10,9,8,7,6,5,4,3]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>[8,1,1]
[3,2,1,10,9,8,7,6,5,4]=>[10,9,8,7,1,6,2,5,3,4]=>[1,2,3,4,10,5,9,6,8,7]=>[5,2,2,1]
[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>[7,1,1,1]
[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>[6,1,1,1,1]
[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>[4,1,1,1,1,1,1]
[1,2,3,4,5,6,7,10,9,8]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,7,10,9]=>[7,10,1,2,3,4,5,6,8,9]=>[4,1,10,9,8,7,6,5,3,2]=>[1,2,1,1,1,1,1,1,1]
[5,2,7,4,1,6,3,8]=>[7,5,2,1,4,6,3,8]=>[2,4,7,8,5,3,6,1]=>[4,1,2,1]
[4,7,3,1,5,6,2,8]=>[1,5,3,7,4,6,2,8]=>[8,4,6,2,5,3,7,1]=>[1,2,2,2,1]
[1,5,8,4,2,6,7,3]=>[2,6,4,8,5,7,1,3]=>[7,3,5,1,4,2,8,6]=>[1,2,2,2,1]
[1,6,3,8,5,2,7,4]=>[8,6,3,2,5,7,1,4]=>[1,3,6,7,4,2,8,5]=>[4,1,2,1]
[5,2,3,7,1,6,4,8]=>[7,2,3,1,5,6,4,8]=>[2,7,6,8,4,3,5,1]=>[2,2,1,2,1]
[6,2,3,7,5,1,4,8]=>[6,7,2,3,1,5,4,8]=>[3,2,7,6,8,4,5,1]=>[1,2,2,2,1]
[1,7,3,4,8,6,2,5]=>[7,8,3,4,2,6,1,5]=>[2,1,6,5,7,3,8,4]=>[1,2,2,2,1]
[6,2,3,4,8,1,7,5]=>[8,2,3,4,1,6,7,5]=>[1,7,6,5,8,3,2,4]=>[2,1,2,1,2]
[8,7,3,2,1,6,5,4]=>[3,8,4,7,5,6,2,1]=>[6,1,5,2,4,3,7,8]=>[1,2,2,3]
[8,7,6,3,1,5,2,4]=>[7,4,8,5,6,3,2,1]=>[2,5,1,4,3,6,7,8]=>[2,2,4]
[8,5,1,7,2,3,4,6]=>[5,6,7,2,8,3,4,1]=>[4,3,2,7,1,6,5,8]=>[1,1,2,2,2]
[9,8,7,6,5,2,1,4,3]=>[6,9,7,8,5,4,3,2,1]=>[4,1,3,2,5,6,7,8,9]=>[1,2,6]
[9,8,7,3,2,1,6,5,4]=>[4,9,5,8,6,7,3,2,1]=>[6,1,5,2,4,3,7,8,9]=>[1,2,2,4]
[9,8,7,6,3,1,5,2,4]=>[8,5,9,6,7,4,3,2,1]=>[2,5,1,4,3,6,7,8,9]=>[2,2,5]
[9,4,3,2,1,8,7,6,5]=>[2,9,3,8,4,7,5,6,1]=>[8,1,7,2,6,3,5,4,9]=>[1,2,2,2,2]
[9,8,7,4,1,6,2,3,5]=>[7,8,4,9,5,6,3,2,1]=>[3,2,6,1,5,4,7,8,9]=>[1,2,2,4]
[10,9,8,7,6,5,2,1,4,3]=>[7,10,8,9,6,5,4,3,2,1]=>[4,1,3,2,5,6,7,8,9,10]=>[1,2,7]
[10,9,8,7,3,2,1,6,5,4]=>[5,10,6,9,7,8,4,3,2,1]=>[6,1,5,2,4,3,7,8,9,10]=>[1,2,2,5]
[10,9,8,7,6,3,1,5,2,4]=>[9,6,10,7,8,5,4,3,2,1]=>[2,5,1,4,3,6,7,8,9,10]=>[2,2,6]
[10,9,4,3,2,1,8,7,6,5]=>[3,10,4,9,5,8,6,7,2,1]=>[8,1,7,2,6,3,5,4,9,10]=>[1,2,2,2,3]
[10,9,8,7,4,1,6,2,3,5]=>[8,9,5,10,6,7,4,3,2,1]=>[3,2,6,1,5,4,7,8,9,10]=>[1,2,2,5]
[2,4,8,5,3,7,1,6]=>[5,2,4,7,8,1,6,3]=>[4,7,5,2,1,8,3,6]=>[2,1,1,2,2]
[2,4,1,8,5,3,7,6]=>[2,5,8,1,6,7,3,4]=>[7,4,1,8,3,2,6,5]=>[1,1,2,1,2,1]
[2,4,8,6,3,1,7,5]=>[5,8,2,6,1,4,7,3]=>[4,1,7,3,8,5,2,6]=>[1,2,2,1,2]
[3,4,6,8,2,1,7,5]=>[5,1,2,3,8,6,7,4]=>[4,8,7,6,1,3,2,5]=>[2,1,1,2,2]
[3,4,1,5,8,2,7,6]=>[1,2,8,4,6,7,3,5]=>[8,7,1,5,3,2,6,4]=>[1,1,2,1,2,1]
[3,5,6,2,1,7,8,4]=>[4,1,2,6,3,8,5,7]=>[5,8,7,3,6,1,4,2]=>[2,1,2,2,1]
[3,4,6,2,7,8,1,5]=>[7,1,2,4,3,5,8,6]=>[2,8,7,5,6,4,1,3]=>[2,1,2,1,2]
[8,1,4,6,3,7,2,5]=>[3,5,7,4,8,2,6,1]=>[6,4,2,5,1,7,3,8]=>[1,1,2,2,2]
[8,1,4,6,3,7,5,2]=>[8,3,5,4,7,2,6,1]=>[1,6,4,5,2,7,3,8]=>[2,2,2,2]
[3,5,6,2,1,7,4,8]=>[4,1,2,7,5,3,6,8]=>[5,8,7,2,4,6,3,1]=>[2,1,3,1,1]
[8,1,5,6,7,3,4,2]=>[3,6,4,8,7,2,5,1]=>[6,3,5,1,2,7,4,8]=>[1,2,3,2]
[8,1,5,6,7,3,2,4]=>[3,7,6,4,8,2,5,1]=>[6,2,3,5,1,7,4,8]=>[1,3,2,2]
[3,4,1,6,8,7,2,5]=>[1,2,4,7,8,6,3,5]=>[8,7,5,2,1,3,6,4]=>[1,1,1,1,3,1]
[8,1,3,2,6,7,5,4]=>[5,8,3,7,2,4,6,1]=>[4,1,6,2,7,5,3,8]=>[1,2,2,1,2]
[2,3,8,6,7,1,5,4]=>[8,6,4,7,1,2,5,3]=>[1,3,5,2,8,7,4,6]=>[3,2,1,2]
[2,4,1,8,6,7,5,3]=>[5,8,2,7,1,6,3,4]=>[4,1,7,2,8,3,6,5]=>[1,2,2,2,1]
[2,5,8,6,1,7,4,3]=>[8,2,7,5,1,4,6,3]=>[1,7,2,4,8,5,3,6]=>[2,3,1,2]
[3,5,6,1,8,7,4,2]=>[2,3,8,1,7,6,4,5]=>[7,6,1,8,2,3,5,4]=>[1,1,2,3,1]
[3,4,1,6,8,7,5,2]=>[8,1,2,4,7,6,3,5]=>[1,8,7,5,2,3,6,4]=>[2,1,1,3,1]
[8,1,4,6,2,7,5,3]=>[8,3,7,5,2,4,6,1]=>[1,6,2,4,7,5,3,8]=>[2,3,1,2]
[3,5,1,6,7,8,4,2]=>[4,1,2,5,8,7,3,6]=>[5,8,7,4,1,2,6,3]=>[2,1,1,3,1]
[3,5,1,6,7,4,8,2]=>[4,1,2,6,5,8,3,7]=>[5,8,7,3,4,1,6,2]=>[2,1,2,2,1]
[8,1,5,6,7,4,2,3]=>[3,7,4,8,6,2,5,1]=>[6,2,5,1,3,7,4,8]=>[1,2,3,2]
[4,5,6,1,7,3,2,8]=>[1,2,7,6,4,3,5,8]=>[8,7,2,3,5,6,4,1]=>[1,1,4,1,1]
[6,5,8,7,4,3,1,2]=>[2,1,7,8,6,5,4,3]=>[7,8,2,1,3,4,5,6]=>[2,1,5]
[6,4,2,7,8,5,1,3]=>[2,7,4,1,8,3,6,5]=>[7,2,5,8,1,6,3,4]=>[1,3,2,2]
[6,1,4,8,7,5,2,3]=>[7,8,3,1,6,5,2,4]=>[2,1,6,8,3,4,7,5]=>[1,3,3,1]
[1,6,4,8,7,5,2,3]=>[7,2,8,3,6,5,1,4]=>[2,7,1,6,3,4,8,5]=>[2,2,3,1]
[1,8,6,2,4,7,3,5]=>[5,7,8,4,3,6,1,2]=>[4,2,1,5,6,3,8,7]=>[1,1,3,2,1]
[8,1,6,2,4,7,3,5]=>[5,7,8,4,2,3,6,1]=>[4,2,1,5,7,6,3,8]=>[1,1,3,1,2]
[7,6,2,1,4,8,3,5]=>[3,5,7,8,4,2,1,6]=>[6,4,2,1,5,7,8,3]=>[1,1,1,4,1]
[6,4,1,7,8,5,2,3]=>[2,7,4,1,8,6,3,5]=>[7,2,5,8,1,3,6,4]=>[1,3,3,1]
[7,6,1,2,4,8,3,5]=>[5,7,8,3,4,2,1,6]=>[4,2,1,6,5,7,8,3]=>[1,1,2,3,1]
[7,6,1,3,4,8,2,5]=>[4,5,7,8,3,2,1,6]=>[5,4,2,1,6,7,8,3]=>[1,1,1,4,1]
[8,1,6,3,4,7,2,5]=>[4,5,7,3,8,2,6,1]=>[5,4,2,6,1,7,3,8]=>[1,1,2,2,2]
[1,8,6,3,4,7,2,5]=>[4,5,7,3,8,6,1,2]=>[5,4,2,6,1,3,8,7]=>[1,1,2,3,1]
[1,7,2,5,4,8,3,6]=>[5,4,7,8,3,1,2,6]=>[4,5,2,1,6,8,7,3]=>[2,1,3,1,1]
[2,7,1,5,4,8,3,6]=>[5,4,7,8,1,3,2,6]=>[4,5,2,1,8,6,7,3]=>[2,1,2,2,1]
[2,8,6,3,4,7,1,5]=>[4,5,7,3,8,1,6,2]=>[5,4,2,6,1,8,3,7]=>[1,1,2,2,2]
[2,8,6,1,4,7,3,5]=>[5,7,8,4,1,3,6,2]=>[4,2,1,5,8,6,3,7]=>[1,1,3,1,2]
[1,2,7,5,4,8,3,6]=>[5,4,7,3,8,1,2,6]=>[4,5,2,6,1,8,7,3]=>[2,2,2,1,1]
[2,5,8,4,7,3,1,6]=>[2,4,7,6,8,1,5,3]=>[7,5,2,3,1,8,4,6]=>[1,1,2,2,2]
[6,8,3,2,4,7,1,5]=>[4,3,5,1,7,8,6,2]=>[5,6,4,8,2,1,3,7]=>[2,2,1,3]
[3,7,2,5,4,8,1,6]=>[5,1,3,4,7,2,8,6]=>[4,8,6,5,2,7,1,3]=>[2,1,1,2,2]
[3,1,7,5,4,8,2,6]=>[5,1,4,7,3,8,2,6]=>[4,8,5,2,6,1,7,3]=>[2,1,2,2,1]
[1,3,7,5,4,8,2,6]=>[5,4,7,2,3,8,1,6]=>[4,5,2,7,6,1,8,3]=>[2,2,1,2,1]
[1,5,8,4,7,3,2,6]=>[2,4,7,6,8,5,1,3]=>[7,5,2,3,1,4,8,6]=>[1,1,2,3,1]
[5,1,8,4,7,3,2,6]=>[4,1,7,6,8,5,2,3]=>[5,8,2,3,1,4,7,6]=>[2,2,3,1]
[5,8,2,4,7,3,1,6]=>[4,1,7,3,6,8,5,2]=>[5,8,2,6,3,1,4,7]=>[2,2,1,3]
[6,8,4,3,7,5,1,2]=>[4,3,1,7,8,6,5,2]=>[5,6,8,2,1,3,4,7]=>[3,1,4]
[8,7,5,6,2,1,4,3]=>[5,8,6,3,7,4,2,1]=>[4,1,3,6,2,5,7,8]=>[1,3,4]
[8,5,2,4,7,3,1,6]=>[4,7,3,2,6,8,5,1]=>[5,2,6,7,3,1,4,8]=>[1,3,1,3]
[8,1,5,4,7,3,2,6]=>[4,3,7,6,8,2,5,1]=>[5,6,2,3,1,7,4,8]=>[2,2,2,2]
[1,8,5,4,7,3,2,6]=>[4,3,7,6,8,5,1,2]=>[5,6,2,3,1,4,8,7]=>[2,2,3,1]
[1,7,3,5,4,8,2,6]=>[5,3,4,7,2,8,1,6]=>[4,6,5,2,7,1,8,3]=>[2,1,2,2,1]
[8,6,3,1,4,7,2,5]=>[5,3,7,8,4,2,6,1]=>[4,6,2,1,5,7,3,8]=>[2,1,3,2]
[8,6,4,2,7,5,1,3]=>[7,3,8,4,2,6,5,1]=>[2,6,1,5,7,3,4,8]=>[2,3,3]
[8,6,4,1,7,2,5,3]=>[8,6,3,7,4,2,5,1]=>[1,3,6,2,5,7,4,8]=>[3,3,2]
[5,3,7,4,6,8,2,1]=>[4,1,5,2,3,8,7,6]=>[5,8,4,7,6,1,2,3]=>[2,2,1,3]
[4,1,3,2,7,8,5,6]=>[7,3,1,5,8,2,4,6]=>[2,6,8,4,1,7,5,3]=>[3,1,2,1,1]
[1,4,3,2,7,8,5,6]=>[2,7,3,5,8,1,4,6]=>[7,2,6,4,1,8,5,3]=>[1,2,1,2,1,1]
[2,4,3,1,7,8,5,6]=>[2,7,1,3,5,8,4,6]=>[7,2,8,6,4,1,5,3]=>[1,2,1,1,2,1]
[2,7,3,5,4,8,1,6]=>[5,3,4,7,1,2,8,6]=>[4,6,5,2,8,7,1,3]=>[2,1,2,1,2]
[2,8,5,4,7,3,1,6]=>[4,3,7,6,8,1,5,2]=>[5,6,2,3,1,8,4,7]=>[2,2,2,2]
[5,7,3,4,6,8,2,1]=>[3,1,4,5,2,8,7,6]=>[6,8,5,4,7,1,2,3]=>[2,1,2,3]
[8,2,5,4,7,3,1,6]=>[4,3,7,2,6,8,5,1]=>[5,6,2,7,3,1,4,8]=>[2,2,1,3]
[7,2,3,5,4,8,1,6]=>[5,2,3,4,7,1,8,6]=>[4,7,6,5,2,8,1,3]=>[2,1,1,2,2]
[3,2,1,4,7,8,5,6]=>[1,7,2,5,8,3,4,6]=>[8,2,7,4,1,6,5,3]=>[1,2,1,2,1,1]
[8,1,7,6,4,3,5,2]=>[6,5,8,7,4,2,3,1]=>[3,4,1,2,5,7,6,8]=>[2,4,2]
[8,6,4,5,2,7,1,3]=>[5,3,7,4,2,8,6,1]=>[4,6,2,5,7,1,3,8]=>[2,3,3]
[7,1,8,6,4,3,5,2]=>[6,5,8,7,4,2,1,3]=>[3,4,1,2,5,7,8,6]=>[2,5,1]
[7,4,2,5,1,6,3,8]=>[7,3,2,5,4,6,1,8]=>[2,6,7,4,5,3,8,1]=>[3,2,2,1]
[7,3,6,5,2,1,8,4]=>[5,8,2,6,4,3,1,7]=>[4,1,7,3,5,6,8,2]=>[1,2,4,1]
[7,5,8,6,4,2,1,3]=>[2,7,6,1,8,5,4,3]=>[7,2,3,8,1,4,5,6]=>[1,3,4]
[5,4,2,8,1,3,7,6]=>[8,3,2,1,5,6,7,4]=>[1,6,7,8,4,3,2,5]=>[4,1,1,2]
[5,8,2,6,4,1,3,7]=>[6,1,7,3,5,4,8,2]=>[3,8,2,6,4,5,1,7]=>[2,2,2,2]
[6,4,2,5,1,8,3,7]=>[7,3,2,4,1,8,5,6]=>[2,6,7,5,8,1,4,3]=>[3,2,2,1]
[2,5,8,6,3,1,4,7]=>[2,6,5,7,1,4,8,3]=>[7,3,4,2,8,5,1,6]=>[1,2,2,1,2]
[2,3,5,8,1,4,7,6]=>[3,8,1,2,5,6,7,4]=>[6,1,8,7,4,3,2,5]=>[1,2,1,1,1,2]
[2,3,6,8,1,5,7,4]=>[6,3,8,1,2,5,7,4]=>[3,6,1,8,7,4,2,5]=>[2,2,1,1,2]
[6,3,7,5,2,1,4,8]=>[6,2,5,1,7,4,3,8]=>[3,7,4,8,2,5,6,1]=>[2,2,3,1]
[2,5,7,6,3,1,4,8]=>[2,6,5,7,1,4,3,8]=>[7,3,4,2,8,5,6,1]=>[1,2,2,2,1]
[2,8,7,6,3,1,5,4]=>[5,8,6,7,4,1,3,2]=>[4,1,3,2,5,8,6,7]=>[1,2,3,2]
[2,5,8,7,6,3,1,4]=>[7,2,6,8,5,1,4,3]=>[2,7,3,1,4,8,5,6]=>[2,1,3,2]
[2,4,8,1,6,5,7,3]=>[6,2,5,8,1,4,7,3]=>[3,7,4,1,8,5,2,6]=>[2,1,2,1,2]
[2,8,7,3,6,1,4,5]=>[4,6,7,8,5,1,3,2]=>[5,3,2,1,4,8,6,7]=>[1,1,1,3,2]
[7,3,5,2,1,4,6,8]=>[2,5,4,6,3,7,1,8]=>[7,4,5,3,6,2,8,1]=>[1,2,2,2,1]
[8,4,2,5,1,3,7,6]=>[8,3,2,5,4,6,7,1]=>[1,6,7,4,5,3,2,8]=>[3,2,1,2]
[2,3,6,8,1,4,7,5]=>[8,5,1,2,3,6,7,4]=>[1,4,8,7,6,3,2,5]=>[3,1,1,1,2]
[2,7,8,6,3,1,4,5]=>[6,5,7,2,8,1,4,3]=>[3,4,2,7,1,8,5,6]=>[2,2,2,2]
[2,3,6,1,8,4,7,5]=>[8,6,1,2,3,7,4,5]=>[1,3,8,7,6,2,5,4]=>[3,1,1,2,1]
[2,8,6,3,1,4,5,7]=>[5,4,6,7,1,3,8,2]=>[4,5,3,2,8,6,1,7]=>[2,1,2,1,2]
[8,3,5,2,1,4,6,7]=>[2,5,4,6,3,7,8,1]=>[7,4,5,3,6,2,1,8]=>[1,2,2,1,2]
[2,4,8,1,3,7,5,6]=>[2,7,8,1,4,5,6,3]=>[7,2,1,8,5,4,3,6]=>[1,1,2,1,1,2]
[2,5,8,1,7,3,6,4]=>[2,8,6,7,1,4,5,3]=>[7,1,3,2,8,5,4,6]=>[1,2,2,1,2]
[3,8,6,1,4,7,5,2]=>[8,5,7,1,4,3,6,2]=>[1,4,2,8,5,6,3,7]=>[2,2,2,2]
[2,6,8,1,5,7,3,4]=>[7,5,2,8,1,4,6,3]=>[2,4,7,1,8,5,3,6]=>[3,2,1,2]
[2,7,1,5,8,3,4,6]=>[6,4,7,8,1,3,2,5]=>[3,5,2,1,8,6,7,4]=>[2,1,2,2,1]
[2,7,1,6,3,8,4,5]=>[7,8,5,1,3,4,2,6]=>[2,1,4,8,6,5,7,3]=>[1,3,1,2,1]
[4,7,6,1,8,5,2,3]=>[7,8,1,6,4,3,2,5]=>[2,1,8,3,5,6,7,4]=>[1,2,4,1]
[3,7,5,8,1,2,6,4]=>[8,5,1,3,6,2,7,4]=>[1,4,8,6,3,7,2,5]=>[3,1,2,2]
[7,3,6,1,2,8,4,5]=>[2,7,8,4,5,3,1,6]=>[7,2,1,5,4,6,8,3]=>[1,1,2,3,1]
[7,4,8,1,6,5,2,3]=>[2,7,8,6,4,1,5,3]=>[7,2,1,3,5,8,4,6]=>[1,1,4,2]
[7,4,6,1,8,2,5,3]=>[2,8,6,7,4,3,1,5]=>[7,1,3,2,5,6,8,4]=>[1,2,4,1]
[7,4,5,8,6,1,2,3]=>[2,6,3,7,1,8,5,4]=>[7,3,6,2,8,1,4,5]=>[1,2,2,3]
[4,6,8,5,1,7,2,3]=>[7,1,2,8,5,4,6,3]=>[2,8,7,1,4,5,3,6]=>[2,1,3,2]
[5,1,7,6,2,3,8,4]=>[8,5,1,6,4,2,3,7]=>[1,4,8,3,5,7,6,2]=>[3,3,1,1]
[5,1,7,6,2,8,3,4]=>[7,1,8,5,4,2,3,6]=>[2,8,1,4,5,7,6,3]=>[2,4,1,1]
[5,1,8,7,6,2,3,4]=>[6,1,7,8,5,4,2,3]=>[3,8,2,1,4,5,7,6]=>[2,1,4,1]
[8,5,1,7,6,2,3,4]=>[6,7,2,8,5,3,4,1]=>[3,2,7,1,4,6,5,8]=>[1,2,3,2]
[8,5,1,6,2,7,3,4]=>[7,8,5,3,2,4,6,1]=>[2,1,4,6,7,5,3,8]=>[1,4,1,2]
[3,6,1,8,4,7,5,2]=>[8,5,1,2,7,6,3,4]=>[1,4,8,7,2,3,6,5]=>[3,1,3,1]
[4,6,1,8,7,5,2,3]=>[7,1,2,8,6,5,3,4]=>[2,8,7,1,3,4,6,5]=>[2,1,4,1]
[4,8,5,1,7,2,3,6]=>[1,6,7,3,8,4,5,2]=>[8,3,2,6,1,5,4,7]=>[1,1,2,2,2]
[4,5,1,8,7,2,3,6]=>[1,6,2,7,8,5,3,4]=>[8,3,7,2,1,4,6,5]=>[1,2,1,3,1]
[3,4,8,7,1,2,5,6]=>[1,2,5,6,7,8,4,3]=>[8,7,4,3,2,1,5,6]=>[1,1,1,1,1,3]
[8,6,4,7,1,2,5,3]=>[8,5,3,6,2,7,4,1]=>[1,4,6,3,7,2,5,8]=>[3,2,3]
[6,4,7,1,2,8,5,3]=>[2,8,7,4,1,5,3,6]=>[7,1,2,5,8,4,6,3]=>[1,4,2,1]
[6,5,1,2,7,3,8,4]=>[8,6,3,4,2,1,5,7]=>[1,3,6,5,7,8,4,2]=>[3,3,1,1]
[6,5,1,8,2,7,3,4]=>[7,8,5,2,1,6,3,4]=>[2,1,4,7,8,3,6,5]=>[1,4,2,1]
[8,6,5,1,2,7,3,4]=>[7,8,4,5,3,2,6,1]=>[2,1,5,4,6,7,3,8]=>[1,2,3,2]
[8,6,5,1,7,2,3,4]=>[6,7,8,4,3,2,5,1]=>[3,2,1,5,6,7,4,8]=>[1,1,4,2]
[6,5,1,8,7,2,3,4]=>[6,7,2,1,8,5,3,4]=>[3,2,7,8,1,4,6,5]=>[1,3,3,1]
[6,5,1,7,2,8,3,4]=>[7,8,5,3,2,1,4,6]=>[2,1,4,6,7,8,5,3]=>[1,5,1,1]
[6,5,1,7,2,3,8,4]=>[8,5,6,3,2,1,4,7]=>[1,4,3,6,7,8,5,2]=>[2,4,1,1]
[5,7,4,1,8,2,3,6]=>[6,1,7,3,8,4,2,5]=>[3,8,2,6,1,5,7,4]=>[2,2,3,1]
[6,8,5,7,4,1,2,3]=>[6,1,7,3,8,5,4,2]=>[3,8,2,6,1,4,5,7]=>[2,2,4]
[7,3,8,1,5,2,4,6]=>[2,6,7,4,5,1,8,3]=>[7,3,2,5,4,8,1,6]=>[1,1,2,2,2]
[1,8,4,2,3,6,7,5]=>[6,3,8,4,5,7,1,2]=>[3,6,1,5,4,2,8,7]=>[2,2,1,2,1]
[2,5,8,3,4,6,7,1]=>[4,2,5,6,8,1,7,3]=>[5,7,4,3,1,8,2,6]=>[2,1,1,2,2]
[4,1,7,2,3,6,8,5]=>[6,1,8,4,5,2,3,7]=>[3,8,1,5,4,7,6,2]=>[2,2,2,1,1]
[4,6,2,1,5,7,8,3]=>[3,1,5,6,2,8,4,7]=>[6,8,4,3,7,1,5,2]=>[2,1,2,2,1]
[4,5,2,3,1,7,8,6]=>[3,1,4,2,6,8,5,7]=>[6,8,5,7,3,1,4,2]=>[2,2,1,2,1]
[3,2,6,7,4,1,8,5]=>[5,1,3,8,2,6,4,7]=>[4,8,6,1,7,3,5,2]=>[2,1,2,2,1]
[5,6,2,7,1,4,8,3]=>[6,1,8,3,2,5,4,7]=>[3,8,1,6,7,4,5,2]=>[2,3,2,1]
[6,2,3,8,1,7,4,5]=>[7,8,2,3,1,5,6,4]=>[2,1,7,6,8,4,3,5]=>[1,2,2,1,2]
[4,6,2,7,5,1,3,8]=>[1,6,7,3,2,5,4,8]=>[8,3,2,6,7,4,5,1]=>[1,1,3,2,1]
[2,6,3,1,8,4,5,7]=>[3,6,7,1,2,8,4,5]=>[6,3,2,8,7,1,5,4]=>[1,1,2,1,2,1]
[5,4,2,3,7,8,6,1]=>[5,2,1,8,3,4,7,6]=>[4,7,8,1,6,5,2,3]=>[3,2,1,2]
[4,1,8,2,5,7,3,6]=>[5,1,7,8,4,6,2,3]=>[4,8,2,1,5,3,7,6]=>[2,1,2,2,1]
[3,1,8,4,7,2,5,6]=>[1,4,6,7,8,5,2,3]=>[8,5,3,2,1,4,7,6]=>[1,1,1,1,3,1]
[6,2,3,8,4,1,7,5]=>[5,8,2,3,1,6,7,4]=>[4,1,7,6,8,3,2,5]=>[1,2,2,1,2]
[2,6,4,1,5,3,8,7]=>[5,3,8,1,4,2,6,7]=>[4,6,1,8,5,7,3,2]=>[2,2,2,1,1]
[3,2,7,6,4,1,8,5]=>[5,8,1,6,2,4,3,7]=>[4,1,8,3,7,5,6,2]=>[1,2,2,2,1]
[2,5,4,1,7,6,8,3]=>[3,2,6,1,5,8,4,7]=>[6,7,3,8,4,1,5,2]=>[2,2,1,2,1]
[6,2,1,4,7,8,3,5]=>[7,2,4,5,1,8,3,6]=>[2,7,5,4,8,1,6,3]=>[2,1,2,2,1]
[2,6,5,1,7,8,3,4]=>[7,5,3,1,2,8,4,6]=>[2,4,6,8,7,1,5,3]=>[4,1,2,1]
[5,8,3,1,7,2,4,6]=>[6,3,1,7,8,4,5,2]=>[3,6,8,2,1,5,4,7]=>[3,1,2,2]
[6,8,3,1,5,2,4,7]=>[6,3,7,4,1,5,8,2]=>[3,6,2,5,8,4,1,7]=>[2,3,1,2]
[4,2,7,1,6,3,5,8]=>[6,1,7,2,4,5,3,8]=>[3,8,2,7,5,4,6,1]=>[2,2,1,2,1]
[5,1,7,4,2,6,3,8]=>[7,5,4,1,6,2,3,8]=>[2,4,5,8,3,7,6,1]=>[4,2,1,1]
[6,8,4,2,1,5,3,7]=>[4,7,5,3,1,6,8,2]=>[5,2,4,6,8,3,1,7]=>[1,4,1,2]
[6,8,5,2,1,7,3,4]=>[4,7,1,8,5,3,6,2]=>[5,2,8,1,4,6,3,7]=>[1,2,3,2]
[5,8,2,1,4,7,3,6]=>[3,5,1,7,8,4,6,2]=>[6,4,8,2,1,5,3,7]=>[1,2,1,2,2]
[6,8,3,2,5,1,7,4]=>[3,8,4,1,6,5,7,2]=>[6,1,5,8,3,4,2,7]=>[1,3,2,2]
[6,8,4,3,1,5,7,2]=>[6,4,3,1,8,5,7,2]=>[3,5,6,8,1,4,2,7]=>[4,2,2]
[6,8,4,2,1,5,7,3]=>[4,6,3,1,8,5,7,2]=>[5,3,6,8,1,4,2,7]=>[1,3,2,2]
[6,8,3,2,1,4,5,7]=>[5,4,3,6,1,7,8,2]=>[4,5,6,3,8,2,1,7]=>[3,2,1,2]
[5,1,7,3,2,4,6,8]=>[5,4,6,1,7,2,3,8]=>[4,5,3,8,2,7,6,1]=>[2,2,2,1,1]
[5,2,1,8,3,6,7,4]=>[6,8,2,1,5,7,3,4]=>[3,1,7,8,4,2,6,5]=>[1,3,1,2,1]
[4,3,8,1,6,2,7,5]=>[1,8,2,6,4,5,7,3]=>[8,1,7,3,5,4,2,6]=>[1,2,2,1,2]
[5,4,7,2,1,6,8,3]=>[4,2,1,6,8,5,3,7]=>[5,7,8,3,1,4,6,2]=>[3,1,3,1]
[5,2,1,7,3,4,8,6]=>[8,2,5,1,6,3,4,7]=>[1,7,4,8,3,6,5,2]=>[2,2,2,1,1]
[6,4,3,1,7,5,8,2]=>[3,2,6,5,1,8,4,7]=>[6,7,3,4,8,1,5,2]=>[2,3,2,1]
[5,3,1,7,2,6,8,4]=>[2,6,1,8,5,3,4,7]=>[7,3,8,1,4,6,5,2]=>[1,2,3,1,1]
[4,2,1,6,5,8,3,7]=>[5,2,1,4,7,8,3,6]=>[4,7,8,5,2,1,6,3]=>[3,1,1,2,1]
[4,2,1,8,5,7,3,6]=>[5,1,7,8,2,6,3,4]=>[4,8,2,1,7,3,6,5]=>[2,1,2,2,1]
[7,4,3,1,8,5,6,2]=>[3,2,6,8,7,4,1,5]=>[6,7,3,1,2,5,8,4]=>[2,1,4,1]
[7,4,2,1,8,5,6,3]=>[6,2,8,3,7,4,1,5]=>[3,7,1,6,2,5,8,4]=>[2,2,3,1]
[6,3,2,1,7,4,5,8]=>[3,2,6,7,4,1,5,8]=>[6,7,3,2,5,8,4,1]=>[2,1,3,1,1]
[6,4,2,1,7,5,3,8]=>[7,3,2,6,4,1,5,8]=>[2,6,7,3,5,8,4,1]=>[3,3,1,1]
[6,1,8,4,2,7,3,5]=>[7,4,8,5,1,6,2,3]=>[2,5,1,4,8,3,7,6]=>[2,3,2,1]
[6,2,1,8,3,7,4,5]=>[7,8,2,5,1,6,3,4]=>[2,1,7,4,8,3,6,5]=>[1,2,2,2,1]
[5,3,2,7,6,1,4,8]=>[2,6,1,7,3,5,4,8]=>[7,3,8,2,6,4,5,1]=>[1,2,2,2,1]
[5,3,2,8,6,1,4,7]=>[2,6,1,7,3,5,8,4]=>[7,3,8,2,6,4,1,5]=>[1,2,2,1,2]
[6,3,2,8,7,1,4,5]=>[2,6,7,1,8,3,5,4]=>[7,3,2,8,1,6,4,5]=>[1,1,2,2,2]
[4,2,8,1,7,3,5,6]=>[6,1,7,8,2,4,5,3]=>[3,8,2,1,7,5,4,6]=>[2,1,2,1,2]
[2,1,5,8,4,7,3,6]=>[3,5,7,8,1,6,2,4]=>[6,4,2,1,8,3,7,5]=>[1,1,1,2,2,1]
[4,3,2,5,8,1,6,7]=>[3,2,1,4,6,7,8,5]=>[6,7,8,5,3,2,1,4]=>[3,1,1,1,2]
[4,3,2,5,7,1,6,8]=>[3,2,1,4,6,7,5,8]=>[6,7,8,5,3,2,4,1]=>[3,1,1,2,1]
[4,3,1,6,2,7,5,8]=>[2,1,7,5,3,4,6,8]=>[7,8,2,4,6,5,3,1]=>[2,3,1,1,1]
[4,3,1,7,2,8,5,6]=>[2,1,7,8,5,3,4,6]=>[7,8,2,1,4,6,5,3]=>[2,1,3,1,1]
[5,4,1,7,2,8,6,3]=>[2,1,8,7,5,3,4,6]=>[7,8,1,2,4,6,5,3]=>[2,4,1,1]
[6,5,3,1,7,8,4,2]=>[3,5,2,1,8,7,4,6]=>[6,4,7,8,1,2,5,3]=>[1,3,3,1]
[6,4,2,1,7,8,3,5]=>[7,3,2,5,1,8,4,6]=>[2,6,7,4,8,1,5,3]=>[3,2,2,1]
[5,4,2,1,6,7,3,8]=>[3,5,2,1,7,4,6,8]=>[6,4,7,8,2,5,3,1]=>[1,3,2,1,1]
[5,3,2,1,6,7,4,8]=>[3,2,5,1,7,4,6,8]=>[6,7,4,8,2,5,3,1]=>[2,2,2,1,1]
[6,4,2,1,7,8,5,3]=>[5,2,8,3,1,7,4,6]=>[4,7,1,6,8,2,5,3]=>[2,3,2,1]
[5,3,2,6,8,1,7,4]=>[2,4,1,8,3,6,7,5]=>[7,5,8,1,6,3,2,4]=>[1,2,2,1,2]
[3,2,1,4,6,8,5,7]=>[2,1,5,7,8,3,4,6]=>[7,8,4,2,1,6,5,3]=>[2,1,1,2,1,1]
[5,3,2,1,6,7,8,4]=>[3,2,5,1,6,8,4,7]=>[6,7,4,8,3,1,5,2]=>[2,2,1,2,1]
[8,6,1,4,5,7,2,3]=>[4,7,5,8,3,2,6,1]=>[5,2,4,1,6,7,3,8]=>[1,2,3,2]
[3,8,6,4,5,7,1,2]=>[4,7,5,1,3,8,6,2]=>[5,2,4,8,6,1,3,7]=>[1,3,1,3]
[5,2,8,3,7,4,6,1]=>[6,1,8,4,7,2,5,3]=>[3,8,1,5,2,7,4,6]=>[2,2,2,2]
[6,2,8,5,4,7,3,1]=>[5,4,1,8,7,2,6,3]=>[4,5,8,1,2,7,3,6]=>[3,3,2]
[1,8,6,3,7,4,2,5]=>[7,4,6,3,8,5,1,2]=>[2,5,3,6,1,4,8,7]=>[2,2,3,1]
[1,8,6,5,7,2,3,4]=>[6,7,4,3,8,5,1,2]=>[3,2,5,6,1,4,8,7]=>[1,3,3,1]
[5,2,8,4,3,6,7,1]=>[5,4,1,6,8,2,7,3]=>[4,5,8,3,1,7,2,6]=>[3,1,2,2]
[5,4,2,8,3,6,1,7]=>[5,2,1,7,3,6,8,4]=>[4,7,8,2,6,3,1,5]=>[3,2,1,2]
[6,5,3,8,4,7,2,1]=>[5,2,1,8,3,7,6,4]=>[4,7,8,1,6,2,3,5]=>[3,2,3]
[5,2,8,4,3,7,1,6]=>[5,4,1,7,8,2,6,3]=>[4,5,8,2,1,7,3,6]=>[3,1,2,2]
[6,2,8,3,7,4,1,5]=>[7,4,6,1,8,2,5,3]=>[2,5,3,8,1,7,4,6]=>[2,2,2,2]
[5,4,2,7,3,1,8,6]=>[5,2,1,8,3,6,4,7]=>[4,7,8,1,6,3,5,2]=>[3,2,2,1]
[6,4,3,7,1,2,8,5]=>[3,2,8,5,1,6,4,7]=>[6,7,1,4,8,3,5,2]=>[2,3,2,1]
[6,4,3,8,1,2,7,5]=>[3,2,8,5,1,6,7,4]=>[6,7,1,4,8,3,2,5]=>[2,3,1,2]
[7,6,3,8,4,2,1,5]=>[7,3,6,5,2,1,8,4]=>[2,6,3,4,7,8,1,5]=>[2,4,2]
[7,2,8,5,1,6,3,4]=>[7,8,5,2,4,1,6,3]=>[2,1,4,7,5,8,3,6]=>[1,3,2,2]
[7,2,8,4,3,1,5,6]=>[6,5,2,4,7,1,8,3]=>[3,4,7,5,2,8,1,6]=>[3,1,2,2]
[7,5,3,8,4,2,6,1]=>[6,3,2,5,1,8,7,4]=>[3,6,7,4,8,1,2,5]=>[3,2,3]
[7,6,4,8,2,3,5,1]=>[5,3,6,2,1,8,7,4]=>[4,6,3,7,8,1,2,5]=>[2,3,3]
[7,6,8,1,2,5,3,4]=>[7,8,4,5,2,1,6,3]=>[2,1,5,4,7,8,3,6]=>[1,2,3,2]
[5,3,1,7,8,4,6,2]=>[6,2,1,4,8,7,3,5]=>[3,7,8,5,1,2,6,4]=>[3,1,3,1]
[5,3,2,7,8,4,6,1]=>[6,2,1,4,8,3,7,5]=>[3,7,8,5,1,6,2,4]=>[3,1,2,2]
[5,4,1,6,3,8,7,2]=>[4,2,1,8,5,7,3,6]=>[5,7,8,1,4,2,6,3]=>[3,2,2,1]
[6,5,1,7,8,2,3,4]=>[6,7,4,2,1,8,3,5]=>[3,2,5,7,8,1,6,4]=>[1,4,2,1]
[6,3,1,7,8,4,2,5]=>[7,2,6,4,1,8,3,5]=>[2,7,3,5,8,1,6,4]=>[2,3,2,1]
[5,4,1,7,3,8,2,6]=>[5,2,1,7,4,8,3,6]=>[4,7,8,2,5,1,6,3]=>[3,2,2,1]
[6,3,2,7,8,4,1,5]=>[7,2,6,3,1,4,8,5]=>[2,7,3,6,8,5,1,4]=>[2,3,1,2]
[6,1,5,4,3,2,8,7]=>[5,4,3,8,2,1,6,7]=>[4,5,6,1,7,8,3,2]=>[3,3,1,1]
[8,7,6,1,3,5,2,4]=>[5,7,8,4,6,3,2,1]=>[4,2,1,5,3,6,7,8]=>[1,1,2,4]
[8,1,6,5,7,3,4,2]=>[6,4,3,8,7,2,5,1]=>[3,5,6,1,2,7,4,8]=>[3,3,2]
[8,4,1,5,7,6,2,3]=>[4,2,7,8,6,3,5,1]=>[5,7,2,1,3,6,4,8]=>[2,1,3,2]
[7,8,6,2,5,3,1,4]=>[7,4,6,1,8,5,3,2]=>[2,5,3,8,1,4,6,7]=>[2,2,4]
[6,1,3,5,2,8,4,7]=>[7,3,4,8,2,1,5,6]=>[2,6,5,1,7,8,4,3]=>[2,1,3,1,1]
[8,1,3,7,4,2,5,6]=>[6,3,5,7,8,2,4,1]=>[3,6,4,2,1,7,5,8]=>[2,1,1,2,2]
[4,3,8,7,5,2,1,6]=>[7,1,6,2,5,8,4,3]=>[2,8,3,7,4,1,5,6]=>[2,2,1,3]
[6,7,1,8,5,3,4,2]=>[6,1,8,7,5,3,2,4]=>[3,8,1,2,4,6,7,5]=>[2,5,1]
[2,7,6,4,8,3,5,1]=>[4,6,3,2,8,1,7,5]=>[5,3,6,7,1,8,2,4]=>[1,3,2,2]
[6,5,2,7,1,4,8,3]=>[6,8,3,2,1,5,4,7]=>[3,1,6,7,8,4,5,2]=>[1,4,2,1]
[7,4,6,1,3,2,8,5]=>[5,2,8,4,6,3,1,7]=>[4,7,1,5,3,6,8,2]=>[2,2,3,1]
[7,5,2,1,3,8,4,6]=>[3,7,8,4,2,5,1,6]=>[6,2,1,5,7,4,8,3]=>[1,1,3,2,1]
[7,4,1,5,6,3,8,2]=>[4,2,6,5,8,3,1,7]=>[5,7,3,4,1,6,8,2]=>[2,2,3,1]
[3,4,7,5,6,1,8,2]=>[4,8,1,2,6,5,3,7]=>[5,1,8,7,3,4,6,2]=>[1,2,1,3,1]
[2,4,7,5,6,3,8,1]=>[4,6,2,5,1,3,8,7]=>[5,3,7,4,8,6,1,2]=>[1,2,2,1,2]
[5,4,1,7,6,2,8,3]=>[2,1,8,6,5,3,4,7]=>[7,8,1,3,4,6,5,2]=>[2,4,1,1]
[3,5,6,7,1,4,8,2]=>[2,6,1,3,8,5,4,7]=>[7,3,8,6,1,4,5,2]=>[1,2,1,3,1]
[5,7,2,1,6,3,8,4]=>[8,3,1,6,4,5,2,7]=>[1,6,8,3,5,4,7,2]=>[3,2,2,1]
[4,7,2,5,6,3,8,1]=>[1,4,6,3,5,2,8,7]=>[8,5,3,6,4,7,1,2]=>[1,1,2,2,2]
[8,6,2,5,7,1,4,3]=>[8,6,3,4,2,7,5,1]=>[1,3,6,5,7,2,4,8]=>[3,2,3]
[2,7,4,5,3,8,1,6]=>[3,5,4,7,1,2,8,6]=>[6,4,5,2,8,7,1,3]=>[1,2,2,1,2]
[6,8,7,1,3,2,5,4]=>[5,8,4,1,6,7,3,2]=>[4,1,5,8,3,2,6,7]=>[1,3,1,3]
[2,8,6,5,7,1,4,3]=>[8,6,4,3,7,1,5,2]=>[1,3,5,6,2,8,4,7]=>[4,2,2]
[1,8,5,6,2,4,7,3]=>[6,3,8,5,4,7,1,2]=>[3,6,1,4,5,2,8,7]=>[2,3,2,1]
[8,1,5,6,2,4,7,3]=>[6,3,8,5,2,4,7,1]=>[3,6,1,4,7,5,2,8]=>[2,3,1,2]
[6,4,8,1,3,2,7,5]=>[5,2,8,4,1,6,7,3]=>[4,7,1,5,8,3,2,6]=>[2,3,1,2]
[1,4,5,2,8,6,7,3]=>[2,3,6,8,7,1,4,5]=>[7,6,3,1,2,8,5,4]=>[1,1,1,3,1,1]
[2,3,1,7,8,6,4,5]=>[7,4,8,1,2,6,3,5]=>[2,5,1,8,7,3,6,4]=>[2,2,1,2,1]
[3,5,7,6,2,8,1,4]=>[2,5,7,1,4,3,8,6]=>[7,4,2,8,5,6,1,3]=>[1,1,2,2,2]
[4,5,6,1,2,8,7,3]=>[1,2,8,7,4,3,5,6]=>[8,7,1,2,5,6,4,3]=>[1,1,4,1,1]
[5,4,1,2,8,6,7,3]=>[6,2,1,8,7,3,4,5]=>[3,7,8,1,2,6,5,4]=>[3,3,1,1]
[8,4,5,2,1,6,7,3]=>[4,2,6,3,8,5,7,1]=>[5,7,3,6,1,4,2,8]=>[2,2,2,2]
[3,1,2,6,8,4,7,5]=>[1,4,8,6,7,2,3,5]=>[8,5,1,3,2,7,6,4]=>[1,1,2,2,1,1]
[5,1,3,2,7,8,4,6]=>[7,3,5,1,8,2,4,6]=>[2,6,4,8,1,7,5,3]=>[2,2,2,1,1]
[1,5,4,2,7,8,3,6]=>[3,2,7,5,8,1,4,6]=>[6,7,2,4,1,8,5,3]=>[2,2,2,1,1]
[4,6,7,8,3,1,5,2]=>[2,8,1,6,5,3,7,4]=>[7,1,8,3,4,6,2,5]=>[1,2,3,2]
[7,6,2,8,4,3,1,5]=>[7,6,3,5,2,1,8,4]=>[2,3,6,4,7,8,1,5]=>[3,3,2]
[5,2,8,6,3,4,7,1]=>[5,1,6,4,8,2,7,3]=>[4,8,3,5,1,7,2,6]=>[2,2,2,2]
[5,6,8,4,3,2,7,1]=>[1,2,6,5,4,8,7,3]=>[8,7,3,4,5,1,2,6]=>[1,1,3,3]
[5,3,8,1,7,2,4,6]=>[2,6,1,7,8,4,5,3]=>[7,3,8,2,1,5,4,6]=>[1,2,1,2,2]
[3,6,7,8,4,2,1,5]=>[2,7,6,1,5,3,8,4]=>[7,2,3,8,4,6,1,5]=>[1,3,2,2]
[6,5,1,8,4,3,7,2]=>[6,5,2,1,8,7,3,4]=>[3,4,7,8,1,2,6,5]=>[4,3,1]
[6,3,8,4,2,1,7,5]=>[5,2,4,1,8,6,7,3]=>[4,7,5,8,1,3,2,6]=>[2,2,2,2]
[2,5,8,3,1,6,7,4]=>[4,2,6,8,1,5,7,3]=>[5,7,3,1,8,4,2,6]=>[2,1,2,1,2]
[3,5,8,1,2,6,7,4]=>[6,1,2,8,4,5,7,3]=>[3,8,7,1,5,4,2,6]=>[2,1,2,1,2]
[3,2,8,1,5,6,7,4]=>[1,5,6,8,2,4,7,3]=>[8,4,3,1,7,5,2,6]=>[1,1,1,2,1,2]
[1,5,8,3,2,6,7,4]=>[4,2,6,8,5,7,1,3]=>[5,7,3,1,4,2,8,6]=>[2,1,2,2,1]
[1,3,8,6,2,4,7,5]=>[8,5,6,2,4,7,1,3]=>[1,4,3,7,5,2,8,6]=>[2,2,1,2,1]
[3,2,7,8,4,6,1,5]=>[5,7,1,3,8,2,6,4]=>[4,2,8,6,1,7,3,5]=>[1,2,1,2,2]
[5,1,8,3,4,6,7,2]=>[4,5,1,6,8,7,2,3]=>[5,4,8,3,1,2,7,6]=>[1,2,1,3,1]
[4,8,7,2,1,6,3,5]=>[1,4,7,8,5,6,3,2]=>[8,5,2,1,4,3,6,7]=>[1,1,1,2,3]
[2,8,1,6,3,4,7,5]=>[8,5,6,1,3,4,7,2]=>[1,4,3,8,6,5,2,7]=>[2,2,1,1,2]
[8,3,4,2,1,6,5,7]=>[2,4,3,7,5,6,8,1]=>[7,5,6,2,4,3,1,8]=>[1,2,2,1,2]
[6,4,7,2,5,8,1,3]=>[2,7,4,1,5,3,8,6]=>[7,2,5,8,4,6,1,3]=>[1,3,2,2]
[8,4,5,2,6,3,1,7]=>[2,7,4,3,6,5,8,1]=>[7,2,5,6,3,4,1,8]=>[1,3,2,2]
[2,4,5,8,3,6,1,7]=>[2,3,5,7,1,6,8,4]=>[7,6,4,2,8,3,1,5]=>[1,1,1,2,1,2]
[3,5,8,1,2,6,4,7]=>[7,1,4,2,5,6,8,3]=>[2,8,5,7,4,3,1,6]=>[2,2,1,1,2]
[8,6,1,3,5,2,4,7]=>[4,6,7,3,5,2,8,1]=>[5,3,2,6,4,7,1,8]=>[1,1,2,2,2]
[8,5,1,2,6,4,3,7]=>[7,6,3,4,2,5,8,1]=>[2,3,6,5,7,4,1,8]=>[3,2,1,2]
[5,8,4,6,1,3,2,7]=>[1,7,5,3,6,4,8,2]=>[8,2,4,6,3,5,1,7]=>[1,3,2,2]
[7,3,4,5,2,8,1,6]=>[2,3,5,4,7,1,8,6]=>[7,6,4,5,2,8,1,3]=>[1,1,2,2,2]
[2,6,4,3,7,8,5,1]=>[3,5,2,8,1,4,7,6]=>[6,4,7,1,8,5,2,3]=>[1,2,2,1,2]
[7,4,1,8,3,2,5,6]=>[6,5,2,7,8,3,1,4]=>[3,4,7,2,1,6,8,5]=>[3,1,3,1]
[6,2,1,7,8,4,5,3]=>[6,4,8,2,1,7,3,5]=>[3,5,1,7,8,2,6,4]=>[2,3,2,1]
[7,6,3,1,5,4,8,2]=>[3,6,5,8,4,2,1,7]=>[6,3,4,1,5,7,8,2]=>[1,2,4,1]
[2,4,6,5,1,7,8,3]=>[6,2,4,1,3,8,5,7]=>[3,7,5,8,6,1,4,2]=>[2,2,1,2,1]
[1,4,7,5,6,8,2,3]=>[4,7,2,5,3,8,1,6]=>[5,2,7,4,6,1,8,3]=>[1,2,2,2,1]
[3,7,5,2,4,6,8,1]=>[4,5,1,3,6,2,8,7]=>[5,4,8,6,3,7,1,2]=>[1,2,1,2,2]
[5,6,1,7,4,2,8,3]=>[1,8,6,5,3,2,4,7]=>[8,1,3,4,6,7,5,2]=>[1,5,1,1]
[3,7,4,8,1,2,6,5]=>[3,8,1,5,6,2,7,4]=>[6,1,8,4,3,7,2,5]=>[1,2,1,2,2]
[6,3,5,7,8,1,4,2]=>[3,8,2,1,6,4,7,5]=>[6,1,7,8,3,5,2,4]=>[1,3,2,2]
[3,6,5,7,1,8,4,2]=>[3,2,8,1,7,5,4,6]=>[6,7,1,8,2,4,5,3]=>[2,2,3,1]
[6,4,7,8,2,1,3,5]=>[2,6,5,1,7,3,8,4]=>[7,3,4,8,2,6,1,5]=>[1,3,2,2]
[6,7,3,8,4,1,2,5]=>[3,6,1,7,5,2,8,4]=>[6,3,8,2,4,7,1,5]=>[1,2,3,2]
[2,7,8,3,4,6,1,5]=>[4,5,7,2,8,1,6,3]=>[5,4,2,7,1,8,3,6]=>[1,1,2,2,2]
[7,5,8,4,1,3,2,6]=>[7,5,2,6,4,1,8,3]=>[2,4,7,3,5,8,1,6]=>[3,3,2]
[4,7,5,8,3,1,2,6]=>[6,1,3,7,5,2,8,4]=>[3,8,6,2,4,7,1,5]=>[2,1,3,2]
[3,6,7,4,8,1,2,5]=>[6,4,1,2,7,3,8,5]=>[3,5,8,7,2,6,1,4]=>[3,1,2,2]
[5,7,3,1,6,8,4,2]=>[3,1,5,8,7,4,2,6]=>[6,8,4,1,2,5,7,3]=>[2,1,4,1]
[2,7,3,1,8,6,4,5]=>[7,8,3,6,1,4,2,5]=>[2,1,6,3,8,5,7,4]=>[1,2,2,2,1]
[2,8,4,3,1,5,7,6]=>[4,3,8,1,5,6,7,2]=>[5,6,1,8,4,3,2,7]=>[2,2,1,1,2]
[4,8,1,2,3,5,7,6]=>[8,3,1,4,5,6,7,2]=>[1,6,8,5,4,3,2,7]=>[3,1,1,1,2]
[7,6,8,1,2,4,3,5]=>[7,4,5,6,2,1,8,3]=>[2,5,4,3,7,8,1,6]=>[2,1,3,2]
[7,6,8,5,1,3,2,4]=>[7,5,6,2,1,8,4,3]=>[2,4,3,7,8,1,5,6]=>[2,3,3]
[8,4,5,2,7,6,1,3]=>[2,7,3,8,4,6,5,1]=>[7,2,6,1,5,3,4,8]=>[1,2,2,3]
[6,7,1,3,5,2,8,4]=>[8,4,6,3,1,5,2,7]=>[1,5,3,6,8,4,7,2]=>[2,3,2,1]
[5,7,2,3,6,8,1,4]=>[7,3,1,4,5,2,8,6]=>[2,6,8,5,4,7,1,3]=>[3,1,2,2]
[8,5,3,2,7,6,1,4]=>[3,7,2,8,4,6,5,1]=>[6,2,7,1,5,3,4,8]=>[1,2,2,3]
[3,4,6,7,5,8,1,2]=>[3,7,1,2,5,4,8,6]=>[6,2,8,7,4,5,1,3]=>[1,2,1,2,2]
[3,4,5,7,6,1,8,2]=>[8,1,2,3,6,5,4,7]=>[1,8,7,6,3,4,5,2]=>[2,1,1,3,1]
[2,6,4,5,7,8,3,1]=>[3,4,2,5,8,1,7,6]=>[6,5,7,4,1,8,2,3]=>[1,2,1,2,2]
[3,8,5,1,6,2,7,4]=>[8,6,1,4,3,5,7,2]=>[1,3,8,5,6,4,2,7]=>[3,2,1,2]
[2,5,1,3,6,8,7,4]=>[8,5,1,2,7,3,4,6]=>[1,4,8,7,2,6,5,3]=>[3,1,2,1,1]
[5,4,6,1,3,7,8,2]=>[5,2,1,6,3,8,4,7]=>[4,7,8,3,6,1,5,2]=>[3,2,2,1]
[6,3,5,7,1,4,8,2]=>[6,2,3,1,8,5,4,7]=>[3,7,6,8,1,4,5,2]=>[2,2,3,1]
[7,3,4,6,8,1,5,2]=>[8,2,3,6,4,1,7,5]=>[1,7,6,3,5,8,2,4]=>[2,1,3,2]
[7,5,2,8,4,1,3,6]=>[6,7,3,2,5,1,8,4]=>[3,2,6,7,4,8,1,5]=>[1,3,2,2]
[3,7,6,4,1,8,2,5]=>[7,4,8,1,5,3,2,6]=>[2,5,1,8,4,6,7,3]=>[2,2,3,1]
[3,7,8,4,1,5,6,2]=>[6,4,8,1,5,2,7,3]=>[3,5,1,8,4,7,2,6]=>[2,2,2,2]
[8,7,5,4,2,1,6,3]=>[5,8,6,4,3,7,2,1]=>[4,1,3,5,6,2,7,8]=>[1,4,3]
[3,5,8,6,7,4,2,1]=>[4,8,2,7,1,6,5,3]=>[5,1,7,2,8,3,4,6]=>[1,2,2,3]
[5,8,1,6,7,3,4,2]=>[1,6,4,8,7,3,5,2]=>[8,3,5,1,2,6,4,7]=>[1,2,3,2]
[6,7,2,5,1,8,4,3]=>[8,7,3,1,5,4,2,6]=>[1,2,6,8,4,5,7,3]=>[4,3,1]
[5,8,2,1,6,7,4,3]=>[5,1,8,3,7,4,6,2]=>[4,8,1,6,2,5,3,7]=>[2,2,2,2]
[4,5,2,8,6,3,7,1]=>[1,2,6,5,8,3,7,4]=>[8,7,3,4,1,6,2,5]=>[1,1,2,2,2]
[3,6,1,2,5,8,4,7]=>[1,5,7,8,3,2,4,6]=>[8,4,2,1,6,7,5,3]=>[1,1,1,3,1,1]
[1,4,5,8,2,3,7,6]=>[2,3,8,5,6,7,1,4]=>[7,6,1,4,3,2,8,5]=>[1,1,2,1,2,1]
[1,2,6,4,5,8,3,7]=>[4,5,3,7,8,1,2,6]=>[5,4,6,2,1,8,7,3]=>[1,2,1,2,1,1]
[1,5,2,4,6,8,3,7]=>[4,5,2,7,8,1,3,6]=>[5,4,7,2,1,8,6,3]=>[1,2,1,2,1,1]
[3,6,1,5,8,2,4,7]=>[6,1,4,7,2,8,3,5]=>[3,8,5,2,7,1,6,4]=>[2,1,2,2,1]
[2,6,5,1,4,8,3,7]=>[5,7,3,1,2,8,4,6]=>[4,2,6,8,7,1,5,3]=>[1,3,1,2,1]
[5,2,6,1,4,8,3,7]=>[5,7,2,1,3,8,4,6]=>[4,2,7,8,6,1,5,3]=>[1,3,1,2,1]
[2,5,1,8,4,7,3,6]=>[5,2,7,8,1,6,3,4]=>[4,7,2,1,8,3,6,5]=>[2,1,2,2,1]
[2,7,1,4,3,6,8,5]=>[4,6,8,1,3,5,2,7]=>[5,3,1,8,6,4,7,2]=>[1,1,2,1,2,1]
[1,3,7,5,8,2,4,6]=>[6,4,7,2,3,8,1,5]=>[3,5,2,7,6,1,8,4]=>[2,2,1,2,1]
[8,2,1,5,7,3,4,6]=>[6,2,4,7,8,3,5,1]=>[3,7,5,2,1,6,4,8]=>[2,1,1,2,2]
[2,5,4,8,1,3,7,6]=>[3,2,8,1,5,6,7,4]=>[6,7,1,8,4,3,2,5]=>[2,2,1,1,2]
[2,4,1,3,8,6,7,5]=>[2,6,8,1,7,3,4,5]=>[7,3,1,8,2,6,5,4]=>[1,1,2,2,1,1]
[8,4,3,7,1,2,6,5]=>[3,2,8,5,6,7,4,1]=>[6,7,1,4,3,2,5,8]=>[2,2,1,3]
[1,7,3,5,8,2,6,4]=>[4,8,3,6,2,7,1,5]=>[5,1,6,3,7,2,8,4]=>[1,2,2,2,1]
[1,8,4,2,6,7,3,5]=>[3,7,5,8,4,6,1,2]=>[6,2,4,1,5,3,8,7]=>[1,2,2,2,1]
[7,2,1,6,8,3,4,5]=>[6,7,2,4,8,3,1,5]=>[3,2,7,5,1,6,8,4]=>[1,2,1,3,1]
[3,1,7,6,8,2,4,5]=>[6,7,1,4,3,8,2,5]=>[3,2,8,5,6,1,7,4]=>[1,2,2,2,1]
[4,1,7,2,6,8,3,5]=>[1,7,5,8,4,2,3,6]=>[8,2,4,1,5,7,6,3]=>[1,2,3,1,1]
[5,1,7,2,3,6,8,4]=>[6,8,4,1,5,2,3,7]=>[3,1,5,8,4,7,6,2]=>[1,3,2,1,1]
[7,1,2,5,3,6,8,4]=>[6,4,8,2,3,5,1,7]=>[3,5,1,7,6,4,8,2]=>[2,2,1,2,1]
[5,4,1,2,7,8,3,6]=>[7,5,2,1,8,3,4,6]=>[2,4,7,8,1,6,5,3]=>[4,2,1,1]
[8,1,3,2,4,6,7,5]=>[3,6,8,2,4,5,7,1]=>[6,3,1,7,5,4,2,8]=>[1,1,2,1,1,2]
[7,3,1,2,4,6,8,5]=>[6,2,8,3,4,5,1,7]=>[3,7,1,6,5,4,8,2]=>[2,2,1,2,1]
[1,8,3,4,7,2,5,6]=>[3,4,6,7,8,5,1,2]=>[6,5,3,2,1,4,8,7]=>[1,1,1,1,3,1]
[3,5,8,1,2,7,4,6]=>[7,1,2,8,4,5,6,3]=>[2,8,7,1,5,4,3,6]=>[2,1,2,1,2]
[3,6,8,1,2,4,7,5]=>[8,1,4,5,2,6,7,3]=>[1,8,5,4,7,3,2,6]=>[2,1,2,1,2]
[4,1,3,8,7,2,6,5]=>[1,8,6,7,3,5,2,4]=>[8,1,3,2,6,4,7,5]=>[1,2,2,2,1]
[1,3,7,4,8,2,6,5]=>[8,4,6,2,3,7,1,5]=>[1,5,3,7,6,2,8,4]=>[2,2,1,2,1]
[1,4,6,8,2,3,7,5]=>[8,2,5,3,6,7,1,4]=>[1,7,4,6,3,2,8,5]=>[2,2,1,2,1]
[3,5,8,1,7,2,4,6]=>[6,1,2,7,8,4,5,3]=>[3,8,7,2,1,5,4,6]=>[2,1,1,2,2]
[2,6,8,1,7,3,4,5]=>[6,7,2,8,1,4,5,3]=>[3,2,7,1,8,5,4,6]=>[1,2,2,1,2]
[6,1,5,8,2,3,7,4]=>[8,5,3,6,1,7,2,4]=>[1,4,6,3,8,2,7,5]=>[3,2,2,1]
[1,8,3,2,7,5,6,4]=>[6,8,3,7,4,5,1,2]=>[3,1,6,2,5,4,8,7]=>[1,2,2,2,1]
[3,1,7,2,8,5,6,4]=>[6,8,1,7,4,2,3,5]=>[3,1,8,2,5,7,6,4]=>[1,2,3,1,1]
[2,6,7,3,8,1,5,4]=>[8,4,2,6,1,3,7,5]=>[1,5,7,3,8,6,2,4]=>[3,2,1,2]
[8,4,1,7,3,6,2,5]=>[5,2,7,8,6,3,4,1]=>[4,7,2,1,3,6,5,8]=>[2,1,3,2]
[3,7,2,8,6,1,5,4]=>[8,6,7,1,3,2,5,4]=>[1,3,2,8,6,7,4,5]=>[2,2,2,2]
[5,1,7,8,4,2,6,3]=>[1,8,6,5,3,7,2,4]=>[8,1,3,4,6,2,7,5]=>[1,4,2,1]
[5,1,8,7,4,2,6,3]=>[1,8,6,5,7,4,2,3]=>[8,1,3,4,2,5,7,6]=>[1,3,3,1]
[4,7,2,8,3,6,5,1]=>[8,1,5,7,3,2,6,4]=>[1,8,4,2,6,7,3,5]=>[2,1,3,2]
[4,1,7,8,5,3,6,2]=>[6,1,5,3,8,7,2,4]=>[3,8,4,6,1,2,7,5]=>[2,2,3,1]
[5,1,7,4,8,3,6,2]=>[4,1,6,3,8,7,2,5]=>[5,8,3,6,1,2,7,4]=>[2,2,3,1]
[4,1,8,7,5,3,6,2]=>[6,1,5,8,7,4,2,3]=>[3,8,4,1,2,5,7,6]=>[2,1,4,1]
[4,8,2,7,3,6,5,1]=>[8,1,5,7,3,6,4,2]=>[1,8,4,2,6,3,5,7]=>[2,1,2,3]
[4,7,2,6,3,5,8,1]=>[1,5,6,3,4,2,8,7]=>[8,4,3,6,5,7,1,2]=>[1,1,2,2,2]
[6,8,2,4,3,7,5,1]=>[4,8,3,1,5,7,6,2]=>[5,1,6,8,4,2,3,7]=>[1,3,1,3]
[6,7,2,4,3,8,5,1]=>[4,8,3,1,5,2,7,6]=>[5,1,6,8,4,7,2,3]=>[1,3,2,2]
[6,8,2,7,3,5,4,1]=>[8,5,1,7,3,6,4,2]=>[1,4,8,2,6,3,5,7]=>[3,2,3]
[3,8,7,2,4,1,5,6]=>[4,6,1,5,7,8,3,2]=>[5,3,8,4,2,1,6,7]=>[1,2,1,1,3]
[3,7,8,2,4,1,5,6]=>[4,6,1,5,7,2,8,3]=>[5,3,8,4,2,7,1,6]=>[1,2,1,2,2]
[3,6,8,2,4,5,7,1]=>[4,5,1,2,6,8,7,3]=>[5,4,8,7,3,1,2,6]=>[1,2,1,1,3]
[3,6,7,2,4,5,8,1]=>[4,5,1,2,6,3,8,7]=>[5,4,8,7,3,6,1,2]=>[1,2,1,2,2]
[8,6,1,7,2,5,4,3]=>[8,7,5,6,3,2,4,1]=>[1,2,4,3,6,7,5,8]=>[3,3,2]
[8,7,6,1,2,3,5,4]=>[8,4,5,6,7,3,2,1]=>[1,5,4,3,2,6,7,8]=>[2,1,1,4]
[5,4,3,1,6,2,8,7]=>[5,3,2,1,8,4,6,7]=>[4,6,7,8,1,5,3,2]=>[4,2,1,1]
[2,8,6,7,5,3,4,1]=>[6,3,8,7,5,1,4,2]=>[3,6,1,2,4,8,5,7]=>[2,4,2]
[2,1,8,7,3,6,4,5]=>[7,8,5,6,1,4,2,3]=>[2,1,4,3,8,5,7,6]=>[1,2,2,2,1]
[3,6,5,8,2,4,7,1]=>[5,3,1,2,6,8,7,4]=>[4,6,8,7,3,1,2,5]=>[3,1,1,3]
[5,2,1,8,7,3,4,6]=>[6,7,1,8,2,5,3,4]=>[3,2,8,1,7,4,6,5]=>[1,2,2,2,1]
[6,5,2,7,4,3,8,1]=>[6,5,3,2,1,4,8,7]=>[3,4,6,7,8,5,1,2]=>[5,1,2]
[4,6,5,2,7,3,8,1]=>[6,1,4,3,2,5,8,7]=>[3,8,5,6,7,4,1,2]=>[2,3,1,2]
[6,2,7,1,8,3,5,4]=>[8,6,7,2,1,4,3,5]=>[1,3,2,7,8,5,6,4]=>[2,3,2,1]
[2,7,5,4,8,3,6,1]=>[4,3,6,2,8,1,7,5]=>[5,6,3,7,1,8,2,4]=>[2,2,2,2]
[8,7,5,1,2,6,4,3]=>[8,7,4,5,3,6,2,1]=>[1,2,5,4,6,3,7,8]=>[3,2,3]
[7,1,6,2,3,8,5,4]=>[8,7,4,5,2,3,1,6]=>[1,2,5,4,7,6,8,3]=>[3,2,2,1]
[4,8,1,3,2,7,5,6]=>[4,1,7,8,3,5,6,2]=>[5,8,2,1,6,4,3,7]=>[2,1,2,1,2]
[3,8,1,4,7,5,2,6]=>[7,1,4,6,8,3,5,2]=>[2,8,5,3,1,6,4,7]=>[2,1,1,2,2]
[6,3,8,7,4,5,1,2]=>[7,5,1,8,2,6,4,3]=>[2,4,8,1,7,3,5,6]=>[3,2,3]
[8,5,7,4,6,2,1,3]=>[2,7,6,4,8,5,3,1]=>[7,2,3,5,1,4,6,8]=>[1,3,4]
[4,6,7,8,2,3,5,1]=>[5,1,2,6,3,8,7,4]=>[4,8,7,3,6,1,2,5]=>[2,1,2,3]
[5,8,3,2,4,6,1,7]=>[4,3,1,5,7,6,8,2]=>[5,6,8,4,2,3,1,7]=>[3,1,2,2]
[8,2,6,5,3,1,7,4]=>[5,8,6,2,4,3,7,1]=>[4,1,3,7,5,6,2,8]=>[1,3,2,2]
[4,8,7,6,5,2,3,1]=>[6,8,7,1,5,4,3,2]=>[3,1,2,8,4,5,6,7]=>[1,3,4]
[2,1,8,6,4,3,7,5]=>[5,8,6,1,4,7,2,3]=>[4,1,3,8,5,2,7,6]=>[1,3,1,2,1]
[7,2,5,4,6,1,8,3]=>[4,3,8,2,6,5,1,7]=>[5,6,1,7,3,4,8,2]=>[2,2,3,1]
[4,7,6,1,2,5,8,3]=>[1,6,8,4,5,3,2,7]=>[8,3,1,5,4,6,7,2]=>[1,1,2,3,1]
[2,4,1,7,6,8,5,3]=>[5,2,4,8,1,7,3,6]=>[4,7,5,1,8,2,6,3]=>[2,1,2,2,1]
[3,4,1,7,8,5,6,2]=>[6,1,2,4,8,7,3,5]=>[3,8,7,5,1,2,6,4]=>[2,1,1,3,1]
[7,5,4,3,1,8,6,2]=>[4,3,2,8,7,5,1,6]=>[5,6,7,1,2,4,8,3]=>[3,4,1]
[8,5,6,2,7,3,1,4]=>[7,4,2,6,3,8,5,1]=>[2,5,7,3,6,1,4,8]=>[3,2,3]
[8,4,2,5,6,1,7,3]=>[4,2,8,3,6,5,7,1]=>[5,7,1,6,3,4,2,8]=>[2,2,2,2]
[4,1,3,6,7,5,8,2]=>[4,1,6,3,5,8,2,7]=>[5,8,3,6,4,1,7,2]=>[2,2,1,2,1]
[1,7,5,3,8,2,4,6]=>[4,6,3,7,2,8,1,5]=>[5,3,6,2,7,1,8,4]=>[1,2,2,2,1]
[1,7,2,4,5,8,3,6]=>[4,5,7,8,3,1,2,6]=>[5,4,2,1,6,8,7,3]=>[1,1,1,3,1,1]
[8,2,5,3,1,6,4,7]=>[4,7,2,5,3,6,8,1]=>[5,2,7,4,6,3,1,8]=>[1,2,2,1,2]
[1,7,4,5,8,3,2,6]=>[3,4,7,6,2,8,1,5]=>[6,5,2,3,7,1,8,4]=>[1,1,3,2,1]
[2,6,4,7,8,3,1,5]=>[7,3,2,6,1,4,8,5]=>[2,6,7,3,8,5,1,4]=>[3,2,1,2]
[1,2,6,4,7,8,3,5]=>[7,4,3,5,8,1,2,6]=>[2,5,6,4,1,8,7,3]=>[3,1,2,1,1]
[2,7,4,5,8,1,3,6]=>[3,6,4,7,1,2,8,5]=>[6,3,5,2,8,7,1,4]=>[1,2,2,1,2]
[2,7,5,3,1,8,4,6]=>[4,7,3,8,1,5,2,6]=>[5,2,6,1,8,4,7,3]=>[1,2,2,2,1]
[6,1,4,7,8,3,5,2]=>[6,3,4,1,8,7,2,5]=>[3,6,5,8,1,2,7,4]=>[2,2,3,1]
[3,6,4,7,8,1,5,2]=>[8,3,1,2,6,4,7,5]=>[1,6,8,7,3,5,2,4]=>[3,1,2,2]
[4,3,6,7,1,8,5,2]=>[1,3,8,2,7,5,4,6]=>[8,6,1,7,2,4,5,3]=>[1,1,2,3,1]
[4,3,6,7,1,8,2,5]=>[1,7,2,3,8,5,4,6]=>[8,2,7,6,1,4,5,3]=>[1,2,1,3,1]
[3,6,4,7,8,1,2,5]=>[3,6,1,2,7,4,8,5]=>[6,3,8,7,2,5,1,4]=>[1,2,1,2,2]
[2,3,6,4,1,7,8,5]=>[4,6,1,2,3,8,5,7]=>[5,3,8,7,6,1,4,2]=>[1,2,1,1,2,1]
[4,7,2,1,5,3,8,6]=>[3,1,5,8,4,6,2,7]=>[6,8,4,1,5,3,7,2]=>[2,1,2,2,1]
[3,7,4,5,2,1,8,6]=>[3,5,1,4,8,6,2,7]=>[6,4,8,5,1,3,7,2]=>[1,2,1,3,1]
[1,3,6,4,7,2,8,5]=>[8,4,2,3,6,1,5,7]=>[1,5,7,6,3,8,4,2]=>[3,1,2,1,1]
[3,6,4,7,2,8,5,1]=>[8,3,1,2,5,4,7,6]=>[1,6,8,7,4,5,2,3]=>[3,1,2,2]
[5,1,3,4,2,7,8,6]=>[3,4,6,1,8,2,5,7]=>[6,5,3,8,1,7,4,2]=>[1,1,2,2,1,1]
[5,4,2,1,3,7,8,6]=>[3,6,2,1,8,4,5,7]=>[6,3,7,8,1,5,4,2]=>[1,3,2,1,1]
[6,1,7,3,8,2,5,4]=>[8,4,6,3,1,7,2,5]=>[1,5,3,6,8,2,7,4]=>[2,3,2,1]
[1,6,7,3,8,2,5,4]=>[8,4,2,6,3,7,1,5]=>[1,5,7,3,6,2,8,4]=>[3,2,2,1]
[6,1,4,7,8,5,2,3]=>[7,3,4,1,8,6,2,5]=>[2,6,5,8,1,3,7,4]=>[2,2,3,1]
[6,3,2,1,7,8,5,4]=>[2,5,8,3,1,7,4,6]=>[7,4,1,6,8,2,5,3]=>[1,1,3,2,1]
[6,2,7,3,1,8,5,4]=>[8,4,7,2,1,5,3,6]=>[1,5,2,7,8,4,6,3]=>[2,3,2,1]
[6,2,4,7,8,1,5,3]=>[8,3,6,2,1,4,7,5]=>[1,6,3,7,8,5,2,4]=>[2,3,1,2]
[2,6,7,3,1,8,5,4]=>[8,4,2,7,1,5,3,6]=>[1,5,7,2,8,4,6,3]=>[3,2,2,1]
[8,6,5,1,3,2,4,7]=>[6,4,5,7,3,2,8,1]=>[3,5,4,2,6,7,1,8]=>[2,1,3,2]
[6,4,7,8,3,2,5,1]=>[6,2,1,5,3,8,7,4]=>[3,7,8,4,6,1,2,5]=>[3,2,3]
[3,8,4,7,1,2,5,6]=>[5,1,3,6,7,8,4,2]=>[4,8,6,3,2,1,5,7]=>[2,1,1,1,3]
[5,8,6,4,1,3,2,7]=>[1,7,5,6,4,3,8,2]=>[8,2,4,3,5,6,1,7]=>[1,2,3,2]
[8,3,6,4,5,2,1,7]=>[4,7,2,6,5,3,8,1]=>[5,2,7,3,4,6,1,8]=>[1,2,3,2]
[6,8,5,7,4,2,3,1]=>[1,6,3,8,7,5,4,2]=>[8,3,6,1,2,4,5,7]=>[1,2,5]
[2,3,8,7,1,6,4,5]=>[7,8,5,6,1,2,4,3]=>[2,1,4,3,8,7,5,6]=>[1,2,2,1,2]
[4,3,7,8,1,6,2,5]=>[1,7,8,2,5,3,6,4]=>[8,2,1,7,4,6,3,5]=>[1,1,2,2,2]
[7,3,8,4,1,2,5,6]=>[2,5,6,4,7,1,8,3]=>[7,4,3,5,2,8,1,6]=>[1,1,2,2,2]
[4,8,1,2,7,3,5,6]=>[6,1,7,8,3,4,5,2]=>[3,8,2,1,6,5,4,7]=>[2,1,2,1,2]
[6,8,1,2,7,4,5,3]=>[6,8,7,3,1,4,5,2]=>[3,1,2,6,8,5,4,7]=>[1,4,1,2]
[5,6,8,4,1,3,7,2]=>[1,6,2,8,5,4,7,3]=>[8,3,7,1,4,5,2,6]=>[1,2,3,2]
[8,5,4,7,1,6,3,2]=>[3,2,8,7,5,6,4,1]=>[6,7,1,2,4,3,5,8]=>[2,3,3]
[2,5,8,7,3,6,4,1]=>[8,2,5,7,6,1,4,3]=>[1,7,4,2,3,8,5,6]=>[2,1,3,2]
[2,4,8,7,5,6,1,3]=>[7,5,8,2,6,1,4,3]=>[2,4,1,7,3,8,5,6]=>[2,2,2,2]
[3,7,4,8,5,6,2,1]=>[5,8,3,1,2,7,6,4]=>[4,1,6,8,7,2,3,5]=>[1,3,1,3]
[6,4,8,7,5,1,2,3]=>[2,6,1,7,8,5,4,3]=>[7,3,8,2,1,4,5,6]=>[1,2,1,4]
[3,8,5,2,4,6,7,1]=>[4,5,1,3,6,8,7,2]=>[5,4,8,6,3,1,2,7]=>[1,2,1,1,3]
[5,7,1,8,4,6,2,3]=>[1,7,5,8,6,3,2,4]=>[8,2,4,1,3,6,7,5]=>[1,2,4,1]
[6,3,8,7,2,1,4,5]=>[6,2,5,1,7,8,4,3]=>[3,7,4,8,2,1,5,6]=>[2,2,1,3]
[2,3,7,8,5,6,1,4]=>[7,5,3,8,1,2,6,4]=>[2,4,6,1,8,7,3,5]=>[3,2,1,2]
[3,7,6,8,5,1,2,4]=>[6,7,3,1,2,8,5,4]=>[3,2,6,8,7,1,4,5]=>[1,3,1,3]
[2,6,7,8,5,1,3,4]=>[6,2,7,3,8,1,5,4]=>[3,7,2,6,1,8,4,5]=>[2,2,2,2]
[2,4,7,8,1,6,3,5]=>[7,8,2,5,1,3,6,4]=>[2,1,7,4,8,6,3,5]=>[1,2,2,1,2]
[5,4,7,8,2,6,3,1]=>[1,8,2,5,3,7,6,4]=>[8,1,7,4,6,2,3,5]=>[1,2,2,3]
[2,8,3,4,1,5,7,6]=>[3,4,8,1,5,6,7,2]=>[6,5,1,8,4,3,2,7]=>[1,1,2,1,1,2]
[6,8,3,4,1,2,7,5]=>[3,8,5,4,1,6,7,2]=>[6,1,4,5,8,3,2,7]=>[1,4,1,2]
[6,8,7,1,5,2,3,4]=>[6,7,1,8,4,5,3,2]=>[3,2,8,1,5,4,6,7]=>[1,2,2,3]
[5,8,3,2,7,6,1,4]=>[3,1,7,8,4,6,5,2]=>[6,8,2,1,5,3,4,7]=>[2,1,2,3]
[2,5,3,1,8,6,7,4]=>[6,2,8,1,3,7,4,5]=>[3,7,1,8,6,2,5,4]=>[2,2,1,2,1]
[3,5,8,6,1,4,7,2]=>[2,6,8,1,5,4,7,3]=>[7,3,1,8,4,5,2,6]=>[1,1,2,2,2]
[4,8,6,1,5,2,7,3]=>[8,1,6,4,5,3,7,2]=>[1,8,3,5,4,6,2,7]=>[2,2,2,2]
[5,8,2,3,7,6,1,4]=>[7,1,8,3,4,6,5,2]=>[2,8,1,6,5,3,4,7]=>[2,2,1,3]
[4,6,8,5,3,2,7,1]=>[2,6,1,5,4,8,7,3]=>[7,3,8,4,5,1,2,6]=>[1,2,2,3]
[2,6,4,8,5,1,7,3]=>[8,3,2,6,1,5,7,4]=>[1,6,7,3,8,4,2,5]=>[3,2,1,2]
[7,6,4,8,5,2,1,3]=>[3,7,6,2,1,8,5,4]=>[6,2,3,7,8,1,4,5]=>[1,4,3]
[3,4,8,6,5,2,7,1]=>[6,5,1,2,4,8,7,3]=>[3,4,8,7,5,1,2,6]=>[3,1,1,3]
[3,4,8,7,5,6,2,1]=>[5,8,7,1,2,6,4,3]=>[4,1,2,8,7,3,5,6]=>[1,3,1,3]
[2,5,1,3,8,6,7,4]=>[6,2,8,1,7,3,4,5]=>[3,7,1,8,2,6,5,4]=>[2,2,2,1,1]
[5,4,8,1,3,6,7,2]=>[5,2,1,6,8,4,7,3]=>[4,7,8,3,1,5,2,6]=>[3,1,2,2]
[8,3,5,4,1,6,7,2]=>[6,2,4,3,8,5,7,1]=>[3,7,5,6,1,4,2,8]=>[2,2,2,2]
[7,3,4,8,5,6,1,2]=>[7,2,3,5,1,8,6,4]=>[2,7,6,4,8,1,3,5]=>[2,1,2,3]
[6,1,5,7,2,4,8,3]=>[6,3,8,5,2,1,4,7]=>[3,6,1,4,7,8,5,2]=>[2,4,1,1]
[7,4,5,1,2,3,8,6]=>[8,4,2,5,3,6,1,7]=>[1,5,7,4,6,3,8,2]=>[3,2,2,1]
[7,4,3,1,2,8,5,6]=>[7,3,2,8,4,5,1,6]=>[2,6,7,1,5,4,8,3]=>[3,2,2,1]
[8,4,7,6,2,1,5,3]=>[2,5,8,6,7,4,3,1]=>[7,4,1,3,2,5,6,8]=>[1,1,2,4]
[8,4,6,5,7,1,3,2]=>[8,2,6,4,3,7,5,1]=>[1,7,3,5,6,2,4,8]=>[2,3,3]
[7,2,1,4,5,8,3,6]=>[2,4,5,7,8,3,1,6]=>[7,5,4,2,1,6,8,3]=>[1,1,1,1,3,1]
[3,5,7,6,4,1,8,2]=>[8,2,6,1,5,4,3,7]=>[1,7,3,8,4,5,6,2]=>[2,2,3,1]
[5,7,2,3,6,4,8,1]=>[6,3,1,4,5,2,8,7]=>[3,6,8,5,4,7,1,2]=>[3,1,2,2]
[8,6,2,3,7,1,4,5]=>[3,4,6,7,2,8,5,1]=>[6,5,3,2,7,1,4,8]=>[1,1,1,2,3]
[5,7,2,4,8,3,6,1]=>[4,1,6,8,3,2,7,5]=>[5,8,3,1,6,7,2,4]=>[2,1,3,2]
[1,7,2,4,8,6,3,5]=>[7,8,4,6,3,1,2,5]=>[2,1,5,3,6,8,7,4]=>[1,2,3,1,1]
[7,6,1,5,4,8,3,2]=>[5,4,8,7,3,2,1,6]=>[4,5,1,2,6,7,8,3]=>[2,5,1]
[4,7,3,2,1,8,5,6]=>[1,4,3,7,8,5,2,6]=>[8,5,6,2,1,4,7,3]=>[1,2,1,3,1]
[4,8,7,6,1,2,5,3]=>[8,1,5,6,7,4,3,2]=>[1,8,4,3,2,5,6,7]=>[2,1,1,4]
[7,8,6,1,3,2,5,4]=>[5,8,4,6,1,7,3,2]=>[4,1,5,3,8,2,6,7]=>[1,2,2,3]
[5,8,6,4,2,3,1,7]=>[1,5,7,6,4,3,8,2]=>[8,4,2,3,5,6,1,7]=>[1,1,4,2]
[2,8,3,1,6,5,4,7]=>[7,3,6,1,4,5,8,2]=>[2,6,3,8,5,4,1,7]=>[2,2,1,1,2]
[3,8,1,2,5,7,4,6]=>[1,5,7,8,3,4,6,2]=>[8,4,2,1,6,5,3,7]=>[1,1,1,2,1,2]
[6,8,5,4,2,7,3,1]=>[1,8,5,4,3,7,6,2]=>[8,1,4,5,6,2,3,7]=>[1,4,3]
[6,8,3,1,2,4,5,7]=>[4,5,3,6,1,7,8,2]=>[5,4,6,3,8,2,1,7]=>[1,2,2,1,2]
[4,6,8,7,3,1,5,2]=>[2,8,1,6,5,7,4,3]=>[7,1,8,3,4,2,5,6]=>[1,2,2,3]
[6,5,3,7,8,4,1,2]=>[7,3,2,1,4,8,6,5]=>[2,6,7,8,5,1,3,4]=>[4,1,3]
[4,1,3,8,7,5,6,2]=>[1,6,8,7,3,5,2,4]=>[8,3,1,2,6,4,7,5]=>[1,1,3,2,1]
[4,3,2,6,8,1,7,5]=>[2,1,4,8,3,6,7,5]=>[7,8,5,1,6,3,2,4]=>[2,1,2,1,2]
[7,1,5,6,3,8,2,4]=>[5,3,7,4,8,2,1,6]=>[4,6,2,5,1,7,8,3]=>[2,2,3,1]
[5,1,2,4,7,8,3,6]=>[7,4,5,1,8,2,3,6]=>[2,5,4,8,1,7,6,3]=>[2,2,2,1,1]
[3,5,4,2,8,1,6,7]=>[4,1,3,2,6,7,8,5]=>[5,8,6,7,3,2,1,4]=>[2,2,1,1,2]
[5,1,3,8,4,2,7,6]=>[5,8,3,1,6,7,2,4]=>[4,1,6,8,3,2,7,5]=>[1,3,1,2,1]
[6,2,8,7,3,5,4,1]=>[8,5,1,7,6,2,4,3]=>[1,4,8,2,3,7,5,6]=>[3,3,2]
[7,1,8,4,3,6,5,2]=>[4,8,5,7,6,2,1,3]=>[5,1,4,2,3,7,8,6]=>[1,2,4,1]
[3,6,8,7,4,1,2,5]=>[6,2,7,1,5,8,4,3]=>[3,7,2,8,4,1,5,6]=>[2,2,1,3]
[5,6,8,1,7,3,2,4]=>[1,7,6,2,8,4,5,3]=>[8,2,3,7,1,5,4,6]=>[1,3,2,2]
[3,1,6,8,7,4,2,5]=>[3,7,1,6,8,5,2,4]=>[6,2,8,3,1,4,7,5]=>[1,2,1,3,1]
[7,4,6,8,2,1,5,3]=>[2,5,8,6,3,1,7,4]=>[7,4,1,3,6,8,2,5]=>[1,1,4,2]
[6,5,8,4,3,1,2,7]=>[6,2,1,7,5,4,8,3]=>[3,7,8,2,4,5,1,6]=>[3,3,2]
[1,5,8,3,7,4,2,6]=>[2,7,4,6,8,5,1,3]=>[7,2,5,3,1,4,8,6]=>[1,2,1,3,1]
[3,8,2,7,1,5,6,4]=>[6,8,1,3,5,7,4,2]=>[3,1,8,6,4,2,5,7]=>[1,2,1,1,3]
[3,5,8,7,4,2,6,1]=>[6,2,5,8,1,7,4,3]=>[3,7,4,1,8,2,5,6]=>[2,1,2,3]
[7,5,1,8,4,2,6,3]=>[8,6,5,2,7,3,1,4]=>[1,3,4,7,2,6,8,5]=>[4,3,1]
[3,6,8,5,2,7,4,1]=>[2,8,5,1,4,7,6,3]=>[7,1,4,8,5,2,3,6]=>[1,3,1,3]
[2,1,6,5,4,8,3,7]=>[5,4,1,3,7,8,2,6]=>[4,5,8,6,2,1,7,3]=>[3,1,1,2,1]
[2,1,7,8,4,6,5,3]=>[8,5,3,7,1,6,2,4]=>[1,4,6,2,8,3,7,5]=>[3,2,2,1]
[2,1,7,4,3,5,8,6]=>[4,8,1,5,6,2,3,7]=>[5,1,8,4,3,7,6,2]=>[1,2,1,2,1,1]
[3,5,7,8,4,6,1,2]=>[7,2,5,1,3,8,6,4]=>[2,7,4,8,6,1,3,5]=>[2,2,1,3]
[8,6,2,3,5,7,1,4]=>[7,3,4,5,2,8,6,1]=>[2,6,5,4,7,1,3,8]=>[2,1,2,3]
[7,8,2,4,3,1,5,6]=>[6,3,5,4,7,1,8,2]=>[3,6,4,5,2,8,1,7]=>[2,2,2,2]
[7,6,3,8,1,5,4,2]=>[8,3,7,5,2,1,6,4]=>[1,6,2,4,7,8,3,5]=>[2,4,2]
[6,1,8,2,3,5,4,7]=>[7,4,5,6,1,8,2,3]=>[2,5,4,3,8,1,7,6]=>[2,1,2,2,1]
[7,2,4,1,6,3,8,5]=>[3,8,2,6,4,5,1,7]=>[6,1,7,3,5,4,8,2]=>[1,2,2,2,1]
[8,4,3,1,7,5,2,6]=>[3,2,7,6,8,4,5,1]=>[6,7,2,3,1,5,4,8]=>[2,2,2,2]
[7,3,1,4,6,8,5,2]=>[2,5,8,4,7,3,1,6]=>[7,4,1,5,2,6,8,3]=>[1,1,2,3,1]
[7,3,8,5,2,6,4,1]=>[8,5,2,4,1,7,6,3]=>[1,4,7,5,8,2,3,6]=>[3,2,3]
[4,3,8,7,1,6,5,2]=>[8,1,7,2,5,6,4,3]=>[1,8,2,7,4,3,5,6]=>[2,2,1,3]
[4,7,1,8,5,2,6,3]=>[8,1,6,5,7,3,2,4]=>[1,8,3,4,2,6,7,5]=>[2,2,3,1]
[5,3,2,4,7,8,6,1]=>[2,5,1,8,3,4,7,6]=>[7,4,8,1,6,5,2,3]=>[1,2,2,1,2]
[5,3,4,2,8,7,1,6]=>[2,3,1,7,8,4,6,5]=>[7,6,8,2,1,5,3,4]=>[1,2,1,2,2]
[5,2,4,3,6,8,1,7]=>[4,2,3,1,5,7,8,6]=>[5,7,6,8,4,2,1,3]=>[2,2,1,1,2]
[3,8,6,5,4,1,2,7]=>[6,7,5,1,4,3,8,2]=>[3,2,4,8,5,6,1,7]=>[1,3,2,2]
[4,7,5,6,3,8,2,1]=>[3,5,1,4,2,8,7,6]=>[6,4,8,5,7,1,2,3]=>[1,2,2,3]
[4,8,5,7,2,3,1,6]=>[5,1,3,7,6,8,4,2]=>[4,8,6,2,3,1,5,7]=>[2,1,2,3]
[4,2,7,5,8,3,6,1]=>[1,4,6,3,8,2,7,5]=>[8,5,3,6,1,7,2,4]=>[1,1,2,2,2]
[3,8,5,7,1,4,6,2]=>[6,3,8,1,5,7,4,2]=>[3,6,1,8,4,2,5,7]=>[2,2,1,3]
[6,8,2,5,4,3,1,7]=>[7,6,3,1,5,4,8,2]=>[2,3,6,8,4,5,1,7]=>[4,2,2]
[6,7,2,4,5,3,8,1]=>[4,6,3,1,5,2,8,7]=>[5,3,6,8,4,7,1,2]=>[1,3,2,2]
[5,7,2,8,3,6,1,4]=>[5,1,7,8,3,2,6,4]=>[4,8,2,1,6,7,3,5]=>[2,1,3,2]
[5,1,3,6,4,2,8,7]=>[5,3,4,1,8,2,6,7]=>[4,6,5,8,1,7,3,2]=>[2,2,2,1,1]
[5,1,8,7,4,6,2,3]=>[1,7,5,8,6,4,2,3]=>[8,2,4,1,3,5,7,6]=>[1,2,4,1]
[6,8,3,7,5,4,2,1]=>[1,8,7,3,6,5,4,2]=>[8,1,2,6,3,4,5,7]=>[1,3,4]
[6,1,3,4,7,5,8,2]=>[6,3,4,5,1,8,2,7]=>[3,6,5,4,8,1,7,2]=>[2,1,2,2,1]
[6,3,2,1,4,8,5,7]=>[3,2,7,8,4,1,5,6]=>[6,7,2,1,5,8,4,3]=>[2,1,3,1,1]
[6,2,3,1,4,7,8,5]=>[2,3,6,8,4,1,5,7]=>[7,6,3,1,5,8,4,2]=>[1,1,1,3,1,1]
[6,2,1,4,8,7,5,3]=>[8,7,2,4,1,6,3,5]=>[1,2,7,5,8,3,6,4]=>[3,2,2,1]
[6,2,8,3,5,7,4,1]=>[5,8,4,1,7,2,6,3]=>[4,1,5,8,2,7,3,6]=>[1,3,2,2]
[5,2,1,3,6,4,8,7]=>[2,5,8,3,1,4,6,7]=>[7,4,1,6,8,5,3,2]=>[1,1,3,1,1,1]
[7,1,8,3,5,4,6,2]=>[6,4,5,8,7,2,1,3]=>[3,5,4,1,2,7,8,6]=>[2,1,4,1]
[7,1,2,4,8,5,6,3]=>[6,8,4,7,2,3,1,5]=>[3,1,5,2,7,6,8,4]=>[1,2,2,2,1]
[7,1,3,2,4,8,6,5]=>[8,3,7,2,4,5,1,6]=>[1,6,2,7,5,4,8,3]=>[2,2,1,2,1]
[7,2,1,3,4,5,8,6]=>[2,8,3,4,5,6,1,7]=>[7,1,6,5,4,3,8,2]=>[1,2,1,1,2,1]
[8,7,3,5,4,2,1,6]=>[7,3,6,5,4,8,2,1]=>[2,6,3,4,5,1,7,8]=>[2,3,3]
[8,4,6,5,3,2,1,7]=>[7,2,6,5,4,3,8,1]=>[2,7,3,4,5,6,1,8]=>[2,4,2]
[8,3,7,1,4,6,5,2]=>[8,2,5,7,4,6,3,1]=>[1,7,4,2,5,3,6,8]=>[2,1,2,3]
[2,8,3,6,4,7,5,1]=>[8,5,3,4,7,1,6,2]=>[1,4,6,5,2,8,3,7]=>[3,1,2,2]
[6,2,1,7,5,8,3,4]=>[7,5,2,4,1,8,3,6]=>[2,4,7,5,8,1,6,3]=>[3,2,2,1]
[6,3,8,7,5,2,1,4]=>[7,6,1,8,2,5,4,3]=>[2,3,8,1,7,4,5,6]=>[3,2,3]
[6,7,2,1,5,8,4,3]=>[5,8,3,1,7,4,2,6]=>[4,1,6,8,2,5,7,3]=>[1,3,3,1]
[9,1,8,7,6,5,4,3,2]=>[9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,8,7,9]=>[7,2]
[7,6,8,1,5,4,3,2]=>[8,7,6,4,2,1,5,3]=>[1,2,3,5,7,8,4,6]=>[6,2]
[7,1,9,8,6,5,4,3,2]=>[1,9,8,7,6,5,4,2,3]=>[9,1,2,3,4,5,6,8,7]=>[1,7,1]
[6,1,9,8,7,5,4,3,2]=>[9,1,8,7,6,5,4,2,3]=>[1,9,2,3,4,5,6,8,7]=>[2,6,1]
[5,4,8,7,6,1,3,2]=>[1,8,2,6,7,5,4,3]=>[8,1,7,3,2,4,5,6]=>[1,2,1,4]
[5,1,9,8,7,6,4,3,2]=>[9,8,1,7,6,5,4,2,3]=>[1,2,9,3,4,5,6,8,7]=>[3,5,1]
[4,1,9,8,7,6,5,3,2]=>[9,8,7,1,6,5,4,2,3]=>[1,2,3,9,4,5,6,8,7]=>[4,4,1]
[3,1,9,8,7,6,5,4,2]=>[9,8,7,6,1,5,4,2,3]=>[1,2,3,4,9,5,6,8,7]=>[5,3,1]
[10,1,9,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,9,8,10]=>[8,2]
[9,8,1,7,6,5,4,3,2]=>[9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,7,6,8,9]=>[6,3]
[7,6,1,8,5,4,3,2]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[7,1]
[8,1,10,9,7,6,5,4,3,2]=>[1,10,9,8,7,6,5,4,2,3]=>[10,1,2,3,4,5,6,7,9,8]=>[1,8,1]
[6,5,8,1,7,4,3,2]=>[2,1,8,7,6,4,5,3]=>[7,8,1,2,3,5,4,6]=>[2,4,2]
[7,1,10,9,8,6,5,4,3,2]=>[10,1,9,8,7,6,5,4,2,3]=>[1,10,2,3,4,5,6,7,9,8]=>[2,7,1]
[6,1,10,9,8,7,5,4,3,2]=>[10,9,1,8,7,6,5,4,2,3]=>[1,2,10,3,4,5,6,7,9,8]=>[3,6,1]
[6,5,8,7,4,1,3,2]=>[2,1,8,6,7,5,4,3]=>[7,8,1,3,2,4,5,6]=>[2,2,4]
[4,1,10,9,8,7,6,5,3,2]=>[10,9,8,7,1,6,5,4,2,3]=>[1,2,3,4,10,5,6,7,9,8]=>[5,4,1]
[3,2,9,8,7,6,5,4,1]=>[9,8,7,6,1,5,2,4,3]=>[1,2,3,4,9,5,8,6,7]=>[5,2,2]
[3,1,10,9,8,7,6,5,4,2]=>[10,9,8,7,6,1,5,4,2,3]=>[1,2,3,4,5,10,6,7,9,8]=>[6,3,1]
[1,6,4,8,3,2,5,7]=>[3,6,5,2,7,8,1,4]=>[6,3,4,7,2,1,8,5]=>[1,3,1,2,1]
[1,8,3,5,6,2,4,7]=>[6,3,4,7,5,8,1,2]=>[3,6,5,2,4,1,8,7]=>[2,1,2,2,1]
[1,4,8,5,6,2,3,7]=>[6,2,4,7,5,8,1,3]=>[3,7,5,2,4,1,8,6]=>[2,1,2,2,1]
[1,2,8,5,3,7,4,6]=>[7,4,8,5,6,1,2,3]=>[2,5,1,4,3,8,7,6]=>[2,2,2,1,1]
[6,1,4,8,2,3,5,7]=>[5,3,6,7,1,8,2,4]=>[4,6,3,2,8,1,7,5]=>[2,1,2,2,1]
[1,8,2,5,4,7,3,6]=>[5,4,7,8,3,6,1,2]=>[4,5,2,1,6,3,8,7]=>[2,1,2,2,1]
[5,7,4,1,2,3,8,6]=>[8,4,1,5,3,6,2,7]=>[1,5,8,4,6,3,7,2]=>[3,2,2,1]
[1,7,4,2,5,3,8,6]=>[5,3,8,4,6,1,2,7]=>[4,6,1,5,3,8,7,2]=>[2,2,2,1,1]
[6,7,4,2,1,3,8,5]=>[4,8,5,3,1,6,2,7]=>[5,1,4,6,8,3,7,2]=>[1,4,2,1]
[6,4,3,8,5,7,1,2]=>[2,7,3,1,5,8,6,4]=>[7,2,6,8,4,1,3,5]=>[1,3,1,3]
[7,2,5,3,4,1,6,8]=>[4,6,2,5,3,7,1,8]=>[5,3,7,4,6,2,8,1]=>[1,2,2,2,1]
[8,3,7,4,5,6,1,2]=>[4,7,2,5,8,6,3,1]=>[5,2,7,4,1,3,6,8]=>[1,2,1,4]
[2,7,4,3,1,5,6,8]=>[5,4,1,3,6,7,2,8]=>[4,5,8,6,3,2,7,1]=>[3,1,1,2,1]
[6,8,4,2,3,1,5,7]=>[4,6,5,3,1,7,8,2]=>[5,3,4,6,8,2,1,7]=>[1,4,1,2]
[3,7,5,2,4,1,6,8]=>[4,6,1,5,3,7,2,8]=>[5,3,8,4,6,2,7,1]=>[1,2,2,2,1]
[2,1,7,4,8,3,5,6]=>[4,6,7,1,3,8,2,5]=>[5,3,2,8,6,1,7,4]=>[1,1,2,1,2,1]
[5,2,8,6,1,3,4,7]=>[5,6,1,7,2,4,8,3]=>[4,3,8,2,7,5,1,6]=>[1,2,2,1,2]
[2,8,3,1,4,5,6,7]=>[4,1,3,5,6,7,8,2]=>[5,8,6,4,3,2,1,7]=>[2,1,1,1,1,2]
[7,4,8,2,3,1,5,6]=>[4,2,6,5,7,1,8,3]=>[5,7,3,4,2,8,1,6]=>[2,2,2,2]
[4,2,7,3,1,5,6,8]=>[5,2,1,4,6,7,3,8]=>[4,7,8,5,3,2,6,1]=>[3,1,1,2,1]
[8,3,7,2,1,4,5,6]=>[2,5,4,6,7,8,3,1]=>[7,4,5,3,2,1,6,8]=>[1,2,1,1,3]
[6,5,2,4,7,1,3,8]=>[6,3,4,2,1,7,5,8]=>[3,6,5,7,8,2,4,1]=>[2,3,2,1]
[6,5,7,4,1,8,2,3]=>[7,2,1,8,5,4,3,6]=>[2,7,8,1,4,5,6,3]=>[3,4,1]
[7,6,4,5,1,8,2,3]=>[7,3,8,5,4,2,1,6]=>[2,6,1,4,5,7,8,3]=>[2,5,1]
[6,4,3,1,8,2,5,7]=>[6,3,2,7,1,8,4,5]=>[3,6,7,2,8,1,5,4]=>[3,2,2,1]
[7,4,1,2,8,3,5,6]=>[6,7,2,8,3,4,1,5]=>[3,2,7,1,6,5,8,4]=>[1,2,2,2,1]
[4,8,1,3,5,7,2,6]=>[4,1,5,7,8,3,6,2]=>[5,8,4,2,1,6,3,7]=>[2,1,1,2,2]
[7,8,4,1,3,6,2,5]=>[5,7,3,8,4,1,6,2]=>[4,2,6,1,5,8,3,7]=>[1,2,3,2]
[6,5,8,1,3,7,2,4]=>[5,7,2,1,8,4,6,3]=>[4,2,7,8,1,5,3,6]=>[1,3,2,2]
[5,3,6,1,8,2,4,7]=>[2,6,1,7,3,8,4,5]=>[7,3,8,2,6,1,5,4]=>[1,2,2,2,1]
[8,3,1,7,2,4,5,6]=>[5,2,6,7,8,3,4,1]=>[4,7,3,2,1,6,5,8]=>[2,1,1,2,2]
[2,8,1,4,7,3,5,6]=>[4,6,7,8,1,3,5,2]=>[5,3,2,1,8,6,4,7]=>[1,1,1,2,1,2]
[3,1,8,5,4,7,6,2]=>[4,8,1,5,7,6,2,3]=>[5,1,8,4,2,3,7,6]=>[1,2,1,3,1]
[4,1,5,8,3,7,6,2]=>[1,8,3,5,7,6,2,4]=>[8,1,6,4,2,3,7,5]=>[1,2,1,3,1]
[4,1,5,3,8,7,6,2]=>[1,8,3,7,4,6,2,5]=>[8,1,6,2,5,3,7,4]=>[1,2,2,2,1]
[4,5,1,8,2,7,6,3]=>[1,2,8,7,5,6,3,4]=>[8,7,1,2,4,3,6,5]=>[1,1,3,2,1]
[4,8,5,3,1,7,6,2]=>[4,1,3,8,7,5,6,2]=>[5,8,6,1,2,4,3,7]=>[2,1,3,2]
[4,5,2,8,1,7,6,3]=>[1,2,8,7,3,5,6,4]=>[8,7,1,2,6,4,3,5]=>[1,1,3,1,2]
[5,6,2,7,8,1,4,3]=>[1,8,6,3,2,4,7,5]=>[8,1,3,6,7,5,2,4]=>[1,4,1,2]
[4,6,2,8,7,1,5,3]=>[8,1,6,2,7,3,5,4]=>[1,8,3,7,2,6,4,5]=>[2,2,2,2]
[4,8,6,3,7,5,1,2]=>[4,7,1,3,8,6,5,2]=>[5,2,8,6,1,3,4,7]=>[1,2,1,4]
[4,6,8,2,7,5,1,3]=>[7,1,2,8,4,6,5,3]=>[2,8,7,1,5,3,4,6]=>[2,1,2,3]
[4,6,2,8,7,5,1,3]=>[7,1,2,8,6,3,5,4]=>[2,8,7,1,3,6,4,5]=>[2,1,3,2]
[5,6,2,7,4,1,8,3]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[1,4,2,1]
[5,6,7,2,3,1,8,4]=>[4,1,5,2,8,6,3,7]=>[5,8,4,7,1,3,6,2]=>[2,2,3,1]
[5,6,7,2,8,3,1,4]=>[1,7,4,2,6,3,8,5]=>[8,2,5,7,3,6,1,4]=>[1,3,2,2]
[5,6,7,2,1,8,3,4]=>[4,1,7,2,8,5,3,6]=>[5,8,2,7,1,4,6,3]=>[2,2,3,1]
[5,6,7,2,1,3,8,4]=>[4,1,8,5,2,6,3,7]=>[5,8,1,4,7,3,6,2]=>[2,3,2,1]
[5,6,1,7,8,2,4,3]=>[1,8,6,4,2,7,3,5]=>[8,1,3,5,7,2,6,4]=>[1,4,2,1]
[5,6,1,7,2,4,8,3]=>[6,1,8,5,3,2,4,7]=>[3,8,1,4,6,7,5,2]=>[2,4,1,1]
[5,1,6,7,8,3,4,2]=>[3,1,6,4,8,7,2,5]=>[6,8,3,5,1,2,7,4]=>[2,2,3,1]
[4,1,6,8,7,3,5,2]=>[1,3,6,8,7,5,2,4]=>[8,6,3,1,2,4,7,5]=>[1,1,1,4,1]
[4,1,6,8,7,5,3,2]=>[8,1,3,7,6,5,2,4]=>[1,8,6,2,3,4,7,5]=>[2,1,4,1]
[5,1,6,7,4,8,3,2]=>[3,1,5,4,8,7,2,6]=>[6,8,4,5,1,2,7,3]=>[2,2,3,1]
[5,6,1,7,8,4,2,3]=>[1,7,4,2,8,6,3,5]=>[8,2,5,7,1,3,6,4]=>[1,3,3,1]
[4,6,8,1,7,5,2,3]=>[7,1,2,8,6,4,5,3]=>[2,8,7,1,3,5,4,6]=>[2,1,3,2]
[4,8,6,1,7,5,3,2]=>[8,7,1,6,4,3,5,2]=>[1,2,8,3,5,6,4,7]=>[3,3,2]
[5,6,7,1,8,3,2,4]=>[1,7,6,2,8,4,3,5]=>[8,2,3,7,1,5,6,4]=>[1,3,3,1]
[5,6,7,1,3,8,2,4]=>[5,1,7,2,8,4,3,6]=>[4,8,2,7,1,5,6,3]=>[2,2,3,1]
[5,6,7,1,3,2,8,4]=>[5,1,8,4,2,6,3,7]=>[4,8,1,5,7,3,6,2]=>[2,3,2,1]
[5,6,7,3,1,2,8,4]=>[1,8,5,4,2,6,3,7]=>[8,1,4,5,7,3,6,2]=>[1,4,2,1]
[5,6,7,3,8,1,2,4]=>[1,6,4,2,7,3,8,5]=>[8,3,5,7,2,6,1,4]=>[1,3,2,2]
[5,6,8,7,4,2,1,3]=>[1,2,7,6,8,5,4,3]=>[8,7,2,3,1,4,5,6]=>[1,1,2,4]
[5,6,7,3,8,2,1,4]=>[1,4,2,7,6,3,8,5]=>[8,5,7,2,3,6,1,4]=>[1,2,3,2]
[7,4,6,2,3,5,1,8]=>[4,2,5,7,6,3,1,8]=>[5,7,4,2,3,6,8,1]=>[2,1,4,1]
[1,4,8,6,3,2,5,7]=>[6,2,5,7,4,8,1,3]=>[3,7,4,2,5,1,8,6]=>[2,1,2,2,1]
[7,4,1,6,3,8,5,2]=>[2,8,5,4,7,3,1,6]=>[7,1,4,5,2,6,8,3]=>[1,3,3,1]
[7,6,3,1,5,8,4,2]=>[3,5,8,7,4,2,1,6]=>[6,4,1,2,5,7,8,3]=>[1,1,5,1]
[6,4,2,5,7,3,1,8]=>[4,2,7,3,1,6,5,8]=>[5,7,2,6,8,3,4,1]=>[2,3,2,1]
[4,2,5,7,6,3,1,8]=>[1,7,3,6,2,5,4,8]=>[8,2,6,3,7,4,5,1]=>[1,2,2,2,1]
[7,4,5,6,1,8,3,2]=>[2,3,8,7,5,4,1,6]=>[7,6,1,2,4,5,8,3]=>[1,1,5,1]
[4,1,5,8,6,3,2,7]=>[1,7,3,6,5,8,2,4]=>[8,2,6,3,4,1,7,5]=>[1,2,2,2,1]
[4,7,5,1,6,8,2,3]=>[7,1,5,3,8,4,2,6]=>[2,8,4,6,1,5,7,3]=>[2,2,3,1]
[8,6,5,1,2,7,4,3]=>[8,7,4,5,3,2,6,1]=>[1,2,5,4,6,7,3,8]=>[3,3,2]
[3,2,5,1,4,8,7,6]=>[1,3,8,2,7,4,5,6]=>[8,6,1,7,2,5,4,3]=>[1,1,2,2,1,1]
[8,5,4,1,3,2,7,6]=>[5,8,4,3,2,6,7,1]=>[4,1,5,6,7,3,2,8]=>[1,4,1,2]
[1,4,2,3,6,8,7,5]=>[2,8,5,7,1,3,4,6]=>[7,1,4,2,8,6,5,3]=>[1,2,2,1,1,1]
[5,4,8,3,7,1,6,2]=>[2,1,4,8,6,7,5,3]=>[7,8,5,1,3,2,4,6]=>[2,1,2,3]
[6,4,1,8,5,3,7,2]=>[2,6,5,1,8,7,3,4]=>[7,3,4,8,1,2,6,5]=>[1,3,3,1]
[8,4,6,1,3,5,2,7]=>[5,2,7,4,6,3,8,1]=>[4,7,2,5,3,6,1,8]=>[2,2,2,2]
[3,2,5,4,7,8,1,6]=>[1,3,7,2,4,5,8,6]=>[8,6,2,7,5,4,1,3]=>[1,1,2,1,1,2]
[5,2,4,3,7,8,1,6]=>[3,7,2,1,4,5,8,6]=>[6,2,7,8,5,4,1,3]=>[1,3,1,1,2]
[8,1,6,7,2,5,3,4]=>[7,8,5,3,6,2,4,1]=>[2,1,4,6,3,7,5,8]=>[1,3,2,2]
[3,1,7,6,5,8,2,4]=>[7,5,1,4,3,8,2,6]=>[2,4,8,5,6,1,7,3]=>[3,2,2,1]
[6,1,4,7,2,8,3,5]=>[3,7,8,5,2,1,4,6]=>[6,2,1,4,7,8,5,3]=>[1,1,4,1,1]
[3,2,8,6,4,7,1,5]=>[5,7,1,4,8,2,6,3]=>[4,2,8,5,1,7,3,6]=>[1,2,1,2,2]
[7,8,4,6,3,2,1,5]=>[3,7,6,5,1,8,4,2]=>[6,2,3,4,8,1,5,7]=>[1,4,3]
[1,8,6,5,3,7,2,4]=>[5,7,4,3,8,6,1,2]=>[4,2,5,6,1,3,8,7]=>[1,3,3,1]
[3,8,5,2,7,6,1,4]=>[7,3,8,1,4,6,5,2]=>[2,6,1,8,5,3,4,7]=>[2,2,1,3]
[4,7,5,3,1,8,6,2]=>[4,1,3,8,7,5,2,6]=>[5,8,6,1,2,4,7,3]=>[2,1,4,1]
[4,5,3,6,8,1,7,2]=>[1,3,2,4,8,6,7,5]=>[8,6,7,5,1,3,2,4]=>[1,2,1,2,2]
[3,5,2,6,1,8,7,4]=>[4,1,2,8,3,7,5,6]=>[5,8,7,1,6,2,4,3]=>[2,1,2,2,1]
[1,6,3,5,7,2,8,4]=>[4,8,3,2,6,1,5,7]=>[5,1,6,7,3,8,4,2]=>[1,3,2,1,1]
[1,5,4,6,7,8,2,3]=>[3,2,4,7,5,8,1,6]=>[6,7,5,2,4,1,8,3]=>[2,1,2,2,1]
[8,4,6,5,7,2,1,3]=>[7,2,6,4,3,8,5,1]=>[2,7,3,5,6,1,4,8]=>[2,3,3]
[7,4,5,2,6,8,1,3]=>[2,7,4,3,5,1,8,6]=>[7,2,5,6,4,8,1,3]=>[1,3,2,2]
[5,4,2,6,8,7,1,3]=>[4,2,1,7,8,3,6,5]=>[5,7,8,2,1,6,3,4]=>[3,1,2,2]
[6,5,1,4,3,2,8,7]=>[5,4,8,3,2,1,6,7]=>[4,5,1,6,7,8,3,2]=>[2,4,1,1]
[2,6,5,1,4,7,3,8]=>[5,7,4,1,3,2,6,8]=>[4,2,5,8,6,7,3,1]=>[1,3,2,1,1]
[3,6,4,5,2,1,8,7]=>[3,5,1,4,2,8,6,7]=>[6,4,8,5,7,1,3,2]=>[1,2,2,2,1]
[5,7,4,1,3,8,6,2]=>[1,8,5,3,7,4,2,6]=>[8,1,4,6,2,5,7,3]=>[1,3,3,1]
[7,5,4,2,3,8,1,6]=>[4,5,3,2,7,1,8,6]=>[5,4,6,7,2,8,1,3]=>[1,3,2,2]
[5,2,6,7,3,1,4,8]=>[6,5,2,1,3,7,4,8]=>[3,4,7,8,6,2,5,1]=>[4,1,2,1]
[2,4,3,8,6,1,5,7]=>[2,6,7,1,3,5,8,4]=>[7,3,2,8,6,4,1,5]=>[1,1,2,1,1,2]
[7,8,1,3,5,6,2,4]=>[7,4,5,8,3,1,6,2]=>[2,5,4,1,6,8,3,7]=>[2,1,3,2]
[7,8,3,1,5,6,2,4]=>[3,7,5,8,4,1,6,2]=>[6,2,4,1,5,8,3,7]=>[1,2,3,2]
[7,1,3,8,5,6,2,4]=>[7,5,8,3,6,2,1,4]=>[2,4,1,6,3,7,8,5]=>[2,2,3,1]
[5,1,7,8,3,4,6,2]=>[5,1,6,3,8,7,2,4]=>[4,8,3,6,1,2,7,5]=>[2,2,3,1]
[3,7,1,5,8,6,2,4]=>[4,7,8,1,6,3,2,5]=>[5,2,1,8,3,6,7,4]=>[1,1,2,3,1]
[1,3,7,8,2,5,6,4]=>[6,8,5,2,3,7,1,4]=>[3,1,4,7,6,2,8,5]=>[1,3,1,2,1]
[3,1,7,8,5,2,6,4]=>[8,6,1,5,3,7,2,4]=>[1,3,8,4,6,2,7,5]=>[3,2,2,1]
[1,3,7,5,8,2,6,4]=>[4,8,6,2,3,7,1,5]=>[5,1,3,7,6,2,8,4]=>[1,3,1,2,1]
[3,1,7,5,8,2,6,4]=>[4,8,1,6,3,7,2,5]=>[5,1,8,3,6,2,7,4]=>[1,2,2,2,1]
[3,5,7,1,8,4,6,2]=>[2,6,8,1,7,4,3,5]=>[7,3,1,8,2,5,6,4]=>[1,1,2,3,1]
[3,5,7,8,1,4,6,2]=>[2,6,8,1,5,3,7,4]=>[7,3,1,8,4,6,2,5]=>[1,1,2,2,2]
[5,3,7,8,4,6,1,2]=>[1,7,5,2,3,8,6,4]=>[8,2,4,7,6,1,3,5]=>[1,3,1,3]
[5,3,7,8,4,1,6,2]=>[1,8,6,2,5,3,7,4]=>[8,1,3,7,4,6,2,5]=>[1,3,2,2]
[5,3,7,8,1,4,6,2]=>[6,1,8,2,5,3,7,4]=>[3,8,1,7,4,6,2,5]=>[2,2,2,2]
[5,3,7,1,8,4,6,2]=>[6,1,8,2,7,4,3,5]=>[3,8,1,7,2,5,6,4]=>[2,2,3,1]
[5,1,3,7,8,4,2,6]=>[7,6,3,1,4,8,2,5]=>[2,3,6,8,5,1,7,4]=>[4,1,2,1]
[3,6,2,1,4,5,8,7]=>[1,3,8,4,5,2,6,7]=>[8,6,1,5,4,7,3,2]=>[1,1,2,2,1,1]
[6,4,2,5,1,3,8,7]=>[8,3,2,5,4,1,6,7]=>[1,6,7,4,5,8,3,2]=>[3,3,1,1]
[2,5,8,1,7,3,4,6]=>[6,2,7,8,1,4,5,3]=>[3,7,2,1,8,5,4,6]=>[2,1,2,1,2]
[6,8,2,7,3,1,4,5]=>[6,3,5,1,7,8,4,2]=>[3,6,4,8,2,1,5,7]=>[2,2,1,3]
[6,8,2,3,7,1,4,5]=>[3,4,6,1,7,8,5,2]=>[6,5,3,8,2,1,4,7]=>[1,1,2,1,3]
[8,6,2,7,4,5,1,3]=>[7,5,8,3,2,6,4,1]=>[2,4,1,6,7,3,5,8]=>[2,3,3]
[5,2,8,1,7,3,4,6]=>[6,7,1,8,2,4,5,3]=>[3,2,8,1,7,5,4,6]=>[1,2,2,1,2]
[4,2,3,8,1,5,6,7]=>[2,3,1,5,6,7,8,4]=>[7,6,8,4,3,2,1,5]=>[1,2,1,1,1,2]
[5,2,8,3,7,1,4,6]=>[4,6,1,7,8,2,5,3]=>[5,3,8,2,1,7,4,6]=>[1,2,1,2,2]
[5,2,8,4,6,1,3,7]=>[6,4,1,7,2,5,8,3]=>[3,5,8,2,7,4,1,6]=>[3,2,1,2]
[2,1,5,8,4,3,6,7]=>[3,6,1,5,7,8,2,4]=>[6,3,8,4,2,1,7,5]=>[1,2,1,1,2,1]
[5,8,3,2,7,1,4,6]=>[4,3,1,6,7,8,5,2]=>[5,6,8,3,2,1,4,7]=>[3,1,1,3]
[4,1,3,8,2,5,6,7]=>[3,5,1,6,7,8,2,4]=>[6,4,8,3,2,1,7,5]=>[1,2,1,1,2,1]
[3,5,8,2,7,1,4,6]=>[4,1,2,6,7,8,5,3]=>[5,8,7,3,2,1,4,6]=>[2,1,1,1,3]
[2,6,8,3,7,1,4,5]=>[4,6,2,7,8,1,5,3]=>[5,3,7,2,1,8,4,6]=>[1,2,1,2,2]
[5,1,8,3,7,2,4,6]=>[4,6,1,7,8,5,2,3]=>[5,3,8,2,1,4,7,6]=>[1,2,1,3,1]
[5,1,8,4,6,2,3,7]=>[6,4,1,7,5,8,2,3]=>[3,5,8,2,4,1,7,6]=>[3,2,2,1]
[4,5,8,1,6,2,3,7]=>[1,6,2,7,4,5,8,3]=>[8,3,7,2,5,4,1,6]=>[1,2,2,1,2]
[5,4,8,1,6,2,3,7]=>[6,2,1,7,4,5,8,3]=>[3,7,8,2,5,4,1,6]=>[3,2,1,2]
[2,1,5,4,8,3,6,7]=>[4,1,3,6,7,8,2,5]=>[5,8,6,3,2,1,7,4]=>[2,1,1,1,2,1]
[2,4,3,8,1,5,6,7]=>[3,1,2,5,6,7,8,4]=>[6,8,7,4,3,2,1,5]=>[2,1,1,1,1,2]
[3,1,8,4,2,5,6,7]=>[1,5,4,6,7,8,2,3]=>[8,4,5,3,2,1,7,6]=>[1,2,1,1,2,1]
[3,8,4,2,1,5,6,7]=>[5,1,4,3,6,7,8,2]=>[4,8,5,6,3,2,1,7]=>[2,2,1,1,2]
[2,3,8,4,1,5,6,7]=>[5,1,2,4,6,7,8,3]=>[4,8,7,5,3,2,1,6]=>[2,1,1,1,1,2]
[3,4,2,8,1,5,6,7]=>[1,3,2,5,6,7,8,4]=>[8,6,7,4,3,2,1,5]=>[1,2,1,1,1,2]
[3,8,5,2,7,1,4,6]=>[4,6,1,3,7,8,5,2]=>[5,3,8,6,2,1,4,7]=>[1,2,1,1,3]
[4,8,5,2,6,1,3,7]=>[1,4,6,3,7,5,8,2]=>[8,5,3,6,2,4,1,7]=>[1,1,2,2,2]
[3,2,8,4,1,5,6,7]=>[1,5,2,4,6,7,8,3]=>[8,4,7,5,3,2,1,6]=>[1,2,1,1,1,2]
[2,8,4,3,1,5,6,7]=>[5,4,1,3,6,7,8,2]=>[4,5,8,6,3,2,1,7]=>[3,1,1,1,2]
[5,7,4,3,8,1,6,2]=>[1,4,3,8,6,2,7,5]=>[8,5,6,1,3,7,2,4]=>[1,2,3,2]
[5,7,4,3,8,2,6,1]=>[1,4,3,6,2,8,7,5]=>[8,5,6,3,7,1,2,4]=>[1,2,2,3]
[3,8,4,2,6,7,5,1]=>[3,5,8,1,4,7,6,2]=>[6,4,1,8,5,2,3,7]=>[1,1,2,1,3]
[3,8,4,1,6,7,5,2]=>[3,5,8,1,7,4,6,2]=>[6,4,1,8,2,5,3,7]=>[1,1,2,2,2]
[6,1,7,5,2,8,4,3]=>[8,7,5,4,2,1,3,6]=>[1,2,4,5,7,8,6,3]=>[6,1,1]
[5,6,4,3,2,8,1,7]=>[1,5,4,3,2,7,8,6]=>[8,4,5,6,7,2,1,3]=>[1,4,1,2]
[2,6,7,5,3,8,4,1]=>[2,8,5,4,1,3,7,6]=>[7,1,4,5,8,6,2,3]=>[1,4,1,2]
[6,7,4,8,2,5,3,1]=>[3,1,8,5,2,7,6,4]=>[6,8,1,4,7,2,3,5]=>[2,3,3]
[2,1,6,7,5,3,8,4]=>[3,8,6,1,5,2,4,7]=>[6,1,3,8,4,7,5,2]=>[1,3,2,1,1]
[3,8,4,2,1,6,7,5]=>[4,1,3,6,8,5,7,2]=>[5,8,6,3,1,4,2,7]=>[2,1,1,2,2]
[5,7,4,3,8,2,1,6]=>[1,4,3,7,6,2,8,5]=>[8,5,6,2,3,7,1,4]=>[1,2,3,2]
[6,7,4,8,1,2,5,3]=>[8,5,3,1,6,2,7,4]=>[1,4,6,8,3,7,2,5]=>[4,2,2]
[6,7,5,8,1,2,4,3]=>[8,5,1,6,3,2,7,4]=>[1,4,8,3,6,7,2,5]=>[3,3,2]
[6,7,4,8,3,1,2,5]=>[6,3,1,7,5,2,8,4]=>[3,6,8,2,4,7,1,5]=>[3,3,2]
[3,4,8,1,2,5,7,6]=>[1,2,8,4,5,6,7,3]=>[8,7,1,5,4,3,2,6]=>[1,1,2,1,1,2]
[6,1,3,4,8,2,5,7]=>[3,4,6,7,1,8,2,5]=>[6,5,3,2,8,1,7,4]=>[1,1,1,2,2,1]
[6,2,3,4,8,1,5,7]=>[2,3,4,6,1,7,8,5]=>[7,6,5,3,8,2,1,4]=>[1,1,1,2,1,2]
[3,4,8,2,1,5,7,6]=>[1,2,4,8,5,6,7,3]=>[8,7,5,1,4,3,2,6]=>[1,1,1,2,1,2]
[6,7,5,8,2,4,3,1]=>[1,8,5,3,2,7,6,4]=>[8,1,4,6,7,2,3,5]=>[1,4,3]
[6,7,5,8,3,1,4,2]=>[1,8,6,5,3,2,7,4]=>[8,1,3,4,6,7,2,5]=>[1,5,2]
[3,4,8,1,5,7,6,2]=>[8,1,2,5,7,4,6,3]=>[1,8,7,4,2,5,3,6]=>[2,1,1,2,2]
[2,5,7,6,1,4,8,3]=>[2,6,8,5,1,4,3,7]=>[7,3,1,4,8,5,6,2]=>[1,1,3,2,1]
[6,7,4,8,2,3,5,1]=>[5,3,1,6,2,8,7,4]=>[4,6,8,3,7,1,2,5]=>[3,2,3]
[6,7,4,8,1,3,5,2]=>[6,3,1,8,5,2,7,4]=>[3,6,8,1,4,7,2,5]=>[3,3,2]
[2,6,7,5,1,3,8,4]=>[8,5,2,6,1,4,3,7]=>[1,4,7,3,8,5,6,2]=>[3,2,2,1]
[6,3,1,4,8,2,5,7]=>[4,2,6,7,1,8,3,5]=>[5,7,3,2,8,1,6,4]=>[2,1,2,2,1]
[6,7,4,8,1,3,2,5]=>[7,5,3,1,6,2,8,4]=>[2,4,6,8,3,7,1,5]=>[4,2,2]
[6,7,5,8,4,1,3,2]=>[1,8,6,3,2,7,5,4]=>[8,1,3,6,7,2,4,5]=>[1,4,3]
[6,7,4,8,2,1,3,5]=>[6,5,3,1,7,2,8,4]=>[3,4,6,8,2,7,1,5]=>[4,2,2]
[6,7,4,8,1,2,3,5]=>[5,6,3,1,7,2,8,4]=>[4,3,6,8,2,7,1,5]=>[1,3,2,2]
[1,5,6,3,4,8,2,7]=>[4,2,5,3,7,8,1,6]=>[5,7,4,6,2,1,8,3]=>[2,2,1,2,1]
[1,4,3,6,5,8,2,7]=>[2,5,3,4,7,8,1,6]=>[7,4,6,5,2,1,8,3]=>[1,2,1,1,2,1]
[8,1,3,4,7,2,6,5]=>[8,3,4,6,7,2,5,1]=>[1,6,5,3,2,7,4,8]=>[2,1,1,2,2]
[5,1,7,3,4,8,2,6]=>[4,5,1,7,3,8,2,6]=>[5,4,8,2,6,1,7,3]=>[1,2,2,2,1]
[6,7,8,2,3,5,4,1]=>[8,4,1,5,2,7,6,3]=>[1,5,8,4,7,2,3,6]=>[3,2,3]
[5,8,6,2,3,7,4,1]=>[1,8,4,5,3,7,6,2]=>[8,1,5,4,6,2,3,7]=>[1,2,2,3]
[2,8,3,4,7,5,6,1]=>[6,8,3,4,7,1,5,2]=>[3,1,6,5,2,8,4,7]=>[1,2,1,2,2]
[1,8,3,4,7,6,2,5]=>[7,8,3,4,6,5,1,2]=>[2,1,6,5,3,4,8,7]=>[1,2,1,3,1]
[8,7,2,3,6,5,4,1]=>[8,7,3,4,6,5,2,1]=>[1,2,6,5,3,4,7,8]=>[3,1,4]
[3,8,1,7,5,2,6,4]=>[8,6,1,5,7,3,4,2]=>[1,3,8,4,2,6,5,7]=>[3,1,2,2]
[4,8,1,6,7,2,5,3]=>[8,1,6,4,7,3,5,2]=>[1,8,3,5,2,6,4,7]=>[2,2,2,2]
[2,1,3,8,4,6,5,7]=>[7,1,5,6,8,2,3,4]=>[2,8,4,3,1,7,6,5]=>[2,1,1,2,1,1]
[8,2,1,7,4,3,6,5]=>[5,8,2,6,7,3,4,1]=>[4,1,7,3,2,6,5,8]=>[1,2,1,2,2]
[1,3,2,8,5,4,6,7]=>[6,2,5,7,8,1,3,4]=>[3,7,4,2,1,8,6,5]=>[2,1,1,2,1,1]
[8,3,1,5,7,2,6,4]=>[2,4,8,6,7,3,5,1]=>[7,5,1,3,2,6,4,8]=>[1,1,2,2,2]
[8,4,5,1,7,2,6,3]=>[2,8,6,3,7,4,5,1]=>[7,1,3,6,2,5,4,8]=>[1,3,2,2]
[1,5,6,8,7,4,2,3]=>[2,3,7,8,6,5,1,4]=>[7,6,2,1,3,4,8,5]=>[1,1,1,4,1]
[8,4,5,7,6,3,2,1]=>[8,2,3,7,6,5,4,1]=>[1,7,6,2,3,4,5,8]=>[2,1,5]
[1,4,8,5,7,6,2,3]=>[4,7,8,2,6,5,1,3]=>[5,2,1,7,3,4,8,6]=>[1,1,2,3,1]
[2,4,8,5,7,3,6,1]=>[4,6,8,2,7,1,5,3]=>[5,3,1,7,2,8,4,6]=>[1,1,2,2,2]
[4,3,8,6,5,7,2,1]=>[5,1,4,8,2,7,6,3]=>[4,8,5,1,7,2,3,6]=>[2,1,2,3]
[6,7,2,8,5,3,4,1]=>[6,1,8,7,3,2,5,4]=>[3,8,1,2,6,7,4,5]=>[2,4,2]
[5,2,7,8,6,3,4,1]=>[1,6,3,8,7,2,5,4]=>[8,3,6,1,2,7,4,5]=>[1,2,3,2]
[4,2,8,6,7,3,5,1]=>[6,1,4,8,7,2,5,3]=>[3,8,5,1,2,7,4,6]=>[2,1,3,2]
[3,2,8,7,5,4,6,1]=>[6,5,8,1,7,2,4,3]=>[3,4,1,8,2,7,5,6]=>[2,2,2,2]
[3,1,8,7,5,6,2,4]=>[7,5,8,1,6,4,2,3]=>[2,4,1,8,3,5,7,6]=>[2,2,3,1]
[4,1,8,6,7,5,2,3]=>[7,1,4,8,6,5,2,3]=>[2,8,5,1,3,4,7,6]=>[2,1,4,1]
[6,7,1,8,5,4,2,3]=>[7,1,8,6,5,3,2,4]=>[2,8,1,3,4,6,7,5]=>[2,5,1]
[7,8,3,2,6,1,4,5]=>[4,3,6,7,1,8,5,2]=>[5,6,3,2,8,1,4,7]=>[2,1,2,3]
[3,4,8,2,6,1,7,5]=>[8,1,2,4,6,5,7,3]=>[1,8,7,5,3,4,2,6]=>[2,1,1,2,2]
[7,8,4,1,5,6,3,2]=>[5,3,8,7,4,1,6,2]=>[4,6,1,2,5,8,3,7]=>[2,4,2]
[7,8,1,4,5,6,3,2]=>[4,5,8,7,3,1,6,2]=>[5,4,1,2,6,8,3,7]=>[1,1,4,2]
[7,8,1,2,6,3,4,5]=>[6,7,8,3,4,1,5,2]=>[3,2,1,6,5,8,4,7]=>[1,1,2,2,2]
[7,8,5,1,4,6,3,2]=>[5,8,7,4,3,1,6,2]=>[4,1,2,5,6,8,3,7]=>[1,5,2]
[7,8,4,5,1,6,3,2]=>[3,8,7,5,4,1,6,2]=>[6,1,2,4,5,8,3,7]=>[1,5,2]
[5,3,8,4,1,6,7,2]=>[6,2,1,4,8,5,7,3]=>[3,7,8,5,1,4,2,6]=>[3,1,2,2]
[6,2,4,8,1,5,3,7]=>[3,7,2,5,1,6,8,4]=>[6,2,7,4,8,3,1,5]=>[1,2,2,1,2]
[3,4,8,5,1,6,7,2]=>[6,1,2,4,8,5,7,3]=>[3,8,7,5,1,4,2,6]=>[2,1,1,2,2]
[3,5,8,1,4,6,7,2]=>[5,1,2,6,8,4,7,3]=>[4,8,7,3,1,5,2,6]=>[2,1,1,2,2]
[1,4,8,2,6,3,7,5]=>[8,2,6,4,5,7,1,3]=>[1,7,3,5,4,2,8,6]=>[2,2,1,2,1]
[5,3,8,1,4,6,7,2]=>[2,5,1,6,8,4,7,3]=>[7,4,8,3,1,5,2,6]=>[1,2,1,2,2]
[4,2,6,8,1,5,3,7]=>[1,7,5,2,3,6,8,4]=>[8,2,4,7,6,3,1,5]=>[1,3,1,1,2]
[7,4,2,8,1,5,3,6]=>[7,3,2,5,6,1,8,4]=>[2,6,7,4,3,8,1,5]=>[3,1,2,2]
[6,1,7,5,8,4,3,2]=>[4,3,1,8,7,6,2,5]=>[5,6,8,1,2,3,7,4]=>[3,4,1]
[6,2,1,8,4,5,3,7]=>[5,7,2,6,1,8,3,4]=>[4,2,7,3,8,1,6,5]=>[1,2,2,2,1]
[1,2,7,8,5,3,4,6]=>[6,7,5,3,8,1,2,4]=>[3,2,4,6,1,8,7,5]=>[1,3,2,1,1]
[6,3,7,8,5,4,1,2]=>[7,3,1,8,2,6,5,4]=>[2,6,8,1,7,3,4,5]=>[3,2,3]
[6,1,5,7,8,4,3,2]=>[3,4,1,8,7,6,2,5]=>[6,5,8,1,2,3,7,4]=>[1,2,4,1]
[1,7,5,6,8,4,3,2]=>[3,4,2,8,7,6,1,5]=>[6,5,7,1,2,3,8,4]=>[1,2,4,1]
[3,1,8,4,5,6,7,2]=>[1,4,5,6,8,7,2,3]=>[8,5,4,3,1,2,7,6]=>[1,1,1,1,3,1]
[2,1,4,8,6,5,3,7]=>[7,6,1,3,5,8,2,4]=>[2,3,8,6,4,1,7,5]=>[3,1,1,2,1]
[2,4,1,8,6,5,3,7]=>[7,2,6,1,5,8,3,4]=>[2,7,3,8,4,1,6,5]=>[2,2,1,2,1]
[4,2,1,8,6,5,3,7]=>[1,7,6,2,5,8,3,4]=>[8,2,3,7,4,1,6,5]=>[1,3,1,2,1]
[3,2,7,8,5,1,4,6]=>[6,7,1,5,2,3,8,4]=>[3,2,8,4,7,6,1,5]=>[1,2,2,1,2]
[2,3,7,8,5,1,4,6]=>[6,7,5,1,2,3,8,4]=>[3,2,4,8,7,6,1,5]=>[1,3,1,1,2]
[2,7,3,8,5,1,4,6]=>[6,7,3,5,1,2,8,4]=>[3,2,6,4,8,7,1,5]=>[1,2,2,1,2]
[3,6,2,8,5,1,4,7]=>[6,7,1,3,2,5,8,4]=>[3,2,8,6,7,4,1,5]=>[1,2,2,1,2]
[4,1,2,8,7,5,3,6]=>[1,7,6,8,5,2,3,4]=>[8,2,3,1,4,7,6,5]=>[1,2,3,1,1]
[1,4,2,8,7,5,3,6]=>[7,2,6,8,5,1,3,4]=>[2,7,3,1,4,8,6,5]=>[2,1,3,1,1]
[7,3,6,8,5,4,1,2]=>[7,3,8,2,1,6,5,4]=>[2,6,1,7,8,3,4,5]=>[2,3,3]
[7,2,1,8,5,3,4,6]=>[6,7,2,5,8,3,1,4]=>[3,2,7,4,1,6,8,5]=>[1,2,1,3,1]
[1,2,6,8,4,5,3,7]=>[5,3,7,6,8,1,2,4]=>[4,6,2,3,1,8,7,5]=>[2,2,2,1,1]
[7,1,6,5,8,4,3,2]=>[4,3,8,7,6,2,1,5]=>[5,6,1,2,3,7,8,4]=>[2,5,1]
[6,5,7,1,8,4,3,2]=>[2,1,8,7,6,4,3,5]=>[7,8,1,2,3,5,6,4]=>[2,5,1]
[5,7,6,1,8,4,3,2]=>[8,1,7,6,4,3,2,5]=>[1,8,2,3,5,6,7,4]=>[2,5,1]
[6,7,1,5,8,4,3,2]=>[4,1,8,7,6,3,2,5]=>[5,8,1,2,3,6,7,4]=>[2,5,1]
[6,7,3,8,5,4,1,2]=>[7,1,8,3,2,6,5,4]=>[2,8,1,6,7,3,4,5]=>[2,3,3]
[7,1,2,8,4,5,3,6]=>[5,7,6,8,2,3,1,4]=>[4,2,3,1,7,6,8,5]=>[1,2,2,2,1]
[7,6,1,5,8,4,3,2]=>[4,8,7,6,3,2,1,5]=>[5,1,2,3,6,7,8,4]=>[1,6,1]
[7,5,6,1,8,4,3,2]=>[2,8,7,6,4,3,1,5]=>[7,1,2,3,5,6,8,4]=>[1,6,1]
[9,10,7,8,5,6,2,1,3,4]=>[8,7,9,5,3,1,10,6,4,2]=>[3,4,2,6,8,10,1,5,7,9]=>[2,4,4]
[9,10,7,8,4,3,5,6,1,2]=>[6,5,9,7,3,1,10,8,4,2]=>[5,6,2,4,8,10,1,3,7,9]=>[2,4,4]
[9,10,7,8,4,2,5,1,3,6]=>[6,8,5,9,7,3,1,10,4,2]=>[5,3,6,2,4,8,10,1,7,9]=>[1,2,4,3]
[9,10,7,8,3,2,1,4,5,6]=>[7,6,5,8,9,3,1,10,4,2]=>[4,5,6,3,2,8,10,1,7,9]=>[3,1,3,3]
[9,10,6,5,7,8,3,4,1,2]=>[4,3,9,7,5,1,10,8,6,2]=>[7,8,2,4,6,10,1,3,5,9]=>[2,4,4]
[9,10,6,5,7,8,2,1,3,4]=>[8,7,4,3,9,5,1,10,6,2]=>[3,4,7,8,2,6,10,1,5,9]=>[4,3,3]
[9,10,6,4,7,3,5,8,1,2]=>[4,6,3,9,7,5,1,10,8,2]=>[7,5,8,2,4,6,10,1,3,9]=>[1,2,4,3]
[9,10,6,4,7,2,5,1,3,8]=>[6,4,8,3,9,7,5,1,10,2]=>[5,7,3,8,2,4,6,10,1,9]=>[2,2,4,2]
[9,10,6,3,7,2,1,4,5,8]=>[4,7,6,8,3,9,5,1,10,2]=>[7,4,5,3,8,2,6,10,1,9]=>[1,2,2,3,2]
[9,10,5,4,3,6,7,8,1,2]=>[5,4,3,6,9,7,1,10,8,2]=>[6,7,8,5,2,4,10,1,3,9]=>[3,1,3,3]
[9,10,5,4,2,6,7,1,3,8]=>[8,5,4,3,6,9,7,1,10,2]=>[3,6,7,8,5,2,4,10,1,9]=>[4,1,3,2]
[9,10,5,3,2,6,1,4,7,8]=>[5,4,7,3,8,6,9,1,10,2]=>[6,7,4,8,3,5,2,10,1,9]=>[2,2,2,2,2]
[9,10,4,3,2,1,5,6,7,8]=>[6,5,4,3,7,8,9,1,10,2]=>[5,6,7,8,4,3,2,10,1,9]=>[4,1,1,2,2]
[8,7,9,10,5,6,3,4,1,2]=>[2,1,9,7,5,3,10,8,6,4]=>[9,10,2,4,6,8,1,3,5,7]=>[2,4,4]
[8,7,9,10,5,6,2,1,3,4]=>[8,7,2,1,9,5,3,10,6,4]=>[3,4,9,10,2,6,8,1,5,7]=>[4,3,3]
[8,7,9,10,4,3,5,6,1,2]=>[6,5,2,1,9,7,3,10,8,4]=>[5,6,9,10,2,4,8,1,3,7]=>[4,3,3]
[8,7,9,10,4,2,5,1,3,6]=>[6,8,5,2,1,9,7,3,10,4]=>[5,3,6,9,10,2,4,8,1,7]=>[1,4,3,2]
[8,7,9,10,3,2,1,4,5,6]=>[7,6,5,8,2,1,9,3,10,4]=>[4,5,6,3,9,10,2,8,1,7]=>[3,3,2,2]
[8,6,9,5,7,10,3,4,1,2]=>[2,4,1,9,7,5,3,10,8,6]=>[9,7,10,2,4,6,8,1,3,5]=>[1,2,4,3]
[8,6,9,5,7,10,2,1,3,4]=>[2,8,7,4,1,9,5,3,10,6]=>[9,3,4,7,10,2,6,8,1,5]=>[1,4,3,2]
[8,6,9,4,7,3,5,10,1,2]=>[4,2,6,1,9,7,5,3,10,8]=>[7,9,5,10,2,4,6,8,1,3]=>[2,2,4,2]
[8,6,9,3,7,2,1,4,5,10]=>[4,7,6,2,8,1,9,5,3,10]=>[7,4,5,9,3,10,2,6,8,1]=>[1,3,2,3,1]
[8,5,9,4,3,6,7,10,1,2]=>[2,5,4,6,1,9,7,3,10,8]=>[9,6,7,5,10,2,4,8,1,3]=>[1,2,2,3,2]
[8,5,9,4,2,6,7,1,3,10]=>[2,8,5,4,6,1,9,7,3,10]=>[9,3,6,7,5,10,2,4,8,1]=>[1,3,2,3,1]
[8,5,9,3,2,6,1,4,7,10]=>[5,4,2,7,8,6,1,9,3,10]=>[6,7,9,4,3,5,10,2,8,1]=>[3,1,3,2,1]
[8,4,9,3,2,1,5,6,7,10]=>[2,6,5,4,7,8,1,9,3,10]=>[9,5,6,7,4,3,10,2,8,1]=>[1,3,1,2,2,1]
[7,6,5,8,9,10,3,4,1,2]=>[3,2,1,4,9,7,5,10,8,6]=>[8,9,10,7,2,4,6,1,3,5]=>[3,1,3,3]
[7,6,5,8,9,10,2,1,3,4]=>[3,2,1,8,7,4,9,5,10,6]=>[8,9,10,3,4,7,2,6,1,5]=>[3,3,2,2]
[7,6,4,8,9,3,5,10,1,2]=>[6,3,2,1,4,9,7,5,10,8]=>[5,8,9,10,7,2,4,6,1,3]=>[4,1,3,2]
[7,6,4,8,9,2,5,1,3,10]=>[3,6,2,1,8,4,9,7,5,10]=>[8,5,9,10,3,7,2,4,6,1]=>[1,3,2,3,1]
[7,6,3,8,9,2,1,4,5,10]=>[7,3,6,2,1,8,4,9,5,10]=>[4,8,5,9,10,3,7,2,6,1]=>[2,3,2,2,1]
[7,5,4,8,3,6,9,10,1,2]=>[3,2,5,1,6,4,9,7,10,8]=>[8,9,6,10,5,7,2,4,1,3]=>[2,2,2,2,2]
[7,4,3,8,2,1,5,6,9,10]=>[3,2,6,5,7,1,8,4,9,10]=>[8,9,5,6,4,10,3,7,2,1]=>[2,2,2,2,1,1]
[6,5,4,3,7,8,9,10,1,2]=>[4,3,2,1,5,6,9,7,10,8]=>[7,8,9,10,6,5,2,4,1,3]=>[4,1,1,2,2]
[11,12,9,10,7,8,5,6,2,1,3,4]=>[10,9,11,7,5,3,1,12,8,6,4,2]=>[3,4,2,6,8,10,12,1,5,7,9,11]=>[2,5,5]
[11,12,9,10,7,8,4,3,5,6,1,2]=>[8,7,11,9,5,3,1,12,10,6,4,2]=>[5,6,2,4,8,10,12,1,3,7,9,11]=>[2,5,5]
[11,12,9,10,7,8,4,2,5,1,3,6]=>[8,10,7,11,9,5,3,1,12,6,4,2]=>[5,3,6,2,4,8,10,12,1,7,9,11]=>[1,2,5,4]
[11,12,9,10,7,8,3,2,1,4,5,6]=>[9,8,7,10,11,5,3,1,12,6,4,2]=>[4,5,6,3,2,8,10,12,1,7,9,11]=>[3,1,4,4]
[11,12,9,10,6,5,7,8,3,4,1,2]=>[6,5,11,9,7,3,1,12,10,8,4,2]=>[7,8,2,4,6,10,12,1,3,5,9,11]=>[2,5,5]
[11,12,9,10,6,5,7,8,2,1,3,4]=>[10,9,6,5,11,7,3,1,12,8,4,2]=>[3,4,7,8,2,6,10,12,1,5,9,11]=>[4,4,4]
[11,12,9,10,6,4,7,3,5,8,1,2]=>[6,8,5,11,9,7,3,1,12,10,4,2]=>[7,5,8,2,4,6,10,12,1,3,9,11]=>[1,2,5,4]
[11,12,9,10,6,4,7,2,5,1,3,8]=>[8,6,10,5,11,9,7,3,1,12,4,2]=>[5,7,3,8,2,4,6,10,12,1,9,11]=>[2,2,5,3]
[11,12,9,10,6,3,7,2,1,4,5,8]=>[6,9,8,10,5,11,7,3,1,12,4,2]=>[7,4,5,3,8,2,6,10,12,1,9,11]=>[1,2,2,4,3]
[11,12,9,10,5,4,3,6,7,8,1,2]=>[7,6,5,8,11,9,3,1,12,10,4,2]=>[6,7,8,5,2,4,10,12,1,3,9,11]=>[3,1,4,4]
[11,12,9,10,5,4,2,6,7,1,3,8]=>[10,7,6,5,8,11,9,3,1,12,4,2]=>[3,6,7,8,5,2,4,10,12,1,9,11]=>[4,1,4,3]
[11,12,9,10,5,3,2,6,1,4,7,8]=>[7,6,9,5,10,8,11,3,1,12,4,2]=>[6,7,4,8,3,5,2,10,12,1,9,11]=>[2,2,2,3,3]
[11,12,9,10,4,3,2,1,5,6,7,8]=>[8,7,6,5,9,10,11,3,1,12,4,2]=>[5,6,7,8,4,3,2,10,12,1,9,11]=>[4,1,1,3,3]
[11,12,8,7,9,10,5,6,3,4,1,2]=>[4,3,11,9,7,5,1,12,10,8,6,2]=>[9,10,2,4,6,8,12,1,3,5,7,11]=>[2,5,5]
[11,12,8,7,9,10,5,6,2,1,3,4]=>[10,9,4,3,11,7,5,1,12,8,6,2]=>[3,4,9,10,2,6,8,12,1,5,7,11]=>[4,4,4]
[11,12,8,7,9,10,4,3,5,6,1,2]=>[8,7,4,3,11,9,5,1,12,10,6,2]=>[5,6,9,10,2,4,8,12,1,3,7,11]=>[4,4,4]
[11,12,8,7,9,10,4,2,5,1,3,6]=>[8,10,7,4,3,11,9,5,1,12,6,2]=>[5,3,6,9,10,2,4,8,12,1,7,11]=>[1,4,4,3]
[11,12,8,7,9,10,3,2,1,4,5,6]=>[9,8,7,10,4,3,11,5,1,12,6,2]=>[4,5,6,3,9,10,2,8,12,1,7,11]=>[3,3,3,3]
[11,12,8,6,9,5,7,10,3,4,1,2]=>[4,6,3,11,9,7,5,1,12,10,8,2]=>[9,7,10,2,4,6,8,12,1,3,5,11]=>[1,2,5,4]
[11,12,8,6,9,5,7,10,2,1,3,4]=>[4,10,9,6,3,11,7,5,1,12,8,2]=>[9,3,4,7,10,2,6,8,12,1,5,11]=>[1,4,4,3]
[11,12,8,6,9,4,7,3,5,10,1,2]=>[6,4,8,3,11,9,7,5,1,12,10,2]=>[7,9,5,10,2,4,6,8,12,1,3,11]=>[2,2,5,3]
[11,12,8,6,9,4,7,2,5,1,3,10]=>[8,6,4,10,3,11,9,7,5,1,12,2]=>[5,7,9,3,10,2,4,6,8,12,1,11]=>[3,2,5,2]
[11,12,8,6,9,3,7,2,1,4,5,10]=>[6,9,8,4,10,3,11,7,5,1,12,2]=>[7,4,5,9,3,10,2,6,8,12,1,11]=>[1,3,2,4,2]
[11,12,8,5,9,4,3,6,7,10,1,2]=>[4,7,6,8,3,11,9,5,1,12,10,2]=>[9,6,7,5,10,2,4,8,12,1,3,11]=>[1,2,2,4,3]
[11,12,8,5,9,4,2,6,7,1,3,10]=>[4,10,7,6,8,3,11,9,5,1,12,2]=>[9,3,6,7,5,10,2,4,8,12,1,11]=>[1,3,2,4,2]
[11,12,8,5,9,3,2,6,1,4,7,10]=>[7,6,4,9,10,8,3,11,5,1,12,2]=>[6,7,9,4,3,5,10,2,8,12,1,11]=>[3,1,3,3,2]
[11,12,8,4,9,3,2,1,5,6,7,10]=>[4,8,7,6,9,10,3,11,5,1,12,2]=>[9,5,6,7,4,3,10,2,8,12,1,11]=>[1,3,1,2,3,2]
[11,12,7,6,5,8,9,10,3,4,1,2]=>[5,4,3,6,11,9,7,1,12,10,8,2]=>[8,9,10,7,2,4,6,12,1,3,5,11]=>[3,1,4,4]
[11,12,7,6,5,8,9,10,2,1,3,4]=>[5,4,3,10,9,6,11,7,1,12,8,2]=>[8,9,10,3,4,7,2,6,12,1,5,11]=>[3,3,3,3]
[11,12,7,6,4,8,9,3,5,10,1,2]=>[8,5,4,3,6,11,9,7,1,12,10,2]=>[5,8,9,10,7,2,4,6,12,1,3,11]=>[4,1,4,3]
[11,12,7,6,4,8,9,2,5,1,3,10]=>[5,8,4,3,10,6,11,9,7,1,12,2]=>[8,5,9,10,3,7,2,4,6,12,1,11]=>[1,3,2,4,2]
[11,12,7,6,3,8,9,2,1,4,5,10]=>[9,5,8,4,3,10,6,11,7,1,12,2]=>[4,8,5,9,10,3,7,2,6,12,1,11]=>[2,3,2,3,2]
[11,12,7,5,4,8,3,6,9,10,1,2]=>[5,4,7,3,8,6,11,9,1,12,10,2]=>[8,9,6,10,5,7,2,4,12,1,3,11]=>[2,2,2,3,3]
[11,12,7,5,3,8,2,6,1,4,9,10]=>[5,7,4,9,3,10,8,6,11,1,12,2]=>[8,6,9,4,10,3,5,7,2,12,1,11]=>[1,2,2,3,2,2]
[11,12,7,4,3,8,2,1,5,6,9,10]=>[5,4,8,7,9,3,10,6,11,1,12,2]=>[8,9,5,6,4,10,3,7,2,12,1,11]=>[2,2,2,2,2,2]
[11,12,6,5,4,3,7,8,9,10,1,2]=>[6,5,4,3,7,8,11,9,1,12,10,2]=>[7,8,9,10,6,5,2,4,12,1,3,11]=>[4,1,1,3,3]
[11,12,6,4,3,2,7,1,5,8,9,10]=>[6,5,4,8,3,9,7,10,11,1,12,2]=>[7,8,9,5,10,4,6,3,2,12,1,11]=>[3,2,2,1,2,2]
[11,12,5,4,3,2,1,6,7,8,9,10]=>[7,6,5,4,3,8,9,10,11,1,12,2]=>[6,7,8,9,10,5,4,3,2,12,1,11]=>[5,1,1,1,2,2]
[10,9,11,12,7,8,5,6,3,4,1,2]=>[2,1,11,9,7,5,3,12,10,8,6,4]=>[11,12,2,4,6,8,10,1,3,5,7,9]=>[2,5,5]
[10,9,11,12,7,8,5,6,2,1,3,4]=>[10,9,2,1,11,7,5,3,12,8,6,4]=>[3,4,11,12,2,6,8,10,1,5,7,9]=>[4,4,4]
[10,9,11,12,7,8,4,3,5,6,1,2]=>[8,7,2,1,11,9,5,3,12,10,6,4]=>[5,6,11,12,2,4,8,10,1,3,7,9]=>[4,4,4]
[10,9,11,12,7,8,4,2,5,1,3,6]=>[8,10,7,2,1,11,9,5,3,12,6,4]=>[5,3,6,11,12,2,4,8,10,1,7,9]=>[1,4,4,3]
[10,9,11,12,7,8,3,2,1,4,5,6]=>[9,8,7,10,2,1,11,5,3,12,6,4]=>[4,5,6,3,11,12,2,8,10,1,7,9]=>[3,3,3,3]
[10,9,11,12,6,5,7,8,3,4,1,2]=>[6,5,2,1,11,9,7,3,12,10,8,4]=>[7,8,11,12,2,4,6,10,1,3,5,9]=>[4,4,4]
[10,9,11,12,6,5,7,8,2,1,3,4]=>[10,9,6,5,2,1,11,7,3,12,8,4]=>[3,4,7,8,11,12,2,6,10,1,5,9]=>[6,3,3]
[10,9,11,12,6,4,7,3,5,8,1,2]=>[6,8,5,2,1,11,9,7,3,12,10,4]=>[7,5,8,11,12,2,4,6,10,1,3,9]=>[1,4,4,3]
[10,9,11,12,6,4,7,2,5,1,3,8]=>[8,6,10,5,2,1,11,9,7,3,12,4]=>[5,7,3,8,11,12,2,4,6,10,1,9]=>[2,4,4,2]
[10,9,11,12,6,3,7,2,1,4,5,8]=>[6,9,8,10,5,2,1,11,7,3,12,4]=>[7,4,5,3,8,11,12,2,6,10,1,9]=>[1,2,4,3,2]
[10,9,11,12,5,4,3,6,7,8,1,2]=>[7,6,5,8,2,1,11,9,3,12,10,4]=>[6,7,8,5,11,12,2,4,10,1,3,9]=>[3,3,3,3]
[10,9,11,12,5,4,2,6,7,1,3,8]=>[10,7,6,5,8,2,1,11,9,3,12,4]=>[3,6,7,8,5,11,12,2,4,10,1,9]=>[4,3,3,2]
[10,9,11,12,5,3,2,6,1,4,7,8]=>[7,6,9,5,10,8,2,1,11,3,12,4]=>[6,7,4,8,3,5,11,12,2,10,1,9]=>[2,2,4,2,2]
[10,9,11,12,4,3,2,1,5,6,7,8]=>[8,7,6,5,9,10,2,1,11,3,12,4]=>[5,6,7,8,4,3,11,12,2,10,1,9]=>[4,1,3,2,2]
[10,8,11,7,9,12,5,6,3,4,1,2]=>[2,4,1,11,9,7,5,3,12,10,8,6]=>[11,9,12,2,4,6,8,10,1,3,5,7]=>[1,2,5,4]
[10,8,11,7,9,12,5,6,2,1,3,4]=>[2,10,9,4,1,11,7,5,3,12,8,6]=>[11,3,4,9,12,2,6,8,10,1,5,7]=>[1,4,4,3]
[10,8,11,7,9,12,4,3,5,6,1,2]=>[2,8,7,4,1,11,9,5,3,12,10,6]=>[11,5,6,9,12,2,4,8,10,1,3,7]=>[1,4,4,3]
[10,8,11,7,9,12,4,2,5,1,3,6]=>[8,2,10,7,4,1,11,9,5,3,12,6]=>[5,11,3,6,9,12,2,4,8,10,1,7]=>[2,4,4,2]
[10,8,11,7,9,12,3,2,1,4,5,6]=>[9,8,7,2,10,4,1,11,5,3,12,6]=>[4,5,6,11,3,9,12,2,8,10,1,7]=>[4,3,3,2]
[10,8,11,6,9,5,7,12,3,4,1,2]=>[4,2,6,1,11,9,7,5,3,12,10,8]=>[9,11,7,12,2,4,6,8,10,1,3,5]=>[2,2,5,3]
[10,8,11,6,9,5,7,12,2,1,3,4]=>[4,2,10,9,6,1,11,7,5,3,12,8]=>[9,11,3,4,7,12,2,6,8,10,1,5]=>[2,4,4,2]
[10,8,11,6,9,4,7,3,5,12,1,2]=>[6,4,2,8,1,11,9,7,5,3,12,10]=>[7,9,11,5,12,2,4,6,8,10,1,3]=>[3,2,5,2]
[10,8,11,6,9,4,7,2,5,1,3,12]=>[8,6,4,2,10,1,11,9,7,5,3,12]=>[5,7,9,11,3,12,2,4,6,8,10,1]=>[4,2,5,1]
[10,8,11,6,9,3,7,2,1,4,5,12]=>[6,9,8,4,2,10,1,11,7,5,3,12]=>[7,4,5,9,11,3,12,2,6,8,10,1]=>[1,4,2,4,1]
[10,8,11,5,9,4,3,6,7,12,1,2]=>[4,7,6,2,8,1,11,9,5,3,12,10]=>[9,6,7,11,5,12,2,4,8,10,1,3]=>[1,3,2,4,2]
[10,8,11,5,9,4,2,6,7,1,3,12]=>[4,10,7,6,2,8,1,11,9,5,3,12]=>[9,3,6,7,11,5,12,2,4,8,10,1]=>[1,4,2,4,1]
[10,8,11,5,9,3,2,6,1,4,7,12]=>[7,6,4,9,2,10,8,1,11,5,3,12]=>[6,7,9,4,11,3,5,12,2,8,10,1]=>[3,2,3,3,1]
[10,8,11,4,9,3,2,1,5,6,7,12]=>[4,8,7,6,9,2,10,1,11,5,3,12]=>[9,5,6,7,4,11,3,12,2,8,10,1]=>[1,3,2,2,3,1]
[10,7,11,6,5,8,9,12,3,4,1,2]=>[2,5,4,6,1,11,9,7,3,12,10,8]=>[11,8,9,7,12,2,4,6,10,1,3,5]=>[1,2,2,4,3]
[10,7,11,6,5,8,9,12,2,1,3,4]=>[2,5,4,10,9,6,1,11,7,3,12,8]=>[11,8,9,3,4,7,12,2,6,10,1,5]=>[1,2,4,3,2]
[10,7,11,6,4,8,9,3,5,12,1,2]=>[2,8,5,4,6,1,11,9,7,3,12,10]=>[11,5,8,9,7,12,2,4,6,10,1,3]=>[1,3,2,4,2]
[10,7,11,6,4,8,9,2,5,1,3,12]=>[5,2,8,4,10,6,1,11,9,7,3,12]=>[8,11,5,9,3,7,12,2,4,6,10,1]=>[2,2,3,4,1]
[10,7,11,6,3,8,9,2,1,4,5,12]=>[9,5,2,8,4,10,6,1,11,7,3,12]=>[4,8,11,5,9,3,7,12,2,6,10,1]=>[3,2,3,3,1]
[10,7,11,5,4,8,3,6,9,12,1,2]=>[5,4,2,7,8,6,1,11,9,3,12,10]=>[8,9,11,6,5,7,12,2,4,10,1,3]=>[3,1,3,3,2]
[10,7,11,5,3,8,2,6,1,4,9,12]=>[5,7,4,2,9,10,8,6,1,11,3,12]=>[8,6,9,11,4,3,5,7,12,2,10,1]=>[1,3,1,4,2,1]
[10,7,11,4,3,8,2,1,5,6,9,12]=>[5,4,8,7,2,9,10,6,1,11,3,12]=>[8,9,5,6,11,4,3,7,12,2,10,1]=>[2,3,1,3,2,1]
[10,6,11,5,4,3,7,8,9,12,1,2]=>[2,6,5,4,7,8,1,11,9,3,12,10]=>[11,7,8,9,6,5,12,2,4,10,1,3]=>[1,3,1,2,3,2]
[10,6,11,4,3,2,7,1,5,8,9,12]=>[6,5,4,2,8,9,7,10,1,11,3,12]=>[7,8,9,11,5,4,6,3,12,2,10,1]=>[4,1,2,2,2,1]
[10,5,11,4,3,2,1,6,7,8,9,12]=>[2,7,6,5,4,8,9,10,1,11,3,12]=>[11,6,7,8,9,5,4,3,12,2,10,1]=>[1,4,1,1,2,2,1]
[9,8,7,10,11,12,5,6,3,4,1,2]=>[3,2,1,4,11,9,7,5,12,10,8,6]=>[10,11,12,9,2,4,6,8,1,3,5,7]=>[3,1,4,4]
[9,8,7,10,11,12,5,6,2,1,3,4]=>[3,2,1,10,9,4,11,7,5,12,8,6]=>[10,11,12,3,4,9,2,6,8,1,5,7]=>[3,3,3,3]
[9,8,7,10,11,12,4,3,5,6,1,2]=>[3,2,1,8,7,4,11,9,5,12,10,6]=>[10,11,12,5,6,9,2,4,8,1,3,7]=>[3,3,3,3]
[9,8,7,10,11,12,4,2,5,1,3,6]=>[8,3,2,1,10,7,4,11,9,5,12,6]=>[5,10,11,12,3,6,9,2,4,8,1,7]=>[4,3,3,2]
[9,8,7,10,11,12,3,2,1,4,5,6]=>[9,8,7,3,2,1,10,4,11,5,12,6]=>[4,5,6,10,11,12,3,9,2,8,1,7]=>[6,2,2,2]
[9,8,6,10,11,5,7,12,3,4,1,2]=>[6,3,2,1,4,11,9,7,5,12,10,8]=>[7,10,11,12,9,2,4,6,8,1,3,5]=>[4,1,4,3]
[9,8,6,10,11,5,7,12,2,1,3,4]=>[10,3,2,1,9,6,4,11,7,5,12,8]=>[3,10,11,12,4,7,9,2,6,8,1,5]=>[4,3,3,2]
[9,8,6,10,11,4,7,3,5,12,1,2]=>[3,6,2,1,8,4,11,9,7,5,12,10]=>[10,7,11,12,5,9,2,4,6,8,1,3]=>[1,3,2,4,2]
[9,8,6,10,11,4,7,2,5,1,3,12]=>[3,8,6,2,1,10,4,11,9,7,5,12]=>[10,5,7,11,12,3,9,2,4,6,8,1]=>[1,4,2,4,1]
[9,8,6,10,11,3,7,2,1,4,5,12]=>[6,3,9,8,2,1,10,4,11,7,5,12]=>[7,10,4,5,11,12,3,9,2,6,8,1]=>[2,4,2,3,1]
[9,8,5,10,11,4,3,6,7,12,1,2]=>[7,3,6,2,1,8,4,11,9,5,12,10]=>[6,10,7,11,12,5,9,2,4,8,1,3]=>[2,3,2,3,2]
[9,8,5,10,11,3,2,6,1,4,7,12]=>[3,7,6,9,2,1,10,8,4,11,5,12]=>[10,6,7,4,11,12,3,5,9,2,8,1]=>[1,2,3,3,2,1]
[9,8,4,10,11,3,2,1,5,6,7,12]=>[8,3,7,6,9,2,1,10,4,11,5,12]=>[5,10,6,7,4,11,12,3,9,2,8,1]=>[2,2,3,2,2,1]
[9,7,6,10,5,8,11,12,3,4,1,2]=>[3,2,5,1,6,4,11,9,7,12,10,8]=>[10,11,8,12,7,9,2,4,6,1,3,5]=>[2,2,2,3,3]
[9,7,6,10,5,8,11,12,2,1,3,4]=>[3,2,5,1,10,9,6,4,11,7,12,8]=>[10,11,8,12,3,4,7,9,2,6,1,5]=>[2,2,4,2,2]
[9,7,6,10,4,8,11,2,5,1,3,12]=>[5,3,2,8,1,10,6,4,11,9,7,12]=>[8,10,11,5,12,3,7,9,2,4,6,1]=>[3,2,3,3,1]
[9,7,6,10,3,8,11,2,1,4,5,12]=>[9,5,3,2,8,1,10,6,4,11,7,12]=>[4,8,10,11,5,12,3,7,9,2,6,1]=>[4,2,3,2,1]
[9,7,5,10,4,8,3,6,11,12,1,2]=>[3,5,2,7,1,8,6,4,11,9,12,10]=>[10,8,11,6,12,5,7,9,2,4,1,3]=>[1,2,2,3,2,2]
[9,7,5,10,3,8,2,6,1,4,11,12]=>[5,3,7,2,9,1,10,8,6,4,11,12]=>[8,10,6,11,4,12,3,5,7,9,2,1]=>[2,2,2,4,1,1]
[9,7,4,10,3,8,2,1,5,6,11,12]=>[3,5,8,7,2,9,1,10,6,4,11,12]=>[10,8,5,6,11,4,12,3,7,9,2,1]=>[1,1,3,2,3,1,1]
[9,6,5,10,4,3,7,8,11,12,1,2]=>[3,2,6,5,7,1,8,4,11,9,12,10]=>[10,11,7,8,6,12,5,9,2,4,1,3]=>[2,2,2,2,2,2]
[9,6,4,10,3,2,7,1,5,8,11,12]=>[3,6,5,2,8,9,7,1,10,4,11,12]=>[10,7,8,11,5,4,6,12,3,9,2,1]=>[1,3,1,3,2,1,1]
[9,5,4,10,3,2,1,6,7,8,11,12]=>[3,2,7,6,5,8,9,1,10,4,11,12]=>[10,11,6,7,8,5,4,12,3,9,2,1]=>[2,3,1,2,2,1,1]
[8,7,6,5,9,10,11,12,3,4,1,2]=>[4,3,2,1,5,6,11,9,7,12,10,8]=>[9,10,11,12,8,7,2,4,6,1,3,5]=>[4,1,1,3,3]
[8,7,6,5,9,10,11,12,2,1,3,4]=>[4,3,2,1,5,10,9,6,11,7,12,8]=>[9,10,11,12,8,3,4,7,2,6,1,5]=>[4,1,3,2,2]
[8,7,6,4,9,10,11,2,5,1,3,12]=>[8,4,3,2,1,5,10,6,11,9,7,12]=>[5,9,10,11,12,8,3,7,2,4,6,1]=>[5,1,2,3,1]
[8,7,6,3,9,10,11,2,1,4,5,12]=>[9,8,4,3,2,1,5,10,6,11,7,12]=>[4,5,9,10,11,12,8,3,7,2,6,1]=>[6,1,2,2,1]
[8,6,5,4,9,3,7,10,11,12,1,2]=>[4,3,2,6,1,7,5,8,11,9,12,10]=>[9,10,11,7,12,6,8,5,2,4,1,3]=>[3,2,2,1,2,2]
[8,6,4,3,9,2,7,1,5,10,11,12]=>[4,3,6,2,8,1,9,7,5,10,11,12]=>[9,10,7,11,5,12,4,6,8,3,2,1]=>[2,2,2,3,1,1,1]
[8,5,4,3,9,2,1,6,7,10,11,12]=>[4,3,2,7,6,8,1,9,5,10,11,12]=>[9,10,11,6,7,5,12,4,8,3,2,1]=>[3,2,2,2,1,1,1]
[7,6,5,4,3,8,9,10,11,12,1,2]=>[5,4,3,2,1,6,7,8,11,9,12,10]=>[8,9,10,11,12,7,6,5,2,4,1,3]=>[5,1,1,1,2,2]
[7,5,4,3,2,8,1,6,9,10,11,12]=>[5,4,3,2,7,1,8,6,9,10,11,12]=>[8,9,10,11,6,12,5,7,4,3,2,1]=>[4,2,2,1,1,1,1]
[6,5,4,3,2,1,7,8,9,10,11,12]=>[6,5,4,3,2,1,7,8,9,10,11,12]=>[7,8,9,10,11,12,6,5,4,3,2,1]=>[6,1,1,1,1,1,1]
[7,1,6,5,3,2,4,8]=>[6,5,7,4,2,3,1,8]=>[3,4,2,5,7,6,8,1]=>[2,3,2,1]
[1,8,7,5,3,2,4,6]=>[6,5,7,4,8,3,1,2]=>[3,4,2,5,1,6,8,7]=>[2,2,3,1]
[1,8,7,4,2,5,3,6]=>[7,5,4,6,8,3,1,2]=>[2,4,5,3,1,6,8,7]=>[3,1,3,1]
[8,7,4,2,5,3,6,1]=>[6,4,3,5,8,7,2,1]=>[3,5,6,4,1,2,7,8]=>[3,1,4]
[7,1,6,4,2,5,3,8]=>[7,5,4,6,2,3,1,8]=>[2,4,5,3,7,6,8,1]=>[3,2,2,1]
[2,6,5,4,7,1,3,8]=>[6,4,3,1,2,7,5,8]=>[3,5,6,8,7,2,4,1]=>[4,1,2,1]
[7,1,5,3,6,4,2,8]=>[7,4,3,6,2,5,1,8]=>[2,5,6,3,7,4,8,1]=>[3,2,2,1]
[5,3,6,4,2,7,1,8]=>[5,2,1,4,3,7,6,8]=>[4,7,8,5,6,2,3,1]=>[3,2,2,1]
[1,5,3,8,7,4,2,6]=>[2,7,6,8,3,5,1,4]=>[7,2,3,1,6,4,8,5]=>[1,2,2,2,1]
[7,4,2,8,6,3,5,1]=>[2,6,8,7,3,1,5,4]=>[7,3,1,2,6,8,4,5]=>[1,1,4,2]
[5,3,6,1,8,7,4,2]=>[3,1,8,2,7,6,4,5]=>[6,8,1,7,2,3,5,4]=>[2,2,3,1]
[6,1,5,3,8,7,4,2]=>[3,8,7,4,1,6,2,5]=>[6,1,2,5,8,3,7,4]=>[1,4,2,1]
[2,3,1,8,7,5,4,6]=>[7,6,8,1,2,5,3,4]=>[2,3,1,8,7,4,6,5]=>[2,2,1,2,1]
[5,3,8,7,4,2,1,6]=>[1,7,6,2,5,8,4,3]=>[8,2,3,7,4,1,5,6]=>[1,3,1,3]
[7,4,2,1,8,6,3,5]=>[7,2,8,3,6,4,1,5]=>[2,7,1,6,3,5,8,4]=>[2,2,3,1]
[8,6,3,5,7,4,2,1]=>[4,8,3,2,7,6,5,1]=>[5,1,6,7,2,3,4,8]=>[1,3,4]
[1,8,6,3,5,7,4,2]=>[5,8,4,3,7,6,1,2]=>[4,1,5,6,2,3,8,7]=>[1,3,3,1]
[6,3,8,5,2,1,7,4]=>[5,8,2,1,6,4,7,3]=>[4,1,7,8,3,5,2,6]=>[1,3,2,2]
[8,6,3,7,4,2,1,5]=>[7,3,6,5,2,8,4,1]=>[2,6,3,4,7,1,5,8]=>[2,3,3]
[2,8,6,4,7,5,1,3]=>[4,7,3,8,6,1,5,2]=>[5,2,6,1,3,8,4,7]=>[1,2,3,2]
[5,1,8,6,3,7,4,2]=>[1,8,5,4,7,6,2,3]=>[8,1,4,5,2,3,7,6]=>[1,3,3,1]
[6,3,7,4,1,8,5,2]=>[4,8,2,1,7,5,3,6]=>[5,1,7,8,2,4,6,3]=>[1,3,3,1]
[8,5,2,6,3,7,4,1]=>[8,5,3,2,4,7,6,1]=>[1,4,6,7,5,2,3,8]=>[4,1,3]
[6,1,8,7,4,2,5,3]=>[8,6,5,1,7,4,2,3]=>[1,3,4,8,2,5,7,6]=>[4,3,1]
[8,6,3,7,4,2,5,1]=>[6,3,5,2,8,7,4,1]=>[3,6,4,7,1,2,5,8]=>[2,2,4]
[1,8,6,3,2,4,7,5]=>[4,8,5,6,3,7,1,2]=>[5,1,4,3,6,2,8,7]=>[1,2,2,2,1]
[8,6,3,2,4,7,5,1]=>[3,8,4,5,2,7,6,1]=>[6,1,5,4,7,2,3,8]=>[1,2,2,3]
[7,5,1,8,6,3,2,4]=>[7,6,2,8,5,3,1,4]=>[2,3,7,1,4,6,8,5]=>[3,4,1]
[6,1,8,7,5,3,2,4]=>[7,6,1,8,5,4,2,3]=>[2,3,8,1,4,5,7,6]=>[3,4,1]
[4,3,2,8,7,6,1,5]=>[1,7,8,2,6,3,5,4]=>[8,2,1,7,3,6,4,5]=>[1,1,2,2,2]
[2,4,5,1,3,8,7,6]=>[2,3,8,1,7,4,5,6]=>[7,6,1,8,2,5,4,3]=>[1,1,2,2,1,1]
[7,5,8,6,3,2,4,1]=>[2,6,5,1,8,7,4,3]=>[7,3,4,8,1,2,5,6]=>[1,3,4]
[8,6,3,1,7,4,2,5]=>[3,7,6,8,4,2,5,1]=>[6,2,3,1,5,7,4,8]=>[1,2,3,2]
[8,7,4,2,5,3,1,6]=>[7,4,3,6,5,8,2,1]=>[2,5,6,3,4,1,7,8]=>[3,2,3]
[4,1,8,7,5,3,2,6]=>[7,1,6,5,8,4,2,3]=>[2,8,3,4,1,5,7,6]=>[2,2,3,1]
[2,8,6,4,1,3,7,5]=>[8,5,4,6,1,3,7,2]=>[1,4,5,3,8,6,2,7]=>[3,2,1,2]
[7,4,2,8,6,3,1,5]=>[2,7,6,8,3,1,5,4]=>[7,2,3,1,6,8,4,5]=>[1,2,3,2]
[6,3,1,8,5,2,7,4]=>[8,2,6,5,1,7,3,4]=>[1,7,3,4,8,2,6,5]=>[2,3,2,1]
[8,5,2,6,3,1,7,4]=>[5,8,3,2,6,4,7,1]=>[4,1,6,7,3,5,2,8]=>[1,3,2,2]
[7,4,8,5,2,6,3,1]=>[8,2,5,4,1,7,6,3]=>[1,7,4,5,8,2,3,6]=>[2,3,3]
[1,8,5,2,7,4,6,3]=>[6,3,8,7,4,5,1,2]=>[3,6,1,2,5,4,8,7]=>[2,3,2,1]
[8,5,2,7,4,6,3,1]=>[5,2,8,7,3,6,4,1]=>[4,7,1,2,6,3,5,8]=>[2,3,3]
[7,4,6,3,1,8,5,2]=>[2,4,8,7,5,3,1,6]=>[7,5,1,2,4,6,8,3]=>[1,1,5,1]
[8,6,3,1,5,7,4,2]=>[3,5,8,7,4,2,6,1]=>[6,4,1,2,5,7,3,8]=>[1,1,4,2]
[4,1,7,5,8,6,3,2]=>[8,1,4,3,7,6,2,5]=>[1,8,5,6,2,3,7,4]=>[2,2,3,1]
[2,3,1,7,5,8,6,4]=>[8,5,1,2,4,7,3,6]=>[1,4,8,7,5,2,6,3]=>[3,1,1,2,1]
[8,5,2,1,7,4,6,3]=>[6,8,3,2,7,4,5,1]=>[3,1,6,7,2,5,4,8]=>[1,3,2,2]
[1,7,4,6,3,8,5,2]=>[8,3,5,4,2,7,1,6]=>[1,6,4,5,7,2,8,3]=>[2,3,2,1]
[3,6,5,2,1,4,8,7]=>[4,8,1,5,3,2,6,7]=>[5,1,8,4,6,7,3,2]=>[1,2,3,1,1]
[3,5,6,2,1,4,8,7]=>[4,1,2,8,5,3,6,7]=>[5,8,7,1,4,6,3,2]=>[2,1,3,1,1]
[3,5,7,8,1,4,2,6]=>[2,7,1,5,6,3,8,4]=>[7,2,8,4,3,6,1,5]=>[1,2,1,2,2]
[4,1,8,5,7,3,2,6]=>[1,4,7,6,8,5,2,3]=>[8,5,2,3,1,4,7,6]=>[1,1,2,3,1]
[4,1,7,5,8,3,2,6]=>[1,4,7,6,3,8,2,5]=>[8,5,2,3,6,1,7,4]=>[1,1,3,2,1]
[2,1,5,8,7,4,3,6]=>[7,3,6,8,1,5,2,4]=>[2,6,3,1,8,4,7,5]=>[2,1,2,2,1]
[2,1,5,7,8,4,3,6]=>[7,3,6,1,4,8,2,5]=>[2,6,3,8,5,1,7,4]=>[2,2,1,2,1]
[5,1,7,4,8,3,2,6]=>[4,1,7,6,3,8,2,5]=>[5,8,2,3,6,1,7,4]=>[2,3,2,1]
[4,7,2,8,3,6,1,5]=>[1,5,7,8,3,2,6,4]=>[8,4,2,1,6,7,3,5]=>[1,1,1,3,2]
[4,6,2,7,3,1,8,5]=>[1,5,8,3,2,6,4,7]=>[8,4,1,6,7,3,5,2]=>[1,1,3,2,1]
[3,7,8,2,4,1,6,5]=>[4,5,8,1,6,2,7,3]=>[5,4,1,8,3,7,2,6]=>[1,1,2,2,2]
[3,8,7,2,4,1,6,5]=>[4,5,8,1,6,7,3,2]=>[5,4,1,8,3,2,6,7]=>[1,1,2,1,3]
[3,8,6,2,4,1,7,5]=>[4,5,8,1,6,3,7,2]=>[5,4,1,8,3,6,2,7]=>[1,1,2,2,2]
[6,2,8,4,1,7,3,5]=>[7,4,8,2,1,5,6,3]=>[2,5,1,7,8,4,3,6]=>[2,3,1,2]
[7,3,4,8,1,6,2,5]=>[2,3,7,8,5,1,6,4]=>[7,6,2,1,4,8,3,5]=>[1,1,1,3,2]
[6,3,4,8,1,7,2,5]=>[2,3,7,1,8,5,6,4]=>[7,6,2,8,1,4,3,5]=>[1,1,2,2,2]
[5,3,4,8,1,2,7,6]=>[2,3,1,8,5,6,7,4]=>[7,6,8,1,4,3,2,5]=>[1,2,2,1,2]
[4,3,5,8,1,2,7,6]=>[2,1,3,8,5,6,7,4]=>[7,8,6,1,4,3,2,5]=>[2,1,2,1,2]
[1,8,5,4,2,3,7,6]=>[8,5,4,3,6,7,1,2]=>[1,4,5,6,3,2,8,7]=>[4,1,2,1]
[3,5,4,8,1,2,7,6]=>[3,1,2,8,5,6,7,4]=>[6,8,7,1,4,3,2,5]=>[2,1,2,1,2]
[4,5,3,8,1,2,7,6]=>[1,3,2,8,5,6,7,4]=>[8,6,7,1,4,3,2,5]=>[1,2,2,1,2]
[6,4,3,8,1,7,2,5]=>[3,2,7,1,8,5,6,4]=>[6,7,2,8,1,4,3,5]=>[2,2,2,2]
[7,4,3,8,1,6,2,5]=>[3,2,7,8,5,1,6,4]=>[6,7,2,1,4,8,3,5]=>[2,1,3,2]
[6,5,3,8,7,1,2,4]=>[3,6,2,1,7,8,5,4]=>[6,3,7,8,2,1,4,5]=>[1,3,1,3]
[5,6,3,8,7,1,2,4]=>[3,1,6,2,7,8,5,4]=>[6,8,3,7,2,1,4,5]=>[2,2,1,3]
[4,6,3,8,1,7,2,5]=>[1,3,7,2,8,5,6,4]=>[8,6,2,7,1,4,3,5]=>[1,1,2,2,2]
[2,6,8,4,1,7,3,5]=>[7,4,2,8,1,5,6,3]=>[2,5,7,1,8,4,3,6]=>[3,2,1,2]
[5,7,3,8,6,1,2,4]=>[3,1,6,7,2,8,5,4]=>[6,8,3,2,7,1,4,5]=>[2,1,2,3]
[3,7,5,8,6,1,2,4]=>[6,3,7,1,2,8,5,4]=>[3,6,2,8,7,1,4,5]=>[2,2,1,3]
[2,7,8,5,6,1,3,4]=>[6,7,4,2,8,1,5,3]=>[3,2,5,7,1,8,4,6]=>[1,3,2,2]
[1,8,7,5,6,2,3,4]=>[6,7,4,8,5,3,1,2]=>[3,2,5,1,4,6,8,7]=>[1,2,4,1]
[2,6,8,5,7,1,3,4]=>[6,2,7,4,8,1,5,3]=>[3,7,2,5,1,8,4,6]=>[2,2,2,2]
[5,3,6,8,7,1,2,4]=>[6,2,1,3,7,8,5,4]=>[3,7,8,6,2,1,4,5]=>[3,1,1,3]
[6,3,5,8,7,1,2,4]=>[6,2,3,1,7,8,5,4]=>[3,7,6,8,2,1,4,5]=>[2,2,1,3]
[7,2,8,5,6,1,3,4]=>[6,7,4,8,2,1,5,3]=>[3,2,5,1,7,8,4,6]=>[1,2,3,2]
[5,2,8,6,7,1,3,4]=>[6,1,7,4,8,2,5,3]=>[3,8,2,5,1,7,4,6]=>[2,2,2,2]
[1,8,3,2,7,6,4,5]=>[7,8,3,6,4,5,1,2]=>[2,1,6,3,5,4,8,7]=>[1,2,2,2,1]
[5,2,8,7,6,1,3,4]=>[6,1,7,8,5,2,4,3]=>[3,8,2,1,4,7,5,6]=>[2,1,3,2]
[6,2,8,7,5,1,3,4]=>[6,7,1,8,5,2,4,3]=>[3,2,8,1,4,7,5,6]=>[1,2,3,2]
[3,4,7,8,1,6,2,5]=>[7,8,1,2,5,3,6,4]=>[2,1,8,7,4,6,3,5]=>[1,2,1,2,2]
[1,8,5,7,6,2,3,4]=>[6,3,7,8,5,4,1,2]=>[3,6,2,1,4,5,8,7]=>[2,1,4,1]
[2,5,8,7,6,1,3,4]=>[2,6,7,8,5,1,4,3]=>[7,3,2,1,4,8,5,6]=>[1,1,1,3,2]
[7,4,6,5,8,1,2,3]=>[2,6,7,4,3,1,8,5]=>[7,3,2,5,6,8,1,4]=>[1,1,4,2]
[3,6,7,8,5,1,2,4]=>[6,2,7,1,3,8,5,4]=>[3,7,2,8,6,1,4,5]=>[2,2,1,3]
[2,6,8,7,5,1,3,4]=>[6,2,7,8,5,1,4,3]=>[3,7,2,1,4,8,5,6]=>[2,1,3,2]
[1,8,6,7,5,2,3,4]=>[6,7,3,8,5,4,1,2]=>[3,2,6,1,4,5,8,7]=>[1,2,4,1]
[2,7,8,6,5,1,3,4]=>[6,7,2,8,5,1,4,3]=>[3,2,7,1,4,8,5,6]=>[1,2,3,2]
[5,7,6,4,8,1,2,3]=>[1,6,7,4,3,2,8,5]=>[8,3,2,5,6,7,1,4]=>[1,1,4,2]
[6,3,8,7,5,1,2,4]=>[6,7,1,8,2,5,4,3]=>[3,2,8,1,7,4,5,6]=>[1,2,2,3]
[2,8,7,4,1,3,5,6]=>[5,6,4,7,8,1,3,2]=>[4,3,5,2,1,8,6,7]=>[1,2,1,2,2]
[5,4,8,7,1,3,2,6]=>[2,1,7,5,6,8,4,3]=>[7,8,2,4,3,1,5,6]=>[2,2,1,3]
[4,8,6,1,3,2,5,7]=>[1,6,4,5,7,3,8,2]=>[8,3,5,4,2,6,1,7]=>[1,2,1,2,2]
[5,4,2,7,6,8,1,3]=>[2,1,7,5,3,4,8,6]=>[7,8,2,4,6,5,1,3]=>[2,3,1,2]
[2,8,7,1,4,5,3,6]=>[5,7,4,6,8,1,3,2]=>[4,2,5,3,1,8,6,7]=>[1,2,1,2,2]
[4,2,1,8,7,3,5,6]=>[6,1,7,8,2,5,3,4]=>[3,8,2,1,7,4,6,5]=>[2,1,2,2,1]
[5,1,6,3,2,8,7,4]=>[8,4,3,1,7,2,5,6]=>[1,5,6,8,2,7,4,3]=>[4,2,1,1]
[4,6,1,8,7,3,2,5]=>[7,1,6,2,8,5,3,4]=>[2,8,3,7,1,4,6,5]=>[2,2,3,1]
[8,7,2,3,5,4,1,6]=>[7,3,4,6,5,8,2,1]=>[2,6,5,3,4,1,7,8]=>[2,1,2,3]
[5,3,1,4,8,7,2,6]=>[2,7,1,8,4,6,3,5]=>[7,2,8,1,5,3,6,4]=>[1,2,2,2,1]
[4,3,5,2,8,7,1,6]=>[2,1,3,7,8,4,6,5]=>[7,8,6,2,1,5,3,4]=>[2,1,1,2,2]
[3,7,6,8,1,5,2,4]=>[7,8,5,1,3,2,6,4]=>[2,1,4,8,6,7,3,5]=>[1,3,2,2]
[8,1,4,2,3,6,7,5]=>[6,3,8,2,4,5,7,1]=>[3,6,1,7,5,4,2,8]=>[2,2,1,1,2]
[3,7,2,1,8,6,4,5]=>[7,8,1,3,6,4,2,5]=>[2,1,8,6,3,5,7,4]=>[1,2,1,3,1]
[2,8,6,1,7,3,5,4]=>[8,6,7,4,1,3,5,2]=>[1,3,2,5,8,6,4,7]=>[2,3,1,2]
[1,7,6,3,5,8,2,4]=>[7,4,5,3,2,8,1,6]=>[2,5,4,6,7,1,8,3]=>[2,3,2,1]
[3,7,5,1,6,8,2,4]=>[7,5,1,3,8,4,2,6]=>[2,4,8,6,1,5,7,3]=>[3,1,3,1]
[3,6,5,8,1,4,7,2]=>[6,3,1,2,8,5,7,4]=>[3,6,8,7,1,4,2,5]=>[3,1,2,2]
[8,1,5,6,4,7,2,3]=>[3,7,5,4,8,2,6,1]=>[6,2,4,5,1,7,3,8]=>[1,3,2,2]
[1,7,4,6,8,2,5,3]=>[8,3,6,4,2,7,1,5]=>[1,6,3,5,7,2,8,4]=>[2,3,2,1]
[7,5,8,2,6,3,1,4]=>[7,4,2,6,1,8,5,3]=>[2,5,7,3,8,1,4,6]=>[3,2,3]
[2,7,1,6,5,4,8,3]=>[6,5,4,8,1,3,2,7]=>[3,4,5,1,8,6,7,2]=>[3,2,2,1]
[6,4,7,2,3,1,8,5]=>[4,2,5,1,8,6,3,7]=>[5,7,4,8,1,3,6,2]=>[2,2,3,1]
[5,3,1,8,4,6,2,7]=>[2,5,1,7,6,8,3,4]=>[7,4,8,2,3,1,6,5]=>[1,2,2,2,1]
[2,7,4,3,6,8,1,5]=>[3,7,4,5,1,2,8,6]=>[6,2,5,4,8,7,1,3]=>[1,2,2,1,2]
[2,8,4,6,1,5,3,7]=>[3,7,5,6,1,4,8,2]=>[6,2,4,3,8,5,1,7]=>[1,2,2,1,2]
[8,4,1,6,3,2,5,7]=>[6,5,2,7,3,4,8,1]=>[3,4,7,2,6,5,1,8]=>[3,2,1,2]
[4,7,3,8,5,2,1,6]=>[7,1,3,6,5,2,8,4]=>[2,8,6,3,4,7,1,5]=>[2,1,3,2]
[3,1,7,4,8,5,2,6]=>[7,1,4,6,3,8,2,5]=>[2,8,5,3,6,1,7,4]=>[2,1,2,2,1]
[7,4,1,6,3,2,8,5]=>[5,2,8,6,3,4,1,7]=>[4,7,1,3,6,5,8,2]=>[2,3,2,1]
[7,3,1,4,5,2,8,6]=>[4,2,5,8,3,6,1,7]=>[5,7,4,1,6,3,8,2]=>[2,1,2,2,1]
[6,1,4,8,5,3,2,7]=>[7,3,6,5,1,8,2,4]=>[2,6,3,4,8,1,7,5]=>[2,3,2,1]
[8,1,2,4,6,7,5,3]=>[5,8,4,7,2,3,6,1]=>[4,1,5,2,7,6,3,8]=>[1,2,2,1,2]
[8,1,3,6,7,5,4,2]=>[4,8,7,3,6,2,5,1]=>[5,1,2,6,3,7,4,8]=>[1,3,2,2]
[7,5,2,3,8,6,1,4]=>[7,8,3,2,4,1,6,5]=>[2,1,6,7,5,8,3,4]=>[1,3,2,2]
[4,7,5,1,8,6,3,2]=>[3,8,1,7,6,4,2,5]=>[6,1,8,2,3,5,7,4]=>[1,2,4,1]
[4,7,3,2,8,5,6,1]=>[1,3,6,8,4,2,7,5]=>[8,6,3,1,5,7,2,4]=>[1,1,1,3,2]
[7,5,8,4,2,3,6,1]=>[5,2,6,4,1,8,7,3]=>[4,7,3,5,8,1,2,6]=>[2,3,3]
[3,8,4,6,1,7,5,2]=>[8,3,7,1,5,4,6,2]=>[1,6,2,8,4,5,3,7]=>[2,2,2,2]
[3,7,4,6,5,2,8,1]=>[6,3,5,1,4,2,8,7]=>[3,6,4,8,5,7,1,2]=>[2,2,2,2]
[4,2,7,6,1,5,8,3]=>[1,6,8,5,2,4,3,7]=>[8,3,1,4,7,5,6,2]=>[1,1,3,2,1]
[8,3,1,4,5,7,6,2]=>[2,8,4,5,7,3,6,1]=>[7,1,5,4,2,6,3,8]=>[1,2,1,2,2]
[5,8,4,7,3,2,6,1]=>[1,3,6,5,8,7,4,2]=>[8,6,3,4,1,2,5,7]=>[1,1,2,4]
[7,2,6,5,8,4,1,3]=>[7,4,3,8,2,1,6,5]=>[2,5,6,1,7,8,3,4]=>[3,3,2]
[2,6,8,3,7,4,1,5]=>[7,4,2,6,8,1,5,3]=>[2,5,7,3,1,8,4,6]=>[3,1,2,2]
[8,1,5,6,4,7,3,2]=>[3,5,4,8,7,2,6,1]=>[6,4,5,1,2,7,3,8]=>[1,2,3,2]
[2,5,8,1,6,4,7,3]=>[2,6,5,8,1,4,7,3]=>[7,3,4,1,8,5,2,6]=>[1,2,2,1,2]
[7,4,1,8,3,2,6,5]=>[5,2,8,6,7,3,1,4]=>[4,7,1,3,2,6,8,5]=>[2,2,3,1]
[5,2,6,8,3,1,7,4]=>[5,3,1,8,2,6,7,4]=>[4,6,8,1,7,3,2,5]=>[3,2,1,2]
[3,6,5,8,4,1,7,2]=>[3,2,8,1,6,5,7,4]=>[6,7,1,8,3,4,2,5]=>[2,2,2,2]
[7,3,6,1,8,4,5,2]=>[6,8,2,7,4,3,1,5]=>[3,1,7,2,5,6,8,4]=>[1,2,4,1]
[8,2,7,3,4,6,5,1]=>[8,4,5,7,2,6,3,1]=>[1,5,4,2,7,3,6,8]=>[2,1,2,3]
[7,3,8,2,5,6,4,1]=>[5,8,2,4,1,7,6,3]=>[4,1,7,5,8,2,3,6]=>[1,2,2,3]
[5,7,3,1,6,4,8,2]=>[3,1,6,5,8,4,2,7]=>[6,8,3,4,1,5,7,2]=>[2,2,3,1]
[6,1,3,2,4,8,7,5]=>[8,3,7,2,4,1,5,6]=>[1,6,2,7,5,8,4,3]=>[2,2,2,1,1]
[8,7,4,2,3,6,1,5]=>[4,5,3,7,8,6,2,1]=>[5,4,6,2,1,3,7,8]=>[1,2,1,4]
[3,7,1,5,2,8,6,4]=>[4,8,1,7,3,5,2,6]=>[5,1,8,2,6,4,7,3]=>[1,2,2,2,1]
[8,7,2,5,3,1,4,6]=>[6,3,5,7,4,8,2,1]=>[3,6,4,2,5,1,7,8]=>[2,1,2,3]
[5,2,8,7,1,4,3,6]=>[7,5,1,6,8,2,4,3]=>[2,4,8,3,1,7,5,6]=>[3,1,2,2]
[7,1,8,6,2,4,3,5]=>[7,5,6,8,4,2,1,3]=>[2,4,3,1,5,7,8,6]=>[2,1,4,1]
[7,1,6,2,8,5,3,4]=>[7,8,6,4,2,3,1,5]=>[2,1,3,5,7,6,8,4]=>[1,4,2,1]
[6,3,4,1,7,2,8,5]=>[2,3,8,6,4,1,5,7]=>[7,6,1,3,5,8,4,2]=>[1,1,4,1,1]
[7,2,4,3,5,1,8,6]=>[4,2,3,5,8,6,1,7]=>[5,7,6,4,1,3,8,2]=>[2,1,1,3,1]
[5,1,7,2,3,8,6,4]=>[8,7,4,1,5,2,3,6]=>[1,2,5,8,4,7,6,3]=>[4,2,1,1]
[8,2,3,5,1,7,6,4]=>[4,8,2,3,7,5,6,1]=>[5,1,7,6,2,4,3,8]=>[1,2,1,2,2]
[7,6,3,1,4,8,2,5]=>[5,3,7,8,4,2,1,6]=>[4,6,2,1,5,7,8,3]=>[2,1,4,1]
[6,1,8,2,7,5,3,4]=>[7,8,6,4,1,5,2,3]=>[2,1,3,5,8,4,7,6]=>[1,4,2,1]
[7,2,8,1,6,5,3,4]=>[7,8,6,2,4,1,5,3]=>[2,1,3,7,5,8,4,6]=>[1,3,2,2]
[5,3,1,7,4,8,2,6]=>[2,5,1,7,4,8,3,6]=>[7,4,8,2,5,1,6,3]=>[1,2,2,2,1]
[8,2,7,5,1,6,4,3]=>[8,7,5,2,4,6,3,1]=>[1,2,4,7,5,3,6,8]=>[4,1,3]
[6,1,7,3,2,8,5,4]=>[8,4,7,5,2,1,3,6]=>[1,5,2,4,7,8,6,3]=>[2,4,1,1]
[4,7,2,1,6,3,8,5]=>[1,8,3,6,4,5,2,7]=>[8,1,6,3,5,4,7,2]=>[1,2,2,2,1]
[6,2,1,5,3,8,4,7]=>[7,2,4,8,3,1,5,6]=>[2,7,5,1,6,8,4,3]=>[2,1,3,1,1]
[5,3,1,6,2,8,4,7]=>[2,7,4,1,8,3,5,6]=>[7,2,5,8,1,6,4,3]=>[1,3,2,1,1]
[6,1,5,2,8,4,3,7]=>[7,6,3,8,2,1,4,5]=>[2,3,6,1,7,8,5,4]=>[3,3,1,1]
[7,4,3,8,1,5,2,6]=>[3,2,7,5,6,1,8,4]=>[6,7,2,4,3,8,1,5]=>[2,2,2,2]
[7,4,8,1,5,3,2,6]=>[2,7,6,4,5,1,8,3]=>[7,2,3,5,4,8,1,6]=>[1,3,2,2]
[6,1,5,3,2,8,4,7]=>[4,7,3,8,2,1,5,6]=>[5,2,6,1,7,8,4,3]=>[1,2,3,1,1]
[6,3,2,8,4,1,5,7]=>[2,6,3,5,1,7,8,4]=>[7,3,6,4,8,2,1,5]=>[1,2,2,1,2]
[7,3,4,2,8,5,1,6]=>[2,3,7,4,6,1,8,5]=>[7,6,2,5,3,8,1,4]=>[1,1,2,2,2]
[7,1,6,3,4,2,8,5]=>[4,5,8,6,2,3,1,7]=>[5,4,1,3,7,6,8,2]=>[1,1,3,2,1]
[8,5,1,3,7,4,2,6]=>[7,4,6,2,8,3,5,1]=>[2,5,3,7,1,6,4,8]=>[2,2,2,2]
[8,6,1,3,7,5,2,4]=>[7,8,4,6,3,2,5,1]=>[2,1,5,3,6,7,4,8]=>[1,2,3,2]
[4,8,5,6,1,7,3,2]=>[3,8,1,7,5,4,6,2]=>[6,1,8,2,4,5,3,7]=>[1,2,3,2]
[6,7,1,3,8,5,2,4]=>[7,8,4,1,6,3,2,5]=>[2,1,5,8,3,6,7,4]=>[1,3,3,1]
[3,6,7,1,5,2,8,4]=>[8,6,1,4,2,5,3,7]=>[1,3,8,5,7,4,6,2]=>[3,2,2,1]
[7,1,3,8,4,2,6,5]=>[5,8,3,6,7,2,1,4]=>[4,1,6,3,2,7,8,5]=>[1,2,1,3,1]
[5,6,2,7,1,3,8,4]=>[8,3,1,5,2,6,4,7]=>[1,6,8,4,7,3,5,2]=>[3,2,2,1]
[5,6,2,8,1,3,7,4]=>[8,3,1,5,2,6,7,4]=>[1,6,8,4,7,3,2,5]=>[3,2,1,2]
[6,1,8,3,7,5,2,4]=>[7,8,4,1,6,5,2,3]=>[2,1,5,8,3,4,7,6]=>[1,3,3,1]
[7,4,2,1,5,8,3,6]=>[3,5,2,7,8,4,1,6]=>[6,4,7,2,1,5,8,3]=>[1,2,1,3,1]
[7,4,1,5,8,3,2,6]=>[4,2,7,6,8,3,1,5]=>[5,7,2,3,1,6,8,4]=>[2,2,3,1]
[6,4,2,7,3,8,1,5]=>[5,2,7,3,1,4,8,6]=>[4,7,2,6,8,5,1,3]=>[2,3,1,2]
[5,1,8,3,7,4,2,6]=>[7,4,1,6,8,5,2,3]=>[2,5,8,3,1,4,7,6]=>[3,1,3,1]
[7,4,8,3,1,5,2,6]=>[2,7,5,4,6,1,8,3]=>[7,2,4,5,3,8,1,6]=>[1,3,2,2]
[5,2,1,7,4,8,3,6]=>[5,7,2,1,4,8,3,6]=>[4,2,7,8,5,1,6,3]=>[1,3,1,2,1]
[6,1,8,4,5,2,7,3]=>[4,8,6,5,1,7,2,3]=>[5,1,3,4,8,2,7,6]=>[1,4,2,1]
[7,1,6,4,5,2,8,3]=>[4,8,6,5,2,3,1,7]=>[5,1,3,4,7,6,8,2]=>[1,4,2,1]
[3,5,2,7,1,6,8,4]=>[6,1,2,8,3,5,4,7]=>[3,8,7,1,6,4,5,2]=>[2,1,2,2,1]
[4,5,7,3,1,6,8,2]=>[1,2,6,4,8,5,3,7]=>[8,7,3,5,1,4,6,2]=>[1,1,2,3,1]
[4,5,7,2,8,6,1,3]=>[1,2,7,8,4,3,6,5]=>[8,7,2,1,5,6,3,4]=>[1,1,1,3,2]
[3,5,1,7,2,6,8,4]=>[6,1,2,8,5,3,4,7]=>[3,8,7,1,4,6,5,2]=>[2,1,3,1,1]
[4,5,7,2,8,1,3,6]=>[1,4,2,6,7,3,8,5]=>[8,5,7,3,2,6,1,4]=>[1,2,1,2,2]
[4,6,7,1,3,8,5,2]=>[8,1,5,2,7,4,3,6]=>[1,8,4,7,2,5,6,3]=>[2,2,3,1]
[3,6,1,5,7,8,4,2]=>[4,5,1,2,8,7,3,6]=>[5,4,8,7,1,2,6,3]=>[1,2,1,3,1]
[4,6,7,1,5,8,3,2]=>[5,1,2,8,7,4,3,6]=>[4,8,7,1,2,5,6,3]=>[2,1,4,1]
[6,1,3,7,4,8,5,2]=>[8,5,3,4,1,7,2,6]=>[1,4,6,5,8,2,7,3]=>[3,2,2,1]
[3,2,1,7,4,8,5,6]=>[1,7,8,2,5,3,4,6]=>[8,2,1,7,4,6,5,3]=>[1,1,2,2,1,1]
[4,1,5,2,7,6,3,8]=>[3,1,7,6,2,4,5,8]=>[6,8,2,3,7,5,4,1]=>[2,3,1,1,1]
[2,5,1,3,7,6,4,8]=>[7,6,1,3,2,4,5,8]=>[2,3,8,6,7,5,4,1]=>[3,2,1,1,1]
[2,5,1,4,3,8,6,7]=>[4,7,1,2,8,3,5,6]=>[5,2,8,7,1,6,4,3]=>[1,2,1,2,1,1]
[3,7,2,1,5,8,6,4]=>[8,1,3,5,7,4,2,6]=>[1,8,6,4,2,5,7,3]=>[2,1,1,3,1]
[6,2,7,1,4,8,5,3]=>[8,5,7,2,1,4,3,6]=>[1,4,2,7,8,5,6,3]=>[2,3,2,1]
[3,7,4,2,1,8,5,6]=>[4,1,3,7,8,5,2,6]=>[5,8,6,2,1,4,7,3]=>[2,1,1,3,1]
[7,2,5,3,1,8,6,4]=>[8,4,2,3,7,5,1,6]=>[1,5,7,6,2,4,8,3]=>[3,1,3,1]
[7,5,1,4,2,8,6,3]=>[4,8,7,3,2,5,1,6]=>[5,1,2,6,7,4,8,3]=>[1,4,2,1]
[5,3,2,1,7,6,4,8]=>[2,7,3,1,6,4,5,8]=>[7,2,6,8,3,5,4,1]=>[1,3,2,1,1]
[6,3,2,8,1,5,7,4]=>[2,6,8,3,1,5,7,4]=>[7,3,1,6,8,4,2,5]=>[1,1,3,1,2]
[7,4,3,2,8,1,6,5]=>[3,2,8,4,6,1,7,5]=>[6,7,1,5,3,8,2,4]=>[2,2,2,2]
[7,6,2,4,8,3,5,1]=>[4,6,8,3,2,1,7,5]=>[5,3,1,6,7,8,2,4]=>[1,1,4,2]
[7,3,6,4,8,1,5,2]=>[4,8,2,6,3,1,7,5]=>[5,1,7,3,6,8,2,4]=>[1,2,3,2]
[2,7,5,3,8,1,4,6]=>[4,6,3,7,1,2,8,5]=>[5,3,6,2,8,7,1,4]=>[1,2,2,1,2]
[1,8,5,3,6,4,2,7]=>[7,4,3,6,5,8,1,2]=>[2,5,6,3,4,1,8,7]=>[3,2,2,1]
[8,6,2,3,7,5,4,1]=>[8,7,3,4,2,6,5,1]=>[1,2,6,5,7,3,4,8]=>[3,2,3]
[8,6,3,2,7,5,4,1]=>[8,3,7,4,2,6,5,1]=>[1,6,2,5,7,3,4,8]=>[2,3,3]
[7,2,6,1,5,4,3,8]=>[7,6,2,4,5,3,1,8]=>[2,3,7,5,4,6,8,1]=>[3,1,3,1]
[8,5,7,4,3,6,2,1]=>[2,5,4,8,7,6,3,1]=>[7,4,5,1,2,3,6,8]=>[1,2,5]
[8,4,6,7,1,3,2,5]=>[2,7,5,6,3,8,4,1]=>[7,2,4,3,6,1,5,8]=>[1,2,2,3]
[2,8,5,6,1,4,3,7]=>[7,5,3,6,1,4,8,2]=>[2,4,6,3,8,5,1,7]=>[3,2,1,2]
[7,2,6,8,4,1,5,3]=>[8,6,5,2,3,1,7,4]=>[1,3,4,7,6,8,2,5]=>[4,2,2]
[7,6,4,8,3,2,5,1]=>[3,6,5,2,1,8,7,4]=>[6,3,4,7,8,1,2,5]=>[1,4,3]
[6,5,8,1,4,2,7,3]=>[8,6,4,2,1,5,7,3]=>[1,3,5,7,8,4,2,6]=>[5,1,2]
[6,5,8,4,1,3,7,2]=>[6,2,1,8,5,4,7,3]=>[3,7,8,1,4,5,2,6]=>[3,3,2]
[5,4,8,3,2,1,7,6]=>[2,1,5,4,8,6,7,3]=>[7,8,4,5,1,3,2,6]=>[2,2,2,2]
[4,3,7,2,1,6,5,8]=>[2,1,4,7,5,6,3,8]=>[7,8,5,2,4,3,6,1]=>[2,1,2,2,1]
[2,5,8,1,4,3,7,6]=>[5,2,8,1,4,6,7,3]=>[4,7,1,8,5,3,2,6]=>[2,2,1,1,2]
[3,6,8,2,1,5,7,4]=>[4,6,1,2,8,5,7,3]=>[5,3,8,7,1,4,2,6]=>[1,2,1,2,2]
[5,7,4,8,1,3,6,2]=>[1,6,3,8,5,2,7,4]=>[8,3,6,1,4,7,2,5]=>[1,2,3,2]
[5,7,1,4,8,2,6,3]=>[4,1,8,6,7,3,2,5]=>[5,8,1,3,2,6,7,4]=>[2,2,3,1]
[2,7,4,1,8,3,6,5]=>[3,8,6,7,1,4,2,5]=>[6,1,3,2,8,5,7,4]=>[1,2,2,2,1]
[3,5,1,8,4,2,7,6]=>[5,1,2,8,6,7,3,4]=>[4,8,7,1,3,2,6,5]=>[2,1,2,2,1]
[4,1,5,7,3,6,2,8]=>[3,1,5,7,6,2,4,8]=>[6,8,4,2,3,7,5,1]=>[2,1,3,1,1]
[4,2,5,8,3,1,7,6]=>[3,1,5,8,2,6,7,4]=>[6,8,4,1,7,3,2,5]=>[2,1,2,1,2]
[6,1,2,7,8,3,5,4]=>[8,6,4,7,2,1,3,5]=>[1,3,5,2,7,8,6,4]=>[3,3,1,1]
[5,3,1,8,6,4,2,7]=>[7,2,1,6,5,8,3,4]=>[2,7,8,3,4,1,6,5]=>[3,2,2,1]
[3,1,8,4,7,5,2,6]=>[7,1,4,6,8,5,2,3]=>[2,8,5,3,1,4,7,6]=>[2,1,1,3,1]
[4,8,1,7,6,2,3,5]=>[1,6,7,8,5,3,4,2]=>[8,3,2,1,4,6,5,7]=>[1,1,1,3,2]
[7,3,8,1,6,4,2,5]=>[7,2,6,8,4,1,5,3]=>[2,7,3,1,5,8,4,6]=>[2,1,3,2]
[4,7,8,1,5,3,2,6]=>[7,1,6,4,5,2,8,3]=>[2,8,3,5,4,7,1,6]=>[2,2,2,2]
[7,1,8,6,2,5,3,4]=>[7,8,5,6,4,2,1,3]=>[2,1,4,3,5,7,8,6]=>[1,2,4,1]
[5,8,7,1,3,6,4,2]=>[1,8,5,7,4,6,3,2]=>[8,1,4,2,5,3,6,7]=>[1,2,2,3]
[3,8,7,2,1,6,4,5]=>[4,7,8,1,5,6,3,2]=>[5,2,1,8,4,3,6,7]=>[1,1,2,1,3]
[2,8,7,1,6,3,5,4]=>[8,6,7,4,5,1,3,2]=>[1,3,2,5,4,8,6,7]=>[2,2,2,2]
[3,7,6,1,5,4,2,8]=>[7,6,1,4,5,3,2,8]=>[2,3,8,5,4,6,7,1]=>[3,1,3,1]
[4,8,7,6,1,3,5,2]=>[6,8,1,5,7,4,3,2]=>[3,1,8,4,2,5,6,7]=>[1,2,1,4]
[5,8,7,2,6,1,4,3]=>[1,8,4,6,7,5,3,2]=>[8,1,5,3,2,4,6,7]=>[1,2,1,4]
[6,8,1,7,5,2,4,3]=>[8,6,1,7,5,3,4,2]=>[1,3,8,2,4,6,5,7]=>[3,3,2]
[7,3,8,6,5,1,2,4]=>[6,7,8,2,1,5,4,3]=>[3,2,1,7,8,4,5,6]=>[1,1,3,3]
[5,7,8,4,3,1,2,6]=>[1,6,7,5,4,2,8,3]=>[8,3,2,4,5,7,1,6]=>[1,1,4,2]
[5,8,6,4,3,2,1,7]=>[7,1,6,5,4,3,8,2]=>[2,8,3,4,5,6,1,7]=>[2,4,2]
[8,7,3,6,4,2,1,5]=>[7,3,6,5,8,4,2,1]=>[2,6,3,4,1,5,7,8]=>[2,2,4]
[6,1,4,2,5,3,7,8]=>[6,4,2,3,5,1,7,8]=>[3,5,7,6,4,8,2,1]=>[3,1,2,1,1]
[1,3,7,5,4,2,8,6]=>[5,4,8,2,6,1,3,7]=>[4,5,1,7,3,8,6,2]=>[2,2,2,1,1]
[6,1,3,5,4,2,7,8]=>[6,3,5,2,4,1,7,8]=>[3,6,4,7,5,8,2,1]=>[2,2,2,1,1]
[5,1,6,3,4,7,8,2]=>[4,5,3,1,6,8,2,7]=>[5,4,6,8,3,1,7,2]=>[1,3,1,2,1]
[5,2,6,3,4,7,1,8]=>[4,5,2,1,3,7,6,8]=>[5,4,7,8,6,2,3,1]=>[1,3,1,2,1]
[3,4,7,5,8,6,1,2]=>[4,7,1,2,3,8,6,5]=>[5,2,8,7,6,1,3,4]=>[1,2,1,1,3]
[2,4,7,1,5,3,8,6]=>[2,5,8,1,4,6,3,7]=>[7,4,1,8,5,3,6,2]=>[1,1,2,1,2,1]
[2,3,6,7,4,8,1,5]=>[5,3,7,1,2,4,8,6]=>[4,6,2,8,7,5,1,3]=>[2,2,1,1,2]
[2,7,6,5,3,1,8,4]=>[5,8,6,4,1,3,2,7]=>[4,1,3,5,8,6,7,2]=>[1,4,2,1]
[5,2,6,1,4,7,8,3]=>[5,6,2,1,3,8,4,7]=>[4,3,7,8,6,1,5,2]=>[1,3,1,2,1]
[4,7,6,5,2,1,8,3]=>[5,8,1,6,4,3,2,7]=>[4,1,8,3,5,6,7,2]=>[1,2,4,1]
[5,3,6,2,4,1,7,8]=>[2,4,1,6,5,3,7,8]=>[7,5,8,3,4,6,2,1]=>[1,2,3,1,1]
[5,7,4,2,1,3,6,8]=>[5,4,1,6,3,7,2,8]=>[4,5,8,3,6,2,7,1]=>[3,2,2,1]
[6,3,1,5,4,7,8,2]=>[2,5,4,6,1,8,3,7]=>[7,4,5,3,8,1,6,2]=>[1,2,2,2,1]
[5,3,6,1,4,2,7,8]=>[2,6,4,1,5,3,7,8]=>[7,3,5,8,4,6,2,1]=>[1,3,2,1,1]
[1,7,4,2,6,3,8,5]=>[3,8,6,4,5,1,2,7]=>[6,1,3,5,4,8,7,2]=>[1,3,2,1,1]
[5,7,4,1,2,3,6,8]=>[4,5,1,6,3,7,2,8]=>[5,4,8,3,6,2,7,1]=>[1,2,2,2,1]
[6,4,1,2,5,3,7,8]=>[6,3,4,2,5,1,7,8]=>[3,6,5,7,4,8,2,1]=>[2,2,2,1,1]
[4,7,6,3,8,5,1,2]=>[4,7,1,3,2,8,6,5]=>[5,2,8,6,7,1,3,4]=>[1,2,2,3]
[3,7,6,5,2,8,1,4]=>[5,7,4,1,3,2,8,6]=>[4,2,5,8,6,7,1,3]=>[1,3,2,2]
[3,7,6,5,1,2,8,4]=>[8,5,6,1,4,3,2,7]=>[1,4,3,8,5,6,7,2]=>[2,2,3,1]
[4,7,2,6,1,3,8,5]=>[1,8,3,5,6,4,2,7]=>[8,1,6,4,3,5,7,2]=>[1,2,1,3,1]
[2,7,1,6,8,3,5,4]=>[8,6,4,7,1,3,2,5]=>[1,3,5,2,8,6,7,4]=>[3,2,2,1]
[2,7,6,5,8,1,4,3]=>[8,6,4,3,1,2,7,5]=>[1,3,5,6,8,7,2,4]=>[5,1,2]
[9,1,2,3,4,5,6,8,7]=>[9,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,9]=>[2,1,1,1,1,1,2]
[10,1,2,3,4,5,6,7,9,8]=>[10,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,10]=>[2,1,1,1,1,1,1,2]
[2,3,4,5,6,7,8,10,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>[1,10,9,8,7,6,5,4,2,3]=>[2,1,1,1,1,1,1,2]
[2,11,10,9,8,7,6,5,4,3,1]=>[11,10,9,8,7,6,5,4,1,3,2]=>[1,2,3,4,5,6,7,8,11,9,10]=>[9,2]
[3,2,10,9,8,7,6,5,4,1]=>[10,9,8,7,6,1,5,2,4,3]=>[1,2,3,4,5,10,6,9,7,8]=>[6,2,2]
[3,9,2,8,7,6,5,4,1]=>[9,8,7,6,1,3,5,4,2]=>[1,2,3,4,9,7,5,6,8]=>[5,1,3]
[4,2,9,8,7,6,5,3,1]=>[9,8,7,1,6,5,2,4,3]=>[1,2,3,9,4,5,8,6,7]=>[4,3,2]
[5,2,8,7,6,4,3,1]=>[8,1,7,6,5,2,4,3]=>[1,8,2,3,4,7,5,6]=>[2,4,2]
[8,2,7,6,1,5,4,3]=>[8,7,5,6,2,4,3,1]=>[1,2,4,3,7,5,6,8]=>[3,2,3]
[9,2,8,1,7,6,5,4,3]=>[9,8,7,6,2,4,5,3,1]=>[1,2,3,4,8,6,5,7,9]=>[5,1,3]
[8,4,1,7,6,5,3,2]=>[8,2,7,6,5,3,4,1]=>[1,7,2,3,4,6,5,8]=>[2,4,2]
[11,1,10,9,8,7,6,5,4,3,2]=>[11,10,9,8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8,10,9,11]=>[9,2]
[4,5,6,2,3,8,1,7]=>[1,4,2,5,3,7,8,6]=>[8,5,7,4,6,2,1,3]=>[1,2,2,1,2]
[4,5,3,2,7,8,1,6]=>[1,3,2,7,4,5,8,6]=>[8,6,7,2,5,4,1,3]=>[1,2,2,1,2]
[6,5,7,3,8,4,2,1]=>[2,1,8,4,3,7,6,5]=>[7,8,1,5,6,2,3,4]=>[2,3,3]
[6,8,7,2,4,3,5,1]=>[6,4,1,5,8,7,3,2]=>[3,5,8,4,1,2,6,7]=>[3,1,4]
[3,2,7,4,5,8,1,6]=>[1,4,5,7,2,3,8,6]=>[8,5,4,2,7,6,1,3]=>[1,1,1,2,1,2]
[6,8,1,5,2,4,3,7]=>[7,5,6,3,1,4,8,2]=>[2,4,3,6,8,5,1,7]=>[2,3,1,2]
[8,3,4,6,1,5,2,7]=>[2,3,7,5,6,4,8,1]=>[7,6,2,4,3,5,1,8]=>[1,1,2,2,2]
[2,3,4,7,5,8,1,6]=>[5,7,1,2,3,4,8,6]=>[4,2,8,7,6,5,1,3]=>[1,2,1,1,1,2]
[6,3,4,7,8,2,5,1]=>[6,2,3,1,4,8,7,5]=>[3,7,6,8,5,1,2,4]=>[2,2,1,3]
[5,3,7,4,8,6,1,2]=>[4,1,7,2,3,8,6,5]=>[5,8,2,7,6,1,3,4]=>[2,2,1,3]
[8,3,6,4,1,7,2,5]=>[7,2,4,8,5,3,6,1]=>[2,7,5,1,4,6,3,8]=>[2,1,3,2]
[1,3,7,4,8,6,2,5]=>[7,8,4,2,3,6,1,5]=>[2,1,5,7,6,3,8,4]=>[1,3,1,2,1]
[3,7,8,5,4,1,2,6]=>[6,7,5,1,4,2,8,3]=>[3,2,4,8,5,7,1,6]=>[1,3,2,2]
[5,4,3,1,7,8,2,6]=>[3,2,1,7,5,8,4,6]=>[6,7,8,2,4,1,5,3]=>[3,2,2,1]
[5,7,6,2,8,4,1,3]=>[1,7,8,4,3,2,6,5]=>[8,2,1,5,6,7,3,4]=>[1,1,4,2]
[6,1,7,5,8,3,4,2]=>[6,4,3,1,8,7,2,5]=>[3,5,6,8,1,2,7,4]=>[4,3,1]
[7,5,6,4,1,3,8,2]=>[6,2,8,5,4,3,1,7]=>[3,7,1,4,5,6,8,2]=>[2,5,1]
[1,5,6,8,4,7,3,2]=>[2,3,5,8,7,6,1,4]=>[7,6,4,1,2,3,8,5]=>[1,1,1,4,1]
[4,1,3,7,6,5,8,2]=>[1,6,5,3,4,8,2,7]=>[8,3,4,6,5,1,7,2]=>[1,3,1,2,1]
[3,4,1,7,5,8,6,2]=>[8,1,2,5,4,7,3,6]=>[1,8,7,4,5,2,6,3]=>[2,1,2,2,1]
[8,5,7,4,3,1,6,2]=>[2,8,6,5,4,7,3,1]=>[7,1,3,4,5,2,6,8]=>[1,4,3]
[6,8,5,1,7,2,4,3]=>[8,6,1,7,4,3,5,2]=>[1,3,8,2,5,6,4,7]=>[3,3,2]
[7,8,3,6,2,1,4,5]=>[3,6,5,7,1,8,4,2]=>[6,3,4,2,8,1,5,7]=>[1,2,2,3]
[8,1,7,4,2,3,6,5]=>[8,5,4,6,7,2,3,1]=>[1,4,5,3,2,7,6,8]=>[3,1,2,2]
[8,2,3,1,5,7,6,4]=>[8,2,3,5,7,4,6,1]=>[1,7,6,4,2,5,3,8]=>[2,1,1,2,2]
[3,8,4,1,2,7,6,5]=>[3,8,1,7,4,5,6,2]=>[6,1,8,2,5,4,3,7]=>[1,2,2,1,2]
[5,4,7,2,3,6,8,1]=>[4,2,1,5,6,3,8,7]=>[5,7,8,4,3,6,1,2]=>[3,1,2,2]
[6,3,2,1,8,4,7,5]=>[2,8,3,6,1,7,4,5]=>[7,1,6,3,8,2,5,4]=>[1,2,2,2,1]
[2,3,7,4,1,8,5,6]=>[4,7,8,1,2,5,3,6]=>[5,2,1,8,7,4,6,3]=>[1,1,2,1,2,1]
[6,4,1,3,2,7,8,5]=>[4,6,2,8,3,1,5,7]=>[5,3,7,1,6,8,4,2]=>[1,2,3,1,1]
[2,7,8,5,1,3,6,4]=>[8,5,6,4,1,2,7,3]=>[1,4,3,5,8,7,2,6]=>[2,3,1,2]
[8,2,5,6,7,1,3,4]=>[6,3,7,2,4,8,5,1]=>[3,6,2,7,5,1,4,8]=>[2,2,1,3]
[2,8,5,4,7,6,1,3]=>[4,3,7,8,6,1,5,2]=>[5,6,2,1,3,8,4,7]=>[2,1,3,2]
[6,7,1,5,8,2,4,3]=>[8,6,4,1,7,3,2,5]=>[1,3,5,8,2,6,7,4]=>[4,3,1]
[4,8,7,6,2,3,5,1]=>[5,6,8,1,7,4,3,2]=>[4,3,1,8,2,5,6,7]=>[1,1,2,4]
[7,8,1,5,3,2,6,4]=>[5,8,6,3,4,1,7,2]=>[4,1,3,6,5,8,2,7]=>[1,3,2,2]
[6,5,7,3,8,2,1,4]=>[4,2,1,7,6,3,8,5]=>[5,7,8,2,3,6,1,4]=>[3,3,2]
[8,1,4,7,2,5,6,3]=>[3,6,8,5,7,2,4,1]=>[6,3,1,4,2,7,5,8]=>[1,1,2,2,2]
[7,3,4,6,1,5,8,2]=>[2,3,6,8,5,4,1,7]=>[7,6,3,1,4,5,8,2]=>[1,1,1,4,1]
[8,3,4,5,7,1,6,2]=>[2,3,4,8,6,7,5,1]=>[7,6,5,1,3,2,4,8]=>[1,1,1,2,3]
[4,2,6,8,3,1,5,7]=>[1,6,5,2,3,7,8,4]=>[8,3,4,7,6,2,1,5]=>[1,3,1,1,2]
[2,3,5,8,6,1,4,7]=>[3,6,7,1,2,5,8,4]=>[6,3,2,8,7,4,1,5]=>[1,1,2,1,1,2]
[4,2,3,8,6,1,5,7]=>[6,1,7,2,3,5,8,4]=>[3,8,2,7,6,4,1,5]=>[2,2,1,1,2]
[6,4,1,2,8,3,5,7]=>[6,7,2,8,3,1,4,5]=>[3,2,7,1,6,8,5,4]=>[1,2,3,1,1]
[1,2,3,7,4,6,8,5]=>[6,8,5,1,2,3,4,7]=>[3,1,4,8,7,6,5,2]=>[1,3,1,1,1,1]
[3,2,7,1,4,5,8,6]=>[1,8,2,4,5,6,3,7]=>[8,1,7,5,4,3,6,2]=>[1,2,1,1,2,1]
[2,1,5,3,8,7,4,6]=>[3,7,8,1,6,2,4,5]=>[6,2,1,8,3,7,5,4]=>[1,1,2,2,1,1]
[5,8,3,2,4,1,6,7]=>[4,3,1,6,5,7,8,2]=>[5,6,8,3,4,2,1,7]=>[3,2,1,2]
[4,2,7,1,8,3,5,6]=>[6,1,7,8,2,4,3,5]=>[3,8,2,1,7,5,6,4]=>[2,1,2,2,1]
[4,1,8,2,7,3,5,6]=>[6,1,7,8,4,5,2,3]=>[3,8,2,1,5,4,7,6]=>[2,1,2,2,1]
[3,2,7,1,4,8,5,6]=>[1,7,8,2,4,5,3,6]=>[8,2,1,7,5,4,6,3]=>[1,1,2,1,2,1]
[1,2,3,7,6,8,4,5]=>[7,5,4,8,1,2,3,6]=>[2,4,5,1,8,7,6,3]=>[3,2,1,1,1]
[1,2,3,6,8,7,4,5]=>[4,7,8,6,1,2,3,5]=>[5,2,1,3,8,7,6,4]=>[1,1,3,1,1,1]
[1,2,3,7,8,6,4,5]=>[7,4,8,6,1,2,3,5]=>[2,5,1,3,8,7,6,4]=>[2,3,1,1,1]
[6,2,8,3,7,5,1,4]=>[7,8,4,1,6,2,5,3]=>[2,1,5,8,3,7,4,6]=>[1,3,2,2]
[4,2,8,3,7,5,6,1]=>[1,6,8,4,7,2,5,3]=>[8,3,1,5,2,7,4,6]=>[1,1,2,2,2]
[7,3,4,8,6,5,1,2]=>[7,8,2,3,1,6,5,4]=>[2,1,7,6,8,3,4,5]=>[1,2,2,3]
[4,6,3,8,5,7,2,1]=>[5,1,2,8,3,7,6,4]=>[4,8,7,1,6,2,3,5]=>[2,1,2,3]
[7,5,3,8,6,2,4,1]=>[6,2,8,3,1,7,5,4]=>[3,7,1,6,8,2,4,5]=>[2,3,3]
[2,6,8,3,7,4,5,1]=>[6,2,8,4,7,1,5,3]=>[3,7,1,5,2,8,4,6]=>[2,2,2,2]
[1,8,4,3,7,5,6,2]=>[3,6,8,4,7,5,1,2]=>[6,3,1,5,2,4,8,7]=>[1,1,2,3,1]
[7,4,3,8,6,2,5,1]=>[2,6,8,3,1,7,5,4]=>[7,3,1,6,8,2,4,5]=>[1,1,3,3]
[4,5,3,8,6,7,2,1]=>[1,2,5,8,3,7,6,4]=>[8,7,4,1,6,2,3,5]=>[1,1,1,2,3]
[3,6,7,8,4,5,2,1]=>[2,5,3,8,1,7,6,4]=>[7,4,6,1,8,2,3,5]=>[1,2,2,3]
[2,6,8,5,4,7,3,1]=>[2,5,4,8,7,1,6,3]=>[7,4,5,1,2,8,3,6]=>[1,2,3,2]
[1,8,5,6,4,7,3,2]=>[3,5,4,8,7,6,1,2]=>[6,4,5,1,2,3,8,7]=>[1,2,4,1]
[2,5,8,6,4,7,3,1]=>[5,2,4,8,7,1,6,3]=>[4,7,5,1,2,8,3,6]=>[2,1,3,2]
[7,4,6,5,8,3,2,1]=>[4,2,3,1,8,7,6,5]=>[5,7,6,8,1,2,3,4]=>[2,2,4]
[6,3,7,8,4,5,2,1]=>[5,3,1,8,2,7,6,4]=>[4,6,8,1,7,2,3,5]=>[3,2,3]
[4,3,7,8,5,6,2,1]=>[5,1,3,8,2,7,6,4]=>[4,8,6,1,7,2,3,5]=>[2,1,2,3]
[5,2,8,6,4,7,3,1]=>[1,5,4,8,7,2,6,3]=>[8,4,5,1,2,7,3,6]=>[1,2,3,2]
[4,2,8,6,5,7,3,1]=>[5,1,4,8,7,2,6,3]=>[4,8,5,1,2,7,3,6]=>[2,1,3,2]
[3,2,8,6,7,4,5,1]=>[6,4,8,1,7,2,5,3]=>[3,5,1,8,2,7,4,6]=>[2,2,2,2]
[2,3,8,7,5,4,6,1]=>[6,5,8,7,1,2,4,3]=>[3,4,1,2,8,7,5,6]=>[2,3,1,2]
[1,8,2,7,4,5,6,3]=>[5,6,8,7,3,4,1,2]=>[4,3,1,2,6,5,8,7]=>[1,1,3,2,1]
[7,2,8,6,3,4,5,1]=>[5,6,8,7,2,1,4,3]=>[4,3,1,2,7,8,5,6]=>[1,1,4,2]
[6,2,8,4,5,7,3,1]=>[4,5,1,8,7,2,6,3]=>[5,4,8,1,2,7,3,6]=>[1,2,3,2]
[5,2,8,4,6,7,3,1]=>[4,1,5,8,7,2,6,3]=>[5,8,4,1,2,7,3,6]=>[2,1,3,2]
[4,2,8,5,6,7,3,1]=>[1,4,5,8,7,2,6,3]=>[8,5,4,1,2,7,3,6]=>[1,1,1,3,2]
[3,4,6,8,7,2,5,1]=>[3,6,8,1,2,7,5,4]=>[6,3,1,8,7,2,4,5]=>[1,1,2,1,3]
[7,3,5,8,6,2,4,1]=>[3,6,8,2,1,7,5,4]=>[6,3,1,7,8,2,4,5]=>[1,1,3,3]
[1,8,3,5,7,4,6,2]=>[4,6,8,3,7,5,1,2]=>[5,3,1,6,2,4,8,7]=>[1,1,2,3,1]
[2,7,8,4,5,6,3,1]=>[4,5,2,8,7,1,6,3]=>[5,4,7,1,2,8,3,6]=>[1,2,3,2]
[3,7,5,8,4,6,2,1]=>[3,5,2,8,1,7,6,4]=>[6,4,7,1,8,2,3,5]=>[1,2,2,3]
[5,7,4,6,8,3,2,1]=>[1,3,4,2,8,7,6,5]=>[8,6,5,7,1,2,3,4]=>[1,1,2,4]
[3,6,5,8,4,7,2,1]=>[3,2,5,8,1,7,6,4]=>[6,7,4,1,8,2,3,5]=>[2,1,2,3]
[2,6,8,4,5,7,3,1]=>[4,2,5,8,7,1,6,3]=>[5,7,4,1,2,8,3,6]=>[2,1,3,2]
[4,2,7,1,3,8,5,6]=>[7,1,8,2,4,5,3,6]=>[2,8,1,7,5,4,6,3]=>[2,2,1,2,1]
[4,2,5,1,3,8,6,7]=>[7,2,1,3,8,4,5,6]=>[2,7,8,6,1,5,4,3]=>[3,1,2,1,1]
[5,3,6,1,7,2,4,8]=>[2,6,1,7,4,3,5,8]=>[7,3,8,2,5,6,4,1]=>[1,2,3,1,1]
[3,7,1,2,5,8,6,4]=>[8,1,5,7,3,4,2,6]=>[1,8,4,2,6,5,7,3]=>[2,1,2,2,1]
[3,7,4,1,2,8,5,6]=>[7,1,3,8,4,5,2,6]=>[2,8,6,1,5,4,7,3]=>[2,1,2,2,1]
[7,5,1,3,4,8,6,2]=>[8,4,5,2,7,3,1,6]=>[1,5,4,7,2,6,8,3]=>[2,2,3,1]
[7,5,1,2,4,8,6,3]=>[8,5,7,3,2,4,1,6]=>[1,4,2,6,7,5,8,3]=>[2,3,2,1]
[6,4,2,3,7,1,5,8]=>[3,4,2,6,1,7,5,8]=>[6,5,7,3,8,2,4,1]=>[1,2,2,2,1]
[7,4,2,3,8,1,6,5]=>[8,3,2,4,6,1,7,5]=>[1,6,7,5,3,8,2,4]=>[3,1,2,2]
[4,7,5,2,8,1,3,6]=>[1,4,6,3,7,2,8,5]=>[8,5,3,6,2,7,1,4]=>[1,1,2,2,2]
[8,2,6,3,7,1,4,5]=>[4,6,7,2,3,8,5,1]=>[5,3,2,7,6,1,4,8]=>[1,1,2,1,3]
[8,5,7,1,2,4,6,3]=>[6,8,4,2,5,7,3,1]=>[3,1,5,7,4,2,6,8]=>[1,3,1,3]
[8,5,7,1,3,4,6,2]=>[5,6,2,8,4,7,3,1]=>[4,3,7,1,5,2,6,8]=>[1,2,2,3]
[8,6,2,7,1,3,5,4]=>[8,3,5,6,2,7,4,1]=>[1,6,4,3,7,2,5,8]=>[2,1,2,3]
[3,8,5,6,1,2,4,7]=>[5,6,1,3,7,4,8,2]=>[4,3,8,6,2,5,1,7]=>[1,2,1,2,2]
[3,7,5,8,1,2,4,6]=>[5,6,1,3,7,2,8,4]=>[4,3,8,6,2,7,1,5]=>[1,2,1,2,2]
[7,6,4,8,1,3,5,2]=>[6,3,8,5,2,1,7,4]=>[3,6,1,4,7,8,2,5]=>[2,4,2]
[6,5,8,1,2,4,7,3]=>[6,8,4,2,1,5,7,3]=>[3,1,5,7,8,4,2,6]=>[1,4,1,2]
[3,6,8,1,2,5,7,4]=>[6,8,1,4,2,5,7,3]=>[3,1,8,5,7,4,2,6]=>[1,2,2,1,2]
[3,7,2,4,8,1,6,5]=>[8,1,3,4,6,2,7,5]=>[1,8,6,5,3,7,2,4]=>[2,1,1,2,2]
[4,6,3,8,1,2,5,7]=>[1,5,3,6,2,7,8,4]=>[8,4,6,3,7,2,1,5]=>[1,2,2,1,2]
[4,6,3,7,1,2,5,8]=>[1,5,3,6,2,7,4,8]=>[8,4,6,3,7,2,5,1]=>[1,2,2,2,1]
[4,1,7,8,2,3,6,5]=>[1,8,5,6,3,7,2,4]=>[8,1,4,3,6,2,7,5]=>[1,2,2,2,1]
[5,1,2,8,6,3,4,7]=>[6,7,5,1,8,2,3,4]=>[3,2,4,8,1,7,6,5]=>[1,3,2,1,1]
[5,3,8,1,6,2,4,7]=>[2,6,1,7,4,5,8,3]=>[7,3,8,2,5,4,1,6]=>[1,2,2,1,2]
[6,1,8,5,2,3,4,7]=>[5,6,7,4,1,8,2,3]=>[4,3,2,5,8,1,7,6]=>[1,1,3,2,1]
[6,1,7,5,2,3,4,8]=>[5,6,7,4,2,1,3,8]=>[4,3,2,5,7,8,6,1]=>[1,1,4,1,1]
[6,8,1,3,7,4,5,2]=>[6,8,4,1,7,3,5,2]=>[3,1,5,8,2,6,4,7]=>[1,3,2,2]
[7,2,8,1,6,3,4,5]=>[6,7,8,2,4,1,5,3]=>[3,2,1,7,5,8,4,6]=>[1,1,2,2,2]
[4,7,8,2,5,1,3,6]=>[1,4,6,7,5,2,8,3]=>[8,5,3,2,4,7,1,6]=>[1,1,1,3,2]
[6,8,2,7,1,4,5,3]=>[6,8,3,1,5,7,4,2]=>[3,1,6,8,4,2,5,7]=>[1,3,1,3]
[4,8,7,1,3,5,6,2]=>[1,5,6,8,4,7,3,2]=>[8,4,3,1,5,2,6,7]=>[1,1,1,2,3]
[3,8,7,1,2,4,6,5]=>[8,1,4,5,6,7,3,2]=>[1,8,5,4,3,2,6,7]=>[2,1,1,1,3]
[4,8,7,1,2,3,6,5]=>[1,8,4,5,6,7,3,2]=>[8,1,5,4,3,2,6,7]=>[1,2,1,1,3]
[5,8,7,1,2,4,6,3]=>[6,1,8,4,5,7,3,2]=>[3,8,1,5,4,2,6,7]=>[2,2,1,3]
[5,8,7,1,3,4,6,2]=>[5,1,6,8,4,7,3,2]=>[4,8,3,1,5,2,6,7]=>[2,1,2,3]
[7,1,8,6,2,3,5,4]=>[8,5,6,7,4,2,1,3]=>[1,4,3,2,5,7,8,6]=>[2,1,4,1]
[5,8,6,4,1,2,3,7]=>[5,1,6,7,4,3,8,2]=>[4,8,3,2,5,6,1,7]=>[2,1,3,2]
[7,8,1,2,6,5,3,4]=>[7,8,6,3,4,1,5,2]=>[2,1,3,6,5,8,4,7]=>[1,3,2,2]
[1,4,8,2,7,5,3,6]=>[7,2,6,8,4,5,1,3]=>[2,7,3,1,5,4,8,6]=>[2,1,2,2,1]
[7,8,2,1,6,3,5,4]=>[8,3,6,7,4,1,5,2]=>[1,6,3,2,5,8,4,7]=>[2,1,3,2]
[6,1,2,7,5,4,3,8]=>[7,6,5,2,3,1,4,8]=>[2,3,4,7,6,8,5,1]=>[4,2,1,1]
[1,2,8,7,5,4,3,6]=>[7,6,5,8,4,1,2,3]=>[2,3,4,1,5,8,7,6]=>[3,3,1,1]
[6,2,1,5,7,4,3,8]=>[4,7,2,6,3,1,5,8]=>[5,2,7,3,6,8,4,1]=>[1,2,3,1,1]
[6,2,3,7,4,1,5,8]=>[6,2,3,5,1,7,4,8]=>[3,7,6,4,8,2,5,1]=>[2,1,2,2,1]
[3,4,8,7,5,6,1,2]=>[7,5,8,1,2,6,4,3]=>[2,4,1,8,7,3,5,6]=>[2,2,1,3]
[2,3,8,7,4,1,5,6]=>[6,5,7,8,1,2,4,3]=>[3,4,2,1,8,7,5,6]=>[2,1,2,1,2]
[2,7,3,8,6,4,1,5]=>[7,6,8,3,1,2,5,4]=>[2,3,1,6,8,7,4,5]=>[2,3,1,2]
[1,8,3,7,6,4,5,2]=>[6,8,7,3,5,4,1,2]=>[3,1,2,6,4,5,8,7]=>[1,3,3,1]
[5,2,7,1,4,6,8,3]=>[5,6,1,8,2,4,3,7]=>[4,3,8,1,7,5,6,2]=>[1,2,2,2,1]
[4,6,7,5,2,1,8,3]=>[5,1,2,8,6,4,3,7]=>[4,8,7,1,3,5,6,2]=>[2,1,4,1]
[6,3,1,4,5,7,8,2]=>[4,2,5,6,1,8,3,7]=>[5,7,4,3,8,1,6,2]=>[2,1,2,2,1]
[5,3,1,4,6,2,7,8]=>[4,2,6,3,1,5,7,8]=>[5,7,3,6,8,4,2,1]=>[2,3,1,1,1]
[5,7,4,1,2,6,3,8]=>[7,4,1,5,3,6,2,8]=>[2,5,8,4,6,3,7,1]=>[3,2,2,1]
[4,8,1,2,6,7,3,5]=>[1,7,5,8,3,4,6,2]=>[8,2,4,1,6,5,3,7]=>[1,2,2,1,2]
[1,2,8,7,6,5,3,4]=>[7,8,6,5,4,1,2,3]=>[2,1,3,4,5,8,7,6]=>[1,5,1,1]
[3,1,2,4,6,8,7,5]=>[1,8,5,7,2,3,4,6]=>[8,1,4,2,7,6,5,3]=>[1,2,2,1,1,1]
[3,1,8,4,5,7,6,2]=>[8,1,4,5,7,6,2,3]=>[1,8,5,4,2,3,7,6]=>[2,1,1,3,1]
[3,2,8,5,4,7,1,6]=>[5,1,4,7,8,2,6,3]=>[4,8,5,2,1,7,3,6]=>[2,1,1,2,2]
[4,2,8,1,5,3,7,6]=>[5,1,8,2,4,6,7,3]=>[4,8,1,7,5,3,2,6]=>[2,2,1,1,2]
[4,3,8,5,7,6,1,2]=>[1,4,7,8,2,6,5,3]=>[8,5,2,1,7,3,4,6]=>[1,1,1,2,3]
[4,8,2,1,6,3,7,5]=>[1,8,3,6,4,5,7,2]=>[8,1,6,3,5,4,2,7]=>[1,2,2,1,2]
[3,8,6,5,2,7,1,4]=>[5,7,4,1,3,8,6,2]=>[4,2,5,8,6,1,3,7]=>[1,3,1,3]
[3,8,5,6,1,7,4,2]=>[3,8,7,1,5,4,6,2]=>[6,1,2,8,4,5,3,7]=>[1,3,2,2]
[3,5,7,8,1,2,6,4]=>[2,8,1,5,6,3,7,4]=>[7,1,8,4,3,6,2,5]=>[1,2,1,2,2]
[3,7,8,5,2,1,6,4]=>[5,8,6,1,4,2,7,3]=>[4,1,3,8,5,7,2,6]=>[1,3,2,2]
[3,7,2,8,4,1,6,5]=>[5,8,1,3,6,2,7,4]=>[4,1,8,6,3,7,2,5]=>[1,2,1,2,2]
[2,8,1,7,4,6,5,3]=>[8,5,7,6,1,3,4,2]=>[1,4,2,3,8,6,5,7]=>[2,3,1,2]
[2,8,7,5,1,6,4,3]=>[8,7,5,4,6,1,3,2]=>[1,2,4,5,3,8,6,7]=>[4,2,2]
[2,8,6,7,5,1,4,3]=>[8,6,3,7,5,1,4,2]=>[1,3,6,2,4,8,5,7]=>[3,3,2]
[5,1,3,4,6,7,2,8]=>[3,4,5,1,7,2,6,8]=>[6,5,4,8,2,7,3,1]=>[1,1,2,2,1,1]
[1,3,4,8,7,5,2,6]=>[7,6,8,2,3,5,1,4]=>[2,3,1,7,6,4,8,5]=>[2,2,1,2,1]
[8,2,4,1,7,3,5,6]=>[6,2,3,7,8,4,5,1]=>[3,7,6,2,1,5,4,8]=>[2,1,1,2,2]
[8,6,1,4,2,3,7,5]=>[8,5,3,4,6,2,7,1]=>[1,4,6,5,3,7,2,8]=>[3,1,2,2]
[3,6,1,4,2,8,7,5]=>[8,1,4,7,3,2,5,6]=>[1,8,5,2,6,7,4,3]=>[2,1,3,1,1]
[6,1,7,4,3,8,2,5]=>[5,4,7,3,1,8,2,6]=>[4,5,2,6,8,1,7,3]=>[2,3,2,1]
[1,8,7,4,3,6,2,5]=>[5,4,7,8,6,3,1,2]=>[4,5,2,1,3,6,8,7]=>[2,1,4,1]
[7,4,1,3,8,2,6,5]=>[8,4,2,6,7,3,1,5]=>[1,5,7,3,2,6,8,4]=>[3,1,3,1]
[4,8,2,3,1,5,7,6]=>[3,1,4,8,5,6,7,2]=>[6,8,5,1,4,3,2,7]=>[2,1,2,1,2]
[4,8,6,2,1,3,7,5]=>[1,4,8,5,6,3,7,2]=>[8,5,1,4,3,6,2,7]=>[1,1,2,2,2]
[1,7,8,4,2,3,6,5]=>[8,5,4,6,2,7,1,3]=>[1,4,5,3,7,2,8,6]=>[3,2,2,1]
[4,7,1,3,8,2,6,5]=>[1,8,4,6,7,3,2,5]=>[8,1,5,3,2,6,7,4]=>[1,2,1,3,1]
[8,7,1,3,4,2,6,5]=>[4,5,8,3,6,7,2,1]=>[5,4,1,6,3,2,7,8]=>[1,1,2,1,3]
[1,7,4,3,6,2,8,5]=>[3,8,4,6,5,1,2,7]=>[6,1,5,3,4,8,7,2]=>[1,2,3,1,1]
[3,8,6,4,5,2,1,7]=>[4,7,6,1,5,3,8,2]=>[5,2,3,8,4,6,1,7]=>[1,3,2,2]
[3,8,4,6,5,2,1,7]=>[7,3,6,1,5,4,8,2]=>[2,6,3,8,4,5,1,7]=>[2,2,2,2]
[2,4,3,7,5,8,1,6]=>[2,5,7,1,3,4,8,6]=>[7,4,2,8,6,5,1,3]=>[1,1,2,1,1,2]
[1,4,7,3,6,2,8,5]=>[8,2,4,6,5,1,3,7]=>[1,7,5,3,4,8,6,2]=>[2,1,3,1,1]
[1,8,3,4,2,6,7,5]=>[3,4,6,8,5,7,1,2]=>[6,5,3,1,4,2,8,7]=>[1,1,1,2,2,1]
[6,4,1,3,7,2,8,5]=>[8,4,2,6,3,1,5,7]=>[1,5,7,3,6,8,4,2]=>[3,3,1,1]
[8,1,4,3,6,2,7,5]=>[3,8,4,6,2,5,7,1]=>[6,1,5,3,7,4,2,8]=>[1,2,2,1,2]
[4,2,3,8,5,7,1,6]=>[5,1,7,8,2,3,6,4]=>[4,8,2,1,7,6,3,5]=>[2,1,2,1,2]
[5,8,2,6,4,3,1,7]=>[1,7,6,3,5,4,8,2]=>[8,2,3,6,4,5,1,7]=>[1,3,2,2]
[7,2,5,8,4,3,1,6]=>[3,7,6,2,5,1,8,4]=>[6,2,3,7,4,8,1,5]=>[1,3,2,2]
[4,2,3,5,8,7,1,6]=>[7,1,8,2,3,4,6,5]=>[2,8,1,7,6,5,3,4]=>[2,2,1,1,2]
[8,2,3,5,4,7,1,6]=>[5,2,3,4,7,8,6,1]=>[4,7,6,5,2,1,3,8]=>[2,1,1,1,3]
[6,1,8,3,4,2,7,5]=>[4,5,8,6,1,7,2,3]=>[5,4,1,3,8,2,7,6]=>[1,1,3,2,1]
[2,4,3,5,7,8,1,6]=>[2,7,1,3,4,5,8,6]=>[7,2,8,6,5,4,1,3]=>[1,2,1,1,1,2]
[3,8,6,5,4,2,1,7]=>[7,6,5,1,4,3,8,2]=>[2,3,4,8,5,6,1,7]=>[4,2,2]
[6,3,1,4,2,8,7,5]=>[2,8,4,7,3,1,5,6]=>[7,1,5,2,6,8,4,3]=>[1,2,3,1,1]
[7,3,8,1,2,6,4,5]=>[2,7,8,4,5,1,6,3]=>[7,2,1,5,4,8,3,6]=>[1,1,2,2,2]
[7,1,4,5,3,2,6,8]=>[3,6,5,2,4,7,1,8]=>[6,3,4,7,5,2,8,1]=>[1,3,1,2,1]
[1,8,4,2,6,5,3,7]=>[3,7,6,4,5,8,1,2]=>[6,2,3,5,4,1,8,7]=>[1,3,1,2,1]
[5,3,1,8,4,7,2,6]=>[2,5,1,7,8,6,3,4]=>[7,4,8,2,1,3,6,5]=>[1,2,1,3,1]
[4,3,8,1,5,7,2,6]=>[2,1,5,7,8,4,6,3]=>[7,8,4,2,1,5,3,6]=>[2,1,1,2,2]
[6,3,1,2,5,7,4,8]=>[5,2,7,3,4,1,6,8]=>[4,7,2,6,5,8,3,1]=>[2,2,2,1,1]
[7,1,4,2,6,5,3,8]=>[3,7,6,2,4,5,1,8]=>[6,2,3,7,5,4,8,1]=>[1,3,1,2,1]
[3,8,4,1,6,5,2,7]=>[3,7,1,6,4,5,8,2]=>[6,2,8,3,5,4,1,7]=>[1,2,2,1,2]
[7,5,3,6,4,8,2,1]=>[5,3,2,4,1,8,7,6]=>[4,6,7,5,8,1,2,3]=>[3,2,3]
[7,3,6,4,5,8,2,1]=>[4,5,2,3,1,8,7,6]=>[5,4,7,6,8,1,2,3]=>[1,2,2,3]
[8,7,2,4,5,1,6,3]=>[4,8,3,6,5,7,2,1]=>[5,1,6,3,4,2,7,8]=>[1,2,2,3]
[7,1,5,4,8,6,3,2]=>[3,8,4,7,6,2,1,5]=>[6,1,5,2,3,7,8,4]=>[1,2,4,1]
[2,7,5,4,8,6,3,1]=>[3,8,4,2,7,1,6,5]=>[6,1,5,7,2,8,3,4]=>[1,3,2,2]
[2,1,8,7,5,3,6,4]=>[8,6,5,7,1,4,2,3]=>[1,3,4,2,8,5,7,6]=>[3,2,2,1]
[5,8,3,7,4,1,6,2]=>[1,8,3,6,5,7,4,2]=>[8,1,6,3,4,2,5,7]=>[1,2,2,3]
[8,1,7,4,2,6,5,3]=>[4,8,7,5,6,2,3,1]=>[5,1,2,4,3,7,6,8]=>[1,3,2,2]
[5,6,3,1,8,4,7,2]=>[3,1,6,2,8,7,4,5]=>[6,8,3,7,1,2,5,4]=>[2,2,3,1]
[5,7,1,4,8,6,3,2]=>[1,8,4,7,6,3,2,5]=>[8,1,5,2,3,6,7,4]=>[1,2,4,1]
[3,5,7,4,8,6,2,1]=>[8,2,4,1,3,7,6,5]=>[1,7,5,8,6,2,3,4]=>[2,2,1,3]
[2,6,7,4,5,8,3,1]=>[4,2,5,3,8,1,7,6]=>[5,7,4,6,1,8,2,3]=>[2,2,2,2]
[6,1,7,4,5,8,3,2]=>[4,5,3,1,8,7,2,6]=>[5,4,6,8,1,2,7,3]=>[1,3,3,1]
[5,3,7,4,8,6,2,1]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[1,3,1,3]
[5,4,3,6,8,2,7,1]=>[3,2,1,4,6,8,7,5]=>[6,7,8,5,3,1,2,4]=>[3,1,1,3]
[6,5,3,7,4,8,2,1]=>[5,3,2,1,4,8,7,6]=>[4,6,7,8,5,1,2,3]=>[4,1,3]
[2,7,8,4,5,1,6,3]=>[4,8,6,5,1,2,7,3]=>[5,1,3,4,8,7,2,6]=>[1,4,1,2]
[5,7,3,8,4,1,6,2]=>[1,8,3,6,5,2,7,4]=>[8,1,6,3,4,7,2,5]=>[1,2,3,2]
[5,6,3,8,1,4,7,2]=>[3,1,6,2,8,5,7,4]=>[6,8,3,7,1,4,2,5]=>[2,2,2,2]
[8,4,1,2,5,6,7,3]=>[5,6,2,8,3,4,7,1]=>[4,3,7,1,6,5,2,8]=>[1,2,2,1,2]
[3,7,8,4,1,6,5,2]=>[4,8,7,1,5,2,6,3]=>[5,1,2,8,4,7,3,6]=>[1,3,2,2]
[6,8,3,1,2,5,7,4]=>[6,3,8,4,1,5,7,2]=>[3,6,1,5,8,4,2,7]=>[2,3,1,2]
[8,7,1,4,5,2,6,3]=>[4,8,6,3,5,7,2,1]=>[5,1,3,6,4,2,7,8]=>[1,3,1,3]
[7,5,1,8,2,6,3,4]=>[7,8,5,2,6,3,1,4]=>[2,1,4,7,3,6,8,5]=>[1,3,3,1]
[8,7,3,1,5,4,2,6]=>[3,7,6,4,5,8,2,1]=>[6,2,3,5,4,1,7,8]=>[1,3,1,3]
[3,6,2,1,5,4,8,7]=>[1,3,5,8,4,2,6,7]=>[8,6,4,1,5,7,3,2]=>[1,1,1,3,1,1]
[5,4,2,6,1,3,8,7]=>[8,3,2,1,5,4,6,7]=>[1,6,7,8,4,5,3,2]=>[4,2,1,1]
[3,2,6,5,1,4,8,7]=>[8,1,5,2,4,3,6,7]=>[1,8,4,7,5,6,3,2]=>[2,2,2,1,1]
[2,5,8,1,7,4,3,6]=>[2,7,6,8,1,4,5,3]=>[7,2,3,1,8,5,4,6]=>[1,2,2,1,2]
[6,8,2,7,4,3,1,5]=>[7,6,3,1,5,8,4,2]=>[2,3,6,8,4,1,5,7]=>[4,1,3]
[6,8,2,3,7,5,1,4]=>[7,8,3,1,4,6,5,2]=>[2,1,6,8,5,3,4,7]=>[1,3,1,3]
[7,6,2,5,4,8,1,3]=>[7,5,3,4,2,1,8,6]=>[2,4,6,5,7,8,1,3]=>[3,3,2]
[2,6,5,1,8,4,3,7]=>[7,6,3,1,2,8,4,5]=>[2,3,6,8,7,1,5,4]=>[4,1,2,1]
[4,2,7,3,1,8,5,6]=>[4,1,7,8,2,5,3,6]=>[5,8,2,1,7,4,6,3]=>[2,1,2,2,1]
[5,2,7,3,8,6,1,4]=>[7,1,8,4,2,3,6,5]=>[2,8,1,5,7,6,3,4]=>[2,3,1,2]
[2,1,5,8,4,3,7,6]=>[3,5,8,1,6,7,2,4]=>[6,4,1,8,3,2,7,5]=>[1,1,2,1,2,1]
[5,8,4,2,6,7,1,3]=>[1,7,4,3,5,8,6,2]=>[8,2,5,6,4,1,3,7]=>[1,3,1,3]
[3,2,4,8,1,5,7,6]=>[1,8,2,3,5,6,7,4]=>[8,1,7,6,4,3,2,5]=>[1,2,1,1,1,2]
[2,4,8,3,1,7,5,6]=>[2,4,7,8,1,5,6,3]=>[7,5,2,1,8,4,3,6]=>[1,1,1,2,1,2]
[4,8,3,2,1,7,6,5]=>[1,3,8,4,7,5,6,2]=>[8,6,1,5,2,4,3,7]=>[1,1,2,2,2]
[4,1,3,7,2,6,8,5]=>[6,1,8,3,5,2,4,7]=>[3,8,1,6,4,7,5,2]=>[2,2,2,1,1]
[3,4,8,2,1,6,5,7]=>[1,2,4,7,5,6,8,3]=>[8,7,5,2,4,3,1,6]=>[1,1,1,2,1,2]
[6,8,3,7,2,1,5,4]=>[3,5,1,8,6,7,4,2]=>[6,4,8,1,3,2,5,7]=>[1,2,2,3]
[3,5,8,1,7,2,6,4]=>[2,8,1,6,7,4,5,3]=>[7,1,8,3,2,5,4,6]=>[1,2,1,2,2]
[7,6,4,8,1,5,3,2]=>[3,8,7,5,2,1,6,4]=>[6,1,2,4,7,8,3,5]=>[1,5,2]
[5,3,7,1,8,2,6,4]=>[8,2,1,6,7,4,3,5]=>[1,7,8,3,2,5,6,4]=>[3,1,3,1]
[2,7,6,3,8,1,4,5]=>[4,6,7,3,1,2,8,5]=>[5,3,2,6,8,7,1,4]=>[1,1,3,1,2]
[2,1,7,6,4,8,3,5]=>[5,7,4,1,3,8,2,6]=>[4,2,5,8,6,1,7,3]=>[1,3,1,2,1]
[2,1,5,4,8,7,3,6]=>[3,7,8,1,4,6,2,5]=>[6,2,1,8,5,3,7,4]=>[1,1,2,1,2,1]
[5,4,8,7,2,6,1,3]=>[2,1,5,7,8,6,4,3]=>[7,8,4,2,1,3,5,6]=>[2,1,1,4]
[2,4,3,8,7,1,5,6]=>[2,6,7,8,1,3,5,4]=>[7,3,2,1,8,6,4,5]=>[1,1,1,2,1,2]
[3,8,5,4,2,1,7,6]=>[5,4,1,3,8,6,7,2]=>[4,5,8,6,1,3,2,7]=>[3,1,2,2]
[4,8,6,5,2,7,1,3]=>[5,7,1,4,3,8,6,2]=>[4,2,8,5,6,1,3,7]=>[1,2,2,3]
[3,2,8,7,5,4,1,6]=>[7,6,1,5,8,2,4,3]=>[2,3,8,4,1,7,5,6]=>[3,1,2,2]
[2,8,6,5,4,3,1,7]=>[7,6,5,4,1,3,8,2]=>[2,3,4,5,8,6,1,7]=>[5,1,2]
[5,4,2,6,3,1,8,7]=>[5,3,2,1,4,8,6,7]=>[4,6,7,8,5,1,3,2]=>[4,1,2,1]
[6,5,2,1,3,4,8,7]=>[3,8,4,5,2,1,6,7]=>[6,1,5,4,7,8,3,2]=>[1,2,3,1,1]
[7,3,6,5,2,8,4,1]=>[8,5,2,4,3,1,7,6]=>[1,4,7,5,6,8,2,3]=>[3,3,2]
[7,6,2,3,4,8,5,1]=>[8,3,4,5,2,1,7,6]=>[1,6,5,4,7,8,2,3]=>[2,1,3,2]
[7,1,5,3,8,4,6,2]=>[6,3,8,4,7,2,1,5]=>[3,6,1,5,2,7,8,4]=>[2,2,3,1]
[2,1,7,6,4,8,5,3]=>[8,5,4,1,3,7,2,6]=>[1,4,5,8,6,2,7,3]=>[4,1,2,1]
[5,8,3,7,2,1,4,6]=>[3,1,6,5,7,8,4,2]=>[6,8,3,4,2,1,5,7]=>[2,2,1,3]
[3,8,7,4,2,1,5,6]=>[6,5,1,4,7,8,3,2]=>[3,4,8,5,2,1,6,7]=>[3,1,1,3]
[7,8,2,3,5,1,4,6]=>[3,4,6,7,5,1,8,2]=>[6,5,3,2,4,8,1,7]=>[1,1,1,3,2]
[8,1,6,3,2,4,5,7]=>[5,4,6,7,2,3,8,1]=>[4,5,3,2,7,6,1,8]=>[2,1,2,1,2]
[5,7,1,4,8,3,6,2]=>[4,1,6,8,7,3,2,5]=>[5,8,3,1,2,6,7,4]=>[2,1,4,1]
[6,1,7,5,4,8,3,2]=>[5,4,3,1,8,7,2,6]=>[4,5,6,8,1,2,7,3]=>[4,3,1]
[6,3,7,5,8,4,2,1]=>[4,3,1,8,2,7,6,5]=>[5,6,8,1,7,2,3,4]=>[3,2,3]
[7,6,1,5,8,3,4,2]=>[6,4,8,7,3,2,1,5]=>[3,5,1,2,6,7,8,4]=>[2,5,1]
[8,6,7,5,1,3,2,4]=>[7,5,6,2,8,4,3,1]=>[2,4,3,7,1,5,6,8]=>[2,2,4]
[5,4,2,6,8,3,7,1]=>[4,2,1,6,8,3,7,5]=>[5,7,8,3,1,6,2,4]=>[3,1,2,2]
[6,5,2,8,1,4,3,7]=>[7,3,5,2,1,6,8,4]=>[2,6,4,7,8,3,1,5]=>[2,3,1,2]
[7,4,2,8,1,3,6,5]=>[8,3,2,5,6,1,7,4]=>[1,6,7,4,3,8,2,5]=>[3,1,2,2]
[2,7,8,4,5,1,3,6]=>[6,4,7,5,1,2,8,3]=>[3,5,2,4,8,7,1,6]=>[2,3,1,2]
[5,7,3,8,4,1,2,6]=>[3,1,6,7,5,2,8,4]=>[6,8,3,2,4,7,1,5]=>[2,1,3,2]
[2,4,8,1,5,6,3,7]=>[2,5,7,1,4,6,8,3]=>[7,4,2,8,5,3,1,6]=>[1,1,2,1,1,2]
[3,6,8,4,1,2,7,5]=>[8,5,1,4,2,6,7,3]=>[1,4,8,5,7,3,2,6]=>[3,2,1,2]
[4,8,1,2,5,3,6,7]=>[6,3,1,4,5,7,8,2]=>[3,6,8,5,4,2,1,7]=>[3,1,1,1,2]
[8,1,2,4,3,5,6,7]=>[5,2,3,4,6,7,8,1]=>[4,7,6,5,3,2,1,8]=>[2,1,1,1,1,2]
[2,3,4,6,5,7,8,9,10,1]=>[5,1,2,3,4,6,7,8,10,9]=>[6,10,9,8,7,5,4,3,1,2]=>[2,1,1,1,1,1,1,2]
[2,3,6,4,5,7,8,9,1]=>[4,5,1,2,3,6,7,9,8]=>[6,5,9,8,7,4,3,1,2]=>[1,2,1,1,1,1,2]
[10,1,2,3,5,4,6,7,8,9]=>[6,2,3,4,5,7,8,9,10,1]=>[5,9,8,7,6,4,3,2,1,10]=>[2,1,1,1,1,1,1,2]
[5,8,7,4,6,3,2,1]=>[4,8,1,7,6,5,3,2]=>[5,1,8,2,3,4,6,7]=>[1,2,5]
[4,8,7,6,3,5,2,1]=>[5,8,7,1,6,4,3,2]=>[4,1,2,8,3,5,6,7]=>[1,3,4]
[3,8,7,6,5,2,4,1]=>[6,8,7,5,1,4,3,2]=>[3,1,2,4,8,5,6,7]=>[1,4,3]
[7,9,6,8,5,4,3,2,1]=>[1,3,9,8,7,6,5,4,2]=>[9,7,1,2,3,4,5,6,8]=>[1,1,7]
[5,8,4,7,6,3,2,1]=>[8,1,3,7,6,5,4,2]=>[1,8,6,2,3,4,5,7]=>[2,1,5]
[6,8,5,4,7,3,2,1]=>[1,4,3,8,7,6,5,2]=>[8,5,6,1,2,3,4,7]=>[1,2,5]
[3,8,7,6,2,5,4,1]=>[8,5,7,6,1,4,3,2]=>[1,4,2,3,8,5,6,7]=>[2,3,3]
[4,9,8,7,6,3,5,2,1]=>[6,9,8,7,1,5,4,3,2]=>[4,1,2,3,9,5,6,7,8]=>[1,4,4]
[4,8,7,6,3,2,5,1]=>[6,5,8,1,7,4,3,2]=>[3,4,1,8,2,5,6,7]=>[2,2,4]
[3,8,7,6,5,2,1,4]=>[7,6,8,5,1,4,3,2]=>[2,3,1,4,8,5,6,7]=>[2,3,3]
[7,5,8,4,6,3,1,2]=>[2,7,4,1,8,6,5,3]=>[7,2,5,8,1,3,4,6]=>[1,3,4]
[9,8,10,6,7,4,5,2,3,1]=>[8,6,4,2,1,10,9,7,5,3]=>[3,5,7,9,10,1,2,4,6,8]=>[5,5]
[3,5,2,4,7,6,1,8]=>[7,1,3,2,4,6,5,8]=>[2,8,6,7,5,3,4,1]=>[2,2,1,2,1]
[3,5,4,7,2,6,1,8]=>[3,1,2,5,7,6,4,8]=>[6,8,7,4,2,3,5,1]=>[2,1,1,3,1]
[3,5,4,7,6,1,8,2]=>[2,8,1,3,6,5,4,7]=>[7,1,8,6,3,4,5,2]=>[1,2,1,3,1]
[3,5,7,4,6,1,8,2]=>[2,4,8,1,6,5,3,7]=>[7,5,1,8,3,4,6,2]=>[1,1,2,3,1]
[3,5,7,4,6,1,2,8]=>[2,6,1,4,7,5,3,8]=>[7,3,8,5,2,4,6,1]=>[1,2,1,3,1]
[3,5,7,4,6,2,1,8]=>[2,4,7,1,6,5,3,8]=>[7,5,2,8,3,4,6,1]=>[1,1,2,3,1]
[3,2,5,7,4,6,1,8]=>[1,3,5,7,2,6,4,8]=>[8,6,4,2,7,3,5,1]=>[1,1,1,2,2,1]
[3,5,2,7,6,4,1,8]=>[2,7,1,6,3,5,4,8]=>[7,2,8,3,6,4,5,1]=>[1,2,2,2,1]
[3,5,7,2,6,4,1,8]=>[2,7,1,4,6,5,3,8]=>[7,2,8,5,3,4,6,1]=>[1,2,1,3,1]
[5,3,7,6,2,4,1,8]=>[5,1,7,2,6,4,3,8]=>[4,8,2,7,3,5,6,1]=>[2,2,3,1]
[5,3,7,6,1,2,8,4]=>[8,2,1,5,6,4,3,7]=>[1,7,8,4,3,5,6,2]=>[3,1,3,1]
[5,3,7,6,1,4,2,8]=>[7,2,1,5,6,4,3,8]=>[2,7,8,4,3,5,6,1]=>[3,1,3,1]
[5,3,7,6,4,1,2,8]=>[6,1,7,2,5,4,3,8]=>[3,8,2,7,4,5,6,1]=>[2,2,3,1]
[3,5,7,2,6,1,4,8]=>[4,1,2,6,7,5,3,8]=>[5,8,7,3,2,4,6,1]=>[2,1,1,3,1]
[3,5,2,7,6,1,4,8]=>[6,1,2,7,3,5,4,8]=>[3,8,7,2,6,4,5,1]=>[2,1,2,2,1]
[5,3,7,6,4,1,8,2]=>[1,8,6,2,5,4,3,7]=>[8,1,3,7,4,5,6,2]=>[1,3,3,1]
[3,7,5,4,1,8,2,6]=>[7,4,1,3,8,5,2,6]=>[2,5,8,6,1,4,7,3]=>[3,1,3,1]
[3,7,5,4,1,8,6,2]=>[4,3,8,1,7,5,2,6]=>[5,6,1,8,2,4,7,3]=>[2,2,3,1]
[3,7,5,1,4,8,6,2]=>[8,5,1,3,7,4,2,6]=>[1,4,8,6,2,5,7,3]=>[3,1,3,1]
[3,7,5,1,4,8,2,6]=>[5,7,1,3,8,4,2,6]=>[4,2,8,6,1,5,7,3]=>[1,2,1,3,1]
[3,5,7,1,2,6,8,4]=>[6,1,2,8,4,5,3,7]=>[3,8,7,1,5,4,6,2]=>[2,1,2,2,1]
[3,5,7,2,1,6,8,4]=>[4,1,2,6,8,5,3,7]=>[5,8,7,3,1,4,6,2]=>[2,1,1,3,1]
[3,5,2,7,1,6,4,8]=>[7,1,3,2,5,6,4,8]=>[2,8,6,7,4,3,5,1]=>[2,2,1,2,1]
[3,5,7,2,1,6,4,8]=>[4,1,2,7,5,6,3,8]=>[5,8,7,2,4,3,6,1]=>[2,1,2,2,1]
[5,3,7,1,6,2,4,8]=>[2,6,1,7,4,5,3,8]=>[7,3,8,2,5,4,6,1]=>[1,2,2,2,1]
[3,5,7,1,4,6,8,2]=>[5,1,2,6,8,4,3,7]=>[4,8,7,3,1,5,6,2]=>[2,1,1,3,1]
[3,5,7,1,4,2,6,8]=>[6,1,4,2,5,7,3,8]=>[3,8,5,7,4,2,6,1]=>[2,2,1,2,1]
[3,5,2,7,1,4,6,8]=>[1,3,5,2,6,7,4,8]=>[8,6,4,7,3,2,5,1]=>[1,1,2,1,2,1]
[3,2,5,7,4,1,6,8]=>[1,3,6,2,5,7,4,8]=>[8,6,3,7,4,2,5,1]=>[1,1,2,1,2,1]
[3,5,7,4,2,1,6,8]=>[2,6,1,5,4,7,3,8]=>[7,3,8,4,5,2,6,1]=>[1,2,2,2,1]
[3,5,7,4,1,2,6,8]=>[5,1,2,6,4,7,3,8]=>[4,8,7,3,5,2,6,1]=>[2,1,2,2,1]
[3,5,4,7,1,6,8,2]=>[3,1,2,6,8,5,4,7]=>[6,8,7,3,1,4,5,2]=>[2,1,1,3,1]
[3,5,4,7,1,2,6,8]=>[5,1,3,2,6,7,4,8]=>[4,8,6,7,3,2,5,1]=>[2,2,1,2,1]
[3,5,4,7,2,1,6,8]=>[3,1,2,6,5,7,4,8]=>[6,8,7,3,4,2,5,1]=>[2,1,2,2,1]
[3,5,4,2,7,1,6,8]=>[4,1,3,2,6,7,5,8]=>[5,8,6,7,3,2,4,1]=>[2,2,1,2,1]
[3,2,5,4,7,1,6,8]=>[1,4,2,3,6,7,5,8]=>[8,5,7,6,3,2,4,1]=>[1,2,1,1,2,1]
[3,5,4,7,2,1,8,6]=>[3,1,2,5,8,6,4,7]=>[6,8,7,4,1,3,5,2]=>[2,1,1,3,1]
[3,5,4,7,1,2,8,6]=>[3,1,2,8,5,6,4,7]=>[6,8,7,1,4,3,5,2]=>[2,1,2,2,1]
[5,7,6,3,1,8,4,2]=>[1,4,8,7,5,3,2,6]=>[8,5,1,2,4,6,7,3]=>[1,1,5,1]
[5,7,6,3,1,8,2,4]=>[1,7,4,8,5,3,2,6]=>[8,2,5,1,4,6,7,3]=>[1,2,4,1]
[3,5,7,4,1,2,8,6]=>[2,8,1,5,4,6,3,7]=>[7,1,8,4,5,3,6,2]=>[1,2,2,2,1]
[3,5,2,7,1,4,8,6]=>[8,1,3,2,5,6,4,7]=>[1,8,6,7,4,3,5,2]=>[2,2,1,2,1]
[3,5,7,2,1,4,8,6]=>[4,1,2,8,5,6,3,7]=>[5,8,7,1,4,3,6,2]=>[2,1,2,2,1]
[3,5,7,1,4,2,8,6]=>[5,1,2,8,4,6,3,7]=>[4,8,7,1,5,3,6,2]=>[2,1,2,2,1]
[3,7,5,2,1,8,6,4]=>[8,4,1,3,7,5,2,6]=>[1,5,8,6,2,4,7,3]=>[3,1,3,1]
[3,7,2,5,1,8,6,4]=>[4,8,1,3,7,5,2,6]=>[5,1,8,6,2,4,7,3]=>[1,2,1,3,1]
[3,2,7,5,1,8,6,4]=>[4,8,1,7,2,5,3,6]=>[5,1,8,2,7,4,6,3]=>[1,2,2,2,1]
[3,2,7,5,1,8,4,6]=>[7,1,4,8,2,5,3,6]=>[2,8,5,1,7,4,6,3]=>[2,1,2,2,1]
[3,7,2,5,1,8,4,6]=>[7,1,3,4,8,5,2,6]=>[2,8,6,5,1,4,7,3]=>[2,1,1,3,1]
[3,7,5,2,1,8,4,6]=>[4,7,1,3,8,5,2,6]=>[5,2,8,6,1,4,7,3]=>[1,2,1,3,1]
[6,1,2,5,7,4,8,3]=>[4,6,5,8,2,1,3,7]=>[5,3,4,1,7,8,6,2]=>[1,2,3,1,1]
[6,3,2,7,4,1,8,5]=>[2,5,8,3,1,6,4,7]=>[7,4,1,6,8,3,5,2]=>[1,1,3,2,1]
[2,1,7,5,8,4,6,3]=>[4,6,3,8,1,7,2,5]=>[5,3,6,1,8,2,7,4]=>[1,2,2,2,1]
[2,7,3,6,8,4,1,5]=>[7,6,3,4,1,2,8,5]=>[2,3,6,5,8,7,1,4]=>[3,2,1,2]
[2,1,8,3,4,7,5,6]=>[7,8,1,4,5,6,2,3]=>[2,1,8,5,4,3,7,6]=>[1,2,1,1,2,1]
[5,1,7,2,4,8,3,6]=>[5,7,1,8,4,2,3,6]=>[4,2,8,1,5,7,6,3]=>[1,2,3,1,1]
[3,4,2,6,7,1,8,5]=>[1,2,4,8,3,6,5,7]=>[8,7,5,1,6,3,4,2]=>[1,1,1,2,2,1]
[3,5,8,7,2,1,6,4]=>[2,5,8,1,6,7,4,3]=>[7,4,1,8,3,2,5,6]=>[1,1,2,1,3]
[1,3,4,5,6,7,9,2,8]=>[2,3,4,5,6,8,9,1,7]=>[8,7,6,5,4,2,1,9,3]=>[1,1,1,1,1,1,2,1]
[2,3,4,5,6,7,1,9,8]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,2,1]
[2,1,4,5,6,7,8,9,3]=>[1,3,4,5,6,7,9,2,8]=>[9,7,6,5,4,3,1,8,2]=>[1,1,1,1,1,1,2,1]
[5,8,3,4,1,7,6,2]=>[3,1,4,8,7,5,6,2]=>[6,8,5,1,2,4,3,7]=>[2,1,3,2]
[5,8,7,2,4,1,6,3]=>[1,8,4,6,5,7,3,2]=>[8,1,5,3,4,2,6,7]=>[1,2,2,3]
[3,8,6,4,1,7,5,2]=>[4,8,7,1,5,3,6,2]=>[5,1,2,8,4,6,3,7]=>[1,3,2,2]
[4,3,5,6,8,1,7,2]=>[2,1,3,4,8,6,7,5]=>[7,8,6,5,1,3,2,4]=>[2,1,1,2,2]
[3,7,6,4,1,8,5,2]=>[4,8,7,1,5,3,2,6]=>[5,1,2,8,4,6,7,3]=>[1,3,3,1]
[3,7,4,1,8,6,5,2]=>[8,3,7,1,6,4,2,5]=>[1,6,2,8,3,5,7,4]=>[2,2,3,1]
[3,8,4,1,7,6,5,2]=>[8,3,7,1,6,4,5,2]=>[1,6,2,8,3,5,4,7]=>[2,2,2,2]
[3,2,7,6,1,5,4,8]=>[7,1,5,6,2,4,3,8]=>[2,8,4,3,7,5,6,1]=>[2,1,2,2,1]
[3,2,8,7,6,1,5,4]=>[8,6,7,1,5,2,4,3]=>[1,3,2,8,4,7,5,6]=>[2,2,2,2]
[5,7,8,2,4,1,6,3]=>[1,8,4,6,5,2,7,3]=>[8,1,5,3,4,7,2,6]=>[1,2,3,2]
[4,2,5,8,1,6,7,3]=>[3,1,6,8,2,5,7,4]=>[6,8,3,1,7,4,2,5]=>[2,1,2,1,2]
[4,2,5,8,1,7,3,6]=>[3,1,7,8,2,5,6,4]=>[6,8,2,1,7,4,3,5]=>[2,1,2,1,2]
[5,8,2,4,1,6,3,7]=>[7,3,1,5,4,6,8,2]=>[2,6,8,4,5,3,1,7]=>[3,2,1,2]
[3,2,6,8,1,5,4,7]=>[7,1,5,2,3,6,8,4]=>[2,8,4,7,6,3,1,5]=>[2,2,1,1,2]
[8,3,2,5,6,1,4,7]=>[2,6,3,4,7,5,8,1]=>[7,3,6,5,2,4,1,8]=>[1,2,1,2,2]
[3,2,8,6,7,1,5,4]=>[8,6,1,4,7,2,5,3]=>[1,3,8,5,2,7,4,6]=>[3,1,2,2]
[3,2,6,8,7,1,5,4]=>[3,8,1,6,7,2,5,4]=>[6,1,8,3,2,7,4,5]=>[1,2,1,2,2]
[3,2,6,7,1,5,4,8]=>[7,1,5,2,3,6,4,8]=>[2,8,4,7,6,3,5,1]=>[2,2,1,2,1]
[7,2,8,1,5,3,6,4]=>[8,6,2,4,5,1,7,3]=>[1,3,7,5,4,8,2,6]=>[3,1,2,2]
[7,4,2,8,5,1,3,6]=>[6,2,7,3,5,1,8,4]=>[3,7,2,6,4,8,1,5]=>[2,2,2,2]
[7,2,4,1,8,3,6,5]=>[3,8,2,6,7,4,1,5]=>[6,1,7,3,2,5,8,4]=>[1,2,1,3,1]
[2,6,5,7,1,8,3,4]=>[7,3,2,8,1,5,4,6]=>[2,6,7,1,8,4,5,3]=>[3,2,2,1]
[2,5,1,8,7,4,3,6]=>[2,7,6,8,1,5,3,4]=>[7,2,3,1,8,4,6,5]=>[1,2,2,2,1]
[8,3,5,4,1,6,2,7]=>[7,2,5,4,3,6,8,1]=>[2,7,4,5,6,3,1,8]=>[2,3,1,2]
[8,6,3,4,1,5,2,7]=>[3,7,5,4,6,2,8,1]=>[6,2,4,5,3,7,1,8]=>[1,3,2,2]
[5,4,7,6,8,2,3,1]=>[1,6,2,4,3,8,7,5]=>[8,3,7,5,6,1,2,4]=>[1,2,2,3]
[4,1,8,2,3,7,6,5]=>[1,8,7,4,5,6,2,3]=>[8,1,2,5,4,3,7,6]=>[1,3,1,2,1]
[2,1,8,5,3,4,7,6]=>[8,5,1,4,6,7,2,3]=>[1,4,8,5,3,2,7,6]=>[3,1,1,2,1]
[5,2,4,6,8,7,3,1]=>[8,3,1,4,7,2,6,5]=>[1,6,8,5,2,7,3,4]=>[3,1,2,2]
[5,7,4,8,6,1,3,2]=>[1,3,8,6,2,7,5,4]=>[8,6,1,3,7,2,4,5]=>[1,1,3,3]
[5,4,2,6,7,8,1,3]=>[4,2,1,7,3,5,8,6]=>[5,7,8,2,6,4,1,3]=>[3,2,1,2]
[7,4,1,8,3,5,6,2]=>[5,2,6,8,7,3,1,4]=>[4,7,3,1,2,6,8,5]=>[2,1,4,1]
[6,5,4,8,7,3,1,2]=>[3,2,1,7,8,6,5,4]=>[6,7,8,2,1,3,4,5]=>[3,1,4]
[8,7,1,3,2,5,6,4]=>[4,6,8,3,5,7,2,1]=>[5,3,1,6,4,2,7,8]=>[1,1,2,1,3]
[6,8,2,3,1,7,5,4]=>[8,3,4,1,7,5,6,2]=>[1,6,5,8,2,4,3,7]=>[2,2,2,2]
[7,4,3,2,6,8,5,1]=>[3,2,5,8,4,1,7,6]=>[6,7,4,1,5,8,2,3]=>[2,1,3,2]
[2,7,4,3,8,5,6,1]=>[3,6,8,4,1,2,7,5]=>[6,3,1,5,8,7,2,4]=>[1,1,3,1,2]
[8,3,7,2,1,5,6,4]=>[2,4,6,8,5,7,3,1]=>[7,5,3,1,4,2,6,8]=>[1,1,1,2,3]
[5,7,8,2,4,3,1,6]=>[1,7,4,6,5,2,8,3]=>[8,2,5,3,4,7,1,6]=>[1,2,3,2]
[8,4,7,3,2,6,1,5]=>[2,5,4,7,8,6,3,1]=>[7,4,5,2,1,3,6,8]=>[1,2,1,4]
[3,2,5,7,4,8,1,6]=>[1,3,5,7,2,4,8,6]=>[8,6,4,2,7,5,1,3]=>[1,1,1,2,1,2]
[8,2,7,3,4,1,5,6]=>[4,6,2,5,7,8,3,1]=>[5,3,7,4,2,1,6,8]=>[1,2,1,1,3]
[7,1,6,3,5,8,2,4]=>[7,4,5,3,8,2,1,6]=>[2,5,4,6,1,7,8,3]=>[2,2,3,1]
[2,8,5,6,7,1,4,3]=>[3,8,6,4,7,1,5,2]=>[6,1,3,5,2,8,4,7]=>[1,3,2,2]
[1,5,2,7,8,6,4,3]=>[2,4,8,7,6,1,3,5]=>[7,5,1,2,3,8,6,4]=>[1,1,4,1,1]
[2,6,8,5,1,4,7,3]=>[6,2,8,5,1,4,7,3]=>[3,7,1,4,8,5,2,6]=>[2,3,1,2]
[1,4,2,8,6,5,7,3]=>[6,2,5,8,7,1,3,4]=>[3,7,4,1,2,8,6,5]=>[2,1,3,1,1]
[3,5,1,6,8,7,2,4]=>[4,1,2,7,8,6,3,5]=>[5,8,7,2,1,3,6,4]=>[2,1,1,3,1]
[5,7,6,2,1,3,8,4]=>[4,1,8,5,6,3,2,7]=>[5,8,1,4,3,6,7,2]=>[2,2,3,1]
[2,5,8,7,4,1,6,3]=>[8,2,6,5,7,1,4,3]=>[1,7,3,4,2,8,5,6]=>[2,2,2,2]
[4,1,7,5,2,6,8,3]=>[1,6,4,8,5,2,3,7]=>[8,3,5,1,4,7,6,2]=>[1,2,3,1,1]
[7,6,2,4,5,1,8,3]=>[4,8,3,6,5,2,1,7]=>[5,1,6,3,4,7,8,2]=>[1,2,4,1]
[7,3,4,2,5,8,6,1]=>[2,3,8,4,5,1,7,6]=>[7,6,1,5,4,8,2,3]=>[1,1,2,2,2]
[8,7,4,2,5,1,6,3]=>[8,4,3,6,5,7,2,1]=>[1,5,6,3,4,2,7,8]=>[3,2,3]
[8,1,4,5,2,6,7,3]=>[3,6,4,8,2,5,7,1]=>[6,3,5,1,7,4,2,8]=>[1,2,2,1,2]
[5,2,4,8,6,7,1,3]=>[7,3,1,5,8,2,6,4]=>[2,6,8,4,1,7,3,5]=>[3,1,2,2]
[8,5,6,2,1,3,7,4]=>[4,8,5,2,6,3,7,1]=>[5,1,4,7,3,6,2,8]=>[1,3,2,2]
[4,2,1,5,6,7,8,3]=>[2,4,1,5,6,8,3,7]=>[7,5,8,4,3,1,6,2]=>[1,2,1,1,2,1]
[3,4,6,5,1,7,8,2]=>[6,1,2,4,3,8,5,7]=>[3,8,7,5,6,1,4,2]=>[2,1,2,2,1]
[7,3,5,2,4,6,1,8]=>[2,4,5,3,7,6,1,8]=>[7,5,4,6,2,3,8,1]=>[1,1,2,3,1]
[5,3,7,2,4,6,1,8]=>[2,4,1,5,7,6,3,8]=>[7,5,8,4,2,3,6,1]=>[1,2,1,3,1]
[3,7,5,2,4,6,1,8]=>[4,5,1,3,7,6,2,8]=>[5,4,8,6,2,3,7,1]=>[1,2,1,3,1]
[1,5,3,2,4,7,6,8]=>[3,7,4,1,2,5,6,8]=>[6,2,5,8,7,4,3,1]=>[1,3,1,1,1,1]
[1,5,3,2,7,4,6,8]=>[3,6,2,7,1,4,5,8]=>[6,3,7,2,8,5,4,1]=>[1,2,2,1,1,1]
[5,7,3,2,4,1,6,8]=>[4,3,1,6,5,7,2,8]=>[5,6,8,3,4,2,7,1]=>[3,2,2,1]
[3,7,2,5,4,1,6,8]=>[6,1,3,5,4,7,2,8]=>[3,8,6,4,5,2,7,1]=>[2,1,2,2,1]
[5,1,3,2,4,7,6,8]=>[3,7,2,4,1,5,6,8]=>[6,2,7,5,8,4,3,1]=>[1,2,2,1,1,1]
[5,1,3,2,7,4,6,8]=>[3,6,7,2,1,4,5,8]=>[6,3,2,7,8,5,4,1]=>[1,1,3,1,1,1]
[7,1,3,2,5,4,6,8]=>[3,6,2,4,5,7,1,8]=>[6,3,7,5,4,2,8,1]=>[1,2,1,1,2,1]
[7,1,3,5,2,4,6,8]=>[3,5,6,2,4,7,1,8]=>[6,4,3,7,5,2,8,1]=>[1,1,2,1,2,1]
[5,1,3,7,2,4,6,8]=>[3,5,6,1,7,2,4,8]=>[6,4,3,8,2,7,5,1]=>[1,1,2,2,1,1]
[3,2,7,5,1,4,6,8]=>[1,5,6,2,4,7,3,8]=>[8,4,3,7,5,2,6,1]=>[1,1,2,1,2,1]
[3,7,5,1,2,4,6,8]=>[1,4,5,6,3,7,2,8]=>[8,5,4,3,6,2,7,1]=>[1,1,1,2,2,1]
[5,7,3,1,2,4,6,8]=>[4,5,3,1,6,7,2,8]=>[5,4,6,8,3,2,7,1]=>[1,3,1,2,1]
[1,5,3,7,2,4,6,8]=>[3,5,2,6,7,1,4,8]=>[6,4,7,3,2,8,5,1]=>[1,2,1,2,1,1]
[5,3,2,4,7,1,6,8]=>[3,2,4,1,6,7,5,8]=>[6,7,5,8,3,2,4,1]=>[2,2,1,2,1]
[5,3,2,1,4,7,6,8]=>[3,2,7,4,1,5,6,8]=>[6,7,2,5,8,4,3,1]=>[2,3,1,1,1]
[5,3,2,1,7,4,6,8]=>[3,2,6,1,7,4,5,8]=>[6,7,3,8,2,5,4,1]=>[2,2,2,1,1]
[1,3,2,7,5,4,6,8]=>[6,2,5,7,1,3,4,8]=>[3,7,4,2,8,6,5,1]=>[2,1,2,1,1,1]
[1,3,7,2,5,4,6,8]=>[6,2,4,5,7,1,3,8]=>[3,7,5,4,2,8,6,1]=>[2,1,1,2,1,1]
[7,3,1,2,5,4,6,8]=>[6,3,2,4,5,7,1,8]=>[3,6,7,5,4,2,8,1]=>[3,1,1,2,1]
[5,3,1,2,7,4,6,8]=>[6,2,7,3,1,4,5,8]=>[3,7,2,6,8,5,4,1]=>[2,3,1,1,1]
[5,3,1,2,4,7,6,8]=>[7,3,2,4,1,5,6,8]=>[2,6,7,5,8,4,3,1]=>[3,2,1,1,1]
[3,2,5,1,4,7,6,8]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[1,2,2,1,1,1]
[7,3,1,5,2,4,6,8]=>[5,2,6,3,4,7,1,8]=>[4,7,3,6,5,2,8,1]=>[2,2,1,2,1]
[1,3,7,5,2,4,6,8]=>[5,6,2,4,7,1,3,8]=>[4,3,7,5,2,8,6,1]=>[1,2,1,2,1,1]
[7,5,1,3,2,4,6,8]=>[5,3,4,6,2,7,1,8]=>[4,6,5,3,7,2,8,1]=>[2,1,2,2,1]
[5,7,1,3,2,4,6,8]=>[5,3,4,1,6,7,2,8]=>[4,6,5,8,3,2,7,1]=>[2,2,1,2,1]
[3,7,1,5,2,4,6,8]=>[1,5,6,3,4,7,2,8]=>[8,4,3,6,5,2,7,1]=>[1,1,2,1,2,1]
[3,7,1,2,5,4,6,8]=>[1,6,3,4,5,7,2,8]=>[8,3,6,5,4,2,7,1]=>[1,2,1,1,2,1]
[3,7,2,1,5,4,6,8]=>[1,3,6,4,5,7,2,8]=>[8,6,3,5,4,2,7,1]=>[1,1,2,1,2,1]
[3,2,1,7,5,4,6,8]=>[1,6,2,5,7,3,4,8]=>[8,3,7,4,2,6,5,1]=>[1,2,1,2,1,1]
[3,1,2,7,5,4,6,8]=>[1,6,5,7,2,3,4,8]=>[8,3,4,2,7,6,5,1]=>[1,2,2,1,1,1]
[3,1,7,2,5,4,6,8]=>[1,6,4,5,7,2,3,8]=>[8,3,5,4,2,7,6,1]=>[1,2,1,2,1,1]
[3,1,7,5,2,4,6,8]=>[1,5,6,4,7,2,3,8]=>[8,4,3,5,2,7,6,1]=>[1,1,2,2,1,1]
[7,1,5,3,2,4,6,8]=>[5,4,6,2,3,7,1,8]=>[4,5,3,7,6,2,8,1]=>[2,2,1,2,1]
[1,7,5,3,2,4,6,8]=>[5,4,6,3,7,1,2,8]=>[4,5,3,6,2,8,7,1]=>[2,2,2,1,1]
[1,3,9,2,4,5,6,7,8]=>[2,4,5,6,7,8,9,1,3]=>[8,6,5,4,3,2,1,9,7]=>[1,1,1,1,1,1,2,1]
[1,9,2,8,7,6,5,4,3]=>[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,7,6,9,8]=>[6,2,1]
[1,10,9,8,7,6,5,2,4,3]=>[10,8,9,7,6,5,4,3,1,2]=>[1,3,2,4,5,6,7,8,10,9]=>[2,7,1]
[1,8,7,4,2,6,5,3]=>[4,8,7,5,6,3,1,2]=>[5,1,2,4,3,6,8,7]=>[1,3,3,1]
[2,8,5,1,7,6,4,3]=>[3,8,7,6,1,4,5,2]=>[6,1,2,3,8,5,4,7]=>[1,4,1,2]
[6,8,5,1,2,7,4,3]=>[8,7,4,1,5,3,6,2]=>[1,2,5,8,4,6,3,7]=>[4,2,2]
[8,1,2,9,7,6,5,4,3]=>[9,8,7,6,5,2,3,1,4]=>[1,2,3,4,5,8,7,9,6]=>[6,2,1]
[2,8,1,4,7,6,5,3]=>[8,7,4,6,1,3,5,2]=>[1,2,5,3,8,6,4,7]=>[3,2,1,2]
[1,7,2,9,8,6,5,4,3]=>[2,9,8,7,6,5,1,3,4]=>[8,1,2,3,4,5,9,7,6]=>[1,6,1,1]
[1,8,5,4,2,7,6,3]=>[4,3,8,7,5,6,1,2]=>[5,6,1,2,4,3,8,7]=>[2,3,2,1]
[8,7,1,2,9,6,5,4,3]=>[9,8,7,6,3,4,2,1,5]=>[1,2,3,4,7,6,8,9,5]=>[5,3,1]
[1,2,11,10,9,8,7,6,5,4,3]=>[11,10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,11,10,9]=>[9,1,1]
[7,5,3,4,2,8,1,6]=>[3,5,4,2,7,1,8,6]=>[6,4,5,7,2,8,1,3]=>[1,3,2,2]
[8,5,3,6,2,4,7,1]=>[3,5,2,6,4,8,7,1]=>[6,4,7,3,5,1,2,8]=>[1,2,2,3]
[8,5,6,3,7,4,2,1]=>[2,8,4,3,7,6,5,1]=>[7,1,5,6,2,3,4,8]=>[1,3,4]
[8,5,6,2,7,4,3,1]=>[2,8,7,4,3,6,5,1]=>[7,1,2,5,6,3,4,8]=>[1,4,3]
[8,7,6,3,4,1,5,2]=>[4,8,6,5,7,3,2,1]=>[5,1,3,4,2,6,7,8]=>[1,3,4]
[1,7,2,3,6,8,5,4]=>[5,8,7,3,4,1,2,6]=>[4,1,2,6,5,8,7,3]=>[1,3,2,1,1]
[3,5,6,4,8,2,7,1]=>[2,4,1,3,6,8,7,5]=>[7,5,8,6,3,1,2,4]=>[1,2,1,1,3]
[3,5,1,4,8,2,7,6]=>[8,1,4,2,6,7,3,5]=>[1,8,5,7,3,2,6,4]=>[2,2,1,2,1]
[1,7,5,4,8,2,6,3]=>[4,3,8,6,2,7,1,5]=>[5,6,1,3,7,2,8,4]=>[2,3,2,1]
[3,7,5,1,6,4,8,2]=>[6,5,1,3,8,4,2,7]=>[3,4,8,6,1,5,7,2]=>[3,1,3,1]
[2,7,5,4,8,1,3,6]=>[6,4,3,7,1,2,8,5]=>[3,5,6,2,8,7,1,4]=>[3,2,1,2]
[2,7,5,4,8,6,1,3]=>[4,3,7,2,8,1,6,5]=>[5,6,2,7,1,8,3,4]=>[2,2,2,2]
[1,7,5,4,8,6,3,2]=>[3,8,4,2,7,6,1,5]=>[6,1,5,7,2,3,8,4]=>[1,3,3,1]
[2,5,1,4,8,7,3,6]=>[7,2,8,1,4,6,3,5]=>[2,7,1,8,5,3,6,4]=>[2,2,1,2,1]
[3,6,4,2,8,7,1,5]=>[3,7,1,2,8,4,6,5]=>[6,2,8,7,1,5,3,4]=>[1,2,1,2,2]
[3,5,2,4,8,1,6,7]=>[1,3,4,2,6,7,8,5]=>[8,6,5,7,3,2,1,4]=>[1,1,2,1,1,2]
[3,5,6,4,8,1,2,7]=>[2,6,1,4,3,7,8,5]=>[7,3,8,5,6,2,1,4]=>[1,2,2,1,2]
[1,5,6,4,8,7,2,3]=>[2,4,3,7,8,6,1,5]=>[7,5,6,2,1,3,8,4]=>[1,2,1,3,1]
[3,6,4,1,8,7,2,5]=>[3,7,1,2,8,6,4,5]=>[6,2,8,7,1,3,5,4]=>[1,2,1,3,1]
[3,6,4,5,8,7,2,1]=>[8,3,1,2,4,7,6,5]=>[1,6,8,7,5,2,3,4]=>[3,1,1,3]
[1,6,4,3,8,5,2,7]=>[3,7,4,2,6,8,1,5]=>[6,2,5,7,3,1,8,4]=>[1,3,1,2,1]
[7,1,3,4,5,8,2,6]=>[3,4,5,7,8,2,1,6]=>[6,5,4,2,1,7,8,3]=>[1,1,1,1,3,1]
[7,6,1,4,5,3,8,2]=>[4,6,5,8,3,2,1,7]=>[5,3,4,1,6,7,8,2]=>[1,2,4,1]
[7,6,1,3,5,4,8,2]=>[6,4,5,8,3,2,1,7]=>[3,5,4,1,6,7,8,2]=>[2,1,4,1]
[7,1,3,2,5,8,4,6]=>[3,5,7,8,2,4,1,6]=>[6,4,2,1,7,5,8,3]=>[1,1,1,2,2,1]
[1,6,4,2,8,5,3,7]=>[3,7,6,2,8,1,4,5]=>[6,2,3,7,1,8,5,4]=>[1,3,2,1,1]
[7,6,5,8,2,4,3,1]=>[8,5,3,2,1,7,6,4]=>[1,4,6,7,8,2,3,5]=>[5,3]
[7,6,5,8,3,1,4,2]=>[8,6,5,3,2,1,7,4]=>[1,3,4,6,7,8,2,5]=>[6,2]
[2,6,4,3,8,1,7,5]=>[3,8,4,1,2,6,7,5]=>[6,1,5,8,7,3,2,4]=>[1,3,1,1,2]
[2,6,4,3,8,5,7,1]=>[3,6,2,8,1,4,7,5]=>[6,3,7,1,8,5,2,4]=>[1,2,2,1,2]
[7,2,3,1,5,8,6,4]=>[8,2,3,5,7,4,1,6]=>[1,7,6,4,2,5,8,3]=>[2,1,1,3,1]
[7,1,5,6,3,8,4,2]=>[3,8,5,4,7,2,1,6]=>[6,1,4,5,2,7,8,3]=>[1,3,3,1]
[7,3,6,5,1,4,8,2]=>[6,8,2,5,4,3,1,7]=>[3,1,7,4,5,6,8,2]=>[1,2,4,1]
[7,2,6,5,3,8,1,4]=>[5,7,4,2,3,1,8,6]=>[4,2,5,7,6,8,1,3]=>[1,3,2,2]
[7,2,3,1,4,8,6,5]=>[8,2,3,7,4,5,1,6]=>[1,7,6,2,5,4,8,3]=>[2,1,2,2,1]
[7,2,3,5,4,8,6,1]=>[4,8,2,3,5,1,7,6]=>[5,1,7,6,4,8,2,3]=>[1,2,1,2,2]
[1,5,6,4,8,3,7,2]=>[2,4,3,6,8,7,1,5]=>[7,5,6,3,1,2,8,4]=>[1,2,1,3,1]
[2,5,6,4,8,3,1,7]=>[2,4,3,7,1,6,8,5]=>[7,5,6,2,8,3,1,4]=>[1,2,2,1,2]
[3,5,6,1,4,7,8,2]=>[5,1,2,6,3,8,4,7]=>[4,8,7,3,6,1,5,2]=>[2,1,2,2,1]
[7,6,1,3,4,5,8,2]=>[4,5,6,8,3,2,1,7]=>[5,4,3,1,6,7,8,2]=>[1,1,1,4,1]
[7,1,3,2,4,8,5,6]=>[3,7,8,2,4,5,1,6]=>[6,2,1,7,5,4,8,3]=>[1,1,2,1,2,1]
[7,6,1,5,3,4,8,2]=>[5,6,4,8,3,2,1,7]=>[4,3,5,1,6,7,8,2]=>[1,2,4,1]
[7,6,1,5,4,3,8,2]=>[6,5,4,8,3,2,1,7]=>[3,4,5,1,6,7,8,2]=>[3,4,1]
[1,6,4,5,8,3,2,7]=>[3,4,2,7,6,8,1,5]=>[6,5,7,2,3,1,8,4]=>[1,2,2,2,1]
[7,6,5,8,1,3,2,4]=>[7,5,6,3,2,1,8,4]=>[2,4,3,6,7,8,1,5]=>[2,4,2]
[3,5,6,8,2,1,7,4]=>[2,5,1,3,8,6,7,4]=>[7,4,8,6,1,3,2,5]=>[1,2,1,2,2]
[4,2,1,5,3,7,8,6]=>[2,4,1,6,8,3,5,7]=>[7,5,8,3,1,6,4,2]=>[1,2,1,2,1,1]
[4,2,5,6,3,1,8,7]=>[3,1,5,2,4,8,6,7]=>[6,8,4,7,5,1,3,2]=>[2,2,1,2,1]
[3,5,6,8,1,7,2,4]=>[2,7,1,3,8,5,6,4]=>[7,2,8,6,1,4,3,5]=>[1,2,1,2,2]
[4,1,5,6,3,2,8,7]=>[3,1,5,4,8,2,6,7]=>[6,8,4,5,1,7,3,2]=>[2,2,2,1,1]
[4,5,3,1,7,2,8,6]=>[1,3,2,8,6,4,5,7]=>[8,6,7,1,3,5,4,2]=>[1,2,3,1,1]
[4,1,3,5,2,7,8,6]=>[3,4,1,6,8,2,5,7]=>[6,5,8,3,1,7,4,2]=>[1,2,1,2,1,1]
[2,5,4,7,3,8,6,1]=>[2,8,3,5,1,4,7,6]=>[7,1,6,4,8,5,2,3]=>[1,2,2,1,2]
[3,5,7,1,8,4,2,6]=>[2,7,1,6,8,4,3,5]=>[7,2,8,3,1,5,6,4]=>[1,2,1,3,1]
[4,5,3,7,1,2,8,6]=>[1,3,2,8,5,6,4,7]=>[8,6,7,1,4,3,5,2]=>[1,2,2,2,1]
[5,1,3,2,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[5,7,6,4,8,3,2,1]=>[2,1,2,1,1,1]
[3,6,1,7,4,5,2,8]=>[5,7,1,6,3,2,4,8]=>[4,2,8,3,6,7,5,1]=>[1,2,3,1,1]
[5,1,3,4,2,6,7,8]=>[3,5,2,4,1,6,7,8]=>[6,4,7,5,8,3,2,1]=>[1,2,2,1,1,1]
[5,3,1,4,2,6,7,8]=>[5,3,2,4,1,6,7,8]=>[4,6,7,5,8,3,2,1]=>[3,2,1,1,1]
[4,5,2,3,7,1,8,6]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[1,3,1,2,1]
[4,2,6,1,3,7,5,8]=>[7,2,1,4,5,3,6,8]=>[2,7,8,5,4,6,3,1]=>[3,1,2,1,1]
[4,6,2,1,3,7,5,8]=>[3,1,7,4,5,2,6,8]=>[6,8,2,5,4,7,3,1]=>[2,2,2,1,1]
[3,6,2,1,7,4,8,5]=>[8,1,3,6,4,2,5,7]=>[1,8,6,3,5,7,4,2]=>[2,1,3,1,1]
[3,1,4,7,6,5,2,8]=>[7,1,6,3,5,2,4,8]=>[2,8,3,6,4,7,5,1]=>[2,2,2,1,1]
[3,6,2,7,1,5,8,4]=>[6,8,1,3,2,5,4,7]=>[3,1,8,6,7,4,5,2]=>[1,2,2,2,1]
[4,6,2,7,1,3,5,8]=>[3,1,5,6,2,7,4,8]=>[6,8,4,3,7,2,5,1]=>[2,1,2,2,1]
[3,5,7,1,8,2,6,4]=>[2,8,1,6,7,4,3,5]=>[7,1,8,3,2,5,6,4]=>[1,2,1,3,1]
[5,1,4,2,3,6,7,8]=>[4,5,2,3,1,6,7,8]=>[5,4,7,6,8,3,2,1]=>[1,2,2,1,1,1]
[3,6,1,7,2,5,8,4]=>[6,8,1,5,3,2,4,7]=>[3,1,8,4,6,7,5,2]=>[1,2,3,1,1]
[2,6,5,3,4,7,8,1]=>[4,5,3,1,2,6,8,7]=>[5,4,6,8,7,3,1,2]=>[1,3,1,1,2]
[3,6,1,7,5,4,2,8]=>[7,6,1,5,3,2,4,8]=>[2,3,8,4,6,7,5,1]=>[3,3,1,1]
[5,1,4,3,2,6,7,8]=>[5,4,2,3,1,6,7,8]=>[4,5,7,6,8,3,2,1]=>[3,2,1,1,1]
[5,4,1,3,2,6,7,8]=>[5,3,4,2,1,6,7,8]=>[4,6,5,7,8,3,2,1]=>[2,3,1,1,1]
[6,4,2,5,3,8,1,7]=>[5,3,2,4,1,7,8,6]=>[4,6,7,5,8,2,1,3]=>[3,2,1,2]
[4,6,2,3,5,1,8,7]=>[3,1,4,5,2,8,6,7]=>[6,8,5,4,7,1,3,2]=>[2,1,2,2,1]
[6,2,4,5,1,8,3,7]=>[3,7,2,4,1,8,5,6]=>[6,2,7,5,8,1,4,3]=>[1,2,2,2,1]
[8,2,6,7,1,4,5,3]=>[6,8,5,2,3,7,4,1]=>[3,1,4,7,6,2,5,8]=>[1,3,1,3]
[2,6,4,1,5,8,3,7]=>[5,3,7,1,2,8,4,6]=>[4,6,2,8,7,1,5,3]=>[2,2,1,2,1]
[2,8,1,6,7,4,5,3]=>[6,4,8,7,1,3,5,2]=>[3,5,1,2,8,6,4,7]=>[2,3,1,2]
[6,8,4,5,7,2,3,1]=>[3,1,6,4,8,7,5,2]=>[6,8,3,5,1,2,4,7]=>[2,2,4]
[2,8,6,1,4,7,5,3]=>[8,5,7,4,1,3,6,2]=>[1,4,2,5,8,6,3,7]=>[2,3,1,2]
[2,8,1,6,4,7,5,3]=>[8,5,4,7,1,3,6,2]=>[1,4,5,2,8,6,3,7]=>[3,2,1,2]
[2,6,1,4,8,5,3,7]=>[7,4,6,1,2,8,3,5]=>[2,5,3,8,7,1,6,4]=>[2,2,1,2,1]
[4,2,3,6,1,8,5,7]=>[7,2,1,3,4,8,5,6]=>[2,7,8,6,5,1,4,3]=>[3,1,1,2,1]
[4,2,3,1,6,8,5,7]=>[2,3,1,5,7,8,4,6]=>[7,6,8,4,2,1,5,3]=>[1,2,1,1,2,1]
[4,2,3,8,6,1,7,5]=>[1,8,6,2,3,5,7,4]=>[8,1,3,7,6,4,2,5]=>[1,3,1,1,2]
[6,4,5,8,2,3,7,1]=>[2,5,3,1,6,8,7,4]=>[7,4,6,8,3,1,2,5]=>[1,3,1,3]
[6,4,8,5,2,3,7,1]=>[2,5,1,6,4,8,7,3]=>[7,4,8,3,5,1,2,6]=>[1,2,2,3]
[4,2,8,3,1,6,7,5]=>[4,1,6,8,2,5,7,3]=>[5,8,3,1,7,4,2,6]=>[2,1,2,1,2]
[2,4,8,1,3,6,7,5]=>[2,6,8,1,4,5,7,3]=>[7,3,1,8,5,4,2,6]=>[1,1,2,1,1,2]
[2,4,1,8,3,6,7,5]=>[2,6,8,1,5,7,3,4]=>[7,3,1,8,4,2,6,5]=>[1,1,2,1,2,1]
[2,1,4,8,6,3,7,5]=>[8,6,1,3,5,7,2,4]=>[1,3,8,6,4,2,7,5]=>[3,1,1,2,1]
[6,4,8,2,5,3,7,1]=>[2,6,4,1,5,8,7,3]=>[7,3,5,8,4,1,2,6]=>[1,3,1,3]
[4,6,8,2,3,5,7,1]=>[1,4,5,2,6,8,7,3]=>[8,5,4,7,3,1,2,6]=>[1,1,2,1,3]
[2,6,8,4,1,5,7,3]=>[6,4,2,8,1,5,7,3]=>[3,5,7,1,8,4,2,6]=>[3,2,1,2]
[2,6,8,1,4,5,7,3]=>[5,6,2,8,1,4,7,3]=>[4,3,7,1,8,5,2,6]=>[1,2,2,1,2]
[2,1,6,8,4,5,7,3]=>[5,3,6,8,1,7,2,4]=>[4,6,3,1,8,2,7,5]=>[2,1,2,2,1]
[2,8,1,4,6,7,3,5]=>[7,4,5,8,1,3,6,2]=>[2,5,4,1,8,6,3,7]=>[2,1,2,1,2]
[4,8,6,2,3,7,5,1]=>[8,1,4,5,3,7,6,2]=>[1,8,5,4,6,2,3,7]=>[2,1,2,3]
[8,4,2,6,7,3,1,5]=>[2,7,6,3,4,8,5,1]=>[7,2,3,6,5,1,4,8]=>[1,3,1,3]
[7,6,4,5,1,3,8,2]=>[6,3,8,5,4,2,1,7]=>[3,6,1,4,5,7,8,2]=>[2,5,1]
[1,6,7,5,3,4,8,2]=>[5,2,6,4,3,8,1,7]=>[4,7,3,5,6,1,8,2]=>[2,3,2,1]
[1,6,7,5,8,2,3,4]=>[6,2,7,4,3,8,1,5]=>[3,7,2,5,6,1,8,4]=>[2,3,2,1]
[6,2,5,8,3,4,7,1]=>[5,3,6,1,8,2,7,4]=>[4,6,3,8,1,7,2,5]=>[2,2,2,2]
[6,2,3,8,7,4,1,5]=>[7,6,8,2,1,3,5,4]=>[2,3,1,7,8,6,4,5]=>[2,3,1,2]
[2,4,7,3,5,8,6,1]=>[8,2,4,5,1,3,7,6]=>[1,7,5,4,8,6,2,3]=>[2,1,2,1,2]
[2,5,3,7,1,8,4,6]=>[7,2,8,1,3,5,4,6]=>[2,7,1,8,6,4,5,3]=>[2,2,1,2,1]
[5,2,8,3,1,4,6,7]=>[5,2,4,1,6,7,8,3]=>[4,7,5,8,3,2,1,6]=>[2,2,1,1,2]
[4,8,2,3,6,5,7,1]=>[1,6,3,4,5,8,7,2]=>[8,3,6,5,4,1,2,7]=>[1,2,1,1,3]
[5,8,1,3,6,4,7,2]=>[6,4,1,5,8,3,7,2]=>[3,5,8,4,1,6,2,7]=>[3,1,2,2]
[5,8,1,4,3,6,2,7]=>[5,4,1,7,3,6,8,2]=>[4,5,8,2,6,3,1,7]=>[3,2,1,2]
[5,8,4,1,3,7,6,2]=>[1,8,5,3,7,4,6,2]=>[8,1,4,6,2,5,3,7]=>[1,3,2,2]
[6,4,5,3,8,1,7,2]=>[2,4,3,1,8,6,7,5]=>[7,5,6,8,1,3,2,4]=>[1,3,2,2]
[4,5,1,3,6,2,8,7]=>[4,1,5,2,8,3,6,7]=>[5,8,4,7,1,6,3,2]=>[2,2,2,1,1]
[4,2,6,5,1,7,3,8]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[1,3,2,1,1]
[4,3,5,7,2,1,6,8]=>[2,1,3,6,5,7,4,8]=>[7,8,6,3,4,2,5,1]=>[2,1,2,2,1]
[3,4,6,2,5,8,7,1]=>[8,1,2,4,3,5,7,6]=>[1,8,7,5,6,4,2,3]=>[2,1,2,1,2]
[3,5,2,4,6,1,8,7]=>[1,3,4,2,5,8,6,7]=>[8,6,5,7,4,1,3,2]=>[1,1,2,1,2,1]
[4,2,5,1,6,8,3,7]=>[5,2,1,3,7,8,4,6]=>[4,7,8,6,2,1,5,3]=>[3,1,1,2,1]
[1,8,2,3,6,5,7,4]=>[6,5,8,3,4,7,1,2]=>[3,4,1,6,5,2,8,7]=>[2,2,1,2,1]
[4,2,8,3,5,7,1,6]=>[4,1,5,7,8,2,6,3]=>[5,8,4,2,1,7,3,6]=>[2,1,1,2,2]
[1,3,7,2,6,5,8,4]=>[6,5,8,2,4,1,3,7]=>[3,4,1,7,5,8,6,2]=>[2,2,2,1,1]
[1,3,6,4,2,5,8,7]=>[4,8,2,5,1,3,6,7]=>[5,1,7,4,8,6,3,2]=>[1,2,2,1,1,1]
[1,5,4,7,3,6,8,2]=>[3,2,5,6,4,8,1,7]=>[6,7,4,3,5,1,8,2]=>[2,1,2,2,1]
[5,2,3,8,4,1,7,6]=>[5,8,2,1,3,6,7,4]=>[4,1,7,8,6,3,2,5]=>[1,3,1,1,2]
[7,5,3,4,8,2,1,6]=>[3,4,2,7,6,1,8,5]=>[6,5,7,2,3,8,1,4]=>[1,2,3,2]
[7,2,8,3,4,1,5,6]=>[4,6,2,5,7,1,8,3]=>[5,3,7,4,2,8,1,6]=>[1,2,1,2,2]
[7,4,3,8,5,2,6,1]=>[2,6,3,5,1,8,7,4]=>[7,3,6,4,8,1,2,5]=>[1,2,2,3]
[4,6,2,7,3,1,5,8]=>[1,6,3,5,2,7,4,8]=>[8,3,6,4,7,2,5,1]=>[1,2,2,2,1]
[7,6,3,8,2,4,5,1]=>[3,5,6,2,1,8,7,4]=>[6,4,3,7,8,1,2,5]=>[1,1,3,3]
[7,2,8,5,1,3,4,6]=>[5,6,7,2,4,1,8,3]=>[4,3,2,7,5,8,1,6]=>[1,1,2,2,2]
[1,5,3,7,6,8,4,2]=>[2,5,4,8,3,7,1,6]=>[7,4,5,1,6,2,8,3]=>[1,2,2,2,1]
[1,6,3,7,8,2,4,5]=>[6,7,3,2,4,8,1,5]=>[3,2,6,7,5,1,8,4]=>[1,3,1,2,1]
[1,4,3,7,8,5,2,6]=>[7,2,6,3,4,8,1,5]=>[2,7,3,6,5,1,8,4]=>[2,2,1,2,1]
[4,2,6,5,7,8,3,1]=>[1,4,3,5,8,2,7,6]=>[8,5,6,4,1,7,2,3]=>[1,2,1,2,2]
[4,2,6,7,5,8,1,3]=>[1,3,7,5,2,4,8,6]=>[8,6,2,4,7,5,1,3]=>[1,1,3,1,2]
[3,2,6,7,8,1,4,5]=>[6,1,3,7,2,4,8,5]=>[3,8,6,2,7,5,1,4]=>[2,1,2,1,2]
[5,1,8,3,6,4,7,2]=>[6,4,1,5,8,7,2,3]=>[3,5,8,4,1,2,7,6]=>[3,1,3,1]
[3,6,8,5,7,2,1,4]=>[2,7,6,1,4,8,5,3]=>[7,2,3,8,5,1,4,6]=>[1,3,1,3]
[5,1,3,8,7,6,4,2]=>[1,8,7,6,3,5,2,4]=>[8,1,2,3,6,4,7,5]=>[1,4,2,1]
[3,8,5,6,1,7,2,4]=>[7,3,8,1,5,4,6,2]=>[2,6,1,8,4,5,3,7]=>[2,2,2,2]
[3,4,8,1,7,6,2,5]=>[7,8,1,2,6,4,5,3]=>[2,1,8,7,3,5,4,6]=>[1,2,1,2,2]
[4,7,6,8,5,1,3,2]=>[8,6,1,3,2,7,5,4]=>[1,3,8,6,7,2,4,5]=>[3,2,3]
[6,7,4,8,5,1,3,2]=>[3,1,8,6,2,7,5,4]=>[6,8,1,3,7,2,4,5]=>[2,3,3]
[5,3,6,8,7,1,4,2]=>[3,1,8,2,6,7,5,4]=>[6,8,1,7,3,2,4,5]=>[2,2,1,3]
[1,8,4,6,7,2,5,3]=>[8,3,6,4,7,5,1,2]=>[1,6,3,5,2,4,8,7]=>[2,2,3,1]
[5,2,8,3,7,1,6,4]=>[8,4,1,6,7,2,5,3]=>[1,5,8,3,2,7,4,6]=>[3,1,2,2]
[7,4,5,8,6,1,3,2]=>[2,3,8,6,1,7,5,4]=>[7,6,1,3,8,2,4,5]=>[1,1,3,3]
[4,3,6,8,7,1,5,2]=>[1,3,8,2,6,7,5,4]=>[8,6,1,7,3,2,4,5]=>[1,1,2,1,3]
[6,4,8,3,1,7,5,2]=>[2,4,1,8,7,5,6,3]=>[7,5,8,1,2,4,3,6]=>[1,2,3,2]
[3,6,5,8,7,1,4,2]=>[3,2,8,1,6,7,5,4]=>[6,7,1,8,3,2,4,5]=>[2,2,1,3]
[5,7,4,8,2,6,3,1]=>[1,3,8,5,2,7,6,4]=>[8,6,1,4,7,2,3,5]=>[1,1,3,3]
[5,6,4,8,2,7,3,1]=>[1,3,2,8,5,7,6,4]=>[8,6,7,1,4,2,3,5]=>[1,2,2,3]
[4,6,3,8,2,7,5,1]=>[8,1,3,2,5,7,6,4]=>[1,8,6,7,4,2,3,5]=>[2,2,1,3]
[5,3,8,1,7,2,6,4]=>[8,2,1,6,7,4,5,3]=>[1,7,8,3,2,5,4,6]=>[3,1,2,2]
[6,5,8,1,3,7,4,2]=>[8,5,2,1,7,4,6,3]=>[1,4,7,8,2,5,3,6]=>[4,2,2]
[6,5,3,8,2,7,4,1]=>[8,3,2,1,5,7,6,4]=>[1,6,7,8,4,2,3,5]=>[4,1,3]
[6,4,8,1,3,7,5,2]=>[2,8,5,1,7,4,6,3]=>[7,1,4,8,2,5,3,6]=>[1,3,2,2]
[6,2,8,3,4,7,5,1]=>[8,4,5,1,7,2,6,3]=>[1,5,4,8,2,7,3,6]=>[2,2,2,2]
[7,6,3,1,4,2,5,8]=>[6,4,3,5,7,2,1,8]=>[3,5,6,4,2,7,8,1]=>[3,1,3,1]
[1,5,4,3,7,8,2,6]=>[3,2,7,4,5,8,1,6]=>[6,7,2,5,4,1,8,3]=>[2,2,1,2,1]
[7,8,4,2,5,3,1,6]=>[7,4,3,6,5,1,8,2]=>[2,5,6,3,4,8,1,7]=>[3,3,2]
[4,2,7,8,5,3,1,6]=>[7,1,6,5,2,3,8,4]=>[2,8,3,4,7,6,1,5]=>[2,3,1,2]
[4,2,5,3,1,7,8,6]=>[4,2,1,3,6,8,5,7]=>[5,7,8,6,3,1,4,2]=>[3,1,1,2,1]
[4,2,8,7,6,3,1,5]=>[7,1,6,8,5,2,4,3]=>[2,8,3,1,4,7,5,6]=>[2,1,3,2]
[4,2,7,6,3,1,5,8]=>[1,6,5,7,2,4,3,8]=>[8,3,4,2,7,5,6,1]=>[1,2,2,2,1]
[6,3,1,8,7,5,2,4]=>[7,8,2,1,6,5,3,4]=>[2,1,7,8,3,4,6,5]=>[1,3,3,1]
[4,2,7,6,3,1,8,5]=>[1,5,8,6,2,4,3,7]=>[8,4,1,3,7,5,6,2]=>[1,1,3,2,1]
[7,6,3,1,8,4,2,5]=>[3,7,6,8,4,2,1,5]=>[6,2,3,1,5,7,8,4]=>[1,2,4,1]
[7,6,4,2,1,8,3,5]=>[4,7,3,8,5,2,1,6]=>[5,2,6,1,4,7,8,3]=>[1,2,4,1]
[1,8,2,7,6,4,3,5]=>[7,6,8,5,3,4,1,2]=>[2,3,1,4,6,5,8,7]=>[2,3,2,1]
[8,3,5,7,6,4,2,1]=>[8,3,7,2,6,5,4,1]=>[1,6,2,7,3,4,5,8]=>[2,2,4]
[8,4,2,5,7,6,3,1]=>[2,8,4,7,3,6,5,1]=>[7,1,5,2,6,3,4,8]=>[1,2,2,3]
[8,7,5,2,4,6,3,1]=>[5,8,4,3,7,6,2,1]=>[4,1,5,6,2,3,7,8]=>[1,3,4]
[7,5,2,4,6,3,1,8]=>[4,7,3,2,6,5,1,8]=>[5,2,6,7,3,4,8,1]=>[1,3,3,1]
[5,2,8,6,3,7,4,1]=>[1,8,5,4,7,2,6,3]=>[8,1,4,5,2,7,3,6]=>[1,3,2,2]
[8,4,7,5,2,6,3,1]=>[8,2,5,4,7,6,3,1]=>[1,7,4,5,2,3,6,8]=>[2,2,4]
[8,3,6,4,7,5,2,1]=>[8,4,2,3,7,6,5,1]=>[1,5,7,6,2,3,4,8]=>[3,1,4]
[1,8,2,7,5,3,6,4]=>[8,6,5,7,3,4,1,2]=>[1,3,4,2,6,5,8,7]=>[3,2,2,1]
[7,5,2,1,8,3,6,4]=>[8,3,6,2,7,4,1,5]=>[1,6,3,7,2,5,8,4]=>[2,2,3,1]
[7,5,2,6,3,1,8,4]=>[5,8,3,2,6,4,1,7]=>[4,1,6,7,3,5,8,2]=>[1,3,3,1]
[8,7,4,1,5,2,6,3]=>[8,6,4,3,5,7,2,1]=>[1,3,5,6,4,2,7,8]=>[4,1,3]
[7,4,1,5,2,8,6,3]=>[4,2,8,7,3,5,1,6]=>[5,7,1,2,6,4,8,3]=>[2,3,2,1]
[7,6,3,1,4,2,8,5]=>[5,3,8,4,6,2,1,7]=>[4,6,1,5,3,7,8,2]=>[2,2,3,1]
[7,5,2,8,6,3,1,4]=>[7,6,2,8,3,1,5,4]=>[2,3,7,1,6,8,4,5]=>[3,3,2]
[8,7,5,2,6,3,1,4]=>[7,4,6,3,8,5,2,1]=>[2,5,3,6,1,4,7,8]=>[2,2,4]
[7,5,2,1,3,6,4,8]=>[3,7,4,5,2,6,1,8]=>[6,2,5,4,7,3,8,1]=>[1,2,2,2,1]
[8,7,5,2,1,3,6,4]=>[4,8,5,6,3,7,2,1]=>[5,1,4,3,6,2,7,8]=>[1,2,2,3]
[7,5,2,1,3,8,6,4]=>[8,3,7,4,2,5,1,6]=>[1,6,2,5,7,4,8,3]=>[2,3,2,1]
[1,3,7,6,5,8,2,4]=>[7,5,4,2,3,8,1,6]=>[2,4,5,7,6,1,8,3]=>[4,1,2,1]
[8,6,4,7,5,2,1,3]=>[3,7,6,2,8,5,4,1]=>[6,2,3,7,1,4,5,8]=>[1,3,4]
[6,4,8,7,5,2,1,3]=>[7,2,1,6,8,5,4,3]=>[2,7,8,3,1,4,5,6]=>[3,1,4]
[6,3,1,4,7,5,2,8]=>[2,7,4,6,3,1,5,8]=>[7,2,5,3,6,8,4,1]=>[1,2,3,1,1]
[8,5,7,6,3,1,4,2]=>[2,8,6,5,7,4,3,1]=>[7,1,3,4,2,5,6,8]=>[1,3,4]
[1,8,2,5,7,6,4,3]=>[8,4,7,6,3,5,1,2]=>[1,5,2,3,6,4,8,7]=>[2,3,2,1]
[1,8,2,6,4,7,5,3]=>[8,5,4,7,3,6,1,2]=>[1,4,5,2,6,3,8,7]=>[3,2,2,1]
[7,5,2,1,6,4,8,3]=>[6,3,5,2,8,4,1,7]=>[3,6,4,7,1,5,8,2]=>[2,2,3,1]
[6,3,8,7,4,1,5,2]=>[8,6,2,1,5,7,4,3]=>[1,3,7,8,4,2,5,6]=>[4,1,3]
[6,3,7,4,1,5,2,8]=>[7,2,5,4,1,6,3,8]=>[2,7,4,5,8,3,6,1]=>[2,3,2,1]
[7,4,1,6,3,5,2,8]=>[5,2,7,6,3,4,1,8]=>[4,7,2,3,6,5,8,1]=>[2,3,2,1]
[7,4,1,8,6,3,5,2]=>[2,6,8,7,5,3,1,4]=>[7,3,1,2,4,6,8,5]=>[1,1,5,1]
[8,4,6,3,1,7,5,2]=>[2,4,8,7,5,3,6,1]=>[7,5,1,2,4,6,3,8]=>[1,1,4,2]
[6,4,7,5,2,1,8,3]=>[2,5,1,8,6,4,3,7]=>[7,4,8,1,3,5,6,2]=>[1,2,4,1]
[1,6,4,7,5,3,8,2]=>[6,3,2,5,4,8,1,7]=>[3,6,7,4,5,1,8,2]=>[3,2,2,1]
[8,6,3,5,2,7,4,1]=>[8,3,5,4,2,7,6,1]=>[1,6,4,5,7,2,3,8]=>[2,3,3]
[6,3,5,2,8,7,4,1]=>[3,8,2,1,7,4,6,5]=>[6,1,7,8,2,5,3,4]=>[1,3,2,2]
[6,3,5,2,7,4,1,8]=>[7,2,4,3,1,6,5,8]=>[2,7,5,6,8,3,4,1]=>[2,3,2,1]
[3,5,8,4,6,1,7,2]=>[2,4,8,1,6,5,7,3]=>[7,5,1,8,3,4,2,6]=>[1,1,2,2,2]
[1,4,7,3,5,2,6,8]=>[2,4,6,5,7,1,3,8]=>[7,5,3,4,2,8,6,1]=>[1,1,2,2,1,1]
[5,7,4,2,6,3,1,8]=>[1,7,4,3,6,5,2,8]=>[8,2,5,6,3,4,7,1]=>[1,3,3,1]
[4,2,6,3,5,7,1,8]=>[4,1,5,2,3,7,6,8]=>[5,8,4,7,6,2,3,1]=>[2,2,1,2,1]
[1,4,5,8,2,7,3,6]=>[2,3,7,8,5,6,1,4]=>[7,6,2,1,4,3,8,5]=>[1,1,1,2,2,1]
[2,4,5,8,1,6,7,3]=>[2,3,6,8,1,5,7,4]=>[7,6,3,1,8,4,2,5]=>[1,1,1,2,1,2]
[8,3,4,7,1,6,5,2]=>[8,2,3,7,5,6,4,1]=>[1,7,6,2,4,3,5,8]=>[2,1,2,3]
[4,2,5,7,8,1,6,3]=>[1,8,3,6,2,4,7,5]=>[8,1,6,3,7,5,2,4]=>[1,2,2,1,2]
[8,3,4,6,5,1,7,2]=>[8,2,3,6,5,4,7,1]=>[1,7,6,3,4,5,2,8]=>[2,1,3,2]
[6,1,3,7,4,2,5,8]=>[6,3,5,7,2,1,4,8]=>[3,6,4,2,7,8,5,1]=>[2,1,3,1,1]
[3,1,6,8,2,7,4,5]=>[7,1,3,8,5,6,2,4]=>[2,8,6,1,4,3,7,5]=>[2,1,2,2,1]
[6,1,3,8,2,5,4,7]=>[7,3,5,6,1,8,2,4]=>[2,6,4,3,8,1,7,5]=>[2,1,2,2,1]
[4,8,2,3,1,6,7,5]=>[3,1,4,6,8,5,7,2]=>[6,8,5,3,1,4,2,7]=>[2,1,1,2,2]
[3,2,6,8,1,5,7,4]=>[6,1,3,8,2,5,7,4]=>[3,8,6,1,7,4,2,5]=>[2,1,2,1,2]
[8,2,6,1,5,4,7,3]=>[6,5,8,2,4,3,7,1]=>[3,4,1,7,5,6,2,8]=>[2,2,2,2]
[8,6,2,7,1,5,4,3]=>[8,7,3,5,2,6,4,1]=>[1,2,6,4,7,3,5,8]=>[3,2,3]
[7,6,8,3,1,5,4,2]=>[4,8,7,5,2,1,6,3]=>[5,1,2,4,7,8,3,6]=>[1,5,2]
[5,7,4,2,8,1,6,3]=>[1,8,4,3,6,2,7,5]=>[8,1,5,6,3,7,2,4]=>[1,3,2,2]
[6,3,7,2,8,1,5,4]=>[8,2,4,1,6,3,7,5]=>[1,7,5,8,3,6,2,4]=>[2,2,2,2]
[7,5,2,8,6,1,4,3]=>[8,6,2,7,3,1,5,4]=>[1,3,7,2,6,8,4,5]=>[3,3,2]
[2,7,3,8,1,5,6,4]=>[6,8,3,5,1,2,7,4]=>[3,1,6,4,8,7,2,5]=>[1,2,2,1,2]
[1,6,8,5,2,4,3,7]=>[7,5,2,6,4,8,1,3]=>[2,4,7,3,5,1,8,6]=>[3,2,2,1]
[4,5,7,2,8,1,6,3]=>[1,2,8,4,6,3,7,5]=>[8,7,1,5,3,6,2,4]=>[1,1,2,2,2]
[4,5,6,8,3,1,7,2]=>[1,2,3,8,6,5,7,4]=>[8,7,6,1,3,4,2,5]=>[1,1,1,3,2]
[8,4,6,5,3,1,7,2]=>[8,2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2,8]=>[2,4,2]
[5,6,4,8,3,1,7,2]=>[1,3,2,8,6,5,7,4]=>[8,6,7,1,3,4,2,5]=>[1,2,3,2]
[3,4,7,1,2,6,5,8]=>[1,2,7,4,5,6,3,8]=>[8,7,2,5,4,3,6,1]=>[1,1,2,1,2,1]
[4,8,1,6,2,3,7,5]=>[1,8,5,6,3,4,7,2]=>[8,1,4,3,6,5,2,7]=>[1,2,2,1,2]
[5,2,7,1,3,6,4,8]=>[7,2,4,1,5,6,3,8]=>[2,7,5,8,4,3,6,1]=>[2,2,1,2,1]
[7,8,1,2,4,3,6,5]=>[5,8,3,4,6,1,7,2]=>[4,1,6,5,3,8,2,7]=>[1,2,1,2,2]
[8,4,1,6,2,3,7,5]=>[8,5,2,6,3,4,7,1]=>[1,4,7,3,6,5,2,8]=>[3,2,1,2]
[4,8,3,1,2,5,7,6]=>[1,8,4,3,5,6,7,2]=>[8,1,5,6,4,3,2,7]=>[1,3,1,1,2]
[4,1,3,6,5,7,8,2]=>[5,3,1,4,6,8,2,7]=>[4,6,8,5,3,1,7,2]=>[3,1,1,2,1]
[6,1,3,4,2,8,5,7]=>[3,4,7,8,2,1,5,6]=>[6,5,2,1,7,8,4,3]=>[1,1,1,3,1,1]
[8,1,4,2,5,7,6,3]=>[3,8,5,7,2,4,6,1]=>[6,1,4,2,7,5,3,8]=>[1,2,2,1,2]
[8,1,4,3,5,7,6,2]=>[3,8,4,5,7,2,6,1]=>[6,1,5,4,2,7,3,8]=>[1,2,1,2,2]
[5,2,4,1,3,7,8,6]=>[6,2,3,1,8,4,5,7]=>[3,7,6,8,1,5,4,2]=>[2,2,2,1,1]
[2,6,5,3,1,7,8,4]=>[4,6,3,1,2,8,5,7]=>[5,3,6,8,7,1,4,2]=>[1,3,1,2,1]
[8,3,2,1,5,7,6,4]=>[2,8,3,5,7,4,6,1]=>[7,1,6,4,2,5,3,8]=>[1,2,1,2,2]
[1,7,4,3,6,8,2,5]=>[3,7,4,5,2,8,1,6]=>[6,2,5,4,7,1,8,3]=>[1,2,2,2,1]
[2,7,6,3,1,8,4,5]=>[4,7,8,5,1,3,2,6]=>[5,2,1,4,8,6,7,3]=>[1,1,3,2,1]
[2,8,4,6,3,7,5,1]=>[8,3,5,4,7,1,6,2]=>[1,6,4,5,2,8,3,7]=>[2,2,2,2]
[8,7,1,3,6,5,4,2]=>[8,7,4,6,3,5,2,1]=>[1,2,5,3,6,4,7,8]=>[3,2,3]
[1,8,5,7,4,2,6,3]=>[3,8,6,5,7,4,1,2]=>[6,1,3,4,2,5,8,7]=>[1,3,3,1]
[3,8,6,5,7,1,4,2]=>[8,6,4,1,3,7,5,2]=>[1,3,5,8,6,2,4,7]=>[4,1,3]
[4,8,6,2,7,1,5,3]=>[8,1,4,6,3,7,5,2]=>[1,8,5,3,6,2,4,7]=>[2,1,2,3]
[4,7,5,3,8,2,1,6]=>[4,1,3,7,6,2,8,5]=>[5,8,6,2,3,7,1,4]=>[2,1,3,2]
[1,6,5,8,3,4,2,7]=>[5,3,2,7,6,8,1,4]=>[4,6,7,2,3,1,8,5]=>[3,2,2,1]
[6,1,5,3,8,4,2,7]=>[7,4,3,6,1,8,2,5]=>[2,5,6,3,8,1,7,4]=>[3,2,2,1]
[8,1,5,4,7,2,6,3]=>[4,3,8,6,7,2,5,1]=>[5,6,1,3,2,7,4,8]=>[2,2,2,2]
[2,1,4,7,5,8,3,6]=>[5,7,1,3,4,8,2,6]=>[4,2,8,6,5,1,7,3]=>[1,2,1,1,2,1]
[6,3,5,8,7,4,1,2]=>[3,7,1,8,2,6,5,4]=>[6,2,8,1,7,3,4,5]=>[1,2,2,3]
[4,7,2,8,5,6,3,1]=>[5,8,1,7,3,2,6,4]=>[4,1,8,2,6,7,3,5]=>[1,2,3,2]
[1,4,8,7,3,5,6,2]=>[5,6,8,2,7,4,1,3]=>[4,3,1,7,2,5,8,6]=>[1,1,2,3,1]
[8,1,7,6,3,5,4,2]=>[8,5,7,6,4,2,3,1]=>[1,4,2,3,5,7,6,8]=>[2,4,2]
[3,6,8,5,7,4,1,2]=>[2,7,4,8,1,6,5,3]=>[7,2,5,1,8,3,4,6]=>[1,2,2,3]
[5,7,2,8,6,4,1,3]=>[1,7,8,6,3,2,5,4]=>[8,2,1,3,6,7,4,5]=>[1,1,4,2]
[3,8,7,5,6,4,2,1]=>[4,8,7,6,1,5,3,2]=>[5,1,2,3,8,4,6,7]=>[1,4,3]
[2,8,7,6,4,5,3,1]=>[5,8,7,6,4,1,3,2]=>[4,1,2,3,5,8,6,7]=>[1,5,2]
[1,8,7,6,5,3,4,2]=>[6,8,7,5,4,3,1,2]=>[3,1,2,4,5,6,8,7]=>[1,6,1]
[4,6,7,2,5,3,1,8]=>[7,1,4,2,6,5,3,8]=>[2,8,5,7,3,4,6,1]=>[2,2,3,1]
[1,4,7,8,2,6,5,3]=>[8,7,2,5,3,6,1,4]=>[1,2,7,4,6,3,8,5]=>[3,2,2,1]
[2,4,7,8,1,6,5,3]=>[8,7,2,5,1,3,6,4]=>[1,2,7,4,8,6,3,5]=>[3,2,1,2]
[4,2,6,8,7,1,5,3]=>[1,3,8,6,7,2,5,4]=>[8,6,1,3,2,7,4,5]=>[1,1,2,2,2]
[3,1,7,8,2,6,5,4]=>[8,7,1,5,3,6,2,4]=>[1,2,8,4,6,3,7,5]=>[3,2,2,1]
[6,1,3,8,2,7,5,4]=>[8,7,3,5,1,6,2,4]=>[1,2,6,4,8,3,7,5]=>[3,2,2,1]
[5,1,8,4,2,7,6,3]=>[4,1,8,7,5,6,2,3]=>[5,8,1,2,4,3,7,6]=>[2,3,2,1]
[8,2,6,1,7,5,4,3]=>[8,7,6,2,4,3,5,1]=>[1,2,3,7,5,6,4,8]=>[4,2,2]
[6,8,3,7,1,5,4,2]=>[8,3,1,7,5,6,4,2]=>[1,6,8,2,4,3,5,7]=>[3,2,3]
[2,7,3,8,1,6,5,4]=>[8,7,3,5,1,2,6,4]=>[1,2,6,4,8,7,3,5]=>[3,2,1,2]
[1,7,3,8,2,6,5,4]=>[8,7,3,5,2,6,1,4]=>[1,2,6,4,7,3,8,5]=>[3,2,2,1]
[2,6,8,4,1,7,5,3]=>[4,2,8,7,1,5,6,3]=>[5,7,1,2,8,4,3,6]=>[2,3,1,2]
[4,5,8,6,3,1,7,2]=>[8,1,2,6,5,4,7,3]=>[1,8,7,3,4,5,2,6]=>[2,1,3,2]
[4,6,7,1,2,8,5,3]=>[8,1,7,4,2,5,3,6]=>[1,8,2,5,7,4,6,3]=>[2,3,2,1]
[3,6,1,8,2,7,5,4]=>[8,7,1,5,2,6,3,4]=>[1,2,8,4,7,3,6,5]=>[3,2,2,1]
[5,7,4,1,2,8,6,3]=>[1,8,7,4,3,5,2,6]=>[8,1,2,5,6,4,7,3]=>[1,4,2,1]
[6,3,7,1,2,8,5,4]=>[8,2,7,4,1,5,3,6]=>[1,7,2,5,8,4,6,3]=>[2,3,2,1]
[6,2,1,8,3,7,5,4]=>[8,7,2,5,1,6,3,4]=>[1,2,7,4,8,3,6,5]=>[3,2,2,1]
[8,1,5,6,3,2,4,7]=>[6,5,3,7,2,4,8,1]=>[3,4,6,2,7,5,1,8]=>[3,2,1,2]
[1,7,8,3,5,2,4,6]=>[4,6,7,5,2,8,1,3]=>[5,3,2,4,7,1,8,6]=>[1,1,3,2,1]
[8,5,3,7,2,4,6,1]=>[3,5,2,6,8,7,4,1]=>[6,4,7,3,1,2,5,8]=>[1,2,1,4]
[1,7,2,4,8,5,3,6]=>[7,4,6,8,3,1,2,5]=>[2,5,3,1,6,8,7,4]=>[2,1,3,1,1]
[1,7,8,5,4,3,2,6]=>[7,6,5,4,2,8,1,3]=>[2,3,4,5,7,1,8,6]=>[5,2,1]
[1,2,6,7,8,4,3,5]=>[3,7,6,4,8,1,2,5]=>[6,2,3,5,1,8,7,4]=>[1,3,2,1,1]
[2,7,5,8,4,1,3,6]=>[6,3,7,5,1,2,8,4]=>[3,6,2,4,8,7,1,5]=>[2,3,1,2]
[2,1,7,8,4,5,3,6]=>[5,7,6,1,3,8,2,4]=>[4,2,3,8,6,1,7,5]=>[1,3,1,2,1]
[3,7,8,2,1,5,4,6]=>[4,7,1,5,6,2,8,3]=>[5,2,8,4,3,7,1,6]=>[1,2,1,2,2]
[8,5,1,4,7,3,6,2]=>[4,6,2,8,7,3,5,1]=>[5,3,7,1,2,6,4,8]=>[1,2,3,2]
[8,1,4,6,7,3,5,2]=>[6,3,4,8,7,2,5,1]=>[3,6,5,1,2,7,4,8]=>[2,1,3,2]
[3,5,8,6,7,4,1,2]=>[7,2,4,8,1,6,5,3]=>[2,7,5,1,8,3,4,6]=>[2,1,2,3]
[3,6,8,4,7,1,5,2]=>[4,2,8,1,6,7,5,3]=>[5,7,1,8,3,2,4,6]=>[2,2,1,3]
[4,7,1,3,6,8,2,5]=>[1,7,4,5,8,3,2,6]=>[8,2,5,4,1,6,7,3]=>[1,2,1,3,1]
[3,7,6,4,8,1,2,5]=>[6,4,7,1,3,2,8,5]=>[3,5,2,8,6,7,1,4]=>[2,2,2,2]
[3,1,7,5,6,8,2,4]=>[4,7,1,5,3,8,2,6]=>[5,2,8,4,6,1,7,3]=>[1,2,2,2,1]
[2,3,6,5,7,1,8,4]=>[4,3,8,1,2,6,5,7]=>[5,6,1,8,7,3,4,2]=>[2,2,1,2,1]
[3,7,5,4,2,1,8,6]=>[5,4,1,3,8,6,2,7]=>[4,5,8,6,1,3,7,2]=>[3,1,3,1]
[1,3,6,7,4,2,8,5]=>[5,3,8,2,6,1,4,7]=>[4,6,1,7,3,8,5,2]=>[2,2,2,1,1]
[3,6,4,8,2,7,5,1]=>[8,3,1,2,5,7,6,4]=>[1,6,8,7,4,2,3,5]=>[3,1,1,3]
[1,4,6,3,2,7,8,5]=>[2,4,6,3,8,1,5,7]=>[7,5,3,6,1,8,4,2]=>[1,1,2,2,1,1]
[8,7,1,5,6,3,2,4]=>[7,6,4,8,3,5,2,1]=>[2,3,5,1,6,4,7,8]=>[3,2,3]
[8,1,6,7,5,3,2,4]=>[7,6,3,8,5,2,4,1]=>[2,3,6,1,4,7,5,8]=>[3,3,2]
[1,7,8,6,5,3,2,4]=>[7,6,2,8,5,4,1,3]=>[2,3,7,1,4,5,8,6]=>[3,4,1]
[8,7,2,4,6,5,3,1]=>[8,4,7,3,6,5,2,1]=>[1,5,2,6,3,4,7,8]=>[2,2,4]
[1,7,8,2,6,4,5,3]=>[6,8,7,4,2,5,1,3]=>[3,1,2,5,7,4,8,6]=>[1,4,2,1]
[8,7,2,5,3,1,6,4]=>[5,8,3,6,4,7,2,1]=>[4,1,6,3,5,2,7,8]=>[1,2,2,3]
[8,7,3,2,1,5,6,4]=>[4,3,6,8,5,7,2,1]=>[5,6,3,1,4,2,7,8]=>[2,1,2,3]
[8,2,6,7,3,1,5,4]=>[5,8,6,2,3,7,4,1]=>[4,1,3,7,6,2,5,8]=>[1,3,1,3]
[1,7,2,8,5,6,4,3]=>[5,8,7,6,3,1,2,4]=>[4,1,2,3,6,8,7,5]=>[1,5,1,1]
[2,7,1,8,4,6,5,3]=>[8,5,7,6,1,3,2,4]=>[1,4,2,3,8,6,7,5]=>[2,3,2,1]
[3,7,8,2,1,6,5,4]=>[8,4,7,1,5,2,6,3]=>[1,5,2,8,4,7,3,6]=>[2,2,2,2]
[8,7,6,1,4,5,3,2]=>[5,8,7,4,6,3,2,1]=>[4,1,2,5,3,6,7,8]=>[1,3,4]
[4,8,1,2,3,7,5,6]=>[7,1,8,3,4,5,6,2]=>[2,8,1,6,5,4,3,7]=>[2,2,1,1,2]
[1,8,2,3,6,5,4,7]=>[7,6,3,4,5,8,1,2]=>[2,3,6,5,4,1,8,7]=>[3,1,1,2,1]
[3,5,8,4,7,2,6,1]=>[2,4,6,8,1,7,5,3]=>[7,5,3,1,8,2,4,6]=>[1,1,1,2,3]
[1,8,5,4,6,2,3,7]=>[6,4,3,7,5,8,1,2]=>[3,5,6,2,4,1,8,7]=>[3,2,2,1]
[3,8,5,4,6,1,2,7]=>[6,4,1,3,7,5,8,2]=>[3,5,8,6,2,4,1,7]=>[3,1,2,2]
[3,8,5,1,6,4,2,7]=>[7,6,1,4,3,5,8,2]=>[2,3,8,5,6,4,1,7]=>[3,2,1,2]
[2,8,5,4,6,1,3,7]=>[6,4,3,7,1,5,8,2]=>[3,5,6,2,8,4,1,7]=>[3,2,1,2]
[2,8,5,4,6,3,1,7]=>[4,3,7,6,1,5,8,2]=>[5,6,2,3,8,4,1,7]=>[2,3,1,2]
[1,8,5,4,6,3,2,7]=>[4,3,7,6,5,8,1,2]=>[5,6,2,3,4,1,8,7]=>[2,3,2,1]
[2,5,8,4,7,3,6,1]=>[2,4,6,8,7,1,5,3]=>[7,5,3,1,2,8,4,6]=>[1,1,1,3,2]
[3,6,4,2,7,8,5,1]=>[3,5,1,2,8,4,7,6]=>[6,4,8,7,1,5,2,3]=>[1,2,1,2,2]
[4,5,8,1,7,6,2,3]=>[1,2,7,8,6,4,5,3]=>[8,7,2,1,3,5,4,6]=>[1,1,1,3,2]
[3,5,8,4,7,1,6,2]=>[2,4,8,1,6,7,5,3]=>[7,5,1,8,3,2,4,6]=>[1,1,2,1,3]
[1,5,8,4,7,3,6,2]=>[2,4,6,8,7,5,1,3]=>[7,5,3,1,2,4,8,6]=>[1,1,1,4,1]
[3,6,4,1,7,8,5,2]=>[3,5,1,2,8,7,4,6]=>[6,4,8,7,1,2,5,3]=>[1,2,1,3,1]
[3,6,4,8,7,5,2,1]=>[2,8,7,1,3,6,5,4]=>[7,1,2,8,6,3,4,5]=>[1,3,1,3]
[1,6,4,3,7,8,5,2]=>[3,5,2,8,4,7,1,6]=>[6,4,7,1,5,2,8,3]=>[1,2,2,2,1]
[7,1,3,4,8,6,5,2]=>[8,7,3,4,6,2,1,5]=>[1,2,6,5,3,7,8,4]=>[3,1,3,1]
[7,6,1,3,8,4,2,5]=>[7,4,6,8,3,2,1,5]=>[2,5,3,1,6,7,8,4]=>[2,1,4,1]
[1,6,4,2,7,8,3,5]=>[3,7,5,2,8,1,4,6]=>[6,2,4,7,1,8,5,3]=>[1,3,2,1,1]
[2,6,4,1,7,8,3,5]=>[3,7,5,1,2,8,4,6]=>[6,2,4,8,7,1,5,3]=>[1,3,1,2,1]
[7,2,3,4,8,6,5,1]=>[8,7,2,3,4,1,6,5]=>[1,2,7,6,5,8,3,4]=>[3,1,2,2]
[7,2,3,1,8,6,4,5]=>[7,8,2,3,6,4,1,5]=>[2,1,7,6,3,5,8,4]=>[1,2,1,3,1]
[7,2,3,4,1,6,8,5]=>[2,3,4,6,8,5,1,7]=>[7,6,5,3,1,4,8,2]=>[1,1,1,1,3,1]
[7,2,8,6,3,4,1,5]=>[5,7,6,8,2,1,4,3]=>[4,2,3,1,7,8,5,6]=>[1,2,3,2]
[7,2,3,1,5,6,8,4]=>[2,3,5,6,8,4,1,7]=>[7,6,4,3,1,5,8,2]=>[1,1,1,1,3,1]
[7,2,3,8,1,6,5,4]=>[8,7,2,3,5,1,6,4]=>[1,2,7,6,4,8,3,5]=>[3,1,2,2]
[7,2,3,8,5,6,4,1]=>[5,8,7,2,3,1,6,4]=>[4,1,2,7,6,8,3,5]=>[1,3,2,2]
[2,6,4,8,7,1,5,3]=>[8,3,2,6,7,1,5,4]=>[1,6,7,3,2,8,4,5]=>[3,1,2,2]
[3,5,8,1,6,7,2,4]=>[2,7,1,5,8,4,6,3]=>[7,2,8,4,1,5,3,6]=>[1,2,1,2,2]
[7,6,1,3,5,8,2,4]=>[7,4,5,8,3,2,1,6]=>[2,5,4,1,6,7,8,3]=>[2,1,4,1]
[7,1,3,2,5,6,8,4]=>[3,5,6,8,2,4,1,7]=>[6,4,3,1,7,5,8,2]=>[1,1,1,2,2,1]
[7,1,3,8,2,6,5,4]=>[8,7,3,5,6,2,1,4]=>[1,2,6,4,3,7,8,5]=>[3,1,3,1]
[7,6,1,8,5,4,2,3]=>[7,8,6,5,3,2,1,4]=>[2,1,3,4,6,7,8,5]=>[1,6,1]
[4,1,6,5,8,2,7,3]=>[1,4,3,8,6,7,2,5]=>[8,5,6,1,3,2,7,4]=>[1,2,2,2,1]
[3,1,6,5,8,4,7,2]=>[4,1,3,6,8,7,2,5]=>[5,8,6,3,1,2,7,4]=>[2,1,1,3,1]
[3,2,6,5,8,4,7,1]=>[4,1,3,6,8,2,7,5]=>[5,8,6,3,1,7,2,4]=>[2,1,1,2,2]
[4,3,7,1,6,5,8,2]=>[1,6,2,5,8,4,3,7]=>[8,3,7,4,1,5,6,2]=>[1,2,1,3,1]
[5,2,6,4,8,3,7,1]=>[4,3,1,6,8,2,7,5]=>[5,6,8,3,1,7,2,4]=>[3,1,2,2]
[5,1,6,4,8,3,7,2]=>[4,3,1,6,8,7,2,5]=>[5,6,8,3,1,2,7,4]=>[3,1,3,1]
[5,1,6,4,8,2,7,3]=>[4,3,1,8,6,7,2,5]=>[5,6,8,1,3,2,7,4]=>[3,2,2,1]
[5,2,6,4,8,1,7,3]=>[4,3,1,8,2,6,7,5]=>[5,6,8,1,7,3,2,4]=>[3,2,1,2]
[4,3,7,5,8,1,6,2]=>[1,4,8,2,6,3,7,5]=>[8,5,1,7,3,6,2,4]=>[1,1,2,2,2]
[4,3,7,5,8,2,6,1]=>[1,4,6,2,3,8,7,5]=>[8,5,3,7,6,1,2,4]=>[1,1,2,1,3]
[5,3,7,4,8,2,6,1]=>[4,1,6,2,3,8,7,5]=>[5,8,3,7,6,1,2,4]=>[2,2,1,3]
[5,3,7,4,8,1,6,2]=>[4,1,8,2,6,3,7,5]=>[5,8,1,7,3,6,2,4]=>[2,2,2,2]
[5,4,8,1,6,2,7,3]=>[2,1,8,6,4,5,7,3]=>[7,8,1,3,5,4,2,6]=>[2,3,1,2]
[4,3,7,2,6,1,8,5]=>[1,8,2,4,6,5,3,7]=>[8,1,7,5,3,4,6,2]=>[1,2,1,3,1]
[4,3,7,1,5,2,8,6]=>[2,1,5,8,4,6,3,7]=>[7,8,4,1,5,3,6,2]=>[2,1,2,2,1]
[4,3,7,1,6,2,8,5]=>[1,8,2,6,4,5,3,7]=>[8,1,7,3,5,4,6,2]=>[1,2,2,2,1]
[5,4,8,2,6,3,7,1]=>[2,1,6,4,5,8,7,3]=>[7,8,3,5,4,1,2,6]=>[2,2,1,3]
[5,4,8,1,6,3,7,2]=>[2,1,6,5,8,4,7,3]=>[7,8,3,4,1,5,2,6]=>[2,2,2,2]
[4,1,7,8,6,3,2,5]=>[7,1,6,3,8,5,2,4]=>[2,8,3,6,1,4,7,5]=>[2,2,3,1]
[4,7,2,8,3,5,1,6]=>[1,5,7,3,6,2,8,4]=>[8,4,2,6,3,7,1,5]=>[1,1,2,2,2]
[1,2,6,8,3,7,4,5]=>[7,3,8,5,6,1,2,4]=>[2,6,1,4,3,8,7,5]=>[2,2,2,1,1]
[6,8,3,2,1,4,7,5]=>[4,3,8,5,1,6,7,2]=>[5,6,1,4,8,3,2,7]=>[2,3,1,2]
[7,2,4,1,6,5,8,3]=>[3,6,2,5,8,4,1,7]=>[6,3,7,4,1,5,8,2]=>[1,2,1,3,1]
[7,5,8,4,3,1,6,2]=>[2,8,6,5,4,1,7,3]=>[7,1,3,4,5,8,2,6]=>[1,5,2]
[6,8,2,4,1,3,7,5]=>[8,3,5,4,1,6,7,2]=>[1,6,4,5,8,3,2,7]=>[2,3,1,2]
[2,8,4,7,6,3,5,1]=>[6,8,3,7,5,1,4,2]=>[3,1,6,2,4,8,5,7]=>[1,2,3,2]
[6,1,2,7,5,8,4,3]=>[5,4,8,7,2,1,3,6]=>[4,5,1,2,7,8,6,3]=>[2,4,1,1]
[4,2,7,3,8,5,6,1]=>[1,6,8,4,2,3,7,5]=>[8,3,1,5,7,6,2,4]=>[1,1,3,1,2]
[4,5,2,6,8,3,7,1]=>[1,4,2,6,8,3,7,5]=>[8,5,7,3,1,6,2,4]=>[1,2,1,2,2]
[7,2,4,3,8,5,6,1]=>[3,6,8,2,4,1,7,5]=>[6,3,1,7,5,8,2,4]=>[1,1,2,2,2]
[6,8,5,3,4,7,2,1]=>[4,1,5,3,8,7,6,2]=>[5,8,4,6,1,2,3,7]=>[2,2,4]
[8,4,7,6,2,3,5,1]=>[2,5,6,8,7,4,3,1]=>[7,4,3,1,2,5,6,8]=>[1,1,1,5]
[6,8,4,1,5,3,7,2]=>[6,5,3,1,8,4,7,2]=>[3,4,6,8,1,5,2,7]=>[4,2,2]
[8,3,4,7,6,2,5,1]=>[6,8,2,3,7,5,4,1]=>[3,1,7,6,2,4,5,8]=>[1,2,1,4]
[1,8,3,5,2,6,7,4]=>[6,3,4,8,5,7,1,2]=>[3,6,5,1,4,2,8,7]=>[2,1,2,2,1]
[6,8,3,5,1,4,7,2]=>[3,6,1,8,5,4,7,2]=>[6,3,8,1,4,5,2,7]=>[1,2,3,2]
[6,8,5,4,2,3,7,1]=>[5,1,6,4,3,8,7,2]=>[4,8,3,5,6,1,2,7]=>[2,3,3]
[5,8,2,4,3,7,6,1]=>[4,1,8,3,5,7,6,2]=>[5,8,1,6,4,2,3,7]=>[2,2,1,3]
[8,2,1,3,5,6,4,7]=>[2,5,7,3,4,6,8,1]=>[7,4,2,6,5,3,1,8]=>[1,1,2,1,1,2]
[8,2,1,3,5,4,7,6]=>[2,5,8,3,4,6,7,1]=>[7,4,1,6,5,3,2,8]=>[1,1,2,1,1,2]
[8,2,1,3,4,6,7,5]=>[2,6,8,3,4,5,7,1]=>[7,3,1,6,5,4,2,8]=>[1,1,2,1,1,2]
[8,1,3,4,2,6,5,7]=>[3,4,7,2,5,6,8,1]=>[6,5,2,7,4,3,1,8]=>[1,1,2,1,1,2]
[8,1,3,4,2,5,7,6]=>[3,4,8,2,5,6,7,1]=>[6,5,1,7,4,3,2,8]=>[1,1,2,1,1,2]
[8,1,3,2,5,6,4,7]=>[3,5,7,2,4,6,8,1]=>[6,4,2,7,5,3,1,8]=>[1,1,2,1,1,2]
[8,1,2,4,5,3,7,6]=>[4,5,8,2,3,6,7,1]=>[5,4,1,7,6,3,2,8]=>[1,1,2,1,1,2]
[8,1,2,4,3,6,7,5]=>[4,6,8,2,3,5,7,1]=>[5,3,1,7,6,4,2,8]=>[1,1,2,1,1,2]
[6,5,3,8,4,2,7,1]=>[6,3,2,1,5,8,7,4]=>[3,6,7,8,4,1,2,5]=>[4,1,3]
[7,4,5,1,6,2,8,3]=>[2,8,6,4,3,5,1,7]=>[7,1,3,5,6,4,8,2]=>[1,4,2,1]
[6,7,8,4,1,3,5,2]=>[6,1,8,5,4,2,7,3]=>[3,8,1,4,5,7,2,6]=>[2,4,2]
[8,3,6,1,5,7,4,2]=>[5,8,2,7,4,3,6,1]=>[4,1,7,2,5,6,3,8]=>[1,2,3,2]
[3,2,7,5,8,6,1,4]=>[4,7,1,3,8,2,6,5]=>[5,2,8,6,1,7,3,4]=>[1,2,1,2,2]
[2,5,4,7,8,1,6,3]=>[2,8,3,6,1,4,7,5]=>[7,1,6,3,8,5,2,4]=>[1,2,2,1,2]
[2,4,6,7,8,1,5,3]=>[3,8,2,6,1,4,7,5]=>[6,1,7,3,8,5,2,4]=>[1,2,2,1,2]
[2,4,6,8,1,7,5,3]=>[3,8,2,7,1,5,6,4]=>[6,1,7,2,8,4,3,5]=>[1,2,2,1,2]
[2,4,7,8,3,5,6,1]=>[5,6,2,3,8,1,7,4]=>[4,3,7,6,1,8,2,5]=>[1,2,1,2,2]
[3,2,7,6,1,8,4,5]=>[7,8,1,5,2,4,3,6]=>[2,1,8,4,7,5,6,3]=>[1,2,2,2,1]
[3,2,6,8,1,7,4,5]=>[7,1,3,8,2,5,6,4]=>[2,8,6,1,7,4,3,5]=>[2,1,2,1,2]
[4,3,6,2,1,8,5,7]=>[2,1,4,7,3,8,5,6]=>[7,8,5,2,6,1,4,3]=>[2,1,2,2,1]
[3,6,4,2,5,8,1,7]=>[4,1,3,5,2,7,8,6]=>[5,8,6,4,7,2,1,3]=>[2,1,2,1,2]
[8,4,5,3,2,1,7,6]=>[2,5,4,3,8,6,7,1]=>[7,4,5,6,1,3,2,8]=>[1,3,2,2]
[5,8,3,4,2,1,7,6]=>[3,1,5,4,8,6,7,2]=>[6,8,4,5,1,3,2,7]=>[2,2,2,2]
[6,8,4,2,3,7,5,1]=>[8,4,3,1,5,7,6,2]=>[1,5,6,8,4,2,3,7]=>[4,1,3]
[6,4,8,3,2,7,1,5]=>[2,5,4,1,7,8,6,3]=>[7,4,5,8,2,1,3,6]=>[1,3,1,3]
[5,8,3,7,2,1,6,4]=>[3,1,5,8,6,7,4,2]=>[6,8,4,1,3,2,5,7]=>[2,1,2,3]
[2,5,6,4,7,1,8,3]=>[2,4,3,8,1,6,5,7]=>[7,5,6,1,8,3,4,2]=>[1,2,2,2,1]
[2,5,4,8,1,6,7,3]=>[3,2,6,8,1,5,7,4]=>[6,7,3,1,8,4,2,5]=>[2,1,2,1,2]
[6,4,7,3,8,2,1,5]=>[2,4,1,7,6,3,8,5]=>[7,5,8,2,3,6,1,4]=>[1,2,3,2]
[6,7,4,3,2,1,8,5]=>[5,4,3,1,8,6,2,7]=>[4,5,6,8,1,3,7,2]=>[4,3,1]
[1,2,6,5,8,7,3,4]=>[4,3,7,8,6,1,2,5]=>[5,6,2,1,3,8,7,4]=>[2,1,3,1,1]
[1,5,2,8,4,6,7,3]=>[5,2,6,8,7,1,3,4]=>[4,7,3,1,2,8,6,5]=>[2,1,3,1,1]
[1,5,2,7,4,6,8,3]=>[5,2,6,4,8,1,3,7]=>[4,7,3,5,1,8,6,2]=>[2,2,2,1,1]
[5,1,2,8,3,6,7,4]=>[6,8,5,1,7,2,3,4]=>[3,1,4,8,2,7,6,5]=>[1,3,2,1,1]
[5,6,3,4,8,7,2,1]=>[1,8,3,2,4,7,6,5]=>[8,1,6,7,5,2,3,4]=>[1,3,1,3]
[6,5,3,4,8,7,2,1]=>[8,3,2,1,4,7,6,5]=>[1,6,7,8,5,2,3,4]=>[4,1,3]
[4,1,2,8,3,6,7,5]=>[6,1,8,5,7,2,3,4]=>[3,8,1,4,2,7,6,5]=>[2,2,2,1,1]
[4,1,2,7,3,6,8,5]=>[6,1,8,5,2,3,4,7]=>[3,8,1,4,7,6,5,2]=>[2,3,1,1,1]
[7,5,3,8,4,6,2,1]=>[5,2,8,3,1,7,6,4]=>[4,7,1,6,8,2,3,5]=>[2,3,3]
[8,5,3,7,4,6,2,1]=>[5,2,8,3,7,6,4,1]=>[4,7,1,6,2,3,5,8]=>[2,2,4]
[7,1,2,8,3,6,4,5]=>[7,8,5,6,2,3,1,4]=>[2,1,4,3,7,6,8,5]=>[1,2,2,2,1]
[6,1,8,2,3,5,7,4]=>[6,8,4,5,1,7,2,3]=>[3,1,5,4,8,2,7,6]=>[1,2,2,2,1]
[6,1,7,2,3,5,8,4]=>[6,8,4,5,2,1,3,7]=>[3,1,5,4,7,8,6,2]=>[1,2,3,1,1]
[1,6,8,2,4,5,7,3]=>[5,6,2,8,4,7,1,3]=>[4,3,7,1,5,2,8,6]=>[1,2,2,2,1]
[4,3,8,7,5,6,2,1]=>[5,8,1,7,2,6,4,3]=>[4,1,8,2,7,3,5,6]=>[1,2,2,3]
[1,8,2,7,4,6,5,3]=>[8,5,7,6,3,4,1,2]=>[1,4,2,3,6,5,8,7]=>[2,3,2,1]
[7,1,6,2,3,5,8,4]=>[6,8,4,5,2,3,1,7]=>[3,1,5,4,7,6,8,2]=>[1,2,2,2,1]
[8,1,6,2,3,5,7,4]=>[6,8,4,5,2,3,7,1]=>[3,1,5,4,7,6,2,8]=>[1,2,2,1,2]
[8,1,7,2,3,5,6,4]=>[6,8,4,5,7,2,3,1]=>[3,1,5,4,2,7,6,8]=>[1,2,1,2,2]
[5,8,3,7,4,6,2,1]=>[1,5,8,3,7,6,4,2]=>[8,4,1,6,2,3,5,7]=>[1,1,2,4]
[6,8,7,3,4,5,2,1]=>[4,1,5,8,7,6,3,2]=>[5,8,4,1,2,3,6,7]=>[2,1,5]
[1,8,7,2,4,5,3,6]=>[5,7,4,6,8,3,1,2]=>[4,2,5,3,1,6,8,7]=>[1,2,1,3,1]
[8,7,1,2,3,4,6,5]=>[8,3,4,5,6,7,2,1]=>[1,6,5,4,3,2,7,8]=>[2,1,1,1,3]
[8,6,1,2,3,4,7,5]=>[8,3,4,5,6,2,7,1]=>[1,6,5,4,3,7,2,8]=>[2,1,1,2,2]
[8,1,6,2,3,5,4,7]=>[7,4,5,6,2,3,8,1]=>[2,5,4,3,7,6,1,8]=>[2,1,2,1,2]
[1,7,6,2,4,5,3,8]=>[5,7,4,6,3,1,2,8]=>[4,2,5,3,6,8,7,1]=>[1,2,3,1,1]
[1,8,7,4,6,3,5,2]=>[4,6,8,7,5,3,1,2]=>[5,3,1,2,4,6,8,7]=>[1,1,5,1]
[6,3,7,5,1,4,8,2]=>[6,8,2,1,5,4,3,7]=>[3,1,7,8,4,5,6,2]=>[1,3,3,1]
[4,2,5,8,7,3,6,1]=>[1,6,8,3,7,2,5,4]=>[8,3,1,6,2,7,4,5]=>[1,1,2,2,2]
[1,8,3,5,7,2,6,4]=>[4,8,3,6,7,5,1,2]=>[5,1,6,3,2,4,8,7]=>[1,2,1,3,1]
[2,3,4,6,8,5,7,1]=>[4,6,8,1,2,3,7,5]=>[5,3,1,8,7,6,2,4]=>[1,1,2,1,1,2]
[2,3,5,7,4,8,6,1]=>[8,3,5,1,2,4,7,6]=>[1,6,4,8,7,5,2,3]=>[2,2,1,1,2]
[2,4,6,3,7,8,5,1]=>[5,2,3,8,1,4,7,6]=>[4,7,6,1,8,5,2,3]=>[2,1,2,1,2]
[8,2,4,5,1,3,7,6]=>[3,8,2,5,4,6,7,1]=>[6,1,7,4,5,3,2,8]=>[1,2,2,1,2]
[1,3,8,5,2,4,6,7]=>[5,6,2,4,7,8,1,3]=>[4,3,7,5,2,1,8,6]=>[1,2,1,1,2,1]
[2,6,7,1,8,4,5,3]=>[6,2,8,7,1,4,3,5]=>[3,7,1,2,8,5,6,4]=>[2,3,2,1]
[5,8,3,1,4,2,6,7]=>[6,4,3,1,5,7,8,2]=>[3,5,6,8,4,2,1,7]=>[4,1,1,2]
[3,8,4,2,6,7,1,5]=>[3,7,1,4,5,8,6,2]=>[6,2,8,5,4,1,3,7]=>[1,2,1,1,3]
[2,4,1,8,5,6,3,7]=>[2,5,7,1,6,8,3,4]=>[7,4,2,8,3,1,6,5]=>[1,1,2,1,2,1]
[1,6,2,7,8,5,3,4]=>[7,4,2,8,6,1,3,5]=>[2,5,7,1,3,8,6,4]=>[3,3,1,1]
[3,5,2,6,7,8,4,1]=>[4,1,2,5,8,3,7,6]=>[5,8,7,4,1,6,2,3]=>[2,1,1,2,2]
[4,5,1,6,7,3,8,2]=>[1,4,2,6,5,8,3,7]=>[8,5,7,3,4,1,6,2]=>[1,2,2,2,1]
[2,8,4,1,7,5,3,6]=>[3,7,6,8,1,4,5,2]=>[6,2,3,1,8,5,4,7]=>[1,2,2,1,2]
[8,5,3,1,7,4,2,6]=>[3,7,6,2,8,4,5,1]=>[6,2,3,7,1,5,4,8]=>[1,3,2,2]
[4,2,8,7,1,5,3,6]=>[1,7,5,6,8,2,4,3]=>[8,2,4,3,1,7,5,6]=>[1,2,1,2,2]
[5,2,6,8,1,7,4,3]=>[3,1,8,7,2,5,6,4]=>[6,8,1,2,7,4,3,5]=>[2,3,1,2]
[5,7,3,2,6,8,1,4]=>[3,1,7,4,5,2,8,6]=>[6,8,2,5,4,7,1,3]=>[2,2,2,2]
[8,4,7,3,1,6,2,5]=>[2,7,4,8,5,6,3,1]=>[7,2,5,1,4,3,6,8]=>[1,2,2,3]
[6,7,1,2,3,5,8,4]=>[6,8,3,4,1,5,2,7]=>[3,1,6,5,8,4,7,2]=>[1,2,2,2,1]
[3,1,6,7,8,4,2,5]=>[3,7,1,6,4,8,2,5]=>[6,2,8,3,5,1,7,4]=>[1,2,2,2,1]
[3,1,4,8,5,6,2,7]=>[1,5,7,3,6,8,2,4]=>[8,4,2,6,3,1,7,5]=>[1,1,2,1,2,1]
[8,3,1,4,5,7,2,6]=>[4,2,5,7,8,3,6,1]=>[5,7,4,2,1,6,3,8]=>[2,1,1,2,2]
[5,6,7,8,9,1,2,3,4,10]=>[1,6,2,7,3,8,4,9,5,10]=>[10,5,9,4,8,3,7,2,6,1]=>[1,2,2,2,2,1]
[8,6,2,3,5,1,4,7]=>[3,4,6,7,5,2,8,1]=>[6,5,3,2,4,7,1,8]=>[1,1,1,3,2]
[8,2,4,5,7,3,1,6]=>[3,4,7,2,6,8,5,1]=>[6,5,2,7,3,1,4,8]=>[1,1,2,1,3]
[2,6,3,8,7,5,4,1]=>[2,8,7,6,1,3,5,4]=>[7,1,2,3,8,6,4,5]=>[1,4,1,2]
[8,2,3,7,5,4,1,6]=>[7,6,2,3,5,8,4,1]=>[2,3,7,6,4,1,5,8]=>[3,1,1,3]
[8,2,6,3,5,4,1,7]=>[7,4,6,2,5,3,8,1]=>[2,5,3,7,4,6,1,8]=>[2,2,2,2]
[8,6,1,5,2,4,3,7]=>[7,5,6,3,4,2,8,1]=>[2,4,3,6,5,7,1,8]=>[2,2,2,2]
[8,4,1,6,5,3,2,7]=>[2,7,6,5,3,4,8,1]=>[7,2,3,4,6,5,1,8]=>[1,4,1,2]
[8,3,6,1,5,4,2,7]=>[7,2,6,4,5,3,8,1]=>[2,7,3,5,4,6,1,8]=>[2,2,2,2]
[8,3,2,6,5,4,1,7]=>[7,2,6,3,5,4,8,1]=>[2,7,3,6,4,5,1,8]=>[2,2,2,2]
[8,3,2,5,7,4,1,6]=>[2,4,7,3,6,8,5,1]=>[7,5,2,6,3,1,4,8]=>[1,1,2,1,3]
[6,1,3,8,7,5,4,2]=>[8,7,6,3,1,5,2,4]=>[1,2,3,6,8,4,7,5]=>[5,2,1]
[3,6,1,8,7,5,4,2]=>[2,8,7,1,6,5,3,4]=>[7,1,2,8,3,4,6,5]=>[1,3,3,1]
[3,8,1,5,7,6,4,2]=>[8,4,7,1,6,3,5,2]=>[1,5,2,8,3,6,4,7]=>[2,2,2,2]
[3,5,2,8,7,6,4,1]=>[8,2,7,1,6,3,5,4]=>[1,7,2,8,3,6,4,5]=>[2,2,2,2]
[3,4,8,2,7,6,5,1]=>[8,7,1,2,4,6,5,3]=>[1,2,8,7,5,3,4,6]=>[3,1,1,3]
[3,4,8,7,1,6,5,2]=>[8,7,1,2,5,6,4,3]=>[1,2,8,7,4,3,5,6]=>[3,1,1,3]
[8,1,3,5,7,6,4,2]=>[8,4,7,3,6,2,5,1]=>[1,5,2,6,3,7,4,8]=>[2,2,2,2]
[4,1,8,5,7,6,3,2]=>[8,1,4,7,6,5,2,3]=>[1,8,5,2,3,4,7,6]=>[2,1,4,1]
[8,1,7,3,4,6,2,5]=>[4,5,7,8,6,2,3,1]=>[5,4,2,1,3,7,6,8]=>[1,1,1,3,2]
[8,3,1,7,2,6,5,4]=>[8,2,7,5,6,3,4,1]=>[1,7,2,4,3,6,5,8]=>[2,2,2,2]
[3,8,2,4,7,6,5,1]=>[8,7,1,3,4,6,5,2]=>[1,2,8,6,5,3,4,7]=>[3,1,1,3]
[2,8,3,7,4,6,5,1]=>[8,5,7,3,6,1,4,2]=>[1,4,2,6,3,8,5,7]=>[2,2,2,2]
[8,2,3,7,1,6,5,4]=>[8,7,2,3,5,6,4,1]=>[1,2,7,6,4,3,5,8]=>[3,1,1,3]
[8,2,7,1,3,6,5,4]=>[8,7,2,4,5,6,3,1]=>[1,2,7,5,4,3,6,8]=>[3,1,1,3]
[8,1,7,2,6,4,3,5]=>[7,6,8,4,5,2,3,1]=>[2,3,1,5,4,7,6,8]=>[2,2,2,2]
[8,1,7,5,2,4,3,6]=>[7,5,6,4,8,2,3,1]=>[2,4,3,5,1,7,6,8]=>[2,2,2,2]
[2,4,8,5,7,6,3,1]=>[8,4,7,2,6,1,5,3]=>[1,5,2,7,3,8,4,6]=>[2,2,2,2]
[8,2,4,3,7,6,1,5]=>[3,7,8,2,4,6,5,1]=>[6,2,1,7,5,3,4,8]=>[1,1,2,1,3]
[8,2,7,3,5,1,4,6]=>[4,6,7,2,5,8,3,1]=>[5,3,2,7,4,1,6,8]=>[1,1,2,1,3]
[8,2,7,3,1,5,6,4]=>[4,6,8,2,5,7,3,1]=>[5,3,1,7,4,2,6,8]=>[1,1,2,1,3]
[8,2,1,5,7,6,4,3]=>[8,4,7,2,6,3,5,1]=>[1,5,2,7,3,6,4,8]=>[2,2,2,2]
[6,2,1,8,7,5,4,3]=>[8,7,6,2,1,5,3,4]=>[1,2,3,7,8,4,6,5]=>[5,2,1]
[6,1,8,2,7,5,4,3]=>[8,7,6,4,1,5,2,3]=>[1,2,3,5,8,4,7,6]=>[5,2,1]
[8,1,7,3,5,2,6,4]=>[8,4,6,5,7,2,3,1]=>[1,5,3,4,2,7,6,8]=>[2,2,2,2]
[8,1,5,2,7,6,4,3]=>[3,8,7,6,2,4,5,1]=>[6,1,2,3,7,5,4,8]=>[1,4,1,2]
[8,1,7,2,4,6,5,3]=>[8,5,7,4,6,2,3,1]=>[1,4,2,5,3,7,6,8]=>[2,2,2,2]
[8,2,4,1,7,6,5,3]=>[8,3,7,2,6,4,5,1]=>[1,6,2,7,3,5,4,8]=>[2,2,2,2]
[4,2,8,3,7,6,5,1]=>[8,1,7,4,6,2,5,3]=>[1,8,2,5,3,7,4,6]=>[2,2,2,2]
[4,8,2,1,7,6,5,3]=>[8,1,7,3,6,4,5,2]=>[1,8,2,6,3,5,4,7]=>[2,2,2,2]
[5,1,8,7,2,6,4,3]=>[1,8,7,5,6,4,2,3]=>[8,1,2,4,3,5,7,6]=>[1,3,3,1]
[8,2,5,4,1,7,6,3]=>[4,3,8,2,7,5,6,1]=>[5,6,1,7,2,4,3,8]=>[2,2,2,2]
[8,1,4,3,7,6,5,2]=>[8,3,7,4,6,2,5,1]=>[1,6,2,5,3,7,4,8]=>[2,2,2,2]
[4,8,1,3,7,6,5,2]=>[8,1,7,4,6,3,5,2]=>[1,8,2,5,3,6,4,7]=>[2,2,2,2]
[4,3,8,1,7,6,5,2]=>[8,1,7,2,6,4,5,3]=>[1,8,2,7,3,5,4,6]=>[2,2,2,2]
[5,7,6,3,2,4,1,8]=>[1,5,4,7,6,3,2,8]=>[8,4,5,2,3,6,7,1]=>[1,2,4,1]
[6,5,7,2,4,3,1,8]=>[7,4,2,1,6,5,3,8]=>[2,5,7,8,3,4,6,1]=>[4,3,1]
[5,7,1,3,2,8,6,4]=>[8,4,1,7,3,5,2,6]=>[1,5,8,2,6,4,7,3]=>[3,2,2,1]
[5,8,1,3,2,7,4,6]=>[4,7,1,8,3,5,6,2]=>[5,2,8,1,6,4,3,7]=>[1,2,2,1,2]
[8,5,1,3,2,4,6,7]=>[5,3,4,6,2,7,8,1]=>[4,6,5,3,7,2,1,8]=>[2,1,2,1,2]
[7,5,1,3,2,4,8,6]=>[4,8,3,5,2,6,1,7]=>[5,1,6,4,7,3,8,2]=>[1,2,2,2,1]
[6,7,1,2,5,4,8,3]=>[6,5,8,3,1,4,2,7]=>[3,4,1,6,8,5,7,2]=>[2,3,2,1]
[6,8,1,2,5,7,4,3]=>[5,8,7,3,1,4,6,2]=>[4,1,2,6,8,5,3,7]=>[1,4,1,2]
[7,1,2,3,8,6,4,5]=>[7,8,6,2,3,4,1,5]=>[2,1,3,7,6,5,8,4]=>[1,3,1,2,1]
[8,1,6,4,2,3,5,7]=>[5,6,4,7,2,3,8,1]=>[4,3,5,2,7,6,1,8]=>[1,2,2,1,2]
[1,5,4,8,2,3,7,6]=>[3,2,8,5,6,7,1,4]=>[6,7,1,4,3,2,8,5]=>[2,2,1,2,1]
[1,7,8,2,3,5,6,4]=>[6,8,4,5,2,7,1,3]=>[3,1,5,4,7,2,8,6]=>[1,2,2,2,1]
[7,5,8,2,3,1,4,6]=>[4,6,5,2,7,1,8,3]=>[5,3,4,7,2,8,1,6]=>[1,3,2,2]
[7,4,1,2,6,8,3,5]=>[7,5,2,8,3,4,1,6]=>[2,4,7,1,6,5,8,3]=>[3,2,2,1]
[7,2,5,4,1,8,6,3]=>[4,3,8,2,7,5,1,6]=>[5,6,1,7,2,4,8,3]=>[2,2,3,1]
[7,3,5,4,2,1,8,6]=>[5,2,4,3,8,6,1,7]=>[4,7,5,6,1,3,8,2]=>[2,2,3,1]
[7,3,2,8,5,6,1,4]=>[7,2,5,8,3,1,6,4]=>[2,7,4,1,6,8,3,5]=>[2,1,3,2]
[1,7,4,3,6,8,5,2]=>[3,5,8,4,2,7,1,6]=>[6,4,1,5,7,2,8,3]=>[1,1,3,2,1]
[4,7,6,5,2,3,8,1]=>[5,6,1,4,3,2,8,7]=>[4,3,8,5,6,7,1,2]=>[1,2,3,2]
[4,7,6,5,1,3,8,2]=>[6,8,1,5,4,3,2,7]=>[3,1,8,4,5,6,7,2]=>[1,2,4,1]
[5,4,6,8,7,2,1,3]=>[2,1,3,7,6,8,5,4]=>[7,8,6,2,3,1,4,5]=>[2,1,2,3]
[6,7,4,2,1,8,5,3]=>[8,4,3,1,7,5,2,6]=>[1,5,6,8,2,4,7,3]=>[4,3,1]
[6,7,3,2,1,8,5,4]=>[3,8,4,1,7,5,2,6]=>[6,1,5,8,2,4,7,3]=>[1,3,3,1]
[1,7,6,3,2,8,4,5]=>[4,7,8,5,3,1,2,6]=>[5,2,1,4,6,8,7,3]=>[1,1,4,1,1]
[5,4,2,1,7,3,6,8]=>[3,6,2,1,7,4,5,8]=>[6,3,7,8,2,5,4,1]=>[1,3,2,1,1]
[6,5,8,1,7,3,4,2]=>[6,2,1,8,7,4,5,3]=>[3,7,8,1,2,5,4,6]=>[3,3,2]
[6,5,8,2,3,7,4,1]=>[8,4,2,1,5,7,6,3]=>[1,5,7,8,4,2,3,6]=>[4,1,3]
[6,5,8,3,4,1,7,2]=>[4,2,1,8,6,5,7,3]=>[5,7,8,1,3,4,2,6]=>[3,3,2]
[4,1,2,8,5,3,6,7]=>[6,5,1,7,8,2,3,4]=>[3,4,8,2,1,7,6,5]=>[3,1,2,1,1]
[3,7,4,1,6,5,2,8]=>[3,7,1,6,4,5,2,8]=>[6,2,8,3,5,4,7,1]=>[1,2,2,2,1]
[3,5,8,2,6,1,7,4]=>[2,8,1,4,6,5,7,3]=>[7,1,8,5,3,4,2,6]=>[1,2,1,2,2]
[1,7,6,2,5,8,4,3]=>[5,8,7,4,3,1,2,6]=>[4,1,2,5,6,8,7,3]=>[1,5,1,1]
[1,7,6,5,8,4,2,3]=>[7,4,3,2,8,6,1,5]=>[2,5,6,7,1,3,8,4]=>[4,3,1]
[3,7,6,2,8,4,5,1]=>[6,8,4,1,3,2,7,5]=>[3,1,5,8,6,7,2,4]=>[1,3,2,2]
[2,7,1,5,8,4,3,6]=>[4,7,6,8,1,3,2,5]=>[5,2,3,1,8,6,7,4]=>[1,2,2,2,1]
[2,7,6,1,8,4,3,5]=>[7,6,8,4,1,3,2,5]=>[2,3,1,5,8,6,7,4]=>[2,3,2,1]
[7,2,6,3,4,5,1,8]=>[4,5,7,2,6,3,1,8]=>[5,4,2,7,3,6,8,1]=>[1,1,2,3,1]
[6,7,8,4,2,5,3,1]=>[1,8,5,4,2,7,6,3]=>[8,1,4,5,7,2,3,6]=>[1,4,3]
[4,1,2,7,8,5,3,6]=>[1,7,6,4,8,2,3,5]=>[8,2,3,5,1,7,6,4]=>[1,3,2,1,1]
[3,7,6,1,5,8,2,4]=>[7,5,8,1,4,3,2,6]=>[2,4,1,8,5,6,7,3]=>[2,2,3,1]
[3,8,5,6,4,2,7,1]=>[3,6,5,1,4,8,7,2]=>[6,3,4,8,5,1,2,7]=>[1,3,1,3]
[3,2,6,4,7,8,5,1]=>[5,1,3,8,2,4,7,6]=>[4,8,6,1,7,5,2,3]=>[2,1,2,1,2]
[4,2,7,5,8,3,1,6]=>[1,4,7,6,2,3,8,5]=>[8,5,2,3,7,6,1,4]=>[1,1,3,1,2]
[4,2,7,1,3,8,6,5]=>[1,8,7,2,4,5,3,6]=>[8,1,2,7,5,4,6,3]=>[1,3,1,2,1]
[5,2,1,4,7,8,3,6]=>[7,2,4,1,5,8,3,6]=>[2,7,5,8,4,1,6,3]=>[2,2,1,2,1]
[6,1,3,8,5,4,7,2]=>[6,5,8,3,1,7,2,4]=>[3,4,1,6,8,2,7,5]=>[2,3,2,1]
[2,7,6,8,5,1,3,4]=>[6,7,3,2,8,1,5,4]=>[3,2,6,7,1,8,4,5]=>[1,3,2,2]
[2,7,6,8,5,3,1,4]=>[7,6,3,2,8,1,5,4]=>[2,3,6,7,1,8,4,5]=>[4,2,2]
[1,5,8,6,4,2,3,7]=>[2,6,7,5,4,8,1,3]=>[7,3,2,4,5,1,8,6]=>[1,1,3,2,1]
[2,5,8,6,4,1,7,3]=>[8,2,6,5,1,4,7,3]=>[1,7,3,4,8,5,2,6]=>[2,3,1,2]
[2,4,6,1,5,7,3,8]=>[2,5,7,1,4,3,6,8]=>[7,4,2,8,5,6,3,1]=>[1,1,2,2,1,1]
[1,6,2,3,5,8,7,4]=>[8,5,7,3,1,2,4,6]=>[1,4,2,6,8,7,5,3]=>[2,3,1,1,1]
[4,7,2,3,1,6,8,5]=>[3,1,4,6,8,5,2,7]=>[6,8,5,3,1,4,7,2]=>[2,1,1,3,1]
[6,7,3,1,5,4,8,2]=>[3,6,5,1,8,4,2,7]=>[6,3,4,8,1,5,7,2]=>[1,3,3,1]
[7,4,6,2,8,3,5,1]=>[2,6,8,4,3,1,7,5]=>[7,3,1,5,6,8,2,4]=>[1,1,4,2]
[7,3,5,1,4,8,2,6]=>[2,5,7,3,8,4,1,6]=>[7,4,2,6,1,5,8,3]=>[1,1,2,3,1]
[3,4,6,5,1,2,7,8]=>[1,2,5,6,4,3,7,8]=>[8,7,4,3,5,6,2,1]=>[1,1,1,3,1,1]
[7,5,4,3,8,6,2,1]=>[3,2,8,4,1,7,6,5]=>[6,7,1,5,8,2,3,4]=>[2,3,3]
[4,3,8,2,6,7,5,1]=>[1,5,8,2,4,7,6,3]=>[8,4,1,7,5,2,3,6]=>[1,1,2,1,3]
[4,3,8,2,5,7,1,6]=>[2,1,4,5,7,8,6,3]=>[7,8,5,4,2,1,3,6]=>[2,1,1,1,3]
[4,1,6,2,5,3,7,8]=>[6,4,1,5,2,3,7,8]=>[3,5,8,4,7,6,2,1]=>[3,2,1,1,1]
[5,1,8,6,4,7,2,3]=>[1,7,5,4,8,6,2,3]=>[8,2,4,5,1,3,7,6]=>[1,3,3,1]
[4,1,8,5,6,3,7,2]=>[1,4,6,5,8,7,2,3]=>[8,5,3,4,1,2,7,6]=>[1,1,2,3,1]
[4,2,6,1,5,3,8,7]=>[5,1,8,2,4,3,6,7]=>[4,8,1,7,5,6,3,2]=>[2,2,2,1,1]
[6,7,2,3,1,5,8,4]=>[3,4,6,1,8,5,2,7]=>[6,5,3,8,1,4,7,2]=>[1,1,2,3,1]
[7,5,2,3,8,1,6,4]=>[8,3,4,2,6,1,7,5]=>[1,6,5,7,3,8,2,4]=>[2,2,2,2]
[7,5,2,3,8,4,1,6]=>[7,3,4,2,6,1,8,5]=>[2,6,5,7,3,8,1,4]=>[2,2,2,2]
[4,5,1,7,6,3,8,2]=>[1,2,6,5,4,8,3,7]=>[8,7,3,4,5,1,6,2]=>[1,1,3,2,1]
[8,1,7,5,2,3,4,6]=>[5,6,7,4,8,2,3,1]=>[4,3,2,5,1,7,6,8]=>[1,1,2,2,2]
[8,6,3,1,4,2,5,7]=>[6,4,3,5,7,2,8,1]=>[3,5,6,4,2,7,1,8]=>[3,1,2,2]
[4,8,3,6,1,7,2,5]=>[1,3,7,8,5,4,6,2]=>[8,6,2,1,4,5,3,7]=>[1,1,1,3,2]
[9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,9,8,1]=>[8,7,6,5,4,3,1,2,9]=>[1,1,1,1,1,1,3]
[8,2,3,4,5,6,7,1,9]=>[2,3,4,5,6,8,7,1,9]=>[8,7,6,5,4,2,3,9,1]=>[1,1,1,1,1,3,1]
[7,2,3,4,5,6,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>[8,7,6,5,3,4,9,2,1]=>[1,1,1,1,3,1,1]
[6,2,3,4,5,1,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>[8,7,6,4,5,9,3,2,1]=>[1,1,1,3,1,1,1]
[5,2,3,4,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[8,7,5,6,9,4,3,2,1]=>[1,1,3,1,1,1,1]
[4,2,3,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[8,6,7,9,5,4,3,2,1]=>[1,3,1,1,1,1,1]
[1,2,4,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[6,9,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]
[1,2,4,6,8,9,7,5,3]=>[5,9,4,8,3,7,1,2,6]=>[5,1,6,2,7,3,9,8,4]=>[1,2,2,2,1,1]
[1,2,4,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[7,10,9,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,2,4,6,8,10,9,7,5,3]=>[10,5,9,4,8,3,7,1,2,6]=>[1,6,2,7,3,8,4,10,9,5]=>[2,2,2,2,1,1]
[1,2,4,6,8,5,7,3]=>[4,6,8,3,7,1,2,5]=>[5,3,1,6,2,8,7,4]=>[1,1,2,2,1,1]
[2,1,7,5,8,6,3,4]=>[4,7,3,8,1,6,2,5]=>[5,2,6,1,8,3,7,4]=>[1,2,2,2,1]
[4,7,3,8,6,5,2,1]=>[8,7,1,3,2,6,5,4]=>[1,2,8,6,7,3,4,5]=>[3,2,3]
[3,8,7,4,6,5,1,2]=>[4,7,8,6,1,5,3,2]=>[5,2,1,3,8,4,6,7]=>[1,1,3,3]
[7,3,8,4,6,5,1,2]=>[4,7,8,2,1,6,5,3]=>[5,2,1,7,8,3,4,6]=>[1,1,3,3]
[7,4,3,6,5,8,1,2]=>[2,7,3,5,4,1,8,6]=>[7,2,6,4,5,8,1,3]=>[1,2,3,2]
[4,5,8,7,2,6,1,3]=>[1,2,5,7,8,6,4,3]=>[8,7,4,2,1,3,5,6]=>[1,1,1,1,4]
[3,8,6,7,5,1,4,2]=>[8,6,3,7,1,5,4,2]=>[1,3,6,2,8,4,5,7]=>[3,2,3]
[4,6,7,8,5,2,3,1]=>[2,6,1,3,8,7,5,4]=>[7,3,8,6,1,2,4,5]=>[1,2,1,4]
[4,5,3,8,2,7,6,1]=>[1,2,8,3,5,7,6,4]=>[8,7,1,6,4,2,3,5]=>[1,1,2,1,3]
[6,4,7,2,5,8,3,1]=>[2,5,1,8,4,3,7,6]=>[7,4,8,1,5,6,2,3]=>[1,2,3,2]
[6,3,8,7,5,1,4,2]=>[8,6,1,7,2,5,4,3]=>[1,3,8,2,7,4,5,6]=>[3,2,3]
[5,3,6,4,1,2,8,7]=>[8,2,1,5,4,3,6,7]=>[1,7,8,4,5,6,3,2]=>[3,3,1,1]
[6,8,4,3,5,7,1,2]=>[4,3,1,7,5,8,6,2]=>[5,6,8,2,4,1,3,7]=>[3,2,3]
[5,2,4,8,7,6,1,3]=>[7,1,8,3,6,2,5,4]=>[2,8,1,6,3,7,4,5]=>[2,2,2,2]
[3,2,4,5,1,8,6,7]=>[2,1,3,4,7,8,5,6]=>[7,8,6,5,2,1,4,3]=>[2,1,1,1,2,1]
[4,2,5,1,7,8,3,6]=>[3,1,7,2,5,8,4,6]=>[6,8,2,7,4,1,5,3]=>[2,2,1,2,1]
[2,5,4,1,3,8,6,7]=>[7,3,1,2,8,4,5,6]=>[2,6,8,7,1,5,4,3]=>[3,1,2,1,1]
[1,4,5,3,8,2,6,7]=>[2,4,3,6,7,8,1,5]=>[7,5,6,3,2,1,8,4]=>[1,2,1,1,2,1]
[5,1,8,2,4,3,6,7]=>[6,4,5,1,7,8,2,3]=>[3,5,4,8,2,1,7,6]=>[2,2,1,2,1]
[1,5,4,8,2,3,6,7]=>[5,3,2,6,7,8,1,4]=>[4,6,7,3,2,1,8,5]=>[3,1,1,2,1]
[3,5,1,4,7,8,2,6]=>[7,1,4,2,5,8,3,6]=>[2,8,5,7,4,1,6,3]=>[2,2,1,2,1]
[4,8,3,1,6,7,2,5]=>[1,3,7,5,8,4,6,2]=>[8,6,2,4,1,5,3,7]=>[1,1,2,2,2]
[3,4,8,2,6,5,7,1]=>[6,1,2,4,5,8,7,3]=>[3,8,7,5,4,1,2,6]=>[2,1,1,1,3]
[3,6,2,4,8,7,1,5]=>[7,8,1,3,2,4,6,5]=>[2,1,8,6,7,5,3,4]=>[1,2,2,1,2]
[4,7,3,2,6,8,1,5]=>[1,3,7,4,5,2,8,6]=>[8,6,2,5,4,7,1,3]=>[1,1,2,2,2]
[7,3,4,6,8,1,2,5]=>[2,3,6,7,4,1,8,5]=>[7,6,3,2,5,8,1,4]=>[1,1,1,3,2]
[3,6,7,2,5,8,1,4]=>[7,4,1,2,5,3,8,6]=>[2,5,8,7,4,6,1,3]=>[3,1,2,2]
[1,5,6,8,3,7,2,4]=>[2,5,3,7,8,6,1,4]=>[7,4,6,2,1,3,8,5]=>[1,2,1,3,1]
[6,1,5,8,3,4,7,2]=>[5,3,6,1,8,7,2,4]=>[4,6,3,8,1,2,7,5]=>[2,2,3,1]
[5,6,8,1,3,4,7,2]=>[5,1,6,2,8,4,7,3]=>[4,8,3,7,1,5,2,6]=>[2,2,2,2]
[2,8,5,6,3,4,7,1]=>[5,3,6,4,8,1,7,2]=>[4,6,3,5,1,8,2,7]=>[2,2,2,2]
[6,8,1,3,5,4,7,2]=>[6,4,5,1,8,3,7,2]=>[3,5,4,8,1,6,2,7]=>[2,2,2,2]
[8,1,6,3,5,4,7,2]=>[6,4,5,3,8,2,7,1]=>[3,5,4,6,1,7,2,8]=>[2,2,2,2]
[1,8,7,3,6,4,5,2]=>[6,8,4,7,5,3,1,2]=>[3,1,5,2,4,6,8,7]=>[1,2,4,1]
[7,1,2,5,8,4,6,3]=>[4,6,8,7,2,3,1,5]=>[5,3,1,2,7,6,8,4]=>[1,1,3,2,1]
[6,2,4,8,1,7,3,5]=>[3,7,8,2,1,5,6,4]=>[6,2,1,7,8,4,3,5]=>[1,1,3,1,2]
[1,6,2,7,4,8,5,3]=>[8,5,4,2,7,1,3,6]=>[1,4,5,7,2,8,6,3]=>[4,2,1,1]
[2,7,1,8,4,3,5,6]=>[6,5,7,8,1,3,2,4]=>[3,4,2,1,8,6,7,5]=>[2,1,2,2,1]
[6,7,1,8,3,2,4,5]=>[6,5,7,1,8,3,2,4]=>[3,4,2,8,1,6,7,5]=>[2,2,3,1]
[2,7,6,3,5,8,1,4]=>[7,4,5,3,1,2,8,6]=>[2,5,4,6,8,7,1,3]=>[2,3,1,2]
[2,7,5,6,8,1,3,4]=>[6,3,7,4,1,2,8,5]=>[3,6,2,5,8,7,1,4]=>[2,3,1,2]
[6,7,2,8,1,3,4,5]=>[3,5,6,1,7,2,8,4]=>[6,4,3,8,2,7,1,5]=>[1,1,2,2,2]
[1,5,7,6,8,2,3,4]=>[2,6,7,4,3,8,1,5]=>[7,3,2,5,6,1,8,4]=>[1,1,3,2,1]
[7,4,6,8,5,3,1,2]=>[7,2,3,1,8,6,5,4]=>[2,7,6,8,1,3,4,5]=>[2,2,4]
[2,1,5,7,8,3,6,4]=>[8,3,6,1,4,7,2,5]=>[1,6,3,8,5,2,7,4]=>[2,2,1,2,1]
[3,8,6,7,5,1,2,4]=>[6,7,3,8,1,5,4,2]=>[3,2,6,1,8,4,5,7]=>[1,2,2,3]
[4,7,5,8,6,3,1,2]=>[3,7,1,2,8,6,5,4]=>[6,2,8,7,1,3,4,5]=>[1,2,1,4]
[7,8,5,1,3,2,6,4]=>[5,8,4,6,3,1,7,2]=>[4,1,5,3,6,8,2,7]=>[1,2,3,2]
[1,5,4,7,6,2,8,3]=>[2,8,3,6,5,1,4,7]=>[7,1,6,3,4,8,5,2]=>[1,2,3,1,1]
[2,3,7,6,5,1,8,4]=>[8,6,5,1,2,4,3,7]=>[1,3,4,8,7,5,6,2]=>[4,1,2,1]
[6,1,5,8,3,2,7,4]=>[5,3,8,6,1,7,2,4]=>[4,6,1,3,8,2,7,5]=>[2,3,2,1]
[2,5,8,4,6,3,1,7]=>[2,4,7,6,1,5,8,3]=>[7,5,2,3,8,4,1,6]=>[1,1,3,1,2]
[7,1,5,4,8,3,2,6]=>[4,3,7,6,8,2,1,5]=>[5,6,2,3,1,7,8,4]=>[2,2,3,1]
[6,4,1,7,5,3,2,8]=>[2,7,6,5,3,1,4,8]=>[7,2,3,4,6,8,5,1]=>[1,5,1,1]
[7,2,5,4,8,1,6,3]=>[4,3,8,2,6,1,7,5]=>[5,6,1,7,3,8,2,4]=>[2,2,2,2]
[1,7,2,5,3,8,6,4]=>[4,8,7,3,5,1,2,6]=>[5,1,2,6,4,8,7,3]=>[1,3,2,1,1]
[7,2,3,8,6,1,5,4]=>[8,6,7,2,3,1,5,4]=>[1,3,2,7,6,8,4,5]=>[2,2,2,2]
[7,3,2,5,8,1,6,4]=>[2,4,8,3,6,1,7,5]=>[7,5,1,6,3,8,2,4]=>[1,1,2,2,2]
[5,3,8,4,1,2,6,7]=>[2,5,1,6,4,7,8,3]=>[7,4,8,3,5,2,1,6]=>[1,2,2,1,2]
[2,4,8,3,7,1,5,6]=>[2,4,6,7,8,1,5,3]=>[7,5,3,2,1,8,4,6]=>[1,1,1,1,2,2]
[5,2,8,4,1,6,3,7]=>[7,5,2,1,4,6,8,3]=>[2,4,7,8,5,3,1,6]=>[4,1,1,2]
[7,6,5,2,1,8,4,3]=>[8,4,7,5,3,2,1,6]=>[1,5,2,4,6,7,8,3]=>[2,5,1]
[2,7,5,1,8,3,6,4]=>[8,6,3,7,1,4,2,5]=>[1,3,6,2,8,5,7,4]=>[3,2,2,1]
[5,1,8,7,4,3,6,2]=>[1,6,5,8,7,4,2,3]=>[8,3,4,1,2,5,7,6]=>[1,2,4,1]
[3,8,7,2,4,6,1,5]=>[4,5,7,8,1,6,3,2]=>[5,4,2,1,8,3,6,7]=>[1,1,1,2,3]
[8,4,7,6,3,5,1,2]=>[7,2,5,8,6,4,3,1]=>[2,7,4,1,3,5,6,8]=>[2,1,5]
[8,1,7,4,2,3,5,6]=>[5,6,4,7,8,2,3,1]=>[4,3,5,2,1,7,6,8]=>[1,2,1,2,2]
[6,5,1,3,8,7,4,2]=>[8,7,4,2,1,6,3,5]=>[1,2,5,7,8,3,6,4]=>[5,2,1]
[4,7,8,3,2,5,1,6]=>[5,1,4,7,6,2,8,3]=>[4,8,5,2,3,7,1,6]=>[2,1,3,2]
[6,1,8,5,3,7,2,4]=>[5,7,4,1,8,6,2,3]=>[4,2,5,8,1,3,7,6]=>[1,3,3,1]
[5,1,6,8,3,7,4,2]=>[3,1,8,5,7,6,2,4]=>[6,8,1,4,2,3,7,5]=>[2,2,3,1]
[8,6,5,1,7,4,3,2]=>[8,7,6,4,3,2,5,1]=>[1,2,3,5,6,7,4,8]=>[6,2]
[7,6,4,1,3,5,8,2]=>[5,6,3,8,4,2,1,7]=>[4,3,6,1,5,7,8,2]=>[1,2,4,1]
[8,2,3,7,1,4,5,6]=>[2,3,5,6,7,8,4,1]=>[7,6,4,3,2,1,5,8]=>[1,1,1,1,1,3]
[2,8,3,7,1,4,5,6]=>[3,5,6,7,8,1,4,2]=>[6,4,3,2,1,8,5,7]=>[1,1,1,1,2,2]
[5,6,2,7,4,3,1,8]=>[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>[1,4,2,1]
[8,6,2,7,4,1,3,5]=>[6,7,3,5,2,8,4,1]=>[3,2,6,4,7,1,5,8]=>[1,2,2,3]
[3,7,8,2,6,1,4,5]=>[4,6,7,1,2,8,5,3]=>[5,3,2,8,7,1,4,6]=>[1,1,2,1,3]
[6,8,4,7,3,1,5,2]=>[3,1,8,6,5,7,4,2]=>[6,8,1,3,4,2,5,7]=>[2,3,3]
[4,8,6,5,1,2,7,3]=>[8,1,5,6,4,3,7,2]=>[1,8,4,3,5,6,2,7]=>[2,1,3,2]
[4,8,6,5,1,2,3,7]=>[1,5,6,7,4,3,8,2]=>[8,4,3,2,5,6,1,7]=>[1,1,1,3,2]
[3,4,5,1,7,6,8,2]=>[1,2,3,6,5,8,4,7]=>[8,7,6,3,4,1,5,2]=>[1,1,1,2,2,1]
[3,8,7,6,5,1,2,4]=>[6,7,8,5,1,4,3,2]=>[3,2,1,4,8,5,6,7]=>[1,1,3,3]
[8,4,6,7,1,2,5,3]=>[2,8,5,6,3,7,4,1]=>[7,1,4,3,6,2,5,8]=>[1,2,2,3]
[5,7,2,6,1,8,4,3]=>[1,8,7,3,5,4,2,6]=>[8,1,2,6,4,5,7,3]=>[1,3,3,1]
[5,7,2,6,1,3,8,4]=>[8,3,1,5,6,4,2,7]=>[1,6,8,4,3,5,7,2]=>[3,1,3,1]
[5,8,2,6,1,4,7,3]=>[6,1,8,3,5,4,7,2]=>[3,8,1,6,4,5,2,7]=>[2,2,2,2]
[3,8,7,5,6,1,4,2]=>[8,6,4,7,1,5,3,2]=>[1,3,5,2,8,4,6,7]=>[3,2,3]
[6,8,4,7,2,1,5,3]=>[5,3,1,8,6,7,4,2]=>[4,6,8,1,3,2,5,7]=>[3,2,3]
[7,4,6,5,1,3,8,2]=>[2,6,8,5,4,3,1,7]=>[7,3,1,4,5,6,8,2]=>[1,1,5,1]
[1,7,3,4,5,2,8,6]=>[3,4,5,8,6,1,2,7]=>[6,5,4,1,3,8,7,2]=>[1,1,1,3,1,1]
[4,8,2,1,3,5,6,7]=>[4,3,1,5,6,7,8,2]=>[5,6,8,4,3,2,1,7]=>[3,1,1,1,2]
[1,7,2,5,4,3,8,6]=>[5,4,8,3,6,1,2,7]=>[4,5,1,6,3,8,7,2]=>[2,2,2,1,1]
[2,6,7,3,4,8,1,5]=>[4,5,2,7,1,3,8,6]=>[5,4,7,2,8,6,1,3]=>[1,2,2,1,2]
[2,1,5,7,4,3,8,6]=>[3,5,8,1,6,2,4,7]=>[6,4,1,8,3,7,5,2]=>[1,1,2,2,1,1]
[4,1,8,7,5,6,2,3]=>[7,1,5,8,6,4,2,3]=>[2,8,4,1,3,5,7,6]=>[2,1,4,1]
[1,5,8,7,4,3,6,2]=>[6,2,5,8,7,4,1,3]=>[3,7,4,1,2,5,8,6]=>[2,1,4,1]
[6,4,1,3,8,7,5,2]=>[2,8,7,4,1,6,3,5]=>[7,1,2,5,8,3,6,4]=>[1,4,2,1]
[2,1,7,4,6,8,3,5]=>[7,4,5,1,3,8,2,6]=>[2,5,4,8,6,1,7,3]=>[2,2,1,2,1]
[1,7,2,4,6,8,3,5]=>[7,4,5,8,3,1,2,6]=>[2,5,4,1,6,8,7,3]=>[2,1,3,1,1]
[8,6,4,2,7,3,5,1]=>[6,3,8,4,2,7,5,1]=>[3,6,1,5,7,2,4,8]=>[2,3,3]
[1,8,6,2,7,3,5,4]=>[8,6,7,4,3,5,1,2]=>[1,3,2,5,6,4,8,7]=>[2,3,2,1]
[1,7,8,6,2,3,5,4]=>[8,5,6,2,7,4,1,3]=>[1,4,3,7,2,5,8,6]=>[2,2,3,1]
[2,1,8,3,5,7,6,4]=>[8,5,7,1,4,6,2,3]=>[1,4,2,8,5,3,7,6]=>[2,2,1,2,1]
[3,5,8,1,7,6,2,4]=>[2,7,8,1,6,4,5,3]=>[7,2,1,8,3,5,4,6]=>[1,1,2,2,2]
[2,8,1,3,6,7,5,4]=>[5,8,7,1,3,4,6,2]=>[4,1,2,8,6,5,3,7]=>[1,3,1,1,2]
[7,2,4,8,6,1,5,3]=>[8,3,6,7,2,1,5,4]=>[1,6,3,2,7,8,4,5]=>[2,1,3,2]
[8,2,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[7,8,6,5,4,3,2,9,1]=>[2,1,1,1,1,2,1]
[6,4,3,2,8,1,7,5]=>[3,2,8,4,1,6,7,5]=>[6,7,1,5,8,3,2,4]=>[2,3,1,2]
[5,8,4,3,1,6,7,2]=>[1,6,4,3,8,5,7,2]=>[8,3,5,6,1,4,2,7]=>[1,3,2,2]
[4,2,8,1,5,7,6,3]=>[1,8,5,7,2,4,6,3]=>[8,1,4,2,7,5,3,6]=>[1,2,2,1,2]
[6,3,7,2,5,4,8,1]=>[6,2,4,1,5,3,8,7]=>[3,7,5,8,4,6,1,2]=>[2,2,2,2]
[5,7,2,6,3,4,8,1]=>[5,1,6,3,4,2,8,7]=>[4,8,3,6,5,7,1,2]=>[2,2,2,2]
[3,7,5,4,6,2,8,1]=>[4,3,6,1,5,2,8,7]=>[5,6,3,8,4,7,1,2]=>[2,2,2,2]
[6,8,3,2,1,7,4,5]=>[4,3,7,1,8,5,6,2]=>[5,6,2,8,1,4,3,7]=>[2,2,2,2]
[4,8,1,7,5,3,2,6]=>[7,1,6,5,8,3,4,2]=>[2,8,3,4,1,6,5,7]=>[2,2,2,2]
[5,4,3,7,2,8,6,1]=>[2,1,8,3,5,4,7,6]=>[7,8,1,6,4,5,2,3]=>[2,2,2,2]
[3,6,5,7,2,8,4,1]=>[3,2,8,1,5,4,7,6]=>[6,7,1,8,4,5,2,3]=>[2,2,2,2]
[4,6,5,3,8,2,1,7]=>[4,1,3,2,7,6,8,5]=>[5,8,6,7,2,3,1,4]=>[2,2,2,2]
[2,6,5,8,7,3,1,4]=>[3,2,7,6,8,1,5,4]=>[6,7,2,3,1,8,4,5]=>[2,2,2,2]
[6,3,8,4,1,7,2,5]=>[7,2,4,1,8,5,6,3]=>[2,7,5,8,1,4,3,6]=>[2,2,2,2]
[7,2,8,1,6,4,3,5]=>[7,6,8,2,4,1,5,3]=>[2,3,1,7,5,8,4,6]=>[2,2,2,2]
[3,2,8,7,6,4,1,5]=>[7,6,8,1,5,2,4,3]=>[2,3,1,8,4,7,5,6]=>[2,2,2,2]
[8,2,6,4,3,5,1,7]=>[5,4,7,2,6,3,8,1]=>[4,5,2,7,3,6,1,8]=>[2,2,2,2]
[5,4,2,8,6,3,7,1]=>[2,1,6,5,8,3,7,4]=>[7,8,3,4,1,6,2,5]=>[2,2,2,2]
[2,8,7,5,3,1,4,6]=>[6,5,7,4,8,1,3,2]=>[3,4,2,5,1,8,6,7]=>[2,2,2,2]
[2,5,6,3,1,4,8,7]=>[4,2,8,1,5,3,6,7]=>[5,7,1,8,4,6,3,2]=>[2,2,2,1,1]
[2,4,7,8,5,3,1,6]=>[7,6,2,5,1,3,8,4]=>[2,3,7,4,8,6,1,5]=>[3,2,1,2]
[6,5,3,2,4,1,8,7]=>[4,3,5,2,1,8,6,7]=>[5,6,4,7,8,1,3,2]=>[2,3,2,1]
[6,5,8,7,3,2,4,1]=>[2,1,6,5,8,7,4,3]=>[7,8,3,4,1,2,5,6]=>[2,2,4]
[2,1,4,7,8,5,3,6]=>[7,6,1,3,4,8,2,5]=>[2,3,8,6,5,1,7,4]=>[3,1,1,2,1]
[8,5,6,7,3,1,4,2]=>[2,8,6,5,3,7,4,1]=>[7,1,3,4,6,2,5,8]=>[1,4,3]
[8,7,5,3,2,6,4,1]=>[4,8,5,3,7,6,2,1]=>[5,1,4,6,2,3,7,8]=>[1,3,4]
[8,5,3,1,4,6,7,2]=>[5,3,6,2,8,4,7,1]=>[4,6,3,7,1,5,2,8]=>[2,2,2,2]
[6,1,4,3,7,8,2,5]=>[3,7,4,5,1,8,2,6]=>[6,2,5,4,8,1,7,3]=>[1,2,2,2,1]
[6,1,2,7,5,8,3,4]=>[7,5,4,8,2,1,3,6]=>[2,4,5,1,7,8,6,3]=>[3,3,1,1]
[2,7,3,1,4,6,8,5]=>[3,6,8,1,4,5,2,7]=>[6,3,1,8,5,4,7,2]=>[1,1,2,1,2,1]
[3,8,5,6,7,1,2,4]=>[6,3,7,1,4,8,5,2]=>[3,6,2,8,5,1,4,7]=>[2,2,1,3]
[6,5,1,2,8,4,7,3]=>[6,8,7,3,2,1,4,5]=>[3,1,2,6,7,8,5,4]=>[1,5,1,1]
[2,5,8,1,4,6,7,3]=>[5,2,6,8,1,4,7,3]=>[4,7,3,1,8,5,2,6]=>[2,1,2,1,2]
[2,1,8,7,5,4,6,3]=>[6,5,8,7,1,4,2,3]=>[3,4,1,2,8,5,7,6]=>[2,3,2,1]
[7,8,3,4,1,6,5,2]=>[3,4,8,7,5,1,6,2]=>[6,5,1,2,4,8,3,7]=>[1,1,4,2]
[8,7,3,4,2,6,5,1]=>[3,4,8,5,7,6,2,1]=>[6,5,1,4,2,3,7,8]=>[1,1,2,4]
[4,7,2,8,6,3,1,5]=>[7,1,6,8,3,2,5,4]=>[2,8,3,1,6,7,4,5]=>[2,1,3,2]
[4,7,5,2,3,8,1,6]=>[1,4,5,3,7,2,8,6]=>[8,5,4,6,2,7,1,3]=>[1,1,2,2,2]
[6,4,7,5,2,8,3,1]=>[8,2,1,5,4,3,7,6]=>[1,7,8,4,5,6,2,3]=>[3,3,2]
[7,5,1,3,6,4,8,2]=>[6,4,5,2,8,3,1,7]=>[3,5,4,7,1,6,8,2]=>[2,2,3,1]
[6,5,2,3,7,8,4,1]=>[5,8,3,2,1,4,7,6]=>[4,1,6,7,8,5,2,3]=>[1,4,1,2]
[7,2,6,3,1,5,8,4]=>[4,6,8,2,5,3,1,7]=>[5,3,1,7,4,6,8,2]=>[1,1,2,3,1]
[4,6,3,8,7,5,1,2]=>[7,1,2,8,3,6,5,4]=>[2,8,7,1,6,3,4,5]=>[2,1,2,3]
[2,8,4,1,5,7,6,3]=>[3,8,5,7,1,4,6,2]=>[6,1,4,2,8,5,3,7]=>[1,2,2,1,2]
[1,8,4,2,5,7,6,3]=>[3,8,5,7,4,6,1,2]=>[6,1,4,2,5,3,8,7]=>[1,2,2,2,1]
[2,8,5,4,1,7,6,3]=>[4,3,8,7,1,5,6,2]=>[5,6,1,2,8,4,3,7]=>[2,3,1,2]
[1,8,5,2,4,7,6,3]=>[8,5,3,7,4,6,1,2]=>[1,4,6,2,5,3,8,7]=>[3,2,2,1]
[1,4,6,2,8,7,5,3]=>[3,8,2,7,6,1,4,5]=>[6,1,7,2,3,8,5,4]=>[1,2,3,1,1]
[7,8,2,4,1,6,5,3]=>[4,8,3,7,5,1,6,2]=>[5,1,6,2,4,8,3,7]=>[1,2,3,2]
[2,4,6,1,8,7,5,3]=>[3,8,2,7,1,6,4,5]=>[6,1,7,2,8,3,5,4]=>[1,2,2,2,1]
[2,8,4,5,1,7,6,3]=>[3,4,8,7,1,5,6,2]=>[6,5,1,2,8,4,3,7]=>[1,1,3,1,2]
[3,5,8,2,7,6,1,4]=>[2,7,8,1,4,6,5,3]=>[7,2,1,8,5,3,4,6]=>[1,1,2,1,3]
[2,1,6,8,7,5,3,4]=>[3,7,8,6,1,5,2,4]=>[6,2,1,3,8,4,7,5]=>[1,1,3,2,1]
[1,8,2,4,5,7,6,3]=>[8,4,5,7,3,6,1,2]=>[1,5,4,2,6,3,8,7]=>[2,1,2,2,1]
[1,2,8,3,5,7,6,4]=>[8,5,7,4,6,1,2,3]=>[1,4,2,5,3,8,7,6]=>[2,2,2,1,1]
[1,3,8,2,5,7,6,4]=>[8,5,7,2,4,6,1,3]=>[1,4,2,7,5,3,8,6]=>[2,2,1,2,1]
[2,3,8,1,5,7,6,4]=>[8,5,7,1,2,4,6,3]=>[1,4,2,8,7,5,3,6]=>[2,2,1,1,2]
[2,6,1,8,7,5,3,4]=>[7,2,8,6,1,5,3,4]=>[2,7,1,3,8,4,6,5]=>[2,3,2,1]
[1,6,2,8,7,5,3,4]=>[7,2,8,6,5,1,3,4]=>[2,7,1,3,4,8,6,5]=>[2,4,1,1]
[1,6,3,8,7,5,2,4]=>[7,2,8,6,3,5,1,4]=>[2,7,1,3,6,4,8,5]=>[2,3,2,1]
[3,2,8,1,5,7,6,4]=>[8,1,5,7,2,4,6,3]=>[1,8,4,2,7,5,3,6]=>[2,1,2,1,2]
[3,1,8,2,5,7,6,4]=>[8,1,5,7,4,6,2,3]=>[1,8,4,2,5,3,7,6]=>[2,1,2,2,1]
[2,8,1,4,5,7,6,3]=>[8,4,5,7,1,3,6,2]=>[1,5,4,2,8,6,3,7]=>[2,1,2,1,2]
[7,8,2,1,4,6,5,3]=>[8,3,5,7,4,1,6,2]=>[1,6,4,2,5,8,3,7]=>[2,1,3,2]
[2,3,6,8,7,5,1,4]=>[3,7,8,6,1,2,5,4]=>[6,2,1,3,8,7,4,5]=>[1,1,3,1,2]
[3,1,6,8,7,2,5,4]=>[3,8,1,6,7,5,2,4]=>[6,1,8,3,2,4,7,5]=>[1,2,1,3,1]
[3,8,4,5,1,6,2,7]=>[3,7,1,5,4,6,8,2]=>[6,2,8,4,5,3,1,7]=>[1,2,2,1,2]
[6,1,4,5,7,2,3,8]=>[3,6,4,7,2,1,5,8]=>[6,3,5,2,7,8,4,1]=>[1,2,3,1,1]
[8,1,4,7,6,3,2,5]=>[7,3,6,8,5,2,4,1]=>[2,6,3,1,4,7,5,8]=>[2,1,3,2]
[8,3,1,6,4,7,2,5]=>[2,5,7,4,8,3,6,1]=>[7,4,2,5,1,6,3,8]=>[1,1,2,2,2]
[5,3,8,6,2,7,1,4]=>[5,1,7,2,4,8,6,3]=>[4,8,2,7,5,1,3,6]=>[2,2,1,3]
[8,4,6,3,1,2,5,7]=>[5,2,6,4,7,3,8,1]=>[4,7,3,5,2,6,1,8]=>[2,2,2,2]
[6,8,1,4,5,2,3,7]=>[6,4,7,3,1,5,8,2]=>[3,5,2,6,8,4,1,7]=>[2,3,1,2]
[1,5,8,4,6,2,3,7]=>[2,6,4,7,5,8,1,3]=>[7,3,5,2,4,1,8,6]=>[1,2,2,2,1]
[2,1,6,5,3,8,4,7]=>[7,4,1,3,8,2,5,6]=>[2,5,8,6,1,7,4,3]=>[3,1,2,1,1]
[5,7,4,8,1,2,3,6]=>[5,1,6,3,7,2,8,4]=>[4,8,3,6,2,7,1,5]=>[2,2,2,2]
[4,7,8,1,2,6,3,5]=>[1,7,8,4,5,2,6,3]=>[8,2,1,5,4,7,3,6]=>[1,1,2,2,2]
[8,7,1,5,6,2,3,4]=>[6,7,4,8,3,5,2,1]=>[3,2,5,1,6,4,7,8]=>[1,2,2,3]
[1,6,5,8,7,2,3,4]=>[6,3,2,7,8,5,1,4]=>[3,6,7,2,1,4,8,5]=>[3,1,3,1]
[3,7,1,6,2,4,8,5]=>[8,1,5,6,3,4,2,7]=>[1,8,4,3,6,5,7,2]=>[2,1,2,2,1]
[5,1,2,7,6,8,3,4]=>[7,5,4,1,8,2,3,6]=>[2,4,5,8,1,7,6,3]=>[4,2,1,1]
[1,7,6,5,8,2,3,4]=>[6,7,4,3,2,8,1,5]=>[3,2,5,6,7,1,8,4]=>[1,4,2,1]
[1,6,8,5,7,2,3,4]=>[6,2,7,4,8,5,1,3]=>[3,7,2,5,1,4,8,6]=>[2,2,3,1]
[7,5,1,2,6,8,3,4]=>[7,5,8,3,2,4,1,6]=>[2,4,1,6,7,5,8,3]=>[2,3,2,1]
[6,1,5,2,7,8,3,4]=>[7,5,3,8,2,1,4,6]=>[2,4,6,1,7,8,5,3]=>[3,3,1,1]
[1,6,3,8,7,2,4,5]=>[6,7,2,8,3,5,1,4]=>[3,2,7,1,6,4,8,5]=>[1,2,2,2,1]
[1,7,3,2,4,6,8,5]=>[3,6,8,4,5,1,2,7]=>[6,3,1,5,4,8,7,2]=>[1,1,2,2,1,1]
[8,3,1,4,2,5,7,6]=>[4,2,8,3,5,6,7,1]=>[5,7,1,6,4,3,2,8]=>[2,2,1,1,2]
[3,1,2,7,8,4,6,5]=>[8,1,6,4,7,2,3,5]=>[1,8,3,5,2,7,6,4]=>[2,2,2,1,1]
[5,1,2,6,8,7,3,4]=>[4,7,1,8,6,2,3,5]=>[5,2,8,1,3,7,6,4]=>[1,2,3,1,1]
[1,8,6,2,5,7,3,4]=>[7,5,8,4,3,6,1,2]=>[2,4,1,5,6,3,8,7]=>[2,3,2,1]
[5,7,8,1,2,6,3,4]=>[7,1,8,4,5,2,6,3]=>[2,8,1,5,4,7,3,6]=>[2,2,2,2]
[7,1,6,8,5,2,3,4]=>[6,7,3,8,5,2,1,4]=>[3,2,6,1,4,7,8,5]=>[1,2,4,1]
[3,7,1,2,8,4,6,5]=>[8,1,6,7,3,4,2,5]=>[1,8,3,2,6,5,7,4]=>[2,1,2,2,1]
[1,5,8,7,6,2,3,4]=>[2,6,7,8,5,4,1,3]=>[7,3,2,1,4,5,8,6]=>[1,1,1,4,1]
[7,8,6,1,5,2,3,4]=>[6,7,8,4,1,5,3,2]=>[3,2,1,5,8,4,6,7]=>[1,1,3,3]
[1,9,3,4,5,6,7,8,2]=>[3,4,5,6,7,9,8,1,2]=>[7,6,5,4,3,1,2,9,8]=>[1,1,1,1,1,3,1]
[1,10,3,4,5,6,7,8,9,2]=>[3,4,5,6,7,8,10,9,1,2]=>[8,7,6,5,4,3,1,2,10,9]=>[1,1,1,1,1,1,3,1]
[7,8,6,3,1,5,2,4]=>[7,4,8,5,1,6,3,2]=>[2,5,1,4,8,3,6,7]=>[2,3,3]
[1,7,4,8,2,5,3,6]=>[3,7,5,6,2,8,1,4]=>[6,2,4,3,7,1,8,5]=>[1,2,2,2,1]
[3,8,6,1,4,2,7,5]=>[5,8,1,4,6,3,7,2]=>[4,1,8,5,3,6,2,7]=>[1,2,1,2,2]
[7,1,8,2,4,6,3,5]=>[5,7,8,4,6,2,1,3]=>[4,2,1,5,3,7,8,6]=>[1,1,2,3,1]
[7,6,8,4,1,5,3,2]=>[8,7,5,4,2,1,6,3]=>[1,2,4,5,7,8,3,6]=>[6,2]
[7,3,2,8,1,5,4,6]=>[2,7,3,5,6,1,8,4]=>[7,2,6,4,3,8,1,5]=>[1,2,1,2,2]
[3,5,4,1,7,2,6,8]=>[6,1,3,2,7,4,5,8]=>[3,8,6,7,2,5,4,1]=>[2,2,2,1,1]
[6,4,7,3,2,5,1,8]=>[2,5,4,1,7,6,3,8]=>[7,4,5,8,2,3,6,1]=>[1,3,3,1]
[7,6,5,3,8,4,1,2]=>[4,7,3,2,1,8,6,5]=>[5,2,6,7,8,1,3,4]=>[1,4,3]
[6,4,5,7,8,1,3,2]=>[2,3,1,8,6,4,7,5]=>[7,6,8,1,3,5,2,4]=>[1,2,3,2]
[3,7,4,1,6,8,5,2]=>[3,5,8,1,7,4,2,6]=>[6,4,1,8,2,5,7,3]=>[1,1,2,3,1]
[3,1,2,7,6,8,5,4]=>[5,1,4,8,7,2,3,6]=>[4,8,5,1,2,7,6,3]=>[2,1,3,1,1]
[6,1,8,3,5,4,2,7]=>[7,4,6,5,1,8,2,3]=>[2,5,3,4,8,1,7,6]=>[2,3,2,1]
[3,8,5,2,4,6,1,7]=>[4,5,1,3,7,6,8,2]=>[5,4,8,6,2,3,1,7]=>[1,2,1,2,2]
[1,6,4,8,3,5,2,7]=>[3,5,2,7,6,8,1,4]=>[6,4,7,2,3,1,8,5]=>[1,2,2,2,1]
[1,5,4,8,6,3,7,2]=>[2,6,3,5,8,7,1,4]=>[7,3,6,4,1,2,8,5]=>[1,2,1,3,1]
[4,8,2,5,3,7,1,6]=>[1,5,3,4,7,8,6,2]=>[8,4,6,5,2,1,3,7]=>[1,2,1,1,3]
[3,8,4,5,2,6,7,1]=>[3,5,1,4,6,8,7,2]=>[6,4,8,5,3,1,2,7]=>[1,2,1,1,3]
[5,7,8,4,6,3,2,1]=>[4,1,2,8,7,6,5,3]=>[5,8,7,1,2,3,4,6]=>[2,1,5]
[5,3,2,8,6,4,7,1]=>[6,2,1,5,8,3,7,4]=>[3,7,8,4,1,6,2,5]=>[3,1,2,2]
[6,8,1,2,7,4,3,5]=>[7,6,8,3,1,4,5,2]=>[2,3,1,6,8,5,4,7]=>[2,3,1,2]
[5,8,7,3,6,2,4,1]=>[1,4,6,8,7,5,3,2]=>[8,5,3,1,2,4,6,7]=>[1,1,1,5]
[7,3,5,4,2,8,6,1]=>[4,2,3,8,5,1,7,6]=>[5,7,6,1,4,8,2,3]=>[2,1,3,2]
[2,5,1,3,7,8,6,4]=>[5,2,8,1,7,3,4,6]=>[4,7,1,8,2,6,5,3]=>[2,2,2,1,1]
[4,3,7,2,1,8,6,5]=>[1,8,2,4,7,5,3,6]=>[8,1,7,5,2,4,6,3]=>[1,2,1,3,1]
[4,6,7,2,1,3,5,8]=>[1,5,4,6,2,7,3,8]=>[8,4,5,3,7,2,6,1]=>[1,2,2,2,1]
[4,6,2,3,1,5,7,8]=>[3,1,5,4,6,2,7,8]=>[6,8,4,5,3,7,2,1]=>[2,2,2,1,1]
[3,6,4,2,5,1,7,8]=>[4,1,3,6,5,2,7,8]=>[5,8,6,3,4,7,2,1]=>[2,1,3,1,1]
[3,1,6,4,7,5,2,8]=>[7,1,4,3,6,2,5,8]=>[2,8,5,6,3,7,4,1]=>[2,2,2,1,1]
[3,6,2,7,5,4,1,8]=>[7,6,1,3,2,5,4,8]=>[2,3,8,6,7,4,5,1]=>[3,2,2,1]
[2,5,7,3,4,1,6,8]=>[4,2,6,1,5,7,3,8]=>[5,7,3,8,4,2,6,1]=>[2,2,1,2,1]
[2,3,5,8,6,4,7,1]=>[6,3,5,8,1,2,7,4]=>[3,6,4,1,8,7,2,5]=>[2,1,2,1,2]
[2,4,7,3,8,6,5,1]=>[8,7,2,4,1,3,6,5]=>[1,2,7,5,8,6,3,4]=>[3,2,1,2]
[3,1,5,4,7,8,6,2]=>[1,3,5,8,4,7,2,6]=>[8,6,4,1,5,2,7,3]=>[1,1,1,2,2,1]
[4,5,7,2,3,1,8,6]=>[1,4,2,5,8,6,3,7]=>[8,5,7,4,1,3,6,2]=>[1,2,1,3,1]
[3,7,8,1,4,6,5,2]=>[8,5,7,1,4,2,6,3]=>[1,4,2,8,5,7,3,6]=>[2,2,2,2]
[2,5,8,7,4,1,3,6]=>[2,6,7,5,8,1,4,3]=>[7,3,2,4,1,8,5,6]=>[1,1,2,2,2]
[2,6,4,7,5,3,8,1]=>[6,3,2,5,1,4,8,7]=>[3,6,7,4,8,5,1,2]=>[3,2,1,2]
[6,2,4,7,1,3,8,5]=>[3,8,2,5,1,6,4,7]=>[6,1,7,4,8,3,5,2]=>[1,2,2,2,1]
[7,3,5,1,4,2,8,6]=>[2,5,8,4,3,6,1,7]=>[7,4,1,5,6,3,8,2]=>[1,1,3,2,1]
[5,4,7,1,3,2,8,6]=>[5,2,1,8,4,6,3,7]=>[4,7,8,1,5,3,6,2]=>[3,2,2,1]
[6,1,4,7,5,3,8,2]=>[6,3,5,4,1,8,2,7]=>[3,6,4,5,8,1,7,2]=>[2,3,2,1]
[8,7,4,3,1,5,6,2]=>[6,4,3,8,5,7,2,1]=>[3,5,6,1,4,2,7,8]=>[3,2,3]
[8,7,1,4,3,5,6,2]=>[5,4,6,8,3,7,2,1]=>[4,5,3,1,6,2,7,8]=>[2,1,2,3]
[6,1,8,4,7,3,2,5]=>[4,7,6,1,8,5,2,3]=>[5,2,3,8,1,4,7,6]=>[1,3,3,1]
[4,7,3,6,1,2,8,5]=>[1,3,8,5,6,4,2,7]=>[8,6,1,4,3,5,7,2]=>[1,1,2,3,1]
[5,2,1,7,4,3,8,6]=>[5,8,2,1,6,3,4,7]=>[4,1,7,8,3,6,5,2]=>[1,3,2,1,1]
[4,7,6,2,3,1,8,5]=>[1,4,5,8,6,3,2,7]=>[8,5,4,1,3,6,7,2]=>[1,1,1,4,1]
[7,6,8,2,5,3,4,1]=>[6,8,4,2,1,7,5,3]=>[3,1,5,7,8,2,4,6]=>[1,4,3]
[2,3,6,1,8,7,5,4]=>[3,8,7,1,2,6,4,5]=>[6,1,2,8,7,3,5,4]=>[1,3,1,2,1]
[2,6,8,7,5,3,1,4]=>[2,7,6,8,5,1,4,3]=>[7,2,3,1,4,8,5,6]=>[1,2,3,2]
[6,4,1,7,5,2,8,3]=>[2,8,6,5,3,1,4,7]=>[7,1,3,4,6,8,5,2]=>[1,5,1,1]
[2,8,7,4,1,5,6,3]=>[6,4,8,5,7,1,3,2]=>[3,5,1,4,2,8,6,7]=>[2,2,2,2]
[8,6,2,1,5,7,4,3]=>[5,8,3,7,4,2,6,1]=>[4,1,6,2,5,7,3,8]=>[1,2,3,2]
[3,8,6,7,5,2,1,4]=>[7,6,3,8,1,5,4,2]=>[2,3,6,1,8,4,5,7]=>[3,2,3]
[6,1,3,7,5,8,2,4]=>[7,5,3,4,1,8,2,6]=>[2,4,6,5,8,1,7,3]=>[3,2,2,1]
[4,7,3,1,8,5,6,2]=>[1,3,6,8,7,4,2,5]=>[8,6,3,1,2,5,7,4]=>[1,1,1,4,1]
[2,6,7,5,3,4,8,1]=>[5,2,6,4,1,3,8,7]=>[4,7,3,5,8,6,1,2]=>[2,3,1,2]
[2,6,4,5,7,3,8,1]=>[3,4,2,6,1,5,8,7]=>[6,5,7,3,8,4,1,2]=>[1,2,2,1,2]
[6,1,4,5,8,3,7,2]=>[3,4,6,1,8,7,2,5]=>[6,5,3,8,1,2,7,4]=>[1,1,2,3,1]
[6,1,8,5,3,4,7,2]=>[5,6,4,1,8,7,2,3]=>[4,3,5,8,1,2,7,6]=>[1,3,3,1]
[4,1,5,6,8,3,7,2]=>[3,1,4,6,8,7,2,5]=>[6,8,5,3,1,2,7,4]=>[2,1,1,3,1]
[6,4,1,8,7,2,5,3]=>[2,8,6,1,7,5,3,4]=>[7,1,3,8,2,4,6,5]=>[1,3,3,1]
[4,5,7,2,6,8,1,3]=>[1,2,7,4,5,3,8,6]=>[8,7,2,5,4,6,1,3]=>[1,1,2,2,2]
[6,9,1,2,3,4,5,7,8]=>[3,4,5,6,1,7,8,9,2]=>[7,6,5,4,9,3,2,1,8]=>[1,1,1,2,1,1,2]
[1,3,8,5,2,7,4,6]=>[7,4,8,2,5,6,1,3]=>[2,5,1,7,4,3,8,6]=>[2,2,1,2,1]
[1,3,8,6,7,2,4,5]=>[6,7,4,8,2,5,1,3]=>[3,2,5,1,7,4,8,6]=>[1,2,2,2,1]
[4,2,7,8,6,1,3,5]=>[1,6,7,3,8,2,5,4]=>[8,3,2,6,1,7,4,5]=>[1,1,2,2,2]
[7,5,3,6,8,2,1,4]=>[7,3,2,6,4,1,8,5]=>[2,6,7,3,5,8,1,4]=>[3,3,2]
[5,2,6,7,8,1,3,4]=>[6,3,1,7,2,4,8,5]=>[3,6,8,2,7,5,1,4]=>[3,2,1,2]
[4,5,6,8,1,2,7,3]=>[1,2,8,5,3,6,7,4]=>[8,7,1,4,6,3,2,5]=>[1,1,3,1,2]
[3,5,8,6,1,2,7,4]=>[2,8,1,5,6,4,7,3]=>[7,1,8,4,3,5,2,6]=>[1,2,1,2,2]
[4,2,6,8,7,1,3,5]=>[1,6,3,7,8,2,5,4]=>[8,3,6,2,1,7,4,5]=>[1,2,1,2,2]
[1,4,6,8,7,2,3,5]=>[6,2,3,7,8,5,1,4]=>[3,7,6,2,1,4,8,5]=>[2,1,1,3,1]
[4,5,3,8,1,7,2,6]=>[1,3,2,7,8,5,6,4]=>[8,6,7,2,1,4,3,5]=>[1,2,1,2,2]
[3,5,8,4,1,7,2,6]=>[2,7,1,4,8,5,6,3]=>[7,2,8,5,1,4,3,6]=>[1,2,1,2,2]
[1,6,5,7,8,2,3,4]=>[6,3,2,7,4,8,1,5]=>[3,6,7,2,5,1,8,4]=>[3,2,2,1]
[5,6,4,8,2,3,7,1]=>[1,5,3,2,6,8,7,4]=>[8,4,6,7,3,1,2,5]=>[1,3,1,3]
[6,5,4,8,1,3,7,2]=>[6,3,2,1,8,5,7,4]=>[3,6,7,8,1,4,2,5]=>[4,2,2]
[7,6,4,8,5,1,3,2]=>[3,8,6,2,1,7,5,4]=>[6,1,3,7,8,2,4,5]=>[1,4,3]
[7,2,6,5,8,1,3,4]=>[6,7,4,2,3,1,8,5]=>[3,2,5,7,6,8,1,4]=>[1,3,2,2]
[8,1,2,7,4,5,3,6]=>[5,7,6,8,2,3,4,1]=>[4,2,3,1,7,6,5,8]=>[1,2,2,1,2]
[2,5,7,4,6,1,3,8]=>[2,6,4,7,1,5,3,8]=>[7,3,5,2,8,4,6,1]=>[1,2,2,2,1]
[6,1,7,4,5,3,8,2]=>[4,6,5,3,1,8,2,7]=>[5,3,4,6,8,1,7,2]=>[1,4,2,1]
[2,6,4,8,3,1,7,5]=>[3,5,2,8,1,6,7,4]=>[6,4,7,1,8,3,2,5]=>[1,2,2,1,2]
[8,1,3,7,5,6,4,2]=>[5,8,7,3,6,2,4,1]=>[4,1,2,6,3,7,5,8]=>[1,3,2,2]
[1,2,5,3,8,6,7,4]=>[3,6,8,7,1,2,4,5]=>[6,3,1,2,8,7,5,4]=>[1,1,3,1,1,1]
[4,1,6,5,7,8,2,3]=>[1,4,3,7,5,8,2,6]=>[8,5,6,2,4,1,7,3]=>[1,2,2,2,1]
[6,1,3,7,4,2,8,5]=>[5,8,3,6,2,1,4,7]=>[4,1,6,3,7,8,5,2]=>[1,2,3,1,1]
[6,7,2,4,1,3,8,5]=>[8,3,5,4,1,6,2,7]=>[1,6,4,5,8,3,7,2]=>[2,3,2,1]
[7,3,8,4,2,6,5,1]=>[4,8,2,5,1,7,6,3]=>[5,1,7,4,8,2,3,6]=>[1,2,2,3]
[1,3,8,2,5,6,7,4]=>[5,6,8,2,4,7,1,3]=>[4,3,1,7,5,2,8,6]=>[1,1,2,1,2,1]
[1,8,6,7,2,5,4,3]=>[8,7,5,3,6,4,1,2]=>[1,2,4,6,3,5,8,7]=>[4,3,1]
[7,6,8,3,5,4,2,1]=>[8,4,2,1,7,6,5,3]=>[1,5,7,8,2,3,4,6]=>[4,4]
[1,6,7,3,8,5,4,2]=>[2,8,7,4,3,6,1,5]=>[7,1,2,5,6,3,8,4]=>[1,4,2,1]
[7,3,4,8,1,6,5,2]=>[8,2,3,7,5,1,6,4]=>[1,7,6,2,4,8,3,5]=>[2,1,3,2]
[8,7,2,4,6,1,5,3]=>[4,8,3,6,7,5,2,1]=>[5,1,6,3,2,4,7,8]=>[1,2,1,4]
[7,8,6,5,2,4,3,1]=>[8,5,1,7,6,4,3,2]=>[1,4,8,2,3,5,6,7]=>[3,5]
[3,6,7,5,2,8,4,1]=>[2,8,5,1,4,3,7,6]=>[7,1,4,8,5,6,2,3]=>[1,3,2,2]
[5,4,6,7,8,1,3,2]=>[2,1,3,8,6,4,7,5]=>[7,8,6,1,3,5,2,4]=>[2,1,3,2]
[7,5,3,2,8,6,4,1]=>[8,3,2,7,4,1,6,5]=>[1,6,7,2,5,8,3,4]=>[3,3,2]
[5,4,8,6,7,2,3,1]=>[1,6,2,4,8,7,5,3]=>[8,3,7,5,1,2,4,6]=>[1,2,1,4]
[5,4,8,6,3,1,2,7]=>[2,1,6,7,5,4,8,3]=>[7,8,3,2,4,5,1,6]=>[2,1,3,2]
[4,5,7,3,6,2,8,1]=>[1,2,4,6,5,3,8,7]=>[8,7,5,3,4,6,1,2]=>[1,1,1,3,2]
[4,5,6,3,8,2,7,1]=>[1,2,4,3,6,8,7,5]=>[8,7,5,6,3,1,2,4]=>[1,1,2,1,3]
[5,4,8,7,2,1,3,6]=>[2,1,6,5,7,8,4,3]=>[7,8,3,4,2,1,5,6]=>[2,2,1,3]
[2,5,4,7,8,1,3,6]=>[3,2,6,7,1,4,8,5]=>[6,7,3,2,8,5,1,4]=>[2,1,2,1,2]
[5,3,6,4,8,2,7,1]=>[4,2,1,3,6,8,7,5]=>[5,7,8,6,3,1,2,4]=>[3,1,1,3]
[8,2,6,3,7,4,5,1]=>[6,8,4,2,3,7,5,1]=>[3,1,5,7,6,2,4,8]=>[1,3,1,3]
[8,2,4,7,3,5,6,1]=>[3,5,6,8,2,7,4,1]=>[6,4,3,1,7,2,5,8]=>[1,1,1,2,3]
[8,2,6,5,7,3,4,1]=>[6,4,3,8,2,7,5,1]=>[3,5,6,1,7,2,4,8]=>[3,2,3]
[4,5,6,2,7,3,8,1]=>[1,2,6,4,3,5,8,7]=>[8,7,3,5,6,4,1,2]=>[1,1,3,1,2]
[5,4,6,2,8,3,7,1]=>[2,1,6,3,8,4,7,5]=>[7,8,3,6,1,5,2,4]=>[2,2,2,2]
[8,4,6,1,7,2,5,3]=>[2,8,6,7,4,3,5,1]=>[7,1,3,2,5,6,4,8]=>[1,2,3,2]
[5,2,1,6,3,8,7,4]=>[4,8,2,1,7,3,5,6]=>[5,1,7,8,2,6,4,3]=>[1,3,2,1,1]
[4,5,6,3,7,1,8,2]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[1,1,2,3,1]
[6,3,2,8,5,4,1,7]=>[7,2,6,3,1,5,8,4]=>[2,7,3,6,8,4,1,5]=>[2,3,1,2]
[4,3,1,5,2,8,6,7]=>[4,2,1,7,8,3,5,6]=>[5,7,8,2,1,6,4,3]=>[3,1,2,1,1]
[3,8,4,1,5,2,6,7]=>[6,1,4,3,5,7,8,2]=>[3,8,5,6,4,2,1,7]=>[2,2,1,1,2]
[2,5,4,3,8,1,6,7]=>[4,3,1,2,6,7,8,5]=>[5,6,8,7,3,2,1,4]=>[3,1,1,1,2]
[5,3,4,2,7,1,6,8]=>[2,4,3,1,6,7,5,8]=>[7,5,6,8,3,2,4,1]=>[1,3,1,2,1]
[3,7,5,4,1,2,6,8]=>[5,6,1,4,3,7,2,8]=>[4,3,8,5,6,2,7,1]=>[1,2,2,2,1]
[4,2,5,1,3,8,7,6]=>[3,1,8,2,7,4,5,6]=>[6,8,1,7,2,5,4,3]=>[2,2,2,1,1]
[4,3,5,1,2,7,6,8]=>[2,1,7,4,3,5,6,8]=>[7,8,2,5,6,4,3,1]=>[2,3,1,1,1]
[4,2,1,8,6,3,7,5]=>[1,8,6,2,5,7,3,4]=>[8,1,3,7,4,2,6,5]=>[1,3,1,2,1]
[3,1,7,2,5,6,4,8]=>[1,5,7,4,6,2,3,8]=>[8,4,2,5,3,7,6,1]=>[1,1,2,2,1,1]
[3,7,5,4,2,1,6,8]=>[6,5,1,4,3,7,2,8]=>[3,4,8,5,6,2,7,1]=>[3,2,2,1]
[3,7,2,4,1,6,5,8]=>[1,3,4,7,5,6,2,8]=>[8,6,5,2,4,3,7,1]=>[1,1,1,2,2,1]
[7,3,2,1,6,4,5,8]=>[3,2,6,7,4,5,1,8]=>[6,7,3,2,5,4,8,1]=>[2,1,2,2,1]
[2,8,6,1,7,4,3,5]=>[7,6,8,4,1,3,5,2]=>[2,3,1,5,8,6,4,7]=>[2,3,1,2]
[2,5,4,6,1,3,7,8]=>[5,3,1,2,6,4,7,8]=>[4,6,8,7,3,5,2,1]=>[3,1,2,1,1]
[2,5,6,4,1,3,7,8]=>[5,2,6,1,4,3,7,8]=>[4,7,3,8,5,6,2,1]=>[2,2,2,1,1]
[8,5,2,6,1,3,7,4]=>[8,3,5,2,6,4,7,1]=>[1,6,4,7,3,5,2,8]=>[2,2,2,2]
[7,1,5,6,3,2,4,8]=>[6,5,3,7,2,4,1,8]=>[3,4,6,2,7,5,8,1]=>[3,2,2,1]
[7,1,2,5,4,6,3,8]=>[5,4,7,2,3,6,1,8]=>[4,5,2,7,6,3,8,1]=>[2,2,1,2,1]
[2,4,1,6,5,3,7,8]=>[2,6,1,5,3,4,7,8]=>[7,3,8,4,6,5,2,1]=>[1,2,2,1,1,1]
[4,1,2,7,5,6,3,8]=>[5,1,7,6,2,3,4,8]=>[4,8,2,3,7,6,5,1]=>[2,3,1,1,1]
[7,1,2,6,5,4,3,8]=>[7,6,5,2,3,4,1,8]=>[2,3,4,7,6,5,8,1]=>[4,1,2,1]
[8,2,1,5,6,3,7,4]=>[4,8,2,6,3,5,7,1]=>[5,1,7,3,6,4,2,8]=>[1,2,2,1,2]
[2,8,5,1,6,4,7,3]=>[6,5,3,8,1,4,7,2]=>[3,4,6,1,8,5,2,7]=>[3,2,1,2]
[6,1,4,5,3,2,7,8]=>[3,6,5,2,4,1,7,8]=>[6,3,4,7,5,8,2,1]=>[1,3,2,1,1]
[3,1,6,5,4,2,7,8]=>[6,1,5,4,2,3,7,8]=>[3,8,4,5,7,6,2,1]=>[2,3,1,1,1]
[3,1,4,6,5,2,7,8]=>[1,6,3,5,2,4,7,8]=>[8,3,6,4,7,5,2,1]=>[1,2,2,1,1,1]
[6,4,1,5,3,2,8,7]=>[5,4,2,8,3,1,6,7]=>[4,5,7,1,6,8,3,2]=>[3,3,1,1]
[2,1,8,6,3,7,5,4]=>[8,7,5,1,4,6,2,3]=>[1,2,4,8,5,3,7,6]=>[4,1,2,1]
[5,8,3,1,7,6,4,2]=>[1,8,3,7,6,4,5,2]=>[8,1,6,2,3,5,4,7]=>[1,2,3,2]
[7,6,3,2,8,5,1,4]=>[3,7,8,4,2,1,6,5]=>[6,2,1,5,7,8,3,4]=>[1,1,4,2]
[5,6,3,8,7,4,1,2]=>[1,7,2,8,3,6,5,4]=>[8,2,7,1,6,3,4,5]=>[1,2,2,3]
[5,2,6,8,7,4,1,3]=>[3,1,7,8,6,2,5,4]=>[6,8,2,1,3,7,4,5]=>[2,1,3,2]
[4,3,8,5,7,2,6,1]=>[1,4,6,8,2,7,5,3]=>[8,5,3,1,7,2,4,6]=>[1,1,1,2,3]
[6,3,8,4,5,1,2,7]=>[6,2,4,1,7,5,8,3]=>[3,7,5,8,2,4,1,6]=>[2,2,2,2]
[5,4,1,3,2,8,6,7]=>[4,7,2,1,8,3,5,6]=>[5,2,7,8,1,6,4,3]=>[1,3,2,1,1]
[5,2,1,4,3,8,6,7]=>[2,4,7,1,8,3,5,6]=>[7,5,2,8,1,6,4,3]=>[1,1,2,2,1,1]
[4,2,7,3,8,5,1,6]=>[1,7,4,6,2,3,8,5]=>[8,2,5,3,7,6,1,4]=>[1,2,2,1,2]
[4,3,7,2,8,5,6,1]=>[1,6,8,2,4,3,7,5]=>[8,3,1,7,5,6,2,4]=>[1,1,2,2,2]
[5,3,1,2,4,8,6,7]=>[7,2,8,3,1,4,5,6]=>[2,7,1,6,8,5,4,3]=>[2,3,1,1,1]
[5,4,3,1,2,8,6,7]=>[7,3,2,1,8,4,5,6]=>[2,6,7,8,1,5,4,3]=>[4,2,1,1]
[5,3,4,1,2,8,6,7]=>[2,7,3,1,8,4,5,6]=>[7,2,6,8,1,5,4,3]=>[1,3,2,1,1]
[5,2,3,4,1,8,6,7]=>[2,3,4,1,7,8,5,6]=>[7,6,5,8,2,1,4,3]=>[1,1,2,1,2,1]
[5,8,7,4,3,1,6,2]=>[8,1,6,5,4,7,3,2]=>[1,8,3,4,5,2,6,7]=>[2,3,3]
[6,8,1,3,4,5,7,2]=>[4,5,6,1,8,3,7,2]=>[5,4,3,8,1,6,2,7]=>[1,1,2,2,2]
[3,1,7,8,2,5,4,6]=>[7,1,5,6,3,8,2,4]=>[2,8,4,3,6,1,7,5]=>[2,1,2,2,1]
[6,3,7,4,1,2,5,8]=>[2,5,6,4,1,7,3,8]=>[7,4,3,5,8,2,6,1]=>[1,1,3,2,1]
[7,2,6,8,4,3,1,5]=>[7,6,5,2,3,1,8,4]=>[2,3,4,7,6,8,1,5]=>[4,2,2]
[3,7,2,8,6,5,1,4]=>[7,8,6,1,3,2,5,4]=>[2,1,3,8,6,7,4,5]=>[1,3,2,2]
[3,6,7,5,1,2,4,8]=>[5,6,1,2,7,4,3,8]=>[4,3,8,7,2,5,6,1]=>[1,2,1,3,1]
[7,4,5,1,8,2,3,6]=>[6,2,7,3,8,4,1,5]=>[3,7,2,6,1,5,8,4]=>[2,2,3,1]
[2,1,4,8,3,7,5,6]=>[7,8,1,3,5,6,2,4]=>[2,1,8,6,4,3,7,5]=>[1,2,1,1,2,1]
[4,8,1,6,7,3,2,5]=>[7,1,6,4,8,3,5,2]=>[2,8,3,5,1,6,4,7]=>[2,2,2,2]
[5,8,1,4,3,2,7,6]=>[5,4,1,8,3,6,7,2]=>[4,5,8,1,6,3,2,7]=>[3,2,1,2]
[4,8,1,3,5,6,2,7]=>[4,1,5,7,3,6,8,2]=>[5,8,4,2,6,3,1,7]=>[2,1,2,1,2]
[5,3,7,8,4,2,6,1]=>[1,6,5,2,3,8,7,4]=>[8,3,4,7,6,1,2,5]=>[1,3,1,3]
[6,3,7,8,2,4,5,1]=>[5,6,2,1,3,8,7,4]=>[4,3,7,8,6,1,2,5]=>[1,3,1,3]
[8,5,2,4,3,1,7,6]=>[5,3,4,2,8,6,7,1]=>[4,6,5,7,1,3,2,8]=>[2,2,2,2]
[7,5,4,2,3,1,8,6]=>[4,5,3,2,8,6,1,7]=>[5,4,6,7,1,3,8,2]=>[1,3,3,1]
[3,5,6,4,8,1,7,2]=>[2,4,1,3,8,6,7,5]=>[7,5,8,6,1,3,2,4]=>[1,2,1,2,2]
[3,5,4,6,7,1,8,2]=>[3,1,2,4,8,6,5,7]=>[6,8,7,5,1,3,4,2]=>[2,1,1,3,1]
[1,4,2,6,5,8,7,3]=>[2,4,8,5,7,1,3,6]=>[7,5,1,4,2,8,6,3]=>[1,1,2,2,1,1]
[1,4,2,5,3,8,7,6]=>[2,8,4,7,1,3,5,6]=>[7,1,5,2,8,6,4,3]=>[1,2,2,1,1,1]
[1,5,2,6,4,8,7,3]=>[4,2,8,5,7,1,3,6]=>[5,7,1,4,2,8,6,3]=>[2,2,2,1,1]
[1,6,2,5,3,8,7,4]=>[4,8,7,3,1,2,5,6]=>[5,1,2,6,8,7,4,3]=>[1,4,1,1,1]
[2,5,1,4,3,8,7,6]=>[8,4,1,2,7,3,5,6]=>[1,5,8,7,2,6,4,3]=>[3,1,2,1,1]
[1,7,3,5,4,8,6,2]=>[4,8,3,5,2,7,1,6]=>[5,1,6,4,7,2,8,3]=>[1,2,2,2,1]
[1,8,2,6,3,7,5,4]=>[8,7,5,3,4,6,1,2]=>[1,2,4,6,5,3,8,7]=>[4,1,2,1]
[1,7,2,6,4,8,5,3]=>[8,5,4,7,3,1,2,6]=>[1,4,5,2,6,8,7,3]=>[3,3,1,1]
[1,7,2,6,3,8,5,4]=>[8,7,5,3,4,1,2,6]=>[1,2,4,6,5,8,7,3]=>[4,2,1,1]
[1,5,2,7,4,8,6,3]=>[2,8,5,4,7,1,3,6]=>[7,1,4,5,2,8,6,3]=>[1,3,2,1,1]
[4,8,1,3,2,6,5,7]=>[4,1,7,3,5,6,8,2]=>[5,8,2,6,4,3,1,7]=>[2,2,1,1,2]
[1,5,3,8,4,7,6,2]=>[2,8,5,7,3,6,1,4]=>[7,1,4,2,6,3,8,5]=>[1,2,2,2,1]
[1,8,4,7,3,6,5,2]=>[8,3,5,7,6,4,1,2]=>[1,6,4,2,3,5,8,7]=>[2,1,4,1]
[2,6,3,8,1,5,4,7]=>[7,3,5,1,2,6,8,4]=>[2,6,4,8,7,3,1,5]=>[2,2,1,1,2]
[8,3,1,4,2,6,5,7]=>[4,2,7,3,5,6,8,1]=>[5,7,2,6,4,3,1,8]=>[2,2,1,1,2]
[4,8,7,3,5,2,1,6]=>[4,7,1,6,5,8,3,2]=>[5,2,8,3,4,1,6,7]=>[1,2,2,3]
[6,8,7,3,5,2,4,1]=>[4,1,6,8,7,5,3,2]=>[5,8,3,1,2,4,6,7]=>[2,1,5]
[8,3,5,1,2,6,4,7]=>[2,7,4,5,3,6,8,1]=>[7,2,5,4,6,3,1,8]=>[1,2,2,1,2]
[8,6,3,1,5,4,2,7]=>[3,7,6,4,5,2,8,1]=>[6,2,3,5,4,7,1,8]=>[1,3,2,2]
[8,6,4,1,5,3,2,7]=>[7,6,4,3,5,2,8,1]=>[2,3,5,6,4,7,1,8]=>[4,2,2]
[8,6,5,4,1,3,2,7]=>[7,5,6,4,3,2,8,1]=>[2,4,3,5,6,7,1,8]=>[2,4,2]
[5,3,8,7,4,6,2,1]=>[1,5,8,7,2,6,4,3]=>[8,4,1,2,7,3,5,6]=>[1,1,3,3]
[2,3,8,7,4,6,1,5]=>[5,7,8,6,1,2,4,3]=>[4,2,1,3,8,7,5,6]=>[1,1,3,1,2]
[4,8,5,3,1,2,7,6]=>[8,1,5,4,3,6,7,2]=>[1,8,4,5,6,3,2,7]=>[2,3,1,2]
[6,8,7,3,1,5,4,2]=>[4,1,8,7,5,6,3,2]=>[5,8,1,2,4,3,6,7]=>[2,3,3]
[6,8,5,4,1,3,7,2]=>[6,1,8,5,4,3,7,2]=>[3,8,1,4,5,6,2,7]=>[2,4,2]
[2,5,8,7,4,6,3,1]=>[5,8,2,7,6,1,4,3]=>[4,1,7,2,3,8,5,6]=>[1,2,3,2]
[4,8,7,6,5,1,3,2]=>[8,6,7,1,5,4,3,2]=>[1,3,2,8,4,5,6,7]=>[2,2,4]
[3,8,7,5,1,6,2,4]=>[7,8,5,1,4,6,3,2]=>[2,1,4,8,5,3,6,7]=>[1,3,1,3]
[2,3,8,7,5,6,1,4]=>[7,5,8,6,1,2,4,3]=>[2,4,1,3,8,7,5,6]=>[2,3,1,2]
[8,5,4,7,2,1,3,6]=>[6,5,3,2,7,8,4,1]=>[3,4,6,7,2,1,5,8]=>[4,1,3]
[6,8,7,3,5,2,1,4]=>[4,1,7,6,8,5,3,2]=>[5,8,2,3,1,4,6,7]=>[2,2,4]
[3,5,8,6,4,2,7,1]=>[6,2,5,1,4,8,7,3]=>[3,7,4,8,5,1,2,6]=>[2,2,1,3]
[6,8,4,1,5,2,7,3]=>[8,6,4,3,1,5,7,2]=>[1,3,5,6,8,4,2,7]=>[5,1,2]
[6,8,2,1,7,5,3,4]=>[7,8,3,1,6,4,5,2]=>[2,1,6,8,3,5,4,7]=>[1,3,2,2]
[5,8,4,6,1,2,7,3]=>[1,8,5,3,6,4,7,2]=>[8,1,4,6,3,5,2,7]=>[1,3,2,2]
[2,4,8,6,5,1,7,3]=>[8,6,2,5,1,4,7,3]=>[1,3,7,4,8,5,2,6]=>[3,2,1,2]
[4,8,7,6,5,2,1,3]=>[7,6,8,1,5,4,3,2]=>[2,3,1,8,4,5,6,7]=>[2,2,4]
[4,8,7,5,1,6,2,3]=>[7,8,1,5,4,6,3,2]=>[2,1,8,4,5,3,6,7]=>[1,2,2,3]
[4,5,2,1,8,6,7,3]=>[1,6,2,8,3,7,4,5]=>[8,3,7,1,6,2,5,4]=>[1,2,2,2,1]
[4,5,8,3,1,6,7,2]=>[1,2,6,4,8,5,7,3]=>[8,7,3,5,1,4,2,6]=>[1,1,2,2,2]
[5,7,2,8,4,6,1,3]=>[1,7,5,8,3,2,6,4]=>[8,2,4,1,6,7,3,5]=>[1,2,3,2]
[6,7,3,2,4,8,5,1]=>[3,8,4,1,5,2,7,6]=>[6,1,5,8,4,7,2,3]=>[1,3,2,2]
[7,2,8,6,4,5,1,3]=>[7,5,8,6,2,1,4,3]=>[2,4,1,3,7,8,5,6]=>[2,4,2]
[8,7,2,6,5,1,3,4]=>[6,7,8,3,5,4,2,1]=>[3,2,1,6,4,5,7,8]=>[1,1,2,4]
[5,2,7,8,4,1,3,6]=>[6,1,7,5,2,3,8,4]=>[3,8,2,4,7,6,1,5]=>[2,3,1,2]
[2,7,8,6,4,1,3,5]=>[6,7,5,2,8,1,4,3]=>[3,2,4,7,1,8,5,6]=>[1,3,2,2]
[6,2,7,4,8,5,3,1]=>[8,4,3,1,7,2,6,5]=>[1,5,6,8,2,7,3,4]=>[4,2,2]
[8,6,5,1,7,2,4,3]=>[8,6,7,4,3,2,5,1]=>[1,3,2,5,6,7,4,8]=>[2,4,2]
[6,8,5,1,7,3,2,4]=>[7,6,1,8,4,3,5,2]=>[2,3,8,1,5,6,4,7]=>[3,3,2]
[1,6,8,3,7,4,2,5]=>[7,4,2,6,8,5,1,3]=>[2,5,7,3,1,4,8,6]=>[3,1,3,1]
[5,1,6,3,4,8,2,7]=>[4,5,3,1,7,8,2,6]=>[5,4,6,8,2,1,7,3]=>[1,3,1,2,1]
[3,5,2,4,8,1,7,6]=>[8,1,3,2,4,6,7,5]=>[1,8,6,7,5,3,2,4]=>[2,2,1,1,2]
[6,3,8,2,4,1,7,5]=>[2,4,5,1,8,6,7,3]=>[7,5,4,8,1,3,2,6]=>[1,1,2,2,2]
[4,6,3,8,7,5,2,1]=>[2,8,1,7,3,6,5,4]=>[7,1,8,2,6,3,4,5]=>[1,2,2,3]
[6,3,8,7,5,4,2,1]=>[1,8,7,6,2,5,4,3]=>[8,1,2,3,7,4,5,6]=>[1,4,3]
[6,8,4,2,1,7,5,3]=>[8,4,3,1,7,5,6,2]=>[1,5,6,8,2,4,3,7]=>[4,2,2]
[5,2,6,4,3,8,1,7]=>[5,4,2,1,3,7,8,6]=>[4,5,7,8,6,2,1,3]=>[4,1,1,2]
[6,5,3,1,4,8,2,7]=>[5,3,7,2,1,8,4,6]=>[4,6,2,7,8,1,5,3]=>[2,3,2,1]
[3,8,1,7,6,2,5,4]=>[8,6,7,1,5,3,4,2]=>[1,3,2,8,4,6,5,7]=>[2,2,2,2]
[8,1,7,6,4,2,5,3]=>[8,6,5,7,4,2,3,1]=>[1,3,4,2,5,7,6,8]=>[3,3,2]
[7,2,6,3,8,5,4,1]=>[8,7,4,2,3,1,6,5]=>[1,2,5,7,6,8,3,4]=>[4,2,2]
[7,3,8,6,4,1,5,2]=>[8,6,2,5,1,7,4,3]=>[1,3,7,4,8,2,5,6]=>[3,2,3]
[1,7,5,8,2,4,3,6]=>[7,5,3,6,2,8,1,4]=>[2,4,6,3,7,1,8,5]=>[3,2,2,1]
[6,1,5,2,4,8,3,7]=>[5,7,3,8,2,1,4,6]=>[4,2,6,1,7,8,5,3]=>[1,2,3,1,1]
[1,5,6,3,8,2,4,7]=>[4,2,6,3,7,8,1,5]=>[5,7,3,6,2,1,8,4]=>[2,2,1,2,1]
[8,7,1,3,6,5,2,4]=>[7,8,4,6,3,5,2,1]=>[2,1,5,3,6,4,7,8]=>[1,2,2,3]
[2,6,7,4,3,8,5,1]=>[4,2,8,5,1,3,7,6]=>[5,7,1,4,8,6,2,3]=>[2,3,1,2]
[5,2,4,7,3,8,6,1]=>[8,3,1,5,2,4,7,6]=>[1,6,8,4,7,5,2,3]=>[3,2,1,2]
[1,5,8,7,2,4,6,3]=>[2,6,8,5,7,4,1,3]=>[7,3,1,4,2,5,8,6]=>[1,1,2,3,1]
[1,4,8,7,3,6,5,2]=>[8,5,7,2,6,4,1,3]=>[1,4,2,7,3,5,8,6]=>[2,2,3,1]
[3,7,2,8,1,5,4,6]=>[7,1,3,5,6,2,8,4]=>[2,8,6,4,3,7,1,5]=>[2,1,1,2,2]
[3,2,6,1,5,8,4,7]=>[1,5,7,2,3,8,4,6]=>[8,4,2,7,6,1,5,3]=>[1,1,2,1,2,1]
[7,2,1,5,8,4,3,6]=>[4,7,2,6,8,3,1,5]=>[5,2,7,3,1,6,8,4]=>[1,2,1,3,1]
[7,2,8,1,4,3,6,5]=>[5,8,2,4,6,1,7,3]=>[4,1,7,5,3,8,2,6]=>[1,2,1,2,2]
[1,7,8,3,2,6,5,4]=>[8,4,7,5,2,6,1,3]=>[1,5,2,4,7,3,8,6]=>[2,3,2,1]
[1,7,4,8,3,2,6,5]=>[3,5,8,6,2,7,1,4]=>[6,4,1,3,7,2,8,5]=>[1,1,3,2,1]
[6,1,5,4,3,8,2,7]=>[5,4,3,7,1,8,2,6]=>[4,5,6,2,8,1,7,3]=>[3,2,2,1]
[1,7,4,5,6,8,2,3]=>[3,4,7,5,2,8,1,6]=>[6,5,2,4,7,1,8,3]=>[1,1,3,2,1]
[1,6,4,2,3,5,7,8]=>[4,5,3,6,1,2,7,8]=>[5,4,6,3,8,7,2,1]=>[1,2,2,1,1,1]
[1,8,7,2,3,4,5,6]=>[4,5,6,7,8,3,1,2]=>[5,4,3,2,1,6,8,7]=>[1,1,1,1,3,1]
[1,5,8,6,2,3,4,7]=>[5,2,6,7,4,8,1,3]=>[4,7,3,2,5,1,8,6]=>[2,1,2,2,1]
[1,6,5,7,2,3,4,8]=>[5,6,3,2,7,1,4,8]=>[4,3,6,7,2,8,5,1]=>[1,3,2,1,1]
[1,3,2,7,6,4,5,8]=>[6,7,2,5,1,3,4,8]=>[3,2,7,4,8,6,5,1]=>[1,2,2,1,1,1]
[1,2,3,7,6,4,5,8]=>[6,7,5,1,2,3,4,8]=>[3,2,4,8,7,6,5,1]=>[1,3,1,1,1,1]
[1,5,4,2,3,7,6,8]=>[7,4,3,1,2,5,6,8]=>[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]
[1,5,4,2,3,8,6,7]=>[7,3,2,8,1,4,5,6]=>[2,6,7,1,8,5,4,3]=>[3,2,1,1,1]
[1,3,2,8,6,4,5,7]=>[6,7,2,5,8,1,3,4]=>[3,2,7,4,1,8,6,5]=>[1,2,1,2,1,1]
[1,7,5,8,2,3,4,6]=>[5,6,3,7,2,8,1,4]=>[4,3,6,2,7,1,8,5]=>[1,2,2,2,1]
[1,8,7,5,2,3,4,6]=>[5,6,7,4,8,3,1,2]=>[4,3,2,5,1,6,8,7]=>[1,1,2,3,1]
[2,1,5,8,6,3,7,4]=>[8,3,6,1,5,7,2,4]=>[1,6,3,8,4,2,7,5]=>[2,2,1,2,1]
[2,5,8,4,6,1,7,3]=>[2,4,8,6,1,5,7,3]=>[7,5,1,3,8,4,2,6]=>[1,1,3,1,2]
[2,5,3,8,6,1,7,4]=>[2,8,6,1,3,5,7,4]=>[7,1,3,8,6,4,2,5]=>[1,3,1,1,2]
[2,6,3,5,8,1,7,4]=>[4,8,3,1,2,6,7,5]=>[5,1,6,8,7,3,2,4]=>[1,3,1,1,2]
[6,3,2,5,8,1,7,4]=>[2,4,8,3,1,6,7,5]=>[7,5,1,6,8,3,2,4]=>[1,1,3,1,2]
[5,3,2,8,6,1,7,4]=>[8,2,1,6,3,5,7,4]=>[1,7,8,3,6,4,2,5]=>[3,2,1,2]
[5,8,4,6,1,3,7,2]=>[1,6,3,8,5,4,7,2]=>[8,3,6,1,4,5,2,7]=>[1,2,3,2]
[5,3,8,6,1,4,7,2]=>[6,1,8,2,5,4,7,3]=>[3,8,1,7,4,5,2,6]=>[2,2,2,2]
[2,6,5,4,8,1,7,3]=>[4,3,2,8,1,6,7,5]=>[5,6,7,1,8,3,2,4]=>[3,2,1,2]
[8,3,5,7,2,6,4,1]=>[3,8,2,5,7,6,4,1]=>[6,1,7,4,2,3,5,8]=>[1,2,1,4]
[2,4,6,8,5,3,7,1]=>[3,6,2,5,8,1,7,4]=>[6,3,7,4,1,8,2,5]=>[1,2,1,2,2]
[2,4,8,1,7,6,5,3]=>[8,7,2,6,1,4,5,3]=>[1,2,7,3,8,5,4,6]=>[3,2,1,2]
[4,3,8,1,5,7,6,2]=>[1,8,2,5,7,4,6,3]=>[8,1,7,4,2,5,3,6]=>[1,2,1,2,2]
[3,8,4,1,5,7,6,2]=>[3,8,1,5,7,4,6,2]=>[6,1,8,4,2,5,3,7]=>[1,2,1,2,2]
[4,3,6,8,5,2,7,1]=>[1,3,6,2,5,8,7,4]=>[8,6,3,7,4,1,2,5]=>[1,1,2,1,3]
[8,5,4,7,2,6,3,1]=>[3,2,8,5,7,6,4,1]=>[6,7,1,4,2,3,5,8]=>[2,2,4]
[3,6,8,5,4,2,7,1]=>[2,6,5,1,4,8,7,3]=>[7,3,4,8,5,1,2,6]=>[1,3,1,3]
[3,6,4,8,5,2,7,1]=>[6,3,1,2,5,8,7,4]=>[3,6,8,7,4,1,2,5]=>[3,1,1,3]
[3,6,4,1,8,2,7,5]=>[3,8,1,6,2,7,4,5]=>[6,1,8,3,7,2,5,4]=>[1,2,2,2,1]
[4,8,6,5,1,3,7,2]=>[6,8,1,5,4,3,7,2]=>[3,1,8,4,5,6,2,7]=>[1,2,3,2]
[2,8,3,5,6,7,1,4]=>[4,7,3,5,8,1,6,2]=>[5,2,6,4,1,8,3,7]=>[1,2,1,2,2]
[5,6,2,4,7,1,8,3]=>[4,1,8,3,2,6,5,7]=>[5,8,1,6,7,3,4,2]=>[2,3,2,1]
[2,7,5,4,6,1,8,3]=>[4,3,8,6,1,5,2,7]=>[5,6,1,3,8,4,7,2]=>[2,3,2,1]
[2,3,7,4,6,1,8,5]=>[8,4,6,1,2,5,3,7]=>[1,5,3,8,7,4,6,2]=>[2,2,1,2,1]
[2,6,7,4,1,3,8,5]=>[8,5,4,1,2,6,3,7]=>[1,4,5,8,7,3,6,2]=>[4,1,2,1]
[6,5,7,4,1,3,8,2]=>[6,2,1,8,5,4,3,7]=>[3,7,8,1,4,5,6,2]=>[3,4,1]
[2,4,6,3,5,7,8,1]=>[2,4,5,1,3,6,8,7]=>[7,5,4,8,6,3,1,2]=>[1,1,2,1,1,2]
[4,1,6,3,5,7,8,2]=>[4,1,5,3,6,8,2,7]=>[5,8,4,6,3,1,7,2]=>[2,2,1,2,1]
[2,3,6,1,5,7,8,4]=>[5,6,1,2,3,8,4,7]=>[4,3,8,7,6,1,5,2]=>[1,2,1,1,2,1]
[4,6,1,2,5,7,8,3]=>[5,1,6,8,3,2,4,7]=>[4,8,3,1,6,7,5,2]=>[2,1,3,1,1]
[2,6,4,1,5,7,8,3]=>[5,3,6,1,2,8,4,7]=>[4,6,3,8,7,1,5,2]=>[2,2,1,2,1]
[2,4,1,6,5,7,8,3]=>[2,5,1,4,6,8,3,7]=>[7,4,8,5,3,1,6,2]=>[1,2,1,1,2,1]
[7,5,4,2,6,1,8,3]=>[8,4,3,2,6,5,1,7]=>[1,5,6,7,3,4,8,2]=>[4,3,1]
[4,7,3,1,8,6,5,2]=>[8,1,3,7,6,4,2,5]=>[1,8,6,2,3,5,7,4]=>[2,1,4,1]
[5,6,4,2,7,1,8,3]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[1,4,2,1]
[4,2,7,5,3,1,8,6]=>[1,5,4,8,2,6,3,7]=>[8,4,5,1,7,3,6,2]=>[1,2,2,2,1]
[5,3,6,4,8,2,1,7]=>[4,2,1,3,7,6,8,5]=>[5,7,8,6,2,3,1,4]=>[3,1,2,2]
[7,3,2,5,4,1,8,6]=>[2,5,3,4,8,6,1,7]=>[7,4,6,5,1,3,8,2]=>[1,2,1,3,1]
[7,3,2,5,1,8,6,4]=>[2,4,8,3,7,5,1,6]=>[7,5,1,6,2,4,8,3]=>[1,1,2,3,1]
[4,6,3,8,7,2,1,5]=>[7,1,3,2,6,8,5,4]=>[2,8,6,7,3,1,4,5]=>[2,2,1,3]
[4,7,6,3,8,2,1,5]=>[4,7,1,6,3,2,8,5]=>[5,2,8,3,6,7,1,4]=>[1,2,3,2]
[4,7,3,8,6,2,1,5]=>[7,1,3,6,2,8,5,4]=>[2,8,6,3,7,1,4,5]=>[2,1,2,3]
[5,7,3,2,6,1,8,4]=>[3,1,8,4,6,5,2,7]=>[6,8,1,5,3,4,7,2]=>[2,2,3,1]
[5,7,3,2,6,4,1,8]=>[3,1,7,4,6,5,2,8]=>[6,8,2,5,3,4,7,1]=>[2,2,3,1]
[7,5,2,8,4,3,1,6]=>[7,6,3,2,5,1,8,4]=>[2,3,6,7,4,8,1,5]=>[4,2,2]
[7,3,2,4,1,8,6,5]=>[2,8,3,4,7,5,1,6]=>[7,1,6,5,2,4,8,3]=>[1,2,1,3,1]
[8,4,3,2,7,5,1,6]=>[3,2,7,4,6,8,5,1]=>[6,7,2,5,3,1,4,8]=>[2,2,1,3]
[4,3,7,5,8,2,1,6]=>[1,4,7,2,6,3,8,5]=>[8,5,2,7,3,6,1,4]=>[1,1,2,2,2]
[4,3,7,5,2,6,1,8]=>[1,5,2,4,7,6,3,8]=>[8,4,7,5,2,3,6,1]=>[1,2,1,3,1]
[8,4,5,3,7,2,1,6]=>[2,4,3,7,6,8,5,1]=>[7,5,6,2,3,1,4,8]=>[1,2,2,3]
[4,3,5,2,8,6,1,7]=>[2,1,3,7,4,6,8,5]=>[7,8,6,2,5,3,1,4]=>[2,1,2,1,2]
[4,5,3,6,8,2,1,7]=>[1,3,2,4,7,6,8,5]=>[8,6,7,5,2,3,1,4]=>[1,2,1,2,2]
[1,2,8,6,4,5,7,3]=>[5,6,4,8,7,1,2,3]=>[4,3,5,1,2,8,7,6]=>[1,2,3,1,1]
[1,8,5,3,4,6,7,2]=>[4,5,3,6,8,7,1,2]=>[5,4,6,3,1,2,8,7]=>[1,2,1,3,1]
[10,2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,10,9,1]=>[9,8,7,6,5,4,3,1,2,10]=>[1,1,1,1,1,1,1,3]
[7,8,4,1,6,3,5,2]=>[6,3,8,7,4,1,5,2]=>[3,6,1,2,5,8,4,7]=>[2,4,2]
[8,7,5,6,1,3,4,2]=>[6,8,5,3,7,4,2,1]=>[3,1,4,6,2,5,7,8]=>[1,3,4]
[3,2,6,4,1,8,5,7]=>[1,4,7,2,3,8,5,6]=>[8,5,2,7,6,1,4,3]=>[1,1,2,1,2,1]
[4,8,7,5,2,3,1,6]=>[5,7,1,6,4,8,3,2]=>[4,2,8,3,5,1,6,7]=>[1,2,2,3]
[3,4,2,8,7,5,1,6]=>[7,1,2,6,8,3,5,4]=>[2,8,7,3,1,6,4,5]=>[2,1,1,2,2]
[8,5,7,6,3,2,4,1]=>[2,6,5,8,7,4,3,1]=>[7,3,4,1,2,5,6,8]=>[1,2,5]
[6,4,1,8,7,3,2,5]=>[2,7,6,1,8,5,3,4]=>[7,2,3,8,1,4,6,5]=>[1,3,3,1]
[3,7,6,1,5,8,4,2]=>[5,8,7,1,4,3,2,6]=>[4,1,2,8,5,6,7,3]=>[1,3,3,1]
[3,6,5,8,2,7,4,1]=>[3,2,8,1,5,7,6,4]=>[6,7,1,8,4,2,3,5]=>[2,2,1,3]
[8,3,2,7,4,6,5,1]=>[8,2,5,7,3,6,4,1]=>[1,7,4,2,6,3,5,8]=>[2,1,2,3]
[7,1,6,2,3,8,4,5]=>[7,8,4,5,2,3,1,6]=>[2,1,5,4,7,6,8,3]=>[1,2,2,2,1]
[6,4,7,1,3,2,8,5]=>[5,2,8,4,1,6,3,7]=>[4,7,1,5,8,3,6,2]=>[2,3,2,1]
[8,7,1,6,2,5,3,4]=>[7,8,5,6,3,4,2,1]=>[2,1,4,3,6,5,7,8]=>[1,2,2,3]
[3,8,5,2,4,7,6,1]=>[8,4,1,3,5,7,6,2]=>[1,5,8,6,4,2,3,7]=>[3,1,1,3]
[3,8,5,1,4,7,2,6]=>[5,7,1,3,8,4,6,2]=>[4,2,8,6,1,5,3,7]=>[1,2,1,2,2]
[7,1,4,8,5,6,2,3]=>[7,3,5,8,6,2,1,4]=>[2,6,4,1,3,7,8,5]=>[2,1,4,1]
[4,9,1,2,3,5,6,7,8]=>[3,4,1,5,6,7,8,9,2]=>[7,6,9,5,4,3,2,1,8]=>[1,2,1,1,1,1,2]
[3,9,1,2,4,5,6,7,8]=>[3,1,4,5,6,7,8,9,2]=>[7,9,6,5,4,3,2,1,8]=>[2,1,1,1,1,1,2]
[7,10,1,2,3,4,5,6,8,9]=>[3,4,5,6,7,1,8,9,10,2]=>[8,7,6,5,4,10,3,2,1,9]=>[1,1,1,1,2,1,1,2]
[6,10,1,2,3,4,5,7,8,9]=>[3,4,5,6,1,7,8,9,10,2]=>[8,7,6,5,10,4,3,2,1,9]=>[1,1,1,2,1,1,1,2]
[4,10,1,2,3,5,6,7,8,9]=>[3,4,1,5,6,7,8,9,10,2]=>[8,7,10,6,5,4,3,2,1,9]=>[1,2,1,1,1,1,1,2]
[3,10,1,2,4,5,6,7,8,9]=>[3,1,4,5,6,7,8,9,10,2]=>[8,10,7,6,5,4,3,2,1,9]=>[2,1,1,1,1,1,1,2]
[1,8,2,3,4,5,6,7,9]=>[3,4,5,6,7,8,1,2,9]=>[7,6,5,4,3,2,9,8,1]=>[1,1,1,1,1,2,1,1]
[7,4,6,1,3,2,5,8]=>[6,4,2,5,7,3,1,8]=>[3,5,7,4,2,6,8,1]=>[3,1,3,1]
[1,4,5,8,6,3,2,7]=>[7,2,3,6,5,8,1,4]=>[2,7,6,3,4,1,8,5]=>[2,1,2,2,1]
[4,5,2,6,7,3,1,8]=>[1,4,2,7,3,6,5,8]=>[8,5,7,2,6,3,4,1]=>[1,2,2,2,1]
[8,1,7,5,3,6,2,4]=>[5,7,4,8,6,2,3,1]=>[4,2,5,1,3,7,6,8]=>[1,2,3,2]
[5,2,8,3,6,1,4,7]=>[4,6,1,7,2,5,8,3]=>[5,3,8,2,7,4,1,6]=>[1,2,2,1,2]
[4,3,5,1,6,7,8,2]=>[2,1,5,3,6,8,4,7]=>[7,8,4,6,3,1,5,2]=>[2,2,1,2,1]
[3,6,7,5,1,2,8,4]=>[8,5,1,2,6,4,3,7]=>[1,4,8,7,3,5,6,2]=>[3,1,3,1]
[1,7,6,8,5,2,4,3]=>[8,6,3,2,7,5,1,4]=>[1,3,6,7,2,4,8,5]=>[4,3,1]
[5,7,6,8,1,2,4,3]=>[1,8,5,6,3,2,7,4]=>[8,1,4,3,6,7,2,5]=>[1,2,3,2]
[5,6,3,7,1,4,8,2]=>[3,1,6,2,8,5,4,7]=>[6,8,3,7,1,4,5,2]=>[2,2,3,1]
[5,3,2,1,8,6,4,7]=>[2,7,3,1,6,8,4,5]=>[7,2,6,8,3,1,5,4]=>[1,3,1,2,1]
[9,8,7,5,6,4,3,2,1]=>[4,9,8,7,6,5,3,2,1]=>[6,1,2,3,4,5,7,8,9]=>[1,8]
[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11]
[10,9,8,7,5,6,4,3,2,1]=>[5,10,9,8,7,6,4,3,2,1]=>[6,1,2,3,4,5,7,8,9,10]=>[1,9]
[9,8,7,5,4,6,3,2,1]=>[5,4,9,8,7,6,3,2,1]=>[5,6,1,2,3,4,7,8,9]=>[2,7]
[9,8,7,4,6,5,3,2,1]=>[9,4,8,7,6,5,3,2,1]=>[1,6,2,3,4,5,7,8,9]=>[2,7]
[1,8,7,6,5,4,3,2,9]=>[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>[7,1,1]
[1,9,8,7,6,5,4,3,2,10]=>[9,8,7,6,5,4,3,1,2,10]=>[2,3,4,5,6,7,8,10,9,1]=>[8,1,1]
[2,8,9,7,6,5,4,3,1]=>[2,9,8,7,6,5,1,4,3]=>[8,1,2,3,4,5,9,6,7]=>[1,6,2]
[7,8,6,1,4,5,2,3]=>[7,5,8,4,1,6,3,2]=>[2,4,1,5,8,3,6,7]=>[2,3,3]
[1,8,5,4,6,7,2,3]=>[4,3,7,5,8,6,1,2]=>[5,6,2,4,1,3,8,7]=>[2,2,3,1]
[6,5,8,3,7,2,1,4]=>[4,2,1,7,6,8,5,3]=>[5,7,8,2,3,1,4,6]=>[3,2,3]
[7,8,5,3,6,2,1,4]=>[4,7,6,3,1,8,5,2]=>[5,2,3,6,8,1,4,7]=>[1,4,3]
[7,8,5,3,6,2,4,1]=>[4,6,3,1,8,7,5,2]=>[5,3,6,8,1,2,4,7]=>[1,3,4]
[1,8,4,3,2,6,7,5]=>[4,3,6,8,5,7,1,2]=>[5,6,3,1,4,2,8,7]=>[2,1,2,2,1]
[5,4,3,8,2,1,7,6]=>[3,2,1,5,8,6,7,4]=>[6,7,8,4,1,3,2,5]=>[3,1,2,2]
[6,4,8,3,2,1,7,5]=>[2,5,4,1,8,6,7,3]=>[7,4,5,8,1,3,2,6]=>[1,3,2,2]
[1,8,4,3,2,7,6,5]=>[3,8,4,7,5,6,1,2]=>[6,1,5,2,4,3,8,7]=>[1,2,2,2,1]
[6,5,8,3,1,2,7,4]=>[8,5,4,2,1,6,7,3]=>[1,4,5,7,8,3,2,6]=>[5,1,2]
[1,8,6,7,3,2,4,5]=>[6,5,7,3,8,4,1,2]=>[3,4,2,6,1,5,8,7]=>[2,2,3,1]
[7,8,6,1,3,2,4,5]=>[6,4,5,7,1,8,3,2]=>[3,5,4,2,8,1,6,7]=>[2,1,2,3]
[1,8,4,3,2,7,5,6]=>[4,3,7,8,5,6,1,2]=>[5,6,2,1,4,3,8,7]=>[2,1,2,2,1]
[5,4,3,8,2,1,6,7]=>[3,2,1,6,5,7,8,4]=>[6,7,8,3,4,2,1,5]=>[3,2,1,2]
[1,8,4,3,2,5,7,6]=>[4,3,8,5,6,7,1,2]=>[5,6,1,4,3,2,8,7]=>[2,2,1,2,1]
[5,4,3,8,2,6,7,1]=>[3,2,1,5,6,8,7,4]=>[6,7,8,4,3,1,2,5]=>[3,1,1,3]
[6,4,2,3,5,1,8,7]=>[3,4,2,5,1,8,6,7]=>[6,5,7,4,8,1,3,2]=>[1,2,2,2,1]
[5,2,3,6,1,4,8,7]=>[8,2,3,1,5,4,6,7]=>[1,7,6,8,4,5,3,2]=>[2,2,2,1,1]
[5,2,3,8,6,4,7,1]=>[6,5,1,8,2,3,7,4]=>[3,4,8,1,7,6,2,5]=>[3,2,1,2]
[5,2,3,7,4,8,1,6]=>[5,7,2,1,3,4,8,6]=>[4,2,7,8,6,5,1,3]=>[1,3,1,1,2]
[8,6,3,2,5,4,7,1]=>[3,6,4,5,2,8,7,1]=>[6,3,5,4,7,1,2,8]=>[1,2,2,3]
[7,2,3,4,5,8,1,6]=>[2,3,4,5,7,1,8,6]=>[7,6,5,4,2,8,1,3]=>[1,1,1,1,2,2]
[7,2,8,1,5,3,4,6]=>[6,7,2,4,5,1,8,3]=>[3,2,7,5,4,8,1,6]=>[1,2,1,2,2]
[3,8,6,4,7,2,5,1]=>[4,6,3,8,1,7,5,2]=>[5,3,6,1,8,2,4,7]=>[1,2,2,3]
[2,1,8,6,4,5,7,3]=>[5,6,4,8,1,7,2,3]=>[4,3,5,1,8,2,7,6]=>[1,2,2,2,1]
[4,8,2,5,7,3,1,6]=>[1,4,7,3,6,8,5,2]=>[8,5,2,6,3,1,4,7]=>[1,1,2,1,3]
[5,8,2,3,4,7,1,6]=>[3,4,1,5,7,8,6,2]=>[6,5,8,4,2,1,3,7]=>[1,2,1,1,3]
[6,3,4,7,8,2,1,5]=>[7,2,3,1,6,4,8,5]=>[2,7,6,8,3,5,1,4]=>[2,2,2,2]
[3,8,5,1,4,7,6,2]=>[8,5,1,3,7,4,6,2]=>[1,4,8,6,2,5,3,7]=>[3,1,2,2]
[4,8,5,1,3,6,7,2]=>[1,5,6,3,8,4,7,2]=>[8,4,3,6,1,5,2,7]=>[1,1,2,2,2]
[4,6,8,5,2,7,3,1]=>[2,8,1,5,4,7,6,3]=>[7,1,8,4,5,2,3,6]=>[1,2,2,3]
[3,7,8,5,2,6,4,1]=>[8,5,4,1,2,7,6,3]=>[1,4,5,8,7,2,3,6]=>[4,1,3]
[3,8,6,2,7,4,5,1]=>[6,8,4,1,3,7,5,2]=>[3,1,5,8,6,2,4,7]=>[1,3,1,3]
[8,5,4,7,1,3,6,2]=>[6,3,2,8,5,7,4,1]=>[3,6,7,1,4,2,5,8]=>[3,2,3]
[7,3,6,2,8,1,5,4]=>[8,2,4,6,3,1,7,5]=>[1,7,5,3,6,8,2,4]=>[2,1,3,2]
[8,1,5,2,3,7,6,4]=>[8,7,4,2,3,5,6,1]=>[1,2,5,7,6,4,3,8]=>[4,1,1,2]
[6,4,2,3,7,8,5,1]=>[5,2,8,3,1,4,7,6]=>[4,7,1,6,8,5,2,3]=>[2,3,1,2]
[8,4,2,3,6,7,1,5]=>[7,3,2,4,5,8,6,1]=>[2,6,7,5,4,1,3,8]=>[3,1,1,3]
[4,5,8,3,7,2,1,6]=>[1,2,4,7,6,8,5,3]=>[8,7,5,2,3,1,4,6]=>[1,1,1,2,3]
[3,7,2,8,4,5,1,6]=>[5,7,1,3,6,2,8,4]=>[4,2,8,6,3,7,1,5]=>[1,2,1,2,2]
[3,5,1,8,4,6,2,7]=>[5,1,2,7,6,8,3,4]=>[4,8,7,2,3,1,6,5]=>[2,1,2,2,1]
[4,2,1,5,6,8,3,7]=>[2,4,1,5,7,8,3,6]=>[7,5,8,4,2,1,6,3]=>[1,2,1,1,2,1]
[4,1,2,6,5,8,3,7]=>[5,4,1,7,8,2,3,6]=>[4,5,8,2,1,7,6,3]=>[3,1,2,1,1]
[4,1,8,3,2,6,7,5]=>[4,1,6,8,5,7,2,3]=>[5,8,3,1,4,2,7,6]=>[2,1,2,2,1]
[4,2,7,5,8,1,3,6]=>[1,6,4,7,2,3,8,5]=>[8,3,5,2,7,6,1,4]=>[1,2,2,1,2]
[4,6,2,7,8,3,1,5]=>[7,1,6,3,2,4,8,5]=>[2,8,3,6,7,5,1,4]=>[2,3,1,2]
[4,6,1,3,8,2,5,7]=>[4,1,6,7,2,8,3,5]=>[5,8,3,2,7,1,6,4]=>[2,1,2,2,1]
[4,3,6,2,1,8,7,5]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[1,2,2,2,1]
[3,7,4,5,1,6,2,8]=>[3,7,1,5,4,6,2,8]=>[6,2,8,4,5,3,7,1]=>[1,2,2,2,1]
[3,6,4,5,8,2,1,7]=>[3,4,1,2,7,6,8,5]=>[6,5,8,7,2,3,1,4]=>[1,2,1,2,2]
[6,1,4,5,2,8,7,3]=>[3,4,8,7,2,1,5,6]=>[6,5,1,2,7,8,4,3]=>[1,1,4,1,1]
[7,2,4,5,1,6,3,8]=>[3,7,2,5,4,6,1,8]=>[6,2,7,4,5,3,8,1]=>[1,2,2,2,1]
[7,5,4,1,6,3,2,8]=>[7,6,4,3,2,5,1,8]=>[2,3,5,6,7,4,8,1]=>[5,2,1]
[1,5,4,8,6,3,2,7]=>[2,7,3,6,5,8,1,4]=>[7,2,6,3,4,1,8,5]=>[1,2,2,2,1]
[7,5,4,8,6,3,1,2]=>[3,2,7,1,8,6,5,4]=>[6,7,2,8,1,3,4,5]=>[2,2,4]
[8,5,4,1,6,3,2,7]=>[7,6,4,3,2,5,8,1]=>[2,3,5,6,7,4,1,8]=>[5,1,2]
[8,2,1,5,6,7,3,4]=>[4,7,2,5,8,3,6,1]=>[5,2,7,4,1,6,3,8]=>[1,2,1,2,2]
[6,3,1,8,4,7,2,5]=>[2,5,7,1,8,6,3,4]=>[7,4,2,8,1,3,6,5]=>[1,1,2,3,1]
[7,1,4,8,6,3,2,5]=>[7,3,6,8,5,2,1,4]=>[2,6,3,1,4,7,8,5]=>[2,1,4,1]
[4,1,8,5,6,7,2,3]=>[1,4,7,5,8,6,2,3]=>[8,5,2,4,1,3,7,6]=>[1,1,2,3,1]
[5,7,4,8,6,2,1,3]=>[1,3,7,6,2,8,5,4]=>[8,6,2,3,7,1,4,5]=>[1,1,3,3]
[5,3,6,8,2,7,1,4]=>[5,2,1,3,7,8,6,4]=>[4,7,8,6,2,1,3,5]=>[3,1,1,3]
[6,3,7,4,8,2,1,5]=>[4,7,2,1,6,3,8,5]=>[5,2,7,8,3,6,1,4]=>[1,3,2,2]
[4,3,6,8,2,7,1,5]=>[1,5,2,3,7,8,6,4]=>[8,4,7,6,2,1,3,5]=>[1,2,1,1,3]
[5,3,7,4,8,2,1,6]=>[4,1,7,2,6,3,8,5]=>[5,8,2,7,3,6,1,4]=>[2,2,2,2]
[5,3,8,4,1,6,2,7]=>[7,2,1,5,4,6,8,3]=>[2,7,8,4,5,3,1,6]=>[3,2,1,2]
[5,3,8,1,4,7,2,6]=>[2,5,1,7,8,4,6,3]=>[7,4,8,2,1,5,3,6]=>[1,2,1,2,2]
[5,8,4,1,6,3,2,7]=>[1,7,6,4,3,5,8,2]=>[8,2,3,5,6,4,1,7]=>[1,4,1,2]
[7,3,8,4,1,6,2,5]=>[7,2,4,8,5,1,6,3]=>[2,7,5,1,4,8,3,6]=>[2,1,3,2]
[1,5,8,3,6,7,4,2]=>[2,5,8,4,7,6,1,3]=>[7,4,1,5,2,3,8,6]=>[1,1,2,3,1]
[1,8,2,5,6,7,3,4]=>[4,7,5,8,3,6,1,2]=>[5,2,4,1,6,3,8,7]=>[1,2,2,2,1]
[7,8,4,1,6,5,2,3]=>[7,3,8,6,4,1,5,2]=>[2,6,1,3,5,8,4,7]=>[2,4,2]
[8,3,1,2,5,7,4,6]=>[5,2,7,8,3,4,6,1]=>[4,7,2,1,6,5,3,8]=>[2,1,2,1,2]
[8,1,4,2,6,5,3,7]=>[3,7,6,2,4,5,8,1]=>[6,2,3,7,5,4,1,8]=>[1,3,1,1,2]
[5,1,3,7,4,8,2,6]=>[5,7,3,1,4,8,2,6]=>[4,2,6,8,5,1,7,3]=>[1,3,1,2,1]
[5,1,3,4,7,8,2,6]=>[7,3,4,1,5,8,2,6]=>[2,6,5,8,4,1,7,3]=>[2,2,1,2,1]
[2,5,8,7,4,3,6,1]=>[6,2,5,8,7,1,4,3]=>[3,7,4,1,2,8,5,6]=>[2,1,3,2]
[5,1,7,8,3,4,2,6]=>[5,1,7,6,3,8,2,4]=>[4,8,2,3,6,1,7,5]=>[2,3,2,1]
[5,6,8,2,3,4,1,7]=>[4,1,5,2,7,6,8,3]=>[5,8,4,7,2,3,1,6]=>[2,2,2,2]
[2,3,5,7,4,6,8,1]=>[3,5,6,1,2,4,8,7]=>[6,4,3,8,7,5,1,2]=>[1,1,2,1,1,2]
[4,5,2,3,8,6,1,7]=>[1,7,3,2,4,6,8,5]=>[8,2,6,7,5,3,1,4]=>[1,3,1,1,2]
[3,7,4,5,8,1,2,6]=>[3,6,1,4,7,2,8,5]=>[6,3,8,5,2,7,1,4]=>[1,2,1,2,2]
[5,8,2,1,6,3,4,7]=>[3,6,1,7,4,5,8,2]=>[6,3,8,2,5,4,1,7]=>[1,2,2,1,2]
[4,8,1,3,7,5,2,6]=>[1,7,4,6,8,3,5,2]=>[8,2,5,3,1,6,4,7]=>[1,2,1,2,2]
[2,4,7,8,5,3,6,1]=>[6,5,2,3,8,1,7,4]=>[3,4,7,6,1,8,2,5]=>[3,1,2,2]
[5,3,1,4,7,2,8,6]=>[2,8,4,1,6,3,5,7]=>[7,1,5,8,3,6,4,2]=>[1,3,2,1,1]
[4,3,8,5,1,2,7,6]=>[1,8,2,5,4,6,7,3]=>[8,1,7,4,5,3,2,6]=>[1,2,2,1,2]
[2,4,7,5,8,3,6,1]=>[4,6,2,3,8,1,7,5]=>[5,3,7,6,1,8,2,4]=>[1,2,1,2,2]
[4,3,5,8,2,1,7,6]=>[2,1,3,5,8,6,7,4]=>[7,8,6,4,1,3,2,5]=>[2,1,1,2,2]
[4,8,5,7,3,1,2,6]=>[6,1,3,7,5,8,4,2]=>[3,8,6,2,4,1,5,7]=>[2,1,2,3]
[4,8,7,5,1,3,2,6]=>[7,1,5,6,4,8,3,2]=>[2,8,4,3,5,1,6,7]=>[2,1,2,3]
[4,2,8,5,1,3,6,7]=>[5,1,6,2,4,7,8,3]=>[4,8,3,7,5,2,1,6]=>[2,2,1,1,2]
[3,7,8,4,1,5,2,6]=>[7,5,1,4,6,2,8,3]=>[2,4,8,5,3,7,1,6]=>[3,1,2,2]
[3,4,7,5,8,2,1,6]=>[4,7,1,2,6,3,8,5]=>[5,2,8,7,3,6,1,4]=>[1,2,1,2,2]
[1,8,5,7,2,4,3,6]=>[7,5,3,6,8,4,1,2]=>[2,4,6,3,1,5,8,7]=>[3,1,3,1]
[1,8,5,4,2,3,6,7]=>[5,6,4,3,7,8,1,2]=>[4,3,5,6,2,1,8,7]=>[1,3,1,2,1]
[1,3,6,8,5,4,2,7]=>[3,7,6,2,5,8,1,4]=>[6,2,3,7,4,1,8,5]=>[1,3,1,2,1]
[1,6,3,8,2,7,4,5]=>[7,8,3,2,5,6,1,4]=>[2,1,6,7,4,3,8,5]=>[1,3,1,2,1]
[1,4,2,7,5,8,3,6]=>[2,5,7,4,8,1,3,6]=>[7,4,2,5,1,8,6,3]=>[1,1,2,2,1,1]
[1,8,2,3,6,7,5,4]=>[5,8,7,3,4,6,1,2]=>[4,1,2,6,5,3,8,7]=>[1,3,1,2,1]
[1,3,6,8,2,7,5,4]=>[3,8,7,2,5,6,1,4]=>[6,1,2,7,4,3,8,5]=>[1,3,1,2,1]
[1,6,5,4,3,8,2,7]=>[5,4,3,2,7,8,1,6]=>[4,5,6,7,2,1,8,3]=>[4,1,2,1]
[1,8,3,4,5,6,2,7]=>[3,4,5,7,6,8,1,2]=>[6,5,4,2,3,1,8,7]=>[1,1,1,2,2,1]
[1,8,3,6,2,4,5,7]=>[3,5,6,7,4,8,1,2]=>[6,4,3,2,5,1,8,7]=>[1,1,1,2,2,1]
[7,2,8,4,3,6,5,1]=>[4,8,5,7,2,1,6,3]=>[5,1,4,2,7,8,3,6]=>[1,2,3,2]
[7,2,8,5,6,3,4,1]=>[6,4,8,7,2,1,5,3]=>[3,5,1,2,7,8,4,6]=>[2,4,2]
[7,6,3,8,5,4,2,1]=>[8,7,3,2,1,6,5,4]=>[1,2,6,7,8,3,4,5]=>[5,3]
[6,2,8,7,5,4,1,3]=>[7,1,8,6,5,2,4,3]=>[2,8,1,3,4,7,5,6]=>[2,4,2]
[6,2,8,4,3,7,1,5]=>[5,4,7,1,8,2,6,3]=>[4,5,2,8,1,7,3,6]=>[2,2,2,2]
[5,2,8,4,3,1,7,6]=>[5,4,1,8,2,6,7,3]=>[4,5,8,1,7,3,2,6]=>[3,2,1,2]
[1,4,7,3,2,6,8,5]=>[2,4,6,8,5,1,3,7]=>[7,5,3,1,4,8,6,2]=>[1,1,1,3,1,1]
[1,5,7,3,6,2,8,4]=>[2,8,4,6,5,1,3,7]=>[7,1,5,3,4,8,6,2]=>[1,2,3,1,1]
[3,6,2,7,1,5,4,8]=>[7,1,3,5,2,6,4,8]=>[2,8,6,4,7,3,5,1]=>[2,1,2,2,1]
[1,4,3,5,8,2,7,6]=>[2,8,3,4,6,7,1,5]=>[7,1,6,5,3,2,8,4]=>[1,2,1,1,2,1]
[1,4,3,6,8,7,2,5]=>[2,4,7,8,3,6,1,5]=>[7,5,2,1,6,3,8,4]=>[1,1,1,2,2,1]
[1,5,3,7,6,8,2,4]=>[2,7,5,3,4,8,1,6]=>[7,2,4,6,5,1,8,3]=>[1,3,1,2,1]
[4,2,6,5,7,8,1,3]=>[1,4,3,7,2,5,8,6]=>[8,5,6,2,7,4,1,3]=>[1,2,2,1,2]
[3,2,5,7,6,8,1,4]=>[7,1,3,5,2,4,8,6]=>[2,8,6,4,7,5,1,3]=>[2,1,2,1,2]
[3,2,4,6,8,7,1,5]=>[1,4,7,8,2,3,6,5]=>[8,5,2,1,7,6,3,4]=>[1,1,1,2,1,2]
[5,3,2,6,8,4,7,1]=>[2,4,1,6,8,3,7,5]=>[7,5,8,3,1,6,2,4]=>[1,2,1,2,2]
[5,3,2,8,7,6,4,1]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[1,3,2,2]
[5,3,8,2,7,6,1,4]=>[7,1,8,2,4,6,5,3]=>[2,8,1,7,5,3,4,6]=>[2,2,1,3]
[6,5,4,8,3,7,2,1]=>[3,2,1,5,8,7,6,4]=>[6,7,8,4,1,2,3,5]=>[3,1,4]
[4,8,5,1,3,7,2,6]=>[1,5,7,3,8,4,6,2]=>[8,4,2,6,1,5,3,7]=>[1,1,2,2,2]
[4,3,8,7,2,6,5,1]=>[8,1,5,7,2,6,4,3]=>[1,8,4,2,7,3,5,6]=>[2,1,2,3]
[2,7,5,1,8,4,6,3]=>[6,3,8,7,1,4,2,5]=>[3,6,1,2,8,5,7,4]=>[2,3,2,1]
[7,8,5,2,1,6,4,3]=>[8,4,7,5,3,1,6,2]=>[1,5,2,4,6,8,3,7]=>[2,4,2]
[7,5,4,8,3,2,6,1]=>[3,2,6,5,1,8,7,4]=>[6,7,3,4,8,1,2,5]=>[2,3,3]
[8,6,4,7,3,2,1,5]=>[3,7,6,5,2,8,4,1]=>[6,2,3,4,7,1,5,8]=>[1,4,3]
[3,8,5,6,2,7,1,4]=>[5,3,7,1,4,8,6,2]=>[4,6,2,8,5,1,3,7]=>[2,2,1,3]
[2,4,5,8,7,3,1,6]=>[7,2,3,6,8,1,5,4]=>[2,7,6,3,1,8,4,5]=>[2,1,1,2,2]
[2,4,5,8,6,7,1,3]=>[7,2,3,5,8,1,6,4]=>[2,7,6,4,1,8,3,5]=>[2,1,1,2,2]
[4,3,1,5,6,2,8,7]=>[4,2,1,5,8,3,6,7]=>[5,7,8,4,1,6,3,2]=>[3,1,2,1,1]
[4,1,5,8,6,7,2,3]=>[1,7,3,5,8,6,2,4]=>[8,2,6,4,1,3,7,5]=>[1,2,1,3,1]
[4,3,7,6,1,2,8,5]=>[1,8,2,5,6,4,3,7]=>[8,1,7,4,3,5,6,2]=>[1,2,1,3,1]
[4,7,5,6,1,2,8,3]=>[8,1,5,3,6,4,2,7]=>[1,8,4,6,3,5,7,2]=>[2,2,3,1]
[4,3,7,5,6,2,8,1]=>[1,4,6,2,5,3,8,7]=>[8,5,3,7,4,6,1,2]=>[1,1,2,2,2]
[4,5,1,8,6,7,3,2]=>[1,2,5,8,7,6,3,4]=>[8,7,4,1,2,3,6,5]=>[1,1,1,4,1]
[3,4,5,8,6,7,2,1]=>[5,8,1,2,3,7,6,4]=>[4,1,8,7,6,2,3,5]=>[1,2,1,1,3]
[2,1,5,8,6,7,4,3]=>[5,8,3,7,1,6,2,4]=>[4,1,6,2,8,3,7,5]=>[1,2,2,2,1]
[3,4,5,8,7,1,2,6]=>[1,2,3,6,7,8,5,4]=>[8,7,6,3,2,1,4,5]=>[1,1,1,1,1,3]
[4,7,1,5,6,2,8,3]=>[1,4,8,6,3,5,2,7]=>[8,5,1,3,6,4,7,2]=>[1,1,3,2,1]
[2,6,4,7,1,3,8,5]=>[3,8,5,1,2,6,4,7]=>[6,1,4,8,7,3,5,2]=>[1,3,1,2,1]
[5,3,8,6,4,7,2,1]=>[1,5,4,8,2,7,6,3]=>[8,4,5,1,7,2,3,6]=>[1,2,2,3]
[6,4,1,5,7,8,3,2]=>[4,2,5,1,8,7,3,6]=>[5,7,4,8,1,2,6,3]=>[2,2,3,1]
[3,8,4,6,1,7,2,5]=>[3,7,8,1,5,4,6,2]=>[6,2,1,8,4,5,3,7]=>[1,1,2,2,2]
[3,8,5,6,4,7,2,1]=>[3,5,4,8,1,7,6,2]=>[6,4,5,1,8,2,3,7]=>[1,2,2,3]
[3,8,4,5,6,7,2,1]=>[3,4,5,8,1,7,6,2]=>[6,5,4,1,8,2,3,7]=>[1,1,1,2,3]
[3,8,6,5,2,7,4,1]=>[8,5,4,1,3,7,6,2]=>[1,4,5,8,6,2,3,7]=>[4,1,3]
[3,8,7,5,2,1,4,6]=>[6,5,7,1,4,8,3,2]=>[3,4,2,8,5,1,6,7]=>[2,2,1,3]
[3,8,6,5,1,7,2,4]=>[7,8,5,1,4,3,6,2]=>[2,1,4,8,5,6,3,7]=>[1,3,2,2]
[6,5,4,7,1,3,8,2]=>[6,3,2,1,8,5,4,7]=>[3,6,7,8,1,4,5,2]=>[4,3,1]
[2,1,6,5,3,7,8,4]=>[6,4,1,3,8,2,5,7]=>[3,5,8,6,1,7,4,2]=>[3,1,2,1,1]
[2,1,3,4,5,6,8,9,7]=>[1,7,9,2,3,4,5,6,8]=>[9,3,1,8,7,6,5,4,2]=>[1,1,2,1,1,1,1,1]
[2,1,3,4,5,6,7,9,8]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,10,11,9]=>[9,11,1,2,3,4,5,6,7,8,10]=>[3,1,11,10,9,8,7,6,5,4,2]=>[1,2,1,1,1,1,1,1,1,1]
[2,3,1,4,5,6,7,9,8]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[1,1,2,1,1,1,1,1]
[1,3,2,4,5,6,7,9,8]=>[2,9,1,3,4,5,6,7,8]=>[8,1,9,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1]
[2,1,3,4,5,6,7,8,10,9]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[1,2,1,1,1,1,1,1,1]
[1,6,2,5,4,8,3,7]=>[5,4,7,2,8,1,3,6]=>[4,5,2,7,1,8,6,3]=>[2,2,2,1,1]
[4,1,2,7,5,8,3,6]=>[5,1,7,4,8,2,3,6]=>[4,8,2,5,1,7,6,3]=>[2,2,2,1,1]
[6,1,3,5,8,2,4,7]=>[6,3,4,7,1,8,2,5]=>[3,6,5,2,8,1,7,4]=>[2,1,2,2,1]
[5,6,4,3,1,8,2,7]=>[1,7,4,3,2,8,5,6]=>[8,2,5,6,7,1,4,3]=>[1,4,2,1]
[6,2,3,5,8,1,4,7]=>[6,2,3,4,1,7,8,5]=>[3,7,6,5,8,2,1,4]=>[2,1,2,1,2]
[6,7,2,3,8,4,5,1]=>[6,8,3,1,4,2,7,5]=>[3,1,6,8,5,7,2,4]=>[1,3,2,2]
[6,7,2,1,3,8,4,5]=>[3,7,8,4,1,5,2,6]=>[6,2,1,5,8,4,7,3]=>[1,1,3,2,1]
[5,7,4,1,8,3,2,6]=>[1,7,6,3,8,4,2,5]=>[8,2,3,6,1,5,7,4]=>[1,3,3,1]
[4,1,7,5,8,3,6,2]=>[1,4,6,3,8,7,2,5]=>[8,5,3,6,1,2,7,4]=>[1,1,2,3,1]
[6,7,1,3,8,4,5,2]=>[6,8,4,1,7,3,2,5]=>[3,1,5,8,2,6,7,4]=>[1,3,3,1]
[1,6,7,4,3,8,5,2]=>[4,2,8,5,3,7,1,6]=>[5,7,1,4,6,2,8,3]=>[2,3,2,1]
[6,1,7,4,2,8,5,3]=>[4,8,7,5,2,1,3,6]=>[5,1,2,4,7,8,6,3]=>[1,5,1,1]
[2,1,6,7,4,3,8,5]=>[5,3,8,1,6,2,4,7]=>[4,6,1,8,3,7,5,2]=>[2,2,2,1,1]
[6,7,3,2,1,8,4,5]=>[4,3,7,1,8,5,2,6]=>[5,6,2,8,1,4,7,3]=>[2,2,3,1]
[2,5,7,3,1,4,8,6]=>[4,2,8,1,5,6,3,7]=>[5,7,1,8,4,3,6,2]=>[2,2,1,2,1]
[6,7,3,2,8,4,5,1]=>[3,6,1,8,4,2,7,5]=>[6,3,8,1,5,7,2,4]=>[1,2,3,2]
[1,2,6,7,4,3,8,5]=>[5,3,8,6,1,2,4,7]=>[4,6,1,3,8,7,5,2]=>[2,3,1,1,1]
[2,7,1,8,4,6,3,5]=>[5,7,8,6,1,3,2,4]=>[4,2,1,3,8,6,7,5]=>[1,1,3,2,1]
[2,7,5,8,1,6,3,4]=>[7,3,8,5,1,2,6,4]=>[2,6,1,4,8,7,3,5]=>[2,3,1,2]
[6,7,1,8,4,5,3,2]=>[5,1,8,7,6,3,2,4]=>[4,8,1,2,3,6,7,5]=>[2,5,1]
[8,3,7,6,1,2,5,4]=>[8,2,5,6,7,4,3,1]=>[1,7,4,3,2,5,6,8]=>[2,1,1,4]
[8,2,5,7,1,4,6,3]=>[6,3,8,2,5,7,4,1]=>[3,6,1,7,4,2,5,8]=>[2,2,1,3]
[8,2,4,7,1,5,6,3]=>[3,6,8,2,5,7,4,1]=>[6,3,1,7,4,2,5,8]=>[1,1,2,1,3]
[8,2,3,4,7,1,5,6]=>[2,3,4,6,7,8,5,1]=>[7,6,5,3,2,1,4,8]=>[1,1,1,1,1,3]
[8,7,4,6,5,2,3,1]=>[3,6,8,7,5,4,2,1]=>[6,3,1,2,4,5,7,8]=>[1,1,6]
[8,4,6,7,5,1,2,3]=>[2,6,7,3,8,5,4,1]=>[7,3,2,6,1,4,5,8]=>[1,1,2,4]
[8,3,5,7,6,1,4,2]=>[3,8,2,6,7,5,4,1]=>[6,1,7,3,2,4,5,8]=>[1,2,1,4]
[8,7,3,6,2,1,5,4]=>[3,5,8,6,7,4,2,1]=>[6,4,1,3,2,5,7,8]=>[1,1,2,4]
[8,7,3,4,6,2,1,5]=>[3,4,7,6,8,5,2,1]=>[6,5,2,3,1,4,7,8]=>[1,1,2,4]
[8,7,4,6,5,2,1,3]=>[3,7,6,8,5,4,2,1]=>[6,2,3,1,4,5,7,8]=>[1,2,5]
[8,6,5,2,7,4,3,1]=>[8,7,4,3,2,6,5,1]=>[1,2,5,6,7,3,4,8]=>[5,3]
[8,4,3,7,6,5,1,2]=>[2,7,8,3,6,5,4,1]=>[7,2,1,6,3,4,5,8]=>[1,1,2,4]
[8,5,7,6,4,1,2,3]=>[6,2,7,8,5,4,3,1]=>[3,7,2,1,4,5,6,8]=>[2,1,5]
[8,4,2,7,5,1,6,3]=>[2,8,6,3,5,7,4,1]=>[7,1,3,6,4,2,5,8]=>[1,3,1,3]
[8,3,4,2,7,5,6,1]=>[2,3,6,8,4,7,5,1]=>[7,6,3,1,5,2,4,8]=>[1,1,1,2,3]
[8,4,7,6,5,1,2,3]=>[2,6,7,8,5,4,3,1]=>[7,3,2,1,4,5,6,8]=>[1,1,1,5]
[8,3,5,2,7,4,6,1]=>[6,2,3,8,4,7,5,1]=>[3,7,6,1,5,2,4,8]=>[2,1,2,3]
[8,5,2,6,7,4,1,3]=>[7,4,2,8,3,6,5,1]=>[2,5,7,1,6,3,4,8]=>[3,2,3]
[8,6,2,5,7,3,1,4]=>[7,6,3,4,2,8,5,1]=>[2,3,6,5,7,1,4,8]=>[3,2,3]
[8,6,2,4,7,3,1,5]=>[4,7,3,6,2,8,5,1]=>[5,2,6,3,7,1,4,8]=>[1,2,2,3]
[8,5,2,3,7,4,1,6]=>[7,3,4,2,6,8,5,1]=>[2,6,5,7,3,1,4,8]=>[2,2,1,3]
[8,5,3,2,7,6,4,1]=>[8,3,2,7,4,6,5,1]=>[1,6,7,2,5,3,4,8]=>[3,2,3]
[8,6,1,5,4,3,2,7]=>[7,6,5,3,4,2,8,1]=>[2,3,4,6,5,7,1,8]=>[4,2,2]
[2,4,5,8,3,1,6,7]=>[2,3,6,1,5,7,8,4]=>[7,6,3,8,4,2,1,5]=>[1,1,2,1,1,2]
[2,7,4,6,1,5,8,3]=>[3,6,8,5,1,4,2,7]=>[6,3,1,4,8,5,7,2]=>[1,1,3,2,1]
[2,4,3,8,5,1,6,7]=>[2,6,1,3,5,7,8,4]=>[7,3,8,6,4,2,1,5]=>[1,2,1,1,1,2]
[7,8,3,2,5,4,6,1]=>[3,6,4,5,1,8,7,2]=>[6,3,5,4,8,1,2,7]=>[1,2,2,3]
[1,5,6,7,3,8,2,4]=>[2,5,3,7,4,8,1,6]=>[7,4,6,2,5,1,8,3]=>[1,2,2,2,1]
[1,6,5,4,8,3,2,7]=>[4,3,2,7,6,8,1,5]=>[5,6,7,2,3,1,8,4]=>[3,2,2,1]
[1,7,3,5,8,4,6,2]=>[4,6,8,3,2,7,1,5]=>[5,3,1,6,7,2,8,4]=>[1,1,3,2,1]
[7,2,1,6,4,8,5,3]=>[8,5,2,4,7,3,1,6]=>[1,4,7,5,2,6,8,3]=>[3,1,3,1]
[7,5,8,3,2,4,6,1]=>[5,4,2,6,1,8,7,3]=>[4,5,7,3,8,1,2,6]=>[3,2,3]
[3,8,7,2,4,6,5,1]=>[8,4,5,7,1,6,3,2]=>[1,5,4,2,8,3,6,7]=>[2,1,2,3]
[1,3,7,6,4,8,5,2]=>[8,5,4,2,3,7,1,6]=>[1,4,5,7,6,2,8,3]=>[4,1,2,1]
[3,1,8,7,6,4,2,5]=>[7,6,8,1,5,4,2,3]=>[2,3,1,8,4,5,7,6]=>[2,2,3,1]
[3,1,8,7,5,4,2,6]=>[7,6,1,5,8,4,2,3]=>[2,3,8,4,1,5,7,6]=>[3,1,3,1]
[3,1,7,6,5,4,2,8]=>[7,6,1,5,4,2,3,8]=>[2,3,8,4,5,7,6,1]=>[3,3,1,1]
[4,8,1,6,5,3,2,7]=>[7,1,6,5,3,4,8,2]=>[2,8,3,4,6,5,1,7]=>[2,3,1,2]
[8,4,1,7,6,3,2,5]=>[2,7,6,8,5,3,4,1]=>[7,2,3,1,4,6,5,8]=>[1,2,3,2]
[5,4,1,8,6,3,2,7]=>[2,1,7,6,5,8,3,4]=>[7,8,2,3,4,1,6,5]=>[2,3,2,1]
[5,4,1,7,6,3,2,8]=>[2,1,7,6,5,3,4,8]=>[7,8,2,3,4,6,5,1]=>[2,4,1,1]
[6,4,1,8,5,3,2,7]=>[2,7,6,5,1,8,3,4]=>[7,2,3,4,8,1,6,5]=>[1,4,2,1]
[8,4,1,7,5,3,2,6]=>[2,7,6,5,8,3,4,1]=>[7,2,3,4,1,6,5,8]=>[1,3,2,2]
[7,4,1,6,5,3,2,8]=>[2,7,6,5,3,4,1,8]=>[7,2,3,4,6,5,8,1]=>[1,4,2,1]
[7,5,6,1,4,3,2,8]=>[7,6,4,2,5,3,1,8]=>[2,3,5,7,4,6,8,1]=>[4,3,1]
[8,5,6,1,4,3,2,7]=>[7,6,4,2,5,3,8,1]=>[2,3,5,7,4,6,1,8]=>[4,2,2]
[5,7,6,1,4,3,2,8]=>[1,7,6,4,5,3,2,8]=>[8,2,3,5,4,6,7,1]=>[1,3,3,1]
[6,7,5,1,4,3,2,8]=>[7,6,4,1,5,3,2,8]=>[2,3,5,8,4,6,7,1]=>[4,3,1]
[8,7,5,1,4,3,2,6]=>[7,6,4,5,3,8,2,1]=>[2,3,5,4,6,1,7,8]=>[3,2,3]
[8,6,5,1,4,3,2,7]=>[7,6,4,5,3,2,8,1]=>[2,3,5,4,6,7,1,8]=>[3,3,2]
[1,8,6,3,4,2,5,7]=>[4,6,5,7,3,8,1,2]=>[5,3,4,2,6,1,8,7]=>[1,2,2,2,1]
[3,1,6,4,5,2,7,8]=>[1,4,6,5,2,3,7,8]=>[8,5,3,4,7,6,2,1]=>[1,1,3,1,1,1]
[3,1,6,4,5,8,2,7]=>[1,4,5,3,7,8,2,6]=>[8,5,4,6,2,1,7,3]=>[1,1,2,1,2,1]
[3,1,6,4,5,7,2,8]=>[1,4,5,3,7,2,6,8]=>[8,5,4,6,2,7,3,1]=>[1,1,2,2,1,1]
[4,6,8,7,2,5,1,3]=>[5,1,2,7,8,6,4,3]=>[4,8,7,2,1,3,5,6]=>[2,1,1,4]
[7,6,3,8,4,5,2,1]=>[5,8,3,2,1,7,6,4]=>[4,1,6,7,8,2,3,5]=>[1,4,3]
[5,2,7,8,1,4,3,6]=>[7,5,1,6,2,3,8,4]=>[2,4,8,3,7,6,1,5]=>[3,2,1,2]
[8,2,7,6,1,4,5,3]=>[6,8,5,7,2,4,3,1]=>[3,1,4,2,7,5,6,8]=>[1,2,2,3]
[5,2,3,4,7,1,6,8]=>[2,3,4,1,6,7,5,8]=>[7,6,5,8,3,2,4,1]=>[1,1,2,1,2,1]
[5,2,3,7,1,6,8,4]=>[6,8,2,1,3,5,4,7]=>[3,1,7,8,6,4,5,2]=>[1,3,1,2,1]
[5,2,3,4,7,8,1,6]=>[7,2,3,1,4,5,8,6]=>[2,7,6,8,5,4,1,3]=>[2,2,1,1,2]
[8,7,5,3,1,6,4,2]=>[4,8,7,5,3,6,2,1]=>[5,1,2,4,6,3,7,8]=>[1,4,3]
[1,4,7,8,5,2,3,6]=>[6,7,2,5,3,8,1,4]=>[3,2,7,4,6,1,8,5]=>[1,2,2,2,1]
[3,2,6,7,4,1,5,8]=>[6,1,5,2,3,7,4,8]=>[3,8,4,7,6,2,5,1]=>[2,2,1,2,1]
[5,8,3,7,6,4,1,2]=>[1,7,8,3,6,5,4,2]=>[8,2,1,6,3,4,5,7]=>[1,1,2,4]
[6,5,1,7,2,4,8,3]=>[6,8,5,3,2,1,4,7]=>[3,1,4,6,7,8,5,2]=>[1,5,1,1]
[3,6,7,1,4,2,5,8]=>[6,1,4,5,2,7,3,8]=>[3,8,5,4,7,2,6,1]=>[2,1,2,2,1]
[4,7,5,8,2,1,3,6]=>[6,1,5,3,7,2,8,4]=>[3,8,4,6,2,7,1,5]=>[2,2,2,2]
[8,1,2,7,5,4,3,6]=>[7,6,5,8,2,3,4,1]=>[2,3,4,1,7,6,5,8]=>[3,2,1,2]
[6,5,1,8,3,7,2,4]=>[5,7,2,1,8,6,3,4]=>[4,2,7,8,1,3,6,5]=>[1,3,3,1]
[1,8,7,5,3,2,6,4]=>[5,8,6,4,7,3,1,2]=>[4,1,3,5,2,6,8,7]=>[1,3,3,1]
[7,8,1,5,4,2,3,6]=>[6,7,5,3,4,1,8,2]=>[3,2,4,6,5,8,1,7]=>[1,3,2,2]
[2,7,5,1,4,6,3,8]=>[5,7,4,1,3,6,2,8]=>[4,2,5,8,6,3,7,1]=>[1,3,1,2,1]
[3,4,6,8,1,5,7,2]=>[6,1,2,3,8,5,7,4]=>[3,8,7,6,1,4,2,5]=>[2,1,1,2,2]
[5,7,6,1,4,3,8,2]=>[1,6,5,8,4,3,2,7]=>[8,3,4,1,5,6,7,2]=>[1,2,4,1]
[6,8,1,7,5,4,2,3]=>[7,1,8,6,5,3,4,2]=>[2,8,1,3,4,6,5,7]=>[2,4,2]
[6,3,5,7,1,4,2,8]=>[7,2,5,3,1,6,4,8]=>[2,7,4,6,8,3,5,1]=>[2,3,2,1]
[5,2,6,7,4,8,1,3]=>[3,1,7,5,2,4,8,6]=>[6,8,2,4,7,5,1,3]=>[2,3,1,2]
[1,7,5,2,6,4,8,3]=>[6,5,3,8,4,1,2,7]=>[3,4,6,1,5,8,7,2]=>[3,3,1,1]
[7,1,3,6,8,2,4,5]=>[6,7,3,4,8,2,1,5]=>[3,2,6,5,1,7,8,4]=>[1,2,1,3,1]
[3,1,2,7,5,4,8,6]=>[1,5,8,6,2,3,4,7]=>[8,4,1,3,7,6,5,2]=>[1,1,3,1,1,1]
[6,7,4,1,3,2,8,5]=>[5,8,4,3,1,6,2,7]=>[4,1,5,6,8,3,7,2]=>[1,4,2,1]
[1,7,2,8,4,3,5,6]=>[6,5,7,8,3,1,2,4]=>[3,4,2,1,6,8,7,5]=>[2,1,3,1,1]
[1,6,3,5,7,8,2,4]=>[4,7,3,2,5,8,1,6]=>[5,2,6,7,4,1,8,3]=>[1,3,1,2,1]
[7,6,4,1,8,3,2,5]=>[7,6,3,8,4,2,1,5]=>[2,3,6,1,5,7,8,4]=>[3,4,1]
[8,4,1,6,5,2,7,3]=>[2,8,6,5,3,4,7,1]=>[7,1,3,4,6,5,2,8]=>[1,4,1,2]
[4,2,1,5,7,8,3,6]=>[7,2,1,4,5,8,3,6]=>[2,7,8,5,4,1,6,3]=>[3,1,1,2,1]
[5,4,1,6,7,8,2,3]=>[4,2,1,7,5,8,3,6]=>[5,7,8,2,4,1,6,3]=>[3,2,2,1]
[5,1,4,6,7,8,2,3]=>[3,4,1,7,5,8,2,6]=>[6,5,8,2,4,1,7,3]=>[1,2,2,2,1]
[4,1,5,3,7,8,2,6]=>[3,1,7,4,5,8,2,6]=>[6,8,2,5,4,1,7,3]=>[2,2,1,2,1]
[7,1,5,4,6,3,2,8]=>[4,3,7,6,2,5,1,8]=>[5,6,2,3,7,4,8,1]=>[2,3,2,1]
[8,2,1,6,7,5,4,3]=>[4,8,7,2,6,3,5,1]=>[5,1,2,7,3,6,4,8]=>[1,3,2,2]
[1,2,4,7,6,3,8,5]=>[8,6,3,5,1,2,4,7]=>[1,3,6,4,8,7,5,2]=>[3,2,1,1,1]
[6,7,4,1,8,5,2,3]=>[7,3,1,8,6,4,2,5]=>[2,6,8,1,3,5,7,4]=>[3,4,1]
[8,6,4,1,5,7,3,2]=>[5,3,8,7,4,2,6,1]=>[4,6,1,2,5,7,3,8]=>[2,4,2]
[5,2,4,3,7,1,6,8]=>[4,2,3,1,6,7,5,8]=>[5,7,6,8,3,2,4,1]=>[2,2,1,2,1]
[3,2,1,7,5,8,4,6]=>[1,5,7,2,4,8,3,6]=>[8,4,2,7,5,1,6,3]=>[1,1,2,1,2,1]
[4,5,1,3,7,8,2,6]=>[1,7,4,2,5,8,3,6]=>[8,2,5,7,4,1,6,3]=>[1,3,1,2,1]
[7,6,4,3,1,5,2,8]=>[7,5,4,3,6,2,1,8]=>[2,4,5,6,3,7,8,1]=>[4,3,1]
[7,5,4,6,1,3,2,8]=>[7,5,3,2,6,4,1,8]=>[2,4,6,7,3,5,8,1]=>[4,3,1]
[1,5,6,3,7,8,2,4]=>[2,7,4,3,5,8,1,6]=>[7,2,5,6,4,1,8,3]=>[1,3,1,2,1]
[6,8,3,5,7,2,4,1]=>[6,3,1,4,8,7,5,2]=>[3,6,8,5,1,2,4,7]=>[3,1,4]
[8,6,5,7,2,1,4,3]=>[5,8,6,3,2,7,4,1]=>[4,1,3,6,7,2,5,8]=>[1,4,3]
[1,6,3,8,4,5,7,2]=>[5,6,2,8,3,7,1,4]=>[4,3,7,1,6,2,8,5]=>[1,2,2,2,1]
[7,5,4,2,6,3,8,1]=>[6,4,3,2,5,1,8,7]=>[3,5,6,7,4,8,1,2]=>[4,2,2]
[7,8,6,5,4,3,2,9,1]=>[1,7,6,5,4,3,2,9,8]=>[9,3,4,5,6,7,8,1,2]=>[1,6,2]
[9,7,6,5,4,3,1,2,8]=>[7,8,6,5,4,3,2,9,1]=>[3,2,4,5,6,7,8,1,9]=>[1,6,2]
[2,3,8,4,7,5,6,1]=>[6,8,4,7,1,2,5,3]=>[3,1,5,2,8,7,4,6]=>[1,2,2,1,2]
[3,7,2,8,6,4,5,1]=>[6,8,7,1,3,2,5,4]=>[3,1,2,8,6,7,4,5]=>[1,3,2,2]
[6,3,7,5,8,2,4,1]=>[6,4,2,1,3,8,7,5]=>[3,5,7,8,6,1,2,4]=>[4,1,3]
[4,3,7,8,6,2,5,1]=>[6,1,3,8,2,7,5,4]=>[3,8,6,1,7,2,4,5]=>[2,1,2,3]
[3,8,1,7,5,2,4,6]=>[6,7,1,5,8,3,4,2]=>[3,2,8,4,1,6,5,7]=>[1,2,1,2,2]
[2,4,7,8,6,1,5,3]=>[8,6,2,3,7,1,5,4]=>[1,3,7,6,2,8,4,5]=>[3,1,2,2]
[2,4,8,5,1,7,3,6]=>[7,2,4,8,1,5,6,3]=>[2,7,5,1,8,4,3,6]=>[2,1,2,1,2]
[2,8,3,5,1,6,4,7]=>[7,3,5,1,4,6,8,2]=>[2,6,4,8,5,3,1,7]=>[2,2,1,1,2]
[8,2,4,6,3,7,5,1]=>[8,3,5,2,4,7,6,1]=>[1,6,4,7,5,2,3,8]=>[2,2,1,3]
[4,5,3,8,2,1,7,6]=>[1,3,2,5,8,6,7,4]=>[8,6,7,4,1,3,2,5]=>[1,2,1,2,2]
[4,8,3,2,5,1,6,7]=>[1,4,3,6,5,7,8,2]=>[8,5,6,3,4,2,1,7]=>[1,2,2,1,2]
[5,2,7,1,3,8,6,4]=>[8,7,2,1,4,5,3,6]=>[1,2,7,8,5,4,6,3]=>[4,1,2,1]
[1,4,6,2,7,5,3,8]=>[7,2,6,4,1,3,5,8]=>[2,7,3,5,8,6,4,1]=>[2,3,1,1,1]
[8,2,7,5,1,4,6,3]=>[6,8,5,2,4,7,3,1]=>[3,1,4,7,5,2,6,8]=>[1,3,1,3]
[1,7,4,6,8,3,5,2]=>[6,3,4,2,8,7,1,5]=>[3,6,5,7,1,2,8,4]=>[2,2,3,1]
[7,3,1,2,5,6,4,8]=>[5,2,7,3,4,6,1,8]=>[4,7,2,6,5,3,8,1]=>[2,2,1,2,1]
[7,2,4,1,5,8,6,3]=>[3,8,2,5,7,4,1,6]=>[6,1,7,4,2,5,8,3]=>[1,2,1,3,1]
[7,8,2,1,5,4,6,3]=>[6,3,5,8,4,1,7,2]=>[3,6,4,1,5,8,2,7]=>[2,1,3,2]
[1,4,2,8,6,5,3,7]=>[7,2,6,5,8,1,3,4]=>[2,7,3,4,1,8,6,5]=>[2,2,2,1,1]
[1,5,2,4,6,3,8,7]=>[4,5,2,8,1,3,6,7]=>[5,4,7,1,8,6,3,2]=>[1,2,2,1,1,1]
[6,4,1,3,2,5,8,7]=>[4,8,3,2,5,1,6,7]=>[5,1,6,7,4,8,3,2]=>[1,3,2,1,1]
[5,2,3,7,8,1,6,4]=>[8,6,2,1,3,4,7,5]=>[1,3,7,8,6,5,2,4]=>[4,1,1,2]
[5,2,8,6,3,1,7,4]=>[5,1,8,6,2,4,7,3]=>[4,8,1,3,7,5,2,6]=>[2,3,1,2]
[7,6,3,4,2,8,1,5]=>[3,5,4,7,2,1,8,6]=>[6,4,5,2,7,8,1,3]=>[1,2,3,2]
[6,2,4,5,7,8,1,3]=>[3,4,7,2,1,5,8,6]=>[6,5,2,7,8,4,1,3]=>[1,1,3,1,2]
[8,6,3,2,5,7,1,4]=>[3,7,4,5,2,8,6,1]=>[6,2,5,4,7,1,3,8]=>[1,2,2,3]
[6,2,5,3,7,1,8,4]=>[8,4,2,3,1,6,5,7]=>[1,5,7,6,8,3,4,2]=>[3,2,2,1]
[8,5,3,6,7,2,1,4]=>[7,3,2,6,4,8,5,1]=>[2,6,7,3,5,1,4,8]=>[3,2,3]
[4,5,7,8,6,2,1,3]=>[7,1,2,6,3,8,5,4]=>[2,8,7,3,6,1,4,5]=>[2,1,2,3]
[1,2,8,4,3,6,7,5]=>[4,6,8,5,7,1,2,3]=>[5,3,1,4,2,8,7,6]=>[1,1,2,2,1,1]
[1,8,3,2,4,6,7,5]=>[3,6,8,4,5,7,1,2]=>[6,3,1,5,4,2,8,7]=>[1,1,2,1,2,1]
[1,7,3,2,6,8,4,5]=>[7,3,5,8,4,1,2,6]=>[2,6,4,1,5,8,7,3]=>[2,1,3,1,1]
[8,2,7,1,4,3,5,6]=>[6,2,4,5,7,8,3,1]=>[3,7,5,4,2,1,6,8]=>[2,1,1,1,3]
[7,2,1,3,6,8,4,5]=>[7,2,5,8,3,4,1,6]=>[2,7,4,1,6,5,8,3]=>[2,1,2,2,1]
[6,2,1,7,8,3,4,5]=>[6,7,2,4,1,8,3,5]=>[3,2,7,5,8,1,6,4]=>[1,2,2,2,1]
[4,7,8,1,6,5,3,2]=>[8,7,1,6,4,2,5,3]=>[1,2,8,3,5,7,4,6]=>[3,3,2]
[3,5,8,6,1,4,2,7]=>[2,7,1,5,6,4,8,3]=>[7,2,8,4,3,5,1,6]=>[1,2,1,2,2]
[8,7,2,6,5,4,3,1]=>[8,7,6,3,5,4,2,1]=>[1,2,3,6,4,5,7,8]=>[4,4]
[7,3,8,1,6,5,4,2]=>[8,7,2,6,4,1,5,3]=>[1,2,7,3,5,8,4,6]=>[3,3,2]
[7,3,8,2,6,5,4,1]=>[8,7,2,4,1,6,5,3]=>[1,2,7,5,8,3,4,6]=>[3,2,3]
[7,1,3,8,6,5,4,2]=>[8,7,6,3,5,2,1,4]=>[1,2,3,6,4,7,8,5]=>[4,3,1]
[8,1,3,7,6,5,4,2]=>[8,7,6,3,5,2,4,1]=>[1,2,3,6,4,7,5,8]=>[4,2,2]
[2,4,1,8,7,3,6,5]=>[8,2,6,7,1,5,3,4]=>[1,7,3,2,8,4,6,5]=>[2,1,2,2,1]
[7,3,8,6,1,5,4,2]=>[8,7,2,5,1,6,4,3]=>[1,2,7,4,8,3,5,6]=>[3,2,3]
[3,5,1,7,8,2,6,4]=>[2,8,1,6,4,7,3,5]=>[7,1,8,3,5,2,6,4]=>[1,2,2,2,1]
[5,4,7,8,2,1,6,3]=>[2,1,5,8,6,3,7,4]=>[7,8,4,1,3,6,2,5]=>[2,1,3,2]
[5,3,6,1,8,4,2,7]=>[7,2,1,6,3,8,4,5]=>[2,7,8,3,6,1,5,4]=>[3,2,2,1]
[6,3,8,7,1,5,4,2]=>[8,7,2,1,5,6,4,3]=>[1,2,7,8,4,3,5,6]=>[4,1,3]
[8,6,4,7,1,5,3,2]=>[3,8,7,5,2,6,4,1]=>[6,1,2,4,7,3,5,8]=>[1,4,3]
[6,4,7,1,5,3,2,8]=>[2,7,6,4,1,5,3,8]=>[7,2,3,5,8,4,6,1]=>[1,4,2,1]
[3,4,6,2,1,8,5,7]=>[1,2,4,7,3,8,5,6]=>[8,7,5,2,6,1,4,3]=>[1,1,1,2,2,1]
[4,5,7,2,1,6,3,8]=>[1,4,2,7,5,6,3,8]=>[8,5,7,2,4,3,6,1]=>[1,2,2,2,1]
[5,6,4,8,3,2,1,7]=>[1,3,2,7,6,5,8,4]=>[8,6,7,2,3,4,1,5]=>[1,2,3,2]
[5,7,4,8,2,1,6,3]=>[1,5,3,8,6,2,7,4]=>[8,4,6,1,3,7,2,5]=>[1,2,3,2]
[5,7,4,2,6,3,8,1]=>[1,6,4,3,5,2,8,7]=>[8,3,5,6,4,7,1,2]=>[1,3,2,2]
[5,7,4,1,6,2,8,3]=>[1,8,6,4,3,5,2,7]=>[8,1,3,5,6,4,7,2]=>[1,4,2,1]
[6,8,7,3,1,4,2,5]=>[7,5,4,1,6,8,3,2]=>[2,4,5,8,3,1,6,7]=>[4,1,3]
[8,5,6,1,7,3,2,4]=>[7,6,2,8,4,3,5,1]=>[2,3,7,1,5,6,4,8]=>[3,3,2]
[4,5,2,6,1,3,8,7]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[1,3,2,1,1]
[6,7,1,2,4,8,5,3]=>[8,5,7,3,1,4,2,6]=>[1,4,2,6,8,5,7,3]=>[2,3,2,1]
[2,3,6,4,7,5,8,1]=>[6,4,1,2,3,5,8,7]=>[3,5,8,7,6,4,1,2]=>[3,1,1,1,2]
[7,8,1,3,4,5,6,2]=>[4,5,6,8,3,1,7,2]=>[5,4,3,1,6,8,2,7]=>[1,1,1,3,2]
[1,8,2,6,7,3,4,5]=>[6,7,4,8,3,5,1,2]=>[3,2,5,1,6,4,8,7]=>[1,2,2,2,1]
[7,1,2,6,3,8,5,4]=>[8,7,5,2,3,4,1,6]=>[1,2,4,7,6,5,8,3]=>[4,1,2,1]
[8,1,2,6,3,7,5,4]=>[8,7,5,2,3,4,6,1]=>[1,2,4,7,6,5,3,8]=>[4,1,1,2]
[8,1,2,7,6,3,5,4]=>[8,6,7,5,2,3,4,1]=>[1,3,2,4,7,6,5,8]=>[2,3,1,2]
[4,8,7,3,1,6,2,5]=>[7,1,4,8,5,6,3,2]=>[2,8,5,1,4,3,6,7]=>[2,1,2,3]
[7,4,3,1,6,2,8,5]=>[3,2,8,6,4,5,1,7]=>[6,7,1,3,5,4,8,2]=>[2,3,2,1]
[3,7,6,2,4,8,1,5]=>[4,5,7,1,3,2,8,6]=>[5,4,2,8,6,7,1,3]=>[1,1,2,2,2]
[4,3,7,2,8,6,1,5]=>[1,7,8,2,4,3,6,5]=>[8,2,1,7,5,6,3,4]=>[1,1,2,2,2]
[6,1,2,7,4,3,8,5]=>[5,8,6,2,3,1,4,7]=>[4,1,3,7,6,8,5,2]=>[1,3,2,1,1]
[5,1,2,6,3,8,7,4]=>[4,8,7,2,1,3,5,6]=>[5,1,2,7,8,6,4,3]=>[1,4,1,1,1]
[6,1,2,8,3,5,7,4]=>[6,8,5,7,2,1,3,4]=>[3,1,4,2,7,8,6,5]=>[1,2,3,1,1]
[7,5,3,2,1,8,6,4]=>[3,8,4,2,7,5,1,6]=>[6,1,5,7,2,4,8,3]=>[1,3,3,1]
[4,2,1,5,3,6,7,8]=>[2,5,3,1,4,6,7,8]=>[7,4,6,8,5,3,2,1]=>[1,3,1,1,1,1]
[3,1,4,2,5,6,7,8,9]=>[4,2,1,3,5,6,7,8,9]=>[6,8,9,7,5,4,3,2,1]=>[3,1,1,1,1,1,1]
[6,2,5,4,1,8,7,3]=>[4,3,8,2,1,7,5,6]=>[5,6,1,7,8,2,4,3]=>[2,3,2,1]
[6,5,3,2,1,8,7,4]=>[3,8,4,2,1,7,5,6]=>[6,1,5,7,8,2,4,3]=>[1,4,2,1]
[8,4,3,2,7,6,1,5]=>[3,2,7,8,4,6,5,1]=>[6,7,2,1,5,3,4,8]=>[2,1,2,3]
[1,5,8,4,7,6,3,2]=>[8,2,4,7,6,5,1,3]=>[1,7,5,2,3,4,8,6]=>[2,1,4,1]
[6,8,3,7,5,2,1,4]=>[7,3,1,6,8,5,4,2]=>[2,6,8,3,1,4,5,7]=>[3,1,4]
[5,7,8,4,3,2,1,6]=>[7,1,6,5,4,2,8,3]=>[2,8,3,4,5,7,1,6]=>[2,4,2]
[6,4,3,8,5,2,1,7]=>[2,7,3,1,6,5,8,4]=>[7,2,6,8,3,4,1,5]=>[1,3,2,2]
[8,2,5,4,7,6,1,3]=>[4,3,7,8,2,6,5,1]=>[5,6,2,1,7,3,4,8]=>[2,1,2,3]
[7,2,5,4,8,6,1,3]=>[4,3,7,8,2,1,6,5]=>[5,6,2,1,7,8,3,4]=>[2,1,3,2]
[4,5,3,2,8,6,1,7]=>[1,3,2,7,4,6,8,5]=>[8,6,7,2,5,3,1,4]=>[1,2,2,1,2]
[3,2,5,4,8,6,1,7]=>[1,3,7,2,4,6,8,5]=>[8,6,2,7,5,3,1,4]=>[1,1,2,1,1,2]
[3,2,8,6,5,4,1,7]=>[7,6,1,5,2,4,8,3]=>[2,3,8,4,7,5,1,6]=>[3,2,1,2]
[8,4,3,6,5,2,1,7]=>[2,7,3,6,5,4,8,1]=>[7,2,6,3,4,5,1,8]=>[1,2,3,2]
[8,4,3,7,5,2,1,6]=>[2,7,3,6,5,8,4,1]=>[7,2,6,3,4,1,5,8]=>[1,2,2,3]
[3,2,7,8,5,4,1,6]=>[7,6,1,5,2,3,8,4]=>[2,3,8,4,7,6,1,5]=>[3,2,1,2]
[6,8,7,4,3,2,1,5]=>[1,7,6,5,4,8,3,2]=>[8,2,3,4,5,1,6,7]=>[1,4,3]
[3,6,1,4,8,7,2,5]=>[7,8,1,4,2,6,3,5]=>[2,1,8,5,7,3,6,4]=>[1,2,2,2,1]
[5,8,1,3,7,2,6,4]=>[8,4,1,6,7,3,5,2]=>[1,5,8,3,2,6,4,7]=>[3,1,2,2]
[4,7,5,1,8,2,6,3]=>[8,1,6,3,7,4,2,5]=>[1,8,3,6,2,5,7,4]=>[2,2,3,1]
[6,3,2,1,8,7,4,5]=>[2,7,8,3,1,6,4,5]=>[7,2,1,6,8,3,5,4]=>[1,1,3,2,1]
[6,2,3,1,8,7,4,5]=>[7,8,2,3,1,6,4,5]=>[2,1,7,6,8,3,5,4]=>[1,2,2,2,1]
[3,4,7,1,8,5,6,2]=>[6,8,1,2,7,4,3,5]=>[3,1,8,7,2,5,6,4]=>[1,2,1,3,1]
[3,4,8,1,7,5,6,2]=>[6,8,1,2,7,4,5,3]=>[3,1,8,7,2,5,4,6]=>[1,2,1,2,2]
[7,2,1,5,8,4,6,3]=>[4,6,8,2,7,3,1,5]=>[5,3,1,7,2,6,8,4]=>[1,1,2,3,1]
[8,3,6,4,1,7,5,2]=>[4,8,2,7,5,3,6,1]=>[5,1,7,2,4,6,3,8]=>[1,2,3,2]
[7,3,1,5,2,8,6,4]=>[2,4,8,7,3,5,1,6]=>[7,5,1,2,6,4,8,3]=>[1,1,3,2,1]
[7,1,6,4,2,8,5,3]=>[4,8,7,5,2,3,1,6]=>[5,1,2,4,7,6,8,3]=>[1,4,2,1]
[3,7,4,1,5,8,6,2]=>[3,8,1,5,7,4,2,6]=>[6,1,8,4,2,5,7,3]=>[1,2,1,3,1]
[5,8,6,1,2,7,4,3]=>[1,8,7,4,5,3,6,2]=>[8,1,2,5,4,6,3,7]=>[1,3,2,2]
[6,8,1,4,3,7,5,2]=>[4,8,5,1,7,3,6,2]=>[5,1,4,8,2,6,3,7]=>[1,3,2,2]
[6,7,1,4,3,8,5,2]=>[4,8,5,1,7,3,2,6]=>[5,1,4,8,2,6,7,3]=>[1,3,3,1]
[4,7,1,5,3,8,6,2]=>[1,4,8,5,7,3,2,6]=>[8,5,1,4,2,6,7,3]=>[1,1,2,3,1]
[6,8,1,2,4,7,5,3]=>[8,5,7,3,1,4,6,2]=>[1,4,2,6,8,5,3,7]=>[2,3,1,2]
[7,1,6,4,8,3,5,2]=>[4,6,3,8,7,2,1,5]=>[5,3,6,1,2,7,8,4]=>[1,2,4,1]
[8,6,4,1,3,7,5,2]=>[8,5,3,7,4,2,6,1]=>[1,4,6,2,5,7,3,8]=>[3,3,2]
[8,5,3,6,1,7,4,2]=>[8,3,2,7,5,4,6,1]=>[1,6,7,2,4,5,3,8]=>[3,3,2]
[8,5,6,1,2,7,4,3]=>[8,7,4,2,5,3,6,1]=>[1,2,5,7,4,6,3,8]=>[4,2,2]
[8,6,2,5,4,7,3,1]=>[5,4,8,3,2,7,6,1]=>[4,5,1,6,7,2,3,8]=>[2,3,3]
[8,5,2,1,4,3,6,7]=>[3,6,4,5,2,7,8,1]=>[6,3,5,4,7,2,1,8]=>[1,2,2,1,2]
[2,8,4,1,3,6,7,5]=>[6,3,8,1,4,5,7,2]=>[3,6,1,8,5,4,2,7]=>[2,2,1,1,2]
[8,1,2,4,5,6,7,3]=>[4,5,6,8,2,3,7,1]=>[5,4,3,1,7,6,2,8]=>[1,1,1,2,1,2]
[6,1,4,3,2,7,8,5]=>[4,3,6,8,2,1,5,7]=>[5,6,3,1,7,8,4,2]=>[2,1,3,1,1]
[1,8,3,6,7,2,4,5]=>[6,7,3,4,8,5,1,2]=>[3,2,6,5,1,4,8,7]=>[1,2,1,3,1]
[1,2,8,3,7,4,6,5]=>[8,6,7,4,5,1,2,3]=>[1,3,2,5,4,8,7,6]=>[2,2,2,1,1]
[1,9,2,3,4,5,6,7,8,10]=>[3,4,5,6,7,8,9,1,2,10]=>[8,7,6,5,4,3,2,10,9,1]=>[1,1,1,1,1,1,2,1,1]
[8,2,6,5,4,3,1,7]=>[7,6,5,2,4,3,8,1]=>[2,3,4,7,5,6,1,8]=>[4,2,2]
[8,2,7,6,4,5,3,1]=>[5,8,7,6,2,4,3,1]=>[4,1,2,3,7,5,6,8]=>[1,4,3]
[8,7,3,5,4,2,6,1]=>[6,3,5,4,8,7,2,1]=>[3,6,4,5,1,2,7,8]=>[2,2,4]
[3,7,1,8,2,5,4,6]=>[7,1,5,6,8,3,2,4]=>[2,8,4,3,1,6,7,5]=>[2,1,1,3,1]
[4,5,8,6,1,3,7,2]=>[1,2,6,8,5,4,7,3]=>[8,7,3,1,4,5,2,6]=>[1,1,1,3,2]
[4,5,8,6,2,7,3,1]=>[8,1,2,5,4,7,6,3]=>[1,8,7,4,5,2,3,6]=>[2,1,2,3]
[4,6,7,1,5,3,8,2]=>[6,1,5,2,8,4,3,7]=>[3,8,4,7,1,5,6,2]=>[2,2,3,1]
[4,6,7,2,1,8,5,3]=>[8,1,4,2,7,5,3,6]=>[1,8,5,7,2,4,6,3]=>[2,2,3,1]
[4,2,5,6,7,8,3,1]=>[3,1,4,5,8,2,7,6]=>[6,8,5,4,1,7,2,3]=>[2,1,1,2,2]
[4,1,3,5,6,7,8,2]=>[3,4,1,5,6,8,2,7]=>[6,5,8,4,3,1,7,2]=>[1,2,1,1,2,1]
[3,7,8,4,5,1,6,2]=>[4,8,6,1,5,2,7,3]=>[5,1,3,8,4,7,2,6]=>[1,3,2,2]
[4,6,8,3,2,7,1,5]=>[5,1,4,2,7,8,6,3]=>[4,8,5,7,2,1,3,6]=>[2,2,1,3]
[4,6,8,2,3,7,1,5]=>[1,4,5,2,7,8,6,3]=>[8,5,4,7,2,1,3,6]=>[1,1,2,1,3]
[3,8,1,7,4,5,2,6]=>[5,7,1,6,8,3,4,2]=>[4,2,8,3,1,6,5,7]=>[1,2,1,2,2]
[4,5,8,3,7,1,2,6]=>[1,2,6,4,7,8,5,3]=>[8,7,3,5,2,1,4,6]=>[1,1,2,1,3]
[3,7,8,4,6,2,5,1]=>[4,6,2,8,1,7,5,3]=>[5,3,7,1,8,2,4,6]=>[1,2,2,3]
[3,8,6,2,5,1,7,4]=>[8,4,6,1,5,3,7,2]=>[1,5,3,8,4,6,2,7]=>[2,2,2,2]
[4,5,8,6,1,2,7,3]=>[1,2,8,5,6,4,7,3]=>[8,7,1,4,3,5,2,6]=>[1,1,2,2,2]
[4,6,8,5,2,7,1,3]=>[5,1,2,7,4,8,6,3]=>[4,8,7,2,5,1,3,6]=>[2,1,2,3]
[3,7,8,5,2,6,1,4]=>[5,7,4,1,2,8,6,3]=>[4,2,5,8,7,1,3,6]=>[1,3,1,3]
[3,7,8,5,4,1,6,2]=>[8,6,5,1,4,2,7,3]=>[1,3,4,8,5,7,2,6]=>[4,2,2]
[4,6,8,5,3,1,7,2]=>[2,8,1,6,5,4,7,3]=>[7,1,8,3,4,5,2,6]=>[1,2,3,2]
[7,8,2,3,5,4,1,6]=>[7,3,4,6,5,1,8,2]=>[2,6,5,3,4,8,1,7]=>[2,1,3,2]
[5,1,3,7,6,4,8,2]=>[6,5,3,1,4,8,2,7]=>[3,4,6,8,5,1,7,2]=>[4,1,2,1]
[4,6,5,2,7,8,1,3]=>[7,1,4,3,2,5,8,6]=>[2,8,5,6,7,4,1,3]=>[2,3,1,2]
[4,6,5,1,7,3,8,2]=>[6,1,5,3,2,8,4,7]=>[3,8,4,6,7,1,5,2]=>[2,3,2,1]
[5,7,3,1,2,4,8,6]=>[8,4,3,1,5,6,2,7]=>[1,5,6,8,4,3,7,2]=>[4,1,2,1]
[6,3,2,5,1,7,4,8]=>[2,7,3,5,4,1,6,8]=>[7,2,6,4,5,8,3,1]=>[1,2,3,1,1]
[6,1,2,4,8,5,3,7]=>[7,4,6,8,2,1,3,5]=>[2,5,3,1,7,8,6,4]=>[2,1,3,1,1]
[6,3,1,7,2,5,8,4]=>[2,6,8,5,3,1,4,7]=>[7,3,1,4,6,8,5,2]=>[1,1,4,1,1]
[3,7,2,8,5,1,4,6]=>[6,7,1,3,5,2,8,4]=>[3,2,8,6,4,7,1,5]=>[1,2,1,2,2]
[3,6,5,2,4,7,1,8]=>[4,5,1,3,2,7,6,8]=>[5,4,8,6,7,2,3,1]=>[1,2,2,2,1]
[1,2,3,4,5,6,8,7,9]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,9,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,7,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1]
[5,2,7,3,4,6,1,8]=>[4,5,1,7,2,6,3,8]=>[5,4,8,2,7,3,6,1]=>[1,2,2,2,1]
[1,3,5,8,6,4,7,2]=>[6,3,5,8,2,7,1,4]=>[3,6,4,1,7,2,8,5]=>[2,1,2,2,1]
[6,1,7,4,8,5,3,2]=>[8,4,3,1,7,6,2,5]=>[1,5,6,8,2,3,7,4]=>[4,3,1]
[5,7,4,1,3,6,8,2]=>[5,1,6,3,8,4,2,7]=>[4,8,3,6,1,5,7,2]=>[2,2,3,1]
[7,4,3,1,6,5,8,2]=>[3,2,6,5,8,4,1,7]=>[6,7,3,4,1,5,8,2]=>[2,2,3,1]
[8,6,1,7,5,3,2,4]=>[7,6,8,5,3,2,4,1]=>[2,3,1,4,6,7,5,8]=>[2,4,2]
[7,8,1,4,6,5,3,2]=>[8,4,7,6,3,1,5,2]=>[1,5,2,3,6,8,4,7]=>[2,4,2]
[7,8,6,1,4,5,3,2]=>[5,8,7,4,1,6,3,2]=>[4,1,2,5,8,3,6,7]=>[1,4,3]
[5,1,7,6,3,4,2,8]=>[5,1,7,6,4,2,3,8]=>[4,8,2,3,5,7,6,1]=>[2,4,1,1]
[6,2,7,3,8,5,4,1]=>[8,7,4,2,1,3,6,5]=>[1,2,5,7,8,6,3,4]=>[5,1,2]
[1,2,7,5,3,4,8,6]=>[8,5,4,6,1,2,3,7]=>[1,4,5,3,8,7,6,2]=>[3,2,1,1,1]
[7,2,8,3,6,4,5,1]=>[6,8,4,7,2,1,5,3]=>[3,1,5,2,7,8,4,6]=>[1,2,3,2]
[6,2,7,8,3,1,4,5]=>[6,5,7,2,1,3,8,4]=>[3,4,2,7,8,6,1,5]=>[2,3,1,2]
[1,7,8,2,5,3,4,6]=>[6,7,4,5,2,8,1,3]=>[3,2,5,4,7,1,8,6]=>[1,2,2,2,1]
[3,7,8,1,2,5,6,4]=>[6,8,1,4,5,2,7,3]=>[3,1,8,5,4,7,2,6]=>[1,2,1,2,2]
[1,2,8,7,3,4,6,5]=>[8,5,6,7,4,1,2,3]=>[1,4,3,2,5,8,7,6]=>[2,1,3,1,1]
[8,2,7,4,5,1,6,3]=>[4,8,6,2,5,7,3,1]=>[5,1,3,7,4,2,6,8]=>[1,3,1,3]
[7,5,4,8,6,1,2,3]=>[6,3,2,7,1,8,5,4]=>[3,6,7,2,8,1,4,5]=>[3,2,3]
[7,1,8,6,4,5,2,3]=>[7,5,8,6,4,2,1,3]=>[2,4,1,3,5,7,8,6]=>[2,5,1]
[8,7,5,1,4,3,6,2]=>[6,5,8,4,3,7,2,1]=>[3,4,1,5,6,2,7,8]=>[2,3,3]
[1,5,7,8,3,4,2,6]=>[2,5,7,6,3,8,1,4]=>[7,4,2,3,6,1,8,5]=>[1,1,3,2,1]
[8,4,1,3,7,5,6,2]=>[6,2,8,4,7,3,5,1]=>[3,7,1,5,2,6,4,8]=>[2,2,2,2]
[1,8,5,7,4,2,3,6]=>[6,3,7,5,8,4,1,2]=>[3,6,2,4,1,5,8,7]=>[2,2,3,1]
[2,1,6,8,5,3,4,7]=>[6,3,7,1,5,8,2,4]=>[3,6,2,8,4,1,7,5]=>[2,2,1,2,1]
[4,5,1,3,8,6,7,2]=>[1,6,2,8,4,7,3,5]=>[8,3,7,1,5,2,6,4]=>[1,2,2,2,1]
[5,6,8,7,3,1,2,4]=>[1,6,2,7,5,8,4,3]=>[8,3,7,2,4,1,5,6]=>[1,2,2,3]
[6,7,5,3,8,1,2,4]=>[6,4,1,7,3,2,8,5]=>[3,5,8,2,6,7,1,4]=>[3,3,2]
[6,2,3,4,7,1,8,5]=>[8,2,3,4,1,6,5,7]=>[1,7,6,5,8,3,4,2]=>[2,1,2,2,1]
[6,8,5,7,3,1,2,4]=>[6,1,7,5,3,8,4,2]=>[3,8,2,4,6,1,5,7]=>[2,3,3]
[5,7,8,6,3,1,2,4]=>[1,6,7,5,2,8,4,3]=>[8,3,2,4,7,1,5,6]=>[1,1,3,3]
[5,1,4,2,6,8,7,3]=>[3,8,5,1,7,2,4,6]=>[6,1,4,8,2,7,5,3]=>[1,3,2,1,1]
[6,3,2,4,7,1,8,5]=>[2,8,3,4,1,6,5,7]=>[7,1,6,5,8,3,4,2]=>[1,2,2,2,1]
[1,5,6,8,4,2,3,7]=>[2,6,3,7,5,8,1,4]=>[7,3,6,2,4,1,8,5]=>[1,2,2,2,1]
[5,7,8,3,6,1,2,4]=>[1,6,4,7,2,8,5,3]=>[8,3,5,2,7,1,4,6]=>[1,2,2,3]
[1,5,8,6,2,4,3,7]=>[2,7,5,6,4,8,1,3]=>[7,2,4,3,5,1,8,6]=>[1,2,2,2,1]
[1,5,3,7,2,6,8,4]=>[6,2,8,3,5,1,4,7]=>[3,7,1,6,4,8,5,2]=>[2,2,2,1,1]
[5,8,6,3,7,1,2,4]=>[1,6,4,7,3,8,5,2]=>[8,3,5,2,6,1,4,7]=>[1,2,2,3]
[1,5,2,4,8,6,7,3]=>[6,2,8,4,7,1,3,5]=>[3,7,1,5,2,8,6,4]=>[2,2,2,1,1]
[1,5,4,2,6,8,7,3]=>[3,2,8,5,7,1,4,6]=>[6,7,1,4,2,8,5,3]=>[2,2,2,1,1]
[5,7,6,3,8,1,2,4]=>[1,6,4,7,3,2,8,5]=>[8,3,5,2,6,7,1,4]=>[1,2,3,2]
[5,7,6,8,3,1,2,4]=>[1,6,7,5,3,2,8,4]=>[8,3,2,4,6,7,1,5]=>[1,1,4,2]
[6,8,7,5,3,1,2,4]=>[6,1,7,5,8,4,3,2]=>[3,8,2,4,1,5,6,7]=>[2,2,4]
[1,2,5,3,6,8,7,4]=>[3,8,5,7,1,2,4,6]=>[6,1,4,2,8,7,5,3]=>[1,2,2,1,1,1]
[7,3,6,1,4,8,2,5]=>[2,5,7,8,4,3,1,6]=>[7,4,2,1,5,6,8,3]=>[1,1,1,4,1]
[7,8,1,6,5,3,4,2]=>[6,8,7,5,3,1,4,2]=>[3,1,2,4,6,8,5,7]=>[1,5,2]
[8,7,3,2,1,4,6,5]=>[4,3,8,5,6,7,2,1]=>[5,6,1,4,3,2,7,8]=>[2,2,1,3]
[8,3,5,1,7,4,2,6]=>[7,2,6,3,8,4,5,1]=>[2,7,3,6,1,5,4,8]=>[2,2,2,2]
[3,5,6,8,4,2,7,1]=>[2,3,6,1,5,8,7,4]=>[7,6,3,8,4,1,2,5]=>[1,1,2,1,3]
[2,8,6,3,4,1,7,5]=>[4,5,8,6,1,3,7,2]=>[5,4,1,3,8,6,2,7]=>[1,1,3,1,2]
[4,3,6,2,8,5,7,1]=>[1,6,2,3,8,4,7,5]=>[8,3,7,6,1,5,2,4]=>[1,2,1,2,2]
[1,7,2,3,5,8,6,4]=>[8,5,7,3,4,1,2,6]=>[1,4,2,6,5,8,7,3]=>[2,2,2,1,1]
[4,6,2,3,5,1,7,8]=>[3,1,4,6,5,2,7,8]=>[6,8,5,3,4,7,2,1]=>[2,1,3,1,1]
[6,4,8,7,2,1,5,3]=>[2,5,1,8,6,7,4,3]=>[7,4,8,1,3,2,5,6]=>[1,2,2,3]
[2,8,4,3,6,7,1,5]=>[3,7,4,5,8,1,6,2]=>[6,2,5,4,1,8,3,7]=>[1,2,1,2,2]
[7,3,2,5,6,1,8,4]=>[2,4,8,3,6,5,1,7]=>[7,5,1,6,3,4,8,2]=>[1,1,2,3,1]
[1,6,7,8,2,4,3,5]=>[7,5,2,6,3,8,1,4]=>[2,4,7,3,6,1,8,5]=>[3,2,2,1]
[4,1,2,8,5,3,7,6]=>[5,1,8,6,7,2,3,4]=>[4,8,1,3,2,7,6,5]=>[2,2,2,1,1]
[3,8,4,2,5,1,7,6]=>[4,1,3,5,8,6,7,2]=>[5,8,6,4,1,3,2,7]=>[2,1,1,2,2]
[1,8,5,6,4,3,2,7]=>[3,7,6,5,4,8,1,2]=>[6,2,3,4,5,1,8,7]=>[1,4,2,1]
[2,8,3,5,6,4,1,7]=>[4,7,3,6,1,5,8,2]=>[5,2,6,3,8,4,1,7]=>[1,2,2,1,2]
[4,1,5,7,6,8,2,3]=>[1,7,3,5,4,8,2,6]=>[8,2,6,4,5,1,7,3]=>[1,2,2,2,1]
[7,6,8,3,2,5,1,4]=>[5,4,7,2,1,8,6,3]=>[4,5,2,7,8,1,3,6]=>[2,3,3]
[2,7,8,1,6,4,5,3]=>[6,8,7,4,1,2,5,3]=>[3,1,2,5,8,7,4,6]=>[1,4,1,2]
[2,7,1,4,5,3,8,6]=>[4,5,8,1,3,6,2,7]=>[5,4,1,8,6,3,7,2]=>[1,1,2,1,2,1]
[1,5,2,7,4,3,6,8]=>[6,5,2,7,1,3,4,8]=>[3,4,7,2,8,6,5,1]=>[3,2,1,1,1]
[5,1,3,8,4,6,2,7]=>[5,7,3,1,6,8,2,4]=>[4,2,6,8,3,1,7,5]=>[1,3,1,2,1]
[6,5,8,7,1,3,2,4]=>[7,5,2,1,6,8,4,3]=>[2,4,7,8,3,1,5,6]=>[4,1,3]
[2,7,3,5,1,6,8,4]=>[6,3,4,8,1,5,2,7]=>[3,6,5,1,8,4,7,2]=>[2,1,2,2,1]
[5,7,6,8,2,1,4,3]=>[1,5,8,6,3,2,7,4]=>[8,4,1,3,6,7,2,5]=>[1,1,4,2]
[1,2,6,5,3,4,7,8]=>[5,6,4,1,2,3,7,8]=>[4,3,5,8,7,6,2,1]=>[1,3,1,1,1,1]
[1,7,2,5,6,8,3,4]=>[4,7,5,8,3,1,2,6]=>[5,2,4,1,6,8,7,3]=>[1,2,3,1,1]
[1,6,2,4,5,3,7,8]=>[4,6,3,5,1,2,7,8]=>[5,3,6,4,8,7,2,1]=>[1,2,2,1,1,1]
[1,3,2,8,4,5,7,6]=>[8,2,5,6,7,1,3,4]=>[1,7,4,3,2,8,6,5]=>[2,1,1,2,1,1]
[1,6,8,2,4,3,5,7]=>[6,4,5,2,7,8,1,3]=>[3,5,4,7,2,1,8,6]=>[2,2,1,2,1]
[1,6,7,2,5,3,4,8]=>[6,7,4,2,5,1,3,8]=>[3,2,5,7,4,8,6,1]=>[1,3,2,1,1]
[1,2,8,3,6,7,4,5]=>[7,5,8,4,6,1,2,3]=>[2,4,1,5,3,8,7,6]=>[2,2,2,1,1]
[1,7,2,5,3,4,8,6]=>[8,5,3,4,6,1,2,7]=>[1,4,6,5,3,8,7,2]=>[3,1,2,1,1]
[7,1,5,6,2,3,8,4]=>[8,5,3,6,2,4,1,7]=>[1,4,6,3,7,5,8,2]=>[3,2,2,1]
[1,7,5,6,2,3,8,4]=>[8,5,3,6,4,1,2,7]=>[1,4,6,3,5,8,7,2]=>[3,3,1,1]
[6,1,5,3,4,8,2,7]=>[4,5,3,7,1,8,2,6]=>[5,4,6,2,8,1,7,3]=>[1,2,2,2,1]
[7,8,4,1,5,6,2,3]=>[7,5,3,8,4,1,6,2]=>[2,4,6,1,5,8,3,7]=>[3,3,2]
[5,8,1,3,6,7,2,4]=>[7,4,1,5,8,3,6,2]=>[2,5,8,4,1,6,3,7]=>[3,1,2,2]
[1,2,5,4,8,3,6,7]=>[4,3,6,7,8,1,2,5]=>[5,6,3,2,1,8,7,4]=>[2,1,1,2,1,1]
[3,5,4,7,8,1,2,6]=>[3,1,2,6,7,4,8,5]=>[6,8,7,3,2,5,1,4]=>[2,1,1,2,2]
[1,6,4,7,8,2,3,5]=>[3,6,2,7,4,8,1,5]=>[6,3,7,2,5,1,8,4]=>[1,2,2,2,1]
[6,2,7,3,8,5,1,4]=>[7,8,4,2,1,3,6,5]=>[2,1,5,7,8,6,3,4]=>[1,4,1,2]
[1,3,7,8,5,6,2,4]=>[7,5,3,8,2,6,1,4]=>[2,4,6,1,7,3,8,5]=>[3,2,2,1]
[8,1,7,4,6,2,3,5]=>[6,4,7,8,5,2,3,1]=>[3,5,2,1,4,7,6,8]=>[2,1,3,2]
[4,5,8,7,1,2,3,6]=>[1,5,2,6,7,8,4,3]=>[8,4,7,3,2,1,5,6]=>[1,2,1,1,3]
[4,1,8,5,7,2,3,6]=>[1,6,4,7,8,5,2,3]=>[8,3,5,2,1,4,7,6]=>[1,2,1,3,1]
[2,6,5,4,1,8,3,7]=>[7,4,3,1,2,8,5,6]=>[2,5,6,8,7,1,4,3]=>[4,1,2,1]
[6,5,4,1,3,8,2,7]=>[5,7,3,2,1,8,4,6]=>[4,2,6,7,8,1,5,3]=>[1,4,2,1]
[1,3,8,7,4,2,6,5]=>[5,8,6,7,2,4,1,3]=>[4,1,3,2,7,5,8,6]=>[1,2,2,2,1]
[8,7,4,3,1,5,2,6]=>[7,5,4,3,6,8,2,1]=>[2,4,5,6,3,1,7,8]=>[4,1,3]
[8,2,5,1,4,6,7,3]=>[5,6,2,3,8,4,7,1]=>[4,3,7,6,1,5,2,8]=>[1,2,1,2,2]
[3,8,4,5,1,6,7,2]=>[3,6,1,4,8,5,7,2]=>[6,3,8,5,1,4,2,7]=>[1,2,1,2,2]
[8,5,4,1,3,6,7,2]=>[5,6,3,2,8,4,7,1]=>[4,3,6,7,1,5,2,8]=>[1,3,2,2]
[8,3,1,7,5,6,4,2]=>[5,8,2,7,6,3,4,1]=>[4,1,7,2,3,6,5,8]=>[1,2,3,2]
[8,4,7,6,5,3,1,2]=>[7,8,2,6,5,4,3,1]=>[2,1,7,3,4,5,6,8]=>[1,2,5]
[8,1,4,5,7,6,3,2]=>[8,3,4,7,6,2,5,1]=>[1,6,5,2,3,7,4,8]=>[2,1,3,2]
[2,4,1,8,5,7,6,3]=>[8,2,5,7,1,6,3,4]=>[1,7,4,2,8,3,6,5]=>[2,1,2,2,1]
[8,3,1,7,4,2,6,5]=>[2,5,8,6,7,3,4,1]=>[7,4,1,3,2,6,5,8]=>[1,1,2,2,2]
[8,2,7,3,1,6,5,4]=>[8,4,7,2,5,6,3,1]=>[1,5,2,7,4,3,6,8]=>[2,2,1,3]
[1,8,4,2,3,7,6,5]=>[3,8,7,4,5,6,1,2]=>[6,1,2,5,4,3,8,7]=>[1,3,1,2,1]
[8,5,1,2,4,3,7,6]=>[5,8,3,4,2,6,7,1]=>[4,1,6,5,7,3,2,8]=>[1,2,2,1,2]
[8,4,5,7,6,2,3,1]=>[2,3,6,8,7,5,4,1]=>[7,6,3,1,2,4,5,8]=>[1,1,1,5]
[2,3,1,8,7,6,4,5]=>[7,8,6,1,2,5,3,4]=>[2,1,3,8,7,4,6,5]=>[1,3,1,2,1]
[4,2,8,7,3,1,5,6]=>[1,6,5,7,8,2,4,3]=>[8,3,4,2,1,7,5,6]=>[1,2,1,2,2]
[1,3,4,8,7,2,5,6]=>[6,7,8,2,3,5,1,4]=>[3,2,1,7,6,4,8,5]=>[1,1,2,1,2,1]
[8,1,3,4,6,7,2,5]=>[7,3,4,5,8,2,6,1]=>[2,6,5,4,1,7,3,8]=>[2,1,1,2,2]
[3,4,8,2,6,7,1,5]=>[7,1,2,4,5,8,6,3]=>[2,8,7,5,4,1,3,6]=>[2,1,1,1,3]
[3,6,8,2,5,1,7,4]=>[8,4,1,2,6,5,7,3]=>[1,5,8,7,3,4,2,6]=>[3,1,2,2]
[3,8,2,5,7,4,6,1]=>[4,6,8,1,3,7,5,2]=>[5,3,1,8,6,2,4,7]=>[1,1,2,1,3]
[8,4,2,1,7,5,6,3]=>[6,2,8,3,7,4,5,1]=>[3,7,1,6,2,5,4,8]=>[2,2,2,2]
[8,2,7,5,6,4,1,3]=>[7,4,8,6,2,5,3,1]=>[2,5,1,3,7,4,6,8]=>[2,3,3]
[6,8,5,4,1,7,2,3]=>[7,1,8,5,4,3,6,2]=>[2,8,1,4,5,6,3,7]=>[2,4,2]
[2,8,1,5,7,6,3,4]=>[4,7,8,6,1,3,5,2]=>[5,2,1,3,8,6,4,7]=>[1,1,3,1,2]
[3,1,8,2,7,5,6,4]=>[6,8,1,7,4,5,2,3]=>[3,1,8,2,5,4,7,6]=>[1,2,2,2,1]
[2,8,4,7,3,6,5,1]=>[8,3,5,7,6,1,4,2]=>[1,6,4,2,3,8,5,7]=>[2,1,3,2]
[8,4,7,2,1,6,5,3]=>[2,8,4,7,5,6,3,1]=>[7,1,5,2,4,3,6,8]=>[1,2,2,3]
[1,8,4,7,6,5,2,3]=>[7,8,3,6,5,4,1,2]=>[2,1,6,3,4,5,8,7]=>[1,2,4,1]
[8,4,7,1,3,6,5,2]=>[2,8,5,7,4,6,3,1]=>[7,1,4,2,5,3,6,8]=>[1,2,2,3]
[2,3,4,7,6,8,1,5]=>[7,5,1,2,3,4,8,6]=>[2,4,8,7,6,5,1,3]=>[3,1,1,1,2]
[3,8,1,2,5,6,4,7]=>[1,5,7,3,4,6,8,2]=>[8,4,2,6,5,3,1,7]=>[1,1,2,1,1,2]
[3,7,1,2,5,6,4,8]=>[1,5,7,3,4,6,2,8]=>[8,4,2,6,5,3,7,1]=>[1,1,2,1,2,1]
[8,5,2,1,4,6,7,3]=>[3,5,6,2,8,4,7,1]=>[6,4,3,7,1,5,2,8]=>[1,1,2,2,2]
[4,2,6,3,8,5,7,1]=>[1,6,3,8,2,4,7,5]=>[8,3,6,1,7,5,2,4]=>[1,2,2,1,2]
[4,5,2,6,7,1,8,3]=>[1,4,2,8,3,6,5,7]=>[8,5,7,1,6,3,4,2]=>[1,2,2,2,1]
[2,8,6,4,7,3,1,5]=>[4,7,6,3,8,1,5,2]=>[5,2,3,6,1,8,4,7]=>[1,3,2,2]
[3,1,8,6,5,2,7,4]=>[8,6,1,5,4,7,2,3]=>[1,3,8,4,5,2,7,6]=>[3,2,2,1]
[8,3,1,5,2,6,7,4]=>[2,6,4,8,3,5,7,1]=>[7,3,5,1,6,4,2,8]=>[1,2,2,1,2]
[3,8,2,4,1,5,7,6]=>[1,3,4,8,5,6,7,2]=>[8,6,5,1,4,3,2,7]=>[1,1,1,2,1,2]
[5,8,3,2,4,1,7,6]=>[4,3,1,5,8,6,7,2]=>[5,6,8,4,1,3,2,7]=>[3,1,2,2]
[7,2,6,8,4,3,5,1]=>[6,5,3,8,2,1,7,4]=>[3,4,6,1,7,8,2,5]=>[3,3,2]
[6,5,3,2,4,8,1,7]=>[4,3,5,2,1,7,8,6]=>[5,6,4,7,8,2,1,3]=>[2,3,1,2]
[5,2,4,6,1,3,8,7]=>[3,8,2,1,5,4,6,7]=>[6,1,7,8,4,5,3,2]=>[1,3,2,1,1]
[7,2,3,4,6,8,1,5]=>[7,2,3,4,5,1,8,6]=>[2,7,6,5,4,8,1,3]=>[2,1,1,2,2]
[8,3,4,6,7,5,1,2]=>[7,2,3,4,8,6,5,1]=>[2,7,6,5,1,3,4,8]=>[2,1,1,4]
[6,8,3,4,7,5,2,1]=>[8,3,1,4,7,6,5,2]=>[1,6,8,5,2,3,4,7]=>[3,1,4]
[4,8,1,5,7,6,3,2]=>[8,1,4,7,6,3,5,2]=>[1,8,5,2,3,6,4,7]=>[2,1,3,2]
[3,7,4,6,8,2,5,1]=>[6,3,4,1,2,8,7,5]=>[3,6,5,8,7,1,2,4]=>[2,2,1,3]
[4,7,1,6,8,3,2,5]=>[7,1,6,4,8,3,2,5]=>[2,8,3,5,1,6,7,4]=>[2,2,3,1]
[4,5,2,8,1,7,3,6]=>[1,7,2,8,3,5,6,4]=>[8,2,7,1,6,4,3,5]=>[1,2,2,1,2]
[3,7,5,2,8,6,1,4]=>[7,3,8,1,4,2,6,5]=>[2,6,1,8,5,7,3,4]=>[2,2,2,2]
[4,8,5,2,6,7,1,3]=>[7,1,4,3,5,8,6,2]=>[2,8,5,6,4,1,3,7]=>[2,2,1,3]
[5,4,8,6,1,2,7,3]=>[2,1,8,5,6,4,7,3]=>[7,8,1,4,3,5,2,6]=>[2,2,2,2]
[8,4,6,5,2,7,3,1]=>[8,2,5,4,3,7,6,1]=>[1,7,4,5,6,2,3,8]=>[2,3,3]
[8,1,6,4,7,5,2,3]=>[4,7,3,8,6,2,5,1]=>[5,2,6,1,3,7,4,8]=>[1,2,3,2]
[8,6,2,3,5,1,7,4]=>[8,3,4,6,5,2,7,1]=>[1,6,5,3,4,7,2,8]=>[2,1,3,2]
[8,2,5,7,4,1,3,6]=>[6,3,7,2,5,8,4,1]=>[3,6,2,7,4,1,5,8]=>[2,2,1,3]
[7,2,4,5,6,8,1,3]=>[3,4,7,2,5,1,8,6]=>[6,5,2,7,4,8,1,3]=>[1,1,2,2,2]
[7,1,3,5,6,2,8,4]=>[4,8,3,6,2,5,1,7]=>[5,1,6,3,7,4,8,2]=>[1,2,2,2,1]
[7,1,5,8,4,6,3,2]=>[3,5,8,7,6,2,1,4]=>[6,4,1,2,3,7,8,5]=>[1,1,5,1]
[6,3,8,4,7,1,5,2]=>[4,8,2,1,6,7,5,3]=>[5,1,7,8,3,2,4,6]=>[1,3,1,3]
[5,3,6,1,4,2,8,7]=>[2,5,1,8,4,3,6,7]=>[7,4,8,1,5,6,3,2]=>[1,2,3,1,1]
[5,7,2,1,4,3,8,6]=>[3,5,1,8,4,6,2,7]=>[6,4,8,1,5,3,7,2]=>[1,2,2,2,1]
[7,1,8,3,5,2,4,6]=>[4,6,7,5,8,2,1,3]=>[5,3,2,4,1,7,8,6]=>[1,1,2,3,1]
[7,2,4,8,1,5,6,3]=>[3,6,8,2,5,1,7,4]=>[6,3,1,7,4,8,2,5]=>[1,1,2,2,2]
[7,1,8,4,2,5,6,3]=>[6,4,8,5,7,2,1,3]=>[3,5,1,4,2,7,8,6]=>[2,2,3,1]
[6,4,2,5,8,1,7,3]=>[4,2,8,3,1,6,7,5]=>[5,7,1,6,8,3,2,4]=>[2,3,1,2]
[7,3,8,5,6,2,1,4]=>[7,6,2,4,1,8,5,3]=>[2,3,7,5,8,1,4,6]=>[3,2,3]
[2,7,4,8,1,5,6,3]=>[3,6,8,5,1,2,7,4]=>[6,3,1,4,8,7,2,5]=>[1,1,3,1,2]
[7,4,8,3,1,5,6,2]=>[2,6,4,8,5,1,7,3]=>[7,3,5,1,4,8,2,6]=>[1,2,3,2]
[6,1,5,8,3,7,4,2]=>[3,8,5,1,7,6,2,4]=>[6,1,4,8,2,3,7,5]=>[1,3,3,1]
[4,8,5,3,7,2,1,6]=>[4,1,3,7,6,8,5,2]=>[5,8,6,2,3,1,4,7]=>[2,1,2,3]
[7,4,8,6,5,3,2,1]=>[8,7,2,1,6,5,4,3]=>[1,2,7,8,3,4,5,6]=>[4,4]
[7,4,8,5,6,3,1,2]=>[7,2,4,1,8,6,5,3]=>[2,7,5,8,1,3,4,6]=>[2,2,4]
[7,8,4,1,3,5,6,2]=>[5,6,3,8,4,1,7,2]=>[4,3,6,1,5,8,2,7]=>[1,2,3,2]
[7,8,3,4,1,5,6,2]=>[3,6,4,8,5,1,7,2]=>[6,3,5,1,4,8,2,7]=>[1,2,3,2]
[7,3,1,8,2,5,6,4]=>[2,6,8,5,7,3,1,4]=>[7,3,1,4,2,6,8,5]=>[1,1,2,3,1]
[7,2,3,8,1,5,6,4]=>[6,8,2,3,5,1,7,4]=>[3,1,7,6,4,8,2,5]=>[1,2,1,2,2]
[6,4,8,7,3,2,1,5]=>[7,2,1,6,5,8,4,3]=>[2,7,8,3,4,1,5,6]=>[3,2,3]
[2,7,4,8,6,3,1,5]=>[7,3,6,2,8,1,5,4]=>[2,6,3,7,1,8,4,5]=>[2,2,2,2]
[6,4,8,2,3,1,7,5]=>[4,2,5,1,8,6,7,3]=>[5,7,4,8,1,3,2,6]=>[2,2,2,2]
[7,2,1,8,3,5,6,4]=>[6,8,2,5,7,3,1,4]=>[3,1,7,4,2,6,8,5]=>[1,2,1,3,1]
[5,1,6,3,8,2,4,7]=>[4,6,3,1,7,8,2,5]=>[5,3,6,8,2,1,7,4]=>[1,3,1,2,1]
[3,6,5,1,4,8,7,2]=>[8,5,1,3,2,7,4,6]=>[1,4,8,6,7,2,5,3]=>[3,2,2,1]
[7,3,6,2,8,4,1,5]=>[7,2,4,6,3,1,8,5]=>[2,7,5,3,6,8,1,4]=>[2,1,3,2]
[6,5,1,8,4,7,2,3]=>[7,5,2,1,8,6,3,4]=>[2,4,7,8,1,3,6,5]=>[4,3,1]
[7,5,4,8,1,6,2,3]=>[7,3,2,8,5,1,6,4]=>[2,6,7,1,4,8,3,5]=>[3,3,2]
[4,3,5,8,7,1,2,6]=>[2,1,3,6,7,8,5,4]=>[7,8,6,3,2,1,4,5]=>[2,1,1,1,3]
[4,3,5,8,2,1,6,7]=>[2,1,3,6,5,7,8,4]=>[7,8,6,3,4,2,1,5]=>[2,1,2,1,2]
[6,4,7,2,3,1,5,8]=>[4,2,6,5,1,7,3,8]=>[5,7,3,4,8,2,6,1]=>[2,3,2,1]
[6,8,1,5,4,2,7,3]=>[8,6,5,3,1,4,7,2]=>[1,3,4,6,8,5,2,7]=>[5,1,2]
[7,8,6,3,1,4,2,5]=>[7,5,4,6,1,8,3,2]=>[2,4,5,3,8,1,6,7]=>[3,2,3]
[7,2,8,5,4,6,3,1]=>[5,4,8,7,2,1,6,3]=>[4,5,1,2,7,8,3,6]=>[2,4,2]
[6,1,8,4,7,2,3,5]=>[6,4,7,1,8,5,2,3]=>[3,5,2,8,1,4,7,6]=>[2,2,3,1]
[5,6,4,3,7,1,8,2]=>[1,4,3,2,8,6,5,7]=>[8,5,6,7,1,3,4,2]=>[1,3,3,1]
[6,5,3,7,2,4,8,1]=>[3,5,2,1,6,4,8,7]=>[6,4,7,8,3,5,1,2]=>[1,3,2,2]
[5,6,2,8,4,3,7,1]=>[1,6,5,2,8,3,7,4]=>[8,3,4,7,1,6,2,5]=>[1,3,2,2]
[4,1,2,6,8,3,7,5]=>[4,1,8,6,7,2,3,5]=>[5,8,1,3,2,7,6,4]=>[2,2,2,1,1]
[7,1,3,6,5,8,4,2]=>[5,4,8,3,7,2,1,6]=>[4,5,1,6,2,7,8,3]=>[2,2,3,1]
[5,7,4,3,6,8,2,1]=>[1,4,3,5,2,8,7,6]=>[8,5,6,4,7,1,2,3]=>[1,2,2,3]
[5,1,2,4,6,7,8,3]=>[4,5,6,1,8,2,3,7]=>[5,4,3,8,1,7,6,2]=>[1,1,2,2,1,1]
[4,6,3,5,2,8,7,1]=>[1,3,4,2,8,5,7,6]=>[8,6,5,7,1,4,2,3]=>[1,1,2,2,2]
[5,6,3,4,8,2,7,1]=>[3,1,4,2,6,8,7,5]=>[6,8,5,7,3,1,2,4]=>[2,2,1,3]
[5,8,4,6,3,2,7,1]=>[1,3,6,5,4,8,7,2]=>[8,6,3,4,5,1,2,7]=>[1,1,3,3]
[5,4,3,8,6,2,7,1]=>[2,1,6,3,5,8,7,4]=>[7,8,3,6,4,1,2,5]=>[2,2,1,3]
[5,7,8,2,4,3,6,1]=>[1,6,4,5,2,8,7,3]=>[8,3,5,4,7,1,2,6]=>[1,2,2,3]
[5,6,2,4,8,3,7,1]=>[4,1,6,2,8,3,7,5]=>[5,8,3,7,1,6,2,4]=>[2,2,2,2]
[6,4,7,8,2,3,5,1]=>[2,5,1,6,3,8,7,4]=>[7,4,8,3,6,1,2,5]=>[1,2,2,3]
[3,7,5,2,4,8,1,6]=>[4,5,1,3,7,2,8,6]=>[5,4,8,6,2,7,1,3]=>[1,2,1,2,2]
[4,7,5,2,3,8,6,1]=>[8,1,4,3,5,2,7,6]=>[1,8,5,6,4,7,2,3]=>[2,2,2,2]
[6,4,7,3,2,5,8,1]=>[2,5,4,1,6,3,8,7]=>[7,4,5,8,3,6,1,2]=>[1,3,2,2]
[5,7,3,2,8,4,6,1]=>[3,1,6,8,4,2,7,5]=>[6,8,3,1,5,7,2,4]=>[2,1,3,2]
[5,3,7,2,8,4,6,1]=>[6,1,8,2,4,3,7,5]=>[3,8,1,7,5,6,2,4]=>[2,2,2,2]
[4,3,7,2,5,8,6,1]=>[1,8,2,4,5,3,7,6]=>[8,1,7,5,4,6,2,3]=>[1,2,1,2,2]
[4,7,3,2,5,8,6,1]=>[1,3,8,4,5,2,7,6]=>[8,6,1,5,4,7,2,3]=>[1,1,2,2,2]
[4,7,3,2,6,8,5,1]=>[1,3,5,8,4,2,7,6]=>[8,6,4,1,5,7,2,3]=>[1,1,1,3,2]
[7,5,3,2,6,4,8,1]=>[3,6,4,2,5,1,8,7]=>[6,3,5,7,4,8,1,2]=>[1,3,2,2]
[8,5,2,6,7,3,4,1]=>[6,4,2,8,3,7,5,1]=>[3,5,7,1,6,2,4,8]=>[3,2,3]
[8,4,2,6,3,7,5,1]=>[2,8,5,3,4,7,6,1]=>[7,1,4,6,5,2,3,8]=>[1,3,1,3]
[7,4,6,2,3,8,5,1]=>[2,8,4,5,3,1,7,6]=>[7,1,5,4,6,8,2,3]=>[1,2,3,2]
[7,5,6,2,8,3,4,1]=>[6,2,8,4,3,1,7,5]=>[3,7,1,5,6,8,2,4]=>[2,4,2]
[5,7,6,2,8,3,4,1]=>[1,6,8,4,3,2,7,5]=>[8,3,1,5,6,7,2,4]=>[1,1,4,2]
[4,7,6,2,3,8,5,1]=>[8,1,4,5,3,2,7,6]=>[1,8,5,4,6,7,2,3]=>[2,1,3,2]
[7,6,3,2,5,8,1,4]=>[3,7,4,5,2,1,8,6]=>[6,2,5,4,7,8,1,3]=>[1,2,3,2]
[7,6,4,2,5,8,3,1]=>[5,3,8,4,2,1,7,6]=>[4,6,1,5,7,8,2,3]=>[2,4,2]
[6,3,8,5,4,7,2,1]=>[5,4,1,8,2,7,6,3]=>[4,5,8,1,7,2,3,6]=>[3,2,3]
[1,3,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[7,9,8,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1]
[1,4,2,3,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[7,6,9,8,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]
[1,3,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[8,10,9,7,6,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[2,4,6,3,8,7,5,1]=>[3,8,2,7,1,4,6,5]=>[6,1,7,2,8,5,3,4]=>[1,2,2,1,2]
[2,4,3,6,8,7,1,5]=>[2,4,7,8,1,3,6,5]=>[7,5,2,1,8,6,3,4]=>[1,1,1,2,1,2]
[2,4,6,3,8,7,1,5]=>[7,2,3,8,1,4,6,5]=>[2,7,6,1,8,5,3,4]=>[2,1,2,1,2]
[2,4,6,5,8,7,1,3]=>[4,2,3,7,8,1,6,5]=>[5,7,6,2,1,8,3,4]=>[2,1,1,2,2]
[2,4,6,8,5,7,3,1]=>[3,5,8,2,7,1,6,4]=>[6,4,1,7,2,8,3,5]=>[1,1,2,2,2]
[2,4,6,8,5,7,1,3]=>[3,7,2,5,8,1,6,4]=>[6,2,7,4,1,8,3,5]=>[1,2,1,2,2]
[2,4,6,8,3,7,1,5]=>[5,2,3,7,8,1,6,4]=>[4,7,6,2,1,8,3,5]=>[2,1,1,2,2]
[2,4,6,8,1,7,3,5]=>[7,2,3,8,1,5,6,4]=>[2,7,6,1,8,4,3,5]=>[2,1,2,1,2]
[2,4,6,5,1,8,7,3]=>[4,2,3,8,1,7,5,6]=>[5,7,6,1,8,2,4,3]=>[2,1,2,2,1]
[2,4,6,5,8,3,7,1]=>[4,2,3,6,8,1,7,5]=>[5,7,6,3,1,8,2,4]=>[2,1,1,2,2]
[2,4,6,5,8,1,7,3]=>[4,2,3,8,1,6,7,5]=>[5,7,6,1,8,3,2,4]=>[2,1,2,1,2]
[2,4,6,8,5,1,7,3]=>[3,8,2,6,1,5,7,4]=>[6,1,7,3,8,4,2,5]=>[1,2,2,1,2]
[2,4,6,8,7,3,5,1]=>[3,6,8,2,7,1,5,4]=>[6,3,1,7,2,8,4,5]=>[1,1,2,2,2]
[2,4,6,8,7,1,5,3]=>[3,8,2,6,7,1,5,4]=>[6,1,7,3,2,8,4,5]=>[1,2,1,2,2]
[2,4,6,8,7,1,3,5]=>[6,2,3,7,8,1,5,4]=>[3,7,6,2,1,8,4,5]=>[2,1,1,2,2]
[2,4,6,8,5,1,3,7]=>[6,2,3,7,1,5,8,4]=>[3,7,6,2,8,4,1,5]=>[2,1,2,1,2]
[2,4,6,5,1,8,3,7]=>[7,2,4,1,3,8,5,6]=>[2,7,5,8,6,1,4,3]=>[2,2,1,2,1]
[2,4,6,5,3,8,1,7]=>[5,2,4,1,3,7,8,6]=>[4,7,5,8,6,2,1,3]=>[2,2,1,1,2]
[2,4,6,5,8,3,1,7]=>[4,2,3,7,1,6,8,5]=>[5,7,6,2,8,3,1,4]=>[2,1,2,1,2]
[2,4,6,8,5,3,1,7]=>[3,7,2,6,1,5,8,4]=>[6,2,7,3,8,4,1,5]=>[1,2,2,1,2]
[2,4,6,8,7,3,1,5]=>[3,7,2,6,8,1,5,4]=>[6,2,7,3,1,8,4,5]=>[1,2,1,2,2]
[2,4,6,8,7,5,1,3]=>[3,7,8,2,6,1,5,4]=>[6,2,1,7,3,8,4,5]=>[1,1,2,2,2]
[4,8,7,5,2,1,3,6]=>[6,1,5,7,4,8,3,2]=>[3,8,4,2,5,1,6,7]=>[2,1,2,3]
[6,1,4,7,5,8,2,3]=>[7,3,5,4,1,8,2,6]=>[2,6,4,5,8,1,7,3]=>[2,3,2,1]
[1,8,6,5,3,2,7,4]=>[5,8,6,4,3,7,1,2]=>[4,1,3,5,6,2,8,7]=>[1,4,2,1]
[1,6,3,5,8,2,4,7]=>[6,3,4,2,7,8,1,5]=>[3,6,5,7,2,1,8,4]=>[2,2,1,2,1]
[6,1,2,7,8,4,5,3]=>[6,4,8,7,2,1,3,5]=>[3,5,1,2,7,8,6,4]=>[2,4,1,1]
[6,1,3,2,7,8,5,4]=>[5,8,3,7,2,1,4,6]=>[4,1,6,2,7,8,5,3]=>[1,2,3,1,1]
[5,6,3,1,7,4,8,2]=>[3,1,6,5,2,8,4,7]=>[6,8,3,4,7,1,5,2]=>[2,3,2,1]
[4,8,3,7,1,6,5,2]=>[8,1,3,7,5,6,4,2]=>[1,8,6,2,4,3,5,7]=>[2,1,2,3]
[8,7,2,6,5,1,4,3]=>[8,6,7,3,5,4,2,1]=>[1,3,2,6,4,5,7,8]=>[2,2,4]
[5,8,3,2,1,7,6,4]=>[3,1,8,4,7,5,6,2]=>[6,8,1,5,2,4,3,7]=>[2,2,2,2]
[5,4,3,8,1,7,6,2]=>[2,1,8,3,7,5,6,4]=>[7,8,1,6,2,4,3,5]=>[2,2,2,2]
[6,5,3,8,7,1,4,2]=>[8,3,2,1,6,7,5,4]=>[1,6,7,8,3,2,4,5]=>[4,1,3]
[4,3,8,2,7,6,5,1]=>[8,1,7,2,4,6,5,3]=>[1,8,2,7,5,3,4,6]=>[2,2,1,3]
[4,8,2,7,6,5,3,1]=>[8,7,1,6,3,5,4,2]=>[1,2,8,3,6,4,5,7]=>[3,2,3]
[3,8,7,6,2,5,1,4]=>[5,7,8,6,1,4,3,2]=>[4,2,1,3,8,5,6,7]=>[1,1,3,3]
[4,8,3,7,2,1,6,5]=>[1,3,5,8,6,7,4,2]=>[8,6,4,1,3,2,5,7]=>[1,1,1,2,3]
[8,6,3,1,7,5,4,2]=>[8,3,7,6,4,2,5,1]=>[1,6,2,3,5,7,4,8]=>[2,4,2]
[8,6,3,7,1,5,4,2]=>[8,3,7,5,2,6,4,1]=>[1,6,2,4,7,3,5,8]=>[2,3,3]
[4,8,3,7,6,2,5,1]=>[6,8,1,3,7,5,4,2]=>[3,1,8,6,2,4,5,7]=>[1,2,1,4]
[5,8,2,7,6,4,1,3]=>[1,7,8,6,3,5,4,2]=>[8,2,1,3,6,4,5,7]=>[1,1,3,3]
[8,4,2,1,7,6,5,3]=>[2,8,7,3,6,4,5,1]=>[7,1,2,6,3,5,4,8]=>[1,3,2,2]
[1,6,4,2,5,3,7,8]=>[6,4,3,5,1,2,7,8]=>[3,5,6,4,8,7,2,1]=>[3,2,1,1,1]
[1,8,6,2,7,3,4,5]=>[6,7,8,4,3,5,1,2]=>[3,2,1,5,6,4,8,7]=>[1,1,3,2,1]
[1,6,3,2,4,5,7,8]=>[4,3,5,6,1,2,7,8]=>[5,6,4,3,8,7,2,1]=>[2,1,2,1,1,1]
[1,5,2,6,4,3,7,8]=>[6,5,3,1,2,4,7,8]=>[3,4,6,8,7,5,2,1]=>[4,1,1,1,1]
[1,8,6,2,3,7,4,5]=>[7,8,4,5,3,6,1,2]=>[2,1,5,4,6,3,8,7]=>[1,2,2,2,1]
[1,5,2,8,6,3,4,7]=>[6,2,7,5,8,1,3,4]=>[3,7,2,4,1,8,6,5]=>[2,2,2,1,1]
[1,3,6,8,2,7,4,5]=>[7,3,8,2,5,6,1,4]=>[2,6,1,7,4,3,8,5]=>[2,2,1,2,1]
[1,4,3,8,2,5,6,7]=>[3,2,5,6,7,8,1,4]=>[6,7,4,3,2,1,8,5]=>[2,1,1,1,2,1]
[1,7,2,3,8,5,4,6]=>[7,6,8,3,4,1,2,5]=>[2,3,1,6,5,8,7,4]=>[2,2,2,1,1]
[1,6,2,8,5,4,3,7]=>[7,6,5,2,8,1,3,4]=>[2,3,4,7,1,8,6,5]=>[4,2,1,1]
[1,7,2,3,8,6,4,5]=>[7,8,6,3,4,1,2,5]=>[2,1,3,6,5,8,7,4]=>[1,3,2,1,1]
[1,5,3,8,2,7,4,6]=>[7,2,8,3,5,6,1,4]=>[2,7,1,6,4,3,8,5]=>[2,2,1,2,1]
[1,5,7,3,2,8,4,6]=>[4,2,7,8,5,1,3,6]=>[5,7,2,1,4,8,6,3]=>[2,1,3,1,1]
[1,2,7,3,6,8,4,5]=>[7,5,8,4,1,2,3,6]=>[2,4,1,5,8,7,6,3]=>[2,3,1,1,1]
[1,7,2,3,6,8,4,5]=>[7,5,8,3,4,1,2,6]=>[2,4,1,6,5,8,7,3]=>[2,2,2,1,1]
[1,7,2,5,8,3,4,6]=>[6,4,7,8,3,1,2,5]=>[3,5,2,1,6,8,7,4]=>[2,1,3,1,1]
[8,2,3,4,5,6,7,9,1]=>[2,3,4,5,6,7,1,9,8]=>[8,7,6,5,4,3,9,1,2]=>[1,1,1,1,1,2,2]
[2,9,3,4,5,6,7,8,1]=>[3,4,5,6,7,9,1,8,2]=>[7,6,5,4,3,1,9,2,8]=>[1,1,1,1,1,2,2]
[6,2,3,5,8,1,7,4]=>[4,8,2,3,1,6,7,5]=>[5,1,7,6,8,3,2,4]=>[1,2,2,1,2]
[5,2,4,8,1,6,7,3]=>[3,6,1,8,2,5,7,4]=>[6,3,8,1,7,4,2,5]=>[1,2,2,1,2]
[2,10,3,4,5,6,7,8,9,1]=>[3,4,5,6,7,8,10,1,9,2]=>[8,7,6,5,4,3,1,10,2,9]=>[1,1,1,1,1,1,2,2]
[2,6,4,5,7,3,1,8]=>[3,4,2,7,1,6,5,8]=>[6,5,7,2,8,3,4,1]=>[1,2,2,2,1]
[1,3,7,5,6,8,4,2]=>[4,5,3,8,2,7,1,6]=>[5,4,6,1,7,2,8,3]=>[1,2,2,2,1]
[1,3,6,7,4,5,8,2]=>[5,3,6,2,4,8,1,7]=>[4,6,3,7,5,1,8,2]=>[2,2,1,2,1]
[1,5,6,3,4,2,7,8]=>[4,2,6,5,1,3,7,8]=>[5,7,3,4,8,6,2,1]=>[2,3,1,1,1]
[1,5,6,3,4,7,2,8]=>[4,2,5,3,7,1,6,8]=>[5,7,4,6,2,8,3,1]=>[2,2,2,1,1]
[1,5,3,6,4,2,7,8]=>[6,3,2,5,1,4,7,8]=>[3,6,7,4,8,5,2,1]=>[3,2,1,1,1]
[1,7,5,6,8,3,4,2]=>[3,6,4,2,8,7,1,5]=>[6,3,5,7,1,2,8,4]=>[1,3,3,1]
[1,7,5,6,3,8,4,2]=>[3,8,5,4,2,7,1,6]=>[6,1,4,5,7,2,8,3]=>[1,4,2,1]
[1,3,7,5,2,8,6,4]=>[4,8,7,2,5,1,3,6]=>[5,1,2,7,4,8,6,3]=>[1,3,2,1,1]
[1,3,7,2,5,8,6,4]=>[8,5,7,2,4,1,3,6]=>[1,4,2,7,5,8,6,3]=>[2,2,2,1,1]
[1,5,3,7,4,6,2,8]=>[5,2,7,3,6,1,4,8]=>[4,7,2,6,3,8,5,1]=>[2,2,2,1,1]
[1,5,6,3,7,4,2,8]=>[2,7,4,3,6,1,5,8]=>[7,2,5,6,3,8,4,1]=>[1,3,2,1,1]
[1,5,7,6,3,4,8,2]=>[2,5,6,4,3,8,1,7]=>[7,4,3,5,6,1,8,2]=>[1,1,3,2,1]
[1,5,7,3,6,4,8,2]=>[2,6,4,5,3,8,1,7]=>[7,3,5,4,6,1,8,2]=>[1,2,2,2,1]
[1,3,7,2,5,6,8,4]=>[5,6,8,2,4,1,3,7]=>[4,3,1,7,5,8,6,2]=>[1,1,2,2,1,1]
[1,3,7,5,6,2,8,4]=>[4,8,6,2,5,1,3,7]=>[5,1,3,7,4,8,6,2]=>[1,3,2,1,1]
[6,7,3,1,8,5,2,4]=>[3,7,1,8,6,4,2,5]=>[6,2,8,1,3,5,7,4]=>[1,2,4,1]
[6,3,1,5,8,7,2,4]=>[2,4,7,1,8,6,3,5]=>[7,5,2,8,1,3,6,4]=>[1,1,2,3,1]
[4,6,3,5,8,2,1,7]=>[1,3,4,2,7,6,8,5]=>[8,6,5,7,2,3,1,4]=>[1,1,2,2,2]
[7,2,4,8,6,3,1,5]=>[7,3,6,8,2,1,5,4]=>[2,6,3,1,7,8,4,5]=>[2,1,3,2]
[2,3,6,4,1,8,7,5]=>[8,4,1,2,3,7,5,6]=>[1,5,8,7,6,2,4,3]=>[3,1,1,2,1]
[4,7,5,2,1,8,6,3]=>[8,1,4,3,7,5,2,6]=>[1,8,5,6,2,4,7,3]=>[2,2,3,1]
[8,5,3,6,2,1,7,4]=>[3,5,2,8,6,4,7,1]=>[6,4,7,1,3,5,2,8]=>[1,2,3,2]
[4,5,7,3,1,2,8,6]=>[1,2,8,5,4,6,3,7]=>[8,7,1,4,5,3,6,2]=>[1,1,3,2,1]
[4,5,1,8,3,2,7,6]=>[1,5,2,8,6,7,3,4]=>[8,4,7,1,3,2,6,5]=>[1,2,2,2,1]
[5,7,4,6,3,2,1,8]=>[1,3,7,6,5,4,2,8]=>[8,6,2,3,4,5,7,1]=>[1,1,5,1]
[2,5,3,8,4,1,7,6]=>[5,2,8,1,3,6,7,4]=>[4,7,1,8,6,3,2,5]=>[2,2,1,1,2]
[8,6,2,3,1,7,5,4]=>[8,3,4,7,5,2,6,1]=>[1,6,5,2,4,7,3,8]=>[2,1,3,2]
[6,3,1,2,4,8,7,5]=>[2,8,7,3,4,1,5,6]=>[7,1,2,6,5,8,4,3]=>[1,3,2,1,1]
[4,7,5,2,3,6,1,8]=>[1,4,5,3,7,6,2,8]=>[8,5,4,6,2,3,7,1]=>[1,1,2,3,1]
[3,6,8,4,5,1,2,7]=>[6,4,1,2,7,5,8,3]=>[3,5,8,7,2,4,1,6]=>[3,1,2,2]
[5,2,3,7,6,4,1,8]=>[7,6,2,1,3,5,4,8]=>[2,3,7,8,6,4,5,1]=>[4,1,2,1]
[6,2,7,3,5,4,1,8]=>[7,4,6,2,1,5,3,8]=>[2,5,3,7,8,4,6,1]=>[2,3,2,1]
[7,2,6,5,3,4,1,8]=>[5,7,6,2,4,3,1,8]=>[4,2,3,7,5,6,8,1]=>[1,3,3,1]
[8,2,6,5,4,1,3,7]=>[6,7,5,2,4,3,8,1]=>[3,2,4,7,5,6,1,8]=>[1,3,2,2]
[6,2,8,4,5,1,3,7]=>[6,4,7,2,1,5,8,3]=>[3,5,2,7,8,4,1,6]=>[2,3,1,2]
[2,3,1,7,8,5,6,4]=>[6,4,8,1,2,7,3,5]=>[3,5,1,8,7,2,6,4]=>[2,2,1,2,1]
[7,2,8,5,1,4,3,6]=>[7,5,6,2,4,1,8,3]=>[2,4,3,7,5,8,1,6]=>[2,2,2,2]
[8,6,7,1,4,2,3,5]=>[6,7,4,5,2,8,3,1]=>[3,2,5,4,7,1,6,8]=>[1,2,2,3]
[6,8,7,1,4,3,2,5]=>[7,6,4,1,5,8,3,2]=>[2,3,5,8,4,1,6,7]=>[4,1,3]
[6,8,2,5,3,1,4,7]=>[6,3,5,1,7,4,8,2]=>[3,6,4,8,2,5,1,7]=>[2,2,2,2]
[3,7,8,5,1,4,2,6]=>[7,5,6,1,4,2,8,3]=>[2,4,3,8,5,7,1,6]=>[2,2,2,2]
[4,8,7,3,1,2,5,6]=>[1,5,6,4,7,8,3,2]=>[8,4,3,5,2,1,6,7]=>[1,1,2,1,3]
[4,8,6,2,3,1,5,7]=>[1,4,6,5,7,3,8,2]=>[8,5,3,4,2,6,1,7]=>[1,1,2,2,2]
[3,8,5,4,2,1,6,7]=>[6,5,1,4,3,7,8,2]=>[3,4,8,5,6,2,1,7]=>[3,2,1,2]
[4,5,3,8,2,1,6,7]=>[1,3,2,6,5,7,8,4]=>[8,6,7,3,4,2,1,5]=>[1,2,2,1,2]
[3,7,4,1,8,2,6,5]=>[3,8,1,6,7,4,2,5]=>[6,1,8,3,2,5,7,4]=>[1,2,1,3,1]
[3,8,4,1,7,6,2,5]=>[3,7,8,1,6,4,5,2]=>[6,2,1,8,3,5,4,7]=>[1,1,2,2,2]
[3,7,2,1,8,4,6,5]=>[8,1,3,6,7,4,2,5]=>[1,8,6,3,2,5,7,4]=>[2,1,1,3,1]
[8,7,1,6,5,2,3,4]=>[6,7,8,5,3,4,2,1]=>[3,2,1,4,6,5,7,8]=>[1,1,3,3]
[8,5,1,2,7,6,3,4]=>[7,8,6,3,2,4,5,1]=>[2,1,3,6,7,5,4,8]=>[1,4,1,2]
[3,8,2,1,7,6,4,5]=>[7,8,1,3,6,4,5,2]=>[2,1,8,6,3,5,4,7]=>[1,2,1,2,2]
[3,5,7,8,2,4,6,1]=>[2,5,6,1,3,8,7,4]=>[7,4,3,8,6,1,2,5]=>[1,1,2,1,3]
[7,8,2,5,4,3,6,1]=>[6,5,3,4,1,8,7,2]=>[3,4,6,5,8,1,2,7]=>[3,2,3]
[4,5,3,7,8,2,6,1]=>[1,2,6,3,4,8,7,5]=>[8,7,3,6,5,1,2,4]=>[1,1,2,1,3]
[1,5,4,7,3,6,2,8]=>[3,2,5,7,6,1,4,8]=>[6,7,4,2,3,8,5,1]=>[2,1,3,1,1]
[1,7,3,6,8,4,5,2]=>[6,4,8,3,2,7,1,5]=>[3,5,1,6,7,2,8,4]=>[2,3,2,1]
[4,7,6,3,5,1,8,2]=>[4,8,1,6,5,3,2,7]=>[5,1,8,3,4,6,7,2]=>[1,2,4,1]
[7,8,3,6,1,5,4,2]=>[8,3,7,5,1,6,4,2]=>[1,6,2,4,8,3,5,7]=>[2,3,3]
[2,5,7,8,4,6,1,3]=>[7,2,5,3,8,1,6,4]=>[2,7,4,6,1,8,3,5]=>[2,2,2,2]
[3,7,5,6,2,1,4,8]=>[6,5,1,3,7,4,2,8]=>[3,4,8,6,2,5,7,1]=>[3,1,3,1]
[6,2,1,7,4,5,3,8]=>[5,7,2,6,3,1,4,8]=>[4,2,7,3,6,8,5,1]=>[1,2,3,1,1]
[1,2,6,4,7,5,3,8]=>[7,4,3,6,1,2,5,8]=>[2,5,6,3,8,7,4,1]=>[3,2,1,1,1]
[7,5,6,3,8,4,2,1]=>[2,8,4,3,1,7,6,5]=>[7,1,5,6,8,2,3,4]=>[1,4,3]
[8,5,4,2,1,6,7,3]=>[4,6,3,2,8,5,7,1]=>[5,3,6,7,1,4,2,8]=>[1,3,2,2]
[2,6,8,4,7,5,1,3]=>[4,2,7,8,6,1,5,3]=>[5,7,2,1,3,8,4,6]=>[2,1,3,2]
[6,7,5,1,4,8,3,2]=>[5,1,8,7,4,3,2,6]=>[4,8,1,2,5,6,7,3]=>[2,5,1]
[7,4,1,6,5,3,8,2]=>[2,6,5,4,8,3,1,7]=>[7,3,4,5,1,6,8,2]=>[1,3,3,1]
[5,8,2,7,3,6,4,1]=>[1,8,5,7,3,6,4,2]=>[8,1,4,2,6,3,5,7]=>[1,2,2,3]
[1,6,5,7,3,8,4,2]=>[3,2,8,5,4,7,1,6]=>[6,7,1,4,5,2,8,3]=>[2,3,2,1]
[1,5,6,8,4,2,7,3]=>[2,3,8,6,5,7,1,4]=>[7,6,1,3,4,2,8,5]=>[1,1,3,2,1]
[7,5,4,1,8,2,6,3]=>[8,6,3,2,7,4,1,5]=>[1,3,6,7,2,5,8,4]=>[4,3,1]
[7,8,5,3,2,6,1,4]=>[5,4,7,3,1,8,6,2]=>[4,5,2,6,8,1,3,7]=>[2,3,3]
[8,2,5,1,7,6,4,3]=>[3,8,7,2,6,4,5,1]=>[6,1,2,7,3,5,4,8]=>[1,3,2,2]
[3,4,2,7,8,6,1,5]=>[7,1,2,4,8,3,6,5]=>[2,8,7,5,1,6,3,4]=>[2,1,1,2,2]
[7,8,6,1,4,3,2,5]=>[7,6,4,5,1,8,3,2]=>[2,3,5,4,8,1,6,7]=>[3,2,3]
[2,4,7,8,6,1,3,5]=>[6,7,2,3,8,1,5,4]=>[3,2,7,6,1,8,4,5]=>[1,2,1,2,2]
[3,7,8,6,5,2,4,1]=>[6,2,8,7,1,5,4,3]=>[3,7,1,2,8,4,5,6]=>[2,3,3]
[4,5,2,7,8,6,3,1]=>[1,2,4,8,7,3,6,5]=>[8,7,5,1,2,6,3,4]=>[1,1,1,3,2]
[4,6,2,5,3,1,7,8]=>[1,6,3,5,4,2,7,8]=>[8,3,6,4,5,7,2,1]=>[1,2,3,1,1]
[4,1,5,6,3,2,7,8]=>[3,1,6,5,2,4,7,8]=>[6,8,3,4,7,5,2,1]=>[2,3,1,1,1]
[2,6,7,5,4,1,3,8]=>[6,2,7,5,1,4,3,8]=>[3,7,2,4,8,5,6,1]=>[2,3,2,1]
[1,7,5,6,4,3,2,8]=>[3,7,6,5,4,1,2,8]=>[6,2,3,4,5,8,7,1]=>[1,5,1,1]
[7,6,5,3,1,8,4,2]=>[4,8,7,5,3,2,1,6]=>[5,1,2,4,6,7,8,3]=>[1,6,1]
[7,8,6,4,3,1,5,2]=>[8,6,5,4,1,7,3,2]=>[1,3,4,5,8,2,6,7]=>[5,3]
[4,1,7,8,6,5,3,2]=>[3,8,1,7,6,5,2,4]=>[6,1,8,2,3,4,7,5]=>[1,2,4,1]
[4,5,7,3,8,6,1,2]=>[1,2,4,7,3,8,6,5]=>[8,7,5,2,6,1,3,4]=>[1,1,1,2,3]
[6,8,5,3,7,2,1,4]=>[4,1,7,6,3,8,5,2]=>[5,8,2,3,6,1,4,7]=>[2,3,3]
[4,7,1,5,8,2,6,3]=>[1,4,8,6,7,3,2,5]=>[8,5,1,3,2,6,7,4]=>[1,1,2,3,1]
[3,7,6,2,1,8,4,5]=>[4,7,8,1,5,3,2,6]=>[5,2,1,8,4,6,7,3]=>[1,1,2,3,1]
[2,7,5,8,3,6,4,1]=>[3,8,5,2,7,1,6,4]=>[6,1,4,7,2,8,3,5]=>[1,3,2,2]
[7,4,8,2,6,5,3,1]=>[8,2,7,4,1,6,5,3]=>[1,7,2,5,8,3,4,6]=>[2,3,3]
[7,5,4,8,2,6,3,1]=>[3,2,8,5,1,7,6,4]=>[6,7,1,4,8,2,3,5]=>[2,3,3]
[2,3,6,5,7,8,1,4]=>[4,3,7,1,2,5,8,6]=>[5,6,2,8,7,4,1,3]=>[2,2,1,1,2]
[8,3,4,1,2,6,7,5]=>[2,6,3,8,4,5,7,1]=>[7,3,6,1,5,4,2,8]=>[1,2,2,1,2]
[7,3,4,8,5,2,1,6]=>[7,2,3,6,5,1,8,4]=>[2,7,6,3,4,8,1,5]=>[2,1,3,2]
[7,3,8,4,1,5,6,2]=>[6,2,4,8,5,1,7,3]=>[3,7,5,1,4,8,2,6]=>[2,1,3,2]
[7,2,4,5,1,8,3,6]=>[3,7,2,4,8,5,1,6]=>[6,2,7,5,1,4,8,3]=>[1,2,1,3,1]
[4,8,2,3,5,7,6,1]=>[1,8,3,4,5,7,6,2]=>[8,1,6,5,4,2,3,7]=>[1,2,1,1,3]
[4,5,2,3,8,6,7,1]=>[1,6,2,8,3,4,7,5]=>[8,3,7,1,6,5,2,4]=>[1,2,2,1,2]
[6,7,4,8,5,3,2,1]=>[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>[1,3,4]
[4,3,5,6,1,7,8,2]=>[2,1,3,6,4,8,5,7]=>[7,8,6,3,5,1,4,2]=>[2,1,2,2,1]
[3,5,2,6,4,7,8,1]=>[5,1,3,2,4,6,8,7]=>[4,8,6,7,5,3,1,2]=>[2,2,1,1,2]
[4,1,2,8,5,7,6,3]=>[1,8,5,7,6,2,3,4]=>[8,1,4,2,3,7,6,5]=>[1,2,3,1,1]
[3,1,5,6,4,7,8,2]=>[1,3,5,4,6,8,2,7]=>[8,6,4,5,3,1,7,2]=>[1,1,2,1,2,1]
[2,6,4,5,8,1,3,7]=>[3,6,4,1,2,7,8,5]=>[6,3,5,8,7,2,1,4]=>[1,3,1,1,2]
[6,4,1,3,5,8,2,7]=>[4,5,2,7,1,8,3,6]=>[5,4,7,2,8,1,6,3]=>[1,2,2,2,1]
[3,4,1,7,2,6,8,5]=>[1,2,6,8,5,3,4,7]=>[8,7,3,1,4,6,5,2]=>[1,1,1,3,1,1]
[2,4,7,5,8,1,3,6]=>[6,2,4,7,1,3,8,5]=>[3,7,5,2,8,6,1,4]=>[2,1,2,1,2]
[3,1,6,4,8,7,5,2]=>[3,8,1,7,4,6,2,5]=>[6,1,8,2,5,3,7,4]=>[1,2,2,2,1]
[3,7,6,2,1,5,8,4]=>[4,6,8,1,5,3,2,7]=>[5,3,1,8,4,6,7,2]=>[1,1,2,3,1]
[4,2,6,1,3,7,8,5]=>[6,1,8,2,4,3,5,7]=>[3,8,1,7,5,6,4,2]=>[2,2,2,1,1]
[2,8,4,6,7,1,3,5]=>[3,6,7,4,8,1,5,2]=>[6,3,2,5,1,8,4,7]=>[1,1,2,2,2]
[5,8,2,1,4,6,7,3]=>[3,5,1,6,8,4,7,2]=>[6,4,8,3,1,5,2,7]=>[1,2,1,2,2]
[8,4,6,1,2,5,7,3]=>[6,2,8,4,5,3,7,1]=>[3,7,1,5,4,6,2,8]=>[2,2,2,2]
[3,7,8,4,2,6,5,1]=>[4,8,5,1,2,7,6,3]=>[5,1,4,8,7,2,3,6]=>[1,3,1,3]
[5,6,2,8,7,1,3,4]=>[6,1,7,2,8,3,5,4]=>[3,8,2,7,1,6,4,5]=>[2,2,2,2]
[7,1,3,8,4,5,6,2]=>[5,6,8,3,7,2,1,4]=>[4,3,1,6,2,7,8,5]=>[1,1,2,3,1]
[7,8,1,4,3,5,6,2]=>[5,4,6,8,3,1,7,2]=>[4,5,3,1,6,8,2,7]=>[2,1,3,2]
[3,6,7,2,8,1,5,4]=>[8,4,1,2,6,3,7,5]=>[1,5,8,7,3,6,2,4]=>[3,1,2,2]
[2,6,7,1,3,5,8,4]=>[6,8,4,1,2,5,3,7]=>[3,1,5,8,7,4,6,2]=>[1,3,1,2,1]
[3,6,7,1,8,2,5,4]=>[8,6,1,2,7,4,3,5]=>[1,3,8,7,2,5,6,4]=>[3,1,3,1]
[3,4,1,8,7,2,6,5]=>[8,1,2,6,7,5,3,4]=>[1,8,7,3,2,4,6,5]=>[2,1,1,3,1]
[3,1,5,7,2,8,6,4]=>[8,1,3,7,5,2,4,6]=>[1,8,6,2,4,7,5,3]=>[2,1,3,1,1]
[3,8,1,4,7,2,6,5]=>[8,1,4,6,7,3,5,2]=>[1,8,5,3,2,6,4,7]=>[2,1,1,2,2]
[4,8,1,3,2,7,6,5]=>[1,8,4,7,3,5,6,2]=>[8,1,5,2,6,4,3,7]=>[1,2,2,1,2]
[4,1,8,3,2,7,6,5]=>[1,8,4,7,5,6,2,3]=>[8,1,5,2,4,3,7,6]=>[1,2,2,2,1]
[4,3,8,1,2,7,6,5]=>[1,8,2,7,4,5,6,3]=>[8,1,7,2,5,4,3,6]=>[1,2,2,1,2]
[4,3,8,2,1,7,6,5]=>[1,8,2,4,7,5,6,3]=>[8,1,7,5,2,4,3,6]=>[1,2,1,2,2]
[3,8,4,2,7,1,6,5]=>[3,8,1,4,6,7,5,2]=>[6,1,8,5,3,2,4,7]=>[1,2,1,1,3]
[2,8,4,3,7,6,1,5]=>[3,7,8,4,6,1,5,2]=>[6,2,1,5,3,8,4,7]=>[1,1,2,2,2]
[3,8,2,4,7,1,6,5]=>[8,1,3,4,6,7,5,2]=>[1,8,6,5,3,2,4,7]=>[2,1,1,1,3]
[3,2,4,8,7,1,6,5]=>[8,1,6,7,2,3,5,4]=>[1,8,3,2,7,6,4,5]=>[2,1,2,1,2]
[3,2,5,7,1,8,6,4]=>[8,1,3,7,2,5,4,6]=>[1,8,6,2,7,4,5,3]=>[2,1,2,2,1]
[4,2,8,3,1,7,6,5]=>[1,8,4,7,2,5,6,3]=>[8,1,5,2,7,4,3,6]=>[1,2,2,1,2]
[4,8,2,1,3,7,6,5]=>[1,8,3,7,4,5,6,2]=>[8,1,6,2,5,4,3,7]=>[1,2,2,1,2]
[4,2,8,1,3,7,6,5]=>[1,8,7,2,4,5,6,3]=>[8,1,2,7,5,4,3,6]=>[1,3,1,1,2]
[2,3,4,6,8,7,1,5]=>[4,7,8,1,2,3,6,5]=>[5,2,1,8,7,6,3,4]=>[1,1,2,1,1,2]
[5,6,4,7,1,2,8,3]=>[1,8,5,3,2,6,4,7]=>[8,1,4,6,7,3,5,2]=>[1,4,2,1]
[4,5,7,1,6,8,3,2]=>[1,2,5,8,7,4,3,6]=>[8,7,4,1,2,5,6,3]=>[1,1,1,4,1]
[3,2,7,6,8,1,4,5]=>[6,7,1,4,2,3,8,5]=>[3,2,8,5,7,6,1,4]=>[1,2,2,1,2]
[4,5,1,7,6,8,2,3]=>[1,2,7,5,4,8,3,6]=>[8,7,2,4,5,1,6,3]=>[1,1,3,2,1]
[6,7,2,8,3,1,4,5]=>[6,3,5,1,7,2,8,4]=>[3,6,4,8,2,7,1,5]=>[2,2,2,2]
[7,6,3,1,2,8,4,5]=>[7,3,8,4,5,2,1,6]=>[2,6,1,5,4,7,8,3]=>[2,2,3,1]
[6,2,7,8,4,1,3,5]=>[6,7,5,2,1,3,8,4]=>[3,2,4,7,8,6,1,5]=>[1,4,1,2]
[6,3,7,8,4,1,2,5]=>[6,7,2,1,5,3,8,4]=>[3,2,7,8,4,6,1,5]=>[1,3,2,2]
[7,8,5,2,4,1,3,6]=>[4,6,7,5,3,1,8,2]=>[5,3,2,4,6,8,1,7]=>[1,1,4,2]
[7,6,2,3,1,8,4,5]=>[3,4,7,8,5,2,1,6]=>[6,5,2,1,4,7,8,3]=>[1,1,1,4,1]
[4,2,5,1,3,7,8,6]=>[6,2,1,3,8,4,5,7]=>[3,7,8,6,1,5,4,2]=>[3,1,2,1,1]
[3,5,1,4,2,7,8,6]=>[1,4,6,2,8,3,5,7]=>[8,5,3,7,1,6,4,2]=>[1,1,2,2,1,1]
[3,4,1,7,8,5,2,6]=>[7,1,2,6,4,8,3,5]=>[2,8,7,3,5,1,6,4]=>[2,1,2,2,1]
[4,1,3,7,8,5,2,6]=>[1,7,6,3,4,8,2,5]=>[8,2,3,6,5,1,7,4]=>[1,3,1,2,1]
[3,1,8,5,4,2,7,6]=>[5,1,4,8,6,7,2,3]=>[4,8,5,1,3,2,7,6]=>[2,1,2,2,1]
[7,6,3,5,8,4,2,1]=>[4,8,3,2,1,7,6,5]=>[5,1,6,7,8,2,3,4]=>[1,4,3]
[4,5,1,3,2,7,8,6]=>[4,1,6,2,8,3,5,7]=>[5,8,3,7,1,6,4,2]=>[2,2,2,1,1]
[5,1,3,2,4,7,8,6]=>[3,6,8,2,1,4,5,7]=>[6,3,1,7,8,5,4,2]=>[1,1,3,1,1,1]
[2,3,7,8,5,4,1,6]=>[7,6,5,1,2,3,8,4]=>[2,3,4,8,7,6,1,5]=>[4,1,1,2]
[8,3,5,6,1,7,2,4]=>[7,2,3,8,5,4,6,1]=>[2,7,6,1,4,5,3,8]=>[2,1,3,2]
[4,5,8,1,2,6,7,3]=>[1,6,2,8,4,5,7,3]=>[8,3,7,1,5,4,2,6]=>[1,2,2,1,2]
[1,3,4,8,6,2,7,5]=>[8,6,2,3,5,7,1,4]=>[1,3,7,6,4,2,8,5]=>[3,1,1,2,1]
[7,2,4,1,3,8,5,6]=>[7,2,3,8,4,5,1,6]=>[2,7,6,1,5,4,8,3]=>[2,1,2,2,1]
[3,8,2,5,4,1,6,7]=>[6,1,3,5,4,7,8,2]=>[3,8,6,4,5,2,1,7]=>[2,1,2,1,2]
[8,4,5,2,6,1,7,3]=>[2,8,4,3,6,5,7,1]=>[7,1,5,6,3,4,2,8]=>[1,3,2,2]
[4,6,8,2,3,7,5,1]=>[8,1,4,2,5,7,6,3]=>[1,8,5,7,4,2,3,6]=>[2,2,1,3]
[2,7,3,4,1,5,6,8]=>[3,5,1,4,6,7,2,8]=>[6,4,8,5,3,2,7,1]=>[1,2,1,1,2,1]
[6,7,2,3,4,8,1,5]=>[3,4,5,1,7,2,8,6]=>[6,5,4,8,2,7,1,3]=>[1,1,2,2,2]
[3,5,2,4,6,7,8,1]=>[1,3,4,2,5,6,8,7]=>[8,6,5,7,4,3,1,2]=>[1,1,2,1,1,2]
[4,2,6,3,5,7,8,1]=>[4,1,5,2,3,6,8,7]=>[5,8,4,7,6,3,1,2]=>[2,2,1,1,2]
[2,3,4,5,6,1,8,7,9]=>[1,2,3,4,5,8,6,7,9]=>[9,8,7,6,5,2,4,3,1]=>[1,1,1,1,1,2,1,1]
[2,3,4,1,6,5,7,8,9]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,4,6,5,3,2,1]=>[1,1,1,2,1,1,1,1]
[2,3,1,5,4,6,7,8,9]=>[1,2,5,3,4,6,7,8,9]=>[9,8,5,7,6,4,3,2,1]=>[1,1,2,1,1,1,1,1]
[1,4,8,5,6,2,7,3]=>[4,8,2,6,5,7,1,3]=>[5,1,7,3,4,2,8,6]=>[1,2,2,2,1]
[2,4,8,5,6,1,7,3]=>[4,8,2,6,1,5,7,3]=>[5,1,7,3,8,4,2,6]=>[1,2,2,1,2]
[6,3,5,8,4,7,1,2]=>[3,7,2,1,5,8,6,4]=>[6,2,7,8,4,1,3,5]=>[1,3,1,3]
[2,8,7,4,5,1,6,3]=>[4,8,6,5,7,1,3,2]=>[5,1,3,4,2,8,6,7]=>[1,3,2,2]
[1,3,8,5,2,6,7,4]=>[6,4,8,2,5,7,1,3]=>[3,5,1,7,4,2,8,6]=>[2,2,1,2,1]
[7,2,8,4,5,1,6,3]=>[4,8,6,2,5,1,7,3]=>[5,1,3,7,4,8,2,6]=>[1,3,2,2]
[6,2,3,5,1,7,8,4]=>[6,2,3,4,1,8,5,7]=>[3,7,6,5,8,1,4,2]=>[2,1,2,2,1]
[8,6,2,4,1,5,7,3]=>[6,3,4,8,5,2,7,1]=>[3,6,5,1,4,7,2,8]=>[2,1,3,2]
[1,6,4,3,2,7,8,5]=>[4,3,6,2,8,1,5,7]=>[5,6,3,7,1,8,4,2]=>[2,2,2,1,1]
[8,5,3,2,1,6,7,4]=>[4,3,6,2,8,5,7,1]=>[5,6,3,7,1,4,2,8]=>[2,2,2,2]
[1,7,5,2,3,6,8,4]=>[6,8,4,3,5,1,2,7]=>[3,1,5,6,4,8,7,2]=>[1,3,2,1,1]
[8,1,2,5,3,6,7,4]=>[6,4,8,2,3,5,7,1]=>[3,5,1,7,6,4,2,8]=>[2,2,1,1,2]
[6,7,5,3,8,2,1,4]=>[4,1,7,6,3,2,8,5]=>[5,8,2,3,6,7,1,4]=>[2,4,2]
[5,2,6,8,3,7,1,4]=>[5,3,1,7,8,2,6,4]=>[4,6,8,2,1,7,3,5]=>[3,1,2,2]
[4,2,5,8,6,7,1,3]=>[1,7,3,5,8,2,6,4]=>[8,2,6,4,1,7,3,5]=>[1,2,1,2,2]
[5,8,6,3,4,1,7,2]=>[1,4,8,6,5,3,7,2]=>[8,5,1,3,4,6,2,7]=>[1,1,4,2]
[3,7,2,4,1,8,6,5]=>[8,1,3,4,7,5,2,6]=>[1,8,6,5,2,4,7,3]=>[2,1,1,3,1]
[2,4,7,8,5,1,3,6]=>[6,7,2,5,1,3,8,4]=>[3,2,7,4,8,6,1,5]=>[1,2,2,1,2]
[5,7,6,8,1,3,4,2]=>[1,6,8,5,3,2,7,4]=>[8,3,1,4,6,7,2,5]=>[1,1,4,2]
[3,1,7,4,5,6,2,8]=>[1,4,5,7,6,2,3,8]=>[8,5,4,2,3,7,6,1]=>[1,1,1,3,1,1]
[2,4,8,3,5,7,1,6]=>[2,4,5,7,8,1,6,3]=>[7,5,4,2,1,8,3,6]=>[1,1,1,1,2,2]
[8,1,7,2,4,3,5,6]=>[6,4,5,7,8,2,3,1]=>[3,5,4,2,1,7,6,8]=>[2,1,1,2,2]
[1,3,8,2,4,7,5,6]=>[7,8,2,4,5,6,1,3]=>[2,1,7,5,4,3,8,6]=>[1,2,1,1,2,1]
[1,3,7,2,4,6,5,8]=>[7,2,4,5,6,1,3,8]=>[2,7,5,4,3,8,6,1]=>[2,1,1,2,1,1]
[1,7,3,2,4,6,5,8]=>[3,7,4,5,6,1,2,8]=>[6,2,5,4,3,8,7,1]=>[1,2,1,2,1,1]
[1,8,3,7,4,2,5,6]=>[6,3,5,7,8,4,1,2]=>[3,6,4,2,1,5,8,7]=>[2,1,1,3,1]
[8,7,3,1,4,2,5,6]=>[6,4,3,5,7,8,2,1]=>[3,5,6,4,2,1,7,8]=>[3,1,1,3]
[2,8,4,3,5,7,1,6]=>[4,3,5,7,8,1,6,2]=>[5,6,4,2,1,8,3,7]=>[2,1,1,2,2]
[3,2,6,5,1,7,8,4]=>[6,1,4,2,3,8,5,7]=>[3,8,5,7,6,1,4,2]=>[2,2,1,2,1]
[5,3,2,6,7,1,8,4]=>[2,4,1,8,3,6,5,7]=>[7,5,8,1,6,3,4,2]=>[1,2,2,2,1]
[3,2,8,6,7,4,1,5]=>[7,6,1,4,8,2,5,3]=>[2,3,8,5,1,7,4,6]=>[3,1,2,2]
[8,4,6,2,7,3,1,5]=>[2,7,4,6,3,8,5,1]=>[7,2,5,3,6,1,4,8]=>[1,2,2,3]
[4,3,8,6,7,2,1,5]=>[7,1,6,2,4,8,5,3]=>[2,8,3,7,5,1,4,6]=>[2,2,1,3]
[4,3,6,2,8,7,1,5]=>[1,7,2,3,8,4,6,5]=>[8,2,7,6,1,5,3,4]=>[1,2,1,2,2]
[3,8,4,7,6,5,1,2]=>[7,8,3,6,1,5,4,2]=>[2,1,6,3,8,4,5,7]=>[1,2,2,3]
[7,8,4,2,6,3,5,1]=>[6,3,8,4,1,7,5,2]=>[3,6,1,5,8,2,4,7]=>[2,3,3]
[3,2,7,8,6,4,5,1]=>[6,3,8,1,7,2,5,4]=>[3,6,1,8,2,7,4,5]=>[2,2,2,2]
[3,2,7,5,6,8,4,1]=>[4,5,1,3,8,2,7,6]=>[5,4,8,6,1,7,2,3]=>[1,2,1,2,2]
[5,7,8,6,3,2,4,1]=>[6,1,5,2,8,7,4,3]=>[3,8,4,7,1,2,5,6]=>[2,2,4]
[6,5,4,2,1,7,8,3]=>[4,6,3,2,1,8,5,7]=>[5,3,6,7,8,1,4,2]=>[1,4,2,1]
[5,4,2,1,7,6,3,8]=>[7,3,2,1,6,4,5,8]=>[2,6,7,8,3,5,4,1]=>[4,2,1,1]
[4,1,6,5,2,7,8,3]=>[1,6,4,3,8,2,5,7]=>[8,3,5,6,1,7,4,2]=>[1,3,2,1,1]
[5,4,1,6,7,2,8,3]=>[4,2,1,8,6,3,5,7]=>[5,7,8,1,3,6,4,2]=>[3,3,1,1]
[5,2,6,3,8,7,1,4]=>[7,3,1,8,2,4,6,5]=>[2,6,8,1,7,5,3,4]=>[3,2,1,2]
[8,6,1,7,3,4,2,5]=>[5,7,6,8,3,2,4,1]=>[4,2,3,1,6,7,5,8]=>[1,2,3,2]
[1,8,3,6,7,4,2,5]=>[7,6,3,4,8,5,1,2]=>[2,3,6,5,1,4,8,7]=>[3,1,3,1]
[1,6,3,5,2,7,8,4]=>[6,3,4,2,8,1,5,7]=>[3,6,5,7,1,8,4,2]=>[2,2,2,1,1]
[5,1,3,7,2,6,4,8]=>[7,3,5,1,6,2,4,8]=>[2,6,4,8,3,7,5,1]=>[2,2,2,1,1]
[8,1,6,7,2,4,3,5]=>[7,5,6,3,8,2,4,1]=>[2,4,3,6,1,7,5,8]=>[2,2,2,2]
[6,1,4,8,2,7,3,5]=>[3,7,8,5,1,6,2,4]=>[6,2,1,4,8,3,7,5]=>[1,1,3,2,1]
[6,2,4,8,3,7,1,5]=>[3,5,7,1,8,2,6,4]=>[6,4,2,8,1,7,3,5]=>[1,1,2,2,2]
[8,7,2,6,3,5,1,4]=>[5,7,8,3,6,4,2,1]=>[4,2,1,6,3,5,7,8]=>[1,1,2,4]
[8,1,7,6,5,2,3,4]=>[6,7,8,5,4,2,3,1]=>[3,2,1,4,5,7,6,8]=>[1,1,4,2]
[7,1,5,6,8,2,4,3]=>[3,8,6,4,7,2,1,5]=>[6,1,3,5,2,7,8,4]=>[1,3,3,1]
[7,6,1,5,2,4,3,8]=>[7,5,6,3,4,2,1,8]=>[2,4,3,6,5,7,8,1]=>[2,2,3,1]
[7,1,6,3,5,4,2,8]=>[7,4,6,5,2,3,1,8]=>[2,5,3,4,7,6,8,1]=>[2,3,2,1]
[1,6,7,3,5,4,8,2]=>[6,4,2,5,3,8,1,7]=>[3,5,7,4,6,1,8,2]=>[3,2,2,1]
[1,7,3,5,6,8,4,2]=>[4,5,8,3,2,7,1,6]=>[5,4,1,6,7,2,8,3]=>[1,1,3,2,1]
[1,7,8,3,6,4,5,2]=>[6,8,4,2,7,5,1,3]=>[3,1,5,7,2,4,8,6]=>[1,3,3,1]
[1,8,7,6,4,5,2,3]=>[7,5,8,6,4,3,1,2]=>[2,4,1,3,5,6,8,7]=>[2,5,1]
[8,2,7,4,6,5,1,3]=>[4,7,8,6,2,5,3,1]=>[5,2,1,3,7,4,6,8]=>[1,1,3,3]
[7,4,5,1,6,8,3,2]=>[2,5,3,8,7,4,1,6]=>[7,4,6,1,2,5,8,3]=>[1,2,4,1]
[4,1,7,5,6,8,3,2]=>[1,4,5,3,8,7,2,6]=>[8,5,4,6,1,2,7,3]=>[1,1,2,3,1]
[5,6,7,4,3,1,8,2]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[1,1,5,1]
[6,7,8,5,3,1,4,2]=>[1,8,6,5,2,7,4,3]=>[8,1,3,4,7,2,5,6]=>[1,4,3]
[1,4,6,2,5,3,7,8]=>[2,6,4,5,1,3,7,8]=>[7,3,5,4,8,6,2,1]=>[1,2,2,1,1,1]
[1,6,3,2,5,4,7,8]=>[3,6,4,5,1,2,7,8]=>[6,3,5,4,8,7,2,1]=>[1,2,2,1,1,1]
[1,6,8,2,5,4,7,3]=>[6,5,2,8,4,7,1,3]=>[3,4,7,1,5,2,8,6]=>[3,2,2,1]
[1,5,4,2,6,3,7,8]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]
[1,2,6,4,3,5,7,8]=>[5,4,6,1,2,3,7,8]=>[4,5,3,8,7,6,2,1]=>[2,2,1,1,1,1]
[1,6,8,2,7,5,4,3]=>[2,8,7,6,4,5,1,3]=>[7,1,2,3,5,4,8,6]=>[1,4,2,1]
[1,5,4,7,2,6,8,3]=>[3,2,6,8,5,1,4,7]=>[6,7,3,1,4,8,5,2]=>[2,1,3,1,1]
[1,3,7,6,2,8,5,4]=>[8,7,5,2,4,1,3,6]=>[1,2,4,7,5,8,6,3]=>[4,2,1,1]
[1,7,6,2,8,4,3,5]=>[7,6,8,4,3,1,2,5]=>[2,3,1,5,6,8,7,4]=>[2,4,1,1]
[1,5,2,8,4,3,7,6]=>[5,2,8,6,7,1,3,4]=>[4,7,1,3,2,8,6,5]=>[2,2,2,1,1]
[1,2,8,4,3,6,5,7]=>[4,7,5,6,8,1,2,3]=>[5,2,4,3,1,8,7,6]=>[1,2,1,2,1,1]
[1,2,8,5,6,3,4,7]=>[6,4,7,5,8,1,2,3]=>[3,5,2,4,1,8,7,6]=>[2,2,2,1,1]
[1,7,3,5,2,8,6,4]=>[4,8,3,7,5,1,2,6]=>[5,1,6,2,4,8,7,3]=>[1,2,3,1,1]
[1,6,7,2,5,8,4,3]=>[5,2,8,7,4,1,3,6]=>[4,7,1,2,5,8,6,3]=>[2,4,1,1]
[1,5,8,3,2,7,4,6]=>[4,2,7,8,5,6,1,3]=>[5,7,2,1,4,3,8,6]=>[2,1,2,2,1]
[1,4,5,8,2,6,3,7]=>[2,3,7,5,6,8,1,4]=>[7,6,2,4,3,1,8,5]=>[1,1,2,1,2,1]
[1,7,6,4,8,2,5,3]=>[4,8,6,3,2,7,1,5]=>[5,1,3,6,7,2,8,4]=>[1,4,2,1]
[1,3,8,2,6,5,4,7]=>[7,6,2,4,5,8,1,3]=>[2,3,7,5,4,1,8,6]=>[3,1,1,2,1]
[1,7,6,3,8,2,4,5]=>[4,6,7,3,2,8,1,5]=>[5,3,2,6,7,1,8,4]=>[1,1,3,2,1]
[1,5,2,7,6,4,8,3]=>[2,6,5,4,8,1,3,7]=>[7,3,4,5,1,8,6,2]=>[1,3,2,1,1]
[1,2,4,3,8,7,5,6]=>[7,8,3,6,1,2,4,5]=>[2,1,6,3,8,7,5,4]=>[1,2,2,1,1,1]
[1,4,3,8,7,2,5,6]=>[2,6,7,8,3,5,1,4]=>[7,3,2,1,6,4,8,5]=>[1,1,1,2,2,1]
[1,3,8,6,2,4,5,7]=>[5,6,7,2,4,8,1,3]=>[4,3,2,7,5,1,8,6]=>[1,1,2,1,2,1]
[1,3,8,5,4,2,6,7]=>[6,5,2,4,7,8,1,3]=>[3,4,7,5,2,1,8,6]=>[3,1,1,2,1]
[1,7,2,4,8,6,5,3]=>[8,7,4,6,3,1,2,5]=>[1,2,5,3,6,8,7,4]=>[3,3,1,1]
[1,6,5,3,2,8,7,4]=>[8,4,3,2,7,1,5,6]=>[1,5,6,7,2,8,4,3]=>[4,2,1,1]
[1,3,2,8,7,5,4,6]=>[7,6,8,2,5,1,3,4]=>[2,3,1,7,4,8,6,5]=>[2,2,2,1,1]
[1,2,8,6,5,4,3,7]=>[7,6,5,4,8,1,2,3]=>[2,3,4,5,1,8,7,6]=>[4,2,1,1]
[8,1,3,4,6,5,2,7]=>[7,3,4,6,2,5,8,1]=>[2,6,5,3,7,4,1,8]=>[2,1,2,1,2]
[8,3,1,4,6,5,2,7]=>[2,7,4,6,3,5,8,1]=>[7,2,5,3,6,4,1,8]=>[1,2,2,1,2]
[5,8,3,1,2,6,4,7]=>[7,4,3,1,5,6,8,2]=>[2,5,6,8,4,3,1,7]=>[4,1,1,2]
[4,8,1,7,5,2,3,6]=>[1,6,7,5,8,3,4,2]=>[8,3,2,4,1,6,5,7]=>[1,1,2,2,2]
[4,8,1,7,5,2,6,3]=>[8,1,6,5,7,3,4,2]=>[1,8,3,4,2,6,5,7]=>[2,2,2,2]
[8,4,1,3,5,6,2,7]=>[4,5,2,7,3,6,8,1]=>[5,4,7,2,6,3,1,8]=>[1,2,2,1,2]
[8,5,3,2,1,6,4,7]=>[4,3,7,5,2,6,8,1]=>[5,6,2,4,7,3,1,8]=>[2,3,1,2]
[8,1,5,4,2,6,3,7]=>[7,5,4,2,3,6,8,1]=>[2,4,5,7,6,3,1,8]=>[4,1,1,2]
[8,5,2,4,1,6,3,7]=>[7,3,5,4,2,6,8,1]=>[2,6,4,5,7,3,1,8]=>[2,3,1,2]
[4,8,7,1,5,2,6,3]=>[8,1,6,4,5,7,3,2]=>[1,8,3,5,4,2,6,7]=>[2,2,1,3]
[4,8,7,1,5,2,3,6]=>[1,6,7,4,5,8,3,2]=>[8,3,2,5,4,1,6,7]=>[1,1,2,1,3]
[7,6,8,4,1,3,2,5]=>[7,5,6,4,2,1,8,3]=>[2,4,3,5,7,8,1,6]=>[2,4,2]
[7,6,8,4,1,3,5,2]=>[6,8,5,4,2,1,7,3]=>[3,1,4,5,7,8,2,6]=>[1,5,2]
[4,8,2,7,5,1,3,6]=>[1,6,7,3,5,8,4,2]=>[8,3,2,6,4,1,5,7]=>[1,1,2,1,3]
[7,6,8,4,1,5,2,3]=>[7,8,5,4,2,1,6,3]=>[2,1,4,5,7,8,3,6]=>[1,5,2]
[8,7,6,1,5,2,3,4]=>[6,7,8,4,5,3,2,1]=>[3,2,1,5,4,6,7,8]=>[1,1,2,4]
[7,1,4,8,6,3,5,2]=>[6,8,3,7,5,2,1,4]=>[3,1,6,2,4,7,8,5]=>[1,2,4,1]
[8,1,6,5,3,4,7,2]=>[5,6,4,3,8,2,7,1]=>[4,3,5,6,1,7,2,8]=>[1,3,2,2]
[8,6,2,5,3,4,7,1]=>[5,6,3,4,2,8,7,1]=>[4,3,6,5,7,1,2,8]=>[1,2,2,3]
[8,6,5,1,3,4,7,2]=>[5,6,8,4,3,2,7,1]=>[4,3,1,5,6,7,2,8]=>[1,1,4,2]
[8,7,5,1,3,6,2,4]=>[5,7,8,4,3,6,2,1]=>[4,2,1,5,6,3,7,8]=>[1,1,3,3]
[8,7,1,5,3,6,2,4]=>[5,7,4,8,3,6,2,1]=>[4,2,5,1,6,3,7,8]=>[1,2,2,3]
[8,6,1,3,5,4,7,2]=>[6,4,5,8,3,2,7,1]=>[3,5,4,1,6,7,2,8]=>[2,1,3,2]
[7,1,4,8,3,6,5,2]=>[8,3,5,7,6,2,1,4]=>[1,6,4,2,3,7,8,5]=>[2,1,4,1]
[7,8,5,2,4,3,6,1]=>[6,4,5,3,1,8,7,2]=>[3,5,4,6,8,1,2,7]=>[2,3,3]
[7,3,8,2,5,4,6,1]=>[6,2,4,5,1,8,7,3]=>[3,7,5,4,8,1,2,6]=>[2,1,2,3]
[8,4,2,5,3,7,6,1]=>[4,2,8,3,5,7,6,1]=>[5,7,1,6,4,2,3,8]=>[2,2,1,3]
[4,8,1,5,3,7,6,2]=>[1,4,8,5,7,3,6,2]=>[8,5,1,4,2,6,3,7]=>[1,1,2,2,2]
[7,4,8,2,6,3,5,1]=>[2,6,8,4,1,7,5,3]=>[7,3,1,5,8,2,4,6]=>[1,1,3,3]
[7,4,8,2,6,3,1,5]=>[2,7,4,6,1,8,5,3]=>[7,2,5,3,8,1,4,6]=>[1,2,2,3]
[8,7,3,1,6,4,2,5]=>[3,7,6,8,4,5,2,1]=>[6,2,3,1,5,4,7,8]=>[1,2,2,3]
[8,7,3,1,4,6,5,2]=>[3,8,5,7,4,6,2,1]=>[6,1,4,2,5,3,7,8]=>[1,2,2,3]
[8,4,3,2,7,5,6,1]=>[3,2,6,8,4,7,5,1]=>[6,7,3,1,5,2,4,8]=>[2,1,2,3]
[6,4,1,7,8,5,3,2]=>[2,4,1,8,7,6,3,5]=>[7,5,8,1,2,3,6,4]=>[1,2,4,1]
[7,6,3,4,1,8,5,2]=>[3,4,8,7,5,2,1,6]=>[6,5,1,2,4,7,8,3]=>[1,1,5,1]
[7,8,6,4,2,5,1,3]=>[5,7,4,1,8,6,3,2]=>[4,2,5,8,1,3,6,7]=>[1,3,4]
[7,8,2,4,6,5,1,3]=>[4,7,8,3,1,6,5,2]=>[5,2,1,6,8,3,4,7]=>[1,1,3,3]
[8,1,7,3,5,6,2,4]=>[7,4,5,8,6,2,3,1]=>[2,5,4,1,3,7,6,8]=>[2,1,3,2]
[8,7,5,2,4,6,1,3]=>[7,4,5,3,8,6,2,1]=>[2,5,4,6,1,3,7,8]=>[2,2,4]
[8,1,7,5,4,6,2,3]=>[7,5,4,8,6,2,3,1]=>[2,4,5,1,3,7,6,8]=>[3,3,2]
[5,3,1,7,6,4,2,8]=>[7,2,1,6,5,3,4,8]=>[2,7,8,3,4,6,5,1]=>[3,3,1,1]
[7,5,3,2,1,6,4,8]=>[4,3,7,5,2,6,1,8]=>[5,6,2,4,7,3,8,1]=>[2,3,2,1]
[7,6,5,3,1,4,2,8]=>[7,5,4,6,3,2,1,8]=>[2,4,5,3,6,7,8,1]=>[3,4,1]
[1,8,6,4,3,2,7,5]=>[5,4,8,6,3,7,1,2]=>[4,5,1,3,6,2,8,7]=>[2,3,2,1]
[1,8,7,6,4,2,5,3]=>[8,6,5,7,4,3,1,2]=>[1,3,4,2,5,6,8,7]=>[3,4,1]
[8,4,6,7,5,3,2,1]=>[3,8,2,7,6,5,4,1]=>[6,1,7,2,3,4,5,8]=>[1,2,5]
[1,4,8,6,7,5,3,2]=>[4,8,7,2,6,5,1,3]=>[5,1,2,7,3,4,8,6]=>[1,3,3,1]
[7,6,2,5,8,4,3,1]=>[4,8,7,3,2,1,6,5]=>[5,1,2,6,7,8,3,4]=>[1,5,2]
[1,7,3,6,8,5,4,2]=>[4,8,7,3,2,6,1,5]=>[5,1,2,6,7,3,8,4]=>[1,4,2,1]
[8,6,2,5,7,4,3,1]=>[4,8,7,3,2,6,5,1]=>[5,1,2,6,7,3,4,8]=>[1,4,3]
[7,1,3,6,8,5,4,2]=>[4,8,7,3,6,2,1,5]=>[5,1,2,6,3,7,8,4]=>[1,3,3,1]
[1,8,3,6,7,5,4,2]=>[4,8,7,3,6,5,1,2]=>[5,1,2,6,3,4,8,7]=>[1,3,3,1]
[8,1,7,6,4,5,3,2]=>[5,8,7,6,4,2,3,1]=>[4,1,2,3,5,7,6,8]=>[1,5,2]
[7,1,8,6,4,5,3,2]=>[5,8,7,6,4,2,1,3]=>[4,1,2,3,5,7,8,6]=>[1,6,1]
[1,6,2,7,4,5,3,8]=>[5,7,6,3,1,2,4,8]=>[4,2,3,6,8,7,5,1]=>[1,4,1,1,1]
[1,8,2,6,4,3,5,7]=>[6,5,7,3,4,8,1,2]=>[3,4,2,6,5,1,8,7]=>[2,2,1,2,1]
[1,7,2,6,4,3,5,8]=>[6,5,7,3,4,1,2,8]=>[3,4,2,6,5,8,7,1]=>[2,2,2,1,1]
[1,7,2,5,4,6,3,8]=>[5,4,7,3,6,1,2,8]=>[4,5,2,6,3,8,7,1]=>[2,2,2,1,1]
[6,5,7,2,8,3,4,1]=>[6,2,1,8,4,3,7,5]=>[3,7,8,1,5,6,2,4]=>[3,3,2]
[6,5,7,2,8,1,4,3]=>[8,4,2,1,6,3,7,5]=>[1,5,7,8,3,6,2,4]=>[4,2,2]
[6,2,7,5,8,1,4,3]=>[8,6,4,2,1,3,7,5]=>[1,3,5,7,8,6,2,4]=>[5,1,2]
[6,5,7,3,8,1,4,2]=>[4,2,1,8,6,3,7,5]=>[5,7,8,1,3,6,2,4]=>[3,3,2]
[6,3,7,4,8,2,5,1]=>[4,6,2,1,3,8,7,5]=>[5,3,7,8,6,1,2,4]=>[1,3,1,3]
[6,3,7,4,8,1,5,2]=>[4,8,2,1,6,3,7,5]=>[5,1,7,8,3,6,2,4]=>[1,3,2,2]
[6,2,7,4,8,1,5,3]=>[4,8,6,2,1,3,7,5]=>[5,1,3,7,8,6,2,4]=>[1,4,1,2]
[8,7,6,4,2,5,3,1]=>[8,5,4,7,6,3,2,1]=>[1,4,5,2,3,6,7,8]=>[3,5]
[8,7,4,6,2,3,5,1]=>[5,3,6,8,7,4,2,1]=>[4,6,3,1,2,5,7,8]=>[2,1,5]
[6,8,4,5,7,3,2,1]=>[3,1,4,8,7,6,5,2]=>[6,8,5,1,2,3,4,7]=>[2,1,5]
[6,7,5,1,4,3,8,2]=>[6,5,1,8,4,3,2,7]=>[3,4,8,1,5,6,7,2]=>[3,4,1]
[7,8,5,1,4,3,6,2]=>[6,5,8,4,3,1,7,2]=>[3,4,1,5,6,8,2,7]=>[2,4,2]
[2,7,6,8,3,5,1,4]=>[5,7,3,2,8,1,6,4]=>[4,2,6,7,1,8,3,5]=>[1,3,2,2]
[7,2,1,5,3,8,6,4]=>[4,8,2,7,3,5,1,6]=>[5,1,7,2,6,4,8,3]=>[1,2,2,2,1]
[5,8,2,7,6,1,3,4]=>[6,1,7,8,3,5,4,2]=>[3,8,2,1,6,4,5,7]=>[2,1,2,3]
[5,1,8,7,3,4,2,6]=>[5,1,7,6,8,4,2,3]=>[4,8,2,3,1,5,7,6]=>[2,2,3,1]
[8,6,5,4,3,2,1,7,9]=>[7,6,5,4,3,2,8,1,9]=>[3,4,5,6,7,8,2,9,1]=>[6,2,1]
[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[9,8,10,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]
[9,7,6,5,4,3,2,1,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>[3,4,5,6,7,8,9,2,10,1]=>[7,2,1]
[2,4,8,7,5,3,1,6]=>[7,6,2,5,8,1,4,3]=>[2,3,7,4,1,8,5,6]=>[3,1,2,2]
[2,6,5,1,4,3,8,7]=>[5,8,4,1,3,2,6,7]=>[4,1,5,8,6,7,3,2]=>[1,3,2,1,1]
[4,6,5,3,1,2,8,7]=>[8,1,5,4,3,2,6,7]=>[1,8,4,5,6,7,3,2]=>[2,4,1,1]
[4,6,8,7,5,3,1,2]=>[2,7,8,1,6,5,4,3]=>[7,2,1,8,3,4,5,6]=>[1,1,2,4]
[6,8,7,5,3,1,4,2]=>[1,8,6,5,7,4,3,2]=>[8,1,3,4,2,5,6,7]=>[1,3,4]
[8,7,5,6,3,1,4,2]=>[8,6,5,3,7,4,2,1]=>[1,3,4,6,2,5,7,8]=>[4,4]
[8,7,3,4,6,5,1,2]=>[3,4,7,8,6,5,2,1]=>[6,5,2,1,3,4,7,8]=>[1,1,1,5]
[2,1,4,8,7,3,6,5]=>[8,6,7,1,3,5,2,4]=>[1,3,2,8,6,4,7,5]=>[2,2,1,2,1]
[4,8,7,3,1,2,6,5]=>[8,1,5,4,6,7,3,2]=>[1,8,4,5,3,2,6,7]=>[2,2,1,3]
[8,7,3,4,1,2,6,5]=>[3,8,5,4,6,7,2,1]=>[6,1,4,5,3,2,7,8]=>[1,3,1,3]
[2,8,7,3,4,6,5,1]=>[8,4,5,7,6,1,3,2]=>[1,5,4,2,3,8,6,7]=>[2,1,3,2]
[2,8,7,1,6,5,3,4]=>[7,8,6,4,5,1,3,2]=>[2,1,3,5,4,8,6,7]=>[1,3,2,2]
[8,7,1,2,6,5,3,4]=>[7,8,6,3,4,5,2,1]=>[2,1,3,6,5,4,7,8]=>[1,3,1,3]
[8,7,1,2,4,3,6,5]=>[5,8,3,4,6,7,2,1]=>[4,1,6,5,3,2,7,8]=>[1,2,1,1,3]
[2,1,8,7,3,4,6,5]=>[8,5,6,7,1,4,2,3]=>[1,4,3,2,8,5,7,6]=>[2,1,2,2,1]
[8,7,5,1,2,4,3,6]=>[7,4,5,6,3,8,2,1]=>[2,5,4,3,6,1,7,8]=>[2,1,2,3]
[2,8,7,1,4,3,6,5]=>[5,8,4,6,7,1,3,2]=>[4,1,5,3,2,8,6,7]=>[1,2,1,2,2]
[2,8,7,3,4,1,6,5]=>[4,5,8,6,7,1,3,2]=>[5,4,1,3,2,8,6,7]=>[1,1,2,2,2]
[2,8,7,5,6,3,4,1]=>[6,4,8,7,5,1,3,2]=>[3,5,1,2,4,8,6,7]=>[2,4,2]
[2,4,8,7,3,1,6,5]=>[5,8,2,6,7,1,4,3]=>[4,1,7,3,2,8,5,6]=>[1,2,1,2,2]
[2,8,7,3,1,4,6,5]=>[4,8,5,6,7,1,3,2]=>[5,1,4,3,2,8,6,7]=>[1,2,1,2,2]
[2,4,3,1,8,7,5,6]=>[2,7,8,1,3,6,4,5]=>[7,2,1,8,6,3,5,4]=>[1,1,2,1,2,1]
[4,3,1,2,6,8,7,5]=>[2,1,8,5,7,3,4,6]=>[7,8,1,4,2,6,5,3]=>[2,2,2,1,1]
[2,8,7,5,6,3,1,4]=>[7,6,4,8,5,1,3,2]=>[2,3,5,1,4,8,6,7]=>[3,3,2]
[2,8,7,5,3,6,4,1]=>[8,5,4,7,6,1,3,2]=>[1,4,5,2,3,8,6,7]=>[3,3,2]
[2,8,7,5,6,1,4,3]=>[8,6,4,7,5,1,3,2]=>[1,3,5,2,4,8,6,7]=>[3,3,2]
[2,6,8,7,5,1,4,3]=>[2,8,6,7,5,1,4,3]=>[7,1,3,2,4,8,5,6]=>[1,2,3,2]
[6,8,7,5,1,2,4,3]=>[8,5,1,6,7,4,3,2]=>[1,4,8,3,2,5,6,7]=>[3,1,4]
[8,7,5,6,1,2,4,3]=>[8,5,6,3,7,4,2,1]=>[1,4,3,6,2,5,7,8]=>[2,2,4]
[2,4,8,7,3,6,5,1]=>[8,5,7,2,6,1,4,3]=>[1,4,2,7,3,8,5,6]=>[2,2,2,2]
[8,7,2,4,3,6,5,1]=>[4,8,3,5,7,6,2,1]=>[5,1,6,4,2,3,7,8]=>[1,2,1,4]
[4,8,7,1,2,6,5,3]=>[8,1,7,4,5,6,3,2]=>[1,8,2,5,4,3,6,7]=>[2,2,1,3]
[8,7,5,3,1,2,6,4]=>[8,5,4,6,3,7,2,1]=>[1,4,5,3,6,2,7,8]=>[3,2,3]
[8,7,5,3,6,4,1,2]=>[4,7,3,8,6,5,2,1]=>[5,2,6,1,3,4,7,8]=>[1,2,5]
[8,7,1,4,3,6,5,2]=>[4,8,5,7,3,6,2,1]=>[5,1,4,2,6,3,7,8]=>[1,2,2,3]
[8,7,3,4,1,6,5,2]=>[3,4,8,7,5,6,2,1]=>[6,5,1,2,4,3,7,8]=>[1,1,3,3]
[8,1,2,3,4,5,7,6,9]=>[8,2,3,4,5,6,7,1,9]=>[2,8,7,6,5,4,3,9,1]=>[2,1,1,1,1,2,1]
[7,1,2,3,5,4,6,8]=>[6,2,3,4,5,7,1,8]=>[3,7,6,5,4,2,8,1]=>[2,1,1,1,2,1]
[1,9,2,3,4,5,6,8,7]=>[9,3,4,5,6,7,8,1,2]=>[1,7,6,5,4,3,2,9,8]=>[2,1,1,1,1,2,1]
[7,1,2,6,4,5,3,8]=>[5,7,6,2,3,4,1,8]=>[4,2,3,7,6,5,8,1]=>[1,3,1,2,1]
[7,1,2,4,3,5,6,8]=>[5,2,3,4,6,7,1,8]=>[4,7,6,5,3,2,8,1]=>[2,1,1,1,2,1]
[7,5,4,2,8,3,1,6]=>[7,4,3,2,6,1,8,5]=>[2,5,6,7,3,8,1,4]=>[4,2,2]
[8,3,6,1,5,2,4,7]=>[2,6,7,4,5,3,8,1]=>[7,3,2,5,4,6,1,8]=>[1,1,2,2,2]
[3,1,6,8,5,7,2,4]=>[3,7,1,5,8,6,2,4]=>[6,2,8,4,1,3,7,5]=>[1,2,1,3,1]
[5,7,2,1,8,4,6,3]=>[6,1,8,3,7,4,2,5]=>[3,8,1,6,2,5,7,4]=>[2,2,3,1]
[7,2,8,6,4,3,1,5]=>[7,6,5,8,2,1,4,3]=>[2,3,4,1,7,8,5,6]=>[3,3,2]
[6,3,8,7,4,2,1,5]=>[7,6,2,1,5,8,4,3]=>[2,3,7,8,4,1,5,6]=>[4,1,3]
[7,6,3,2,8,4,1,5]=>[3,7,4,6,2,1,8,5]=>[6,2,5,3,7,8,1,4]=>[1,2,3,2]
[5,8,3,7,4,2,1,6]=>[1,7,3,6,5,8,4,2]=>[8,2,6,3,4,1,5,7]=>[1,2,2,3]
[4,1,7,3,5,8,6,2]=>[1,8,4,5,3,7,2,6]=>[8,1,5,4,6,2,7,3]=>[1,2,2,2,1]
[8,4,7,3,5,2,1,6]=>[2,4,7,6,5,8,3,1]=>[7,5,2,3,4,1,6,8]=>[1,1,3,3]
[5,4,8,1,3,2,6,7]=>[6,4,2,1,5,7,8,3]=>[3,5,7,8,4,2,1,6]=>[4,1,1,2]
[4,5,8,2,1,3,6,7]=>[1,5,4,2,6,7,8,3]=>[8,4,5,7,3,2,1,6]=>[1,3,1,1,2]
[8,1,3,5,2,4,6,7]=>[3,5,6,2,4,7,8,1]=>[6,4,3,7,5,2,1,8]=>[1,1,2,1,1,2]
[1,8,3,5,7,2,4,6]=>[6,3,4,7,8,5,1,2]=>[3,6,5,2,1,4,8,7]=>[2,1,1,3,1]
[1,7,3,8,6,2,4,5]=>[6,7,8,3,2,5,1,4]=>[3,2,1,6,7,4,8,5]=>[1,1,3,2,1]
[8,6,2,1,3,7,5,4]=>[8,3,7,4,5,2,6,1]=>[1,6,2,5,4,7,3,8]=>[2,2,2,2]
[1,3,4,5,6,7,8,2,9]=>[2,3,4,5,6,8,1,7,9]=>[8,7,6,5,4,2,9,3,1]=>[1,1,1,1,1,2,1,1]
[1,3,4,5,6,7,8,10,2,9]=>[2,3,4,5,6,7,9,10,1,8]=>[9,8,7,6,5,4,2,1,10,3]=>[1,1,1,1,1,1,1,2,1]
[1,5,7,3,6,8,2,4]=>[2,7,4,5,3,8,1,6]=>[7,2,5,4,6,1,8,3]=>[1,2,2,2,1]
[8,4,6,2,5,7,1,3]=>[2,7,4,5,3,8,6,1]=>[7,2,5,4,6,1,3,8]=>[1,2,2,3]
[1,3,4,7,6,8,2,5]=>[7,5,2,3,4,8,1,6]=>[2,4,7,6,5,1,8,3]=>[3,1,1,2,1]
[1,2,4,7,8,5,3,6]=>[7,6,3,4,8,1,2,5]=>[2,3,6,5,1,8,7,4]=>[3,1,2,1,1]
[3,1,4,7,6,8,2,5]=>[7,1,5,3,4,8,2,6]=>[2,8,4,6,5,1,7,3]=>[2,2,1,2,1]
[4,1,3,7,6,8,2,5]=>[1,7,5,3,4,8,2,6]=>[8,2,4,6,5,1,7,3]=>[1,3,1,2,1]
[5,1,7,3,6,8,2,4]=>[7,4,1,5,3,8,2,6]=>[2,5,8,4,6,1,7,3]=>[3,2,2,1]
[6,7,8,2,4,5,1,3]=>[7,4,1,5,2,8,6,3]=>[2,5,8,4,7,1,3,6]=>[3,2,3]
[5,8,6,2,4,7,1,3]=>[1,7,4,5,3,8,6,2]=>[8,2,5,4,6,1,3,7]=>[1,2,2,3]
[3,8,2,6,5,7,1,4]=>[7,5,1,3,4,8,6,2]=>[2,4,8,6,5,1,3,7]=>[3,1,1,3]
[8,7,1,6,4,3,2,5]=>[7,6,5,8,3,4,2,1]=>[2,3,4,1,6,5,7,8]=>[3,2,3]
[1,8,2,7,5,4,3,6]=>[7,6,5,8,3,4,1,2]=>[2,3,4,1,6,5,8,7]=>[3,2,2,1]
[3,8,1,7,5,4,2,6]=>[7,6,1,5,8,3,4,2]=>[2,3,8,4,1,6,5,7]=>[3,1,2,2]
[5,8,6,1,7,3,2,4]=>[1,7,6,8,4,3,5,2]=>[8,2,3,1,5,6,4,7]=>[1,2,3,2]
[6,7,1,2,8,4,3,5]=>[7,6,8,3,1,4,2,5]=>[2,3,1,6,8,5,7,4]=>[2,3,2,1]
[2,1,3,8,6,5,4,7]=>[7,6,1,5,8,2,3,4]=>[2,3,8,4,1,7,6,5]=>[3,1,2,1,1]
[1,3,2,8,6,5,4,7]=>[7,6,2,5,8,1,3,4]=>[2,3,7,4,1,8,6,5]=>[3,1,2,1,1]
[3,4,1,7,6,8,2,5]=>[7,1,2,5,4,8,3,6]=>[2,8,7,4,5,1,6,3]=>[2,1,2,2,1]
[2,5,7,1,8,4,3,6]=>[2,7,6,8,1,4,3,5]=>[7,2,3,1,8,5,6,4]=>[1,2,2,2,1]
[3,5,7,1,6,8,2,4]=>[2,7,1,5,8,4,3,6]=>[7,2,8,4,1,5,6,3]=>[1,2,1,3,1]
[4,5,7,6,1,8,2,3]=>[1,2,7,8,5,4,3,6]=>[8,7,2,1,4,5,6,3]=>[1,1,1,4,1]
[5,4,7,6,8,3,1,2]=>[1,7,2,4,3,8,6,5]=>[8,2,7,5,6,1,3,4]=>[1,2,2,3]
[1,5,7,8,6,3,2,4]=>[7,2,6,3,8,5,1,4]=>[2,7,3,6,1,4,8,5]=>[2,2,3,1]
[8,4,6,7,5,2,1,3]=>[7,2,6,3,8,5,4,1]=>[2,7,3,6,1,4,5,8]=>[2,2,4]
[1,4,8,6,7,3,2,5]=>[7,6,2,4,8,5,1,3]=>[2,3,7,5,1,4,8,6]=>[3,1,3,1]
[2,4,8,6,7,3,1,5]=>[7,6,2,4,8,1,5,3]=>[2,3,7,5,1,8,4,6]=>[3,1,2,2]
[2,3,8,7,5,4,1,6]=>[7,6,5,8,1,2,4,3]=>[2,3,4,1,8,7,5,6]=>[3,2,1,2]
[1,3,8,7,5,4,2,6]=>[7,6,5,8,2,4,1,3]=>[2,3,4,1,7,5,8,6]=>[3,2,2,1]
[8,2,7,6,4,3,1,5]=>[7,6,5,8,2,4,3,1]=>[2,3,4,1,7,5,6,8]=>[3,2,3]
[8,1,7,6,4,3,2,5]=>[7,6,5,8,4,2,3,1]=>[2,3,4,1,5,7,6,8]=>[3,3,2]
[4,1,8,6,7,3,2,5]=>[7,1,6,4,8,5,2,3]=>[2,8,3,5,1,4,7,6]=>[2,2,3,1]
[4,8,7,5,6,2,1,3]=>[7,6,1,4,8,5,3,2]=>[2,3,8,5,1,4,6,7]=>[3,1,4]
[5,6,8,1,7,4,3,2]=>[1,2,8,7,6,4,5,3]=>[8,7,1,2,3,5,4,6]=>[1,1,4,2]
[1,3,9,8,7,6,5,4,2]=>[9,8,7,6,5,2,4,1,3]=>[1,2,3,4,5,8,6,9,7]=>[6,2,1]
[8,7,1,9,6,5,4,3,2]=>[9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,7,8,9,6]=>[8,1]
[1,8,10,9,7,6,5,4,3,2]=>[10,2,9,8,7,6,5,4,1,3]=>[1,9,2,3,4,5,6,7,10,8]=>[2,7,1]
[4,1,8,7,3,6,5,2]=>[8,1,5,7,6,4,2,3]=>[1,8,4,2,3,5,7,6]=>[2,1,4,1]
[5,6,8,4,1,7,3,2]=>[1,2,8,7,5,4,6,3]=>[8,7,1,2,4,5,3,6]=>[1,1,4,2]
[4,5,8,7,3,1,6,2]=>[8,1,2,6,5,7,4,3]=>[1,8,7,3,4,2,5,6]=>[2,1,2,3]
[9,8,1,10,7,6,5,4,3,2]=>[10,9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,6,8,9,10,7]=>[9,1]
[8,7,6,1,9,5,4,3,2]=>[9,8,7,6,4,3,2,1,5]=>[1,2,3,4,6,7,8,9,5]=>[8,1]
[3,1,8,4,7,6,5,2]=>[8,7,1,4,6,5,2,3]=>[1,2,8,5,3,4,7,6]=>[3,1,3,1]
[1,5,8,4,3,7,6,2]=>[2,4,8,5,7,6,1,3]=>[7,5,1,4,2,3,8,6]=>[1,1,2,3,1]
[8,1,7,2,5,6,4,3]=>[5,8,7,4,6,2,3,1]=>[4,1,2,5,3,7,6,8]=>[1,3,2,2]
[8,1,3,5,2,7,6,4]=>[4,8,3,7,2,5,6,1]=>[5,1,6,2,7,4,3,8]=>[1,2,2,1,2]
[2,7,1,5,4,8,6,3]=>[4,8,5,7,1,3,2,6]=>[5,1,4,2,8,6,7,3]=>[1,2,2,2,1]
[2,4,1,6,7,5,8,3]=>[2,4,6,1,5,8,3,7]=>[7,5,3,8,4,1,6,2]=>[1,1,2,1,2,1]
[8,1,4,5,6,3,7,2]=>[3,4,6,5,8,2,7,1]=>[6,5,3,4,1,7,2,8]=>[1,1,2,2,2]
[8,1,4,5,6,2,7,3]=>[3,4,8,6,2,5,7,1]=>[6,5,1,3,7,4,2,8]=>[1,1,3,1,2]
[8,1,4,7,6,2,5,3]=>[8,3,6,7,5,2,4,1]=>[1,6,3,2,4,7,5,8]=>[2,1,3,2]
[2,5,1,7,8,6,4,3]=>[2,4,8,7,1,6,3,5]=>[7,5,1,2,8,3,6,4]=>[1,1,3,2,1]
[3,5,6,2,8,7,4,1]=>[2,3,8,1,7,4,6,5]=>[7,6,1,8,2,5,3,4]=>[1,1,2,2,2]
[2,4,5,1,7,6,3,8]=>[2,3,7,1,6,4,5,8]=>[7,6,2,8,3,5,4,1]=>[1,1,2,2,1,1]
[8,4,5,3,7,6,2,1]=>[2,3,8,4,7,6,5,1]=>[7,6,1,5,2,3,4,8]=>[1,1,2,4]
[3,4,5,6,2,8,1,7]=>[1,2,3,5,4,7,8,6]=>[8,7,6,4,5,2,1,3]=>[1,1,1,2,1,2]
[7,3,4,1,6,8,2,5]=>[2,3,7,5,8,4,1,6]=>[7,6,2,4,1,5,8,3]=>[1,1,2,3,1]
[2,6,3,1,4,7,5,8]=>[3,7,1,4,5,2,6,8]=>[6,2,8,5,4,7,3,1]=>[1,2,1,2,1,1]
[7,2,1,6,3,4,8,5]=>[8,2,5,6,3,4,1,7]=>[1,7,4,3,6,5,8,2]=>[2,1,2,2,1]
[3,7,4,2,5,8,6,1]=>[3,8,1,4,5,2,7,6]=>[6,1,8,5,4,7,2,3]=>[1,2,1,2,2]
[2,3,5,1,4,8,7,6]=>[3,8,1,2,7,4,5,6]=>[6,1,8,7,2,5,4,3]=>[1,2,1,2,1,1]
[2,7,1,3,6,8,5,4]=>[5,8,7,1,3,4,2,6]=>[4,1,2,8,6,5,7,3]=>[1,3,1,2,1]
[2,7,1,3,8,4,6,5]=>[8,6,7,1,3,4,2,5]=>[1,3,2,8,6,5,7,4]=>[2,2,1,2,1]
[3,8,7,1,6,2,5,4]=>[8,6,7,1,4,5,3,2]=>[1,3,2,8,5,4,6,7]=>[2,2,1,3]
[3,8,7,1,4,5,2,6]=>[5,7,1,4,6,8,3,2]=>[4,2,8,5,3,1,6,7]=>[1,2,1,1,3]
[3,7,4,2,1,8,6,5]=>[3,8,1,4,7,5,2,6]=>[6,1,8,5,2,4,7,3]=>[1,2,1,3,1]
[4,8,5,7,2,6,3,1]=>[3,8,1,5,7,6,4,2]=>[6,1,8,4,2,3,5,7]=>[1,2,1,4]
[8,4,5,7,3,2,6,1]=>[2,3,6,5,8,7,4,1]=>[7,6,3,4,1,2,5,8]=>[1,1,2,4]
[8,3,7,2,4,1,5,6]=>[2,4,6,5,7,8,3,1]=>[7,5,3,4,2,1,6,8]=>[1,1,2,1,3]
[8,6,7,2,1,4,3,5]=>[4,7,5,6,2,8,3,1]=>[5,2,4,3,7,1,6,8]=>[1,2,2,3]
[7,3,4,6,2,1,5,8]=>[2,3,6,5,7,4,1,8]=>[7,6,3,4,2,5,8,1]=>[1,1,2,3,1]
[3,4,7,6,1,2,8,5]=>[8,1,2,5,6,4,3,7]=>[1,8,7,4,3,5,6,2]=>[2,1,1,3,1]
[4,5,8,7,6,1,3,2]=>[8,1,2,6,7,5,4,3]=>[1,8,7,3,2,4,5,6]=>[2,1,1,4]
[8,6,3,7,5,1,4,2]=>[8,3,6,2,7,5,4,1]=>[1,6,3,7,2,4,5,8]=>[2,2,4]
[8,7,3,5,6,1,4,2]=>[8,3,6,4,7,5,2,1]=>[1,6,3,5,2,4,7,8]=>[2,2,4]
[7,6,3,8,1,4,5,2]=>[3,6,8,5,2,1,7,4]=>[6,3,1,4,7,8,2,5]=>[1,1,4,2]
[8,5,2,7,6,1,3,4]=>[6,7,2,8,3,5,4,1]=>[3,2,7,1,6,4,5,8]=>[1,2,2,3]
[8,7,3,1,4,5,2,6]=>[5,3,7,4,6,8,2,1]=>[4,6,2,5,3,1,7,8]=>[2,2,1,3]
[6,4,7,2,1,5,8,3]=>[4,2,6,1,8,5,3,7]=>[5,7,3,8,1,4,6,2]=>[2,2,3,1]
[8,5,3,1,6,4,7,2]=>[3,6,5,2,8,4,7,1]=>[6,3,4,7,1,5,2,8]=>[1,3,2,2]
[8,7,3,1,4,5,6,2]=>[5,3,6,8,4,7,2,1]=>[4,6,3,1,5,2,7,8]=>[2,1,2,3]
[8,7,4,1,5,6,2,3]=>[7,5,3,8,4,6,2,1]=>[2,4,6,1,5,3,7,8]=>[3,2,3]
[8,6,3,1,7,4,5,2]=>[3,6,8,7,4,2,5,1]=>[6,3,1,2,5,7,4,8]=>[1,1,4,2]
[8,5,3,1,6,7,4,2]=>[3,5,2,8,7,4,6,1]=>[6,4,7,1,2,5,3,8]=>[1,2,3,2]
[8,5,3,7,1,6,4,2]=>[8,3,2,7,5,6,4,1]=>[1,6,7,2,4,3,5,8]=>[3,2,3]
[7,4,8,2,6,1,5,3]=>[2,8,4,6,1,7,5,3]=>[7,1,5,3,8,2,4,6]=>[1,2,2,3]
[8,5,3,1,6,4,2,7]=>[3,7,6,4,2,5,8,1]=>[6,2,3,5,7,4,1,8]=>[1,4,1,2]
[8,7,5,1,2,6,3,4]=>[7,8,4,5,3,6,2,1]=>[2,1,5,4,6,3,7,8]=>[1,2,2,3]
[8,6,4,1,2,7,5,3]=>[8,7,4,3,5,2,6,1]=>[1,2,5,6,4,7,3,8]=>[4,2,2]
[8,7,4,1,2,5,3,6]=>[7,4,5,3,6,8,2,1]=>[2,5,4,6,3,1,7,8]=>[2,2,1,3]
[8,7,5,1,2,3,6,4]=>[8,4,5,6,3,7,2,1]=>[1,5,4,3,6,2,7,8]=>[2,1,2,3]
[6,5,3,7,4,2,1,8]=>[7,3,2,1,6,5,4,8]=>[2,6,7,8,3,4,5,1]=>[4,3,1]
[1,6,3,8,4,2,5,7]=>[6,3,5,2,7,8,1,4]=>[3,6,4,7,2,1,8,5]=>[2,2,1,2,1]
[4,7,2,5,3,6,1,8]=>[1,5,3,4,7,6,2,8]=>[8,4,6,5,2,3,7,1]=>[1,2,1,3,1]
[1,8,3,4,5,2,6,7]=>[3,4,6,5,7,8,1,2]=>[6,5,3,4,2,1,8,7]=>[1,1,2,1,2,1]
[1,8,6,4,2,5,3,7]=>[7,5,4,6,3,8,1,2]=>[2,4,5,3,6,1,8,7]=>[3,2,2,1]
[8,2,6,4,1,5,7,3]=>[6,4,8,2,5,3,7,1]=>[3,5,1,7,4,6,2,8]=>[2,2,2,2]
[7,8,3,4,6,1,5,2]=>[3,4,8,6,1,7,5,2]=>[6,5,1,3,8,2,4,7]=>[1,1,3,3]
[4,8,7,5,3,1,6,2]=>[8,6,1,5,4,7,3,2]=>[1,3,8,4,5,2,6,7]=>[3,2,3]
[4,1,8,5,3,2,6,7]=>[1,6,5,4,7,8,2,3]=>[8,3,4,5,2,1,7,6]=>[1,3,1,2,1]
[8,1,6,4,2,7,3,5]=>[7,4,8,5,2,3,6,1]=>[2,5,1,4,7,6,3,8]=>[2,3,1,2]
[3,1,7,4,2,5,8,6]=>[1,4,8,5,6,2,3,7]=>[8,5,1,4,3,7,6,2]=>[1,1,2,2,1,1]
[1,2,7,4,3,5,6,8]=>[5,4,6,7,1,2,3,8]=>[4,5,3,2,8,7,6,1]=>[2,1,2,1,1,1]
[6,1,8,5,2,4,3,7]=>[7,5,6,4,1,8,2,3]=>[2,4,3,5,8,1,7,6]=>[2,3,2,1]
[4,5,2,1,6,8,7,3]=>[1,8,3,2,5,7,4,6]=>[8,1,6,7,4,2,5,3]=>[1,3,1,2,1]
[7,2,8,6,5,1,4,3]=>[8,6,7,5,2,1,4,3]=>[1,3,2,4,7,8,5,6]=>[2,4,2]
[7,4,8,6,1,5,3,2]=>[8,2,7,5,1,6,4,3]=>[1,7,2,4,8,3,5,6]=>[2,3,3]
[7,6,3,1,2,5,4,8]=>[7,4,3,5,6,2,1,8]=>[2,5,6,4,3,7,8,1]=>[3,1,3,1]
[8,5,3,1,2,4,7,6]=>[8,4,3,5,2,6,7,1]=>[1,5,6,4,7,3,2,8]=>[3,2,1,2]
[8,2,1,6,5,3,4,7]=>[6,7,2,5,3,4,8,1]=>[3,2,7,4,6,5,1,8]=>[1,2,2,1,2]
[3,8,1,5,6,2,4,7]=>[6,1,4,7,3,5,8,2]=>[3,8,5,2,6,4,1,7]=>[2,1,2,1,2]
[6,8,4,1,5,2,3,7]=>[6,7,4,3,1,5,8,2]=>[3,2,5,6,8,4,1,7]=>[1,4,1,2]
[3,2,8,1,6,4,5,7]=>[1,6,7,2,4,5,8,3]=>[8,3,2,7,5,4,1,6]=>[1,1,2,1,1,2]
[5,2,1,3,7,6,4,8]=>[7,2,6,3,1,4,5,8]=>[2,7,3,6,8,5,4,1]=>[2,3,1,1,1]
[5,4,1,2,8,3,7,6]=>[8,6,2,1,7,3,4,5]=>[1,3,7,8,2,6,5,4]=>[4,2,1,1]
[7,1,2,5,3,4,6,8]=>[5,6,2,3,4,7,1,8]=>[4,3,7,6,5,2,8,1]=>[1,2,1,1,2,1]
[1,8,6,3,2,7,4,5]=>[4,7,8,5,3,6,1,2]=>[5,2,1,4,6,3,8,7]=>[1,1,3,2,1]
[1,4,6,2,8,5,3,7]=>[7,2,6,3,8,1,4,5]=>[2,7,3,6,1,8,5,4]=>[2,2,2,1,1]
[1,5,6,2,8,4,3,7]=>[2,7,6,3,8,1,4,5]=>[7,2,3,6,1,8,5,4]=>[1,3,2,1,1]
[2,4,6,3,1,7,5,8]=>[2,4,7,1,5,3,6,8]=>[7,5,2,8,4,6,3,1]=>[1,1,2,2,1,1]
[3,4,8,6,5,7,2,1]=>[5,4,8,1,2,7,6,3]=>[4,5,1,8,7,2,3,6]=>[2,2,1,3]
[1,2,4,7,3,6,5,8]=>[7,3,5,6,1,2,4,8]=>[2,6,4,3,8,7,5,1]=>[2,1,2,1,1,1]
[1,2,5,7,4,3,6,8]=>[3,6,5,7,1,2,4,8]=>[6,3,4,2,8,7,5,1]=>[1,2,2,1,1,1]
[1,2,5,7,4,6,8,3]=>[3,5,6,4,8,1,2,7]=>[6,4,3,5,1,8,7,2]=>[1,1,2,2,1,1]
[1,2,4,7,6,8,3,5]=>[7,5,3,4,8,1,2,6]=>[2,4,6,5,1,8,7,3]=>[3,1,2,1,1]
[3,5,8,6,1,7,2,4]=>[2,7,8,1,5,4,6,3]=>[7,2,1,8,4,5,3,6]=>[1,1,2,2,2]
[2,3,6,8,1,7,4,5]=>[7,3,8,1,2,5,6,4]=>[2,6,1,8,7,4,3,5]=>[2,2,1,1,2]
[2,3,7,1,8,6,4,5]=>[7,8,6,1,2,4,3,5]=>[2,1,3,8,7,5,6,4]=>[1,3,1,2,1]
[2,6,1,7,8,5,3,4]=>[7,4,2,8,1,6,3,5]=>[2,5,7,1,8,3,6,4]=>[3,2,2,1]
[2,4,8,5,6,7,1,3]=>[4,7,2,5,8,1,6,3]=>[5,2,7,4,1,8,3,6]=>[1,2,1,2,2]
[1,4,8,5,6,7,3,2]=>[4,5,8,2,7,6,1,3]=>[5,4,1,7,2,3,8,6]=>[1,1,2,3,1]
[4,8,3,1,6,5,7,2]=>[1,3,6,5,8,4,7,2]=>[8,6,3,4,1,5,2,7]=>[1,1,2,2,2]
[1,6,8,5,4,2,7,3]=>[2,8,6,5,4,7,1,3]=>[7,1,3,4,5,2,8,6]=>[1,4,2,1]
[6,5,8,4,2,1,7,3]=>[5,2,1,8,6,4,7,3]=>[4,7,8,1,3,5,2,6]=>[3,3,2]
[1,7,8,6,5,4,2,3]=>[7,2,8,6,5,4,1,3]=>[2,7,1,3,4,5,8,6]=>[2,5,1]
[6,8,7,4,5,1,3,2]=>[1,8,6,4,7,5,3,2]=>[8,1,3,5,2,4,6,7]=>[1,3,4]
[6,1,3,5,4,2,8,7]=>[5,3,4,8,2,1,6,7]=>[4,6,5,1,7,8,3,2]=>[2,1,3,1,1]
[2,1,5,8,6,4,7,3]=>[6,3,5,8,1,7,2,4]=>[3,6,4,1,8,2,7,5]=>[2,1,2,2,1]
[4,2,8,5,6,3,7,1]=>[1,4,6,5,8,2,7,3]=>[8,5,3,4,1,7,2,6]=>[1,1,2,2,2]
[5,3,7,2,6,8,4,1]=>[5,1,8,2,4,3,7,6]=>[4,8,1,7,5,6,2,3]=>[2,2,2,2]
[5,7,2,3,4,6,8,1]=>[3,4,1,5,6,2,8,7]=>[6,5,8,4,3,7,1,2]=>[1,2,1,2,2]
[1,8,7,3,2,5,6,4]=>[4,6,8,5,7,3,1,2]=>[5,3,1,4,2,6,8,7]=>[1,1,2,3,1]
[5,7,1,2,3,8,6,4]=>[8,7,3,1,4,5,2,6]=>[1,2,6,8,5,4,7,3]=>[4,1,2,1]
[7,8,6,2,4,1,5,3]=>[8,4,6,5,1,7,3,2]=>[1,5,3,4,8,2,6,7]=>[2,3,3]
[7,2,8,4,6,1,5,3]=>[4,8,6,7,2,1,5,3]=>[5,1,3,2,7,8,4,6]=>[1,2,3,2]
[7,4,6,2,8,1,5,3]=>[2,8,4,6,3,1,7,5]=>[7,1,5,3,6,8,2,4]=>[1,2,3,2]
[7,1,5,8,2,3,6,4]=>[8,5,3,6,7,2,1,4]=>[1,4,6,3,2,7,8,5]=>[3,1,3,1]
[7,6,4,8,2,1,5,3]=>[5,3,8,6,2,1,7,4]=>[4,6,1,3,7,8,2,5]=>[2,4,2]
[6,1,8,4,2,3,5,7]=>[5,6,4,7,1,8,2,3]=>[4,3,5,2,8,1,7,6]=>[1,2,2,2,1]
[1,8,6,4,2,5,7,3]=>[6,4,8,5,3,7,1,2]=>[3,5,1,4,6,2,8,7]=>[2,3,2,1]
[5,6,2,1,8,4,7,3]=>[6,1,8,3,2,7,4,5]=>[3,8,1,6,7,2,5,4]=>[2,3,2,1]
[2,8,1,6,5,7,3,4]=>[7,5,4,8,1,3,6,2]=>[2,4,5,1,8,6,3,7]=>[3,2,1,2]
[5,1,6,4,3,8,7,2]=>[4,3,1,8,5,7,2,6]=>[5,6,8,1,4,2,7,3]=>[3,2,2,1]
[5,4,6,8,1,3,7,2]=>[2,1,6,3,8,5,7,4]=>[7,8,3,6,1,4,2,5]=>[2,2,2,2]
[3,7,1,6,4,5,8,2]=>[5,6,1,4,8,3,2,7]=>[4,3,8,5,1,6,7,2]=>[1,2,1,3,1]
[3,5,2,1,4,6,7,8]=>[1,4,3,5,2,6,7,8]=>[8,5,6,4,7,3,2,1]=>[1,2,2,1,1,1]
[1,3,8,7,5,4,6,2]=>[6,5,8,7,2,4,1,3]=>[3,4,1,2,7,5,8,6]=>[2,3,2,1]
[1,2,3,4,5,7,9,8,6]=>[9,6,8,1,2,3,4,5,7]=>[1,4,2,9,8,7,6,5,3]=>[2,2,1,1,1,1,1]
[1,2,3,4,6,8,9,7,5]=>[6,9,5,8,1,2,3,4,7]=>[4,1,5,2,9,8,7,6,3]=>[1,2,2,1,1,1,1]
[1,2,3,4,6,9,8,7,5]=>[9,8,5,7,1,2,3,4,6]=>[1,2,5,3,9,8,7,6,4]=>[3,2,1,1,1,1]
[1,2,3,5,7,9,8,6,4]=>[9,5,8,4,7,1,2,3,6]=>[1,5,2,6,3,9,8,7,4]=>[2,2,2,1,1,1]
[1,2,3,5,9,8,7,6,4]=>[9,8,7,4,6,1,2,3,5]=>[1,2,3,6,4,9,8,7,5]=>[4,2,1,1,1]
[1,2,4,6,9,8,7,5,3]=>[9,8,4,7,3,6,1,2,5]=>[1,2,6,3,7,4,9,8,5]=>[3,2,2,1,1]
[1,2,4,9,8,7,6,5,3]=>[9,8,7,6,3,5,1,2,4]=>[1,2,3,4,7,5,9,8,6]=>[5,2,1,1]
[1,3,5,7,9,8,6,4,2]=>[9,4,8,3,7,2,6,1,5]=>[1,6,2,7,3,8,4,9,5]=>[2,2,2,2,1]
[1,3,5,9,8,7,6,4,2]=>[9,8,7,3,6,2,5,1,4]=>[1,2,3,7,4,8,5,9,6]=>[4,2,2,1]
[1,2,3,4,5,6,8,10,9,7]=>[10,7,9,1,2,3,4,5,6,8]=>[1,4,2,10,9,8,7,6,5,3]=>[2,2,1,1,1,1,1,1]
[1,2,3,4,5,7,9,10,8,6]=>[7,10,6,9,1,2,3,4,5,8]=>[4,1,5,2,10,9,8,7,6,3]=>[1,2,2,1,1,1,1,1]
[1,2,3,4,5,7,10,9,8,6]=>[10,9,6,8,1,2,3,4,5,7]=>[1,2,5,3,10,9,8,7,6,4]=>[3,2,1,1,1,1,1]
[1,2,3,4,6,8,10,9,7,5]=>[10,6,9,5,8,1,2,3,4,7]=>[1,5,2,6,3,10,9,8,7,4]=>[2,2,2,1,1,1,1]
[1,2,3,4,6,10,9,8,7,5]=>[10,9,8,5,7,1,2,3,4,6]=>[1,2,3,6,4,10,9,8,7,5]=>[4,2,1,1,1,1]
[1,2,3,5,7,9,10,8,6,4]=>[6,10,5,9,4,8,1,2,3,7]=>[5,1,6,2,7,3,10,9,8,4]=>[1,2,2,2,1,1,1]
[1,2,3,5,7,10,9,8,6,4]=>[10,9,5,8,4,7,1,2,3,6]=>[1,2,6,3,7,4,10,9,8,5]=>[3,2,2,1,1,1]
[1,2,3,5,10,9,8,7,6,4]=>[10,9,8,7,4,6,1,2,3,5]=>[1,2,3,4,7,5,10,9,8,6]=>[5,2,1,1,1]
[1,2,4,6,10,9,8,7,5,3]=>[10,9,8,4,7,3,6,1,2,5]=>[1,2,3,7,4,8,5,10,9,6]=>[4,2,2,1,1]
[1,2,4,10,9,8,7,6,5,3]=>[10,9,8,7,6,3,5,1,2,4]=>[1,2,3,4,5,8,6,10,9,7]=>[6,2,1,1]
[1,3,5,7,9,10,8,6,4,2]=>[5,10,4,9,3,8,2,7,1,6]=>[6,1,7,2,8,3,9,4,10,5]=>[1,2,2,2,2,1]
[1,3,5,7,10,9,8,6,4,2]=>[10,9,4,8,3,7,2,6,1,5]=>[1,2,7,3,8,4,9,5,10,6]=>[3,2,2,2,1]
[1,3,5,10,9,8,7,6,4,2]=>[10,9,8,7,3,6,2,5,1,4]=>[1,2,3,4,8,5,9,6,10,7]=>[5,2,2,1]
[1,3,10,9,8,7,6,5,4,2]=>[10,9,8,7,6,5,2,4,1,3]=>[1,2,3,4,5,6,9,7,10,8]=>[7,2,1]
[7,4,1,8,2,5,6,3]=>[6,2,8,5,7,3,1,4]=>[3,7,1,4,2,6,8,5]=>[2,2,3,1]
[3,1,7,2,5,6,8,4]=>[1,5,6,8,4,2,3,7]=>[8,4,3,1,5,7,6,2]=>[1,1,1,3,1,1]
[4,1,5,7,3,2,8,6]=>[3,1,5,8,6,2,4,7]=>[6,8,4,1,3,7,5,2]=>[2,1,3,1,1]
[6,4,1,7,2,8,5,3]=>[2,8,7,5,3,1,4,6]=>[7,1,2,4,6,8,5,3]=>[1,5,1,1]
[7,3,1,6,2,8,5,4]=>[8,2,7,5,3,4,1,6]=>[1,7,2,4,6,5,8,3]=>[2,3,2,1]
[4,8,2,5,3,1,6,7]=>[1,6,3,5,4,7,8,2]=>[8,3,6,4,5,2,1,7]=>[1,2,2,1,2]
[5,1,3,4,8,2,6,7]=>[3,4,6,1,7,8,2,5]=>[6,5,3,8,2,1,7,4]=>[1,1,2,1,2,1]
[7,8,5,1,3,4,6,2]=>[5,6,8,4,3,1,7,2]=>[4,3,1,5,6,8,2,7]=>[1,1,4,2]
[7,1,3,4,5,6,8,2]=>[3,4,5,6,8,2,1,7]=>[6,5,4,3,1,7,8,2]=>[1,1,1,1,3,1]
[8,5,2,7,6,3,1,4]=>[7,6,2,8,3,5,4,1]=>[2,3,7,1,6,4,5,8]=>[3,2,3]
[1,8,3,5,6,2,7,4]=>[4,8,3,6,5,7,1,2]=>[5,1,6,3,4,2,8,7]=>[1,2,2,2,1]
[8,3,2,5,6,1,7,4]=>[2,4,8,3,6,5,7,1]=>[7,5,1,6,3,4,2,8]=>[1,1,2,2,2]
[4,2,5,1,6,8,7,3]=>[3,1,8,2,5,7,4,6]=>[6,8,1,7,4,2,5,3]=>[2,2,1,2,1]
[5,4,2,7,8,6,1,3]=>[2,1,7,4,8,3,6,5]=>[7,8,2,5,1,6,3,4]=>[2,2,2,2]
[6,8,7,2,1,3,4,5]=>[5,4,6,1,7,8,3,2]=>[4,5,3,8,2,1,6,7]=>[2,2,1,3]
[3,7,6,8,5,2,4,1]=>[6,3,2,8,1,7,5,4]=>[3,6,7,1,8,2,4,5]=>[3,2,3]
[1,7,8,5,2,6,3,4]=>[7,8,5,4,2,6,1,3]=>[2,1,4,5,7,3,8,6]=>[1,4,2,1]
[5,8,7,2,6,3,4,1]=>[1,6,8,4,7,5,3,2]=>[8,3,1,5,2,4,6,7]=>[1,1,2,4]
[7,6,2,4,8,1,5,3]=>[4,8,3,6,2,1,7,5]=>[5,1,6,3,7,8,2,4]=>[1,2,3,2]
[6,7,5,1,8,2,3,4]=>[6,7,1,8,4,3,2,5]=>[3,2,8,1,5,6,7,4]=>[1,2,4,1]
[7,6,1,2,4,3,8,5]=>[5,8,3,4,6,2,1,7]=>[4,1,6,5,3,7,8,2]=>[1,2,1,3,1]
[6,7,2,1,5,3,8,4]=>[8,3,6,4,1,5,2,7]=>[1,6,3,5,8,4,7,2]=>[2,3,2,1]
[4,3,2,8,7,1,6,5]=>[1,8,2,6,7,3,5,4]=>[8,1,7,3,2,6,4,5]=>[1,2,1,2,2]
[4,8,3,2,7,1,6,5]=>[1,3,8,4,6,7,5,2]=>[8,6,1,5,3,2,4,7]=>[1,1,2,1,3]
[4,8,3,1,7,6,5,2]=>[8,1,3,7,6,4,5,2]=>[1,8,6,2,3,5,4,7]=>[2,1,3,2]
[5,8,7,3,1,6,4,2]=>[1,4,8,7,5,6,3,2]=>[8,5,1,2,4,3,6,7]=>[1,1,3,3]
[3,8,7,2,6,5,1,4]=>[7,8,4,6,1,5,3,2]=>[2,1,5,3,8,4,6,7]=>[1,2,2,3]
[7,4,1,8,6,5,3,2]=>[8,2,7,6,5,3,1,4]=>[1,7,2,3,4,6,8,5]=>[2,5,1]
[5,4,2,8,1,7,6,3]=>[2,1,8,7,3,5,6,4]=>[7,8,1,2,6,4,3,5]=>[2,3,1,2]
[5,8,4,2,1,7,6,3]=>[1,8,4,3,7,5,6,2]=>[8,1,5,6,2,4,3,7]=>[1,3,2,2]
[5,8,4,7,1,6,3,2]=>[1,3,8,7,5,6,4,2]=>[8,6,1,2,4,3,5,7]=>[1,1,3,3]
[5,4,8,3,1,7,6,2]=>[2,1,4,8,7,5,6,3]=>[7,8,5,1,2,4,3,6]=>[2,1,3,2]
[6,7,4,1,2,5,8,3]=>[6,8,4,3,1,5,2,7]=>[3,1,5,6,8,4,7,2]=>[1,4,2,1]
[1,6,7,4,2,5,8,3]=>[6,4,2,8,5,1,3,7]=>[3,5,7,1,4,8,6,2]=>[3,3,1,1]
[3,6,7,5,8,1,2,4]=>[6,2,7,1,4,3,8,5]=>[3,7,2,8,5,6,1,4]=>[2,2,2,2]
[1,6,7,5,8,3,2,4]=>[2,7,6,4,3,8,1,5]=>[7,2,3,5,6,1,8,4]=>[1,4,2,1]
[3,8,6,5,7,4,1,2]=>[7,4,3,8,1,6,5,2]=>[2,5,6,1,8,3,4,7]=>[3,2,3]
[8,1,6,5,7,4,3,2]=>[4,3,8,7,6,2,5,1]=>[5,6,1,2,3,7,4,8]=>[2,4,2]
[5,2,1,6,8,4,7,3]=>[4,6,1,8,2,7,3,5]=>[5,3,8,1,7,2,6,4]=>[1,2,2,2,1]
[6,5,8,7,4,2,3,1]=>[2,1,6,8,7,5,4,3]=>[7,8,3,1,2,4,5,6]=>[2,1,5]
[6,8,5,7,4,2,1,3]=>[1,7,6,3,8,5,4,2]=>[8,2,3,6,1,4,5,7]=>[1,3,4]
[3,6,7,5,8,2,1,4]=>[2,7,6,1,4,3,8,5]=>[7,2,3,8,5,6,1,4]=>[1,3,2,2]
[4,7,5,3,8,1,2,6]=>[6,1,4,3,7,2,8,5]=>[3,8,5,6,2,7,1,4]=>[2,2,2,2]
[4,7,5,3,6,1,2,8]=>[6,1,4,3,7,5,2,8]=>[3,8,5,6,2,4,7,1]=>[2,2,3,1]
[4,7,5,3,1,6,2,8]=>[7,1,5,4,3,6,2,8]=>[2,8,4,5,6,3,7,1]=>[2,3,2,1]
[2,7,5,8,6,3,4,1]=>[3,6,2,8,7,1,5,4]=>[6,3,7,1,2,8,4,5]=>[1,2,3,2]
[2,7,5,6,8,3,4,1]=>[3,6,4,2,8,1,7,5]=>[6,3,5,7,1,8,2,4]=>[1,3,2,2]
[2,7,5,6,8,3,1,4]=>[3,7,6,4,1,2,8,5]=>[6,2,3,5,8,7,1,4]=>[1,4,1,2]
[4,7,5,3,6,8,1,2]=>[4,1,3,7,5,2,8,6]=>[5,8,6,2,4,7,1,3]=>[2,1,3,2]
[2,7,5,3,6,8,1,4]=>[7,4,3,5,1,2,8,6]=>[2,5,6,4,8,7,1,3]=>[3,2,1,2]
[8,7,5,3,1,4,6,2]=>[6,4,8,5,3,7,2,1]=>[3,5,1,4,6,2,7,8]=>[2,3,3]
[2,7,5,3,1,4,8,6]=>[4,8,5,1,3,6,2,7]=>[5,1,4,8,6,3,7,2]=>[1,3,1,2,1]
[2,7,5,3,4,8,6,1]=>[8,4,3,5,1,2,7,6]=>[1,5,6,4,8,7,2,3]=>[3,2,1,2]
[5,7,6,2,8,3,1,4]=>[1,7,4,6,3,2,8,5]=>[8,2,5,3,6,7,1,4]=>[1,2,3,2]
[5,1,6,3,2,4,8,7]=>[4,8,5,2,1,3,6,7]=>[5,1,4,7,8,6,3,2]=>[1,4,1,1,1]
[5,7,6,1,8,3,2,4]=>[1,7,6,8,4,3,2,5]=>[8,2,3,1,5,6,7,4]=>[1,2,4,1]
[3,8,7,2,1,5,4,6]=>[4,7,1,5,6,8,3,2]=>[5,2,8,4,3,1,6,7]=>[1,2,1,1,3]
[6,1,7,2,8,4,3,5]=>[7,6,8,4,2,1,3,5]=>[2,3,1,5,7,8,6,4]=>[2,4,1,1]
[4,8,5,6,7,3,1,2]=>[3,7,1,4,8,6,5,2]=>[6,2,8,5,1,3,4,7]=>[1,2,1,4]
[3,7,6,2,8,5,1,4]=>[7,8,4,1,3,2,6,5]=>[2,1,5,8,6,7,3,4]=>[1,3,2,2]
[6,1,7,3,8,5,2,4]=>[7,8,4,3,1,6,2,5]=>[2,1,5,6,8,3,7,4]=>[1,4,2,1]
[7,1,8,3,2,5,4,6]=>[4,7,5,6,8,2,1,3]=>[5,2,4,3,1,7,8,6]=>[1,2,1,3,1]
[2,7,8,3,1,5,4,6]=>[4,7,5,6,1,2,8,3]=>[5,2,4,3,8,7,1,6]=>[1,2,2,1,2]
[4,8,5,6,7,2,1,3]=>[3,7,1,6,4,8,5,2]=>[6,2,8,3,5,1,4,7]=>[1,2,2,3]
[5,8,6,2,7,4,1,3]=>[1,7,8,4,3,6,5,2]=>[8,2,1,5,6,3,4,7]=>[1,1,3,3]
[2,4,6,7,8,5,1,3]=>[3,7,2,4,8,1,6,5]=>[6,2,7,5,1,8,3,4]=>[1,2,1,2,2]
[2,4,6,7,8,3,1,5]=>[3,7,2,6,1,4,8,5]=>[6,2,7,3,8,5,1,4]=>[1,2,2,1,2]
[4,7,6,2,8,5,1,3]=>[7,8,1,4,3,2,6,5]=>[2,1,8,5,6,7,3,4]=>[1,2,3,2]
[5,8,7,3,2,4,1,6]=>[1,5,4,7,6,8,3,2]=>[8,4,5,2,3,1,6,7]=>[1,2,2,3]
[4,6,5,8,7,3,1,2]=>[3,1,2,7,8,6,5,4]=>[6,8,7,2,1,3,4,5]=>[2,1,1,4]
[8,3,1,7,2,6,4,5]=>[2,7,8,5,6,3,4,1]=>[7,2,1,4,3,6,5,8]=>[1,1,2,2,2]
[4,5,1,2,8,7,3,6]=>[1,7,2,8,6,3,4,5]=>[8,2,7,1,3,6,5,4]=>[1,2,3,1,1]
[5,6,1,2,8,3,7,4]=>[8,6,1,7,3,2,4,5]=>[1,3,8,2,6,7,5,4]=>[3,3,1,1]
[7,5,6,1,3,8,4,2]=>[8,5,2,7,4,3,1,6]=>[1,4,7,2,5,6,8,3]=>[3,4,1]
[5,7,6,1,3,8,4,2]=>[1,8,5,7,4,3,2,6]=>[8,1,4,2,5,6,7,3]=>[1,2,4,1]
[6,7,1,4,2,8,5,3]=>[4,8,7,3,1,5,2,6]=>[5,1,2,6,8,4,7,3]=>[1,4,2,1]
[2,1,6,4,8,3,7,5]=>[8,4,1,3,6,7,2,5]=>[1,5,8,6,3,2,7,4]=>[3,1,1,2,1]
[1,4,5,7,8,3,6,2]=>[6,2,3,4,8,7,1,5]=>[3,7,6,5,1,2,8,4]=>[2,1,1,3,1]
[1,5,7,8,3,6,2,4]=>[2,5,7,3,8,6,1,4]=>[7,4,2,6,1,3,8,5]=>[1,1,2,3,1]
[1,5,7,8,2,4,3,6]=>[2,7,5,6,3,8,1,4]=>[7,2,4,3,6,1,8,5]=>[1,2,2,2,1]
[6,8,4,7,3,2,1,5]=>[3,1,7,6,5,8,4,2]=>[6,8,2,3,4,1,5,7]=>[2,3,3]
[6,8,5,4,2,7,1,3]=>[5,1,7,4,3,8,6,2]=>[4,8,2,5,6,1,3,7]=>[2,3,3]
[1,8,4,6,3,2,7,5]=>[3,5,8,6,4,7,1,2]=>[6,4,1,3,5,2,8,7]=>[1,1,3,2,1]
[6,4,8,5,3,2,1,7]=>[7,2,1,6,5,4,8,3]=>[2,7,8,3,4,5,1,6]=>[3,3,2]
[3,5,6,1,4,2,7,8]=>[6,1,4,2,5,3,7,8]=>[3,8,5,7,4,6,2,1]=>[2,2,2,1,1]
[1,6,3,8,4,2,7,5]=>[5,8,3,2,6,7,1,4]=>[4,1,6,7,3,2,8,5]=>[1,3,1,2,1]
[7,1,3,2,4,6,8,5]=>[3,6,8,2,4,5,1,7]=>[6,3,1,7,5,4,8,2]=>[1,1,2,1,2,1]
[4,1,8,2,6,7,5,3]=>[1,5,8,7,4,6,2,3]=>[8,4,1,2,5,3,7,6]=>[1,1,3,2,1]
[3,6,7,8,2,1,4,5]=>[6,5,1,2,7,3,8,4]=>[3,4,8,7,2,6,1,5]=>[3,1,2,2]
[2,5,7,1,6,3,4,8]=>[6,2,7,1,4,5,3,8]=>[3,7,2,8,5,4,6,1]=>[2,2,1,2,1]
[4,2,8,3,6,5,1,7]=>[1,7,4,6,2,5,8,3]=>[8,2,5,3,7,4,1,6]=>[1,2,2,1,2]
[6,3,8,7,2,4,5,1]=>[5,6,1,8,2,7,4,3]=>[4,3,8,1,7,2,5,6]=>[1,2,2,3]
[7,6,1,8,2,4,5,3]=>[6,8,5,7,3,2,1,4]=>[3,1,4,2,6,7,8,5]=>[1,2,4,1]
[2,5,6,3,4,8,1,7]=>[4,2,5,1,3,7,8,6]=>[5,7,4,8,6,2,1,3]=>[2,2,1,1,2]
[5,2,4,7,8,6,1,3]=>[7,3,1,4,8,2,6,5]=>[2,6,8,5,1,7,3,4]=>[3,1,2,2]
[2,4,5,7,1,8,6,3]=>[8,2,3,7,1,5,4,6]=>[1,7,6,2,8,4,5,3]=>[2,1,2,2,1]
[6,1,4,2,5,7,8,3]=>[5,3,6,8,2,1,4,7]=>[4,6,3,1,7,8,5,2]=>[2,1,3,1,1]
[1,6,7,2,4,3,5,8]=>[6,4,5,2,7,1,3,8]=>[3,5,4,7,2,8,6,1]=>[2,2,2,1,1]
[1,8,3,4,5,2,7,6]=>[3,4,5,8,6,7,1,2]=>[6,5,4,1,3,2,8,7]=>[1,1,1,2,2,1]
[1,8,3,6,4,7,2,5]=>[5,7,3,4,8,6,1,2]=>[4,2,6,5,1,3,8,7]=>[1,2,1,3,1]
[1,4,7,2,5,6,3,8]=>[2,5,7,4,6,1,3,8]=>[7,4,2,5,3,8,6,1]=>[1,1,2,2,1,1]
[7,3,5,8,2,6,1,4]=>[5,2,3,7,1,8,6,4]=>[4,7,6,2,8,1,3,5]=>[2,1,2,3]
[3,4,8,2,5,1,7,6]=>[1,2,4,5,8,6,7,3]=>[8,7,5,4,1,3,2,6]=>[1,1,1,1,2,2]
[1,7,2,5,8,4,3,6]=>[4,7,6,8,3,1,2,5]=>[5,2,3,1,6,8,7,4]=>[1,2,3,1,1]
[1,4,6,7,8,3,5,2]=>[3,6,2,4,8,7,1,5]=>[6,3,7,5,1,2,8,4]=>[1,2,1,3,1]
[3,7,5,1,6,8,4,2]=>[5,3,8,1,7,4,2,6]=>[4,6,1,8,2,5,7,3]=>[2,2,3,1]
[5,8,7,4,6,2,3,1]=>[6,1,4,8,7,5,3,2]=>[3,8,5,1,2,4,6,7]=>[2,1,5]
[2,7,8,4,6,5,1,3]=>[4,7,2,8,6,1,5,3]=>[5,2,7,1,3,8,4,6]=>[1,2,3,2]
[3,7,8,5,4,6,2,1]=>[5,4,2,8,1,7,6,3]=>[4,5,7,1,8,2,3,6]=>[3,2,3]
[4,8,7,5,2,6,3,1]=>[8,5,1,4,7,6,3,2]=>[1,4,8,5,2,3,6,7]=>[3,1,4]
[2,8,7,4,6,1,5,3]=>[4,8,6,7,5,1,3,2]=>[5,1,3,2,4,8,6,7]=>[1,2,3,2]
[4,8,7,2,5,6,3,1]=>[5,8,1,4,7,6,3,2]=>[4,1,8,5,2,3,6,7]=>[1,2,1,4]
[4,7,8,5,3,6,2,1]=>[5,4,1,2,8,7,6,3]=>[4,5,8,7,1,2,3,6]=>[3,1,4]
[6,4,8,1,5,7,3,2]=>[2,5,1,8,7,4,6,3]=>[7,4,8,1,2,5,3,6]=>[1,2,3,2]
[1,6,8,3,5,2,7,4]=>[8,4,2,6,5,7,1,3]=>[1,5,7,3,4,2,8,6]=>[3,2,2,1]
[4,5,8,6,3,7,2,1]=>[5,1,2,4,8,7,6,3]=>[4,8,7,5,1,2,3,6]=>[2,1,1,4]
[2,6,7,8,4,5,1,3]=>[2,7,5,3,8,1,6,4]=>[7,2,4,6,1,8,3,5]=>[1,3,2,2]
[6,1,2,8,4,7,5,3]=>[8,5,7,6,2,1,3,4]=>[1,4,2,3,7,8,6,5]=>[2,4,1,1]
[4,7,1,8,5,6,3,2]=>[5,8,1,7,6,3,2,4]=>[4,1,8,2,3,6,7,5]=>[1,2,4,1]
[5,7,1,8,2,6,4,3]=>[1,8,7,5,6,3,2,4]=>[8,1,2,4,3,6,7,5]=>[1,3,3,1]
[7,2,1,8,6,4,5,3]=>[6,8,7,2,5,3,1,4]=>[3,1,2,7,4,6,8,5]=>[1,3,3,1]
[5,3,8,4,7,6,2,1]=>[1,8,4,7,2,6,5,3]=>[8,1,5,2,7,3,4,6]=>[1,2,2,3]
[4,5,8,3,7,6,2,1]=>[8,1,2,4,7,6,5,3]=>[1,8,7,5,2,3,4,6]=>[2,1,1,4]
[1,7,2,8,6,4,5,3]=>[6,8,7,5,3,1,2,4]=>[3,1,2,4,6,8,7,5]=>[1,5,1,1]
[2,4,7,8,5,6,1,3]=>[7,5,2,3,8,1,6,4]=>[2,4,7,6,1,8,3,5]=>[3,1,2,2]
[3,5,8,6,4,7,2,1]=>[5,2,4,8,1,7,6,3]=>[4,7,5,1,8,2,3,6]=>[2,1,2,3]
[2,4,8,5,7,6,1,3]=>[4,7,8,2,6,1,5,3]=>[5,2,1,7,3,8,4,6]=>[1,1,2,2,2]
[2,6,3,8,5,1,7,4]=>[8,6,3,1,2,5,7,4]=>[1,3,6,8,7,4,2,5]=>[4,1,1,2]
[4,1,5,8,6,7,3,2]=>[1,5,8,3,7,6,2,4]=>[8,4,1,6,2,3,7,5]=>[1,1,2,3,1]
[4,5,8,2,6,3,1,7]=>[1,2,7,4,6,5,8,3]=>[8,7,2,5,3,4,1,6]=>[1,1,2,2,2]
[6,2,1,4,8,3,7,5]=>[8,2,4,6,1,7,3,5]=>[1,7,5,3,8,2,6,4]=>[2,1,2,2,1]
[2,8,5,4,1,3,7,6]=>[8,5,4,1,3,6,7,2]=>[1,4,5,8,6,3,2,7]=>[4,1,1,2]
[4,2,8,7,1,3,5,6]=>[5,1,6,7,8,2,4,3]=>[4,8,3,2,1,7,5,6]=>[2,1,1,2,2]
[5,4,6,3,1,7,2,8]=>[2,1,7,5,4,3,6,8]=>[7,8,2,4,5,6,3,1]=>[2,4,1,1]
[4,3,6,5,1,8,2,7]=>[1,7,2,4,3,8,5,6]=>[8,2,7,5,6,1,4,3]=>[1,2,2,2,1]
[1,4,8,3,6,5,2,7]=>[7,2,4,6,5,8,1,3]=>[2,7,5,3,4,1,8,6]=>[2,1,2,2,1]
[1,3,8,6,4,7,2,5]=>[5,7,4,8,2,6,1,3]=>[4,2,5,1,7,3,8,6]=>[1,2,2,2,1]
[1,2,8,6,4,3,7,5]=>[5,8,6,4,7,1,2,3]=>[4,1,3,5,2,8,7,6]=>[1,3,2,1,1]
[6,5,1,8,7,3,2,4]=>[7,6,2,1,8,5,3,4]=>[2,3,7,8,1,4,6,5]=>[4,3,1]
[4,1,7,6,8,3,2,5]=>[7,1,6,4,3,8,2,5]=>[2,8,3,5,6,1,7,4]=>[2,3,2,1]
[8,1,4,5,7,3,2,6]=>[3,4,7,6,8,2,5,1]=>[6,5,2,3,1,7,4,8]=>[1,1,2,2,2]
[1,8,4,7,6,2,3,5]=>[3,6,7,8,5,4,1,2]=>[6,3,2,1,4,5,8,7]=>[1,1,1,4,1]
[1,6,3,7,4,5,2,8]=>[5,7,3,2,6,1,4,8]=>[4,2,6,7,3,8,5,1]=>[1,3,2,1,1]
[2,6,3,7,4,8,5,1]=>[8,5,3,1,2,4,7,6]=>[1,4,6,8,7,5,2,3]=>[4,1,1,2]
[4,6,1,7,8,2,5,3]=>[8,1,6,4,2,7,3,5]=>[1,8,3,5,7,2,6,4]=>[2,3,2,1]
[7,2,3,8,4,5,6,1]=>[5,6,8,2,3,1,7,4]=>[4,3,1,7,6,8,2,5]=>[1,1,2,2,2]
[5,2,6,7,8,3,4,1]=>[3,1,6,4,8,2,7,5]=>[6,8,3,5,1,7,2,4]=>[2,2,2,2]
[6,5,8,1,2,7,4,3]=>[8,7,4,2,1,5,6,3]=>[1,2,5,7,8,4,3,6]=>[5,1,2]
[6,5,1,8,7,2,4,3]=>[8,6,2,1,7,5,3,4]=>[1,3,7,8,2,4,6,5]=>[4,3,1]
[5,8,4,3,7,2,1,6]=>[1,4,3,7,6,8,5,2]=>[8,5,6,2,3,1,4,7]=>[1,2,2,3]
[6,1,2,8,7,3,4,5]=>[6,7,8,5,2,1,3,4]=>[3,2,1,4,7,8,6,5]=>[1,1,4,1,1]
[7,3,2,8,4,6,1,5]=>[2,5,7,8,3,1,6,4]=>[7,4,2,1,6,8,3,5]=>[1,1,1,3,2]
[4,5,1,7,6,2,8,3]=>[1,2,8,6,5,3,4,7]=>[8,7,1,3,4,6,5,2]=>[1,1,4,1,1]
[1,5,2,7,6,3,4,8]=>[6,2,7,5,1,3,4,8]=>[3,7,2,4,8,6,5,1]=>[2,3,1,1,1]
[7,2,6,8,3,5,4,1]=>[8,5,3,7,2,1,6,4]=>[1,4,6,2,7,8,3,5]=>[3,3,2]
[4,8,1,7,6,2,5,3]=>[8,1,6,7,5,3,4,2]=>[1,8,3,2,4,6,5,7]=>[2,1,3,2]
[7,2,8,6,5,3,4,1]=>[6,8,7,5,2,1,4,3]=>[3,1,2,4,7,8,5,6]=>[1,5,2]
[4,1,8,7,6,5,2,3]=>[7,8,1,6,5,4,2,3]=>[2,1,8,3,4,5,7,6]=>[1,2,4,1]
[7,6,5,2,8,4,3,1]=>[8,7,4,3,2,1,6,5]=>[1,2,5,6,7,8,3,4]=>[6,2]
[6,5,1,8,7,4,3,2]=>[2,1,8,7,6,5,3,4]=>[7,8,1,2,3,4,6,5]=>[2,5,1]
[7,5,1,8,6,4,3,2]=>[2,8,7,6,5,3,1,4]=>[7,1,2,3,4,6,8,5]=>[1,6,1]
[8,5,1,7,6,4,3,2]=>[2,8,7,6,5,3,4,1]=>[7,1,2,3,4,6,5,8]=>[1,5,2]
[8,5,3,7,6,1,4,2]=>[8,3,2,6,7,5,4,1]=>[1,6,7,3,2,4,5,8]=>[3,1,4]
[3,8,7,6,1,5,4,2]=>[8,7,5,6,1,4,3,2]=>[1,2,4,3,8,5,6,7]=>[3,2,3]
[8,3,7,5,4,1,6,2]=>[8,6,2,5,4,7,3,1]=>[1,3,7,4,5,2,6,8]=>[3,2,3]
[4,5,3,1,8,7,2,6]=>[1,3,2,7,8,6,4,5]=>[8,6,7,2,1,3,5,4]=>[1,2,1,3,1]
[3,4,8,1,5,2,6,7]=>[1,2,6,4,5,7,8,3]=>[8,7,3,5,4,2,1,6]=>[1,1,2,1,1,2]
[8,6,5,7,1,3,2,4]=>[7,5,6,3,2,8,4,1]=>[2,4,3,6,7,1,5,8]=>[2,3,3]
[1,5,8,6,2,7,4,3]=>[8,2,7,5,4,6,1,3]=>[1,7,2,4,5,3,8,6]=>[2,3,2,1]
[3,1,8,5,7,2,6,4]=>[4,8,1,6,7,5,2,3]=>[5,1,8,3,2,4,7,6]=>[1,2,1,3,1]
[6,8,5,3,4,2,1,7]=>[4,1,7,6,5,3,8,2]=>[5,8,2,3,4,6,1,7]=>[2,4,2]
[8,5,2,6,4,3,1,7]=>[7,6,3,2,5,4,8,1]=>[2,3,6,7,4,5,1,8]=>[4,2,2]
[8,6,4,5,2,1,7,3]=>[5,3,8,6,4,2,7,1]=>[4,6,1,3,5,7,2,8]=>[2,4,2]
[8,5,2,6,1,4,7,3]=>[6,8,3,2,5,4,7,1]=>[3,1,6,7,4,5,2,8]=>[1,3,2,2]
[2,7,5,8,1,4,6,3]=>[6,3,8,5,1,2,7,4]=>[3,6,1,4,8,7,2,5]=>[2,3,1,2]
[3,2,6,7,1,8,5,4]=>[3,8,1,7,2,5,4,6]=>[6,1,8,2,7,4,5,3]=>[1,2,2,2,1]
[3,4,6,7,8,2,1,5]=>[3,7,1,2,6,4,8,5]=>[6,2,8,7,3,5,1,4]=>[1,2,1,2,2]
[3,2,6,7,8,4,1,5]=>[3,7,1,6,2,4,8,5]=>[6,2,8,3,7,5,1,4]=>[1,2,2,1,2]
[6,2,7,4,8,5,1,3]=>[4,7,3,1,8,2,6,5]=>[5,2,6,8,1,7,3,4]=>[1,3,2,2]
[6,7,1,3,8,5,4,2]=>[8,7,4,1,6,3,2,5]=>[1,2,5,8,3,6,7,4]=>[4,3,1]
[6,7,1,8,5,2,4,3]=>[8,6,1,7,5,3,2,4]=>[1,3,8,2,4,6,7,5]=>[3,4,1]
[1,2,6,7,8,5,3,4]=>[3,7,4,8,6,1,2,5]=>[6,2,5,1,3,8,7,4]=>[1,2,3,1,1]
[1,6,7,4,8,3,2,5]=>[4,2,7,6,3,8,1,5]=>[5,7,2,3,6,1,8,4]=>[2,3,2,1]
[1,4,6,7,8,3,2,5]=>[3,7,2,6,4,8,1,5]=>[6,2,7,3,5,1,8,4]=>[1,2,2,2,1]
[6,1,2,4,5,3,7,8]=>[4,6,2,3,5,1,7,8]=>[5,3,7,6,4,8,2,1]=>[1,2,1,2,1,1]
[8,1,7,3,2,6,4,5]=>[4,7,8,5,6,2,3,1]=>[5,2,1,4,3,7,6,8]=>[1,1,2,2,2]
[4,1,3,2,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[6,8,7,9,5,4,3,2,1]=>[2,2,1,1,1,1,1]
[8,7,2,1,5,4,6,3]=>[6,3,5,8,4,7,2,1]=>[3,6,4,1,5,2,7,8]=>[2,1,2,3]
[2,7,4,8,6,5,3,1]=>[8,7,3,2,6,1,5,4]=>[1,2,6,7,3,8,4,5]=>[4,2,2]
[7,6,5,2,4,1,8,3]=>[8,4,6,5,3,2,1,7]=>[1,5,3,4,6,7,8,2]=>[2,5,1]
[7,6,4,3,1,5,8,2]=>[6,4,3,8,5,2,1,7]=>[3,5,6,1,4,7,8,2]=>[3,4,1]
[6,1,8,7,2,3,5,4]=>[8,5,6,1,7,4,2,3]=>[1,4,3,8,2,5,7,6]=>[2,2,3,1]
[8,6,1,2,7,3,4,5]=>[6,7,8,3,4,2,5,1]=>[3,2,1,6,5,7,4,8]=>[1,1,2,2,2]
[3,6,8,2,7,1,5,4]=>[8,4,1,2,6,7,5,3]=>[1,5,8,7,3,2,4,6]=>[3,1,1,3]
[2,8,6,1,4,5,7,3]=>[5,6,8,4,1,3,7,2]=>[4,3,1,5,8,6,2,7]=>[1,1,3,1,2]
[6,8,7,2,5,4,1,3]=>[7,1,8,4,6,5,3,2]=>[2,8,1,5,3,4,6,7]=>[2,2,4]
[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[9,8,7,10,6,5,4,3,2,1]=>[1,1,2,1,1,1,1,1,1]
[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[9,8,7,6,10,5,4,3,2,1]=>[1,1,1,2,1,1,1,1,1]
[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[9,8,7,6,5,4,3,10,2,1]=>[1,1,1,1,1,1,2,1,1]
[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[9,8,7,6,5,4,10,3,2,1]=>[1,1,1,1,1,2,1,1,1]
[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[9,8,7,6,5,10,4,3,2,1]=>[1,1,1,1,2,1,1,1,1]
[3,2,6,4,8,7,5,1]=>[3,8,1,7,2,4,6,5]=>[6,1,8,2,7,5,3,4]=>[1,2,2,1,2]
[4,7,2,8,6,5,1,3]=>[7,8,1,6,3,2,5,4]=>[2,1,8,3,6,7,4,5]=>[1,2,3,2]
[4,7,1,8,6,5,3,2]=>[8,7,1,6,5,3,2,4]=>[1,2,8,3,4,6,7,5]=>[3,4,1]
[2,7,4,8,3,6,1,5]=>[3,5,7,2,8,1,6,4]=>[6,4,2,7,1,8,3,5]=>[1,1,2,2,2]
[4,7,3,8,6,1,5,2]=>[8,1,3,6,2,7,5,4]=>[1,8,6,3,7,2,4,5]=>[2,1,2,3]
[4,3,6,8,7,2,5,1]=>[1,3,6,8,2,7,5,4]=>[8,6,3,1,7,2,4,5]=>[1,1,1,2,3]
[4,3,8,2,5,7,6,1]=>[1,8,2,4,5,7,6,3]=>[8,1,7,5,4,2,3,6]=>[1,2,1,1,3]
[4,1,2,6,8,7,5,3]=>[1,8,4,7,6,2,3,5]=>[8,1,5,2,3,7,6,4]=>[1,2,3,1,1]
[3,1,6,4,8,7,2,5]=>[7,1,3,8,4,6,2,5]=>[2,8,6,1,5,3,7,4]=>[2,1,2,2,1]
[4,1,6,8,7,5,2,3]=>[1,3,7,8,6,5,2,4]=>[8,6,2,1,3,4,7,5]=>[1,1,1,4,1]
[3,8,1,4,5,7,2,6]=>[1,4,5,7,8,3,6,2]=>[8,5,4,2,1,6,3,7]=>[1,1,1,1,2,2]
[3,8,1,4,2,5,7,6]=>[1,4,8,3,5,6,7,2]=>[8,5,1,6,4,3,2,7]=>[1,1,2,1,1,2]
[4,1,8,3,5,2,7,6]=>[4,1,5,8,6,7,2,3]=>[5,8,4,1,3,2,7,6]=>[2,1,2,2,1]
[3,8,1,2,5,4,7,6]=>[1,5,8,3,4,6,7,2]=>[8,4,1,6,5,3,2,7]=>[1,1,2,1,1,2]
[4,2,3,6,8,7,1,5]=>[4,1,7,8,2,3,6,5]=>[5,8,2,1,7,6,3,4]=>[2,1,2,1,2]
[4,2,8,3,5,1,7,6]=>[4,1,5,8,2,6,7,3]=>[5,8,4,1,7,3,2,6]=>[2,1,2,1,2]
[4,2,8,3,5,7,6,1]=>[1,8,4,5,7,2,6,3]=>[8,1,5,4,2,7,3,6]=>[1,2,1,2,2]
[3,8,2,4,5,7,6,1]=>[8,1,3,4,5,7,6,2]=>[1,8,6,5,4,2,3,7]=>[2,1,1,1,3]
[4,2,8,5,7,1,3,6]=>[1,6,4,7,8,2,5,3]=>[8,3,5,2,1,7,4,6]=>[1,2,1,2,2]
[3,8,1,5,2,4,7,6]=>[8,1,5,3,4,6,7,2]=>[1,8,4,6,5,3,2,7]=>[2,2,1,1,2]
[7,5,6,4,1,3,2,8]=>[7,5,2,6,4,3,1,8]=>[2,4,7,3,5,6,8,1]=>[3,4,1]
[7,8,6,4,1,3,2,5]=>[7,5,6,4,1,8,3,2]=>[2,4,3,5,8,1,6,7]=>[2,3,3]
[7,1,4,2,5,6,3,8]=>[5,3,7,2,4,6,1,8]=>[4,6,2,7,5,3,8,1]=>[2,2,1,2,1]
[7,3,2,1,4,6,5,8]=>[3,2,7,4,5,6,1,8]=>[6,7,2,5,4,3,8,1]=>[2,2,1,2,1]
[7,6,1,4,3,2,5,8]=>[6,5,3,4,7,2,1,8]=>[3,4,6,5,2,7,8,1]=>[3,1,3,1]
[7,4,1,3,5,6,2,8]=>[4,5,2,7,3,6,1,8]=>[5,4,7,2,6,3,8,1]=>[1,2,2,2,1]
[2,7,1,3,5,6,8,4]=>[5,6,8,1,3,4,2,7]=>[4,3,1,8,6,5,7,2]=>[1,1,2,1,2,1]
[3,6,2,1,5,8,7,4]=>[8,1,3,5,2,7,4,6]=>[1,8,6,4,7,2,5,3]=>[2,1,2,2,1]
[2,3,6,1,5,8,7,4]=>[8,5,1,2,3,7,4,6]=>[1,4,8,7,6,2,5,3]=>[3,1,1,2,1]
[3,4,7,1,5,6,8,2]=>[1,2,5,6,8,4,3,7]=>[8,7,4,3,1,5,6,2]=>[1,1,1,1,3,1]
[3,6,7,4,1,2,8,5]=>[8,5,1,4,2,6,3,7]=>[1,4,8,5,7,3,6,2]=>[3,2,2,1]
[4,3,2,7,1,6,8,5]=>[2,1,6,8,3,5,4,7]=>[7,8,3,1,6,4,5,2]=>[2,1,2,2,1]
[7,3,2,8,1,6,4,5]=>[2,7,8,3,5,1,6,4]=>[7,2,1,6,4,8,3,5]=>[1,1,2,2,2]
[7,4,8,1,5,6,3,2]=>[2,5,8,7,4,1,6,3]=>[7,4,1,2,5,8,3,6]=>[1,1,4,2]
[6,8,2,1,5,3,7,4]=>[8,3,6,4,1,5,7,2]=>[1,6,3,5,8,4,2,7]=>[2,3,1,2]
[4,5,8,2,3,6,7,1]=>[1,4,2,5,6,8,7,3]=>[8,5,7,4,3,1,2,6]=>[1,2,1,1,3]
[2,4,8,5,3,6,7,1]=>[5,2,4,6,8,1,7,3]=>[4,7,5,3,1,8,2,6]=>[2,1,1,2,2]
[5,3,2,6,4,8,7,1]=>[2,4,1,8,3,5,7,6]=>[7,5,8,1,6,4,2,3]=>[1,2,2,1,2]
[2,4,5,3,8,6,7,1]=>[2,3,6,8,1,4,7,5]=>[7,6,3,1,8,5,2,4]=>[1,1,1,2,1,2]
[4,3,5,2,8,6,7,1]=>[2,1,3,6,8,4,7,5]=>[7,8,6,3,1,5,2,4]=>[2,1,1,2,2]
[4,8,5,3,2,6,7,1]=>[5,1,4,3,6,8,7,2]=>[4,8,5,6,3,1,2,7]=>[2,2,1,3]
[3,5,4,2,8,6,7,1]=>[3,1,2,6,8,4,7,5]=>[6,8,7,3,1,5,2,4]=>[2,1,1,2,2]
[4,1,2,7,5,6,8,3]=>[5,1,6,4,8,2,3,7]=>[4,8,3,5,1,7,6,2]=>[2,2,2,1,1]
[5,6,7,4,2,8,3,1]=>[1,2,8,5,4,3,7,6]=>[8,7,1,4,5,6,2,3]=>[1,1,4,2]
[2,5,7,4,6,8,3,1]=>[2,4,5,3,8,1,7,6]=>[7,5,4,6,1,8,2,3]=>[1,1,2,2,2]
[7,5,2,4,3,8,6,1]=>[4,8,3,2,5,1,7,6]=>[5,1,6,7,4,8,2,3]=>[1,3,2,2]
[6,4,1,8,5,2,7,3]=>[2,8,6,5,1,7,3,4]=>[7,1,3,4,8,2,6,5]=>[1,4,2,1]
[2,6,1,8,5,4,7,3]=>[6,5,2,8,1,7,3,4]=>[3,4,7,1,8,2,6,5]=>[3,2,2,1]
[7,1,2,8,5,6,4,3]=>[5,8,7,6,2,3,1,4]=>[4,1,2,3,7,6,8,5]=>[1,4,2,1]
[4,3,2,6,8,5,7,1]=>[2,1,4,6,8,3,7,5]=>[7,8,5,3,1,6,2,4]=>[2,1,1,2,2]
[3,7,6,4,8,5,2,1]=>[8,4,3,1,2,7,6,5]=>[1,5,6,8,7,2,3,4]=>[4,1,3]
[2,3,5,8,4,6,7,1]=>[3,5,6,8,1,2,7,4]=>[6,4,3,1,8,7,2,5]=>[1,1,1,2,1,2]
[3,5,2,8,4,6,7,1]=>[5,1,2,6,8,3,7,4]=>[4,8,7,3,1,6,2,5]=>[2,1,1,2,2]
[3,4,5,8,2,6,7,1]=>[1,2,3,5,6,8,7,4]=>[8,7,6,4,3,1,2,5]=>[1,1,1,1,1,3]
[5,4,2,8,3,6,7,1]=>[5,2,1,6,8,3,7,4]=>[4,7,8,3,1,6,2,5]=>[3,1,2,2]
[5,3,4,8,2,6,7,1]=>[2,3,1,5,6,8,7,4]=>[7,6,8,4,3,1,2,5]=>[1,2,1,1,3]
[2,5,4,8,3,6,7,1]=>[3,2,5,6,8,1,7,4]=>[6,7,4,3,1,8,2,5]=>[2,1,1,2,2]
[6,3,2,5,8,4,7,1]=>[2,4,6,1,8,3,7,5]=>[7,5,3,8,1,6,2,4]=>[1,1,2,2,2]
[6,1,8,3,5,4,7,2]=>[6,4,5,1,8,7,2,3]=>[3,5,4,8,1,2,7,6]=>[2,2,3,1]
[5,8,2,3,4,6,7,1]=>[3,4,1,5,6,8,7,2]=>[6,5,8,4,3,1,2,7]=>[1,2,1,1,3]
[6,2,1,7,8,5,4,3]=>[4,8,7,2,1,6,3,5]=>[5,1,2,7,8,3,6,4]=>[1,4,2,1]
[7,4,6,8,3,2,5,1]=>[6,2,5,3,1,8,7,4]=>[3,7,4,6,8,1,2,5]=>[2,3,3]
[3,4,5,2,7,1,6,8]=>[1,2,4,3,6,7,5,8]=>[8,7,5,6,3,2,4,1]=>[1,1,2,1,2,1]
[7,5,6,1,2,3,8,4]=>[8,4,5,2,6,3,1,7]=>[1,5,4,7,3,6,8,2]=>[2,2,3,1]
[1,5,7,6,3,2,8,4]=>[2,5,8,6,4,1,3,7]=>[7,4,1,3,5,8,6,2]=>[1,1,4,1,1]
[8,4,6,2,3,1,5,7]=>[4,2,6,5,7,3,8,1]=>[5,7,3,4,2,6,1,8]=>[2,2,2,2]
[3,1,7,8,5,4,2,6]=>[7,6,1,5,3,8,2,4]=>[2,3,8,4,6,1,7,5]=>[3,2,2,1]
[3,4,5,2,1,8,6,7]=>[1,2,4,3,7,8,5,6]=>[8,7,5,6,2,1,4,3]=>[1,1,2,1,2,1]
[7,6,4,8,3,1,2,5]=>[6,3,7,5,2,1,8,4]=>[3,6,2,4,7,8,1,5]=>[2,4,2]
[7,4,8,5,6,1,2,3]=>[2,6,7,4,1,8,5,3]=>[7,3,2,5,8,1,4,6]=>[1,1,3,3]
[6,2,8,5,1,3,4,7]=>[5,6,7,2,1,4,8,3]=>[4,3,2,7,8,5,1,6]=>[1,1,3,1,2]
[6,8,2,5,1,3,7,4]=>[8,3,5,1,6,4,7,2]=>[1,6,4,8,3,5,2,7]=>[2,2,2,2]
[6,7,4,2,1,5,3,8]=>[4,7,5,3,1,6,2,8]=>[5,2,4,6,8,3,7,1]=>[1,4,2,1]
[5,7,4,1,3,6,2,8]=>[5,1,7,4,3,6,2,8]=>[4,8,2,5,6,3,7,1]=>[2,3,2,1]
[4,2,7,5,1,8,3,6]=>[1,7,4,8,2,5,3,6]=>[8,2,5,1,7,4,6,3]=>[1,2,2,2,1]
[4,1,6,5,3,8,2,7]=>[1,5,4,3,7,8,2,6]=>[8,4,5,6,2,1,7,3]=>[1,3,1,2,1]
[1,5,4,6,3,8,2,7]=>[3,2,5,4,7,8,1,6]=>[6,7,4,5,2,1,8,3]=>[2,2,1,2,1]
[1,8,6,4,7,3,2,5]=>[4,7,6,3,8,5,1,2]=>[5,2,3,6,1,4,8,7]=>[1,3,3,1]
[4,7,1,8,6,3,5,2]=>[6,8,1,7,5,3,2,4]=>[3,1,8,2,4,6,7,5]=>[1,2,4,1]
[5,4,8,1,7,3,6,2]=>[2,1,6,8,7,4,5,3]=>[7,8,3,1,2,5,4,6]=>[2,1,3,2]
[4,3,8,6,2,1,7,5]=>[1,5,8,2,6,4,7,3]=>[8,4,1,7,3,5,2,6]=>[1,1,2,2,2]
[8,3,6,2,4,1,7,5]=>[2,4,5,8,6,3,7,1]=>[7,5,4,1,3,6,2,8]=>[1,1,1,3,2]
[7,8,3,2,4,6,5,1]=>[3,8,4,5,1,7,6,2]=>[6,1,5,4,8,2,3,7]=>[1,2,2,3]
[7,2,8,5,3,1,6,4]=>[5,8,6,2,4,1,7,3]=>[4,1,3,7,5,8,2,6]=>[1,3,2,2]
[2,5,4,8,7,3,6,1]=>[2,6,8,3,7,1,5,4]=>[7,3,1,6,2,8,4,5]=>[1,1,2,2,2]
[6,4,2,8,7,3,1,5]=>[2,7,6,1,8,3,5,4]=>[7,2,3,8,1,6,4,5]=>[1,3,2,2]
[3,6,8,1,7,4,2,5]=>[7,6,1,2,8,4,5,3]=>[2,3,8,7,1,5,4,6]=>[3,1,2,2]
[7,8,6,3,1,4,5,2]=>[6,4,8,5,1,7,3,2]=>[3,5,1,4,8,2,6,7]=>[2,3,3]
[6,8,7,5,2,1,3,4]=>[6,5,1,7,8,4,3,2]=>[3,4,8,2,1,5,6,7]=>[3,1,4]
[7,6,2,8,5,1,3,4]=>[6,7,8,3,2,1,5,4]=>[3,2,1,6,7,8,4,5]=>[1,1,4,2]
[1,5,7,6,2,8,4,3]=>[8,2,7,5,4,1,3,6]=>[1,7,2,4,5,8,6,3]=>[2,4,1,1]
[1,6,5,2,7,8,4,3]=>[5,3,2,8,7,1,4,6]=>[4,6,7,1,2,8,5,3]=>[3,3,1,1]
[4,7,8,5,6,2,3,1]=>[6,4,1,2,8,7,5,3]=>[3,5,8,7,1,2,4,6]=>[3,1,4]
[2,7,8,5,6,1,4,3]=>[8,6,4,2,7,1,5,3]=>[1,3,5,7,2,8,4,6]=>[4,2,2]
[6,7,8,4,2,1,5,3]=>[5,1,8,6,4,2,7,3]=>[4,8,1,3,5,7,2,6]=>[2,4,2]
[4,7,8,1,2,5,6,3]=>[1,6,8,4,5,2,7,3]=>[8,3,1,5,4,7,2,6]=>[1,1,2,2,2]
[6,1,4,7,2,5,8,3]=>[3,6,8,5,2,1,4,7]=>[6,3,1,4,7,8,5,2]=>[1,1,4,1,1]
[6,7,8,3,5,4,2,1]=>[1,8,4,2,7,6,5,3]=>[8,1,5,7,2,3,4,6]=>[1,3,4]
[6,7,8,2,1,5,3,4]=>[4,7,1,8,5,2,6,3]=>[5,2,8,1,4,7,3,6]=>[1,2,3,2]
[5,6,3,2,7,4,1,8]=>[3,1,7,4,2,6,5,8]=>[6,8,2,5,7,3,4,1]=>[2,3,2,1]
[2,6,4,3,7,5,8,1]=>[3,6,4,1,2,5,8,7]=>[6,3,5,8,7,4,1,2]=>[1,3,1,1,2]
[7,2,3,6,1,8,4,5]=>[7,8,2,3,5,4,1,6]=>[2,1,7,6,4,5,8,3]=>[1,2,1,3,1]
[3,4,6,5,7,1,2,8]=>[6,1,2,4,3,7,5,8]=>[3,8,7,5,6,2,4,1]=>[2,1,2,2,1]
[7,6,2,3,5,4,8,1]=>[6,3,4,5,2,1,8,7]=>[3,6,5,4,7,8,1,2]=>[2,1,3,2]
[8,5,2,4,3,6,1,7]=>[5,3,4,2,7,6,8,1]=>[4,6,5,7,2,3,1,8]=>[2,2,2,2]
[8,5,7,2,4,1,6,3]=>[8,4,2,6,5,7,3,1]=>[1,5,7,3,4,2,6,8]=>[3,2,3]
[2,6,7,5,8,1,4,3]=>[2,8,6,4,1,3,7,5]=>[7,1,3,5,8,6,2,4]=>[1,4,1,2]
[7,4,8,2,1,5,6,3]=>[4,2,6,8,5,1,7,3]=>[5,7,3,1,4,8,2,6]=>[2,1,3,2]
[2,3,6,7,8,5,1,4]=>[3,7,4,8,1,2,6,5]=>[6,2,5,1,8,7,3,4]=>[1,2,2,1,2]
[5,7,4,1,6,8,2,3]=>[1,7,5,3,8,4,2,6]=>[8,2,4,6,1,5,7,3]=>[1,3,3,1]
[6,5,1,2,8,3,4,7]=>[6,7,8,3,2,1,4,5]=>[3,2,1,6,7,8,5,4]=>[1,1,4,1,1]
[3,7,4,8,6,1,2,5]=>[3,6,7,1,2,8,5,4]=>[6,3,2,8,7,1,4,5]=>[1,1,2,1,3]
[1,6,8,5,3,2,4,7]=>[6,5,2,7,4,8,1,3]=>[3,4,7,2,5,1,8,6]=>[3,2,2,1]
[6,2,7,4,3,8,1,5]=>[5,4,7,2,1,3,8,6]=>[4,5,2,7,8,6,1,3]=>[2,3,1,2]
[1,7,8,4,6,2,3,5]=>[6,4,7,2,8,5,1,3]=>[3,5,2,7,1,4,8,6]=>[2,2,3,1]
[7,1,8,4,6,2,3,5]=>[6,4,7,8,5,2,1,3]=>[3,5,2,1,4,7,8,6]=>[2,1,4,1]
[8,1,6,5,4,7,2,3]=>[7,5,4,3,8,2,6,1]=>[2,4,5,6,1,7,3,8]=>[4,2,2]
[4,1,6,8,7,3,2,5]=>[1,3,7,6,8,5,2,4]=>[8,6,2,3,1,4,7,5]=>[1,1,2,3,1]
[5,1,4,6,7,3,8,2]=>[3,4,1,6,5,8,2,7]=>[6,5,8,3,4,1,7,2]=>[1,2,2,2,1]
[7,1,3,4,6,2,8,5]=>[8,3,4,6,2,5,1,7]=>[1,6,5,3,7,4,8,2]=>[2,1,2,2,1]
[4,7,2,8,5,3,1,6]=>[7,1,6,3,5,2,8,4]=>[2,8,3,6,4,7,1,5]=>[2,2,2,2]
[6,5,2,8,4,7,1,3]=>[7,5,2,1,8,3,6,4]=>[2,4,7,8,1,6,3,5]=>[4,2,2]
[1,4,7,5,8,6,3,2]=>[8,4,2,3,7,6,1,5]=>[1,5,7,6,2,3,8,4]=>[3,1,3,1]
[6,1,8,3,4,7,2,5]=>[4,5,7,1,8,6,2,3]=>[5,4,2,8,1,3,7,6]=>[1,1,2,3,1]
[4,7,1,6,8,3,5,2]=>[6,1,4,8,7,3,2,5]=>[3,8,5,1,2,6,7,4]=>[2,1,4,1]
[3,6,5,2,8,4,1,7]=>[7,4,1,3,2,6,8,5]=>[2,5,8,6,7,3,1,4]=>[3,2,1,2]
[8,2,5,6,3,1,7,4]=>[5,3,8,2,6,4,7,1]=>[4,6,1,7,3,5,2,8]=>[2,2,2,2]
[7,1,8,4,2,5,3,6]=>[7,5,4,6,8,2,1,3]=>[2,4,5,3,1,7,8,6]=>[3,1,3,1]
[1,4,8,7,5,2,6,3]=>[8,6,2,5,7,4,1,3]=>[1,3,7,4,2,5,8,6]=>[3,1,3,1]
[1,5,6,4,2,3,7,8]=>[5,2,6,4,1,3,7,8]=>[4,7,3,5,8,6,2,1]=>[2,3,1,1,1]
[5,7,3,6,8,4,2,1]=>[1,4,8,3,2,7,6,5]=>[8,5,1,6,7,2,3,4]=>[1,1,3,3]
[3,1,5,2,7,8,6,4]=>[1,3,5,8,7,2,4,6]=>[8,6,4,1,2,7,5,3]=>[1,1,1,3,1,1]
[1,8,7,3,2,5,4,6]=>[4,7,5,6,8,3,1,2]=>[5,2,4,3,1,6,8,7]=>[1,2,1,3,1]
[1,2,5,4,8,7,3,6]=>[3,7,8,4,6,1,2,5]=>[6,2,1,5,3,8,7,4]=>[1,1,2,2,1,1]
[1,2,4,8,6,3,5,7]=>[6,7,3,5,8,1,2,4]=>[3,2,6,4,1,8,7,5]=>[1,2,1,2,1,1]
[1,5,2,4,7,3,8,6]=>[8,4,2,6,1,3,5,7]=>[1,5,7,3,8,6,4,2]=>[3,2,1,1,1]
[8,6,3,5,7,4,1,2]=>[7,3,4,2,8,6,5,1]=>[2,6,5,7,1,3,4,8]=>[2,2,4]
[1,6,3,2,5,7,8,4]=>[3,5,6,2,8,1,4,7]=>[6,4,3,7,1,8,5,2]=>[1,1,2,2,1,1]
[1,5,6,3,2,8,4,7]=>[4,2,7,3,8,1,5,6]=>[5,7,2,6,1,8,4,3]=>[2,2,2,1,1]
[1,2,5,8,4,6,3,7]=>[3,5,7,6,8,1,2,4]=>[6,4,2,3,1,8,7,5]=>[1,1,2,2,1,1]
[1,5,3,2,7,8,4,6]=>[7,3,2,5,8,1,4,6]=>[2,6,7,4,1,8,5,3]=>[3,1,2,1,1]
[4,1,8,6,2,3,7,5]=>[1,8,5,6,4,7,2,3]=>[8,1,4,3,5,2,7,6]=>[1,2,2,2,1]
[7,5,8,6,2,3,4,1]=>[5,2,6,1,8,7,4,3]=>[4,7,3,8,1,2,5,6]=>[2,2,4]
[1,7,6,4,3,8,5,2]=>[4,8,5,3,2,7,1,6]=>[5,1,4,6,7,2,8,3]=>[1,4,2,1]
[1,8,5,7,6,3,2,4]=>[3,7,6,8,5,4,1,2]=>[6,2,3,1,4,5,8,7]=>[1,2,4,1]
[1,4,7,3,6,8,5,2]=>[5,8,2,4,3,7,1,6]=>[4,1,7,5,6,2,8,3]=>[1,2,2,2,1]
[1,6,3,5,7,8,4,2]=>[4,5,2,8,3,7,1,6]=>[5,4,7,1,6,2,8,3]=>[1,2,2,2,1]
[1,5,6,3,2,7,8,4]=>[4,2,6,3,8,1,5,7]=>[5,7,3,6,1,8,4,2]=>[2,2,2,1,1]
[1,2,7,6,8,4,5,3]=>[6,4,3,8,7,1,2,5]=>[3,5,6,1,2,8,7,4]=>[3,3,1,1]
[1,8,4,7,5,3,2,6]=>[7,3,6,5,8,4,1,2]=>[2,6,3,4,1,5,8,7]=>[2,2,3,1]
[1,2,6,8,4,3,7,5]=>[5,3,8,6,7,1,2,4]=>[4,6,1,3,2,8,7,5]=>[2,2,2,1,1]
[5,3,7,2,6,4,1,8]=>[7,2,1,4,6,5,3,8]=>[2,7,8,5,3,4,6,1]=>[3,1,3,1]
[5,3,8,2,6,1,7,4]=>[8,2,1,4,6,5,7,3]=>[1,7,8,5,3,4,2,6]=>[3,1,2,2]
[7,6,2,5,3,4,1,8]=>[5,7,3,6,4,2,1,8]=>[4,2,6,3,5,7,8,1]=>[1,2,4,1]
[7,6,2,4,5,3,1,8]=>[4,7,3,6,5,2,1,8]=>[5,2,6,3,4,7,8,1]=>[1,2,4,1]
[7,6,2,4,3,5,1,8]=>[5,3,4,7,6,2,1,8]=>[4,6,5,2,3,7,8,1]=>[2,1,4,1]
[7,6,2,3,5,4,1,8]=>[7,3,4,6,5,2,1,8]=>[2,6,5,3,4,7,8,1]=>[2,1,4,1]
[8,4,2,7,1,6,3,5]=>[7,2,8,3,5,6,4,1]=>[2,7,1,6,4,3,5,8]=>[2,2,1,3]
[4,6,3,2,8,1,7,5]=>[1,3,8,4,2,6,7,5]=>[8,6,1,5,7,3,2,4]=>[1,1,3,1,2]
[8,7,6,1,5,3,2,4]=>[7,6,8,4,5,3,2,1]=>[2,3,1,5,4,6,7,8]=>[2,2,4]
[8,7,6,1,4,3,5,2]=>[6,5,8,4,7,3,2,1]=>[3,4,1,5,2,6,7,8]=>[2,2,4]
[8,7,6,1,3,5,4,2]=>[8,5,7,4,6,3,2,1]=>[1,4,2,5,3,6,7,8]=>[2,2,4]
[8,7,6,1,5,4,2,3]=>[7,8,6,4,5,3,2,1]=>[2,1,3,5,4,6,7,8]=>[1,3,4]
[8,3,5,4,2,1,6,7]=>[6,2,5,4,3,7,8,1]=>[3,7,4,5,6,2,1,8]=>[2,3,1,2]
[7,8,4,3,1,5,2,6]=>[7,5,4,3,6,1,8,2]=>[2,4,5,6,3,8,1,7]=>[4,2,2]
[8,7,6,1,2,5,3,4]=>[7,8,4,5,6,3,2,1]=>[2,1,5,4,3,6,7,8]=>[1,2,1,4]
[8,7,6,1,2,5,4,3]=>[8,7,4,5,6,3,2,1]=>[1,2,5,4,3,6,7,8]=>[3,1,4]
[8,7,6,1,4,2,5,3]=>[8,6,4,5,7,3,2,1]=>[1,3,5,4,2,6,7,8]=>[3,1,4]
[4,7,5,8,6,1,3,2]=>[3,8,1,6,2,7,5,4]=>[6,1,8,3,7,2,4,5]=>[1,2,2,3]
[6,5,7,3,8,4,1,2]=>[4,2,1,7,3,8,6,5]=>[5,7,8,2,6,1,3,4]=>[3,2,3]
[8,7,5,4,1,2,6,3]=>[8,5,6,4,3,7,2,1]=>[1,4,3,5,6,2,7,8]=>[2,3,3]
[8,6,7,1,5,3,2,4]=>[7,6,8,4,2,5,3,1]=>[2,3,1,5,7,4,6,8]=>[2,3,3]
[7,5,6,1,3,4,2,8]=>[5,7,4,2,6,3,1,8]=>[4,2,5,7,3,6,8,1]=>[1,3,3,1]
[5,7,8,1,3,4,2,6]=>[5,1,7,4,6,2,8,3]=>[4,8,2,5,3,7,1,6]=>[2,2,2,2]
[5,7,8,3,4,6,1,2]=>[1,4,7,5,2,8,6,3]=>[8,5,2,4,7,1,3,6]=>[1,1,3,3]
[7,5,1,3,4,2,6,8]=>[4,6,3,5,2,7,1,8]=>[5,3,6,4,7,2,8,1]=>[1,2,2,2,1]
[5,7,1,3,4,2,8,6]=>[4,5,1,8,3,6,2,7]=>[5,4,8,1,6,3,7,2]=>[1,2,2,2,1]
[7,3,5,6,4,8,1,2]=>[3,7,2,5,4,1,8,6]=>[6,2,7,4,5,8,1,3]=>[1,2,3,2]
[1,7,3,8,2,5,6,4]=>[6,8,3,5,2,7,1,4]=>[3,1,6,4,7,2,8,5]=>[1,2,2,2,1]
[1,5,3,7,8,4,6,2]=>[2,6,4,8,3,7,1,5]=>[7,3,5,1,6,2,8,4]=>[1,2,2,2,1]
[1,5,7,3,8,2,6,4]=>[2,8,4,6,3,7,1,5]=>[7,1,5,3,6,2,8,4]=>[1,2,2,2,1]
[7,1,5,3,6,2,4,8]=>[4,6,3,7,2,5,1,8]=>[5,3,6,2,7,4,8,1]=>[1,2,2,2,1]
[1,7,3,5,8,4,2,6]=>[4,7,3,6,2,8,1,5]=>[5,2,6,3,7,1,8,4]=>[1,2,2,2,1]
[1,3,7,5,8,6,2,4]=>[4,7,3,8,2,6,1,5]=>[5,2,6,1,7,3,8,4]=>[1,2,2,2,1]
[1,7,8,5,3,6,2,4]=>[5,7,4,2,8,6,1,3]=>[4,2,5,7,1,3,8,6]=>[1,3,3,1]
[1,7,5,8,3,4,2,6]=>[5,3,7,6,2,8,1,4]=>[4,6,2,3,7,1,8,5]=>[2,3,2,1]
[7,1,5,6,3,4,2,8]=>[5,3,7,6,2,4,1,8]=>[4,6,2,3,7,5,8,1]=>[2,3,2,1]
[7,3,5,6,4,1,2,8]=>[6,2,3,7,5,4,1,8]=>[3,7,6,2,4,5,8,1]=>[2,1,4,1]
[3,7,5,8,4,1,2,6]=>[6,3,7,1,5,2,8,4]=>[3,6,2,8,4,7,1,5]=>[2,2,2,2]
[7,5,6,8,1,3,4,2]=>[6,2,8,5,3,1,7,4]=>[3,7,1,4,6,8,2,5]=>[2,4,2]
[5,3,4,7,8,1,2,6]=>[2,3,1,6,7,4,8,5]=>[7,6,8,3,2,5,1,4]=>[1,2,1,2,2]
[5,3,7,6,8,1,2,4]=>[6,1,7,2,4,3,8,5]=>[3,8,2,7,5,6,1,4]=>[2,2,2,2]
[3,7,1,2,5,8,4,6]=>[1,5,7,8,3,4,2,6]=>[8,4,2,1,6,5,7,3]=>[1,1,1,2,2,1]
[3,1,2,7,5,8,4,6]=>[1,5,7,4,8,2,3,6]=>[8,4,2,5,1,7,6,3]=>[1,1,2,2,1,1]
[3,1,2,5,7,8,6,4]=>[1,5,8,4,7,2,3,6]=>[8,4,1,5,2,7,6,3]=>[1,1,2,2,1,1]
[7,3,1,5,4,6,2,8]=>[2,5,4,7,3,6,1,8]=>[7,4,5,2,6,3,8,1]=>[1,2,2,2,1]
[7,3,5,1,2,6,4,8]=>[2,7,4,5,3,6,1,8]=>[7,2,5,4,6,3,8,1]=>[1,2,2,2,1]
[3,7,1,2,8,5,6,4]=>[6,8,1,7,3,4,2,5]=>[3,1,8,2,6,5,7,4]=>[1,2,2,2,1]
[5,3,1,7,4,6,8,2]=>[2,5,1,6,4,8,3,7]=>[7,4,8,3,5,1,6,2]=>[1,2,2,2,1]
[5,3,7,1,2,6,8,4]=>[2,6,1,8,4,5,3,7]=>[7,3,8,1,5,4,6,2]=>[1,2,2,2,1]
[7,4,8,3,5,6,1,2]=>[2,4,7,5,1,8,6,3]=>[7,5,2,4,8,1,3,6]=>[1,1,3,3]
[5,7,6,4,2,3,1,8]=>[1,5,7,6,4,3,2,8]=>[8,4,2,3,5,6,7,1]=>[1,1,5,1]
[7,4,8,2,5,6,1,3]=>[2,7,4,5,1,8,6,3]=>[7,2,5,4,8,1,3,6]=>[1,2,2,3]
[5,8,2,4,6,1,3,7]=>[6,3,1,4,7,5,8,2]=>[3,6,8,5,2,4,1,7]=>[3,1,2,2]
[6,1,4,8,5,2,7,3]=>[8,3,6,5,1,7,2,4]=>[1,6,3,4,8,2,7,5]=>[2,3,2,1]
[3,4,5,8,1,6,7,2]=>[1,2,3,6,8,5,7,4]=>[8,7,6,3,1,4,2,5]=>[1,1,1,1,2,2]
[6,8,7,4,2,1,5,3]=>[5,1,8,6,4,7,3,2]=>[4,8,1,3,5,2,6,7]=>[2,3,3]
[5,6,8,4,7,3,1,2]=>[1,2,7,4,8,6,5,3]=>[8,7,2,5,1,3,4,6]=>[1,1,2,4]
[3,1,6,8,5,2,7,4]=>[3,8,1,6,5,7,2,4]=>[6,1,8,3,4,2,7,5]=>[1,2,2,2,1]
[2,3,8,1,5,6,4,7]=>[5,7,1,2,4,6,8,3]=>[4,2,8,7,5,3,1,6]=>[1,2,1,1,1,2]
[5,1,8,2,4,6,7,3]=>[5,6,1,8,4,7,2,3]=>[4,3,8,1,5,2,7,6]=>[1,2,2,2,1]
[4,1,8,2,3,6,7,5]=>[6,1,8,4,5,7,2,3]=>[3,8,1,5,4,2,7,6]=>[2,2,1,2,1]
[5,2,3,8,1,7,4,6]=>[7,8,2,1,3,5,6,4]=>[2,1,7,8,6,4,3,5]=>[1,3,1,1,2]
[2,3,5,7,1,6,4,8]=>[3,7,1,2,5,6,4,8]=>[6,2,8,7,4,3,5,1]=>[1,2,1,1,2,1]
[1,5,3,8,2,4,6,7]=>[3,5,2,6,7,8,1,4]=>[6,4,7,3,2,1,8,5]=>[1,2,1,1,2,1]
[8,6,2,7,5,1,4,3]=>[8,6,7,3,2,5,4,1]=>[1,3,2,6,7,4,5,8]=>[2,3,3]
[2,7,1,8,6,3,5,4]=>[8,6,7,5,1,3,2,4]=>[1,3,2,4,8,6,7,5]=>[2,3,2,1]
[5,7,6,1,3,2,8,4]=>[5,1,8,4,6,3,2,7]=>[4,8,1,5,3,6,7,2]=>[2,2,3,1]
[8,1,7,5,3,6,4,2]=>[8,5,4,7,6,2,3,1]=>[1,4,5,2,3,7,6,8]=>[3,3,2]
[8,6,5,3,7,4,2,1]=>[8,4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4,8]=>[4,4]
[3,5,4,6,1,7,8,2]=>[3,1,2,6,4,8,5,7]=>[6,8,7,3,5,1,4,2]=>[2,1,2,2,1]
[8,1,5,4,6,3,7,2]=>[4,3,6,5,8,2,7,1]=>[5,6,3,4,1,7,2,8]=>[2,2,2,2]
[2,7,1,5,6,4,3,8]=>[4,7,6,1,3,5,2,8]=>[5,2,3,8,6,4,7,1]=>[1,3,1,2,1]
[8,4,6,3,1,7,2,5]=>[2,7,4,8,5,3,6,1]=>[7,2,5,1,4,6,3,8]=>[1,2,3,2]
[8,4,2,5,6,3,7,1]=>[4,2,6,3,5,8,7,1]=>[5,7,3,6,4,1,2,8]=>[2,2,1,3]
[8,6,2,7,5,4,3,1]=>[8,7,6,3,2,5,4,1]=>[1,2,3,6,7,4,5,8]=>[5,3]
[5,4,7,2,8,6,1,3]=>[2,1,7,8,4,3,6,5]=>[7,8,2,1,5,6,3,4]=>[2,1,3,2]
[3,5,6,4,1,7,2,8]=>[2,7,1,5,4,3,6,8]=>[7,2,8,4,5,6,3,1]=>[1,2,3,1,1]
[2,5,6,1,7,4,3,8]=>[2,7,6,1,4,3,5,8]=>[7,2,3,8,5,6,4,1]=>[1,3,2,1,1]
[2,7,1,8,6,5,4,3]=>[8,7,6,5,1,3,2,4]=>[1,2,3,4,8,6,7,5]=>[5,2,1]
[3,7,6,1,8,5,4,2]=>[8,7,6,1,4,3,2,5]=>[1,2,3,8,5,6,7,4]=>[4,3,1]
[8,6,4,2,1,3,5,7,9]=>[5,4,6,3,7,2,8,1,9]=>[5,6,4,7,3,8,2,9,1]=>[2,2,2,2,1]
[8,6,4,2,9,1,3,5,7]=>[4,6,3,7,2,8,1,9,5]=>[6,4,7,3,8,2,9,1,5]=>[1,2,2,2,2]
[9,7,5,3,1,2,4,6,8]=>[5,6,4,7,3,8,2,9,1]=>[5,4,6,3,7,2,8,1,9]=>[1,2,2,2,2]
[10,8,6,4,2,1,3,5,7,9]=>[6,5,7,4,8,3,9,2,10,1]=>[5,6,4,7,3,8,2,9,1,10]=>[2,2,2,2,2]
[6,2,8,3,1,4,5,7]=>[5,2,4,6,1,7,8,3]=>[4,7,5,3,8,2,1,6]=>[2,1,2,1,2]
[2,7,8,3,1,4,5,6]=>[5,4,6,7,1,2,8,3]=>[4,5,3,2,8,7,1,6]=>[2,1,2,1,2]
[9,7,5,2,3,1,4,6,8,10]=>[4,6,5,7,3,8,2,9,1,10]=>[7,5,6,4,8,3,9,2,10,1]=>[1,2,2,2,2,1]
[9,7,5,3,1,2,4,6,8,10]=>[5,6,4,7,3,8,2,9,1,10]=>[6,5,7,4,8,3,9,2,10,1]=>[1,2,2,2,2,1]
[1,5,3,2,8,6,7,4]=>[6,2,8,3,7,1,4,5]=>[3,7,1,6,2,8,5,4]=>[2,2,2,1,1]
[1,8,5,3,2,6,7,4]=>[4,6,3,8,5,7,1,2]=>[5,3,6,1,4,2,8,7]=>[1,2,2,2,1]
[1,7,8,5,6,3,2,4]=>[7,6,4,2,8,5,1,3]=>[2,3,5,7,1,4,8,6]=>[4,3,1]
[1,5,6,7,3,2,8,4]=>[2,5,3,8,6,1,4,7]=>[7,4,6,1,3,8,5,2]=>[1,2,3,1,1]
[1,7,5,2,3,4,8,6]=>[8,4,5,3,6,1,2,7]=>[1,5,4,6,3,8,7,2]=>[2,2,2,1,1]
[1,7,5,2,4,8,6,3]=>[8,5,3,7,4,1,2,6]=>[1,4,6,2,5,8,7,3]=>[3,3,1,1]
[1,4,8,6,2,3,5,7]=>[2,5,6,7,4,8,1,3]=>[7,4,3,2,5,1,8,6]=>[1,1,1,2,2,1]
[1,2,8,6,3,4,5,7]=>[5,6,7,4,8,1,2,3]=>[4,3,2,5,1,8,7,6]=>[1,1,2,2,1,1]
[1,2,8,6,3,5,7,4]=>[6,8,5,4,7,1,2,3]=>[3,1,4,5,2,8,7,6]=>[1,3,2,1,1]
[1,2,7,8,4,3,5,6]=>[6,5,7,3,8,1,2,4]=>[3,4,2,6,1,8,7,5]=>[2,2,2,1,1]
[1,8,6,7,4,2,3,5]=>[6,7,5,3,8,4,1,2]=>[3,2,4,6,1,5,8,7]=>[1,3,3,1]
[1,6,7,8,4,2,3,5]=>[6,2,7,5,3,8,1,4]=>[3,7,2,4,6,1,8,5]=>[2,3,2,1]
[1,6,7,8,3,4,2,5]=>[5,2,7,6,3,8,1,4]=>[4,7,2,3,6,1,8,5]=>[2,3,2,1]
[1,7,4,2,3,8,5,6]=>[7,3,8,4,5,1,2,6]=>[2,6,1,5,4,8,7,3]=>[2,2,2,1,1]
[1,7,8,4,2,3,5,6]=>[5,6,4,7,2,8,1,3]=>[4,3,5,2,7,1,8,6]=>[1,2,2,2,1]
[1,7,8,3,4,2,5,6]=>[4,6,5,7,2,8,1,3]=>[5,3,4,2,7,1,8,6]=>[1,2,2,2,1]
[1,2,3,7,8,5,4,6]=>[7,6,4,8,1,2,3,5]=>[2,3,5,1,8,7,6,4]=>[3,2,1,1,1]
[1,2,7,4,6,3,8,5]=>[8,4,6,5,1,2,3,7]=>[1,5,3,4,8,7,6,2]=>[2,3,1,1,1]
[1,7,4,5,2,3,8,6]=>[3,8,5,4,6,1,2,7]=>[6,1,4,5,3,8,7,2]=>[1,3,2,1,1]
[1,7,8,4,5,2,3,6]=>[6,4,7,5,2,8,1,3]=>[3,5,2,4,7,1,8,6]=>[2,3,2,1]
[1,7,8,3,4,5,2,6]=>[4,5,7,6,2,8,1,3]=>[5,4,2,3,7,1,8,6]=>[1,1,3,2,1]
[1,2,8,4,5,6,3,7]=>[4,5,7,6,8,1,2,3]=>[5,4,2,3,1,8,7,6]=>[1,1,2,2,1,1]
[1,8,4,5,6,2,3,7]=>[3,6,4,7,5,8,1,2]=>[6,3,5,2,4,1,8,7]=>[1,2,2,2,1]
[5,8,2,7,3,4,1,6]=>[5,1,7,3,6,8,4,2]=>[4,8,2,6,3,1,5,7]=>[2,2,1,3]
[6,8,7,2,3,4,1,5]=>[4,5,1,7,6,8,3,2]=>[5,4,8,2,3,1,6,7]=>[1,2,2,3]
[3,8,7,5,2,6,1,4]=>[5,7,4,8,1,6,3,2]=>[4,2,5,1,8,3,6,7]=>[1,2,2,3]
[4,8,7,3,2,5,1,6]=>[5,1,4,7,6,8,3,2]=>[4,8,5,2,3,1,6,7]=>[2,1,2,3]
[5,3,8,1,6,7,4,2]=>[5,1,8,2,7,4,6,3]=>[4,8,1,7,2,5,3,6]=>[2,2,2,2]
[5,1,8,2,6,4,7,3]=>[6,5,1,8,4,7,2,3]=>[3,4,8,1,5,2,7,6]=>[3,2,2,1]
[8,4,1,6,5,2,3,7]=>[6,2,7,5,3,4,8,1]=>[3,7,2,4,6,5,1,8]=>[2,3,1,2]
[1,8,7,6,4,3,5,2]=>[6,5,8,7,4,3,1,2]=>[3,4,1,2,5,6,8,7]=>[2,5,1]
[6,1,8,7,5,3,4,2]=>[6,1,8,7,5,4,2,3]=>[3,8,1,2,4,5,7,6]=>[2,5,1]
[6,8,7,3,2,4,1,5]=>[5,4,1,7,6,8,3,2]=>[4,5,8,2,3,1,6,7]=>[3,2,3]
[2,3,7,5,6,8,4,1]=>[4,5,3,8,1,2,7,6]=>[5,4,6,1,8,7,2,3]=>[1,2,2,1,2]
[3,2,4,7,5,8,1,6]=>[1,5,7,2,3,4,8,6]=>[8,4,2,7,6,5,1,3]=>[1,1,2,1,1,2]
[2,8,7,6,4,5,1,3]=>[7,5,8,6,4,1,3,2]=>[2,4,1,3,5,8,6,7]=>[2,4,2]
[4,8,7,6,3,1,5,2]=>[8,6,1,5,7,4,3,2]=>[1,3,8,4,2,5,6,7]=>[3,1,4]
[3,5,2,4,7,6,8,1]=>[6,1,3,2,4,5,8,7]=>[3,8,6,7,5,4,1,2]=>[2,2,1,1,2]
[5,3,2,6,4,7,8,1]=>[2,5,3,1,4,6,8,7]=>[7,4,6,8,5,3,1,2]=>[1,3,1,1,2]
[5,3,2,6,7,4,8,1]=>[2,4,1,6,3,5,8,7]=>[7,5,8,3,6,4,1,2]=>[1,2,2,1,2]
[5,3,2,7,6,4,8,1]=>[6,2,1,5,3,4,8,7]=>[3,7,8,4,6,5,1,2]=>[3,2,1,2]
[7,3,5,2,8,4,6,1]=>[6,2,3,8,4,1,7,5]=>[3,7,6,1,5,8,2,4]=>[2,1,3,2]
[3,5,2,7,4,6,8,1]=>[5,1,2,6,3,4,8,7]=>[4,8,7,3,6,5,1,2]=>[2,1,2,1,2]
[3,2,5,7,4,6,8,1]=>[1,3,5,6,2,4,8,7]=>[8,6,4,3,7,5,1,2]=>[1,1,1,2,1,2]
[3,2,7,5,4,8,6,1]=>[4,8,1,5,2,3,7,6]=>[5,1,8,4,7,6,2,3]=>[1,2,2,1,2]
[3,7,5,2,4,8,6,1]=>[8,4,1,3,5,2,7,6]=>[1,5,8,6,4,7,2,3]=>[3,1,2,2]
[8,3,5,1,6,4,7,2]=>[6,2,5,3,8,4,7,1]=>[3,7,4,6,1,5,2,8]=>[2,2,2,2]
[8,4,5,6,1,3,7,2]=>[2,6,3,8,5,4,7,1]=>[7,3,6,1,4,5,2,8]=>[1,2,3,2]
[3,4,7,6,8,2,5,1]=>[6,4,1,2,3,8,7,5]=>[3,5,8,7,6,1,2,4]=>[3,1,1,3]
[5,2,8,4,1,3,6,7]=>[5,6,2,1,4,7,8,3]=>[4,3,7,8,5,2,1,6]=>[1,3,1,1,2]
[7,6,4,1,8,2,5,3]=>[8,6,3,7,4,2,1,5]=>[1,3,6,2,5,7,8,4]=>[3,4,1]
[8,1,6,7,3,4,2,5]=>[5,7,6,3,8,2,4,1]=>[4,2,3,6,1,7,5,8]=>[1,3,2,2]
[8,2,1,6,7,4,3,5]=>[7,6,2,4,8,3,5,1]=>[2,3,7,5,1,6,4,8]=>[3,1,2,2]
[5,2,8,6,3,7,1,4]=>[5,1,7,4,8,2,6,3]=>[4,8,2,5,1,7,3,6]=>[2,2,2,2]
[7,6,8,1,2,5,4,3]=>[8,7,4,5,2,1,6,3]=>[1,2,5,4,7,8,3,6]=>[3,3,2]
[1,2,3,4,9,5,6,8,7]=>[9,6,7,8,1,2,3,4,5]=>[1,4,3,2,9,8,7,6,5]=>[2,1,2,1,1,1,1]
[2,1,3,4,8,5,7,6]=>[8,1,6,7,2,3,4,5]=>[1,8,3,2,7,6,5,4]=>[2,1,2,1,1,1]
[1,2,3,4,5,9,6,8,7]=>[9,7,8,1,2,3,4,5,6]=>[1,3,2,9,8,7,6,5,4]=>[2,2,1,1,1,1,1]
[1,2,3,4,10,5,6,7,9,8]=>[10,6,7,8,9,1,2,3,4,5]=>[1,5,4,3,2,10,9,8,7,6]=>[2,1,1,2,1,1,1,1]
[1,2,3,4,5,10,6,7,9,8]=>[10,7,8,9,1,2,3,4,5,6]=>[1,4,3,2,10,9,8,7,6,5]=>[2,1,2,1,1,1,1,1]
[5,7,1,2,6,8,3,4]=>[7,5,1,8,3,4,2,6]=>[2,4,8,1,6,5,7,3]=>[3,2,2,1]
[1,4,2,3,5,6,9,8,7]=>[2,9,8,1,3,4,5,6,7]=>[8,1,2,9,7,6,5,4,3]=>[1,3,1,1,1,1,1]
[1,5,2,3,6,8,7,4]=>[8,5,2,7,1,3,4,6]=>[1,4,7,2,8,6,5,3]=>[3,2,1,1,1]
[3,4,1,2,5,6,8,9,7]=>[1,7,2,9,3,4,5,6,8]=>[9,3,8,1,7,6,5,4,2]=>[1,2,2,1,1,1,1]
[1,2,3,4,5,6,7,8,11,10,9]=>[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,11,10,9,8,7,6,5,4,3]=>[3,1,1,1,1,1,1,1,1]
[3,5,7,4,1,8,2,6]=>[2,7,1,4,8,5,3,6]=>[7,2,8,5,1,4,6,3]=>[1,2,1,3,1]
[8,6,4,7,5,1,2,3]=>[6,3,7,2,8,5,4,1]=>[3,6,2,7,1,4,5,8]=>[2,2,4]
[8,6,4,1,2,5,3,7]=>[7,4,5,3,6,2,8,1]=>[2,5,4,6,3,7,1,8]=>[2,2,2,2]
[2,8,4,3,1,6,5,7]=>[4,3,7,1,5,6,8,2]=>[5,6,2,8,4,3,1,7]=>[2,2,1,1,2]
[3,8,4,6,1,5,2,7]=>[3,7,1,5,6,4,8,2]=>[6,2,8,4,3,5,1,7]=>[1,2,1,2,2]
[8,3,5,6,1,4,7,2]=>[6,2,3,8,5,4,7,1]=>[3,7,6,1,4,5,2,8]=>[2,1,3,2]
[6,8,7,3,5,4,2,1]=>[1,8,4,7,6,5,3,2]=>[8,1,5,2,3,4,6,7]=>[1,2,5]
[3,1,2,8,5,7,4,6]=>[1,5,7,8,6,2,3,4]=>[8,4,2,1,3,7,6,5]=>[1,1,1,3,1,1]
[7,3,1,2,5,8,4,6]=>[5,2,7,8,3,4,1,6]=>[4,7,2,1,6,5,8,3]=>[2,1,2,2,1]
[2,1,3,8,5,7,4,6]=>[5,7,8,1,6,2,3,4]=>[4,2,1,8,3,7,6,5]=>[1,1,2,2,1,1]
[7,3,1,2,8,4,5,6]=>[6,2,7,8,3,4,1,5]=>[3,7,2,1,6,5,8,4]=>[2,1,2,2,1]
[2,1,4,7,6,3,5,8]=>[6,7,1,3,5,2,4,8]=>[3,2,8,6,4,7,5,1]=>[1,2,1,2,1,1]
[7,2,4,5,3,8,1,6]=>[3,5,2,4,7,1,8,6]=>[6,4,7,5,2,8,1,3]=>[1,2,1,2,2]
[8,4,2,5,6,7,3,1]=>[4,2,5,8,3,7,6,1]=>[5,7,4,1,6,2,3,8]=>[2,1,2,3]
[5,4,1,6,3,7,8,2]=>[5,4,2,1,6,8,3,7]=>[4,5,7,8,3,1,6,2]=>[4,1,2,1]
[4,5,1,3,6,7,8,2]=>[4,1,5,2,6,8,3,7]=>[5,8,4,7,3,1,6,2]=>[2,2,1,2,1]
[6,1,7,5,4,8,2,3]=>[7,5,4,3,1,8,2,6]=>[2,4,5,6,8,1,7,3]=>[5,2,1]
[5,7,2,1,8,4,3,6]=>[7,3,1,6,8,4,2,5]=>[2,6,8,3,1,5,7,4]=>[3,1,3,1]
[5,6,2,1,8,3,4,7]=>[3,6,1,7,2,8,4,5]=>[6,3,8,2,7,1,5,4]=>[1,2,2,2,1]
[2,4,8,6,5,7,3,1]=>[5,4,8,2,7,1,6,3]=>[4,5,1,7,2,8,3,6]=>[2,2,2,2]
[6,2,8,4,7,5,1,3]=>[4,7,1,8,6,2,5,3]=>[5,2,8,1,3,7,4,6]=>[1,2,3,2]
[4,5,7,3,6,8,1,2]=>[1,2,4,7,5,3,8,6]=>[8,7,5,2,4,6,1,3]=>[1,1,1,3,2]
[3,4,7,8,6,5,1,2]=>[7,3,8,1,2,6,5,4]=>[2,6,1,8,7,3,4,5]=>[2,2,1,3]
[1,4,7,2,6,8,5,3]=>[5,8,2,7,4,1,3,6]=>[4,1,7,2,5,8,6,3]=>[1,2,3,1,1]
[3,2,7,6,4,1,5,8]=>[6,1,5,7,2,4,3,8]=>[3,8,4,2,7,5,6,1]=>[2,1,2,2,1]
[6,2,3,5,7,1,4,8]=>[6,2,3,4,1,7,5,8]=>[3,7,6,5,8,2,4,1]=>[2,1,2,2,1]
[7,8,1,2,5,6,4,3]=>[5,8,7,3,4,1,6,2]=>[4,1,2,6,5,8,3,7]=>[1,3,2,2]
[7,1,3,6,8,5,2,4]=>[7,4,8,3,6,2,1,5]=>[2,5,1,6,3,7,8,4]=>[2,2,3,1]
[4,2,8,5,1,6,3,7]=>[1,7,5,2,4,6,8,3]=>[8,2,4,7,5,3,1,6]=>[1,3,1,1,2]
[6,5,8,1,4,2,3,7]=>[6,7,4,2,1,5,8,3]=>[3,2,5,7,8,4,1,6]=>[1,4,1,2]
[3,8,2,4,5,1,6,7]=>[1,3,4,6,5,7,8,2]=>[8,6,5,3,4,2,1,7]=>[1,1,1,2,1,2]
[3,6,2,4,1,5,7,8]=>[1,3,5,4,6,2,7,8]=>[8,6,4,5,3,7,2,1]=>[1,1,2,2,1,1]
[2,3,8,4,1,6,5,7]=>[4,7,1,2,5,6,8,3]=>[5,2,8,7,4,3,1,6]=>[1,2,1,1,1,2]
[4,5,7,3,1,6,2,8]=>[1,2,7,5,4,6,3,8]=>[8,7,2,4,5,3,6,1]=>[1,1,3,2,1]
[2,3,1,4,8,5,7,6]=>[8,1,2,6,7,3,4,5]=>[1,8,7,3,2,6,5,4]=>[2,1,1,2,1,1]
[4,2,6,1,5,8,7,3]=>[1,8,5,2,3,7,4,6]=>[8,1,4,7,6,2,5,3]=>[1,3,1,2,1]
[7,5,1,8,4,3,6,2]=>[6,5,2,8,7,3,1,4]=>[3,4,7,1,2,6,8,5]=>[3,4,1]
[3,1,8,5,7,6,4,2]=>[8,4,7,1,6,5,2,3]=>[1,5,2,8,3,4,7,6]=>[2,2,3,1]
[2,4,8,7,5,1,3,6]=>[6,7,2,5,8,1,4,3]=>[3,2,7,4,1,8,5,6]=>[1,2,1,2,2]
[3,5,7,6,1,8,4,2]=>[8,2,7,1,5,4,3,6]=>[1,7,2,8,4,5,6,3]=>[2,2,3,1]
[3,5,7,6,2,8,4,1]=>[8,2,5,1,4,3,7,6]=>[1,7,4,8,5,6,2,3]=>[2,2,2,2]
[1,5,3,2,8,7,6,4]=>[2,8,7,3,6,1,4,5]=>[7,1,2,6,3,8,5,4]=>[1,3,2,1,1]
[6,1,4,3,8,7,5,2]=>[8,3,7,4,1,6,2,5]=>[1,6,2,5,8,3,7,4]=>[2,3,2,1]
[6,3,1,8,7,4,2,5]=>[7,2,6,1,8,5,3,4]=>[2,7,3,8,1,4,6,5]=>[2,2,3,1]
[6,3,5,2,1,8,7,4]=>[8,2,4,3,1,7,5,6]=>[1,7,5,6,8,2,4,3]=>[2,3,2,1]
[2,8,4,1,3,7,6,5]=>[3,8,7,1,4,5,6,2]=>[6,1,2,8,5,4,3,7]=>[1,3,1,1,2]
[3,8,1,4,7,6,5,2]=>[8,7,1,4,6,3,5,2]=>[1,2,8,5,3,6,4,7]=>[3,1,2,2]
[6,2,3,8,7,5,4,1]=>[8,7,6,2,1,3,5,4]=>[1,2,3,7,8,6,4,5]=>[5,1,2]
[4,1,3,5,8,7,6,2]=>[1,8,7,3,4,6,2,5]=>[8,1,2,6,5,3,7,4]=>[1,3,1,2,1]
[3,4,7,5,8,1,2,6]=>[6,1,2,4,7,3,8,5]=>[3,8,7,5,2,6,1,4]=>[2,1,1,2,2]
[2,8,6,7,5,4,3,1]=>[3,8,7,6,5,1,4,2]=>[6,1,2,3,4,8,5,7]=>[1,5,2]
[7,2,6,8,1,4,3,5]=>[7,5,6,2,3,1,8,4]=>[2,4,3,7,6,8,1,5]=>[2,2,2,2]
[8,1,6,3,7,4,5,2]=>[6,8,4,3,7,2,5,1]=>[3,1,5,6,2,7,4,8]=>[1,3,2,2]
[2,4,3,7,1,8,6,5]=>[8,2,7,1,3,5,4,6]=>[1,7,2,8,6,4,5,3]=>[2,2,1,2,1]
[2,6,5,7,3,8,4,1]=>[3,2,8,5,1,4,7,6]=>[6,7,1,4,8,5,2,3]=>[2,3,1,2]
[6,8,2,7,4,1,5,3]=>[8,6,3,1,5,7,4,2]=>[1,3,6,8,4,2,5,7]=>[4,1,3]
[6,1,7,8,5,3,2,4]=>[7,6,3,1,8,5,2,4]=>[2,3,6,8,1,4,7,5]=>[4,3,1]
[2,6,5,4,7,1,8,3]=>[4,3,2,8,1,6,5,7]=>[5,6,7,1,8,3,4,2]=>[3,2,2,1]
[5,8,3,4,6,1,7,2]=>[3,1,4,8,6,5,7,2]=>[6,8,5,1,3,4,2,7]=>[2,1,3,2]
[6,8,7,1,5,4,2,3]=>[7,1,8,6,4,5,3,2]=>[2,8,1,3,5,4,6,7]=>[2,3,3]
[4,8,3,1,5,7,6,2]=>[1,3,8,5,7,4,6,2]=>[8,6,1,4,2,5,3,7]=>[1,1,2,2,2]
[8,3,4,5,2,7,1,6]=>[2,3,5,4,7,8,6,1]=>[7,6,4,5,2,1,3,8]=>[1,1,2,1,3]
[8,2,6,7,1,5,3,4]=>[7,8,5,2,3,6,4,1]=>[2,1,4,7,6,3,5,8]=>[1,3,1,3]
[7,1,5,2,6,3,4,8]=>[6,7,4,2,3,5,1,8]=>[3,2,5,7,6,4,8,1]=>[1,3,1,2,1]
[3,7,1,5,2,6,8,4]=>[6,1,4,8,3,5,2,7]=>[3,8,5,1,6,4,7,2]=>[2,1,2,2,1]
[6,7,1,8,3,4,5,2]=>[5,6,1,8,7,3,2,4]=>[4,3,8,1,2,6,7,5]=>[1,2,4,1]
[3,7,1,6,8,4,5,2]=>[6,4,8,1,7,3,2,5]=>[3,5,1,8,2,6,7,4]=>[2,2,3,1]
[3,6,5,2,7,1,4,8]=>[4,6,1,3,2,7,5,8]=>[5,3,8,6,7,2,4,1]=>[1,2,2,2,1]
[6,8,3,4,7,1,5,2]=>[3,4,1,8,6,7,5,2]=>[6,5,8,1,3,2,4,7]=>[1,2,2,3]
[3,7,1,6,5,2,8,4]=>[8,6,1,5,3,4,2,7]=>[1,3,8,4,6,5,7,2]=>[3,2,2,1]
[8,3,5,2,7,1,6,4]=>[8,2,4,3,6,7,5,1]=>[1,7,5,6,3,2,4,8]=>[2,2,1,3]
[7,1,8,4,6,3,5,2]=>[4,6,8,7,5,2,1,3]=>[5,3,1,2,4,7,8,6]=>[1,1,5,1]
[3,8,6,4,7,1,5,2]=>[4,8,6,1,3,7,5,2]=>[5,1,3,8,6,2,4,7]=>[1,3,1,3]
[3,7,1,4,8,6,5,2]=>[8,7,1,4,6,3,2,5]=>[1,2,8,5,3,6,7,4]=>[3,1,3,1]
[3,7,1,4,5,2,8,6]=>[1,4,5,8,3,6,2,7]=>[8,5,4,1,6,3,7,2]=>[1,1,1,2,2,1]
[2,3,7,6,5,8,1,4]=>[7,5,4,1,2,3,8,6]=>[2,4,5,8,7,6,1,3]=>[4,1,1,2]
[6,7,8,5,4,3,2,1,9]=>[1,2,8,7,6,5,4,3,9]=>[9,8,2,3,4,5,6,7,1]=>[1,1,6,1]
[7,8,9,6,5,4,3,2,1,10]=>[1,2,9,8,7,6,5,4,3,10]=>[10,9,2,3,4,5,6,7,8,1]=>[1,1,7,1]
[6,2,4,3,7,5,1,8]=>[3,7,2,4,1,6,5,8]=>[6,2,7,5,8,3,4,1]=>[1,2,2,2,1]
[1,3,6,4,7,5,2,8]=>[7,4,2,3,6,1,5,8]=>[2,5,7,6,3,8,4,1]=>[3,1,2,1,1]
[8,2,5,3,6,4,1,7]=>[7,4,2,3,6,5,8,1]=>[2,5,7,6,3,4,1,8]=>[3,1,2,2]
[6,2,5,3,7,4,1,8]=>[7,4,2,3,1,6,5,8]=>[2,5,7,6,8,3,4,1]=>[3,2,2,1]
[4,2,6,3,7,5,1,8]=>[1,7,4,2,3,6,5,8]=>[8,2,5,7,6,3,4,1]=>[1,3,1,2,1]
[5,2,7,3,6,4,1,8]=>[7,4,1,6,2,5,3,8]=>[2,5,8,3,7,4,6,1]=>[3,2,2,1]
[7,3,6,2,5,4,1,8]=>[7,2,4,6,5,3,1,8]=>[2,7,5,3,4,6,8,1]=>[2,1,4,1]
[6,3,8,2,5,4,1,7]=>[7,2,4,1,6,5,8,3]=>[2,7,5,8,3,4,1,6]=>[2,2,2,2]
[7,3,1,4,6,5,2,8]=>[2,7,4,6,3,5,1,8]=>[7,2,5,3,6,4,8,1]=>[1,2,2,2,1]
[8,3,7,2,5,4,1,6]=>[7,2,4,6,5,8,3,1]=>[2,7,5,3,4,1,6,8]=>[2,1,2,3]
[3,2,8,4,6,5,1,7]=>[7,1,4,6,2,5,8,3]=>[2,8,5,3,7,4,1,6]=>[2,1,2,1,2]
[1,4,7,3,6,5,2,8]=>[7,2,4,6,5,1,3,8]=>[2,7,5,3,4,8,6,1]=>[2,1,3,1,1]
[8,2,5,4,1,6,3,7]=>[7,5,2,4,3,6,8,1]=>[2,4,7,5,6,3,1,8]=>[3,2,1,2]
[8,2,6,4,1,5,3,7]=>[7,5,2,4,6,3,8,1]=>[2,4,7,5,3,6,1,8]=>[3,1,2,2]
[1,4,8,3,7,5,2,6]=>[7,2,4,6,8,5,1,3]=>[2,7,5,3,1,4,8,6]=>[2,1,1,3,1]
[6,2,1,4,8,5,3,7]=>[7,2,4,6,1,8,3,5]=>[2,7,5,3,8,1,6,4]=>[2,1,2,2,1]
[5,2,1,4,8,6,3,7]=>[7,2,4,1,6,8,3,5]=>[2,7,5,8,3,1,6,4]=>[2,2,1,2,1]
[3,2,1,5,8,6,4,7]=>[1,7,2,4,6,8,3,5]=>[8,2,7,5,3,1,6,4]=>[1,2,1,1,2,1]
[4,2,8,3,7,5,1,6]=>[1,7,4,6,8,2,5,3]=>[8,2,5,3,1,7,4,6]=>[1,2,1,2,2]
[5,2,8,3,7,4,1,6]=>[7,4,1,6,8,2,5,3]=>[2,5,8,3,1,7,4,6]=>[3,1,2,2]
[8,3,7,2,6,4,1,5]=>[7,2,4,6,8,5,3,1]=>[2,7,5,3,1,4,6,8]=>[2,1,1,4]
[7,3,1,4,8,5,2,6]=>[2,7,4,6,8,3,1,5]=>[7,2,5,3,1,6,8,4]=>[1,2,1,3,1]
[1,3,7,4,8,5,2,6]=>[7,4,6,2,3,8,1,5]=>[2,5,3,7,6,1,8,4]=>[2,2,1,2,1]
[7,2,6,3,8,4,1,5]=>[7,4,6,2,3,1,8,5]=>[2,5,3,7,6,8,1,4]=>[2,2,2,2]
[5,2,7,3,8,4,1,6]=>[7,4,1,6,2,3,8,5]=>[2,5,8,3,7,6,1,4]=>[3,2,1,2]
[5,2,6,3,8,4,1,7]=>[7,4,2,1,3,6,8,5]=>[2,5,7,8,6,3,1,4]=>[4,1,1,2]
[6,2,5,3,8,4,1,7]=>[7,4,2,3,1,6,8,5]=>[2,5,7,6,8,3,1,4]=>[3,2,1,2]
[8,2,5,3,7,4,1,6]=>[7,4,2,3,6,8,5,1]=>[2,5,7,6,3,1,4,8]=>[3,1,1,3]
[1,3,6,4,8,5,2,7]=>[7,4,2,3,6,8,1,5]=>[2,5,7,6,3,1,8,4]=>[3,1,1,2,1]
[1,3,5,4,8,6,2,7]=>[3,7,2,4,6,8,1,5]=>[6,2,7,5,3,1,8,4]=>[1,2,1,1,2,1]
[8,2,4,3,7,5,1,6]=>[3,7,2,4,6,8,5,1]=>[6,2,7,5,3,1,4,8]=>[1,2,1,1,3]
[7,2,4,3,8,5,1,6]=>[3,7,2,4,6,1,8,5]=>[6,2,7,5,3,8,1,4]=>[1,2,1,2,2]
[6,2,4,3,8,5,1,7]=>[3,7,2,4,1,6,8,5]=>[6,2,7,5,8,3,1,4]=>[1,2,2,1,2]
[5,2,4,3,8,6,1,7]=>[3,7,2,1,4,6,8,5]=>[6,2,7,8,5,3,1,4]=>[1,3,1,1,2]
[4,2,5,3,8,6,1,7]=>[3,1,7,2,4,6,8,5]=>[6,8,2,7,5,3,1,4]=>[2,2,1,1,2]
[4,2,5,3,1,7,6,8]=>[4,2,1,3,7,5,6,8]=>[5,7,8,6,2,4,3,1]=>[3,1,2,1,1]
[6,2,4,3,1,7,5,8]=>[4,2,3,7,5,1,6,8]=>[5,7,6,2,4,8,3,1]=>[2,1,3,1,1]
[8,4,1,3,6,5,2,7]=>[7,4,2,6,3,5,8,1]=>[2,5,7,3,6,4,1,8]=>[3,2,1,2]
[1,5,2,4,7,6,3,8]=>[7,4,2,6,1,3,5,8]=>[2,5,7,3,8,6,4,1]=>[3,2,1,1,1]
[7,2,5,3,1,6,4,8]=>[4,7,2,5,3,6,1,8]=>[5,2,7,4,6,3,8,1]=>[1,2,2,2,1]
[6,2,5,3,1,7,4,8]=>[4,7,2,5,3,1,6,8]=>[5,2,7,4,6,8,3,1]=>[1,2,3,1,1]
[4,2,6,3,1,7,5,8]=>[4,1,7,2,5,3,6,8]=>[5,8,2,7,4,6,3,1]=>[2,2,2,1,1]
[3,2,6,4,1,7,5,8]=>[1,4,7,2,5,3,6,8]=>[8,5,2,7,4,6,3,1]=>[1,1,2,2,1,1]
[3,2,7,4,1,6,5,8]=>[1,4,7,2,5,6,3,8]=>[8,5,2,7,4,3,6,1]=>[1,1,2,1,2,1]
[4,2,7,3,1,6,5,8]=>[4,1,7,2,5,6,3,8]=>[5,8,2,7,4,3,6,1]=>[2,2,1,2,1]
[7,2,6,3,1,5,4,8]=>[4,7,2,5,6,3,1,8]=>[5,2,7,4,3,6,8,1]=>[1,2,1,3,1]
[1,5,2,4,8,6,3,7]=>[7,4,2,6,8,1,3,5]=>[2,5,7,3,1,8,6,4]=>[3,1,2,1,1]
[8,4,1,3,7,5,2,6]=>[7,4,2,6,8,3,5,1]=>[2,5,7,3,1,6,4,8]=>[3,1,2,2]
[6,2,1,5,3,7,4,8]=>[7,2,5,3,4,1,6,8]=>[2,7,4,6,5,8,3,1]=>[2,2,2,1,1]
[3,2,1,6,4,7,5,8]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[1,2,2,1,1,1]
[3,2,8,5,1,6,4,7]=>[7,1,5,2,4,6,8,3]=>[2,8,4,7,5,3,1,6]=>[2,2,1,1,2]
[6,2,8,4,1,5,3,7]=>[7,5,2,4,1,6,8,3]=>[2,4,7,5,8,3,1,6]=>[3,2,1,2]
[8,3,7,4,1,5,2,6]=>[7,2,5,4,6,8,3,1]=>[2,7,4,5,3,1,6,8]=>[2,2,1,3]
[7,1,3,2,5,6,4,8]=>[3,5,7,2,4,6,1,8]=>[6,4,2,7,5,3,8,1]=>[1,1,2,1,2,1]
[6,3,5,2,4,8,1,7]=>[2,4,5,3,1,7,8,6]=>[7,5,4,6,8,2,1,3]=>[1,1,3,1,2]
[1,5,2,8,7,4,3,6]=>[2,7,6,8,5,1,3,4]=>[7,2,3,1,4,8,6,5]=>[1,2,3,1,1]
[5,7,2,8,1,4,3,6]=>[7,3,1,5,6,2,8,4]=>[2,6,8,4,3,7,1,5]=>[3,1,2,2]
[5,8,2,7,1,4,3,6]=>[7,3,1,5,6,8,4,2]=>[2,6,8,4,3,1,5,7]=>[3,1,1,3]
[4,8,3,1,5,2,7,6]=>[1,5,3,8,4,6,7,2]=>[8,4,6,1,5,3,2,7]=>[1,2,2,1,2]
[7,1,5,3,2,6,8,4]=>[4,6,3,8,2,5,1,7]=>[5,3,6,1,7,4,8,2]=>[1,2,2,2,1]
[3,1,5,7,8,6,2,4]=>[7,1,3,4,8,6,2,5]=>[2,8,6,5,1,3,7,4]=>[2,1,1,3,1]
[8,7,6,5,4,1,2,3,9]=>[6,7,8,5,4,3,2,1,9]=>[4,3,2,5,6,7,8,9,1]=>[1,1,6,1]
[6,7,5,4,3,2,1,8,9]=>[1,7,6,5,4,3,2,8,9]=>[9,3,4,5,6,7,8,2,1]=>[1,6,1,1]
[8,6,2,3,1,5,7,4]=>[3,4,6,8,5,2,7,1]=>[6,5,3,1,4,7,2,8]=>[1,1,1,3,2]
[1,4,2,7,3,6,8,5]=>[2,6,8,5,1,3,4,7]=>[7,3,1,4,8,6,5,2]=>[1,1,3,1,1,1]
[3,2,1,7,8,5,4,6]=>[7,1,6,2,4,8,3,5]=>[2,8,3,7,5,1,6,4]=>[2,2,1,2,1]
[7,3,4,2,1,5,8,6]=>[2,4,3,8,5,6,1,7]=>[7,5,6,1,4,3,8,2]=>[1,2,2,2,1]
[1,7,6,3,2,4,8,5]=>[4,8,5,6,3,1,2,7]=>[5,1,4,3,6,8,7,2]=>[1,2,3,1,1]
[2,1,6,4,7,8,5,3]=>[5,3,8,1,4,7,2,6]=>[4,6,1,8,5,2,7,3]=>[2,2,1,2,1]
[1,2,3,7,5,8,4,6]=>[5,7,4,8,1,2,3,6]=>[4,2,5,1,8,7,6,3]=>[1,2,2,1,1,1]
[1,8,5,3,2,4,7,6]=>[4,8,5,3,6,7,1,2]=>[5,1,4,6,3,2,8,7]=>[1,3,1,2,1]
[4,7,8,1,5,6,2,3]=>[7,1,5,8,4,2,6,3]=>[2,8,4,1,5,7,3,6]=>[2,1,3,2]
[3,6,7,1,8,4,2,5]=>[7,6,1,2,8,4,3,5]=>[2,3,8,7,1,5,6,4]=>[3,1,3,1]
[2,7,3,8,4,5,6,1]=>[5,6,8,3,1,2,7,4]=>[4,3,1,6,8,7,2,5]=>[1,1,3,1,2]
[7,1,4,3,8,5,6,2]=>[3,6,8,4,7,2,1,5]=>[6,3,1,5,2,7,8,4]=>[1,1,2,3,1]
[5,6,2,7,8,3,4,1]=>[1,6,4,2,8,3,7,5]=>[8,3,5,7,1,6,2,4]=>[1,3,2,2]
[7,4,1,8,5,6,2,3]=>[2,7,5,8,6,3,1,4]=>[7,2,4,1,3,6,8,5]=>[1,2,4,1]
[7,2,5,8,1,6,3,4]=>[7,3,8,2,5,1,6,4]=>[2,6,1,7,4,8,3,5]=>[2,2,2,2]
[6,4,8,1,5,7,2,3]=>[2,7,5,1,8,4,6,3]=>[7,2,4,8,1,5,3,6]=>[1,3,2,2]
[2,7,4,1,3,6,8,5]=>[6,3,8,1,4,5,2,7]=>[3,6,1,8,5,4,7,2]=>[2,2,1,2,1]
[6,2,1,4,7,5,8,3]=>[6,2,4,5,1,8,3,7]=>[3,7,5,4,8,1,6,2]=>[2,1,2,2,1]
[1,2,8,4,6,3,5,7]=>[4,6,7,5,8,1,2,3]=>[5,3,2,4,1,8,7,6]=>[1,1,2,2,1,1]
[2,6,1,5,4,7,3,8]=>[5,4,7,1,3,2,6,8]=>[4,5,2,8,6,7,3,1]=>[2,2,2,1,1]
[1,2,8,5,4,6,3,7]=>[5,4,7,6,8,1,2,3]=>[4,5,2,3,1,8,7,6]=>[2,2,2,1,1]
[1,3,6,8,4,5,7,2]=>[5,3,6,8,2,7,1,4]=>[4,6,3,1,7,2,8,5]=>[2,1,2,2,1]
[1,2,8,4,6,3,7,5]=>[8,4,6,5,7,1,2,3]=>[1,5,3,4,2,8,7,6]=>[2,2,2,1,1]
[4,6,3,5,7,8,1,2]=>[1,3,4,2,7,5,8,6]=>[8,6,5,7,2,4,1,3]=>[1,1,2,2,2]
[2,7,6,5,1,4,8,3]=>[6,8,5,4,1,3,2,7]=>[3,1,4,5,8,6,7,2]=>[1,4,2,1]
[2,7,4,8,1,3,6,5]=>[3,8,5,6,1,2,7,4]=>[6,1,4,3,8,7,2,5]=>[1,2,2,1,2]
[2,3,6,8,4,1,7,5]=>[5,3,8,1,2,6,7,4]=>[4,6,1,8,7,3,2,5]=>[2,2,1,1,2]
[1,2,6,8,4,7,5,3]=>[3,8,5,7,6,1,2,4]=>[6,1,4,2,3,8,7,5]=>[1,2,3,1,1]
[1,7,2,8,6,3,5,4]=>[8,6,7,5,3,1,2,4]=>[1,3,2,4,6,8,7,5]=>[2,4,1,1]
[2,3,8,5,4,7,1,6]=>[5,4,7,8,1,2,6,3]=>[4,5,2,1,8,7,3,6]=>[2,1,2,1,2]
[1,2,8,4,7,3,5,6]=>[4,6,7,8,5,1,2,3]=>[5,3,2,1,4,8,7,6]=>[1,1,1,3,1,1]
[2,6,1,4,8,3,7,5]=>[8,4,6,1,2,7,3,5]=>[1,5,3,8,7,2,6,4]=>[2,2,1,2,1]
[3,7,6,5,2,1,4,8]=>[6,5,7,1,4,3,2,8]=>[3,4,2,8,5,6,7,1]=>[2,2,3,1]
[2,5,6,1,4,8,7,3]=>[2,8,5,1,3,7,4,6]=>[7,1,4,8,6,2,5,3]=>[1,3,1,2,1]
[8,4,2,3,7,1,6,5]=>[8,3,2,4,6,7,5,1]=>[1,6,7,5,3,2,4,8]=>[3,1,1,3]
[5,2,4,8,7,3,1,6]=>[7,3,1,6,8,2,5,4]=>[2,6,8,3,1,7,4,5]=>[3,1,2,2]
[3,2,4,6,7,8,1,5]=>[1,4,7,2,3,5,8,6]=>[8,5,2,7,6,4,1,3]=>[1,1,2,1,1,2]
[5,2,6,8,1,3,7,4]=>[8,5,2,1,3,6,7,4]=>[1,4,7,8,6,3,2,5]=>[4,1,1,2]
[4,8,1,6,3,7,5,2]=>[8,1,5,4,7,3,6,2]=>[1,8,4,5,2,6,3,7]=>[2,2,2,2]
[7,1,5,2,6,4,3,8]=>[7,6,4,2,3,5,1,8]=>[2,3,5,7,6,4,8,1]=>[4,1,2,1]
[8,3,5,2,6,1,4,7]=>[2,4,6,3,7,5,8,1]=>[7,5,3,6,2,4,1,8]=>[1,1,2,2,2]
[1,8,5,6,2,7,4,3]=>[3,8,7,5,4,6,1,2]=>[6,1,2,4,5,3,8,7]=>[1,4,2,1]
[4,2,7,6,1,8,5,3]=>[8,1,7,5,2,4,3,6]=>[1,8,2,4,7,5,6,3]=>[2,3,2,1]
[7,2,4,8,6,3,5,1]=>[6,8,3,7,2,1,5,4]=>[3,1,6,2,7,8,4,5]=>[1,2,3,2]
[7,3,2,1,8,5,4,6]=>[2,7,3,6,8,4,1,5]=>[7,2,6,3,1,5,8,4]=>[1,2,1,3,1]
[7,3,2,1,6,4,8,5]=>[2,8,3,6,4,5,1,7]=>[7,1,6,3,5,4,8,2]=>[1,2,2,2,1]
[3,6,5,2,1,8,4,7]=>[4,7,1,3,2,8,5,6]=>[5,2,8,6,7,1,4,3]=>[1,2,2,2,1]
[6,7,2,4,3,5,8,1]=>[5,3,4,1,6,2,8,7]=>[4,6,5,8,3,7,1,2]=>[2,2,2,2]
[4,5,3,7,2,1,6,8]=>[1,3,2,6,5,7,4,8]=>[8,6,7,3,4,2,5,1]=>[1,2,2,2,1]
[4,3,8,2,1,5,7,6]=>[2,1,4,8,5,6,7,3]=>[7,8,5,1,4,3,2,6]=>[2,1,2,1,2]
[4,3,2,8,1,6,7,5]=>[2,1,6,8,3,5,7,4]=>[7,8,3,1,6,4,2,5]=>[2,1,2,1,2]
[6,8,5,2,7,3,4,1]=>[6,1,8,4,3,7,5,2]=>[3,8,1,5,6,2,4,7]=>[2,3,3]
[5,4,7,8,2,3,6,1]=>[2,1,5,6,3,8,7,4]=>[7,8,4,3,6,1,2,5]=>[2,1,2,3]
[4,3,8,2,1,6,7,5]=>[2,1,4,6,8,5,7,3]=>[7,8,5,3,1,4,2,6]=>[2,1,1,2,2]
[3,6,7,4,5,2,8,1]=>[4,2,6,1,5,3,8,7]=>[5,7,3,8,4,6,1,2]=>[2,2,2,2]
[3,5,7,4,6,2,8,1]=>[2,4,6,1,5,3,8,7]=>[7,5,3,8,4,6,1,2]=>[1,1,2,2,2]
[5,3,7,6,2,4,8,1]=>[5,1,6,2,4,3,8,7]=>[4,8,3,7,5,6,1,2]=>[2,2,2,2]
[6,4,7,8,3,1,5,2]=>[8,2,1,6,5,3,7,4]=>[1,7,8,3,4,6,2,5]=>[3,3,2]
[8,4,7,3,1,5,6,2]=>[2,6,4,8,5,7,3,1]=>[7,3,5,1,4,2,6,8]=>[1,2,2,3]
[5,6,7,1,8,3,4,2]=>[1,6,2,8,7,4,3,5]=>[8,3,7,1,2,5,6,4]=>[1,2,4,1]
[7,1,8,6,2,5,4,3]=>[8,7,5,6,4,2,1,3]=>[1,2,4,3,5,7,8,6]=>[3,4,1]
[1,5,8,2,6,4,7,3]=>[2,6,5,8,4,7,1,3]=>[7,3,4,1,5,2,8,6]=>[1,2,2,2,1]
[1,5,7,4,6,8,3,2]=>[2,4,5,3,8,7,1,6]=>[7,5,4,6,1,2,8,3]=>[1,1,2,3,1]
[1,4,7,5,6,8,3,2]=>[4,5,2,3,8,7,1,6]=>[5,4,7,6,1,2,8,3]=>[1,2,1,3,1]
[5,6,7,4,8,1,3,2]=>[1,2,8,6,4,3,7,5]=>[8,7,1,3,5,6,2,4]=>[1,1,4,2]
[8,1,2,6,4,5,7,3]=>[5,6,4,8,2,3,7,1]=>[4,3,5,1,7,6,2,8]=>[1,2,2,1,2]
[4,8,1,7,2,5,6,3]=>[1,6,8,5,7,3,4,2]=>[8,3,1,4,2,6,5,7]=>[1,1,2,2,2]
[2,6,7,1,5,4,8,3]=>[6,5,2,8,1,4,3,7]=>[3,4,7,1,8,5,6,2]=>[3,2,2,1]
[3,2,7,6,5,8,1,4]=>[7,5,1,4,2,3,8,6]=>[2,4,8,5,7,6,1,3]=>[3,2,1,2]
[1,7,3,4,5,8,2,6]=>[3,4,5,7,2,8,1,6]=>[6,5,4,2,7,1,8,3]=>[1,1,1,2,2,1]
[7,1,8,4,5,6,3,2]=>[4,5,8,7,6,2,1,3]=>[5,4,1,2,3,7,8,6]=>[1,1,5,1]
[1,2,3,4,5,6,7,8,11,9,10]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,1,11,10,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,7,8,9,12,10,11]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[1,2,1,1,1,1,1,1,1,1,1]
[6,7,3,2,5,8,1,4]=>[3,7,4,1,5,2,8,6]=>[6,2,5,8,4,7,1,3]=>[1,3,2,2]
[6,1,8,4,5,3,7,2]=>[4,6,5,1,8,7,2,3]=>[5,3,4,8,1,2,7,6]=>[1,3,3,1]
[4,6,2,5,1,8,7,3]=>[1,4,8,3,2,7,5,6]=>[8,5,1,6,7,2,4,3]=>[1,1,3,2,1]
[5,1,4,6,2,8,7,3]=>[3,4,1,8,7,2,5,6]=>[6,5,8,1,2,7,4,3]=>[1,2,3,1,1]
[7,3,5,2,1,6,8,4]=>[2,4,6,3,8,5,1,7]=>[7,5,3,6,1,4,8,2]=>[1,1,2,3,1]
[8,5,1,2,6,3,7,4]=>[8,6,3,4,2,5,7,1]=>[1,3,6,5,7,4,2,8]=>[3,2,1,2]
[1,5,8,7,4,6,3,2]=>[5,8,2,7,6,4,1,3]=>[4,1,7,2,3,5,8,6]=>[1,2,4,1]
[5,7,2,1,3,6,8,4]=>[3,6,1,8,4,5,2,7]=>[6,3,8,1,5,4,7,2]=>[1,2,2,2,1]
[3,7,2,6,8,1,5,4]=>[8,6,1,3,4,2,7,5]=>[1,3,8,6,5,7,2,4]=>[3,1,2,2]
[7,4,8,6,5,1,3,2]=>[8,2,6,1,7,5,4,3]=>[1,7,3,8,2,4,5,6]=>[2,2,4]
[2,7,6,8,5,1,4,3]=>[8,6,3,2,7,1,5,4]=>[1,3,6,7,2,8,4,5]=>[4,2,2]
[1,5,4,7,8,6,2,3]=>[2,7,3,4,8,6,1,5]=>[7,2,6,5,1,3,8,4]=>[1,2,1,3,1]
[7,3,1,6,8,2,5,4]=>[8,2,6,4,7,3,1,5]=>[1,7,3,5,2,6,8,4]=>[2,2,3,1]
[7,1,6,8,5,2,4,3]=>[8,6,3,7,5,2,1,4]=>[1,3,6,2,4,7,8,5]=>[3,4,1]
[3,5,8,7,6,4,1,2]=>[7,8,2,6,1,5,4,3]=>[2,1,7,3,8,4,5,6]=>[1,2,2,3]
[1,5,7,8,6,2,4,3]=>[8,2,6,3,7,5,1,4]=>[1,7,3,6,2,4,8,5]=>[2,2,3,1]
[3,6,2,1,4,7,8,5]=>[1,3,6,8,4,2,5,7]=>[8,6,3,1,5,7,4,2]=>[1,1,1,3,1,1]
[6,8,2,7,5,4,3,1]=>[1,8,7,6,3,5,4,2]=>[8,1,2,3,6,4,5,7]=>[1,4,3]
[5,8,1,7,6,4,3,2]=>[8,1,7,6,5,3,4,2]=>[1,8,2,3,4,6,5,7]=>[2,4,2]
[2,3,4,5,6,7,8,10,11,1,9]=>[10,1,2,3,4,5,6,7,8,11,9]=>[2,11,10,9,8,7,6,5,4,1,3]=>[2,1,1,1,1,1,1,1,2]
[8,6,3,2,1,5,4,7]=>[4,3,7,5,6,2,8,1]=>[5,6,2,4,3,7,1,8]=>[2,2,2,2]
[8,5,3,2,4,1,7,6]=>[4,3,5,2,8,6,7,1]=>[5,6,4,7,1,3,2,8]=>[2,2,2,2]
[7,5,2,4,3,6,8,1]=>[5,3,4,2,6,1,8,7]=>[4,6,5,7,3,8,1,2]=>[2,2,2,2]
[8,5,1,4,6,3,2,7]=>[4,7,6,3,2,5,8,1]=>[5,2,3,6,7,4,1,8]=>[1,4,1,2]
[8,5,1,6,3,4,2,7]=>[5,7,6,3,2,4,8,1]=>[4,2,3,6,7,5,1,8]=>[1,4,1,2]
[8,4,3,6,1,5,2,7]=>[3,2,7,5,6,4,8,1]=>[6,7,2,4,3,5,1,8]=>[2,2,2,2]
[8,4,3,5,2,1,7,6]=>[3,2,5,4,8,6,7,1]=>[6,7,4,5,1,3,2,8]=>[2,2,2,2]
[6,4,3,2,8,7,1,5]=>[3,2,7,1,8,4,6,5]=>[6,7,2,8,1,5,3,4]=>[2,2,2,2]
[8,5,1,4,3,7,2,6]=>[5,4,7,2,8,3,6,1]=>[4,5,2,7,1,6,3,8]=>[2,2,2,2]
[8,5,4,2,1,3,7,6]=>[4,8,5,3,2,6,7,1]=>[5,1,4,6,7,3,2,8]=>[1,4,1,2]
[4,7,3,6,1,8,5,2]=>[8,1,3,7,5,4,2,6]=>[1,8,6,2,4,5,7,3]=>[2,1,4,1]
[7,6,2,4,1,5,8,3]=>[6,3,4,8,5,2,1,7]=>[3,6,5,1,4,7,8,2]=>[2,1,4,1]
[8,1,6,3,7,4,2,5]=>[7,4,6,3,8,2,5,1]=>[2,5,3,6,1,7,4,8]=>[2,2,2,2]
[5,3,8,2,6,7,1,4]=>[7,2,1,4,5,8,6,3]=>[2,7,8,5,4,1,3,6]=>[3,1,1,3]
[8,2,5,1,7,6,3,4]=>[7,3,8,2,6,4,5,1]=>[2,6,1,7,3,5,4,8]=>[2,2,2,2]
[8,2,4,6,3,7,1,5]=>[3,5,7,2,4,8,6,1]=>[6,4,2,7,5,1,3,8]=>[1,1,2,1,3]
[7,2,6,4,3,5,8,1]=>[5,4,6,2,3,1,8,7]=>[4,5,3,7,6,8,1,2]=>[2,2,2,2]
[7,3,6,2,4,5,8,1]=>[2,4,5,6,3,1,8,7]=>[7,5,4,3,6,8,1,2]=>[1,1,1,3,2]
[8,3,7,2,1,4,6,5]=>[2,4,8,5,6,7,3,1]=>[7,5,1,4,3,2,6,8]=>[1,1,2,1,3]
[7,6,4,1,3,2,8,5]=>[5,8,4,3,6,2,1,7]=>[4,1,5,6,3,7,8,2]=>[1,3,3,1]
[7,3,8,2,1,5,6,4]=>[2,4,6,8,5,1,7,3]=>[7,5,3,1,4,8,2,6]=>[1,1,1,3,2]
[6,2,5,7,4,3,8,1]=>[3,6,5,2,1,4,8,7]=>[6,3,4,7,8,5,1,2]=>[1,4,1,2]
[6,2,5,4,8,7,1,3]=>[4,3,7,1,8,2,6,5]=>[5,6,2,8,1,7,3,4]=>[2,2,2,2]
[7,2,4,8,5,1,6,3]=>[8,3,6,2,5,1,7,4]=>[1,6,3,7,4,8,2,5]=>[2,2,2,2]
[4,2,7,6,8,5,1,3]=>[7,1,4,3,8,2,6,5]=>[2,8,5,6,1,7,3,4]=>[2,2,2,2]
[7,1,6,2,8,5,4,3]=>[8,7,6,4,2,3,1,5]=>[1,2,3,5,7,6,8,4]=>[5,2,1]
[7,1,6,3,8,5,2,4]=>[7,8,4,3,6,2,1,5]=>[2,1,5,6,3,7,8,4]=>[1,3,3,1]
[7,2,6,8,1,3,5,4]=>[8,5,6,2,3,1,7,4]=>[1,4,3,7,6,8,2,5]=>[2,2,2,2]
[7,2,8,5,1,3,6,4]=>[8,5,6,2,4,1,7,3]=>[1,4,3,7,5,8,2,6]=>[2,2,2,2]
[7,1,8,5,3,2,6,4]=>[5,8,6,4,7,2,1,3]=>[4,1,3,5,2,7,8,6]=>[1,3,3,1]
[7,1,8,2,5,6,4,3]=>[5,8,7,4,6,2,1,3]=>[4,1,2,5,3,7,8,6]=>[1,3,3,1]
[6,1,5,7,4,8,3,2]=>[3,5,4,1,8,7,2,6]=>[6,4,5,8,1,2,7,3]=>[1,3,3,1]
[4,6,7,3,1,8,5,2]=>[4,1,2,8,7,5,3,6]=>[5,8,7,1,2,4,6,3]=>[2,1,4,1]
[4,2,6,3,1,8,7,5]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[1,3,1,2,1]
[6,1,4,2,5,8,7,3]=>[3,8,5,7,2,1,4,6]=>[6,1,4,2,7,8,5,3]=>[1,2,3,1,1]
[1,5,3,8,4,6,2,7]=>[5,2,7,3,6,8,1,4]=>[4,7,2,6,3,1,8,5]=>[2,2,1,2,1]
[7,2,3,5,8,4,1,6]=>[4,7,2,3,6,1,8,5]=>[5,2,7,6,3,8,1,4]=>[1,2,1,2,2]
[7,6,4,2,8,5,1,3]=>[7,3,8,4,2,1,6,5]=>[2,6,1,5,7,8,3,4]=>[2,4,2]
[1,7,6,4,8,5,3,2]=>[8,4,3,2,7,6,1,5]=>[1,5,6,7,2,3,8,4]=>[4,3,1]
[8,7,4,2,1,5,6,3]=>[4,6,3,8,5,7,2,1]=>[5,3,6,1,4,2,7,8]=>[1,2,2,3]
[8,2,3,5,1,4,6,7]=>[2,3,5,6,4,7,8,1]=>[7,6,4,3,5,2,1,8]=>[1,1,1,2,1,2]
[8,7,4,1,3,2,6,5]=>[5,8,4,3,6,7,2,1]=>[4,1,5,6,3,2,7,8]=>[1,3,1,3]
[7,1,4,8,3,6,2,5]=>[3,5,7,8,6,2,1,4]=>[6,4,2,1,3,7,8,5]=>[1,1,1,4,1]
[3,7,5,8,4,2,1,6]=>[3,7,6,1,5,2,8,4]=>[6,2,3,8,4,7,1,5]=>[1,3,2,2]
[6,1,5,8,3,4,2,7]=>[5,3,7,6,1,8,2,4]=>[4,6,2,3,8,1,7,5]=>[2,3,2,1]
[6,7,5,1,3,2,4,8]=>[6,4,5,1,7,3,2,8]=>[3,5,4,8,2,6,7,1]=>[2,2,3,1]
[5,2,6,1,7,3,4,8]=>[6,7,2,1,4,3,5,8]=>[3,2,7,8,5,6,4,1]=>[1,3,2,1,1]
[4,2,6,8,3,7,1,5]=>[1,5,3,7,8,2,6,4]=>[8,4,6,2,1,7,3,5]=>[1,2,1,2,2]
[6,8,5,1,4,2,3,7]=>[6,7,4,1,5,3,8,2]=>[3,2,5,8,4,6,1,7]=>[1,3,2,2]
[7,8,4,5,1,3,6,2]=>[6,3,8,5,4,1,7,2]=>[3,6,1,4,5,8,2,7]=>[2,4,2]
[6,3,8,1,4,2,7,5]=>[2,5,8,4,1,6,7,3]=>[7,4,1,5,8,3,2,6]=>[1,1,3,1,2]
[4,8,1,5,6,3,7,2]=>[1,4,6,5,8,3,7,2]=>[8,5,3,4,1,6,2,7]=>[1,1,2,2,2]
[1,8,2,6,5,3,7,4]=>[8,6,5,3,4,7,1,2]=>[1,3,4,6,5,2,8,7]=>[4,1,2,1]
[3,8,1,7,2,6,5,4]=>[8,7,1,5,6,3,4,2]=>[1,2,8,4,3,6,5,7]=>[3,1,2,2]
[7,3,8,1,2,6,5,4]=>[8,2,7,4,5,1,6,3]=>[1,7,2,5,4,8,3,6]=>[2,2,2,2]
[8,1,4,2,3,5,7,6]=>[8,4,2,3,5,6,7,1]=>[1,5,7,6,4,3,2,8]=>[3,1,1,1,2]
[8,1,2,4,6,5,7,3]=>[6,4,5,8,2,3,7,1]=>[3,5,4,1,7,6,2,8]=>[2,1,2,1,2]
[5,1,8,3,7,4,6,2]=>[6,1,8,4,7,5,2,3]=>[3,8,1,5,2,4,7,6]=>[2,2,3,1]
[8,4,7,1,5,3,6,2]=>[2,6,5,8,4,7,3,1]=>[7,3,4,1,5,2,6,8]=>[1,2,2,3]
[7,2,5,3,4,6,1,8]=>[4,5,2,3,7,6,1,8]=>[5,4,7,6,2,3,8,1]=>[1,2,1,3,1]
[7,6,4,2,5,3,1,8]=>[7,4,3,6,5,2,1,8]=>[2,5,6,3,4,7,8,1]=>[3,4,1]
[1,7,2,6,3,4,8,5]=>[8,5,6,3,4,1,2,7]=>[1,4,3,6,5,8,7,2]=>[2,2,2,1,1]
[7,2,5,1,6,3,4,8]=>[6,7,2,4,3,5,1,8]=>[3,2,7,5,6,4,8,1]=>[1,2,2,2,1]
[7,3,1,4,6,2,5,8]=>[4,2,6,7,3,5,1,8]=>[5,7,3,2,6,4,8,1]=>[2,1,2,2,1]
[5,8,4,3,1,7,2,6]=>[1,7,4,3,8,5,6,2]=>[8,2,5,6,1,4,3,7]=>[1,3,2,2]
[3,6,8,5,2,4,7,1]=>[5,2,6,1,4,8,7,3]=>[4,7,3,8,5,1,2,6]=>[2,2,1,3]
[1,3,8,4,7,2,6,5]=>[8,4,6,7,2,5,1,3]=>[1,5,3,2,7,4,8,6]=>[2,1,2,2,1]
[3,2,1,4,5,8,6,7]=>[2,1,7,8,3,4,5,6]=>[7,8,2,1,6,5,4,3]=>[2,1,2,1,1,1]
[6,7,1,3,2,8,5,4]=>[8,4,7,3,1,5,2,6]=>[1,5,2,6,8,4,7,3]=>[2,3,2,1]
[1,5,3,2,6,8,4,7]=>[3,5,2,7,8,1,4,6]=>[6,4,7,2,1,8,5,3]=>[1,2,1,2,1,1]
[5,4,3,1,7,2,8,6]=>[3,2,1,8,6,4,5,7]=>[6,7,8,1,3,5,4,2]=>[3,3,1,1]
[5,7,4,2,8,6,1,3]=>[1,7,3,8,4,2,6,5]=>[8,2,6,1,5,7,3,4]=>[1,2,3,2]
[5,4,3,7,8,2,6,1]=>[2,1,6,3,4,8,7,5]=>[7,8,3,6,5,1,2,4]=>[2,2,1,3]
[1,3,6,8,7,2,5,4]=>[3,8,6,7,2,5,1,4]=>[6,1,3,2,7,4,8,5]=>[1,2,2,2,1]
[5,8,7,1,4,2,3,6]=>[6,1,7,4,5,8,3,2]=>[3,8,2,5,4,1,6,7]=>[2,2,1,3]
[2,6,3,7,1,4,5,8]=>[3,5,6,1,2,7,4,8]=>[6,4,3,8,7,2,5,1]=>[1,1,2,1,2,1]
[6,5,1,2,4,7,8,3]=>[5,6,8,3,2,1,4,7]=>[4,3,1,6,7,8,5,2]=>[1,1,4,1,1]
[7,6,8,4,3,1,5,2]=>[8,6,5,4,2,1,7,3]=>[1,3,4,5,7,8,2,6]=>[6,2]
[1,7,6,5,3,2,4,8]=>[6,5,7,4,3,1,2,8]=>[3,4,2,5,6,8,7,1]=>[2,4,1,1]
[2,7,6,5,4,1,3,8]=>[6,7,5,4,1,3,2,8]=>[3,2,4,5,8,6,7,1]=>[1,4,2,1]
[6,2,3,5,8,4,1,7]=>[4,7,2,3,1,6,8,5]=>[5,2,7,6,8,3,1,4]=>[1,2,2,1,2]
[4,7,6,1,5,8,3,2]=>[5,8,1,7,4,3,2,6]=>[4,1,8,2,5,6,7,3]=>[1,2,4,1]
[9,8,7,6,5,4,2,3,1]=>[7,9,8,6,5,4,3,2,1]=>[3,1,2,4,5,6,7,8,9]=>[1,8]
[9,1,3,2,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[6,8,7,5,4,3,2,1,9]=>[2,1,1,1,1,1,2]
[6,8,7,1,5,4,3,2]=>[1,8,7,6,4,5,3,2]=>[8,1,2,3,5,4,6,7]=>[1,4,3]
[9,8,7,1,6,5,4,3,2]=>[9,8,7,6,4,5,3,2,1]=>[1,2,3,4,6,5,7,8,9]=>[5,4]
[9,8,7,6,1,5,4,3,2]=>[9,8,7,5,6,4,3,2,1]=>[1,2,3,5,4,6,7,8,9]=>[4,5]
[9,8,7,6,5,1,4,3,2]=>[9,8,6,7,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9]=>[3,6]
[9,10,1,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,3,1,4,2]=>[1,2,3,4,5,6,8,10,7,9]=>[8,2]
[10,9,1,8,7,6,5,4,3,2]=>[10,9,8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,8,7,9,10]=>[7,3]
[10,9,8,1,7,6,5,4,3,2]=>[10,9,8,7,6,4,5,3,2,1]=>[1,2,3,4,5,7,6,8,9,10]=>[6,4]
[10,9,8,7,1,6,5,4,3,2]=>[10,9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9,10]=>[5,5]
[10,9,8,7,6,1,5,4,3,2]=>[10,9,8,6,7,5,4,3,2,1]=>[1,2,3,5,4,6,7,8,9,10]=>[4,6]
[10,9,8,7,6,5,1,4,3,2]=>[10,9,7,8,6,5,4,3,2,1]=>[1,2,4,3,5,6,7,8,9,10]=>[3,7]
[10,9,8,7,6,5,4,1,3,2]=>[10,8,9,7,6,5,4,3,2,1]=>[1,3,2,4,5,6,7,8,9,10]=>[2,8]
[7,2,6,1,5,8,3,4]=>[7,5,8,2,4,3,1,6]=>[2,4,1,7,5,6,8,3]=>[2,2,3,1]
[4,7,3,8,6,2,5,1]=>[6,8,1,3,2,7,5,4]=>[3,1,8,6,7,2,4,5]=>[1,2,2,3]
[5,4,7,3,8,2,1,6]=>[2,1,4,7,6,3,8,5]=>[7,8,5,2,3,6,1,4]=>[2,1,3,2]
[8,7,2,4,6,3,5,1]=>[4,6,8,3,7,5,2,1]=>[5,3,1,6,2,4,7,8]=>[1,1,2,4]
[1,7,2,8,5,4,3,6]=>[7,6,5,8,3,1,2,4]=>[2,3,4,1,6,8,7,5]=>[3,3,1,1]
[5,4,8,3,6,2,1,7]=>[2,1,4,7,6,5,8,3]=>[7,8,5,2,3,4,1,6]=>[2,1,3,2]
[6,8,2,5,7,1,4,3]=>[8,6,3,1,4,7,5,2]=>[1,3,6,8,5,2,4,7]=>[4,1,3]
[5,8,4,2,7,3,6,1]=>[1,6,3,8,4,7,5,2]=>[8,3,6,1,5,2,4,7]=>[1,2,2,3]
[8,2,7,3,4,5,1,6]=>[4,5,7,2,6,8,3,1]=>[5,4,2,7,3,1,6,8]=>[1,1,2,1,3]
[8,1,5,2,4,6,3,7]=>[5,7,4,2,3,6,8,1]=>[4,2,5,7,6,3,1,8]=>[1,3,1,1,2]
[8,6,1,3,4,5,7,2]=>[4,5,6,8,3,2,7,1]=>[5,4,3,1,6,7,2,8]=>[1,1,1,3,2]
[2,6,8,7,3,4,5,1]=>[5,2,6,8,7,1,4,3]=>[4,7,3,1,2,8,5,6]=>[2,1,3,2]
[1,7,8,5,6,4,2,3]=>[7,4,2,8,6,5,1,3]=>[2,5,7,1,3,4,8,6]=>[3,4,1]
[3,1,7,5,8,2,4,6]=>[6,1,4,7,3,8,2,5]=>[3,8,5,2,6,1,7,4]=>[2,1,2,2,1]
[8,1,3,2,4,6,5,7]=>[3,7,2,4,5,6,8,1]=>[6,2,7,5,4,3,1,8]=>[1,2,1,1,1,2]
[8,1,5,6,4,2,3,7]=>[6,3,7,5,2,4,8,1]=>[3,6,2,4,7,5,1,8]=>[2,3,1,2]
[8,1,6,5,4,3,2,7]=>[7,6,5,4,2,3,8,1]=>[2,3,4,5,7,6,1,8]=>[5,1,2]
[2,6,8,1,5,4,3,7]=>[7,6,4,1,2,5,8,3]=>[2,3,5,8,7,4,1,6]=>[4,1,1,2]
[5,2,1,7,6,3,8,4]=>[8,6,2,1,5,3,4,7]=>[1,3,7,8,4,6,5,2]=>[4,2,1,1]
[3,5,8,2,1,4,7,6]=>[4,1,2,8,5,6,7,3]=>[5,8,7,1,4,3,2,6]=>[2,1,2,1,2]
[4,2,7,5,3,8,6,1]=>[1,4,8,5,2,3,7,6]=>[8,5,1,4,7,6,2,3]=>[1,1,3,1,2]
[6,4,5,1,8,3,2,7]=>[2,7,6,3,1,8,4,5]=>[7,2,3,6,8,1,5,4]=>[1,4,2,1]
[5,4,7,8,3,1,2,6]=>[2,1,6,7,5,3,8,4]=>[7,8,3,2,4,6,1,5]=>[2,1,3,2]
[4,5,8,1,3,7,2,6]=>[1,5,2,7,8,4,6,3]=>[8,4,7,2,1,5,3,6]=>[1,2,1,2,2]
[1,5,3,6,8,7,2,4]=>[4,2,7,8,3,6,1,5]=>[5,7,2,1,6,3,8,4]=>[2,1,2,2,1]
[4,7,2,6,8,3,5,1]=>[6,1,4,8,3,2,7,5]=>[3,8,5,1,6,7,2,4]=>[2,1,3,2]
[6,3,2,8,7,4,5,1]=>[6,8,2,1,7,3,5,4]=>[3,1,7,8,2,6,4,5]=>[1,3,2,2]
[7,4,3,8,5,6,2,1]=>[2,5,8,3,1,7,6,4]=>[7,4,1,6,8,2,3,5]=>[1,1,3,3]
[3,1,5,8,7,6,2,4]=>[7,8,1,3,6,5,2,4]=>[2,1,8,6,3,4,7,5]=>[1,2,1,3,1]
[3,1,8,6,5,7,2,4]=>[7,5,1,4,8,6,2,3]=>[2,4,8,5,1,3,7,6]=>[3,1,3,1]
[1,2,7,6,4,5,8,3]=>[5,6,4,3,8,1,2,7]=>[4,3,5,6,1,8,7,2]=>[1,3,2,1,1]
[7,2,6,5,1,8,3,4]=>[7,8,5,2,4,3,1,6]=>[2,1,4,7,5,6,8,3]=>[1,3,3,1]
[4,2,8,5,6,3,1,7]=>[1,4,7,6,2,5,8,3]=>[8,5,2,3,7,4,1,6]=>[1,1,3,1,2]
[6,4,2,1,8,7,3,5]=>[7,2,8,3,1,6,4,5]=>[2,7,1,6,8,3,5,4]=>[2,3,2,1]
[4,7,3,2,5,1,6,8]=>[1,4,3,6,5,7,2,8]=>[8,5,6,3,4,2,7,1]=>[1,2,2,2,1]
[4,2,5,3,8,7,1,6]=>[3,1,7,8,2,4,6,5]=>[6,8,2,1,7,5,3,4]=>[2,1,2,1,2]
[7,2,5,3,8,4,6,1]=>[6,3,8,2,4,1,7,5]=>[3,6,1,7,5,8,2,4]=>[2,2,2,2]
[3,6,8,1,7,4,5,2]=>[6,2,8,1,7,4,5,3]=>[3,7,1,8,2,5,4,6]=>[2,2,2,2]
[8,7,3,2,5,4,6,1]=>[3,6,4,5,8,7,2,1]=>[6,3,5,4,1,2,7,8]=>[1,2,1,4]
[7,5,6,1,8,3,2,4]=>[7,6,2,8,4,3,1,5]=>[2,3,7,1,5,6,8,4]=>[3,4,1]
[4,5,6,2,7,3,1,8]=>[1,2,7,4,3,6,5,8]=>[8,7,2,5,6,3,4,1]=>[1,1,3,2,1]
[5,3,4,7,1,6,2,8]=>[2,3,1,7,5,6,4,8]=>[7,6,8,2,4,3,5,1]=>[1,2,2,2,1]
[3,5,1,4,6,8,2,7]=>[1,4,5,2,7,8,3,6]=>[8,5,4,7,2,1,6,3]=>[1,1,2,1,2,1]
[2,3,7,4,1,8,6,5]=>[8,4,7,1,2,5,3,6]=>[1,5,2,8,7,4,6,3]=>[2,2,1,2,1]
[2,4,5,1,8,6,3,7]=>[2,3,7,1,6,8,4,5]=>[7,6,2,8,3,1,5,4]=>[1,1,2,1,2,1]
[6,3,7,1,5,2,4,8]=>[2,6,7,4,1,5,3,8]=>[7,3,2,5,8,4,6,1]=>[1,1,3,2,1]
[4,1,3,7,8,2,6,5]=>[1,8,6,3,4,7,2,5]=>[8,1,3,6,5,2,7,4]=>[1,3,1,2,1]
[7,1,4,8,6,5,2,3]=>[7,8,3,6,5,2,1,4]=>[2,1,6,3,4,7,8,5]=>[1,2,4,1]
[8,3,4,2,1,7,5,6]=>[2,4,3,7,8,5,6,1]=>[7,5,6,2,1,4,3,8]=>[1,2,1,2,2]
[6,5,2,4,8,7,1,3]=>[4,7,2,1,8,3,6,5]=>[5,2,7,8,1,6,3,4]=>[1,3,2,2]
[8,5,2,4,1,3,7,6]=>[8,3,5,4,2,6,7,1]=>[1,6,4,5,7,3,2,8]=>[2,3,1,2]
[5,1,2,4,3,6,8,7]=>[4,8,2,3,1,5,6,7]=>[5,1,7,6,8,4,3,2]=>[1,2,2,1,1,1]
[8,6,2,7,5,3,1,4]=>[7,6,8,3,2,5,4,1]=>[2,3,1,6,7,4,5,8]=>[2,3,3]
[6,2,1,5,8,3,4,7]=>[6,2,4,7,1,8,3,5]=>[3,7,5,2,8,1,6,4]=>[2,1,2,2,1]
[2,3,8,7,1,5,4,6]=>[7,5,6,8,1,2,4,3]=>[2,4,3,1,8,7,5,6]=>[2,1,2,1,2]
[4,3,8,1,5,2,6,7]=>[2,1,6,4,5,7,8,3]=>[7,8,3,5,4,2,1,6]=>[2,2,1,1,2]
[4,1,3,6,7,2,8,5]=>[4,1,8,3,6,2,5,7]=>[5,8,1,6,3,7,4,2]=>[2,2,2,1,1]
[7,1,4,5,8,2,6,3]=>[3,4,8,6,7,2,1,5]=>[6,5,1,3,2,7,8,4]=>[1,1,2,3,1]
[6,1,3,2,4,5,8,7]=>[3,8,2,4,5,1,6,7]=>[6,1,7,5,4,8,3,2]=>[1,2,1,2,1,1]
[7,8,1,6,5,2,4,3]=>[8,6,7,5,3,1,4,2]=>[1,3,2,4,6,8,5,7]=>[2,4,2]
[7,4,8,6,5,1,2,3]=>[2,6,7,1,8,5,4,3]=>[7,3,2,8,1,4,5,6]=>[1,1,2,4]
[3,7,8,6,5,1,2,4]=>[6,7,2,8,1,5,4,3]=>[3,2,7,1,8,4,5,6]=>[1,2,2,3]
[8,4,5,7,2,6,3,1]=>[2,3,8,5,7,6,4,1]=>[7,6,1,4,2,3,5,8]=>[1,1,2,4]
[4,5,8,2,7,3,1,6]=>[1,2,7,4,6,8,5,3]=>[8,7,2,5,3,1,4,6]=>[1,1,2,1,3]
[6,5,8,2,7,3,1,4]=>[7,4,2,1,6,8,5,3]=>[2,5,7,8,3,1,4,6]=>[4,1,3]
[6,4,8,2,7,3,1,5]=>[2,7,4,1,6,8,5,3]=>[7,2,5,8,3,1,4,6]=>[1,3,1,3]
[7,8,1,3,6,4,2,5]=>[7,4,6,8,3,1,5,2]=>[2,5,3,1,6,8,4,7]=>[2,1,3,2]
[4,5,7,8,3,2,1,6]=>[7,1,2,6,5,3,8,4]=>[2,8,7,3,4,6,1,5]=>[2,1,3,2]
[5,7,4,2,3,6,8,1]=>[4,1,5,3,6,2,8,7]=>[5,8,4,6,3,7,1,2]=>[2,2,2,2]
[5,4,7,3,2,8,1,6]=>[2,1,5,4,7,3,8,6]=>[7,8,4,5,2,6,1,3]=>[2,2,2,2]
[6,8,3,2,4,5,1,7]=>[4,3,5,1,7,6,8,2]=>[5,6,4,8,2,3,1,7]=>[2,2,2,2]
[6,4,3,8,5,1,2,7]=>[3,2,6,1,7,5,8,4]=>[6,7,3,8,2,4,1,5]=>[2,2,2,2]
[5,4,6,8,2,3,1,7]=>[2,1,5,3,7,6,8,4]=>[7,8,4,6,2,3,1,5]=>[2,2,2,2]
[6,4,8,5,1,2,3,7]=>[5,2,6,1,7,4,8,3]=>[4,7,3,8,2,5,1,6]=>[2,2,2,2]
[5,4,7,8,2,1,3,6]=>[2,1,6,5,7,3,8,4]=>[7,8,3,4,2,6,1,5]=>[2,2,2,2]
[5,8,6,3,1,2,4,7]=>[5,1,6,4,7,3,8,2]=>[4,8,3,5,2,6,1,7]=>[2,2,2,2]
[5,6,1,3,2,4,8,7]=>[4,8,3,1,5,2,6,7]=>[5,1,6,8,4,7,3,2]=>[1,3,2,1,1]
[8,1,5,4,6,2,7,3]=>[4,3,8,6,2,5,7,1]=>[5,6,1,3,7,4,2,8]=>[2,3,1,2]
[4,3,8,1,2,5,7,6]=>[2,1,8,4,5,6,7,3]=>[7,8,1,5,4,3,2,6]=>[2,2,1,1,2]
[4,6,3,2,8,5,7,1]=>[1,3,6,2,8,4,7,5]=>[8,6,3,7,1,5,2,4]=>[1,1,2,2,2]
[5,3,7,2,1,8,6,4]=>[8,2,1,4,7,5,3,6]=>[1,7,8,5,2,4,6,3]=>[3,1,3,1]
[7,4,3,2,5,1,8,6]=>[4,3,2,5,8,6,1,7]=>[5,6,7,4,1,3,8,2]=>[3,1,3,1]
[5,4,8,3,7,2,1,6]=>[2,1,4,7,6,8,5,3]=>[7,8,5,2,3,1,4,6]=>[2,1,2,3]
[3,6,8,5,2,1,7,4]=>[5,2,8,1,6,4,7,3]=>[4,7,1,8,3,5,2,6]=>[2,2,2,2]
[6,1,5,4,7,2,8,3]=>[4,3,8,6,2,1,5,7]=>[5,6,1,3,7,8,4,2]=>[2,4,1,1]
[1,3,6,5,8,2,7,4]=>[4,3,8,2,6,7,1,5]=>[5,6,1,7,3,2,8,4]=>[2,2,1,2,1]
[5,4,8,3,2,7,1,6]=>[2,1,5,4,7,8,6,3]=>[7,8,4,5,2,1,3,6]=>[2,2,1,3]
[5,4,3,7,8,2,1,6]=>[2,1,7,3,6,4,8,5]=>[7,8,2,6,3,5,1,4]=>[2,2,2,2]
[3,4,5,6,7,8,2,9,1]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,2,2]
[3,4,5,6,7,8,9,2,10,1]=>[1,2,3,4,5,6,8,7,10,9]=>[10,9,8,7,6,5,3,4,1,2]=>[1,1,1,1,1,1,2,2]
[3,4,5,6,7,2,1,9,8]=>[1,2,3,4,6,5,9,7,8]=>[9,8,7,6,4,5,1,3,2]=>[1,1,1,1,2,2,1]
[1,4,8,6,3,2,7,5]=>[5,8,2,6,4,7,1,3]=>[4,1,7,3,5,2,8,6]=>[1,2,2,2,1]
[6,7,2,5,3,8,4,1]=>[8,5,3,1,4,2,7,6]=>[1,4,6,8,5,7,2,3]=>[4,2,2]
[6,3,4,8,1,2,7,5]=>[2,3,8,5,1,6,7,4]=>[7,6,1,4,8,3,2,5]=>[1,1,3,1,2]
[2,6,3,1,5,8,7,4]=>[8,3,5,1,2,7,4,6]=>[1,6,4,8,7,2,5,3]=>[2,2,1,2,1]
[6,1,3,5,8,7,4,2]=>[8,4,7,3,1,6,2,5]=>[1,5,2,6,8,3,7,4]=>[2,3,2,1]
[3,5,8,7,4,6,2,1]=>[5,8,2,7,1,6,4,3]=>[4,1,7,2,8,3,5,6]=>[1,2,2,3]
[6,8,5,7,3,4,2,1]=>[1,5,3,8,7,6,4,2]=>[8,4,6,1,2,3,5,7]=>[1,2,5]
[5,3,6,8,4,2,1,7]=>[3,1,7,2,6,5,8,4]=>[6,8,2,7,3,4,1,5]=>[2,2,2,2]
[5,1,6,8,4,7,3,2]=>[3,1,5,8,7,6,2,4]=>[6,8,4,1,2,3,7,5]=>[2,1,4,1]
[6,2,8,3,4,1,5,7]=>[4,6,2,5,1,7,8,3]=>[5,3,7,4,8,2,1,6]=>[1,2,2,1,2]
[2,4,1,8,7,6,3,5]=>[7,8,2,6,1,5,3,4]=>[2,1,7,3,8,4,6,5]=>[1,2,2,2,1]
[1,3,5,8,4,7,2,6]=>[3,5,7,8,2,6,1,4]=>[6,4,2,1,7,3,8,5]=>[1,1,1,2,2,1]
[5,8,7,2,4,1,3,6]=>[4,1,6,7,5,8,3,2]=>[5,8,3,2,4,1,6,7]=>[2,1,2,3]
[4,1,3,5,6,2,8,7]=>[3,4,1,5,8,2,6,7]=>[6,5,8,4,1,7,3,2]=>[1,2,1,2,1,1]
[6,3,8,5,1,7,4,2]=>[8,7,2,1,5,4,6,3]=>[1,2,7,8,4,5,3,6]=>[4,2,2]
[6,4,8,7,3,5,2,1]=>[5,1,8,2,7,6,4,3]=>[4,8,1,7,2,3,5,6]=>[2,2,4]
[8,2,3,5,6,1,4,7]=>[6,2,3,4,7,5,8,1]=>[3,7,6,5,2,4,1,8]=>[2,1,1,2,2]
[4,3,5,6,8,2,7,1]=>[2,1,3,4,6,8,7,5]=>[7,8,6,5,3,1,2,4]=>[2,1,1,1,3]
[8,2,3,4,6,1,7,5]=>[8,2,3,4,6,5,7,1]=>[1,7,6,5,3,4,2,8]=>[2,1,1,2,2]
[2,7,4,3,8,1,5,6]=>[4,3,6,7,1,2,8,5]=>[5,6,3,2,8,7,1,4]=>[2,1,2,1,2]
[3,8,2,7,6,4,1,5]=>[7,6,8,1,3,5,4,2]=>[2,3,1,8,6,4,5,7]=>[2,2,1,3]
[5,3,6,2,1,8,4,7]=>[2,4,1,7,3,8,5,6]=>[7,5,8,2,6,1,4,3]=>[1,2,2,2,1]
[4,3,8,6,2,7,1,5]=>[1,5,7,2,4,8,6,3]=>[8,4,2,7,5,1,3,6]=>[1,1,2,1,3]
[3,1,6,8,2,7,5,4]=>[3,8,1,7,5,6,2,4]=>[6,1,8,2,4,3,7,5]=>[1,2,2,2,1]
[5,8,7,2,4,6,1,3]=>[1,7,4,5,8,6,3,2]=>[8,2,5,4,1,3,6,7]=>[1,2,1,4]
[1,5,2,8,7,6,4,3]=>[8,2,7,6,5,1,3,4]=>[1,7,2,3,4,8,6,5]=>[2,4,1,1]
[4,7,1,2,6,5,8,3]=>[1,6,5,8,3,4,2,7]=>[8,3,4,1,6,5,7,2]=>[1,2,2,2,1]
[4,2,5,6,8,7,3,1]=>[1,8,3,4,7,2,6,5]=>[8,1,6,5,2,7,3,4]=>[1,2,1,2,2]
[8,2,5,1,6,3,7,4]=>[8,6,2,4,3,5,7,1]=>[1,3,7,5,6,4,2,8]=>[3,2,1,2]
[8,3,4,5,1,6,7,2]=>[2,3,6,4,8,5,7,1]=>[7,6,3,5,1,4,2,8]=>[1,1,2,2,2]
[7,8,1,5,6,3,2,4]=>[7,6,4,8,3,1,5,2]=>[2,3,5,1,6,8,4,7]=>[3,3,2]
[1,7,8,3,2,5,4,6]=>[4,7,5,6,2,8,1,3]=>[5,2,4,3,7,1,8,6]=>[1,2,2,2,1]
[7,8,1,3,2,5,6,4]=>[4,6,8,3,5,1,7,2]=>[5,3,1,6,4,8,2,7]=>[1,1,2,2,2]
[7,8,1,3,5,2,4,6]=>[4,6,7,3,5,1,8,2]=>[5,3,2,6,4,8,1,7]=>[1,1,2,2,2]
[1,3,7,8,5,2,4,6]=>[6,7,5,2,3,8,1,4]=>[3,2,4,7,6,1,8,5]=>[1,3,1,2,1]
[1,7,8,3,5,2,6,4]=>[8,4,6,5,2,7,1,3]=>[1,5,3,4,7,2,8,6]=>[2,3,2,1]
[1,7,8,3,2,5,6,4]=>[4,6,8,5,2,7,1,3]=>[5,3,1,4,7,2,8,6]=>[1,1,3,2,1]
[3,7,8,5,4,6,1,2]=>[7,5,4,1,2,8,6,3]=>[2,4,5,8,7,1,3,6]=>[4,1,3]
[3,5,7,6,4,8,1,2]=>[7,2,5,1,4,3,8,6]=>[2,7,4,8,5,6,1,3]=>[2,2,2,2]
[1,3,7,8,5,4,6,2]=>[6,5,3,8,2,7,1,4]=>[3,4,6,1,7,2,8,5]=>[3,2,2,1]
[1,3,7,8,5,4,2,6]=>[7,6,5,2,3,8,1,4]=>[2,3,4,7,6,1,8,5]=>[4,1,2,1]
[1,3,7,8,2,5,4,6]=>[7,5,6,2,3,8,1,4]=>[2,4,3,7,6,1,8,5]=>[2,2,1,2,1]
[1,3,2,7,8,5,4,6]=>[7,6,2,4,8,1,3,5]=>[2,3,7,5,1,8,6,4]=>[3,1,2,1,1]
[1,5,7,6,8,3,2,4]=>[7,2,6,4,3,8,1,5]=>[2,7,3,5,6,1,8,4]=>[2,3,2,1]
[3,5,4,7,8,6,1,2]=>[2,7,1,3,4,8,6,5]=>[7,2,8,6,5,1,3,4]=>[1,2,1,1,3]
[3,5,7,6,8,4,1,2]=>[7,2,4,1,3,8,6,5]=>[2,7,5,8,6,1,3,4]=>[2,2,1,3]
[3,5,7,4,6,8,1,2]=>[2,4,7,1,5,3,8,6]=>[7,5,2,8,4,6,1,3]=>[1,1,2,2,2]
[6,5,8,4,3,7,1,2]=>[2,1,7,5,4,8,6,3]=>[7,8,2,4,5,1,3,6]=>[2,3,3]
[6,7,3,1,5,2,4,8]=>[6,3,7,4,1,5,2,8]=>[3,6,2,5,8,4,7,1]=>[2,3,2,1]
[5,2,4,1,8,3,6,7]=>[6,2,3,1,7,8,4,5]=>[3,7,6,8,2,1,5,4]=>[2,2,1,2,1]
[2,1,7,4,3,8,5,6]=>[4,7,8,1,5,2,3,6]=>[5,2,1,8,4,7,6,3]=>[1,1,2,2,1,1]
[4,1,5,7,6,3,8,2]=>[1,6,3,5,4,8,2,7]=>[8,3,6,4,5,1,7,2]=>[1,2,2,2,1]
[1,4,6,7,3,5,2,8]=>[5,2,3,7,6,1,4,8]=>[4,7,6,2,3,8,5,1]=>[2,1,3,1,1]
[1,4,8,2,6,7,5,3]=>[5,8,2,7,4,6,1,3]=>[4,1,7,2,5,3,8,6]=>[1,2,2,2,1]
[1,7,3,2,4,5,6,8]=>[4,3,5,6,7,1,2,8]=>[5,6,4,3,2,8,7,1]=>[2,1,1,2,1,1]
[1,7,3,2,4,5,8,6]=>[3,8,4,5,6,1,2,7]=>[6,1,5,4,3,8,7,2]=>[1,2,1,2,1,1]
[1,6,4,3,2,5,7,8]=>[5,4,3,6,1,2,7,8]=>[4,5,6,3,8,7,2,1]=>[3,2,1,1,1]
[4,2,6,5,3,1,7,8]=>[1,6,5,2,4,3,7,8]=>[8,3,4,7,5,6,2,1]=>[1,3,2,1,1]
[5,2,1,6,8,7,4,3]=>[8,4,1,7,2,6,3,5]=>[1,5,8,2,7,3,6,4]=>[3,2,2,1]
[1,3,5,8,6,2,7,4]=>[8,3,6,2,5,7,1,4]=>[1,6,3,7,4,2,8,5]=>[2,2,1,2,1]
[2,3,8,4,1,7,6,5]=>[8,4,7,1,2,5,6,3]=>[1,5,2,8,7,4,3,6]=>[2,2,1,1,2]
[3,7,8,5,4,2,6,1]=>[6,5,4,1,2,8,7,3]=>[3,4,5,8,7,1,2,6]=>[4,1,3]
[8,3,2,7,5,6,1,4]=>[7,2,5,8,3,6,4,1]=>[2,7,4,1,6,3,5,8]=>[2,1,2,3]
[1,3,8,5,7,4,2,6]=>[4,7,6,8,2,5,1,3]=>[5,2,3,1,7,4,8,6]=>[1,2,2,2,1]
[1,2,3,7,5,4,6,8]=>[6,5,7,1,2,3,4,8]=>[3,4,2,8,7,6,5,1]=>[2,2,1,1,1,1]
[1,4,2,8,6,3,5,7]=>[2,6,7,5,8,1,3,4]=>[7,3,2,4,1,8,6,5]=>[1,1,2,2,1,1]
[2,8,6,3,5,7,4,1]=>[5,8,4,3,7,1,6,2]=>[4,1,5,6,2,8,3,7]=>[1,3,2,2]
[6,1,8,2,5,3,4,7]=>[6,7,4,5,1,8,2,3]=>[3,2,5,4,8,1,7,6]=>[1,2,2,2,1]
[3,8,6,4,2,7,1,5]=>[5,4,7,1,3,8,6,2]=>[4,5,2,8,6,1,3,7]=>[2,2,1,3]
[1,5,4,2,3,6,8,7]=>[8,4,3,1,2,5,6,7]=>[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]
[6,1,5,2,3,4,8,7]=>[8,4,5,2,3,1,6,7]=>[1,5,4,7,6,8,3,2]=>[2,2,2,1,1]
[3,1,2,5,8,7,4,6]=>[1,7,8,4,6,2,3,5]=>[8,2,1,5,3,7,6,4]=>[1,1,2,2,1,1]
[6,5,2,1,8,4,7,3]=>[6,8,3,2,1,7,4,5]=>[3,1,6,7,8,2,5,4]=>[1,4,2,1]
[5,6,2,4,3,8,1,7]=>[5,3,1,4,2,7,8,6]=>[4,6,8,5,7,2,1,3]=>[3,2,1,2]
[3,7,5,2,8,1,4,6]=>[4,6,1,3,7,2,8,5]=>[5,3,8,6,2,7,1,4]=>[1,2,1,2,2]
[5,1,4,7,3,2,8,6]=>[3,5,1,8,6,2,4,7]=>[6,4,8,1,3,7,5,2]=>[1,2,3,1,1]
[2,3,5,4,8,6,1,7]=>[3,7,1,2,4,6,8,5]=>[6,2,8,7,5,3,1,4]=>[1,2,1,1,1,2]
[2,3,6,4,7,5,1,8]=>[7,4,1,2,3,6,5,8]=>[2,5,8,7,6,3,4,1]=>[3,1,1,2,1]
[2,3,5,7,4,8,1,6]=>[3,5,7,1,2,4,8,6]=>[6,4,2,8,7,5,1,3]=>[1,1,2,1,1,2]
[2,3,7,6,1,5,8,4]=>[6,8,5,1,2,4,3,7]=>[3,1,4,8,7,5,6,2]=>[1,3,1,2,1]
[8,3,2,4,1,7,6,5]=>[2,8,3,4,7,5,6,1]=>[7,1,6,5,2,4,3,8]=>[1,2,1,2,2]
[3,7,6,1,2,5,8,4]=>[6,8,1,4,5,3,2,7]=>[3,1,8,5,4,6,7,2]=>[1,2,1,3,1]
[4,7,1,6,8,5,3,2]=>[4,8,1,7,6,3,2,5]=>[5,1,8,2,3,6,7,4]=>[1,2,4,1]
[4,1,5,8,6,2,3,7]=>[3,1,6,7,5,8,2,4]=>[6,8,3,2,4,1,7,5]=>[2,1,2,2,1]
[5,3,4,6,2,8,7,1]=>[2,3,1,4,8,5,7,6]=>[7,6,8,5,1,4,2,3]=>[1,2,1,2,2]
[5,4,8,6,3,7,1,2]=>[1,7,2,5,4,8,6,3]=>[8,2,7,4,5,1,3,6]=>[1,2,2,3]
[5,7,3,4,8,2,6,1]=>[3,1,4,6,2,8,7,5]=>[6,8,5,3,7,1,2,4]=>[2,1,2,3]
[5,6,4,2,7,8,3,1]=>[1,5,3,2,8,4,7,6]=>[8,4,6,7,1,5,2,3]=>[1,3,2,2]
[6,5,2,3,7,4,1,8]=>[7,3,4,2,1,6,5,8]=>[2,6,5,7,8,3,4,1]=>[2,3,2,1]
[6,5,2,3,1,8,7,4]=>[8,3,4,2,1,7,5,6]=>[1,6,5,7,8,2,4,3]=>[2,3,2,1]
[6,5,3,7,4,1,2,8]=>[3,6,2,1,7,5,4,8]=>[6,3,7,8,2,4,5,1]=>[1,3,3,1]
[6,4,7,5,3,8,1,2]=>[7,2,1,5,4,3,8,6]=>[2,7,8,4,5,6,1,3]=>[3,3,2]
[5,7,6,4,8,3,1,2]=>[7,1,4,3,2,8,6,5]=>[2,8,5,6,7,1,3,4]=>[2,3,3]
[5,7,4,8,3,1,6,2]=>[1,3,8,6,5,2,7,4]=>[8,6,1,3,4,7,2,5]=>[1,1,4,2]
[3,1,4,7,5,2,8,6]=>[1,5,8,3,6,2,4,7]=>[8,4,1,6,3,7,5,2]=>[1,1,2,2,1,1]
[4,3,5,1,8,7,2,6]=>[2,1,3,7,8,6,4,5]=>[7,8,6,2,1,3,5,4]=>[2,1,1,3,1]
[2,5,6,8,3,1,7,4]=>[2,5,3,8,1,6,7,4]=>[7,4,6,1,8,3,2,5]=>[1,2,2,1,2]
[7,1,4,5,3,6,2,8]=>[3,5,4,7,2,6,1,8]=>[6,4,5,2,7,3,8,1]=>[1,2,2,2,1]
[1,7,2,4,5,3,6,8]=>[4,6,3,5,7,1,2,8]=>[5,3,6,4,2,8,7,1]=>[1,2,1,2,1,1]
[1,7,4,5,3,2,6,8]=>[3,6,5,4,7,1,2,8]=>[6,3,4,5,2,8,7,1]=>[1,3,2,1,1]
[1,6,4,7,3,5,2,8]=>[3,5,2,7,6,1,4,8]=>[6,4,7,2,3,8,5,1]=>[1,2,3,1,1]
[3,5,6,4,8,2,1,7]=>[2,4,1,3,7,6,8,5]=>[7,5,8,6,2,3,1,4]=>[1,2,1,2,2]
[1,6,4,7,5,2,3,8]=>[3,6,2,7,5,1,4,8]=>[6,3,7,2,4,8,5,1]=>[1,2,3,1,1]
[1,5,2,6,7,4,3,8]=>[4,2,7,6,1,3,5,8]=>[5,7,2,3,8,6,4,1]=>[2,3,1,1,1]
[8,5,6,1,4,3,7,2]=>[6,5,2,8,4,3,7,1]=>[3,4,7,1,5,6,2,8]=>[3,3,2]
[6,4,5,8,2,3,1,7]=>[2,5,3,1,7,6,8,4]=>[7,4,6,8,2,3,1,5]=>[1,3,2,2]
[8,6,1,3,2,5,7,4]=>[4,6,8,3,5,2,7,1]=>[5,3,1,6,4,7,2,8]=>[1,1,2,2,2]
[7,5,8,1,4,6,3,2]=>[5,2,8,7,4,1,6,3]=>[4,7,1,2,5,8,3,6]=>[2,4,2]
[4,2,6,7,8,1,5,3]=>[1,3,8,6,2,4,7,5]=>[8,6,1,3,7,5,2,4]=>[1,1,3,1,2]
[3,4,6,7,8,1,5,2]=>[3,8,1,2,6,4,7,5]=>[6,1,8,7,3,5,2,4]=>[1,2,1,2,2]
[4,7,3,8,5,1,6,2]=>[8,1,3,6,5,2,7,4]=>[1,8,6,3,4,7,2,5]=>[2,1,3,2]
[4,3,2,7,5,8,1,6]=>[2,1,5,7,3,4,8,6]=>[7,8,4,2,6,5,1,3]=>[2,1,2,1,2]
[4,8,5,3,2,6,1,7]=>[5,1,4,3,7,6,8,2]=>[4,8,5,6,2,3,1,7]=>[2,2,2,2]
[2,8,4,5,3,6,1,7]=>[3,5,4,7,1,6,8,2]=>[6,4,5,2,8,3,1,7]=>[1,2,2,1,2]
[8,1,5,3,2,4,7,6]=>[4,8,5,2,3,6,7,1]=>[5,1,4,7,6,3,2,8]=>[1,3,1,1,2]
[7,8,4,1,3,6,5,2]=>[8,5,3,7,4,1,6,2]=>[1,4,6,2,5,8,3,7]=>[3,3,2]
[8,6,1,3,2,7,4,5]=>[4,7,8,3,5,2,6,1]=>[5,2,1,6,4,7,3,8]=>[1,1,2,2,2]
[7,3,8,2,4,1,6,5]=>[2,4,5,8,6,1,7,3]=>[7,5,4,1,3,8,2,6]=>[1,1,1,3,2]
[6,2,3,7,8,1,5,4]=>[8,6,2,3,1,4,7,5]=>[1,3,7,6,8,5,2,4]=>[3,2,1,2]
[6,3,7,8,1,5,4,2]=>[8,7,2,1,5,3,6,4]=>[1,2,7,8,4,6,3,5]=>[4,2,2]
[2,6,3,7,8,1,5,4]=>[8,6,3,1,2,4,7,5]=>[1,3,6,8,7,5,2,4]=>[4,1,1,2]
[7,5,8,1,6,4,2,3]=>[7,2,8,6,4,1,5,3]=>[2,7,1,3,5,8,4,6]=>[2,4,2]
[8,1,4,3,7,5,6,2]=>[3,6,8,4,7,2,5,1]=>[6,3,1,5,2,7,4,8]=>[1,1,2,2,2]
[1,4,8,5,3,2,6,7]=>[6,2,5,4,7,8,1,3]=>[3,7,4,5,2,1,8,6]=>[2,2,1,2,1]
[8,2,7,6,4,1,5,3]=>[8,6,5,7,2,4,3,1]=>[1,3,4,2,7,5,6,8]=>[3,2,3]
[6,8,2,7,3,1,5,4]=>[5,8,3,1,6,7,4,2]=>[4,1,6,8,3,2,5,7]=>[1,3,1,3]
[8,2,6,3,4,1,7,5]=>[4,5,8,2,6,3,7,1]=>[5,4,1,7,3,6,2,8]=>[1,1,2,2,2]
[6,1,2,8,5,3,7,4]=>[8,6,5,7,2,1,3,4]=>[1,3,4,2,7,8,6,5]=>[3,3,1,1]
[7,5,2,8,1,6,3,4]=>[7,8,3,2,5,1,6,4]=>[2,1,6,7,4,8,3,5]=>[1,3,2,2]
[4,8,5,7,1,3,2,6]=>[7,1,5,3,6,8,4,2]=>[2,8,4,6,3,1,5,7]=>[2,2,1,3]
[3,4,7,2,1,5,8,6]=>[1,2,4,8,5,6,3,7]=>[8,7,5,1,4,3,6,2]=>[1,1,1,2,2,1]
[4,8,2,7,1,3,6,5]=>[1,8,3,5,6,7,4,2]=>[8,1,6,4,3,2,5,7]=>[1,2,1,1,3]
[5,2,1,8,7,4,6,3]=>[6,1,8,7,2,5,3,4]=>[3,8,1,2,7,4,6,5]=>[2,3,2,1]
[8,2,1,7,4,6,3,5]=>[5,7,8,2,6,3,4,1]=>[4,2,1,7,3,6,5,8]=>[1,1,2,2,2]
[4,2,5,8,3,6,7,1]=>[3,1,5,6,8,2,7,4]=>[6,8,4,3,1,7,2,5]=>[2,1,1,2,2]
[4,1,5,6,8,2,7,3]=>[3,1,4,8,6,7,2,5]=>[6,8,5,1,3,2,7,4]=>[2,1,2,2,1]
[4,5,2,8,7,3,1,6]=>[1,2,7,6,8,3,5,4]=>[8,7,2,3,1,6,4,5]=>[1,1,2,2,2]
[4,8,5,3,1,6,7,2]=>[6,1,4,3,8,5,7,2]=>[3,8,5,6,1,4,2,7]=>[2,2,2,2]
[6,2,3,1,7,8,5,4]=>[5,8,2,3,1,7,4,6]=>[4,1,7,6,8,2,5,3]=>[1,2,2,2,1]
[5,2,3,6,8,4,7,1]=>[4,6,1,8,2,3,7,5]=>[5,3,8,1,7,6,2,4]=>[1,2,2,1,2]
[6,2,1,7,8,4,3,5]=>[7,6,2,4,1,8,3,5]=>[2,3,7,5,8,1,6,4]=>[3,2,2,1]
[5,2,1,3,8,4,7,6]=>[8,2,6,1,7,3,4,5]=>[1,7,3,8,2,6,5,4]=>[2,2,2,1,1]
[6,2,7,8,3,5,4,1]=>[8,5,3,1,7,2,6,4]=>[1,4,6,8,2,7,3,5]=>[4,2,2]
[5,1,2,8,4,3,7,6]=>[5,8,6,1,7,2,3,4]=>[4,1,3,8,2,7,6,5]=>[1,3,2,1,1]
[6,7,8,3,2,5,4,1]=>[4,1,8,5,2,7,6,3]=>[5,8,1,4,7,2,3,6]=>[2,3,3]
[5,7,2,6,4,8,1,3]=>[1,7,5,3,4,2,8,6]=>[8,2,4,6,5,7,1,3]=>[1,3,2,2]
[6,2,3,4,7,8,5,1]=>[5,8,2,3,1,4,7,6]=>[4,1,7,6,8,5,2,3]=>[1,2,2,1,2]
[7,2,1,8,4,3,5,6]=>[6,2,5,7,8,3,1,4]=>[3,7,4,2,1,6,8,5]=>[2,1,1,3,1]
[6,2,1,3,7,5,8,4]=>[6,2,5,8,3,1,4,7]=>[3,7,4,1,6,8,5,2]=>[2,1,3,1,1]
[6,8,7,3,4,5,1,2]=>[4,1,7,5,8,6,3,2]=>[5,8,2,4,1,3,6,7]=>[2,2,4]
[6,2,3,7,8,1,4,5]=>[6,7,2,3,1,4,8,5]=>[3,2,7,6,8,5,1,4]=>[1,2,2,1,2]
[7,4,3,2,5,8,1,6]=>[4,3,2,5,7,1,8,6]=>[5,6,7,4,2,8,1,3]=>[3,1,2,2]
[7,2,4,3,5,8,1,6]=>[4,2,3,5,7,1,8,6]=>[5,7,6,4,2,8,1,3]=>[2,1,1,2,2]
[1,7,6,4,2,3,5,8]=>[5,6,4,7,3,1,2,8]=>[4,3,5,2,6,8,7,1]=>[1,2,3,1,1]
[1,3,2,5,8,6,4,7]=>[7,2,4,6,8,1,3,5]=>[2,7,5,3,1,8,6,4]=>[2,1,1,2,1,1]
[1,7,5,8,4,2,3,6]=>[6,3,7,5,2,8,1,4]=>[3,6,2,4,7,1,8,5]=>[2,3,2,1]
[5,7,2,4,3,6,8,1]=>[5,3,1,4,6,2,8,7]=>[4,6,8,5,3,7,1,2]=>[3,1,2,2]
[2,8,3,6,1,7,4,5]=>[7,8,3,5,1,4,6,2]=>[2,1,6,4,8,5,3,7]=>[1,2,2,1,2]
[4,3,1,8,5,2,6,7]=>[2,1,6,5,7,8,3,4]=>[7,8,3,4,2,1,6,5]=>[2,2,1,2,1]
[1,8,4,5,6,2,7,3]=>[3,4,8,6,5,7,1,2]=>[6,5,1,3,4,2,8,7]=>[1,1,3,2,1]
[8,2,5,3,1,7,4,6]=>[4,7,2,3,8,5,6,1]=>[5,2,7,6,1,4,3,8]=>[1,2,1,2,2]
[6,3,5,8,1,7,4,2]=>[3,8,2,1,7,5,6,4]=>[6,1,7,8,2,4,3,5]=>[1,3,2,2]
[3,5,4,8,6,1,7,2]=>[2,8,1,3,6,5,7,4]=>[7,1,8,6,3,4,2,5]=>[1,2,1,2,2]
[5,7,6,1,2,8,3,4]=>[7,1,8,4,5,3,2,6]=>[2,8,1,5,4,6,7,3]=>[2,2,3,1]
[7,4,6,5,1,8,2,3]=>[2,7,8,5,4,3,1,6]=>[7,2,1,4,5,6,8,3]=>[1,1,5,1]
[1,7,3,8,2,4,6,5]=>[8,3,5,6,2,7,1,4]=>[1,6,4,3,7,2,8,5]=>[2,1,2,2,1]
[3,6,1,5,8,4,7,2]=>[4,6,1,2,8,7,3,5]=>[5,3,8,7,1,2,6,4]=>[1,2,1,3,1]
[3,5,8,2,4,1,7,6]=>[4,1,2,5,8,6,7,3]=>[5,8,7,4,1,3,2,6]=>[2,1,1,2,2]
[7,2,8,4,1,3,6,5]=>[8,5,2,4,6,1,7,3]=>[1,4,7,5,3,8,2,6]=>[3,1,2,2]
[8,4,3,5,7,2,6,1]=>[3,2,4,6,8,7,5,1]=>[6,7,5,3,1,2,4,8]=>[2,1,1,4]
[6,3,5,8,2,4,7,1]=>[5,2,3,1,6,8,7,4]=>[4,7,6,8,3,1,2,5]=>[2,2,1,3]
[2,8,7,1,4,6,3,5]=>[5,7,8,4,6,1,3,2]=>[4,2,1,5,3,8,6,7]=>[1,1,2,2,2]
[1,8,5,3,7,4,2,6]=>[7,4,3,6,8,5,1,2]=>[2,5,6,3,1,4,8,7]=>[3,1,3,1]
[7,5,6,2,8,4,3,1]=>[2,8,7,4,3,1,6,5]=>[7,1,2,5,6,8,3,4]=>[1,5,2]
[5,7,6,2,8,1,4,3]=>[1,8,4,6,3,2,7,5]=>[8,1,5,3,6,7,2,4]=>[1,2,3,2]
[6,3,8,1,2,5,4,7]=>[2,7,4,5,1,6,8,3]=>[7,2,5,4,8,3,1,6]=>[1,2,2,1,2]
[7,6,4,8,5,3,2,1]=>[8,3,2,1,7,6,5,4]=>[1,6,7,8,2,3,4,5]=>[4,4]
[7,6,5,3,8,4,2,1]=>[8,4,3,2,1,7,6,5]=>[1,5,6,7,8,2,3,4]=>[5,3]
[7,6,5,4,2,8,3,1]=>[8,5,4,3,2,1,7,6]=>[1,4,5,6,7,8,2,3]=>[6,2]
[8,6,9,7,5,4,3,2,1]=>[9,2,1,8,7,6,5,4,3]=>[1,8,9,2,3,4,5,6,7]=>[3,6]
[7,5,4,8,6,3,2,1]=>[2,8,3,1,7,6,5,4]=>[7,1,6,8,2,3,4,5]=>[1,3,4]
[8,7,5,9,6,4,3,2,1]=>[9,3,2,1,8,7,6,5,4]=>[1,7,8,9,2,3,4,5,6]=>[4,5]
[8,7,6,4,9,5,3,2,1]=>[9,4,3,2,1,8,7,6,5]=>[1,6,7,8,9,2,3,4,5]=>[5,4]
[7,6,5,3,2,8,4,1]=>[4,8,5,3,2,1,7,6]=>[5,1,4,6,7,8,2,3]=>[1,5,2]
[8,7,6,5,3,9,4,2,1]=>[9,5,4,3,2,1,8,7,6]=>[1,5,6,7,8,9,2,3,4]=>[6,3]
[8,7,6,5,4,2,9,3,1]=>[9,6,5,4,3,2,1,8,7]=>[1,4,5,6,7,8,9,2,3]=>[7,2]
[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[11,1]
[1,12,11,10,9,8,7,6,5,4,3,2]=>[12,11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,10,12,11]=>[11,1]
[1,5,7,2,4,3,6,8]=>[6,4,2,5,7,1,3,8]=>[3,5,7,4,2,8,6,1]=>[3,1,2,1,1]
[1,6,5,3,2,4,7,8]=>[5,4,6,3,1,2,7,8]=>[4,5,3,6,8,7,2,1]=>[2,3,1,1,1]
[1,7,2,4,6,5,3,8]=>[7,4,6,3,5,1,2,8]=>[2,5,3,6,4,8,7,1]=>[2,2,2,1,1]
[1,2,6,8,7,4,3,5]=>[3,7,6,8,5,1,2,4]=>[6,2,3,1,4,8,7,5]=>[1,2,3,1,1]
[1,6,2,8,7,4,3,5]=>[7,6,2,8,5,1,3,4]=>[2,3,7,1,4,8,6,5]=>[3,3,1,1]
[1,7,4,2,3,5,8,6]=>[8,4,3,5,6,1,2,7]=>[1,5,6,4,3,8,7,2]=>[3,1,2,1,1]
[1,8,5,2,3,6,4,7]=>[7,4,5,3,6,8,1,2]=>[2,5,4,6,3,1,8,7]=>[2,2,1,2,1]
[1,7,4,8,5,2,3,6]=>[3,6,7,5,2,8,1,4]=>[6,3,2,4,7,1,8,5]=>[1,1,3,2,1]
[1,4,7,5,2,8,6,3]=>[4,8,2,7,5,1,3,6]=>[5,1,7,2,4,8,6,3]=>[1,2,3,1,1]
[1,6,3,7,4,2,8,5]=>[5,8,3,2,6,1,4,7]=>[4,1,6,7,3,8,5,2]=>[1,3,2,1,1]
[1,8,5,2,7,4,3,6]=>[7,6,3,8,4,5,1,2]=>[2,3,6,1,5,4,8,7]=>[3,2,2,1]
[1,4,8,7,5,3,2,6]=>[7,6,2,5,8,4,1,3]=>[2,3,7,4,1,5,8,6]=>[3,1,3,1]
[1,2,5,8,6,3,7,4]=>[8,3,6,5,7,1,2,4]=>[1,6,3,4,2,8,7,5]=>[2,2,2,1,1]
[1,2,4,7,5,8,6,3]=>[8,5,3,4,7,1,2,6]=>[1,4,6,5,2,8,7,3]=>[3,1,2,1,1]
[1,5,8,7,6,2,4,3]=>[8,2,6,7,5,4,1,3]=>[1,7,3,2,4,5,8,6]=>[2,1,4,1]
[1,3,5,8,7,6,2,4]=>[7,8,3,6,2,5,1,4]=>[2,1,6,3,7,4,8,5]=>[1,2,2,2,1]
[1,5,2,4,3,6,8,7]=>[4,8,3,1,2,5,6,7]=>[5,1,6,8,7,4,3,2]=>[1,3,1,1,1,1]
[1,6,8,7,5,3,2,4]=>[2,7,6,8,5,4,1,3]=>[7,2,3,1,4,5,8,6]=>[1,2,4,1]
[1,2,5,7,4,3,8,6]=>[3,5,8,6,1,2,4,7]=>[6,4,1,3,8,7,5,2]=>[1,1,3,1,1,1]
[1,5,3,2,6,8,7,4]=>[8,3,2,5,7,1,4,6]=>[1,6,7,4,2,8,5,3]=>[3,1,2,1,1]
[1,4,2,6,8,7,5,3]=>[8,2,4,7,6,1,3,5]=>[1,7,5,2,3,8,6,4]=>[2,1,3,1,1]
[1,5,8,6,3,2,7,4]=>[2,5,8,6,4,7,1,3]=>[7,4,1,3,5,2,8,6]=>[1,1,3,2,1]
[1,8,5,2,6,3,4,7]=>[6,7,4,3,5,8,1,2]=>[3,2,5,6,4,1,8,7]=>[1,3,1,2,1]
[1,7,4,6,3,2,8,5]=>[3,5,8,6,4,1,2,7]=>[6,4,1,3,5,8,7,2]=>[1,1,4,1,1]
[1,6,3,2,8,5,4,7]=>[7,3,6,2,8,1,4,5]=>[2,6,3,7,1,8,5,4]=>[2,2,2,1,1]
[1,3,8,6,4,2,5,7]=>[6,5,7,2,4,8,1,3]=>[3,4,2,7,5,1,8,6]=>[2,2,1,2,1]
[1,5,7,4,2,3,8,6]=>[2,8,5,4,6,1,3,7]=>[7,1,4,5,3,8,6,2]=>[1,3,2,1,1]
[2,7,3,6,8,5,4,1]=>[4,8,7,3,1,2,6,5]=>[5,1,2,6,8,7,3,4]=>[1,4,1,2]
[8,5,2,4,6,7,3,1]=>[4,5,2,8,3,7,6,1]=>[5,4,7,1,6,2,3,8]=>[1,2,2,3]
[2,5,8,7,1,4,3,6]=>[2,7,5,6,8,1,4,3]=>[7,2,4,3,1,8,5,6]=>[1,2,1,2,2]
[3,4,6,5,8,2,7,1]=>[4,1,2,3,6,8,7,5]=>[5,8,7,6,3,1,2,4]=>[2,1,1,1,3]
[5,2,4,1,6,7,8,3]=>[5,2,3,1,6,8,4,7]=>[4,7,6,8,3,1,5,2]=>[2,2,1,2,1]
[4,2,7,1,6,8,3,5]=>[1,7,5,8,2,4,3,6]=>[8,2,4,1,7,5,6,3]=>[1,2,2,2,1]
[5,2,8,6,4,7,1,3]=>[1,7,5,4,8,2,6,3]=>[8,2,4,5,1,7,3,6]=>[1,3,2,2]
[6,1,3,4,7,2,8,5]=>[8,3,4,6,2,1,5,7]=>[1,6,5,3,7,8,4,2]=>[2,1,3,1,1]
[8,4,7,2,5,3,1,6]=>[2,7,4,6,5,8,3,1]=>[7,2,5,3,4,1,6,8]=>[1,2,2,3]
[8,6,1,4,7,3,5,2]=>[4,6,8,7,3,2,5,1]=>[5,3,1,2,6,7,4,8]=>[1,1,4,2]
[5,3,6,7,2,4,8,1]=>[5,2,1,3,6,4,8,7]=>[4,7,8,6,3,5,1,2]=>[3,1,2,2]
[8,6,4,2,7,1,5,3]=>[8,4,3,6,2,7,5,1]=>[1,5,6,3,7,2,4,8]=>[3,2,3]
[8,6,1,4,7,5,2,3]=>[4,7,8,6,3,2,5,1]=>[5,2,1,3,6,7,4,8]=>[1,1,4,2]
[1,5,8,2,6,7,4,3]=>[2,5,8,7,4,6,1,3]=>[7,4,1,2,5,3,8,6]=>[1,1,3,2,1]
[7,1,3,6,5,2,8,4]=>[8,6,3,5,2,4,1,7]=>[1,3,6,4,7,5,8,2]=>[3,2,2,1]
[1,4,7,5,2,3,8,6]=>[8,2,5,4,6,1,3,7]=>[1,7,4,5,3,8,6,2]=>[2,2,2,1,1]
[2,8,6,4,7,3,5,1]=>[4,6,3,8,7,1,5,2]=>[5,3,6,1,2,8,4,7]=>[1,2,3,2]
[8,7,1,4,6,5,3,2]=>[8,4,7,6,3,5,2,1]=>[1,5,2,3,6,4,7,8]=>[2,3,3]
[1,2,4,6,8,5,3,7]=>[4,7,3,6,8,1,2,5]=>[5,2,6,3,1,8,7,4]=>[1,2,1,2,1,1]
[3,1,5,8,6,2,4,7]=>[1,3,6,7,5,8,2,4]=>[8,6,3,2,4,1,7,5]=>[1,1,1,2,2,1]
[2,4,3,8,7,1,6,5]=>[8,2,6,7,1,3,5,4]=>[1,7,3,2,8,6,4,5]=>[2,1,2,1,2]
[6,8,7,5,4,3,1,2]=>[1,7,8,6,5,4,3,2]=>[8,2,1,3,4,5,6,7]=>[1,1,6]
[5,6,4,7,3,8,2,9,1]=>[1,3,2,5,4,7,6,9,8]=>[9,7,8,5,6,3,4,1,2]=>[1,2,2,2,2]
[5,3,4,8,6,2,7,1]=>[6,2,1,3,5,8,7,4]=>[3,7,8,6,4,1,2,5]=>[3,1,1,3]
[5,4,6,3,7,2,8,1,9]=>[2,1,4,3,6,5,8,7,9]=>[8,9,6,7,4,5,2,3,1]=>[2,2,2,2,1]
[6,5,7,4,8,3,9,2,10,1]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2]
[3,4,5,8,6,2,7,1]=>[6,1,2,3,5,8,7,4]=>[3,8,7,6,4,1,2,5]=>[2,1,1,1,3]
[5,6,4,7,3,8,2,9,1,10]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>[1,2,2,2,2,1]
[5,4,2,3,6,1,8,7]=>[3,4,2,1,5,8,6,7]=>[6,5,7,8,4,1,3,2]=>[1,3,1,2,1]
[5,1,7,4,3,6,8,2]=>[5,4,1,6,3,8,2,7]=>[4,5,8,3,6,1,7,2]=>[3,2,2,1]
[4,3,7,6,8,2,1,5]=>[7,1,6,2,4,3,8,5]=>[2,8,3,7,5,6,1,4]=>[2,2,2,2]
[8,1,4,7,2,3,5,6]=>[5,3,6,7,8,2,4,1]=>[4,6,3,2,1,7,5,8]=>[2,1,1,2,2]
[6,1,8,5,2,7,3,4]=>[7,8,5,4,1,6,2,3]=>[2,1,4,5,8,3,7,6]=>[1,4,2,1]
[8,7,2,6,3,1,4,5]=>[6,3,5,7,8,4,2,1]=>[3,6,4,2,1,5,7,8]=>[2,1,1,4]
[8,7,1,6,4,5,2,3]=>[7,5,8,6,3,4,2,1]=>[2,4,1,3,6,5,7,8]=>[2,3,3]
[5,4,1,3,7,2,8,6]=>[8,4,2,1,6,3,5,7]=>[1,5,7,8,3,6,4,2]=>[4,2,1,1]
[8,3,4,7,6,2,1,5]=>[7,2,3,6,8,5,4,1]=>[2,7,6,3,1,4,5,8]=>[2,1,1,4]
[6,5,8,7,2,4,3,1]=>[2,1,8,5,7,6,4,3]=>[7,8,1,4,2,3,5,6]=>[2,2,4]
[4,3,6,5,8,2,1,7]=>[1,4,2,3,7,6,8,5]=>[8,5,7,6,2,3,1,4]=>[1,2,1,2,2]
[7,6,3,2,8,5,4,1]=>[8,3,7,4,2,1,6,5]=>[1,6,2,5,7,8,3,4]=>[2,4,2]
[3,2,6,8,7,1,4,5]=>[6,1,3,7,8,2,5,4]=>[3,8,6,2,1,7,4,5]=>[2,1,1,2,2]
[4,3,7,1,8,5,2,6]=>[1,7,2,6,8,4,3,5]=>[8,2,7,3,1,5,6,4]=>[1,2,1,3,1]
[3,2,8,5,6,7,1,4]=>[4,7,1,5,8,2,6,3]=>[5,2,8,4,1,7,3,6]=>[1,2,1,2,2]
[4,7,3,1,8,5,2,6]=>[1,3,7,6,8,4,2,5]=>[8,6,2,3,1,5,7,4]=>[1,1,2,3,1]
[3,7,8,2,5,6,1,4]=>[7,4,5,1,2,8,6,3]=>[2,5,4,8,7,1,3,6]=>[2,2,1,3]
[7,5,1,4,2,3,6,8]=>[5,6,3,4,2,7,1,8]=>[4,3,6,5,7,2,8,1]=>[1,2,2,2,1]
[1,5,3,4,7,8,6,2]=>[5,2,8,3,4,7,1,6]=>[4,7,1,6,5,2,8,3]=>[2,2,1,2,1]
[5,1,2,4,7,8,6,3]=>[5,8,4,1,7,2,3,6]=>[4,1,5,8,2,7,6,3]=>[1,3,2,1,1]
[5,1,7,8,6,2,3,4]=>[6,1,7,3,8,5,2,4]=>[3,8,2,6,1,4,7,5]=>[2,2,3,1]
[8,5,1,6,7,2,3,4]=>[6,7,4,2,8,3,5,1]=>[3,2,5,7,1,6,4,8]=>[1,3,2,2]
[6,1,5,2,7,3,4,8]=>[6,7,4,2,3,1,5,8]=>[3,2,5,7,6,8,4,1]=>[1,3,2,1,1]
[7,1,2,6,4,5,8,3]=>[5,6,4,8,2,3,1,7]=>[4,3,5,1,7,6,8,2]=>[1,2,2,2,1]
[1,7,3,6,4,5,8,2]=>[5,6,3,4,2,8,1,7]=>[4,3,6,5,7,1,8,2]=>[1,2,2,2,1]
[1,8,3,6,4,5,7,2]=>[5,6,3,4,8,7,1,2]=>[4,3,6,5,1,2,8,7]=>[1,2,1,3,1]
[8,1,6,2,7,3,4,5]=>[6,7,8,4,2,3,5,1]=>[3,2,1,5,7,6,4,8]=>[1,1,3,1,2]
[7,1,6,2,5,3,4,8]=>[6,7,4,5,2,3,1,8]=>[3,2,5,4,7,6,8,1]=>[1,2,2,2,1]
[8,1,6,2,5,3,4,7]=>[6,7,4,5,2,3,8,1]=>[3,2,5,4,7,6,1,8]=>[1,2,2,1,2]
[8,1,7,2,5,3,4,6]=>[6,7,4,5,8,2,3,1]=>[3,2,5,4,1,7,6,8]=>[1,2,1,2,2]
[1,8,3,7,4,5,6,2]=>[5,6,8,3,7,4,1,2]=>[4,3,1,6,2,5,8,7]=>[1,1,2,3,1]
[8,1,6,7,5,2,3,4]=>[6,7,3,8,5,2,4,1]=>[3,2,6,1,4,7,5,8]=>[1,2,3,2]
[3,1,2,8,5,6,7,4]=>[1,5,6,8,7,2,3,4]=>[8,4,3,1,2,7,6,5]=>[1,1,1,3,1,1]
[6,3,1,2,7,4,5,8]=>[6,2,7,3,4,1,5,8]=>[3,7,2,6,5,8,4,1]=>[2,2,2,1,1]
[1,7,3,4,6,8,5,2]=>[5,8,3,4,2,7,1,6]=>[4,1,6,5,7,2,8,3]=>[1,2,2,2,1]
[1,7,3,8,4,5,6,2]=>[5,6,8,3,2,7,1,4]=>[4,3,1,6,7,2,8,5]=>[1,1,3,2,1]
[7,1,8,2,5,3,4,6]=>[6,7,4,5,8,2,1,3]=>[3,2,5,4,1,7,8,6]=>[1,2,1,3,1]
[6,1,7,2,5,3,4,8]=>[6,7,4,5,2,1,3,8]=>[3,2,5,4,7,8,6,1]=>[1,2,3,1,1]
[5,1,7,2,6,3,4,8]=>[6,7,4,1,5,2,3,8]=>[3,2,5,8,4,7,6,1]=>[1,3,2,1,1]
[5,1,8,2,6,3,4,7]=>[6,7,4,1,5,8,2,3]=>[3,2,5,8,4,1,7,6]=>[1,3,1,2,1]
[1,6,3,7,4,5,8,2]=>[5,6,3,2,4,8,1,7]=>[4,3,6,7,5,1,8,2]=>[1,3,1,2,1]
[2,4,7,3,5,1,6,8]=>[2,4,6,1,5,7,3,8]=>[7,5,3,8,4,2,6,1]=>[1,1,2,1,2,1]
[2,4,8,6,3,5,1,7]=>[5,7,2,6,1,4,8,3]=>[4,2,7,3,8,5,1,6]=>[1,2,2,1,2]
[2,3,7,5,4,1,6,8]=>[6,5,1,2,4,7,3,8]=>[3,4,8,7,5,2,6,1]=>[3,1,1,2,1]
[3,4,6,2,1,5,8,7]=>[1,2,4,8,5,3,6,7]=>[8,7,5,1,4,6,3,2]=>[1,1,1,3,1,1]
[3,4,7,2,1,6,5,8]=>[1,2,4,7,5,6,3,8]=>[8,7,5,2,4,3,6,1]=>[1,1,1,2,2,1]
[2,6,8,3,5,1,4,7]=>[4,6,2,7,1,5,8,3]=>[5,3,7,2,8,4,1,6]=>[1,2,2,1,2]
[2,3,6,1,5,8,4,7]=>[5,7,1,2,3,8,4,6]=>[4,2,8,7,6,1,5,3]=>[1,2,1,1,2,1]
[2,3,7,1,6,5,8,4]=>[6,5,8,1,2,4,3,7]=>[3,4,1,8,7,5,6,2]=>[2,2,1,2,1]
[2,4,7,1,3,6,8,5]=>[2,6,8,1,4,5,3,7]=>[7,3,1,8,5,4,6,2]=>[1,1,2,1,2,1]
[5,4,7,8,1,3,2,6]=>[2,1,7,5,6,3,8,4]=>[7,8,2,4,3,6,1,5]=>[2,2,2,2]
[2,5,7,1,4,6,3,8]=>[5,2,7,1,4,6,3,8]=>[4,7,2,8,5,3,6,1]=>[2,2,1,2,1]
[2,4,7,1,6,3,5,8]=>[2,6,7,1,4,5,3,8]=>[7,3,2,8,5,4,6,1]=>[1,1,2,1,2,1]
[2,3,7,1,6,5,4,8]=>[7,6,1,2,4,5,3,8]=>[2,3,8,7,5,4,6,1]=>[3,1,1,2,1]
[2,5,7,1,4,3,6,8]=>[6,4,1,2,5,7,3,8]=>[3,5,8,7,4,2,6,1]=>[3,1,1,2,1]
[2,5,7,3,1,4,6,8]=>[5,4,1,2,6,7,3,8]=>[4,5,8,7,3,2,6,1]=>[3,1,1,2,1]
[3,4,7,2,1,6,8,5]=>[1,2,4,6,8,5,3,7]=>[8,7,5,3,1,4,6,2]=>[1,1,1,1,3,1]
[4,6,3,7,1,5,2,8]=>[1,3,7,5,2,6,4,8]=>[8,6,2,4,7,3,5,1]=>[1,1,3,2,1]
[5,7,3,2,8,1,4,6]=>[4,3,1,6,7,2,8,5]=>[5,6,8,3,2,7,1,4]=>[3,1,2,2]
[3,6,8,5,4,1,7,2]=>[2,8,6,1,5,4,7,3]=>[7,1,3,8,4,5,2,6]=>[1,3,2,2]
[5,4,7,8,1,3,6,2]=>[2,1,6,8,5,3,7,4]=>[7,8,3,1,4,6,2,5]=>[2,1,3,2]
[2,5,7,1,4,6,8,3]=>[5,2,6,8,1,4,3,7]=>[4,7,3,1,8,5,6,2]=>[2,1,2,2,1]
[2,4,7,1,6,3,8,5]=>[8,2,6,1,4,5,3,7]=>[1,7,3,8,5,4,6,2]=>[2,2,1,2,1]
[2,4,7,1,6,8,3,5]=>[7,2,5,8,1,4,3,6]=>[2,7,4,1,8,5,6,3]=>[2,1,2,2,1]
[2,4,8,3,1,7,6,5]=>[8,2,4,7,1,5,6,3]=>[1,7,5,2,8,4,3,6]=>[2,1,2,1,2]
[7,2,3,4,5,6,1,9,8]=>[2,3,4,5,6,1,9,7,8]=>[8,7,6,5,4,9,1,3,2]=>[1,1,1,1,2,2,1]
[8,6,5,1,2,4,3,7]=>[7,4,5,6,3,2,8,1]=>[2,5,4,3,6,7,1,8]=>[2,1,3,2]
[7,6,1,4,2,3,5,8]=>[5,6,3,4,7,2,1,8]=>[4,3,6,5,2,7,8,1]=>[1,2,1,3,1]
[6,5,1,4,8,3,2,7]=>[4,7,6,2,1,8,3,5]=>[5,2,3,7,8,1,6,4]=>[1,4,2,1]
[8,7,5,1,4,2,3,6]=>[6,7,4,5,3,8,2,1]=>[3,2,5,4,6,1,7,8]=>[1,2,2,3]
[8,7,5,1,4,2,6,3]=>[8,6,4,5,3,7,2,1]=>[1,3,5,4,6,2,7,8]=>[3,2,3]
[8,6,1,4,2,5,3,7]=>[7,5,3,4,6,2,8,1]=>[2,4,6,5,3,7,1,8]=>[3,1,2,2]
[8,7,1,4,3,2,6,5]=>[5,4,8,3,6,7,2,1]=>[4,5,1,6,3,2,7,8]=>[2,2,1,3]
[8,7,6,3,1,5,4,2]=>[4,8,7,5,6,3,2,1]=>[5,1,2,4,3,6,7,8]=>[1,3,4]
[2,8,3,7,4,5,6,1]=>[5,6,8,3,7,1,4,2]=>[4,3,1,6,2,8,5,7]=>[1,1,2,2,2]
[2,9,1,8,7,6,5,4,3]=>[9,8,7,6,5,1,3,4,2]=>[1,2,3,4,5,9,7,6,8]=>[6,1,2]
[4,2,5,7,3,1,6,8]=>[3,1,6,2,5,7,4,8]=>[6,8,3,7,4,2,5,1]=>[2,2,1,2,1]
[8,4,5,1,3,2,6,7]=>[6,4,2,5,3,7,8,1]=>[3,5,7,4,6,2,1,8]=>[3,2,1,2]
[4,3,7,5,2,1,6,8]=>[1,6,2,5,4,7,3,8]=>[8,3,7,4,5,2,6,1]=>[1,2,2,2,1]
[1,6,7,4,3,2,5,8]=>[6,5,4,2,7,1,3,8]=>[3,4,5,7,2,8,6,1]=>[4,2,1,1]
[3,5,1,4,7,2,6,8]=>[1,4,6,2,7,3,5,8]=>[8,5,3,7,2,6,4,1]=>[1,1,2,2,1,1]
[2,5,1,4,7,8,3,6]=>[7,4,1,2,5,8,3,6]=>[2,5,8,7,4,1,6,3]=>[3,1,1,2,1]
[6,4,3,1,7,2,5,8]=>[6,3,2,7,4,1,5,8]=>[3,6,7,2,5,8,4,1]=>[3,3,1,1]
[6,2,7,4,3,1,5,8]=>[6,5,2,4,1,7,3,8]=>[3,4,7,5,8,2,6,1]=>[3,2,2,1]
[7,2,4,1,3,6,8,5]=>[6,2,3,8,4,5,1,7]=>[3,7,6,1,5,4,8,2]=>[2,1,2,2,1]
[6,3,2,5,7,1,4,8]=>[2,6,3,4,1,7,5,8]=>[7,3,6,5,8,2,4,1]=>[1,2,2,2,1]
[1,7,3,2,5,6,4,8]=>[3,5,7,4,6,1,2,8]=>[6,4,2,5,3,8,7,1]=>[1,1,2,2,1,1]
[2,1,7,3,5,6,8,4]=>[5,6,8,1,4,2,3,7]=>[4,3,1,8,5,7,6,2]=>[1,1,2,2,1,1]
[2,1,6,3,5,7,8,4]=>[5,6,1,3,8,2,4,7]=>[4,3,8,6,1,7,5,2]=>[1,2,1,2,1,1]
[1,6,3,2,5,7,4,8]=>[3,5,7,4,1,2,6,8]=>[6,4,2,5,8,7,3,1]=>[1,1,3,1,1,1]
[5,6,2,1,4,3,7,8]=>[3,6,4,1,5,2,7,8]=>[6,3,5,8,4,7,2,1]=>[1,3,2,1,1]
[2,5,4,1,6,3,7,8]=>[6,4,1,3,2,5,7,8]=>[3,5,8,6,7,4,2,1]=>[3,2,1,1,1]
[4,6,1,5,2,7,3,8]=>[1,7,5,3,4,2,6,8]=>[8,2,4,6,5,7,3,1]=>[1,3,2,1,1]
[1,6,5,3,7,2,4,8]=>[4,6,3,2,7,1,5,8]=>[5,3,6,7,2,8,4,1]=>[1,3,2,1,1]
[1,2,5,3,4,8,7,6]=>[3,8,7,1,2,4,5,6]=>[6,1,2,8,7,5,4,3]=>[1,3,1,1,1,1]
[5,2,7,6,1,8,4,3]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[1,4,2,1]
[5,8,2,6,1,7,4,3]=>[1,8,7,3,5,4,6,2]=>[8,1,2,6,4,5,3,7]=>[1,3,2,2]
[1,7,8,2,4,6,5,3]=>[8,5,7,4,2,6,1,3]=>[1,4,2,5,7,3,8,6]=>[2,3,2,1]
[1,5,8,3,6,2,7,4]=>[2,8,4,6,5,7,1,3]=>[7,1,5,3,4,2,8,6]=>[1,2,2,2,1]
[6,8,7,1,4,5,2,3]=>[7,5,1,8,4,6,3,2]=>[2,4,8,1,5,3,6,7]=>[3,2,3]
[1,2,6,4,7,3,8,5]=>[8,4,3,6,1,2,5,7]=>[1,5,6,3,8,7,4,2]=>[3,2,1,1,1]
[1,2,7,8,3,5,6,4]=>[6,8,5,3,7,1,2,4]=>[3,1,4,6,2,8,7,5]=>[1,3,2,1,1]
[4,8,7,6,2,1,5,3]=>[5,8,1,6,7,4,3,2]=>[4,1,8,3,2,5,6,7]=>[1,2,1,4]
[2,7,4,5,8,1,6,3]=>[3,4,8,6,1,2,7,5]=>[6,5,1,3,8,7,2,4]=>[1,1,3,1,2]
[2,6,1,8,5,4,3,7]=>[7,6,5,1,2,8,3,4]=>[2,3,4,8,7,1,6,5]=>[4,1,2,1]
[5,8,6,2,3,4,1,7]=>[4,1,5,7,6,3,8,2]=>[5,8,4,2,3,6,1,7]=>[2,1,3,2]
[5,8,6,2,1,4,3,7]=>[4,1,7,5,6,3,8,2]=>[5,8,2,4,3,6,1,7]=>[2,2,2,2]
[4,5,8,6,2,1,3,7]=>[1,2,6,5,7,4,8,3]=>[8,7,3,4,2,5,1,6]=>[1,1,2,2,2]
[6,4,7,5,8,2,1,3]=>[7,2,1,6,4,3,8,5]=>[2,7,8,3,5,6,1,4]=>[3,3,2]
[6,3,7,4,2,5,8,1]=>[5,2,4,1,6,3,8,7]=>[4,7,5,8,3,6,1,2]=>[2,2,2,2]
[6,2,1,5,8,4,3,7]=>[4,7,2,6,1,8,3,5]=>[5,2,7,3,8,1,6,4]=>[1,2,2,2,1]
[7,5,6,2,4,3,8,1]=>[6,4,2,5,3,1,8,7]=>[3,5,7,4,6,8,1,2]=>[3,3,2]
[4,6,2,5,7,3,8,1]=>[1,4,6,3,2,5,8,7]=>[8,5,3,6,7,4,1,2]=>[1,1,3,1,2]
[4,2,8,5,3,6,1,7]=>[1,5,4,7,2,6,8,3]=>[8,4,5,2,7,3,1,6]=>[1,2,2,1,2]
[8,1,7,4,5,6,2,3]=>[4,7,5,8,6,2,3,1]=>[5,2,4,1,3,7,6,8]=>[1,2,3,2]
[7,6,5,3,1,2,8,4]=>[8,5,4,6,3,2,1,7]=>[1,4,5,3,6,7,8,2]=>[3,4,1]
[6,2,3,1,7,8,4,5]=>[7,2,3,5,1,8,4,6]=>[2,7,6,4,8,1,5,3]=>[2,1,2,2,1]
[3,1,8,6,7,2,4,5]=>[6,7,1,4,8,5,2,3]=>[3,2,8,5,1,4,7,6]=>[1,2,1,3,1]
[4,2,5,1,8,6,7,3]=>[3,1,6,8,2,7,4,5]=>[6,8,3,1,7,2,5,4]=>[2,1,2,2,1]
[4,2,8,5,3,6,7,1]=>[1,5,4,6,8,2,7,3]=>[8,4,5,3,1,7,2,6]=>[1,2,1,2,2]
[2,8,6,3,5,4,7,1]=>[6,4,5,3,8,1,7,2]=>[3,5,4,6,1,8,2,7]=>[2,2,2,2]
[3,5,2,8,6,4,7,1]=>[2,6,1,5,8,3,7,4]=>[7,3,8,4,1,6,2,5]=>[1,2,1,2,2]
[7,3,5,1,6,4,8,2]=>[6,2,5,3,8,4,1,7]=>[3,7,4,6,1,5,8,2]=>[2,2,3,1]
[5,1,4,7,2,6,8,3]=>[3,6,1,8,5,2,4,7]=>[6,3,8,1,4,7,5,2]=>[1,2,3,1,1]
[1,8,2,5,6,4,7,3]=>[4,6,5,8,3,7,1,2]=>[5,3,4,1,6,2,8,7]=>[1,2,2,2,1]
[2,7,1,4,8,5,6,3]=>[6,8,4,7,1,3,2,5]=>[3,1,5,2,8,6,7,4]=>[1,2,2,2,1]
[2,8,4,6,1,3,7,5]=>[3,8,5,6,1,4,7,2]=>[6,1,4,3,8,5,2,7]=>[1,2,2,1,2]
[8,4,6,2,5,3,7,1]=>[2,6,4,5,3,8,7,1]=>[7,3,5,4,6,1,2,8]=>[1,2,2,3]
[8,3,7,6,2,1,5,4]=>[5,8,2,6,7,4,3,1]=>[4,1,7,3,2,5,6,8]=>[1,2,1,4]
[8,5,2,7,6,1,4,3]=>[8,6,2,7,3,5,4,1]=>[1,3,7,2,6,4,5,8]=>[3,2,3]
[8,3,7,6,2,5,1,4]=>[5,7,8,2,6,4,3,1]=>[4,2,1,7,3,5,6,8]=>[1,1,2,4]
[7,3,8,6,5,1,4,2]=>[8,6,7,2,1,5,4,3]=>[1,3,2,7,8,4,5,6]=>[2,3,3]
[9,8,7,6,1,2,3,4,5,10]=>[5,6,7,8,9,4,3,2,1,10]=>[6,5,4,3,2,7,8,9,10,1]=>[1,1,1,1,5,1]
[5,4,7,1,3,8,6,2]=>[2,1,8,5,7,4,3,6]=>[7,8,1,4,2,5,6,3]=>[2,2,3,1]
[8,1,7,6,3,4,2,5]=>[5,7,6,8,4,2,3,1]=>[4,2,3,1,5,7,6,8]=>[1,2,3,2]
[8,1,4,2,5,7,3,6]=>[5,3,7,8,2,4,6,1]=>[4,6,2,1,7,5,3,8]=>[2,1,2,1,2]
[3,4,8,5,6,2,7,1]=>[4,6,1,2,5,8,7,3]=>[5,3,8,7,4,1,2,6]=>[1,2,1,1,3]
[5,8,2,3,4,6,1,7]=>[3,4,1,5,7,6,8,2]=>[6,5,8,4,2,3,1,7]=>[1,2,1,2,2]
[1,5,6,3,2,4,7,8]=>[5,4,2,6,1,3,7,8]=>[4,5,7,3,8,6,2,1]=>[3,2,1,1,1]
[6,3,5,2,4,1,7,8]=>[2,4,6,5,3,1,7,8]=>[7,5,3,4,6,8,2,1]=>[1,1,4,1,1]
[7,8,3,5,2,4,6,1]=>[3,5,6,4,1,8,7,2]=>[6,4,3,5,8,1,2,7]=>[1,1,3,3]
[2,4,5,7,3,6,1,8]=>[2,3,5,7,1,6,4,8]=>[7,6,4,2,8,3,5,1]=>[1,1,1,2,2,1]
[2,5,3,1,6,4,7,8]=>[3,6,1,4,2,5,7,8]=>[6,3,8,5,7,4,2,1]=>[1,2,2,1,1,1]
[6,5,1,3,4,2,7,8]=>[4,6,3,5,2,1,7,8]=>[5,3,6,4,7,8,2,1]=>[1,2,3,1,1]
[2,6,7,8,4,3,5,1]=>[2,6,5,3,8,1,7,4]=>[7,3,4,6,1,8,2,5]=>[1,3,2,2]
[1,7,8,4,5,3,6,2]=>[4,6,5,2,8,7,1,3]=>[5,3,4,7,1,2,8,6]=>[1,3,3,1]
[7,1,8,5,3,4,6,2]=>[5,6,4,8,7,2,1,3]=>[4,3,5,1,2,7,8,6]=>[1,2,4,1]
[5,7,4,2,1,6,3,8]=>[4,1,7,5,3,6,2,8]=>[5,8,2,4,6,3,7,1]=>[2,3,2,1]
[7,4,8,6,3,5,2,1]=>[5,8,2,1,7,6,4,3]=>[4,1,7,8,2,3,5,6]=>[1,3,4]
[4,7,6,3,5,2,1,8]=>[4,7,1,6,5,3,2,8]=>[5,2,8,3,4,6,7,1]=>[1,2,4,1]
[1,6,5,8,7,4,2,3]=>[3,2,7,8,6,5,1,4]=>[6,7,2,1,3,4,8,5]=>[2,1,4,1]
[6,1,3,8,7,5,2,4]=>[7,8,6,3,1,5,2,4]=>[2,1,3,6,8,4,7,5]=>[1,4,2,1]
[7,6,2,1,8,3,5,4]=>[8,3,6,7,4,2,1,5]=>[1,6,3,2,5,7,8,4]=>[2,1,4,1]
[7,1,3,6,8,2,5,4]=>[8,6,3,4,7,2,1,5]=>[1,3,6,5,2,7,8,4]=>[3,1,3,1]
[1,7,5,6,8,2,4,3]=>[3,8,6,4,2,7,1,5]=>[6,1,3,5,7,2,8,4]=>[1,4,2,1]
[3,6,7,5,8,2,4,1]=>[2,6,4,1,3,8,7,5]=>[7,3,5,8,6,1,2,4]=>[1,3,1,3]
[1,7,4,5,2,8,6,3]=>[3,4,8,7,5,1,2,6]=>[6,5,1,2,4,8,7,3]=>[1,1,4,1,1]
[7,5,4,2,1,8,6,3]=>[8,4,3,2,7,5,1,6]=>[1,5,6,7,2,4,8,3]=>[4,3,1]
[3,6,7,4,2,8,5,1]=>[4,2,8,1,5,3,7,6]=>[5,7,1,8,4,6,2,3]=>[2,2,2,2]
[4,6,3,2,7,8,5,1]=>[1,3,5,2,8,4,7,6]=>[8,6,4,7,1,5,2,3]=>[1,1,2,2,2]
[7,8,2,6,4,5,3,1]=>[5,8,7,3,1,6,4,2]=>[4,1,2,6,8,3,5,7]=>[1,4,3]
[7,1,2,4,5,6,3,8]=>[4,5,7,2,3,6,1,8]=>[5,4,2,7,6,3,8,1]=>[1,1,2,1,2,1]
[7,3,2,1,5,6,4,8]=>[3,2,5,7,4,6,1,8]=>[6,7,4,2,5,3,8,1]=>[2,1,2,2,1]
[3,6,2,1,7,5,4,8]=>[7,1,3,6,4,2,5,8]=>[2,8,6,3,5,7,4,1]=>[2,1,3,1,1]
[2,1,6,4,7,5,3,8]=>[7,4,1,3,6,2,5,8]=>[2,5,8,6,3,7,4,1]=>[3,1,2,1,1]
[7,2,8,5,6,4,3,1]=>[4,8,7,6,2,1,5,3]=>[5,1,2,3,7,8,4,6]=>[1,5,2]
[7,6,8,5,4,1,3,2]=>[8,6,2,1,7,5,4,3]=>[1,3,7,8,2,4,5,6]=>[4,4]
[7,1,8,4,6,5,3,2]=>[8,4,7,6,5,2,1,3]=>[1,5,2,3,4,7,8,6]=>[2,5,1]
[7,8,6,3,1,5,4,2]=>[4,8,7,5,1,6,3,2]=>[5,1,2,4,8,3,6,7]=>[1,4,3]
[7,6,1,4,5,3,2,8]=>[4,7,6,3,5,2,1,8]=>[5,2,3,6,4,7,8,1]=>[1,3,3,1]
[7,1,5,6,4,3,2,8]=>[3,7,6,5,2,4,1,8]=>[6,2,3,4,7,5,8,1]=>[1,4,2,1]
[4,1,3,8,6,2,7,5]=>[1,8,6,3,5,7,2,4]=>[8,1,3,6,4,2,7,5]=>[1,3,1,2,1]
[5,1,2,8,4,6,7,3]=>[5,6,1,8,7,2,3,4]=>[4,3,8,1,2,7,6,5]=>[1,2,3,1,1]
[5,6,3,2,8,1,7,4]=>[3,1,8,4,2,6,7,5]=>[6,8,1,5,7,3,2,4]=>[2,3,1,2]
[8,2,6,3,1,5,7,4]=>[4,6,8,2,5,3,7,1]=>[5,3,1,7,4,6,2,8]=>[1,1,2,2,2]
[8,2,5,6,7,4,3,1]=>[3,4,8,7,2,6,5,1]=>[6,5,1,2,7,3,4,8]=>[1,1,3,3]
[8,2,5,3,4,7,6,1]=>[8,4,2,3,5,7,6,1]=>[1,5,7,6,4,2,3,8]=>[3,1,1,3]
[7,5,3,2,4,1,8,6]=>[4,3,5,2,8,6,1,7]=>[5,6,4,7,1,3,8,2]=>[2,2,3,1]
[6,7,2,8,3,4,5,1]=>[5,6,1,8,3,2,7,4]=>[4,3,8,1,6,7,2,5]=>[1,2,3,2]
[6,1,2,3,8,4,7,5]=>[8,6,7,2,3,1,4,5]=>[1,3,2,7,6,8,5,4]=>[2,2,2,1,1]
[8,1,6,7,4,2,3,5]=>[6,7,5,3,8,2,4,1]=>[3,2,4,6,1,7,5,8]=>[1,3,2,2]
[8,1,6,4,5,2,3,7]=>[6,4,7,5,2,3,8,1]=>[3,5,2,4,7,6,1,8]=>[2,3,1,2]
[8,6,4,7,2,3,5,1]=>[5,3,6,2,8,7,4,1]=>[4,6,3,7,1,2,5,8]=>[2,2,4]
[8,6,4,1,2,3,7,5]=>[8,4,5,3,6,2,7,1]=>[1,5,4,6,3,7,2,8]=>[2,2,2,2]
[8,6,1,4,2,5,7,3]=>[6,4,8,3,5,2,7,1]=>[3,5,1,6,4,7,2,8]=>[2,2,2,2]
[8,6,7,4,2,5,1,3]=>[5,7,4,2,8,6,3,1]=>[4,2,5,7,1,3,6,8]=>[1,3,4]
[8,6,4,2,5,3,1,7]=>[7,4,3,6,5,2,8,1]=>[2,5,6,3,4,7,1,8]=>[3,3,2]
[8,6,4,2,7,3,1,5]=>[7,4,3,6,2,8,5,1]=>[2,5,6,3,7,1,4,8]=>[3,2,3]
[8,6,4,1,5,7,2,3]=>[7,5,3,8,4,2,6,1]=>[2,4,6,1,5,7,3,8]=>[3,3,2]
[8,6,4,2,1,5,7,3]=>[4,6,3,8,5,2,7,1]=>[5,3,6,1,4,7,2,8]=>[1,2,3,2]
[8,6,1,4,7,2,5,3]=>[4,8,6,7,3,2,5,1]=>[5,1,3,2,6,7,4,8]=>[1,2,3,2]
[8,6,4,5,2,7,3,1]=>[3,8,5,4,2,7,6,1]=>[6,1,4,5,7,2,3,8]=>[1,4,3]
[8,6,7,4,2,1,5,3]=>[5,8,6,4,2,7,3,1]=>[4,1,3,5,7,2,6,8]=>[1,4,3]
[8,6,4,7,2,1,5,3]=>[5,3,8,6,2,7,4,1]=>[4,6,1,3,7,2,5,8]=>[2,3,3]
[8,6,4,2,5,7,3,1]=>[5,3,8,4,2,7,6,1]=>[4,6,1,5,7,2,3,8]=>[2,3,3]
[8,6,4,2,5,1,7,3]=>[8,4,3,6,5,2,7,1]=>[1,5,6,3,4,7,2,8]=>[3,3,2]
[8,6,4,2,5,7,1,3]=>[7,4,3,5,2,8,6,1]=>[2,5,6,4,7,1,3,8]=>[3,2,3]
[3,4,7,5,8,2,6,1]=>[4,6,1,2,3,8,7,5]=>[5,3,8,7,6,1,2,4]=>[1,2,1,1,3]
[5,3,8,6,4,1,7,2]=>[1,8,6,2,5,4,7,3]=>[8,1,3,7,4,5,2,6]=>[1,3,2,2]
[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[8,7,6,5,4,9,3,2,1]=>[1,1,1,1,2,1,1,1]
[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[8,7,6,5,9,4,3,2,1]=>[1,1,1,2,1,1,1,1]
[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[8,7,6,9,5,4,3,2,1]=>[1,1,2,1,1,1,1,1]
[2,3,4,5,6,7,8,9,10,11,12,1]=>[1,2,3,4,5,6,7,8,9,10,12,11]=>[12,11,10,9,8,7,6,5,4,3,1,2]=>[1,1,1,1,1,1,1,1,1,1,2]
[7,4,5,1,2,8,6,3]=>[2,8,7,4,3,5,1,6]=>[7,1,2,5,6,4,8,3]=>[1,4,2,1]
[6,4,7,1,8,5,2,3]=>[2,7,1,8,6,4,3,5]=>[7,2,8,1,3,5,6,4]=>[1,2,4,1]
[5,7,4,2,3,8,6,1]=>[1,8,4,3,5,2,7,6]=>[8,1,5,6,4,7,2,3]=>[1,3,2,2]
[4,8,5,2,1,7,3,6]=>[1,4,7,3,8,5,6,2]=>[8,5,2,6,1,4,3,7]=>[1,1,2,2,2]
[8,5,7,6,1,2,4,3]=>[8,5,2,6,7,4,3,1]=>[1,4,7,3,2,5,6,8]=>[3,1,4]
[6,8,7,5,2,4,1,3]=>[5,1,7,8,6,4,3,2]=>[4,8,2,1,3,5,6,7]=>[2,1,5]
[5,7,6,8,4,1,3,2]=>[8,1,6,3,2,7,5,4]=>[1,8,3,6,7,2,4,5]=>[2,3,3]
[7,3,1,6,8,5,4,2]=>[4,8,2,7,6,3,1,5]=>[5,1,7,2,3,6,8,4]=>[1,2,4,1]
[7,3,1,8,6,4,5,2]=>[6,8,2,7,5,3,1,4]=>[3,1,7,2,4,6,8,5]=>[1,2,4,1]
[8,6,4,1,7,3,2,5]=>[7,6,3,8,4,2,5,1]=>[2,3,6,1,5,7,4,8]=>[3,3,2]
[3,5,2,8,4,7,1,6]=>[5,1,2,7,8,3,6,4]=>[4,8,7,2,1,6,3,5]=>[2,1,1,2,2]
[6,4,8,3,7,2,1,5]=>[2,4,1,7,6,8,5,3]=>[7,5,8,2,3,1,4,6]=>[1,2,2,3]
[3,6,2,8,7,4,1,5]=>[7,6,1,2,8,3,5,4]=>[2,3,8,7,1,6,4,5]=>[3,1,2,2]
[6,8,4,2,7,3,1,5]=>[7,4,3,1,6,8,5,2]=>[2,5,6,8,3,1,4,7]=>[4,1,3]
[9,8,2,3,4,5,6,7,1]=>[3,4,5,6,7,9,8,2,1]=>[7,6,5,4,3,1,2,8,9]=>[1,1,1,1,1,4]
[9,8,7,6,4,5,3,2,1]=>[5,9,8,7,6,4,3,2,1]=>[5,1,2,3,4,6,7,8,9]=>[1,8]
[3,2,7,6,4,5,8,1]=>[5,6,1,4,2,3,8,7]=>[4,3,8,5,7,6,1,2]=>[1,2,2,1,2]
[1,7,3,6,8,4,2,5]=>[7,6,3,4,2,8,1,5]=>[2,3,6,5,7,1,8,4]=>[3,2,2,1]
[2,3,6,5,1,8,7,4]=>[4,3,8,1,2,7,5,6]=>[5,6,1,8,7,2,4,3]=>[2,2,1,2,1]
[8,3,1,2,6,4,7,5]=>[2,8,6,3,4,5,7,1]=>[7,1,3,6,5,4,2,8]=>[1,3,1,1,2]
[1,7,8,2,4,3,5,6]=>[6,4,5,7,2,8,1,3]=>[3,5,4,2,7,1,8,6]=>[2,1,2,2,1]
[3,6,4,7,1,2,8,5]=>[3,8,1,5,2,6,4,7]=>[6,1,8,4,7,3,5,2]=>[1,2,2,2,1]
[5,7,4,8,1,3,2,6]=>[1,7,5,3,6,2,8,4]=>[8,2,4,6,3,7,1,5]=>[1,3,2,2]
[8,5,4,2,6,1,7,3]=>[8,4,3,2,6,5,7,1]=>[1,5,6,7,3,4,2,8]=>[4,2,2]
[3,2,6,8,7,4,1,5]=>[3,7,1,6,8,2,5,4]=>[6,2,8,3,1,7,4,5]=>[1,2,1,2,2]
[2,3,7,5,1,8,6,4]=>[4,8,7,1,2,5,3,6]=>[5,1,2,8,7,4,6,3]=>[1,3,1,2,1]
[6,3,1,2,8,7,4,5]=>[2,7,8,6,3,1,4,5]=>[7,2,1,3,6,8,5,4]=>[1,1,4,1,1]
[5,2,1,3,8,7,6,4]=>[8,7,2,1,6,3,4,5]=>[1,2,7,8,3,6,5,4]=>[4,2,1,1]
[1,5,8,2,4,3,6,7]=>[6,4,2,5,7,8,1,3]=>[3,5,7,4,2,1,8,6]=>[3,1,1,2,1]
[4,3,6,8,1,5,2,7]=>[1,7,2,5,3,6,8,4]=>[8,2,7,4,6,3,1,5]=>[1,2,2,1,2]
[5,4,6,8,3,1,7,2]=>[2,1,3,8,6,5,7,4]=>[7,8,6,1,3,4,2,5]=>[2,1,3,2]
[2,3,7,6,1,8,5,4]=>[8,7,5,1,2,4,3,6]=>[1,2,4,8,7,5,6,3]=>[4,1,2,1]
[3,2,7,8,6,4,1,5]=>[7,6,1,3,8,2,5,4]=>[2,3,8,6,1,7,4,5]=>[3,1,2,2]
[6,2,8,3,1,4,7,5]=>[4,8,2,5,1,6,7,3]=>[5,1,7,4,8,3,2,6]=>[1,2,2,1,2]
[3,1,2,8,7,4,5,6]=>[1,6,7,8,5,2,3,4]=>[8,3,2,1,4,7,6,5]=>[1,1,1,3,1,1]
[2,1,3,8,7,4,6,5]=>[8,6,7,1,5,2,3,4]=>[1,3,2,8,4,7,6,5]=>[2,2,2,1,1]
[2,1,3,8,7,4,5,6]=>[6,7,8,1,5,2,3,4]=>[3,2,1,8,4,7,6,5]=>[1,1,2,2,1,1]
[1,6,8,3,2,4,7,5]=>[4,8,5,2,6,7,1,3]=>[5,1,4,7,3,2,8,6]=>[1,3,1,2,1]
[8,5,1,7,2,4,3,6]=>[7,5,6,2,8,3,4,1]=>[2,4,3,7,1,6,5,8]=>[2,2,2,2]
[8,4,1,7,3,2,5,6]=>[6,5,2,7,8,3,4,1]=>[3,4,7,2,1,6,5,8]=>[3,1,2,2]
[8,3,1,6,2,7,5,4]=>[8,2,7,5,3,4,6,1]=>[1,7,2,4,6,5,3,8]=>[2,3,1,2]
[1,3,2,8,7,6,4,5]=>[7,8,6,2,5,1,3,4]=>[2,1,3,7,4,8,6,5]=>[1,3,2,1,1]
[2,1,3,8,7,6,4,5]=>[7,8,6,1,5,2,3,4]=>[2,1,3,8,4,7,6,5]=>[1,3,2,1,1]
[1,6,3,7,2,5,4,8]=>[7,3,5,2,6,1,4,8]=>[2,6,4,7,3,8,5,1]=>[2,2,2,1,1]
[1,7,2,4,6,3,5,8]=>[4,6,7,3,5,1,2,8]=>[5,3,2,6,4,8,7,1]=>[1,1,2,2,1,1]
[5,7,2,8,4,1,3,6]=>[6,1,7,3,5,2,8,4]=>[3,8,2,6,4,7,1,5]=>[2,2,2,2]
[2,4,8,3,1,6,7,5]=>[2,4,6,8,1,5,7,3]=>[7,5,3,1,8,4,2,6]=>[1,1,1,2,1,2]
[3,5,8,4,2,1,6,7]=>[2,6,1,5,4,7,8,3]=>[7,3,8,4,5,2,1,6]=>[1,2,2,1,2]
[2,5,8,3,1,4,6,7]=>[5,4,1,2,6,7,8,3]=>[4,5,8,7,3,2,1,6]=>[3,1,1,1,2]
[2,8,1,3,5,7,4,6]=>[5,7,8,1,3,4,6,2]=>[4,2,1,8,6,5,3,7]=>[1,1,2,1,1,2]
[5,4,7,8,3,2,6,1]=>[1,6,2,5,3,8,7,4]=>[8,3,7,4,6,1,2,5]=>[1,2,2,3]
[3,4,8,5,7,1,2,6]=>[6,1,2,4,7,8,5,3]=>[3,8,7,5,2,1,4,6]=>[2,1,1,1,3]
[3,6,8,2,5,1,4,7]=>[4,6,1,2,7,5,8,3]=>[5,3,8,7,2,4,1,6]=>[1,2,1,2,2]
[3,4,6,5,8,2,1,7]=>[4,1,2,3,7,6,8,5]=>[5,8,7,6,2,3,1,4]=>[2,1,1,2,2]
[2,4,6,7,8,3,5,1]=>[3,6,2,4,8,1,7,5]=>[6,3,7,5,1,8,2,4]=>[1,2,1,2,2]
[1,4,2,5,7,6,3,8]=>[2,7,4,6,1,3,5,8]=>[7,2,5,3,8,6,4,1]=>[1,2,2,1,1,1]
[1,4,2,6,8,5,3,7]=>[2,4,7,6,8,1,3,5]=>[7,5,2,3,1,8,6,4]=>[1,1,2,2,1,1]
[1,2,6,8,3,5,4,7]=>[7,5,3,6,8,1,2,4]=>[2,4,6,3,1,8,7,5]=>[3,1,2,1,1]
[1,6,8,3,5,4,2,7]=>[7,4,2,6,5,8,1,3]=>[2,5,7,3,4,1,8,6]=>[3,2,2,1]
[1,5,3,2,4,6,8,7]=>[3,8,4,1,2,5,6,7]=>[6,1,5,8,7,4,3,2]=>[1,3,1,1,1,1]
[1,5,8,7,6,3,2,4]=>[7,2,6,8,5,4,1,3]=>[2,7,3,1,4,5,8,6]=>[2,1,4,1]
[1,5,7,6,3,2,4,8]=>[2,6,5,7,4,1,3,8]=>[7,3,4,2,5,8,6,1]=>[1,2,3,1,1]
[1,6,3,2,4,8,7,5]=>[8,3,7,4,1,2,5,6]=>[1,6,2,5,8,7,4,3]=>[2,3,1,1,1]
[1,2,7,6,4,3,5,8]=>[6,5,7,4,1,2,3,8]=>[3,4,2,5,8,7,6,1]=>[2,3,1,1,1]
[1,7,4,2,5,3,6,8]=>[6,4,3,5,7,1,2,8]=>[3,5,6,4,2,8,7,1]=>[3,1,2,1,1]
[1,8,4,7,5,2,6,3]=>[8,3,6,5,7,4,1,2]=>[1,6,3,4,2,5,8,7]=>[2,2,3,1]
[1,6,3,7,4,2,5,8]=>[6,3,5,2,7,1,4,8]=>[3,6,4,7,2,8,5,1]=>[2,2,2,1,1]
[1,6,3,2,7,5,4,8]=>[7,3,6,4,1,2,5,8]=>[2,6,3,5,8,7,4,1]=>[2,3,1,1,1]
[1,4,7,5,2,6,3,8]=>[7,2,5,4,6,1,3,8]=>[2,7,4,5,3,8,6,1]=>[2,2,2,1,1]
[1,3,6,4,8,7,5,2]=>[3,8,7,2,4,6,1,5]=>[6,1,2,7,5,3,8,4]=>[1,3,1,2,1]
[1,3,7,6,4,2,5,8]=>[6,5,7,2,4,1,3,8]=>[3,4,2,7,5,8,6,1]=>[2,2,2,1,1]
[1,3,2,4,8,5,7,6]=>[8,2,6,7,1,3,4,5]=>[1,7,3,2,8,6,5,4]=>[2,1,2,1,1,1]
[1,3,8,7,5,2,4,6]=>[6,7,5,8,2,4,1,3]=>[3,2,4,1,7,5,8,6]=>[1,2,2,2,1]
[1,4,6,3,2,7,5,8]=>[2,4,7,5,1,3,6,8]=>[7,5,2,4,8,6,3,1]=>[1,1,3,1,1,1]
[1,4,6,3,2,8,7,5]=>[8,2,4,3,7,1,5,6]=>[1,7,5,6,2,8,4,3]=>[2,2,2,1,1]
[1,6,3,2,8,4,7,5]=>[8,3,6,2,7,1,4,5]=>[1,6,3,7,2,8,5,4]=>[2,2,2,1,1]
[1,6,3,5,2,7,4,8]=>[7,3,5,4,1,2,6,8]=>[2,6,4,5,8,7,3,1]=>[2,3,1,1,1]
[1,6,3,5,2,8,7,4]=>[4,8,3,2,7,1,5,6]=>[5,1,6,7,2,8,4,3]=>[1,3,2,1,1]
[1,8,3,7,5,2,4,6]=>[6,7,3,5,8,4,1,2]=>[3,2,6,4,1,5,8,7]=>[1,2,1,3,1]
[6,4,7,1,5,3,8,2]=>[2,6,5,1,8,4,3,7]=>[7,3,4,8,1,5,6,2]=>[1,3,3,1]
[5,3,8,2,6,4,7,1]=>[6,2,1,4,5,8,7,3]=>[3,7,8,5,4,1,2,6]=>[3,1,1,3]
[4,3,8,2,6,5,7,1]=>[1,6,2,4,5,8,7,3]=>[8,3,7,5,4,1,2,6]=>[1,2,1,1,3]
[5,7,1,4,8,2,3,6]=>[6,4,1,7,8,3,2,5]=>[3,5,8,2,1,6,7,4]=>[3,1,3,1]
[6,5,7,1,4,3,8,2]=>[6,5,2,1,8,4,3,7]=>[3,4,7,8,1,5,6,2]=>[4,3,1]
[4,8,3,5,7,6,1,2]=>[1,3,4,7,8,6,5,2]=>[8,6,5,2,1,3,4,7]=>[1,1,1,1,4]
[5,7,6,1,2,4,8,3]=>[6,1,8,4,5,3,2,7]=>[3,8,1,5,4,6,7,2]=>[2,2,3,1]
[4,8,3,5,7,6,2,1]=>[8,1,3,4,7,6,5,2]=>[1,8,6,5,2,3,4,7]=>[2,1,1,4]
[5,7,6,2,4,8,3,1]=>[1,5,8,4,3,2,7,6]=>[8,4,1,5,6,7,2,3]=>[1,1,4,2]
[6,7,5,2,3,8,4,1]=>[8,4,1,5,3,2,7,6]=>[1,5,8,4,6,7,2,3]=>[3,3,2]
[6,7,5,3,8,4,2,1]=>[1,8,4,3,2,7,6,5]=>[8,1,5,6,7,2,3,4]=>[1,4,3]
[3,2,1,4,8,5,7,6]=>[1,8,2,6,7,3,4,5]=>[8,1,7,3,2,6,5,4]=>[1,2,1,2,1,1]
[5,4,1,8,2,6,3,7]=>[7,5,2,1,6,8,3,4]=>[2,4,7,8,3,1,6,5]=>[4,1,2,1]
[4,7,1,5,2,6,3,8]=>[1,7,5,3,4,6,2,8]=>[8,2,4,6,5,3,7,1]=>[1,3,1,2,1]
[6,5,1,4,2,7,3,8]=>[7,5,3,4,2,1,6,8]=>[2,4,6,5,7,8,3,1]=>[3,3,1,1]
[1,8,7,3,4,5,2,6]=>[4,5,7,6,8,3,1,2]=>[5,4,2,3,1,6,8,7]=>[1,1,2,3,1]
[1,2,6,8,7,3,4,5]=>[6,3,7,8,5,1,2,4]=>[3,6,2,1,4,8,7,5]=>[2,1,3,1,1]
[1,3,7,8,4,5,6,2]=>[5,6,3,8,2,7,1,4]=>[4,3,6,1,7,2,8,5]=>[1,2,2,2,1]
[1,3,4,5,6,7,8,9,10,11,12,2]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[11,10,9,8,7,6,5,4,3,1,12,2]=>[1,1,1,1,1,1,1,1,1,2,1]
[8,4,2,3,1,6,5,7]=>[3,4,2,7,5,6,8,1]=>[6,5,7,2,4,3,1,8]=>[1,2,2,1,2]
[6,4,5,2,8,1,7,3]=>[2,8,4,3,1,6,7,5]=>[7,1,5,6,8,3,2,4]=>[1,4,1,2]
[4,8,6,2,3,1,7,5]=>[1,4,5,8,6,3,7,2]=>[8,5,4,1,3,6,2,7]=>[1,1,1,3,2]
[6,4,2,1,8,5,3,7]=>[7,3,2,6,1,8,4,5]=>[2,6,7,3,8,1,5,4]=>[3,2,2,1]
[4,2,6,1,5,8,3,7]=>[5,1,7,2,3,8,4,6]=>[4,8,2,7,6,1,5,3]=>[2,2,1,2,1]
[6,4,2,3,5,8,1,7]=>[3,4,2,5,1,7,8,6]=>[6,5,7,4,8,2,1,3]=>[1,2,2,1,2]
[2,8,6,4,5,1,7,3]=>[4,8,6,5,1,3,7,2]=>[5,1,3,4,8,6,2,7]=>[1,4,1,2]
[8,2,4,6,7,1,5,3]=>[8,3,6,2,4,7,5,1]=>[1,6,3,7,5,2,4,8]=>[2,2,1,3]
[6,5,1,8,3,2,7,4]=>[5,8,6,2,1,7,3,4]=>[4,1,3,7,8,2,6,5]=>[1,4,2,1]
[1,4,3,7,2,8,6,5]=>[8,2,7,3,5,1,4,6]=>[1,7,2,6,4,8,5,3]=>[2,2,2,1,1]
[1,8,7,4,5,3,2,6]=>[4,7,6,5,8,3,1,2]=>[5,2,3,4,1,6,8,7]=>[1,3,3,1]
[2,8,3,1,4,5,7,6]=>[3,8,1,4,5,6,7,2]=>[6,1,8,5,4,3,2,7]=>[1,2,1,1,1,2]
[6,1,7,2,8,4,5,3]=>[6,8,7,4,2,1,3,5]=>[3,1,2,5,7,8,6,4]=>[1,5,1,1]
[8,3,2,1,5,6,7,4]=>[3,2,5,6,8,4,7,1]=>[6,7,4,3,1,5,2,8]=>[2,1,1,2,2]
[1,7,4,6,3,8,2,5]=>[3,5,7,4,2,8,1,6]=>[6,4,2,5,7,1,8,3]=>[1,1,3,2,1]
[5,6,4,1,3,8,2,7]=>[5,1,7,3,2,8,4,6]=>[4,8,2,6,7,1,5,3]=>[2,3,2,1]
[4,5,3,1,8,7,6,2]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[1,1,2,3,1]
[6,3,4,2,7,8,5,1]=>[2,3,5,1,8,4,7,6]=>[7,6,4,8,1,5,2,3]=>[1,1,2,2,2]
[8,7,4,5,1,6,3,2]=>[3,8,7,5,4,6,2,1]=>[6,1,2,4,5,3,7,8]=>[1,4,3]
[6,2,7,8,1,3,5,4]=>[8,5,6,2,1,3,7,4]=>[1,4,3,7,8,6,2,5]=>[2,3,1,2]
[5,1,8,4,3,7,2,6]=>[5,4,1,7,8,6,2,3]=>[4,5,8,2,1,3,7,6]=>[3,1,3,1]
[7,2,8,1,4,5,6,3]=>[5,6,8,2,4,1,7,3]=>[4,3,1,7,5,8,2,6]=>[1,1,2,2,2]
[1,4,8,2,5,6,7,3]=>[2,5,6,8,4,7,1,3]=>[7,4,3,1,5,2,8,6]=>[1,1,1,2,2,1]
[2,1,4,3,6,5,8,10,9,7]=>[10,1,3,5,7,9,2,4,6,8]=>[1,10,8,6,4,2,9,7,5,3]=>[2,1,1,1,2,1,1,1]
[8,1,6,7,2,5,4,3]=>[8,7,5,3,6,2,4,1]=>[1,2,4,6,3,7,5,8]=>[4,2,2]
[7,5,2,3,6,8,4,1]=>[5,8,3,2,4,1,7,6]=>[4,1,6,7,5,8,2,3]=>[1,3,2,2]
[8,1,4,6,5,3,2,7]=>[7,3,6,5,2,4,8,1]=>[2,6,3,4,7,5,1,8]=>[2,3,1,2]
[8,1,4,7,6,5,2,3]=>[7,8,3,6,5,2,4,1]=>[2,1,6,3,4,7,5,8]=>[1,2,3,2]
[8,1,2,7,6,5,4,3]=>[8,7,6,5,2,3,4,1]=>[1,2,3,4,7,6,5,8]=>[5,1,2]
[4,5,8,1,6,7,2,3]=>[1,2,7,5,8,4,6,3]=>[8,7,2,4,1,5,3,6]=>[1,1,2,2,2]
[3,2,8,6,1,5,7,4]=>[6,8,1,5,2,4,7,3]=>[3,1,8,4,7,5,2,6]=>[1,2,2,1,2]
[6,2,8,3,5,1,4,7]=>[4,6,7,2,1,5,8,3]=>[5,3,2,7,8,4,1,6]=>[1,1,3,1,2]
[6,8,2,5,3,4,1,7]=>[5,7,3,1,6,4,8,2]=>[4,2,6,8,3,5,1,7]=>[1,3,2,2]
[6,8,7,5,4,1,2,3]=>[6,1,7,8,5,4,3,2]=>[3,8,2,1,4,5,6,7]=>[2,1,5]
[6,3,5,2,8,1,7,4]=>[8,2,4,3,1,6,7,5]=>[1,7,5,6,8,3,2,4]=>[2,3,1,2]
[4,8,7,1,6,3,2,5]=>[7,1,6,8,4,5,3,2]=>[2,8,3,1,5,4,6,7]=>[2,1,2,3]
[4,8,2,7,5,3,6,1]=>[6,1,5,8,3,7,4,2]=>[3,8,4,1,6,2,5,7]=>[2,1,2,3]
[1,3,2,6,8,7,4,5]=>[4,7,8,2,6,1,3,5]=>[5,2,1,7,3,8,6,4]=>[1,1,2,2,1,1]
[1,6,2,5,8,7,3,4]=>[4,7,2,8,6,1,3,5]=>[5,2,7,1,3,8,6,4]=>[1,2,3,1,1]
[1,6,8,7,2,3,5,4]=>[8,5,2,6,7,4,1,3]=>[1,4,7,3,2,5,8,6]=>[3,1,3,1]
[1,6,8,7,2,5,3,4]=>[7,2,8,5,6,4,1,3]=>[2,7,1,4,3,5,8,6]=>[2,2,3,1]
[1,5,2,4,8,3,6,7]=>[4,6,2,7,8,1,3,5]=>[5,3,7,2,1,8,6,4]=>[1,2,1,2,1,1]
[1,2,4,5,8,6,3,7]=>[7,3,4,6,8,1,2,5]=>[2,6,5,3,1,8,7,4]=>[2,1,1,2,1,1]
[1,2,8,3,5,4,7,6]=>[5,8,4,6,7,1,2,3]=>[4,1,5,3,2,8,7,6]=>[1,2,1,2,1,1]
[1,3,8,2,5,4,7,6]=>[5,8,2,4,6,7,1,3]=>[4,1,7,5,3,2,8,6]=>[1,2,1,1,2,1]
[1,6,7,5,2,4,8,3]=>[6,2,8,5,4,1,3,7]=>[3,7,1,4,5,8,6,2]=>[2,4,1,1]
[1,7,4,2,5,8,3,6]=>[5,3,7,8,4,1,2,6]=>[4,6,2,1,5,8,7,3]=>[2,1,3,1,1]
[1,6,4,3,7,5,2,8]=>[3,7,4,2,6,1,5,8]=>[6,2,5,7,3,8,4,1]=>[1,3,2,1,1]
[1,6,5,4,7,2,3,8]=>[6,4,3,2,7,1,5,8]=>[3,5,6,7,2,8,4,1]=>[4,2,1,1]
[1,7,3,2,6,4,8,5]=>[8,3,6,4,5,1,2,7]=>[1,6,3,5,4,8,7,2]=>[2,2,2,1,1]
[1,5,8,2,3,6,7,4]=>[6,2,8,4,5,7,1,3]=>[3,7,1,5,4,2,8,6]=>[2,2,1,2,1]
[1,3,2,6,8,5,4,7]=>[4,7,2,6,8,1,3,5]=>[5,2,7,3,1,8,6,4]=>[1,2,1,2,1,1]
[1,6,3,2,7,4,5,8]=>[3,6,7,4,1,2,5,8]=>[6,3,2,5,8,7,4,1]=>[1,1,3,1,1,1]
[1,7,8,5,4,2,3,6]=>[6,7,5,4,2,8,1,3]=>[3,2,4,5,7,1,8,6]=>[1,4,2,1]
[1,8,4,7,3,2,6,5]=>[3,5,8,6,7,4,1,2]=>[6,4,1,3,2,5,8,7]=>[1,1,2,3,1]
[1,3,8,4,2,6,5,7]=>[4,7,2,5,6,8,1,3]=>[5,2,7,4,3,1,8,6]=>[1,2,1,1,2,1]
[1,7,4,2,6,5,8,3]=>[3,6,5,8,4,1,2,7]=>[6,3,4,1,5,8,7,2]=>[1,2,3,1,1]
[1,6,5,8,3,7,4,2]=>[3,2,8,5,7,6,1,4]=>[6,7,1,4,2,3,8,5]=>[2,2,3,1]
[1,7,4,8,3,2,5,6]=>[3,6,5,7,2,8,1,4]=>[6,3,4,2,7,1,8,5]=>[1,2,2,2,1]
[1,4,8,3,2,7,5,6]=>[2,4,7,8,5,6,1,3]=>[7,5,2,1,4,3,8,6]=>[1,1,1,2,2,1]
[1,8,3,6,4,5,2,7]=>[5,7,3,6,4,8,1,2]=>[4,2,6,3,5,1,8,7]=>[1,2,2,2,1]
[1,6,4,7,3,2,8,5]=>[3,5,2,8,6,1,4,7]=>[6,4,7,1,3,8,5,2]=>[1,2,3,1,1]
[8,2,3,7,4,5,6,1]=>[5,6,8,2,3,7,4,1]=>[4,3,1,7,6,2,5,8]=>[1,1,2,1,3]
[8,5,7,2,3,6,4,1]=>[8,4,2,5,7,6,3,1]=>[1,5,7,4,2,3,6,8]=>[3,1,4]
[7,6,1,5,4,8,2,3]=>[7,5,4,8,3,2,1,6]=>[2,4,5,1,6,7,8,3]=>[3,4,1]
[7,6,3,2,1,8,4,5]=>[4,3,7,8,5,2,1,6]=>[5,6,2,1,4,7,8,3]=>[2,1,4,1]
[2,8,7,3,4,6,1,5]=>[4,5,7,8,6,1,3,2]=>[5,4,2,1,3,8,6,7]=>[1,1,1,3,2]
[6,5,1,3,7,2,8,4]=>[8,4,6,3,2,1,5,7]=>[1,5,3,6,7,8,4,2]=>[2,4,1,1]
[8,1,7,3,4,5,2,6]=>[4,5,7,6,8,2,3,1]=>[5,4,2,3,1,7,6,8]=>[1,1,2,2,2]
[7,1,8,3,4,5,2,6]=>[4,5,7,6,8,2,1,3]=>[5,4,2,3,1,7,8,6]=>[1,1,2,3,1]
[6,8,7,3,4,2,1,5]=>[4,1,7,6,5,8,3,2]=>[5,8,2,3,4,1,6,7]=>[2,3,3]
[3,8,7,1,2,4,5,6]=>[1,4,5,6,7,8,3,2]=>[8,5,4,3,2,1,6,7]=>[1,1,1,1,1,3]
[1,8,5,3,4,6,2,7]=>[4,5,3,7,6,8,1,2]=>[5,4,6,2,3,1,8,7]=>[1,2,2,2,1]
[7,1,6,5,4,3,8,2]=>[6,5,4,3,8,2,1,7]=>[3,4,5,6,1,7,8,2]=>[4,3,1]
[7,1,3,6,4,5,8,2]=>[5,6,3,4,8,2,1,7]=>[4,3,6,5,1,7,8,2]=>[1,2,1,3,1]
[7,1,5,3,6,4,8,2]=>[6,4,3,5,8,2,1,7]=>[3,5,6,4,1,7,8,2]=>[3,1,3,1]
[6,1,5,3,7,8,2,4]=>[7,4,3,5,1,8,2,6]=>[2,5,6,4,8,1,7,3]=>[3,2,2,1]
[5,8,7,1,2,6,3,4]=>[7,1,8,4,5,6,3,2]=>[2,8,1,5,4,3,6,7]=>[2,2,1,3]
[6,8,2,3,4,7,1,5]=>[3,4,5,1,7,8,6,2]=>[6,5,4,8,2,1,3,7]=>[1,1,2,1,3]
[5,1,7,3,8,6,2,4]=>[7,1,8,4,3,6,2,5]=>[2,8,1,5,6,3,7,4]=>[2,3,2,1]
[6,1,3,2,4,7,8,5]=>[3,6,8,2,4,1,5,7]=>[6,3,1,7,5,8,4,2]=>[1,1,2,2,1,1]
[6,2,1,3,4,7,8,5]=>[2,6,8,3,4,1,5,7]=>[7,3,1,6,5,8,4,2]=>[1,1,2,2,1,1]
[3,2,5,8,7,4,1,6]=>[7,1,3,6,8,2,5,4]=>[2,8,6,3,1,7,4,5]=>[2,1,1,2,2]
[4,2,5,8,7,3,1,6]=>[1,7,3,6,8,2,5,4]=>[8,2,6,3,1,7,4,5]=>[1,2,1,2,2]
[8,3,4,1,6,5,2,7]=>[2,3,7,6,4,5,8,1]=>[7,6,2,3,5,4,1,8]=>[1,1,3,1,2]
[3,4,8,5,7,2,1,6]=>[4,7,1,2,6,8,5,3]=>[5,2,8,7,3,1,4,6]=>[1,2,1,1,3]
[3,6,4,8,5,7,2,1]=>[5,2,8,1,3,7,6,4]=>[4,7,1,8,6,2,3,5]=>[2,2,1,3]
[5,8,4,7,3,6,2,1]=>[1,3,5,8,7,6,4,2]=>[8,6,4,1,2,3,5,7]=>[1,1,1,5]
[6,5,8,2,1,7,4,3]=>[8,4,2,1,7,5,6,3]=>[1,5,7,8,2,4,3,6]=>[4,2,2]
[6,1,4,3,8,7,2,5]=>[3,7,8,4,1,6,2,5]=>[6,2,1,5,8,3,7,4]=>[1,1,3,2,1]
[5,1,3,2,6,8,7,4]=>[8,3,5,1,7,2,4,6]=>[1,6,4,8,2,7,5,3]=>[2,2,2,1,1]
[6,1,3,8,7,2,4,5]=>[6,7,8,3,1,5,2,4]=>[3,2,1,6,8,4,7,5]=>[1,1,3,2,1]
[1,2,8,4,5,7,3,6]=>[4,5,7,8,6,1,2,3]=>[5,4,2,1,3,8,7,6]=>[1,1,1,3,1,1]
[4,2,1,8,7,6,3,5]=>[1,7,8,6,2,5,3,4]=>[8,2,1,3,7,4,6,5]=>[1,1,3,2,1]
[3,2,5,8,7,1,4,6]=>[1,3,6,7,8,2,5,4]=>[8,6,3,2,1,7,4,5]=>[1,1,1,1,2,2]
[2,5,8,4,7,1,6,3]=>[2,4,8,6,7,1,5,3]=>[7,5,1,3,2,8,4,6]=>[1,1,2,2,2]
[1,6,2,4,8,5,7,3]=>[6,8,4,2,7,1,3,5]=>[3,1,5,7,2,8,6,4]=>[1,3,2,1,1]
[3,1,6,5,8,7,2,4]=>[4,1,3,7,8,6,2,5]=>[5,8,6,2,1,3,7,4]=>[2,1,1,3,1]
[4,8,5,3,6,7,1,2]=>[4,1,3,7,5,8,6,2]=>[5,8,6,2,4,1,3,7]=>[2,1,2,3]
[1,8,5,3,4,7,6,2]=>[8,4,3,5,7,6,1,2]=>[1,5,6,4,2,3,8,7]=>[3,1,3,1]
[2,7,1,3,6,4,5,8]=>[6,7,1,3,4,5,2,8]=>[3,2,8,6,5,4,7,1]=>[1,2,1,1,2,1]
[8,1,7,3,5,4,6,2]=>[6,4,5,8,7,2,3,1]=>[3,5,4,1,2,7,6,8]=>[2,1,3,2]
[1,8,6,3,2,5,4,7]=>[4,7,5,6,3,8,1,2]=>[5,2,4,3,6,1,8,7]=>[1,2,2,2,1]
[3,2,4,8,5,7,1,6]=>[1,5,7,8,2,3,6,4]=>[8,4,2,1,7,6,3,5]=>[1,1,1,2,1,2]
[8,1,2,4,7,5,6,3]=>[6,8,4,7,2,3,5,1]=>[3,1,5,2,7,6,4,8]=>[1,2,2,1,2]
[6,4,5,8,3,1,7,2]=>[2,3,1,8,6,5,7,4]=>[7,6,8,1,3,4,2,5]=>[1,2,3,2]
[8,6,2,1,5,7,3,4]=>[7,3,5,8,4,2,6,1]=>[2,6,4,1,5,7,3,8]=>[2,1,3,2]
[8,7,2,4,1,5,3,6]=>[7,3,5,4,6,8,2,1]=>[2,6,4,5,3,1,7,8]=>[2,2,1,3]
[7,5,3,4,8,6,2,1]=>[8,3,2,4,1,7,6,5]=>[1,6,7,5,8,2,3,4]=>[3,2,3]
[4,3,6,5,1,2,7,8]=>[2,1,5,6,4,3,7,8]=>[7,8,4,3,5,6,2,1]=>[2,1,3,1,1]
[5,8,3,7,6,4,2,1]=>[8,1,7,3,6,5,4,2]=>[1,8,2,6,3,4,5,7]=>[2,2,4]
[1,3,8,7,6,5,2,4]=>[7,8,6,5,2,4,1,3]=>[2,1,3,4,7,5,8,6]=>[1,4,2,1]
[4,8,7,2,6,3,1,5]=>[7,1,4,6,8,5,3,2]=>[2,8,5,3,1,4,6,7]=>[2,1,1,4]
[1,8,7,2,6,3,5,4]=>[8,6,7,4,5,3,1,2]=>[1,3,2,5,4,6,8,7]=>[2,2,3,1]
[8,7,2,1,4,3,5,6]=>[3,6,4,5,7,8,2,1]=>[6,3,5,4,2,1,7,8]=>[1,2,1,1,3]
[2,8,7,1,6,3,4,5]=>[6,7,8,4,5,1,3,2]=>[3,2,1,5,4,8,6,7]=>[1,1,2,2,2]
[4,2,8,7,6,5,1,3]=>[7,8,1,6,5,2,4,3]=>[2,1,8,3,4,7,5,6]=>[1,2,3,2]
[8,4,2,7,6,5,3,1]=>[8,2,7,6,3,5,4,1]=>[1,7,2,3,6,4,5,8]=>[2,3,3]
[6,8,7,5,2,4,3,1]=>[1,8,5,7,6,4,3,2]=>[8,1,4,2,3,5,6,7]=>[1,2,5]
[1,2,5,7,4,8,6,3]=>[8,3,5,4,7,1,2,6]=>[1,6,4,5,2,8,7,3]=>[2,2,2,1,1]
[6,2,1,8,7,5,3,4]=>[7,8,6,2,1,5,3,4]=>[2,1,3,7,8,4,6,5]=>[1,4,2,1]
[6,3,8,7,4,5,2,1]=>[5,1,8,7,2,6,4,3]=>[4,8,1,2,7,3,5,6]=>[2,3,3]
[4,6,5,3,2,8,1,7]=>[5,1,4,3,2,7,8,6]=>[4,8,5,6,7,2,1,3]=>[2,3,1,2]
[2,8,3,4,1,5,6,7]=>[3,5,1,4,6,7,8,2]=>[6,4,8,5,3,2,1,7]=>[1,2,1,1,1,2]
[4,5,6,3,1,8,2,7]=>[1,2,7,4,3,8,5,6]=>[8,7,2,5,6,1,4,3]=>[1,1,3,2,1]
[5,2,1,4,3,6,8,7]=>[2,4,8,3,1,5,6,7]=>[7,5,1,6,8,4,3,2]=>[1,1,3,1,1,1]
[1,5,6,3,8,4,2,7]=>[2,7,4,3,6,8,1,5]=>[7,2,5,6,3,1,8,4]=>[1,3,1,2,1]
[2,6,5,3,8,4,1,7]=>[7,4,3,1,2,6,8,5]=>[2,5,6,8,7,3,1,4]=>[4,1,1,2]
[5,7,3,8,4,2,6,1]=>[1,6,3,5,2,8,7,4]=>[8,3,6,4,7,1,2,5]=>[1,2,2,3]
[5,3,6,2,8,4,1,7]=>[7,2,1,4,3,6,8,5]=>[2,7,8,5,6,3,1,4]=>[3,2,1,2]
[2,3,6,5,4,8,1,7]=>[5,4,1,2,3,7,8,6]=>[4,5,8,7,6,2,1,3]=>[3,1,1,1,2]
[3,7,5,4,8,2,6,1]=>[4,3,6,1,2,8,7,5]=>[5,6,3,8,7,1,2,4]=>[2,2,1,3]
[5,3,7,1,2,8,4,6]=>[2,7,1,8,4,5,3,6]=>[7,2,8,1,5,4,6,3]=>[1,2,2,2,1]
[6,3,8,7,2,5,4,1]=>[8,5,1,7,2,6,4,3]=>[1,4,8,2,7,3,5,6]=>[3,2,3]
[2,8,7,6,1,5,3,4]=>[7,8,5,6,4,1,3,2]=>[2,1,4,3,5,8,6,7]=>[1,2,3,2]
[9,7,8,5,4,3,2,1,6]=>[8,7,6,5,4,2,9,3,1]=>[2,3,4,5,6,8,1,7,9]=>[6,3]
[1,2,3,4,6,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[4,9,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1]
[1,2,3,5,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[5,9,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1]
[6,8,4,1,7,5,2,3]=>[7,3,1,8,6,4,5,2]=>[2,6,8,1,3,5,4,7]=>[3,3,2]
[8,1,4,6,7,5,2,3]=>[7,3,4,8,6,2,5,1]=>[2,6,5,1,3,7,4,8]=>[2,1,3,2]
[2,6,8,1,4,7,5,3]=>[8,5,2,7,1,4,6,3]=>[1,4,7,2,8,5,3,6]=>[3,2,1,2]
[8,1,4,6,7,2,5,3]=>[8,3,6,4,7,2,5,1]=>[1,6,3,5,2,7,4,8]=>[2,2,2,2]
[8,2,1,6,7,4,5,3]=>[6,4,8,2,7,3,5,1]=>[3,5,1,7,2,6,4,8]=>[2,2,2,2]
[8,2,6,1,7,4,5,3]=>[6,8,7,2,4,3,5,1]=>[3,1,2,7,5,6,4,8]=>[1,3,2,2]
[4,2,8,1,6,7,5,3]=>[1,5,8,7,2,4,6,3]=>[8,4,1,2,7,5,3,6]=>[1,1,3,1,2]
[8,1,2,6,4,7,5,3]=>[8,5,4,7,2,3,6,1]=>[1,4,5,2,7,6,3,8]=>[3,2,1,2]
[4,8,1,2,6,7,5,3]=>[1,5,8,7,3,4,6,2]=>[8,4,1,2,6,5,3,7]=>[1,1,3,1,2]
[8,1,6,2,4,7,5,3]=>[8,5,7,4,2,3,6,1]=>[1,4,2,5,7,6,3,8]=>[2,3,1,2]
[8,2,4,6,1,7,5,3]=>[8,3,7,2,5,4,6,1]=>[1,6,2,7,4,5,3,8]=>[2,2,2,2]
[2,1,4,5,6,7,8,9,10,3]=>[1,3,4,5,6,7,8,10,2,9]=>[10,8,7,6,5,4,3,1,9,2]=>[1,1,1,1,1,1,1,2,1]
[2,3,4,5,6,7,8,1,10,9]=>[1,2,3,4,5,6,7,10,8,9]=>[10,9,8,7,6,5,4,1,3,2]=>[1,1,1,1,1,1,1,2,1]
[5,4,7,6,3,1,2,8]=>[2,1,6,7,5,4,3,8]=>[7,8,3,2,4,5,6,1]=>[2,1,4,1]
[3,6,4,8,1,5,2,7]=>[3,7,1,5,2,6,8,4]=>[6,2,8,4,7,3,1,5]=>[1,2,2,1,2]
[3,6,8,4,1,5,2,7]=>[7,5,1,4,2,6,8,3]=>[2,4,8,5,7,3,1,6]=>[3,2,1,2]
[8,7,1,4,2,3,5,6]=>[5,6,3,4,7,8,2,1]=>[4,3,6,5,2,1,7,8]=>[1,2,1,1,3]
[3,8,6,4,1,5,2,7]=>[7,5,1,4,6,3,8,2]=>[2,4,8,5,3,6,1,7]=>[3,1,2,2]
[8,2,6,5,7,1,3,4]=>[6,7,4,2,3,8,5,1]=>[3,2,5,7,6,1,4,8]=>[1,3,1,3]
[4,6,1,3,2,8,7,5]=>[1,8,4,7,3,2,5,6]=>[8,1,5,2,6,7,4,3]=>[1,2,3,1,1]
[7,1,4,8,2,3,6,5]=>[3,8,5,6,7,2,1,4]=>[6,1,4,3,2,7,8,5]=>[1,2,1,3,1]
[4,5,3,6,7,1,8,2]=>[1,3,2,4,8,6,5,7]=>[8,6,7,5,1,3,4,2]=>[1,2,1,3,1]
[1,4,7,8,3,5,2,6]=>[5,7,2,6,3,8,1,4]=>[4,2,7,3,6,1,8,5]=>[1,2,2,2,1]
[4,6,1,3,5,2,8,7]=>[4,1,5,8,3,2,6,7]=>[5,8,4,1,6,7,3,2]=>[2,1,3,1,1]
[2,5,1,4,8,3,7,6]=>[8,4,1,2,6,7,3,5]=>[1,5,8,7,3,2,6,4]=>[3,1,1,2,1]
[6,1,2,5,4,8,7,3]=>[4,8,5,7,2,1,3,6]=>[5,1,4,2,7,8,6,3]=>[1,2,3,1,1]
[8,4,1,7,3,5,6,2]=>[5,2,6,8,7,3,4,1]=>[4,7,3,1,2,6,5,8]=>[2,1,3,2]
[8,4,1,2,5,7,3,6]=>[5,7,2,8,3,4,6,1]=>[4,2,7,1,6,5,3,8]=>[1,2,2,1,2]
[2,4,5,6,8,3,1,7]=>[2,3,4,7,1,6,8,5]=>[7,6,5,2,8,3,1,4]=>[1,1,1,2,1,2]
[3,4,5,8,6,2,1,7]=>[7,1,2,3,6,5,8,4]=>[2,8,7,6,3,4,1,5]=>[2,1,1,2,2]
[4,5,1,8,6,3,7,2]=>[1,2,6,5,8,7,3,4]=>[8,7,3,4,1,2,6,5]=>[1,1,2,3,1]
[8,3,7,2,1,6,5,4]=>[8,2,4,7,5,6,3,1]=>[1,7,5,2,4,3,6,8]=>[2,1,2,3]
[8,4,7,3,6,2,1,5]=>[2,4,7,6,8,5,3,1]=>[7,5,2,3,1,4,6,8]=>[1,1,2,4]
[3,8,7,5,6,4,1,2]=>[7,4,8,6,1,5,3,2]=>[2,5,1,3,8,4,6,7]=>[2,3,3]
[3,8,7,5,6,2,1,4]=>[7,6,4,8,1,5,3,2]=>[2,3,5,1,8,4,6,7]=>[3,2,3]
[3,8,7,5,6,2,4,1]=>[6,4,8,7,1,5,3,2]=>[3,5,1,2,8,4,6,7]=>[2,3,3]
[2,8,7,5,6,4,1,3]=>[7,4,8,6,5,1,3,2]=>[2,5,1,3,4,8,6,7]=>[2,4,2]
[6,7,8,9,2,3,4,5,10,1]=>[5,1,6,2,7,3,8,4,10,9]=>[6,10,5,9,4,8,3,7,1,2]=>[2,2,2,2,2]
[10,1,9,2,8,3,7,4,6,5]=>[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>[2,2,2,2,2]
[1,5,6,3,8,2,7,4]=>[2,8,4,3,6,7,1,5]=>[7,1,5,6,3,2,8,4]=>[1,3,1,2,1]
[2,6,3,8,4,7,1,5]=>[5,7,2,8,1,3,6,4]=>[4,2,7,1,8,6,3,5]=>[1,2,2,1,2]
[2,6,3,5,7,8,1,4]=>[4,7,3,1,2,5,8,6]=>[5,2,6,8,7,4,1,3]=>[1,3,1,1,2]
[1,5,6,3,7,2,8,4]=>[2,8,4,3,6,1,5,7]=>[7,1,5,6,3,8,4,2]=>[1,3,2,1,1]
[1,7,5,3,6,2,8,4]=>[8,4,3,6,5,1,2,7]=>[1,5,6,3,4,8,7,2]=>[3,3,1,1]
[1,5,7,3,4,2,8,6]=>[4,2,5,8,6,1,3,7]=>[5,7,4,1,3,8,6,2]=>[2,1,3,1,1]
[1,5,8,3,4,2,7,6]=>[4,2,5,8,6,7,1,3]=>[5,7,4,1,3,2,8,6]=>[2,1,2,2,1]
[1,4,5,3,7,2,8,6]=>[2,3,8,4,6,1,5,7]=>[7,6,1,5,3,8,4,2]=>[1,1,2,2,1,1]
[1,4,5,3,8,2,7,6]=>[2,3,8,4,6,7,1,5]=>[7,6,1,5,3,2,8,4]=>[1,1,2,1,2,1]
[6,5,1,4,2,7,8,3]=>[6,4,8,3,2,1,5,7]=>[3,5,1,6,7,8,4,2]=>[2,4,1,1]
[6,5,1,4,2,8,7,3]=>[4,8,7,3,2,1,5,6]=>[5,1,2,6,7,8,4,3]=>[1,5,1,1]
[1,7,5,4,2,8,6,3]=>[4,3,8,7,5,1,2,6]=>[5,6,1,2,4,8,7,3]=>[2,4,1,1]
[5,1,6,8,3,7,2,4]=>[5,3,1,7,8,6,2,4]=>[4,6,8,2,1,3,7,5]=>[3,1,3,1]
[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1,1,1,1,1]
[3,8,5,2,1,4,7,6]=>[4,8,1,5,3,6,7,2]=>[5,1,8,4,6,3,2,7]=>[1,2,2,1,2]
[3,5,4,8,2,6,7,1]=>[3,1,2,5,6,8,7,4]=>[6,8,7,4,3,1,2,5]=>[2,1,1,1,3]
[5,4,7,1,8,6,3,2]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[1,2,4,1]
[1,4,8,2,6,5,3,7]=>[7,2,6,4,5,8,1,3]=>[2,7,3,5,4,1,8,6]=>[2,2,1,2,1]
[8,5,1,3,6,2,4,7]=>[4,6,7,3,2,5,8,1]=>[5,3,2,6,7,4,1,8]=>[1,1,3,1,2]
[1,4,8,2,6,7,3,5]=>[7,2,5,8,4,6,1,3]=>[2,7,4,1,5,3,8,6]=>[2,1,2,2,1]
[1,2,5,6,8,7,3,4]=>[3,4,7,8,6,1,2,5]=>[6,5,2,1,3,8,7,4]=>[1,1,1,3,1,1]
[1,5,6,8,2,7,4,3]=>[2,3,8,7,5,6,1,4]=>[7,6,1,2,4,3,8,5]=>[1,1,3,2,1]
[2,6,7,3,4,1,8,5]=>[4,5,2,8,1,6,3,7]=>[5,4,7,1,8,3,6,2]=>[1,2,2,2,1]
[1,6,5,7,8,2,4,3]=>[3,2,8,6,4,7,1,5]=>[6,7,1,3,5,2,8,4]=>[2,3,2,1]
[3,7,6,1,8,2,4,5]=>[6,7,8,1,4,3,2,5]=>[3,2,1,8,5,6,7,4]=>[1,1,2,3,1]
[1,3,7,2,6,4,8,5]=>[8,6,2,4,5,1,3,7]=>[1,3,7,5,4,8,6,2]=>[3,1,2,1,1]
[1,5,8,6,7,3,4,2]=>[6,2,4,8,7,5,1,3]=>[3,7,5,1,2,4,8,6]=>[2,1,4,1]
[1,6,5,8,7,2,4,3]=>[3,2,8,6,7,5,1,4]=>[6,7,1,3,2,4,8,5]=>[2,2,3,1]
[1,5,7,6,2,8,3,4]=>[2,7,8,5,4,1,3,6]=>[7,2,1,4,5,8,6,3]=>[1,1,4,1,1]
[1,2,5,8,6,7,4,3]=>[5,8,3,7,6,1,2,4]=>[4,1,6,2,3,8,7,5]=>[1,2,3,1,1]
[1,2,6,5,7,3,8,4]=>[4,3,8,6,1,2,5,7]=>[5,6,1,3,8,7,4,2]=>[2,3,1,1,1]
[1,7,5,8,6,4,2,3]=>[3,7,2,8,6,5,1,4]=>[6,2,7,1,3,4,8,5]=>[1,2,4,1]
[3,6,5,8,1,2,7,4]=>[8,5,1,3,2,6,7,4]=>[1,4,8,6,7,3,2,5]=>[3,2,1,2]
[5,4,7,8,1,6,3,2]=>[1,8,2,7,5,3,6,4]=>[8,1,7,2,4,6,3,5]=>[1,2,3,2]
[2,5,6,8,1,3,7,4]=>[2,8,5,1,3,6,7,4]=>[7,1,4,8,6,3,2,5]=>[1,3,1,1,2]
[5,3,6,8,1,2,7,4]=>[8,2,1,5,3,6,7,4]=>[1,7,8,4,6,3,2,5]=>[3,2,1,2]
[4,6,5,8,3,2,7,1]=>[3,1,2,6,5,8,7,4]=>[6,8,7,3,4,1,2,5]=>[2,1,2,3]
[2,5,8,7,1,6,4,3]=>[8,2,7,5,6,1,4,3]=>[1,7,2,4,3,8,5,6]=>[2,2,2,2]
[7,3,6,8,5,2,1,4]=>[7,6,2,3,1,8,5,4]=>[2,3,7,6,8,1,4,5]=>[3,2,3]
[8,3,6,7,5,2,4,1]=>[6,3,8,2,7,5,4,1]=>[3,6,1,7,2,4,5,8]=>[2,2,4]
[8,4,5,7,3,6,2,1]=>[2,3,5,8,7,6,4,1]=>[7,6,4,1,2,3,5,8]=>[1,1,1,5]
[2,4,7,8,5,6,3,1]=>[5,3,8,2,7,1,6,4]=>[4,6,1,7,2,8,3,5]=>[2,2,2,2]
[3,6,8,7,5,2,4,1]=>[2,6,8,7,1,5,4,3]=>[7,3,1,2,8,4,5,6]=>[1,1,3,3]
[6,4,7,8,5,1,3,2]=>[8,2,1,6,3,7,5,4]=>[1,7,8,3,6,2,4,5]=>[3,2,3]
[7,8,4,6,5,3,1,2]=>[3,7,1,8,6,5,4,2]=>[6,2,8,1,3,4,5,7]=>[1,2,5]
[6,8,4,7,5,1,3,2]=>[3,1,8,6,7,5,4,2]=>[6,8,1,3,2,4,5,7]=>[2,2,4]
[7,6,1,2,3,5,4,8]=>[7,3,4,5,6,2,1,8]=>[2,6,5,4,3,7,8,1]=>[2,1,1,3,1]
[8,7,6,4,2,1,5,3]=>[5,8,6,4,7,3,2,1]=>[4,1,3,5,2,6,7,8]=>[1,3,4]
[3,8,7,5,2,6,4,1]=>[8,5,4,7,1,6,3,2]=>[1,4,5,2,8,3,6,7]=>[3,2,3]
[3,8,7,4,2,6,5,1]=>[4,8,5,7,1,6,3,2]=>[5,1,4,2,8,3,6,7]=>[1,2,2,3]
[5,8,3,2,4,7,6,1]=>[3,1,8,4,5,7,6,2]=>[6,8,1,5,4,2,3,7]=>[2,2,1,3]
[1,3,4,7,2,6,5,8]=>[7,2,3,5,6,1,4,8]=>[2,7,6,4,3,8,5,1]=>[2,1,1,2,1,1]
[2,5,1,4,3,6,7,8]=>[5,1,3,4,2,6,7,8]=>[4,8,6,5,7,3,2,1]=>[2,1,2,1,1,1]
[4,5,8,3,2,6,1,7]=>[1,2,5,4,7,6,8,3]=>[8,7,4,5,2,3,1,6]=>[1,1,2,2,2]
[5,8,2,1,4,6,3,7]=>[3,5,1,7,4,6,8,2]=>[6,4,8,2,5,3,1,7]=>[1,2,2,1,2]
[4,1,5,8,3,6,2,7]=>[3,1,5,7,6,8,2,4]=>[6,8,4,2,3,1,7,5]=>[2,1,2,2,1]
[4,5,8,3,6,1,2,7]=>[1,2,6,4,7,5,8,3]=>[8,7,3,5,2,4,1,6]=>[1,1,2,2,2]
[3,2,7,1,8,5,4,6]=>[7,1,6,8,2,4,3,5]=>[2,8,3,1,7,5,6,4]=>[2,1,2,2,1]
[4,7,8,5,2,3,1,6]=>[5,7,1,6,4,2,8,3]=>[4,2,8,3,5,7,1,6]=>[1,2,3,2]
[6,2,7,8,1,5,3,4]=>[7,8,5,2,1,3,6,4]=>[2,1,4,7,8,6,3,5]=>[1,4,1,2]
[2,7,1,3,8,5,4,6]=>[7,6,8,1,3,4,2,5]=>[2,3,1,8,6,5,7,4]=>[2,2,1,2,1]
[2,6,7,8,4,1,3,5]=>[6,2,7,5,1,3,8,4]=>[3,7,2,4,8,6,1,5]=>[2,3,1,2]
[2,6,7,8,4,3,1,5]=>[2,7,6,5,1,3,8,4]=>[7,2,3,4,8,6,1,5]=>[1,4,1,2]
[7,1,2,6,3,8,4,5]=>[7,8,5,2,3,4,1,6]=>[2,1,4,7,6,5,8,3]=>[1,3,1,2,1]
[8,5,4,6,1,2,7,3]=>[8,5,3,2,6,4,7,1]=>[1,4,6,7,3,5,2,8]=>[4,2,2]
[7,4,1,8,2,5,3,6]=>[7,5,2,6,8,3,1,4]=>[2,4,7,3,1,6,8,5]=>[3,1,3,1]
[7,2,1,8,3,6,4,5]=>[7,8,2,5,6,3,1,4]=>[2,1,7,4,3,6,8,5]=>[1,2,1,3,1]
[6,8,7,3,1,2,4,5]=>[5,6,4,1,7,8,3,2]=>[4,3,5,8,2,1,6,7]=>[1,3,1,3]
[7,4,8,3,1,2,6,5]=>[2,8,5,4,6,1,7,3]=>[7,1,4,5,3,8,2,6]=>[1,3,2,2]
[8,4,5,3,1,6,7,2]=>[2,6,4,3,8,5,7,1]=>[7,3,5,6,1,4,2,8]=>[1,3,2,2]
[8,2,1,7,4,3,5,6]=>[6,2,5,7,8,3,4,1]=>[3,7,4,2,1,6,5,8]=>[2,1,1,2,2]
[7,2,6,8,4,1,3,5]=>[6,7,5,2,3,1,8,4]=>[3,2,4,7,6,8,1,5]=>[1,3,2,2]
[7,2,5,1,6,8,3,4]=>[7,5,2,3,8,4,1,6]=>[2,4,7,6,1,5,8,3]=>[3,1,3,1]
[6,2,1,7,4,8,3,5]=>[5,7,2,4,1,8,3,6]=>[4,2,7,5,8,1,6,3]=>[1,2,2,2,1]
[1,7,4,3,2,5,6,8]=>[5,4,3,6,7,1,2,8]=>[4,5,6,3,2,8,7,1]=>[3,1,2,1,1]
[3,7,5,8,2,4,6,1]=>[5,3,6,1,2,8,7,4]=>[4,6,3,8,7,1,2,5]=>[2,2,1,3]
[5,2,1,6,3,4,8,7]=>[8,2,5,3,1,4,6,7]=>[1,7,4,6,8,5,3,2]=>[2,3,1,1,1]
[3,8,4,5,7,2,6,1]=>[3,4,6,8,1,7,5,2]=>[6,5,3,1,8,2,4,7]=>[1,1,1,2,3]
[3,8,4,7,5,6,2,1]=>[5,8,3,7,1,6,4,2]=>[4,1,6,2,8,3,5,7]=>[1,2,2,3]
[4,2,8,6,3,7,5,1]=>[8,1,5,4,7,2,6,3]=>[1,8,4,5,2,7,3,6]=>[2,2,2,2]
[4,1,7,6,3,8,5,2]=>[8,1,5,4,3,7,2,6]=>[1,8,4,5,6,2,7,3]=>[2,3,2,1]
[7,4,1,8,5,3,6,2]=>[2,6,5,8,7,3,1,4]=>[7,3,4,1,2,6,8,5]=>[1,2,4,1]
[3,5,6,8,4,7,1,2]=>[2,3,7,1,5,8,6,4]=>[7,6,2,8,4,1,3,5]=>[1,1,2,1,3]
[5,4,1,8,6,7,2,3]=>[2,1,7,5,8,6,3,4]=>[7,8,2,4,1,3,6,5]=>[2,2,3,1]
[6,2,8,4,5,3,7,1]=>[4,6,5,1,8,2,7,3]=>[5,3,4,8,1,7,2,6]=>[1,3,2,2]
[4,5,2,1,8,7,3,6]=>[1,7,2,8,3,6,4,5]=>[8,2,7,1,6,3,5,4]=>[1,2,2,2,1]
[4,7,3,8,2,6,5,1]=>[8,1,3,5,2,7,6,4]=>[1,8,6,4,7,2,3,5]=>[2,1,2,3]
[4,7,3,1,8,6,2,5]=>[1,3,7,8,6,4,2,5]=>[8,6,2,1,3,5,7,4]=>[1,1,1,4,1]
[6,3,7,1,2,5,8,4]=>[2,6,8,4,1,5,3,7]=>[7,3,1,5,8,4,6,2]=>[1,1,3,2,1]
[5,1,4,7,8,2,6,3]=>[8,3,1,6,4,7,2,5]=>[1,6,8,3,5,2,7,4]=>[3,2,2,1]
[7,2,5,8,1,3,6,4]=>[8,5,2,3,6,1,7,4]=>[1,4,7,6,3,8,2,5]=>[3,1,2,2]
[3,8,7,5,2,1,6,4]=>[5,8,6,1,4,7,3,2]=>[4,1,3,8,5,2,6,7]=>[1,3,1,3]
[3,8,5,6,2,7,4,1]=>[3,8,5,1,4,7,6,2]=>[6,1,4,8,5,2,3,7]=>[1,3,1,3]
[3,6,5,8,4,2,7,1]=>[3,2,6,1,5,8,7,4]=>[6,7,3,8,4,1,2,5]=>[2,2,1,3]
[6,8,3,2,5,7,4,1]=>[3,5,1,8,4,7,6,2]=>[6,4,8,1,5,2,3,7]=>[1,2,2,3]
[4,1,5,6,8,7,3,2]=>[1,8,3,4,7,6,2,5]=>[8,1,6,5,2,3,7,4]=>[1,2,1,3,1]
[8,4,2,3,6,7,5,1]=>[5,2,8,3,4,7,6,1]=>[4,7,1,6,5,2,3,8]=>[2,2,1,3]
[4,5,1,3,7,6,8,2]=>[1,6,4,2,5,8,3,7]=>[8,3,5,7,4,1,6,2]=>[1,3,1,2,1]
[3,5,4,8,6,2,7,1]=>[2,6,1,3,5,8,7,4]=>[7,3,8,6,4,1,2,5]=>[1,2,1,1,3]
[3,6,2,4,5,8,7,1]=>[8,1,3,4,2,5,7,6]=>[1,8,6,5,7,4,2,3]=>[2,1,2,1,2]
[8,1,3,7,4,5,6,2]=>[5,6,8,3,7,2,4,1]=>[4,3,1,6,2,7,5,8]=>[1,1,2,2,2]
[8,1,5,3,6,4,7,2]=>[6,4,3,5,8,2,7,1]=>[3,5,6,4,1,7,2,8]=>[3,1,2,2]
[2,6,4,8,3,1,5,7]=>[3,6,5,1,2,7,8,4]=>[6,3,4,8,7,2,1,5]=>[1,3,1,1,2]
[2,6,4,1,5,8,7,3]=>[3,8,5,1,2,7,4,6]=>[6,1,4,8,7,2,5,3]=>[1,3,1,2,1]
[3,5,1,4,6,2,7,8]=>[1,4,6,3,2,5,7,8]=>[8,5,3,6,7,4,2,1]=>[1,1,3,1,1,1]
[7,6,5,2,4,3,8,1]=>[6,4,5,3,2,1,8,7]=>[3,5,4,6,7,8,1,2]=>[2,4,2]
[3,6,4,5,2,8,1,7]=>[3,5,1,4,2,7,8,6]=>[6,4,8,5,7,2,1,3]=>[1,2,2,1,2]
[8,1,5,4,7,3,6,2]=>[4,3,6,8,7,2,5,1]=>[5,6,3,1,2,7,4,8]=>[2,1,3,2]
[7,6,5,4,1,8,2,3]=>[7,8,5,4,3,2,1,6]=>[2,1,4,5,6,7,8,3]=>[1,6,1]
[3,6,4,1,5,7,2,8]=>[5,1,3,7,4,2,6,8]=>[4,8,6,2,5,7,3,1]=>[2,1,3,1,1]
[8,1,5,4,7,6,3,2]=>[3,8,4,7,6,2,5,1]=>[6,1,5,2,3,7,4,8]=>[1,2,3,2]
[3,6,4,1,5,7,8,2]=>[5,1,3,6,2,8,4,7]=>[4,8,6,3,7,1,5,2]=>[2,1,2,2,1]
[7,6,5,2,8,4,1,3]=>[7,8,4,3,2,1,6,5]=>[2,1,5,6,7,8,3,4]=>[1,5,2]
[3,1,6,5,2,8,7,4]=>[4,1,3,8,7,2,5,6]=>[5,8,6,1,2,7,4,3]=>[2,1,3,1,1]
[1,7,2,4,3,5,8,6]=>[4,8,3,5,6,1,2,7]=>[5,1,6,4,3,8,7,2]=>[1,2,1,2,1,1]
[3,8,1,7,4,2,6,5]=>[5,8,1,6,7,3,4,2]=>[4,1,8,3,2,6,5,7]=>[1,2,1,2,2]
[8,1,7,4,3,5,6,2]=>[5,4,6,8,7,2,3,1]=>[4,5,3,1,2,7,6,8]=>[2,1,3,2]
[6,8,2,4,5,3,7,1]=>[4,6,3,1,5,8,7,2]=>[5,3,6,8,4,1,2,7]=>[1,3,1,3]
[4,8,5,3,6,1,7,2]=>[4,1,3,8,6,5,7,2]=>[5,8,6,1,3,4,2,7]=>[2,1,3,2]
[2,8,3,1,4,7,5,6]=>[3,7,8,1,4,5,6,2]=>[6,2,1,8,5,4,3,7]=>[1,1,2,1,1,2]
[8,6,3,2,7,4,1,5]=>[3,7,4,6,2,8,5,1]=>[6,2,5,3,7,1,4,8]=>[1,2,2,3]
[2,7,3,1,8,4,5,6]=>[3,6,7,8,1,4,2,5]=>[6,3,2,1,8,5,7,4]=>[1,1,1,2,2,1]
[1,2,8,3,5,6,4,7]=>[5,7,4,6,8,1,2,3]=>[4,2,5,3,1,8,7,6]=>[1,2,1,2,1,1]
[3,5,7,4,8,1,6,2]=>[2,4,8,1,6,3,7,5]=>[7,5,1,8,3,6,2,4]=>[1,1,2,2,2]
[2,8,1,3,5,4,6,7]=>[6,1,3,4,5,7,8,2]=>[3,8,6,5,4,2,1,7]=>[2,1,1,1,1,2]
[1,5,2,8,6,4,3,7]=>[2,7,6,5,8,1,3,4]=>[7,2,3,4,1,8,6,5]=>[1,3,2,1,1]
[7,4,8,6,3,1,2,5]=>[2,6,7,5,1,8,4,3]=>[7,3,2,4,8,1,5,6]=>[1,1,3,3]
[4,7,8,5,2,1,3,6]=>[6,1,5,7,4,2,8,3]=>[3,8,4,2,5,7,1,6]=>[2,1,3,2]
[6,1,5,2,8,7,3,4]=>[7,3,8,6,2,1,4,5]=>[2,6,1,3,7,8,5,4]=>[2,4,1,1]
[8,1,3,5,7,4,2,6]=>[4,7,3,6,8,2,5,1]=>[5,2,6,3,1,7,4,8]=>[1,2,1,2,2]
[3,1,8,5,4,7,2,6]=>[5,1,4,7,8,6,2,3]=>[4,8,5,2,1,3,7,6]=>[2,1,1,3,1]
[3,1,6,4,8,5,2,7]=>[7,1,4,3,6,8,2,5]=>[2,8,5,6,3,1,7,4]=>[2,2,1,2,1]
[5,1,3,4,2,6,8,7]=>[3,4,8,2,1,5,6,7]=>[6,5,1,7,8,4,3,2]=>[1,1,3,1,1,1]
[3,2,6,4,1,5,7,8]=>[1,5,2,4,6,3,7,8]=>[8,4,7,5,3,6,2,1]=>[1,2,1,2,1,1]
[5,4,2,1,8,3,6,7]=>[3,6,2,1,7,8,4,5]=>[6,3,7,8,2,1,5,4]=>[1,3,1,2,1]
[4,2,5,1,8,7,3,6]=>[3,1,7,8,2,6,4,5]=>[6,8,2,1,7,3,5,4]=>[2,1,2,2,1]
[6,8,2,7,1,4,3,5]=>[7,3,5,1,6,8,4,2]=>[2,6,4,8,3,1,5,7]=>[2,2,1,3]
[1,8,4,7,3,2,5,6]=>[3,6,5,7,8,4,1,2]=>[6,3,4,2,1,5,8,7]=>[1,2,1,3,1]
[5,8,3,1,4,7,6,2]=>[3,1,8,5,7,4,6,2]=>[6,8,1,4,2,5,3,7]=>[2,2,2,2]
[1,2,5,4,7,8,3,6]=>[3,7,4,5,8,1,2,6]=>[6,2,5,4,1,8,7,3]=>[1,2,1,2,1,1]
[4,7,1,2,5,3,6,8]=>[6,3,1,4,5,7,2,8]=>[3,6,8,5,4,2,7,1]=>[3,1,1,2,1]
[6,8,4,1,3,7,2,5]=>[5,7,3,1,8,4,6,2]=>[4,2,6,8,1,5,3,7]=>[1,3,2,2]
[3,2,6,1,7,8,5,4]=>[5,1,3,8,2,7,4,6]=>[4,8,6,1,7,2,5,3]=>[2,1,2,2,1]
[5,4,1,6,7,3,2,8]=>[4,2,1,7,6,3,5,8]=>[5,7,8,2,3,6,4,1]=>[3,3,1,1]
[7,4,1,6,5,8,2,3]=>[2,7,5,4,8,3,1,6]=>[7,2,4,5,1,6,8,3]=>[1,3,3,1]
[8,5,4,1,6,7,3,2]=>[5,3,2,8,7,4,6,1]=>[4,6,7,1,2,5,3,8]=>[3,3,2]
[5,2,1,6,4,7,8,3]=>[5,2,4,1,6,8,3,7]=>[4,7,5,8,3,1,6,2]=>[2,2,1,2,1]
[1,6,2,3,5,7,8,4]=>[5,6,8,3,1,2,4,7]=>[4,3,1,6,8,7,5,2]=>[1,1,3,1,1,1]
[8,2,4,6,1,7,3,5]=>[3,7,8,2,5,4,6,1]=>[6,2,1,7,4,5,3,8]=>[1,1,2,2,2]
[1,5,7,2,3,6,8,4]=>[6,2,8,4,5,1,3,7]=>[3,7,1,5,4,8,6,2]=>[2,2,2,1,1]
[7,3,1,4,2,5,8,6]=>[4,2,8,3,5,6,1,7]=>[5,7,1,6,4,3,8,2]=>[2,2,1,2,1]
[4,3,5,1,6,2,7,8]=>[2,1,6,4,3,5,7,8]=>[7,8,3,5,6,4,2,1]=>[2,3,1,1,1]
[8,6,3,5,4,1,2,7]=>[3,6,7,5,4,2,8,1]=>[6,3,2,4,5,7,1,8]=>[1,1,4,2]
[8,3,2,6,1,5,4,7]=>[2,7,3,5,6,4,8,1]=>[7,2,6,4,3,5,1,8]=>[1,2,1,2,2]
[8,5,1,7,4,6,2,3]=>[7,5,2,8,6,3,4,1]=>[2,4,7,1,3,6,5,8]=>[3,3,2]
[4,8,1,7,6,3,5,2]=>[6,8,1,7,5,3,4,2]=>[3,1,8,2,4,6,5,7]=>[1,2,3,2]
[8,5,7,6,2,1,3,4]=>[6,5,2,7,8,4,3,1]=>[3,4,7,2,1,5,6,8]=>[3,1,4]
[5,4,8,3,1,7,2,6]=>[2,1,7,4,8,5,6,3]=>[7,8,2,5,1,4,3,6]=>[2,2,2,2]
[5,1,4,8,3,2,7,6]=>[3,5,1,8,6,7,2,4]=>[6,4,8,1,3,2,7,5]=>[1,2,2,2,1]
[4,3,8,7,2,6,1,5]=>[1,5,7,8,2,6,4,3]=>[8,4,2,1,7,3,5,6]=>[1,1,1,2,3]
[3,8,7,2,6,4,1,5]=>[7,4,6,8,1,5,3,2]=>[2,5,3,1,8,4,6,7]=>[2,1,2,3]
[8,2,5,7,4,3,6,1]=>[3,6,5,8,2,7,4,1]=>[6,3,4,1,7,2,5,8]=>[1,2,2,3]
[3,8,7,4,6,1,2,5]=>[6,4,7,8,1,5,3,2]=>[3,5,2,1,8,4,6,7]=>[2,1,2,3]
[8,7,6,3,5,4,1,2]=>[4,7,8,6,5,3,2,1]=>[5,2,1,3,4,6,7,8]=>[1,1,6]
[2,8,4,7,6,1,5,3]=>[8,3,6,7,5,1,4,2]=>[1,6,3,2,4,8,5,7]=>[2,1,3,2]
[2,5,4,8,3,1,7,6]=>[3,2,5,8,1,6,7,4]=>[6,7,4,1,8,3,2,5]=>[2,1,2,1,2]
[5,4,8,2,1,3,7,6]=>[4,2,1,8,5,6,7,3]=>[5,7,8,1,4,3,2,6]=>[3,2,1,2]
[3,8,7,2,6,1,5,4]=>[8,4,6,7,1,5,3,2]=>[1,5,3,2,8,4,6,7]=>[2,1,2,3]
[1,8,4,7,6,3,5,2]=>[6,8,3,7,5,4,1,2]=>[3,1,6,2,4,5,8,7]=>[1,2,4,1]
[1,8,3,7,6,5,2,4]=>[7,8,6,3,5,4,1,2]=>[2,1,3,6,4,5,8,7]=>[1,3,3,1]
[1,4,3,8,7,2,6,5]=>[8,2,6,7,3,5,1,4]=>[1,7,3,2,6,4,8,5]=>[2,1,2,2,1]
[7,1,5,4,6,2,3,8]=>[6,4,3,7,2,5,1,8]=>[3,5,6,2,7,4,8,1]=>[3,2,2,1]
[5,4,3,1,7,6,2,8]=>[3,2,1,7,6,4,5,8]=>[6,7,8,2,3,5,4,1]=>[3,3,1,1]
[4,1,3,7,5,6,2,8]=>[5,1,7,3,6,2,4,8]=>[4,8,2,6,3,7,5,1]=>[2,2,2,1,1]
[2,6,8,3,1,7,4,5]=>[4,7,2,8,1,5,6,3]=>[5,2,7,1,8,4,3,6]=>[1,2,2,1,2]
[2,5,4,8,1,7,3,6]=>[3,2,7,8,1,5,6,4]=>[6,7,2,1,8,4,3,5]=>[2,1,2,1,2]
[7,5,2,4,8,3,6,1]=>[4,6,2,8,3,1,7,5]=>[5,3,7,1,6,8,2,4]=>[1,2,3,2]
[7,8,2,6,3,5,4,1]=>[8,5,7,3,1,6,4,2]=>[1,4,2,6,8,3,5,7]=>[2,3,3]
[5,6,3,1,4,2,7,8]=>[6,4,3,1,5,2,7,8]=>[3,5,6,8,4,7,2,1]=>[4,2,1,1]
[2,6,5,3,4,8,7,1]=>[8,4,3,1,2,5,7,6]=>[1,5,6,8,7,4,2,3]=>[4,1,1,2]
[2,6,1,5,3,4,7,8]=>[5,6,1,3,4,2,7,8]=>[4,3,8,6,5,7,2,1]=>[1,2,1,2,1,1]
[3,6,2,7,4,5,1,8]=>[5,7,1,3,2,6,4,8]=>[4,2,8,6,7,3,5,1]=>[1,2,2,2,1]
[3,4,7,8,5,1,6,2]=>[8,6,1,2,5,3,7,4]=>[1,3,8,7,4,6,2,5]=>[3,1,2,2]
[3,6,2,4,7,8,5,1]=>[5,8,1,3,2,4,7,6]=>[4,1,8,6,7,5,2,3]=>[1,2,2,1,2]
[1,5,4,8,6,2,7,3]=>[2,8,3,6,5,7,1,4]=>[7,1,6,3,4,2,8,5]=>[1,2,2,2,1]
[4,5,2,7,6,3,8,1]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[1,1,3,1,2]
[4,8,5,1,2,3,6,7]=>[4,1,5,6,3,7,8,2]=>[5,8,4,3,6,2,1,7]=>[2,1,2,1,2]
[8,6,2,4,5,1,3,7]=>[6,3,4,7,5,2,8,1]=>[3,6,5,2,4,7,1,8]=>[2,1,3,2]
[7,4,2,3,6,8,5,1]=>[5,2,8,3,4,1,7,6]=>[4,7,1,6,5,8,2,3]=>[2,2,2,2]
[2,1,6,7,4,8,3,5]=>[5,3,7,1,4,8,2,6]=>[4,6,2,8,5,1,7,3]=>[2,2,1,2,1]
[7,8,1,3,6,4,5,2]=>[6,8,4,7,3,1,5,2]=>[3,1,5,2,6,8,4,7]=>[1,2,3,2]
[7,2,6,8,4,5,3,1]=>[5,3,8,7,2,1,6,4]=>[4,6,1,2,7,8,3,5]=>[2,4,2]
[7,5,8,1,6,2,4,3]=>[8,6,2,7,4,1,5,3]=>[1,3,7,2,5,8,4,6]=>[3,3,2]
[7,2,6,8,5,1,4,3]=>[8,6,3,7,2,1,5,4]=>[1,3,6,2,7,8,4,5]=>[3,3,2]
[6,7,8,4,3,1,5,2]=>[1,8,6,5,4,2,7,3]=>[8,1,3,4,5,7,2,6]=>[1,5,2]
[7,3,8,1,6,4,5,2]=>[6,8,2,7,4,1,5,3]=>[3,1,7,2,5,8,4,6]=>[1,2,3,2]
[1,7,5,8,2,4,6,3]=>[6,3,8,5,2,7,1,4]=>[3,6,1,4,7,2,8,5]=>[2,3,2,1]
[3,7,8,2,6,5,1,4]=>[7,8,4,1,2,6,5,3]=>[2,1,5,8,7,3,4,6]=>[1,3,1,3]
[3,7,8,2,1,6,4,5]=>[4,7,8,1,5,2,6,3]=>[5,2,1,8,4,7,3,6]=>[1,1,2,2,2]
[7,8,1,6,3,5,4,2]=>[8,5,7,6,3,1,4,2]=>[1,4,2,3,6,8,5,7]=>[2,4,2]
[6,7,8,2,5,4,3,1]=>[1,8,7,4,2,6,5,3]=>[8,1,2,5,7,3,4,6]=>[1,4,3]
[6,7,8,3,1,5,4,2]=>[4,1,8,7,5,2,6,3]=>[5,8,1,2,4,7,3,6]=>[2,4,2]
[7,8,1,6,2,5,4,3]=>[8,7,5,6,3,1,4,2]=>[1,2,4,3,6,8,5,7]=>[3,3,2]
[5,1,6,8,3,4,7,2]=>[5,3,1,6,8,7,2,4]=>[4,6,8,3,1,2,7,5]=>[3,1,3,1]
[7,1,6,8,5,4,3,2]=>[3,8,7,6,5,2,1,4]=>[6,1,2,3,4,7,8,5]=>[1,6,1]
[5,6,8,1,2,3,7,4]=>[8,4,1,5,2,6,7,3]=>[1,5,8,4,7,3,2,6]=>[3,2,1,2]
[4,8,1,2,7,6,5,3]=>[8,1,7,6,3,4,5,2]=>[1,8,2,3,6,5,4,7]=>[2,3,1,2]
[6,4,7,3,5,2,1,8]=>[2,4,1,7,6,5,3,8]=>[7,5,8,2,3,4,6,1]=>[1,2,4,1]
[5,7,8,4,2,1,3,6]=>[1,6,5,7,4,2,8,3]=>[8,3,4,2,5,7,1,6]=>[1,2,3,2]
[3,1,6,2,5,7,8,4]=>[1,5,6,3,8,2,4,7]=>[8,4,3,6,1,7,5,2]=>[1,1,2,2,1,1]
[2,1,6,3,5,7,4,8]=>[5,7,1,4,2,3,6,8]=>[4,2,8,5,7,6,3,1]=>[1,2,2,1,1,1]
[1,6,4,5,2,7,3,8]=>[3,7,5,4,1,2,6,8]=>[6,2,4,5,8,7,3,1]=>[1,4,1,1,1]
[1,4,7,3,2,5,6,8]=>[2,5,4,6,7,1,3,8]=>[7,4,5,3,2,8,6,1]=>[1,2,1,2,1,1]
[6,2,1,4,5,3,7,8]=>[2,4,6,3,5,1,7,8]=>[7,5,3,6,4,8,2,1]=>[1,1,2,2,1,1]
[6,2,1,5,7,3,4,8]=>[6,2,4,7,3,1,5,8]=>[3,7,5,2,6,8,4,1]=>[2,1,3,1,1]
[1,2,4,6,8,3,7,5]=>[4,8,3,6,7,1,2,5]=>[5,1,6,3,2,8,7,4]=>[1,2,1,2,1,1]
[1,3,5,8,2,6,7,4]=>[3,6,8,2,5,7,1,4]=>[6,3,1,7,4,2,8,5]=>[1,1,2,1,2,1]
[6,1,3,7,2,8,5,4]=>[8,7,3,5,2,1,4,6]=>[1,2,6,4,7,8,5,3]=>[3,3,1,1]
[6,4,5,8,3,7,1,2]=>[2,3,1,7,5,8,6,4]=>[7,6,8,2,4,1,3,5]=>[1,2,2,3]
[8,1,4,3,6,7,2,5]=>[3,7,4,5,8,2,6,1]=>[6,2,5,4,1,7,3,8]=>[1,2,1,2,2]
[8,1,5,2,6,4,3,7]=>[7,6,4,2,3,5,8,1]=>[2,3,5,7,6,4,1,8]=>[4,1,1,2]
[1,6,7,4,2,8,3,5]=>[7,4,2,8,5,1,3,6]=>[2,5,7,1,4,8,6,3]=>[3,3,1,1]
[1,5,8,7,4,3,2,6]=>[7,2,6,5,8,4,1,3]=>[2,7,3,4,1,5,8,6]=>[2,2,3,1]
[1,4,7,2,3,6,8,5]=>[2,6,8,4,5,1,3,7]=>[7,3,1,5,4,8,6,2]=>[1,1,2,2,1,1]
[3,1,2,6,7,8,5,4]=>[1,4,5,8,7,2,3,6]=>[8,5,4,1,2,7,6,3]=>[1,1,1,3,1,1]
[3,8,1,6,4,2,7,5]=>[5,8,1,6,3,4,7,2]=>[4,1,8,3,6,5,2,7]=>[1,2,2,1,2]
[1,6,3,4,7,8,2,5]=>[7,3,4,2,5,8,1,6]=>[2,6,5,7,4,1,8,3]=>[2,2,1,2,1]
[3,1,5,7,6,2,8,4]=>[8,1,3,6,5,2,4,7]=>[1,8,6,3,4,7,5,2]=>[2,1,3,1,1]
[6,3,1,4,2,7,8,5]=>[4,2,6,8,3,1,5,7]=>[5,7,3,1,6,8,4,2]=>[2,1,3,1,1]
[2,4,3,7,6,1,8,5]=>[8,2,6,1,3,5,4,7]=>[1,7,3,8,6,4,5,2]=>[2,2,1,2,1]
[1,4,7,6,8,3,2,5]=>[7,6,2,4,3,8,1,5]=>[2,3,7,5,6,1,8,4]=>[3,2,2,1]
[7,2,1,5,6,3,8,4]=>[4,8,2,6,3,5,1,7]=>[5,1,7,3,6,4,8,2]=>[1,2,2,2,1]
[4,3,1,8,6,2,7,5]=>[1,8,2,6,5,7,3,4]=>[8,1,7,3,4,2,6,5]=>[1,2,2,2,1]
[3,1,5,2,8,7,6,4]=>[8,1,3,7,6,2,4,5]=>[1,8,6,2,3,7,5,4]=>[2,1,3,1,1]
[1,2,8,4,3,7,6,5]=>[8,4,7,5,6,1,2,3]=>[1,5,2,4,3,8,7,6]=>[2,2,2,1,1]
[7,5,1,8,3,2,6,4]=>[5,8,6,2,7,3,1,4]=>[4,1,3,7,2,6,8,5]=>[1,3,3,1]
[4,7,6,3,1,8,2,5]=>[7,1,4,8,5,3,2,6]=>[2,8,5,1,4,6,7,3]=>[2,1,4,1]
[5,3,1,8,6,2,4,7]=>[2,6,1,7,5,8,3,4]=>[7,3,8,2,4,1,6,5]=>[1,2,2,2,1]
[5,1,8,6,3,2,4,7]=>[6,5,1,7,4,8,2,3]=>[3,4,8,2,5,1,7,6]=>[3,2,2,1]
[1,5,4,2,8,6,3,7]=>[3,2,7,6,8,1,4,5]=>[6,7,2,3,1,8,5,4]=>[2,2,2,1,1]
[1,4,2,8,5,3,7,6]=>[2,5,8,6,7,1,3,4]=>[7,4,1,3,2,8,6,5]=>[1,1,2,2,1,1]
[8,3,1,6,4,2,5,7]=>[2,6,5,7,3,4,8,1]=>[7,3,4,2,6,5,1,8]=>[1,2,2,1,2]
[1,7,4,8,3,5,2,6]=>[3,5,7,6,2,8,1,4]=>[6,4,2,3,7,1,8,5]=>[1,1,3,2,1]
[7,3,2,4,8,5,1,6]=>[2,7,3,4,6,1,8,5]=>[7,2,6,5,3,8,1,4]=>[1,2,1,2,2]
[5,7,8,1,4,2,6,3]=>[1,8,6,4,5,2,7,3]=>[8,1,3,5,4,7,2,6]=>[1,3,2,2]
[2,6,3,8,1,7,5,4]=>[8,7,3,1,2,5,6,4]=>[1,2,6,8,7,4,3,5]=>[4,1,1,2]
[2,5,1,8,6,3,7,4]=>[2,8,6,1,5,7,3,4]=>[7,1,3,8,4,2,6,5]=>[1,3,1,2,1]
[1,8,4,2,7,5,3,6]=>[3,7,6,8,4,5,1,2]=>[6,2,3,1,5,4,8,7]=>[1,2,2,2,1]
[6,5,1,7,2,8,4,3]=>[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>[6,1,1]
[2,8,1,7,5,3,6,4]=>[8,6,5,7,1,3,4,2]=>[1,3,4,2,8,6,5,7]=>[3,2,1,2]
[1,2,8,7,6,4,3,5]=>[7,6,8,5,4,1,2,3]=>[2,3,1,4,5,8,7,6]=>[2,4,1,1]
[4,1,8,7,6,3,5,2]=>[6,8,1,7,5,4,2,3]=>[3,1,8,2,4,5,7,6]=>[1,2,4,1]
[4,8,2,6,3,5,1,7]=>[1,5,7,3,6,4,8,2]=>[8,4,2,6,3,5,1,7]=>[1,1,2,2,2]
[4,1,8,5,3,6,2,7]=>[1,5,4,7,6,8,2,3]=>[8,4,5,2,3,1,7,6]=>[1,2,2,2,1]
[6,4,2,5,3,1,7,8]=>[6,3,2,5,4,1,7,8]=>[3,6,7,4,5,8,2,1]=>[3,3,1,1]
[3,1,5,8,2,7,4,6]=>[1,3,7,8,5,6,2,4]=>[8,6,2,1,4,3,7,5]=>[1,1,1,2,2,1]
[6,4,1,5,3,2,7,8]=>[6,5,3,2,4,1,7,8]=>[3,4,6,7,5,8,2,1]=>[4,2,1,1]
[6,2,1,5,4,3,7,8]=>[6,2,5,3,4,1,7,8]=>[3,7,4,6,5,8,2,1]=>[2,2,2,1,1]
[3,1,8,5,4,6,2,7]=>[5,1,4,7,6,8,2,3]=>[4,8,5,2,3,1,7,6]=>[2,1,2,2,1]
[6,1,8,4,5,3,2,7]=>[4,7,6,5,1,8,2,3]=>[5,2,3,4,8,1,7,6]=>[1,4,2,1]
[4,3,5,7,1,6,8,2]=>[2,1,3,6,8,5,4,7]=>[7,8,6,3,1,4,5,2]=>[2,1,1,3,1]
[6,3,8,4,5,1,7,2]=>[4,8,2,1,6,5,7,3]=>[5,1,7,8,3,4,2,6]=>[1,3,2,2]
[3,1,6,8,5,7,4,2]=>[3,5,8,1,7,6,2,4]=>[6,4,1,8,2,3,7,5]=>[1,1,2,3,1]
[2,6,1,8,5,7,4,3]=>[5,2,8,7,1,6,3,4]=>[4,7,1,2,8,3,6,5]=>[2,3,2,1]
[6,5,8,7,2,3,4,1]=>[5,2,1,6,8,7,4,3]=>[4,7,8,3,1,2,5,6]=>[3,1,4]
[6,3,8,4,5,2,7,1]=>[4,6,2,1,5,8,7,3]=>[5,3,7,8,4,1,2,6]=>[1,3,1,3]
[2,1,6,8,5,3,7,4]=>[3,8,6,1,5,7,2,4]=>[6,1,3,8,4,2,7,5]=>[1,3,1,2,1]
[3,2,6,8,5,4,7,1]=>[3,6,1,5,8,2,7,4]=>[6,3,8,4,1,7,2,5]=>[1,2,1,2,2]
[4,1,8,5,2,6,3,7]=>[1,7,5,4,6,8,2,3]=>[8,2,4,5,3,1,7,6]=>[1,3,1,2,1]
[3,1,6,8,5,2,4,7]=>[6,1,3,7,5,8,2,4]=>[3,8,6,2,4,1,7,5]=>[2,1,2,2,1]
[6,5,8,7,4,1,2,3]=>[6,2,1,7,8,5,4,3]=>[3,7,8,2,1,4,5,6]=>[3,1,4]
[6,5,8,7,4,2,1,3]=>[2,1,7,6,8,5,4,3]=>[7,8,2,3,1,4,5,6]=>[2,2,4]
[6,5,8,7,2,4,1,3]=>[5,2,1,7,8,6,4,3]=>[4,7,8,2,1,3,5,6]=>[3,1,4]
[6,2,8,4,5,7,1,3]=>[4,7,5,1,8,2,6,3]=>[5,2,4,8,1,7,3,6]=>[1,3,2,2]
[6,1,8,4,5,7,3,2]=>[4,5,1,8,7,6,2,3]=>[5,4,8,1,2,3,7,6]=>[1,2,4,1]
[2,8,1,9,3,4,5,6,7]=>[5,6,7,8,9,1,3,2,4]=>[5,4,3,2,1,9,7,8,6]=>[1,1,1,1,2,2,1]
[4,2,7,3,5,8,6,1]=>[1,8,4,5,2,3,7,6]=>[8,1,5,4,7,6,2,3]=>[1,2,2,1,2]
[3,6,2,4,8,5,7,1]=>[6,8,1,3,2,4,7,5]=>[3,1,8,6,7,5,2,4]=>[1,2,2,1,2]
[2,7,5,4,3,8,6,1]=>[4,3,8,5,1,2,7,6]=>[5,6,1,4,8,7,2,3]=>[2,3,1,2]
[3,5,1,8,4,7,6,2]=>[2,8,1,5,7,6,3,4]=>[7,1,8,4,2,3,6,5]=>[1,2,1,3,1]
[3,6,1,8,5,4,7,2]=>[6,5,1,2,8,7,3,4]=>[3,4,8,7,1,2,6,5]=>[3,1,3,1]
[2,4,8,3,7,6,5,1]=>[8,7,2,4,6,1,5,3]=>[1,2,7,5,3,8,4,6]=>[3,1,2,2]
[3,6,8,2,5,7,4,1]=>[5,2,8,1,4,7,6,3]=>[4,7,1,8,5,2,3,6]=>[2,2,1,3]
[3,6,8,2,5,4,7,1]=>[6,4,1,2,5,8,7,3]=>[3,5,8,7,4,1,2,6]=>[3,1,1,3]
[4,6,8,3,2,5,7,1]=>[5,1,4,2,6,8,7,3]=>[4,8,5,7,3,1,2,6]=>[2,2,1,3]
[4,6,2,8,3,5,7,1]=>[1,5,6,2,8,3,7,4]=>[8,4,3,7,1,6,2,5]=>[1,1,2,2,2]
[3,6,1,8,5,7,4,2]=>[5,2,8,1,7,6,3,4]=>[4,7,1,8,2,3,6,5]=>[2,2,3,1]
[5,2,6,8,4,1,7,3]=>[3,1,8,6,2,5,7,4]=>[6,8,1,3,7,4,2,5]=>[2,3,1,2]
[4,6,3,8,7,2,5,1]=>[6,1,2,8,3,7,5,4]=>[3,8,7,1,6,2,4,5]=>[2,1,2,3]
[2,6,8,5,7,4,3,1]=>[2,4,8,7,6,1,5,3]=>[7,5,1,2,3,8,4,6]=>[1,1,4,2]
[2,4,8,7,6,3,5,1]=>[6,8,7,2,5,1,4,3]=>[3,1,2,7,4,8,5,6]=>[1,3,2,2]
[7,5,1,6,3,2,8,4]=>[5,8,6,3,2,4,1,7]=>[4,1,3,6,7,5,8,2]=>[1,4,2,1]
[2,7,6,3,4,1,8,5]=>[4,5,8,6,1,3,2,7]=>[5,4,1,3,8,6,7,2]=>[1,1,3,2,1]
[5,7,6,3,1,2,8,4]=>[1,8,5,4,6,3,2,7]=>[8,1,4,5,3,6,7,2]=>[1,3,3,1]
[4,8,2,1,7,5,6,3]=>[1,6,8,3,7,4,5,2]=>[8,3,1,6,2,5,4,7]=>[1,1,2,2,2]
[6,3,8,5,7,2,4,1]=>[6,4,1,8,2,7,5,3]=>[3,5,8,1,7,2,4,6]=>[3,2,3]
[1,5,4,8,6,2,3,7]=>[3,2,6,7,5,8,1,4]=>[6,7,3,2,4,1,8,5]=>[2,1,2,2,1]
[8,2,1,6,7,3,5,4]=>[8,6,2,4,7,3,5,1]=>[1,3,7,5,2,6,4,8]=>[3,1,2,2]
[3,5,1,8,7,6,2,4]=>[2,7,8,1,6,5,3,4]=>[7,2,1,8,3,4,6,5]=>[1,1,2,3,1]
[5,6,2,7,8,1,3,4]=>[6,1,7,3,2,4,8,5]=>[3,8,2,6,7,5,1,4]=>[2,3,1,2]
[4,7,8,3,5,6,1,2]=>[4,7,1,5,2,8,6,3]=>[5,2,8,4,7,1,3,6]=>[1,2,2,3]
[2,1,3,4,5,6,9,7,8]=>[1,8,9,2,3,4,5,6,7]=>[9,2,1,8,7,6,5,4,3]=>[1,1,2,1,1,1,1,1]
[1,2,3,4,5,6,7,8,10,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,11,10,9,8,7,6,5,4,3,1]=>[2,1,1,1,1,1,1,1,1,1]
[1,2,3,4,5,7,8,6,9]=>[6,8,1,2,3,4,5,7,9]=>[4,2,9,8,7,6,5,3,1]=>[1,2,1,1,1,1,1,1]
[2,1,3,4,5,6,7,10,8,9]=>[1,9,10,2,3,4,5,6,7,8]=>[10,2,1,9,8,7,6,5,4,3]=>[1,1,2,1,1,1,1,1,1]
[3,2,5,6,8,4,7,1]=>[1,3,4,6,8,2,7,5]=>[8,6,5,3,1,7,2,4]=>[1,1,1,1,2,2]
[8,4,5,2,6,3,7,1]=>[2,6,4,3,5,8,7,1]=>[7,3,5,6,4,1,2,8]=>[1,3,1,3]
[2,5,6,4,8,3,7,1]=>[2,4,3,6,8,1,7,5]=>[7,5,6,3,1,8,2,4]=>[1,2,1,2,2]
[5,3,2,4,7,8,1,6]=>[2,7,3,1,4,5,8,6]=>[7,2,6,8,5,4,1,3]=>[1,3,1,1,2]
[4,2,5,7,3,8,1,6]=>[3,1,5,7,2,4,8,6]=>[6,8,4,2,7,5,1,3]=>[2,1,2,1,2]
[4,7,3,1,6,8,2,5]=>[1,3,7,5,8,4,2,6]=>[8,6,2,4,1,5,7,3]=>[1,1,2,3,1]
[4,2,7,6,8,1,3,5]=>[1,6,7,4,2,3,8,5]=>[8,3,2,5,7,6,1,4]=>[1,1,3,1,2]
[4,7,2,5,6,3,1,8]=>[1,4,7,3,6,5,2,8]=>[8,5,2,6,3,4,7,1]=>[1,1,2,3,1]
[5,4,1,3,7,8,2,6]=>[7,4,2,1,5,8,3,6]=>[2,5,7,8,4,1,6,3]=>[4,1,2,1]
[6,1,5,8,3,7,2,4]=>[5,3,7,1,8,6,2,4]=>[4,6,2,8,1,3,7,5]=>[2,2,3,1]
[6,1,5,8,4,3,2,7]=>[3,7,6,5,1,8,2,4]=>[6,2,3,4,8,1,7,5]=>[1,4,2,1]
[7,2,1,6,8,3,5,4]=>[8,6,2,4,7,3,1,5]=>[1,3,7,5,2,6,8,4]=>[3,1,3,1]
[5,6,4,1,8,3,2,7]=>[1,7,6,3,2,8,4,5]=>[8,2,3,6,7,1,5,4]=>[1,4,2,1]
[4,5,2,1,7,8,3,6]=>[1,7,3,2,5,8,4,6]=>[8,2,6,7,4,1,5,3]=>[1,3,1,2,1]
[2,3,7,8,5,1,6,4]=>[8,6,5,1,2,3,7,4]=>[1,3,4,8,7,6,2,5]=>[4,1,1,2]
[4,1,7,6,2,3,8,5]=>[1,8,5,6,4,2,3,7]=>[8,1,4,3,5,7,6,2]=>[1,2,3,1,1]
[1,2,6,7,4,3,5,8]=>[6,5,3,7,1,2,4,8]=>[3,4,6,2,8,7,5,1]=>[3,2,1,1,1]
[5,8,6,3,4,1,2,7]=>[1,6,4,7,5,3,8,2]=>[8,3,5,2,4,6,1,7]=>[1,2,3,2]
[6,2,3,1,8,5,4,7]=>[7,2,3,6,1,8,4,5]=>[2,7,6,3,8,1,5,4]=>[2,1,2,2,1]
[5,1,2,6,4,8,3,7]=>[5,4,7,1,8,2,3,6]=>[4,5,2,8,1,7,6,3]=>[2,2,2,1,1]
[8,6,2,3,7,5,1,4]=>[7,8,3,4,2,6,5,1]=>[2,1,6,5,7,3,4,8]=>[1,2,2,3]
[4,5,2,8,6,1,3,7]=>[1,6,2,7,3,5,8,4]=>[8,3,7,2,6,4,1,5]=>[1,2,2,1,2]
[3,4,8,2,5,6,1,7]=>[1,2,4,5,7,6,8,3]=>[8,7,5,4,2,3,1,6]=>[1,1,1,1,2,2]
[2,8,3,6,7,4,5,1]=>[6,4,8,3,7,1,5,2]=>[3,5,1,6,2,8,4,7]=>[2,2,2,2]
[6,8,2,7,5,3,1,4]=>[7,6,1,8,3,5,4,2]=>[2,3,8,1,6,4,5,7]=>[3,2,3]
[5,8,3,6,4,1,7,2]=>[1,8,3,6,5,4,7,2]=>[8,1,6,3,4,5,2,7]=>[1,2,3,2]
[4,3,8,5,2,7,1,6]=>[1,5,2,4,7,8,6,3]=>[8,4,7,5,2,1,3,6]=>[1,2,1,1,3]
[2,8,4,5,1,6,3,7]=>[3,7,5,1,4,6,8,2]=>[6,2,4,8,5,3,1,7]=>[1,3,1,1,2]
[3,2,5,8,4,7,1,6]=>[1,3,5,7,8,2,6,4]=>[8,6,4,2,1,7,3,5]=>[1,1,1,1,2,2]
[2,5,8,1,3,4,7,6]=>[8,4,1,2,5,6,7,3]=>[1,5,8,7,4,3,2,6]=>[3,1,1,1,2]
[4,6,1,3,8,2,7,5]=>[1,8,4,6,2,7,3,5]=>[8,1,5,3,7,2,6,4]=>[1,2,2,2,1]
[8,6,1,2,3,5,7,4]=>[6,8,3,4,5,2,7,1]=>[3,1,6,5,4,7,2,8]=>[1,2,1,2,2]
[5,1,7,8,3,2,4,6]=>[6,5,1,7,3,8,2,4]=>[3,4,8,2,6,1,7,5]=>[3,2,2,1]
[3,1,7,6,2,8,5,4]=>[8,7,1,5,4,2,3,6]=>[1,2,8,4,5,7,6,3]=>[3,3,1,1]
[5,4,2,8,6,7,3,1]=>[2,1,5,8,7,3,6,4]=>[7,8,4,1,2,6,3,5]=>[2,1,3,2]
[6,1,4,2,8,7,3,5]=>[3,7,8,6,2,1,4,5]=>[6,2,1,3,7,8,5,4]=>[1,1,4,1,1]
[3,7,2,6,8,4,5,1]=>[6,4,8,1,3,2,7,5]=>[3,5,1,8,6,7,2,4]=>[2,2,2,2]
[5,4,6,2,7,8,3,1]=>[2,1,5,3,8,4,7,6]=>[7,8,4,6,1,5,2,3]=>[2,2,2,2]
[5,1,8,6,4,2,7,3]=>[1,8,6,5,4,7,2,3]=>[8,1,3,4,5,2,7,6]=>[1,4,2,1]
[6,2,1,8,5,7,4,3]=>[5,8,7,2,1,6,3,4]=>[4,1,2,7,8,3,6,5]=>[1,4,2,1]
[6,5,7,8,1,3,4,2]=>[6,2,1,8,5,3,7,4]=>[3,7,8,1,4,6,2,5]=>[3,3,2]
[2,1,7,6,8,4,5,3]=>[6,4,3,8,1,7,2,5]=>[3,5,6,1,8,2,7,4]=>[3,2,2,1]
[6,4,7,2,8,3,1,5]=>[2,7,4,1,6,3,8,5]=>[7,2,5,8,3,6,1,4]=>[1,3,2,2]
[6,3,2,7,8,4,5,1]=>[6,2,4,1,8,3,7,5]=>[3,7,5,8,1,6,2,4]=>[2,2,2,2]
[1,4,8,2,7,6,5,3]=>[8,7,2,6,4,5,1,3]=>[1,2,7,3,5,4,8,6]=>[3,2,2,1]
[4,7,3,1,5,2,8,6]=>[1,5,3,8,4,6,2,7]=>[8,4,6,1,5,3,7,2]=>[1,2,2,2,1]
[2,1,4,7,5,3,8,6]=>[5,8,1,3,6,2,4,7]=>[4,1,8,6,3,7,5,2]=>[1,2,1,2,1,1]
[4,7,3,6,5,2,8,1]=>[6,1,3,5,4,2,8,7]=>[3,8,6,4,5,7,1,2]=>[2,1,3,2]
[4,7,6,3,1,5,8,2]=>[6,1,4,8,5,3,2,7]=>[3,8,5,1,4,6,7,2]=>[2,1,4,1]
[2,4,7,3,8,5,1,6]=>[7,2,4,6,1,3,8,5]=>[2,7,5,3,8,6,1,4]=>[2,1,2,1,2]
[2,7,3,1,8,5,4,6]=>[7,3,6,8,1,4,2,5]=>[2,6,3,1,8,5,7,4]=>[2,1,2,2,1]
[2,8,3,1,7,4,5,6]=>[3,6,7,8,1,4,5,2]=>[6,3,2,1,8,5,4,7]=>[1,1,1,2,1,2]
[6,7,5,2,1,4,8,3]=>[4,6,1,8,5,3,2,7]=>[5,3,8,1,4,6,7,2]=>[1,2,4,1]
[1,2,6,8,3,4,7,5]=>[8,5,3,6,7,1,2,4]=>[1,4,6,3,2,8,7,5]=>[3,1,2,1,1]
[1,5,6,8,3,2,4,7]=>[2,6,5,3,7,8,1,4]=>[7,3,4,6,2,1,8,5]=>[1,3,1,2,1]
[1,8,2,7,3,5,6,4]=>[6,8,5,7,3,4,1,2]=>[3,1,4,2,6,5,8,7]=>[1,2,2,2,1]
[1,7,4,8,6,5,3,2]=>[8,7,3,2,6,5,1,4]=>[1,2,6,7,3,4,8,5]=>[4,3,1]
[1,6,3,5,7,4,8,2]=>[4,6,3,2,5,8,1,7]=>[5,3,6,7,4,1,8,2]=>[1,3,1,2,1]
[1,5,4,7,2,8,3,6]=>[3,2,7,8,5,1,4,6]=>[6,7,2,1,4,8,5,3]=>[2,1,3,1,1]
[3,8,5,2,6,1,7,4]=>[8,4,1,3,6,5,7,2]=>[1,5,8,6,3,4,2,7]=>[3,1,2,2]
[3,7,4,8,5,2,6,1]=>[6,3,5,1,2,8,7,4]=>[3,6,4,8,7,1,2,5]=>[2,2,1,3]
[8,1,2,6,5,3,4,7]=>[6,7,5,2,3,4,8,1]=>[3,2,4,7,6,5,1,8]=>[1,3,1,1,2]
[6,8,7,1,3,4,2,5]=>[5,7,4,1,6,8,3,2]=>[4,2,5,8,3,1,6,7]=>[1,3,1,3]
[3,7,8,6,1,4,2,5]=>[7,5,6,1,2,8,4,3]=>[2,4,3,8,7,1,5,6]=>[2,2,1,3]
[3,6,1,5,2,7,8,4]=>[6,1,4,8,3,2,5,7]=>[3,8,5,1,6,7,4,2]=>[2,1,3,1,1]
[8,1,2,6,3,5,7,4]=>[6,8,5,2,3,4,7,1]=>[3,1,4,7,6,5,2,8]=>[1,3,1,1,2]
[3,4,2,8,5,1,6,7]=>[1,2,6,3,5,7,8,4]=>[8,7,3,6,4,2,1,5]=>[1,1,2,1,1,2]
[1,4,3,2,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>[6,7,9,8,5,4,3,2,1]=>[3,1,1,1,1,1,1]
[6,8,2,7,5,4,1,3]=>[7,1,8,6,3,5,4,2]=>[2,8,1,3,6,4,5,7]=>[2,3,3]
[1,8,4,3,7,6,2,5]=>[3,7,8,4,6,5,1,2]=>[6,2,1,5,3,4,8,7]=>[1,1,2,3,1]
[4,3,8,7,1,2,6,5]=>[1,8,2,5,6,7,4,3]=>[8,1,7,4,3,2,5,6]=>[1,2,1,1,3]
[1,8,4,5,7,6,2,3]=>[3,4,7,8,6,5,1,2]=>[6,5,2,1,3,4,8,7]=>[1,1,1,4,1]
[4,3,8,5,7,1,6,2]=>[1,4,8,2,6,7,5,3]=>[8,5,1,7,3,2,4,6]=>[1,1,2,1,3]
[6,3,4,8,7,2,1,5]=>[7,2,3,1,6,8,5,4]=>[2,7,6,8,3,1,4,5]=>[2,2,1,3]
[5,3,8,4,7,1,6,2]=>[4,1,8,2,6,7,5,3]=>[5,8,1,7,3,2,4,6]=>[2,2,1,3]
[3,2,8,7,1,6,4,5]=>[7,8,1,5,6,2,4,3]=>[2,1,8,4,3,7,5,6]=>[1,2,1,2,2]
[2,7,8,3,1,6,4,5]=>[4,7,8,5,1,2,6,3]=>[5,2,1,4,8,7,3,6]=>[1,1,3,1,2]
[2,7,8,5,1,4,6,3]=>[6,8,5,4,1,2,7,3]=>[3,1,4,5,8,7,2,6]=>[1,4,1,2]
[3,5,8,7,4,1,6,2]=>[8,2,6,1,5,7,4,3]=>[1,7,3,8,4,2,5,6]=>[2,2,1,3]
[7,4,6,8,3,5,1,2]=>[7,2,5,3,1,8,6,4]=>[2,7,4,6,8,1,3,5]=>[2,3,3]
[2,7,8,1,3,6,4,5]=>[7,8,4,5,1,2,6,3]=>[2,1,5,4,8,7,3,6]=>[1,2,2,1,2]
[2,7,8,1,4,5,6,3]=>[5,6,8,4,1,2,7,3]=>[4,3,1,5,8,7,2,6]=>[1,1,3,1,2]
[3,6,7,8,2,4,1,5]=>[5,2,7,1,6,3,8,4]=>[4,7,2,8,3,6,1,5]=>[2,2,2,2]
[4,5,7,8,6,3,1,2]=>[7,1,2,3,8,6,5,4]=>[2,8,7,6,1,3,4,5]=>[2,1,1,4]
[5,4,6,8,7,3,1,2]=>[2,1,3,7,8,6,5,4]=>[7,8,6,2,1,3,4,5]=>[2,1,1,4]
[5,7,6,8,2,1,3,4]=>[1,6,5,7,3,2,8,4]=>[8,3,4,2,6,7,1,5]=>[1,2,3,2]
[3,7,6,8,2,4,1,5]=>[5,7,6,1,3,2,8,4]=>[4,2,3,8,6,7,1,5]=>[1,3,2,2]
[5,4,7,8,6,3,1,2]=>[1,7,2,3,8,6,5,4]=>[8,2,7,6,1,3,4,5]=>[1,2,1,4]
[4,5,7,8,2,6,1,3]=>[1,2,5,7,3,8,6,4]=>[8,7,4,2,6,1,3,5]=>[1,1,1,2,3]
[4,5,6,8,7,3,1,2]=>[1,2,3,7,8,6,5,4]=>[8,7,6,2,1,3,4,5]=>[1,1,1,1,4]
[5,7,3,4,2,1,6,8]=>[3,1,6,5,4,7,2,8]=>[6,8,3,4,5,2,7,1]=>[2,3,2,1]
[6,1,5,3,8,4,7,2]=>[6,3,8,4,1,7,2,5]=>[3,6,1,5,8,2,7,4]=>[2,3,2,1]
[1,8,6,2,5,4,7,3]=>[6,5,8,4,3,7,1,2]=>[3,4,1,5,6,2,8,7]=>[2,3,2,1]
[6,2,7,4,8,3,1,5]=>[4,7,6,2,1,3,8,5]=>[5,2,3,7,8,6,1,4]=>[1,4,1,2]
[2,8,5,1,4,3,7,6]=>[5,8,4,1,3,6,7,2]=>[4,1,5,8,6,3,2,7]=>[1,3,1,1,2]
[6,8,2,7,5,1,4,3]=>[8,6,1,7,3,5,4,2]=>[1,3,8,2,6,4,5,7]=>[3,2,3]
[8,3,4,5,6,1,7,2]=>[2,3,4,8,6,5,7,1]=>[7,6,5,1,3,4,2,8]=>[1,1,1,3,2]
[5,3,6,4,7,2,1,8]=>[4,2,1,3,7,6,5,8]=>[5,7,8,6,2,3,4,1]=>[3,1,3,1]
[4,2,6,5,7,3,1,8]=>[1,4,3,7,2,6,5,8]=>[8,5,6,2,7,3,4,1]=>[1,2,2,2,1]
[3,2,6,5,8,4,1,7]=>[4,1,3,7,2,6,8,5]=>[5,8,6,2,7,3,1,4]=>[2,1,2,1,2]
[3,2,6,5,8,7,1,4]=>[4,1,3,7,8,2,6,5]=>[5,8,6,2,1,7,3,4]=>[2,1,1,2,2]
[5,2,6,4,8,7,1,3]=>[4,3,1,7,8,2,6,5]=>[5,6,8,2,1,7,3,4]=>[3,1,2,2]
[5,4,7,6,8,2,1,3]=>[1,7,2,6,4,3,8,5]=>[8,2,7,3,5,6,1,4]=>[1,2,3,2]
[6,4,7,5,8,3,1,2]=>[7,2,1,4,3,8,6,5]=>[2,7,8,5,6,1,3,4]=>[3,2,3]
[4,2,7,5,8,6,1,3]=>[1,4,7,3,8,2,6,5]=>[8,5,2,6,1,7,3,4]=>[1,1,2,2,2]
[3,2,7,5,8,4,1,6]=>[4,7,1,6,2,3,8,5]=>[5,2,8,3,7,6,1,4]=>[1,2,2,1,2]
[4,3,6,2,8,5,1,7]=>[1,7,2,4,3,6,8,5]=>[8,2,7,5,6,3,1,4]=>[1,2,2,1,2]
[4,3,7,6,8,5,1,2]=>[7,1,4,2,3,8,6,5]=>[2,8,5,7,6,1,3,4]=>[2,2,1,3]
[5,3,7,6,8,2,1,4]=>[1,7,6,2,4,3,8,5]=>[8,2,3,7,5,6,1,4]=>[1,3,2,2]
[5,3,7,2,8,6,1,4]=>[7,1,8,2,4,3,6,5]=>[2,8,1,7,5,6,3,4]=>[2,2,2,2]
[3,2,6,4,8,7,1,5]=>[7,1,3,8,2,4,6,5]=>[2,8,6,1,7,5,3,4]=>[2,1,2,1,2]
[4,2,7,3,8,6,1,5]=>[1,7,8,4,2,3,6,5]=>[8,2,1,5,7,6,3,4]=>[1,1,3,1,2]
[5,2,7,6,8,3,1,4]=>[1,7,6,4,2,3,8,5]=>[8,2,3,5,7,6,1,4]=>[1,4,1,2]
[3,2,7,6,8,5,1,4]=>[7,4,1,3,8,2,6,5]=>[2,5,8,6,1,7,3,4]=>[3,1,2,2]
[6,2,7,5,8,4,1,3]=>[7,4,3,1,8,2,6,5]=>[2,5,6,8,1,7,3,4]=>[4,2,2]
[4,8,1,7,3,2,5,6]=>[1,6,5,7,8,3,4,2]=>[8,3,4,2,1,6,5,7]=>[1,2,1,2,2]
[3,7,4,8,2,1,5,6]=>[3,6,1,5,7,2,8,4]=>[6,3,8,4,2,7,1,5]=>[1,2,1,2,2]
[3,7,8,2,5,4,6,1]=>[6,4,5,1,2,8,7,3]=>[3,5,4,8,7,1,2,6]=>[2,2,1,3]
[4,7,5,8,3,2,6,1]=>[3,6,1,5,2,8,7,4]=>[6,3,8,4,7,1,2,5]=>[1,2,2,3]
[6,7,1,3,2,5,8,4]=>[4,6,8,3,1,5,2,7]=>[5,3,1,6,8,4,7,2]=>[1,1,3,2,1]
[8,7,6,4,1,5,3,2]=>[8,7,5,4,6,3,2,1]=>[1,2,4,5,3,6,7,8]=>[4,4]
[3,8,5,2,6,4,7,1]=>[6,4,1,3,5,8,7,2]=>[3,5,8,6,4,1,2,7]=>[3,1,1,3]
[7,2,5,3,4,8,1,6]=>[4,5,2,3,7,1,8,6]=>[5,4,7,6,2,8,1,3]=>[1,2,1,2,2]
[4,2,5,3,7,8,6,1]=>[3,1,5,8,2,4,7,6]=>[6,8,4,1,7,5,2,3]=>[2,1,2,1,2]
[5,3,6,2,4,1,8,7]=>[2,4,1,5,3,8,6,7]=>[7,5,8,4,6,1,3,2]=>[1,2,2,2,1]
[7,8,6,2,3,5,4,1]=>[8,4,5,1,7,6,3,2]=>[1,5,4,8,2,3,6,7]=>[2,2,4]
[5,8,2,6,3,7,4,1]=>[1,8,5,3,4,7,6,2]=>[8,1,4,6,5,2,3,7]=>[1,3,1,3]
[4,8,2,3,7,5,6,1]=>[1,6,8,3,4,7,5,2]=>[8,3,1,6,5,2,4,7]=>[1,1,2,1,3]
[7,5,6,2,3,8,4,1]=>[8,4,2,5,3,1,7,6]=>[1,5,7,4,6,8,2,3]=>[3,3,2]
[2,7,5,6,4,3,8,1]=>[3,6,5,4,1,2,8,7]=>[6,3,4,5,8,7,1,2]=>[1,4,1,2]
[2,8,4,3,7,5,6,1]=>[3,6,8,4,7,1,5,2]=>[6,3,1,5,2,8,4,7]=>[1,1,2,2,2]
[3,8,5,7,6,4,2,1]=>[8,3,7,6,1,5,4,2]=>[1,6,2,3,8,4,5,7]=>[2,3,3]
[7,8,6,3,5,4,2,1]=>[8,4,1,7,6,5,3,2]=>[1,5,8,2,3,4,6,7]=>[3,5]
[2,7,6,3,8,5,4,1]=>[8,7,4,3,1,2,6,5]=>[1,2,5,6,8,7,3,4]=>[5,1,2]
[7,4,2,5,6,3,8,1]=>[4,2,6,3,5,1,8,7]=>[5,7,3,6,4,8,1,2]=>[2,2,2,2]
[6,2,7,5,3,8,4,1]=>[8,5,4,2,1,3,7,6]=>[1,4,5,7,8,6,2,3]=>[5,1,2]
[2,4,8,3,7,5,6,1]=>[6,8,2,4,7,1,5,3]=>[3,1,7,5,2,8,4,6]=>[1,2,1,2,2]
[4,8,3,7,5,6,2,1]=>[5,8,1,3,7,6,4,2]=>[4,1,8,6,2,3,5,7]=>[1,2,1,4]
[6,2,5,8,3,7,4,1]=>[3,8,5,1,7,2,6,4]=>[6,1,4,8,2,7,3,5]=>[1,3,2,2]
[4,7,3,8,2,5,6,1]=>[1,3,5,6,2,8,7,4]=>[8,6,4,3,7,1,2,5]=>[1,1,1,2,3]
[4,5,3,7,1,2,6,8]=>[1,5,3,2,6,7,4,8]=>[8,4,6,7,3,2,5,1]=>[1,3,1,2,1]
[8,5,6,4,1,3,2,7]=>[7,5,2,6,4,3,8,1]=>[2,4,7,3,5,6,1,8]=>[3,3,2]
[6,7,2,8,4,3,1,5]=>[7,6,3,1,5,2,8,4]=>[2,3,6,8,4,7,1,5]=>[4,2,2]
[6,7,3,2,8,4,1,5]=>[3,7,4,1,6,2,8,5]=>[6,2,5,8,3,7,1,4]=>[1,3,2,2]
[4,7,8,3,1,5,2,6]=>[7,1,5,4,6,2,8,3]=>[2,8,4,5,3,7,1,6]=>[2,2,2,2]
[4,5,8,1,3,2,6,7]=>[1,6,4,2,5,7,8,3]=>[8,3,5,7,4,2,1,6]=>[1,3,1,1,2]
[4,7,1,3,8,6,5,2]=>[8,1,7,4,6,3,2,5]=>[1,8,2,5,3,6,7,4]=>[2,2,3,1]
[2,6,7,4,3,8,1,5]=>[5,4,2,7,1,3,8,6]=>[4,5,7,2,8,6,1,3]=>[3,2,1,2]
[3,7,6,4,5,8,1,2]=>[4,7,5,1,3,2,8,6]=>[5,2,4,8,6,7,1,3]=>[1,3,2,2]
[5,7,2,8,3,4,6,1]=>[5,1,6,8,3,2,7,4]=>[4,8,3,1,6,7,2,5]=>[2,1,3,2]
[3,7,2,8,5,6,4,1]=>[5,8,7,1,3,2,6,4]=>[4,1,2,8,6,7,3,5]=>[1,3,2,2]
[2,3,8,6,4,5,7,1]=>[5,6,4,8,1,2,7,3]=>[4,3,5,1,8,7,2,6]=>[1,2,2,1,2]
[3,6,2,8,7,4,5,1]=>[6,2,8,1,7,3,5,4]=>[3,7,1,8,2,6,4,5]=>[2,2,2,2]
[2,5,6,1,8,7,3,4]=>[2,7,3,8,1,6,4,5]=>[7,2,6,1,8,3,5,4]=>[1,2,2,2,1]
[3,6,2,8,4,7,5,1]=>[8,5,1,2,7,3,6,4]=>[1,4,8,7,2,6,3,5]=>[3,1,2,2]
[2,3,8,5,7,4,6,1]=>[4,6,8,7,1,2,5,3]=>[5,3,1,2,8,7,4,6]=>[1,1,3,1,2]
[2,3,8,6,7,5,4,1]=>[4,8,7,6,1,2,5,3]=>[5,1,2,3,8,7,4,6]=>[1,4,1,2]
[8,5,6,3,1,4,2,7]=>[7,5,4,2,6,3,8,1]=>[2,4,5,7,3,6,1,8]=>[4,2,2]
[8,3,5,1,6,4,2,7]=>[7,2,6,4,3,5,8,1]=>[2,7,3,5,6,4,1,8]=>[2,3,1,2]
[5,7,8,3,4,6,2,1]=>[1,4,5,2,8,7,6,3]=>[8,5,4,7,1,2,3,6]=>[1,1,2,4]
[5,1,3,8,6,4,2,7]=>[7,6,3,1,5,8,2,4]=>[2,3,6,8,4,1,7,5]=>[4,1,2,1]
[1,5,8,3,6,4,2,7]=>[2,7,4,6,5,8,1,3]=>[7,2,5,3,4,1,8,6]=>[1,2,2,2,1]
[7,5,8,3,6,4,2,1]=>[2,8,4,1,7,6,5,3]=>[7,1,5,8,2,3,4,6]=>[1,3,4]
[1,5,8,6,3,4,2,7]=>[2,5,7,6,4,8,1,3]=>[7,4,2,3,5,1,8,6]=>[1,1,3,2,1]
[3,7,5,8,2,6,4,1]=>[3,8,5,1,2,7,6,4]=>[6,1,4,8,7,2,3,5]=>[1,3,1,3]
[5,7,8,1,4,6,2,3]=>[1,7,5,8,4,2,6,3]=>[8,2,4,1,5,7,3,6]=>[1,2,3,2]
[1,3,7,8,4,2,6,5]=>[5,8,6,2,3,7,1,4]=>[4,1,3,7,6,2,8,5]=>[1,3,1,2,1]
[6,1,2,5,3,4,7,8]=>[5,6,2,3,4,1,7,8]=>[4,3,7,6,5,8,2,1]=>[1,2,1,2,1,1]
[6,1,2,3,5,4,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[4,8,7,6,5,9,3,2,1]=>[2,1,1,2,1,1,1]
[6,1,2,5,4,3,7,8]=>[6,5,2,3,4,1,7,8]=>[3,4,7,6,5,8,2,1]=>[3,1,2,1,1]
[5,1,4,6,7,3,2,8]=>[3,4,1,7,6,2,5,8]=>[6,5,8,2,3,7,4,1]=>[1,2,3,1,1]
[1,4,6,5,7,2,3,8]=>[6,2,4,3,7,1,5,8]=>[3,7,5,6,2,8,4,1]=>[2,2,2,1,1]
[6,7,3,5,4,1,2,8]=>[3,6,1,7,5,4,2,8]=>[6,3,8,2,4,5,7,1]=>[1,2,4,1]
[8,1,6,7,3,5,4,2]=>[8,5,3,7,6,2,4,1]=>[1,4,6,2,3,7,5,8]=>[3,3,2]
[4,2,5,1,3,7,6,8]=>[7,2,1,4,3,5,6,8]=>[2,7,8,5,6,4,3,1]=>[3,2,1,1,1]
[8,2,5,4,1,6,7,3]=>[6,4,2,3,8,5,7,1]=>[3,5,7,6,1,4,2,8]=>[3,1,2,2]
[8,1,7,5,4,2,6,3]=>[8,6,5,4,7,2,3,1]=>[1,3,4,5,2,7,6,8]=>[4,2,2]
[1,2,6,4,7,3,5,8]=>[4,6,3,7,1,2,5,8]=>[5,3,6,2,8,7,4,1]=>[1,2,2,1,1,1]
[1,6,4,3,7,2,5,8]=>[4,3,6,2,7,1,5,8]=>[5,6,3,7,2,8,4,1]=>[2,2,2,1,1]
[7,5,6,8,1,3,2,4]=>[7,5,2,6,3,1,8,4]=>[2,4,7,3,6,8,1,5]=>[3,3,2]
[6,8,7,5,4,2,3,1]=>[1,6,8,7,5,4,3,2]=>[8,3,1,2,4,5,6,7]=>[1,1,6]
[7,3,1,8,6,5,2,4]=>[7,8,2,6,5,3,1,4]=>[2,1,7,3,4,6,8,5]=>[1,2,4,1]
[2,7,3,1,4,8,6,5]=>[8,3,7,1,4,5,2,6]=>[1,6,2,8,5,4,7,3]=>[2,2,1,2,1]
[3,1,6,5,7,8,4,2]=>[4,1,3,5,8,7,2,6]=>[5,8,6,4,1,2,7,3]=>[2,1,1,3,1]
[4,3,1,5,8,7,6,2]=>[1,8,2,7,4,6,3,5]=>[8,1,7,2,5,3,6,4]=>[1,2,2,2,1]
[4,7,1,3,2,5,6,8]=>[5,3,1,4,6,7,2,8]=>[4,6,8,5,3,2,7,1]=>[3,1,1,2,1]
[4,1,6,7,3,2,8,5]=>[1,5,3,8,6,2,4,7]=>[8,4,6,1,3,7,5,2]=>[1,2,3,1,1]
[5,4,8,6,1,7,3,2]=>[1,8,2,7,5,4,6,3]=>[8,1,7,2,4,5,3,6]=>[1,2,3,2]
[3,5,4,7,1,8,6,2]=>[2,8,1,3,7,5,4,6]=>[7,1,8,6,2,4,5,3]=>[1,2,1,3,1]
[7,1,5,4,2,3,6,8]=>[5,6,4,2,3,7,1,8]=>[4,3,5,7,6,2,8,1]=>[1,3,1,2,1]
[7,1,3,6,4,5,2,8]=>[5,7,3,6,2,4,1,8]=>[4,2,6,3,7,5,8,1]=>[1,2,2,2,1]
[6,1,3,8,4,5,2,7]=>[5,7,3,6,1,8,2,4]=>[4,2,6,3,8,1,7,5]=>[1,2,2,2,1]
[2,1,8,7,3,6,5,4]=>[8,7,5,6,1,4,2,3]=>[1,2,4,3,8,5,7,6]=>[3,2,2,1]
[5,8,6,3,1,2,7,4]=>[1,8,5,4,6,3,7,2]=>[8,1,4,5,3,6,2,7]=>[1,3,2,2]
[5,8,2,7,1,3,6,4]=>[8,3,1,5,6,7,4,2]=>[1,6,8,4,3,2,5,7]=>[3,1,1,3]
[2,6,5,4,1,3,7,8]=>[5,6,4,1,3,2,7,8]=>[4,3,5,8,6,7,2,1]=>[1,3,2,1,1]
[4,1,5,7,6,3,2,8]=>[1,7,3,6,5,2,4,8]=>[8,2,6,3,4,7,5,1]=>[1,2,3,1,1]
[4,5,1,7,6,3,2,8]=>[1,2,7,6,5,3,4,8]=>[8,7,2,3,4,6,5,1]=>[1,1,4,1,1]
[6,2,1,5,4,3,8,7]=>[5,2,4,8,3,1,6,7]=>[4,7,5,1,6,8,3,2]=>[2,1,3,1,1]
[1,4,2,6,7,8,5,3]=>[2,4,5,8,7,1,3,6]=>[7,5,4,1,2,8,6,3]=>[1,1,1,3,1,1]
[1,4,2,5,6,8,7,3]=>[2,8,4,5,7,1,3,6]=>[7,1,5,4,2,8,6,3]=>[1,2,1,2,1,1]
[2,5,3,6,7,8,4,1]=>[4,2,5,8,1,3,7,6]=>[5,7,4,1,8,6,2,3]=>[2,1,2,1,2]
[1,8,6,2,4,3,5,7]=>[6,4,5,7,3,8,1,2]=>[3,5,4,2,6,1,8,7]=>[2,1,2,2,1]
[3,2,4,5,7,8,1,6]=>[1,7,2,3,4,5,8,6]=>[8,2,7,6,5,4,1,3]=>[1,2,1,1,1,2]
[2,3,4,7,5,8,6,1]=>[8,5,1,2,3,4,7,6]=>[1,4,8,7,6,5,2,3]=>[3,1,1,1,2]
[6,5,2,8,7,4,3,1]=>[2,1,8,7,6,3,5,4]=>[7,8,1,2,3,6,4,5]=>[2,4,2]
[7,5,2,8,6,4,3,1]=>[2,8,7,6,3,1,5,4]=>[7,1,2,3,6,8,4,5]=>[1,5,2]
[7,8,3,2,6,5,4,1]=>[8,3,7,4,1,6,5,2]=>[1,6,2,5,8,3,4,7]=>[2,3,3]
[8,2,6,3,7,5,1,4]=>[7,8,4,2,3,6,5,1]=>[2,1,5,7,6,3,4,8]=>[1,3,1,3]
[8,6,7,2,5,3,1,4]=>[7,4,6,2,8,5,3,1]=>[2,5,3,7,1,4,6,8]=>[2,2,4]
[1,6,2,7,8,4,5,3]=>[6,4,2,8,7,1,3,5]=>[3,5,7,1,2,8,6,4]=>[3,3,1,1]
[1,6,8,2,7,5,3,4]=>[7,2,8,6,4,5,1,3]=>[2,7,1,3,5,4,8,6]=>[2,3,2,1]
[5,1,7,4,3,8,6,2]=>[4,1,8,5,3,7,2,6]=>[5,8,1,4,6,2,7,3]=>[2,3,2,1]
[8,6,3,7,2,4,1,5]=>[3,5,7,6,2,8,4,1]=>[6,4,2,3,7,1,5,8]=>[1,1,3,3]
[1,7,8,6,4,2,3,5]=>[6,7,5,2,8,4,1,3]=>[3,2,4,7,1,5,8,6]=>[1,3,3,1]
[7,2,8,6,4,1,3,5]=>[6,7,5,8,2,1,4,3]=>[3,2,4,1,7,8,5,6]=>[1,2,3,2]
[1,5,3,7,4,2,6,8]=>[6,3,2,5,7,1,4,8]=>[3,6,7,4,2,8,5,1]=>[3,1,2,1,1]
[1,7,6,4,3,2,8,5]=>[5,4,8,6,3,1,2,7]=>[4,5,1,3,6,8,7,2]=>[2,4,1,1]
[1,2,7,4,3,8,6,5]=>[8,4,7,5,1,2,3,6]=>[1,5,2,4,8,7,6,3]=>[2,3,1,1,1]
[1,5,3,2,4,6,7,8]=>[4,3,5,1,2,6,7,8]=>[5,6,4,8,7,3,2,1]=>[2,2,1,1,1,1]
[1,5,4,2,3,7,8,6]=>[6,3,2,8,1,4,5,7]=>[3,6,7,1,8,5,4,2]=>[3,2,1,1,1]
[4,3,7,2,8,1,6,5]=>[1,8,2,4,6,3,7,5]=>[8,1,7,5,3,6,2,4]=>[1,2,1,2,2]
[3,2,7,5,6,1,8,4]=>[4,8,1,6,2,5,3,7]=>[5,1,8,3,7,4,6,2]=>[1,2,2,2,1]
[7,4,5,1,6,3,8,2]=>[2,6,5,3,8,4,1,7]=>[7,3,4,6,1,5,8,2]=>[1,3,3,1]
[7,5,6,1,4,3,8,2]=>[6,5,2,8,4,3,1,7]=>[3,4,7,1,5,6,8,2]=>[3,4,1]
[4,2,7,6,8,3,5,1]=>[6,1,4,3,8,2,7,5]=>[3,8,5,6,1,7,2,4]=>[2,2,2,2]
[3,2,6,4,8,5,7,1]=>[6,1,3,8,2,4,7,5]=>[3,8,6,1,7,5,2,4]=>[2,1,2,1,2]
[6,2,8,5,7,1,4,3]=>[8,6,4,1,7,2,5,3]=>[1,3,5,8,2,7,4,6]=>[4,2,2]
[6,4,8,5,7,1,3,2]=>[8,2,1,6,4,7,5,3]=>[1,7,8,3,5,2,4,6]=>[3,2,3]
[5,3,4,1,6,2,8,7]=>[2,5,3,1,8,4,6,7]=>[7,4,6,8,1,5,3,2]=>[1,3,2,1,1]
[6,5,7,3,4,1,8,2]=>[4,2,1,8,6,5,3,7]=>[5,7,8,1,3,4,6,2]=>[3,4,1]
[5,2,7,6,8,1,4,3]=>[1,8,6,4,2,3,7,5]=>[8,1,3,5,7,6,2,4]=>[1,4,1,2]
[7,5,6,1,8,2,4,3]=>[8,6,2,7,4,3,1,5]=>[1,3,7,2,5,6,8,4]=>[3,4,1]
[7,3,6,1,8,2,5,4]=>[8,2,6,7,4,3,1,5]=>[1,7,3,2,5,6,8,4]=>[2,1,4,1]
[7,2,8,1,6,3,5,4]=>[8,6,7,2,4,1,5,3]=>[1,3,2,7,5,8,4,6]=>[2,2,2,2]
[10,5,9,4,8,3,7,2,6,1]=>[2,4,6,8,10,9,7,5,3,1]=>[9,7,5,3,1,2,4,6,8,10]=>[1,1,1,1,6]
[8,3,6,5,4,1,2,7]=>[6,7,2,5,4,3,8,1]=>[3,2,7,4,5,6,1,8]=>[1,2,3,2]
[1,7,5,8,4,6,3,2]=>[3,5,2,8,7,6,1,4]=>[6,4,7,1,2,3,8,5]=>[1,2,4,1]
[6,5,7,1,2,8,3,4]=>[7,8,4,2,1,5,3,6]=>[2,1,5,7,8,4,6,3]=>[1,4,2,1]
[7,1,4,2,3,8,6,5]=>[3,8,7,2,4,5,1,6]=>[6,1,2,7,5,4,8,3]=>[1,3,1,2,1]
[3,7,5,6,8,1,2,4]=>[6,3,7,1,4,2,8,5]=>[3,6,2,8,5,7,1,4]=>[2,2,2,2]
[8,1,2,5,3,7,6,4]=>[4,8,7,2,3,5,6,1]=>[5,1,2,7,6,4,3,8]=>[1,3,1,1,2]
[8,6,5,2,4,1,7,3]=>[8,4,6,5,3,2,7,1]=>[1,5,3,4,6,7,2,8]=>[2,4,2]
[3,6,5,2,4,1,7,8]=>[4,6,1,5,3,2,7,8]=>[5,3,8,4,6,7,2,1]=>[1,2,3,1,1]
[6,8,5,2,4,3,1,7]=>[7,4,1,6,5,3,8,2]=>[2,5,8,3,4,6,1,7]=>[3,3,2]
[3,4,2,8,6,7,1,5]=>[7,1,2,5,8,3,6,4]=>[2,8,7,4,1,6,3,5]=>[2,1,1,2,2]
[3,7,1,6,2,5,8,4]=>[6,8,1,5,3,4,2,7]=>[3,1,8,4,6,5,7,2]=>[1,2,2,2,1]
[4,6,7,2,5,1,8,3]=>[8,1,4,2,6,5,3,7]=>[1,8,5,7,3,4,6,2]=>[2,2,3,1]
[3,6,2,5,1,7,8,4]=>[6,1,3,4,2,8,5,7]=>[3,8,6,5,7,1,4,2]=>[2,1,2,2,1]
[3,4,2,7,8,1,5,6]=>[1,2,6,7,3,4,8,5]=>[8,7,3,2,6,5,1,4]=>[1,1,1,2,1,2]
[3,8,5,2,4,7,1,6]=>[4,5,1,3,7,8,6,2]=>[5,4,8,6,2,1,3,7]=>[1,2,1,1,3]
[7,1,4,2,5,8,6,3]=>[3,8,5,7,2,4,1,6]=>[6,1,4,2,7,5,8,3]=>[1,2,2,2,1]
[7,8,5,1,2,4,3,6]=>[7,4,5,6,3,1,8,2]=>[2,5,4,3,6,8,1,7]=>[2,1,3,2]
[5,8,1,4,3,6,7,2]=>[5,4,1,6,8,3,7,2]=>[4,5,8,3,1,6,2,7]=>[3,1,2,2]
[7,2,3,8,6,4,1,5]=>[7,6,8,2,3,1,5,4]=>[2,3,1,7,6,8,4,5]=>[2,2,2,2]
[4,6,2,7,8,1,3,5]=>[1,6,7,3,2,4,8,5]=>[8,3,2,6,7,5,1,4]=>[1,1,3,1,2]
[6,2,3,7,1,4,5,8]=>[2,3,5,6,1,7,4,8]=>[7,6,4,3,8,2,5,1]=>[1,1,1,2,2,1]
[4,6,7,8,2,1,3,5]=>[6,1,5,2,7,3,8,4]=>[3,8,4,7,2,6,1,5]=>[2,2,2,2]
[5,3,4,1,7,8,2,6]=>[2,3,1,7,5,8,4,6]=>[7,6,8,2,4,1,5,3]=>[1,2,2,2,1]
[9,7,10,8,6,5,4,3,2,1]=>[10,2,1,9,8,7,6,5,4,3]=>[1,9,10,2,3,4,5,6,7,8]=>[3,7]
[6,1,3,4,2,5,8,7]=>[3,4,8,2,5,1,6,7]=>[6,5,1,7,4,8,3,2]=>[1,1,2,2,1,1]
[5,1,3,6,2,4,8,7]=>[8,3,5,2,1,4,6,7]=>[1,6,4,7,8,5,3,2]=>[2,3,1,1,1]
[1,5,7,6,8,2,4,3]=>[8,2,6,4,3,7,1,5]=>[1,7,3,5,6,2,8,4]=>[2,3,2,1]
[5,7,1,3,8,4,2,6]=>[7,4,1,6,8,3,2,5]=>[2,5,8,3,1,6,7,4]=>[3,1,3,1]
[2,6,1,4,3,7,8,5]=>[4,6,8,1,3,2,5,7]=>[5,3,1,8,6,7,4,2]=>[1,1,2,2,1,1]
[1,6,2,4,3,5,8,7]=>[4,8,3,5,1,2,6,7]=>[5,1,6,4,8,7,3,2]=>[1,2,2,1,1,1]
[5,3,7,6,1,8,4,2]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[1,3,3,1]
[1,5,6,3,7,8,4,2]=>[2,5,3,8,4,7,1,6]=>[7,4,6,1,5,2,8,3]=>[1,2,2,2,1]
[7,3,5,6,1,8,4,2]=>[3,8,2,7,5,4,1,6]=>[6,1,7,2,4,5,8,3]=>[1,2,4,1]
[7,3,6,1,5,8,4,2]=>[5,8,2,7,4,3,1,6]=>[4,1,7,2,5,6,8,3]=>[1,2,4,1]
[1,6,3,7,8,5,4,2]=>[4,2,8,7,3,6,1,5]=>[5,7,1,2,6,3,8,4]=>[2,3,2,1]
[1,7,8,6,3,5,4,2]=>[8,5,2,7,6,4,1,3]=>[1,4,7,2,3,5,8,6]=>[3,4,1]
[3,7,5,6,1,8,4,2]=>[3,8,7,1,5,4,2,6]=>[6,1,2,8,4,5,7,3]=>[1,3,3,1]
[5,6,2,8,4,7,3,1]=>[1,5,2,8,7,3,6,4]=>[8,4,7,1,2,6,3,5]=>[1,2,3,2]
[3,7,5,4,6,1,2,8]=>[6,4,1,3,7,5,2,8]=>[3,5,8,6,2,4,7,1]=>[3,1,3,1]
[5,3,4,7,6,8,1,2]=>[7,2,1,3,5,4,8,6]=>[2,7,8,6,4,5,1,3]=>[3,1,2,2]
[7,8,3,5,4,1,2,6]=>[3,6,7,5,4,1,8,2]=>[6,3,2,4,5,8,1,7]=>[1,1,4,2]
[3,5,4,1,2,7,6,8]=>[7,1,4,3,2,5,6,8]=>[2,8,5,6,7,4,3,1]=>[2,3,1,1,1]
[5,3,4,1,2,7,6,8]=>[2,7,4,3,1,5,6,8]=>[7,2,5,6,8,4,3,1]=>[1,4,1,1,1]
[7,8,3,1,2,5,4,6]=>[7,4,3,5,6,1,8,2]=>[2,5,6,4,3,8,1,7]=>[3,1,2,2]
[7,8,5,1,3,2,4,6]=>[6,4,5,7,3,1,8,2]=>[3,5,4,2,6,8,1,7]=>[2,1,3,2]
[7,5,6,1,3,2,4,8]=>[6,4,5,2,7,3,1,8]=>[3,5,4,7,2,6,8,1]=>[2,2,3,1]
[7,5,1,3,8,6,2,4]=>[7,8,4,2,6,3,1,5]=>[2,1,5,7,3,6,8,4]=>[1,3,3,1]
[5,7,6,1,3,8,2,4]=>[5,1,7,8,4,3,2,6]=>[4,8,2,1,5,6,7,3]=>[2,1,4,1]
[5,7,6,3,8,1,4,2]=>[1,4,8,6,3,2,7,5]=>[8,5,1,3,6,7,2,4]=>[1,1,4,2]
[5,1,3,7,6,2,4,8]=>[6,7,3,1,5,2,4,8]=>[3,2,6,8,4,7,5,1]=>[1,3,2,1,1]
[1,6,3,7,2,4,5,8]=>[3,5,6,2,7,1,4,8]=>[6,4,3,7,2,8,5,1]=>[1,1,2,2,1,1]
[5,3,2,4,8,1,7,6]=>[2,8,3,1,4,6,7,5]=>[7,1,6,8,5,3,2,4]=>[1,3,1,1,2]
[6,8,5,3,2,7,1,4]=>[5,4,1,7,3,8,6,2]=>[4,5,8,2,6,1,3,7]=>[3,2,3]
[4,6,2,7,1,3,8,5]=>[1,8,3,5,2,6,4,7]=>[8,1,6,4,7,3,5,2]=>[1,2,2,2,1]
[3,4,6,5,1,8,7,2]=>[4,1,2,3,8,7,5,6]=>[5,8,7,6,1,2,4,3]=>[2,1,1,3,1]
[8,7,1,5,3,2,6,4]=>[5,8,6,3,4,7,2,1]=>[4,1,3,6,5,2,7,8]=>[1,3,1,3]
[3,5,1,4,7,2,8,6]=>[8,1,4,2,6,3,5,7]=>[1,8,5,7,3,6,4,2]=>[2,2,2,1,1]
[5,1,4,8,7,3,2,6]=>[7,3,1,6,8,5,2,4]=>[2,6,8,3,1,4,7,5]=>[3,1,3,1]
[2,1,4,3,6,5,8,10,7,9]=>[1,3,5,7,9,10,2,4,6,8]=>[10,8,6,4,2,1,9,7,5,3]=>[1,1,1,1,1,2,1,1,1]
[6,1,3,4,2,7,8,5]=>[3,4,6,8,2,1,5,7]=>[6,5,3,1,7,8,4,2]=>[1,1,1,3,1,1]
[6,5,2,3,7,8,1,4]=>[7,3,4,2,1,5,8,6]=>[2,6,5,7,8,4,1,3]=>[2,3,1,2]
[1,5,3,8,4,2,7,6]=>[5,2,8,3,6,7,1,4]=>[4,7,1,6,3,2,8,5]=>[2,2,1,2,1]
[5,4,2,1,8,3,7,6]=>[8,3,2,1,6,7,4,5]=>[1,6,7,8,3,2,5,4]=>[4,1,2,1]
[3,1,7,4,2,6,8,5]=>[1,4,6,8,5,2,3,7]=>[8,5,3,1,4,7,6,2]=>[1,1,1,3,1,1]
[7,4,8,2,3,5,1,6]=>[4,2,5,7,6,1,8,3]=>[5,7,4,2,3,8,1,6]=>[2,1,3,2]
[8,4,1,3,2,6,7,5]=>[4,6,2,8,3,5,7,1]=>[5,3,7,1,6,4,2,8]=>[1,2,2,1,2]
[8,1,7,3,2,5,6,4]=>[4,6,8,5,7,2,3,1]=>[5,3,1,4,2,7,6,8]=>[1,1,2,2,2]
[8,6,5,2,7,3,1,4]=>[7,4,6,3,2,8,5,1]=>[2,5,3,6,7,1,4,8]=>[2,3,3]
[3,1,6,8,4,2,7,5]=>[5,1,3,8,6,7,2,4]=>[4,8,6,1,3,2,7,5]=>[2,1,2,2,1]
[1,5,2,8,3,6,7,4]=>[6,2,8,5,7,1,3,4]=>[3,7,1,4,2,8,6,5]=>[2,2,2,1,1]
[2,3,4,9,5,6,7,8,1]=>[5,6,7,9,1,2,3,8,4]=>[5,4,3,1,9,8,7,2,6]=>[1,1,1,2,1,1,2]
[6,2,4,7,3,5,1,8]=>[3,5,7,2,1,6,4,8]=>[6,4,2,7,8,3,5,1]=>[1,1,3,2,1]
[1,4,8,5,3,6,7,2]=>[5,2,4,6,8,7,1,3]=>[4,7,5,3,1,2,8,6]=>[2,1,1,3,1]
[2,5,6,3,1,8,4,7]=>[4,2,7,1,3,8,5,6]=>[5,7,2,8,6,1,4,3]=>[2,2,1,2,1]
[4,5,1,2,7,8,6,3]=>[1,5,2,8,7,3,4,6]=>[8,4,7,1,2,6,5,3]=>[1,2,3,1,1]
[4,8,5,1,2,6,7,3]=>[1,6,8,4,3,5,7,2]=>[8,3,1,5,6,4,2,7]=>[1,1,3,1,2]
[4,6,7,5,1,2,8,3]=>[8,1,5,2,6,4,3,7]=>[1,8,4,7,3,5,6,2]=>[2,2,3,1]
[6,1,4,7,3,8,2,5]=>[3,5,7,4,1,8,2,6]=>[6,4,2,5,8,1,7,3]=>[1,1,3,2,1]
[7,1,6,3,4,8,2,5]=>[4,5,7,3,8,2,1,6]=>[5,4,2,6,1,7,8,3]=>[1,1,2,3,1]
[2,8,4,6,3,1,5,7]=>[3,6,5,7,1,4,8,2]=>[6,3,4,2,8,5,1,7]=>[1,2,2,1,2]
[8,2,6,3,5,1,4,7]=>[4,6,7,2,5,3,8,1]=>[5,3,2,7,4,6,1,8]=>[1,1,2,2,2]
[3,7,4,1,5,8,2,6]=>[5,1,3,7,8,4,2,6]=>[4,8,6,2,1,5,7,3]=>[2,1,1,3,1]
[6,7,5,1,3,8,2,4]=>[5,7,1,8,4,3,2,6]=>[4,2,8,1,5,6,7,3]=>[1,2,4,1]
[7,8,6,2,4,1,3,5]=>[4,6,7,5,1,8,3,2]=>[5,3,2,4,8,1,6,7]=>[1,1,3,3]
[8,2,4,1,3,6,7,5]=>[6,2,3,8,4,5,7,1]=>[3,7,6,1,5,4,2,8]=>[2,1,2,1,2]
[8,1,3,6,2,5,7,4]=>[6,8,3,5,2,4,7,1]=>[3,1,6,4,7,5,2,8]=>[1,2,2,1,2]
[1,5,6,3,8,4,7,2]=>[2,6,3,8,4,7,1,5]=>[7,3,6,1,5,2,8,4]=>[1,2,2,2,1]
[5,6,1,3,7,2,8,4]=>[8,4,1,6,3,2,5,7]=>[1,5,8,3,6,7,4,2]=>[3,3,1,1]
[5,6,1,8,2,3,7,4]=>[8,5,1,6,2,7,3,4]=>[1,4,8,3,7,2,6,5]=>[3,2,2,1]
[3,7,8,1,6,4,2,5]=>[7,6,8,1,4,2,5,3]=>[2,3,1,8,5,7,4,6]=>[2,2,2,2]
[1,7,8,6,3,4,2,5]=>[5,7,6,2,8,4,1,3]=>[4,2,3,7,1,5,8,6]=>[1,3,3,1]
[1,7,3,8,6,4,2,5]=>[7,6,8,3,2,5,1,4]=>[2,3,1,6,7,4,8,5]=>[2,3,2,1]
[5,7,1,8,6,4,2,3]=>[1,7,8,6,5,3,2,4]=>[8,2,1,3,4,6,7,5]=>[1,1,5,1]
[7,8,1,5,6,4,2,3]=>[7,4,8,6,3,1,5,2]=>[2,5,1,3,6,8,4,7]=>[2,4,2]
[7,1,8,5,6,4,2,3]=>[7,4,8,6,5,2,1,3]=>[2,5,1,3,4,7,8,6]=>[2,5,1]
[7,1,5,8,6,4,2,3]=>[3,7,8,6,5,2,1,4]=>[6,2,1,3,4,7,8,5]=>[1,1,5,1]
[8,1,3,5,6,4,2,7]=>[4,7,3,6,2,5,8,1]=>[5,2,6,3,7,4,1,8]=>[1,2,2,1,2]
[1,3,8,5,6,4,2,7]=>[4,7,6,2,5,8,1,3]=>[5,2,3,7,4,1,8,6]=>[1,3,1,2,1]
[1,3,5,8,6,4,2,7]=>[7,3,6,2,5,8,1,4]=>[2,6,3,7,4,1,8,5]=>[2,2,1,2,1]
[1,5,7,8,6,4,2,3]=>[7,2,3,8,6,5,1,4]=>[2,7,6,1,3,4,8,5]=>[2,1,4,1]
[7,6,8,5,9,4,10,3,11,2,12,1]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,2,2,2,2,2]
[1,8,2,6,5,3,4,7]=>[6,7,5,3,4,8,1,2]=>[3,2,4,6,5,1,8,7]=>[1,3,1,2,1]
[8,6,1,5,2,3,4,7]=>[5,6,7,3,4,2,8,1]=>[4,3,2,6,5,7,1,8]=>[1,1,2,2,2]
[8,5,1,6,2,3,4,7]=>[5,6,7,3,2,4,8,1]=>[4,3,2,6,7,5,1,8]=>[1,1,3,1,2]
[7,6,1,2,3,8,4,5]=>[7,8,3,4,5,2,1,6]=>[2,1,6,5,4,7,8,3]=>[1,2,1,3,1]
[2,7,8,4,1,3,5,6]=>[5,6,4,7,1,2,8,3]=>[4,3,5,2,8,7,1,6]=>[1,2,2,1,2]
[6,8,1,2,3,7,4,5]=>[7,8,3,4,1,5,6,2]=>[2,1,6,5,8,4,3,7]=>[1,2,2,1,2]
[8,1,3,5,6,7,2,4]=>[4,7,3,5,8,2,6,1]=>[5,2,6,4,1,7,3,8]=>[1,2,1,2,2]
[8,1,2,5,3,4,7,6]=>[8,5,2,3,4,6,7,1]=>[1,4,7,6,5,3,2,8]=>[3,1,1,1,2]
[3,7,6,2,5,8,4,1]=>[5,8,4,1,3,2,7,6]=>[4,1,5,8,6,7,2,3]=>[1,3,2,2]
[5,2,7,3,4,8,1,6]=>[4,5,1,7,2,3,8,6]=>[5,4,8,2,7,6,1,3]=>[1,2,2,1,2]
[8,6,4,7,3,5,2,1]=>[3,5,2,8,7,6,4,1]=>[6,4,7,1,2,3,5,8]=>[1,2,5]
[4,2,1,6,5,7,8,3]=>[5,2,1,4,6,8,3,7]=>[4,7,8,5,3,1,6,2]=>[3,1,1,2,1]
[2,7,5,4,1,3,6,8]=>[5,6,4,1,3,7,2,8]=>[4,3,5,8,6,2,7,1]=>[1,3,1,2,1]
[2,7,4,6,5,1,8,3]=>[8,3,6,5,1,4,2,7]=>[1,6,3,4,8,5,7,2]=>[2,3,2,1]
[6,8,7,5,2,1,4,3]=>[5,1,8,6,7,4,3,2]=>[4,8,1,3,2,5,6,7]=>[2,2,4]
[2,8,6,3,5,1,4,7]=>[4,6,7,5,1,3,8,2]=>[5,3,2,4,8,6,1,7]=>[1,1,3,1,2]
[1,2,8,6,4,5,3,7]=>[5,7,6,4,8,1,2,3]=>[4,2,3,5,1,8,7,6]=>[1,3,2,1,1]
[1,5,8,7,6,3,4,2]=>[6,8,2,7,5,4,1,3]=>[3,1,7,2,4,5,8,6]=>[1,2,4,1]
[1,4,7,8,5,6,3,2]=>[5,3,8,2,7,6,1,4]=>[4,6,1,7,2,3,8,5]=>[2,2,3,1]
[1,6,4,8,5,7,3,2]=>[5,2,8,3,7,6,1,4]=>[4,7,1,6,2,3,8,5]=>[2,2,3,1]
[1,6,8,5,2,7,3,4]=>[7,2,8,5,4,6,1,3]=>[2,7,1,4,5,3,8,6]=>[2,3,2,1]
[1,3,4,8,5,2,7,6]=>[5,8,2,3,6,7,1,4]=>[4,1,7,6,3,2,8,5]=>[1,2,1,1,2,1]
[3,5,8,7,6,2,4,1]=>[6,8,2,7,1,5,4,3]=>[3,1,7,2,8,4,5,6]=>[1,2,2,3]
[6,5,3,7,4,1,8,2]=>[8,3,2,1,6,5,4,7]=>[1,6,7,8,3,4,5,2]=>[4,3,1]
[3,1,5,4,6,8,7,2]=>[1,3,8,4,5,7,2,6]=>[8,6,1,5,4,2,7,3]=>[1,1,2,1,2,1]
[3,1,6,4,2,5,8,7]=>[1,4,8,5,2,3,6,7]=>[8,5,1,4,7,6,3,2]=>[1,1,3,1,1,1]
[3,6,1,4,5,7,8,2]=>[1,4,5,6,2,8,3,7]=>[8,5,4,3,7,1,6,2]=>[1,1,1,2,2,1]
[1,8,4,7,2,3,6,5]=>[3,8,5,6,7,4,1,2]=>[6,1,4,3,2,5,8,7]=>[1,2,1,3,1]
[5,4,2,3,6,8,1,7]=>[3,4,2,1,5,7,8,6]=>[6,5,7,8,4,2,1,3]=>[1,3,1,1,2]
[7,3,2,1,8,6,4,5]=>[2,7,8,3,6,4,1,5]=>[7,2,1,6,3,5,8,4]=>[1,1,2,3,1]
[8,7,2,4,1,3,6,5]=>[8,3,5,4,6,7,2,1]=>[1,6,4,5,3,2,7,8]=>[2,2,1,3]
[8,2,6,3,5,7,1,4]=>[7,4,5,2,3,8,6,1]=>[2,5,4,7,6,1,3,8]=>[2,2,1,3]
[1,8,3,7,4,6,5,2]=>[8,5,7,3,6,4,1,2]=>[1,4,2,6,3,5,8,7]=>[2,2,3,1]
[8,2,3,1,7,4,5,6]=>[2,3,6,7,8,4,5,1]=>[7,6,3,2,1,5,4,8]=>[1,1,1,1,2,2]
[3,1,7,8,6,2,5,4]=>[8,6,1,3,7,5,2,4]=>[1,3,8,6,2,4,7,5]=>[3,1,3,1]
[4,8,1,2,6,5,7,3]=>[1,6,5,8,3,4,7,2]=>[8,3,4,1,6,5,2,7]=>[1,2,2,1,2]
[5,6,1,8,3,7,2,4]=>[5,1,7,2,8,6,3,4]=>[4,8,2,7,1,3,6,5]=>[2,2,3,1]
[2,8,1,6,5,3,7,4]=>[8,6,5,1,3,4,7,2]=>[1,3,4,8,6,5,2,7]=>[4,1,1,2]
[2,1,5,7,6,3,8,4]=>[8,3,6,1,5,2,4,7]=>[1,6,3,8,4,7,5,2]=>[2,2,2,1,1]
[1,8,5,2,3,4,7,6]=>[8,4,5,3,6,7,1,2]=>[1,5,4,6,3,2,8,7]=>[2,2,1,2,1]
[1,5,8,2,3,4,7,6]=>[8,4,2,5,6,7,1,3]=>[1,5,7,4,3,2,8,6]=>[3,1,1,2,1]
[1,2,7,8,4,5,6,3]=>[5,6,3,8,7,1,2,4]=>[4,3,6,1,2,8,7,5]=>[1,2,3,1,1]
[1,2,3,4,5,6,9,7,10,8]=>[10,8,1,2,3,4,5,6,7,9]=>[1,3,10,9,8,7,6,5,4,2]=>[3,1,1,1,1,1,1,1]
[2,3,4,5,6,9,10,1,7,8]=>[8,9,1,2,3,4,5,6,10,7]=>[3,2,10,9,8,7,6,5,1,4]=>[1,2,1,1,1,1,1,2]
[4,3,8,7,6,2,5,1]=>[6,8,1,7,2,5,4,3]=>[3,1,8,2,7,4,5,6]=>[1,2,2,3]
[5,4,8,2,7,6,3,1]=>[1,8,2,7,4,6,5,3]=>[8,1,7,2,5,3,4,6]=>[1,2,2,3]
[3,2,5,6,4,8,1,7]=>[1,3,5,2,4,7,8,6]=>[8,6,4,7,5,2,1,3]=>[1,1,2,1,1,2]
[2,3,6,4,1,7,5,8]=>[4,7,1,2,5,3,6,8]=>[5,2,8,7,4,6,3,1]=>[1,2,1,2,1,1]
[2,3,7,1,5,8,4,6]=>[5,7,8,1,2,4,3,6]=>[4,2,1,8,7,5,6,3]=>[1,1,2,1,2,1]
[2,3,6,1,7,5,8,4]=>[6,5,1,2,3,8,4,7]=>[3,4,8,7,6,1,5,2]=>[3,1,1,2,1]
[2,3,6,5,1,7,4,8]=>[7,5,1,2,4,3,6,8]=>[2,4,8,7,5,6,3,1]=>[3,1,2,1,1]
[4,3,2,6,5,8,1,7]=>[2,1,5,3,4,7,8,6]=>[7,8,4,6,5,2,1,3]=>[2,2,1,1,2]
[4,6,1,7,5,8,3,2]=>[5,1,4,2,8,7,3,6]=>[4,8,5,7,1,2,6,3]=>[2,2,3,1]
[4,2,6,5,1,7,8,3]=>[1,6,4,2,3,8,5,7]=>[8,3,5,7,6,1,4,2]=>[1,3,1,2,1]
[4,1,5,7,6,8,3,2]=>[1,5,3,4,8,7,2,6]=>[8,4,6,5,1,2,7,3]=>[1,2,1,3,1]
[4,2,5,7,6,8,3,1]=>[1,5,3,4,8,2,7,6]=>[8,4,6,5,1,7,2,3]=>[1,2,1,2,2]
[4,3,6,5,2,8,1,7]=>[1,5,2,4,3,7,8,6]=>[8,4,7,5,6,2,1,3]=>[1,2,2,1,2]
[4,3,6,5,1,7,8,2]=>[1,6,2,4,3,8,5,7]=>[8,3,7,5,6,1,4,2]=>[1,2,2,2,1]
[3,6,4,5,2,1,7,8]=>[3,6,1,5,4,2,7,8]=>[6,3,8,4,5,7,2,1]=>[1,2,3,1,1]
[3,5,6,4,2,8,1,7]=>[2,5,1,4,3,7,8,6]=>[7,4,8,5,6,2,1,3]=>[1,2,2,1,2]
[4,6,5,3,1,7,8,2]=>[6,1,4,3,2,8,5,7]=>[3,8,5,6,7,1,4,2]=>[2,3,2,1]
[1,2,3,4,5,7,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[4,10,9,8,7,6,5,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,5,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[6,10,9,8,7,5,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[5,8,1,4,2,3,6,7]=>[5,6,3,1,4,7,8,2]=>[4,3,6,8,5,2,1,7]=>[1,3,1,1,2]
[3,5,4,8,1,7,2,6]=>[3,1,2,7,8,5,6,4]=>[6,8,7,2,1,4,3,5]=>[2,1,1,2,2]
[5,3,6,8,1,4,7,2]=>[6,2,1,3,8,5,7,4]=>[3,7,8,6,1,4,2,5]=>[3,1,2,2]
[3,5,1,8,6,4,7,2]=>[2,6,1,5,8,7,3,4]=>[7,3,8,4,1,2,6,5]=>[1,2,1,3,1]
[4,7,2,8,3,1,6,5]=>[1,5,8,3,6,2,7,4]=>[8,4,1,6,3,7,2,5]=>[1,1,2,2,2]
[5,3,8,4,6,2,7,1]=>[4,1,6,2,5,8,7,3]=>[5,8,3,7,4,1,2,6]=>[2,2,1,3]
[7,4,8,1,5,2,6,3]=>[2,8,6,4,5,1,7,3]=>[7,1,3,5,4,8,2,6]=>[1,3,2,2]
[4,1,5,6,8,7,2,3]=>[3,1,4,7,8,6,2,5]=>[6,8,5,2,1,3,7,4]=>[2,1,1,3,1]
[1,2,5,6,8,4,7,3]=>[3,4,6,8,7,1,2,5]=>[6,5,3,1,2,8,7,4]=>[1,1,1,3,1,1]
[1,5,6,8,4,7,2,3]=>[2,3,7,5,8,6,1,4]=>[7,6,2,4,1,3,8,5]=>[1,1,2,3,1]
[5,6,8,1,2,4,7,3]=>[6,1,8,4,2,5,7,3]=>[3,8,1,5,7,4,2,6]=>[2,3,1,2]
[6,8,1,4,5,7,2,3]=>[4,7,5,1,8,3,6,2]=>[5,2,4,8,1,6,3,7]=>[1,3,2,2]
[4,3,5,1,8,6,7,2]=>[2,1,3,6,8,7,4,5]=>[7,8,6,3,1,2,5,4]=>[2,1,1,3,1]
[1,3,5,6,8,4,7,2]=>[3,4,6,8,2,7,1,5]=>[6,5,3,1,7,2,8,4]=>[1,1,1,2,2,1]
[5,6,8,2,3,4,7,1]=>[4,1,5,2,6,8,7,3]=>[5,8,4,7,3,1,2,6]=>[2,2,1,3]
[6,5,1,2,4,8,7,3]=>[8,5,7,3,2,1,4,6]=>[1,4,2,6,7,8,5,3]=>[2,4,1,1]
[5,8,7,2,1,3,6,4]=>[4,1,8,5,6,7,3,2]=>[5,8,1,4,3,2,6,7]=>[2,2,1,3]
[5,1,7,2,8,6,3,4]=>[7,1,8,6,4,2,3,5]=>[2,8,1,3,5,7,6,4]=>[2,4,1,1]
[6,1,5,3,4,8,7,2]=>[8,4,3,5,1,7,2,6]=>[1,5,6,4,8,2,7,3]=>[3,2,2,1]
[5,8,6,3,2,1,4,7]=>[1,6,5,4,7,3,8,2]=>[8,3,4,5,2,6,1,7]=>[1,3,2,2]
[8,7,1,6,3,5,4,2]=>[8,5,7,6,3,4,2,1]=>[1,4,2,3,6,5,7,8]=>[2,3,3]
[3,2,1,7,8,6,4,5]=>[7,1,4,8,2,6,3,5]=>[2,8,5,1,7,3,6,4]=>[2,1,2,2,1]
[8,6,7,1,2,5,3,4]=>[7,8,4,5,2,6,3,1]=>[2,1,5,4,7,3,6,8]=>[1,2,2,3]
[1,5,6,4,2,8,7,3]=>[2,4,3,8,7,1,5,6]=>[7,5,6,1,2,8,4,3]=>[1,2,3,1,1]
[7,5,1,4,8,2,3,6]=>[6,4,7,2,8,3,1,5]=>[3,5,2,7,1,6,8,4]=>[2,2,3,1]
[3,2,8,1,7,5,6,4]=>[6,8,1,7,2,4,5,3]=>[3,1,8,2,7,5,4,6]=>[1,2,2,1,2]
[8,4,3,1,7,5,6,2]=>[3,2,6,8,7,4,5,1]=>[6,7,3,1,2,5,4,8]=>[2,1,3,2]
[6,1,7,8,4,2,3,5]=>[6,7,5,3,1,8,2,4]=>[3,2,4,6,8,1,7,5]=>[1,4,2,1]
[7,4,3,1,8,5,2,6]=>[3,2,7,6,8,4,1,5]=>[6,7,2,3,1,5,8,4]=>[2,2,3,1]
[7,8,1,6,3,4,5,2]=>[5,6,8,7,3,1,4,2]=>[4,3,1,2,6,8,5,7]=>[1,1,4,2]
[6,8,1,7,3,4,2,5]=>[5,7,6,1,8,3,4,2]=>[4,2,3,8,1,6,5,7]=>[1,3,2,2]
[3,4,2,1,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[1,3,1,1,1,1,1]
[4,3,1,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[7,6,8,9,5,4,3,2,1]=>[1,3,1,1,1,1,1]
[2,3,1,4,5,6,7,8,9,10,11]=>[1,3,2,4,5,6,7,8,9,10,11]=>[11,9,10,8,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1,1]
[5,3,1,2,4,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>[7,6,8,5,9,4,3,2,1]=>[1,2,2,1,1,1,1]
[3,1,2,4,5,6,7,8,9,10,11]=>[2,3,1,4,5,6,7,8,9,10,11]=>[10,9,11,8,7,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1,1]
[4,5,6,3,8,1,7,2]=>[1,2,4,3,8,6,7,5]=>[8,7,5,6,1,3,2,4]=>[1,1,2,2,2]
[7,8,3,5,2,1,6,4]=>[3,5,8,6,4,1,7,2]=>[6,4,1,3,5,8,2,7]=>[1,1,4,2]
[6,3,7,5,2,4,1,8]=>[5,7,2,1,6,4,3,8]=>[4,2,7,8,3,5,6,1]=>[1,3,3,1]
[7,8,1,5,6,4,3,2]=>[4,8,7,6,3,1,5,2]=>[5,1,2,3,6,8,4,7]=>[1,5,2]
[6,3,7,5,1,4,2,8]=>[7,2,5,1,6,4,3,8]=>[2,7,4,8,3,5,6,1]=>[2,2,3,1]
[1,3,8,2,4,6,7,5]=>[6,8,2,4,5,7,1,3]=>[3,1,7,5,4,2,8,6]=>[1,2,1,1,2,1]
[3,1,7,2,5,8,6,4]=>[8,1,5,7,4,2,3,6]=>[1,8,4,2,5,7,6,3]=>[2,1,3,1,1]
[2,8,7,6,3,5,1,4]=>[5,7,8,6,4,1,3,2]=>[4,2,1,3,5,8,6,7]=>[1,1,4,2]
[2,8,7,1,5,6,4,3]=>[5,8,7,4,6,1,3,2]=>[4,1,2,5,3,8,6,7]=>[1,3,2,2]
[3,1,4,6,8,2,7,5]=>[1,4,8,3,6,7,2,5]=>[8,5,1,6,3,2,7,4]=>[1,1,2,1,2,1]
[4,1,5,7,3,8,2,6]=>[3,1,5,7,4,8,2,6]=>[6,8,4,2,5,1,7,3]=>[2,1,2,2,1]
[6,2,5,8,4,7,3,1]=>[3,5,1,8,7,2,6,4]=>[6,4,8,1,2,7,3,5]=>[1,2,3,2]
[7,2,8,5,4,3,6,1]=>[6,5,4,8,2,1,7,3]=>[3,4,5,1,7,8,2,6]=>[3,3,2]
[7,1,6,8,2,5,3,4]=>[7,8,5,3,6,2,1,4]=>[2,1,4,6,3,7,8,5]=>[1,3,3,1]
[2,6,5,7,8,4,1,3]=>[3,2,7,4,8,1,6,5]=>[6,7,2,5,1,8,3,4]=>[2,2,2,2]
[3,6,5,7,4,1,8,2]=>[3,2,8,1,6,5,4,7]=>[6,7,1,8,3,4,5,2]=>[2,2,3,1]
[1,6,5,7,4,2,3,8]=>[6,3,2,7,5,1,4,8]=>[3,6,7,2,4,8,5,1]=>[3,3,1,1]
[3,4,7,5,2,1,8,6]=>[5,1,2,4,8,6,3,7]=>[4,8,7,5,1,3,6,2]=>[2,1,1,3,1]
[3,6,7,5,8,4,1,2]=>[2,7,4,1,3,8,6,5]=>[7,2,5,8,6,1,3,4]=>[1,3,1,3]
[3,4,7,2,5,6,8,1]=>[1,2,4,5,6,3,8,7]=>[8,7,5,4,3,6,1,2]=>[1,1,1,1,2,2]
[2,5,3,7,8,6,4,1]=>[2,4,8,7,1,3,6,5]=>[7,5,1,2,8,6,3,4]=>[1,1,3,1,2]
[7,2,8,4,5,6,3,1]=>[4,5,8,7,2,1,6,3]=>[5,4,1,2,7,8,3,6]=>[1,1,4,2]
[6,2,3,8,5,4,7,1]=>[6,5,8,2,1,3,7,4]=>[3,4,1,7,8,6,2,5]=>[2,3,1,2]
[5,4,3,1,2,6,7,8,9]=>[4,5,3,2,1,6,7,8,9]=>[6,5,7,8,9,4,3,2,1]=>[1,4,1,1,1,1]
[6,5,4,3,1,2,7,8,9]=>[5,6,4,3,2,1,7,8,9]=>[5,4,6,7,8,9,3,2,1]=>[1,5,1,1,1]
[7,5,8,6,4,1,3,2]=>[2,8,6,1,7,5,4,3]=>[7,1,3,8,2,4,5,6]=>[1,3,4]
[2,7,6,3,8,5,1,4]=>[7,8,4,3,1,2,6,5]=>[2,1,5,6,8,7,3,4]=>[1,4,1,2]
[2,3,1,7,6,8,4,5]=>[7,5,1,2,4,8,3,6]=>[2,4,8,7,5,1,6,3]=>[3,1,1,2,1]
[2,3,1,8,4,6,7,5]=>[6,8,1,2,5,7,3,4]=>[3,1,8,7,4,2,6,5]=>[1,2,1,1,2,1]
[6,2,3,4,5,1,9,7,8]=>[2,3,4,5,1,8,9,6,7]=>[8,7,6,5,9,2,1,4,3]=>[1,1,1,2,1,2,1]
[4,2,3,5,1,8,6,7]=>[2,3,1,4,7,8,5,6]=>[7,6,8,5,2,1,4,3]=>[1,2,1,1,2,1]
[2,3,4,5,6,10,1,7,8,9]=>[1,2,3,4,5,7,8,9,10,6]=>[10,9,8,7,6,4,3,2,1,5]=>[1,1,1,1,1,1,1,1,2]
[2,3,4,5,10,1,6,7,8,9]=>[1,2,3,4,6,7,8,9,10,5]=>[10,9,8,7,5,4,3,2,1,6]=>[1,1,1,1,1,1,1,1,2]
[2,3,4,10,1,5,6,7,8,9]=>[1,2,3,5,6,7,8,9,10,4]=>[10,9,8,6,5,4,3,2,1,7]=>[1,1,1,1,1,1,1,1,2]
[5,8,7,2,6,4,1,3]=>[1,7,8,4,6,5,3,2]=>[8,2,1,5,3,4,6,7]=>[1,1,2,4]
[6,8,5,1,7,4,3,2]=>[1,8,7,6,4,3,5,2]=>[8,1,2,3,5,6,4,7]=>[1,5,2]
[6,8,5,2,7,4,1,3]=>[7,1,8,4,3,6,5,2]=>[2,8,1,5,6,3,4,7]=>[2,3,3]
[7,3,8,6,5,2,1,4]=>[7,6,8,2,1,5,4,3]=>[2,3,1,7,8,4,5,6]=>[2,3,3]
[7,5,8,1,6,4,3,2]=>[2,8,7,6,4,1,5,3]=>[7,1,2,3,5,8,4,6]=>[1,5,2]
[7,5,8,2,6,4,1,3]=>[7,2,8,4,1,6,5,3]=>[2,7,1,5,8,3,4,6]=>[2,3,3]
[2,1,3,4,5,6,8,7,9]=>[1,8,2,3,4,5,6,7,9]=>[9,2,8,7,6,5,4,3,1]=>[1,2,1,1,1,1,1,1]
[2,3,4,5,6,8,7,9,1]=>[7,1,2,3,4,5,6,9,8]=>[3,9,8,7,6,5,4,1,2]=>[2,1,1,1,1,1,2]
[2,6,8,7,1,3,5,4]=>[8,5,2,6,7,1,4,3]=>[1,4,7,3,2,8,5,6]=>[3,1,2,2]
[3,7,6,1,4,5,2,8]=>[5,7,1,4,6,3,2,8]=>[4,2,8,5,3,6,7,1]=>[1,2,1,3,1]
[4,1,6,2,7,5,3,8]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[1,4,1,1,1]
[7,6,2,5,3,1,4,8]=>[6,3,5,7,4,2,1,8]=>[3,6,4,2,5,7,8,1]=>[2,1,4,1]
[4,3,1,7,6,2,5,8]=>[2,1,6,7,5,3,4,8]=>[7,8,3,2,4,6,5,1]=>[2,1,3,1,1]
[4,5,3,1,2,8,6,7]=>[1,7,3,2,8,4,5,6]=>[8,2,6,7,1,5,4,3]=>[1,3,2,1,1]
[2,4,5,3,1,8,6,7]=>[2,4,1,3,7,8,5,6]=>[7,5,8,6,2,1,4,3]=>[1,2,1,1,2,1]
[5,7,6,2,3,1,4,8]=>[4,1,6,5,7,3,2,8]=>[5,8,3,4,2,6,7,1]=>[2,2,3,1]
[4,1,3,7,5,2,6,8]=>[6,3,1,5,7,2,4,8]=>[3,6,8,4,2,7,5,1]=>[3,1,2,1,1]
[4,1,6,3,2,7,5,8]=>[4,1,7,5,2,3,6,8]=>[5,8,2,4,7,6,3,1]=>[2,3,1,1,1]
[7,5,4,1,3,2,6,8]=>[6,4,5,3,2,7,1,8]=>[3,5,4,6,7,2,8,1]=>[2,3,2,1]
[2,4,8,5,6,3,1,7]=>[4,7,2,6,1,5,8,3]=>[5,2,7,3,8,4,1,6]=>[1,2,2,1,2]
[5,7,4,1,3,2,6,8]=>[6,4,1,5,3,7,2,8]=>[3,5,8,4,6,2,7,1]=>[3,2,2,1]
[2,6,8,4,5,3,1,7]=>[4,2,7,6,1,5,8,3]=>[5,7,2,3,8,4,1,6]=>[2,3,1,2]
[5,2,3,7,4,1,6,8]=>[6,2,3,1,5,7,4,8]=>[3,7,6,8,4,2,5,1]=>[2,2,1,2,1]
[5,1,6,3,2,4,7,8]=>[5,4,6,2,1,3,7,8]=>[4,5,3,7,8,6,2,1]=>[2,3,1,1,1]
[4,2,5,1,6,3,7,8]=>[6,2,1,4,3,5,7,8]=>[3,7,8,5,6,4,2,1]=>[3,2,1,1,1]
[5,1,6,2,4,3,7,8]=>[6,4,5,2,1,3,7,8]=>[3,5,4,7,8,6,2,1]=>[2,3,1,1,1]
[5,3,4,8,7,6,2,1]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[1,3,1,3]
[1,8,2,6,7,4,5,3]=>[6,4,8,7,3,5,1,2]=>[3,5,1,2,6,4,8,7]=>[2,3,2,1]
[8,5,7,2,4,3,6,1]=>[6,4,2,5,8,7,3,1]=>[3,5,7,4,1,2,6,8]=>[3,1,4]
[8,5,3,6,4,7,2,1]=>[5,3,2,4,8,7,6,1]=>[4,6,7,5,1,2,3,8]=>[3,1,4]
[8,2,5,3,6,7,4,1]=>[5,3,8,2,4,7,6,1]=>[4,6,1,7,5,2,3,8]=>[2,2,1,3]
[1,2,8,3,4,7,6,5]=>[8,7,4,5,6,1,2,3]=>[1,2,5,4,3,8,7,6]=>[3,1,2,1,1]
[6,8,5,2,7,1,3,4]=>[4,6,1,7,3,8,5,2]=>[5,3,8,2,6,1,4,7]=>[1,2,2,3]
[8,2,4,7,6,3,1,5]=>[7,3,6,8,2,5,4,1]=>[2,6,3,1,7,4,5,8]=>[2,1,2,3]
[8,7,5,1,4,6,3,2]=>[5,8,7,4,3,6,2,1]=>[4,1,2,5,6,3,7,8]=>[1,4,3]
[7,3,8,5,4,2,1,6]=>[7,6,2,5,4,1,8,3]=>[2,3,7,4,5,8,1,6]=>[3,3,2]
[6,3,4,7,2,8,5,1]=>[8,2,3,1,5,4,7,6]=>[1,7,6,8,4,5,2,3]=>[2,2,2,2]
[8,1,7,3,6,4,2,5]=>[7,4,6,8,5,2,3,1]=>[2,5,3,1,4,7,6,8]=>[2,1,3,2]
[7,1,8,5,3,4,2,6]=>[5,7,6,4,8,2,1,3]=>[4,2,3,5,1,7,8,6]=>[1,3,3,1]
[6,8,4,3,1,5,2,7]=>[7,5,4,3,1,6,8,2]=>[2,4,5,6,8,3,1,7]=>[5,1,2]
[1,4,5,8,3,2,6,7]=>[2,3,6,5,7,8,1,4]=>[7,6,3,4,2,1,8,5]=>[1,1,2,1,2,1]
[5,2,7,4,3,8,6,1]=>[4,1,8,5,2,3,7,6]=>[5,8,1,4,7,6,2,3]=>[2,3,1,2]
[2,7,3,4,8,5,6,1]=>[6,8,3,4,1,2,7,5]=>[3,1,6,5,8,7,2,4]=>[1,2,2,1,2]
[2,7,6,8,3,5,4,1]=>[8,5,3,2,7,1,6,4]=>[1,4,6,7,2,8,3,5]=>[4,2,2]
[6,2,3,7,4,5,8,1]=>[5,6,2,3,1,4,8,7]=>[4,3,7,6,8,5,1,2]=>[1,2,2,1,2]
[1,6,3,2,7,5,8,4]=>[6,3,5,2,8,1,4,7]=>[3,6,4,7,1,8,5,2]=>[2,2,2,1,1]
[7,3,5,2,6,8,1,4]=>[7,2,4,3,5,1,8,6]=>[2,7,5,6,4,8,1,3]=>[2,2,2,2]
[6,4,2,7,1,5,8,3]=>[6,2,8,3,1,5,4,7]=>[3,7,1,6,8,4,5,2]=>[2,3,2,1]
[2,5,3,6,4,7,8,1]=>[5,3,1,2,4,6,8,7]=>[4,6,8,7,5,3,1,2]=>[3,1,1,1,2]
[1,8,7,2,4,6,3,5]=>[5,7,8,4,6,3,1,2]=>[4,2,1,5,3,6,8,7]=>[1,1,2,3,1]
[1,8,7,2,5,4,3,6]=>[7,6,4,5,8,3,1,2]=>[2,3,5,4,1,6,8,7]=>[3,1,3,1]
[1,5,4,2,7,3,6,8]=>[6,3,2,7,1,4,5,8]=>[3,6,7,2,8,5,4,1]=>[3,2,1,1,1]
[1,5,4,2,8,7,3,6]=>[3,2,7,8,6,1,4,5]=>[6,7,2,1,3,8,5,4]=>[2,1,3,1,1]
[1,6,8,3,5,2,4,7]=>[4,6,2,7,5,8,1,3]=>[5,3,7,2,4,1,8,6]=>[1,2,2,2,1]
[1,7,6,2,3,5,8,4]=>[6,8,4,5,3,1,2,7]=>[3,1,5,4,6,8,7,2]=>[1,2,3,1,1]
[1,2,8,3,6,5,4,7]=>[7,6,4,5,8,1,2,3]=>[2,3,5,4,1,8,7,6]=>[3,1,2,1,1]
[1,3,8,6,5,2,4,7]=>[6,7,5,2,4,8,1,3]=>[3,2,4,7,5,1,8,6]=>[1,3,1,2,1]
[1,4,7,3,2,8,6,5]=>[8,2,4,7,5,1,3,6]=>[1,7,5,2,4,8,6,3]=>[2,1,3,1,1]
[1,8,6,5,2,4,7,3]=>[6,8,5,4,3,7,1,2]=>[3,1,4,5,6,2,8,7]=>[1,4,2,1]
[1,6,8,4,3,2,5,7]=>[6,5,4,2,7,8,1,3]=>[3,4,5,7,2,1,8,6]=>[4,1,2,1]
[1,2,6,5,3,8,4,7]=>[7,4,3,8,1,2,5,6]=>[2,5,6,1,8,7,4,3]=>[3,2,1,1,1]
[1,7,3,2,8,4,6,5]=>[8,3,6,7,4,1,2,5]=>[1,6,3,2,5,8,7,4]=>[2,1,3,1,1]
[1,6,5,2,8,4,7,3]=>[6,3,2,8,7,1,4,5]=>[3,6,7,1,2,8,5,4]=>[3,3,1,1]
[1,8,3,7,2,4,6,5]=>[8,3,5,6,7,4,1,2]=>[1,6,4,3,2,5,8,7]=>[2,1,1,3,1]
[5,4,2,8,7,6,1,3]=>[2,1,7,8,6,3,5,4]=>[7,8,2,1,3,6,4,5]=>[2,1,3,2]
[8,6,3,2,5,7,4,1]=>[3,5,8,4,2,7,6,1]=>[6,4,1,5,7,2,3,8]=>[1,1,3,3]
[6,8,5,2,7,1,4,3]=>[8,4,1,6,3,7,5,2]=>[1,5,8,3,6,2,4,7]=>[3,2,3]
[6,8,2,5,1,7,4,3]=>[8,7,3,1,5,4,6,2]=>[1,2,6,8,4,5,3,7]=>[4,2,2]
[6,8,5,7,2,1,4,3]=>[5,1,8,6,3,7,4,2]=>[4,8,1,3,6,2,5,7]=>[2,3,3]
[6,5,8,2,7,4,1,3]=>[7,2,1,8,4,6,5,3]=>[2,7,8,1,5,3,4,6]=>[3,2,3]
[6,2,1,7,5,8,4,3]=>[5,4,8,2,1,7,3,6]=>[4,5,1,7,8,2,6,3]=>[2,3,2,1]
[1,6,4,8,5,3,7,2]=>[6,3,2,5,8,7,1,4]=>[3,6,7,4,1,2,8,5]=>[3,1,3,1]
[3,5,6,2,8,7,1,4]=>[2,7,1,3,8,4,6,5]=>[7,2,8,6,1,5,3,4]=>[1,2,1,2,2]
[1,6,5,3,4,7,8,2]=>[4,5,3,2,6,8,1,7]=>[5,4,6,7,3,1,8,2]=>[1,3,1,2,1]
[4,2,6,7,8,1,3,5]=>[1,6,3,7,2,4,8,5]=>[8,3,6,2,7,5,1,4]=>[1,2,2,1,2]
[5,1,7,2,6,4,8,3]=>[6,5,1,8,4,2,3,7]=>[3,4,8,1,5,7,6,2]=>[3,3,1,1]
[4,1,7,6,5,8,2,3]=>[7,1,5,4,3,8,2,6]=>[2,8,4,5,6,1,7,3]=>[2,3,2,1]
[5,2,1,7,6,4,8,3]=>[6,5,2,1,4,8,3,7]=>[3,4,7,8,5,1,6,2]=>[4,1,2,1]
[4,2,3,6,7,8,1,5]=>[4,1,7,2,3,5,8,6]=>[5,8,2,7,6,4,1,3]=>[2,2,1,1,2]
[2,7,6,4,1,5,8,3]=>[6,4,8,5,1,3,2,7]=>[3,5,1,4,8,6,7,2]=>[2,3,2,1]
[2,4,3,6,7,8,1,5]=>[2,4,7,1,3,5,8,6]=>[7,5,2,8,6,4,1,3]=>[1,1,2,1,1,2]
[6,8,5,2,7,3,1,4]=>[7,4,1,6,3,8,5,2]=>[2,5,8,3,6,1,4,7]=>[3,2,3]
[7,5,2,4,1,8,3,6]=>[7,3,4,2,8,5,1,6]=>[2,6,5,7,1,4,8,3]=>[2,2,3,1]
[6,5,1,3,7,8,2,4]=>[7,4,5,2,1,8,3,6]=>[2,5,4,7,8,1,6,3]=>[2,3,2,1]
[6,1,2,4,3,7,8,5]=>[4,6,8,2,3,1,5,7]=>[5,3,1,7,6,8,4,2]=>[1,1,2,2,1,1]
[8,1,5,4,2,3,6,7]=>[5,6,4,2,3,7,8,1]=>[4,3,5,7,6,2,1,8]=>[1,3,1,1,2]
[7,1,2,4,6,3,8,5]=>[8,4,6,2,3,5,1,7]=>[1,5,3,7,6,4,8,2]=>[2,2,1,2,1]
[7,1,2,6,5,3,8,4]=>[8,6,5,2,3,4,1,7]=>[1,3,4,7,6,5,8,2]=>[4,1,2,1]
[7,1,4,5,2,3,6,8]=>[5,3,6,2,4,7,1,8]=>[4,6,3,7,5,2,8,1]=>[2,2,1,2,1]
[6,1,4,8,7,2,3,5]=>[3,6,7,1,8,5,2,4]=>[6,3,2,8,1,4,7,5]=>[1,1,2,3,1]
[1,6,7,5,8,3,4,2]=>[2,6,4,3,8,7,1,5]=>[7,3,5,6,1,2,8,4]=>[1,3,3,1]
[6,1,7,5,8,2,3,4]=>[6,7,4,3,1,8,2,5]=>[3,2,5,6,8,1,7,4]=>[1,4,2,1]
[6,1,4,7,8,2,3,5]=>[3,6,7,4,1,8,2,5]=>[6,3,2,5,8,1,7,4]=>[1,1,3,2,1]
[8,1,2,3,7,5,4,6]=>[7,6,8,2,3,4,5,1]=>[2,3,1,7,6,5,4,8]=>[2,2,1,1,2]
[5,8,6,1,2,4,7,3]=>[6,1,8,4,5,3,7,2]=>[3,8,1,5,4,6,2,7]=>[2,2,2,2]
[1,6,8,7,5,3,4,2]=>[2,6,8,7,5,4,1,3]=>[7,3,1,2,4,5,8,6]=>[1,1,5,1]
[6,1,8,7,5,2,3,4]=>[6,7,1,8,5,4,2,3]=>[3,2,8,1,4,5,7,6]=>[1,2,4,1]
[8,3,1,2,4,6,5,7]=>[7,3,2,4,5,6,8,1]=>[2,6,7,5,4,3,1,8]=>[3,1,1,1,2]
[8,3,1,2,4,5,7,6]=>[8,3,2,4,5,6,7,1]=>[1,6,7,5,4,3,2,8]=>[3,1,1,1,2]
[6,3,1,2,4,7,5,8]=>[7,3,2,4,5,1,6,8]=>[2,6,7,5,4,8,3,1]=>[3,1,2,1,1]
[6,7,1,4,2,3,5,8]=>[5,6,3,4,1,7,2,8]=>[4,3,6,5,8,2,7,1]=>[1,2,2,2,1]
[6,1,7,4,8,2,3,5]=>[6,4,7,3,1,8,2,5]=>[3,5,2,6,8,1,7,4]=>[2,3,2,1]
[6,7,8,5,1,2,4,3]=>[8,5,1,6,2,7,4,3]=>[1,4,8,3,7,2,5,6]=>[3,2,3]
[8,7,6,5,4,3,2,9,1,10]=>[7,6,5,4,3,2,1,9,8,10]=>[4,5,6,7,8,9,10,2,3,1]=>[7,2,1]
[4,3,8,5,6,2,7,1]=>[1,4,6,2,5,8,7,3]=>[8,5,3,7,4,1,2,6]=>[1,1,2,1,3]
[4,3,8,6,7,2,5,1]=>[6,1,4,8,2,7,5,3]=>[3,8,5,1,7,2,4,6]=>[2,1,2,3]
[7,6,8,1,5,3,4,2]=>[6,8,7,4,2,1,5,3]=>[3,1,2,5,7,8,4,6]=>[1,5,2]
[7,4,6,1,5,3,8,2]=>[2,6,5,8,4,3,1,7]=>[7,3,4,1,5,6,8,2]=>[1,2,4,1]
[6,3,8,1,7,2,5,4]=>[8,2,6,1,7,4,5,3]=>[1,7,3,8,2,5,4,6]=>[2,2,2,2]
[6,2,5,4,7,1,8,3]=>[4,3,8,2,1,6,5,7]=>[5,6,1,7,8,3,4,2]=>[2,3,2,1]
[2,6,3,4,8,7,5,1]=>[8,7,3,1,2,4,6,5]=>[1,2,6,8,7,5,3,4]=>[4,1,1,2]
[2,7,4,5,1,8,3,6]=>[3,7,4,8,1,5,2,6]=>[6,2,5,1,8,4,7,3]=>[1,2,2,2,1]
[8,4,5,7,6,1,2,3]=>[2,6,3,7,8,5,4,1]=>[7,3,6,2,1,4,5,8]=>[1,2,1,4]
[8,1,3,4,6,7,5,2]=>[5,8,3,4,7,2,6,1]=>[4,1,6,5,2,7,3,8]=>[1,2,1,2,2]
[8,7,6,2,3,5,4,1]=>[8,4,5,7,6,3,2,1]=>[1,5,4,2,3,6,7,8]=>[2,1,5]
[8,3,6,7,5,1,2,4]=>[6,7,2,3,8,5,4,1]=>[3,2,7,6,1,4,5,8]=>[1,2,1,4]
[8,2,1,6,5,7,4,3]=>[5,4,8,2,7,3,6,1]=>[4,5,1,7,2,6,3,8]=>[2,2,2,2]
[2,7,1,8,5,6,4,3]=>[5,8,7,6,1,3,2,4]=>[4,1,2,3,8,6,7,5]=>[1,4,2,1]
[2,7,8,6,1,5,3,4]=>[7,8,5,2,6,1,4,3]=>[2,1,4,7,3,8,5,6]=>[1,3,2,2]
[6,8,2,1,3,5,4,7]=>[3,7,4,5,1,6,8,2]=>[6,2,5,4,8,3,1,7]=>[1,2,2,1,2]
[3,5,1,6,4,8,2,7]=>[5,1,4,2,7,8,3,6]=>[4,8,5,7,2,1,6,3]=>[2,2,1,2,1]
[3,5,8,6,2,1,4,7]=>[2,6,1,5,7,4,8,3]=>[7,3,8,4,2,5,1,6]=>[1,2,1,2,2]
[2,4,8,5,6,1,3,7]=>[6,2,4,7,1,5,8,3]=>[3,7,5,2,8,4,1,6]=>[2,1,2,1,2]
[5,3,8,4,2,7,6,1]=>[4,1,8,2,5,7,6,3]=>[5,8,1,7,4,2,3,6]=>[2,2,1,3]
[2,8,5,3,1,4,7,6]=>[4,8,5,1,3,6,7,2]=>[5,1,4,8,6,3,2,7]=>[1,3,1,1,2]
[8,7,3,2,1,6,4,5]=>[4,3,7,8,5,6,2,1]=>[5,6,2,1,4,3,7,8]=>[2,1,2,3]
[7,8,3,4,6,5,2,1]=>[8,3,4,1,7,6,5,2]=>[1,6,5,8,2,3,4,7]=>[2,2,4]
[8,7,3,6,5,2,4,1]=>[6,8,3,7,5,4,2,1]=>[3,1,6,2,4,5,7,8]=>[1,2,5]
[3,1,2,8,6,5,7,4]=>[6,1,5,8,7,2,3,4]=>[3,8,4,1,2,7,6,5]=>[2,1,3,1,1]
[3,8,2,7,5,4,6,1]=>[6,5,8,1,3,7,4,2]=>[3,4,1,8,6,2,5,7]=>[2,2,1,3]
[8,7,1,4,5,3,6,2]=>[4,6,5,8,3,7,2,1]=>[5,3,4,1,6,2,7,8]=>[1,2,2,3]
[2,8,7,4,6,3,5,1]=>[4,6,8,7,5,1,3,2]=>[5,3,1,2,4,8,6,7]=>[1,1,4,2]
[2,8,7,4,6,3,1,5]=>[4,7,6,8,5,1,3,2]=>[5,2,3,1,4,8,6,7]=>[1,2,3,2]
[8,3,4,1,2,5,7,6]=>[2,8,4,3,5,6,7,1]=>[7,1,5,6,4,3,2,8]=>[1,3,1,1,2]
[8,4,1,3,2,5,7,6]=>[4,8,3,2,5,6,7,1]=>[5,1,6,7,4,3,2,8]=>[1,3,1,1,2]
[7,3,8,6,2,1,4,5]=>[6,2,5,7,1,8,4,3]=>[3,7,4,2,8,1,5,6]=>[2,1,2,3]
[7,2,8,4,6,5,1,3]=>[4,7,8,6,2,1,5,3]=>[5,2,1,3,7,8,4,6]=>[1,1,4,2]
[5,8,6,4,7,2,3,1]=>[6,1,4,3,8,7,5,2]=>[3,8,5,6,1,2,4,7]=>[2,2,4]
[4,7,2,6,5,8,3,1]=>[5,1,4,8,3,2,7,6]=>[4,8,5,1,6,7,2,3]=>[2,1,3,2]
[3,6,8,5,7,4,2,1]=>[2,4,8,7,1,6,5,3]=>[7,5,1,2,8,3,4,6]=>[1,1,3,3]
[6,7,5,2,4,8,3,1]=>[5,1,8,4,3,2,7,6]=>[4,8,1,5,6,7,2,3]=>[2,4,2]
[8,1,2,7,5,6,3,4]=>[7,5,8,6,2,3,4,1]=>[2,4,1,3,7,6,5,8]=>[2,3,1,2]
[8,2,7,3,4,6,1,5]=>[4,5,7,8,2,6,3,1]=>[5,4,2,1,7,3,6,8]=>[1,1,1,2,3]
[6,7,5,4,8,1,3,2]=>[1,8,6,4,3,2,7,5]=>[8,1,3,5,6,7,2,4]=>[1,5,2]
[8,3,5,6,4,7,2,1]=>[3,5,2,4,8,7,6,1]=>[6,4,7,5,1,2,3,8]=>[1,2,1,4]
[8,5,6,2,4,3,7,1]=>[6,4,2,5,3,8,7,1]=>[3,5,7,4,6,1,2,8]=>[3,2,3]
[6,8,4,5,1,3,2,7]=>[7,5,3,1,6,4,8,2]=>[2,4,6,8,3,5,1,7]=>[4,2,2]
[6,4,8,7,5,3,2,1]=>[1,8,7,2,6,5,4,3]=>[8,1,2,7,3,4,5,6]=>[1,3,4]
[6,7,1,4,3,2,8,5]=>[5,4,8,3,1,6,2,7]=>[4,5,1,6,8,3,7,2]=>[2,3,2,1]
[7,2,5,1,4,8,3,6]=>[5,7,2,3,8,4,1,6]=>[4,2,7,6,1,5,8,3]=>[1,2,1,3,1]
[5,8,1,3,4,2,7,6]=>[4,5,1,8,3,6,7,2]=>[5,4,8,1,6,3,2,7]=>[1,2,2,1,2]
[1,6,7,3,2,8,5,4]=>[8,4,2,7,5,1,3,6]=>[1,5,7,2,4,8,6,3]=>[3,3,1,1]
[3,2,7,6,8,4,5,1]=>[6,4,1,3,8,2,7,5]=>[3,5,8,6,1,7,2,4]=>[3,1,2,2]
[6,4,1,5,2,8,7,3]=>[4,2,8,7,3,1,5,6]=>[5,7,1,2,6,8,4,3]=>[2,4,1,1]
[7,6,5,3,1,8,2,4]=>[7,4,8,5,3,2,1,6]=>[2,5,1,4,6,7,8,3]=>[2,5,1]
[2,5,1,4,7,3,6,8]=>[4,6,1,2,7,3,5,8]=>[5,3,8,7,2,6,4,1]=>[1,2,1,2,1,1]
[3,1,6,5,7,2,4,8]=>[6,1,4,3,7,2,5,8]=>[3,8,5,6,2,7,4,1]=>[2,2,2,1,1]
[2,6,1,5,7,4,3,8]=>[4,7,6,1,3,2,5,8]=>[5,2,3,8,6,7,4,1]=>[1,3,2,1,1]
[3,1,6,5,2,4,7,8]=>[1,5,6,4,2,3,7,8]=>[8,4,3,5,7,6,2,1]=>[1,1,3,1,1,1]
[3,6,5,1,4,2,7,8]=>[6,1,4,5,3,2,7,8]=>[3,8,5,4,6,7,2,1]=>[2,1,3,1,1]
[3,6,5,1,7,2,4,8]=>[6,7,1,4,3,2,5,8]=>[3,2,8,5,6,7,4,1]=>[1,2,3,1,1]
[5,4,3,6,1,7,2,8]=>[3,2,1,7,5,4,6,8]=>[6,7,8,2,4,5,3,1]=>[3,3,1,1]
[4,5,2,7,6,1,3,8]=>[1,6,2,7,3,5,4,8]=>[8,3,7,2,6,4,5,1]=>[1,2,2,2,1]
[4,6,5,3,1,2,7,8]=>[1,5,6,4,3,2,7,8]=>[8,4,3,5,6,7,2,1]=>[1,1,4,1,1]
[5,4,1,6,3,7,2,8]=>[5,4,2,1,7,3,6,8]=>[4,5,7,8,2,6,3,1]=>[4,2,1,1]
[5,4,2,6,3,7,8,1]=>[5,3,2,1,4,6,8,7]=>[4,6,7,8,5,3,1,2]=>[4,1,1,2]
[3,6,5,7,1,4,2,8]=>[7,5,1,3,2,6,4,8]=>[2,4,8,6,7,3,5,1]=>[3,2,2,1]
[3,6,5,1,4,7,2,8]=>[5,7,1,4,3,2,6,8]=>[4,2,8,5,6,7,3,1]=>[1,2,3,1,1]
[4,3,6,5,7,1,2,8]=>[1,6,2,4,3,7,5,8]=>[8,3,7,5,6,2,4,1]=>[1,2,2,2,1]
[4,2,6,5,1,3,7,8]=>[5,1,6,2,4,3,7,8]=>[4,8,3,7,5,6,2,1]=>[2,2,2,1,1]
[4,1,6,5,3,7,8,2]=>[1,5,4,3,6,8,2,7]=>[8,4,5,6,3,1,7,2]=>[1,3,1,2,1]
[3,4,7,6,1,2,5,8]=>[1,2,5,6,7,4,3,8]=>[8,7,4,3,2,5,6,1]=>[1,1,1,1,3,1]
[4,2,5,7,6,3,8,1]=>[1,6,3,5,2,4,8,7]=>[8,3,6,4,7,5,1,2]=>[1,2,2,1,2]
[4,1,6,5,2,7,3,8]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[1,4,1,1,1]
[3,6,5,7,2,1,4,8]=>[6,5,1,3,2,7,4,8]=>[3,4,8,6,7,2,5,1]=>[3,2,2,1]
[3,5,7,6,2,4,1,8]=>[2,5,7,1,6,4,3,8]=>[7,4,2,8,3,5,6,1]=>[1,1,2,3,1]
[5,4,2,6,3,7,1,8]=>[5,3,2,1,4,7,6,8]=>[4,6,7,8,5,2,3,1]=>[4,1,2,1]
[4,6,5,2,1,7,3,8]=>[1,4,7,5,3,2,6,8]=>[8,5,2,4,6,7,3,1]=>[1,1,4,1,1]
[3,5,8,2,1,4,6,7]=>[5,1,4,2,6,7,8,3]=>[4,8,5,7,3,2,1,6]=>[2,2,1,1,2]
[3,5,8,2,4,6,7,1]=>[4,1,2,5,6,8,7,3]=>[5,8,7,4,3,1,2,6]=>[2,1,1,1,3]
[5,3,8,2,1,4,6,7]=>[2,5,4,1,6,7,8,3]=>[7,4,5,8,3,2,1,6]=>[1,3,1,1,2]
[5,3,1,8,2,4,6,7]=>[5,2,6,1,7,8,3,4]=>[4,7,3,8,2,1,6,5]=>[2,2,1,2,1]
[5,1,3,8,2,4,6,7]=>[3,5,6,1,7,8,2,4]=>[6,4,3,8,2,1,7,5]=>[1,1,2,1,2,1]
[1,5,8,4,2,3,6,7]=>[5,2,6,4,7,8,1,3]=>[4,7,3,5,2,1,8,6]=>[2,2,1,2,1]
[5,8,2,1,4,3,6,7]=>[3,6,4,1,5,7,8,2]=>[6,3,5,8,4,2,1,7]=>[1,3,1,1,2]
[5,8,2,4,1,6,7,3]=>[6,3,1,4,8,5,7,2]=>[3,6,8,5,1,4,2,7]=>[3,1,2,2]
[5,8,2,4,6,3,1,7]=>[4,1,7,3,6,5,8,2]=>[5,8,2,6,3,4,1,7]=>[2,2,2,2]
[5,8,2,4,3,6,1,7]=>[5,3,1,4,7,6,8,2]=>[4,6,8,5,2,3,1,7]=>[3,1,2,2]
[5,8,1,4,6,2,3,7]=>[6,4,1,7,3,5,8,2]=>[3,5,8,2,6,4,1,7]=>[3,2,1,2]
[1,5,8,4,6,7,2,3]=>[2,4,7,5,8,6,1,3]=>[7,5,2,4,1,3,8,6]=>[1,1,2,3,1]
[5,1,8,4,6,7,2,3]=>[4,1,7,5,8,6,2,3]=>[5,8,2,4,1,3,7,6]=>[2,2,3,1]
[5,8,2,4,6,3,7,1]=>[4,1,6,3,5,8,7,2]=>[5,8,3,6,4,1,2,7]=>[2,2,1,3]
[3,8,4,6,7,2,1,5]=>[7,3,6,1,4,8,5,2]=>[2,6,3,8,5,1,4,7]=>[2,2,1,3]
[3,8,4,6,7,2,5,1]=>[6,3,4,8,1,7,5,2]=>[3,6,5,1,8,2,4,7]=>[2,1,2,3]
[8,4,3,6,7,2,5,1]=>[2,6,3,4,8,7,5,1]=>[7,3,6,5,1,2,4,8]=>[1,2,1,4]
[8,4,3,6,7,2,1,5]=>[2,7,3,6,4,8,5,1]=>[7,2,6,3,5,1,4,8]=>[1,2,2,3]
[8,6,2,4,5,3,7,1]=>[4,6,3,5,2,8,7,1]=>[5,3,6,4,7,1,2,8]=>[1,2,2,3]
[1,8,6,4,5,7,2,3]=>[4,7,5,3,8,6,1,2]=>[5,2,4,6,1,3,8,7]=>[1,3,3,1]
[8,6,2,4,5,3,1,7]=>[4,7,3,6,5,2,8,1]=>[5,2,6,3,4,7,1,8]=>[1,2,3,2]
[1,8,6,4,2,3,5,7]=>[5,6,4,7,3,8,1,2]=>[4,3,5,2,6,1,8,7]=>[1,2,2,2,1]
[3,8,1,6,2,4,5,7]=>[1,5,6,7,3,4,8,2]=>[8,4,3,2,6,5,1,7]=>[1,1,1,2,1,2]
[3,8,6,2,1,4,5,7]=>[5,1,4,6,7,3,8,2]=>[4,8,5,3,2,6,1,7]=>[2,1,1,2,2]
[3,8,6,2,4,5,7,1]=>[4,5,6,1,3,8,7,2]=>[5,4,3,8,6,1,2,7]=>[1,1,2,1,3]
[8,3,6,2,4,5,1,7]=>[2,4,5,7,6,3,8,1]=>[7,5,4,2,3,6,1,8]=>[1,1,1,3,2]
[8,3,6,7,2,1,4,5]=>[6,2,5,7,3,8,4,1]=>[3,7,4,2,6,1,5,8]=>[2,1,2,3]
[3,8,6,7,2,1,4,5]=>[6,5,7,1,3,8,4,2]=>[3,4,2,8,6,1,5,7]=>[2,2,1,3]
[8,2,6,4,5,1,7,3]=>[4,8,6,2,5,3,7,1]=>[5,1,3,7,4,6,2,8]=>[1,3,2,2]
[1,8,4,6,7,5,2,3]=>[7,3,4,8,6,5,1,2]=>[2,6,5,1,3,4,8,7]=>[2,1,4,1]
[8,4,6,2,3,7,5,1]=>[2,8,4,5,3,7,6,1]=>[7,1,5,4,6,2,3,8]=>[1,2,2,3]
[8,4,7,2,1,3,6,5]=>[4,2,8,5,6,7,3,1]=>[5,7,1,4,3,2,6,8]=>[2,2,1,3]
[2,7,1,6,3,5,8,4]=>[6,8,5,1,3,4,2,7]=>[3,1,4,8,6,5,7,2]=>[1,3,1,2,1]
[8,4,2,1,5,3,7,6]=>[3,5,2,8,4,6,7,1]=>[6,4,7,1,5,3,2,8]=>[1,2,2,1,2]
[1,6,2,5,8,4,7,3]=>[4,6,2,8,7,1,3,5]=>[5,3,7,1,2,8,6,4]=>[1,2,3,1,1]
[3,2,1,7,4,5,8,6]=>[1,8,2,5,6,3,4,7]=>[8,1,7,4,3,6,5,2]=>[1,2,1,2,1,1]
[2,6,8,5,1,7,4,3]=>[2,8,7,5,1,4,6,3]=>[7,1,2,4,8,5,3,6]=>[1,4,1,2]
[2,1,5,8,7,3,6,4]=>[8,3,6,7,1,5,2,4]=>[1,6,3,2,8,4,7,5]=>[2,1,2,2,1]
[3,2,1,6,7,4,8,5]=>[1,4,8,2,6,3,5,7]=>[8,5,1,7,3,6,4,2]=>[1,1,2,2,1,1]
[4,3,1,7,8,5,2,6]=>[1,7,2,6,4,8,3,5]=>[8,2,7,3,5,1,6,4]=>[1,2,2,2,1]
[5,6,8,2,4,3,7,1]=>[1,6,4,2,5,8,7,3]=>[8,3,5,7,4,1,2,6]=>[1,3,1,3]
[1,2,8,6,4,7,3,5]=>[5,7,4,8,6,1,2,3]=>[4,2,5,1,3,8,7,6]=>[1,2,3,1,1]
[5,3,2,7,8,6,4,1]=>[4,1,8,2,7,3,6,5]=>[5,8,1,7,2,6,3,4]=>[2,2,2,2]
[4,2,7,8,3,5,6,1]=>[1,5,6,3,8,2,7,4]=>[8,4,3,6,1,7,2,5]=>[1,1,2,2,2]
[2,8,7,1,5,3,6,4]=>[8,6,4,5,7,1,3,2]=>[1,3,5,4,2,8,6,7]=>[3,1,2,2]
[7,3,5,6,4,2,8,1]=>[3,6,2,5,4,1,8,7]=>[6,3,7,4,5,8,1,2]=>[1,2,3,2]
[3,8,4,2,7,6,5,1]=>[8,3,7,1,4,6,5,2]=>[1,6,2,8,5,3,4,7]=>[2,2,1,3]
[4,8,3,2,7,5,6,1]=>[1,3,6,8,4,7,5,2]=>[8,6,3,1,5,2,4,7]=>[1,1,1,2,3]
[2,6,8,1,5,3,4,7]=>[6,7,4,1,2,5,8,3]=>[3,2,5,8,7,4,1,6]=>[1,3,1,1,2]
[3,2,5,6,8,1,4,7]=>[1,3,6,2,4,7,8,5]=>[8,6,3,7,5,2,1,4]=>[1,1,2,1,1,2]
[3,8,1,6,4,5,2,7]=>[5,7,1,6,3,4,8,2]=>[4,2,8,3,6,5,1,7]=>[1,2,2,1,2]
[7,4,3,6,2,1,8,5]=>[3,2,5,8,6,4,1,7]=>[6,7,4,1,3,5,8,2]=>[2,1,4,1]
[1,2,4,8,6,3,7,5]=>[8,6,3,5,7,1,2,4]=>[1,3,6,4,2,8,7,5]=>[3,1,2,1,1]
[7,2,1,5,3,4,8,6]=>[8,2,5,3,4,6,1,7]=>[1,7,4,6,5,3,8,2]=>[2,2,1,2,1]
[5,7,2,3,1,4,8,6]=>[3,4,1,8,5,6,2,7]=>[6,5,8,1,4,3,7,2]=>[1,2,2,2,1]
[7,1,5,2,4,6,8,3]=>[5,6,3,8,2,4,1,7]=>[4,3,6,1,7,5,8,2]=>[1,2,2,2,1]
[1,8,6,4,7,5,3,2]=>[8,4,3,7,6,5,1,2]=>[1,5,6,2,3,4,8,7]=>[3,4,1]
[7,4,1,5,8,6,3,2]=>[2,8,4,7,6,3,1,5]=>[7,1,5,2,3,6,8,4]=>[1,2,4,1]
[4,5,8,7,3,1,2,6]=>[1,2,6,7,5,8,4,3]=>[8,7,3,2,4,1,5,6]=>[1,1,1,2,3]
[1,8,6,4,7,5,2,3]=>[4,7,3,8,6,5,1,2]=>[5,2,6,1,3,4,8,7]=>[1,2,4,1]
[2,7,4,6,3,8,5,1]=>[8,3,5,4,1,2,7,6]=>[1,6,4,5,8,7,2,3]=>[2,3,1,2]
[1,2,8,6,4,7,5,3]=>[8,5,4,7,6,1,2,3]=>[1,4,5,2,3,8,7,6]=>[3,3,1,1]
[3,4,5,6,7,9,1,2,8]=>[1,2,3,4,7,5,8,9,6]=>[9,8,7,6,3,5,2,1,4]=>[1,1,1,1,2,1,2]
[3,4,5,6,9,1,2,7,8]=>[1,2,3,6,4,7,8,9,5]=>[9,8,7,4,6,3,2,1,5]=>[1,1,1,2,1,1,2]
[7,5,4,3,8,1,6,2]=>[4,3,2,8,6,1,7,5]=>[5,6,7,1,3,8,2,4]=>[3,3,2]
[3,5,4,1,7,8,2,6]=>[3,1,2,7,5,8,4,6]=>[6,8,7,2,4,1,5,3]=>[2,1,2,2,1]
[6,4,2,1,5,7,3,8]=>[3,5,2,7,4,1,6,8]=>[6,4,7,2,5,8,3,1]=>[1,2,3,1,1]
[3,1,5,8,7,2,4,6]=>[1,3,6,7,8,5,2,4]=>[8,6,3,2,1,4,7,5]=>[1,1,1,1,3,1]
[3,2,5,7,8,4,6,1]=>[6,1,3,4,8,2,7,5]=>[3,8,6,5,1,7,2,4]=>[2,1,1,2,2]
[5,3,7,4,2,6,8,1]=>[5,2,1,4,6,3,8,7]=>[4,7,8,5,3,6,1,2]=>[3,1,2,2]
[5,3,7,4,2,6,1,8]=>[5,2,1,4,7,6,3,8]=>[4,7,8,5,2,3,6,1]=>[3,1,3,1]
[5,2,8,4,3,1,6,7]=>[6,5,2,1,4,7,8,3]=>[3,4,7,8,5,2,1,6]=>[4,1,1,2]
[5,1,8,4,3,2,6,7]=>[6,5,4,1,7,8,2,3]=>[3,4,5,8,2,1,7,6]=>[4,1,2,1]
[5,2,7,4,3,6,1,8]=>[5,4,1,7,2,6,3,8]=>[4,5,8,2,7,3,6,1]=>[3,2,2,1]
[5,2,7,4,3,6,8,1]=>[5,4,1,6,2,3,8,7]=>[4,5,8,3,7,6,1,2]=>[3,2,1,2]
[5,3,7,4,1,6,8,2]=>[6,2,1,4,8,5,3,7]=>[3,7,8,5,1,4,6,2]=>[3,1,3,1]
[3,1,5,7,8,4,2,6]=>[7,1,3,6,4,8,2,5]=>[2,8,6,3,5,1,7,4]=>[2,1,2,2,1]
[5,2,7,4,1,3,8,6]=>[8,5,2,1,4,6,3,7]=>[1,4,7,8,5,3,6,2]=>[4,1,2,1]
[6,2,3,7,4,8,5,1]=>[8,5,2,3,1,4,7,6]=>[1,4,7,6,8,5,2,3]=>[3,2,1,2]
[6,2,3,7,4,8,1,5]=>[5,7,2,3,1,4,8,6]=>[4,2,7,6,8,5,1,3]=>[1,2,2,1,2]
[6,2,3,7,4,5,1,8]=>[5,7,2,3,1,6,4,8]=>[4,2,7,6,8,3,5,1]=>[1,2,2,2,1]
[6,1,3,7,4,5,8,2]=>[5,6,3,4,1,8,2,7]=>[4,3,6,5,8,1,7,2]=>[1,2,2,2,1]
[1,2,8,6,4,3,5,7]=>[6,5,7,4,8,1,2,3]=>[3,4,2,5,1,8,7,6]=>[2,2,2,1,1]
[1,8,6,3,5,4,2,7]=>[7,4,6,5,3,8,1,2]=>[2,5,3,4,6,1,8,7]=>[2,3,2,1]
[2,6,1,8,5,3,4,7]=>[6,7,5,1,2,8,3,4]=>[3,2,4,8,7,1,6,5]=>[1,3,1,2,1]
[4,5,7,8,1,6,3,2]=>[8,1,2,7,5,3,6,4]=>[1,8,7,2,4,6,3,5]=>[2,1,3,2]
[1,8,2,7,5,3,4,6]=>[6,7,5,8,3,4,1,2]=>[3,2,4,1,6,5,8,7]=>[1,2,2,2,1]
[2,5,4,1,8,6,7,3]=>[3,2,6,8,1,7,4,5]=>[6,7,3,1,8,2,5,4]=>[2,1,2,2,1]
[4,1,5,3,8,6,7,2]=>[3,1,6,8,4,7,2,5]=>[6,8,3,1,5,2,7,4]=>[2,1,2,2,1]
[7,3,5,1,4,8,6,2]=>[8,2,5,3,7,4,1,6]=>[1,7,4,6,2,5,8,3]=>[2,2,3,1]
[7,1,3,2,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[5,7,6,4,3,2,8,1]=>[2,1,1,1,2,1]
[3,8,7,1,4,2,5,6]=>[6,1,4,5,7,8,3,2]=>[3,8,5,4,2,1,6,7]=>[2,1,1,1,3]
[5,1,7,8,2,4,3,6]=>[7,5,1,6,3,8,2,4]=>[2,4,8,3,6,1,7,5]=>[3,2,2,1]
[8,5,4,6,1,7,3,2]=>[3,2,8,7,5,4,6,1]=>[6,7,1,2,4,5,3,8]=>[2,4,2]
[5,3,2,1,4,6,8,7]=>[3,2,8,4,1,5,6,7]=>[6,7,1,5,8,4,3,2]=>[2,3,1,1,1]
[5,3,2,4,8,1,6,7]=>[3,2,4,1,6,7,8,5]=>[6,7,5,8,3,2,1,4]=>[2,2,1,1,2]
[5,3,2,4,7,1,8,6]=>[2,8,3,1,4,6,5,7]=>[7,1,6,8,5,3,4,2]=>[1,3,1,2,1]
[8,4,5,3,7,1,2,6]=>[2,6,4,3,7,8,5,1]=>[7,3,5,6,2,1,4,8]=>[1,3,1,3]
[4,8,1,7,3,5,6,2]=>[1,5,6,8,7,3,4,2]=>[8,4,3,1,2,6,5,7]=>[1,1,1,3,2]
[5,3,2,4,6,8,1,7]=>[3,2,4,1,5,7,8,6]=>[6,7,5,8,4,2,1,3]=>[2,2,1,1,2]
[2,7,6,3,1,4,8,5]=>[4,8,5,6,1,3,2,7]=>[5,1,4,3,8,6,7,2]=>[1,2,2,2,1]
[3,7,4,5,6,8,2,1]=>[3,4,5,1,2,8,7,6]=>[6,5,4,8,7,1,2,3]=>[1,1,2,1,3]
[8,7,1,4,2,5,3,6]=>[7,5,3,4,6,8,2,1]=>[2,4,6,5,3,1,7,8]=>[3,1,1,3]
[8,4,3,5,7,1,6,2]=>[3,2,4,8,6,7,5,1]=>[6,7,5,1,3,2,4,8]=>[2,1,2,3]
[1,7,6,4,2,5,3,8]=>[7,5,4,6,3,1,2,8]=>[2,4,5,3,6,8,7,1]=>[3,3,1,1]
[7,6,4,2,8,3,1,5]=>[7,4,3,6,2,1,8,5]=>[2,5,6,3,7,8,1,4]=>[3,3,2]
[8,5,2,4,3,7,1,6]=>[5,3,4,2,7,8,6,1]=>[4,6,5,7,2,1,3,8]=>[2,2,1,3]
[8,5,1,4,3,7,6,2]=>[4,8,5,2,7,3,6,1]=>[5,1,4,7,2,6,3,8]=>[1,3,2,2]
[7,5,4,1,3,6,8,2]=>[5,6,3,2,8,4,1,7]=>[4,3,6,7,1,5,8,2]=>[1,3,3,1]
[3,6,7,2,5,1,8,4]=>[8,4,1,2,6,5,3,7]=>[1,5,8,7,3,4,6,2]=>[3,1,3,1]
[2,6,5,7,1,4,8,3]=>[6,3,2,8,1,5,4,7]=>[3,6,7,1,8,4,5,2]=>[3,2,2,1]
[3,5,1,7,8,4,6,2]=>[2,6,1,4,8,7,3,5]=>[7,3,8,5,1,2,6,4]=>[1,2,1,3,1]
[1,5,2,4,6,8,7,3]=>[8,4,2,5,7,1,3,6]=>[1,5,7,4,2,8,6,3]=>[3,1,2,1,1]
[8,1,2,4,7,6,5,3]=>[8,7,4,6,2,3,5,1]=>[1,2,5,3,7,6,4,8]=>[3,2,1,2]
[3,4,1,8,6,7,5,2]=>[5,8,1,2,7,6,3,4]=>[4,1,8,7,2,3,6,5]=>[1,2,1,3,1]
[4,3,8,5,1,7,6,2]=>[1,4,8,2,7,5,6,3]=>[8,5,1,7,2,4,3,6]=>[1,1,2,2,2]
[6,1,3,2,8,5,7,4]=>[6,8,3,7,2,1,4,5]=>[3,1,6,2,7,8,5,4]=>[1,2,3,1,1]
[3,1,2,4,5,6,7,9,8]=>[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>[3,1,1,1,1,1,1]
[6,7,4,2,5,8,3,1]=>[5,3,1,8,4,2,7,6]=>[4,6,8,1,5,7,2,3]=>[3,3,2]
[8,5,4,2,6,3,1,7]=>[7,4,3,2,6,5,8,1]=>[2,5,6,7,3,4,1,8]=>[4,2,2]
[1,3,8,4,7,5,2,6]=>[7,4,6,8,2,5,1,3]=>[2,5,3,1,7,4,8,6]=>[2,1,2,2,1]
[5,3,7,1,4,6,8,2]=>[2,5,1,6,8,4,3,7]=>[7,4,8,3,1,5,6,2]=>[1,2,1,3,1]
[5,7,2,6,1,4,8,3]=>[6,1,8,3,5,4,2,7]=>[3,8,1,6,4,5,7,2]=>[2,2,3,1]
[3,8,6,4,7,2,1,5]=>[4,7,6,1,3,8,5,2]=>[5,2,3,8,6,1,4,7]=>[1,3,1,3]
[5,2,7,4,6,8,3,1]=>[4,1,5,3,8,2,7,6]=>[5,8,4,6,1,7,2,3]=>[2,2,2,2]
[4,8,6,3,7,2,1,5]=>[4,7,1,6,3,8,5,2]=>[5,2,8,3,6,1,4,7]=>[1,2,2,3]
[2,8,3,1,7,6,4,5]=>[7,8,3,6,1,4,5,2]=>[2,1,6,3,8,5,4,7]=>[1,2,2,1,2]
[2,5,6,4,8,1,7,3]=>[2,4,3,8,1,6,7,5]=>[7,5,6,1,8,3,2,4]=>[1,2,2,1,2]
[5,7,2,1,6,8,3,4]=>[7,3,1,5,8,4,2,6]=>[2,6,8,4,1,5,7,3]=>[3,1,3,1]
[4,7,8,5,1,6,2,3]=>[7,8,1,5,4,2,6,3]=>[2,1,8,4,5,7,3,6]=>[1,2,3,2]
[4,5,2,1,6,7,8,3]=>[3,1,5,2,6,8,4,7]=>[6,8,4,7,3,1,5,2]=>[2,2,1,2,1]
[4,5,6,3,1,7,8,2]=>[1,2,6,4,3,8,5,7]=>[8,7,3,5,6,1,4,2]=>[1,1,3,2,1]
[3,5,6,7,4,1,8,2]=>[2,3,8,1,6,5,4,7]=>[7,6,1,8,3,4,5,2]=>[1,1,2,3,1]
[3,5,1,4,2,8,7,6]=>[8,1,4,2,7,3,5,6]=>[1,8,5,7,2,6,4,3]=>[2,2,2,1,1]
[3,5,1,4,2,6,8,7]=>[1,4,8,3,2,5,6,7]=>[8,5,1,6,7,4,3,2]=>[1,1,3,1,1,1]
[3,5,1,4,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[8,4,6,5,7,3,2,1]=>[1,2,2,1,1,1]
[1,3,8,4,6,2,5,7]=>[4,6,7,2,5,8,1,3]=>[5,3,2,7,4,1,8,6]=>[1,1,2,1,2,1]
[1,8,4,2,3,7,5,6]=>[7,3,8,4,5,6,1,2]=>[2,6,1,5,4,3,8,7]=>[2,2,1,2,1]
[1,4,8,3,2,7,6,5]=>[8,2,4,7,5,6,1,3]=>[1,7,5,2,4,3,8,6]=>[2,1,2,2,1]
[1,3,7,6,5,2,4,8]=>[6,7,5,2,4,1,3,8]=>[3,2,4,7,5,8,6,1]=>[1,3,2,1,1]
[1,2,8,6,7,5,4,3]=>[4,8,7,6,5,1,2,3]=>[5,1,2,3,4,8,7,6]=>[1,5,1,1]
[1,7,5,4,3,2,6,8]=>[6,5,4,3,7,1,2,8]=>[3,4,5,6,2,8,7,1]=>[4,2,1,1]
[3,8,5,7,4,6,2,1]=>[3,5,8,7,1,6,4,2]=>[6,4,1,2,8,3,5,7]=>[1,1,3,3]
[8,6,2,4,5,7,1,3]=>[4,7,3,5,2,8,6,1]=>[5,2,6,4,7,1,3,8]=>[1,2,2,3]
[3,8,7,4,5,2,6,1]=>[4,6,5,8,1,7,3,2]=>[5,3,4,1,8,2,6,7]=>[1,2,2,3]
[6,5,2,4,1,3,8,7]=>[8,3,5,4,2,1,6,7]=>[1,6,4,5,7,8,3,2]=>[2,4,1,1]
[7,6,3,2,5,1,8,4]=>[3,8,4,6,5,2,1,7]=>[6,1,5,3,4,7,8,2]=>[1,2,4,1]
[4,2,7,8,3,6,1,5]=>[1,5,7,3,8,2,6,4]=>[8,4,2,6,1,7,3,5]=>[1,1,2,2,2]
[4,6,3,7,5,8,2,1]=>[5,1,3,2,4,8,7,6]=>[4,8,6,7,5,1,2,3]=>[2,2,1,3]
[4,2,5,7,8,6,3,1]=>[1,4,8,3,7,2,6,5]=>[8,5,1,6,2,7,3,4]=>[1,1,2,2,2]
[8,2,5,7,3,6,1,4]=>[5,3,7,8,2,6,4,1]=>[4,6,2,1,7,3,5,8]=>[2,1,2,3]
[4,2,5,8,7,6,3,1]=>[8,1,7,3,6,2,5,4]=>[1,8,2,6,3,7,4,5]=>[2,2,2,2]
[6,7,2,4,5,1,8,3]=>[4,8,3,1,6,5,2,7]=>[5,1,6,8,3,4,7,2]=>[1,3,3,1]
[5,2,7,8,3,6,1,4]=>[5,1,7,3,8,2,6,4]=>[4,8,2,6,1,7,3,5]=>[2,2,2,2]
[7,2,8,3,1,6,4,5]=>[4,7,8,2,5,1,6,3]=>[5,2,1,7,4,8,3,6]=>[1,1,2,2,2]
[7,2,3,4,1,8,5,6]=>[2,3,4,7,8,5,1,6]=>[7,6,5,2,1,4,8,3]=>[1,1,1,1,3,1]
[2,4,7,8,1,3,6,5]=>[8,2,5,6,1,3,7,4]=>[1,7,4,3,8,6,2,5]=>[2,1,2,1,2]
[5,2,8,3,1,4,7,6]=>[4,8,2,1,5,6,7,3]=>[5,1,7,8,4,3,2,6]=>[1,3,1,1,2]
[8,7,2,5,1,4,3,6]=>[7,3,5,6,4,8,2,1]=>[2,6,4,3,5,1,7,8]=>[2,1,2,3]
[8,4,1,3,2,7,6,5]=>[8,4,2,7,3,5,6,1]=>[1,5,7,2,6,4,3,8]=>[3,2,1,2]
[8,3,5,1,2,4,7,6]=>[2,8,4,5,3,6,7,1]=>[7,1,5,4,6,3,2,8]=>[1,2,2,1,2]
[3,8,6,2,7,1,5,4]=>[8,4,6,1,3,7,5,2]=>[1,5,3,8,6,2,4,7]=>[2,2,1,3]
[3,8,4,2,1,7,6,5]=>[3,8,1,4,7,5,6,2]=>[6,1,8,5,2,4,3,7]=>[1,2,1,2,2]
[8,3,1,7,5,6,2,4]=>[7,2,5,8,6,3,4,1]=>[2,7,4,1,3,6,5,8]=>[2,1,3,2]
[8,4,1,7,5,2,6,3]=>[2,8,6,5,7,3,4,1]=>[7,1,3,4,2,6,5,8]=>[1,3,2,2]
[8,4,3,7,5,1,2,6]=>[3,2,6,7,5,8,4,1]=>[6,7,3,2,4,1,5,8]=>[2,1,2,3]
[8,5,7,6,4,3,1,2]=>[2,7,8,6,5,4,3,1]=>[7,2,1,3,4,5,6,8]=>[1,1,6]
[8,4,7,6,5,2,1,3]=>[7,2,6,8,5,4,3,1]=>[2,7,3,1,4,5,6,8]=>[2,1,5]
[8,3,1,4,7,6,2,5]=>[2,7,8,4,6,3,5,1]=>[7,2,1,5,3,6,4,8]=>[1,1,2,2,2]
[8,3,5,7,6,2,4,1]=>[3,6,8,2,7,5,4,1]=>[6,3,1,7,2,4,5,8]=>[1,1,2,4]
[3,6,2,4,8,1,7,5]=>[8,1,3,4,2,6,7,5]=>[1,8,6,5,7,3,2,4]=>[2,1,2,1,2]
[7,3,8,2,4,6,1,5]=>[2,4,5,7,1,8,6,3]=>[7,5,4,2,8,1,3,6]=>[1,1,1,2,3]
[1,5,2,6,8,3,7,4]=>[4,2,8,6,7,1,3,5]=>[5,7,1,3,2,8,6,4]=>[2,2,2,1,1]
[4,5,3,1,8,2,6,7]=>[1,6,3,2,7,8,4,5]=>[8,3,6,7,2,1,5,4]=>[1,3,1,2,1]
[5,1,7,8,3,6,2,4]=>[5,1,7,3,8,6,2,4]=>[4,8,2,6,1,3,7,5]=>[2,2,3,1]
[7,2,8,4,1,3,5,6]=>[5,6,2,4,7,1,8,3]=>[4,3,7,5,2,8,1,6]=>[1,2,1,2,2]
[6,1,7,3,2,8,4,5]=>[4,7,8,5,2,1,3,6]=>[5,2,1,4,7,8,6,3]=>[1,1,4,1,1]
[5,8,2,1,3,4,6,7]=>[4,3,5,1,6,7,8,2]=>[5,6,4,8,3,2,1,7]=>[2,2,1,1,2]
[4,2,5,1,8,3,6,7]=>[6,2,1,3,7,8,4,5]=>[3,7,8,6,2,1,5,4]=>[3,1,1,2,1]
[7,4,2,8,3,5,1,6]=>[5,2,7,3,6,1,8,4]=>[4,7,2,6,3,8,1,5]=>[2,2,2,2]
[6,7,8,5,2,1,4,3]=>[5,1,8,6,2,7,4,3]=>[4,8,1,3,7,2,5,6]=>[2,3,3]
[1,6,2,7,8,4,3,5]=>[7,6,4,2,8,1,3,5]=>[2,3,5,7,1,8,6,4]=>[4,2,1,1]
[7,3,4,1,8,6,2,5]=>[2,3,7,8,6,4,1,5]=>[7,6,2,1,3,5,8,4]=>[1,1,1,4,1]
[4,7,6,3,5,8,2,1]=>[4,5,1,3,2,8,7,6]=>[5,4,8,6,7,1,2,3]=>[1,2,2,3]
[3,7,6,5,2,4,8,1]=>[5,6,4,1,3,2,8,7]=>[4,3,5,8,6,7,1,2]=>[1,3,2,2]
[1,4,7,8,6,2,5,3]=>[8,6,2,3,7,5,1,4]=>[1,3,7,6,2,4,8,5]=>[3,1,3,1]
[1,3,2,7,8,4,6,5]=>[8,6,2,4,7,1,3,5]=>[1,3,7,5,2,8,6,4]=>[3,1,2,1,1]
[6,8,2,3,5,7,4,1]=>[5,8,3,1,4,7,6,2]=>[4,1,6,8,5,2,3,7]=>[1,3,1,3]
[5,7,1,4,6,2,8,3]=>[4,1,8,6,3,5,2,7]=>[5,8,1,3,6,4,7,2]=>[2,3,2,1]
[6,3,1,4,7,8,2,5]=>[2,7,4,5,1,8,3,6]=>[7,2,5,4,8,1,6,3]=>[1,2,2,2,1]
[9,8,7,6,5,1,3,4,2]=>[7,9,6,8,5,4,3,2,1]=>[3,1,4,2,5,6,7,8,9]=>[1,2,6]
[9,1,7,8,6,5,4,3,2]=>[3,9,8,7,6,5,2,4,1]=>[7,1,2,3,4,5,8,6,9]=>[1,6,2]
[4,5,7,1,8,6,2,3]=>[1,2,7,8,6,4,3,5]=>[8,7,2,1,3,5,6,4]=>[1,1,1,4,1]
[4,3,8,6,5,2,7,1]=>[6,1,5,2,4,8,7,3]=>[3,8,4,7,5,1,2,6]=>[2,2,1,3]
[2,3,8,6,5,1,7,4]=>[8,6,5,1,2,4,7,3]=>[1,3,4,8,7,5,2,6]=>[4,1,1,2]
[7,6,2,1,5,4,3,8]=>[7,3,6,4,5,2,1,8]=>[2,6,3,5,4,7,8,1]=>[2,2,3,1]
[3,1,2,6,5,7,8,4]=>[1,5,4,6,8,2,3,7]=>[8,4,5,3,1,7,6,2]=>[1,2,1,2,1,1]
[7,3,2,6,1,4,8,5]=>[2,8,3,5,6,4,1,7]=>[7,1,6,4,3,5,8,2]=>[1,2,1,3,1]
[3,2,5,6,8,4,1,7]=>[1,3,4,7,2,6,8,5]=>[8,6,5,2,7,3,1,4]=>[1,1,1,2,1,2]
[7,2,6,8,5,4,3,1]=>[3,8,7,6,2,1,5,4]=>[6,1,2,3,7,8,4,5]=>[1,5,2]
[3,7,5,6,2,4,1,8]=>[5,3,7,1,6,4,2,8]=>[4,6,2,8,3,5,7,1]=>[2,2,3,1]
[1,3,4,5,6,7,2,9,8]=>[2,3,4,5,6,9,1,7,8]=>[8,7,6,5,4,1,9,3,2]=>[1,1,1,1,1,2,1,1]
[3,2,5,4,6,1,8,7,9]=>[1,4,2,3,5,8,6,7,9]=>[9,6,8,7,5,2,4,3,1]=>[1,2,1,1,2,1,1]
[4,2,5,1,3,6,8,7]=>[8,2,1,4,3,5,6,7]=>[1,7,8,5,6,4,3,2]=>[3,2,1,1,1]
[5,3,4,2,7,1,8,6]=>[2,3,1,8,4,6,5,7]=>[7,6,8,1,5,3,4,2]=>[1,2,2,2,1]
[5,6,8,2,1,3,4,7]=>[5,4,1,6,2,7,8,3]=>[4,5,8,3,7,2,1,6]=>[3,2,1,2]
[6,5,2,1,3,8,4,7]=>[3,7,8,4,2,1,5,6]=>[6,2,1,5,7,8,4,3]=>[1,1,4,1,1]
[2,4,3,5,6,8,1,7]=>[3,1,2,4,5,7,8,6]=>[6,8,7,5,4,2,1,3]=>[2,1,1,1,1,2]
[6,3,2,4,8,5,1,7]=>[2,7,3,4,1,6,8,5]=>[7,2,6,5,8,3,1,4]=>[1,2,2,1,2]
[6,3,1,2,7,8,4,5]=>[2,7,5,8,3,1,4,6]=>[7,2,4,1,6,8,5,3]=>[1,2,3,1,1]
[8,4,7,1,2,5,3,6]=>[7,4,2,5,6,8,3,1]=>[2,5,7,4,3,1,6,8]=>[3,1,1,3]
[7,4,6,1,8,5,2,3]=>[2,7,8,6,4,3,1,5]=>[7,2,1,3,5,6,8,4]=>[1,1,5,1]
[8,5,6,7,2,1,4,3]=>[5,2,8,6,3,7,4,1]=>[4,7,1,3,6,2,5,8]=>[2,3,3]
[2,5,6,3,8,4,7,1]=>[2,6,3,8,1,4,7,5]=>[7,3,6,1,8,5,2,4]=>[1,2,2,1,2]
[6,8,4,2,3,1,7,5]=>[4,5,3,1,8,6,7,2]=>[5,4,6,8,1,3,2,7]=>[1,3,2,2]
[1,7,6,2,8,3,5,4]=>[8,6,7,4,3,1,2,5]=>[1,3,2,5,6,8,7,4]=>[2,4,1,1]
[4,1,3,8,5,2,7,6]=>[5,1,8,3,6,7,2,4]=>[4,8,1,6,3,2,7,5]=>[2,2,1,2,1]
[1,8,5,4,7,2,3,6]=>[6,4,3,7,8,5,1,2]=>[3,5,6,2,1,4,8,7]=>[3,1,3,1]
[8,2,5,6,4,3,1,7]=>[3,7,6,2,5,4,8,1]=>[6,2,3,7,4,5,1,8]=>[1,3,2,2]
[2,4,3,8,6,5,1,7]=>[7,2,6,1,3,5,8,4]=>[2,7,3,8,6,4,1,5]=>[2,2,1,1,2]
[1,8,3,2,5,4,6,7]=>[3,6,4,5,7,8,1,2]=>[6,3,5,4,2,1,8,7]=>[1,2,1,1,2,1]
[5,1,7,3,2,8,4,6]=>[4,7,1,8,5,2,3,6]=>[5,2,8,1,4,7,6,3]=>[1,2,3,1,1]
[5,7,8,1,3,2,4,6]=>[6,4,1,5,7,2,8,3]=>[3,5,8,4,2,7,1,6]=>[3,1,2,2]
[8,2,4,1,6,7,3,5]=>[3,7,2,5,8,4,6,1]=>[6,2,7,4,1,5,3,8]=>[1,2,1,2,2]
[1,7,4,8,3,6,2,5]=>[3,5,7,2,8,6,1,4]=>[6,4,2,7,1,3,8,5]=>[1,1,2,3,1]
[1,7,5,8,4,3,2,6]=>[3,7,6,5,2,8,1,4]=>[6,2,3,4,7,1,8,5]=>[1,4,2,1]
[6,3,1,2,7,8,5,4]=>[2,5,8,7,3,1,4,6]=>[7,4,1,2,6,8,5,3]=>[1,1,4,1,1]
[8,2,7,5,3,4,1,6]=>[5,7,6,2,4,8,3,1]=>[4,2,3,7,5,1,6,8]=>[1,3,1,3]
[6,3,1,2,8,7,5,4]=>[8,2,7,6,3,1,4,5]=>[1,7,2,3,6,8,5,4]=>[2,4,1,1]
[8,4,7,2,6,3,1,5]=>[2,7,4,6,8,5,3,1]=>[7,2,5,3,1,4,6,8]=>[1,2,1,4]
[1,2,5,7,8,3,6,4]=>[8,3,6,4,7,1,2,5]=>[1,6,3,5,2,8,7,4]=>[2,2,2,1,1]
[8,4,6,2,3,7,1,5]=>[4,2,5,7,3,8,6,1]=>[5,7,4,2,6,1,3,8]=>[2,1,2,3]
[3,4,5,8,1,7,2,6]=>[1,2,3,7,8,5,6,4]=>[8,7,6,2,1,4,3,5]=>[1,1,1,1,2,2]
[6,3,4,2,7,8,1,5]=>[2,3,7,4,1,5,8,6]=>[7,6,2,5,8,4,1,3]=>[1,1,3,1,2]
[8,6,3,4,7,2,1,5]=>[3,4,7,6,2,8,5,1]=>[6,5,2,3,7,1,4,8]=>[1,1,3,3]
[4,3,8,6,7,5,1,2]=>[7,1,4,8,2,6,5,3]=>[2,8,5,1,7,3,4,6]=>[2,1,2,3]
[4,5,6,2,7,8,3,1]=>[1,2,5,3,8,4,7,6]=>[8,7,4,6,1,5,2,3]=>[1,1,2,2,2]
[4,5,6,2,1,7,8,3]=>[1,4,2,6,3,8,5,7]=>[8,5,7,3,6,1,4,2]=>[1,2,2,2,1]
[4,5,6,2,1,7,3,8]=>[1,4,2,7,5,3,6,8]=>[8,5,7,2,4,6,3,1]=>[1,2,3,1,1]
[6,8,7,2,3,1,4,5]=>[4,6,5,1,7,8,3,2]=>[5,3,4,8,2,1,6,7]=>[1,3,1,3]
[4,5,1,6,7,3,2,8]=>[1,4,2,7,6,3,5,8]=>[8,5,7,2,3,6,4,1]=>[1,2,3,1,1]
[2,5,1,8,3,7,4,6]=>[7,2,8,1,5,6,3,4]=>[2,7,1,8,4,3,6,5]=>[2,2,1,2,1]
[5,7,2,1,3,8,4,6]=>[3,7,1,8,4,5,2,6]=>[6,2,8,1,5,4,7,3]=>[1,2,2,2,1]
[3,7,5,4,1,6,8,2]=>[6,4,1,3,8,5,2,7]=>[3,5,8,6,1,4,7,2]=>[3,1,3,1]
[7,1,5,4,2,6,3,8]=>[7,5,4,2,3,6,1,8]=>[2,4,5,7,6,3,8,1]=>[4,1,2,1]
[8,5,6,3,7,2,1,4]=>[4,2,7,6,3,8,5,1]=>[5,7,2,3,6,1,4,8]=>[2,3,3]
[7,6,5,4,3,1,2,9,8]=>[9,6,5,4,3,2,1,7,8]=>[1,4,5,6,7,8,9,3,2]=>[7,1,1]
[8,7,6,5,4,3,1,2,10,9]=>[10,7,6,5,4,3,2,1,8,9]=>[1,4,5,6,7,8,9,10,3,2]=>[8,1,1]
[7,6,5,4,1,3,2,9,8]=>[6,9,5,4,3,2,1,7,8]=>[4,1,5,6,7,8,9,3,2]=>[1,6,1,1]
[9,8,7,6,5,3,2,4,1]=>[7,6,9,8,5,4,3,2,1]=>[3,4,1,2,5,6,7,8,9]=>[2,7]
[9,8,7,6,5,2,4,3,1]=>[9,6,8,7,5,4,3,2,1]=>[1,4,2,3,5,6,7,8,9]=>[2,7]
[10,9,8,7,6,5,4,2,3,1]=>[8,10,9,7,6,5,4,3,2,1]=>[3,1,2,4,5,6,7,8,9,10]=>[1,9]
[2,7,4,5,6,8,1,3]=>[3,4,7,5,1,2,8,6]=>[6,5,2,4,8,7,1,3]=>[1,1,3,1,2]
[2,3,4,6,8,1,7,5]=>[4,8,1,2,3,6,7,5]=>[5,1,8,7,6,3,2,4]=>[1,2,1,1,1,2]
[2,3,5,8,1,6,7,4]=>[3,6,8,1,2,5,7,4]=>[6,3,1,8,7,4,2,5]=>[1,1,2,1,1,2]
[2,4,7,5,6,8,1,3]=>[4,7,2,5,1,3,8,6]=>[5,2,7,4,8,6,1,3]=>[1,2,2,1,2]
[4,7,6,5,2,8,3,1]=>[8,5,1,4,3,2,7,6]=>[1,4,8,5,6,7,2,3]=>[3,3,2]
[2,5,4,8,6,7,3,1]=>[2,5,8,3,7,1,6,4]=>[7,4,1,6,2,8,3,5]=>[1,1,2,2,2]
[7,5,4,1,6,8,2,3]=>[7,5,3,2,8,4,1,6]=>[2,4,6,7,1,5,8,3]=>[4,3,1]
[2,7,3,6,4,1,8,5]=>[5,8,3,6,1,4,2,7]=>[4,1,6,3,8,5,7,2]=>[1,2,2,2,1]
[7,2,1,8,5,6,4,3]=>[5,8,7,2,6,3,1,4]=>[4,1,2,7,3,6,8,5]=>[1,3,3,1]
[3,6,5,1,4,8,2,7]=>[5,7,1,3,2,8,4,6]=>[4,2,8,6,7,1,5,3]=>[1,2,2,2,1]
[2,5,1,4,6,3,8,7]=>[4,5,1,2,8,3,6,7]=>[5,4,8,7,1,6,3,2]=>[1,2,1,2,1,1]
[8,5,6,4,3,1,7,2]=>[2,8,6,5,4,3,7,1]=>[7,1,3,4,5,6,2,8]=>[1,5,2]
[8,3,5,6,7,1,2,4]=>[6,2,3,7,4,8,5,1]=>[3,7,6,2,5,1,4,8]=>[2,1,2,3]
[2,1,4,7,3,6,8,5]=>[6,8,1,3,5,2,4,7]=>[3,1,8,6,4,7,5,2]=>[1,2,1,2,1,1]
[5,3,7,6,4,8,2,1]=>[1,5,4,2,3,8,7,6]=>[8,4,5,7,6,1,2,3]=>[1,3,1,3]
[3,7,6,4,2,8,1,5]=>[5,4,7,1,3,2,8,6]=>[4,5,2,8,6,7,1,3]=>[2,2,2,2]
[8,6,1,4,3,7,2,5]=>[5,4,7,8,3,2,6,1]=>[4,5,2,1,6,7,3,8]=>[2,1,3,2]
[8,4,7,5,1,6,3,2]=>[8,2,7,5,4,6,3,1]=>[1,7,2,4,5,3,6,8]=>[2,3,3]
[2,1,5,3,7,8,6,4]=>[3,5,8,1,7,2,4,6]=>[6,4,1,8,2,7,5,3]=>[1,1,2,2,1,1]
[5,1,4,7,6,8,2,3]=>[7,3,1,5,4,8,2,6]=>[2,6,8,4,5,1,7,3]=>[3,2,2,1]
[8,3,4,1,6,7,5,2]=>[2,3,5,8,7,4,6,1]=>[7,6,4,1,2,5,3,8]=>[1,1,1,3,2]
[8,1,4,2,6,5,7,3]=>[3,6,5,8,2,4,7,1]=>[6,3,4,1,7,5,2,8]=>[1,2,2,1,2]
[8,6,4,3,7,2,1,5]=>[4,3,7,6,2,8,5,1]=>[5,6,2,3,7,1,4,8]=>[2,3,3]
[5,8,1,4,3,2,6,7]=>[6,5,3,1,4,7,8,2]=>[3,4,6,8,5,2,1,7]=>[4,1,1,2]
[5,6,4,3,8,2,7,1]=>[1,4,3,2,6,8,7,5]=>[8,5,6,7,3,1,2,4]=>[1,3,1,3]
[7,8,1,4,3,2,5,6]=>[6,5,3,4,7,1,8,2]=>[3,4,6,5,2,8,1,7]=>[3,1,2,2]
[7,1,8,4,5,3,6,2]=>[4,6,5,8,7,2,1,3]=>[5,3,4,1,2,7,8,6]=>[1,2,4,1]
[4,3,1,8,6,5,7,2]=>[1,6,2,5,8,7,3,4]=>[8,3,7,4,1,2,6,5]=>[1,2,1,3,1]
[4,3,2,7,5,1,8,6]=>[2,1,5,8,3,6,4,7]=>[7,8,4,1,6,3,5,2]=>[2,1,2,2,1]
[5,2,3,7,4,1,8,6]=>[5,8,2,1,3,6,4,7]=>[4,1,7,8,6,3,5,2]=>[1,3,1,2,1]
[2,1,7,4,3,6,8,5]=>[4,6,8,1,5,2,3,7]=>[5,3,1,8,4,7,6,2]=>[1,1,2,2,1,1]
[7,1,2,4,5,6,8,3]=>[4,5,6,8,2,3,1,7]=>[5,4,3,1,7,6,8,2]=>[1,1,1,2,2,1]
[2,8,7,1,4,5,6,3]=>[5,6,8,4,7,1,3,2]=>[4,3,1,5,2,8,6,7]=>[1,1,2,2,2]
[8,7,1,3,4,5,6,2]=>[4,5,6,8,3,7,2,1]=>[5,4,3,1,6,2,7,8]=>[1,1,1,2,3]
[1,7,2,5,4,6,8,3]=>[5,4,6,8,3,1,2,7]=>[4,5,3,1,6,8,7,2]=>[2,1,3,1,1]
[2,5,3,8,1,6,7,4]=>[6,2,8,1,3,5,7,4]=>[3,7,1,8,6,4,2,5]=>[2,2,1,1,2]
[1,6,4,2,5,7,8,3]=>[5,3,6,2,8,1,4,7]=>[4,6,3,7,1,8,5,2]=>[2,2,2,1,1]
[6,5,3,4,1,7,8,2]=>[3,6,4,2,1,8,5,7]=>[6,3,5,7,8,1,4,2]=>[1,4,2,1]
[2,5,3,1,4,7,8,6]=>[3,6,1,2,8,4,5,7]=>[6,3,8,7,1,5,4,2]=>[1,2,1,2,1,1]
[6,8,2,3,1,5,7,4]=>[3,4,6,1,8,5,7,2]=>[6,5,3,8,1,4,2,7]=>[1,1,2,2,2]
[4,3,1,5,2,7,8,6]=>[4,2,1,6,8,3,5,7]=>[5,7,8,3,1,6,4,2]=>[3,1,2,1,1]
[5,2,3,1,4,7,8,6]=>[2,3,6,1,8,4,5,7]=>[7,6,3,8,1,5,4,2]=>[1,1,2,2,1,1]
[7,2,1,3,5,6,8,4]=>[2,5,6,8,3,4,1,7]=>[7,4,3,1,6,5,8,2]=>[1,1,1,2,2,1]
[7,3,6,4,5,8,1,2]=>[4,7,2,5,3,1,8,6]=>[5,2,7,4,6,8,1,3]=>[1,2,3,2]
[6,4,3,7,5,8,2,1]=>[2,5,3,1,4,8,7,6]=>[7,4,6,8,5,1,2,3]=>[1,3,1,3]
[5,2,4,7,8,6,3,1]=>[4,1,8,3,7,2,6,5]=>[5,8,1,6,2,7,3,4]=>[2,2,2,2]
[5,4,8,7,2,3,1,6]=>[2,1,5,7,6,8,4,3]=>[7,8,4,2,3,1,5,6]=>[2,1,2,3]
[5,8,2,1,7,4,3,6]=>[7,3,1,6,8,4,5,2]=>[2,6,8,3,1,5,4,7]=>[3,1,2,2]
[6,5,7,2,1,8,4,3]=>[8,4,2,1,7,5,3,6]=>[1,5,7,8,2,4,6,3]=>[4,3,1]
[1,5,4,7,3,8,6,2]=>[2,8,3,5,4,7,1,6]=>[7,1,6,4,5,2,8,3]=>[1,2,2,2,1]
[7,4,1,3,8,5,6,2]=>[6,2,8,4,7,3,1,5]=>[3,7,1,5,2,6,8,4]=>[2,2,3,1]
[3,6,8,4,1,7,2,5]=>[7,4,1,2,8,5,6,3]=>[2,5,8,7,1,4,3,6]=>[3,1,2,2]
[2,1,8,4,7,6,3,5]=>[7,8,4,6,1,5,2,3]=>[2,1,5,3,8,4,7,6]=>[1,2,2,2,1]
[2,7,5,6,8,4,3,1]=>[3,4,2,8,7,1,6,5]=>[6,5,7,1,2,8,3,4]=>[1,2,3,2]
[3,5,2,4,7,8,6,1]=>[5,1,2,8,3,4,7,6]=>[4,8,7,1,6,5,2,3]=>[2,1,2,1,2]
[7,5,6,3,8,2,1,4]=>[4,2,7,6,3,1,8,5]=>[5,7,2,3,6,8,1,4]=>[2,4,2]
[7,4,2,6,1,5,8,3]=>[6,2,8,3,5,4,1,7]=>[3,7,1,6,4,5,8,2]=>[2,2,3,1]
[8,4,1,6,2,5,7,3]=>[6,2,8,5,3,4,7,1]=>[3,7,1,4,6,5,2,8]=>[2,3,1,2]
[7,3,4,5,1,6,8,2]=>[2,3,6,4,8,5,1,7]=>[7,6,3,5,1,4,8,2]=>[1,1,2,3,1]
[8,4,2,7,6,1,5,3]=>[2,8,6,7,3,5,4,1]=>[7,1,3,2,6,4,5,8]=>[1,2,2,3]
[8,4,7,6,1,2,5,3]=>[2,8,5,6,7,4,3,1]=>[7,1,4,3,2,5,6,8]=>[1,2,1,4]
[8,7,6,2,1,5,3,4]=>[4,7,8,5,6,3,2,1]=>[5,2,1,4,3,6,7,8]=>[1,1,2,4]
[5,7,8,1,6,2,4,3]=>[1,8,6,7,4,2,5,3]=>[8,1,3,2,5,7,4,6]=>[1,2,3,2]
[6,8,4,7,5,2,1,3]=>[3,1,7,6,8,5,4,2]=>[6,8,2,3,1,4,5,7]=>[2,2,4]
[6,8,2,7,1,5,4,3]=>[8,7,3,1,5,6,4,2]=>[1,2,6,8,4,3,5,7]=>[4,1,3]
[6,8,7,4,2,5,1,3]=>[5,1,7,4,8,6,3,2]=>[4,8,2,5,1,3,6,7]=>[2,2,4]
[6,8,4,2,5,1,3,7]=>[4,6,3,1,7,5,8,2]=>[5,3,6,8,2,4,1,7]=>[1,3,2,2]
[6,5,4,3,2,7,1,8,9]=>[5,4,3,2,1,7,6,8,9]=>[5,6,7,8,9,3,4,2,1]=>[5,2,1,1]
[5,4,3,2,6,1,7,8,9]=>[4,3,2,1,6,5,7,8,9]=>[6,7,8,9,4,5,3,2,1]=>[4,2,1,1,1]
[4,3,2,5,1,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>[7,8,9,5,6,4,3,2,1]=>[3,2,1,1,1,1]
[3,2,4,1,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[8,9,6,7,5,4,3,2,1]=>[2,2,1,1,1,1,1]
[2,5,3,7,6,4,8,1]=>[2,6,5,1,3,4,8,7]=>[7,3,4,8,6,5,1,2]=>[1,3,1,1,2]
[3,1,5,7,6,4,2,8]=>[7,1,3,6,5,2,4,8]=>[2,8,6,3,4,7,5,1]=>[2,1,3,1,1]
[3,1,6,5,4,7,2,8]=>[5,1,4,3,7,2,6,8]=>[4,8,5,6,2,7,3,1]=>[2,2,2,1,1]
[2,5,6,8,3,4,7,1]=>[2,5,3,6,8,1,7,4]=>[7,4,6,3,1,8,2,5]=>[1,2,1,2,2]
[4,1,3,6,5,2,7,8]=>[6,3,1,5,2,4,7,8]=>[3,6,8,4,7,5,2,1]=>[3,2,1,1,1]
[3,6,2,4,5,7,1,8]=>[1,3,4,5,2,7,6,8]=>[8,6,5,4,7,2,3,1]=>[1,1,1,2,2,1]
[3,6,2,5,4,7,1,8]=>[5,1,3,4,2,7,6,8]=>[4,8,6,5,7,2,3,1]=>[2,1,2,2,1]
[3,6,1,4,5,7,2,8]=>[1,4,5,7,3,2,6,8]=>[8,5,4,2,6,7,3,1]=>[1,1,1,3,1,1]
[4,3,1,6,5,2,7,8]=>[2,1,6,5,3,4,7,8]=>[7,8,3,4,6,5,2,1]=>[2,3,1,1,1]
[4,1,2,6,5,3,7,8]=>[6,5,2,1,3,4,7,8]=>[3,4,7,8,6,5,2,1]=>[4,1,1,1,1]
[4,6,1,3,5,2,7,8]=>[4,1,6,3,5,2,7,8]=>[5,8,3,6,4,7,2,1]=>[2,2,2,1,1]
[3,6,4,2,5,7,1,8]=>[4,1,3,5,2,7,6,8]=>[5,8,6,4,7,2,3,1]=>[2,1,2,2,1]
[4,2,6,3,5,1,7,8]=>[4,1,6,2,5,3,7,8]=>[5,8,3,7,4,6,2,1]=>[2,2,2,1,1]
[3,4,7,6,5,1,2,8]=>[6,7,1,2,5,4,3,8]=>[3,2,8,7,4,5,6,1]=>[1,2,1,3,1]
[4,5,2,7,1,3,6,8]=>[3,1,5,2,6,7,4,8]=>[6,8,4,7,3,2,5,1]=>[2,2,1,2,1]
[2,6,5,1,4,8,7,3]=>[8,5,3,1,2,7,4,6]=>[1,4,6,8,7,2,5,3]=>[4,1,2,1]
[6,4,7,1,3,5,2,8]=>[5,2,7,4,1,6,3,8]=>[4,7,2,5,8,3,6,1]=>[2,3,2,1]
[6,8,1,3,5,7,4,2]=>[5,8,4,1,7,3,6,2]=>[4,1,5,8,2,6,3,7]=>[1,3,2,2]
[5,8,3,2,7,4,6,1]=>[3,1,6,8,4,7,5,2]=>[6,8,3,1,5,2,4,7]=>[2,1,2,3]
[6,8,3,1,5,4,7,2]=>[3,6,5,1,8,4,7,2]=>[6,3,4,8,1,5,2,7]=>[1,3,2,2]
[5,2,8,3,4,6,7,1]=>[4,5,1,6,8,2,7,3]=>[5,4,8,3,1,7,2,6]=>[1,2,1,2,2]
[5,2,7,1,6,4,8,3]=>[6,5,1,8,2,4,3,7]=>[3,4,8,1,7,5,6,2]=>[3,2,2,1]
[4,5,2,6,1,3,7,8]=>[3,1,5,2,6,4,7,8]=>[6,8,4,7,3,5,2,1]=>[2,2,2,1,1]
[4,3,5,8,6,1,7,2]=>[1,8,2,3,6,5,7,4]=>[8,1,7,6,3,4,2,5]=>[1,2,1,2,2]
[5,1,3,6,7,4,2,8]=>[4,7,3,1,6,2,5,8]=>[5,2,6,8,3,7,4,1]=>[1,3,2,1,1]
[4,2,8,3,6,7,5,1]=>[1,5,8,4,7,2,6,3]=>[8,4,1,5,2,7,3,6]=>[1,1,2,2,2]
[3,1,7,8,5,6,2,4]=>[7,5,1,3,8,6,2,4]=>[2,4,8,6,1,3,7,5]=>[3,1,3,1]
[4,2,8,6,7,1,3,5]=>[1,6,7,4,8,2,5,3]=>[8,3,2,5,1,7,4,6]=>[1,1,2,2,2]
[5,3,1,6,4,7,2,8]=>[2,5,4,1,7,3,6,8]=>[7,4,5,8,2,6,3,1]=>[1,3,2,1,1]
[1,2,4,5,8,7,3,6]=>[7,8,3,4,6,1,2,5]=>[2,1,6,5,3,8,7,4]=>[1,2,1,2,1,1]
[1,5,2,3,7,8,6,4]=>[5,2,8,7,1,3,4,6]=>[4,7,1,2,8,6,5,3]=>[2,3,1,1,1]
[4,2,8,1,6,5,7,3]=>[1,6,5,8,2,4,7,3]=>[8,3,4,1,7,5,2,6]=>[1,2,2,1,2]
[4,3,7,8,2,1,5,9,6]=>[1,5,9,2,6,3,7,4,8]=>[9,5,1,8,4,7,3,6,2]=>[1,1,2,2,2,1]
[5,2,6,3,7,8,4,1]=>[5,3,1,8,2,4,7,6]=>[4,6,8,1,7,5,2,3]=>[3,2,1,2]
[2,4,1,3,7,8,6,5]=>[2,5,8,1,7,3,4,6]=>[7,4,1,8,2,6,5,3]=>[1,1,2,2,1,1]
[5,1,6,4,7,8,2,3]=>[4,3,1,7,5,8,2,6]=>[5,6,8,2,4,1,7,3]=>[3,2,2,1]
[8,4,6,3,7,5,1,2]=>[2,4,7,3,8,6,5,1]=>[7,5,2,6,1,3,4,8]=>[1,1,2,4]
[4,7,6,8,2,3,5,1]=>[5,6,1,3,2,8,7,4]=>[4,3,8,6,7,1,2,5]=>[1,2,2,3]
[5,7,4,8,1,2,6,3]=>[1,8,5,3,6,2,7,4]=>[8,1,4,6,3,7,2,5]=>[1,3,2,2]
[3,6,7,5,8,1,4,2]=>[2,8,6,1,4,3,7,5]=>[7,1,3,8,5,6,2,4]=>[1,3,2,2]
[3,7,5,6,8,2,4,1]=>[3,6,4,1,2,8,7,5]=>[6,3,5,8,7,1,2,4]=>[1,3,1,3]
[2,7,1,6,8,4,5,3]=>[6,4,8,7,1,3,2,5]=>[3,5,1,2,8,6,7,4]=>[2,3,2,1]
[1,5,4,7,2,6,3,8]=>[3,2,7,5,6,1,4,8]=>[6,7,2,4,3,8,5,1]=>[2,2,2,1,1]
[2,4,5,8,3,1,7,6]=>[2,3,5,8,1,6,7,4]=>[7,6,4,1,8,3,2,5]=>[1,1,1,2,1,2]
[1,4,7,5,8,3,6,2]=>[4,6,2,3,8,7,1,5]=>[5,3,7,6,1,2,8,4]=>[1,2,1,3,1]
[4,7,8,6,2,5,1,3]=>[5,7,1,2,8,6,4,3]=>[4,2,8,7,1,3,5,6]=>[1,2,1,4]
[4,8,7,3,5,6,2,1]=>[4,5,8,1,7,6,3,2]=>[5,4,1,8,2,3,6,7]=>[1,1,2,4]
[1,7,6,3,5,4,2,8]=>[7,4,6,5,3,1,2,8]=>[2,5,3,4,6,8,7,1]=>[2,4,1,1]
[4,3,8,1,6,5,7,2]=>[1,6,2,5,8,4,7,3]=>[8,3,7,4,1,5,2,6]=>[1,2,1,2,2]
[1,3,6,2,5,8,7,4]=>[8,5,2,3,7,1,4,6]=>[1,4,7,6,2,8,5,3]=>[3,1,2,1,1]
[5,8,7,1,4,6,3,2]=>[1,5,8,7,4,6,3,2]=>[8,4,1,2,5,3,6,7]=>[1,1,3,3]
[6,2,5,1,3,4,8,7]=>[8,2,4,5,3,1,6,7]=>[1,7,5,4,6,8,3,2]=>[2,1,3,1,1]
[4,6,5,1,2,7,3,8]=>[1,7,4,5,3,2,6,8]=>[8,2,5,4,6,7,3,1]=>[1,2,3,1,1]
[5,6,4,1,2,7,3,8]=>[7,4,1,5,3,2,6,8]=>[2,5,8,4,6,7,3,1]=>[3,3,1,1]
[8,1,5,6,2,4,3,7]=>[7,5,3,6,2,4,8,1]=>[2,4,6,3,7,5,1,8]=>[3,2,1,2]
[6,4,5,1,2,7,3,8]=>[7,4,2,5,3,1,6,8]=>[2,5,7,4,6,8,3,1]=>[3,3,1,1]
[5,4,6,1,3,2,7,8]=>[6,4,2,1,5,3,7,8]=>[3,5,7,8,4,6,2,1]=>[4,2,1,1]
[5,7,1,4,3,2,6,8]=>[6,5,3,1,4,7,2,8]=>[3,4,6,8,5,2,7,1]=>[4,1,2,1]
[2,6,4,1,3,7,5,8]=>[7,4,1,3,5,2,6,8]=>[2,5,8,6,4,7,3,1]=>[3,1,2,1,1]
[7,8,5,3,2,1,6,4]=>[5,4,8,6,3,1,7,2]=>[4,5,1,3,6,8,2,7]=>[2,4,2]
[1,2,6,7,8,4,5,3]=>[3,6,4,8,7,1,2,5]=>[6,3,5,1,2,8,7,4]=>[1,2,3,1,1]
[5,2,3,7,1,8,4,6]=>[7,8,2,1,3,5,4,6]=>[2,1,7,8,6,4,5,3]=>[1,3,1,2,1]
[7,2,3,1,8,4,6,5]=>[8,2,3,6,7,4,1,5]=>[1,7,6,3,2,5,8,4]=>[2,1,1,3,1]
[7,3,4,5,1,8,6,2]=>[2,3,4,8,7,5,1,6]=>[7,6,5,1,2,4,8,3]=>[1,1,1,4,1]
[1,5,6,7,4,8,2,3]=>[2,3,7,5,4,8,1,6]=>[7,6,2,4,5,1,8,3]=>[1,1,3,2,1]
[6,3,2,5,7,4,8,1]=>[2,4,6,3,1,5,8,7]=>[7,5,3,6,8,4,1,2]=>[1,1,3,1,2]
[5,7,3,8,1,2,4,6]=>[5,3,1,6,7,2,8,4]=>[4,6,8,3,2,7,1,5]=>[3,1,2,2]
[4,5,2,1,7,6,3,8]=>[1,7,3,2,6,4,5,8]=>[8,2,6,7,3,5,4,1]=>[1,3,2,1,1]
[2,6,7,8,3,1,4,5]=>[6,5,2,7,1,3,8,4]=>[3,4,7,2,8,6,1,5]=>[3,2,1,2]
[6,3,2,5,1,7,8,4]=>[2,6,3,4,1,8,5,7]=>[7,3,6,5,8,1,4,2]=>[1,2,2,2,1]
[5,6,7,1,8,4,2,3]=>[1,7,2,8,6,4,3,5]=>[8,2,7,1,3,5,6,4]=>[1,2,4,1]
[1,7,8,4,6,5,2,3]=>[4,7,2,8,6,5,1,3]=>[5,2,7,1,3,4,8,6]=>[1,2,4,1]
[1,7,3,2,8,6,5,4]=>[8,7,3,6,4,1,2,5]=>[1,2,6,3,5,8,7,4]=>[3,3,1,1]
[2,7,8,1,6,5,3,4]=>[7,8,6,4,1,2,5,3]=>[2,1,3,5,8,7,4,6]=>[1,4,1,2]
[2,5,8,1,7,6,3,4]=>[2,7,8,6,1,4,5,3]=>[7,2,1,3,8,5,4,6]=>[1,1,3,1,2]
[8,1,5,7,3,4,6,2]=>[5,3,6,8,7,2,4,1]=>[4,6,3,1,2,7,5,8]=>[2,1,3,2]
[2,8,4,7,6,3,1,5]=>[7,3,6,8,5,1,4,2]=>[2,6,3,1,4,8,5,7]=>[2,1,3,2]
[1,8,2,4,7,6,3,5]=>[7,8,4,6,3,5,1,2]=>[2,1,5,3,6,4,8,7]=>[1,2,2,2,1]
[4,5,8,7,1,6,2,3]=>[1,2,7,8,5,6,4,3]=>[8,7,2,1,4,3,5,6]=>[1,1,1,2,3]
[1,8,2,4,6,7,5,3]=>[5,8,4,7,3,6,1,2]=>[4,1,5,2,6,3,8,7]=>[1,2,2,2,1]
[2,5,1,8,4,7,6,3]=>[2,8,5,7,1,6,3,4]=>[7,1,4,2,8,3,6,5]=>[1,2,2,2,1]
[3,4,2,8,1,7,6,5]=>[8,1,2,7,3,5,6,4]=>[1,8,7,2,6,4,3,5]=>[2,1,2,1,2]
[2,4,5,8,1,7,6,3]=>[8,2,3,7,1,5,6,4]=>[1,7,6,2,8,4,3,5]=>[2,1,2,1,2]
[3,1,8,2,6,7,5,4]=>[5,8,1,7,4,6,2,3]=>[4,1,8,2,5,3,7,6]=>[1,2,2,2,1]
[2,6,8,1,4,3,7,5]=>[5,8,4,1,2,6,7,3]=>[4,1,5,8,7,3,2,6]=>[1,3,1,1,2]
[4,1,8,2,6,7,3,5]=>[1,7,5,8,4,6,2,3]=>[8,2,4,1,5,3,7,6]=>[1,2,2,2,1]
[1,6,5,2,8,7,3,4]=>[7,3,2,8,6,1,4,5]=>[2,6,7,1,3,8,5,4]=>[3,3,1,1]
[2,6,1,5,8,7,3,4]=>[4,7,2,8,1,6,3,5]=>[5,2,7,1,8,3,6,4]=>[1,2,2,2,1]
[8,1,7,3,5,2,4,6]=>[4,6,7,5,8,2,3,1]=>[5,3,2,4,1,7,6,8]=>[1,1,2,2,2]
[8,1,3,2,7,6,4,5]=>[7,8,3,6,2,4,5,1]=>[2,1,6,3,7,5,4,8]=>[1,2,2,1,2]
[7,3,4,8,6,2,5,1]=>[6,8,2,3,1,7,5,4]=>[3,1,7,6,8,2,4,5]=>[1,2,2,3]
[7,5,8,1,6,2,3,4]=>[6,7,2,8,4,1,5,3]=>[3,2,7,1,5,8,4,6]=>[1,2,3,2]
[6,7,5,3,2,8,4,1]=>[4,1,8,5,3,2,7,6]=>[5,8,1,4,6,7,2,3]=>[2,4,2]
[6,2,5,3,8,1,4,7]=>[4,6,2,3,1,7,8,5]=>[5,3,7,6,8,2,1,4]=>[1,2,2,1,2]
[7,6,1,3,5,2,4,8]=>[4,6,7,3,5,2,1,8]=>[5,3,2,6,4,7,8,1]=>[1,1,2,3,1]
[6,2,4,5,3,8,1,7]=>[3,5,2,4,1,7,8,6]=>[6,4,7,5,8,2,1,3]=>[1,2,2,1,2]
[6,1,5,4,7,2,3,8]=>[6,4,3,7,2,1,5,8]=>[3,5,6,2,7,8,4,1]=>[3,3,1,1]
[6,8,5,4,7,1,3,2]=>[1,8,6,4,3,7,5,2]=>[8,1,3,5,6,2,4,7]=>[1,4,3]
[1,6,8,4,2,5,7,3]=>[6,4,2,8,5,7,1,3]=>[3,5,7,1,4,2,8,6]=>[3,2,2,1]
[7,5,8,1,3,4,2,6]=>[5,7,4,2,6,1,8,3]=>[4,2,5,7,3,8,1,6]=>[1,3,2,2]
[1,4,2,8,3,5,7,6]=>[2,8,5,6,7,1,3,4]=>[7,1,4,3,2,8,6,5]=>[1,2,1,2,1,1]
[1,3,5,4,8,7,2,6]=>[3,7,8,2,4,6,1,5]=>[6,2,1,7,5,3,8,4]=>[1,1,2,1,2,1]
[1,6,2,4,8,3,7,5]=>[8,4,6,2,7,1,3,5]=>[1,5,3,7,2,8,6,4]=>[2,2,2,1,1]
[1,7,8,5,4,2,6,3]=>[8,6,5,4,2,7,1,3]=>[1,3,4,5,7,2,8,6]=>[5,2,1]
[1,5,2,8,6,4,7,3]=>[2,6,5,8,7,1,3,4]=>[7,3,4,1,2,8,6,5]=>[1,2,3,1,1]
[1,6,5,2,7,4,8,3]=>[6,5,3,2,8,1,4,7]=>[3,4,6,7,1,8,5,2]=>[4,2,1,1]
[5,1,6,7,4,2,8,3]=>[3,1,8,6,5,2,4,7]=>[6,8,1,3,4,7,5,2]=>[2,4,1,1]
[6,8,1,5,2,3,7,4]=>[8,5,6,3,1,4,7,2]=>[1,4,3,6,8,5,2,7]=>[2,3,1,2]
[1,5,4,2,8,6,7,3]=>[3,2,6,8,7,1,4,5]=>[6,7,3,1,2,8,5,4]=>[2,1,3,1,1]
[1,8,5,4,6,2,7,3]=>[4,3,8,6,5,7,1,2]=>[5,6,1,3,4,2,8,7]=>[2,3,2,1]
[1,7,5,4,6,2,8,3]=>[4,3,8,6,5,1,2,7]=>[5,6,1,3,4,8,7,2]=>[2,4,1,1]
[5,8,4,1,6,2,7,3]=>[1,8,6,4,3,5,7,2]=>[8,1,3,5,6,4,2,7]=>[1,4,1,2]
[6,4,5,1,7,2,8,3]=>[2,8,6,4,3,1,5,7]=>[7,1,3,5,6,8,4,2]=>[1,5,1,1]
[4,5,3,1,2,8,7,6]=>[1,3,2,8,7,4,5,6]=>[8,6,7,1,2,5,4,3]=>[1,2,3,1,1]
[6,4,2,3,1,8,7,5]=>[8,3,2,4,1,7,5,6]=>[1,6,7,5,8,2,4,3]=>[3,2,2,1]
[7,6,1,8,2,5,3,4]=>[7,8,5,6,3,2,1,4]=>[2,1,4,3,6,7,8,5]=>[1,2,4,1]
[5,7,8,1,2,4,3,6]=>[7,4,1,5,6,2,8,3]=>[2,5,8,4,3,7,1,6]=>[3,1,2,2]
[1,7,6,8,3,5,4,2]=>[8,5,3,2,7,6,1,4]=>[1,4,6,7,2,3,8,5]=>[4,3,1]
[5,7,6,4,2,1,3,8]=>[1,6,5,7,4,3,2,8]=>[8,3,4,2,5,6,7,1]=>[1,2,4,1]
[6,5,7,4,1,3,2,8]=>[7,5,2,1,6,4,3,8]=>[2,4,7,8,3,5,6,1]=>[4,3,1]
[4,6,1,8,3,5,2,7]=>[1,5,7,6,2,8,3,4]=>[8,4,2,3,7,1,6,5]=>[1,1,3,2,1]
[7,1,6,8,2,5,4,3]=>[8,7,5,3,6,2,1,4]=>[1,2,4,6,3,7,8,5]=>[4,3,1]
[4,7,1,8,3,2,5,6]=>[1,6,5,7,8,3,2,4]=>[8,3,4,2,1,6,7,5]=>[1,2,1,3,1]
[4,8,3,6,1,5,2,7]=>[1,3,7,5,6,4,8,2]=>[8,6,2,4,3,5,1,7]=>[1,1,2,2,2]
[1,7,8,6,4,5,3,2]=>[5,2,8,7,6,4,1,3]=>[4,7,1,2,3,5,8,6]=>[2,5,1]
[3,2,8,6,4,5,1,7]=>[5,7,1,6,2,4,8,3]=>[4,2,8,3,7,5,1,6]=>[1,2,2,1,2]
[8,4,3,6,2,5,1,7]=>[3,2,5,7,6,4,8,1]=>[6,7,4,2,3,5,1,8]=>[2,1,3,2]
[1,6,8,7,4,3,5,2]=>[2,6,5,8,7,4,1,3]=>[7,3,4,1,2,5,8,6]=>[1,2,4,1]
[3,1,2,6,8,7,5,4]=>[8,1,4,7,6,2,3,5]=>[1,8,5,2,3,7,6,4]=>[2,1,3,1,1]
[5,7,4,2,1,8,6,3]=>[1,8,4,3,7,5,2,6]=>[8,1,5,6,2,4,7,3]=>[1,3,3,1]
[8,6,5,7,2,4,3,1]=>[8,5,3,2,7,6,4,1]=>[1,4,6,7,2,3,5,8]=>[4,4]
[7,4,6,1,8,5,3,2]=>[8,2,7,6,4,3,1,5]=>[1,7,2,3,5,6,8,4]=>[2,5,1]
[7,4,6,3,8,1,5,2]=>[2,4,8,6,3,1,7,5]=>[7,5,1,3,6,8,2,4]=>[1,1,4,2]
[7,4,8,3,6,2,1,5]=>[2,4,7,6,1,8,5,3]=>[7,5,2,3,8,1,4,6]=>[1,1,3,3]
[6,4,8,2,3,5,7,1]=>[4,2,5,1,6,8,7,3]=>[5,7,4,8,3,1,2,6]=>[2,2,1,3]
[4,6,8,2,5,7,1,3]=>[7,1,4,2,5,8,6,3]=>[2,8,5,7,4,1,3,6]=>[2,2,1,3]
[6,4,8,2,5,7,1,3]=>[2,7,4,1,5,8,6,3]=>[7,2,5,8,4,1,3,6]=>[1,3,1,3]
[6,2,4,5,8,3,7,1]=>[3,4,6,1,8,2,7,5]=>[6,5,3,8,1,7,2,4]=>[1,1,2,2,2]
[6,8,2,4,7,3,5,1]=>[4,6,1,8,3,7,5,2]=>[5,3,8,1,6,2,4,7]=>[1,2,2,3]
[8,4,6,2,7,1,3,5]=>[4,2,6,7,3,8,5,1]=>[5,7,3,2,6,1,4,8]=>[2,1,2,3]
[6,8,4,2,7,1,3,5]=>[4,6,3,1,7,8,5,2]=>[5,3,6,8,2,1,4,7]=>[1,3,1,3]
[6,8,2,4,1,7,3,5]=>[7,3,4,1,8,5,6,2]=>[2,6,5,8,1,4,3,7]=>[2,2,2,2]
[7,5,1,6,2,4,8,3]=>[6,8,5,3,2,4,1,7]=>[3,1,4,6,7,5,8,2]=>[1,4,2,1]
[2,4,8,5,6,7,3,1]=>[4,5,8,2,7,1,6,3]=>[5,4,1,7,2,8,3,6]=>[1,1,2,2,2]
[4,5,2,3,8,7,1,6]=>[1,7,2,8,3,4,6,5]=>[8,2,7,1,6,5,3,4]=>[1,2,2,1,2]
[2,5,4,7,6,1,3,8]=>[3,2,6,7,1,5,4,8]=>[6,7,3,2,8,4,5,1]=>[2,1,2,2,1]
[5,2,3,7,6,1,4,8]=>[6,7,2,1,3,5,4,8]=>[3,2,7,8,6,4,5,1]=>[1,3,1,2,1]
[4,2,3,7,6,1,5,8]=>[6,1,7,2,3,5,4,8]=>[3,8,2,7,6,4,5,1]=>[2,2,1,2,1]
[4,2,7,3,5,1,6,8]=>[4,1,6,2,5,7,3,8]=>[5,8,3,7,4,2,6,1]=>[2,2,1,2,1]
[5,6,2,3,8,4,7,1]=>[6,1,8,3,2,4,7,5]=>[3,8,1,6,7,5,2,4]=>[2,3,1,2]
[5,6,2,3,1,7,8,4]=>[3,4,1,6,2,8,5,7]=>[6,5,8,3,7,1,4,2]=>[1,2,2,2,1]
[5,7,2,3,4,1,6,8]=>[3,4,1,6,5,7,2,8]=>[6,5,8,3,4,2,7,1]=>[1,2,2,2,1]
[6,2,7,3,5,1,4,8]=>[4,6,7,2,1,5,3,8]=>[5,3,2,7,8,4,6,1]=>[1,1,3,2,1]
[7,2,6,3,5,1,4,8]=>[4,6,7,2,5,3,1,8]=>[5,3,2,7,4,6,8,1]=>[1,1,2,3,1]
[6,5,2,3,1,7,8,4]=>[3,4,6,2,1,8,5,7]=>[6,5,3,7,8,1,4,2]=>[1,1,3,2,1]
[6,5,2,3,8,4,7,1]=>[6,8,3,2,1,4,7,5]=>[3,1,6,7,8,5,2,4]=>[1,4,1,2]
[7,5,2,1,4,6,8,3]=>[3,5,6,2,8,4,1,7]=>[6,4,3,7,1,5,8,2]=>[1,1,2,3,1]
[8,5,2,3,1,6,4,7]=>[3,4,7,5,2,6,8,1]=>[6,5,2,4,7,3,1,8]=>[1,1,3,1,2]
[8,6,2,3,1,5,4,7]=>[3,4,7,5,6,2,8,1]=>[6,5,2,4,3,7,1,8]=>[1,1,2,2,2]
[8,2,6,3,1,7,4,5]=>[4,7,8,2,5,3,6,1]=>[5,2,1,7,4,6,3,8]=>[1,1,2,2,2]
[1,6,3,4,2,7,5,8]=>[3,4,7,5,1,2,6,8]=>[6,5,2,4,8,7,3,1]=>[1,1,3,1,1,1]
[8,5,2,7,3,4,6,1]=>[5,6,2,8,3,7,4,1]=>[4,3,7,1,6,2,5,8]=>[1,2,2,3]
[1,7,2,4,5,6,8,3]=>[4,5,6,8,3,1,2,7]=>[5,4,3,1,6,8,7,2]=>[1,1,1,3,1,1]
[1,8,3,2,5,6,4,7]=>[3,5,7,4,6,8,1,2]=>[6,4,2,5,3,1,8,7]=>[1,1,2,1,2,1]
[7,2,8,1,4,6,3,5]=>[5,7,8,2,4,1,6,3]=>[4,2,1,7,5,8,3,6]=>[1,1,2,2,2]
[2,7,8,1,5,6,3,4]=>[7,5,8,4,1,2,6,3]=>[2,4,1,5,8,7,3,6]=>[2,3,1,2]
[5,8,2,3,1,6,4,7]=>[3,4,1,7,5,6,8,2]=>[6,5,8,2,4,3,1,7]=>[1,2,2,1,2]
[5,7,2,1,4,6,8,3]=>[3,5,1,6,8,4,2,7]=>[6,4,8,3,1,5,7,2]=>[1,2,1,3,1]
[4,2,7,1,5,6,8,3]=>[5,1,6,8,2,4,3,7]=>[4,8,3,1,7,5,6,2]=>[2,1,2,2,1]
[4,2,3,8,1,7,5,6]=>[7,1,8,2,3,5,6,4]=>[2,8,1,7,6,4,3,5]=>[2,2,1,1,2]
[4,2,1,5,3,7,6,8]=>[2,4,1,7,3,5,6,8]=>[7,5,8,2,6,4,3,1]=>[1,2,2,1,1,1]
[5,1,3,8,4,6,7,2]=>[5,6,1,8,3,7,2,4]=>[4,3,8,1,6,2,7,5]=>[1,2,2,2,1]
[5,1,3,2,6,7,8,4]=>[3,5,6,1,8,2,4,7]=>[6,4,3,8,1,7,5,2]=>[1,1,2,2,1,1]
[5,1,3,4,2,7,6,8]=>[3,4,7,2,1,5,6,8]=>[6,5,2,7,8,4,3,1]=>[1,1,3,1,1,1]
[6,1,3,4,2,7,5,8]=>[3,4,7,2,5,1,6,8]=>[6,5,2,7,4,8,3,1]=>[1,1,2,2,1,1]
[7,2,1,3,5,8,4,6]=>[2,5,7,8,3,4,1,6]=>[7,4,2,1,6,5,8,3]=>[1,1,1,2,2,1]
[6,8,7,2,3,4,5,1]=>[4,5,1,6,8,7,3,2]=>[5,4,8,3,1,2,6,7]=>[1,2,1,4]
[10,9,11,8,7,6,5,4,3,2,1]=>[2,1,11,10,9,8,7,6,5,4,3]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,9]
[3,7,2,8,1,4,5,6]=>[1,3,5,6,7,2,8,4]=>[8,6,4,3,2,7,1,5]=>[1,1,1,1,2,2]
[5,2,3,7,4,6,1,8]=>[5,7,2,1,3,6,4,8]=>[4,2,7,8,6,3,5,1]=>[1,3,1,2,1]
[2,6,7,3,4,5,1,8]=>[4,5,2,7,1,6,3,8]=>[5,4,7,2,8,3,6,1]=>[1,2,2,2,1]
[6,2,7,3,4,5,1,8]=>[4,5,7,2,1,6,3,8]=>[5,4,2,7,8,3,6,1]=>[1,1,3,2,1]
[3,8,4,5,2,1,6,7]=>[3,6,1,5,4,7,8,2]=>[6,3,8,4,5,2,1,7]=>[1,2,2,1,2]
[2,7,6,3,4,5,1,8]=>[4,5,7,6,1,3,2,8]=>[5,4,2,3,8,6,7,1]=>[1,1,3,2,1]
[2,8,7,5,1,3,4,6]=>[5,6,7,4,8,1,3,2]=>[4,3,2,5,1,8,6,7]=>[1,1,2,2,2]
[2,1,10,3,4,5,6,7,8,9]=>[1,4,5,6,7,8,9,10,2,3]=>[10,7,6,5,4,3,2,1,9,8]=>[1,1,1,1,1,1,1,2,1]
[4,5,7,2,8,3,6,1]=>[1,2,6,8,4,3,7,5]=>[8,7,3,1,5,6,2,4]=>[1,1,1,3,2]
[5,2,1,3,6,7,8,4]=>[2,5,6,1,8,3,4,7]=>[7,4,3,8,1,6,5,2]=>[1,1,2,2,1,1]
[7,5,2,6,1,8,4,3]=>[8,7,3,2,5,4,1,6]=>[1,2,6,7,4,5,8,3]=>[4,3,1]
[6,1,5,2,7,8,4,3]=>[5,3,8,7,2,1,4,6]=>[4,6,1,2,7,8,5,3]=>[2,4,1,1]
[1,6,5,7,2,8,4,3]=>[3,2,8,7,5,1,4,6]=>[6,7,1,2,4,8,5,3]=>[2,4,1,1]
[1,5,4,6,2,8,3,7]=>[3,2,7,4,8,1,5,6]=>[6,7,2,5,1,8,4,3]=>[2,2,2,1,1]
[6,2,1,5,8,4,7,3]=>[4,6,8,2,1,7,3,5]=>[5,3,1,7,8,2,6,4]=>[1,1,3,2,1]
[7,5,6,8,4,1,3,2]=>[2,8,6,3,1,7,5,4]=>[7,1,3,6,8,2,4,5]=>[1,4,3]
[8,3,7,5,1,4,2,6]=>[7,2,5,6,4,8,3,1]=>[2,7,4,3,5,1,6,8]=>[2,1,2,3]
[8,1,5,7,3,6,2,4]=>[5,3,7,8,6,2,4,1]=>[4,6,2,1,3,7,5,8]=>[2,1,3,2]
[8,3,2,6,4,5,1,7]=>[2,5,7,3,6,4,8,1]=>[7,4,2,6,3,5,1,8]=>[1,1,2,2,2]
[8,5,6,2,7,1,3,4]=>[4,6,2,7,3,8,5,1]=>[5,3,7,2,6,1,4,8]=>[1,2,2,3]
[8,1,2,3,6,4,7,5]=>[8,6,2,3,4,5,7,1]=>[1,3,7,6,5,4,2,8]=>[3,1,1,1,2]
[7,6,2,3,5,8,1,4]=>[7,3,4,5,2,1,8,6]=>[2,6,5,4,7,8,1,3]=>[2,1,3,2]
[4,5,3,7,8,1,6,2]=>[1,2,8,3,6,4,7,5]=>[8,7,1,6,3,5,2,4]=>[1,1,2,2,2]
[3,4,2,8,1,6,7,5]=>[1,2,6,8,3,5,7,4]=>[8,7,3,1,6,4,2,5]=>[1,1,1,2,1,2]
[8,3,4,1,5,7,6,2]=>[2,3,8,5,7,4,6,1]=>[7,6,1,4,2,5,3,8]=>[1,1,2,2,2]
[4,3,7,5,1,6,2,8]=>[1,7,2,5,4,6,3,8]=>[8,2,7,4,5,3,6,1]=>[1,2,2,2,1]
[5,2,6,1,4,3,7,8]=>[6,2,4,1,5,3,7,8]=>[3,7,5,8,4,6,2,1]=>[2,2,2,1,1]
[3,5,2,8,6,7,4,1]=>[2,5,8,1,7,3,6,4]=>[7,4,1,8,2,6,3,5]=>[1,1,2,2,2]
[5,3,7,4,2,8,6,1]=>[4,1,8,2,5,3,7,6]=>[5,8,1,7,4,6,2,3]=>[2,2,2,2]
[7,4,8,2,3,5,6,1]=>[4,2,5,6,1,8,7,3]=>[5,7,4,3,8,1,2,6]=>[2,1,2,3]
[5,6,2,8,7,1,4,3]=>[1,8,6,2,7,3,5,4]=>[8,1,3,7,2,6,4,5]=>[1,3,2,2]
[4,6,3,5,2,7,8,1]=>[1,3,5,4,2,6,8,7]=>[8,6,4,5,7,3,1,2]=>[1,1,3,1,2]
[4,1,6,3,5,7,2,8]=>[4,1,5,3,7,2,6,8]=>[5,8,4,6,2,7,3,1]=>[2,2,2,1,1]
[7,2,5,8,6,1,4,3]=>[3,8,6,7,2,1,5,4]=>[6,1,3,2,7,8,4,5]=>[1,2,3,2]
[4,3,6,1,5,7,8,2]=>[2,1,5,6,3,8,4,7]=>[7,8,4,3,6,1,5,2]=>[2,1,2,2,1]
[3,5,4,1,2,6,7,8]=>[1,4,5,3,2,6,7,8]=>[8,5,4,6,7,3,2,1]=>[1,1,3,1,1,1]
[5,3,1,4,6,7,8,2]=>[4,2,5,1,6,8,3,7]=>[5,7,4,8,3,1,6,2]=>[2,2,1,2,1]
[4,6,7,1,3,5,8,2]=>[1,5,6,2,8,4,3,7]=>[8,4,3,7,1,5,6,2]=>[1,1,2,3,1]
[5,6,1,3,4,7,2,8]=>[4,5,1,7,3,2,6,8]=>[5,4,8,2,6,7,3,1]=>[1,2,3,1,1]
[2,5,3,7,8,4,6,1]=>[2,6,4,8,1,3,7,5]=>[7,3,5,1,8,6,2,4]=>[1,2,2,1,2]
[4,6,2,1,3,7,8,5]=>[3,1,6,8,4,2,5,7]=>[6,8,3,1,5,7,4,2]=>[2,1,3,1,1]
[3,2,6,7,4,8,5,1]=>[3,8,1,5,2,4,7,6]=>[6,1,8,4,7,5,2,3]=>[1,2,2,1,2]
[7,1,3,8,4,5,2,6]=>[5,7,3,6,8,2,1,4]=>[4,2,6,3,1,7,8,5]=>[1,2,1,3,1]
[7,1,8,3,4,6,2,5]=>[4,5,7,8,6,2,1,3]=>[5,4,2,1,3,7,8,6]=>[1,1,1,4,1]
[6,3,2,7,5,8,4,1]=>[5,2,4,1,8,3,7,6]=>[4,7,5,8,1,6,2,3]=>[2,2,2,2]
[6,2,7,1,4,5,3,8]=>[5,7,2,4,1,6,3,8]=>[4,2,7,5,8,3,6,1]=>[1,2,2,2,1]
[2,5,4,1,3,6,7,8]=>[4,5,1,3,2,6,7,8]=>[5,4,8,6,7,3,2,1]=>[1,2,2,1,1,1]
[5,4,1,2,6,7,3,8]=>[5,7,3,2,1,4,6,8]=>[4,2,6,7,8,5,3,1]=>[1,4,1,1,1]
[6,5,2,7,4,1,3,8]=>[6,7,3,2,1,5,4,8]=>[3,2,6,7,8,4,5,1]=>[1,4,2,1]
[7,4,5,6,2,1,8,3]=>[2,5,3,8,6,4,1,7]=>[7,4,6,1,3,5,8,2]=>[1,2,4,1]
[6,4,5,2,7,1,8,3]=>[2,8,4,3,1,6,5,7]=>[7,1,5,6,8,3,4,2]=>[1,4,2,1]
[3,7,5,6,2,1,8,4]=>[5,3,8,1,6,4,2,7]=>[4,6,1,8,3,5,7,2]=>[2,2,3,1]
[1,7,6,3,8,4,5,2]=>[6,8,4,3,2,7,1,5]=>[3,1,5,6,7,2,8,4]=>[1,4,2,1]
[6,4,1,3,5,2,7,8]=>[4,6,3,2,5,1,7,8]=>[5,3,6,7,4,8,2,1]=>[1,3,2,1,1]
[5,1,8,3,4,6,2,7]=>[4,5,1,7,6,8,2,3]=>[5,4,8,2,3,1,7,6]=>[1,2,2,2,1]
[4,5,8,2,3,7,1,6]=>[1,4,2,5,7,8,6,3]=>[8,5,7,4,2,1,3,6]=>[1,2,1,1,3]
[7,3,4,8,2,5,1,6]=>[2,3,5,7,6,1,8,4]=>[7,6,4,2,3,8,1,5]=>[1,1,1,3,2]
[4,7,2,5,1,6,8,3]=>[1,6,3,4,8,5,2,7]=>[8,3,6,5,1,4,7,2]=>[1,2,1,3,1]
[6,5,4,7,2,8,3,1]=>[3,2,1,8,5,4,7,6]=>[6,7,8,1,4,5,2,3]=>[3,3,2]
[3,2,4,6,5,8,1,7]=>[1,5,2,3,4,7,8,6]=>[8,4,7,6,5,2,1,3]=>[1,2,1,1,1,2]
[3,5,4,8,7,1,6,2]=>[2,8,1,3,6,7,5,4]=>[7,1,8,6,3,2,4,5]=>[1,2,1,1,3]
[7,5,2,1,6,3,4,8]=>[3,6,7,4,2,5,1,8]=>[6,3,2,5,7,4,8,1]=>[1,1,3,2,1]
[6,3,1,7,4,2,5,8]=>[2,6,5,7,3,1,4,8]=>[7,3,4,2,6,8,5,1]=>[1,2,3,1,1]
[8,7,2,1,5,3,6,4]=>[8,3,6,4,5,7,2,1]=>[1,6,3,5,4,2,7,8]=>[2,2,1,3]
[7,2,8,1,5,6,4,3]=>[5,8,7,2,4,1,6,3]=>[4,1,2,7,5,8,3,6]=>[1,3,2,2]
[8,3,6,4,1,5,7,2]=>[6,2,4,8,5,3,7,1]=>[3,7,5,1,4,6,2,8]=>[2,1,3,2]
[7,5,6,1,4,8,2,3]=>[7,5,2,8,4,3,1,6]=>[2,4,7,1,5,6,8,3]=>[3,4,1]
[5,7,2,6,3,8,4,1]=>[1,8,5,3,4,2,7,6]=>[8,1,4,6,5,7,2,3]=>[1,3,2,2]
[6,8,1,3,2,7,5,4]=>[8,4,7,3,1,5,6,2]=>[1,5,2,6,8,4,3,7]=>[2,3,1,2]
[5,7,3,6,4,1,2,8]=>[3,1,6,7,5,4,2,8]=>[6,8,3,2,4,5,7,1]=>[2,1,4,1]
[7,2,4,3,8,1,5,6]=>[4,2,3,6,7,1,8,5]=>[5,7,6,3,2,8,1,4]=>[2,1,1,2,2]
[2,5,4,6,1,3,8,7]=>[3,2,8,1,5,4,6,7]=>[6,7,1,8,4,5,3,2]=>[2,2,2,1,1]
[2,4,3,5,8,1,6,7]=>[3,1,2,4,6,7,8,5]=>[6,8,7,5,3,2,1,4]=>[2,1,1,1,1,2]
[5,8,2,6,7,4,3,1]=>[1,4,8,7,3,6,5,2]=>[8,5,1,2,6,3,4,7]=>[1,1,3,3]
[2,6,5,3,8,1,4,7]=>[4,6,3,1,2,7,8,5]=>[5,3,6,8,7,2,1,4]=>[1,3,1,1,2]
[6,1,2,4,3,5,7,8]=>[5,2,3,4,6,1,7,8]=>[4,7,6,5,3,8,2,1]=>[2,1,1,2,1,1]
[6,5,8,2,7,3,4,1]=>[6,2,1,8,4,7,5,3]=>[3,7,8,1,5,2,4,6]=>[3,2,3]
[1,7,6,8,4,3,2,5]=>[7,6,5,3,2,8,1,4]=>[2,3,4,6,7,1,8,5]=>[5,2,1]
[1,7,6,5,3,8,2,4]=>[5,7,4,3,2,8,1,6]=>[4,2,5,6,7,1,8,3]=>[1,4,2,1]
[4,6,1,3,7,8,5,2]=>[1,5,8,4,2,7,3,6]=>[8,4,1,5,7,2,6,3]=>[1,1,3,2,1]
[8,4,1,5,2,6,7,3]=>[6,4,2,8,3,5,7,1]=>[3,5,7,1,6,4,2,8]=>[3,2,1,2]
[1,5,6,3,8,7,2,4]=>[2,7,3,8,4,6,1,5]=>[7,2,6,1,5,3,8,4]=>[1,2,2,2,1]
[5,3,2,6,8,7,1,4]=>[2,4,1,7,8,3,6,5]=>[7,5,8,2,1,6,3,4]=>[1,2,1,2,2]
[6,3,5,2,7,1,4,8]=>[2,4,6,3,1,7,5,8]=>[7,5,3,6,8,2,4,1]=>[1,1,3,2,1]
[8,5,2,6,7,1,4,3]=>[8,6,3,2,4,7,5,1]=>[1,3,6,7,5,2,4,8]=>[4,1,3]
[5,3,8,7,1,4,2,6]=>[7,2,1,5,6,8,4,3]=>[2,7,8,4,3,1,5,6]=>[3,1,1,3]
[6,4,5,3,1,8,7,2]=>[2,4,3,1,8,7,5,6]=>[7,5,6,8,1,2,4,3]=>[1,3,3,1]
[8,5,1,2,3,6,7,4]=>[6,8,3,4,2,5,7,1]=>[3,1,6,5,7,4,2,8]=>[1,2,2,1,2]
[2,8,6,1,5,4,7,3]=>[6,5,8,4,1,3,7,2]=>[3,4,1,5,8,6,2,7]=>[2,3,1,2]
[8,3,2,6,1,5,7,4]=>[2,6,8,3,5,4,7,1]=>[7,3,1,6,4,5,2,8]=>[1,1,2,2,2]
[3,8,6,4,7,1,2,5]=>[6,4,7,1,3,8,5,2]=>[3,5,2,8,6,1,4,7]=>[2,2,1,3]
[1,8,7,5,4,3,2,6]=>[7,6,5,4,8,3,1,2]=>[2,3,4,5,1,6,8,7]=>[4,3,1]
[5,3,4,1,6,2,7,8]=>[2,6,4,3,1,5,7,8]=>[7,3,5,6,8,4,2,1]=>[1,4,1,1,1]
[2,7,1,4,6,3,5,8]=>[4,6,7,1,3,5,2,8]=>[5,3,2,8,6,4,7,1]=>[1,1,2,1,2,1]
[7,1,5,2,4,6,3,8]=>[5,7,4,2,3,6,1,8]=>[4,2,5,7,6,3,8,1]=>[1,3,1,2,1]
[6,1,4,5,2,7,3,8]=>[3,7,5,2,4,1,6,8]=>[6,2,4,7,5,8,3,1]=>[1,3,2,1,1]
[6,1,5,8,2,7,4,3]=>[3,8,7,5,1,6,2,4]=>[6,1,2,4,8,3,7,5]=>[1,4,2,1]
[7,1,2,3,6,4,5,8]=>[6,7,2,3,4,5,1,8]=>[3,2,7,6,5,4,8,1]=>[1,2,1,1,2,1]
[6,3,1,8,5,4,7,2]=>[6,2,5,1,8,7,3,4]=>[3,7,4,8,1,2,6,5]=>[2,2,3,1]
[6,1,3,8,7,4,5,2]=>[6,8,7,3,1,5,2,4]=>[3,1,2,6,8,4,7,5]=>[1,4,2,1]
[2,8,4,6,5,1,7,3]=>[8,3,6,5,1,4,7,2]=>[1,6,3,4,8,5,2,7]=>[2,3,1,2]
[5,7,2,8,1,3,6,4]=>[8,3,1,5,6,2,7,4]=>[1,6,8,4,3,7,2,5]=>[3,1,2,2]
[5,4,1,2,6,3,8,7]=>[5,8,3,2,1,4,6,7]=>[4,1,6,7,8,5,3,2]=>[1,4,1,1,1]
[6,5,1,4,7,3,2,8]=>[4,7,6,3,2,1,5,8]=>[5,2,3,6,7,8,4,1]=>[1,5,1,1]
[2,7,8,4,1,3,6,5]=>[8,5,4,6,1,2,7,3]=>[1,4,5,3,8,7,2,6]=>[3,2,1,2]
[2,4,6,5,7,8,1,3]=>[4,2,3,7,1,5,8,6]=>[5,7,6,2,8,4,1,3]=>[2,1,2,1,2]
[2,4,6,7,5,8,1,3]=>[3,7,2,5,1,4,8,6]=>[6,2,7,4,8,5,1,3]=>[1,2,2,1,2]
[2,4,5,6,8,7,1,3]=>[2,3,4,7,8,1,6,5]=>[7,6,5,2,1,8,3,4]=>[1,1,1,1,2,2]
[2,4,5,6,8,3,7,1]=>[2,3,4,6,8,1,7,5]=>[7,6,5,3,1,8,2,4]=>[1,1,1,1,2,2]
[2,4,5,6,3,8,1,7]=>[2,3,5,1,4,7,8,6]=>[7,6,4,8,5,2,1,3]=>[1,1,2,1,1,2]
[2,3,4,6,8,5,1,7]=>[4,7,1,2,3,6,8,5]=>[5,2,8,7,6,3,1,4]=>[1,2,1,1,1,2]
[5,2,8,3,4,1,6,7]=>[4,6,2,1,5,7,8,3]=>[5,3,7,8,4,2,1,6]=>[1,3,1,1,2]
[3,6,4,1,2,7,8,5]=>[6,1,3,8,4,2,5,7]=>[3,8,6,1,5,7,4,2]=>[2,1,3,1,1]
[4,1,7,3,8,6,2,5]=>[1,7,8,4,3,6,2,5]=>[8,2,1,5,6,3,7,4]=>[1,1,3,2,1]
[8,4,1,2,5,3,7,6]=>[5,8,3,2,4,6,7,1]=>[4,1,6,7,5,3,2,8]=>[1,3,1,1,2]
[1,5,2,7,6,8,4,3]=>[2,5,4,8,7,1,3,6]=>[7,4,5,1,2,8,6,3]=>[1,2,3,1,1]
[4,8,2,7,6,5,1,3]=>[7,8,1,6,3,5,4,2]=>[2,1,8,3,6,4,5,7]=>[1,2,2,3]
[7,4,2,8,6,5,1,3]=>[2,7,8,6,3,1,5,4]=>[7,2,1,3,6,8,4,5]=>[1,1,4,2]
[6,5,8,2,7,1,4,3]=>[8,4,2,1,6,7,5,3]=>[1,5,7,8,3,2,4,6]=>[4,1,3]
[7,5,8,2,1,6,4,3]=>[8,4,2,7,5,1,6,3]=>[1,5,7,2,4,8,3,6]=>[3,3,2]
[3,2,1,6,5,8,4,7]=>[1,5,2,4,7,8,3,6]=>[8,4,7,5,2,1,6,3]=>[1,2,1,1,2,1]
[2,6,4,8,5,7,3,1]=>[5,2,8,3,7,1,6,4]=>[4,7,1,6,2,8,3,5]=>[2,2,2,2]
[3,4,8,5,2,1,7,6]=>[5,1,2,4,8,6,7,3]=>[4,8,7,5,1,3,2,6]=>[2,1,1,2,2]
[4,8,7,1,3,2,6,5]=>[1,5,8,4,6,7,3,2]=>[8,4,1,5,3,2,6,7]=>[1,1,2,1,3]
[3,4,1,8,7,6,2,5]=>[7,8,1,2,6,5,3,4]=>[2,1,8,7,3,4,6,5]=>[1,2,1,3,1]
[1,3,5,6,8,7,2,4]=>[3,4,7,8,2,6,1,5]=>[6,5,2,1,7,3,8,4]=>[1,1,1,2,2,1]
[2,8,7,5,4,1,6,3]=>[8,6,5,4,7,1,3,2]=>[1,3,4,5,2,8,6,7]=>[4,2,2]
[8,1,5,7,4,2,6,3]=>[3,8,6,5,7,2,4,1]=>[6,1,3,4,2,7,5,8]=>[1,3,2,2]
[5,8,7,3,4,1,6,2]=>[1,4,8,6,5,7,3,2]=>[8,5,1,3,4,2,6,7]=>[1,1,3,3]
[4,6,1,3,2,8,5,7]=>[4,1,7,8,3,2,5,6]=>[5,8,2,1,6,7,4,3]=>[2,1,3,1,1]
[2,6,5,8,3,1,4,7]=>[6,5,3,1,2,7,8,4]=>[3,4,6,8,7,2,1,5]=>[4,1,1,2]
[6,7,8,2,4,5,3,1]=>[5,1,8,4,2,7,6,3]=>[4,8,1,5,7,2,3,6]=>[2,3,3]
[3,2,8,4,5,7,1,6]=>[1,4,5,7,8,2,6,3]=>[8,5,4,2,1,7,3,6]=>[1,1,1,1,2,2]
[6,1,8,2,4,5,3,7]=>[5,7,4,6,1,8,2,3]=>[4,2,5,3,8,1,7,6]=>[1,2,2,2,1]
[8,3,6,4,2,7,1,5]=>[5,2,4,7,3,8,6,1]=>[4,7,5,2,6,1,3,8]=>[2,1,2,3]
[1,3,8,4,7,6,2,5]=>[7,8,4,6,2,5,1,3]=>[2,1,5,3,7,4,8,6]=>[1,2,2,2,1]
[8,3,7,5,4,1,2,6]=>[6,7,2,5,4,8,3,1]=>[3,2,7,4,5,1,6,8]=>[1,2,2,3]
[2,6,4,7,8,5,1,3]=>[7,3,2,4,8,1,6,5]=>[2,6,7,5,1,8,3,4]=>[3,1,2,2]
[5,4,3,7,6,1,8,2]=>[2,1,8,3,6,5,4,7]=>[7,8,1,6,3,4,5,2]=>[2,2,3,1]
[3,1,2,8,7,6,4,5]=>[7,8,1,6,5,2,3,4]=>[2,1,8,3,4,7,6,5]=>[1,2,3,1,1]
[8,5,4,1,2,3,7,6]=>[8,4,5,3,2,6,7,1]=>[1,5,4,6,7,3,2,8]=>[2,3,1,2]
[8,3,2,1,6,4,7,5]=>[2,8,3,6,4,5,7,1]=>[7,1,6,3,5,4,2,8]=>[1,2,2,1,2]
[2,3,8,4,1,7,5,6]=>[4,7,8,1,2,5,6,3]=>[5,2,1,8,7,4,3,6]=>[1,1,2,1,1,2]
[4,6,1,3,2,7,8,5]=>[4,1,6,8,3,2,5,7]=>[5,8,3,1,6,7,4,2]=>[2,1,3,1,1]
[6,7,2,5,8,4,1,3]=>[7,4,1,8,3,2,6,5]=>[2,5,8,1,6,7,3,4]=>[3,3,2]
[4,1,7,8,2,5,6,3]=>[1,6,8,5,3,7,2,4]=>[8,3,1,4,6,2,7,5]=>[1,1,3,2,1]
[3,4,6,7,1,5,8,2]=>[6,1,2,3,8,5,4,7]=>[3,8,7,6,1,4,5,2]=>[2,1,1,3,1]
[3,4,5,7,8,1,6,2]=>[8,1,2,3,6,4,7,5]=>[1,8,7,6,3,5,2,4]=>[2,1,1,2,2]
[1,8,7,4,3,5,2,6]=>[5,4,7,6,8,3,1,2]=>[4,5,2,3,1,6,8,7]=>[2,2,3,1]
[2,4,5,8,1,3,7,6]=>[2,3,8,1,5,6,7,4]=>[7,6,1,8,4,3,2,5]=>[1,1,2,1,1,2]
[2,7,8,6,5,3,1,4]=>[7,6,2,8,5,1,4,3]=>[2,3,7,1,4,8,5,6]=>[3,3,2]
[6,3,1,5,8,4,2,7]=>[2,4,7,6,1,8,3,5]=>[7,5,2,3,8,1,6,4]=>[1,1,3,2,1]
[2,8,3,5,6,1,4,7]=>[6,3,4,7,1,5,8,2]=>[3,6,5,2,8,4,1,7]=>[2,1,2,1,2]
[1,3,6,4,2,7,5,8]=>[4,7,2,5,1,3,6,8]=>[5,2,7,4,8,6,3,1]=>[1,2,2,1,1,1]
[3,2,8,5,6,1,4,7]=>[6,1,4,7,2,5,8,3]=>[3,8,5,2,7,4,1,6]=>[2,1,2,1,2]
[7,2,5,8,1,4,6,3]=>[6,3,8,2,5,1,7,4]=>[3,6,1,7,4,8,2,5]=>[2,2,2,2]
[4,7,5,8,1,2,6,3]=>[8,1,5,3,6,2,7,4]=>[1,8,4,6,3,7,2,5]=>[2,2,2,2]
[4,3,2,5,7,8,1,6]=>[2,1,7,3,4,5,8,6]=>[7,8,2,6,5,4,1,3]=>[2,2,1,1,2]
[2,4,7,5,8,3,1,6]=>[4,7,2,6,1,3,8,5]=>[5,2,7,3,8,6,1,4]=>[1,2,2,1,2]
[2,5,4,7,3,8,1,6]=>[3,2,5,7,1,4,8,6]=>[6,7,4,2,8,5,1,3]=>[2,1,2,1,2]
[3,7,8,4,2,1,6,5]=>[5,4,8,1,6,2,7,3]=>[4,5,1,8,3,7,2,6]=>[2,2,2,2]
[8,5,4,7,6,3,1,2]=>[3,2,7,8,6,5,4,1]=>[6,7,2,1,3,4,5,8]=>[2,1,5]
[1,5,4,8,7,6,2,3]=>[2,7,8,3,6,5,1,4]=>[7,2,1,6,3,4,8,5]=>[1,1,2,3,1]
[3,2,4,5,8,1,6,7]=>[2,1,3,4,6,7,8,5]=>[7,8,6,5,3,2,1,4]=>[2,1,1,1,1,2]
[4,8,3,7,6,2,1,5]=>[7,1,3,6,8,5,4,2]=>[2,8,6,3,1,4,5,7]=>[2,1,1,4]
[1,4,7,6,3,8,2,5]=>[5,7,2,4,3,8,1,6]=>[4,2,7,5,6,1,8,3]=>[1,2,2,2,1]
[3,6,5,1,7,2,8,4]=>[8,6,1,4,3,2,5,7]=>[1,3,8,5,6,7,4,2]=>[3,3,1,1]
[7,4,1,6,2,8,5,3]=>[2,8,7,5,3,4,1,6]=>[7,1,2,4,6,5,8,3]=>[1,4,2,1]
[1,3,6,8,2,4,7,5]=>[8,5,2,3,6,7,1,4]=>[1,4,7,6,3,2,8,5]=>[3,1,1,2,1]
[1,6,7,4,3,8,2,5]=>[5,4,2,7,3,8,1,6]=>[4,5,7,2,6,1,8,3]=>[3,2,2,1]
[7,3,1,6,5,2,8,4]=>[8,2,6,5,3,4,1,7]=>[1,7,3,4,6,5,8,2]=>[2,3,2,1]
[8,5,4,1,6,2,7,3]=>[8,6,4,3,2,5,7,1]=>[1,3,5,6,7,4,2,8]=>[5,1,2]
[4,7,2,8,5,1,6,3]=>[8,1,6,3,5,2,7,4]=>[1,8,3,6,4,7,2,5]=>[2,2,2,2]
[7,8,6,2,1,5,4,3]=>[8,4,7,5,1,6,3,2]=>[1,5,2,4,8,3,6,7]=>[2,3,3]
[8,6,2,7,3,5,1,4]=>[5,7,8,3,2,6,4,1]=>[4,2,1,6,7,3,5,8]=>[1,1,3,3]
[2,1,3,8,7,5,6,4]=>[6,8,7,1,5,2,3,4]=>[3,1,2,8,4,7,6,5]=>[1,3,2,1,1]
[1,6,4,7,3,8,5,2]=>[8,3,2,5,4,7,1,6]=>[1,6,7,4,5,2,8,3]=>[3,2,2,1]
[4,8,1,6,3,7,2,5]=>[1,5,7,4,8,3,6,2]=>[8,4,2,5,1,6,3,7]=>[1,1,2,2,2]
[8,5,4,1,6,3,7,2]=>[6,5,3,2,8,4,7,1]=>[3,4,6,7,1,5,2,8]=>[4,2,2]
[1,7,6,2,4,8,5,3]=>[8,5,7,4,3,1,2,6]=>[1,4,2,5,6,8,7,3]=>[2,4,1,1]
[5,7,3,2,4,8,6,1]=>[3,1,8,4,5,2,7,6]=>[6,8,1,5,4,7,2,3]=>[2,2,2,2]
[2,6,8,5,4,3,1,7]=>[2,7,6,5,1,4,8,3]=>[7,2,3,4,8,5,1,6]=>[1,4,1,2]
[2,8,4,6,3,5,1,7]=>[3,5,7,6,1,4,8,2]=>[6,4,2,3,8,5,1,7]=>[1,1,3,1,2]
[2,7,8,3,6,4,5,1]=>[6,8,4,2,7,1,5,3]=>[3,1,5,7,2,8,4,6]=>[1,3,2,2]
[3,8,1,4,6,5,2,7]=>[7,1,4,6,3,5,8,2]=>[2,8,5,3,6,4,1,7]=>[2,1,2,1,2]
[2,7,5,4,1,8,3,6]=>[7,4,3,8,1,5,2,6]=>[2,5,6,1,8,4,7,3]=>[3,2,2,1]
[4,6,1,8,5,3,2,7]=>[7,1,6,5,2,8,3,4]=>[2,8,3,4,7,1,6,5]=>[2,3,2,1]
[3,8,5,2,1,6,4,7]=>[4,7,1,5,3,6,8,2]=>[5,2,8,4,6,3,1,7]=>[1,2,2,1,2]
[5,1,4,8,2,6,3,7]=>[3,7,5,1,6,8,2,4]=>[6,2,4,8,3,1,7,5]=>[1,3,1,2,1]
[4,5,8,1,3,7,6,2]=>[1,2,8,5,7,4,6,3]=>[8,7,1,4,2,5,3,6]=>[1,1,2,2,2]
[1,4,7,8,6,3,5,2]=>[6,3,8,2,7,5,1,4]=>[3,6,1,7,2,4,8,5]=>[2,2,3,1]
[8,5,2,6,3,4,7,1]=>[5,6,3,2,4,8,7,1]=>[4,3,6,7,5,1,2,8]=>[1,3,1,3]
[8,3,6,1,2,7,4,5]=>[2,7,8,4,5,3,6,1]=>[7,2,1,5,4,6,3,8]=>[1,1,2,2,2]
[3,8,6,1,2,5,7,4]=>[6,8,1,4,5,3,7,2]=>[3,1,8,5,4,6,2,7]=>[1,2,1,2,2]
[3,7,6,2,1,8,5,4]=>[8,4,7,1,5,3,2,6]=>[1,5,2,8,4,6,7,3]=>[2,2,3,1]
[4,3,7,6,1,8,5,2]=>[8,1,7,2,5,4,3,6]=>[1,8,2,7,4,5,6,3]=>[2,2,3,1]
[8,6,3,2,7,1,5,4]=>[3,8,4,6,2,7,5,1]=>[6,1,5,3,7,2,4,8]=>[1,2,2,3]
[6,8,1,5,4,7,2,3]=>[7,5,4,1,8,3,6,2]=>[2,4,5,8,1,6,3,7]=>[4,2,2]
[6,7,2,5,4,8,1,3]=>[7,5,3,1,4,2,8,6]=>[2,4,6,8,5,7,1,3]=>[4,2,2]
[7,6,2,4,8,5,1,3]=>[4,7,8,3,2,1,6,5]=>[5,2,1,6,7,8,3,4]=>[1,1,4,2]
[4,6,8,7,3,1,2,5]=>[6,1,2,7,5,8,4,3]=>[3,8,7,2,4,1,5,6]=>[2,1,2,3]
[4,7,5,2,6,3,8,1]=>[6,1,4,3,5,2,8,7]=>[3,8,5,6,4,7,1,2]=>[2,2,2,2]
[3,5,6,2,8,1,4,7]=>[4,1,2,6,3,7,8,5]=>[5,8,7,3,6,2,1,4]=>[2,1,2,1,2]
[5,1,2,4,3,7,6,8]=>[4,7,2,3,1,5,6,8]=>[5,2,7,6,8,4,3,1]=>[1,2,2,1,1,1]
[6,1,8,2,4,3,5,7]=>[6,4,5,7,1,8,2,3]=>[3,5,4,2,8,1,7,6]=>[2,1,2,2,1]
[1,6,8,2,5,3,4,7]=>[6,7,4,2,5,8,1,3]=>[3,2,5,7,4,1,8,6]=>[1,3,1,2,1]
[8,5,2,7,3,6,4,1]=>[8,5,2,7,3,6,4,1]=>[1,4,7,2,6,3,5,8]=>[3,2,3]
[8,7,6,2,4,5,1,3]=>[7,4,5,8,6,3,2,1]=>[2,5,4,1,3,6,7,8]=>[2,1,5]
[8,7,6,2,4,5,3,1]=>[5,8,4,7,6,3,2,1]=>[4,1,5,2,3,6,7,8]=>[1,2,5]
[5,4,8,7,1,2,6,3]=>[2,1,8,5,6,7,4,3]=>[7,8,1,4,3,2,5,6]=>[2,2,1,3]
[2,5,6,4,3,8,1,7]=>[2,5,4,1,3,7,8,6]=>[7,4,5,8,6,2,1,3]=>[1,3,1,1,2]
[8,6,3,5,2,1,4,7]=>[3,6,5,7,4,2,8,1]=>[6,3,4,2,5,7,1,8]=>[1,2,3,2]
[8,7,3,5,2,4,6,1]=>[3,5,6,4,8,7,2,1]=>[6,4,3,5,1,2,7,8]=>[1,1,2,4]
[8,4,2,7,6,5,1,3]=>[2,7,8,6,3,5,4,1]=>[7,2,1,3,6,4,5,8]=>[1,1,3,3]
[4,1,3,8,5,6,2,7]=>[5,1,7,3,6,8,2,4]=>[4,8,2,6,3,1,7,5]=>[2,2,1,2,1]
[5,2,8,3,1,6,7,4]=>[4,6,1,8,2,5,7,3]=>[5,3,8,1,7,4,2,6]=>[1,2,2,1,2]
[1,7,8,6,3,2,5,4]=>[5,8,6,2,7,4,1,3]=>[4,1,3,7,2,5,8,6]=>[1,3,3,1]
[3,7,2,4,5,6,1,8]=>[1,3,4,5,7,6,2,8]=>[8,6,5,4,2,3,7,1]=>[1,1,1,1,3,1]
[3,2,8,1,5,7,4,6]=>[1,5,7,8,2,4,6,3]=>[8,4,2,1,7,5,3,6]=>[1,1,1,2,1,2]
[3,4,6,7,2,1,5,8]=>[6,1,2,5,3,7,4,8]=>[3,8,7,4,6,2,5,1]=>[2,1,2,2,1]
[5,7,6,2,1,8,3,4]=>[4,1,7,8,5,3,2,6]=>[5,8,2,1,4,6,7,3]=>[2,1,4,1]
[4,2,5,3,8,6,7,1]=>[3,1,6,8,2,4,7,5]=>[6,8,3,1,7,5,2,4]=>[2,1,2,1,2]
[3,2,7,4,8,5,6,1]=>[6,8,1,4,2,3,7,5]=>[3,1,8,5,7,6,2,4]=>[1,2,2,1,2]
[6,3,8,5,4,2,7,1]=>[6,5,2,1,4,8,7,3]=>[3,4,7,8,5,1,2,6]=>[4,1,3]
[1,5,3,8,7,4,6,2]=>[2,6,8,7,3,5,1,4]=>[7,3,1,2,6,4,8,5]=>[1,1,3,2,1]
[5,1,3,8,7,4,6,2]=>[6,1,8,7,3,5,2,4]=>[3,8,1,2,6,4,7,5]=>[2,3,2,1]
[2,5,3,8,7,4,1,6]=>[2,7,6,8,1,3,5,4]=>[7,2,3,1,8,6,4,5]=>[1,2,2,1,2]
[6,8,3,5,1,2,7,4]=>[3,8,5,1,6,4,7,2]=>[6,1,4,8,3,5,2,7]=>[1,3,2,2]
[5,8,2,7,4,6,3,1]=>[1,5,8,7,3,6,4,2]=>[8,4,1,2,6,3,5,7]=>[1,1,3,3]
[4,5,2,8,3,7,1,6]=>[1,5,2,7,8,3,6,4]=>[8,4,7,2,1,6,3,5]=>[1,2,1,2,2]
[7,8,5,1,6,4,3,2]=>[8,7,6,4,3,1,5,2]=>[1,2,3,5,6,8,4,7]=>[6,2]
[8,7,5,1,6,4,3,2]=>[8,7,6,4,3,5,2,1]=>[1,2,3,5,6,4,7,8]=>[5,3]
[4,5,8,3,1,2,7,6]=>[1,2,8,5,4,6,7,3]=>[8,7,1,4,5,3,2,6]=>[1,1,3,1,2]
[4,6,8,3,2,1,7,5]=>[5,1,4,2,8,6,7,3]=>[4,8,5,7,1,3,2,6]=>[2,2,2,2]
[4,6,8,3,5,1,2,7]=>[6,1,4,2,7,5,8,3]=>[3,8,5,7,2,4,1,6]=>[2,2,2,2]
[1,4,6,3,7,5,2,8]=>[7,2,4,3,6,1,5,8]=>[2,7,5,6,3,8,4,1]=>[2,2,2,1,1]
[4,5,2,6,8,7,3,1]=>[1,2,8,4,7,3,6,5]=>[8,7,1,5,2,6,3,4]=>[1,1,2,2,2]
[1,7,6,3,8,5,2,4]=>[7,8,4,3,2,6,1,5]=>[2,1,5,6,7,3,8,4]=>[1,4,2,1]
[1,3,8,7,4,5,6,2]=>[5,6,8,7,2,4,1,3]=>[4,3,1,2,7,5,8,6]=>[1,1,3,2,1]
[7,3,1,8,4,5,6,2]=>[2,5,6,8,7,3,1,4]=>[7,4,3,1,2,6,8,5]=>[1,1,1,4,1]
[3,2,8,7,4,5,6,1]=>[5,6,8,1,7,2,4,3]=>[4,3,1,8,2,7,5,6]=>[1,1,2,2,2]
[6,2,4,3,7,5,8,1]=>[3,6,2,4,1,5,8,7]=>[6,3,7,5,8,4,1,2]=>[1,2,2,1,2]
[6,4,2,5,1,7,8,3]=>[6,3,2,4,1,8,5,7]=>[3,6,7,5,8,1,4,2]=>[3,2,2,1]
[3,8,2,1,5,7,6,4]=>[8,1,3,5,7,4,6,2]=>[1,8,6,4,2,5,3,7]=>[2,1,1,2,2]
[1,3,2,8,7,4,6,5]=>[8,6,7,2,5,1,3,4]=>[1,3,2,7,4,8,6,5]=>[2,2,2,1,1]
[5,4,2,7,3,8,6,1]=>[2,1,8,5,3,4,7,6]=>[7,8,1,4,6,5,2,3]=>[2,3,1,2]
[4,6,3,7,8,1,2,5]=>[1,3,6,2,7,4,8,5]=>[8,6,3,7,2,5,1,4]=>[1,1,2,2,2]
[6,2,5,4,1,7,8,3]=>[6,4,2,3,1,8,5,7]=>[3,5,7,6,8,1,4,2]=>[3,2,2,1]
[4,1,5,6,3,8,7,2]=>[3,1,4,8,5,7,2,6]=>[6,8,5,1,4,2,7,3]=>[2,1,2,2,1]
[8,5,1,6,3,2,4,7]=>[6,5,7,3,2,4,8,1]=>[3,4,2,6,7,5,1,8]=>[2,3,1,2]
[6,8,7,4,3,2,5,1]=>[1,6,5,4,8,7,3,2]=>[8,3,4,5,1,2,6,7]=>[1,3,4]
[8,1,5,4,6,7,3,2]=>[4,3,5,8,7,2,6,1]=>[5,6,4,1,2,7,3,8]=>[2,1,3,2]
[2,8,5,1,3,7,6,4]=>[8,7,4,1,3,5,6,2]=>[1,2,5,8,6,4,3,7]=>[4,1,1,2]
[2,4,5,8,3,7,6,1]=>[8,2,3,5,7,1,6,4]=>[1,7,6,4,2,8,3,5]=>[2,1,1,2,2]
[6,4,5,1,3,8,7,2]=>[2,8,5,3,1,7,4,6]=>[7,1,4,6,8,2,5,3]=>[1,4,2,1]
[6,1,3,5,4,8,2,7]=>[5,3,4,7,1,8,2,6]=>[4,6,5,2,8,1,7,3]=>[2,1,2,2,1]
[1,3,8,7,2,5,6,4]=>[6,8,5,7,2,4,1,3]=>[3,1,4,2,7,5,8,6]=>[1,2,2,2,1]
[2,5,4,1,8,3,7,6]=>[3,2,8,1,6,7,4,5]=>[6,7,1,8,3,2,5,4]=>[2,2,1,2,1]
[5,1,4,8,3,7,6,2]=>[8,3,1,5,7,6,2,4]=>[1,6,8,4,2,3,7,5]=>[3,1,3,1]
[8,4,1,2,7,6,5,3]=>[2,8,7,6,3,4,5,1]=>[7,1,2,3,6,5,4,8]=>[1,4,1,2]
[4,8,3,2,7,6,5,1]=>[8,1,3,7,4,6,5,2]=>[1,8,6,2,5,3,4,7]=>[2,1,2,3]
[1,8,7,3,4,6,5,2]=>[8,4,5,7,6,3,1,2]=>[1,5,4,2,3,6,8,7]=>[2,1,4,1]
[10,9,7,5,3,1,2,4,6,8]=>[6,7,5,8,4,9,3,10,2,1]=>[5,4,6,3,7,2,8,1,9,10]=>[1,2,2,2,3]
[5,3,1,2,4,6,8,7]=>[8,3,2,4,1,5,6,7]=>[1,6,7,5,8,4,3,2]=>[3,2,1,1,1]
[3,1,2,8,7,5,4,6]=>[7,1,6,8,5,2,3,4]=>[2,8,3,1,4,7,6,5]=>[2,1,3,1,1]
[1,4,3,8,5,7,2,6]=>[2,5,7,8,3,6,1,4]=>[7,4,2,1,6,3,8,5]=>[1,1,1,2,2,1]
[6,7,1,5,2,8,4,3]=>[8,7,5,3,1,4,2,6]=>[1,2,4,6,8,5,7,3]=>[5,2,1]
[4,8,1,3,6,2,7,5]=>[1,8,4,6,3,5,7,2]=>[8,1,5,3,6,4,2,7]=>[1,2,2,1,2]
[2,7,3,4,8,6,5,1]=>[8,7,3,4,1,2,6,5]=>[1,2,6,5,8,7,3,4]=>[3,2,1,2]
[2,7,1,6,5,8,3,4]=>[7,5,4,8,1,3,2,6]=>[2,4,5,1,8,6,7,3]=>[3,2,2,1]
[6,2,3,8,1,5,7,4]=>[6,8,2,3,1,5,7,4]=>[3,1,7,6,8,4,2,5]=>[1,2,2,1,2]
[2,5,7,4,8,3,6,1]=>[2,4,6,3,8,1,7,5]=>[7,5,3,6,1,8,2,4]=>[1,1,2,2,2]
[8,5,6,2,4,7,1,3]=>[7,4,2,5,3,8,6,1]=>[2,5,7,4,6,1,3,8]=>[3,2,3]
[4,8,5,6,7,1,3,2]=>[3,8,1,6,4,7,5,2]=>[6,1,8,3,5,2,4,7]=>[1,2,2,3]
[4,3,7,1,2,8,5,6]=>[2,1,7,8,4,5,3,6]=>[7,8,2,1,5,4,6,3]=>[2,1,2,2,1]
[4,8,1,6,2,5,3,7]=>[1,7,5,6,3,4,8,2]=>[8,2,4,3,6,5,1,7]=>[1,2,2,1,2]
[5,8,3,1,2,4,6,7]=>[4,5,3,1,6,7,8,2]=>[5,4,6,8,3,2,1,7]=>[1,3,1,1,2]
[1,4,8,5,2,3,6,7]=>[2,5,6,4,7,8,1,3]=>[7,4,3,5,2,1,8,6]=>[1,1,2,1,2,1]
[1,4,8,5,2,3,7,6]=>[8,2,5,4,6,7,1,3]=>[1,7,4,5,3,2,8,6]=>[2,2,1,2,1]
[7,1,4,2,6,8,3,5]=>[3,7,5,8,2,4,1,6]=>[6,2,4,1,7,5,8,3]=>[1,2,2,2,1]
[1,5,8,7,2,4,3,6]=>[2,7,5,6,8,4,1,3]=>[7,2,4,3,1,5,8,6]=>[1,2,1,3,1]
[1,5,4,2,8,3,7,6]=>[3,2,8,6,7,1,4,5]=>[6,7,1,3,2,8,5,4]=>[2,2,2,1,1]
[1,2,8,7,3,5,4,6]=>[7,5,6,8,4,1,2,3]=>[2,4,3,1,5,8,7,6]=>[2,1,3,1,1]
[8,7,1,3,2,5,4,6]=>[4,7,3,5,6,8,2,1]=>[5,2,6,4,3,1,7,8]=>[1,2,1,1,3]
[6,7,4,2,8,1,3,5]=>[4,6,3,1,7,2,8,5]=>[5,3,6,8,2,7,1,4]=>[1,3,2,2]
[4,1,6,8,7,2,3,5]=>[1,6,3,7,8,5,2,4]=>[8,3,6,2,1,4,7,5]=>[1,2,1,3,1]
[4,7,5,6,2,8,3,1]=>[3,8,1,5,4,2,7,6]=>[6,1,8,4,5,7,2,3]=>[1,2,3,2]
[8,4,3,6,7,5,2,1]=>[2,4,8,3,7,6,5,1]=>[7,5,1,6,2,3,4,8]=>[1,1,2,4]
[6,7,5,2,8,4,3,1]=>[1,8,7,4,3,2,6,5]=>[8,1,2,5,6,7,3,4]=>[1,5,2]
[6,8,4,3,2,7,5,1]=>[4,3,1,8,5,7,6,2]=>[5,6,8,1,4,2,3,7]=>[3,2,3]
[1,3,7,6,4,8,2,5]=>[5,7,4,2,3,8,1,6]=>[4,2,5,7,6,1,8,3]=>[1,3,1,2,1]
[2,6,4,8,7,3,1,5]=>[7,3,2,6,8,1,5,4]=>[2,6,7,3,1,8,4,5]=>[3,1,2,2]
[2,1,8,7,3,5,4,6]=>[7,5,6,8,1,4,2,3]=>[2,4,3,1,8,5,7,6]=>[2,1,2,2,1]
[6,1,5,8,7,4,3,2]=>[8,3,1,7,6,5,2,4]=>[1,6,8,2,3,4,7,5]=>[3,4,1]
[6,1,8,5,7,4,3,2]=>[4,1,8,7,6,5,2,3]=>[5,8,1,2,3,4,7,6]=>[2,5,1]
[8,5,1,4,7,6,3,2]=>[8,4,2,7,6,3,5,1]=>[1,5,7,2,3,6,4,8]=>[3,3,2]
[8,1,3,7,2,4,6,5]=>[8,3,5,6,7,2,4,1]=>[1,6,4,3,2,7,5,8]=>[2,1,1,2,2]
[2,6,7,3,5,8,4,1]=>[5,2,8,4,1,3,7,6]=>[4,7,1,5,8,6,2,3]=>[2,3,1,2]
[2,6,7,3,5,8,1,4]=>[7,4,2,5,1,3,8,6]=>[2,5,7,4,8,6,1,3]=>[3,2,1,2]
[5,3,1,6,4,8,2,7]=>[2,5,4,1,7,8,3,6]=>[7,4,5,8,2,1,6,3]=>[1,3,1,2,1]
[2,5,6,7,1,4,8,3]=>[2,6,3,8,1,5,4,7]=>[7,3,6,1,8,4,5,2]=>[1,2,2,2,1]
[4,7,5,3,2,8,1,6]=>[5,1,4,3,7,2,8,6]=>[4,8,5,6,2,7,1,3]=>[2,2,2,2]
[4,7,5,2,8,6,1,3]=>[7,1,3,8,4,2,6,5]=>[2,8,6,1,5,7,3,4]=>[2,1,3,2]
[3,8,6,7,2,5,4,1]=>[8,5,3,7,1,6,4,2]=>[1,4,6,2,8,3,5,7]=>[3,2,3]
[5,8,1,2,7,4,3,6]=>[7,6,1,8,3,4,5,2]=>[2,3,8,1,6,5,4,7]=>[3,2,1,2]
[6,3,1,8,2,4,5,7]=>[5,2,6,7,1,8,3,4]=>[4,7,3,2,8,1,6,5]=>[2,1,2,2,1]
[6,3,1,8,4,5,2,7]=>[2,5,7,6,1,8,3,4]=>[7,4,2,3,8,1,6,5]=>[1,1,3,2,1]
[2,1,4,7,5,8,6,3]=>[8,5,1,3,4,7,2,6]=>[1,4,8,6,5,2,7,3]=>[3,1,1,2,1]
[7,6,2,4,8,3,1,5]=>[4,7,3,6,2,1,8,5]=>[5,2,6,3,7,8,1,4]=>[1,2,3,2]
[6,5,8,1,4,3,7,2]=>[6,5,2,1,8,4,7,3]=>[3,4,7,8,1,5,2,6]=>[4,2,2]
[8,6,3,5,2,1,7,4]=>[3,5,8,6,4,2,7,1]=>[6,4,1,3,5,7,2,8]=>[1,1,4,2]
[6,8,3,1,2,5,4,7]=>[7,4,3,5,1,6,8,2]=>[2,5,6,4,8,3,1,7]=>[3,2,1,2]
[5,8,6,4,7,1,2,3]=>[1,6,7,4,3,8,5,2]=>[8,3,2,5,6,1,4,7]=>[1,1,3,3]
[2,5,1,8,7,3,4,6]=>[6,2,7,8,1,5,3,4]=>[3,7,2,1,8,4,6,5]=>[2,1,2,2,1]
[7,2,4,3,8,6,1,5]=>[3,7,8,2,4,1,6,5]=>[6,2,1,7,5,8,3,4]=>[1,1,2,2,2]
[6,8,4,3,5,1,7,2]=>[4,3,1,8,6,5,7,2]=>[5,6,8,1,3,4,2,7]=>[3,3,2]
[1,4,7,3,6,8,2,5]=>[7,2,4,5,3,8,1,6]=>[2,7,5,4,6,1,8,3]=>[2,1,2,2,1]
[3,7,1,4,6,8,2,5]=>[7,1,4,5,8,3,2,6]=>[2,8,5,4,1,6,7,3]=>[2,1,1,3,1]
[2,4,7,3,6,8,1,5]=>[7,2,4,5,1,3,8,6]=>[2,7,5,4,8,6,1,3]=>[2,1,2,1,2]
[2,7,5,6,1,8,4,3]=>[3,8,7,5,1,4,2,6]=>[6,1,2,4,8,5,7,3]=>[1,4,2,1]
[1,2,6,7,4,5,8,3]=>[5,3,6,4,8,1,2,7]=>[4,6,3,5,1,8,7,2]=>[2,2,2,1,1]
[6,5,2,8,7,1,4,3]=>[8,6,2,1,7,3,5,4]=>[1,3,7,8,2,6,4,5]=>[4,2,2]
[7,2,3,6,8,1,4,5]=>[6,7,2,3,4,1,8,5]=>[3,2,7,6,5,8,1,4]=>[1,2,1,2,2]
[5,8,1,4,2,7,3,6]=>[7,4,1,8,3,5,6,2]=>[2,5,8,1,6,4,3,7]=>[3,2,1,2]
[2,3,1,6,8,7,4,5]=>[4,7,8,1,2,6,3,5]=>[5,2,1,8,7,3,6,4]=>[1,1,2,1,2,1]
[6,4,8,2,1,7,3,5]=>[4,2,7,1,8,5,6,3]=>[5,7,2,8,1,4,3,6]=>[2,2,2,2]
[2,3,1,8,7,5,6,4]=>[6,8,7,1,2,5,3,4]=>[3,1,2,8,7,4,6,5]=>[1,3,1,2,1]
[1,5,6,7,2,4,3,8]=>[2,7,5,3,6,1,4,8]=>[7,2,4,6,3,8,5,1]=>[1,3,2,1,1]
[6,8,3,7,1,2,5,4]=>[3,8,5,1,6,7,4,2]=>[6,1,4,8,3,2,5,7]=>[1,3,1,3]
[2,8,6,4,1,5,3,7]=>[7,5,4,6,1,3,8,2]=>[2,4,5,3,8,6,1,7]=>[3,2,1,2]
[1,5,7,3,6,2,4,8]=>[4,2,6,7,5,1,3,8]=>[5,7,3,2,4,8,6,1]=>[2,1,3,1,1]
[6,7,4,5,1,3,8,2]=>[6,3,1,8,5,4,2,7]=>[3,6,8,1,4,5,7,2]=>[3,4,1]
[1,6,5,3,8,2,4,7]=>[4,6,3,2,7,8,1,5]=>[5,3,6,7,2,1,8,4]=>[1,3,1,2,1]
[8,7,4,5,1,3,2,6]=>[7,5,3,6,4,8,2,1]=>[2,4,6,3,5,1,7,8]=>[3,2,3]
[8,5,1,2,7,4,3,6]=>[7,6,8,3,2,4,5,1]=>[2,3,1,6,7,5,4,8]=>[2,3,1,2]
[2,6,3,8,4,1,7,5]=>[5,8,3,1,2,6,7,4]=>[4,1,6,8,7,3,2,5]=>[1,3,1,1,2]
[3,2,4,6,1,8,7,5]=>[1,4,8,2,3,7,5,6]=>[8,5,1,7,6,2,4,3]=>[1,1,2,1,2,1]
[3,6,7,4,1,2,5,8]=>[5,6,1,4,2,7,3,8]=>[4,3,8,5,7,2,6,1]=>[1,2,2,2,1]
[1,4,7,5,8,2,3,6]=>[6,2,4,7,3,8,1,5]=>[3,7,5,2,6,1,8,4]=>[2,1,2,2,1]
[1,6,8,4,7,3,2,5]=>[4,2,7,6,8,5,1,3]=>[5,7,2,3,1,4,8,6]=>[2,2,3,1]
[3,6,7,5,4,8,1,2]=>[2,7,5,1,4,3,8,6]=>[7,2,4,8,5,6,1,3]=>[1,3,2,2]
[2,3,5,7,8,1,6,4]=>[8,3,6,1,2,4,7,5]=>[1,6,3,8,7,5,2,4]=>[2,2,1,1,2]
[1,5,7,4,2,3,6,8]=>[5,2,6,4,7,1,3,8]=>[4,7,3,5,2,8,6,1]=>[2,2,2,1,1]
[2,4,7,5,3,6,8,1]=>[5,2,4,6,1,3,8,7]=>[4,7,5,3,8,6,1,2]=>[2,1,2,1,2]
[8,1,7,2,4,6,3,5]=>[5,7,8,4,6,2,3,1]=>[4,2,1,5,3,7,6,8]=>[1,1,2,2,2]
[1,2,4,7,8,6,3,5]=>[7,4,8,3,6,1,2,5]=>[2,5,1,6,3,8,7,4]=>[2,2,2,1,1]
[2,4,7,8,3,5,1,6]=>[5,7,2,6,1,3,8,4]=>[4,2,7,3,8,6,1,5]=>[1,2,2,1,2]
[1,3,6,2,5,8,4,7]=>[5,7,2,3,8,1,4,6]=>[4,2,7,6,1,8,5,3]=>[1,2,1,2,1,1]
[1,5,3,6,8,2,4,7]=>[6,3,2,4,7,8,1,5]=>[3,6,7,5,2,1,8,4]=>[3,1,1,2,1]
[4,8,1,2,6,3,7,5]=>[1,8,6,3,4,5,7,2]=>[8,1,3,6,5,4,2,7]=>[1,3,1,1,2]
[5,8,1,2,6,3,7,4]=>[8,6,3,1,4,5,7,2]=>[1,3,6,8,5,4,2,7]=>[4,1,1,2]
[1,6,2,3,7,5,8,4]=>[6,5,8,3,1,2,4,7]=>[3,4,1,6,8,7,5,2]=>[2,3,1,1,1]
[4,1,2,6,5,7,8,3]=>[5,4,1,6,8,2,3,7]=>[4,5,8,3,1,7,6,2]=>[3,1,2,1,1]
[1,8,4,2,7,3,6,5]=>[3,8,6,7,4,5,1,2]=>[6,1,3,2,5,4,8,7]=>[1,2,2,2,1]
[1,7,5,2,3,8,6,4]=>[8,7,4,3,5,1,2,6]=>[1,2,5,6,4,8,7,3]=>[4,2,1,1]
[8,1,4,7,3,5,2,6]=>[3,5,7,6,8,2,4,1]=>[6,4,2,3,1,7,5,8]=>[1,1,2,2,2]
[2,6,1,8,3,7,4,5]=>[7,8,5,1,2,6,3,4]=>[2,1,4,8,7,3,6,5]=>[1,3,1,2,1]
[8,4,2,1,3,7,5,6]=>[3,7,2,8,4,5,6,1]=>[6,2,7,1,5,4,3,8]=>[1,2,2,1,2]
[2,5,1,7,6,8,3,4]=>[2,7,5,1,4,8,3,6]=>[7,2,4,8,5,1,6,3]=>[1,3,1,2,1]
[5,3,1,8,2,4,7,6]=>[2,8,5,1,6,7,3,4]=>[7,1,4,8,3,2,6,5]=>[1,3,1,2,1]
[1,2,6,3,7,5,8,4]=>[6,5,3,8,1,2,4,7]=>[3,4,6,1,8,7,5,2]=>[3,2,1,1,1]
[5,1,8,3,2,4,7,6]=>[4,8,5,1,6,7,2,3]=>[5,1,4,8,3,2,7,6]=>[1,3,1,2,1]
[3,1,5,4,6,7,8,2]=>[1,4,3,5,6,8,2,7]=>[8,5,6,4,3,1,7,2]=>[1,2,1,1,2,1]
[2,8,5,7,3,1,4,6]=>[6,5,3,7,8,1,4,2]=>[3,4,6,2,1,8,5,7]=>[3,1,2,2]
[2,6,8,7,3,1,4,5]=>[6,5,2,7,8,1,4,3]=>[3,4,7,2,1,8,5,6]=>[3,1,2,2]
[7,2,1,3,8,5,4,6]=>[7,2,6,8,3,4,1,5]=>[2,7,3,1,6,5,8,4]=>[2,1,2,2,1]
[2,1,7,3,8,6,4,5]=>[7,8,6,1,4,2,3,5]=>[2,1,3,8,5,7,6,4]=>[1,3,2,1,1]
[1,7,5,3,2,4,8,6]=>[4,8,5,3,6,1,2,7]=>[5,1,4,6,3,8,7,2]=>[1,3,2,1,1]
[1,4,2,7,6,5,8,3]=>[6,2,5,4,8,1,3,7]=>[3,7,4,5,1,8,6,2]=>[2,2,2,1,1]
[2,8,7,3,4,1,5,6]=>[4,6,5,7,8,1,3,2]=>[5,3,4,2,1,8,6,7]=>[1,2,1,2,2]
[5,7,6,2,3,8,1,4]=>[4,1,5,7,3,2,8,6]=>[5,8,4,2,6,7,1,3]=>[2,1,3,2]
[4,5,7,6,2,8,1,3]=>[1,2,5,7,4,3,8,6]=>[8,7,4,2,5,6,1,3]=>[1,1,1,3,2]
[3,1,8,7,5,2,6,4]=>[8,6,1,5,7,4,2,3]=>[1,3,8,4,2,5,7,6]=>[3,1,3,1]
[4,5,6,8,7,2,1,3]=>[1,2,3,7,6,8,5,4]=>[8,7,6,2,3,1,4,5]=>[1,1,1,2,3]
[2,8,3,1,5,4,7,6]=>[3,5,8,1,4,6,7,2]=>[6,4,1,8,5,3,2,7]=>[1,1,2,1,1,2]
[3,8,4,1,5,2,7,6]=>[5,1,3,8,4,6,7,2]=>[4,8,6,1,5,3,2,7]=>[2,1,2,1,2]
[5,1,7,8,3,2,6,4]=>[5,1,8,6,3,7,2,4]=>[4,8,1,3,6,2,7,5]=>[2,3,2,1]
[1,8,6,2,4,3,7,5]=>[5,8,4,6,3,7,1,2]=>[4,1,5,3,6,2,8,7]=>[1,2,2,2,1]
[4,8,3,1,6,2,7,5]=>[1,3,8,6,4,5,7,2]=>[8,6,1,3,5,4,2,7]=>[1,1,3,1,2]
[2,8,3,1,6,4,7,5]=>[8,3,6,1,4,5,7,2]=>[1,6,3,8,5,4,2,7]=>[2,2,1,1,2]
[1,4,5,6,7,8,9,3,2]=>[2,3,4,5,6,9,8,1,7]=>[8,7,6,5,4,1,2,9,3]=>[1,1,1,1,1,3,1]
[1,4,5,6,7,8,9,10,3,2]=>[2,3,4,5,6,7,10,9,1,8]=>[9,8,7,6,5,4,1,2,10,3]=>[1,1,1,1,1,1,3,1]
[5,4,3,1,2,7,6,8]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[5,1,1,1]
[4,1,6,5,2,3,7,8]=>[5,1,6,4,2,3,7,8]=>[4,8,3,5,7,6,2,1]=>[2,3,1,1,1]
[7,1,5,2,3,6,4,8]=>[7,4,5,2,3,6,1,8]=>[2,5,4,7,6,3,8,1]=>[2,2,1,2,1]
[4,6,1,2,8,3,7,5]=>[1,8,6,7,3,2,4,5]=>[8,1,3,2,6,7,5,4]=>[1,2,3,1,1]
[4,1,3,6,7,2,5,8]=>[6,3,1,4,7,2,5,8]=>[3,6,8,5,2,7,4,1]=>[3,1,2,1,1]
[2,6,7,4,3,1,5,8]=>[6,5,4,1,2,7,3,8]=>[3,4,5,8,7,2,6,1]=>[4,1,2,1]
[2,6,3,1,7,4,5,8]=>[3,6,7,1,4,2,5,8]=>[6,3,2,8,5,7,4,1]=>[1,1,2,2,1,1]
[6,5,3,7,2,4,1,8]=>[3,5,2,1,7,6,4,8]=>[6,4,7,8,2,3,5,1]=>[1,3,3,1]
[2,3,6,7,1,5,4,8]=>[7,5,1,2,3,6,4,8]=>[2,4,8,7,6,3,5,1]=>[3,1,1,2,1]
[2,7,5,8,1,3,6,4]=>[8,5,3,6,1,2,7,4]=>[1,4,6,3,8,7,2,5]=>[3,2,1,2]
[5,1,6,7,3,2,4,8]=>[6,5,3,1,7,2,4,8]=>[3,4,6,8,2,7,5,1]=>[4,2,1,1]
[1,2,5,7,8,6,3,4]=>[7,3,4,8,6,1,2,5]=>[2,6,5,1,3,8,7,4]=>[2,1,3,1,1]
[1,2,6,7,4,5,3,8]=>[5,3,7,6,1,2,4,8]=>[4,6,2,3,8,7,5,1]=>[2,3,1,1,1]
[1,2,7,8,4,6,3,5]=>[5,7,3,8,6,1,2,4]=>[4,2,6,1,3,8,7,5]=>[1,2,3,1,1]
[8,6,5,2,1,7,4,3]=>[8,4,7,5,3,2,6,1]=>[1,5,2,4,6,7,3,8]=>[2,4,2]
[4,3,8,6,7,1,5,2]=>[8,1,6,2,4,7,5,3]=>[1,8,3,7,5,2,4,6]=>[2,2,1,3]
[7,3,2,8,6,1,5,4]=>[8,2,6,7,3,1,5,4]=>[1,7,3,2,6,8,4,5]=>[2,1,3,2]
[7,5,8,2,6,1,4,3]=>[8,4,2,6,1,7,5,3]=>[1,5,7,3,8,2,4,6]=>[3,2,3]
[5,6,8,2,7,4,1,3]=>[1,7,2,8,4,6,5,3]=>[8,2,7,1,5,3,4,6]=>[1,2,2,3]
[5,2,7,4,6,1,8,3]=>[4,1,8,6,2,5,3,7]=>[5,8,1,3,7,4,6,2]=>[2,3,2,1]
[5,4,8,6,3,2,1,7]=>[1,7,2,6,5,4,8,3]=>[8,2,7,3,4,5,1,6]=>[1,2,3,2]
[4,6,8,5,1,2,7,3]=>[8,1,5,2,6,4,7,3]=>[1,8,4,7,3,5,2,6]=>[2,2,2,2]
[6,3,5,7,1,2,8,4]=>[8,2,5,3,1,6,4,7]=>[1,7,4,6,8,3,5,2]=>[2,3,2,1]
[1,8,5,3,2,4,6,7]=>[5,4,6,3,7,8,1,2]=>[4,5,3,6,2,1,8,7]=>[2,2,1,2,1]
[1,8,7,5,3,4,2,6]=>[5,7,6,4,8,3,1,2]=>[4,2,3,5,1,6,8,7]=>[1,3,3,1]
[1,7,8,5,3,4,2,6]=>[5,7,6,4,2,8,1,3]=>[4,2,3,5,7,1,8,6]=>[1,4,2,1]
[1,7,6,8,4,2,3,5]=>[6,7,5,3,2,8,1,4]=>[3,2,4,6,7,1,8,5]=>[1,4,2,1]
[1,7,8,6,4,3,2,5]=>[7,6,5,2,8,4,1,3]=>[2,3,4,7,1,5,8,6]=>[4,3,1]
[9,8,7,6,5,2,1,3,4]=>[7,6,8,9,5,4,3,2,1]=>[3,4,2,1,5,6,7,8,9]=>[2,1,6]
[9,7,8,6,5,4,3,2,1]=>[2,9,8,7,6,5,4,3,1]=>[8,1,2,3,4,5,6,7,9]=>[1,8]
[5,1,7,8,4,2,3,6]=>[6,1,7,5,3,8,2,4]=>[3,8,2,4,6,1,7,5]=>[2,3,2,1]
[2,8,3,1,7,5,6,4]=>[6,8,3,7,1,4,5,2]=>[3,1,6,2,8,5,4,7]=>[1,2,2,1,2]
[8,5,6,2,1,4,7,3]=>[4,6,2,8,5,3,7,1]=>[5,3,7,1,4,6,2,8]=>[1,2,3,2]
[12,10,8,6,4,2,1,3,5,7,9,11]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[2,2,2,2,2,2]
[2,1,6,4,7,8,3,5]=>[7,4,1,3,5,8,2,6]=>[2,5,8,6,4,1,7,3]=>[3,1,1,2,1]
[5,7,8,3,4,2,1,6]=>[1,4,7,6,5,2,8,3]=>[8,5,2,3,4,7,1,6]=>[1,1,4,2]
[4,7,5,3,8,2,6,1]=>[4,1,3,6,2,8,7,5]=>[5,8,6,3,7,1,2,4]=>[2,1,2,3]
[2,6,4,7,8,5,3,1]=>[4,2,8,3,7,1,6,5]=>[5,7,1,6,2,8,3,4]=>[2,2,2,2]
[7,8,4,5,6,1,3,2]=>[3,8,6,4,1,7,5,2]=>[6,1,3,5,8,2,4,7]=>[1,4,3]
[2,5,1,8,4,6,7,3]=>[5,2,6,8,1,7,3,4]=>[4,7,3,1,8,2,6,5]=>[2,1,2,2,1]
[6,5,8,3,4,2,1,7]=>[4,2,1,7,6,5,8,3]=>[5,7,8,2,3,4,1,6]=>[3,3,2]
[1,3,5,8,4,6,7,2]=>[3,5,6,8,2,7,1,4]=>[6,4,3,1,7,2,8,5]=>[1,1,1,2,2,1]
[3,4,5,8,2,1,6,7]=>[1,2,3,6,5,7,8,4]=>[8,7,6,3,4,2,1,5]=>[1,1,1,2,1,2]
[8,2,7,6,3,4,5,1]=>[5,6,8,7,2,4,3,1]=>[4,3,1,2,7,5,6,8]=>[1,1,3,3]
[6,8,7,3,2,1,4,5]=>[6,5,4,1,7,8,3,2]=>[3,4,5,8,2,1,6,7]=>[4,1,3]
[3,4,8,2,7,1,5,6]=>[1,2,4,6,7,8,5,3]=>[8,7,5,3,2,1,4,6]=>[1,1,1,1,1,3]
[7,2,6,1,4,8,3,5]=>[5,7,8,2,4,3,1,6]=>[4,2,1,7,5,6,8,3]=>[1,1,2,3,1]
[7,8,1,2,4,6,3,5]=>[5,7,8,3,4,1,6,2]=>[4,2,1,6,5,8,3,7]=>[1,1,2,2,2]
[7,2,8,3,4,5,1,6]=>[4,5,7,2,6,1,8,3]=>[5,4,2,7,3,8,1,6]=>[1,1,2,2,2]
[7,5,1,2,4,3,8,6]=>[5,8,3,4,2,6,1,7]=>[4,1,6,5,7,3,8,2]=>[1,2,2,2,1]
[7,6,8,1,4,2,3,5]=>[6,7,4,5,2,1,8,3]=>[3,2,5,4,7,8,1,6]=>[1,2,3,2]
[2,4,3,7,8,5,6,1]=>[6,2,4,8,1,3,7,5]=>[3,7,5,1,8,6,2,4]=>[2,1,2,1,2]
[2,1,7,6,3,4,5,8]=>[5,6,7,1,4,2,3,8]=>[4,3,2,8,5,7,6,1]=>[1,1,2,2,1,1]
[6,3,5,2,1,8,4,7]=>[2,4,7,3,1,8,5,6]=>[7,5,2,6,8,1,4,3]=>[1,1,3,2,1]
[6,1,5,3,8,2,4,7]=>[4,6,3,7,1,8,2,5]=>[5,3,6,2,8,1,7,4]=>[1,2,2,2,1]
[3,2,4,8,6,1,7,5]=>[8,1,6,2,3,5,7,4]=>[1,8,3,7,6,4,2,5]=>[2,2,1,1,2]
[2,1,3,8,4,5,7,6]=>[8,1,5,6,7,2,3,4]=>[1,8,4,3,2,7,6,5]=>[2,1,1,2,1,1]
[3,1,2,8,5,4,7,6]=>[1,5,8,6,7,2,3,4]=>[8,4,1,3,2,7,6,5]=>[1,1,2,2,1,1]
[2,1,3,7,8,4,6,5]=>[8,6,1,4,7,2,3,5]=>[1,3,8,5,2,7,6,4]=>[3,1,2,1,1]
[2,1,3,8,4,7,6,5]=>[8,7,1,5,6,2,3,4]=>[1,2,8,4,3,7,6,5]=>[3,1,2,1,1]
[3,1,2,8,4,5,7,6]=>[1,8,5,6,7,2,3,4]=>[8,1,4,3,2,7,6,5]=>[1,2,1,2,1,1]
[1,2,8,7,5,4,6,3]=>[6,5,8,7,4,1,2,3]=>[3,4,1,2,5,8,7,6]=>[2,4,1,1]
[4,6,7,2,3,8,1,5]=>[1,4,5,2,7,3,8,6]=>[8,5,4,7,2,6,1,3]=>[1,1,2,2,2]
[3,2,6,5,7,8,1,4]=>[4,1,3,7,2,5,8,6]=>[5,8,6,2,7,4,1,3]=>[2,1,2,1,2]
[3,2,7,5,6,8,1,4]=>[4,7,1,5,2,3,8,6]=>[5,2,8,4,7,6,1,3]=>[1,2,2,1,2]
[2,1,8,7,4,6,5,3]=>[8,5,7,6,1,4,2,3]=>[1,4,2,3,8,5,7,6]=>[2,3,2,1]
[6,1,5,8,4,7,3,2]=>[3,5,1,8,7,6,2,4]=>[6,4,8,1,2,3,7,5]=>[1,2,4,1]
[2,4,7,1,8,3,6,5]=>[8,2,6,7,1,4,3,5]=>[1,7,3,2,8,5,6,4]=>[2,1,2,2,1]
[6,1,5,4,2,3,8,7]=>[8,5,4,2,3,1,6,7]=>[1,4,5,7,6,8,3,2]=>[4,2,1,1]
[6,4,5,1,2,8,3,7]=>[7,2,8,4,3,1,5,6]=>[2,7,1,5,6,8,4,3]=>[2,4,1,1]
[8,4,1,5,7,6,3,2]=>[2,8,4,7,6,3,5,1]=>[7,1,5,2,3,6,4,8]=>[1,2,3,2]
[8,1,6,3,5,2,4,7]=>[4,6,7,5,2,3,8,1]=>[5,3,2,4,7,6,1,8]=>[1,1,3,1,2]
[4,6,2,5,3,8,1,7]=>[1,5,3,4,2,7,8,6]=>[8,4,6,5,7,2,1,3]=>[1,2,2,1,2]
[4,6,5,2,1,8,3,7]=>[1,4,7,3,2,8,5,6]=>[8,5,2,6,7,1,4,3]=>[1,1,3,2,1]
[5,8,4,3,6,7,2,1]=>[1,4,3,5,8,7,6,2]=>[8,5,6,4,1,2,3,7]=>[1,2,1,4]
[6,8,2,1,5,3,4,7]=>[3,6,7,4,1,5,8,2]=>[6,3,2,5,8,4,1,7]=>[1,1,3,1,2]
[2,5,3,8,6,7,4,1]=>[2,5,8,7,1,3,6,4]=>[7,4,1,2,8,6,3,5]=>[1,1,3,1,2]
[3,2,6,5,1,8,4,7]=>[7,1,4,2,3,8,5,6]=>[2,8,5,7,6,1,4,3]=>[2,2,1,2,1]
[7,4,5,8,1,6,2,3]=>[2,7,3,8,5,1,6,4]=>[7,2,6,1,4,8,3,5]=>[1,2,3,2]
[4,5,8,1,6,7,3,2]=>[1,2,5,8,7,4,6,3]=>[8,7,4,1,2,5,3,6]=>[1,1,1,3,2]
[5,1,8,4,6,7,3,2]=>[4,1,5,8,7,6,2,3]=>[5,8,4,1,2,3,7,6]=>[2,1,4,1]
[6,5,3,8,1,7,2,4]=>[3,7,2,1,8,5,6,4]=>[6,2,7,8,1,4,3,5]=>[1,3,2,2]
[8,3,7,1,6,2,4,5]=>[2,6,7,8,4,5,3,1]=>[7,3,2,1,5,4,6,8]=>[1,1,1,2,3]
[8,1,7,5,6,4,2,3]=>[7,4,8,6,5,2,3,1]=>[2,5,1,3,4,7,6,8]=>[2,4,2]
[7,2,3,6,8,1,5,4]=>[8,6,2,3,4,1,7,5]=>[1,3,7,6,5,8,2,4]=>[3,1,2,2]
[2,6,3,7,8,1,4,5]=>[6,7,3,1,2,4,8,5]=>[3,2,6,8,7,5,1,4]=>[1,3,1,1,2]
[6,3,8,7,2,1,5,4]=>[5,8,2,1,6,7,4,3]=>[4,1,7,8,3,2,5,6]=>[1,3,1,3]
[7,2,5,6,3,4,8,1]=>[5,3,6,2,4,1,8,7]=>[4,6,3,7,5,8,1,2]=>[2,2,2,2]
[7,2,8,6,3,1,5,4]=>[5,8,6,7,2,1,4,3]=>[4,1,3,2,7,8,5,6]=>[1,2,3,2]
[7,2,4,5,8,6,3,1]=>[8,3,4,7,2,1,6,5]=>[1,6,5,2,7,8,3,4]=>[2,1,3,2]
[6,3,8,4,7,2,5,1]=>[4,6,1,8,2,7,5,3]=>[5,3,8,1,7,2,4,6]=>[1,2,2,3]
[7,2,3,6,8,5,4,1]=>[4,8,7,2,3,1,6,5]=>[5,1,2,7,6,8,3,4]=>[1,3,2,2]
[7,2,8,5,4,1,3,6]=>[6,7,5,2,4,1,8,3]=>[3,2,4,7,5,8,1,6]=>[1,3,2,2]
[7,4,5,2,8,1,6,3]=>[2,8,4,3,6,1,7,5]=>[7,1,5,6,3,8,2,4]=>[1,3,2,2]
[7,5,4,2,8,1,6,3]=>[8,4,3,2,6,1,7,5]=>[1,5,6,7,3,8,2,4]=>[4,2,2]
[7,6,3,2,8,4,5,1]=>[3,6,8,4,2,1,7,5]=>[6,3,1,5,7,8,2,4]=>[1,1,4,2]
[7,2,3,6,8,4,5,1]=>[6,4,8,2,3,1,7,5]=>[3,5,1,7,6,8,2,4]=>[2,2,2,2]
[7,2,5,4,8,3,6,1]=>[4,3,6,8,2,1,7,5]=>[5,6,3,1,7,8,2,4]=>[2,1,3,2]
[7,2,8,3,6,1,4,5]=>[4,6,7,8,2,1,5,3]=>[5,3,2,1,7,8,4,6]=>[1,1,1,3,2]
[3,1,6,7,4,5,2,8]=>[5,1,3,7,6,2,4,8]=>[4,8,6,2,3,7,5,1]=>[2,1,3,1,1]
[3,1,5,4,7,6,2,8]=>[1,3,7,4,6,2,5,8]=>[8,6,2,5,3,7,4,1]=>[1,1,2,2,1,1]
[7,3,6,8,2,4,5,1]=>[5,6,2,3,1,8,7,4]=>[4,3,7,6,8,1,2,5]=>[1,2,2,3]
[5,1,3,2,4,6,8,7]=>[3,8,2,4,1,5,6,7]=>[6,1,7,5,8,4,3,2]=>[1,2,2,1,1,1]
[8,4,2,5,1,7,3,6]=>[7,3,2,4,8,5,6,1]=>[2,6,7,5,1,4,3,8]=>[3,1,2,2]
[6,4,2,5,7,3,8,1]=>[4,2,6,3,1,5,8,7]=>[5,7,3,6,8,4,1,2]=>[2,3,1,2]
[5,7,8,4,2,3,6,1]=>[1,5,6,4,2,8,7,3]=>[8,4,3,5,7,1,2,6]=>[1,1,3,3]
[6,4,5,2,8,3,7,1]=>[2,6,3,1,8,4,7,5]=>[7,3,6,8,1,5,2,4]=>[1,3,2,2]
[6,5,2,4,3,8,7,1]=>[4,8,3,2,1,5,7,6]=>[5,1,6,7,8,4,2,3]=>[1,4,1,2]
[6,5,3,4,1,8,2,7]=>[3,7,4,2,1,8,5,6]=>[6,2,5,7,8,1,4,3]=>[1,4,2,1]
[5,6,4,8,3,1,2,7]=>[1,6,3,2,7,5,8,4]=>[8,3,6,7,2,4,1,5]=>[1,3,2,2]
[7,2,4,6,3,8,5,1]=>[8,3,5,2,4,1,7,6]=>[1,6,4,7,5,8,2,3]=>[2,2,2,2]
[2,8,3,7,6,1,5,4]=>[8,6,7,3,5,1,4,2]=>[1,3,2,6,4,8,5,7]=>[2,2,2,2]
[4,6,5,3,8,1,7,2]=>[4,1,3,2,8,6,7,5]=>[5,8,6,7,1,3,2,4]=>[2,2,2,2]
[2,4,8,7,6,1,5,3]=>[8,6,7,2,5,1,4,3]=>[1,3,2,7,4,8,5,6]=>[2,2,2,2]
[3,2,8,7,4,6,5,1]=>[8,5,7,1,6,2,4,3]=>[1,4,2,8,3,7,5,6]=>[2,2,2,2]
[8,2,6,5,1,4,3,7]=>[7,5,6,2,4,3,8,1]=>[2,4,3,7,5,6,1,8]=>[2,2,2,2]
[4,8,5,2,7,6,3,1]=>[3,8,1,7,4,6,5,2]=>[6,1,8,2,5,3,4,7]=>[1,2,2,3]
[2,8,6,5,7,1,3,4]=>[6,7,4,3,8,1,5,2]=>[3,2,5,6,1,8,4,7]=>[1,3,2,2]
[3,8,4,7,2,1,6,5]=>[3,5,8,1,6,7,4,2]=>[6,4,1,8,3,2,5,7]=>[1,1,2,1,3]
[4,8,5,1,7,6,3,2]=>[3,8,1,7,6,4,5,2]=>[6,1,8,2,3,5,4,7]=>[1,2,3,2]
[5,8,1,7,6,2,3,4]=>[6,1,7,8,5,3,4,2]=>[3,8,2,1,4,6,5,7]=>[2,1,3,2]
[3,4,6,2,5,7,1,8]=>[1,2,4,5,3,7,6,8]=>[8,7,5,4,6,2,3,1]=>[1,1,1,2,2,1]
[1,7,5,2,6,8,3,4]=>[7,5,3,8,4,1,2,6]=>[2,4,6,1,5,8,7,3]=>[3,3,1,1]
[5,1,7,2,4,6,3,8]=>[5,7,4,1,6,2,3,8]=>[4,2,5,8,3,7,6,1]=>[1,3,2,1,1]
[6,8,2,1,3,4,7,5]=>[3,8,4,5,1,6,7,2]=>[6,1,5,4,8,3,2,7]=>[1,2,2,1,2]
[6,4,8,5,1,7,2,3]=>[2,7,1,8,5,4,6,3]=>[7,2,8,1,4,5,3,6]=>[1,2,3,2]
[5,2,8,1,3,6,7,4]=>[6,8,2,1,4,5,7,3]=>[3,1,7,8,5,4,2,6]=>[1,3,1,1,2]
[7,4,3,8,5,6,1,2]=>[2,7,3,5,1,8,6,4]=>[7,2,6,4,8,1,3,5]=>[1,2,2,3]
[6,2,1,8,7,4,5,3]=>[6,8,7,2,1,5,3,4]=>[3,1,2,7,8,4,6,5]=>[1,4,2,1]
[6,2,1,8,7,3,5,4]=>[8,6,7,2,1,5,3,4]=>[1,3,2,7,8,4,6,5]=>[2,3,2,1]
[5,2,1,7,6,3,4,8]=>[6,7,2,1,5,3,4,8]=>[3,2,7,8,4,6,5,1]=>[1,3,2,1,1]
[4,2,6,8,5,7,1,3]=>[1,3,7,5,8,2,6,4]=>[8,6,2,4,1,7,3,5]=>[1,1,2,2,2]
[8,6,4,3,2,7,5,1]=>[4,3,8,5,2,7,6,1]=>[5,6,1,4,7,2,3,8]=>[2,3,3]
[1,3,4,7,8,2,6,5]=>[8,6,2,3,4,7,1,5]=>[1,3,7,6,5,2,8,4]=>[3,1,1,2,1]
[1,5,4,3,8,7,2,6]=>[3,2,7,8,4,6,1,5]=>[6,7,2,1,5,3,8,4]=>[2,1,2,2,1]
[1,2,5,8,4,3,6,7]=>[3,6,5,7,8,1,2,4]=>[6,3,4,2,1,8,7,5]=>[1,2,1,2,1,1]
[1,5,8,2,6,4,3,7]=>[2,7,6,4,5,8,1,3]=>[7,2,3,5,4,1,8,6]=>[1,3,1,2,1]
[10,9,8,6,4,2,1,3,5,7]=>[7,6,8,5,9,4,10,3,2,1]=>[4,5,3,6,2,7,1,8,9,10]=>[2,2,2,4]
[10,9,8,7,6,4,2,1,3,5]=>[8,7,9,6,10,5,4,3,2,1]=>[3,4,2,5,1,6,7,8,9,10]=>[2,2,6]
[3,5,6,2,4,7,8,1]=>[4,1,2,5,3,6,8,7]=>[5,8,7,4,6,3,1,2]=>[2,1,2,1,2]
[3,5,6,7,2,4,8,1]=>[2,5,1,3,6,4,8,7]=>[7,4,8,6,3,5,1,2]=>[1,2,1,2,2]
[3,5,7,6,8,2,4,1]=>[6,2,4,1,3,8,7,5]=>[3,7,5,8,6,1,2,4]=>[2,2,1,3]
[3,5,7,2,6,8,4,1]=>[2,5,8,1,4,3,7,6]=>[7,4,1,8,5,6,2,3]=>[1,1,2,2,2]
[3,5,2,7,6,8,4,1]=>[2,5,1,4,8,3,7,6]=>[7,4,8,5,1,6,2,3]=>[1,2,1,2,2]
[3,5,4,7,2,6,8,1]=>[3,1,2,5,6,4,8,7]=>[6,8,7,4,3,5,1,2]=>[2,1,1,2,2]
[3,4,5,7,2,6,8,1]=>[1,2,3,5,6,4,8,7]=>[8,7,6,4,3,5,1,2]=>[1,1,1,1,2,2]
[3,4,5,7,2,8,6,1]=>[8,1,2,3,5,4,7,6]=>[1,8,7,6,4,5,2,3]=>[2,1,1,2,2]
[3,5,4,7,8,2,6,1]=>[2,6,1,3,4,8,7,5]=>[7,3,8,6,5,1,2,4]=>[1,2,1,1,3]
[3,5,4,7,2,8,6,1]=>[2,8,1,3,5,4,7,6]=>[7,1,8,6,4,5,2,3]=>[1,2,1,2,2]
[3,2,5,7,4,8,6,1]=>[8,1,3,5,2,4,7,6]=>[1,8,6,4,7,5,2,3]=>[2,1,2,1,2]
[3,5,7,4,2,8,6,1]=>[2,4,8,1,5,3,7,6]=>[7,5,1,8,4,6,2,3]=>[1,1,2,2,2]
[3,5,7,8,4,2,6,1]=>[6,2,5,1,3,8,7,4]=>[3,7,4,8,6,1,2,5]=>[2,2,1,3]
[3,5,2,7,8,6,4,1]=>[2,4,8,1,7,3,6,5]=>[7,5,1,8,2,6,3,4]=>[1,1,2,2,2]
[3,5,7,8,2,6,4,1]=>[8,2,5,1,3,7,6,4]=>[1,7,4,8,6,2,3,5]=>[2,2,1,3]
[3,5,7,8,6,2,4,1]=>[6,2,3,8,1,7,5,4]=>[3,7,6,1,8,2,4,5]=>[2,1,2,3]
[4,2,5,6,7,3,8,1]=>[3,1,4,6,2,5,8,7]=>[6,8,5,3,7,4,1,2]=>[2,1,2,1,2]
[8,6,1,4,3,5,2,7]=>[5,4,7,3,6,2,8,1]=>[4,5,2,6,3,7,1,8]=>[2,2,2,2]
[6,1,8,4,3,5,2,7]=>[5,4,7,6,1,8,2,3]=>[4,5,2,3,8,1,7,6]=>[2,3,2,1]
[5,1,6,4,8,2,3,7]=>[6,4,3,1,7,8,2,5]=>[3,5,6,8,2,1,7,4]=>[4,1,2,1]
[8,1,4,2,5,3,6,7]=>[6,4,2,3,5,7,8,1]=>[3,5,7,6,4,2,1,8]=>[3,1,1,1,2]
[2,8,4,1,5,3,6,7]=>[6,4,1,3,5,7,8,2]=>[3,5,8,6,4,2,1,7]=>[3,1,1,1,2]
[4,1,8,3,5,2,6,7]=>[4,1,6,5,7,8,2,3]=>[5,8,3,4,2,1,7,6]=>[2,2,1,2,1]
[3,1,8,2,5,4,6,7]=>[1,6,4,5,7,8,2,3]=>[8,3,5,4,2,1,7,6]=>[1,2,1,1,2,1]
[4,2,5,1,8,7,6,3]=>[1,8,3,7,2,6,4,5]=>[8,1,6,2,7,3,5,4]=>[1,2,2,2,1]
[5,2,4,8,1,7,6,3]=>[8,3,1,7,2,5,6,4]=>[1,6,8,2,7,4,3,5]=>[3,2,1,2]
[7,3,2,4,6,8,1,5]=>[2,7,3,4,5,1,8,6]=>[7,2,6,5,4,8,1,3]=>[1,2,1,2,2]
[1,4,8,6,7,2,5,3]=>[8,6,2,4,7,5,1,3]=>[1,3,7,5,2,4,8,6]=>[3,1,3,1]
[1,4,5,7,3,8,2,6]=>[2,3,5,7,4,8,1,6]=>[7,6,4,2,5,1,8,3]=>[1,1,1,2,2,1]
[4,6,8,1,2,5,3,7]=>[1,7,4,5,2,6,8,3]=>[8,2,5,4,7,3,1,6]=>[1,2,2,1,2]
[3,5,6,8,2,1,4,7]=>[2,6,1,5,3,7,8,4]=>[7,3,8,4,6,2,1,5]=>[1,2,2,1,2]
[8,2,5,4,1,3,7,6]=>[8,5,2,4,3,6,7,1]=>[1,4,7,5,6,3,2,8]=>[3,2,1,2]
[2,4,5,8,6,3,1,7]=>[7,2,3,6,1,5,8,4]=>[2,7,6,3,8,4,1,5]=>[2,1,2,1,2]
[5,4,8,2,3,1,7,6]=>[4,2,1,5,8,6,7,3]=>[5,7,8,4,1,3,2,6]=>[3,1,2,2]
[4,7,5,8,2,3,1,6]=>[5,1,3,7,6,2,8,4]=>[4,8,6,2,3,7,1,5]=>[2,1,3,2]
[4,6,7,5,1,8,3,2]=>[2,8,1,7,5,4,3,6]=>[7,1,8,2,4,5,6,3]=>[1,2,4,1]
[1,7,3,6,5,8,2,4]=>[7,5,3,4,2,8,1,6]=>[2,4,6,5,7,1,8,3]=>[3,2,2,1]
[7,5,3,8,6,2,1,4]=>[7,3,2,6,1,8,5,4]=>[2,6,7,3,8,1,4,5]=>[3,2,3]
[4,6,7,5,2,8,3,1]=>[2,8,1,5,4,3,7,6]=>[7,1,8,4,5,6,2,3]=>[1,2,3,2]
[5,8,7,2,4,3,1,6]=>[1,7,4,6,5,8,3,2]=>[8,2,5,3,4,1,6,7]=>[1,2,2,3]
[5,1,2,8,6,7,3,4]=>[7,5,1,8,6,2,3,4]=>[2,4,8,1,3,7,6,5]=>[3,3,1,1]
[2,5,7,8,6,1,4,3]=>[8,2,6,3,7,1,5,4]=>[1,7,3,6,2,8,4,5]=>[2,2,2,2]
[7,2,6,8,4,5,1,3]=>[7,5,3,8,2,1,6,4]=>[2,4,6,1,7,8,3,5]=>[3,3,2]
[5,1,7,6,8,2,3,4]=>[6,1,7,4,3,8,2,5]=>[3,8,2,5,6,1,7,4]=>[2,3,2,1]
[1,7,6,2,4,3,8,5]=>[5,8,4,6,3,1,2,7]=>[4,1,5,3,6,8,7,2]=>[1,2,3,1,1]
[7,1,6,2,4,5,3,8]=>[5,7,4,6,2,3,1,8]=>[4,2,5,3,7,6,8,1]=>[1,2,2,2,1]
[5,7,1,6,2,3,4,8]=>[5,6,1,7,3,4,2,8]=>[4,3,8,2,6,5,7,1]=>[1,2,2,2,1]
[6,2,5,8,3,4,1,7]=>[5,3,7,2,1,6,8,4]=>[4,6,2,7,8,3,1,5]=>[2,3,1,2]
[5,6,8,7,1,3,2,4]=>[1,7,5,2,6,8,4,3]=>[8,2,4,7,3,1,5,6]=>[1,3,1,3]
[2,1,3,6,5,8,4,7]=>[5,1,4,7,8,2,3,6]=>[4,8,5,2,1,7,6,3]=>[2,1,1,2,1,1]
[2,8,6,5,7,4,3,1]=>[4,3,8,7,6,1,5,2]=>[5,6,1,2,3,8,4,7]=>[2,4,2]
[2,8,6,5,7,4,1,3]=>[7,4,3,8,6,1,5,2]=>[2,5,6,1,3,8,4,7]=>[3,3,2]
[6,5,2,7,4,3,1,8]=>[7,6,3,2,1,5,4,8]=>[2,3,6,7,8,4,5,1]=>[5,2,1]
[6,5,2,8,4,3,7,1]=>[6,5,2,1,8,3,7,4]=>[3,4,7,8,1,6,2,5]=>[4,2,2]
[7,6,8,5,2,4,1,3]=>[5,7,2,1,8,6,4,3]=>[4,2,7,8,1,3,5,6]=>[1,3,4]
[5,3,7,2,4,1,8,6]=>[2,4,1,5,8,6,3,7]=>[7,5,8,4,1,3,6,2]=>[1,2,1,3,1]
[5,1,2,8,6,3,7,4]=>[8,6,5,1,7,2,3,4]=>[1,3,4,8,2,7,6,5]=>[4,2,1,1]
[6,1,5,7,2,4,3,8]=>[7,5,3,6,2,1,4,8]=>[2,4,6,3,7,8,5,1]=>[3,3,1,1]
[4,1,8,2,6,5,7,3]=>[1,6,5,8,4,7,2,3]=>[8,3,4,1,5,2,7,6]=>[1,2,2,2,1]
[6,1,4,7,8,5,3,2]=>[4,8,3,1,7,6,2,5]=>[5,1,6,8,2,3,7,4]=>[1,3,3,1]
[6,1,5,7,8,4,2,3]=>[3,7,4,1,8,6,2,5]=>[6,2,5,8,1,3,7,4]=>[1,3,3,1]
[5,6,8,3,7,4,2,1]=>[1,2,8,4,7,6,5,3]=>[8,7,1,5,2,3,4,6]=>[1,1,2,4]
[4,6,1,5,7,2,8,3]=>[1,4,8,6,3,2,5,7]=>[8,5,1,3,6,7,4,2]=>[1,1,4,1,1]
[2,5,8,4,6,3,7,1]=>[2,4,6,5,8,1,7,3]=>[7,5,3,4,1,8,2,6]=>[1,1,2,2,2]
[4,3,7,1,2,6,8,5]=>[2,1,6,8,4,5,3,7]=>[7,8,3,1,5,4,6,2]=>[2,1,2,2,1]
[8,1,6,5,2,7,4,3]=>[8,7,5,4,2,3,6,1]=>[1,2,4,5,7,6,3,8]=>[5,1,2]
[6,8,1,5,2,7,4,3]=>[8,7,5,3,1,4,6,2]=>[1,2,4,6,8,5,3,7]=>[5,1,2]
[4,5,8,2,3,7,6,1]=>[1,2,8,4,5,7,6,3]=>[8,7,1,5,4,2,3,6]=>[1,1,2,1,3]
[1,7,3,2,4,8,6,5]=>[8,3,7,4,5,1,2,6]=>[1,6,2,5,4,8,7,3]=>[2,2,2,1,1]
[4,3,1,8,2,6,7,5]=>[2,1,6,8,5,7,3,4]=>[7,8,3,1,4,2,6,5]=>[2,1,2,2,1]
[4,8,1,3,2,5,7,6]=>[4,1,8,3,5,6,7,2]=>[5,8,1,6,4,3,2,7]=>[2,2,1,1,2]
[1,7,5,3,8,6,2,4]=>[7,3,8,4,2,6,1,5]=>[2,6,1,5,7,3,8,4]=>[2,3,2,1]
[4,2,5,8,1,3,7,6]=>[3,1,8,2,5,6,7,4]=>[6,8,1,7,4,3,2,5]=>[2,2,1,1,2]
[3,1,8,2,6,5,4,7]=>[7,1,6,4,5,8,2,3]=>[2,8,3,5,4,1,7,6]=>[2,2,1,2,1]
[2,3,8,4,1,5,7,6]=>[4,8,1,2,5,6,7,3]=>[5,1,8,7,4,3,2,6]=>[1,2,1,1,1,2]
[7,1,6,2,4,8,3,5]=>[5,7,8,4,2,3,1,6]=>[4,2,1,5,7,6,8,3]=>[1,1,3,2,1]
[6,5,8,1,3,2,4,7]=>[6,4,5,2,1,7,8,3]=>[3,5,4,7,8,2,1,6]=>[2,3,1,2]
[2,1,8,5,3,4,6,7]=>[5,6,1,4,7,8,2,3]=>[4,3,8,5,2,1,7,6]=>[1,2,1,1,2,1]
[8,4,1,3,2,5,6,7]=>[5,3,4,2,6,7,8,1]=>[4,6,5,7,3,2,1,8]=>[2,2,1,1,2]
[8,6,1,2,3,5,4,7]=>[7,3,4,5,6,2,8,1]=>[2,6,5,4,3,7,1,8]=>[2,1,1,2,2]
[7,8,1,5,2,4,6,3]=>[6,8,5,3,4,1,7,2]=>[3,1,4,6,5,8,2,7]=>[1,3,2,2]
[2,8,6,3,1,5,4,7]=>[4,7,5,6,1,3,8,2]=>[5,2,4,3,8,6,1,7]=>[1,2,2,1,2]
[5,7,2,8,4,1,6,3]=>[1,8,6,3,5,2,7,4]=>[8,1,3,6,4,7,2,5]=>[1,3,2,2]
[2,5,6,3,8,1,4,7]=>[4,2,6,1,3,7,8,5]=>[5,7,3,8,6,2,1,4]=>[2,2,1,1,2]
[1,3,4,5,6,7,2,8,9]=>[2,3,4,5,7,1,6,8,9]=>[8,7,6,5,3,9,4,2,1]=>[1,1,1,1,2,1,1,1]
[7,4,5,6,8,1,3,2]=>[2,3,8,6,4,1,7,5]=>[7,6,1,3,5,8,2,4]=>[1,1,4,2]
[7,6,8,1,4,5,3,2]=>[5,8,7,4,2,1,6,3]=>[4,1,2,5,7,8,3,6]=>[1,5,2]
[1,7,8,5,6,4,3,2]=>[4,2,8,7,6,5,1,3]=>[5,7,1,2,3,4,8,6]=>[2,5,1]
[2,8,1,7,4,5,3,6]=>[5,7,6,8,1,3,4,2]=>[4,2,3,1,8,6,5,7]=>[1,2,2,1,2]
[7,3,6,2,5,4,8,1]=>[6,2,4,5,3,1,8,7]=>[3,7,5,4,6,8,1,2]=>[2,1,3,2]
[1,6,2,3,5,8,4,7]=>[5,7,8,3,1,2,4,6]=>[4,2,1,6,8,7,5,3]=>[1,1,3,1,1,1]
[1,8,5,6,4,3,7,2]=>[3,6,5,4,8,7,1,2]=>[6,3,4,5,1,2,8,7]=>[1,3,3,1]
[2,6,8,4,5,1,7,3]=>[4,2,8,6,1,5,7,3]=>[5,7,1,3,8,4,2,6]=>[2,3,1,2]
[4,6,5,7,8,1,3,2]=>[3,1,2,8,6,4,7,5]=>[6,8,7,1,3,5,2,4]=>[2,1,3,2]
[2,5,8,6,4,7,1,3]=>[7,2,5,4,8,1,6,3]=>[2,7,4,5,1,8,3,6]=>[2,2,2,2]
[5,3,2,1,7,8,4,6]=>[2,7,3,1,5,8,4,6]=>[7,2,6,8,4,1,5,3]=>[1,3,1,2,1]
[8,4,1,3,6,7,2,5]=>[7,4,2,5,8,3,6,1]=>[2,5,7,4,1,6,3,8]=>[3,1,2,2]
[1,6,5,3,8,4,7,2]=>[6,3,2,8,4,7,1,5]=>[3,6,7,1,5,2,8,4]=>[3,2,2,1]
[7,6,2,3,5,1,4,8]=>[3,4,6,7,5,2,1,8]=>[6,5,3,2,4,7,8,1]=>[1,1,1,4,1]
[6,2,5,3,4,8,1,7]=>[4,5,2,3,1,7,8,6]=>[5,4,7,6,8,2,1,3]=>[1,2,2,1,2]
[6,2,5,3,4,8,7,1]=>[8,4,2,3,1,5,7,6]=>[1,5,7,6,8,4,2,3]=>[3,2,1,2]
[2,6,5,3,4,8,1,7]=>[4,5,3,1,2,7,8,6]=>[5,4,6,8,7,2,1,3]=>[1,3,1,1,2]
[5,1,3,4,8,7,2,6]=>[7,8,3,1,4,6,2,5]=>[2,1,6,8,5,3,7,4]=>[1,3,1,2,1]
[1,5,3,4,8,7,2,6]=>[7,2,8,3,4,6,1,5]=>[2,7,1,6,5,3,8,4]=>[2,2,1,2,1]
[5,1,3,8,4,7,6,2]=>[8,5,1,7,3,6,2,4]=>[1,4,8,2,6,3,7,5]=>[3,2,2,1]
[4,3,5,8,1,7,6,2]=>[1,8,2,3,7,5,6,4]=>[8,1,7,6,2,4,3,5]=>[1,2,1,2,2]
[3,6,5,4,8,1,2,7]=>[6,4,1,3,2,7,8,5]=>[3,5,8,6,7,2,1,4]=>[3,2,1,2]
[3,6,5,4,8,2,7,1]=>[4,3,1,2,6,8,7,5]=>[5,6,8,7,3,1,2,4]=>[3,1,1,3]
[2,5,3,6,8,4,1,7]=>[4,2,7,1,3,6,8,5]=>[5,7,2,8,6,3,1,4]=>[2,2,1,1,2]
[4,6,2,5,1,7,8,3]=>[1,6,3,4,2,8,5,7]=>[8,3,6,5,7,1,4,2]=>[1,2,2,2,1]
[2,3,6,5,8,4,1,7]=>[4,3,7,1,2,6,8,5]=>[5,6,2,8,7,3,1,4]=>[2,2,1,1,2]
[2,3,5,1,7,6,4,8]=>[3,7,1,2,6,4,5,8]=>[6,2,8,7,3,5,4,1]=>[1,2,1,2,1,1]
[2,3,1,7,4,8,6,5]=>[8,7,1,2,5,3,4,6]=>[1,2,8,7,4,6,5,3]=>[3,1,2,1,1]
[2,3,8,7,6,4,1,5]=>[7,6,8,5,1,2,4,3]=>[2,3,1,4,8,7,5,6]=>[2,3,1,2]
[2,6,3,7,4,1,5,8]=>[6,3,5,1,2,7,4,8]=>[3,6,4,8,7,2,5,1]=>[2,2,1,2,1]
[7,5,2,3,1,6,4,8]=>[3,4,7,5,2,6,1,8]=>[6,5,2,4,7,3,8,1]=>[1,1,3,2,1]
[1,8,3,6,4,2,7,5]=>[5,8,3,6,4,7,1,2]=>[4,1,6,3,5,2,8,7]=>[1,2,2,2,1]
[2,1,7,4,8,5,3,6]=>[7,4,6,1,3,8,2,5]=>[2,5,3,8,6,1,7,4]=>[2,2,1,2,1]
[8,1,7,3,2,5,4,6]=>[4,7,5,6,8,2,3,1]=>[5,2,4,3,1,7,6,8]=>[1,2,1,2,2]
[7,8,5,2,6,4,3,1]=>[8,7,4,3,1,6,5,2]=>[1,2,5,6,8,3,4,7]=>[5,3]
[4,2,8,1,3,6,7,5]=>[6,1,8,2,4,5,7,3]=>[3,8,1,7,5,4,2,6]=>[2,2,1,1,2]
[8,1,2,5,7,4,6,3]=>[4,6,8,7,2,3,5,1]=>[5,3,1,2,7,6,4,8]=>[1,1,3,1,2]
[7,4,6,3,1,2,5,8]=>[5,2,6,4,7,3,1,8]=>[4,7,3,5,2,6,8,1]=>[2,2,3,1]
[6,4,1,3,7,2,5,8]=>[4,6,2,7,3,1,5,8]=>[5,3,7,2,6,8,4,1]=>[1,2,3,1,1]
[8,2,5,3,6,1,4,7]=>[4,6,2,3,7,5,8,1]=>[5,3,7,6,2,4,1,8]=>[1,2,1,2,2]
[3,7,5,1,4,6,2,8]=>[5,7,1,4,3,6,2,8]=>[4,2,8,5,6,3,7,1]=>[1,2,2,2,1]
[8,6,4,7,5,1,3,2]=>[3,8,6,2,7,5,4,1]=>[6,1,3,7,2,4,5,8]=>[1,3,4]
[6,1,2,4,7,8,3,5]=>[7,4,5,8,2,1,3,6]=>[2,5,4,1,7,8,6,3]=>[2,1,3,1,1]
[2,4,6,5,7,1,8,3]=>[4,2,3,8,1,6,5,7]=>[5,7,6,1,8,3,4,2]=>[2,1,2,2,1]
[4,2,6,7,8,5,3,1]=>[1,3,4,8,7,2,6,5]=>[8,6,5,1,2,7,3,4]=>[1,1,1,3,2]
[6,2,4,7,8,5,3,1]=>[4,8,3,1,7,2,6,5]=>[5,1,6,8,2,7,3,4]=>[1,3,2,2]
[3,5,2,1,7,8,6,4]=>[5,1,2,8,3,7,4,6]=>[4,8,7,1,6,2,5,3]=>[2,1,2,2,1]
[1,2,7,8,6,4,5,3]=>[6,3,8,7,5,1,2,4]=>[3,6,1,2,4,8,7,5]=>[2,4,1,1]
[7,1,6,3,2,4,8,5]=>[4,8,5,6,2,3,1,7]=>[5,1,4,3,7,6,8,2]=>[1,2,2,2,1]
[6,4,8,1,2,3,7,5]=>[8,4,2,5,1,6,7,3]=>[1,5,7,4,8,3,2,6]=>[3,2,1,2]
[7,4,1,3,6,8,5,2]=>[5,2,8,4,7,3,1,6]=>[4,7,1,5,2,6,8,3]=>[2,2,3,1]
[7,2,5,1,6,4,3,8]=>[7,6,2,4,3,5,1,8]=>[2,3,7,5,6,4,8,1]=>[3,2,2,1]
[5,2,7,1,4,6,3,8]=>[5,7,2,1,4,6,3,8]=>[4,2,7,8,5,3,6,1]=>[1,3,1,2,1]
[6,3,8,5,7,1,4,2]=>[8,6,2,1,4,7,5,3]=>[1,3,7,8,5,2,4,6]=>[4,1,3]
[2,4,3,8,5,7,1,6]=>[2,5,7,8,1,3,6,4]=>[7,4,2,1,8,6,3,5]=>[1,1,1,2,1,2]
[2,8,3,1,4,6,5,7]=>[3,7,1,4,5,6,8,2]=>[6,2,8,5,4,3,1,7]=>[1,2,1,1,1,2]
[4,5,7,6,1,3,8,2]=>[1,2,6,8,5,4,3,7]=>[8,7,3,1,4,5,6,2]=>[1,1,1,4,1]
[3,7,1,6,5,8,2,4]=>[7,5,1,4,8,3,2,6]=>[2,4,8,5,1,6,7,3]=>[3,1,3,1]
[7,4,3,6,8,2,1,5]=>[2,7,3,6,4,1,8,5]=>[7,2,6,3,5,8,1,4]=>[1,2,3,2]
[3,8,5,4,7,6,1,2]=>[4,3,7,8,1,6,5,2]=>[5,6,2,1,8,3,4,7]=>[2,1,2,3]
[4,6,5,1,3,8,7,2]=>[8,1,5,3,2,7,4,6]=>[1,8,4,6,7,2,5,3]=>[2,3,2,1]
[5,4,6,2,1,8,7,3]=>[2,1,8,4,3,7,5,6]=>[7,8,1,5,6,2,4,3]=>[2,3,2,1]
[3,2,8,5,1,4,6,7]=>[1,5,6,2,4,7,8,3]=>[8,4,3,7,5,2,1,6]=>[1,1,2,1,1,2]
[3,5,4,1,2,8,6,7]=>[7,1,3,2,8,4,5,6]=>[2,8,6,7,1,5,4,3]=>[2,2,2,1,1]
[5,3,8,1,4,2,6,7]=>[2,6,4,1,5,7,8,3]=>[7,3,5,8,4,2,1,6]=>[1,3,1,1,2]
[5,3,8,1,4,2,7,6]=>[2,5,1,8,4,6,7,3]=>[7,4,8,1,5,3,2,6]=>[1,2,2,1,2]
[7,5,2,6,1,4,8,3]=>[6,8,3,2,5,4,1,7]=>[3,1,6,7,4,5,8,2]=>[1,3,3,1]
[2,4,5,1,8,3,7,6]=>[2,3,8,1,6,7,4,5]=>[7,6,1,8,3,2,5,4]=>[1,1,2,1,2,1]
[6,4,5,3,1,7,8,2]=>[2,6,4,3,1,8,5,7]=>[7,3,5,6,8,1,4,2]=>[1,4,2,1]
[7,3,5,6,4,1,8,2]=>[3,8,2,6,5,4,1,7]=>[6,1,7,3,4,5,8,2]=>[1,2,4,1]
[2,5,6,3,4,1,8,7]=>[4,2,5,1,3,8,6,7]=>[5,7,4,8,6,1,3,2]=>[2,2,1,2,1]
[4,6,2,1,5,8,3,7]=>[3,1,5,7,2,8,4,6]=>[6,8,4,2,7,1,5,3]=>[2,1,2,2,1]
[2,3,5,8,7,4,1,6]=>[7,3,6,8,1,2,5,4]=>[2,6,3,1,8,7,4,5]=>[2,1,2,1,2]
[2,3,5,8,7,4,6,1]=>[6,8,3,7,1,2,5,4]=>[3,1,6,2,8,7,4,5]=>[1,2,2,1,2]
[1,7,4,5,8,3,6,2]=>[3,4,6,2,8,7,1,5]=>[6,5,3,7,1,2,8,4]=>[1,1,2,3,1]
[8,6,1,5,4,2,7,3]=>[8,6,5,3,4,2,7,1]=>[1,3,4,6,5,7,2,8]=>[4,2,2]
[2,8,5,6,3,1,4,7]=>[6,5,3,7,1,4,8,2]=>[3,4,6,2,8,5,1,7]=>[3,2,1,2]
[2,3,7,8,1,5,4,6]=>[7,5,6,1,2,3,8,4]=>[2,4,3,8,7,6,1,5]=>[2,2,1,1,2]
[5,2,6,7,8,3,1,4]=>[3,1,7,6,2,4,8,5]=>[6,8,2,3,7,5,1,4]=>[2,3,1,2]
[5,6,2,7,8,3,1,4]=>[1,7,6,3,2,4,8,5]=>[8,2,3,6,7,5,1,4]=>[1,4,1,2]
[2,3,7,5,8,4,6,1]=>[4,6,3,8,1,2,7,5]=>[5,3,6,1,8,7,2,4]=>[1,2,2,1,2]
[2,5,6,7,1,8,4,3]=>[2,3,8,7,1,5,4,6]=>[7,6,1,2,8,4,5,3]=>[1,1,3,2,1]
[8,5,3,6,4,2,1,7]=>[7,3,2,6,5,4,8,1]=>[2,6,7,3,4,5,1,8]=>[3,3,2]
[2,3,7,8,5,4,6,1]=>[6,5,3,8,1,2,7,4]=>[3,4,6,1,8,7,2,5]=>[3,2,1,2]
[6,4,7,8,1,2,5,3]=>[2,8,5,1,6,3,7,4]=>[7,1,4,8,3,6,2,5]=>[1,3,2,2]
[7,5,8,1,2,3,6,4]=>[8,4,5,2,6,1,7,3]=>[1,5,4,7,3,8,2,6]=>[2,2,2,2]
[1,2,8,7,4,6,5,3]=>[8,5,7,6,4,1,2,3]=>[1,4,2,3,5,8,7,6]=>[2,4,1,1]
[5,1,4,8,7,3,6,2]=>[6,1,8,3,7,5,2,4]=>[3,8,1,6,2,4,7,5]=>[2,2,3,1]
[4,3,1,8,7,5,6,2]=>[1,6,8,2,7,5,3,4]=>[8,3,1,7,2,4,6,5]=>[1,1,2,3,1]
[7,2,6,5,3,1,4,8]=>[6,5,7,2,4,3,1,8]=>[3,4,2,7,5,6,8,1]=>[2,2,3,1]
[1,3,7,6,2,4,8,5]=>[8,5,6,2,4,1,3,7]=>[1,4,3,7,5,8,6,2]=>[2,2,2,1,1]
[1,3,8,2,7,4,6,5]=>[8,6,7,2,4,5,1,3]=>[1,3,2,7,5,4,8,6]=>[2,2,1,2,1]
[8,2,7,1,6,4,3,5]=>[7,6,8,2,4,5,3,1]=>[2,3,1,7,5,4,6,8]=>[2,2,1,3]
[7,5,4,1,6,3,8,2]=>[6,5,3,2,8,4,1,7]=>[3,4,6,7,1,5,8,2]=>[4,3,1]
[1,6,5,3,2,4,8,7]=>[4,8,5,3,1,2,6,7]=>[5,1,4,6,8,7,3,2]=>[1,4,1,1,1]
[4,3,7,2,5,1,6,8]=>[2,1,4,6,5,7,3,8]=>[7,8,5,3,4,2,6,1]=>[2,1,2,2,1]
[5,1,4,3,2,6,8,7]=>[4,3,8,2,1,5,6,7]=>[5,6,1,7,8,4,3,2]=>[2,3,1,1,1]
[7,2,1,3,5,4,6,8]=>[2,6,3,4,5,7,1,8]=>[7,3,6,5,4,2,8,1]=>[1,2,1,1,2,1]
[1,6,8,7,5,2,3,4]=>[6,2,7,8,5,4,1,3]=>[3,7,2,1,4,5,8,6]=>[2,1,4,1]
[4,3,6,1,8,5,2,7]=>[1,7,2,6,3,8,4,5]=>[8,2,7,3,6,1,5,4]=>[1,2,2,2,1]
[1,3,6,2,5,4,8,7]=>[5,8,2,4,1,3,6,7]=>[4,1,7,5,8,6,3,2]=>[1,2,2,1,1,1]
[1,4,8,7,3,6,2,5]=>[5,7,8,2,6,4,1,3]=>[4,2,1,7,3,5,8,6]=>[1,1,2,3,1]
[4,5,7,6,3,1,8,2]=>[8,1,2,6,5,4,3,7]=>[1,8,7,3,4,5,6,2]=>[2,1,4,1]
[4,6,7,5,1,3,8,2]=>[6,1,2,8,5,4,3,7]=>[3,8,7,1,4,5,6,2]=>[2,1,4,1]
[3,6,5,1,4,7,8,2]=>[5,6,1,3,2,8,4,7]=>[4,3,8,6,7,1,5,2]=>[1,2,2,2,1]
[5,4,1,8,7,3,6,2]=>[2,1,6,8,7,5,3,4]=>[7,8,3,1,2,4,6,5]=>[2,1,4,1]
[6,2,4,7,5,3,1,8]=>[7,3,6,2,1,5,4,8]=>[2,6,3,7,8,4,5,1]=>[2,3,2,1]
[6,2,5,1,8,7,3,4]=>[7,3,8,2,1,6,4,5]=>[2,6,1,7,8,3,5,4]=>[2,3,2,1]
[3,2,6,1,5,8,7,4]=>[8,1,5,2,3,7,4,6]=>[1,8,4,7,6,2,5,3]=>[2,2,1,2,1]
[4,2,3,6,7,5,1,8]=>[4,1,7,2,3,6,5,8]=>[5,8,2,7,6,3,4,1]=>[2,2,1,2,1]
[6,2,3,5,7,4,1,8]=>[4,7,2,3,1,6,5,8]=>[5,2,7,6,8,3,4,1]=>[1,2,2,2,1]
[1,6,3,8,4,7,2,5]=>[5,7,2,8,3,6,1,4]=>[4,2,7,1,6,3,8,5]=>[1,2,2,2,1]
[7,5,8,1,4,2,3,6]=>[6,7,4,2,5,1,8,3]=>[3,2,5,7,4,8,1,6]=>[1,3,2,2]
[1,3,4,8,5,6,2,7]=>[5,7,2,3,6,8,1,4]=>[4,2,7,6,3,1,8,5]=>[1,2,1,1,2,1]
[1,3,8,5,6,7,2,4]=>[4,7,5,8,2,6,1,3]=>[5,2,4,1,7,3,8,6]=>[1,2,2,2,1]
[6,2,4,1,5,7,8,3]=>[5,2,3,6,1,8,4,7]=>[4,7,6,3,8,1,5,2]=>[2,1,2,2,1]
[5,8,4,1,3,6,7,2]=>[5,1,6,3,8,4,7,2]=>[4,8,3,6,1,5,2,7]=>[2,2,2,2]
[6,7,2,3,8,1,4,5]=>[3,4,6,1,7,2,8,5]=>[6,5,3,8,2,7,1,4]=>[1,1,2,2,2]
[3,2,7,4,8,1,5,6]=>[1,4,6,7,2,3,8,5]=>[8,5,3,2,7,6,1,4]=>[1,1,1,2,1,2]
[2,5,4,7,3,1,8,6]=>[3,2,5,8,1,6,4,7]=>[6,7,4,1,8,3,5,2]=>[2,1,2,2,1]
[4,6,3,1,2,5,7,8]=>[4,1,5,3,6,2,7,8]=>[5,8,4,6,3,7,2,1]=>[2,2,2,1,1]
[7,4,6,8,3,1,2,5]=>[2,6,7,5,3,1,8,4]=>[7,3,2,4,6,8,1,5]=>[1,1,4,2]
[7,3,2,1,5,4,8,6]=>[3,2,5,8,4,6,1,7]=>[6,7,4,1,5,3,8,2]=>[2,1,2,2,1]
[2,5,6,4,8,1,3,7]=>[2,6,4,1,3,7,8,5]=>[7,3,5,8,6,2,1,4]=>[1,3,1,1,2]
[5,4,1,6,2,3,7,8]=>[5,6,3,2,1,4,7,8]=>[4,3,6,7,8,5,2,1]=>[1,4,1,1,1]
[1,3,6,5,2,4,7,8]=>[5,6,2,4,1,3,7,8]=>[4,3,7,5,8,6,2,1]=>[1,2,2,1,1,1]
[6,4,5,1,2,8,7,3]=>[2,8,7,4,3,1,5,6]=>[7,1,2,5,6,8,4,3]=>[1,5,1,1]
[5,4,1,2,7,6,3,8]=>[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>[5,1,1,1]
[5,8,7,3,1,2,4,6]=>[5,1,6,4,7,8,3,2]=>[4,8,3,5,2,1,6,7]=>[2,2,1,3]
[2,7,8,1,4,5,3,6]=>[5,7,4,6,1,2,8,3]=>[4,2,5,3,8,7,1,6]=>[1,2,2,1,2]
[4,1,2,8,7,3,6,5]=>[1,8,6,7,5,2,3,4]=>[8,1,3,2,4,7,6,5]=>[1,2,3,1,1]
[6,1,2,4,3,8,7,5]=>[8,4,7,2,3,1,5,6]=>[1,5,2,7,6,8,4,3]=>[2,2,2,1,1]
[3,7,8,1,2,4,6,5]=>[8,1,4,5,6,2,7,3]=>[1,8,5,4,3,7,2,6]=>[2,1,1,2,2]
[8,4,3,1,2,6,5,7]=>[7,4,3,2,5,6,8,1]=>[2,5,6,7,4,3,1,8]=>[4,1,1,2]
[3,8,2,7,4,5,1,6]=>[5,7,1,3,6,8,4,2]=>[4,2,8,6,3,1,5,7]=>[1,2,1,1,3]
[8,6,2,3,5,4,1,7]=>[7,3,4,6,5,2,8,1]=>[2,6,5,3,4,7,1,8]=>[2,1,3,2]
[8,2,6,1,3,5,4,7]=>[7,2,4,5,6,3,8,1]=>[2,7,5,4,3,6,1,8]=>[2,1,1,2,2]
[8,4,3,7,2,5,6,1]=>[3,2,5,6,8,7,4,1]=>[6,7,4,3,1,2,5,8]=>[2,1,1,4]
[8,3,1,7,4,5,2,6]=>[2,5,7,6,8,3,4,1]=>[7,4,2,3,1,6,5,8]=>[1,1,2,2,2]
[6,8,2,4,5,1,7,3]=>[4,8,3,1,6,5,7,2]=>[5,1,6,8,3,4,2,7]=>[1,3,2,2]
[4,3,8,1,7,5,6,2]=>[1,6,8,2,7,4,5,3]=>[8,3,1,7,2,5,4,6]=>[1,1,2,2,2]
[8,4,3,7,1,5,6,2]=>[3,2,6,8,5,7,4,1]=>[6,7,3,1,4,2,5,8]=>[2,1,2,3]
[8,3,4,7,2,6,5,1]=>[8,2,3,5,7,6,4,1]=>[1,7,6,4,2,3,5,8]=>[2,1,1,4]
[8,1,3,7,6,4,5,2]=>[6,8,7,3,5,2,4,1]=>[3,1,2,6,4,7,5,8]=>[1,3,2,2]
[8,3,7,1,4,5,6,2]=>[2,5,6,8,4,7,3,1]=>[7,4,3,1,5,2,6,8]=>[1,1,1,2,3]
[8,3,7,6,2,4,5,1]=>[5,6,8,2,7,4,3,1]=>[4,3,1,7,2,5,6,8]=>[1,1,2,4]
[8,7,2,3,6,1,5,4]=>[8,3,4,6,7,5,2,1]=>[1,6,5,3,2,4,7,8]=>[2,1,1,4]
[8,2,7,1,3,4,6,5]=>[8,2,4,5,6,7,3,1]=>[1,7,5,4,3,2,6,8]=>[2,1,1,1,3]
[5,1,8,4,2,3,7,6]=>[8,5,4,1,6,7,2,3]=>[1,4,5,8,3,2,7,6]=>[4,1,2,1]
[8,2,4,7,3,1,6,5]=>[3,5,8,2,6,7,4,1]=>[6,4,1,7,3,2,5,8]=>[1,1,2,1,3]
[6,8,1,4,7,3,2,5]=>[4,7,6,1,8,3,5,2]=>[5,2,3,8,1,6,4,7]=>[1,3,2,2]
[8,5,7,2,6,3,1,4]=>[7,4,2,6,8,5,3,1]=>[2,5,7,3,1,4,6,8]=>[3,1,4]
[5,8,2,7,3,1,6,4]=>[5,1,8,3,6,7,4,2]=>[4,8,1,6,3,2,5,7]=>[2,2,1,3]
[8,1,2,6,7,5,4,3]=>[4,8,7,6,2,3,5,1]=>[5,1,2,3,7,6,4,8]=>[1,4,1,2]
[8,4,1,7,5,6,2,3]=>[2,7,5,8,6,3,4,1]=>[7,2,4,1,3,6,5,8]=>[1,2,3,2]
[8,2,4,7,6,5,1,3]=>[7,8,3,6,2,5,4,1]=>[2,1,6,3,7,4,5,8]=>[1,2,2,3]
[8,2,7,6,4,5,1,3]=>[7,5,8,6,2,4,3,1]=>[2,4,1,3,7,5,6,8]=>[2,3,3]
[8,4,7,2,3,6,5,1]=>[2,8,4,5,7,6,3,1]=>[7,1,5,4,2,3,6,8]=>[1,2,1,4]
[8,2,4,7,3,6,5,1]=>[8,3,5,7,2,6,4,1]=>[1,6,4,2,7,3,5,8]=>[2,1,2,3]
[8,1,7,6,4,5,2,3]=>[7,5,8,6,4,2,3,1]=>[2,4,1,3,5,7,6,8]=>[2,4,2]
[8,1,4,7,3,6,5,2]=>[8,3,5,7,6,2,4,1]=>[1,6,4,2,3,7,5,8]=>[2,1,3,2]
[2,8,1,5,3,7,6,4]=>[4,8,7,1,3,5,6,2]=>[5,1,2,8,6,4,3,7]=>[1,3,1,1,2]
[1,8,2,4,7,5,6,3]=>[6,8,4,7,3,5,1,2]=>[3,1,5,2,6,4,8,7]=>[1,2,2,2,1]
[2,3,8,4,7,1,6,5]=>[8,4,6,7,1,2,5,3]=>[1,5,3,2,8,7,4,6]=>[2,1,2,1,2]
[1,8,2,3,5,6,4,7]=>[5,7,3,4,6,8,1,2]=>[4,2,6,5,3,1,8,7]=>[1,2,1,1,2,1]
[1,4,7,6,2,3,5,8]=>[2,5,6,7,4,1,3,8]=>[7,4,3,2,5,8,6,1]=>[1,1,1,3,1,1]
[1,7,6,2,3,8,4,5]=>[7,8,4,5,3,1,2,6]=>[2,1,5,4,6,8,7,3]=>[1,2,3,1,1]
[1,7,3,8,6,2,5,4]=>[8,6,7,3,2,5,1,4]=>[1,3,2,6,7,4,8,5]=>[2,3,2,1]
[5,8,2,3,7,4,1,6]=>[7,3,1,4,6,8,5,2]=>[2,6,8,5,3,1,4,7]=>[3,1,1,3]
[4,2,8,3,7,6,1,5]=>[1,7,8,4,6,2,5,3]=>[8,2,1,5,3,7,4,6]=>[1,1,2,2,2]
[1,3,5,6,4,8,2,7]=>[3,5,2,4,7,8,1,6]=>[6,4,7,5,2,1,8,3]=>[1,2,1,1,2,1]
[3,1,7,8,5,2,4,6]=>[6,7,1,5,3,8,2,4]=>[3,2,8,4,6,1,7,5]=>[1,2,2,2,1]
[4,6,1,8,2,7,5,3]=>[8,1,7,5,2,6,3,4]=>[1,8,2,4,7,3,6,5]=>[2,3,2,1]
[6,3,5,2,8,4,7,1]=>[6,2,3,1,8,4,7,5]=>[3,7,6,8,1,5,2,4]=>[2,2,2,2]
[1,6,3,5,2,8,4,7]=>[7,3,4,2,8,1,5,6]=>[2,6,5,7,1,8,4,3]=>[2,2,2,1,1]
[5,4,8,6,3,7,2,1]=>[1,5,2,4,8,7,6,3]=>[8,4,7,5,1,2,3,6]=>[1,2,1,4]
[6,3,5,1,8,4,7,2]=>[6,2,3,1,8,7,4,5]=>[3,7,6,8,1,2,5,4]=>[2,2,3,1]
[2,6,3,1,5,8,4,7]=>[3,5,7,1,2,8,4,6]=>[6,4,2,8,7,1,5,3]=>[1,1,2,1,2,1]
[2,5,4,8,6,3,1,7]=>[2,7,3,6,1,5,8,4]=>[7,2,6,3,8,4,1,5]=>[1,2,2,1,2]
[2,5,4,8,6,3,7,1]=>[2,6,3,5,8,1,7,4]=>[7,3,6,4,1,8,2,5]=>[1,2,1,2,2]
[1,2,5,4,8,6,3,7]=>[3,7,4,6,8,1,2,5]=>[6,2,5,3,1,8,7,4]=>[1,2,1,2,1,1]
[6,4,5,8,2,1,7,3]=>[2,5,3,1,8,6,7,4]=>[7,4,6,8,1,3,2,5]=>[1,3,2,2]
[5,3,4,1,2,6,8,7]=>[2,8,4,3,1,5,6,7]=>[7,1,5,6,8,4,3,2]=>[1,4,1,1,1]
[1,4,3,5,2,8,6,7]=>[3,2,4,7,8,1,5,6]=>[6,7,5,2,1,8,4,3]=>[2,1,1,2,1,1]
[1,3,5,4,8,2,6,7]=>[4,2,3,6,7,8,1,5]=>[5,7,6,3,2,1,8,4]=>[2,1,1,1,2,1]
[3,5,4,8,2,6,1,7]=>[3,1,2,5,7,6,8,4]=>[6,8,7,4,2,3,1,5]=>[2,1,1,2,2]
[3,6,4,5,1,2,8,7]=>[3,8,1,5,4,2,6,7]=>[6,1,8,4,5,7,3,2]=>[1,2,3,1,1]
[4,3,5,1,8,6,2,7]=>[2,1,3,7,6,8,4,5]=>[7,8,6,2,3,1,5,4]=>[2,1,2,2,1]
[3,5,4,8,1,6,2,7]=>[3,1,2,7,5,6,8,4]=>[6,8,7,2,4,3,1,5]=>[2,1,2,1,2]
[3,4,8,5,6,1,2,7]=>[6,1,2,4,7,5,8,3]=>[3,8,7,5,2,4,1,6]=>[2,1,1,2,2]
[3,4,8,5,6,2,1,7]=>[4,7,1,2,6,5,8,3]=>[5,2,8,7,3,4,1,6]=>[1,2,1,2,2]
[3,5,4,8,1,6,7,2]=>[3,1,2,6,8,5,7,4]=>[6,8,7,3,1,4,2,5]=>[2,1,1,2,2]
[2,4,3,1,5,8,6,7]=>[3,1,2,7,8,4,5,6]=>[6,8,7,2,1,5,4,3]=>[2,1,1,2,1,1]
[1,7,6,2,5,4,8,3]=>[6,5,8,4,3,1,2,7]=>[3,4,1,5,6,8,7,2]=>[2,4,1,1]
[5,6,1,7,4,3,8,2]=>[1,6,5,4,2,8,3,7]=>[8,3,4,5,7,1,6,2]=>[1,4,2,1]
[3,7,2,1,5,6,8,4]=>[1,3,5,6,8,4,2,7]=>[8,6,4,3,1,5,7,2]=>[1,1,1,1,3,1]
[8,1,6,4,3,5,2,7]=>[5,4,7,6,2,3,8,1]=>[4,5,2,3,7,6,1,8]=>[2,3,1,2]
[1,3,7,8,2,6,4,5]=>[7,8,5,2,3,6,1,4]=>[2,1,4,7,6,3,8,5]=>[1,3,1,2,1]
[2,1,6,5,3,8,7,4]=>[4,3,8,1,7,2,5,6]=>[5,6,1,8,2,7,4,3]=>[2,2,2,1,1]
[3,4,5,6,7,9,2,1,8]=>[1,2,3,4,5,8,7,9,6]=>[9,8,7,6,5,2,3,1,4]=>[1,1,1,1,1,2,2]
[3,4,5,6,9,2,1,7,8]=>[1,2,3,4,7,6,8,9,5]=>[9,8,7,6,3,4,2,1,5]=>[1,1,1,1,2,1,2]
[3,7,5,6,4,2,1,8]=>[3,7,6,1,5,4,2,8]=>[6,2,3,8,4,5,7,1]=>[1,3,3,1]
[6,1,4,3,7,5,8,2]=>[3,6,4,5,1,8,2,7]=>[6,3,5,4,8,1,7,2]=>[1,2,2,2,1]
[3,8,6,4,5,2,7,1]=>[4,6,5,1,3,8,7,2]=>[5,3,4,8,6,1,2,7]=>[1,3,1,3]
[4,5,8,6,2,3,7,1]=>[1,2,5,6,4,8,7,3]=>[8,7,4,3,5,1,2,6]=>[1,1,1,2,3]
[3,7,4,5,1,6,8,2]=>[3,6,1,4,8,5,2,7]=>[6,3,8,5,1,4,7,2]=>[1,2,1,3,1]
[4,6,8,5,1,3,7,2]=>[6,1,2,8,5,4,7,3]=>[3,8,7,1,4,5,2,6]=>[2,1,3,2]
[3,7,4,5,2,8,6,1]=>[3,4,8,1,5,2,7,6]=>[6,5,1,8,4,7,2,3]=>[1,1,2,2,2]
[4,5,1,6,8,3,7,2]=>[1,4,2,6,8,7,3,5]=>[8,5,7,3,1,2,6,4]=>[1,2,1,3,1]
[8,3,5,4,6,1,2,7]=>[6,2,4,3,7,5,8,1]=>[3,7,5,6,2,4,1,8]=>[2,2,2,2]
[1,7,4,5,2,6,8,3]=>[3,6,4,8,5,1,2,7]=>[6,3,5,1,4,8,7,2]=>[1,2,3,1,1]
[1,4,2,6,5,3,8,7]=>[2,5,4,8,1,3,6,7]=>[7,4,5,1,8,6,3,2]=>[1,2,2,1,1,1]
[3,1,5,8,4,6,2,7]=>[1,3,5,7,6,8,2,4]=>[8,6,4,2,3,1,7,5]=>[1,1,1,2,2,1]
[8,2,6,3,4,1,5,7]=>[4,6,2,5,7,3,8,1]=>[5,3,7,4,2,6,1,8]=>[1,2,1,2,2]
[4,6,5,8,2,1,3,7]=>[6,1,5,3,2,7,8,4]=>[3,8,4,6,7,2,1,5]=>[2,3,1,2]
[1,4,8,3,5,6,2,7]=>[2,4,5,7,6,8,1,3]=>[7,5,4,2,3,1,8,6]=>[1,1,1,2,2,1]
[1,8,7,4,2,3,6,5]=>[8,5,4,6,7,3,1,2]=>[1,4,5,3,2,6,8,7]=>[3,1,3,1]
[4,3,1,8,5,7,2,6]=>[2,1,5,7,8,6,3,4]=>[7,8,4,2,1,3,6,5]=>[2,1,1,3,1]
[7,3,2,4,8,1,6,5]=>[2,8,3,4,6,1,7,5]=>[7,1,6,5,3,8,2,4]=>[1,2,1,2,2]
[3,7,2,4,5,8,1,6]=>[1,3,4,5,7,2,8,6]=>[8,6,5,4,2,7,1,3]=>[1,1,1,1,2,2]
[3,2,7,4,6,1,8,5]=>[8,1,4,6,2,5,3,7]=>[1,8,5,3,7,4,6,2]=>[2,1,2,2,1]
[8,3,2,4,5,7,1,6]=>[3,2,4,5,7,8,6,1]=>[6,7,5,4,2,1,3,8]=>[2,1,1,1,3]
[7,4,6,2,1,3,8,5]=>[4,2,8,5,6,3,1,7]=>[5,7,1,4,3,6,8,2]=>[2,2,3,1]
[3,6,7,2,4,1,8,5]=>[4,5,1,2,8,6,3,7]=>[5,4,8,7,1,3,6,2]=>[1,2,1,3,1]
[8,4,7,2,3,5,6,1]=>[4,2,5,6,8,7,3,1]=>[5,7,4,3,1,2,6,8]=>[2,1,1,4]
[3,8,6,7,1,5,4,2]=>[8,7,5,1,3,6,4,2]=>[1,2,4,8,6,3,5,7]=>[4,1,3]
[4,3,2,8,6,1,5,7]=>[2,1,6,7,3,5,8,4]=>[7,8,3,2,6,4,1,5]=>[2,1,2,1,2]
[4,1,6,3,2,5,7,8]=>[5,4,1,6,2,3,7,8]=>[4,5,8,3,7,6,2,1]=>[3,2,1,1,1]
[5,7,1,8,4,3,6,2]=>[1,6,5,8,7,3,2,4]=>[8,3,4,1,2,6,7,5]=>[1,2,4,1]
[5,4,8,7,6,2,3,1]=>[1,6,8,2,7,5,4,3]=>[8,3,1,7,2,4,5,6]=>[1,1,2,4]
[8,4,6,3,1,5,2,7]=>[2,7,5,4,6,3,8,1]=>[7,2,4,5,3,6,1,8]=>[1,3,2,2]
[3,6,1,5,2,4,7,8]=>[1,5,6,3,4,2,7,8]=>[8,4,3,6,5,7,2,1]=>[1,1,2,2,1,1]
[3,7,6,2,5,4,1,8]=>[7,4,6,1,5,3,2,8]=>[2,5,3,8,4,6,7,1]=>[2,2,3,1]
[2,7,1,5,3,4,6,8]=>[5,6,1,3,4,7,2,8]=>[4,3,8,6,5,2,7,1]=>[1,2,1,1,2,1]
[5,2,3,8,7,1,6,4]=>[8,6,1,7,2,3,5,4]=>[1,3,8,2,7,6,4,5]=>[3,2,1,2]
[7,5,2,4,1,3,8,6]=>[8,3,5,4,2,6,1,7]=>[1,6,4,5,7,3,8,2]=>[2,3,2,1]
[7,2,6,8,5,1,3,4]=>[6,7,3,8,2,1,5,4]=>[3,2,6,1,7,8,4,5]=>[1,2,3,2]
[8,6,5,4,1,3,7,2]=>[6,8,5,4,3,2,7,1]=>[3,1,4,5,6,7,2,8]=>[1,5,2]
[8,2,3,4,1,6,7,5]=>[2,3,4,6,8,5,7,1]=>[7,6,5,3,1,4,2,8]=>[1,1,1,1,2,2]
[7,4,3,8,1,6,5,2]=>[2,8,3,7,5,1,6,4]=>[7,1,6,2,4,8,3,5]=>[1,2,3,2]
[6,5,1,4,3,8,7,2]=>[4,8,5,2,1,7,3,6]=>[5,1,4,7,8,2,6,3]=>[1,4,2,1]
[4,7,6,2,5,8,1,3]=>[7,1,4,5,3,2,8,6]=>[2,8,5,4,6,7,1,3]=>[2,1,3,2]
[6,3,2,4,5,8,1,7]=>[3,2,4,5,1,7,8,6]=>[6,7,5,4,8,2,1,3]=>[2,1,2,1,2]
[2,6,4,5,8,3,1,7]=>[3,4,2,7,1,6,8,5]=>[6,5,7,2,8,3,1,4]=>[1,2,2,1,2]
[3,7,4,8,6,2,5,1]=>[6,8,3,1,2,7,5,4]=>[3,1,6,8,7,2,4,5]=>[1,3,1,3]
[7,3,5,2,8,1,4,6]=>[2,4,6,3,7,1,8,5]=>[7,5,3,6,2,8,1,4]=>[1,1,2,2,2]
[1,5,8,7,4,2,3,6]=>[2,6,7,5,8,4,1,3]=>[7,3,2,4,1,5,8,6]=>[1,1,2,3,1]
[1,7,2,4,5,8,6,3]=>[8,4,5,7,3,1,2,6]=>[1,5,4,2,6,8,7,3]=>[2,1,3,1,1]
[1,4,6,8,7,2,5,3]=>[3,8,2,6,7,5,1,4]=>[6,1,7,3,2,4,8,5]=>[1,2,1,3,1]
[1,3,7,2,6,4,5,8]=>[6,7,2,4,5,1,3,8]=>[3,2,7,5,4,8,6,1]=>[1,2,1,2,1,1]
[1,7,3,2,8,5,6,4]=>[6,8,3,7,4,1,2,5]=>[3,1,6,2,5,8,7,4]=>[1,2,3,1,1]
[1,6,5,2,4,8,3,7]=>[5,7,3,2,8,1,4,6]=>[4,2,6,7,1,8,5,3]=>[1,3,2,1,1]
[1,7,3,8,4,2,5,6]=>[6,3,5,7,2,8,1,4]=>[3,6,4,2,7,1,8,5]=>[2,1,2,2,1]
[1,6,2,4,7,5,8,3]=>[6,4,5,2,8,1,3,7]=>[3,5,4,7,1,8,6,2]=>[2,2,2,1,1]
[1,6,2,7,4,3,8,5]=>[5,8,6,3,1,2,4,7]=>[4,1,3,6,8,7,5,2]=>[1,4,1,1,1]
[2,5,3,6,7,1,4,8]=>[6,3,1,2,4,7,5,8]=>[3,6,8,7,5,2,4,1]=>[3,1,1,2,1]
[6,4,1,5,7,2,3,8]=>[6,4,2,7,3,1,5,8]=>[3,5,7,2,6,8,4,1]=>[3,3,1,1]
[6,4,1,5,7,3,8,2]=>[4,2,6,5,1,8,3,7]=>[5,7,3,4,8,1,6,2]=>[2,3,2,1]
[1,2,7,3,8,5,6,4]=>[6,8,7,4,1,2,3,5]=>[3,1,2,5,8,7,6,4]=>[1,4,1,1,1]
[7,4,1,6,3,8,2,5]=>[5,2,7,4,8,3,1,6]=>[4,7,2,5,1,6,8,3]=>[2,2,3,1]
[1,5,7,4,3,8,6,2]=>[2,4,8,5,3,7,1,6]=>[7,5,1,4,6,2,8,3]=>[1,1,3,2,1]
[2,7,3,1,4,5,8,6]=>[3,8,1,4,5,6,2,7]=>[6,1,8,5,4,3,7,2]=>[1,2,1,1,2,1]
[2,3,4,5,1,7,6,9,8]=>[1,2,3,4,6,9,5,7,8]=>[9,8,7,6,4,1,5,3,2]=>[1,1,1,1,1,2,1,1]
[6,5,8,3,2,7,1,4]=>[5,4,2,1,7,8,6,3]=>[4,5,7,8,2,1,3,6]=>[4,1,3]
[8,4,3,1,7,6,5,2]=>[2,8,3,7,6,4,5,1]=>[7,1,6,2,3,5,4,8]=>[1,2,3,2]
[1,2,6,7,5,3,4,8]=>[6,3,7,5,1,2,4,8]=>[3,6,2,4,8,7,5,1]=>[2,3,1,1,1]
[1,2,6,8,7,4,5,3]=>[3,6,8,7,5,1,2,4]=>[6,3,1,2,4,8,7,5]=>[1,1,4,1,1]
[3,4,5,6,8,2,7,1]=>[1,2,3,4,6,8,7,5]=>[8,7,6,5,3,1,2,4]=>[1,1,1,1,1,3]
[7,2,1,4,5,6,3,8]=>[2,4,5,7,3,6,1,8]=>[7,5,4,2,6,3,8,1]=>[1,1,1,2,2,1]
[1,5,6,7,3,4,2,8]=>[2,5,3,7,6,1,4,8]=>[7,4,6,2,3,8,5,1]=>[1,2,3,1,1]
[4,6,8,5,2,1,7,3]=>[5,1,2,8,6,4,7,3]=>[4,8,7,1,3,5,2,6]=>[2,1,3,2]
[5,7,8,3,2,4,6,1]=>[1,5,4,6,2,8,7,3]=>[8,4,5,3,7,1,2,6]=>[1,2,2,3]
[5,7,8,2,3,1,6,4]=>[4,1,5,8,6,2,7,3]=>[5,8,4,1,3,7,2,6]=>[2,1,3,2]
[4,5,2,7,8,6,1,3]=>[1,2,7,4,8,3,6,5]=>[8,7,2,5,1,6,3,4]=>[1,1,2,2,2]
[1,3,5,8,7,2,6,4]=>[8,3,6,7,2,5,1,4]=>[1,6,3,2,7,4,8,5]=>[2,1,2,2,1]
[6,4,1,8,5,7,3,2]=>[2,5,1,8,7,6,3,4]=>[7,4,8,1,2,3,6,5]=>[1,2,4,1]
[8,5,1,6,7,2,4,3]=>[8,6,4,2,7,3,5,1]=>[1,3,5,7,2,6,4,8]=>[4,2,2]
[2,5,6,1,3,8,7,4]=>[2,8,7,1,4,3,5,6]=>[7,1,2,8,5,6,4,3]=>[1,3,2,1,1]
[3,8,5,7,2,4,6,1]=>[5,3,6,8,1,7,4,2]=>[4,6,3,1,8,2,5,7]=>[2,1,2,3]
[6,7,1,4,5,2,8,3]=>[4,8,6,3,1,5,2,7]=>[5,1,3,6,8,4,7,2]=>[1,4,2,1]
[6,4,1,2,5,8,3,7]=>[5,7,2,8,3,1,4,6]=>[4,2,7,1,6,8,5,3]=>[1,2,3,1,1]
[4,6,3,5,7,1,8,2]=>[1,3,4,2,8,6,5,7]=>[8,6,5,7,1,3,4,2]=>[1,1,2,3,1]
[2,3,5,4,7,1,8,6]=>[3,8,1,2,4,6,5,7]=>[6,1,8,7,5,3,4,2]=>[1,2,1,1,2,1]
[6,8,4,1,5,7,3,2]=>[5,3,1,8,7,4,6,2]=>[4,6,8,1,2,5,3,7]=>[3,3,2]
[8,1,6,2,3,7,5,4]=>[8,7,4,5,2,3,6,1]=>[1,2,5,4,7,6,3,8]=>[3,2,1,2]
[2,8,3,6,4,1,7,5]=>[5,8,3,6,1,4,7,2]=>[4,1,6,3,8,5,2,7]=>[1,2,2,1,2]
[5,1,8,7,3,2,6,4]=>[5,1,8,6,7,4,2,3]=>[4,8,1,3,2,5,7,6]=>[2,2,3,1]
[6,5,3,4,8,2,1,7]=>[3,4,2,1,7,6,8,5]=>[6,5,7,8,2,3,1,4]=>[1,3,2,2]
[5,4,8,7,3,6,2,1]=>[1,5,8,2,7,6,4,3]=>[8,4,1,7,2,3,5,6]=>[1,1,2,4]
[5,2,7,6,8,3,4,1]=>[1,6,4,3,8,2,7,5]=>[8,3,5,6,1,7,2,4]=>[1,3,2,2]
[8,4,5,2,7,3,6,1]=>[2,6,3,8,4,7,5,1]=>[7,3,6,1,5,2,4,8]=>[1,2,2,3]
[6,3,7,4,5,2,8,1]=>[4,6,2,1,5,3,8,7]=>[5,3,7,8,4,6,1,2]=>[1,3,2,2]
[7,3,4,2,8,5,6,1]=>[2,3,6,8,4,1,7,5]=>[7,6,3,1,5,8,2,4]=>[1,1,1,3,2]
[4,3,6,5,8,2,7,1]=>[1,4,2,3,6,8,7,5]=>[8,5,7,6,3,1,2,4]=>[1,2,1,1,3]
[8,2,7,4,5,3,6,1]=>[4,6,5,8,2,7,3,1]=>[5,3,4,1,7,2,6,8]=>[1,2,2,3]
[7,2,8,4,5,3,6,1]=>[4,6,5,8,2,1,7,3]=>[5,3,4,1,7,8,2,6]=>[1,2,3,2]
[6,3,8,2,7,4,5,1]=>[6,8,2,1,4,7,5,3]=>[3,1,7,8,5,2,4,6]=>[1,3,1,3]
[3,2,8,4,7,5,6,1]=>[6,8,1,4,7,2,5,3]=>[3,1,8,5,2,7,4,6]=>[1,2,1,2,2]
[8,3,6,2,7,4,5,1]=>[6,8,2,4,3,7,5,1]=>[3,1,7,5,6,2,4,8]=>[1,2,2,3]
[1,7,8,3,6,5,4,2]=>[8,7,4,2,6,5,1,3]=>[1,2,5,7,3,4,8,6]=>[4,3,1]
[6,4,5,8,7,2,1,3]=>[2,3,1,7,6,8,5,4]=>[7,6,8,2,3,1,4,5]=>[1,2,2,3]
[5,8,1,7,2,4,3,6]=>[7,5,1,6,8,3,4,2]=>[2,4,8,3,1,6,5,7]=>[3,1,2,2]
[2,5,7,3,8,1,4,6]=>[4,2,6,7,1,3,8,5]=>[5,7,3,2,8,6,1,4]=>[2,1,2,1,2]
[8,3,5,2,1,6,7,4]=>[2,4,6,3,8,5,7,1]=>[7,5,3,6,1,4,2,8]=>[1,1,2,2,2]
[2,6,4,7,1,8,5,3]=>[8,3,2,7,1,5,4,6]=>[1,6,7,2,8,4,5,3]=>[3,2,2,1]
[1,6,5,7,3,8,2,4]=>[5,3,2,7,4,8,1,6]=>[4,6,7,2,5,1,8,3]=>[3,2,2,1]
[1,8,5,3,7,6,2,4]=>[7,3,8,4,6,5,1,2]=>[2,6,1,5,3,4,8,7]=>[2,2,3,1]
[6,4,2,3,8,7,5,1]=>[2,8,7,3,1,4,6,5]=>[7,1,2,6,8,5,3,4]=>[1,4,1,2]
[6,5,1,3,8,4,2,7]=>[7,4,6,2,1,8,3,5]=>[2,5,3,7,8,1,6,4]=>[2,3,2,1]
[6,1,4,2,7,8,3,5]=>[3,7,5,8,2,1,4,6]=>[6,2,4,1,7,8,5,3]=>[1,2,3,1,1]
[6,5,1,3,7,8,4,2]=>[5,8,4,2,1,7,3,6]=>[4,1,5,7,8,2,6,3]=>[1,4,2,1]
[5,1,3,2,7,8,6,4]=>[5,8,3,1,7,2,4,6]=>[4,1,6,8,2,7,5,3]=>[1,3,2,1,1]
[5,6,8,2,4,7,1,3]=>[1,7,4,2,5,8,6,3]=>[8,2,5,7,4,1,3,6]=>[1,3,1,3]
[5,1,3,2,6,8,4,7]=>[3,5,7,1,8,2,4,6]=>[6,4,2,8,1,7,5,3]=>[1,1,2,2,1,1]
[5,7,1,4,6,8,2,3]=>[4,1,7,5,8,3,2,6]=>[5,8,2,4,1,6,7,3]=>[2,2,3,1]
[2,4,1,7,5,6,3,8]=>[2,5,7,1,6,3,4,8]=>[7,4,2,8,3,6,5,1]=>[1,1,2,2,1,1]
[1,4,3,7,6,2,8,5]=>[8,2,6,3,5,1,4,7]=>[1,7,3,6,4,8,5,2]=>[2,2,2,1,1]
[1,4,3,8,2,5,7,6]=>[2,8,3,5,6,7,1,4]=>[7,1,6,4,3,2,8,5]=>[1,2,1,1,2,1]
[1,5,7,3,6,4,2,8]=>[2,7,4,6,5,1,3,8]=>[7,2,5,3,4,8,6,1]=>[1,2,3,1,1]
[1,6,7,2,4,8,3,5]=>[5,7,2,8,4,1,3,6]=>[4,2,7,1,5,8,6,3]=>[1,2,3,1,1]
[3,7,2,8,4,1,5,6]=>[6,1,3,5,7,2,8,4]=>[3,8,6,4,2,7,1,5]=>[2,1,1,2,2]
[2,3,8,4,5,7,1,6]=>[4,5,7,8,1,2,6,3]=>[5,4,2,1,8,7,3,6]=>[1,1,1,2,1,2]
[4,1,8,3,2,6,5,7]=>[4,1,7,5,6,8,2,3]=>[5,8,2,4,3,1,7,6]=>[2,2,1,2,1]
[1,2,6,8,4,3,5,7]=>[6,5,3,7,8,1,2,4]=>[3,4,6,2,1,8,7,5]=>[3,1,2,1,1]
[7,2,6,3,1,8,4,5]=>[4,7,8,2,5,3,1,6]=>[5,2,1,7,4,6,8,3]=>[1,1,2,3,1]
[3,4,2,1,6,8,5,7]=>[1,3,2,5,7,8,4,6]=>[8,6,7,4,2,1,5,3]=>[1,2,1,1,2,1]
[3,4,7,1,5,6,2,8]=>[1,2,5,7,4,6,3,8]=>[8,7,4,2,5,3,6,1]=>[1,1,1,2,2,1]
[4,8,7,2,5,6,1,3]=>[7,1,4,5,8,6,3,2]=>[2,8,5,4,1,3,6,7]=>[2,1,1,4]
[5,8,6,4,7,3,2,1]=>[4,1,3,8,7,6,5,2]=>[5,8,6,1,2,3,4,7]=>[2,1,5]
[8,5,2,3,1,6,7,4]=>[3,4,6,2,8,5,7,1]=>[6,5,3,7,1,4,2,8]=>[1,1,2,2,2]
[2,8,6,3,5,1,7,4]=>[8,4,6,5,1,3,7,2]=>[1,5,3,4,8,6,2,7]=>[2,3,1,2]
[8,3,2,6,4,1,7,5]=>[2,5,8,3,6,4,7,1]=>[7,4,1,6,3,5,2,8]=>[1,1,2,2,2]
[8,4,1,5,3,6,7,2]=>[5,4,2,6,8,3,7,1]=>[4,5,7,3,1,6,2,8]=>[3,1,2,2]
[8,5,1,3,4,6,7,2]=>[4,5,6,2,8,3,7,1]=>[5,4,3,7,1,6,2,8]=>[1,1,2,2,2]
[3,8,6,2,5,4,7,1]=>[6,4,5,1,3,8,7,2]=>[3,5,4,8,6,1,2,7]=>[2,2,1,3]
[8,1,7,4,2,5,3,6]=>[7,5,4,6,8,2,3,1]=>[2,4,5,3,1,7,6,8]=>[3,1,2,2]
[8,1,5,2,4,6,7,3]=>[5,6,3,8,2,4,7,1]=>[4,3,6,1,7,5,2,8]=>[1,2,2,1,2]
[5,2,6,4,1,3,8,7]=>[8,5,2,1,4,3,6,7]=>[1,4,7,8,5,6,3,2]=>[4,2,1,1]
[7,1,3,5,2,8,6,4]=>[4,8,3,7,2,5,1,6]=>[5,1,6,2,7,4,8,3]=>[1,2,2,2,1]
[8,6,4,7,1,3,5,2]=>[6,3,8,5,2,7,4,1]=>[3,6,1,4,7,2,5,8]=>[2,3,3]
[6,8,4,3,2,1,7,5]=>[5,4,3,1,8,6,7,2]=>[4,5,6,8,1,3,2,7]=>[4,2,2]
[2,1,8,5,4,3,7,6]=>[5,4,8,1,6,7,2,3]=>[4,5,1,8,3,2,7,6]=>[2,2,1,2,1]
[6,2,8,5,4,1,3,7]=>[6,7,5,2,1,4,8,3]=>[3,2,4,7,8,5,1,6]=>[1,4,1,2]
[6,4,8,5,3,2,7,1]=>[6,2,1,5,4,8,7,3]=>[3,7,8,4,5,1,2,6]=>[3,2,3]
[8,5,4,6,2,7,1,3]=>[5,3,2,7,4,8,6,1]=>[4,6,7,2,5,1,3,8]=>[3,2,3]
[6,8,5,4,7,2,3,1]=>[1,6,4,3,8,7,5,2]=>[8,3,5,6,1,2,4,7]=>[1,3,4]
[2,5,7,3,4,8,1,6]=>[4,2,5,7,1,3,8,6]=>[5,7,4,2,8,6,1,3]=>[2,1,2,1,2]
[5,2,4,7,8,1,3,6]=>[3,6,1,7,2,4,8,5]=>[6,3,8,2,7,5,1,4]=>[1,2,2,1,2]
[4,8,5,6,1,2,7,3]=>[8,1,5,3,6,4,7,2]=>[1,8,4,6,3,5,2,7]=>[2,2,2,2]
[2,5,6,8,7,1,4,3]=>[2,3,8,6,7,1,5,4]=>[7,6,1,3,2,8,4,5]=>[1,1,2,2,2]
[1,7,8,5,4,6,2,3]=>[7,5,4,2,8,6,1,3]=>[2,4,5,7,1,3,8,6]=>[4,3,1]
[4,6,8,1,5,2,7,3]=>[8,1,6,4,2,5,7,3]=>[1,8,3,5,7,4,2,6]=>[2,3,1,2]
[5,3,8,1,2,6,7,4]=>[2,6,1,8,4,5,7,3]=>[7,3,8,1,5,4,2,6]=>[1,2,2,1,2]
[8,2,3,6,4,1,7,5]=>[5,8,2,3,6,4,7,1]=>[4,1,7,6,3,5,2,8]=>[1,2,1,2,2]
[2,3,7,5,8,6,1,4]=>[4,7,3,8,1,2,6,5]=>[5,2,6,1,8,7,3,4]=>[1,2,2,1,2]
[3,8,5,1,2,4,7,6]=>[8,1,4,5,3,6,7,2]=>[1,8,5,4,6,3,2,7]=>[2,1,2,1,2]
[1,3,6,4,8,2,7,5]=>[8,4,2,3,6,7,1,5]=>[1,5,7,6,3,2,8,4]=>[3,1,1,2,1]
[1,2,3,4,6,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[5,10,9,8,7,6,4,3,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,2,3,4,5,6,8,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[3,10,9,8,7,6,5,4,2,1]=>[2,1,1,1,1,1,1,1,1]
[1,7,6,2,8,5,3,4]=>[7,8,6,4,3,1,2,5]=>[2,1,3,5,6,8,7,4]=>[1,5,1,1]
[1,5,8,6,4,7,2,3]=>[7,2,5,4,8,6,1,3]=>[2,7,4,5,1,3,8,6]=>[2,2,3,1]
[6,8,4,5,1,3,7,2]=>[6,3,1,8,5,4,7,2]=>[3,6,8,1,4,5,2,7]=>[3,3,2]
[5,2,3,8,1,4,6,7]=>[2,3,5,1,6,7,8,4]=>[7,6,4,8,3,2,1,5]=>[1,1,2,1,1,2]
[1,6,8,3,2,4,5,7]=>[5,4,6,2,7,8,1,3]=>[4,5,3,7,2,1,8,6]=>[2,2,1,2,1]
[9,6,5,4,3,2,1,7,8]=>[7,6,5,4,3,2,8,9,1]=>[3,4,5,6,7,8,2,1,9]=>[6,1,2]
[10,7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,2,9,10,1]=>[3,4,5,6,7,8,9,2,1,10]=>[7,1,2]
[9,8,5,4,3,2,1,6,7]=>[7,6,5,4,3,8,9,2,1]=>[3,4,5,6,7,2,1,8,9]=>[5,1,3]
[6,2,5,3,7,4,8,1]=>[6,4,2,3,1,5,8,7]=>[3,5,7,6,8,4,1,2]=>[3,2,1,2]
[8,5,4,2,6,3,7,1]=>[6,4,3,2,5,8,7,1]=>[3,5,6,7,4,1,2,8]=>[4,1,3]
[7,3,6,5,8,2,4,1]=>[6,4,2,3,1,8,7,5]=>[3,5,7,6,8,1,2,4]=>[3,2,3]
[7,3,6,4,8,2,5,1]=>[4,6,2,3,1,8,7,5]=>[5,3,7,6,8,1,2,4]=>[1,2,2,3]
[7,3,5,4,8,2,6,1]=>[4,2,3,6,1,8,7,5]=>[5,7,6,3,8,1,2,4]=>[2,1,2,3]
[7,3,6,8,4,5,1,2]=>[7,5,2,3,1,8,6,4]=>[2,4,7,6,8,1,3,5]=>[3,2,3]
[1,6,5,7,4,2,8,3]=>[3,2,8,6,5,1,4,7]=>[6,7,1,3,4,8,5,2]=>[2,4,1,1]
[1,2,7,4,8,5,6,3]=>[6,8,4,3,7,1,2,5]=>[3,1,5,6,2,8,7,4]=>[1,3,2,1,1]
[2,6,7,4,8,5,1,3]=>[4,2,7,3,8,1,6,5]=>[5,7,2,6,1,8,3,4]=>[2,2,2,2]
[3,2,7,5,8,4,6,1]=>[4,6,1,3,8,2,7,5]=>[5,3,8,6,1,7,2,4]=>[1,2,1,2,2]
[2,5,8,6,4,3,7,1]=>[6,2,5,4,8,1,7,3]=>[3,7,4,5,1,8,2,6]=>[2,2,2,2]
[6,4,2,5,7,1,8,3]=>[4,2,8,3,1,6,5,7]=>[5,7,1,6,8,3,4,2]=>[2,3,2,1]
[2,7,5,4,6,8,1,3]=>[4,3,7,5,1,2,8,6]=>[5,6,2,4,8,7,1,3]=>[2,3,1,2]
[9,1,2,3,4,5,8,7,6]=>[9,8,2,3,4,5,6,7,1]=>[1,2,8,7,6,5,4,3,9]=>[3,1,1,1,1,2]
[8,1,4,7,3,5,6,2]=>[3,5,6,8,7,2,4,1]=>[6,4,3,1,2,7,5,8]=>[1,1,1,3,2]
[8,1,4,5,7,3,6,2]=>[3,4,6,8,7,2,5,1]=>[6,5,3,1,2,7,4,8]=>[1,1,1,3,2]
[2,5,7,4,6,8,1,3]=>[2,4,7,5,1,3,8,6]=>[7,5,2,4,8,6,1,3]=>[1,1,3,1,2]
[2,5,6,4,1,3,8,7]=>[2,8,5,1,4,3,6,7]=>[7,1,4,8,5,6,3,2]=>[1,3,2,1,1]
[4,6,1,3,5,7,2,8]=>[4,1,5,7,3,2,6,8]=>[5,8,4,2,6,7,3,1]=>[2,1,3,1,1]
[3,2,7,5,8,1,6,4]=>[4,8,1,6,2,3,7,5]=>[5,1,8,3,7,6,2,4]=>[1,2,2,1,2]
[4,3,6,8,5,2,1,7]=>[1,3,7,2,6,5,8,4]=>[8,6,2,7,3,4,1,5]=>[1,1,2,2,2]
[4,5,3,2,1,8,6,7]=>[1,4,3,2,7,8,5,6]=>[8,5,6,7,2,1,4,3]=>[1,3,1,2,1]
[3,6,5,8,1,7,4,2]=>[3,2,8,1,7,5,6,4]=>[6,7,1,8,2,4,3,5]=>[2,2,2,2]
[4,1,6,8,5,2,3,7]=>[1,6,3,7,5,8,2,4]=>[8,3,6,2,4,1,7,5]=>[1,2,2,2,1]
[4,5,2,8,6,7,1,3]=>[1,2,7,5,8,3,6,4]=>[8,7,2,4,1,6,3,5]=>[1,1,2,2,2]
[4,5,2,8,6,7,3,1]=>[1,2,5,8,7,3,6,4]=>[8,7,4,1,2,6,3,5]=>[1,1,1,3,2]
[2,5,1,6,4,8,3,7]=>[5,4,1,2,7,8,3,6]=>[4,5,8,7,2,1,6,3]=>[3,1,1,2,1]
[3,2,4,5,8,6,1,7]=>[1,7,2,3,4,6,8,5]=>[8,2,7,6,5,3,1,4]=>[1,2,1,1,1,2]
[4,5,2,1,3,8,6,7]=>[3,1,7,2,8,4,5,6]=>[6,8,2,7,1,5,4,3]=>[2,2,2,1,1]
[4,2,3,6,8,5,1,7]=>[4,1,7,2,3,6,8,5]=>[5,8,2,7,6,3,1,4]=>[2,2,1,1,2]
[4,5,1,3,2,8,6,7]=>[4,1,7,2,8,3,5,6]=>[5,8,2,7,1,6,4,3]=>[2,2,2,1,1]
[3,4,5,8,6,1,7,2]=>[8,1,2,3,6,5,7,4]=>[1,8,7,6,3,4,2,5]=>[2,1,1,2,2]
[3,4,5,8,6,1,2,7]=>[1,2,3,6,7,5,8,4]=>[8,7,6,3,2,4,1,5]=>[1,1,1,1,2,2]
[6,3,1,2,5,4,8,7]=>[5,2,8,3,4,1,6,7]=>[4,7,1,6,5,8,3,2]=>[2,2,2,1,1]
[7,3,1,2,5,4,8,6]=>[5,2,8,3,4,6,1,7]=>[4,7,1,6,5,3,8,2]=>[2,2,1,2,1]
[1,5,8,2,4,3,7,6]=>[5,2,8,4,6,7,1,3]=>[4,7,1,5,3,2,8,6]=>[2,2,1,2,1]
[4,3,7,8,2,6,5,1]=>[8,1,5,2,3,7,6,4]=>[1,8,4,7,6,2,3,5]=>[2,2,1,3]
[3,8,5,1,2,6,7,4]=>[6,8,1,4,3,5,7,2]=>[3,1,8,5,6,4,2,7]=>[1,2,2,1,2]
[2,4,7,8,3,6,5,1]=>[8,5,2,3,7,1,6,4]=>[1,4,7,6,2,8,3,5]=>[3,1,2,2]
[5,4,7,8,3,6,1,2]=>[1,7,2,5,3,8,6,4]=>[8,2,7,4,6,1,3,5]=>[1,2,2,3]
[6,8,1,3,2,5,7,4]=>[4,6,8,3,1,5,7,2]=>[5,3,1,6,8,4,2,7]=>[1,1,3,1,2]
[1,4,8,5,7,2,3,6]=>[6,2,4,7,8,5,1,3]=>[3,7,5,2,1,4,8,6]=>[2,1,1,3,1]
[1,8,7,3,2,4,5,6]=>[5,4,6,7,8,3,1,2]=>[4,5,3,2,1,6,8,7]=>[2,1,1,3,1]
[8,6,2,7,3,4,1,5]=>[5,7,3,6,2,8,4,1]=>[4,2,6,3,7,1,5,8]=>[1,2,2,3]
[8,6,2,7,3,4,5,1]=>[5,6,8,3,2,7,4,1]=>[4,3,1,6,7,2,5,8]=>[1,1,3,3]
[5,6,3,2,8,7,1,4]=>[3,1,7,2,8,4,6,5]=>[6,8,2,7,1,5,3,4]=>[2,2,2,2]
[1,5,6,3,7,2,4,8]=>[4,2,6,3,7,1,5,8]=>[5,7,3,6,2,8,4,1]=>[2,2,2,1,1]
[5,1,6,7,3,4,2,8]=>[5,3,1,7,6,2,4,8]=>[4,6,8,2,3,7,5,1]=>[3,3,1,1]
[6,8,5,1,7,4,2,3]=>[7,1,8,6,4,3,5,2]=>[2,8,1,3,5,6,4,7]=>[2,4,2]
[8,4,2,3,5,7,6,1]=>[8,3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3,8]=>[3,1,1,3]
[5,4,8,3,1,2,6,7]=>[5,2,1,6,4,7,8,3]=>[4,7,8,3,5,2,1,6]=>[3,2,1,2]
[6,8,5,1,7,3,4,2]=>[6,1,8,7,4,3,5,2]=>[3,8,1,2,5,6,4,7]=>[2,4,2]
[1,7,8,3,6,5,2,4]=>[7,8,4,2,6,5,1,3]=>[2,1,5,7,3,4,8,6]=>[1,3,3,1]
[4,6,7,5,1,8,2,3]=>[7,1,2,8,5,4,3,6]=>[2,8,7,1,4,5,6,3]=>[2,1,4,1]
[7,3,6,8,4,1,2,5]=>[6,7,2,5,3,1,8,4]=>[3,2,7,4,6,8,1,5]=>[1,2,3,2]
[6,4,2,3,7,5,8,1]=>[6,3,2,4,1,5,8,7]=>[3,6,7,5,8,4,1,2]=>[3,2,1,2]
[6,3,7,5,1,2,8,4]=>[8,2,5,1,6,4,3,7]=>[1,7,4,8,3,5,6,2]=>[2,2,3,1]
[7,2,5,4,8,6,3,1]=>[3,8,4,7,2,1,6,5]=>[6,1,5,2,7,8,3,4]=>[1,2,3,2]
[6,2,3,8,7,4,5,1]=>[6,8,7,2,1,3,5,4]=>[3,1,2,7,8,6,4,5]=>[1,4,1,2]
[7,1,2,8,4,6,5,3]=>[8,5,7,6,2,3,1,4]=>[1,4,2,3,7,6,8,5]=>[2,3,2,1]
[3,5,8,1,2,7,6,4]=>[2,8,1,7,4,5,6,3]=>[7,1,8,2,5,4,3,6]=>[1,2,2,1,2]
[1,4,3,6,8,5,2,7]=>[2,4,7,3,6,8,1,5]=>[7,5,2,6,3,1,8,4]=>[1,1,2,1,2,1]
[7,6,2,8,5,3,4,1]=>[6,8,7,3,2,1,5,4]=>[3,1,2,6,7,8,4,5]=>[1,5,2]
[6,8,3,5,4,7,2,1]=>[5,3,1,4,8,7,6,2]=>[4,6,8,5,1,2,3,7]=>[3,1,4]
[8,2,7,6,4,1,3,5]=>[6,7,5,8,2,4,3,1]=>[3,2,4,1,7,5,6,8]=>[1,2,2,3]
[8,5,7,1,4,2,6,3]=>[8,6,4,2,5,7,3,1]=>[1,3,5,7,4,2,6,8]=>[4,1,3]
[4,8,2,5,6,3,7,1]=>[1,4,6,3,5,8,7,2]=>[8,5,3,6,4,1,2,7]=>[1,1,2,1,3]
[8,1,5,7,4,6,2,3]=>[3,7,5,8,6,2,4,1]=>[6,2,4,1,3,7,5,8]=>[1,2,3,2]
[4,7,1,5,6,3,2,8]=>[1,4,7,6,3,5,2,8]=>[8,5,2,3,6,4,7,1]=>[1,1,3,2,1]
[4,5,7,1,6,3,8,2]=>[1,2,6,5,8,4,3,7]=>[8,7,3,4,1,5,6,2]=>[1,1,2,3,1]
[2,7,1,4,8,3,6,5]=>[8,4,6,7,1,3,2,5]=>[1,5,3,2,8,6,7,4]=>[2,1,2,2,1]
[2,7,1,5,6,8,4,3]=>[4,5,8,7,1,3,2,6]=>[5,4,1,2,8,6,7,3]=>[1,1,3,2,1]
[2,3,1,8,7,4,6,5]=>[8,6,7,1,2,5,3,4]=>[1,3,2,8,7,4,6,5]=>[2,2,1,2,1]
[4,6,8,2,1,5,3,7]=>[1,4,7,5,2,6,8,3]=>[8,5,2,4,7,3,1,6]=>[1,1,3,1,2]
[5,6,8,4,7,2,3,1]=>[1,2,6,4,8,7,5,3]=>[8,7,3,5,1,2,4,6]=>[1,1,2,4]
[4,5,7,3,6,1,2,8]=>[1,2,6,4,7,5,3,8]=>[8,7,3,5,2,4,6,1]=>[1,1,2,3,1]
[3,4,5,7,2,1,6,8]=>[1,2,3,6,5,7,4,8]=>[8,7,6,3,4,2,5,1]=>[1,1,1,2,2,1]
[4,5,6,8,3,2,7,1]=>[1,2,3,6,5,8,7,4]=>[8,7,6,3,4,1,2,5]=>[1,1,1,2,3]
[4,5,7,2,6,1,8,3]=>[1,2,8,4,6,5,3,7]=>[8,7,1,5,3,4,6,2]=>[1,1,2,3,1]
[3,9,2,1,4,5,6,7,8]=>[1,4,3,5,6,7,8,9,2]=>[9,6,7,5,4,3,2,1,8]=>[1,2,1,1,1,1,2]
[4,6,5,7,2,3,8,1]=>[5,1,3,2,6,4,8,7]=>[4,8,6,7,3,5,1,2]=>[2,2,2,2]
[5,2,4,8,6,7,3,1]=>[5,1,8,3,7,2,6,4]=>[4,8,1,6,2,7,3,5]=>[2,2,2,2]
[5,2,6,7,8,1,4,3]=>[3,1,8,6,2,4,7,5]=>[6,8,1,3,7,5,2,4]=>[2,3,1,2]
[4,8,2,7,5,3,1,6]=>[7,1,6,3,5,8,4,2]=>[2,8,3,6,4,1,5,7]=>[2,2,1,3]
[1,2,4,6,5,8,3,7]=>[5,3,4,7,8,1,2,6]=>[4,6,5,2,1,8,7,3]=>[2,1,1,2,1,1]
[5,4,2,3,1,7,8,6]=>[3,4,2,1,6,8,5,7]=>[6,5,7,8,3,1,4,2]=>[1,3,1,2,1]
[5,8,6,1,7,2,3,4]=>[6,1,7,8,4,3,5,2]=>[3,8,2,1,5,6,4,7]=>[2,1,3,2]
[5,1,4,3,8,2,6,7]=>[4,3,6,1,7,8,2,5]=>[5,6,3,8,2,1,7,4]=>[2,2,1,2,1]
[8,4,7,5,6,2,1,3]=>[7,2,6,4,8,5,3,1]=>[2,7,3,5,1,4,6,8]=>[2,2,4]
[3,8,6,7,5,2,4,1]=>[6,3,8,7,1,5,4,2]=>[3,6,1,2,8,4,5,7]=>[2,3,3]
[8,2,5,4,7,3,6,1]=>[4,3,6,8,2,7,5,1]=>[5,6,3,1,7,2,4,8]=>[2,1,2,3]
[4,2,8,7,3,6,5,1]=>[8,1,5,7,6,2,4,3]=>[1,8,4,2,3,7,5,6]=>[2,1,3,2]
[3,7,8,6,1,4,5,2]=>[6,8,5,1,2,7,4,3]=>[3,1,4,8,7,2,5,6]=>[1,3,1,3]
[4,6,7,8,2,1,5,3]=>[5,1,2,8,6,3,7,4]=>[4,8,7,1,3,6,2,5]=>[2,1,3,2]
[4,7,6,3,8,1,5,2]=>[4,8,1,6,3,2,7,5]=>[5,1,8,3,6,7,2,4]=>[1,2,3,2]
[3,8,1,4,6,2,5,7]=>[1,4,6,7,3,5,8,2]=>[8,5,3,2,6,4,1,7]=>[1,1,1,2,1,2]
[4,7,5,6,2,8,1,3]=>[5,1,3,7,4,2,8,6]=>[4,8,6,2,5,7,1,3]=>[2,1,3,2]
[8,7,5,1,6,3,2,4]=>[7,6,8,4,3,5,2,1]=>[2,3,1,5,6,4,7,8]=>[2,3,3]
[7,8,6,2,3,5,1,4]=>[4,5,7,1,8,6,3,2]=>[5,4,2,8,1,3,6,7]=>[1,1,2,4]
[2,8,4,6,7,3,5,1]=>[6,3,4,8,7,1,5,2]=>[3,6,5,1,2,8,4,7]=>[2,1,3,2]
[4,1,6,7,8,2,5,3]=>[1,3,8,6,4,7,2,5]=>[8,6,1,3,5,2,7,4]=>[1,1,3,2,1]
[4,7,8,6,5,1,3,2]=>[8,6,1,2,7,5,4,3]=>[1,3,8,7,2,4,5,6]=>[3,1,4]
[8,4,6,7,3,5,2,1]=>[5,2,3,8,7,6,4,1]=>[4,7,6,1,2,3,5,8]=>[2,1,5]
[6,8,4,7,3,5,2,1]=>[3,1,5,8,7,6,4,2]=>[6,8,4,1,2,3,5,7]=>[2,1,5]
[7,4,5,8,3,6,2,1]=>[2,3,5,1,8,7,6,4]=>[7,6,4,8,1,2,3,5]=>[1,1,2,4]
[8,4,7,3,5,6,2,1]=>[2,4,5,8,7,6,3,1]=>[7,5,4,1,2,3,6,8]=>[1,1,1,5]
[3,6,4,2,8,1,7,5]=>[3,8,1,4,2,6,7,5]=>[6,1,8,5,7,3,2,4]=>[1,2,2,1,2]
[3,4,8,6,2,1,7,5]=>[5,8,1,2,6,4,7,3]=>[4,1,8,7,3,5,2,6]=>[1,2,1,2,2]
[3,8,6,2,1,7,4,5]=>[4,7,8,1,5,3,6,2]=>[5,2,1,8,4,6,3,7]=>[1,1,2,2,2]
[3,1,8,2,4,6,5,7]=>[1,7,4,5,6,8,2,3]=>[8,2,5,4,3,1,7,6]=>[1,2,1,1,2,1]
[8,1,7,6,2,5,4,3]=>[8,7,5,6,4,2,3,1]=>[1,2,4,3,5,7,6,8]=>[3,3,2]
[8,5,4,3,7,6,1,2]=>[4,3,2,7,8,6,5,1]=>[5,6,7,2,1,3,4,8]=>[3,1,4]
[4,8,1,3,6,7,5,2]=>[1,5,8,4,7,3,6,2]=>[8,4,1,5,2,6,3,7]=>[1,1,2,2,2]
[3,5,8,6,1,7,4,2]=>[8,2,7,1,5,4,6,3]=>[1,7,2,8,4,5,3,6]=>[2,2,2,2]
[8,1,4,7,5,2,6,3]=>[8,3,6,5,7,2,4,1]=>[1,6,3,4,2,7,5,8]=>[2,2,2,2]
[1,4,8,6,7,3,5,2]=>[6,4,8,2,7,5,1,3]=>[3,5,1,7,2,4,8,6]=>[2,2,3,1]
[4,1,6,7,8,5,3,2]=>[1,3,4,8,7,6,2,5]=>[8,6,5,1,2,3,7,4]=>[1,1,1,4,1]
[3,7,8,6,4,1,5,2]=>[8,6,5,1,2,7,4,3]=>[1,3,4,8,7,2,5,6]=>[4,1,3]
[4,6,1,5,7,2,3,8]=>[1,6,4,7,3,2,5,8]=>[8,3,5,2,6,7,4,1]=>[1,2,3,1,1]
[4,8,5,3,2,7,1,6]=>[5,1,4,3,7,8,6,2]=>[4,8,5,6,2,1,3,7]=>[2,2,1,3]
[5,4,8,1,3,7,2,6]=>[5,2,1,7,8,4,6,3]=>[4,7,8,2,1,5,3,6]=>[3,1,2,2]
[8,4,5,3,1,7,2,6]=>[2,7,4,3,8,5,6,1]=>[7,2,5,6,1,4,3,8]=>[1,3,2,2]
[7,4,5,3,1,8,6,2]=>[2,4,3,8,7,5,1,6]=>[7,5,6,1,2,4,8,3]=>[1,2,4,1]
[5,6,8,7,2,4,3,1]=>[1,2,8,5,7,6,4,3]=>[8,7,1,4,2,3,5,6]=>[1,1,2,4]
[5,7,8,6,4,2,3,1]=>[6,1,2,8,7,5,4,3]=>[3,8,7,1,2,4,5,6]=>[2,1,5]
[6,8,7,5,1,3,2,4]=>[7,5,1,6,8,4,3,2]=>[2,4,8,3,1,5,6,7]=>[3,1,4]
[6,7,4,1,8,2,5,3]=>[8,6,3,1,7,4,2,5]=>[1,3,6,8,2,5,7,4]=>[4,3,1]
[5,7,6,8,3,2,4,1]=>[6,1,5,3,2,8,7,4]=>[3,8,4,6,7,1,2,5]=>[2,3,3]
[6,3,4,8,7,1,2,5]=>[2,3,6,1,7,8,5,4]=>[7,6,3,8,2,1,4,5]=>[1,1,2,1,3]
[2,7,4,8,1,6,3,5]=>[3,7,8,5,1,2,6,4]=>[6,2,1,4,8,7,3,5]=>[1,1,3,1,2]
[5,3,1,6,7,8,2,4]=>[2,4,1,7,5,8,3,6]=>[7,5,8,2,4,1,6,3]=>[1,2,2,2,1]
[3,4,7,8,6,1,2,5]=>[6,7,1,2,3,8,5,4]=>[3,2,8,7,6,1,4,5]=>[1,2,1,1,3]
[2,1,4,7,8,6,3,5]=>[7,4,8,1,3,6,2,5]=>[2,5,1,8,6,3,7,4]=>[2,2,1,2,1]
[2,4,5,8,1,6,3,7]=>[2,3,7,1,5,6,8,4]=>[7,6,2,8,4,3,1,5]=>[1,1,2,1,1,2]
[3,4,6,8,2,5,7,1]=>[5,1,2,3,6,8,7,4]=>[4,8,7,6,3,1,2,5]=>[2,1,1,1,3]
[1,8,5,6,4,2,3,7]=>[6,3,7,5,4,8,1,2]=>[3,6,2,4,5,1,8,7]=>[2,3,2,1]
[1,8,7,6,2,4,5,3]=>[6,8,5,7,4,3,1,2]=>[3,1,4,2,5,6,8,7]=>[1,2,4,1]
[6,4,8,5,7,3,1,2]=>[7,2,1,4,8,6,5,3]=>[2,7,8,5,1,3,4,6]=>[3,1,4]
[1,6,4,7,2,5,8,3]=>[3,6,2,8,5,1,4,7]=>[6,3,7,1,4,8,5,2]=>[1,2,3,1,1]
[2,7,5,1,8,6,3,4]=>[7,3,8,6,1,4,2,5]=>[2,6,1,3,8,5,7,4]=>[2,3,2,1]
[4,7,1,6,5,3,8,2]=>[6,1,5,4,8,3,2,7]=>[3,8,4,5,1,6,7,2]=>[2,2,3,1]
[1,7,5,6,4,8,2,3]=>[3,7,5,4,2,8,1,6]=>[6,2,4,5,7,1,8,3]=>[1,4,2,1]
[2,4,8,5,7,3,1,6]=>[4,7,2,6,8,1,5,3]=>[5,2,7,3,1,8,4,6]=>[1,2,1,2,2]
[8,3,1,4,6,2,7,5]=>[2,8,4,6,3,5,7,1]=>[7,1,5,3,6,4,2,8]=>[1,2,2,1,2]
[7,2,6,4,5,8,1,3]=>[4,7,5,2,3,1,8,6]=>[5,2,4,7,6,8,1,3]=>[1,3,2,2]
[7,2,5,4,6,8,1,3]=>[4,3,7,2,5,1,8,6]=>[5,6,2,7,4,8,1,3]=>[2,2,2,2]
[6,4,5,7,3,8,2,9,1,10]=>[2,3,1,5,4,7,6,9,8,10]=>[9,8,10,6,7,4,5,2,3,1]=>[1,2,2,2,2,1]
[2,7,1,5,3,8,6,4]=>[4,8,7,1,3,5,2,6]=>[5,1,2,8,6,4,7,3]=>[1,3,1,2,1]
[3,5,7,2,8,4,1,6]=>[2,7,1,4,6,3,8,5]=>[7,2,8,5,3,6,1,4]=>[1,2,1,2,2]
[2,4,3,8,5,1,7,6]=>[2,5,8,1,3,6,7,4]=>[7,4,1,8,6,3,2,5]=>[1,1,2,1,1,2]
[2,8,3,4,1,7,6,5]=>[8,3,4,7,1,5,6,2]=>[1,6,5,2,8,4,3,7]=>[2,1,2,1,2]
[4,7,6,8,2,5,3,1]=>[8,5,1,3,2,7,6,4]=>[1,4,8,6,7,2,3,5]=>[3,2,3]
[2,6,7,1,4,5,8,3]=>[5,6,2,8,1,4,3,7]=>[4,3,7,1,8,5,6,2]=>[1,2,2,2,1]
[8,7,1,6,3,5,2,4]=>[5,7,8,6,3,4,2,1]=>[4,2,1,3,6,5,7,8]=>[1,1,3,3]
[8,7,2,6,1,5,3,4]=>[7,8,3,5,6,4,2,1]=>[2,1,6,4,3,5,7,8]=>[1,2,1,4]
[7,1,3,8,2,6,4,5]=>[7,8,3,5,6,2,1,4]=>[2,1,6,4,3,7,8,5]=>[1,2,1,3,1]
[6,2,5,3,4,7,1,8]=>[4,5,2,3,1,7,6,8]=>[5,4,7,6,8,2,3,1]=>[1,2,2,2,1]
[2,7,3,4,1,5,8,6]=>[3,4,8,1,5,6,2,7]=>[6,5,1,8,4,3,7,2]=>[1,1,2,1,2,1]
[2,5,8,1,6,7,3,4]=>[2,7,5,8,1,4,6,3]=>[7,2,4,1,8,5,3,6]=>[1,2,2,1,2]
[6,2,8,3,4,5,1,7]=>[4,5,7,2,1,6,8,3]=>[5,4,2,7,8,3,1,6]=>[1,1,3,1,2]
[7,3,4,6,8,2,1,5]=>[7,2,3,6,4,1,8,5]=>[2,7,6,3,5,8,1,4]=>[2,1,3,2]
[5,1,3,7,2,8,4,6]=>[7,8,3,1,5,2,4,6]=>[2,1,6,8,4,7,5,3]=>[1,3,2,1,1]
[5,2,4,6,1,7,8,3]=>[3,6,2,1,4,8,5,7]=>[6,3,7,8,5,1,4,2]=>[1,3,1,2,1]
[3,8,4,6,1,5,7,2]=>[3,6,8,1,5,4,7,2]=>[6,3,1,8,4,5,2,7]=>[1,1,2,2,2]
[8,7,3,2,5,1,6,4]=>[3,8,4,6,5,7,2,1]=>[6,1,5,3,4,2,7,8]=>[1,2,2,3]
[3,6,4,1,2,5,8,7]=>[8,1,4,3,5,2,6,7]=>[1,8,5,6,4,7,3,2]=>[2,2,2,1,1]
[6,3,1,4,2,5,8,7]=>[4,2,8,3,5,1,6,7]=>[5,7,1,6,4,8,3,2]=>[2,2,2,1,1]
[5,2,3,1,4,6,8,7]=>[2,3,8,4,1,5,6,7]=>[7,6,1,5,8,4,3,2]=>[1,1,3,1,1,1]
[4,2,7,1,3,5,8,6]=>[8,2,1,4,5,6,3,7]=>[1,7,8,5,4,3,6,2]=>[3,1,1,2,1]
[3,5,4,1,6,2,8,7]=>[5,1,3,2,8,4,6,7]=>[4,8,6,7,1,5,3,2]=>[2,2,2,1,1]
[4,5,7,2,8,3,1,6]=>[1,2,7,4,6,3,8,5]=>[8,7,2,5,3,6,1,4]=>[1,1,2,2,2]
[3,5,1,7,6,2,8,4]=>[2,8,1,6,5,3,4,7]=>[7,1,8,3,4,6,5,2]=>[1,2,3,1,1]
[8,3,6,2,7,5,4,1]=>[8,7,2,4,3,6,5,1]=>[1,2,7,5,6,3,4,8]=>[3,2,3]
[8,4,2,6,5,3,7,1]=>[2,6,5,3,4,8,7,1]=>[7,3,4,6,5,1,2,8]=>[1,3,1,3]
[4,1,7,6,5,3,2,8]=>[7,1,6,5,4,2,3,8]=>[2,8,3,4,5,7,6,1]=>[2,4,1,1]
[2,3,6,7,1,8,5,4]=>[3,8,7,1,2,5,4,6]=>[6,1,2,8,7,4,5,3]=>[1,3,1,2,1]
[3,6,1,2,7,8,5,4]=>[5,8,1,7,3,2,4,6]=>[4,1,8,2,6,7,5,3]=>[1,2,3,1,1]
[4,5,1,8,7,6,3,2]=>[8,1,2,7,6,5,3,4]=>[1,8,7,2,3,4,6,5]=>[2,1,4,1]
[4,1,3,6,7,5,2,8]=>[4,1,7,3,6,2,5,8]=>[5,8,2,6,3,7,4,1]=>[2,2,2,1,1]
[3,1,4,5,7,6,2,8]=>[1,7,3,4,6,2,5,8]=>[8,2,6,5,3,7,4,1]=>[1,2,1,2,1,1]
[4,5,1,3,6,8,7,2]=>[1,8,4,2,5,7,3,6]=>[8,1,5,7,4,2,6,3]=>[1,3,1,2,1]
[3,8,5,1,2,4,6,7]=>[1,4,5,6,3,7,8,2]=>[8,5,4,3,6,2,1,7]=>[1,1,1,2,1,2]
[8,5,1,2,4,3,6,7]=>[6,3,4,5,2,7,8,1]=>[3,6,5,4,7,2,1,8]=>[2,1,2,1,2]
[5,8,4,1,2,3,6,7]=>[4,5,1,6,3,7,8,2]=>[5,4,8,3,6,2,1,7]=>[1,2,2,1,2]
[3,5,8,1,4,2,7,6]=>[5,1,2,8,4,6,7,3]=>[4,8,7,1,5,3,2,6]=>[2,1,2,1,2]
[2,8,5,7,1,4,3,6]=>[7,5,3,6,8,1,4,2]=>[2,4,6,3,1,8,5,7]=>[3,1,2,2]
[8,1,2,4,6,3,7,5]=>[8,4,6,2,3,5,7,1]=>[1,5,3,7,6,4,2,8]=>[2,2,1,1,2]
[7,6,1,4,2,3,8,5]=>[8,5,3,4,6,2,1,7]=>[1,4,6,5,3,7,8,2]=>[3,1,3,1]
[6,1,2,7,8,4,3,5]=>[7,6,4,8,2,1,3,5]=>[2,3,5,1,7,8,6,4]=>[3,3,1,1]
[7,8,1,2,5,3,4,6]=>[6,7,3,4,5,1,8,2]=>[3,2,6,5,4,8,1,7]=>[1,2,1,2,2]
[1,8,4,7,5,2,3,6]=>[3,6,7,5,8,4,1,2]=>[6,3,2,4,1,5,8,7]=>[1,1,2,3,1]
[4,5,8,2,1,6,7,3]=>[1,4,2,6,8,5,7,3]=>[8,5,7,3,1,4,2,6]=>[1,2,1,2,2]
[7,4,2,5,3,6,1,8]=>[5,3,2,4,7,6,1,8]=>[4,6,7,5,2,3,8,1]=>[3,1,3,1]
[3,1,6,7,5,2,4,8]=>[6,1,3,7,5,2,4,8]=>[3,8,6,2,4,7,5,1]=>[2,1,3,1,1]
[4,8,1,5,3,6,7,2]=>[1,5,4,6,8,3,7,2]=>[8,4,5,3,1,6,2,7]=>[1,2,1,2,2]
[5,1,4,6,3,7,8,2]=>[3,5,4,1,6,8,2,7]=>[6,4,5,8,3,1,7,2]=>[1,3,1,2,1]
[7,1,5,3,6,8,2,4]=>[7,4,3,5,8,2,1,6]=>[2,5,6,4,1,7,8,3]=>[3,1,3,1]
[8,1,5,3,6,7,2,4]=>[7,4,3,5,8,2,6,1]=>[2,5,6,4,1,7,3,8]=>[3,1,2,2]
[3,6,5,2,4,7,8,1]=>[4,5,1,3,2,6,8,7]=>[5,4,8,6,7,3,1,2]=>[1,2,2,1,2]
[1,7,5,4,6,8,2,3]=>[4,3,7,5,2,8,1,6]=>[5,6,2,4,7,1,8,3]=>[2,3,2,1]
[4,7,8,2,5,6,1,3]=>[7,1,4,5,2,8,6,3]=>[2,8,5,4,7,1,3,6]=>[2,1,2,3]
[2,8,5,4,6,7,1,3]=>[4,3,7,5,8,1,6,2]=>[5,6,2,4,1,8,3,7]=>[2,2,2,2]
[9,8,1,7,2,3,4,5,6]=>[5,6,7,8,9,3,4,2,1]=>[5,4,3,2,1,7,6,8,9]=>[1,1,1,1,2,3]
[4,5,2,6,1,8,3,7]=>[1,7,3,2,4,8,5,6]=>[8,2,6,7,5,1,4,3]=>[1,3,1,2,1]
[5,1,8,6,7,3,4,2]=>[1,6,4,8,7,5,2,3]=>[8,3,5,1,2,4,7,6]=>[1,2,4,1]
[6,8,3,2,4,1,5,7]=>[4,3,6,5,1,7,8,2]=>[5,6,3,4,8,2,1,7]=>[2,3,1,2]
[6,5,2,4,1,7,8,3]=>[6,3,4,2,1,8,5,7]=>[3,6,5,7,8,1,4,2]=>[2,3,2,1]
[5,4,8,2,1,3,6,7]=>[5,4,2,1,6,7,8,3]=>[4,5,7,8,3,2,1,6]=>[4,1,1,2]
[1,4,8,3,2,6,5,7]=>[2,4,7,5,6,8,1,3]=>[7,5,2,4,3,1,8,6]=>[1,1,2,1,2,1]
[1,3,8,4,2,7,5,6]=>[4,7,8,2,5,6,1,3]=>[5,2,1,7,4,3,8,6]=>[1,1,2,1,2,1]
[7,2,8,3,1,4,5,6]=>[5,2,4,6,7,1,8,3]=>[4,7,5,3,2,8,1,6]=>[2,1,1,2,2]
[8,1,3,2,7,5,4,6]=>[7,3,6,8,2,4,5,1]=>[2,6,3,1,7,5,4,8]=>[2,1,2,1,2]
[2,3,4,5,6,1,9,8,7]=>[9,1,2,3,4,5,8,6,7]=>[1,9,8,7,6,5,2,4,3]=>[2,1,1,1,1,2,1]
[7,6,1,8,2,5,4,3]=>[8,7,5,6,3,2,1,4]=>[1,2,4,3,6,7,8,5]=>[3,4,1]
[8,4,1,6,7,3,5,2]=>[2,6,4,8,7,3,5,1]=>[7,3,5,1,2,6,4,8]=>[1,2,3,2]
[5,8,4,2,1,6,3,7]=>[4,1,7,5,3,6,8,2]=>[5,8,2,4,6,3,1,7]=>[2,3,1,2]
[7,6,4,1,2,5,3,8]=>[7,4,5,3,6,2,1,8]=>[2,5,4,6,3,7,8,1]=>[2,2,3,1]
[5,4,2,8,1,6,3,7]=>[7,3,2,1,5,6,8,4]=>[2,6,7,8,4,3,1,5]=>[4,1,1,2]
[8,7,2,6,4,5,3,1]=>[5,8,7,3,6,4,2,1]=>[4,1,2,6,3,5,7,8]=>[1,3,4]
[7,2,8,4,3,6,1,5]=>[5,4,7,8,2,1,6,3]=>[4,5,2,1,7,8,3,6]=>[2,1,3,2]
[1,7,5,4,8,6,2,3]=>[4,3,7,2,8,6,1,5]=>[5,6,2,7,1,3,8,4]=>[2,2,3,1]
[4,8,6,3,5,2,1,7]=>[4,7,1,6,5,3,8,2]=>[5,2,8,3,4,6,1,7]=>[1,2,3,2]
[5,8,6,3,2,7,1,4]=>[1,5,4,7,3,8,6,2]=>[8,4,5,2,6,1,3,7]=>[1,2,2,3]
[5,7,3,2,8,6,4,1]=>[1,8,3,7,4,2,6,5]=>[8,1,6,2,5,7,3,4]=>[1,2,3,2]
[4,5,1,6,8,2,7,3]=>[1,4,2,8,6,7,3,5]=>[8,5,7,1,3,2,6,4]=>[1,2,2,2,1]
[1,6,3,7,2,4,8,5]=>[8,3,5,2,6,1,4,7]=>[1,6,4,7,3,8,5,2]=>[2,2,2,1,1]
[8,9,7,6,5,4,3,1,2]=>[8,1,9,7,6,5,4,3,2]=>[2,9,1,3,4,5,6,7,8]=>[2,7]
[8,6,7,5,4,3,2,1,9]=>[2,8,7,6,5,4,3,1,9]=>[8,2,3,4,5,6,7,9,1]=>[1,7,1]
[8,7,9,6,5,4,3,1,2]=>[8,2,1,9,7,6,5,4,3]=>[2,8,9,1,3,4,5,6,7]=>[3,6]
[9,7,8,6,5,4,3,1,2]=>[8,2,9,7,6,5,4,3,1]=>[2,8,1,3,4,5,6,7,9]=>[2,7]
[4,3,7,1,6,2,5,8]=>[2,1,6,7,4,5,3,8]=>[7,8,3,2,5,4,6,1]=>[2,1,2,2,1]
[4,3,1,6,7,2,5,8]=>[2,1,6,4,7,3,5,8]=>[7,8,3,5,2,6,4,1]=>[2,2,2,1,1]
[5,2,1,4,8,6,7,3]=>[6,8,2,1,4,7,3,5]=>[3,1,7,8,5,2,6,4]=>[1,3,1,2,1]
[8,2,7,4,1,6,5,3]=>[4,8,7,2,5,6,3,1]=>[5,1,2,7,4,3,6,8]=>[1,3,1,3]
[3,2,8,4,1,6,5,7]=>[1,4,7,2,5,6,8,3]=>[8,5,2,7,4,3,1,6]=>[1,1,2,1,1,2]
[3,7,6,4,1,5,8,2]=>[6,4,8,1,5,3,2,7]=>[3,5,1,8,4,6,7,2]=>[2,2,3,1]
[7,1,6,5,4,2,8,3]=>[8,6,5,4,2,3,1,7]=>[1,3,4,5,7,6,8,2]=>[5,2,1]
[7,1,8,4,2,3,6,5]=>[8,5,4,6,7,2,1,3]=>[1,4,5,3,2,7,8,6]=>[3,1,3,1]
[2,7,6,4,5,1,8,3]=>[4,8,6,5,1,3,2,7]=>[5,1,3,4,8,6,7,2]=>[1,4,2,1]
[4,6,8,1,7,3,5,2]=>[6,1,2,8,7,4,5,3]=>[3,8,7,1,2,5,4,6]=>[2,1,3,2]
[3,6,8,1,5,7,4,2]=>[5,2,8,1,7,4,6,3]=>[4,7,1,8,2,5,3,6]=>[2,2,2,2]
[4,5,6,8,2,1,7,3]=>[1,2,5,3,8,6,7,4]=>[8,7,4,6,1,3,2,5]=>[1,1,2,2,2]
[4,5,6,8,1,3,7,2]=>[1,2,6,3,8,5,7,4]=>[8,7,3,6,1,4,2,5]=>[1,1,2,2,2]
[4,5,8,3,2,1,7,6]=>[1,2,5,4,8,6,7,3]=>[8,7,4,5,1,3,2,6]=>[1,1,2,2,2]
[4,5,1,3,2,6,7,8]=>[5,3,1,4,2,6,7,8]=>[4,6,8,5,7,3,2,1]=>[3,2,1,1,1]
[4,7,3,2,1,6,5,8]=>[1,4,3,7,5,6,2,8]=>[8,5,6,2,4,3,7,1]=>[1,2,2,2,1]
[4,7,1,3,5,6,2,8]=>[4,1,5,7,3,6,2,8]=>[5,8,4,2,6,3,7,1]=>[2,1,2,2,1]
[4,8,3,2,1,6,7,5]=>[1,4,3,6,8,5,7,2]=>[8,5,6,3,1,4,2,7]=>[1,2,1,2,2]
[5,2,8,1,4,6,7,3]=>[5,6,1,8,2,4,7,3]=>[4,3,8,1,7,5,2,6]=>[1,2,2,1,2]
[5,6,3,7,8,1,4,2]=>[1,8,3,2,6,4,7,5]=>[8,1,6,7,3,5,2,4]=>[1,3,2,2]
[5,7,1,4,3,6,2,8]=>[5,4,1,7,3,6,2,8]=>[4,5,8,2,6,3,7,1]=>[3,2,2,1]
[6,2,3,7,1,5,4,8]=>[7,2,3,5,1,6,4,8]=>[2,7,6,4,8,3,5,1]=>[2,1,2,2,1]
[6,2,8,1,5,4,7,3]=>[6,5,8,2,1,4,7,3]=>[3,4,1,7,8,5,2,6]=>[2,3,1,2]
[6,1,3,4,5,2,7,8]=>[3,4,6,2,5,1,7,8]=>[6,5,3,7,4,8,2,1]=>[1,1,2,2,1,1]
[7,1,3,4,5,6,2,8]=>[3,4,5,7,2,6,1,8]=>[6,5,4,2,7,3,8,1]=>[1,1,1,2,2,1]
[7,2,5,1,3,6,4,8]=>[7,2,4,5,3,6,1,8]=>[2,7,5,4,6,3,8,1]=>[2,1,2,2,1]
[6,5,2,7,8,4,3,1]=>[4,2,1,8,7,3,6,5]=>[5,7,8,1,2,6,3,4]=>[3,3,2]
[7,5,3,6,4,2,1,8]=>[7,3,2,6,5,4,1,8]=>[2,6,7,3,4,5,8,1]=>[3,4,1]
[2,3,6,5,8,4,7,1]=>[4,3,6,8,1,2,7,5]=>[5,6,3,1,8,7,2,4]=>[2,1,2,1,2]
[1,3,6,7,5,2,4,8]=>[6,3,7,2,5,1,4,8]=>[3,6,2,7,4,8,5,1]=>[2,2,2,1,1]
[1,5,2,6,8,7,3,4]=>[4,2,7,8,6,1,3,5]=>[5,7,2,1,3,8,6,4]=>[2,1,3,1,1]
[5,3,4,7,2,1,6,8]=>[2,3,1,6,5,7,4,8]=>[7,6,8,3,4,2,5,1]=>[1,2,2,2,1]
[4,8,5,7,1,2,3,6]=>[1,5,6,3,7,8,4,2]=>[8,4,3,6,2,1,5,7]=>[1,1,2,1,3]
[4,2,3,7,6,1,8,5]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[1,3,1,2,1]
[4,6,3,2,5,8,7,1]=>[1,3,8,4,2,5,7,6]=>[8,6,1,5,7,4,2,3]=>[1,1,3,1,2]
[5,8,4,3,2,6,1,7]=>[1,5,4,3,7,6,8,2]=>[8,4,5,6,2,3,1,7]=>[1,3,2,2]
[1,5,7,4,8,6,2,3]=>[2,4,7,3,8,6,1,5]=>[7,5,2,6,1,3,8,4]=>[1,1,2,3,1]
[1,2,7,8,6,4,3,5]=>[7,6,3,8,5,1,2,4]=>[2,3,6,1,4,8,7,5]=>[3,3,1,1]
[3,5,1,7,8,6,2,4]=>[2,7,1,4,8,6,3,5]=>[7,2,8,5,1,3,6,4]=>[1,2,1,3,1]
[5,2,4,1,7,6,8,3]=>[3,6,2,1,5,8,4,7]=>[6,3,7,8,4,1,5,2]=>[1,3,1,2,1]
[1,3,2,5,4,7,6,9,10,8]=>[2,4,6,8,10,1,3,5,7,9]=>[9,7,5,3,1,10,8,6,4,2]=>[1,1,1,1,2,1,1,1,1]
[1,3,2,5,4,6,8,9,10,7]=>[2,4,7,8,10,1,3,5,6,9]=>[9,7,4,3,1,10,8,6,5,2]=>[1,1,1,1,2,1,1,1,1]
[1,3,2,4,6,7,5,9,10,8]=>[2,5,6,8,10,1,3,4,7,9]=>[9,6,5,3,1,10,8,7,4,2]=>[1,1,1,1,2,1,1,1,1]
[1,3,2,4,6,5,8,9,10,7]=>[2,5,7,8,10,1,3,4,6,9]=>[9,6,4,3,1,10,8,7,5,2]=>[1,1,1,1,2,1,1,1,1]
[1,3,2,4,5,7,8,9,10,6]=>[2,6,7,8,10,1,3,4,5,9]=>[9,5,4,3,1,10,8,7,6,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,4,5,3,7,6,9,10,8]=>[3,4,6,8,10,1,2,5,7,9]=>[8,7,5,3,1,10,9,6,4,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,4,5,3,6,8,9,10,7]=>[3,4,7,8,10,1,2,5,6,9]=>[8,7,4,3,1,10,9,6,5,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,4,3,6,7,5,9,10,8]=>[3,5,6,8,10,1,2,4,7,9]=>[8,6,5,3,1,10,9,7,4,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,4,3,6,5,8,9,10,7]=>[3,5,7,8,10,1,2,4,6,9]=>[8,6,4,3,1,10,9,7,5,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,4,3,5,7,8,9,10,6]=>[3,6,7,8,10,1,2,4,5,9]=>[8,5,4,3,1,10,9,7,6,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,3,5,6,7,4,9,10,8]=>[4,5,6,8,10,1,2,3,7,9]=>[7,6,5,3,1,10,9,8,4,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,3,5,6,4,8,9,10,7]=>[4,5,7,8,10,1,2,3,6,9]=>[7,6,4,3,1,10,9,8,5,2]=>[1,1,1,1,2,1,1,1,1]
[1,2,3,5,4,7,8,9,10,6]=>[4,6,7,8,10,1,2,3,5,9]=>[7,5,4,3,1,10,9,8,6,2]=>[1,1,1,1,2,1,1,1,1]
[1,3,2,5,4,7,6,9,8,11,12,10]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[11,9,7,5,3,1,12,10,8,6,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,5,4,7,6,8,10,11,12,9]=>[2,4,6,9,10,12,1,3,5,7,8,11]=>[11,9,7,4,3,1,12,10,8,6,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,5,4,6,8,9,7,11,12,10]=>[2,4,7,8,10,12,1,3,5,6,9,11]=>[11,9,6,5,3,1,12,10,8,7,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,5,4,6,8,7,10,11,12,9]=>[2,4,7,9,10,12,1,3,5,6,8,11]=>[11,9,6,4,3,1,12,10,8,7,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,5,4,6,7,9,10,11,12,8]=>[2,4,8,9,10,12,1,3,5,6,7,11]=>[11,9,5,4,3,1,12,10,8,7,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,6,7,5,9,8,11,12,10]=>[2,5,6,8,10,12,1,3,4,7,9,11]=>[11,8,7,5,3,1,12,10,9,6,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,6,7,5,8,10,11,12,9]=>[2,5,6,9,10,12,1,3,4,7,8,11]=>[11,8,7,4,3,1,12,10,9,6,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,6,5,8,9,7,11,12,10]=>[2,5,7,8,10,12,1,3,4,6,9,11]=>[11,8,6,5,3,1,12,10,9,7,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,6,5,8,7,10,11,12,9]=>[2,5,7,9,10,12,1,3,4,6,8,11]=>[11,8,6,4,3,1,12,10,9,7,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,6,5,7,9,10,11,12,8]=>[2,5,8,9,10,12,1,3,4,6,7,11]=>[11,8,5,4,3,1,12,10,9,7,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,5,7,8,9,6,11,12,10]=>[2,6,7,8,10,12,1,3,4,5,9,11]=>[11,7,6,5,3,1,12,10,9,8,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,5,7,8,6,10,11,12,9]=>[2,6,7,9,10,12,1,3,4,5,8,11]=>[11,7,6,4,3,1,12,10,9,8,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,5,7,6,9,10,11,12,8]=>[2,6,8,9,10,12,1,3,4,5,7,11]=>[11,7,5,4,3,1,12,10,9,8,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,3,2,4,5,6,8,9,10,11,12,7]=>[2,7,8,9,10,12,1,3,4,5,6,11]=>[11,6,5,4,3,1,12,10,9,8,7,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,5,3,7,6,9,8,11,12,10]=>[3,4,6,8,10,12,1,2,5,7,9,11]=>[10,9,7,5,3,1,12,11,8,6,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,5,3,7,6,8,10,11,12,9]=>[3,4,6,9,10,12,1,2,5,7,8,11]=>[10,9,7,4,3,1,12,11,8,6,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,5,3,6,8,9,7,11,12,10]=>[3,4,7,8,10,12,1,2,5,6,9,11]=>[10,9,6,5,3,1,12,11,8,7,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,5,3,6,8,7,10,11,12,9]=>[3,4,7,9,10,12,1,2,5,6,8,11]=>[10,9,6,4,3,1,12,11,8,7,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,5,3,6,7,9,10,11,12,8]=>[3,4,8,9,10,12,1,2,5,6,7,11]=>[10,9,5,4,3,1,12,11,8,7,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,6,7,5,9,8,11,12,10]=>[3,5,6,8,10,12,1,2,4,7,9,11]=>[10,8,7,5,3,1,12,11,9,6,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,6,7,5,8,10,11,12,9]=>[3,5,6,9,10,12,1,2,4,7,8,11]=>[10,8,7,4,3,1,12,11,9,6,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,6,5,8,9,7,11,12,10]=>[3,5,7,8,10,12,1,2,4,6,9,11]=>[10,8,6,5,3,1,12,11,9,7,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,6,5,8,7,10,11,12,9]=>[3,5,7,9,10,12,1,2,4,6,8,11]=>[10,8,6,4,3,1,12,11,9,7,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,6,5,7,9,10,11,12,8]=>[3,5,8,9,10,12,1,2,4,6,7,11]=>[10,8,5,4,3,1,12,11,9,7,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,5,7,8,9,6,11,12,10]=>[3,6,7,8,10,12,1,2,4,5,9,11]=>[10,7,6,5,3,1,12,11,9,8,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,5,7,8,6,10,11,12,9]=>[3,6,7,9,10,12,1,2,4,5,8,11]=>[10,7,6,4,3,1,12,11,9,8,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,5,7,6,9,10,11,12,8]=>[3,6,8,9,10,12,1,2,4,5,7,11]=>[10,7,5,4,3,1,12,11,9,8,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,4,3,5,6,8,9,10,11,12,7]=>[3,7,8,9,10,12,1,2,4,5,6,11]=>[10,6,5,4,3,1,12,11,9,8,7,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,6,7,4,9,8,11,12,10]=>[4,5,6,8,10,12,1,2,3,7,9,11]=>[9,8,7,5,3,1,12,11,10,6,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,6,7,4,8,10,11,12,9]=>[4,5,6,9,10,12,1,2,3,7,8,11]=>[9,8,7,4,3,1,12,11,10,6,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,6,4,8,9,7,11,12,10]=>[4,5,7,8,10,12,1,2,3,6,9,11]=>[9,8,6,5,3,1,12,11,10,7,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,6,4,8,7,10,11,12,9]=>[4,5,7,9,10,12,1,2,3,6,8,11]=>[9,8,6,4,3,1,12,11,10,7,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,6,4,7,9,10,11,12,8]=>[4,5,8,9,10,12,1,2,3,6,7,11]=>[9,8,5,4,3,1,12,11,10,7,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,4,7,8,9,6,11,12,10]=>[4,6,7,8,10,12,1,2,3,5,9,11]=>[9,7,6,5,3,1,12,11,10,8,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,4,7,8,6,10,11,12,9]=>[4,6,7,9,10,12,1,2,3,5,8,11]=>[9,7,6,4,3,1,12,11,10,8,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,4,7,6,9,10,11,12,8]=>[4,6,8,9,10,12,1,2,3,5,7,11]=>[9,7,5,4,3,1,12,11,10,8,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,5,4,6,8,9,10,11,12,7]=>[4,7,8,9,10,12,1,2,3,5,6,11]=>[9,6,5,4,3,1,12,11,10,8,7,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,4,6,7,8,9,5,11,12,10]=>[5,6,7,8,10,12,1,2,3,4,9,11]=>[8,7,6,5,3,1,12,11,10,9,4,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,4,6,7,8,5,10,11,12,9]=>[5,6,7,9,10,12,1,2,3,4,8,11]=>[8,7,6,4,3,1,12,11,10,9,5,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,4,6,7,5,9,10,11,12,8]=>[5,6,8,9,10,12,1,2,3,4,7,11]=>[8,7,5,4,3,1,12,11,10,9,6,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,4,6,5,8,9,10,11,12,7]=>[5,7,8,9,10,12,1,2,3,4,6,11]=>[8,6,5,4,3,1,12,11,10,9,7,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[1,2,3,4,5,7,8,9,10,11,12,6]=>[6,7,8,9,10,12,1,2,3,4,5,11]=>[7,6,5,4,3,1,12,11,10,9,8,2]=>[1,1,1,1,1,2,1,1,1,1,1]
[9,3,4,5,6,7,8,2,1]=>[2,3,4,5,6,9,8,7,1]=>[8,7,6,5,4,1,2,3,9]=>[1,1,1,1,1,4]
[9,1,8,2,7,3,6,4,5]=>[8,9,6,7,4,5,2,3,1]=>[2,1,4,3,6,5,8,7,9]=>[1,2,2,2,2]
[5,4,3,8,1,7,2,6]=>[3,2,1,7,8,5,6,4]=>[6,7,8,2,1,4,3,5]=>[3,1,2,2]
[5,4,6,3,7,2,9,1,8]=>[2,1,4,3,6,5,8,9,7]=>[8,9,6,7,4,5,2,1,3]=>[2,2,2,1,2]
[5,10,1,9,2,8,3,7,4,6]=>[1,9,10,7,8,5,6,3,4,2]=>[10,2,1,4,3,6,5,8,7,9]=>[1,1,2,2,2,2]
[5,6,4,7,3,8,2,10,1,9]=>[1,3,2,5,4,7,6,9,10,8]=>[10,8,9,6,7,4,5,2,1,3]=>[1,2,2,2,1,2]
[7,3,1,5,6,8,4,2]=>[2,4,5,8,7,3,1,6]=>[7,5,4,1,2,6,8,3]=>[1,1,1,4,1]
[7,2,3,1,6,8,4,5]=>[7,2,3,5,8,4,1,6]=>[2,7,6,4,1,5,8,3]=>[2,1,1,3,1]
[4,1,8,2,5,6,3,7]=>[5,1,7,4,6,8,2,3]=>[4,8,2,5,3,1,7,6]=>[2,2,1,2,1]
[5,7,8,1,6,2,3,4]=>[6,1,7,8,4,2,5,3]=>[3,8,2,1,5,7,4,6]=>[2,1,3,2]
[1,4,2,5,8,6,3,7]=>[2,7,4,6,8,1,3,5]=>[7,2,5,3,1,8,6,4]=>[1,2,1,2,1,1]
[4,8,2,5,1,6,3,7]=>[1,7,3,5,4,6,8,2]=>[8,2,6,4,5,3,1,7]=>[1,2,2,1,2]
[5,8,1,2,4,6,3,7]=>[5,7,3,1,4,6,8,2]=>[4,2,6,8,5,3,1,7]=>[1,3,1,1,2]
[3,2,7,5,6,1,4,8]=>[6,1,4,7,2,5,3,8]=>[3,8,5,2,7,4,6,1]=>[2,1,2,2,1]
[3,2,7,1,6,4,5,8]=>[1,6,7,2,4,5,3,8]=>[8,3,2,7,5,4,6,1]=>[1,1,2,1,2,1]
[6,2,8,7,3,4,5,1]=>[5,6,1,8,7,2,4,3]=>[4,3,8,1,2,7,5,6]=>[1,2,3,2]
[7,3,4,8,5,6,2,1]=>[5,8,2,3,1,7,6,4]=>[4,1,7,6,8,2,3,5]=>[1,2,2,3]
[7,3,6,8,4,5,2,1]=>[5,3,8,2,1,7,6,4]=>[4,6,1,7,8,2,3,5]=>[2,3,3]
[5,6,2,8,3,1,7,4]=>[5,1,8,3,2,6,7,4]=>[4,8,1,6,7,3,2,5]=>[2,3,1,2]
[1,7,4,8,3,5,6,2]=>[3,5,6,2,8,7,1,4]=>[6,4,3,7,1,2,8,5]=>[1,1,2,3,1]
[5,3,1,4,8,6,2,7]=>[2,7,4,1,6,8,3,5]=>[7,2,5,8,3,1,6,4]=>[1,3,1,2,1]
[5,2,4,8,3,1,6,7]=>[3,6,2,1,5,7,8,4]=>[6,3,7,8,4,2,1,5]=>[1,3,1,1,2]
[8,7,3,5,4,1,6,2]=>[8,3,6,5,4,7,2,1]=>[1,6,3,4,5,2,7,8]=>[2,3,3]
[1,8,6,7,5,3,2,4]=>[7,6,3,8,5,4,1,2]=>[2,3,6,1,4,5,8,7]=>[3,4,1]
[7,4,8,3,1,6,5,2]=>[2,4,8,7,5,1,6,3]=>[7,5,1,2,4,8,3,6]=>[1,1,4,2]
[8,1,5,3,7,6,2,4]=>[7,3,8,4,6,2,5,1]=>[2,6,1,5,3,7,4,8]=>[2,2,2,2]
[6,4,8,7,3,5,1,2]=>[7,2,1,5,8,6,4,3]=>[2,7,8,4,1,3,5,6]=>[3,1,4]
[6,1,4,2,3,5,7,8]=>[4,5,2,3,6,1,7,8]=>[5,4,7,6,3,8,2,1]=>[1,2,1,2,1,1]
[6,5,1,8,3,7,4,2]=>[8,5,2,1,7,6,3,4]=>[1,4,7,8,2,3,6,5]=>[4,3,1]
[7,1,4,3,8,6,5,2]=>[8,3,7,4,6,2,1,5]=>[1,6,2,5,3,7,8,4]=>[2,2,3,1]
[8,5,4,1,7,3,2,6]=>[7,6,3,2,8,4,5,1]=>[2,3,6,7,1,5,4,8]=>[4,2,2]
[4,5,3,8,1,7,6,2]=>[1,2,8,3,7,5,6,4]=>[8,7,1,6,2,4,3,5]=>[1,1,2,2,2]
[4,7,6,3,2,8,5,1]=>[4,8,1,5,3,2,7,6]=>[5,1,8,4,6,7,2,3]=>[1,2,3,2]
[5,7,6,3,8,2,4,1]=>[1,4,6,3,2,8,7,5]=>[8,5,3,6,7,1,2,4]=>[1,1,3,3]
[6,8,4,7,1,2,5,3]=>[8,5,3,1,6,7,4,2]=>[1,4,6,8,3,2,5,7]=>[4,1,3]
[1,3,7,6,8,4,5,2]=>[6,4,3,8,2,7,1,5]=>[3,5,6,1,7,2,8,4]=>[3,2,2,1]
[6,1,5,7,2,8,3,4]=>[7,3,8,5,2,1,4,6]=>[2,6,1,4,7,8,5,3]=>[2,4,1,1]
[1,8,7,2,5,6,3,4]=>[7,5,8,4,6,3,1,2]=>[2,4,1,5,3,6,8,7]=>[2,2,3,1]
[1,8,2,6,7,4,3,5]=>[7,6,4,8,3,5,1,2]=>[2,3,5,1,6,4,8,7]=>[3,2,2,1]
[2,5,4,8,7,6,1,3]=>[2,7,8,3,6,1,5,4]=>[7,2,1,6,3,8,4,5]=>[1,1,2,2,2]
[1,8,7,6,3,5,4,2]=>[8,5,7,6,4,3,1,2]=>[1,4,2,3,5,6,8,7]=>[2,5,1]
[1,8,5,7,6,4,3,2]=>[8,3,7,6,5,4,1,2]=>[1,6,2,3,4,5,8,7]=>[2,5,1]
[1,6,2,7,3,8,4,9,5]=>[9,7,5,3,1,2,4,6,8]=>[1,3,5,7,9,8,6,4,2]=>[5,1,1,1,1]
[7,2,4,1,8,5,3,6]=>[3,7,2,6,8,4,1,5]=>[6,2,7,3,1,5,8,4]=>[1,2,1,3,1]
[7,3,2,1,4,6,8,5]=>[3,2,6,8,4,5,1,7]=>[6,7,3,1,5,4,8,2]=>[2,1,2,2,1]
[4,7,2,6,1,8,3,5]=>[1,7,8,3,5,4,2,6]=>[8,2,1,6,4,5,7,3]=>[1,1,2,3,1]
[8,7,3,5,2,1,6,4]=>[3,5,8,6,4,7,2,1]=>[6,4,1,3,5,2,7,8]=>[1,1,3,3]
[7,5,3,2,1,6,8,4]=>[4,3,6,2,8,5,1,7]=>[5,6,3,7,1,4,8,2]=>[2,2,3,1]
[6,8,1,3,4,2,5,7]=>[4,6,3,5,1,7,8,2]=>[5,3,6,4,8,2,1,7]=>[1,2,2,1,2]
[2,5,7,1,3,6,4,8]=>[7,4,1,2,5,6,3,8]=>[2,5,8,7,4,3,6,1]=>[3,1,1,2,1]
[1,4,7,2,5,3,6,8]=>[2,6,4,5,7,1,3,8]=>[7,3,5,4,2,8,6,1]=>[1,2,1,2,1,1]
[4,5,3,1,2,6,8,7]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[1,4,1,1,1]
[4,5,1,3,8,2,6,7]=>[4,1,6,2,7,8,3,5]=>[5,8,3,7,2,1,6,4]=>[2,2,1,2,1]
[4,1,5,3,2,7,6,8]=>[4,3,1,7,2,5,6,8]=>[5,6,8,2,7,4,3,1]=>[3,2,1,1,1]
[7,3,5,1,4,2,6,8]=>[2,6,4,5,3,7,1,8]=>[7,3,5,4,6,2,8,1]=>[1,2,2,2,1]
[6,2,1,7,4,3,8,5]=>[5,8,2,6,3,1,4,7]=>[4,1,7,3,6,8,5,2]=>[1,2,3,1,1]
[2,4,3,6,7,1,5,8]=>[2,6,1,3,4,7,5,8]=>[7,3,8,6,5,2,4,1]=>[1,2,1,1,2,1]
[6,1,5,3,7,2,4,8]=>[4,6,3,7,2,1,5,8]=>[5,3,6,2,7,8,4,1]=>[1,2,3,1,1]
[3,6,5,4,1,7,2,8]=>[7,5,1,4,3,2,6,8]=>[2,4,8,5,6,7,3,1]=>[3,3,1,1]
[6,8,7,5,4,2,1,3]=>[1,7,6,8,5,4,3,2]=>[8,2,3,1,4,5,6,7]=>[1,2,5]
[1,6,8,7,3,2,4,5]=>[6,5,2,7,8,4,1,3]=>[3,4,7,2,1,5,8,6]=>[3,1,3,1]
[8,7,5,4,6,1,3,2]=>[8,6,4,3,7,5,2,1]=>[1,3,5,6,2,4,7,8]=>[4,4]
[1,7,8,2,4,6,3,5]=>[5,7,8,4,2,6,1,3]=>[4,2,1,5,7,3,8,6]=>[1,1,3,2,1]
[7,5,4,8,1,3,6,2]=>[6,3,2,8,5,1,7,4]=>[3,6,7,1,4,8,2,5]=>[3,3,2]
[5,6,1,8,4,3,7,2]=>[1,6,5,2,8,7,3,4]=>[8,3,4,7,1,2,6,5]=>[1,3,3,1]
[1,8,2,6,7,5,4,3]=>[4,8,7,6,3,5,1,2]=>[5,1,2,3,6,4,8,7]=>[1,4,2,1]
[2,7,5,1,6,8,3,4]=>[7,5,3,8,1,4,2,6]=>[2,4,6,1,8,5,7,3]=>[3,2,2,1]
[3,8,6,1,2,4,5,7]=>[1,4,5,6,7,3,8,2]=>[8,5,4,3,2,6,1,7]=>[1,1,1,1,2,2]
[1,8,5,3,2,7,4,6]=>[4,7,3,8,5,6,1,2]=>[5,2,6,1,4,3,8,7]=>[1,2,2,2,1]
[1,8,4,7,2,3,5,6]=>[5,3,6,7,8,4,1,2]=>[4,6,3,2,1,5,8,7]=>[2,1,1,3,1]
[3,4,5,6,2,1,7,8,9]=>[1,2,3,6,5,4,7,8,9]=>[9,8,7,4,5,6,3,2,1]=>[1,1,1,3,1,1,1]
[7,1,5,6,2,3,4,8]=>[5,6,3,7,2,4,1,8]=>[4,3,6,2,7,5,8,1]=>[1,2,2,2,1]
[6,5,1,7,2,3,4,8]=>[5,6,7,3,2,1,4,8]=>[4,3,2,6,7,8,5,1]=>[1,1,4,1,1]
[1,6,8,2,7,3,4,5]=>[6,7,2,8,4,5,1,3]=>[3,2,7,1,5,4,8,6]=>[1,2,2,2,1]
[1,6,8,7,3,4,2,5]=>[5,2,7,6,8,4,1,3]=>[4,7,2,3,1,5,8,6]=>[2,2,3,1]
[4,1,3,6,7,8,5,2]=>[4,1,5,8,3,7,2,6]=>[5,8,4,1,6,2,7,3]=>[2,1,2,2,1]
[7,4,1,5,6,8,3,2]=>[4,2,5,8,7,3,1,6]=>[5,7,4,1,2,6,8,3]=>[2,1,4,1]
[4,1,2,6,7,8,5,3]=>[4,1,5,8,7,2,3,6]=>[5,8,4,1,2,7,6,3]=>[2,1,3,1,1]
[5,4,3,2,10,9,8,7,1,6]=>[1,9,10,2,8,3,7,4,6,5]=>[10,2,1,9,3,8,4,7,5,6]=>[1,1,2,2,2,2]
[5,4,3,2,10,1,9,8,7,6]=>[1,10,2,9,3,8,4,6,7,5]=>[10,1,9,2,8,3,7,5,4,6]=>[1,2,2,2,1,2]
[6,5,4,3,2,12,11,10,9,8,1,7]=>[1,11,12,2,10,3,9,4,8,5,7,6]=>[12,2,1,11,3,10,4,9,5,8,6,7]=>[1,1,2,2,2,2,2]
[6,5,4,3,2,12,1,11,10,9,8,7]=>[1,12,2,11,3,10,4,9,5,7,8,6]=>[12,1,11,2,10,3,9,4,8,6,5,7]=>[1,2,2,2,2,1,2]
[3,7,8,2,1,4,5,6]=>[5,1,4,6,7,2,8,3]=>[4,8,5,3,2,7,1,6]=>[2,1,1,2,2]
[3,7,8,1,5,2,6,4]=>[8,6,1,4,5,2,7,3]=>[1,3,8,5,4,7,2,6]=>[3,1,2,2]
[1,5,4,7,8,3,6,2]=>[2,6,3,4,8,7,1,5]=>[7,3,6,5,1,2,8,4]=>[1,2,1,3,1]
[5,2,4,7,8,3,6,1]=>[6,3,1,4,8,2,7,5]=>[3,6,8,5,1,7,2,4]=>[3,1,2,2]
[5,1,4,7,8,3,6,2]=>[6,3,1,4,8,7,2,5]=>[3,6,8,5,1,2,7,4]=>[3,1,3,1]
[4,8,1,5,6,2,3,7]=>[1,6,4,7,3,5,8,2]=>[8,3,5,2,6,4,1,7]=>[1,2,2,1,2]
[5,6,4,1,7,3,8,2]=>[1,6,5,3,2,8,4,7]=>[8,3,4,6,7,1,5,2]=>[1,4,2,1]
[3,7,8,5,4,2,1,6]=>[7,6,5,1,4,2,8,3]=>[2,3,4,8,5,7,1,6]=>[4,2,2]
[1,7,4,5,6,8,3,2]=>[3,4,5,2,8,7,1,6]=>[6,5,4,7,1,2,8,3]=>[1,1,2,3,1]
[7,2,4,5,6,8,3,1]=>[3,4,5,8,2,1,7,6]=>[6,5,4,1,7,8,2,3]=>[1,1,1,3,2]
[2,7,4,5,6,8,3,1]=>[3,4,5,2,8,1,7,6]=>[6,5,4,7,1,8,2,3]=>[1,1,2,2,2]
[2,4,7,8,3,1,6,5]=>[5,8,2,6,1,3,7,4]=>[4,1,7,3,8,6,2,5]=>[1,2,2,1,2]
[5,4,3,6,8,1,7,2]=>[3,2,1,4,8,6,7,5]=>[6,7,8,5,1,3,2,4]=>[3,1,2,2]
[3,7,4,5,8,1,6,2]=>[3,4,8,1,6,2,7,5]=>[6,5,1,8,3,7,2,4]=>[1,1,2,2,2]
[1,4,3,5,6,8,2,7]=>[3,2,4,5,7,8,1,6]=>[6,7,5,4,2,1,8,3]=>[2,1,1,1,2,1]
[1,4,6,5,8,2,7,3]=>[4,2,3,8,6,7,1,5]=>[5,7,6,1,3,2,8,4]=>[2,1,2,2,1]
[4,6,1,7,3,2,8,5]=>[1,5,8,6,3,2,4,7]=>[8,4,1,3,6,7,5,2]=>[1,1,4,1,1]
[1,7,3,6,4,2,8,5]=>[5,8,3,6,4,1,2,7]=>[4,1,6,3,5,8,7,2]=>[1,2,3,1,1]
[1,6,8,4,7,5,3,2]=>[2,8,4,7,6,5,1,3]=>[7,1,5,2,3,4,8,6]=>[1,2,4,1]
[8,7,3,1,5,2,6,4]=>[3,8,6,4,5,7,2,1]=>[6,1,3,5,4,2,7,8]=>[1,3,1,3]
[4,7,1,6,8,2,3,5]=>[1,6,7,4,8,3,2,5]=>[8,3,2,5,1,6,7,4]=>[1,1,2,3,1]
[4,6,5,8,2,3,7,1]=>[5,1,3,2,6,8,7,4]=>[4,8,6,7,3,1,2,5]=>[2,2,1,3]
[7,1,8,2,4,5,3,6]=>[5,7,4,6,8,2,1,3]=>[4,2,5,3,1,7,8,6]=>[1,2,1,3,1]
[5,7,8,2,3,4,1,6]=>[4,1,5,7,6,2,8,3]=>[5,8,4,2,3,7,1,6]=>[2,1,3,2]
[5,2,3,8,7,1,4,6]=>[6,7,1,8,2,3,5,4]=>[3,2,8,1,7,6,4,5]=>[1,2,2,1,2]
[8,7,1,3,2,6,4,5]=>[4,7,8,3,5,6,2,1]=>[5,2,1,6,4,3,7,8]=>[1,1,2,1,3]
[2,6,3,7,5,8,4,1]=>[5,4,2,8,1,3,7,6]=>[4,5,7,1,8,6,2,3]=>[3,2,1,2]
[7,5,1,2,3,8,4,6]=>[7,8,3,4,2,5,1,6]=>[2,1,6,5,7,4,8,3]=>[1,2,2,2,1]
[4,3,5,2,6,1,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[8,9,6,7,4,5,3,2,1]=>[2,2,2,1,1,1]
[3,2,4,1,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[9,10,7,8,6,5,4,3,2,1]=>[2,2,1,1,1,1,1,1]
[4,3,5,2,6,1,7,8,9,10]=>[2,1,4,3,6,5,7,8,9,10]=>[9,10,7,8,5,6,4,3,2,1]=>[2,2,2,1,1,1,1]
[5,4,6,3,7,2,8,1,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[9,10,7,8,5,6,3,4,2,1]=>[2,2,2,2,1,1]
[8,6,2,1,3,7,4,5]=>[3,7,8,4,5,2,6,1]=>[6,2,1,5,4,7,3,8]=>[1,1,2,2,2]
[4,2,3,6,8,5,7,1]=>[4,1,6,8,2,3,7,5]=>[5,8,3,1,7,6,2,4]=>[2,1,2,1,2]
[4,7,3,2,6,5,1,8]=>[1,3,7,4,6,5,2,8]=>[8,6,2,5,3,4,7,1]=>[1,1,2,3,1]
[4,3,7,8,2,1,6,5]=>[1,5,8,2,6,3,7,4]=>[8,4,1,7,3,6,2,5]=>[1,1,2,2,2]
[4,8,7,2,1,5,6,3]=>[1,4,6,8,5,7,3,2]=>[8,5,3,1,4,2,6,7]=>[1,1,1,2,3]
[4,5,3,8,6,1,2,7]=>[1,3,2,6,7,5,8,4]=>[8,6,7,3,2,4,1,5]=>[1,2,1,2,2]
[6,3,5,8,4,1,2,7]=>[6,2,3,1,7,5,8,4]=>[3,7,6,8,2,4,1,5]=>[2,2,2,2]
[7,3,8,4,5,1,2,6]=>[6,2,4,7,5,1,8,3]=>[3,7,5,2,4,8,1,6]=>[2,1,3,2]
[4,8,7,5,1,2,6,3]=>[8,1,5,6,4,7,3,2]=>[1,8,4,3,5,2,6,7]=>[2,1,2,3]
[7,8,4,6,1,3,5,2]=>[6,3,8,5,1,7,4,2]=>[3,6,1,4,8,2,5,7]=>[2,3,3]
[4,8,7,5,1,3,6,2]=>[6,8,1,5,4,7,3,2]=>[3,1,8,4,5,2,6,7]=>[1,2,2,3]
[4,5,3,6,8,1,2,7]=>[1,3,2,6,4,7,8,5]=>[8,6,7,3,5,2,1,4]=>[1,2,2,1,2]
[7,8,6,2,1,4,3,5]=>[4,7,5,6,1,8,3,2]=>[5,2,4,3,8,1,6,7]=>[1,2,2,3]
[7,8,6,3,1,2,5,4]=>[8,5,4,6,1,7,3,2]=>[1,4,5,3,8,2,6,7]=>[3,2,3]
[3,7,6,4,1,5,2,8]=>[7,5,1,4,6,3,2,8]=>[2,4,8,5,3,6,7,1]=>[3,1,3,1]
[7,3,1,2,8,6,5,4]=>[8,2,7,6,3,4,1,5]=>[1,7,2,3,6,5,8,4]=>[2,3,2,1]
[4,1,3,6,5,7,2,8]=>[5,3,1,4,7,2,6,8]=>[4,6,8,5,2,7,3,1]=>[3,1,2,1,1]
[4,1,3,5,7,2,8,6]=>[8,3,1,4,6,2,5,7]=>[1,6,8,5,3,7,4,2]=>[3,1,2,1,1]
[5,1,8,2,4,6,3,7]=>[5,7,4,1,6,8,2,3]=>[4,2,5,8,3,1,7,6]=>[1,3,1,2,1]
[6,8,2,1,4,5,3,7]=>[3,5,7,4,1,6,8,2]=>[6,4,2,5,8,3,1,7]=>[1,1,3,1,2]
[4,2,7,3,6,8,5,1]=>[1,5,8,4,2,3,7,6]=>[8,4,1,5,7,6,2,3]=>[1,1,3,1,2]
[3,1,5,8,6,7,2,4]=>[7,1,3,5,8,6,2,4]=>[2,8,6,4,1,3,7,5]=>[2,1,1,3,1]
[6,8,2,1,4,5,7,3]=>[3,5,6,1,8,4,7,2]=>[6,4,3,8,1,5,2,7]=>[1,1,2,2,2]
[12,1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[1,1,1,1,1,1,1,1,1,1,2]
[1,5,4,8,7,3,2,6]=>[2,7,3,6,8,5,1,4]=>[7,2,6,3,1,4,8,5]=>[1,2,1,3,1]
[4,3,1,2,6,5,7,8]=>[6,3,2,1,4,5,7,8]=>[3,6,7,8,5,4,2,1]=>[4,1,1,1,1]
[7,1,4,5,8,3,6,2]=>[3,4,6,8,7,2,1,5]=>[6,5,3,1,2,7,8,4]=>[1,1,1,4,1]
[7,5,8,1,2,4,6,3]=>[6,8,4,2,5,1,7,3]=>[3,1,5,7,4,8,2,6]=>[1,3,2,2]
[6,1,5,2,8,7,4,3]=>[3,8,7,6,2,1,4,5]=>[6,1,2,3,7,8,5,4]=>[1,5,1,1]
[8,4,6,3,1,2,7,5]=>[2,8,5,4,6,3,7,1]=>[7,1,4,5,3,6,2,8]=>[1,3,2,2]
[3,8,6,4,1,5,7,2]=>[6,4,8,1,5,3,7,2]=>[3,5,1,8,4,6,2,7]=>[2,2,2,2]
[3,8,6,4,5,1,7,2]=>[4,8,6,1,5,3,7,2]=>[5,1,3,8,4,6,2,7]=>[1,3,2,2]
[3,7,6,4,5,1,2,8]=>[6,4,7,1,5,3,2,8]=>[3,5,2,8,4,6,7,1]=>[2,2,3,1]
[7,4,6,3,1,2,8,5]=>[2,8,5,4,6,3,1,7]=>[7,1,4,5,3,6,8,2]=>[1,3,3,1]
[4,6,2,5,7,8,1,3]=>[1,4,7,3,2,5,8,6]=>[8,5,2,6,7,4,1,3]=>[1,1,3,1,2]
[4,6,3,5,7,1,2,8]=>[1,3,6,4,2,7,5,8]=>[8,6,3,5,7,2,4,1]=>[1,1,3,2,1]
[4,7,3,5,8,6,1,2]=>[1,3,4,7,2,8,6,5]=>[8,6,5,2,7,1,3,4]=>[1,1,1,2,3]
[4,8,3,5,7,1,6,2]=>[1,3,4,8,6,7,5,2]=>[8,6,5,1,3,2,4,7]=>[1,1,1,2,3]
[4,8,3,5,6,1,2,7]=>[1,3,6,4,7,5,8,2]=>[8,6,3,5,2,4,1,7]=>[1,1,2,2,2]
[1,4,7,2,6,5,8,3]=>[6,2,5,8,4,1,3,7]=>[3,7,4,1,5,8,6,2]=>[2,1,3,1,1]
[1,5,7,2,6,4,8,3]=>[2,6,5,8,4,1,3,7]=>[7,3,4,1,5,8,6,2]=>[1,2,3,1,1]
[1,2,7,8,3,5,4,6]=>[7,5,6,3,8,1,2,4]=>[2,4,3,6,1,8,7,5]=>[2,2,2,1,1]
[1,7,6,2,8,5,4,3]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>[6,1,1]
[1,2,7,8,3,4,6,5]=>[8,5,6,3,7,1,2,4]=>[1,4,3,6,2,8,7,5]=>[2,2,2,1,1]
[1,7,6,8,3,4,2,5]=>[5,7,6,3,2,8,1,4]=>[4,2,3,6,7,1,8,5]=>[1,4,2,1]
[2,4,8,6,5,7,1,3]=>[7,5,2,4,8,1,6,3]=>[2,4,7,5,1,8,3,6]=>[3,1,2,2]
[8,2,1,5,6,4,7,3]=>[4,6,2,5,8,3,7,1]=>[5,3,7,4,1,6,2,8]=>[1,2,1,2,2]
[3,2,7,5,8,6,4,1]=>[8,4,1,3,7,2,6,5]=>[1,5,8,6,2,7,3,4]=>[3,1,2,2]
[2,4,8,3,6,5,7,1]=>[6,2,4,5,8,1,7,3]=>[3,7,5,4,1,8,2,6]=>[2,1,1,2,2]
[3,1,8,2,6,5,7,4]=>[6,1,5,8,4,7,2,3]=>[3,8,4,1,5,2,7,6]=>[2,1,2,2,1]
[4,6,7,8,5,2,1,3]=>[2,7,1,6,3,8,5,4]=>[7,2,8,3,6,1,4,5]=>[1,2,2,3]
[4,7,2,1,8,6,5,3]=>[8,1,7,3,6,4,2,5]=>[1,8,2,6,3,5,7,4]=>[2,2,3,1]
[5,6,2,8,4,1,7,3]=>[1,8,6,3,2,5,7,4]=>[8,1,3,6,7,4,2,5]=>[1,4,1,2]
[5,7,2,4,8,6,1,3]=>[4,1,7,8,3,2,6,5]=>[5,8,2,1,6,7,3,4]=>[2,1,3,2]
[6,7,2,4,8,5,1,3]=>[4,7,1,8,3,2,6,5]=>[5,2,8,1,6,7,3,4]=>[1,2,3,2]
[6,7,3,2,8,5,1,4]=>[3,7,1,8,4,2,6,5]=>[6,2,8,1,5,7,3,4]=>[1,2,3,2]
[7,2,3,1,8,6,5,4]=>[8,7,2,3,6,4,1,5]=>[1,2,7,6,3,5,8,4]=>[3,1,3,1]
[7,2,8,3,5,6,1,4]=>[7,4,5,8,2,1,6,3]=>[2,5,4,1,7,8,3,6]=>[2,1,3,2]
[1,7,3,4,8,5,2,6]=>[7,3,4,6,2,8,1,5]=>[2,6,5,3,7,1,8,4]=>[2,1,2,2,1]
[1,7,3,8,5,4,2,6]=>[7,6,3,5,2,8,1,4]=>[2,3,6,4,7,1,8,5]=>[3,2,2,1]
[7,2,8,4,5,3,1,6]=>[4,7,6,2,5,1,8,3]=>[5,2,3,7,4,8,1,6]=>[1,3,2,2]
[2,8,6,4,3,1,7,5]=>[5,4,8,6,1,3,7,2]=>[4,5,1,3,8,6,2,7]=>[2,3,1,2]
[1,7,3,4,8,2,5,6]=>[3,4,6,7,2,8,1,5]=>[6,5,3,2,7,1,8,4]=>[1,1,1,2,2,1]
[1,8,4,6,7,2,3,5]=>[3,6,7,4,8,5,1,2]=>[6,3,2,5,1,4,8,7]=>[1,1,2,3,1]
[1,4,2,3,7,8,6,5]=>[2,5,8,7,1,3,4,6]=>[7,4,1,2,8,6,5,3]=>[1,1,3,1,1,1]
[5,7,1,6,4,8,3,2]=>[1,5,4,8,7,3,2,6]=>[8,4,5,1,2,6,7,3]=>[1,2,4,1]
[7,4,5,8,1,3,6,2]=>[2,6,3,8,5,1,7,4]=>[7,3,6,1,4,8,2,5]=>[1,2,3,2]
[1,4,3,6,2,5,8,7]=>[2,8,3,5,1,4,6,7]=>[7,1,6,4,8,5,3,2]=>[1,2,2,1,1,1]
[1,4,6,3,2,5,8,7]=>[2,4,8,5,1,3,6,7]=>[7,5,1,4,8,6,3,2]=>[1,1,3,1,1,1]
[1,4,6,3,2,8,5,7]=>[2,4,7,3,8,1,5,6]=>[7,5,2,6,1,8,4,3]=>[1,1,2,2,1,1]
[6,8,4,1,5,7,2,3]=>[7,5,3,1,8,4,6,2]=>[2,4,6,8,1,5,3,7]=>[4,2,2]
[5,2,6,7,4,1,8,3]=>[3,1,8,6,2,5,4,7]=>[6,8,1,3,7,4,5,2]=>[2,3,2,1]
[8,5,6,4,1,7,3,2]=>[2,8,7,5,4,3,6,1]=>[7,1,2,4,5,6,3,8]=>[1,5,2]
[7,8,3,1,6,4,5,2]=>[3,6,8,7,4,1,5,2]=>[6,3,1,2,5,8,4,7]=>[1,1,4,2]
[5,8,2,6,3,1,7,4]=>[5,1,8,3,6,4,7,2]=>[4,8,1,6,3,5,2,7]=>[2,2,2,2]
[4,5,8,1,6,3,7,2]=>[1,2,6,5,8,4,7,3]=>[8,7,3,4,1,5,2,6]=>[1,1,2,2,2]
[8,1,4,6,2,5,7,3]=>[3,6,8,5,2,4,7,1]=>[6,3,1,4,7,5,2,8]=>[1,1,3,1,2]
[4,5,8,1,6,2,7,3]=>[1,2,8,6,4,5,7,3]=>[8,7,1,3,5,4,2,6]=>[1,1,3,1,2]
[5,2,6,8,1,4,3,7]=>[7,5,2,1,3,6,8,4]=>[2,4,7,8,6,3,1,5]=>[4,1,1,2]
[6,7,3,8,2,1,4,5]=>[3,6,5,1,7,2,8,4]=>[6,3,4,8,2,7,1,5]=>[1,3,2,2]
[2,6,3,7,4,1,8,5]=>[5,8,3,1,2,6,4,7]=>[4,1,6,8,7,3,5,2]=>[1,3,1,2,1]
[2,1,4,8,5,3,7,6]=>[5,8,1,3,6,7,2,4]=>[4,1,8,6,3,2,7,5]=>[1,2,1,1,2,1]
[2,7,3,8,4,1,6,5]=>[5,8,3,6,1,2,7,4]=>[4,1,6,3,8,7,2,5]=>[1,2,2,1,2]
[2,6,3,1,5,4,8,7]=>[3,5,8,1,4,2,6,7]=>[6,4,1,8,5,7,3,2]=>[1,1,2,2,1,1]
[1,5,8,3,4,7,2,6]=>[4,2,5,7,8,6,1,3]=>[5,7,4,2,1,3,8,6]=>[2,1,1,3,1]
[5,3,8,1,4,6,2,7]=>[2,5,1,7,4,6,8,3]=>[7,4,8,2,5,3,1,6]=>[1,2,2,1,2]
[4,5,8,1,3,6,2,7]=>[1,5,2,7,4,6,8,3]=>[8,4,7,2,5,3,1,6]=>[1,2,2,1,2]
[7,4,6,5,2,8,3,1]=>[8,2,5,4,3,1,7,6]=>[1,7,4,5,6,8,2,3]=>[2,4,2]
[4,1,3,8,5,7,6,2]=>[1,8,5,7,3,6,2,4]=>[8,1,4,2,6,3,7,5]=>[1,2,2,2,1]
[4,1,3,7,2,8,6,5]=>[1,8,7,3,5,2,4,6]=>[8,1,2,6,4,7,5,3]=>[1,3,2,1,1]
[4,6,3,1,7,2,8,5]=>[1,3,8,6,4,2,5,7]=>[8,6,1,3,5,7,4,2]=>[1,1,4,1,1]
[7,2,6,3,1,8,5,4]=>[8,4,7,2,5,3,1,6]=>[1,5,2,7,4,6,8,3]=>[2,2,3,1]
[4,8,7,2,5,3,1,6]=>[7,1,4,6,5,8,3,2]=>[2,8,5,3,4,1,6,7]=>[2,1,2,3]
[1,6,3,2,8,7,4,5]=>[7,8,3,2,6,1,4,5]=>[2,1,6,7,3,8,5,4]=>[1,3,2,1,1]
[2,8,1,7,5,4,6,3]=>[6,5,8,7,1,3,4,2]=>[3,4,1,2,8,6,5,7]=>[2,3,1,2]
[6,8,3,1,5,7,2,4]=>[3,7,5,1,8,4,6,2]=>[6,2,4,8,1,5,3,7]=>[1,3,2,2]
[8,7,3,1,2,5,6,4]=>[6,3,8,4,5,7,2,1]=>[3,6,1,5,4,2,7,8]=>[2,2,1,3]
[7,4,5,1,2,6,8,3]=>[6,2,8,4,3,5,1,7]=>[3,7,1,5,6,4,8,2]=>[2,3,2,1]
[1,9,8,7,5,4,3,2,6]=>[8,7,6,5,9,4,3,1,2]=>[2,3,4,5,1,6,7,9,8]=>[4,4,1]
[1,9,7,6,5,4,3,2,8]=>[8,7,6,5,4,3,9,1,2]=>[2,3,4,5,6,7,1,9,8]=>[6,2,1]
[1,9,8,7,6,5,2,3,4]=>[7,8,9,6,5,4,3,1,2]=>[3,2,1,4,5,6,7,9,8]=>[1,1,6,1]
[1,8,4,5,6,3,2,7]=>[3,4,7,6,5,8,1,2]=>[6,5,2,3,4,1,8,7]=>[1,1,3,2,1]
[1,10,8,7,6,5,4,3,2,9]=>[9,8,7,6,5,4,3,10,1,2]=>[2,3,4,5,6,7,8,1,10,9]=>[7,2,1]
[4,7,6,1,5,8,2,3]=>[7,1,5,8,4,3,2,6]=>[2,8,4,1,5,6,7,3]=>[2,1,4,1]
[3,4,8,1,6,7,2,5]=>[7,1,2,5,8,4,6,3]=>[2,8,7,4,1,5,3,6]=>[2,1,1,2,2]
[3,6,7,8,4,1,5,2]=>[2,8,6,1,5,3,7,4]=>[7,1,3,8,4,6,2,5]=>[1,3,2,2]
[2,3,7,8,4,6,1,5]=>[5,7,3,8,1,2,6,4]=>[4,2,6,1,8,7,3,5]=>[1,2,2,1,2]
[1,3,7,8,4,6,2,5]=>[5,7,3,8,2,6,1,4]=>[4,2,6,1,7,3,8,5]=>[1,2,2,2,1]
[3,1,7,8,4,6,2,5]=>[5,7,1,3,8,6,2,4]=>[4,2,8,6,1,3,7,5]=>[1,2,1,3,1]
[4,3,8,1,6,7,2,5]=>[1,7,2,5,8,4,6,3]=>[8,2,7,4,1,5,3,6]=>[1,2,1,2,2]
[4,8,7,3,6,1,2,5]=>[6,1,4,7,8,5,3,2]=>[3,8,5,2,1,4,6,7]=>[2,1,1,4]
[5,8,4,3,7,1,2,6]=>[1,6,4,3,7,8,5,2]=>[8,3,5,6,2,1,4,7]=>[1,3,1,3]
[2,4,8,3,6,7,1,5]=>[7,2,4,5,8,1,6,3]=>[2,7,5,4,1,8,3,6]=>[2,1,1,2,2]
[1,6,5,8,7,3,2,4]=>[3,2,7,6,8,5,1,4]=>[6,7,2,3,1,4,8,5]=>[2,2,3,1]
[5,6,4,8,7,2,1,3]=>[1,3,2,7,6,8,5,4]=>[8,6,7,2,3,1,4,5]=>[1,2,2,3]
[7,2,6,8,3,5,1,4]=>[5,7,3,8,2,1,6,4]=>[4,2,6,1,7,8,3,5]=>[1,2,3,2]
[7,2,8,6,5,3,1,4]=>[7,6,8,5,2,1,4,3]=>[2,3,1,4,7,8,5,6]=>[2,4,2]
[4,8,3,7,6,1,2,5]=>[1,3,6,7,8,5,4,2]=>[8,6,3,2,1,4,5,7]=>[1,1,1,1,4]
[2,8,4,7,1,3,6,5]=>[3,8,5,6,7,1,4,2]=>[6,1,4,3,2,8,5,7]=>[1,2,1,2,2]
[6,8,3,4,5,2,1,7]=>[3,4,1,7,6,5,8,2]=>[6,5,8,2,3,4,1,7]=>[1,2,3,2]
[3,7,1,4,5,6,2,8]=>[1,4,5,7,3,6,2,8]=>[8,5,4,2,6,3,7,1]=>[1,1,1,2,2,1]
[3,6,1,4,5,2,7,8]=>[1,4,6,3,5,2,7,8]=>[8,5,3,6,4,7,2,1]=>[1,1,2,2,1,1]
[3,8,2,4,5,1,7,6]=>[1,3,4,5,8,6,7,2]=>[8,6,5,4,1,3,2,7]=>[1,1,1,1,2,2]
[3,7,2,1,5,6,4,8]=>[1,3,5,7,4,6,2,8]=>[8,6,4,2,5,3,7,1]=>[1,1,1,2,2,1]
[3,6,8,1,5,4,7,2]=>[6,5,1,2,8,4,7,3]=>[3,4,8,7,1,5,2,6]=>[3,1,2,2]
[1,7,4,6,3,5,2,8]=>[3,5,7,6,4,1,2,8]=>[6,4,2,3,5,8,7,1]=>[1,1,4,1,1]
[1,3,6,5,7,2,4,8]=>[6,4,2,3,7,1,5,8]=>[3,5,7,6,2,8,4,1]=>[3,1,2,1,1]
[1,7,2,5,6,4,3,8]=>[4,7,6,3,5,1,2,8]=>[5,2,3,6,4,8,7,1]=>[1,3,2,1,1]
[1,6,8,5,4,3,7,2]=>[2,6,5,4,8,7,1,3]=>[7,3,4,5,1,2,8,6]=>[1,3,3,1]
[2,5,7,8,4,3,1,6]=>[7,2,6,5,1,3,8,4]=>[2,7,3,4,8,6,1,5]=>[2,3,1,2]
[6,8,5,3,2,4,1,7]=>[5,4,1,7,6,3,8,2]=>[4,5,8,2,3,6,1,7]=>[3,3,2]
[1,6,8,5,3,2,7,4]=>[5,2,8,6,4,7,1,3]=>[4,7,1,3,5,2,8,6]=>[2,3,2,1]
[1,3,7,6,8,5,2,4]=>[7,4,3,8,2,6,1,5]=>[2,5,6,1,7,3,8,4]=>[3,2,2,1]
[4,1,7,8,6,5,2,3]=>[7,1,3,8,6,5,2,4]=>[2,8,6,1,3,4,7,5]=>[2,1,4,1]
[5,4,3,7,6,1,2,8]=>[3,2,1,6,7,5,4,8]=>[6,7,8,3,2,4,5,1]=>[3,1,3,1]
[4,7,6,1,2,3,8,5]=>[1,8,4,5,6,3,2,7]=>[8,1,5,4,3,6,7,2]=>[1,2,1,3,1]
[4,5,2,6,7,8,1,3]=>[1,4,2,7,3,5,8,6]=>[8,5,7,2,6,4,1,3]=>[1,2,2,1,2]
[2,8,7,6,5,4,3,1,9]=>[8,7,6,5,4,1,3,2,9]=>[2,3,4,5,6,9,7,8,1]=>[6,2,1]
[1,7,6,2,3,8,5,4]=>[8,7,4,5,3,1,2,6]=>[1,2,5,4,6,8,7,3]=>[3,3,1,1]
[4,5,1,3,7,6,2,8]=>[1,7,4,2,6,3,5,8]=>[8,2,5,7,3,6,4,1]=>[1,3,2,1,1]
[1,5,4,3,8,6,2,7]=>[3,2,7,4,6,8,1,5]=>[6,7,2,5,3,1,8,4]=>[2,2,1,2,1]
[1,3,7,5,8,4,6,2]=>[4,6,3,8,2,7,1,5]=>[5,3,6,1,7,2,8,4]=>[1,2,2,2,1]
[7,8,1,5,3,4,6,2]=>[5,6,4,8,3,1,7,2]=>[4,3,5,1,6,8,2,7]=>[1,2,3,2]
[7,3,5,4,1,6,2,8]=>[7,2,5,4,3,6,1,8]=>[2,7,4,5,6,3,8,1]=>[2,3,2,1]
[3,5,7,1,6,4,2,8]=>[2,7,1,6,4,5,3,8]=>[7,2,8,3,5,4,6,1]=>[1,2,2,2,1]
[3,7,5,6,1,4,2,8]=>[7,5,1,3,6,4,2,8]=>[2,4,8,6,3,5,7,1]=>[3,1,3,1]
[1,7,5,6,3,4,8,2]=>[5,3,6,4,2,8,1,7]=>[4,6,3,5,7,1,8,2]=>[2,3,2,1]
[5,1,3,7,8,2,6,4]=>[8,6,3,1,4,7,2,5]=>[1,3,6,8,5,2,7,4]=>[4,1,2,1]
[5,8,1,2,7,6,4,3]=>[1,8,7,6,3,4,5,2]=>[8,1,2,3,6,5,4,7]=>[1,4,1,2]
[1,6,7,4,5,3,2,8]=>[4,2,7,6,5,1,3,8]=>[5,7,2,3,4,8,6,1]=>[2,4,1,1]
[1,4,2,6,7,5,3,8]=>[2,4,7,6,1,3,5,8]=>[7,5,2,3,8,6,4,1]=>[1,1,3,1,1,1]
[1,8,2,4,6,5,3,7]=>[7,4,6,3,5,8,1,2]=>[2,5,3,6,4,1,8,7]=>[2,2,1,2,1]
[7,2,1,6,4,3,8,5]=>[5,8,2,6,3,4,1,7]=>[4,1,7,3,6,5,8,2]=>[1,2,2,2,1]
[1,4,8,7,2,3,6,5]=>[8,2,5,6,7,4,1,3]=>[1,7,4,3,2,5,8,6]=>[2,1,1,3,1]
[4,1,3,6,5,8,2,7]=>[5,3,1,4,7,8,2,6]=>[4,6,8,5,2,1,7,3]=>[3,1,1,2,1]
[4,3,7,1,5,8,2,6]=>[2,1,5,7,8,4,3,6]=>[7,8,4,2,1,5,6,3]=>[2,1,1,3,1]
[1,8,6,5,2,7,4,3]=>[8,7,5,4,3,6,1,2]=>[1,2,4,5,6,3,8,7]=>[5,2,1]
[6,4,1,8,3,7,5,2]=>[2,8,5,1,7,6,3,4]=>[7,1,4,8,2,3,6,5]=>[1,3,3,1]
[4,5,8,7,3,6,2,1]=>[5,8,1,2,7,6,4,3]=>[4,1,8,7,2,3,5,6]=>[1,2,1,4]
[6,8,7,2,1,5,4,3]=>[8,4,1,7,5,6,3,2]=>[1,5,8,2,4,3,6,7]=>[3,2,3]
[8,1,6,3,7,5,4,2]=>[8,7,4,3,6,2,5,1]=>[1,2,5,6,3,7,4,8]=>[4,2,2]
[8,5,1,3,7,6,4,2]=>[8,7,4,2,6,3,5,1]=>[1,2,5,7,3,6,4,8]=>[4,2,2]
[8,3,6,5,4,2,1,7]=>[7,6,2,5,4,3,8,1]=>[2,3,7,4,5,6,1,8]=>[3,3,2]
[6,1,3,5,7,2,8,4]=>[4,8,3,6,2,1,5,7]=>[5,1,6,3,7,8,4,2]=>[1,2,3,1,1]
[2,8,1,5,6,4,3,7]=>[4,7,6,1,3,5,8,2]=>[5,2,3,8,6,4,1,7]=>[1,3,1,1,2]
[1,6,7,5,8,4,2,3]=>[2,7,4,3,8,6,1,5]=>[7,2,5,6,1,3,8,4]=>[1,3,3,1]
[7,4,1,6,5,2,8,3]=>[2,8,6,5,3,4,1,7]=>[7,1,3,4,6,5,8,2]=>[1,4,2,1]
[6,8,4,7,3,2,5,1]=>[3,1,6,5,8,7,4,2]=>[6,8,3,4,1,2,5,7]=>[2,2,4]
[5,8,7,3,2,1,6,4]=>[1,5,4,8,6,7,3,2]=>[8,4,5,1,3,2,6,7]=>[1,2,2,3]
[5,8,7,2,6,4,3,1]=>[8,1,7,4,6,5,3,2]=>[1,8,2,5,3,4,6,7]=>[2,2,4]
[6,8,7,3,5,1,4,2]=>[4,1,8,6,7,5,3,2]=>[5,8,1,3,2,4,6,7]=>[2,2,4]
[7,2,5,6,8,3,4,1]=>[3,6,4,8,2,1,7,5]=>[6,3,5,1,7,8,2,4]=>[1,2,3,2]
[5,4,8,6,7,3,1,2]=>[1,7,2,4,8,6,5,3]=>[8,2,7,5,1,3,4,6]=>[1,2,1,4]
[4,2,7,3,1,6,8,5]=>[4,1,6,8,2,5,3,7]=>[5,8,3,1,7,4,6,2]=>[2,1,2,2,1]
[7,3,6,4,2,1,8,5]=>[5,2,4,8,6,3,1,7]=>[4,7,5,1,3,6,8,2]=>[2,1,4,1]
[4,8,5,2,7,3,1,6]=>[7,1,4,3,6,8,5,2]=>[2,8,5,6,3,1,4,7]=>[2,2,1,3]
[6,4,3,1,8,5,2,7]=>[3,2,7,6,1,8,4,5]=>[6,7,2,3,8,1,5,4]=>[2,3,2,1]
[7,4,8,6,5,3,1,2]=>[7,8,2,1,6,5,4,3]=>[2,1,7,8,3,4,5,6]=>[1,3,4]
[7,3,2,1,8,5,6,4]=>[2,6,8,3,7,4,1,5]=>[7,3,1,6,2,5,8,4]=>[1,1,2,3,1]
[9,1,2,3,4,5,7,6,8]=>[8,2,3,4,5,6,7,9,1]=>[2,8,7,6,5,4,3,1,9]=>[2,1,1,1,1,1,2]
[2,1,3,4,5,9,6,7,8]=>[1,7,8,9,2,3,4,5,6]=>[9,3,2,1,8,7,6,5,4]=>[1,1,1,2,1,1,1,1]
[1,5,7,2,4,3,8,6]=>[5,2,8,4,6,1,3,7]=>[4,7,1,5,3,8,6,2]=>[2,2,2,1,1]
[1,2,7,5,8,4,3,6]=>[4,7,6,3,8,1,2,5]=>[5,2,3,6,1,8,7,4]=>[1,3,2,1,1]
[5,1,3,8,2,7,4,6]=>[7,8,3,1,5,6,2,4]=>[2,1,6,8,4,3,7,5]=>[1,3,1,2,1]
[5,7,1,3,2,8,4,6]=>[4,7,1,8,3,5,2,6]=>[5,2,8,1,6,4,7,3]=>[1,2,2,2,1]
[7,1,6,3,2,8,4,5]=>[4,7,8,5,2,3,1,6]=>[5,2,1,4,7,6,8,3]=>[1,1,3,2,1]
[8,1,7,2,3,6,5,4]=>[8,7,4,5,6,2,3,1]=>[1,2,5,4,3,7,6,8]=>[3,1,2,2]
[7,1,2,6,4,3,8,5]=>[5,8,6,2,3,4,1,7]=>[4,1,3,7,6,5,8,2]=>[1,3,1,2,1]
[8,7,1,3,2,4,6,5]=>[4,8,3,5,6,7,2,1]=>[5,1,6,4,3,2,7,8]=>[1,2,1,1,3]
[1,8,2,7,6,3,5,4]=>[8,6,7,5,3,4,1,2]=>[1,3,2,4,6,5,8,7]=>[2,3,2,1]
[8,1,6,3,2,7,4,5]=>[4,7,8,5,2,3,6,1]=>[5,2,1,4,7,6,3,8]=>[1,1,3,1,2]
[8,2,1,7,6,3,4,5]=>[6,7,8,2,5,3,4,1]=>[3,2,1,7,4,6,5,8]=>[1,1,2,2,2]
[6,8,4,3,5,1,2,7]=>[6,4,3,1,7,5,8,2]=>[3,5,6,8,2,4,1,7]=>[4,2,2]
[8,7,3,5,4,1,2,6]=>[3,6,7,5,4,8,2,1]=>[6,3,2,4,5,1,7,8]=>[1,1,3,3]
[6,3,8,5,7,2,1,4]=>[7,6,2,1,4,8,5,3]=>[2,3,7,8,5,1,4,6]=>[4,1,3]
[8,7,3,6,4,1,2,5]=>[3,6,7,5,8,4,2,1]=>[6,3,2,4,1,5,7,8]=>[1,1,2,4]
[5,2,7,4,6,1,3,8]=>[6,4,1,7,2,5,3,8]=>[3,5,8,2,7,4,6,1]=>[3,2,2,1]
[8,7,2,3,5,1,4,6]=>[3,4,6,7,5,8,2,1]=>[6,5,3,2,4,1,7,8]=>[1,1,1,2,3]
[7,6,3,4,1,8,2,5]=>[3,7,4,8,5,2,1,6]=>[6,2,5,1,4,7,8,3]=>[1,2,4,1]
[6,3,5,2,8,1,4,7]=>[2,4,6,3,1,7,8,5]=>[7,5,3,6,8,2,1,4]=>[1,1,3,1,2]
[6,4,5,3,1,7,2,8]=>[2,7,5,4,3,1,6,8]=>[7,2,4,5,6,8,3,1]=>[1,5,1,1]
[8,7,2,4,3,1,5,6]=>[6,3,5,4,7,8,2,1]=>[3,6,4,5,2,1,7,8]=>[2,2,1,3]
[4,7,6,2,3,1,5,8]=>[1,4,6,5,7,3,2,8]=>[8,5,3,4,2,6,7,1]=>[1,1,2,3,1]
[4,7,6,1,3,2,8,5]=>[1,5,8,4,6,3,2,7]=>[8,4,1,5,3,6,7,2]=>[1,1,2,3,1]
[2,8,1,3,5,6,4,7]=>[5,7,1,3,4,6,8,2]=>[4,2,8,6,5,3,1,7]=>[1,2,1,1,1,2]
[2,6,3,4,7,8,5,1]=>[5,8,3,1,2,4,7,6]=>[4,1,6,8,7,5,2,3]=>[1,3,1,1,2]
[7,6,3,1,8,5,2,4]=>[3,7,8,6,4,2,1,5]=>[6,2,1,3,5,7,8,4]=>[1,1,5,1]
[7,2,1,3,6,8,5,4]=>[5,8,2,7,3,4,1,6]=>[4,1,7,2,6,5,8,3]=>[1,2,2,2,1]
[7,6,3,8,1,5,2,4]=>[3,7,8,5,2,1,6,4]=>[6,2,1,4,7,8,3,5]=>[1,1,4,2]
[1,6,4,7,8,5,3,2]=>[4,2,8,3,7,6,1,5]=>[5,7,1,6,2,3,8,4]=>[2,2,3,1]
[7,2,5,8,6,1,3,4]=>[6,3,7,8,2,1,5,4]=>[3,6,2,1,7,8,4,5]=>[2,1,3,2]
[4,1,3,6,2,5,8,7]=>[8,3,1,5,2,4,6,7]=>[1,6,8,4,7,5,3,2]=>[3,2,1,1,1]
[7,1,4,6,3,2,5,8]=>[3,6,5,7,2,4,1,8]=>[6,3,4,2,7,5,8,1]=>[1,2,2,2,1]
[6,7,2,3,8,4,1,5]=>[7,3,4,1,6,2,8,5]=>[2,6,5,8,3,7,1,4]=>[2,2,2,2]
[2,7,8,1,5,4,3,6]=>[7,6,4,5,1,2,8,3]=>[2,3,5,4,8,7,1,6]=>[3,2,1,2]
[1,5,2,6,8,7,4,3]=>[2,8,4,7,6,1,3,5]=>[7,1,5,2,3,8,6,4]=>[1,2,3,1,1]
[1,8,3,7,5,2,6,4]=>[8,6,3,5,7,4,1,2]=>[1,3,6,4,2,5,8,7]=>[3,1,3,1]
[8,1,3,6,5,2,7,4]=>[8,6,3,5,2,4,7,1]=>[1,3,6,4,7,5,2,8]=>[3,2,1,2]
[4,7,1,5,2,6,8,3]=>[1,6,4,8,3,5,2,7]=>[8,3,5,1,6,4,7,2]=>[1,2,2,2,1]
[7,4,1,5,2,6,8,3]=>[6,4,2,8,3,5,1,7]=>[3,5,7,1,6,4,8,2]=>[3,2,2,1]
[3,1,6,7,5,2,8,4]=>[3,8,1,6,5,2,4,7]=>[6,1,8,3,4,7,5,2]=>[1,2,3,1,1]
[7,1,4,5,2,6,8,3]=>[3,6,4,8,2,5,1,7]=>[6,3,5,1,7,4,8,2]=>[1,2,2,2,1]
[4,1,6,2,3,8,7,5]=>[1,8,7,4,2,3,5,6]=>[8,1,2,5,7,6,4,3]=>[1,4,1,1,1]
[4,1,7,6,5,2,8,3]=>[8,1,6,5,4,2,3,7]=>[1,8,3,4,5,7,6,2]=>[2,4,1,1]
[8,4,5,3,6,1,7,2]=>[2,4,3,8,6,5,7,1]=>[7,5,6,1,3,4,2,8]=>[1,2,3,2]
[2,8,4,7,3,5,6,1]=>[3,5,6,8,7,1,4,2]=>[6,4,3,1,2,8,5,7]=>[1,1,1,3,2]
[1,5,4,8,3,2,6,7]=>[3,2,6,5,7,8,1,4]=>[6,7,3,4,2,1,8,5]=>[2,2,1,2,1]
[2,6,3,1,7,8,4,5]=>[7,3,5,1,2,8,4,6]=>[2,6,4,8,7,1,5,3]=>[2,2,1,2,1]
[2,1,7,8,3,5,4,6]=>[7,5,6,1,3,8,2,4]=>[2,4,3,8,6,1,7,5]=>[2,2,1,2,1]
[1,5,8,6,7,4,2,3]=>[7,2,4,8,6,5,1,3]=>[2,7,5,1,3,4,8,6]=>[2,1,4,1]
[8,7,1,3,5,2,6,4]=>[8,4,6,3,5,7,2,1]=>[1,5,3,6,4,2,7,8]=>[2,2,1,3]
[3,7,8,2,5,4,1,6]=>[7,4,6,1,5,2,8,3]=>[2,5,3,8,4,7,1,6]=>[2,2,2,2]
[4,7,6,5,8,1,3,2]=>[8,6,1,4,3,2,7,5]=>[1,3,8,5,6,7,2,4]=>[3,3,2]
[4,7,8,6,2,1,5,3]=>[5,8,1,6,2,7,4,3]=>[4,1,8,3,7,2,5,6]=>[1,2,2,3]
[4,8,6,3,2,1,7,5]=>[5,1,4,8,6,3,7,2]=>[4,8,5,1,3,6,2,7]=>[2,1,3,2]
[5,1,4,7,6,8,3,2]=>[5,3,1,4,8,7,2,6]=>[4,6,8,5,1,2,7,3]=>[3,1,3,1]
[5,3,7,4,6,1,8,2]=>[4,1,8,2,6,5,3,7]=>[5,8,1,7,3,4,6,2]=>[2,2,3,1]
[3,6,7,1,5,4,8,2]=>[6,5,1,2,8,4,3,7]=>[3,4,8,7,1,5,6,2]=>[3,1,3,1]
[3,6,4,7,5,8,2,1]=>[5,3,1,2,4,8,7,6]=>[4,6,8,7,5,1,2,3]=>[3,1,1,3]
[8,1,7,3,2,4,5,6]=>[5,4,6,7,8,2,3,1]=>[4,5,3,2,1,7,6,8]=>[2,1,1,2,2]
[6,4,7,1,5,2,8,3]=>[2,8,6,4,1,5,3,7]=>[7,1,3,5,8,4,6,2]=>[1,4,2,1]
[4,8,1,3,5,2,7,6]=>[4,1,5,8,3,6,7,2]=>[5,8,4,1,6,3,2,7]=>[2,1,2,1,2]
[1,6,5,2,8,7,4,3]=>[3,2,8,7,6,1,4,5]=>[6,7,1,2,3,8,5,4]=>[2,4,1,1]
[1,3,4,5,2,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>[8,7,5,9,6,4,3,2,1]=>[1,1,2,1,1,1,1,1]
[2,3,4,5,7,9,1,6,8]=>[7,1,2,3,4,5,8,9,6]=>[3,9,8,7,6,5,2,1,4]=>[2,1,1,1,1,1,2]
[2,3,4,5,1,6,7,9,8]=>[1,2,3,4,9,5,6,7,8]=>[9,8,7,6,1,5,4,3,2]=>[1,1,1,1,2,1,1,1]
[4,1,7,2,5,8,3,6]=>[5,1,7,8,4,2,3,6]=>[4,8,2,1,5,7,6,3]=>[2,1,3,1,1]
[3,2,5,8,6,1,7,4]=>[8,1,3,6,2,5,7,4]=>[1,8,6,3,7,4,2,5]=>[2,1,2,1,2]
[4,5,1,7,2,8,6,3]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[1,1,4,1,1]
[2,8,5,3,6,7,4,1]=>[5,3,8,4,7,1,6,2]=>[4,6,1,5,2,8,3,7]=>[2,2,2,2]
[8,3,5,2,6,7,4,1]=>[5,2,3,8,4,7,6,1]=>[4,7,6,1,5,2,3,8]=>[2,1,2,3]
[2,8,6,3,4,7,5,1]=>[8,4,5,3,7,1,6,2]=>[1,5,4,6,2,8,3,7]=>[2,2,2,2]
[4,7,1,8,5,3,6,2]=>[6,1,5,8,7,3,2,4]=>[3,8,4,1,2,6,7,5]=>[2,1,4,1]
[6,4,7,2,5,3,1,8]=>[2,7,4,1,6,5,3,8]=>[7,2,5,8,3,4,6,1]=>[1,3,3,1]
[7,1,4,3,6,8,2,5]=>[3,7,4,5,8,2,1,6]=>[6,2,5,4,1,7,8,3]=>[1,2,1,3,1]
[6,3,1,5,4,8,7,2]=>[2,4,8,5,1,7,3,6]=>[7,5,1,4,8,2,6,3]=>[1,1,3,2,1]
[7,1,3,8,5,4,2,6]=>[7,6,3,5,8,2,1,4]=>[2,3,6,4,1,7,8,5]=>[3,1,3,1]
[4,8,7,3,5,1,6,2]=>[4,8,1,6,5,7,3,2]=>[5,1,8,3,4,2,6,7]=>[1,2,2,3]
[5,3,8,7,1,6,2,4]=>[7,1,8,2,5,6,4,3]=>[2,8,1,7,4,3,5,6]=>[2,2,1,3]
[3,4,1,6,2,8,7,5]=>[1,2,4,8,7,3,5,6]=>[8,7,5,1,2,6,4,3]=>[1,1,1,3,1,1]
[5,2,6,7,4,3,1,8]=>[3,1,7,6,2,5,4,8]=>[6,8,2,3,7,4,5,1]=>[2,3,2,1]
[8,5,1,6,4,3,2,7]=>[7,6,5,3,2,4,8,1]=>[2,3,4,6,7,5,1,8]=>[5,1,2]
[8,4,6,2,1,5,7,3]=>[4,2,6,8,5,3,7,1]=>[5,7,3,1,4,6,2,8]=>[2,1,3,2]
[8,5,2,1,6,4,7,3]=>[6,3,5,2,8,4,7,1]=>[3,6,4,7,1,5,2,8]=>[2,2,2,2]
[1,7,2,8,5,4,6,3]=>[6,5,8,7,3,1,2,4]=>[3,4,1,2,6,8,7,5]=>[2,4,1,1]
[6,7,1,4,8,5,3,2]=>[8,4,1,7,6,3,2,5]=>[1,5,8,2,3,6,7,4]=>[3,4,1]
[7,3,2,8,5,1,4,6]=>[2,6,7,3,5,1,8,4]=>[7,3,2,6,4,8,1,5]=>[1,1,2,2,2]
[4,1,7,3,2,8,5,6]=>[4,1,7,8,5,2,3,6]=>[5,8,2,1,4,7,6,3]=>[2,1,3,1,1]
[8,3,5,2,4,7,1,6]=>[2,4,5,3,7,8,6,1]=>[7,5,4,6,2,1,3,8]=>[1,1,2,1,3]
[4,3,7,8,6,1,5,2]=>[8,1,6,2,3,7,5,4]=>[1,8,3,7,6,2,4,5]=>[2,2,1,3]
[1,2,6,3,7,8,5,4]=>[5,3,8,7,1,2,4,6]=>[4,6,1,2,8,7,5,3]=>[2,3,1,1,1]
[6,1,3,7,8,5,4,2]=>[4,8,7,3,1,6,2,5]=>[5,1,2,6,8,3,7,4]=>[1,4,2,1]
[2,6,4,7,5,3,1,8]=>[7,3,2,6,1,5,4,8]=>[2,6,7,3,8,4,5,1]=>[3,2,2,1]
[5,6,3,7,2,8,4,1]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[1,3,2,2]
[4,5,1,8,6,2,7,3]=>[1,2,8,6,5,7,3,4]=>[8,7,1,3,4,2,6,5]=>[1,1,3,2,1]
[4,5,1,6,8,7,3,2]=>[1,2,8,4,7,6,3,5]=>[8,7,1,5,2,3,6,4]=>[1,1,2,3,1]
[3,9,2,4,5,6,7,8,1]=>[1,3,4,5,6,7,9,8,2]=>[9,7,6,5,4,3,1,2,8]=>[1,1,1,1,1,1,3]
[3,8,6,1,5,2,4,7]=>[6,7,1,4,5,3,8,2]=>[3,2,8,5,4,6,1,7]=>[1,2,1,2,2]
[3,2,8,1,5,6,4,7]=>[1,5,7,2,4,6,8,3]=>[8,4,2,7,5,3,1,6]=>[1,1,2,1,1,2]
[5,8,7,3,2,1,4,6]=>[1,6,5,4,7,8,3,2]=>[8,3,4,5,2,1,6,7]=>[1,3,1,3]
[3,4,7,6,8,2,1,5]=>[7,6,1,2,4,3,8,5]=>[2,3,8,7,5,6,1,4]=>[3,1,2,2]
[2,8,1,3,7,5,6,4]=>[6,8,7,1,3,4,5,2]=>[3,1,2,8,6,5,4,7]=>[1,3,1,1,2]
[7,6,1,2,5,8,4,3]=>[5,8,7,3,4,2,1,6]=>[4,1,2,6,5,7,8,3]=>[1,3,3,1]
[3,4,7,1,5,8,2,6]=>[1,2,5,7,8,4,3,6]=>[8,7,4,2,1,5,6,3]=>[1,1,1,1,3,1]
[4,2,7,1,5,8,3,6]=>[5,1,7,8,2,4,3,6]=>[4,8,2,1,7,5,6,3]=>[2,1,2,2,1]
[4,1,2,3,5,6,8,7,9]=>[8,2,3,1,4,5,6,7,9]=>[2,8,7,9,6,5,4,3,1]=>[2,2,1,1,1,1,1]
[2,4,6,3,5,1,7,8]=>[2,4,6,1,5,3,7,8]=>[7,5,3,8,4,6,2,1]=>[1,1,2,2,1,1]
[4,1,6,2,5,8,3,7]=>[5,1,7,3,8,2,4,6]=>[4,8,2,6,1,7,5,3]=>[2,2,2,1,1]
[1,4,6,3,8,5,2,7]=>[7,2,4,3,6,8,1,5]=>[2,7,5,6,3,1,8,4]=>[2,2,1,2,1]
[4,5,6,3,1,7,2,8]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[1,1,4,1,1]
[3,4,6,2,5,1,7,8]=>[1,2,4,6,5,3,7,8]=>[8,7,5,3,4,6,2,1]=>[1,1,1,3,1,1]
[1,4,7,5,2,3,6,8]=>[2,5,6,4,7,1,3,8]=>[7,4,3,5,2,8,6,1]=>[1,1,2,2,1,1]
[1,4,6,5,8,2,3,7]=>[6,2,4,3,7,8,1,5]=>[3,7,5,6,2,1,8,4]=>[2,2,1,2,1]
[1,4,5,3,7,2,6,8]=>[2,4,3,6,7,1,5,8]=>[7,5,6,3,2,8,4,1]=>[1,2,1,2,1,1]
[1,5,3,6,8,4,7,2]=>[4,2,6,8,3,7,1,5]=>[5,7,3,1,6,2,8,4]=>[2,1,2,2,1]
[6,5,1,3,8,4,7,2]=>[6,8,4,2,1,7,3,5]=>[3,1,5,7,8,2,6,4]=>[1,4,2,1]
[7,3,1,6,8,4,5,2]=>[6,2,4,8,7,3,1,5]=>[3,7,5,1,2,6,8,4]=>[2,1,4,1]
[7,4,2,3,6,5,1,8]=>[7,3,2,4,6,5,1,8]=>[2,6,7,5,3,4,8,1]=>[3,1,3,1]
[7,2,4,3,1,5,6,8]=>[5,2,4,3,6,7,1,8]=>[4,7,5,6,3,2,8,1]=>[2,2,1,2,1]
[6,3,1,4,8,5,7,2]=>[2,6,8,4,1,7,3,5]=>[7,3,1,5,8,2,6,4]=>[1,1,3,2,1]
[6,3,5,4,8,7,1,2]=>[4,2,3,1,7,8,6,5]=>[5,7,6,8,2,1,3,4]=>[2,2,1,3]
[2,6,4,3,1,7,5,8]=>[4,3,7,1,5,2,6,8]=>[5,6,2,8,4,7,3,1]=>[2,2,2,1,1]
[4,8,1,7,5,6,3,2]=>[5,8,1,7,6,3,4,2]=>[4,1,8,2,3,6,5,7]=>[1,2,3,2]
[1,5,7,2,8,4,6,3]=>[2,6,8,7,4,1,3,5]=>[7,3,1,2,5,8,6,4]=>[1,1,4,1,1]
[5,8,7,2,3,6,4,1]=>[1,8,4,5,7,6,3,2]=>[8,1,5,4,2,3,6,7]=>[1,2,1,4]
[4,6,5,1,2,3,7,8]=>[4,1,5,6,3,2,7,8]=>[5,8,4,3,6,7,2,1]=>[2,1,3,1,1]
[1,8,7,5,2,6,3,4]=>[7,8,5,4,6,3,1,2]=>[2,1,4,5,3,6,8,7]=>[1,3,3,1]
[1,7,6,3,4,5,8,2]=>[4,5,6,3,2,8,1,7]=>[5,4,3,6,7,1,8,2]=>[1,1,3,2,1]
[1,8,7,4,5,6,2,3]=>[4,7,5,8,6,3,1,2]=>[5,2,4,1,3,6,8,7]=>[1,2,4,1]
[1,8,7,3,6,4,2,5]=>[7,4,6,8,5,3,1,2]=>[2,5,3,1,4,6,8,7]=>[2,1,4,1]
[1,4,7,5,8,2,6,3]=>[4,8,2,6,3,7,1,5]=>[5,1,7,3,6,2,8,4]=>[1,2,2,2,1]
[1,4,7,2,3,6,5,8]=>[2,7,4,5,6,1,3,8]=>[7,2,5,4,3,8,6,1]=>[1,2,1,2,1,1]
[1,7,2,5,6,3,4,8]=>[6,4,7,3,5,1,2,8]=>[3,5,2,6,4,8,7,1]=>[2,2,2,1,1]
[1,2,6,5,8,3,4,7]=>[6,4,3,7,8,1,2,5]=>[3,5,6,2,1,8,7,4]=>[3,1,2,1,1]
[1,5,8,2,6,3,4,7]=>[6,2,7,4,5,8,1,3]=>[3,7,2,5,4,1,8,6]=>[2,2,1,2,1]
[7,3,6,8,1,2,5,4]=>[8,2,5,6,3,1,7,4]=>[1,7,4,3,6,8,2,5]=>[2,1,3,2]
[4,1,5,7,2,6,3,8]=>[3,1,7,5,6,2,4,8]=>[6,8,2,4,3,7,5,1]=>[2,2,2,1,1]
[5,7,2,1,3,6,4,8]=>[3,7,4,1,5,6,2,8]=>[6,2,5,8,4,3,7,1]=>[1,3,1,2,1]
[3,5,6,7,2,4,1,8]=>[2,5,1,3,7,6,4,8]=>[7,4,8,6,2,3,5,1]=>[1,2,1,3,1]
[1,5,6,4,8,3,2,7]=>[2,4,3,7,6,8,1,5]=>[7,5,6,2,3,1,8,4]=>[1,2,2,2,1]
[2,1,5,6,4,8,3,7]=>[3,5,1,4,7,8,2,6]=>[6,4,8,5,2,1,7,3]=>[1,2,1,1,2,1]
[5,1,4,7,8,6,2,3]=>[7,3,1,4,8,6,2,5]=>[2,6,8,5,1,3,7,4]=>[3,1,3,1]
[1,6,7,2,8,5,4,3]=>[2,8,7,6,4,1,3,5]=>[7,1,2,3,5,8,6,4]=>[1,5,1,1]
[5,3,2,1,7,8,6,4]=>[2,5,1,8,3,7,4,6]=>[7,4,8,1,6,2,5,3]=>[1,2,2,2,1]
[7,4,3,8,6,1,5,2]=>[2,8,3,6,1,7,5,4]=>[7,1,6,3,8,2,4,5]=>[1,2,2,3]
[4,3,7,1,5,8,6,2]=>[1,8,2,5,7,4,3,6]=>[8,1,7,4,2,5,6,3]=>[1,2,1,3,1]
[1,4,3,2,7,5,8,6]=>[2,8,3,6,1,4,5,7]=>[7,1,6,3,8,5,4,2]=>[1,2,2,1,1,1]
[4,8,7,2,6,1,3,5]=>[1,4,6,7,8,5,3,2]=>[8,5,3,2,1,4,6,7]=>[1,1,1,1,4]
[4,5,8,2,1,7,3,6]=>[1,4,2,7,8,5,6,3]=>[8,5,7,2,1,4,3,6]=>[1,2,1,2,2]
[6,8,4,1,7,3,2,5]=>[7,6,3,1,8,4,5,2]=>[2,3,6,8,1,5,4,7]=>[4,2,2]
[6,7,9,8,5,4,3,2,1]=>[9,1,2,8,7,6,5,4,3]=>[1,9,8,2,3,4,5,6,7]=>[2,1,6]
[9,11,10,8,7,6,5,4,3,2,1]=>[11,1,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[2,9]
[7,8,10,9,6,5,4,3,2,1]=>[10,1,2,9,8,7,6,5,4,3]=>[1,10,9,2,3,4,5,6,7,8]=>[2,1,7]
[6,7,5,9,8,4,3,2,1]=>[1,2,9,3,8,7,6,5,4]=>[9,8,1,7,2,3,4,5,6]=>[1,1,2,5]
[5,7,9,8,6,4,3,2,1]=>[9,2,8,1,7,6,5,4,3]=>[1,8,2,9,3,4,5,6,7]=>[2,2,5]
[6,3,1,8,2,7,5,4]=>[8,2,7,5,1,6,3,4]=>[1,7,2,4,8,3,6,5]=>[2,3,2,1]
[6,4,1,3,2,5,7,8]=>[5,3,4,2,6,1,7,8]=>[4,6,5,7,3,8,2,1]=>[2,2,2,1,1]
[4,1,7,8,3,2,5,6]=>[1,6,5,7,3,8,2,4]=>[8,3,4,2,6,1,7,5]=>[1,2,2,2,1]
[5,8,2,1,3,6,4,7]=>[3,7,4,1,5,6,8,2]=>[6,2,5,8,4,3,1,7]=>[1,3,1,1,2]
[5,7,6,3,4,1,8,2]=>[1,4,8,6,5,3,2,7]=>[8,5,1,3,4,6,7,2]=>[1,1,5,1]
[1,8,3,5,2,6,4,7]=>[7,3,5,4,6,8,1,2]=>[2,6,4,5,3,1,8,7]=>[2,2,1,2,1]
[3,4,6,1,8,5,7,2]=>[6,1,2,3,8,7,4,5]=>[3,8,7,6,1,2,5,4]=>[2,1,1,3,1]
[2,3,8,7,4,5,1,6]=>[5,7,6,8,1,2,4,3]=>[4,2,3,1,8,7,5,6]=>[1,2,2,1,2]
[1,8,3,5,7,4,2,6]=>[4,7,3,6,8,5,1,2]=>[5,2,6,3,1,4,8,7]=>[1,2,1,3,1]
[2,5,8,4,6,7,1,3]=>[2,4,7,5,8,1,6,3]=>[7,5,2,4,1,8,3,6]=>[1,1,2,2,2]
[9,8,6,1,2,3,4,5,7]=>[4,5,6,7,8,3,9,2,1]=>[6,5,4,3,2,7,1,8,9]=>[1,1,1,1,2,3]
[9,8,7,5,1,2,3,4,6]=>[5,6,7,8,4,9,3,2,1]=>[5,4,3,2,6,1,7,8,9]=>[1,1,1,2,4]
[9,8,7,6,4,1,2,3,5]=>[6,7,8,5,9,4,3,2,1]=>[4,3,2,5,1,6,7,8,9]=>[1,1,2,5]
[9,8,7,6,5,3,1,2,4]=>[7,8,6,9,5,4,3,2,1]=>[3,2,4,1,5,6,7,8,9]=>[1,2,6]
[4,7,8,6,2,3,5,1]=>[5,6,1,2,8,7,4,3]=>[4,3,8,7,1,2,5,6]=>[1,2,1,4]
[7,1,2,4,8,6,5,3]=>[8,7,4,6,2,3,1,5]=>[1,2,5,3,7,6,8,4]=>[3,2,2,1]
[2,8,3,6,5,7,1,4]=>[7,5,3,4,8,1,6,2]=>[2,4,6,5,1,8,3,7]=>[3,1,2,2]
[9,2,8,7,6,5,4,3,1]=>[9,8,7,6,5,2,4,3,1]=>[1,2,3,4,5,8,6,7,9]=>[6,3]
[10,9,4,8,7,6,5,3,2,1]=>[10,9,8,3,7,6,5,4,2,1]=>[1,2,3,8,4,5,6,7,9,10]=>[4,6]
[10,2,9,8,7,6,5,4,3,1]=>[10,9,8,7,6,5,2,4,3,1]=>[1,2,3,4,5,6,9,7,8,10]=>[7,3]
[5,4,1,2,3,7,8,6]=>[6,8,3,2,1,4,5,7]=>[3,1,6,7,8,5,4,2]=>[1,4,1,1,1]
[1,6,7,2,5,8,3,4]=>[7,5,2,8,4,1,3,6]=>[2,4,7,1,5,8,6,3]=>[3,3,1,1]
[7,8,5,6,2,4,3,1]=>[8,5,3,1,7,6,4,2]=>[1,4,6,8,2,3,5,7]=>[4,4]
[5,3,8,6,2,4,1,7]=>[5,1,7,2,6,4,8,3]=>[4,8,2,7,3,5,1,6]=>[2,2,2,2]
[2,7,4,6,3,8,1,5]=>[3,5,7,4,1,2,8,6]=>[6,4,2,5,8,7,1,3]=>[1,1,3,1,2]
[5,4,7,8,6,2,1,3]=>[1,7,2,6,3,8,5,4]=>[8,2,7,3,6,1,4,5]=>[1,2,2,3]
[2,7,4,8,3,1,5,6]=>[3,6,5,7,1,2,8,4]=>[6,3,4,2,8,7,1,5]=>[1,2,2,1,2]
[6,5,8,2,3,4,7,1]=>[4,5,2,1,6,8,7,3]=>[5,4,7,8,3,1,2,6]=>[1,3,1,3]
[7,8,2,3,6,4,5,1]=>[6,8,3,4,1,7,5,2]=>[3,1,6,5,8,2,4,7]=>[1,2,2,3]
[8,1,2,7,5,3,4,6]=>[6,7,5,8,2,3,4,1]=>[3,2,4,1,7,6,5,8]=>[1,2,2,1,2]
[4,2,8,1,3,7,5,6]=>[7,1,8,2,4,5,6,3]=>[2,8,1,7,5,4,3,6]=>[2,2,1,1,2]
[7,5,1,8,2,3,4,6]=>[5,6,7,2,8,3,1,4]=>[4,3,2,7,1,6,8,5]=>[1,1,2,3,1]
[8,2,4,1,3,7,5,6]=>[7,2,3,8,4,5,6,1]=>[2,7,6,1,5,4,3,8]=>[2,1,2,1,2]
[8,1,6,2,3,7,4,5]=>[7,8,4,5,2,3,6,1]=>[2,1,5,4,7,6,3,8]=>[1,2,2,1,2]
[7,1,8,2,3,6,4,5]=>[7,8,4,5,6,2,1,3]=>[2,1,5,4,3,7,8,6]=>[1,2,1,3,1]
[4,7,2,5,3,8,1,6]=>[1,5,3,4,7,2,8,6]=>[8,4,6,5,2,7,1,3]=>[1,2,1,2,2]
[3,5,7,4,2,8,1,6]=>[2,5,1,4,7,3,8,6]=>[7,4,8,5,2,6,1,3]=>[1,2,1,2,2]
[2,4,7,6,3,8,1,5]=>[5,7,2,4,1,3,8,6]=>[4,2,7,5,8,6,1,3]=>[1,2,2,1,2]
[4,6,5,7,1,2,3,8]=>[1,5,6,3,2,7,4,8]=>[8,4,3,6,7,2,5,1]=>[1,1,3,2,1]
[4,6,5,7,1,3,8,2]=>[6,1,3,2,8,5,4,7]=>[3,8,6,7,1,4,5,2]=>[2,2,3,1]
[3,4,7,6,1,8,2,5]=>[7,8,1,2,5,4,3,6]=>[2,1,8,7,4,5,6,3]=>[1,2,1,3,1]
[8,5,2,1,6,3,4,7]=>[3,6,7,4,2,5,8,1]=>[6,3,2,5,7,4,1,8]=>[1,1,3,1,2]
[7,1,8,5,3,2,4,6]=>[6,5,7,4,8,2,1,3]=>[3,4,2,5,1,7,8,6]=>[2,2,3,1]
[9,1,10,7,5,3,2,4,6,8]=>[7,6,8,5,9,4,10,2,1,3]=>[4,5,3,6,2,7,1,9,10,8]=>[2,2,2,3,1]
[8,1,9,2,10,6,4,3,5,7]=>[8,7,9,6,10,4,2,1,3,5]=>[3,4,2,5,1,7,9,10,8,6]=>[2,2,4,1,1]
[10,5,1,6,2,7,3,8,4,9]=>[9,7,5,3,2,4,6,8,10,1]=>[2,4,6,8,9,7,5,3,1,10]=>[5,1,1,1,2]
[12,6,1,7,2,8,3,9,4,10,5,11]=>[11,9,7,5,3,2,4,6,8,10,12,1]=>[2,4,6,8,10,11,9,7,5,3,1,12]=>[6,1,1,1,1,2]
[8,6,1,3,2,7,5,4]=>[8,4,7,3,5,2,6,1]=>[1,5,2,6,4,7,3,8]=>[2,2,2,2]
[8,1,7,5,2,4,6,3]=>[6,8,5,4,7,2,3,1]=>[3,1,4,5,2,7,6,8]=>[1,3,2,2]
[8,6,1,2,7,3,5,4]=>[8,6,7,3,4,2,5,1]=>[1,3,2,6,5,7,4,8]=>[2,2,2,2]
[4,2,8,5,7,1,6,3]=>[1,4,8,6,7,2,5,3]=>[8,5,1,3,2,7,4,6]=>[1,1,2,2,2]
[6,8,7,4,5,3,2,1]=>[1,4,8,7,6,5,3,2]=>[8,5,1,2,3,4,6,7]=>[1,1,6]
[5,2,6,7,4,8,3,1]=>[3,1,5,4,8,2,7,6]=>[6,8,4,5,1,7,2,3]=>[2,2,2,2]
[6,5,8,1,7,3,2,4]=>[7,6,2,1,8,4,5,3]=>[2,3,7,8,1,5,4,6]=>[4,2,2]
[7,2,4,1,6,3,5,8]=>[6,2,3,7,4,5,1,8]=>[3,7,6,2,5,4,8,1]=>[2,1,2,2,1]
[2,6,1,5,3,4,8,7]=>[8,5,1,3,4,2,6,7]=>[1,4,8,6,5,7,3,2]=>[3,1,2,1,1]
[3,8,7,5,4,2,6,1]=>[6,5,4,8,1,7,3,2]=>[3,4,5,1,8,2,6,7]=>[3,2,3]
[5,7,8,2,3,6,4,1]=>[1,8,4,5,2,7,6,3]=>[8,1,5,4,7,2,3,6]=>[1,2,2,3]
[2,8,7,3,1,4,5,6]=>[5,4,6,7,8,1,3,2]=>[4,5,3,2,1,8,6,7]=>[2,1,1,2,2]
[5,6,1,2,4,7,8,3]=>[5,6,1,8,3,2,4,7]=>[4,3,8,1,6,7,5,2]=>[1,2,3,1,1]
[3,8,6,7,5,4,2,1]=>[3,8,7,6,1,5,4,2]=>[6,1,2,3,8,4,5,7]=>[1,4,3]
[7,8,5,1,4,6,2,3]=>[7,5,8,4,3,1,6,2]=>[2,4,1,5,6,8,3,7]=>[2,4,2]
[8,2,7,5,4,6,1,3]=>[7,5,4,8,2,6,3,1]=>[2,4,5,1,7,3,6,8]=>[3,2,3]
[8,4,7,6,3,1,2,5]=>[2,6,7,5,8,4,3,1]=>[7,3,2,4,1,5,6,8]=>[1,1,2,4]
[4,6,7,1,3,2,8,5]=>[1,5,8,4,2,6,3,7]=>[8,4,1,5,7,3,6,2]=>[1,1,3,2,1]
[6,4,7,5,3,2,8,1]=>[6,2,1,5,4,3,8,7]=>[3,7,8,4,5,6,1,2]=>[3,3,2]
[8,4,6,3,1,5,7,2]=>[2,6,4,8,5,3,7,1]=>[7,3,5,1,4,6,2,8]=>[1,2,3,2]
[7,3,1,4,5,6,8,2]=>[4,2,5,6,8,3,1,7]=>[5,7,4,3,1,6,8,2]=>[2,1,1,3,1]
[6,7,3,4,2,1,8,5]=>[3,5,4,1,8,6,2,7]=>[6,4,5,8,1,3,7,2]=>[1,3,3,1]
[6,4,8,3,1,5,7,2]=>[2,6,4,1,8,5,7,3]=>[7,3,5,8,1,4,2,6]=>[1,3,2,2]
[7,4,2,3,5,1,8,6]=>[3,4,2,5,8,6,1,7]=>[6,5,7,4,1,3,8,2]=>[1,2,1,3,1]
[3,1,6,5,2,4,8,7]=>[8,1,5,4,2,3,6,7]=>[1,8,4,5,7,6,3,2]=>[2,3,1,1,1]
[2,5,3,8,6,4,1,7]=>[2,7,6,1,3,5,8,4]=>[7,2,3,8,6,4,1,5]=>[1,3,1,1,2]
[6,7,1,5,4,3,2,8]=>[7,6,5,3,1,4,2,8]=>[2,3,4,6,8,5,7,1]=>[5,2,1]
[5,3,4,7,6,1,8,2]=>[8,2,1,3,6,5,4,7]=>[1,7,8,6,3,4,5,2]=>[3,1,3,1]
[1,6,4,3,8,7,5,2]=>[8,3,2,7,4,6,1,5]=>[1,6,7,2,5,3,8,4]=>[3,2,2,1]
[4,5,1,6,8,7,2,3]=>[1,4,2,7,8,6,3,5]=>[8,5,7,2,1,3,6,4]=>[1,2,1,3,1]
[3,4,7,2,5,8,6,1]=>[8,1,2,4,5,3,7,6]=>[1,8,7,5,4,6,2,3]=>[2,1,1,2,2]
[2,5,1,8,6,4,7,3]=>[2,6,5,8,1,7,3,4]=>[7,3,4,1,8,2,6,5]=>[1,2,2,2,1]
[9,8,7,4,3,2,1,5,6]=>[7,6,5,4,8,9,3,2,1]=>[3,4,5,6,2,1,7,8,9]=>[4,1,4]
[8,4,7,3,1,5,2,6]=>[2,7,5,4,6,8,3,1]=>[7,2,4,5,3,1,6,8]=>[1,3,1,3]
[2,5,1,8,3,6,4,7]=>[7,5,1,2,6,8,3,4]=>[2,4,8,7,3,1,6,5]=>[3,1,1,2,1]
[5,8,4,7,3,2,1,6]=>[1,3,7,6,5,8,4,2]=>[8,6,2,3,4,1,5,7]=>[1,1,3,3]
[4,3,8,6,1,2,5,7]=>[2,1,5,6,7,4,8,3]=>[7,8,4,3,2,5,1,6]=>[2,1,1,2,2]
[4,8,6,5,7,1,3,2]=>[8,6,1,4,3,7,5,2]=>[1,3,8,5,6,2,4,7]=>[3,2,3]
[7,2,3,5,6,8,4,1]=>[4,5,8,2,3,1,7,6]=>[5,4,1,7,6,8,2,3]=>[1,1,2,2,2]
[8,3,4,2,7,6,1,5]=>[2,3,7,8,4,6,5,1]=>[7,6,2,1,5,3,4,8]=>[1,1,1,2,3]
[8,7,5,6,4,1,3,2]=>[8,6,3,7,5,4,2,1]=>[1,3,6,2,4,5,7,8]=>[3,5]
[8,7,4,2,3,6,5,1]=>[8,4,3,5,7,6,2,1]=>[1,5,6,4,2,3,7,8]=>[3,1,4]
[8,4,2,3,7,6,5,1]=>[2,8,7,3,4,6,5,1]=>[7,1,2,6,5,3,4,8]=>[1,3,1,3]
[7,2,4,5,3,1,6,8]=>[3,6,2,5,4,7,1,8]=>[6,3,7,4,5,2,8,1]=>[1,2,2,2,1]
[7,6,3,1,4,5,8,2]=>[5,3,6,8,4,2,1,7]=>[4,6,3,1,5,7,8,2]=>[2,1,4,1]
[3,7,4,6,2,1,8,5]=>[3,5,8,1,6,4,2,7]=>[6,4,1,8,3,5,7,2]=>[1,1,2,3,1]
[5,4,1,7,8,6,2,3]=>[2,1,7,4,8,6,3,5]=>[7,8,2,5,1,3,6,4]=>[2,2,3,1]
[5,3,4,7,8,1,6,2]=>[8,2,1,3,6,4,7,5]=>[1,7,8,6,3,5,2,4]=>[3,1,2,2]
[4,3,7,6,5,1,8,2]=>[8,1,6,2,5,4,3,7]=>[1,8,3,7,4,5,6,2]=>[2,2,3,1]
[5,1,4,8,2,3,7,6]=>[3,8,5,1,6,7,2,4]=>[6,1,4,8,3,2,7,5]=>[1,3,1,2,1]
[3,2,8,5,4,1,6,7]=>[6,1,5,2,4,7,8,3]=>[3,8,4,7,5,2,1,6]=>[2,2,1,1,2]
[3,1,2,4,5,6,9,7,8]=>[8,1,9,2,3,4,5,6,7]=>[2,9,1,8,7,6,5,4,3]=>[2,2,1,1,1,1,1]
[1,2,8,3,4,6,5,7]=>[7,4,5,6,8,1,2,3]=>[2,5,4,3,1,8,7,6]=>[2,1,1,2,1,1]
[5,7,1,2,6,3,4,8]=>[6,7,3,1,4,5,2,8]=>[3,2,6,8,5,4,7,1]=>[1,3,1,2,1]
[1,2,7,5,6,3,4,8]=>[6,4,7,5,1,2,3,8]=>[3,5,2,4,8,7,6,1]=>[2,3,1,1,1]
[5,1,4,7,2,3,6,8]=>[5,3,6,1,7,2,4,8]=>[4,6,3,8,2,7,5,1]=>[2,2,2,1,1]
[4,8,1,2,3,6,5,7]=>[7,3,1,4,5,6,8,2]=>[2,6,8,5,4,3,1,7]=>[3,1,1,1,2]
[1,3,4,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>[8,6,9,7,5,4,3,2,1]=>[1,2,1,1,1,1,1,1]
[1,3,5,6,4,2,7,8,9]=>[3,6,2,5,1,4,7,8,9]=>[7,4,8,5,9,6,3,2,1]=>[1,2,2,1,1,1,1]
[1,3,5,7,8,6,4,2,9]=>[4,8,3,7,2,6,1,5,9]=>[6,2,7,3,8,4,9,5,1]=>[1,2,2,2,1,1]
[1,3,4,2,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>[9,7,10,8,6,5,4,3,2,1]=>[1,2,1,1,1,1,1,1,1]
[1,3,5,6,4,2,7,8,9,10]=>[3,6,2,5,1,4,7,8,9,10]=>[8,5,9,6,10,7,4,3,2,1]=>[1,2,2,1,1,1,1,1]
[1,3,5,7,8,6,4,2,9,10]=>[4,8,3,7,2,6,1,5,9,10]=>[7,3,8,4,9,5,10,6,2,1]=>[1,2,2,2,1,1,1]
[6,2,3,8,7,1,4,5]=>[6,7,8,2,1,3,5,4]=>[3,2,1,7,8,6,4,5]=>[1,1,3,1,2]
[8,2,3,6,4,7,5,1]=>[8,5,2,3,4,7,6,1]=>[1,4,7,6,5,2,3,8]=>[3,1,1,3]
[7,2,3,6,4,8,1,5]=>[5,7,2,3,4,1,8,6]=>[4,2,7,6,5,8,1,3]=>[1,2,1,2,2]
[4,5,1,3,2,6,8,7]=>[4,1,8,3,2,5,6,7]=>[5,8,1,6,7,4,3,2]=>[2,3,1,1,1]
[6,4,7,5,1,3,2,8]=>[2,7,5,1,6,4,3,8]=>[7,2,4,8,3,5,6,1]=>[1,3,3,1]
[5,3,1,6,2,7,8,4]=>[2,6,4,1,8,3,5,7]=>[7,3,5,8,1,6,4,2]=>[1,3,2,1,1]
[6,7,2,4,1,8,3,5]=>[7,3,4,1,8,5,2,6]=>[2,6,5,8,1,4,7,3]=>[2,2,3,1]
[5,1,6,3,2,7,8,4]=>[4,6,3,1,8,2,5,7]=>[5,3,6,8,1,7,4,2]=>[1,3,2,1,1]
[5,2,1,6,4,7,3,8]=>[5,2,4,1,7,3,6,8]=>[4,7,5,8,2,6,3,1]=>[2,2,2,1,1]
[5,4,1,6,2,7,8,3]=>[6,4,2,1,8,3,5,7]=>[3,5,7,8,1,6,4,2]=>[4,2,1,1]
[6,7,2,5,4,1,3,8]=>[6,7,3,1,5,4,2,8]=>[3,2,6,8,4,5,7,1]=>[1,3,3,1]
[7,1,3,5,4,2,8,6]=>[5,3,4,8,2,6,1,7]=>[4,6,5,1,7,3,8,2]=>[2,1,2,2,1]
[7,6,8,2,4,5,3,1]=>[5,8,4,2,1,7,6,3]=>[4,1,5,7,8,2,3,6]=>[1,4,3]
[3,8,5,4,7,1,2,6]=>[6,4,1,3,7,8,5,2]=>[3,5,8,6,2,1,4,7]=>[3,1,1,3]
[7,3,2,6,5,8,1,4]=>[7,2,5,3,4,1,8,6]=>[2,7,4,6,5,8,1,3]=>[2,2,2,2]
[3,6,2,5,7,4,8,1]=>[4,6,1,3,2,5,8,7]=>[5,3,8,6,7,4,1,2]=>[1,2,2,1,2]
[2,7,1,5,8,6,4,3]=>[8,4,7,6,1,3,2,5]=>[1,5,2,3,8,6,7,4]=>[2,3,2,1]
[7,2,4,1,6,8,5,3]=>[3,5,8,2,7,4,1,6]=>[6,4,1,7,2,5,8,3]=>[1,1,2,3,1]
[6,4,7,2,3,8,5,1]=>[2,8,4,1,5,3,7,6]=>[7,1,5,8,4,6,2,3]=>[1,3,2,2]
[6,1,8,5,7,4,2,3]=>[7,4,1,8,6,5,2,3]=>[2,5,8,1,3,4,7,6]=>[3,4,1]
[7,1,4,3,6,5,8,2]=>[3,6,4,5,8,2,1,7]=>[6,3,5,4,1,7,8,2]=>[1,2,1,3,1]
[7,1,5,6,3,4,8,2]=>[5,3,6,4,8,2,1,7]=>[4,6,3,5,1,7,8,2]=>[2,2,3,1]
[6,1,8,5,4,7,3,2]=>[5,4,1,8,7,6,2,3]=>[4,5,8,1,2,3,7,6]=>[3,4,1]
[7,6,1,5,4,2,8,3]=>[8,6,5,3,4,2,1,7]=>[1,3,4,6,5,7,8,2]=>[4,3,1]
[5,1,6,8,7,2,4,3]=>[3,1,8,6,7,5,2,4]=>[6,8,1,3,2,4,7,5]=>[2,2,3,1]
[4,6,7,5,3,1,8,2]=>[2,8,1,6,5,4,3,7]=>[7,1,8,3,4,5,6,2]=>[1,2,4,1]
[5,3,2,6,8,7,4,1]=>[8,2,1,4,7,3,6,5]=>[1,7,8,5,2,6,3,4]=>[3,1,2,2]
[5,4,6,2,8,7,3,1]=>[2,1,3,8,7,4,6,5]=>[7,8,6,1,2,5,3,4]=>[2,1,3,2]
[4,5,8,6,7,2,3,1]=>[6,1,2,4,8,7,5,3]=>[3,8,7,5,1,2,4,6]=>[2,1,1,4]
[4,5,7,6,1,2,8,3]=>[1,2,8,5,6,4,3,7]=>[8,7,1,4,3,5,6,2]=>[1,1,2,3,1]
[4,6,5,7,2,1,8,3]=>[5,1,3,2,8,6,4,7]=>[4,8,6,7,1,3,5,2]=>[2,2,3,1]
[7,4,8,6,3,5,1,2]=>[7,2,5,1,8,6,4,3]=>[2,7,4,8,1,3,5,6]=>[2,2,4]
[7,2,4,3,6,1,8,5]=>[3,8,2,4,6,5,1,7]=>[6,1,7,5,3,4,8,2]=>[1,2,1,3,1]
[2,3,4,7,8,6,1,5]=>[7,4,8,1,2,3,6,5]=>[2,5,1,8,7,6,3,4]=>[2,2,1,1,2]
[6,3,7,1,4,2,8,5]=>[2,5,8,4,1,6,3,7]=>[7,4,1,5,8,3,6,2]=>[1,1,3,2,1]
[4,6,3,5,1,8,2,7]=>[1,3,7,4,2,8,5,6]=>[8,6,2,5,7,1,4,3]=>[1,1,3,2,1]
[8,5,7,6,2,3,4,1]=>[5,2,6,8,7,4,3,1]=>[4,7,3,1,2,5,6,8]=>[2,1,5]
[3,4,6,7,8,2,5,1]=>[3,6,1,2,4,8,7,5]=>[6,3,8,7,5,1,2,4]=>[1,2,1,1,3]
[2,5,6,7,3,8,1,4]=>[2,5,3,7,1,4,8,6]=>[7,4,6,2,8,5,1,3]=>[1,2,2,1,2]
[5,8,4,6,2,1,7,3]=>[1,5,3,8,6,4,7,2]=>[8,4,6,1,3,5,2,7]=>[1,2,3,2]
[2,4,7,5,8,6,3,1]=>[8,4,2,3,7,1,6,5]=>[1,5,7,6,2,8,3,4]=>[3,1,2,2]
[1,6,8,3,4,2,7,5]=>[4,5,2,8,6,7,1,3]=>[5,4,7,1,3,2,8,6]=>[1,2,2,2,1]
[4,1,7,6,2,8,3,5]=>[1,7,8,5,4,2,3,6]=>[8,2,1,4,5,7,6,3]=>[1,1,4,1,1]
[4,1,8,2,7,5,3,6]=>[1,7,6,8,4,5,2,3]=>[8,2,3,1,5,4,7,6]=>[1,2,2,2,1]
[4,1,7,2,8,5,3,6]=>[1,7,6,8,4,2,3,5]=>[8,2,3,1,5,7,6,4]=>[1,2,3,1,1]
[2,5,6,3,7,4,8,1]=>[2,6,4,1,3,5,8,7]=>[7,3,5,8,6,4,1,2]=>[1,3,1,1,2]
[2,6,5,3,8,4,7,1]=>[6,3,2,8,1,4,7,5]=>[3,6,7,1,8,5,2,4]=>[3,2,1,2]
[2,6,5,3,7,4,8,1]=>[6,4,3,1,2,5,8,7]=>[3,5,6,8,7,4,1,2]=>[4,1,1,2]
[7,1,6,3,5,4,8,2]=>[6,4,5,3,8,2,1,7]=>[3,5,4,6,1,7,8,2]=>[2,2,3,1]
[5,7,3,2,8,4,1,6]=>[3,1,7,4,6,2,8,5]=>[6,8,2,5,3,7,1,4]=>[2,2,2,2]
[7,1,4,2,8,5,3,6]=>[3,7,6,8,2,4,1,5]=>[6,2,3,1,7,5,8,4]=>[1,2,2,2,1]
[2,6,8,1,7,5,3,4]=>[7,2,8,6,1,4,5,3]=>[2,7,1,3,8,5,4,6]=>[2,3,1,2]
[1,4,6,5,3,8,2,7]=>[5,2,4,3,7,8,1,6]=>[4,7,5,6,2,1,8,3]=>[2,2,1,2,1]
[2,4,5,8,7,1,3,6]=>[2,3,6,7,8,1,5,4]=>[7,6,3,2,1,8,4,5]=>[1,1,1,1,2,2]
[3,1,6,8,7,5,4,2]=>[8,3,7,1,6,5,2,4]=>[1,6,2,8,3,4,7,5]=>[2,2,3,1]
[3,1,8,7,5,6,4,2]=>[5,8,7,1,6,4,2,3]=>[4,1,2,8,3,5,7,6]=>[1,3,3,1]
[5,1,8,7,6,3,4,2]=>[1,6,8,7,5,4,2,3]=>[8,3,1,2,4,5,7,6]=>[1,1,5,1]
[8,2,7,5,3,6,4,1]=>[8,5,4,7,2,6,3,1]=>[1,4,5,2,7,3,6,8]=>[3,2,3]
[8,7,2,3,1,5,6,4]=>[3,4,6,8,5,7,2,1]=>[6,5,3,1,4,2,7,8]=>[1,1,1,2,3]
[2,8,5,7,6,1,3,4]=>[6,3,7,8,5,1,4,2]=>[3,6,2,1,4,8,5,7]=>[2,1,3,2]
[1,8,7,2,6,4,5,3]=>[6,8,7,4,5,3,1,2]=>[3,1,2,5,4,6,8,7]=>[1,3,3,1]
[8,7,2,1,6,4,5,3]=>[6,8,3,7,4,5,2,1]=>[3,1,6,2,5,4,7,8]=>[1,2,2,3]
[8,7,1,6,4,3,5,2]=>[6,5,8,7,3,4,2,1]=>[3,4,1,2,6,5,7,8]=>[2,3,3]
[8,3,6,2,1,5,4,7]=>[2,4,7,5,6,3,8,1]=>[7,5,2,4,3,6,1,8]=>[1,1,2,2,2]
[4,5,1,8,7,3,6,2]=>[1,2,6,8,7,5,3,4]=>[8,7,3,1,2,4,6,5]=>[1,1,1,4,1]
[3,8,5,2,6,7,4,1]=>[5,3,8,1,4,7,6,2]=>[4,6,1,8,5,2,3,7]=>[2,2,1,3]
[4,3,8,5,2,6,1,7]=>[1,5,2,4,7,6,8,3]=>[8,4,7,5,2,3,1,6]=>[1,2,1,2,2]
[3,6,4,7,5,2,1,8]=>[7,3,1,2,6,5,4,8]=>[2,6,8,7,3,4,5,1]=>[3,1,3,1]
[5,7,4,1,2,6,8,3]=>[6,1,8,4,3,5,2,7]=>[3,8,1,5,6,4,7,2]=>[2,3,2,1]
[2,8,6,7,5,3,1,4]=>[7,6,3,8,5,1,4,2]=>[2,3,6,1,4,8,5,7]=>[3,3,2]
[7,4,5,2,6,3,1,8]=>[2,7,4,3,6,5,1,8]=>[7,2,5,6,3,4,8,1]=>[1,3,3,1]
[8,6,3,4,5,1,7,2]=>[3,4,8,6,5,2,7,1]=>[6,5,1,3,4,7,2,8]=>[1,1,4,2]
[8,6,3,5,4,1,7,2]=>[8,3,6,5,4,2,7,1]=>[1,6,3,4,5,7,2,8]=>[2,4,2]
[8,7,4,5,1,3,6,2]=>[6,3,8,5,4,7,2,1]=>[3,6,1,4,5,2,7,8]=>[2,3,3]
[8,6,2,5,3,1,4,7]=>[6,3,5,7,4,2,8,1]=>[3,6,4,2,5,7,1,8]=>[2,1,3,2]
[8,4,7,3,1,2,5,6]=>[5,2,6,4,7,8,3,1]=>[4,7,3,5,2,1,6,8]=>[2,2,1,3]
[8,7,3,5,1,6,4,2]=>[8,3,7,5,4,6,2,1]=>[1,6,2,4,5,3,7,8]=>[2,3,3]
[4,3,7,6,1,5,2,8]=>[1,7,2,5,6,4,3,8]=>[8,2,7,4,3,5,6,1]=>[1,2,1,3,1]
[7,5,4,3,6,1,8,2]=>[4,3,2,8,6,5,1,7]=>[5,6,7,1,3,4,8,2]=>[3,4,1]
[5,6,8,4,3,7,2,1]=>[1,2,5,4,8,7,6,3]=>[8,7,4,5,1,2,3,6]=>[1,1,2,4]
[7,5,8,4,2,1,6,3]=>[5,2,8,6,4,1,7,3]=>[4,7,1,3,5,8,2,6]=>[2,4,2]
[1,4,8,7,6,2,5,3]=>[8,6,7,2,5,4,1,3]=>[1,3,2,7,4,5,8,6]=>[2,2,3,1]
[7,2,4,1,5,3,8,6]=>[5,2,3,8,4,6,1,7]=>[4,7,6,1,5,3,8,2]=>[2,1,2,2,1]
[8,5,3,4,1,7,2,6]=>[3,7,4,2,8,5,6,1]=>[6,2,5,7,1,4,3,8]=>[1,3,2,2]
[8,6,5,3,1,2,7,4]=>[8,5,4,6,3,2,7,1]=>[1,4,5,3,6,7,2,8]=>[3,3,2]
[7,4,6,5,3,2,8,1]=>[6,2,5,4,3,1,8,7]=>[3,7,4,5,6,8,1,2]=>[2,4,2]
[1,7,4,2,8,5,6,3]=>[3,6,8,7,4,1,2,5]=>[6,3,1,2,5,8,7,4]=>[1,1,4,1,1]
[3,2,1,7,4,6,8,5]=>[1,6,8,2,5,3,4,7]=>[8,3,1,7,4,6,5,2]=>[1,1,2,2,1,1]
[6,2,5,7,1,4,3,8]=>[7,5,2,3,1,6,4,8]=>[2,4,7,6,8,3,5,1]=>[3,2,2,1]
[4,8,5,3,1,2,6,7]=>[1,5,6,4,3,7,8,2]=>[8,4,3,5,6,2,1,7]=>[1,1,3,1,2]
[8,5,2,4,6,1,3,7]=>[6,3,4,2,7,5,8,1]=>[3,6,5,7,2,4,1,8]=>[2,2,2,2]
[1,5,3,4,7,2,6,8]=>[3,4,2,6,7,1,5,8]=>[6,5,7,3,2,8,4,1]=>[1,2,1,2,1,1]
[8,4,6,1,5,7,3,2]=>[2,5,8,7,4,3,6,1]=>[7,4,1,2,5,6,3,8]=>[1,1,4,2]
[6,4,7,2,1,3,8,5]=>[4,2,8,5,1,6,3,7]=>[5,7,1,4,8,3,6,2]=>[2,3,2,1]
[6,7,3,1,2,4,8,5]=>[8,4,3,5,1,6,2,7]=>[1,5,6,4,8,3,7,2]=>[3,2,2,1]
[3,1,8,7,6,2,5,4]=>[8,6,7,1,5,4,2,3]=>[1,3,2,8,4,5,7,6]=>[2,2,3,1]
[1,3,8,6,7,2,5,4]=>[8,6,4,7,2,5,1,3]=>[1,3,5,2,7,4,8,6]=>[3,2,2,1]
[5,2,3,6,1,8,4,7]=>[7,2,3,1,4,8,5,6]=>[2,7,6,8,5,1,4,3]=>[2,2,1,2,1]
[3,2,6,4,7,1,5,8]=>[1,4,6,2,3,7,5,8]=>[8,5,3,7,6,2,4,1]=>[1,1,2,1,2,1]
[3,6,2,5,7,8,4,1]=>[4,5,1,2,8,3,7,6]=>[5,4,8,7,1,6,2,3]=>[1,2,1,2,2]
[2,7,4,6,8,3,5,1]=>[6,3,4,2,8,1,7,5]=>[3,6,5,7,1,8,2,4]=>[2,2,2,2]
[1,5,7,6,8,4,2,3]=>[7,2,4,3,8,6,1,5]=>[2,7,5,6,1,3,8,4]=>[2,2,3,1]
[2,7,4,6,8,5,3,1]=>[4,8,3,2,7,1,6,5]=>[5,1,6,7,2,8,3,4]=>[1,3,2,2]
[3,7,6,8,5,1,4,2]=>[8,6,3,1,2,7,5,4]=>[1,3,6,8,7,2,4,5]=>[4,1,3]
[7,1,3,8,6,2,4,5]=>[6,7,8,3,5,2,1,4]=>[3,2,1,6,4,7,8,5]=>[1,1,2,3,1]
[2,7,1,8,6,5,3,4]=>[7,8,6,5,1,3,2,4]=>[2,1,3,4,8,6,7,5]=>[1,4,2,1]
[4,6,7,5,1,2,3,8]=>[1,5,6,2,7,4,3,8]=>[8,4,3,7,2,5,6,1]=>[1,1,2,3,1]
[5,3,4,7,6,2,1,8]=>[7,2,1,3,6,5,4,8]=>[2,7,8,6,3,4,5,1]=>[3,1,3,1]
[4,1,8,5,7,2,6,3]=>[1,4,8,6,7,5,2,3]=>[8,5,1,3,2,4,7,6]=>[1,1,2,3,1]
[7,6,8,2,4,3,5,1]=>[6,4,5,2,1,8,7,3]=>[3,5,4,7,8,1,2,6]=>[2,3,3]
[7,4,5,3,8,1,6,2]=>[2,4,3,8,6,1,7,5]=>[7,5,6,1,3,8,2,4]=>[1,2,3,2]
[7,3,6,1,4,2,8,5]=>[2,5,8,4,6,3,1,7]=>[7,4,1,5,3,6,8,2]=>[1,1,2,3,1]
[8,7,2,6,4,5,1,3]=>[7,5,8,3,6,4,2,1]=>[2,4,1,6,3,5,7,8]=>[2,2,4]
[2,6,4,8,3,5,1,7]=>[3,5,2,7,1,6,8,4]=>[6,4,7,2,8,3,1,5]=>[1,2,2,1,2]
[1,4,8,5,3,2,7,6]=>[5,2,4,8,6,7,1,3]=>[4,7,5,1,3,2,8,6]=>[2,1,2,2,1]
[3,5,8,4,6,7,1,2]=>[2,4,7,1,5,8,6,3]=>[7,5,2,8,4,1,3,6]=>[1,1,2,1,3]
[1,2,4,8,5,7,3,6]=>[5,7,8,3,6,1,2,4]=>[4,2,1,6,3,8,7,5]=>[1,1,2,2,1,1]
[5,6,3,1,8,2,4,7]=>[6,3,1,7,2,8,4,5]=>[3,6,8,2,7,1,5,4]=>[3,2,2,1]
[7,3,6,5,1,8,4,2]=>[8,7,2,5,4,3,1,6]=>[1,2,7,4,5,6,8,3]=>[3,4,1]
[5,7,2,1,4,8,6,3]=>[8,3,1,5,7,4,2,6]=>[1,6,8,4,2,5,7,3]=>[3,1,3,1]
[7,6,3,5,2,1,8,4]=>[3,5,8,6,4,2,1,7]=>[6,4,1,3,5,7,8,2]=>[1,1,5,1]
[7,1,4,6,8,5,3,2]=>[4,8,3,7,6,2,1,5]=>[5,1,6,2,3,7,8,4]=>[1,2,4,1]
[2,7,1,5,6,4,8,3]=>[4,6,5,8,1,3,2,7]=>[5,3,4,1,8,6,7,2]=>[1,2,2,2,1]
[1,5,7,8,4,6,3,2]=>[5,2,3,8,7,6,1,4]=>[4,7,6,1,2,3,8,5]=>[2,1,4,1]
[1,4,8,5,7,6,3,2]=>[8,4,7,2,6,5,1,3]=>[1,5,2,7,3,4,8,6]=>[2,2,3,1]
[2,8,1,5,6,4,7,3]=>[4,6,5,8,1,3,7,2]=>[5,3,4,1,8,6,2,7]=>[1,2,2,1,2]
[3,7,2,8,1,5,6,4]=>[6,8,1,3,5,2,7,4]=>[3,1,8,6,4,7,2,5]=>[1,2,1,2,2]
[7,3,2,5,1,6,8,4]=>[2,6,3,4,8,5,1,7]=>[7,3,6,5,1,4,8,2]=>[1,2,1,3,1]
[8,7,2,1,3,6,5,4]=>[8,3,7,4,5,6,2,1]=>[1,6,2,5,4,3,7,8]=>[2,2,1,3]
[7,3,2,8,1,4,6,5]=>[2,8,3,5,6,1,7,4]=>[7,1,6,4,3,8,2,5]=>[1,2,1,2,2]
[3,6,2,1,8,4,7,5]=>[8,1,3,6,2,7,4,5]=>[1,8,6,3,7,2,5,4]=>[2,1,2,2,1]
[3,5,1,7,6,4,8,2]=>[2,6,1,5,4,8,3,7]=>[7,3,8,4,5,1,6,2]=>[1,2,2,2,1]
[5,4,7,6,2,1,8,3]=>[2,1,5,8,6,4,3,7]=>[7,8,4,1,3,5,6,2]=>[2,1,4,1]
[3,5,2,8,7,1,6,4]=>[2,8,1,6,7,3,5,4]=>[7,1,8,3,2,6,4,5]=>[1,2,1,2,2]
[3,7,6,5,4,1,8,2]=>[8,6,5,1,4,3,2,7]=>[1,3,4,8,5,6,7,2]=>[4,3,1]
[4,6,5,3,1,8,7,2]=>[4,1,3,2,8,7,5,6]=>[5,8,6,7,1,2,4,3]=>[2,2,3,1]
[4,5,2,6,7,3,8,1]=>[1,4,2,6,3,5,8,7]=>[8,5,7,3,6,4,1,2]=>[1,2,2,1,2]
[8,6,7,4,3,1,5,2]=>[8,6,5,4,2,7,3,1]=>[1,3,4,5,7,2,6,8]=>[5,3]
[4,7,1,8,5,3,2,6]=>[7,1,6,5,8,3,2,4]=>[2,8,3,4,1,6,7,5]=>[2,2,3,1]
[8,6,7,1,4,3,5,2]=>[6,5,8,4,2,7,3,1]=>[3,4,1,5,7,2,6,8]=>[2,3,3]
[8,6,7,2,1,3,5,4]=>[4,8,5,6,2,7,3,1]=>[5,1,4,3,7,2,6,8]=>[1,2,2,3]
[8,5,6,1,7,4,2,3]=>[7,2,8,6,4,3,5,1]=>[2,7,1,3,5,6,4,8]=>[2,4,2]
[6,4,1,2,5,7,8,3]=>[5,6,2,8,3,1,4,7]=>[4,3,7,1,6,8,5,2]=>[1,2,3,1,1]
[3,4,6,1,8,2,7,5]=>[8,1,2,6,3,7,4,5]=>[1,8,7,3,6,2,5,4]=>[2,1,2,2,1]
[5,3,1,4,7,6,2,8]=>[2,7,4,1,6,3,5,8]=>[7,2,5,8,3,6,4,1]=>[1,3,2,1,1]
[6,4,5,2,7,1,3,8]=>[4,2,6,3,1,7,5,8]=>[5,7,3,6,8,2,4,1]=>[2,3,2,1]
[7,4,3,5,1,6,2,8]=>[3,2,7,5,4,6,1,8]=>[6,7,2,4,5,3,8,1]=>[2,3,2,1]
[7,5,3,6,2,1,4,8]=>[3,6,5,2,7,4,1,8]=>[6,3,4,7,2,5,8,1]=>[1,3,3,1]
[6,4,3,7,1,8,2,5]=>[3,2,7,1,8,5,4,6]=>[6,7,2,8,1,4,5,3]=>[2,2,3,1]
[3,1,2,7,6,4,5,8]=>[1,6,7,5,2,3,4,8]=>[8,3,2,4,7,6,5,1]=>[1,1,3,1,1,1]
[5,1,2,7,6,3,4,8]=>[6,7,5,2,1,3,4,8]=>[3,2,4,7,8,6,5,1]=>[1,4,1,1,1]
[3,5,6,8,1,2,7,4]=>[2,8,1,5,3,6,7,4]=>[7,1,8,4,6,3,2,5]=>[1,2,2,1,2]
[2,6,5,7,1,3,4,8]=>[5,6,3,1,2,7,4,8]=>[4,3,6,8,7,2,5,1]=>[1,3,1,2,1]
[2,3,7,1,5,6,4,8]=>[5,7,1,2,4,6,3,8]=>[4,2,8,7,5,3,6,1]=>[1,2,1,1,2,1]
[4,6,1,5,2,8,7,3]=>[1,4,8,7,3,2,5,6]=>[8,5,1,2,6,7,4,3]=>[1,1,4,1,1]
[6,1,5,4,2,7,8,3]=>[6,4,3,8,2,1,5,7]=>[3,5,6,1,7,8,4,2]=>[3,3,1,1]
[4,6,1,5,2,7,8,3]=>[1,6,4,8,3,2,5,7]=>[8,3,5,1,6,7,4,2]=>[1,2,3,1,1]
[2,8,6,5,1,3,7,4]=>[8,5,6,4,1,3,7,2]=>[1,4,3,5,8,6,2,7]=>[2,3,1,2]
[5,1,8,6,2,7,4,3]=>[1,8,7,5,4,6,2,3]=>[8,1,2,4,5,3,7,6]=>[1,4,2,1]
[3,6,8,2,7,5,1,4]=>[7,2,8,1,4,6,5,3]=>[2,7,1,8,5,3,4,6]=>[2,2,1,3]
[5,6,4,1,7,2,8,3]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[1,5,1,1]
[3,8,6,1,5,7,4,2]=>[5,8,7,1,4,3,6,2]=>[4,1,2,8,5,6,3,7]=>[1,3,2,2]
[8,1,6,3,4,2,5,7]=>[4,6,5,7,2,3,8,1]=>[5,3,4,2,7,6,1,8]=>[1,2,2,1,2]
[7,4,2,3,1,6,8,5]=>[3,4,2,6,8,5,1,7]=>[6,5,7,3,1,4,8,2]=>[1,2,1,3,1]
[6,4,2,3,7,8,1,5]=>[7,3,2,4,1,5,8,6]=>[2,6,7,5,8,4,1,3]=>[3,2,1,2]
[4,3,6,2,5,8,1,7]=>[2,1,4,5,3,7,8,6]=>[7,8,5,4,6,2,1,3]=>[2,1,2,1,2]
[9,8,10,7,6,5,4,3,1,2]=>[9,2,1,10,8,7,6,5,4,3]=>[2,9,10,1,3,4,5,6,7,8]=>[3,7]
[8,9,7,6,5,4,2,1,3]=>[8,7,1,9,6,5,4,3,2]=>[2,3,9,1,4,5,6,7,8]=>[3,6]
[8,9,7,6,5,4,2,3,1]=>[7,1,9,8,6,5,4,3,2]=>[3,9,1,2,4,5,6,7,8]=>[2,7]
[1,6,4,5,7,3,2,8]=>[3,4,2,7,6,1,5,8]=>[6,5,7,2,3,8,4,1]=>[1,2,3,1,1]
[1,6,4,5,7,2,8,3]=>[3,4,2,8,6,1,5,7]=>[6,5,7,1,3,8,4,2]=>[1,2,3,1,1]
[1,7,5,6,4,8,3,2]=>[3,5,4,2,8,7,1,6]=>[6,4,5,7,1,2,8,3]=>[1,3,3,1]
[1,5,6,7,3,2,4,8]=>[2,6,5,3,7,1,4,8]=>[7,3,4,6,2,8,5,1]=>[1,3,2,1,1]
[8,2,1,4,3,7,5,6]=>[2,4,7,8,3,5,6,1]=>[7,5,2,1,6,4,3,8]=>[1,1,1,2,1,2]
[7,6,8,2,1,5,3,4]=>[4,7,8,5,2,1,6,3]=>[5,2,1,4,7,8,3,6]=>[1,1,4,2]
[7,1,6,8,3,2,4,5]=>[6,5,7,3,8,2,1,4]=>[3,4,2,6,1,7,8,5]=>[2,2,3,1]
[4,5,6,1,3,8,2,7]=>[1,5,2,7,3,8,4,6]=>[8,4,7,2,6,1,5,3]=>[1,2,2,2,1]
[6,3,5,7,4,2,8,1]=>[3,6,2,1,5,4,8,7]=>[6,3,7,8,4,5,1,2]=>[1,3,2,2]
[7,6,4,8,5,3,1,2]=>[3,7,2,1,8,6,5,4]=>[6,2,7,8,1,3,4,5]=>[1,3,4]
[8,2,1,6,4,7,3,5]=>[5,7,2,4,8,3,6,1]=>[4,2,7,5,1,6,3,8]=>[1,2,1,2,2]
[1,3,8,6,5,2,7,4]=>[8,6,5,2,4,7,1,3]=>[1,3,4,7,5,2,8,6]=>[4,1,2,1]
[2,7,3,8,5,6,4,1]=>[5,8,7,3,1,2,6,4]=>[4,1,2,6,8,7,3,5]=>[1,4,1,2]
[1,2,8,5,7,4,6,3]=>[4,6,8,7,5,1,2,3]=>[5,3,1,2,4,8,7,6]=>[1,1,4,1,1]
[1,6,8,5,4,7,2,3]=>[2,7,5,4,8,6,1,3]=>[7,2,4,5,1,3,8,6]=>[1,3,3,1]
[2,1,3,8,6,4,7,5]=>[8,6,1,5,7,2,3,4]=>[1,3,8,4,2,7,6,5]=>[3,1,2,1,1]
[8,2,5,4,3,7,1,6]=>[5,4,2,3,7,8,6,1]=>[4,5,7,6,2,1,3,8]=>[3,1,1,3]
[5,8,4,3,7,6,2,1]=>[1,3,8,4,7,6,5,2]=>[8,6,1,5,2,3,4,7]=>[1,1,2,4]
[8,1,5,3,4,7,2,6]=>[4,5,3,7,8,2,6,1]=>[5,4,6,2,1,7,3,8]=>[1,2,1,2,2]
[6,1,8,7,4,5,3,2]=>[5,1,8,7,6,4,2,3]=>[4,8,1,2,3,5,7,6]=>[2,5,1]
[5,8,6,4,2,1,7,3]=>[1,5,8,6,4,3,7,2]=>[8,4,1,3,5,6,2,7]=>[1,1,4,2]
[2,6,1,8,4,7,5,3]=>[8,5,2,7,1,6,3,4]=>[1,4,7,2,8,3,6,5]=>[3,2,2,1]
[5,3,8,6,1,2,7,4]=>[8,2,1,5,6,4,7,3]=>[1,7,8,4,3,5,2,6]=>[3,1,2,2]
[3,7,6,2,1,4,8,5]=>[4,8,1,5,6,3,2,7]=>[5,1,8,4,3,6,7,2]=>[1,2,1,3,1]
[4,6,2,3,7,1,8,5]=>[1,8,3,4,2,6,5,7]=>[8,1,6,5,7,3,4,2]=>[1,2,2,2,1]
[6,8,7,5,1,3,4,2]=>[6,1,8,5,7,4,3,2]=>[3,8,1,4,2,5,6,7]=>[2,2,4]
[6,4,3,2,7,8,5,1]=>[3,2,5,1,8,4,7,6]=>[6,7,4,8,1,5,2,3]=>[2,2,2,2]
[7,8,6,4,2,5,3,1]=>[8,5,4,1,7,6,3,2]=>[1,4,5,8,2,3,6,7]=>[4,4]
[6,4,5,8,7,1,3,2]=>[2,3,1,8,6,7,5,4]=>[7,6,8,1,3,2,4,5]=>[1,2,2,3]
[6,4,1,7,8,3,2,5]=>[2,7,6,4,1,8,3,5]=>[7,2,3,5,8,1,6,4]=>[1,4,2,1]
[2,3,4,5,8,6,7,9,1]=>[6,7,1,2,3,4,5,9,8]=>[4,3,9,8,7,6,5,1,2]=>[1,2,1,1,1,1,2]
[6,4,3,8,7,2,5,1]=>[2,6,1,8,3,7,5,4]=>[7,3,8,1,6,2,4,5]=>[1,2,2,3]
[5,4,7,2,1,3,8,6]=>[4,2,1,8,5,6,3,7]=>[5,7,8,1,4,3,6,2]=>[3,2,2,1]
[2,6,4,5,7,1,8,3]=>[3,4,2,8,1,6,5,7]=>[6,5,7,1,8,3,4,2]=>[1,2,2,2,1]
[3,7,4,6,1,5,8,2]=>[3,6,8,1,5,4,2,7]=>[6,3,1,8,4,5,7,2]=>[1,1,2,3,1]
[3,4,6,5,2,8,1,7]=>[5,1,2,4,3,7,8,6]=>[4,8,7,5,6,2,1,3]=>[2,1,2,1,2]
[4,6,7,5,8,2,1,3]=>[2,7,1,6,4,3,8,5]=>[7,2,8,3,5,6,1,4]=>[1,2,3,2]
[2,5,7,6,4,1,8,3]=>[8,2,6,5,1,4,3,7]=>[1,7,3,4,8,5,6,2]=>[2,3,2,1]
[5,1,4,6,2,7,8,3]=>[3,6,4,1,8,2,5,7]=>[6,3,5,8,1,7,4,2]=>[1,3,2,1,1]
[1,2,5,3,7,8,6,4]=>[3,5,8,7,1,2,4,6]=>[6,4,1,2,8,7,5,3]=>[1,1,3,1,1,1]
[4,8,3,5,1,2,7,6]=>[1,3,8,5,4,6,7,2]=>[8,6,1,4,5,3,2,7]=>[1,1,3,1,2]
[6,1,3,7,2,8,4,5]=>[7,8,3,5,2,1,4,6]=>[2,1,6,4,7,8,5,3]=>[1,2,3,1,1]
[3,8,5,4,1,7,2,6]=>[7,4,1,3,8,5,6,2]=>[2,5,8,6,1,4,3,7]=>[3,1,2,2]
[3,1,5,8,2,6,7,4]=>[1,3,6,8,5,7,2,4]=>[8,6,3,1,4,2,7,5]=>[1,1,1,2,2,1]
[2,8,5,3,1,7,4,6]=>[4,7,3,8,1,5,6,2]=>[5,2,6,1,8,4,3,7]=>[1,2,2,1,2]
[6,5,2,3,7,1,8,4]=>[8,3,4,2,1,6,5,7]=>[1,6,5,7,8,3,4,2]=>[2,3,2,1]
[7,2,1,6,4,8,3,5]=>[5,7,2,4,8,3,1,6]=>[4,2,7,5,1,6,8,3]=>[1,2,1,3,1]
[2,1,3,7,5,8,4,6]=>[5,7,1,4,8,2,3,6]=>[4,2,8,5,1,7,6,3]=>[1,2,1,2,1,1]
[6,2,4,5,7,1,8,3]=>[3,4,8,2,1,6,5,7]=>[6,5,1,7,8,3,4,2]=>[1,1,3,2,1]
[2,3,8,7,1,4,6,5]=>[8,5,6,7,1,2,4,3]=>[1,4,3,2,8,7,5,6]=>[2,1,2,1,2]
[6,8,2,5,4,7,3,1]=>[5,4,1,8,3,7,6,2]=>[4,5,8,1,6,2,3,7]=>[3,2,3]
[9,2,3,4,5,1,6,7,8]=>[2,3,4,6,5,7,8,9,1]=>[8,7,6,4,5,3,2,1,9]=>[1,1,1,2,1,1,2]
[10,2,3,4,5,6,1,7,8,9]=>[2,3,4,5,7,6,8,9,10,1]=>[9,8,7,6,4,5,3,2,1,10]=>[1,1,1,1,2,1,1,2]
[10,2,3,4,5,1,6,7,8,9]=>[2,3,4,6,5,7,8,9,10,1]=>[9,8,7,5,6,4,3,2,1,10]=>[1,1,1,2,1,1,1,2]
[3,2,9,1,4,5,6,7,8]=>[2,1,4,5,6,7,8,9,3]=>[8,9,6,5,4,3,2,1,7]=>[2,1,1,1,1,1,2]
[2,7,6,3,8,4,5,1]=>[6,8,4,3,1,2,7,5]=>[3,1,5,6,8,7,2,4]=>[1,4,1,2]
[4,6,8,2,3,1,7,5]=>[1,4,5,2,8,6,7,3]=>[8,5,4,7,1,3,2,6]=>[1,1,2,2,2]
[4,7,2,3,5,1,8,6]=>[3,1,4,5,8,6,2,7]=>[6,8,5,4,1,3,7,2]=>[2,1,1,3,1]
[6,4,2,1,3,7,5,8]=>[3,7,4,2,5,1,6,8]=>[6,2,5,7,4,8,3,1]=>[1,3,2,1,1]
[5,3,2,7,6,1,8,4]=>[8,2,1,6,3,5,4,7]=>[1,7,8,3,6,4,5,2]=>[3,2,2,1]
[5,6,4,2,8,7,1,3]=>[1,7,3,2,8,4,6,5]=>[8,2,6,7,1,5,3,4]=>[1,3,2,2]
[5,7,4,2,6,1,8,3]=>[1,8,4,3,6,5,2,7]=>[8,1,5,6,3,4,7,2]=>[1,3,3,1]
[5,4,7,1,6,2,8,3]=>[2,1,8,6,4,5,3,7]=>[7,8,1,3,5,4,6,2]=>[2,3,2,1]
[4,5,8,7,6,2,1,3]=>[7,1,2,6,8,5,4,3]=>[2,8,7,3,1,4,5,6]=>[2,1,1,4]
[6,4,7,1,2,3,8,5]=>[8,4,2,5,1,6,3,7]=>[1,5,7,4,8,3,6,2]=>[3,2,2,1]
[6,1,7,3,8,4,5,2]=>[6,8,4,3,1,7,2,5]=>[3,1,5,6,8,2,7,4]=>[1,4,2,1]
[8,2,3,1,6,4,7,5]=>[8,2,3,6,4,5,7,1]=>[1,7,6,3,5,4,2,8]=>[2,1,2,1,2]
[1,8,7,2,3,4,6,5]=>[8,4,5,6,7,3,1,2]=>[1,5,4,3,2,6,8,7]=>[2,1,1,3,1]
[1,3,8,2,5,6,4,7]=>[5,7,2,4,6,8,1,3]=>[4,2,7,5,3,1,8,6]=>[1,2,1,1,2,1]
[1,3,2,7,4,6,8,5]=>[6,8,2,5,1,3,4,7]=>[3,1,7,4,8,6,5,2]=>[1,2,2,1,1,1]
[1,3,8,4,6,2,7,5]=>[8,4,6,2,5,7,1,3]=>[1,5,3,7,4,2,8,6]=>[2,2,1,2,1]
[2,5,7,6,3,8,4,1]=>[8,2,5,4,1,3,7,6]=>[1,7,4,5,8,6,2,3]=>[2,3,1,2]
[6,4,7,1,2,5,3,8]=>[7,4,2,5,1,6,3,8]=>[2,5,7,4,8,3,6,1]=>[3,2,2,1]
[7,4,5,1,6,8,2,3]=>[2,7,5,3,8,4,1,6]=>[7,2,4,6,1,5,8,3]=>[1,3,3,1]
[1,7,8,4,2,6,3,5]=>[7,4,8,5,2,6,1,3]=>[2,5,1,4,7,3,8,6]=>[2,3,2,1]
[6,2,1,5,3,7,8,4]=>[6,2,4,8,3,1,5,7]=>[3,7,5,1,6,8,4,2]=>[2,1,3,1,1]
[6,2,5,1,3,8,7,4]=>[8,7,2,4,3,1,5,6]=>[1,2,7,5,6,8,4,3]=>[3,3,1,1]
[6,2,8,5,1,3,7,4]=>[8,5,6,2,1,4,7,3]=>[1,4,3,7,8,5,2,6]=>[2,3,1,2]
[4,1,7,8,3,6,5,2]=>[8,1,5,3,7,6,2,4]=>[1,8,4,6,2,3,7,5]=>[2,2,3,1]
[6,4,2,1,7,3,5,8]=>[3,6,2,7,4,1,5,8]=>[6,3,7,2,5,8,4,1]=>[1,2,3,1,1]
[5,8,4,2,1,3,6,7]=>[5,4,1,6,3,7,8,2]=>[4,5,8,3,6,2,1,7]=>[3,2,1,2]
[6,5,1,2,7,4,8,3]=>[6,5,8,3,2,1,4,7]=>[3,4,1,6,7,8,5,2]=>[2,4,1,1]
[2,8,4,3,5,1,7,6]=>[4,3,5,8,1,6,7,2]=>[5,6,4,1,8,3,2,7]=>[2,1,2,1,2]
[5,2,4,7,6,8,1,3]=>[7,3,1,5,2,4,8,6]=>[2,6,8,4,7,5,1,3]=>[3,2,1,2]
[3,1,5,7,4,8,6,2]=>[8,1,3,5,4,7,2,6]=>[1,8,6,4,5,2,7,3]=>[2,1,2,2,1]
[4,1,7,6,8,2,5,3]=>[8,1,6,4,3,7,2,5]=>[1,8,3,5,6,2,7,4]=>[2,3,2,1]
[7,2,6,4,1,5,3,8]=>[7,5,2,4,6,3,1,8]=>[2,4,7,5,3,6,8,1]=>[3,1,3,1]
[1,2,6,5,8,3,7,4]=>[4,3,8,6,7,1,2,5]=>[5,6,1,3,2,8,7,4]=>[2,2,2,1,1]
[7,3,5,6,1,4,2,8]=>[7,2,5,3,6,4,1,8]=>[2,7,4,6,3,5,8,1]=>[2,2,3,1]
[5,8,3,1,6,7,4,2]=>[3,1,5,8,7,4,6,2]=>[6,8,4,1,2,5,3,7]=>[2,1,3,2]
[4,7,1,6,8,5,2,3]=>[7,1,4,8,6,3,2,5]=>[2,8,5,1,3,6,7,4]=>[2,1,4,1]
[1,7,3,8,2,5,4,6]=>[7,3,5,6,2,8,1,4]=>[2,6,4,3,7,1,8,5]=>[2,1,2,2,1]
[8,4,1,3,6,7,5,2]=>[5,2,8,4,7,3,6,1]=>[4,7,1,5,2,6,3,8]=>[2,2,2,2]
[5,3,1,8,6,7,4,2]=>[5,1,8,2,7,6,3,4]=>[4,8,1,7,2,3,6,5]=>[2,2,3,1]
[2,7,1,6,5,8,4,3]=>[5,4,8,7,1,3,2,6]=>[4,5,1,2,8,6,7,3]=>[2,3,2,1]
[2,3,6,1,7,5,4,8]=>[7,6,1,2,4,3,5,8]=>[2,3,8,7,5,6,4,1]=>[3,1,2,1,1]
[2,7,1,4,8,6,5,3]=>[8,7,4,6,1,3,2,5]=>[1,2,5,3,8,6,7,4]=>[3,2,2,1]
[6,2,7,1,4,3,5,8]=>[6,2,4,5,1,7,3,8]=>[3,7,5,4,8,2,6,1]=>[2,1,2,2,1]
[8,3,2,6,5,1,7,4]=>[8,2,6,3,5,4,7,1]=>[1,7,3,6,4,5,2,8]=>[2,2,2,2]
[2,6,8,4,7,1,3,5]=>[6,4,2,7,8,1,5,3]=>[3,5,7,2,1,8,4,6]=>[3,1,2,2]
[7,8,6,3,2,5,4,1]=>[4,8,5,1,7,6,3,2]=>[5,1,4,8,2,3,6,7]=>[1,3,4]
[5,2,8,6,3,1,4,7]=>[6,5,1,7,2,4,8,3]=>[3,4,8,2,7,5,1,6]=>[3,2,1,2]
[1,6,4,8,2,3,5,7]=>[5,3,6,2,7,8,1,4]=>[4,6,3,7,2,1,8,5]=>[2,2,1,2,1]
[2,8,5,6,4,1,7,3]=>[3,8,6,5,1,4,7,2]=>[6,1,3,4,8,5,2,7]=>[1,4,1,2]
[1,4,7,3,5,8,6,2]=>[8,2,4,5,3,7,1,6]=>[1,7,5,4,6,2,8,3]=>[2,1,2,2,1]
[8,6,1,4,3,2,7,5]=>[5,4,8,3,6,2,7,1]=>[4,5,1,6,3,7,2,8]=>[2,2,2,2]
[7,3,8,2,4,1,5,6]=>[2,4,6,5,7,1,8,3]=>[7,5,3,4,2,8,1,6]=>[1,1,2,2,2]
[6,3,7,8,1,2,5,4]=>[8,2,5,1,6,3,7,4]=>[1,7,4,8,3,6,2,5]=>[2,2,2,2]
[7,6,1,5,2,3,8,4]=>[8,5,6,3,4,2,1,7]=>[1,4,3,6,5,7,8,2]=>[2,2,3,1]
[5,1,8,6,7,2,3,4]=>[6,1,7,4,8,5,2,3]=>[3,8,2,5,1,4,7,6]=>[2,2,3,1]
[5,7,1,6,8,2,3,4]=>[6,1,7,4,8,3,2,5]=>[3,8,2,5,1,6,7,4]=>[2,2,3,1]
[6,8,4,2,1,7,3,5]=>[4,7,3,1,8,5,6,2]=>[5,2,6,8,1,4,3,7]=>[1,3,2,2]
[6,4,1,3,7,8,5,2]=>[5,2,8,4,1,7,3,6]=>[4,7,1,5,8,2,6,3]=>[2,3,2,1]
[6,8,5,4,3,7,1,2]=>[1,7,5,4,3,8,6,2]=>[8,2,4,5,6,1,3,7]=>[1,4,3]
[6,1,2,4,8,3,7,5]=>[8,4,6,7,2,1,3,5]=>[1,5,3,2,7,8,6,4]=>[2,1,3,1,1]
[2,5,6,8,1,4,7,3]=>[2,6,3,8,1,5,7,4]=>[7,3,6,1,8,4,2,5]=>[1,2,2,1,2]
[4,1,6,5,2,3,8,7]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[1,4,1,1,1]
[4,5,1,7,8,6,2,3]=>[1,2,7,4,8,6,3,5]=>[8,7,2,5,1,3,6,4]=>[1,1,2,3,1]
[8,5,7,3,4,6,2,1]=>[4,2,5,8,7,6,3,1]=>[5,7,4,1,2,3,6,8]=>[2,1,5]
[6,8,7,4,3,5,2,1]=>[1,5,4,8,7,6,3,2]=>[8,4,5,1,2,3,6,7]=>[1,2,5]
[6,8,7,5,3,4,2,1]=>[1,5,8,7,6,4,3,2]=>[8,4,1,2,3,5,6,7]=>[1,1,6]
[5,8,6,2,4,7,3,1]=>[1,5,8,4,3,7,6,2]=>[8,4,1,5,6,2,3,7]=>[1,1,3,3]
[4,8,6,2,5,7,3,1]=>[5,8,1,4,3,7,6,2]=>[4,1,8,5,6,2,3,7]=>[1,2,2,3]
[1,6,4,7,5,3,2,8]=>[7,3,2,6,5,1,4,8]=>[2,6,7,3,4,8,5,1]=>[3,3,1,1]
[1,6,5,3,2,7,4,8]=>[4,7,5,3,1,2,6,8]=>[5,2,4,6,8,7,3,1]=>[1,4,1,1,1]
[1,6,8,7,4,5,3,2]=>[2,5,8,7,6,4,1,3]=>[7,4,1,2,3,5,8,6]=>[1,1,5,1]
[1,4,7,5,3,2,6,8]=>[6,2,5,4,7,1,3,8]=>[3,7,4,5,2,8,6,1]=>[2,2,2,1,1]
[1,7,5,4,3,2,8,6]=>[5,4,3,8,6,1,2,7]=>[4,5,6,1,3,8,7,2]=>[3,3,1,1]
[1,4,7,5,3,2,8,6]=>[5,2,4,8,6,1,3,7]=>[4,7,5,1,3,8,6,2]=>[2,1,3,1,1]
[1,7,4,6,8,5,3,2]=>[4,8,3,2,7,6,1,5]=>[5,1,6,7,2,3,8,4]=>[1,3,3,1]
[6,8,7,2,3,5,4,1]=>[8,4,1,5,7,6,3,2]=>[1,5,8,4,2,3,6,7]=>[3,1,4]
[5,7,6,1,8,2,4,3]=>[1,8,6,7,4,3,2,5]=>[8,1,3,2,5,6,7,4]=>[1,2,4,1]
[4,8,6,5,7,2,3,1]=>[6,4,1,3,8,7,5,2]=>[3,5,8,6,1,2,4,7]=>[3,1,4]
[8,5,6,2,4,7,3,1]=>[5,2,8,4,3,7,6,1]=>[4,7,1,5,6,2,3,8]=>[2,3,3]
[8,1,3,6,4,5,2,7]=>[5,7,3,6,2,4,8,1]=>[4,2,6,3,7,5,1,8]=>[1,2,2,1,2]
[1,2,3,7,4,8,5,9,6]=>[9,7,5,1,2,3,4,6,8]=>[1,3,5,9,8,7,6,4,2]=>[4,1,1,1,1,1]
[1,2,3,4,8,5,9,6,10,7]=>[10,8,6,1,2,3,4,5,7,9]=>[1,3,5,10,9,8,7,6,4,2]=>[4,1,1,1,1,1,1]
[4,3,1,6,2,5,8,7]=>[2,1,8,5,3,4,6,7]=>[7,8,1,4,6,5,3,2]=>[2,3,1,1,1]
[7,1,2,4,8,3,5,6]=>[4,6,7,8,2,3,1,5]=>[5,3,2,1,7,6,8,4]=>[1,1,1,2,2,1]
[8,6,1,3,5,7,4,2]=>[5,8,4,7,3,2,6,1]=>[4,1,5,2,6,7,3,8]=>[1,2,3,2]
[7,1,5,8,2,3,4,6]=>[5,6,3,7,8,2,1,4]=>[4,3,6,2,1,7,8,5]=>[1,2,1,3,1]
[3,6,8,5,1,4,2,7]=>[7,5,1,2,6,4,8,3]=>[2,4,8,7,3,5,1,6]=>[3,1,2,2]
[5,2,4,1,6,8,3,7]=>[5,2,3,1,7,8,4,6]=>[4,7,6,8,2,1,5,3]=>[2,2,1,2,1]
[1,3,2,5,4,7,9,6,8]=>[2,4,6,8,9,1,3,5,7]=>[8,6,4,2,1,9,7,5,3]=>[1,1,1,1,2,1,1,1]
[1,3,2,5,4,7,6,10,8,9]=>[2,4,6,9,10,1,3,5,7,8]=>[9,7,5,2,1,10,8,6,4,3]=>[1,1,1,1,2,1,1,1,1]
[2,5,3,4,6,8,1,7]=>[3,4,1,2,5,7,8,6]=>[6,5,8,7,4,2,1,3]=>[1,2,1,1,1,2]
[4,7,1,2,5,6,3,8]=>[5,1,7,3,4,6,2,8]=>[4,8,2,6,5,3,7,1]=>[2,2,1,2,1]
[6,7,3,1,8,2,4,5]=>[6,3,7,1,8,4,2,5]=>[3,6,2,8,1,5,7,4]=>[2,2,3,1]
[7,3,1,4,6,2,8,5]=>[2,8,4,6,3,5,1,7]=>[7,1,5,3,6,4,8,2]=>[1,2,2,2,1]
[7,4,1,2,5,6,3,8]=>[5,7,3,2,4,6,1,8]=>[4,2,6,7,5,3,8,1]=>[1,3,1,2,1]
[5,4,1,3,6,8,7,2]=>[8,4,2,1,5,7,3,6]=>[1,5,7,8,4,2,6,3]=>[4,1,2,1]
[5,7,4,8,1,6,3,2]=>[1,3,8,7,5,2,6,4]=>[8,6,1,2,4,7,3,5]=>[1,1,4,2]
[4,3,1,2,5,7,6,8]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]
[1,2,4,7,8,5,6,3]=>[6,4,8,3,7,1,2,5]=>[3,5,1,6,2,8,7,4]=>[2,2,2,1,1]
[8,3,6,5,7,4,2,1]=>[4,3,8,2,7,6,5,1]=>[5,6,1,7,2,3,4,8]=>[2,2,4]
[8,2,6,5,7,4,3,1]=>[4,3,8,7,2,6,5,1]=>[5,6,1,2,7,3,4,8]=>[2,3,3]
[8,4,7,1,5,2,6,3]=>[2,8,6,4,5,7,3,1]=>[7,1,3,5,4,2,6,8]=>[1,3,1,3]
[8,2,6,3,7,5,4,1]=>[8,7,4,2,3,6,5,1]=>[1,2,5,7,6,3,4,8]=>[4,1,3]
[8,5,7,1,4,3,6,2]=>[6,5,2,8,4,7,3,1]=>[3,4,7,1,5,2,6,8]=>[3,2,3]
[5,3,1,8,4,2,6,7]=>[2,6,5,1,7,8,3,4]=>[7,3,4,8,2,1,6,5]=>[1,3,1,2,1]
[4,5,3,6,8,7,1,2]=>[1,3,2,4,7,8,6,5]=>[8,6,7,5,2,1,3,4]=>[1,2,1,1,3]
[2,1,6,5,8,7,3,4]=>[4,3,7,8,1,6,2,5]=>[5,6,2,1,8,3,7,4]=>[2,1,2,2,1]
[6,1,5,4,7,3,8,2]=>[4,3,6,5,1,8,2,7]=>[5,6,3,4,8,1,7,2]=>[2,3,2,1]
[3,1,8,4,2,7,6,5]=>[8,1,4,7,5,6,2,3]=>[1,8,5,2,4,3,7,6]=>[2,1,2,2,1]
[8,2,3,1,7,6,4,5]=>[7,8,2,3,6,4,5,1]=>[2,1,7,6,3,5,4,8]=>[1,2,1,2,2]
[7,2,5,8,3,1,4,6]=>[6,5,2,3,7,1,8,4]=>[3,4,7,6,2,8,1,5]=>[3,1,2,2]
[6,8,2,3,1,7,4,5]=>[3,4,7,1,8,5,6,2]=>[6,5,2,8,1,4,3,7]=>[1,1,2,2,2]
[8,6,7,4,1,3,5,2]=>[6,8,5,4,2,7,3,1]=>[3,1,4,5,7,2,6,8]=>[1,4,3]
[4,1,3,6,5,2,8,7]=>[5,3,1,4,8,2,6,7]=>[4,6,8,5,1,7,3,2]=>[3,1,2,1,1]
[4,6,3,2,5,1,8,7]=>[1,4,3,5,2,8,6,7]=>[8,5,6,4,7,1,3,2]=>[1,2,2,2,1]
[4,8,3,2,6,5,7,1]=>[1,3,6,4,5,8,7,2]=>[8,6,3,5,4,1,2,7]=>[1,1,2,1,3]
[4,8,3,6,5,2,7,1]=>[6,1,3,5,4,8,7,2]=>[3,8,6,4,5,1,2,7]=>[2,1,2,3]
[8,1,6,2,5,4,7,3]=>[6,5,8,4,2,3,7,1]=>[3,4,1,5,7,6,2,8]=>[2,3,1,2]
[2,4,3,8,6,1,7,5]=>[8,2,6,1,3,5,7,4]=>[1,7,3,8,6,4,2,5]=>[2,2,1,1,2]
[2,6,3,8,5,4,7,1]=>[6,5,2,8,1,3,7,4]=>[3,4,7,1,8,6,2,5]=>[3,2,1,2]
[6,1,3,2,5,8,7,4]=>[8,3,5,7,2,1,4,6]=>[1,6,4,2,7,8,5,3]=>[2,1,3,1,1]
[6,8,4,2,5,3,7,1]=>[6,4,3,1,5,8,7,2]=>[3,5,6,8,4,1,2,7]=>[4,1,3]
[6,8,4,3,5,2,7,1]=>[4,3,1,6,5,8,7,2]=>[5,6,8,3,4,1,2,7]=>[3,2,3]
[8,1,4,6,5,3,7,2]=>[6,3,5,4,8,2,7,1]=>[3,6,4,5,1,7,2,8]=>[2,2,2,2]
[3,5,4,6,1,2,8,7]=>[3,1,2,8,5,4,6,7]=>[6,8,7,1,4,5,3,2]=>[2,1,3,1,1]
[7,3,5,6,1,8,2,4]=>[7,2,3,8,5,4,1,6]=>[2,7,6,1,4,5,8,3]=>[2,1,4,1]
[5,7,6,3,4,2,8,1]=>[1,4,6,5,3,2,8,7]=>[8,5,3,4,6,7,1,2]=>[1,1,4,2]
[4,6,7,2,3,5,8,1]=>[1,4,5,2,6,3,8,7]=>[8,5,4,7,3,6,1,2]=>[1,1,2,2,2]
[6,5,4,8,7,2,3,1]=>[3,2,1,6,8,7,5,4]=>[6,7,8,3,1,2,4,5]=>[3,1,4]
[4,8,7,6,5,3,2,1,9]=>[8,7,6,1,5,4,3,2,9]=>[2,3,4,9,5,6,7,8,1]=>[4,4,1]
[5,9,8,7,6,4,3,2,1,10]=>[9,8,7,1,6,5,4,3,2,10]=>[2,3,4,10,5,6,7,8,9,1]=>[4,5,1]
[2,1,3,4,5,9,8,6,7]=>[8,9,1,7,2,3,4,5,6]=>[2,1,9,3,8,7,6,5,4]=>[1,2,2,1,1,1,1]
[1,2,3,4,5,9,6,7,10,8]=>[10,7,8,1,2,3,4,5,6,9]=>[1,4,3,10,9,8,7,6,5,2]=>[2,2,1,1,1,1,1,1]
[1,8,5,6,2,3,7,4]=>[8,5,3,6,4,7,1,2]=>[1,4,6,3,5,2,8,7]=>[3,2,2,1]
[7,2,4,6,8,1,5,3]=>[8,3,6,2,4,1,7,5]=>[1,6,3,7,5,8,2,4]=>[2,2,2,2]
[6,2,5,4,7,8,1,3]=>[4,3,7,2,1,5,8,6]=>[5,6,2,7,8,4,1,3]=>[2,3,1,2]
[3,8,2,6,1,7,4,5]=>[7,8,1,3,5,4,6,2]=>[2,1,8,6,4,5,3,7]=>[1,2,1,2,2]
[8,5,6,1,3,2,7,4]=>[5,8,4,2,6,3,7,1]=>[4,1,5,7,3,6,2,8]=>[1,3,2,2]
[5,3,7,8,2,6,1,4]=>[5,1,7,2,3,8,6,4]=>[4,8,2,7,6,1,3,5]=>[2,2,1,3]
[4,5,8,3,6,1,7,2]=>[1,2,4,8,6,5,7,3]=>[8,7,5,1,3,4,2,6]=>[1,1,1,3,2]
[6,3,1,8,7,4,5,2]=>[6,8,2,1,7,5,3,4]=>[3,1,7,8,2,4,6,5]=>[1,3,3,1]
[8,6,3,2,7,4,5,1]=>[3,6,8,4,2,7,5,1]=>[6,3,1,5,7,2,4,8]=>[1,1,3,3]
[1,3,6,8,7,4,5,2]=>[3,6,8,7,2,5,1,4]=>[6,3,1,2,7,4,8,5]=>[1,1,3,2,1]
[5,7,1,3,6,2,4,8]=>[4,6,1,7,3,5,2,8]=>[5,3,8,2,6,4,7,1]=>[1,2,2,2,1]
[3,6,4,1,2,5,7,8]=>[1,4,5,3,6,2,7,8]=>[8,5,4,6,3,7,2,1]=>[1,1,2,2,1,1]
[4,7,1,3,2,5,8,6]=>[4,1,8,3,5,6,2,7]=>[5,8,1,6,4,3,7,2]=>[2,2,1,2,1]
[4,7,1,3,2,6,8,5]=>[4,1,6,8,3,5,2,7]=>[5,8,3,1,6,4,7,2]=>[2,1,2,2,1]
[5,7,1,3,6,2,8,4]=>[8,4,1,6,3,5,2,7]=>[1,5,8,3,6,4,7,2]=>[3,2,2,1]
[6,8,2,5,7,3,1,4]=>[7,6,3,1,4,8,5,2]=>[2,3,6,8,5,1,4,7]=>[4,1,3]
[5,8,6,3,4,7,2,1]=>[1,4,5,3,8,7,6,2]=>[8,5,4,6,1,2,3,7]=>[1,1,2,4]
[3,7,5,4,2,8,1,6]=>[5,4,1,3,7,2,8,6]=>[4,5,8,6,2,7,1,3]=>[3,1,2,2]
[4,6,5,1,7,8,2,3]=>[7,1,5,3,2,8,4,6]=>[2,8,4,6,7,1,5,3]=>[2,3,2,1]
[3,6,5,1,8,2,4,7]=>[6,7,1,3,2,8,4,5]=>[3,2,8,6,7,1,5,4]=>[1,2,2,2,1]
[5,8,7,3,4,2,6,1]=>[1,4,6,5,8,7,3,2]=>[8,5,3,4,1,2,6,7]=>[1,1,2,4]
[8,7,6,5,4,1,9,3,2]=>[9,8,6,5,4,3,2,1,7]=>[1,2,4,5,6,7,8,9,3]=>[8,1]
[6,9,5,4,3,2,1,7,8]=>[1,7,6,5,4,3,8,9,2]=>[9,3,4,5,6,7,2,1,8]=>[1,5,1,2]
[9,8,7,6,5,4,1,10,3,2]=>[10,9,7,6,5,4,3,2,1,8]=>[1,2,4,5,6,7,8,9,10,3]=>[9,1]
[8,7,6,5,1,9,4,3,2]=>[9,8,7,5,4,3,2,1,6]=>[1,2,3,5,6,7,8,9,4]=>[8,1]
[8,5,2,3,7,4,6,1]=>[6,8,3,2,4,7,5,1]=>[3,1,6,7,5,2,4,8]=>[1,3,1,3]
[6,3,1,5,4,8,2,7]=>[2,5,4,7,1,8,3,6]=>[7,4,5,2,8,1,6,3]=>[1,2,2,2,1]
[4,7,6,3,5,2,8,1]=>[4,6,1,5,3,2,8,7]=>[5,3,8,4,6,7,1,2]=>[1,2,3,2]
[1,7,5,3,4,8,6,2]=>[8,4,3,5,2,7,1,6]=>[1,5,6,4,7,2,8,3]=>[3,2,2,1]
[5,8,2,3,4,7,6,1]=>[8,3,1,4,5,7,6,2]=>[1,6,8,5,4,2,3,7]=>[3,1,1,3]
[8,3,1,4,7,5,2,6]=>[2,7,4,6,8,3,5,1]=>[7,2,5,3,1,6,4,8]=>[1,2,1,2,2]
[5,3,1,6,4,8,7,2]=>[2,4,1,8,5,7,3,6]=>[7,5,8,1,4,2,6,3]=>[1,2,2,2,1]
[3,4,8,5,7,2,6,1]=>[4,6,8,1,2,7,5,3]=>[5,3,1,8,7,2,4,6]=>[1,1,2,1,3]
[8,5,1,2,7,6,4,3]=>[8,7,6,3,2,4,5,1]=>[1,2,3,6,7,5,4,8]=>[5,1,2]
[8,2,6,3,1,5,4,7]=>[4,7,2,5,6,3,8,1]=>[5,2,7,4,3,6,1,8]=>[1,2,1,2,2]
[3,7,8,5,6,2,4,1]=>[6,4,2,8,1,7,5,3]=>[3,5,7,1,8,2,4,6]=>[3,2,3]
[7,4,3,6,2,5,8,1]=>[3,2,5,6,4,1,8,7]=>[6,7,4,3,5,8,1,2]=>[2,1,3,2]
[4,3,8,7,1,6,2,5]=>[1,7,8,2,5,6,4,3]=>[8,2,1,7,4,3,5,6]=>[1,1,2,1,3]
[1,5,3,8,4,7,2,6]=>[5,2,7,8,3,6,1,4]=>[4,7,2,1,6,3,8,5]=>[2,1,2,2,1]
[8,2,3,1,6,5,7,4]=>[6,2,3,5,8,4,7,1]=>[3,7,6,4,1,5,2,8]=>[2,1,1,2,2]
[8,4,2,7,1,3,6,5]=>[8,3,2,5,6,7,4,1]=>[1,6,7,4,3,2,5,8]=>[3,1,1,3]
[4,7,2,3,6,5,8,1]=>[1,6,3,4,5,2,8,7]=>[8,3,6,5,4,7,1,2]=>[1,2,1,2,2]
[3,8,2,6,4,7,1,5]=>[5,7,1,3,4,8,6,2]=>[4,2,8,6,5,1,3,7]=>[1,2,1,1,3]
[1,7,5,8,6,2,4,3]=>[3,8,6,2,7,5,1,4]=>[6,1,3,7,2,4,8,5]=>[1,3,3,1]
[6,5,1,7,4,8,3,2]=>[5,4,2,1,8,7,3,6]=>[4,5,7,8,1,2,6,3]=>[4,3,1]
[10,9,8,6,7,5,4,3,2,1]=>[4,10,9,8,7,6,5,3,2,1]=>[7,1,2,3,4,5,6,8,9,10]=>[1,9]
[7,6,3,5,1,4,8,2]=>[3,6,8,5,4,2,1,7]=>[6,3,1,4,5,7,8,2]=>[1,1,5,1]
[6,5,4,1,7,2,3,8]=>[6,7,4,3,2,1,5,8]=>[3,2,5,6,7,8,4,1]=>[1,5,1,1]
[8,3,6,1,7,4,5,2]=>[6,8,2,7,4,3,5,1]=>[3,1,7,2,5,6,4,8]=>[1,2,3,2]
[7,1,2,6,4,8,3,5]=>[5,7,4,8,2,3,1,6]=>[4,2,5,1,7,6,8,3]=>[1,2,2,2,1]
[3,5,1,8,6,2,4,7]=>[6,1,2,7,5,8,3,4]=>[3,8,7,2,4,1,6,5]=>[2,1,2,2,1]
[9,8,7,6,4,3,2,5,1]=>[7,6,5,9,8,4,3,2,1]=>[3,4,5,1,2,6,7,8,9]=>[3,6]
[10,9,7,6,8,5,4,3,2,1]=>[4,3,10,9,8,7,6,5,2,1]=>[7,8,1,2,3,4,5,6,9,10]=>[2,8]
[10,8,7,6,9,5,4,3,2,1]=>[4,3,2,10,9,8,7,6,5,1]=>[7,8,9,1,2,3,4,5,6,10]=>[3,7]
[8,9,7,6,4,3,2,1,5]=>[8,7,6,5,1,9,4,3,2]=>[2,3,4,5,9,1,6,7,8]=>[5,4]
[9,8,7,6,5,3,4,2,1]=>[6,9,8,7,5,4,3,2,1]=>[4,1,2,3,5,6,7,8,9]=>[1,8]
[8,1,6,7,4,5,3,2]=>[5,3,8,7,6,2,4,1]=>[4,6,1,2,3,7,5,8]=>[2,4,2]
[8,1,6,4,7,5,3,2]=>[8,4,3,7,6,2,5,1]=>[1,5,6,2,3,7,4,8]=>[3,3,2]
[6,4,8,1,5,3,7,2]=>[2,6,5,1,8,4,7,3]=>[7,3,4,8,1,5,2,6]=>[1,3,2,2]
[1,6,4,3,5,8,2,7]=>[4,3,5,2,7,8,1,6]=>[5,6,4,7,2,1,8,3]=>[2,2,1,2,1]
[5,1,4,3,7,8,6,2]=>[3,5,1,8,4,7,2,6]=>[6,4,8,1,5,2,7,3]=>[1,2,2,2,1]
[5,7,6,3,4,2,1,8]=>[1,4,7,6,5,3,2,8]=>[8,5,2,3,4,6,7,1]=>[1,1,5,1]
[4,1,3,7,6,5,2,8]=>[1,7,6,3,5,2,4,8]=>[8,2,3,6,4,7,5,1]=>[1,3,2,1,1]
[8,7,6,5,4,2,3,1,9]=>[6,8,7,5,4,3,2,1,9]=>[4,2,3,5,6,7,8,9,1]=>[1,7,1]
[4,3,6,1,2,7,8,5]=>[2,1,6,8,4,3,5,7]=>[7,8,3,1,5,6,4,2]=>[2,1,3,1,1]
[6,2,7,1,5,8,3,4]=>[7,5,8,2,1,4,3,6]=>[2,4,1,7,8,5,6,3]=>[2,3,2,1]
[5,8,3,6,7,2,4,1]=>[1,6,3,4,8,7,5,2]=>[8,3,6,5,1,2,4,7]=>[1,2,1,4]
[8,1,6,2,5,7,4,3]=>[5,8,7,4,2,3,6,1]=>[4,1,2,5,7,6,3,8]=>[1,4,1,2]
[2,7,1,5,3,6,8,4]=>[6,4,8,1,3,5,2,7]=>[3,5,1,8,6,4,7,2]=>[2,2,1,2,1]
[6,8,7,3,4,2,5,1]=>[4,1,6,5,8,7,3,2]=>[5,8,3,4,1,2,6,7]=>[2,2,4]
[1,8,6,2,4,7,5,3]=>[8,5,7,4,3,6,1,2]=>[1,4,2,5,6,3,8,7]=>[2,3,2,1]
[5,7,3,6,4,2,1,8]=>[1,7,3,6,5,4,2,8]=>[8,2,6,3,4,5,7,1]=>[1,2,4,1]
[5,7,3,6,4,1,8,2]=>[1,8,3,6,5,4,2,7]=>[8,1,6,3,4,5,7,2]=>[1,2,4,1]
[3,7,5,6,4,1,8,2]=>[3,8,6,1,5,4,2,7]=>[6,1,3,8,4,5,7,2]=>[1,3,3,1]
[8,9,6,7,4,5,2,1,3]=>[8,7,5,3,1,9,6,4,2]=>[2,3,5,7,9,1,4,6,8]=>[5,4]
[10,8,9,6,7,4,5,2,1,3]=>[9,8,6,4,2,10,7,5,3,1]=>[2,3,5,7,9,1,4,6,8,10]=>[5,5]
[6,7,2,3,5,8,1,4]=>[7,3,4,1,5,2,8,6]=>[2,6,5,8,4,7,1,3]=>[2,2,2,2]
[7,4,5,8,2,3,1,6]=>[2,5,3,7,6,1,8,4]=>[7,4,6,2,3,8,1,5]=>[1,2,3,2]
[2,1,3,8,5,4,6,7]=>[6,1,5,7,8,2,3,4]=>[3,8,4,2,1,7,6,5]=>[2,1,1,2,1,1]
[5,3,6,8,2,4,1,7]=>[5,2,1,3,7,6,8,4]=>[4,7,8,6,2,3,1,5]=>[3,1,2,2]
[1,7,8,6,3,2,4,5]=>[6,5,7,2,8,4,1,3]=>[3,4,2,7,1,5,8,6]=>[2,2,3,1]
[7,1,2,5,3,8,4,6]=>[7,4,8,2,3,5,1,6]=>[2,5,1,7,6,4,8,3]=>[2,2,1,2,1]
[3,7,4,2,5,1,8,6]=>[4,1,3,5,8,6,2,7]=>[5,8,6,4,1,3,7,2]=>[2,1,1,3,1]
[1,8,3,4,5,7,2,6]=>[3,4,5,7,8,6,1,2]=>[6,5,4,2,1,3,8,7]=>[1,1,1,1,3,1]
[2,6,7,5,3,8,1,4]=>[5,2,7,4,1,3,8,6]=>[4,7,2,5,8,6,1,3]=>[2,3,1,2]
[4,5,2,6,8,7,1,3]=>[1,4,2,7,8,3,6,5]=>[8,5,7,2,1,6,3,4]=>[1,2,1,2,2]
[4,5,2,6,8,3,1,7]=>[1,4,2,7,3,6,8,5]=>[8,5,7,2,6,3,1,4]=>[1,2,2,1,2]
[5,1,2,4,3,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[5,8,7,6,9,4,3,2,1]=>[2,1,2,1,1,1,1]
[7,1,2,3,4,6,5,8,9]=>[7,2,3,4,5,6,1,8,9]=>[3,8,7,6,5,4,9,2,1]=>[2,1,1,1,2,1,1]
[4,5,7,6,2,1,3,8]=>[1,2,6,5,7,4,3,8]=>[8,7,3,4,2,5,6,1]=>[1,1,2,3,1]
[7,8,2,6,5,4,3,1]=>[8,7,6,3,1,5,4,2]=>[1,2,3,6,8,4,5,7]=>[5,3]
[5,3,7,8,4,2,1,6]=>[1,7,6,2,5,3,8,4]=>[8,2,3,7,4,6,1,5]=>[1,3,2,2]
[7,3,6,8,1,5,4,2]=>[8,7,2,5,3,1,6,4]=>[1,2,7,4,6,8,3,5]=>[3,3,2]
[7,5,8,2,4,3,6,1]=>[6,4,2,5,1,8,7,3]=>[3,5,7,4,8,1,2,6]=>[3,2,3]
[8,1,5,3,4,6,2,7]=>[4,5,3,7,2,6,8,1]=>[5,4,6,2,7,3,1,8]=>[1,2,2,1,2]
[5,8,7,2,4,3,6,1]=>[1,6,4,5,8,7,3,2]=>[8,3,5,4,1,2,6,7]=>[1,2,1,4]
[1,7,2,4,8,5,6,3]=>[6,8,4,7,3,1,2,5]=>[3,1,5,2,6,8,7,4]=>[1,2,3,1,1]
[5,8,2,3,7,4,6,1]=>[6,1,8,3,4,7,5,2]=>[3,8,1,6,5,2,4,7]=>[2,2,1,3]
[7,8,2,3,5,4,6,1]=>[6,3,4,5,1,8,7,2]=>[3,6,5,4,8,1,2,7]=>[2,1,2,3]
[8,4,1,3,2,6,5,7]=>[4,7,3,2,5,6,8,1]=>[5,2,6,7,4,3,1,8]=>[1,3,1,1,2]
[8,7,2,3,5,4,6,1]=>[6,3,4,5,8,7,2,1]=>[3,6,5,4,1,2,7,8]=>[2,1,1,4]
[1,7,6,8,4,5,3,2]=>[5,3,2,8,7,6,1,4]=>[4,6,7,1,2,3,8,5]=>[3,4,1]
[2,7,3,1,8,5,6,4]=>[6,8,3,7,1,4,2,5]=>[3,1,6,2,8,5,7,4]=>[1,2,2,2,1]
[3,8,5,2,1,6,7,4]=>[4,6,1,3,8,5,7,2]=>[5,3,8,6,1,4,2,7]=>[1,2,1,2,2]
[8,3,5,1,7,6,4,2]=>[3,8,2,7,6,4,5,1]=>[6,1,7,2,3,5,4,8]=>[1,2,3,2]
[8,3,5,4,7,1,6,2]=>[4,2,3,8,6,7,5,1]=>[5,7,6,1,3,2,4,8]=>[2,1,2,3]
[6,4,1,5,7,8,2,3]=>[4,2,7,5,1,8,3,6]=>[5,7,2,4,8,1,6,3]=>[2,3,2,1]
[8,7,2,6,1,4,3,5]=>[7,3,5,6,8,4,2,1]=>[2,6,4,3,1,5,7,8]=>[2,1,1,4]
[6,1,7,3,8,2,4,5]=>[4,6,7,3,1,8,2,5]=>[5,3,2,6,8,1,7,4]=>[1,1,3,2,1]
[7,1,8,6,4,2,3,5]=>[6,7,5,8,4,2,1,3]=>[3,2,4,1,5,7,8,6]=>[1,2,4,1]
[4,1,3,5,8,2,6,7]=>[3,4,1,6,7,8,2,5]=>[6,5,8,3,2,1,7,4]=>[1,2,1,1,2,1]
[1,8,5,7,4,6,3,2]=>[3,5,8,7,6,4,1,2]=>[6,4,1,2,3,5,8,7]=>[1,1,5,1]
[1,7,2,8,6,5,3,4]=>[7,8,6,5,3,1,2,4]=>[2,1,3,4,6,8,7,5]=>[1,5,1,1]
[5,7,1,6,4,2,3,8]=>[6,1,7,5,3,4,2,8]=>[3,8,2,4,6,5,7,1]=>[2,3,2,1]
[4,8,2,7,5,1,6,3]=>[8,1,6,3,5,7,4,2]=>[1,8,3,6,4,2,5,7]=>[2,2,1,3]
[2,8,4,6,7,1,5,3]=>[8,3,6,4,7,1,5,2]=>[1,6,3,5,2,8,4,7]=>[2,2,2,2]
[3,8,5,1,4,2,6,7]=>[6,1,4,5,3,7,8,2]=>[3,8,5,4,6,2,1,7]=>[2,1,2,1,2]
[1,7,6,2,5,3,8,4]=>[8,6,4,5,3,1,2,7]=>[1,3,5,4,6,8,7,2]=>[3,3,1,1]
[1,7,5,2,4,3,8,6]=>[5,8,4,3,6,1,2,7]=>[4,1,5,6,3,8,7,2]=>[1,3,2,1,1]
[2,8,5,1,4,3,6,7]=>[6,4,5,1,3,7,8,2]=>[3,5,4,8,6,2,1,7]=>[2,2,1,1,2]
[9,7,6,5,4,3,2,8,1]=>[7,6,5,4,3,2,9,8,1]=>[3,4,5,6,7,8,1,2,9]=>[6,3]
[7,6,3,5,4,8,2,1]=>[5,3,4,2,1,8,7,6]=>[4,6,5,7,8,1,2,3]=>[2,3,3]
[3,1,2,5,7,6,8,4]=>[1,6,4,5,8,2,3,7]=>[8,3,5,4,1,7,6,2]=>[1,2,1,2,1,1]
[5,1,7,3,2,6,8,4]=>[4,6,1,8,5,2,3,7]=>[5,3,8,1,4,7,6,2]=>[1,2,3,1,1]
[4,8,2,3,7,5,1,6]=>[1,7,3,4,6,8,5,2]=>[8,2,6,5,3,1,4,7]=>[1,2,1,1,3]
[8,7,2,4,3,5,6,1]=>[5,3,4,6,8,7,2,1]=>[4,6,5,3,1,2,7,8]=>[2,1,1,4]
[8,1,2,4,7,3,5,6]=>[4,6,7,8,2,3,5,1]=>[5,3,2,1,7,6,4,8]=>[1,1,1,2,1,2]
[7,6,2,8,4,5,1,3]=>[7,5,8,3,2,1,6,4]=>[2,4,1,6,7,8,3,5]=>[2,4,2]
[6,8,1,5,7,3,2,4]=>[7,6,4,1,8,3,5,2]=>[2,3,5,8,1,6,4,7]=>[4,2,2]
[4,1,7,5,6,8,2,3]=>[1,4,7,5,3,8,2,6]=>[8,5,2,4,6,1,7,3]=>[1,1,3,2,1]
[3,7,6,2,1,4,5,8]=>[5,1,4,6,7,3,2,8]=>[4,8,5,3,2,6,7,1]=>[2,1,1,3,1]
[1,6,8,7,2,5,4,3]=>[2,8,7,5,6,4,1,3]=>[7,1,2,4,3,5,8,6]=>[1,3,3,1]
[1,4,8,7,6,3,5,2]=>[6,8,7,2,5,4,1,3]=>[3,1,2,7,4,5,8,6]=>[1,3,3,1]
[1,2,3,4,7,5,6,9,8]=>[9,6,1,2,3,4,5,7,8]=>[1,4,9,8,7,6,5,3,2]=>[3,1,1,1,1,1,1]
[3,1,8,4,5,2,7,6]=>[1,4,5,8,6,7,2,3]=>[8,5,4,1,3,2,7,6]=>[1,1,1,2,2,1]
[2,3,7,6,1,8,4,5]=>[7,8,5,1,2,4,3,6]=>[2,1,4,8,7,5,6,3]=>[1,3,1,2,1]
[4,8,5,2,1,3,7,6]=>[1,4,8,5,3,6,7,2]=>[8,5,1,4,6,3,2,7]=>[1,1,3,1,2]
[5,8,4,2,1,3,7,6]=>[4,1,8,5,3,6,7,2]=>[5,8,1,4,6,3,2,7]=>[2,3,1,2]
[9,8,7,6,5,3,1,4,2]=>[9,7,6,8,5,4,3,2,1]=>[1,3,4,2,5,6,7,8,9]=>[3,6]
[9,8,7,6,4,1,5,3,2]=>[9,8,6,5,7,4,3,2,1]=>[1,2,4,5,3,6,7,8,9]=>[4,5]
[9,7,1,8,6,5,4,3,2]=>[9,8,7,6,5,3,2,4,1]=>[1,2,3,4,5,7,8,6,9]=>[7,2]
[6,2,5,3,1,8,7,4]=>[8,4,2,3,1,7,5,6]=>[1,5,7,6,8,2,4,3]=>[3,2,2,1]
[6,4,5,3,8,7,1,2]=>[2,4,3,1,7,8,6,5]=>[7,5,6,8,2,1,3,4]=>[1,3,1,3]
[1,6,4,5,8,7,3,2]=>[8,3,2,4,7,6,1,5]=>[1,6,7,5,2,3,8,4]=>[3,1,3,1]
[8,4,7,5,2,3,1,6]=>[2,5,7,6,4,8,3,1]=>[7,4,2,3,5,1,6,8]=>[1,1,3,3]
[8,2,7,4,5,3,1,6]=>[4,7,6,2,5,8,3,1]=>[5,2,3,7,4,1,6,8]=>[1,3,1,3]
[8,2,4,7,5,3,1,6]=>[7,3,6,2,5,8,4,1]=>[2,6,3,7,4,1,5,8]=>[2,2,1,3]
[8,2,6,7,5,3,1,4]=>[7,6,3,8,2,5,4,1]=>[2,3,6,1,7,4,5,8]=>[3,2,3]
[8,4,6,7,5,3,1,2]=>[7,2,3,8,6,5,4,1]=>[2,7,6,1,3,4,5,8]=>[2,1,5]
[6,4,5,8,7,3,1,2]=>[2,3,1,7,8,6,5,4]=>[7,6,8,2,1,3,4,5]=>[1,2,1,4]
[6,2,8,7,5,3,1,4]=>[7,6,1,8,5,2,4,3]=>[2,3,8,1,4,7,5,6]=>[3,3,2]
[4,6,5,3,8,7,1,2]=>[4,1,3,2,7,8,6,5]=>[5,8,6,7,2,1,3,4]=>[2,2,1,3]
[6,7,2,4,5,3,1,8]=>[4,7,3,1,6,5,2,8]=>[5,2,6,8,3,4,7,1]=>[1,3,3,1]
[2,8,4,7,5,3,1,6]=>[7,3,6,5,8,1,4,2]=>[2,6,3,4,1,8,5,7]=>[2,2,2,2]
[5,8,7,4,6,3,1,2]=>[7,1,4,8,6,5,3,2]=>[2,8,5,1,3,4,6,7]=>[2,1,5]
[6,5,8,4,7,2,1,3]=>[2,1,7,6,4,8,5,3]=>[7,8,2,3,5,1,4,6]=>[2,3,3]
[4,8,6,2,5,7,1,3]=>[7,1,4,5,3,8,6,2]=>[2,8,5,4,6,1,3,7]=>[2,1,2,3]
[8,1,6,2,5,7,3,4]=>[7,5,8,4,2,3,6,1]=>[2,4,1,5,7,6,3,8]=>[2,3,1,2]
[6,8,1,2,4,7,3,5]=>[5,7,8,3,1,4,6,2]=>[4,2,1,6,8,5,3,7]=>[1,1,3,1,2]
[8,1,5,3,2,7,4,6]=>[4,7,3,8,2,5,6,1]=>[5,2,6,1,7,4,3,8]=>[1,2,2,1,2]
[8,3,7,6,2,5,4,1]=>[8,5,7,2,6,4,3,1]=>[1,4,2,7,3,5,6,8]=>[2,2,4]
[4,6,1,3,5,8,2,7]=>[4,1,5,7,2,8,3,6]=>[5,8,4,2,7,1,6,3]=>[2,1,2,2,1]
[4,5,1,3,8,7,2,6]=>[1,7,2,8,4,6,3,5]=>[8,2,7,1,5,3,6,4]=>[1,2,2,2,1]
[6,2,7,1,8,3,4,5]=>[6,7,8,2,1,4,3,5]=>[3,2,1,7,8,5,6,4]=>[1,1,3,2,1]
[6,4,5,8,1,7,2,3]=>[2,7,3,1,8,5,6,4]=>[7,2,6,8,1,4,3,5]=>[1,3,2,2]
[6,2,8,5,1,4,7,3]=>[6,8,5,2,1,4,7,3]=>[3,1,4,7,8,5,2,6]=>[1,4,1,2]
[2,4,7,6,1,8,3,5]=>[7,8,2,5,1,4,3,6]=>[2,1,7,4,8,5,6,3]=>[1,2,2,2,1]
[10,8,9,7,6,5,4,3,2,1]=>[2,10,9,8,7,6,5,4,3,1]=>[9,1,2,3,4,5,6,7,8,10]=>[1,9]
[7,4,5,8,6,3,2,1]=>[8,2,3,1,7,6,5,4]=>[1,7,6,8,2,3,4,5]=>[2,2,4]
[11,9,10,8,7,6,5,4,3,2,1]=>[2,11,10,9,8,7,6,5,4,3,1]=>[10,1,2,3,4,5,6,7,8,9,11]=>[1,10]
[9,6,7,8,5,4,3,2,1]=>[2,3,9,8,7,6,5,4,1]=>[8,7,1,2,3,4,5,6,9]=>[1,1,7]
[7,9,8,5,4,3,2,1,6]=>[1,8,7,6,5,4,9,3,2]=>[9,2,3,4,5,6,1,7,8]=>[1,5,3]
[1,6,2,3,8,5,7,4]=>[6,8,7,3,1,2,4,5]=>[3,1,2,6,8,7,5,4]=>[1,4,1,1,1]
[3,4,2,6,8,5,7,1]=>[1,2,4,6,8,3,7,5]=>[8,7,5,3,1,6,2,4]=>[1,1,1,1,2,2]
[1,6,8,5,7,4,3,2]=>[2,4,8,7,6,5,1,3]=>[7,5,1,2,3,4,8,6]=>[1,1,5,1]
[3,8,1,2,4,7,6,5]=>[8,1,7,3,4,5,6,2]=>[1,8,2,6,5,4,3,7]=>[2,2,1,1,2]
[1,4,5,7,3,6,8,2]=>[2,3,5,6,4,8,1,7]=>[7,6,4,3,5,1,8,2]=>[1,1,1,2,2,1]
[2,3,8,1,4,6,5,7]=>[7,1,2,4,5,6,8,3]=>[2,8,7,5,4,3,1,6]=>[2,1,1,1,1,2]
[3,6,2,4,7,5,8,1]=>[6,1,3,4,2,5,8,7]=>[3,8,6,5,7,4,1,2]=>[2,1,2,1,2]
[3,1,8,4,6,2,5,7]=>[1,4,6,7,5,8,2,3]=>[8,5,3,2,4,1,7,6]=>[1,1,1,2,2,1]
[4,2,7,3,5,8,1,6]=>[4,1,5,7,2,3,8,6]=>[5,8,4,2,7,6,1,3]=>[2,1,2,1,2]
[3,1,8,4,5,6,2,7]=>[1,4,5,7,6,8,2,3]=>[8,5,4,2,3,1,7,6]=>[1,1,1,2,2,1]
[4,2,7,8,6,3,1,5]=>[7,1,6,3,8,2,5,4]=>[2,8,3,6,1,7,4,5]=>[2,2,2,2]
[7,1,4,2,8,6,3,5]=>[3,7,8,6,2,4,1,5]=>[6,2,1,3,7,5,8,4]=>[1,1,3,2,1]
[2,3,7,4,8,1,6,5]=>[8,4,6,1,2,3,7,5]=>[1,5,3,8,7,6,2,4]=>[2,2,1,1,2]
[7,3,2,6,8,4,5,1]=>[6,2,4,8,3,1,7,5]=>[3,7,5,1,6,8,2,4]=>[2,1,3,2]
[2,4,5,7,1,6,8,3]=>[2,3,6,8,1,5,4,7]=>[7,6,3,1,8,4,5,2]=>[1,1,1,2,2,1]
[8,4,2,6,7,3,5,1]=>[2,6,4,8,3,7,5,1]=>[7,3,5,1,6,2,4,8]=>[1,2,2,3]
[4,1,5,7,8,6,2,3]=>[1,7,3,4,8,6,2,5]=>[8,2,6,5,1,3,7,4]=>[1,2,1,3,1]
[7,6,2,3,5,8,4,1]=>[5,8,3,4,2,1,7,6]=>[4,1,6,5,7,8,2,3]=>[1,2,3,2]
[2,8,5,7,6,3,4,1]=>[3,6,8,7,5,1,4,2]=>[6,3,1,2,4,8,5,7]=>[1,1,4,2]
[2,5,7,8,6,4,1,3]=>[7,2,3,8,6,1,5,4]=>[2,7,6,1,3,8,4,5]=>[2,1,3,2]
[8,7,4,6,2,5,3,1]=>[3,8,5,7,6,4,2,1]=>[6,1,4,2,3,5,7,8]=>[1,2,5]
[1,7,5,4,6,2,3,8]=>[6,4,3,7,5,1,2,8]=>[3,5,6,2,4,8,7,1]=>[3,3,1,1]
[6,2,7,5,3,1,4,8]=>[6,5,7,2,1,4,3,8]=>[3,4,2,7,8,5,6,1]=>[2,3,2,1]
[6,1,7,4,8,5,2,3]=>[4,7,3,1,8,6,2,5]=>[5,2,6,8,1,3,7,4]=>[1,3,3,1]
[8,2,4,6,3,1,7,5]=>[3,5,8,2,6,4,7,1]=>[6,4,1,7,3,5,2,8]=>[1,1,2,2,2]
[5,6,2,4,8,7,3,1]=>[1,8,4,2,7,3,6,5]=>[8,1,5,7,2,6,3,4]=>[1,3,2,2]
[7,8,1,4,5,6,2,3]=>[4,7,5,8,3,1,6,2]=>[5,2,4,1,6,8,3,7]=>[1,2,3,2]
[8,9,1,6,7,5,4,3,2]=>[4,9,8,7,6,3,1,5,2]=>[6,1,2,3,4,7,9,5,8]=>[1,6,2]
[8,3,1,2,5,4,7,6]=>[5,2,8,3,4,6,7,1]=>[4,7,1,6,5,3,2,8]=>[2,2,1,1,2]
[8,1,5,3,7,4,2,6]=>[7,4,3,6,8,2,5,1]=>[2,5,6,3,1,7,4,8]=>[3,1,2,2]
[1,2,6,7,8,3,5,4]=>[3,8,6,4,7,1,2,5]=>[6,1,3,5,2,8,7,4]=>[1,3,2,1,1]
[1,2,4,8,6,7,3,5]=>[7,5,8,3,6,1,2,4]=>[2,4,1,6,3,8,7,5]=>[2,2,2,1,1]
[8,1,2,6,5,7,3,4]=>[7,5,4,8,2,3,6,1]=>[2,4,5,1,7,6,3,8]=>[3,2,1,2]
[7,1,2,6,5,8,3,4]=>[7,5,4,8,2,3,1,6]=>[2,4,5,1,7,6,8,3]=>[3,2,2,1]
[7,4,8,3,5,6,2,1]=>[2,4,5,1,8,7,6,3]=>[7,5,4,8,1,2,3,6]=>[1,1,2,4]
[3,1,5,7,2,6,8,4]=>[1,3,6,8,5,2,4,7]=>[8,6,3,1,4,7,5,2]=>[1,1,1,3,1,1]
[3,1,7,5,2,6,8,4]=>[6,1,4,8,5,2,3,7]=>[3,8,5,1,4,7,6,2]=>[2,1,3,1,1]
[5,2,7,3,1,6,8,4]=>[4,6,1,8,2,5,3,7]=>[5,3,8,1,7,4,6,2]=>[1,2,2,2,1]
[4,6,3,1,2,7,8,5]=>[1,6,3,8,4,2,5,7]=>[8,3,6,1,5,7,4,2]=>[1,2,3,1,1]
[2,3,5,6,8,4,7,1]=>[3,4,6,8,1,2,7,5]=>[6,5,3,1,8,7,2,4]=>[1,1,1,2,1,2]
[2,4,5,8,3,6,7,1]=>[2,3,5,6,8,1,7,4]=>[7,6,4,3,1,8,2,5]=>[1,1,1,1,2,2]
[4,5,8,7,6,3,1,2]=>[7,8,1,2,6,5,4,3]=>[2,1,8,7,3,4,5,6]=>[1,2,1,4]
[8,7,4,6,5,3,1,2]=>[3,7,8,6,5,4,2,1]=>[6,2,1,3,4,5,7,8]=>[1,1,6]
[9,5,8,7,6,4,3,1,2]=>[8,9,2,7,6,5,4,3,1]=>[2,1,8,3,4,5,6,7,9]=>[1,2,6]
[8,1,4,3,6,2,5,7]=>[4,3,6,7,2,5,8,1]=>[5,6,3,2,7,4,1,8]=>[2,1,2,1,2]
[8,1,5,7,6,4,3,2]=>[8,3,7,6,5,2,4,1]=>[1,6,2,3,4,7,5,8]=>[2,4,2]
[1,6,3,7,8,4,2,5]=>[7,6,3,2,4,8,1,5]=>[2,3,6,7,5,1,8,4]=>[4,1,2,1]
[4,3,5,8,6,7,2,1]=>[1,5,8,2,3,7,6,4]=>[8,4,1,7,6,2,3,5]=>[1,1,2,1,3]
[7,1,4,8,5,6,3,2]=>[5,8,3,7,6,2,1,4]=>[4,1,6,2,3,7,8,5]=>[1,2,4,1]
[4,3,8,7,2,5,6,1]=>[1,5,6,8,2,7,4,3]=>[8,4,3,1,7,2,5,6]=>[1,1,1,2,3]
[1,7,3,8,6,4,5,2]=>[6,8,7,3,2,5,1,4]=>[3,1,2,6,7,4,8,5]=>[1,4,2,1]
[7,4,2,8,5,6,3,1]=>[2,5,8,7,3,1,6,4]=>[7,4,1,2,6,8,3,5]=>[1,1,4,2]
[3,4,8,2,6,7,5,1]=>[5,8,1,2,4,7,6,3]=>[4,1,8,7,5,2,3,6]=>[1,2,1,1,3]
[1,4,5,8,7,6,2,3]=>[7,8,2,3,6,5,1,4]=>[2,1,7,6,3,4,8,5]=>[1,2,1,3,1]
[5,2,1,3,8,4,6,7]=>[2,6,7,1,8,3,4,5]=>[7,3,2,8,1,6,5,4]=>[1,1,2,2,1,1]
[1,4,3,5,8,2,6,7]=>[3,2,4,6,7,8,1,5]=>[6,7,5,3,2,1,8,4]=>[2,1,1,1,2,1]
[2,1,3,8,6,4,5,7]=>[6,7,1,5,8,2,3,4]=>[3,2,8,4,1,7,6,5]=>[1,2,1,2,1,1]
[1,3,6,4,5,8,2,7]=>[4,5,2,3,7,8,1,6]=>[5,4,7,6,2,1,8,3]=>[1,2,1,1,2,1]
[6,1,4,3,5,8,2,7]=>[4,3,5,7,1,8,2,6]=>[5,6,4,2,8,1,7,3]=>[2,1,2,2,1]
[6,5,1,3,8,2,4,7]=>[4,6,7,2,1,8,3,5]=>[5,3,2,7,8,1,6,4]=>[1,1,3,2,1]
[1,4,3,8,6,2,5,7]=>[2,6,7,3,5,8,1,4]=>[7,3,2,6,4,1,8,5]=>[1,1,2,1,2,1]
[7,1,5,4,6,3,8,2]=>[4,3,6,5,8,2,1,7]=>[5,6,3,4,1,7,8,2]=>[2,2,3,1]
[8,9,7,6,5,4,3,2,10,1]=>[1,8,7,6,5,4,3,2,10,9]=>[10,3,4,5,6,7,8,9,1,2]=>[1,7,2]
[6,4,7,8,3,5,1,2]=>[7,2,1,5,3,8,6,4]=>[2,7,8,4,6,1,3,5]=>[3,2,3]
[3,5,6,7,1,8,4,2]=>[2,3,8,1,7,5,4,6]=>[7,6,1,8,2,4,5,3]=>[1,1,2,3,1]
[3,5,2,4,8,6,7,1]=>[6,1,2,8,3,4,7,5]=>[3,8,7,1,6,5,2,4]=>[2,1,2,1,2]
[3,7,6,1,4,8,5,2]=>[8,5,7,1,4,3,2,6]=>[1,4,2,8,5,6,7,3]=>[2,2,3,1]
[8,4,7,1,5,6,2,3]=>[2,7,5,8,4,6,3,1]=>[7,2,4,1,5,3,6,8]=>[1,2,2,3]
[2,7,8,3,6,1,5,4]=>[8,4,6,2,7,1,5,3]=>[1,5,3,7,2,8,4,6]=>[2,2,2,2]
[1,7,8,3,6,2,5,4]=>[8,4,6,2,7,5,1,3]=>[1,5,3,7,2,4,8,6]=>[2,2,3,1]
[7,4,3,5,8,1,6,2]=>[3,2,4,8,6,1,7,5]=>[6,7,5,1,3,8,2,4]=>[2,1,3,2]
[7,3,6,4,1,8,5,2]=>[4,8,2,7,5,3,1,6]=>[5,1,7,2,4,6,8,3]=>[1,2,4,1]
[7,1,6,4,3,8,5,2]=>[4,8,5,3,7,2,1,6]=>[5,1,4,6,2,7,8,3]=>[1,3,3,1]
[8,7,3,4,1,5,2,6]=>[3,7,5,4,6,8,2,1]=>[6,2,4,5,3,1,7,8]=>[1,3,1,3]
[7,2,6,4,3,8,5,1]=>[4,8,5,2,3,1,7,6]=>[5,1,4,7,6,8,2,3]=>[1,3,2,2]
[1,7,5,4,3,8,2,6]=>[5,4,3,7,2,8,1,6]=>[4,5,6,2,7,1,8,3]=>[3,2,2,1]
[4,6,7,1,3,8,2,5]=>[1,5,7,2,8,4,3,6]=>[8,4,2,7,1,5,6,3]=>[1,1,2,3,1]
[2,3,4,5,6,1,8,9,7]=>[1,2,3,4,5,7,9,6,8]=>[9,8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,2,1]
[2,3,4,5,6,7,1,9,10,8]=>[1,2,3,4,5,6,8,10,7,9]=>[10,9,8,7,6,5,3,1,4,2]=>[1,1,1,1,1,1,1,2,1]
[2,7,3,4,1,8,5,6]=>[3,4,7,8,1,5,2,6]=>[6,5,2,1,8,4,7,3]=>[1,1,1,2,2,1]
[8,6,4,5,1,3,7,2]=>[6,3,8,5,4,2,7,1]=>[3,6,1,4,5,7,2,8]=>[2,4,2]
[7,4,8,5,3,6,1,2]=>[7,2,5,4,1,8,6,3]=>[2,7,4,5,8,1,3,6]=>[2,3,3]
[8,4,6,5,1,3,7,2]=>[2,6,8,5,4,3,7,1]=>[7,3,1,4,5,6,2,8]=>[1,1,4,2]
[4,5,3,8,7,1,2,6]=>[1,3,2,6,7,8,5,4]=>[8,6,7,3,2,1,4,5]=>[1,2,1,1,3]
[8,5,4,7,6,1,2,3]=>[6,3,2,7,8,5,4,1]=>[3,6,7,2,1,4,5,8]=>[3,1,4]
[7,5,8,2,4,3,1,6]=>[7,4,2,6,5,1,8,3]=>[2,5,7,3,4,8,1,6]=>[3,3,2]
[8,2,3,5,4,1,7,6]=>[5,2,3,4,8,6,7,1]=>[4,7,6,5,1,3,2,8]=>[2,1,1,2,2]
[7,1,3,8,2,4,6,5]=>[8,3,5,6,7,2,1,4]=>[1,6,4,3,2,7,8,5]=>[2,1,1,3,1]
[7,2,3,6,4,1,8,5]=>[5,8,2,3,6,4,1,7]=>[4,1,7,6,3,5,8,2]=>[1,2,1,3,1]
[4,2,6,3,5,8,1,7]=>[4,1,5,2,3,7,8,6]=>[5,8,4,7,6,2,1,3]=>[2,2,1,1,2]
[7,4,2,6,8,5,3,1]=>[2,4,8,7,3,1,6,5]=>[7,5,1,2,6,8,3,4]=>[1,1,4,2]
[6,4,1,8,5,2,3,7]=>[6,2,7,5,1,8,3,4]=>[3,7,2,4,8,1,6,5]=>[2,3,2,1]
[8,4,1,6,3,5,2,7]=>[5,2,7,6,3,4,8,1]=>[4,7,2,3,6,5,1,8]=>[2,3,1,2]
[7,3,4,1,6,8,5,2]=>[2,3,5,8,7,4,1,6]=>[7,6,4,1,2,5,8,3]=>[1,1,1,4,1]
[8,6,2,5,7,3,4,1]=>[6,4,8,3,2,7,5,1]=>[3,5,1,6,7,2,4,8]=>[2,3,3]
[6,3,4,8,5,1,2,7]=>[2,3,6,1,7,5,8,4]=>[7,6,3,8,2,4,1,5]=>[1,1,2,2,2]
[7,2,6,8,3,4,5,1]=>[5,6,3,8,2,1,7,4]=>[4,3,6,1,7,8,2,5]=>[1,2,3,2]
[1,6,7,5,4,8,2,3]=>[2,7,5,4,3,8,1,6]=>[7,2,4,5,6,1,8,3]=>[1,4,2,1]
[1,8,5,4,2,6,3,7]=>[7,5,4,3,6,8,1,2]=>[2,4,5,6,3,1,8,7]=>[4,1,2,1]
[8,9,7,6,5,4,1,3,2]=>[9,7,1,8,6,5,4,3,2]=>[1,3,9,2,4,5,6,7,8]=>[3,6]
[9,10,8,7,6,5,4,1,3,2]=>[10,8,1,9,7,6,5,4,3,2]=>[1,3,10,2,4,5,6,7,8,9]=>[3,7]
[10,8,7,6,5,4,3,2,9,1]=>[8,7,6,5,4,3,2,10,9,1]=>[3,4,5,6,7,8,9,1,2,10]=>[7,3]
[5,7,3,6,2,1,4,8]=>[3,1,6,5,7,4,2,8]=>[6,8,3,4,2,5,7,1]=>[2,2,3,1]
[5,8,6,1,2,4,3,7]=>[7,4,1,5,6,3,8,2]=>[2,5,8,4,3,6,1,7]=>[3,1,2,2]
[4,1,5,7,3,6,8,2]=>[3,1,5,6,4,8,2,7]=>[6,8,4,3,5,1,7,2]=>[2,1,2,2,1]
[1,4,5,7,6,8,2,3]=>[7,2,3,5,4,8,1,6]=>[2,7,6,4,5,1,8,3]=>[2,1,2,2,1]
[5,7,2,1,6,8,4,3]=>[5,1,8,3,7,4,2,6]=>[4,8,1,6,2,5,7,3]=>[2,2,3,1]
[2,6,3,1,7,8,5,4]=>[5,8,3,1,2,7,4,6]=>[4,1,6,8,7,2,5,3]=>[1,3,1,2,1]
[6,2,5,7,4,1,8,3]=>[3,8,6,2,1,5,4,7]=>[6,1,3,7,8,4,5,2]=>[1,4,2,1]
[3,6,1,8,7,4,5,2]=>[6,2,8,1,7,5,3,4]=>[3,7,1,8,2,4,6,5]=>[2,2,3,1]
[4,7,1,3,5,6,8,2]=>[4,1,5,6,8,3,2,7]=>[5,8,4,3,1,6,7,2]=>[2,1,1,3,1]
[4,3,5,7,8,2,6,1]=>[1,6,2,3,4,8,7,5]=>[8,3,7,6,5,1,2,4]=>[1,2,1,1,3]
[5,3,2,7,6,4,1,8]=>[7,2,1,6,3,5,4,8]=>[2,7,8,3,6,4,5,1]=>[3,2,2,1]
[5,3,7,4,6,2,1,8]=>[4,1,7,2,6,5,3,8]=>[5,8,2,7,3,4,6,1]=>[2,2,3,1]
[5,7,3,2,1,8,6,4]=>[3,1,8,4,7,5,2,6]=>[6,8,1,5,2,4,7,3]=>[2,2,3,1]
[5,7,6,3,2,1,8,4]=>[1,5,4,8,6,3,2,7]=>[8,4,5,1,3,6,7,2]=>[1,2,4,1]
[1,7,3,5,4,2,6,8]=>[6,3,5,4,7,1,2,8]=>[3,6,4,5,2,8,7,1]=>[2,2,2,1,1]
[5,3,7,4,1,8,6,2]=>[4,1,8,2,7,5,3,6]=>[5,8,1,7,2,4,6,3]=>[2,2,3,1]
[7,3,5,4,1,6,8,2]=>[6,2,4,3,8,5,1,7]=>[3,7,5,6,1,4,8,2]=>[2,2,3,1]
[7,5,1,6,8,3,2,4]=>[7,6,4,2,8,3,1,5]=>[2,3,5,7,1,6,8,4]=>[4,3,1]
[5,3,1,7,6,8,2,4]=>[7,2,1,5,4,8,3,6]=>[2,7,8,4,5,1,6,3]=>[3,2,2,1]
[7,1,5,2,4,3,6,8]=>[6,4,5,2,3,7,1,8]=>[3,5,4,7,6,2,8,1]=>[2,2,1,2,1]
[6,8,7,3,2,1,5,4]=>[5,4,1,8,6,7,3,2]=>[4,5,8,1,3,2,6,7]=>[3,2,3]
[3,6,8,7,2,4,1,5]=>[5,2,7,1,6,8,4,3]=>[4,7,2,8,3,1,5,6]=>[2,2,1,3]
[5,7,3,6,2,1,8,4]=>[3,1,5,8,6,4,2,7]=>[6,8,4,1,3,5,7,2]=>[2,1,4,1]
[8,9,5,6,4,3,2,1,7]=>[3,8,7,6,5,4,1,9,2]=>[7,2,3,4,5,6,9,1,8]=>[1,6,2]
[9,10,7,6,5,4,3,2,1,8]=>[9,8,7,6,5,4,3,1,10,2]=>[2,3,4,5,6,7,8,10,1,9]=>[8,2]
[10,7,8,6,5,4,3,2,1,9]=>[2,9,8,7,6,5,4,3,10,1]=>[9,2,3,4,5,6,7,8,1,10]=>[1,7,2]
[6,8,2,1,5,4,3,7]=>[7,3,6,4,1,5,8,2]=>[2,6,3,5,8,4,1,7]=>[2,3,1,2]
[6,3,2,1,5,8,4,7]=>[3,2,5,7,1,8,4,6]=>[6,7,4,2,8,1,5,3]=>[2,1,2,2,1]
[4,3,5,6,2,8,1,7]=>[2,1,3,5,4,7,8,6]=>[7,8,6,4,5,2,1,3]=>[2,1,2,1,2]
[3,4,6,7,5,1,8,2]=>[3,8,1,2,6,5,4,7]=>[6,1,8,7,3,4,5,2]=>[1,2,1,3,1]
[7,4,1,2,5,6,8,3]=>[5,6,2,8,3,4,1,7]=>[4,3,7,1,6,5,8,2]=>[1,2,2,2,1]
[6,5,8,3,7,1,4,2]=>[4,2,1,8,6,7,5,3]=>[5,7,8,1,3,2,4,6]=>[3,2,3]
[9,8,7,6,4,1,5,2,3]=>[8,9,6,5,7,4,3,2,1]=>[2,1,4,5,3,6,7,8,9]=>[1,3,5]
[10,9,8,7,6,5,3,1,4,2]=>[10,8,7,9,6,5,4,3,2,1]=>[1,3,4,2,5,6,7,8,9,10]=>[3,7]
[1,5,2,4,7,6,8,3]=>[6,4,2,5,8,1,3,7]=>[3,5,7,4,1,8,6,2]=>[3,1,2,1,1]
[2,5,4,7,1,8,3,6]=>[3,2,7,8,1,5,4,6]=>[6,7,2,1,8,4,5,3]=>[2,1,2,2,1]
[1,5,4,7,3,8,2,6]=>[3,2,5,7,4,8,1,6]=>[6,7,4,2,5,1,8,3]=>[2,1,2,2,1]
[1,2,6,7,3,5,4,8]=>[7,5,3,6,1,2,4,8]=>[2,4,6,3,8,7,5,1]=>[3,2,1,1,1]
[8,1,2,4,6,3,5,7]=>[4,6,7,2,3,5,8,1]=>[5,3,2,7,6,4,1,8]=>[1,1,2,1,1,2]
[3,7,8,4,5,6,1,2]=>[4,7,5,1,2,8,6,3]=>[5,2,4,8,7,1,3,6]=>[1,3,1,3]
[1,3,8,6,7,4,5,2]=>[6,4,8,7,2,5,1,3]=>[3,5,1,2,7,4,8,6]=>[2,3,2,1]
[2,6,5,3,7,1,8,4]=>[8,4,3,1,2,6,5,7]=>[1,5,6,8,7,3,4,2]=>[4,1,2,1]
[5,7,1,3,6,4,8,2]=>[6,4,1,5,8,3,2,7]=>[3,5,8,4,1,6,7,2]=>[3,1,3,1]
[8,1,7,6,4,2,3,5]=>[6,7,5,8,4,2,3,1]=>[3,2,4,1,5,7,6,8]=>[1,2,3,2]
[1,8,6,3,7,4,5,2]=>[6,8,4,3,7,5,1,2]=>[3,1,5,6,2,4,8,7]=>[1,3,3,1]
[7,6,4,2,3,8,5,1]=>[8,4,3,5,2,1,7,6]=>[1,5,6,4,7,8,2,3]=>[3,3,2]
[3,5,6,8,2,4,7,1]=>[2,5,1,3,6,8,7,4]=>[7,4,8,6,3,1,2,5]=>[1,2,1,1,3]
[4,8,7,3,2,5,6,1]=>[5,1,4,6,8,7,3,2]=>[4,8,5,3,1,2,6,7]=>[2,1,1,4]
[5,6,2,8,7,4,3,1]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[1,1,4,2]
[6,2,8,3,7,4,5,1]=>[6,8,4,1,7,2,5,3]=>[3,1,5,8,2,7,4,6]=>[1,3,2,2]
[5,2,3,8,6,1,4,7]=>[6,7,2,1,3,5,8,4]=>[3,2,7,8,6,4,1,5]=>[1,3,1,1,2]
[1,4,3,8,5,6,2,7]=>[2,5,7,3,6,8,1,4]=>[7,4,2,6,3,1,8,5]=>[1,1,2,1,2,1]
[7,8,2,6,4,3,5,1]=>[6,5,8,3,1,7,4,2]=>[3,4,1,6,8,2,5,7]=>[2,3,3]
[4,5,8,7,2,3,6,1]=>[1,2,5,6,8,7,4,3]=>[8,7,4,3,1,2,5,6]=>[1,1,1,1,4]
[7,8,6,1,4,2,5,3]=>[8,6,4,5,1,7,3,2]=>[1,3,5,4,8,2,6,7]=>[3,2,3]
[5,1,3,6,4,2,7,8]=>[6,3,5,2,1,4,7,8]=>[3,6,4,7,8,5,2,1]=>[2,3,1,1,1]
[6,1,2,4,7,5,3,8]=>[7,4,6,2,3,1,5,8]=>[2,5,3,7,6,8,4,1]=>[2,2,2,1,1]
[8,3,1,4,6,7,2,5]=>[2,7,4,5,8,3,6,1]=>[7,2,5,4,1,6,3,8]=>[1,2,1,2,2]
[7,8,5,1,2,6,3,4]=>[7,8,4,5,3,1,6,2]=>[2,1,5,4,6,8,3,7]=>[1,2,3,2]
[6,4,5,1,8,7,3,2]=>[2,3,1,8,7,6,4,5]=>[7,6,8,1,2,3,5,4]=>[1,2,4,1]
[8,6,2,1,7,3,5,4]=>[8,3,6,7,4,2,5,1]=>[1,6,3,2,5,7,4,8]=>[2,1,3,2]
[5,6,3,4,7,2,8,1,9]=>[3,1,4,2,6,5,8,7,9]=>[7,9,6,8,4,5,2,3,1]=>[2,2,2,2,1]
[1,6,5,7,3,4,8,2]=>[5,3,2,6,4,8,1,7]=>[4,6,7,3,5,1,8,2]=>[3,2,2,1]
[7,6,4,1,2,5,8,3]=>[6,8,4,3,5,2,1,7]=>[3,1,5,6,4,7,8,2]=>[1,3,3,1]
[2,6,5,4,8,7,1,3]=>[4,3,2,7,8,1,6,5]=>[5,6,7,2,1,8,3,4]=>[3,1,2,2]
[5,6,7,1,3,2,4,8]=>[6,4,1,5,2,7,3,8]=>[3,5,8,4,7,2,6,1]=>[3,2,2,1]
[7,1,8,4,3,2,6,5]=>[5,4,8,6,7,2,1,3]=>[4,5,1,3,2,7,8,6]=>[2,2,3,1]
[2,1,4,9,3,5,6,7,8]=>[1,3,5,6,7,8,9,2,4]=>[9,7,5,4,3,2,1,8,6]=>[1,1,1,1,1,1,2,1]
[1,8,5,2,7,6,4,3]=>[3,8,7,6,4,5,1,2]=>[6,1,2,3,5,4,8,7]=>[1,4,2,1]
[1,7,6,8,2,5,4,3]=>[8,7,5,3,2,6,1,4]=>[1,2,4,6,7,3,8,5]=>[5,2,1]
[1,7,8,6,2,5,4,3]=>[8,7,5,2,6,4,1,3]=>[1,2,4,7,3,5,8,6]=>[4,3,1]
[4,6,5,7,1,8,2,3]=>[7,1,3,2,8,5,4,6]=>[2,8,6,7,1,4,5,3]=>[2,2,3,1]
[7,2,5,6,4,8,3,1]=>[3,5,4,8,2,1,7,6]=>[6,4,5,1,7,8,2,3]=>[1,2,3,2]
[7,4,6,2,8,5,3,1]=>[8,2,7,4,3,1,6,5]=>[1,7,2,5,6,8,3,4]=>[2,4,2]
[9,7,6,5,4,3,8,2,1]=>[6,5,4,3,2,9,8,7,1]=>[4,5,6,7,8,1,2,3,9]=>[5,4]
[10,9,7,6,5,4,8,3,2,1]=>[6,5,4,3,10,9,8,7,2,1]=>[5,6,7,8,1,2,3,4,9,10]=>[4,6]
[1,6,3,4,2,5,8,7]=>[3,4,8,5,1,2,6,7]=>[6,5,1,4,8,7,3,2]=>[1,1,3,1,1,1]
[1,4,3,7,6,2,5,8]=>[2,6,7,3,5,1,4,8]=>[7,3,2,6,4,8,5,1]=>[1,1,2,2,1,1]
[1,3,7,4,6,8,5,2]=>[5,8,4,2,3,7,1,6]=>[4,1,5,7,6,2,8,3]=>[1,3,1,2,1]
[4,8,3,1,7,6,2,5]=>[1,3,7,8,6,4,5,2]=>[8,6,2,1,3,5,4,7]=>[1,1,1,3,2]
[2,6,7,5,3,4,1,8]=>[5,2,7,6,1,4,3,8]=>[4,7,2,3,8,5,6,1]=>[2,3,2,1]
[2,4,1,7,5,6,8,3]=>[2,5,6,1,4,8,3,7]=>[7,4,3,8,5,1,6,2]=>[1,1,2,1,2,1]
[7,2,4,8,3,5,1,6]=>[3,5,7,2,6,1,8,4]=>[6,4,2,7,3,8,1,5]=>[1,1,2,2,2]
[5,6,1,4,3,8,7,2]=>[4,1,8,5,2,7,3,6]=>[5,8,1,4,7,2,6,3]=>[2,3,2,1]
[5,8,6,4,3,1,7,2]=>[8,1,6,5,4,3,7,2]=>[1,8,3,4,5,6,2,7]=>[2,4,2]
[4,1,3,7,8,6,5,2]=>[1,4,8,7,3,6,2,5]=>[8,5,1,2,6,3,7,4]=>[1,1,3,2,1]
Map
Lehmer-code to major-code bijection
Description
Sends a permutation to the unique permutation such that the Lehmer code is sent to the major code.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation σ is given by L(σ)=l1…ln with li=#{j>i:σj<σi}. In particular, li is the number of boxes in the i-th column of the Rothe diagram. For example, the Lehmer code of σ=[4,3,1,5,2] is 32010. The Lehmer code L:Sn ˜⟶ Sn is a bijection between permutations of size n and sequences l1…ln∈Nn with li≤i.
* The major code M(σ) of a permutation σ∈Sn is a way to encode a permutation as a sequence m1m2…mn with mi≥i. To define mi, let deli(σ) be the normalized permutation obtained by removing all σj<i from the one-line notation of σ. The i-th index is then given by
mi=maj(deli(σ))−maj(deli−1(σ)).
For example, the permutation [9,3,5,7,2,1,4,6,8] has major code [5,0,1,0,1,2,0,1,0] since
maj([8,2,4,6,1,3,5,7])=5,maj([7,1,3,5,2,4,6])=5,maj([6,2,4,1,3,5])=4,
maj([5,1,3,2,4])=4,maj([4,2,1,3])=3,maj([3,1,2])=1,maj([2,1])=1.
Observe that the sum of the major code of σ equals the major index of σ.
The Lehmer code encodes the inversions of a permutation and the major code encodes its major index. In particular, the number of inversions of a permutation equals the major index of its image under this map.
* The Lehmer code of a permutation σ is given by L(σ)=l1…ln with li=#{j>i:σj<σi}. In particular, li is the number of boxes in the i-th column of the Rothe diagram. For example, the Lehmer code of σ=[4,3,1,5,2] is 32010. The Lehmer code L:Sn ˜⟶ Sn is a bijection between permutations of size n and sequences l1…ln∈Nn with li≤i.
* The major code M(σ) of a permutation σ∈Sn is a way to encode a permutation as a sequence m1m2…mn with mi≥i. To define mi, let deli(σ) be the normalized permutation obtained by removing all σj<i from the one-line notation of σ. The i-th index is then given by
mi=maj(deli(σ))−maj(deli−1(σ)).
For example, the permutation [9,3,5,7,2,1,4,6,8] has major code [5,0,1,0,1,2,0,1,0] since
maj([8,2,4,6,1,3,5,7])=5,maj([7,1,3,5,2,4,6])=5,maj([6,2,4,1,3,5])=4,
maj([5,1,3,2,4])=4,maj([4,2,1,3])=3,maj([3,1,2])=1,maj([2,1])=1.
Observe that the sum of the major code of σ equals the major index of σ.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
The complement of a permutation σ of length n is the permutation τ with τ(i)=n+1−σ(i)
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
The descent composition of a permutation π of length n is the integer composition of n whose descent set equals the descent set of π. The descent set of a permutation π is {i∣1≤i<n,π(i)>π(i+1)}. The descent set of a composition c=(i1,i2,…,ik) is the set {i1,i1+i2,i1+i2+i3,…,i1+i2+⋯+ik−1}.
searching the database
Sorry, this map was not found in the database.