Identifier
Mp00235:
Permutations
—descent views to invisible inversion bottoms⟶
Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00167: Signed permutations —inverse Kreweras complement⟶ Signed permutations
Images
=>
[1]=>[1]=>[1]=>[-1]
[1,2]=>[1,2]=>[1,2]=>[2,-1]
[2,1]=>[2,1]=>[2,1]=>[1,-2]
[1,2,3]=>[1,2,3]=>[1,2,3]=>[2,3,-1]
[1,3,2]=>[1,3,2]=>[1,3,2]=>[3,2,-1]
[2,1,3]=>[2,1,3]=>[2,1,3]=>[1,3,-2]
[2,3,1]=>[3,2,1]=>[3,2,1]=>[2,1,-3]
[3,1,2]=>[3,1,2]=>[3,1,2]=>[3,1,-2]
[3,2,1]=>[2,3,1]=>[2,3,1]=>[1,2,-3]
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[2,3,4,-1]
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>[2,4,3,-1]
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>[3,2,4,-1]
[1,3,4,2]=>[1,4,3,2]=>[1,4,3,2]=>[4,3,2,-1]
[1,4,2,3]=>[1,4,2,3]=>[1,4,2,3]=>[3,4,2,-1]
[1,4,3,2]=>[1,3,4,2]=>[1,3,4,2]=>[4,2,3,-1]
[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[1,3,4,-2]
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>[1,4,3,-2]
[2,3,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[2,1,4,-3]
[2,3,4,1]=>[4,2,3,1]=>[4,2,3,1]=>[2,3,1,-4]
[2,4,1,3]=>[4,2,1,3]=>[4,2,1,3]=>[2,4,1,-3]
[2,4,3,1]=>[3,2,4,1]=>[3,2,4,1]=>[2,1,3,-4]
[3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]=>[3,1,4,-2]
[3,1,4,2]=>[3,4,1,2]=>[3,4,1,2]=>[4,1,2,-3]
[3,2,1,4]=>[2,3,1,4]=>[2,3,1,4]=>[1,2,4,-3]
[3,2,4,1]=>[4,3,2,1]=>[4,3,2,1]=>[3,2,1,-4]
[3,4,1,2]=>[4,1,3,2]=>[4,1,3,2]=>[4,3,1,-2]
[3,4,2,1]=>[2,4,3,1]=>[2,4,3,1]=>[1,3,2,-4]
[4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]=>[3,4,1,-2]
[4,1,3,2]=>[4,3,1,2]=>[4,3,1,2]=>[4,2,1,-3]
[4,2,1,3]=>[2,4,1,3]=>[2,4,1,3]=>[1,4,2,-3]
[4,2,3,1]=>[3,4,2,1]=>[3,4,2,1]=>[3,1,2,-4]
[4,3,1,2]=>[3,1,4,2]=>[3,1,4,2]=>[4,1,3,-2]
[4,3,2,1]=>[2,3,4,1]=>[2,3,4,1]=>[1,2,3,-4]
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[2,3,4,5,-1]
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[2,3,5,4,-1]
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[2,4,3,5,-1]
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[2,5,4,3,-1]
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[2,4,5,3,-1]
[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,4,5,3]=>[2,5,3,4,-1]
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[3,2,4,5,-1]
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[3,2,5,4,-1]
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[4,3,2,5,-1]
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,5,3,4,2]=>[5,3,4,2,-1]
[1,3,5,2,4]=>[1,5,3,2,4]=>[1,5,3,2,4]=>[4,3,5,2,-1]
[1,3,5,4,2]=>[1,4,3,5,2]=>[1,4,3,5,2]=>[5,3,2,4,-1]
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[3,4,2,5,-1]
[1,4,2,5,3]=>[1,4,5,2,3]=>[1,4,5,2,3]=>[4,5,2,3,-1]
[1,4,3,2,5]=>[1,3,4,2,5]=>[1,3,4,2,5]=>[4,2,3,5,-1]
[1,4,3,5,2]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[5,4,3,2,-1]
[1,4,5,2,3]=>[1,5,2,4,3]=>[1,5,2,4,3]=>[3,5,4,2,-1]
[1,4,5,3,2]=>[1,3,5,4,2]=>[1,3,5,4,2]=>[5,2,4,3,-1]
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[3,4,5,2,-1]
[1,5,2,4,3]=>[1,5,4,2,3]=>[1,5,4,2,3]=>[4,5,3,2,-1]
[1,5,3,2,4]=>[1,3,5,2,4]=>[1,3,5,2,4]=>[4,2,5,3,-1]
[1,5,3,4,2]=>[1,4,5,3,2]=>[1,4,5,3,2]=>[5,4,2,3,-1]
[1,5,4,2,3]=>[1,4,2,5,3]=>[1,4,2,5,3]=>[3,5,2,4,-1]
[1,5,4,3,2]=>[1,3,4,5,2]=>[1,3,4,5,2]=>[5,2,3,4,-1]
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[1,3,4,5,-2]
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[1,3,5,4,-2]
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[1,4,3,5,-2]
[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[1,5,4,3,-2]
[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[1,4,5,3,-2]
[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,4,5,3]=>[1,5,3,4,-2]
[2,3,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[2,1,4,5,-3]
[2,3,1,5,4]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[2,1,5,4,-3]
[2,3,4,1,5]=>[4,2,3,1,5]=>[4,2,3,1,5]=>[2,3,1,5,-4]
[2,3,4,5,1]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[2,3,4,1,-5]
[2,3,5,1,4]=>[5,2,3,1,4]=>[5,2,3,1,4]=>[2,3,5,1,-4]
[2,3,5,4,1]=>[4,2,3,5,1]=>[4,2,3,5,1]=>[2,3,1,4,-5]
[2,4,1,3,5]=>[4,2,1,3,5]=>[4,2,1,3,5]=>[2,4,1,5,-3]
[2,4,1,5,3]=>[4,2,5,1,3]=>[4,2,5,1,3]=>[2,5,1,3,-4]
[2,4,3,1,5]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[2,1,3,5,-4]
[2,4,3,5,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[2,4,3,1,-5]
[2,4,5,1,3]=>[5,2,1,4,3]=>[5,2,1,4,3]=>[2,5,4,1,-3]
[2,4,5,3,1]=>[3,2,5,4,1]=>[3,2,5,4,1]=>[2,1,4,3,-5]
[2,5,1,3,4]=>[5,2,1,3,4]=>[5,2,1,3,4]=>[2,4,5,1,-3]
[2,5,1,4,3]=>[5,2,4,1,3]=>[5,2,4,1,3]=>[2,5,3,1,-4]
[2,5,3,1,4]=>[3,2,5,1,4]=>[3,2,5,1,4]=>[2,1,5,3,-4]
[2,5,3,4,1]=>[4,2,5,3,1]=>[4,2,5,3,1]=>[2,4,1,3,-5]
[2,5,4,1,3]=>[4,2,1,5,3]=>[4,2,1,5,3]=>[2,5,1,4,-3]
[2,5,4,3,1]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[2,1,3,4,-5]
[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,4,5,-2]
[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,5,4,-2]
[3,1,4,2,5]=>[3,4,1,2,5]=>[3,4,1,2,5]=>[4,1,2,5,-3]
[3,1,4,5,2]=>[3,5,1,4,2]=>[3,5,1,4,2]=>[5,1,4,2,-3]
[3,1,5,2,4]=>[3,5,1,2,4]=>[3,5,1,2,4]=>[4,1,5,2,-3]
[3,1,5,4,2]=>[3,4,1,5,2]=>[3,4,1,5,2]=>[5,1,2,4,-3]
[3,2,1,4,5]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[1,2,4,5,-3]
[3,2,1,5,4]=>[2,3,1,5,4]=>[2,3,1,5,4]=>[1,2,5,4,-3]
[3,2,4,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[3,2,1,5,-4]
[3,2,4,5,1]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[3,2,4,1,-5]
[3,2,5,1,4]=>[5,3,2,1,4]=>[5,3,2,1,4]=>[3,2,5,1,-4]
[3,2,5,4,1]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[3,2,1,4,-5]
[3,4,1,2,5]=>[4,1,3,2,5]=>[4,1,3,2,5]=>[4,3,1,5,-2]
[3,4,1,5,2]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[5,3,1,2,-4]
[3,4,2,1,5]=>[2,4,3,1,5]=>[2,4,3,1,5]=>[1,3,2,5,-4]
[3,4,2,5,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[4,3,2,1,-5]
[3,4,5,1,2]=>[5,1,3,4,2]=>[5,1,3,4,2]=>[5,3,4,1,-2]
[3,4,5,2,1]=>[2,5,3,4,1]=>[2,5,3,4,1]=>[1,3,4,2,-5]
[3,5,1,2,4]=>[5,1,3,2,4]=>[5,1,3,2,4]=>[4,3,5,1,-2]
[3,5,1,4,2]=>[5,4,3,1,2]=>[5,4,3,1,2]=>[5,3,2,1,-4]
[3,5,2,1,4]=>[2,5,3,1,4]=>[2,5,3,1,4]=>[1,3,5,2,-4]
[3,5,2,4,1]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[4,3,1,2,-5]
[3,5,4,1,2]=>[4,1,3,5,2]=>[4,1,3,5,2]=>[5,3,1,4,-2]
[3,5,4,2,1]=>[2,4,3,5,1]=>[2,4,3,5,1]=>[1,3,2,4,-5]
[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[3,4,1,5,-2]
[4,1,2,5,3]=>[4,1,5,2,3]=>[4,1,5,2,3]=>[4,5,1,3,-2]
[4,1,3,2,5]=>[4,3,1,2,5]=>[4,3,1,2,5]=>[4,2,1,5,-3]
[4,1,3,5,2]=>[4,5,1,3,2]=>[4,5,1,3,2]=>[5,4,1,2,-3]
[4,1,5,2,3]=>[4,5,2,1,3]=>[4,5,2,1,3]=>[3,5,1,2,-4]
[4,1,5,3,2]=>[4,3,5,1,2]=>[4,3,5,1,2]=>[5,2,1,3,-4]
[4,2,1,3,5]=>[2,4,1,3,5]=>[2,4,1,3,5]=>[1,4,2,5,-3]
[4,2,1,5,3]=>[2,4,5,1,3]=>[2,4,5,1,3]=>[1,5,2,3,-4]
[4,2,3,1,5]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[3,1,2,5,-4]
[4,2,3,5,1]=>[5,4,2,3,1]=>[5,4,2,3,1]=>[3,4,2,1,-5]
[4,2,5,1,3]=>[5,4,1,2,3]=>[5,4,1,2,3]=>[4,5,2,1,-3]
[4,2,5,3,1]=>[3,5,4,1,2]=>[3,5,4,1,2]=>[5,1,3,2,-4]
[4,3,1,2,5]=>[3,1,4,2,5]=>[3,1,4,2,5]=>[4,1,3,5,-2]
[4,3,1,5,2]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[4,1,2,3,-5]
[4,3,2,1,5]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[1,2,3,5,-4]
[4,3,2,5,1]=>[5,3,4,2,1]=>[5,3,4,2,1]=>[4,2,3,1,-5]
[4,3,5,1,2]=>[5,1,4,3,2]=>[5,1,4,3,2]=>[5,4,3,1,-2]
[4,3,5,2,1]=>[2,5,4,3,1]=>[2,5,4,3,1]=>[1,4,3,2,-5]
[4,5,1,2,3]=>[5,1,2,4,3]=>[5,1,2,4,3]=>[3,5,4,1,-2]
[4,5,1,3,2]=>[5,3,1,4,2]=>[5,3,1,4,2]=>[5,2,4,1,-3]
[4,5,2,1,3]=>[2,5,1,4,3]=>[2,5,1,4,3]=>[1,5,4,2,-3]
[4,5,2,3,1]=>[3,5,2,4,1]=>[3,5,2,4,1]=>[3,1,4,2,-5]
[4,5,3,1,2]=>[3,1,5,4,2]=>[3,1,5,4,2]=>[5,1,4,3,-2]
[4,5,3,2,1]=>[2,3,5,4,1]=>[2,3,5,4,1]=>[1,2,4,3,-5]
[5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[3,4,5,1,-2]
[5,1,2,4,3]=>[5,1,4,2,3]=>[5,1,4,2,3]=>[4,5,3,1,-2]
[5,1,3,2,4]=>[5,3,1,2,4]=>[5,3,1,2,4]=>[4,2,5,1,-3]
[5,1,3,4,2]=>[5,4,1,3,2]=>[5,4,1,3,2]=>[5,4,2,1,-3]
[5,1,4,2,3]=>[5,4,2,1,3]=>[5,4,2,1,3]=>[3,5,2,1,-4]
[5,1,4,3,2]=>[5,3,4,1,2]=>[5,3,4,1,2]=>[5,2,3,1,-4]
[5,2,1,3,4]=>[2,5,1,3,4]=>[2,5,1,3,4]=>[1,4,5,2,-3]
[5,2,1,4,3]=>[2,5,4,1,3]=>[2,5,4,1,3]=>[1,5,3,2,-4]
[5,2,3,1,4]=>[3,5,2,1,4]=>[3,5,2,1,4]=>[3,1,5,2,-4]
[5,2,3,4,1]=>[4,5,2,3,1]=>[4,5,2,3,1]=>[3,4,1,2,-5]
[5,2,4,1,3]=>[4,5,1,2,3]=>[4,5,1,2,3]=>[4,5,1,2,-3]
[5,2,4,3,1]=>[3,4,5,1,2]=>[3,4,5,1,2]=>[5,1,2,3,-4]
[5,3,1,2,4]=>[3,1,5,2,4]=>[3,1,5,2,4]=>[4,1,5,3,-2]
[5,3,1,4,2]=>[3,5,4,2,1]=>[3,5,4,2,1]=>[4,1,3,2,-5]
[5,3,2,1,4]=>[2,3,5,1,4]=>[2,3,5,1,4]=>[1,2,5,3,-4]
[5,3,2,4,1]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[4,2,1,3,-5]
[5,3,4,1,2]=>[4,1,5,3,2]=>[4,1,5,3,2]=>[5,4,1,3,-2]
[5,3,4,2,1]=>[2,4,5,3,1]=>[2,4,5,3,1]=>[1,4,2,3,-5]
[5,4,1,2,3]=>[4,1,2,5,3]=>[4,1,2,5,3]=>[3,5,1,4,-2]
[5,4,1,3,2]=>[4,3,1,5,2]=>[4,3,1,5,2]=>[5,2,1,4,-3]
[5,4,2,1,3]=>[2,4,1,5,3]=>[2,4,1,5,3]=>[1,5,2,4,-3]
[5,4,2,3,1]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[3,1,2,4,-5]
[5,4,3,1,2]=>[3,1,4,5,2]=>[3,1,4,5,2]=>[5,1,3,4,-2]
[5,4,3,2,1]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[1,2,3,4,-5]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[2,3,4,5,6,-1]
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[2,3,4,6,5,-1]
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[2,3,5,4,6,-1]
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[2,3,6,5,4,-1]
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[2,3,5,6,4,-1]
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,5,6,4]=>[2,3,6,4,5,-1]
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[2,4,3,5,6,-1]
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[2,4,3,6,5,-1]
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[2,5,4,3,6,-1]
[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[1,2,5,4,6,3]=>[2,6,4,3,5,-1]
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[2,4,5,3,6,-1]
[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[1,2,5,6,3,4]=>[2,5,6,3,4,-1]
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>[2,5,3,4,6,-1]
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[2,6,5,4,3,-1]
[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[1,2,4,6,5,3]=>[2,6,3,5,4,-1]
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[2,4,5,6,3,-1]
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>[2,5,3,6,4,-1]
[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>[1,2,5,6,4,3]=>[2,6,5,3,4,-1]
[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[1,2,5,3,6,4]=>[2,4,6,3,5,-1]
[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[1,2,4,5,6,3]=>[2,6,3,4,5,-1]
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[3,2,4,5,6,-1]
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[3,2,4,6,5,-1]
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[3,2,5,4,6,-1]
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[3,2,6,5,4,-1]
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[3,2,5,6,4,-1]
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,5,6,4]=>[3,2,6,4,5,-1]
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[4,3,2,5,6,-1]
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[4,3,2,6,5,-1]
[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[1,5,3,6,2,4]=>[5,3,6,2,4,-1]
[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[1,4,3,5,2,6]=>[5,3,2,4,6,-1]
[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[1,4,3,6,5,2]=>[6,3,2,5,4,-1]
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,6,3,2,4,5]=>[4,3,5,6,2,-1]
[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>[1,4,3,6,2,5]=>[5,3,2,6,4,-1]
[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[1,4,3,5,6,2]=>[6,3,2,4,5,-1]
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[3,4,2,5,6,-1]
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[3,4,2,6,5,-1]
[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>[4,5,2,3,6,-1]
[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>[4,6,2,5,3,-1]
[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>[4,5,2,6,3,-1]
[1,4,2,6,5,3]=>[1,4,5,2,6,3]=>[1,4,5,2,6,3]=>[4,6,2,3,5,-1]
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>[4,2,3,5,6,-1]
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,3,4,2,6,5]=>[4,2,3,6,5,-1]
[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[5,4,3,2,6,-1]
[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[1,5,4,3,6,2]=>[6,4,3,2,5,-1]
[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[1,3,5,4,2,6]=>[5,2,4,3,6,-1]
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[6,5,4,3,2,-1]
[1,4,6,3,5,2]=>[1,5,6,4,3,2]=>[1,5,6,4,3,2]=>[6,5,4,2,3,-1]
[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[1,3,5,4,6,2]=>[6,2,4,3,5,-1]
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[3,4,5,2,6,-1]
[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[1,5,2,6,3,4]=>[3,5,6,2,4,-1]
[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[1,5,6,3,2,4]=>[5,4,6,2,3,-1]
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>[4,2,5,3,6,-1]
[1,5,3,2,6,4]=>[1,3,5,6,2,4]=>[1,3,5,6,2,4]=>[5,2,6,3,4,-1]
[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>[1,4,5,3,2,6]=>[5,4,2,3,6,-1]
[1,5,3,4,6,2]=>[1,6,5,3,4,2]=>[1,6,5,3,4,2]=>[6,4,5,3,2,-1]
[1,5,3,6,2,4]=>[1,6,5,2,3,4]=>[1,6,5,2,3,4]=>[4,5,6,3,2,-1]
[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>[3,5,2,4,6,-1]
[1,5,4,2,6,3]=>[1,4,5,6,3,2]=>[1,4,5,6,3,2]=>[6,5,2,3,4,-1]
[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>[5,2,3,4,6,-1]
[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[1,3,6,5,4,2]=>[6,2,5,4,3,-1]
[1,5,6,2,4,3]=>[1,6,4,2,5,3]=>[1,6,4,2,5,3]=>[4,6,3,5,2,-1]
[1,5,6,4,2,3]=>[1,4,2,6,5,3]=>[1,4,2,6,5,3]=>[3,6,2,5,4,-1]
[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[1,3,4,6,5,2]=>[6,2,3,5,4,-1]
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[3,4,5,6,2,-1]
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>[4,2,5,6,3,-1]
[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>[1,5,6,3,4,2]=>[6,4,5,2,3,-1]
[1,6,3,5,2,4]=>[1,5,6,2,3,4]=>[1,5,6,2,3,4]=>[4,5,6,2,3,-1]
[1,6,3,5,4,2]=>[1,4,5,6,2,3]=>[1,4,5,6,2,3]=>[5,6,2,3,4,-1]
[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>[3,5,2,6,4,-1]
[1,6,4,2,5,3]=>[1,4,6,5,3,2]=>[1,4,6,5,3,2]=>[6,5,2,4,3,-1]
[1,6,4,3,2,5]=>[1,3,4,6,2,5]=>[1,3,4,6,2,5]=>[5,2,3,6,4,-1]
[1,6,4,3,5,2]=>[1,5,4,6,3,2]=>[1,5,4,6,3,2]=>[6,5,3,2,4,-1]
[1,6,4,5,2,3]=>[1,5,2,6,4,3]=>[1,5,2,6,4,3]=>[3,6,5,2,4,-1]
[1,6,4,5,3,2]=>[1,3,5,6,4,2]=>[1,3,5,6,4,2]=>[6,2,5,3,4,-1]
[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[1,5,2,3,6,4]=>[3,4,6,2,5,-1]
[1,6,5,2,4,3]=>[1,5,4,2,6,3]=>[1,5,4,2,6,3]=>[4,6,3,2,5,-1]
[1,6,5,3,2,4]=>[1,3,5,2,6,4]=>[1,3,5,2,6,4]=>[4,2,6,3,5,-1]
[1,6,5,3,4,2]=>[1,4,5,3,6,2]=>[1,4,5,3,6,2]=>[6,4,2,3,5,-1]
[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[1,4,2,5,6,3]=>[3,6,2,4,5,-1]
[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[1,3,4,5,6,2]=>[6,2,3,4,5,-1]
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[1,3,4,5,6,-2]
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[1,3,4,6,5,-2]
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[1,3,5,4,6,-2]
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[1,3,6,5,4,-2]
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[1,3,5,6,4,-2]
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,5,6,4]=>[1,3,6,4,5,-2]
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[1,4,3,5,6,-2]
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[1,4,3,6,5,-2]
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[1,5,4,3,6,-2]
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,6,4,5,3]=>[1,6,4,5,3,-2]
[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[2,1,5,4,6,3]=>[1,6,4,3,5,-2]
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[1,4,5,3,6,-2]
[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[2,1,5,6,3,4]=>[1,5,6,3,4,-2]
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,4,5,3,6]=>[1,5,3,4,6,-2]
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[1,6,5,4,3,-2]
[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,6,3,5,4]=>[1,4,6,5,3,-2]
[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[2,1,4,6,5,3]=>[1,6,3,5,4,-2]
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[1,4,5,6,3,-2]
[2,1,6,3,5,4]=>[2,1,6,5,3,4]=>[2,1,6,5,3,4]=>[1,5,6,4,3,-2]
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[2,1,4,6,3,5]=>[1,5,3,6,4,-2]
[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>[2,1,5,6,4,3]=>[1,6,5,3,4,-2]
[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[2,1,5,3,6,4]=>[1,4,6,3,5,-2]
[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[2,1,4,5,6,3]=>[1,6,3,4,5,-2]
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[2,1,4,5,6,-3]
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[2,1,4,6,5,-3]
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[2,1,5,4,6,-3]
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[2,1,6,5,4,-3]
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[3,2,1,6,4,5]=>[2,1,5,6,4,-3]
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[3,2,1,5,6,4]=>[2,1,6,4,5,-3]
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[2,3,1,5,6,-4]
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[4,2,3,1,6,5]=>[2,3,1,6,5,-4]
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[2,3,4,1,6,-5]
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[2,3,4,5,1,-6]
[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[6,2,3,4,1,5]=>[2,3,4,6,1,-5]
[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[5,2,3,4,6,1]=>[2,3,4,1,5,-6]
[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[5,2,3,1,4,6]=>[2,3,5,1,6,-4]
[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[4,2,3,5,1,6]=>[2,3,1,4,6,-5]
[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[6,2,3,1,5,4]=>[2,3,6,5,1,-4]
[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[6,2,3,1,4,5]=>[2,3,5,6,1,-4]
[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[4,2,3,5,6,1]=>[2,3,1,4,5,-6]
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,1,5,6,-3]
[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[4,2,5,1,3,6]=>[2,5,1,3,6,-4]
[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[2,6,1,5,3,-4]
[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[4,2,6,1,3,5]=>[2,5,1,6,3,-4]
[2,4,1,6,5,3]=>[4,2,5,1,6,3]=>[4,2,5,1,6,3]=>[2,6,1,3,5,-4]
[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[2,1,3,5,6,-4]
[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[3,2,4,1,6,5]=>[2,1,3,6,5,-4]
[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[3,2,5,4,1,6]=>[2,1,4,3,6,-5]
[2,4,6,3,1,5]=>[3,2,6,4,1,5]=>[3,2,6,4,1,5]=>[2,1,4,6,3,-5]
[2,4,6,5,1,3]=>[5,2,1,4,6,3]=>[5,2,1,4,6,3]=>[2,6,4,1,5,-3]
[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[3,2,5,4,6,1]=>[2,1,4,3,5,-6]
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[5,2,1,3,4,6]=>[2,4,5,1,6,-3]
[2,5,1,4,6,3]=>[5,2,6,1,4,3]=>[5,2,6,1,4,3]=>[2,6,5,1,3,-4]
[2,5,3,4,6,1]=>[6,2,5,3,4,1]=>[6,2,5,3,4,1]=>[2,4,5,3,1,-6]
[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[2,1,3,4,6,-5]
[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[3,2,6,5,4,1]=>[2,1,5,4,3,-6]
[2,5,6,3,1,4]=>[3,2,6,1,5,4]=>[3,2,6,1,5,4]=>[2,1,6,5,3,-4]
[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[3,2,4,6,5,1]=>[2,1,3,5,4,-6]
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[6,2,1,3,4,5]=>[2,4,5,6,1,-3]
[2,6,1,4,5,3]=>[6,2,5,1,4,3]=>[6,2,5,1,4,3]=>[2,6,5,3,1,-4]
[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>[3,2,6,1,4,5]=>[2,1,5,6,3,-4]
[2,6,4,5,3,1]=>[3,2,5,6,4,1]=>[3,2,5,6,4,1]=>[2,1,5,3,4,-6]
[2,6,5,3,1,4]=>[3,2,5,1,6,4]=>[3,2,5,1,6,4]=>[2,1,6,3,5,-4]
[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[2,1,3,4,5,-6]
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,4,5,6,-2]
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,4,6,5,-2]
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,5,4,6,-2]
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,1,2,6,5,4]=>[3,1,6,5,4,-2]
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,5,6,4,-2]
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>[3,1,2,5,6,4]=>[3,1,6,4,5,-2]
[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[4,1,2,5,6,-3]
[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[3,4,1,2,6,5]=>[4,1,2,6,5,-3]
[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[3,6,1,4,5,2]=>[6,1,4,5,2,-3]
[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[3,5,1,2,4,6]=>[4,1,5,2,6,-3]
[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[3,5,1,6,2,4]=>[5,1,6,2,4,-3]
[3,1,5,4,2,6]=>[3,4,1,5,2,6]=>[3,4,1,5,2,6]=>[5,1,2,4,6,-3]
[3,1,5,4,6,2]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[6,1,5,4,2,-3]
[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[3,6,1,2,4,5]=>[4,1,5,6,2,-3]
[3,1,6,2,5,4]=>[3,6,1,5,2,4]=>[3,6,1,5,2,4]=>[5,1,6,4,2,-3]
[3,1,6,4,2,5]=>[3,4,1,6,2,5]=>[3,4,1,6,2,5]=>[5,1,2,6,4,-3]
[3,1,6,4,5,2]=>[3,5,1,6,4,2]=>[3,5,1,6,4,2]=>[6,1,5,2,4,-3]
[3,1,6,5,2,4]=>[3,5,1,2,6,4]=>[3,5,1,2,6,4]=>[4,1,6,2,5,-3]
[3,1,6,5,4,2]=>[3,4,1,5,6,2]=>[3,4,1,5,6,2]=>[6,1,2,4,5,-3]
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[1,2,4,5,6,-3]
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[2,3,1,4,6,5]=>[1,2,4,6,5,-3]
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[2,3,1,5,4,6]=>[1,2,5,4,6,-3]
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[2,3,1,6,5,4]=>[1,2,6,5,4,-3]
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[2,3,1,6,4,5]=>[1,2,5,6,4,-3]
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[2,3,1,5,6,4]=>[1,2,6,4,5,-3]
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[3,2,1,5,6,-4]
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[3,2,1,6,5,-4]
[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[3,2,4,1,6,-5]
[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[3,2,4,5,1,-6]
[3,2,4,6,1,5]=>[6,3,2,4,1,5]=>[6,3,2,4,1,5]=>[3,2,4,6,1,-5]
[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[5,3,2,4,6,1]=>[3,2,4,1,5,-6]
[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[5,3,2,1,4,6]=>[3,2,5,1,6,-4]
[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[3,2,1,4,6,-5]
[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[3,2,5,4,1,-6]
[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[4,3,2,6,5,1]=>[3,2,1,5,4,-6]
[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[6,3,2,1,4,5]=>[3,2,5,6,1,-4]
[3,2,6,1,5,4]=>[6,3,2,5,1,4]=>[6,3,2,5,1,4]=>[3,2,6,4,1,-5]
[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[3,2,1,4,5,-6]
[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[4,1,3,2,6,5]=>[4,3,1,6,5,-2]
[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[5,3,1,2,6,-4]
[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[6,3,1,5,2,-4]
[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[4,6,3,1,2,5]=>[5,3,1,6,2,-4]
[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[2,4,3,1,5,6]=>[1,3,2,5,6,-4]
[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[2,4,3,1,6,5]=>[1,3,2,6,5,-4]
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[4,3,2,1,6,-5]
[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[4,3,2,5,1,-6]
[3,4,2,6,1,5]=>[6,4,3,2,1,5]=>[6,4,3,2,1,5]=>[4,3,2,6,1,-5]
[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[4,3,2,1,5,-6]
[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[6,3,4,1,2,-5]
[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[5,3,4,2,1,-6]
[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[6,1,3,4,2,5]=>[5,3,4,6,1,-2]
[3,4,6,1,5,2]=>[6,5,3,4,1,2]=>[6,5,3,4,1,2]=>[6,3,4,2,1,-5]
[3,4,6,2,5,1]=>[5,6,3,4,2,1]=>[5,6,3,4,2,1]=>[5,3,4,1,2,-6]
[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[2,5,3,4,6,1]=>[1,3,4,2,5,-6]
[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[5,1,3,6,2,4]=>[5,3,6,1,4,-2]
[3,5,1,4,2,6]=>[5,4,3,1,2,6]=>[5,4,3,1,2,6]=>[5,3,2,1,6,-4]
[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[5,6,3,2,1,4]=>[4,3,6,1,2,-5]
[3,5,1,6,4,2]=>[5,4,3,6,1,2]=>[5,4,3,6,1,2]=>[6,3,2,1,4,-5]
[3,5,2,4,1,6]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[4,3,1,2,6,-5]
[3,5,2,4,6,1]=>[6,5,3,2,4,1]=>[6,5,3,2,4,1]=>[4,3,5,2,1,-6]
[3,5,2,6,1,4]=>[6,5,3,1,2,4]=>[6,5,3,1,2,4]=>[5,3,6,2,1,-4]
[3,5,2,6,4,1]=>[4,6,3,5,1,2]=>[4,6,3,5,1,2]=>[6,3,1,4,2,-5]
[3,5,4,1,6,2]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[5,3,1,2,4,-6]
[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[2,4,3,5,1,6]=>[1,3,2,4,6,-5]
[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[6,4,3,5,2,1]=>[5,3,2,4,1,-6]
[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[6,1,3,2,5,4]=>[4,3,6,5,1,-2]
[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[2,4,3,6,5,1]=>[1,3,2,5,4,-6]
[3,6,1,4,2,5]=>[6,4,3,1,2,5]=>[6,4,3,1,2,5]=>[5,3,2,6,1,-4]
[3,6,1,5,2,4]=>[6,5,3,2,1,4]=>[6,5,3,2,1,4]=>[4,3,6,2,1,-5]
[3,6,1,5,4,2]=>[6,4,3,5,1,2]=>[6,4,3,5,1,2]=>[6,3,2,4,1,-5]
[3,6,2,4,5,1]=>[5,6,3,2,4,1]=>[5,6,3,2,4,1]=>[4,3,5,1,2,-6]
[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[5,6,3,1,2,4]=>[5,3,6,1,2,-4]
[3,6,2,5,4,1]=>[4,5,3,6,1,2]=>[4,5,3,6,1,2]=>[6,3,1,2,4,-5]
[3,6,4,1,2,5]=>[4,1,3,6,2,5]=>[4,1,3,6,2,5]=>[5,3,1,6,4,-2]
[3,6,4,1,5,2]=>[4,6,3,5,2,1]=>[4,6,3,5,2,1]=>[5,3,1,4,2,-6]
[3,6,4,2,5,1]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[5,3,2,1,4,-6]
[3,6,5,1,2,4]=>[5,1,3,2,6,4]=>[5,1,3,2,6,4]=>[4,3,6,1,5,-2]
[3,6,5,2,4,1]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[4,3,1,2,5,-6]
[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[2,4,3,5,6,1]=>[1,3,2,4,5,-6]
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[3,4,1,5,6,-2]
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[3,4,1,6,5,-2]
[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[4,1,5,2,3,6]=>[4,5,1,3,6,-2]
[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[4,1,6,2,5,3]=>[4,6,1,5,3,-2]
[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[4,1,6,2,3,5]=>[4,5,1,6,3,-2]
[4,1,2,6,5,3]=>[4,1,5,2,6,3]=>[4,1,5,2,6,3]=>[4,6,1,3,5,-2]
[4,1,3,2,5,6]=>[4,3,1,2,5,6]=>[4,3,1,2,5,6]=>[4,2,1,5,6,-3]
[4,1,3,2,6,5]=>[4,3,1,2,6,5]=>[4,3,1,2,6,5]=>[4,2,1,6,5,-3]
[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[4,5,2,1,3,6]=>[3,5,1,2,6,-4]
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[5,6,1,2,3,-4]
[4,1,5,3,2,6]=>[4,3,5,1,2,6]=>[4,3,5,1,2,6]=>[5,2,1,3,6,-4]
[4,1,5,3,6,2]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[6,5,1,3,2,-4]
[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[4,6,2,1,5,3]=>[3,6,1,5,2,-4]
[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[4,6,2,1,3,5]=>[3,5,1,6,2,-4]
[4,1,6,2,5,3]=>[4,6,5,1,2,3]=>[4,6,5,1,2,3]=>[5,6,1,3,2,-4]
[4,1,6,3,5,2]=>[4,5,6,1,3,2]=>[4,5,6,1,3,2]=>[6,5,1,2,3,-4]
[4,1,6,5,2,3]=>[4,5,2,1,6,3]=>[4,5,2,1,6,3]=>[3,6,1,2,5,-4]
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[2,4,1,3,5,6]=>[1,4,2,5,6,-3]
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[2,4,1,3,6,5]=>[1,4,2,6,5,-3]
[4,2,1,5,3,6]=>[2,4,5,1,3,6]=>[2,4,5,1,3,6]=>[1,5,2,3,6,-4]
[4,2,1,5,6,3]=>[2,4,6,1,5,3]=>[2,4,6,1,5,3]=>[1,6,2,5,3,-4]
[4,2,1,6,3,5]=>[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>[1,5,2,6,3,-4]
[4,2,1,6,5,3]=>[2,4,5,1,6,3]=>[2,4,5,1,6,3]=>[1,6,2,3,5,-4]
[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[3,1,2,5,6,-4]
[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>[3,4,2,1,6,5]=>[3,1,2,6,5,-4]
[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[5,4,2,3,1,6]=>[3,4,2,1,6,-5]
[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[6,4,2,3,5,1]=>[3,4,2,5,1,-6]
[4,2,3,6,1,5]=>[6,4,2,3,1,5]=>[6,4,2,3,1,5]=>[3,4,2,6,1,-5]
[4,2,3,6,5,1]=>[5,4,2,3,6,1]=>[5,4,2,3,6,1]=>[3,4,2,1,5,-6]
[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[5,4,1,2,3,6]=>[4,5,2,1,6,-3]
[4,2,5,1,6,3]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[4,6,2,1,3,-5]
[4,2,5,3,6,1]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[4,5,2,3,1,-6]
[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[6,4,1,2,3,5]=>[4,5,2,6,1,-3]
[4,2,6,1,5,3]=>[6,4,5,2,1,3]=>[6,4,5,2,1,3]=>[4,6,2,3,1,-5]
[4,2,6,3,5,1]=>[5,4,6,2,3,1]=>[5,4,6,2,3,1]=>[4,5,2,1,3,-6]
[4,2,6,5,1,3]=>[5,4,1,2,6,3]=>[5,4,1,2,6,3]=>[4,6,2,1,5,-3]
[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[3,1,4,2,5,6]=>[4,1,3,5,6,-2]
[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[3,1,4,2,6,5]=>[4,1,3,6,5,-2]
[4,3,1,5,2,6]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[4,1,2,3,6,-5]
[4,3,1,6,5,2]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[4,1,2,3,5,-6]
[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[1,2,3,5,6,-4]
[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[2,3,4,1,6,5]=>[1,2,3,6,5,-4]
[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[5,3,4,2,1,6]=>[4,2,3,1,6,-5]
[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[6,3,4,2,5,1]=>[4,2,3,5,1,-6]
[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[6,3,4,2,1,5]=>[4,2,3,6,1,-5]
[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[5,3,4,2,6,1]=>[4,2,3,1,5,-6]
[4,3,5,1,6,2]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[6,4,3,1,2,-5]
[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[2,5,4,3,1,6]=>[1,4,3,2,6,-5]
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[5,4,3,2,1,-6]
[4,3,6,1,5,2]=>[6,5,4,3,1,2]=>[6,5,4,3,1,2]=>[6,4,3,2,1,-5]
[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[5,4,3,1,2,-6]
[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[2,5,4,3,6,1]=>[1,4,3,2,5,-6]
[4,5,1,3,2,6]=>[5,3,1,4,2,6]=>[5,3,1,4,2,6]=>[5,2,4,1,6,-3]
[4,5,1,3,6,2]=>[5,6,1,4,3,2]=>[5,6,1,4,3,2]=>[6,5,4,1,2,-3]
[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[5,6,2,4,1,3]=>[3,6,4,1,2,-5]
[4,5,1,6,3,2]=>[5,3,6,4,1,2]=>[5,3,6,4,1,2]=>[6,2,4,1,3,-5]
[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[3,5,2,4,1,6]=>[3,1,4,2,6,-5]
[4,5,3,1,6,2]=>[3,5,6,4,2,1]=>[3,5,6,4,2,1]=>[5,1,4,2,3,-6]
[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[2,3,5,4,1,6]=>[1,2,4,3,6,-5]
[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[2,6,5,4,3,1]=>[1,5,4,3,2,-6]
[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[6,1,2,4,5,3]=>[3,6,4,5,1,-2]
[4,5,6,1,3,2]=>[6,3,1,4,5,2]=>[6,3,1,4,5,2]=>[6,2,4,5,1,-3]
[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[2,6,1,4,5,3]=>[1,6,4,5,2,-3]
[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[3,6,2,4,5,1]=>[3,1,4,5,2,-6]
[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[3,1,6,4,5,2]=>[6,1,4,5,3,-2]
[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[2,3,6,4,5,1]=>[1,2,4,5,3,-6]
[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[5,6,1,4,2,3]=>[5,6,4,1,2,-3]
[4,6,3,1,5,2]=>[3,6,5,4,2,1]=>[3,6,5,4,2,1]=>[5,1,4,3,2,-6]
[4,6,3,5,2,1]=>[2,5,6,4,3,1]=>[2,5,6,4,3,1]=>[1,5,4,2,3,-6]
[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[2,3,5,4,6,1]=>[1,2,4,3,5,-6]
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[3,4,5,1,6,-2]
[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[5,1,2,6,3,4]=>[3,5,6,1,4,-2]
[5,1,2,4,6,3]=>[5,1,6,2,4,3]=>[5,1,6,2,4,3]=>[4,6,5,1,3,-2]
[5,1,3,2,4,6]=>[5,3,1,2,4,6]=>[5,3,1,2,4,6]=>[4,2,5,1,6,-3]
[5,1,3,2,6,4]=>[5,3,1,6,2,4]=>[5,3,1,6,2,4]=>[5,2,6,1,4,-3]
[5,1,3,4,6,2]=>[5,6,1,3,4,2]=>[5,6,1,3,4,2]=>[6,4,5,1,2,-3]
[5,1,3,6,2,4]=>[5,6,1,2,3,4]=>[5,6,1,2,3,4]=>[4,5,6,1,2,-3]
[5,1,4,2,3,6]=>[5,4,2,1,3,6]=>[5,4,2,1,3,6]=>[3,5,2,1,6,-4]
[5,1,4,2,6,3]=>[5,4,6,1,2,3]=>[5,4,6,1,2,3]=>[5,6,2,1,3,-4]
[5,1,4,3,2,6]=>[5,3,4,1,2,6]=>[5,3,4,1,2,6]=>[5,2,3,1,6,-4]
[5,1,4,6,2,3]=>[5,6,2,1,4,3]=>[5,6,2,1,4,3]=>[3,6,5,1,2,-4]
[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[5,6,2,3,1,4]=>[3,4,6,1,2,-5]
[5,1,6,2,4,3]=>[5,6,4,2,1,3]=>[5,6,4,2,1,3]=>[4,6,3,1,2,-5]
[5,1,6,3,2,4]=>[5,3,6,2,1,4]=>[5,3,6,2,1,4]=>[4,2,6,1,3,-5]
[5,1,6,3,4,2]=>[5,4,6,3,1,2]=>[5,4,6,3,1,2]=>[6,4,2,1,3,-5]
[5,1,6,4,3,2]=>[5,3,4,6,1,2]=>[5,3,4,6,1,2]=>[6,2,3,1,4,-5]
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[2,5,1,3,4,6]=>[1,4,5,2,6,-3]
[5,2,1,3,6,4]=>[2,5,1,6,3,4]=>[2,5,1,6,3,4]=>[1,5,6,2,4,-3]
[5,2,3,1,6,4]=>[3,5,2,6,1,4]=>[3,5,2,6,1,4]=>[3,1,6,2,4,-5]
[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[4,5,2,3,1,6]=>[3,4,1,2,6,-5]
[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[6,5,2,3,4,1]=>[3,4,5,2,1,-6]
[5,2,3,6,1,4]=>[6,5,2,1,3,4]=>[6,5,2,1,3,4]=>[3,5,6,2,1,-4]
[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[4,5,1,2,3,6]=>[4,5,1,2,6,-3]
[5,2,4,1,6,3]=>[4,5,6,2,1,3]=>[4,5,6,2,1,3]=>[4,6,1,2,3,-5]
[5,2,4,3,1,6]=>[3,4,5,1,2,6]=>[3,4,5,1,2,6]=>[5,1,2,3,6,-4]
[5,2,4,3,6,1]=>[6,5,4,2,3,1]=>[6,5,4,2,3,1]=>[4,5,3,2,1,-6]
[5,2,6,1,4,3]=>[6,5,4,1,2,3]=>[6,5,4,1,2,3]=>[5,6,3,2,1,-4]
[5,2,6,3,4,1]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[5,4,1,2,3,-6]
[5,2,6,4,3,1]=>[3,4,6,5,2,1]=>[3,4,6,5,2,1]=>[5,1,2,4,3,-6]
[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[3,1,5,2,4,6]=>[4,1,5,3,6,-2]
[5,3,1,2,6,4]=>[3,1,5,6,2,4]=>[3,1,5,6,2,4]=>[5,1,6,3,4,-2]
[5,3,1,4,2,6]=>[3,5,4,2,1,6]=>[3,5,4,2,1,6]=>[4,1,3,2,6,-5]
[5,3,1,6,2,4]=>[3,5,6,1,2,4]=>[3,5,6,1,2,4]=>[5,1,6,2,3,-4]
[5,3,1,6,4,2]=>[3,5,4,6,2,1]=>[3,5,4,6,2,1]=>[5,1,3,2,4,-6]
[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[2,3,5,1,4,6]=>[1,2,5,3,6,-4]
[5,3,2,1,6,4]=>[2,3,5,6,1,4]=>[2,3,5,6,1,4]=>[1,2,6,3,4,-5]
[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[4,2,1,3,6,-5]
[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[6,3,5,2,4,1]=>[4,2,5,3,1,-6]
[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[6,3,5,1,2,4]=>[5,2,6,3,1,-4]
[5,3,2,6,4,1]=>[4,3,6,5,1,2]=>[4,3,6,5,1,2]=>[6,2,1,4,3,-5]
[5,3,4,1,6,2]=>[4,6,5,3,1,2]=>[4,6,5,3,1,2]=>[6,4,1,3,2,-5]
[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[2,4,5,3,1,6]=>[1,4,2,3,6,-5]
[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[6,4,5,3,2,1]=>[5,4,2,3,1,-6]
[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[6,1,5,3,4,2]=>[6,4,5,3,1,-2]
[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[6,1,5,2,3,4]=>[4,5,6,3,1,-2]
[5,3,6,1,4,2]=>[6,4,5,1,3,2]=>[6,4,5,1,3,2]=>[6,5,2,3,1,-4]
[5,3,6,2,1,4]=>[2,6,5,1,3,4]=>[2,6,5,1,3,4]=>[1,5,6,3,2,-4]
[5,3,6,2,4,1]=>[4,6,5,2,3,1]=>[4,6,5,2,3,1]=>[4,5,1,3,2,-6]
[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[4,1,2,5,3,6]=>[3,5,1,4,6,-2]
[5,4,1,2,6,3]=>[4,1,5,6,3,2]=>[4,1,5,6,3,2]=>[6,5,1,3,4,-2]
[5,4,1,3,6,2]=>[4,5,2,6,3,1]=>[4,5,2,6,3,1]=>[3,5,1,2,4,-6]
[5,4,1,6,2,3]=>[4,5,1,6,2,3]=>[4,5,1,6,2,3]=>[5,6,1,2,4,-3]
[5,4,1,6,3,2]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[5,2,1,3,4,-6]
[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[2,4,1,5,3,6]=>[1,5,2,4,6,-3]
[5,4,2,1,6,3]=>[2,4,5,6,3,1]=>[2,4,5,6,3,1]=>[1,5,2,3,4,-6]
[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[3,1,2,4,6,-5]
[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[6,4,1,5,2,3]=>[5,6,2,4,1,-3]
[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[3,1,4,5,2,6]=>[5,1,3,4,6,-2]
[5,4,3,1,6,2]=>[3,4,5,6,1,2]=>[3,4,5,6,1,2]=>[6,1,2,3,4,-5]
[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[1,2,3,4,6,-5]
[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[6,3,4,5,2,1]=>[5,2,3,4,1,-6]
[5,4,6,1,3,2]=>[6,3,1,5,4,2]=>[6,3,1,5,4,2]=>[6,2,5,4,1,-3]
[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[3,6,2,5,4,1]=>[3,1,5,4,2,-6]
[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[2,3,6,5,4,1]=>[1,2,5,4,3,-6]
[5,6,1,2,4,3]=>[6,1,4,2,5,3]=>[6,1,4,2,5,3]=>[4,6,3,5,1,-2]
[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[3,6,2,1,5,4]=>[3,1,6,5,2,-4]
[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[3,1,6,2,5,4]=>[4,1,6,5,3,-2]
[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[4,1,2,6,5,3]=>[3,6,1,5,4,-2]
[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[3,4,2,6,5,1]=>[3,1,2,5,4,-6]
[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[2,3,4,6,5,1]=>[1,2,3,5,4,-6]
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[3,4,5,6,1,-2]
[6,1,2,3,5,4]=>[6,1,2,5,3,4]=>[6,1,2,5,3,4]=>[3,5,6,4,1,-2]
[6,1,2,4,3,5]=>[6,1,4,2,3,5]=>[6,1,4,2,3,5]=>[4,5,3,6,1,-2]
[6,1,2,4,5,3]=>[6,1,5,2,4,3]=>[6,1,5,2,4,3]=>[4,6,5,3,1,-2]
[6,1,2,5,3,4]=>[6,1,5,3,2,4]=>[6,1,5,3,2,4]=>[5,4,6,3,1,-2]
[6,1,2,5,4,3]=>[6,1,4,5,2,3]=>[6,1,4,5,2,3]=>[5,6,3,4,1,-2]
[6,1,3,2,4,5]=>[6,3,1,2,4,5]=>[6,3,1,2,4,5]=>[4,2,5,6,1,-3]
[6,1,3,2,5,4]=>[6,3,1,5,2,4]=>[6,3,1,5,2,4]=>[5,2,6,4,1,-3]
[6,1,3,5,2,4]=>[6,5,1,2,3,4]=>[6,5,1,2,3,4]=>[4,5,6,2,1,-3]
[6,1,4,2,3,5]=>[6,4,2,1,3,5]=>[6,4,2,1,3,5]=>[3,5,2,6,1,-4]
[6,1,4,2,5,3]=>[6,4,5,1,2,3]=>[6,4,5,1,2,3]=>[5,6,2,3,1,-4]
[6,1,4,3,2,5]=>[6,3,4,1,2,5]=>[6,3,4,1,2,5]=>[5,2,3,6,1,-4]
[6,1,4,3,5,2]=>[6,5,4,1,3,2]=>[6,5,4,1,3,2]=>[6,5,3,2,1,-4]
[6,1,4,5,3,2]=>[6,3,5,1,4,2]=>[6,3,5,1,4,2]=>[6,2,5,3,1,-4]
[6,1,5,2,3,4]=>[6,5,2,3,1,4]=>[6,5,2,3,1,4]=>[3,4,6,2,1,-5]
[6,1,5,2,4,3]=>[6,5,4,2,1,3]=>[6,5,4,2,1,3]=>[4,6,3,2,1,-5]
[6,1,5,3,4,2]=>[6,4,5,3,1,2]=>[6,4,5,3,1,2]=>[6,4,2,3,1,-5]
[6,1,5,4,2,3]=>[6,4,2,5,1,3]=>[6,4,2,5,1,3]=>[3,6,2,4,1,-5]
[6,1,5,4,3,2]=>[6,3,4,5,1,2]=>[6,3,4,5,1,2]=>[6,2,3,4,1,-5]
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[2,6,1,3,4,5]=>[1,4,5,6,2,-3]
[6,2,1,3,5,4]=>[2,6,1,5,3,4]=>[2,6,1,5,3,4]=>[1,5,6,4,2,-3]
[6,2,1,4,3,5]=>[2,6,4,1,3,5]=>[2,6,4,1,3,5]=>[1,5,3,6,2,-4]
[6,2,1,5,4,3]=>[2,6,4,5,1,3]=>[2,6,4,5,1,3]=>[1,6,3,4,2,-5]
[6,2,3,1,5,4]=>[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>[3,1,6,4,2,-5]
[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[5,6,2,3,4,1]=>[3,4,5,1,2,-6]
[6,2,3,5,1,4]=>[5,6,2,1,3,4]=>[5,6,2,1,3,4]=>[3,5,6,1,2,-4]
[6,2,3,5,4,1]=>[4,5,1,6,3,2]=>[4,5,1,6,3,2]=>[6,5,1,2,4,-3]
[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[4,6,1,2,3,5]=>[4,5,1,6,2,-3]
[6,2,4,1,5,3]=>[4,6,5,2,1,3]=>[4,6,5,2,1,3]=>[4,6,1,3,2,-5]
[6,2,4,3,1,5]=>[3,4,6,1,2,5]=>[3,4,6,1,2,5]=>[5,1,2,6,3,-4]
[6,2,4,3,5,1]=>[5,6,4,2,3,1]=>[5,6,4,2,3,1]=>[4,5,3,1,2,-6]
[6,2,4,5,1,3]=>[5,6,1,2,4,3]=>[5,6,1,2,4,3]=>[4,6,5,1,2,-3]
[6,2,4,5,3,1]=>[3,5,6,1,4,2]=>[3,5,6,1,4,2]=>[6,1,5,2,3,-4]
[6,2,5,1,3,4]=>[5,6,1,3,2,4]=>[5,6,1,3,2,4]=>[5,4,6,1,2,-3]
[6,2,5,1,4,3]=>[5,6,4,1,2,3]=>[5,6,4,1,2,3]=>[5,6,3,1,2,-4]
[6,2,5,3,4,1]=>[4,6,5,3,2,1]=>[4,6,5,3,2,1]=>[5,4,1,3,2,-6]
[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[5,1,2,3,4,-6]
[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[3,1,6,2,4,5]=>[4,1,5,6,3,-2]
[6,3,1,2,5,4]=>[3,1,6,5,2,4]=>[3,1,6,5,2,4]=>[5,1,6,4,3,-2]
[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[2,3,6,1,4,5]=>[1,2,5,6,3,-4]
[6,3,2,1,5,4]=>[2,3,6,5,1,4]=>[2,3,6,5,1,4]=>[1,2,6,4,3,-5]
[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[5,3,6,2,4,1]=>[4,2,5,1,3,-6]
[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>[4,3,5,6,1,2]=>[6,2,1,3,4,-5]
[6,3,4,1,5,2]=>[4,5,6,3,1,2]=>[4,5,6,3,1,2]=>[6,4,1,2,3,-5]
[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[5,4,2,1,3,-6]
[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[5,1,6,2,3,4]=>[4,5,6,1,3,-2]
[6,3,5,2,1,4]=>[2,5,6,1,3,4]=>[2,5,6,1,3,4]=>[1,5,6,2,3,-4]
[6,3,5,2,4,1]=>[4,5,6,2,3,1]=>[4,5,6,2,3,1]=>[4,5,1,2,3,-6]
[6,3,5,4,1,2]=>[4,1,5,6,2,3]=>[4,1,5,6,2,3]=>[5,6,1,3,4,-2]
[6,3,5,4,2,1]=>[2,4,5,6,1,3]=>[2,4,5,6,1,3]=>[1,6,2,3,4,-5]
[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[4,1,2,6,3,5]=>[3,5,1,6,4,-2]
[6,4,1,3,2,5]=>[4,3,1,6,2,5]=>[4,3,1,6,2,5]=>[5,2,1,6,4,-3]
[6,4,1,5,3,2]=>[4,3,6,5,2,1]=>[4,3,6,5,2,1]=>[5,2,1,4,3,-6]
[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[2,4,1,6,3,5]=>[1,5,2,6,4,-3]
[6,4,2,1,5,3]=>[2,4,6,5,3,1]=>[2,4,6,5,3,1]=>[1,5,2,4,3,-6]
[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[3,4,2,6,1,5]=>[3,1,2,6,4,-5]
[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[3,1,4,6,2,5]=>[5,1,3,6,4,-2]
[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>[3,4,6,5,1,2]=>[6,1,2,4,3,-5]
[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[2,3,4,6,1,5]=>[1,2,3,6,4,-5]
[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[5,3,4,6,2,1]=>[5,2,3,1,4,-6]
[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[2,5,4,6,3,1]=>[1,5,3,2,4,-6]
[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[3,5,2,6,4,1]=>[3,1,5,2,4,-6]
[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[2,3,5,6,4,1]=>[1,2,5,3,4,-6]
[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[5,1,2,3,6,4]=>[3,4,6,1,5,-2]
[6,5,1,2,4,3]=>[5,1,4,2,6,3]=>[5,1,4,2,6,3]=>[4,6,3,1,5,-2]
[6,5,1,3,2,4]=>[5,3,1,2,6,4]=>[5,3,1,2,6,4]=>[4,2,6,1,5,-3]
[6,5,1,4,3,2]=>[5,3,4,1,6,2]=>[5,3,4,1,6,2]=>[6,2,3,1,5,-4]
[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[2,5,1,3,6,4]=>[1,4,6,2,5,-3]
[6,5,2,1,4,3]=>[2,5,4,1,6,3]=>[2,5,4,1,6,3]=>[1,6,3,2,5,-4]
[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[4,5,2,3,6,1]=>[3,4,1,2,5,-6]
[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[4,5,1,2,6,3]=>[4,6,1,2,5,-3]
[6,5,2,4,3,1]=>[3,4,5,1,6,2]=>[3,4,5,1,6,2]=>[6,1,2,3,5,-4]
[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[3,1,5,2,6,4]=>[4,1,6,3,5,-2]
[6,5,3,1,4,2]=>[3,5,4,2,6,1]=>[3,5,4,2,6,1]=>[4,1,3,2,5,-6]
[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[2,3,5,1,6,4]=>[1,2,6,3,5,-4]
[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[4,2,1,3,5,-6]
[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[2,4,5,3,6,1]=>[1,4,2,3,5,-6]
[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[4,1,2,5,6,3]=>[3,6,1,4,5,-2]
[6,5,4,1,3,2]=>[4,3,1,5,6,2]=>[4,3,1,5,6,2]=>[6,2,1,4,5,-3]
[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[2,4,1,5,6,3]=>[1,6,2,4,5,-3]
[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[3,1,2,4,5,-6]
[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[3,1,4,5,6,2]=>[6,1,3,4,5,-2]
[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[1,2,3,4,5,-6]
[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>[7,4,1,2,3,5,6]=>[4,5,2,6,7,1,-3]
[4,2,7,1,3,6,5]=>[7,4,1,2,6,3,5]=>[7,4,1,2,6,3,5]=>[4,6,2,7,5,1,-3]
[4,2,7,5,1,3,6]=>[5,4,1,2,7,3,6]=>[5,4,1,2,7,3,6]=>[4,6,2,1,7,5,-3]
[4,2,7,6,1,3,5]=>[6,4,1,2,3,7,5]=>[6,4,1,2,3,7,5]=>[4,5,2,7,1,6,-3]
[4,2,7,6,5,1,3]=>[5,4,1,2,6,7,3]=>[5,4,1,2,6,7,3]=>[4,7,2,1,5,6,-3]
[5,1,3,7,2,4,6]=>[5,7,1,2,3,4,6]=>[5,7,1,2,3,4,6]=>[4,5,6,1,7,2,-3]
[5,1,3,7,6,2,4]=>[5,6,1,2,3,7,4]=>[5,6,1,2,3,7,4]=>[4,5,7,1,2,6,-3]
[5,2,7,1,4,3,6]=>[7,5,4,1,2,3,6]=>[7,5,4,1,2,3,6]=>[5,6,3,2,7,1,-4]
[5,2,7,6,1,4,3]=>[6,5,4,1,2,7,3]=>[6,5,4,1,2,7,3]=>[5,7,3,2,1,6,-4]
[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>[7,3,5,1,2,4,6]=>[5,2,6,3,7,1,-4]
[5,3,2,7,6,1,4]=>[6,3,5,1,2,7,4]=>[6,3,5,1,2,7,4]=>[5,2,7,3,1,6,-4]
[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>[7,1,5,2,3,4,6]=>[4,5,6,3,7,1,-2]
[5,3,7,2,1,4,6]=>[2,7,5,1,3,4,6]=>[2,7,5,1,3,4,6]=>[1,5,6,3,7,2,-4]
[5,3,7,6,1,2,4]=>[6,1,5,2,3,7,4]=>[6,1,5,2,3,7,4]=>[4,5,7,3,1,6,-2]
[5,3,7,6,2,1,4]=>[2,6,5,1,3,7,4]=>[2,6,5,1,3,7,4]=>[1,5,7,3,2,6,-4]
[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>[7,4,1,5,2,3,6]=>[5,6,2,4,7,1,-3]
[5,4,2,7,6,1,3]=>[6,4,1,5,2,7,3]=>[6,4,1,5,2,7,3]=>[5,7,2,4,1,6,-3]
[6,1,2,4,7,3,5]=>[6,1,7,2,3,4,5]=>[6,1,7,2,3,4,5]=>[4,5,6,7,1,3,-2]
[6,1,3,7,2,5,4]=>[6,7,1,5,2,3,4]=>[6,7,1,5,2,3,4]=>[5,6,7,4,1,2,-3]
[6,1,4,3,7,2,5]=>[6,7,4,1,2,3,5]=>[6,7,4,1,2,3,5]=>[5,6,3,7,1,2,-4]
[6,1,4,7,3,2,5]=>[6,3,7,1,2,4,5]=>[6,3,7,1,2,4,5]=>[5,2,6,7,1,3,-4]
[6,2,1,4,7,3,5]=>[2,6,7,1,3,4,5]=>[2,6,7,1,3,4,5]=>[1,5,6,7,2,3,-4]
[6,2,3,7,5,1,4]=>[5,7,1,2,6,3,4]=>[5,7,1,2,6,3,4]=>[4,6,7,1,5,2,-3]
[6,2,4,7,1,3,5]=>[7,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>[4,5,6,7,2,1,-3]
[6,2,7,1,5,4,3]=>[7,6,4,5,1,2,3]=>[7,6,4,5,1,2,3]=>[6,7,3,4,2,1,-5]
[6,3,2,7,1,5,4]=>[7,3,6,5,1,2,4]=>[7,3,6,5,1,2,4]=>[6,2,7,4,3,1,-5]
[6,3,7,1,2,5,4]=>[7,1,6,5,2,3,4]=>[7,1,6,5,2,3,4]=>[5,6,7,4,3,1,-2]
[6,3,7,2,1,5,4]=>[2,7,6,5,1,3,4]=>[2,7,6,5,1,3,4]=>[1,6,7,4,3,2,-5]
[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>[7,3,4,6,1,2,5]=>[6,2,3,7,4,1,-5]
[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>[7,1,4,6,2,3,5]=>[5,6,3,7,4,1,-2]
[6,4,3,7,2,1,5]=>[2,7,4,6,1,3,5]=>[2,7,4,6,1,3,5]=>[1,6,3,7,4,2,-5]
[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[7,1,2,6,3,4,5]=>[3,5,6,7,4,1,-2]
[6,4,7,1,3,2,5]=>[7,3,1,6,2,4,5]=>[7,3,1,6,2,4,5]=>[5,2,6,7,4,1,-3]
[6,4,7,2,1,3,5]=>[2,7,1,6,3,4,5]=>[2,7,1,6,3,4,5]=>[1,5,6,7,4,2,-3]
[6,4,7,3,1,2,5]=>[3,1,7,6,2,4,5]=>[3,1,7,6,2,4,5]=>[5,1,6,7,4,3,-2]
[6,4,7,3,2,1,5]=>[2,3,7,6,1,4,5]=>[2,3,7,6,1,4,5]=>[1,2,6,7,4,3,-5]
[6,5,2,7,1,4,3]=>[7,5,4,1,6,2,3]=>[7,5,4,1,6,2,3]=>[6,7,3,2,5,1,-4]
[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>[7,3,5,1,6,2,4]=>[6,2,7,3,5,1,-4]
[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>[7,1,5,2,6,3,4]=>[4,6,7,3,5,1,-2]
[6,5,3,7,2,1,4]=>[2,7,5,1,6,3,4]=>[2,7,5,1,6,3,4]=>[1,6,7,3,5,2,-4]
[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>[7,4,1,5,6,2,3]=>[6,7,2,4,5,1,-3]
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[3,4,5,6,7,1,-2]
[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>[7,1,2,3,6,4,5]=>[3,4,6,7,5,1,-2]
[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]=>[7,1,2,5,3,4,6]=>[3,5,6,4,7,1,-2]
[7,1,2,3,6,5,4]=>[7,1,2,5,6,3,4]=>[7,1,2,5,6,3,4]=>[3,6,7,4,5,1,-2]
[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]=>[7,1,4,2,3,5,6]=>[4,5,3,6,7,1,-2]
[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]=>[7,1,4,2,6,3,5]=>[4,6,3,7,5,1,-2]
[7,1,2,5,4,3,6]=>[7,1,4,5,2,3,6]=>[7,1,4,5,2,3,6]=>[5,6,3,4,7,1,-2]
[7,1,2,6,5,4,3]=>[7,1,4,5,6,2,3]=>[7,1,4,5,6,2,3]=>[6,7,3,4,5,1,-2]
[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]=>[7,3,1,2,4,5,6]=>[4,2,5,6,7,1,-3]
[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]=>[7,3,1,2,6,4,5]=>[4,2,6,7,5,1,-3]
[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]=>[7,3,1,5,2,4,6]=>[5,2,6,4,7,1,-3]
[7,1,3,2,6,5,4]=>[7,3,1,5,6,2,4]=>[7,3,1,5,6,2,4]=>[6,2,7,4,5,1,-3]
[7,1,3,6,4,2,5]=>[7,4,1,6,2,3,5]=>[7,4,1,6,2,3,5]=>[5,6,2,7,4,1,-3]
[7,1,4,3,2,5,6]=>[7,3,4,1,2,5,6]=>[7,3,4,1,2,5,6]=>[5,2,3,6,7,1,-4]
[7,1,4,3,2,6,5]=>[7,3,4,1,6,2,5]=>[7,3,4,1,6,2,5]=>[6,2,3,7,5,1,-4]
[7,1,5,4,3,2,6]=>[7,3,4,5,1,2,6]=>[7,3,4,5,1,2,6]=>[6,2,3,4,7,1,-5]
[7,1,6,5,4,3,2]=>[7,3,4,5,6,1,2]=>[7,3,4,5,6,1,2]=>[7,2,3,4,5,1,-6]
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[1,4,5,6,7,2,-3]
[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]=>[2,7,1,3,6,4,5]=>[1,4,6,7,5,2,-3]
[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]=>[2,7,1,5,3,4,6]=>[1,5,6,4,7,2,-3]
[7,2,1,3,6,5,4]=>[2,7,1,5,6,3,4]=>[2,7,1,5,6,3,4]=>[1,6,7,4,5,2,-3]
[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]=>[2,7,4,1,3,5,6]=>[1,5,3,6,7,2,-4]
[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]=>[2,7,4,1,6,3,5]=>[1,6,3,7,5,2,-4]
[7,2,1,5,4,3,6]=>[2,7,4,5,1,3,6]=>[2,7,4,5,1,3,6]=>[1,6,3,4,7,2,-5]
[7,2,1,6,5,4,3]=>[2,7,4,5,6,1,3]=>[2,7,4,5,6,1,3]=>[1,7,3,4,5,2,-6]
[7,2,5,3,6,1,4]=>[6,7,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>[5,6,7,3,1,2,-4]
[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[3,1,7,2,4,5,6]=>[4,1,5,6,7,3,-2]
[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]=>[3,1,7,2,6,4,5]=>[4,1,6,7,5,3,-2]
[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]=>[3,1,7,5,2,4,6]=>[5,1,6,4,7,3,-2]
[7,3,1,2,6,5,4]=>[3,1,7,5,6,2,4]=>[3,1,7,5,6,2,4]=>[6,1,7,4,5,3,-2]
[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[2,3,7,1,4,5,6]=>[1,2,5,6,7,3,-4]
[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]=>[2,3,7,1,6,4,5]=>[1,2,6,7,5,3,-4]
[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]=>[2,3,7,5,1,4,6]=>[1,2,6,4,7,3,-5]
[7,3,2,1,6,5,4]=>[2,3,7,5,6,1,4]=>[2,3,7,5,6,1,4]=>[1,2,7,4,5,3,-6]
[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[4,1,2,7,3,5,6]=>[3,5,1,6,7,4,-2]
[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]=>[4,1,2,7,6,3,5]=>[3,6,1,7,5,4,-2]
[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]=>[4,3,1,7,2,5,6]=>[5,2,1,6,7,4,-3]
[7,4,1,3,2,6,5]=>[4,3,1,7,6,2,5]=>[4,3,1,7,6,2,5]=>[6,2,1,7,5,4,-3]
[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[2,4,1,7,3,5,6]=>[1,5,2,6,7,4,-3]
[7,4,2,1,3,6,5]=>[2,4,1,7,6,3,5]=>[2,4,1,7,6,3,5]=>[1,6,2,7,5,4,-3]
[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[3,1,4,7,2,5,6]=>[5,1,3,6,7,4,-2]
[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]=>[3,1,4,7,6,2,5]=>[6,1,3,7,5,4,-2]
[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[2,3,4,7,1,5,6]=>[1,2,3,6,7,4,-5]
[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]=>[2,3,4,7,6,1,5]=>[1,2,3,7,5,4,-6]
[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[5,1,2,3,7,4,6]=>[3,4,6,1,7,5,-2]
[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]=>[5,1,4,2,7,3,6]=>[4,6,3,1,7,5,-2]
[7,5,1,3,2,4,6]=>[5,3,1,2,7,4,6]=>[5,3,1,2,7,4,6]=>[4,2,6,1,7,5,-3]
[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]=>[5,3,4,1,7,2,6]=>[6,2,3,1,7,5,-4]
[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[2,5,1,3,7,4,6]=>[1,4,6,2,7,5,-3]
[7,5,2,1,4,3,6]=>[2,5,4,1,7,3,6]=>[2,5,4,1,7,3,6]=>[1,6,3,2,7,5,-4]
[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[3,1,5,2,7,4,6]=>[4,1,6,3,7,5,-2]
[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[2,3,5,1,7,4,6]=>[1,2,6,3,7,5,-4]
[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[4,1,2,5,7,3,6]=>[3,6,1,4,7,5,-2]
[7,5,4,1,3,2,6]=>[4,3,1,5,7,2,6]=>[4,3,1,5,7,2,6]=>[6,2,1,4,7,5,-3]
[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[2,4,1,5,7,3,6]=>[1,6,2,4,7,5,-3]
[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[3,1,4,5,7,2,6]=>[6,1,3,4,7,5,-2]
[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[2,3,4,5,7,1,6]=>[1,2,3,4,7,5,-6]
[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[6,1,2,3,4,7,5]=>[3,4,5,7,1,6,-2]
[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]=>[6,1,2,5,3,7,4]=>[3,5,7,4,1,6,-2]
[7,6,1,2,4,3,5]=>[6,1,4,2,3,7,5]=>[6,1,4,2,3,7,5]=>[4,5,3,7,1,6,-2]
[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]=>[6,1,4,5,2,7,3]=>[5,7,3,4,1,6,-2]
[7,6,1,3,2,4,5]=>[6,3,1,2,4,7,5]=>[6,3,1,2,4,7,5]=>[4,2,5,7,1,6,-3]
[7,6,1,3,2,5,4]=>[6,3,1,5,2,7,4]=>[6,3,1,5,2,7,4]=>[5,2,7,4,1,6,-3]
[7,6,1,4,3,2,5]=>[6,3,4,1,2,7,5]=>[6,3,4,1,2,7,5]=>[5,2,3,7,1,6,-4]
[7,6,1,5,4,3,2]=>[6,3,4,5,1,7,2]=>[6,3,4,5,1,7,2]=>[7,2,3,4,1,6,-5]
[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[2,6,1,3,4,7,5]=>[1,4,5,7,2,6,-3]
[7,6,2,1,3,5,4]=>[2,6,1,5,3,7,4]=>[2,6,1,5,3,7,4]=>[1,5,7,4,2,6,-3]
[7,6,2,1,4,3,5]=>[2,6,4,1,3,7,5]=>[2,6,4,1,3,7,5]=>[1,5,3,7,2,6,-4]
[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]=>[2,6,4,5,1,7,3]=>[1,7,3,4,2,6,-5]
[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[3,1,6,2,4,7,5]=>[4,1,5,7,3,6,-2]
[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]=>[3,1,6,5,2,7,4]=>[5,1,7,4,3,6,-2]
[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[2,3,6,1,4,7,5]=>[1,2,5,7,3,6,-4]
[7,6,3,2,1,5,4]=>[2,3,6,5,1,7,4]=>[2,3,6,5,1,7,4]=>[1,2,7,4,3,6,-5]
[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[4,1,2,6,3,7,5]=>[3,5,1,7,4,6,-2]
[7,6,4,1,3,2,5]=>[4,3,1,6,2,7,5]=>[4,3,1,6,2,7,5]=>[5,2,1,7,4,6,-3]
[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[2,4,1,6,3,7,5]=>[1,5,2,7,4,6,-3]
[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[3,1,4,6,2,7,5]=>[5,1,3,7,4,6,-2]
[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[2,3,4,6,1,7,5]=>[1,2,3,7,4,6,-5]
[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[5,1,2,3,6,7,4]=>[3,4,7,1,5,6,-2]
[7,6,5,1,2,4,3]=>[5,1,4,2,6,7,3]=>[5,1,4,2,6,7,3]=>[4,7,3,1,5,6,-2]
[7,6,5,1,3,2,4]=>[5,3,1,2,6,7,4]=>[5,3,1,2,6,7,4]=>[4,2,7,1,5,6,-3]
[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]=>[5,3,4,1,6,7,2]=>[7,2,3,1,5,6,-4]
[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[2,5,1,3,6,7,4]=>[1,4,7,2,5,6,-3]
[7,6,5,2,1,4,3]=>[2,5,4,1,6,7,3]=>[2,5,4,1,6,7,3]=>[1,7,3,2,5,6,-4]
[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[3,1,5,2,6,7,4]=>[4,1,7,3,5,6,-2]
[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[2,3,5,1,6,7,4]=>[1,2,7,3,5,6,-4]
[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[4,1,2,5,6,7,3]=>[3,7,1,4,5,6,-2]
[7,6,5,4,1,3,2]=>[4,3,1,5,6,7,2]=>[4,3,1,5,6,7,2]=>[7,2,1,4,5,6,-3]
[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[2,4,1,5,6,7,3]=>[1,7,2,4,5,6,-3]
[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[7,1,3,4,5,6,-2]
[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,-7]
[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[2,3,4,8,5,6,7,1]=>[1,2,3,5,6,7,4,-8]
[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[2,4,8,3,5,6,7,1]=>[1,4,2,5,6,7,3,-8]
[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[2,6,4,7,3,5,8,1]=>[1,5,3,6,2,4,7,-8]
[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[3,4,2,8,5,6,7,1]=>[3,1,2,5,6,7,4,-8]
[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[3,5,2,7,4,8,6,1]=>[3,1,5,2,7,4,6,-8]
[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[3,8,2,7,6,5,4,1]=>[3,1,7,6,5,4,2,-8]
[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[4,3,8,2,5,6,7,1]=>[4,2,1,5,6,7,3,-8]
[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[4,8,2,3,5,6,7,1]=>[3,4,1,5,6,7,2,-8]
[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[7,4,5,3,8,2,6,1]=>[6,4,2,3,7,1,5,-8]
[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[7,4,2,5,8,3,6,1]=>[3,6,2,4,7,1,5,-8]
[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1,-8]
[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[7,6,4,5,3,2,1,-8]
[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[3,1,4,8,5,6,7,2]=>[8,1,3,5,6,7,4,-2]
[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[4,1,8,3,5,6,7,2]=>[8,4,1,5,6,7,3,-2]
[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[2,4,1,8,5,6,7,3]=>[1,8,2,5,6,7,4,-3]
[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[4,1,2,7,8,5,6,3]=>[3,8,1,6,7,4,5,-2]
[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[4,1,2,8,7,5,6,3]=>[3,8,1,6,7,5,4,-2]
[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[4,1,2,8,5,6,7,3]=>[3,8,1,5,6,7,4,-2]
[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[2,3,8,1,5,6,7,4]=>[1,2,8,5,6,7,3,-4]
[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[3,8,2,1,7,6,5,4]=>[3,1,8,7,6,5,2,-4]
[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[3,8,2,1,5,6,7,4]=>[3,1,8,5,6,7,2,-4]
[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[3,1,8,2,5,6,7,4]=>[4,1,8,5,6,7,3,-2]
[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[2,8,1,3,5,6,7,4]=>[1,4,8,5,6,7,2,-3]
[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[8,1,2,3,5,6,7,4]=>[3,4,8,5,6,7,1,-2]
[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[4,1,2,6,3,8,7,5]=>[3,5,1,8,4,7,6,-2]
[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[4,1,2,7,3,8,6,5]=>[3,5,1,8,7,4,6,-2]
[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[3,1,6,2,4,8,7,5]=>[4,1,5,8,3,7,6,-2]
[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[2,4,5,3,7,1,8,6]=>[1,4,2,3,8,5,7,-6]
[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[4,5,2,3,8,1,7,6]=>[3,4,1,2,8,7,5,-6]
[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[4,1,5,3,7,2,8,6]=>[6,4,1,3,8,5,7,-2]
[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[3,1,5,2,7,4,8,6]=>[4,1,6,3,8,5,7,-2]
[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[3,1,5,2,8,4,7,6]=>[4,1,6,3,8,7,5,-2]
[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[5,3,6,2,4,8,1,7]=>[4,2,5,1,3,8,6,-7]
[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[4,1,2,6,3,8,5,7]=>[3,5,1,7,4,8,6,-2]
[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[4,5,2,3,8,1,6,7]=>[3,4,1,2,7,8,5,-6]
[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[4,1,5,3,8,2,6,7]=>[6,4,1,3,7,8,5,-2]
[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[3,1,5,2,8,4,6,7]=>[4,1,6,3,7,8,5,-2]
[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[3,5,2,7,4,6,1,8]=>[3,1,5,2,6,4,8,-7]
[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[4,5,2,3,7,6,1,8]=>[3,4,1,2,6,5,8,-7]
[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[6,4,2,7,3,5,1,8]=>[3,5,2,6,1,4,8,-7]
[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[7,4,2,6,3,5,1,8]=>[3,5,2,6,4,1,8,-7]
[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[3,6,2,1,4,7,5,8]=>[3,1,5,7,2,6,8,-4]
[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[4,5,2,3,7,1,6,8]=>[3,4,1,2,7,5,8,-6]
[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[3,1,5,2,7,4,6,8]=>[4,1,6,3,7,5,8,-2]
[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[4,3,6,2,5,1,7,8]=>[4,2,1,5,3,7,8,-6]
[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[4,3,2,1,6,7,8,-5]
[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[3,2,1,5,6,7,8,-4]
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,-1]
[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[2,3,7,4,5,6,8,1]=>[1,2,4,5,6,3,7,-8]
[3,2,5,6,8,7,4,1]=>[4,3,2,7,5,6,8,1]=>[4,3,2,7,5,6,8,1]=>[3,2,1,5,6,4,7,-8]
[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[7,3,6,5,4,2,1,-8]
[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[7,4,3,6,5,2,1,-8]
[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[3,2,7,6,5,4,1,-8]
[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[5,4,3,2,7,6,1,-8]
[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[8,3,2,5,4,7,6,1]=>[3,2,5,4,7,6,1,-8]
[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[1,4,3,6,5,8,7,2]=>[8,3,2,5,4,7,6,-1]
[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[2,1,4,5,8,6,7,3]=>[1,8,3,4,6,7,5,-2]
[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[1,8,7,6,5,4,3,-2]
[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,5,6,4,3]=>[1,8,7,5,6,4,3,-2]
[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,8,5,4,7,6,3]=>[1,8,5,4,7,6,3,-2]
[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[2,3,8,4,5,6,7,-1]
[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[2,3,8,7,6,5,4,-1]
[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[2,3,4,1,8,7,6,5]=>[1,2,3,8,7,6,5,-4]
[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[2,4,3,1,6,8,7,5]=>[1,3,2,8,5,7,6,-4]
[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[2,4,3,1,8,7,6,5]=>[1,3,2,8,7,6,5,-4]
[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[3,2,4,1,8,7,6,5]=>[2,1,3,8,7,6,5,-4]
[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,6,7,8,5]=>[3,2,1,8,5,6,7,-4]
[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,6,8,7,5]=>[3,2,1,8,5,7,6,-4]
[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,7,6,8,5]=>[3,2,1,8,6,5,7,-4]
[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[3,2,1,8,7,6,5,-4]
[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,6,7,5]=>[3,2,1,8,6,7,5,-4]
[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[4,2,3,1,8,7,6,5]=>[2,3,1,8,7,6,5,-4]
[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[4,2,3,1,8,6,7,5]=>[2,3,1,8,6,7,5,-4]
[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[1,3,4,2,8,7,6,5]=>[4,2,3,8,7,6,5,-1]
[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[4,3,2,8,7,6,5,-1]
[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,6,8,7,5]=>[1,4,3,8,5,7,6,-2]
[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[1,4,3,8,7,6,5,-2]
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,8,6,7,5]=>[1,4,3,8,6,7,5,-2]
[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[2,4,3,8,7,6,5,-1]
[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[2,3,1,4,8,7,6,5]=>[1,2,4,8,7,6,5,-3]
[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[2,1,4,8,7,6,5,-3]
[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[3,2,4,8,7,6,5,-1]
[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[1,3,4,8,7,6,5,-2]
[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[2,3,4,8,7,6,5,-1]
[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,7,8,6]=>[3,2,1,5,8,6,7,-4]
[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[3,2,1,5,8,7,6,-4]
[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[2,3,6,4,5,1,8,7]=>[1,2,4,5,3,8,7,-6]
[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[5,4,3,2,1,8,7,-6]
[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[6,5,3,4,2,1,8,7]=>[5,3,4,2,1,8,7,-6]
[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,5,4,1,8,7]=>[3,2,5,4,1,8,7,-6]
[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[2,1,4,6,5,3,8,7]=>[1,6,3,5,4,8,7,-2]
[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[1,6,5,4,3,8,7,-2]
[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,6,4,5,3,8,7]=>[1,6,4,5,3,8,7,-2]
[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[1,3,2,6,5,8,7,-4]
[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[3,2,1,6,5,8,7,-4]
[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,3,1,6,5,8,7,-4]
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[1,4,3,6,5,8,7,-2]
[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[1,5,4,3,6,8,7,-2]
[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[3,2,1,5,6,8,7,-4]
[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[3,2,5,4,7,6,1,8]=>[2,1,4,3,6,5,8,-7]
[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[3,2,1,7,5,6,4,8]=>[2,1,7,5,6,4,8,-3]
[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,6,7,5,8]=>[3,2,1,7,5,6,8,-4]
[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[3,2,1,7,6,5,8,-4]
[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[2,1,4,7,6,5,8,-3]
[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,1,5,4,7,6,8,-3]
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[3,2,5,4,7,6,8,-1]
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[2,3,5,4,7,6,8,-1]
[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[3,2,1,5,7,6,8,-4]
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[3,2,4,5,7,6,8,-1]
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,7,6,8,-1]
[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[3,2,1,6,5,7,8,-4]
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[3,2,5,4,6,7,8,-1]
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[2,3,5,4,6,7,8,-1]
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[3,2,4,5,6,7,8,-1]
[1,2,8,4,7,6,5,3]=>[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,8,4,3]=>[2,8,7,3,4,5,6,-1]
[1,3,8,5,6,7,4,2]=>[1,4,3,7,8,5,6,2]=>[1,4,3,7,8,5,6,2]=>[8,3,2,6,7,4,5,-1]
[1,8,4,7,6,5,3,2]=>[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,8,4,2]=>[8,2,7,3,4,5,6,-1]
[2,1,4,3,8,6,7,5]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,7,8,6,5]=>[1,4,3,8,7,5,6,-2]
[2,1,4,7,5,6,8,3]=>[2,1,8,4,7,5,6,3]=>[2,1,8,4,7,5,6,3]=>[1,8,4,6,7,5,3,-2]
[2,1,6,4,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>[2,1,5,6,4,3,8,7]=>[1,6,5,3,4,8,7,-2]
[2,1,7,4,6,5,8,3]=>[2,1,8,7,6,4,5,3]=>[2,1,8,7,6,4,5,3]=>[1,8,6,7,5,4,3,-2]
[2,1,8,4,7,6,5,3]=>[2,1,5,6,7,8,4,3]=>[2,1,5,6,7,8,4,3]=>[1,8,7,3,4,5,6,-2]
[2,1,7,5,4,6,8,3]=>[2,1,8,5,7,4,6,3]=>[2,1,8,5,7,4,6,3]=>[1,8,6,4,7,5,3,-2]
[2,5,3,4,6,1,8,7]=>[6,2,5,3,4,1,8,7]=>[6,2,5,3,4,1,8,7]=>[2,4,5,3,1,8,7,-6]
[2,6,3,4,5,8,7,1]=>[7,2,6,3,4,5,8,1]=>[7,2,6,3,4,5,8,1]=>[2,4,5,6,3,1,7,-8]
[2,7,4,5,6,3,1,8]=>[3,2,6,7,4,5,1,8]=>[3,2,6,7,4,5,1,8]=>[2,1,5,6,3,4,8,-7]
[2,8,5,4,3,6,7,1]=>[7,2,4,5,8,3,6,1]=>[7,2,4,5,8,3,6,1]=>[2,6,3,4,7,1,5,-8]
[3,2,4,1,8,6,7,5]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,7,8,6,5]=>[3,2,1,8,7,5,6,-4]
[3,2,7,4,6,5,8,1]=>[8,3,2,7,6,4,5,1]=>[8,3,2,7,6,4,5,1]=>[3,2,6,7,5,4,1,-8]
[4,2,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[3,1,2,6,5,8,7,-4]
[4,2,3,1,7,6,8,5]=>[3,4,2,1,8,7,6,5]=>[3,4,2,1,8,7,6,5]=>[3,1,2,8,7,6,5,-4]
[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>[3,4,2,1,7,8,6,5]=>[3,1,2,8,7,5,6,-4]
[5,2,4,3,6,1,8,7]=>[6,5,4,2,3,1,8,7]=>[6,5,4,2,3,1,8,7]=>[4,5,3,2,1,8,7,-6]
[5,2,4,3,7,6,8,1]=>[8,5,4,2,3,7,6,1]=>[8,5,4,2,3,7,6,1]=>[4,5,3,2,7,6,1,-8]
[7,2,4,3,6,5,8,1]=>[8,7,4,2,6,3,5,1]=>[8,7,4,2,6,3,5,1]=>[4,6,3,7,5,2,1,-8]
[7,2,5,4,6,3,8,1]=>[8,7,6,5,2,4,3,1]=>[8,7,6,5,2,4,3,1]=>[5,7,6,4,3,2,1,-8]
[5,3,2,4,6,1,8,7]=>[6,3,5,2,4,1,8,7]=>[6,3,5,2,4,1,8,7]=>[4,2,5,3,1,8,7,-6]
[7,3,2,4,6,5,8,1]=>[8,3,7,2,6,4,5,1]=>[8,3,7,2,6,4,5,1]=>[4,2,6,7,5,3,1,-8]
[8,3,2,5,7,6,4,1]=>[4,3,6,7,2,8,5,1]=>[4,3,6,7,2,8,5,1]=>[5,2,1,7,3,4,6,-8]
[7,3,2,6,5,4,8,1]=>[8,3,7,5,6,2,4,1]=>[8,3,7,5,6,2,4,1]=>[6,2,7,4,5,3,1,-8]
[7,3,4,2,6,5,8,1]=>[8,4,7,3,6,2,5,1]=>[8,4,7,3,6,2,5,1]=>[6,4,2,7,5,3,1,-8]
[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[4,2,6,1,7,3,5,8]=>[2,6,1,7,3,5,8,-4]
[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,7,8,5,6]=>[1,4,3,7,8,5,6,-2]
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,5,7,6]=>[1,4,3,6,8,7,5,-2]
[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[2,1,7,4,5,8,3,6]=>[1,7,4,5,8,3,6,-2]
[2,1,4,5,7,8,3,6]=>[2,1,8,4,5,3,7,6]=>[2,1,8,4,5,3,7,6]=>[1,6,4,5,8,7,3,-2]
[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[4,2,6,1,5,3,7,8]=>[2,6,1,5,3,7,8,-4]
[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,6,4,1,3,7,8]=>[2,6,4,1,3,7,8,-5]
[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,5,6,3,4,8,7]=>[1,5,6,3,4,8,7,-2]
[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,6,3,5,4,8,7]=>[1,4,6,5,3,8,7,-2]
[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[5,2,6,7,1,3,4,8]=>[2,6,7,1,3,4,8,-5]
[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[2,1,5,8,3,6,7,4]=>[1,5,8,3,6,7,4,-2]
[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[2,1,5,7,3,8,4,6]=>[1,5,7,3,8,4,6,-2]
[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,4,3,6]=>[2,1,7,8,5,4,3,6]=>[1,7,6,5,8,3,4,-2]
[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,8,3,5,4,7,6]=>[1,4,6,5,8,7,3,-2]
[2,3,5,7,8,1,4,6]=>[8,2,3,1,5,4,7,6]=>[8,2,3,1,5,4,7,6]=>[2,3,6,5,8,7,1,-4]
[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[6,2,3,1,5,4,8,7]=>[2,3,6,5,1,8,7,-4]
[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[2,1,6,7,8,3,4,5]=>[1,6,7,8,3,4,5,-2]
[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,8,3,4,6,7,5]=>[1,4,5,8,6,7,3,-2]
[2,1,6,3,4,7,8,5]=>[2,1,6,3,8,4,7,5]=>[2,1,6,3,8,4,7,5]=>[1,4,6,8,3,7,5,-2]
[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[4,2,3,1,8,5,7,6]=>[2,3,1,6,8,7,5,-4]
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[2,1,4,6,7,8,5,-3]
[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[4,1,2,6,5,8,7,-3]
[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,3,1,6,5,8,7,-2]
[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[4,6,3,1,7,2,5,8]=>[6,3,1,7,2,5,8,-4]
[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[4,1,3,2,8,6,7,5]=>[4,3,1,8,6,7,5,-2]
[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[3,4,1,2,7,8,5,6]=>[4,1,2,7,8,5,6,-3]
[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[4,1,3,2,8,5,7,6]=>[4,3,1,6,8,7,5,-2]
[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[5,1,4,2,7,6,8,-3]
[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[4,3,1,6,7,8,5,-2]
[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[3,6,1,4,5,2,8,7]=>[6,1,4,5,2,8,7,-3]
[3,4,5,1,6,2,8,7]=>[5,6,3,4,1,2,8,7]=>[5,6,3,4,1,2,8,7]=>[6,3,4,1,2,8,7,-5]
[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[4,6,3,1,5,2,7,8]=>[6,3,1,5,2,7,8,-4]
[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>[6,3,4,1,2,7,8,-5]
[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[3,5,1,6,2,4,8,7]=>[5,1,6,2,4,8,7,-3]
[3,5,1,6,2,4,8,7]=>[5,6,3,2,1,4,8,7]=>[5,6,3,2,1,4,8,7]=>[4,3,6,1,2,8,7,-5]
[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[6,1,3,2,5,4,8,7]=>[4,3,6,5,1,8,7,-2]
[3,5,1,6,2,4,7,8]=>[5,6,3,2,1,4,7,8]=>[5,6,3,2,1,4,7,8]=>[4,3,6,1,2,7,8,-5]
[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[5,6,3,7,1,2,4,8]=>[6,3,7,1,2,4,8,-5]
[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[5,7,3,8,1,6,2,4]=>[7,3,8,1,6,2,4,-5]
[3,1,5,6,7,8,2,4]=>[3,8,1,2,5,6,7,4]=>[3,8,1,2,5,6,7,4]=>[4,1,8,5,6,7,2,-3]
[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[3,5,1,7,2,8,4,6]=>[5,1,7,2,8,4,6,-3]
[3,5,1,7,2,8,4,6]=>[5,7,3,8,1,4,2,6]=>[5,7,3,8,1,4,2,6]=>[7,3,6,1,8,2,4,-5]
[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[8,1,3,2,5,4,7,6]=>[4,3,6,5,8,7,1,-2]
[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>[8,1,3,2,5,4,6,7]=>[4,3,6,5,7,8,1,-2]
[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[4,3,5,1,7,8,6,-2]
[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[1,5,3,7,2,6,4,8]=>[5,3,7,2,6,4,8,-1]
[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[3,6,1,7,8,2,4,5]=>[6,1,7,8,2,4,5,-3]
[3,6,1,7,8,2,4,5]=>[6,8,3,2,4,1,7,5]=>[6,8,3,2,4,1,7,5]=>[4,3,5,8,1,7,2,-6]
[3,6,1,2,4,7,8,5]=>[6,1,3,2,8,4,7,5]=>[6,1,3,2,8,4,7,5]=>[4,3,6,8,1,7,5,-2]
[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[4,5,6,1,2,3,8,7]=>[5,6,1,2,3,8,7,-4]
[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[6,1,2,4,5,3,8,7]=>[3,6,4,5,1,8,7,-2]
[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[8,1,2,4,5,6,3,7]=>[3,7,4,5,6,8,1,-2]
[4,1,5,6,2,3,7,8]=>[4,6,2,1,5,3,7,8]=>[4,6,2,1,5,3,7,8]=>[3,6,1,5,2,7,8,-4]
[4,5,1,6,2,3,7,8]=>[5,6,2,4,1,3,7,8]=>[5,6,2,4,1,3,7,8]=>[3,6,4,1,2,7,8,-5]
[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3,8]=>[6,7,4,1,2,3,8,-5]
[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[5,7,8,4,1,6,2,3]=>[7,8,4,1,6,2,3,-5]
[4,1,5,6,7,8,2,3]=>[4,8,2,1,5,6,7,3]=>[4,8,2,1,5,6,7,3]=>[3,8,1,5,6,7,2,-4]
[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[4,5,7,1,2,8,3,6]=>[5,7,1,2,8,3,6,-4]
[4,5,1,7,2,8,3,6]=>[5,7,8,4,1,3,2,6]=>[5,7,8,4,1,3,2,6]=>[7,6,4,1,8,2,3,-5]
[4,5,7,1,2,8,3,6]=>[7,1,8,4,5,3,2,6]=>[7,1,8,4,5,3,2,6]=>[7,6,4,5,8,1,3,-2]
[4,1,2,5,7,8,3,6]=>[4,1,8,2,5,3,7,6]=>[4,1,8,2,5,3,7,6]=>[4,6,1,5,8,7,3,-2]
[4,1,2,5,6,3,8,7]=>[4,1,6,2,5,3,8,7]=>[4,1,6,2,5,3,8,7]=>[4,6,1,5,3,8,7,-2]
[4,1,2,5,6,7,8,3]=>[4,1,8,2,5,6,7,3]=>[4,1,8,2,5,6,7,3]=>[4,8,1,5,6,7,3,-2]
[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[4,6,7,1,8,2,3,5]=>[6,7,1,8,2,3,5,-4]
[4,6,7,1,8,2,3,5]=>[7,8,2,4,3,6,1,5]=>[7,8,2,4,3,6,1,5]=>[3,5,4,8,6,1,2,-7]
[4,1,6,2,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[4,6,7,1,3,2,5,8]=>[6,5,1,7,2,3,8,-4]
[4,1,6,2,3,7,5,8]=>[4,6,2,1,7,3,5,8]=>[4,6,2,1,7,3,5,8]=>[3,6,1,7,2,5,8,-4]
[4,1,2,6,3,7,8,5]=>[4,1,6,2,8,3,7,5]=>[4,1,6,2,8,3,7,5]=>[4,6,1,8,3,7,5,-2]
[1,4,6,2,3,8,5,7]=>[1,6,2,4,8,3,5,7]=>[1,6,2,4,8,3,5,7]=>[3,6,4,7,2,8,5,-1]
[1,2,4,7,3,8,5,6]=>[1,2,7,4,8,5,3,6]=>[1,2,7,4,8,5,3,6]=>[2,7,4,6,8,3,5,-1]
[1,2,4,5,7,8,3,6]=>[1,2,8,4,5,3,7,6]=>[1,2,8,4,5,3,7,6]=>[2,6,4,5,8,7,3,-1]
[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[2,5,4,3,7,8,6,-1]
[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[6,7,8,1,2,3,4,-5]
[5,6,1,7,2,3,8,4]=>[6,7,2,8,5,1,3,4]=>[6,7,2,8,5,1,3,4]=>[3,7,8,5,1,2,4,-6]
[5,1,6,7,2,8,3,4]=>[5,7,8,3,1,6,2,4]=>[5,7,8,3,1,6,2,4]=>[7,4,8,1,6,2,3,-5]
[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[5,6,7,3,1,2,4,8]=>[6,4,7,1,2,3,8,-5]
[5,1,6,2,3,7,4,8]=>[5,6,2,7,1,3,4,8]=>[5,6,2,7,1,3,4,8]=>[3,6,7,1,2,4,8,-5]
[1,5,6,2,3,7,8,4]=>[1,6,2,8,5,3,7,4]=>[1,6,2,8,5,3,7,4]=>[3,6,8,5,2,7,4,-1]
[5,1,6,2,3,8,4,7]=>[5,6,2,8,1,3,4,7]=>[5,6,2,8,1,3,4,7]=>[3,6,7,1,2,8,4,-5]
[5,1,7,2,8,3,4,6]=>[5,7,8,3,1,4,2,6]=>[5,7,8,3,1,4,2,6]=>[7,4,6,1,8,2,3,-5]
[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[1,2,7,3,5,8,4,6]=>[2,4,7,5,8,3,6,-1]
[1,5,2,3,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,2,8,3,4,6,7]=>[3,5,6,2,7,8,4,-1]
[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[6,7,2,8,4,1,3,5]=>[3,7,5,8,1,2,4,-6]
[6,1,2,3,7,8,4,5]=>[6,1,2,8,4,3,7,5]=>[6,1,2,8,4,3,7,5]=>[3,6,5,8,1,7,4,-2]
[1,7,2,3,8,4,5,6]=>[1,7,2,8,4,5,3,6]=>[1,7,2,8,4,5,3,6]=>[3,7,5,6,8,2,4,-1]
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[2,3,5,6,7,8,4,-1]
[6,4,5,2,3,1,8,7]=>[3,5,2,6,4,1,8,7]=>[3,5,2,6,4,1,8,7]=>[3,1,5,2,4,8,7,-6]
[2,1,8,6,7,4,5,3]=>[2,1,5,7,4,8,6,3]=>[2,1,5,7,4,8,6,3]=>[1,8,5,3,7,4,6,-2]
[8,4,6,2,7,3,5,1]=>[5,6,7,8,3,4,2,1]=>[5,6,7,8,3,4,2,1]=>[7,5,6,1,2,3,4,-8]
[8,4,7,2,6,5,3,1]=>[3,5,6,7,8,4,2,1]=>[3,5,6,7,8,4,2,1]=>[7,1,6,2,3,4,5,-8]
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[1,4,3,6,5,8,7,10,9,-2]
[6,4,5,2,3,1,8,7,10,9]=>[3,5,2,6,4,1,8,7,10,9]=>[3,5,2,6,4,1,8,7,10,9]=>[3,1,5,2,4,8,7,10,9,-6]
[2,1,8,6,7,4,5,3,10,9]=>[2,1,5,7,4,8,6,3,10,9]=>[2,1,5,7,4,8,6,3,10,9]=>[1,8,5,3,7,4,6,10,9,-2]
[10,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,10,8,1]=>[3,5,2,7,4,9,6,10,8,1]=>[3,1,5,2,7,4,9,6,8,-10]
[2,1,4,3,10,8,9,6,7,5]=>[2,1,4,3,7,9,6,10,8,5]=>[2,1,4,3,7,9,6,10,8,5]=>[1,4,3,10,7,5,9,6,8,-2]
[6,2,8,1,3,4,5,7]=>[8,6,1,3,4,2,5,7]=>[8,6,1,3,4,2,5,7]=>[6,4,5,7,2,8,1,-3]
[8,4,6,1,2,3,5,7]=>[6,1,2,8,3,4,5,7]=>[6,1,2,8,3,4,5,7]=>[3,5,6,7,1,8,4,-2]
[8,4,7,1,2,3,5,6]=>[7,1,2,8,3,5,4,6]=>[7,1,2,8,3,5,4,6]=>[3,5,7,6,8,1,4,-2]
[7,3,6,8,1,2,4,5]=>[8,1,7,2,4,3,6,5]=>[8,1,7,2,4,3,6,5]=>[4,6,5,8,7,3,1,-2]
[8,2,6,7,1,3,4,5]=>[7,8,1,3,4,2,6,5]=>[7,8,1,3,4,2,6,5]=>[6,4,5,8,7,1,2,-3]
[5,8,4,7,1,2,3,6]=>[7,1,2,8,5,3,4,6]=>[7,1,2,8,5,3,4,6]=>[3,6,7,5,8,1,4,-2]
[7,5,2,4,1,3,6,8]=>[4,5,1,2,7,3,6,8]=>[4,5,1,2,7,3,6,8]=>[4,6,1,2,7,5,8,-3]
[8,5,2,4,1,3,6,7]=>[4,5,1,2,8,3,6,7]=>[4,5,1,2,8,3,6,7]=>[4,6,1,2,7,8,5,-3]
[8,6,3,5,1,2,4,7]=>[5,1,6,2,3,8,4,7]=>[5,1,6,2,3,8,4,7]=>[4,5,7,1,3,8,6,-2]
[6,8,2,5,7,1,3,4]=>[7,8,1,3,2,6,5,4]=>[7,8,1,3,2,6,5,4]=>[5,4,8,7,6,1,2,-3]
[6,5,3,7,8,1,2,4]=>[8,1,5,2,6,3,7,4]=>[8,1,5,2,6,3,7,4]=>[4,6,8,3,5,7,1,-2]
[7,4,2,5,8,1,3,6]=>[8,4,1,7,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>[5,6,2,7,8,4,1,-3]
[7,5,2,4,8,1,3,6]=>[8,5,1,2,7,3,4,6]=>[8,5,1,2,7,3,4,6]=>[4,6,7,2,8,5,1,-3]
[7,3,2,6,8,1,4,5]=>[8,3,7,1,4,2,6,5]=>[8,3,7,1,4,2,6,5]=>[6,2,5,8,7,3,1,-4]
[8,4,2,5,7,1,3,6]=>[7,4,1,8,2,3,5,6]=>[7,4,1,8,2,3,5,6]=>[5,6,2,7,8,1,4,-3]
[8,5,2,4,7,1,3,6]=>[7,5,1,2,8,3,4,6]=>[7,5,1,2,8,3,4,6]=>[4,6,7,2,8,1,5,-3]
[8,3,2,6,7,1,4,5]=>[7,3,8,1,4,2,6,5]=>[7,3,8,1,4,2,6,5]=>[6,2,5,8,7,1,3,-4]
[6,3,7,2,5,1,4,8]=>[5,7,6,1,2,3,4,8]=>[5,7,6,1,2,3,4,8]=>[5,6,7,1,3,2,8,-4]
[7,3,6,2,5,1,4,8]=>[5,6,7,1,2,3,4,8]=>[5,6,7,1,2,3,4,8]=>[5,6,7,1,2,3,8,-4]
[6,3,8,2,5,1,4,7]=>[5,8,6,1,2,3,4,7]=>[5,8,6,1,2,3,4,7]=>[5,6,7,1,3,8,2,-4]
[7,4,8,3,6,1,2,5]=>[6,1,8,7,2,3,4,5]=>[6,1,8,7,2,3,4,5]=>[5,6,7,8,1,4,3,-2]
[8,3,6,2,5,1,4,7]=>[5,6,8,1,2,3,4,7]=>[5,6,8,1,2,3,4,7]=>[5,6,7,1,2,8,3,-4]
[8,3,7,2,6,1,4,5]=>[6,7,8,1,4,2,3,5]=>[6,7,8,1,4,2,3,5]=>[6,7,5,8,1,2,3,-4]
[8,4,7,3,6,1,2,5]=>[6,1,7,8,2,3,4,5]=>[6,1,7,8,2,3,4,5]=>[5,6,7,8,1,3,4,-2]
[6,5,4,2,7,1,3,8]=>[7,4,1,5,6,2,3,8]=>[7,4,1,5,6,2,3,8]=>[6,7,2,4,5,1,8,-3]
[6,5,4,3,8,1,2,7]=>[8,1,4,5,6,3,2,7]=>[8,1,4,5,6,3,2,7]=>[7,6,3,4,5,8,1,-2]
[8,7,5,3,6,1,2,4]=>[6,1,5,2,7,3,8,4]=>[6,1,5,2,7,3,8,4]=>[4,6,8,3,1,5,7,-2]
[5,8,3,7,2,6,1,4]=>[6,7,8,1,5,2,3,4]=>[6,7,8,1,5,2,3,4]=>[6,7,8,5,1,2,3,-4]
[5,1,2,3,8,7,4,6]=>[5,1,2,7,3,4,8,6]=>[5,1,2,7,3,4,8,6]=>[3,5,6,1,8,4,7,-2]
[8,1,2,5,3,4,6,7]=>[8,1,5,3,2,4,6,7]=>[8,1,5,3,2,4,6,7]=>[5,4,6,3,7,8,1,-2]
[7,1,2,6,3,4,8,5]=>[7,1,6,3,8,2,4,5]=>[7,1,6,3,8,2,4,5]=>[6,4,7,8,3,1,5,-2]
[4,1,2,5,8,7,3,6]=>[4,1,7,2,5,3,8,6]=>[4,1,7,2,5,3,8,6]=>[4,6,1,5,8,3,7,-2]
[3,1,7,2,6,4,8,5]=>[3,7,1,6,8,2,4,5]=>[3,7,1,6,8,2,4,5]=>[6,1,7,8,4,2,5,-3]
[5,1,4,2,7,3,8,6]=>[5,4,7,1,2,8,3,6]=>[5,4,7,1,2,8,3,6]=>[5,7,2,1,8,3,6,-4]
[7,1,4,2,6,3,8,5]=>[7,4,6,1,8,2,3,5]=>[7,4,6,1,8,2,3,5]=>[6,7,2,8,3,1,5,-4]
[7,1,5,2,6,3,8,4]=>[7,5,6,8,1,2,3,4]=>[7,5,6,8,1,2,3,4]=>[6,7,8,2,3,1,4,-5]
[8,1,4,2,6,7,3,5]=>[8,4,7,1,3,2,6,5]=>[8,4,7,1,3,2,6,5]=>[6,5,2,8,7,3,1,-4]
[2,8,1,7,6,3,4,5]=>[8,2,6,3,4,7,1,5]=>[8,2,6,3,4,7,1,5]=>[2,4,5,8,3,6,1,-7]
[6,3,1,2,4,7,8,5]=>[3,1,6,2,8,4,7,5]=>[3,1,6,2,8,4,7,5]=>[4,1,6,8,3,7,5,-2]
[5,4,1,2,8,3,6,7]=>[4,1,5,8,3,2,6,7]=>[4,1,5,8,3,2,6,7]=>[6,5,1,3,7,8,4,-2]
[7,4,1,5,2,3,8,6]=>[4,7,1,5,2,8,3,6]=>[4,7,1,5,2,8,3,6]=>[5,7,1,4,8,2,6,-3]
[8,3,1,7,6,2,4,5]=>[3,8,6,1,4,7,2,5]=>[3,8,6,1,4,7,2,5]=>[7,1,5,8,3,6,2,-4]
[8,4,1,5,7,2,3,6]=>[4,8,1,7,2,3,5,6]=>[4,8,1,7,2,3,5,6]=>[5,6,1,7,8,4,2,-3]
[4,3,1,5,6,7,8,2]=>[3,4,8,2,5,6,7,1]=>[3,4,8,2,5,6,7,1]=>[4,1,2,5,6,7,3,-8]
[2,5,4,1,8,3,6,7]=>[4,2,5,8,3,1,6,7]=>[4,2,5,8,3,1,6,7]=>[2,5,1,3,7,8,4,-6]
[7,3,4,1,6,2,8,5]=>[4,6,7,3,8,1,2,5]=>[4,6,7,3,8,1,2,5]=>[7,4,1,8,2,3,5,-6]
[8,3,5,1,6,2,4,7]=>[5,6,8,2,3,1,4,7]=>[5,6,8,2,3,1,4,7]=>[4,5,7,1,2,8,3,-6]
[7,3,5,1,6,2,8,4]=>[5,6,7,8,3,1,2,4]=>[5,6,7,8,3,1,2,4]=>[7,5,8,1,2,3,4,-6]
[8,5,4,1,6,7,2,3]=>[4,5,2,8,7,1,6,3]=>[4,5,2,8,7,1,6,3]=>[3,8,1,2,7,5,4,-6]
[7,3,6,5,1,2,8,4]=>[5,1,6,7,8,4,3,2]=>[5,1,6,7,8,4,3,2]=>[8,7,6,1,3,4,5,-2]
[4,6,7,3,8,5,1,2]=>[5,1,8,4,7,6,2,3]=>[5,1,8,4,7,6,2,3]=>[7,8,4,1,6,5,3,-2]
[6,2,8,4,5,1,7,3]=>[5,6,7,8,4,2,1,3]=>[5,6,7,8,4,2,1,3]=>[6,8,5,1,2,3,4,-7]
[5,1,4,8,6,2,3,7]=>[5,6,2,1,4,8,3,7]=>[5,6,2,1,4,8,3,7]=>[3,7,5,1,2,8,6,-4]
[3,5,2,7,1,8,6,4]=>[7,5,3,6,2,8,1,4]=>[7,5,3,6,2,8,1,4]=>[5,3,8,2,4,1,6,-7]
[2,6,7,3,1,5,8,4]=>[3,2,7,8,1,6,5,4]=>[3,2,7,8,1,6,5,4]=>[2,1,8,7,6,3,4,-5]
[4,6,7,2,8,1,5,3]=>[8,7,5,4,1,6,2,3]=>[8,7,5,4,1,6,2,3]=>[7,8,4,3,6,2,1,-5]
[5,6,7,8,2,1,4,3]=>[2,8,4,1,5,6,7,3]=>[2,8,4,1,5,6,7,3]=>[1,8,3,5,6,7,2,-4]
[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>[3,1,4,2,7,5,8,6]=>[4,1,3,6,8,5,7,-2]
[4,6,2,7,3,5,1,8]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>[6,5,4,1,2,3,8,-7]
[4,8,2,6,5,1,3,7]=>[5,6,2,4,8,1,3,7]=>[5,6,2,4,8,1,3,7]=>[3,7,4,1,2,8,5,-6]
[3,2,5,1,6,4,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,6,1,4,8,7]=>[3,2,6,1,4,8,7,-5]
[4,2,5,3,6,1,8,7]=>[6,4,5,2,3,1,8,7]=>[6,4,5,2,3,1,8,7]=>[4,5,2,3,1,8,7,-6]
[4,3,6,5,7,1,8,2]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[8,4,3,6,5,1,2,-7]
[5,3,6,4,7,1,8,2]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[8,5,6,3,4,1,2,-7]
[2,1,6,4,7,5,8,3]=>[2,1,8,6,7,4,5,3]=>[2,1,8,6,7,4,5,3]=>[1,8,6,7,4,5,3,-2]
[5,2,6,1,7,3,8,4]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]=>[5,7,8,2,1,3,4,-6]
[4,2,6,1,7,3,8,5]=>[6,4,7,2,8,1,3,5]=>[6,4,7,2,8,1,3,5]=>[4,7,2,8,1,3,5,-6]
[3,2,5,1,7,4,8,6]=>[5,3,2,7,1,8,4,6]=>[5,3,2,7,1,8,4,6]=>[3,2,7,1,8,4,6,-5]
[3,2,4,1,7,5,8,6]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,7,8,5,6]=>[3,2,1,7,8,5,6,-4]
[3,1,4,2,7,6,8,5]=>[3,4,1,2,8,7,6,5]=>[3,4,1,2,8,7,6,5]=>[4,1,2,8,7,6,5,-3]
[3,2,5,1,7,6,8,4]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[3,2,8,1,7,6,4,-5]
[4,2,6,1,7,5,8,3]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[4,8,2,7,1,5,3,-6]
[3,1,5,2,7,6,8,4]=>[3,5,1,8,2,7,6,4]=>[3,5,1,8,2,7,6,4]=>[5,1,8,2,7,6,4,-3]
[2,1,5,3,7,6,8,4]=>[2,1,5,8,3,7,6,4]=>[2,1,5,8,3,7,6,4]=>[1,5,8,3,7,6,4,-2]
[4,1,6,2,7,5,8,3]=>[4,6,8,1,7,2,5,3]=>[4,6,8,1,7,2,5,3]=>[6,8,1,7,2,5,3,-4]
[5,1,6,2,7,4,8,3]=>[5,6,8,7,1,2,4,3]=>[5,6,8,7,1,2,4,3]=>[6,8,7,1,2,4,3,-5]
[5,2,6,1,7,4,8,3]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[5,8,7,2,1,4,3,-6]
[3,1,6,5,7,4,8,2]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[8,1,7,6,5,4,2,-3]
[4,1,6,5,7,3,8,2]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[8,7,1,6,5,3,2,-4]
[5,1,6,4,7,3,8,2]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[8,7,6,1,4,3,2,-5]
[3,2,5,1,6,8,4,7]=>[5,3,2,8,1,6,4,7]=>[5,3,2,8,1,6,4,7]=>[3,2,7,1,6,8,4,-5]
[7,2,5,8,4,1,3,6]=>[4,8,2,7,1,3,5,6]=>[4,8,2,7,1,3,5,6]=>[3,6,1,7,8,4,2,-5]
[7,6,5,3,2,1,8,4]=>[2,3,5,6,7,8,1,4]=>[2,3,5,6,7,8,1,4]=>[1,2,8,3,4,5,6,-7]
[7,3,6,2,4,1,8,5]=>[4,6,7,2,8,3,1,5]=>[4,6,7,2,8,3,1,5]=>[4,6,1,8,2,3,5,-7]
[3,5,2,7,1,8,4,6]=>[7,5,3,8,2,4,1,6]=>[7,5,3,8,2,4,1,6]=>[5,3,6,2,8,1,4,-7]
[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[4,2,1,6,5,8,7,-3]
[3,5,2,6,4,1,8,7]=>[4,6,3,5,1,2,8,7]=>[4,6,3,5,1,2,8,7]=>[6,3,1,4,2,8,7,-5]
[6,1,2,4,5,3,8,7]=>[6,1,5,2,4,3,8,7]=>[6,1,5,2,4,3,8,7]=>[4,6,5,3,1,8,7,-2]
[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,6,5,3,4,8,7]=>[1,5,6,4,3,8,7,-2]
[2,1,5,7,4,8,6,3]=>[2,1,6,8,5,7,3,4]=>[2,1,6,8,5,7,3,4]=>[1,7,8,5,3,6,4,-2]
[2,1,8,3,4,6,7,5]=>[2,1,8,3,7,4,6,5]=>[2,1,8,3,7,4,6,5]=>[1,4,6,8,7,5,3,-2]
[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]=>[4,3,1,2,8,7,5,6]=>[4,2,1,7,8,6,5,-3]
[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,8,7,5,6]=>[1,4,3,7,8,6,5,-2]
[5,1,7,3,8,4,6,2]=>[5,6,7,8,1,4,3,2]=>[5,6,7,8,1,4,3,2]=>[8,7,6,1,2,3,4,-5]
[7,5,2,4,8,1,6,3]=>[8,5,7,3,6,1,4,2]=>[8,5,7,3,6,1,4,2]=>[8,4,7,2,5,3,1,-6]
[5,7,1,6,8,2,4,3]=>[7,8,4,2,5,1,6,3]=>[7,8,4,2,5,1,6,3]=>[4,8,3,5,7,1,2,-6]
[2,3,8,1,4,6,7,5]=>[8,2,3,1,7,4,6,5]=>[8,2,3,1,7,4,6,5]=>[2,3,6,8,7,5,1,-4]
[7,8,4,1,2,3,6,5]=>[4,1,2,8,6,3,7,5]=>[4,1,2,8,6,3,7,5]=>[3,6,1,8,5,7,4,-2]
[7,8,2,6,4,1,3,5]=>[4,6,2,8,3,1,7,5]=>[4,6,2,8,3,1,7,5]=>[3,5,1,8,2,7,4,-6]
[5,2,8,1,4,7,3,6]=>[8,5,7,1,2,3,4,6]=>[8,5,7,1,2,3,4,6]=>[5,6,7,2,8,3,1,-4]
[4,5,7,6,1,8,3,2]=>[6,3,7,4,5,8,2,1]=>[6,3,7,4,5,8,2,1]=>[7,2,4,5,1,3,6,-8]
[3,7,8,5,1,2,4,6]=>[5,1,3,2,8,4,7,6]=>[5,1,3,2,8,4,7,6]=>[4,3,6,1,8,7,5,-2]
[4,1,8,6,2,3,5,7]=>[4,6,2,1,3,8,5,7]=>[4,6,2,1,3,8,5,7]=>[3,5,1,7,2,8,6,-4]
[2,8,5,3,4,1,6,7]=>[4,2,5,3,8,1,6,7]=>[4,2,5,3,8,1,6,7]=>[2,4,1,3,7,8,5,-6]
[3,4,1,2,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[4,3,1,8,7,6,5,-2]
[3,5,2,6,4,8,7,1]=>[7,5,3,6,2,4,8,1]=>[7,5,3,6,2,4,8,1]=>[5,3,6,2,4,1,7,-8]
[2,7,3,5,8,6,1,4]=>[6,2,8,3,1,7,5,4]=>[6,2,8,3,1,7,5,4]=>[2,4,8,7,1,6,3,-5]
[3,2,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]=>[4,3,2,1,8,5,7,6]=>[3,2,1,6,8,7,5,-4]
[3,6,4,7,8,2,5,1]=>[5,8,3,6,2,4,7,1]=>[5,8,3,6,2,4,7,1]=>[5,3,6,1,4,7,2,-8]
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[1,4,3,6,5,8,7,10,9,12,11,-2]
[8,1,5,3,7,2,6,4]=>[8,7,5,6,1,2,3,4]=>[8,7,5,6,1,2,3,4]=>[6,7,8,3,4,2,1,-5]
[7,4,6,1,8,3,5,2]=>[6,5,8,7,3,4,1,2]=>[6,5,8,7,3,4,1,2]=>[8,5,6,2,1,4,3,-7]
[7,3,5,1,8,4,6,2]=>[5,6,7,8,3,4,1,2]=>[5,6,7,8,3,4,1,2]=>[8,5,6,1,2,3,4,-7]
[7,3,4,1,8,5,6,2]=>[4,6,7,3,8,5,1,2]=>[4,6,7,3,8,5,1,2]=>[8,4,1,6,2,3,5,-7]
[4,5,7,3,1,8,6,2]=>[3,7,6,4,5,8,2,1]=>[3,7,6,4,5,8,2,1]=>[7,1,4,5,3,2,6,-8]
[7,5,6,1,8,3,4,2]=>[6,4,8,3,7,5,1,2]=>[6,4,8,3,7,5,1,2]=>[8,4,2,6,1,5,3,-7]
[4,5,7,1,3,8,2,6]=>[7,8,1,4,5,2,3,6]=>[7,8,1,4,5,2,3,6]=>[6,7,4,5,8,1,2,-3]
[5,3,1,2,8,6,4,7]=>[3,1,5,6,2,8,4,7]=>[3,1,5,6,2,8,4,7]=>[5,1,7,3,4,8,6,-2]
[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>[3,1,4,2,6,8,5,7]=>[4,1,3,7,5,8,6,-2]
[3,6,7,1,5,8,2,4]=>[7,8,3,2,1,6,5,4]=>[7,8,3,2,1,6,5,4]=>[4,3,8,7,6,1,2,-5]
[7,1,6,5,8,2,4,3]=>[7,8,4,2,6,1,5,3]=>[7,8,4,2,6,1,5,3]=>[4,8,3,7,5,1,2,-6]
[5,2,3,1,8,6,7,4]=>[3,5,2,7,1,8,6,4]=>[3,5,2,7,1,8,6,4]=>[3,1,8,2,7,4,6,-5]
[6,2,4,1,8,5,7,3]=>[4,6,7,2,8,1,5,3]=>[4,6,7,2,8,1,5,3]=>[4,8,1,7,2,3,5,-6]
[6,2,5,1,8,4,7,3]=>[5,6,7,8,2,1,4,3]=>[5,6,7,8,2,1,4,3]=>[5,8,7,1,2,3,4,-6]
[7,1,6,4,8,2,5,3]=>[7,8,5,6,2,1,4,3]=>[7,8,5,6,2,1,4,3]=>[5,8,7,3,4,1,2,-6]
[7,1,5,3,8,2,6,4]=>[7,8,5,6,1,2,3,4]=>[7,8,5,6,1,2,3,4]=>[6,7,8,3,4,1,2,-5]
[6,1,5,2,8,3,7,4]=>[6,5,8,7,1,2,3,4]=>[6,5,8,7,1,2,3,4]=>[6,7,8,2,1,4,3,-5]
[6,2,1,4,8,7,3,5]=>[2,6,7,1,3,4,8,5]=>[2,6,7,1,3,4,8,5]=>[1,5,6,8,2,3,7,-4]
[5,2,1,3,8,7,4,6]=>[2,5,1,7,3,4,8,6]=>[2,5,1,7,3,4,8,6]=>[1,5,6,2,8,4,7,-3]
[6,1,4,2,8,3,7,5]=>[6,4,8,1,7,2,3,5]=>[6,4,8,1,7,2,3,5]=>[6,7,2,8,1,5,3,-4]
[7,1,4,3,8,2,6,5]=>[7,8,4,1,6,2,3,5]=>[7,8,4,1,6,2,3,5]=>[6,7,3,8,5,1,2,-4]
[7,6,1,4,8,3,2,5]=>[6,3,7,2,1,8,4,5]=>[6,3,7,2,1,8,4,5]=>[4,2,7,8,1,3,6,-5]
[5,1,3,2,8,4,7,6]=>[5,3,1,8,2,7,4,6]=>[5,3,1,8,2,7,4,6]=>[5,2,7,1,8,6,4,-3]
[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>[2,4,1,3,7,5,8,6]=>[1,4,2,6,8,5,7,-3]
[2,4,8,5,3,1,6,7]=>[3,2,5,4,8,1,6,7]=>[3,2,5,4,8,1,6,7]=>[2,1,4,3,7,8,5,-6]
[2,1,8,4,7,3,6,5]=>[2,1,7,8,6,3,4,5]=>[2,1,7,8,6,3,4,5]=>[1,6,7,8,5,3,4,-2]
[1,6,2,4,7,3,8,5]=>[1,6,7,2,8,4,3,5]=>[1,6,7,2,8,4,3,5]=>[4,7,6,8,2,3,5,-1]
[7,1,5,3,4,2,8,6]=>[7,4,5,3,1,8,2,6]=>[7,4,5,3,1,8,2,6]=>[7,4,2,3,8,1,6,-5]
[7,4,2,6,5,1,3,8]=>[5,4,2,6,7,1,3,8]=>[5,4,2,6,7,1,3,8]=>[3,7,2,1,4,5,8,-6]
[7,2,3,5,4,1,6,8]=>[4,5,1,7,3,2,6,8]=>[4,5,1,7,3,2,6,8]=>[6,5,1,2,7,4,8,-3]
[5,1,8,4,6,2,7,3]=>[5,6,7,8,1,4,2,3]=>[5,6,7,8,1,4,2,3]=>[7,8,6,1,2,3,4,-5]
[3,5,6,1,8,4,7,2]=>[6,7,3,8,5,1,4,2]=>[6,7,3,8,5,1,4,2]=>[8,3,7,5,1,2,4,-6]
[4,2,5,6,1,8,7,3]=>[6,4,7,2,5,1,8,3]=>[6,4,7,2,5,1,8,3]=>[4,8,2,5,1,3,7,-6]
[7,1,4,2,5,3,8,6]=>[7,4,5,1,2,8,3,6]=>[7,4,5,1,2,8,3,6]=>[5,7,2,3,8,1,6,-4]
[4,1,6,2,8,3,7,5]=>[4,6,8,1,7,2,3,5]=>[4,6,8,1,7,2,3,5]=>[6,7,1,8,2,5,3,-4]
[6,8,5,3,1,7,4,2]=>[3,5,4,8,7,6,1,2]=>[3,5,4,8,7,6,1,2]=>[8,1,3,2,6,5,4,-7]
[3,8,2,4,6,7,1,5]=>[7,8,3,2,1,4,6,5]=>[7,8,3,2,1,4,6,5]=>[4,3,6,8,7,1,2,-5]
[5,1,7,3,6,2,4,8]=>[5,6,7,2,1,3,4,8]=>[5,6,7,2,1,3,4,8]=>[4,6,7,1,2,3,8,-5]
[1,2,8,3,7,4,5,6]=>[1,2,8,7,4,5,3,6]=>[1,2,8,7,4,5,3,6]=>[2,7,5,6,8,4,3,-1]
[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,3,2,1,4]=>[6,5,8,4,3,2,1,-7]
[7,6,8,1,4,3,5,2]=>[8,5,4,1,3,7,6,2]=>[8,5,4,1,3,7,6,2]=>[8,5,3,2,7,6,1,-4]
[3,2,5,4,8,1,7,6]=>[8,3,2,5,4,7,1,6]=>[8,3,2,5,4,7,1,6]=>[3,2,5,4,8,6,1,-7]
[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[3,5,2,4,6,7,8,-1]
[2,8,3,1,5,7,4,6]=>[3,2,8,7,1,4,5,6]=>[3,2,8,7,1,4,5,6]=>[2,1,6,7,8,4,3,-5]
[6,3,4,5,8,7,2,1]=>[2,7,6,3,4,5,8,1]=>[2,7,6,3,4,5,8,1]=>[1,4,5,6,3,2,7,-8]
[6,3,7,4,2,8,5,1]=>[5,4,8,7,6,1,2,3]=>[5,4,8,7,6,1,2,3]=>[7,8,2,1,5,4,3,-6]
[7,2,6,3,5,4,8,1]=>[8,7,6,5,3,2,4,1]=>[8,7,6,5,3,2,4,1]=>[6,5,7,4,3,2,1,-8]
[6,7,3,1,8,4,2,5]=>[3,7,4,8,1,6,2,5]=>[3,7,4,8,1,6,2,5]=>[7,1,3,8,6,2,4,-5]
[7,2,6,1,8,4,3,5]=>[6,7,4,8,3,2,1,5]=>[6,7,4,8,3,2,1,5]=>[6,5,3,8,1,2,4,-7]
[5,4,8,1,7,2,6,3]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,2,1,3]=>[6,8,5,4,3,2,1,-7]
[4,7,3,6,2,5,1,8]=>[5,6,7,4,2,3,1,8]=>[5,6,7,4,2,3,1,8]=>[5,6,4,1,2,3,8,-7]
[5,4,6,1,3,2,8,7]=>[6,3,1,5,4,2,8,7]=>[6,3,1,5,4,2,8,7]=>[6,2,5,4,1,8,7,-3]
[8,4,7,3,6,2,5,1]=>[5,6,7,8,2,3,4,1]=>[5,6,7,8,2,3,4,1]=>[5,6,7,1,2,3,4,-8]
[2,1,7,6,8,3,5,4]=>[2,1,8,5,3,7,6,4]=>[2,1,8,5,3,7,6,4]=>[1,5,8,4,7,6,3,-2]
[2,6,4,1,8,5,7,3]=>[4,2,6,7,8,3,5,1]=>[4,2,6,7,8,3,5,1]=>[2,6,1,7,3,4,5,-8]
[6,2,7,3,5,1,8,4]=>[5,6,7,8,3,2,1,4]=>[5,6,7,8,3,2,1,4]=>[6,5,8,1,2,3,4,-7]
[1,7,5,3,4,6,8,2]=>[1,8,5,3,7,4,6,2]=>[1,8,5,3,7,4,6,2]=>[8,4,6,3,7,5,2,-1]
[4,5,7,2,1,8,6,3]=>[2,7,6,4,5,8,1,3]=>[2,7,6,4,5,8,1,3]=>[1,8,4,5,3,2,6,-7]
[5,7,3,8,1,6,2,4]=>[8,6,7,2,5,1,3,4]=>[8,6,7,2,5,1,3,4]=>[4,7,8,5,2,3,1,-6]
[2,8,5,7,1,6,3,4]=>[7,2,6,3,8,1,5,4]=>[7,2,6,3,8,1,5,4]=>[2,4,8,7,3,1,5,-6]
[1,8,4,7,3,6,2,5]=>[1,6,7,8,2,3,4,5]=>[1,6,7,8,2,3,4,5]=>[5,6,7,8,2,3,4,-1]
[6,8,3,7,1,5,2,4]=>[7,5,8,2,1,6,3,4]=>[7,5,8,2,1,6,3,4]=>[4,7,8,2,6,1,3,-5]
[7,1,8,3,5,6,2,4]=>[7,6,8,2,3,5,1,4]=>[7,6,8,2,3,5,1,4]=>[4,5,8,6,2,1,3,-7]
[6,4,3,1,2,8,5,7]=>[3,1,4,6,8,2,5,7]=>[3,1,4,6,8,2,5,7]=>[6,1,3,7,4,8,5,-2]
[6,3,8,1,4,7,2,5]=>[8,7,6,1,2,3,4,5]=>[8,7,6,1,2,3,4,5]=>[5,6,7,8,3,2,1,-4]
[6,5,1,2,8,7,3,4]=>[5,1,6,2,7,3,8,4]=>[5,1,6,2,7,3,8,4]=>[4,6,8,1,3,5,7,-2]
[3,7,2,5,4,8,6,1]=>[6,8,3,5,1,7,4,2]=>[6,8,3,5,1,7,4,2]=>[8,3,7,4,1,6,2,-5]
[8,3,6,1,4,7,2,5]=>[6,7,8,1,2,3,4,5]=>[6,7,8,1,2,3,4,5]=>[5,6,7,8,1,2,3,-4]
[8,2,6,1,4,3,7,5]=>[6,8,4,1,7,2,3,5]=>[6,8,4,1,7,2,3,5]=>[6,7,3,8,1,5,2,-4]
[7,6,1,8,3,2,4,5]=>[6,3,7,1,4,8,2,5]=>[6,3,7,1,4,8,2,5]=>[7,2,5,8,1,3,6,-4]
[4,2,6,1,8,5,7,3]=>[6,4,7,2,8,1,5,3]=>[6,4,7,2,8,1,5,3]=>[4,8,2,7,1,3,5,-6]
[7,5,8,4,1,2,3,6]=>[4,1,2,8,7,3,5,6]=>[4,1,2,8,7,3,5,6]=>[3,6,1,7,8,5,4,-2]
[5,8,7,1,2,4,3,6]=>[7,1,4,2,5,3,8,6]=>[7,1,4,2,5,3,8,6]=>[4,6,3,5,8,1,7,-2]
[8,1,6,5,7,2,4,3]=>[8,7,4,2,6,1,5,3]=>[8,7,4,2,6,1,5,3]=>[4,8,3,7,5,2,1,-6]
[7,1,6,5,8,3,2,4]=>[7,3,8,2,6,1,5,4]=>[7,3,8,2,6,1,5,4]=>[4,2,8,7,5,1,3,-6]
[2,1,7,5,6,8,3,4]=>[2,1,8,3,7,5,6,4]=>[2,1,8,3,7,5,6,4]=>[1,4,8,6,7,5,3,-2]
[3,8,6,4,2,7,5,1]=>[5,4,3,7,6,8,1,2]=>[5,4,3,7,6,8,1,2]=>[8,3,2,1,5,4,6,-7]
[6,4,2,1,8,3,5,7]=>[2,4,6,8,1,3,5,7]=>[2,4,6,8,1,3,5,7]=>[1,6,2,7,3,8,4,-5]
[8,2,6,4,1,3,5,7]=>[4,6,2,8,3,1,5,7]=>[4,6,2,8,3,1,5,7]=>[3,5,1,7,2,8,4,-6]
[3,2,6,1,5,4,8,7]=>[6,3,2,5,1,4,8,7]=>[6,3,2,5,1,4,8,7]=>[3,2,6,4,1,8,7,-5]
[5,2,4,3,8,1,7,6]=>[8,5,4,2,3,7,1,6]=>[8,5,4,2,3,7,1,6]=>[4,5,3,2,8,6,1,-7]
[6,1,5,2,4,3,8,7]=>[6,5,4,2,1,3,8,7]=>[6,5,4,2,1,3,8,7]=>[4,6,3,2,1,8,7,-5]
[6,1,3,2,5,4,8,7]=>[6,3,1,5,2,4,8,7]=>[6,3,1,5,2,4,8,7]=>[5,2,6,4,1,8,7,-3]
[4,3,6,1,5,2,8,7]=>[6,5,4,3,1,2,8,7]=>[6,5,4,3,1,2,8,7]=>[6,4,3,2,1,8,7,-5]
[4,3,5,2,8,1,7,6]=>[8,5,4,3,2,7,1,6]=>[8,5,4,3,2,7,1,6]=>[5,4,3,2,8,6,1,-7]
[4,3,7,2,6,5,8,1]=>[8,7,4,3,6,2,5,1]=>[8,7,4,3,6,2,5,1]=>[6,4,3,7,5,2,1,-8]
[4,3,8,1,7,2,6,5]=>[8,7,4,3,6,2,1,5]=>[8,7,4,3,6,2,1,5]=>[6,4,3,8,5,2,1,-7]
[4,3,8,1,5,2,7,6]=>[8,5,4,3,1,7,2,6]=>[8,5,4,3,1,7,2,6]=>[7,4,3,2,8,6,1,-5]
[2,1,5,4,8,3,7,6]=>[2,1,8,5,4,7,3,6]=>[2,1,8,5,4,7,3,6]=>[1,7,5,4,8,6,3,-2]
[5,4,7,6,8,1,3,2]=>[8,3,1,5,4,7,6,2]=>[8,3,1,5,4,7,6,2]=>[8,2,5,4,7,6,1,-3]
[4,3,7,6,8,1,5,2]=>[8,5,4,3,1,7,6,2]=>[8,5,4,3,1,7,6,2]=>[8,4,3,2,7,6,1,-5]
[4,3,6,5,8,1,7,2]=>[8,7,4,3,6,5,1,2]=>[8,7,4,3,6,5,1,2]=>[8,4,3,6,5,2,1,-7]
[6,3,5,4,7,2,8,1]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,3,4,2,1]=>[7,5,6,4,3,2,1,-8]
[6,3,5,4,8,1,7,2]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,3,4,1,2]=>[8,5,6,4,3,2,1,-7]
[7,4,6,5,8,1,3,2]=>[8,3,1,7,6,4,5,2]=>[8,3,1,7,6,4,5,2]=>[8,2,6,7,5,4,1,-3]
[8,1,6,3,7,2,5,4]=>[8,7,6,5,2,1,3,4]=>[8,7,6,5,2,1,3,4]=>[5,7,8,4,3,2,1,-6]
[8,1,7,2,4,3,6,5]=>[8,7,4,2,6,3,1,5]=>[8,7,4,2,6,3,1,5]=>[4,6,3,8,5,2,1,-7]
[8,1,3,2,7,4,6,5]=>[8,3,1,7,6,4,2,5]=>[8,3,1,7,6,4,2,5]=>[7,2,6,8,5,4,1,-3]
[2,1,8,3,7,4,6,5]=>[2,1,8,7,6,4,3,5]=>[2,1,8,7,6,4,3,5]=>[1,7,6,8,5,4,3,-2]
[2,1,8,3,5,4,7,6]=>[2,1,8,5,3,7,4,6]=>[2,1,8,5,3,7,4,6]=>[1,5,7,4,8,6,3,-2]
[8,1,3,2,5,4,7,6]=>[8,3,1,5,2,7,4,6]=>[8,3,1,5,2,7,4,6]=>[5,2,7,4,8,6,1,-3]
[8,1,5,2,4,3,7,6]=>[8,5,4,2,1,7,3,6]=>[8,5,4,2,1,7,3,6]=>[4,7,3,2,8,6,1,-5]
[3,2,8,1,7,4,6,5]=>[8,3,2,7,6,4,1,5]=>[8,3,2,7,6,4,1,5]=>[3,2,6,8,5,4,1,-7]
[3,2,8,1,5,4,7,6]=>[8,3,2,5,1,7,4,6]=>[8,3,2,5,1,7,4,6]=>[3,2,7,4,8,6,1,-5]
[3,2,4,1,8,5,7,6]=>[4,3,2,1,8,7,5,6]=>[4,3,2,1,8,7,5,6]=>[3,2,1,7,8,6,5,-4]
[4,1,3,2,7,6,8,5]=>[4,3,1,2,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[4,2,1,8,7,6,5,-3]
[3,2,7,6,8,1,5,4]=>[8,3,2,5,1,7,6,4]=>[8,3,2,5,1,7,6,4]=>[3,2,8,4,7,6,1,-5]
[3,2,6,5,8,1,7,4]=>[8,3,2,7,6,5,1,4]=>[8,3,2,7,6,5,1,4]=>[3,2,8,6,5,4,1,-7]
[7,6,8,1,5,2,4,3]=>[8,5,4,2,1,7,6,3]=>[8,5,4,2,1,7,6,3]=>[4,8,3,2,7,6,1,-5]
[7,6,8,1,3,2,5,4]=>[8,3,1,5,2,7,6,4]=>[8,3,1,5,2,7,6,4]=>[5,2,8,4,7,6,1,-3]
[7,2,8,1,5,4,6,3]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,1,4,2,3]=>[7,8,6,4,3,2,1,-5]
[5,4,7,2,6,3,8,1]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,2,3,1]=>[6,7,5,4,3,2,1,-8]
[6,5,8,1,3,2,7,4]=>[8,3,1,7,6,5,2,4]=>[8,3,1,7,6,5,2,4]=>[7,2,8,6,5,4,1,-3]
[2,1,6,5,8,3,7,4]=>[2,1,8,7,6,5,3,4]=>[2,1,8,7,6,5,3,4]=>[1,7,8,6,5,4,3,-2]
[6,5,7,4,8,1,3,2]=>[8,3,1,7,6,5,4,2]=>[8,3,1,7,6,5,4,2]=>[8,2,7,6,5,4,1,-3]
[5,4,6,3,8,1,7,2]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,1,2]=>[8,6,5,4,3,2,1,-7]
[6,3,7,1,4,8,2,5]=>[7,8,6,1,2,3,4,5]=>[7,8,6,1,2,3,4,5]=>[5,6,7,8,3,1,2,-4]
[6,5,3,1,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>[3,1,5,2,6,4,8,7]=>[4,1,6,3,5,8,7,-2]
[8,1,4,7,3,6,2,5]=>[8,6,7,1,2,3,4,5]=>[8,6,7,1,2,3,4,5]=>[5,6,7,8,2,3,1,-4]
[2,1,8,7,5,3,4,6]=>[2,1,5,3,7,4,8,6]=>[2,1,5,3,7,4,8,6]=>[1,4,6,3,8,5,7,-2]
[3,5,6,4,7,1,8,2]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[8,3,6,5,4,1,2,-7]
[7,2,5,1,4,3,8,6]=>[5,7,4,1,2,8,3,6]=>[5,7,4,1,2,8,3,6]=>[5,7,3,1,8,2,6,-4]
[2,7,3,6,4,8,1,5]=>[8,2,7,6,1,3,4,5]=>[8,2,7,6,1,3,4,5]=>[2,6,7,8,4,3,1,-5]
[1,8,5,7,4,3,6,2]=>[1,6,4,7,8,3,5,2]=>[1,6,4,7,8,3,5,2]=>[8,6,3,7,2,4,5,-1]
[3,8,6,1,7,2,5,4]=>[6,8,3,5,1,7,2,4]=>[6,8,3,5,1,7,2,4]=>[7,3,8,4,1,6,2,-5]
[7,8,5,3,6,1,2,4]=>[6,1,5,2,8,3,7,4]=>[6,1,5,2,8,3,7,4]=>[4,6,8,3,1,7,5,-2]
[3,6,8,2,5,7,1,4]=>[7,8,3,1,2,6,5,4]=>[7,8,3,1,2,6,5,4]=>[5,3,8,7,6,1,2,-4]
[1,2,5,8,3,6,7,4]=>[1,2,8,7,5,3,6,4]=>[1,2,8,7,5,3,6,4]=>[2,6,8,5,7,4,3,-1]
[1,8,4,3,5,2,7,6]=>[1,5,4,8,3,7,2,6]=>[1,5,4,8,3,7,2,6]=>[7,5,3,2,8,6,4,-1]
[7,3,6,8,5,1,2,4]=>[5,1,8,3,7,2,6,4]=>[5,1,8,3,7,2,6,4]=>[6,4,8,1,7,5,3,-2]
[1,2,5,7,8,4,3,6]=>[1,2,4,8,5,3,7,6]=>[1,2,4,8,5,3,7,6]=>[2,6,3,5,8,7,4,-1]
[3,6,2,4,7,8,1,5]=>[8,6,3,2,1,4,7,5]=>[8,6,3,2,1,4,7,5]=>[4,3,6,8,2,7,1,-5]
[5,6,7,8,1,3,4,2]=>[8,4,1,3,5,6,7,2]=>[8,4,1,3,5,6,7,2]=>[8,4,2,5,6,7,1,-3]
[2,4,6,1,7,5,8,3]=>[6,2,8,4,7,1,5,3]=>[6,2,8,4,7,1,5,3]=>[2,8,4,7,1,5,3,-6]
[4,7,5,2,8,1,6,3]=>[8,5,7,4,6,1,3,2]=>[8,5,7,4,6,1,3,2]=>[8,7,4,2,5,3,1,-6]
[1,8,3,4,7,2,6,5]=>[1,7,8,3,6,2,4,5]=>[1,7,8,3,6,2,4,5]=>[6,4,7,8,5,2,3,-1]
[4,2,6,1,8,3,7,5]=>[6,4,8,2,7,1,3,5]=>[6,4,8,2,7,1,3,5]=>[4,7,2,8,1,5,3,-6]
[1,7,3,6,4,8,2,5]=>[1,8,7,6,2,3,4,5]=>[1,8,7,6,2,3,4,5]=>[5,6,7,8,4,3,2,-1]
[6,7,3,4,1,8,2,5]=>[4,8,7,3,2,6,1,5]=>[4,8,7,3,2,6,1,5]=>[5,4,1,8,6,3,2,-7]
[2,3,1,7,5,8,4,6]=>[3,2,1,8,7,4,5,6]=>[3,2,1,8,7,4,5,6]=>[2,1,6,7,8,5,4,-3]
[3,6,5,1,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>[5,1,3,2,6,4,8,7]=>[4,3,6,1,5,8,7,-2]
[6,1,4,5,3,2,8,7]=>[6,3,5,1,4,2,8,7]=>[6,3,5,1,4,2,8,7]=>[6,2,5,3,1,8,7,-4]
[5,6,7,8,1,4,3,2]=>[8,3,4,1,5,6,7,2]=>[8,3,4,1,5,6,7,2]=>[8,2,3,5,6,7,1,-4]
[2,1,5,8,7,3,4,6]=>[2,1,7,3,5,4,8,6]=>[2,1,7,3,5,4,8,6]=>[1,4,6,5,8,3,7,-2]
[8,5,7,3,6,1,4,2]=>[6,4,7,1,8,3,5,2]=>[6,4,7,1,8,3,5,2]=>[8,6,2,7,1,3,5,-4]
[2,1,8,3,6,7,5,4]=>[2,1,8,5,7,3,6,4]=>[2,1,8,5,7,3,6,4]=>[1,6,8,4,7,5,3,-2]
[4,1,2,3,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[3,4,1,8,7,6,5,-2]
[3,2,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[3,2,1,6,7,8,5,-4]
[2,8,3,1,6,4,5,7]=>[3,2,8,6,4,1,5,7]=>[3,2,8,6,4,1,5,7]=>[2,1,5,7,4,8,3,-6]
[5,1,8,3,6,7,2,4]=>[5,7,8,2,1,3,6,4]=>[5,7,8,2,1,3,6,4]=>[4,6,8,1,7,2,3,-5]
[7,6,1,4,3,8,2,5]=>[6,7,4,2,1,8,3,5]=>[6,7,4,2,1,8,3,5]=>[4,7,3,8,1,2,6,-5]
[1,8,6,4,5,2,3,7]=>[1,5,2,6,4,8,3,7]=>[1,5,2,6,4,8,3,7]=>[3,7,5,2,4,8,6,-1]
[6,3,8,1,4,7,5,2]=>[8,5,7,1,6,2,4,3]=>[8,5,7,1,6,2,4,3]=>[6,8,7,2,5,3,1,-4]
[5,6,2,8,1,4,7,3]=>[8,6,7,1,5,2,4,3]=>[8,6,7,1,5,2,4,3]=>[6,8,7,5,2,3,1,-4]
[8,4,6,1,7,3,5,2]=>[6,5,7,8,3,4,1,2]=>[6,5,7,8,3,4,1,2]=>[8,5,6,2,1,3,4,-7]
[6,4,2,7,5,1,3,8]=>[5,4,2,7,6,1,3,8]=>[5,4,2,7,6,1,3,8]=>[3,7,2,1,5,4,8,-6]
[5,8,3,6,1,4,7,2]=>[6,7,8,1,5,3,4,2]=>[6,7,8,1,5,3,4,2]=>[8,6,7,5,1,2,3,-4]
[2,8,7,6,1,4,3,5]=>[6,2,4,1,3,7,8,5]=>[6,2,4,1,3,7,8,5]=>[2,5,3,8,1,6,7,-4]
[2,8,1,6,5,4,3,7]=>[8,2,4,5,6,1,3,7]=>[8,2,4,5,6,1,3,7]=>[2,7,3,4,5,8,1,-6]
[4,5,8,1,7,2,3,6]=>[8,7,2,4,5,3,1,6]=>[8,7,2,4,5,3,1,6]=>[3,6,4,5,8,2,1,-7]
[7,4,2,6,8,5,1,3]=>[5,4,2,8,7,1,6,3]=>[5,4,2,8,7,1,6,3]=>[3,8,2,1,7,5,4,-6]
[7,3,2,5,8,6,1,4]=>[6,3,8,2,1,7,5,4]=>[6,3,8,2,1,7,5,4]=>[4,2,8,7,1,6,3,-5]
[7,3,1,8,6,2,4,5]=>[3,7,6,1,4,8,2,5]=>[3,7,6,1,4,8,2,5]=>[7,1,5,8,3,2,6,-4]
[3,1,7,2,5,4,8,6]=>[3,7,1,5,2,8,4,6]=>[3,7,1,5,2,8,4,6]=>[5,1,7,4,8,2,6,-3]
[7,4,1,8,5,2,3,6]=>[4,7,1,5,8,3,2,6]=>[4,7,1,5,8,3,2,6]=>[7,6,1,4,8,2,5,-3]
[7,3,8,4,5,1,6,2]=>[5,6,7,8,4,1,3,2]=>[5,6,7,8,4,1,3,2]=>[8,7,5,1,2,3,4,-6]
[3,8,2,4,7,5,1,6]=>[5,7,3,1,8,2,4,6]=>[5,7,3,1,8,2,4,6]=>[6,3,7,1,8,2,5,-4]
[3,5,2,7,4,8,6,1]=>[6,5,3,8,2,7,1,4]=>[6,5,3,8,2,7,1,4]=>[5,3,8,2,1,6,4,-7]
[3,6,2,7,8,5,4,1]=>[4,5,3,8,6,2,7,1]=>[4,5,3,8,6,2,7,1]=>[6,3,1,2,5,7,4,-8]
[4,1,5,6,7,8,3,2]=>[4,3,8,1,5,6,7,2]=>[4,3,8,1,5,6,7,2]=>[8,2,1,5,6,7,3,-4]
[4,1,7,3,8,5,6,2]=>[4,6,7,1,8,5,3,2]=>[4,6,7,1,8,5,3,2]=>[8,7,1,6,2,3,5,-4]
[4,5,7,3,2,8,6,1]=>[6,3,8,4,5,7,1,2]=>[6,3,8,4,5,7,1,2]=>[8,2,4,5,1,6,3,-7]
[4,5,7,3,8,1,6,2]=>[8,6,7,4,5,1,3,2]=>[8,6,7,4,5,1,3,2]=>[8,7,4,5,2,3,1,-6]
[2,5,3,8,7,6,1,4]=>[6,2,5,1,3,7,8,4]=>[6,2,5,1,3,7,8,4]=>[2,5,8,3,1,6,7,-4]
[7,2,5,8,3,6,1,4]=>[6,7,8,1,2,3,5,4]=>[6,7,8,1,2,3,5,4]=>[5,6,8,7,1,2,3,-4]
[3,4,6,5,7,1,8,2]=>[7,8,3,4,6,5,1,2]=>[7,8,3,4,6,5,1,2]=>[8,3,4,6,5,1,2,-7]
[6,3,1,4,7,2,8,5]=>[3,6,7,2,8,4,1,5]=>[3,6,7,2,8,4,1,5]=>[4,1,6,8,2,3,5,-7]
[8,3,2,5,7,6,1,4]=>[6,3,7,2,1,8,5,4]=>[6,3,7,2,1,8,5,4]=>[4,2,8,7,1,3,6,-5]
[2,8,6,1,5,7,3,4]=>[6,2,8,1,3,7,5,4]=>[6,2,8,1,3,7,5,4]=>[2,5,8,7,1,6,3,-4]
[4,3,5,6,7,1,8,2]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,5,6,1,2]=>[8,4,3,5,6,1,2,-7]
[8,4,7,6,5,3,2,1]=>[2,3,5,6,7,8,4,1]=>[2,3,5,6,7,8,4,1]=>[1,2,7,3,4,5,6,-8]
[8,4,7,3,6,5,2,1]=>[2,5,6,7,8,4,1,3]=>[2,5,6,7,8,4,1,3]=>[1,8,6,2,3,4,5,-7]
[8,2,7,3,6,4,5,1]=>[5,8,7,6,4,3,2,1]=>[5,8,7,6,4,3,2,1]=>[7,6,5,1,4,3,2,-8]
[8,5,7,3,6,2,4,1]=>[4,6,7,2,8,3,5,1]=>[4,6,7,2,8,3,5,1]=>[4,6,1,7,2,3,5,-8]
[8,6,7,3,5,2,4,1]=>[4,5,7,2,3,8,6,1]=>[4,5,7,2,3,8,6,1]=>[4,5,1,2,7,3,6,-8]
[8,5,7,4,6,2,3,1]=>[3,6,2,7,8,4,5,1]=>[3,6,2,7,8,4,5,1]=>[3,1,6,7,2,4,5,-8]
[8,3,7,2,6,1,5,4]=>[6,7,8,5,1,2,3,4]=>[6,7,8,5,1,2,3,4]=>[6,7,8,4,1,2,3,-5]
[4,6,7,3,8,5,2,1]=>[2,5,8,4,7,6,1,3]=>[2,5,8,4,7,6,1,3]=>[1,8,4,2,6,5,3,-7]
[4,7,1,3,2,8,6,5]=>[7,3,1,4,6,8,2,5]=>[7,3,1,4,6,8,2,5]=>[7,2,4,8,5,1,6,-3]
[2,7,3,1,5,8,4,6]=>[3,2,7,8,1,4,5,6]=>[3,2,7,8,1,4,5,6]=>[2,1,6,7,8,3,4,-5]
[7,4,1,5,8,2,3,6]=>[4,7,1,8,2,3,5,6]=>[4,7,1,8,2,3,5,6]=>[5,6,1,7,8,2,4,-3]
[5,3,8,6,1,2,4,7]=>[6,1,5,2,3,8,4,7]=>[6,1,5,2,3,8,4,7]=>[4,5,7,3,1,8,6,-2]
[1,2,8,3,7,5,4,6]=>[1,2,8,5,7,4,3,6]=>[1,2,8,5,7,4,3,6]=>[2,7,6,4,8,5,3,-1]
[4,3,8,1,2,6,7,5]=>[8,1,4,3,7,2,6,5]=>[8,1,4,3,7,2,6,5]=>[6,4,3,8,7,5,1,-2]
[7,3,8,1,4,2,6,5]=>[8,4,7,1,6,2,3,5]=>[8,4,7,1,6,2,3,5]=>[6,7,2,8,5,3,1,-4]
[6,4,2,8,7,5,1,3]=>[5,4,2,7,6,1,8,3]=>[5,4,2,7,6,1,8,3]=>[3,8,2,1,5,4,7,-6]
[6,3,8,1,5,4,7,2]=>[8,7,6,5,1,3,4,2]=>[8,7,6,5,1,3,4,2]=>[8,6,7,4,3,2,1,-5]
[5,8,3,2,6,7,1,4]=>[7,3,8,1,5,2,6,4]=>[7,3,8,1,5,2,6,4]=>[6,2,8,5,7,1,3,-4]
[2,1,5,3,8,4,7,6]=>[2,1,5,8,3,7,4,6]=>[2,1,5,8,3,7,4,6]=>[1,5,7,3,8,6,4,-2]
[3,1,8,2,5,4,7,6]=>[3,8,1,5,2,7,4,6]=>[3,8,1,5,2,7,4,6]=>[5,1,7,4,8,6,2,-3]
[8,1,3,2,6,4,7,5]=>[8,3,1,6,7,2,4,5]=>[8,3,1,6,7,2,4,5]=>[6,2,7,8,4,5,1,-3]
[3,1,8,2,6,4,7,5]=>[3,8,1,6,7,2,4,5]=>[3,8,1,6,7,2,4,5]=>[6,1,7,8,4,5,2,-3]
[2,1,8,3,6,4,7,5]=>[2,1,8,6,7,3,4,5]=>[2,1,8,6,7,3,4,5]=>[1,6,7,8,4,5,3,-2]
[2,1,6,3,8,4,7,5]=>[2,1,6,8,7,3,4,5]=>[2,1,6,8,7,3,4,5]=>[1,6,7,8,3,5,4,-2]
[2,1,7,3,5,4,8,6]=>[2,1,7,5,3,8,4,6]=>[2,1,7,5,3,8,4,6]=>[1,5,7,4,8,3,6,-2]
[2,1,7,3,6,4,8,5]=>[2,1,7,6,8,3,4,5]=>[2,1,7,6,8,3,4,5]=>[1,6,7,8,4,3,5,-2]
[3,1,6,2,5,4,8,7]=>[3,6,1,5,2,4,8,7]=>[3,6,1,5,2,4,8,7]=>[5,1,6,4,2,8,7,-3]
[7,1,3,2,5,4,8,6]=>[7,3,1,5,2,8,4,6]=>[7,3,1,5,2,8,4,6]=>[5,2,7,4,8,1,6,-3]
[7,1,3,2,6,4,8,5]=>[7,3,1,6,8,2,4,5]=>[7,3,1,6,8,2,4,5]=>[6,2,7,8,4,1,5,-3]
[6,1,4,2,5,3,8,7]=>[6,4,5,1,2,3,8,7]=>[6,4,5,1,2,3,8,7]=>[5,6,2,3,1,8,7,-4]
[4,1,6,2,5,3,8,7]=>[4,6,5,1,2,3,8,7]=>[4,6,5,1,2,3,8,7]=>[5,6,1,3,2,8,7,-4]
[4,1,7,2,5,3,8,6]=>[4,7,5,1,2,8,3,6]=>[4,7,5,1,2,8,3,6]=>[5,7,1,3,8,2,6,-4]
[4,1,7,2,6,3,8,5]=>[4,7,6,1,8,2,3,5]=>[4,7,6,1,8,2,3,5]=>[6,7,1,8,3,2,5,-4]
[5,1,7,2,6,3,8,4]=>[5,7,6,8,1,2,3,4]=>[5,7,6,8,1,2,3,4]=>[6,7,8,1,3,2,4,-5]
[8,1,5,2,6,3,7,4]=>[8,5,6,7,1,2,3,4]=>[8,5,6,7,1,2,3,4]=>[6,7,8,2,3,4,1,-5]
[5,1,8,2,6,3,7,4]=>[5,8,6,7,1,2,3,4]=>[5,8,6,7,1,2,3,4]=>[6,7,8,1,3,4,2,-5]
[5,1,6,2,8,3,7,4]=>[5,6,8,7,1,2,3,4]=>[5,6,8,7,1,2,3,4]=>[6,7,8,1,2,4,3,-5]
[3,1,6,2,8,4,7,5]=>[3,6,1,8,7,2,4,5]=>[3,6,1,8,7,2,4,5]=>[6,1,7,8,2,5,4,-3]
[4,1,8,2,6,3,7,5]=>[4,8,6,1,7,2,3,5]=>[4,8,6,1,7,2,3,5]=>[6,7,1,8,3,5,2,-4]
[8,1,4,2,6,3,7,5]=>[8,4,6,1,7,2,3,5]=>[8,4,6,1,7,2,3,5]=>[6,7,2,8,3,5,1,-4]
[8,1,4,2,5,3,7,6]=>[8,4,5,1,2,7,3,6]=>[8,4,5,1,2,7,3,6]=>[5,7,2,3,8,6,1,-4]
[4,1,8,2,5,3,7,6]=>[4,8,5,1,2,7,3,6]=>[4,8,5,1,2,7,3,6]=>[5,7,1,3,8,6,2,-4]
[4,1,5,2,8,3,7,6]=>[4,5,8,1,2,7,3,6]=>[4,5,8,1,2,7,3,6]=>[5,7,1,2,8,6,3,-4]
[3,1,5,2,8,4,7,6]=>[3,5,1,8,2,7,4,6]=>[3,5,1,8,2,7,4,6]=>[5,1,7,2,8,6,4,-3]
[3,1,4,2,8,5,7,6]=>[3,4,1,2,8,7,5,6]=>[3,4,1,2,8,7,5,6]=>[4,1,2,7,8,6,5,-3]
[4,1,3,2,7,5,8,6]=>[4,3,1,2,7,8,5,6]=>[4,3,1,2,7,8,5,6]=>[4,2,1,7,8,5,6,-3]
[5,1,4,2,8,3,7,6]=>[5,4,8,1,2,7,3,6]=>[5,4,8,1,2,7,3,6]=>[5,7,2,1,8,6,3,-4]
[6,1,3,2,8,4,7,5]=>[6,3,1,8,7,2,4,5]=>[6,3,1,8,7,2,4,5]=>[6,2,7,8,1,5,4,-3]
[6,1,3,2,7,4,8,5]=>[6,3,1,7,8,2,4,5]=>[6,3,1,7,8,2,4,5]=>[6,2,7,8,1,4,5,-3]
[5,1,3,2,7,4,8,6]=>[5,3,1,7,2,8,4,6]=>[5,3,1,7,2,8,4,6]=>[5,2,7,1,8,4,6,-3]
[5,1,3,2,6,4,8,7]=>[5,3,1,6,2,4,8,7]=>[5,3,1,6,2,4,8,7]=>[5,2,6,1,4,8,7,-3]
[5,1,4,2,6,3,8,7]=>[5,4,6,1,2,3,8,7]=>[5,4,6,1,2,3,8,7]=>[5,6,2,1,3,8,7,-4]
[6,1,4,2,7,3,8,5]=>[6,4,7,1,8,2,3,5]=>[6,4,7,1,8,2,3,5]=>[6,7,2,8,1,3,5,-4]
[6,1,5,2,7,3,8,4]=>[6,5,7,8,1,2,3,4]=>[6,5,7,8,1,2,3,4]=>[6,7,8,2,1,3,4,-5]
[4,2,1,3,7,6,8,5]=>[2,4,1,3,8,7,6,5]=>[2,4,1,3,8,7,6,5]=>[1,4,2,8,7,6,5,-3]
[3,2,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>[4,3,2,1,6,8,5,7]=>[3,2,1,7,5,8,6,-4]
[5,3,2,1,7,6,8,4]=>[2,3,5,8,1,7,6,4]=>[2,3,5,8,1,7,6,4]=>[1,2,8,3,7,6,4,-5]
[5,6,1,4,7,2,8,3]=>[6,7,8,1,5,4,2,3]=>[6,7,8,1,5,4,2,3]=>[7,8,6,5,1,2,3,-4]
[6,4,7,3,5,1,8,2]=>[5,8,7,6,3,4,1,2]=>[5,8,7,6,3,4,1,2]=>[8,5,6,1,4,3,2,-7]
[1,8,2,3,5,7,4,6]=>[1,8,2,7,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>[3,5,6,7,8,4,2,-1]
[1,2,8,6,3,4,7,5]=>[1,2,6,3,8,7,5,4]=>[1,2,6,3,8,7,5,4]=>[2,4,8,7,3,6,5,-1]
[5,2,6,3,4,1,8,7]=>[4,5,6,3,2,1,8,7]=>[4,5,6,3,2,1,8,7]=>[5,4,1,2,3,8,7,-6]
[4,1,2,6,5,3,8,7]=>[4,1,5,2,6,3,8,7]=>[4,1,5,2,6,3,8,7]=>[4,6,1,3,5,8,7,-2]
[8,2,6,4,7,3,5,1]=>[5,8,7,6,3,2,4,1]=>[5,8,7,6,3,2,4,1]=>[6,5,7,1,4,3,2,-8]
[2,1,7,4,8,5,6,3]=>[2,1,6,7,8,5,4,3]=>[2,1,6,7,8,5,4,3]=>[1,8,7,6,3,4,5,-2]
[2,1,6,3,4,8,7,5]=>[2,1,6,3,7,4,8,5]=>[2,1,6,3,7,4,8,5]=>[1,4,6,8,3,5,7,-2]
[4,6,7,2,5,8,3,1]=>[3,8,7,4,1,6,5,2]=>[3,8,7,4,1,6,5,2]=>[8,1,4,7,6,3,2,-5]
[3,2,8,7,4,5,1,6]=>[5,3,2,7,4,1,8,6]=>[5,3,2,7,4,1,8,6]=>[3,2,5,1,8,4,7,-6]
[5,8,3,7,6,1,4,2]=>[6,4,7,3,5,8,1,2]=>[6,4,7,3,5,8,1,2]=>[8,4,2,5,1,3,6,-7]
[7,4,2,8,1,6,5,3]=>[8,4,7,5,6,1,3,2]=>[8,4,7,5,6,1,3,2]=>[8,7,2,4,5,3,1,-6]
[4,1,8,5,7,3,6,2]=>[4,6,7,1,8,3,5,2]=>[4,6,7,1,8,3,5,2]=>[8,6,1,7,2,3,5,-4]
[3,2,8,1,6,5,7,4]=>[8,3,2,7,6,1,5,4]=>[8,3,2,7,6,1,5,4]=>[3,2,8,7,5,4,1,-6]
[7,2,4,8,1,5,3,6]=>[8,7,5,2,1,3,4,6]=>[8,7,5,2,1,3,4,6]=>[4,6,7,3,8,2,1,-5]
[3,5,1,7,2,8,6,4]=>[5,7,3,6,1,8,2,4]=>[5,7,3,6,1,8,2,4]=>[7,3,8,1,4,2,6,-5]
[8,6,1,4,2,3,5,7]=>[6,4,2,1,3,8,5,7]=>[6,4,2,1,3,8,5,7]=>[3,5,2,7,1,8,6,-4]
[8,2,3,6,4,1,5,7]=>[4,6,1,8,2,3,5,7]=>[4,6,1,8,2,3,5,7]=>[5,6,1,7,2,8,4,-3]
[6,2,3,8,4,1,5,7]=>[4,8,1,6,2,3,5,7]=>[4,8,1,6,2,3,5,7]=>[5,6,1,7,4,8,2,-3]
[6,2,4,3,8,1,5,7]=>[8,6,4,2,1,3,5,7]=>[8,6,4,2,1,3,5,7]=>[4,6,3,7,2,8,1,-5]
[1,2,7,3,5,8,6,4]=>[1,2,7,6,3,8,5,4]=>[1,2,7,6,3,8,5,4]=>[2,5,8,7,4,3,6,-1]
[8,1,4,3,6,5,7,2]=>[8,7,4,1,6,3,5,2]=>[8,7,4,1,6,3,5,2]=>[8,6,3,7,5,2,1,-4]
[1,8,4,6,3,5,7,2]=>[1,7,6,8,3,4,5,2]=>[1,7,6,8,3,4,5,2]=>[8,5,6,7,3,2,4,-1]
[1,6,4,8,3,5,7,2]=>[1,7,8,6,3,4,5,2]=>[1,7,8,6,3,4,5,2]=>[8,5,6,7,4,2,3,-1]
[6,1,4,8,3,5,7,2]=>[6,7,8,1,3,4,5,2]=>[6,7,8,1,3,4,5,2]=>[8,5,6,7,1,2,3,-4]
[2,1,6,3,8,5,7,4]=>[2,1,6,7,8,3,5,4]=>[2,1,6,7,8,3,5,4]=>[1,6,8,7,3,4,5,-2]
[2,1,8,3,6,5,7,4]=>[2,1,8,7,6,3,5,4]=>[2,1,8,7,6,3,5,4]=>[1,6,8,7,5,4,3,-2]
[6,1,8,4,3,5,7,2]=>[6,7,4,8,3,1,5,2]=>[6,7,4,8,3,1,5,2]=>[8,5,3,7,1,2,4,-6]
[5,8,1,4,7,3,2,6]=>[8,3,7,1,5,2,4,6]=>[8,3,7,1,5,2,4,6]=>[6,2,7,5,8,3,1,-4]
[8,7,4,2,6,5,1,3]=>[5,4,2,6,7,1,8,3]=>[5,4,2,6,7,1,8,3]=>[3,8,2,1,4,5,7,-6]
[8,7,6,1,4,5,2,3]=>[6,5,2,1,4,7,8,3]=>[6,5,2,1,4,7,8,3]=>[3,8,5,2,1,6,7,-4]
[8,5,6,4,1,7,2,3]=>[4,6,1,7,8,5,2,3]=>[4,6,1,7,8,5,2,3]=>[7,8,1,6,2,4,5,-3]
[4,5,8,6,1,7,3,2]=>[6,3,8,4,5,7,2,1]=>[6,3,8,4,5,7,2,1]=>[7,2,4,5,1,6,3,-8]
[8,2,4,3,6,7,1,5]=>[7,8,4,2,1,3,6,5]=>[7,8,4,2,1,3,6,5]=>[4,6,3,8,7,1,2,-5]
[2,7,3,6,5,8,1,4]=>[8,2,7,1,6,3,5,4]=>[8,2,7,1,6,3,5,4]=>[2,6,8,7,5,3,1,-4]
[1,6,2,8,4,3,7,5]=>[1,6,4,8,7,2,3,5]=>[1,6,4,8,7,2,3,5]=>[6,7,3,8,2,5,4,-1]
[2,1,8,3,5,7,4,6]=>[2,1,8,7,3,4,5,6]=>[2,1,8,7,3,4,5,6]=>[1,5,6,7,8,4,3,-2]
[7,2,8,4,3,5,6,1]=>[6,7,4,8,3,5,2,1]=>[6,7,4,8,3,5,2,1]=>[7,5,3,6,1,2,4,-8]
[3,8,4,7,2,5,6,1]=>[6,7,3,8,2,5,4,1]=>[6,7,3,8,2,5,4,1]=>[5,3,7,6,1,2,4,-8]
[8,3,2,4,6,1,5,7]=>[6,3,8,2,1,4,5,7]=>[6,3,8,2,1,4,5,7]=>[4,2,6,7,1,8,3,-5]
[8,3,7,4,2,5,6,1]=>[6,4,7,8,3,5,2,1]=>[6,4,7,8,3,5,2,1]=>[7,5,2,6,1,3,4,-8]
[6,8,2,5,7,4,1,3]=>[4,7,2,8,1,6,5,3]=>[4,7,2,8,1,6,5,3]=>[3,8,1,7,6,2,4,-5]
[3,1,2,7,5,6,8,4]=>[3,1,2,8,7,5,6,4]=>[3,1,2,8,7,5,6,4]=>[3,1,8,6,7,5,4,-2]
[2,7,3,1,5,6,8,4]=>[3,2,7,8,1,5,6,4]=>[3,2,7,8,1,5,6,4]=>[2,1,8,6,7,3,4,-5]
[5,6,7,8,1,4,2,3]=>[8,4,2,1,5,6,7,3]=>[8,4,2,1,5,6,7,3]=>[3,8,2,5,6,7,1,-4]
[5,1,7,2,4,6,8,3]=>[5,7,8,2,1,4,6,3]=>[5,7,8,2,1,4,6,3]=>[4,8,6,1,7,2,3,-5]
[5,7,4,8,2,1,3,6]=>[2,8,1,7,5,3,4,6]=>[2,8,1,7,5,3,4,6]=>[1,6,7,5,8,4,2,-3]
[4,2,3,8,5,1,6,7]=>[5,4,2,3,8,1,6,7]=>[5,4,2,3,8,1,6,7]=>[3,4,2,1,7,8,5,-6]
[6,5,7,3,8,2,4,1]=>[4,8,7,2,6,5,3,1]=>[4,8,7,2,6,5,3,1]=>[4,7,1,6,5,3,2,-8]
[6,4,7,3,8,2,5,1]=>[5,8,7,6,2,4,3,1]=>[5,8,7,6,2,4,3,1]=>[5,7,6,1,4,3,2,-8]
[3,7,8,2,6,4,1,5]=>[4,6,3,8,2,1,7,5]=>[4,6,3,8,2,1,7,5]=>[5,3,1,8,2,7,4,-6]
[1,3,6,7,4,2,5,8]=>[1,4,3,7,2,6,5,8]=>[1,4,3,7,2,6,5,8]=>[5,3,2,7,6,4,8,-1]
[2,6,8,4,7,3,1,5]=>[3,2,7,8,1,6,4,5]=>[3,2,7,8,1,6,4,5]=>[2,1,7,8,6,3,4,-5]
[3,2,7,4,8,1,6,5]=>[8,3,2,7,6,1,4,5]=>[8,3,2,7,6,1,4,5]=>[3,2,7,8,5,4,1,-6]
[4,7,1,5,8,2,3,6]=>[7,8,2,4,1,3,5,6]=>[7,8,2,4,1,3,5,6]=>[3,6,4,7,8,1,2,-5]
[1,3,5,2,7,6,8,4]=>[1,5,3,8,2,7,6,4]=>[1,5,3,8,2,7,6,4]=>[5,3,8,2,7,6,4,-1]
[1,3,5,7,4,2,8,6]=>[1,4,3,7,5,8,2,6]=>[1,4,3,7,5,8,2,6]=>[7,3,2,5,8,4,6,-1]
[2,5,6,3,7,8,1,4]=>[8,2,6,1,5,3,7,4]=>[8,2,6,1,5,3,7,4]=>[2,6,8,5,3,7,1,-4]
[4,1,6,2,8,5,7,3]=>[4,6,7,1,8,2,5,3]=>[4,6,7,1,8,2,5,3]=>[6,8,1,7,2,3,5,-4]
[6,4,2,1,3,8,7,5]=>[2,4,1,6,7,3,8,5]=>[2,4,1,6,7,3,8,5]=>[1,6,2,8,4,5,7,-3]
[8,1,4,7,2,5,3,6]=>[8,7,5,1,2,3,4,6]=>[8,7,5,1,2,3,4,6]=>[5,6,7,3,8,2,1,-4]
[2,5,8,7,3,6,1,4]=>[6,2,7,1,5,3,8,4]=>[6,2,7,1,5,3,8,4]=>[2,6,8,5,1,3,7,-4]
[3,1,8,4,7,2,6,5]=>[3,7,1,8,6,2,4,5]=>[3,7,1,8,6,2,4,5]=>[6,1,7,8,5,2,4,-3]
[2,6,5,4,3,8,1,7]=>[8,2,4,5,6,3,1,7]=>[8,2,4,5,6,3,1,7]=>[2,6,3,4,5,8,1,-7]
[6,2,4,5,1,7,8,3]=>[5,6,8,2,4,1,7,3]=>[5,6,8,2,4,1,7,3]=>[4,8,5,1,2,7,3,-6]
[3,7,1,5,6,8,2,4]=>[7,8,3,2,1,5,6,4]=>[7,8,3,2,1,5,6,4]=>[4,3,8,6,7,1,2,-5]
[5,7,3,8,6,1,4,2]=>[6,4,8,3,5,7,1,2]=>[6,4,8,3,5,7,1,2]=>[8,4,2,5,1,6,3,-7]
[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>[4,1,3,6,5,8,7,-2]
[6,1,4,3,5,2,8,7]=>[6,5,4,1,3,2,8,7]=>[6,5,4,1,3,2,8,7]=>[6,5,3,2,1,8,7,-4]
[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>[2,1,5,3,6,4,8,7]=>[1,4,6,3,5,8,7,-2]
[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,5,8,6]=>[1,4,3,6,8,5,7,-2]
[2,5,7,8,3,6,1,4]=>[6,2,8,1,5,3,7,4]=>[6,2,8,1,5,3,7,4]=>[2,6,8,5,1,7,3,-4]
[2,7,6,3,1,4,5,8]=>[3,2,6,1,4,7,5,8]=>[3,2,6,1,4,7,5,8]=>[2,1,5,7,3,6,8,-4]
[5,6,1,2,4,3,8,7]=>[6,1,4,2,5,3,8,7]=>[6,1,4,2,5,3,8,7]=>[4,6,3,5,1,8,7,-2]
[5,7,4,2,8,3,6,1]=>[6,4,7,8,5,2,3,1]=>[6,4,7,8,5,2,3,1]=>[6,7,2,5,1,3,4,-8]
[5,7,8,2,6,4,1,3]=>[4,6,2,8,5,1,7,3]=>[4,6,2,8,5,1,7,3]=>[3,8,1,5,2,7,4,-6]
[3,6,2,5,7,8,1,4]=>[8,6,3,1,2,5,7,4]=>[8,6,3,1,2,5,7,4]=>[5,3,8,6,2,7,1,-4]
[4,8,2,6,5,7,1,3]=>[7,8,1,4,6,2,5,3]=>[7,8,1,4,6,2,5,3]=>[6,8,4,7,5,1,2,-3]
[3,7,8,5,2,4,1,6]=>[4,5,3,2,8,1,7,6]=>[4,5,3,2,8,1,7,6]=>[4,3,1,2,8,7,5,-6]
[3,5,2,7,4,8,1,6]=>[8,5,3,7,2,1,4,6]=>[8,5,3,7,2,1,4,6]=>[5,3,7,2,8,4,1,-6]
[4,7,2,3,1,8,5,6]=>[3,7,2,4,8,5,1,6]=>[3,7,2,4,8,5,1,6]=>[3,1,4,6,8,2,5,-7]
[2,8,4,6,7,3,1,5]=>[3,2,7,8,1,4,6,5]=>[3,2,7,8,1,4,6,5]=>[2,1,6,8,7,3,4,-5]
[6,2,1,8,4,3,7,5]=>[2,6,4,8,7,1,3,5]=>[2,6,4,8,7,1,3,5]=>[1,7,3,8,2,5,4,-6]
[3,5,1,6,4,2,8,7]=>[5,4,3,6,1,2,8,7]=>[5,4,3,6,1,2,8,7]=>[6,3,2,1,4,8,7,-5]
[7,3,4,6,8,5,1,2]=>[5,1,8,2,7,4,6,3]=>[5,1,8,2,7,4,6,3]=>[4,8,6,1,7,5,3,-2]
[4,6,7,1,8,5,3,2]=>[7,3,5,4,8,6,1,2]=>[7,3,5,4,8,6,1,2]=>[8,2,4,3,6,1,5,-7]
[3,6,1,7,8,5,4,2]=>[6,4,3,5,8,1,7,2]=>[6,4,3,5,8,1,7,2]=>[8,3,2,4,1,7,5,-6]
[2,1,5,7,3,8,6,4]=>[2,1,7,6,5,8,3,4]=>[2,1,7,6,5,8,3,4]=>[1,7,8,5,4,3,6,-2]
[8,1,3,6,4,7,2,5]=>[8,7,1,6,2,3,4,5]=>[8,7,1,6,2,3,4,5]=>[5,6,7,8,4,2,1,-3]
[6,3,7,4,8,1,2,5]=>[8,1,6,7,2,3,4,5]=>[8,1,6,7,2,3,4,5]=>[5,6,7,8,3,4,1,-2]
[5,2,6,3,8,1,4,7]=>[8,5,6,1,2,3,4,7]=>[8,5,6,1,2,3,4,7]=>[5,6,7,2,3,8,1,-4]
[2,7,8,3,6,1,4,5]=>[6,2,8,1,4,3,7,5]=>[6,2,8,1,4,3,7,5]=>[2,6,5,8,1,7,3,-4]
[2,6,3,1,8,4,5,7]=>[3,2,6,8,4,1,5,7]=>[3,2,6,8,4,1,5,7]=>[2,1,5,7,3,8,4,-6]
[8,6,1,3,5,2,4,7]=>[6,5,1,2,3,8,4,7]=>[6,5,1,2,3,8,4,7]=>[4,5,7,2,1,8,6,-3]
[7,5,8,4,1,3,2,6]=>[4,3,1,8,7,2,5,6]=>[4,3,1,8,7,2,5,6]=>[6,2,1,7,8,5,4,-3]
[4,6,7,2,8,3,1,5]=>[3,8,7,4,2,6,1,5]=>[3,8,7,4,2,6,1,5]=>[5,1,4,8,6,3,2,-7]
[2,1,7,6,5,3,8,4]=>[2,1,5,6,7,8,3,4]=>[2,1,5,6,7,8,3,4]=>[1,7,8,3,4,5,6,-2]
[7,2,5,4,6,1,8,3]=>[6,7,8,5,2,4,1,3]=>[6,7,8,5,2,4,1,3]=>[5,8,6,4,1,2,3,-7]
[6,1,5,7,2,4,8,3]=>[6,7,8,2,1,5,4,3]=>[6,7,8,2,1,5,4,3]=>[4,8,7,6,1,2,3,-5]
[7,4,5,1,2,3,8,6]=>[5,1,2,7,4,8,3,6]=>[5,1,2,7,4,8,3,6]=>[3,7,5,1,8,4,6,-2]
[7,1,2,3,5,8,4,6]=>[7,1,2,8,3,4,5,6]=>[7,1,2,8,3,4,5,6]=>[3,5,6,7,8,1,4,-2]
[2,1,7,8,3,4,6,5]=>[2,1,8,3,6,4,7,5]=>[2,1,8,3,6,4,7,5]=>[1,4,6,8,5,7,3,-2]
[6,2,5,1,7,4,8,3]=>[5,6,8,7,2,1,4,3]=>[5,6,8,7,2,1,4,3]=>[5,8,7,1,2,4,3,-6]
[3,4,1,2,7,8,6,5]=>[4,1,3,2,6,8,7,5]=>[4,1,3,2,6,8,7,5]=>[4,3,1,8,5,7,6,-2]
[3,1,2,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[3,1,4,8,7,6,5,-2]
[8,4,7,6,2,3,1,5]=>[3,6,2,7,4,8,1,5]=>[3,6,2,7,4,8,1,5]=>[3,1,5,8,2,4,6,-7]
[6,1,4,7,2,8,3,5]=>[6,7,8,1,3,4,2,5]=>[6,7,8,1,3,4,2,5]=>[7,5,6,8,1,2,3,-4]
[1,3,2,8,5,4,6,7]=>[1,3,2,5,8,4,6,7]=>[1,3,2,5,8,4,6,7]=>[3,2,6,4,7,8,5,-1]
[2,8,7,1,4,5,3,6]=>[7,2,5,1,4,3,8,6]=>[7,2,5,1,4,3,8,6]=>[2,6,5,3,8,1,7,-4]
[3,6,7,4,1,8,2,5]=>[4,7,3,8,1,6,2,5]=>[4,7,3,8,1,6,2,5]=>[7,3,1,8,6,2,4,-5]
[8,1,2,4,6,7,5,3]=>[8,1,5,2,7,4,6,3]=>[8,1,5,2,7,4,6,3]=>[4,8,6,3,7,5,1,-2]
[6,4,2,8,5,1,3,7]=>[5,4,2,8,6,1,3,7]=>[5,4,2,8,6,1,3,7]=>[3,7,2,1,5,8,4,-6]
[6,2,4,1,7,5,8,3]=>[4,6,8,2,7,1,5,3]=>[4,6,8,2,7,1,5,3]=>[4,8,1,7,2,5,3,-6]
[4,6,7,2,8,1,3,5]=>[8,7,1,4,3,6,2,5]=>[8,7,1,4,3,6,2,5]=>[7,5,4,8,6,2,1,-3]
[7,2,5,8,6,3,1,4]=>[3,6,8,1,2,7,5,4]=>[3,6,8,1,2,7,5,4]=>[5,1,8,7,2,6,3,-4]
[6,1,4,2,7,5,3,8]=>[6,4,5,1,7,2,3,8]=>[6,4,5,1,7,2,3,8]=>[6,7,2,3,1,5,8,-4]
[6,2,3,7,4,1,5,8]=>[4,7,1,6,2,3,5,8]=>[4,7,1,6,2,3,5,8]=>[5,6,1,7,4,2,8,-3]
[6,2,4,1,7,3,5,8]=>[4,6,7,2,3,1,5,8]=>[4,6,7,2,3,1,5,8]=>[4,5,1,7,2,3,8,-6]
[4,6,7,5,2,1,8,3]=>[2,5,7,4,8,6,3,1]=>[2,5,7,4,8,6,3,1]=>[1,7,4,2,6,3,5,-8]
[5,1,7,3,6,2,8,4]=>[5,6,7,8,1,3,2,4]=>[5,6,7,8,1,3,2,4]=>[7,6,8,1,2,3,4,-5]
[5,6,3,1,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>[3,1,6,2,5,4,8,7]=>[4,1,6,5,3,8,7,-2]
[3,7,6,4,2,8,5,1]=>[5,4,3,8,6,7,1,2]=>[5,4,3,8,6,7,1,2]=>[8,3,2,1,5,6,4,-7]
[7,1,8,5,4,2,3,6]=>[7,4,2,5,8,3,1,6]=>[7,4,2,5,8,3,1,6]=>[3,6,2,4,8,1,5,-7]
[2,1,7,8,5,3,4,6]=>[2,1,5,3,8,4,7,6]=>[2,1,5,3,8,4,7,6]=>[1,4,6,3,8,7,5,-2]
[5,1,7,2,4,8,3,6]=>[5,7,8,2,1,3,4,6]=>[5,7,8,2,1,3,4,6]=>[4,6,7,1,8,2,3,-5]
[8,1,3,2,6,5,4,7]=>[8,3,1,5,6,2,4,7]=>[8,3,1,5,6,2,4,7]=>[6,2,7,4,5,8,1,-3]
[4,2,1,5,6,7,8,3]=>[2,4,8,1,5,6,7,3]=>[2,4,8,1,5,6,7,3]=>[1,8,2,5,6,7,3,-4]
[7,3,5,2,4,6,1,8]=>[6,5,7,2,3,4,1,8]=>[6,5,7,2,3,4,1,8]=>[4,5,6,2,1,3,8,-7]
[5,3,7,2,4,6,1,8]=>[6,7,5,2,3,4,1,8]=>[6,7,5,2,3,4,1,8]=>[4,5,6,3,1,2,8,-7]
[3,2,5,7,4,1,6,8]=>[4,3,2,7,5,1,6,8]=>[4,3,2,7,5,1,6,8]=>[3,2,1,5,7,4,8,-6]
[3,2,5,1,7,4,6,8]=>[5,3,2,7,1,4,6,8]=>[5,3,2,7,1,4,6,8]=>[3,2,6,1,7,4,8,-5]
[7,6,2,8,3,1,4,5]=>[3,8,6,2,4,7,1,5]=>[3,8,6,2,4,7,1,5]=>[4,1,5,8,3,6,2,-7]
[3,2,5,1,7,8,4,6]=>[5,3,2,8,1,4,7,6]=>[5,3,2,8,1,4,7,6]=>[3,2,6,1,8,7,4,-5]
[6,1,3,7,4,2,5,8]=>[6,4,1,7,2,3,5,8]=>[6,4,1,7,2,3,5,8]=>[5,6,2,7,1,4,8,-3]
[6,3,7,2,8,1,5,4]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,1,3,2,4]=>[7,6,8,4,3,2,1,-5]
[3,6,2,7,8,1,5,4]=>[8,6,3,5,1,2,7,4]=>[8,6,3,5,1,2,7,4]=>[6,3,8,4,2,7,1,-5]
[8,4,6,5,3,1,7,2]=>[3,5,6,7,8,2,1,4]=>[3,5,6,7,8,2,1,4]=>[6,1,8,2,3,4,5,-7]
[7,8,1,2,4,3,6,5]=>[8,1,4,2,6,3,7,5]=>[8,1,4,2,6,3,7,5]=>[4,6,3,8,5,7,1,-2]
[5,2,4,1,3,7,8,6]=>[4,5,1,2,3,8,7,6]=>[4,5,1,2,3,8,7,6]=>[4,5,1,2,8,7,6,-3]
[3,5,1,6,4,7,8,2]=>[5,8,3,6,1,4,7,2]=>[5,8,3,6,1,4,7,2]=>[8,3,6,1,4,7,2,-5]
[8,1,5,4,7,2,6,3]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,1,2,4,3]=>[6,8,7,4,3,2,1,-5]
[8,2,5,3,7,1,6,4]=>[7,8,5,6,2,1,3,4]=>[7,8,5,6,2,1,3,4]=>[5,7,8,3,4,1,2,-6]
[1,7,2,4,8,5,3,6]=>[1,7,5,2,8,3,4,6]=>[1,7,5,2,8,3,4,6]=>[4,6,7,3,8,2,5,-1]
[2,6,8,7,4,3,5,1]=>[5,2,4,7,3,6,8,1]=>[5,2,4,7,3,6,8,1]=>[2,5,3,1,6,4,7,-8]
[3,1,7,4,5,2,8,6]=>[3,5,1,7,4,8,2,6]=>[3,5,1,7,4,8,2,6]=>[7,1,5,2,8,4,6,-3]
[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]=>[2,1,6,3,4,7,8,5]=>[1,4,5,8,3,6,7,-2]
[6,8,5,4,2,7,1,3]=>[7,4,1,5,8,6,2,3]=>[7,4,1,5,8,6,2,3]=>[7,8,2,4,6,1,5,-3]
[5,2,8,6,7,3,4,1]=>[4,5,7,3,2,8,6,1]=>[4,5,7,3,2,8,6,1]=>[5,4,1,2,7,3,6,-8]
[8,4,5,1,7,3,6,2]=>[5,6,7,8,4,3,1,2]=>[5,6,7,8,4,3,1,2]=>[8,6,5,1,2,3,4,-7]
[7,4,8,5,6,2,3,1]=>[3,6,2,7,8,5,4,1]=>[3,6,2,7,8,5,4,1]=>[3,1,7,6,2,4,5,-8]
[2,1,8,7,3,4,6,5]=>[2,1,7,3,6,4,8,5]=>[2,1,7,3,6,4,8,5]=>[1,4,6,8,5,3,7,-2]
[4,1,2,8,7,5,3,6]=>[4,1,5,2,7,3,8,6]=>[4,1,5,2,7,3,8,6]=>[4,6,1,3,8,5,7,-2]
[2,6,3,7,8,1,4,5]=>[8,2,6,1,4,3,7,5]=>[8,2,6,1,4,3,7,5]=>[2,6,5,8,3,7,1,-4]
[3,5,1,7,4,8,6,2]=>[5,6,3,8,1,7,2,4]=>[5,6,3,8,1,7,2,4]=>[7,3,8,1,2,6,4,-5]
[4,5,7,3,8,6,1,2]=>[6,1,8,4,5,7,2,3]=>[6,1,8,4,5,7,2,3]=>[7,8,4,5,1,6,3,-2]
[5,6,7,8,4,1,3,2]=>[4,3,1,8,5,6,7,2]=>[4,3,1,8,5,6,7,2]=>[8,2,1,5,6,7,4,-3]
[8,5,1,2,4,3,6,7]=>[5,1,4,2,8,3,6,7]=>[5,1,4,2,8,3,6,7]=>[4,6,3,1,7,8,5,-2]
[2,8,5,7,3,1,4,6]=>[3,2,7,1,8,4,5,6]=>[3,2,7,1,8,4,5,6]=>[2,1,6,7,8,3,5,-4]
[8,7,6,2,1,4,3,5]=>[2,6,4,1,3,7,8,5]=>[2,6,4,1,3,7,8,5]=>[1,5,3,8,2,6,7,-4]
[5,4,8,1,6,3,7,2]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,1,3,2]=>[8,7,5,4,3,2,1,-6]
[5,4,7,2,8,1,6,3]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,1,2,3]=>[7,8,5,4,3,2,1,-6]
[8,1,5,4,6,3,7,2]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,1,4,3,2]=>[8,7,6,4,3,2,1,-5]
[2,1,5,8,3,7,4,6]=>[2,1,8,7,5,4,3,6]=>[2,1,8,7,5,4,3,6]=>[1,7,6,5,8,4,3,-2]
[2,1,7,4,8,3,6,5]=>[2,1,8,7,6,3,4,5]=>[2,1,8,7,6,3,4,5]=>[1,6,7,8,5,4,3,-2]
[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>[4,1,3,2,7,5,8,6]=>[4,3,1,6,8,5,7,-2]
[6,2,5,1,7,3,8,4]=>[5,6,7,8,2,1,3,4]=>[5,6,7,8,2,1,3,4]=>[5,7,8,1,2,3,4,-6]
[7,1,2,3,6,8,4,5]=>[7,1,2,8,4,3,6,5]=>[7,1,2,8,4,3,6,5]=>[3,6,5,8,7,1,4,-2]
[3,1,5,2,8,6,7,4]=>[3,5,1,7,2,8,6,4]=>[3,5,1,7,2,8,6,4]=>[5,1,8,2,7,4,6,-3]
[6,2,5,1,8,3,4,7]=>[5,6,8,3,2,1,4,7]=>[5,6,8,3,2,1,4,7]=>[5,4,7,1,2,8,3,-6]
[3,5,6,1,4,2,7,8]=>[6,4,3,1,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>[6,3,2,5,1,7,8,-4]
[3,6,2,7,8,5,1,4]=>[5,8,3,2,6,1,7,4]=>[5,8,3,2,6,1,7,4]=>[4,3,8,1,5,7,2,-6]
[3,6,2,7,8,1,4,5]=>[8,6,3,1,4,2,7,5]=>[8,6,3,1,4,2,7,5]=>[6,3,5,8,2,7,1,-4]
[7,5,4,1,6,8,2,3]=>[4,5,2,7,8,1,6,3]=>[4,5,2,7,8,1,6,3]=>[3,8,1,2,7,4,5,-6]
[7,3,6,1,4,8,2,5]=>[6,8,7,1,2,3,4,5]=>[6,8,7,1,2,3,4,5]=>[5,6,7,8,1,3,2,-4]
[6,2,5,1,8,7,3,4]=>[5,6,7,3,2,1,8,4]=>[5,6,7,3,2,1,8,4]=>[5,4,8,1,2,3,7,-6]
[7,3,5,1,8,2,6,4]=>[5,8,7,6,3,2,1,4]=>[5,8,7,6,3,2,1,4]=>[6,5,8,1,4,3,2,-7]
[4,6,7,1,8,5,2,3]=>[7,5,2,4,8,6,1,3]=>[7,5,2,4,8,6,1,3]=>[3,8,4,2,6,1,5,-7]
[8,4,7,1,3,2,6,5]=>[7,3,1,8,6,2,4,5]=>[7,3,1,8,6,2,4,5]=>[6,2,7,8,5,1,4,-3]
[3,5,2,8,4,6,7,1]=>[7,5,3,8,2,4,6,1]=>[7,5,3,8,2,4,6,1]=>[5,3,6,2,7,1,4,-8]
[3,7,1,5,8,2,4,6]=>[7,8,3,2,1,4,5,6]=>[7,8,3,2,1,4,5,6]=>[4,3,6,7,8,1,2,-5]
[5,2,3,4,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>[3,4,1,2,7,8,6,-5]
[3,8,1,2,4,6,7,5]=>[8,1,3,2,7,4,6,5]=>[8,1,3,2,7,4,6,5]=>[4,3,6,8,7,5,1,-2]
[1,2,8,5,3,7,4,6]=>[1,2,5,8,7,3,4,6]=>[1,2,5,8,7,3,4,6]=>[2,6,7,3,8,5,4,-1]
[7,1,4,2,6,8,3,5]=>[7,4,8,1,3,2,6,5]=>[7,4,8,1,3,2,6,5]=>[6,5,2,8,7,1,3,-4]
[1,2,8,3,5,7,6,4]=>[1,2,8,6,3,7,5,4]=>[1,2,8,6,3,7,5,4]=>[2,5,8,7,4,6,3,-1]
[8,3,4,5,1,6,2,7]=>[5,6,8,3,4,1,2,7]=>[5,6,8,3,4,1,2,7]=>[7,4,5,1,2,8,3,-6]
[5,7,3,4,8,1,6,2]=>[8,6,7,3,5,1,4,2]=>[8,6,7,3,5,1,4,2]=>[8,4,7,5,2,3,1,-6]
[4,6,7,3,8,1,2,5]=>[8,1,7,4,2,6,3,5]=>[8,1,7,4,2,6,3,5]=>[5,7,4,8,6,3,1,-2]
[6,1,2,8,3,4,7,5]=>[6,1,8,3,7,2,4,5]=>[6,1,8,3,7,2,4,5]=>[6,4,7,8,1,5,3,-2]
[3,1,8,2,5,4,6,7]=>[3,8,1,5,2,4,6,7]=>[3,8,1,5,2,4,6,7]=>[5,1,6,4,7,8,2,-3]
[6,3,5,1,8,2,4,7]=>[5,8,6,2,3,1,4,7]=>[5,8,6,2,3,1,4,7]=>[4,5,7,1,3,8,2,-6]
[5,3,8,7,6,2,1,4]=>[2,6,5,1,3,7,8,4]=>[2,6,5,1,3,7,8,4]=>[1,5,8,3,2,6,7,-4]
[3,6,1,7,8,4,2,5]=>[6,4,3,8,2,1,7,5]=>[6,4,3,8,2,1,7,5]=>[5,3,2,8,1,7,4,-6]
[4,5,7,2,1,8,3,6]=>[2,7,8,4,5,3,1,6]=>[2,7,8,4,5,3,1,6]=>[1,6,4,5,8,2,3,-7]
[4,6,8,5,2,1,7,3]=>[2,5,8,4,7,6,3,1]=>[2,5,8,4,7,6,3,1]=>[1,7,4,2,6,5,3,-8]
[8,6,7,3,4,1,5,2]=>[4,5,7,3,1,8,6,2]=>[4,5,7,3,1,8,6,2]=>[8,4,1,2,7,3,6,-5]
[4,3,8,1,6,5,7,2]=>[8,7,4,3,6,1,5,2]=>[8,7,4,3,6,1,5,2]=>[8,4,3,7,5,2,1,-6]
[7,2,6,3,8,1,5,4]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,1,2,3,4]=>[6,7,8,4,3,2,1,-5]
[7,2,8,1,6,3,5,4]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,3,1,2,4]=>[7,5,8,4,3,2,1,-6]
[6,3,8,1,7,2,5,4]=>[8,7,6,5,2,3,1,4]=>[8,7,6,5,2,3,1,4]=>[5,6,8,4,3,2,1,-7]
[1,2,5,3,7,6,8,4]=>[1,2,5,8,3,7,6,4]=>[1,2,5,8,3,7,6,4]=>[2,5,8,3,7,6,4,-1]
[3,6,8,2,5,7,4,1]=>[4,7,3,8,1,6,5,2]=>[4,7,3,8,1,6,5,2]=>[8,3,1,7,6,2,4,-5]
[4,5,6,2,7,3,8,1]=>[8,6,7,4,5,2,3,1]=>[8,6,7,4,5,2,3,1]=>[6,7,4,5,2,3,1,-8]
[8,4,5,7,6,2,3,1]=>[3,6,2,7,1,8,5,4]=>[3,6,2,7,1,8,5,4]=>[3,1,8,7,2,4,6,-5]
[8,1,2,3,5,7,4,6]=>[8,1,2,7,3,4,5,6]=>[8,1,2,7,3,4,5,6]=>[3,5,6,7,8,4,1,-2]
[5,2,8,1,4,3,7,6]=>[8,5,4,1,2,7,3,6]=>[8,5,4,1,2,7,3,6]=>[5,7,3,2,8,6,1,-4]
[5,2,4,1,6,3,8,7]=>[4,5,6,2,1,3,8,7]=>[4,5,6,2,1,3,8,7]=>[4,6,1,2,3,8,7,-5]
[2,1,7,4,6,3,8,5]=>[2,1,6,7,8,4,3,5]=>[2,1,6,7,8,4,3,5]=>[1,7,6,8,3,4,5,-2]
[7,2,4,3,6,1,8,5]=>[6,7,4,2,8,3,1,5]=>[6,7,4,2,8,3,1,5]=>[4,6,3,8,1,2,5,-7]
[8,4,3,5,7,2,6,1]=>[6,7,4,8,3,2,5,1]=>[6,7,4,8,3,2,5,1]=>[6,5,3,7,1,2,4,-8]
[3,5,2,6,1,4,8,7]=>[6,5,3,1,2,4,8,7]=>[6,5,3,1,2,4,8,7]=>[5,3,6,2,1,8,7,-4]
[4,5,7,2,3,8,6,1]=>[6,8,1,4,5,7,3,2]=>[6,8,1,4,5,7,3,2]=>[8,7,4,5,1,6,2,-3]
[4,5,7,2,3,8,1,6]=>[8,7,2,4,5,1,3,6]=>[8,7,2,4,5,1,3,6]=>[3,7,4,5,8,2,1,-6]
[4,5,6,2,3,1,8,7]=>[3,6,2,4,5,1,8,7]=>[3,6,2,4,5,1,8,7]=>[3,1,4,5,2,8,7,-6]
[4,5,6,2,1,3,8,7]=>[2,6,1,4,5,3,8,7]=>[2,6,1,4,5,3,8,7]=>[1,6,4,5,2,8,7,-3]
[4,5,6,1,3,2,8,7]=>[6,3,1,4,5,2,8,7]=>[6,3,1,4,5,2,8,7]=>[6,2,4,5,1,8,7,-3]
[4,5,6,3,1,2,8,7]=>[3,1,6,4,5,2,8,7]=>[3,1,6,4,5,2,8,7]=>[6,1,4,5,3,8,7,-2]
[4,5,7,3,2,8,1,6]=>[8,3,7,4,5,1,2,6]=>[8,3,7,4,5,1,2,6]=>[7,2,4,5,8,3,1,-6]
[4,6,7,3,8,2,5,1]=>[5,8,7,4,2,6,3,1]=>[5,8,7,4,2,6,3,1]=>[5,7,4,1,6,3,2,-8]
[4,6,7,3,8,2,1,5]=>[2,8,7,4,1,6,3,5]=>[2,8,7,4,1,6,3,5]=>[1,7,4,8,6,3,2,-5]
[4,5,7,3,1,8,2,6]=>[3,7,8,4,5,1,2,6]=>[3,7,8,4,5,1,2,6]=>[7,1,4,5,8,2,3,-6]
[3,5,1,7,4,8,2,6]=>[5,8,3,7,1,2,4,6]=>[5,8,3,7,1,2,4,6]=>[6,3,7,1,8,4,2,-5]
[2,1,5,7,4,8,3,6]=>[2,1,8,7,5,3,4,6]=>[2,1,8,7,5,3,4,6]=>[1,6,7,5,8,4,3,-2]
[4,5,7,1,3,8,6,2]=>[7,6,1,4,5,8,3,2]=>[7,6,1,4,5,8,3,2]=>[8,7,4,5,2,1,6,-3]
[4,6,7,3,8,1,5,2]=>[8,5,7,4,1,6,3,2]=>[8,5,7,4,1,6,3,2]=>[8,7,4,2,6,3,1,-5]
[5,6,7,8,3,1,4,2]=>[3,8,4,2,5,6,7,1]=>[3,8,4,2,5,6,7,1]=>[4,1,3,5,6,7,2,-8]
[4,6,7,1,8,3,5,2]=>[7,5,8,4,3,6,1,2]=>[7,5,8,4,3,6,1,2]=>[8,5,4,2,6,1,3,-7]
[3,6,1,7,8,4,5,2]=>[6,5,3,8,4,1,7,2]=>[6,5,3,8,4,1,7,2]=>[8,3,5,2,1,7,4,-6]
[2,1,6,7,8,4,5,3]=>[2,1,5,8,4,6,7,3]=>[2,1,5,8,4,6,7,3]=>[1,8,5,3,6,7,4,-2]
[2,1,6,7,8,4,3,5]=>[2,1,4,8,3,6,7,5]=>[2,1,4,8,3,6,7,5]=>[1,5,3,8,6,7,4,-2]
[4,6,7,1,8,3,2,5]=>[7,3,8,4,2,6,1,5]=>[7,3,8,4,2,6,1,5]=>[5,2,4,8,6,1,3,-7]
[5,6,7,8,1,3,2,4]=>[8,3,1,2,5,6,7,4]=>[8,3,1,2,5,6,7,4]=>[4,2,8,5,6,7,1,-3]
[4,6,7,2,8,3,5,1]=>[5,7,8,4,3,6,2,1]=>[5,7,8,4,3,6,2,1]=>[7,5,4,1,6,2,3,-8]
[3,6,2,7,8,4,5,1]=>[5,6,3,8,4,2,7,1]=>[5,6,3,8,4,2,7,1]=>[6,3,5,1,2,7,4,-8]
[3,6,2,7,8,4,1,5]=>[4,8,3,6,2,1,7,5]=>[4,8,3,6,2,1,7,5]=>[5,3,1,8,4,7,2,-6]
[3,4,2,1,7,8,5,6]=>[2,4,3,1,8,5,7,6]=>[2,4,3,1,8,5,7,6]=>[1,3,2,6,8,7,5,-4]
[4,6,7,2,8,5,3,1]=>[3,5,8,4,7,6,2,1]=>[3,5,8,4,7,6,2,1]=>[7,1,4,2,6,5,3,-8]
[4,6,7,2,8,5,1,3]=>[5,8,2,4,7,6,1,3]=>[5,8,2,4,7,6,1,3]=>[3,8,4,1,6,5,2,-7]
[4,5,7,1,2,8,6,3]=>[7,1,6,4,5,8,2,3]=>[7,1,6,4,5,8,2,3]=>[7,8,4,5,3,1,6,-2]
[2,1,6,7,8,3,5,4]=>[2,1,8,5,3,6,7,4]=>[2,1,8,5,3,6,7,4]=>[1,5,8,4,6,7,3,-2]
[3,6,1,7,8,2,5,4]=>[6,8,3,5,2,1,7,4]=>[6,8,3,5,2,1,7,4]=>[5,3,8,4,1,7,2,-6]
[4,6,7,1,8,2,5,3]=>[7,8,5,4,2,6,1,3]=>[7,8,5,4,2,6,1,3]=>[5,8,4,3,6,1,2,-7]
[5,6,7,8,1,2,4,3]=>[8,1,4,2,5,6,7,3]=>[8,1,4,2,5,6,7,3]=>[4,8,3,5,6,7,1,-2]
[5,6,7,8,2,4,1,3]=>[4,8,1,2,5,6,7,3]=>[4,8,1,2,5,6,7,3]=>[4,8,1,5,6,7,2,-3]
[5,6,7,8,2,4,3,1]=>[3,4,8,1,5,6,7,2]=>[3,4,8,1,5,6,7,2]=>[8,1,2,5,6,7,3,-4]
[3,6,1,7,8,5,2,4]=>[6,5,3,2,8,1,7,4]=>[6,5,3,2,8,1,7,4]=>[4,3,8,2,1,7,5,-6]
[2,1,6,7,8,5,3,4]=>[2,1,5,3,8,6,7,4]=>[2,1,5,3,8,6,7,4]=>[1,4,8,3,6,7,5,-2]
[3,6,1,5,2,4,8,7]=>[6,5,3,2,1,4,8,7]=>[6,5,3,2,1,4,8,7]=>[4,3,6,2,1,8,7,-5]
[4,3,1,2,7,8,5,6]=>[3,1,4,2,8,5,7,6]=>[3,1,4,2,8,5,7,6]=>[4,1,3,6,8,7,5,-2]
[5,4,2,6,7,1,8,3]=>[7,4,5,8,3,6,1,2]=>[7,4,5,8,3,6,1,2]=>[8,5,2,3,6,1,4,-7]
[6,4,8,2,5,1,7,3]=>[5,8,7,6,2,4,1,3]=>[5,8,7,6,2,4,1,3]=>[5,8,6,1,4,3,2,-7]
[3,5,2,8,1,7,6,4]=>[8,5,3,6,2,7,1,4]=>[8,5,3,6,2,7,1,4]=>[5,3,8,2,4,6,1,-7]
[6,2,5,1,4,3,8,7]=>[5,6,4,1,2,3,8,7]=>[5,6,4,1,2,3,8,7]=>[5,6,3,1,2,8,7,-4]
[5,2,6,1,4,3,8,7]=>[6,5,4,1,2,3,8,7]=>[6,5,4,1,2,3,8,7]=>[5,6,3,2,1,8,7,-4]
[5,2,7,1,4,3,8,6]=>[7,5,4,1,2,8,3,6]=>[7,5,4,1,2,8,3,6]=>[5,7,3,2,8,1,6,-4]
[6,2,8,1,4,3,7,5]=>[8,6,4,1,7,2,3,5]=>[8,6,4,1,7,2,3,5]=>[6,7,3,8,2,5,1,-4]
[6,2,7,1,4,3,8,5]=>[7,6,4,1,8,2,3,5]=>[7,6,4,1,8,2,3,5]=>[6,7,3,8,2,1,5,-4]
[7,2,6,1,4,3,8,5]=>[6,7,4,1,8,2,3,5]=>[6,7,4,1,8,2,3,5]=>[6,7,3,8,1,2,5,-4]
[8,2,5,1,4,3,7,6]=>[5,8,4,1,2,7,3,6]=>[5,8,4,1,2,7,3,6]=>[5,7,3,1,8,6,2,-4]
[8,1,4,3,7,2,6,5]=>[8,7,4,1,6,2,3,5]=>[8,7,4,1,6,2,3,5]=>[6,7,3,8,5,2,1,-4]
[8,2,6,1,5,3,7,4]=>[6,8,5,7,1,2,3,4]=>[6,8,5,7,1,2,3,4]=>[6,7,8,3,1,4,2,-5]
[7,2,6,1,5,3,8,4]=>[6,7,5,8,1,2,3,4]=>[6,7,5,8,1,2,3,4]=>[6,7,8,3,1,2,4,-5]
[6,2,7,1,5,3,8,4]=>[7,6,5,8,1,2,3,4]=>[7,6,5,8,1,2,3,4]=>[6,7,8,3,2,1,4,-5]
[6,2,8,1,5,3,7,4]=>[8,6,5,7,1,2,3,4]=>[8,6,5,7,1,2,3,4]=>[6,7,8,3,2,4,1,-5]
[7,4,8,1,3,2,6,5]=>[8,3,1,7,6,2,4,5]=>[8,3,1,7,6,2,4,5]=>[6,2,7,8,5,4,1,-3]
[8,3,7,1,4,2,6,5]=>[7,4,8,1,6,2,3,5]=>[7,4,8,1,6,2,3,5]=>[6,7,2,8,5,1,3,-4]
[8,3,7,1,5,2,6,4]=>[7,5,8,6,1,2,3,4]=>[7,5,8,6,1,2,3,4]=>[6,7,8,2,4,1,3,-5]
[7,3,8,1,5,2,6,4]=>[8,5,7,6,1,2,3,4]=>[8,5,7,6,1,2,3,4]=>[6,7,8,2,4,3,1,-5]
[6,2,7,3,8,1,5,4]=>[8,6,7,5,1,2,3,4]=>[8,6,7,5,1,2,3,4]=>[6,7,8,4,2,3,1,-5]
[6,2,8,3,7,1,5,4]=>[7,6,8,5,1,2,3,4]=>[7,6,8,5,1,2,3,4]=>[6,7,8,4,2,1,3,-5]
[5,1,8,3,7,2,6,4]=>[5,7,8,6,1,2,3,4]=>[5,7,8,6,1,2,3,4]=>[6,7,8,1,4,2,3,-5]
[4,1,8,3,7,2,6,5]=>[4,7,8,1,6,2,3,5]=>[4,7,8,1,6,2,3,5]=>[6,7,1,8,5,2,3,-4]
[3,1,7,4,8,2,6,5]=>[3,8,1,7,6,2,4,5]=>[3,8,1,7,6,2,4,5]=>[6,1,7,8,5,4,2,-3]
[4,1,7,3,8,2,6,5]=>[4,8,7,1,6,2,3,5]=>[4,8,7,1,6,2,3,5]=>[6,7,1,8,5,3,2,-4]
[5,1,7,3,8,2,6,4]=>[5,8,7,6,1,2,3,4]=>[5,8,7,6,1,2,3,4]=>[6,7,8,1,4,3,2,-5]
[7,3,8,2,6,1,5,4]=>[6,8,7,5,1,2,3,4]=>[6,8,7,5,1,2,3,4]=>[6,7,8,4,1,3,2,-5]
[8,2,6,3,7,1,5,4]=>[7,8,6,5,1,2,3,4]=>[7,8,6,5,1,2,3,4]=>[6,7,8,4,3,1,2,-5]
[5,3,7,8,1,4,2,6]=>[8,4,5,1,3,2,7,6]=>[8,4,5,1,3,2,7,6]=>[6,5,2,3,8,7,1,-4]
[5,1,6,7,3,2,8,4]=>[5,3,7,8,1,6,2,4]=>[5,3,7,8,1,6,2,4]=>[7,2,8,1,6,3,4,-5]
[3,7,8,1,4,6,2,5]=>[8,6,3,1,2,4,7,5]=>[8,6,3,1,2,4,7,5]=>[5,3,6,8,2,7,1,-4]
[3,1,5,6,7,8,4,2]=>[3,4,1,8,5,6,7,2]=>[3,4,1,8,5,6,7,2]=>[8,1,2,5,6,7,4,-3]
[1,6,4,7,8,5,2,3]=>[1,5,2,8,6,3,7,4]=>[1,5,2,8,6,3,7,4]=>[3,6,8,2,5,7,4,-1]
[1,7,8,6,3,4,5,2]=>[1,5,6,3,4,8,7,2]=>[1,5,6,3,4,8,7,2]=>[8,4,5,2,3,7,6,-1]
[2,6,1,4,5,3,8,7]=>[6,2,5,1,4,3,8,7]=>[6,2,5,1,4,3,8,7]=>[2,6,5,3,1,8,7,-4]
[3,1,6,4,5,2,8,7]=>[3,5,1,6,4,2,8,7]=>[3,5,1,6,4,2,8,7]=>[6,1,5,2,4,8,7,-3]
[2,1,4,8,3,6,7,5]=>[2,1,8,4,7,3,6,5]=>[2,1,8,4,7,3,6,5]=>[1,6,4,8,7,5,3,-2]
[2,1,5,3,8,6,7,4]=>[2,1,5,7,3,8,6,4]=>[2,1,5,7,3,8,6,4]=>[1,5,8,3,7,4,6,-2]
[3,7,8,4,1,6,2,5]=>[4,8,3,6,1,2,7,5]=>[4,8,3,6,1,2,7,5]=>[6,3,1,8,4,7,2,-5]
[6,5,1,2,7,8,3,4]=>[5,1,6,2,8,3,7,4]=>[5,1,6,2,8,3,7,4]=>[4,6,8,1,3,7,5,-2]
[8,3,7,6,1,2,4,5]=>[6,1,7,3,4,8,2,5]=>[6,1,7,3,4,8,2,5]=>[7,4,5,8,1,3,6,-2]
[3,5,8,7,1,2,4,6]=>[7,1,3,2,5,4,8,6]=>[7,1,3,2,5,4,8,6]=>[4,3,6,5,8,1,7,-2]
[4,1,7,5,8,2,3,6]=>[4,8,2,1,7,3,5,6]=>[4,8,2,1,7,3,5,6]=>[3,6,1,7,8,5,2,-4]
[8,1,6,7,3,2,4,5]=>[8,3,7,2,4,1,6,5]=>[8,3,7,2,4,1,6,5]=>[4,2,5,8,7,3,1,-6]
[5,7,8,3,1,2,4,6]=>[3,1,8,2,5,4,7,6]=>[3,1,8,2,5,4,7,6]=>[4,1,6,5,8,7,3,-2]
[8,3,5,1,7,4,6,2]=>[5,6,8,7,3,4,1,2]=>[5,6,8,7,3,4,1,2]=>[8,5,6,1,2,4,3,-7]
[8,3,4,1,7,5,6,2]=>[4,6,8,3,7,5,1,2]=>[4,6,8,3,7,5,1,2]=>[8,4,1,6,2,5,3,-7]
[4,6,2,1,7,5,8,3]=>[2,6,8,4,7,1,5,3]=>[2,6,8,4,7,1,5,3]=>[1,8,4,7,2,5,3,-6]
[1,4,6,2,7,5,8,3]=>[1,6,8,4,7,2,5,3]=>[1,6,8,4,7,2,5,3]=>[6,8,4,7,2,5,3,-1]
[4,7,5,6,1,8,3,2]=>[6,3,8,4,7,5,1,2]=>[6,3,8,4,7,5,1,2]=>[8,2,4,6,1,5,3,-7]
[1,5,3,2,7,6,8,4]=>[1,3,5,8,2,7,6,4]=>[1,3,5,8,2,7,6,4]=>[5,2,8,3,7,6,4,-1]
[2,5,3,1,7,6,8,4]=>[3,2,5,8,1,7,6,4]=>[3,2,5,8,1,7,6,4]=>[2,1,8,3,7,6,4,-5]
[4,7,1,6,5,8,2,3]=>[7,8,2,4,6,1,5,3]=>[7,8,2,4,6,1,5,3]=>[3,8,4,7,5,1,2,-6]
[4,6,1,2,7,5,8,3]=>[6,1,8,4,7,2,5,3]=>[6,1,8,4,7,2,5,3]=>[6,8,4,7,1,5,3,-2]
[5,3,1,2,7,6,8,4]=>[3,1,5,8,2,7,6,4]=>[3,1,5,8,2,7,6,4]=>[5,1,8,3,7,6,4,-2]
[4,3,1,2,7,6,8,5]=>[3,1,4,2,8,7,6,5]=>[3,1,4,2,8,7,6,5]=>[4,1,3,8,7,6,5,-2]
[3,5,1,2,7,6,8,4]=>[5,1,3,8,2,7,6,4]=>[5,1,3,8,2,7,6,4]=>[5,3,8,1,7,6,4,-2]
[6,7,1,5,8,2,3,4]=>[7,8,2,3,1,6,5,4]=>[7,8,2,3,1,6,5,4]=>[3,4,8,7,6,1,2,-5]
[2,7,6,1,5,8,3,4]=>[6,2,7,1,3,8,5,4]=>[6,2,7,1,3,8,5,4]=>[2,5,8,7,1,3,6,-4]
[2,3,5,1,7,6,8,4]=>[5,2,3,8,1,7,6,4]=>[5,2,3,8,1,7,6,4]=>[2,3,8,1,7,6,4,-5]
[5,2,3,1,7,6,8,4]=>[3,5,2,8,1,7,6,4]=>[3,5,2,8,1,7,6,4]=>[3,1,8,2,7,6,4,-5]
[3,5,2,1,7,6,8,4]=>[2,5,3,8,1,7,6,4]=>[2,5,3,8,1,7,6,4]=>[1,3,8,2,7,6,4,-5]
[7,6,2,1,5,8,3,4]=>[2,6,7,1,3,8,5,4]=>[2,6,7,1,3,8,5,4]=>[1,5,8,7,2,3,6,-4]
[8,2,6,4,7,1,5,3]=>[7,8,5,6,1,2,4,3]=>[7,8,5,6,1,2,4,3]=>[6,8,7,3,4,1,2,-5]
[6,1,5,2,7,4,8,3]=>[6,5,8,7,1,2,4,3]=>[6,5,8,7,1,2,4,3]=>[6,8,7,2,1,4,3,-5]
[1,5,2,3,7,6,8,4]=>[1,5,2,8,3,7,6,4]=>[1,5,2,8,3,7,6,4]=>[3,5,8,2,7,6,4,-1]
[5,2,1,3,7,6,8,4]=>[2,5,1,8,3,7,6,4]=>[2,5,1,8,3,7,6,4]=>[1,5,8,2,7,6,4,-3]
[8,4,2,6,7,5,1,3]=>[5,4,2,7,8,1,6,3]=>[5,4,2,7,8,1,6,3]=>[3,8,2,1,7,4,5,-6]
[6,1,4,2,7,5,8,3]=>[6,4,8,1,7,2,5,3]=>[6,4,8,1,7,2,5,3]=>[6,8,2,7,1,5,3,-4]
[8,2,6,5,7,1,4,3]=>[7,8,4,1,6,2,5,3]=>[7,8,4,1,6,2,5,3]=>[6,8,3,7,5,1,2,-4]
[5,1,3,2,7,6,8,4]=>[5,3,1,8,2,7,6,4]=>[5,3,1,8,2,7,6,4]=>[5,2,8,1,7,6,4,-3]
[1,4,2,3,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[3,4,2,8,7,6,5,-1]
[2,4,1,3,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[2,4,1,8,7,6,5,-3]
[2,5,1,3,7,6,8,4]=>[5,2,1,8,3,7,6,4]=>[5,2,1,8,3,7,6,4]=>[2,5,8,1,7,6,4,-3]
[6,8,2,3,5,7,1,4]=>[7,8,2,1,3,6,5,4]=>[7,8,2,1,3,6,5,4]=>[3,5,8,7,6,1,2,-4]
[6,7,1,3,5,8,2,4]=>[7,8,1,2,3,6,5,4]=>[7,8,1,2,3,6,5,4]=>[4,5,8,7,6,1,2,-3]
[5,1,2,3,7,6,8,4]=>[5,1,2,8,3,7,6,4]=>[5,1,2,8,3,7,6,4]=>[3,5,8,1,7,6,4,-2]
[8,2,5,6,7,4,1,3]=>[4,7,2,8,1,5,6,3]=>[4,7,2,8,1,5,6,3]=>[3,8,1,6,7,2,4,-5]
[8,7,4,2,6,3,5,1]=>[5,4,7,6,2,3,8,1]=>[5,4,7,6,2,3,8,1]=>[5,6,2,1,4,3,7,-8]
[5,2,3,1,6,4,8,7]=>[3,5,2,6,1,4,8,7]=>[3,5,2,6,1,4,8,7]=>[3,1,6,2,4,8,7,-5]
[7,4,5,2,3,1,8,6]=>[3,5,2,7,4,8,1,6]=>[3,5,2,7,4,8,1,6]=>[3,1,5,2,8,4,6,-7]
[7,3,5,2,4,1,8,6]=>[4,5,7,2,3,8,1,6]=>[4,5,7,2,3,8,1,6]=>[4,5,1,2,8,3,6,-7]
[6,3,5,2,4,1,8,7]=>[4,5,6,2,3,1,8,7]=>[4,5,6,2,3,1,8,7]=>[4,5,1,2,3,8,7,-6]
[4,1,6,3,5,2,8,7]=>[4,5,6,1,3,2,8,7]=>[4,5,6,1,3,2,8,7]=>[6,5,1,2,3,8,7,-4]
[6,3,4,1,5,2,8,7]=>[4,5,6,3,1,2,8,7]=>[4,5,6,3,1,2,8,7]=>[6,4,1,2,3,8,7,-5]
[5,2,7,3,4,1,8,6]=>[4,5,7,3,2,8,1,6]=>[4,5,7,3,2,8,1,6]=>[5,4,1,2,8,3,6,-7]
[6,2,8,5,7,3,4,1]=>[4,6,7,3,8,2,5,1]=>[4,6,7,3,8,2,5,1]=>[6,4,1,7,2,3,5,-8]
[6,2,7,3,4,1,8,5]=>[4,6,7,3,8,2,1,5]=>[4,6,7,3,8,2,1,5]=>[6,4,1,8,2,3,5,-7]
[7,3,4,1,5,2,8,6]=>[4,5,7,3,1,8,2,6]=>[4,5,7,3,1,8,2,6]=>[7,4,1,2,8,3,6,-5]
[4,1,7,3,5,2,8,6]=>[4,5,7,1,3,8,2,6]=>[4,5,7,1,3,8,2,6]=>[7,5,1,2,8,3,6,-4]
[2,1,7,4,5,3,8,6]=>[2,1,5,7,4,8,3,6]=>[2,1,5,7,4,8,3,6]=>[1,7,5,3,8,4,6,-2]
[3,1,8,6,7,4,5,2]=>[3,5,1,7,4,8,6,2]=>[3,5,1,7,4,8,6,2]=>[8,1,5,2,7,4,6,-3]
[4,1,8,6,7,3,5,2]=>[4,5,7,1,3,8,6,2]=>[4,5,7,1,3,8,6,2]=>[8,5,1,2,7,3,6,-4]
[8,5,7,3,4,1,6,2]=>[4,6,7,3,8,1,5,2]=>[4,6,7,3,8,1,5,2]=>[8,4,1,7,2,3,5,-6]
[8,5,6,2,7,3,4,1]=>[4,6,7,3,8,5,2,1]=>[4,6,7,3,8,5,2,1]=>[7,4,1,6,2,3,5,-8]
[8,4,7,3,5,1,6,2]=>[5,6,7,8,3,1,4,2]=>[5,6,7,8,3,1,4,2]=>[8,5,7,1,2,3,4,-6]
[5,1,8,4,7,3,6,2]=>[5,6,7,8,1,3,4,2]=>[5,6,7,8,1,3,4,2]=>[8,6,7,1,2,3,4,-5]
[3,1,8,5,7,4,6,2]=>[3,6,1,7,8,4,5,2]=>[3,6,1,7,8,4,5,2]=>[8,1,6,7,2,4,5,-3]
[2,1,8,5,7,4,6,3]=>[2,1,6,7,8,4,5,3]=>[2,1,6,7,8,4,5,3]=>[1,8,6,7,3,4,5,-2]
[3,1,7,4,6,2,8,5]=>[3,6,1,7,8,4,2,5]=>[3,6,1,7,8,4,2,5]=>[7,1,6,8,2,4,5,-3]
[4,1,7,3,6,2,8,5]=>[4,6,7,1,8,3,2,5]=>[4,6,7,1,8,3,2,5]=>[7,6,1,8,2,3,5,-4]
[6,2,8,4,7,3,5,1]=>[5,6,7,8,3,2,4,1]=>[5,6,7,8,3,2,4,1]=>[6,5,7,1,2,3,4,-8]
[7,3,6,2,5,1,8,4]=>[5,6,7,8,2,3,1,4]=>[5,6,7,8,2,3,1,4]=>[5,6,8,1,2,3,4,-7]
[5,2,4,1,7,3,8,6]=>[4,5,7,2,1,8,3,6]=>[4,5,7,2,1,8,3,6]=>[4,7,1,2,8,3,6,-5]
[6,2,4,1,7,3,8,5]=>[4,6,7,2,8,1,3,5]=>[4,6,7,2,8,1,3,5]=>[4,7,1,8,2,3,5,-6]
[7,4,6,2,3,1,8,5]=>[3,6,2,7,8,4,1,5]=>[3,6,2,7,8,4,1,5]=>[3,1,6,8,2,4,5,-7]
[6,2,3,1,7,4,8,5]=>[3,6,2,7,8,1,4,5]=>[3,6,2,7,8,1,4,5]=>[3,1,7,8,2,4,5,-6]
[5,2,3,1,7,4,8,6]=>[3,5,2,7,1,8,4,6]=>[3,5,2,7,1,8,4,6]=>[3,1,7,2,8,4,6,-5]
[4,2,3,1,7,5,8,6]=>[3,4,2,1,7,8,5,6]=>[3,4,2,1,7,8,5,6]=>[3,1,2,7,8,5,6,-4]
[3,1,4,2,8,6,7,5]=>[3,4,1,2,7,8,6,5]=>[3,4,1,2,7,8,6,5]=>[4,1,2,8,7,5,6,-3]
[6,2,3,1,8,5,7,4]=>[3,6,2,7,8,1,5,4]=>[3,6,2,7,8,1,5,4]=>[3,1,8,7,2,4,5,-6]
[8,5,6,2,3,1,7,4]=>[3,6,2,7,8,5,1,4]=>[3,6,2,7,8,5,1,4]=>[3,1,8,6,2,4,5,-7]
[7,3,8,5,6,2,4,1]=>[4,6,7,2,8,5,3,1]=>[4,6,7,2,8,5,3,1]=>[4,7,1,6,2,3,5,-8]
[8,5,6,2,4,1,7,3]=>[4,6,7,2,8,5,1,3]=>[4,6,7,2,8,5,1,3]=>[4,8,1,6,2,3,5,-7]
[5,2,4,1,8,6,7,3]=>[4,5,7,2,1,8,6,3]=>[4,5,7,2,1,8,6,3]=>[4,8,1,2,7,3,6,-5]
[4,1,5,2,8,6,7,3]=>[4,5,7,1,2,8,6,3]=>[4,5,7,1,2,8,6,3]=>[5,8,1,2,7,3,6,-4]
[3,1,6,2,8,5,7,4]=>[3,6,1,7,8,2,5,4]=>[3,6,1,7,8,2,5,4]=>[6,1,8,7,2,4,5,-3]
[5,1,6,2,8,4,7,3]=>[5,6,7,8,1,2,4,3]=>[5,6,7,8,1,2,4,3]=>[6,8,7,1,2,3,4,-5]
[8,4,6,2,5,1,7,3]=>[5,6,7,8,2,4,1,3]=>[5,6,7,8,2,4,1,3]=>[5,8,6,1,2,3,4,-7]
[7,3,8,4,6,2,5,1]=>[5,6,7,8,2,4,3,1]=>[5,6,7,8,2,4,3,1]=>[5,7,6,1,2,3,4,-8]
[6,2,7,3,8,4,5,1]=>[5,6,7,8,4,2,3,1]=>[5,6,7,8,4,2,3,1]=>[6,7,5,1,2,3,4,-8]
[8,4,5,1,6,2,7,3]=>[5,6,7,8,4,1,2,3]=>[5,6,7,8,4,1,2,3]=>[7,8,5,1,2,3,4,-6]
[4,1,8,5,6,2,7,3]=>[4,6,7,1,8,5,2,3]=>[4,6,7,1,8,5,2,3]=>[7,8,1,6,2,3,5,-4]
[3,1,8,5,6,2,7,4]=>[3,6,1,7,8,5,2,4]=>[3,6,1,7,8,5,2,4]=>[7,1,8,6,2,4,5,-3]
[2,1,8,5,6,3,7,4]=>[2,1,6,7,8,5,3,4]=>[2,1,6,7,8,5,3,4]=>[1,7,8,6,3,4,5,-2]
[3,1,7,4,8,5,6,2]=>[3,6,1,7,8,5,4,2]=>[3,6,1,7,8,5,4,2]=>[8,1,7,6,2,4,5,-3]
[7,3,6,2,8,4,5,1]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>[7,6,5,1,2,3,4,-8]
[4,1,2,6,3,8,7,5]=>[4,1,6,2,7,3,8,5]=>[4,1,6,2,7,3,8,5]=>[4,6,1,8,3,5,7,-2]
[7,6,2,1,8,3,4,5]=>[2,6,7,1,4,8,3,5]=>[2,6,7,1,4,8,3,5]=>[1,7,5,8,2,3,6,-4]
[1,2,7,6,5,3,8,4]=>[1,2,5,6,7,8,3,4]=>[1,2,5,6,7,8,3,4]=>[2,7,8,3,4,5,6,-1]
[2,6,1,8,5,7,3,4]=>[6,2,7,3,8,1,5,4]=>[6,2,7,3,8,1,5,4]=>[2,4,8,7,1,3,5,-6]
[3,1,2,6,4,8,7,5]=>[3,1,2,6,7,4,8,5]=>[3,1,2,6,7,4,8,5]=>[3,1,6,8,4,5,7,-2]
[3,5,6,1,7,4,8,2]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[8,3,7,5,1,4,2,-6]
[8,2,4,3,7,1,6,5]=>[7,8,4,2,6,1,3,5]=>[7,8,4,2,6,1,3,5]=>[4,7,3,8,5,1,2,-6]
[5,8,2,4,3,7,1,6]=>[7,8,4,2,5,1,3,6]=>[7,8,4,2,5,1,3,6]=>[4,7,3,5,8,1,2,-6]
[4,2,5,6,1,8,3,7]=>[6,4,8,2,5,1,3,7]=>[6,4,8,2,5,1,3,7]=>[4,7,2,5,1,8,3,-6]
[4,2,5,6,1,7,3,8]=>[6,4,7,2,5,1,3,8]=>[6,4,7,2,5,1,3,8]=>[4,7,2,5,1,3,8,-6]
[6,1,5,7,3,2,4,8]=>[6,3,7,2,1,5,4,8]=>[6,3,7,2,1,5,4,8]=>[4,2,7,6,1,3,8,-5]
[6,1,5,8,3,2,4,7]=>[6,3,8,2,1,5,4,7]=>[6,3,8,2,1,5,4,7]=>[4,2,7,6,1,8,3,-5]
[3,8,2,4,7,1,5,6]=>[7,8,3,2,1,5,4,6]=>[7,8,3,2,1,5,4,6]=>[4,3,7,6,8,1,2,-5]
[3,6,8,2,4,7,1,5]=>[7,8,3,2,1,6,4,5]=>[7,8,3,2,1,6,4,5]=>[4,3,7,8,6,1,2,-5]
[7,3,2,4,6,1,5,8]=>[6,3,7,2,1,4,5,8]=>[6,3,7,2,1,4,5,8]=>[4,2,6,7,1,3,8,-5]
[3,2,5,1,8,4,6,7]=>[5,3,2,8,1,4,6,7]=>[5,3,2,8,1,4,6,7]=>[3,2,6,1,7,8,4,-5]
[7,8,3,2,4,6,1,5]=>[6,3,8,2,1,4,7,5]=>[6,3,8,2,1,4,7,5]=>[4,2,6,8,1,7,3,-5]
[6,1,5,7,8,3,2,4]=>[6,3,8,2,1,5,7,4]=>[6,3,8,2,1,5,7,4]=>[4,2,8,6,1,7,3,-5]
[4,2,5,6,1,7,8,3]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,5,1,7,3]=>[4,8,2,5,1,7,3,-6]
[6,1,5,8,7,3,2,4]=>[6,3,7,2,1,5,8,4]=>[6,3,7,2,1,5,8,4]=>[4,2,8,6,1,3,7,-5]
[8,7,3,2,4,6,1,5]=>[6,3,7,2,1,4,8,5]=>[6,3,7,2,1,4,8,5]=>[4,2,6,8,1,3,7,-5]
[3,2,5,1,8,7,4,6]=>[5,3,2,7,1,4,8,6]=>[5,3,2,7,1,4,8,6]=>[3,2,6,1,8,4,7,-5]
[3,2,5,1,6,4,7,8]=>[5,3,2,6,1,4,7,8]=>[5,3,2,6,1,4,7,8]=>[3,2,6,1,4,7,8,-5]
[3,2,4,1,8,7,5,6]=>[4,3,2,1,7,5,8,6]=>[4,3,2,1,7,5,8,6]=>[3,2,1,6,8,5,7,-4]
[3,2,5,1,6,8,7,4]=>[5,3,2,7,1,6,8,4]=>[5,3,2,7,1,6,8,4]=>[3,2,8,1,6,4,7,-5]
[3,8,6,5,1,7,4,2]=>[5,4,3,6,8,7,1,2]=>[5,4,3,6,8,7,1,2]=>[8,3,2,1,4,6,5,-7]
[3,7,6,5,1,8,4,2]=>[5,4,3,6,7,8,1,2]=>[5,4,3,6,7,8,1,2]=>[8,3,2,1,4,5,6,-7]
[3,2,5,1,6,7,8,4]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,6,7,4]=>[3,2,8,1,6,7,4,-5]
[3,2,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>[3,2,1,6,7,5,8,-4]
[3,2,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>[4,3,2,1,8,6,5,7]=>[3,2,1,7,6,8,5,-4]
[3,2,5,1,8,4,7,6]=>[5,3,2,8,1,7,4,6]=>[5,3,2,8,1,7,4,6]=>[3,2,7,1,8,6,4,-5]
[3,2,5,1,6,7,4,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,7,1,6,4,8]=>[3,2,7,1,6,4,8,-5]
[5,2,6,1,8,3,7,4]=>[6,5,8,7,2,1,3,4]=>[6,5,8,7,2,1,3,4]=>[5,7,8,2,1,4,3,-6]
[5,2,6,1,8,4,7,3]=>[6,5,7,8,2,1,4,3]=>[6,5,7,8,2,1,4,3]=>[5,8,7,2,1,3,4,-6]
[3,2,5,1,7,6,4,8]=>[5,3,2,6,1,7,4,8]=>[5,3,2,6,1,7,4,8]=>[3,2,7,1,4,6,8,-5]
[3,2,5,1,8,6,4,7]=>[5,3,2,6,1,8,4,7]=>[5,3,2,6,1,8,4,7]=>[3,2,7,1,4,8,6,-5]
[8,6,1,5,7,3,2,4]=>[6,3,8,1,2,7,5,4]=>[6,3,8,1,2,7,5,4]=>[5,2,8,7,1,6,3,-4]
[8,5,6,1,7,3,4,2]=>[6,4,7,3,8,5,1,2]=>[6,4,7,3,8,5,1,2]=>[8,4,2,6,1,3,5,-7]
[8,5,1,6,7,4,2,3]=>[5,4,1,8,7,2,6,3]=>[5,4,1,8,7,2,6,3]=>[6,8,2,1,7,5,4,-3]
[3,2,5,1,8,6,7,4]=>[5,3,2,7,1,8,6,4]=>[5,3,2,7,1,8,6,4]=>[3,2,8,1,7,4,6,-5]
[3,2,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>[3,2,1,5,7,8,6,-4]
[3,2,5,1,7,8,6,4]=>[5,3,2,6,1,8,7,4]=>[5,3,2,6,1,8,7,4]=>[3,2,8,1,4,7,6,-5]
[3,2,5,1,8,7,6,4]=>[5,3,2,6,1,7,8,4]=>[5,3,2,6,1,7,8,4]=>[3,2,8,1,4,6,7,-5]
[1,2,4,8,7,5,3,6]=>[1,2,5,4,7,3,8,6]=>[1,2,5,4,7,3,8,6]=>[2,6,4,3,8,5,7,-1]
[4,8,3,5,1,6,2,7]=>[5,6,8,4,3,1,2,7]=>[5,6,8,4,3,1,2,7]=>[7,5,4,1,2,8,3,-6]
[4,6,2,5,1,8,3,7]=>[5,6,8,4,2,1,3,7]=>[5,6,8,4,2,1,3,7]=>[5,7,4,1,2,8,3,-6]
[4,5,1,8,3,7,2,6]=>[5,7,8,4,1,2,3,6]=>[5,7,8,4,1,2,3,6]=>[6,7,4,1,8,2,3,-5]
[6,8,3,5,1,7,4,2]=>[5,4,7,8,2,6,1,3]=>[5,4,7,8,2,6,1,3]=>[5,8,2,1,6,3,4,-7]
[3,5,6,1,8,2,7,4]=>[6,8,3,7,5,1,2,4]=>[6,8,3,7,5,1,2,4]=>[7,3,8,5,1,4,2,-6]
[2,4,1,6,8,3,7,5]=>[4,2,8,1,7,6,3,5]=>[4,2,8,1,7,6,3,5]=>[2,7,1,8,6,5,3,-4]
[1,5,3,2,8,4,6,7]=>[1,3,5,8,2,4,6,7]=>[1,3,5,8,2,4,6,7]=>[5,2,6,3,7,8,4,-1]
[4,2,6,7,1,3,8,5]=>[7,4,1,2,8,6,3,5]=>[7,4,1,2,8,6,3,5]=>[4,7,2,8,6,1,5,-3]
[5,1,8,7,4,3,2,6]=>[5,3,4,7,1,2,8,6]=>[5,3,4,7,1,2,8,6]=>[6,2,3,1,8,4,7,-5]
[4,6,7,2,5,8,1,3]=>[8,7,1,4,2,6,5,3]=>[8,7,1,4,2,6,5,3]=>[5,8,4,7,6,2,1,-3]
[5,7,1,6,3,8,2,4]=>[7,8,6,2,5,1,3,4]=>[7,8,6,2,5,1,3,4]=>[4,7,8,5,3,1,2,-6]
[6,1,4,2,8,5,7,3]=>[6,4,7,1,8,2,5,3]=>[6,4,7,1,8,2,5,3]=>[6,8,2,7,1,3,5,-4]
[5,1,3,7,8,6,2,4]=>[5,6,1,2,3,8,7,4]=>[5,6,1,2,3,8,7,4]=>[4,5,8,1,2,7,6,-3]
[8,1,6,5,7,3,2,4]=>[8,3,7,2,6,1,5,4]=>[8,3,7,2,6,1,5,4]=>[4,2,8,7,5,3,1,-6]
[1,4,5,7,3,2,8,6]=>[1,3,7,4,5,8,2,6]=>[1,3,7,4,5,8,2,6]=>[7,2,4,5,8,3,6,-1]
[1,2,5,3,8,4,7,6]=>[1,2,5,8,3,7,4,6]=>[1,2,5,8,3,7,4,6]=>[2,5,7,3,8,6,4,-1]
[4,8,2,3,7,6,1,5]=>[6,7,1,4,2,8,3,5]=>[6,7,1,4,2,8,3,5]=>[5,7,4,8,1,2,6,-3]
[4,8,2,3,7,1,6,5]=>[7,8,2,4,6,1,3,5]=>[7,8,2,4,6,1,3,5]=>[3,7,4,8,5,1,2,-6]
[5,3,6,2,4,7,1,8]=>[7,6,5,2,3,4,1,8]=>[7,6,5,2,3,4,1,8]=>[4,5,6,3,2,1,8,-7]
[1,7,6,5,3,2,8,4]=>[1,3,5,6,7,8,2,4]=>[1,3,5,6,7,8,2,4]=>[7,2,8,3,4,5,6,-1]
[1,2,8,5,4,7,3,6]=>[1,2,7,5,8,3,4,6]=>[1,2,7,5,8,3,4,6]=>[2,6,7,4,8,3,5,-1]
[8,1,2,6,7,5,3,4]=>[8,1,5,3,7,2,6,4]=>[8,1,5,3,7,2,6,4]=>[6,4,8,3,7,5,1,-2]
[8,2,5,7,1,3,6,4]=>[7,8,1,6,2,3,5,4]=>[7,8,1,6,2,3,5,4]=>[5,6,8,7,4,1,2,-3]
[8,5,7,4,2,6,1,3]=>[6,4,1,7,8,2,5,3]=>[6,4,1,7,8,2,5,3]=>[6,8,2,7,1,4,5,-3]
[8,4,7,1,3,6,2,5]=>[7,6,1,8,2,3,4,5]=>[7,6,1,8,2,3,4,5]=>[5,6,7,8,2,1,4,-3]
[8,7,1,3,4,6,2,5]=>[7,6,1,3,2,4,8,5]=>[7,6,1,3,2,4,8,5]=>[5,4,6,8,2,1,7,-3]
[8,6,1,2,5,7,3,4]=>[6,1,8,2,3,7,5,4]=>[6,1,8,2,3,7,5,4]=>[4,5,8,7,1,6,3,-2]
[7,1,2,4,6,8,5,3]=>[7,1,5,2,8,4,6,3]=>[7,1,5,2,8,4,6,3]=>[4,8,6,3,7,1,5,-2]
[7,1,2,6,8,5,3,4]=>[7,1,5,3,8,2,6,4]=>[7,1,5,3,8,2,6,4]=>[6,4,8,3,7,1,5,-2]
[1,2,3,5,8,6,4,7]=>[1,2,3,6,5,8,4,7]=>[1,2,3,6,5,8,4,7]=>[2,3,7,5,4,8,6,-1]
[7,4,1,3,8,2,5,6]=>[4,7,2,8,1,5,3,6]=>[4,7,2,8,1,5,3,6]=>[3,7,1,6,8,2,4,-5]
[6,1,8,3,7,2,5,4]=>[6,7,8,5,2,1,3,4]=>[6,7,8,5,2,1,3,4]=>[5,7,8,4,1,2,3,-6]
[8,1,7,2,5,4,6,3]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,2,4,1,3]=>[5,8,6,4,3,2,1,-7]
[8,5,2,7,1,6,3,4]=>[7,5,8,2,6,1,3,4]=>[7,5,8,2,6,1,3,4]=>[4,7,8,2,5,1,3,-6]
[8,7,4,1,2,3,6,5]=>[4,1,2,7,6,3,8,5]=>[4,1,2,7,6,3,8,5]=>[3,6,1,8,5,4,7,-2]
[8,3,2,6,5,1,4,7]=>[5,3,6,2,8,1,4,7]=>[5,3,6,2,8,1,4,7]=>[4,2,7,1,3,8,5,-6]
[8,7,3,1,2,4,6,5]=>[3,1,7,2,6,4,8,5]=>[3,1,7,2,6,4,8,5]=>[4,1,6,8,5,3,7,-2]
[7,6,3,1,5,2,4,8]=>[3,6,5,1,2,7,4,8]=>[3,6,5,1,2,7,4,8]=>[5,1,7,3,2,6,8,-4]
[5,3,8,1,7,6,2,4]=>[8,6,5,2,3,7,1,4]=>[8,6,5,2,3,7,1,4]=>[4,5,8,3,2,6,1,-7]
[3,2,5,7,6,1,4,8]=>[6,3,2,1,5,7,4,8]=>[6,3,2,1,5,7,4,8]=>[3,2,7,5,1,6,8,-4]
[3,8,4,7,2,5,1,6]=>[5,7,3,8,2,1,4,6]=>[5,7,3,8,2,1,4,6]=>[5,3,7,1,8,2,4,-6]
[1,7,3,5,8,6,2,4]=>[1,6,8,3,2,7,5,4]=>[1,6,8,3,2,7,5,4]=>[5,4,8,7,2,6,3,-1]
[7,3,5,8,6,1,2,4]=>[6,1,8,3,2,7,5,4]=>[6,1,8,3,2,7,5,4]=>[5,4,8,7,1,6,3,-2]
[7,3,5,8,6,2,1,4]=>[2,6,8,3,1,7,5,4]=>[2,6,8,3,1,7,5,4]=>[1,4,8,7,2,6,3,-5]
[1,2,7,6,8,3,5,4]=>[1,2,8,5,3,7,6,4]=>[1,2,8,5,3,7,6,4]=>[2,5,8,4,7,6,3,-1]
[7,2,6,8,5,4,1,3]=>[4,5,1,8,7,2,6,3]=>[4,5,1,8,7,2,6,3]=>[6,8,1,2,7,5,4,-3]
[5,6,1,4,2,3,7,8]=>[6,4,2,1,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>[3,6,2,5,1,7,8,-4]
[5,4,1,3,7,2,6,8]=>[4,5,2,7,3,1,6,8]=>[4,5,2,7,3,1,6,8]=>[3,5,1,2,7,4,8,-6]
[5,1,6,3,4,2,7,8]=>[5,4,6,3,1,2,7,8]=>[5,4,6,3,1,2,7,8]=>[6,4,2,1,3,7,8,-5]
[3,4,8,1,6,2,5,7]=>[8,6,3,4,2,1,5,7]=>[8,6,3,4,2,1,5,7]=>[5,3,4,7,2,8,1,-6]
[7,3,8,2,6,4,5,1]=>[5,8,7,6,4,2,3,1]=>[5,8,7,6,4,2,3,1]=>[6,7,5,1,4,3,2,-8]
[5,7,8,6,4,1,2,3]=>[4,1,2,6,5,8,7,3]=>[4,1,2,6,5,8,7,3]=>[3,8,1,5,4,7,6,-2]
[2,5,6,3,1,7,8,4]=>[3,2,6,8,5,1,7,4]=>[3,2,6,8,5,1,7,4]=>[2,1,8,5,3,7,4,-6]
[4,5,2,1,3,8,7,6]=>[2,5,1,4,3,7,8,6]=>[2,5,1,4,3,7,8,6]=>[1,5,4,2,8,6,7,-3]
[3,5,2,7,6,1,8,4]=>[6,5,3,7,2,8,4,1]=>[6,5,3,7,2,8,4,1]=>[5,3,7,2,1,4,6,-8]
[1,2,6,8,5,7,3,4]=>[1,2,7,3,8,6,5,4]=>[1,2,7,3,8,6,5,4]=>[2,4,8,7,6,3,5,-1]
[1,3,6,4,2,8,7,5]=>[1,4,3,6,7,2,8,5]=>[1,4,3,6,7,2,8,5]=>[6,3,2,8,4,5,7,-1]
[1,3,7,4,2,8,6,5]=>[1,4,3,7,6,8,2,5]=>[1,4,3,7,6,8,2,5]=>[7,3,2,8,5,4,6,-1]
[1,2,5,8,7,3,6,4]=>[1,2,7,6,5,3,8,4]=>[1,2,7,6,5,3,8,4]=>[2,6,8,5,4,3,7,-1]
[1,2,7,8,6,3,5,4]=>[1,2,6,5,3,8,7,4]=>[1,2,6,5,3,8,7,4]=>[2,5,8,4,3,7,6,-1]
[2,6,1,7,5,8,3,4]=>[6,2,8,3,7,1,5,4]=>[6,2,8,3,7,1,5,4]=>[2,4,8,7,1,5,3,-6]
[3,6,4,1,7,8,2,5]=>[4,6,3,8,1,2,7,5]=>[4,6,3,8,1,2,7,5]=>[6,3,1,8,2,7,4,-5]
[4,7,3,6,5,8,1,2]=>[8,1,7,4,6,3,5,2]=>[8,1,7,4,6,3,5,2]=>[8,6,4,7,5,3,1,-2]
[5,3,6,7,1,8,2,4]=>[7,8,5,2,3,6,1,4]=>[7,8,5,2,3,6,1,4]=>[4,5,8,3,6,1,2,-7]
[7,1,5,8,4,2,3,6]=>[7,4,2,8,1,3,5,6]=>[7,4,2,8,1,3,5,6]=>[3,6,2,7,8,1,4,-5]
[8,1,5,7,4,2,3,6]=>[8,4,2,7,1,3,5,6]=>[8,4,2,7,1,3,5,6]=>[3,6,2,7,8,4,1,-5]
[7,8,3,1,2,4,6,5]=>[3,1,8,2,6,4,7,5]=>[3,1,8,2,6,4,7,5]=>[4,1,6,8,5,7,3,-2]
[2,8,7,3,4,5,6,1]=>[6,2,7,3,4,5,8,1]=>[6,2,7,3,4,5,8,1]=>[2,4,5,6,1,3,7,-8]
[1,7,3,6,5,2,8,4]=>[1,5,6,7,8,4,3,2]=>[1,5,6,7,8,4,3,2]=>[8,7,6,2,3,4,5,-1]
[8,4,6,7,1,5,3,2]=>[7,3,5,8,1,4,6,2]=>[7,3,5,8,1,4,6,2]=>[8,2,6,3,7,1,4,-5]
[1,8,5,4,2,6,7,3]=>[1,4,5,8,7,2,6,3]=>[1,4,5,8,7,2,6,3]=>[6,8,2,3,7,5,4,-1]
[7,4,8,2,1,3,5,6]=>[2,8,1,7,3,5,4,6]=>[2,8,1,7,3,5,4,6]=>[1,5,7,6,8,4,2,-3]
[5,3,1,2,4,7,8,6]=>[3,1,5,2,4,8,7,6]=>[3,1,5,2,4,8,7,6]=>[4,1,5,3,8,7,6,-2]
[4,1,2,7,8,3,6,5]=>[4,1,8,2,6,3,7,5]=>[4,1,8,2,6,3,7,5]=>[4,6,1,8,5,7,3,-2]
[1,2,8,4,3,7,5,6]=>[1,2,4,8,7,5,3,6]=>[1,2,4,8,7,5,3,6]=>[2,7,3,6,8,5,4,-1]
[7,6,3,8,4,5,1,2]=>[5,1,6,7,3,8,4,2]=>[5,1,6,7,3,8,4,2]=>[8,5,7,1,3,4,6,-2]
[7,6,5,1,2,4,8,3]=>[5,1,6,2,7,8,4,3]=>[5,1,6,2,7,8,4,3]=>[4,8,7,1,3,5,6,-2]
[7,6,5,1,4,8,2,3]=>[5,6,2,1,7,8,4,3]=>[5,6,2,1,7,8,4,3]=>[3,8,7,1,2,5,6,-4]
[8,1,6,5,3,7,2,4]=>[8,7,5,2,6,1,3,4]=>[8,7,5,2,6,1,3,4]=>[4,7,8,3,5,2,1,-6]
[7,5,4,1,2,6,8,3]=>[4,1,5,7,8,2,6,3]=>[4,1,5,7,8,2,6,3]=>[6,8,1,3,7,4,5,-2]
[7,8,1,4,5,3,2,6]=>[8,3,5,1,4,2,7,6]=>[8,3,5,1,4,2,7,6]=>[6,2,5,3,8,7,1,-4]
[3,8,1,5,4,7,2,6]=>[8,7,3,5,1,2,4,6]=>[8,7,3,5,1,2,4,6]=>[6,3,7,4,8,2,1,-5]
[7,8,4,2,6,5,1,3]=>[5,4,2,6,8,1,7,3]=>[5,4,2,6,8,1,7,3]=>[3,8,2,1,4,7,5,-6]
[5,8,1,4,7,3,6,2]=>[8,6,7,1,5,3,4,2]=>[8,6,7,1,5,3,4,2]=>[8,6,7,5,2,3,1,-4]
[2,3,1,8,6,4,5,7]=>[3,2,1,6,4,8,5,7]=>[3,2,1,6,4,8,5,7]=>[2,1,5,7,4,8,6,-3]
[1,8,4,5,2,3,6,7]=>[1,5,2,8,4,3,6,7]=>[1,5,2,8,4,3,6,7]=>[3,6,5,2,7,8,4,-1]
[3,4,8,7,5,2,6,1]=>[6,5,3,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>[6,3,4,2,1,5,7,-8]
[3,8,7,2,5,4,6,1]=>[6,7,3,5,2,4,8,1]=>[6,7,3,5,2,4,8,1]=>[5,3,6,4,1,2,7,-8]
[5,3,6,2,4,8,7,1]=>[7,6,5,2,3,4,8,1]=>[7,6,5,2,3,4,8,1]=>[4,5,6,3,2,1,7,-8]
[1,8,2,6,3,4,7,5]=>[1,8,6,3,7,2,4,5]=>[1,8,6,3,7,2,4,5]=>[6,4,7,8,3,5,2,-1]
[7,1,3,6,4,8,2,5]=>[7,8,1,6,2,3,4,5]=>[7,8,1,6,2,3,4,5]=>[5,6,7,8,4,1,2,-3]
[8,2,1,3,5,7,4,6]=>[2,8,1,7,3,4,5,6]=>[2,8,1,7,3,4,5,6]=>[1,5,6,7,8,4,2,-3]
[7,5,4,1,3,8,2,6]=>[4,5,1,7,8,2,3,6]=>[4,5,1,7,8,2,3,6]=>[6,7,1,2,8,4,5,-3]
[7,2,3,6,1,4,8,5]=>[6,7,2,1,8,3,4,5]=>[6,7,2,1,8,3,4,5]=>[3,6,7,8,1,2,5,-4]
[1,7,2,3,5,8,4,6]=>[1,7,2,8,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>[3,5,6,7,8,2,4,-1]
[7,4,8,1,3,6,2,5]=>[8,6,1,7,2,3,4,5]=>[8,6,1,7,2,3,4,5]=>[5,6,7,8,2,4,1,-3]
[8,6,1,4,7,3,2,5]=>[6,3,8,2,1,7,4,5]=>[6,3,8,2,1,7,4,5]=>[4,2,7,8,1,6,3,-5]
[3,5,2,6,7,1,8,4]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[5,3,8,2,6,1,4,-7]
[3,7,2,5,6,1,8,4]=>[6,7,3,8,2,5,1,4]=>[6,7,3,8,2,5,1,4]=>[5,3,8,6,1,2,4,-7]
[8,3,2,1,5,7,4,6]=>[2,3,8,7,1,4,5,6]=>[2,3,8,7,1,4,5,6]=>[1,2,6,7,8,4,3,-5]
[2,8,3,6,4,7,1,5]=>[7,2,8,6,1,3,4,5]=>[7,2,8,6,1,3,4,5]=>[2,6,7,8,4,1,3,-5]
[7,3,6,4,8,1,2,5]=>[8,1,7,6,2,3,4,5]=>[8,1,7,6,2,3,4,5]=>[5,6,7,8,4,3,1,-2]
[8,3,6,4,7,1,2,5]=>[7,1,8,6,2,3,4,5]=>[7,1,8,6,2,3,4,5]=>[5,6,7,8,4,1,3,-2]
[1,2,8,3,5,7,4,6]=>[1,2,8,7,3,4,5,6]=>[1,2,8,7,3,4,5,6]=>[2,5,6,7,8,4,3,-1]
[1,8,3,2,5,7,4,6]=>[1,3,8,7,2,4,5,6]=>[1,3,8,7,2,4,5,6]=>[5,2,6,7,8,4,3,-1]
[7,3,6,4,8,2,1,5]=>[2,8,7,6,1,3,4,5]=>[2,8,7,6,1,3,4,5]=>[1,6,7,8,4,3,2,-5]
[5,1,6,4,2,3,7,8]=>[5,4,2,6,1,3,7,8]=>[5,4,2,6,1,3,7,8]=>[3,6,2,1,4,7,8,-5]
[3,6,7,5,2,4,1,8]=>[4,5,3,2,7,6,1,8]=>[4,5,3,2,7,6,1,8]=>[4,3,1,2,6,5,8,-7]
[3,5,6,2,4,1,7,8]=>[4,6,3,2,5,1,7,8]=>[4,6,3,2,5,1,7,8]=>[4,3,1,5,2,7,8,-6]
[8,3,6,1,4,5,7,2]=>[6,7,8,1,4,3,5,2]=>[6,7,8,1,4,3,5,2]=>[8,6,5,7,1,2,3,-4]
[8,4,6,1,2,3,7,5]=>[6,1,2,8,7,4,3,5]=>[6,1,2,8,7,4,3,5]=>[3,7,6,8,1,5,4,-2]
[3,5,4,1,8,7,2,6]=>[4,5,3,7,2,1,8,6]=>[4,5,3,7,2,1,8,6]=>[5,3,1,2,8,4,7,-6]
[4,2,7,3,6,5,8,1]=>[8,4,7,2,6,3,5,1]=>[8,4,7,2,6,3,5,1]=>[4,6,2,7,5,3,1,-8]
[3,7,8,5,1,6,2,4]=>[5,8,3,1,6,2,7,4]=>[5,8,3,1,6,2,7,4]=>[6,3,8,1,5,7,2,-4]
[7,8,6,1,3,5,2,4]=>[6,5,1,2,3,8,7,4]=>[6,5,1,2,3,8,7,4]=>[4,5,8,2,1,7,6,-3]
[4,2,8,1,6,7,3,5]=>[8,4,7,2,3,1,6,5]=>[8,4,7,2,3,1,6,5]=>[4,5,2,8,7,3,1,-6]
[6,1,3,7,4,8,2,5]=>[6,8,1,7,2,3,4,5]=>[6,8,1,7,2,3,4,5]=>[5,6,7,8,1,4,2,-3]
[3,8,7,5,1,2,4,6]=>[5,1,3,2,7,4,8,6]=>[5,1,3,2,7,4,8,6]=>[4,3,6,1,8,5,7,-2]
[8,5,7,4,1,2,3,6]=>[4,1,2,7,8,3,5,6]=>[4,1,2,7,8,3,5,6]=>[3,6,1,7,8,4,5,-2]
[1,7,2,8,6,3,4,5]=>[1,7,6,3,4,8,2,5]=>[1,7,6,3,4,8,2,5]=>[7,4,5,8,3,2,6,-1]
[4,1,8,7,2,3,5,6]=>[4,7,2,1,3,5,8,6]=>[4,7,2,1,3,5,8,6]=>[3,5,1,6,8,2,7,-4]
[3,4,7,1,6,8,2,5]=>[7,8,3,4,2,1,6,5]=>[7,8,3,4,2,1,6,5]=>[5,3,4,8,7,1,2,-6]
[4,8,3,1,2,6,7,5]=>[3,1,8,4,7,2,6,5]=>[3,1,8,4,7,2,6,5]=>[6,1,4,8,7,5,3,-2]
[6,5,8,2,3,1,7,4]=>[3,8,2,7,6,5,1,4]=>[3,8,2,7,6,5,1,4]=>[3,1,8,6,5,4,2,-7]
[4,3,6,1,8,5,7,2]=>[6,7,4,3,8,1,5,2]=>[6,7,4,3,8,1,5,2]=>[8,4,3,7,1,2,5,-6]
[1,5,2,6,8,4,3,7]=>[1,5,4,8,2,6,3,7]=>[1,5,4,8,2,6,3,7]=>[5,7,3,2,6,8,4,-1]
[2,3,7,5,6,8,1,4]=>[8,2,3,1,7,5,6,4]=>[8,2,3,1,7,5,6,4]=>[2,3,8,6,7,5,1,-4]
[2,4,8,7,1,3,6,5]=>[7,2,1,4,6,3,8,5]=>[7,2,1,4,6,3,8,5]=>[2,6,4,8,5,1,7,-3]
[4,6,3,7,5,2,8,1]=>[8,5,7,4,6,2,3,1]=>[8,5,7,4,6,2,3,1]=>[6,7,4,2,5,3,1,-8]
[8,2,3,6,7,5,1,4]=>[5,7,1,2,8,3,6,4]=>[5,7,1,2,8,3,6,4]=>[4,6,8,1,7,2,5,-3]
[8,3,7,2,5,6,1,4]=>[6,7,8,1,2,5,3,4]=>[6,7,8,1,2,5,3,4]=>[5,7,8,6,1,2,3,-4]
[1,2,8,6,7,3,5,4]=>[1,2,7,5,3,8,6,4]=>[1,2,7,5,3,8,6,4]=>[2,5,8,4,7,3,6,-1]
[6,7,4,3,1,8,2,5]=>[3,4,7,8,2,6,1,5]=>[3,4,7,8,2,6,1,5]=>[5,1,2,8,6,3,4,-7]
[6,7,1,3,2,5,4,8]=>[7,3,1,5,2,6,4,8]=>[7,3,1,5,2,6,4,8]=>[5,2,7,4,6,1,8,-3]
[4,5,1,3,2,7,6,8]=>[5,3,1,4,2,7,6,8]=>[5,3,1,4,2,7,6,8]=>[5,2,4,1,7,6,8,-3]
[4,5,2,3,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>[3,1,4,2,7,6,8,-5]
[5,1,6,3,2,7,4,8]=>[5,3,6,7,1,2,4,8]=>[5,3,6,7,1,2,4,8]=>[6,2,7,1,3,4,8,-5]
[5,1,6,2,7,4,3,8]=>[5,6,4,7,1,2,3,8]=>[5,6,4,7,1,2,3,8]=>[6,7,3,1,2,4,8,-5]
[3,6,8,4,2,7,5,1]=>[5,4,3,7,8,6,1,2]=>[5,4,3,7,8,6,1,2]=>[8,3,2,1,6,4,5,-7]
[8,4,1,5,3,2,6,7]=>[4,3,8,5,2,1,6,7]=>[4,3,8,5,2,1,6,7]=>[5,2,1,4,7,8,3,-6]
[6,7,4,1,3,8,2,5]=>[4,7,2,8,1,6,3,5]=>[4,7,2,8,1,6,3,5]=>[3,7,1,8,6,2,4,-5]
[4,5,7,3,8,6,2,1]=>[2,6,8,4,5,7,1,3]=>[2,6,8,4,5,7,1,3]=>[1,8,4,5,2,6,3,-7]
[6,3,1,8,7,5,4,2]=>[3,6,4,5,7,2,8,1]=>[3,6,4,5,7,2,8,1]=>[6,1,3,4,2,5,7,-8]
[6,4,2,7,8,5,1,3]=>[5,4,2,8,6,1,7,3]=>[5,4,2,8,6,1,7,3]=>[3,8,2,1,5,7,4,-6]
[1,6,4,8,7,5,2,3]=>[1,5,2,7,6,3,8,4]=>[1,5,2,7,6,3,8,4]=>[3,6,8,2,5,4,7,-1]
[3,7,2,5,4,8,1,6]=>[8,7,3,5,2,1,4,6]=>[8,7,3,5,2,1,4,6]=>[5,3,7,4,8,2,1,-6]
[5,8,2,4,7,3,1,6]=>[3,7,8,1,5,2,4,6]=>[3,7,8,1,5,2,4,6]=>[6,1,7,5,8,2,3,-4]
[7,3,6,5,2,1,8,4]=>[2,5,6,7,8,4,3,1]=>[2,5,6,7,8,4,3,1]=>[1,7,6,2,3,4,5,-8]
[5,8,2,6,4,1,3,7]=>[4,6,2,8,5,1,3,7]=>[4,6,2,8,5,1,3,7]=>[3,7,1,5,2,8,4,-6]
[2,5,7,6,3,1,4,8]=>[3,2,6,1,5,7,4,8]=>[3,2,6,1,5,7,4,8]=>[2,1,7,5,3,6,8,-4]
[2,4,8,1,6,5,7,3]=>[8,2,7,4,6,1,5,3]=>[8,2,7,4,6,1,5,3]=>[2,8,4,7,5,3,1,-6]
[2,8,7,3,6,1,4,5]=>[6,2,7,1,4,3,8,5]=>[6,2,7,1,4,3,8,5]=>[2,6,5,8,1,3,7,-4]
[2,8,6,3,1,4,5,7]=>[3,2,6,1,4,8,5,7]=>[3,2,6,1,4,8,5,7]=>[2,1,5,7,3,8,6,-4]
[4,6,8,5,1,7,2,3]=>[5,8,1,4,7,6,2,3]=>[5,8,1,4,7,6,2,3]=>[7,8,4,1,6,5,2,-3]
[5,1,7,6,2,3,8,4]=>[5,6,2,7,1,8,4,3]=>[5,6,2,7,1,8,4,3]=>[3,8,7,1,2,4,6,-5]
[6,5,1,7,2,8,3,4]=>[5,6,7,1,8,2,3,4]=>[5,6,7,1,8,2,3,4]=>[6,7,8,1,2,3,5,-4]
[5,3,2,7,6,1,4,8]=>[6,3,5,1,2,7,4,8]=>[6,3,5,1,2,7,4,8]=>[5,2,7,3,1,6,8,-4]
[8,1,6,5,7,3,4,2]=>[8,4,7,3,6,1,5,2]=>[8,4,7,3,6,1,5,2]=>[8,4,2,7,5,3,1,-6]
[5,1,8,3,4,6,7,2]=>[5,7,8,3,1,4,6,2]=>[5,7,8,3,1,4,6,2]=>[8,4,6,1,7,2,3,-5]
[7,3,1,2,4,6,8,5]=>[3,1,7,2,8,4,6,5]=>[3,1,7,2,8,4,6,5]=>[4,1,6,8,7,3,5,-2]
[3,7,2,8,6,1,5,4]=>[6,8,3,5,2,7,1,4]=>[6,8,3,5,2,7,1,4]=>[5,3,8,4,1,6,2,-7]
[5,3,6,1,8,2,4,7]=>[6,8,5,2,3,1,4,7]=>[6,8,5,2,3,1,4,7]=>[4,5,7,3,1,8,2,-6]
[6,8,2,7,3,1,4,5]=>[3,7,8,2,4,6,1,5]=>[3,7,8,2,4,6,1,5]=>[4,1,5,8,6,2,3,-7]
[5,1,8,3,7,2,4,6]=>[5,7,8,2,1,4,3,6]=>[5,7,8,2,1,4,3,6]=>[4,7,6,1,8,2,3,-5]
[2,4,5,1,3,8,7,6]=>[5,2,1,4,3,7,8,6]=>[5,2,1,4,3,7,8,6]=>[2,5,4,1,8,6,7,-3]
[7,4,2,8,6,3,1,5]=>[3,6,4,8,1,7,2,5]=>[3,6,4,8,1,7,2,5]=>[7,1,3,8,2,6,4,-5]
[4,1,8,5,7,3,2,6]=>[4,3,7,1,8,2,5,6]=>[4,3,7,1,8,2,5,6]=>[6,2,1,7,8,3,5,-4]
[4,1,7,5,8,3,2,6]=>[4,3,8,1,7,2,5,6]=>[4,3,8,1,7,2,5,6]=>[6,2,1,7,8,5,3,-4]
[6,5,3,8,7,1,2,4]=>[7,1,5,2,6,3,8,4]=>[7,1,5,2,6,3,8,4]=>[4,6,8,3,5,1,7,-2]
[7,6,3,1,4,8,2,5]=>[3,6,7,1,2,8,4,5]=>[3,6,7,1,2,8,4,5]=>[5,1,7,8,2,3,6,-4]
[8,5,1,3,7,4,2,6]=>[5,4,2,8,7,1,3,6]=>[5,4,2,8,7,1,3,6]=>[3,7,2,1,8,5,4,-6]
[4,5,7,3,1,6,8,2]=>[3,7,8,4,5,2,6,1]=>[3,7,8,4,5,2,6,1]=>[6,1,4,5,7,2,3,-8]
[4,5,7,2,8,6,1,3]=>[6,8,2,4,5,7,1,3]=>[6,8,2,4,5,7,1,3]=>[3,8,4,5,1,6,2,-7]
[4,5,7,2,8,1,3,6]=>[8,7,1,4,5,3,2,6]=>[8,7,1,4,5,3,2,6]=>[7,6,4,5,8,2,1,-3]
[1,8,3,5,7,4,6,2]=>[1,6,8,7,3,4,5,2]=>[1,6,8,7,3,4,5,2]=>[8,5,6,7,2,4,3,-1]
[5,3,8,1,6,2,4,7]=>[8,6,5,2,3,1,4,7]=>[8,6,5,2,3,1,4,7]=>[4,5,7,3,2,8,1,-6]
[3,8,7,1,2,4,6,5]=>[7,1,3,2,6,4,8,5]=>[7,1,3,2,6,4,8,5]=>[4,3,6,8,5,1,7,-2]
[5,6,3,1,8,4,7,2]=>[3,6,7,8,5,2,4,1]=>[3,6,7,8,5,2,4,1]=>[6,1,7,5,2,3,4,-8]
[3,7,2,5,1,8,4,6]=>[5,7,3,8,2,4,1,6]=>[5,7,3,8,2,4,1,6]=>[5,3,6,1,8,2,4,-7]
[8,4,2,6,5,1,3,7]=>[5,4,2,6,8,1,3,7]=>[5,4,2,6,8,1,3,7]=>[3,7,2,1,4,8,5,-6]
[3,2,6,8,1,5,4,7]=>[8,3,2,5,1,6,4,7]=>[8,3,2,5,1,6,4,7]=>[3,2,7,4,6,8,1,-5]
[2,5,1,4,8,7,3,6]=>[5,2,7,1,4,3,8,6]=>[5,2,7,1,4,3,8,6]=>[2,6,5,1,8,3,7,-4]
[6,2,4,5,1,8,3,7]=>[5,6,8,2,4,1,3,7]=>[5,6,8,2,4,1,3,7]=>[4,7,5,1,2,8,3,-6]
[2,4,1,8,3,6,7,5]=>[4,2,8,1,7,3,6,5]=>[4,2,8,1,7,3,6,5]=>[2,6,1,8,7,5,3,-4]
[4,2,7,6,3,1,5,8]=>[3,6,4,1,2,7,5,8]=>[3,6,4,1,2,7,5,8]=>[5,1,3,7,2,6,8,-4]
[3,6,4,1,7,8,5,2]=>[4,6,3,5,8,2,7,1]=>[4,6,3,5,8,2,7,1]=>[6,3,1,4,2,7,5,-8]
[5,1,2,7,6,3,8,4]=>[5,1,6,7,2,8,4,3]=>[5,1,6,7,2,8,4,3]=>[5,8,7,1,3,4,6,-2]
[6,7,2,8,5,4,3,1]=>[3,4,5,8,7,6,1,2]=>[3,4,5,8,7,6,1,2]=>[8,1,2,3,6,5,4,-7]
[8,2,3,7,5,4,1,6]=>[4,5,2,7,8,1,3,6]=>[4,5,2,7,8,1,3,6]=>[3,7,1,2,8,4,5,-6]
[2,5,3,4,7,8,1,6]=>[8,2,5,3,4,1,7,6]=>[8,2,5,3,4,1,7,6]=>[2,4,5,3,8,7,1,-6]
[2,7,4,3,6,8,5,1]=>[5,2,4,8,7,1,6,3]=>[5,2,4,8,7,1,6,3]=>[2,8,3,1,7,5,4,-6]
[1,7,4,3,6,8,5,2]=>[1,5,4,8,7,2,6,3]=>[1,5,4,8,7,2,6,3]=>[6,8,3,2,7,5,4,-1]
[4,1,2,7,8,5,3,6]=>[4,1,5,2,8,3,7,6]=>[4,1,5,2,8,3,7,6]=>[4,6,1,3,8,7,5,-2]
[4,7,3,1,2,6,8,5]=>[3,1,7,4,8,2,6,5]=>[3,1,7,4,8,2,6,5]=>[6,1,4,8,7,3,5,-2]
[5,6,2,7,3,4,8,1]=>[8,6,7,3,5,2,4,1]=>[8,6,7,3,5,2,4,1]=>[6,4,7,5,2,3,1,-8]
[4,7,6,8,2,1,3,5]=>[2,8,1,4,3,7,6,5]=>[2,8,1,4,3,7,6,5]=>[1,5,4,8,7,6,2,-3]
[1,5,8,6,4,2,3,7]=>[1,4,2,6,5,8,3,7]=>[1,4,2,6,5,8,3,7]=>[3,7,2,5,4,8,6,-1]
[8,3,1,6,4,7,2,5]=>[3,8,7,6,1,2,4,5]=>[3,8,7,6,1,2,4,5]=>[6,1,7,8,4,3,2,-5]
[8,4,6,3,1,2,5,7]=>[3,1,6,8,2,4,5,7]=>[3,1,6,8,2,4,5,7]=>[5,1,6,7,3,8,4,-2]
[1,8,6,2,5,7,3,4]=>[1,6,8,2,3,7,5,4]=>[1,6,8,2,3,7,5,4]=>[4,5,8,7,2,6,3,-1]
[4,7,3,6,1,2,8,5]=>[6,1,7,4,8,3,2,5]=>[6,1,7,4,8,3,2,5]=>[7,6,4,8,1,3,5,-2]
[4,2,7,8,6,1,3,5]=>[6,4,1,2,3,8,7,5]=>[6,4,1,2,3,8,7,5]=>[4,5,2,8,1,7,6,-3]
[5,3,2,4,1,8,6,7]=>[4,3,5,2,1,8,6,7]=>[4,3,5,2,1,8,6,7]=>[4,2,1,3,7,8,6,-5]
[1,4,2,6,3,8,7,5]=>[1,4,6,2,7,3,8,5]=>[1,4,6,2,7,3,8,5]=>[4,6,2,8,3,5,7,-1]
[5,2,8,3,6,1,4,7]=>[6,5,8,1,2,3,4,7]=>[6,5,8,1,2,3,4,7]=>[5,6,7,2,1,8,3,-4]
[8,3,1,2,5,7,4,6]=>[3,1,8,7,2,4,5,6]=>[3,1,8,7,2,4,5,6]=>[5,1,6,7,8,4,3,-2]
[2,7,5,8,1,6,3,4]=>[8,2,6,3,7,1,5,4]=>[8,2,6,3,7,1,5,4]=>[2,4,8,7,3,5,1,-6]
[1,7,3,5,8,4,6,2]=>[1,6,7,8,3,4,5,2]=>[1,6,7,8,3,4,5,2]=>[8,5,6,7,2,3,4,-1]
[8,1,6,3,4,7,5,2]=>[8,5,7,2,6,1,4,3]=>[8,5,7,2,6,1,4,3]=>[4,8,7,2,5,3,1,-6]
[4,6,7,3,5,1,8,2]=>[5,8,7,4,3,6,1,2]=>[5,8,7,4,3,6,1,2]=>[8,5,4,1,6,3,2,-7]
[7,6,4,1,8,3,2,5]=>[4,3,6,7,2,8,1,5]=>[4,3,6,7,2,8,1,5]=>[5,2,1,8,3,4,6,-7]
[3,7,2,5,4,1,8,6]=>[4,5,3,7,1,8,2,6]=>[4,5,3,7,1,8,2,6]=>[7,3,1,2,8,4,6,-5]
[3,7,2,8,1,5,4,6]=>[8,7,3,5,1,4,2,6]=>[8,7,3,5,1,4,2,6]=>[7,3,6,4,8,2,1,-5]
[3,5,1,7,8,2,6,4]=>[5,8,3,6,1,2,7,4]=>[5,8,3,6,1,2,7,4]=>[6,3,8,1,4,7,2,-5]
[2,3,1,8,5,7,4,6]=>[3,2,1,7,8,4,5,6]=>[3,2,1,7,8,4,5,6]=>[2,1,6,7,8,4,5,-3]
[3,6,4,1,5,2,8,7]=>[4,6,3,5,2,1,8,7]=>[4,6,3,5,2,1,8,7]=>[5,3,1,4,2,8,7,-6]
[4,5,8,6,1,3,7,2]=>[6,8,2,4,5,7,3,1]=>[6,8,2,4,5,7,3,1]=>[3,7,4,5,1,6,2,-8]
[4,1,3,5,6,7,8,2]=>[4,8,1,3,5,6,7,2]=>[4,8,1,3,5,6,7,2]=>[8,4,1,5,6,7,2,-3]
[2,1,5,8,6,3,7,4]=>[2,1,6,8,5,7,4,3]=>[2,1,6,8,5,7,4,3]=>[1,8,7,5,3,6,4,-2]
[3,7,8,5,4,1,6,2]=>[4,5,3,8,6,1,7,2]=>[4,5,3,8,6,1,7,2]=>[8,3,1,2,5,7,4,-6]
[4,6,8,5,3,1,7,2]=>[3,5,8,4,7,6,1,2]=>[3,5,8,4,7,6,1,2]=>[8,1,4,2,6,5,3,-7]
[1,6,5,3,7,8,2,4]=>[1,8,5,2,6,3,7,4]=>[1,8,5,2,6,3,7,4]=>[4,6,8,3,5,7,2,-1]
[1,8,5,7,4,2,3,6]=>[1,4,2,7,8,3,5,6]=>[1,4,2,7,8,3,5,6]=>[3,6,2,7,8,4,5,-1]
[7,2,6,1,3,4,8,5]=>[6,7,1,3,8,2,4,5]=>[6,7,1,3,8,2,4,5]=>[6,4,7,8,1,2,5,-3]
[6,3,8,4,7,1,2,5]=>[7,1,6,8,2,3,4,5]=>[7,1,6,8,2,3,4,5]=>[5,6,7,8,3,1,4,-2]
[1,2,5,4,8,3,6,7]=>[1,2,8,5,4,3,6,7]=>[1,2,8,5,4,3,6,7]=>[2,6,5,4,7,8,3,-1]
[4,1,8,5,7,2,3,6]=>[4,7,2,1,8,3,5,6]=>[4,7,2,1,8,3,5,6]=>[3,6,1,7,8,2,5,-4]
[8,4,7,6,5,3,1,2]=>[3,1,5,6,7,8,4,2]=>[3,1,5,6,7,8,4,2]=>[8,1,7,3,4,5,6,-2]
[2,3,1,8,7,6,4,5]=>[3,2,1,6,4,7,8,5]=>[3,2,1,6,4,7,8,5]=>[2,1,5,8,4,6,7,-3]
[1,3,4,8,7,2,5,6]=>[1,7,3,4,2,5,8,6]=>[1,7,3,4,2,5,8,6]=>[5,3,4,6,8,2,7,-1]
[8,4,7,6,5,1,2,3]=>[5,1,2,6,7,8,4,3]=>[5,1,2,6,7,8,4,3]=>[3,8,7,1,4,5,6,-2]
[2,8,4,7,3,6,5,1]=>[5,2,6,7,8,4,1,3]=>[5,2,6,7,8,4,1,3]=>[2,8,6,1,3,4,5,-7]
[1,8,4,7,6,5,2,3]=>[1,5,2,6,7,8,4,3]=>[1,5,2,6,7,8,4,3]=>[3,8,7,2,4,5,6,-1]
[5,3,6,1,4,2,8,7]=>[6,4,5,1,3,2,8,7]=>[6,4,5,1,3,2,8,7]=>[6,5,2,3,1,8,7,-4]
[2,1,7,5,8,3,6,4]=>[2,1,8,6,7,3,5,4]=>[2,1,8,6,7,3,5,4]=>[1,6,8,7,4,5,3,-2]
[5,1,3,6,2,8,7,4]=>[5,6,1,7,3,2,8,4]=>[5,6,1,7,3,2,8,4]=>[6,5,8,1,2,4,7,-3]
[6,3,7,5,2,4,8,1]=>[8,5,7,3,6,2,4,1]=>[8,5,7,3,6,2,4,1]=>[6,4,7,2,5,3,1,-8]
[8,6,3,1,7,5,4,2]=>[3,6,4,5,8,7,1,2]=>[3,6,4,5,8,7,1,2]=>[8,1,3,4,2,6,5,-7]
[4,6,8,3,1,7,2,5]=>[3,8,7,4,1,6,2,5]=>[3,8,7,4,1,6,2,5]=>[7,1,4,8,6,3,2,-5]
[3,6,1,2,4,8,7,5]=>[6,1,3,2,7,4,8,5]=>[6,1,3,2,7,4,8,5]=>[4,3,6,8,1,5,7,-2]
[6,3,1,2,4,8,7,5]=>[3,1,6,2,7,4,8,5]=>[3,1,6,2,7,4,8,5]=>[4,1,6,8,3,5,7,-2]
[4,2,6,1,3,7,8,5]=>[6,4,1,2,8,3,7,5]=>[6,4,1,2,8,3,7,5]=>[4,6,2,8,1,7,5,-3]
[8,4,6,1,2,5,7,3]=>[6,1,7,8,2,4,5,3]=>[6,1,7,8,2,4,5,3]=>[5,8,6,7,1,3,4,-2]
[3,1,7,6,2,8,4,5]=>[3,6,1,7,2,8,4,5]=>[3,6,1,7,2,8,4,5]=>[5,1,7,8,2,4,6,-3]
[4,2,5,1,3,7,8,6]=>[5,4,1,2,3,8,7,6]=>[5,4,1,2,3,8,7,6]=>[4,5,2,1,8,7,6,-3]
[8,1,6,3,5,4,7,2]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,3,1,4,2]=>[8,5,7,4,3,2,1,-6]
[7,1,3,6,8,5,4,2]=>[7,4,1,5,8,3,6,2]=>[7,4,1,5,8,3,6,2]=>[8,6,2,4,7,1,5,-3]
[6,5,7,2,8,1,4,3]=>[8,7,4,1,6,5,2,3]=>[8,7,4,1,6,5,2,3]=>[7,8,3,6,5,2,1,-4]
[7,3,4,1,6,8,2,5]=>[4,8,7,3,2,1,6,5]=>[4,8,7,3,2,1,6,5]=>[5,4,1,8,7,3,2,-6]
[7,3,4,1,6,5,8,2]=>[4,8,7,3,6,1,5,2]=>[4,8,7,3,6,1,5,2]=>[8,4,1,7,5,3,2,-6]
[8,5,7,2,6,4,1,3]=>[4,6,2,7,8,1,5,3]=>[4,6,2,7,8,1,5,3]=>[3,8,1,7,2,4,5,-6]
[8,7,3,1,4,5,6,2]=>[3,7,6,2,4,5,8,1]=>[3,7,6,2,4,5,8,1]=>[4,1,5,6,3,2,7,-8]
[8,7,5,1,2,6,3,4]=>[5,1,7,2,6,3,8,4]=>[5,1,7,2,6,3,8,4]=>[4,6,8,1,5,3,7,-2]
[8,7,3,1,4,2,5,6]=>[3,7,4,2,1,5,8,6]=>[3,7,4,2,1,5,8,6]=>[4,1,3,6,8,2,7,-5]
[5,6,1,8,3,4,7,2]=>[6,7,8,3,5,1,4,2]=>[6,7,8,3,5,1,4,2]=>[8,4,7,5,1,2,3,-6]
[7,2,5,6,1,4,8,3]=>[6,7,8,1,2,5,4,3]=>[6,7,8,1,2,5,4,3]=>[5,8,7,6,1,2,3,-4]
[6,3,5,2,4,7,1,8]=>[7,5,6,2,3,4,1,8]=>[7,5,6,2,3,4,1,8]=>[4,5,6,2,3,1,8,-7]
[6,3,5,1,2,8,7,4]=>[5,1,6,7,3,2,8,4]=>[5,1,6,7,3,2,8,4]=>[6,5,8,1,3,4,7,-2]
[7,8,1,3,4,6,2,5]=>[8,6,1,3,2,4,7,5]=>[8,6,1,3,2,4,7,5]=>[5,4,6,8,2,7,1,-3]
[7,6,1,4,3,2,5,8]=>[6,3,4,1,2,7,5,8]=>[6,3,4,1,2,7,5,8]=>[5,2,3,7,1,6,8,-4]
[7,4,1,3,5,6,2,8]=>[4,7,2,6,3,5,1,8]=>[4,7,2,6,3,5,1,8]=>[3,5,1,6,4,2,8,-7]
[5,4,2,8,3,6,7,1]=>[7,4,5,8,3,2,6,1]=>[7,4,5,8,3,2,6,1]=>[6,5,2,3,7,1,4,-8]
[3,4,5,2,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>[1,3,4,2,7,8,6,-5]
[7,2,6,5,1,3,8,4]=>[5,6,2,7,8,4,3,1]=>[5,6,2,7,8,4,3,1]=>[3,7,6,1,2,4,5,-8]
[2,5,7,4,6,3,1,8]=>[3,2,6,7,5,4,1,8]=>[3,2,6,7,5,4,1,8]=>[2,1,6,5,3,4,8,-7]
[4,5,1,8,3,6,7,2]=>[5,7,8,4,1,3,6,2]=>[5,7,8,4,1,3,6,2]=>[8,6,4,1,7,2,3,-5]
[1,3,7,5,6,8,4,2]=>[1,4,3,8,7,5,6,2]=>[1,4,3,8,7,5,6,2]=>[8,3,2,6,7,5,4,-1]
[4,1,2,8,6,5,3,7]=>[4,1,5,2,6,8,3,7]=>[4,1,5,2,6,8,3,7]=>[4,7,1,3,5,8,6,-2]
[1,8,5,6,2,7,4,3]=>[1,6,4,7,8,5,2,3]=>[1,6,4,7,8,5,2,3]=>[7,8,3,6,2,4,5,-1]
[8,3,5,7,2,6,1,4]=>[6,7,8,1,3,2,5,4]=>[6,7,8,1,3,2,5,4]=>[6,5,8,7,1,2,3,-4]
[1,3,7,6,5,2,8,4]=>[1,5,3,6,7,8,2,4]=>[1,5,3,6,7,8,2,4]=>[7,3,8,2,4,5,6,-1]
[1,6,4,7,3,5,8,2]=>[1,8,7,6,3,4,5,2]=>[1,8,7,6,3,4,5,2]=>[8,5,6,7,4,3,2,-1]
[8,2,6,5,7,3,4,1]=>[4,8,7,3,6,2,5,1]=>[4,8,7,3,6,2,5,1]=>[6,4,1,7,5,3,2,-8]
[8,1,2,6,7,3,4,5]=>[8,1,7,3,4,2,6,5]=>[8,1,7,3,4,2,6,5]=>[6,4,5,8,7,3,1,-2]
[1,8,6,3,5,2,4,7]=>[1,5,6,2,3,8,4,7]=>[1,5,6,2,3,8,4,7]=>[4,5,7,2,3,8,6,-1]
[5,1,7,6,2,4,8,3]=>[5,6,7,3,1,8,4,2]=>[5,6,7,3,1,8,4,2]=>[8,4,7,1,2,3,6,-5]
[8,3,5,6,1,4,7,2]=>[6,7,8,1,3,5,4,2]=>[6,7,8,1,3,5,4,2]=>[8,5,7,6,1,2,3,-4]
[8,1,4,5,3,2,7,6]=>[8,3,5,1,4,7,2,6]=>[8,3,5,1,4,7,2,6]=>[7,2,5,3,8,6,1,-4]
[1,5,4,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>[3,5,2,4,7,6,8,-1]
[1,3,6,4,2,5,7,8]=>[1,4,3,6,2,5,7,8]=>[1,4,3,6,2,5,7,8]=>[5,3,2,6,4,7,8,-1]
[1,3,7,4,2,5,6,8]=>[1,4,3,7,2,5,6,8]=>[1,4,3,7,2,5,6,8]=>[5,3,2,6,7,4,8,-1]
[1,7,6,4,2,3,5,8]=>[1,4,2,6,3,7,5,8]=>[1,4,2,6,3,7,5,8]=>[3,5,2,7,4,6,8,-1]
[1,3,2,7,6,4,5,8]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,4,7,5,8]=>[3,2,5,7,4,6,8,-1]
[1,2,3,7,6,4,5,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,4,7,5,8]=>[2,3,5,7,4,6,8,-1]
[1,3,2,5,8,6,4,7]=>[1,3,2,6,5,8,4,7]=>[1,3,2,6,5,8,4,7]=>[3,2,7,5,4,8,6,-1]
[3,8,2,5,6,7,4,1]=>[4,7,3,8,1,5,6,2]=>[4,7,3,8,1,5,6,2]=>[8,3,1,6,7,2,4,-5]
[4,6,8,2,1,7,3,5]=>[2,8,7,4,3,6,1,5]=>[2,8,7,4,3,6,1,5]=>[1,5,4,8,6,3,2,-7]
[3,1,2,5,7,8,6,4]=>[3,1,2,6,5,8,7,4]=>[3,1,2,6,5,8,7,4]=>[3,1,8,5,4,7,6,-2]
[7,8,6,1,2,4,5,3]=>[6,1,5,2,4,8,7,3]=>[6,1,5,2,4,8,7,3]=>[4,8,5,3,1,7,6,-2]
[1,5,3,4,7,8,6,2]=>[1,6,5,3,4,8,7,2]=>[1,6,5,3,4,8,7,2]=>[8,4,5,3,2,7,6,-1]
[5,1,2,4,7,8,6,3]=>[5,1,6,2,4,8,7,3]=>[5,1,6,2,4,8,7,3]=>[4,8,5,1,3,7,6,-2]
[1,8,5,3,4,6,7,2]=>[1,7,5,3,8,4,6,2]=>[1,7,5,3,8,4,6,2]=>[8,4,6,3,7,2,5,-1]
[8,1,6,4,2,3,5,7]=>[8,4,2,6,3,1,5,7]=>[8,4,2,6,3,1,5,7]=>[3,5,2,7,4,8,1,-6]
[8,3,1,2,4,6,7,5]=>[3,1,8,2,7,4,6,5]=>[3,1,8,2,7,4,6,5]=>[4,1,6,8,7,5,3,-2]
[3,1,2,8,5,6,7,4]=>[3,1,2,7,8,5,6,4]=>[3,1,2,7,8,5,6,4]=>[3,1,8,6,7,4,5,-2]
[6,1,8,4,2,3,5,7]=>[6,4,2,8,3,1,5,7]=>[6,4,2,8,3,1,5,7]=>[3,5,2,7,1,8,4,-6]
[3,6,8,5,4,1,7,2]=>[4,5,3,8,7,6,1,2]=>[4,5,3,8,7,6,1,2]=>[8,3,1,2,6,5,4,-7]
[2,5,1,4,7,8,3,6]=>[5,2,8,1,4,3,7,6]=>[5,2,8,1,4,3,7,6]=>[2,6,5,1,8,7,3,-4]
[3,5,1,6,4,2,7,8]=>[5,4,3,6,1,2,7,8]=>[5,4,3,6,1,2,7,8]=>[6,3,2,1,4,7,8,-5]
[7,2,4,1,3,6,8,5]=>[4,7,1,2,8,3,6,5]=>[4,7,1,2,8,3,6,5]=>[4,6,1,8,7,2,5,-3]
[4,5,8,6,2,1,3,7]=>[2,6,1,4,5,8,3,7]=>[2,6,1,4,5,8,3,7]=>[1,7,4,5,2,8,6,-3]
[8,2,4,1,6,5,7,3]=>[4,8,7,2,6,1,5,3]=>[4,8,7,2,6,1,5,3]=>[4,8,1,7,5,3,2,-6]
[1,5,8,2,4,3,6,7]=>[1,8,4,2,5,3,6,7]=>[1,8,4,2,5,3,6,7]=>[4,6,3,5,7,8,2,-1]
[2,6,1,8,3,4,7,5]=>[6,2,8,3,7,1,4,5]=>[6,2,8,3,7,1,4,5]=>[2,4,7,8,1,5,3,-6]
[6,4,2,3,1,8,5,7]=>[3,4,2,6,8,1,5,7]=>[3,4,2,6,8,1,5,7]=>[3,1,2,7,4,8,5,-6]
[1,3,7,4,5,2,8,6]=>[1,5,3,7,4,8,2,6]=>[1,5,3,7,4,8,2,6]=>[7,3,5,2,8,4,6,-1]
[6,5,1,3,8,7,2,4]=>[5,6,2,1,7,3,8,4]=>[5,6,2,1,7,3,8,4]=>[3,6,8,1,2,5,7,-4]
[8,5,7,2,3,6,4,1]=>[4,6,1,7,8,3,5,2]=>[4,6,1,7,8,3,5,2]=>[8,6,1,7,2,4,5,-3]
[8,7,1,2,4,3,6,5]=>[7,1,4,2,6,3,8,5]=>[7,1,4,2,6,3,8,5]=>[4,6,3,8,5,1,7,-2]
[7,3,6,2,4,5,1,8]=>[5,6,7,2,4,3,1,8]=>[5,6,7,2,4,3,1,8]=>[4,6,5,1,2,3,8,-7]
[6,5,1,4,2,8,7,3]=>[5,4,6,3,7,2,8,1]=>[5,4,6,3,7,2,8,1]=>[6,4,2,1,3,5,7,-8]
[8,1,3,6,7,5,2,4]=>[8,5,1,2,7,3,6,4]=>[8,5,1,2,7,3,6,4]=>[4,6,8,2,7,5,1,-3]
[5,1,6,8,3,7,2,4]=>[5,7,8,2,1,6,3,4]=>[5,7,8,2,1,6,3,4]=>[4,7,8,1,6,2,3,-5]
[6,1,3,8,4,2,5,7]=>[6,4,1,8,2,3,5,7]=>[6,4,1,8,2,3,5,7]=>[5,6,2,7,1,8,4,-3]
[4,1,5,6,3,2,7,8]=>[4,3,6,1,5,2,7,8]=>[4,3,6,1,5,2,7,8]=>[6,2,1,5,3,7,8,-4]
[7,6,3,5,1,8,4,2]=>[5,4,8,6,2,7,1,3]=>[5,4,8,6,2,7,1,3]=>[5,8,2,1,4,6,3,-7]
[3,6,4,1,5,7,2,8]=>[4,6,3,7,2,5,1,8]=>[4,6,3,7,2,5,1,8]=>[5,3,1,6,2,4,8,-7]
[5,4,8,2,1,3,7,6]=>[2,8,1,5,4,7,3,6]=>[2,8,1,5,4,7,3,6]=>[1,7,5,4,8,6,2,-3]
[7,2,8,1,4,3,6,5]=>[8,7,4,1,6,3,2,5]=>[8,7,4,1,6,3,2,5]=>[7,6,3,8,5,2,1,-4]
[1,8,3,6,4,7,2,5]=>[1,7,8,6,2,3,4,5]=>[1,7,8,6,2,3,4,5]=>[5,6,7,8,4,2,3,-1]
[4,1,2,7,5,3,8,6]=>[4,1,5,2,7,8,3,6]=>[4,1,5,2,7,8,3,6]=>[4,7,1,3,8,5,6,-2]
[6,2,1,8,5,7,4,3]=>[2,6,4,7,8,1,5,3]=>[2,6,4,7,8,1,5,3]=>[1,8,3,7,2,4,5,-6]
[7,1,3,4,8,5,2,6]=>[7,5,1,3,8,2,4,6]=>[7,5,1,3,8,2,4,6]=>[6,4,7,2,8,1,5,-3]
[1,8,4,3,7,6,2,5]=>[1,6,4,7,3,8,2,5]=>[1,6,4,7,3,8,2,5]=>[7,5,3,8,2,4,6,-1]
[1,8,4,5,7,6,2,3]=>[1,6,2,7,3,8,5,4]=>[1,6,2,7,3,8,5,4]=>[3,5,8,7,2,4,6,-1]
[6,4,7,3,1,2,5,8]=>[3,1,7,6,2,4,5,8]=>[3,1,7,6,2,4,5,8]=>[5,1,6,7,4,3,8,-2]
[5,2,6,3,7,1,4,8]=>[7,5,6,1,2,3,4,8]=>[7,5,6,1,2,3,4,8]=>[5,6,7,2,3,1,8,-4]
[6,7,2,8,4,3,1,5]=>[3,4,8,7,1,6,2,5]=>[3,4,8,7,1,6,2,5]=>[7,1,2,8,6,4,3,-5]
[6,2,7,3,5,8,1,4]=>[8,6,7,1,3,2,5,4]=>[8,6,7,1,3,2,5,4]=>[6,5,8,7,2,3,1,-4]
[1,5,4,2,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[3,5,2,4,7,8,6,-1]
[2,1,4,3,6,5,10,8,9,7]=>[2,1,4,3,6,5,9,10,8,7]=>[2,1,4,3,6,5,9,10,8,7]=>[1,4,3,6,5,10,9,7,8,-2]
[2,1,4,3,8,6,7,5,10,9]=>[2,1,4,3,7,8,6,5,10,9]=>[2,1,4,3,7,8,6,5,10,9]=>[1,4,3,8,7,5,6,10,9,-2]
[2,1,6,4,5,3,8,7,10,9]=>[2,1,5,6,4,3,8,7,10,9]=>[2,1,5,6,4,3,8,7,10,9]=>[1,6,5,3,4,8,7,10,9,-2]
[2,1,6,4,5,3,10,8,9,7]=>[2,1,5,6,4,3,9,10,8,7]=>[2,1,5,6,4,3,9,10,8,7]=>[1,6,5,3,4,10,9,7,8,-2]
[2,1,10,8,9,6,7,4,5,3]=>[2,1,5,7,4,9,6,10,8,3]=>[2,1,5,7,4,9,6,10,8,3]=>[1,10,5,3,7,4,9,6,8,-2]
[4,2,3,1,6,5,8,7,10,9]=>[3,4,2,1,6,5,8,7,10,9]=>[3,4,2,1,6,5,8,7,10,9]=>[3,1,2,6,5,8,7,10,9,-4]
[4,2,3,1,6,5,10,8,9,7]=>[3,4,2,1,6,5,9,10,8,7]=>[3,4,2,1,6,5,9,10,8,7]=>[3,1,2,6,5,10,9,7,8,-4]
[4,2,3,1,8,6,7,5,10,9]=>[3,4,2,1,7,8,6,5,10,9]=>[3,4,2,1,7,8,6,5,10,9]=>[3,1,2,8,7,5,6,10,9,-4]
[4,2,3,1,10,8,9,6,7,5]=>[3,4,2,1,7,9,6,10,8,5]=>[3,4,2,1,7,9,6,10,8,5]=>[3,1,2,10,7,5,9,6,8,-4]
[6,4,5,2,3,1,10,8,9,7]=>[3,5,2,6,4,1,9,10,8,7]=>[3,5,2,6,4,1,9,10,8,7]=>[3,1,5,2,4,10,9,7,8,-6]
[8,6,7,4,5,2,3,1,10,9]=>[3,5,2,7,4,8,6,1,10,9]=>[3,5,2,7,4,8,6,1,10,9]=>[3,1,5,2,7,4,6,10,9,-8]
[2,1,4,3,6,5,8,7,12,10,11,9]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>[1,4,3,6,5,8,7,12,11,9,10,-2]
[2,1,4,3,6,5,10,8,9,7,12,11]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>[1,4,3,6,5,10,9,7,8,12,11,-2]
[2,1,4,3,6,5,12,10,11,8,9,7]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>[1,4,3,6,5,12,9,7,11,8,10,-2]
[2,1,4,3,8,6,7,5,10,9,12,11]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>[1,4,3,8,7,5,6,10,9,12,11,-2]
[2,1,4,3,8,6,7,5,12,10,11,9]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>[1,4,3,8,7,5,6,12,11,9,10,-2]
[2,1,4,3,10,8,9,6,7,5,12,11]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>[1,4,3,10,7,5,9,6,8,12,11,-2]
[2,1,4,3,12,10,11,8,9,6,7,5]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>[1,4,3,12,7,5,9,6,11,8,10,-2]
[2,1,6,4,5,3,8,7,10,9,12,11]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>[1,6,5,3,4,8,7,10,9,12,11,-2]
[2,1,6,4,5,3,8,7,12,10,11,9]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>[1,6,5,3,4,8,7,12,11,9,10,-2]
[2,1,6,4,5,3,10,8,9,7,12,11]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>[1,6,5,3,4,10,9,7,8,12,11,-2]
[2,1,6,4,5,3,12,10,11,8,9,7]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>[1,6,5,3,4,12,9,7,11,8,10,-2]
[2,1,8,6,7,4,5,3,10,9,12,11]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>[1,8,5,3,7,4,6,10,9,12,11,-2]
[2,1,8,6,7,4,5,3,12,10,11,9]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>[1,8,5,3,7,4,6,12,11,9,10,-2]
[2,1,10,8,9,6,7,4,5,3,12,11]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>[1,10,5,3,7,4,9,6,8,12,11,-2]
[2,1,12,10,11,8,9,6,7,4,5,3]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>[1,12,5,3,7,4,9,6,11,8,10,-2]
[4,2,3,1,6,5,8,7,10,9,12,11]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>[3,1,2,6,5,8,7,10,9,12,11,-4]
[4,2,3,1,6,5,8,7,12,10,11,9]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>[3,1,2,6,5,8,7,12,11,9,10,-4]
[4,2,3,1,6,5,10,8,9,7,12,11]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>[3,1,2,6,5,10,9,7,8,12,11,-4]
[4,2,3,1,6,5,12,10,11,8,9,7]=>[3,4,2,1,6,5,9,11,8,12,10,7]=>[3,4,2,1,6,5,9,11,8,12,10,7]=>[3,1,2,6,5,12,9,7,11,8,10,-4]
[4,2,3,1,8,6,7,5,10,9,12,11]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>[3,1,2,8,7,5,6,10,9,12,11,-4]
[4,2,3,1,8,6,7,5,12,10,11,9]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>[3,1,2,8,7,5,6,12,11,9,10,-4]
[4,2,3,1,10,8,9,6,7,5,12,11]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>[3,1,2,10,7,5,9,6,8,12,11,-4]
[4,2,3,1,12,10,11,8,9,6,7,5]=>[3,4,2,1,7,9,6,11,8,12,10,5]=>[3,4,2,1,7,9,6,11,8,12,10,5]=>[3,1,2,12,7,5,9,6,11,8,10,-4]
[6,4,5,2,3,1,8,7,10,9,12,11]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>[3,1,5,2,4,8,7,10,9,12,11,-6]
[6,4,5,2,3,1,8,7,12,10,11,9]=>[3,5,2,6,4,1,8,7,11,12,10,9]=>[3,5,2,6,4,1,8,7,11,12,10,9]=>[3,1,5,2,4,8,7,12,11,9,10,-6]
[6,4,5,2,3,1,10,8,9,7,12,11]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>[3,1,5,2,4,10,9,7,8,12,11,-6]
[6,4,5,2,3,1,12,10,11,8,9,7]=>[3,5,2,6,4,1,9,11,8,12,10,7]=>[3,5,2,6,4,1,9,11,8,12,10,7]=>[3,1,5,2,4,12,9,7,11,8,10,-6]
[8,6,7,4,5,2,3,1,10,9,12,11]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>[3,1,5,2,7,4,6,10,9,12,11,-8]
[8,6,7,4,5,2,3,1,12,10,11,9]=>[3,5,2,7,4,8,6,1,11,12,10,9]=>[3,5,2,7,4,8,6,1,11,12,10,9]=>[3,1,5,2,7,4,6,12,11,9,10,-8]
[10,8,9,6,7,4,5,2,3,1,12,11]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>[3,1,5,2,7,4,9,6,8,12,11,-10]
[12,10,11,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>[3,1,5,2,7,4,9,6,11,8,10,-12]
[3,8,5,2,4,1,6,7]=>[4,5,3,2,8,1,6,7]=>[4,5,3,2,8,1,6,7]=>[4,3,1,2,7,8,5,-6]
[3,7,1,6,8,4,5,2]=>[7,5,3,8,4,1,6,2]=>[7,5,3,8,4,1,6,2]=>[8,3,5,2,7,1,4,-6]
[3,7,1,6,4,8,5,2]=>[7,5,3,8,6,1,2,4]=>[7,5,3,8,6,1,2,4]=>[7,3,8,2,5,1,4,-6]
[5,1,6,8,3,4,7,2]=>[5,7,8,3,1,6,4,2]=>[5,7,8,3,1,6,4,2]=>[8,4,7,1,6,2,3,-5]
[5,7,4,1,3,2,8,6]=>[4,3,1,7,5,8,2,6]=>[4,3,1,7,5,8,2,6]=>[7,2,1,5,8,4,6,-3]
[2,6,8,7,1,3,5,4]=>[7,2,1,5,3,6,8,4]=>[7,2,1,5,3,6,8,4]=>[2,5,8,4,6,1,7,-3]
[3,7,6,1,4,5,2,8]=>[6,5,3,1,4,7,2,8]=>[6,5,3,1,4,7,2,8]=>[7,3,5,2,1,6,8,-4]
[4,1,6,2,7,5,3,8]=>[4,6,5,1,7,2,3,8]=>[4,6,5,1,7,2,3,8]=>[6,7,1,3,2,5,8,-4]
[4,5,3,1,2,8,6,7]=>[3,1,5,4,2,8,6,7]=>[3,1,5,4,2,8,6,7]=>[5,1,4,3,7,8,6,-2]
[2,4,5,3,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>[2,1,4,3,7,8,6,-5]
[5,7,6,2,3,1,4,8]=>[3,6,2,1,5,7,4,8]=>[3,6,2,1,5,7,4,8]=>[3,1,7,5,2,6,8,-4]
[4,1,3,7,5,2,6,8]=>[4,5,1,3,7,2,6,8]=>[4,5,1,3,7,2,6,8]=>[6,4,1,2,7,5,8,-3]
[4,1,6,3,2,7,5,8]=>[4,3,6,1,7,2,5,8]=>[4,3,6,1,7,2,5,8]=>[6,2,1,7,3,5,8,-4]
[2,7,5,4,1,3,6,8]=>[4,2,1,5,7,3,6,8]=>[4,2,1,5,7,3,6,8]=>[2,6,1,4,7,5,8,-3]
[7,5,4,1,3,2,6,8]=>[4,3,1,5,7,2,6,8]=>[4,3,1,5,7,2,6,8]=>[6,2,1,4,7,5,8,-3]
[2,4,8,5,6,3,1,7]=>[3,2,6,4,8,5,1,7]=>[3,2,6,4,8,5,1,7]=>[2,1,4,6,3,8,5,-7]
[2,5,7,4,1,3,6,8]=>[4,2,1,7,5,3,6,8]=>[4,2,1,7,5,3,6,8]=>[2,6,1,5,7,4,8,-3]
[5,7,4,1,3,2,6,8]=>[4,3,1,7,5,2,6,8]=>[4,3,1,7,5,2,6,8]=>[6,2,1,5,7,4,8,-3]
[2,6,8,4,5,3,1,7]=>[3,2,5,8,4,6,1,7]=>[3,2,5,8,4,6,1,7]=>[2,1,5,3,6,8,4,-7]
[4,5,1,6,3,2,7,8]=>[5,3,6,4,1,2,7,8]=>[5,3,6,4,1,2,7,8]=>[6,2,4,1,3,7,8,-5]
[5,1,6,3,2,4,7,8]=>[5,3,6,2,1,4,7,8]=>[5,3,6,2,1,4,7,8]=>[4,2,6,1,3,7,8,-5]
[4,2,5,1,6,3,7,8]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7,8]=>[4,6,2,1,3,7,8,-5]
[5,1,6,2,4,3,7,8]=>[5,6,4,2,1,3,7,8]=>[5,6,4,2,1,3,7,8]=>[4,6,3,1,2,7,8,-5]
[4,3,5,1,6,2,7,8]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7,8]=>[6,4,3,1,2,7,8,-5]
[2,8,1,6,5,4,7,3]=>[8,2,7,5,6,1,4,3]=>[8,2,7,5,6,1,4,3]=>[2,8,7,4,5,3,1,-6]
[5,1,7,2,6,8,3,4]=>[5,7,8,3,1,2,6,4]=>[5,7,8,3,1,2,6,4]=>[6,4,8,1,7,2,3,-5]
[5,8,1,6,2,4,7,3]=>[8,6,7,2,5,1,4,3]=>[8,6,7,2,5,1,4,3]=>[4,8,7,5,2,3,1,-6]
[6,1,2,4,3,7,8,5]=>[6,1,4,2,8,3,7,5]=>[6,1,4,2,8,3,7,5]=>[4,6,3,8,1,7,5,-2]
[7,1,2,4,6,3,8,5]=>[7,1,6,2,8,4,3,5]=>[7,1,6,2,8,4,3,5]=>[4,7,6,8,3,1,5,-2]
[1,5,8,4,2,3,6,7]=>[1,4,2,8,5,3,6,7]=>[1,4,2,8,5,3,6,7]=>[3,6,2,5,7,8,4,-1]
[3,8,4,6,7,2,5,1]=>[5,7,3,8,2,4,6,1]=>[5,7,3,8,2,4,6,1]=>[5,3,6,1,7,2,4,-8]
[8,6,2,4,5,3,1,7]=>[3,5,6,1,4,8,2,7]=>[3,5,6,1,4,8,2,7]=>[7,1,5,2,3,8,6,-4]
[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>[3,5,2,7,4,8,6,-1]
[8,2,6,4,5,1,7,3]=>[5,8,7,6,4,2,1,3]=>[5,8,7,6,4,2,1,3]=>[6,8,5,1,4,3,2,-7]
[6,1,4,5,8,3,7,2]=>[6,7,8,1,4,5,3,2]=>[6,7,8,1,4,5,3,2]=>[8,7,5,6,1,2,3,-4]
[7,3,2,6,4,1,8,5]=>[4,3,6,7,8,1,2,5]=>[4,3,6,7,8,1,2,5]=>[7,2,1,8,3,4,5,-6]
[3,5,2,6,4,8,1,7]=>[8,5,3,6,2,4,1,7]=>[8,5,3,6,2,4,1,7]=>[5,3,6,2,4,8,1,-7]
[8,1,5,2,4,6,3,7]=>[8,5,6,2,1,4,3,7]=>[8,5,6,2,1,4,3,7]=>[4,7,6,2,3,8,1,-5]
[3,8,1,6,4,5,2,7]=>[8,5,3,6,4,1,2,7]=>[8,5,3,6,4,1,2,7]=>[7,3,5,2,4,8,1,-6]
[8,1,3,6,5,4,2,7]=>[8,4,1,5,6,3,2,7]=>[8,4,1,5,6,3,2,7]=>[7,6,2,4,5,8,1,-3]
[7,1,5,2,4,6,8,3]=>[7,5,8,2,1,4,6,3]=>[7,5,8,2,1,4,6,3]=>[4,8,6,2,7,1,3,-5]
[8,6,2,1,5,7,3,4]=>[2,6,8,1,3,7,5,4]=>[2,6,8,1,3,7,5,4]=>[1,5,8,7,2,6,3,-4]
[2,7,5,8,3,1,4,6]=>[3,2,8,1,7,4,5,6]=>[3,2,8,1,7,4,5,6]=>[2,1,6,7,8,5,3,-4]
[1,8,5,2,4,6,7,3]=>[1,5,8,3,7,4,6,2]=>[1,5,8,3,7,4,6,2]=>[8,4,6,2,7,5,3,-1]
[5,3,2,4,7,8,1,6]=>[8,3,5,2,4,1,7,6]=>[8,3,5,2,4,1,7,6]=>[4,2,5,3,8,7,1,-6]
[7,5,4,1,3,6,8,2]=>[4,5,1,7,8,3,6,2]=>[4,5,1,7,8,3,6,2]=>[8,6,1,2,7,4,5,-3]
[2,7,3,6,5,1,8,4]=>[5,2,6,7,8,4,3,1]=>[5,2,6,7,8,4,3,1]=>[2,7,6,1,3,4,5,-8]
[5,1,7,3,2,8,4,6]=>[5,3,7,8,1,4,2,6]=>[5,3,7,8,1,4,2,6]=>[7,2,6,1,8,3,4,-5]
[1,7,4,8,3,6,2,5]=>[1,6,8,7,2,3,4,5]=>[1,6,8,7,2,3,4,5]=>[5,6,7,8,2,4,3,-1]
[7,1,8,5,3,4,2,6]=>[7,4,5,3,8,2,1,6]=>[7,4,5,3,8,2,1,6]=>[6,4,2,3,8,1,5,-7]
[8,2,4,7,6,3,1,5]=>[3,6,7,2,1,8,4,5]=>[3,6,7,2,1,8,4,5]=>[4,1,7,8,2,3,6,-5]
[1,2,5,7,8,3,6,4]=>[1,2,8,6,5,3,7,4]=>[1,2,8,6,5,3,7,4]=>[2,6,8,5,4,7,3,-1]
[4,5,1,6,7,3,8,2]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[8,7,4,1,6,3,2,-5]
[1,6,5,3,8,7,2,4]=>[1,7,5,2,6,3,8,4]=>[1,7,5,2,6,3,8,4]=>[4,6,8,3,5,2,7,-1]
[6,8,2,3,1,5,7,4]=>[3,8,2,7,1,6,5,4]=>[3,8,2,7,1,6,5,4]=>[3,1,8,7,6,4,2,-5]
[6,2,5,3,8,1,4,7]=>[8,6,5,1,2,3,4,7]=>[8,6,5,1,2,3,4,7]=>[5,6,7,3,2,8,1,-4]
[6,2,5,3,7,1,4,8]=>[7,6,5,1,2,3,4,8]=>[7,6,5,1,2,3,4,8]=>[5,6,7,3,2,1,8,-4]
[3,6,2,4,7,8,5,1]=>[5,8,3,1,6,4,7,2]=>[5,8,3,1,6,4,7,2]=>[8,3,6,1,5,7,2,-4]
[5,6,1,4,8,3,7,2]=>[6,7,8,1,5,4,3,2]=>[6,7,8,1,5,4,3,2]=>[8,7,6,5,1,2,3,-4]
[8,1,3,2,6,5,7,4]=>[8,3,1,7,6,2,5,4]=>[8,3,1,7,6,2,5,4]=>[6,2,8,7,5,4,1,-3]
[6,1,3,7,2,5,8,4]=>[6,7,1,8,2,3,5,4]=>[6,7,1,8,2,3,5,4]=>[5,6,8,7,1,2,4,-3]
[4,6,8,2,5,1,7,3]=>[5,8,7,4,2,6,1,3]=>[5,8,7,4,2,6,1,3]=>[5,8,4,1,6,3,2,-7]
[7,2,1,3,5,8,4,6]=>[2,7,1,8,3,4,5,6]=>[2,7,1,8,3,4,5,6]=>[1,5,6,7,8,2,4,-3]
[6,2,7,3,4,5,1,8]=>[5,6,7,3,4,2,1,8]=>[5,6,7,3,4,2,1,8]=>[6,4,5,1,2,3,8,-7]
[7,5,1,4,8,2,3,6]=>[5,7,1,2,8,3,4,6]=>[5,7,1,2,8,3,4,6]=>[4,6,7,1,8,2,5,-3]
[6,5,8,2,7,3,4,1]=>[4,8,7,3,6,5,2,1]=>[4,8,7,3,6,5,2,1]=>[7,4,1,6,5,3,2,-8]
[8,2,4,7,1,5,3,6]=>[7,8,5,2,1,3,4,6]=>[7,8,5,2,1,3,4,6]=>[4,6,7,3,8,1,2,-5]
[8,1,4,6,5,7,3,2]=>[8,3,7,1,6,4,5,2]=>[8,3,7,1,6,4,5,2]=>[8,2,6,7,5,3,1,-4]
[5,6,3,1,7,2,8,4]=>[3,6,7,8,5,2,1,4]=>[3,6,7,8,5,2,1,4]=>[6,1,8,5,2,3,4,-7]
[4,2,3,5,1,8,6,7]=>[5,4,2,3,1,8,6,7]=>[5,4,2,3,1,8,6,7]=>[3,4,2,1,7,8,6,-5]
[4,6,8,2,7,3,5,1]=>[5,8,7,4,3,6,2,1]=>[5,8,7,4,3,6,2,1]=>[7,5,4,1,6,3,2,-8]
[4,5,2,6,7,1,8,3]=>[7,5,8,4,2,6,1,3]=>[7,5,8,4,2,6,1,3]=>[5,8,4,2,6,1,3,-7]
[8,1,2,6,5,4,7,3]=>[8,1,7,5,6,2,4,3]=>[8,1,7,5,6,2,4,3]=>[6,8,7,4,5,3,1,-2]
[8,5,1,2,7,4,3,6]=>[5,1,4,8,7,2,3,6]=>[5,1,4,8,7,2,3,6]=>[6,7,3,1,8,5,4,-2]
[1,6,3,7,4,8,2,5]=>[1,8,6,7,2,3,4,5]=>[1,8,6,7,2,3,4,5]=>[5,6,7,8,3,4,2,-1]
[2,8,1,6,7,3,4,5]=>[8,2,7,3,4,1,6,5]=>[8,2,7,3,4,1,6,5]=>[2,4,5,8,7,3,1,-6]
[1,5,7,2,3,6,8,4]=>[1,7,2,8,5,3,6,4]=>[1,7,2,8,5,3,6,4]=>[3,6,8,5,7,2,4,-1]
[4,2,7,1,3,6,8,5]=>[7,4,1,2,8,3,6,5]=>[7,4,1,2,8,3,6,5]=>[4,6,2,8,7,1,5,-3]
[8,5,7,2,4,3,6,1]=>[6,7,4,2,8,3,5,1]=>[6,7,4,2,8,3,5,1]=>[4,6,3,7,1,2,5,-8]
[7,8,6,2,4,1,3,5]=>[4,6,1,2,3,8,7,5]=>[4,6,1,2,3,8,7,5]=>[4,5,1,8,2,7,6,-3]
[7,2,6,1,4,8,3,5]=>[6,7,8,1,3,2,4,5]=>[6,7,8,1,3,2,4,5]=>[6,5,7,8,1,2,3,-4]
[4,6,7,2,3,8,1,5]=>[8,7,2,4,1,6,3,5]=>[8,7,2,4,1,6,3,5]=>[3,7,4,8,6,2,1,-5]
[8,1,6,3,5,2,4,7]=>[8,5,6,2,3,1,4,7]=>[8,5,6,2,3,1,4,7]=>[4,5,7,2,3,8,1,-6]
[4,3,7,2,8,1,6,5]=>[8,7,4,3,6,1,2,5]=>[8,7,4,3,6,1,2,5]=>[7,4,3,8,5,2,1,-6]
[4,1,8,6,5,2,3,7]=>[4,5,2,1,6,8,3,7]=>[4,5,2,1,6,8,3,7]=>[3,7,1,2,5,8,6,-4]
[4,8,1,3,7,6,2,5]=>[8,6,1,4,2,7,3,5]=>[8,6,1,4,2,7,3,5]=>[5,7,4,8,2,6,1,-3]
[6,3,7,2,5,4,8,1]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,2,3,4,1]=>[5,6,7,4,3,2,1,-8]
[7,1,4,8,2,5,3,6]=>[7,8,5,1,2,3,4,6]=>[7,8,5,1,2,3,4,6]=>[5,6,7,3,8,1,2,-4]
[7,5,2,6,3,4,8,1]=>[8,5,7,2,6,3,4,1]=>[8,5,7,2,6,3,4,1]=>[4,6,7,2,5,3,1,-8]
[7,1,2,4,8,5,3,6]=>[7,1,5,2,8,3,4,6]=>[7,1,5,2,8,3,4,6]=>[4,6,7,3,8,1,5,-2]
[4,6,2,5,1,7,8,3]=>[5,6,8,4,2,1,7,3]=>[5,6,8,4,2,1,7,3]=>[5,8,4,1,2,7,3,-6]
[4,2,8,5,1,3,6,7]=>[5,4,1,2,8,3,6,7]=>[5,4,1,2,8,3,6,7]=>[4,6,2,1,7,8,5,-3]
[4,2,7,5,1,3,6,8]=>[5,4,1,2,7,3,6,8]=>[5,4,1,2,7,3,6,8]=>[4,6,2,1,7,5,8,-3]
[7,1,3,6,8,5,2,4]=>[7,5,1,2,8,3,6,4]=>[7,5,1,2,8,3,6,4]=>[4,6,8,2,7,1,5,-3]
[4,2,8,1,3,6,7,5]=>[8,4,1,2,7,3,6,5]=>[8,4,1,2,7,3,6,5]=>[4,6,2,8,7,5,1,-3]
[8,1,3,6,4,2,5,7]=>[8,4,1,6,2,3,5,7]=>[8,4,1,6,2,3,5,7]=>[5,6,2,7,4,8,1,-3]
[7,1,3,6,4,2,5,8]=>[7,4,1,6,2,3,5,8]=>[7,4,1,6,2,3,5,8]=>[5,6,2,7,4,1,8,-3]
[8,1,3,6,2,5,7,4]=>[8,6,1,7,2,3,5,4]=>[8,6,1,7,2,3,5,4]=>[5,6,8,7,2,4,1,-3]
[8,1,2,5,7,4,6,3]=>[8,1,6,7,2,4,5,3]=>[8,1,6,7,2,4,5,3]=>[5,8,6,7,3,4,1,-2]
[1,7,4,6,3,5,8,2]=>[1,8,6,7,3,4,5,2]=>[1,8,6,7,3,4,5,2]=>[8,5,6,7,3,4,2,-1]
[7,1,2,5,8,4,6,3]=>[7,1,6,8,2,4,5,3]=>[7,1,6,8,2,4,5,3]=>[5,8,6,7,3,1,4,-2]
[7,1,3,6,2,5,8,4]=>[7,6,1,8,2,3,5,4]=>[7,6,1,8,2,3,5,4]=>[5,6,8,7,2,1,4,-3]
[7,1,4,8,3,6,2,5]=>[7,6,8,1,2,3,4,5]=>[7,6,8,1,2,3,4,5]=>[5,6,7,8,2,1,3,-4]
[5,2,7,1,4,8,3,6]=>[7,5,8,1,2,3,4,6]=>[7,5,8,1,2,3,4,6]=>[5,6,7,2,8,1,3,-4]
[5,2,7,3,6,1,4,8]=>[6,5,7,1,2,3,4,8]=>[6,5,7,1,2,3,4,8]=>[5,6,7,2,1,3,8,-4]
[7,2,5,1,4,8,3,6]=>[5,7,8,1,2,3,4,6]=>[5,7,8,1,2,3,4,6]=>[5,6,7,1,8,2,3,-4]
[7,4,6,3,1,2,5,8]=>[3,1,6,7,2,4,5,8]=>[3,1,6,7,2,4,5,8]=>[5,1,6,7,3,4,8,-2]
[7,3,1,2,5,8,4,6]=>[3,1,7,8,2,4,5,6]=>[3,1,7,8,2,4,5,6]=>[5,1,6,7,8,3,4,-2]
[6,4,8,3,1,2,5,7]=>[3,1,8,6,2,4,5,7]=>[3,1,8,6,2,4,5,7]=>[5,1,6,7,4,8,3,-2]
[8,2,5,7,4,1,3,6]=>[4,7,2,8,1,3,5,6]=>[4,7,2,8,1,3,5,6]=>[3,6,1,7,8,2,4,-5]
[8,2,4,1,3,6,7,5]=>[4,8,1,2,7,3,6,5]=>[4,8,1,2,7,3,6,5]=>[4,6,1,8,7,5,2,-3]
[7,4,6,1,2,5,8,3]=>[6,1,8,7,2,4,5,3]=>[6,1,8,7,2,4,5,3]=>[5,8,6,7,1,4,3,-2]
[6,1,3,8,2,5,7,4]=>[6,8,1,7,2,3,5,4]=>[6,8,1,7,2,3,5,4]=>[5,6,8,7,1,4,2,-3]
[8,2,5,1,4,7,3,6]=>[5,8,7,1,2,3,4,6]=>[5,8,7,1,2,3,4,6]=>[5,6,7,1,8,3,2,-4]
[7,2,5,3,6,1,4,8]=>[6,7,5,1,2,3,4,8]=>[6,7,5,1,2,3,4,8]=>[5,6,7,3,1,2,8,-4]
[8,2,5,3,6,1,4,7]=>[6,8,5,1,2,3,4,7]=>[6,8,5,1,2,3,4,7]=>[5,6,7,3,1,8,2,-4]
[6,4,7,1,2,5,8,3]=>[7,1,8,6,2,4,5,3]=>[7,1,8,6,2,4,5,3]=>[5,8,6,7,4,1,3,-2]
[6,4,8,1,2,5,7,3]=>[8,1,7,6,2,4,5,3]=>[8,1,7,6,2,4,5,3]=>[5,8,6,7,4,3,1,-2]
[7,2,5,8,1,3,6,4]=>[8,7,1,6,2,3,5,4]=>[8,7,1,6,2,3,5,4]=>[5,6,8,7,4,2,1,-3]
[1,5,2,3,8,6,7,4]=>[1,5,2,7,3,8,6,4]=>[1,5,2,7,3,8,6,4]=>[3,5,8,2,7,4,6,-1]
[4,6,7,2,3,8,5,1]=>[5,8,1,4,7,6,3,2]=>[5,8,1,4,7,6,3,2]=>[8,7,4,1,6,5,2,-3]
[4,5,7,6,3,1,8,2]=>[3,6,7,4,5,8,1,2]=>[3,6,7,4,5,8,1,2]=>[8,1,4,5,2,3,6,-7]
[4,2,3,6,7,5,1,8]=>[5,4,2,3,7,6,1,8]=>[5,4,2,3,7,6,1,8]=>[3,4,2,1,6,5,8,-7]
[6,2,4,7,3,5,1,8]=>[5,6,7,2,3,4,1,8]=>[5,6,7,2,3,4,1,8]=>[4,5,6,1,2,3,8,-7]
[2,6,4,5,7,3,1,8]=>[3,2,7,6,4,5,1,8]=>[3,2,7,6,4,5,1,8]=>[2,1,5,6,4,3,8,-7]
[7,2,4,6,3,5,1,8]=>[5,7,6,2,3,4,1,8]=>[5,7,6,2,3,4,1,8]=>[4,5,6,1,3,2,8,-7]
[1,5,3,8,6,2,4,7]=>[1,6,5,2,3,8,4,7]=>[1,6,5,2,3,8,4,7]=>[4,5,7,3,2,8,6,-1]
[8,1,2,4,7,5,3,6]=>[8,1,5,2,7,3,4,6]=>[8,1,5,2,7,3,4,6]=>[4,6,7,3,8,5,1,-2]
[1,8,2,4,7,5,3,6]=>[1,8,5,2,7,3,4,6]=>[1,8,5,2,7,3,4,6]=>[4,6,7,3,8,5,2,-1]
[5,1,8,2,4,7,3,6]=>[5,8,7,2,1,3,4,6]=>[5,8,7,2,1,3,4,6]=>[4,6,7,1,8,3,2,-5]
[1,6,3,8,4,7,2,5]=>[1,7,6,8,2,3,4,5]=>[1,7,6,8,2,3,4,5]=>[5,6,7,8,3,2,4,-1]
[6,1,8,3,5,2,4,7]=>[6,5,8,2,3,1,4,7]=>[6,5,8,2,3,1,4,7]=>[4,5,7,2,1,8,3,-6]
[7,1,5,2,4,8,3,6]=>[7,5,8,2,1,3,4,6]=>[7,5,8,2,1,3,4,6]=>[4,6,7,2,8,1,3,-5]
[8,1,5,2,4,7,3,6]=>[8,5,7,2,1,3,4,6]=>[8,5,7,2,1,3,4,6]=>[4,6,7,2,8,3,1,-5]
[8,5,7,1,4,2,3,6]=>[7,4,2,1,8,3,5,6]=>[7,4,2,1,8,3,5,6]=>[3,6,2,7,8,1,5,-4]
[7,5,8,1,4,2,3,6]=>[8,4,2,1,7,3,5,6]=>[8,4,2,1,7,3,5,6]=>[3,6,2,7,8,5,1,-4]
[1,7,5,8,4,2,3,6]=>[1,4,2,8,7,3,5,6]=>[1,4,2,8,7,3,5,6]=>[3,6,2,7,8,5,4,-1]
[5,1,3,8,6,2,4,7]=>[5,6,1,2,3,8,4,7]=>[5,6,1,2,3,8,4,7]=>[4,5,7,1,2,8,6,-3]
[7,2,4,8,5,1,3,6]=>[5,8,2,1,7,3,4,6]=>[5,8,2,1,7,3,4,6]=>[3,6,7,1,8,5,2,-4]
[6,1,3,8,4,7,2,5]=>[6,7,1,8,2,3,4,5]=>[6,7,1,8,2,3,4,5]=>[5,6,7,8,1,2,4,-3]
[8,2,4,7,5,1,3,6]=>[5,7,2,1,8,3,4,6]=>[5,7,2,1,8,3,4,6]=>[3,6,7,1,8,2,5,-4]
[6,4,1,3,5,7,2,8]=>[4,6,2,7,3,5,1,8]=>[4,6,2,7,3,5,1,8]=>[3,5,1,6,2,4,8,-7]
[5,7,8,1,2,4,3,6]=>[8,1,4,2,5,3,7,6]=>[8,1,4,2,5,3,7,6]=>[4,6,3,5,8,7,1,-2]
[6,5,1,2,4,3,8,7]=>[5,1,4,2,6,3,8,7]=>[5,1,4,2,6,3,8,7]=>[4,6,3,1,5,8,7,-2]
[2,5,1,4,6,3,8,7]=>[5,2,6,1,4,3,8,7]=>[5,2,6,1,4,3,8,7]=>[2,6,5,1,3,8,7,-4]
[2,6,3,8,7,1,4,5]=>[7,2,6,1,4,3,8,5]=>[7,2,6,1,4,3,8,5]=>[2,6,5,8,3,1,7,-4]
[5,8,7,3,1,2,4,6]=>[3,1,7,2,5,4,8,6]=>[3,1,7,2,5,4,8,6]=>[4,1,6,5,8,3,7,-2]
[2,7,8,1,4,5,3,6]=>[8,2,5,1,4,3,7,6]=>[8,2,5,1,4,3,7,6]=>[2,6,5,3,8,7,1,-4]
[4,3,7,1,2,6,8,5]=>[7,1,4,3,8,2,6,5]=>[7,1,4,3,8,2,6,5]=>[6,4,3,8,7,1,5,-2]
[4,1,2,8,7,3,6,5]=>[4,1,7,2,6,3,8,5]=>[4,1,7,2,6,3,8,5]=>[4,6,1,8,5,3,7,-2]
[2,5,6,3,8,7,1,4]=>[7,2,6,1,5,3,8,4]=>[7,2,6,1,5,3,8,4]=>[2,6,8,5,3,1,7,-4]
[8,7,5,1,2,4,3,6]=>[5,1,4,2,7,3,8,6]=>[5,1,4,2,7,3,8,6]=>[4,6,3,1,8,5,7,-2]
[6,1,2,4,3,8,7,5]=>[6,1,4,2,7,3,8,5]=>[6,1,4,2,7,3,8,5]=>[4,6,3,8,1,5,7,-2]
[3,7,8,1,2,4,6,5]=>[8,1,3,2,6,4,7,5]=>[8,1,3,2,6,4,7,5]=>[4,3,6,8,5,7,1,-2]
[7,8,5,1,2,4,3,6]=>[5,1,4,2,8,3,7,6]=>[5,1,4,2,8,3,7,6]=>[4,6,3,1,8,7,5,-2]
[5,7,3,2,6,8,1,4]=>[8,3,7,1,5,2,6,4]=>[8,3,7,1,5,2,6,4]=>[6,2,8,5,7,3,1,-4]
[8,3,4,1,2,6,7,5]=>[4,1,8,3,7,2,6,5]=>[4,1,8,3,7,2,6,5]=>[6,4,1,8,7,5,3,-2]
[2,1,4,7,3,6,8,5]=>[2,1,7,4,8,3,6,5]=>[2,1,7,4,8,3,6,5]=>[1,6,4,8,7,3,5,-2]
[7,3,4,1,2,6,8,5]=>[4,1,7,3,8,2,6,5]=>[4,1,7,3,8,2,6,5]=>[6,4,1,8,7,3,5,-2]
[8,6,2,3,5,4,1,7]=>[4,5,1,6,3,8,2,7]=>[4,5,1,6,3,8,2,7]=>[7,5,1,2,4,8,6,-3]
[8,4,7,2,3,6,5,1]=>[5,6,1,7,8,4,3,2]=>[5,6,1,7,8,4,3,2]=>[8,7,6,1,2,4,5,-3]
[3,8,1,7,2,5,4,6]=>[8,7,3,5,2,4,1,6]=>[8,7,3,5,2,4,1,6]=>[5,3,6,4,8,2,1,-7]
[4,5,1,6,8,3,7,2]=>[5,7,8,4,1,6,3,2]=>[5,7,8,4,1,6,3,2]=>[8,7,4,1,6,2,3,-5]
[1,8,5,7,6,4,2,3]=>[1,4,2,6,7,8,3,5]=>[1,4,2,6,7,8,3,5]=>[3,7,2,8,4,5,6,-1]
[3,6,5,1,7,8,2,4]=>[5,6,3,1,8,2,7,4]=>[5,6,3,1,8,2,7,4]=>[6,3,8,1,2,7,5,-4]
[1,2,7,6,8,5,3,4]=>[1,2,5,3,8,7,6,4]=>[1,2,5,3,8,7,6,4]=>[2,4,8,3,7,6,5,-1]
[8,5,4,2,1,6,7,3]=>[2,4,5,8,7,1,6,3]=>[2,4,5,8,7,1,6,3]=>[1,8,2,3,7,5,4,-6]
[8,3,4,6,7,5,1,2]=>[5,1,7,2,8,4,6,3]=>[5,1,7,2,8,4,6,3]=>[4,8,6,1,7,3,5,-2]
[4,2,5,3,7,8,1,6]=>[8,4,5,2,3,1,7,6]=>[8,4,5,2,3,1,7,6]=>[4,5,2,3,8,7,1,-6]
[3,5,4,1,6,2,8,7]=>[4,5,3,6,2,1,8,7]=>[4,5,3,6,2,1,8,7]=>[5,3,1,2,4,8,7,-6]
[4,5,7,6,1,3,8,2]=>[6,7,2,4,5,8,3,1]=>[6,7,2,4,5,8,3,1]=>[3,7,4,5,1,2,6,-8]
[4,5,7,2,8,3,1,6]=>[3,8,7,4,5,2,1,6]=>[3,8,7,4,5,2,1,6]=>[6,1,4,5,8,3,2,-7]
[2,1,5,7,6,3,8,4]=>[2,1,6,7,5,8,4,3]=>[2,1,6,7,5,8,4,3]=>[1,8,7,5,3,4,6,-2]
[3,5,1,7,6,2,8,4]=>[5,6,3,7,1,8,4,2]=>[5,6,3,7,1,8,4,2]=>[8,3,7,1,2,4,6,-5]
[4,6,7,5,1,2,8,3]=>[5,1,7,4,8,6,3,2]=>[5,1,7,4,8,6,3,2]=>[8,7,4,1,6,3,5,-2]
[4,6,7,3,1,8,2,5]=>[3,7,8,4,1,6,2,5]=>[3,7,8,4,1,6,2,5]=>[7,1,4,8,6,2,3,-5]
[4,6,7,5,1,8,2,3]=>[5,7,1,4,8,6,2,3]=>[5,7,1,4,8,6,2,3]=>[7,8,4,1,6,2,5,-3]
[8,1,2,4,6,3,7,5]=>[8,1,6,2,7,4,3,5]=>[8,1,6,2,7,4,3,5]=>[4,7,6,8,3,5,1,-2]
[1,8,4,7,5,2,3,6]=>[1,5,2,7,8,4,3,6]=>[1,5,2,7,8,4,3,6]=>[3,7,6,2,8,4,5,-1]
[8,2,1,3,6,7,4,5]=>[2,8,1,7,4,3,6,5]=>[2,8,1,7,4,3,6,5]=>[1,6,5,8,7,4,2,-3]
[7,4,3,1,5,8,2,6]=>[3,4,7,8,1,2,5,6]=>[3,4,7,8,1,2,5,6]=>[6,1,2,7,8,3,4,-5]
[4,5,1,6,8,2,7,3]=>[5,8,7,4,1,6,2,3]=>[5,8,7,4,1,6,2,3]=>[7,8,4,1,6,3,2,-5]
[5,4,1,2,8,6,3,7]=>[4,1,5,6,3,8,2,7]=>[4,1,5,6,3,8,2,7]=>[7,5,1,3,4,8,6,-2]
[7,3,4,6,2,5,1,8]=>[5,6,7,3,2,4,1,8]=>[5,6,7,3,2,4,1,8]=>[5,4,6,1,2,3,8,-7]
[2,4,7,8,5,3,1,6]=>[3,2,5,4,8,1,7,6]=>[3,2,5,4,8,1,7,6]=>[2,1,4,3,8,7,5,-6]
[3,8,2,6,4,1,5,7]=>[4,6,3,8,2,1,5,7]=>[4,6,3,8,2,1,5,7]=>[5,3,1,7,2,8,4,-6]
[6,2,5,1,7,8,3,4]=>[5,6,8,3,2,1,7,4]=>[5,6,8,3,2,1,7,4]=>[5,4,8,1,2,7,3,-6]
[5,1,7,3,6,4,2,8]=>[5,4,6,7,1,2,3,8]=>[5,4,6,7,1,2,3,8]=>[6,7,2,1,3,4,8,-5]
[7,2,8,5,6,3,1,4]=>[3,6,7,2,8,5,1,4]=>[3,6,7,2,8,5,1,4]=>[4,1,8,6,2,3,5,-7]
[5,2,4,8,3,7,1,6]=>[7,5,8,2,4,1,3,6]=>[7,5,8,2,4,1,3,6]=>[4,7,5,2,8,1,3,-6]
[2,5,3,6,8,1,4,7]=>[8,2,5,1,3,6,4,7]=>[8,2,5,1,3,6,4,7]=>[2,5,7,3,6,8,1,-4]
[5,1,8,3,4,7,6,2]=>[5,6,7,2,1,8,4,3]=>[5,6,7,2,1,8,4,3]=>[4,8,7,1,2,3,6,-5]
[6,1,4,3,7,2,8,5]=>[6,7,4,1,8,3,2,5]=>[6,7,4,1,8,3,2,5]=>[7,6,3,8,1,2,5,-4]
[7,3,4,6,5,8,1,2]=>[8,1,7,3,6,4,5,2]=>[8,1,7,3,6,4,5,2]=>[8,4,6,7,5,3,1,-2]
[7,3,6,5,8,1,2,4]=>[8,1,7,2,6,3,5,4]=>[8,1,7,2,6,3,5,4]=>[4,6,8,7,5,3,1,-2]
[4,2,8,1,6,5,7,3]=>[8,4,7,2,6,1,5,3]=>[8,4,7,2,6,1,5,3]=>[4,8,2,7,5,3,1,-6]
[7,3,5,2,6,8,1,4]=>[8,5,7,1,3,2,6,4]=>[8,5,7,1,3,2,6,4]=>[6,5,8,2,7,3,1,-4]
[3,4,7,5,2,8,6,1]=>[6,5,3,4,8,7,1,2]=>[6,5,3,4,8,7,1,2]=>[8,3,4,2,1,6,5,-7]
[8,5,7,3,2,6,4,1]=>[4,3,6,7,8,1,5,2]=>[4,3,6,7,8,1,5,2]=>[8,2,1,7,3,4,5,-6]
[1,3,8,5,2,4,6,7]=>[1,5,3,2,8,4,6,7]=>[1,5,3,2,8,4,6,7]=>[4,3,6,2,7,8,5,-1]
[2,7,3,5,1,4,8,6]=>[5,2,7,1,3,8,4,6]=>[5,2,7,1,3,8,4,6]=>[2,5,7,1,8,3,6,-4]
[6,1,3,2,8,5,7,4]=>[6,3,1,7,8,2,5,4]=>[6,3,1,7,8,2,5,4]=>[6,2,8,7,1,4,5,-3]
[8,1,4,3,5,2,7,6]=>[8,5,4,1,3,7,2,6]=>[8,5,4,1,3,7,2,6]=>[7,5,3,2,8,6,1,-4]
[1,5,6,2,3,8,7,4]=>[1,6,2,7,5,3,8,4]=>[1,6,2,7,5,3,8,4]=>[3,6,8,5,2,4,7,-1]
[7,2,3,6,8,5,1,4]=>[5,8,1,2,7,3,6,4]=>[5,8,1,2,7,3,6,4]=>[4,6,8,1,7,5,2,-3]
[2,6,3,1,7,8,4,5]=>[3,2,6,8,4,1,7,5]=>[3,2,6,8,4,1,7,5]=>[2,1,5,8,3,7,4,-6]
[4,7,1,3,8,6,2,5]=>[7,6,1,4,2,8,3,5]=>[7,6,1,4,2,8,3,5]=>[5,7,4,8,2,1,6,-3]
[2,8,4,7,3,1,5,6]=>[3,2,7,8,1,5,4,6]=>[3,2,7,8,1,5,4,6]=>[2,1,7,6,8,3,4,-5]
[1,7,4,2,3,8,5,6]=>[1,4,2,7,8,5,3,6]=>[1,4,2,7,8,5,3,6]=>[3,7,2,6,8,4,5,-1]
[5,8,6,1,4,2,3,7]=>[6,4,2,1,5,8,3,7]=>[6,4,2,1,5,8,3,7]=>[3,7,2,5,1,8,6,-4]
[1,8,3,4,7,5,2,6]=>[1,5,7,2,8,3,4,6]=>[1,5,7,2,8,3,4,6]=>[4,6,7,2,8,3,5,-1]
[7,2,4,6,5,1,8,3]=>[5,6,7,3,8,4,2,1]=>[5,6,7,3,8,4,2,1]=>[7,4,6,1,2,3,5,-8]
[5,2,8,6,3,4,1,7]=>[4,5,6,3,2,8,1,7]=>[4,5,6,3,2,8,1,7]=>[5,4,1,2,3,8,6,-7]
[5,2,4,6,7,1,8,3]=>[7,5,8,2,4,6,1,3]=>[7,5,8,2,4,6,1,3]=>[4,8,5,2,6,1,3,-7]
[8,3,4,6,1,5,7,2]=>[6,7,8,3,1,4,5,2]=>[6,7,8,3,1,4,5,2]=>[8,4,6,7,1,2,3,-5]
[8,4,5,6,1,7,2,3]=>[6,7,2,8,4,5,1,3]=>[6,7,2,8,4,5,1,3]=>[3,8,5,6,1,2,4,-7]
[6,2,3,5,1,8,7,4]=>[5,6,2,7,3,1,8,4]=>[5,6,2,7,3,1,8,4]=>[3,5,8,1,2,4,7,-6]
[7,1,5,4,2,3,8,6]=>[7,4,2,5,1,8,3,6]=>[7,4,2,5,1,8,3,6]=>[3,7,2,4,8,1,6,-5]
[3,6,7,2,5,1,8,4]=>[5,7,3,8,2,6,1,4]=>[5,7,3,8,2,6,1,4]=>[5,3,8,1,6,2,4,-7]
[5,3,4,6,1,2,8,7]=>[6,1,5,3,4,2,8,7]=>[6,1,5,3,4,2,8,7]=>[6,4,5,3,1,8,7,-2]
[3,6,2,5,7,8,4,1]=>[4,8,3,6,1,5,7,2]=>[4,8,3,6,1,5,7,2]=>[8,3,1,6,4,7,2,-5]
[6,5,8,1,4,3,7,2]=>[8,7,4,1,6,5,3,2]=>[8,7,4,1,6,5,3,2]=>[8,7,3,6,5,2,1,-4]
[3,8,1,6,4,7,5,2]=>[8,5,3,7,6,1,2,4]=>[8,5,3,7,6,1,2,4]=>[7,3,8,2,5,4,1,-6]
[7,2,8,3,5,6,4,1]=>[4,6,7,8,1,5,3,2]=>[4,6,7,8,1,5,3,2]=>[8,7,1,6,2,3,4,-5]
[7,3,6,4,5,1,8,2]=>[5,8,7,6,4,3,1,2]=>[5,8,7,6,4,3,1,2]=>[8,6,5,1,4,3,2,-7]
[1,8,7,5,4,2,3,6]=>[1,4,2,5,7,3,8,6]=>[1,4,2,5,7,3,8,6]=>[3,6,2,4,8,5,7,-1]
[1,2,4,8,5,7,3,6]=>[1,2,7,4,8,3,5,6]=>[1,2,7,4,8,3,5,6]=>[2,6,4,7,8,3,5,-1]
[7,1,2,3,8,4,6,5]=>[7,1,2,8,6,4,3,5]=>[7,1,2,8,6,4,3,5]=>[3,7,6,8,5,1,4,-2]
[3,7,8,2,5,1,6,4]=>[5,8,3,6,2,1,7,4]=>[5,8,3,6,2,1,7,4]=>[5,3,8,1,4,7,2,-6]
[4,6,8,5,1,2,7,3]=>[5,1,8,4,7,6,3,2]=>[5,1,8,4,7,6,3,2]=>[8,7,4,1,6,5,3,-2]
[6,7,3,1,8,2,4,5]=>[3,7,8,1,4,6,2,5]=>[3,7,8,1,4,6,2,5]=>[7,1,5,8,6,2,3,-4]
[8,1,4,2,6,5,7,3]=>[8,4,7,1,6,2,5,3]=>[8,4,7,1,6,2,5,3]=>[6,8,2,7,5,3,1,-4]
[7,8,3,5,1,6,2,4]=>[5,6,8,2,3,1,7,4]=>[5,6,8,2,3,1,7,4]=>[4,5,8,1,2,7,3,-6]
[4,8,5,1,2,3,6,7]=>[5,1,2,4,8,3,6,7]=>[5,1,2,4,8,3,6,7]=>[3,6,4,1,7,8,5,-2]
[2,8,1,4,6,5,7,3]=>[8,2,7,1,6,4,5,3]=>[8,2,7,1,6,4,5,3]=>[2,8,6,7,5,3,1,-4]
[7,6,2,8,4,5,1,3]=>[5,6,1,7,2,8,4,3]=>[5,6,1,7,2,8,4,3]=>[5,8,7,1,2,4,6,-3]
[4,5,1,7,2,6,8,3]=>[5,7,8,4,1,2,6,3]=>[5,7,8,4,1,2,6,3]=>[6,8,4,1,7,2,3,-5]
[7,3,4,1,8,2,6,5]=>[4,8,7,3,6,2,1,5]=>[4,8,7,3,6,2,1,5]=>[6,4,1,8,5,3,2,-7]
[7,4,1,3,6,8,2,5]=>[4,7,2,8,1,3,6,5]=>[4,7,2,8,1,3,6,5]=>[3,6,1,8,7,2,4,-5]
[8,1,2,6,5,7,3,4]=>[8,1,7,3,6,2,5,4]=>[8,1,7,3,6,2,5,4]=>[6,4,8,7,5,3,1,-2]
[5,7,3,6,2,4,8,1]=>[8,6,7,2,5,3,4,1]=>[8,6,7,2,5,3,4,1]=>[4,6,7,5,2,3,1,-8]
[5,3,4,7,8,1,2,6]=>[8,1,5,3,4,2,7,6]=>[8,1,5,3,4,2,7,6]=>[6,4,5,3,8,7,1,-2]
[5,7,2,6,1,4,8,3]=>[6,7,8,1,5,2,4,3]=>[6,7,8,1,5,2,4,3]=>[6,8,7,5,1,2,3,-4]
[3,7,5,6,8,1,2,4]=>[8,1,3,2,7,5,6,4]=>[8,1,3,2,7,5,6,4]=>[4,3,8,6,7,5,1,-2]
[4,5,8,1,7,3,2,6]=>[8,3,7,4,5,2,1,6]=>[8,3,7,4,5,2,1,6]=>[6,2,4,5,8,3,1,-7]
[7,4,3,6,8,5,2,1]=>[2,5,4,8,7,1,6,3]=>[2,5,4,8,7,1,6,3]=>[1,8,3,2,7,5,4,-6]
[2,8,1,6,5,7,3,4]=>[8,2,7,3,6,1,5,4]=>[8,2,7,3,6,1,5,4]=>[2,4,8,7,5,3,1,-6]
[6,5,1,4,7,2,8,3]=>[5,6,7,2,8,4,3,1]=>[5,6,7,2,8,4,3,1]=>[4,7,6,1,2,3,5,-8]
[1,2,4,8,3,7,5,6]=>[1,2,8,4,7,5,3,6]=>[1,2,8,4,7,5,3,6]=>[2,7,4,6,8,5,3,-1]
[7,3,4,8,5,1,2,6]=>[5,1,8,2,7,3,4,6]=>[5,1,8,2,7,3,4,6]=>[4,6,7,1,8,5,3,-2]
[7,3,2,6,5,8,1,4]=>[8,3,7,1,6,2,5,4]=>[8,3,7,1,6,2,5,4]=>[6,2,8,7,5,3,1,-4]
[7,8,5,1,2,6,3,4]=>[5,1,8,2,6,3,7,4]=>[5,1,8,2,6,3,7,4]=>[4,6,8,1,5,7,3,-2]
[8,3,6,7,5,1,2,4]=>[5,1,7,3,8,2,6,4]=>[5,1,7,3,8,2,6,4]=>[6,4,8,1,7,3,5,-2]
[7,2,8,4,6,5,3,1]=>[3,5,6,7,8,2,4,1]=>[3,5,6,7,8,2,4,1]=>[6,1,7,2,3,4,5,-8]
[6,1,4,7,2,5,8,3]=>[6,7,8,1,2,4,5,3]=>[6,7,8,1,2,4,5,3]=>[5,8,6,7,1,2,3,-4]
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
Map
to signed permutation
Description
The signed permutation with all signs positive.
Map
inverse Kreweras complement
Description
The inverse Kreweras complement of a signed permutation.
This is the signed permutation $c \pi^{-1}$ where $c = (1,\ldots,n,-1,-2,\dots,-n)$ is the long cycle.
The order of the inverse Kreweras complement on signed permutations of $\{\pm 1,\dots, \pm n\}$ is $2n$.
This is the signed permutation $c \pi^{-1}$ where $c = (1,\ldots,n,-1,-2,\dots,-n)$ is the long cycle.
The order of the inverse Kreweras complement on signed permutations of $\{\pm 1,\dots, \pm n\}$ is $2n$.
searching the database
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