Identifier
Mp00237:
Permutations
—descent views to invisible inversion bottoms⟶
Permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00190: Signed permutations —Foata-Han⟶ Signed permutations
Mp00170: Permutations —to signed permutation⟶ Signed permutations
Mp00190: Signed permutations —Foata-Han⟶ Signed permutations
Images
=>
[1]=>[1]=>[1]=>[1]
[1,2]=>[1,2]=>[1,2]=>[1,2]
[2,1]=>[2,1]=>[2,1]=>[-2,1]
[1,2,3]=>[1,2,3]=>[1,2,3]=>[1,2,3]
[1,3,2]=>[1,3,2]=>[1,3,2]=>[1,-3,2]
[2,1,3]=>[2,1,3]=>[2,1,3]=>[-2,1,3]
[2,3,1]=>[3,2,1]=>[3,2,1]=>[-2,-3,1]
[3,1,2]=>[3,1,2]=>[3,1,2]=>[3,1,2]
[3,2,1]=>[2,3,1]=>[2,3,1]=>[3,-2,1]
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>[1,2,-4,3]
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>[1,-3,2,4]
[1,3,4,2]=>[1,4,3,2]=>[1,4,3,2]=>[1,-3,-4,2]
[1,4,2,3]=>[1,4,2,3]=>[1,4,2,3]=>[-4,1,2,3]
[1,4,3,2]=>[1,3,4,2]=>[1,3,4,2]=>[1,4,-3,2]
[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>[-2,1,3,4]
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>[-2,1,-4,3]
[2,3,1,4]=>[3,2,1,4]=>[3,2,1,4]=>[-2,-3,1,4]
[2,3,4,1]=>[4,2,3,1]=>[4,2,3,1]=>[2,3,-4,1]
[2,4,1,3]=>[4,2,1,3]=>[4,2,1,3]=>[-4,-2,1,3]
[2,4,3,1]=>[3,2,4,1]=>[3,2,4,1]=>[-2,4,-3,1]
[3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]
[3,1,4,2]=>[3,4,1,2]=>[3,4,1,2]=>[3,4,1,2]
[3,2,1,4]=>[2,3,1,4]=>[2,3,1,4]=>[3,-2,1,4]
[3,2,4,1]=>[4,3,2,1]=>[4,3,2,1]=>[-2,-3,-4,1]
[3,4,1,2]=>[4,1,3,2]=>[4,1,3,2]=>[3,1,-4,2]
[3,4,2,1]=>[2,4,3,1]=>[2,4,3,1]=>[3,-2,-4,1]
[4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]=>[1,4,2,3]
[4,1,3,2]=>[4,3,1,2]=>[4,3,1,2]=>[-4,3,1,2]
[4,2,1,3]=>[2,4,1,3]=>[2,4,1,3]=>[-2,4,1,3]
[4,2,3,1]=>[3,4,2,1]=>[3,4,2,1]=>[2,-4,-3,1]
[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]=>[3,4,-2,1]
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,-5,4]
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,-4,3,5]
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[1,2,-4,-5,3]
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[1,-5,2,3,4]
[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,4,5,3]=>[1,2,5,-4,3]
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[1,-3,2,4,5]
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[1,-3,2,-5,4]
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[1,-3,-4,2,5]
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,5,3,4,2]=>[-3,1,4,-5,2]
[1,3,5,2,4]=>[1,5,3,2,4]=>[1,5,3,2,4]=>[1,-5,-3,2,4]
[1,3,5,4,2]=>[1,4,3,5,2]=>[1,4,3,5,2]=>[1,-3,5,-4,2]
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[-4,1,2,3,5]
[1,4,2,5,3]=>[1,4,5,2,3]=>[1,4,5,2,3]=>[-4,1,5,2,3]
[1,4,3,2,5]=>[1,3,4,2,5]=>[1,3,4,2,5]=>[1,4,-3,2,5]
[1,4,3,5,2]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[1,-3,-4,-5,2]
[1,4,5,2,3]=>[1,5,2,4,3]=>[1,5,2,4,3]=>[-4,1,2,-5,3]
[1,4,5,3,2]=>[1,3,5,4,2]=>[1,3,5,4,2]=>[1,4,-3,-5,2]
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[5,1,2,3,4]
[1,5,2,4,3]=>[1,5,4,2,3]=>[1,5,4,2,3]=>[-4,-5,1,2,3]
[1,5,3,2,4]=>[1,3,5,2,4]=>[1,3,5,2,4]=>[1,-3,5,2,4]
[1,5,3,4,2]=>[1,4,5,3,2]=>[1,4,5,3,2]=>[1,3,-5,-4,2]
[1,5,4,2,3]=>[1,4,2,5,3]=>[1,4,2,5,3]=>[1,-5,2,-4,3]
[1,5,4,3,2]=>[1,3,4,5,2]=>[1,3,4,5,2]=>[1,4,5,-3,2]
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[-2,1,3,4,5]
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[-2,1,3,-5,4]
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[-2,1,-4,3,5]
[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[-2,1,-4,-5,3]
[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[-2,-5,1,3,4]
[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,4,5,3]=>[-2,1,5,-4,3]
[2,3,1,4,5]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[-2,-3,1,4,5]
[2,3,1,5,4]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[-2,-3,1,-5,4]
[2,3,4,1,5]=>[4,2,3,1,5]=>[4,2,3,1,5]=>[2,3,-4,1,5]
[2,3,4,5,1]=>[5,2,3,4,1]=>[5,2,3,4,1]=>[5,3,4,-2,1]
[2,3,5,1,4]=>[5,2,3,1,4]=>[5,2,3,1,4]=>[2,-5,3,1,4]
[2,3,5,4,1]=>[4,2,3,5,1]=>[4,2,3,5,1]=>[2,3,5,-4,1]
[2,4,1,3,5]=>[4,2,1,3,5]=>[4,2,1,3,5]=>[-4,-2,1,3,5]
[2,4,1,5,3]=>[4,2,5,1,3]=>[4,2,5,1,3]=>[-4,-2,5,1,3]
[2,4,3,1,5]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[-2,4,-3,1,5]
[2,4,3,5,1]=>[5,2,4,3,1]=>[5,2,4,3,1]=>[2,3,-4,-5,1]
[2,4,5,1,3]=>[5,2,1,4,3]=>[5,2,1,4,3]=>[-4,-2,1,-5,3]
[2,4,5,3,1]=>[3,2,5,4,1]=>[3,2,5,4,1]=>[-2,4,-3,-5,1]
[2,5,1,3,4]=>[5,2,1,3,4]=>[5,2,1,3,4]=>[5,-2,1,3,4]
[2,5,1,4,3]=>[5,2,4,1,3]=>[5,2,4,1,3]=>[-5,2,4,1,3]
[2,5,3,1,4]=>[3,2,5,1,4]=>[3,2,5,1,4]=>[-2,-3,5,1,4]
[2,5,3,4,1]=>[4,2,5,3,1]=>[4,2,5,3,1]=>[-2,3,-5,-4,1]
[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]=>[-2,4,5,-3,1]
[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]
[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,2,-5,4]
[3,1,4,2,5]=>[3,4,1,2,5]=>[3,4,1,2,5]=>[3,4,1,2,5]
[3,1,4,5,2]=>[3,5,1,4,2]=>[3,5,1,4,2]=>[-5,4,1,-3,2]
[3,1,5,2,4]=>[3,5,1,2,4]=>[3,5,1,2,4]=>[3,1,5,2,4]
[3,1,5,4,2]=>[3,4,1,5,2]=>[3,4,1,5,2]=>[5,-4,1,-3,2]
[3,2,1,4,5]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[3,-2,1,4,5]
[3,2,1,5,4]=>[2,3,1,5,4]=>[2,3,1,5,4]=>[3,-2,1,-5,4]
[3,2,4,1,5]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[-2,-3,-4,1,5]
[3,2,4,5,1]=>[5,3,2,4,1]=>[5,3,2,4,1]=>[-2,-5,4,-3,1]
[3,2,5,1,4]=>[5,3,2,1,4]=>[5,3,2,1,4]=>[-2,-5,-3,1,4]
[3,2,5,4,1]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[-2,-3,5,-4,1]
[3,4,1,2,5]=>[4,1,3,2,5]=>[4,1,3,2,5]=>[3,1,-4,2,5]
[3,4,1,5,2]=>[4,5,3,1,2]=>[4,5,3,1,2]=>[5,-4,3,1,2]
[3,4,2,1,5]=>[2,4,3,1,5]=>[2,4,3,1,5]=>[3,-2,-4,1,5]
[3,4,2,5,1]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[-2,-3,-4,-5,1]
[3,4,5,1,2]=>[5,1,3,4,2]=>[5,1,3,4,2]=>[1,3,4,-5,2]
[3,4,5,2,1]=>[2,5,3,4,1]=>[2,5,3,4,1]=>[-2,3,4,-5,1]
[3,5,1,2,4]=>[5,1,3,2,4]=>[5,1,3,2,4]=>[3,-5,1,2,4]
[3,5,1,4,2]=>[5,4,3,1,2]=>[5,4,3,1,2]=>[-4,-5,3,1,2]
[3,5,2,1,4]=>[2,5,3,1,4]=>[2,5,3,1,4]=>[3,-5,-2,1,4]
[3,5,2,4,1]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[2,-3,-5,-4,1]
[3,5,4,1,2]=>[4,1,3,5,2]=>[4,1,3,5,2]=>[3,1,5,-4,2]
[3,5,4,2,1]=>[2,4,3,5,1]=>[2,4,3,5,1]=>[3,-2,5,-4,1]
[4,1,2,3,5]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[1,4,2,3,5]
[4,1,2,5,3]=>[4,1,5,2,3]=>[4,1,5,2,3]=>[5,-4,1,2,3]
[4,1,3,2,5]=>[4,3,1,2,5]=>[4,3,1,2,5]=>[-4,3,1,2,5]
[4,1,3,5,2]=>[4,5,1,3,2]=>[4,5,1,3,2]=>[5,3,1,-4,2]
[4,1,5,2,3]=>[4,5,2,1,3]=>[4,5,2,1,3]=>[-5,-4,2,1,3]
[4,1,5,3,2]=>[4,3,5,1,2]=>[4,3,5,1,2]=>[-4,3,5,1,2]
[4,2,1,3,5]=>[2,4,1,3,5]=>[2,4,1,3,5]=>[-2,4,1,3,5]
[4,2,1,5,3]=>[2,4,5,1,3]=>[2,4,5,1,3]=>[-2,4,5,1,3]
[4,2,3,1,5]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[2,-4,-3,1,5]
[4,2,3,5,1]=>[5,4,2,3,1]=>[5,4,2,3,1]=>[-4,2,3,-5,1]
[4,2,5,1,3]=>[5,4,1,2,3]=>[5,4,1,2,3]=>[5,1,4,2,3]
[4,2,5,3,1]=>[3,5,4,1,2]=>[3,5,4,1,2]=>[3,-5,4,1,2]
[4,3,1,2,5]=>[3,1,4,2,5]=>[3,1,4,2,5]=>[-4,1,-3,2,5]
[4,3,1,5,2]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[5,2,-4,-3,1]
[4,3,2,1,5]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[3,4,-2,1,5]
[4,3,2,5,1]=>[5,3,4,2,1]=>[5,3,4,2,1]=>[4,2,-3,-5,1]
[4,3,5,1,2]=>[5,1,4,3,2]=>[5,1,4,3,2]=>[3,1,-4,-5,2]
[4,3,5,2,1]=>[2,5,4,3,1]=>[2,5,4,3,1]=>[3,-2,-4,-5,1]
[4,5,1,2,3]=>[5,1,2,4,3]=>[5,1,2,4,3]=>[1,4,2,-5,3]
[4,5,1,3,2]=>[5,3,1,4,2]=>[5,3,1,4,2]=>[-4,-5,1,-3,2]
[4,5,2,1,3]=>[2,5,1,4,3]=>[2,5,1,4,3]=>[-2,4,1,-5,3]
[4,5,2,3,1]=>[3,5,2,4,1]=>[3,5,2,4,1]=>[-5,2,4,-3,1]
[4,5,3,1,2]=>[3,1,5,4,2]=>[3,1,5,4,2]=>[-4,1,-3,-5,2]
[4,5,3,2,1]=>[2,3,5,4,1]=>[2,3,5,4,1]=>[3,4,-2,-5,1]
[5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[1,2,5,3,4]
[5,1,2,4,3]=>[5,1,4,2,3]=>[5,1,4,2,3]=>[1,-5,4,2,3]
[5,1,3,2,4]=>[5,3,1,2,4]=>[5,3,1,2,4]=>[5,3,1,2,4]
[5,1,3,4,2]=>[5,4,1,3,2]=>[5,4,1,3,2]=>[-4,3,1,-5,2]
[5,1,4,2,3]=>[5,4,2,1,3]=>[5,4,2,1,3]=>[-4,-5,-2,1,3]
[5,1,4,3,2]=>[5,3,4,1,2]=>[5,3,4,1,2]=>[5,3,4,1,2]
[5,2,1,3,4]=>[2,5,1,3,4]=>[2,5,1,3,4]=>[-2,1,5,3,4]
[5,2,1,4,3]=>[2,5,4,1,3]=>[2,5,4,1,3]=>[-2,-5,4,1,3]
[5,2,3,1,4]=>[3,5,2,1,4]=>[3,5,2,1,4]=>[-5,2,-3,1,4]
[5,2,3,4,1]=>[4,5,2,3,1]=>[4,5,2,3,1]=>[5,2,3,-4,1]
[5,2,4,1,3]=>[4,5,1,2,3]=>[4,5,1,2,3]=>[1,4,5,2,3]
[5,2,4,3,1]=>[3,4,5,1,2]=>[3,4,5,1,2]=>[3,4,5,1,2]
[5,3,1,2,4]=>[3,1,5,2,4]=>[3,1,5,2,4]=>[5,1,-3,2,4]
[5,3,1,4,2]=>[3,5,4,2,1]=>[3,5,4,2,1]=>[2,-4,-3,-5,1]
[5,3,2,1,4]=>[2,3,5,1,4]=>[2,3,5,1,4]=>[3,-2,5,1,4]
[5,3,2,4,1]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[-5,2,-3,-4,1]
[5,3,4,1,2]=>[4,1,5,3,2]=>[4,1,5,3,2]=>[-3,1,-5,-4,2]
[5,3,4,2,1]=>[2,4,5,3,1]=>[2,4,5,3,1]=>[5,3,-2,-4,1]
[5,4,1,2,3]=>[4,1,2,5,3]=>[4,1,2,5,3]=>[5,1,2,-4,3]
[5,4,1,3,2]=>[4,3,1,5,2]=>[4,3,1,5,2]=>[-5,-3,1,-4,2]
[5,4,2,1,3]=>[2,4,1,5,3]=>[2,4,1,5,3]=>[5,-2,1,-4,3]
[5,4,2,3,1]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[2,-4,5,-3,1]
[5,4,3,1,2]=>[3,1,4,5,2]=>[3,1,4,5,2]=>[-4,1,5,-3,2]
[5,4,3,2,1]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[3,4,5,-2,1]
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,-6,5]
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,-5,4,6]
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[1,2,3,-5,-6,4]
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,-6,3,4,5]
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,5,6,4]=>[1,2,3,6,-5,4]
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,-4,3,5,6]
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,-4,3,-6,5]
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[1,2,-4,-5,3,6]
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,6,4,5,3]=>[1,-4,2,5,-6,3]
[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[1,2,5,4,6,3]=>[1,2,-4,6,-5,3]
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,-5,2,3,4,6]
[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[1,2,5,6,3,4]=>[1,-5,2,6,3,4]
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>[1,2,5,-4,3,6]
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[1,2,-4,-5,-6,3]
[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[1,2,4,6,5,3]=>[1,2,5,-4,-6,3]
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[-6,1,2,3,4,5]
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>[1,2,-4,6,3,5]
[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>[1,2,5,6,4,3]=>[1,2,4,-6,-5,3]
[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[1,2,5,3,6,4]=>[1,2,-6,3,-5,4]
[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[1,2,4,5,6,3]=>[1,2,5,6,-4,3]
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,-3,2,4,5,6]
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,-3,2,4,-6,5]
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,-3,2,-5,4,6]
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[1,-3,2,-5,-6,4]
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,-3,-6,2,4,5]
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,5,6,4]=>[1,-3,2,6,-5,4]
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[1,-3,-4,2,5,6]
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[1,-3,-4,2,-6,5]
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,5,3,4,2,6]=>[-3,1,4,-5,2,6]
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,6,3,4,5,2]=>[3,1,4,5,-6,2]
[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[1,5,3,4,6,2]=>[-3,1,4,6,-5,2]
[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[1,5,3,6,2,4]=>[1,-5,-3,6,2,4]
[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[1,4,3,5,2,6]=>[1,-3,5,-4,2,6]
[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[1,6,3,5,4,2]=>[-3,1,4,-5,-6,2]
[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[1,4,3,6,5,2]=>[1,-3,5,-4,-6,2]
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,6,3,2,4,5]=>[-6,1,-3,2,4,5]
[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>[1,4,3,6,2,5]=>[1,-3,-4,6,2,5]
[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[1,4,3,5,6,2]=>[1,-3,5,6,-4,2]
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[-4,1,2,3,5,6]
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[-4,1,2,3,-6,5]
[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>[-4,1,5,2,3,6]
[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>[1,-6,5,2,-4,3]
[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>[-4,1,2,6,3,5]
[1,4,2,6,5,3]=>[1,4,5,2,6,3]=>[1,4,5,2,6,3]=>[1,6,-5,2,-4,3]
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>[1,4,-3,2,5,6]
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,3,4,2,6,5]=>[1,4,-3,2,-6,5]
[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[1,-3,-4,-5,2,6]
[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[1,6,4,3,5,2]=>[1,-3,-6,5,-4,2]
[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[1,5,4,3,6,2]=>[1,-3,-4,6,-5,2]
[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[1,3,5,4,2,6]=>[1,4,-3,-5,2,6]
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[1,-3,-4,-5,-6,2]
[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[1,3,6,4,5,2]=>[1,-3,4,5,-6,2]
[1,4,6,3,5,2]=>[1,5,6,4,3,2]=>[1,5,6,4,3,2]=>[1,3,-4,-6,-5,2]
[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[1,3,5,4,6,2]=>[1,4,-3,6,-5,2]
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[5,1,2,3,4,6]
[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[1,5,2,6,3,4]=>[-6,1,-5,2,3,4]
[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[1,5,6,3,2,4]=>[1,-6,-5,3,2,4]
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>[1,-3,5,2,4,6]
[1,5,3,2,6,4]=>[1,3,5,6,2,4]=>[1,3,5,6,2,4]=>[1,-3,5,6,2,4]
[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>[1,4,5,3,2,6]=>[1,3,-5,-4,2,6]
[1,5,3,4,6,2]=>[1,6,5,3,4,2]=>[1,6,5,3,4,2]=>[-3,-5,1,4,-6,2]
[1,5,3,6,2,4]=>[1,6,5,2,3,4]=>[1,6,5,2,3,4]=>[-6,5,1,2,3,4]
[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>[1,-5,2,-4,3,6]
[1,5,4,2,6,3]=>[1,4,5,6,3,2]=>[1,4,5,6,3,2]=>[1,6,3,-5,-4,2]
[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>[1,4,5,-3,2,6]
[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[1,6,4,5,3,2]=>[-5,1,3,-4,-6,2]
[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[1,3,6,5,4,2]=>[1,4,-3,-5,-6,2]
[1,5,6,2,4,3]=>[1,6,4,2,5,3]=>[1,6,4,2,5,3]=>[1,-5,-6,2,-4,3]
[1,5,6,4,2,3]=>[1,4,2,6,5,3]=>[1,4,2,6,5,3]=>[1,-5,2,-4,-6,3]
[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[1,3,4,6,5,2]=>[1,4,5,-3,-6,2]
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>[1,-3,2,6,4,5]
[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>[1,5,6,3,4,2]=>[-6,1,3,4,-5,2]
[1,6,3,5,2,4]=>[1,5,6,2,3,4]=>[1,5,6,2,3,4]=>[5,1,2,6,3,4]
[1,6,3,5,4,2]=>[1,4,5,6,2,3]=>[1,4,5,6,2,3]=>[-4,1,5,6,2,3]
[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>[-6,1,2,-4,3,5]
[1,6,4,2,5,3]=>[1,4,6,5,3,2]=>[1,4,6,5,3,2]=>[1,3,-5,-4,-6,2]
[1,6,4,3,2,5]=>[1,3,4,6,2,5]=>[1,3,4,6,2,5]=>[1,4,-3,6,2,5]
[1,6,4,3,5,2]=>[1,5,4,6,3,2]=>[1,5,4,6,3,2]=>[1,-6,3,-4,-5,2]
[1,6,4,5,2,3]=>[1,5,2,6,4,3]=>[1,5,2,6,4,3]=>[1,-4,2,-6,-5,3]
[1,6,4,5,3,2]=>[1,3,5,6,4,2]=>[1,3,5,6,4,2]=>[1,6,4,-3,-5,2]
[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[1,5,2,3,6,4]=>[-6,1,2,3,-5,4]
[1,6,5,2,4,3]=>[1,5,4,2,6,3]=>[1,5,4,2,6,3]=>[1,-6,-4,2,-5,3]
[1,6,5,3,2,4]=>[1,3,5,2,6,4]=>[1,3,5,2,6,4]=>[1,6,-3,2,-5,4]
[1,6,5,3,4,2]=>[1,4,5,3,6,2]=>[1,4,5,3,6,2]=>[1,3,-5,6,-4,2]
[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[1,4,2,5,6,3]=>[1,-5,2,6,-4,3]
[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[1,3,4,5,6,2]=>[1,4,5,6,-3,2]
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[-2,1,3,4,5,6]
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[-2,1,3,4,-6,5]
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[-2,1,3,-5,4,6]
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[-2,1,3,-5,-6,4]
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[-2,1,-6,3,4,5]
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,5,6,4]=>[-2,1,3,6,-5,4]
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[-2,1,-4,3,5,6]
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[-2,1,-4,3,-6,5]
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[-2,1,-4,-5,3,6]
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,6,4,5,3]=>[-2,-4,1,5,-6,3]
[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[2,1,5,4,6,3]=>[-2,1,-4,6,-5,3]
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[-2,-5,1,3,4,6]
[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[2,1,5,6,3,4]=>[-2,-5,1,6,3,4]
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,4,5,3,6]=>[-2,1,5,-4,3,6]
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[-2,1,-4,-5,-6,3]
[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,6,3,5,4]=>[-2,-5,1,3,-6,4]
[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[2,1,4,6,5,3]=>[-2,1,5,-4,-6,3]
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[-6,-2,1,3,4,5]
[2,1,6,3,5,4]=>[2,1,6,5,3,4]=>[2,1,6,5,3,4]=>[-2,-5,-6,1,3,4]
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[2,1,4,6,3,5]=>[-2,1,-4,6,3,5]
[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>[2,1,5,6,4,3]=>[-2,1,4,-6,-5,3]
[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[2,1,5,3,6,4]=>[-2,1,-6,3,-5,4]
[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[2,1,4,5,6,3]=>[-2,1,5,6,-4,3]
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[-2,-3,1,4,5,6]
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[-2,-3,1,4,-6,5]
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[-2,-3,1,-5,4,6]
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[-2,-3,1,-5,-6,4]
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[3,2,1,6,4,5]=>[-2,-3,-6,1,4,5]
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[3,2,1,5,6,4]=>[-2,-3,1,6,-5,4]
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[4,2,3,1,5,6]=>[2,3,-4,1,5,6]
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[4,2,3,1,6,5]=>[2,3,-4,1,-6,5]
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[5,2,3,4,1,6]=>[5,3,4,-2,1,6]
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[6,2,3,4,5,1]=>[3,6,4,5,-2,1]
[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[6,2,3,4,1,5]=>[3,6,4,-2,1,5]
[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[5,2,3,4,6,1]=>[5,3,4,6,-2,1]
[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[5,2,3,1,4,6]=>[2,-5,3,1,4,6]
[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[4,2,3,5,1,6]=>[2,3,5,-4,1,6]
[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[6,2,3,5,4,1]=>[5,3,4,-2,-6,1]
[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[6,2,3,1,5,4]=>[2,-5,3,1,-6,4]
[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[4,2,3,6,5,1]=>[2,3,5,-4,-6,1]
[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[6,2,3,1,4,5]=>[-6,2,3,1,4,5]
[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[4,2,3,5,6,1]=>[2,3,5,6,-4,1]
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[4,2,1,3,5,6]=>[-4,-2,1,3,5,6]
[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[4,2,5,1,3,6]=>[-4,-2,5,1,3,6]
[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[4,2,6,1,5,3]=>[-2,-6,5,1,-4,3]
[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[4,2,6,1,3,5]=>[-4,-2,1,6,3,5]
[2,4,1,6,5,3]=>[4,2,5,1,6,3]=>[4,2,5,1,6,3]=>[-2,6,-5,1,-4,3]
[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[-2,4,-3,1,5,6]
[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[3,2,4,1,6,5]=>[-2,4,-3,1,-6,5]
[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[5,2,4,3,1,6]=>[2,3,-4,-5,1,6]
[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[6,2,4,3,5,1]=>[2,-4,3,5,-6,1]
[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[5,2,4,3,6,1]=>[2,3,-4,6,-5,1]
[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[3,2,5,4,1,6]=>[-2,4,-3,-5,1,6]
[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[6,2,5,4,3,1]=>[2,3,-4,-5,-6,1]
[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[3,2,6,4,5,1]=>[-2,-3,4,5,-6,1]
[2,4,6,3,1,5]=>[3,2,6,4,1,5]=>[3,2,6,4,1,5]=>[-2,4,-6,-3,1,5]
[2,4,6,5,1,3]=>[5,2,1,4,6,3]=>[5,2,1,4,6,3]=>[-4,-2,1,6,-5,3]
[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[3,2,5,4,6,1]=>[-2,4,-3,6,-5,1]
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[5,2,1,3,4,6]=>[5,-2,1,3,4,6]
[2,5,1,4,3,6]=>[5,2,4,1,3,6]=>[5,2,4,1,3,6]=>[-5,2,4,1,3,6]
[2,5,1,4,6,3]=>[5,2,6,1,4,3]=>[5,2,6,1,4,3]=>[-6,-2,4,1,-5,3]
[2,5,3,1,4,6]=>[3,2,5,1,4,6]=>[3,2,5,1,4,6]=>[-2,-3,5,1,4,6]
[2,5,3,4,6,1]=>[6,2,5,3,4,1]=>[6,2,5,3,4,1]=>[5,-2,3,4,-6,1]
[2,5,3,6,1,4]=>[6,2,5,1,3,4]=>[6,2,5,1,3,4]=>[6,2,1,5,3,4]
[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[-2,4,5,-3,1,6]
[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[6,2,4,5,3,1]=>[4,5,3,-2,-6,1]
[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[3,2,6,5,4,1]=>[-2,4,-3,-5,-6,1]
[2,5,6,3,1,4]=>[3,2,6,1,5,4]=>[3,2,6,1,5,4]=>[-2,-3,5,1,-6,4]
[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[3,2,4,6,5,1]=>[-2,4,5,-3,-6,1]
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[6,2,1,3,4,5]=>[-2,6,1,3,4,5]
[2,6,1,4,3,5]=>[6,2,4,1,3,5]=>[6,2,4,1,3,5]=>[6,2,4,1,3,5]
[2,6,1,4,5,3]=>[6,2,5,1,4,3]=>[6,2,5,1,4,3]=>[-5,2,4,1,-6,3]
[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>[3,2,6,1,4,5]=>[-2,-3,1,6,4,5]
[2,6,3,5,1,4]=>[5,2,6,1,3,4]=>[5,2,6,1,3,4]=>[5,-2,1,6,3,4]
[2,6,4,5,3,1]=>[3,2,5,6,4,1]=>[3,2,5,6,4,1]=>[-2,6,4,-3,-5,1]
[2,6,5,3,1,4]=>[3,2,5,1,6,4]=>[3,2,5,1,6,4]=>[-2,6,-3,1,-5,4]
[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[-2,4,5,6,-3,1]
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,-6,5]
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,-5,4,6]
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,1,2,6,5,4]=>[3,1,2,-5,-6,4]
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,-6,2,4,5]
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>[3,1,2,5,6,4]=>[3,1,2,6,-5,4]
[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]=>[3,4,1,2,5,6]
[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[3,4,1,2,6,5]=>[3,4,1,2,-6,5]
[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[3,6,1,4,5,2]=>[-6,1,4,5,-3,2]
[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[3,5,1,2,4,6]=>[3,1,5,2,4,6]
[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[3,5,1,6,2,4]=>[5,6,1,-3,2,4]
[3,1,5,4,2,6]=>[3,4,1,5,2,6]=>[3,4,1,5,2,6]=>[5,-4,1,-3,2,6]
[3,1,5,4,6,2]=>[3,6,1,5,4,2]=>[3,6,1,5,4,2]=>[-5,4,1,-3,-6,2]
[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[3,6,1,2,4,5]=>[3,1,2,6,4,5]
[3,1,6,2,5,4]=>[3,6,1,5,2,4]=>[3,6,1,5,2,4]=>[6,1,5,-3,2,4]
[3,1,6,4,2,5]=>[3,4,1,6,2,5]=>[3,4,1,6,2,5]=>[-4,6,1,-3,2,5]
[3,1,6,4,5,2]=>[3,5,1,6,4,2]=>[3,5,1,6,4,2]=>[4,-6,1,-3,-5,2]
[3,1,6,5,2,4]=>[3,5,1,2,6,4]=>[3,5,1,2,6,4]=>[3,6,1,2,-5,4]
[3,1,6,5,4,2]=>[3,4,1,5,6,2]=>[3,4,1,5,6,2]=>[5,-4,1,6,-3,2]
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[3,-2,1,4,5,6]
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[2,3,1,4,6,5]=>[3,-2,1,4,-6,5]
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[2,3,1,5,4,6]=>[3,-2,1,-5,4,6]
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[2,3,1,6,5,4]=>[3,-2,1,-5,-6,4]
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[2,3,1,6,4,5]=>[3,-2,-6,1,4,5]
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[2,3,1,5,6,4]=>[3,-2,1,6,-5,4]
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[-2,-3,-4,1,5,6]
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[-2,-3,-4,1,-6,5]
[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[5,3,2,4,1,6]=>[-2,-5,4,-3,1,6]
[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[6,3,2,4,5,1]=>[2,-6,4,5,-3,1]
[3,2,4,6,1,5]=>[6,3,2,4,1,5]=>[6,3,2,4,1,5]=>[-6,-2,4,-3,1,5]
[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[5,3,2,4,6,1]=>[-2,-5,4,6,-3,1]
[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[5,3,2,1,4,6]=>[-2,-5,-3,1,4,6]
[3,2,5,1,6,4]=>[5,3,2,6,1,4]=>[5,3,2,6,1,4]=>[-2,-5,-3,6,1,4]
[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[-2,-3,5,-4,1,6]
[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[6,3,2,5,4,1]=>[-2,-5,4,-3,-6,1]
[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[4,3,2,6,5,1]=>[-2,-3,5,-4,-6,1]
[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[6,3,2,1,4,5]=>[-6,-2,-3,1,4,5]
[3,2,6,1,5,4]=>[6,3,2,5,1,4]=>[6,3,2,5,1,4]=>[-6,-2,-3,5,1,4]
[3,2,6,4,1,5]=>[4,3,2,6,1,5]=>[4,3,2,6,1,5]=>[-2,-3,-4,6,1,5]
[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[-2,-3,5,6,-4,1]
[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[4,1,3,2,6,5]=>[3,1,-4,2,-6,5]
[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[4,5,3,1,2,6]=>[5,-4,3,1,2,6]
[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[4,6,3,1,5,2]=>[-3,5,-6,1,-4,2]
[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[4,6,3,1,2,5]=>[-4,6,3,1,2,5]
[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[2,4,3,1,5,6]=>[3,-2,-4,1,5,6]
[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[2,4,3,1,6,5]=>[3,-2,-4,1,-6,5]
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[-2,-3,-4,-5,1,6]
[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[6,4,3,2,5,1]=>[-2,-3,-6,5,-4,1]
[3,4,2,6,1,5]=>[6,4,3,2,1,5]=>[6,4,3,2,1,5]=>[-2,-3,-6,-4,1,5]
[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[-2,-3,-4,6,-5,1]
[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]=>[5,6,3,4,1,2]
[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[2,5,3,4,1,6]=>[-2,3,4,-5,1,6]
[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[6,5,3,4,2,1]=>[-3,4,2,-5,-6,1]
[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[2,6,3,4,5,1]=>[2,3,4,5,-6,1]
[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[6,1,3,4,2,5]=>[1,3,-6,4,2,5]
[3,4,6,1,5,2]=>[6,5,3,4,1,2]=>[6,5,3,4,1,2]=>[-6,5,3,4,1,2]
[3,4,6,2,5,1]=>[5,6,3,4,2,1]=>[5,6,3,4,2,1]=>[3,4,2,-6,-5,1]
[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[2,5,3,4,6,1]=>[-2,3,4,6,-5,1]
[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[5,1,3,6,2,4]=>[3,-5,1,6,2,4]
[3,5,1,4,2,6]=>[5,4,3,1,2,6]=>[5,4,3,1,2,6]=>[-4,-5,3,1,2,6]
[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[5,6,3,2,1,4]=>[2,-6,-5,-3,1,4]
[3,5,1,6,4,2]=>[5,4,3,6,1,2]=>[5,4,3,6,1,2]=>[-4,-5,3,6,1,2]
[3,5,2,4,1,6]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[2,-3,-5,-4,1,6]
[3,5,2,4,6,1]=>[6,5,3,2,4,1]=>[6,5,3,2,4,1]=>[-2,-5,-6,4,-3,1]
[3,5,2,6,1,4]=>[6,5,3,1,2,4]=>[6,5,3,1,2,4]=>[-6,5,3,1,2,4]
[3,5,2,6,4,1]=>[4,6,3,5,1,2]=>[4,6,3,5,1,2]=>[-4,6,3,5,1,2]
[3,5,4,1,6,2]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[6,-3,2,-5,-4,1]
[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[2,4,3,5,1,6]=>[3,-2,5,-4,1,6]
[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[6,4,3,5,2,1]=>[-5,-3,2,-6,-4,1]
[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[2,6,3,5,4,1]=>[-2,3,4,-5,-6,1]
[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[6,1,3,2,5,4]=>[3,-5,1,2,-6,4]
[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[2,4,3,6,5,1]=>[3,-2,5,-4,-6,1]
[3,6,1,4,2,5]=>[6,4,3,1,2,5]=>[6,4,3,1,2,5]=>[-6,-4,3,1,2,5]
[3,6,1,5,2,4]=>[6,5,3,2,1,4]=>[6,5,3,2,1,4]=>[-2,-5,-6,-3,1,4]
[3,6,1,5,4,2]=>[6,4,3,5,1,2]=>[6,4,3,5,1,2]=>[-6,-4,3,5,1,2]
[3,6,2,4,5,1]=>[5,6,3,2,4,1]=>[5,6,3,2,4,1]=>[-3,-6,2,4,-5,1]
[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[5,6,3,1,2,4]=>[5,6,3,1,2,4]
[3,6,2,5,4,1]=>[4,5,3,6,1,2]=>[4,5,3,6,1,2]=>[5,-4,3,6,1,2]
[3,6,4,1,2,5]=>[4,1,3,6,2,5]=>[4,1,3,6,2,5]=>[3,1,-4,6,2,5]
[3,6,4,1,5,2]=>[4,6,3,5,2,1]=>[4,6,3,5,2,1]=>[-3,5,2,-6,-4,1]
[3,6,4,2,5,1]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[-6,-3,2,-4,-5,1]
[3,6,5,1,2,4]=>[5,1,3,2,6,4]=>[5,1,3,2,6,4]=>[3,1,-6,2,-5,4]
[3,6,5,2,4,1]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[2,-3,-5,6,-4,1]
[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[2,4,3,5,6,1]=>[3,-2,5,6,-4,1]
[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[1,4,2,3,5,6]
[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[1,4,2,3,-6,5]
[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[4,1,5,2,3,6]=>[5,-4,1,2,3,6]
[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[4,1,6,2,5,3]=>[5,1,-6,2,-4,3]
[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[4,1,6,2,3,5]=>[-4,6,1,2,3,5]
[4,1,2,6,5,3]=>[4,1,5,2,6,3]=>[4,1,5,2,6,3]=>[-6,1,-5,2,-4,3]
[4,1,3,2,5,6]=>[4,3,1,2,5,6]=>[4,3,1,2,5,6]=>[-4,3,1,2,5,6]
[4,1,3,2,6,5]=>[4,3,1,2,6,5]=>[4,3,1,2,6,5]=>[-4,3,1,2,-6,5]
[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[4,5,2,1,3,6]=>[-5,-4,2,1,3,6]
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[4,5,6,1,2,3]=>[1,4,5,6,2,3]
[4,1,5,3,2,6]=>[4,3,5,1,2,6]=>[4,3,5,1,2,6]=>[-4,3,5,1,2,6]
[4,1,5,3,6,2]=>[4,6,5,1,3,2]=>[4,6,5,1,3,2]=>[5,-4,3,1,-6,2]
[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[4,6,2,1,5,3]=>[-5,2,-6,1,-4,3]
[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[4,6,2,1,3,5]=>[6,-4,2,1,3,5]
[4,1,6,2,5,3]=>[4,6,5,1,2,3]=>[4,6,5,1,2,3]=>[6,4,1,5,2,3]
[4,1,6,3,2,5]=>[4,3,6,1,2,5]=>[4,3,6,1,2,5]=>[-4,3,1,6,2,5]
[4,1,6,3,5,2]=>[4,5,6,1,3,2]=>[4,5,6,1,3,2]=>[5,6,3,1,-4,2]
[4,1,6,5,2,3]=>[4,5,2,1,6,3]=>[4,5,2,1,6,3]=>[2,-6,-5,1,-4,3]
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[2,4,1,3,5,6]=>[-2,4,1,3,5,6]
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[2,4,1,3,6,5]=>[-2,4,1,3,-6,5]
[4,2,1,5,3,6]=>[2,4,5,1,3,6]=>[2,4,5,1,3,6]=>[-2,4,5,1,3,6]
[4,2,1,5,6,3]=>[2,4,6,1,5,3]=>[2,4,6,1,5,3]=>[6,-2,5,1,-4,3]
[4,2,1,6,3,5]=>[2,4,6,1,3,5]=>[2,4,6,1,3,5]=>[-2,4,1,6,3,5]
[4,2,1,6,5,3]=>[2,4,5,1,6,3]=>[2,4,5,1,6,3]=>[5,6,-2,1,-4,3]
[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[2,-4,-3,1,5,6]
[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>[3,4,2,1,6,5]=>[2,-4,-3,1,-6,5]
[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[5,4,2,3,1,6]=>[-4,2,3,-5,1,6]
[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[6,4,2,3,5,1]=>[4,2,3,5,-6,1]
[4,2,3,6,1,5]=>[6,4,2,3,1,5]=>[6,4,2,3,1,5]=>[-4,2,-6,3,1,5]
[4,2,3,6,5,1]=>[5,4,2,3,6,1]=>[5,4,2,3,6,1]=>[-4,2,3,6,-5,1]
[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[5,4,1,2,3,6]=>[5,1,4,2,3,6]
[4,2,5,1,6,3]=>[5,4,6,2,1,3]=>[5,4,6,2,1,3]=>[6,-4,-5,2,1,3]
[4,2,5,3,6,1]=>[6,4,5,2,3,1]=>[6,4,5,2,3,1]=>[4,5,2,3,-6,1]
[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[6,4,1,2,3,5]=>[1,6,4,2,3,5]
[4,2,6,1,5,3]=>[6,4,5,2,1,3]=>[6,4,5,2,1,3]=>[2,-4,-6,5,1,3]
[4,2,6,3,5,1]=>[5,4,6,2,3,1]=>[5,4,6,2,3,1]=>[-4,6,2,3,-5,1]
[4,2,6,5,1,3]=>[5,4,1,2,6,3]=>[5,4,1,2,6,3]=>[-4,6,1,2,-5,3]
[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[3,1,4,2,5,6]=>[-4,1,-3,2,5,6]
[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[3,1,4,2,6,5]=>[-4,1,-3,2,-6,5]
[4,3,1,5,2,6]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[5,2,-4,-3,1,6]
[4,3,1,6,5,2]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[5,2,-4,6,-3,1]
[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[3,4,-2,1,5,6]
[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[2,3,4,1,6,5]=>[3,4,-2,1,-6,5]
[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[5,3,4,2,1,6]=>[4,2,-3,-5,1,6]
[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[6,3,4,2,5,1]=>[4,-3,2,5,-6,1]
[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[6,3,4,2,1,5]=>[4,2,-6,-3,1,5]
[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[5,3,4,2,6,1]=>[4,2,-3,6,-5,1]
[4,3,5,1,6,2]=>[5,6,4,3,1,2]=>[5,6,4,3,1,2]=>[4,-6,-5,3,1,2]
[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[2,5,4,3,1,6]=>[3,-2,-4,-5,1,6]
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[-2,-3,-4,-5,-6,1]
[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[2,6,4,3,5,1]=>[3,-2,-6,5,-4,1]
[4,3,6,1,5,2]=>[6,5,4,3,1,2]=>[6,5,4,3,1,2]=>[-4,-5,-6,3,1,2]
[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[2,-3,-4,-6,-5,1]
[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[2,5,4,3,6,1]=>[3,-2,-4,6,-5,1]
[4,5,1,3,2,6]=>[5,3,1,4,2,6]=>[5,3,1,4,2,6]=>[-4,-5,1,-3,2,6]
[4,5,1,3,6,2]=>[5,6,1,4,3,2]=>[5,6,1,4,3,2]=>[4,3,1,-6,-5,2]
[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[5,6,2,4,1,3]=>[2,-5,6,4,1,3]
[4,5,1,6,3,2]=>[5,3,6,4,1,2]=>[5,3,6,4,1,2]=>[-6,3,-5,4,1,2]
[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[3,5,2,4,1,6]=>[-5,2,4,-3,1,6]
[4,5,3,1,6,2]=>[3,5,6,4,2,1]=>[3,5,6,4,2,1]=>[4,2,-6,-3,-5,1]
[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[2,3,5,4,1,6]=>[3,4,-2,-5,1,6]
[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[6,3,5,4,2,1]=>[4,2,-3,-5,-6,1]
[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[2,6,5,4,3,1]=>[3,-2,-4,-5,-6,1]
[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[6,1,2,4,5,3]=>[1,2,4,5,-6,3]
[4,5,6,1,3,2]=>[6,3,1,4,5,2]=>[6,3,1,4,5,2]=>[4,-6,1,5,-3,2]
[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[2,6,1,4,5,3]=>[-2,1,4,5,-6,3]
[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[3,6,2,4,5,1]=>[-2,6,4,5,-3,1]
[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[3,1,6,4,5,2]=>[-4,-3,1,5,-6,2]
[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[2,3,6,4,5,1]=>[3,-2,4,5,-6,1]
[4,6,1,5,2,3]=>[6,5,2,4,1,3]=>[6,5,2,4,1,3]=>[5,-6,2,4,1,3]
[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[5,6,1,4,2,3]=>[1,6,-5,4,2,3]
[4,6,3,1,5,2]=>[3,6,5,4,2,1]=>[3,6,5,4,2,1]=>[2,-4,-3,-5,-6,1]
[4,6,3,5,2,1]=>[2,5,6,4,3,1]=>[2,5,6,4,3,1]=>[4,3,-2,-6,-5,1]
[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[2,3,5,4,6,1]=>[3,4,-2,6,-5,1]
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[1,2,5,3,4,6]
[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[5,1,2,6,3,4]=>[1,6,-5,2,3,4]
[5,1,2,4,6,3]=>[5,1,6,2,4,3]=>[5,1,6,2,4,3]=>[4,-6,1,2,-5,3]
[5,1,3,2,4,6]=>[5,3,1,2,4,6]=>[5,3,1,2,4,6]=>[5,3,1,2,4,6]
[5,1,3,2,6,4]=>[5,3,1,6,2,4]=>[5,3,1,6,2,4]=>[6,-3,-5,1,2,4]
[5,1,3,4,6,2]=>[5,6,1,2,3,4]=>[5,6,1,2,3,4]=>[1,2,5,6,3,4]
[5,1,3,6,2,4]=>[5,6,1,3,4,2]=>[5,6,1,3,4,2]=>[1,6,3,4,-5,2]
[5,1,4,2,3,6]=>[5,4,2,1,3,6]=>[5,4,2,1,3,6]=>[-4,-5,-2,1,3,6]
[5,1,4,2,6,3]=>[5,4,6,1,2,3]=>[5,4,6,1,2,3]=>[5,1,4,6,2,3]
[5,1,4,3,2,6]=>[5,3,4,1,2,6]=>[5,3,4,1,2,6]=>[5,3,4,1,2,6]
[5,1,4,6,2,3]=>[5,6,2,1,4,3]=>[5,6,2,1,4,3]=>[-4,-6,2,1,-5,3]
[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[5,6,2,3,1,4]=>[2,6,-5,3,1,4]
[5,1,6,2,4,3]=>[5,6,4,2,1,3]=>[5,6,4,2,1,3]=>[-4,-6,-5,2,1,3]
[5,1,6,3,2,4]=>[5,3,6,2,1,4]=>[5,3,6,2,1,4]=>[6,2,-5,-3,1,4]
[5,1,6,3,4,2]=>[5,4,6,3,1,2]=>[5,4,6,3,1,2]=>[-4,6,-5,3,1,2]
[5,1,6,4,2,3]=>[5,4,2,6,1,3]=>[5,4,2,6,1,3]=>[-4,-5,-2,6,1,3]
[5,1,6,4,3,2]=>[5,3,4,6,1,2]=>[5,3,4,6,1,2]=>[5,3,4,6,1,2]
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[2,5,1,3,4,6]=>[-2,1,5,3,4,6]
[5,2,1,3,6,4]=>[2,5,1,6,3,4]=>[2,5,1,6,3,4]=>[-2,6,-5,1,3,4]
[5,2,3,1,6,4]=>[3,5,2,6,1,4]=>[3,5,2,6,1,4]=>[-5,2,-3,6,1,4]
[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[4,5,2,3,1,6]=>[5,2,3,-4,1,6]
[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[6,5,2,3,4,1]=>[2,5,3,4,-6,1]
[5,2,3,6,1,4]=>[6,5,2,1,3,4]=>[6,5,2,1,3,4]=>[-6,5,-2,1,3,4]
[5,2,3,6,4,1]=>[4,6,2,5,1,3]=>[4,6,2,5,1,3]=>[6,-4,2,5,1,3]
[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[4,5,1,2,3,6]=>[1,4,5,2,3,6]
[5,2,4,1,6,3]=>[4,5,6,2,1,3]=>[4,5,6,2,1,3]=>[2,-5,-4,6,1,3]
[5,2,4,3,1,6]=>[3,4,5,1,2,6]=>[3,4,5,1,2,6]=>[3,4,5,1,2,6]
[5,2,4,3,6,1]=>[6,5,4,2,3,1]=>[6,5,4,2,3,1]=>[-4,-5,2,3,-6,1]
[5,2,6,1,4,3]=>[6,5,4,1,2,3]=>[6,5,4,1,2,3]=>[-6,5,1,4,2,3]
[5,2,6,3,4,1]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[3,2,-6,-5,-4,1]
[5,2,6,4,3,1]=>[3,4,6,5,2,1]=>[3,4,6,5,2,1]=>[5,2,-4,-3,-6,1]
[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[3,1,5,2,4,6]=>[5,1,-3,2,4,6]
[5,3,1,2,6,4]=>[3,1,5,6,2,4]=>[3,1,5,6,2,4]=>[5,1,-3,6,2,4]
[5,3,1,4,2,6]=>[3,5,4,2,1,6]=>[3,5,4,2,1,6]=>[2,-4,-3,-5,1,6]
[5,3,1,4,6,2]=>[3,5,6,1,2,4]=>[3,5,6,1,2,4]=>[3,1,5,6,2,4]
[5,3,1,6,4,2]=>[3,5,4,6,2,1]=>[3,5,4,6,2,1]=>[6,-4,2,-3,-5,1]
[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[2,3,5,1,4,6]=>[3,-2,5,1,4,6]
[5,3,2,1,6,4]=>[2,3,5,6,1,4]=>[2,3,5,6,1,4]=>[3,-2,5,6,1,4]
[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[-5,2,-3,-4,1,6]
[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[6,3,5,2,4,1]=>[-3,5,2,4,-6,1]
[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[6,3,5,1,2,4]=>[3,6,1,5,2,4]
[5,3,2,6,4,1]=>[4,3,6,5,1,2]=>[4,3,6,5,1,2]=>[-4,3,-6,5,1,2]
[5,3,4,1,6,2]=>[4,6,5,3,1,2]=>[4,6,5,3,1,2]=>[5,-4,-6,3,1,2]
[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[2,4,5,3,1,6]=>[5,3,-2,-4,1,6]
[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[6,4,5,3,2,1]=>[3,2,-5,-4,-6,1]
[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[6,1,5,3,4,2]=>[1,-5,3,4,-6,2]
[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[6,1,5,2,3,4]=>[-6,1,2,5,3,4]
[5,3,6,1,4,2]=>[6,4,5,1,3,2]=>[6,4,5,1,3,2]=>[4,5,3,1,-6,2]
[5,3,6,2,1,4]=>[2,6,5,1,3,4]=>[2,6,5,1,3,4]=>[-6,-2,1,5,3,4]
[5,3,6,2,4,1]=>[4,6,5,2,3,1]=>[4,6,5,2,3,1]=>[5,-4,2,3,-6,1]
[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[4,1,2,5,3,6]=>[5,1,2,-4,3,6]
[5,4,1,2,6,3]=>[4,1,5,6,3,2]=>[4,1,5,6,3,2]=>[-6,1,3,-5,-4,2]
[5,4,1,3,6,2]=>[4,5,1,6,2,3]=>[4,5,1,6,2,3]=>[5,6,-4,1,2,3]
[5,4,1,6,2,3]=>[4,5,2,6,3,1]=>[4,5,2,6,3,1]=>[2,-6,3,-5,-4,1]
[5,4,1,6,3,2]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[-5,6,2,-3,-4,1]
[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[2,4,1,5,3,6]=>[5,-2,1,-4,3,6]
[5,4,2,1,6,3]=>[2,4,5,6,3,1]=>[2,4,5,6,3,1]=>[5,6,3,-2,-4,1]
[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[2,-4,5,-3,1,6]
[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[6,4,1,5,2,3]=>[-6,5,-4,1,2,3]
[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[3,1,4,5,2,6]=>[-4,1,5,-3,2,6]
[5,4,3,1,6,2]=>[3,4,5,6,1,2]=>[3,4,5,6,1,2]=>[3,4,5,6,1,2]
[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[3,4,5,-2,1,6]
[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[6,3,4,5,2,1]=>[4,5,2,-6,-3,1]
[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[2,6,4,5,3,1]=>[-2,5,3,-4,-6,1]
[5,4,6,1,3,2]=>[6,3,1,5,4,2]=>[6,3,1,5,4,2]=>[-4,-5,1,-3,-6,2]
[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[3,6,2,5,4,1]=>[-5,2,4,-3,-6,1]
[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[2,3,6,5,4,1]=>[3,4,-2,-5,-6,1]
[5,6,1,2,4,3]=>[6,1,4,2,5,3]=>[6,1,4,2,5,3]=>[5,-4,1,2,-6,3]
[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[3,6,2,1,5,4]=>[-5,2,-3,1,-6,4]
[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[3,1,6,2,5,4]=>[5,1,-3,2,-6,4]
[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[4,1,2,6,5,3]=>[5,1,2,-4,-6,3]
[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[3,4,2,6,5,1]=>[2,-4,5,-3,-6,1]
[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[2,3,4,6,5,1]=>[3,4,5,-2,-6,1]
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[1,2,3,6,4,5]
[6,1,2,3,5,4]=>[6,1,2,5,3,4]=>[6,1,2,5,3,4]=>[1,2,-6,5,3,4]
[6,1,2,4,3,5]=>[6,1,4,2,3,5]=>[6,1,4,2,3,5]=>[-6,1,4,2,3,5]
[6,1,2,4,5,3]=>[6,1,5,2,4,3]=>[6,1,5,2,4,3]=>[1,-5,4,2,-6,3]
[6,1,2,5,3,4]=>[6,1,5,3,2,4]=>[6,1,5,3,2,4]=>[3,-5,-6,1,2,4]
[6,1,2,5,4,3]=>[6,1,4,5,2,3]=>[6,1,4,5,2,3]=>[-6,1,4,5,2,3]
[6,1,3,2,4,5]=>[6,3,1,2,4,5]=>[6,3,1,2,4,5]=>[3,6,1,2,4,5]
[6,1,3,2,5,4]=>[6,3,1,5,2,4]=>[6,3,1,5,2,4]=>[-6,5,1,-3,2,4]
[6,1,3,4,5,2]=>[6,5,1,2,3,4]=>[6,5,1,2,3,4]=>[1,6,2,5,3,4]
[6,1,4,2,3,5]=>[6,4,2,1,3,5]=>[6,4,2,1,3,5]=>[-6,-4,-2,1,3,5]
[6,1,4,2,5,3]=>[6,4,5,1,2,3]=>[6,4,5,1,2,3]=>[1,6,4,5,2,3]
[6,1,4,3,2,5]=>[6,3,4,1,2,5]=>[6,3,4,1,2,5]=>[3,6,4,1,2,5]
[6,1,4,3,5,2]=>[6,5,4,1,3,2]=>[6,5,4,1,3,2]=>[-4,-5,3,1,-6,2]
[6,1,4,5,3,2]=>[6,3,5,1,4,2]=>[6,3,5,1,4,2]=>[-3,5,4,1,-6,2]
[6,1,5,2,3,4]=>[6,5,2,3,1,4]=>[6,5,2,3,1,4]=>[5,2,-6,3,1,4]
[6,1,5,2,4,3]=>[6,5,4,2,1,3]=>[6,5,4,2,1,3]=>[-4,-5,-6,-2,1,3]
[6,1,5,3,4,2]=>[6,4,5,3,1,2]=>[6,4,5,3,1,2]=>[4,5,-6,3,1,2]
[6,1,5,4,2,3]=>[6,4,2,5,1,3]=>[6,4,2,5,1,3]=>[-6,-4,-2,5,1,3]
[6,1,5,4,3,2]=>[6,3,4,5,1,2]=>[6,3,4,5,1,2]=>[3,6,4,5,1,2]
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[2,6,1,3,4,5]=>[-2,1,3,6,4,5]
[6,2,1,3,5,4]=>[2,6,1,5,3,4]=>[2,6,1,5,3,4]=>[-2,1,-6,5,3,4]
[6,2,1,4,3,5]=>[2,6,4,1,3,5]=>[2,6,4,1,3,5]=>[-6,-2,4,1,3,5]
[6,2,1,5,4,3]=>[2,6,4,5,1,3]=>[2,6,4,5,1,3]=>[-6,-2,4,5,1,3]
[6,2,3,1,5,4]=>[3,6,2,5,1,4]=>[3,6,2,5,1,4]=>[6,2,-3,5,1,4]
[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[5,6,2,3,4,1]=>[5,6,3,4,-2,1]
[6,2,3,5,1,4]=>[5,6,2,1,3,4]=>[5,6,2,1,3,4]=>[-5,6,2,1,3,4]
[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[4,6,1,2,3,5]=>[1,4,2,6,3,5]
[6,2,4,1,5,3]=>[4,6,5,2,1,3]=>[4,6,5,2,1,3]=>[-5,-4,-6,2,1,3]
[6,2,4,3,1,5]=>[3,4,6,1,2,5]=>[3,4,6,1,2,5]=>[3,4,1,6,2,5]
[6,2,4,3,5,1]=>[5,6,4,2,3,1]=>[5,6,4,2,3,1]=>[4,-6,2,3,-5,1]
[6,2,4,5,1,3]=>[5,6,1,3,2,4]=>[5,6,1,3,2,4]=>[3,6,-5,1,2,4]
[6,2,5,1,3,4]=>[5,6,1,2,4,3]=>[5,6,1,2,4,3]=>[1,6,4,2,-5,3]
[6,2,5,1,4,3]=>[5,6,4,1,2,3]=>[5,6,4,1,2,3]=>[5,6,1,4,2,3]
[6,2,5,3,1,4]=>[3,5,6,1,4,2]=>[3,5,6,1,4,2]=>[-5,6,4,1,-3,2]
[6,2,5,3,4,1]=>[4,6,5,3,2,1]=>[4,6,5,3,2,1]=>[2,-3,-5,-4,-6,1]
[6,2,5,4,1,3]=>[4,5,1,6,3,2]=>[4,5,1,6,3,2]=>[3,-6,1,-5,-4,2]
[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[5,6,2,-4,-3,1]
[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[3,1,6,2,4,5]=>[1,6,-3,2,4,5]
[6,3,1,2,5,4]=>[3,1,6,5,2,4]=>[3,1,6,5,2,4]=>[5,1,-6,-3,2,4]
[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[2,3,6,1,4,5]=>[3,-2,1,6,4,5]
[6,3,2,1,5,4]=>[2,3,6,5,1,4]=>[2,3,6,5,1,4]=>[3,-2,-6,5,1,4]
[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[5,3,6,2,4,1]=>[-6,-5,2,4,-3,1]
[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>[5,3,6,1,2,4]=>[5,3,1,6,2,4]
[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>[4,3,5,6,1,2]=>[-4,3,5,6,1,2]
[6,3,4,1,5,2]=>[4,5,6,3,1,2]=>[4,5,6,3,1,2]=>[5,6,-4,3,1,2]
[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[-3,2,-6,-4,-5,1]
[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[5,1,6,2,3,4]=>[5,6,1,2,3,4]
[6,3,5,2,1,4]=>[2,5,6,1,3,4]=>[2,5,6,1,3,4]=>[-2,1,5,6,3,4]
[6,3,5,2,4,1]=>[4,5,6,2,3,1]=>[4,5,6,2,3,1]=>[5,6,2,3,-4,1]
[6,3,5,4,1,2]=>[4,1,5,6,2,3]=>[4,1,5,6,2,3]=>[5,-4,1,6,2,3]
[6,3,5,4,2,1]=>[2,4,5,6,1,3]=>[2,4,5,6,1,3]=>[-2,4,5,6,1,3]
[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[4,1,2,6,3,5]=>[1,6,2,-4,3,5]
[6,4,1,3,2,5]=>[4,3,1,6,2,5]=>[4,3,1,6,2,5]=>[6,-3,1,-4,2,5]
[6,4,1,5,3,2]=>[4,3,6,5,2,1]=>[4,3,6,5,2,1]=>[-5,2,-3,-4,-6,1]
[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[2,4,1,6,3,5]=>[-2,6,1,-4,3,5]
[6,4,2,1,5,3]=>[2,4,6,5,3,1]=>[2,4,6,5,3,1]=>[5,3,-2,-4,-6,1]
[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[3,4,2,6,1,5]=>[2,-4,-3,6,1,5]
[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[3,1,4,6,2,5]=>[-4,1,-3,6,2,5]
[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>[3,4,6,5,1,2]=>[3,4,-6,5,1,2]
[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[2,3,4,6,1,5]=>[3,4,-2,6,1,5]
[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[5,3,4,6,2,1]=>[4,6,2,-3,-5,1]
[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[2,5,4,6,3,1]=>[6,-2,3,-4,-5,1]
[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[3,5,2,6,4,1]=>[2,-6,4,-3,-5,1]
[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[2,3,5,6,4,1]=>[3,6,4,-2,-5,1]
[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[5,1,2,3,6,4]=>[1,6,2,3,-5,4]
[6,5,1,2,4,3]=>[5,1,4,2,6,3]=>[5,1,4,2,6,3]=>[6,1,-4,2,-5,3]
[6,5,1,3,2,4]=>[5,3,1,2,6,4]=>[5,3,1,2,6,4]=>[-6,3,1,2,-5,4]
[6,5,1,4,3,2]=>[5,3,4,1,6,2]=>[5,3,4,1,6,2]=>[4,6,-3,1,-5,2]
[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[2,5,1,3,6,4]=>[-2,6,1,3,-5,4]
[6,5,2,1,4,3]=>[2,5,4,1,6,3]=>[2,5,4,1,6,3]=>[6,-2,-4,1,-5,3]
[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[4,5,2,3,6,1]=>[5,2,3,6,-4,1]
[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[4,5,1,2,6,3]=>[5,6,1,2,-4,3]
[6,5,2,4,3,1]=>[3,4,5,1,6,2]=>[3,4,5,1,6,2]=>[5,6,-4,1,-3,2]
[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[3,1,5,2,6,4]=>[-6,1,-3,2,-5,4]
[6,5,3,1,4,2]=>[3,5,4,2,6,1]=>[3,5,4,2,6,1]=>[2,-4,-3,6,-5,1]
[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[2,3,5,1,6,4]=>[3,6,-2,1,-5,4]
[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[-5,2,-3,6,-4,1]
[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[2,4,5,3,6,1]=>[5,3,-2,6,-4,1]
[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[4,1,2,5,6,3]=>[5,1,2,6,-4,3]
[6,5,4,1,3,2]=>[4,3,1,5,6,2]=>[4,3,1,5,6,2]=>[-5,-3,1,6,-4,2]
[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[2,4,1,5,6,3]=>[5,-2,1,6,-4,3]
[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[2,-4,5,6,-3,1]
[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[3,1,4,5,6,2]=>[-4,1,5,6,-3,2]
[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[3,4,5,6,-2,1]
[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>[7,4,1,2,3,5,6]=>[1,4,7,2,3,5,6]
[4,2,7,1,3,6,5]=>[7,4,1,2,6,3,5]=>[7,4,1,2,6,3,5]=>[4,1,6,-7,2,3,5]
[4,2,7,5,1,3,6]=>[5,4,1,2,7,3,6]=>[5,4,1,2,7,3,6]=>[-4,1,7,2,-5,3,6]
[4,2,7,6,1,3,5]=>[6,4,1,2,3,7,5]=>[6,4,1,2,3,7,5]=>[7,1,4,2,3,-6,5]
[4,2,7,6,5,1,3]=>[5,4,1,2,6,7,3]=>[5,4,1,2,6,7,3]=>[-4,6,1,2,7,-5,3]
[5,1,3,4,7,2,6]=>[5,7,1,2,3,4,6]=>[5,7,1,2,3,4,6]=>[1,2,5,3,7,4,6]
[5,1,3,4,7,6,2]=>[5,6,1,2,3,7,4]=>[5,6,1,2,3,7,4]=>[1,6,7,2,3,-5,4]
[5,2,7,1,4,3,6]=>[7,5,4,1,2,3,6]=>[7,5,4,1,2,3,6]=>[7,5,1,4,2,3,6]
[5,2,7,6,1,4,3]=>[6,5,4,1,2,7,3]=>[6,5,4,1,2,7,3]=>[-4,-5,7,1,2,-6,3]
[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>[7,3,5,1,2,4,6]=>[3,1,7,5,2,4,6]
[5,3,2,7,6,1,4]=>[6,3,5,1,2,7,4]=>[6,3,5,1,2,7,4]=>[5,3,7,1,2,-6,4]
[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>[7,1,5,2,3,4,6]=>[7,1,2,5,3,4,6]
[5,3,7,2,1,4,6]=>[2,7,5,1,3,4,6]=>[2,7,5,1,3,4,6]=>[7,-2,1,5,3,4,6]
[5,3,7,6,1,2,4]=>[6,1,5,2,3,7,4]=>[6,1,5,2,3,7,4]=>[1,-5,7,2,3,-6,4]
[5,3,7,6,2,1,4]=>[2,6,5,1,3,7,4]=>[2,6,5,1,3,7,4]=>[-2,-5,7,1,3,-6,4]
[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>[7,4,1,5,2,3,6]=>[7,5,-4,1,2,3,6]
[5,4,2,7,6,1,3]=>[6,4,1,5,2,7,3]=>[6,4,1,5,2,7,3]=>[-7,-5,1,-6,2,-4,3]
[6,1,2,4,5,7,3]=>[6,1,7,2,3,4,5]=>[6,1,7,2,3,4,5]=>[1,6,7,2,3,4,5]
[6,1,3,5,4,7,2]=>[6,7,1,5,2,3,4]=>[6,7,1,5,2,3,4]=>[-6,1,7,2,5,3,4]
[6,1,4,3,5,7,2]=>[6,7,4,1,2,3,5]=>[6,7,4,1,2,3,5]=>[1,6,7,4,2,3,5]
[6,1,4,5,7,3,2]=>[6,3,7,1,2,4,5]=>[6,3,7,1,2,4,5]=>[3,6,1,2,7,4,5]
[6,2,1,4,5,7,3]=>[2,6,7,1,3,4,5]=>[2,6,7,1,3,4,5]=>[-2,1,3,6,7,4,5]
[6,2,7,1,3,4,5]=>[7,6,1,2,3,4,5]=>[7,6,1,2,3,4,5]=>[1,2,7,3,6,4,5]
[6,2,7,1,5,4,3]=>[7,6,4,5,1,2,3]=>[7,6,4,5,1,2,3]=>[7,1,6,4,5,2,3]
[6,2,7,5,1,3,4]=>[5,7,1,2,6,3,4]=>[5,7,1,2,6,3,4]=>[1,7,2,-5,6,3,4]
[6,3,2,7,1,5,4]=>[7,3,6,5,1,2,4]=>[7,3,6,5,1,2,4]=>[3,-7,6,1,5,2,4]
[6,3,7,1,2,5,4]=>[7,1,6,5,2,3,4]=>[7,1,6,5,2,3,4]=>[-6,-7,1,2,5,3,4]
[6,3,7,2,1,5,4]=>[2,7,6,5,1,3,4]=>[2,7,6,5,1,3,4]=>[-6,-7,-2,1,5,3,4]
[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>[7,3,4,6,1,2,5]=>[3,4,7,1,6,2,5]
[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>[7,1,4,6,2,3,5]=>[7,1,4,2,6,3,5]
[6,4,3,7,2,1,5]=>[2,7,4,6,1,3,5]=>[2,7,4,6,1,3,5]=>[7,-2,4,1,6,3,5]
[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[7,1,2,6,3,4,5]=>[1,-7,2,3,6,4,5]
[6,4,7,1,3,2,5]=>[7,3,1,6,2,4,5]=>[7,3,1,6,2,4,5]=>[7,1,6,-3,2,4,5]
[6,4,7,2,1,3,5]=>[2,7,1,6,3,4,5]=>[2,7,1,6,3,4,5]=>[-2,-7,1,3,6,4,5]
[6,4,7,3,1,2,5]=>[3,1,7,6,2,4,5]=>[3,1,7,6,2,4,5]=>[1,-7,6,-3,2,4,5]
[6,4,7,3,2,1,5]=>[2,3,7,6,1,4,5]=>[2,3,7,6,1,4,5]=>[3,-7,-2,1,6,4,5]
[6,5,2,7,1,4,3]=>[7,5,4,1,6,2,3]=>[7,5,4,1,6,2,3]=>[-4,-7,6,-5,1,2,3]
[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>[7,3,5,1,6,2,4]=>[-3,5,1,-7,6,2,4]
[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>[7,1,5,2,6,3,4]=>[5,6,1,-7,2,3,4]
[6,5,3,7,2,1,4]=>[2,7,5,1,6,3,4]=>[2,7,5,1,6,3,4]=>[5,6,-2,-7,1,3,4]
[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>[7,4,1,5,6,2,3]=>[7,5,-4,1,6,2,3]
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[1,2,3,4,7,5,6]
[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>[7,1,2,3,6,4,5]=>[1,2,3,-7,6,4,5]
[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]=>[7,1,2,5,3,4,6]=>[1,-7,2,5,3,4,6]
[7,1,2,3,6,5,4]=>[7,1,2,5,6,3,4]=>[7,1,2,5,6,3,4]=>[1,-7,2,5,6,3,4]
[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]=>[7,1,4,2,3,5,6]=>[7,1,4,2,3,5,6]
[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]=>[7,1,4,2,6,3,5]=>[-4,6,1,-7,2,3,5]
[7,1,2,5,4,3,6]=>[7,1,4,5,2,3,6]=>[7,1,4,5,2,3,6]=>[7,1,4,5,2,3,6]
[7,1,2,6,5,4,3]=>[7,1,4,5,6,2,3]=>[7,1,4,5,6,2,3]=>[-4,1,7,5,6,2,3]
[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]
[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]=>[7,3,1,2,6,4,5]=>[3,6,1,-7,2,4,5]
[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]=>[7,3,1,5,2,4,6]=>[7,5,1,-3,2,4,6]
[7,1,3,2,6,5,4]=>[7,3,1,5,6,2,4]=>[7,3,1,5,6,2,4]=>[7,5,1,-3,6,2,4]
[7,1,3,5,6,4,2]=>[7,4,1,6,2,3,5]=>[7,4,1,6,2,3,5]=>[7,-4,6,1,2,3,5]
[7,1,4,3,2,5,6]=>[7,3,4,1,2,5,6]=>[7,3,4,1,2,5,6]=>[3,4,7,1,2,5,6]
[7,1,4,3,2,6,5]=>[7,3,4,1,6,2,5]=>[7,3,4,1,6,2,5]=>[4,-3,1,-7,6,2,5]
[7,1,5,4,3,2,6]=>[7,3,4,5,1,2,6]=>[7,3,4,5,1,2,6]=>[3,4,7,5,1,2,6]
[7,1,6,5,4,3,2]=>[7,3,4,5,6,1,2]=>[7,3,4,5,6,1,2]=>[3,4,7,5,6,1,2]
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[-2,1,3,4,7,5,6]
[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]=>[2,7,1,3,6,4,5]=>[-2,1,3,-7,6,4,5]
[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]=>[2,7,1,5,3,4,6]=>[-2,-7,1,5,3,4,6]
[7,2,1,3,6,5,4]=>[2,7,1,5,6,3,4]=>[2,7,1,5,6,3,4]=>[-2,-7,1,5,6,3,4]
[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]=>[2,7,4,1,3,5,6]=>[7,-2,4,1,3,5,6]
[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]=>[2,7,4,1,6,3,5]=>[-4,6,-2,-7,1,3,5]
[7,2,1,5,4,3,6]=>[2,7,4,5,1,3,6]=>[2,7,4,5,1,3,6]=>[7,-2,4,5,1,3,6]
[7,2,1,6,5,4,3]=>[2,7,4,5,6,1,3]=>[2,7,4,5,6,1,3]=>[-7,2,4,5,6,1,3]
[7,2,6,1,4,5,3]=>[6,7,5,1,2,3,4]=>[6,7,5,1,2,3,4]=>[1,6,7,2,5,3,4]
[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[3,1,7,2,4,5,6]=>[1,-3,7,2,4,5,6]
[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]=>[3,1,7,2,6,4,5]=>[1,6,-3,-7,2,4,5]
[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]=>[3,1,7,5,2,4,6]=>[5,-7,1,-3,2,4,6]
[7,3,1,2,6,5,4]=>[3,1,7,5,6,2,4]=>[3,1,7,5,6,2,4]=>[5,-3,-7,1,6,2,4]
[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[2,3,7,1,4,5,6]=>[3,-2,1,4,7,5,6]
[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]=>[2,3,7,1,6,4,5]=>[3,-2,1,-7,6,4,5]
[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]=>[2,3,7,5,1,4,6]=>[3,-7,-2,5,1,4,6]
[7,3,2,1,6,5,4]=>[2,3,7,5,6,1,4]=>[2,3,7,5,6,1,4]=>[3,-7,-2,5,6,1,4]
[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[4,1,2,7,3,5,6]=>[1,2,7,-4,3,5,6]
[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]=>[4,1,2,7,6,3,5]=>[1,6,2,-7,-4,3,5]
[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]=>[4,3,1,7,2,5,6]=>[-3,7,1,-4,2,5,6]
[7,4,1,3,2,6,5]=>[4,3,1,7,6,2,5]=>[4,3,1,7,6,2,5]=>[6,-3,1,-7,-4,2,5]
[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[2,4,1,7,3,5,6]=>[-2,1,7,-4,3,5,6]
[7,4,2,1,3,6,5]=>[2,4,1,7,6,3,5]=>[2,4,1,7,6,3,5]=>[-2,6,1,-7,-4,3,5]
[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[3,1,4,7,2,5,6]=>[-4,1,-3,2,7,5,6]
[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]=>[3,1,4,7,6,2,5]=>[-4,1,-3,-7,6,2,5]
[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[2,3,4,7,1,5,6]=>[3,4,-2,1,7,5,6]
[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]=>[2,3,4,7,6,1,5]=>[3,4,-2,-7,6,1,5]
[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[5,1,2,3,7,4,6]=>[1,2,7,3,-5,4,6]
[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]=>[5,1,4,2,7,3,6]=>[1,7,-4,2,-5,3,6]
[7,5,1,3,2,4,6]=>[5,3,1,2,7,4,6]=>[5,3,1,2,7,4,6]=>[7,3,1,2,-5,4,6]
[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]=>[5,3,4,1,7,2,6]=>[4,-3,7,1,-5,2,6]
[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[2,5,1,3,7,4,6]=>[-2,1,7,3,-5,4,6]
[7,5,2,1,4,3,6]=>[2,5,4,1,7,3,6]=>[2,5,4,1,7,3,6]=>[-2,7,-4,1,-5,3,6]
[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[3,1,5,2,7,4,6]=>[7,1,-3,2,-5,4,6]
[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[2,3,5,1,7,4,6]=>[3,-2,7,1,-5,4,6]
[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[4,1,2,5,7,3,6]=>[5,1,2,-4,7,3,6]
[7,5,4,1,3,2,6]=>[4,3,1,5,7,2,6]=>[4,3,1,5,7,2,6]=>[-5,-3,1,-4,7,2,6]
[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[2,4,1,5,7,3,6]=>[5,-2,1,-4,7,3,6]
[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[3,1,4,5,7,2,6]=>[-4,1,5,-3,7,2,6]
[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[2,3,4,5,7,1,6]=>[3,4,5,-2,7,1,6]
[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[6,1,2,3,4,7,5]=>[1,2,7,3,4,-6,5]
[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]=>[6,1,2,5,3,7,4]=>[1,7,2,-5,3,-6,4]
[7,6,1,2,4,3,5]=>[6,1,4,2,3,7,5]=>[6,1,4,2,3,7,5]=>[1,-7,4,2,3,-6,5]
[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]=>[6,1,4,5,2,7,3]=>[1,5,7,-4,2,-6,3]
[7,6,1,3,2,4,5]=>[6,3,1,2,4,7,5]=>[6,3,1,2,4,7,5]=>[7,3,1,2,4,-6,5]
[7,6,1,3,2,5,4]=>[6,3,1,5,2,7,4]=>[6,3,1,5,2,7,4]=>[-7,-5,1,-3,2,-6,4]
[7,6,1,4,3,2,5]=>[6,3,4,1,2,7,5]=>[6,3,4,1,2,7,5]=>[7,3,4,1,2,-6,5]
[7,6,1,5,4,3,2]=>[6,3,4,5,1,7,2]=>[6,3,4,5,1,7,2]=>[4,5,7,-6,1,-3,2]
[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[2,6,1,3,4,7,5]=>[-2,1,7,3,4,-6,5]
[7,6,2,1,3,5,4]=>[2,6,1,5,3,7,4]=>[2,6,1,5,3,7,4]=>[-2,7,1,-5,3,-6,4]
[7,6,2,1,4,3,5]=>[2,6,4,1,3,7,5]=>[2,6,4,1,3,7,5]=>[-2,-7,4,1,3,-6,5]
[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]=>[2,6,4,5,1,7,3]=>[-2,5,7,-4,1,-6,3]
[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[3,1,6,2,4,7,5]=>[7,1,-3,2,4,-6,5]
[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]=>[3,1,6,5,2,7,4]=>[-7,1,-3,-5,2,-6,4]
[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[2,3,6,1,4,7,5]=>[3,-2,7,1,4,-6,5]
[7,6,3,2,1,5,4]=>[2,3,6,5,1,7,4]=>[2,3,6,5,1,7,4]=>[3,7,-2,-5,1,-6,4]
[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[4,1,2,6,3,7,5]=>[7,1,2,-4,3,-6,5]
[7,6,4,1,3,2,5]=>[4,3,1,6,2,7,5]=>[4,3,1,6,2,7,5]=>[-7,-3,1,-4,2,-6,5]
[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[2,4,1,6,3,7,5]=>[7,-2,1,-4,3,-6,5]
[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[3,1,4,6,2,7,5]=>[-4,1,7,-3,2,-6,5]
[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[2,3,4,6,1,7,5]=>[3,4,7,-2,1,-6,5]
[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[5,1,2,3,6,7,4]=>[1,6,2,3,7,-5,4]
[7,6,5,1,2,4,3]=>[5,1,4,2,6,7,3]=>[5,1,4,2,6,7,3]=>[6,1,-4,2,7,-5,3]
[7,6,5,1,3,2,4]=>[5,3,1,2,6,7,4]=>[5,3,1,2,6,7,4]=>[-6,3,1,2,7,-5,4]
[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]=>[5,3,4,1,6,7,2]=>[4,6,-3,1,7,-5,2]
[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[2,5,1,3,6,7,4]=>[-2,6,1,3,7,-5,4]
[7,6,5,2,1,4,3]=>[2,5,4,1,6,7,3]=>[2,5,4,1,6,7,3]=>[6,-2,-4,1,7,-5,3]
[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[3,1,5,2,6,7,4]=>[-6,1,-3,2,7,-5,4]
[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[2,3,5,1,6,7,4]=>[3,6,-2,1,7,-5,4]
[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[4,1,2,5,6,7,3]=>[5,1,2,6,7,-4,3]
[7,6,5,4,1,3,2]=>[4,3,1,5,6,7,2]=>[4,3,1,5,6,7,2]=>[-5,-3,1,6,7,-4,2]
[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[2,4,1,5,6,7,3]=>[5,-2,1,6,7,-4,3]
[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>[-4,1,5,6,7,-3,2]
[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>[3,4,5,6,7,-2,1]
[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[2,3,4,8,5,6,7,1]=>[3,-2,4,5,6,7,-8,1]
[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[2,4,8,3,5,6,7,1]=>[3,-2,5,8,6,7,-4,1]
[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[2,6,4,7,3,5,8,1]=>[7,-2,-6,3,5,8,-4,1]
[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[3,4,2,8,5,6,7,1]=>[2,-4,-8,5,6,7,-3,1]
[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[3,5,2,7,4,8,6,1]=>[2,-8,4,-3,6,-5,-7,1]
[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[3,8,2,7,6,5,4,1]=>[-5,2,4,-3,-6,-7,-8,1]
[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[4,3,8,2,5,6,7,1]=>[-2,-3,5,8,6,7,-4,1]
[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[4,8,2,3,5,6,7,1]=>[2,3,5,8,6,7,-4,1]
[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[7,4,5,3,8,2,6,1]=>[3,8,-5,-7,2,6,-4,1]
[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[7,4,2,5,8,3,6,1]=>[-2,-7,8,-5,3,6,-4,1]
[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[-2,-3,-4,-5,-6,-7,-8,1]
[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[3,1,4,8,5,6,7,2]=>[-4,-3,1,5,6,7,-8,2]
[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[4,1,8,3,5,6,7,2]=>[1,-8,3,5,6,7,-4,2]
[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[2,4,1,8,5,6,7,3]=>[5,-4,-2,1,6,7,-8,3]
[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[4,1,2,7,8,5,6,3]=>[8,1,-4,2,5,6,-7,3]
[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[4,1,2,8,7,5,6,3]=>[5,1,-4,-7,2,6,-8,3]
[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[4,1,2,8,5,6,7,3]=>[5,-4,1,2,6,7,-8,3]
[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[2,3,8,1,5,6,7,4]=>[3,-2,1,8,6,7,-5,4]
[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[3,8,2,1,7,6,5,4]=>[-5,2,-3,1,-6,-7,-8,4]
[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[3,8,2,1,5,6,7,4]=>[2,5,-3,1,6,7,-8,4]
[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[3,1,8,2,5,6,7,4]=>[1,-3,5,2,6,7,-8,4]
[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[2,8,1,3,5,6,7,4]=>[-2,1,3,8,6,7,-5,4]
[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[8,1,2,3,5,6,7,4]=>[1,2,3,8,6,7,-5,4]
[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[4,1,2,6,3,8,7,5]=>[7,1,2,-4,3,-6,-8,5]
[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[3,1,6,2,4,8,7,5]=>[7,1,-3,2,4,-6,-8,5]
[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[2,4,5,3,7,1,8,6]=>[5,3,-2,8,-4,1,-7,6]
[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[4,1,5,3,7,2,8,6]=>[-3,1,-5,8,-4,2,-7,6]
[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[3,1,5,2,7,4,8,6]=>[-8,1,-3,2,-5,4,-7,6]
[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[3,1,5,2,8,4,7,6]=>[7,1,-3,2,-5,4,-8,6]
[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[5,3,6,2,4,8,1,7]=>[-6,-5,2,4,-3,8,1,7]
[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[4,1,2,6,3,8,5,7]=>[1,8,2,-4,3,-6,5,7]
[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[4,5,2,3,8,1,6,7]=>[5,2,3,-4,1,8,6,7]
[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[4,1,5,3,8,2,6,7]=>[-3,1,-5,-4,2,8,6,7]
[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[3,1,5,2,8,4,6,7]=>[1,8,-3,2,-5,4,6,7]
[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[3,5,2,7,4,6,1,8]=>[-7,2,4,-3,6,-5,1,8]
[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[4,5,2,3,7,6,1,8]=>[5,2,3,6,-4,-7,1,8]
[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[6,4,2,7,3,5,1,8]=>[2,-7,-4,3,5,-6,1,8]
[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[7,4,2,6,3,5,1,8]=>[-6,2,3,-7,5,-4,1,8]
[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[3,6,2,1,4,7,5,8]=>[-7,2,-3,1,4,-6,5,8]
[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[4,5,2,3,7,1,6,8]=>[5,2,3,-4,7,1,6,8]
[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[3,1,5,2,7,4,6,8]=>[7,1,-3,2,-5,4,6,8]
[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[4,3,6,2,5,1,7,8]=>[-6,-3,2,5,-4,1,7,8]
[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[-2,-3,-4,-5,1,6,7,8]
[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[-2,-3,-4,1,5,6,7,8]
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]
[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[2,3,7,4,5,6,8,1]=>[-2,3,4,5,6,8,-7,1]
[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[8,7,3,6,5,4,2,1]=>[-3,4,2,-5,-6,-7,-8,1]
[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[8,7,4,3,6,5,2,1]=>[-5,-3,-6,2,-7,-4,-8,1]
[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[8,3,2,7,6,5,4,1]=>[-2,-5,4,-3,-6,-7,-8,1]
[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[8,5,4,3,2,7,6,1]=>[-2,-3,-4,-7,6,-5,-8,1]
[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[8,3,2,5,4,7,6,1]=>[-2,-5,-3,4,6,-7,-8,1]
[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[1,4,3,6,5,8,7,2]=>[1,-3,5,-4,7,-6,-8,2]
[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[2,1,4,5,8,6,7,3]=>[-2,1,5,-4,6,7,-8,3]
[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[-2,1,-4,-5,-6,-7,-8,3]
[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,8,7,5,6,4,3]=>[-2,-6,-5,1,4,-7,-8,3]
[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,8,5,4,7,6,3]=>[-2,1,-4,-7,6,-5,-8,3]
[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,6,7,8,-5,4]
[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[1,2,3,-5,-6,-7,-8,4]
[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[2,3,4,1,8,7,6,5]=>[3,4,-2,1,-6,-7,-8,5]
[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[2,4,3,1,6,8,7,5]=>[3,-2,-4,1,7,-6,-8,5]
[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[2,4,3,1,8,7,6,5]=>[3,-2,-4,1,-6,-7,-8,5]
[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[3,2,4,1,8,7,6,5]=>[-2,4,-3,1,-6,-7,-8,5]
[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,6,7,8,5]=>[-2,-3,-4,1,7,8,-6,5]
[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,6,8,7,5]=>[-2,-3,-4,1,7,-6,-8,5]
[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,7,6,8,5]=>[-2,-3,-4,1,-6,8,-7,5]
[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[-2,-3,-4,1,-6,-7,-8,5]
[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[4,3,2,1,8,6,7,5]=>[-2,-3,-4,-6,1,7,-8,5]
[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,-4,1,-6,-7,-8,5]
[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,-4,-6,1,7,-8,5]
[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[1,3,4,2,8,7,6,5]=>[1,4,-3,2,-6,-7,-8,5]
[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[1,-3,-4,2,-6,-7,-8,5]
[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,6,8,7,5]=>[-2,1,-4,3,7,-6,-8,5]
[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[-2,1,-4,3,-6,-7,-8,5]
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,8,6,7,5]=>[-2,1,-4,-6,3,7,-8,5]
[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[1,2,-4,3,-6,-7,-8,5]
[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[2,3,1,4,8,7,6,5]=>[3,-2,1,4,-6,-7,-8,5]
[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,-3,1,4,-6,-7,-8,5]
[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[1,-3,2,4,-6,-7,-8,5]
[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[-2,1,3,4,-6,-7,-8,5]
[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,-6,-7,-8,5]
[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,7,8,6]=>[-2,-3,-4,1,5,8,-7,6]
[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[-2,-3,-4,1,5,-7,-8,6]
[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[2,3,6,4,5,1,8,7]=>[3,-2,4,5,-6,1,-8,7]
[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[-2,-3,-4,-5,-6,1,-8,7]
[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[6,3,2,5,4,1,8,7]=>[-2,-5,4,-3,-6,1,-8,7]
[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[2,1,4,6,5,3,8,7]=>[-2,1,5,-4,-6,3,-8,7]
[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[-2,1,-4,-5,-6,3,-8,7]
[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,6,4,5,3,8,7]=>[-2,-4,1,5,-6,3,-8,7]
[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[3,-2,-4,1,-6,5,-8,7]
[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[-2,-3,-4,1,-6,5,-8,7]
[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,-4,1,-6,5,-8,7]
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[-2,1,-4,3,-6,5,-8,7]
[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[-2,1,-4,-5,3,6,-8,7]
[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[-2,-3,-4,1,5,6,-8,7]
[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[3,2,5,4,7,6,1,8]=>[-2,4,-3,6,-5,-7,1,8]
[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,-3,-5,1,6,-7,4,8]
[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,6,7,5,8]=>[-2,-3,-4,1,7,-6,5,8]
[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[-2,-3,-4,1,-6,-7,5,8]
[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,-3,1,4,-6,-7,5,8]
[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,-3,1,-5,4,-7,6,8]
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,-3,2,-5,4,-7,6,8]
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,-5,4,-7,6,8]
[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[-2,-3,-4,1,5,-7,6,8]
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,-3,2,4,5,-7,6,8]
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,-7,6,8]
[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[-2,-3,-4,1,-6,5,7,8]
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,-3,2,-5,4,6,7,8]
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,-5,4,6,7,8]
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,-3,2,4,5,6,7,8]
[1,2,8,4,7,6,5,3]=>[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,8,4,3]=>[1,2,7,8,4,-6,-5,3]
[1,3,8,5,6,7,4,2]=>[1,4,3,7,8,5,6,2]=>[1,4,3,7,8,5,6,2]=>[1,-3,-4,8,5,6,-7,2]
[1,8,4,3,5,7,6,2]=>[1,6,4,7,3,8,2,5]=>[1,6,4,7,3,8,2,5]=>[-7,1,3,-6,-4,8,2,5]
[1,8,4,7,6,5,3,2]=>[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,8,4,2]=>[1,6,7,8,4,-3,-5,2]
[2,1,4,3,8,6,7,5]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,7,8,6,5]=>[-2,1,-4,3,6,-8,-7,5]
[2,1,6,4,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>[2,1,5,6,4,3,8,7]=>[-2,1,4,-6,-5,3,-8,7]
[2,1,8,4,7,6,5,3]=>[2,1,5,6,7,8,4,3]=>[2,1,5,6,7,8,4,3]=>[-2,1,7,8,4,-6,-5,3]
[2,1,7,5,4,6,8,3]=>[2,1,8,5,7,4,6,3]=>[2,1,8,5,7,4,6,3]=>[-2,-7,-5,1,4,6,-8,3]
[2,6,3,4,5,8,7,1]=>[7,2,6,3,4,5,8,1]=>[7,2,6,3,4,5,8,1]=>[-2,3,6,4,5,8,-7,1]
[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,-3,7,4,5,-6,1,8]
[2,8,5,4,3,6,7,1]=>[7,2,4,5,8,3,6,1]=>[7,2,4,5,8,3,6,1]=>[4,5,-2,8,3,6,-7,1]
[3,2,4,1,8,6,7,5]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,7,8,6,5]=>[-2,-3,-4,1,6,-8,-7,5]
[3,2,7,4,6,5,8,1]=>[8,3,2,7,6,4,5,1]=>[8,3,2,7,6,4,5,1]=>[2,-6,-3,-7,4,5,-8,1]
[4,2,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[2,-4,-3,1,-6,5,-8,7]
[4,2,3,1,7,6,8,5]=>[3,4,2,1,8,7,6,5]=>[3,4,2,1,8,7,6,5]=>[2,-4,-3,1,-6,-7,-8,5]
[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>[3,4,2,1,7,8,6,5]=>[2,-4,-3,1,6,-8,-7,5]
[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,-5,2,3,-6,1,-8,7]
[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,-7,2,3,6,-5,-8,1]
[7,2,4,3,6,5,8,1]=>[8,7,4,2,6,3,5,1]=>[8,7,4,2,6,3,5,1]=>[-6,-7,2,3,-8,5,-4,1]
[5,3,2,4,6,1,8,7]=>[6,3,5,2,4,1,8,7]=>[6,3,5,2,4,1,8,7]=>[-3,5,2,4,-6,1,-8,7]
[8,3,2,5,7,6,4,1]=>[4,3,6,7,2,8,5,1]=>[4,3,6,7,2,8,5,1]=>[-7,8,2,-3,5,-4,-6,1]
[7,3,4,2,6,5,8,1]=>[8,4,7,3,6,2,5,1]=>[8,4,7,3,6,2,5,1]=>[-3,7,-4,6,2,5,-8,1]
[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[4,2,6,1,7,3,5,8]=>[-6,-2,7,1,-4,3,5,8]
[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,7,8,5,6]=>[-2,1,-4,-7,3,8,5,6]
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,5,7,6]=>[-2,1,-4,-7,3,5,-8,6]
[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[2,1,7,4,5,8,3,6]=>[-2,-4,1,-7,5,8,3,6]
[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,-6,5,1,-4,3,7,8]
[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[5,2,6,4,1,3,7,8]=>[-6,-2,-5,4,1,3,7,8]
[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,5,6,3,4,8,7]=>[-2,-5,1,6,3,4,-8,7]
[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,6,3,5,4,8,7]=>[-2,-5,1,3,-6,4,-8,7]
[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[5,2,6,7,1,3,4,8]=>[5,-2,1,6,7,3,4,8]
[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[2,1,5,8,3,6,7,4]=>[-2,1,-8,3,6,7,-5,4]
[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[2,1,5,7,3,8,4,6]=>[-2,-7,1,8,3,-5,4,6]
[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,4,3,6]=>[2,1,7,8,5,4,3,6]=>[-2,1,4,-8,-7,-5,3,6]
[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,8,3,5,4,7,6]=>[-2,-5,1,-7,3,4,-8,6]
[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[2,1,6,7,8,3,4,5]=>[-6,-2,1,3,7,8,4,5]
[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,8,3,4,6,7,5]=>[6,-2,1,3,4,7,-8,5]
[2,1,6,3,4,7,8,5]=>[2,1,6,3,8,4,7,5]=>[2,1,6,3,8,4,7,5]=>[-2,-7,1,3,-8,4,-6,5]
[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,-4,-7,1,5,-8,6]
[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,-3,-8,1,4,5,6,7]
[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[3,4,1,2,-6,5,-8,7]
[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[3,1,-4,2,-6,5,-8,7]
[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[4,6,3,1,7,2,5,8]=>[-3,-6,7,1,-4,2,5,8]
[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[4,1,3,2,8,6,7,5]=>[3,1,-4,-6,2,7,-8,5]
[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[3,4,1,2,7,8,5,6]=>[3,4,1,-7,2,8,5,6]
[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[4,1,3,2,8,5,7,6]=>[3,1,-4,-7,2,5,-8,6]
[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[-5,4,1,-3,2,-7,6,8]
[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[3,1,-8,-4,2,5,6,7]
[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,-3,2,-8,7]
[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[4,6,3,1,5,2,7,8]=>[-3,5,-6,1,-4,2,7,8]
[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]=>[5,6,3,4,1,2,7,8]
[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[3,5,1,6,2,4,8,7]=>[5,6,1,-3,2,4,-8,7]
[3,5,1,6,2,4,8,7]=>[5,6,3,2,1,4,8,7]=>[5,6,3,2,1,4,8,7]=>[2,-6,-5,-3,1,4,-8,7]
[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[6,1,3,2,5,4,8,7]=>[3,-5,1,2,-6,4,-8,7]
[3,5,1,6,2,4,7,8]=>[5,6,3,2,1,4,7,8]=>[5,6,3,2,1,4,7,8]=>[2,-6,-5,-3,1,4,7,8]
[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[5,6,3,7,1,2,4,8]=>[5,6,3,1,7,2,4,8]
[3,1,5,6,7,8,2,4]=>[3,8,1,2,5,6,7,4]=>[3,8,1,2,5,6,7,4]=>[3,1,2,8,6,7,-5,4]
[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[3,5,1,7,2,8,4,6]=>[7,8,1,-3,2,-5,4,6]
[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,-3,4,8,1,-5,2,6]
[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[8,1,3,2,5,4,7,6]=>[3,-5,1,-7,2,4,-8,6]
[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[3,-5,1,2,-8,4,6,7]
[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[1,5,3,7,2,6,4,8]=>[1,-3,-7,6,2,-5,4,8]
[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[3,6,1,7,8,2,4,5]=>[1,6,7,-3,2,8,4,5]
[3,6,1,7,8,2,4,5]=>[6,8,3,2,4,1,7,5]=>[6,8,3,2,4,1,7,5]=>[-7,-3,2,4,-8,1,-6,5]
[3,6,1,2,4,7,8,5]=>[6,1,3,2,8,4,7,5]=>[6,1,3,2,8,4,7,5]=>[3,-7,1,2,-8,4,-6,5]
[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[4,5,6,1,2,3,8,7]=>[1,4,5,6,2,3,-8,7]
[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[6,1,2,4,5,3,8,7]=>[1,2,4,5,-6,3,-8,7]
[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[8,1,2,4,5,6,3,7]=>[1,2,5,8,6,-4,3,7]
[4,1,5,6,2,3,7,8]=>[4,6,2,1,5,3,7,8]=>[4,6,2,1,5,3,7,8]=>[-5,2,-6,1,-4,3,7,8]
[4,5,1,6,2,3,7,8]=>[5,6,2,4,1,3,7,8]=>[5,6,2,4,1,3,7,8]=>[2,-5,6,4,1,3,7,8]
[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[5,6,7,4,1,2,3,8]=>[5,6,7,1,4,2,3,8]
[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[5,7,8,4,1,6,2,3]=>[4,-7,8,6,-5,1,2,3]
[4,1,5,6,7,8,2,3]=>[4,8,2,1,5,6,7,3]=>[4,8,2,1,5,6,7,3]=>[2,5,-8,1,6,7,-4,3]
[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[4,5,7,1,2,8,3,6]=>[5,1,7,8,2,-4,3,6]
[4,5,1,7,2,8,3,6]=>[5,7,8,4,1,3,2,6]=>[5,7,8,4,1,3,2,6]=>[4,-7,8,3,1,-5,2,6]
[4,5,7,1,2,8,3,6]=>[7,1,8,4,5,3,2,6]=>[7,1,8,4,5,3,2,6]=>[5,-4,1,-8,-7,3,2,6]
[4,1,2,5,7,8,3,6]=>[4,1,8,2,5,3,7,6]=>[4,1,8,2,5,3,7,6]=>[5,-7,1,2,-4,3,-8,6]
[4,1,2,5,6,3,8,7]=>[4,1,6,2,5,3,8,7]=>[4,1,6,2,5,3,8,7]=>[5,1,-6,2,-4,3,-8,7]
[4,1,2,5,6,7,8,3]=>[4,1,8,2,5,6,7,3]=>[4,1,8,2,5,6,7,3]=>[1,-8,5,2,6,7,-4,3]
[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[4,6,7,1,8,2,3,5]=>[-4,6,7,8,1,2,3,5]
[4,6,7,1,8,2,3,5]=>[7,8,2,4,3,6,1,5]=>[7,8,2,4,3,6,1,5]=>[2,8,-4,-7,3,6,1,5]
[4,1,6,2,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[4,6,7,1,3,2,5,8]=>[3,6,7,1,-4,2,5,8]
[4,1,6,2,3,7,5,8]=>[4,6,2,1,7,3,5,8]=>[4,6,2,1,7,3,5,8]=>[-7,-6,2,1,-4,3,5,8]
[4,1,2,6,3,7,8,5]=>[4,1,6,2,8,3,7,5]=>[4,1,6,2,8,3,7,5]=>[7,1,-8,2,-4,3,-6,5]
[1,4,6,2,3,8,5,7]=>[1,6,2,4,8,3,5,7]=>[1,6,2,4,8,3,5,7]=>[-4,1,-6,2,3,8,5,7]
[1,2,4,7,3,8,5,6]=>[1,2,7,4,8,5,3,6]=>[1,2,7,4,8,5,3,6]=>[1,2,-4,-8,-7,5,3,6]
[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[1,2,-4,-5,-8,3,6,7]
[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[5,6,7,8,1,2,3,4]=>[1,2,5,6,7,8,3,4]
[5,6,1,7,2,3,8,4]=>[6,7,2,8,5,1,3,4]=>[6,7,2,8,5,1,3,4]=>[-7,8,-6,2,1,5,3,4]
[5,1,6,7,2,8,3,4]=>[5,7,8,3,1,6,2,4]=>[5,7,8,3,1,6,2,4]=>[-3,-7,8,6,-5,1,2,4]
[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[5,6,7,3,1,2,4,8]=>[5,6,7,3,1,2,4,8]
[5,1,6,2,3,7,4,8]=>[5,6,2,7,1,3,4,8]=>[5,6,2,7,1,3,4,8]=>[-5,6,2,1,7,3,4,8]
[1,5,6,2,3,7,8,4]=>[1,6,2,8,5,3,7,4]=>[1,6,2,8,5,3,7,4]=>[1,-7,-5,2,-8,3,-6,4]
[5,1,6,2,3,8,4,7]=>[5,6,2,8,1,3,4,7]=>[5,6,2,8,1,3,4,7]=>[-5,6,2,1,3,8,4,7]
[5,1,7,2,8,3,4,6]=>[5,7,8,3,1,4,2,6]=>[5,7,8,3,1,4,2,6]=>[-3,-7,8,4,1,-5,2,6]
[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[1,2,7,3,5,8,4,6]=>[1,-5,2,-7,3,8,4,6]
[1,5,2,3,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,8,-5,2,3,4,6,7]
[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[6,7,2,8,4,1,3,5]=>[-7,8,-6,2,4,1,3,5]
[6,1,2,3,7,8,4,5]=>[6,1,2,8,4,3,7,5]=>[6,1,2,8,4,3,7,5]=>[4,1,-7,2,-8,3,-6,5]
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[-8,1,2,3,4,5,6,7]
[6,4,5,2,3,1,8,7]=>[3,5,2,6,4,1,8,7]=>[3,5,2,6,4,1,8,7]=>[2,-6,4,-3,-5,1,-8,7]
[2,1,8,6,7,4,5,3]=>[2,1,5,7,4,8,6,3]=>[2,1,5,7,4,8,6,3]=>[-2,1,4,-8,6,-5,-7,3]
[8,4,6,2,7,3,5,1]=>[5,6,7,8,3,4,2,1]=>[5,6,7,8,3,4,2,1]=>[7,8,3,4,2,-6,-5,1]
[8,4,7,2,6,5,3,1]=>[3,5,6,7,8,2,1,4]=>[3,5,6,7,8,2,1,4]=>[2,6,7,-5,8,-3,1,4]
[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]=>[-2,1,-4,3,-6,5,-8,7,-10,9]
[7,3,5,8,1,2,4,6]=>[8,1,7,2,4,3,6,5]=>[8,1,7,2,4,3,6,5]=>[-6,1,4,-7,2,3,-8,5]
[8,4,6,7,1,2,3,5]=>[7,1,2,8,3,5,4,6]=>[7,1,2,8,3,5,4,6]=>[1,-8,5,2,-7,3,4,6]
[5,8,4,7,1,2,3,6]=>[7,1,2,8,5,3,4,6]=>[7,1,2,8,5,3,4,6]=>[1,-8,-7,5,2,3,4,6]
[7,4,2,8,1,3,5,6]=>[8,4,1,7,2,3,5,6]=>[8,4,1,7,2,3,5,6]=>[-4,8,1,7,2,3,5,6]
[8,4,2,7,1,3,5,6]=>[7,4,1,8,2,3,5,6]=>[7,4,1,8,2,3,5,6]=>[7,-4,1,8,2,3,5,6]
[8,5,2,7,1,3,4,6]=>[7,5,1,2,8,3,4,6]=>[7,5,1,2,8,3,4,6]=>[5,-7,1,8,2,3,4,6]
[6,3,7,2,5,1,4,8]=>[5,7,6,1,2,3,4,8]=>[5,7,6,1,2,3,4,8]=>[1,7,5,2,6,3,4,8]
[7,3,6,2,5,1,4,8]=>[5,6,7,1,2,3,4,8]=>[5,6,7,1,2,3,4,8]=>[1,2,5,6,7,3,4,8]
[7,3,8,2,6,1,4,5]=>[6,8,7,1,2,3,4,5]=>[6,8,7,1,2,3,4,5]=>[1,2,8,6,3,7,4,5]
[8,3,6,2,5,1,4,7]=>[5,6,8,1,2,3,4,7]=>[5,6,8,1,2,3,4,7]=>[1,2,5,6,3,8,4,7]
[8,3,7,2,6,1,4,5]=>[6,7,8,1,2,3,4,5]=>[6,7,8,1,2,3,4,5]=>[1,2,3,6,7,8,4,5]
[8,4,7,3,6,1,2,5]=>[6,1,7,8,2,3,4,5]=>[6,1,7,8,2,3,4,5]=>[1,6,7,2,3,8,4,5]
[6,5,4,2,7,1,3,8]=>[7,4,1,5,6,2,3,8]=>[7,4,1,5,6,2,3,8]=>[7,5,-4,1,6,2,3,8]
[6,5,4,3,8,1,2,7]=>[8,1,4,5,6,3,2,7]=>[8,1,4,5,6,3,2,7]=>[1,5,6,-8,3,-4,2,7]
[8,7,5,3,6,1,2,4]=>[6,1,5,2,7,3,8,4]=>[6,1,5,2,7,3,8,4]=>[8,1,-7,2,-5,3,-6,4]
[5,8,3,7,2,6,1,4]=>[6,7,8,1,5,2,3,4]=>[6,7,8,1,5,2,3,4]=>[-6,1,7,8,2,5,3,4]
[8,1,2,5,3,4,6,7]=>[8,1,5,3,2,4,6,7]=>[8,1,5,3,2,4,6,7]=>[-8,3,-5,1,2,4,6,7]
[7,1,2,5,6,3,8,4]=>[7,1,6,8,2,4,5,3]=>[7,1,6,8,2,4,5,3]=>[-6,1,2,8,4,5,-7,3]
[4,1,2,5,8,7,3,6]=>[4,1,7,2,5,3,8,6]=>[4,1,7,2,5,3,8,6]=>[5,1,-8,2,-4,3,-7,6]
[3,1,7,2,6,4,8,5]=>[3,7,1,6,8,2,4,5]=>[3,7,1,6,8,2,4,5]=>[1,7,-3,6,2,8,4,5]
[5,1,4,2,7,3,8,6]=>[5,4,7,1,2,8,3,6]=>[5,4,7,1,2,8,3,6]=>[-4,1,7,8,2,-5,3,6]
[7,1,4,2,6,3,8,5]=>[7,4,6,1,8,2,3,5]=>[7,4,6,1,8,2,3,5]=>[-7,4,6,8,1,2,3,5]
[7,1,5,2,6,3,8,4]=>[7,5,6,8,1,2,3,4]=>[7,5,6,8,1,2,3,4]=>[1,2,7,5,6,8,3,4]
[8,1,4,2,6,7,3,5]=>[8,4,7,1,3,2,6,5]=>[8,4,7,1,3,2,6,5]=>[4,3,6,-7,1,2,-8,5]
[2,8,1,7,6,3,4,5]=>[8,2,6,3,4,7,1,5]=>[8,2,6,3,4,7,1,5]=>[-2,3,6,-8,4,7,1,5]
[6,3,1,2,4,7,8,5]=>[3,1,6,2,8,4,7,5]=>[3,1,6,2,8,4,7,5]=>[7,1,-3,2,-8,4,-6,5]
[5,4,1,2,8,3,6,7]=>[4,1,5,8,3,2,6,7]=>[4,1,5,8,3,2,6,7]=>[1,8,3,-5,-4,2,6,7]
[4,3,1,5,6,7,8,2]=>[3,4,8,2,5,6,7,1]=>[3,4,8,2,5,6,7,1]=>[2,-4,5,8,6,7,-3,1]
[7,3,4,1,6,2,8,5]=>[4,6,7,3,8,1,2,5]=>[4,6,7,3,8,1,2,5]=>[-4,6,7,3,1,8,2,5]
[7,3,8,1,6,2,4,5]=>[8,6,7,2,3,1,5,4]=>[8,6,7,2,3,1,5,4]=>[2,7,5,-6,3,1,-8,4]
[7,3,5,1,6,2,8,4]=>[5,6,7,8,3,1,2,4]=>[5,6,7,8,3,1,2,4]=>[5,6,7,8,3,1,2,4]
[7,3,8,5,1,2,4,6]=>[5,1,8,2,7,3,4,6]=>[5,1,8,2,7,3,4,6]=>[-8,1,-5,7,2,3,4,6]
[4,6,7,3,8,5,1,2]=>[5,1,8,4,7,6,2,3]=>[5,1,8,4,7,6,2,3]=>[1,-7,-5,4,-8,6,2,3]
[6,2,8,4,5,1,7,3]=>[5,6,7,8,4,2,1,3]=>[5,6,7,8,4,2,1,3]=>[2,8,-7,-6,-5,4,1,3]
[5,1,4,8,6,2,3,7]=>[5,6,2,1,4,8,3,7]=>[5,6,2,1,4,8,3,7]=>[-4,-6,2,1,-5,8,3,7]
[3,5,2,7,1,8,6,4]=>[7,5,3,6,2,8,1,4]=>[7,5,3,6,2,8,1,4]=>[6,-3,-7,-5,2,8,1,4]
[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,-3,6,5,1,-8,-7,4]
[4,6,7,2,8,1,5,3]=>[8,7,5,4,1,6,2,3]=>[8,7,5,4,1,6,2,3]=>[-4,-7,-8,6,-5,1,2,3]
[5,6,7,8,2,1,4,3]=>[2,8,4,1,5,6,7,3]=>[2,8,4,1,5,6,7,3]=>[4,5,-2,1,6,7,-8,3]
[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,-3,2,-8,5,-7,6]
[4,6,2,7,3,5,1,8]=>[5,6,7,4,3,2,1,8]=>[5,6,7,4,3,2,1,8]=>[3,2,-4,-7,-6,-5,1,8]
[3,2,5,1,6,4,8,7]=>[5,3,2,6,1,4,8,7]=>[5,3,2,6,1,4,8,7]=>[-2,-5,-3,6,1,4,-8,7]
[3,2,5,4,7,1,8,6]=>[7,3,2,5,4,8,1,6]=>[7,3,2,5,4,8,1,6]=>[-2,-5,4,-7,-3,8,1,6]
[4,2,5,3,7,6,8,1]=>[8,4,5,2,3,7,6,1]=>[8,4,5,2,3,7,6,1]=>[7,5,2,3,6,-4,-8,1]
[4,2,5,3,7,1,8,6]=>[7,4,5,2,3,8,1,6]=>[7,4,5,2,3,8,1,6]=>[4,5,2,-7,3,8,1,6]
[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,-6,1,-8,7]
[4,2,5,1,6,3,8,7]=>[5,4,6,2,1,3,8,7]=>[5,4,6,2,1,3,8,7]=>[6,-4,-5,2,1,3,-8,7]
[3,1,5,4,6,2,8,7]=>[3,6,1,5,4,2,8,7]=>[3,6,1,5,4,2,8,7]=>[-5,4,1,-3,-6,2,-8,7]
[4,1,5,3,6,2,8,7]=>[4,6,5,1,3,2,8,7]=>[4,6,5,1,3,2,8,7]=>[5,-4,3,1,-6,2,-8,7]
[4,3,5,2,7,1,8,6]=>[7,5,4,3,2,8,1,6]=>[7,5,4,3,2,8,1,6]=>[-2,-3,-4,-7,-5,8,1,6]
[4,3,5,1,7,2,8,6]=>[5,7,4,3,1,8,2,6]=>[5,7,4,3,1,8,2,6]=>[-3,8,-7,-4,1,-5,2,6]
[4,1,5,3,7,2,8,6]=>[4,7,5,1,3,8,2,6]=>[4,7,5,1,3,8,2,6]=>[5,-4,3,-7,1,8,2,6]
[3,1,5,4,7,2,8,6]=>[3,7,1,5,4,8,2,6]=>[3,7,1,5,4,8,2,6]=>[-5,4,1,-7,-3,8,2,6]
[2,1,5,4,7,3,8,6]=>[2,1,7,5,4,8,3,6]=>[2,1,7,5,4,8,3,6]=>[-2,1,-4,-7,-5,8,3,6]
[3,1,5,4,7,6,8,2]=>[3,8,1,5,4,7,6,2]=>[3,8,1,5,4,7,6,2]=>[-5,4,-3,1,6,-7,-8,2]
[4,1,5,3,7,6,8,2]=>[4,8,5,1,3,7,6,2]=>[4,8,5,1,3,7,6,2]=>[-4,5,3,1,6,-7,-8,2]
[4,3,6,5,7,1,8,2]=>[7,8,4,3,6,5,1,2]=>[7,8,4,3,6,5,1,2]=>[-6,-8,4,3,-7,5,1,2]
[5,3,6,4,7,1,8,2]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]=>[7,8,5,6,3,4,1,2]
[5,1,6,3,7,4,8,2]=>[5,8,6,7,1,3,4,2]=>[5,8,6,7,1,3,4,2]=>[5,1,6,7,3,4,-8,2]
[4,1,6,3,7,5,8,2]=>[4,8,6,1,7,3,5,2]=>[4,8,6,1,7,3,5,2]=>[7,-6,3,1,-8,5,-4,2]
[3,1,6,4,7,5,8,2]=>[3,8,1,6,7,4,5,2]=>[3,8,1,6,7,4,5,2]=>[-6,-3,1,7,4,5,-8,2]
[2,1,6,4,7,5,8,3]=>[2,1,8,6,7,4,5,3]=>[2,1,8,6,7,4,5,3]=>[-7,-2,-6,1,4,5,-8,3]
[2,1,6,4,7,3,8,5]=>[2,1,7,6,8,4,3,5]=>[2,1,7,6,8,4,3,5]=>[-2,-8,1,-6,-7,4,3,5]
[3,1,6,4,7,2,8,5]=>[3,7,1,6,8,4,2,5]=>[3,7,1,6,8,4,2,5]=>[6,1,8,4,-7,-3,2,5]
[4,1,6,3,7,2,8,5]=>[4,7,6,1,8,3,2,5]=>[4,7,6,1,8,3,2,5]=>[-8,-6,3,1,-7,-4,2,5]
[5,1,6,3,7,2,8,4]=>[5,7,6,8,1,3,2,4]=>[5,7,6,8,1,3,2,4]=>[5,6,3,8,-7,1,2,4]
[5,3,6,2,7,4,8,1]=>[8,6,5,7,3,2,4,1]=>[8,6,5,7,3,2,4,1]=>[-7,3,-5,-8,2,4,-6,1]
[5,2,6,3,7,4,8,1]=>[8,5,6,7,2,3,4,1]=>[8,5,6,7,2,3,4,1]=>[5,8,6,7,3,4,-2,1]
[5,2,6,3,7,1,8,4]=>[7,5,6,8,2,3,1,4]=>[7,5,6,8,2,3,1,4]=>[2,5,6,8,-7,3,1,4]
[5,2,6,1,7,3,8,4]=>[6,5,7,8,2,1,3,4]=>[6,5,7,8,2,1,3,4]=>[2,-5,-6,7,1,8,3,4]
[4,2,5,1,7,3,8,6]=>[5,4,7,2,1,8,3,6]=>[5,4,7,2,1,8,3,6]=>[8,-7,2,-4,1,-5,3,6]
[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,-6,7,2,1,8,3,5]
[4,2,6,3,7,1,8,5]=>[7,4,6,2,8,3,1,5]=>[7,4,6,2,8,3,1,5]=>[2,-6,8,3,-7,-4,1,5]
[4,2,6,3,7,5,8,1]=>[8,4,6,2,7,3,5,1]=>[8,4,6,2,7,3,5,1]=>[-6,2,7,-4,3,5,-8,1]
[3,2,6,4,7,5,8,1]=>[8,3,2,6,7,4,5,1]=>[8,3,2,6,7,4,5,1]=>[-6,2,-3,7,4,5,-8,1]
[3,2,6,4,7,1,8,5]=>[7,3,2,6,8,4,1,5]=>[7,3,2,6,8,4,1,5]=>[-6,-2,4,8,-7,-3,1,5]
[3,2,6,1,7,4,8,5]=>[6,3,2,7,8,1,4,5]=>[6,3,2,7,8,1,4,5]=>[-6,-2,-3,1,7,8,4,5]
[3,2,5,1,7,4,8,6]=>[5,3,2,7,1,8,4,6]=>[5,3,2,7,1,8,4,6]=>[-2,-7,-3,8,1,-5,4,6]
[3,2,4,1,7,5,8,6]=>[4,3,2,1,7,8,5,6]=>[4,3,2,1,7,8,5,6]=>[-2,-3,-4,-7,1,8,5,6]
[3,1,4,2,7,6,8,5]=>[3,4,1,2,8,7,6,5]=>[3,4,1,2,8,7,6,5]=>[3,4,1,2,-6,-7,-8,5]
[3,2,5,1,7,6,8,4]=>[5,3,2,8,1,7,6,4]=>[5,3,2,8,1,7,6,4]=>[-2,-3,-7,6,1,-5,-8,4]
[3,2,6,1,7,5,8,4]=>[6,3,2,8,7,1,5,4]=>[6,3,2,8,7,1,5,4]=>[-2,-7,-3,-6,5,1,-8,4]
[4,2,6,1,7,5,8,3]=>[6,4,8,2,7,1,5,3]=>[6,4,8,2,7,1,5,3]=>[7,-8,-4,2,5,1,-6,3]
[4,2,5,1,7,6,8,3]=>[5,4,8,2,1,7,6,3]=>[5,4,8,2,1,7,6,3]=>[6,2,-7,-4,1,-5,-8,3]
[4,1,5,2,7,6,8,3]=>[4,5,8,1,2,7,6,3]=>[4,5,8,1,2,7,6,3]=>[5,7,1,6,2,-4,-8,3]
[3,1,5,2,7,6,8,4]=>[3,5,1,8,2,7,6,4]=>[3,5,1,8,2,7,6,4]=>[-7,6,1,-3,2,-5,-8,4]
[2,1,5,3,7,6,8,4]=>[2,1,5,8,3,7,6,4]=>[2,1,5,8,3,7,6,4]=>[-2,1,-7,6,3,-5,-8,4]
[2,1,6,3,7,5,8,4]=>[2,1,6,8,7,3,5,4]=>[2,1,6,8,7,3,5,4]=>[-2,-7,1,-6,5,3,-8,4]
[3,1,6,2,7,5,8,4]=>[3,6,1,8,7,2,5,4]=>[3,6,1,8,7,2,5,4]=>[7,5,1,-6,-3,2,-8,4]
[4,1,6,2,7,5,8,3]=>[4,6,8,1,7,2,5,3]=>[4,6,8,1,7,2,5,3]=>[8,7,1,5,-6,2,-4,3]
[5,1,6,2,7,4,8,3]=>[5,6,8,7,1,2,4,3]=>[5,6,8,7,1,2,4,3]=>[5,6,7,1,4,2,-8,3]
[5,2,6,1,7,4,8,3]=>[6,5,8,7,2,1,4,3]=>[6,5,8,7,2,1,4,3]=>[4,-7,-5,-6,2,1,-8,3]
[5,4,6,2,7,1,8,3]=>[7,6,8,5,4,2,1,3]=>[7,6,8,5,4,2,1,3]=>[4,-5,-8,-6,-7,2,1,3]
[5,1,6,4,7,2,8,3]=>[5,7,8,6,1,4,2,3]=>[5,7,8,6,1,4,2,3]=>[5,8,6,1,-7,4,2,3]
[3,1,6,5,7,2,8,4]=>[3,7,1,8,6,5,2,4]=>[3,7,1,8,6,5,2,4]=>[6,5,1,-8,-7,-3,2,4]
[3,1,6,5,7,4,8,2]=>[3,8,1,7,6,5,4,2]=>[3,8,1,7,6,5,4,2]=>[-5,4,1,-3,-6,-7,-8,2]
[4,1,6,5,7,3,8,2]=>[4,8,7,1,6,5,3,2]=>[4,8,7,1,6,5,3,2]=>[-5,-6,3,1,-4,-7,-8,2]
[5,1,6,4,7,3,8,2]=>[5,8,7,6,1,4,3,2]=>[5,8,7,6,1,4,3,2]=>[4,-6,-5,3,1,-7,-8,2]
[3,2,5,1,6,8,4,7]=>[5,3,2,8,1,6,4,7]=>[5,3,2,8,1,6,4,7]=>[-2,-8,-3,6,1,-5,4,7]
[7,3,6,2,4,1,8,5]=>[4,6,7,2,8,3,1,5]=>[4,6,7,2,8,3,1,5]=>[2,-7,8,-6,3,-4,1,5]
[3,5,2,7,1,8,4,6]=>[7,5,3,8,2,4,1,6]=>[7,5,3,8,2,4,1,6]=>[8,-7,-5,2,4,-3,1,6]
[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[-4,3,1,2,-6,5,-8,7]
[3,5,2,6,4,1,8,7]=>[4,6,3,5,1,2,8,7]=>[4,6,3,5,1,2,8,7]=>[-4,6,3,5,1,2,-8,7]
[6,1,2,4,5,3,8,7]=>[6,1,5,2,4,3,8,7]=>[6,1,5,2,4,3,8,7]=>[1,-5,4,2,-6,3,-8,7]
[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,6,5,3,4,8,7]=>[-2,-5,-6,1,3,4,-8,7]
[2,1,5,7,4,8,6,3]=>[2,1,6,8,5,7,3,4]=>[2,1,6,8,5,7,3,4]=>[-2,-8,-6,1,5,7,3,4]
[8,1,2,3,5,6,7,4]=>[8,1,2,7,3,4,5,6]=>[8,1,2,7,3,4,5,6]=>[-8,1,2,3,4,7,5,6]
[2,1,8,3,4,6,7,5]=>[2,1,8,3,7,4,6,5]=>[2,1,8,3,7,4,6,5]=>[-6,-2,1,-7,3,4,-8,5]
[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]=>[4,3,1,2,8,7,5,6]=>[-4,3,1,-7,-8,2,5,6]
[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,8,7,5,6]=>[-2,1,-4,-7,-8,3,5,6]
[5,1,7,3,8,4,6,2]=>[5,6,7,8,1,4,3,2]=>[5,6,7,8,1,4,3,2]=>[7,8,4,3,1,-6,-5,2]
[5,7,1,6,8,2,4,3]=>[7,8,4,2,5,1,6,3]=>[7,8,4,2,5,1,6,3]=>[-5,-8,2,-4,6,1,-7,3]
[7,8,4,1,2,3,6,5]=>[4,1,2,8,6,3,7,5]=>[4,1,2,8,6,3,7,5]=>[7,1,2,-6,-4,3,-8,5]
[4,5,7,6,1,8,3,2]=>[6,3,7,4,5,8,2,1]=>[6,3,7,4,5,8,2,1]=>[4,-3,5,8,2,-7,-6,1]
[3,7,8,5,1,2,4,6]=>[5,1,3,2,8,4,7,6]=>[5,1,3,2,8,4,7,6]=>[3,-7,1,2,-5,4,-8,6]
[4,1,8,6,2,3,5,7]=>[4,6,2,1,3,8,5,7]=>[4,6,2,1,3,8,5,7]=>[8,-4,2,1,3,-6,5,7]
[2,8,5,3,4,1,6,7]=>[4,2,5,3,8,1,6,7]=>[4,2,5,3,8,1,6,7]=>[-2,3,-5,-4,1,8,6,7]
[3,4,1,2,7,6,8,5]=>[4,1,3,2,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[3,1,-4,2,-6,-7,-8,5]
[3,5,2,6,4,8,7,1]=>[7,5,3,6,2,4,8,1]=>[7,5,3,6,2,4,8,1]=>[-6,-7,-5,2,4,8,-3,1]
[3,2,4,1,7,8,5,6]=>[4,3,2,1,8,5,7,6]=>[4,3,2,1,8,5,7,6]=>[-2,-3,-4,-7,1,5,-8,6]
[7,3,5,1,6,2,4,8]=>[5,6,7,2,4,3,1,8]=>[5,6,7,2,4,3,1,8]=>[7,4,2,3,-6,-5,1,8]
[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]=>[-2,1,-4,3,-6,5,-8,7,-10,9,-12,11]
[8,1,3,5,6,2,7,4]=>[8,6,1,7,2,3,5,4]=>[8,6,1,7,2,3,5,4]=>[-8,7,5,1,2,3,-6,4]
[7,4,6,1,8,3,5,2]=>[6,5,8,7,3,4,1,2]=>[6,5,8,7,3,4,1,2]=>[-6,5,-8,7,3,4,1,2]
[7,3,5,1,8,4,6,2]=>[5,6,7,8,3,4,1,2]=>[5,6,7,8,3,4,1,2]=>[5,6,7,8,3,4,1,2]
[7,3,4,1,8,5,6,2]=>[4,6,7,3,8,5,1,2]=>[4,6,7,3,8,5,1,2]=>[7,8,-4,3,-6,5,1,2]
[4,5,7,3,1,8,6,2]=>[3,7,6,4,5,8,2,1]=>[3,7,6,4,5,8,2,1]=>[-4,-3,5,8,2,-6,-7,1]
[7,5,6,1,8,3,4,2]=>[6,4,8,3,7,5,1,2]=>[6,4,8,3,7,5,1,2]=>[-4,-8,7,3,-6,5,1,2]
[4,5,7,1,3,8,2,6]=>[7,8,1,4,5,3,6,2]=>[7,8,1,4,5,3,6,2]=>[1,8,5,-4,3,6,-7,2]
[5,3,1,2,8,6,4,7]=>[3,1,5,6,2,8,4,7]=>[3,1,5,6,2,8,4,7]=>[-6,1,-3,8,2,-5,4,7]
[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,-3,2,-6,8,5,7]
[7,6,1,5,8,3,2,4]=>[6,3,7,2,1,8,4,5]=>[6,3,7,2,1,8,4,5]=>[8,2,-7,-3,-6,1,4,5]
[3,6,7,1,5,8,2,4]=>[7,8,3,2,1,6,5,4]=>[7,8,3,2,1,6,5,4]=>[2,-5,-6,-3,1,-8,-7,4]
[7,1,6,5,8,2,4,3]=>[7,8,4,2,6,1,5,3]=>[7,8,4,2,6,1,5,3]=>[-6,-8,-4,2,5,1,-7,3]
[7,5,1,6,8,4,2,3]=>[5,4,2,7,8,1,3,6]=>[5,4,2,7,8,1,3,6]=>[-4,-5,-2,1,7,8,3,6]
[5,2,3,1,8,6,7,4]=>[3,5,2,7,1,8,6,4]=>[3,5,2,7,1,8,6,4]=>[2,-8,6,-3,1,-5,-7,4]
[6,2,4,1,8,5,7,3]=>[4,6,7,2,8,1,5,3]=>[4,6,7,2,8,1,5,3]=>[2,-7,8,-6,5,1,-4,3]
[6,2,5,1,8,4,7,3]=>[5,6,7,8,2,1,4,3]=>[5,6,7,8,2,1,4,3]=>[2,8,-7,-6,4,1,-5,3]
[7,1,6,4,8,2,5,3]=>[7,8,5,6,2,1,4,3]=>[7,8,5,6,2,1,4,3]=>[2,6,-5,-8,4,1,-7,3]
[6,1,5,2,8,3,7,4]=>[6,5,8,7,1,2,3,4]=>[6,5,8,7,1,2,3,4]=>[8,1,6,5,2,7,3,4]
[7,3,1,4,8,6,2,5]=>[3,7,6,1,4,8,2,5]=>[3,7,6,1,4,8,2,5]=>[6,-3,4,-7,1,8,2,5]
[5,2,1,3,8,7,4,6]=>[2,5,1,7,3,4,8,6]=>[2,5,1,7,3,4,8,6]=>[-2,8,-5,1,3,4,-7,6]
[7,4,1,3,8,5,2,6]=>[4,7,1,5,8,3,2,6]=>[4,7,1,5,8,3,2,6]=>[-5,1,8,-7,3,-4,2,6]
[6,1,4,2,8,3,7,5]=>[6,4,8,1,7,2,3,5]=>[6,4,8,1,7,2,3,5]=>[-4,1,-6,8,2,7,3,5]
[7,6,1,4,8,3,2,5]=>[6,3,7,1,4,8,2,5]=>[6,3,7,1,4,8,2,5]=>[-6,7,4,1,-3,8,2,5]
[5,1,3,2,8,4,7,6]=>[5,3,1,8,2,7,4,6]=>[5,3,1,8,2,7,4,6]=>[-3,7,-8,1,2,-5,4,6]
[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>[2,4,1,3,7,5,8,6]=>[-2,4,1,3,-8,5,-7,6]
[2,4,8,5,3,1,6,7]=>[3,2,5,4,8,1,6,7]=>[3,2,5,4,8,1,6,7]=>[-2,4,-3,-5,1,8,6,7]
[2,1,8,4,7,3,6,5]=>[2,1,7,8,6,3,4,5]=>[2,1,7,8,6,3,4,5]=>[-8,-2,-7,1,3,6,4,5]
[1,6,2,4,7,3,8,5]=>[1,6,7,2,8,4,3,5]=>[1,6,7,2,8,4,3,5]=>[1,-8,4,-7,-6,2,3,5]
[5,1,8,4,6,2,7,3]=>[5,6,7,8,1,4,2,3]=>[5,6,7,8,1,4,2,3]=>[1,6,7,8,-5,4,2,3]
[3,5,6,1,8,4,7,2]=>[6,7,3,8,5,1,4,2]=>[6,7,3,8,5,1,4,2]=>[-3,-8,5,-7,4,1,-6,2]
[4,2,5,6,1,8,7,3]=>[6,4,7,2,5,1,8,3]=>[6,4,7,2,5,1,8,3]=>[-5,-7,2,8,-6,1,-4,3]
[7,1,4,2,5,3,8,6]=>[7,4,5,1,2,8,3,6]=>[7,4,5,1,2,8,3,6]=>[4,5,1,8,-7,2,3,6]
[4,1,6,2,8,3,7,5]=>[4,6,8,1,7,2,3,5]=>[4,6,8,1,7,2,3,5]=>[1,6,8,-4,2,7,3,5]
[6,8,5,3,1,7,4,2]=>[3,5,4,8,7,6,1,2]=>[3,5,4,8,7,6,1,2]=>[3,-5,4,-7,-8,6,1,2]
[3,8,2,4,6,7,1,5]=>[7,8,3,2,1,5,4,6]=>[7,8,3,2,1,5,4,6]=>[2,-8,-5,-3,-7,1,4,6]
[5,1,7,3,6,2,4,8]=>[5,6,7,2,1,3,4,8]=>[5,6,7,2,1,3,4,8]=>[-6,-5,2,1,7,3,4,8]
[1,2,8,3,7,4,5,6]=>[1,2,8,7,4,5,3,6]=>[1,2,8,7,4,5,3,6]=>[1,-7,-4,2,-8,5,3,6]
[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]=>[8,7,6,5,3,2,1,4]=>[-2,-5,-6,-7,-8,-3,1,4]
[7,6,8,1,4,3,5,2]=>[8,5,4,1,3,7,6,2]=>[8,5,4,1,3,7,6,2]=>[-4,-7,3,1,6,-5,-8,2]
[3,2,5,4,8,1,7,6]=>[8,3,2,5,4,7,1,6]=>[8,3,2,5,4,7,1,6]=>[-2,-5,-3,-8,4,7,1,6]
[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,-5,2,-4,3,6,7,8]
[6,7,3,1,5,8,4,2]=>[3,7,4,8,1,6,2,5]=>[3,7,4,8,1,6,2,5]=>[-4,-7,8,1,6,-3,2,5]
[6,3,4,5,8,7,2,1]=>[2,7,6,3,4,5,8,1]=>[2,7,6,3,4,5,8,1]=>[-6,2,3,4,5,8,-7,1]
[6,3,7,4,2,8,5,1]=>[5,4,8,7,6,1,2,3]=>[5,4,8,7,6,1,2,3]=>[-7,5,-8,4,1,6,2,3]
[5,1,8,3,7,6,2,4]=>[5,6,7,2,1,8,4,3]=>[5,6,7,2,1,8,4,3]=>[4,2,-8,-7,1,-6,-5,3]
[5,4,8,1,7,2,6,3]=>[8,7,6,5,4,2,1,3]=>[8,7,6,5,4,2,1,3]=>[-4,-5,-6,-7,-8,-2,1,3]
[4,7,3,6,2,5,1,8]=>[5,6,7,4,2,3,1,8]=>[5,6,7,4,2,3,1,8]=>[7,4,-6,2,3,-5,1,8]
[5,4,6,1,3,2,8,7]=>[6,3,1,5,4,2,8,7]=>[6,3,1,5,4,2,8,7]=>[-4,-5,1,-3,-6,2,-8,7]
[8,4,7,3,6,2,5,1]=>[5,6,7,8,2,3,4,1]=>[5,6,7,8,2,3,4,1]=>[5,6,7,8,3,4,-2,1]
[2,1,7,6,8,3,5,4]=>[2,1,8,5,3,7,6,4]=>[2,1,8,5,3,7,6,4]=>[-2,1,-6,-7,3,-5,-8,4]
[2,6,4,1,8,5,7,3]=>[4,2,6,7,8,3,5,1]=>[4,2,6,7,8,3,5,1]=>[2,7,-6,8,3,5,-4,1]
[1,7,3,8,5,2,4,6]=>[1,5,8,2,7,3,4,6]=>[1,5,8,2,7,3,4,6]=>[8,1,2,-5,3,7,4,6]
[6,2,7,3,5,1,8,4]=>[5,6,7,8,3,2,1,4]=>[5,6,7,8,3,2,1,4]=>[3,8,-7,-6,-5,2,1,4]
[1,7,5,3,4,6,8,2]=>[1,8,5,3,7,4,6,2]=>[1,8,5,3,7,4,6,2]=>[-3,-7,1,4,-8,6,-5,2]
[4,5,7,2,1,8,6,3]=>[2,7,6,4,5,8,1,3]=>[2,7,6,4,5,8,1,3]=>[-6,-7,-2,4,5,8,1,3]
[5,7,3,8,1,6,2,4]=>[8,6,7,2,5,1,3,4]=>[8,6,7,2,5,1,3,4]=>[-8,2,6,1,7,5,3,4]
[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,-8,-6,3,5,1,-7,4]
[1,8,4,7,3,6,2,5]=>[1,6,7,8,2,3,4,5]=>[1,6,7,8,2,3,4,5]=>[1,6,2,3,7,8,4,5]
[6,8,3,7,1,5,2,4]=>[7,5,8,2,1,6,3,4]=>[7,5,8,2,1,6,3,4]=>[2,-8,-7,6,-5,1,3,4]
[6,4,3,1,2,8,5,7]=>[3,1,4,6,8,2,5,7]=>[3,1,4,6,8,2,5,7]=>[-4,1,-3,6,2,8,5,7]
[3,7,2,5,4,8,6,1]=>[6,8,3,5,2,7,1,4]=>[6,8,3,5,2,7,1,4]=>[2,8,5,-6,-3,7,1,4]
[8,3,6,1,4,7,2,5]=>[6,7,8,1,3,5,4,2]=>[6,7,8,1,3,5,4,2]=>[1,8,5,3,4,-7,-6,2]
[8,2,6,1,4,3,7,5]=>[6,8,4,1,7,2,3,5]=>[6,8,4,1,7,2,3,5]=>[8,-6,4,7,1,2,3,5]
[4,2,6,1,8,5,7,3]=>[6,4,7,2,8,1,5,3]=>[6,4,7,2,8,1,5,3]=>[8,2,-7,-6,5,1,-4,3]
[5,8,7,1,2,4,3,6]=>[7,1,4,2,5,3,8,6]=>[7,1,4,2,5,3,8,6]=>[5,-4,1,2,-8,3,-7,6]
[8,1,6,5,7,2,4,3]=>[8,7,4,2,6,1,5,3]=>[8,7,4,2,6,1,5,3]=>[-6,-7,-2,-8,5,1,-4,3]
[7,1,6,5,8,3,2,4]=>[7,3,8,2,6,1,5,4]=>[7,3,8,2,6,1,5,4]=>[-8,6,2,-3,5,1,-7,4]
[3,8,6,4,2,7,5,1]=>[5,4,3,7,6,8,1,2]=>[5,4,3,7,6,8,1,2]=>[-4,-5,3,-7,6,8,1,2]
[3,2,6,1,5,4,8,7]=>[6,3,2,5,1,4,8,7]=>[6,3,2,5,1,4,8,7]=>[-6,-2,-3,5,1,4,-8,7]
[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,-5,-6,-2,1,3,-8,7]
[6,1,3,2,5,4,8,7]=>[6,3,1,5,2,4,8,7]=>[6,3,1,5,2,4,8,7]=>[-6,5,1,-3,2,4,-8,7]
[4,3,6,1,5,2,8,7]=>[6,5,4,3,1,2,8,7]=>[6,5,4,3,1,2,8,7]=>[-4,-5,-6,3,1,2,-8,7]
[4,3,5,2,8,1,7,6]=>[8,5,4,3,2,7,1,6]=>[8,5,4,3,2,7,1,6]=>[-2,-3,-8,-4,-5,7,1,6]
[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,-7,-8,-3,2,5,-4,1]
[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,-7,-3,-8,2,-4,1,5]
[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,-3,-8,-4,1,-5,2,6]
[2,1,5,4,8,3,7,6]=>[2,1,8,5,4,7,3,6]=>[2,1,8,5,4,7,3,6]=>[-2,1,-8,-4,-5,7,3,6]
[5,4,7,6,8,1,3,2]=>[8,3,1,5,4,7,6,2]=>[8,3,1,5,4,7,6,2]=>[-4,-5,-3,1,6,-7,-8,2]
[4,3,7,6,8,1,5,2]=>[8,5,4,3,1,7,6,2]=>[8,5,4,3,1,7,6,2]=>[-6,-3,-4,-7,1,-5,-8,2]
[4,3,6,5,8,1,7,2]=>[8,7,4,3,6,5,1,2]=>[8,7,4,3,6,5,1,2]=>[-6,-7,-4,3,-8,5,1,2]
[6,3,5,4,7,2,8,1]=>[8,7,6,5,3,4,2,1]=>[8,7,6,5,3,4,2,1]=>[-3,-5,-6,4,2,-7,-8,1]
[6,3,5,4,8,1,7,2]=>[8,7,6,5,3,4,1,2]=>[8,7,6,5,3,4,1,2]=>[-6,-7,-8,5,3,4,1,2]
[7,4,6,5,8,1,3,2]=>[8,3,1,7,6,4,5,2]=>[8,3,1,7,6,4,5,2]=>[4,-6,-3,-7,1,5,-8,2]
[8,2,7,1,5,3,6,4]=>[7,8,5,6,1,2,4,3]=>[7,8,5,6,1,2,4,3]=>[1,8,5,6,4,2,-7,3]
[8,1,7,2,4,3,6,5]=>[8,7,4,2,6,3,1,5]=>[8,7,4,2,6,3,1,5]=>[-6,-7,-2,-8,3,-4,1,5]
[8,1,3,2,7,4,6,5]=>[8,3,1,7,6,4,2,5]=>[8,3,1,7,6,4,2,5]=>[-6,-4,1,-7,-8,-3,2,5]
[2,1,8,3,7,4,6,5]=>[2,1,8,7,6,4,3,5]=>[2,1,8,7,6,4,3,5]=>[-2,1,-6,-7,-8,-4,3,5]
[2,1,8,3,5,4,7,6]=>[2,1,8,5,3,7,4,6]=>[2,1,8,5,3,7,4,6]=>[-2,-7,-8,1,3,-5,4,6]
[8,1,3,2,5,4,7,6]=>[8,3,1,5,2,7,4,6]=>[8,3,1,5,2,7,4,6]=>[-8,7,1,-3,2,-5,4,6]
[8,1,5,2,4,3,7,6]=>[8,5,4,2,1,7,3,6]=>[8,5,4,2,1,7,3,6]=>[-7,-2,-8,-4,1,-5,3,6]
[3,2,8,1,7,4,6,5]=>[8,3,2,7,6,4,1,5]=>[8,3,2,7,6,4,1,5]=>[-6,-2,4,-7,-8,-3,1,5]
[3,2,8,1,5,4,7,6]=>[8,3,2,5,1,7,4,6]=>[8,3,2,5,1,7,4,6]=>[-5,-2,-3,7,-8,1,4,6]
[3,2,4,1,8,5,7,6]=>[4,3,2,1,8,7,5,6]=>[4,3,2,1,8,7,5,6]=>[-2,-3,-4,-7,-8,1,5,6]
[4,1,3,2,7,6,8,5]=>[4,3,1,2,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[-4,3,1,2,-6,-7,-8,5]
[3,2,7,6,8,1,5,4]=>[8,3,2,5,1,7,6,4]=>[8,3,2,5,1,7,6,4]=>[-5,-2,6,-3,1,-7,-8,4]
[3,2,6,5,8,1,7,4]=>[8,3,2,7,6,5,1,4]=>[8,3,2,7,6,5,1,4]=>[-6,-2,-3,-7,-8,5,1,4]
[7,6,8,1,5,2,4,3]=>[8,5,4,2,1,7,6,3]=>[8,5,4,2,1,7,6,3]=>[-2,-6,-4,-7,1,-5,-8,3]
[7,6,8,1,3,2,5,4]=>[8,3,1,5,2,7,6,4]=>[8,3,1,5,2,7,6,4]=>[-6,-7,1,-3,2,-5,-8,4]
[7,2,8,1,5,4,6,3]=>[8,7,6,5,1,2,3,4]=>[8,7,6,5,1,2,3,4]=>[-8,7,1,6,2,5,3,4]
[5,4,7,2,6,3,8,1]=>[8,7,6,5,4,2,3,1]=>[8,7,6,5,4,2,3,1]=>[-4,-5,-6,-7,2,3,-8,1]
[6,5,8,1,3,2,7,4]=>[8,3,1,7,6,5,2,4]=>[8,3,1,7,6,5,2,4]=>[-6,5,1,-7,-8,-3,2,4]
[2,1,6,5,8,3,7,4]=>[2,1,8,7,6,5,3,4]=>[2,1,8,7,6,5,3,4]=>[-2,-5,-6,-7,-8,1,3,4]
[6,5,7,4,8,1,3,2]=>[8,3,1,7,6,5,4,2]=>[8,3,1,7,6,5,4,2]=>[-4,-5,1,-3,-6,-7,-8,2]
[5,4,6,3,8,1,7,2]=>[8,7,6,5,4,3,1,2]=>[8,7,6,5,4,3,1,2]=>[-4,-5,-6,-7,-8,3,1,2]
[6,5,3,1,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>[3,1,5,2,6,4,8,7]=>[-6,1,-3,2,-5,4,-8,7]
[4,7,1,3,5,8,6,2]=>[7,6,1,4,2,8,3,5]=>[7,6,1,4,2,8,3,5]=>[-4,1,-6,8,-7,2,3,5]
[2,1,8,7,5,3,4,6]=>[2,1,5,3,7,4,8,6]=>[2,1,5,3,7,4,8,6]=>[-2,1,-8,3,-5,4,-7,6]
[3,5,6,4,7,1,8,2]=>[7,8,3,6,5,4,1,2]=>[7,8,3,6,5,4,1,2]=>[6,5,3,-8,-7,4,1,2]
[7,2,5,1,4,3,8,6]=>[5,7,4,1,2,8,3,6]=>[5,7,4,1,2,8,3,6]=>[-7,4,1,8,2,-5,3,6]
[1,8,5,7,4,3,6,2]=>[1,6,4,7,8,3,5,2]=>[1,6,4,7,8,3,5,2]=>[1,-7,-6,8,3,5,-4,2]
[3,8,6,1,7,2,5,4]=>[6,8,3,5,2,7,4,1]=>[6,8,3,5,2,7,4,1]=>[5,7,2,-3,4,-8,-6,1]
[7,8,5,3,6,1,2,4]=>[6,1,5,2,8,3,7,4]=>[6,1,5,2,8,3,7,4]=>[1,7,-8,2,-5,3,-6,4]
[1,2,5,8,3,6,7,4]=>[1,2,8,7,5,3,6,4]=>[1,2,8,7,5,3,6,4]=>[1,2,-6,-7,-8,3,-5,4]
[7,3,6,8,5,1,2,4]=>[5,1,8,2,7,4,6,3]=>[5,1,8,2,7,4,6,3]=>[1,-7,4,2,-8,6,-5,3]
[1,2,5,7,8,4,3,6]=>[1,2,4,8,5,3,7,6]=>[1,2,4,8,5,3,7,6]=>[1,2,5,-7,-4,3,-8,6]
[3,6,2,4,7,8,1,5]=>[8,6,3,2,1,4,7,5]=>[8,6,3,2,1,4,7,5]=>[-2,-7,-8,-3,1,4,-6,5]
[5,6,7,8,1,3,4,2]=>[8,4,1,3,5,6,7,2]=>[8,4,1,3,5,6,7,2]=>[8,1,3,5,6,7,-4,2]
[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,-4,-8,7,5,1,-6,3]
[4,7,5,2,8,1,6,3]=>[8,5,7,4,6,1,3,2]=>[8,5,7,4,6,1,3,2]=>[-5,7,4,6,3,1,-8,2]
[1,8,3,4,7,2,6,5]=>[1,7,8,3,6,2,4,5]=>[1,7,8,3,6,2,4,5]=>[1,-7,8,3,2,6,4,5]
[4,2,6,1,8,3,7,5]=>[6,4,8,2,7,1,3,5]=>[6,4,8,2,7,1,3,5]=>[-6,-4,8,2,1,7,3,5]
[6,7,3,4,1,8,2,5]=>[4,8,7,3,1,6,5,2]=>[4,8,7,3,1,6,5,2]=>[-3,5,-6,-7,1,-4,-8,2]
[3,6,5,1,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>[5,1,3,2,6,4,8,7]=>[3,1,-6,2,-5,4,-8,7]
[6,1,4,5,3,2,8,7]=>[6,3,5,1,4,2,8,7]=>[6,3,5,1,4,2,8,7]=>[-3,5,4,1,-6,2,-8,7]
[5,6,7,8,1,4,3,2]=>[8,3,4,1,5,6,7,2]=>[8,3,4,1,5,6,7,2]=>[3,4,5,1,6,7,-8,2]
[2,1,5,8,7,3,4,6]=>[2,1,7,3,5,4,8,6]=>[2,1,7,3,5,4,8,6]=>[-2,-5,1,3,-8,4,-7,6]
[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,-7,3,-4,1,5,-6,2]
[2,1,8,3,6,7,5,4]=>[2,1,8,5,7,3,6,4]=>[2,1,8,5,7,3,6,4]=>[-2,-7,-5,1,6,3,-8,4]
[4,1,2,3,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[1,4,2,3,-6,-7,-8,5]
[3,2,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[-2,-3,-8,-4,1,5,6,7]
[5,1,8,3,6,7,2,4]=>[5,7,8,2,1,4,3,6]=>[5,7,8,2,1,4,3,6]=>[-8,-7,2,4,1,-5,3,6]
[1,8,6,4,5,2,3,7]=>[1,5,2,6,4,8,3,7]=>[1,5,2,6,4,8,3,7]=>[1,-4,2,-6,-5,8,3,7]
[1,8,3,2,5,6,7,4]=>[1,3,8,7,2,4,5,6]=>[1,3,8,7,2,4,5,6]=>[-8,1,-3,2,4,7,5,6]
[7,5,1,3,2,6,8,4]=>[5,3,1,7,8,2,4,6]=>[5,3,1,7,8,2,4,6]=>[-3,7,-5,1,2,8,4,6]
[8,4,6,1,7,3,5,2]=>[6,5,7,8,3,4,1,2]=>[6,5,7,8,3,4,1,2]=>[-6,5,7,8,3,4,1,2]
[5,8,3,6,1,4,7,2]=>[6,7,8,1,5,3,4,2]=>[6,7,8,1,5,3,4,2]=>[1,8,5,-7,3,4,-6,2]
[2,8,7,6,1,4,3,5]=>[6,2,4,1,3,7,8,5]=>[6,2,4,1,3,7,8,5]=>[-7,2,4,1,3,8,-6,5]
[6,4,2,1,5,8,3,7]=>[2,4,6,8,1,3,5,7]=>[2,4,6,8,1,3,5,7]=>[-2,4,1,6,3,8,5,7]
[2,8,1,6,5,4,3,7]=>[8,2,4,5,6,1,3,7]=>[8,2,4,5,6,1,3,7]=>[-2,4,5,8,6,1,3,7]
[4,5,8,1,7,2,3,6]=>[8,7,2,4,5,3,1,6]=>[8,7,2,4,5,3,1,6]=>[2,4,5,-7,-8,3,1,6]
[3,1,7,2,5,4,8,6]=>[3,7,1,5,2,8,4,6]=>[3,7,1,5,2,8,4,6]=>[-5,1,8,-3,-7,2,4,6]
[7,3,8,4,5,1,6,2]=>[5,6,7,8,4,3,2,1]=>[5,6,7,8,4,3,2,1]=>[4,3,2,-8,-7,-6,-5,1]
[3,5,2,7,4,8,6,1]=>[6,5,3,8,2,7,1,4]=>[6,5,3,8,2,7,1,4]=>[8,-5,-3,-6,2,7,1,4]
[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,-3,2,-5,-8,7,-4,1]
[4,1,5,6,7,8,3,2]=>[4,3,8,1,5,6,7,2]=>[4,3,8,1,5,6,7,2]=>[-5,-3,1,8,6,7,-4,2]
[4,1,7,3,8,5,6,2]=>[4,6,7,1,8,5,3,2]=>[4,6,7,1,8,5,3,2]=>[5,3,-8,1,-7,-4,-6,2]
[4,5,7,3,2,8,6,1]=>[6,3,8,4,5,7,1,2]=>[6,3,8,4,5,7,1,2]=>[-6,8,3,4,5,7,1,2]
[2,5,3,8,7,6,1,4]=>[6,2,5,1,3,7,8,4]=>[6,2,5,1,3,7,8,4]=>[-5,2,7,1,3,8,-6,4]
[7,2,5,8,3,6,1,4]=>[6,7,8,1,3,5,2,4]=>[6,7,8,1,3,5,2,4]=>[1,3,7,-6,8,5,2,4]
[3,4,6,5,7,1,8,2]=>[7,8,3,4,6,5,1,2]=>[7,8,3,4,6,5,1,2]=>[3,8,6,4,-7,5,1,2]
[1,2,8,3,5,6,7,4]=>[1,2,8,7,3,4,5,6]=>[1,2,8,7,3,4,5,6]=>[-8,7,1,2,3,4,5,6]
[4,3,5,6,7,1,8,2]=>[7,8,4,3,5,6,1,2]=>[7,8,4,3,5,6,1,2]=>[-7,8,4,3,5,6,1,2]
[8,4,7,6,5,3,2,1]=>[2,3,5,6,7,8,4,1]=>[2,3,5,6,7,8,4,1]=>[3,6,7,8,4,-2,-5,1]
[8,2,7,3,6,4,5,1]=>[5,8,7,6,4,3,2,1]=>[5,8,7,6,4,3,2,1]=>[2,-3,-4,-6,-5,-7,-8,1]
[8,5,7,3,6,2,4,1]=>[4,6,7,2,8,3,5,1]=>[4,6,7,2,8,3,5,1]=>[7,8,2,3,-6,5,-4,1]
[8,6,7,3,5,2,4,1]=>[4,5,7,2,3,8,6,1]=>[4,5,7,2,3,8,6,1]=>[5,8,2,3,6,-4,-7,1]
[8,5,7,4,6,2,3,1]=>[3,6,2,7,8,4,5,1]=>[3,6,2,7,8,4,5,1]=>[-7,2,-3,8,4,5,-6,1]
[8,3,7,2,6,1,5,4]=>[6,7,8,5,1,2,3,4]=>[6,7,8,5,1,2,3,4]=>[1,6,7,8,2,5,3,4]
[4,6,7,3,8,5,2,1]=>[2,5,8,4,7,6,1,3]=>[2,5,8,4,7,6,1,3]=>[-2,-5,7,4,-8,6,1,3]
[4,7,1,3,2,8,6,5]=>[7,3,1,4,6,8,2,5]=>[7,3,1,4,6,8,2,5]=>[-7,4,1,-3,6,8,2,5]
[2,7,3,1,5,8,4,6]=>[3,2,7,8,1,5,6,4]=>[3,2,7,8,1,5,6,4]=>[-2,-3,1,8,5,6,-7,4]
[6,7,1,3,4,5,8,2]=>[7,8,1,2,3,6,5,4]=>[7,8,1,2,3,6,5,4]=>[1,2,6,5,3,-8,-7,4]
[7,4,1,5,8,2,3,6]=>[4,7,2,8,1,5,3,6]=>[4,7,2,8,1,5,3,6]=>[8,-7,2,5,1,-4,3,6]
[5,3,8,6,1,2,4,7]=>[6,1,5,2,3,8,4,7]=>[6,1,5,2,3,8,4,7]=>[1,-5,2,8,3,-6,4,7]
[8,2,1,3,5,6,7,4]=>[2,8,1,7,3,4,5,6]=>[2,8,1,7,3,4,5,6]=>[-8,-2,1,3,4,7,5,6]
[7,3,2,4,8,6,1,5]=>[6,3,8,2,1,7,5,4]=>[6,3,8,2,1,7,5,4]=>[5,2,-3,-7,1,-8,-6,4]
[7,6,2,4,5,8,3,1]=>[3,8,6,2,4,7,1,5]=>[3,8,6,2,4,7,1,5]=>[-8,6,2,4,-3,7,1,5]
[1,2,8,3,7,5,4,6]=>[1,2,8,5,7,4,3,6]=>[1,2,8,5,7,4,3,6]=>[-7,1,2,4,-8,-5,3,6]
[4,3,8,1,2,6,7,5]=>[8,1,4,3,7,2,6,5]=>[8,1,4,3,7,2,6,5]=>[3,-4,-7,1,6,2,-8,5]
[7,3,8,1,4,2,6,5]=>[8,4,7,1,6,2,3,5]=>[8,4,7,1,6,2,3,5]=>[4,-8,1,7,2,6,3,5]
[2,1,5,3,8,4,7,6]=>[2,1,5,8,3,7,4,6]=>[2,1,5,8,3,7,4,6]=>[-2,-8,1,3,7,-5,4,6]
[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,-3,-8,2,4,6]
[8,1,3,2,6,4,7,5]=>[8,3,1,6,7,2,4,5]=>[8,3,1,6,7,2,4,5]=>[1,8,6,-3,2,7,4,5]
[3,1,8,2,6,4,7,5]=>[3,8,1,6,7,2,4,5]=>[3,8,1,6,7,2,4,5]=>[1,8,-3,2,6,7,4,5]
[2,1,8,3,6,4,7,5]=>[2,1,8,6,7,3,4,5]=>[2,1,8,6,7,3,4,5]=>[6,-8,-2,1,3,7,4,5]
[2,1,6,3,8,4,7,5]=>[2,1,6,8,7,3,4,5]=>[2,1,6,8,7,3,4,5]=>[-6,-2,-8,1,3,7,4,5]
[2,1,7,3,5,4,8,6]=>[2,1,7,5,3,8,4,6]=>[2,1,7,5,3,8,4,6]=>[-2,-8,1,-5,-7,3,4,6]
[2,1,7,3,6,4,8,5]=>[2,1,7,6,8,3,4,5]=>[2,1,7,6,8,3,4,5]=>[-6,-7,-2,1,3,8,4,5]
[3,1,6,2,5,4,8,7]=>[3,6,1,5,2,4,8,7]=>[3,6,1,5,2,4,8,7]=>[6,1,5,-3,2,4,-8,7]
[7,1,3,2,5,4,8,6]=>[7,3,1,5,2,8,4,6]=>[7,3,1,5,2,8,4,6]=>[8,-5,1,-3,-7,2,4,6]
[7,1,3,2,6,4,8,5]=>[7,3,1,6,8,2,4,5]=>[7,3,1,6,8,2,4,5]=>[7,1,6,-3,2,8,4,5]
[6,1,4,2,5,3,8,7]=>[6,4,5,1,2,3,8,7]=>[6,4,5,1,2,3,8,7]=>[1,6,4,5,2,3,-8,7]
[4,1,6,2,5,3,8,7]=>[4,6,5,1,2,3,8,7]=>[4,6,5,1,2,3,8,7]=>[6,4,1,5,2,3,-8,7]
[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,-4,1,8,-7,2,3,6]
[4,1,7,2,6,3,8,5]=>[4,7,6,1,8,2,3,5]=>[4,7,6,1,8,2,3,5]=>[-4,-7,6,8,1,2,3,5]
[5,1,7,2,6,3,8,4]=>[5,7,6,8,1,2,3,4]=>[5,7,6,8,1,2,3,4]=>[1,7,5,2,6,8,3,4]
[8,1,5,2,6,3,7,4]=>[8,5,6,7,1,2,3,4]=>[8,5,6,7,1,2,3,4]=>[1,2,5,8,6,7,3,4]
[5,1,8,2,6,3,7,4]=>[5,8,6,7,1,2,3,4]=>[5,8,6,7,1,2,3,4]=>[1,8,2,5,6,7,3,4]
[5,1,6,2,8,3,7,4]=>[5,6,8,7,1,2,3,4]=>[5,6,8,7,1,2,3,4]=>[1,8,5,6,2,7,3,4]
[3,1,6,2,8,4,7,5]=>[3,6,1,8,7,2,4,5]=>[3,6,1,8,7,2,4,5]=>[1,6,-8,7,-3,2,4,5]
[4,1,8,2,6,3,7,5]=>[4,8,6,1,7,2,3,5]=>[4,8,6,1,7,2,3,5]=>[8,6,-4,7,1,2,3,5]
[8,1,4,2,6,3,7,5]=>[8,4,6,1,7,2,3,5]=>[8,4,6,1,7,2,3,5]=>[4,1,-8,6,2,7,3,5]
[8,1,4,2,5,3,7,6]=>[8,4,5,1,2,7,3,6]=>[8,4,5,1,2,7,3,6]=>[5,8,1,7,2,-4,3,6]
[4,1,8,2,5,3,7,6]=>[4,8,5,1,2,7,3,6]=>[4,8,5,1,2,7,3,6]=>[-4,5,1,7,-8,2,3,6]
[4,1,5,2,8,3,7,6]=>[4,5,8,1,2,7,3,6]=>[4,5,8,1,2,7,3,6]=>[5,1,8,2,7,-4,3,6]
[3,1,5,2,8,4,7,6]=>[3,5,1,8,2,7,4,6]=>[3,5,1,8,2,7,4,6]=>[8,1,7,-3,2,-5,4,6]
[3,1,4,2,8,5,7,6]=>[3,4,1,2,8,7,5,6]=>[3,4,1,2,8,7,5,6]=>[3,4,1,-7,-8,2,5,6]
[4,1,3,2,7,5,8,6]=>[4,3,1,2,7,8,5,6]=>[4,3,1,2,7,8,5,6]=>[-4,3,1,-7,2,8,5,6]
[5,1,4,2,8,3,7,6]=>[5,4,8,1,2,7,3,6]=>[5,4,8,1,2,7,3,6]=>[-4,1,8,2,7,-5,3,6]
[6,1,3,2,8,4,7,5]=>[6,3,1,8,7,2,4,5]=>[6,3,1,8,7,2,4,5]=>[-3,-6,-8,7,1,2,4,5]
[6,1,3,2,7,4,8,5]=>[6,3,1,7,8,2,4,5]=>[6,3,1,7,8,2,4,5]=>[-3,-6,7,1,2,8,4,5]
[5,1,3,2,7,4,8,6]=>[5,3,1,7,2,8,4,6]=>[5,3,1,7,2,8,4,6]=>[8,-3,-7,1,2,-5,4,6]
[5,1,3,2,6,4,8,7]=>[5,3,1,6,2,4,8,7]=>[5,3,1,6,2,4,8,7]=>[6,-3,-5,1,2,4,-8,7]
[5,1,4,2,6,3,8,7]=>[5,4,6,1,2,3,8,7]=>[5,4,6,1,2,3,8,7]=>[5,1,4,6,2,3,-8,7]
[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,-4,7,8,1,2,3,5]
[6,1,5,2,7,3,8,4]=>[6,5,7,8,1,2,3,4]=>[6,5,7,8,1,2,3,4]=>[1,6,2,5,7,8,3,4]
[4,2,1,3,7,6,8,5]=>[2,4,1,3,8,7,6,5]=>[2,4,1,3,8,7,6,5]=>[-2,4,1,3,-6,-7,-8,5]
[3,2,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>[4,3,2,1,6,8,5,7]=>[-2,-3,-4,1,-6,8,5,7]
[3,6,7,4,1,5,8,2]=>[4,7,3,8,1,6,2,5]=>[4,7,3,8,1,6,2,5]=>[-7,-3,8,1,6,-4,2,5]
[5,3,2,1,7,6,8,4]=>[2,3,5,8,1,7,6,4]=>[2,3,5,8,1,7,6,4]=>[3,7,-2,6,1,-5,-8,4]
[5,6,1,4,7,2,8,3]=>[6,7,8,1,5,4,2,3]=>[6,7,8,1,5,4,2,3]=>[1,8,5,-7,-6,4,2,3]
[6,4,7,3,5,1,8,2]=>[5,8,7,6,3,4,1,2]=>[5,8,7,6,3,4,1,2]=>[5,-7,-8,6,3,4,1,2]
[1,2,8,6,3,4,7,5]=>[1,2,6,3,8,7,5,4]=>[1,2,6,3,8,7,5,4]=>[1,2,-5,3,-7,-6,-8,4]
[5,2,6,3,4,1,8,7]=>[4,5,6,3,2,1,8,7]=>[4,5,6,3,2,1,8,7]=>[3,2,-6,-5,-4,1,-8,7]
[4,1,2,6,5,3,8,7]=>[4,1,5,2,6,3,8,7]=>[4,1,5,2,6,3,8,7]=>[-6,1,-5,2,-4,3,-8,7]
[2,1,7,4,8,5,6,3]=>[2,1,6,7,8,5,4,3]=>[2,1,6,7,8,5,4,3]=>[-2,1,5,4,-8,-7,-6,3]
[2,1,6,3,4,8,7,5]=>[2,1,6,3,7,4,8,5]=>[2,1,6,3,7,4,8,5]=>[-2,1,-8,3,-7,4,-6,5]
[4,6,7,2,5,8,3,1]=>[3,8,7,4,2,6,1,5]=>[3,8,7,4,2,6,1,5]=>[2,-7,-8,-4,-3,6,1,5]
[3,2,8,7,4,5,1,6]=>[5,3,2,7,4,1,8,6]=>[5,3,2,7,4,1,8,6]=>[-2,-3,4,-8,-5,1,-7,6]
[7,4,2,8,1,6,5,3]=>[8,4,7,5,6,1,3,2]=>[8,4,7,5,6,1,3,2]=>[7,-4,5,6,3,1,-8,2]
[4,1,8,5,7,3,6,2]=>[4,6,7,1,8,3,5,2]=>[4,6,7,1,8,3,5,2]=>[7,8,3,1,-6,5,-4,2]
[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,-3,6,8,-5,1,2,4]
[8,6,1,4,2,3,5,7]=>[6,4,2,1,3,8,5,7]=>[6,4,2,1,3,8,5,7]=>[-8,-4,-2,1,3,-6,5,7]
[6,2,4,3,8,1,5,7]=>[8,6,4,2,1,3,5,7]=>[8,6,4,2,1,3,5,7]=>[-8,-6,-4,-2,1,3,5,7]
[1,2,7,3,5,8,6,4]=>[1,2,7,6,3,8,5,4]=>[1,2,7,6,3,8,5,4]=>[1,2,-5,-8,3,-6,-7,4]
[8,1,4,3,6,5,7,2]=>[8,7,4,1,6,2,3,5]=>[8,7,4,1,6,2,3,5]=>[-8,7,-4,6,1,2,3,5]
[6,1,4,8,3,5,7,2]=>[6,7,8,1,4,5,3,2]=>[6,7,8,1,4,5,3,2]=>[1,8,4,5,3,-7,-6,2]
[4,6,8,1,3,5,7,2]=>[8,7,1,4,2,6,3,5]=>[8,7,1,4,2,6,3,5]=>[-7,4,6,1,-8,2,3,5]
[2,1,6,3,8,5,7,4]=>[2,1,6,7,8,3,5,4]=>[2,1,6,7,8,3,5,4]=>[-2,-7,1,8,5,3,-6,4]
[2,1,8,3,6,5,7,4]=>[2,1,8,7,6,3,5,4]=>[2,1,8,7,6,3,5,4]=>[-2,-5,-6,-7,1,3,-8,4]
[8,7,6,1,4,5,2,3]=>[6,5,2,1,4,7,8,3]=>[6,5,2,1,4,7,8,3]=>[-4,-5,-2,1,7,8,-6,3]
[2,8,3,1,5,6,7,4]=>[3,2,8,7,1,4,5,6]=>[3,2,8,7,1,4,5,6]=>[-8,-2,-3,1,4,7,5,6]
[8,2,7,1,5,4,6,3]=>[7,8,6,5,1,2,3,4]=>[7,8,6,5,1,2,3,4]=>[7,8,1,6,2,5,3,4]
[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,-4,-8,1,2,7,3,5]
[7,2,8,4,3,5,6,1]=>[6,7,4,8,3,5,2,1]=>[6,7,4,8,3,5,2,1]=>[-8,-4,3,5,2,-7,-6,1]
[6,2,4,5,8,1,3,7]=>[8,6,1,3,4,2,5,7]=>[8,6,1,3,4,2,5,7]=>[1,6,-8,3,4,2,5,7]
[8,6,2,5,4,1,3,7]=>[4,5,1,6,3,8,2,7]=>[4,5,1,6,3,8,2,7]=>[3,-6,1,-5,-4,8,2,7]
[8,3,2,4,6,1,5,7]=>[6,3,8,2,1,4,5,7]=>[6,3,8,2,1,4,5,7]=>[2,-6,-3,8,1,4,5,7]
[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,-5,-7,2,6,-8,4]
[2,7,3,1,5,6,8,4]=>[3,2,7,8,1,4,5,6]=>[3,2,7,8,1,4,5,6]=>[-2,-3,1,4,7,8,5,6]
[5,6,7,8,1,4,2,3]=>[8,4,2,1,5,6,7,3]=>[8,4,2,1,5,6,7,3]=>[5,-2,-8,1,6,7,-4,3]
[5,1,7,2,4,6,8,3]=>[5,7,8,2,1,3,4,6]=>[5,7,8,2,1,3,4,6]=>[7,-5,2,1,3,8,4,6]
[5,7,4,8,2,1,3,6]=>[2,8,1,7,5,3,4,6]=>[2,8,1,7,5,3,4,6]=>[-2,-7,-8,1,5,3,4,6]
[7,4,3,8,5,2,1,6]=>[2,5,4,8,7,1,6,3]=>[2,5,4,8,7,1,6,3]=>[7,-2,-4,-5,6,1,-8,3]
[4,2,3,8,5,1,6,7]=>[5,4,2,3,8,1,6,7]=>[5,4,2,3,8,1,6,7]=>[-4,2,3,-5,1,8,6,7]
[6,5,7,3,8,2,4,1]=>[4,8,7,2,6,5,3,1]=>[4,8,7,2,6,5,3,1]=>[-5,-6,2,3,-4,-7,-8,1]
[6,4,7,3,8,2,5,1]=>[5,8,7,6,2,4,3,1]=>[5,8,7,6,2,4,3,1]=>[4,-6,-5,2,3,-7,-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,-3,1,8,-7,6,4,5]
[1,3,5,2,7,6,8,4]=>[1,5,3,8,2,7,6,4]=>[1,5,3,8,2,7,6,4]=>[1,-3,-7,6,2,-5,-8,4]
[1,3,5,7,4,2,8,6]=>[1,4,3,7,5,8,2,6]=>[1,4,3,7,5,8,2,6]=>[1,-3,5,-7,-4,8,2,6]
[4,1,6,2,8,5,7,3]=>[4,6,7,1,8,2,5,3]=>[4,6,7,1,8,2,5,3]=>[7,8,5,1,-6,2,-4,3]
[6,4,2,1,3,8,7,5]=>[2,4,1,6,7,3,8,5]=>[2,4,1,6,7,3,8,5]=>[7,-2,1,8,-4,3,-6,5]
[2,5,8,7,3,6,1,4]=>[6,2,7,1,5,3,8,4]=>[6,2,7,1,5,3,8,4]=>[-5,-2,8,1,-7,3,-6,4]
[3,2,8,4,7,6,1,5]=>[6,3,2,7,1,8,5,4]=>[6,3,2,7,1,8,5,4]=>[-2,-3,5,-8,1,-7,-6,4]
[3,1,8,4,7,2,6,5]=>[3,7,1,8,6,2,4,5]=>[3,7,1,8,6,2,4,5]=>[1,8,-7,6,-3,2,4,5]
[7,3,4,8,6,2,1,5]=>[2,6,8,3,1,7,5,4]=>[2,6,8,3,1,7,5,4]=>[3,5,-2,-7,1,-8,-6,4]
[2,6,5,4,3,8,1,7]=>[8,2,4,5,6,3,1,7]=>[8,2,4,5,6,3,1,7]=>[5,8,6,3,-2,-4,1,7]
[3,7,1,5,6,8,2,4]=>[7,8,3,2,1,4,5,6]=>[7,8,3,2,1,4,5,6]=>[-7,8,2,-3,1,4,5,6]
[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,-3,2,-6,5,-8,7]
[6,1,4,3,5,2,8,7]=>[6,5,4,1,3,2,8,7]=>[6,5,4,1,3,2,8,7]=>[-4,-5,3,1,-6,2,-8,7]
[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>[2,1,5,3,6,4,8,7]=>[-2,1,-6,3,-5,4,-8,7]
[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,5,8,6]=>[-2,1,-4,3,-8,5,-7,6]
[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,-3,7,1,4,-6,5,8]
[5,6,1,2,4,3,8,7]=>[6,1,4,2,5,3,8,7]=>[6,1,4,2,5,3,8,7]=>[5,-4,1,2,-6,3,-8,7]
[5,7,4,2,8,3,6,1]=>[6,4,7,8,5,3,1,2]=>[6,4,7,8,5,3,1,2]=>[-4,8,5,-7,-6,3,1,2]
[3,6,2,5,7,8,1,4]=>[8,6,3,1,4,2,7,5]=>[8,6,3,1,4,2,7,5]=>[-4,-7,-8,1,-3,2,-6,5]
[3,5,2,7,4,8,1,6]=>[8,5,3,7,2,1,4,6]=>[8,5,3,7,2,1,4,6]=>[-3,-8,7,-5,2,1,4,6]
[4,7,2,3,1,8,5,6]=>[3,7,2,4,8,5,1,6]=>[3,7,2,4,8,5,1,6]=>[8,2,4,5,-7,-3,1,6]
[2,8,4,6,7,3,1,5]=>[3,2,7,8,1,5,4,6]=>[3,2,7,8,1,5,4,6]=>[-2,-3,5,8,-7,1,4,6]
[6,2,1,8,4,3,7,5]=>[2,6,4,8,7,1,3,5]=>[2,6,4,8,7,1,3,5]=>[-6,-2,-8,4,1,7,3,5]
[3,5,1,6,4,2,8,7]=>[5,4,3,6,1,2,8,7]=>[5,4,3,6,1,2,8,7]=>[-4,-5,3,6,1,2,-8,7]
[4,6,7,1,8,5,3,2]=>[7,3,5,4,8,6,1,2]=>[7,3,5,4,8,6,1,2]=>[5,3,-8,4,-7,6,1,2]
[3,6,1,7,8,5,4,2]=>[6,4,3,5,8,1,7,2]=>[6,4,3,5,8,1,7,2]=>[-5,-3,8,-6,7,1,-4,2]
[2,1,5,7,3,8,6,4]=>[2,1,7,6,5,8,3,4]=>[2,1,7,6,5,8,3,4]=>[-2,-5,-6,-7,1,8,3,4]
[5,2,6,3,8,1,4,7]=>[8,5,6,1,2,3,4,7]=>[8,5,6,1,2,3,4,7]=>[1,2,5,8,6,3,4,7]
[8,6,1,3,5,2,4,7]=>[6,5,1,3,4,8,2,7]=>[6,5,1,3,4,8,2,7]=>[5,1,3,4,-6,8,2,7]
[7,5,8,4,1,3,2,6]=>[4,3,1,8,7,2,5,6]=>[4,3,1,8,7,2,5,6]=>[-3,7,-8,1,-4,2,5,6]
[4,6,7,2,8,3,1,5]=>[3,8,7,4,1,6,5,2]=>[3,8,7,4,1,6,5,2]=>[5,-4,-6,-7,1,-3,-8,2]
[3,7,8,4,1,5,6,2]=>[4,8,3,6,1,2,7,5]=>[4,8,3,6,1,2,7,5]=>[-4,3,6,7,1,2,-8,5]
[6,1,5,7,2,4,8,3]=>[6,7,8,2,1,5,4,3]=>[6,7,8,2,1,5,4,3]=>[2,-5,-8,4,1,-7,-6,3]
[7,4,5,1,2,3,8,6]=>[5,1,2,7,4,8,3,6]=>[5,1,2,7,4,8,3,6]=>[4,1,-7,2,-5,8,3,6]
[2,1,7,8,3,4,6,5]=>[2,1,8,3,6,4,7,5]=>[2,1,8,3,6,4,7,5]=>[-2,-7,1,-6,3,4,-8,5]
[6,2,5,1,7,4,8,3]=>[5,6,8,7,2,1,4,3]=>[5,6,8,7,2,1,4,3]=>[2,-7,-6,-5,4,1,-8,3]
[3,4,1,2,7,8,6,5]=>[4,1,3,2,6,8,7,5]=>[4,1,3,2,6,8,7,5]=>[3,1,-4,2,7,-6,-8,5]
[3,1,2,4,7,6,8,5]=>[3,1,2,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[3,1,2,4,-6,-7,-8,5]
[8,4,7,6,2,3,1,5]=>[3,6,2,7,1,8,5,4]=>[3,6,2,7,1,8,5,4]=>[2,-8,5,-3,1,-7,-6,4]
[1,3,2,8,5,4,6,7]=>[1,3,2,5,8,4,6,7]=>[1,3,2,5,8,4,6,7]=>[1,-3,2,-5,4,8,6,7]
[2,8,7,1,4,5,3,6]=>[7,2,5,1,4,3,8,6]=>[7,2,5,1,4,3,8,6]=>[-5,2,4,1,-8,3,-7,6]
[8,1,2,4,6,7,5,3]=>[8,1,5,2,7,3,4,6]=>[8,1,5,2,7,3,4,6]=>[5,1,-8,7,2,3,4,6]
[6,2,4,1,7,5,8,3]=>[4,6,8,2,7,1,5,3]=>[4,6,8,2,7,1,5,3]=>[8,7,2,-6,5,1,-4,3]
[4,6,7,2,8,1,3,5]=>[8,7,1,4,2,6,5,3]=>[8,7,1,4,2,6,5,3]=>[4,5,-6,1,2,-7,-8,3]
[6,1,4,2,7,5,3,8]=>[6,4,5,1,7,2,3,8]=>[6,4,5,1,7,2,3,8]=>[4,5,7,-6,1,2,3,8]
[6,2,4,1,7,3,5,8]=>[4,6,7,2,3,1,5,8]=>[4,6,7,2,3,1,5,8]=>[2,6,7,3,-4,1,5,8]
[5,1,7,3,6,2,8,4]=>[5,6,7,8,1,3,2,4]=>[5,6,7,8,1,3,2,4]=>[3,6,7,8,-5,1,2,4]
[5,6,3,1,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>[3,1,6,2,5,4,8,7]=>[5,1,-3,2,-6,4,-8,7]
[3,7,6,4,2,8,5,1]=>[5,4,3,8,6,7,1,2]=>[5,4,3,8,6,7,1,2]=>[-4,-5,-8,3,6,7,1,2]
[7,1,8,5,4,2,3,6]=>[7,4,2,5,8,3,1,6]=>[7,4,2,5,8,3,1,6]=>[-2,-5,3,-7,8,-4,1,6]
[2,1,7,8,5,3,4,6]=>[2,1,5,3,8,4,7,6]=>[2,1,5,3,8,4,7,6]=>[-2,-7,1,3,-5,4,-8,6]
[8,1,3,2,6,5,4,7]=>[8,3,1,5,6,2,4,7]=>[8,3,1,5,6,2,4,7]=>[5,8,1,-3,6,2,4,7]
[8,4,6,5,2,1,7,3]=>[2,5,6,7,8,4,1,3]=>[2,5,6,7,8,4,1,3]=>[-2,6,7,8,-5,4,1,3]
[4,2,1,5,6,7,8,3]=>[2,4,8,1,5,6,7,3]=>[2,4,8,1,5,6,7,3]=>[5,-2,1,8,6,7,-4,3]
[7,3,5,2,4,6,1,8]=>[6,5,7,2,3,4,1,8]=>[6,5,7,2,3,4,1,8]=>[2,5,7,3,4,-6,1,8]
[5,3,7,2,4,6,1,8]=>[6,7,5,2,3,4,1,8]=>[6,7,5,2,3,4,1,8]=>[7,2,5,3,4,-6,1,8]
[3,2,5,7,4,1,6,8]=>[4,3,2,7,5,1,6,8]=>[4,3,2,7,5,1,6,8]=>[-2,-3,5,-7,-4,1,6,8]
[3,2,5,1,7,4,6,8]=>[5,3,2,7,1,4,6,8]=>[5,3,2,7,1,4,6,8]=>[-2,-5,-3,1,7,4,6,8]
[3,2,5,1,7,8,4,6]=>[5,3,2,8,1,4,7,6]=>[5,3,2,8,1,4,7,6]=>[-2,-5,-3,1,7,4,-8,6]
[7,2,8,5,1,3,4,6]=>[5,8,1,2,7,3,6,4]=>[5,8,1,2,7,3,6,4]=>[1,7,2,6,-8,3,-5,4]
[6,3,7,2,8,1,5,4]=>[8,7,6,5,1,3,2,4]=>[8,7,6,5,1,3,2,4]=>[-6,-7,5,3,-8,1,2,4]
[3,6,2,7,8,1,5,4]=>[8,6,3,5,1,2,7,4]=>[8,6,3,5,1,2,7,4]=>[6,5,3,7,1,2,-8,4]
[2,7,3,8,1,5,6,4]=>[8,2,7,6,1,3,4,5]=>[8,2,7,6,1,3,4,5]=>[8,7,2,1,3,6,4,5]
[8,4,6,5,3,1,7,2]=>[3,5,6,7,8,4,2,1]=>[3,5,6,7,8,4,2,1]=>[7,8,4,2,-6,-3,-5,1]
[7,8,1,2,4,3,6,5]=>[8,1,4,2,6,3,7,5]=>[8,1,4,2,6,3,7,5]=>[7,-4,1,-6,2,3,-8,5]
[5,2,4,1,3,7,8,6]=>[4,5,1,2,3,8,7,6]=>[4,5,1,2,3,8,7,6]=>[1,4,5,2,3,-7,-8,6]
[3,5,1,6,4,7,8,2]=>[5,8,3,6,1,4,7,2]=>[5,8,3,6,1,4,7,2]=>[-8,3,6,4,1,7,-5,2]
[8,1,5,4,7,2,6,3]=>[8,7,6,5,1,4,3,2]=>[8,7,6,5,1,4,3,2]=>[-4,-5,-6,3,1,-7,-8,2]
[8,2,5,3,7,1,6,4]=>[7,8,5,6,2,1,3,4]=>[7,8,5,6,2,1,3,4]=>[-8,2,-7,5,1,6,3,4]
[2,6,8,7,4,3,5,1]=>[5,2,4,7,3,6,8,1]=>[5,2,4,7,3,6,8,1]=>[2,7,-4,3,6,8,-5,1]
[3,1,7,4,5,2,8,6]=>[3,5,1,7,4,8,2,6]=>[3,5,1,7,4,8,2,6]=>[-7,4,1,-3,-5,8,2,6]
[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]=>[2,1,6,3,4,7,8,5]=>[-2,-7,1,3,4,8,-6,5]
[6,8,5,4,2,7,1,3]=>[7,4,1,5,8,6,2,3]=>[7,4,1,5,8,6,2,3]=>[-8,5,-4,1,-7,6,2,3]
[5,2,8,6,7,3,4,1]=>[4,5,7,3,2,8,6,1]=>[4,5,7,3,2,8,6,1]=>[3,2,-8,-5,6,-4,-7,1]
[8,4,5,1,7,3,6,2]=>[5,6,7,8,4,1,2,3]=>[5,6,7,8,4,1,2,3]=>[5,6,7,8,1,4,2,3]
[7,4,8,5,6,2,3,1]=>[3,6,2,7,8,5,4,1]=>[3,6,2,7,8,5,4,1]=>[2,-8,5,4,-3,-7,-6,1]
[2,1,8,7,3,4,6,5]=>[2,1,7,3,6,4,8,5]=>[2,1,7,3,6,4,8,5]=>[-2,-8,1,3,-6,4,-7,5]
[4,1,2,8,7,5,3,6]=>[4,1,5,2,7,3,8,6]=>[4,1,5,2,7,3,8,6]=>[-8,1,-5,2,-4,3,-7,6]
[3,5,1,7,4,8,6,2]=>[5,6,3,8,1,7,2,4]=>[5,6,3,8,1,7,2,4]=>[-3,-6,8,1,-5,7,2,4]
[4,5,7,3,8,6,1,2]=>[6,1,8,4,5,7,2,3]=>[6,1,8,4,5,7,2,3]=>[8,1,-6,4,5,7,2,3]
[5,6,7,8,4,1,3,2]=>[4,3,1,8,5,6,7,2]=>[4,3,1,8,5,6,7,2]=>[-5,-3,-8,1,6,7,-4,2]
[8,5,1,2,4,3,6,7]=>[5,1,4,2,8,3,6,7]=>[5,1,4,2,8,3,6,7]=>[1,-4,8,2,-5,3,6,7]
[7,6,2,1,4,8,3,5]=>[2,6,7,1,4,8,3,5]=>[2,6,7,1,4,8,3,5]=>[-2,4,7,-6,1,8,3,5]
[8,7,6,2,1,4,3,5]=>[2,6,4,1,3,7,8,5]=>[2,6,4,1,3,7,8,5]=>[-2,-7,4,1,3,8,-6,5]
[5,4,8,1,6,3,7,2]=>[8,7,6,5,4,1,3,2]=>[8,7,6,5,4,1,3,2]=>[-4,-5,-6,-7,3,1,-8,2]
[5,4,7,2,8,1,6,3]=>[8,7,6,5,4,1,2,3]=>[8,7,6,5,4,1,2,3]=>[-6,-7,-8,5,1,4,2,3]
[8,1,5,4,6,3,7,2]=>[8,7,6,5,1,2,4,3]=>[8,7,6,5,1,2,4,3]=>[-6,-7,5,1,4,2,-8,3]
[2,1,5,8,3,7,4,6]=>[2,1,8,7,5,4,3,6]=>[2,1,8,7,5,4,3,6]=>[-2,1,-4,-7,-8,-5,3,6]
[2,1,7,4,8,3,6,5]=>[2,1,8,7,6,3,4,5]=>[2,1,8,7,6,3,4,5]=>[-6,-7,-8,-2,1,3,4,5]
[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>[4,1,3,2,7,5,8,6]=>[3,1,-4,2,-8,5,-7,6]
[6,2,5,1,7,3,8,4]=>[5,6,7,8,2,1,3,4]=>[5,6,7,8,2,1,3,4]=>[-6,2,-5,7,1,8,3,4]
[7,1,2,3,6,8,4,5]=>[7,1,2,8,4,3,6,5]=>[7,1,2,8,4,3,6,5]=>[4,1,-6,-8,2,3,-7,5]
[3,1,5,2,8,6,7,4]=>[3,5,1,7,2,8,6,4]=>[3,5,1,7,2,8,6,4]=>[6,-8,1,-3,2,-5,-7,4]
[6,2,5,1,8,3,4,7]=>[5,6,8,3,2,1,4,7]=>[5,6,8,3,2,1,4,7]=>[-8,3,-6,-5,2,1,4,7]
[3,5,6,1,4,2,7,8]=>[6,4,3,1,5,2,7,8]=>[6,4,3,1,5,2,7,8]=>[-5,-3,-6,1,-4,2,7,8]
[3,6,2,7,8,5,1,4]=>[5,8,3,1,6,4,7,2]=>[5,8,3,1,6,4,7,2]=>[-3,-6,4,1,-8,7,-5,2]
[3,6,2,7,8,1,4,5]=>[8,6,3,1,2,5,7,4]=>[8,6,3,1,2,5,7,4]=>[6,5,3,1,2,7,-8,4]
[8,1,4,5,3,6,7,2]=>[8,7,5,1,2,3,4,6]=>[8,7,5,1,2,3,4,6]=>[1,8,2,7,5,3,4,6]
[7,3,5,1,8,2,6,4]=>[5,8,7,6,3,1,4,2]=>[5,8,7,6,3,1,4,2]=>[-3,-6,-5,-7,4,1,-8,2]
[4,6,7,1,8,5,2,3]=>[7,5,2,4,8,6,1,3]=>[7,5,2,4,8,6,1,3]=>[5,-8,2,4,-7,6,1,3]
[8,4,7,1,3,2,6,5]=>[7,3,1,8,6,2,4,5]=>[7,3,1,8,6,2,4,5]=>[-3,-8,-7,6,1,2,4,5]
[3,5,2,8,4,6,7,1]=>[7,5,3,8,2,4,6,1]=>[7,5,3,8,2,4,6,1]=>[-2,-7,-5,8,4,6,-3,1]
[3,7,1,5,8,2,4,6]=>[7,8,3,2,1,5,6,4]=>[7,8,3,2,1,5,6,4]=>[-5,-8,2,-3,1,6,-7,4]
[5,2,3,4,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>[4,5,2,3,1,8,6,7]=>[5,2,3,-4,-8,1,6,7]
[7,1,4,2,6,8,3,5]=>[7,4,8,1,3,2,6,5]=>[7,4,8,1,3,2,6,5]=>[-4,3,6,-8,1,2,-7,5]
[1,2,8,3,5,7,6,4]=>[1,2,8,6,3,7,5,4]=>[1,2,8,6,3,7,5,4]=>[1,2,-5,-7,3,-8,-6,4]
[5,7,3,4,8,1,6,2]=>[8,6,7,3,5,1,4,2]=>[8,6,7,3,5,1,4,2]=>[6,7,-3,5,4,1,-8,2]
[4,6,7,3,8,1,2,5]=>[8,1,7,4,2,6,3,5]=>[8,1,7,4,2,6,3,5]=>[-4,-7,6,1,-8,2,3,5]
[4,6,8,3,1,5,7,2]=>[3,8,7,4,1,6,2,5]=>[3,8,7,4,1,6,2,5]=>[-4,-7,-8,6,1,-3,2,5]
[6,1,2,8,3,4,7,5]=>[6,1,8,3,7,2,4,5]=>[6,1,8,3,7,2,4,5]=>[-8,-6,3,1,2,7,4,5]
[3,1,8,2,5,4,6,7]=>[3,8,1,5,2,4,6,7]=>[3,8,1,5,2,4,6,7]=>[1,5,8,-3,2,4,6,7]
[5,3,8,7,6,2,1,4]=>[2,6,5,1,3,7,8,4]=>[2,6,5,1,3,7,8,4]=>[-2,-5,7,1,3,8,-6,4]
[3,6,1,7,8,4,2,5]=>[6,4,3,8,2,1,7,5]=>[6,4,3,8,2,1,7,5]=>[7,-3,2,-4,-8,1,-6,5]
[4,5,7,2,1,8,3,6]=>[2,7,8,4,5,3,1,6]=>[2,7,8,4,5,3,1,6]=>[-2,4,5,-8,-7,3,1,6]
[8,6,7,3,4,1,5,2]=>[4,5,7,3,1,8,6,2]=>[4,5,7,3,1,8,6,2]=>[3,6,-8,-5,1,-4,-7,2]
[6,8,2,7,3,4,1,5]=>[4,8,7,3,2,6,5,1]=>[4,8,7,3,2,6,5,1]=>[-3,2,-6,-7,5,-4,-8,1]
[4,3,8,1,6,5,7,2]=>[8,7,4,3,6,1,5,2]=>[8,7,4,3,6,1,5,2]=>[-6,-7,-8,-3,5,1,-4,2]
[7,2,6,3,8,1,5,4]=>[8,7,6,5,1,4,2,3]=>[8,7,6,5,1,4,2,3]=>[-6,-7,5,1,-8,4,2,3]
[7,2,8,1,6,3,5,4]=>[8,7,6,5,3,1,2,4]=>[8,7,6,5,3,1,2,4]=>[-6,-7,-8,5,3,1,2,4]
[1,2,5,3,7,6,8,4]=>[1,2,5,8,3,7,6,4]=>[1,2,5,8,3,7,6,4]=>[1,2,-7,6,3,-5,-8,4]
[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,-8,1]
[8,4,5,7,6,2,3,1]=>[3,6,2,7,4,8,1,5]=>[3,6,2,7,4,8,1,5]=>[-7,2,4,-6,-3,8,1,5]
[5,2,8,1,4,3,7,6]=>[8,5,4,1,2,7,3,6]=>[8,5,4,1,2,7,3,6]=>[-8,-4,1,7,2,-5,3,6]
[5,2,4,1,6,3,8,7]=>[4,5,6,2,1,3,8,7]=>[4,5,6,2,1,3,8,7]=>[2,-5,-4,6,1,3,-8,7]
[2,1,7,4,6,3,8,5]=>[2,1,6,7,8,4,3,5]=>[2,1,6,7,8,4,3,5]=>[-2,1,4,-7,-6,8,3,5]
[8,4,3,5,7,2,6,1]=>[6,7,4,8,3,2,5,1]=>[6,7,4,8,3,2,5,1]=>[-8,3,-4,-7,2,5,-6,1]
[8,6,1,2,4,5,7,3]=>[6,1,8,2,3,7,5,4]=>[6,1,8,2,3,7,5,4]=>[-7,5,1,2,3,-8,-6,4]
[3,5,2,6,1,4,8,7]=>[6,5,3,1,2,4,8,7]=>[6,5,3,1,2,4,8,7]=>[-6,5,3,1,2,4,-8,7]
[4,5,7,2,3,8,6,1]=>[6,8,2,4,5,7,1,3]=>[6,8,2,4,5,7,1,3]=>[-2,6,4,8,5,7,1,3]
[4,5,7,2,3,8,1,6]=>[8,7,2,4,5,1,3,6]=>[8,7,2,4,5,1,3,6]=>[8,2,4,7,5,1,3,6]
[4,5,6,2,3,1,8,7]=>[3,6,2,4,5,1,8,7]=>[3,6,2,4,5,1,8,7]=>[-2,6,4,5,-3,1,-8,7]
[4,5,6,2,1,3,8,7]=>[2,6,1,4,5,3,8,7]=>[2,6,1,4,5,3,8,7]=>[-2,1,4,5,-6,3,-8,7]
[4,5,6,1,3,2,8,7]=>[6,3,1,4,5,2,8,7]=>[6,3,1,4,5,2,8,7]=>[4,-6,1,5,-3,2,-8,7]
[4,5,6,3,1,2,8,7]=>[3,1,6,4,5,2,8,7]=>[3,1,6,4,5,2,8,7]=>[-4,-3,1,5,-6,2,-8,7]
[4,5,7,3,2,8,1,6]=>[8,3,7,4,5,1,2,6]=>[8,3,7,4,5,1,2,6]=>[-8,3,4,7,5,1,2,6]
[4,6,7,3,8,2,5,1]=>[5,8,7,4,2,6,3,1]=>[5,8,7,4,2,6,3,1]=>[-6,2,-4,-7,3,-8,-5,1]
[4,6,7,3,8,2,1,5]=>[2,8,7,4,1,6,3,5]=>[2,8,7,4,1,6,3,5]=>[-4,-7,6,-2,-8,1,3,5]
[4,5,7,3,1,8,2,6]=>[3,7,8,4,5,2,6,1]=>[3,7,8,4,5,2,6,1]=>[-4,8,5,-3,2,6,-7,1]
[3,5,1,7,4,8,2,6]=>[5,8,3,7,1,2,4,6]=>[5,8,3,7,1,2,4,6]=>[5,3,1,8,2,7,4,6]
[2,1,5,7,4,8,3,6]=>[2,1,8,7,5,3,4,6]=>[2,1,8,7,5,3,4,6]=>[-2,-7,-8,-5,1,3,4,6]
[4,5,7,1,3,8,6,2]=>[7,6,1,4,5,8,3,2]=>[7,6,1,4,5,8,3,2]=>[4,1,5,8,3,-6,-7,2]
[4,6,7,3,8,1,5,2]=>[8,5,7,4,1,6,3,2]=>[8,5,7,4,1,6,3,2]=>[6,3,-7,-4,1,-8,-5,2]
[5,6,7,8,3,1,4,2]=>[3,8,4,2,5,6,7,1]=>[3,8,4,2,5,6,7,1]=>[4,2,-8,5,6,7,-3,1]
[4,6,7,1,8,3,5,2]=>[7,5,8,4,3,6,1,2]=>[7,5,8,4,3,6,1,2]=>[8,4,-7,-5,3,6,1,2]
[3,6,1,7,8,4,5,2]=>[6,5,3,8,4,1,7,2]=>[6,5,3,8,4,1,7,2]=>[-4,-8,7,-3,-5,1,-6,2]
[2,1,6,7,8,4,5,3]=>[2,1,5,8,4,6,7,3]=>[2,1,5,8,4,6,7,3]=>[-2,1,-4,8,6,7,-5,3]
[2,1,6,7,8,4,3,5]=>[2,1,4,8,3,6,7,5]=>[2,1,4,8,3,6,7,5]=>[-2,1,-4,3,6,7,-8,5]
[4,6,7,1,8,3,2,5]=>[7,3,8,4,2,6,1,5]=>[7,3,8,4,2,6,1,5]=>[-4,-8,-3,-7,2,6,1,5]
[5,6,7,8,1,3,2,4]=>[8,3,1,2,5,6,7,4]=>[8,3,1,2,5,6,7,4]=>[3,1,5,2,6,7,-8,4]
[4,6,7,2,8,3,5,1]=>[5,7,8,4,3,6,2,1]=>[5,7,8,4,3,6,2,1]=>[3,-8,6,-4,2,-7,-5,1]
[3,6,2,7,8,4,5,1]=>[5,6,3,8,4,2,7,1]=>[5,6,3,8,4,2,7,1]=>[-3,4,2,-8,-6,7,-5,1]
[3,6,2,7,8,4,1,5]=>[4,8,3,6,1,5,7,2]=>[4,8,3,6,1,5,7,2]=>[8,6,-3,5,1,7,-4,2]
[3,4,2,1,7,8,5,6]=>[2,4,3,1,8,5,7,6]=>[2,4,3,1,8,5,7,6]=>[3,-2,-4,-7,1,5,-8,6]
[4,6,7,2,8,5,3,1]=>[3,5,8,4,7,6,2,1]=>[3,5,8,4,7,6,2,1]=>[4,-7,6,2,-3,-5,-8,1]
[4,6,7,2,8,5,1,3]=>[5,8,1,4,7,6,3,2]=>[5,8,1,4,7,6,3,2]=>[4,1,6,3,-7,-5,-8,2]
[4,5,7,1,2,8,6,3]=>[7,1,6,4,5,8,2,3]=>[7,1,6,4,5,8,2,3]=>[-6,-7,1,4,5,8,2,3]
[2,1,6,7,8,3,5,4]=>[2,1,8,5,3,6,7,4]=>[2,1,8,5,3,6,7,4]=>[-2,-6,1,-8,3,7,-5,4]
[3,6,1,7,8,2,5,4]=>[6,8,3,5,2,1,7,4]=>[6,8,3,5,2,1,7,4]=>[3,7,-5,2,-8,1,-6,4]
[4,6,7,1,8,2,5,3]=>[7,8,5,4,2,6,1,3]=>[7,8,5,4,2,6,1,3]=>[-4,-8,-7,-5,2,6,1,3]
[5,6,7,8,1,2,4,3]=>[8,1,4,2,5,6,7,3]=>[8,1,4,2,5,6,7,3]=>[4,5,1,2,6,7,-8,3]
[5,6,7,8,2,4,1,3]=>[4,8,1,2,5,6,7,3]=>[4,8,1,2,5,6,7,3]=>[5,1,2,8,6,7,-4,3]
[5,6,7,8,2,4,3,1]=>[3,4,8,1,5,6,7,2]=>[3,4,8,1,5,6,7,2]=>[5,-4,1,8,6,7,-3,2]
[3,6,1,7,8,5,2,4]=>[6,5,3,2,8,1,7,4]=>[6,5,3,2,8,1,7,4]=>[-2,-3,-8,-5,7,1,-6,4]
[2,1,6,7,8,5,3,4]=>[2,1,5,3,8,6,7,4]=>[2,1,5,3,8,6,7,4]=>[-2,1,-6,-5,3,7,-8,4]
[3,6,1,5,2,4,8,7]=>[6,5,3,2,1,4,8,7]=>[6,5,3,2,1,4,8,7]=>[-2,-5,-6,-3,1,4,-8,7]
[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,-7,2,5,-8,6]
[5,4,2,6,7,1,8,3]=>[7,4,5,8,3,6,1,2]=>[7,4,5,8,3,6,1,2]=>[4,-7,5,8,3,6,1,2]
[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,-7,6,-8,2,4,1,3]
[3,5,2,8,1,7,6,4]=>[8,5,3,6,2,7,1,4]=>[8,5,3,6,2,7,1,4]=>[-8,6,2,-5,-3,7,1,4]
[6,2,5,1,4,3,8,7]=>[5,6,4,1,2,3,8,7]=>[5,6,4,1,2,3,8,7]=>[5,6,1,4,2,3,-8,7]
[5,2,6,1,4,3,8,7]=>[6,5,4,1,2,3,8,7]=>[6,5,4,1,2,3,8,7]=>[-6,5,1,4,2,3,-8,7]
[5,2,7,1,4,3,8,6]=>[7,5,4,1,2,8,3,6]=>[7,5,4,1,2,8,3,6]=>[-4,-5,1,8,-7,2,3,6]
[6,2,8,1,4,3,7,5]=>[8,6,4,1,7,2,3,5]=>[8,6,4,1,7,2,3,5]=>[-8,-6,-4,7,1,2,3,5]
[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,-4,8,1,2,3,5]
[7,2,6,1,4,3,8,5]=>[6,7,4,1,8,2,3,5]=>[6,7,4,1,8,2,3,5]=>[-7,-6,4,8,1,2,3,5]
[8,2,5,1,4,3,7,6]=>[5,8,4,1,2,7,3,6]=>[5,8,4,1,2,7,3,6]=>[8,4,1,7,2,-5,3,6]
[8,1,4,3,7,2,6,5]=>[8,7,4,1,6,3,5,2]=>[8,7,4,1,6,3,5,2]=>[-6,-7,3,1,-8,5,-4,2]
[8,2,6,1,5,3,7,4]=>[6,8,5,7,1,2,3,4]=>[6,8,5,7,1,2,3,4]=>[1,6,2,8,5,7,3,4]
[7,2,6,1,5,3,8,4]=>[6,7,5,8,1,2,3,4]=>[6,7,5,8,1,2,3,4]=>[1,6,7,2,5,8,3,4]
[6,2,7,1,5,3,8,4]=>[7,6,5,8,1,2,3,4]=>[7,6,5,8,1,2,3,4]=>[7,1,6,2,5,8,3,4]
[6,2,8,1,5,3,7,4]=>[8,6,5,7,1,2,3,4]=>[8,6,5,7,1,2,3,4]=>[6,1,8,2,5,7,3,4]
[7,4,8,1,3,2,6,5]=>[8,3,1,7,6,2,4,5]=>[8,3,1,7,6,2,4,5]=>[7,1,-8,6,-3,2,4,5]
[8,3,7,1,4,2,6,5]=>[7,4,8,1,6,2,3,5]=>[7,4,8,1,6,2,3,5]=>[7,1,8,-4,2,6,3,5]
[8,3,7,1,5,2,6,4]=>[7,5,8,6,1,2,3,4]=>[7,5,8,6,1,2,3,4]=>[7,1,8,5,2,6,3,4]
[7,3,8,1,5,2,6,4]=>[8,5,7,6,1,2,3,4]=>[8,5,7,6,1,2,3,4]=>[1,8,7,5,2,6,3,4]
[6,2,7,3,8,1,5,4]=>[8,6,7,5,1,2,3,4]=>[8,6,7,5,1,2,3,4]=>[1,8,6,7,2,5,3,4]
[6,2,8,3,7,1,5,4]=>[7,6,8,5,1,2,3,4]=>[7,6,8,5,1,2,3,4]=>[7,1,6,8,2,5,3,4]
[5,1,8,3,7,2,6,4]=>[5,7,8,6,1,2,3,4]=>[5,7,8,6,1,2,3,4]=>[1,7,5,8,2,6,3,4]
[4,1,8,3,7,2,6,5]=>[4,7,8,1,6,2,3,5]=>[4,7,8,1,6,2,3,5]=>[1,7,-4,8,2,6,3,5]
[3,1,7,4,8,2,6,5]=>[3,8,1,7,6,2,4,5]=>[3,8,1,7,6,2,4,5]=>[1,-8,7,6,-3,2,4,5]
[4,1,7,3,8,2,6,5]=>[4,8,7,1,6,2,3,5]=>[4,8,7,1,6,2,3,5]=>[-4,1,-8,7,2,6,3,5]
[5,1,7,3,8,2,6,4]=>[5,8,7,6,1,2,3,4]=>[5,8,7,6,1,2,3,4]=>[8,7,1,5,2,6,3,4]
[7,3,8,2,6,1,5,4]=>[6,8,7,5,1,2,3,4]=>[6,8,7,5,1,2,3,4]=>[8,6,1,7,2,5,3,4]
[7,4,2,5,8,3,6,1]=>[6,4,7,8,2,5,3,1]=>[6,4,7,8,2,5,3,1]=>[-8,-7,5,2,3,-6,-4,1]
[5,3,7,8,1,4,2,6]=>[8,4,5,1,3,2,7,6]=>[8,4,5,1,3,2,7,6]=>[4,5,3,-7,1,2,-8,6]
[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,-3,1,8,-5,6,2,4]
[3,1,5,6,7,8,4,2]=>[3,4,1,8,5,6,7,2]=>[3,4,1,8,5,6,7,2]=>[5,-4,-8,1,6,7,-3,2]
[1,6,4,7,8,5,2,3]=>[1,5,2,8,6,3,7,4]=>[1,5,2,8,6,3,7,4]=>[1,-7,2,-6,-8,3,-5,4]
[6,4,1,7,2,3,5,8]=>[4,6,2,7,3,5,1,8]=>[4,6,2,7,3,5,1,8]=>[7,2,3,-6,5,-4,1,8]
[7,4,1,6,2,3,5,8]=>[4,7,2,6,3,5,1,8]=>[4,7,2,6,3,5,1,8]=>[2,6,3,-7,5,-4,1,8]
[1,7,8,6,3,4,5,2]=>[1,5,6,3,4,8,7,2]=>[1,5,6,3,4,8,7,2]=>[-6,1,3,4,7,-5,-8,2]
[2,6,1,4,5,3,8,7]=>[6,2,5,1,4,3,8,7]=>[6,2,5,1,4,3,8,7]=>[-5,2,4,1,-6,3,-8,7]
[3,1,6,4,5,2,8,7]=>[3,5,1,6,4,2,8,7]=>[3,5,1,6,4,2,8,7]=>[4,-6,1,-3,-5,2,-8,7]
[8,4,1,3,5,6,7,2]=>[4,8,1,7,2,3,5,6]=>[4,8,1,7,2,3,5,6]=>[1,-4,8,2,3,7,5,6]
[2,1,4,8,3,6,7,5]=>[2,1,8,4,7,3,6,5]=>[2,1,8,4,7,3,6,5]=>[-2,-4,-7,1,6,3,-8,5]
[8,3,1,2,5,6,7,4]=>[3,1,8,7,2,4,5,6]=>[3,1,8,7,2,4,5,6]=>[-8,1,-3,7,2,4,5,6]
[2,1,5,3,8,6,7,4]=>[2,1,5,7,3,8,6,4]=>[2,1,5,7,3,8,6,4]=>[-2,1,6,-8,3,-5,-7,4]
[1,7,5,2,8,3,4,6]=>[1,5,7,3,8,4,6,2]=>[1,5,7,3,8,4,6,2]=>[-8,1,3,4,-7,6,-5,2]
[1,8,5,2,7,3,4,6]=>[1,5,8,3,7,4,6,2]=>[1,5,8,3,7,4,6,2]=>[-3,1,7,4,-8,6,-5,2]
[3,6,8,2,7,1,4,5]=>[7,8,3,1,2,6,5,4]=>[7,8,3,1,2,6,5,4]=>[6,5,3,1,2,-8,-7,4]
[3,5,8,7,1,2,4,6]=>[7,1,3,2,5,4,8,6]=>[7,1,3,2,5,4,8,6]=>[3,-5,1,2,-8,4,-7,6]
[4,1,7,5,8,2,3,6]=>[4,8,2,1,7,3,5,6]=>[4,8,2,1,7,3,5,6]=>[8,7,2,1,-4,3,5,6]
[8,1,6,7,3,2,4,5]=>[8,3,7,2,4,1,6,5]=>[8,3,7,2,4,1,6,5]=>[-3,2,6,-7,4,1,-8,5]
[5,7,8,3,1,2,4,6]=>[3,1,8,2,5,4,7,6]=>[3,1,8,2,5,4,7,6]=>[5,1,-3,-7,2,4,-8,6]
[8,3,5,1,7,4,6,2]=>[5,6,8,7,3,4,1,2]=>[5,6,8,7,3,4,1,2]=>[5,6,-8,7,3,4,1,2]
[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,-4,7,3,-6,5,1,2]
[4,6,2,1,7,5,8,3]=>[2,6,8,4,7,1,5,3]=>[2,6,8,4,7,1,5,3]=>[-2,4,-8,7,5,1,-6,3]
[1,4,6,2,7,5,8,3]=>[1,6,8,4,7,2,5,3]=>[1,6,8,4,7,2,5,3]=>[-4,1,-8,7,5,2,-6,3]
[4,7,5,6,1,8,3,2]=>[6,3,8,4,7,5,1,2]=>[6,3,8,4,7,5,1,2]=>[7,3,-8,4,-6,5,1,2]
[1,5,3,2,7,6,8,4]=>[1,3,5,8,2,7,6,4]=>[1,3,5,8,2,7,6,4]=>[1,7,-3,6,2,-5,-8,4]
[2,5,3,1,7,6,8,4]=>[3,2,5,8,1,7,6,4]=>[3,2,5,8,1,7,6,4]=>[-2,7,-3,6,1,-5,-8,4]
[4,7,1,6,5,8,2,3]=>[7,8,2,4,6,1,5,3]=>[7,8,2,4,6,1,5,3]=>[7,8,6,-2,5,1,-4,3]
[4,6,1,2,7,5,8,3]=>[6,1,8,4,7,2,5,3]=>[6,1,8,4,7,2,5,3]=>[7,-4,-8,1,5,2,-6,3]
[5,3,1,2,7,6,8,4]=>[3,1,5,8,2,7,6,4]=>[3,1,5,8,2,7,6,4]=>[-7,1,-3,6,2,-5,-8,4]
[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,-3,2,-6,-7,-8,5]
[3,5,1,2,7,6,8,4]=>[5,1,3,8,2,7,6,4]=>[5,1,3,8,2,7,6,4]=>[3,1,-7,6,2,-5,-8,4]
[6,7,1,5,8,2,3,4]=>[7,8,2,3,1,6,5,4]=>[7,8,2,3,1,6,5,4]=>[2,5,-6,3,1,-8,-7,4]
[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,-7,6,1,-5,-8,4]
[5,2,3,1,7,6,8,4]=>[3,5,2,8,1,7,6,4]=>[3,5,2,8,1,7,6,4]=>[2,-7,-3,6,1,-5,-8,4]
[3,5,2,1,7,6,8,4]=>[2,5,3,8,1,7,6,4]=>[2,5,3,8,1,7,6,4]=>[3,-2,-7,6,1,-5,-8,4]
[6,1,5,2,7,4,8,3]=>[6,5,8,7,1,2,4,3]=>[6,5,8,7,1,2,4,3]=>[-6,5,7,1,4,2,-8,3]
[1,5,2,3,7,6,8,4]=>[1,5,2,8,3,7,6,4]=>[1,5,2,8,3,7,6,4]=>[-6,1,2,-7,3,-5,-8,4]
[5,2,1,3,7,6,8,4]=>[2,5,1,8,3,7,6,4]=>[2,5,1,8,3,7,6,4]=>[-2,6,1,-7,3,-5,-8,4]
[6,1,4,2,7,5,8,3]=>[6,4,8,1,7,2,5,3]=>[6,4,8,1,7,2,5,3]=>[7,-8,1,-4,5,2,-6,3]
[5,1,3,2,7,6,8,4]=>[5,3,1,8,2,7,6,4]=>[5,3,1,8,2,7,6,4]=>[6,-3,1,-7,2,-5,-8,4]
[1,4,2,3,7,6,8,5]=>[1,4,2,3,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[-4,1,2,3,-6,-7,-8,5]
[2,4,1,3,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[-4,-2,1,3,-6,-7,-8,5]
[2,5,1,3,7,6,8,4]=>[5,2,1,8,3,7,6,4]=>[5,2,1,8,3,7,6,4]=>[-6,-2,1,-7,3,-5,-8,4]
[5,1,2,3,7,6,8,4]=>[5,1,2,8,3,7,6,4]=>[5,1,2,8,3,7,6,4]=>[1,6,2,-7,3,-5,-8,4]
[5,2,3,1,6,4,8,7]=>[3,5,2,6,1,4,8,7]=>[3,5,2,6,1,4,8,7]=>[-5,2,-3,6,1,4,-8,7]
[7,4,5,2,3,1,8,6]=>[3,5,2,7,4,8,1,6]=>[3,5,2,7,4,8,1,6]=>[-7,2,4,-3,-5,8,1,6]
[7,3,5,2,4,1,8,6]=>[4,5,7,2,3,8,1,6]=>[4,5,7,2,3,8,1,6]=>[5,2,7,3,-4,8,1,6]
[6,3,5,2,4,1,8,7]=>[4,5,6,2,3,1,8,7]=>[4,5,6,2,3,1,8,7]=>[5,6,2,3,-4,1,-8,7]
[4,1,6,3,5,2,8,7]=>[4,5,6,1,3,2,8,7]=>[4,5,6,1,3,2,8,7]=>[5,6,3,1,-4,2,-8,7]
[6,3,4,1,5,2,8,7]=>[4,5,6,3,1,2,8,7]=>[4,5,6,3,1,2,8,7]=>[5,6,-4,3,1,2,-8,7]
[5,2,7,3,4,1,8,6]=>[4,5,7,3,2,8,1,6]=>[4,5,7,3,2,8,1,6]=>[3,-7,2,-5,-4,8,1,6]
[6,2,8,5,7,3,4,1]=>[4,6,7,3,8,2,5,1]=>[4,6,7,3,8,2,5,1]=>[7,-3,8,-6,2,5,-4,1]
[6,2,7,3,4,1,8,5]=>[4,6,7,3,8,2,1,5]=>[4,6,7,3,8,2,1,5]=>[-7,3,8,-6,2,-4,1,5]
[7,3,4,1,5,2,8,6]=>[4,5,7,3,1,8,2,6]=>[4,5,7,3,1,8,2,6]=>[-7,3,8,-5,1,-4,2,6]
[4,1,7,3,5,2,8,6]=>[4,5,7,1,3,8,2,6]=>[4,5,7,1,3,8,2,6]=>[5,3,7,1,-4,8,2,6]
[2,1,7,4,5,3,8,6]=>[2,1,5,7,4,8,3,6]=>[2,1,5,7,4,8,3,6]=>[-2,1,-7,4,-5,8,3,6]
[3,1,8,6,7,4,5,2]=>[3,5,1,7,4,8,6,2]=>[3,5,1,7,4,8,6,2]=>[4,-8,1,-3,6,-5,-7,2]
[4,1,8,6,7,3,5,2]=>[4,5,7,1,3,8,6,2]=>[4,5,7,1,3,8,6,2]=>[5,8,3,1,6,-4,-7,2]
[8,5,7,3,4,1,6,2]=>[4,6,7,3,8,1,5,2]=>[4,6,7,3,8,1,5,2]=>[7,-3,8,-6,5,1,-4,2]
[8,5,6,2,7,3,4,1]=>[4,6,7,3,8,5,2,1]=>[4,6,7,3,8,5,2,1]=>[3,5,-8,2,-7,-4,-6,1]
[8,4,7,3,5,1,6,2]=>[5,6,7,8,3,1,4,2]=>[5,6,7,8,3,1,4,2]=>[7,8,-3,-6,4,1,-5,2]
[5,1,8,4,7,3,6,2]=>[5,6,7,8,1,3,4,2]=>[5,6,7,8,1,3,4,2]=>[1,6,7,8,3,4,-5,2]
[3,1,8,5,7,4,6,2]=>[3,6,1,7,8,4,5,2]=>[3,6,1,7,8,4,5,2]=>[-7,8,-3,1,4,5,-6,2]
[2,1,8,5,7,4,6,3]=>[2,1,6,7,8,4,5,3]=>[2,1,6,7,8,4,5,3]=>[-2,-7,1,8,4,5,-6,3]
[3,1,7,4,6,2,8,5]=>[3,6,1,7,8,4,2,5]=>[3,6,1,7,8,4,2,5]=>[7,8,1,4,-6,-3,2,5]
[4,1,7,3,6,2,8,5]=>[4,6,7,1,8,3,2,5]=>[4,6,7,1,8,3,2,5]=>[3,-7,8,-6,1,-4,2,5]
[6,2,8,4,7,3,5,1]=>[5,6,7,8,3,2,4,1]=>[5,6,7,8,3,2,4,1]=>[7,8,-3,-6,2,4,-5,1]
[7,3,6,2,5,1,8,4]=>[5,6,7,8,2,3,1,4]=>[5,6,7,8,2,3,1,4]=>[2,6,7,8,-5,3,1,4]
[5,2,4,1,7,3,8,6]=>[4,5,7,2,1,8,3,6]=>[4,5,7,2,1,8,3,6]=>[2,-7,8,-5,1,-4,3,6]
[6,2,4,1,7,3,8,5]=>[4,6,7,2,8,1,3,5]=>[4,6,7,2,8,1,3,5]=>[-6,2,-4,1,7,8,3,5]
[7,4,6,2,3,1,8,5]=>[3,6,2,7,8,4,1,5]=>[3,6,2,7,8,4,1,5]=>[-7,2,4,8,-6,-3,1,5]
[6,2,3,1,7,4,8,5]=>[3,6,2,7,8,1,4,5]=>[3,6,2,7,8,1,4,5]=>[6,2,-3,1,7,8,4,5]
[5,2,3,1,7,4,8,6]=>[3,5,2,7,1,8,4,6]=>[3,5,2,7,1,8,4,6]=>[-7,2,-3,8,1,-5,4,6]
[4,2,3,1,7,5,8,6]=>[3,4,2,1,7,8,5,6]=>[3,4,2,1,7,8,5,6]=>[2,-4,-3,-7,1,8,5,6]
[3,1,4,2,8,6,7,5]=>[3,4,1,2,7,8,6,5]=>[3,4,1,2,7,8,6,5]=>[3,4,1,2,6,-8,-7,5]
[6,2,3,1,8,5,7,4]=>[3,6,2,7,8,1,5,4]=>[3,6,2,7,8,1,5,4]=>[-7,2,-3,8,5,1,-6,4]
[8,5,6,2,3,1,7,4]=>[3,6,2,7,8,5,1,4]=>[3,6,2,7,8,5,1,4]=>[-7,2,-3,8,-6,5,1,4]
[7,3,8,5,6,2,4,1]=>[4,6,7,2,8,5,3,1]=>[4,6,7,2,8,5,3,1]=>[5,2,-8,3,-7,-4,-6,1]
[8,5,6,2,4,1,7,3]=>[4,6,7,2,8,5,1,3]=>[4,6,7,2,8,5,1,3]=>[2,-7,-4,8,-6,5,1,3]
[5,2,4,1,8,6,7,3]=>[4,5,7,2,1,8,6,3]=>[4,5,7,2,1,8,6,3]=>[6,2,-8,-5,1,-4,-7,3]
[4,1,5,2,8,6,7,3]=>[4,5,7,1,2,8,6,3]=>[4,5,7,1,2,8,6,3]=>[5,8,6,1,2,-4,-7,3]
[3,1,6,2,8,5,7,4]=>[3,6,1,7,8,2,5,4]=>[3,6,1,7,8,2,5,4]=>[7,8,1,-3,5,2,-6,4]
[5,1,6,2,8,4,7,3]=>[5,6,7,8,1,2,4,3]=>[5,6,7,8,1,2,4,3]=>[1,6,7,8,4,2,-5,3]
[8,4,6,2,5,1,7,3]=>[5,6,7,8,2,4,1,3]=>[5,6,7,8,2,4,1,3]=>[2,6,7,-5,8,4,1,3]
[7,3,8,4,6,2,5,1]=>[5,6,7,8,2,4,3,1]=>[5,6,7,8,2,4,3,1]=>[7,8,4,2,3,-6,-5,1]
[6,2,7,3,8,4,5,1]=>[5,6,7,8,4,2,3,1]=>[5,6,7,8,4,2,3,1]=>[7,8,4,-6,2,3,-5,1]
[8,4,5,1,6,2,7,3]=>[5,6,7,8,4,3,1,2]=>[5,6,7,8,4,3,1,2]=>[7,8,4,-6,-5,3,1,2]
[4,1,8,5,6,2,7,3]=>[4,6,7,1,8,5,2,3]=>[4,6,7,1,8,5,2,3]=>[7,8,5,-4,-6,1,2,3]
[3,1,8,5,6,2,7,4]=>[3,6,1,7,8,5,2,4]=>[3,6,1,7,8,5,2,4]=>[7,8,1,-3,-6,5,2,4]
[2,1,8,5,6,3,7,4]=>[2,1,6,7,8,5,3,4]=>[2,1,6,7,8,5,3,4]=>[-2,-7,1,8,-6,5,3,4]
[3,1,7,4,8,5,6,2]=>[3,6,1,7,8,5,4,2]=>[3,6,1,7,8,5,4,2]=>[5,-8,1,4,-3,-7,-6,2]
[7,3,6,2,8,4,5,1]=>[5,6,7,8,4,1,3,2]=>[5,6,7,8,4,1,3,2]=>[7,8,4,-6,3,1,-5,2]
[4,1,2,6,3,8,7,5]=>[4,1,6,2,7,3,8,5]=>[4,1,6,2,7,3,8,5]=>[-8,1,-7,2,-4,3,-6,5]
[1,2,7,6,5,3,8,4]=>[1,2,5,6,7,8,3,4]=>[1,2,5,6,7,8,3,4]=>[1,-5,2,6,7,8,3,4]
[7,1,4,5,3,6,8,2]=>[7,8,5,1,2,3,4,6]=>[7,8,5,1,2,3,4,6]=>[1,2,7,8,5,3,4,6]
[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,-8,-7,3,5,1,-6,4]
[3,1,2,6,4,8,7,5]=>[3,1,2,6,7,4,8,5]=>[3,1,2,6,7,4,8,5]=>[3,1,2,8,-7,4,-6,5]
[3,5,6,1,7,4,8,2]=>[6,8,3,7,5,1,4,2]=>[6,8,3,7,5,1,4,2]=>[3,-7,5,-8,4,1,-6,2]
[8,2,4,3,7,1,6,5]=>[7,8,4,2,6,1,3,5]=>[7,8,4,2,6,1,3,5]=>[8,-7,4,2,1,6,3,5]
[5,8,2,4,3,7,1,6]=>[7,8,4,2,5,1,3,6]=>[7,8,4,2,5,1,3,6]=>[8,-7,4,2,5,1,3,6]
[4,2,5,6,1,8,3,7]=>[6,4,8,2,5,1,3,7]=>[6,4,8,2,5,1,3,7]=>[-6,-4,8,2,5,1,3,7]
[4,2,5,6,1,7,3,8]=>[6,4,7,2,5,1,3,8]=>[6,4,7,2,5,1,3,8]=>[-6,7,-4,2,5,1,3,8]
[6,1,5,7,3,2,4,8]=>[6,3,7,2,1,5,4,8]=>[6,3,7,2,1,5,4,8]=>[5,2,-7,-3,1,-6,4,8]
[6,1,5,8,3,2,4,7]=>[6,3,8,2,1,5,4,7]=>[6,3,8,2,1,5,4,7]=>[5,-8,2,-3,1,-6,4,7]
[3,8,2,4,7,1,5,6]=>[7,8,3,2,1,4,6,5]=>[7,8,3,2,1,4,6,5]=>[-6,-8,2,-3,1,4,-7,5]
[3,6,8,2,4,7,1,5]=>[7,8,3,2,1,6,4,5]=>[7,8,3,2,1,6,4,5]=>[-6,-8,2,-3,-7,1,4,5]
[7,3,2,4,6,1,5,8]=>[6,3,7,2,1,4,5,8]=>[6,3,7,2,1,4,5,8]=>[2,-6,7,-3,1,4,5,8]
[3,2,5,1,8,4,6,7]=>[5,3,2,8,1,4,6,7]=>[5,3,2,8,1,4,6,7]=>[-2,-5,-3,1,4,8,6,7]
[7,8,3,2,4,6,1,5]=>[6,3,8,2,1,4,7,5]=>[6,3,8,2,1,4,7,5]=>[2,7,-8,-3,1,4,-6,5]
[6,1,5,7,8,3,2,4]=>[6,3,8,2,1,5,7,4]=>[6,3,8,2,1,5,7,4]=>[2,5,-8,-3,1,7,-6,4]
[4,2,5,6,1,7,8,3]=>[6,4,8,2,5,1,7,3]=>[6,4,8,2,5,1,7,3]=>[5,-8,2,7,-6,1,-4,3]
[6,1,5,8,7,3,2,4]=>[6,3,7,2,1,5,8,4]=>[6,3,7,2,1,5,8,4]=>[5,2,-7,-3,1,8,-6,4]
[8,7,3,2,4,6,1,5]=>[6,3,7,2,1,4,8,5]=>[6,3,7,2,1,4,8,5]=>[8,2,-7,-3,1,4,-6,5]
[3,2,5,1,8,7,4,6]=>[5,3,2,7,1,4,8,6]=>[5,3,2,7,1,4,8,6]=>[-2,-5,-3,8,1,4,-7,6]
[3,2,5,1,6,4,7,8]=>[5,3,2,6,1,4,7,8]=>[5,3,2,6,1,4,7,8]=>[-2,-5,-3,6,1,4,7,8]
[3,2,4,1,8,7,5,6]=>[4,3,2,1,7,5,8,6]=>[4,3,2,1,7,5,8,6]=>[-2,-3,-4,1,-8,5,-7,6]
[3,2,5,1,6,8,7,4]=>[5,3,2,7,1,6,8,4]=>[5,3,2,7,1,6,8,4]=>[-2,-3,-7,6,1,8,-5,4]
[3,8,6,5,1,7,4,2]=>[5,4,3,6,8,7,1,2]=>[5,4,3,6,8,7,1,2]=>[-4,-5,3,6,-8,7,1,2]
[3,7,6,5,1,8,4,2]=>[5,4,3,6,7,8,1,2]=>[5,4,3,6,7,8,1,2]=>[-4,-5,3,6,7,8,1,2]
[3,2,5,1,6,7,8,4]=>[5,3,2,8,1,6,7,4]=>[5,3,2,8,1,6,7,4]=>[-2,-3,-8,1,6,7,-5,4]
[3,2,4,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>[-2,-3,-4,-7,1,5,6,8]
[3,2,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>[4,3,2,1,8,6,5,7]=>[-2,-3,-4,1,-8,-6,5,7]
[8,3,2,4,7,6,1,5]=>[6,3,7,2,1,8,5,4]=>[6,3,7,2,1,8,5,4]=>[-5,2,-3,-8,1,-7,-6,4]
[3,2,5,1,8,4,7,6]=>[5,3,2,8,1,7,4,6]=>[5,3,2,8,1,7,4,6]=>[-2,-8,-3,1,7,-5,4,6]
[3,2,5,1,6,7,4,8]=>[5,3,2,7,1,6,4,8]=>[5,3,2,7,1,6,4,8]=>[-2,-3,-7,6,1,-5,4,8]
[8,4,2,3,7,5,1,6]=>[5,4,2,7,8,1,6,3]=>[5,4,2,7,8,1,6,3]=>[-2,-7,-4,8,6,1,-5,3]
[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,-6,-8,7,2,1,3,4]
[5,2,6,1,8,4,7,3]=>[6,5,7,8,2,1,4,3]=>[6,5,7,8,2,1,4,3]=>[8,2,-7,-5,4,1,-6,3]
[7,4,2,3,8,5,1,6]=>[5,4,2,8,7,1,6,3]=>[5,4,2,8,7,1,6,3]=>[-2,-7,-4,-5,6,1,-8,3]
[3,2,5,1,7,6,4,8]=>[5,3,2,6,1,7,4,8]=>[5,3,2,6,1,7,4,8]=>[-2,-3,7,-6,1,-5,4,8]
[3,2,5,1,8,6,4,7]=>[5,3,2,6,1,8,4,7]=>[5,3,2,6,1,8,4,7]=>[-2,-3,-6,8,1,-5,4,7]
[8,6,1,5,7,3,2,4]=>[6,3,8,2,1,7,4,5]=>[6,3,8,2,1,7,4,5]=>[2,7,-8,-3,-6,1,4,5]
[8,5,6,1,7,3,4,2]=>[6,4,7,3,8,5,1,2]=>[6,4,7,3,8,5,1,2]=>[-4,8,-7,3,-6,5,1,2]
[8,5,1,6,7,4,2,3]=>[5,4,2,8,7,1,3,6]=>[5,4,2,8,7,1,3,6]=>[-4,-5,-8,-2,1,7,3,6]
[3,2,5,1,8,6,7,4]=>[5,3,2,7,1,8,6,4]=>[5,3,2,7,1,8,6,4]=>[-2,-3,6,-8,1,-5,-7,4]
[3,2,4,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>[-2,-3,-4,1,-8,5,6,7]
[3,2,5,1,7,8,6,4]=>[5,3,2,6,1,8,7,4]=>[5,3,2,6,1,8,7,4]=>[-2,-3,7,-6,1,-5,-8,4]
[3,2,5,1,8,7,6,4]=>[5,3,2,6,1,7,8,4]=>[5,3,2,6,1,7,8,4]=>[-2,-3,7,-6,1,8,-5,4]
[8,2,7,1,4,3,6,5]=>[7,8,4,1,6,2,5,3]=>[7,8,4,1,6,2,5,3]=>[-6,-8,1,-4,5,2,-7,3]
[8,2,7,3,4,1,6,5]=>[4,8,7,3,6,2,5,1]=>[4,8,7,3,6,2,5,1]=>[3,-7,-4,6,2,5,-8,1]
[2,7,3,8,4,6,5,1]=>[5,2,6,7,8,4,3,1]=>[5,2,6,7,8,4,3,1]=>[-2,8,4,3,-7,-6,-5,1]
[1,2,4,8,7,5,3,6]=>[1,2,5,4,7,3,8,6]=>[1,2,5,4,7,3,8,6]=>[1,2,-4,8,-5,3,-7,6]
[4,8,3,5,1,6,2,7]=>[5,6,8,4,3,1,2,7]=>[5,6,8,4,3,1,2,7]=>[4,8,-6,-5,3,1,2,7]
[4,6,2,5,1,8,3,7]=>[5,6,8,4,2,1,3,7]=>[5,6,8,4,2,1,3,7]=>[-8,2,-6,-5,4,1,3,7]
[4,5,1,8,3,7,2,6]=>[5,7,8,4,1,2,3,6]=>[5,7,8,4,1,2,3,6]=>[5,1,7,8,4,2,3,6]
[6,8,2,4,5,7,3,1]=>[3,7,8,2,4,6,1,5]=>[3,7,8,2,4,6,1,5]=>[-2,4,7,8,-3,6,1,5]
[3,5,6,1,8,2,7,4]=>[6,8,3,7,5,1,2,4]=>[6,8,3,7,5,1,2,4]=>[8,3,-6,7,1,5,2,4]
[2,4,1,6,8,3,7,5]=>[4,2,8,1,7,6,3,5]=>[4,2,8,1,7,6,3,5]=>[-7,-2,1,6,-8,-4,3,5]
[1,5,3,2,8,4,6,7]=>[1,3,5,8,2,4,6,7]=>[1,3,5,8,2,4,6,7]=>[1,-3,5,2,4,8,6,7]
[4,2,6,7,1,3,8,5]=>[7,4,1,2,8,6,3,5]=>[7,4,1,2,8,6,3,5]=>[-4,1,6,-8,-7,2,3,5]
[5,1,8,7,4,3,2,6]=>[5,3,4,7,1,2,8,6]=>[5,3,4,7,1,2,8,6]=>[5,3,4,8,1,2,-7,6]
[4,6,7,2,5,8,1,3]=>[8,7,1,4,3,6,2,5]=>[8,7,1,4,3,6,2,5]=>[4,-7,3,-8,1,6,2,5]
[5,7,1,6,3,8,2,4]=>[7,8,6,2,5,1,3,4]=>[7,8,6,2,5,1,3,4]=>[7,8,6,2,1,5,3,4]
[6,1,4,2,8,5,7,3]=>[6,4,7,1,8,2,5,3]=>[6,4,7,1,8,2,5,3]=>[8,-7,5,-4,1,2,-6,3]
[8,1,2,5,6,3,7,4]=>[8,1,6,7,2,4,5,3]=>[8,1,6,7,2,4,5,3]=>[6,1,2,7,4,5,-8,3]
[8,1,6,5,7,3,2,4]=>[8,3,7,2,6,1,5,4]=>[8,3,7,2,6,1,5,4]=>[-3,2,-7,6,5,1,-8,4]
[1,4,5,7,3,2,8,6]=>[1,3,7,4,5,8,2,6]=>[1,3,7,4,5,8,2,6]=>[1,-3,4,-7,5,8,2,6]
[7,2,8,3,6,5,1,4]=>[5,6,7,1,8,4,3,2]=>[5,6,7,1,8,4,3,2]=>[4,3,-8,1,-7,-6,-5,2]
[1,2,5,3,8,4,7,6]=>[1,2,5,8,3,7,4,6]=>[1,2,5,8,3,7,4,6]=>[1,-8,2,3,7,-5,4,6]
[4,8,2,3,7,1,6,5]=>[7,8,2,4,6,1,3,5]=>[7,8,2,4,6,1,3,5]=>[-2,4,7,8,1,6,3,5]
[5,3,6,2,4,7,1,8]=>[7,6,5,2,3,4,1,8]=>[7,6,5,2,3,4,1,8]=>[-6,2,5,3,4,-7,1,8]
[1,7,6,5,3,2,8,4]=>[1,3,5,6,7,8,2,4]=>[1,3,5,6,7,8,2,4]=>[1,-3,5,6,7,8,2,4]
[7,1,2,3,5,6,8,4]=>[7,1,2,8,3,4,5,6]=>[7,1,2,8,3,4,5,6]=>[7,1,2,8,3,4,5,6]
[1,2,8,5,4,7,3,6]=>[1,2,7,5,8,3,4,6]=>[1,2,7,5,8,3,4,6]=>[1,-7,-5,2,3,8,4,6]
[8,1,2,6,7,5,3,4]=>[8,1,5,3,7,2,6,4]=>[8,1,5,3,7,2,6,4]=>[3,-7,-5,1,6,2,-8,4]
[8,5,7,4,2,6,1,3]=>[6,4,1,7,8,2,5,3]=>[6,4,1,7,8,2,5,3]=>[8,-7,-4,1,5,2,-6,3]
[8,5,2,4,7,1,6,3]=>[7,5,8,2,6,1,3,4]=>[7,5,8,2,6,1,3,4]=>[-5,7,8,2,1,6,3,4]
[7,1,2,4,6,8,5,3]=>[7,1,5,2,8,3,4,6]=>[7,1,5,2,8,3,4,6]=>[1,-7,-5,8,2,3,4,6]
[7,1,2,6,8,5,3,4]=>[7,1,5,3,8,2,6,4]=>[7,1,5,3,8,2,6,4]=>[3,1,-8,-7,6,2,-5,4]
[1,2,3,5,8,6,4,7]=>[1,2,3,6,5,8,4,7]=>[1,2,3,6,5,8,4,7]=>[1,2,3,-5,-6,8,4,7]
[6,1,8,3,7,2,5,4]=>[6,7,8,5,2,1,3,4]=>[6,7,8,5,2,1,3,4]=>[-8,-7,-6,2,1,5,3,4]
[2,6,3,5,8,7,1,4]=>[7,2,6,1,4,3,8,5]=>[7,2,6,1,4,3,8,5]=>[-8,2,4,1,-6,3,-7,5]
[2,8,3,7,1,5,6,4]=>[7,2,8,6,1,3,4,5]=>[7,2,8,6,1,3,4,5]=>[7,8,-2,1,3,6,4,5]
[2,1,8,3,5,6,7,4]=>[2,1,8,7,3,4,5,6]=>[2,1,8,7,3,4,5,6]=>[-8,7,-2,1,3,4,5,6]
[8,1,7,2,5,4,6,3]=>[8,7,6,5,2,4,1,3]=>[8,7,6,5,2,4,1,3]=>[-6,-7,5,-8,2,4,1,3]
[8,7,4,1,2,3,6,5]=>[4,1,2,7,6,3,8,5]=>[4,1,2,7,6,3,8,5]=>[8,1,2,-4,-6,3,-7,5]
[8,7,3,1,6,2,4,5]=>[3,7,6,2,4,5,8,1]=>[3,7,6,2,4,5,8,1]=>[-2,-7,6,4,5,8,-3,1]
[8,7,3,1,2,4,6,5]=>[3,1,7,2,6,4,8,5]=>[3,1,7,2,6,4,8,5]=>[8,1,-3,2,-6,4,-7,5]
[5,3,8,1,7,6,2,4]=>[8,6,5,2,3,7,1,4]=>[8,6,5,2,3,7,1,4]=>[-8,5,2,-6,3,7,1,4]
[3,2,5,7,6,1,4,8]=>[6,3,2,1,5,7,4,8]=>[6,3,2,1,5,7,4,8]=>[-2,-5,-3,1,7,-6,4,8]
[3,8,4,7,2,5,1,6]=>[5,7,3,8,2,1,4,6]=>[5,7,3,8,2,1,4,6]=>[-7,-3,8,-5,2,1,4,6]
[1,2,7,6,8,3,5,4]=>[1,2,8,5,3,7,6,4]=>[1,2,8,5,3,7,6,4]=>[1,2,-6,-7,3,-5,-8,4]
[5,6,1,4,2,3,7,8]=>[6,4,2,1,5,3,7,8]=>[6,4,2,1,5,3,7,8]=>[-2,-5,-6,1,-4,3,7,8]
[5,1,6,3,4,2,7,8]=>[5,4,6,3,1,2,7,8]=>[5,4,6,3,1,2,7,8]=>[-4,6,-5,3,1,2,7,8]
[3,4,8,1,6,2,5,7]=>[8,6,3,4,2,1,5,7]=>[8,6,3,4,2,1,5,7]=>[-3,4,-8,-6,2,1,5,7]
[1,7,3,8,4,6,5,2]=>[1,5,6,7,8,4,3,2]=>[1,5,6,7,8,4,3,2]=>[1,8,4,3,-7,-6,-5,2]
[7,3,8,2,6,4,5,1]=>[5,8,7,6,4,2,3,1]=>[5,8,7,6,4,2,3,1]=>[4,-6,-5,-7,2,3,-8,1]
[5,7,8,6,4,1,2,3]=>[4,1,2,6,5,8,7,3]=>[4,1,2,6,5,8,7,3]=>[5,1,2,-4,7,-6,-8,3]
[2,5,6,3,1,7,8,4]=>[3,2,6,8,5,1,7,4]=>[3,2,6,8,5,1,7,4]=>[-2,8,7,-3,-5,1,-6,4]
[4,5,2,1,3,8,7,6]=>[2,5,1,4,3,7,8,6]=>[2,5,1,4,3,7,8,6]=>[-2,4,1,-5,3,8,-7,6]
[3,5,2,7,6,1,8,4]=>[6,5,3,7,2,8,4,1]=>[6,5,3,7,2,8,4,1]=>[-8,-3,2,-7,4,-5,-6,1]
[8,3,2,4,6,5,1,7]=>[5,3,6,2,8,1,4,7]=>[5,3,6,2,8,1,4,7]=>[6,2,-5,-3,1,8,4,7]
[1,2,6,8,5,7,3,4]=>[1,2,7,3,8,6,5,4]=>[1,2,7,3,8,6,5,4]=>[1,2,-5,3,-6,-8,-7,4]
[1,3,6,4,2,8,7,5]=>[1,4,3,6,7,2,8,5]=>[1,4,3,6,7,2,8,5]=>[1,-3,7,8,-4,2,-6,5]
[1,3,7,4,2,8,6,5]=>[1,4,3,7,6,8,2,5]=>[1,4,3,7,6,8,2,5]=>[1,-3,-4,-7,6,8,2,5]
[1,2,5,8,7,3,6,4]=>[1,2,7,6,5,3,8,4]=>[1,2,7,6,5,3,8,4]=>[1,2,-8,-5,-6,3,-7,4]
[1,2,7,8,6,3,5,4]=>[1,2,6,5,3,8,7,4]=>[1,2,6,5,3,8,7,4]=>[1,2,-7,-5,3,-6,-8,4]
[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,-7,-8,3,5,1,-6,4]
[4,7,3,6,5,8,1,2]=>[8,1,7,4,6,3,5,2]=>[8,1,7,4,6,3,5,2]=>[-4,1,-7,6,3,5,-8,2]
[5,3,6,7,1,8,2,4]=>[7,8,5,2,3,6,1,4]=>[7,8,5,2,3,6,1,4]=>[2,8,5,-7,3,6,1,4]
[7,8,3,1,2,4,6,5]=>[3,1,8,2,6,4,7,5]=>[3,1,8,2,6,4,7,5]=>[7,1,-3,-6,2,4,-8,5]
[7,3,8,1,2,4,6,5]=>[8,1,7,2,6,3,5,4]=>[8,1,7,2,6,3,5,4]=>[-6,1,2,-7,5,3,-8,4]
[8,3,7,5,1,2,4,6]=>[5,1,7,2,8,3,4,6]=>[5,1,7,2,8,3,4,6]=>[7,8,1,-5,2,3,4,6]
[2,8,7,3,4,5,6,1]=>[6,2,7,3,4,5,8,1]=>[6,2,7,3,4,5,8,1]=>[7,2,3,4,5,8,-6,1]
[7,8,3,6,2,4,5,1]=>[5,6,8,2,3,1,7,4]=>[5,6,8,2,3,1,7,4]=>[8,2,7,3,-6,1,-5,4]
[8,4,6,7,1,5,3,2]=>[7,3,5,8,1,4,6,2]=>[7,3,5,8,1,4,6,2]=>[3,5,8,1,4,6,-7,2]
[1,8,5,4,2,6,7,3]=>[1,4,5,8,7,2,6,3]=>[1,4,5,8,7,2,6,3]=>[1,7,-5,-4,6,2,-8,3]
[7,2,8,6,3,1,4,5]=>[3,6,8,1,2,7,5,4]=>[3,6,8,1,2,7,5,4]=>[3,7,1,5,2,-8,-6,4]
[5,3,1,2,4,7,8,6]=>[3,1,5,2,4,8,7,6]=>[3,1,5,2,4,8,7,6]=>[5,1,-3,2,4,-7,-8,6]
[4,1,2,7,8,3,6,5]=>[4,1,8,2,6,3,7,5]=>[4,1,8,2,6,3,7,5]=>[7,-6,1,2,-4,3,-8,5]
[1,2,8,4,3,7,5,6]=>[1,2,4,8,7,5,3,6]=>[1,2,4,8,7,5,3,6]=>[1,2,5,-7,-8,-4,3,6]
[7,2,3,8,5,1,4,6]=>[5,8,2,1,7,3,4,6]=>[5,8,2,1,7,3,4,6]=>[8,7,2,-5,1,3,4,6]
[7,2,3,8,4,1,5,6]=>[4,8,2,7,1,3,5,6]=>[4,8,2,7,1,3,5,6]=>[-4,2,8,1,3,7,5,6]
[7,6,5,1,2,4,8,3]=>[5,1,6,2,7,8,4,3]=>[5,1,6,2,7,8,4,3]=>[-8,1,-7,2,4,-6,-5,3]
[7,6,5,1,4,8,2,3]=>[5,6,2,1,7,8,4,3]=>[5,6,2,1,7,8,4,3]=>[2,-8,-7,1,4,-6,-5,3]
[8,1,6,5,3,7,2,4]=>[8,7,5,2,6,1,3,4]=>[8,7,5,2,6,1,3,4]=>[-8,-5,7,-2,1,6,3,4]
[7,5,4,1,2,6,8,3]=>[4,1,5,7,8,2,6,3]=>[4,1,5,7,8,2,6,3]=>[-7,1,-5,8,6,2,-4,3]
[3,8,1,5,4,6,7,2]=>[8,7,3,5,1,2,4,6]=>[8,7,3,5,1,2,4,6]=>[3,8,1,7,5,2,4,6]
[7,8,1,4,5,3,2,6]=>[8,3,5,1,4,2,7,6]=>[8,3,5,1,4,2,7,6]=>[-3,5,4,-7,1,2,-8,6]
[7,3,8,1,4,5,2,6]=>[8,5,7,1,3,2,6,4]=>[8,5,7,1,3,2,6,4]=>[7,3,6,-5,1,2,-8,4]
[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,-3,-8,1,4,-6,5,7]
[1,8,4,5,2,3,6,7]=>[1,5,2,8,4,3,6,7]=>[1,5,2,8,4,3,6,7]=>[1,-8,-4,2,-5,3,6,7]
[3,4,8,7,5,2,6,1]=>[6,5,3,4,7,2,8,1]=>[6,5,3,4,7,2,8,1]=>[-3,4,7,2,-5,8,-6,1]
[3,8,7,2,5,4,6,1]=>[6,7,3,5,2,4,8,1]=>[6,7,3,5,2,4,8,1]=>[7,-3,5,2,4,8,-6,1]
[5,3,6,2,4,8,7,1]=>[7,6,5,2,3,4,8,1]=>[7,6,5,2,3,4,8,1]=>[-6,2,5,3,4,8,-7,1]
[1,8,2,6,3,4,7,5]=>[1,8,6,3,7,2,4,5]=>[1,8,6,3,7,2,4,5]=>[-8,-6,1,-3,2,7,4,5]
[7,5,4,1,3,8,2,6]=>[4,5,1,7,8,3,6,2]=>[4,5,1,7,8,3,6,2]=>[-7,8,1,-5,3,6,-4,2]
[7,2,3,6,1,4,8,5]=>[6,7,2,1,8,3,4,5]=>[6,7,2,1,8,3,4,5]=>[-7,8,-6,2,1,3,4,5]
[3,5,2,6,7,1,8,4]=>[7,5,3,8,2,6,1,4]=>[7,5,3,8,2,6,1,4]=>[8,-7,-3,-5,2,6,1,4]
[5,1,6,4,2,3,7,8]=>[5,4,2,6,1,3,7,8]=>[5,4,2,6,1,3,7,8]=>[-4,-5,-2,6,1,3,7,8]
[8,2,6,1,4,5,3,7]=>[6,8,5,1,2,3,4,7]=>[6,8,5,1,2,3,4,7]=>[1,6,2,8,5,3,4,7]
[6,2,8,1,4,5,3,7]=>[8,6,5,1,2,3,4,7]=>[8,6,5,1,2,3,4,7]=>[1,8,6,2,5,3,4,7]
[3,6,7,5,2,4,1,8]=>[4,5,3,2,7,6,1,8]=>[4,5,3,2,7,6,1,8]=>[2,-3,-5,6,-4,-7,1,8]
[3,5,6,2,4,1,7,8]=>[4,6,3,2,5,1,7,8]=>[4,6,3,2,5,1,7,8]=>[-3,2,-6,5,-4,1,7,8]
[8,3,6,1,4,5,7,2]=>[6,7,8,1,2,5,3,4]=>[6,7,8,1,2,5,3,4]=>[1,2,7,8,-6,5,3,4]
[8,4,6,1,2,3,7,5]=>[6,1,2,8,7,4,3,5]=>[6,1,2,8,7,4,3,5]=>[4,1,-7,-6,-8,2,3,5]
[3,5,4,1,8,7,2,6]=>[4,5,3,7,2,1,8,6]=>[4,5,3,7,2,1,8,6]=>[8,-3,2,-5,-4,1,-7,6]
[1,7,2,3,5,6,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>[7,8,1,2,3,4,5,6]
[4,2,7,3,6,5,8,1]=>[8,4,7,2,6,3,5,1]=>[8,4,7,2,6,3,5,1]=>[-2,7,6,-4,3,5,-8,1]
[8,7,1,3,5,6,2,4]=>[7,6,1,3,2,4,8,5]=>[7,6,1,3,2,4,8,5]=>[8,3,-6,1,2,4,-7,5]
[4,2,8,1,6,7,3,5]=>[8,4,7,2,3,1,6,5]=>[8,4,7,2,3,1,6,5]=>[4,2,6,-7,3,1,-8,5]
[3,8,7,5,1,2,4,6]=>[5,1,3,2,7,4,8,6]=>[5,1,3,2,7,4,8,6]=>[3,1,-8,2,-5,4,-7,6]
[8,5,7,4,1,2,3,6]=>[4,1,2,7,8,3,5,6]=>[4,1,2,7,8,3,5,6]=>[1,2,7,-4,3,8,5,6]
[1,7,2,8,6,3,4,5]=>[1,7,6,3,4,8,2,5]=>[1,7,6,3,4,8,2,5]=>[-6,-3,1,-7,4,8,2,5]
[4,1,8,7,2,3,5,6]=>[4,7,2,1,3,5,8,6]=>[4,7,2,1,3,5,8,6]=>[8,-4,2,1,3,5,-7,6]
[3,4,7,1,6,8,2,5]=>[7,8,3,4,2,1,6,5]=>[7,8,3,4,2,1,6,5]=>[3,4,-6,-8,2,1,-7,5]
[6,4,2,3,8,5,1,7]=>[5,4,2,8,6,1,3,7]=>[5,4,2,8,6,1,3,7]=>[-4,-5,-8,-2,6,1,3,7]
[4,8,3,1,2,6,7,5]=>[3,1,8,4,7,2,6,5]=>[3,1,8,4,7,2,6,5]=>[-4,-3,-7,1,6,2,-8,5]
[6,7,3,1,4,8,2,5]=>[3,7,8,1,4,6,2,5]=>[3,7,8,1,4,6,2,5]=>[7,1,4,8,-3,6,2,5]
[6,3,8,2,4,5,1,7]=>[5,8,6,2,3,1,4,7]=>[5,8,6,2,3,1,4,7]=>[5,6,-8,2,3,1,4,7]
[7,8,6,1,3,4,5,2]=>[6,5,1,2,3,8,7,4]=>[6,5,1,2,3,8,7,4]=>[5,1,7,2,3,-6,-8,4]
[6,5,8,2,3,1,7,4]=>[3,8,2,7,6,5,1,4]=>[3,8,2,7,6,5,1,4]=>[6,2,-3,-7,-8,5,1,4]
[1,8,2,3,5,6,7,4]=>[1,8,2,7,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>[-8,1,2,7,3,4,5,6]
[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,-3,-7,-6,5,1,-4,2]
[1,5,2,6,8,4,3,7]=>[1,5,4,8,2,6,3,7]=>[1,5,4,8,2,6,3,7]=>[-8,1,-4,6,2,-5,3,7]
[6,3,1,8,5,7,2,4]=>[3,6,7,2,8,4,5,1]=>[3,6,7,2,8,4,5,1]=>[-7,8,2,-3,4,5,-6,1]
[2,3,7,5,6,8,1,4]=>[8,2,3,1,7,5,6,4]=>[8,2,3,1,7,5,6,4]=>[-5,2,3,-7,1,6,-8,4]
[8,2,7,5,1,3,4,6]=>[5,7,1,2,8,3,6,4]=>[5,7,1,2,8,3,6,4]=>[1,8,6,2,-7,3,-5,4]
[2,4,8,7,1,3,6,5]=>[7,2,1,4,6,3,8,5]=>[7,2,1,4,6,3,8,5]=>[4,-2,1,8,-6,3,-7,5]
[4,6,3,7,5,2,8,1]=>[8,5,7,4,6,2,3,1]=>[8,5,7,4,6,2,3,1]=>[-5,7,4,6,2,3,-8,1]
[8,7,5,1,2,4,6,3]=>[5,1,7,2,6,3,8,4]=>[5,1,7,2,6,3,8,4]=>[8,1,-6,2,-7,3,-5,4]
[1,8,3,7,2,5,6,4]=>[1,7,8,6,2,3,4,5]=>[1,7,8,6,2,3,4,5]=>[7,8,1,2,3,6,4,5]
[2,8,7,3,5,6,1,4]=>[6,2,7,1,4,3,8,5]=>[6,2,7,1,4,3,8,5]=>[-8,-2,4,1,-7,3,-6,5]
[8,3,7,2,5,6,1,4]=>[6,7,8,1,3,2,5,4]=>[6,7,8,1,3,2,5,4]=>[3,8,5,-7,1,2,-6,4]
[1,2,8,6,7,3,5,4]=>[1,2,7,5,3,8,6,4]=>[1,2,7,5,3,8,6,4]=>[1,2,-6,-5,3,-8,-7,4]
[8,3,7,1,2,5,6,4]=>[7,1,8,6,2,3,4,5]=>[7,1,8,6,2,3,4,5]=>[7,8,1,6,2,3,4,5]
[6,7,4,3,1,8,2,5]=>[3,4,7,8,2,6,1,5]=>[3,4,7,8,2,6,1,5]=>[-4,7,2,8,-3,6,1,5]
[6,7,1,3,2,5,4,8]=>[7,3,1,5,2,6,4,8]=>[7,3,1,5,2,6,4,8]=>[-6,-7,1,-3,2,-5,4,8]
[4,5,1,3,2,7,6,8]=>[5,3,1,4,2,7,6,8]=>[5,3,1,4,2,7,6,8]=>[-4,-5,1,-3,2,-7,6,8]
[4,5,2,3,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>[3,5,2,4,1,7,6,8]=>[-5,2,4,-3,1,-7,6,8]
[5,1,6,3,2,7,4,8]=>[5,3,6,7,1,2,4,8]=>[5,3,6,7,1,2,4,8]=>[5,3,1,6,7,2,4,8]
[5,1,6,2,7,4,3,8]=>[5,6,4,7,1,2,3,8]=>[5,6,4,7,1,2,3,8]=>[5,6,1,4,7,2,3,8]
[3,6,8,4,2,7,5,1]=>[5,4,3,7,8,6,1,2]=>[5,4,3,7,8,6,1,2]=>[-4,-5,3,8,-7,6,1,2]
[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,-8,-3,-4,1,6,7]
[4,5,7,3,8,6,2,1]=>[2,6,8,4,5,7,1,3]=>[2,6,8,4,5,7,1,3]=>[-6,-2,4,8,5,7,1,3]
[6,3,1,8,7,5,4,2]=>[3,6,4,5,7,2,8,1]=>[3,6,4,5,7,2,8,1]=>[-4,5,7,2,-3,8,-6,1]
[1,6,4,8,7,5,2,3]=>[1,5,2,7,6,3,8,4]=>[1,5,2,7,6,3,8,4]=>[1,-8,2,-6,-5,3,-7,4]
[3,7,2,5,4,8,1,6]=>[8,7,3,5,2,1,4,6]=>[8,7,3,5,2,1,4,6]=>[-3,-7,-8,2,5,1,4,6]
[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,-3,5,1,7,-6,4,8]
[2,4,8,1,6,5,7,3]=>[8,2,7,4,6,1,5,3]=>[8,2,7,4,6,1,5,3]=>[-2,4,-7,6,5,1,-8,3]
[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,-3,1,8,4,-6,5,7]
[5,1,7,6,2,3,8,4]=>[5,6,2,7,1,8,4,3]=>[5,6,2,7,1,8,4,3]=>[2,-8,4,-7,1,-6,-5,3]
[5,1,7,6,2,8,3,4]=>[5,6,7,3,1,8,4,2]=>[5,6,7,3,1,8,4,2]=>[3,4,-8,-7,1,-6,-5,2]
[5,3,2,7,6,1,4,8]=>[6,3,5,1,2,7,4,8]=>[6,3,5,1,2,7,4,8]=>[5,3,7,1,2,-6,4,8]
[8,1,6,5,7,3,4,2]=>[8,4,7,3,6,1,5,2]=>[8,4,7,3,6,1,5,2]=>[-3,7,-4,6,5,1,-8,2]
[5,1,8,3,4,6,7,2]=>[5,7,8,3,1,4,6,2]=>[5,7,8,3,1,4,6,2]=>[-3,8,-7,1,4,6,-5,2]
[7,3,1,2,4,6,8,5]=>[3,1,7,2,8,4,6,5]=>[3,1,7,2,8,4,6,5]=>[6,1,-3,-8,2,4,-7,5]
[3,7,2,8,6,1,5,4]=>[6,8,3,5,1,7,4,2]=>[6,8,3,5,1,7,4,2]=>[5,7,4,-3,1,-8,-6,2]
[5,3,6,1,8,2,4,7]=>[6,8,5,2,3,1,4,7]=>[6,8,5,2,3,1,4,7]=>[5,8,2,-6,3,1,4,7]
[7,8,1,3,5,6,2,4]=>[8,6,1,3,2,4,7,5]=>[8,6,1,3,2,4,7,5]=>[7,-6,3,1,2,4,-8,5]
[6,8,2,3,7,1,4,5]=>[7,8,2,1,3,6,5,4]=>[7,8,2,1,3,6,5,4]=>[-6,5,2,1,3,-8,-7,4]
[5,8,3,2,7,1,4,6]=>[7,3,8,1,5,2,6,4]=>[7,3,8,1,5,2,6,4]=>[-8,5,6,1,-3,2,-7,4]
[5,1,8,3,7,2,4,6]=>[5,7,8,2,1,3,6,4]=>[5,7,8,2,1,3,6,4]=>[-8,2,-7,1,6,3,-5,4]
[2,4,5,1,3,8,7,6]=>[5,2,1,4,3,7,8,6]=>[5,2,1,4,3,7,8,6]=>[-4,-2,1,-5,3,8,-7,6]
[7,4,2,8,6,3,1,5]=>[3,6,4,8,1,7,2,5]=>[3,6,4,8,1,7,2,5]=>[-4,8,-3,1,-6,7,2,5]
[4,1,8,5,7,3,2,6]=>[4,3,7,1,8,2,5,6]=>[4,3,7,1,8,2,5,6]=>[-3,7,1,8,-4,2,5,6]
[4,1,7,5,8,3,2,6]=>[4,3,8,1,7,2,5,6]=>[4,3,8,1,7,2,5,6]=>[-3,8,1,-4,7,2,5,6]
[6,5,3,8,7,1,2,4]=>[7,1,5,2,6,3,8,4]=>[7,1,5,2,6,3,8,4]=>[8,-6,1,2,-5,3,-7,4]
[7,6,3,1,4,8,2,5]=>[3,6,7,1,4,8,5,2]=>[3,6,7,1,4,8,5,2]=>[-7,8,4,1,5,-3,-6,2]
[4,5,7,3,1,6,8,2]=>[3,7,8,4,5,1,2,6]=>[3,7,8,4,5,1,2,6]=>[7,3,4,8,5,1,2,6]
[4,5,7,2,8,6,1,3]=>[6,8,1,4,5,7,3,2]=>[6,8,1,4,5,7,3,2]=>[1,8,5,7,3,-4,-6,2]
[5,3,8,1,6,2,4,7]=>[8,6,5,2,3,1,4,7]=>[8,6,5,2,3,1,4,7]=>[-6,5,-8,2,3,1,4,7]
[3,8,7,1,2,4,6,5]=>[7,1,3,2,6,4,8,5]=>[7,1,3,2,6,4,8,5]=>[3,-8,1,2,-6,4,-7,5]
[5,6,3,1,8,4,7,2]=>[3,6,7,8,5,2,4,1]=>[3,6,7,8,5,2,4,1]=>[-7,8,5,-3,2,4,-6,1]
[3,7,2,5,1,8,4,6]=>[5,7,3,8,2,4,1,6]=>[5,7,3,8,2,4,1,6]=>[-7,-3,2,8,4,-5,1,6]
[3,2,6,8,1,5,4,7]=>[8,3,2,5,1,6,4,7]=>[8,3,2,5,1,6,4,7]=>[-5,-2,6,-3,-8,1,4,7]
[2,5,1,4,8,7,3,6]=>[5,2,7,1,4,3,8,6]=>[5,2,7,1,4,3,8,6]=>[-8,-2,4,1,-5,3,-7,6]
[2,4,1,8,3,6,7,5]=>[4,2,8,1,7,3,6,5]=>[4,2,8,1,7,3,6,5]=>[-7,-2,1,6,-4,3,-8,5]
[4,2,7,6,3,1,5,8]=>[3,6,4,1,2,7,5,8]=>[3,6,4,1,2,7,5,8]=>[3,-7,4,1,2,-6,5,8]
[3,6,4,1,7,8,5,2]=>[4,6,3,5,8,2,7,1]=>[4,6,3,5,8,2,7,1]=>[-3,5,8,-6,2,7,-4,1]
[8,2,3,7,5,4,1,6]=>[4,5,2,7,8,1,3,6]=>[4,5,2,7,8,1,3,6]=>[-5,-4,2,1,7,8,3,6]
[4,1,2,7,8,5,3,6]=>[4,1,5,2,8,3,7,6]=>[4,1,5,2,8,3,7,6]=>[7,1,-5,2,-4,3,-8,6]
[4,7,3,1,2,6,8,5]=>[3,1,7,4,8,2,6,5]=>[3,1,7,4,8,2,6,5]=>[-4,1,-8,-3,6,2,-7,5]
[5,6,2,7,3,4,8,1]=>[8,6,7,3,5,2,4,1]=>[8,6,7,3,5,2,4,1]=>[6,7,-3,5,2,4,-8,1]
[1,5,8,6,4,2,3,7]=>[1,4,2,6,5,8,3,7]=>[1,4,2,6,5,8,3,7]=>[1,-5,2,-4,-6,8,3,7]
[8,4,6,3,1,2,5,7]=>[3,1,6,8,2,4,5,7]=>[3,1,6,8,2,4,5,7]=>[1,6,-3,2,4,8,5,7]
[4,7,3,6,1,2,8,5]=>[6,1,7,4,8,3,2,5]=>[6,1,7,4,8,3,2,5]=>[8,1,-4,-7,-6,3,2,5]
[5,2,8,3,6,1,4,7]=>[6,5,8,1,2,3,4,7]=>[6,5,8,1,2,3,4,7]=>[1,6,2,5,3,8,4,7]
[7,2,4,5,1,6,3,8]=>[5,7,6,2,3,4,1,8]=>[5,7,6,2,3,4,1,8]=>[5,2,6,3,4,-7,1,8]
[3,8,4,6,1,7,2,5]=>[6,7,3,8,2,5,4,1]=>[6,7,3,8,2,5,4,1]=>[-3,-8,5,2,4,-7,-6,1]
[2,7,5,8,1,6,3,4]=>[8,2,6,3,7,1,5,4]=>[8,2,6,3,7,1,5,4]=>[-7,2,-6,3,5,1,-8,4]
[7,6,4,1,8,3,2,5]=>[4,3,6,7,2,8,1,5]=>[4,3,6,7,2,8,1,5]=>[6,2,7,-3,-4,8,1,5]
[3,5,1,7,8,2,6,4]=>[5,8,3,6,1,2,7,4]=>[5,8,3,6,1,2,7,4]=>[-8,3,6,7,1,2,-5,4]
[3,6,4,1,5,2,8,7]=>[4,6,3,5,2,1,8,7]=>[4,6,3,5,2,1,8,7]=>[-3,5,2,-6,-4,1,-8,7]
[4,1,3,5,6,7,8,2]=>[4,8,1,3,5,6,7,2]=>[4,8,1,3,5,6,7,2]=>[3,1,5,8,6,7,-4,2]
[2,1,5,8,6,3,7,4]=>[2,1,6,8,5,7,4,3]=>[2,1,6,8,5,7,4,3]=>[-2,1,-5,7,4,-8,-6,3]
[3,7,8,5,4,1,6,2]=>[4,5,3,8,6,1,7,2]=>[4,5,3,8,6,1,7,2]=>[6,-3,7,-5,-8,1,-4,2]
[4,6,8,5,3,1,7,2]=>[3,5,8,4,7,6,1,2]=>[3,5,8,4,7,6,1,2]=>[3,-5,7,4,-8,6,1,2]
[1,8,5,7,4,2,3,6]=>[1,4,2,7,8,3,5,6]=>[1,4,2,7,8,3,5,6]=>[7,1,2,-4,3,8,5,6]
[6,3,8,4,7,1,2,5]=>[7,1,6,8,2,3,4,5]=>[7,1,6,8,2,3,4,5]=>[7,1,2,3,6,8,4,5]
[1,2,5,4,8,3,6,7]=>[1,2,8,5,4,3,6,7]=>[1,2,8,5,4,3,6,7]=>[1,2,-8,-4,-5,3,6,7]
[4,1,8,5,7,2,3,6]=>[4,7,2,1,8,3,5,6]=>[4,7,2,1,8,3,5,6]=>[-7,8,2,1,-4,3,5,6]
[8,2,5,1,4,6,7,3]=>[5,8,7,1,2,3,4,6]=>[5,8,7,1,2,3,4,6]=>[1,5,8,2,3,7,4,6]
[8,4,7,6,5,3,1,2]=>[3,1,5,6,7,8,4,2]=>[3,1,5,6,7,8,4,2]=>[-6,1,7,8,4,-3,-5,2]
[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,-3,1,-7,4,8,-6,5]
[1,3,4,8,7,2,5,6]=>[1,7,3,4,2,5,8,6]=>[1,7,3,4,2,5,8,6]=>[-3,1,-8,4,2,5,-7,6]
[8,4,7,6,5,1,2,3]=>[5,1,2,6,7,8,4,3]=>[5,1,2,6,7,8,4,3]=>[7,1,2,8,4,-6,-5,3]
[1,8,4,7,6,5,2,3]=>[1,5,2,6,7,8,4,3]=>[1,5,2,6,7,8,4,3]=>[1,-7,2,8,4,-6,-5,3]
[5,3,6,1,4,2,8,7]=>[6,4,5,1,3,2,8,7]=>[6,4,5,1,3,2,8,7]=>[4,5,3,1,-6,2,-8,7]
[2,1,7,5,8,3,6,4]=>[2,1,8,6,7,3,5,4]=>[2,1,8,6,7,3,5,4]=>[-7,-2,-6,1,5,3,-8,4]
[8,6,3,1,7,5,4,2]=>[3,6,4,5,8,7,1,2]=>[3,6,4,5,8,7,1,2]=>[-6,3,4,5,-8,7,1,2]
[3,6,1,2,4,8,7,5]=>[6,1,3,2,7,4,8,5]=>[6,1,3,2,7,4,8,5]=>[3,1,-8,2,-7,4,-6,5]
[6,3,1,2,4,8,7,5]=>[3,1,6,2,7,4,8,5]=>[3,1,6,2,7,4,8,5]=>[-8,1,-3,2,-7,4,-6,5]
[4,2,6,1,3,7,8,5]=>[6,4,1,2,8,3,7,5]=>[6,4,1,2,8,3,7,5]=>[-4,1,7,2,-8,3,-6,5]
[7,6,2,3,1,8,4,5]=>[3,6,2,7,4,8,5,1]=>[3,6,2,7,4,8,5,1]=>[2,-8,4,-3,5,-7,-6,1]
[8,1,6,3,5,4,7,2]=>[8,7,6,5,3,1,4,2]=>[8,7,6,5,3,1,4,2]=>[-4,-5,-6,-7,-8,1,-3,2]
[4,5,7,6,1,8,2,3]=>[6,7,2,4,5,8,3,1]=>[6,7,2,4,5,8,3,1]=>[7,4,5,8,3,-2,-6,1]
[8,1,4,5,6,2,7,3]=>[8,6,7,1,2,3,4,5]=>[8,6,7,1,2,3,4,5]=>[1,2,3,8,6,7,4,5]
[7,3,4,1,6,5,8,2]=>[4,8,7,3,6,2,1,5]=>[4,8,7,3,6,2,1,5]=>[-7,-3,2,6,-8,-4,1,5]
[8,7,3,1,4,2,5,6]=>[3,7,4,2,1,5,8,6]=>[3,7,4,2,1,5,8,6]=>[2,-4,-8,-3,1,5,-7,6]
[1,8,3,5,6,2,7,4]=>[1,6,8,7,3,4,5,2]=>[1,6,8,7,3,4,5,2]=>[3,-6,1,7,4,5,-8,2]
[2,8,6,1,4,5,7,3]=>[6,2,8,1,3,7,5,4]=>[6,2,8,1,3,7,5,4]=>[-7,-2,1,5,3,-8,-6,4]
[7,6,1,4,3,2,5,8]=>[6,3,4,1,2,7,5,8]=>[6,3,4,1,2,7,5,8]=>[7,3,4,1,2,-6,5,8]
[5,4,2,8,3,6,7,1]=>[7,4,5,8,3,2,6,1]=>[7,4,5,8,3,2,6,1]=>[3,8,2,-5,-7,6,-4,1]
[3,4,5,2,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>[-2,3,4,-5,-8,1,6,7]
[5,1,8,2,4,6,7,3]=>[5,8,7,2,1,3,4,6]=>[5,8,7,2,1,3,4,6]=>[-8,-5,2,7,1,3,4,6]
[1,3,7,5,6,8,4,2]=>[1,4,3,8,7,5,6,2]=>[1,4,3,8,7,5,6,2]=>[1,-3,-4,-7,5,6,-8,2]
[1,8,5,6,2,7,4,3]=>[1,6,4,7,8,5,2,3]=>[1,6,4,7,8,5,2,3]=>[-4,-7,1,8,-6,5,2,3]
[3,7,2,6,8,1,5,4]=>[8,7,3,5,1,4,2,6]=>[8,7,3,5,1,4,2,6]=>[-7,3,5,4,-8,1,2,6]
[8,2,4,6,1,3,7,5]=>[6,8,1,3,7,2,4,5]=>[6,8,1,3,7,2,4,5]=>[-6,1,8,3,2,7,4,5]
[8,3,5,6,1,4,7,2]=>[6,7,8,1,4,3,5,2]=>[6,7,8,1,4,3,5,2]=>[7,8,3,-4,1,5,-6,2]
[8,1,4,5,3,2,7,6]=>[8,3,5,1,4,7,2,6]=>[8,3,5,1,4,7,2,6]=>[3,5,4,-8,1,7,2,6]
[1,3,6,4,2,5,7,8]=>[1,4,3,6,2,5,7,8]=>[1,4,3,6,2,5,7,8]=>[1,-3,-4,6,2,5,7,8]
[1,7,6,4,2,3,5,8]=>[1,4,2,6,3,7,5,8]=>[1,4,2,6,3,7,5,8]=>[1,-7,2,-4,3,-6,5,8]
[1,2,3,7,6,4,5,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,-7,4,-6,5,8]
[1,3,2,5,8,6,4,7]=>[1,3,2,6,5,8,4,7]=>[1,3,2,6,5,8,4,7]=>[1,-3,2,-5,-6,8,4,7]
[4,8,2,7,1,3,6,5]=>[7,8,1,4,6,2,5,3]=>[7,8,1,4,6,2,5,3]=>[1,8,-4,6,5,2,-7,3]
[3,1,2,5,7,8,6,4]=>[3,1,2,6,5,8,7,4]=>[3,1,2,6,5,8,7,4]=>[3,1,2,-5,7,-6,-8,4]
[7,8,6,1,2,4,5,3]=>[6,1,5,2,4,8,7,3]=>[6,1,5,2,4,8,7,3]=>[1,-5,4,2,7,-6,-8,3]
[1,5,3,4,7,8,6,2]=>[1,6,5,3,4,8,7,2]=>[1,6,5,3,4,8,7,2]=>[-3,-5,1,4,7,-6,-8,2]
[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,-6,1,2,7,-5,-8,3]
[1,8,5,3,4,6,7,2]=>[1,7,5,3,8,4,6,2]=>[1,7,5,3,8,4,6,2]=>[-3,1,-8,-5,4,6,-7,2]
[8,1,6,4,2,3,5,7]=>[8,4,2,6,3,1,5,7]=>[8,4,2,6,3,1,5,7]=>[-6,-8,-2,3,-4,1,5,7]
[8,3,1,2,4,6,7,5]=>[3,1,8,2,7,4,6,5]=>[3,1,8,2,7,4,6,5]=>[1,6,-3,-7,2,4,-8,5]
[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,-8,2,5,6,-7,4]
[6,1,8,4,2,3,5,7]=>[6,4,2,8,3,1,5,7]=>[6,4,2,8,3,1,5,7]=>[8,-2,3,-6,-4,1,5,7]
[2,7,4,3,8,5,1,6]=>[5,2,4,8,7,1,6,3]=>[5,2,4,8,7,1,6,3]=>[2,7,-4,-5,6,1,-8,3]
[5,7,3,2,8,1,4,6]=>[8,3,7,1,5,2,6,4]=>[8,3,7,1,5,2,6,4]=>[-3,7,6,-5,1,2,-8,4]
[3,6,8,5,4,1,7,2]=>[4,5,3,8,7,6,1,2]=>[4,5,3,8,7,6,1,2]=>[5,-4,3,-7,-8,6,1,2]
[2,5,1,4,7,8,3,6]=>[5,2,8,1,4,3,7,6]=>[5,2,8,1,4,3,7,6]=>[7,-2,4,1,-5,3,-8,6]
[3,5,1,6,4,2,7,8]=>[5,4,3,6,1,2,7,8]=>[5,4,3,6,1,2,7,8]=>[-4,-5,3,6,1,2,7,8]
[7,2,4,1,3,6,8,5]=>[4,7,1,2,8,3,6,5]=>[4,7,1,2,8,3,6,5]=>[1,8,6,2,-4,3,-7,5]
[4,5,8,6,2,1,3,7]=>[2,6,1,4,5,8,3,7]=>[2,6,1,4,5,8,3,7]=>[-2,1,4,5,-6,8,3,7]
[1,5,8,2,4,3,6,7]=>[1,8,4,2,5,3,6,7]=>[1,8,4,2,5,3,6,7]=>[-8,1,-5,2,-4,3,6,7]
[1,8,3,7,5,2,4,6]=>[1,5,7,2,8,3,4,6]=>[1,5,7,2,8,3,4,6]=>[7,1,-5,8,2,3,4,6]
[2,6,1,8,3,4,7,5]=>[6,2,8,3,7,1,4,5]=>[6,2,8,3,7,1,4,5]=>[-8,-6,2,3,1,7,4,5]
[8,3,2,1,5,6,7,4]=>[2,3,8,7,1,4,5,6]=>[2,3,8,7,1,4,5,6]=>[-8,3,-2,1,4,7,5,6]
[8,5,7,2,3,6,4,1]=>[4,6,2,7,8,1,5,3]=>[4,6,2,7,8,1,5,3]=>[-7,2,-6,8,5,1,-4,3]
[7,1,5,3,6,4,8,2]=>[7,8,5,6,1,2,3,4]=>[7,8,5,6,1,2,3,4]=>[1,2,7,8,5,6,3,4]
[8,7,1,2,4,3,6,5]=>[7,1,4,2,6,3,8,5]=>[7,1,4,2,6,3,8,5]=>[8,-4,1,2,-6,3,-7,5]
[2,6,3,5,7,8,1,4]=>[8,2,6,1,4,3,7,5]=>[8,2,6,1,4,3,7,5]=>[-7,2,4,-6,1,3,-8,5]
[5,1,6,8,3,7,2,4]=>[5,7,8,2,1,6,3,4]=>[5,7,8,2,1,6,3,4]=>[-8,-7,2,6,-5,1,3,4]
[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,-3,5,1,-4,2,7,8]
[8,1,5,3,6,4,7,2]=>[8,7,5,6,1,2,3,4]=>[8,7,5,6,1,2,3,4]=>[1,8,2,7,5,6,3,4]
[3,6,4,1,5,7,8,2]=>[4,6,3,8,1,2,7,5]=>[4,6,3,8,1,2,7,5]=>[8,-4,3,1,7,2,-6,5]
[5,4,8,2,1,3,7,6]=>[2,8,1,5,4,7,3,6]=>[2,8,1,5,4,7,3,6]=>[-2,4,-5,-8,1,7,3,6]
[7,2,8,1,4,3,6,5]=>[8,7,4,1,6,2,5,3]=>[8,7,4,1,6,2,5,3]=>[-6,-7,5,1,-8,2,-4,3]
[6,2,1,8,5,7,4,3]=>[2,6,4,7,8,1,5,3]=>[2,6,4,7,8,1,5,3]=>[7,-4,-2,8,5,1,-6,3]
[6,7,2,8,4,3,1,5]=>[3,4,8,7,1,6,2,5]=>[3,4,8,7,1,6,2,5]=>[-4,7,-3,1,-8,6,2,5]
[1,5,4,2,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[1,-5,2,-4,-8,3,6,7]
[3,7,1,6,8,4,5,2]=>[7,5,3,8,4,1,6,2]=>[7,5,3,8,4,1,6,2]=>[-4,-8,6,-3,-7,1,-5,2]
[3,7,2,5,8,4,6,1]=>[6,7,3,8,2,5,1,4]=>[6,7,3,8,2,5,1,4]=>[-7,-3,2,-6,8,5,1,4]
[5,1,6,8,3,4,7,2]=>[5,7,8,3,1,6,4,2]=>[5,7,8,3,1,6,4,2]=>[6,-3,4,-8,1,-7,-5,2]
[2,6,8,7,1,3,5,4]=>[7,2,1,5,3,6,8,4]=>[7,2,1,5,3,6,8,4]=>[-6,-2,-5,1,3,8,-7,4]
[3,7,6,1,4,5,2,8]=>[6,5,3,1,4,7,2,8]=>[6,5,3,1,4,7,2,8]=>[-4,-5,-6,1,7,-3,2,8]
[4,1,6,2,7,5,3,8]=>[4,6,5,1,7,2,3,8]=>[4,6,5,1,7,2,3,8]=>[5,-4,7,-6,1,2,3,8]
[4,5,3,1,2,8,6,7]=>[3,1,5,4,2,8,6,7]=>[3,1,5,4,2,8,6,7]=>[-4,1,-3,-5,-8,2,6,7]
[2,4,5,3,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>[3,2,5,4,1,8,6,7]=>[-2,4,-3,-5,-8,1,6,7]
[5,7,6,2,3,1,4,8]=>[3,6,2,1,5,7,4,8]=>[3,6,2,1,5,7,4,8]=>[-5,2,-3,1,7,-6,4,8]
[4,1,3,7,5,2,6,8]=>[4,5,1,3,7,2,6,8]=>[4,5,1,3,7,2,6,8]=>[5,3,1,-4,7,2,6,8]
[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,-3,7,1,-4,2,5,8]
[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,-5,1,-4,7,3,6,8]
[7,5,4,1,3,2,6,8]=>[4,3,1,5,7,2,6,8]=>[4,3,1,5,7,2,6,8]=>[-5,-3,1,-4,7,2,6,8]
[2,4,8,5,6,3,1,7]=>[3,2,6,4,8,5,1,7]=>[3,2,6,4,8,5,1,7]=>[-2,4,-3,-8,5,-6,1,7]
[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,-5,1,-7,-4,3,6,8]
[5,7,4,1,3,2,6,8]=>[4,3,1,7,5,2,6,8]=>[4,3,1,7,5,2,6,8]=>[-5,-3,1,-7,-4,2,6,8]
[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,-3,8,4,6,-5,1,7]
[4,5,1,6,3,2,7,8]=>[5,3,6,4,1,2,7,8]=>[5,3,6,4,1,2,7,8]=>[-6,3,-5,4,1,2,7,8]
[5,1,6,3,2,4,7,8]=>[5,3,6,2,1,4,7,8]=>[5,3,6,2,1,4,7,8]=>[6,2,-5,-3,1,4,7,8]
[4,2,5,1,6,3,7,8]=>[5,4,6,2,1,3,7,8]=>[5,4,6,2,1,3,7,8]=>[6,-4,-5,2,1,3,7,8]
[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,-5,2,1,3,7,8]
[4,3,5,1,6,2,7,8]=>[5,6,4,3,1,2,7,8]=>[5,6,4,3,1,2,7,8]=>[4,-6,-5,3,1,2,7,8]
[6,1,2,4,3,7,8,5]=>[6,1,4,2,8,3,7,5]=>[6,1,4,2,8,3,7,5]=>[1,7,-4,2,-8,3,-6,5]
[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,-8,1,-6,-7,2,3,5]
[1,5,8,4,2,3,6,7]=>[1,4,2,8,5,3,6,7]=>[1,4,2,8,5,3,6,7]=>[1,-5,-8,2,-4,3,6,7]
[3,8,4,6,7,2,5,1]=>[5,7,3,8,2,4,6,1]=>[5,7,3,8,2,4,6,1]=>[3,-7,2,8,4,6,-5,1]
[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>[-8,1,2,-4,3,-6,5,7]
[8,3,6,2,4,5,1,7]=>[5,6,8,2,3,1,4,7]=>[5,6,8,2,3,1,4,7]=>[2,6,-5,8,3,1,4,7]
[8,2,6,4,5,1,7,3]=>[5,8,7,6,4,2,1,3]=>[5,8,7,6,4,2,1,3]=>[-4,-6,-5,-7,-8,2,1,3]
[1,8,4,6,7,5,2,3]=>[1,5,2,7,8,4,3,6]=>[1,5,2,7,8,4,3,6]=>[-8,1,2,-7,4,-5,3,6]
[3,5,2,6,4,8,1,7]=>[8,5,3,6,2,4,1,7]=>[8,5,3,6,2,4,1,7]=>[-8,-6,-5,2,4,-3,1,7]
[8,1,5,2,4,6,3,7]=>[8,5,6,2,1,4,3,7]=>[8,5,6,2,1,4,3,7]=>[2,-6,-5,4,-8,1,3,7]
[3,8,1,6,4,5,2,7]=>[8,5,3,6,4,1,2,7]=>[8,5,3,6,4,1,2,7]=>[-8,-6,3,-5,4,1,2,7]
[8,1,3,6,5,4,2,7]=>[8,4,1,5,6,3,2,7]=>[8,4,1,5,6,3,2,7]=>[6,-5,1,-8,3,-4,2,7]
[7,1,5,2,4,6,8,3]=>[7,5,8,2,1,3,4,6]=>[7,5,8,2,1,3,4,6]=>[-7,5,2,8,1,3,4,6]
[7,5,4,1,3,6,8,2]=>[4,5,1,7,8,2,3,6]=>[4,5,1,7,8,2,3,6]=>[5,-4,7,1,2,8,3,6]
[8,3,1,4,7,6,2,5]=>[3,8,6,1,4,7,2,5]=>[3,8,6,1,4,7,2,5]=>[-8,6,4,1,-3,7,2,5]
[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,-5,4,8,1,-3,2,6]
[1,7,4,8,3,6,2,5]=>[1,6,8,7,2,3,4,5]=>[1,6,8,7,2,3,4,5]=>[8,6,1,2,3,7,4,5]
[7,1,8,5,3,4,2,6]=>[7,4,5,3,8,2,1,6]=>[7,4,5,3,8,2,1,6]=>[3,-5,8,2,-7,-4,1,6]
[8,2,4,7,6,3,1,5]=>[3,6,7,2,1,8,4,5]=>[3,6,7,2,1,8,4,5]=>[2,-7,8,-3,-6,1,4,5]
[1,2,5,7,8,3,6,4]=>[1,2,8,6,5,3,7,4]=>[1,2,8,6,5,3,7,4]=>[1,2,-7,-5,-8,3,-6,4]
[4,5,1,6,7,3,8,2]=>[5,8,7,4,1,6,3,2]=>[5,8,7,4,1,6,3,2]=>[-6,3,-4,-7,1,-8,-5,2]
[6,8,2,3,1,5,7,4]=>[3,8,2,7,1,6,5,4]=>[3,8,2,7,1,6,5,4]=>[6,2,-3,5,1,-7,-8,4]
[7,2,1,3,5,6,8,4]=>[2,7,1,8,3,4,5,6]=>[2,7,1,8,3,4,5,6]=>[7,-2,1,8,3,4,5,6]
[3,6,2,4,7,8,5,1]=>[5,8,3,2,6,1,7,4]=>[5,8,3,2,6,1,7,4]=>[-3,-6,2,7,-8,1,-5,4]
[8,1,3,2,6,5,7,4]=>[8,3,1,7,6,2,5,4]=>[8,3,1,7,6,2,5,4]=>[-6,5,1,-7,-3,2,-8,4]
[6,2,7,3,4,5,1,8]=>[5,6,7,3,4,2,1,8]=>[5,6,7,3,4,2,1,8]=>[7,3,4,2,-6,-5,1,8]
[6,2,7,1,4,5,3,8]=>[7,6,5,1,2,3,4,8]=>[7,6,5,1,2,3,4,8]=>[7,1,6,2,5,3,4,8]
[6,5,8,2,7,3,4,1]=>[4,8,7,3,6,5,2,1]=>[4,8,7,3,6,5,2,1]=>[-3,-6,5,2,-4,-7,-8,1]
[2,8,4,6,5,1,7,3]=>[5,2,6,7,8,4,1,3]=>[5,2,6,7,8,4,1,3]=>[-6,-2,7,8,-5,4,1,3]
[4,2,3,5,1,8,6,7]=>[5,4,2,3,1,8,6,7]=>[5,4,2,3,1,8,6,7]=>[-4,2,3,-5,-8,1,6,7]
[1,5,7,2,3,6,8,4]=>[1,7,2,8,5,3,6,4]=>[1,7,2,8,5,3,6,4]=>[1,-6,-5,-8,2,3,-7,4]
[8,5,7,2,4,3,6,1]=>[6,7,4,2,8,3,5,1]=>[6,7,4,2,8,3,5,1]=>[-8,-4,2,-7,3,5,-6,1]
[7,8,6,2,4,1,3,5]=>[4,6,1,2,3,8,7,5]=>[4,6,1,2,3,8,7,5]=>[1,4,7,2,3,-6,-8,5]
[7,2,6,1,4,8,3,5]=>[6,7,8,1,4,2,5,3]=>[6,7,8,1,4,2,5,3]=>[7,8,5,-4,1,2,-6,3]
[8,1,6,3,5,2,4,7]=>[8,5,6,2,3,1,4,7]=>[8,5,6,2,3,1,4,7]=>[2,5,-8,6,3,1,4,7]
[6,3,7,2,5,4,8,1]=>[8,7,6,5,2,3,4,1]=>[8,7,6,5,2,3,4,1]=>[-6,-7,2,5,3,4,-8,1]
[4,2,8,5,1,3,6,7]=>[5,4,1,2,8,3,6,7]=>[5,4,1,2,8,3,6,7]=>[-4,1,2,8,-5,3,6,7]
[7,4,6,3,1,2,5,8]=>[3,1,6,7,2,4,5,8]=>[3,1,6,7,2,4,5,8]=>[1,6,-3,2,7,4,5,8]
[4,6,7,2,3,8,5,1]=>[5,8,2,4,7,6,1,3]=>[5,8,2,4,7,6,1,3]=>[-5,2,7,4,-8,6,1,3]
[4,5,7,6,3,1,8,2]=>[3,6,7,4,5,8,1,2]=>[3,6,7,4,5,8,1,2]=>[-6,3,7,4,5,8,1,2]
[4,6,7,5,1,3,8,2]=>[5,7,1,4,8,6,2,3]=>[5,7,1,4,8,6,2,3]=>[1,8,-5,4,-7,6,2,3]
[3,6,5,1,4,7,8,2]=>[5,6,3,1,8,2,7,4]=>[5,6,3,1,8,2,7,4]=>[-3,7,-8,1,-6,2,-5,4]
[4,6,7,3,1,5,8,2]=>[3,7,8,4,1,6,2,5]=>[3,7,8,4,1,6,2,5]=>[-4,8,-7,6,1,-3,2,5]
[4,2,3,6,7,5,1,8]=>[5,4,2,3,7,6,1,8]=>[5,4,2,3,7,6,1,8]=>[-4,2,3,6,-5,-7,1,8]
[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,-3,-6,4,5,-7,1,8]
[7,1,5,2,4,8,3,6]=>[7,5,8,2,1,4,6,3]=>[7,5,8,2,1,4,6,3]=>[-8,-5,4,2,1,6,-7,3]
[7,5,8,1,4,2,3,6]=>[8,4,2,1,7,3,5,6]=>[8,4,2,1,7,3,5,6]=>[-8,7,-2,1,-4,3,5,6]
[1,7,5,8,4,2,3,6]=>[1,4,2,8,7,3,5,6]=>[1,4,2,8,7,3,5,6]=>[7,1,-8,2,-4,3,5,6]
[5,7,8,1,2,4,3,6]=>[8,1,4,2,5,3,7,6]=>[8,1,4,2,5,3,7,6]=>[5,-4,1,-7,2,3,-8,6]
[6,5,1,2,4,3,8,7]=>[5,1,4,2,6,3,8,7]=>[5,1,4,2,6,3,8,7]=>[6,1,-4,2,-5,3,-8,7]
[2,5,1,4,6,3,8,7]=>[5,2,6,1,4,3,8,7]=>[5,2,6,1,4,3,8,7]=>[-6,-2,4,1,-5,3,-8,7]
[5,8,7,3,1,2,4,6]=>[3,1,7,2,5,4,8,6]=>[3,1,7,2,5,4,8,6]=>[5,1,-3,2,-8,4,-7,6]
[2,7,8,1,4,5,3,6]=>[8,2,5,1,4,3,7,6]=>[8,2,5,1,4,3,7,6]=>[-5,2,4,-7,1,3,-8,6]
[4,3,7,1,2,6,8,5]=>[7,1,4,3,8,2,6,5]=>[7,1,4,3,8,2,6,5]=>[3,1,-8,-4,6,2,-7,5]
[4,1,2,8,7,3,6,5]=>[4,1,7,2,6,3,8,5]=>[4,1,7,2,6,3,8,5]=>[8,1,-6,2,-4,3,-7,5]
[8,7,5,1,2,4,3,6]=>[5,1,4,2,7,3,8,6]=>[5,1,4,2,7,3,8,6]=>[8,1,-4,2,-5,3,-7,6]
[6,1,2,4,3,8,7,5]=>[6,1,4,2,7,3,8,5]=>[6,1,4,2,7,3,8,5]=>[8,1,-4,2,-7,3,-6,5]
[3,7,8,1,2,4,6,5]=>[8,1,3,2,6,4,7,5]=>[8,1,3,2,6,4,7,5]=>[3,-7,1,-6,2,4,-8,5]
[7,8,5,1,2,4,3,6]=>[5,1,4,2,8,3,7,6]=>[5,1,4,2,8,3,7,6]=>[1,7,-4,2,-5,3,-8,6]
[8,3,4,1,2,6,7,5]=>[4,1,8,3,7,2,6,5]=>[4,1,8,3,7,2,6,5]=>[3,-7,1,-4,6,2,-8,5]
[2,1,4,7,3,6,8,5]=>[2,1,7,4,8,3,6,5]=>[2,1,7,4,8,3,6,5]=>[-2,1,-8,-4,6,3,-7,5]
[7,3,4,1,2,6,8,5]=>[4,1,7,3,8,2,6,5]=>[4,1,7,3,8,2,6,5]=>[-3,-8,1,-4,6,2,-7,5]
[3,7,8,5,1,4,6,2]=>[5,8,3,1,6,2,7,4]=>[5,8,3,1,6,2,7,4]=>[-3,-6,7,1,-8,2,-5,4]
[4,6,8,5,1,3,7,2]=>[5,8,1,4,7,6,2,3]=>[5,8,1,4,7,6,2,3]=>[1,-5,7,4,-8,6,2,3]
[4,5,1,6,8,3,7,2]=>[5,7,8,4,1,6,3,2]=>[5,7,8,4,1,6,3,2]=>[6,-8,3,-4,1,-7,-5,2]
[6,4,2,3,8,7,5,1]=>[5,4,2,7,6,1,8,3]=>[5,4,2,7,6,1,8,3]=>[-2,-6,8,-4,-5,1,-7,3]
[6,4,2,3,7,8,5,1]=>[5,4,2,8,6,1,7,3]=>[5,4,2,8,6,1,7,3]=>[-2,-6,7,-4,-8,1,-5,3]
[8,1,3,5,6,4,7,2]=>[8,7,1,6,2,3,4,5]=>[8,7,1,6,2,3,4,5]=>[-8,1,2,7,3,6,4,5]
[8,5,4,2,1,6,7,3]=>[2,4,5,8,7,1,6,3]=>[2,4,5,8,7,1,6,3]=>[5,7,-2,-4,6,1,-8,3]
[8,5,1,3,4,6,7,2]=>[5,8,1,2,7,3,4,6]=>[5,8,1,2,7,3,4,6]=>[1,2,8,-5,3,7,4,6]
[8,1,5,2,4,6,7,3]=>[8,5,7,2,1,3,4,6]=>[8,5,7,2,1,3,4,6]=>[-8,-5,2,1,3,7,4,6]
[7,2,8,5,4,1,3,6]=>[4,5,1,8,7,2,6,3]=>[4,5,1,8,7,2,6,3]=>[-7,6,1,-5,-8,2,-4,3]
[4,5,7,2,6,8,1,3]=>[8,7,1,4,5,3,2,6]=>[8,7,1,4,5,3,2,6]=>[4,1,5,-7,-8,3,2,6]
[8,1,2,4,6,3,7,5]=>[8,1,6,2,7,4,3,5]=>[8,1,6,2,7,4,3,5]=>[-7,4,1,-6,-8,2,3,5]
[4,5,1,6,8,2,7,3]=>[5,8,7,4,1,6,2,3]=>[5,8,7,4,1,6,2,3]=>[-7,4,-8,6,-5,1,2,3]
[5,1,7,3,6,4,2,8]=>[5,4,6,7,1,2,3,8]=>[5,4,6,7,1,2,3,8]=>[5,1,4,6,7,2,3,8]
[4,2,8,1,6,5,7,3]=>[8,4,7,2,6,1,5,3]=>[8,4,7,2,6,1,5,3]=>[-7,2,-4,6,5,1,-8,3]
[1,3,8,5,2,4,6,7]=>[1,5,3,2,8,4,6,7]=>[1,5,3,2,8,4,6,7]=>[-8,1,-3,2,-5,4,6,7]
[6,1,3,2,8,5,7,4]=>[6,3,1,7,8,2,5,4]=>[6,3,1,7,8,2,5,4]=>[8,-3,-7,1,5,2,-6,4]
[8,1,4,3,5,2,7,6]=>[8,5,4,1,3,7,2,6]=>[8,5,4,1,3,7,2,6]=>[-8,-4,3,1,-5,7,2,6]
[1,7,4,2,3,8,5,6]=>[1,4,2,7,8,5,3,6]=>[1,4,2,7,8,5,3,6]=>[-8,1,2,5,-7,-4,3,6]
[8,7,4,2,3,6,5,1]=>[5,4,2,6,7,1,8,3]=>[5,4,2,6,7,1,8,3]=>[-2,-6,7,8,-4,1,-5,3]
[7,1,4,3,6,5,8,2]=>[7,8,4,1,6,2,3,5]=>[7,8,4,1,6,2,3,5]=>[8,4,-7,1,2,6,3,5]
[8,6,2,5,3,1,4,7]=>[3,5,6,1,4,8,2,7]=>[3,5,6,1,4,8,2,7]=>[-5,6,4,1,-3,8,2,7]
[3,6,2,5,7,8,4,1]=>[4,8,3,6,2,1,7,5]=>[4,8,3,6,2,1,7,5]=>[-3,7,-6,2,-4,1,-8,5]
[7,3,2,8,1,4,6,5]=>[8,3,7,1,6,2,5,4]=>[8,3,7,1,6,2,5,4]=>[-3,1,6,-7,5,2,-8,4]
[6,5,8,1,4,3,7,2]=>[8,7,4,1,6,5,3,2]=>[8,7,4,1,6,5,3,2]=>[-3,-5,-6,1,-7,-4,-8,2]
[5,8,1,4,6,2,7,3]=>[8,6,7,1,5,3,4,2]=>[8,6,7,1,5,3,4,2]=>[1,7,5,-6,3,4,-8,2]
[1,2,4,8,5,7,3,6]=>[1,2,7,4,8,3,5,6]=>[1,2,7,4,8,3,5,6]=>[1,-7,2,-4,3,8,5,6]
[3,7,8,2,5,1,6,4]=>[5,8,3,6,2,1,7,4]=>[5,8,3,6,2,1,7,4]=>[-3,7,-6,2,-8,1,-5,4]
[8,1,3,5,6,4,2,7]=>[8,4,1,6,2,3,5,7]=>[8,4,1,6,2,3,5,7]=>[-4,8,6,1,2,3,5,7]
[4,6,8,5,1,2,7,3]=>[5,1,8,4,7,6,3,2]=>[5,1,8,4,7,6,3,2]=>[6,1,-4,3,-7,-5,-8,2]
[8,1,4,2,6,5,7,3]=>[8,4,7,1,6,2,5,3]=>[8,4,7,1,6,2,5,3]=>[-7,1,6,-4,5,2,-8,3]
[4,8,5,1,2,3,6,7]=>[5,1,2,4,8,3,6,7]=>[5,1,2,4,8,3,6,7]=>[1,4,2,-5,3,8,6,7]
[8,1,2,6,5,7,3,4]=>[8,1,7,3,6,2,5,4]=>[8,1,7,3,6,2,5,4]=>[-6,1,-7,3,5,2,-8,4]
[4,5,8,1,7,3,2,6]=>[8,3,7,4,5,2,1,6]=>[8,3,7,4,5,2,1,6]=>[-7,4,5,2,-8,-3,1,6]
[2,8,1,6,5,7,3,4]=>[8,2,7,3,6,1,5,4]=>[8,2,7,3,6,1,5,4]=>[-2,6,-7,3,5,1,-8,4]
[8,4,6,5,1,3,7,2]=>[5,6,1,7,8,4,3,2]=>[5,6,1,7,8,4,3,2]=>[4,-8,1,3,-7,-6,-5,2]
[5,7,3,4,2,8,6,1]=>[6,4,8,3,5,7,1,2]=>[6,4,8,3,5,7,1,2]=>[-6,-4,3,8,5,7,1,2]
[5,8,3,4,2,7,6,1]=>[6,4,7,3,5,8,1,2]=>[6,4,7,3,5,8,1,2]=>[-6,-4,7,3,5,8,1,2]
[8,3,6,7,5,1,2,4]=>[5,1,7,2,8,4,6,3]=>[5,1,7,2,8,4,6,3]=>[4,-8,1,2,-7,6,-5,3]
[6,1,4,7,2,5,8,3]=>[6,7,8,1,3,4,2,5]=>[6,7,8,1,3,4,2,5]=>[1,3,7,8,-6,4,2,5]
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.
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
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
This map is similar to Mp00235descent views to invisible inversion bottoms, but different beginning with permutations of six elements.
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
Foata-Han
searching the database
Sorry, this map was not found in the database.