Identifier
Mp00237:
Permutations
—descent views to invisible inversion bottoms⟶
Permutations
Mp00239: Permutations —Corteel⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Mp00239: Permutations —Corteel⟶ Permutations
Mp00240: Permutations —weak exceedance partition⟶ Set partitions
Images
=>
Cc0009;cc-rep-3
[1]=>[1]=>[1]=>{{1}}
[1,2]=>[1,2]=>[1,2]=>{{1},{2}}
[2,1]=>[2,1]=>[2,1]=>{{1,2}}
[1,2,3]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[1,3,2]=>[1,3,2]=>[1,3,2]=>{{1},{2,3}}
[2,1,3]=>[2,1,3]=>[2,1,3]=>{{1,2},{3}}
[2,3,1]=>[3,2,1]=>[2,3,1]=>{{1,2,3}}
[3,1,2]=>[3,1,2]=>[3,1,2]=>{{1,3},{2}}
[3,2,1]=>[2,3,1]=>[3,2,1]=>{{1,3},{2}}
[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},{3,4}}
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}}
[1,3,4,2]=>[1,4,3,2]=>[1,3,4,2]=>{{1},{2,3,4}}
[1,4,2,3]=>[1,4,2,3]=>[1,4,2,3]=>{{1},{2,4},{3}}
[1,4,3,2]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}}
[2,1,3,4]=>[2,1,3,4]=>[2,1,3,4]=>{{1,2},{3},{4}}
[2,1,4,3]=>[2,1,4,3]=>[2,1,4,3]=>{{1,2},{3,4}}
[2,3,1,4]=>[3,2,1,4]=>[2,3,1,4]=>{{1,2,3},{4}}
[2,3,4,1]=>[4,2,3,1]=>[2,3,4,1]=>{{1,2,3,4}}
[2,4,1,3]=>[4,2,1,3]=>[2,4,1,3]=>{{1,2,4},{3}}
[2,4,3,1]=>[3,2,4,1]=>[2,4,3,1]=>{{1,2,4},{3}}
[3,1,2,4]=>[3,1,2,4]=>[3,1,2,4]=>{{1,3},{2},{4}}
[3,1,4,2]=>[3,4,1,2]=>[4,3,2,1]=>{{1,4},{2,3}}
[3,2,1,4]=>[2,3,1,4]=>[3,2,1,4]=>{{1,3},{2},{4}}
[3,2,4,1]=>[4,3,2,1]=>[3,4,1,2]=>{{1,3},{2,4}}
[3,4,1,2]=>[4,1,3,2]=>[3,1,4,2]=>{{1,3,4},{2}}
[3,4,2,1]=>[2,4,3,1]=>[3,2,4,1]=>{{1,3,4},{2}}
[4,1,2,3]=>[4,1,2,3]=>[4,1,2,3]=>{{1,4},{2},{3}}
[4,1,3,2]=>[4,3,1,2]=>[3,4,2,1]=>{{1,3},{2,4}}
[4,2,1,3]=>[2,4,1,3]=>[4,2,1,3]=>{{1,4},{2},{3}}
[4,2,3,1]=>[3,4,2,1]=>[4,3,1,2]=>{{1,4},{2,3}}
[4,3,1,2]=>[3,1,4,2]=>[4,1,3,2]=>{{1,4},{2},{3}}
[4,3,2,1]=>[2,3,4,1]=>[4,2,3,1]=>{{1,4},{2},{3}}
[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},{4,5}}
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[1,2,4,5,3]=>[1,2,5,4,3]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,5,3,4]=>{{1},{2},{3,5},{4}}
[1,2,5,4,3]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[1,3,4,2,5]=>[1,4,3,2,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[1,3,4,5,2]=>[1,5,3,4,2]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[1,3,5,2,4]=>[1,5,3,2,4]=>[1,3,5,2,4]=>{{1},{2,3,5},{4}}
[1,3,5,4,2]=>[1,4,3,5,2]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,4,2,3,5]=>{{1},{2,4},{3},{5}}
[1,4,2,5,3]=>[1,4,5,2,3]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}}
[1,4,3,2,5]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[1,4,3,5,2]=>[1,5,4,3,2]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[1,4,5,2,3]=>[1,5,2,4,3]=>[1,4,2,5,3]=>{{1},{2,4,5},{3}}
[1,4,5,3,2]=>[1,3,5,4,2]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,5,2,3,4]=>{{1},{2,5},{3},{4}}
[1,5,2,4,3]=>[1,5,4,2,3]=>[1,4,5,3,2]=>{{1},{2,4},{3,5}}
[1,5,3,2,4]=>[1,3,5,2,4]=>[1,5,3,2,4]=>{{1},{2,5},{3},{4}}
[1,5,3,4,2]=>[1,4,5,3,2]=>[1,5,4,2,3]=>{{1},{2,5},{3,4}}
[1,5,4,2,3]=>[1,4,2,5,3]=>[1,5,2,4,3]=>{{1},{2,5},{3},{4}}
[1,5,4,3,2]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}
[2,1,3,4,5]=>[2,1,3,4,5]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}
[2,1,3,5,4]=>[2,1,3,5,4]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}
[2,1,4,3,5]=>[2,1,4,3,5]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}
[2,1,4,5,3]=>[2,1,5,4,3]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}
[2,1,5,3,4]=>[2,1,5,3,4]=>[2,1,5,3,4]=>{{1,2},{3,5},{4}}
[2,1,5,4,3]=>[2,1,4,5,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}}
[2,3,1,4,5]=>[3,2,1,4,5]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}
[2,3,1,5,4]=>[3,2,1,5,4]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}
[2,3,4,1,5]=>[4,2,3,1,5]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}
[2,3,4,5,1]=>[5,2,3,4,1]=>[2,3,4,5,1]=>{{1,2,3,4,5}}
[2,3,5,1,4]=>[5,2,3,1,4]=>[2,3,5,1,4]=>{{1,2,3,5},{4}}
[2,3,5,4,1]=>[4,2,3,5,1]=>[2,3,5,4,1]=>{{1,2,3,5},{4}}
[2,4,1,3,5]=>[4,2,1,3,5]=>[2,4,1,3,5]=>{{1,2,4},{3},{5}}
[2,4,1,5,3]=>[4,2,5,1,3]=>[2,5,4,3,1]=>{{1,2,5},{3,4}}
[2,4,3,1,5]=>[3,2,4,1,5]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}}
[2,4,3,5,1]=>[5,2,4,3,1]=>[2,4,5,1,3]=>{{1,2,4},{3,5}}
[2,4,5,1,3]=>[5,2,1,4,3]=>[2,4,1,5,3]=>{{1,2,4,5},{3}}
[2,4,5,3,1]=>[3,2,5,4,1]=>[2,4,3,5,1]=>{{1,2,4,5},{3}}
[2,5,1,3,4]=>[5,2,1,3,4]=>[2,5,1,3,4]=>{{1,2,5},{3},{4}}
[2,5,1,4,3]=>[5,2,4,1,3]=>[2,4,5,3,1]=>{{1,2,4},{3,5}}
[2,5,3,1,4]=>[3,2,5,1,4]=>[2,5,3,1,4]=>{{1,2,5},{3},{4}}
[2,5,3,4,1]=>[4,2,5,3,1]=>[2,5,4,1,3]=>{{1,2,5},{3,4}}
[2,5,4,1,3]=>[4,2,1,5,3]=>[2,5,1,4,3]=>{{1,2,5},{3},{4}}
[2,5,4,3,1]=>[3,2,4,5,1]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}}
[3,1,2,4,5]=>[3,1,2,4,5]=>[3,1,2,4,5]=>{{1,3},{2},{4},{5}}
[3,1,2,5,4]=>[3,1,2,5,4]=>[3,1,2,5,4]=>{{1,3},{2},{4,5}}
[3,1,4,2,5]=>[3,4,1,2,5]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}
[3,1,4,5,2]=>[3,5,1,4,2]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}
[3,1,5,2,4]=>[3,5,1,2,4]=>[5,3,2,1,4]=>{{1,5},{2,3},{4}}
[3,1,5,4,2]=>[3,4,1,5,2]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}
[3,2,1,4,5]=>[2,3,1,4,5]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}
[3,2,1,5,4]=>[2,3,1,5,4]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}}
[3,2,4,1,5]=>[4,3,2,1,5]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}}
[3,2,4,5,1]=>[5,3,2,4,1]=>[3,4,1,5,2]=>{{1,3},{2,4,5}}
[3,2,5,1,4]=>[5,3,2,1,4]=>[3,5,1,2,4]=>{{1,3},{2,5},{4}}
[3,2,5,4,1]=>[4,3,2,5,1]=>[3,5,1,4,2]=>{{1,3},{2,5},{4}}
[3,4,1,2,5]=>[4,1,3,2,5]=>[3,1,4,2,5]=>{{1,3,4},{2},{5}}
[3,4,1,5,2]=>[4,5,3,1,2]=>[4,3,5,2,1]=>{{1,4},{2,3,5}}
[3,4,2,1,5]=>[2,4,3,1,5]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}
[3,4,2,5,1]=>[5,4,3,2,1]=>[3,4,5,1,2]=>{{1,3,5},{2,4}}
[3,4,5,1,2]=>[5,1,3,4,2]=>[3,1,4,5,2]=>{{1,3,4,5},{2}}
[3,4,5,2,1]=>[2,5,3,4,1]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}
[3,5,1,2,4]=>[5,1,3,2,4]=>[3,1,5,2,4]=>{{1,3,5},{2},{4}}
[3,5,1,4,2]=>[5,4,3,1,2]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}
[3,5,2,1,4]=>[2,5,3,1,4]=>[3,2,5,1,4]=>{{1,3,5},{2},{4}}
[3,5,2,4,1]=>[4,5,3,2,1]=>[4,3,5,1,2]=>{{1,4},{2,3,5}}
[3,5,4,1,2]=>[4,1,3,5,2]=>[3,1,5,4,2]=>{{1,3,5},{2},{4}}
[3,5,4,2,1]=>[2,4,3,5,1]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}}
[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]=>[5,1,4,3,2]=>{{1,5},{2},{3,4}}
[4,1,3,2,5]=>[4,3,1,2,5]=>[3,4,2,1,5]=>{{1,3},{2,4},{5}}
[4,1,3,5,2]=>[4,5,1,3,2]=>[5,4,2,1,3]=>{{1,5},{2,4},{3}}
[4,1,5,2,3]=>[4,5,2,1,3]=>[5,4,1,3,2]=>{{1,5},{2,4},{3}}
[4,1,5,3,2]=>[4,3,5,1,2]=>[4,5,3,2,1]=>{{1,4},{2,5},{3}}
[4,2,1,3,5]=>[2,4,1,3,5]=>[4,2,1,3,5]=>{{1,4},{2},{3},{5}}
[4,2,1,5,3]=>[2,4,5,1,3]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}}
[4,2,3,1,5]=>[3,4,2,1,5]=>[4,3,1,2,5]=>{{1,4},{2,3},{5}}
[4,2,3,5,1]=>[5,4,2,3,1]=>[4,5,1,2,3]=>{{1,4},{2,5},{3}}
[4,2,5,1,3]=>[5,4,1,2,3]=>[4,5,2,3,1]=>{{1,4},{2,5},{3}}
[4,2,5,3,1]=>[3,5,4,1,2]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}
[4,3,1,2,5]=>[3,1,4,2,5]=>[4,1,3,2,5]=>{{1,4},{2},{3},{5}}
[4,3,1,5,2]=>[3,4,5,2,1]=>[5,4,3,1,2]=>{{1,5},{2,4},{3}}
[4,3,2,1,5]=>[2,3,4,1,5]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}
[4,3,2,5,1]=>[5,3,4,2,1]=>[3,5,4,1,2]=>{{1,3,4},{2,5}}
[4,3,5,1,2]=>[5,1,4,3,2]=>[4,1,5,2,3]=>{{1,4},{2},{3,5}}
[4,3,5,2,1]=>[2,5,4,3,1]=>[4,2,5,1,3]=>{{1,4},{2},{3,5}}
[4,5,1,2,3]=>[5,1,2,4,3]=>[4,1,2,5,3]=>{{1,4,5},{2},{3}}
[4,5,1,3,2]=>[5,3,1,4,2]=>[3,4,2,5,1]=>{{1,3},{2,4,5}}
[4,5,2,1,3]=>[2,5,1,4,3]=>[4,2,1,5,3]=>{{1,4,5},{2},{3}}
[4,5,2,3,1]=>[3,5,2,4,1]=>[4,3,1,5,2]=>{{1,4,5},{2,3}}
[4,5,3,1,2]=>[3,1,5,4,2]=>[4,1,3,5,2]=>{{1,4,5},{2},{3}}
[4,5,3,2,1]=>[2,3,5,4,1]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}
[5,1,2,3,4]=>[5,1,2,3,4]=>[5,1,2,3,4]=>{{1,5},{2},{3},{4}}
[5,1,2,4,3]=>[5,1,4,2,3]=>[4,1,5,3,2]=>{{1,4},{2},{3,5}}
[5,1,3,2,4]=>[5,3,1,2,4]=>[3,5,2,1,4]=>{{1,3},{2,5},{4}}
[5,1,3,4,2]=>[5,4,1,3,2]=>[4,5,2,1,3]=>{{1,4},{2,5},{3}}
[5,1,4,2,3]=>[5,4,2,1,3]=>[4,5,1,3,2]=>{{1,4},{2,5},{3}}
[5,1,4,3,2]=>[5,3,4,1,2]=>[3,5,4,2,1]=>{{1,3,4},{2,5}}
[5,2,1,3,4]=>[2,5,1,3,4]=>[5,2,1,3,4]=>{{1,5},{2},{3},{4}}
[5,2,1,4,3]=>[2,5,4,1,3]=>[4,2,5,3,1]=>{{1,4},{2},{3,5}}
[5,2,3,1,4]=>[3,5,2,1,4]=>[5,3,1,2,4]=>{{1,5},{2,3},{4}}
[5,2,3,4,1]=>[4,5,2,3,1]=>[5,4,1,2,3]=>{{1,5},{2,4},{3}}
[5,2,4,1,3]=>[4,5,1,2,3]=>[5,4,2,3,1]=>{{1,5},{2,4},{3}}
[5,2,4,3,1]=>[3,4,5,1,2]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}
[5,3,1,2,4]=>[3,1,5,2,4]=>[5,1,3,2,4]=>{{1,5},{2},{3},{4}}
[5,3,1,4,2]=>[3,5,4,2,1]=>[5,3,4,1,2]=>{{1,5},{2,3,4}}
[5,3,2,1,4]=>[2,3,5,1,4]=>[5,2,3,1,4]=>{{1,5},{2},{3},{4}}
[5,3,2,4,1]=>[4,3,5,2,1]=>[4,5,3,1,2]=>{{1,4},{2,5},{3}}
[5,3,4,1,2]=>[4,1,5,3,2]=>[5,1,4,2,3]=>{{1,5},{2},{3,4}}
[5,3,4,2,1]=>[2,4,5,3,1]=>[5,2,4,1,3]=>{{1,5},{2},{3,4}}
[5,4,1,2,3]=>[4,1,2,5,3]=>[5,1,2,4,3]=>{{1,5},{2},{3},{4}}
[5,4,1,3,2]=>[4,3,1,5,2]=>[3,5,2,4,1]=>{{1,3},{2,5},{4}}
[5,4,2,1,3]=>[2,4,1,5,3]=>[5,2,1,4,3]=>{{1,5},{2},{3},{4}}
[5,4,2,3,1]=>[3,4,2,5,1]=>[5,3,1,4,2]=>{{1,5},{2,3},{4}}
[5,4,3,1,2]=>[3,1,4,5,2]=>[5,1,3,4,2]=>{{1,5},{2},{3},{4}}
[5,4,3,2,1]=>[2,3,4,5,1]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}
[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},{5,6}}
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,6},{5}}
[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,6},{5}}
[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>{{1},{2},{3,5},{4},{6}}
[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}
[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[1,2,5,3,6,4]=>{{1},{2},{3,5,6},{4}}
[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>{{1},{2},{3,6},{4},{5}}
[1,2,6,3,5,4]=>[1,2,6,5,3,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,5},{4,6}}
[1,2,6,4,3,5]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>{{1},{2},{3,6},{4},{5}}
[1,2,6,4,5,3]=>[1,2,5,6,4,3]=>[1,2,6,5,3,4]=>{{1},{2},{3,6},{4,5}}
[1,2,6,5,3,4]=>[1,2,5,3,6,4]=>[1,2,6,3,5,4]=>{{1},{2},{3,6},{4},{5}}
[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,6},{5}}
[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[1,3,4,6,2,5]=>{{1},{2,3,4,6},{5}}
[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>{{1},{2,3,5},{4},{6}}
[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}
[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[1,3,5,2,6,4]=>{{1},{2,3,5,6},{4}}
[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>{{1},{2,3,6},{4},{5}}
[1,3,6,2,5,4]=>[1,6,3,5,2,4]=>[1,3,5,6,4,2]=>{{1},{2,3,5},{4,6}}
[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>[1,3,6,4,2,5]=>{{1},{2,3,6},{4},{5}}
[1,3,6,4,5,2]=>[1,5,3,6,4,2]=>[1,3,6,5,2,4]=>{{1},{2,3,6},{4,5}}
[1,3,6,5,2,4]=>[1,5,3,2,6,4]=>[1,3,6,2,5,4]=>{{1},{2,3,6},{4},{5}}
[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>{{1},{2,4},{3},{5},{6}}
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>{{1},{2,4},{3},{5,6}}
[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}
[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}
[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[1,6,4,3,2,5]=>{{1},{2,6},{3,4},{5}}
[1,4,2,6,5,3]=>[1,4,5,2,6,3]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}
[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[1,4,3,6,2,5]=>[1,6,4,3,2,5]=>[1,4,6,2,3,5]=>{{1},{2,4},{3,6},{5}}
[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[1,4,2,5,3,6]=>{{1},{2,4,5},{3},{6}}
[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[1,5,4,6,3,2]=>{{1},{2,5},{3,4,6}}
[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[1,4,5,6,2,3]=>{{1},{2,4,6},{3,5}}
[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[1,4,2,5,6,3]=>{{1},{2,4,5,6},{3}}
[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[1,4,2,6,3,5]=>{{1},{2,4,6},{3},{5}}
[1,4,6,2,5,3]=>[1,6,5,4,2,3]=>[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}
[1,4,6,3,2,5]=>[1,3,6,4,2,5]=>[1,4,3,6,2,5]=>{{1},{2,4,6},{3},{5}}
[1,4,6,3,5,2]=>[1,5,6,4,3,2]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,4,6,5,2,3]=>[1,5,2,4,6,3]=>[1,4,2,6,5,3]=>{{1},{2,4,6},{3},{5}}
[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>{{1},{2,5},{3},{4},{6}}
[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[1,6,2,5,4,3]=>{{1},{2,6},{3},{4,5}}
[1,5,2,4,3,6]=>[1,5,4,2,3,6]=>[1,4,5,3,2,6]=>{{1},{2,4},{3,5},{6}}
[1,5,2,4,6,3]=>[1,5,6,2,4,3]=>[1,6,5,3,2,4]=>{{1},{2,6},{3,5},{4}}
[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[1,6,5,2,4,3]=>{{1},{2,6},{3,5},{4}}
[1,5,2,6,4,3]=>[1,5,4,6,2,3]=>[1,5,6,4,3,2]=>{{1},{2,5},{3,6},{4}}
[1,5,3,2,4,6]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>{{1},{2,5},{3},{4},{6}}
[1,5,3,2,6,4]=>[1,3,5,6,2,4]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}
[1,5,3,4,2,6]=>[1,4,5,3,2,6]=>[1,5,4,2,3,6]=>{{1},{2,5},{3,4},{6}}
[1,5,3,4,6,2]=>[1,6,5,3,4,2]=>[1,5,6,2,3,4]=>{{1},{2,5},{3,6},{4}}
[1,5,3,6,2,4]=>[1,6,5,2,3,4]=>[1,5,6,3,4,2]=>{{1},{2,5},{3,6},{4}}
[1,5,3,6,4,2]=>[1,4,6,5,2,3]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}
[1,5,4,2,3,6]=>[1,4,2,5,3,6]=>[1,5,2,4,3,6]=>{{1},{2,5},{3},{4},{6}}
[1,5,4,2,6,3]=>[1,4,5,6,3,2]=>[1,6,5,4,2,3]=>{{1},{2,6},{3,5},{4}}
[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[1,5,4,6,2,3]=>[1,6,2,5,4,3]=>[1,5,2,6,3,4]=>{{1},{2,5},{3},{4,6}}
[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[1,5,2,3,6,4]=>{{1},{2,5,6},{3},{4}}
[1,5,6,2,4,3]=>[1,6,4,2,5,3]=>[1,4,5,3,6,2]=>{{1},{2,4},{3,5,6}}
[1,5,6,3,2,4]=>[1,3,6,2,5,4]=>[1,5,3,2,6,4]=>{{1},{2,5,6},{3},{4}}
[1,5,6,3,4,2]=>[1,4,6,3,5,2]=>[1,5,4,2,6,3]=>{{1},{2,5,6},{3,4}}
[1,5,6,4,2,3]=>[1,4,2,6,5,3]=>[1,5,2,4,6,3]=>{{1},{2,5,6},{3},{4}}
[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>{{1},{2,6},{3},{4},{5}}
[1,6,2,3,5,4]=>[1,6,2,5,3,4]=>[1,5,2,6,4,3]=>{{1},{2,5},{3},{4,6}}
[1,6,2,4,3,5]=>[1,6,4,2,3,5]=>[1,4,6,3,2,5]=>{{1},{2,4},{3,6},{5}}
[1,6,2,4,5,3]=>[1,6,5,2,4,3]=>[1,5,6,3,2,4]=>{{1},{2,5},{3,6},{4}}
[1,6,2,5,3,4]=>[1,6,5,3,2,4]=>[1,5,6,2,4,3]=>{{1},{2,5},{3,6},{4}}
[1,6,2,5,4,3]=>[1,6,4,5,2,3]=>[1,4,6,5,3,2]=>{{1},{2,4,5},{3,6}}
[1,6,3,2,4,5]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>{{1},{2,6},{3},{4},{5}}
[1,6,3,2,5,4]=>[1,3,6,5,2,4]=>[1,5,3,6,4,2]=>{{1},{2,5},{3},{4,6}}
[1,6,3,4,2,5]=>[1,4,6,3,2,5]=>[1,6,4,2,3,5]=>{{1},{2,6},{3,4},{5}}
[1,6,3,4,5,2]=>[1,5,6,3,4,2]=>[1,6,5,2,3,4]=>{{1},{2,6},{3,5},{4}}
[1,6,3,5,2,4]=>[1,5,6,2,3,4]=>[1,6,5,3,4,2]=>{{1},{2,6},{3,5},{4}}
[1,6,3,5,4,2]=>[1,4,5,6,2,3]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}
[1,6,4,2,3,5]=>[1,4,2,6,3,5]=>[1,6,2,4,3,5]=>{{1},{2,6},{3},{4},{5}}
[1,6,4,2,5,3]=>[1,4,6,5,3,2]=>[1,6,4,5,2,3]=>{{1},{2,6},{3,4,5}}
[1,6,4,3,2,5]=>[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>{{1},{2,6},{3},{4},{5}}
[1,6,4,3,5,2]=>[1,5,4,6,3,2]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[1,6,4,5,2,3]=>[1,5,2,6,4,3]=>[1,6,2,5,3,4]=>{{1},{2,6},{3},{4,5}}
[1,6,4,5,3,2]=>[1,3,5,6,4,2]=>[1,6,3,5,2,4]=>{{1},{2,6},{3},{4,5}}
[1,6,5,2,3,4]=>[1,5,2,3,6,4]=>[1,6,2,3,5,4]=>{{1},{2,6},{3},{4},{5}}
[1,6,5,2,4,3]=>[1,5,4,2,6,3]=>[1,4,6,3,5,2]=>{{1},{2,4},{3,6},{5}}
[1,6,5,3,2,4]=>[1,3,5,2,6,4]=>[1,6,3,2,5,4]=>{{1},{2,6},{3},{4},{5}}
[1,6,5,3,4,2]=>[1,4,5,3,6,2]=>[1,6,4,2,5,3]=>{{1},{2,6},{3,4},{5}}
[1,6,5,4,2,3]=>[1,4,2,5,6,3]=>[1,6,2,4,5,3]=>{{1},{2,6},{3},{4},{5}}
[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}
[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}
[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}
[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}
[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}
[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,6},{5}}
[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}
[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}
[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}
[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}
[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}
[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>{{1,2},{3,4,6},{5}}
[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}
[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>{{1,2},{3,5},{4},{6}}
[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}
[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}
[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}
[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[2,1,5,3,6,4]=>{{1,2},{3,5,6},{4}}
[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}
[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>{{1,2},{3,6},{4},{5}}
[2,1,6,3,5,4]=>[2,1,6,5,3,4]=>[2,1,5,6,4,3]=>{{1,2},{3,5},{4,6}}
[2,1,6,4,3,5]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>{{1,2},{3,6},{4},{5}}
[2,1,6,4,5,3]=>[2,1,5,6,4,3]=>[2,1,6,5,3,4]=>{{1,2},{3,6},{4,5}}
[2,1,6,5,3,4]=>[2,1,5,3,6,4]=>[2,1,6,3,5,4]=>{{1,2},{3,6},{4},{5}}
[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}
[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}
[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}
[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}
[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}
[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>{{1,2,3},{4,6},{5}}
[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}
[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}
[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}
[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}
[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[2,3,4,6,1,5]=>{{1,2,3,4,6},{5}}
[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}
[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[2,3,5,1,4,6]=>{{1,2,3,5},{4},{6}}
[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}
[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}
[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}
[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[2,3,5,1,6,4]=>{{1,2,3,5,6},{4}}
[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}
[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[2,3,6,1,4,5]=>{{1,2,3,6},{4},{5}}
[2,3,6,1,5,4]=>[6,2,3,5,1,4]=>[2,3,5,6,4,1]=>{{1,2,3,5},{4,6}}
[2,3,6,4,1,5]=>[4,2,3,6,1,5]=>[2,3,6,4,1,5]=>{{1,2,3,6},{4},{5}}
[2,3,6,4,5,1]=>[5,2,3,6,4,1]=>[2,3,6,5,1,4]=>{{1,2,3,6},{4,5}}
[2,3,6,5,1,4]=>[5,2,3,1,6,4]=>[2,3,6,1,5,4]=>{{1,2,3,6},{4},{5}}
[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}
[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>{{1,2,4},{3},{5},{6}}
[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>{{1,2,4},{3},{5,6}}
[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}
[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}
[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[2,6,4,3,1,5]=>{{1,2,6},{3,4},{5}}
[2,4,1,6,5,3]=>[4,2,5,1,6,3]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}
[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}
[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}
[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}
[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}
[2,4,3,6,1,5]=>[6,2,4,3,1,5]=>[2,4,6,1,3,5]=>{{1,2,4},{3,6},{5}}
[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[2,4,6,1,5,3]=>{{1,2,4},{3,6},{5}}
[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[2,4,1,5,3,6]=>{{1,2,4,5},{3},{6}}
[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[2,5,4,6,3,1]=>{{1,2,5},{3,4,6}}
[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}
[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[2,4,5,6,1,3]=>{{1,2,4,6},{3,5}}
[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[2,4,1,5,6,3]=>{{1,2,4,5,6},{3}}
[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}
[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[2,4,1,6,3,5]=>{{1,2,4,6},{3},{5}}
[2,4,6,1,5,3]=>[6,2,5,4,1,3]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}
[2,4,6,3,1,5]=>[3,2,6,4,1,5]=>[2,4,3,6,1,5]=>{{1,2,4,6},{3},{5}}
[2,4,6,3,5,1]=>[5,2,6,4,3,1]=>[2,5,4,6,1,3]=>{{1,2,5},{3,4,6}}
[2,4,6,5,1,3]=>[5,2,1,4,6,3]=>[2,4,1,6,5,3]=>{{1,2,4,6},{3},{5}}
[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}
[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>{{1,2,5},{3},{4},{6}}
[2,5,1,3,6,4]=>[5,2,1,6,3,4]=>[2,6,1,5,4,3]=>{{1,2,6},{3},{4,5}}
[2,5,1,4,3,6]=>[5,2,4,1,3,6]=>[2,4,5,3,1,6]=>{{1,2,4},{3,5},{6}}
[2,5,1,4,6,3]=>[5,2,6,1,4,3]=>[2,6,5,3,1,4]=>{{1,2,6},{3,5},{4}}
[2,5,1,6,3,4]=>[5,2,6,3,1,4]=>[2,6,5,1,4,3]=>{{1,2,6},{3,5},{4}}
[2,5,1,6,4,3]=>[5,2,4,6,1,3]=>[2,5,6,4,3,1]=>{{1,2,5},{3,6},{4}}
[2,5,3,1,4,6]=>[3,2,5,1,4,6]=>[2,5,3,1,4,6]=>{{1,2,5},{3},{4},{6}}
[2,5,3,1,6,4]=>[3,2,5,6,1,4]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}
[2,5,3,4,1,6]=>[4,2,5,3,1,6]=>[2,5,4,1,3,6]=>{{1,2,5},{3,4},{6}}
[2,5,3,4,6,1]=>[6,2,5,3,4,1]=>[2,5,6,1,3,4]=>{{1,2,5},{3,6},{4}}
[2,5,3,6,1,4]=>[6,2,5,1,3,4]=>[2,5,6,3,4,1]=>{{1,2,5},{3,6},{4}}
[2,5,3,6,4,1]=>[4,2,6,5,1,3]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}
[2,5,4,1,3,6]=>[4,2,1,5,3,6]=>[2,5,1,4,3,6]=>{{1,2,5},{3},{4},{6}}
[2,5,4,1,6,3]=>[4,2,5,6,3,1]=>[2,6,5,4,1,3]=>{{1,2,6},{3,5},{4}}
[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}
[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[2,4,6,5,1,3]=>{{1,2,4,5},{3,6}}
[2,5,4,6,1,3]=>[6,2,1,5,4,3]=>[2,5,1,6,3,4]=>{{1,2,5},{3},{4,6}}
[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[2,5,3,6,1,4]=>{{1,2,5},{3},{4,6}}
[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[2,5,1,3,6,4]=>{{1,2,5,6},{3},{4}}
[2,5,6,1,4,3]=>[6,2,4,1,5,3]=>[2,4,5,3,6,1]=>{{1,2,4},{3,5,6}}
[2,5,6,3,1,4]=>[3,2,6,1,5,4]=>[2,5,3,1,6,4]=>{{1,2,5,6},{3},{4}}
[2,5,6,3,4,1]=>[4,2,6,3,5,1]=>[2,5,4,1,6,3]=>{{1,2,5,6},{3,4}}
[2,5,6,4,1,3]=>[4,2,1,6,5,3]=>[2,5,1,4,6,3]=>{{1,2,5,6},{3},{4}}
[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}
[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>{{1,2,6},{3},{4},{5}}
[2,6,1,3,5,4]=>[6,2,1,5,3,4]=>[2,5,1,6,4,3]=>{{1,2,5},{3},{4,6}}
[2,6,1,4,3,5]=>[6,2,4,1,3,5]=>[2,4,6,3,1,5]=>{{1,2,4},{3,6},{5}}
[2,6,1,4,5,3]=>[6,2,5,1,4,3]=>[2,5,6,3,1,4]=>{{1,2,5},{3,6},{4}}
[2,6,1,5,3,4]=>[6,2,5,3,1,4]=>[2,5,6,1,4,3]=>{{1,2,5},{3,6},{4}}
[2,6,1,5,4,3]=>[6,2,4,5,1,3]=>[2,4,6,5,3,1]=>{{1,2,4,5},{3,6}}
[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>[2,6,3,1,4,5]=>{{1,2,6},{3},{4},{5}}
[2,6,3,1,5,4]=>[3,2,6,5,1,4]=>[2,5,3,6,4,1]=>{{1,2,5},{3},{4,6}}
[2,6,3,4,1,5]=>[4,2,6,3,1,5]=>[2,6,4,1,3,5]=>{{1,2,6},{3,4},{5}}
[2,6,3,4,5,1]=>[5,2,6,3,4,1]=>[2,6,5,1,3,4]=>{{1,2,6},{3,5},{4}}
[2,6,3,5,1,4]=>[5,2,6,1,3,4]=>[2,6,5,3,4,1]=>{{1,2,6},{3,5},{4}}
[2,6,3,5,4,1]=>[4,2,5,6,1,3]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}
[2,6,4,1,3,5]=>[4,2,1,6,3,5]=>[2,6,1,4,3,5]=>{{1,2,6},{3},{4},{5}}
[2,6,4,1,5,3]=>[4,2,6,5,3,1]=>[2,6,4,5,1,3]=>{{1,2,6},{3,4,5}}
[2,6,4,3,1,5]=>[3,2,4,6,1,5]=>[2,6,3,4,1,5]=>{{1,2,6},{3},{4},{5}}
[2,6,4,3,5,1]=>[5,2,4,6,3,1]=>[2,5,6,4,1,3]=>{{1,2,5},{3,6},{4}}
[2,6,4,5,1,3]=>[5,2,1,6,4,3]=>[2,6,1,5,3,4]=>{{1,2,6},{3},{4,5}}
[2,6,4,5,3,1]=>[3,2,5,6,4,1]=>[2,6,3,5,1,4]=>{{1,2,6},{3},{4,5}}
[2,6,5,1,3,4]=>[5,2,1,3,6,4]=>[2,6,1,3,5,4]=>{{1,2,6},{3},{4},{5}}
[2,6,5,1,4,3]=>[5,2,4,1,6,3]=>[2,4,6,3,5,1]=>{{1,2,4},{3,6},{5}}
[2,6,5,3,1,4]=>[3,2,5,1,6,4]=>[2,6,3,1,5,4]=>{{1,2,6},{3},{4},{5}}
[2,6,5,3,4,1]=>[4,2,5,3,6,1]=>[2,6,4,1,5,3]=>{{1,2,6},{3,4},{5}}
[2,6,5,4,1,3]=>[4,2,1,5,6,3]=>[2,6,1,4,5,3]=>{{1,2,6},{3},{4},{5}}
[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}
[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>{{1,3},{2},{4},{5,6}}
[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>{{1,3},{2},{4,5},{6}}
[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>{{1,3},{2},{4,5,6}}
[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>{{1,3},{2},{4,6},{5}}
[3,1,2,6,5,4]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>{{1,3},{2},{4,6},{5}}
[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}
[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}
[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}
[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}
[3,1,4,6,2,5]=>[3,6,1,4,2,5]=>[4,3,2,6,1,5]=>{{1,4,6},{2,3},{5}}
[3,1,4,6,5,2]=>[3,5,1,4,6,2]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}
[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[5,3,2,1,4,6]=>{{1,5},{2,3},{4},{6}}
[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}
[3,1,5,4,2,6]=>[3,4,1,5,2,6]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}
[3,1,5,4,6,2]=>[3,6,1,5,4,2]=>[5,3,2,6,1,4]=>{{1,5},{2,3},{4,6}}
[3,1,5,6,2,4]=>[3,6,1,2,5,4]=>[5,3,2,1,6,4]=>{{1,5,6},{2,3},{4}}
[3,1,5,6,4,2]=>[3,4,1,6,5,2]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}
[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[6,3,2,1,4,5]=>{{1,6},{2,3},{4},{5}}
[3,1,6,2,5,4]=>[3,6,1,5,2,4]=>[5,3,2,6,4,1]=>{{1,5},{2,3},{4,6}}
[3,1,6,4,2,5]=>[3,4,1,6,2,5]=>[6,3,2,4,1,5]=>{{1,6},{2,3},{4},{5}}
[3,1,6,4,5,2]=>[3,5,1,6,4,2]=>[6,3,2,5,1,4]=>{{1,6},{2,3},{4,5}}
[3,1,6,5,2,4]=>[3,5,1,2,6,4]=>[6,3,2,1,5,4]=>{{1,6},{2,3},{4},{5}}
[3,1,6,5,4,2]=>[3,4,1,5,6,2]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}
[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}
[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}
[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}
[3,2,1,6,4,5]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>{{1,3},{2},{4,6},{5}}
[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}
[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}
[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}
[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}
[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}
[3,2,4,6,1,5]=>[6,3,2,4,1,5]=>[3,4,1,6,2,5]=>{{1,3},{2,4,6},{5}}
[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[3,4,1,6,5,2]=>{{1,3},{2,4,6},{5}}
[3,2,5,1,4,6]=>[5,3,2,1,4,6]=>[3,5,1,2,4,6]=>{{1,3},{2,5},{4},{6}}
[3,2,5,1,6,4]=>[5,3,2,6,1,4]=>[3,6,1,5,4,2]=>{{1,3},{2,6},{4,5}}
[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[3,5,1,4,2,6]=>{{1,3},{2,5},{4},{6}}
[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}
[3,2,5,6,1,4]=>[6,3,2,1,5,4]=>[3,5,1,2,6,4]=>{{1,3},{2,5,6},{4}}
[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[3,5,1,4,6,2]=>{{1,3},{2,5,6},{4}}
[3,2,6,1,4,5]=>[6,3,2,1,4,5]=>[3,6,1,2,4,5]=>{{1,3},{2,6},{4},{5}}
[3,2,6,1,5,4]=>[6,3,2,5,1,4]=>[3,5,1,6,4,2]=>{{1,3},{2,5},{4,6}}
[3,2,6,4,1,5]=>[4,3,2,6,1,5]=>[3,6,1,4,2,5]=>{{1,3},{2,6},{4},{5}}
[3,2,6,4,5,1]=>[5,3,2,6,4,1]=>[3,6,1,5,2,4]=>{{1,3},{2,6},{4,5}}
[3,2,6,5,1,4]=>[5,3,2,1,6,4]=>[3,6,1,2,5,4]=>{{1,3},{2,6},{4},{5}}
[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[3,6,1,4,5,2]=>{{1,3},{2,6},{4},{5}}
[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[3,1,4,2,5,6]=>{{1,3,4},{2},{5},{6}}
[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[3,1,4,2,6,5]=>{{1,3,4},{2},{5,6}}
[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[4,3,5,2,1,6]=>{{1,4},{2,3,5},{6}}
[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[4,3,5,2,6,1]=>{{1,4},{2,3,5,6}}
[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[4,3,6,2,1,5]=>{{1,4},{2,3,6},{5}}
[3,4,1,6,5,2]=>[4,5,3,1,6,2]=>[4,3,6,2,5,1]=>{{1,4},{2,3,6},{5}}
[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}
[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}
[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[3,4,5,1,2,6]=>{{1,3,5},{2,4},{6}}
[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[3,4,5,1,6,2]=>{{1,3,5,6},{2,4}}
[3,4,2,6,1,5]=>[6,4,3,2,1,5]=>[3,4,6,1,2,5]=>{{1,3,6},{2,4},{5}}
[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[3,4,6,1,5,2]=>{{1,3,6},{2,4},{5}}
[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[3,1,4,5,2,6]=>{{1,3,4,5},{2},{6}}
[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}
[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}
[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}
[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[3,1,4,5,6,2]=>{{1,3,4,5,6},{2}}
[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}
[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[3,1,4,6,2,5]=>{{1,3,4,6},{2},{5}}
[3,4,6,1,5,2]=>[6,5,3,4,1,2]=>[3,4,5,6,2,1]=>{{1,3,5},{2,4,6}}
[3,4,6,2,1,5]=>[2,6,3,4,1,5]=>[3,2,4,6,1,5]=>{{1,3,4,6},{2},{5}}
[3,4,6,2,5,1]=>[5,6,3,4,2,1]=>[4,3,5,6,1,2]=>{{1,4,6},{2,3,5}}
[3,4,6,5,1,2]=>[5,1,3,4,6,2]=>[3,1,4,6,5,2]=>{{1,3,4,6},{2},{5}}
[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}
[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[3,1,5,2,4,6]=>{{1,3,5},{2},{4},{6}}
[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[3,1,6,5,4,2]=>{{1,3,6},{2},{4,5}}
[3,5,1,4,2,6]=>[5,4,3,1,2,6]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}
[3,5,1,4,6,2]=>[5,6,3,1,4,2]=>[5,3,6,2,1,4]=>{{1,5},{2,3,6},{4}}
[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[5,3,6,1,4,2]=>{{1,5},{2,3,6},{4}}
[3,5,1,6,4,2]=>[5,4,3,6,1,2]=>[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}
[3,5,2,1,4,6]=>[2,5,3,1,4,6]=>[3,2,5,1,4,6]=>{{1,3,5},{2},{4},{6}}
[3,5,2,1,6,4]=>[2,5,3,6,1,4]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}
[3,5,2,4,1,6]=>[4,5,3,2,1,6]=>[4,3,5,1,2,6]=>{{1,4},{2,3,5},{6}}
[3,5,2,4,6,1]=>[6,5,3,2,4,1]=>[3,5,6,1,2,4]=>{{1,3,6},{2,5},{4}}
[3,5,2,6,1,4]=>[6,5,3,1,2,4]=>[3,5,6,2,4,1]=>{{1,3,6},{2,5},{4}}
[3,5,2,6,4,1]=>[4,6,3,5,1,2]=>[4,3,6,5,2,1]=>{{1,4,5},{2,3,6}}
[3,5,4,1,2,6]=>[4,1,3,5,2,6]=>[3,1,5,4,2,6]=>{{1,3,5},{2},{4},{6}}
[3,5,4,1,6,2]=>[4,5,3,6,2,1]=>[5,3,6,4,1,2]=>{{1,5},{2,3,6},{4}}
[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}
[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[3,4,6,5,1,2]=>{{1,3,6},{2,4,5}}
[3,5,4,6,1,2]=>[6,1,3,5,4,2]=>[3,1,5,6,2,4]=>{{1,3,5},{2},{4,6}}
[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[3,2,5,6,1,4]=>{{1,3,5},{2},{4,6}}
[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[3,1,5,2,6,4]=>{{1,3,5,6},{2},{4}}
[3,5,6,1,4,2]=>[6,4,3,1,5,2]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}
[3,5,6,2,1,4]=>[2,6,3,1,5,4]=>[3,2,5,1,6,4]=>{{1,3,5,6},{2},{4}}
[3,5,6,2,4,1]=>[4,6,3,2,5,1]=>[4,3,5,1,6,2]=>{{1,4},{2,3,5,6}}
[3,5,6,4,1,2]=>[4,1,3,6,5,2]=>[3,1,5,4,6,2]=>{{1,3,5,6},{2},{4}}
[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}
[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[3,1,6,2,4,5]=>{{1,3,6},{2},{4},{5}}
[3,6,1,2,5,4]=>[6,1,3,5,2,4]=>[3,1,5,6,4,2]=>{{1,3,5},{2},{4,6}}
[3,6,1,4,2,5]=>[6,4,3,1,2,5]=>[3,4,6,2,1,5]=>{{1,3,6},{2,4},{5}}
[3,6,1,4,5,2]=>[6,5,3,1,4,2]=>[3,5,6,2,1,4]=>{{1,3,6},{2,5},{4}}
[3,6,1,5,2,4]=>[6,5,3,2,1,4]=>[3,5,6,1,4,2]=>{{1,3,6},{2,5},{4}}
[3,6,1,5,4,2]=>[6,4,3,5,1,2]=>[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}
[3,6,2,1,4,5]=>[2,6,3,1,4,5]=>[3,2,6,1,4,5]=>{{1,3,6},{2},{4},{5}}
[3,6,2,1,5,4]=>[2,6,3,5,1,4]=>[3,2,5,6,4,1]=>{{1,3,5},{2},{4,6}}
[3,6,2,4,1,5]=>[4,6,3,2,1,5]=>[4,3,6,1,2,5]=>{{1,4},{2,3,6},{5}}
[3,6,2,4,5,1]=>[5,6,3,2,4,1]=>[5,3,6,1,2,4]=>{{1,5},{2,3,6},{4}}
[3,6,2,5,1,4]=>[5,6,3,1,2,4]=>[5,3,6,2,4,1]=>{{1,5},{2,3,6},{4}}
[3,6,2,5,4,1]=>[4,5,3,6,1,2]=>[5,3,6,4,2,1]=>{{1,5},{2,3,6},{4}}
[3,6,4,1,2,5]=>[4,1,3,6,2,5]=>[3,1,6,4,2,5]=>{{1,3,6},{2},{4},{5}}
[3,6,4,1,5,2]=>[4,6,3,5,2,1]=>[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}
[3,6,4,2,1,5]=>[2,4,3,6,1,5]=>[3,2,6,4,1,5]=>{{1,3,6},{2},{4},{5}}
[3,6,4,2,5,1]=>[5,4,3,6,2,1]=>[3,5,6,4,1,2]=>{{1,3,6},{2,5},{4}}
[3,6,4,5,1,2]=>[5,1,3,6,4,2]=>[3,1,6,5,2,4]=>{{1,3,6},{2},{4,5}}
[3,6,4,5,2,1]=>[2,5,3,6,4,1]=>[3,2,6,5,1,4]=>{{1,3,6},{2},{4,5}}
[3,6,5,1,2,4]=>[5,1,3,2,6,4]=>[3,1,6,2,5,4]=>{{1,3,6},{2},{4},{5}}
[3,6,5,1,4,2]=>[5,4,3,1,6,2]=>[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}
[3,6,5,2,1,4]=>[2,5,3,1,6,4]=>[3,2,6,1,5,4]=>{{1,3,6},{2},{4},{5}}
[3,6,5,2,4,1]=>[4,5,3,2,6,1]=>[4,3,6,1,5,2]=>{{1,4},{2,3,6},{5}}
[3,6,5,4,1,2]=>[4,1,3,5,6,2]=>[3,1,6,4,5,2]=>{{1,3,6},{2},{4},{5}}
[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}
[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},{5,6}}
[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[5,1,4,3,2,6]=>{{1,5},{2},{3,4},{6}}
[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[5,1,4,3,6,2]=>{{1,5,6},{2},{3,4}}
[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[6,1,4,3,2,5]=>{{1,6},{2},{3,4},{5}}
[4,1,2,6,5,3]=>[4,1,5,2,6,3]=>[6,1,4,3,5,2]=>{{1,6},{2},{3,4},{5}}
[4,1,3,2,5,6]=>[4,3,1,2,5,6]=>[3,4,2,1,5,6]=>{{1,3},{2,4},{5},{6}}
[4,1,3,2,6,5]=>[4,3,1,2,6,5]=>[3,4,2,1,6,5]=>{{1,3},{2,4},{5,6}}
[4,1,3,5,2,6]=>[4,5,1,3,2,6]=>[5,4,2,1,3,6]=>{{1,5},{2,4},{3},{6}}
[4,1,3,5,6,2]=>[4,6,1,3,5,2]=>[5,4,2,1,6,3]=>{{1,5,6},{2,4},{3}}
[4,1,3,6,2,5]=>[4,6,1,3,2,5]=>[6,4,2,1,3,5]=>{{1,6},{2,4},{3},{5}}
[4,1,3,6,5,2]=>[4,5,1,3,6,2]=>[6,4,2,1,5,3]=>{{1,6},{2,4},{3},{5}}
[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[5,4,1,3,2,6]=>{{1,5},{2,4},{3},{6}}
[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}
[4,1,5,3,2,6]=>[4,3,5,1,2,6]=>[4,5,3,2,1,6]=>{{1,4},{2,5},{3},{6}}
[4,1,5,3,6,2]=>[4,6,5,1,3,2]=>[6,4,5,3,1,2]=>{{1,6},{2,4},{3,5}}
[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[5,4,1,3,6,2]=>{{1,5,6},{2,4},{3}}
[4,1,5,6,3,2]=>[4,3,6,1,5,2]=>[4,5,3,2,6,1]=>{{1,4},{2,5,6},{3}}
[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[6,4,1,3,2,5]=>{{1,6},{2,4},{3},{5}}
[4,1,6,2,5,3]=>[4,6,5,1,2,3]=>[6,4,5,3,2,1]=>{{1,6},{2,4},{3,5}}
[4,1,6,3,2,5]=>[4,3,6,1,2,5]=>[4,6,3,2,1,5]=>{{1,4},{2,6},{3},{5}}
[4,1,6,3,5,2]=>[4,5,6,1,3,2]=>[6,5,4,3,1,2]=>{{1,6},{2,5},{3,4}}
[4,1,6,5,2,3]=>[4,5,2,1,6,3]=>[6,4,1,3,5,2]=>{{1,6},{2,4},{3},{5}}
[4,1,6,5,3,2]=>[4,3,5,1,6,2]=>[4,6,3,2,5,1]=>{{1,4},{2,6},{3},{5}}
[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>{{1,4},{2},{3},{5},{6}}
[4,2,1,3,6,5]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>{{1,4},{2},{3},{5,6}}
[4,2,1,5,3,6]=>[2,4,5,1,3,6]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}
[4,2,1,5,6,3]=>[2,4,6,1,5,3]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}
[4,2,1,6,3,5]=>[2,4,6,1,3,5]=>[6,2,4,3,1,5]=>{{1,6},{2},{3,4},{5}}
[4,2,1,6,5,3]=>[2,4,5,1,6,3]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}
[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>{{1,4},{2,3},{5},{6}}
[4,2,3,1,6,5]=>[3,4,2,1,6,5]=>[4,3,1,2,6,5]=>{{1,4},{2,3},{5,6}}
[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[4,5,1,2,3,6]=>{{1,4},{2,5},{3},{6}}
[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[4,5,1,2,6,3]=>{{1,4},{2,5,6},{3}}
[4,2,3,6,1,5]=>[6,4,2,3,1,5]=>[4,6,1,2,3,5]=>{{1,4},{2,6},{3},{5}}
[4,2,3,6,5,1]=>[5,4,2,3,6,1]=>[4,6,1,2,5,3]=>{{1,4},{2,6},{3},{5}}
[4,2,5,1,3,6]=>[5,4,1,2,3,6]=>[4,5,2,3,1,6]=>{{1,4},{2,5},{3},{6}}
[4,2,5,1,6,3]=>[5,4,6,2,1,3]=>[5,6,4,2,3,1]=>{{1,5},{2,6},{3,4}}
[4,2,5,3,1,6]=>[3,5,4,1,2,6]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}
[4,2,5,3,6,1]=>[6,4,5,2,3,1]=>[4,6,5,2,1,3]=>{{1,4},{2,6},{3,5}}
[4,2,5,6,1,3]=>[6,4,1,2,5,3]=>[4,5,2,3,6,1]=>{{1,4},{2,5,6},{3}}
[4,2,5,6,3,1]=>[3,6,4,1,5,2]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}
[4,2,6,1,3,5]=>[6,4,1,2,3,5]=>[4,6,2,3,1,5]=>{{1,4},{2,6},{3},{5}}
[4,2,6,1,5,3]=>[6,4,5,2,1,3]=>[4,6,5,2,3,1]=>{{1,4},{2,6},{3,5}}
[4,2,6,3,1,5]=>[3,6,4,1,2,5]=>[6,3,4,2,1,5]=>{{1,6},{2,3,4},{5}}
[4,2,6,3,5,1]=>[5,4,6,2,3,1]=>[5,6,4,2,1,3]=>{{1,5},{2,6},{3,4}}
[4,2,6,5,1,3]=>[5,4,1,2,6,3]=>[4,6,2,3,5,1]=>{{1,4},{2,6},{3},{5}}
[4,2,6,5,3,1]=>[3,5,4,1,6,2]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}
[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[4,1,3,2,5,6]=>{{1,4},{2},{3},{5},{6}}
[4,3,1,2,6,5]=>[3,1,4,2,6,5]=>[4,1,3,2,6,5]=>{{1,4},{2},{3},{5,6}}
[4,3,1,5,2,6]=>[3,4,5,2,1,6]=>[5,4,3,1,2,6]=>{{1,5},{2,4},{3},{6}}
[4,3,1,5,6,2]=>[3,4,6,2,5,1]=>[5,4,3,1,6,2]=>{{1,5,6},{2,4},{3}}
[4,3,1,6,2,5]=>[3,4,6,2,1,5]=>[6,4,3,1,2,5]=>{{1,6},{2,4},{3},{5}}
[4,3,1,6,5,2]=>[3,4,5,2,6,1]=>[6,4,3,1,5,2]=>{{1,6},{2,4},{3},{5}}
[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}
[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}
[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}
[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[3,5,4,1,6,2]=>{{1,3,4},{2,5,6}}
[4,3,2,6,1,5]=>[6,3,4,2,1,5]=>[3,6,4,1,2,5]=>{{1,3,4},{2,6},{5}}
[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[3,6,4,1,5,2]=>{{1,3,4},{2,6},{5}}
[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[4,1,5,2,3,6]=>{{1,4},{2},{3,5},{6}}
[4,3,5,1,6,2]=>[5,6,4,3,1,2]=>[5,4,6,1,3,2]=>{{1,5},{2,4},{3,6}}
[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[4,2,5,1,3,6]=>{{1,4},{2},{3,5},{6}}
[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}
[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[4,1,5,2,6,3]=>{{1,4},{2},{3,5,6}}
[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[4,2,5,1,6,3]=>{{1,4},{2},{3,5,6}}
[4,3,6,1,2,5]=>[6,1,4,3,2,5]=>[4,1,6,2,3,5]=>{{1,4},{2},{3,6},{5}}
[4,3,6,1,5,2]=>[6,5,4,3,1,2]=>[4,5,6,1,3,2]=>{{1,4},{2,5},{3,6}}
[4,3,6,2,1,5]=>[2,6,4,3,1,5]=>[4,2,6,1,3,5]=>{{1,4},{2},{3,6},{5}}
[4,3,6,2,5,1]=>[5,6,4,3,2,1]=>[5,4,6,1,2,3]=>{{1,5},{2,4},{3,6}}
[4,3,6,5,1,2]=>[5,1,4,3,6,2]=>[4,1,6,2,5,3]=>{{1,4},{2},{3,6},{5}}
[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[4,2,6,1,5,3]=>{{1,4},{2},{3,6},{5}}
[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[4,1,2,5,3,6]=>{{1,4,5},{2},{3},{6}}
[4,5,1,2,6,3]=>[5,1,6,4,2,3]=>[5,1,4,6,3,2]=>{{1,5},{2},{3,4,6}}
[4,5,1,3,2,6]=>[5,3,1,4,2,6]=>[3,4,2,5,1,6]=>{{1,3},{2,4,5},{6}}
[4,5,1,3,6,2]=>[5,6,1,4,3,2]=>[5,4,2,6,1,3]=>{{1,5},{2,4,6},{3}}
[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[5,4,1,6,3,2]=>{{1,5},{2,4,6},{3}}
[4,5,1,6,3,2]=>[5,3,6,4,1,2]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}
[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[4,2,1,5,3,6]=>{{1,4,5},{2},{3},{6}}
[4,5,2,1,6,3]=>[2,5,6,4,1,3]=>[5,2,4,6,3,1]=>{{1,5},{2},{3,4,6}}
[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[4,3,1,5,2,6]=>{{1,4,5},{2,3},{6}}
[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[4,5,1,6,2,3]=>{{1,4,6},{2,5},{3}}
[4,5,2,6,1,3]=>[6,5,1,4,2,3]=>[4,5,2,6,3,1]=>{{1,4,6},{2,5},{3}}
[4,5,2,6,3,1]=>[3,6,5,4,1,2]=>[5,3,4,6,2,1]=>{{1,5},{2,3,4,6}}
[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[4,1,3,5,2,6]=>{{1,4,5},{2},{3},{6}}
[4,5,3,1,6,2]=>[3,5,6,4,2,1]=>[5,4,3,6,1,2]=>{{1,5},{2,4,6},{3}}
[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}
[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[3,5,4,6,1,2]=>{{1,3,4,6},{2,5}}
[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[4,1,5,6,2,3]=>{{1,4,6},{2},{3,5}}
[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[4,2,5,6,1,3]=>{{1,4,6},{2},{3,5}}
[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[4,1,2,5,6,3]=>{{1,4,5,6},{2},{3}}
[4,5,6,1,3,2]=>[6,3,1,4,5,2]=>[3,4,2,5,6,1]=>{{1,3},{2,4,5,6}}
[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[4,2,1,5,6,3]=>{{1,4,5,6},{2},{3}}
[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[4,3,1,5,6,2]=>{{1,4,5,6},{2,3}}
[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[4,1,3,5,6,2]=>{{1,4,5,6},{2},{3}}
[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}
[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[4,1,2,6,3,5]=>{{1,4,6},{2},{3},{5}}
[4,6,1,2,5,3]=>[6,1,5,4,2,3]=>[4,1,5,6,3,2]=>{{1,4,6},{2},{3,5}}
[4,6,1,3,2,5]=>[6,3,1,4,2,5]=>[3,4,2,6,1,5]=>{{1,3},{2,4,6},{5}}
[4,6,1,3,5,2]=>[6,5,1,4,3,2]=>[4,5,2,6,1,3]=>{{1,4,6},{2,5},{3}}
[4,6,1,5,2,3]=>[6,5,2,4,1,3]=>[4,5,1,6,3,2]=>{{1,4,6},{2,5},{3}}
[4,6,1,5,3,2]=>[6,3,5,4,1,2]=>[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}
[4,6,2,1,3,5]=>[2,6,1,4,3,5]=>[4,2,1,6,3,5]=>{{1,4,6},{2},{3},{5}}
[4,6,2,1,5,3]=>[2,6,5,4,1,3]=>[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}
[4,6,2,3,1,5]=>[3,6,2,4,1,5]=>[4,3,1,6,2,5]=>{{1,4,6},{2,3},{5}}
[4,6,2,3,5,1]=>[5,6,2,4,3,1]=>[5,4,1,6,2,3]=>{{1,5},{2,4,6},{3}}
[4,6,2,5,1,3]=>[5,6,1,4,2,3]=>[5,4,2,6,3,1]=>{{1,5},{2,4,6},{3}}
[4,6,2,5,3,1]=>[3,5,6,4,1,2]=>[5,4,3,6,2,1]=>{{1,5},{2,4,6},{3}}
[4,6,3,1,2,5]=>[3,1,6,4,2,5]=>[4,1,3,6,2,5]=>{{1,4,6},{2},{3},{5}}
[4,6,3,1,5,2]=>[3,6,5,4,2,1]=>[5,3,4,6,1,2]=>{{1,5},{2,3,4,6}}
[4,6,3,2,1,5]=>[2,3,6,4,1,5]=>[4,2,3,6,1,5]=>{{1,4,6},{2},{3},{5}}
[4,6,3,2,5,1]=>[5,3,6,4,2,1]=>[4,5,3,6,1,2]=>{{1,4,6},{2,5},{3}}
[4,6,3,5,1,2]=>[5,1,6,4,3,2]=>[5,1,4,6,2,3]=>{{1,5},{2},{3,4,6}}
[4,6,3,5,2,1]=>[2,5,6,4,3,1]=>[5,2,4,6,1,3]=>{{1,5},{2},{3,4,6}}
[4,6,5,1,2,3]=>[5,1,2,4,6,3]=>[4,1,2,6,5,3]=>{{1,4,6},{2},{3},{5}}
[4,6,5,1,3,2]=>[5,3,1,4,6,2]=>[3,4,2,6,5,1]=>{{1,3},{2,4,6},{5}}
[4,6,5,2,1,3]=>[2,5,1,4,6,3]=>[4,2,1,6,5,3]=>{{1,4,6},{2},{3},{5}}
[4,6,5,2,3,1]=>[3,5,2,4,6,1]=>[4,3,1,6,5,2]=>{{1,4,6},{2,3},{5}}
[4,6,5,3,1,2]=>[3,1,5,4,6,2]=>[4,1,3,6,5,2]=>{{1,4,6},{2},{3},{5}}
[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}
[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>{{1,5},{2},{3},{4},{6}}
[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[6,1,2,5,4,3]=>{{1,6},{2},{3},{4,5}}
[5,1,2,4,3,6]=>[5,1,4,2,3,6]=>[4,1,5,3,2,6]=>{{1,4},{2},{3,5},{6}}
[5,1,2,4,6,3]=>[5,1,6,2,4,3]=>[6,1,5,3,2,4]=>{{1,6},{2},{3,5},{4}}
[5,1,2,6,3,4]=>[5,1,6,3,2,4]=>[6,1,5,2,4,3]=>{{1,6},{2},{3,5},{4}}
[5,1,2,6,4,3]=>[5,1,4,6,2,3]=>[5,1,6,4,3,2]=>{{1,5},{2},{3,6},{4}}
[5,1,3,2,4,6]=>[5,3,1,2,4,6]=>[3,5,2,1,4,6]=>{{1,3},{2,5},{4},{6}}
[5,1,3,2,6,4]=>[5,3,1,6,2,4]=>[3,6,2,5,4,1]=>{{1,3},{2,6},{4,5}}
[5,1,3,4,2,6]=>[5,4,1,3,2,6]=>[4,5,2,1,3,6]=>{{1,4},{2,5},{3},{6}}
[5,1,3,4,6,2]=>[5,6,1,2,3,4]=>[6,5,2,3,4,1]=>{{1,6},{2,5},{3},{4}}
[5,1,3,6,2,4]=>[5,6,1,3,4,2]=>[6,5,2,1,3,4]=>{{1,6},{2,5},{3},{4}}
[5,1,3,6,4,2]=>[5,4,1,6,3,2]=>[5,6,2,4,1,3]=>{{1,5},{2,6},{3},{4}}
[5,1,4,2,3,6]=>[5,4,2,1,3,6]=>[4,5,1,3,2,6]=>{{1,4},{2,5},{3},{6}}
[5,1,4,2,6,3]=>[5,4,6,1,2,3]=>[5,6,4,3,2,1]=>{{1,5},{2,6},{3,4}}
[5,1,4,3,2,6]=>[5,3,4,1,2,6]=>[3,5,4,2,1,6]=>{{1,3,4},{2,5},{6}}
[5,1,4,3,6,2]=>[5,6,4,1,3,2]=>[5,4,6,3,1,2]=>{{1,5},{2,4},{3,6}}
[5,1,4,6,2,3]=>[5,6,2,1,4,3]=>[6,5,1,3,2,4]=>{{1,6},{2,5},{3},{4}}
[5,1,4,6,3,2]=>[5,3,6,1,4,2]=>[5,6,3,2,1,4]=>{{1,5},{2,6},{3},{4}}
[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[6,5,1,2,4,3]=>{{1,6},{2,5},{3},{4}}
[5,1,6,2,4,3]=>[5,6,4,2,1,3]=>[5,4,6,2,3,1]=>{{1,5},{2,4},{3,6}}
[5,1,6,3,2,4]=>[5,3,6,2,1,4]=>[5,6,3,1,4,2]=>{{1,5},{2,6},{3},{4}}
[5,1,6,3,4,2]=>[5,4,6,3,1,2]=>[5,6,4,1,3,2]=>{{1,5},{2,6},{3,4}}
[5,1,6,4,2,3]=>[5,4,2,6,1,3]=>[5,6,1,4,3,2]=>{{1,5},{2,6},{3},{4}}
[5,1,6,4,3,2]=>[5,3,4,6,1,2]=>[3,6,5,4,2,1]=>{{1,3,5},{2,6},{4}}
[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>{{1,5},{2},{3},{4},{6}}
[5,2,1,3,6,4]=>[2,5,1,6,3,4]=>[6,2,1,5,4,3]=>{{1,6},{2},{3},{4,5}}
[5,2,1,4,3,6]=>[2,5,4,1,3,6]=>[4,2,5,3,1,6]=>{{1,4},{2},{3,5},{6}}
[5,2,1,4,6,3]=>[2,5,6,1,4,3]=>[6,2,5,3,1,4]=>{{1,6},{2},{3,5},{4}}
[5,2,1,6,3,4]=>[2,5,6,3,1,4]=>[6,2,5,1,4,3]=>{{1,6},{2},{3,5},{4}}
[5,2,1,6,4,3]=>[2,5,4,6,1,3]=>[5,2,6,4,3,1]=>{{1,5},{2},{3,6},{4}}
[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[5,3,1,2,4,6]=>{{1,5},{2,3},{4},{6}}
[5,2,3,1,6,4]=>[3,5,2,6,1,4]=>[6,3,1,5,4,2]=>{{1,6},{2,3},{4,5}}
[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[5,4,1,2,3,6]=>{{1,5},{2,4},{3},{6}}
[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[5,6,1,2,3,4]=>{{1,5},{2,6},{3},{4}}
[5,2,3,6,1,4]=>[6,5,2,1,3,4]=>[5,6,1,3,4,2]=>{{1,5},{2,6},{3},{4}}
[5,2,3,6,4,1]=>[4,6,2,5,1,3]=>[6,4,1,5,3,2]=>{{1,6},{2,4,5},{3}}
[5,2,4,1,3,6]=>[4,5,1,2,3,6]=>[5,4,2,3,1,6]=>{{1,5},{2,4},{3},{6}}
[5,2,4,1,6,3]=>[4,5,6,2,1,3]=>[6,5,4,2,3,1]=>{{1,6},{2,5},{3,4}}
[5,2,4,3,1,6]=>[3,4,5,1,2,6]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}
[5,2,4,3,6,1]=>[6,5,4,2,3,1]=>[4,5,6,2,1,3]=>{{1,4},{2,5},{3,6}}
[5,2,4,6,1,3]=>[6,5,1,3,2,4]=>[5,6,2,1,4,3]=>{{1,5},{2,6},{3},{4}}
[5,2,4,6,3,1]=>[3,6,5,2,1,4]=>[6,3,5,1,4,2]=>{{1,6},{2,3,5},{4}}
[5,2,6,1,3,4]=>[6,5,1,2,4,3]=>[5,6,2,3,1,4]=>{{1,5},{2,6},{3},{4}}
[5,2,6,1,4,3]=>[6,5,4,1,2,3]=>[4,5,6,3,2,1]=>{{1,4},{2,5},{3,6}}
[5,2,6,3,1,4]=>[3,6,5,1,4,2]=>[6,3,5,2,1,4]=>{{1,6},{2,3,5},{4}}
[5,2,6,3,4,1]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>{{1,6},{2,5},{3,4}}
[5,2,6,4,1,3]=>[4,6,1,5,3,2]=>[6,4,2,5,1,3]=>{{1,6},{2,4,5},{3}}
[5,2,6,4,3,1]=>[3,4,6,5,2,1]=>[6,4,3,5,1,2]=>{{1,6},{2,4,5},{3}}
[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[5,1,3,2,4,6]=>{{1,5},{2},{3},{4},{6}}
[5,3,1,2,6,4]=>[3,1,5,6,2,4]=>[6,1,3,5,4,2]=>{{1,6},{2},{3},{4,5}}
[5,3,1,4,2,6]=>[3,5,4,2,1,6]=>[5,3,4,1,2,6]=>{{1,5},{2,3,4},{6}}
[5,3,1,4,6,2]=>[3,5,6,1,2,4]=>[6,5,3,2,4,1]=>{{1,6},{2,5},{3},{4}}
[5,3,1,6,2,4]=>[3,5,6,2,4,1]=>[6,5,3,1,2,4]=>{{1,6},{2,5},{3},{4}}
[5,3,1,6,4,2]=>[3,5,4,6,2,1]=>[6,3,5,4,1,2]=>{{1,6},{2,3,5},{4}}
[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>{{1,5},{2},{3},{4},{6}}
[5,3,2,1,6,4]=>[2,3,5,6,1,4]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}
[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[4,5,3,1,2,6]=>{{1,4},{2,5},{3},{6}}
[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[3,6,5,1,2,4]=>{{1,3,5},{2,6},{4}}
[5,3,2,6,1,4]=>[6,3,5,1,2,4]=>[3,6,5,2,4,1]=>{{1,3,5},{2,6},{4}}
[5,3,2,6,4,1]=>[4,3,6,5,1,2]=>[4,6,3,5,2,1]=>{{1,4,5},{2,6},{3}}
[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[5,1,4,2,3,6]=>{{1,5},{2},{3,4},{6}}
[5,3,4,1,6,2]=>[4,6,5,3,1,2]=>[6,4,5,1,3,2]=>{{1,6},{2,4},{3,5}}
[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>{{1,5},{2},{3,4},{6}}
[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[4,6,5,1,2,3]=>{{1,4},{2,6},{3,5}}
[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[5,1,6,2,3,4]=>{{1,5},{2},{3,6},{4}}
[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[5,2,6,1,3,4]=>{{1,5},{2},{3,6},{4}}
[5,3,6,1,2,4]=>[6,1,5,2,3,4]=>[5,1,6,3,4,2]=>{{1,5},{2},{3,6},{4}}
[5,3,6,1,4,2]=>[6,4,5,1,3,2]=>[4,6,5,3,1,2]=>{{1,4},{2,6},{3,5}}
[5,3,6,2,1,4]=>[2,6,5,1,3,4]=>[5,2,6,3,4,1]=>{{1,5},{2},{3,6},{4}}
[5,3,6,2,4,1]=>[4,6,5,2,3,1]=>[6,4,5,2,1,3]=>{{1,6},{2,4},{3,5}}
[5,3,6,4,1,2]=>[4,1,6,5,2,3]=>[6,1,4,5,3,2]=>{{1,6},{2},{3,4,5}}
[5,3,6,4,2,1]=>[2,4,6,5,1,3]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}
[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[5,1,2,4,3,6]=>{{1,5},{2},{3},{4},{6}}
[5,4,1,2,6,3]=>[4,1,5,6,3,2]=>[6,1,5,4,2,3]=>{{1,6},{2},{3,5},{4}}
[5,4,1,3,2,6]=>[4,3,1,5,2,6]=>[3,5,2,4,1,6]=>{{1,3},{2,5},{4},{6}}
[5,4,1,3,6,2]=>[4,5,1,6,2,3]=>[6,5,2,4,3,1]=>{{1,6},{2,5},{3},{4}}
[5,4,1,6,2,3]=>[4,5,2,6,3,1]=>[6,5,1,4,2,3]=>{{1,6},{2,5},{3},{4}}
[5,4,1,6,3,2]=>[4,3,5,6,2,1]=>[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}}
[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[5,2,1,4,3,6]=>{{1,5},{2},{3},{4},{6}}
[5,4,2,1,6,3]=>[2,4,5,6,3,1]=>[6,2,5,4,1,3]=>{{1,6},{2},{3,5},{4}}
[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[5,3,1,4,2,6]=>{{1,5},{2,3},{4},{6}}
[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[4,6,1,5,2,3]=>{{1,4,5},{2,6},{3}}
[5,4,2,6,1,3]=>[6,4,1,5,2,3]=>[4,6,2,5,3,1]=>{{1,4,5},{2,6},{3}}
[5,4,2,6,3,1]=>[3,6,4,5,1,2]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}
[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[5,1,3,4,2,6]=>{{1,5},{2},{3},{4},{6}}
[5,4,3,1,6,2]=>[3,4,5,6,1,2]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}
[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}
[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}}
[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[4,1,6,5,2,3]=>{{1,4,5},{2},{3,6}}
[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[4,2,6,5,1,3]=>{{1,4,5},{2},{3,6}}
[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[5,1,2,6,3,4]=>{{1,5},{2},{3},{4,6}}
[5,4,6,1,3,2]=>[6,3,1,5,4,2]=>[3,5,2,6,1,4]=>{{1,3},{2,5},{4,6}}
[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[5,2,1,6,3,4]=>{{1,5},{2},{3},{4,6}}
[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[5,3,1,6,2,4]=>{{1,5},{2,3},{4,6}}
[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[5,1,3,6,2,4]=>{{1,5},{2},{3},{4,6}}
[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[5,2,3,6,1,4]=>{{1,5},{2},{3},{4,6}}
[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[5,1,2,3,6,4]=>{{1,5,6},{2},{3},{4}}
[5,6,1,2,4,3]=>[6,1,4,2,5,3]=>[4,1,5,3,6,2]=>{{1,4},{2},{3,5,6}}
[5,6,1,3,2,4]=>[6,3,1,2,5,4]=>[3,5,2,1,6,4]=>{{1,3},{2,5,6},{4}}
[5,6,1,3,4,2]=>[6,4,1,3,5,2]=>[4,5,2,1,6,3]=>{{1,4},{2,5,6},{3}}
[5,6,1,4,2,3]=>[6,4,2,1,5,3]=>[4,5,1,3,6,2]=>{{1,4},{2,5,6},{3}}
[5,6,1,4,3,2]=>[6,3,4,1,5,2]=>[3,5,4,2,6,1]=>{{1,3,4},{2,5,6}}
[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[5,2,1,3,6,4]=>{{1,5,6},{2},{3},{4}}
[5,6,2,1,4,3]=>[2,6,4,1,5,3]=>[4,2,5,3,6,1]=>{{1,4},{2},{3,5,6}}
[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[5,3,1,2,6,4]=>{{1,5,6},{2,3},{4}}
[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[5,4,1,2,6,3]=>{{1,5,6},{2,4},{3}}
[5,6,2,4,1,3]=>[4,6,1,2,5,3]=>[5,4,2,3,6,1]=>{{1,5,6},{2,4},{3}}
[5,6,2,4,3,1]=>[3,4,6,1,5,2]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}
[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[5,1,3,2,6,4]=>{{1,5,6},{2},{3},{4}}
[5,6,3,1,4,2]=>[3,6,4,2,5,1]=>[5,3,4,1,6,2]=>{{1,5,6},{2,3,4}}
[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[5,2,3,1,6,4]=>{{1,5,6},{2},{3},{4}}
[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[4,5,3,1,6,2]=>{{1,4},{2,5,6},{3}}
[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[5,1,4,2,6,3]=>{{1,5,6},{2},{3,4}}
[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[5,2,4,1,6,3]=>{{1,5,6},{2},{3,4}}
[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[5,1,2,4,6,3]=>{{1,5,6},{2},{3},{4}}
[5,6,4,1,3,2]=>[4,3,1,6,5,2]=>[3,5,2,4,6,1]=>{{1,3},{2,5,6},{4}}
[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[5,2,1,4,6,3]=>{{1,5,6},{2},{3},{4}}
[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[5,3,1,4,6,2]=>{{1,5,6},{2,3},{4}}
[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[5,1,3,4,6,2]=>{{1,5,6},{2},{3},{4}}
[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}
[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>{{1,6},{2},{3},{4},{5}}
[6,1,2,3,5,4]=>[6,1,2,5,3,4]=>[5,1,2,6,4,3]=>{{1,5},{2},{3},{4,6}}
[6,1,2,4,3,5]=>[6,1,4,2,3,5]=>[4,1,6,3,2,5]=>{{1,4},{2},{3,6},{5}}
[6,1,2,4,5,3]=>[6,1,5,2,4,3]=>[5,1,6,3,2,4]=>{{1,5},{2},{3,6},{4}}
[6,1,2,5,3,4]=>[6,1,5,3,2,4]=>[5,1,6,2,4,3]=>{{1,5},{2},{3,6},{4}}
[6,1,2,5,4,3]=>[6,1,4,5,2,3]=>[4,1,6,5,3,2]=>{{1,4,5},{2},{3,6}}
[6,1,3,2,4,5]=>[6,3,1,2,4,5]=>[3,6,2,1,4,5]=>{{1,3},{2,6},{4},{5}}
[6,1,3,2,5,4]=>[6,3,1,5,2,4]=>[3,5,2,6,4,1]=>{{1,3},{2,5},{4,6}}
[6,1,3,4,2,5]=>[6,4,1,3,2,5]=>[4,6,2,1,3,5]=>{{1,4},{2,6},{3},{5}}
[6,1,3,4,5,2]=>[6,5,1,2,3,4]=>[5,6,2,3,4,1]=>{{1,5},{2,6},{3},{4}}
[6,1,3,5,2,4]=>[6,5,1,3,4,2]=>[5,6,2,1,3,4]=>{{1,5},{2,6},{3},{4}}
[6,1,3,5,4,2]=>[6,4,1,5,3,2]=>[4,6,2,5,1,3]=>{{1,4,5},{2,6},{3}}
[6,1,4,2,3,5]=>[6,4,2,1,3,5]=>[4,6,1,3,2,5]=>{{1,4},{2,6},{3},{5}}
[6,1,4,2,5,3]=>[6,4,5,1,2,3]=>[4,6,5,3,2,1]=>{{1,4},{2,6},{3,5}}
[6,1,4,3,2,5]=>[6,3,4,1,2,5]=>[3,6,4,2,1,5]=>{{1,3,4},{2,6},{5}}
[6,1,4,3,5,2]=>[6,5,4,1,3,2]=>[4,5,6,3,1,2]=>{{1,4},{2,5},{3,6}}
[6,1,4,5,2,3]=>[6,5,2,1,4,3]=>[5,6,1,3,2,4]=>{{1,5},{2,6},{3},{4}}
[6,1,4,5,3,2]=>[6,3,5,1,4,2]=>[3,6,5,2,1,4]=>{{1,3,5},{2,6},{4}}
[6,1,5,2,3,4]=>[6,5,2,3,1,4]=>[5,6,1,2,4,3]=>{{1,5},{2,6},{3},{4}}
[6,1,5,2,4,3]=>[6,5,4,2,1,3]=>[4,5,6,2,3,1]=>{{1,4},{2,5},{3,6}}
[6,1,5,3,2,4]=>[6,3,5,2,1,4]=>[3,6,5,1,4,2]=>{{1,3,5},{2,6},{4}}
[6,1,5,3,4,2]=>[6,4,5,3,1,2]=>[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}}
[6,1,5,4,2,3]=>[6,4,2,5,1,3]=>[4,6,1,5,3,2]=>{{1,4,5},{2,6},{3}}
[6,1,5,4,3,2]=>[6,3,4,5,1,2]=>[3,6,4,5,2,1]=>{{1,3,4,5},{2,6}}
[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>{{1,6},{2},{3},{4},{5}}
[6,2,1,3,5,4]=>[2,6,1,5,3,4]=>[5,2,1,6,4,3]=>{{1,5},{2},{3},{4,6}}
[6,2,1,4,3,5]=>[2,6,4,1,3,5]=>[4,2,6,3,1,5]=>{{1,4},{2},{3,6},{5}}
[6,2,1,4,5,3]=>[2,6,5,1,4,3]=>[5,2,6,3,1,4]=>{{1,5},{2},{3,6},{4}}
[6,2,1,5,3,4]=>[2,6,5,3,1,4]=>[5,2,6,1,4,3]=>{{1,5},{2},{3,6},{4}}
[6,2,1,5,4,3]=>[2,6,4,5,1,3]=>[4,2,6,5,3,1]=>{{1,4,5},{2},{3,6}}
[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[6,3,1,2,4,5]=>{{1,6},{2,3},{4},{5}}
[6,2,3,1,5,4]=>[3,6,2,5,1,4]=>[5,3,1,6,4,2]=>{{1,5},{2,3},{4,6}}
[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[6,4,1,2,3,5]=>{{1,6},{2,4},{3},{5}}
[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[6,5,1,2,3,4]=>{{1,6},{2,5},{3},{4}}
[6,2,3,5,1,4]=>[5,6,2,1,3,4]=>[6,5,1,3,4,2]=>{{1,6},{2,5},{3},{4}}
[6,2,3,5,4,1]=>[4,5,2,6,1,3]=>[6,5,1,4,3,2]=>{{1,6},{2,5},{3},{4}}
[6,2,4,1,3,5]=>[4,6,1,2,3,5]=>[6,4,2,3,1,5]=>{{1,6},{2,4},{3},{5}}
[6,2,4,1,5,3]=>[4,6,5,2,1,3]=>[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}}
[6,2,4,3,1,5]=>[3,4,6,1,2,5]=>[6,4,3,2,1,5]=>{{1,6},{2,4},{3},{5}}
[6,2,4,3,5,1]=>[5,6,4,2,3,1]=>[5,4,6,2,1,3]=>{{1,5},{2,4},{3,6}}
[6,2,4,5,1,3]=>[5,6,1,3,2,4]=>[6,5,2,1,4,3]=>{{1,6},{2,5},{3},{4}}
[6,2,4,5,3,1]=>[3,5,6,2,1,4]=>[6,5,3,1,4,2]=>{{1,6},{2,5},{3},{4}}
[6,2,5,1,3,4]=>[5,6,1,2,4,3]=>[6,5,2,3,1,4]=>{{1,6},{2,5},{3},{4}}
[6,2,5,1,4,3]=>[5,6,4,1,2,3]=>[5,4,6,3,2,1]=>{{1,5},{2,4},{3,6}}
[6,2,5,3,1,4]=>[3,5,6,1,4,2]=>[6,5,3,2,1,4]=>{{1,6},{2,5},{3},{4}}
[6,2,5,3,4,1]=>[4,6,5,3,2,1]=>[6,4,5,1,2,3]=>{{1,6},{2,4},{3,5}}
[6,2,5,4,1,3]=>[4,5,1,6,3,2]=>[6,5,2,4,1,3]=>{{1,6},{2,5},{3},{4}}
[6,2,5,4,3,1]=>[3,4,5,6,2,1]=>[6,5,3,4,1,2]=>{{1,6},{2,5},{3},{4}}
[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[6,1,3,2,4,5]=>{{1,6},{2},{3},{4},{5}}
[6,3,1,2,5,4]=>[3,1,6,5,2,4]=>[5,1,3,6,4,2]=>{{1,5},{2},{3},{4,6}}
[6,3,1,4,2,5]=>[3,6,4,2,1,5]=>[6,3,4,1,2,5]=>{{1,6},{2,3,4},{5}}
[6,3,1,4,5,2]=>[3,6,5,1,2,4]=>[6,3,5,2,4,1]=>{{1,6},{2,3,5},{4}}
[6,3,1,5,2,4]=>[3,6,5,2,4,1]=>[6,3,5,1,2,4]=>{{1,6},{2,3,5},{4}}
[6,3,1,5,4,2]=>[3,6,4,5,2,1]=>[6,3,4,5,1,2]=>{{1,6},{2,3,4,5}}
[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>{{1,6},{2},{3},{4},{5}}
[6,3,2,1,5,4]=>[2,3,6,5,1,4]=>[5,2,3,6,4,1]=>{{1,5},{2},{3},{4,6}}
[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[4,6,3,1,2,5]=>{{1,4},{2,6},{3},{5}}
[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[5,6,3,1,2,4]=>{{1,5},{2,6},{3},{4}}
[6,3,2,5,1,4]=>[5,3,6,1,2,4]=>[5,6,3,2,4,1]=>{{1,5},{2,6},{3},{4}}
[6,3,2,5,4,1]=>[4,3,5,6,1,2]=>[5,6,3,4,2,1]=>{{1,5},{2,6},{3},{4}}
[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[6,1,4,2,3,5]=>{{1,6},{2},{3,4},{5}}
[6,3,4,1,5,2]=>[4,5,6,3,1,2]=>[6,5,4,1,3,2]=>{{1,6},{2,5},{3,4}}
[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[6,2,4,1,3,5]=>{{1,6},{2},{3,4},{5}}
[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[5,6,4,1,2,3]=>{{1,5},{2,6},{3,4}}
[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[6,1,5,2,3,4]=>{{1,6},{2},{3,5},{4}}
[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[6,2,5,1,3,4]=>{{1,6},{2},{3,5},{4}}
[6,3,5,1,2,4]=>[5,1,6,2,3,4]=>[6,1,5,3,4,2]=>{{1,6},{2},{3,5},{4}}
[6,3,5,1,4,2]=>[5,4,6,1,3,2]=>[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}}
[6,3,5,2,1,4]=>[2,5,6,1,3,4]=>[6,2,5,3,4,1]=>{{1,6},{2},{3,5},{4}}
[6,3,5,2,4,1]=>[4,5,6,2,3,1]=>[6,5,4,2,1,3]=>{{1,6},{2,5},{3,4}}
[6,3,5,4,1,2]=>[4,1,5,6,2,3]=>[6,1,5,4,3,2]=>{{1,6},{2},{3,5},{4}}
[6,3,5,4,2,1]=>[2,4,5,6,1,3]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}
[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[6,1,2,4,3,5]=>{{1,6},{2},{3},{4},{5}}
[6,4,1,2,5,3]=>[4,1,6,5,3,2]=>[6,1,4,5,2,3]=>{{1,6},{2},{3,4,5}}
[6,4,1,3,2,5]=>[4,3,1,6,2,5]=>[3,6,2,4,1,5]=>{{1,3},{2,6},{4},{5}}
[6,4,1,3,5,2]=>[4,6,1,5,2,3]=>[6,4,2,5,3,1]=>{{1,6},{2,4,5},{3}}
[6,4,1,5,2,3]=>[4,6,2,5,3,1]=>[6,4,1,5,2,3]=>{{1,6},{2,4,5},{3}}
[6,4,1,5,3,2]=>[4,3,6,5,2,1]=>[4,6,3,5,1,2]=>{{1,4,5},{2,6},{3}}
[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[6,2,1,4,3,5]=>{{1,6},{2},{3},{4},{5}}
[6,4,2,1,5,3]=>[2,4,6,5,3,1]=>[6,2,4,5,1,3]=>{{1,6},{2},{3,4,5}}
[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[6,3,1,4,2,5]=>{{1,6},{2,3},{4},{5}}
[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[5,6,1,4,2,3]=>{{1,5},{2,6},{3},{4}}
[6,4,2,5,1,3]=>[5,4,1,6,2,3]=>[5,6,2,4,3,1]=>{{1,5},{2,6},{3},{4}}
[6,4,2,5,3,1]=>[3,5,4,6,1,2]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}
[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[6,1,3,4,2,5]=>{{1,6},{2},{3},{4},{5}}
[6,4,3,1,5,2]=>[3,4,6,5,1,2]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}
[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>{{1,6},{2},{3},{4},{5}}
[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}}
[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[5,1,6,4,2,3]=>{{1,5},{2},{3,6},{4}}
[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[5,2,6,4,1,3]=>{{1,5},{2},{3,6},{4}}
[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[6,1,2,5,3,4]=>{{1,6},{2},{3},{4,5}}
[6,4,5,1,3,2]=>[5,3,1,6,4,2]=>[3,6,2,5,1,4]=>{{1,3},{2,6},{4,5}}
[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[6,2,1,5,3,4]=>{{1,6},{2},{3},{4,5}}
[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[6,3,1,5,2,4]=>{{1,6},{2,3},{4,5}}
[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[6,1,3,5,2,4]=>{{1,6},{2},{3},{4,5}}
[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>{{1,6},{2},{3},{4,5}}
[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[6,1,2,3,5,4]=>{{1,6},{2},{3},{4},{5}}
[6,5,1,2,4,3]=>[5,1,4,2,6,3]=>[4,1,6,3,5,2]=>{{1,4},{2},{3,6},{5}}
[6,5,1,3,2,4]=>[5,3,1,2,6,4]=>[3,6,2,1,5,4]=>{{1,3},{2,6},{4},{5}}
[6,5,1,3,4,2]=>[5,4,1,3,6,2]=>[4,6,2,1,5,3]=>{{1,4},{2,6},{3},{5}}
[6,5,1,4,2,3]=>[5,4,2,1,6,3]=>[4,6,1,3,5,2]=>{{1,4},{2,6},{3},{5}}
[6,5,1,4,3,2]=>[5,3,4,1,6,2]=>[3,6,4,2,5,1]=>{{1,3,4},{2,6},{5}}
[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[6,2,1,3,5,4]=>{{1,6},{2},{3},{4},{5}}
[6,5,2,1,4,3]=>[2,5,4,1,6,3]=>[4,2,6,3,5,1]=>{{1,4},{2},{3,6},{5}}
[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[6,3,1,2,5,4]=>{{1,6},{2,3},{4},{5}}
[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[6,4,1,2,5,3]=>{{1,6},{2,4},{3},{5}}
[6,5,2,4,1,3]=>[4,5,1,2,6,3]=>[6,4,2,3,5,1]=>{{1,6},{2,4},{3},{5}}
[6,5,2,4,3,1]=>[3,4,5,1,6,2]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}
[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[6,1,3,2,5,4]=>{{1,6},{2},{3},{4},{5}}
[6,5,3,1,4,2]=>[3,5,4,2,6,1]=>[6,3,4,1,5,2]=>{{1,6},{2,3,4},{5}}
[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[6,2,3,1,5,4]=>{{1,6},{2},{3},{4},{5}}
[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[4,6,3,1,5,2]=>{{1,4},{2,6},{3},{5}}
[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[6,1,4,2,5,3]=>{{1,6},{2},{3,4},{5}}
[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[6,2,4,1,5,3]=>{{1,6},{2},{3,4},{5}}
[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[6,1,2,4,5,3]=>{{1,6},{2},{3},{4},{5}}
[6,5,4,1,3,2]=>[4,3,1,5,6,2]=>[3,6,2,4,5,1]=>{{1,3},{2,6},{4},{5}}
[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[6,2,1,4,5,3]=>{{1,6},{2},{3},{4},{5}}
[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[6,3,1,4,5,2]=>{{1,6},{2,3},{4},{5}}
[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[6,1,3,4,5,2]=>{{1,6},{2},{3},{4},{5}}
[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,7},{6}}
[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,7},{6}}
[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,6},{5},{7}}
[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}
[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,6,7},{5}}
[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,7},{5},{6}}
[1,2,3,7,4,6,5]=>[1,2,3,7,6,4,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,6},{5,7}}
[1,2,3,7,5,4,6]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>{{1},{2},{3},{4,7},{5},{6}}
[1,2,3,7,5,6,4]=>[1,2,3,6,7,5,4]=>[1,2,3,7,6,4,5]=>{{1},{2},{3},{4,7},{5,6}}
[1,2,3,7,6,4,5]=>[1,2,3,6,4,7,5]=>[1,2,3,7,4,6,5]=>{{1},{2},{3},{4,7},{5},{6}}
[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,7},{6}}
[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,7},{6}}
[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}
[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[1,2,4,6,3,7,5]=>{{1},{2},{3,4,6,7},{5}}
[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,4,7,3,6,5]=>[1,2,7,4,6,3,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,6},{5,7}}
[1,2,4,7,5,3,6]=>[1,2,5,4,7,3,6]=>[1,2,4,7,5,3,6]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,4,7,5,6,3]=>[1,2,6,4,7,5,3]=>[1,2,4,7,6,3,5]=>{{1},{2},{3,4,7},{5,6}}
[1,2,4,7,6,3,5]=>[1,2,6,4,3,7,5]=>[1,2,4,7,3,6,5]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}
[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}
[1,2,5,3,7,4,6]=>[1,2,5,7,3,4,6]=>[1,2,7,5,4,3,6]=>{{1},{2},{3,7},{4,5},{6}}
[1,2,5,3,7,6,4]=>[1,2,5,6,3,7,4]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}}
[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,4,7,3,6]=>[1,2,7,5,4,3,6]=>[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[1,2,5,3,6,4,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,6},{4,5,7}}
[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,5,7},{4,6}}
[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[1,2,5,3,6,7,4]=>{{1},{2},{3,5,6,7},{4}}
[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[1,2,5,3,7,4,6]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,5,7,3,6,4]=>[1,2,7,6,5,3,4]=>[1,2,5,6,7,4,3]=>{{1},{2},{3,5,7},{4,6}}
[1,2,5,7,4,3,6]=>[1,2,4,7,5,3,6]=>[1,2,5,4,7,3,6]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,5,7,4,6,3]=>[1,2,6,7,5,4,3]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,5,7,6,3,4]=>[1,2,6,3,5,7,4]=>[1,2,5,3,7,6,4]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,2,6,3,4,7,5]=>[1,2,6,3,7,4,5]=>[1,2,7,3,6,5,4]=>{{1},{2},{3,7},{4},{5,6}}
[1,2,6,3,5,4,7]=>[1,2,6,5,3,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,5},{4,6},{7}}
[1,2,6,3,5,7,4]=>[1,2,6,7,3,5,4]=>[1,2,7,6,4,3,5]=>{{1},{2},{3,7},{4,6},{5}}
[1,2,6,3,7,4,5]=>[1,2,6,7,4,3,5]=>[1,2,7,6,3,5,4]=>{{1},{2},{3,7},{4,6},{5}}
[1,2,6,3,7,5,4]=>[1,2,6,5,7,3,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,6,4,3,5,7]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,2,6,4,3,7,5]=>[1,2,4,6,7,3,5]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}}
[1,2,6,4,5,3,7]=>[1,2,5,6,4,3,7]=>[1,2,6,5,3,4,7]=>{{1},{2},{3,6},{4,5},{7}}
[1,2,6,4,5,7,3]=>[1,2,7,6,4,5,3]=>[1,2,6,7,3,4,5]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,6,4,7,3,5]=>[1,2,7,6,3,4,5]=>[1,2,6,7,4,5,3]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,6,4,7,5,3]=>[1,2,5,7,6,3,4]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}}
[1,2,6,5,3,4,7]=>[1,2,5,3,6,4,7]=>[1,2,6,3,5,4,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,2,6,5,3,7,4]=>[1,2,5,6,7,4,3]=>[1,2,7,6,5,3,4]=>{{1},{2},{3,7},{4,6},{5}}
[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[1,2,6,5,7,3,4]=>[1,2,7,3,6,5,4]=>[1,2,6,3,7,4,5]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[1,2,6,3,4,7,5]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,6,7,3,5,4]=>[1,2,7,5,3,6,4]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,5},{4,6,7}}
[1,2,6,7,4,3,5]=>[1,2,4,7,3,6,5]=>[1,2,6,4,3,7,5]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,6,7,4,5,3]=>[1,2,5,7,4,6,3]=>[1,2,6,5,3,7,4]=>{{1},{2},{3,6,7},{4,5}}
[1,2,6,7,5,3,4]=>[1,2,5,3,7,6,4]=>[1,2,6,3,5,7,4]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,3,4,6,5]=>[1,2,7,3,6,4,5]=>[1,2,6,3,7,5,4]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,7,3,5,4,6]=>[1,2,7,5,3,4,6]=>[1,2,5,7,4,3,6]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,7,3,5,6,4]=>[1,2,7,6,3,5,4]=>[1,2,6,7,4,3,5]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,7,3,6,4,5]=>[1,2,7,6,4,3,5]=>[1,2,6,7,3,5,4]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,7,3,6,5,4]=>[1,2,7,5,6,3,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,5,6},{4,7}}
[1,2,7,4,3,5,6]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,4,3,6,5]=>[1,2,4,7,6,3,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,7,4,5,3,6]=>[1,2,5,7,4,3,6]=>[1,2,7,5,3,4,6]=>{{1},{2},{3,7},{4,5},{6}}
[1,2,7,4,5,6,3]=>[1,2,6,7,4,5,3]=>[1,2,7,6,3,4,5]=>{{1},{2},{3,7},{4,6},{5}}
[1,2,7,4,6,3,5]=>[1,2,6,7,3,4,5]=>[1,2,7,6,4,5,3]=>{{1},{2},{3,7},{4,6},{5}}
[1,2,7,4,6,5,3]=>[1,2,5,6,7,3,4]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}
[1,2,7,5,3,4,6]=>[1,2,5,3,7,4,6]=>[1,2,7,3,5,4,6]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,5,3,6,4]=>[1,2,5,7,6,4,3]=>[1,2,7,5,6,3,4]=>{{1},{2},{3,7},{4,5,6}}
[1,2,7,5,4,3,6]=>[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,5,4,6,3]=>[1,2,6,5,7,4,3]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,7,5,6,3,4]=>[1,2,6,3,7,5,4]=>[1,2,7,3,6,4,5]=>{{1},{2},{3,7},{4},{5,6}}
[1,2,7,5,6,4,3]=>[1,2,4,6,7,5,3]=>[1,2,7,4,6,3,5]=>{{1},{2},{3,7},{4},{5,6}}
[1,2,7,6,3,4,5]=>[1,2,6,3,4,7,5]=>[1,2,7,3,4,6,5]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,6,3,5,4]=>[1,2,6,5,3,7,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,7,6,4,3,5]=>[1,2,4,6,3,7,5]=>[1,2,7,4,3,6,5]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,6,4,5,3]=>[1,2,5,6,4,7,3]=>[1,2,7,5,3,6,4]=>{{1},{2},{3,7},{4,5},{6}}
[1,2,7,6,5,3,4]=>[1,2,5,3,6,7,4]=>[1,2,7,3,5,6,4]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,7},{6}}
[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,7},{6}}
[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>{{1},{2,3},{4,6},{5},{7}}
[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}
[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[1,3,2,6,4,7,5]=>{{1},{2,3},{4,6,7},{5}}
[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>{{1},{2,3},{4,7},{5},{6}}
[1,3,2,7,4,6,5]=>[1,3,2,7,6,4,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,6},{5,7}}
[1,3,2,7,5,4,6]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>{{1},{2,3},{4,7},{5},{6}}
[1,3,2,7,5,6,4]=>[1,3,2,6,7,5,4]=>[1,3,2,7,6,4,5]=>{{1},{2,3},{4,7},{5,6}}
[1,3,2,7,6,4,5]=>[1,3,2,6,4,7,5]=>[1,3,2,7,4,6,5]=>{{1},{2,3},{4,7},{5},{6}}
[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,7},{6}}
[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,7},{6}}
[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[1,3,4,6,2,5,7]=>{{1},{2,3,4,6},{5},{7}}
[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}
[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[1,3,4,6,2,7,5]=>{{1},{2,3,4,6,7},{5}}
[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[1,3,4,7,2,5,6]=>{{1},{2,3,4,7},{5},{6}}
[1,3,4,7,2,6,5]=>[1,7,3,4,6,2,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,6},{5,7}}
[1,3,4,7,5,2,6]=>[1,5,3,4,7,2,6]=>[1,3,4,7,5,2,6]=>{{1},{2,3,4,7},{5},{6}}
[1,3,4,7,5,6,2]=>[1,6,3,4,7,5,2]=>[1,3,4,7,6,2,5]=>{{1},{2,3,4,7},{5,6}}
[1,3,4,7,6,2,5]=>[1,6,3,4,2,7,5]=>[1,3,4,7,2,6,5]=>{{1},{2,3,4,7},{5},{6}}
[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>{{1},{2,3,5},{4},{6,7}}
[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}
[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}
[1,3,5,2,7,4,6]=>[1,5,3,7,2,4,6]=>[1,3,7,5,4,2,6]=>{{1},{2,3,7},{4,5},{6}}
[1,3,5,2,7,6,4]=>[1,5,3,6,2,7,4]=>[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}}
[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,3,5,4,7,2,6]=>[1,7,3,5,4,2,6]=>[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,7},{6}}
[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[1,3,5,2,6,4,7]=>{{1},{2,3,5,6},{4},{7}}
[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[1,3,6,5,7,4,2]=>{{1},{2,3,6},{4,5,7}}
[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[1,3,5,6,7,2,4]=>{{1},{2,3,5,7},{4,6}}
[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[1,3,5,2,6,7,4]=>{{1},{2,3,5,6,7},{4}}
[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[1,3,5,2,7,4,6]=>{{1},{2,3,5,7},{4},{6}}
[1,3,5,7,2,6,4]=>[1,7,3,6,5,2,4]=>[1,3,5,6,7,4,2]=>{{1},{2,3,5,7},{4,6}}
[1,3,5,7,4,2,6]=>[1,4,3,7,5,2,6]=>[1,3,5,4,7,2,6]=>{{1},{2,3,5,7},{4},{6}}
[1,3,5,7,4,6,2]=>[1,6,3,7,5,4,2]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,3,5,7,6,2,4]=>[1,6,3,2,5,7,4]=>[1,3,5,2,7,6,4]=>{{1},{2,3,5,7},{4},{6}}
[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,3,6,2,4,7,5]=>[1,6,3,2,7,4,5]=>[1,3,7,2,6,5,4]=>{{1},{2,3,7},{4},{5,6}}
[1,3,6,2,5,4,7]=>[1,6,3,5,2,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,5},{4,6},{7}}
[1,3,6,2,5,7,4]=>[1,6,3,7,2,5,4]=>[1,3,7,6,4,2,5]=>{{1},{2,3,7},{4,6},{5}}
[1,3,6,2,7,4,5]=>[1,6,3,7,4,2,5]=>[1,3,7,6,2,5,4]=>{{1},{2,3,7},{4,6},{5}}
[1,3,6,2,7,5,4]=>[1,6,3,5,7,2,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,6},{4,7},{5}}
[1,3,6,4,2,5,7]=>[1,4,3,6,2,5,7]=>[1,3,6,4,2,5,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,3,6,4,2,7,5]=>[1,4,3,6,7,2,5]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}}
[1,3,6,4,5,2,7]=>[1,5,3,6,4,2,7]=>[1,3,6,5,2,4,7]=>{{1},{2,3,6},{4,5},{7}}
[1,3,6,4,5,7,2]=>[1,7,3,6,4,5,2]=>[1,3,6,7,2,4,5]=>{{1},{2,3,6},{4,7},{5}}
[1,3,6,4,7,2,5]=>[1,7,3,6,2,4,5]=>[1,3,6,7,4,5,2]=>{{1},{2,3,6},{4,7},{5}}
[1,3,6,4,7,5,2]=>[1,5,3,7,6,2,4]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}}
[1,3,6,5,2,4,7]=>[1,5,3,2,6,4,7]=>[1,3,6,2,5,4,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,3,6,5,2,7,4]=>[1,5,3,6,7,4,2]=>[1,3,7,6,5,2,4]=>{{1},{2,3,7},{4,6},{5}}
[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,3,6,5,7,2,4]=>[1,7,3,2,6,5,4]=>[1,3,6,2,7,4,5]=>{{1},{2,3,6},{4},{5,7}}
[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[1,3,6,2,4,7,5]=>{{1},{2,3,6,7},{4},{5}}
[1,3,6,7,2,5,4]=>[1,7,3,5,2,6,4]=>[1,3,5,6,4,7,2]=>{{1},{2,3,5},{4,6,7}}
[1,3,6,7,4,2,5]=>[1,4,3,7,2,6,5]=>[1,3,6,4,2,7,5]=>{{1},{2,3,6,7},{4},{5}}
[1,3,6,7,4,5,2]=>[1,5,3,7,4,6,2]=>[1,3,6,5,2,7,4]=>{{1},{2,3,6,7},{4,5}}
[1,3,6,7,5,2,4]=>[1,5,3,2,7,6,4]=>[1,3,6,2,5,7,4]=>{{1},{2,3,6,7},{4},{5}}
[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,2,4,6,5]=>[1,7,3,2,6,4,5]=>[1,3,6,2,7,5,4]=>{{1},{2,3,6},{4},{5,7}}
[1,3,7,2,5,4,6]=>[1,7,3,5,2,4,6]=>[1,3,5,7,4,2,6]=>{{1},{2,3,5},{4,7},{6}}
[1,3,7,2,5,6,4]=>[1,7,3,6,2,5,4]=>[1,3,6,7,4,2,5]=>{{1},{2,3,6},{4,7},{5}}
[1,3,7,2,6,4,5]=>[1,7,3,6,4,2,5]=>[1,3,6,7,2,5,4]=>{{1},{2,3,6},{4,7},{5}}
[1,3,7,2,6,5,4]=>[1,7,3,5,6,2,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,5,6},{4,7}}
[1,3,7,4,2,5,6]=>[1,4,3,7,2,5,6]=>[1,3,7,4,2,5,6]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,4,2,6,5]=>[1,4,3,7,6,2,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,6},{4},{5,7}}
[1,3,7,4,5,2,6]=>[1,5,3,7,4,2,6]=>[1,3,7,5,2,4,6]=>{{1},{2,3,7},{4,5},{6}}
[1,3,7,4,5,6,2]=>[1,6,3,7,4,5,2]=>[1,3,7,6,2,4,5]=>{{1},{2,3,7},{4,6},{5}}
[1,3,7,4,6,2,5]=>[1,6,3,7,2,4,5]=>[1,3,7,6,4,5,2]=>{{1},{2,3,7},{4,6},{5}}
[1,3,7,4,6,5,2]=>[1,5,3,6,7,2,4]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}
[1,3,7,5,2,4,6]=>[1,5,3,2,7,4,6]=>[1,3,7,2,5,4,6]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,5,2,6,4]=>[1,5,3,7,6,4,2]=>[1,3,7,5,6,2,4]=>{{1},{2,3,7},{4,5,6}}
[1,3,7,5,4,2,6]=>[1,4,3,5,7,2,6]=>[1,3,7,4,5,2,6]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,5,4,6,2]=>[1,6,3,5,7,4,2]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[1,3,7,5,6,2,4]=>[1,6,3,2,7,5,4]=>[1,3,7,2,6,4,5]=>{{1},{2,3,7},{4},{5,6}}
[1,3,7,5,6,4,2]=>[1,4,3,6,7,5,2]=>[1,3,7,4,6,2,5]=>{{1},{2,3,7},{4},{5,6}}
[1,3,7,6,2,4,5]=>[1,6,3,2,4,7,5]=>[1,3,7,2,4,6,5]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,6,2,5,4]=>[1,6,3,5,2,7,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,5},{4,7},{6}}
[1,3,7,6,4,2,5]=>[1,4,3,6,2,7,5]=>[1,3,7,4,2,6,5]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,6,4,5,2]=>[1,5,3,6,4,7,2]=>[1,3,7,5,2,6,4]=>{{1},{2,3,7},{4,5},{6}}
[1,3,7,6,5,2,4]=>[1,5,3,2,6,7,4]=>[1,3,7,2,5,6,4]=>{{1},{2,3,7},{4},{5},{6}}
[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[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},{5},{6},{7}}
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>{{1},{2,4},{3},{5,7},{6}}
[1,4,2,3,7,6,5]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}
[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}
[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}
[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}
[1,4,2,5,7,3,6]=>[1,4,7,2,5,3,6]=>[1,5,4,3,7,2,6]=>{{1},{2,5,7},{3,4},{6}}
[1,4,2,5,7,6,3]=>[1,4,6,2,5,7,3]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}
[1,4,2,6,3,5,7]=>[1,4,6,2,3,5,7]=>[1,6,4,3,2,5,7]=>{{1},{2,6},{3,4},{5},{7}}
[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}}
[1,4,2,6,5,3,7]=>[1,4,5,2,6,3,7]=>[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}}
[1,4,2,6,5,7,3]=>[1,4,7,2,6,5,3]=>[1,6,4,3,7,2,5]=>{{1},{2,6},{3,4},{5,7}}
[1,4,2,6,7,3,5]=>[1,4,7,2,3,6,5]=>[1,6,4,3,2,7,5]=>{{1},{2,6,7},{3,4},{5}}
[1,4,2,6,7,5,3]=>[1,4,5,2,7,6,3]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}}
[1,4,2,7,3,5,6]=>[1,4,7,2,3,5,6]=>[1,7,4,3,2,5,6]=>{{1},{2,7},{3,4},{5},{6}}
[1,4,2,7,3,6,5]=>[1,4,7,2,6,3,5]=>[1,6,4,3,7,5,2]=>{{1},{2,6},{3,4},{5,7}}
[1,4,2,7,5,3,6]=>[1,4,5,2,7,3,6]=>[1,7,4,3,5,2,6]=>{{1},{2,7},{3,4},{5},{6}}
[1,4,2,7,5,6,3]=>[1,4,6,2,7,5,3]=>[1,7,4,3,6,2,5]=>{{1},{2,7},{3,4},{5,6}}
[1,4,2,7,6,3,5]=>[1,4,6,2,3,7,5]=>[1,7,4,3,2,6,5]=>{{1},{2,7},{3,4},{5},{6}}
[1,4,2,7,6,5,3]=>[1,4,5,2,6,7,3]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}}
[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[1,4,3,2,7,5,6]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>{{1},{2,4},{3},{5,7},{6}}
[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,5,7,2,6]=>[1,7,4,3,5,2,6]=>[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,7},{6}}
[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[1,4,3,6,2,5,7]=>[1,6,4,3,2,5,7]=>[1,4,6,2,3,5,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,4,3,6,2,7,5]=>[1,6,4,3,7,2,5]=>[1,4,7,2,6,5,3]=>{{1},{2,4},{3,7},{5,6}}
[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[1,4,3,6,7,2,5]=>[1,7,4,3,2,6,5]=>[1,4,6,2,3,7,5]=>{{1},{2,4},{3,6,7},{5}}
[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[1,4,3,7,2,5,6]=>[1,7,4,3,2,5,6]=>[1,4,7,2,3,5,6]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,3,7,2,6,5]=>[1,7,4,3,6,2,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,6},{5,7}}
[1,4,3,7,5,2,6]=>[1,5,4,3,7,2,6]=>[1,4,7,2,5,3,6]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,3,7,5,6,2]=>[1,6,4,3,7,5,2]=>[1,4,7,2,6,3,5]=>{{1},{2,4},{3,7},{5,6}}
[1,4,3,7,6,2,5]=>[1,6,4,3,2,7,5]=>[1,4,7,2,3,6,5]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[1,4,2,5,3,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[1,4,2,5,3,7,6]=>{{1},{2,4,5},{3},{6,7}}
[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[1,5,4,6,3,2,7]=>{{1},{2,5},{3,4,6},{7}}
[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[1,5,4,6,3,7,2]=>{{1},{2,5},{3,4,6,7}}
[1,4,5,2,7,3,6]=>[1,5,7,4,2,3,6]=>[1,5,4,7,3,2,6]=>{{1},{2,5},{3,4,7},{6}}
[1,4,5,2,7,6,3]=>[1,5,6,4,2,7,3]=>[1,5,4,7,3,6,2]=>{{1},{2,5},{3,4,7},{6}}
[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[1,4,5,6,2,3,7]=>{{1},{2,4,6},{3,5},{7}}
[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[1,4,5,6,2,7,3]=>{{1},{2,4,6,7},{3,5}}
[1,4,5,3,7,2,6]=>[1,7,5,4,3,2,6]=>[1,4,5,7,2,3,6]=>{{1},{2,4,7},{3,5},{6}}
[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>[1,4,5,7,2,6,3]=>{{1},{2,4,7},{3,5},{6}}
[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[1,4,2,5,6,3,7]=>{{1},{2,4,5,6},{3},{7}}
[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[1,5,4,6,7,3,2]=>{{1},{2,5,7},{3,4,6}}
[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[1,4,2,5,6,7,3]=>{{1},{2,4,5,6,7},{3}}
[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[1,4,2,5,7,3,6]=>{{1},{2,4,5,7},{3},{6}}
[1,4,5,7,2,6,3]=>[1,7,6,4,5,2,3]=>[1,4,5,6,7,3,2]=>{{1},{2,4,6},{3,5,7}}
[1,4,5,7,3,2,6]=>[1,3,7,4,5,2,6]=>[1,4,3,5,7,2,6]=>{{1},{2,4,5,7},{3},{6}}
[1,4,5,7,3,6,2]=>[1,6,7,4,5,3,2]=>[1,5,4,6,7,2,3]=>{{1},{2,5,7},{3,4,6}}
[1,4,5,7,6,2,3]=>[1,6,2,4,5,7,3]=>[1,4,2,5,7,6,3]=>{{1},{2,4,5,7},{3},{6}}
[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[1,4,2,6,3,5,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,4,6,2,3,7,5]=>[1,6,2,4,7,3,5]=>[1,4,2,7,6,5,3]=>{{1},{2,4,7},{3},{5,6}}
[1,4,6,2,5,3,7]=>[1,6,5,4,2,3,7]=>[1,4,5,6,3,2,7]=>{{1},{2,4,6},{3,5},{7}}
[1,4,6,2,5,7,3]=>[1,6,7,4,2,5,3]=>[1,6,4,7,3,2,5]=>{{1},{2,6},{3,4,7},{5}}
[1,4,6,2,7,3,5]=>[1,6,7,4,3,2,5]=>[1,6,4,7,2,5,3]=>{{1},{2,6},{3,4,7},{5}}
[1,4,6,2,7,5,3]=>[1,6,5,4,7,2,3]=>[1,4,6,7,5,3,2]=>{{1},{2,4,7},{3,6},{5}}
[1,4,6,3,2,5,7]=>[1,3,6,4,2,5,7]=>[1,4,3,6,2,5,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,4,6,3,2,7,5]=>[1,3,6,4,7,2,5]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}
[1,4,6,3,5,2,7]=>[1,5,6,4,3,2,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,4,6,3,5,7,2]=>[1,7,6,4,3,5,2]=>[1,4,6,7,2,3,5]=>{{1},{2,4,7},{3,6},{5}}
[1,4,6,3,7,2,5]=>[1,7,6,4,2,3,5]=>[1,4,6,7,3,5,2]=>{{1},{2,4,7},{3,6},{5}}
[1,4,6,3,7,5,2]=>[1,5,7,4,6,2,3]=>[1,5,4,7,6,3,2]=>{{1},{2,5,6},{3,4,7}}
[1,4,6,5,2,3,7]=>[1,5,2,4,6,3,7]=>[1,4,2,6,5,3,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,4,6,5,2,7,3]=>[1,5,6,4,7,3,2]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>[1,4,5,7,6,2,3]=>{{1},{2,4,7},{3,5,6}}
[1,4,6,5,7,2,3]=>[1,7,2,4,6,5,3]=>[1,4,2,6,7,3,5]=>{{1},{2,4,6},{3},{5,7}}
[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[1,4,2,6,3,7,5]=>{{1},{2,4,6,7},{3},{5}}
[1,4,6,7,2,5,3]=>[1,7,5,4,2,6,3]=>[1,4,5,6,3,7,2]=>{{1},{2,4,6,7},{3,5}}
[1,4,6,7,3,2,5]=>[1,3,7,4,2,6,5]=>[1,4,3,6,2,7,5]=>{{1},{2,4,6,7},{3},{5}}
[1,4,6,7,3,5,2]=>[1,5,7,4,3,6,2]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,4,6,7,5,2,3]=>[1,5,2,4,7,6,3]=>[1,4,2,6,5,7,3]=>{{1},{2,4,6,7},{3},{5}}
[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[1,4,2,7,3,5,6]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,2,3,6,5]=>[1,7,2,4,6,3,5]=>[1,4,2,6,7,5,3]=>{{1},{2,4,6},{3},{5,7}}
[1,4,7,2,5,3,6]=>[1,7,5,4,2,3,6]=>[1,4,5,7,3,2,6]=>{{1},{2,4,7},{3,5},{6}}
[1,4,7,2,5,6,3]=>[1,7,6,4,2,5,3]=>[1,4,6,7,3,2,5]=>{{1},{2,4,7},{3,6},{5}}
[1,4,7,2,6,3,5]=>[1,7,6,4,3,2,5]=>[1,4,6,7,2,5,3]=>{{1},{2,4,7},{3,6},{5}}
[1,4,7,2,6,5,3]=>[1,7,5,4,6,2,3]=>[1,4,5,7,6,3,2]=>{{1},{2,4,7},{3,5,6}}
[1,4,7,3,2,5,6]=>[1,3,7,4,2,5,6]=>[1,4,3,7,2,5,6]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,3,2,6,5]=>[1,3,7,4,6,2,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,6},{3},{5,7}}
[1,4,7,3,5,2,6]=>[1,5,7,4,3,2,6]=>[1,5,4,7,2,3,6]=>{{1},{2,5},{3,4,7},{6}}
[1,4,7,3,5,6,2]=>[1,6,7,4,3,5,2]=>[1,6,4,7,2,3,5]=>{{1},{2,6},{3,4,7},{5}}
[1,4,7,3,6,2,5]=>[1,6,7,4,2,3,5]=>[1,6,4,7,3,5,2]=>{{1},{2,6},{3,4,7},{5}}
[1,4,7,3,6,5,2]=>[1,5,6,4,7,2,3]=>[1,6,4,7,5,3,2]=>{{1},{2,6},{3,4,7},{5}}
[1,4,7,5,2,3,6]=>[1,5,2,4,7,3,6]=>[1,4,2,7,5,3,6]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,5,2,6,3]=>[1,5,7,4,6,3,2]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,4,7,5,3,2,6]=>[1,3,5,4,7,2,6]=>[1,4,3,7,5,2,6]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,5,3,6,2]=>[1,6,5,4,7,3,2]=>[1,4,6,7,5,2,3]=>{{1},{2,4,7},{3,6},{5}}
[1,4,7,5,6,2,3]=>[1,6,2,4,7,5,3]=>[1,4,2,7,6,3,5]=>{{1},{2,4,7},{3},{5,6}}
[1,4,7,5,6,3,2]=>[1,3,6,4,7,5,2]=>[1,4,3,7,6,2,5]=>{{1},{2,4,7},{3},{5,6}}
[1,4,7,6,2,3,5]=>[1,6,2,4,3,7,5]=>[1,4,2,7,3,6,5]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,6,2,5,3]=>[1,6,5,4,2,7,3]=>[1,4,5,7,3,6,2]=>{{1},{2,4,7},{3,5},{6}}
[1,4,7,6,3,2,5]=>[1,3,6,4,2,7,5]=>[1,4,3,7,2,6,5]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,6,3,5,2]=>[1,5,6,4,3,7,2]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,4,7,6,5,2,3]=>[1,5,2,4,6,7,3]=>[1,4,2,7,5,6,3]=>{{1},{2,4,7},{3},{5},{6}}
[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[1,5,2,3,6,4,7]=>[1,5,2,6,3,4,7]=>[1,6,2,5,4,3,7]=>{{1},{2,6},{3},{4,5},{7}}
[1,5,2,3,6,7,4]=>[1,5,2,7,3,6,4]=>[1,6,2,5,4,7,3]=>{{1},{2,6,7},{3},{4,5}}
[1,5,2,3,7,4,6]=>[1,5,2,7,3,4,6]=>[1,7,2,5,4,3,6]=>{{1},{2,7},{3},{4,5},{6}}
[1,5,2,3,7,6,4]=>[1,5,2,6,3,7,4]=>[1,7,2,5,4,6,3]=>{{1},{2,7},{3},{4,5},{6}}
[1,5,2,4,3,6,7]=>[1,5,4,2,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[1,5,2,4,3,7,6]=>[1,5,4,2,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,4},{3,5},{6,7}}
[1,5,2,4,6,3,7]=>[1,5,6,2,4,3,7]=>[1,6,5,3,2,4,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,5,2,4,6,7,3]=>[1,5,7,2,4,6,3]=>[1,6,5,3,2,7,4]=>{{1},{2,6,7},{3,5},{4}}
[1,5,2,4,7,3,6]=>[1,5,7,2,4,3,6]=>[1,7,5,3,2,4,6]=>{{1},{2,7},{3,5},{4},{6}}
[1,5,2,4,7,6,3]=>[1,5,6,2,4,7,3]=>[1,7,5,3,2,6,4]=>{{1},{2,7},{3,5},{4},{6}}
[1,5,2,6,3,4,7]=>[1,5,6,3,2,4,7]=>[1,6,5,2,4,3,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}
[1,5,2,6,4,3,7]=>[1,5,4,6,2,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,5,2,6,4,7,3]=>[1,5,7,6,2,4,3]=>[1,7,5,6,4,2,3]=>{{1},{2,7},{3,5},{4,6}}
[1,5,2,6,7,3,4]=>[1,5,7,3,2,6,4]=>[1,6,5,2,4,7,3]=>{{1},{2,6,7},{3,5},{4}}
[1,5,2,6,7,4,3]=>[1,5,4,7,2,6,3]=>[1,5,6,4,3,7,2]=>{{1},{2,5},{3,6,7},{4}}
[1,5,2,7,3,4,6]=>[1,5,7,3,2,4,6]=>[1,7,5,2,4,3,6]=>{{1},{2,7},{3,5},{4},{6}}
[1,5,2,7,3,6,4]=>[1,5,7,6,2,3,4]=>[1,7,5,6,4,3,2]=>{{1},{2,7},{3,5},{4,6}}
[1,5,2,7,4,3,6]=>[1,5,4,7,2,3,6]=>[1,5,7,4,3,2,6]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,2,7,4,6,3]=>[1,5,6,7,2,4,3]=>[1,7,6,5,4,2,3]=>{{1},{2,7},{3,6},{4,5}}
[1,5,2,7,6,3,4]=>[1,5,6,3,2,7,4]=>[1,7,5,2,4,6,3]=>{{1},{2,7},{3,5},{4},{6}}
[1,5,2,7,6,4,3]=>[1,5,4,6,2,7,3]=>[1,5,7,4,3,6,2]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,3,2,4,6,7]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,5,3,2,4,7,6]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[1,5,3,2,6,4,7]=>[1,3,5,6,2,4,7]=>[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}}
[1,5,3,2,6,7,4]=>[1,3,5,7,2,6,4]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}}
[1,5,3,2,7,4,6]=>[1,3,5,7,2,4,6]=>[1,7,3,5,4,2,6]=>{{1},{2,7},{3},{4,5},{6}}
[1,5,3,2,7,6,4]=>[1,3,5,6,2,7,4]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}}
[1,5,3,4,2,6,7]=>[1,4,5,3,2,6,7]=>[1,5,4,2,3,6,7]=>{{1},{2,5},{3,4},{6},{7}}
[1,5,3,4,2,7,6]=>[1,4,5,3,2,7,6]=>[1,5,4,2,3,7,6]=>{{1},{2,5},{3,4},{6,7}}
[1,5,3,4,6,2,7]=>[1,6,5,3,4,2,7]=>[1,5,6,2,3,4,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,5,3,4,6,7,2]=>[1,7,5,3,4,6,2]=>[1,5,6,2,3,7,4]=>{{1},{2,5},{3,6,7},{4}}
[1,5,3,4,7,2,6]=>[1,7,5,3,4,2,6]=>[1,5,7,2,3,4,6]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,3,4,7,6,2]=>[1,6,5,3,4,7,2]=>[1,5,7,2,3,6,4]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,3,6,2,4,7]=>[1,6,5,2,3,4,7]=>[1,5,6,3,4,2,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,5,3,6,2,7,4]=>[1,6,5,7,3,2,4]=>[1,6,7,5,3,4,2]=>{{1},{2,6},{3,7},{4,5}}
[1,5,3,6,4,2,7]=>[1,4,6,5,2,3,7]=>[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}}
[1,5,3,6,4,7,2]=>[1,7,5,6,3,4,2]=>[1,5,7,6,3,2,4]=>{{1},{2,5},{3,7},{4,6}}
[1,5,3,6,7,2,4]=>[1,7,5,2,3,6,4]=>[1,5,6,3,4,7,2]=>{{1},{2,5},{3,6,7},{4}}
[1,5,3,6,7,4,2]=>[1,4,7,5,2,6,3]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}}
[1,5,3,7,2,4,6]=>[1,7,5,2,3,4,6]=>[1,5,7,3,4,2,6]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,3,7,2,6,4]=>[1,7,5,6,3,2,4]=>[1,5,7,6,3,4,2]=>{{1},{2,5},{3,7},{4,6}}
[1,5,3,7,4,2,6]=>[1,4,7,5,2,3,6]=>[1,7,4,5,3,2,6]=>{{1},{2,7},{3,4,5},{6}}
[1,5,3,7,4,6,2]=>[1,6,5,7,3,4,2]=>[1,6,7,5,3,2,4]=>{{1},{2,6},{3,7},{4,5}}
[1,5,3,7,6,2,4]=>[1,6,5,2,3,7,4]=>[1,5,7,3,4,6,2]=>{{1},{2,5},{3,7},{4},{6}}
[1,5,3,7,6,4,2]=>[1,4,6,5,2,7,3]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}}
[1,5,4,2,3,6,7]=>[1,4,2,5,3,6,7]=>[1,5,2,4,3,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,5,4,2,3,7,6]=>[1,4,2,5,3,7,6]=>[1,5,2,4,3,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[1,5,4,2,6,3,7]=>[1,4,5,6,3,2,7]=>[1,6,5,4,2,3,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,5,4,2,6,7,3]=>[1,4,5,7,3,6,2]=>[1,6,5,4,2,7,3]=>{{1},{2,6,7},{3,5},{4}}
[1,5,4,2,7,3,6]=>[1,4,5,7,3,2,6]=>[1,7,5,4,2,3,6]=>{{1},{2,7},{3,5},{4},{6}}
[1,5,4,2,7,6,3]=>[1,4,5,6,3,7,2]=>[1,7,5,4,2,6,3]=>{{1},{2,7},{3,5},{4},{6}}
[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,5,4,3,7,2,6]=>[1,7,4,5,3,2,6]=>[1,4,7,5,2,3,6]=>{{1},{2,4,5},{3,7},{6}}
[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[1,5,4,6,2,3,7]=>[1,6,2,5,4,3,7]=>[1,5,2,6,3,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,5,4,6,2,7,3]=>[1,6,7,5,4,2,3]=>[1,6,5,7,2,4,3]=>{{1},{2,6},{3,5},{4,7}}
[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,4,6,7,2,3]=>[1,7,2,5,4,6,3]=>[1,5,2,6,3,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,5,4,7,2,3,6]=>[1,7,2,5,4,3,6]=>[1,5,2,7,3,4,6]=>{{1},{2,5},{3},{4,7},{6}}
[1,5,4,7,2,6,3]=>[1,7,6,5,4,2,3]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,6},{4,7}}
[1,5,4,7,3,2,6]=>[1,3,7,5,4,2,6]=>[1,5,3,7,2,4,6]=>{{1},{2,5},{3},{4,7},{6}}
[1,5,4,7,3,6,2]=>[1,6,7,5,4,3,2]=>[1,6,5,7,2,3,4]=>{{1},{2,6},{3,5},{4,7}}
[1,5,4,7,6,2,3]=>[1,6,2,5,4,7,3]=>[1,5,2,7,3,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[1,5,2,3,6,4,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,6,2,3,7,4]=>[1,6,2,7,5,3,4]=>[1,6,2,5,7,4,3]=>{{1},{2,6},{3},{4,5,7}}
[1,5,6,2,4,3,7]=>[1,6,4,2,5,3,7]=>[1,4,5,3,6,2,7]=>{{1},{2,4},{3,5,6},{7}}
[1,5,6,2,4,7,3]=>[1,6,7,2,5,4,3]=>[1,6,5,3,7,2,4]=>{{1},{2,6},{3,5,7},{4}}
[1,5,6,2,7,3,4]=>[1,6,7,3,5,2,4]=>[1,6,5,2,7,4,3]=>{{1},{2,6},{3,5,7},{4}}
[1,5,6,2,7,4,3]=>[1,6,4,7,5,2,3]=>[1,5,6,4,7,3,2]=>{{1},{2,5,7},{3,6},{4}}
[1,5,6,3,2,4,7]=>[1,3,6,2,5,4,7]=>[1,5,3,2,6,4,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,6,3,2,7,4]=>[1,3,6,7,5,2,4]=>[1,6,3,5,7,4,2]=>{{1},{2,6},{3},{4,5,7}}
[1,5,6,3,4,2,7]=>[1,4,6,3,5,2,7]=>[1,5,4,2,6,3,7]=>{{1},{2,5,6},{3,4},{7}}
[1,5,6,3,4,7,2]=>[1,7,6,3,5,4,2]=>[1,5,6,2,7,3,4]=>{{1},{2,5,7},{3,6},{4}}
[1,5,6,3,7,2,4]=>[1,7,6,2,5,3,4]=>[1,5,6,3,7,4,2]=>{{1},{2,5,7},{3,6},{4}}
[1,5,6,3,7,4,2]=>[1,4,7,6,5,2,3]=>[1,6,4,5,7,3,2]=>{{1},{2,6},{3,4,5,7}}
[1,5,6,4,2,3,7]=>[1,4,2,6,5,3,7]=>[1,5,2,4,6,3,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,6,4,2,7,3]=>[1,4,6,7,5,3,2]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>[1,4,6,5,7,2,3]=>{{1},{2,4,5,7},{3,6}}
[1,5,6,4,7,2,3]=>[1,7,2,6,5,4,3]=>[1,5,2,6,7,3,4]=>{{1},{2,5,7},{3},{4,6}}
[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>[1,5,3,6,7,2,4]=>{{1},{2,5,7},{3},{4,6}}
[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[1,5,2,3,6,7,4]=>{{1},{2,5,6,7},{3},{4}}
[1,5,6,7,2,4,3]=>[1,7,4,2,5,6,3]=>[1,4,5,3,6,7,2]=>{{1},{2,4},{3,5,6,7}}
[1,5,6,7,3,2,4]=>[1,3,7,2,5,6,4]=>[1,5,3,2,6,7,4]=>{{1},{2,5,6,7},{3},{4}}
[1,5,6,7,3,4,2]=>[1,4,7,3,5,6,2]=>[1,5,4,2,6,7,3]=>{{1},{2,5,6,7},{3,4}}
[1,5,6,7,4,2,3]=>[1,4,2,7,5,6,3]=>[1,5,2,4,6,7,3]=>{{1},{2,5,6,7},{3},{4}}
[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[1,5,2,3,7,4,6]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,2,3,6,4]=>[1,7,2,6,5,3,4]=>[1,5,2,6,7,4,3]=>{{1},{2,5,7},{3},{4,6}}
[1,5,7,2,4,3,6]=>[1,7,4,2,5,3,6]=>[1,4,5,3,7,2,6]=>{{1},{2,4},{3,5,7},{6}}
[1,5,7,2,4,6,3]=>[1,7,6,2,5,4,3]=>[1,5,6,3,7,2,4]=>{{1},{2,5,7},{3,6},{4}}
[1,5,7,2,6,3,4]=>[1,7,6,3,5,2,4]=>[1,5,6,2,7,4,3]=>{{1},{2,5,7},{3,6},{4}}
[1,5,7,2,6,4,3]=>[1,7,4,6,5,2,3]=>[1,4,6,5,7,3,2]=>{{1},{2,4,5,7},{3,6}}
[1,5,7,3,2,4,6]=>[1,3,7,2,5,4,6]=>[1,5,3,2,7,4,6]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,3,2,6,4]=>[1,3,7,6,5,2,4]=>[1,5,3,6,7,4,2]=>{{1},{2,5,7},{3},{4,6}}
[1,5,7,3,4,2,6]=>[1,4,7,3,5,2,6]=>[1,5,4,2,7,3,6]=>{{1},{2,5,7},{3,4},{6}}
[1,5,7,3,4,6,2]=>[1,6,7,3,5,4,2]=>[1,6,5,2,7,3,4]=>{{1},{2,6},{3,5,7},{4}}
[1,5,7,3,6,2,4]=>[1,6,7,2,5,3,4]=>[1,6,5,3,7,4,2]=>{{1},{2,6},{3,5,7},{4}}
[1,5,7,3,6,4,2]=>[1,4,6,7,5,2,3]=>[1,6,5,4,7,3,2]=>{{1},{2,6},{3,5,7},{4}}
[1,5,7,4,2,3,6]=>[1,4,2,7,5,3,6]=>[1,5,2,4,7,3,6]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,4,2,6,3]=>[1,4,7,6,5,3,2]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,5,7,4,3,2,6]=>[1,3,4,7,5,2,6]=>[1,5,3,4,7,2,6]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,4,3,6,2]=>[1,6,4,7,5,3,2]=>[1,5,6,4,7,2,3]=>{{1},{2,5,7},{3,6},{4}}
[1,5,7,4,6,2,3]=>[1,6,2,7,5,4,3]=>[1,6,2,5,7,3,4]=>{{1},{2,6},{3},{4,5,7}}
[1,5,7,4,6,3,2]=>[1,3,6,7,5,4,2]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,5,7,6,2,3,4]=>[1,6,2,3,5,7,4]=>[1,5,2,3,7,6,4]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,6,2,4,3]=>[1,6,4,2,5,7,3]=>[1,4,5,3,7,6,2]=>{{1},{2,4},{3,5,7},{6}}
[1,5,7,6,3,2,4]=>[1,3,6,2,5,7,4]=>[1,5,3,2,7,6,4]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,6,3,4,2]=>[1,4,6,3,5,7,2]=>[1,5,4,2,7,6,3]=>{{1},{2,5,7},{3,4},{6}}
[1,5,7,6,4,2,3]=>[1,4,2,6,5,7,3]=>[1,5,2,4,7,6,3]=>{{1},{2,5,7},{3},{4},{6}}
[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,2,3,4,7,5]=>[1,6,2,3,7,4,5]=>[1,7,2,3,6,5,4]=>{{1},{2,7},{3},{4},{5,6}}
[1,6,2,3,5,4,7]=>[1,6,2,5,3,4,7]=>[1,5,2,6,4,3,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,6,2,3,5,7,4]=>[1,6,2,7,3,5,4]=>[1,7,2,6,4,3,5]=>{{1},{2,7},{3},{4,6},{5}}
[1,6,2,3,7,4,5]=>[1,6,2,7,4,3,5]=>[1,7,2,6,3,5,4]=>{{1},{2,7},{3},{4,6},{5}}
[1,6,2,3,7,5,4]=>[1,6,2,5,7,3,4]=>[1,6,2,7,5,4,3]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,2,4,3,5,7]=>[1,6,4,2,3,5,7]=>[1,4,6,3,2,5,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,6,2,4,3,7,5]=>[1,6,4,2,7,3,5]=>[1,4,7,3,6,5,2]=>{{1},{2,4},{3,7},{5,6}}
[1,6,2,4,5,3,7]=>[1,6,5,2,4,3,7]=>[1,5,6,3,2,4,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,6,2,4,5,7,3]=>[1,6,7,2,3,4,5]=>[1,7,6,3,4,5,2]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,2,4,7,3,5]=>[1,6,7,2,4,5,3]=>[1,7,6,3,2,4,5]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,2,4,7,5,3]=>[1,6,5,2,7,4,3]=>[1,6,7,3,5,2,4]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,2,5,3,4,7]=>[1,6,5,3,2,4,7]=>[1,5,6,2,4,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,6,2,5,3,7,4]=>[1,6,5,7,2,3,4]=>[1,6,7,5,4,3,2]=>{{1},{2,6},{3,7},{4,5}}
[1,6,2,5,4,3,7]=>[1,6,4,5,2,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,4,5},{3,6},{7}}
[1,6,2,5,4,7,3]=>[1,6,7,5,2,4,3]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,5},{4,7}}
[1,6,2,5,7,3,4]=>[1,6,7,3,2,5,4]=>[1,7,6,2,4,3,5]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,2,5,7,4,3]=>[1,6,4,7,2,5,3]=>[1,6,7,4,3,2,5]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,2,7,3,4,5]=>[1,6,7,3,4,2,5]=>[1,7,6,2,3,5,4]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,2,7,3,5,4]=>[1,6,7,5,3,2,4]=>[1,6,5,7,3,4,2]=>{{1},{2,6},{3,5},{4,7}}
[1,6,2,7,4,3,5]=>[1,6,4,7,3,2,5]=>[1,6,7,4,2,5,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,2,7,4,5,3]=>[1,6,5,7,4,2,3]=>[1,6,7,5,2,4,3]=>{{1},{2,6},{3,7},{4,5}}
[1,6,2,7,5,3,4]=>[1,6,5,3,7,2,4]=>[1,6,7,2,5,4,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,2,7,5,4,3]=>[1,6,4,5,7,2,3]=>[1,4,7,6,5,3,2]=>{{1},{2,4,6},{3,7},{5}}
[1,6,3,2,4,5,7]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,3,2,4,7,5]=>[1,3,6,2,7,4,5]=>[1,7,3,2,6,5,4]=>{{1},{2,7},{3},{4},{5,6}}
[1,6,3,2,5,4,7]=>[1,3,6,5,2,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,6,3,2,5,7,4]=>[1,3,6,7,2,5,4]=>[1,7,3,6,4,2,5]=>{{1},{2,7},{3},{4,6},{5}}
[1,6,3,2,7,4,5]=>[1,3,6,7,4,2,5]=>[1,7,3,6,2,5,4]=>{{1},{2,7},{3},{4,6},{5}}
[1,6,3,2,7,5,4]=>[1,3,6,5,7,2,4]=>[1,6,3,7,5,4,2]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,3,4,2,5,7]=>[1,4,6,3,2,5,7]=>[1,6,4,2,3,5,7]=>{{1},{2,6},{3,4},{5},{7}}
[1,6,3,4,2,7,5]=>[1,4,6,3,7,2,5]=>[1,7,4,2,6,5,3]=>{{1},{2,7},{3,4},{5,6}}
[1,6,3,4,5,2,7]=>[1,5,6,3,4,2,7]=>[1,6,5,2,3,4,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,6,3,4,5,7,2]=>[1,7,6,3,4,5,2]=>[1,6,7,2,3,4,5]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,3,4,7,2,5]=>[1,7,6,3,2,4,5]=>[1,6,7,2,4,5,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,3,4,7,5,2]=>[1,5,7,3,6,2,4]=>[1,7,5,2,6,4,3]=>{{1},{2,7},{3,5,6},{4}}
[1,6,3,5,2,4,7]=>[1,5,6,2,3,4,7]=>[1,6,5,3,4,2,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,6,3,5,2,7,4]=>[1,5,6,7,3,2,4]=>[1,7,6,5,3,4,2]=>{{1},{2,7},{3,6},{4,5}}
[1,6,3,5,4,2,7]=>[1,4,5,6,2,3,7]=>[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,6,3,5,4,7,2]=>[1,7,6,5,3,4,2]=>[1,5,6,7,3,2,4]=>{{1},{2,5},{3,6},{4,7}}
[1,6,3,5,7,2,4]=>[1,7,6,2,4,3,5]=>[1,6,7,3,2,5,4]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,3,5,7,4,2]=>[1,4,7,6,3,2,5]=>[1,7,4,6,2,5,3]=>{{1},{2,7},{3,4,6},{5}}
[1,6,3,7,2,4,5]=>[1,7,6,2,3,5,4]=>[1,6,7,3,4,2,5]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,3,7,2,5,4]=>[1,7,6,5,2,3,4]=>[1,5,6,7,4,3,2]=>{{1},{2,5},{3,6},{4,7}}
[1,6,3,7,4,2,5]=>[1,4,7,6,2,5,3]=>[1,7,4,6,3,2,5]=>{{1},{2,7},{3,4,6},{5}}
[1,6,3,7,4,5,2]=>[1,5,6,7,4,3,2]=>[1,7,6,5,2,3,4]=>{{1},{2,7},{3,6},{4,5}}
[1,6,3,7,5,2,4]=>[1,5,7,2,6,4,3]=>[1,7,5,3,6,2,4]=>{{1},{2,7},{3,5,6},{4}}
[1,6,3,7,5,4,2]=>[1,4,5,7,6,3,2]=>[1,7,5,4,6,2,3]=>{{1},{2,7},{3,5,6},{4}}
[1,6,4,2,3,5,7]=>[1,4,2,6,3,5,7]=>[1,6,2,4,3,5,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,4,2,3,7,5]=>[1,4,2,6,7,3,5]=>[1,7,2,4,6,5,3]=>{{1},{2,7},{3},{4},{5,6}}
[1,6,4,2,5,3,7]=>[1,4,6,5,3,2,7]=>[1,6,4,5,2,3,7]=>{{1},{2,6},{3,4,5},{7}}
[1,6,4,2,5,7,3]=>[1,4,6,7,2,3,5]=>[1,7,6,4,3,5,2]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,4,2,7,3,5]=>[1,4,6,7,3,5,2]=>[1,7,6,4,2,3,5]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,4,2,7,5,3]=>[1,4,6,5,7,3,2]=>[1,7,4,6,5,2,3]=>{{1},{2,7},{3,4,6},{5}}
[1,6,4,3,2,5,7]=>[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,4,3,2,7,5]=>[1,3,4,6,7,2,5]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}}
[1,6,4,3,5,2,7]=>[1,5,4,6,3,2,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,6,4,3,5,7,2]=>[1,7,4,6,3,5,2]=>[1,4,7,6,2,3,5]=>{{1},{2,4,6},{3,7},{5}}
[1,6,4,3,7,2,5]=>[1,7,4,6,2,3,5]=>[1,4,7,6,3,5,2]=>{{1},{2,4,6},{3,7},{5}}
[1,6,4,3,7,5,2]=>[1,5,4,7,6,2,3]=>[1,5,7,4,6,3,2]=>{{1},{2,5,6},{3,7},{4}}
[1,6,4,5,2,3,7]=>[1,5,2,6,4,3,7]=>[1,6,2,5,3,4,7]=>{{1},{2,6},{3},{4,5},{7}}
[1,6,4,5,2,7,3]=>[1,5,7,6,4,2,3]=>[1,7,5,6,2,4,3]=>{{1},{2,7},{3,5},{4,6}}
[1,6,4,5,3,2,7]=>[1,3,5,6,4,2,7]=>[1,6,3,5,2,4,7]=>{{1},{2,6},{3},{4,5},{7}}
[1,6,4,5,3,7,2]=>[1,7,5,6,4,3,2]=>[1,5,7,6,2,3,4]=>{{1},{2,5},{3,7},{4,6}}
[1,6,4,5,7,2,3]=>[1,7,2,6,4,5,3]=>[1,6,2,7,3,4,5]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,4,5,7,3,2]=>[1,3,7,6,4,5,2]=>[1,6,3,7,2,4,5]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,4,7,2,3,5]=>[1,7,2,6,3,4,5]=>[1,6,2,7,4,5,3]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,4,7,2,5,3]=>[1,7,5,6,2,4,3]=>[1,5,7,6,4,2,3]=>{{1},{2,5},{3,7},{4,6}}
[1,6,4,7,3,2,5]=>[1,3,7,6,2,4,5]=>[1,6,3,7,4,5,2]=>{{1},{2,6},{3},{4,7},{5}}
[1,6,4,7,3,5,2]=>[1,5,7,6,3,4,2]=>[1,7,5,6,3,2,4]=>{{1},{2,7},{3,5},{4,6}}
[1,6,4,7,5,2,3]=>[1,5,2,7,6,3,4]=>[1,7,2,5,6,4,3]=>{{1},{2,7},{3},{4,5,6}}
[1,6,4,7,5,3,2]=>[1,3,5,7,6,2,4]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}}
[1,6,5,2,3,4,7]=>[1,5,2,3,6,4,7]=>[1,6,2,3,5,4,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,5,2,3,7,4]=>[1,5,2,6,7,4,3]=>[1,7,2,6,5,3,4]=>{{1},{2,7},{3},{4,6},{5}}
[1,6,5,2,4,3,7]=>[1,5,4,2,6,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,6,5,2,4,7,3]=>[1,5,6,2,7,3,4]=>[1,7,6,3,5,4,2]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,5,2,7,3,4]=>[1,5,6,3,7,4,2]=>[1,7,6,2,5,3,4]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,5,2,7,4,3]=>[1,5,4,6,7,3,2]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,6,5,3,2,4,7]=>[1,3,5,2,6,4,7]=>[1,6,3,2,5,4,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,5,3,2,7,4]=>[1,3,5,6,7,4,2]=>[1,7,3,6,5,2,4]=>{{1},{2,7},{3},{4,6},{5}}
[1,6,5,3,4,2,7]=>[1,4,5,3,6,2,7]=>[1,6,4,2,5,3,7]=>{{1},{2,6},{3,4},{5},{7}}
[1,6,5,3,4,7,2]=>[1,7,5,3,6,4,2]=>[1,5,7,2,6,3,4]=>{{1},{2,5,6},{3,7},{4}}
[1,6,5,3,7,2,4]=>[1,7,5,2,6,3,4]=>[1,5,7,3,6,4,2]=>{{1},{2,5,6},{3,7},{4}}
[1,6,5,3,7,4,2]=>[1,4,7,5,6,2,3]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}}
[1,6,5,4,2,3,7]=>[1,4,2,5,6,3,7]=>[1,6,2,4,5,3,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,5,4,2,7,3]=>[1,4,5,6,7,2,3]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}}
[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[1,6,5,4,7,2,3]=>[1,7,2,5,6,4,3]=>[1,5,2,7,6,3,4]=>{{1},{2,5,6},{3},{4,7}}
[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[1,6,5,7,2,3,4]=>[1,7,2,3,6,5,4]=>[1,6,2,3,7,4,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,6,5,7,2,4,3]=>[1,7,4,2,6,5,3]=>[1,4,6,3,7,2,5]=>{{1},{2,4},{3,6},{5,7}}
[1,6,5,7,3,2,4]=>[1,3,7,2,6,5,4]=>[1,6,3,2,7,4,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,6,5,7,3,4,2]=>[1,4,7,3,6,5,2]=>[1,6,4,2,7,3,5]=>{{1},{2,6},{3,4},{5,7}}
[1,6,5,7,4,2,3]=>[1,4,2,7,6,5,3]=>[1,6,2,4,7,3,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[1,6,2,3,4,7,5]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,2,3,5,4]=>[1,7,2,5,3,6,4]=>[1,5,2,6,4,7,3]=>{{1},{2,5},{3},{4,6,7}}
[1,6,7,2,4,3,5]=>[1,7,4,2,3,6,5]=>[1,4,6,3,2,7,5]=>{{1},{2,4},{3,6,7},{5}}
[1,6,7,2,4,5,3]=>[1,7,5,2,4,6,3]=>[1,5,6,3,2,7,4]=>{{1},{2,5},{3,6,7},{4}}
[1,6,7,2,5,3,4]=>[1,7,5,3,2,6,4]=>[1,5,6,2,4,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,6,7,2,5,4,3]=>[1,7,4,5,2,6,3]=>[1,4,6,5,3,7,2]=>{{1},{2,4,5},{3,6,7}}
[1,6,7,3,2,4,5]=>[1,3,7,2,4,6,5]=>[1,6,3,2,4,7,5]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,3,2,5,4]=>[1,3,7,5,2,6,4]=>[1,5,3,6,4,7,2]=>{{1},{2,5},{3},{4,6,7}}
[1,6,7,3,4,2,5]=>[1,4,7,3,2,6,5]=>[1,6,4,2,3,7,5]=>{{1},{2,6,7},{3,4},{5}}
[1,6,7,3,4,5,2]=>[1,5,7,3,4,6,2]=>[1,6,5,2,3,7,4]=>{{1},{2,6,7},{3,5},{4}}
[1,6,7,3,5,2,4]=>[1,5,7,2,3,6,4]=>[1,6,5,3,4,7,2]=>{{1},{2,6,7},{3,5},{4}}
[1,6,7,3,5,4,2]=>[1,4,5,7,2,6,3]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}
[1,6,7,4,2,3,5]=>[1,4,2,7,3,6,5]=>[1,6,2,4,3,7,5]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,4,2,5,3]=>[1,4,7,5,3,6,2]=>[1,6,4,5,2,7,3]=>{{1},{2,6,7},{3,4,5}}
[1,6,7,4,3,2,5]=>[1,3,4,7,2,6,5]=>[1,6,3,4,2,7,5]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,4,3,5,2]=>[1,5,4,7,3,6,2]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,6,7,4,5,2,3]=>[1,5,2,7,4,6,3]=>[1,6,2,5,3,7,4]=>{{1},{2,6,7},{3},{4,5}}
[1,6,7,4,5,3,2]=>[1,3,5,7,4,6,2]=>[1,6,3,5,2,7,4]=>{{1},{2,6,7},{3},{4,5}}
[1,6,7,5,2,3,4]=>[1,5,2,3,7,6,4]=>[1,6,2,3,5,7,4]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,5,2,4,3]=>[1,5,4,2,7,6,3]=>[1,4,6,3,5,7,2]=>{{1},{2,4},{3,6,7},{5}}
[1,6,7,5,3,2,4]=>[1,3,5,2,7,6,4]=>[1,6,3,2,5,7,4]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,5,3,4,2]=>[1,4,5,3,7,6,2]=>[1,6,4,2,5,7,3]=>{{1},{2,6,7},{3,4},{5}}
[1,6,7,5,4,2,3]=>[1,4,2,5,7,6,3]=>[1,6,2,4,5,7,3]=>{{1},{2,6,7},{3},{4},{5}}
[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,2,3,4,6,5]=>[1,7,2,3,6,4,5]=>[1,6,2,3,7,5,4]=>{{1},{2,6},{3},{4},{5,7}}
[1,7,2,3,5,4,6]=>[1,7,2,5,3,4,6]=>[1,5,2,7,4,3,6]=>{{1},{2,5},{3},{4,7},{6}}
[1,7,2,3,5,6,4]=>[1,7,2,6,3,5,4]=>[1,6,2,7,4,3,5]=>{{1},{2,6},{3},{4,7},{5}}
[1,7,2,3,6,4,5]=>[1,7,2,6,4,3,5]=>[1,6,2,7,3,5,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,7,2,3,6,5,4]=>[1,7,2,5,6,3,4]=>[1,5,2,7,6,4,3]=>{{1},{2,5,6},{3},{4,7}}
[1,7,2,4,3,5,6]=>[1,7,4,2,3,5,6]=>[1,4,7,3,2,5,6]=>{{1},{2,4},{3,7},{5},{6}}
[1,7,2,4,3,6,5]=>[1,7,4,2,6,3,5]=>[1,4,6,3,7,5,2]=>{{1},{2,4},{3,6},{5,7}}
[1,7,2,4,5,3,6]=>[1,7,5,2,4,3,6]=>[1,5,7,3,2,4,6]=>{{1},{2,5},{3,7},{4},{6}}
[1,7,2,4,5,6,3]=>[1,7,6,2,3,4,5]=>[1,6,7,3,4,5,2]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,2,4,6,3,5]=>[1,7,6,2,4,5,3]=>[1,6,7,3,2,4,5]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,2,4,6,5,3]=>[1,7,5,2,6,4,3]=>[1,5,7,3,6,2,4]=>{{1},{2,5,6},{3,7},{4}}
[1,7,2,5,3,4,6]=>[1,7,5,3,2,4,6]=>[1,5,7,2,4,3,6]=>{{1},{2,5},{3,7},{4},{6}}
[1,7,2,5,3,6,4]=>[1,7,5,6,2,3,4]=>[1,5,7,6,4,3,2]=>{{1},{2,5},{3,7},{4,6}}
[1,7,2,5,4,3,6]=>[1,7,4,5,2,3,6]=>[1,4,7,5,3,2,6]=>{{1},{2,4,5},{3,7},{6}}
[1,7,2,5,4,6,3]=>[1,7,6,5,2,4,3]=>[1,5,6,7,4,2,3]=>{{1},{2,5},{3,6},{4,7}}
[1,7,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>[1,6,7,2,4,3,5]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,2,5,6,4,3]=>[1,7,4,6,2,5,3]=>[1,4,7,6,3,2,5]=>{{1},{2,4,6},{3,7},{5}}
[1,7,2,6,3,4,5]=>[1,7,6,3,4,2,5]=>[1,6,7,2,3,5,4]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,2,6,3,5,4]=>[1,7,6,5,3,2,4]=>[1,5,6,7,3,4,2]=>{{1},{2,5},{3,6},{4,7}}
[1,7,2,6,4,3,5]=>[1,7,4,6,3,2,5]=>[1,4,7,6,2,5,3]=>{{1},{2,4,6},{3,7},{5}}
[1,7,2,6,4,5,3]=>[1,7,5,6,4,2,3]=>[1,5,7,6,2,4,3]=>{{1},{2,5},{3,7},{4,6}}
[1,7,2,6,5,3,4]=>[1,7,5,3,6,2,4]=>[1,5,7,2,6,4,3]=>{{1},{2,5,6},{3,7},{4}}
[1,7,2,6,5,4,3]=>[1,7,4,5,6,2,3]=>[1,4,7,5,6,3,2]=>{{1},{2,4,5,6},{3,7}}
[1,7,3,2,4,5,6]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,3,2,4,6,5]=>[1,3,7,2,6,4,5]=>[1,6,3,2,7,5,4]=>{{1},{2,6},{3},{4},{5,7}}
[1,7,3,2,5,4,6]=>[1,3,7,5,2,4,6]=>[1,5,3,7,4,2,6]=>{{1},{2,5},{3},{4,7},{6}}
[1,7,3,2,5,6,4]=>[1,3,7,6,2,5,4]=>[1,6,3,7,4,2,5]=>{{1},{2,6},{3},{4,7},{5}}
[1,7,3,2,6,4,5]=>[1,3,7,6,4,2,5]=>[1,6,3,7,2,5,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,7,3,2,6,5,4]=>[1,3,7,5,6,2,4]=>[1,5,3,7,6,4,2]=>{{1},{2,5,6},{3},{4,7}}
[1,7,3,4,2,5,6]=>[1,4,7,3,2,5,6]=>[1,7,4,2,3,5,6]=>{{1},{2,7},{3,4},{5},{6}}
[1,7,3,4,2,6,5]=>[1,4,7,3,6,2,5]=>[1,6,4,2,7,5,3]=>{{1},{2,6},{3,4},{5,7}}
[1,7,3,4,5,2,6]=>[1,5,7,3,4,2,6]=>[1,7,5,2,3,4,6]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,3,4,5,6,2]=>[1,6,7,3,4,5,2]=>[1,7,6,2,3,4,5]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,4,6,2,5]=>[1,6,7,3,2,4,5]=>[1,7,6,2,4,5,3]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,4,6,5,2]=>[1,5,6,3,7,2,4]=>[1,7,6,2,5,4,3]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,5,2,4,6]=>[1,5,7,2,3,4,6]=>[1,7,5,3,4,2,6]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,3,5,2,6,4]=>[1,5,7,6,3,2,4]=>[1,7,5,6,3,4,2]=>{{1},{2,7},{3,5},{4,6}}
[1,7,3,5,4,2,6]=>[1,4,5,7,2,3,6]=>[1,7,5,4,3,2,6]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,3,5,4,6,2]=>[1,6,7,5,3,4,2]=>[1,6,5,7,3,2,4]=>{{1},{2,6},{3,5},{4,7}}
[1,7,3,5,6,2,4]=>[1,6,7,2,4,3,5]=>[1,7,6,3,2,5,4]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,5,6,4,2]=>[1,4,6,7,3,2,5]=>[1,7,6,4,2,5,3]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,6,2,4,5]=>[1,6,7,2,3,5,4]=>[1,7,6,3,4,2,5]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,6,2,5,4]=>[1,6,7,5,2,3,4]=>[1,6,5,7,4,3,2]=>{{1},{2,6},{3,5},{4,7}}
[1,7,3,6,4,2,5]=>[1,4,6,7,2,5,3]=>[1,7,6,4,3,2,5]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,6,4,5,2]=>[1,5,7,6,4,3,2]=>[1,7,5,6,2,3,4]=>{{1},{2,7},{3,5},{4,6}}
[1,7,3,6,5,2,4]=>[1,5,6,2,7,4,3]=>[1,7,6,3,5,2,4]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,3,6,5,4,2]=>[1,4,5,6,7,3,2]=>[1,7,6,4,5,2,3]=>{{1},{2,7},{3,6},{4},{5}}
[1,7,4,2,3,5,6]=>[1,4,2,7,3,5,6]=>[1,7,2,4,3,5,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,4,2,3,6,5]=>[1,4,2,7,6,3,5]=>[1,6,2,4,7,5,3]=>{{1},{2,6},{3},{4},{5,7}}
[1,7,4,2,5,3,6]=>[1,4,7,5,3,2,6]=>[1,7,4,5,2,3,6]=>{{1},{2,7},{3,4,5},{6}}
[1,7,4,2,5,6,3]=>[1,4,7,6,2,3,5]=>[1,7,4,6,3,5,2]=>{{1},{2,7},{3,4,6},{5}}
[1,7,4,2,6,3,5]=>[1,4,7,6,3,5,2]=>[1,7,4,6,2,3,5]=>{{1},{2,7},{3,4,6},{5}}
[1,7,4,2,6,5,3]=>[1,4,7,5,6,3,2]=>[1,7,4,5,6,2,3]=>{{1},{2,7},{3,4,5,6}}
[1,7,4,3,2,5,6]=>[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,4,3,2,6,5]=>[1,3,4,7,6,2,5]=>[1,6,3,4,7,5,2]=>{{1},{2,6},{3},{4},{5,7}}
[1,7,4,3,5,2,6]=>[1,5,4,7,3,2,6]=>[1,5,7,4,2,3,6]=>{{1},{2,5},{3,7},{4},{6}}
[1,7,4,3,5,6,2]=>[1,6,4,7,3,5,2]=>[1,6,7,4,2,3,5]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,4,3,6,2,5]=>[1,6,4,7,2,3,5]=>[1,6,7,4,3,5,2]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,4,3,6,5,2]=>[1,5,4,6,7,2,3]=>[1,6,7,4,5,3,2]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,4,5,2,3,6]=>[1,5,2,7,4,3,6]=>[1,7,2,5,3,4,6]=>{{1},{2,7},{3},{4,5},{6}}
[1,7,4,5,2,6,3]=>[1,5,6,7,4,2,3]=>[1,7,6,5,2,4,3]=>{{1},{2,7},{3,6},{4,5}}
[1,7,4,5,3,2,6]=>[1,3,5,7,4,2,6]=>[1,7,3,5,2,4,6]=>{{1},{2,7},{3},{4,5},{6}}
[1,7,4,5,3,6,2]=>[1,6,5,7,4,3,2]=>[1,6,7,5,2,3,4]=>{{1},{2,6},{3,7},{4,5}}
[1,7,4,5,6,2,3]=>[1,6,2,7,4,5,3]=>[1,7,2,6,3,4,5]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,4,5,6,3,2]=>[1,3,6,7,4,5,2]=>[1,7,3,6,2,4,5]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,4,6,2,3,5]=>[1,6,2,7,3,4,5]=>[1,7,2,6,4,5,3]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,4,6,2,5,3]=>[1,6,5,7,2,4,3]=>[1,6,7,5,4,2,3]=>{{1},{2,6},{3,7},{4,5}}
[1,7,4,6,3,2,5]=>[1,3,6,7,2,4,5]=>[1,7,3,6,4,5,2]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,4,6,3,5,2]=>[1,5,6,7,3,4,2]=>[1,7,6,5,3,2,4]=>{{1},{2,7},{3,6},{4,5}}
[1,7,4,6,5,2,3]=>[1,5,2,6,7,3,4]=>[1,7,2,6,5,4,3]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,4,6,5,3,2]=>[1,3,5,6,7,2,4]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}}
[1,7,5,2,3,4,6]=>[1,5,2,3,7,4,6]=>[1,7,2,3,5,4,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,5,2,3,6,4]=>[1,5,2,7,6,4,3]=>[1,7,2,5,6,3,4]=>{{1},{2,7},{3},{4,5,6}}
[1,7,5,2,4,3,6]=>[1,5,4,2,7,3,6]=>[1,4,7,3,5,2,6]=>{{1},{2,4},{3,7},{5},{6}}
[1,7,5,2,4,6,3]=>[1,5,7,2,6,3,4]=>[1,7,5,3,6,4,2]=>{{1},{2,7},{3,5,6},{4}}
[1,7,5,2,6,3,4]=>[1,5,7,3,6,4,2]=>[1,7,5,2,6,3,4]=>{{1},{2,7},{3,5,6},{4}}
[1,7,5,2,6,4,3]=>[1,5,4,7,6,3,2]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[1,7,5,3,2,4,6]=>[1,3,5,2,7,4,6]=>[1,7,3,2,5,4,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,5,3,2,6,4]=>[1,3,5,7,6,4,2]=>[1,7,3,5,6,2,4]=>{{1},{2,7},{3},{4,5,6}}
[1,7,5,3,4,2,6]=>[1,4,5,3,7,2,6]=>[1,7,4,2,5,3,6]=>{{1},{2,7},{3,4},{5},{6}}
[1,7,5,3,4,6,2]=>[1,6,5,3,7,4,2]=>[1,6,7,2,5,3,4]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,5,3,6,2,4]=>[1,6,5,2,7,3,4]=>[1,6,7,3,5,4,2]=>{{1},{2,6},{3,7},{4},{5}}
[1,7,5,3,6,4,2]=>[1,4,6,5,7,2,3]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}}
[1,7,5,4,2,3,6]=>[1,4,2,5,7,3,6]=>[1,7,2,4,5,3,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,5,4,2,6,3]=>[1,4,5,7,6,2,3]=>[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}}
[1,7,5,4,3,2,6]=>[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,5,4,3,6,2]=>[1,6,4,5,7,3,2]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[1,7,5,4,6,2,3]=>[1,6,2,5,7,4,3]=>[1,6,2,7,5,3,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,7,5,4,6,3,2]=>[1,3,6,5,7,4,2]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,7,5,6,2,3,4]=>[1,6,2,3,7,5,4]=>[1,7,2,3,6,4,5]=>{{1},{2,7},{3},{4},{5,6}}
[1,7,5,6,2,4,3]=>[1,6,4,2,7,5,3]=>[1,4,7,3,6,2,5]=>{{1},{2,4},{3,7},{5,6}}
[1,7,5,6,3,2,4]=>[1,3,6,2,7,5,4]=>[1,7,3,2,6,4,5]=>{{1},{2,7},{3},{4},{5,6}}
[1,7,5,6,3,4,2]=>[1,4,6,3,7,5,2]=>[1,7,4,2,6,3,5]=>{{1},{2,7},{3,4},{5,6}}
[1,7,5,6,4,2,3]=>[1,4,2,6,7,5,3]=>[1,7,2,4,6,3,5]=>{{1},{2,7},{3},{4},{5,6}}
[1,7,5,6,4,3,2]=>[1,3,4,6,7,5,2]=>[1,7,3,4,6,2,5]=>{{1},{2,7},{3},{4},{5,6}}
[1,7,6,2,3,4,5]=>[1,6,2,3,4,7,5]=>[1,7,2,3,4,6,5]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,2,3,5,4]=>[1,6,2,5,3,7,4]=>[1,5,2,7,4,6,3]=>{{1},{2,5},{3},{4,7},{6}}
[1,7,6,2,4,3,5]=>[1,6,4,2,3,7,5]=>[1,4,7,3,2,6,5]=>{{1},{2,4},{3,7},{5},{6}}
[1,7,6,2,4,5,3]=>[1,6,5,2,4,7,3]=>[1,5,7,3,2,6,4]=>{{1},{2,5},{3,7},{4},{6}}
[1,7,6,2,5,3,4]=>[1,6,5,3,2,7,4]=>[1,5,7,2,4,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[1,7,6,2,5,4,3]=>[1,6,4,5,2,7,3]=>[1,4,7,5,3,6,2]=>{{1},{2,4,5},{3,7},{6}}
[1,7,6,3,2,4,5]=>[1,3,6,2,4,7,5]=>[1,7,3,2,4,6,5]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,3,2,5,4]=>[1,3,6,5,2,7,4]=>[1,5,3,7,4,6,2]=>{{1},{2,5},{3},{4,7},{6}}
[1,7,6,3,4,2,5]=>[1,4,6,3,2,7,5]=>[1,7,4,2,3,6,5]=>{{1},{2,7},{3,4},{5},{6}}
[1,7,6,3,4,5,2]=>[1,5,6,3,4,7,2]=>[1,7,5,2,3,6,4]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,6,3,5,2,4]=>[1,5,6,2,3,7,4]=>[1,7,5,3,4,6,2]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,6,3,5,4,2]=>[1,4,5,6,2,7,3]=>[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}}
[1,7,6,4,2,3,5]=>[1,4,2,6,3,7,5]=>[1,7,2,4,3,6,5]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,4,2,5,3]=>[1,4,6,5,3,7,2]=>[1,7,4,5,2,6,3]=>{{1},{2,7},{3,4,5},{6}}
[1,7,6,4,3,2,5]=>[1,3,4,6,2,7,5]=>[1,7,3,4,2,6,5]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,4,3,5,2]=>[1,5,4,6,3,7,2]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[1,7,6,4,5,2,3]=>[1,5,2,6,4,7,3]=>[1,7,2,5,3,6,4]=>{{1},{2,7},{3},{4,5},{6}}
[1,7,6,4,5,3,2]=>[1,3,5,6,4,7,2]=>[1,7,3,5,2,6,4]=>{{1},{2,7},{3},{4,5},{6}}
[1,7,6,5,2,3,4]=>[1,5,2,3,6,7,4]=>[1,7,2,3,5,6,4]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,5,2,4,3]=>[1,5,4,2,6,7,3]=>[1,4,7,3,5,6,2]=>{{1},{2,4},{3,7},{5},{6}}
[1,7,6,5,3,2,4]=>[1,3,5,2,6,7,4]=>[1,7,3,2,5,6,4]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,5,3,4,2]=>[1,4,5,3,6,7,2]=>[1,7,4,2,5,6,3]=>{{1},{2,7},{3,4},{5},{6}}
[1,7,6,5,4,2,3]=>[1,4,2,5,6,7,3]=>[1,7,2,4,5,6,3]=>{{1},{2,7},{3},{4},{5},{6}}
[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}
[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}
[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}
[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}
[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}
[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,7},{6}}
[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}
[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}
[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}
[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}
[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}
[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,7},{6}}
[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}
[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>{{1,2},{3},{4,6},{5},{7}}
[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}
[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}
[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}}
[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[2,1,3,6,4,7,5]=>{{1,2},{3},{4,6,7},{5}}
[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}
[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>{{1,2},{3},{4,7},{5},{6}}
[2,1,3,7,4,6,5]=>[2,1,3,7,6,4,5]=>[2,1,3,6,7,5,4]=>{{1,2},{3},{4,6},{5,7}}
[2,1,3,7,5,4,6]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>{{1,2},{3},{4,7},{5},{6}}
[2,1,3,7,5,6,4]=>[2,1,3,6,7,5,4]=>[2,1,3,7,6,4,5]=>{{1,2},{3},{4,7},{5,6}}
[2,1,3,7,6,4,5]=>[2,1,3,6,4,7,5]=>[2,1,3,7,4,6,5]=>{{1,2},{3},{4,7},{5},{6}}
[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}}
[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}
[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}
[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}
[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}
[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,7},{6}}
[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}
[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}
[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}
[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}
[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}
[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,7},{6}}
[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}
[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>{{1,2},{3,4,6},{5},{7}}
[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}
[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}
[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}}
[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[2,1,4,6,3,7,5]=>{{1,2},{3,4,6,7},{5}}
[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}
[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>{{1,2},{3,4,7},{5},{6}}
[2,1,4,7,3,6,5]=>[2,1,7,4,6,3,5]=>[2,1,4,6,7,5,3]=>{{1,2},{3,4,6},{5,7}}
[2,1,4,7,5,3,6]=>[2,1,5,4,7,3,6]=>[2,1,4,7,5,3,6]=>{{1,2},{3,4,7},{5},{6}}
[2,1,4,7,5,6,3]=>[2,1,6,4,7,5,3]=>[2,1,4,7,6,3,5]=>{{1,2},{3,4,7},{5,6}}
[2,1,4,7,6,3,5]=>[2,1,6,4,3,7,5]=>[2,1,4,7,3,6,5]=>{{1,2},{3,4,7},{5},{6}}
[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}}
[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>{{1,2},{3,5},{4},{6},{7}}
[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>{{1,2},{3,5},{4},{6,7}}
[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}
[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}
[2,1,5,3,7,4,6]=>[2,1,5,7,3,4,6]=>[2,1,7,5,4,3,6]=>{{1,2},{3,7},{4,5},{6}}
[2,1,5,3,7,6,4]=>[2,1,5,6,3,7,4]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}}
[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}
[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}
[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}}
[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}}
[2,1,5,4,7,3,6]=>[2,1,7,5,4,3,6]=>[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,7},{6}}
[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>[2,1,5,7,3,6,4]=>{{1,2},{3,5},{4,7},{6}}
[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[2,1,5,3,6,4,7]=>{{1,2},{3,5,6},{4},{7}}
[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[2,1,6,5,7,4,3]=>{{1,2},{3,6},{4,5,7}}
[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}
[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[2,1,5,6,7,3,4]=>{{1,2},{3,5,7},{4,6}}
[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[2,1,5,3,6,7,4]=>{{1,2},{3,5,6,7},{4}}
[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}
[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[2,1,5,3,7,4,6]=>{{1,2},{3,5,7},{4},{6}}
[2,1,5,7,3,6,4]=>[2,1,7,6,5,3,4]=>[2,1,5,6,7,4,3]=>{{1,2},{3,5,7},{4,6}}
[2,1,5,7,4,3,6]=>[2,1,4,7,5,3,6]=>[2,1,5,4,7,3,6]=>{{1,2},{3,5,7},{4},{6}}
[2,1,5,7,4,6,3]=>[2,1,6,7,5,4,3]=>[2,1,6,5,7,3,4]=>{{1,2},{3,6},{4,5,7}}
[2,1,5,7,6,3,4]=>[2,1,6,3,5,7,4]=>[2,1,5,3,7,6,4]=>{{1,2},{3,5,7},{4},{6}}
[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}
[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>{{1,2},{3,6},{4},{5},{7}}
[2,1,6,3,4,7,5]=>[2,1,6,3,7,4,5]=>[2,1,7,3,6,5,4]=>{{1,2},{3,7},{4},{5,6}}
[2,1,6,3,5,4,7]=>[2,1,6,5,3,4,7]=>[2,1,5,6,4,3,7]=>{{1,2},{3,5},{4,6},{7}}
[2,1,6,3,5,7,4]=>[2,1,6,7,3,5,4]=>[2,1,7,6,4,3,5]=>{{1,2},{3,7},{4,6},{5}}
[2,1,6,3,7,4,5]=>[2,1,6,7,4,3,5]=>[2,1,7,6,3,5,4]=>{{1,2},{3,7},{4,6},{5}}
[2,1,6,3,7,5,4]=>[2,1,6,5,7,3,4]=>[2,1,6,7,5,4,3]=>{{1,2},{3,6},{4,7},{5}}
[2,1,6,4,3,5,7]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>{{1,2},{3,6},{4},{5},{7}}
[2,1,6,4,3,7,5]=>[2,1,4,6,7,3,5]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}}
[2,1,6,4,5,3,7]=>[2,1,5,6,4,3,7]=>[2,1,6,5,3,4,7]=>{{1,2},{3,6},{4,5},{7}}
[2,1,6,4,5,7,3]=>[2,1,7,6,4,5,3]=>[2,1,6,7,3,4,5]=>{{1,2},{3,6},{4,7},{5}}
[2,1,6,4,7,3,5]=>[2,1,7,6,3,4,5]=>[2,1,6,7,4,5,3]=>{{1,2},{3,6},{4,7},{5}}
[2,1,6,4,7,5,3]=>[2,1,5,7,6,3,4]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}}
[2,1,6,5,3,4,7]=>[2,1,5,3,6,4,7]=>[2,1,6,3,5,4,7]=>{{1,2},{3,6},{4},{5},{7}}
[2,1,6,5,3,7,4]=>[2,1,5,6,7,4,3]=>[2,1,7,6,5,3,4]=>{{1,2},{3,7},{4,6},{5}}
[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}}
[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>[2,1,5,7,6,3,4]=>{{1,2},{3,5,6},{4,7}}
[2,1,6,5,7,3,4]=>[2,1,7,3,6,5,4]=>[2,1,6,3,7,4,5]=>{{1,2},{3,6},{4},{5,7}}
[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>[2,1,6,4,7,3,5]=>{{1,2},{3,6},{4},{5,7}}
[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[2,1,6,3,4,7,5]=>{{1,2},{3,6,7},{4},{5}}
[2,1,6,7,3,5,4]=>[2,1,7,5,3,6,4]=>[2,1,5,6,4,7,3]=>{{1,2},{3,5},{4,6,7}}
[2,1,6,7,4,3,5]=>[2,1,4,7,3,6,5]=>[2,1,6,4,3,7,5]=>{{1,2},{3,6,7},{4},{5}}
[2,1,6,7,4,5,3]=>[2,1,5,7,4,6,3]=>[2,1,6,5,3,7,4]=>{{1,2},{3,6,7},{4,5}}
[2,1,6,7,5,3,4]=>[2,1,5,3,7,6,4]=>[2,1,6,3,5,7,4]=>{{1,2},{3,6,7},{4},{5}}
[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}}
[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,3,4,6,5]=>[2,1,7,3,6,4,5]=>[2,1,6,3,7,5,4]=>{{1,2},{3,6},{4},{5,7}}
[2,1,7,3,5,4,6]=>[2,1,7,5,3,4,6]=>[2,1,5,7,4,3,6]=>{{1,2},{3,5},{4,7},{6}}
[2,1,7,3,5,6,4]=>[2,1,7,6,3,5,4]=>[2,1,6,7,4,3,5]=>{{1,2},{3,6},{4,7},{5}}
[2,1,7,3,6,4,5]=>[2,1,7,6,4,3,5]=>[2,1,6,7,3,5,4]=>{{1,2},{3,6},{4,7},{5}}
[2,1,7,3,6,5,4]=>[2,1,7,5,6,3,4]=>[2,1,5,7,6,4,3]=>{{1,2},{3,5,6},{4,7}}
[2,1,7,4,3,5,6]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,4,3,6,5]=>[2,1,4,7,6,3,5]=>[2,1,6,4,7,5,3]=>{{1,2},{3,6},{4},{5,7}}
[2,1,7,4,5,3,6]=>[2,1,5,7,4,3,6]=>[2,1,7,5,3,4,6]=>{{1,2},{3,7},{4,5},{6}}
[2,1,7,4,5,6,3]=>[2,1,6,7,4,5,3]=>[2,1,7,6,3,4,5]=>{{1,2},{3,7},{4,6},{5}}
[2,1,7,4,6,3,5]=>[2,1,6,7,3,4,5]=>[2,1,7,6,4,5,3]=>{{1,2},{3,7},{4,6},{5}}
[2,1,7,4,6,5,3]=>[2,1,5,6,7,3,4]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}
[2,1,7,5,3,4,6]=>[2,1,5,3,7,4,6]=>[2,1,7,3,5,4,6]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,5,3,6,4]=>[2,1,5,7,6,4,3]=>[2,1,7,5,6,3,4]=>{{1,2},{3,7},{4,5,6}}
[2,1,7,5,4,3,6]=>[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,5,4,6,3]=>[2,1,6,5,7,4,3]=>[2,1,6,7,5,3,4]=>{{1,2},{3,6},{4,7},{5}}
[2,1,7,5,6,3,4]=>[2,1,6,3,7,5,4]=>[2,1,7,3,6,4,5]=>{{1,2},{3,7},{4},{5,6}}
[2,1,7,5,6,4,3]=>[2,1,4,6,7,5,3]=>[2,1,7,4,6,3,5]=>{{1,2},{3,7},{4},{5,6}}
[2,1,7,6,3,4,5]=>[2,1,6,3,4,7,5]=>[2,1,7,3,4,6,5]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,6,3,5,4]=>[2,1,6,5,3,7,4]=>[2,1,5,7,4,6,3]=>{{1,2},{3,5},{4,7},{6}}
[2,1,7,6,4,3,5]=>[2,1,4,6,3,7,5]=>[2,1,7,4,3,6,5]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,6,4,5,3]=>[2,1,5,6,4,7,3]=>[2,1,7,5,3,6,4]=>{{1,2},{3,7},{4,5},{6}}
[2,1,7,6,5,3,4]=>[2,1,5,3,6,7,4]=>[2,1,7,3,5,6,4]=>{{1,2},{3,7},{4},{5},{6}}
[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}}
[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}
[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}
[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}
[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,7},{6}}
[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}
[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}
[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}
[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}
[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}
[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,7},{6}}
[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}
[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>{{1,2,3},{4,6},{5},{7}}
[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}
[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}
[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}
[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[2,3,1,6,4,7,5]=>{{1,2,3},{4,6,7},{5}}
[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}
[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>{{1,2,3},{4,7},{5},{6}}
[2,3,1,7,4,6,5]=>[3,2,1,7,6,4,5]=>[2,3,1,6,7,5,4]=>{{1,2,3},{4,6},{5,7}}
[2,3,1,7,5,4,6]=>[3,2,1,5,7,4,6]=>[2,3,1,7,5,4,6]=>{{1,2,3},{4,7},{5},{6}}
[2,3,1,7,5,6,4]=>[3,2,1,6,7,5,4]=>[2,3,1,7,6,4,5]=>{{1,2,3},{4,7},{5,6}}
[2,3,1,7,6,4,5]=>[3,2,1,6,4,7,5]=>[2,3,1,7,4,6,5]=>{{1,2,3},{4,7},{5},{6}}
[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}
[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,7},{6}}
[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,7},{6}}
[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,6},{5},{7}}
[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}
[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,6,7},{5}}
[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}
[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,7},{5},{6}}
[2,3,4,7,1,6,5]=>[7,2,3,4,6,1,5]=>[2,3,4,6,7,5,1]=>{{1,2,3,4,6},{5,7}}
[2,3,4,7,5,1,6]=>[5,2,3,4,7,1,6]=>[2,3,4,7,5,1,6]=>{{1,2,3,4,7},{5},{6}}
[2,3,4,7,5,6,1]=>[6,2,3,4,7,5,1]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,7},{5,6}}
[2,3,4,7,6,1,5]=>[6,2,3,4,1,7,5]=>[2,3,4,7,1,6,5]=>{{1,2,3,4,7},{5},{6}}
[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[2,3,5,1,4,6,7]=>{{1,2,3,5},{4},{6},{7}}
[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[2,3,5,1,4,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}
[2,3,5,1,7,4,6]=>[5,2,3,7,1,4,6]=>[2,3,7,5,4,1,6]=>{{1,2,3,7},{4,5},{6}}
[2,3,5,1,7,6,4]=>[5,2,3,6,1,7,4]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}
[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}
[2,3,5,4,7,1,6]=>[7,2,3,5,4,1,6]=>[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,7},{6}}
[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>[2,3,5,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}
[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[2,3,5,1,6,4,7]=>{{1,2,3,5,6},{4},{7}}
[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[2,3,6,5,7,4,1]=>{{1,2,3,6},{4,5,7}}
[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}
[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[2,3,5,6,7,1,4]=>{{1,2,3,5,7},{4,6}}
[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[2,3,5,1,6,7,4]=>{{1,2,3,5,6,7},{4}}
[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[2,3,5,1,7,4,6]=>{{1,2,3,5,7},{4},{6}}
[2,3,5,7,1,6,4]=>[7,2,3,6,5,1,4]=>[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}}
[2,3,5,7,4,1,6]=>[4,2,3,7,5,1,6]=>[2,3,5,4,7,1,6]=>{{1,2,3,5,7},{4},{6}}
[2,3,5,7,4,6,1]=>[6,2,3,7,5,4,1]=>[2,3,6,5,7,1,4]=>{{1,2,3,6},{4,5,7}}
[2,3,5,7,6,1,4]=>[6,2,3,1,5,7,4]=>[2,3,5,1,7,6,4]=>{{1,2,3,5,7},{4},{6}}
[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}
[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[2,3,6,1,4,5,7]=>{{1,2,3,6},{4},{5},{7}}
[2,3,6,1,4,7,5]=>[6,2,3,1,7,4,5]=>[2,3,7,1,6,5,4]=>{{1,2,3,7},{4},{5,6}}
[2,3,6,1,5,4,7]=>[6,2,3,5,1,4,7]=>[2,3,5,6,4,1,7]=>{{1,2,3,5},{4,6},{7}}
[2,3,6,1,5,7,4]=>[6,2,3,7,1,5,4]=>[2,3,7,6,4,1,5]=>{{1,2,3,7},{4,6},{5}}
[2,3,6,1,7,4,5]=>[6,2,3,7,4,1,5]=>[2,3,7,6,1,5,4]=>{{1,2,3,7},{4,6},{5}}
[2,3,6,1,7,5,4]=>[6,2,3,5,7,1,4]=>[2,3,6,7,5,4,1]=>{{1,2,3,6},{4,7},{5}}
[2,3,6,4,1,5,7]=>[4,2,3,6,1,5,7]=>[2,3,6,4,1,5,7]=>{{1,2,3,6},{4},{5},{7}}
[2,3,6,4,1,7,5]=>[4,2,3,6,7,1,5]=>[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}
[2,3,6,4,5,1,7]=>[5,2,3,6,4,1,7]=>[2,3,6,5,1,4,7]=>{{1,2,3,6},{4,5},{7}}
[2,3,6,4,5,7,1]=>[7,2,3,6,4,5,1]=>[2,3,6,7,1,4,5]=>{{1,2,3,6},{4,7},{5}}
[2,3,6,4,7,1,5]=>[7,2,3,6,1,4,5]=>[2,3,6,7,4,5,1]=>{{1,2,3,6},{4,7},{5}}
[2,3,6,4,7,5,1]=>[5,2,3,7,6,1,4]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[2,3,6,5,1,4,7]=>[5,2,3,1,6,4,7]=>[2,3,6,1,5,4,7]=>{{1,2,3,6},{4},{5},{7}}
[2,3,6,5,1,7,4]=>[5,2,3,6,7,4,1]=>[2,3,7,6,5,1,4]=>{{1,2,3,7},{4,6},{5}}
[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>[2,3,5,7,6,1,4]=>{{1,2,3,5,6},{4,7}}
[2,3,6,5,7,1,4]=>[7,2,3,1,6,5,4]=>[2,3,6,1,7,4,5]=>{{1,2,3,6},{4},{5,7}}
[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>[2,3,6,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}
[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[2,3,6,1,4,7,5]=>{{1,2,3,6,7},{4},{5}}
[2,3,6,7,1,5,4]=>[7,2,3,5,1,6,4]=>[2,3,5,6,4,7,1]=>{{1,2,3,5},{4,6,7}}
[2,3,6,7,4,1,5]=>[4,2,3,7,1,6,5]=>[2,3,6,4,1,7,5]=>{{1,2,3,6,7},{4},{5}}
[2,3,6,7,4,5,1]=>[5,2,3,7,4,6,1]=>[2,3,6,5,1,7,4]=>{{1,2,3,6,7},{4,5}}
[2,3,6,7,5,1,4]=>[5,2,3,1,7,6,4]=>[2,3,6,1,5,7,4]=>{{1,2,3,6,7},{4},{5}}
[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[2,3,7,1,4,5,6]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,1,4,6,5]=>[7,2,3,1,6,4,5]=>[2,3,6,1,7,5,4]=>{{1,2,3,6},{4},{5,7}}
[2,3,7,1,5,4,6]=>[7,2,3,5,1,4,6]=>[2,3,5,7,4,1,6]=>{{1,2,3,5},{4,7},{6}}
[2,3,7,1,5,6,4]=>[7,2,3,6,1,5,4]=>[2,3,6,7,4,1,5]=>{{1,2,3,6},{4,7},{5}}
[2,3,7,1,6,4,5]=>[7,2,3,6,4,1,5]=>[2,3,6,7,1,5,4]=>{{1,2,3,6},{4,7},{5}}
[2,3,7,1,6,5,4]=>[7,2,3,5,6,1,4]=>[2,3,5,7,6,4,1]=>{{1,2,3,5,6},{4,7}}
[2,3,7,4,1,5,6]=>[4,2,3,7,1,5,6]=>[2,3,7,4,1,5,6]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,4,1,6,5]=>[4,2,3,7,6,1,5]=>[2,3,6,4,7,5,1]=>{{1,2,3,6},{4},{5,7}}
[2,3,7,4,5,1,6]=>[5,2,3,7,4,1,6]=>[2,3,7,5,1,4,6]=>{{1,2,3,7},{4,5},{6}}
[2,3,7,4,5,6,1]=>[6,2,3,7,4,5,1]=>[2,3,7,6,1,4,5]=>{{1,2,3,7},{4,6},{5}}
[2,3,7,4,6,1,5]=>[6,2,3,7,1,4,5]=>[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,6},{5}}
[2,3,7,4,6,5,1]=>[5,2,3,6,7,1,4]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[2,3,7,5,1,4,6]=>[5,2,3,1,7,4,6]=>[2,3,7,1,5,4,6]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,5,1,6,4]=>[5,2,3,7,6,4,1]=>[2,3,7,5,6,1,4]=>{{1,2,3,7},{4,5,6}}
[2,3,7,5,4,1,6]=>[4,2,3,5,7,1,6]=>[2,3,7,4,5,1,6]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,5,4,6,1]=>[6,2,3,5,7,4,1]=>[2,3,6,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}
[2,3,7,5,6,1,4]=>[6,2,3,1,7,5,4]=>[2,3,7,1,6,4,5]=>{{1,2,3,7},{4},{5,6}}
[2,3,7,5,6,4,1]=>[4,2,3,6,7,5,1]=>[2,3,7,4,6,1,5]=>{{1,2,3,7},{4},{5,6}}
[2,3,7,6,1,4,5]=>[6,2,3,1,4,7,5]=>[2,3,7,1,4,6,5]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,6,1,5,4]=>[6,2,3,5,1,7,4]=>[2,3,5,7,4,6,1]=>{{1,2,3,5},{4,7},{6}}
[2,3,7,6,4,1,5]=>[4,2,3,6,1,7,5]=>[2,3,7,4,1,6,5]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,6,4,5,1]=>[5,2,3,6,4,7,1]=>[2,3,7,5,1,6,4]=>{{1,2,3,7},{4,5},{6}}
[2,3,7,6,5,1,4]=>[5,2,3,1,6,7,4]=>[2,3,7,1,5,6,4]=>{{1,2,3,7},{4},{5},{6}}
[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>{{1,2,4},{3},{5,7},{6}}
[2,4,1,3,7,6,5]=>[4,2,1,3,6,7,5]=>[2,4,1,3,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}
[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}
[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}
[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}
[2,4,1,5,7,3,6]=>[4,2,7,1,5,3,6]=>[2,5,4,3,7,1,6]=>{{1,2,5,7},{3,4},{6}}
[2,4,1,5,7,6,3]=>[4,2,6,1,5,7,3]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}
[2,4,1,6,3,5,7]=>[4,2,6,1,3,5,7]=>[2,6,4,3,1,5,7]=>{{1,2,6},{3,4},{5},{7}}
[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}}
[2,4,1,6,5,3,7]=>[4,2,5,1,6,3,7]=>[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}}
[2,4,1,6,5,7,3]=>[4,2,7,1,6,5,3]=>[2,6,4,3,7,1,5]=>{{1,2,6},{3,4},{5,7}}
[2,4,1,6,7,3,5]=>[4,2,7,1,3,6,5]=>[2,6,4,3,1,7,5]=>{{1,2,6,7},{3,4},{5}}
[2,4,1,6,7,5,3]=>[4,2,5,1,7,6,3]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}}
[2,4,1,7,3,5,6]=>[4,2,7,1,3,5,6]=>[2,7,4,3,1,5,6]=>{{1,2,7},{3,4},{5},{6}}
[2,4,1,7,3,6,5]=>[4,2,7,1,6,3,5]=>[2,6,4,3,7,5,1]=>{{1,2,6},{3,4},{5,7}}
[2,4,1,7,5,3,6]=>[4,2,5,1,7,3,6]=>[2,7,4,3,5,1,6]=>{{1,2,7},{3,4},{5},{6}}
[2,4,1,7,5,6,3]=>[4,2,6,1,7,5,3]=>[2,7,4,3,6,1,5]=>{{1,2,7},{3,4},{5,6}}
[2,4,1,7,6,3,5]=>[4,2,6,1,3,7,5]=>[2,7,4,3,1,6,5]=>{{1,2,7},{3,4},{5},{6}}
[2,4,1,7,6,5,3]=>[4,2,5,1,6,7,3]=>[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}}
[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[2,4,3,1,7,5,6]=>[3,2,4,1,7,5,6]=>[2,4,3,1,7,5,6]=>{{1,2,4},{3},{5,7},{6}}
[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}}
[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}}
[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}}
[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}}
[2,4,3,5,7,1,6]=>[7,2,4,3,5,1,6]=>[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,7},{6}}
[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>[2,4,5,1,7,6,3]=>{{1,2,4},{3,5,7},{6}}
[2,4,3,6,1,5,7]=>[6,2,4,3,1,5,7]=>[2,4,6,1,3,5,7]=>{{1,2,4},{3,6},{5},{7}}
[2,4,3,6,1,7,5]=>[6,2,4,3,7,1,5]=>[2,4,7,1,6,5,3]=>{{1,2,4},{3,7},{5,6}}
[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>[2,4,6,1,5,3,7]=>{{1,2,4},{3,6},{5},{7}}
[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}}
[2,4,3,6,7,1,5]=>[7,2,4,3,1,6,5]=>[2,4,6,1,3,7,5]=>{{1,2,4},{3,6,7},{5}}
[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>[2,4,6,1,5,7,3]=>{{1,2,4},{3,6,7},{5}}
[2,4,3,7,1,5,6]=>[7,2,4,3,1,5,6]=>[2,4,7,1,3,5,6]=>{{1,2,4},{3,7},{5},{6}}
[2,4,3,7,1,6,5]=>[7,2,4,3,6,1,5]=>[2,4,6,1,7,5,3]=>{{1,2,4},{3,6},{5,7}}
[2,4,3,7,5,1,6]=>[5,2,4,3,7,1,6]=>[2,4,7,1,5,3,6]=>{{1,2,4},{3,7},{5},{6}}
[2,4,3,7,5,6,1]=>[6,2,4,3,7,5,1]=>[2,4,7,1,6,3,5]=>{{1,2,4},{3,7},{5,6}}
[2,4,3,7,6,1,5]=>[6,2,4,3,1,7,5]=>[2,4,7,1,3,6,5]=>{{1,2,4},{3,7},{5},{6}}
[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>[2,4,7,1,5,6,3]=>{{1,2,4},{3,7},{5},{6}}
[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[2,4,1,5,3,6,7]=>{{1,2,4,5},{3},{6},{7}}
[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[2,4,1,5,3,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[2,5,4,6,3,1,7]=>{{1,2,5},{3,4,6},{7}}
[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[2,5,4,6,3,7,1]=>{{1,2,5},{3,4,6,7}}
[2,4,5,1,7,3,6]=>[5,2,7,4,1,3,6]=>[2,5,4,7,3,1,6]=>{{1,2,5},{3,4,7},{6}}
[2,4,5,1,7,6,3]=>[5,2,6,4,1,7,3]=>[2,5,4,7,3,6,1]=>{{1,2,5},{3,4,7},{6}}
[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[2,4,5,6,1,3,7]=>{{1,2,4,6},{3,5},{7}}
[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[2,4,5,6,1,7,3]=>{{1,2,4,6,7},{3,5}}
[2,4,5,3,7,1,6]=>[7,2,5,4,3,1,6]=>[2,4,5,7,1,3,6]=>{{1,2,4,7},{3,5},{6}}
[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>[2,4,5,7,1,6,3]=>{{1,2,4,7},{3,5},{6}}
[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[2,4,1,5,6,3,7]=>{{1,2,4,5,6},{3},{7}}
[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}}
[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}
[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[2,4,1,5,6,7,3]=>{{1,2,4,5,6,7},{3}}
[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}
[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[2,4,1,5,7,3,6]=>{{1,2,4,5,7},{3},{6}}
[2,4,5,7,1,6,3]=>[7,2,6,4,5,1,3]=>[2,4,5,6,7,3,1]=>{{1,2,4,6},{3,5,7}}
[2,4,5,7,3,1,6]=>[3,2,7,4,5,1,6]=>[2,4,3,5,7,1,6]=>{{1,2,4,5,7},{3},{6}}
[2,4,5,7,3,6,1]=>[6,2,7,4,5,3,1]=>[2,5,4,6,7,1,3]=>{{1,2,5,7},{3,4,6}}
[2,4,5,7,6,1,3]=>[6,2,1,4,5,7,3]=>[2,4,1,5,7,6,3]=>{{1,2,4,5,7},{3},{6}}
[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}
[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[2,4,1,6,3,5,7]=>{{1,2,4,6},{3},{5},{7}}
[2,4,6,1,3,7,5]=>[6,2,1,4,7,3,5]=>[2,4,1,7,6,5,3]=>{{1,2,4,7},{3},{5,6}}
[2,4,6,1,5,3,7]=>[6,2,5,4,1,3,7]=>[2,4,5,6,3,1,7]=>{{1,2,4,6},{3,5},{7}}
[2,4,6,1,5,7,3]=>[6,2,7,4,1,5,3]=>[2,6,4,7,3,1,5]=>{{1,2,6},{3,4,7},{5}}
[2,4,6,1,7,3,5]=>[6,2,7,4,3,1,5]=>[2,6,4,7,1,5,3]=>{{1,2,6},{3,4,7},{5}}
[2,4,6,1,7,5,3]=>[6,2,5,4,7,1,3]=>[2,4,6,7,5,3,1]=>{{1,2,4,7},{3,6},{5}}
[2,4,6,3,1,5,7]=>[3,2,6,4,1,5,7]=>[2,4,3,6,1,5,7]=>{{1,2,4,6},{3},{5},{7}}
[2,4,6,3,1,7,5]=>[3,2,6,4,7,1,5]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}
[2,4,6,3,5,1,7]=>[5,2,6,4,3,1,7]=>[2,5,4,6,1,3,7]=>{{1,2,5},{3,4,6},{7}}
[2,4,6,3,5,7,1]=>[7,2,6,4,3,5,1]=>[2,4,6,7,1,3,5]=>{{1,2,4,7},{3,6},{5}}
[2,4,6,3,7,1,5]=>[7,2,6,4,1,3,5]=>[2,4,6,7,3,5,1]=>{{1,2,4,7},{3,6},{5}}
[2,4,6,3,7,5,1]=>[5,2,7,4,6,1,3]=>[2,5,4,7,6,3,1]=>{{1,2,5,6},{3,4,7}}
[2,4,6,5,1,3,7]=>[5,2,1,4,6,3,7]=>[2,4,1,6,5,3,7]=>{{1,2,4,6},{3},{5},{7}}
[2,4,6,5,1,7,3]=>[5,2,6,4,7,3,1]=>[2,6,4,7,5,1,3]=>{{1,2,6},{3,4,7},{5}}
[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>[2,4,5,7,6,1,3]=>{{1,2,4,7},{3,5,6}}
[2,4,6,5,7,1,3]=>[7,2,1,4,6,5,3]=>[2,4,1,6,7,3,5]=>{{1,2,4,6},{3},{5,7}}
[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>[2,4,3,6,7,1,5]=>{{1,2,4,6},{3},{5,7}}
[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[2,4,1,6,3,7,5]=>{{1,2,4,6,7},{3},{5}}
[2,4,6,7,1,5,3]=>[7,2,5,4,1,6,3]=>[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}}
[2,4,6,7,3,1,5]=>[3,2,7,4,1,6,5]=>[2,4,3,6,1,7,5]=>{{1,2,4,6,7},{3},{5}}
[2,4,6,7,3,5,1]=>[5,2,7,4,3,6,1]=>[2,5,4,6,1,7,3]=>{{1,2,5},{3,4,6,7}}
[2,4,6,7,5,1,3]=>[5,2,1,4,7,6,3]=>[2,4,1,6,5,7,3]=>{{1,2,4,6,7},{3},{5}}
[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[2,4,1,7,3,5,6]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,1,3,6,5]=>[7,2,1,4,6,3,5]=>[2,4,1,6,7,5,3]=>{{1,2,4,6},{3},{5,7}}
[2,4,7,1,5,3,6]=>[7,2,5,4,1,3,6]=>[2,4,5,7,3,1,6]=>{{1,2,4,7},{3,5},{6}}
[2,4,7,1,5,6,3]=>[7,2,6,4,1,5,3]=>[2,4,6,7,3,1,5]=>{{1,2,4,7},{3,6},{5}}
[2,4,7,1,6,3,5]=>[7,2,6,4,3,1,5]=>[2,4,6,7,1,5,3]=>{{1,2,4,7},{3,6},{5}}
[2,4,7,1,6,5,3]=>[7,2,5,4,6,1,3]=>[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}}
[2,4,7,3,1,5,6]=>[3,2,7,4,1,5,6]=>[2,4,3,7,1,5,6]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,3,1,6,5]=>[3,2,7,4,6,1,5]=>[2,4,3,6,7,5,1]=>{{1,2,4,6},{3},{5,7}}
[2,4,7,3,5,1,6]=>[5,2,7,4,3,1,6]=>[2,5,4,7,1,3,6]=>{{1,2,5},{3,4,7},{6}}
[2,4,7,3,5,6,1]=>[6,2,7,4,3,5,1]=>[2,6,4,7,1,3,5]=>{{1,2,6},{3,4,7},{5}}
[2,4,7,3,6,1,5]=>[6,2,7,4,1,3,5]=>[2,6,4,7,3,5,1]=>{{1,2,6},{3,4,7},{5}}
[2,4,7,3,6,5,1]=>[5,2,6,4,7,1,3]=>[2,6,4,7,5,3,1]=>{{1,2,6},{3,4,7},{5}}
[2,4,7,5,1,3,6]=>[5,2,1,4,7,3,6]=>[2,4,1,7,5,3,6]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,5,1,6,3]=>[5,2,7,4,6,3,1]=>[2,5,4,7,6,1,3]=>{{1,2,5,6},{3,4,7}}
[2,4,7,5,3,1,6]=>[3,2,5,4,7,1,6]=>[2,4,3,7,5,1,6]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,5,3,6,1]=>[6,2,5,4,7,3,1]=>[2,4,6,7,5,1,3]=>{{1,2,4,7},{3,6},{5}}
[2,4,7,5,6,1,3]=>[6,2,1,4,7,5,3]=>[2,4,1,7,6,3,5]=>{{1,2,4,7},{3},{5,6}}
[2,4,7,5,6,3,1]=>[3,2,6,4,7,5,1]=>[2,4,3,7,6,1,5]=>{{1,2,4,7},{3},{5,6}}
[2,4,7,6,1,3,5]=>[6,2,1,4,3,7,5]=>[2,4,1,7,3,6,5]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,6,1,5,3]=>[6,2,5,4,1,7,3]=>[2,4,5,7,3,6,1]=>{{1,2,4,7},{3,5},{6}}
[2,4,7,6,3,1,5]=>[3,2,6,4,1,7,5]=>[2,4,3,7,1,6,5]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,6,3,5,1]=>[5,2,6,4,3,7,1]=>[2,5,4,7,1,6,3]=>{{1,2,5},{3,4,7},{6}}
[2,4,7,6,5,1,3]=>[5,2,1,4,6,7,3]=>[2,4,1,7,5,6,3]=>{{1,2,4,7},{3},{5},{6}}
[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,5,1,3,6,4,7]=>[5,2,1,6,3,4,7]=>[2,6,1,5,4,3,7]=>{{1,2,6},{3},{4,5},{7}}
[2,5,1,3,6,7,4]=>[5,2,1,7,3,6,4]=>[2,6,1,5,4,7,3]=>{{1,2,6,7},{3},{4,5}}
[2,5,1,3,7,4,6]=>[5,2,1,7,3,4,6]=>[2,7,1,5,4,3,6]=>{{1,2,7},{3},{4,5},{6}}
[2,5,1,3,7,6,4]=>[5,2,1,6,3,7,4]=>[2,7,1,5,4,6,3]=>{{1,2,7},{3},{4,5},{6}}
[2,5,1,4,3,6,7]=>[5,2,4,1,3,6,7]=>[2,4,5,3,1,6,7]=>{{1,2,4},{3,5},{6},{7}}
[2,5,1,4,3,7,6]=>[5,2,4,1,3,7,6]=>[2,4,5,3,1,7,6]=>{{1,2,4},{3,5},{6,7}}
[2,5,1,4,6,3,7]=>[5,2,6,1,4,3,7]=>[2,6,5,3,1,4,7]=>{{1,2,6},{3,5},{4},{7}}
[2,5,1,4,6,7,3]=>[5,2,7,1,4,6,3]=>[2,6,5,3,1,7,4]=>{{1,2,6,7},{3,5},{4}}
[2,5,1,4,7,3,6]=>[5,2,7,1,4,3,6]=>[2,7,5,3,1,4,6]=>{{1,2,7},{3,5},{4},{6}}
[2,5,1,4,7,6,3]=>[5,2,6,1,4,7,3]=>[2,7,5,3,1,6,4]=>{{1,2,7},{3,5},{4},{6}}
[2,5,1,6,3,4,7]=>[5,2,6,3,1,4,7]=>[2,6,5,1,4,3,7]=>{{1,2,6},{3,5},{4},{7}}
[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}
[2,5,1,6,4,3,7]=>[5,2,4,6,1,3,7]=>[2,5,6,4,3,1,7]=>{{1,2,5},{3,6},{4},{7}}
[2,5,1,6,4,7,3]=>[5,2,7,6,1,4,3]=>[2,7,5,6,4,1,3]=>{{1,2,7},{3,5},{4,6}}
[2,5,1,6,7,3,4]=>[5,2,7,3,1,6,4]=>[2,6,5,1,4,7,3]=>{{1,2,6,7},{3,5},{4}}
[2,5,1,6,7,4,3]=>[5,2,4,7,1,6,3]=>[2,5,6,4,3,7,1]=>{{1,2,5},{3,6,7},{4}}
[2,5,1,7,3,4,6]=>[5,2,7,3,1,4,6]=>[2,7,5,1,4,3,6]=>{{1,2,7},{3,5},{4},{6}}
[2,5,1,7,3,6,4]=>[5,2,7,6,1,3,4]=>[2,7,5,6,4,3,1]=>{{1,2,7},{3,5},{4,6}}
[2,5,1,7,4,3,6]=>[5,2,4,7,1,3,6]=>[2,5,7,4,3,1,6]=>{{1,2,5},{3,7},{4},{6}}
[2,5,1,7,4,6,3]=>[5,2,6,7,1,4,3]=>[2,7,6,5,4,1,3]=>{{1,2,7},{3,6},{4,5}}
[2,5,1,7,6,3,4]=>[5,2,6,3,1,7,4]=>[2,7,5,1,4,6,3]=>{{1,2,7},{3,5},{4},{6}}
[2,5,1,7,6,4,3]=>[5,2,4,6,1,7,3]=>[2,5,7,4,3,6,1]=>{{1,2,5},{3,7},{4},{6}}
[2,5,3,1,4,6,7]=>[3,2,5,1,4,6,7]=>[2,5,3,1,4,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[2,5,3,1,4,7,6]=>[3,2,5,1,4,7,6]=>[2,5,3,1,4,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,5,3,1,6,4,7]=>[3,2,5,6,1,4,7]=>[2,6,3,5,4,1,7]=>{{1,2,6},{3},{4,5},{7}}
[2,5,3,1,6,7,4]=>[3,2,5,7,1,6,4]=>[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}}
[2,5,3,1,7,4,6]=>[3,2,5,7,1,4,6]=>[2,7,3,5,4,1,6]=>{{1,2,7},{3},{4,5},{6}}
[2,5,3,1,7,6,4]=>[3,2,5,6,1,7,4]=>[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}}
[2,5,3,4,1,6,7]=>[4,2,5,3,1,6,7]=>[2,5,4,1,3,6,7]=>{{1,2,5},{3,4},{6},{7}}
[2,5,3,4,1,7,6]=>[4,2,5,3,1,7,6]=>[2,5,4,1,3,7,6]=>{{1,2,5},{3,4},{6,7}}
[2,5,3,4,6,1,7]=>[6,2,5,3,4,1,7]=>[2,5,6,1,3,4,7]=>{{1,2,5},{3,6},{4},{7}}
[2,5,3,4,6,7,1]=>[7,2,5,3,4,6,1]=>[2,5,6,1,3,7,4]=>{{1,2,5},{3,6,7},{4}}
[2,5,3,4,7,1,6]=>[7,2,5,3,4,1,6]=>[2,5,7,1,3,4,6]=>{{1,2,5},{3,7},{4},{6}}
[2,5,3,4,7,6,1]=>[6,2,5,3,4,7,1]=>[2,5,7,1,3,6,4]=>{{1,2,5},{3,7},{4},{6}}
[2,5,3,6,1,4,7]=>[6,2,5,1,3,4,7]=>[2,5,6,3,4,1,7]=>{{1,2,5},{3,6},{4},{7}}
[2,5,3,6,1,7,4]=>[6,2,5,7,3,1,4]=>[2,6,7,5,3,4,1]=>{{1,2,6},{3,7},{4,5}}
[2,5,3,6,4,1,7]=>[4,2,6,5,1,3,7]=>[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}}
[2,5,3,6,4,7,1]=>[7,2,5,6,3,4,1]=>[2,5,7,6,3,1,4]=>{{1,2,5},{3,7},{4,6}}
[2,5,3,6,7,1,4]=>[7,2,5,1,3,6,4]=>[2,5,6,3,4,7,1]=>{{1,2,5},{3,6,7},{4}}
[2,5,3,6,7,4,1]=>[4,2,7,5,1,6,3]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}}
[2,5,3,7,1,4,6]=>[7,2,5,1,3,4,6]=>[2,5,7,3,4,1,6]=>{{1,2,5},{3,7},{4},{6}}
[2,5,3,7,1,6,4]=>[7,2,5,6,3,1,4]=>[2,5,7,6,3,4,1]=>{{1,2,5},{3,7},{4,6}}
[2,5,3,7,4,1,6]=>[4,2,7,5,1,3,6]=>[2,7,4,5,3,1,6]=>{{1,2,7},{3,4,5},{6}}
[2,5,3,7,4,6,1]=>[6,2,5,7,3,4,1]=>[2,6,7,5,3,1,4]=>{{1,2,6},{3,7},{4,5}}
[2,5,3,7,6,1,4]=>[6,2,5,1,3,7,4]=>[2,5,7,3,4,6,1]=>{{1,2,5},{3,7},{4},{6}}
[2,5,3,7,6,4,1]=>[4,2,6,5,1,7,3]=>[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}}
[2,5,4,1,3,6,7]=>[4,2,1,5,3,6,7]=>[2,5,1,4,3,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[2,5,4,1,3,7,6]=>[4,2,1,5,3,7,6]=>[2,5,1,4,3,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,5,4,1,6,3,7]=>[4,2,5,6,3,1,7]=>[2,6,5,4,1,3,7]=>{{1,2,6},{3,5},{4},{7}}
[2,5,4,1,6,7,3]=>[4,2,5,7,3,6,1]=>[2,6,5,4,1,7,3]=>{{1,2,6,7},{3,5},{4}}
[2,5,4,1,7,3,6]=>[4,2,5,7,3,1,6]=>[2,7,5,4,1,3,6]=>{{1,2,7},{3,5},{4},{6}}
[2,5,4,1,7,6,3]=>[4,2,5,6,3,7,1]=>[2,7,5,4,1,6,3]=>{{1,2,7},{3,5},{4},{6}}
[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>[2,4,6,5,1,3,7]=>{{1,2,4,5},{3,6},{7}}
[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>[2,4,6,5,1,7,3]=>{{1,2,4,5},{3,6,7}}
[2,5,4,3,7,1,6]=>[7,2,4,5,3,1,6]=>[2,4,7,5,1,3,6]=>{{1,2,4,5},{3,7},{6}}
[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>[2,4,7,5,1,6,3]=>{{1,2,4,5},{3,7},{6}}
[2,5,4,6,1,3,7]=>[6,2,1,5,4,3,7]=>[2,5,1,6,3,4,7]=>{{1,2,5},{3},{4,6},{7}}
[2,5,4,6,1,7,3]=>[6,2,7,5,4,1,3]=>[2,6,5,7,1,4,3]=>{{1,2,6},{3,5},{4,7}}
[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>[2,5,3,6,1,4,7]=>{{1,2,5},{3},{4,6},{7}}
[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}}
[2,5,4,6,7,1,3]=>[7,2,1,5,4,6,3]=>[2,5,1,6,3,7,4]=>{{1,2,5},{3},{4,6,7}}
[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>[2,5,3,6,1,7,4]=>{{1,2,5},{3},{4,6,7}}
[2,5,4,7,1,3,6]=>[7,2,1,5,4,3,6]=>[2,5,1,7,3,4,6]=>{{1,2,5},{3},{4,7},{6}}
[2,5,4,7,1,6,3]=>[7,2,6,5,4,1,3]=>[2,5,6,7,1,4,3]=>{{1,2,5},{3,6},{4,7}}
[2,5,4,7,3,1,6]=>[3,2,7,5,4,1,6]=>[2,5,3,7,1,4,6]=>{{1,2,5},{3},{4,7},{6}}
[2,5,4,7,3,6,1]=>[6,2,7,5,4,3,1]=>[2,6,5,7,1,3,4]=>{{1,2,6},{3,5},{4,7}}
[2,5,4,7,6,1,3]=>[6,2,1,5,4,7,3]=>[2,5,1,7,3,6,4]=>{{1,2,5},{3},{4,7},{6}}
[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>[2,5,3,7,1,6,4]=>{{1,2,5},{3},{4,7},{6}}
[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[2,5,1,3,6,4,7]=>{{1,2,5,6},{3},{4},{7}}
[2,5,6,1,3,7,4]=>[6,2,1,7,5,3,4]=>[2,6,1,5,7,4,3]=>{{1,2,6},{3},{4,5,7}}
[2,5,6,1,4,3,7]=>[6,2,4,1,5,3,7]=>[2,4,5,3,6,1,7]=>{{1,2,4},{3,5,6},{7}}
[2,5,6,1,4,7,3]=>[6,2,7,1,5,4,3]=>[2,6,5,3,7,1,4]=>{{1,2,6},{3,5,7},{4}}
[2,5,6,1,7,3,4]=>[6,2,7,3,5,1,4]=>[2,6,5,1,7,4,3]=>{{1,2,6},{3,5,7},{4}}
[2,5,6,1,7,4,3]=>[6,2,4,7,5,1,3]=>[2,5,6,4,7,3,1]=>{{1,2,5,7},{3,6},{4}}
[2,5,6,3,1,4,7]=>[3,2,6,1,5,4,7]=>[2,5,3,1,6,4,7]=>{{1,2,5,6},{3},{4},{7}}
[2,5,6,3,1,7,4]=>[3,2,6,7,5,1,4]=>[2,6,3,5,7,4,1]=>{{1,2,6},{3},{4,5,7}}
[2,5,6,3,4,1,7]=>[4,2,6,3,5,1,7]=>[2,5,4,1,6,3,7]=>{{1,2,5,6},{3,4},{7}}
[2,5,6,3,4,7,1]=>[7,2,6,3,5,4,1]=>[2,5,6,1,7,3,4]=>{{1,2,5,7},{3,6},{4}}
[2,5,6,3,7,1,4]=>[7,2,6,1,5,3,4]=>[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,6},{4}}
[2,5,6,3,7,4,1]=>[4,2,7,6,5,1,3]=>[2,6,4,5,7,3,1]=>{{1,2,6},{3,4,5,7}}
[2,5,6,4,1,3,7]=>[4,2,1,6,5,3,7]=>[2,5,1,4,6,3,7]=>{{1,2,5,6},{3},{4},{7}}
[2,5,6,4,1,7,3]=>[4,2,6,7,5,3,1]=>[2,6,5,4,7,1,3]=>{{1,2,6},{3,5,7},{4}}
[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}}
[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>[2,4,6,5,7,1,3]=>{{1,2,4,5,7},{3,6}}
[2,5,6,4,7,1,3]=>[7,2,1,6,5,4,3]=>[2,5,1,6,7,3,4]=>{{1,2,5,7},{3},{4,6}}
[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>[2,5,3,6,7,1,4]=>{{1,2,5,7},{3},{4,6}}
[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[2,5,1,3,6,7,4]=>{{1,2,5,6,7},{3},{4}}
[2,5,6,7,1,4,3]=>[7,2,4,1,5,6,3]=>[2,4,5,3,6,7,1]=>{{1,2,4},{3,5,6,7}}
[2,5,6,7,3,1,4]=>[3,2,7,1,5,6,4]=>[2,5,3,1,6,7,4]=>{{1,2,5,6,7},{3},{4}}
[2,5,6,7,3,4,1]=>[4,2,7,3,5,6,1]=>[2,5,4,1,6,7,3]=>{{1,2,5,6,7},{3,4}}
[2,5,6,7,4,1,3]=>[4,2,1,7,5,6,3]=>[2,5,1,4,6,7,3]=>{{1,2,5,6,7},{3},{4}}
[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}}
[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[2,5,1,3,7,4,6]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,1,3,6,4]=>[7,2,1,6,5,3,4]=>[2,5,1,6,7,4,3]=>{{1,2,5,7},{3},{4,6}}
[2,5,7,1,4,3,6]=>[7,2,4,1,5,3,6]=>[2,4,5,3,7,1,6]=>{{1,2,4},{3,5,7},{6}}
[2,5,7,1,4,6,3]=>[7,2,6,1,5,4,3]=>[2,5,6,3,7,1,4]=>{{1,2,5,7},{3,6},{4}}
[2,5,7,1,6,3,4]=>[7,2,6,3,5,1,4]=>[2,5,6,1,7,4,3]=>{{1,2,5,7},{3,6},{4}}
[2,5,7,1,6,4,3]=>[7,2,4,6,5,1,3]=>[2,4,6,5,7,3,1]=>{{1,2,4,5,7},{3,6}}
[2,5,7,3,1,4,6]=>[3,2,7,1,5,4,6]=>[2,5,3,1,7,4,6]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,3,1,6,4]=>[3,2,7,6,5,1,4]=>[2,5,3,6,7,4,1]=>{{1,2,5,7},{3},{4,6}}
[2,5,7,3,4,1,6]=>[4,2,7,3,5,1,6]=>[2,5,4,1,7,3,6]=>{{1,2,5,7},{3,4},{6}}
[2,5,7,3,4,6,1]=>[6,2,7,3,5,4,1]=>[2,6,5,1,7,3,4]=>{{1,2,6},{3,5,7},{4}}
[2,5,7,3,6,1,4]=>[6,2,7,1,5,3,4]=>[2,6,5,3,7,4,1]=>{{1,2,6},{3,5,7},{4}}
[2,5,7,3,6,4,1]=>[4,2,6,7,5,1,3]=>[2,6,5,4,7,3,1]=>{{1,2,6},{3,5,7},{4}}
[2,5,7,4,1,3,6]=>[4,2,1,7,5,3,6]=>[2,5,1,4,7,3,6]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,4,1,6,3]=>[4,2,7,6,5,3,1]=>[2,6,4,5,7,1,3]=>{{1,2,6},{3,4,5,7}}
[2,5,7,4,3,1,6]=>[3,2,4,7,5,1,6]=>[2,5,3,4,7,1,6]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,4,3,6,1]=>[6,2,4,7,5,3,1]=>[2,5,6,4,7,1,3]=>{{1,2,5,7},{3,6},{4}}
[2,5,7,4,6,1,3]=>[6,2,1,7,5,4,3]=>[2,6,1,5,7,3,4]=>{{1,2,6},{3},{4,5,7}}
[2,5,7,4,6,3,1]=>[3,2,6,7,5,4,1]=>[2,6,3,5,7,1,4]=>{{1,2,6},{3},{4,5,7}}
[2,5,7,6,1,3,4]=>[6,2,1,3,5,7,4]=>[2,5,1,3,7,6,4]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,6,1,4,3]=>[6,2,4,1,5,7,3]=>[2,4,5,3,7,6,1]=>{{1,2,4},{3,5,7},{6}}
[2,5,7,6,3,1,4]=>[3,2,6,1,5,7,4]=>[2,5,3,1,7,6,4]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,6,3,4,1]=>[4,2,6,3,5,7,1]=>[2,5,4,1,7,6,3]=>{{1,2,5,7},{3,4},{6}}
[2,5,7,6,4,1,3]=>[4,2,1,6,5,7,3]=>[2,5,1,4,7,6,3]=>{{1,2,5,7},{3},{4},{6}}
[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}}
[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,1,3,4,7,5]=>[6,2,1,3,7,4,5]=>[2,7,1,3,6,5,4]=>{{1,2,7},{3},{4},{5,6}}
[2,6,1,3,5,4,7]=>[6,2,1,5,3,4,7]=>[2,5,1,6,4,3,7]=>{{1,2,5},{3},{4,6},{7}}
[2,6,1,3,5,7,4]=>[6,2,1,7,3,5,4]=>[2,7,1,6,4,3,5]=>{{1,2,7},{3},{4,6},{5}}
[2,6,1,3,7,4,5]=>[6,2,1,7,4,3,5]=>[2,7,1,6,3,5,4]=>{{1,2,7},{3},{4,6},{5}}
[2,6,1,3,7,5,4]=>[6,2,1,5,7,3,4]=>[2,6,1,7,5,4,3]=>{{1,2,6},{3},{4,7},{5}}
[2,6,1,4,3,5,7]=>[6,2,4,1,3,5,7]=>[2,4,6,3,1,5,7]=>{{1,2,4},{3,6},{5},{7}}
[2,6,1,4,3,7,5]=>[6,2,4,1,7,3,5]=>[2,4,7,3,6,5,1]=>{{1,2,4},{3,7},{5,6}}
[2,6,1,4,5,3,7]=>[6,2,5,1,4,3,7]=>[2,5,6,3,1,4,7]=>{{1,2,5},{3,6},{4},{7}}
[2,6,1,4,5,7,3]=>[6,2,7,1,3,4,5]=>[2,7,6,3,4,5,1]=>{{1,2,7},{3,6},{4},{5}}
[2,6,1,4,7,3,5]=>[6,2,7,1,4,5,3]=>[2,7,6,3,1,4,5]=>{{1,2,7},{3,6},{4},{5}}
[2,6,1,4,7,5,3]=>[6,2,5,1,7,4,3]=>[2,6,7,3,5,1,4]=>{{1,2,6},{3,7},{4},{5}}
[2,6,1,5,3,4,7]=>[6,2,5,3,1,4,7]=>[2,5,6,1,4,3,7]=>{{1,2,5},{3,6},{4},{7}}
[2,6,1,5,3,7,4]=>[6,2,5,7,1,3,4]=>[2,6,7,5,4,3,1]=>{{1,2,6},{3,7},{4,5}}
[2,6,1,5,4,3,7]=>[6,2,4,5,1,3,7]=>[2,4,6,5,3,1,7]=>{{1,2,4,5},{3,6},{7}}
[2,6,1,5,4,7,3]=>[6,2,7,5,1,4,3]=>[2,6,5,7,4,1,3]=>{{1,2,6},{3,5},{4,7}}
[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>[2,7,6,1,4,3,5]=>{{1,2,7},{3,6},{4},{5}}
[2,6,1,5,7,4,3]=>[6,2,4,7,1,5,3]=>[2,6,7,4,3,1,5]=>{{1,2,6},{3,7},{4},{5}}
[2,6,1,7,3,4,5]=>[6,2,7,3,4,1,5]=>[2,7,6,1,3,5,4]=>{{1,2,7},{3,6},{4},{5}}
[2,6,1,7,3,5,4]=>[6,2,7,5,3,1,4]=>[2,6,5,7,3,4,1]=>{{1,2,6},{3,5},{4,7}}
[2,6,1,7,4,3,5]=>[6,2,4,7,3,1,5]=>[2,6,7,4,1,5,3]=>{{1,2,6},{3,7},{4},{5}}
[2,6,1,7,4,5,3]=>[6,2,5,7,4,1,3]=>[2,6,7,5,1,4,3]=>{{1,2,6},{3,7},{4,5}}
[2,6,1,7,5,3,4]=>[6,2,5,3,7,1,4]=>[2,6,7,1,5,4,3]=>{{1,2,6},{3,7},{4},{5}}
[2,6,1,7,5,4,3]=>[6,2,4,5,7,1,3]=>[2,4,7,6,5,3,1]=>{{1,2,4,6},{3,7},{5}}
[2,6,3,1,4,5,7]=>[3,2,6,1,4,5,7]=>[2,6,3,1,4,5,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,3,1,4,7,5]=>[3,2,6,1,7,4,5]=>[2,7,3,1,6,5,4]=>{{1,2,7},{3},{4},{5,6}}
[2,6,3,1,5,4,7]=>[3,2,6,5,1,4,7]=>[2,5,3,6,4,1,7]=>{{1,2,5},{3},{4,6},{7}}
[2,6,3,1,5,7,4]=>[3,2,6,7,1,5,4]=>[2,7,3,6,4,1,5]=>{{1,2,7},{3},{4,6},{5}}
[2,6,3,1,7,4,5]=>[3,2,6,7,4,1,5]=>[2,7,3,6,1,5,4]=>{{1,2,7},{3},{4,6},{5}}
[2,6,3,1,7,5,4]=>[3,2,6,5,7,1,4]=>[2,6,3,7,5,4,1]=>{{1,2,6},{3},{4,7},{5}}
[2,6,3,4,1,5,7]=>[4,2,6,3,1,5,7]=>[2,6,4,1,3,5,7]=>{{1,2,6},{3,4},{5},{7}}
[2,6,3,4,1,7,5]=>[4,2,6,3,7,1,5]=>[2,7,4,1,6,5,3]=>{{1,2,7},{3,4},{5,6}}
[2,6,3,4,5,1,7]=>[5,2,6,3,4,1,7]=>[2,6,5,1,3,4,7]=>{{1,2,6},{3,5},{4},{7}}
[2,6,3,4,5,7,1]=>[7,2,6,3,4,5,1]=>[2,6,7,1,3,4,5]=>{{1,2,6},{3,7},{4},{5}}
[2,6,3,4,7,1,5]=>[7,2,6,3,1,4,5]=>[2,6,7,1,4,5,3]=>{{1,2,6},{3,7},{4},{5}}
[2,6,3,4,7,5,1]=>[5,2,7,3,6,1,4]=>[2,7,5,1,6,4,3]=>{{1,2,7},{3,5,6},{4}}
[2,6,3,5,1,4,7]=>[5,2,6,1,3,4,7]=>[2,6,5,3,4,1,7]=>{{1,2,6},{3,5},{4},{7}}
[2,6,3,5,1,7,4]=>[5,2,6,7,3,1,4]=>[2,7,6,5,3,4,1]=>{{1,2,7},{3,6},{4,5}}
[2,6,3,5,4,1,7]=>[4,2,5,6,1,3,7]=>[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}
[2,6,3,5,4,7,1]=>[7,2,6,5,3,4,1]=>[2,5,6,7,3,1,4]=>{{1,2,5},{3,6},{4,7}}
[2,6,3,5,7,1,4]=>[7,2,6,1,4,3,5]=>[2,6,7,3,1,5,4]=>{{1,2,6},{3,7},{4},{5}}
[2,6,3,5,7,4,1]=>[4,2,7,6,3,1,5]=>[2,7,4,6,1,5,3]=>{{1,2,7},{3,4,6},{5}}
[2,6,3,7,1,4,5]=>[7,2,6,1,3,5,4]=>[2,6,7,3,4,1,5]=>{{1,2,6},{3,7},{4},{5}}
[2,6,3,7,1,5,4]=>[7,2,6,5,1,3,4]=>[2,5,6,7,4,3,1]=>{{1,2,5},{3,6},{4,7}}
[2,6,3,7,4,1,5]=>[4,2,7,6,1,5,3]=>[2,7,4,6,3,1,5]=>{{1,2,7},{3,4,6},{5}}
[2,6,3,7,4,5,1]=>[5,2,6,7,4,3,1]=>[2,7,6,5,1,3,4]=>{{1,2,7},{3,6},{4,5}}
[2,6,3,7,5,1,4]=>[5,2,7,1,6,4,3]=>[2,7,5,3,6,1,4]=>{{1,2,7},{3,5,6},{4}}
[2,6,3,7,5,4,1]=>[4,2,5,7,6,3,1]=>[2,7,5,4,6,1,3]=>{{1,2,7},{3,5,6},{4}}
[2,6,4,1,3,5,7]=>[4,2,1,6,3,5,7]=>[2,6,1,4,3,5,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,4,1,3,7,5]=>[4,2,1,6,7,3,5]=>[2,7,1,4,6,5,3]=>{{1,2,7},{3},{4},{5,6}}
[2,6,4,1,5,3,7]=>[4,2,6,5,3,1,7]=>[2,6,4,5,1,3,7]=>{{1,2,6},{3,4,5},{7}}
[2,6,4,1,5,7,3]=>[4,2,6,7,1,3,5]=>[2,7,6,4,3,5,1]=>{{1,2,7},{3,6},{4},{5}}
[2,6,4,1,7,3,5]=>[4,2,6,7,3,5,1]=>[2,7,6,4,1,3,5]=>{{1,2,7},{3,6},{4},{5}}
[2,6,4,1,7,5,3]=>[4,2,6,5,7,3,1]=>[2,7,4,6,5,1,3]=>{{1,2,7},{3,4,6},{5}}
[2,6,4,3,1,5,7]=>[3,2,4,6,1,5,7]=>[2,6,3,4,1,5,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,4,3,1,7,5]=>[3,2,4,6,7,1,5]=>[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}}
[2,6,4,3,5,1,7]=>[5,2,4,6,3,1,7]=>[2,5,6,4,1,3,7]=>{{1,2,5},{3,6},{4},{7}}
[2,6,4,3,5,7,1]=>[7,2,4,6,3,5,1]=>[2,4,7,6,1,3,5]=>{{1,2,4,6},{3,7},{5}}
[2,6,4,3,7,1,5]=>[7,2,4,6,1,3,5]=>[2,4,7,6,3,5,1]=>{{1,2,4,6},{3,7},{5}}
[2,6,4,3,7,5,1]=>[5,2,4,7,6,1,3]=>[2,5,7,4,6,3,1]=>{{1,2,5,6},{3,7},{4}}
[2,6,4,5,1,3,7]=>[5,2,1,6,4,3,7]=>[2,6,1,5,3,4,7]=>{{1,2,6},{3},{4,5},{7}}
[2,6,4,5,1,7,3]=>[5,2,7,6,4,1,3]=>[2,7,5,6,1,4,3]=>{{1,2,7},{3,5},{4,6}}
[2,6,4,5,3,1,7]=>[3,2,5,6,4,1,7]=>[2,6,3,5,1,4,7]=>{{1,2,6},{3},{4,5},{7}}
[2,6,4,5,3,7,1]=>[7,2,5,6,4,3,1]=>[2,5,7,6,1,3,4]=>{{1,2,5},{3,7},{4,6}}
[2,6,4,5,7,1,3]=>[7,2,1,6,4,5,3]=>[2,6,1,7,3,4,5]=>{{1,2,6},{3},{4,7},{5}}
[2,6,4,5,7,3,1]=>[3,2,7,6,4,5,1]=>[2,6,3,7,1,4,5]=>{{1,2,6},{3},{4,7},{5}}
[2,6,4,7,1,3,5]=>[7,2,1,6,3,4,5]=>[2,6,1,7,4,5,3]=>{{1,2,6},{3},{4,7},{5}}
[2,6,4,7,1,5,3]=>[7,2,5,6,1,4,3]=>[2,5,7,6,4,1,3]=>{{1,2,5},{3,7},{4,6}}
[2,6,4,7,3,1,5]=>[3,2,7,6,1,4,5]=>[2,6,3,7,4,5,1]=>{{1,2,6},{3},{4,7},{5}}
[2,6,4,7,3,5,1]=>[5,2,7,6,3,4,1]=>[2,7,5,6,3,1,4]=>{{1,2,7},{3,5},{4,6}}
[2,6,4,7,5,1,3]=>[5,2,1,7,6,3,4]=>[2,7,1,5,6,4,3]=>{{1,2,7},{3},{4,5,6}}
[2,6,4,7,5,3,1]=>[3,2,5,7,6,1,4]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}}
[2,6,5,1,3,4,7]=>[5,2,1,3,6,4,7]=>[2,6,1,3,5,4,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,5,1,3,7,4]=>[5,2,1,6,7,4,3]=>[2,7,1,6,5,3,4]=>{{1,2,7},{3},{4,6},{5}}
[2,6,5,1,4,3,7]=>[5,2,4,1,6,3,7]=>[2,4,6,3,5,1,7]=>{{1,2,4},{3,6},{5},{7}}
[2,6,5,1,4,7,3]=>[5,2,6,1,7,3,4]=>[2,7,6,3,5,4,1]=>{{1,2,7},{3,6},{4},{5}}
[2,6,5,1,7,3,4]=>[5,2,6,3,7,4,1]=>[2,7,6,1,5,3,4]=>{{1,2,7},{3,6},{4},{5}}
[2,6,5,1,7,4,3]=>[5,2,4,6,7,3,1]=>[2,6,7,4,5,1,3]=>{{1,2,6},{3,7},{4},{5}}
[2,6,5,3,1,4,7]=>[3,2,5,1,6,4,7]=>[2,6,3,1,5,4,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,5,3,1,7,4]=>[3,2,5,6,7,4,1]=>[2,7,3,6,5,1,4]=>{{1,2,7},{3},{4,6},{5}}
[2,6,5,3,4,1,7]=>[4,2,5,3,6,1,7]=>[2,6,4,1,5,3,7]=>{{1,2,6},{3,4},{5},{7}}
[2,6,5,3,4,7,1]=>[7,2,5,3,6,4,1]=>[2,5,7,1,6,3,4]=>{{1,2,5,6},{3,7},{4}}
[2,6,5,3,7,1,4]=>[7,2,5,1,6,3,4]=>[2,5,7,3,6,4,1]=>{{1,2,5,6},{3,7},{4}}
[2,6,5,3,7,4,1]=>[4,2,7,5,6,1,3]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}}
[2,6,5,4,1,3,7]=>[4,2,1,5,6,3,7]=>[2,6,1,4,5,3,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,5,4,1,7,3]=>[4,2,5,6,7,1,3]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}}
[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}}
[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>[2,4,7,5,6,1,3]=>{{1,2,4,5,6},{3,7}}
[2,6,5,4,7,1,3]=>[7,2,1,5,6,4,3]=>[2,5,1,7,6,3,4]=>{{1,2,5,6},{3},{4,7}}
[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>[2,5,3,7,6,1,4]=>{{1,2,5,6},{3},{4,7}}
[2,6,5,7,1,3,4]=>[7,2,1,3,6,5,4]=>[2,6,1,3,7,4,5]=>{{1,2,6},{3},{4},{5,7}}
[2,6,5,7,1,4,3]=>[7,2,4,1,6,5,3]=>[2,4,6,3,7,1,5]=>{{1,2,4},{3,6},{5,7}}
[2,6,5,7,3,1,4]=>[3,2,7,1,6,5,4]=>[2,6,3,1,7,4,5]=>{{1,2,6},{3},{4},{5,7}}
[2,6,5,7,3,4,1]=>[4,2,7,3,6,5,1]=>[2,6,4,1,7,3,5]=>{{1,2,6},{3,4},{5,7}}
[2,6,5,7,4,1,3]=>[4,2,1,7,6,5,3]=>[2,6,1,4,7,3,5]=>{{1,2,6},{3},{4},{5,7}}
[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>[2,6,3,4,7,1,5]=>{{1,2,6},{3},{4},{5,7}}
[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[2,6,1,3,4,7,5]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,1,3,5,4]=>[7,2,1,5,3,6,4]=>[2,5,1,6,4,7,3]=>{{1,2,5},{3},{4,6,7}}
[2,6,7,1,4,3,5]=>[7,2,4,1,3,6,5]=>[2,4,6,3,1,7,5]=>{{1,2,4},{3,6,7},{5}}
[2,6,7,1,4,5,3]=>[7,2,5,1,4,6,3]=>[2,5,6,3,1,7,4]=>{{1,2,5},{3,6,7},{4}}
[2,6,7,1,5,3,4]=>[7,2,5,3,1,6,4]=>[2,5,6,1,4,7,3]=>{{1,2,5},{3,6,7},{4}}
[2,6,7,1,5,4,3]=>[7,2,4,5,1,6,3]=>[2,4,6,5,3,7,1]=>{{1,2,4,5},{3,6,7}}
[2,6,7,3,1,4,5]=>[3,2,7,1,4,6,5]=>[2,6,3,1,4,7,5]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,3,1,5,4]=>[3,2,7,5,1,6,4]=>[2,5,3,6,4,7,1]=>{{1,2,5},{3},{4,6,7}}
[2,6,7,3,4,1,5]=>[4,2,7,3,1,6,5]=>[2,6,4,1,3,7,5]=>{{1,2,6,7},{3,4},{5}}
[2,6,7,3,4,5,1]=>[5,2,7,3,4,6,1]=>[2,6,5,1,3,7,4]=>{{1,2,6,7},{3,5},{4}}
[2,6,7,3,5,1,4]=>[5,2,7,1,3,6,4]=>[2,6,5,3,4,7,1]=>{{1,2,6,7},{3,5},{4}}
[2,6,7,3,5,4,1]=>[4,2,5,7,1,6,3]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}
[2,6,7,4,1,3,5]=>[4,2,1,7,3,6,5]=>[2,6,1,4,3,7,5]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,4,1,5,3]=>[4,2,7,5,3,6,1]=>[2,6,4,5,1,7,3]=>{{1,2,6,7},{3,4,5}}
[2,6,7,4,3,1,5]=>[3,2,4,7,1,6,5]=>[2,6,3,4,1,7,5]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,4,3,5,1]=>[5,2,4,7,3,6,1]=>[2,5,6,4,1,7,3]=>{{1,2,5},{3,6,7},{4}}
[2,6,7,4,5,1,3]=>[5,2,1,7,4,6,3]=>[2,6,1,5,3,7,4]=>{{1,2,6,7},{3},{4,5}}
[2,6,7,4,5,3,1]=>[3,2,5,7,4,6,1]=>[2,6,3,5,1,7,4]=>{{1,2,6,7},{3},{4,5}}
[2,6,7,5,1,3,4]=>[5,2,1,3,7,6,4]=>[2,6,1,3,5,7,4]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,5,1,4,3]=>[5,2,4,1,7,6,3]=>[2,4,6,3,5,7,1]=>{{1,2,4},{3,6,7},{5}}
[2,6,7,5,3,1,4]=>[3,2,5,1,7,6,4]=>[2,6,3,1,5,7,4]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,5,3,4,1]=>[4,2,5,3,7,6,1]=>[2,6,4,1,5,7,3]=>{{1,2,6,7},{3,4},{5}}
[2,6,7,5,4,1,3]=>[4,2,1,5,7,6,3]=>[2,6,1,4,5,7,3]=>{{1,2,6,7},{3},{4},{5}}
[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}}
[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,1,3,4,6,5]=>[7,2,1,3,6,4,5]=>[2,6,1,3,7,5,4]=>{{1,2,6},{3},{4},{5,7}}
[2,7,1,3,5,4,6]=>[7,2,1,5,3,4,6]=>[2,5,1,7,4,3,6]=>{{1,2,5},{3},{4,7},{6}}
[2,7,1,3,5,6,4]=>[7,2,1,6,3,5,4]=>[2,6,1,7,4,3,5]=>{{1,2,6},{3},{4,7},{5}}
[2,7,1,3,6,4,5]=>[7,2,1,6,4,3,5]=>[2,6,1,7,3,5,4]=>{{1,2,6},{3},{4,7},{5}}
[2,7,1,3,6,5,4]=>[7,2,1,5,6,3,4]=>[2,5,1,7,6,4,3]=>{{1,2,5,6},{3},{4,7}}
[2,7,1,4,3,5,6]=>[7,2,4,1,3,5,6]=>[2,4,7,3,1,5,6]=>{{1,2,4},{3,7},{5},{6}}
[2,7,1,4,3,6,5]=>[7,2,4,1,6,3,5]=>[2,4,6,3,7,5,1]=>{{1,2,4},{3,6},{5,7}}
[2,7,1,4,5,3,6]=>[7,2,5,1,4,3,6]=>[2,5,7,3,1,4,6]=>{{1,2,5},{3,7},{4},{6}}
[2,7,1,4,5,6,3]=>[7,2,6,1,3,4,5]=>[2,6,7,3,4,5,1]=>{{1,2,6},{3,7},{4},{5}}
[2,7,1,4,6,3,5]=>[7,2,6,1,4,5,3]=>[2,6,7,3,1,4,5]=>{{1,2,6},{3,7},{4},{5}}
[2,7,1,4,6,5,3]=>[7,2,5,1,6,4,3]=>[2,5,7,3,6,1,4]=>{{1,2,5,6},{3,7},{4}}
[2,7,1,5,3,4,6]=>[7,2,5,3,1,4,6]=>[2,5,7,1,4,3,6]=>{{1,2,5},{3,7},{4},{6}}
[2,7,1,5,3,6,4]=>[7,2,5,6,1,3,4]=>[2,5,7,6,4,3,1]=>{{1,2,5},{3,7},{4,6}}
[2,7,1,5,4,3,6]=>[7,2,4,5,1,3,6]=>[2,4,7,5,3,1,6]=>{{1,2,4,5},{3,7},{6}}
[2,7,1,5,4,6,3]=>[7,2,6,5,1,4,3]=>[2,5,6,7,4,1,3]=>{{1,2,5},{3,6},{4,7}}
[2,7,1,5,6,3,4]=>[7,2,6,3,1,5,4]=>[2,6,7,1,4,3,5]=>{{1,2,6},{3,7},{4},{5}}
[2,7,1,5,6,4,3]=>[7,2,4,6,1,5,3]=>[2,4,7,6,3,1,5]=>{{1,2,4,6},{3,7},{5}}
[2,7,1,6,3,4,5]=>[7,2,6,3,4,1,5]=>[2,6,7,1,3,5,4]=>{{1,2,6},{3,7},{4},{5}}
[2,7,1,6,3,5,4]=>[7,2,6,5,3,1,4]=>[2,5,6,7,3,4,1]=>{{1,2,5},{3,6},{4,7}}
[2,7,1,6,4,3,5]=>[7,2,4,6,3,1,5]=>[2,4,7,6,1,5,3]=>{{1,2,4,6},{3,7},{5}}
[2,7,1,6,4,5,3]=>[7,2,5,6,4,1,3]=>[2,5,7,6,1,4,3]=>{{1,2,5},{3,7},{4,6}}
[2,7,1,6,5,3,4]=>[7,2,5,3,6,1,4]=>[2,5,7,1,6,4,3]=>{{1,2,5,6},{3,7},{4}}
[2,7,1,6,5,4,3]=>[7,2,4,5,6,1,3]=>[2,4,7,5,6,3,1]=>{{1,2,4,5,6},{3,7}}
[2,7,3,1,4,5,6]=>[3,2,7,1,4,5,6]=>[2,7,3,1,4,5,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,3,1,4,6,5]=>[3,2,7,1,6,4,5]=>[2,6,3,1,7,5,4]=>{{1,2,6},{3},{4},{5,7}}
[2,7,3,1,5,4,6]=>[3,2,7,5,1,4,6]=>[2,5,3,7,4,1,6]=>{{1,2,5},{3},{4,7},{6}}
[2,7,3,1,5,6,4]=>[3,2,7,6,1,5,4]=>[2,6,3,7,4,1,5]=>{{1,2,6},{3},{4,7},{5}}
[2,7,3,1,6,4,5]=>[3,2,7,6,4,1,5]=>[2,6,3,7,1,5,4]=>{{1,2,6},{3},{4,7},{5}}
[2,7,3,1,6,5,4]=>[3,2,7,5,6,1,4]=>[2,5,3,7,6,4,1]=>{{1,2,5,6},{3},{4,7}}
[2,7,3,4,1,5,6]=>[4,2,7,3,1,5,6]=>[2,7,4,1,3,5,6]=>{{1,2,7},{3,4},{5},{6}}
[2,7,3,4,1,6,5]=>[4,2,7,3,6,1,5]=>[2,6,4,1,7,5,3]=>{{1,2,6},{3,4},{5,7}}
[2,7,3,4,5,1,6]=>[5,2,7,3,4,1,6]=>[2,7,5,1,3,4,6]=>{{1,2,7},{3,5},{4},{6}}
[2,7,3,4,5,6,1]=>[6,2,7,3,4,5,1]=>[2,7,6,1,3,4,5]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,4,6,1,5]=>[6,2,7,3,1,4,5]=>[2,7,6,1,4,5,3]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,4,6,5,1]=>[5,2,6,3,7,1,4]=>[2,7,6,1,5,4,3]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,5,1,4,6]=>[5,2,7,1,3,4,6]=>[2,7,5,3,4,1,6]=>{{1,2,7},{3,5},{4},{6}}
[2,7,3,5,1,6,4]=>[5,2,7,6,3,1,4]=>[2,7,5,6,3,4,1]=>{{1,2,7},{3,5},{4,6}}
[2,7,3,5,4,1,6]=>[4,2,5,7,1,3,6]=>[2,7,5,4,3,1,6]=>{{1,2,7},{3,5},{4},{6}}
[2,7,3,5,4,6,1]=>[6,2,7,5,3,4,1]=>[2,6,5,7,3,1,4]=>{{1,2,6},{3,5},{4,7}}
[2,7,3,5,6,1,4]=>[6,2,7,1,4,3,5]=>[2,7,6,3,1,5,4]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,5,6,4,1]=>[4,2,6,7,3,1,5]=>[2,7,6,4,1,5,3]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,6,1,4,5]=>[6,2,7,1,3,5,4]=>[2,7,6,3,4,1,5]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,6,1,5,4]=>[6,2,7,5,1,3,4]=>[2,6,5,7,4,3,1]=>{{1,2,6},{3,5},{4,7}}
[2,7,3,6,4,1,5]=>[4,2,6,7,1,5,3]=>[2,7,6,4,3,1,5]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,6,4,5,1]=>[5,2,7,6,4,3,1]=>[2,7,5,6,1,3,4]=>{{1,2,7},{3,5},{4,6}}
[2,7,3,6,5,1,4]=>[5,2,6,1,7,4,3]=>[2,7,6,3,5,1,4]=>{{1,2,7},{3,6},{4},{5}}
[2,7,3,6,5,4,1]=>[4,2,5,6,7,3,1]=>[2,7,6,4,5,1,3]=>{{1,2,7},{3,6},{4},{5}}
[2,7,4,1,3,5,6]=>[4,2,1,7,3,5,6]=>[2,7,1,4,3,5,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,4,1,3,6,5]=>[4,2,1,7,6,3,5]=>[2,6,1,4,7,5,3]=>{{1,2,6},{3},{4},{5,7}}
[2,7,4,1,5,3,6]=>[4,2,7,5,3,1,6]=>[2,7,4,5,1,3,6]=>{{1,2,7},{3,4,5},{6}}
[2,7,4,1,5,6,3]=>[4,2,7,6,1,3,5]=>[2,7,4,6,3,5,1]=>{{1,2,7},{3,4,6},{5}}
[2,7,4,1,6,3,5]=>[4,2,7,6,3,5,1]=>[2,7,4,6,1,3,5]=>{{1,2,7},{3,4,6},{5}}
[2,7,4,1,6,5,3]=>[4,2,7,5,6,3,1]=>[2,7,4,5,6,1,3]=>{{1,2,7},{3,4,5,6}}
[2,7,4,3,1,5,6]=>[3,2,4,7,1,5,6]=>[2,7,3,4,1,5,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,4,3,1,6,5]=>[3,2,4,7,6,1,5]=>[2,6,3,4,7,5,1]=>{{1,2,6},{3},{4},{5,7}}
[2,7,4,3,5,1,6]=>[5,2,4,7,3,1,6]=>[2,5,7,4,1,3,6]=>{{1,2,5},{3,7},{4},{6}}
[2,7,4,3,5,6,1]=>[6,2,4,7,3,5,1]=>[2,6,7,4,1,3,5]=>{{1,2,6},{3,7},{4},{5}}
[2,7,4,3,6,1,5]=>[6,2,4,7,1,3,5]=>[2,6,7,4,3,5,1]=>{{1,2,6},{3,7},{4},{5}}
[2,7,4,3,6,5,1]=>[5,2,4,6,7,1,3]=>[2,6,7,4,5,3,1]=>{{1,2,6},{3,7},{4},{5}}
[2,7,4,5,1,3,6]=>[5,2,1,7,4,3,6]=>[2,7,1,5,3,4,6]=>{{1,2,7},{3},{4,5},{6}}
[2,7,4,5,1,6,3]=>[5,2,6,7,4,1,3]=>[2,7,6,5,1,4,3]=>{{1,2,7},{3,6},{4,5}}
[2,7,4,5,3,1,6]=>[3,2,5,7,4,1,6]=>[2,7,3,5,1,4,6]=>{{1,2,7},{3},{4,5},{6}}
[2,7,4,5,3,6,1]=>[6,2,5,7,4,3,1]=>[2,6,7,5,1,3,4]=>{{1,2,6},{3,7},{4,5}}
[2,7,4,5,6,1,3]=>[6,2,1,7,4,5,3]=>[2,7,1,6,3,4,5]=>{{1,2,7},{3},{4,6},{5}}
[2,7,4,5,6,3,1]=>[3,2,6,7,4,5,1]=>[2,7,3,6,1,4,5]=>{{1,2,7},{3},{4,6},{5}}
[2,7,4,6,1,3,5]=>[6,2,1,7,3,4,5]=>[2,7,1,6,4,5,3]=>{{1,2,7},{3},{4,6},{5}}
[2,7,4,6,1,5,3]=>[6,2,5,7,1,4,3]=>[2,6,7,5,4,1,3]=>{{1,2,6},{3,7},{4,5}}
[2,7,4,6,3,1,5]=>[3,2,6,7,1,4,5]=>[2,7,3,6,4,5,1]=>{{1,2,7},{3},{4,6},{5}}
[2,7,4,6,3,5,1]=>[5,2,6,7,3,4,1]=>[2,7,6,5,3,1,4]=>{{1,2,7},{3,6},{4,5}}
[2,7,4,6,5,1,3]=>[5,2,1,6,7,3,4]=>[2,7,1,6,5,4,3]=>{{1,2,7},{3},{4,6},{5}}
[2,7,4,6,5,3,1]=>[3,2,5,6,7,1,4]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}}
[2,7,5,1,3,4,6]=>[5,2,1,3,7,4,6]=>[2,7,1,3,5,4,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,5,1,3,6,4]=>[5,2,1,7,6,4,3]=>[2,7,1,5,6,3,4]=>{{1,2,7},{3},{4,5,6}}
[2,7,5,1,4,3,6]=>[5,2,4,1,7,3,6]=>[2,4,7,3,5,1,6]=>{{1,2,4},{3,7},{5},{6}}
[2,7,5,1,4,6,3]=>[5,2,7,1,6,3,4]=>[2,7,5,3,6,4,1]=>{{1,2,7},{3,5,6},{4}}
[2,7,5,1,6,3,4]=>[5,2,7,3,6,4,1]=>[2,7,5,1,6,3,4]=>{{1,2,7},{3,5,6},{4}}
[2,7,5,1,6,4,3]=>[5,2,4,7,6,3,1]=>[2,5,7,4,6,1,3]=>{{1,2,5,6},{3,7},{4}}
[2,7,5,3,1,4,6]=>[3,2,5,1,7,4,6]=>[2,7,3,1,5,4,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,5,3,1,6,4]=>[3,2,5,7,6,4,1]=>[2,7,3,5,6,1,4]=>{{1,2,7},{3},{4,5,6}}
[2,7,5,3,4,1,6]=>[4,2,5,3,7,1,6]=>[2,7,4,1,5,3,6]=>{{1,2,7},{3,4},{5},{6}}
[2,7,5,3,4,6,1]=>[6,2,5,3,7,4,1]=>[2,6,7,1,5,3,4]=>{{1,2,6},{3,7},{4},{5}}
[2,7,5,3,6,1,4]=>[6,2,5,1,7,3,4]=>[2,6,7,3,5,4,1]=>{{1,2,6},{3,7},{4},{5}}
[2,7,5,3,6,4,1]=>[4,2,6,5,7,1,3]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}}
[2,7,5,4,1,3,6]=>[4,2,1,5,7,3,6]=>[2,7,1,4,5,3,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,5,4,1,6,3]=>[4,2,5,7,6,1,3]=>[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}}
[2,7,5,4,3,1,6]=>[3,2,4,5,7,1,6]=>[2,7,3,4,5,1,6]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,5,4,3,6,1]=>[6,2,4,5,7,3,1]=>[2,4,7,6,5,1,3]=>{{1,2,4,6},{3,7},{5}}
[2,7,5,4,6,1,3]=>[6,2,1,5,7,4,3]=>[2,6,1,7,5,3,4]=>{{1,2,6},{3},{4,7},{5}}
[2,7,5,4,6,3,1]=>[3,2,6,5,7,4,1]=>[2,6,3,7,5,1,4]=>{{1,2,6},{3},{4,7},{5}}
[2,7,5,6,1,3,4]=>[6,2,1,3,7,5,4]=>[2,7,1,3,6,4,5]=>{{1,2,7},{3},{4},{5,6}}
[2,7,5,6,1,4,3]=>[6,2,4,1,7,5,3]=>[2,4,7,3,6,1,5]=>{{1,2,4},{3,7},{5,6}}
[2,7,5,6,3,1,4]=>[3,2,6,1,7,5,4]=>[2,7,3,1,6,4,5]=>{{1,2,7},{3},{4},{5,6}}
[2,7,5,6,3,4,1]=>[4,2,6,3,7,5,1]=>[2,7,4,1,6,3,5]=>{{1,2,7},{3,4},{5,6}}
[2,7,5,6,4,1,3]=>[4,2,1,6,7,5,3]=>[2,7,1,4,6,3,5]=>{{1,2,7},{3},{4},{5,6}}
[2,7,5,6,4,3,1]=>[3,2,4,6,7,5,1]=>[2,7,3,4,6,1,5]=>{{1,2,7},{3},{4},{5,6}}
[2,7,6,1,3,4,5]=>[6,2,1,3,4,7,5]=>[2,7,1,3,4,6,5]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,1,3,5,4]=>[6,2,1,5,3,7,4]=>[2,5,1,7,4,6,3]=>{{1,2,5},{3},{4,7},{6}}
[2,7,6,1,4,3,5]=>[6,2,4,1,3,7,5]=>[2,4,7,3,1,6,5]=>{{1,2,4},{3,7},{5},{6}}
[2,7,6,1,4,5,3]=>[6,2,5,1,4,7,3]=>[2,5,7,3,1,6,4]=>{{1,2,5},{3,7},{4},{6}}
[2,7,6,1,5,3,4]=>[6,2,5,3,1,7,4]=>[2,5,7,1,4,6,3]=>{{1,2,5},{3,7},{4},{6}}
[2,7,6,1,5,4,3]=>[6,2,4,5,1,7,3]=>[2,4,7,5,3,6,1]=>{{1,2,4,5},{3,7},{6}}
[2,7,6,3,1,4,5]=>[3,2,6,1,4,7,5]=>[2,7,3,1,4,6,5]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,3,1,5,4]=>[3,2,6,5,1,7,4]=>[2,5,3,7,4,6,1]=>{{1,2,5},{3},{4,7},{6}}
[2,7,6,3,4,1,5]=>[4,2,6,3,1,7,5]=>[2,7,4,1,3,6,5]=>{{1,2,7},{3,4},{5},{6}}
[2,7,6,3,4,5,1]=>[5,2,6,3,4,7,1]=>[2,7,5,1,3,6,4]=>{{1,2,7},{3,5},{4},{6}}
[2,7,6,3,5,1,4]=>[5,2,6,1,3,7,4]=>[2,7,5,3,4,6,1]=>{{1,2,7},{3,5},{4},{6}}
[2,7,6,3,5,4,1]=>[4,2,5,6,1,7,3]=>[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}}
[2,7,6,4,1,3,5]=>[4,2,1,6,3,7,5]=>[2,7,1,4,3,6,5]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,4,1,5,3]=>[4,2,6,5,3,7,1]=>[2,7,4,5,1,6,3]=>{{1,2,7},{3,4,5},{6}}
[2,7,6,4,3,1,5]=>[3,2,4,6,1,7,5]=>[2,7,3,4,1,6,5]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,4,3,5,1]=>[5,2,4,6,3,7,1]=>[2,5,7,4,1,6,3]=>{{1,2,5},{3,7},{4},{6}}
[2,7,6,4,5,1,3]=>[5,2,1,6,4,7,3]=>[2,7,1,5,3,6,4]=>{{1,2,7},{3},{4,5},{6}}
[2,7,6,4,5,3,1]=>[3,2,5,6,4,7,1]=>[2,7,3,5,1,6,4]=>{{1,2,7},{3},{4,5},{6}}
[2,7,6,5,1,3,4]=>[5,2,1,3,6,7,4]=>[2,7,1,3,5,6,4]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,5,1,4,3]=>[5,2,4,1,6,7,3]=>[2,4,7,3,5,6,1]=>{{1,2,4},{3,7},{5},{6}}
[2,7,6,5,3,1,4]=>[3,2,5,1,6,7,4]=>[2,7,3,1,5,6,4]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,5,3,4,1]=>[4,2,5,3,6,7,1]=>[2,7,4,1,5,6,3]=>{{1,2,7},{3,4},{5},{6}}
[2,7,6,5,4,1,3]=>[4,2,1,5,6,7,3]=>[2,7,1,4,5,6,3]=>{{1,2,7},{3},{4},{5},{6}}
[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}
[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}
[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}
[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}
[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>{{1,3},{2},{4},{5,7},{6}}
[3,1,2,4,7,6,5]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}
[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}
[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}
[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}
[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[3,1,2,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}
[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>{{1,3},{2},{4,5,7},{6}}
[3,1,2,5,7,6,4]=>[3,1,2,6,5,7,4]=>[3,1,2,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}
[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>{{1,3},{2},{4,6},{5},{7}}
[3,1,2,6,4,7,5]=>[3,1,2,6,7,4,5]=>[3,1,2,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}
[3,1,2,6,5,4,7]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}
[3,1,2,6,5,7,4]=>[3,1,2,7,6,5,4]=>[3,1,2,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}}
[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[3,1,2,6,4,7,5]=>{{1,3},{2},{4,6,7},{5}}
[3,1,2,6,7,5,4]=>[3,1,2,5,7,6,4]=>[3,1,2,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}
[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>{{1,3},{2},{4,7},{5},{6}}
[3,1,2,7,4,6,5]=>[3,1,2,7,6,4,5]=>[3,1,2,6,7,5,4]=>{{1,3},{2},{4,6},{5,7}}
[3,1,2,7,5,4,6]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>{{1,3},{2},{4,7},{5},{6}}
[3,1,2,7,5,6,4]=>[3,1,2,6,7,5,4]=>[3,1,2,7,6,4,5]=>{{1,3},{2},{4,7},{5,6}}
[3,1,2,7,6,4,5]=>[3,1,2,6,4,7,5]=>[3,1,2,7,4,6,5]=>{{1,3},{2},{4,7},{5},{6}}
[3,1,2,7,6,5,4]=>[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}
[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}
[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}
[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}
[3,1,4,2,7,5,6]=>[3,4,1,2,7,5,6]=>[4,3,2,1,7,5,6]=>{{1,4},{2,3},{5,7},{6}}
[3,1,4,2,7,6,5]=>[3,4,1,2,6,7,5]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}
[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}
[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}
[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}
[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}
[3,1,4,5,7,2,6]=>[3,7,1,4,5,2,6]=>[4,3,2,5,7,1,6]=>{{1,4,5,7},{2,3},{6}}
[3,1,4,5,7,6,2]=>[3,6,1,4,5,7,2]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}
[3,1,4,6,2,5,7]=>[3,6,1,4,2,5,7]=>[4,3,2,6,1,5,7]=>{{1,4,6},{2,3},{5},{7}}
[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}
[3,1,4,6,5,2,7]=>[3,5,1,4,6,2,7]=>[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}
[3,1,4,6,5,7,2]=>[3,7,1,4,6,5,2]=>[4,3,2,6,7,1,5]=>{{1,4,6},{2,3},{5,7}}
[3,1,4,6,7,2,5]=>[3,7,1,4,2,6,5]=>[4,3,2,6,1,7,5]=>{{1,4,6,7},{2,3},{5}}
[3,1,4,6,7,5,2]=>[3,5,1,4,7,6,2]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}
[3,1,4,7,2,5,6]=>[3,7,1,4,2,5,6]=>[4,3,2,7,1,5,6]=>{{1,4,7},{2,3},{5},{6}}
[3,1,4,7,2,6,5]=>[3,7,1,4,6,2,5]=>[4,3,2,6,7,5,1]=>{{1,4,6},{2,3},{5,7}}
[3,1,4,7,5,2,6]=>[3,5,1,4,7,2,6]=>[4,3,2,7,5,1,6]=>{{1,4,7},{2,3},{5},{6}}
[3,1,4,7,5,6,2]=>[3,6,1,4,7,5,2]=>[4,3,2,7,6,1,5]=>{{1,4,7},{2,3},{5,6}}
[3,1,4,7,6,2,5]=>[3,6,1,4,2,7,5]=>[4,3,2,7,1,6,5]=>{{1,4,7},{2,3},{5},{6}}
[3,1,4,7,6,5,2]=>[3,5,1,4,6,7,2]=>[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}}
[3,1,5,2,4,6,7]=>[3,5,1,2,4,6,7]=>[5,3,2,1,4,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[3,1,5,2,4,7,6]=>[3,5,1,2,4,7,6]=>[5,3,2,1,4,7,6]=>{{1,5},{2,3},{4},{6,7}}
[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}}
[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}}
[3,1,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>[7,3,2,5,4,1,6]=>{{1,7},{2,3},{4,5},{6}}
[3,1,5,2,7,6,4]=>[3,5,1,6,2,7,4]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}}
[3,1,5,4,2,6,7]=>[3,4,1,5,2,6,7]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[3,1,5,4,2,7,6]=>[3,4,1,5,2,7,6]=>[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}}
[3,1,5,4,6,2,7]=>[3,6,1,5,4,2,7]=>[5,3,2,6,1,4,7]=>{{1,5},{2,3},{4,6},{7}}
[3,1,5,4,6,7,2]=>[3,7,1,5,4,6,2]=>[5,3,2,6,1,7,4]=>{{1,5},{2,3},{4,6,7}}
[3,1,5,4,7,2,6]=>[3,7,1,5,4,2,6]=>[5,3,2,7,1,4,6]=>{{1,5},{2,3},{4,7},{6}}
[3,1,5,4,7,6,2]=>[3,6,1,5,4,7,2]=>[5,3,2,7,1,6,4]=>{{1,5},{2,3},{4,7},{6}}
[3,1,5,6,2,4,7]=>[3,6,1,2,5,4,7]=>[5,3,2,1,6,4,7]=>{{1,5,6},{2,3},{4},{7}}
[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[6,3,2,5,7,4,1]=>{{1,6},{2,3},{4,5,7}}
[3,1,5,6,4,2,7]=>[3,4,1,6,5,2,7]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}
[3,1,5,6,4,7,2]=>[3,7,1,6,5,4,2]=>[5,3,2,6,7,1,4]=>{{1,5,7},{2,3},{4,6}}
[3,1,5,6,7,2,4]=>[3,7,1,2,5,6,4]=>[5,3,2,1,6,7,4]=>{{1,5,6,7},{2,3},{4}}
[3,1,5,6,7,4,2]=>[3,4,1,7,5,6,2]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}
[3,1,5,7,2,4,6]=>[3,7,1,2,5,4,6]=>[5,3,2,1,7,4,6]=>{{1,5,7},{2,3},{4},{6}}
[3,1,5,7,2,6,4]=>[3,7,1,6,5,2,4]=>[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}}
[3,1,5,7,4,2,6]=>[3,4,1,7,5,2,6]=>[5,3,2,4,7,1,6]=>{{1,5,7},{2,3},{4},{6}}
[3,1,5,7,4,6,2]=>[3,6,1,7,5,4,2]=>[6,3,2,5,7,1,4]=>{{1,6},{2,3},{4,5,7}}
[3,1,5,7,6,2,4]=>[3,6,1,2,5,7,4]=>[5,3,2,1,7,6,4]=>{{1,5,7},{2,3},{4},{6}}
[3,1,5,7,6,4,2]=>[3,4,1,6,5,7,2]=>[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}}
[3,1,6,2,4,5,7]=>[3,6,1,2,4,5,7]=>[6,3,2,1,4,5,7]=>{{1,6},{2,3},{4},{5},{7}}
[3,1,6,2,4,7,5]=>[3,6,1,2,7,4,5]=>[7,3,2,1,6,5,4]=>{{1,7},{2,3},{4},{5,6}}
[3,1,6,2,5,4,7]=>[3,6,1,5,2,4,7]=>[5,3,2,6,4,1,7]=>{{1,5},{2,3},{4,6},{7}}
[3,1,6,2,5,7,4]=>[3,6,1,7,2,5,4]=>[7,3,2,6,4,1,5]=>{{1,7},{2,3},{4,6},{5}}
[3,1,6,2,7,4,5]=>[3,6,1,7,4,2,5]=>[7,3,2,6,1,5,4]=>{{1,7},{2,3},{4,6},{5}}
[3,1,6,2,7,5,4]=>[3,6,1,5,7,2,4]=>[6,3,2,7,5,4,1]=>{{1,6},{2,3},{4,7},{5}}
[3,1,6,4,2,5,7]=>[3,4,1,6,2,5,7]=>[6,3,2,4,1,5,7]=>{{1,6},{2,3},{4},{5},{7}}
[3,1,6,4,2,7,5]=>[3,4,1,6,7,2,5]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}}
[3,1,6,4,5,2,7]=>[3,5,1,6,4,2,7]=>[6,3,2,5,1,4,7]=>{{1,6},{2,3},{4,5},{7}}
[3,1,6,4,5,7,2]=>[3,7,1,6,4,5,2]=>[6,3,2,7,1,4,5]=>{{1,6},{2,3},{4,7},{5}}
[3,1,6,4,7,2,5]=>[3,7,1,6,2,4,5]=>[6,3,2,7,4,5,1]=>{{1,6},{2,3},{4,7},{5}}
[3,1,6,4,7,5,2]=>[3,5,1,7,6,2,4]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}}
[3,1,6,5,2,4,7]=>[3,5,1,2,6,4,7]=>[6,3,2,1,5,4,7]=>{{1,6},{2,3},{4},{5},{7}}
[3,1,6,5,2,7,4]=>[3,5,1,6,7,4,2]=>[7,3,2,6,5,1,4]=>{{1,7},{2,3},{4,6},{5}}
[3,1,6,5,4,2,7]=>[3,4,1,5,6,2,7]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}
[3,1,6,5,4,7,2]=>[3,7,1,5,6,4,2]=>[5,3,2,7,6,1,4]=>{{1,5,6},{2,3},{4,7}}
[3,1,6,5,7,2,4]=>[3,7,1,2,6,5,4]=>[6,3,2,1,7,4,5]=>{{1,6},{2,3},{4},{5,7}}
[3,1,6,5,7,4,2]=>[3,4,1,7,6,5,2]=>[6,3,2,4,7,1,5]=>{{1,6},{2,3},{4},{5,7}}
[3,1,6,7,2,4,5]=>[3,7,1,2,4,6,5]=>[6,3,2,1,4,7,5]=>{{1,6,7},{2,3},{4},{5}}
[3,1,6,7,2,5,4]=>[3,7,1,5,2,6,4]=>[5,3,2,6,4,7,1]=>{{1,5},{2,3},{4,6,7}}
[3,1,6,7,4,2,5]=>[3,4,1,7,2,6,5]=>[6,3,2,4,1,7,5]=>{{1,6,7},{2,3},{4},{5}}
[3,1,6,7,4,5,2]=>[3,5,1,7,4,6,2]=>[6,3,2,5,1,7,4]=>{{1,6,7},{2,3},{4,5}}
[3,1,6,7,5,2,4]=>[3,5,1,2,7,6,4]=>[6,3,2,1,5,7,4]=>{{1,6,7},{2,3},{4},{5}}
[3,1,6,7,5,4,2]=>[3,4,1,5,7,6,2]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}
[3,1,7,2,4,5,6]=>[3,7,1,2,4,5,6]=>[7,3,2,1,4,5,6]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,2,4,6,5]=>[3,7,1,2,6,4,5]=>[6,3,2,1,7,5,4]=>{{1,6},{2,3},{4},{5,7}}
[3,1,7,2,5,4,6]=>[3,7,1,5,2,4,6]=>[5,3,2,7,4,1,6]=>{{1,5},{2,3},{4,7},{6}}
[3,1,7,2,5,6,4]=>[3,7,1,6,2,5,4]=>[6,3,2,7,4,1,5]=>{{1,6},{2,3},{4,7},{5}}
[3,1,7,2,6,4,5]=>[3,7,1,6,4,2,5]=>[6,3,2,7,1,5,4]=>{{1,6},{2,3},{4,7},{5}}
[3,1,7,2,6,5,4]=>[3,7,1,5,6,2,4]=>[5,3,2,7,6,4,1]=>{{1,5,6},{2,3},{4,7}}
[3,1,7,4,2,5,6]=>[3,4,1,7,2,5,6]=>[7,3,2,4,1,5,6]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,4,2,6,5]=>[3,4,1,7,6,2,5]=>[6,3,2,4,7,5,1]=>{{1,6},{2,3},{4},{5,7}}
[3,1,7,4,5,2,6]=>[3,5,1,7,4,2,6]=>[7,3,2,5,1,4,6]=>{{1,7},{2,3},{4,5},{6}}
[3,1,7,4,5,6,2]=>[3,6,1,7,4,5,2]=>[7,3,2,6,1,4,5]=>{{1,7},{2,3},{4,6},{5}}
[3,1,7,4,6,2,5]=>[3,6,1,7,2,4,5]=>[7,3,2,6,4,5,1]=>{{1,7},{2,3},{4,6},{5}}
[3,1,7,4,6,5,2]=>[3,5,1,6,7,2,4]=>[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}}
[3,1,7,5,2,4,6]=>[3,5,1,2,7,4,6]=>[7,3,2,1,5,4,6]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,5,2,6,4]=>[3,5,1,7,6,4,2]=>[7,3,2,5,6,1,4]=>{{1,7},{2,3},{4,5,6}}
[3,1,7,5,4,2,6]=>[3,4,1,5,7,2,6]=>[7,3,2,4,5,1,6]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,5,4,6,2]=>[3,6,1,5,7,4,2]=>[6,3,2,7,5,1,4]=>{{1,6},{2,3},{4,7},{5}}
[3,1,7,5,6,2,4]=>[3,6,1,2,7,5,4]=>[7,3,2,1,6,4,5]=>{{1,7},{2,3},{4},{5,6}}
[3,1,7,5,6,4,2]=>[3,4,1,6,7,5,2]=>[7,3,2,4,6,1,5]=>{{1,7},{2,3},{4},{5,6}}
[3,1,7,6,2,4,5]=>[3,6,1,2,4,7,5]=>[7,3,2,1,4,6,5]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,6,2,5,4]=>[3,6,1,5,2,7,4]=>[5,3,2,7,4,6,1]=>{{1,5},{2,3},{4,7},{6}}
[3,1,7,6,4,2,5]=>[3,4,1,6,2,7,5]=>[7,3,2,4,1,6,5]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,6,4,5,2]=>[3,5,1,6,4,7,2]=>[7,3,2,5,1,6,4]=>{{1,7},{2,3},{4,5},{6}}
[3,1,7,6,5,2,4]=>[3,5,1,2,6,7,4]=>[7,3,2,1,5,6,4]=>{{1,7},{2,3},{4},{5},{6}}
[3,1,7,6,5,4,2]=>[3,4,1,5,6,7,2]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}
[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}
[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}
[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}
[3,2,1,4,7,5,6]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>{{1,3},{2},{4},{5,7},{6}}
[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}
[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}
[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}
[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}
[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}
[3,2,1,5,7,4,6]=>[2,3,1,7,5,4,6]=>[3,2,1,5,7,4,6]=>{{1,3},{2},{4,5,7},{6}}
[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}
[3,2,1,6,4,5,7]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>{{1,3},{2},{4,6},{5},{7}}
[3,2,1,6,4,7,5]=>[2,3,1,6,7,4,5]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}
[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}
[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>[3,2,1,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}}
[3,2,1,6,7,4,5]=>[2,3,1,7,4,6,5]=>[3,2,1,6,4,7,5]=>{{1,3},{2},{4,6,7},{5}}
[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}
[3,2,1,7,4,5,6]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>{{1,3},{2},{4,7},{5},{6}}
[3,2,1,7,4,6,5]=>[2,3,1,7,6,4,5]=>[3,2,1,6,7,5,4]=>{{1,3},{2},{4,6},{5,7}}
[3,2,1,7,5,4,6]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>{{1,3},{2},{4,7},{5},{6}}
[3,2,1,7,5,6,4]=>[2,3,1,6,7,5,4]=>[3,2,1,7,6,4,5]=>{{1,3},{2},{4,7},{5,6}}
[3,2,1,7,6,4,5]=>[2,3,1,6,4,7,5]=>[3,2,1,7,4,6,5]=>{{1,3},{2},{4,7},{5},{6}}
[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}
[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}
[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}}
[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}}
[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}}
[3,2,4,1,7,5,6]=>[4,3,2,1,7,5,6]=>[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,7},{6}}
[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>[3,4,1,2,7,6,5]=>{{1,3},{2,4},{5,7},{6}}
[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}}
[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}}
[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}}
[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}}
[3,2,4,5,7,1,6]=>[7,3,2,4,5,1,6]=>[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,7},{6}}
[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>[3,4,1,5,7,6,2]=>{{1,3},{2,4,5,7},{6}}
[3,2,4,6,1,5,7]=>[6,3,2,4,1,5,7]=>[3,4,1,6,2,5,7]=>{{1,3},{2,4,6},{5},{7}}
[3,2,4,6,1,7,5]=>[6,3,2,4,7,1,5]=>[3,4,1,7,6,5,2]=>{{1,3},{2,4,7},{5,6}}
[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>[3,4,1,6,5,2,7]=>{{1,3},{2,4,6},{5},{7}}
[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}}
[3,2,4,6,7,1,5]=>[7,3,2,4,1,6,5]=>[3,4,1,6,2,7,5]=>{{1,3},{2,4,6,7},{5}}
[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>[3,4,1,6,5,7,2]=>{{1,3},{2,4,6,7},{5}}
[3,2,4,7,1,5,6]=>[7,3,2,4,1,5,6]=>[3,4,1,7,2,5,6]=>{{1,3},{2,4,7},{5},{6}}
[3,2,4,7,1,6,5]=>[7,3,2,4,6,1,5]=>[3,4,1,6,7,5,2]=>{{1,3},{2,4,6},{5,7}}
[3,2,4,7,5,1,6]=>[5,3,2,4,7,1,6]=>[3,4,1,7,5,2,6]=>{{1,3},{2,4,7},{5},{6}}
[3,2,4,7,5,6,1]=>[6,3,2,4,7,5,1]=>[3,4,1,7,6,2,5]=>{{1,3},{2,4,7},{5,6}}
[3,2,4,7,6,1,5]=>[6,3,2,4,1,7,5]=>[3,4,1,7,2,6,5]=>{{1,3},{2,4,7},{5},{6}}
[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>[3,4,1,7,5,6,2]=>{{1,3},{2,4,7},{5},{6}}
[3,2,5,1,4,6,7]=>[5,3,2,1,4,6,7]=>[3,5,1,2,4,6,7]=>{{1,3},{2,5},{4},{6},{7}}
[3,2,5,1,4,7,6]=>[5,3,2,1,4,7,6]=>[3,5,1,2,4,7,6]=>{{1,3},{2,5},{4},{6,7}}
[3,2,5,1,6,4,7]=>[5,3,2,6,1,4,7]=>[3,6,1,5,4,2,7]=>{{1,3},{2,6},{4,5},{7}}
[3,2,5,1,6,7,4]=>[5,3,2,7,1,6,4]=>[3,6,1,5,4,7,2]=>{{1,3},{2,6,7},{4,5}}
[3,2,5,1,7,4,6]=>[5,3,2,7,1,4,6]=>[3,7,1,5,4,2,6]=>{{1,3},{2,7},{4,5},{6}}
[3,2,5,1,7,6,4]=>[5,3,2,6,1,7,4]=>[3,7,1,5,4,6,2]=>{{1,3},{2,7},{4,5},{6}}
[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[3,5,1,4,2,6,7]=>{{1,3},{2,5},{4},{6},{7}}
[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>[3,5,1,4,2,7,6]=>{{1,3},{2,5},{4},{6,7}}
[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}}
[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}}
[3,2,5,4,7,1,6]=>[7,3,2,5,4,1,6]=>[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,7},{6}}
[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>[3,5,1,7,2,6,4]=>{{1,3},{2,5},{4,7},{6}}
[3,2,5,6,1,4,7]=>[6,3,2,1,5,4,7]=>[3,5,1,2,6,4,7]=>{{1,3},{2,5,6},{4},{7}}
[3,2,5,6,1,7,4]=>[6,3,2,7,5,1,4]=>[3,6,1,5,7,4,2]=>{{1,3},{2,6},{4,5,7}}
[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>[3,5,1,4,6,2,7]=>{{1,3},{2,5,6},{4},{7}}
[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[3,5,1,6,7,2,4]=>{{1,3},{2,5,7},{4,6}}
[3,2,5,6,7,1,4]=>[7,3,2,1,5,6,4]=>[3,5,1,2,6,7,4]=>{{1,3},{2,5,6,7},{4}}
[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>[3,5,1,4,6,7,2]=>{{1,3},{2,5,6,7},{4}}
[3,2,5,7,1,4,6]=>[7,3,2,1,5,4,6]=>[3,5,1,2,7,4,6]=>{{1,3},{2,5,7},{4},{6}}
[3,2,5,7,1,6,4]=>[7,3,2,6,5,1,4]=>[3,5,1,6,7,4,2]=>{{1,3},{2,5,7},{4,6}}
[3,2,5,7,4,1,6]=>[4,3,2,7,5,1,6]=>[3,5,1,4,7,2,6]=>{{1,3},{2,5,7},{4},{6}}
[3,2,5,7,4,6,1]=>[6,3,2,7,5,4,1]=>[3,6,1,5,7,2,4]=>{{1,3},{2,6},{4,5,7}}
[3,2,5,7,6,1,4]=>[6,3,2,1,5,7,4]=>[3,5,1,2,7,6,4]=>{{1,3},{2,5,7},{4},{6}}
[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>[3,5,1,4,7,6,2]=>{{1,3},{2,5,7},{4},{6}}
[3,2,6,1,4,5,7]=>[6,3,2,1,4,5,7]=>[3,6,1,2,4,5,7]=>{{1,3},{2,6},{4},{5},{7}}
[3,2,6,1,4,7,5]=>[6,3,2,1,7,4,5]=>[3,7,1,2,6,5,4]=>{{1,3},{2,7},{4},{5,6}}
[3,2,6,1,5,4,7]=>[6,3,2,5,1,4,7]=>[3,5,1,6,4,2,7]=>{{1,3},{2,5},{4,6},{7}}
[3,2,6,1,5,7,4]=>[6,3,2,7,1,5,4]=>[3,7,1,6,4,2,5]=>{{1,3},{2,7},{4,6},{5}}
[3,2,6,1,7,4,5]=>[6,3,2,7,4,1,5]=>[3,7,1,6,2,5,4]=>{{1,3},{2,7},{4,6},{5}}
[3,2,6,1,7,5,4]=>[6,3,2,5,7,1,4]=>[3,6,1,7,5,4,2]=>{{1,3},{2,6},{4,7},{5}}
[3,2,6,4,1,5,7]=>[4,3,2,6,1,5,7]=>[3,6,1,4,2,5,7]=>{{1,3},{2,6},{4},{5},{7}}
[3,2,6,4,1,7,5]=>[4,3,2,6,7,1,5]=>[3,7,1,4,6,5,2]=>{{1,3},{2,7},{4},{5,6}}
[3,2,6,4,5,1,7]=>[5,3,2,6,4,1,7]=>[3,6,1,5,2,4,7]=>{{1,3},{2,6},{4,5},{7}}
[3,2,6,4,5,7,1]=>[7,3,2,6,4,5,1]=>[3,6,1,7,2,4,5]=>{{1,3},{2,6},{4,7},{5}}
[3,2,6,4,7,1,5]=>[7,3,2,6,1,4,5]=>[3,6,1,7,4,5,2]=>{{1,3},{2,6},{4,7},{5}}
[3,2,6,4,7,5,1]=>[5,3,2,7,6,1,4]=>[3,7,1,5,6,4,2]=>{{1,3},{2,7},{4,5,6}}
[3,2,6,5,1,4,7]=>[5,3,2,1,6,4,7]=>[3,6,1,2,5,4,7]=>{{1,3},{2,6},{4},{5},{7}}
[3,2,6,5,1,7,4]=>[5,3,2,6,7,4,1]=>[3,7,1,6,5,2,4]=>{{1,3},{2,7},{4,6},{5}}
[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>[3,6,1,4,5,2,7]=>{{1,3},{2,6},{4},{5},{7}}
[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>[3,5,1,7,6,2,4]=>{{1,3},{2,5,6},{4,7}}
[3,2,6,5,7,1,4]=>[7,3,2,1,6,5,4]=>[3,6,1,2,7,4,5]=>{{1,3},{2,6},{4},{5,7}}
[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>[3,6,1,4,7,2,5]=>{{1,3},{2,6},{4},{5,7}}
[3,2,6,7,1,4,5]=>[7,3,2,1,4,6,5]=>[3,6,1,2,4,7,5]=>{{1,3},{2,6,7},{4},{5}}
[3,2,6,7,1,5,4]=>[7,3,2,5,1,6,4]=>[3,5,1,6,4,7,2]=>{{1,3},{2,5},{4,6,7}}
[3,2,6,7,4,1,5]=>[4,3,2,7,1,6,5]=>[3,6,1,4,2,7,5]=>{{1,3},{2,6,7},{4},{5}}
[3,2,6,7,4,5,1]=>[5,3,2,7,4,6,1]=>[3,6,1,5,2,7,4]=>{{1,3},{2,6,7},{4,5}}
[3,2,6,7,5,1,4]=>[5,3,2,1,7,6,4]=>[3,6,1,2,5,7,4]=>{{1,3},{2,6,7},{4},{5}}
[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>[3,6,1,4,5,7,2]=>{{1,3},{2,6,7},{4},{5}}
[3,2,7,1,4,5,6]=>[7,3,2,1,4,5,6]=>[3,7,1,2,4,5,6]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,1,4,6,5]=>[7,3,2,1,6,4,5]=>[3,6,1,2,7,5,4]=>{{1,3},{2,6},{4},{5,7}}
[3,2,7,1,5,4,6]=>[7,3,2,5,1,4,6]=>[3,5,1,7,4,2,6]=>{{1,3},{2,5},{4,7},{6}}
[3,2,7,1,5,6,4]=>[7,3,2,6,1,5,4]=>[3,6,1,7,4,2,5]=>{{1,3},{2,6},{4,7},{5}}
[3,2,7,1,6,4,5]=>[7,3,2,6,4,1,5]=>[3,6,1,7,2,5,4]=>{{1,3},{2,6},{4,7},{5}}
[3,2,7,1,6,5,4]=>[7,3,2,5,6,1,4]=>[3,5,1,7,6,4,2]=>{{1,3},{2,5,6},{4,7}}
[3,2,7,4,1,5,6]=>[4,3,2,7,1,5,6]=>[3,7,1,4,2,5,6]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,4,1,6,5]=>[4,3,2,7,6,1,5]=>[3,6,1,4,7,5,2]=>{{1,3},{2,6},{4},{5,7}}
[3,2,7,4,5,1,6]=>[5,3,2,7,4,1,6]=>[3,7,1,5,2,4,6]=>{{1,3},{2,7},{4,5},{6}}
[3,2,7,4,5,6,1]=>[6,3,2,7,4,5,1]=>[3,7,1,6,2,4,5]=>{{1,3},{2,7},{4,6},{5}}
[3,2,7,4,6,1,5]=>[6,3,2,7,1,4,5]=>[3,7,1,6,4,5,2]=>{{1,3},{2,7},{4,6},{5}}
[3,2,7,4,6,5,1]=>[5,3,2,6,7,1,4]=>[3,7,1,6,5,4,2]=>{{1,3},{2,7},{4,6},{5}}
[3,2,7,5,1,4,6]=>[5,3,2,1,7,4,6]=>[3,7,1,2,5,4,6]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,5,1,6,4]=>[5,3,2,7,6,4,1]=>[3,7,1,5,6,2,4]=>{{1,3},{2,7},{4,5,6}}
[3,2,7,5,4,1,6]=>[4,3,2,5,7,1,6]=>[3,7,1,4,5,2,6]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,5,4,6,1]=>[6,3,2,5,7,4,1]=>[3,6,1,7,5,2,4]=>{{1,3},{2,6},{4,7},{5}}
[3,2,7,5,6,1,4]=>[6,3,2,1,7,5,4]=>[3,7,1,2,6,4,5]=>{{1,3},{2,7},{4},{5,6}}
[3,2,7,5,6,4,1]=>[4,3,2,6,7,5,1]=>[3,7,1,4,6,2,5]=>{{1,3},{2,7},{4},{5,6}}
[3,2,7,6,1,4,5]=>[6,3,2,1,4,7,5]=>[3,7,1,2,4,6,5]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,6,1,5,4]=>[6,3,2,5,1,7,4]=>[3,5,1,7,4,6,2]=>{{1,3},{2,5},{4,7},{6}}
[3,2,7,6,4,1,5]=>[4,3,2,6,1,7,5]=>[3,7,1,4,2,6,5]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,6,4,5,1]=>[5,3,2,6,4,7,1]=>[3,7,1,5,2,6,4]=>{{1,3},{2,7},{4,5},{6}}
[3,2,7,6,5,1,4]=>[5,3,2,1,6,7,4]=>[3,7,1,2,5,6,4]=>{{1,3},{2,7},{4},{5},{6}}
[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>[3,7,1,4,5,6,2]=>{{1,3},{2,7},{4},{5},{6}}
[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[3,1,4,2,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[3,1,4,2,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[3,1,4,2,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[3,1,4,2,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[3,1,4,2,7,5,6]=>{{1,3,4},{2},{5,7},{6}}
[3,4,1,2,7,6,5]=>[4,1,3,2,6,7,5]=>[3,1,4,2,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[4,3,5,2,1,6,7]=>{{1,4},{2,3,5},{6},{7}}
[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[4,3,5,2,1,7,6]=>{{1,4},{2,3,5},{6,7}}
[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[4,3,5,2,6,1,7]=>{{1,4},{2,3,5,6},{7}}
[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[4,3,5,2,6,7,1]=>{{1,4},{2,3,5,6,7}}
[3,4,1,5,7,2,6]=>[4,7,3,1,5,2,6]=>[4,3,5,2,7,1,6]=>{{1,4},{2,3,5,7},{6}}
[3,4,1,5,7,6,2]=>[4,6,3,1,5,7,2]=>[4,3,5,2,7,6,1]=>{{1,4},{2,3,5,7},{6}}
[3,4,1,6,2,5,7]=>[4,6,3,1,2,5,7]=>[4,3,6,2,1,5,7]=>{{1,4},{2,3,6},{5},{7}}
[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[4,3,7,2,6,5,1]=>{{1,4},{2,3,7},{5,6}}
[3,4,1,6,5,2,7]=>[4,5,3,1,6,2,7]=>[4,3,6,2,5,1,7]=>{{1,4},{2,3,6},{5},{7}}
[3,4,1,6,5,7,2]=>[4,7,3,1,6,5,2]=>[4,3,6,2,7,1,5]=>{{1,4},{2,3,6},{5,7}}
[3,4,1,6,7,2,5]=>[4,7,3,1,2,6,5]=>[4,3,6,2,1,7,5]=>{{1,4},{2,3,6,7},{5}}
[3,4,1,6,7,5,2]=>[4,5,3,1,7,6,2]=>[4,3,6,2,5,7,1]=>{{1,4},{2,3,6,7},{5}}
[3,4,1,7,2,5,6]=>[4,7,3,1,2,5,6]=>[4,3,7,2,1,5,6]=>{{1,4},{2,3,7},{5},{6}}
[3,4,1,7,2,6,5]=>[4,7,3,1,6,2,5]=>[4,3,6,2,7,5,1]=>{{1,4},{2,3,6},{5,7}}
[3,4,1,7,5,2,6]=>[4,5,3,1,7,2,6]=>[4,3,7,2,5,1,6]=>{{1,4},{2,3,7},{5},{6}}
[3,4,1,7,5,6,2]=>[4,6,3,1,7,5,2]=>[4,3,7,2,6,1,5]=>{{1,4},{2,3,7},{5,6}}
[3,4,1,7,6,2,5]=>[4,6,3,1,2,7,5]=>[4,3,7,2,1,6,5]=>{{1,4},{2,3,7},{5},{6}}
[3,4,1,7,6,5,2]=>[4,5,3,1,6,7,2]=>[4,3,7,2,5,6,1]=>{{1,4},{2,3,7},{5},{6}}
[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[3,4,2,1,7,5,6]=>[2,4,3,1,7,5,6]=>[3,2,4,1,7,5,6]=>{{1,3,4},{2},{5,7},{6}}
[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[3,4,5,1,2,6,7]=>{{1,3,5},{2,4},{6},{7}}
[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[3,4,5,1,2,7,6]=>{{1,3,5},{2,4},{6,7}}
[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[3,4,5,1,6,2,7]=>{{1,3,5,6},{2,4},{7}}
[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[3,4,5,1,6,7,2]=>{{1,3,5,6,7},{2,4}}
[3,4,2,5,7,1,6]=>[7,4,3,2,5,1,6]=>[3,4,5,1,7,2,6]=>{{1,3,5,7},{2,4},{6}}
[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>[3,4,5,1,7,6,2]=>{{1,3,5,7},{2,4},{6}}
[3,4,2,6,1,5,7]=>[6,4,3,2,1,5,7]=>[3,4,6,1,2,5,7]=>{{1,3,6},{2,4},{5},{7}}
[3,4,2,6,1,7,5]=>[6,4,3,2,7,1,5]=>[3,4,7,1,6,5,2]=>{{1,3,7},{2,4},{5,6}}
[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>[3,4,6,1,5,2,7]=>{{1,3,6},{2,4},{5},{7}}
[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[3,4,6,1,7,2,5]=>{{1,3,6},{2,4},{5,7}}
[3,4,2,6,7,1,5]=>[7,4,3,2,1,6,5]=>[3,4,6,1,2,7,5]=>{{1,3,6,7},{2,4},{5}}
[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>[3,4,6,1,5,7,2]=>{{1,3,6,7},{2,4},{5}}
[3,4,2,7,1,5,6]=>[7,4,3,2,1,5,6]=>[3,4,7,1,2,5,6]=>{{1,3,7},{2,4},{5},{6}}
[3,4,2,7,1,6,5]=>[7,4,3,2,6,1,5]=>[3,4,6,1,7,5,2]=>{{1,3,6},{2,4},{5,7}}
[3,4,2,7,5,1,6]=>[5,4,3,2,7,1,6]=>[3,4,7,1,5,2,6]=>{{1,3,7},{2,4},{5},{6}}
[3,4,2,7,5,6,1]=>[6,4,3,2,7,5,1]=>[3,4,7,1,6,2,5]=>{{1,3,7},{2,4},{5,6}}
[3,4,2,7,6,1,5]=>[6,4,3,2,1,7,5]=>[3,4,7,1,2,6,5]=>{{1,3,7},{2,4},{5},{6}}
[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>[3,4,7,1,5,6,2]=>{{1,3,7},{2,4},{5},{6}}
[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[3,1,4,5,2,6,7]=>{{1,3,4,5},{2},{6},{7}}
[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[3,1,4,5,2,7,6]=>{{1,3,4,5},{2},{6,7}}
[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}
[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}
[3,4,5,1,7,2,6]=>[5,7,3,4,1,2,6]=>[4,3,5,7,2,1,6]=>{{1,4,7},{2,3,5},{6}}
[3,4,5,1,7,6,2]=>[5,6,3,4,1,7,2]=>[4,3,5,7,2,6,1]=>{{1,4,7},{2,3,5},{6}}
[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}
[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}}
[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}
[3,4,5,2,7,1,6]=>[7,5,3,4,2,1,6]=>[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,7},{6}}
[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>[3,4,5,7,1,6,2]=>{{1,3,5},{2,4,7},{6}}
[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[3,1,4,5,6,2,7]=>{{1,3,4,5,6},{2},{7}}
[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[4,3,5,6,7,2,1]=>{{1,4,6},{2,3,5,7}}
[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[3,4,5,6,7,1,2]=>{{1,3,5,7},{2,4,6}}
[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[3,1,4,5,6,7,2]=>{{1,3,4,5,6,7},{2}}
[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}
[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[3,1,4,5,7,2,6]=>{{1,3,4,5,7},{2},{6}}
[3,4,5,7,1,6,2]=>[7,6,3,4,5,1,2]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}
[3,4,5,7,2,1,6]=>[2,7,3,4,5,1,6]=>[3,2,4,5,7,1,6]=>{{1,3,4,5,7},{2},{6}}
[3,4,5,7,2,6,1]=>[6,7,3,4,5,2,1]=>[4,3,5,6,7,1,2]=>{{1,4,6},{2,3,5,7}}
[3,4,5,7,6,1,2]=>[6,1,3,4,5,7,2]=>[3,1,4,5,7,6,2]=>{{1,3,4,5,7},{2},{6}}
[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}
[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[3,1,4,6,2,5,7]=>{{1,3,4,6},{2},{5},{7}}
[3,4,6,1,2,7,5]=>[6,1,3,4,7,2,5]=>[3,1,4,7,6,5,2]=>{{1,3,4,7},{2},{5,6}}
[3,4,6,1,5,2,7]=>[6,5,3,4,1,2,7]=>[3,4,5,6,2,1,7]=>{{1,3,5},{2,4,6},{7}}
[3,4,6,1,5,7,2]=>[6,7,3,4,1,5,2]=>[4,3,6,7,2,1,5]=>{{1,4,7},{2,3,6},{5}}
[3,4,6,1,7,2,5]=>[6,7,3,4,2,1,5]=>[4,3,6,7,1,5,2]=>{{1,4,7},{2,3,6},{5}}
[3,4,6,1,7,5,2]=>[6,5,3,4,7,1,2]=>[3,4,6,7,5,2,1]=>{{1,3,6},{2,4,7},{5}}
[3,4,6,2,1,5,7]=>[2,6,3,4,1,5,7]=>[3,2,4,6,1,5,7]=>{{1,3,4,6},{2},{5},{7}}
[3,4,6,2,1,7,5]=>[2,6,3,4,7,1,5]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}
[3,4,6,2,5,1,7]=>[5,6,3,4,2,1,7]=>[4,3,5,6,1,2,7]=>{{1,4,6},{2,3,5},{7}}
[3,4,6,2,5,7,1]=>[7,6,3,4,2,5,1]=>[3,4,6,7,1,2,5]=>{{1,3,6},{2,4,7},{5}}
[3,4,6,2,7,1,5]=>[7,6,3,4,1,2,5]=>[3,4,6,7,2,5,1]=>{{1,3,6},{2,4,7},{5}}
[3,4,6,2,7,5,1]=>[5,7,3,4,6,1,2]=>[4,3,5,7,6,2,1]=>{{1,4,7},{2,3,5,6}}
[3,4,6,5,1,2,7]=>[5,1,3,4,6,2,7]=>[3,1,4,6,5,2,7]=>{{1,3,4,6},{2},{5},{7}}
[3,4,6,5,1,7,2]=>[5,6,3,4,7,2,1]=>[4,3,6,7,5,1,2]=>{{1,4,7},{2,3,6},{5}}
[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}
[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>[3,4,5,7,6,1,2]=>{{1,3,5,6},{2,4,7}}
[3,4,6,5,7,1,2]=>[7,1,3,4,6,5,2]=>[3,1,4,6,7,2,5]=>{{1,3,4,6},{2},{5,7}}
[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>[3,2,4,6,7,1,5]=>{{1,3,4,6},{2},{5,7}}
[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[3,1,4,6,2,7,5]=>{{1,3,4,6,7},{2},{5}}
[3,4,6,7,1,5,2]=>[7,5,3,4,1,6,2]=>[3,4,5,6,2,7,1]=>{{1,3,5},{2,4,6,7}}
[3,4,6,7,2,1,5]=>[2,7,3,4,1,6,5]=>[3,2,4,6,1,7,5]=>{{1,3,4,6,7},{2},{5}}
[3,4,6,7,2,5,1]=>[5,7,3,4,2,6,1]=>[4,3,5,6,1,7,2]=>{{1,4,6,7},{2,3,5}}
[3,4,6,7,5,1,2]=>[5,1,3,4,7,6,2]=>[3,1,4,6,5,7,2]=>{{1,3,4,6,7},{2},{5}}
[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}
[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[3,1,4,7,2,5,6]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,1,2,6,5]=>[7,1,3,4,6,2,5]=>[3,1,4,6,7,5,2]=>{{1,3,4,6},{2},{5,7}}
[3,4,7,1,5,2,6]=>[7,5,3,4,1,2,6]=>[3,4,5,7,2,1,6]=>{{1,3,5},{2,4,7},{6}}
[3,4,7,1,5,6,2]=>[7,6,3,4,1,5,2]=>[3,4,6,7,2,1,5]=>{{1,3,6},{2,4,7},{5}}
[3,4,7,1,6,2,5]=>[7,6,3,4,2,1,5]=>[3,4,6,7,1,5,2]=>{{1,3,6},{2,4,7},{5}}
[3,4,7,1,6,5,2]=>[7,5,3,4,6,1,2]=>[3,4,5,7,6,2,1]=>{{1,3,5,6},{2,4,7}}
[3,4,7,2,1,5,6]=>[2,7,3,4,1,5,6]=>[3,2,4,7,1,5,6]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,2,1,6,5]=>[2,7,3,4,6,1,5]=>[3,2,4,6,7,5,1]=>{{1,3,4,6},{2},{5,7}}
[3,4,7,2,5,1,6]=>[5,7,3,4,2,1,6]=>[4,3,5,7,1,2,6]=>{{1,4,7},{2,3,5},{6}}
[3,4,7,2,5,6,1]=>[6,7,3,4,2,5,1]=>[4,3,6,7,1,2,5]=>{{1,4,7},{2,3,6},{5}}
[3,4,7,2,6,1,5]=>[6,7,3,4,1,2,5]=>[4,3,6,7,2,5,1]=>{{1,4,7},{2,3,6},{5}}
[3,4,7,2,6,5,1]=>[5,6,3,4,7,1,2]=>[4,3,6,7,5,2,1]=>{{1,4,7},{2,3,6},{5}}
[3,4,7,5,1,2,6]=>[5,1,3,4,7,2,6]=>[3,1,4,7,5,2,6]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,5,1,6,2]=>[5,7,3,4,6,2,1]=>[4,3,5,7,6,1,2]=>{{1,4,7},{2,3,5,6}}
[3,4,7,5,2,1,6]=>[2,5,3,4,7,1,6]=>[3,2,4,7,5,1,6]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,5,2,6,1]=>[6,5,3,4,7,2,1]=>[3,4,6,7,5,1,2]=>{{1,3,6},{2,4,7},{5}}
[3,4,7,5,6,1,2]=>[6,1,3,4,7,5,2]=>[3,1,4,7,6,2,5]=>{{1,3,4,7},{2},{5,6}}
[3,4,7,5,6,2,1]=>[2,6,3,4,7,5,1]=>[3,2,4,7,6,1,5]=>{{1,3,4,7},{2},{5,6}}
[3,4,7,6,1,2,5]=>[6,1,3,4,2,7,5]=>[3,1,4,7,2,6,5]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,6,1,5,2]=>[6,5,3,4,1,7,2]=>[3,4,5,7,2,6,1]=>{{1,3,5},{2,4,7},{6}}
[3,4,7,6,2,1,5]=>[2,6,3,4,1,7,5]=>[3,2,4,7,1,6,5]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,6,2,5,1]=>[5,6,3,4,2,7,1]=>[4,3,5,7,1,6,2]=>{{1,4,7},{2,3,5},{6}}
[3,4,7,6,5,1,2]=>[5,1,3,4,6,7,2]=>[3,1,4,7,5,6,2]=>{{1,3,4,7},{2},{5},{6}}
[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}}
[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[3,1,5,2,4,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[3,1,5,2,4,7,6]=>{{1,3,5},{2},{4},{6,7}}
[3,5,1,2,6,4,7]=>[5,1,3,6,2,4,7]=>[3,1,6,5,4,2,7]=>{{1,3,6},{2},{4,5},{7}}
[3,5,1,2,6,7,4]=>[5,1,3,7,2,6,4]=>[3,1,6,5,4,7,2]=>{{1,3,6,7},{2},{4,5}}
[3,5,1,2,7,4,6]=>[5,1,3,7,2,4,6]=>[3,1,7,5,4,2,6]=>{{1,3,7},{2},{4,5},{6}}
[3,5,1,2,7,6,4]=>[5,1,3,6,2,7,4]=>[3,1,7,5,4,6,2]=>{{1,3,7},{2},{4,5},{6}}
[3,5,1,4,2,6,7]=>[5,4,3,1,2,6,7]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}
[3,5,1,4,2,7,6]=>[5,4,3,1,2,7,6]=>[3,4,5,2,1,7,6]=>{{1,3,5},{2,4},{6,7}}
[3,5,1,4,6,2,7]=>[5,6,3,1,4,2,7]=>[5,3,6,2,1,4,7]=>{{1,5},{2,3,6},{4},{7}}
[3,5,1,4,6,7,2]=>[5,7,3,1,4,6,2]=>[5,3,6,2,1,7,4]=>{{1,5},{2,3,6,7},{4}}
[3,5,1,4,7,2,6]=>[5,7,3,1,4,2,6]=>[5,3,7,2,1,4,6]=>{{1,5},{2,3,7},{4},{6}}
[3,5,1,4,7,6,2]=>[5,6,3,1,4,7,2]=>[5,3,7,2,1,6,4]=>{{1,5},{2,3,7},{4},{6}}
[3,5,1,6,2,4,7]=>[5,6,3,2,1,4,7]=>[5,3,6,1,4,2,7]=>{{1,5},{2,3,6},{4},{7}}
[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[6,3,7,5,4,2,1]=>{{1,6},{2,3,7},{4,5}}
[3,5,1,6,4,2,7]=>[5,4,3,6,1,2,7]=>[3,5,6,4,2,1,7]=>{{1,3,6},{2,5},{4},{7}}
[3,5,1,6,4,7,2]=>[5,7,3,6,1,4,2]=>[5,3,7,6,4,1,2]=>{{1,5},{2,3,7},{4,6}}
[3,5,1,6,7,2,4]=>[5,7,3,2,1,6,4]=>[5,3,6,1,4,7,2]=>{{1,5},{2,3,6,7},{4}}
[3,5,1,6,7,4,2]=>[5,4,3,7,1,6,2]=>[3,5,6,4,2,7,1]=>{{1,3,6,7},{2,5},{4}}
[3,5,1,7,2,4,6]=>[5,7,3,2,1,4,6]=>[5,3,7,1,4,2,6]=>{{1,5},{2,3,7},{4},{6}}
[3,5,1,7,2,6,4]=>[5,7,3,6,1,2,4]=>[5,3,7,6,4,2,1]=>{{1,5},{2,3,7},{4,6}}
[3,5,1,7,4,2,6]=>[5,4,3,7,1,2,6]=>[3,5,7,4,2,1,6]=>{{1,3,7},{2,5},{4},{6}}
[3,5,1,7,4,6,2]=>[5,6,3,7,1,4,2]=>[6,3,7,5,4,1,2]=>{{1,6},{2,3,7},{4,5}}
[3,5,1,7,6,2,4]=>[5,6,3,2,1,7,4]=>[5,3,7,1,4,6,2]=>{{1,5},{2,3,7},{4},{6}}
[3,5,1,7,6,4,2]=>[5,4,3,6,1,7,2]=>[3,5,7,4,2,6,1]=>{{1,3,7},{2,5},{4},{6}}
[3,5,2,1,4,6,7]=>[2,5,3,1,4,6,7]=>[3,2,5,1,4,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[3,5,2,1,4,7,6]=>[2,5,3,1,4,7,6]=>[3,2,5,1,4,7,6]=>{{1,3,5},{2},{4},{6,7}}
[3,5,2,1,6,4,7]=>[2,5,3,6,1,4,7]=>[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}
[3,5,2,1,6,7,4]=>[2,5,3,7,1,6,4]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}
[3,5,2,1,7,4,6]=>[2,5,3,7,1,4,6]=>[3,2,7,5,4,1,6]=>{{1,3,7},{2},{4,5},{6}}
[3,5,2,1,7,6,4]=>[2,5,3,6,1,7,4]=>[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}}
[3,5,2,4,1,6,7]=>[4,5,3,2,1,6,7]=>[4,3,5,1,2,6,7]=>{{1,4},{2,3,5},{6},{7}}
[3,5,2,4,1,7,6]=>[4,5,3,2,1,7,6]=>[4,3,5,1,2,7,6]=>{{1,4},{2,3,5},{6,7}}
[3,5,2,4,6,1,7]=>[6,5,3,2,4,1,7]=>[3,5,6,1,2,4,7]=>{{1,3,6},{2,5},{4},{7}}
[3,5,2,4,6,7,1]=>[7,5,3,2,4,6,1]=>[3,5,6,1,2,7,4]=>{{1,3,6,7},{2,5},{4}}
[3,5,2,4,7,1,6]=>[7,5,3,2,4,1,6]=>[3,5,7,1,2,4,6]=>{{1,3,7},{2,5},{4},{6}}
[3,5,2,4,7,6,1]=>[6,5,3,2,4,7,1]=>[3,5,7,1,2,6,4]=>{{1,3,7},{2,5},{4},{6}}
[3,5,2,6,1,4,7]=>[6,5,3,1,2,4,7]=>[3,5,6,2,4,1,7]=>{{1,3,6},{2,5},{4},{7}}
[3,5,2,6,1,7,4]=>[6,5,3,7,2,1,4]=>[3,6,7,5,2,4,1]=>{{1,3,7},{2,6},{4,5}}
[3,5,2,6,4,1,7]=>[4,6,3,5,1,2,7]=>[4,3,6,5,2,1,7]=>{{1,4,5},{2,3,6},{7}}
[3,5,2,6,4,7,1]=>[7,5,3,6,2,4,1]=>[3,5,7,6,2,1,4]=>{{1,3,7},{2,5},{4,6}}
[3,5,2,6,7,1,4]=>[7,5,3,1,2,6,4]=>[3,5,6,2,4,7,1]=>{{1,3,6,7},{2,5},{4}}
[3,5,2,6,7,4,1]=>[4,7,3,5,1,6,2]=>[4,3,6,5,2,7,1]=>{{1,4,5},{2,3,6,7}}
[3,5,2,7,1,4,6]=>[7,5,3,1,2,4,6]=>[3,5,7,2,4,1,6]=>{{1,3,7},{2,5},{4},{6}}
[3,5,2,7,1,6,4]=>[7,5,3,6,2,1,4]=>[3,5,7,6,2,4,1]=>{{1,3,7},{2,5},{4,6}}
[3,5,2,7,4,1,6]=>[4,7,3,5,1,2,6]=>[4,3,7,5,2,1,6]=>{{1,4,5},{2,3,7},{6}}
[3,5,2,7,4,6,1]=>[6,5,3,7,2,4,1]=>[3,6,7,5,2,1,4]=>{{1,3,7},{2,6},{4,5}}
[3,5,2,7,6,1,4]=>[6,5,3,1,2,7,4]=>[3,5,7,2,4,6,1]=>{{1,3,7},{2,5},{4},{6}}
[3,5,2,7,6,4,1]=>[4,6,3,5,1,7,2]=>[4,3,7,5,2,6,1]=>{{1,4,5},{2,3,7},{6}}
[3,5,4,1,2,6,7]=>[4,1,3,5,2,6,7]=>[3,1,5,4,2,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[3,5,4,1,2,7,6]=>[4,1,3,5,2,7,6]=>[3,1,5,4,2,7,6]=>{{1,3,5},{2},{4},{6,7}}
[3,5,4,1,6,2,7]=>[4,5,3,6,2,1,7]=>[5,3,6,4,1,2,7]=>{{1,5},{2,3,6},{4},{7}}
[3,5,4,1,6,7,2]=>[4,5,3,7,2,6,1]=>[5,3,6,4,1,7,2]=>{{1,5},{2,3,6,7},{4}}
[3,5,4,1,7,2,6]=>[4,5,3,7,2,1,6]=>[5,3,7,4,1,2,6]=>{{1,5},{2,3,7},{4},{6}}
[3,5,4,1,7,6,2]=>[4,5,3,6,2,7,1]=>[5,3,7,4,1,6,2]=>{{1,5},{2,3,7},{4},{6}}
[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}
[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>[3,4,6,5,1,2,7]=>{{1,3,6},{2,4,5},{7}}
[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>[3,4,6,5,1,7,2]=>{{1,3,6,7},{2,4,5}}
[3,5,4,2,7,1,6]=>[7,4,3,5,2,1,6]=>[3,4,7,5,1,2,6]=>{{1,3,7},{2,4,5},{6}}
[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>[3,4,7,5,1,6,2]=>{{1,3,7},{2,4,5},{6}}
[3,5,4,6,1,2,7]=>[6,1,3,5,4,2,7]=>[3,1,5,6,2,4,7]=>{{1,3,5},{2},{4,6},{7}}
[3,5,4,6,1,7,2]=>[6,7,3,5,4,1,2]=>[5,3,6,7,1,4,2]=>{{1,5},{2,3,6},{4,7}}
[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>[3,2,5,6,1,4,7]=>{{1,3,5},{2},{4,6},{7}}
[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[3,5,6,7,1,2,4]=>{{1,3,6},{2,5},{4,7}}
[3,5,4,6,7,1,2]=>[7,1,3,5,4,6,2]=>[3,1,5,6,2,7,4]=>{{1,3,5},{2},{4,6,7}}
[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>[3,2,5,6,1,7,4]=>{{1,3,5},{2},{4,6,7}}
[3,5,4,7,1,2,6]=>[7,1,3,5,4,2,6]=>[3,1,5,7,2,4,6]=>{{1,3,5},{2},{4,7},{6}}
[3,5,4,7,1,6,2]=>[7,6,3,5,4,1,2]=>[3,5,6,7,1,4,2]=>{{1,3,6},{2,5},{4,7}}
[3,5,4,7,2,1,6]=>[2,7,3,5,4,1,6]=>[3,2,5,7,1,4,6]=>{{1,3,5},{2},{4,7},{6}}
[3,5,4,7,2,6,1]=>[6,7,3,5,4,2,1]=>[5,3,6,7,1,2,4]=>{{1,5},{2,3,6},{4,7}}
[3,5,4,7,6,1,2]=>[6,1,3,5,4,7,2]=>[3,1,5,7,2,6,4]=>{{1,3,5},{2},{4,7},{6}}
[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>[3,2,5,7,1,6,4]=>{{1,3,5},{2},{4,7},{6}}
[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[3,1,5,2,6,4,7]=>{{1,3,5,6},{2},{4},{7}}
[3,5,6,1,2,7,4]=>[6,1,3,7,5,2,4]=>[3,1,6,5,7,4,2]=>{{1,3,6},{2},{4,5,7}}
[3,5,6,1,4,2,7]=>[6,4,3,1,5,2,7]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}
[3,5,6,1,4,7,2]=>[6,7,3,1,5,4,2]=>[5,3,6,2,7,1,4]=>{{1,5,7},{2,3,6},{4}}
[3,5,6,1,7,2,4]=>[6,7,3,2,5,1,4]=>[5,3,6,1,7,4,2]=>{{1,5,7},{2,3,6},{4}}
[3,5,6,1,7,4,2]=>[6,4,3,7,5,1,2]=>[3,5,6,4,7,2,1]=>{{1,3,6},{2,5,7},{4}}
[3,5,6,2,1,4,7]=>[2,6,3,1,5,4,7]=>[3,2,5,1,6,4,7]=>{{1,3,5,6},{2},{4},{7}}
[3,5,6,2,1,7,4]=>[2,6,3,7,5,1,4]=>[3,2,6,5,7,4,1]=>{{1,3,6},{2},{4,5,7}}
[3,5,6,2,4,1,7]=>[4,6,3,2,5,1,7]=>[4,3,5,1,6,2,7]=>{{1,4},{2,3,5,6},{7}}
[3,5,6,2,4,7,1]=>[7,6,3,2,5,4,1]=>[3,5,6,1,7,2,4]=>{{1,3,6},{2,5,7},{4}}
[3,5,6,2,7,1,4]=>[7,6,3,1,5,2,4]=>[3,5,6,2,7,4,1]=>{{1,3,6},{2,5,7},{4}}
[3,5,6,2,7,4,1]=>[4,7,3,6,5,1,2]=>[4,3,6,5,7,2,1]=>{{1,4,5,7},{2,3,6}}
[3,5,6,4,1,2,7]=>[4,1,3,6,5,2,7]=>[3,1,5,4,6,2,7]=>{{1,3,5,6},{2},{4},{7}}
[3,5,6,4,1,7,2]=>[4,6,3,7,5,2,1]=>[5,3,6,4,7,1,2]=>{{1,5,7},{2,3,6},{4}}
[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}
[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>[3,4,6,5,7,1,2]=>{{1,3,6},{2,4,5,7}}
[3,5,6,4,7,1,2]=>[7,1,3,6,5,4,2]=>[3,1,5,6,7,2,4]=>{{1,3,5,7},{2},{4,6}}
[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>[3,2,5,6,7,1,4]=>{{1,3,5,7},{2},{4,6}}
[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[3,1,5,2,6,7,4]=>{{1,3,5,6,7},{2},{4}}
[3,5,6,7,1,4,2]=>[7,4,3,1,5,6,2]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}
[3,5,6,7,2,1,4]=>[2,7,3,1,5,6,4]=>[3,2,5,1,6,7,4]=>{{1,3,5,6,7},{2},{4}}
[3,5,6,7,2,4,1]=>[4,7,3,2,5,6,1]=>[4,3,5,1,6,7,2]=>{{1,4},{2,3,5,6,7}}
[3,5,6,7,4,1,2]=>[4,1,3,7,5,6,2]=>[3,1,5,4,6,7,2]=>{{1,3,5,6,7},{2},{4}}
[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}
[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[3,1,5,2,7,4,6]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,1,2,6,4]=>[7,1,3,6,5,2,4]=>[3,1,5,6,7,4,2]=>{{1,3,5,7},{2},{4,6}}
[3,5,7,1,4,2,6]=>[7,4,3,1,5,2,6]=>[3,4,5,2,7,1,6]=>{{1,3,5,7},{2,4},{6}}
[3,5,7,1,4,6,2]=>[7,6,3,1,5,4,2]=>[3,5,6,2,7,1,4]=>{{1,3,6},{2,5,7},{4}}
[3,5,7,1,6,2,4]=>[7,6,3,2,5,1,4]=>[3,5,6,1,7,4,2]=>{{1,3,6},{2,5,7},{4}}
[3,5,7,1,6,4,2]=>[7,4,3,6,5,1,2]=>[3,4,6,5,7,2,1]=>{{1,3,6},{2,4,5,7}}
[3,5,7,2,1,4,6]=>[2,7,3,1,5,4,6]=>[3,2,5,1,7,4,6]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,2,1,6,4]=>[2,7,3,6,5,1,4]=>[3,2,5,6,7,4,1]=>{{1,3,5,7},{2},{4,6}}
[3,5,7,2,4,1,6]=>[4,7,3,2,5,1,6]=>[4,3,5,1,7,2,6]=>{{1,4},{2,3,5,7},{6}}
[3,5,7,2,4,6,1]=>[6,7,3,2,5,4,1]=>[5,3,6,1,7,2,4]=>{{1,5,7},{2,3,6},{4}}
[3,5,7,2,6,1,4]=>[6,7,3,1,5,2,4]=>[5,3,6,2,7,4,1]=>{{1,5,7},{2,3,6},{4}}
[3,5,7,2,6,4,1]=>[4,6,3,7,5,1,2]=>[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}}
[3,5,7,4,1,2,6]=>[4,1,3,7,5,2,6]=>[3,1,5,4,7,2,6]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,4,1,6,2]=>[4,7,3,6,5,2,1]=>[4,3,6,5,7,1,2]=>{{1,4,5,7},{2,3,6}}
[3,5,7,4,2,1,6]=>[2,4,3,7,5,1,6]=>[3,2,5,4,7,1,6]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,4,2,6,1]=>[6,4,3,7,5,2,1]=>[3,5,6,4,7,1,2]=>{{1,3,6},{2,5,7},{4}}
[3,5,7,4,6,1,2]=>[6,1,3,7,5,4,2]=>[3,1,6,5,7,2,4]=>{{1,3,6},{2},{4,5,7}}
[3,5,7,4,6,2,1]=>[2,6,3,7,5,4,1]=>[3,2,6,5,7,1,4]=>{{1,3,6},{2},{4,5,7}}
[3,5,7,6,1,2,4]=>[6,1,3,2,5,7,4]=>[3,1,5,2,7,6,4]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,6,1,4,2]=>[6,4,3,1,5,7,2]=>[3,4,5,2,7,6,1]=>{{1,3,5,7},{2,4},{6}}
[3,5,7,6,2,1,4]=>[2,6,3,1,5,7,4]=>[3,2,5,1,7,6,4]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,6,2,4,1]=>[4,6,3,2,5,7,1]=>[4,3,5,1,7,6,2]=>{{1,4},{2,3,5,7},{6}}
[3,5,7,6,4,1,2]=>[4,1,3,6,5,7,2]=>[3,1,5,4,7,6,2]=>{{1,3,5,7},{2},{4},{6}}
[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}
[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[3,1,6,2,4,5,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,1,2,4,7,5]=>[6,1,3,2,7,4,5]=>[3,1,7,2,6,5,4]=>{{1,3,7},{2},{4},{5,6}}
[3,6,1,2,5,4,7]=>[6,1,3,5,2,4,7]=>[3,1,5,6,4,2,7]=>{{1,3,5},{2},{4,6},{7}}
[3,6,1,2,5,7,4]=>[6,1,3,7,2,5,4]=>[3,1,7,6,4,2,5]=>{{1,3,7},{2},{4,6},{5}}
[3,6,1,2,7,4,5]=>[6,1,3,7,4,2,5]=>[3,1,7,6,2,5,4]=>{{1,3,7},{2},{4,6},{5}}
[3,6,1,2,7,5,4]=>[6,1,3,5,7,2,4]=>[3,1,6,7,5,4,2]=>{{1,3,6},{2},{4,7},{5}}
[3,6,1,4,2,5,7]=>[6,4,3,1,2,5,7]=>[3,4,6,2,1,5,7]=>{{1,3,6},{2,4},{5},{7}}
[3,6,1,4,2,7,5]=>[6,4,3,1,7,2,5]=>[3,4,7,2,6,5,1]=>{{1,3,7},{2,4},{5,6}}
[3,6,1,4,5,2,7]=>[6,5,3,1,4,2,7]=>[3,5,6,2,1,4,7]=>{{1,3,6},{2,5},{4},{7}}
[3,6,1,4,5,7,2]=>[6,7,3,1,2,4,5]=>[6,3,7,2,4,5,1]=>{{1,6},{2,3,7},{4},{5}}
[3,6,1,4,7,2,5]=>[6,7,3,1,4,5,2]=>[6,3,7,2,1,4,5]=>{{1,6},{2,3,7},{4},{5}}
[3,6,1,4,7,5,2]=>[6,5,3,1,7,4,2]=>[3,6,7,2,5,1,4]=>{{1,3,7},{2,6},{4},{5}}
[3,6,1,5,2,4,7]=>[6,5,3,2,1,4,7]=>[3,5,6,1,4,2,7]=>{{1,3,6},{2,5},{4},{7}}
[3,6,1,5,2,7,4]=>[6,5,3,7,1,2,4]=>[3,6,7,5,4,2,1]=>{{1,3,7},{2,6},{4,5}}
[3,6,1,5,4,2,7]=>[6,4,3,5,1,2,7]=>[3,4,6,5,2,1,7]=>{{1,3,6},{2,4,5},{7}}
[3,6,1,5,4,7,2]=>[6,7,3,5,1,4,2]=>[5,3,6,7,4,1,2]=>{{1,5},{2,3,6},{4,7}}
[3,6,1,5,7,2,4]=>[6,7,3,2,1,5,4]=>[6,3,7,1,4,2,5]=>{{1,6},{2,3,7},{4},{5}}
[3,6,1,5,7,4,2]=>[6,4,3,7,1,5,2]=>[3,6,7,4,2,1,5]=>{{1,3,7},{2,6},{4},{5}}
[3,6,1,7,2,4,5]=>[6,7,3,2,4,1,5]=>[6,3,7,1,2,5,4]=>{{1,6},{2,3,7},{4},{5}}
[3,6,1,7,2,5,4]=>[6,7,3,5,2,1,4]=>[5,3,6,7,2,4,1]=>{{1,5},{2,3,6},{4,7}}
[3,6,1,7,4,2,5]=>[6,4,3,7,2,1,5]=>[3,6,7,4,1,5,2]=>{{1,3,7},{2,6},{4},{5}}
[3,6,1,7,4,5,2]=>[6,5,3,7,4,1,2]=>[3,6,7,5,1,4,2]=>{{1,3,7},{2,6},{4,5}}
[3,6,1,7,5,2,4]=>[6,5,3,2,7,1,4]=>[3,6,7,1,5,4,2]=>{{1,3,7},{2,6},{4},{5}}
[3,6,1,7,5,4,2]=>[6,4,3,5,7,1,2]=>[3,4,7,6,5,2,1]=>{{1,3,7},{2,4,6},{5}}
[3,6,2,1,4,5,7]=>[2,6,3,1,4,5,7]=>[3,2,6,1,4,5,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,2,1,4,7,5]=>[2,6,3,1,7,4,5]=>[3,2,7,1,6,5,4]=>{{1,3,7},{2},{4},{5,6}}
[3,6,2,1,5,4,7]=>[2,6,3,5,1,4,7]=>[3,2,5,6,4,1,7]=>{{1,3,5},{2},{4,6},{7}}
[3,6,2,1,5,7,4]=>[2,6,3,7,1,5,4]=>[3,2,7,6,4,1,5]=>{{1,3,7},{2},{4,6},{5}}
[3,6,2,1,7,4,5]=>[2,6,3,7,4,1,5]=>[3,2,7,6,1,5,4]=>{{1,3,7},{2},{4,6},{5}}
[3,6,2,1,7,5,4]=>[2,6,3,5,7,1,4]=>[3,2,6,7,5,4,1]=>{{1,3,6},{2},{4,7},{5}}
[3,6,2,4,1,5,7]=>[4,6,3,2,1,5,7]=>[4,3,6,1,2,5,7]=>{{1,4},{2,3,6},{5},{7}}
[3,6,2,4,1,7,5]=>[4,6,3,2,7,1,5]=>[4,3,7,1,6,5,2]=>{{1,4},{2,3,7},{5,6}}
[3,6,2,4,5,1,7]=>[5,6,3,2,4,1,7]=>[5,3,6,1,2,4,7]=>{{1,5},{2,3,6},{4},{7}}
[3,6,2,4,5,7,1]=>[7,6,3,2,4,5,1]=>[3,6,7,1,2,4,5]=>{{1,3,7},{2,6},{4},{5}}
[3,6,2,4,7,1,5]=>[7,6,3,2,1,4,5]=>[3,6,7,1,4,5,2]=>{{1,3,7},{2,6},{4},{5}}
[3,6,2,4,7,5,1]=>[5,7,3,2,6,1,4]=>[5,3,7,1,6,4,2]=>{{1,5,6},{2,3,7},{4}}
[3,6,2,5,1,4,7]=>[5,6,3,1,2,4,7]=>[5,3,6,2,4,1,7]=>{{1,5},{2,3,6},{4},{7}}
[3,6,2,5,1,7,4]=>[5,6,3,7,2,1,4]=>[6,3,7,5,2,4,1]=>{{1,6},{2,3,7},{4,5}}
[3,6,2,5,4,1,7]=>[4,5,3,6,1,2,7]=>[5,3,6,4,2,1,7]=>{{1,5},{2,3,6},{4},{7}}
[3,6,2,5,4,7,1]=>[7,6,3,5,2,4,1]=>[3,5,6,7,2,1,4]=>{{1,3,6},{2,5},{4,7}}
[3,6,2,5,7,1,4]=>[7,6,3,1,4,2,5]=>[3,6,7,2,1,5,4]=>{{1,3,7},{2,6},{4},{5}}
[3,6,2,5,7,4,1]=>[4,7,3,6,2,1,5]=>[4,3,7,6,1,5,2]=>{{1,4,6},{2,3,7},{5}}
[3,6,2,7,1,4,5]=>[7,6,3,1,2,5,4]=>[3,6,7,2,4,1,5]=>{{1,3,7},{2,6},{4},{5}}
[3,6,2,7,1,5,4]=>[7,6,3,5,1,2,4]=>[3,5,6,7,4,2,1]=>{{1,3,6},{2,5},{4,7}}
[3,6,2,7,4,1,5]=>[4,7,3,6,1,5,2]=>[4,3,7,6,2,1,5]=>{{1,4,6},{2,3,7},{5}}
[3,6,2,7,4,5,1]=>[5,6,3,7,4,2,1]=>[6,3,7,5,1,2,4]=>{{1,6},{2,3,7},{4,5}}
[3,6,2,7,5,1,4]=>[5,7,3,1,6,4,2]=>[5,3,7,2,6,1,4]=>{{1,5,6},{2,3,7},{4}}
[3,6,2,7,5,4,1]=>[4,5,3,7,6,2,1]=>[5,3,7,4,6,1,2]=>{{1,5,6},{2,3,7},{4}}
[3,6,4,1,2,5,7]=>[4,1,3,6,2,5,7]=>[3,1,6,4,2,5,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,4,1,2,7,5]=>[4,1,3,6,7,2,5]=>[3,1,7,4,6,5,2]=>{{1,3,7},{2},{4},{5,6}}
[3,6,4,1,5,2,7]=>[4,6,3,5,2,1,7]=>[4,3,6,5,1,2,7]=>{{1,4,5},{2,3,6},{7}}
[3,6,4,1,5,7,2]=>[4,6,3,7,1,2,5]=>[6,3,7,4,2,5,1]=>{{1,6},{2,3,7},{4},{5}}
[3,6,4,1,7,2,5]=>[4,6,3,7,2,5,1]=>[6,3,7,4,1,2,5]=>{{1,6},{2,3,7},{4},{5}}
[3,6,4,1,7,5,2]=>[4,6,3,5,7,2,1]=>[4,3,7,6,5,1,2]=>{{1,4,6},{2,3,7},{5}}
[3,6,4,2,1,5,7]=>[2,4,3,6,1,5,7]=>[3,2,6,4,1,5,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,4,2,1,7,5]=>[2,4,3,6,7,1,5]=>[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}}
[3,6,4,2,5,1,7]=>[5,4,3,6,2,1,7]=>[3,5,6,4,1,2,7]=>{{1,3,6},{2,5},{4},{7}}
[3,6,4,2,5,7,1]=>[7,4,3,6,2,5,1]=>[3,4,7,6,1,2,5]=>{{1,3,7},{2,4,6},{5}}
[3,6,4,2,7,1,5]=>[7,4,3,6,1,2,5]=>[3,4,7,6,2,5,1]=>{{1,3,7},{2,4,6},{5}}
[3,6,4,2,7,5,1]=>[5,4,3,7,6,1,2]=>[3,5,7,4,6,2,1]=>{{1,3,7},{2,5,6},{4}}
[3,6,4,5,1,2,7]=>[5,1,3,6,4,2,7]=>[3,1,6,5,2,4,7]=>{{1,3,6},{2},{4,5},{7}}
[3,6,4,5,1,7,2]=>[5,7,3,6,4,1,2]=>[5,3,7,6,1,4,2]=>{{1,5},{2,3,7},{4,6}}
[3,6,4,5,2,1,7]=>[2,5,3,6,4,1,7]=>[3,2,6,5,1,4,7]=>{{1,3,6},{2},{4,5},{7}}
[3,6,4,5,2,7,1]=>[7,5,3,6,4,2,1]=>[3,5,7,6,1,2,4]=>{{1,3,7},{2,5},{4,6}}
[3,6,4,5,7,1,2]=>[7,1,3,6,4,5,2]=>[3,1,6,7,2,4,5]=>{{1,3,6},{2},{4,7},{5}}
[3,6,4,5,7,2,1]=>[2,7,3,6,4,5,1]=>[3,2,6,7,1,4,5]=>{{1,3,6},{2},{4,7},{5}}
[3,6,4,7,1,2,5]=>[7,1,3,6,2,4,5]=>[3,1,6,7,4,5,2]=>{{1,3,6},{2},{4,7},{5}}
[3,6,4,7,1,5,2]=>[7,5,3,6,1,4,2]=>[3,5,7,6,4,1,2]=>{{1,3,7},{2,5},{4,6}}
[3,6,4,7,2,1,5]=>[2,7,3,6,1,4,5]=>[3,2,6,7,4,5,1]=>{{1,3,6},{2},{4,7},{5}}
[3,6,4,7,2,5,1]=>[5,7,3,6,2,4,1]=>[5,3,7,6,2,1,4]=>{{1,5},{2,3,7},{4,6}}
[3,6,4,7,5,1,2]=>[5,1,3,7,6,2,4]=>[3,1,7,5,6,4,2]=>{{1,3,7},{2},{4,5,6}}
[3,6,4,7,5,2,1]=>[2,5,3,7,6,1,4]=>[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}}
[3,6,5,1,2,4,7]=>[5,1,3,2,6,4,7]=>[3,1,6,2,5,4,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,5,1,2,7,4]=>[5,1,3,6,7,4,2]=>[3,1,7,6,5,2,4]=>{{1,3,7},{2},{4,6},{5}}
[3,6,5,1,4,2,7]=>[5,4,3,1,6,2,7]=>[3,4,6,2,5,1,7]=>{{1,3,6},{2,4},{5},{7}}
[3,6,5,1,4,7,2]=>[5,6,3,1,7,2,4]=>[6,3,7,2,5,4,1]=>{{1,6},{2,3,7},{4},{5}}
[3,6,5,1,7,2,4]=>[5,6,3,2,7,4,1]=>[6,3,7,1,5,2,4]=>{{1,6},{2,3,7},{4},{5}}
[3,6,5,1,7,4,2]=>[5,4,3,6,7,2,1]=>[3,6,7,4,5,1,2]=>{{1,3,7},{2,6},{4},{5}}
[3,6,5,2,1,4,7]=>[2,5,3,1,6,4,7]=>[3,2,6,1,5,4,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,5,2,1,7,4]=>[2,5,3,6,7,4,1]=>[3,2,7,6,5,1,4]=>{{1,3,7},{2},{4,6},{5}}
[3,6,5,2,4,1,7]=>[4,5,3,2,6,1,7]=>[4,3,6,1,5,2,7]=>{{1,4},{2,3,6},{5},{7}}
[3,6,5,2,4,7,1]=>[7,5,3,2,6,4,1]=>[3,5,7,1,6,2,4]=>{{1,3,7},{2,5,6},{4}}
[3,6,5,2,7,1,4]=>[7,5,3,1,6,2,4]=>[3,5,7,2,6,4,1]=>{{1,3,7},{2,5,6},{4}}
[3,6,5,2,7,4,1]=>[4,7,3,5,6,1,2]=>[4,3,7,5,6,2,1]=>{{1,4,5,6},{2,3,7}}
[3,6,5,4,1,2,7]=>[4,1,3,5,6,2,7]=>[3,1,6,4,5,2,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,5,4,1,7,2]=>[4,5,3,6,7,1,2]=>[6,3,7,4,5,2,1]=>{{1,6},{2,3,7},{4},{5}}
[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}}
[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>[3,4,7,5,6,1,2]=>{{1,3,7},{2,4,5,6}}
[3,6,5,4,7,1,2]=>[7,1,3,5,6,4,2]=>[3,1,5,7,6,2,4]=>{{1,3,5,6},{2},{4,7}}
[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>[3,2,5,7,6,1,4]=>{{1,3,5,6},{2},{4,7}}
[3,6,5,7,1,2,4]=>[7,1,3,2,6,5,4]=>[3,1,6,2,7,4,5]=>{{1,3,6},{2},{4},{5,7}}
[3,6,5,7,1,4,2]=>[7,4,3,1,6,5,2]=>[3,4,6,2,7,1,5]=>{{1,3,6},{2,4},{5,7}}
[3,6,5,7,2,1,4]=>[2,7,3,1,6,5,4]=>[3,2,6,1,7,4,5]=>{{1,3,6},{2},{4},{5,7}}
[3,6,5,7,2,4,1]=>[4,7,3,2,6,5,1]=>[4,3,6,1,7,2,5]=>{{1,4},{2,3,6},{5,7}}
[3,6,5,7,4,1,2]=>[4,1,3,7,6,5,2]=>[3,1,6,4,7,2,5]=>{{1,3,6},{2},{4},{5,7}}
[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>[3,2,6,4,7,1,5]=>{{1,3,6},{2},{4},{5,7}}
[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[3,1,6,2,4,7,5]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,1,2,5,4]=>[7,1,3,5,2,6,4]=>[3,1,5,6,4,7,2]=>{{1,3,5},{2},{4,6,7}}
[3,6,7,1,4,2,5]=>[7,4,3,1,2,6,5]=>[3,4,6,2,1,7,5]=>{{1,3,6,7},{2,4},{5}}
[3,6,7,1,4,5,2]=>[7,5,3,1,4,6,2]=>[3,5,6,2,1,7,4]=>{{1,3,6,7},{2,5},{4}}
[3,6,7,1,5,2,4]=>[7,5,3,2,1,6,4]=>[3,5,6,1,4,7,2]=>{{1,3,6,7},{2,5},{4}}
[3,6,7,1,5,4,2]=>[7,4,3,5,1,6,2]=>[3,4,6,5,2,7,1]=>{{1,3,6,7},{2,4,5}}
[3,6,7,2,1,4,5]=>[2,7,3,1,4,6,5]=>[3,2,6,1,4,7,5]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,2,1,5,4]=>[2,7,3,5,1,6,4]=>[3,2,5,6,4,7,1]=>{{1,3,5},{2},{4,6,7}}
[3,6,7,2,4,1,5]=>[4,7,3,2,1,6,5]=>[4,3,6,1,2,7,5]=>{{1,4},{2,3,6,7},{5}}
[3,6,7,2,4,5,1]=>[5,7,3,2,4,6,1]=>[5,3,6,1,2,7,4]=>{{1,5},{2,3,6,7},{4}}
[3,6,7,2,5,1,4]=>[5,7,3,1,2,6,4]=>[5,3,6,2,4,7,1]=>{{1,5},{2,3,6,7},{4}}
[3,6,7,2,5,4,1]=>[4,5,3,7,1,6,2]=>[5,3,6,4,2,7,1]=>{{1,5},{2,3,6,7},{4}}
[3,6,7,4,1,2,5]=>[4,1,3,7,2,6,5]=>[3,1,6,4,2,7,5]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,4,1,5,2]=>[4,7,3,5,2,6,1]=>[4,3,6,5,1,7,2]=>{{1,4,5},{2,3,6,7}}
[3,6,7,4,2,1,5]=>[2,4,3,7,1,6,5]=>[3,2,6,4,1,7,5]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,4,2,5,1]=>[5,4,3,7,2,6,1]=>[3,5,6,4,1,7,2]=>{{1,3,6,7},{2,5},{4}}
[3,6,7,4,5,1,2]=>[5,1,3,7,4,6,2]=>[3,1,6,5,2,7,4]=>{{1,3,6,7},{2},{4,5}}
[3,6,7,4,5,2,1]=>[2,5,3,7,4,6,1]=>[3,2,6,5,1,7,4]=>{{1,3,6,7},{2},{4,5}}
[3,6,7,5,1,2,4]=>[5,1,3,2,7,6,4]=>[3,1,6,2,5,7,4]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,5,1,4,2]=>[5,4,3,1,7,6,2]=>[3,4,6,2,5,7,1]=>{{1,3,6,7},{2,4},{5}}
[3,6,7,5,2,1,4]=>[2,5,3,1,7,6,4]=>[3,2,6,1,5,7,4]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,5,2,4,1]=>[4,5,3,2,7,6,1]=>[4,3,6,1,5,7,2]=>{{1,4},{2,3,6,7},{5}}
[3,6,7,5,4,1,2]=>[4,1,3,5,7,6,2]=>[3,1,6,4,5,7,2]=>{{1,3,6,7},{2},{4},{5}}
[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}}
[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[3,1,7,2,4,5,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,1,2,4,6,5]=>[7,1,3,2,6,4,5]=>[3,1,6,2,7,5,4]=>{{1,3,6},{2},{4},{5,7}}
[3,7,1,2,5,4,6]=>[7,1,3,5,2,4,6]=>[3,1,5,7,4,2,6]=>{{1,3,5},{2},{4,7},{6}}
[3,7,1,2,5,6,4]=>[7,1,3,6,2,5,4]=>[3,1,6,7,4,2,5]=>{{1,3,6},{2},{4,7},{5}}
[3,7,1,2,6,4,5]=>[7,1,3,6,4,2,5]=>[3,1,6,7,2,5,4]=>{{1,3,6},{2},{4,7},{5}}
[3,7,1,2,6,5,4]=>[7,1,3,5,6,2,4]=>[3,1,5,7,6,4,2]=>{{1,3,5,6},{2},{4,7}}
[3,7,1,4,2,5,6]=>[7,4,3,1,2,5,6]=>[3,4,7,2,1,5,6]=>{{1,3,7},{2,4},{5},{6}}
[3,7,1,4,2,6,5]=>[7,4,3,1,6,2,5]=>[3,4,6,2,7,5,1]=>{{1,3,6},{2,4},{5,7}}
[3,7,1,4,5,2,6]=>[7,5,3,1,4,2,6]=>[3,5,7,2,1,4,6]=>{{1,3,7},{2,5},{4},{6}}
[3,7,1,4,5,6,2]=>[7,6,3,1,2,4,5]=>[3,6,7,2,4,5,1]=>{{1,3,7},{2,6},{4},{5}}
[3,7,1,4,6,2,5]=>[7,6,3,1,4,5,2]=>[3,6,7,2,1,4,5]=>{{1,3,7},{2,6},{4},{5}}
[3,7,1,4,6,5,2]=>[7,5,3,1,6,4,2]=>[3,5,7,2,6,1,4]=>{{1,3,7},{2,5,6},{4}}
[3,7,1,5,2,4,6]=>[7,5,3,2,1,4,6]=>[3,5,7,1,4,2,6]=>{{1,3,7},{2,5},{4},{6}}
[3,7,1,5,2,6,4]=>[7,5,3,6,1,2,4]=>[3,5,7,6,4,2,1]=>{{1,3,7},{2,5},{4,6}}
[3,7,1,5,4,2,6]=>[7,4,3,5,1,2,6]=>[3,4,7,5,2,1,6]=>{{1,3,7},{2,4,5},{6}}
[3,7,1,5,4,6,2]=>[7,6,3,5,1,4,2]=>[3,5,6,7,4,1,2]=>{{1,3,6},{2,5},{4,7}}
[3,7,1,5,6,2,4]=>[7,6,3,2,1,5,4]=>[3,6,7,1,4,2,5]=>{{1,3,7},{2,6},{4},{5}}
[3,7,1,5,6,4,2]=>[7,4,3,6,1,5,2]=>[3,4,7,6,2,1,5]=>{{1,3,7},{2,4,6},{5}}
[3,7,1,6,2,4,5]=>[7,6,3,2,4,1,5]=>[3,6,7,1,2,5,4]=>{{1,3,7},{2,6},{4},{5}}
[3,7,1,6,2,5,4]=>[7,6,3,5,2,1,4]=>[3,5,6,7,2,4,1]=>{{1,3,6},{2,5},{4,7}}
[3,7,1,6,4,2,5]=>[7,4,3,6,2,1,5]=>[3,4,7,6,1,5,2]=>{{1,3,7},{2,4,6},{5}}
[3,7,1,6,4,5,2]=>[7,5,3,6,4,1,2]=>[3,5,7,6,1,4,2]=>{{1,3,7},{2,5},{4,6}}
[3,7,1,6,5,2,4]=>[7,5,3,2,6,1,4]=>[3,5,7,1,6,4,2]=>{{1,3,7},{2,5,6},{4}}
[3,7,1,6,5,4,2]=>[7,4,3,5,6,1,2]=>[3,4,7,5,6,2,1]=>{{1,3,7},{2,4,5,6}}
[3,7,2,1,4,5,6]=>[2,7,3,1,4,5,6]=>[3,2,7,1,4,5,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,2,1,4,6,5]=>[2,7,3,1,6,4,5]=>[3,2,6,1,7,5,4]=>{{1,3,6},{2},{4},{5,7}}
[3,7,2,1,5,4,6]=>[2,7,3,5,1,4,6]=>[3,2,5,7,4,1,6]=>{{1,3,5},{2},{4,7},{6}}
[3,7,2,1,5,6,4]=>[2,7,3,6,1,5,4]=>[3,2,6,7,4,1,5]=>{{1,3,6},{2},{4,7},{5}}
[3,7,2,1,6,4,5]=>[2,7,3,6,4,1,5]=>[3,2,6,7,1,5,4]=>{{1,3,6},{2},{4,7},{5}}
[3,7,2,1,6,5,4]=>[2,7,3,5,6,1,4]=>[3,2,5,7,6,4,1]=>{{1,3,5,6},{2},{4,7}}
[3,7,2,4,1,5,6]=>[4,7,3,2,1,5,6]=>[4,3,7,1,2,5,6]=>{{1,4},{2,3,7},{5},{6}}
[3,7,2,4,1,6,5]=>[4,7,3,2,6,1,5]=>[4,3,6,1,7,5,2]=>{{1,4},{2,3,6},{5,7}}
[3,7,2,4,5,1,6]=>[5,7,3,2,4,1,6]=>[5,3,7,1,2,4,6]=>{{1,5},{2,3,7},{4},{6}}
[3,7,2,4,5,6,1]=>[6,7,3,2,4,5,1]=>[6,3,7,1,2,4,5]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,4,6,1,5]=>[6,7,3,2,1,4,5]=>[6,3,7,1,4,5,2]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,4,6,5,1]=>[5,6,3,2,7,1,4]=>[6,3,7,1,5,4,2]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,5,1,4,6]=>[5,7,3,1,2,4,6]=>[5,3,7,2,4,1,6]=>{{1,5},{2,3,7},{4},{6}}
[3,7,2,5,1,6,4]=>[5,7,3,6,2,1,4]=>[5,3,7,6,2,4,1]=>{{1,5},{2,3,7},{4,6}}
[3,7,2,5,4,1,6]=>[4,5,3,7,1,2,6]=>[5,3,7,4,2,1,6]=>{{1,5},{2,3,7},{4},{6}}
[3,7,2,5,4,6,1]=>[6,7,3,5,2,4,1]=>[5,3,6,7,2,1,4]=>{{1,5},{2,3,6},{4,7}}
[3,7,2,5,6,1,4]=>[6,7,3,1,4,2,5]=>[6,3,7,2,1,5,4]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,5,6,4,1]=>[4,6,3,7,2,1,5]=>[6,3,7,4,1,5,2]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,6,1,4,5]=>[6,7,3,1,2,5,4]=>[6,3,7,2,4,1,5]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,6,1,5,4]=>[6,7,3,5,1,2,4]=>[5,3,6,7,4,2,1]=>{{1,5},{2,3,6},{4,7}}
[3,7,2,6,4,1,5]=>[4,6,3,7,1,5,2]=>[6,3,7,4,2,1,5]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,6,4,5,1]=>[5,7,3,6,4,2,1]=>[5,3,7,6,1,2,4]=>{{1,5},{2,3,7},{4,6}}
[3,7,2,6,5,1,4]=>[5,6,3,1,7,4,2]=>[6,3,7,2,5,1,4]=>{{1,6},{2,3,7},{4},{5}}
[3,7,2,6,5,4,1]=>[4,5,3,6,7,2,1]=>[6,3,7,4,5,1,2]=>{{1,6},{2,3,7},{4},{5}}
[3,7,4,1,2,5,6]=>[4,1,3,7,2,5,6]=>[3,1,7,4,2,5,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,4,1,2,6,5]=>[4,1,3,7,6,2,5]=>[3,1,6,4,7,5,2]=>{{1,3,6},{2},{4},{5,7}}
[3,7,4,1,5,2,6]=>[4,7,3,5,2,1,6]=>[4,3,7,5,1,2,6]=>{{1,4,5},{2,3,7},{6}}
[3,7,4,1,5,6,2]=>[4,7,3,6,1,2,5]=>[4,3,7,6,2,5,1]=>{{1,4,6},{2,3,7},{5}}
[3,7,4,1,6,2,5]=>[4,7,3,6,2,5,1]=>[4,3,7,6,1,2,5]=>{{1,4,6},{2,3,7},{5}}
[3,7,4,1,6,5,2]=>[4,7,3,5,6,2,1]=>[4,3,7,5,6,1,2]=>{{1,4,5,6},{2,3,7}}
[3,7,4,2,1,5,6]=>[2,4,3,7,1,5,6]=>[3,2,7,4,1,5,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,4,2,1,6,5]=>[2,4,3,7,6,1,5]=>[3,2,6,4,7,5,1]=>{{1,3,6},{2},{4},{5,7}}
[3,7,4,2,5,1,6]=>[5,4,3,7,2,1,6]=>[3,5,7,4,1,2,6]=>{{1,3,7},{2,5},{4},{6}}
[3,7,4,2,5,6,1]=>[6,4,3,7,2,5,1]=>[3,6,7,4,1,2,5]=>{{1,3,7},{2,6},{4},{5}}
[3,7,4,2,6,1,5]=>[6,4,3,7,1,2,5]=>[3,6,7,4,2,5,1]=>{{1,3,7},{2,6},{4},{5}}
[3,7,4,2,6,5,1]=>[5,4,3,6,7,1,2]=>[3,6,7,4,5,2,1]=>{{1,3,7},{2,6},{4},{5}}
[3,7,4,5,1,2,6]=>[5,1,3,7,4,2,6]=>[3,1,7,5,2,4,6]=>{{1,3,7},{2},{4,5},{6}}
[3,7,4,5,1,6,2]=>[5,6,3,7,4,1,2]=>[6,3,7,5,1,4,2]=>{{1,6},{2,3,7},{4,5}}
[3,7,4,5,2,1,6]=>[2,5,3,7,4,1,6]=>[3,2,7,5,1,4,6]=>{{1,3,7},{2},{4,5},{6}}
[3,7,4,5,2,6,1]=>[6,5,3,7,4,2,1]=>[3,6,7,5,1,2,4]=>{{1,3,7},{2,6},{4,5}}
[3,7,4,5,6,1,2]=>[6,1,3,7,4,5,2]=>[3,1,7,6,2,4,5]=>{{1,3,7},{2},{4,6},{5}}
[3,7,4,5,6,2,1]=>[2,6,3,7,4,5,1]=>[3,2,7,6,1,4,5]=>{{1,3,7},{2},{4,6},{5}}
[3,7,4,6,1,2,5]=>[6,1,3,7,2,4,5]=>[3,1,7,6,4,5,2]=>{{1,3,7},{2},{4,6},{5}}
[3,7,4,6,1,5,2]=>[6,5,3,7,1,4,2]=>[3,6,7,5,4,1,2]=>{{1,3,7},{2,6},{4,5}}
[3,7,4,6,2,1,5]=>[2,6,3,7,1,4,5]=>[3,2,7,6,4,5,1]=>{{1,3,7},{2},{4,6},{5}}
[3,7,4,6,2,5,1]=>[5,6,3,7,2,4,1]=>[6,3,7,5,2,1,4]=>{{1,6},{2,3,7},{4,5}}
[3,7,4,6,5,1,2]=>[5,1,3,6,7,2,4]=>[3,1,7,6,5,4,2]=>{{1,3,7},{2},{4,6},{5}}
[3,7,4,6,5,2,1]=>[2,5,3,6,7,1,4]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}
[3,7,5,1,2,4,6]=>[5,1,3,2,7,4,6]=>[3,1,7,2,5,4,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,5,1,2,6,4]=>[5,1,3,7,6,4,2]=>[3,1,7,5,6,2,4]=>{{1,3,7},{2},{4,5,6}}
[3,7,5,1,4,2,6]=>[5,4,3,1,7,2,6]=>[3,4,7,2,5,1,6]=>{{1,3,7},{2,4},{5},{6}}
[3,7,5,1,4,6,2]=>[5,7,3,1,6,2,4]=>[5,3,7,2,6,4,1]=>{{1,5,6},{2,3,7},{4}}
[3,7,5,1,6,2,4]=>[5,7,3,2,6,4,1]=>[5,3,7,1,6,2,4]=>{{1,5,6},{2,3,7},{4}}
[3,7,5,1,6,4,2]=>[5,4,3,7,6,2,1]=>[3,5,7,4,6,1,2]=>{{1,3,7},{2,5,6},{4}}
[3,7,5,2,1,4,6]=>[2,5,3,1,7,4,6]=>[3,2,7,1,5,4,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,5,2,1,6,4]=>[2,5,3,7,6,4,1]=>[3,2,7,5,6,1,4]=>{{1,3,7},{2},{4,5,6}}
[3,7,5,2,4,1,6]=>[4,5,3,2,7,1,6]=>[4,3,7,1,5,2,6]=>{{1,4},{2,3,7},{5},{6}}
[3,7,5,2,4,6,1]=>[6,5,3,2,7,4,1]=>[3,6,7,1,5,2,4]=>{{1,3,7},{2,6},{4},{5}}
[3,7,5,2,6,1,4]=>[6,5,3,1,7,2,4]=>[3,6,7,2,5,4,1]=>{{1,3,7},{2,6},{4},{5}}
[3,7,5,2,6,4,1]=>[4,6,3,5,7,1,2]=>[4,3,7,6,5,2,1]=>{{1,4,6},{2,3,7},{5}}
[3,7,5,4,1,2,6]=>[4,1,3,5,7,2,6]=>[3,1,7,4,5,2,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,5,4,1,6,2]=>[4,5,3,7,6,1,2]=>[5,3,7,4,6,2,1]=>{{1,5,6},{2,3,7},{4}}
[3,7,5,4,2,1,6]=>[2,4,3,5,7,1,6]=>[3,2,7,4,5,1,6]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,5,4,2,6,1]=>[6,4,3,5,7,2,1]=>[3,4,7,6,5,1,2]=>{{1,3,7},{2,4,6},{5}}
[3,7,5,4,6,1,2]=>[6,1,3,5,7,4,2]=>[3,1,6,7,5,2,4]=>{{1,3,6},{2},{4,7},{5}}
[3,7,5,4,6,2,1]=>[2,6,3,5,7,4,1]=>[3,2,6,7,5,1,4]=>{{1,3,6},{2},{4,7},{5}}
[3,7,5,6,1,2,4]=>[6,1,3,2,7,5,4]=>[3,1,7,2,6,4,5]=>{{1,3,7},{2},{4},{5,6}}
[3,7,5,6,1,4,2]=>[6,4,3,1,7,5,2]=>[3,4,7,2,6,1,5]=>{{1,3,7},{2,4},{5,6}}
[3,7,5,6,2,1,4]=>[2,6,3,1,7,5,4]=>[3,2,7,1,6,4,5]=>{{1,3,7},{2},{4},{5,6}}
[3,7,5,6,2,4,1]=>[4,6,3,2,7,5,1]=>[4,3,7,1,6,2,5]=>{{1,4},{2,3,7},{5,6}}
[3,7,5,6,4,1,2]=>[4,1,3,6,7,5,2]=>[3,1,7,4,6,2,5]=>{{1,3,7},{2},{4},{5,6}}
[3,7,5,6,4,2,1]=>[2,4,3,6,7,5,1]=>[3,2,7,4,6,1,5]=>{{1,3,7},{2},{4},{5,6}}
[3,7,6,1,2,4,5]=>[6,1,3,2,4,7,5]=>[3,1,7,2,4,6,5]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,1,2,5,4]=>[6,1,3,5,2,7,4]=>[3,1,5,7,4,6,2]=>{{1,3,5},{2},{4,7},{6}}
[3,7,6,1,4,2,5]=>[6,4,3,1,2,7,5]=>[3,4,7,2,1,6,5]=>{{1,3,7},{2,4},{5},{6}}
[3,7,6,1,4,5,2]=>[6,5,3,1,4,7,2]=>[3,5,7,2,1,6,4]=>{{1,3,7},{2,5},{4},{6}}
[3,7,6,1,5,2,4]=>[6,5,3,2,1,7,4]=>[3,5,7,1,4,6,2]=>{{1,3,7},{2,5},{4},{6}}
[3,7,6,1,5,4,2]=>[6,4,3,5,1,7,2]=>[3,4,7,5,2,6,1]=>{{1,3,7},{2,4,5},{6}}
[3,7,6,2,1,4,5]=>[2,6,3,1,4,7,5]=>[3,2,7,1,4,6,5]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,2,1,5,4]=>[2,6,3,5,1,7,4]=>[3,2,5,7,4,6,1]=>{{1,3,5},{2},{4,7},{6}}
[3,7,6,2,4,1,5]=>[4,6,3,2,1,7,5]=>[4,3,7,1,2,6,5]=>{{1,4},{2,3,7},{5},{6}}
[3,7,6,2,4,5,1]=>[5,6,3,2,4,7,1]=>[5,3,7,1,2,6,4]=>{{1,5},{2,3,7},{4},{6}}
[3,7,6,2,5,1,4]=>[5,6,3,1,2,7,4]=>[5,3,7,2,4,6,1]=>{{1,5},{2,3,7},{4},{6}}
[3,7,6,2,5,4,1]=>[4,5,3,6,1,7,2]=>[5,3,7,4,2,6,1]=>{{1,5},{2,3,7},{4},{6}}
[3,7,6,4,1,2,5]=>[4,1,3,6,2,7,5]=>[3,1,7,4,2,6,5]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,4,1,5,2]=>[4,6,3,5,2,7,1]=>[4,3,7,5,1,6,2]=>{{1,4,5},{2,3,7},{6}}
[3,7,6,4,2,1,5]=>[2,4,3,6,1,7,5]=>[3,2,7,4,1,6,5]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,4,2,5,1]=>[5,4,3,6,2,7,1]=>[3,5,7,4,1,6,2]=>{{1,3,7},{2,5},{4},{6}}
[3,7,6,4,5,1,2]=>[5,1,3,6,4,7,2]=>[3,1,7,5,2,6,4]=>{{1,3,7},{2},{4,5},{6}}
[3,7,6,4,5,2,1]=>[2,5,3,6,4,7,1]=>[3,2,7,5,1,6,4]=>{{1,3,7},{2},{4,5},{6}}
[3,7,6,5,1,2,4]=>[5,1,3,2,6,7,4]=>[3,1,7,2,5,6,4]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,5,1,4,2]=>[5,4,3,1,6,7,2]=>[3,4,7,2,5,6,1]=>{{1,3,7},{2,4},{5},{6}}
[3,7,6,5,2,1,4]=>[2,5,3,1,6,7,4]=>[3,2,7,1,5,6,4]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,5,2,4,1]=>[4,5,3,2,6,7,1]=>[4,3,7,1,5,6,2]=>{{1,4},{2,3,7},{5},{6}}
[3,7,6,5,4,1,2]=>[4,1,3,5,6,7,2]=>[3,1,7,4,5,6,2]=>{{1,3,7},{2},{4},{5},{6}}
[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}}
[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>{{1,4},{2},{3},{5,7},{6}}
[4,1,2,3,7,6,5]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[4,1,2,5,3,6,7]=>[4,1,5,2,3,6,7]=>[5,1,4,3,2,6,7]=>{{1,5},{2},{3,4},{6},{7}}
[4,1,2,5,3,7,6]=>[4,1,5,2,3,7,6]=>[5,1,4,3,2,7,6]=>{{1,5},{2},{3,4},{6,7}}
[4,1,2,5,6,3,7]=>[4,1,6,2,5,3,7]=>[5,1,4,3,6,2,7]=>{{1,5,6},{2},{3,4},{7}}
[4,1,2,5,6,7,3]=>[4,1,7,2,5,6,3]=>[5,1,4,3,6,7,2]=>{{1,5,6,7},{2},{3,4}}
[4,1,2,5,7,3,6]=>[4,1,7,2,5,3,6]=>[5,1,4,3,7,2,6]=>{{1,5,7},{2},{3,4},{6}}
[4,1,2,5,7,6,3]=>[4,1,6,2,5,7,3]=>[5,1,4,3,7,6,2]=>{{1,5,7},{2},{3,4},{6}}
[4,1,2,6,3,5,7]=>[4,1,6,2,3,5,7]=>[6,1,4,3,2,5,7]=>{{1,6},{2},{3,4},{5},{7}}
[4,1,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>[7,1,4,3,6,5,2]=>{{1,7},{2},{3,4},{5,6}}
[4,1,2,6,5,3,7]=>[4,1,5,2,6,3,7]=>[6,1,4,3,5,2,7]=>{{1,6},{2},{3,4},{5},{7}}
[4,1,2,6,5,7,3]=>[4,1,7,2,6,5,3]=>[6,1,4,3,7,2,5]=>{{1,6},{2},{3,4},{5,7}}
[4,1,2,6,7,3,5]=>[4,1,7,2,3,6,5]=>[6,1,4,3,2,7,5]=>{{1,6,7},{2},{3,4},{5}}
[4,1,2,6,7,5,3]=>[4,1,5,2,7,6,3]=>[6,1,4,3,5,7,2]=>{{1,6,7},{2},{3,4},{5}}
[4,1,2,7,3,5,6]=>[4,1,7,2,3,5,6]=>[7,1,4,3,2,5,6]=>{{1,7},{2},{3,4},{5},{6}}
[4,1,2,7,3,6,5]=>[4,1,7,2,6,3,5]=>[6,1,4,3,7,5,2]=>{{1,6},{2},{3,4},{5,7}}
[4,1,2,7,5,3,6]=>[4,1,5,2,7,3,6]=>[7,1,4,3,5,2,6]=>{{1,7},{2},{3,4},{5},{6}}
[4,1,2,7,5,6,3]=>[4,1,6,2,7,5,3]=>[7,1,4,3,6,2,5]=>{{1,7},{2},{3,4},{5,6}}
[4,1,2,7,6,3,5]=>[4,1,6,2,3,7,5]=>[7,1,4,3,2,6,5]=>{{1,7},{2},{3,4},{5},{6}}
[4,1,2,7,6,5,3]=>[4,1,5,2,6,7,3]=>[7,1,4,3,5,6,2]=>{{1,7},{2},{3,4},{5},{6}}
[4,1,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[3,4,2,1,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}
[4,1,3,2,5,7,6]=>[4,3,1,2,5,7,6]=>[3,4,2,1,5,7,6]=>{{1,3},{2,4},{5},{6,7}}
[4,1,3,2,6,5,7]=>[4,3,1,2,6,5,7]=>[3,4,2,1,6,5,7]=>{{1,3},{2,4},{5,6},{7}}
[4,1,3,2,6,7,5]=>[4,3,1,2,7,6,5]=>[3,4,2,1,6,7,5]=>{{1,3},{2,4},{5,6,7}}
[4,1,3,2,7,5,6]=>[4,3,1,2,7,5,6]=>[3,4,2,1,7,5,6]=>{{1,3},{2,4},{5,7},{6}}
[4,1,3,2,7,6,5]=>[4,3,1,2,6,7,5]=>[3,4,2,1,7,6,5]=>{{1,3},{2,4},{5,7},{6}}
[4,1,3,5,2,6,7]=>[4,5,1,3,2,6,7]=>[5,4,2,1,3,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[4,1,3,5,2,7,6]=>[4,5,1,3,2,7,6]=>[5,4,2,1,3,7,6]=>{{1,5},{2,4},{3},{6,7}}
[4,1,3,5,6,2,7]=>[4,6,1,3,5,2,7]=>[5,4,2,1,6,3,7]=>{{1,5,6},{2,4},{3},{7}}
[4,1,3,5,6,7,2]=>[4,7,1,3,5,6,2]=>[5,4,2,1,6,7,3]=>{{1,5,6,7},{2,4},{3}}
[4,1,3,5,7,2,6]=>[4,7,1,3,5,2,6]=>[5,4,2,1,7,3,6]=>{{1,5,7},{2,4},{3},{6}}
[4,1,3,5,7,6,2]=>[4,6,1,3,5,7,2]=>[5,4,2,1,7,6,3]=>{{1,5,7},{2,4},{3},{6}}
[4,1,3,6,2,5,7]=>[4,6,1,3,2,5,7]=>[6,4,2,1,3,5,7]=>{{1,6},{2,4},{3},{5},{7}}
[4,1,3,6,2,7,5]=>[4,6,1,3,7,2,5]=>[7,4,2,1,6,5,3]=>{{1,7},{2,4},{3},{5,6}}
[4,1,3,6,5,2,7]=>[4,5,1,3,6,2,7]=>[6,4,2,1,5,3,7]=>{{1,6},{2,4},{3},{5},{7}}
[4,1,3,6,5,7,2]=>[4,7,1,3,6,5,2]=>[6,4,2,1,7,3,5]=>{{1,6},{2,4},{3},{5,7}}
[4,1,3,6,7,2,5]=>[4,7,1,3,2,6,5]=>[6,4,2,1,3,7,5]=>{{1,6,7},{2,4},{3},{5}}
[4,1,3,6,7,5,2]=>[4,5,1,3,7,6,2]=>[6,4,2,1,5,7,3]=>{{1,6,7},{2,4},{3},{5}}
[4,1,3,7,2,5,6]=>[4,7,1,3,2,5,6]=>[7,4,2,1,3,5,6]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,3,7,2,6,5]=>[4,7,1,3,6,2,5]=>[6,4,2,1,7,5,3]=>{{1,6},{2,4},{3},{5,7}}
[4,1,3,7,5,2,6]=>[4,5,1,3,7,2,6]=>[7,4,2,1,5,3,6]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,3,7,5,6,2]=>[4,6,1,3,7,5,2]=>[7,4,2,1,6,3,5]=>{{1,7},{2,4},{3},{5,6}}
[4,1,3,7,6,2,5]=>[4,6,1,3,2,7,5]=>[7,4,2,1,3,6,5]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,3,7,6,5,2]=>[4,5,1,3,6,7,2]=>[7,4,2,1,5,6,3]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[5,4,1,3,2,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[4,1,5,2,3,7,6]=>[4,5,2,1,3,7,6]=>[5,4,1,3,2,7,6]=>{{1,5},{2,4},{3},{6,7}}
[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}
[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}
[4,1,5,2,7,3,6]=>[4,5,7,1,2,3,6]=>[7,5,4,3,2,1,6]=>{{1,7},{2,5},{3,4},{6}}
[4,1,5,2,7,6,3]=>[4,5,6,1,2,7,3]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}
[4,1,5,3,2,6,7]=>[4,3,5,1,2,6,7]=>[4,5,3,2,1,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[4,1,5,3,2,7,6]=>[4,3,5,1,2,7,6]=>[4,5,3,2,1,7,6]=>{{1,4},{2,5},{3},{6,7}}
[4,1,5,3,6,2,7]=>[4,6,5,1,3,2,7]=>[6,4,5,3,1,2,7]=>{{1,6},{2,4},{3,5},{7}}
[4,1,5,3,6,7,2]=>[4,7,5,1,3,6,2]=>[6,4,5,3,1,7,2]=>{{1,6,7},{2,4},{3,5}}
[4,1,5,3,7,2,6]=>[4,7,5,1,3,2,6]=>[7,4,5,3,1,2,6]=>{{1,7},{2,4},{3,5},{6}}
[4,1,5,3,7,6,2]=>[4,6,5,1,3,7,2]=>[7,4,5,3,1,6,2]=>{{1,7},{2,4},{3,5},{6}}
[4,1,5,6,2,3,7]=>[4,6,2,1,5,3,7]=>[5,4,1,3,6,2,7]=>{{1,5,6},{2,4},{3},{7}}
[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[6,5,4,3,7,2,1]=>{{1,6},{2,5,7},{3,4}}
[4,1,5,6,3,2,7]=>[4,3,6,1,5,2,7]=>[4,5,3,2,6,1,7]=>{{1,4},{2,5,6},{3},{7}}
[4,1,5,6,3,7,2]=>[4,7,6,1,5,3,2]=>[6,4,5,3,7,1,2]=>{{1,6},{2,4},{3,5,7}}
[4,1,5,6,7,2,3]=>[4,7,2,1,5,6,3]=>[5,4,1,3,6,7,2]=>{{1,5,6,7},{2,4},{3}}
[4,1,5,6,7,3,2]=>[4,3,7,1,5,6,2]=>[4,5,3,2,6,7,1]=>{{1,4},{2,5,6,7},{3}}
[4,1,5,7,2,3,6]=>[4,7,2,1,5,3,6]=>[5,4,1,3,7,2,6]=>{{1,5,7},{2,4},{3},{6}}
[4,1,5,7,2,6,3]=>[4,7,6,1,5,2,3]=>[6,4,5,3,7,2,1]=>{{1,6},{2,4},{3,5,7}}
[4,1,5,7,3,2,6]=>[4,3,7,1,5,2,6]=>[4,5,3,2,7,1,6]=>{{1,4},{2,5,7},{3},{6}}
[4,1,5,7,3,6,2]=>[4,6,7,1,5,3,2]=>[6,5,4,3,7,1,2]=>{{1,6},{2,5,7},{3,4}}
[4,1,5,7,6,2,3]=>[4,6,2,1,5,7,3]=>[5,4,1,3,7,6,2]=>{{1,5,7},{2,4},{3},{6}}
[4,1,5,7,6,3,2]=>[4,3,6,1,5,7,2]=>[4,5,3,2,7,6,1]=>{{1,4},{2,5,7},{3},{6}}
[4,1,6,2,3,5,7]=>[4,6,2,1,3,5,7]=>[6,4,1,3,2,5,7]=>{{1,6},{2,4},{3},{5},{7}}
[4,1,6,2,3,7,5]=>[4,6,2,1,7,3,5]=>[7,4,1,3,6,5,2]=>{{1,7},{2,4},{3},{5,6}}
[4,1,6,2,5,3,7]=>[4,6,5,1,2,3,7]=>[6,4,5,3,2,1,7]=>{{1,6},{2,4},{3,5},{7}}
[4,1,6,2,5,7,3]=>[4,6,7,1,2,5,3]=>[7,6,4,3,2,1,5]=>{{1,7},{2,6},{3,4},{5}}
[4,1,6,2,7,3,5]=>[4,6,7,1,3,2,5]=>[7,6,4,3,1,5,2]=>{{1,7},{2,6},{3,4},{5}}
[4,1,6,2,7,5,3]=>[4,6,5,1,7,2,3]=>[7,4,6,3,5,2,1]=>{{1,7},{2,4},{3,6},{5}}
[4,1,6,3,2,5,7]=>[4,3,6,1,2,5,7]=>[4,6,3,2,1,5,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,1,6,3,2,7,5]=>[4,3,6,1,7,2,5]=>[4,7,3,2,6,5,1]=>{{1,4},{2,7},{3},{5,6}}
[4,1,6,3,5,2,7]=>[4,5,6,1,3,2,7]=>[6,5,4,3,1,2,7]=>{{1,6},{2,5},{3,4},{7}}
[4,1,6,3,5,7,2]=>[4,7,6,1,3,5,2]=>[7,4,6,3,1,2,5]=>{{1,7},{2,4},{3,6},{5}}
[4,1,6,3,7,2,5]=>[4,7,6,1,2,3,5]=>[7,4,6,3,2,5,1]=>{{1,7},{2,4},{3,6},{5}}
[4,1,6,3,7,5,2]=>[4,5,7,1,6,2,3]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}
[4,1,6,5,2,3,7]=>[4,5,2,1,6,3,7]=>[6,4,1,3,5,2,7]=>{{1,6},{2,4},{3},{5},{7}}
[4,1,6,5,2,7,3]=>[4,5,6,1,7,3,2]=>[7,6,4,3,5,1,2]=>{{1,7},{2,6},{3,4},{5}}
[4,1,6,5,3,2,7]=>[4,3,5,1,6,2,7]=>[4,6,3,2,5,1,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,1,6,5,3,7,2]=>[4,7,5,1,6,3,2]=>[7,4,5,3,6,1,2]=>{{1,7},{2,4},{3,5,6}}
[4,1,6,5,7,2,3]=>[4,7,2,1,6,5,3]=>[6,4,1,3,7,2,5]=>{{1,6},{2,4},{3},{5,7}}
[4,1,6,5,7,3,2]=>[4,3,7,1,6,5,2]=>[4,6,3,2,7,1,5]=>{{1,4},{2,6},{3},{5,7}}
[4,1,6,7,2,3,5]=>[4,7,2,1,3,6,5]=>[6,4,1,3,2,7,5]=>{{1,6,7},{2,4},{3},{5}}
[4,1,6,7,2,5,3]=>[4,7,5,1,2,6,3]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,4},{3,5}}
[4,1,6,7,3,2,5]=>[4,3,7,1,2,6,5]=>[4,6,3,2,1,7,5]=>{{1,4},{2,6,7},{3},{5}}
[4,1,6,7,3,5,2]=>[4,5,7,1,3,6,2]=>[6,5,4,3,1,7,2]=>{{1,6,7},{2,5},{3,4}}
[4,1,6,7,5,2,3]=>[4,5,2,1,7,6,3]=>[6,4,1,3,5,7,2]=>{{1,6,7},{2,4},{3},{5}}
[4,1,6,7,5,3,2]=>[4,3,5,1,7,6,2]=>[4,6,3,2,5,7,1]=>{{1,4},{2,6,7},{3},{5}}
[4,1,7,2,3,5,6]=>[4,7,2,1,3,5,6]=>[7,4,1,3,2,5,6]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,7,2,3,6,5]=>[4,7,2,1,6,3,5]=>[6,4,1,3,7,5,2]=>{{1,6},{2,4},{3},{5,7}}
[4,1,7,2,5,3,6]=>[4,7,5,1,2,3,6]=>[7,4,5,3,2,1,6]=>{{1,7},{2,4},{3,5},{6}}
[4,1,7,2,5,6,3]=>[4,7,6,1,2,5,3]=>[7,4,6,3,2,1,5]=>{{1,7},{2,4},{3,6},{5}}
[4,1,7,2,6,3,5]=>[4,7,6,1,3,2,5]=>[7,4,6,3,1,5,2]=>{{1,7},{2,4},{3,6},{5}}
[4,1,7,2,6,5,3]=>[4,7,5,1,6,2,3]=>[7,4,5,3,6,2,1]=>{{1,7},{2,4},{3,5,6}}
[4,1,7,3,2,5,6]=>[4,3,7,1,2,5,6]=>[4,7,3,2,1,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[4,1,7,3,2,6,5]=>[4,3,7,1,6,2,5]=>[4,6,3,2,7,5,1]=>{{1,4},{2,6},{3},{5,7}}
[4,1,7,3,5,2,6]=>[4,5,7,1,3,2,6]=>[7,5,4,3,1,2,6]=>{{1,7},{2,5},{3,4},{6}}
[4,1,7,3,5,6,2]=>[4,6,7,1,3,5,2]=>[7,6,4,3,1,2,5]=>{{1,7},{2,6},{3,4},{5}}
[4,1,7,3,6,2,5]=>[4,6,7,1,2,3,5]=>[7,6,4,3,2,5,1]=>{{1,7},{2,6},{3,4},{5}}
[4,1,7,3,6,5,2]=>[4,5,6,1,7,2,3]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}
[4,1,7,5,2,3,6]=>[4,5,2,1,7,3,6]=>[7,4,1,3,5,2,6]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,7,5,2,6,3]=>[4,5,7,1,6,3,2]=>[7,5,4,3,6,1,2]=>{{1,7},{2,5,6},{3,4}}
[4,1,7,5,3,2,6]=>[4,3,5,1,7,2,6]=>[4,7,3,2,5,1,6]=>{{1,4},{2,7},{3},{5},{6}}
[4,1,7,5,3,6,2]=>[4,6,5,1,7,3,2]=>[7,4,6,3,5,1,2]=>{{1,7},{2,4},{3,6},{5}}
[4,1,7,5,6,2,3]=>[4,6,2,1,7,5,3]=>[7,4,1,3,6,2,5]=>{{1,7},{2,4},{3},{5,6}}
[4,1,7,5,6,3,2]=>[4,3,6,1,7,5,2]=>[4,7,3,2,6,1,5]=>{{1,4},{2,7},{3},{5,6}}
[4,1,7,6,2,3,5]=>[4,6,2,1,3,7,5]=>[7,4,1,3,2,6,5]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,7,6,2,5,3]=>[4,6,5,1,2,7,3]=>[7,4,5,3,2,6,1]=>{{1,7},{2,4},{3,5},{6}}
[4,1,7,6,3,2,5]=>[4,3,6,1,2,7,5]=>[4,7,3,2,1,6,5]=>{{1,4},{2,7},{3},{5},{6}}
[4,1,7,6,3,5,2]=>[4,5,6,1,3,7,2]=>[7,5,4,3,1,6,2]=>{{1,7},{2,5},{3,4},{6}}
[4,1,7,6,5,2,3]=>[4,5,2,1,6,7,3]=>[7,4,1,3,5,6,2]=>{{1,7},{2,4},{3},{5},{6}}
[4,1,7,6,5,3,2]=>[4,3,5,1,6,7,2]=>[4,7,3,2,5,6,1]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[4,2,1,3,5,7,6]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[4,2,1,3,6,5,7]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[4,2,1,3,6,7,5]=>[2,4,1,3,7,6,5]=>[4,2,1,3,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[4,2,1,3,7,5,6]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>{{1,4},{2},{3},{5,7},{6}}
[4,2,1,3,7,6,5]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[4,2,1,5,3,6,7]=>[2,4,5,1,3,6,7]=>[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}}
[4,2,1,5,3,7,6]=>[2,4,5,1,3,7,6]=>[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}}
[4,2,1,5,6,3,7]=>[2,4,6,1,5,3,7]=>[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}}
[4,2,1,5,6,7,3]=>[2,4,7,1,5,6,3]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}}
[4,2,1,5,7,3,6]=>[2,4,7,1,5,3,6]=>[5,2,4,3,7,1,6]=>{{1,5,7},{2},{3,4},{6}}
[4,2,1,5,7,6,3]=>[2,4,6,1,5,7,3]=>[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}}
[4,2,1,6,3,5,7]=>[2,4,6,1,3,5,7]=>[6,2,4,3,1,5,7]=>{{1,6},{2},{3,4},{5},{7}}
[4,2,1,6,3,7,5]=>[2,4,6,1,7,3,5]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}}
[4,2,1,6,5,3,7]=>[2,4,5,1,6,3,7]=>[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}}
[4,2,1,6,5,7,3]=>[2,4,7,1,6,5,3]=>[6,2,4,3,7,1,5]=>{{1,6},{2},{3,4},{5,7}}
[4,2,1,6,7,3,5]=>[2,4,7,1,3,6,5]=>[6,2,4,3,1,7,5]=>{{1,6,7},{2},{3,4},{5}}
[4,2,1,6,7,5,3]=>[2,4,5,1,7,6,3]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}}
[4,2,1,7,3,5,6]=>[2,4,7,1,3,5,6]=>[7,2,4,3,1,5,6]=>{{1,7},{2},{3,4},{5},{6}}
[4,2,1,7,3,6,5]=>[2,4,7,1,6,3,5]=>[6,2,4,3,7,5,1]=>{{1,6},{2},{3,4},{5,7}}
[4,2,1,7,5,3,6]=>[2,4,5,1,7,3,6]=>[7,2,4,3,5,1,6]=>{{1,7},{2},{3,4},{5},{6}}
[4,2,1,7,5,6,3]=>[2,4,6,1,7,5,3]=>[7,2,4,3,6,1,5]=>{{1,7},{2},{3,4},{5,6}}
[4,2,1,7,6,3,5]=>[2,4,6,1,3,7,5]=>[7,2,4,3,1,6,5]=>{{1,7},{2},{3,4},{5},{6}}
[4,2,1,7,6,5,3]=>[2,4,5,1,6,7,3]=>[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}}
[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[4,2,3,1,5,7,6]=>[3,4,2,1,5,7,6]=>[4,3,1,2,5,7,6]=>{{1,4},{2,3},{5},{6,7}}
[4,2,3,1,6,5,7]=>[3,4,2,1,6,5,7]=>[4,3,1,2,6,5,7]=>{{1,4},{2,3},{5,6},{7}}
[4,2,3,1,6,7,5]=>[3,4,2,1,7,6,5]=>[4,3,1,2,6,7,5]=>{{1,4},{2,3},{5,6,7}}
[4,2,3,1,7,5,6]=>[3,4,2,1,7,5,6]=>[4,3,1,2,7,5,6]=>{{1,4},{2,3},{5,7},{6}}
[4,2,3,1,7,6,5]=>[3,4,2,1,6,7,5]=>[4,3,1,2,7,6,5]=>{{1,4},{2,3},{5,7},{6}}
[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[4,5,1,2,3,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[4,2,3,5,1,7,6]=>[5,4,2,3,1,7,6]=>[4,5,1,2,3,7,6]=>{{1,4},{2,5},{3},{6,7}}
[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[4,5,1,2,6,3,7]=>{{1,4},{2,5,6},{3},{7}}
[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[4,5,1,2,6,7,3]=>{{1,4},{2,5,6,7},{3}}
[4,2,3,5,7,1,6]=>[7,4,2,3,5,1,6]=>[4,5,1,2,7,3,6]=>{{1,4},{2,5,7},{3},{6}}
[4,2,3,5,7,6,1]=>[6,4,2,3,5,7,1]=>[4,5,1,2,7,6,3]=>{{1,4},{2,5,7},{3},{6}}
[4,2,3,6,1,5,7]=>[6,4,2,3,1,5,7]=>[4,6,1,2,3,5,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,2,3,6,1,7,5]=>[6,4,2,3,7,1,5]=>[4,7,1,2,6,5,3]=>{{1,4},{2,7},{3},{5,6}}
[4,2,3,6,5,1,7]=>[5,4,2,3,6,1,7]=>[4,6,1,2,5,3,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,2,3,6,5,7,1]=>[7,4,2,3,6,5,1]=>[4,6,1,2,7,3,5]=>{{1,4},{2,6},{3},{5,7}}
[4,2,3,6,7,1,5]=>[7,4,2,3,1,6,5]=>[4,6,1,2,3,7,5]=>{{1,4},{2,6,7},{3},{5}}
[4,2,3,6,7,5,1]=>[5,4,2,3,7,6,1]=>[4,6,1,2,5,7,3]=>{{1,4},{2,6,7},{3},{5}}
[4,2,3,7,1,5,6]=>[7,4,2,3,1,5,6]=>[4,7,1,2,3,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,3,7,1,6,5]=>[7,4,2,3,6,1,5]=>[4,6,1,2,7,5,3]=>{{1,4},{2,6},{3},{5,7}}
[4,2,3,7,5,1,6]=>[5,4,2,3,7,1,6]=>[4,7,1,2,5,3,6]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,3,7,5,6,1]=>[6,4,2,3,7,5,1]=>[4,7,1,2,6,3,5]=>{{1,4},{2,7},{3},{5,6}}
[4,2,3,7,6,1,5]=>[6,4,2,3,1,7,5]=>[4,7,1,2,3,6,5]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,3,7,6,5,1]=>[5,4,2,3,6,7,1]=>[4,7,1,2,5,6,3]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,5,1,3,6,7]=>[5,4,1,2,3,6,7]=>[4,5,2,3,1,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[4,2,5,1,3,7,6]=>[5,4,1,2,3,7,6]=>[4,5,2,3,1,7,6]=>{{1,4},{2,5},{3},{6,7}}
[4,2,5,1,6,3,7]=>[5,4,6,2,1,3,7]=>[5,6,4,2,3,1,7]=>{{1,5},{2,6},{3,4},{7}}
[4,2,5,1,6,7,3]=>[5,4,7,2,1,6,3]=>[5,6,4,2,3,7,1]=>{{1,5},{2,6,7},{3,4}}
[4,2,5,1,7,3,6]=>[5,4,7,2,1,3,6]=>[5,7,4,2,3,1,6]=>{{1,5},{2,7},{3,4},{6}}
[4,2,5,1,7,6,3]=>[5,4,6,2,1,7,3]=>[5,7,4,2,3,6,1]=>{{1,5},{2,7},{3,4},{6}}
[4,2,5,3,1,6,7]=>[3,5,4,1,2,6,7]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[4,2,5,3,1,7,6]=>[3,5,4,1,2,7,6]=>[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}}
[4,2,5,3,6,1,7]=>[6,4,5,2,3,1,7]=>[4,6,5,2,1,3,7]=>{{1,4},{2,6},{3,5},{7}}
[4,2,5,3,6,7,1]=>[7,4,5,2,3,6,1]=>[4,6,5,2,1,7,3]=>{{1,4},{2,6,7},{3,5}}
[4,2,5,3,7,1,6]=>[7,4,5,2,3,1,6]=>[4,7,5,2,1,3,6]=>{{1,4},{2,7},{3,5},{6}}
[4,2,5,3,7,6,1]=>[6,4,5,2,3,7,1]=>[4,7,5,2,1,6,3]=>{{1,4},{2,7},{3,5},{6}}
[4,2,5,6,1,3,7]=>[6,4,1,2,5,3,7]=>[4,5,2,3,6,1,7]=>{{1,4},{2,5,6},{3},{7}}
[4,2,5,6,1,7,3]=>[6,4,7,2,5,1,3]=>[5,6,4,2,7,3,1]=>{{1,5,7},{2,6},{3,4}}
[4,2,5,6,3,1,7]=>[3,6,4,1,5,2,7]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[4,2,5,6,3,7,1]=>[7,4,6,2,5,3,1]=>[4,6,5,2,7,1,3]=>{{1,4},{2,6},{3,5,7}}
[4,2,5,6,7,1,3]=>[7,4,1,2,5,6,3]=>[4,5,2,3,6,7,1]=>{{1,4},{2,5,6,7},{3}}
[4,2,5,6,7,3,1]=>[3,7,4,1,5,6,2]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}
[4,2,5,7,1,3,6]=>[7,4,1,2,5,3,6]=>[4,5,2,3,7,1,6]=>{{1,4},{2,5,7},{3},{6}}
[4,2,5,7,1,6,3]=>[7,4,6,2,5,1,3]=>[4,6,5,2,7,3,1]=>{{1,4},{2,6},{3,5,7}}
[4,2,5,7,3,1,6]=>[3,7,4,1,5,2,6]=>[5,3,4,2,7,1,6]=>{{1,5,7},{2,3,4},{6}}
[4,2,5,7,3,6,1]=>[6,4,7,2,5,3,1]=>[5,6,4,2,7,1,3]=>{{1,5,7},{2,6},{3,4}}
[4,2,5,7,6,1,3]=>[6,4,1,2,5,7,3]=>[4,5,2,3,7,6,1]=>{{1,4},{2,5,7},{3},{6}}
[4,2,5,7,6,3,1]=>[3,6,4,1,5,7,2]=>[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}}
[4,2,6,1,3,5,7]=>[6,4,1,2,3,5,7]=>[4,6,2,3,1,5,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,2,6,1,3,7,5]=>[6,4,1,2,7,3,5]=>[4,7,2,3,6,5,1]=>{{1,4},{2,7},{3},{5,6}}
[4,2,6,1,5,3,7]=>[6,4,5,2,1,3,7]=>[4,6,5,2,3,1,7]=>{{1,4},{2,6},{3,5},{7}}
[4,2,6,1,5,7,3]=>[6,4,7,2,1,5,3]=>[6,7,4,2,3,1,5]=>{{1,6},{2,7},{3,4},{5}}
[4,2,6,1,7,3,5]=>[6,4,7,2,3,1,5]=>[6,7,4,2,1,5,3]=>{{1,6},{2,7},{3,4},{5}}
[4,2,6,1,7,5,3]=>[6,4,5,2,7,1,3]=>[4,7,6,2,5,3,1]=>{{1,4},{2,7},{3,6},{5}}
[4,2,6,3,1,5,7]=>[3,6,4,1,2,5,7]=>[6,3,4,2,1,5,7]=>{{1,6},{2,3,4},{5},{7}}
[4,2,6,3,1,7,5]=>[3,6,4,1,7,2,5]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}}
[4,2,6,3,5,1,7]=>[5,4,6,2,3,1,7]=>[5,6,4,2,1,3,7]=>{{1,5},{2,6},{3,4},{7}}
[4,2,6,3,5,7,1]=>[7,4,6,2,3,5,1]=>[4,7,6,2,1,3,5]=>{{1,4},{2,7},{3,6},{5}}
[4,2,6,3,7,1,5]=>[7,4,6,2,1,3,5]=>[4,7,6,2,3,5,1]=>{{1,4},{2,7},{3,6},{5}}
[4,2,6,3,7,5,1]=>[5,4,7,2,6,1,3]=>[5,7,4,2,6,3,1]=>{{1,5,6},{2,7},{3,4}}
[4,2,6,5,1,3,7]=>[5,4,1,2,6,3,7]=>[4,6,2,3,5,1,7]=>{{1,4},{2,6},{3},{5},{7}}
[4,2,6,5,1,7,3]=>[5,4,6,2,7,3,1]=>[6,7,4,2,5,1,3]=>{{1,6},{2,7},{3,4},{5}}
[4,2,6,5,3,1,7]=>[3,5,4,1,6,2,7]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[4,2,6,5,3,7,1]=>[7,4,5,2,6,3,1]=>[4,7,5,2,6,1,3]=>{{1,4},{2,7},{3,5,6}}
[4,2,6,5,7,1,3]=>[7,4,1,2,6,5,3]=>[4,6,2,3,7,1,5]=>{{1,4},{2,6},{3},{5,7}}
[4,2,6,5,7,3,1]=>[3,7,4,1,6,5,2]=>[6,3,4,2,7,1,5]=>{{1,6},{2,3,4},{5,7}}
[4,2,6,7,1,3,5]=>[7,4,1,2,3,6,5]=>[4,6,2,3,1,7,5]=>{{1,4},{2,6,7},{3},{5}}
[4,2,6,7,1,5,3]=>[7,4,5,2,1,6,3]=>[4,6,5,2,3,7,1]=>{{1,4},{2,6,7},{3,5}}
[4,2,6,7,3,1,5]=>[3,7,4,1,2,6,5]=>[6,3,4,2,1,7,5]=>{{1,6,7},{2,3,4},{5}}
[4,2,6,7,3,5,1]=>[5,4,7,2,3,6,1]=>[5,6,4,2,1,7,3]=>{{1,5},{2,6,7},{3,4}}
[4,2,6,7,5,1,3]=>[5,4,1,2,7,6,3]=>[4,6,2,3,5,7,1]=>{{1,4},{2,6,7},{3},{5}}
[4,2,6,7,5,3,1]=>[3,5,4,1,7,6,2]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[4,2,7,1,3,5,6]=>[7,4,1,2,3,5,6]=>[4,7,2,3,1,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,7,1,3,6,5]=>[7,4,1,2,6,3,5]=>[4,6,2,3,7,5,1]=>{{1,4},{2,6},{3},{5,7}}
[4,2,7,1,5,3,6]=>[7,4,5,2,1,3,6]=>[4,7,5,2,3,1,6]=>{{1,4},{2,7},{3,5},{6}}
[4,2,7,1,5,6,3]=>[7,4,6,2,1,5,3]=>[4,7,6,2,3,1,5]=>{{1,4},{2,7},{3,6},{5}}
[4,2,7,1,6,3,5]=>[7,4,6,2,3,1,5]=>[4,7,6,2,1,5,3]=>{{1,4},{2,7},{3,6},{5}}
[4,2,7,1,6,5,3]=>[7,4,5,2,6,1,3]=>[4,7,5,2,6,3,1]=>{{1,4},{2,7},{3,5,6}}
[4,2,7,3,1,5,6]=>[3,7,4,1,2,5,6]=>[7,3,4,2,1,5,6]=>{{1,7},{2,3,4},{5},{6}}
[4,2,7,3,1,6,5]=>[3,7,4,1,6,2,5]=>[6,3,4,2,7,5,1]=>{{1,6},{2,3,4},{5,7}}
[4,2,7,3,5,1,6]=>[5,4,7,2,3,1,6]=>[5,7,4,2,1,3,6]=>{{1,5},{2,7},{3,4},{6}}
[4,2,7,3,5,6,1]=>[6,4,7,2,3,5,1]=>[6,7,4,2,1,3,5]=>{{1,6},{2,7},{3,4},{5}}
[4,2,7,3,6,1,5]=>[6,4,7,2,1,3,5]=>[6,7,4,2,3,5,1]=>{{1,6},{2,7},{3,4},{5}}
[4,2,7,3,6,5,1]=>[5,4,6,2,7,1,3]=>[6,7,4,2,5,3,1]=>{{1,6},{2,7},{3,4},{5}}
[4,2,7,5,1,3,6]=>[5,4,1,2,7,3,6]=>[4,7,2,3,5,1,6]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,7,5,1,6,3]=>[5,4,7,2,6,3,1]=>[5,7,4,2,6,1,3]=>{{1,5,6},{2,7},{3,4}}
[4,2,7,5,3,1,6]=>[3,5,4,1,7,2,6]=>[7,3,4,2,5,1,6]=>{{1,7},{2,3,4},{5},{6}}
[4,2,7,5,3,6,1]=>[6,4,5,2,7,3,1]=>[4,7,6,2,5,1,3]=>{{1,4},{2,7},{3,6},{5}}
[4,2,7,5,6,1,3]=>[6,4,1,2,7,5,3]=>[4,7,2,3,6,1,5]=>{{1,4},{2,7},{3},{5,6}}
[4,2,7,5,6,3,1]=>[3,6,4,1,7,5,2]=>[7,3,4,2,6,1,5]=>{{1,7},{2,3,4},{5,6}}
[4,2,7,6,1,3,5]=>[6,4,1,2,3,7,5]=>[4,7,2,3,1,6,5]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,7,6,1,5,3]=>[6,4,5,2,1,7,3]=>[4,7,5,2,3,6,1]=>{{1,4},{2,7},{3,5},{6}}
[4,2,7,6,3,1,5]=>[3,6,4,1,2,7,5]=>[7,3,4,2,1,6,5]=>{{1,7},{2,3,4},{5},{6}}
[4,2,7,6,3,5,1]=>[5,4,6,2,3,7,1]=>[5,7,4,2,1,6,3]=>{{1,5},{2,7},{3,4},{6}}
[4,2,7,6,5,1,3]=>[5,4,1,2,6,7,3]=>[4,7,2,3,5,6,1]=>{{1,4},{2,7},{3},{5},{6}}
[4,2,7,6,5,3,1]=>[3,5,4,1,6,7,2]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[4,1,3,2,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[4,3,1,2,5,7,6]=>[3,1,4,2,5,7,6]=>[4,1,3,2,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[4,3,1,2,6,5,7]=>[3,1,4,2,6,5,7]=>[4,1,3,2,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[4,3,1,2,6,7,5]=>[3,1,4,2,7,6,5]=>[4,1,3,2,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[4,3,1,2,7,5,6]=>[3,1,4,2,7,5,6]=>[4,1,3,2,7,5,6]=>{{1,4},{2},{3},{5,7},{6}}
[4,3,1,2,7,6,5]=>[3,1,4,2,6,7,5]=>[4,1,3,2,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[4,3,1,5,2,6,7]=>[3,4,5,2,1,6,7]=>[5,4,3,1,2,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[4,3,1,5,2,7,6]=>[3,4,5,2,1,7,6]=>[5,4,3,1,2,7,6]=>{{1,5},{2,4},{3},{6,7}}
[4,3,1,5,6,2,7]=>[3,4,6,2,5,1,7]=>[5,4,3,1,6,2,7]=>{{1,5,6},{2,4},{3},{7}}
[4,3,1,5,6,7,2]=>[3,4,7,2,5,6,1]=>[5,4,3,1,6,7,2]=>{{1,5,6,7},{2,4},{3}}
[4,3,1,5,7,2,6]=>[3,4,7,2,5,1,6]=>[5,4,3,1,7,2,6]=>{{1,5,7},{2,4},{3},{6}}
[4,3,1,5,7,6,2]=>[3,4,6,2,5,7,1]=>[5,4,3,1,7,6,2]=>{{1,5,7},{2,4},{3},{6}}
[4,3,1,6,2,5,7]=>[3,4,6,2,1,5,7]=>[6,4,3,1,2,5,7]=>{{1,6},{2,4},{3},{5},{7}}
[4,3,1,6,2,7,5]=>[3,4,6,2,7,1,5]=>[7,4,3,1,6,5,2]=>{{1,7},{2,4},{3},{5,6}}
[4,3,1,6,5,2,7]=>[3,4,5,2,6,1,7]=>[6,4,3,1,5,2,7]=>{{1,6},{2,4},{3},{5},{7}}
[4,3,1,6,5,7,2]=>[3,4,7,2,6,5,1]=>[6,4,3,1,7,2,5]=>{{1,6},{2,4},{3},{5,7}}
[4,3,1,6,7,2,5]=>[3,4,7,2,1,6,5]=>[6,4,3,1,2,7,5]=>{{1,6,7},{2,4},{3},{5}}
[4,3,1,6,7,5,2]=>[3,4,5,2,7,6,1]=>[6,4,3,1,5,7,2]=>{{1,6,7},{2,4},{3},{5}}
[4,3,1,7,2,5,6]=>[3,4,7,2,1,5,6]=>[7,4,3,1,2,5,6]=>{{1,7},{2,4},{3},{5},{6}}
[4,3,1,7,2,6,5]=>[3,4,7,2,6,1,5]=>[6,4,3,1,7,5,2]=>{{1,6},{2,4},{3},{5,7}}
[4,3,1,7,5,2,6]=>[3,4,5,2,7,1,6]=>[7,4,3,1,5,2,6]=>{{1,7},{2,4},{3},{5},{6}}
[4,3,1,7,5,6,2]=>[3,4,6,2,7,5,1]=>[7,4,3,1,6,2,5]=>{{1,7},{2,4},{3},{5,6}}
[4,3,1,7,6,2,5]=>[3,4,6,2,1,7,5]=>[7,4,3,1,2,6,5]=>{{1,7},{2,4},{3},{5},{6}}
[4,3,1,7,6,5,2]=>[3,4,5,2,6,7,1]=>[7,4,3,1,5,6,2]=>{{1,7},{2,4},{3},{5},{6}}
[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[4,3,2,1,7,5,6]=>[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>{{1,4},{2},{3},{5,7},{6}}
[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[3,5,4,1,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>[3,5,4,1,2,7,6]=>{{1,3,4},{2,5},{6,7}}
[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[3,5,4,1,6,2,7]=>{{1,3,4},{2,5,6},{7}}
[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[3,5,4,1,6,7,2]=>{{1,3,4},{2,5,6,7}}
[4,3,2,5,7,1,6]=>[7,3,4,2,5,1,6]=>[3,5,4,1,7,2,6]=>{{1,3,4},{2,5,7},{6}}
[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>[3,5,4,1,7,6,2]=>{{1,3,4},{2,5,7},{6}}
[4,3,2,6,1,5,7]=>[6,3,4,2,1,5,7]=>[3,6,4,1,2,5,7]=>{{1,3,4},{2,6},{5},{7}}
[4,3,2,6,1,7,5]=>[6,3,4,2,7,1,5]=>[3,7,4,1,6,5,2]=>{{1,3,4},{2,7},{5,6}}
[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>[3,6,4,1,5,2,7]=>{{1,3,4},{2,6},{5},{7}}
[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>[3,6,4,1,7,2,5]=>{{1,3,4},{2,6},{5,7}}
[4,3,2,6,7,1,5]=>[7,3,4,2,1,6,5]=>[3,6,4,1,2,7,5]=>{{1,3,4},{2,6,7},{5}}
[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>[3,6,4,1,5,7,2]=>{{1,3,4},{2,6,7},{5}}
[4,3,2,7,1,5,6]=>[7,3,4,2,1,5,6]=>[3,7,4,1,2,5,6]=>{{1,3,4},{2,7},{5},{6}}
[4,3,2,7,1,6,5]=>[7,3,4,2,6,1,5]=>[3,6,4,1,7,5,2]=>{{1,3,4},{2,6},{5,7}}
[4,3,2,7,5,1,6]=>[5,3,4,2,7,1,6]=>[3,7,4,1,5,2,6]=>{{1,3,4},{2,7},{5},{6}}
[4,3,2,7,5,6,1]=>[6,3,4,2,7,5,1]=>[3,7,4,1,6,2,5]=>{{1,3,4},{2,7},{5,6}}
[4,3,2,7,6,1,5]=>[6,3,4,2,1,7,5]=>[3,7,4,1,2,6,5]=>{{1,3,4},{2,7},{5},{6}}
[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>[3,7,4,1,5,6,2]=>{{1,3,4},{2,7},{5},{6}}
[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[4,1,5,2,3,6,7]=>{{1,4},{2},{3,5},{6},{7}}
[4,3,5,1,2,7,6]=>[5,1,4,3,2,7,6]=>[4,1,5,2,3,7,6]=>{{1,4},{2},{3,5},{6,7}}
[4,3,5,1,6,2,7]=>[5,6,4,3,1,2,7]=>[5,4,6,1,3,2,7]=>{{1,5},{2,4},{3,6},{7}}
[4,3,5,1,6,7,2]=>[5,7,4,3,1,6,2]=>[5,4,6,1,3,7,2]=>{{1,5},{2,4},{3,6,7}}
[4,3,5,1,7,2,6]=>[5,7,4,3,1,2,6]=>[5,4,7,1,3,2,6]=>{{1,5},{2,4},{3,7},{6}}
[4,3,5,1,7,6,2]=>[5,6,4,3,1,7,2]=>[5,4,7,1,3,6,2]=>{{1,5},{2,4},{3,7},{6}}
[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[4,2,5,1,3,6,7]=>{{1,4},{2},{3,5},{6},{7}}
[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>[4,2,5,1,3,7,6]=>{{1,4},{2},{3,5},{6,7}}
[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}}
[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}}
[4,3,5,2,7,1,6]=>[7,5,4,3,2,1,6]=>[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,7},{6}}
[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>[4,5,7,1,2,6,3]=>{{1,4},{2,5},{3,7},{6}}
[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[4,1,5,2,6,3,7]=>{{1,4},{2},{3,5,6},{7}}
[4,3,5,6,1,7,2]=>[6,7,4,3,5,1,2]=>[5,4,6,1,7,3,2]=>{{1,5,7},{2,4},{3,6}}
[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[4,2,5,1,6,3,7]=>{{1,4},{2},{3,5,6},{7}}
[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[4,5,6,1,7,2,3]=>{{1,4},{2,5,7},{3,6}}
[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[4,1,5,2,6,7,3]=>{{1,4},{2},{3,5,6,7}}
[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[4,2,5,1,6,7,3]=>{{1,4},{2},{3,5,6,7}}
[4,3,5,7,1,2,6]=>[7,1,4,3,5,2,6]=>[4,1,5,2,7,3,6]=>{{1,4},{2},{3,5,7},{6}}
[4,3,5,7,1,6,2]=>[7,6,4,3,5,1,2]=>[4,5,6,1,7,3,2]=>{{1,4},{2,5,7},{3,6}}
[4,3,5,7,2,1,6]=>[2,7,4,3,5,1,6]=>[4,2,5,1,7,3,6]=>{{1,4},{2},{3,5,7},{6}}
[4,3,5,7,2,6,1]=>[6,7,4,3,5,2,1]=>[5,4,6,1,7,2,3]=>{{1,5,7},{2,4},{3,6}}
[4,3,5,7,6,1,2]=>[6,1,4,3,5,7,2]=>[4,1,5,2,7,6,3]=>{{1,4},{2},{3,5,7},{6}}
[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>[4,2,5,1,7,6,3]=>{{1,4},{2},{3,5,7},{6}}
[4,3,6,1,2,5,7]=>[6,1,4,3,2,5,7]=>[4,1,6,2,3,5,7]=>{{1,4},{2},{3,6},{5},{7}}
[4,3,6,1,2,7,5]=>[6,1,4,3,7,2,5]=>[4,1,7,2,6,5,3]=>{{1,4},{2},{3,7},{5,6}}
[4,3,6,1,5,2,7]=>[6,5,4,3,1,2,7]=>[4,5,6,1,3,2,7]=>{{1,4},{2,5},{3,6},{7}}
[4,3,6,1,5,7,2]=>[6,7,4,3,1,5,2]=>[6,4,7,1,3,2,5]=>{{1,6},{2,4},{3,7},{5}}
[4,3,6,1,7,2,5]=>[6,7,4,3,2,1,5]=>[6,4,7,1,2,5,3]=>{{1,6},{2,4},{3,7},{5}}
[4,3,6,1,7,5,2]=>[6,5,4,3,7,1,2]=>[4,6,7,1,5,3,2]=>{{1,4},{2,6},{3,7},{5}}
[4,3,6,2,1,5,7]=>[2,6,4,3,1,5,7]=>[4,2,6,1,3,5,7]=>{{1,4},{2},{3,6},{5},{7}}
[4,3,6,2,1,7,5]=>[2,6,4,3,7,1,5]=>[4,2,7,1,6,5,3]=>{{1,4},{2},{3,7},{5,6}}
[4,3,6,2,5,1,7]=>[5,6,4,3,2,1,7]=>[5,4,6,1,2,3,7]=>{{1,5},{2,4},{3,6},{7}}
[4,3,6,2,5,7,1]=>[7,6,4,3,2,5,1]=>[4,6,7,1,2,3,5]=>{{1,4},{2,6},{3,7},{5}}
[4,3,6,2,7,1,5]=>[7,6,4,3,1,2,5]=>[4,6,7,1,3,5,2]=>{{1,4},{2,6},{3,7},{5}}
[4,3,6,2,7,5,1]=>[5,7,4,3,6,1,2]=>[5,4,7,1,6,3,2]=>{{1,5,6},{2,4},{3,7}}
[4,3,6,5,1,2,7]=>[5,1,4,3,6,2,7]=>[4,1,6,2,5,3,7]=>{{1,4},{2},{3,6},{5},{7}}
[4,3,6,5,1,7,2]=>[5,6,4,3,7,2,1]=>[6,4,7,1,5,2,3]=>{{1,6},{2,4},{3,7},{5}}
[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>[4,2,6,1,5,3,7]=>{{1,4},{2},{3,6},{5},{7}}
[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>[4,5,7,1,6,2,3]=>{{1,4},{2,5,6},{3,7}}
[4,3,6,5,7,1,2]=>[7,1,4,3,6,5,2]=>[4,1,6,2,7,3,5]=>{{1,4},{2},{3,6},{5,7}}
[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>[4,2,6,1,7,3,5]=>{{1,4},{2},{3,6},{5,7}}
[4,3,6,7,1,2,5]=>[7,1,4,3,2,6,5]=>[4,1,6,2,3,7,5]=>{{1,4},{2},{3,6,7},{5}}
[4,3,6,7,1,5,2]=>[7,5,4,3,1,6,2]=>[4,5,6,1,3,7,2]=>{{1,4},{2,5},{3,6,7}}
[4,3,6,7,2,1,5]=>[2,7,4,3,1,6,5]=>[4,2,6,1,3,7,5]=>{{1,4},{2},{3,6,7},{5}}
[4,3,6,7,2,5,1]=>[5,7,4,3,2,6,1]=>[5,4,6,1,2,7,3]=>{{1,5},{2,4},{3,6,7}}
[4,3,6,7,5,1,2]=>[5,1,4,3,7,6,2]=>[4,1,6,2,5,7,3]=>{{1,4},{2},{3,6,7},{5}}
[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>[4,2,6,1,5,7,3]=>{{1,4},{2},{3,6,7},{5}}
[4,3,7,1,2,5,6]=>[7,1,4,3,2,5,6]=>[4,1,7,2,3,5,6]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,1,2,6,5]=>[7,1,4,3,6,2,5]=>[4,1,6,2,7,5,3]=>{{1,4},{2},{3,6},{5,7}}
[4,3,7,1,5,2,6]=>[7,5,4,3,1,2,6]=>[4,5,7,1,3,2,6]=>{{1,4},{2,5},{3,7},{6}}
[4,3,7,1,5,6,2]=>[7,6,4,3,1,5,2]=>[4,6,7,1,3,2,5]=>{{1,4},{2,6},{3,7},{5}}
[4,3,7,1,6,2,5]=>[7,6,4,3,2,1,5]=>[4,6,7,1,2,5,3]=>{{1,4},{2,6},{3,7},{5}}
[4,3,7,1,6,5,2]=>[7,5,4,3,6,1,2]=>[4,5,7,1,6,3,2]=>{{1,4},{2,5,6},{3,7}}
[4,3,7,2,1,5,6]=>[2,7,4,3,1,5,6]=>[4,2,7,1,3,5,6]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,2,1,6,5]=>[2,7,4,3,6,1,5]=>[4,2,6,1,7,5,3]=>{{1,4},{2},{3,6},{5,7}}
[4,3,7,2,5,1,6]=>[5,7,4,3,2,1,6]=>[5,4,7,1,2,3,6]=>{{1,5},{2,4},{3,7},{6}}
[4,3,7,2,5,6,1]=>[6,7,4,3,2,5,1]=>[6,4,7,1,2,3,5]=>{{1,6},{2,4},{3,7},{5}}
[4,3,7,2,6,1,5]=>[6,7,4,3,1,2,5]=>[6,4,7,1,3,5,2]=>{{1,6},{2,4},{3,7},{5}}
[4,3,7,2,6,5,1]=>[5,6,4,3,7,1,2]=>[6,4,7,1,5,3,2]=>{{1,6},{2,4},{3,7},{5}}
[4,3,7,5,1,2,6]=>[5,1,4,3,7,2,6]=>[4,1,7,2,5,3,6]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,5,1,6,2]=>[5,7,4,3,6,2,1]=>[5,4,7,1,6,2,3]=>{{1,5,6},{2,4},{3,7}}
[4,3,7,5,2,1,6]=>[2,5,4,3,7,1,6]=>[4,2,7,1,5,3,6]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,5,2,6,1]=>[6,5,4,3,7,2,1]=>[4,6,7,1,5,2,3]=>{{1,4},{2,6},{3,7},{5}}
[4,3,7,5,6,1,2]=>[6,1,4,3,7,5,2]=>[4,1,7,2,6,3,5]=>{{1,4},{2},{3,7},{5,6}}
[4,3,7,5,6,2,1]=>[2,6,4,3,7,5,1]=>[4,2,7,1,6,3,5]=>{{1,4},{2},{3,7},{5,6}}
[4,3,7,6,1,2,5]=>[6,1,4,3,2,7,5]=>[4,1,7,2,3,6,5]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,6,1,5,2]=>[6,5,4,3,1,7,2]=>[4,5,7,1,3,6,2]=>{{1,4},{2,5},{3,7},{6}}
[4,3,7,6,2,1,5]=>[2,6,4,3,1,7,5]=>[4,2,7,1,3,6,5]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,6,2,5,1]=>[5,6,4,3,2,7,1]=>[5,4,7,1,2,6,3]=>{{1,5},{2,4},{3,7},{6}}
[4,3,7,6,5,1,2]=>[5,1,4,3,6,7,2]=>[4,1,7,2,5,6,3]=>{{1,4},{2},{3,7},{5},{6}}
[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>[4,2,7,1,5,6,3]=>{{1,4},{2},{3,7},{5},{6}}
[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[4,1,2,5,3,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[4,1,2,5,3,7,6]=>{{1,4,5},{2},{3},{6,7}}
[4,5,1,2,6,3,7]=>[5,1,6,4,2,3,7]=>[5,1,4,6,3,2,7]=>{{1,5},{2},{3,4,6},{7}}
[4,5,1,2,6,7,3]=>[5,1,7,4,2,6,3]=>[5,1,4,6,3,7,2]=>{{1,5},{2},{3,4,6,7}}
[4,5,1,2,7,3,6]=>[5,1,7,4,2,3,6]=>[5,1,4,7,3,2,6]=>{{1,5},{2},{3,4,7},{6}}
[4,5,1,2,7,6,3]=>[5,1,6,4,2,7,3]=>[5,1,4,7,3,6,2]=>{{1,5},{2},{3,4,7},{6}}
[4,5,1,3,2,6,7]=>[5,3,1,4,2,6,7]=>[3,4,2,5,1,6,7]=>{{1,3},{2,4,5},{6},{7}}
[4,5,1,3,2,7,6]=>[5,3,1,4,2,7,6]=>[3,4,2,5,1,7,6]=>{{1,3},{2,4,5},{6,7}}
[4,5,1,3,6,2,7]=>[5,6,1,4,3,2,7]=>[5,4,2,6,1,3,7]=>{{1,5},{2,4,6},{3},{7}}
[4,5,1,3,6,7,2]=>[5,7,1,4,3,6,2]=>[5,4,2,6,1,7,3]=>{{1,5},{2,4,6,7},{3}}
[4,5,1,3,7,2,6]=>[5,7,1,4,3,2,6]=>[5,4,2,7,1,3,6]=>{{1,5},{2,4,7},{3},{6}}
[4,5,1,3,7,6,2]=>[5,6,1,4,3,7,2]=>[5,4,2,7,1,6,3]=>{{1,5},{2,4,7},{3},{6}}
[4,5,1,6,2,3,7]=>[5,6,2,4,1,3,7]=>[5,4,1,6,3,2,7]=>{{1,5},{2,4,6},{3},{7}}
[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[6,5,4,7,3,2,1]=>{{1,6},{2,5},{3,4,7}}
[4,5,1,6,3,2,7]=>[5,3,6,4,1,2,7]=>[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}
[4,5,1,6,3,7,2]=>[5,7,6,4,1,3,2]=>[6,4,5,7,3,1,2]=>{{1,6},{2,4,7},{3,5}}
[4,5,1,6,7,2,3]=>[5,7,2,4,1,6,3]=>[5,4,1,6,3,7,2]=>{{1,5},{2,4,6,7},{3}}
[4,5,1,6,7,3,2]=>[5,3,7,4,1,6,2]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}
[4,5,1,7,2,3,6]=>[5,7,2,4,1,3,6]=>[5,4,1,7,3,2,6]=>{{1,5},{2,4,7},{3},{6}}
[4,5,1,7,2,6,3]=>[5,7,6,4,1,2,3]=>[6,4,5,7,3,2,1]=>{{1,6},{2,4,7},{3,5}}
[4,5,1,7,3,2,6]=>[5,3,7,4,1,2,6]=>[4,5,3,7,2,1,6]=>{{1,4,7},{2,5},{3},{6}}
[4,5,1,7,3,6,2]=>[5,6,7,4,1,3,2]=>[6,5,4,7,3,1,2]=>{{1,6},{2,5},{3,4,7}}
[4,5,1,7,6,2,3]=>[5,6,2,4,1,7,3]=>[5,4,1,7,3,6,2]=>{{1,5},{2,4,7},{3},{6}}
[4,5,1,7,6,3,2]=>[5,3,6,4,1,7,2]=>[4,5,3,7,2,6,1]=>{{1,4,7},{2,5},{3},{6}}
[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[4,2,1,5,3,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[4,5,2,1,3,7,6]=>[2,5,1,4,3,7,6]=>[4,2,1,5,3,7,6]=>{{1,4,5},{2},{3},{6,7}}
[4,5,2,1,6,3,7]=>[2,5,6,4,1,3,7]=>[5,2,4,6,3,1,7]=>{{1,5},{2},{3,4,6},{7}}
[4,5,2,1,6,7,3]=>[2,5,7,4,1,6,3]=>[5,2,4,6,3,7,1]=>{{1,5},{2},{3,4,6,7}}
[4,5,2,1,7,3,6]=>[2,5,7,4,1,3,6]=>[5,2,4,7,3,1,6]=>{{1,5},{2},{3,4,7},{6}}
[4,5,2,1,7,6,3]=>[2,5,6,4,1,7,3]=>[5,2,4,7,3,6,1]=>{{1,5},{2},{3,4,7},{6}}
[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[4,3,1,5,2,6,7]=>{{1,4,5},{2,3},{6},{7}}
[4,5,2,3,1,7,6]=>[3,5,2,4,1,7,6]=>[4,3,1,5,2,7,6]=>{{1,4,5},{2,3},{6,7}}
[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[4,5,1,6,2,3,7]=>{{1,4,6},{2,5},{3},{7}}
[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[4,5,1,6,2,7,3]=>{{1,4,6,7},{2,5},{3}}
[4,5,2,3,7,1,6]=>[7,5,2,4,3,1,6]=>[4,5,1,7,2,3,6]=>{{1,4,7},{2,5},{3},{6}}
[4,5,2,3,7,6,1]=>[6,5,2,4,3,7,1]=>[4,5,1,7,2,6,3]=>{{1,4,7},{2,5},{3},{6}}
[4,5,2,6,1,3,7]=>[6,5,1,4,2,3,7]=>[4,5,2,6,3,1,7]=>{{1,4,6},{2,5},{3},{7}}
[4,5,2,6,1,7,3]=>[6,5,7,4,2,1,3]=>[5,6,4,7,2,3,1]=>{{1,5},{2,6},{3,4,7}}
[4,5,2,6,3,1,7]=>[3,6,5,4,1,2,7]=>[5,3,4,6,2,1,7]=>{{1,5},{2,3,4,6},{7}}
[4,5,2,6,3,7,1]=>[7,5,6,4,2,3,1]=>[4,6,5,7,2,1,3]=>{{1,4,7},{2,6},{3,5}}
[4,5,2,6,7,1,3]=>[7,5,1,4,2,6,3]=>[4,5,2,6,3,7,1]=>{{1,4,6,7},{2,5},{3}}
[4,5,2,6,7,3,1]=>[3,7,5,4,1,6,2]=>[5,3,4,6,2,7,1]=>{{1,5},{2,3,4,6,7}}
[4,5,2,7,1,3,6]=>[7,5,1,4,2,3,6]=>[4,5,2,7,3,1,6]=>{{1,4,7},{2,5},{3},{6}}
[4,5,2,7,1,6,3]=>[7,5,6,4,2,1,3]=>[4,6,5,7,2,3,1]=>{{1,4,7},{2,6},{3,5}}
[4,5,2,7,3,1,6]=>[3,7,5,4,1,2,6]=>[5,3,4,7,2,1,6]=>{{1,5},{2,3,4,7},{6}}
[4,5,2,7,3,6,1]=>[6,5,7,4,2,3,1]=>[5,6,4,7,2,1,3]=>{{1,5},{2,6},{3,4,7}}
[4,5,2,7,6,1,3]=>[6,5,1,4,2,7,3]=>[4,5,2,7,3,6,1]=>{{1,4,7},{2,5},{3},{6}}
[4,5,2,7,6,3,1]=>[3,6,5,4,1,7,2]=>[5,3,4,7,2,6,1]=>{{1,5},{2,3,4,7},{6}}
[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[4,1,3,5,2,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[4,5,3,1,2,7,6]=>[3,1,5,4,2,7,6]=>[4,1,3,5,2,7,6]=>{{1,4,5},{2},{3},{6,7}}
[4,5,3,1,6,2,7]=>[3,5,6,4,2,1,7]=>[5,4,3,6,1,2,7]=>{{1,5},{2,4,6},{3},{7}}
[4,5,3,1,6,7,2]=>[3,5,7,4,2,6,1]=>[5,4,3,6,1,7,2]=>{{1,5},{2,4,6,7},{3}}
[4,5,3,1,7,2,6]=>[3,5,7,4,2,1,6]=>[5,4,3,7,1,2,6]=>{{1,5},{2,4,7},{3},{6}}
[4,5,3,1,7,6,2]=>[3,5,6,4,2,7,1]=>[5,4,3,7,1,6,2]=>{{1,5},{2,4,7},{3},{6}}
[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}}
[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[3,5,4,6,1,2,7]=>{{1,3,4,6},{2,5},{7}}
[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[3,5,4,6,1,7,2]=>{{1,3,4,6,7},{2,5}}
[4,5,3,2,7,1,6]=>[7,3,5,4,2,1,6]=>[3,5,4,7,1,2,6]=>{{1,3,4,7},{2,5},{6}}
[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>[3,5,4,7,1,6,2]=>{{1,3,4,7},{2,5},{6}}
[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[4,1,5,6,2,3,7]=>{{1,4,6},{2},{3,5},{7}}
[4,5,3,6,1,7,2]=>[6,7,5,4,3,1,2]=>[5,4,6,7,1,3,2]=>{{1,5},{2,4,7},{3,6}}
[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[4,2,5,6,1,3,7]=>{{1,4,6},{2},{3,5},{7}}
[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[4,5,6,7,1,2,3]=>{{1,4,7},{2,5},{3,6}}
[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[4,1,5,6,2,7,3]=>{{1,4,6,7},{2},{3,5}}
[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[4,2,5,6,1,7,3]=>{{1,4,6,7},{2},{3,5}}
[4,5,3,7,1,2,6]=>[7,1,5,4,3,2,6]=>[4,1,5,7,2,3,6]=>{{1,4,7},{2},{3,5},{6}}
[4,5,3,7,1,6,2]=>[7,6,5,4,3,1,2]=>[4,5,6,7,1,3,2]=>{{1,4,7},{2,5},{3,6}}
[4,5,3,7,2,1,6]=>[2,7,5,4,3,1,6]=>[4,2,5,7,1,3,6]=>{{1,4,7},{2},{3,5},{6}}
[4,5,3,7,2,6,1]=>[6,7,5,4,3,2,1]=>[5,4,6,7,1,2,3]=>{{1,5},{2,4,7},{3,6}}
[4,5,3,7,6,1,2]=>[6,1,5,4,3,7,2]=>[4,1,5,7,2,6,3]=>{{1,4,7},{2},{3,5},{6}}
[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>[4,2,5,7,1,6,3]=>{{1,4,7},{2},{3,5},{6}}
[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[4,1,2,5,6,3,7]=>{{1,4,5,6},{2},{3},{7}}
[4,5,6,1,2,7,3]=>[6,1,7,4,5,2,3]=>[5,1,4,6,7,3,2]=>{{1,5,7},{2},{3,4,6}}
[4,5,6,1,3,2,7]=>[6,3,1,4,5,2,7]=>[3,4,2,5,6,1,7]=>{{1,3},{2,4,5,6},{7}}
[4,5,6,1,3,7,2]=>[6,7,1,4,5,3,2]=>[5,4,2,6,7,1,3]=>{{1,5,7},{2,4,6},{3}}
[4,5,6,1,7,2,3]=>[6,7,2,4,5,1,3]=>[5,4,1,6,7,3,2]=>{{1,5,7},{2,4,6},{3}}
[4,5,6,1,7,3,2]=>[6,3,7,4,5,1,2]=>[4,5,3,6,7,2,1]=>{{1,4,6},{2,5,7},{3}}
[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[4,2,1,5,6,3,7]=>{{1,4,5,6},{2},{3},{7}}
[4,5,6,2,1,7,3]=>[2,6,7,4,5,1,3]=>[5,2,4,6,7,3,1]=>{{1,5,7},{2},{3,4,6}}
[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[4,3,1,5,6,2,7]=>{{1,4,5,6},{2,3},{7}}
[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[4,5,1,6,7,2,3]=>{{1,4,6},{2,5,7},{3}}
[4,5,6,2,7,1,3]=>[7,6,1,4,5,2,3]=>[4,5,2,6,7,3,1]=>{{1,4,6},{2,5,7},{3}}
[4,5,6,2,7,3,1]=>[3,7,6,4,5,1,2]=>[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}}
[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[4,1,3,5,6,2,7]=>{{1,4,5,6},{2},{3},{7}}
[4,5,6,3,1,7,2]=>[3,6,7,4,5,2,1]=>[5,4,3,6,7,1,2]=>{{1,5,7},{2,4,6},{3}}
[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}
[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[3,5,4,6,7,1,2]=>{{1,3,4,6},{2,5,7}}
[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[4,1,5,6,7,2,3]=>{{1,4,6},{2},{3,5,7}}
[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[4,2,5,6,7,1,3]=>{{1,4,6},{2},{3,5,7}}
[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[4,1,2,5,6,7,3]=>{{1,4,5,6,7},{2},{3}}
[4,5,6,7,1,3,2]=>[7,3,1,4,5,6,2]=>[3,4,2,5,6,7,1]=>{{1,3},{2,4,5,6,7}}
[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[4,2,1,5,6,7,3]=>{{1,4,5,6,7},{2},{3}}
[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[4,3,1,5,6,7,2]=>{{1,4,5,6,7},{2,3}}
[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[4,1,3,5,6,7,2]=>{{1,4,5,6,7},{2},{3}}
[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}
[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[4,1,2,5,7,3,6]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,1,2,6,3]=>[7,1,6,4,5,2,3]=>[4,1,5,6,7,3,2]=>{{1,4,6},{2},{3,5,7}}
[4,5,7,1,3,2,6]=>[7,3,1,4,5,2,6]=>[3,4,2,5,7,1,6]=>{{1,3},{2,4,5,7},{6}}
[4,5,7,1,3,6,2]=>[7,6,1,4,5,3,2]=>[4,5,2,6,7,1,3]=>{{1,4,6},{2,5,7},{3}}
[4,5,7,1,6,2,3]=>[7,6,2,4,5,1,3]=>[4,5,1,6,7,3,2]=>{{1,4,6},{2,5,7},{3}}
[4,5,7,1,6,3,2]=>[7,3,6,4,5,1,2]=>[3,5,4,6,7,2,1]=>{{1,3,4,6},{2,5,7}}
[4,5,7,2,1,3,6]=>[2,7,1,4,5,3,6]=>[4,2,1,5,7,3,6]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,2,1,6,3]=>[2,7,6,4,5,1,3]=>[4,2,5,6,7,3,1]=>{{1,4,6},{2},{3,5,7}}
[4,5,7,2,3,1,6]=>[3,7,2,4,5,1,6]=>[4,3,1,5,7,2,6]=>{{1,4,5,7},{2,3},{6}}
[4,5,7,2,3,6,1]=>[6,7,2,4,5,3,1]=>[5,4,1,6,7,2,3]=>{{1,5,7},{2,4,6},{3}}
[4,5,7,2,6,1,3]=>[6,7,1,4,5,2,3]=>[5,4,2,6,7,3,1]=>{{1,5,7},{2,4,6},{3}}
[4,5,7,2,6,3,1]=>[3,6,7,4,5,1,2]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}
[4,5,7,3,1,2,6]=>[3,1,7,4,5,2,6]=>[4,1,3,5,7,2,6]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,3,1,6,2]=>[3,7,6,4,5,2,1]=>[5,3,4,6,7,1,2]=>{{1,5,7},{2,3,4,6}}
[4,5,7,3,2,1,6]=>[2,3,7,4,5,1,6]=>[4,2,3,5,7,1,6]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,3,2,6,1]=>[6,3,7,4,5,2,1]=>[4,5,3,6,7,1,2]=>{{1,4,6},{2,5,7},{3}}
[4,5,7,3,6,1,2]=>[6,1,7,4,5,3,2]=>[5,1,4,6,7,2,3]=>{{1,5,7},{2},{3,4,6}}
[4,5,7,3,6,2,1]=>[2,6,7,4,5,3,1]=>[5,2,4,6,7,1,3]=>{{1,5,7},{2},{3,4,6}}
[4,5,7,6,1,2,3]=>[6,1,2,4,5,7,3]=>[4,1,2,5,7,6,3]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,6,1,3,2]=>[6,3,1,4,5,7,2]=>[3,4,2,5,7,6,1]=>{{1,3},{2,4,5,7},{6}}
[4,5,7,6,2,1,3]=>[2,6,1,4,5,7,3]=>[4,2,1,5,7,6,3]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,6,2,3,1]=>[3,6,2,4,5,7,1]=>[4,3,1,5,7,6,2]=>{{1,4,5,7},{2,3},{6}}
[4,5,7,6,3,1,2]=>[3,1,6,4,5,7,2]=>[4,1,3,5,7,6,2]=>{{1,4,5,7},{2},{3},{6}}
[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}}
[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[4,1,2,6,3,5,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,1,2,3,7,5]=>[6,1,2,4,7,3,5]=>[4,1,2,7,6,5,3]=>{{1,4,7},{2},{3},{5,6}}
[4,6,1,2,5,3,7]=>[6,1,5,4,2,3,7]=>[4,1,5,6,3,2,7]=>{{1,4,6},{2},{3,5},{7}}
[4,6,1,2,5,7,3]=>[6,1,7,4,2,5,3]=>[6,1,4,7,3,2,5]=>{{1,6},{2},{3,4,7},{5}}
[4,6,1,2,7,3,5]=>[6,1,7,4,3,2,5]=>[6,1,4,7,2,5,3]=>{{1,6},{2},{3,4,7},{5}}
[4,6,1,2,7,5,3]=>[6,1,5,4,7,2,3]=>[4,1,6,7,5,3,2]=>{{1,4,7},{2},{3,6},{5}}
[4,6,1,3,2,5,7]=>[6,3,1,4,2,5,7]=>[3,4,2,6,1,5,7]=>{{1,3},{2,4,6},{5},{7}}
[4,6,1,3,2,7,5]=>[6,3,1,4,7,2,5]=>[3,4,2,7,6,5,1]=>{{1,3},{2,4,7},{5,6}}
[4,6,1,3,5,2,7]=>[6,5,1,4,3,2,7]=>[4,5,2,6,1,3,7]=>{{1,4,6},{2,5},{3},{7}}
[4,6,1,3,5,7,2]=>[6,7,1,4,2,3,5]=>[6,4,2,7,3,5,1]=>{{1,6},{2,4,7},{3},{5}}
[4,6,1,3,7,2,5]=>[6,7,1,4,3,5,2]=>[6,4,2,7,1,3,5]=>{{1,6},{2,4,7},{3},{5}}
[4,6,1,3,7,5,2]=>[6,5,1,4,7,3,2]=>[4,6,2,7,5,1,3]=>{{1,4,7},{2,6},{3},{5}}
[4,6,1,5,2,3,7]=>[6,5,2,4,1,3,7]=>[4,5,1,6,3,2,7]=>{{1,4,6},{2,5},{3},{7}}
[4,6,1,5,2,7,3]=>[6,5,7,4,1,2,3]=>[5,6,4,7,3,2,1]=>{{1,5},{2,6},{3,4,7}}
[4,6,1,5,3,2,7]=>[6,3,5,4,1,2,7]=>[3,5,4,6,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[4,6,1,5,3,7,2]=>[6,7,5,4,1,3,2]=>[5,4,6,7,3,1,2]=>{{1,5},{2,4,7},{3,6}}
[4,6,1,5,7,2,3]=>[6,7,2,4,1,5,3]=>[6,4,1,7,3,2,5]=>{{1,6},{2,4,7},{3},{5}}
[4,6,1,5,7,3,2]=>[6,3,7,4,1,5,2]=>[4,6,3,7,2,1,5]=>{{1,4,7},{2,6},{3},{5}}
[4,6,1,7,2,3,5]=>[6,7,2,4,3,1,5]=>[6,4,1,7,2,5,3]=>{{1,6},{2,4,7},{3},{5}}
[4,6,1,7,2,5,3]=>[6,7,5,4,2,1,3]=>[5,4,6,7,2,3,1]=>{{1,5},{2,4,7},{3,6}}
[4,6,1,7,3,2,5]=>[6,3,7,4,2,1,5]=>[4,6,3,7,1,5,2]=>{{1,4,7},{2,6},{3},{5}}
[4,6,1,7,3,5,2]=>[6,5,7,4,3,1,2]=>[5,6,4,7,1,3,2]=>{{1,5},{2,6},{3,4,7}}
[4,6,1,7,5,2,3]=>[6,5,2,4,7,1,3]=>[4,6,1,7,5,3,2]=>{{1,4,7},{2,6},{3},{5}}
[4,6,1,7,5,3,2]=>[6,3,5,4,7,1,2]=>[3,6,4,7,5,2,1]=>{{1,3,4,7},{2,6},{5}}
[4,6,2,1,3,5,7]=>[2,6,1,4,3,5,7]=>[4,2,1,6,3,5,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,2,1,3,7,5]=>[2,6,1,4,7,3,5]=>[4,2,1,7,6,5,3]=>{{1,4,7},{2},{3},{5,6}}
[4,6,2,1,5,3,7]=>[2,6,5,4,1,3,7]=>[4,2,5,6,3,1,7]=>{{1,4,6},{2},{3,5},{7}}
[4,6,2,1,5,7,3]=>[2,6,7,4,1,5,3]=>[6,2,4,7,3,1,5]=>{{1,6},{2},{3,4,7},{5}}
[4,6,2,1,7,3,5]=>[2,6,7,4,3,1,5]=>[6,2,4,7,1,5,3]=>{{1,6},{2},{3,4,7},{5}}
[4,6,2,1,7,5,3]=>[2,6,5,4,7,1,3]=>[4,2,6,7,5,3,1]=>{{1,4,7},{2},{3,6},{5}}
[4,6,2,3,1,5,7]=>[3,6,2,4,1,5,7]=>[4,3,1,6,2,5,7]=>{{1,4,6},{2,3},{5},{7}}
[4,6,2,3,1,7,5]=>[3,6,2,4,7,1,5]=>[4,3,1,7,6,5,2]=>{{1,4,7},{2,3},{5,6}}
[4,6,2,3,5,1,7]=>[5,6,2,4,3,1,7]=>[5,4,1,6,2,3,7]=>{{1,5},{2,4,6},{3},{7}}
[4,6,2,3,5,7,1]=>[7,6,2,4,3,5,1]=>[4,6,1,7,2,3,5]=>{{1,4,7},{2,6},{3},{5}}
[4,6,2,3,7,1,5]=>[7,6,2,4,1,3,5]=>[4,6,1,7,3,5,2]=>{{1,4,7},{2,6},{3},{5}}
[4,6,2,3,7,5,1]=>[5,7,2,4,6,1,3]=>[5,4,1,7,6,3,2]=>{{1,5,6},{2,4,7},{3}}
[4,6,2,5,1,3,7]=>[5,6,1,4,2,3,7]=>[5,4,2,6,3,1,7]=>{{1,5},{2,4,6},{3},{7}}
[4,6,2,5,1,7,3]=>[5,6,7,4,2,1,3]=>[6,5,4,7,2,3,1]=>{{1,6},{2,5},{3,4,7}}
[4,6,2,5,3,1,7]=>[3,5,6,4,1,2,7]=>[5,4,3,6,2,1,7]=>{{1,5},{2,4,6},{3},{7}}
[4,6,2,5,3,7,1]=>[7,6,5,4,2,3,1]=>[4,5,6,7,2,1,3]=>{{1,4,7},{2,5},{3,6}}
[4,6,2,5,7,1,3]=>[7,6,1,4,3,2,5]=>[4,6,2,7,1,5,3]=>{{1,4,7},{2,6},{3},{5}}
[4,6,2,5,7,3,1]=>[3,7,6,4,2,1,5]=>[6,3,4,7,1,5,2]=>{{1,6},{2,3,4,7},{5}}
[4,6,2,7,1,3,5]=>[7,6,1,4,2,5,3]=>[4,6,2,7,3,1,5]=>{{1,4,7},{2,6},{3},{5}}
[4,6,2,7,1,5,3]=>[7,6,5,4,1,2,3]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,5},{3,6}}
[4,6,2,7,3,1,5]=>[3,7,6,4,1,5,2]=>[6,3,4,7,2,1,5]=>{{1,6},{2,3,4,7},{5}}
[4,6,2,7,3,5,1]=>[5,6,7,4,3,2,1]=>[6,5,4,7,1,2,3]=>{{1,6},{2,5},{3,4,7}}
[4,6,2,7,5,1,3]=>[5,7,1,4,6,3,2]=>[5,4,2,7,6,1,3]=>{{1,5,6},{2,4,7},{3}}
[4,6,2,7,5,3,1]=>[3,5,7,4,6,2,1]=>[5,4,3,7,6,1,2]=>{{1,5,6},{2,4,7},{3}}
[4,6,3,1,2,5,7]=>[3,1,6,4,2,5,7]=>[4,1,3,6,2,5,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,3,1,2,7,5]=>[3,1,6,4,7,2,5]=>[4,1,3,7,6,5,2]=>{{1,4,7},{2},{3},{5,6}}
[4,6,3,1,5,2,7]=>[3,6,5,4,2,1,7]=>[5,3,4,6,1,2,7]=>{{1,5},{2,3,4,6},{7}}
[4,6,3,1,5,7,2]=>[3,6,7,4,1,2,5]=>[6,4,3,7,2,5,1]=>{{1,6},{2,4,7},{3},{5}}
[4,6,3,1,7,2,5]=>[3,6,7,4,2,5,1]=>[6,4,3,7,1,2,5]=>{{1,6},{2,4,7},{3},{5}}
[4,6,3,1,7,5,2]=>[3,6,5,4,7,2,1]=>[6,3,4,7,5,1,2]=>{{1,6},{2,3,4,7},{5}}
[4,6,3,2,1,5,7]=>[2,3,6,4,1,5,7]=>[4,2,3,6,1,5,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,3,2,1,7,5]=>[2,3,6,4,7,1,5]=>[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}}
[4,6,3,2,5,1,7]=>[5,3,6,4,2,1,7]=>[4,5,3,6,1,2,7]=>{{1,4,6},{2,5},{3},{7}}
[4,6,3,2,5,7,1]=>[7,3,6,4,2,5,1]=>[3,6,4,7,1,2,5]=>{{1,3,4,7},{2,6},{5}}
[4,6,3,2,7,1,5]=>[7,3,6,4,1,2,5]=>[3,6,4,7,2,5,1]=>{{1,3,4,7},{2,6},{5}}
[4,6,3,2,7,5,1]=>[5,3,7,4,6,1,2]=>[4,5,3,7,6,2,1]=>{{1,4,7},{2,5,6},{3}}
[4,6,3,5,1,2,7]=>[5,1,6,4,3,2,7]=>[5,1,4,6,2,3,7]=>{{1,5},{2},{3,4,6},{7}}
[4,6,3,5,1,7,2]=>[5,7,6,4,3,1,2]=>[6,4,5,7,1,3,2]=>{{1,6},{2,4,7},{3,5}}
[4,6,3,5,2,1,7]=>[2,5,6,4,3,1,7]=>[5,2,4,6,1,3,7]=>{{1,5},{2},{3,4,6},{7}}
[4,6,3,5,2,7,1]=>[7,5,6,4,3,2,1]=>[4,6,5,7,1,2,3]=>{{1,4,7},{2,6},{3,5}}
[4,6,3,5,7,1,2]=>[7,1,6,4,3,5,2]=>[4,1,6,7,2,3,5]=>{{1,4,7},{2},{3,6},{5}}
[4,6,3,5,7,2,1]=>[2,7,6,4,3,5,1]=>[4,2,6,7,1,3,5]=>{{1,4,7},{2},{3,6},{5}}
[4,6,3,7,1,2,5]=>[7,1,6,4,2,3,5]=>[4,1,6,7,3,5,2]=>{{1,4,7},{2},{3,6},{5}}
[4,6,3,7,1,5,2]=>[7,5,6,4,1,3,2]=>[4,6,5,7,3,1,2]=>{{1,4,7},{2,6},{3,5}}
[4,6,3,7,2,1,5]=>[2,7,6,4,1,3,5]=>[4,2,6,7,3,5,1]=>{{1,4,7},{2},{3,6},{5}}
[4,6,3,7,2,5,1]=>[5,7,6,4,2,3,1]=>[6,4,5,7,2,1,3]=>{{1,6},{2,4,7},{3,5}}
[4,6,3,7,5,1,2]=>[5,1,7,4,6,2,3]=>[5,1,4,7,6,3,2]=>{{1,5,6},{2},{3,4,7}}
[4,6,3,7,5,2,1]=>[2,5,7,4,6,1,3]=>[5,2,4,7,6,3,1]=>{{1,5,6},{2},{3,4,7}}
[4,6,5,1,2,3,7]=>[5,1,2,4,6,3,7]=>[4,1,2,6,5,3,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,5,1,2,7,3]=>[5,1,6,4,7,3,2]=>[6,1,4,7,5,2,3]=>{{1,6},{2},{3,4,7},{5}}
[4,6,5,1,3,2,7]=>[5,3,1,4,6,2,7]=>[3,4,2,6,5,1,7]=>{{1,3},{2,4,6},{5},{7}}
[4,6,5,1,3,7,2]=>[5,6,1,4,7,2,3]=>[6,4,2,7,5,3,1]=>{{1,6},{2,4,7},{3},{5}}
[4,6,5,1,7,2,3]=>[5,6,2,4,7,3,1]=>[6,4,1,7,5,2,3]=>{{1,6},{2,4,7},{3},{5}}
[4,6,5,1,7,3,2]=>[5,3,6,4,7,2,1]=>[4,6,3,7,5,1,2]=>{{1,4,7},{2,6},{3},{5}}
[4,6,5,2,1,3,7]=>[2,5,1,4,6,3,7]=>[4,2,1,6,5,3,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,5,2,1,7,3]=>[2,5,6,4,7,3,1]=>[6,2,4,7,5,1,3]=>{{1,6},{2},{3,4,7},{5}}
[4,6,5,2,3,1,7]=>[3,5,2,4,6,1,7]=>[4,3,1,6,5,2,7]=>{{1,4,6},{2,3},{5},{7}}
[4,6,5,2,3,7,1]=>[7,5,2,4,6,3,1]=>[4,5,1,7,6,2,3]=>{{1,4,7},{2,5,6},{3}}
[4,6,5,2,7,1,3]=>[7,5,1,4,6,2,3]=>[4,5,2,7,6,3,1]=>{{1,4,7},{2,5,6},{3}}
[4,6,5,2,7,3,1]=>[3,7,5,4,6,1,2]=>[5,3,4,7,6,2,1]=>{{1,5,6},{2,3,4,7}}
[4,6,5,3,1,2,7]=>[3,1,5,4,6,2,7]=>[4,1,3,6,5,2,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,5,3,1,7,2]=>[3,5,6,4,7,1,2]=>[6,4,3,7,5,2,1]=>{{1,6},{2,4,7},{3},{5}}
[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}}
[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>[3,5,4,7,6,1,2]=>{{1,3,4,7},{2,5,6}}
[4,6,5,3,7,1,2]=>[7,1,5,4,6,3,2]=>[4,1,5,7,6,2,3]=>{{1,4,7},{2},{3,5,6}}
[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>[4,2,5,7,6,1,3]=>{{1,4,7},{2},{3,5,6}}
[4,6,5,7,1,2,3]=>[7,1,2,4,6,5,3]=>[4,1,2,6,7,3,5]=>{{1,4,6},{2},{3},{5,7}}
[4,6,5,7,1,3,2]=>[7,3,1,4,6,5,2]=>[3,4,2,6,7,1,5]=>{{1,3},{2,4,6},{5,7}}
[4,6,5,7,2,1,3]=>[2,7,1,4,6,5,3]=>[4,2,1,6,7,3,5]=>{{1,4,6},{2},{3},{5,7}}
[4,6,5,7,2,3,1]=>[3,7,2,4,6,5,1]=>[4,3,1,6,7,2,5]=>{{1,4,6},{2,3},{5,7}}
[4,6,5,7,3,1,2]=>[3,1,7,4,6,5,2]=>[4,1,3,6,7,2,5]=>{{1,4,6},{2},{3},{5,7}}
[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>[4,2,3,6,7,1,5]=>{{1,4,6},{2},{3},{5,7}}
[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[4,1,2,6,3,7,5]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,1,2,5,3]=>[7,1,5,4,2,6,3]=>[4,1,5,6,3,7,2]=>{{1,4,6,7},{2},{3,5}}
[4,6,7,1,3,2,5]=>[7,3,1,4,2,6,5]=>[3,4,2,6,1,7,5]=>{{1,3},{2,4,6,7},{5}}
[4,6,7,1,3,5,2]=>[7,5,1,4,3,6,2]=>[4,5,2,6,1,7,3]=>{{1,4,6,7},{2,5},{3}}
[4,6,7,1,5,2,3]=>[7,5,2,4,1,6,3]=>[4,5,1,6,3,7,2]=>{{1,4,6,7},{2,5},{3}}
[4,6,7,1,5,3,2]=>[7,3,5,4,1,6,2]=>[3,5,4,6,2,7,1]=>{{1,3,4,6,7},{2,5}}
[4,6,7,2,1,3,5]=>[2,7,1,4,3,6,5]=>[4,2,1,6,3,7,5]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,2,1,5,3]=>[2,7,5,4,1,6,3]=>[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}}
[4,6,7,2,3,1,5]=>[3,7,2,4,1,6,5]=>[4,3,1,6,2,7,5]=>{{1,4,6,7},{2,3},{5}}
[4,6,7,2,3,5,1]=>[5,7,2,4,3,6,1]=>[5,4,1,6,2,7,3]=>{{1,5},{2,4,6,7},{3}}
[4,6,7,2,5,1,3]=>[5,7,1,4,2,6,3]=>[5,4,2,6,3,7,1]=>{{1,5},{2,4,6,7},{3}}
[4,6,7,2,5,3,1]=>[3,5,7,4,1,6,2]=>[5,4,3,6,2,7,1]=>{{1,5},{2,4,6,7},{3}}
[4,6,7,3,1,2,5]=>[3,1,7,4,2,6,5]=>[4,1,3,6,2,7,5]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,3,1,5,2]=>[3,7,5,4,2,6,1]=>[5,3,4,6,1,7,2]=>{{1,5},{2,3,4,6,7}}
[4,6,7,3,2,1,5]=>[2,3,7,4,1,6,5]=>[4,2,3,6,1,7,5]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,3,2,5,1]=>[5,3,7,4,2,6,1]=>[4,5,3,6,1,7,2]=>{{1,4,6,7},{2,5},{3}}
[4,6,7,3,5,1,2]=>[5,1,7,4,3,6,2]=>[5,1,4,6,2,7,3]=>{{1,5},{2},{3,4,6,7}}
[4,6,7,3,5,2,1]=>[2,5,7,4,3,6,1]=>[5,2,4,6,1,7,3]=>{{1,5},{2},{3,4,6,7}}
[4,6,7,5,1,2,3]=>[5,1,2,4,7,6,3]=>[4,1,2,6,5,7,3]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,5,1,3,2]=>[5,3,1,4,7,6,2]=>[3,4,2,6,5,7,1]=>{{1,3},{2,4,6,7},{5}}
[4,6,7,5,2,1,3]=>[2,5,1,4,7,6,3]=>[4,2,1,6,5,7,3]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,5,2,3,1]=>[3,5,2,4,7,6,1]=>[4,3,1,6,5,7,2]=>{{1,4,6,7},{2,3},{5}}
[4,6,7,5,3,1,2]=>[3,1,5,4,7,6,2]=>[4,1,3,6,5,7,2]=>{{1,4,6,7},{2},{3},{5}}
[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}}
[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[4,1,2,7,3,5,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,1,2,3,6,5]=>[7,1,2,4,6,3,5]=>[4,1,2,6,7,5,3]=>{{1,4,6},{2},{3},{5,7}}
[4,7,1,2,5,3,6]=>[7,1,5,4,2,3,6]=>[4,1,5,7,3,2,6]=>{{1,4,7},{2},{3,5},{6}}
[4,7,1,2,5,6,3]=>[7,1,6,4,2,5,3]=>[4,1,6,7,3,2,5]=>{{1,4,7},{2},{3,6},{5}}
[4,7,1,2,6,3,5]=>[7,1,6,4,3,2,5]=>[4,1,6,7,2,5,3]=>{{1,4,7},{2},{3,6},{5}}
[4,7,1,2,6,5,3]=>[7,1,5,4,6,2,3]=>[4,1,5,7,6,3,2]=>{{1,4,7},{2},{3,5,6}}
[4,7,1,3,2,5,6]=>[7,3,1,4,2,5,6]=>[3,4,2,7,1,5,6]=>{{1,3},{2,4,7},{5},{6}}
[4,7,1,3,2,6,5]=>[7,3,1,4,6,2,5]=>[3,4,2,6,7,5,1]=>{{1,3},{2,4,6},{5,7}}
[4,7,1,3,5,2,6]=>[7,5,1,4,3,2,6]=>[4,5,2,7,1,3,6]=>{{1,4,7},{2,5},{3},{6}}
[4,7,1,3,5,6,2]=>[7,6,1,4,2,3,5]=>[4,6,2,7,3,5,1]=>{{1,4,7},{2,6},{3},{5}}
[4,7,1,3,6,2,5]=>[7,6,1,4,3,5,2]=>[4,6,2,7,1,3,5]=>{{1,4,7},{2,6},{3},{5}}
[4,7,1,3,6,5,2]=>[7,5,1,4,6,3,2]=>[4,5,2,7,6,1,3]=>{{1,4,7},{2,5,6},{3}}
[4,7,1,5,2,3,6]=>[7,5,2,4,1,3,6]=>[4,5,1,7,3,2,6]=>{{1,4,7},{2,5},{3},{6}}
[4,7,1,5,2,6,3]=>[7,5,6,4,1,2,3]=>[4,6,5,7,3,2,1]=>{{1,4,7},{2,6},{3,5}}
[4,7,1,5,3,2,6]=>[7,3,5,4,1,2,6]=>[3,5,4,7,2,1,6]=>{{1,3,4,7},{2,5},{6}}
[4,7,1,5,3,6,2]=>[7,6,5,4,1,3,2]=>[4,5,6,7,3,1,2]=>{{1,4,7},{2,5},{3,6}}
[4,7,1,5,6,2,3]=>[7,6,2,4,1,5,3]=>[4,6,1,7,3,2,5]=>{{1,4,7},{2,6},{3},{5}}
[4,7,1,5,6,3,2]=>[7,3,6,4,1,5,2]=>[3,6,4,7,2,1,5]=>{{1,3,4,7},{2,6},{5}}
[4,7,1,6,2,3,5]=>[7,6,2,4,3,1,5]=>[4,6,1,7,2,5,3]=>{{1,4,7},{2,6},{3},{5}}
[4,7,1,6,2,5,3]=>[7,6,5,4,2,1,3]=>[4,5,6,7,2,3,1]=>{{1,4,7},{2,5},{3,6}}
[4,7,1,6,3,2,5]=>[7,3,6,4,2,1,5]=>[3,6,4,7,1,5,2]=>{{1,3,4,7},{2,6},{5}}
[4,7,1,6,3,5,2]=>[7,5,6,4,3,1,2]=>[4,6,5,7,1,3,2]=>{{1,4,7},{2,6},{3,5}}
[4,7,1,6,5,2,3]=>[7,5,2,4,6,1,3]=>[4,5,1,7,6,3,2]=>{{1,4,7},{2,5,6},{3}}
[4,7,1,6,5,3,2]=>[7,3,5,4,6,1,2]=>[3,5,4,7,6,2,1]=>{{1,3,4,7},{2,5,6}}
[4,7,2,1,3,5,6]=>[2,7,1,4,3,5,6]=>[4,2,1,7,3,5,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,2,1,3,6,5]=>[2,7,1,4,6,3,5]=>[4,2,1,6,7,5,3]=>{{1,4,6},{2},{3},{5,7}}
[4,7,2,1,5,3,6]=>[2,7,5,4,1,3,6]=>[4,2,5,7,3,1,6]=>{{1,4,7},{2},{3,5},{6}}
[4,7,2,1,5,6,3]=>[2,7,6,4,1,5,3]=>[4,2,6,7,3,1,5]=>{{1,4,7},{2},{3,6},{5}}
[4,7,2,1,6,3,5]=>[2,7,6,4,3,1,5]=>[4,2,6,7,1,5,3]=>{{1,4,7},{2},{3,6},{5}}
[4,7,2,1,6,5,3]=>[2,7,5,4,6,1,3]=>[4,2,5,7,6,3,1]=>{{1,4,7},{2},{3,5,6}}
[4,7,2,3,1,5,6]=>[3,7,2,4,1,5,6]=>[4,3,1,7,2,5,6]=>{{1,4,7},{2,3},{5},{6}}
[4,7,2,3,1,6,5]=>[3,7,2,4,6,1,5]=>[4,3,1,6,7,5,2]=>{{1,4,6},{2,3},{5,7}}
[4,7,2,3,5,1,6]=>[5,7,2,4,3,1,6]=>[5,4,1,7,2,3,6]=>{{1,5},{2,4,7},{3},{6}}
[4,7,2,3,5,6,1]=>[6,7,2,4,3,5,1]=>[6,4,1,7,2,3,5]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,3,6,1,5]=>[6,7,2,4,1,3,5]=>[6,4,1,7,3,5,2]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,3,6,5,1]=>[5,6,2,4,7,1,3]=>[6,4,1,7,5,3,2]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,5,1,3,6]=>[5,7,1,4,2,3,6]=>[5,4,2,7,3,1,6]=>{{1,5},{2,4,7},{3},{6}}
[4,7,2,5,1,6,3]=>[5,7,6,4,2,1,3]=>[6,4,5,7,2,3,1]=>{{1,6},{2,4,7},{3,5}}
[4,7,2,5,3,1,6]=>[3,5,7,4,1,2,6]=>[5,4,3,7,2,1,6]=>{{1,5},{2,4,7},{3},{6}}
[4,7,2,5,3,6,1]=>[6,7,5,4,2,3,1]=>[5,4,6,7,2,1,3]=>{{1,5},{2,4,7},{3,6}}
[4,7,2,5,6,1,3]=>[6,7,1,4,3,2,5]=>[6,4,2,7,1,5,3]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,5,6,3,1]=>[3,6,7,4,2,1,5]=>[6,4,3,7,1,5,2]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,6,1,3,5]=>[6,7,1,4,2,5,3]=>[6,4,2,7,3,1,5]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,6,1,5,3]=>[6,7,5,4,1,2,3]=>[5,4,6,7,3,2,1]=>{{1,5},{2,4,7},{3,6}}
[4,7,2,6,3,1,5]=>[3,6,7,4,1,5,2]=>[6,4,3,7,2,1,5]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,6,3,5,1]=>[5,7,6,4,3,2,1]=>[6,4,5,7,1,2,3]=>{{1,6},{2,4,7},{3,5}}
[4,7,2,6,5,1,3]=>[5,6,1,4,7,3,2]=>[6,4,2,7,5,1,3]=>{{1,6},{2,4,7},{3},{5}}
[4,7,2,6,5,3,1]=>[3,5,6,4,7,2,1]=>[6,4,3,7,5,1,2]=>{{1,6},{2,4,7},{3},{5}}
[4,7,3,1,2,5,6]=>[3,1,7,4,2,5,6]=>[4,1,3,7,2,5,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,3,1,2,6,5]=>[3,1,7,4,6,2,5]=>[4,1,3,6,7,5,2]=>{{1,4,6},{2},{3},{5,7}}
[4,7,3,1,5,2,6]=>[3,7,5,4,2,1,6]=>[5,3,4,7,1,2,6]=>{{1,5},{2,3,4,7},{6}}
[4,7,3,1,5,6,2]=>[3,7,6,4,1,2,5]=>[6,3,4,7,2,5,1]=>{{1,6},{2,3,4,7},{5}}
[4,7,3,1,6,2,5]=>[3,7,6,4,2,5,1]=>[6,3,4,7,1,2,5]=>{{1,6},{2,3,4,7},{5}}
[4,7,3,1,6,5,2]=>[3,7,5,4,6,2,1]=>[5,3,4,7,6,1,2]=>{{1,5,6},{2,3,4,7}}
[4,7,3,2,1,5,6]=>[2,3,7,4,1,5,6]=>[4,2,3,7,1,5,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,3,2,1,6,5]=>[2,3,7,4,6,1,5]=>[4,2,3,6,7,5,1]=>{{1,4,6},{2},{3},{5,7}}
[4,7,3,2,5,1,6]=>[5,3,7,4,2,1,6]=>[4,5,3,7,1,2,6]=>{{1,4,7},{2,5},{3},{6}}
[4,7,3,2,5,6,1]=>[6,3,7,4,2,5,1]=>[4,6,3,7,1,2,5]=>{{1,4,7},{2,6},{3},{5}}
[4,7,3,2,6,1,5]=>[6,3,7,4,1,2,5]=>[4,6,3,7,2,5,1]=>{{1,4,7},{2,6},{3},{5}}
[4,7,3,2,6,5,1]=>[5,3,6,4,7,1,2]=>[4,6,3,7,5,2,1]=>{{1,4,7},{2,6},{3},{5}}
[4,7,3,5,1,2,6]=>[5,1,7,4,3,2,6]=>[5,1,4,7,2,3,6]=>{{1,5},{2},{3,4,7},{6}}
[4,7,3,5,1,6,2]=>[5,6,7,4,3,1,2]=>[6,5,4,7,1,3,2]=>{{1,6},{2,5},{3,4,7}}
[4,7,3,5,2,1,6]=>[2,5,7,4,3,1,6]=>[5,2,4,7,1,3,6]=>{{1,5},{2},{3,4,7},{6}}
[4,7,3,5,2,6,1]=>[6,5,7,4,3,2,1]=>[5,6,4,7,1,2,3]=>{{1,5},{2,6},{3,4,7}}
[4,7,3,5,6,1,2]=>[6,1,7,4,3,5,2]=>[6,1,4,7,2,3,5]=>{{1,6},{2},{3,4,7},{5}}
[4,7,3,5,6,2,1]=>[2,6,7,4,3,5,1]=>[6,2,4,7,1,3,5]=>{{1,6},{2},{3,4,7},{5}}
[4,7,3,6,1,2,5]=>[6,1,7,4,2,3,5]=>[6,1,4,7,3,5,2]=>{{1,6},{2},{3,4,7},{5}}
[4,7,3,6,1,5,2]=>[6,5,7,4,1,3,2]=>[5,6,4,7,3,1,2]=>{{1,5},{2,6},{3,4,7}}
[4,7,3,6,2,1,5]=>[2,6,7,4,1,3,5]=>[6,2,4,7,3,5,1]=>{{1,6},{2},{3,4,7},{5}}
[4,7,3,6,2,5,1]=>[5,6,7,4,2,3,1]=>[6,5,4,7,2,1,3]=>{{1,6},{2,5},{3,4,7}}
[4,7,3,6,5,1,2]=>[5,1,6,4,7,2,3]=>[6,1,4,7,5,3,2]=>{{1,6},{2},{3,4,7},{5}}
[4,7,3,6,5,2,1]=>[2,5,6,4,7,1,3]=>[6,2,4,7,5,3,1]=>{{1,6},{2},{3,4,7},{5}}
[4,7,5,1,2,3,6]=>[5,1,2,4,7,3,6]=>[4,1,2,7,5,3,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,5,1,2,6,3]=>[5,1,7,4,6,3,2]=>[5,1,4,7,6,2,3]=>{{1,5,6},{2},{3,4,7}}
[4,7,5,1,3,2,6]=>[5,3,1,4,7,2,6]=>[3,4,2,7,5,1,6]=>{{1,3},{2,4,7},{5},{6}}
[4,7,5,1,3,6,2]=>[5,7,1,4,6,2,3]=>[5,4,2,7,6,3,1]=>{{1,5,6},{2,4,7},{3}}
[4,7,5,1,6,2,3]=>[5,7,2,4,6,3,1]=>[5,4,1,7,6,2,3]=>{{1,5,6},{2,4,7},{3}}
[4,7,5,1,6,3,2]=>[5,3,7,4,6,2,1]=>[4,5,3,7,6,1,2]=>{{1,4,7},{2,5,6},{3}}
[4,7,5,2,1,3,6]=>[2,5,1,4,7,3,6]=>[4,2,1,7,5,3,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,5,2,1,6,3]=>[2,5,7,4,6,3,1]=>[5,2,4,7,6,1,3]=>{{1,5,6},{2},{3,4,7}}
[4,7,5,2,3,1,6]=>[3,5,2,4,7,1,6]=>[4,3,1,7,5,2,6]=>{{1,4,7},{2,3},{5},{6}}
[4,7,5,2,3,6,1]=>[6,5,2,4,7,3,1]=>[4,6,1,7,5,2,3]=>{{1,4,7},{2,6},{3},{5}}
[4,7,5,2,6,1,3]=>[6,5,1,4,7,2,3]=>[4,6,2,7,5,3,1]=>{{1,4,7},{2,6},{3},{5}}
[4,7,5,2,6,3,1]=>[3,6,5,4,7,1,2]=>[6,3,4,7,5,2,1]=>{{1,6},{2,3,4,7},{5}}
[4,7,5,3,1,2,6]=>[3,1,5,4,7,2,6]=>[4,1,3,7,5,2,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,5,3,1,6,2]=>[3,5,7,4,6,1,2]=>[5,4,3,7,6,2,1]=>{{1,5,6},{2,4,7},{3}}
[4,7,5,3,2,1,6]=>[2,3,5,4,7,1,6]=>[4,2,3,7,5,1,6]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,5,3,2,6,1]=>[6,3,5,4,7,2,1]=>[3,6,4,7,5,1,2]=>{{1,3,4,7},{2,6},{5}}
[4,7,5,3,6,1,2]=>[6,1,5,4,7,3,2]=>[4,1,6,7,5,2,3]=>{{1,4,7},{2},{3,6},{5}}
[4,7,5,3,6,2,1]=>[2,6,5,4,7,3,1]=>[4,2,6,7,5,1,3]=>{{1,4,7},{2},{3,6},{5}}
[4,7,5,6,1,2,3]=>[6,1,2,4,7,5,3]=>[4,1,2,7,6,3,5]=>{{1,4,7},{2},{3},{5,6}}
[4,7,5,6,1,3,2]=>[6,3,1,4,7,5,2]=>[3,4,2,7,6,1,5]=>{{1,3},{2,4,7},{5,6}}
[4,7,5,6,2,1,3]=>[2,6,1,4,7,5,3]=>[4,2,1,7,6,3,5]=>{{1,4,7},{2},{3},{5,6}}
[4,7,5,6,2,3,1]=>[3,6,2,4,7,5,1]=>[4,3,1,7,6,2,5]=>{{1,4,7},{2,3},{5,6}}
[4,7,5,6,3,1,2]=>[3,1,6,4,7,5,2]=>[4,1,3,7,6,2,5]=>{{1,4,7},{2},{3},{5,6}}
[4,7,5,6,3,2,1]=>[2,3,6,4,7,5,1]=>[4,2,3,7,6,1,5]=>{{1,4,7},{2},{3},{5,6}}
[4,7,6,1,2,3,5]=>[6,1,2,4,3,7,5]=>[4,1,2,7,3,6,5]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,1,2,5,3]=>[6,1,5,4,2,7,3]=>[4,1,5,7,3,6,2]=>{{1,4,7},{2},{3,5},{6}}
[4,7,6,1,3,2,5]=>[6,3,1,4,2,7,5]=>[3,4,2,7,1,6,5]=>{{1,3},{2,4,7},{5},{6}}
[4,7,6,1,3,5,2]=>[6,5,1,4,3,7,2]=>[4,5,2,7,1,6,3]=>{{1,4,7},{2,5},{3},{6}}
[4,7,6,1,5,2,3]=>[6,5,2,4,1,7,3]=>[4,5,1,7,3,6,2]=>{{1,4,7},{2,5},{3},{6}}
[4,7,6,1,5,3,2]=>[6,3,5,4,1,7,2]=>[3,5,4,7,2,6,1]=>{{1,3,4,7},{2,5},{6}}
[4,7,6,2,1,3,5]=>[2,6,1,4,3,7,5]=>[4,2,1,7,3,6,5]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,2,1,5,3]=>[2,6,5,4,1,7,3]=>[4,2,5,7,3,6,1]=>{{1,4,7},{2},{3,5},{6}}
[4,7,6,2,3,1,5]=>[3,6,2,4,1,7,5]=>[4,3,1,7,2,6,5]=>{{1,4,7},{2,3},{5},{6}}
[4,7,6,2,3,5,1]=>[5,6,2,4,3,7,1]=>[5,4,1,7,2,6,3]=>{{1,5},{2,4,7},{3},{6}}
[4,7,6,2,5,1,3]=>[5,6,1,4,2,7,3]=>[5,4,2,7,3,6,1]=>{{1,5},{2,4,7},{3},{6}}
[4,7,6,2,5,3,1]=>[3,5,6,4,1,7,2]=>[5,4,3,7,2,6,1]=>{{1,5},{2,4,7},{3},{6}}
[4,7,6,3,1,2,5]=>[3,1,6,4,2,7,5]=>[4,1,3,7,2,6,5]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,3,1,5,2]=>[3,6,5,4,2,7,1]=>[5,3,4,7,1,6,2]=>{{1,5},{2,3,4,7},{6}}
[4,7,6,3,2,1,5]=>[2,3,6,4,1,7,5]=>[4,2,3,7,1,6,5]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,3,2,5,1]=>[5,3,6,4,2,7,1]=>[4,5,3,7,1,6,2]=>{{1,4,7},{2,5},{3},{6}}
[4,7,6,3,5,1,2]=>[5,1,6,4,3,7,2]=>[5,1,4,7,2,6,3]=>{{1,5},{2},{3,4,7},{6}}
[4,7,6,3,5,2,1]=>[2,5,6,4,3,7,1]=>[5,2,4,7,1,6,3]=>{{1,5},{2},{3,4,7},{6}}
[4,7,6,5,1,2,3]=>[5,1,2,4,6,7,3]=>[4,1,2,7,5,6,3]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,5,1,3,2]=>[5,3,1,4,6,7,2]=>[3,4,2,7,5,6,1]=>{{1,3},{2,4,7},{5},{6}}
[4,7,6,5,2,1,3]=>[2,5,1,4,6,7,3]=>[4,2,1,7,5,6,3]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,5,2,3,1]=>[3,5,2,4,6,7,1]=>[4,3,1,7,5,6,2]=>{{1,4,7},{2,3},{5},{6}}
[4,7,6,5,3,1,2]=>[3,1,5,4,6,7,2]=>[4,1,3,7,5,6,2]=>{{1,4,7},{2},{3},{5},{6}}
[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}
[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,1,2,3,6,4,7]=>[5,1,2,6,3,4,7]=>[6,1,2,5,4,3,7]=>{{1,6},{2},{3},{4,5},{7}}
[5,1,2,3,6,7,4]=>[5,1,2,7,3,6,4]=>[6,1,2,5,4,7,3]=>{{1,6,7},{2},{3},{4,5}}
[5,1,2,3,7,4,6]=>[5,1,2,7,3,4,6]=>[7,1,2,5,4,3,6]=>{{1,7},{2},{3},{4,5},{6}}
[5,1,2,3,7,6,4]=>[5,1,2,6,3,7,4]=>[7,1,2,5,4,6,3]=>{{1,7},{2},{3},{4,5},{6}}
[5,1,2,4,3,6,7]=>[5,1,4,2,3,6,7]=>[4,1,5,3,2,6,7]=>{{1,4},{2},{3,5},{6},{7}}
[5,1,2,4,3,7,6]=>[5,1,4,2,3,7,6]=>[4,1,5,3,2,7,6]=>{{1,4},{2},{3,5},{6,7}}
[5,1,2,4,6,3,7]=>[5,1,6,2,4,3,7]=>[6,1,5,3,2,4,7]=>{{1,6},{2},{3,5},{4},{7}}
[5,1,2,4,6,7,3]=>[5,1,7,2,4,6,3]=>[6,1,5,3,2,7,4]=>{{1,6,7},{2},{3,5},{4}}
[5,1,2,4,7,3,6]=>[5,1,7,2,4,3,6]=>[7,1,5,3,2,4,6]=>{{1,7},{2},{3,5},{4},{6}}
[5,1,2,4,7,6,3]=>[5,1,6,2,4,7,3]=>[7,1,5,3,2,6,4]=>{{1,7},{2},{3,5},{4},{6}}
[5,1,2,6,3,4,7]=>[5,1,6,3,2,4,7]=>[6,1,5,2,4,3,7]=>{{1,6},{2},{3,5},{4},{7}}
[5,1,2,6,3,7,4]=>[5,1,6,7,2,3,4]=>[7,1,6,5,4,3,2]=>{{1,7},{2},{3,6},{4,5}}
[5,1,2,6,4,3,7]=>[5,1,4,6,2,3,7]=>[5,1,6,4,3,2,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,1,2,6,4,7,3]=>[5,1,7,6,2,4,3]=>[7,1,5,6,4,2,3]=>{{1,7},{2},{3,5},{4,6}}
[5,1,2,6,7,3,4]=>[5,1,7,3,2,6,4]=>[6,1,5,2,4,7,3]=>{{1,6,7},{2},{3,5},{4}}
[5,1,2,6,7,4,3]=>[5,1,4,7,2,6,3]=>[5,1,6,4,3,7,2]=>{{1,5},{2},{3,6,7},{4}}
[5,1,2,7,3,4,6]=>[5,1,7,3,2,4,6]=>[7,1,5,2,4,3,6]=>{{1,7},{2},{3,5},{4},{6}}
[5,1,2,7,3,6,4]=>[5,1,7,6,2,3,4]=>[7,1,5,6,4,3,2]=>{{1,7},{2},{3,5},{4,6}}
[5,1,2,7,4,3,6]=>[5,1,4,7,2,3,6]=>[5,1,7,4,3,2,6]=>{{1,5},{2},{3,7},{4},{6}}
[5,1,2,7,4,6,3]=>[5,1,6,7,2,4,3]=>[7,1,6,5,4,2,3]=>{{1,7},{2},{3,6},{4,5}}
[5,1,2,7,6,3,4]=>[5,1,6,3,2,7,4]=>[7,1,5,2,4,6,3]=>{{1,7},{2},{3,5},{4},{6}}
[5,1,2,7,6,4,3]=>[5,1,4,6,2,7,3]=>[5,1,7,4,3,6,2]=>{{1,5},{2},{3,7},{4},{6}}
[5,1,3,2,4,6,7]=>[5,3,1,2,4,6,7]=>[3,5,2,1,4,6,7]=>{{1,3},{2,5},{4},{6},{7}}
[5,1,3,2,4,7,6]=>[5,3,1,2,4,7,6]=>[3,5,2,1,4,7,6]=>{{1,3},{2,5},{4},{6,7}}
[5,1,3,2,6,4,7]=>[5,3,1,6,2,4,7]=>[3,6,2,5,4,1,7]=>{{1,3},{2,6},{4,5},{7}}
[5,1,3,2,6,7,4]=>[5,3,1,7,2,6,4]=>[3,6,2,5,4,7,1]=>{{1,3},{2,6,7},{4,5}}
[5,1,3,2,7,4,6]=>[5,3,1,7,2,4,6]=>[3,7,2,5,4,1,6]=>{{1,3},{2,7},{4,5},{6}}
[5,1,3,2,7,6,4]=>[5,3,1,6,2,7,4]=>[3,7,2,5,4,6,1]=>{{1,3},{2,7},{4,5},{6}}
[5,1,3,4,2,6,7]=>[5,4,1,3,2,6,7]=>[4,5,2,1,3,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[5,1,3,4,2,7,6]=>[5,4,1,3,2,7,6]=>[4,5,2,1,3,7,6]=>{{1,4},{2,5},{3},{6,7}}
[5,1,3,4,6,2,7]=>[5,6,1,2,3,4,7]=>[6,5,2,3,4,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,1,3,4,6,7,2]=>[5,7,1,2,3,6,4]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,5},{3},{4}}
[5,1,3,4,7,2,6]=>[5,7,1,2,3,4,6]=>[7,5,2,3,4,1,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,3,4,7,6,2]=>[5,6,1,2,3,7,4]=>[7,5,2,3,4,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,3,6,2,4,7]=>[5,6,1,3,4,2,7]=>[6,5,2,1,3,4,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,1,3,6,2,7,4]=>[5,6,1,7,3,2,4]=>[7,6,2,5,3,4,1]=>{{1,7},{2,6},{3},{4,5}}
[5,1,3,6,4,2,7]=>[5,4,1,6,3,2,7]=>[5,6,2,4,1,3,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,1,3,6,4,7,2]=>[5,7,1,6,3,4,2]=>[7,5,2,6,3,1,4]=>{{1,7},{2,5},{3},{4,6}}
[5,1,3,6,7,2,4]=>[5,7,1,3,4,6,2]=>[6,5,2,1,3,7,4]=>{{1,6,7},{2,5},{3},{4}}
[5,1,3,6,7,4,2]=>[5,4,1,7,3,6,2]=>[5,6,2,4,1,7,3]=>{{1,5},{2,6,7},{3},{4}}
[5,1,3,7,2,4,6]=>[5,7,1,3,4,2,6]=>[7,5,2,1,3,4,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,3,7,2,6,4]=>[5,7,1,6,3,2,4]=>[7,5,2,6,3,4,1]=>{{1,7},{2,5},{3},{4,6}}
[5,1,3,7,4,2,6]=>[5,4,1,7,3,2,6]=>[5,7,2,4,1,3,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,3,7,4,6,2]=>[5,6,1,7,3,4,2]=>[7,6,2,5,3,1,4]=>{{1,7},{2,6},{3},{4,5}}
[5,1,3,7,6,2,4]=>[5,6,1,3,4,7,2]=>[7,5,2,1,3,6,4]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,3,7,6,4,2]=>[5,4,1,6,3,7,2]=>[5,7,2,4,1,6,3]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,4,2,3,6,7]=>[5,4,2,1,3,6,7]=>[4,5,1,3,2,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[5,1,4,2,3,7,6]=>[5,4,2,1,3,7,6]=>[4,5,1,3,2,7,6]=>{{1,4},{2,5},{3},{6,7}}
[5,1,4,2,6,3,7]=>[5,4,6,1,2,3,7]=>[5,6,4,3,2,1,7]=>{{1,5},{2,6},{3,4},{7}}
[5,1,4,2,6,7,3]=>[5,4,7,1,2,6,3]=>[5,6,4,3,2,7,1]=>{{1,5},{2,6,7},{3,4}}
[5,1,4,2,7,3,6]=>[5,4,7,1,2,3,6]=>[5,7,4,3,2,1,6]=>{{1,5},{2,7},{3,4},{6}}
[5,1,4,2,7,6,3]=>[5,4,6,1,2,7,3]=>[5,7,4,3,2,6,1]=>{{1,5},{2,7},{3,4},{6}}
[5,1,4,3,2,6,7]=>[5,3,4,1,2,6,7]=>[3,5,4,2,1,6,7]=>{{1,3,4},{2,5},{6},{7}}
[5,1,4,3,2,7,6]=>[5,3,4,1,2,7,6]=>[3,5,4,2,1,7,6]=>{{1,3,4},{2,5},{6,7}}
[5,1,4,3,6,2,7]=>[5,6,4,1,3,2,7]=>[5,4,6,3,1,2,7]=>{{1,5},{2,4},{3,6},{7}}
[5,1,4,3,6,7,2]=>[5,7,4,1,3,6,2]=>[5,4,6,3,1,7,2]=>{{1,5},{2,4},{3,6,7}}
[5,1,4,3,7,2,6]=>[5,7,4,1,3,2,6]=>[5,4,7,3,1,2,6]=>{{1,5},{2,4},{3,7},{6}}
[5,1,4,3,7,6,2]=>[5,6,4,1,3,7,2]=>[5,4,7,3,1,6,2]=>{{1,5},{2,4},{3,7},{6}}
[5,1,4,6,2,3,7]=>[5,6,2,1,4,3,7]=>[6,5,1,3,2,4,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,1,4,6,2,7,3]=>[5,6,7,1,4,2,3]=>[7,6,5,3,1,4,2]=>{{1,7},{2,6},{3,5},{4}}
[5,1,4,6,3,2,7]=>[5,3,6,1,4,2,7]=>[5,6,3,2,1,4,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,1,4,6,3,7,2]=>[5,7,6,1,4,3,2]=>[7,5,6,3,1,2,4]=>{{1,7},{2,5},{3,6},{4}}
[5,1,4,6,7,2,3]=>[5,7,2,1,4,6,3]=>[6,5,1,3,2,7,4]=>{{1,6,7},{2,5},{3},{4}}
[5,1,4,6,7,3,2]=>[5,3,7,1,4,6,2]=>[5,6,3,2,1,7,4]=>{{1,5},{2,6,7},{3},{4}}
[5,1,4,7,2,3,6]=>[5,7,2,1,4,3,6]=>[7,5,1,3,2,4,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,4,7,2,6,3]=>[5,7,6,1,4,2,3]=>[7,5,6,3,1,4,2]=>{{1,7},{2,5},{3,6},{4}}
[5,1,4,7,3,2,6]=>[5,3,7,1,4,2,6]=>[5,7,3,2,1,4,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,4,7,3,6,2]=>[5,6,7,1,4,3,2]=>[7,6,5,3,1,2,4]=>{{1,7},{2,6},{3,5},{4}}
[5,1,4,7,6,2,3]=>[5,6,2,1,4,7,3]=>[7,5,1,3,2,6,4]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,4,7,6,3,2]=>[5,3,6,1,4,7,2]=>[5,7,3,2,1,6,4]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,6,2,3,4,7]=>[5,6,2,3,1,4,7]=>[6,5,1,2,4,3,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,1,6,2,3,7,4]=>[5,6,2,7,1,3,4]=>[7,6,1,5,4,3,2]=>{{1,7},{2,6},{3},{4,5}}
[5,1,6,2,4,3,7]=>[5,6,4,2,1,3,7]=>[5,4,6,2,3,1,7]=>{{1,5},{2,4},{3,6},{7}}
[5,1,6,2,4,7,3]=>[5,6,7,2,1,4,3]=>[7,6,5,2,4,1,3]=>{{1,7},{2,6},{3,5},{4}}
[5,1,6,2,7,3,4]=>[5,6,7,3,1,2,4]=>[7,6,5,1,4,3,2]=>{{1,7},{2,6},{3,5},{4}}
[5,1,6,2,7,4,3]=>[5,6,4,7,1,2,3]=>[6,5,7,4,3,2,1]=>{{1,6},{2,5},{3,7},{4}}
[5,1,6,3,2,4,7]=>[5,3,6,2,1,4,7]=>[5,6,3,1,4,2,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,1,6,3,2,7,4]=>[5,3,6,7,1,2,4]=>[6,7,3,5,4,2,1]=>{{1,6},{2,7},{3},{4,5}}
[5,1,6,3,4,2,7]=>[5,4,6,3,1,2,7]=>[5,6,4,1,3,2,7]=>{{1,5},{2,6},{3,4},{7}}
[5,1,6,3,4,7,2]=>[5,7,6,3,1,4,2]=>[7,5,6,1,4,2,3]=>{{1,7},{2,5},{3,6},{4}}
[5,1,6,3,7,2,4]=>[5,7,6,2,1,3,4]=>[7,5,6,2,4,3,1]=>{{1,7},{2,5},{3,6},{4}}
[5,1,6,3,7,4,2]=>[5,4,7,6,1,2,3]=>[6,7,4,5,3,2,1]=>{{1,6},{2,7},{3,4,5}}
[5,1,6,4,2,3,7]=>[5,4,2,6,1,3,7]=>[5,6,1,4,3,2,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,1,6,4,2,7,3]=>[5,4,6,7,1,3,2]=>[6,7,5,4,3,1,2]=>{{1,6},{2,7},{3,5},{4}}
[5,1,6,4,3,2,7]=>[5,3,4,6,1,2,7]=>[3,6,5,4,2,1,7]=>{{1,3,5},{2,6},{4},{7}}
[5,1,6,4,3,7,2]=>[5,7,4,6,1,3,2]=>[6,4,7,5,3,1,2]=>{{1,6},{2,4,5},{3,7}}
[5,1,6,4,7,2,3]=>[5,7,2,6,1,4,3]=>[7,5,1,6,4,2,3]=>{{1,7},{2,5},{3},{4,6}}
[5,1,6,4,7,3,2]=>[5,3,7,6,1,4,2]=>[5,7,3,6,4,1,2]=>{{1,5},{2,7},{3},{4,6}}
[5,1,6,7,2,3,4]=>[5,7,2,3,1,6,4]=>[6,5,1,2,4,7,3]=>{{1,6,7},{2,5},{3},{4}}
[5,1,6,7,2,4,3]=>[5,7,4,2,1,6,3]=>[5,4,6,2,3,7,1]=>{{1,5},{2,4},{3,6,7}}
[5,1,6,7,3,2,4]=>[5,3,7,2,1,6,4]=>[5,6,3,1,4,7,2]=>{{1,5},{2,6,7},{3},{4}}
[5,1,6,7,3,4,2]=>[5,4,7,3,1,6,2]=>[5,6,4,1,3,7,2]=>{{1,5},{2,6,7},{3,4}}
[5,1,6,7,4,2,3]=>[5,4,2,7,1,6,3]=>[5,6,1,4,3,7,2]=>{{1,5},{2,6,7},{3},{4}}
[5,1,6,7,4,3,2]=>[5,3,4,7,1,6,2]=>[3,6,5,4,2,7,1]=>{{1,3,5},{2,6,7},{4}}
[5,1,7,2,3,4,6]=>[5,7,2,3,1,4,6]=>[7,5,1,2,4,3,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,7,2,3,6,4]=>[5,7,2,6,1,3,4]=>[7,5,1,6,4,3,2]=>{{1,7},{2,5},{3},{4,6}}
[5,1,7,2,4,3,6]=>[5,7,4,2,1,3,6]=>[5,4,7,2,3,1,6]=>{{1,5},{2,4},{3,7},{6}}
[5,1,7,2,4,6,3]=>[5,7,6,2,1,4,3]=>[7,5,6,2,4,1,3]=>{{1,7},{2,5},{3,6},{4}}
[5,1,7,2,6,3,4]=>[5,7,6,3,1,2,4]=>[7,5,6,1,4,3,2]=>{{1,7},{2,5},{3,6},{4}}
[5,1,7,2,6,4,3]=>[5,7,4,6,1,2,3]=>[6,4,7,5,3,2,1]=>{{1,6},{2,4,5},{3,7}}
[5,1,7,3,2,4,6]=>[5,3,7,2,1,4,6]=>[5,7,3,1,4,2,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,7,3,2,6,4]=>[5,3,7,6,1,2,4]=>[5,7,3,6,4,2,1]=>{{1,5},{2,7},{3},{4,6}}
[5,1,7,3,4,2,6]=>[5,4,7,3,1,2,6]=>[5,7,4,1,3,2,6]=>{{1,5},{2,7},{3,4},{6}}
[5,1,7,3,4,6,2]=>[5,6,7,3,1,4,2]=>[7,6,5,1,4,2,3]=>{{1,7},{2,6},{3,5},{4}}
[5,1,7,3,6,2,4]=>[5,6,7,2,1,3,4]=>[7,6,5,2,4,3,1]=>{{1,7},{2,6},{3,5},{4}}
[5,1,7,3,6,4,2]=>[5,4,6,7,1,2,3]=>[6,7,5,4,3,2,1]=>{{1,6},{2,7},{3,5},{4}}
[5,1,7,4,2,3,6]=>[5,4,2,7,1,3,6]=>[5,7,1,4,3,2,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,7,4,2,6,3]=>[5,4,7,6,1,3,2]=>[6,7,4,5,3,1,2]=>{{1,6},{2,7},{3,4,5}}
[5,1,7,4,3,2,6]=>[5,3,4,7,1,2,6]=>[3,7,5,4,2,1,6]=>{{1,3,5},{2,7},{4},{6}}
[5,1,7,4,3,6,2]=>[5,6,4,7,1,3,2]=>[6,5,7,4,3,1,2]=>{{1,6},{2,5},{3,7},{4}}
[5,1,7,4,6,2,3]=>[5,6,2,7,1,4,3]=>[7,6,1,5,4,2,3]=>{{1,7},{2,6},{3},{4,5}}
[5,1,7,4,6,3,2]=>[5,3,6,7,1,4,2]=>[6,7,3,5,4,1,2]=>{{1,6},{2,7},{3},{4,5}}
[5,1,7,6,2,3,4]=>[5,6,2,3,1,7,4]=>[7,5,1,2,4,6,3]=>{{1,7},{2,5},{3},{4},{6}}
[5,1,7,6,2,4,3]=>[5,6,4,2,1,7,3]=>[5,4,7,2,3,6,1]=>{{1,5},{2,4},{3,7},{6}}
[5,1,7,6,3,2,4]=>[5,3,6,2,1,7,4]=>[5,7,3,1,4,6,2]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,7,6,3,4,2]=>[5,4,6,3,1,7,2]=>[5,7,4,1,3,6,2]=>{{1,5},{2,7},{3,4},{6}}
[5,1,7,6,4,2,3]=>[5,4,2,6,1,7,3]=>[5,7,1,4,3,6,2]=>{{1,5},{2,7},{3},{4},{6}}
[5,1,7,6,4,3,2]=>[5,3,4,6,1,7,2]=>[3,7,5,4,2,6,1]=>{{1,3,5},{2,7},{4},{6}}
[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,2,1,3,4,7,6]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,2,1,3,6,4,7]=>[2,5,1,6,3,4,7]=>[6,2,1,5,4,3,7]=>{{1,6},{2},{3},{4,5},{7}}
[5,2,1,3,6,7,4]=>[2,5,1,7,3,6,4]=>[6,2,1,5,4,7,3]=>{{1,6,7},{2},{3},{4,5}}
[5,2,1,3,7,4,6]=>[2,5,1,7,3,4,6]=>[7,2,1,5,4,3,6]=>{{1,7},{2},{3},{4,5},{6}}
[5,2,1,3,7,6,4]=>[2,5,1,6,3,7,4]=>[7,2,1,5,4,6,3]=>{{1,7},{2},{3},{4,5},{6}}
[5,2,1,4,3,6,7]=>[2,5,4,1,3,6,7]=>[4,2,5,3,1,6,7]=>{{1,4},{2},{3,5},{6},{7}}
[5,2,1,4,3,7,6]=>[2,5,4,1,3,7,6]=>[4,2,5,3,1,7,6]=>{{1,4},{2},{3,5},{6,7}}
[5,2,1,4,6,3,7]=>[2,5,6,1,4,3,7]=>[6,2,5,3,1,4,7]=>{{1,6},{2},{3,5},{4},{7}}
[5,2,1,4,6,7,3]=>[2,5,7,1,4,6,3]=>[6,2,5,3,1,7,4]=>{{1,6,7},{2},{3,5},{4}}
[5,2,1,4,7,3,6]=>[2,5,7,1,4,3,6]=>[7,2,5,3,1,4,6]=>{{1,7},{2},{3,5},{4},{6}}
[5,2,1,4,7,6,3]=>[2,5,6,1,4,7,3]=>[7,2,5,3,1,6,4]=>{{1,7},{2},{3,5},{4},{6}}
[5,2,1,6,3,4,7]=>[2,5,6,3,1,4,7]=>[6,2,5,1,4,3,7]=>{{1,6},{2},{3,5},{4},{7}}
[5,2,1,6,3,7,4]=>[2,5,6,7,1,3,4]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}}
[5,2,1,6,4,3,7]=>[2,5,4,6,1,3,7]=>[5,2,6,4,3,1,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,2,1,6,4,7,3]=>[2,5,7,6,1,4,3]=>[7,2,5,6,4,1,3]=>{{1,7},{2},{3,5},{4,6}}
[5,2,1,6,7,3,4]=>[2,5,7,3,1,6,4]=>[6,2,5,1,4,7,3]=>{{1,6,7},{2},{3,5},{4}}
[5,2,1,6,7,4,3]=>[2,5,4,7,1,6,3]=>[5,2,6,4,3,7,1]=>{{1,5},{2},{3,6,7},{4}}
[5,2,1,7,3,4,6]=>[2,5,7,3,1,4,6]=>[7,2,5,1,4,3,6]=>{{1,7},{2},{3,5},{4},{6}}
[5,2,1,7,3,6,4]=>[2,5,7,6,1,3,4]=>[7,2,5,6,4,3,1]=>{{1,7},{2},{3,5},{4,6}}
[5,2,1,7,4,3,6]=>[2,5,4,7,1,3,6]=>[5,2,7,4,3,1,6]=>{{1,5},{2},{3,7},{4},{6}}
[5,2,1,7,4,6,3]=>[2,5,6,7,1,4,3]=>[7,2,6,5,4,1,3]=>{{1,7},{2},{3,6},{4,5}}
[5,2,1,7,6,3,4]=>[2,5,6,3,1,7,4]=>[7,2,5,1,4,6,3]=>{{1,7},{2},{3,5},{4},{6}}
[5,2,1,7,6,4,3]=>[2,5,4,6,1,7,3]=>[5,2,7,4,3,6,1]=>{{1,5},{2},{3,7},{4},{6}}
[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[5,3,1,2,4,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[5,2,3,1,4,7,6]=>[3,5,2,1,4,7,6]=>[5,3,1,2,4,7,6]=>{{1,5},{2,3},{4},{6,7}}
[5,2,3,1,6,4,7]=>[3,5,2,6,1,4,7]=>[6,3,1,5,4,2,7]=>{{1,6},{2,3},{4,5},{7}}
[5,2,3,1,6,7,4]=>[3,5,2,7,1,6,4]=>[6,3,1,5,4,7,2]=>{{1,6,7},{2,3},{4,5}}
[5,2,3,1,7,4,6]=>[3,5,2,7,1,4,6]=>[7,3,1,5,4,2,6]=>{{1,7},{2,3},{4,5},{6}}
[5,2,3,1,7,6,4]=>[3,5,2,6,1,7,4]=>[7,3,1,5,4,6,2]=>{{1,7},{2,3},{4,5},{6}}
[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[5,4,1,2,3,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[5,2,3,4,1,7,6]=>[4,5,2,3,1,7,6]=>[5,4,1,2,3,7,6]=>{{1,5},{2,4},{3},{6,7}}
[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[5,6,1,2,3,4,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[5,6,1,2,3,7,4]=>{{1,5},{2,6,7},{3},{4}}
[5,2,3,4,7,1,6]=>[7,5,2,3,4,1,6]=>[5,7,1,2,3,4,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,3,4,7,6,1]=>[6,5,2,3,4,7,1]=>[5,7,1,2,3,6,4]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,3,6,1,4,7]=>[6,5,2,1,3,4,7]=>[5,6,1,3,4,2,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,2,3,6,1,7,4]=>[6,5,2,7,3,1,4]=>[6,7,1,5,3,4,2]=>{{1,6},{2,7},{3},{4,5}}
[5,2,3,6,4,1,7]=>[4,6,2,5,1,3,7]=>[6,4,1,5,3,2,7]=>{{1,6},{2,4,5},{3},{7}}
[5,2,3,6,4,7,1]=>[7,5,2,6,3,4,1]=>[5,7,1,6,3,2,4]=>{{1,5},{2,7},{3},{4,6}}
[5,2,3,6,7,1,4]=>[7,5,2,1,3,6,4]=>[5,6,1,3,4,7,2]=>{{1,5},{2,6,7},{3},{4}}
[5,2,3,6,7,4,1]=>[4,7,2,5,1,6,3]=>[6,4,1,5,3,7,2]=>{{1,6,7},{2,4,5},{3}}
[5,2,3,7,1,4,6]=>[7,5,2,1,3,4,6]=>[5,7,1,3,4,2,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,3,7,1,6,4]=>[7,5,2,6,3,1,4]=>[5,7,1,6,3,4,2]=>{{1,5},{2,7},{3},{4,6}}
[5,2,3,7,4,1,6]=>[4,7,2,5,1,3,6]=>[7,4,1,5,3,2,6]=>{{1,7},{2,4,5},{3},{6}}
[5,2,3,7,4,6,1]=>[6,5,2,7,3,4,1]=>[6,7,1,5,3,2,4]=>{{1,6},{2,7},{3},{4,5}}
[5,2,3,7,6,1,4]=>[6,5,2,1,3,7,4]=>[5,7,1,3,4,6,2]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,3,7,6,4,1]=>[4,6,2,5,1,7,3]=>[7,4,1,5,3,6,2]=>{{1,7},{2,4,5},{3},{6}}
[5,2,4,1,3,6,7]=>[4,5,1,2,3,6,7]=>[5,4,2,3,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[5,2,4,1,3,7,6]=>[4,5,1,2,3,7,6]=>[5,4,2,3,1,7,6]=>{{1,5},{2,4},{3},{6,7}}
[5,2,4,1,6,3,7]=>[4,5,6,2,1,3,7]=>[6,5,4,2,3,1,7]=>{{1,6},{2,5},{3,4},{7}}
[5,2,4,1,6,7,3]=>[4,5,7,2,1,6,3]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,5},{3,4}}
[5,2,4,1,7,3,6]=>[4,5,7,2,1,3,6]=>[7,5,4,2,3,1,6]=>{{1,7},{2,5},{3,4},{6}}
[5,2,4,1,7,6,3]=>[4,5,6,2,1,7,3]=>[7,5,4,2,3,6,1]=>{{1,7},{2,5},{3,4},{6}}
[5,2,4,3,1,6,7]=>[3,4,5,1,2,6,7]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[5,2,4,3,1,7,6]=>[3,4,5,1,2,7,6]=>[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}
[5,2,4,3,6,1,7]=>[6,5,4,2,3,1,7]=>[4,5,6,2,1,3,7]=>{{1,4},{2,5},{3,6},{7}}
[5,2,4,3,6,7,1]=>[7,5,4,2,3,6,1]=>[4,5,6,2,1,7,3]=>{{1,4},{2,5},{3,6,7}}
[5,2,4,3,7,1,6]=>[7,5,4,2,3,1,6]=>[4,5,7,2,1,3,6]=>{{1,4},{2,5},{3,7},{6}}
[5,2,4,3,7,6,1]=>[6,5,4,2,3,7,1]=>[4,5,7,2,1,6,3]=>{{1,4},{2,5},{3,7},{6}}
[5,2,4,6,1,3,7]=>[6,5,1,3,2,4,7]=>[5,6,2,1,4,3,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,2,4,6,1,7,3]=>[6,5,7,2,4,1,3]=>[6,7,5,2,1,4,3]=>{{1,6},{2,7},{3,5},{4}}
[5,2,4,6,3,1,7]=>[3,6,5,2,1,4,7]=>[6,3,5,1,4,2,7]=>{{1,6},{2,3,5},{4},{7}}
[5,2,4,6,3,7,1]=>[7,5,6,2,4,3,1]=>[5,7,6,2,1,3,4]=>{{1,5},{2,7},{3,6},{4}}
[5,2,4,6,7,1,3]=>[7,5,1,3,2,6,4]=>[5,6,2,1,4,7,3]=>{{1,5},{2,6,7},{3},{4}}
[5,2,4,6,7,3,1]=>[3,7,5,2,1,6,4]=>[6,3,5,1,4,7,2]=>{{1,6,7},{2,3,5},{4}}
[5,2,4,7,1,3,6]=>[7,5,1,3,2,4,6]=>[5,7,2,1,4,3,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,4,7,1,6,3]=>[7,5,6,2,4,1,3]=>[5,7,6,2,1,4,3]=>{{1,5},{2,7},{3,6},{4}}
[5,2,4,7,3,1,6]=>[3,7,5,2,1,4,6]=>[7,3,5,1,4,2,6]=>{{1,7},{2,3,5},{4},{6}}
[5,2,4,7,3,6,1]=>[6,5,7,2,4,3,1]=>[6,7,5,2,1,3,4]=>{{1,6},{2,7},{3,5},{4}}
[5,2,4,7,6,1,3]=>[6,5,1,3,2,7,4]=>[5,7,2,1,4,6,3]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,4,7,6,3,1]=>[3,6,5,2,1,7,4]=>[7,3,5,1,4,6,2]=>{{1,7},{2,3,5},{4},{6}}
[5,2,6,1,3,4,7]=>[6,5,1,2,4,3,7]=>[5,6,2,3,1,4,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,2,6,1,3,7,4]=>[6,5,1,7,2,3,4]=>[6,7,2,5,4,3,1]=>{{1,6},{2,7},{3},{4,5}}
[5,2,6,1,4,3,7]=>[6,5,4,1,2,3,7]=>[4,5,6,3,2,1,7]=>{{1,4},{2,5},{3,6},{7}}
[5,2,6,1,4,7,3]=>[6,5,7,1,2,4,3]=>[6,7,5,3,4,1,2]=>{{1,6},{2,7},{3,5},{4}}
[5,2,6,1,7,3,4]=>[6,5,7,3,2,1,4]=>[6,7,5,1,3,4,2]=>{{1,6},{2,7},{3,5},{4}}
[5,2,6,1,7,4,3]=>[6,5,4,7,2,1,3]=>[5,6,7,4,2,3,1]=>{{1,5},{2,6},{3,7},{4}}
[5,2,6,3,1,4,7]=>[3,6,5,1,4,2,7]=>[6,3,5,2,1,4,7]=>{{1,6},{2,3,5},{4},{7}}
[5,2,6,3,1,7,4]=>[3,6,5,7,1,2,4]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}}
[5,2,6,3,4,1,7]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>{{1,6},{2,5},{3,4},{7}}
[5,2,6,3,4,7,1]=>[7,5,6,3,2,4,1]=>[5,7,6,1,3,2,4]=>{{1,5},{2,7},{3,6},{4}}
[5,2,6,3,7,1,4]=>[7,5,6,1,2,3,4]=>[5,7,6,3,4,2,1]=>{{1,5},{2,7},{3,6},{4}}
[5,2,6,3,7,4,1]=>[4,7,5,6,3,1,2]=>[7,4,6,5,1,3,2]=>{{1,7},{2,4,5},{3,6}}
[5,2,6,4,1,3,7]=>[4,6,1,5,3,2,7]=>[6,4,2,5,1,3,7]=>{{1,6},{2,4,5},{3},{7}}
[5,2,6,4,1,7,3]=>[4,6,5,7,3,2,1]=>[7,5,6,4,1,2,3]=>{{1,7},{2,5},{3,6},{4}}
[5,2,6,4,3,1,7]=>[3,4,6,5,2,1,7]=>[6,4,3,5,1,2,7]=>{{1,6},{2,4,5},{3},{7}}
[5,2,6,4,3,7,1]=>[7,5,4,6,2,3,1]=>[4,6,7,5,2,1,3]=>{{1,4,5},{2,6},{3,7}}
[5,2,6,4,7,1,3]=>[7,5,1,6,2,4,3]=>[5,7,2,6,4,1,3]=>{{1,5},{2,7},{3},{4,6}}
[5,2,6,4,7,3,1]=>[3,7,5,6,1,4,2]=>[7,3,5,6,4,1,2]=>{{1,7},{2,3,5},{4,6}}
[5,2,6,7,1,3,4]=>[7,5,1,2,4,6,3]=>[5,6,2,3,1,7,4]=>{{1,5},{2,6,7},{3},{4}}
[5,2,6,7,1,4,3]=>[7,5,4,1,2,6,3]=>[4,5,6,3,2,7,1]=>{{1,4},{2,5},{3,6,7}}
[5,2,6,7,3,1,4]=>[3,7,5,1,4,6,2]=>[6,3,5,2,1,7,4]=>{{1,6,7},{2,3,5},{4}}
[5,2,6,7,3,4,1]=>[4,5,7,3,2,6,1]=>[6,5,4,1,2,7,3]=>{{1,6,7},{2,5},{3,4}}
[5,2,6,7,4,1,3]=>[4,7,1,5,3,6,2]=>[6,4,2,5,1,7,3]=>{{1,6,7},{2,4,5},{3}}
[5,2,6,7,4,3,1]=>[3,4,7,5,2,6,1]=>[6,4,3,5,1,7,2]=>{{1,6,7},{2,4,5},{3}}
[5,2,7,1,3,4,6]=>[7,5,1,2,4,3,6]=>[5,7,2,3,1,4,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,7,1,3,6,4]=>[7,5,1,6,2,3,4]=>[5,7,2,6,4,3,1]=>{{1,5},{2,7},{3},{4,6}}
[5,2,7,1,4,3,6]=>[7,5,4,1,2,3,6]=>[4,5,7,3,2,1,6]=>{{1,4},{2,5},{3,7},{6}}
[5,2,7,1,4,6,3]=>[7,5,6,1,2,4,3]=>[5,7,6,3,4,1,2]=>{{1,5},{2,7},{3,6},{4}}
[5,2,7,1,6,3,4]=>[7,5,6,3,2,1,4]=>[5,7,6,1,3,4,2]=>{{1,5},{2,7},{3,6},{4}}
[5,2,7,1,6,4,3]=>[7,5,4,6,2,1,3]=>[4,6,7,5,2,3,1]=>{{1,4,5},{2,6},{3,7}}
[5,2,7,3,1,4,6]=>[3,7,5,1,4,2,6]=>[7,3,5,2,1,4,6]=>{{1,7},{2,3,5},{4},{6}}
[5,2,7,3,1,6,4]=>[3,7,5,6,1,2,4]=>[7,3,5,6,4,2,1]=>{{1,7},{2,3,5},{4,6}}
[5,2,7,3,4,1,6]=>[4,5,7,3,2,1,6]=>[7,5,4,1,2,3,6]=>{{1,7},{2,5},{3,4},{6}}
[5,2,7,3,4,6,1]=>[6,5,7,3,2,4,1]=>[6,7,5,1,3,2,4]=>{{1,6},{2,7},{3,5},{4}}
[5,2,7,3,6,1,4]=>[6,5,7,1,2,3,4]=>[6,7,5,3,4,2,1]=>{{1,6},{2,7},{3,5},{4}}
[5,2,7,3,6,4,1]=>[4,6,5,7,3,1,2]=>[7,5,6,4,1,3,2]=>{{1,7},{2,5},{3,6},{4}}
[5,2,7,4,1,3,6]=>[4,7,1,5,3,2,6]=>[7,4,2,5,1,3,6]=>{{1,7},{2,4,5},{3},{6}}
[5,2,7,4,1,6,3]=>[4,7,5,6,3,2,1]=>[7,4,6,5,1,2,3]=>{{1,7},{2,4,5},{3,6}}
[5,2,7,4,3,1,6]=>[3,4,7,5,2,1,6]=>[7,4,3,5,1,2,6]=>{{1,7},{2,4,5},{3},{6}}
[5,2,7,4,3,6,1]=>[6,5,4,7,2,3,1]=>[5,6,7,4,2,1,3]=>{{1,5},{2,6},{3,7},{4}}
[5,2,7,4,6,1,3]=>[6,5,1,7,2,4,3]=>[6,7,2,5,4,1,3]=>{{1,6},{2,7},{3},{4,5}}
[5,2,7,4,6,3,1]=>[3,6,5,7,1,4,2]=>[7,3,6,5,4,1,2]=>{{1,7},{2,3,6},{4,5}}
[5,2,7,6,1,3,4]=>[6,5,1,2,4,7,3]=>[5,7,2,3,1,6,4]=>{{1,5},{2,7},{3},{4},{6}}
[5,2,7,6,1,4,3]=>[6,5,4,1,2,7,3]=>[4,5,7,3,2,6,1]=>{{1,4},{2,5},{3,7},{6}}
[5,2,7,6,3,1,4]=>[3,6,5,1,4,7,2]=>[7,3,5,2,1,6,4]=>{{1,7},{2,3,5},{4},{6}}
[5,2,7,6,3,4,1]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,6,3]=>{{1,7},{2,5},{3,4},{6}}
[5,2,7,6,4,1,3]=>[4,6,1,5,3,7,2]=>[7,4,2,5,1,6,3]=>{{1,7},{2,4,5},{3},{6}}
[5,2,7,6,4,3,1]=>[3,4,6,5,2,7,1]=>[7,4,3,5,1,6,2]=>{{1,7},{2,4,5},{3},{6}}
[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[5,1,3,2,4,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,3,1,2,4,7,6]=>[3,1,5,2,4,7,6]=>[5,1,3,2,4,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,3,1,2,6,4,7]=>[3,1,5,6,2,4,7]=>[6,1,3,5,4,2,7]=>{{1,6},{2},{3},{4,5},{7}}
[5,3,1,2,6,7,4]=>[3,1,5,7,2,6,4]=>[6,1,3,5,4,7,2]=>{{1,6,7},{2},{3},{4,5}}
[5,3,1,2,7,4,6]=>[3,1,5,7,2,4,6]=>[7,1,3,5,4,2,6]=>{{1,7},{2},{3},{4,5},{6}}
[5,3,1,2,7,6,4]=>[3,1,5,6,2,7,4]=>[7,1,3,5,4,6,2]=>{{1,7},{2},{3},{4,5},{6}}
[5,3,1,4,2,6,7]=>[3,5,4,2,1,6,7]=>[5,3,4,1,2,6,7]=>{{1,5},{2,3,4},{6},{7}}
[5,3,1,4,2,7,6]=>[3,5,4,2,1,7,6]=>[5,3,4,1,2,7,6]=>{{1,5},{2,3,4},{6,7}}
[5,3,1,4,6,2,7]=>[3,5,6,1,2,4,7]=>[6,5,3,2,4,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,3,1,4,6,7,2]=>[3,5,7,1,2,6,4]=>[6,5,3,2,4,7,1]=>{{1,6,7},{2,5},{3},{4}}
[5,3,1,4,7,2,6]=>[3,5,7,1,2,4,6]=>[7,5,3,2,4,1,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,3,1,4,7,6,2]=>[3,5,6,1,2,7,4]=>[7,5,3,2,4,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[5,3,1,6,2,4,7]=>[3,5,6,2,4,1,7]=>[6,5,3,1,2,4,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,3,1,6,2,7,4]=>[3,5,6,7,2,1,4]=>[7,6,3,5,2,4,1]=>{{1,7},{2,6},{3},{4,5}}
[5,3,1,6,4,2,7]=>[3,5,4,6,2,1,7]=>[6,3,5,4,1,2,7]=>{{1,6},{2,3,5},{4},{7}}
[5,3,1,6,4,7,2]=>[3,5,7,6,2,4,1]=>[7,5,3,6,2,1,4]=>{{1,7},{2,5},{3},{4,6}}
[5,3,1,6,7,2,4]=>[3,5,7,2,4,6,1]=>[6,5,3,1,2,7,4]=>{{1,6,7},{2,5},{3},{4}}
[5,3,1,6,7,4,2]=>[3,5,4,7,2,6,1]=>[6,3,5,4,1,7,2]=>{{1,6,7},{2,3,5},{4}}
[5,3,1,7,2,4,6]=>[3,5,7,2,4,1,6]=>[7,5,3,1,2,4,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,3,1,7,2,6,4]=>[3,5,7,6,2,1,4]=>[7,5,3,6,2,4,1]=>{{1,7},{2,5},{3},{4,6}}
[5,3,1,7,4,2,6]=>[3,5,4,7,2,1,6]=>[7,3,5,4,1,2,6]=>{{1,7},{2,3,5},{4},{6}}
[5,3,1,7,4,6,2]=>[3,5,6,7,2,4,1]=>[7,6,3,5,2,1,4]=>{{1,7},{2,6},{3},{4,5}}
[5,3,1,7,6,2,4]=>[3,5,6,2,4,7,1]=>[7,5,3,1,2,6,4]=>{{1,7},{2,5},{3},{4},{6}}
[5,3,1,7,6,4,2]=>[3,5,4,6,2,7,1]=>[7,3,5,4,1,6,2]=>{{1,7},{2,3,5},{4},{6}}
[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,3,2,1,4,7,6]=>[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,3,2,1,6,4,7]=>[2,3,5,6,1,4,7]=>[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}}
[5,3,2,1,6,7,4]=>[2,3,5,7,1,6,4]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}}
[5,3,2,1,7,4,6]=>[2,3,5,7,1,4,6]=>[7,2,3,5,4,1,6]=>{{1,7},{2},{3},{4,5},{6}}
[5,3,2,1,7,6,4]=>[2,3,5,6,1,7,4]=>[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}}
[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[4,5,3,1,2,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[5,3,2,4,1,7,6]=>[4,3,5,2,1,7,6]=>[4,5,3,1,2,7,6]=>{{1,4},{2,5},{3},{6,7}}
[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[3,6,5,1,2,4,7]=>{{1,3,5},{2,6},{4},{7}}
[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[3,6,5,1,2,7,4]=>{{1,3,5},{2,6,7},{4}}
[5,3,2,4,7,1,6]=>[7,3,5,2,4,1,6]=>[3,7,5,1,2,4,6]=>{{1,3,5},{2,7},{4},{6}}
[5,3,2,4,7,6,1]=>[6,3,5,2,4,7,1]=>[3,7,5,1,2,6,4]=>{{1,3,5},{2,7},{4},{6}}
[5,3,2,6,1,4,7]=>[6,3,5,1,2,4,7]=>[3,6,5,2,4,1,7]=>{{1,3,5},{2,6},{4},{7}}
[5,3,2,6,1,7,4]=>[6,3,5,7,2,1,4]=>[3,7,6,5,2,4,1]=>{{1,3,6},{2,7},{4,5}}
[5,3,2,6,4,1,7]=>[4,3,6,5,1,2,7]=>[4,6,3,5,2,1,7]=>{{1,4,5},{2,6},{3},{7}}
[5,3,2,6,4,7,1]=>[7,3,5,6,2,4,1]=>[3,7,5,6,2,1,4]=>{{1,3,5},{2,7},{4,6}}
[5,3,2,6,7,1,4]=>[7,3,5,1,2,6,4]=>[3,6,5,2,4,7,1]=>{{1,3,5},{2,6,7},{4}}
[5,3,2,6,7,4,1]=>[4,3,7,5,1,6,2]=>[4,6,3,5,2,7,1]=>{{1,4,5},{2,6,7},{3}}
[5,3,2,7,1,4,6]=>[7,3,5,1,2,4,6]=>[3,7,5,2,4,1,6]=>{{1,3,5},{2,7},{4},{6}}
[5,3,2,7,1,6,4]=>[7,3,5,6,2,1,4]=>[3,7,5,6,2,4,1]=>{{1,3,5},{2,7},{4,6}}
[5,3,2,7,4,1,6]=>[4,3,7,5,1,2,6]=>[4,7,3,5,2,1,6]=>{{1,4,5},{2,7},{3},{6}}
[5,3,2,7,4,6,1]=>[6,3,5,7,2,4,1]=>[3,7,6,5,2,1,4]=>{{1,3,6},{2,7},{4,5}}
[5,3,2,7,6,1,4]=>[6,3,5,1,2,7,4]=>[3,7,5,2,4,6,1]=>{{1,3,5},{2,7},{4},{6}}
[5,3,2,7,6,4,1]=>[4,3,6,5,1,7,2]=>[4,7,3,5,2,6,1]=>{{1,4,5},{2,7},{3},{6}}
[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[5,1,4,2,3,6,7]=>{{1,5},{2},{3,4},{6},{7}}
[5,3,4,1,2,7,6]=>[4,1,5,3,2,7,6]=>[5,1,4,2,3,7,6]=>{{1,5},{2},{3,4},{6,7}}
[5,3,4,1,6,2,7]=>[4,6,5,3,1,2,7]=>[6,4,5,1,3,2,7]=>{{1,6},{2,4},{3,5},{7}}
[5,3,4,1,6,7,2]=>[4,7,5,3,1,6,2]=>[6,4,5,1,3,7,2]=>{{1,6,7},{2,4},{3,5}}
[5,3,4,1,7,2,6]=>[4,7,5,3,1,2,6]=>[7,4,5,1,3,2,6]=>{{1,7},{2,4},{3,5},{6}}
[5,3,4,1,7,6,2]=>[4,6,5,3,1,7,2]=>[7,4,5,1,3,6,2]=>{{1,7},{2,4},{3,5},{6}}
[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>{{1,5},{2},{3,4},{6},{7}}
[5,3,4,2,1,7,6]=>[2,4,5,3,1,7,6]=>[5,2,4,1,3,7,6]=>{{1,5},{2},{3,4},{6,7}}
[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[4,6,5,1,2,3,7]=>{{1,4},{2,6},{3,5},{7}}
[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[4,6,5,1,2,7,3]=>{{1,4},{2,6,7},{3,5}}
[5,3,4,2,7,1,6]=>[7,4,5,3,2,1,6]=>[4,7,5,1,2,3,6]=>{{1,4},{2,7},{3,5},{6}}
[5,3,4,2,7,6,1]=>[6,4,5,3,2,7,1]=>[4,7,5,1,2,6,3]=>{{1,4},{2,7},{3,5},{6}}
[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[5,1,6,2,3,4,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,3,4,6,1,7,2]=>[6,7,5,3,4,1,2]=>[6,5,7,1,2,4,3]=>{{1,6},{2,5},{3,7},{4}}
[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[5,2,6,1,3,4,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[5,6,7,1,2,3,4]=>{{1,5},{2,6},{3,7},{4}}
[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[5,1,6,2,3,7,4]=>{{1,5},{2},{3,6,7},{4}}
[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[5,2,6,1,3,7,4]=>{{1,5},{2},{3,6,7},{4}}
[5,3,4,7,1,2,6]=>[7,1,5,3,4,2,6]=>[5,1,7,2,3,4,6]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,4,7,1,6,2]=>[7,6,5,3,4,1,2]=>[5,6,7,1,2,4,3]=>{{1,5},{2,6},{3,7},{4}}
[5,3,4,7,2,1,6]=>[2,7,5,3,4,1,6]=>[5,2,7,1,3,4,6]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,4,7,2,6,1]=>[6,7,5,3,4,2,1]=>[6,5,7,1,2,3,4]=>{{1,6},{2,5},{3,7},{4}}
[5,3,4,7,6,1,2]=>[6,1,5,3,4,7,2]=>[5,1,7,2,3,6,4]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,4,7,6,2,1]=>[2,6,5,3,4,7,1]=>[5,2,7,1,3,6,4]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,6,1,2,4,7]=>[6,1,5,2,3,4,7]=>[5,1,6,3,4,2,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,3,6,1,2,7,4]=>[6,1,5,7,3,2,4]=>[6,1,7,5,3,4,2]=>{{1,6},{2},{3,7},{4,5}}
[5,3,6,1,4,2,7]=>[6,4,5,1,3,2,7]=>[4,6,5,3,1,2,7]=>{{1,4},{2,6},{3,5},{7}}
[5,3,6,1,4,7,2]=>[6,7,5,1,3,4,2]=>[6,5,7,3,2,1,4]=>{{1,6},{2,5},{3,7},{4}}
[5,3,6,1,7,2,4]=>[6,7,5,2,3,1,4]=>[6,5,7,2,3,4,1]=>{{1,6},{2,5},{3,7},{4}}
[5,3,6,1,7,4,2]=>[6,4,7,5,2,1,3]=>[5,7,4,6,2,3,1]=>{{1,5},{2,7},{3,4,6}}
[5,3,6,2,1,4,7]=>[2,6,5,1,3,4,7]=>[5,2,6,3,4,1,7]=>{{1,5},{2},{3,6},{4},{7}}
[5,3,6,2,1,7,4]=>[2,6,5,7,3,1,4]=>[6,2,7,5,3,4,1]=>{{1,6},{2},{3,7},{4,5}}
[5,3,6,2,4,1,7]=>[4,6,5,2,3,1,7]=>[6,4,5,2,1,3,7]=>{{1,6},{2,4},{3,5},{7}}
[5,3,6,2,4,7,1]=>[7,6,5,2,3,4,1]=>[5,6,7,2,3,1,4]=>{{1,5},{2,6},{3,7},{4}}
[5,3,6,2,7,1,4]=>[7,6,5,1,3,2,4]=>[5,6,7,3,2,4,1]=>{{1,5},{2,6},{3,7},{4}}
[5,3,6,2,7,4,1]=>[4,7,6,5,1,3,2]=>[7,4,5,6,3,1,2]=>{{1,7},{2,4,6},{3,5}}
[5,3,6,4,1,2,7]=>[4,1,6,5,2,3,7]=>[6,1,4,5,3,2,7]=>{{1,6},{2},{3,4,5},{7}}
[5,3,6,4,1,7,2]=>[4,6,7,5,1,2,3]=>[7,5,4,6,3,2,1]=>{{1,7},{2,5},{3,4,6}}
[5,3,6,4,2,1,7]=>[2,4,6,5,1,3,7]=>[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}}
[5,3,6,4,2,7,1]=>[7,4,6,5,2,3,1]=>[4,7,5,6,2,1,3]=>{{1,4,6},{2,7},{3,5}}
[5,3,6,4,7,1,2]=>[7,1,5,6,3,4,2]=>[5,1,7,6,3,2,4]=>{{1,5},{2},{3,7},{4,6}}
[5,3,6,4,7,2,1]=>[2,7,5,6,3,4,1]=>[5,2,7,6,3,1,4]=>{{1,5},{2},{3,7},{4,6}}
[5,3,6,7,1,2,4]=>[7,1,5,2,3,6,4]=>[5,1,6,3,4,7,2]=>{{1,5},{2},{3,6,7},{4}}
[5,3,6,7,1,4,2]=>[7,4,5,1,3,6,2]=>[4,6,5,3,1,7,2]=>{{1,4},{2,6,7},{3,5}}
[5,3,6,7,2,1,4]=>[2,7,5,1,3,6,4]=>[5,2,6,3,4,7,1]=>{{1,5},{2},{3,6,7},{4}}
[5,3,6,7,2,4,1]=>[4,7,5,2,3,6,1]=>[6,4,5,2,1,7,3]=>{{1,6,7},{2,4},{3,5}}
[5,3,6,7,4,1,2]=>[4,1,7,5,2,6,3]=>[6,1,4,5,3,7,2]=>{{1,6,7},{2},{3,4,5}}
[5,3,6,7,4,2,1]=>[2,4,7,5,1,6,3]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}}
[5,3,7,1,2,4,6]=>[7,1,5,2,3,4,6]=>[5,1,7,3,4,2,6]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,7,1,2,6,4]=>[7,1,5,6,3,2,4]=>[5,1,7,6,3,4,2]=>{{1,5},{2},{3,7},{4,6}}
[5,3,7,1,4,2,6]=>[7,4,5,1,3,2,6]=>[4,7,5,3,1,2,6]=>{{1,4},{2,7},{3,5},{6}}
[5,3,7,1,4,6,2]=>[7,6,5,1,3,4,2]=>[5,6,7,3,2,1,4]=>{{1,5},{2,6},{3,7},{4}}
[5,3,7,1,6,2,4]=>[7,6,5,2,3,1,4]=>[5,6,7,2,3,4,1]=>{{1,5},{2,6},{3,7},{4}}
[5,3,7,1,6,4,2]=>[7,4,6,5,2,1,3]=>[4,7,5,6,2,3,1]=>{{1,4,6},{2,7},{3,5}}
[5,3,7,2,1,4,6]=>[2,7,5,1,3,4,6]=>[5,2,7,3,4,1,6]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,7,2,1,6,4]=>[2,7,5,6,3,1,4]=>[5,2,7,6,3,4,1]=>{{1,5},{2},{3,7},{4,6}}
[5,3,7,2,4,1,6]=>[4,7,5,2,3,1,6]=>[7,4,5,2,1,3,6]=>{{1,7},{2,4},{3,5},{6}}
[5,3,7,2,4,6,1]=>[6,7,5,2,3,4,1]=>[6,5,7,2,3,1,4]=>{{1,6},{2,5},{3,7},{4}}
[5,3,7,2,6,1,4]=>[6,7,5,1,3,2,4]=>[6,5,7,3,2,4,1]=>{{1,6},{2,5},{3,7},{4}}
[5,3,7,2,6,4,1]=>[4,6,7,5,1,3,2]=>[7,5,4,6,3,1,2]=>{{1,7},{2,5},{3,4,6}}
[5,3,7,4,1,2,6]=>[4,1,7,5,2,3,6]=>[7,1,4,5,3,2,6]=>{{1,7},{2},{3,4,5},{6}}
[5,3,7,4,1,6,2]=>[4,7,6,5,1,2,3]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}}
[5,3,7,4,2,1,6]=>[2,4,7,5,1,3,6]=>[7,2,4,5,3,1,6]=>{{1,7},{2},{3,4,5},{6}}
[5,3,7,4,2,6,1]=>[6,4,7,5,2,3,1]=>[5,7,4,6,2,1,3]=>{{1,5},{2,7},{3,4,6}}
[5,3,7,4,6,1,2]=>[6,1,5,7,3,4,2]=>[6,1,7,5,3,2,4]=>{{1,6},{2},{3,7},{4,5}}
[5,3,7,4,6,2,1]=>[2,6,5,7,3,4,1]=>[6,2,7,5,3,1,4]=>{{1,6},{2},{3,7},{4,5}}
[5,3,7,6,1,2,4]=>[6,1,5,2,3,7,4]=>[5,1,7,3,4,6,2]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,7,6,1,4,2]=>[6,4,5,1,3,7,2]=>[4,7,5,3,1,6,2]=>{{1,4},{2,7},{3,5},{6}}
[5,3,7,6,2,1,4]=>[2,6,5,1,3,7,4]=>[5,2,7,3,4,6,1]=>{{1,5},{2},{3,7},{4},{6}}
[5,3,7,6,2,4,1]=>[4,6,5,2,3,7,1]=>[7,4,5,2,1,6,3]=>{{1,7},{2,4},{3,5},{6}}
[5,3,7,6,4,1,2]=>[4,1,6,5,2,7,3]=>[7,1,4,5,3,6,2]=>{{1,7},{2},{3,4,5},{6}}
[5,3,7,6,4,2,1]=>[2,4,6,5,1,7,3]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}}
[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[5,1,2,4,3,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,4,1,2,3,7,6]=>[4,1,2,5,3,7,6]=>[5,1,2,4,3,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,4,1,2,6,3,7]=>[4,1,5,6,3,2,7]=>[6,1,5,4,2,3,7]=>{{1,6},{2},{3,5},{4},{7}}
[5,4,1,2,6,7,3]=>[4,1,5,7,3,6,2]=>[6,1,5,4,2,7,3]=>{{1,6,7},{2},{3,5},{4}}
[5,4,1,2,7,3,6]=>[4,1,5,7,3,2,6]=>[7,1,5,4,2,3,6]=>{{1,7},{2},{3,5},{4},{6}}
[5,4,1,2,7,6,3]=>[4,1,5,6,3,7,2]=>[7,1,5,4,2,6,3]=>{{1,7},{2},{3,5},{4},{6}}
[5,4,1,3,2,6,7]=>[4,3,1,5,2,6,7]=>[3,5,2,4,1,6,7]=>{{1,3},{2,5},{4},{6},{7}}
[5,4,1,3,2,7,6]=>[4,3,1,5,2,7,6]=>[3,5,2,4,1,7,6]=>{{1,3},{2,5},{4},{6,7}}
[5,4,1,3,6,2,7]=>[4,5,1,6,2,3,7]=>[6,5,2,4,3,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,4,1,3,6,7,2]=>[4,5,1,7,2,6,3]=>[6,5,2,4,3,7,1]=>{{1,6,7},{2,5},{3},{4}}
[5,4,1,3,7,2,6]=>[4,5,1,7,2,3,6]=>[7,5,2,4,3,1,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,4,1,3,7,6,2]=>[4,5,1,6,2,7,3]=>[7,5,2,4,3,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[5,4,1,6,2,3,7]=>[4,5,2,6,3,1,7]=>[6,5,1,4,2,3,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,4,1,6,2,7,3]=>[4,5,6,7,2,3,1]=>[7,6,5,4,2,1,3]=>{{1,7},{2,6},{3,5},{4}}
[5,4,1,6,3,2,7]=>[4,3,5,6,2,1,7]=>[5,6,3,4,1,2,7]=>{{1,5},{2,6},{3},{4},{7}}
[5,4,1,6,3,7,2]=>[4,5,7,6,2,1,3]=>[7,6,4,5,2,3,1]=>{{1,7},{2,6},{3,4,5}}
[5,4,1,6,7,2,3]=>[4,5,2,7,3,6,1]=>[6,5,1,4,2,7,3]=>{{1,6,7},{2,5},{3},{4}}
[5,4,1,6,7,3,2]=>[4,3,5,7,2,6,1]=>[5,6,3,4,1,7,2]=>{{1,5},{2,6,7},{3},{4}}
[5,4,1,7,2,3,6]=>[4,5,2,7,3,1,6]=>[7,5,1,4,2,3,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,4,1,7,2,6,3]=>[4,5,7,6,2,3,1]=>[7,6,4,5,2,1,3]=>{{1,7},{2,6},{3,4,5}}
[5,4,1,7,3,2,6]=>[4,3,5,7,2,1,6]=>[5,7,3,4,1,2,6]=>{{1,5},{2,7},{3},{4},{6}}
[5,4,1,7,3,6,2]=>[4,5,6,7,2,1,3]=>[7,6,5,4,2,3,1]=>{{1,7},{2,6},{3,5},{4}}
[5,4,1,7,6,2,3]=>[4,5,2,6,3,7,1]=>[7,5,1,4,2,6,3]=>{{1,7},{2,5},{3},{4},{6}}
[5,4,1,7,6,3,2]=>[4,3,5,6,2,7,1]=>[5,7,3,4,1,6,2]=>{{1,5},{2,7},{3},{4},{6}}
[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[5,2,1,4,3,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,4,2,1,3,7,6]=>[2,4,1,5,3,7,6]=>[5,2,1,4,3,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,4,2,1,6,3,7]=>[2,4,5,6,3,1,7]=>[6,2,5,4,1,3,7]=>{{1,6},{2},{3,5},{4},{7}}
[5,4,2,1,6,7,3]=>[2,4,5,7,3,6,1]=>[6,2,5,4,1,7,3]=>{{1,6,7},{2},{3,5},{4}}
[5,4,2,1,7,3,6]=>[2,4,5,7,3,1,6]=>[7,2,5,4,1,3,6]=>{{1,7},{2},{3,5},{4},{6}}
[5,4,2,1,7,6,3]=>[2,4,5,6,3,7,1]=>[7,2,5,4,1,6,3]=>{{1,7},{2},{3,5},{4},{6}}
[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[5,3,1,4,2,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[5,4,2,3,1,7,6]=>[3,4,2,5,1,7,6]=>[5,3,1,4,2,7,6]=>{{1,5},{2,3},{4},{6,7}}
[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[4,6,1,5,2,3,7]=>{{1,4,5},{2,6},{3},{7}}
[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[4,6,1,5,2,7,3]=>{{1,4,5},{2,6,7},{3}}
[5,4,2,3,7,1,6]=>[7,4,2,5,3,1,6]=>[4,7,1,5,2,3,6]=>{{1,4,5},{2,7},{3},{6}}
[5,4,2,3,7,6,1]=>[6,4,2,5,3,7,1]=>[4,7,1,5,2,6,3]=>{{1,4,5},{2,7},{3},{6}}
[5,4,2,6,1,3,7]=>[6,4,1,5,2,3,7]=>[4,6,2,5,3,1,7]=>{{1,4,5},{2,6},{3},{7}}
[5,4,2,6,1,7,3]=>[6,4,5,7,3,1,2]=>[5,7,6,4,1,3,2]=>{{1,5},{2,7},{3,6},{4}}
[5,4,2,6,3,1,7]=>[3,6,4,5,1,2,7]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[5,4,2,6,3,7,1]=>[7,4,5,6,3,2,1]=>[4,7,6,5,1,2,3]=>{{1,4,5},{2,7},{3,6}}
[5,4,2,6,7,1,3]=>[7,4,1,5,2,6,3]=>[4,6,2,5,3,7,1]=>{{1,4,5},{2,6,7},{3}}
[5,4,2,6,7,3,1]=>[3,7,4,5,1,6,2]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}
[5,4,2,7,1,3,6]=>[7,4,1,5,2,3,6]=>[4,7,2,5,3,1,6]=>{{1,4,5},{2,7},{3},{6}}
[5,4,2,7,1,6,3]=>[7,4,5,6,3,1,2]=>[4,7,6,5,1,3,2]=>{{1,4,5},{2,7},{3,6}}
[5,4,2,7,3,1,6]=>[3,7,4,5,1,2,6]=>[7,3,4,5,2,1,6]=>{{1,7},{2,3,4,5},{6}}
[5,4,2,7,3,6,1]=>[6,4,5,7,3,2,1]=>[5,7,6,4,1,2,3]=>{{1,5},{2,7},{3,6},{4}}
[5,4,2,7,6,1,3]=>[6,4,1,5,2,7,3]=>[4,7,2,5,3,6,1]=>{{1,4,5},{2,7},{3},{6}}
[5,4,2,7,6,3,1]=>[3,6,4,5,1,7,2]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[5,1,3,4,2,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,4,3,1,2,7,6]=>[3,1,4,5,2,7,6]=>[5,1,3,4,2,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,4,3,1,6,2,7]=>[3,4,5,6,1,2,7]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[5,4,3,1,6,7,2]=>[3,4,5,7,1,6,2]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}
[5,4,3,1,7,2,6]=>[3,4,5,7,1,2,6]=>[7,5,3,4,2,1,6]=>{{1,7},{2,5},{3},{4},{6}}
[5,4,3,1,7,6,2]=>[3,4,5,6,1,7,2]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[3,6,4,5,1,2,7]=>{{1,3,4,5},{2,6},{7}}
[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[3,6,4,5,1,7,2]=>{{1,3,4,5},{2,6,7}}
[5,4,3,2,7,1,6]=>[7,3,4,5,2,1,6]=>[3,7,4,5,1,2,6]=>{{1,3,4,5},{2,7},{6}}
[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>[3,7,4,5,1,6,2]=>{{1,3,4,5},{2,7},{6}}
[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[4,1,6,5,2,3,7]=>{{1,4,5},{2},{3,6},{7}}
[5,4,3,6,1,7,2]=>[6,7,4,5,3,1,2]=>[5,4,7,6,1,3,2]=>{{1,5},{2,4,6},{3,7}}
[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[4,2,6,5,1,3,7]=>{{1,4,5},{2},{3,6},{7}}
[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[4,5,7,6,1,2,3]=>{{1,4,6},{2,5},{3,7}}
[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[4,1,6,5,2,7,3]=>{{1,4,5},{2},{3,6,7}}
[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[4,2,6,5,1,7,3]=>{{1,4,5},{2},{3,6,7}}
[5,4,3,7,1,2,6]=>[7,1,4,5,3,2,6]=>[4,1,7,5,2,3,6]=>{{1,4,5},{2},{3,7},{6}}
[5,4,3,7,1,6,2]=>[7,6,4,5,3,1,2]=>[4,5,7,6,1,3,2]=>{{1,4,6},{2,5},{3,7}}
[5,4,3,7,2,1,6]=>[2,7,4,5,3,1,6]=>[4,2,7,5,1,3,6]=>{{1,4,5},{2},{3,7},{6}}
[5,4,3,7,2,6,1]=>[6,7,4,5,3,2,1]=>[5,4,7,6,1,2,3]=>{{1,5},{2,4,6},{3,7}}
[5,4,3,7,6,1,2]=>[6,1,4,5,3,7,2]=>[4,1,7,5,2,6,3]=>{{1,4,5},{2},{3,7},{6}}
[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>[4,2,7,5,1,6,3]=>{{1,4,5},{2},{3,7},{6}}
[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[5,1,2,6,3,4,7]=>{{1,5},{2},{3},{4,6},{7}}
[5,4,6,1,2,7,3]=>[6,1,7,5,4,2,3]=>[6,1,5,7,2,4,3]=>{{1,6},{2},{3,5},{4,7}}
[5,4,6,1,3,2,7]=>[6,3,1,5,4,2,7]=>[3,5,2,6,1,4,7]=>{{1,3},{2,5},{4,6},{7}}
[5,4,6,1,3,7,2]=>[6,7,1,5,4,3,2]=>[6,5,2,7,1,3,4]=>{{1,6},{2,5},{3},{4,7}}
[5,4,6,1,7,2,3]=>[6,7,2,5,4,1,3]=>[6,5,1,7,2,4,3]=>{{1,6},{2,5},{3},{4,7}}
[5,4,6,1,7,3,2]=>[6,3,7,5,4,1,2]=>[5,6,3,7,1,4,2]=>{{1,5},{2,6},{3},{4,7}}
[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[5,2,1,6,3,4,7]=>{{1,5},{2},{3},{4,6},{7}}
[5,4,6,2,1,7,3]=>[2,6,7,5,4,1,3]=>[6,2,5,7,1,4,3]=>{{1,6},{2},{3,5},{4,7}}
[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[5,3,1,6,2,4,7]=>{{1,5},{2,3},{4,6},{7}}
[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[5,6,1,7,2,3,4]=>{{1,5},{2,6},{3},{4,7}}
[5,4,6,2,7,1,3]=>[7,6,1,5,4,2,3]=>[5,6,2,7,1,4,3]=>{{1,5},{2,6},{3},{4,7}}
[5,4,6,2,7,3,1]=>[3,7,6,5,4,1,2]=>[6,3,5,7,1,4,2]=>{{1,6},{2,3,5},{4,7}}
[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[5,1,3,6,2,4,7]=>{{1,5},{2},{3},{4,6},{7}}
[5,4,6,3,1,7,2]=>[3,6,7,5,4,2,1]=>[6,5,3,7,1,2,4]=>{{1,6},{2,5},{3},{4,7}}
[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[5,2,3,6,1,4,7]=>{{1,5},{2},{3},{4,6},{7}}
[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[3,6,5,7,1,2,4]=>{{1,3,5},{2,6},{4,7}}
[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[5,1,6,7,2,3,4]=>{{1,5},{2},{3,6},{4,7}}
[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[5,2,6,7,1,3,4]=>{{1,5},{2},{3,6},{4,7}}
[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[5,1,2,6,3,7,4]=>{{1,5},{2},{3},{4,6,7}}
[5,4,6,7,1,3,2]=>[7,3,1,5,4,6,2]=>[3,5,2,6,1,7,4]=>{{1,3},{2,5},{4,6,7}}
[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[5,2,1,6,3,7,4]=>{{1,5},{2},{3},{4,6,7}}
[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[5,3,1,6,2,7,4]=>{{1,5},{2,3},{4,6,7}}
[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[5,1,3,6,2,7,4]=>{{1,5},{2},{3},{4,6,7}}
[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[5,2,3,6,1,7,4]=>{{1,5},{2},{3},{4,6,7}}
[5,4,7,1,2,3,6]=>[7,1,2,5,4,3,6]=>[5,1,2,7,3,4,6]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,1,2,6,3]=>[7,1,6,5,4,2,3]=>[5,1,6,7,2,4,3]=>{{1,5},{2},{3,6},{4,7}}
[5,4,7,1,3,2,6]=>[7,3,1,5,4,2,6]=>[3,5,2,7,1,4,6]=>{{1,3},{2,5},{4,7},{6}}
[5,4,7,1,3,6,2]=>[7,6,1,5,4,3,2]=>[5,6,2,7,1,3,4]=>{{1,5},{2,6},{3},{4,7}}
[5,4,7,1,6,2,3]=>[7,6,2,5,4,1,3]=>[5,6,1,7,2,4,3]=>{{1,5},{2,6},{3},{4,7}}
[5,4,7,1,6,3,2]=>[7,3,6,5,4,1,2]=>[3,6,5,7,1,4,2]=>{{1,3,5},{2,6},{4,7}}
[5,4,7,2,1,3,6]=>[2,7,1,5,4,3,6]=>[5,2,1,7,3,4,6]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,2,1,6,3]=>[2,7,6,5,4,1,3]=>[5,2,6,7,1,4,3]=>{{1,5},{2},{3,6},{4,7}}
[5,4,7,2,3,1,6]=>[3,7,2,5,4,1,6]=>[5,3,1,7,2,4,6]=>{{1,5},{2,3},{4,7},{6}}
[5,4,7,2,3,6,1]=>[6,7,2,5,4,3,1]=>[6,5,1,7,2,3,4]=>{{1,6},{2,5},{3},{4,7}}
[5,4,7,2,6,1,3]=>[6,7,1,5,4,2,3]=>[6,5,2,7,1,4,3]=>{{1,6},{2,5},{3},{4,7}}
[5,4,7,2,6,3,1]=>[3,6,7,5,4,1,2]=>[6,5,3,7,1,4,2]=>{{1,6},{2,5},{3},{4,7}}
[5,4,7,3,1,2,6]=>[3,1,7,5,4,2,6]=>[5,1,3,7,2,4,6]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,3,1,6,2]=>[3,7,6,5,4,2,1]=>[6,3,5,7,1,2,4]=>{{1,6},{2,3,5},{4,7}}
[5,4,7,3,2,1,6]=>[2,3,7,5,4,1,6]=>[5,2,3,7,1,4,6]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,3,2,6,1]=>[6,3,7,5,4,2,1]=>[5,6,3,7,1,2,4]=>{{1,5},{2,6},{3},{4,7}}
[5,4,7,3,6,1,2]=>[6,1,7,5,4,3,2]=>[6,1,5,7,2,3,4]=>{{1,6},{2},{3,5},{4,7}}
[5,4,7,3,6,2,1]=>[2,6,7,5,4,3,1]=>[6,2,5,7,1,3,4]=>{{1,6},{2},{3,5},{4,7}}
[5,4,7,6,1,2,3]=>[6,1,2,5,4,7,3]=>[5,1,2,7,3,6,4]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,6,1,3,2]=>[6,3,1,5,4,7,2]=>[3,5,2,7,1,6,4]=>{{1,3},{2,5},{4,7},{6}}
[5,4,7,6,2,1,3]=>[2,6,1,5,4,7,3]=>[5,2,1,7,3,6,4]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,6,2,3,1]=>[3,6,2,5,4,7,1]=>[5,3,1,7,2,6,4]=>{{1,5},{2,3},{4,7},{6}}
[5,4,7,6,3,1,2]=>[3,1,6,5,4,7,2]=>[5,1,3,7,2,6,4]=>{{1,5},{2},{3},{4,7},{6}}
[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>[5,2,3,7,1,6,4]=>{{1,5},{2},{3},{4,7},{6}}
[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[5,1,2,3,6,4,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,1,2,3,7,4]=>[6,1,2,7,5,3,4]=>[6,1,2,5,7,4,3]=>{{1,6},{2},{3},{4,5,7}}
[5,6,1,2,4,3,7]=>[6,1,4,2,5,3,7]=>[4,1,5,3,6,2,7]=>{{1,4},{2},{3,5,6},{7}}
[5,6,1,2,4,7,3]=>[6,1,7,2,5,4,3]=>[6,1,5,3,7,2,4]=>{{1,6},{2},{3,5,7},{4}}
[5,6,1,2,7,3,4]=>[6,1,7,3,5,2,4]=>[6,1,5,2,7,4,3]=>{{1,6},{2},{3,5,7},{4}}
[5,6,1,2,7,4,3]=>[6,1,4,7,5,2,3]=>[5,1,6,4,7,3,2]=>{{1,5,7},{2},{3,6},{4}}
[5,6,1,3,2,4,7]=>[6,3,1,2,5,4,7]=>[3,5,2,1,6,4,7]=>{{1,3},{2,5,6},{4},{7}}
[5,6,1,3,2,7,4]=>[6,3,1,7,5,2,4]=>[3,6,2,5,7,4,1]=>{{1,3},{2,6},{4,5,7}}
[5,6,1,3,4,2,7]=>[6,4,1,3,5,2,7]=>[4,5,2,1,6,3,7]=>{{1,4},{2,5,6},{3},{7}}
[5,6,1,3,4,7,2]=>[6,7,1,2,5,3,4]=>[6,5,2,3,7,4,1]=>{{1,6},{2,5,7},{3},{4}}
[5,6,1,3,7,2,4]=>[6,7,1,3,5,4,2]=>[6,5,2,1,7,3,4]=>{{1,6},{2,5,7},{3},{4}}
[5,6,1,3,7,4,2]=>[6,4,1,7,5,3,2]=>[5,6,2,4,7,1,3]=>{{1,5,7},{2,6},{3},{4}}
[5,6,1,4,2,3,7]=>[6,4,2,1,5,3,7]=>[4,5,1,3,6,2,7]=>{{1,4},{2,5,6},{3},{7}}
[5,6,1,4,2,7,3]=>[6,4,7,1,5,2,3]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}
[5,6,1,4,3,2,7]=>[6,3,4,1,5,2,7]=>[3,5,4,2,6,1,7]=>{{1,3,4},{2,5,6},{7}}
[5,6,1,4,3,7,2]=>[6,7,4,1,5,3,2]=>[5,4,6,3,7,1,2]=>{{1,5,7},{2,4},{3,6}}
[5,6,1,4,7,2,3]=>[6,7,2,1,5,4,3]=>[6,5,1,3,7,2,4]=>{{1,6},{2,5,7},{3},{4}}
[5,6,1,4,7,3,2]=>[6,3,7,1,5,4,2]=>[5,6,3,2,7,1,4]=>{{1,5,7},{2,6},{3},{4}}
[5,6,1,7,2,3,4]=>[6,7,2,3,5,1,4]=>[6,5,1,2,7,4,3]=>{{1,6},{2,5,7},{3},{4}}
[5,6,1,7,2,4,3]=>[6,7,4,2,5,1,3]=>[5,4,6,2,7,3,1]=>{{1,5,7},{2,4},{3,6}}
[5,6,1,7,3,2,4]=>[6,3,7,2,5,1,4]=>[5,6,3,1,7,4,2]=>{{1,5,7},{2,6},{3},{4}}
[5,6,1,7,3,4,2]=>[6,4,7,3,5,1,2]=>[5,6,4,1,7,3,2]=>{{1,5,7},{2,6},{3,4}}
[5,6,1,7,4,2,3]=>[6,4,2,7,5,1,3]=>[5,6,1,4,7,3,2]=>{{1,5,7},{2,6},{3},{4}}
[5,6,1,7,4,3,2]=>[6,3,4,7,5,1,2]=>[3,6,5,4,7,2,1]=>{{1,3,5,7},{2,6},{4}}
[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[5,2,1,3,6,4,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,2,1,3,7,4]=>[2,6,1,7,5,3,4]=>[6,2,1,5,7,4,3]=>{{1,6},{2},{3},{4,5,7}}
[5,6,2,1,4,3,7]=>[2,6,4,1,5,3,7]=>[4,2,5,3,6,1,7]=>{{1,4},{2},{3,5,6},{7}}
[5,6,2,1,4,7,3]=>[2,6,7,1,5,4,3]=>[6,2,5,3,7,1,4]=>{{1,6},{2},{3,5,7},{4}}
[5,6,2,1,7,3,4]=>[2,6,7,3,5,1,4]=>[6,2,5,1,7,4,3]=>{{1,6},{2},{3,5,7},{4}}
[5,6,2,1,7,4,3]=>[2,6,4,7,5,1,3]=>[5,2,6,4,7,3,1]=>{{1,5,7},{2},{3,6},{4}}
[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[5,3,1,2,6,4,7]=>{{1,5,6},{2,3},{4},{7}}
[5,6,2,3,1,7,4]=>[3,6,2,7,5,1,4]=>[6,3,1,5,7,4,2]=>{{1,6},{2,3},{4,5,7}}
[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[5,4,1,2,6,3,7]=>{{1,5,6},{2,4},{3},{7}}
[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[5,6,1,2,7,3,4]=>{{1,5,7},{2,6},{3},{4}}
[5,6,2,3,7,1,4]=>[7,6,2,1,5,3,4]=>[5,6,1,3,7,4,2]=>{{1,5,7},{2,6},{3},{4}}
[5,6,2,3,7,4,1]=>[4,7,2,6,5,1,3]=>[6,4,1,5,7,3,2]=>{{1,6},{2,4,5,7},{3}}
[5,6,2,4,1,3,7]=>[4,6,1,2,5,3,7]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[5,6,2,4,1,7,3]=>[4,6,7,2,5,1,3]=>[6,5,4,2,7,3,1]=>{{1,6},{2,5,7},{3,4}}
[5,6,2,4,3,1,7]=>[3,4,6,1,5,2,7]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[5,6,2,4,3,7,1]=>[7,6,4,2,5,3,1]=>[4,5,6,2,7,1,3]=>{{1,4},{2,5,7},{3,6}}
[5,6,2,4,7,1,3]=>[7,6,1,3,5,2,4]=>[5,6,2,1,7,4,3]=>{{1,5,7},{2,6},{3},{4}}
[5,6,2,4,7,3,1]=>[3,7,6,2,5,1,4]=>[6,3,5,1,7,4,2]=>{{1,6},{2,3,5,7},{4}}
[5,6,2,7,1,3,4]=>[7,6,1,2,5,4,3]=>[5,6,2,3,7,1,4]=>{{1,5,7},{2,6},{3},{4}}
[5,6,2,7,1,4,3]=>[7,6,4,1,5,2,3]=>[4,5,6,3,7,2,1]=>{{1,4},{2,5,7},{3,6}}
[5,6,2,7,3,1,4]=>[3,7,6,1,5,4,2]=>[6,3,5,2,7,1,4]=>{{1,6},{2,3,5,7},{4}}
[5,6,2,7,3,4,1]=>[4,6,7,3,5,2,1]=>[6,5,4,1,7,2,3]=>{{1,6},{2,5,7},{3,4}}
[5,6,2,7,4,1,3]=>[4,7,1,6,5,3,2]=>[6,4,2,5,7,1,3]=>{{1,6},{2,4,5,7},{3}}
[5,6,2,7,4,3,1]=>[3,4,7,6,5,2,1]=>[6,4,3,5,7,1,2]=>{{1,6},{2,4,5,7},{3}}
[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[5,1,3,2,6,4,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,3,1,2,7,4]=>[3,1,6,7,5,2,4]=>[6,1,3,5,7,4,2]=>{{1,6},{2},{3},{4,5,7}}
[5,6,3,1,4,2,7]=>[3,6,4,2,5,1,7]=>[5,3,4,1,6,2,7]=>{{1,5,6},{2,3,4},{7}}
[5,6,3,1,4,7,2]=>[3,6,7,1,5,2,4]=>[6,5,3,2,7,4,1]=>{{1,6},{2,5,7},{3},{4}}
[5,6,3,1,7,2,4]=>[3,6,7,2,5,4,1]=>[6,5,3,1,7,2,4]=>{{1,6},{2,5,7},{3},{4}}
[5,6,3,1,7,4,2]=>[3,6,4,7,5,2,1]=>[6,3,5,4,7,1,2]=>{{1,6},{2,3,5,7},{4}}
[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[5,2,3,1,6,4,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,3,2,1,7,4]=>[2,3,6,7,5,1,4]=>[6,2,3,5,7,4,1]=>{{1,6},{2},{3},{4,5,7}}
[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[4,5,3,1,6,2,7]=>{{1,4},{2,5,6},{3},{7}}
[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[3,6,5,1,7,2,4]=>{{1,3,5,7},{2,6},{4}}
[5,6,3,2,7,1,4]=>[7,3,6,1,5,2,4]=>[3,6,5,2,7,4,1]=>{{1,3,5,7},{2,6},{4}}
[5,6,3,2,7,4,1]=>[4,3,7,6,5,1,2]=>[4,6,3,5,7,2,1]=>{{1,4,5,7},{2,6},{3}}
[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[5,1,4,2,6,3,7]=>{{1,5,6},{2},{3,4},{7}}
[5,6,3,4,1,7,2]=>[4,7,6,3,5,1,2]=>[6,4,5,1,7,3,2]=>{{1,6},{2,4},{3,5,7}}
[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[5,2,4,1,6,3,7]=>{{1,5,6},{2},{3,4},{7}}
[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[4,6,5,1,7,2,3]=>{{1,4},{2,6},{3,5,7}}
[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[5,1,6,2,7,3,4]=>{{1,5,7},{2},{3,6},{4}}
[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[5,2,6,1,7,3,4]=>{{1,5,7},{2},{3,6},{4}}
[5,6,3,7,1,2,4]=>[7,1,6,2,5,3,4]=>[5,1,6,3,7,4,2]=>{{1,5,7},{2},{3,6},{4}}
[5,6,3,7,1,4,2]=>[7,4,6,1,5,3,2]=>[4,6,5,3,7,1,2]=>{{1,4},{2,6},{3,5,7}}
[5,6,3,7,2,1,4]=>[2,7,6,1,5,3,4]=>[5,2,6,3,7,4,1]=>{{1,5,7},{2},{3,6},{4}}
[5,6,3,7,2,4,1]=>[4,7,6,2,5,3,1]=>[6,4,5,2,7,1,3]=>{{1,6},{2,4},{3,5,7}}
[5,6,3,7,4,1,2]=>[4,1,7,6,5,2,3]=>[6,1,4,5,7,3,2]=>{{1,6},{2},{3,4,5,7}}
[5,6,3,7,4,2,1]=>[2,4,7,6,5,1,3]=>[6,2,4,5,7,3,1]=>{{1,6},{2},{3,4,5,7}}
[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[5,1,2,4,6,3,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,4,1,2,7,3]=>[4,1,6,7,5,3,2]=>[6,1,5,4,7,2,3]=>{{1,6},{2},{3,5,7},{4}}
[5,6,4,1,3,2,7]=>[4,3,1,6,5,2,7]=>[3,5,2,4,6,1,7]=>{{1,3},{2,5,6},{4},{7}}
[5,6,4,1,3,7,2]=>[4,6,1,7,5,2,3]=>[6,5,2,4,7,3,1]=>{{1,6},{2,5,7},{3},{4}}
[5,6,4,1,7,2,3]=>[4,6,2,7,5,3,1]=>[6,5,1,4,7,2,3]=>{{1,6},{2,5,7},{3},{4}}
[5,6,4,1,7,3,2]=>[4,3,6,7,5,2,1]=>[5,6,3,4,7,1,2]=>{{1,5,7},{2,6},{3},{4}}
[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[5,2,1,4,6,3,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,4,2,1,7,3]=>[2,4,6,7,5,3,1]=>[6,2,5,4,7,1,3]=>{{1,6},{2},{3,5,7},{4}}
[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[5,3,1,4,6,2,7]=>{{1,5,6},{2,3},{4},{7}}
[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[4,6,1,5,7,2,3]=>{{1,4,5,7},{2,6},{3}}
[5,6,4,2,7,1,3]=>[7,4,1,6,5,2,3]=>[4,6,2,5,7,3,1]=>{{1,4,5,7},{2,6},{3}}
[5,6,4,2,7,3,1]=>[3,7,4,6,5,1,2]=>[6,3,4,5,7,2,1]=>{{1,6},{2,3,4,5,7}}
[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[5,1,3,4,6,2,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,4,3,1,7,2]=>[3,4,6,7,5,1,2]=>[6,5,3,4,7,2,1]=>{{1,6},{2,5,7},{3},{4}}
[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}
[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[3,6,4,5,7,1,2]=>{{1,3,4,5,7},{2,6}}
[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[4,1,6,5,7,2,3]=>{{1,4,5,7},{2},{3,6}}
[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[4,2,6,5,7,1,3]=>{{1,4,5,7},{2},{3,6}}
[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[5,1,2,6,7,3,4]=>{{1,5,7},{2},{3},{4,6}}
[5,6,4,7,1,3,2]=>[7,3,1,6,5,4,2]=>[3,5,2,6,7,1,4]=>{{1,3},{2,5,7},{4,6}}
[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[5,2,1,6,7,3,4]=>{{1,5,7},{2},{3},{4,6}}
[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[5,3,1,6,7,2,4]=>{{1,5,7},{2,3},{4,6}}
[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[5,1,3,6,7,2,4]=>{{1,5,7},{2},{3},{4,6}}
[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[5,2,3,6,7,1,4]=>{{1,5,7},{2},{3},{4,6}}
[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[5,1,2,3,6,7,4]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,1,2,4,3]=>[7,1,4,2,5,6,3]=>[4,1,5,3,6,7,2]=>{{1,4},{2},{3,5,6,7}}
[5,6,7,1,3,2,4]=>[7,3,1,2,5,6,4]=>[3,5,2,1,6,7,4]=>{{1,3},{2,5,6,7},{4}}
[5,6,7,1,3,4,2]=>[7,4,1,3,5,6,2]=>[4,5,2,1,6,7,3]=>{{1,4},{2,5,6,7},{3}}
[5,6,7,1,4,2,3]=>[7,4,2,1,5,6,3]=>[4,5,1,3,6,7,2]=>{{1,4},{2,5,6,7},{3}}
[5,6,7,1,4,3,2]=>[7,3,4,1,5,6,2]=>[3,5,4,2,6,7,1]=>{{1,3,4},{2,5,6,7}}
[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[5,2,1,3,6,7,4]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,2,1,4,3]=>[2,7,4,1,5,6,3]=>[4,2,5,3,6,7,1]=>{{1,4},{2},{3,5,6,7}}
[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[5,3,1,2,6,7,4]=>{{1,5,6,7},{2,3},{4}}
[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[5,4,1,2,6,7,3]=>{{1,5,6,7},{2,4},{3}}
[5,6,7,2,4,1,3]=>[4,7,1,2,5,6,3]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[5,6,7,2,4,3,1]=>[3,4,7,1,5,6,2]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[5,1,3,2,6,7,4]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,3,1,4,2]=>[3,7,4,2,5,6,1]=>[5,3,4,1,6,7,2]=>{{1,5,6,7},{2,3,4}}
[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[5,2,3,1,6,7,4]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[4,5,3,1,6,7,2]=>{{1,4},{2,5,6,7},{3}}
[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[5,1,4,2,6,7,3]=>{{1,5,6,7},{2},{3,4}}
[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[5,2,4,1,6,7,3]=>{{1,5,6,7},{2},{3,4}}
[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[5,1,2,4,6,7,3]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,4,1,3,2]=>[4,3,1,7,5,6,2]=>[3,5,2,4,6,7,1]=>{{1,3},{2,5,6,7},{4}}
[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[5,2,1,4,6,7,3]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[5,3,1,4,6,7,2]=>{{1,5,6,7},{2,3},{4}}
[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[5,1,3,4,6,7,2]=>{{1,5,6,7},{2},{3},{4}}
[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}
[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[5,1,2,3,7,4,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,1,2,3,6,4]=>[7,1,2,6,5,3,4]=>[5,1,2,6,7,4,3]=>{{1,5,7},{2},{3},{4,6}}
[5,7,1,2,4,3,6]=>[7,1,4,2,5,3,6]=>[4,1,5,3,7,2,6]=>{{1,4},{2},{3,5,7},{6}}
[5,7,1,2,4,6,3]=>[7,1,6,2,5,4,3]=>[5,1,6,3,7,2,4]=>{{1,5,7},{2},{3,6},{4}}
[5,7,1,2,6,3,4]=>[7,1,6,3,5,2,4]=>[5,1,6,2,7,4,3]=>{{1,5,7},{2},{3,6},{4}}
[5,7,1,2,6,4,3]=>[7,1,4,6,5,2,3]=>[4,1,6,5,7,3,2]=>{{1,4,5,7},{2},{3,6}}
[5,7,1,3,2,4,6]=>[7,3,1,2,5,4,6]=>[3,5,2,1,7,4,6]=>{{1,3},{2,5,7},{4},{6}}
[5,7,1,3,2,6,4]=>[7,3,1,6,5,2,4]=>[3,5,2,6,7,4,1]=>{{1,3},{2,5,7},{4,6}}
[5,7,1,3,4,2,6]=>[7,4,1,3,5,2,6]=>[4,5,2,1,7,3,6]=>{{1,4},{2,5,7},{3},{6}}
[5,7,1,3,4,6,2]=>[7,6,1,2,5,3,4]=>[5,6,2,3,7,4,1]=>{{1,5,7},{2,6},{3},{4}}
[5,7,1,3,6,2,4]=>[7,6,1,3,5,4,2]=>[5,6,2,1,7,3,4]=>{{1,5,7},{2,6},{3},{4}}
[5,7,1,3,6,4,2]=>[7,4,1,6,5,3,2]=>[4,6,2,5,7,1,3]=>{{1,4,5,7},{2,6},{3}}
[5,7,1,4,2,3,6]=>[7,4,2,1,5,3,6]=>[4,5,1,3,7,2,6]=>{{1,4},{2,5,7},{3},{6}}
[5,7,1,4,2,6,3]=>[7,4,6,1,5,2,3]=>[4,6,5,3,7,2,1]=>{{1,4},{2,6},{3,5,7}}
[5,7,1,4,3,2,6]=>[7,3,4,1,5,2,6]=>[3,5,4,2,7,1,6]=>{{1,3,4},{2,5,7},{6}}
[5,7,1,4,3,6,2]=>[7,6,4,1,5,3,2]=>[4,5,6,3,7,1,2]=>{{1,4},{2,5,7},{3,6}}
[5,7,1,4,6,2,3]=>[7,6,2,1,5,4,3]=>[5,6,1,3,7,2,4]=>{{1,5,7},{2,6},{3},{4}}
[5,7,1,4,6,3,2]=>[7,3,6,1,5,4,2]=>[3,6,5,2,7,1,4]=>{{1,3,5,7},{2,6},{4}}
[5,7,1,6,2,3,4]=>[7,6,2,3,5,1,4]=>[5,6,1,2,7,4,3]=>{{1,5,7},{2,6},{3},{4}}
[5,7,1,6,2,4,3]=>[7,6,4,2,5,1,3]=>[4,5,6,2,7,3,1]=>{{1,4},{2,5,7},{3,6}}
[5,7,1,6,3,2,4]=>[7,3,6,2,5,1,4]=>[3,6,5,1,7,4,2]=>{{1,3,5,7},{2,6},{4}}
[5,7,1,6,3,4,2]=>[7,4,6,3,5,1,2]=>[4,6,5,1,7,3,2]=>{{1,4},{2,6},{3,5,7}}
[5,7,1,6,4,2,3]=>[7,4,2,6,5,1,3]=>[4,6,1,5,7,3,2]=>{{1,4,5,7},{2,6},{3}}
[5,7,1,6,4,3,2]=>[7,3,4,6,5,1,2]=>[3,6,4,5,7,2,1]=>{{1,3,4,5,7},{2,6}}
[5,7,2,1,3,4,6]=>[2,7,1,3,5,4,6]=>[5,2,1,3,7,4,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,2,1,3,6,4]=>[2,7,1,6,5,3,4]=>[5,2,1,6,7,4,3]=>{{1,5,7},{2},{3},{4,6}}
[5,7,2,1,4,3,6]=>[2,7,4,1,5,3,6]=>[4,2,5,3,7,1,6]=>{{1,4},{2},{3,5,7},{6}}
[5,7,2,1,4,6,3]=>[2,7,6,1,5,4,3]=>[5,2,6,3,7,1,4]=>{{1,5,7},{2},{3,6},{4}}
[5,7,2,1,6,3,4]=>[2,7,6,3,5,1,4]=>[5,2,6,1,7,4,3]=>{{1,5,7},{2},{3,6},{4}}
[5,7,2,1,6,4,3]=>[2,7,4,6,5,1,3]=>[4,2,6,5,7,3,1]=>{{1,4,5,7},{2},{3,6}}
[5,7,2,3,1,4,6]=>[3,7,2,1,5,4,6]=>[5,3,1,2,7,4,6]=>{{1,5,7},{2,3},{4},{6}}
[5,7,2,3,1,6,4]=>[3,7,2,6,5,1,4]=>[5,3,1,6,7,4,2]=>{{1,5,7},{2,3},{4,6}}
[5,7,2,3,4,1,6]=>[4,7,2,3,5,1,6]=>[5,4,1,2,7,3,6]=>{{1,5,7},{2,4},{3},{6}}
[5,7,2,3,4,6,1]=>[6,7,2,3,5,4,1]=>[6,5,1,2,7,3,4]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,3,6,1,4]=>[6,7,2,1,5,3,4]=>[6,5,1,3,7,4,2]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,3,6,4,1]=>[4,6,2,7,5,1,3]=>[6,5,1,4,7,3,2]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,4,1,3,6]=>[4,7,1,2,5,3,6]=>[5,4,2,3,7,1,6]=>{{1,5,7},{2,4},{3},{6}}
[5,7,2,4,1,6,3]=>[4,7,6,2,5,1,3]=>[6,4,5,2,7,3,1]=>{{1,6},{2,4},{3,5,7}}
[5,7,2,4,3,1,6]=>[3,4,7,1,5,2,6]=>[5,4,3,2,7,1,6]=>{{1,5,7},{2,4},{3},{6}}
[5,7,2,4,3,6,1]=>[6,7,4,2,5,3,1]=>[5,4,6,2,7,1,3]=>{{1,5,7},{2,4},{3,6}}
[5,7,2,4,6,1,3]=>[6,7,1,3,5,2,4]=>[6,5,2,1,7,4,3]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,4,6,3,1]=>[3,6,7,2,5,1,4]=>[6,5,3,1,7,4,2]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,6,1,3,4]=>[6,7,1,2,5,4,3]=>[6,5,2,3,7,1,4]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,6,1,4,3]=>[6,7,4,1,5,2,3]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,4},{3,6}}
[5,7,2,6,3,1,4]=>[3,6,7,1,5,4,2]=>[6,5,3,2,7,1,4]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,6,3,4,1]=>[4,7,6,3,5,2,1]=>[6,4,5,1,7,2,3]=>{{1,6},{2,4},{3,5,7}}
[5,7,2,6,4,1,3]=>[4,6,1,7,5,3,2]=>[6,5,2,4,7,1,3]=>{{1,6},{2,5,7},{3},{4}}
[5,7,2,6,4,3,1]=>[3,4,6,7,5,2,1]=>[6,5,3,4,7,1,2]=>{{1,6},{2,5,7},{3},{4}}
[5,7,3,1,2,4,6]=>[3,1,7,2,5,4,6]=>[5,1,3,2,7,4,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,3,1,2,6,4]=>[3,1,7,6,5,2,4]=>[5,1,3,6,7,4,2]=>{{1,5,7},{2},{3},{4,6}}
[5,7,3,1,4,2,6]=>[3,7,4,2,5,1,6]=>[5,3,4,1,7,2,6]=>{{1,5,7},{2,3,4},{6}}
[5,7,3,1,4,6,2]=>[3,7,6,1,5,2,4]=>[6,3,5,2,7,4,1]=>{{1,6},{2,3,5,7},{4}}
[5,7,3,1,6,2,4]=>[3,7,6,2,5,4,1]=>[6,3,5,1,7,2,4]=>{{1,6},{2,3,5,7},{4}}
[5,7,3,1,6,4,2]=>[3,7,4,6,5,2,1]=>[6,3,4,5,7,1,2]=>{{1,6},{2,3,4,5,7}}
[5,7,3,2,1,4,6]=>[2,3,7,1,5,4,6]=>[5,2,3,1,7,4,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,3,2,1,6,4]=>[2,3,7,6,5,1,4]=>[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}}
[5,7,3,2,4,1,6]=>[4,3,7,2,5,1,6]=>[4,5,3,1,7,2,6]=>{{1,4},{2,5,7},{3},{6}}
[5,7,3,2,4,6,1]=>[6,3,7,2,5,4,1]=>[5,6,3,1,7,2,4]=>{{1,5,7},{2,6},{3},{4}}
[5,7,3,2,6,1,4]=>[6,3,7,1,5,2,4]=>[5,6,3,2,7,4,1]=>{{1,5,7},{2,6},{3},{4}}
[5,7,3,2,6,4,1]=>[4,3,6,7,5,1,2]=>[5,6,3,4,7,2,1]=>{{1,5,7},{2,6},{3},{4}}
[5,7,3,4,1,2,6]=>[4,1,7,3,5,2,6]=>[5,1,4,2,7,3,6]=>{{1,5,7},{2},{3,4},{6}}
[5,7,3,4,1,6,2]=>[4,6,7,3,5,1,2]=>[6,5,4,1,7,3,2]=>{{1,6},{2,5,7},{3,4}}
[5,7,3,4,2,1,6]=>[2,4,7,3,5,1,6]=>[5,2,4,1,7,3,6]=>{{1,5,7},{2},{3,4},{6}}
[5,7,3,4,2,6,1]=>[6,4,7,3,5,2,1]=>[5,6,4,1,7,2,3]=>{{1,5,7},{2,6},{3,4}}
[5,7,3,4,6,1,2]=>[6,1,7,3,5,4,2]=>[6,1,5,2,7,3,4]=>{{1,6},{2},{3,5,7},{4}}
[5,7,3,4,6,2,1]=>[2,6,7,3,5,4,1]=>[6,2,5,1,7,3,4]=>{{1,6},{2},{3,5,7},{4}}
[5,7,3,6,1,2,4]=>[6,1,7,2,5,3,4]=>[6,1,5,3,7,4,2]=>{{1,6},{2},{3,5,7},{4}}
[5,7,3,6,1,4,2]=>[6,4,7,1,5,3,2]=>[5,6,4,3,7,1,2]=>{{1,5,7},{2,6},{3,4}}
[5,7,3,6,2,1,4]=>[2,6,7,1,5,3,4]=>[6,2,5,3,7,4,1]=>{{1,6},{2},{3,5,7},{4}}
[5,7,3,6,2,4,1]=>[4,6,7,2,5,3,1]=>[6,5,4,2,7,1,3]=>{{1,6},{2,5,7},{3,4}}
[5,7,3,6,4,1,2]=>[4,1,6,7,5,2,3]=>[6,1,5,4,7,3,2]=>{{1,6},{2},{3,5,7},{4}}
[5,7,3,6,4,2,1]=>[2,4,6,7,5,1,3]=>[6,2,5,4,7,3,1]=>{{1,6},{2},{3,5,7},{4}}
[5,7,4,1,2,3,6]=>[4,1,2,7,5,3,6]=>[5,1,2,4,7,3,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,4,1,2,6,3]=>[4,1,7,6,5,3,2]=>[6,1,4,5,7,2,3]=>{{1,6},{2},{3,4,5,7}}
[5,7,4,1,3,2,6]=>[4,3,1,7,5,2,6]=>[3,5,2,4,7,1,6]=>{{1,3},{2,5,7},{4},{6}}
[5,7,4,1,3,6,2]=>[4,7,1,6,5,2,3]=>[6,4,2,5,7,3,1]=>{{1,6},{2,4,5,7},{3}}
[5,7,4,1,6,2,3]=>[4,7,2,6,5,3,1]=>[6,4,1,5,7,2,3]=>{{1,6},{2,4,5,7},{3}}
[5,7,4,1,6,3,2]=>[4,3,7,6,5,2,1]=>[4,6,3,5,7,1,2]=>{{1,4,5,7},{2,6},{3}}
[5,7,4,2,1,3,6]=>[2,4,1,7,5,3,6]=>[5,2,1,4,7,3,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,4,2,1,6,3]=>[2,4,7,6,5,3,1]=>[6,2,4,5,7,1,3]=>{{1,6},{2},{3,4,5,7}}
[5,7,4,2,3,1,6]=>[3,4,2,7,5,1,6]=>[5,3,1,4,7,2,6]=>{{1,5,7},{2,3},{4},{6}}
[5,7,4,2,3,6,1]=>[6,4,2,7,5,3,1]=>[5,6,1,4,7,2,3]=>{{1,5,7},{2,6},{3},{4}}
[5,7,4,2,6,1,3]=>[6,4,1,7,5,2,3]=>[5,6,2,4,7,3,1]=>{{1,5,7},{2,6},{3},{4}}
[5,7,4,2,6,3,1]=>[3,6,4,7,5,1,2]=>[6,3,5,4,7,2,1]=>{{1,6},{2,3,5,7},{4}}
[5,7,4,3,1,2,6]=>[3,1,4,7,5,2,6]=>[5,1,3,4,7,2,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,4,3,1,6,2]=>[3,4,7,6,5,1,2]=>[6,4,3,5,7,2,1]=>{{1,6},{2,4,5,7},{3}}
[5,7,4,3,2,1,6]=>[2,3,4,7,5,1,6]=>[5,2,3,4,7,1,6]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,4,3,2,6,1]=>[6,3,4,7,5,2,1]=>[3,6,5,4,7,1,2]=>{{1,3,5,7},{2,6},{4}}
[5,7,4,3,6,1,2]=>[6,1,4,7,5,3,2]=>[5,1,6,4,7,2,3]=>{{1,5,7},{2},{3,6},{4}}
[5,7,4,3,6,2,1]=>[2,6,4,7,5,3,1]=>[5,2,6,4,7,1,3]=>{{1,5,7},{2},{3,6},{4}}
[5,7,4,6,1,2,3]=>[6,1,2,7,5,4,3]=>[6,1,2,5,7,3,4]=>{{1,6},{2},{3},{4,5,7}}
[5,7,4,6,1,3,2]=>[6,3,1,7,5,4,2]=>[3,6,2,5,7,1,4]=>{{1,3},{2,6},{4,5,7}}
[5,7,4,6,2,1,3]=>[2,6,1,7,5,4,3]=>[6,2,1,5,7,3,4]=>{{1,6},{2},{3},{4,5,7}}
[5,7,4,6,2,3,1]=>[3,6,2,7,5,4,1]=>[6,3,1,5,7,2,4]=>{{1,6},{2,3},{4,5,7}}
[5,7,4,6,3,1,2]=>[3,1,6,7,5,4,2]=>[6,1,3,5,7,2,4]=>{{1,6},{2},{3},{4,5,7}}
[5,7,4,6,3,2,1]=>[2,3,6,7,5,4,1]=>[6,2,3,5,7,1,4]=>{{1,6},{2},{3},{4,5,7}}
[5,7,6,1,2,3,4]=>[6,1,2,3,5,7,4]=>[5,1,2,3,7,6,4]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,1,2,4,3]=>[6,1,4,2,5,7,3]=>[4,1,5,3,7,6,2]=>{{1,4},{2},{3,5,7},{6}}
[5,7,6,1,3,2,4]=>[6,3,1,2,5,7,4]=>[3,5,2,1,7,6,4]=>{{1,3},{2,5,7},{4},{6}}
[5,7,6,1,3,4,2]=>[6,4,1,3,5,7,2]=>[4,5,2,1,7,6,3]=>{{1,4},{2,5,7},{3},{6}}
[5,7,6,1,4,2,3]=>[6,4,2,1,5,7,3]=>[4,5,1,3,7,6,2]=>{{1,4},{2,5,7},{3},{6}}
[5,7,6,1,4,3,2]=>[6,3,4,1,5,7,2]=>[3,5,4,2,7,6,1]=>{{1,3,4},{2,5,7},{6}}
[5,7,6,2,1,3,4]=>[2,6,1,3,5,7,4]=>[5,2,1,3,7,6,4]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,2,1,4,3]=>[2,6,4,1,5,7,3]=>[4,2,5,3,7,6,1]=>{{1,4},{2},{3,5,7},{6}}
[5,7,6,2,3,1,4]=>[3,6,2,1,5,7,4]=>[5,3,1,2,7,6,4]=>{{1,5,7},{2,3},{4},{6}}
[5,7,6,2,3,4,1]=>[4,6,2,3,5,7,1]=>[5,4,1,2,7,6,3]=>{{1,5,7},{2,4},{3},{6}}
[5,7,6,2,4,1,3]=>[4,6,1,2,5,7,3]=>[5,4,2,3,7,6,1]=>{{1,5,7},{2,4},{3},{6}}
[5,7,6,2,4,3,1]=>[3,4,6,1,5,7,2]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}
[5,7,6,3,1,2,4]=>[3,1,6,2,5,7,4]=>[5,1,3,2,7,6,4]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,3,1,4,2]=>[3,6,4,2,5,7,1]=>[5,3,4,1,7,6,2]=>{{1,5,7},{2,3,4},{6}}
[5,7,6,3,2,1,4]=>[2,3,6,1,5,7,4]=>[5,2,3,1,7,6,4]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,3,2,4,1]=>[4,3,6,2,5,7,1]=>[4,5,3,1,7,6,2]=>{{1,4},{2,5,7},{3},{6}}
[5,7,6,3,4,1,2]=>[4,1,6,3,5,7,2]=>[5,1,4,2,7,6,3]=>{{1,5,7},{2},{3,4},{6}}
[5,7,6,3,4,2,1]=>[2,4,6,3,5,7,1]=>[5,2,4,1,7,6,3]=>{{1,5,7},{2},{3,4},{6}}
[5,7,6,4,1,2,3]=>[4,1,2,6,5,7,3]=>[5,1,2,4,7,6,3]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,4,1,3,2]=>[4,3,1,6,5,7,2]=>[3,5,2,4,7,6,1]=>{{1,3},{2,5,7},{4},{6}}
[5,7,6,4,2,1,3]=>[2,4,1,6,5,7,3]=>[5,2,1,4,7,6,3]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,4,2,3,1]=>[3,4,2,6,5,7,1]=>[5,3,1,4,7,6,2]=>{{1,5,7},{2,3},{4},{6}}
[5,7,6,4,3,1,2]=>[3,1,4,6,5,7,2]=>[5,1,3,4,7,6,2]=>{{1,5,7},{2},{3},{4},{6}}
[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}
[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,1,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>[7,1,2,3,6,5,4]=>{{1,7},{2},{3},{4},{5,6}}
[6,1,2,3,5,4,7]=>[6,1,2,5,3,4,7]=>[5,1,2,6,4,3,7]=>{{1,5},{2},{3},{4,6},{7}}
[6,1,2,3,5,7,4]=>[6,1,2,7,3,5,4]=>[7,1,2,6,4,3,5]=>{{1,7},{2},{3},{4,6},{5}}
[6,1,2,3,7,4,5]=>[6,1,2,7,4,3,5]=>[7,1,2,6,3,5,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,1,2,3,7,5,4]=>[6,1,2,5,7,3,4]=>[6,1,2,7,5,4,3]=>{{1,6},{2},{3},{4,7},{5}}
[6,1,2,4,3,5,7]=>[6,1,4,2,3,5,7]=>[4,1,6,3,2,5,7]=>{{1,4},{2},{3,6},{5},{7}}
[6,1,2,4,3,7,5]=>[6,1,4,2,7,3,5]=>[4,1,7,3,6,5,2]=>{{1,4},{2},{3,7},{5,6}}
[6,1,2,4,5,3,7]=>[6,1,5,2,4,3,7]=>[5,1,6,3,2,4,7]=>{{1,5},{2},{3,6},{4},{7}}
[6,1,2,4,5,7,3]=>[6,1,7,2,3,4,5]=>[7,1,6,3,4,5,2]=>{{1,7},{2},{3,6},{4},{5}}
[6,1,2,4,7,3,5]=>[6,1,7,2,4,5,3]=>[7,1,6,3,2,4,5]=>{{1,7},{2},{3,6},{4},{5}}
[6,1,2,4,7,5,3]=>[6,1,5,2,7,4,3]=>[6,1,7,3,5,2,4]=>{{1,6},{2},{3,7},{4},{5}}
[6,1,2,5,3,4,7]=>[6,1,5,3,2,4,7]=>[5,1,6,2,4,3,7]=>{{1,5},{2},{3,6},{4},{7}}
[6,1,2,5,3,7,4]=>[6,1,5,7,2,3,4]=>[6,1,7,5,4,3,2]=>{{1,6},{2},{3,7},{4,5}}
[6,1,2,5,4,3,7]=>[6,1,4,5,2,3,7]=>[4,1,6,5,3,2,7]=>{{1,4,5},{2},{3,6},{7}}
[6,1,2,5,4,7,3]=>[6,1,7,5,2,4,3]=>[6,1,5,7,4,2,3]=>{{1,6},{2},{3,5},{4,7}}
[6,1,2,5,7,3,4]=>[6,1,7,3,2,5,4]=>[7,1,6,2,4,3,5]=>{{1,7},{2},{3,6},{4},{5}}
[6,1,2,5,7,4,3]=>[6,1,4,7,2,5,3]=>[6,1,7,4,3,2,5]=>{{1,6},{2},{3,7},{4},{5}}
[6,1,2,7,3,4,5]=>[6,1,7,3,4,2,5]=>[7,1,6,2,3,5,4]=>{{1,7},{2},{3,6},{4},{5}}
[6,1,2,7,3,5,4]=>[6,1,7,5,3,2,4]=>[6,1,5,7,3,4,2]=>{{1,6},{2},{3,5},{4,7}}
[6,1,2,7,4,3,5]=>[6,1,4,7,3,2,5]=>[6,1,7,4,2,5,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,1,2,7,4,5,3]=>[6,1,5,7,4,2,3]=>[6,1,7,5,2,4,3]=>{{1,6},{2},{3,7},{4,5}}
[6,1,2,7,5,3,4]=>[6,1,5,3,7,2,4]=>[6,1,7,2,5,4,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,1,2,7,5,4,3]=>[6,1,4,5,7,2,3]=>[4,1,7,6,5,3,2]=>{{1,4,6},{2},{3,7},{5}}
[6,1,3,2,4,5,7]=>[6,3,1,2,4,5,7]=>[3,6,2,1,4,5,7]=>{{1,3},{2,6},{4},{5},{7}}
[6,1,3,2,4,7,5]=>[6,3,1,2,7,4,5]=>[3,7,2,1,6,5,4]=>{{1,3},{2,7},{4},{5,6}}
[6,1,3,2,5,4,7]=>[6,3,1,5,2,4,7]=>[3,5,2,6,4,1,7]=>{{1,3},{2,5},{4,6},{7}}
[6,1,3,2,5,7,4]=>[6,3,1,7,2,5,4]=>[3,7,2,6,4,1,5]=>{{1,3},{2,7},{4,6},{5}}
[6,1,3,2,7,4,5]=>[6,3,1,7,4,2,5]=>[3,7,2,6,1,5,4]=>{{1,3},{2,7},{4,6},{5}}
[6,1,3,2,7,5,4]=>[6,3,1,5,7,2,4]=>[3,6,2,7,5,4,1]=>{{1,3},{2,6},{4,7},{5}}
[6,1,3,4,2,5,7]=>[6,4,1,3,2,5,7]=>[4,6,2,1,3,5,7]=>{{1,4},{2,6},{3},{5},{7}}
[6,1,3,4,2,7,5]=>[6,4,1,3,7,2,5]=>[4,7,2,1,6,5,3]=>{{1,4},{2,7},{3},{5,6}}
[6,1,3,4,5,2,7]=>[6,5,1,2,3,4,7]=>[5,6,2,3,4,1,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,1,3,4,5,7,2]=>[6,7,1,2,3,5,4]=>[7,6,2,3,4,1,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,3,4,7,2,5]=>[6,7,1,2,4,3,5]=>[7,6,2,3,1,5,4]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,3,4,7,5,2]=>[6,5,1,2,7,3,4]=>[6,7,2,3,5,4,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,3,5,2,4,7]=>[6,5,1,3,4,2,7]=>[5,6,2,1,3,4,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,1,3,5,2,7,4]=>[6,5,1,7,3,2,4]=>[6,7,2,5,3,4,1]=>{{1,6},{2,7},{3},{4,5}}
[6,1,3,5,4,2,7]=>[6,4,1,5,3,2,7]=>[4,6,2,5,1,3,7]=>{{1,4,5},{2,6},{3},{7}}
[6,1,3,5,4,7,2]=>[6,7,1,5,2,3,4]=>[6,5,2,7,4,3,1]=>{{1,6},{2,5},{3},{4,7}}
[6,1,3,5,7,2,4]=>[6,7,1,3,2,4,5]=>[7,6,2,1,4,5,3]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,3,5,7,4,2]=>[6,4,1,7,2,3,5]=>[6,7,2,4,3,5,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,3,7,2,4,5]=>[6,7,1,3,4,5,2]=>[7,6,2,1,3,4,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,3,7,2,5,4]=>[6,7,1,5,3,4,2]=>[6,5,2,7,3,1,4]=>{{1,6},{2,5},{3},{4,7}}
[6,1,3,7,4,2,5]=>[6,4,1,7,3,5,2]=>[6,7,2,4,1,3,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,3,7,4,5,2]=>[6,5,1,7,4,3,2]=>[6,7,2,5,1,3,4]=>{{1,6},{2,7},{3},{4,5}}
[6,1,3,7,5,2,4]=>[6,5,1,3,7,4,2]=>[6,7,2,1,5,3,4]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,3,7,5,4,2]=>[6,4,1,5,7,3,2]=>[4,7,2,6,5,1,3]=>{{1,4,6},{2,7},{3},{5}}
[6,1,4,2,3,5,7]=>[6,4,2,1,3,5,7]=>[4,6,1,3,2,5,7]=>{{1,4},{2,6},{3},{5},{7}}
[6,1,4,2,3,7,5]=>[6,4,2,1,7,3,5]=>[4,7,1,3,6,5,2]=>{{1,4},{2,7},{3},{5,6}}
[6,1,4,2,5,3,7]=>[6,4,5,1,2,3,7]=>[4,6,5,3,2,1,7]=>{{1,4},{2,6},{3,5},{7}}
[6,1,4,2,5,7,3]=>[6,4,7,1,2,5,3]=>[6,7,4,3,2,1,5]=>{{1,6},{2,7},{3,4},{5}}
[6,1,4,2,7,3,5]=>[6,4,7,1,3,2,5]=>[6,7,4,3,1,5,2]=>{{1,6},{2,7},{3,4},{5}}
[6,1,4,2,7,5,3]=>[6,4,5,1,7,2,3]=>[4,7,6,3,5,2,1]=>{{1,4},{2,7},{3,6},{5}}
[6,1,4,3,2,5,7]=>[6,3,4,1,2,5,7]=>[3,6,4,2,1,5,7]=>{{1,3,4},{2,6},{5},{7}}
[6,1,4,3,2,7,5]=>[6,3,4,1,7,2,5]=>[3,7,4,2,6,5,1]=>{{1,3,4},{2,7},{5,6}}
[6,1,4,3,5,2,7]=>[6,5,4,1,3,2,7]=>[4,5,6,3,1,2,7]=>{{1,4},{2,5},{3,6},{7}}
[6,1,4,3,5,7,2]=>[6,7,4,1,2,3,5]=>[6,4,7,3,2,5,1]=>{{1,6},{2,4},{3,7},{5}}
[6,1,4,3,7,2,5]=>[6,7,4,1,3,5,2]=>[6,4,7,3,1,2,5]=>{{1,6},{2,4},{3,7},{5}}
[6,1,4,3,7,5,2]=>[6,5,4,1,7,3,2]=>[4,6,7,3,5,1,2]=>{{1,4},{2,6},{3,7},{5}}
[6,1,4,5,2,3,7]=>[6,5,2,1,4,3,7]=>[5,6,1,3,2,4,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,1,4,5,2,7,3]=>[6,5,7,1,3,4,2]=>[6,7,5,3,2,1,4]=>{{1,6},{2,7},{3,5},{4}}
[6,1,4,5,3,2,7]=>[6,3,5,1,4,2,7]=>[3,6,5,2,1,4,7]=>{{1,3,5},{2,6},{4},{7}}
[6,1,4,5,3,7,2]=>[6,7,5,1,2,4,3]=>[6,5,7,3,4,1,2]=>{{1,6},{2,5},{3,7},{4}}
[6,1,4,5,7,2,3]=>[6,7,2,1,3,4,5]=>[7,6,1,3,4,5,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,4,5,7,3,2]=>[6,3,7,1,2,4,5]=>[6,7,3,2,4,5,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,4,7,2,3,5]=>[6,7,2,1,4,5,3]=>[7,6,1,3,2,4,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,4,7,2,5,3]=>[6,7,5,1,4,3,2]=>[6,5,7,3,1,2,4]=>{{1,6},{2,5},{3,7},{4}}
[6,1,4,7,3,2,5]=>[6,3,7,1,4,5,2]=>[6,7,3,2,1,4,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,4,7,3,5,2]=>[6,5,7,1,4,2,3]=>[6,7,5,3,1,4,2]=>{{1,6},{2,7},{3,5},{4}}
[6,1,4,7,5,2,3]=>[6,5,2,1,7,4,3]=>[6,7,1,3,5,2,4]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,4,7,5,3,2]=>[6,3,5,1,7,4,2]=>[3,7,6,2,5,1,4]=>{{1,3,6},{2,7},{4},{5}}
[6,1,5,2,3,4,7]=>[6,5,2,3,1,4,7]=>[5,6,1,2,4,3,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,1,5,2,3,7,4]=>[6,5,2,7,1,3,4]=>[6,7,1,5,4,3,2]=>{{1,6},{2,7},{3},{4,5}}
[6,1,5,2,4,3,7]=>[6,5,4,2,1,3,7]=>[4,5,6,2,3,1,7]=>{{1,4},{2,5},{3,6},{7}}
[6,1,5,2,4,7,3]=>[6,5,7,2,1,4,3]=>[6,7,5,2,4,1,3]=>{{1,6},{2,7},{3,5},{4}}
[6,1,5,2,7,3,4]=>[6,5,7,3,1,2,4]=>[6,7,5,1,4,3,2]=>{{1,6},{2,7},{3,5},{4}}
[6,1,5,2,7,4,3]=>[6,5,4,7,1,2,3]=>[5,6,7,4,3,2,1]=>{{1,5},{2,6},{3,7},{4}}
[6,1,5,3,2,4,7]=>[6,3,5,2,1,4,7]=>[3,6,5,1,4,2,7]=>{{1,3,5},{2,6},{4},{7}}
[6,1,5,3,2,7,4]=>[6,3,5,7,1,2,4]=>[3,7,6,5,4,2,1]=>{{1,3,6},{2,7},{4,5}}
[6,1,5,3,4,2,7]=>[6,4,5,3,1,2,7]=>[4,6,5,1,3,2,7]=>{{1,4},{2,6},{3,5},{7}}
[6,1,5,3,4,7,2]=>[6,7,5,3,1,4,2]=>[6,5,7,1,4,2,3]=>{{1,6},{2,5},{3,7},{4}}
[6,1,5,3,7,2,4]=>[6,7,5,2,1,3,4]=>[6,5,7,2,4,3,1]=>{{1,6},{2,5},{3,7},{4}}
[6,1,5,3,7,4,2]=>[6,4,7,5,1,2,3]=>[5,7,4,6,3,2,1]=>{{1,5},{2,7},{3,4,6}}
[6,1,5,4,2,3,7]=>[6,4,2,5,1,3,7]=>[4,6,1,5,3,2,7]=>{{1,4,5},{2,6},{3},{7}}
[6,1,5,4,2,7,3]=>[6,4,5,7,1,3,2]=>[5,7,6,4,3,1,2]=>{{1,5},{2,7},{3,6},{4}}
[6,1,5,4,3,2,7]=>[6,3,4,5,1,2,7]=>[3,6,4,5,2,1,7]=>{{1,3,4,5},{2,6},{7}}
[6,1,5,4,3,7,2]=>[6,7,4,5,1,3,2]=>[5,4,7,6,3,1,2]=>{{1,5},{2,4,6},{3,7}}
[6,1,5,4,7,2,3]=>[6,7,2,5,1,4,3]=>[6,5,1,7,4,2,3]=>{{1,6},{2,5},{3},{4,7}}
[6,1,5,4,7,3,2]=>[6,3,7,5,1,4,2]=>[5,6,3,7,4,1,2]=>{{1,5},{2,6},{3},{4,7}}
[6,1,5,7,2,3,4]=>[6,7,2,3,1,5,4]=>[7,6,1,2,4,3,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,5,7,2,4,3]=>[6,7,4,2,1,5,3]=>[6,4,7,2,3,1,5]=>{{1,6},{2,4},{3,7},{5}}
[6,1,5,7,3,2,4]=>[6,3,7,2,1,5,4]=>[6,7,3,1,4,2,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,5,7,3,4,2]=>[6,4,7,3,1,5,2]=>[6,7,4,1,3,2,5]=>{{1,6},{2,7},{3,4},{5}}
[6,1,5,7,4,2,3]=>[6,4,2,7,1,5,3]=>[6,7,1,4,3,2,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,5,7,4,3,2]=>[6,3,4,7,1,5,2]=>[3,7,6,4,2,1,5]=>{{1,3,6},{2,7},{4},{5}}
[6,1,7,2,3,4,5]=>[6,7,2,3,4,1,5]=>[7,6,1,2,3,5,4]=>{{1,7},{2,6},{3},{4},{5}}
[6,1,7,2,3,5,4]=>[6,7,2,5,3,1,4]=>[6,5,1,7,3,4,2]=>{{1,6},{2,5},{3},{4,7}}
[6,1,7,2,4,3,5]=>[6,7,4,2,3,1,5]=>[6,4,7,2,1,5,3]=>{{1,6},{2,4},{3,7},{5}}
[6,1,7,2,4,5,3]=>[6,7,5,2,4,1,3]=>[6,5,7,2,1,4,3]=>{{1,6},{2,5},{3,7},{4}}
[6,1,7,2,5,3,4]=>[6,7,5,3,2,1,4]=>[6,5,7,1,3,4,2]=>{{1,6},{2,5},{3,7},{4}}
[6,1,7,2,5,4,3]=>[6,7,4,5,2,1,3]=>[5,4,7,6,2,3,1]=>{{1,5},{2,4,6},{3,7}}
[6,1,7,3,2,4,5]=>[6,3,7,2,4,1,5]=>[6,7,3,1,2,5,4]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,7,3,2,5,4]=>[6,3,7,5,2,1,4]=>[5,6,3,7,2,4,1]=>{{1,5},{2,6},{3},{4,7}}
[6,1,7,3,4,2,5]=>[6,4,7,3,2,1,5]=>[6,7,4,1,2,5,3]=>{{1,6},{2,7},{3,4},{5}}
[6,1,7,3,4,5,2]=>[6,5,7,3,4,1,2]=>[6,7,5,1,2,4,3]=>{{1,6},{2,7},{3,5},{4}}
[6,1,7,3,5,2,4]=>[6,5,7,2,3,1,4]=>[6,7,5,2,3,4,1]=>{{1,6},{2,7},{3,5},{4}}
[6,1,7,3,5,4,2]=>[6,4,5,7,2,1,3]=>[5,7,6,4,2,3,1]=>{{1,5},{2,7},{3,6},{4}}
[6,1,7,4,2,3,5]=>[6,4,2,7,3,1,5]=>[6,7,1,4,2,5,3]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,7,4,2,5,3]=>[6,4,7,5,3,1,2]=>[5,7,4,6,1,3,2]=>{{1,5},{2,7},{3,4,6}}
[6,1,7,4,3,2,5]=>[6,3,4,7,2,1,5]=>[3,7,6,4,1,5,2]=>{{1,3,6},{2,7},{4},{5}}
[6,1,7,4,3,5,2]=>[6,5,4,7,3,1,2]=>[5,6,7,4,1,3,2]=>{{1,5},{2,6},{3,7},{4}}
[6,1,7,4,5,2,3]=>[6,5,2,7,4,1,3]=>[6,7,1,5,2,4,3]=>{{1,6},{2,7},{3},{4,5}}
[6,1,7,4,5,3,2]=>[6,3,5,7,4,1,2]=>[3,7,6,5,1,4,2]=>{{1,3,6},{2,7},{4,5}}
[6,1,7,5,2,3,4]=>[6,5,2,3,7,1,4]=>[6,7,1,2,5,4,3]=>{{1,6},{2,7},{3},{4},{5}}
[6,1,7,5,2,4,3]=>[6,5,4,2,7,1,3]=>[4,6,7,2,5,3,1]=>{{1,4},{2,6},{3,7},{5}}
[6,1,7,5,3,2,4]=>[6,3,5,2,7,1,4]=>[3,7,6,1,5,4,2]=>{{1,3,6},{2,7},{4},{5}}
[6,1,7,5,3,4,2]=>[6,4,5,3,7,1,2]=>[4,7,6,1,5,3,2]=>{{1,4},{2,7},{3,6},{5}}
[6,1,7,5,4,2,3]=>[6,4,2,5,7,1,3]=>[4,7,1,6,5,3,2]=>{{1,4,6},{2,7},{3},{5}}
[6,1,7,5,4,3,2]=>[6,3,4,5,7,1,2]=>[3,7,4,6,5,2,1]=>{{1,3,4,6},{2,7},{5}}
[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,2,1,3,4,7,5]=>[2,6,1,3,7,4,5]=>[7,2,1,3,6,5,4]=>{{1,7},{2},{3},{4},{5,6}}
[6,2,1,3,5,4,7]=>[2,6,1,5,3,4,7]=>[5,2,1,6,4,3,7]=>{{1,5},{2},{3},{4,6},{7}}
[6,2,1,3,5,7,4]=>[2,6,1,7,3,5,4]=>[7,2,1,6,4,3,5]=>{{1,7},{2},{3},{4,6},{5}}
[6,2,1,3,7,4,5]=>[2,6,1,7,4,3,5]=>[7,2,1,6,3,5,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,2,1,3,7,5,4]=>[2,6,1,5,7,3,4]=>[6,2,1,7,5,4,3]=>{{1,6},{2},{3},{4,7},{5}}
[6,2,1,4,3,5,7]=>[2,6,4,1,3,5,7]=>[4,2,6,3,1,5,7]=>{{1,4},{2},{3,6},{5},{7}}
[6,2,1,4,3,7,5]=>[2,6,4,1,7,3,5]=>[4,2,7,3,6,5,1]=>{{1,4},{2},{3,7},{5,6}}
[6,2,1,4,5,3,7]=>[2,6,5,1,4,3,7]=>[5,2,6,3,1,4,7]=>{{1,5},{2},{3,6},{4},{7}}
[6,2,1,4,5,7,3]=>[2,6,7,1,3,4,5]=>[7,2,6,3,4,5,1]=>{{1,7},{2},{3,6},{4},{5}}
[6,2,1,4,7,3,5]=>[2,6,7,1,4,5,3]=>[7,2,6,3,1,4,5]=>{{1,7},{2},{3,6},{4},{5}}
[6,2,1,4,7,5,3]=>[2,6,5,1,7,4,3]=>[6,2,7,3,5,1,4]=>{{1,6},{2},{3,7},{4},{5}}
[6,2,1,5,3,4,7]=>[2,6,5,3,1,4,7]=>[5,2,6,1,4,3,7]=>{{1,5},{2},{3,6},{4},{7}}
[6,2,1,5,3,7,4]=>[2,6,5,7,1,3,4]=>[6,2,7,5,4,3,1]=>{{1,6},{2},{3,7},{4,5}}
[6,2,1,5,4,3,7]=>[2,6,4,5,1,3,7]=>[4,2,6,5,3,1,7]=>{{1,4,5},{2},{3,6},{7}}
[6,2,1,5,4,7,3]=>[2,6,7,5,1,4,3]=>[6,2,5,7,4,1,3]=>{{1,6},{2},{3,5},{4,7}}
[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>[7,2,6,1,4,3,5]=>{{1,7},{2},{3,6},{4},{5}}
[6,2,1,5,7,4,3]=>[2,6,4,7,1,5,3]=>[6,2,7,4,3,1,5]=>{{1,6},{2},{3,7},{4},{5}}
[6,2,1,7,3,4,5]=>[2,6,7,3,4,1,5]=>[7,2,6,1,3,5,4]=>{{1,7},{2},{3,6},{4},{5}}
[6,2,1,7,3,5,4]=>[2,6,7,5,3,1,4]=>[6,2,5,7,3,4,1]=>{{1,6},{2},{3,5},{4,7}}
[6,2,1,7,4,3,5]=>[2,6,4,7,3,1,5]=>[6,2,7,4,1,5,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,2,1,7,4,5,3]=>[2,6,5,7,4,1,3]=>[6,2,7,5,1,4,3]=>{{1,6},{2},{3,7},{4,5}}
[6,2,1,7,5,3,4]=>[2,6,5,3,7,1,4]=>[6,2,7,1,5,4,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,2,1,7,5,4,3]=>[2,6,4,5,7,1,3]=>[4,2,7,6,5,3,1]=>{{1,4,6},{2},{3,7},{5}}
[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[6,3,1,2,4,5,7]=>{{1,6},{2,3},{4},{5},{7}}
[6,2,3,1,4,7,5]=>[3,6,2,1,7,4,5]=>[7,3,1,2,6,5,4]=>{{1,7},{2,3},{4},{5,6}}
[6,2,3,1,5,4,7]=>[3,6,2,5,1,4,7]=>[5,3,1,6,4,2,7]=>{{1,5},{2,3},{4,6},{7}}
[6,2,3,1,5,7,4]=>[3,6,2,7,1,5,4]=>[7,3,1,6,4,2,5]=>{{1,7},{2,3},{4,6},{5}}
[6,2,3,1,7,4,5]=>[3,6,2,7,4,1,5]=>[7,3,1,6,2,5,4]=>{{1,7},{2,3},{4,6},{5}}
[6,2,3,1,7,5,4]=>[3,6,2,5,7,1,4]=>[6,3,1,7,5,4,2]=>{{1,6},{2,3},{4,7},{5}}
[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[6,4,1,2,3,5,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,2,3,4,1,7,5]=>[4,6,2,3,7,1,5]=>[7,4,1,2,6,5,3]=>{{1,7},{2,4},{3},{5,6}}
[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[6,5,1,2,3,4,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[6,7,1,2,3,4,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,3,4,7,1,5]=>[7,6,2,3,1,4,5]=>[6,7,1,2,4,5,3]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,3,4,7,5,1]=>[5,7,2,3,6,1,4]=>[7,5,1,2,6,4,3]=>{{1,7},{2,5,6},{3},{4}}
[6,2,3,5,1,4,7]=>[5,6,2,1,3,4,7]=>[6,5,1,3,4,2,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,3,5,1,7,4]=>[5,6,2,7,3,1,4]=>[7,6,1,5,3,4,2]=>{{1,7},{2,6},{3},{4,5}}
[6,2,3,5,4,1,7]=>[4,5,2,6,1,3,7]=>[6,5,1,4,3,2,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,3,5,4,7,1]=>[7,6,2,5,3,4,1]=>[5,6,1,7,3,2,4]=>{{1,5},{2,6},{3},{4,7}}
[6,2,3,5,7,1,4]=>[7,6,2,1,4,3,5]=>[6,7,1,3,2,5,4]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,3,5,7,4,1]=>[4,7,2,6,3,1,5]=>[7,4,1,6,2,5,3]=>{{1,7},{2,4,6},{3},{5}}
[6,2,3,7,1,4,5]=>[7,6,2,1,3,5,4]=>[6,7,1,3,4,2,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,3,7,1,5,4]=>[7,6,2,5,1,3,4]=>[5,6,1,7,4,3,2]=>{{1,5},{2,6},{3},{4,7}}
[6,2,3,7,4,1,5]=>[4,7,2,6,1,5,3]=>[7,4,1,6,3,2,5]=>{{1,7},{2,4,6},{3},{5}}
[6,2,3,7,4,5,1]=>[5,6,2,7,4,3,1]=>[7,6,1,5,2,3,4]=>{{1,7},{2,6},{3},{4,5}}
[6,2,3,7,5,1,4]=>[5,7,2,1,6,4,3]=>[7,5,1,3,6,2,4]=>{{1,7},{2,5,6},{3},{4}}
[6,2,3,7,5,4,1]=>[4,5,2,7,6,3,1]=>[7,5,1,4,6,2,3]=>{{1,7},{2,5,6},{3},{4}}
[6,2,4,1,3,5,7]=>[4,6,1,2,3,5,7]=>[6,4,2,3,1,5,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,2,4,1,3,7,5]=>[4,6,1,2,7,3,5]=>[7,4,2,3,6,5,1]=>{{1,7},{2,4},{3},{5,6}}
[6,2,4,1,5,3,7]=>[4,6,5,2,1,3,7]=>[6,4,5,2,3,1,7]=>{{1,6},{2,4},{3,5},{7}}
[6,2,4,1,5,7,3]=>[4,6,7,2,1,5,3]=>[7,6,4,2,3,1,5]=>{{1,7},{2,6},{3,4},{5}}
[6,2,4,1,7,3,5]=>[4,6,7,2,3,1,5]=>[7,6,4,2,1,5,3]=>{{1,7},{2,6},{3,4},{5}}
[6,2,4,1,7,5,3]=>[4,6,5,2,7,1,3]=>[7,4,6,2,5,3,1]=>{{1,7},{2,4},{3,6},{5}}
[6,2,4,3,1,5,7]=>[3,4,6,1,2,5,7]=>[6,4,3,2,1,5,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,2,4,3,1,7,5]=>[3,4,6,1,7,2,5]=>[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}}
[6,2,4,3,5,1,7]=>[5,6,4,2,3,1,7]=>[5,4,6,2,1,3,7]=>{{1,5},{2,4},{3,6},{7}}
[6,2,4,3,5,7,1]=>[7,6,4,2,3,5,1]=>[4,6,7,2,1,3,5]=>{{1,4},{2,6},{3,7},{5}}
[6,2,4,3,7,1,5]=>[7,6,4,2,1,3,5]=>[4,6,7,2,3,5,1]=>{{1,4},{2,6},{3,7},{5}}
[6,2,4,3,7,5,1]=>[5,7,4,2,6,1,3]=>[5,4,7,2,6,3,1]=>{{1,5,6},{2,4},{3,7}}
[6,2,4,5,1,3,7]=>[5,6,1,3,2,4,7]=>[6,5,2,1,4,3,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,4,5,1,7,3]=>[5,6,7,2,3,4,1]=>[7,6,5,2,3,1,4]=>{{1,7},{2,6},{3,5},{4}}
[6,2,4,5,3,1,7]=>[3,5,6,2,1,4,7]=>[6,5,3,1,4,2,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,4,5,3,7,1]=>[7,6,5,2,4,3,1]=>[5,6,7,2,1,3,4]=>{{1,5},{2,6},{3,7},{4}}
[6,2,4,5,7,1,3]=>[7,6,1,3,4,2,5]=>[6,7,2,1,3,5,4]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,4,5,7,3,1]=>[3,7,6,2,4,1,5]=>[7,3,6,1,2,5,4]=>{{1,7},{2,3,6},{4},{5}}
[6,2,4,7,1,3,5]=>[7,6,1,3,2,5,4]=>[6,7,2,1,4,3,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,4,7,1,5,3]=>[7,6,5,2,1,4,3]=>[5,6,7,2,4,1,3]=>{{1,5},{2,6},{3,7},{4}}
[6,2,4,7,3,1,5]=>[3,7,6,2,1,5,4]=>[7,3,6,1,4,2,5]=>{{1,7},{2,3,6},{4},{5}}
[6,2,4,7,3,5,1]=>[5,6,7,2,4,1,3]=>[7,6,5,2,1,4,3]=>{{1,7},{2,6},{3,5},{4}}
[6,2,4,7,5,1,3]=>[5,7,1,3,6,4,2]=>[7,5,2,1,6,3,4]=>{{1,7},{2,5,6},{3},{4}}
[6,2,4,7,5,3,1]=>[3,5,7,2,6,4,1]=>[7,5,3,1,6,2,4]=>{{1,7},{2,5,6},{3},{4}}
[6,2,5,1,3,4,7]=>[5,6,1,2,4,3,7]=>[6,5,2,3,1,4,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,5,1,3,7,4]=>[5,6,1,7,2,3,4]=>[7,6,2,5,4,3,1]=>{{1,7},{2,6},{3},{4,5}}
[6,2,5,1,4,3,7]=>[5,6,4,1,2,3,7]=>[5,4,6,3,2,1,7]=>{{1,5},{2,4},{3,6},{7}}
[6,2,5,1,4,7,3]=>[5,6,7,1,2,4,3]=>[7,6,5,3,4,1,2]=>{{1,7},{2,6},{3,5},{4}}
[6,2,5,1,7,3,4]=>[5,6,7,3,2,1,4]=>[7,6,5,1,3,4,2]=>{{1,7},{2,6},{3,5},{4}}
[6,2,5,1,7,4,3]=>[5,6,4,7,2,1,3]=>[6,5,7,4,2,3,1]=>{{1,6},{2,5},{3,7},{4}}
[6,2,5,3,1,4,7]=>[3,5,6,1,4,2,7]=>[6,5,3,2,1,4,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,5,3,1,7,4]=>[3,5,6,7,1,2,4]=>[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}}
[6,2,5,3,4,1,7]=>[4,6,5,3,2,1,7]=>[6,4,5,1,2,3,7]=>{{1,6},{2,4},{3,5},{7}}
[6,2,5,3,4,7,1]=>[7,6,5,3,2,4,1]=>[5,6,7,1,3,2,4]=>{{1,5},{2,6},{3,7},{4}}
[6,2,5,3,7,1,4]=>[7,6,5,1,4,2,3]=>[5,6,7,3,1,4,2]=>{{1,5},{2,6},{3,7},{4}}
[6,2,5,3,7,4,1]=>[4,7,6,5,3,1,2]=>[7,4,5,6,1,3,2]=>{{1,7},{2,4,6},{3,5}}
[6,2,5,4,1,3,7]=>[4,5,1,6,3,2,7]=>[6,5,2,4,1,3,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,5,4,1,7,3]=>[4,5,6,7,1,3,2]=>[7,6,5,4,3,1,2]=>{{1,7},{2,6},{3,5},{4}}
[6,2,5,4,3,1,7]=>[3,4,5,6,2,1,7]=>[6,5,3,4,1,2,7]=>{{1,6},{2,5},{3},{4},{7}}
[6,2,5,4,3,7,1]=>[7,6,4,5,2,3,1]=>[4,5,7,6,2,1,3]=>{{1,4,6},{2,5},{3,7}}
[6,2,5,4,7,1,3]=>[7,6,1,5,3,2,4]=>[5,6,2,7,3,4,1]=>{{1,5},{2,6},{3},{4,7}}
[6,2,5,4,7,3,1]=>[3,7,6,5,2,1,4]=>[6,3,5,7,2,4,1]=>{{1,6},{2,3,5},{4,7}}
[6,2,5,7,1,3,4]=>[7,6,1,2,4,5,3]=>[6,7,2,3,1,4,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,5,7,1,4,3]=>[7,6,4,1,3,2,5]=>[4,6,7,3,1,5,2]=>{{1,4},{2,6},{3,7},{5}}
[6,2,5,7,3,1,4]=>[3,7,6,1,4,5,2]=>[7,3,6,2,1,4,5]=>{{1,7},{2,3,6},{4},{5}}
[6,2,5,7,3,4,1]=>[4,6,7,3,1,2,5]=>[7,6,4,1,3,5,2]=>{{1,7},{2,6},{3,4},{5}}
[6,2,5,7,4,1,3]=>[4,7,1,6,3,5,2]=>[7,4,2,6,1,3,5]=>{{1,7},{2,4,6},{3},{5}}
[6,2,5,7,4,3,1]=>[3,4,7,6,2,5,1]=>[7,4,3,6,1,2,5]=>{{1,7},{2,4,6},{3},{5}}
[6,2,7,1,3,4,5]=>[7,6,1,2,3,4,5]=>[6,7,2,3,4,5,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,2,7,1,3,5,4]=>[7,6,1,5,2,4,3]=>[5,6,2,7,4,1,3]=>{{1,5},{2,6},{3},{4,7}}
[6,2,7,1,4,3,5]=>[7,6,4,1,2,5,3]=>[4,6,7,3,2,1,5]=>{{1,4},{2,6},{3,7},{5}}
[6,2,7,1,4,5,3]=>[7,6,5,1,2,3,4]=>[5,6,7,3,4,2,1]=>{{1,5},{2,6},{3,7},{4}}
[6,2,7,1,5,3,4]=>[7,6,5,3,1,2,4]=>[5,6,7,1,4,3,2]=>{{1,5},{2,6},{3,7},{4}}
[6,2,7,1,5,4,3]=>[7,6,4,5,1,2,3]=>[4,5,7,6,3,2,1]=>{{1,4,6},{2,5},{3,7}}
[6,2,7,3,1,4,5]=>[3,7,6,1,2,4,5]=>[7,3,6,2,4,5,1]=>{{1,7},{2,3,6},{4},{5}}
[6,2,7,3,1,5,4]=>[3,7,6,5,1,4,2]=>[6,3,5,7,4,1,2]=>{{1,6},{2,3,5},{4,7}}
[6,2,7,3,4,1,5]=>[4,6,7,3,2,5,1]=>[7,6,4,1,2,3,5]=>{{1,7},{2,6},{3,4},{5}}
[6,2,7,3,4,5,1]=>[5,6,7,3,4,2,1]=>[7,6,5,1,2,3,4]=>{{1,7},{2,6},{3,5},{4}}
[6,2,7,3,5,1,4]=>[5,6,7,1,3,2,4]=>[7,6,5,3,2,4,1]=>{{1,7},{2,6},{3,5},{4}}
[6,2,7,3,5,4,1]=>[4,5,6,7,3,2,1]=>[7,6,5,4,1,2,3]=>{{1,7},{2,6},{3,5},{4}}
[6,2,7,4,1,3,5]=>[4,7,1,6,2,3,5]=>[7,4,2,6,3,5,1]=>{{1,7},{2,4,6},{3},{5}}
[6,2,7,4,1,5,3]=>[4,7,6,5,2,3,1]=>[7,4,5,6,2,1,3]=>{{1,7},{2,4,6},{3,5}}
[6,2,7,4,3,1,5]=>[3,4,7,6,1,2,5]=>[7,4,3,6,2,5,1]=>{{1,7},{2,4,6},{3},{5}}
[6,2,7,4,3,5,1]=>[5,6,4,7,3,2,1]=>[6,5,7,4,1,2,3]=>{{1,6},{2,5},{3,7},{4}}
[6,2,7,4,5,1,3]=>[5,6,1,7,4,2,3]=>[7,6,2,5,1,4,3]=>{{1,7},{2,6},{3},{4,5}}
[6,2,7,4,5,3,1]=>[3,5,6,7,4,1,2]=>[7,6,3,5,1,4,2]=>{{1,7},{2,6},{3},{4,5}}
[6,2,7,5,1,3,4]=>[5,7,1,2,6,3,4]=>[7,5,2,3,6,4,1]=>{{1,7},{2,5,6},{3},{4}}
[6,2,7,5,1,4,3]=>[5,7,4,1,6,3,2]=>[5,4,7,3,6,1,2]=>{{1,5,6},{2,4},{3,7}}
[6,2,7,5,3,1,4]=>[3,5,7,1,6,2,4]=>[7,5,3,2,6,4,1]=>{{1,7},{2,5,6},{3},{4}}
[6,2,7,5,3,4,1]=>[4,6,5,3,7,2,1]=>[7,4,6,1,5,2,3]=>{{1,7},{2,4},{3,6},{5}}
[6,2,7,5,4,1,3]=>[4,5,1,7,6,2,3]=>[7,5,2,4,6,3,1]=>{{1,7},{2,5,6},{3},{4}}
[6,2,7,5,4,3,1]=>[3,4,5,7,6,1,2]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}
[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[6,1,3,2,4,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,3,1,2,4,7,5]=>[3,1,6,2,7,4,5]=>[7,1,3,2,6,5,4]=>{{1,7},{2},{3},{4},{5,6}}
[6,3,1,2,5,4,7]=>[3,1,6,5,2,4,7]=>[5,1,3,6,4,2,7]=>{{1,5},{2},{3},{4,6},{7}}
[6,3,1,2,5,7,4]=>[3,1,6,7,2,5,4]=>[7,1,3,6,4,2,5]=>{{1,7},{2},{3},{4,6},{5}}
[6,3,1,2,7,4,5]=>[3,1,6,7,4,2,5]=>[7,1,3,6,2,5,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,3,1,2,7,5,4]=>[3,1,6,5,7,2,4]=>[6,1,3,7,5,4,2]=>{{1,6},{2},{3},{4,7},{5}}
[6,3,1,4,2,5,7]=>[3,6,4,2,1,5,7]=>[6,3,4,1,2,5,7]=>{{1,6},{2,3,4},{5},{7}}
[6,3,1,4,2,7,5]=>[3,6,4,2,7,1,5]=>[7,3,4,1,6,5,2]=>{{1,7},{2,3,4},{5,6}}
[6,3,1,4,5,2,7]=>[3,6,5,1,2,4,7]=>[6,3,5,2,4,1,7]=>{{1,6},{2,3,5},{4},{7}}
[6,3,1,4,5,7,2]=>[3,6,7,1,2,5,4]=>[7,6,3,2,4,1,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,3,1,4,7,2,5]=>[3,6,7,1,4,2,5]=>[7,6,3,2,1,5,4]=>{{1,7},{2,6},{3},{4},{5}}
[6,3,1,4,7,5,2]=>[3,6,5,1,7,2,4]=>[7,3,6,2,5,4,1]=>{{1,7},{2,3,6},{4},{5}}
[6,3,1,5,2,4,7]=>[3,6,5,2,4,1,7]=>[6,3,5,1,2,4,7]=>{{1,6},{2,3,5},{4},{7}}
[6,3,1,5,2,7,4]=>[3,6,5,7,2,1,4]=>[7,3,6,5,2,4,1]=>{{1,7},{2,3,6},{4,5}}
[6,3,1,5,4,2,7]=>[3,6,4,5,2,1,7]=>[6,3,4,5,1,2,7]=>{{1,6},{2,3,4,5},{7}}
[6,3,1,5,4,7,2]=>[3,6,7,5,1,2,4]=>[6,5,3,7,4,2,1]=>{{1,6},{2,5},{3},{4,7}}
[6,3,1,5,7,2,4]=>[3,6,7,2,1,4,5]=>[7,6,3,1,4,5,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,3,1,5,7,4,2]=>[3,6,4,7,1,2,5]=>[7,3,6,4,2,5,1]=>{{1,7},{2,3,6},{4},{5}}
[6,3,1,7,2,4,5]=>[3,6,7,2,4,5,1]=>[7,6,3,1,2,4,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,3,1,7,2,5,4]=>[3,6,7,5,2,4,1]=>[6,5,3,7,2,1,4]=>{{1,6},{2,5},{3},{4,7}}
[6,3,1,7,4,2,5]=>[3,6,4,7,2,5,1]=>[7,3,6,4,1,2,5]=>{{1,7},{2,3,6},{4},{5}}
[6,3,1,7,4,5,2]=>[3,6,5,7,4,2,1]=>[7,3,6,5,1,2,4]=>{{1,7},{2,3,6},{4,5}}
[6,3,1,7,5,2,4]=>[3,6,5,2,7,4,1]=>[7,3,6,1,5,2,4]=>{{1,7},{2,3,6},{4},{5}}
[6,3,1,7,5,4,2]=>[3,6,4,5,7,2,1]=>[7,3,4,6,5,1,2]=>{{1,7},{2,3,4,6},{5}}
[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,3,2,1,4,7,5]=>[2,3,6,1,7,4,5]=>[7,2,3,1,6,5,4]=>{{1,7},{2},{3},{4},{5,6}}
[6,3,2,1,5,4,7]=>[2,3,6,5,1,4,7]=>[5,2,3,6,4,1,7]=>{{1,5},{2},{3},{4,6},{7}}
[6,3,2,1,5,7,4]=>[2,3,6,7,1,5,4]=>[7,2,3,6,4,1,5]=>{{1,7},{2},{3},{4,6},{5}}
[6,3,2,1,7,4,5]=>[2,3,6,7,4,1,5]=>[7,2,3,6,1,5,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,3,2,1,7,5,4]=>[2,3,6,5,7,1,4]=>[6,2,3,7,5,4,1]=>{{1,6},{2},{3},{4,7},{5}}
[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[4,6,3,1,2,5,7]=>{{1,4},{2,6},{3},{5},{7}}
[6,3,2,4,1,7,5]=>[4,3,6,2,7,1,5]=>[4,7,3,1,6,5,2]=>{{1,4},{2,7},{3},{5,6}}
[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[5,6,3,1,2,4,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[3,7,6,1,2,4,5]=>{{1,3,6},{2,7},{4},{5}}
[6,3,2,4,7,1,5]=>[7,3,6,2,1,4,5]=>[3,7,6,1,4,5,2]=>{{1,3,6},{2,7},{4},{5}}
[6,3,2,4,7,5,1]=>[5,3,7,2,6,1,4]=>[5,7,3,1,6,4,2]=>{{1,5,6},{2,7},{3},{4}}
[6,3,2,5,1,4,7]=>[5,3,6,1,2,4,7]=>[5,6,3,2,4,1,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,3,2,5,1,7,4]=>[5,3,6,7,2,1,4]=>[6,7,3,5,2,4,1]=>{{1,6},{2,7},{3},{4,5}}
[6,3,2,5,4,1,7]=>[4,3,5,6,1,2,7]=>[5,6,3,4,2,1,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,3,2,5,4,7,1]=>[7,3,6,5,2,4,1]=>[3,6,5,7,2,1,4]=>{{1,3,5},{2,6},{4,7}}
[6,3,2,5,7,1,4]=>[7,3,6,1,4,2,5]=>[3,7,6,2,1,5,4]=>{{1,3,6},{2,7},{4},{5}}
[6,3,2,5,7,4,1]=>[4,3,7,6,2,1,5]=>[4,7,3,6,1,5,2]=>{{1,4,6},{2,7},{3},{5}}
[6,3,2,7,1,4,5]=>[7,3,6,1,2,5,4]=>[3,7,6,2,4,1,5]=>{{1,3,6},{2,7},{4},{5}}
[6,3,2,7,1,5,4]=>[7,3,6,5,1,2,4]=>[3,6,5,7,4,2,1]=>{{1,3,5},{2,6},{4,7}}
[6,3,2,7,4,1,5]=>[4,3,7,6,1,5,2]=>[4,7,3,6,2,1,5]=>{{1,4,6},{2,7},{3},{5}}
[6,3,2,7,4,5,1]=>[5,3,6,7,4,2,1]=>[6,7,3,5,1,2,4]=>{{1,6},{2,7},{3},{4,5}}
[6,3,2,7,5,1,4]=>[5,3,7,1,6,4,2]=>[5,7,3,2,6,1,4]=>{{1,5,6},{2,7},{3},{4}}
[6,3,2,7,5,4,1]=>[4,3,5,7,6,2,1]=>[5,7,3,4,6,1,2]=>{{1,5,6},{2,7},{3},{4}}
[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[6,1,4,2,3,5,7]=>{{1,6},{2},{3,4},{5},{7}}
[6,3,4,1,2,7,5]=>[4,1,6,3,7,2,5]=>[7,1,4,2,6,5,3]=>{{1,7},{2},{3,4},{5,6}}
[6,3,4,1,5,2,7]=>[4,5,6,3,1,2,7]=>[6,5,4,1,3,2,7]=>{{1,6},{2,5},{3,4},{7}}
[6,3,4,1,5,7,2]=>[4,7,6,3,2,1,5]=>[7,4,6,1,2,5,3]=>{{1,7},{2,4},{3,6},{5}}
[6,3,4,1,7,2,5]=>[4,7,6,3,1,5,2]=>[7,4,6,1,3,2,5]=>{{1,7},{2,4},{3,6},{5}}
[6,3,4,1,7,5,2]=>[4,5,7,3,6,2,1]=>[7,5,4,1,6,2,3]=>{{1,7},{2,5,6},{3,4}}
[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[6,2,4,1,3,5,7]=>{{1,6},{2},{3,4},{5},{7}}
[6,3,4,2,1,7,5]=>[2,4,6,3,7,1,5]=>[7,2,4,1,6,5,3]=>{{1,7},{2},{3,4},{5,6}}
[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[5,6,4,1,2,3,7]=>{{1,5},{2,6},{3,4},{7}}
[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[4,7,6,1,2,3,5]=>{{1,4},{2,7},{3,6},{5}}
[6,3,4,2,7,1,5]=>[7,4,6,3,1,2,5]=>[4,7,6,1,3,5,2]=>{{1,4},{2,7},{3,6},{5}}
[6,3,4,2,7,5,1]=>[5,4,7,3,6,1,2]=>[5,7,4,1,6,3,2]=>{{1,5,6},{2,7},{3,4}}
[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[6,1,5,2,3,4,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,3,4,5,1,7,2]=>[5,7,6,3,4,1,2]=>[7,5,6,1,2,4,3]=>{{1,7},{2,5},{3,6},{4}}
[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[6,2,5,1,3,4,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[5,7,6,1,2,3,4]=>{{1,5},{2,7},{3,6},{4}}
[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[6,1,7,2,3,4,5]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[6,2,7,1,3,4,5]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,4,7,1,2,5]=>[7,1,6,3,2,4,5]=>[6,1,7,2,4,5,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,4,7,1,5,2]=>[7,5,6,3,1,4,2]=>[5,7,6,1,4,2,3]=>{{1,5},{2,7},{3,6},{4}}
[6,3,4,7,2,1,5]=>[2,7,6,3,1,4,5]=>[6,2,7,1,4,5,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,4,7,2,5,1]=>[5,7,6,3,2,4,1]=>[7,5,6,1,3,2,4]=>{{1,7},{2,5},{3,6},{4}}
[6,3,4,7,5,1,2]=>[5,1,7,3,6,2,4]=>[7,1,5,2,6,4,3]=>{{1,7},{2},{3,5,6},{4}}
[6,3,4,7,5,2,1]=>[2,5,7,3,6,1,4]=>[7,2,5,1,6,4,3]=>{{1,7},{2},{3,5,6},{4}}
[6,3,5,1,2,4,7]=>[5,1,6,2,3,4,7]=>[6,1,5,3,4,2,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,3,5,1,2,7,4]=>[5,1,6,7,3,2,4]=>[7,1,6,5,3,4,2]=>{{1,7},{2},{3,6},{4,5}}
[6,3,5,1,4,2,7]=>[5,4,6,1,3,2,7]=>[5,6,4,3,1,2,7]=>{{1,5},{2,6},{3,4},{7}}
[6,3,5,1,4,7,2]=>[5,7,6,1,3,4,2]=>[7,5,6,3,2,1,4]=>{{1,7},{2,5},{3,6},{4}}
[6,3,5,1,7,2,4]=>[5,7,6,2,4,3,1]=>[7,5,6,2,1,3,4]=>{{1,7},{2,5},{3,6},{4}}
[6,3,5,1,7,4,2]=>[5,4,7,6,3,2,1]=>[6,7,4,5,1,2,3]=>{{1,6},{2,7},{3,4,5}}
[6,3,5,2,1,4,7]=>[2,5,6,1,3,4,7]=>[6,2,5,3,4,1,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,3,5,2,1,7,4]=>[2,5,6,7,3,1,4]=>[7,2,6,5,3,4,1]=>{{1,7},{2},{3,6},{4,5}}
[6,3,5,2,4,1,7]=>[4,5,6,2,3,1,7]=>[6,5,4,2,1,3,7]=>{{1,6},{2,5},{3,4},{7}}
[6,3,5,2,4,7,1]=>[7,5,6,2,3,4,1]=>[5,7,6,2,3,1,4]=>{{1,5},{2,7},{3,6},{4}}
[6,3,5,2,7,1,4]=>[7,5,6,1,4,3,2]=>[5,7,6,3,1,2,4]=>{{1,5},{2,7},{3,6},{4}}
[6,3,5,2,7,4,1]=>[4,7,5,6,2,1,3]=>[7,4,6,5,2,3,1]=>{{1,7},{2,4,5},{3,6}}
[6,3,5,4,1,2,7]=>[4,1,5,6,2,3,7]=>[6,1,5,4,3,2,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,3,5,4,1,7,2]=>[4,5,7,6,3,1,2]=>[7,6,4,5,1,3,2]=>{{1,7},{2,6},{3,4,5}}
[6,3,5,4,2,1,7]=>[2,4,5,6,1,3,7]=>[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}}
[6,3,5,4,2,7,1]=>[7,4,5,6,2,3,1]=>[4,7,6,5,2,1,3]=>{{1,4,5},{2,7},{3,6}}
[6,3,5,4,7,1,2]=>[7,1,6,5,3,4,2]=>[5,1,6,7,3,2,4]=>{{1,5},{2},{3,6},{4,7}}
[6,3,5,4,7,2,1]=>[2,7,6,5,3,4,1]=>[5,2,6,7,3,1,4]=>{{1,5},{2},{3,6},{4,7}}
[6,3,5,7,1,2,4]=>[7,1,6,2,4,3,5]=>[6,1,7,3,2,5,4]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,5,7,1,4,2]=>[7,4,6,1,3,5,2]=>[4,7,6,3,1,2,5]=>{{1,4},{2,7},{3,6},{5}}
[6,3,5,7,2,1,4]=>[2,7,6,1,4,3,5]=>[6,2,7,3,1,5,4]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,5,7,2,4,1]=>[4,7,6,2,3,5,1]=>[7,4,6,2,1,3,5]=>{{1,7},{2,4},{3,6},{5}}
[6,3,5,7,4,1,2]=>[4,1,7,6,3,2,5]=>[7,1,4,6,2,5,3]=>{{1,7},{2},{3,4,6},{5}}
[6,3,5,7,4,2,1]=>[2,4,7,6,3,1,5]=>[7,2,4,6,1,5,3]=>{{1,7},{2},{3,4,6},{5}}
[6,3,7,1,2,4,5]=>[7,1,6,2,3,5,4]=>[6,1,7,3,4,2,5]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,7,1,2,5,4]=>[7,1,6,5,2,3,4]=>[5,1,6,7,4,3,2]=>{{1,5},{2},{3,6},{4,7}}
[6,3,7,1,4,2,5]=>[7,4,6,1,2,3,5]=>[4,7,6,3,2,5,1]=>{{1,4},{2,7},{3,6},{5}}
[6,3,7,1,4,5,2]=>[7,5,6,1,3,2,4]=>[5,7,6,3,2,4,1]=>{{1,5},{2,7},{3,6},{4}}
[6,3,7,1,5,2,4]=>[7,5,6,2,1,3,4]=>[5,7,6,2,4,3,1]=>{{1,5},{2,7},{3,6},{4}}
[6,3,7,1,5,4,2]=>[7,4,5,6,1,2,3]=>[4,7,6,5,3,2,1]=>{{1,4,5},{2,7},{3,6}}
[6,3,7,2,1,4,5]=>[2,7,6,1,3,5,4]=>[6,2,7,3,4,1,5]=>{{1,6},{2},{3,7},{4},{5}}
[6,3,7,2,1,5,4]=>[2,7,6,5,1,3,4]=>[5,2,6,7,4,3,1]=>{{1,5},{2},{3,6},{4,7}}
[6,3,7,2,4,1,5]=>[4,7,6,2,1,3,5]=>[7,4,6,2,3,5,1]=>{{1,7},{2,4},{3,6},{5}}
[6,3,7,2,4,5,1]=>[5,7,6,2,3,1,4]=>[7,5,6,2,3,4,1]=>{{1,7},{2,5},{3,6},{4}}
[6,3,7,2,5,1,4]=>[5,7,6,1,2,3,4]=>[7,5,6,3,4,2,1]=>{{1,7},{2,5},{3,6},{4}}
[6,3,7,2,5,4,1]=>[4,5,7,6,1,2,3]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}
[6,3,7,4,1,2,5]=>[4,1,7,6,2,5,3]=>[7,1,4,6,3,2,5]=>{{1,7},{2},{3,4,6},{5}}
[6,3,7,4,1,5,2]=>[4,7,5,6,1,3,2]=>[7,4,6,5,3,1,2]=>{{1,7},{2,4,5},{3,6}}
[6,3,7,4,2,1,5]=>[2,4,7,6,1,5,3]=>[7,2,4,6,3,1,5]=>{{1,7},{2},{3,4,6},{5}}
[6,3,7,4,2,5,1]=>[5,4,7,6,2,1,3]=>[6,7,4,5,2,3,1]=>{{1,6},{2,7},{3,4,5}}
[6,3,7,4,5,1,2]=>[5,1,6,7,4,3,2]=>[7,1,6,5,2,3,4]=>{{1,7},{2},{3,6},{4,5}}
[6,3,7,4,5,2,1]=>[2,5,6,7,4,3,1]=>[7,2,6,5,1,3,4]=>{{1,7},{2},{3,6},{4,5}}
[6,3,7,5,1,2,4]=>[5,1,7,2,6,4,3]=>[7,1,5,3,6,2,4]=>{{1,7},{2},{3,5,6},{4}}
[6,3,7,5,1,4,2]=>[5,4,7,1,6,2,3]=>[5,7,4,3,6,2,1]=>{{1,5,6},{2,7},{3,4}}
[6,3,7,5,2,1,4]=>[2,5,7,1,6,4,3]=>[7,2,5,3,6,1,4]=>{{1,7},{2},{3,5,6},{4}}
[6,3,7,5,2,4,1]=>[4,5,7,2,6,1,3]=>[7,5,4,2,6,3,1]=>{{1,7},{2,5,6},{3,4}}
[6,3,7,5,4,1,2]=>[4,1,5,7,6,3,2]=>[7,1,5,4,6,2,3]=>{{1,7},{2},{3,5,6},{4}}
[6,3,7,5,4,2,1]=>[2,4,5,7,6,3,1]=>[7,2,5,4,6,1,3]=>{{1,7},{2},{3,5,6},{4}}
[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[6,1,2,4,3,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,4,1,2,3,7,5]=>[4,1,2,6,7,3,5]=>[7,1,2,4,6,5,3]=>{{1,7},{2},{3},{4},{5,6}}
[6,4,1,2,5,3,7]=>[4,1,6,5,3,2,7]=>[6,1,4,5,2,3,7]=>{{1,6},{2},{3,4,5},{7}}
[6,4,1,2,5,7,3]=>[4,1,6,7,2,3,5]=>[7,1,6,4,3,5,2]=>{{1,7},{2},{3,6},{4},{5}}
[6,4,1,2,7,3,5]=>[4,1,6,7,3,5,2]=>[7,1,6,4,2,3,5]=>{{1,7},{2},{3,6},{4},{5}}
[6,4,1,2,7,5,3]=>[4,1,6,5,7,3,2]=>[7,1,4,6,5,2,3]=>{{1,7},{2},{3,4,6},{5}}
[6,4,1,3,2,5,7]=>[4,3,1,6,2,5,7]=>[3,6,2,4,1,5,7]=>{{1,3},{2,6},{4},{5},{7}}
[6,4,1,3,2,7,5]=>[4,3,1,6,7,2,5]=>[3,7,2,4,6,5,1]=>{{1,3},{2,7},{4},{5,6}}
[6,4,1,3,5,2,7]=>[4,6,1,5,2,3,7]=>[6,4,2,5,3,1,7]=>{{1,6},{2,4,5},{3},{7}}
[6,4,1,3,5,7,2]=>[4,6,1,7,2,5,3]=>[7,6,2,4,3,1,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,4,1,3,7,2,5]=>[4,6,1,7,3,2,5]=>[7,6,2,4,1,5,3]=>{{1,7},{2,6},{3},{4},{5}}
[6,4,1,3,7,5,2]=>[4,6,1,5,7,2,3]=>[7,4,2,6,5,3,1]=>{{1,7},{2,4,6},{3},{5}}
[6,4,1,5,2,3,7]=>[4,6,2,5,3,1,7]=>[6,4,1,5,2,3,7]=>{{1,6},{2,4,5},{3},{7}}
[6,4,1,5,2,7,3]=>[4,6,5,7,1,2,3]=>[7,5,6,4,3,2,1]=>{{1,7},{2,5},{3,6},{4}}
[6,4,1,5,3,2,7]=>[4,3,6,5,2,1,7]=>[4,6,3,5,1,2,7]=>{{1,4,5},{2,6},{3},{7}}
[6,4,1,5,3,7,2]=>[4,6,7,5,2,1,3]=>[7,5,4,6,2,3,1]=>{{1,7},{2,5},{3,4,6}}
[6,4,1,5,7,2,3]=>[4,6,2,7,1,3,5]=>[7,6,1,4,3,5,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,4,1,5,7,3,2]=>[4,3,6,7,1,2,5]=>[6,7,3,4,2,5,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,4,1,7,2,3,5]=>[4,6,2,7,3,5,1]=>[7,6,1,4,2,3,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,4,1,7,2,5,3]=>[4,6,7,5,3,2,1]=>[7,5,4,6,1,2,3]=>{{1,7},{2,5},{3,4,6}}
[6,4,1,7,3,2,5]=>[4,3,6,7,2,5,1]=>[6,7,3,4,1,2,5]=>{{1,6},{2,7},{3},{4},{5}}
[6,4,1,7,3,5,2]=>[4,6,5,7,2,3,1]=>[7,5,6,4,2,1,3]=>{{1,7},{2,5},{3,6},{4}}
[6,4,1,7,5,2,3]=>[4,6,2,5,7,3,1]=>[7,4,1,6,5,2,3]=>{{1,7},{2,4,6},{3},{5}}
[6,4,1,7,5,3,2]=>[4,3,6,5,7,2,1]=>[4,7,3,6,5,1,2]=>{{1,4,6},{2,7},{3},{5}}
[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[6,2,1,4,3,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,4,2,1,3,7,5]=>[2,4,1,6,7,3,5]=>[7,2,1,4,6,5,3]=>{{1,7},{2},{3},{4},{5,6}}
[6,4,2,1,5,3,7]=>[2,4,6,5,3,1,7]=>[6,2,4,5,1,3,7]=>{{1,6},{2},{3,4,5},{7}}
[6,4,2,1,5,7,3]=>[2,4,6,7,1,3,5]=>[7,2,6,4,3,5,1]=>{{1,7},{2},{3,6},{4},{5}}
[6,4,2,1,7,3,5]=>[2,4,6,7,3,5,1]=>[7,2,6,4,1,3,5]=>{{1,7},{2},{3,6},{4},{5}}
[6,4,2,1,7,5,3]=>[2,4,6,5,7,3,1]=>[7,2,4,6,5,1,3]=>{{1,7},{2},{3,4,6},{5}}
[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[6,3,1,4,2,5,7]=>{{1,6},{2,3},{4},{5},{7}}
[6,4,2,3,1,7,5]=>[3,4,2,6,7,1,5]=>[7,3,1,4,6,5,2]=>{{1,7},{2,3},{4},{5,6}}
[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[5,6,1,4,2,3,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[4,7,1,6,2,3,5]=>{{1,4,6},{2,7},{3},{5}}
[6,4,2,3,7,1,5]=>[7,4,2,6,1,3,5]=>[4,7,1,6,3,5,2]=>{{1,4,6},{2,7},{3},{5}}
[6,4,2,3,7,5,1]=>[5,4,2,7,6,1,3]=>[5,7,1,4,6,3,2]=>{{1,5,6},{2,7},{3},{4}}
[6,4,2,5,1,3,7]=>[5,4,1,6,2,3,7]=>[5,6,2,4,3,1,7]=>{{1,5},{2,6},{3},{4},{7}}
[6,4,2,5,1,7,3]=>[5,4,6,7,2,3,1]=>[6,7,5,4,2,1,3]=>{{1,6},{2,7},{3,5},{4}}
[6,4,2,5,3,1,7]=>[3,5,4,6,1,2,7]=>[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}}
[6,4,2,5,3,7,1]=>[7,4,6,5,3,2,1]=>[4,7,5,6,1,2,3]=>{{1,4,6},{2,7},{3,5}}
[6,4,2,5,7,1,3]=>[7,4,1,6,3,2,5]=>[4,7,2,6,1,5,3]=>{{1,4,6},{2,7},{3},{5}}
[6,4,2,5,7,3,1]=>[3,7,4,6,2,1,5]=>[7,3,4,6,1,5,2]=>{{1,7},{2,3,4,6},{5}}
[6,4,2,7,1,3,5]=>[7,4,1,6,2,5,3]=>[4,7,2,6,3,1,5]=>{{1,4,6},{2,7},{3},{5}}
[6,4,2,7,1,5,3]=>[7,4,6,5,1,3,2]=>[4,7,5,6,3,1,2]=>{{1,4,6},{2,7},{3,5}}
[6,4,2,7,3,1,5]=>[3,7,4,6,1,5,2]=>[7,3,4,6,2,1,5]=>{{1,7},{2,3,4,6},{5}}
[6,4,2,7,3,5,1]=>[5,4,6,7,3,1,2]=>[6,7,5,4,1,3,2]=>{{1,6},{2,7},{3,5},{4}}
[6,4,2,7,5,1,3]=>[5,4,1,7,6,3,2]=>[5,7,2,4,6,1,3]=>{{1,5,6},{2,7},{3},{4}}
[6,4,2,7,5,3,1]=>[3,5,4,7,6,2,1]=>[7,3,5,4,6,1,2]=>{{1,7},{2,3,5,6},{4}}
[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[6,1,3,4,2,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,4,3,1,2,7,5]=>[3,1,4,6,7,2,5]=>[7,1,3,4,6,5,2]=>{{1,7},{2},{3},{4},{5,6}}
[6,4,3,1,5,2,7]=>[3,4,6,5,1,2,7]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}
[6,4,3,1,5,7,2]=>[3,4,6,7,1,5,2]=>[7,6,3,4,2,1,5]=>{{1,7},{2,6},{3},{4},{5}}
[6,4,3,1,7,2,5]=>[3,4,6,7,2,1,5]=>[7,6,3,4,1,5,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,4,3,1,7,5,2]=>[3,4,6,5,7,1,2]=>[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}}
[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,4,3,2,1,7,5]=>[2,3,4,6,7,1,5]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}}
[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[3,6,5,4,1,2,7]=>{{1,3,5},{2,6},{4},{7}}
[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[3,7,4,6,1,2,5]=>{{1,3,4,6},{2,7},{5}}
[6,4,3,2,7,1,5]=>[7,3,4,6,1,2,5]=>[3,7,4,6,2,5,1]=>{{1,3,4,6},{2,7},{5}}
[6,4,3,2,7,5,1]=>[5,3,4,7,6,1,2]=>[3,7,5,4,6,2,1]=>{{1,3,5,6},{2,7},{4}}
[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[5,1,6,4,2,3,7]=>{{1,5},{2},{3,6},{4},{7}}
[6,4,3,5,1,7,2]=>[5,7,4,6,3,1,2]=>[6,4,7,5,1,3,2]=>{{1,6},{2,4,5},{3,7}}
[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[5,2,6,4,1,3,7]=>{{1,5},{2},{3,6},{4},{7}}
[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[4,6,7,5,1,2,3]=>{{1,4,5},{2,6},{3,7}}
[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[4,1,7,6,2,3,5]=>{{1,4,6},{2},{3,7},{5}}
[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[4,2,7,6,1,3,5]=>{{1,4,6},{2},{3,7},{5}}
[6,4,3,7,1,2,5]=>[7,1,4,6,2,3,5]=>[4,1,7,6,3,5,2]=>{{1,4,6},{2},{3,7},{5}}
[6,4,3,7,1,5,2]=>[7,5,4,6,1,3,2]=>[4,6,7,5,3,1,2]=>{{1,4,5},{2,6},{3,7}}
[6,4,3,7,2,1,5]=>[2,7,4,6,1,3,5]=>[4,2,7,6,3,5,1]=>{{1,4,6},{2},{3,7},{5}}
[6,4,3,7,2,5,1]=>[5,7,4,6,2,3,1]=>[6,4,7,5,2,1,3]=>{{1,6},{2,4,5},{3,7}}
[6,4,3,7,5,1,2]=>[5,1,4,7,6,2,3]=>[5,1,7,4,6,3,2]=>{{1,5,6},{2},{3,7},{4}}
[6,4,3,7,5,2,1]=>[2,5,4,7,6,1,3]=>[5,2,7,4,6,3,1]=>{{1,5,6},{2},{3,7},{4}}
[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[6,1,2,5,3,4,7]=>{{1,6},{2},{3},{4,5},{7}}
[6,4,5,1,2,7,3]=>[5,1,7,6,4,2,3]=>[7,1,5,6,2,4,3]=>{{1,7},{2},{3,5},{4,6}}
[6,4,5,1,3,2,7]=>[5,3,1,6,4,2,7]=>[3,6,2,5,1,4,7]=>{{1,3},{2,6},{4,5},{7}}
[6,4,5,1,3,7,2]=>[5,7,1,6,4,3,2]=>[7,5,2,6,1,3,4]=>{{1,7},{2,5},{3},{4,6}}
[6,4,5,1,7,2,3]=>[5,7,2,6,4,1,3]=>[7,5,1,6,2,4,3]=>{{1,7},{2,5},{3},{4,6}}
[6,4,5,1,7,3,2]=>[5,3,7,6,4,1,2]=>[5,7,3,6,1,4,2]=>{{1,5},{2,7},{3},{4,6}}
[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[6,2,1,5,3,4,7]=>{{1,6},{2},{3},{4,5},{7}}
[6,4,5,2,1,7,3]=>[2,5,7,6,4,1,3]=>[7,2,5,6,1,4,3]=>{{1,7},{2},{3,5},{4,6}}
[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[6,3,1,5,2,4,7]=>{{1,6},{2,3},{4,5},{7}}
[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[5,7,1,6,2,3,4]=>{{1,5},{2,7},{3},{4,6}}
[6,4,5,2,7,1,3]=>[7,5,1,6,4,2,3]=>[5,7,2,6,1,4,3]=>{{1,5},{2,7},{3},{4,6}}
[6,4,5,2,7,3,1]=>[3,7,5,6,4,1,2]=>[7,3,5,6,1,4,2]=>{{1,7},{2,3,5},{4,6}}
[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[6,1,3,5,2,4,7]=>{{1,6},{2},{3},{4,5},{7}}
[6,4,5,3,1,7,2]=>[3,5,7,6,4,2,1]=>[7,5,3,6,1,2,4]=>{{1,7},{2,5},{3},{4,6}}
[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>{{1,6},{2},{3},{4,5},{7}}
[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[3,7,5,6,1,2,4]=>{{1,3,5},{2,7},{4,6}}
[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[5,1,7,6,2,3,4]=>{{1,5},{2},{3,7},{4,6}}
[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[5,2,7,6,1,3,4]=>{{1,5},{2},{3,7},{4,6}}
[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[6,1,2,7,3,4,5]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,5,7,1,3,2]=>[7,3,1,6,4,5,2]=>[3,6,2,7,1,4,5]=>{{1,3},{2,6},{4,7},{5}}
[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[6,2,1,7,3,4,5]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[6,3,1,7,2,4,5]=>{{1,6},{2,3},{4,7},{5}}
[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[6,1,3,7,2,4,5]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[6,2,3,7,1,4,5]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,7,1,2,3,5]=>[7,1,2,6,3,4,5]=>[6,1,2,7,4,5,3]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,7,1,2,5,3]=>[7,1,5,6,2,4,3]=>[5,1,7,6,4,2,3]=>{{1,5},{2},{3,7},{4,6}}
[6,4,7,1,3,2,5]=>[7,3,1,6,2,4,5]=>[3,6,2,7,4,5,1]=>{{1,3},{2,6},{4,7},{5}}
[6,4,7,1,3,5,2]=>[7,5,1,6,3,4,2]=>[5,7,2,6,3,1,4]=>{{1,5},{2,7},{3},{4,6}}
[6,4,7,1,5,2,3]=>[7,5,2,6,1,4,3]=>[5,7,1,6,4,2,3]=>{{1,5},{2,7},{3},{4,6}}
[6,4,7,1,5,3,2]=>[7,3,5,6,1,4,2]=>[3,7,5,6,4,1,2]=>{{1,3,5},{2,7},{4,6}}
[6,4,7,2,1,3,5]=>[2,7,1,6,3,4,5]=>[6,2,1,7,4,5,3]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,7,2,1,5,3]=>[2,7,5,6,1,4,3]=>[5,2,7,6,4,1,3]=>{{1,5},{2},{3,7},{4,6}}
[6,4,7,2,3,1,5]=>[3,7,2,6,1,4,5]=>[6,3,1,7,4,5,2]=>{{1,6},{2,3},{4,7},{5}}
[6,4,7,2,3,5,1]=>[5,7,2,6,3,4,1]=>[7,5,1,6,3,2,4]=>{{1,7},{2,5},{3},{4,6}}
[6,4,7,2,5,1,3]=>[5,7,1,6,2,4,3]=>[7,5,2,6,4,1,3]=>{{1,7},{2,5},{3},{4,6}}
[6,4,7,2,5,3,1]=>[3,5,7,6,1,4,2]=>[7,5,3,6,4,1,2]=>{{1,7},{2,5},{3},{4,6}}
[6,4,7,3,1,2,5]=>[3,1,7,6,2,4,5]=>[6,1,3,7,4,5,2]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,7,3,1,5,2]=>[3,7,5,6,2,4,1]=>[7,3,5,6,2,1,4]=>{{1,7},{2,3,5},{4,6}}
[6,4,7,3,2,1,5]=>[2,3,7,6,1,4,5]=>[6,2,3,7,4,5,1]=>{{1,6},{2},{3},{4,7},{5}}
[6,4,7,3,2,5,1]=>[5,3,7,6,2,4,1]=>[5,7,3,6,2,1,4]=>{{1,5},{2,7},{3},{4,6}}
[6,4,7,3,5,1,2]=>[5,1,7,6,3,4,2]=>[7,1,5,6,3,2,4]=>{{1,7},{2},{3,5},{4,6}}
[6,4,7,3,5,2,1]=>[2,5,7,6,3,4,1]=>[7,2,5,6,3,1,4]=>{{1,7},{2},{3,5},{4,6}}
[6,4,7,5,1,2,3]=>[5,1,2,7,6,3,4]=>[7,1,2,5,6,4,3]=>{{1,7},{2},{3},{4,5,6}}
[6,4,7,5,1,3,2]=>[5,3,1,7,6,2,4]=>[3,7,2,5,6,4,1]=>{{1,3},{2,7},{4,5,6}}
[6,4,7,5,2,1,3]=>[2,5,1,7,6,3,4]=>[7,2,1,5,6,4,3]=>{{1,7},{2},{3},{4,5,6}}
[6,4,7,5,2,3,1]=>[3,5,2,7,6,1,4]=>[7,3,1,5,6,4,2]=>{{1,7},{2,3},{4,5,6}}
[6,4,7,5,3,1,2]=>[3,1,5,7,6,2,4]=>[7,1,3,5,6,4,2]=>{{1,7},{2},{3},{4,5,6}}
[6,4,7,5,3,2,1]=>[2,3,5,7,6,1,4]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}}
[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[6,1,2,3,5,4,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,1,2,3,7,4]=>[5,1,2,6,7,4,3]=>[7,1,2,6,5,3,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,5,1,2,4,3,7]=>[5,1,4,2,6,3,7]=>[4,1,6,3,5,2,7]=>{{1,4},{2},{3,6},{5},{7}}
[6,5,1,2,4,7,3]=>[5,1,6,2,7,3,4]=>[7,1,6,3,5,4,2]=>{{1,7},{2},{3,6},{4},{5}}
[6,5,1,2,7,3,4]=>[5,1,6,3,7,4,2]=>[7,1,6,2,5,3,4]=>{{1,7},{2},{3,6},{4},{5}}
[6,5,1,2,7,4,3]=>[5,1,4,6,7,3,2]=>[6,1,7,4,5,2,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,5,1,3,2,4,7]=>[5,3,1,2,6,4,7]=>[3,6,2,1,5,4,7]=>{{1,3},{2,6},{4},{5},{7}}
[6,5,1,3,2,7,4]=>[5,3,1,6,7,4,2]=>[3,7,2,6,5,1,4]=>{{1,3},{2,7},{4,6},{5}}
[6,5,1,3,4,2,7]=>[5,4,1,3,6,2,7]=>[4,6,2,1,5,3,7]=>{{1,4},{2,6},{3},{5},{7}}
[6,5,1,3,4,7,2]=>[5,6,1,2,7,4,3]=>[7,6,2,3,5,1,4]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,1,3,7,2,4]=>[5,6,1,3,7,2,4]=>[7,6,2,1,5,4,3]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,1,3,7,4,2]=>[5,4,1,6,7,2,3]=>[6,7,2,4,5,3,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,5,1,4,2,3,7]=>[5,4,2,1,6,3,7]=>[4,6,1,3,5,2,7]=>{{1,4},{2,6},{3},{5},{7}}
[6,5,1,4,2,7,3]=>[5,4,6,1,7,3,2]=>[6,7,4,3,5,1,2]=>{{1,6},{2,7},{3,4},{5}}
[6,5,1,4,3,2,7]=>[5,3,4,1,6,2,7]=>[3,6,4,2,5,1,7]=>{{1,3,4},{2,6},{5},{7}}
[6,5,1,4,3,7,2]=>[5,6,4,1,7,2,3]=>[6,4,7,3,5,2,1]=>{{1,6},{2,4},{3,7},{5}}
[6,5,1,4,7,2,3]=>[5,6,2,1,7,3,4]=>[7,6,1,3,5,4,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,1,4,7,3,2]=>[5,3,6,1,7,2,4]=>[6,7,3,2,5,4,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,5,1,7,2,3,4]=>[5,6,2,3,7,4,1]=>[7,6,1,2,5,3,4]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,1,7,2,4,3]=>[5,6,4,2,7,3,1]=>[6,4,7,2,5,1,3]=>{{1,6},{2,4},{3,7},{5}}
[6,5,1,7,3,2,4]=>[5,3,6,2,7,4,1]=>[6,7,3,1,5,2,4]=>{{1,6},{2,7},{3},{4},{5}}
[6,5,1,7,3,4,2]=>[5,4,6,3,7,2,1]=>[6,7,4,1,5,2,3]=>{{1,6},{2,7},{3,4},{5}}
[6,5,1,7,4,2,3]=>[5,4,2,6,7,3,1]=>[6,7,1,4,5,2,3]=>{{1,6},{2,7},{3},{4},{5}}
[6,5,1,7,4,3,2]=>[5,3,4,6,7,2,1]=>[3,7,6,4,5,1,2]=>{{1,3,6},{2,7},{4},{5}}
[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[6,2,1,3,5,4,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,2,1,3,7,4]=>[2,5,1,6,7,4,3]=>[7,2,1,6,5,3,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,5,2,1,4,3,7]=>[2,5,4,1,6,3,7]=>[4,2,6,3,5,1,7]=>{{1,4},{2},{3,6},{5},{7}}
[6,5,2,1,4,7,3]=>[2,5,6,1,7,3,4]=>[7,2,6,3,5,4,1]=>{{1,7},{2},{3,6},{4},{5}}
[6,5,2,1,7,3,4]=>[2,5,6,3,7,4,1]=>[7,2,6,1,5,3,4]=>{{1,7},{2},{3,6},{4},{5}}
[6,5,2,1,7,4,3]=>[2,5,4,6,7,3,1]=>[6,2,7,4,5,1,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[6,3,1,2,5,4,7]=>{{1,6},{2,3},{4},{5},{7}}
[6,5,2,3,1,7,4]=>[3,5,2,6,7,4,1]=>[7,3,1,6,5,2,4]=>{{1,7},{2,3},{4,6},{5}}
[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[6,4,1,2,5,3,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[5,7,1,2,6,3,4]=>{{1,5,6},{2,7},{3},{4}}
[6,5,2,3,7,1,4]=>[7,5,2,1,6,3,4]=>[5,7,1,3,6,4,2]=>{{1,5,6},{2,7},{3},{4}}
[6,5,2,3,7,4,1]=>[4,7,2,5,6,1,3]=>[7,4,1,5,6,3,2]=>{{1,7},{2,4,5,6},{3}}
[6,5,2,4,1,3,7]=>[4,5,1,2,6,3,7]=>[6,4,2,3,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,5,2,4,1,7,3]=>[4,5,6,2,7,3,1]=>[7,6,4,2,5,1,3]=>{{1,7},{2,6},{3,4},{5}}
[6,5,2,4,3,1,7]=>[3,4,5,1,6,2,7]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[6,5,2,4,3,7,1]=>[7,5,4,2,6,3,1]=>[4,5,7,2,6,1,3]=>{{1,4},{2,5,6},{3,7}}
[6,5,2,4,7,1,3]=>[7,5,1,3,6,2,4]=>[5,7,2,1,6,4,3]=>{{1,5,6},{2,7},{3},{4}}
[6,5,2,4,7,3,1]=>[3,7,5,2,6,1,4]=>[7,3,5,1,6,4,2]=>{{1,7},{2,3,5,6},{4}}
[6,5,2,7,1,3,4]=>[7,5,1,2,6,4,3]=>[5,7,2,3,6,1,4]=>{{1,5,6},{2,7},{3},{4}}
[6,5,2,7,1,4,3]=>[7,5,4,1,6,2,3]=>[4,5,7,3,6,2,1]=>{{1,4},{2,5,6},{3,7}}
[6,5,2,7,3,1,4]=>[3,7,5,1,6,4,2]=>[7,3,5,2,6,1,4]=>{{1,7},{2,3,5,6},{4}}
[6,5,2,7,3,4,1]=>[4,5,6,3,7,1,2]=>[7,6,4,1,5,3,2]=>{{1,7},{2,6},{3,4},{5}}
[6,5,2,7,4,1,3]=>[4,7,1,5,6,3,2]=>[7,4,2,5,6,1,3]=>{{1,7},{2,4,5,6},{3}}
[6,5,2,7,4,3,1]=>[3,4,7,5,6,2,1]=>[7,4,3,5,6,1,2]=>{{1,7},{2,4,5,6},{3}}
[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[6,1,3,2,5,4,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,3,1,2,7,4]=>[3,1,5,6,7,4,2]=>[7,1,3,6,5,2,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,5,3,1,4,2,7]=>[3,5,4,2,6,1,7]=>[6,3,4,1,5,2,7]=>{{1,6},{2,3,4},{5},{7}}
[6,5,3,1,4,7,2]=>[3,5,6,1,7,4,2]=>[7,6,3,2,5,1,4]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,3,1,7,2,4]=>[3,5,6,2,7,1,4]=>[7,6,3,1,5,4,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,3,1,7,4,2]=>[3,5,4,6,7,1,2]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}}
[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[6,2,3,1,5,4,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,3,2,1,7,4]=>[2,3,5,6,7,4,1]=>[7,2,3,6,5,1,4]=>{{1,7},{2},{3},{4,6},{5}}
[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[4,6,3,1,5,2,7]=>{{1,4},{2,6},{3},{5},{7}}
[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[3,7,5,1,6,2,4]=>{{1,3,5,6},{2,7},{4}}
[6,5,3,2,7,1,4]=>[7,3,5,1,6,2,4]=>[3,7,5,2,6,4,1]=>{{1,3,5,6},{2,7},{4}}
[6,5,3,2,7,4,1]=>[4,3,7,5,6,1,2]=>[4,7,3,5,6,2,1]=>{{1,4,5,6},{2,7},{3}}
[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[6,1,4,2,5,3,7]=>{{1,6},{2},{3,4},{5},{7}}
[6,5,3,4,1,7,2]=>[4,7,5,3,6,1,2]=>[7,4,5,1,6,3,2]=>{{1,7},{2,4},{3,5,6}}
[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[6,2,4,1,5,3,7]=>{{1,6},{2},{3,4},{5},{7}}
[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[4,7,5,1,6,2,3]=>{{1,4},{2,7},{3,5,6}}
[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[5,1,7,2,6,3,4]=>{{1,5,6},{2},{3,7},{4}}
[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[5,2,7,1,6,3,4]=>{{1,5,6},{2},{3,7},{4}}
[6,5,3,7,1,2,4]=>[7,1,5,2,6,3,4]=>[5,1,7,3,6,4,2]=>{{1,5,6},{2},{3,7},{4}}
[6,5,3,7,1,4,2]=>[7,4,5,1,6,3,2]=>[4,7,5,3,6,1,2]=>{{1,4},{2,7},{3,5,6}}
[6,5,3,7,2,1,4]=>[2,7,5,1,6,3,4]=>[5,2,7,3,6,4,1]=>{{1,5,6},{2},{3,7},{4}}
[6,5,3,7,2,4,1]=>[4,7,5,2,6,3,1]=>[7,4,5,2,6,1,3]=>{{1,7},{2,4},{3,5,6}}
[6,5,3,7,4,1,2]=>[4,1,7,5,6,2,3]=>[7,1,4,5,6,3,2]=>{{1,7},{2},{3,4,5,6}}
[6,5,3,7,4,2,1]=>[2,4,7,5,6,1,3]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}}
[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[6,1,2,4,5,3,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,4,1,2,7,3]=>[4,1,5,6,7,2,3]=>[7,1,6,4,5,3,2]=>{{1,7},{2},{3,6},{4},{5}}
[6,5,4,1,3,2,7]=>[4,3,1,5,6,2,7]=>[3,6,2,4,5,1,7]=>{{1,3},{2,6},{4},{5},{7}}
[6,5,4,1,3,7,2]=>[4,5,1,6,7,3,2]=>[7,6,2,4,5,1,3]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,4,1,7,2,3]=>[4,5,2,6,7,1,3]=>[7,6,1,4,5,3,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,4,1,7,3,2]=>[4,3,5,6,7,1,2]=>[6,7,3,4,5,2,1]=>{{1,6},{2,7},{3},{4},{5}}
[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[6,2,1,4,5,3,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,4,2,1,7,3]=>[2,4,5,6,7,1,3]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}}
[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[6,3,1,4,5,2,7]=>{{1,6},{2,3},{4},{5},{7}}
[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[4,7,1,5,6,2,3]=>{{1,4,5,6},{2,7},{3}}
[6,5,4,2,7,1,3]=>[7,4,1,5,6,2,3]=>[4,7,2,5,6,3,1]=>{{1,4,5,6},{2,7},{3}}
[6,5,4,2,7,3,1]=>[3,7,4,5,6,1,2]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}
[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[6,1,3,4,5,2,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,4,3,1,7,2]=>[3,4,5,6,7,2,1]=>[7,6,3,4,5,1,2]=>{{1,7},{2,6},{3},{4},{5}}
[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}
[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[3,7,4,5,6,1,2]=>{{1,3,4,5,6},{2,7}}
[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[4,1,7,5,6,2,3]=>{{1,4,5,6},{2},{3,7}}
[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[4,2,7,5,6,1,3]=>{{1,4,5,6},{2},{3,7}}
[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[5,1,2,7,6,3,4]=>{{1,5,6},{2},{3},{4,7}}
[6,5,4,7,1,3,2]=>[7,3,1,5,6,4,2]=>[3,5,2,7,6,1,4]=>{{1,3},{2,5,6},{4,7}}
[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[5,2,1,7,6,3,4]=>{{1,5,6},{2},{3},{4,7}}
[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[5,3,1,7,6,2,4]=>{{1,5,6},{2,3},{4,7}}
[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[5,1,3,7,6,2,4]=>{{1,5,6},{2},{3},{4,7}}
[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[5,2,3,7,6,1,4]=>{{1,5,6},{2},{3},{4,7}}
[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[6,1,2,3,7,4,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,1,2,4,3]=>[7,1,4,2,6,5,3]=>[4,1,6,3,7,2,5]=>{{1,4},{2},{3,6},{5,7}}
[6,5,7,1,3,2,4]=>[7,3,1,2,6,5,4]=>[3,6,2,1,7,4,5]=>{{1,3},{2,6},{4},{5,7}}
[6,5,7,1,3,4,2]=>[7,4,1,3,6,5,2]=>[4,6,2,1,7,3,5]=>{{1,4},{2,6},{3},{5,7}}
[6,5,7,1,4,2,3]=>[7,4,2,1,6,5,3]=>[4,6,1,3,7,2,5]=>{{1,4},{2,6},{3},{5,7}}
[6,5,7,1,4,3,2]=>[7,3,4,1,6,5,2]=>[3,6,4,2,7,1,5]=>{{1,3,4},{2,6},{5,7}}
[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[6,2,1,3,7,4,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,2,1,4,3]=>[2,7,4,1,6,5,3]=>[4,2,6,3,7,1,5]=>{{1,4},{2},{3,6},{5,7}}
[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[6,3,1,2,7,4,5]=>{{1,6},{2,3},{4},{5,7}}
[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[6,4,1,2,7,3,5]=>{{1,6},{2,4},{3},{5,7}}
[6,5,7,2,4,1,3]=>[4,7,1,2,6,5,3]=>[6,4,2,3,7,1,5]=>{{1,6},{2,4},{3},{5,7}}
[6,5,7,2,4,3,1]=>[3,4,7,1,6,5,2]=>[6,4,3,2,7,1,5]=>{{1,6},{2,4},{3},{5,7}}
[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[6,1,3,2,7,4,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,3,1,4,2]=>[3,7,4,2,6,5,1]=>[6,3,4,1,7,2,5]=>{{1,6},{2,3,4},{5,7}}
[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[6,2,3,1,7,4,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[4,6,3,1,7,2,5]=>{{1,4},{2,6},{3},{5,7}}
[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[6,1,4,2,7,3,5]=>{{1,6},{2},{3,4},{5,7}}
[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[6,2,4,1,7,3,5]=>{{1,6},{2},{3,4},{5,7}}
[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[6,1,2,4,7,3,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,4,1,3,2]=>[4,3,1,7,6,5,2]=>[3,6,2,4,7,1,5]=>{{1,3},{2,6},{4},{5,7}}
[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[6,2,1,4,7,3,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[6,3,1,4,7,2,5]=>{{1,6},{2,3},{4},{5,7}}
[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[6,1,3,4,7,2,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[6,2,3,4,7,1,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[6,1,2,3,4,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,1,2,3,5,4]=>[7,1,2,5,3,6,4]=>[5,1,2,6,4,7,3]=>{{1,5},{2},{3},{4,6,7}}
[6,7,1,2,4,3,5]=>[7,1,4,2,3,6,5]=>[4,1,6,3,2,7,5]=>{{1,4},{2},{3,6,7},{5}}
[6,7,1,2,4,5,3]=>[7,1,5,2,4,6,3]=>[5,1,6,3,2,7,4]=>{{1,5},{2},{3,6,7},{4}}
[6,7,1,2,5,3,4]=>[7,1,5,3,2,6,4]=>[5,1,6,2,4,7,3]=>{{1,5},{2},{3,6,7},{4}}
[6,7,1,2,5,4,3]=>[7,1,4,5,2,6,3]=>[4,1,6,5,3,7,2]=>{{1,4,5},{2},{3,6,7}}
[6,7,1,3,2,4,5]=>[7,3,1,2,4,6,5]=>[3,6,2,1,4,7,5]=>{{1,3},{2,6,7},{4},{5}}
[6,7,1,3,2,5,4]=>[7,3,1,5,2,6,4]=>[3,5,2,6,4,7,1]=>{{1,3},{2,5},{4,6,7}}
[6,7,1,3,4,2,5]=>[7,4,1,3,2,6,5]=>[4,6,2,1,3,7,5]=>{{1,4},{2,6,7},{3},{5}}
[6,7,1,3,4,5,2]=>[7,5,1,2,3,6,4]=>[5,6,2,3,4,7,1]=>{{1,5},{2,6,7},{3},{4}}
[6,7,1,3,5,2,4]=>[7,5,1,3,4,6,2]=>[5,6,2,1,3,7,4]=>{{1,5},{2,6,7},{3},{4}}
[6,7,1,3,5,4,2]=>[7,4,1,5,3,6,2]=>[4,6,2,5,1,7,3]=>{{1,4,5},{2,6,7},{3}}
[6,7,1,4,2,3,5]=>[7,4,2,1,3,6,5]=>[4,6,1,3,2,7,5]=>{{1,4},{2,6,7},{3},{5}}
[6,7,1,4,2,5,3]=>[7,4,5,1,2,6,3]=>[4,6,5,3,2,7,1]=>{{1,4},{2,6,7},{3,5}}
[6,7,1,4,3,2,5]=>[7,3,4,1,2,6,5]=>[3,6,4,2,1,7,5]=>{{1,3,4},{2,6,7},{5}}
[6,7,1,4,3,5,2]=>[7,5,4,1,3,6,2]=>[4,5,6,3,1,7,2]=>{{1,4},{2,5},{3,6,7}}
[6,7,1,4,5,2,3]=>[7,5,2,1,4,6,3]=>[5,6,1,3,2,7,4]=>{{1,5},{2,6,7},{3},{4}}
[6,7,1,4,5,3,2]=>[7,3,5,1,4,6,2]=>[3,6,5,2,1,7,4]=>{{1,3,5},{2,6,7},{4}}
[6,7,1,5,2,3,4]=>[7,5,2,3,1,6,4]=>[5,6,1,2,4,7,3]=>{{1,5},{2,6,7},{3},{4}}
[6,7,1,5,2,4,3]=>[7,5,4,2,1,6,3]=>[4,5,6,2,3,7,1]=>{{1,4},{2,5},{3,6,7}}
[6,7,1,5,3,2,4]=>[7,3,5,2,1,6,4]=>[3,6,5,1,4,7,2]=>{{1,3,5},{2,6,7},{4}}
[6,7,1,5,3,4,2]=>[7,4,5,3,1,6,2]=>[4,6,5,1,3,7,2]=>{{1,4},{2,6,7},{3,5}}
[6,7,1,5,4,2,3]=>[7,4,2,5,1,6,3]=>[4,6,1,5,3,7,2]=>{{1,4,5},{2,6,7},{3}}
[6,7,1,5,4,3,2]=>[7,3,4,5,1,6,2]=>[3,6,4,5,2,7,1]=>{{1,3,4,5},{2,6,7}}
[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[6,2,1,3,4,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,2,1,3,5,4]=>[2,7,1,5,3,6,4]=>[5,2,1,6,4,7,3]=>{{1,5},{2},{3},{4,6,7}}
[6,7,2,1,4,3,5]=>[2,7,4,1,3,6,5]=>[4,2,6,3,1,7,5]=>{{1,4},{2},{3,6,7},{5}}
[6,7,2,1,4,5,3]=>[2,7,5,1,4,6,3]=>[5,2,6,3,1,7,4]=>{{1,5},{2},{3,6,7},{4}}
[6,7,2,1,5,3,4]=>[2,7,5,3,1,6,4]=>[5,2,6,1,4,7,3]=>{{1,5},{2},{3,6,7},{4}}
[6,7,2,1,5,4,3]=>[2,7,4,5,1,6,3]=>[4,2,6,5,3,7,1]=>{{1,4,5},{2},{3,6,7}}
[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[6,3,1,2,4,7,5]=>{{1,6,7},{2,3},{4},{5}}
[6,7,2,3,1,5,4]=>[3,7,2,5,1,6,4]=>[5,3,1,6,4,7,2]=>{{1,5},{2,3},{4,6,7}}
[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[6,4,1,2,3,7,5]=>{{1,6,7},{2,4},{3},{5}}
[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[6,5,1,2,3,7,4]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,3,5,1,4]=>[5,7,2,1,3,6,4]=>[6,5,1,3,4,7,2]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,3,5,4,1]=>[4,5,2,7,1,6,3]=>[6,5,1,4,3,7,2]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,4,1,3,5]=>[4,7,1,2,3,6,5]=>[6,4,2,3,1,7,5]=>{{1,6,7},{2,4},{3},{5}}
[6,7,2,4,1,5,3]=>[4,7,5,2,1,6,3]=>[6,4,5,2,3,7,1]=>{{1,6,7},{2,4},{3,5}}
[6,7,2,4,3,1,5]=>[3,4,7,1,2,6,5]=>[6,4,3,2,1,7,5]=>{{1,6,7},{2,4},{3},{5}}
[6,7,2,4,3,5,1]=>[5,7,4,2,3,6,1]=>[5,4,6,2,1,7,3]=>{{1,5},{2,4},{3,6,7}}
[6,7,2,4,5,1,3]=>[5,7,1,3,2,6,4]=>[6,5,2,1,4,7,3]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,4,5,3,1]=>[3,5,7,2,1,6,4]=>[6,5,3,1,4,7,2]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,5,1,3,4]=>[5,7,1,2,4,6,3]=>[6,5,2,3,1,7,4]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,5,1,4,3]=>[5,7,4,1,2,6,3]=>[5,4,6,3,2,7,1]=>{{1,5},{2,4},{3,6,7}}
[6,7,2,5,3,1,4]=>[3,5,7,1,4,6,2]=>[6,5,3,2,1,7,4]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,5,3,4,1]=>[4,7,5,3,2,6,1]=>[6,4,5,1,2,7,3]=>{{1,6,7},{2,4},{3,5}}
[6,7,2,5,4,1,3]=>[4,5,1,7,3,6,2]=>[6,5,2,4,1,7,3]=>{{1,6,7},{2,5},{3},{4}}
[6,7,2,5,4,3,1]=>[3,4,5,7,2,6,1]=>[6,5,3,4,1,7,2]=>{{1,6,7},{2,5},{3},{4}}
[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[6,1,3,2,4,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,3,1,2,5,4]=>[3,1,7,5,2,6,4]=>[5,1,3,6,4,7,2]=>{{1,5},{2},{3},{4,6,7}}
[6,7,3,1,4,2,5]=>[3,7,4,2,1,6,5]=>[6,3,4,1,2,7,5]=>{{1,6,7},{2,3,4},{5}}
[6,7,3,1,4,5,2]=>[3,7,5,1,2,6,4]=>[6,3,5,2,4,7,1]=>{{1,6,7},{2,3,5},{4}}
[6,7,3,1,5,2,4]=>[3,7,5,2,4,6,1]=>[6,3,5,1,2,7,4]=>{{1,6,7},{2,3,5},{4}}
[6,7,3,1,5,4,2]=>[3,7,4,5,2,6,1]=>[6,3,4,5,1,7,2]=>{{1,6,7},{2,3,4,5}}
[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[6,2,3,1,4,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,3,2,1,5,4]=>[2,3,7,5,1,6,4]=>[5,2,3,6,4,7,1]=>{{1,5},{2},{3},{4,6,7}}
[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[4,6,3,1,2,7,5]=>{{1,4},{2,6,7},{3},{5}}
[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[5,6,3,1,2,7,4]=>{{1,5},{2,6,7},{3},{4}}
[6,7,3,2,5,1,4]=>[5,3,7,1,2,6,4]=>[5,6,3,2,4,7,1]=>{{1,5},{2,6,7},{3},{4}}
[6,7,3,2,5,4,1]=>[4,3,5,7,1,6,2]=>[5,6,3,4,2,7,1]=>{{1,5},{2,6,7},{3},{4}}
[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[6,1,4,2,3,7,5]=>{{1,6,7},{2},{3,4},{5}}
[6,7,3,4,1,5,2]=>[4,5,7,3,1,6,2]=>[6,5,4,1,3,7,2]=>{{1,6,7},{2,5},{3,4}}
[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[6,2,4,1,3,7,5]=>{{1,6,7},{2},{3,4},{5}}
[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[5,6,4,1,2,7,3]=>{{1,5},{2,6,7},{3,4}}
[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[6,1,5,2,3,7,4]=>{{1,6,7},{2},{3,5},{4}}
[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[6,2,5,1,3,7,4]=>{{1,6,7},{2},{3,5},{4}}
[6,7,3,5,1,2,4]=>[5,1,7,2,3,6,4]=>[6,1,5,3,4,7,2]=>{{1,6,7},{2},{3,5},{4}}
[6,7,3,5,1,4,2]=>[5,4,7,1,3,6,2]=>[5,6,4,3,1,7,2]=>{{1,5},{2,6,7},{3,4}}
[6,7,3,5,2,1,4]=>[2,5,7,1,3,6,4]=>[6,2,5,3,4,7,1]=>{{1,6,7},{2},{3,5},{4}}
[6,7,3,5,2,4,1]=>[4,5,7,2,3,6,1]=>[6,5,4,2,1,7,3]=>{{1,6,7},{2,5},{3,4}}
[6,7,3,5,4,1,2]=>[4,1,5,7,2,6,3]=>[6,1,5,4,3,7,2]=>{{1,6,7},{2},{3,5},{4}}
[6,7,3,5,4,2,1]=>[2,4,5,7,1,6,3]=>[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}}
[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[6,1,2,4,3,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,4,1,2,5,3]=>[4,1,7,5,3,6,2]=>[6,1,4,5,2,7,3]=>{{1,6,7},{2},{3,4,5}}
[6,7,4,1,3,2,5]=>[4,3,1,7,2,6,5]=>[3,6,2,4,1,7,5]=>{{1,3},{2,6,7},{4},{5}}
[6,7,4,1,3,5,2]=>[4,7,1,5,2,6,3]=>[6,4,2,5,3,7,1]=>{{1,6,7},{2,4,5},{3}}
[6,7,4,1,5,2,3]=>[4,7,2,5,3,6,1]=>[6,4,1,5,2,7,3]=>{{1,6,7},{2,4,5},{3}}
[6,7,4,1,5,3,2]=>[4,3,7,5,2,6,1]=>[4,6,3,5,1,7,2]=>{{1,4,5},{2,6,7},{3}}
[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[6,2,1,4,3,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,4,2,1,5,3]=>[2,4,7,5,3,6,1]=>[6,2,4,5,1,7,3]=>{{1,6,7},{2},{3,4,5}}
[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[6,3,1,4,2,7,5]=>{{1,6,7},{2,3},{4},{5}}
[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[5,6,1,4,2,7,3]=>{{1,5},{2,6,7},{3},{4}}
[6,7,4,2,5,1,3]=>[5,4,1,7,2,6,3]=>[5,6,2,4,3,7,1]=>{{1,5},{2,6,7},{3},{4}}
[6,7,4,2,5,3,1]=>[3,5,4,7,1,6,2]=>[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}}
[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[6,1,3,4,2,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,4,3,1,5,2]=>[3,4,7,5,1,6,2]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}
[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[6,2,3,4,1,7,5]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[3,6,5,4,1,7,2]=>{{1,3,5},{2,6,7},{4}}
[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[5,1,6,4,2,7,3]=>{{1,5},{2},{3,6,7},{4}}
[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[5,2,6,4,1,7,3]=>{{1,5},{2},{3,6,7},{4}}
[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[6,1,2,5,3,7,4]=>{{1,6,7},{2},{3},{4,5}}
[6,7,4,5,1,3,2]=>[5,3,1,7,4,6,2]=>[3,6,2,5,1,7,4]=>{{1,3},{2,6,7},{4,5}}
[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[6,2,1,5,3,7,4]=>{{1,6,7},{2},{3},{4,5}}
[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[6,3,1,5,2,7,4]=>{{1,6,7},{2,3},{4,5}}
[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[6,1,3,5,2,7,4]=>{{1,6,7},{2},{3},{4,5}}
[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[6,2,3,5,1,7,4]=>{{1,6,7},{2},{3},{4,5}}
[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[6,1,2,3,5,7,4]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,1,2,4,3]=>[5,1,4,2,7,6,3]=>[4,1,6,3,5,7,2]=>{{1,4},{2},{3,6,7},{5}}
[6,7,5,1,3,2,4]=>[5,3,1,2,7,6,4]=>[3,6,2,1,5,7,4]=>{{1,3},{2,6,7},{4},{5}}
[6,7,5,1,3,4,2]=>[5,4,1,3,7,6,2]=>[4,6,2,1,5,7,3]=>{{1,4},{2,6,7},{3},{5}}
[6,7,5,1,4,2,3]=>[5,4,2,1,7,6,3]=>[4,6,1,3,5,7,2]=>{{1,4},{2,6,7},{3},{5}}
[6,7,5,1,4,3,2]=>[5,3,4,1,7,6,2]=>[3,6,4,2,5,7,1]=>{{1,3,4},{2,6,7},{5}}
[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[6,2,1,3,5,7,4]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,2,1,4,3]=>[2,5,4,1,7,6,3]=>[4,2,6,3,5,7,1]=>{{1,4},{2},{3,6,7},{5}}
[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[6,3,1,2,5,7,4]=>{{1,6,7},{2,3},{4},{5}}
[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[6,4,1,2,5,7,3]=>{{1,6,7},{2,4},{3},{5}}
[6,7,5,2,4,1,3]=>[4,5,1,2,7,6,3]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[6,7,5,2,4,3,1]=>[3,4,5,1,7,6,2]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[6,1,3,2,5,7,4]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,3,1,4,2]=>[3,5,4,2,7,6,1]=>[6,3,4,1,5,7,2]=>{{1,6,7},{2,3,4},{5}}
[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[6,2,3,1,5,7,4]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[4,6,3,1,5,7,2]=>{{1,4},{2,6,7},{3},{5}}
[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[6,1,4,2,5,7,3]=>{{1,6,7},{2},{3,4},{5}}
[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[6,2,4,1,5,7,3]=>{{1,6,7},{2},{3,4},{5}}
[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[6,1,2,4,5,7,3]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,4,1,3,2]=>[4,3,1,5,7,6,2]=>[3,6,2,4,5,7,1]=>{{1,3},{2,6,7},{4},{5}}
[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[6,2,1,4,5,7,3]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[6,3,1,4,5,7,2]=>{{1,6,7},{2,3},{4},{5}}
[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[6,1,3,4,5,7,2]=>{{1,6,7},{2},{3},{4},{5}}
[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}
[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,1,2,3,4,6,5]=>[7,1,2,3,6,4,5]=>[6,1,2,3,7,5,4]=>{{1,6},{2},{3},{4},{5,7}}
[7,1,2,3,5,4,6]=>[7,1,2,5,3,4,6]=>[5,1,2,7,4,3,6]=>{{1,5},{2},{3},{4,7},{6}}
[7,1,2,3,5,6,4]=>[7,1,2,6,3,5,4]=>[6,1,2,7,4,3,5]=>{{1,6},{2},{3},{4,7},{5}}
[7,1,2,3,6,4,5]=>[7,1,2,6,4,3,5]=>[6,1,2,7,3,5,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,1,2,3,6,5,4]=>[7,1,2,5,6,3,4]=>[5,1,2,7,6,4,3]=>{{1,5,6},{2},{3},{4,7}}
[7,1,2,4,3,5,6]=>[7,1,4,2,3,5,6]=>[4,1,7,3,2,5,6]=>{{1,4},{2},{3,7},{5},{6}}
[7,1,2,4,3,6,5]=>[7,1,4,2,6,3,5]=>[4,1,6,3,7,5,2]=>{{1,4},{2},{3,6},{5,7}}
[7,1,2,4,5,3,6]=>[7,1,5,2,4,3,6]=>[5,1,7,3,2,4,6]=>{{1,5},{2},{3,7},{4},{6}}
[7,1,2,4,5,6,3]=>[7,1,6,2,3,4,5]=>[6,1,7,3,4,5,2]=>{{1,6},{2},{3,7},{4},{5}}
[7,1,2,4,6,3,5]=>[7,1,6,2,4,5,3]=>[6,1,7,3,2,4,5]=>{{1,6},{2},{3,7},{4},{5}}
[7,1,2,4,6,5,3]=>[7,1,5,2,6,4,3]=>[5,1,7,3,6,2,4]=>{{1,5,6},{2},{3,7},{4}}
[7,1,2,5,3,4,6]=>[7,1,5,3,2,4,6]=>[5,1,7,2,4,3,6]=>{{1,5},{2},{3,7},{4},{6}}
[7,1,2,5,3,6,4]=>[7,1,5,6,2,3,4]=>[5,1,7,6,4,3,2]=>{{1,5},{2},{3,7},{4,6}}
[7,1,2,5,4,3,6]=>[7,1,4,5,2,3,6]=>[4,1,7,5,3,2,6]=>{{1,4,5},{2},{3,7},{6}}
[7,1,2,5,4,6,3]=>[7,1,6,5,2,4,3]=>[5,1,6,7,4,2,3]=>{{1,5},{2},{3,6},{4,7}}
[7,1,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>[6,1,7,2,4,3,5]=>{{1,6},{2},{3,7},{4},{5}}
[7,1,2,5,6,4,3]=>[7,1,4,6,2,5,3]=>[4,1,7,6,3,2,5]=>{{1,4,6},{2},{3,7},{5}}
[7,1,2,6,3,4,5]=>[7,1,6,3,4,2,5]=>[6,1,7,2,3,5,4]=>{{1,6},{2},{3,7},{4},{5}}
[7,1,2,6,3,5,4]=>[7,1,6,5,3,2,4]=>[5,1,6,7,3,4,2]=>{{1,5},{2},{3,6},{4,7}}
[7,1,2,6,4,3,5]=>[7,1,4,6,3,2,5]=>[4,1,7,6,2,5,3]=>{{1,4,6},{2},{3,7},{5}}
[7,1,2,6,4,5,3]=>[7,1,5,6,4,2,3]=>[5,1,7,6,2,4,3]=>{{1,5},{2},{3,7},{4,6}}
[7,1,2,6,5,3,4]=>[7,1,5,3,6,2,4]=>[5,1,7,2,6,4,3]=>{{1,5,6},{2},{3,7},{4}}
[7,1,2,6,5,4,3]=>[7,1,4,5,6,2,3]=>[4,1,7,5,6,3,2]=>{{1,4,5,6},{2},{3,7}}
[7,1,3,2,4,5,6]=>[7,3,1,2,4,5,6]=>[3,7,2,1,4,5,6]=>{{1,3},{2,7},{4},{5},{6}}
[7,1,3,2,4,6,5]=>[7,3,1,2,6,4,5]=>[3,6,2,1,7,5,4]=>{{1,3},{2,6},{4},{5,7}}
[7,1,3,2,5,4,6]=>[7,3,1,5,2,4,6]=>[3,5,2,7,4,1,6]=>{{1,3},{2,5},{4,7},{6}}
[7,1,3,2,5,6,4]=>[7,3,1,6,2,5,4]=>[3,6,2,7,4,1,5]=>{{1,3},{2,6},{4,7},{5}}
[7,1,3,2,6,4,5]=>[7,3,1,6,4,2,5]=>[3,6,2,7,1,5,4]=>{{1,3},{2,6},{4,7},{5}}
[7,1,3,2,6,5,4]=>[7,3,1,5,6,2,4]=>[3,5,2,7,6,4,1]=>{{1,3},{2,5,6},{4,7}}
[7,1,3,4,2,5,6]=>[7,4,1,3,2,5,6]=>[4,7,2,1,3,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[7,1,3,4,2,6,5]=>[7,4,1,3,6,2,5]=>[4,6,2,1,7,5,3]=>{{1,4},{2,6},{3},{5,7}}
[7,1,3,4,5,2,6]=>[7,5,1,2,3,4,6]=>[5,7,2,3,4,1,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,1,3,4,5,6,2]=>[7,6,1,2,3,5,4]=>[6,7,2,3,4,1,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,3,4,6,2,5]=>[7,6,1,2,4,3,5]=>[6,7,2,3,1,5,4]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,3,4,6,5,2]=>[7,5,1,2,6,3,4]=>[5,7,2,3,6,4,1]=>{{1,5,6},{2,7},{3},{4}}
[7,1,3,5,2,4,6]=>[7,5,1,3,4,2,6]=>[5,7,2,1,3,4,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,1,3,5,2,6,4]=>[7,5,1,6,3,2,4]=>[5,7,2,6,3,4,1]=>{{1,5},{2,7},{3},{4,6}}
[7,1,3,5,4,2,6]=>[7,4,1,5,3,2,6]=>[4,7,2,5,1,3,6]=>{{1,4,5},{2,7},{3},{6}}
[7,1,3,5,4,6,2]=>[7,6,1,5,2,3,4]=>[5,6,2,7,4,3,1]=>{{1,5},{2,6},{3},{4,7}}
[7,1,3,5,6,2,4]=>[7,6,1,3,2,4,5]=>[6,7,2,1,4,5,3]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,3,5,6,4,2]=>[7,4,1,6,2,3,5]=>[4,7,2,6,3,5,1]=>{{1,4,6},{2,7},{3},{5}}
[7,1,3,6,2,4,5]=>[7,6,1,3,4,5,2]=>[6,7,2,1,3,4,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,3,6,2,5,4]=>[7,6,1,5,3,4,2]=>[5,6,2,7,3,1,4]=>{{1,5},{2,6},{3},{4,7}}
[7,1,3,6,4,2,5]=>[7,4,1,6,3,5,2]=>[4,7,2,6,1,3,5]=>{{1,4,6},{2,7},{3},{5}}
[7,1,3,6,4,5,2]=>[7,5,1,6,4,3,2]=>[5,7,2,6,1,3,4]=>{{1,5},{2,7},{3},{4,6}}
[7,1,3,6,5,2,4]=>[7,5,1,3,6,4,2]=>[5,7,2,1,6,3,4]=>{{1,5,6},{2,7},{3},{4}}
[7,1,3,6,5,4,2]=>[7,4,1,5,6,3,2]=>[4,7,2,5,6,1,3]=>{{1,4,5,6},{2,7},{3}}
[7,1,4,2,3,5,6]=>[7,4,2,1,3,5,6]=>[4,7,1,3,2,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[7,1,4,2,3,6,5]=>[7,4,2,1,6,3,5]=>[4,6,1,3,7,5,2]=>{{1,4},{2,6},{3},{5,7}}
[7,1,4,2,5,3,6]=>[7,4,5,1,2,3,6]=>[4,7,5,3,2,1,6]=>{{1,4},{2,7},{3,5},{6}}
[7,1,4,2,5,6,3]=>[7,4,6,1,2,5,3]=>[4,7,6,3,2,1,5]=>{{1,4},{2,7},{3,6},{5}}
[7,1,4,2,6,3,5]=>[7,4,6,1,3,2,5]=>[4,7,6,3,1,5,2]=>{{1,4},{2,7},{3,6},{5}}
[7,1,4,2,6,5,3]=>[7,4,5,1,6,2,3]=>[4,7,5,3,6,2,1]=>{{1,4},{2,7},{3,5,6}}
[7,1,4,3,2,5,6]=>[7,3,4,1,2,5,6]=>[3,7,4,2,1,5,6]=>{{1,3,4},{2,7},{5},{6}}
[7,1,4,3,2,6,5]=>[7,3,4,1,6,2,5]=>[3,6,4,2,7,5,1]=>{{1,3,4},{2,6},{5,7}}
[7,1,4,3,5,2,6]=>[7,5,4,1,3,2,6]=>[4,5,7,3,1,2,6]=>{{1,4},{2,5},{3,7},{6}}
[7,1,4,3,5,6,2]=>[7,6,4,1,2,3,5]=>[4,6,7,3,2,5,1]=>{{1,4},{2,6},{3,7},{5}}
[7,1,4,3,6,2,5]=>[7,6,4,1,3,5,2]=>[4,6,7,3,1,2,5]=>{{1,4},{2,6},{3,7},{5}}
[7,1,4,3,6,5,2]=>[7,5,4,1,6,3,2]=>[4,5,7,3,6,1,2]=>{{1,4},{2,5,6},{3,7}}
[7,1,4,5,2,3,6]=>[7,5,2,1,4,3,6]=>[5,7,1,3,2,4,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,1,4,5,2,6,3]=>[7,5,6,1,3,4,2]=>[5,7,6,3,2,1,4]=>{{1,5},{2,7},{3,6},{4}}
[7,1,4,5,3,2,6]=>[7,3,5,1,4,2,6]=>[3,7,5,2,1,4,6]=>{{1,3,5},{2,7},{4},{6}}
[7,1,4,5,3,6,2]=>[7,6,5,1,2,4,3]=>[5,6,7,3,4,1,2]=>{{1,5},{2,6},{3,7},{4}}
[7,1,4,5,6,2,3]=>[7,6,2,1,3,4,5]=>[6,7,1,3,4,5,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,4,5,6,3,2]=>[7,3,6,1,2,4,5]=>[3,7,6,2,4,5,1]=>{{1,3,6},{2,7},{4},{5}}
[7,1,4,6,2,3,5]=>[7,6,2,1,4,5,3]=>[6,7,1,3,2,4,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,4,6,2,5,3]=>[7,6,5,1,4,3,2]=>[5,6,7,3,1,2,4]=>{{1,5},{2,6},{3,7},{4}}
[7,1,4,6,3,2,5]=>[7,3,6,1,4,5,2]=>[3,7,6,2,1,4,5]=>{{1,3,6},{2,7},{4},{5}}
[7,1,4,6,3,5,2]=>[7,5,6,1,4,2,3]=>[5,7,6,3,1,4,2]=>{{1,5},{2,7},{3,6},{4}}
[7,1,4,6,5,2,3]=>[7,5,2,1,6,4,3]=>[5,7,1,3,6,2,4]=>{{1,5,6},{2,7},{3},{4}}
[7,1,4,6,5,3,2]=>[7,3,5,1,6,4,2]=>[3,7,5,2,6,1,4]=>{{1,3,5,6},{2,7},{4}}
[7,1,5,2,3,4,6]=>[7,5,2,3,1,4,6]=>[5,7,1,2,4,3,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,1,5,2,3,6,4]=>[7,5,2,6,1,3,4]=>[5,7,1,6,4,3,2]=>{{1,5},{2,7},{3},{4,6}}
[7,1,5,2,4,3,6]=>[7,5,4,2,1,3,6]=>[4,5,7,2,3,1,6]=>{{1,4},{2,5},{3,7},{6}}
[7,1,5,2,4,6,3]=>[7,5,6,2,1,4,3]=>[5,7,6,2,4,1,3]=>{{1,5},{2,7},{3,6},{4}}
[7,1,5,2,6,3,4]=>[7,5,6,3,1,2,4]=>[5,7,6,1,4,3,2]=>{{1,5},{2,7},{3,6},{4}}
[7,1,5,2,6,4,3]=>[7,5,4,6,1,2,3]=>[4,6,7,5,3,2,1]=>{{1,4,5},{2,6},{3,7}}
[7,1,5,3,2,4,6]=>[7,3,5,2,1,4,6]=>[3,7,5,1,4,2,6]=>{{1,3,5},{2,7},{4},{6}}
[7,1,5,3,2,6,4]=>[7,3,5,6,1,2,4]=>[3,7,5,6,4,2,1]=>{{1,3,5},{2,7},{4,6}}
[7,1,5,3,4,2,6]=>[7,4,5,3,1,2,6]=>[4,7,5,1,3,2,6]=>{{1,4},{2,7},{3,5},{6}}
[7,1,5,3,4,6,2]=>[7,6,5,3,1,4,2]=>[5,6,7,1,4,2,3]=>{{1,5},{2,6},{3,7},{4}}
[7,1,5,3,6,2,4]=>[7,6,5,2,1,3,4]=>[5,6,7,2,4,3,1]=>{{1,5},{2,6},{3,7},{4}}
[7,1,5,3,6,4,2]=>[7,4,6,5,1,2,3]=>[4,7,5,6,3,2,1]=>{{1,4,6},{2,7},{3,5}}
[7,1,5,4,2,3,6]=>[7,4,2,5,1,3,6]=>[4,7,1,5,3,2,6]=>{{1,4,5},{2,7},{3},{6}}
[7,1,5,4,2,6,3]=>[7,4,5,6,1,3,2]=>[4,7,6,5,3,1,2]=>{{1,4,5},{2,7},{3,6}}
[7,1,5,4,3,2,6]=>[7,3,4,5,1,2,6]=>[3,7,4,5,2,1,6]=>{{1,3,4,5},{2,7},{6}}
[7,1,5,4,3,6,2]=>[7,6,4,5,1,3,2]=>[4,5,7,6,3,1,2]=>{{1,4,6},{2,5},{3,7}}
[7,1,5,4,6,2,3]=>[7,6,2,5,1,4,3]=>[5,6,1,7,4,2,3]=>{{1,5},{2,6},{3},{4,7}}
[7,1,5,4,6,3,2]=>[7,3,6,5,1,4,2]=>[3,6,5,7,4,1,2]=>{{1,3,5},{2,6},{4,7}}
[7,1,5,6,2,3,4]=>[7,6,2,3,1,5,4]=>[6,7,1,2,4,3,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,5,6,2,4,3]=>[7,6,4,2,1,5,3]=>[4,6,7,2,3,1,5]=>{{1,4},{2,6},{3,7},{5}}
[7,1,5,6,3,2,4]=>[7,3,6,2,1,5,4]=>[3,7,6,1,4,2,5]=>{{1,3,6},{2,7},{4},{5}}
[7,1,5,6,3,4,2]=>[7,4,6,3,1,5,2]=>[4,7,6,1,3,2,5]=>{{1,4},{2,7},{3,6},{5}}
[7,1,5,6,4,2,3]=>[7,4,2,6,1,5,3]=>[4,7,1,6,3,2,5]=>{{1,4,6},{2,7},{3},{5}}
[7,1,5,6,4,3,2]=>[7,3,4,6,1,5,2]=>[3,7,4,6,2,1,5]=>{{1,3,4,6},{2,7},{5}}
[7,1,6,2,3,4,5]=>[7,6,2,3,4,1,5]=>[6,7,1,2,3,5,4]=>{{1,6},{2,7},{3},{4},{5}}
[7,1,6,2,3,5,4]=>[7,6,2,5,3,1,4]=>[5,6,1,7,3,4,2]=>{{1,5},{2,6},{3},{4,7}}
[7,1,6,2,4,3,5]=>[7,6,4,2,3,1,5]=>[4,6,7,2,1,5,3]=>{{1,4},{2,6},{3,7},{5}}
[7,1,6,2,4,5,3]=>[7,6,5,2,4,1,3]=>[5,6,7,2,1,4,3]=>{{1,5},{2,6},{3,7},{4}}
[7,1,6,2,5,3,4]=>[7,6,5,3,2,1,4]=>[5,6,7,1,3,4,2]=>{{1,5},{2,6},{3,7},{4}}
[7,1,6,2,5,4,3]=>[7,6,4,5,2,1,3]=>[4,5,7,6,2,3,1]=>{{1,4,6},{2,5},{3,7}}
[7,1,6,3,2,4,5]=>[7,3,6,2,4,1,5]=>[3,7,6,1,2,5,4]=>{{1,3,6},{2,7},{4},{5}}
[7,1,6,3,2,5,4]=>[7,3,6,5,2,1,4]=>[3,6,5,7,2,4,1]=>{{1,3,5},{2,6},{4,7}}
[7,1,6,3,4,2,5]=>[7,4,6,3,2,1,5]=>[4,7,6,1,2,5,3]=>{{1,4},{2,7},{3,6},{5}}
[7,1,6,3,4,5,2]=>[7,5,6,3,4,1,2]=>[5,7,6,1,2,4,3]=>{{1,5},{2,7},{3,6},{4}}
[7,1,6,3,5,2,4]=>[7,5,6,2,3,1,4]=>[5,7,6,2,3,4,1]=>{{1,5},{2,7},{3,6},{4}}
[7,1,6,3,5,4,2]=>[7,4,5,6,2,1,3]=>[4,7,6,5,2,3,1]=>{{1,4,5},{2,7},{3,6}}
[7,1,6,4,2,3,5]=>[7,4,2,6,3,1,5]=>[4,7,1,6,2,5,3]=>{{1,4,6},{2,7},{3},{5}}
[7,1,6,4,2,5,3]=>[7,4,6,5,3,1,2]=>[4,7,5,6,1,3,2]=>{{1,4,6},{2,7},{3,5}}
[7,1,6,4,3,2,5]=>[7,3,4,6,2,1,5]=>[3,7,4,6,1,5,2]=>{{1,3,4,6},{2,7},{5}}
[7,1,6,4,3,5,2]=>[7,5,4,6,3,1,2]=>[4,6,7,5,1,3,2]=>{{1,4,5},{2,6},{3,7}}
[7,1,6,4,5,2,3]=>[7,5,2,6,4,1,3]=>[5,7,1,6,2,4,3]=>{{1,5},{2,7},{3},{4,6}}
[7,1,6,4,5,3,2]=>[7,3,5,6,4,1,2]=>[3,7,5,6,1,4,2]=>{{1,3,5},{2,7},{4,6}}
[7,1,6,5,2,3,4]=>[7,5,2,3,6,1,4]=>[5,7,1,2,6,4,3]=>{{1,5,6},{2,7},{3},{4}}
[7,1,6,5,2,4,3]=>[7,5,4,2,6,1,3]=>[4,5,7,2,6,3,1]=>{{1,4},{2,5,6},{3,7}}
[7,1,6,5,3,2,4]=>[7,3,5,2,6,1,4]=>[3,7,5,1,6,4,2]=>{{1,3,5,6},{2,7},{4}}
[7,1,6,5,3,4,2]=>[7,4,5,3,6,1,2]=>[4,7,5,1,6,3,2]=>{{1,4},{2,7},{3,5,6}}
[7,1,6,5,4,2,3]=>[7,4,2,5,6,1,3]=>[4,7,1,5,6,3,2]=>{{1,4,5,6},{2,7},{3}}
[7,1,6,5,4,3,2]=>[7,3,4,5,6,1,2]=>[3,7,4,5,6,2,1]=>{{1,3,4,5,6},{2,7}}
[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,2,1,3,4,6,5]=>[2,7,1,3,6,4,5]=>[6,2,1,3,7,5,4]=>{{1,6},{2},{3},{4},{5,7}}
[7,2,1,3,5,4,6]=>[2,7,1,5,3,4,6]=>[5,2,1,7,4,3,6]=>{{1,5},{2},{3},{4,7},{6}}
[7,2,1,3,5,6,4]=>[2,7,1,6,3,5,4]=>[6,2,1,7,4,3,5]=>{{1,6},{2},{3},{4,7},{5}}
[7,2,1,3,6,4,5]=>[2,7,1,6,4,3,5]=>[6,2,1,7,3,5,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,2,1,3,6,5,4]=>[2,7,1,5,6,3,4]=>[5,2,1,7,6,4,3]=>{{1,5,6},{2},{3},{4,7}}
[7,2,1,4,3,5,6]=>[2,7,4,1,3,5,6]=>[4,2,7,3,1,5,6]=>{{1,4},{2},{3,7},{5},{6}}
[7,2,1,4,3,6,5]=>[2,7,4,1,6,3,5]=>[4,2,6,3,7,5,1]=>{{1,4},{2},{3,6},{5,7}}
[7,2,1,4,5,3,6]=>[2,7,5,1,4,3,6]=>[5,2,7,3,1,4,6]=>{{1,5},{2},{3,7},{4},{6}}
[7,2,1,4,5,6,3]=>[2,7,6,1,3,4,5]=>[6,2,7,3,4,5,1]=>{{1,6},{2},{3,7},{4},{5}}
[7,2,1,4,6,3,5]=>[2,7,6,1,4,5,3]=>[6,2,7,3,1,4,5]=>{{1,6},{2},{3,7},{4},{5}}
[7,2,1,4,6,5,3]=>[2,7,5,1,6,4,3]=>[5,2,7,3,6,1,4]=>{{1,5,6},{2},{3,7},{4}}
[7,2,1,5,3,4,6]=>[2,7,5,3,1,4,6]=>[5,2,7,1,4,3,6]=>{{1,5},{2},{3,7},{4},{6}}
[7,2,1,5,3,6,4]=>[2,7,5,6,1,3,4]=>[5,2,7,6,4,3,1]=>{{1,5},{2},{3,7},{4,6}}
[7,2,1,5,4,3,6]=>[2,7,4,5,1,3,6]=>[4,2,7,5,3,1,6]=>{{1,4,5},{2},{3,7},{6}}
[7,2,1,5,4,6,3]=>[2,7,6,5,1,4,3]=>[5,2,6,7,4,1,3]=>{{1,5},{2},{3,6},{4,7}}
[7,2,1,5,6,3,4]=>[2,7,6,3,1,5,4]=>[6,2,7,1,4,3,5]=>{{1,6},{2},{3,7},{4},{5}}
[7,2,1,5,6,4,3]=>[2,7,4,6,1,5,3]=>[4,2,7,6,3,1,5]=>{{1,4,6},{2},{3,7},{5}}
[7,2,1,6,3,4,5]=>[2,7,6,3,4,1,5]=>[6,2,7,1,3,5,4]=>{{1,6},{2},{3,7},{4},{5}}
[7,2,1,6,3,5,4]=>[2,7,6,5,3,1,4]=>[5,2,6,7,3,4,1]=>{{1,5},{2},{3,6},{4,7}}
[7,2,1,6,4,3,5]=>[2,7,4,6,3,1,5]=>[4,2,7,6,1,5,3]=>{{1,4,6},{2},{3,7},{5}}
[7,2,1,6,4,5,3]=>[2,7,5,6,4,1,3]=>[5,2,7,6,1,4,3]=>{{1,5},{2},{3,7},{4,6}}
[7,2,1,6,5,3,4]=>[2,7,5,3,6,1,4]=>[5,2,7,1,6,4,3]=>{{1,5,6},{2},{3,7},{4}}
[7,2,1,6,5,4,3]=>[2,7,4,5,6,1,3]=>[4,2,7,5,6,3,1]=>{{1,4,5,6},{2},{3,7}}
[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[7,3,1,2,4,5,6]=>{{1,7},{2,3},{4},{5},{6}}
[7,2,3,1,4,6,5]=>[3,7,2,1,6,4,5]=>[6,3,1,2,7,5,4]=>{{1,6},{2,3},{4},{5,7}}
[7,2,3,1,5,4,6]=>[3,7,2,5,1,4,6]=>[5,3,1,7,4,2,6]=>{{1,5},{2,3},{4,7},{6}}
[7,2,3,1,5,6,4]=>[3,7,2,6,1,5,4]=>[6,3,1,7,4,2,5]=>{{1,6},{2,3},{4,7},{5}}
[7,2,3,1,6,4,5]=>[3,7,2,6,4,1,5]=>[6,3,1,7,2,5,4]=>{{1,6},{2,3},{4,7},{5}}
[7,2,3,1,6,5,4]=>[3,7,2,5,6,1,4]=>[5,3,1,7,6,4,2]=>{{1,5,6},{2,3},{4,7}}
[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[7,4,1,2,3,5,6]=>{{1,7},{2,4},{3},{5},{6}}
[7,2,3,4,1,6,5]=>[4,7,2,3,6,1,5]=>[6,4,1,2,7,5,3]=>{{1,6},{2,4},{3},{5,7}}
[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[7,5,1,2,3,4,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[7,6,1,2,3,4,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,4,6,1,5]=>[6,7,2,3,1,4,5]=>[7,6,1,2,4,5,3]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,4,6,5,1]=>[5,6,2,3,7,1,4]=>[7,6,1,2,5,4,3]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,5,1,4,6]=>[5,7,2,1,3,4,6]=>[7,5,1,3,4,2,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,3,5,1,6,4]=>[5,7,2,6,3,1,4]=>[7,5,1,6,3,4,2]=>{{1,7},{2,5},{3},{4,6}}
[7,2,3,5,4,1,6]=>[4,5,2,7,1,3,6]=>[7,5,1,4,3,2,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,3,5,4,6,1]=>[6,7,2,5,3,4,1]=>[6,5,1,7,3,2,4]=>{{1,6},{2,5},{3},{4,7}}
[7,2,3,5,6,1,4]=>[6,7,2,1,4,3,5]=>[7,6,1,3,2,5,4]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,5,6,4,1]=>[4,6,2,7,3,1,5]=>[7,6,1,4,2,5,3]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,6,1,4,5]=>[6,7,2,1,3,5,4]=>[7,6,1,3,4,2,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,6,1,5,4]=>[6,7,2,5,1,3,4]=>[6,5,1,7,4,3,2]=>{{1,6},{2,5},{3},{4,7}}
[7,2,3,6,4,1,5]=>[4,6,2,7,1,5,3]=>[7,6,1,4,3,2,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,6,4,5,1]=>[5,7,2,6,4,3,1]=>[7,5,1,6,2,3,4]=>{{1,7},{2,5},{3},{4,6}}
[7,2,3,6,5,1,4]=>[5,6,2,1,7,4,3]=>[7,6,1,3,5,2,4]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,3,6,5,4,1]=>[4,5,2,6,7,3,1]=>[7,6,1,4,5,2,3]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,4,1,3,5,6]=>[4,7,1,2,3,5,6]=>[7,4,2,3,1,5,6]=>{{1,7},{2,4},{3},{5},{6}}
[7,2,4,1,3,6,5]=>[4,7,1,2,6,3,5]=>[6,4,2,3,7,5,1]=>{{1,6},{2,4},{3},{5,7}}
[7,2,4,1,5,3,6]=>[4,7,5,2,1,3,6]=>[7,4,5,2,3,1,6]=>{{1,7},{2,4},{3,5},{6}}
[7,2,4,1,5,6,3]=>[4,7,6,2,1,5,3]=>[7,4,6,2,3,1,5]=>{{1,7},{2,4},{3,6},{5}}
[7,2,4,1,6,3,5]=>[4,7,6,2,3,1,5]=>[7,4,6,2,1,5,3]=>{{1,7},{2,4},{3,6},{5}}
[7,2,4,1,6,5,3]=>[4,7,5,2,6,1,3]=>[7,4,5,2,6,3,1]=>{{1,7},{2,4},{3,5,6}}
[7,2,4,3,1,5,6]=>[3,4,7,1,2,5,6]=>[7,4,3,2,1,5,6]=>{{1,7},{2,4},{3},{5},{6}}
[7,2,4,3,1,6,5]=>[3,4,7,1,6,2,5]=>[6,4,3,2,7,5,1]=>{{1,6},{2,4},{3},{5,7}}
[7,2,4,3,5,1,6]=>[5,7,4,2,3,1,6]=>[5,4,7,2,1,3,6]=>{{1,5},{2,4},{3,7},{6}}
[7,2,4,3,5,6,1]=>[6,7,4,2,3,5,1]=>[6,4,7,2,1,3,5]=>{{1,6},{2,4},{3,7},{5}}
[7,2,4,3,6,1,5]=>[6,7,4,2,1,3,5]=>[6,4,7,2,3,5,1]=>{{1,6},{2,4},{3,7},{5}}
[7,2,4,3,6,5,1]=>[5,6,4,2,7,1,3]=>[6,4,7,2,5,3,1]=>{{1,6},{2,4},{3,7},{5}}
[7,2,4,5,1,3,6]=>[5,7,1,3,2,4,6]=>[7,5,2,1,4,3,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,4,5,1,6,3]=>[5,7,6,2,3,4,1]=>[7,5,6,2,3,1,4]=>{{1,7},{2,5},{3,6},{4}}
[7,2,4,5,3,1,6]=>[3,5,7,2,1,4,6]=>[7,5,3,1,4,2,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,4,5,3,6,1]=>[6,7,5,2,4,3,1]=>[6,5,7,2,1,3,4]=>{{1,6},{2,5},{3,7},{4}}
[7,2,4,5,6,1,3]=>[6,7,1,3,4,2,5]=>[7,6,2,1,3,5,4]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,4,5,6,3,1]=>[3,6,7,2,4,1,5]=>[7,6,3,1,2,5,4]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,4,6,1,3,5]=>[6,7,1,3,2,5,4]=>[7,6,2,1,4,3,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,4,6,1,5,3]=>[6,7,5,2,1,4,3]=>[6,5,7,2,4,1,3]=>{{1,6},{2,5},{3,7},{4}}
[7,2,4,6,3,1,5]=>[3,6,7,2,1,5,4]=>[7,6,3,1,4,2,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,4,6,3,5,1]=>[5,7,6,2,4,1,3]=>[7,5,6,2,1,4,3]=>{{1,7},{2,5},{3,6},{4}}
[7,2,4,6,5,1,3]=>[5,6,1,3,7,4,2]=>[7,6,2,1,5,3,4]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,4,6,5,3,1]=>[3,5,6,2,7,4,1]=>[7,6,3,1,5,2,4]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,5,1,3,4,6]=>[5,7,1,2,4,3,6]=>[7,5,2,3,1,4,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,5,1,3,6,4]=>[5,7,1,6,2,3,4]=>[7,5,2,6,4,3,1]=>{{1,7},{2,5},{3},{4,6}}
[7,2,5,1,4,3,6]=>[5,7,4,1,2,3,6]=>[5,4,7,3,2,1,6]=>{{1,5},{2,4},{3,7},{6}}
[7,2,5,1,4,6,3]=>[5,7,6,1,2,4,3]=>[7,5,6,3,4,1,2]=>{{1,7},{2,5},{3,6},{4}}
[7,2,5,1,6,3,4]=>[5,7,6,3,2,1,4]=>[7,5,6,1,3,4,2]=>{{1,7},{2,5},{3,6},{4}}
[7,2,5,1,6,4,3]=>[5,7,4,6,2,1,3]=>[6,4,7,5,2,3,1]=>{{1,6},{2,4,5},{3,7}}
[7,2,5,3,1,4,6]=>[3,5,7,1,4,2,6]=>[7,5,3,2,1,4,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,5,3,1,6,4]=>[3,5,7,6,1,2,4]=>[7,5,3,6,4,2,1]=>{{1,7},{2,5},{3},{4,6}}
[7,2,5,3,4,1,6]=>[4,7,5,3,2,1,6]=>[7,4,5,1,2,3,6]=>{{1,7},{2,4},{3,5},{6}}
[7,2,5,3,4,6,1]=>[6,7,5,3,2,4,1]=>[6,5,7,1,3,2,4]=>{{1,6},{2,5},{3,7},{4}}
[7,2,5,3,6,1,4]=>[6,7,5,1,4,2,3]=>[6,5,7,3,1,4,2]=>{{1,6},{2,5},{3,7},{4}}
[7,2,5,3,6,4,1]=>[4,6,7,5,3,1,2]=>[7,5,4,6,1,3,2]=>{{1,7},{2,5},{3,4,6}}
[7,2,5,4,1,3,6]=>[4,5,1,7,3,2,6]=>[7,5,2,4,1,3,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,5,4,1,6,3]=>[4,5,7,6,1,3,2]=>[7,6,4,5,3,1,2]=>{{1,7},{2,6},{3,4,5}}
[7,2,5,4,3,1,6]=>[3,4,5,7,2,1,6]=>[7,5,3,4,1,2,6]=>{{1,7},{2,5},{3},{4},{6}}
[7,2,5,4,3,6,1]=>[6,7,4,5,2,3,1]=>[5,4,7,6,2,1,3]=>{{1,5},{2,4,6},{3,7}}
[7,2,5,4,6,1,3]=>[6,7,1,5,3,2,4]=>[6,5,2,7,3,4,1]=>{{1,6},{2,5},{3},{4,7}}
[7,2,5,4,6,3,1]=>[3,6,7,5,2,1,4]=>[6,5,3,7,2,4,1]=>{{1,6},{2,5},{3},{4,7}}
[7,2,5,6,1,3,4]=>[6,7,1,2,4,5,3]=>[7,6,2,3,1,4,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,5,6,1,4,3]=>[6,7,4,1,3,2,5]=>[6,4,7,3,1,5,2]=>{{1,6},{2,4},{3,7},{5}}
[7,2,5,6,3,1,4]=>[3,6,7,1,4,5,2]=>[7,6,3,2,1,4,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,5,6,3,4,1]=>[4,7,6,3,1,2,5]=>[7,4,6,1,3,5,2]=>{{1,7},{2,4},{3,6},{5}}
[7,2,5,6,4,1,3]=>[4,6,1,7,3,5,2]=>[7,6,2,4,1,3,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,5,6,4,3,1]=>[3,4,6,7,2,5,1]=>[7,6,3,4,1,2,5]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,1,3,4,5]=>[6,7,1,2,3,4,5]=>[7,6,2,3,4,5,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,1,3,5,4]=>[6,7,1,5,2,4,3]=>[6,5,2,7,4,1,3]=>{{1,6},{2,5},{3},{4,7}}
[7,2,6,1,4,3,5]=>[6,7,4,1,2,5,3]=>[6,4,7,3,2,1,5]=>{{1,6},{2,4},{3,7},{5}}
[7,2,6,1,4,5,3]=>[6,7,5,1,2,3,4]=>[6,5,7,3,4,2,1]=>{{1,6},{2,5},{3,7},{4}}
[7,2,6,1,5,3,4]=>[6,7,5,3,1,2,4]=>[6,5,7,1,4,3,2]=>{{1,6},{2,5},{3,7},{4}}
[7,2,6,1,5,4,3]=>[6,7,4,5,1,2,3]=>[5,4,7,6,3,2,1]=>{{1,5},{2,4,6},{3,7}}
[7,2,6,3,1,4,5]=>[3,6,7,1,2,4,5]=>[7,6,3,2,4,5,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,3,1,5,4]=>[3,6,7,5,1,4,2]=>[6,5,3,7,4,1,2]=>{{1,6},{2,5},{3},{4,7}}
[7,2,6,3,4,1,5]=>[4,7,6,3,2,5,1]=>[7,4,6,1,2,3,5]=>{{1,7},{2,4},{3,6},{5}}
[7,2,6,3,4,5,1]=>[5,7,6,3,4,2,1]=>[7,5,6,1,2,3,4]=>{{1,7},{2,5},{3,6},{4}}
[7,2,6,3,5,1,4]=>[5,7,6,1,3,2,4]=>[7,5,6,3,2,4,1]=>{{1,7},{2,5},{3,6},{4}}
[7,2,6,3,5,4,1]=>[4,5,7,6,3,2,1]=>[7,6,4,5,1,2,3]=>{{1,7},{2,6},{3,4,5}}
[7,2,6,4,1,3,5]=>[4,6,1,7,2,3,5]=>[7,6,2,4,3,5,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,4,1,5,3]=>[4,6,7,5,2,3,1]=>[7,5,4,6,2,1,3]=>{{1,7},{2,5},{3,4,6}}
[7,2,6,4,3,1,5]=>[3,4,6,7,1,2,5]=>[7,6,3,4,2,5,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,4,3,5,1]=>[5,7,4,6,3,2,1]=>[6,4,7,5,1,2,3]=>{{1,6},{2,4,5},{3,7}}
[7,2,6,4,5,1,3]=>[5,7,1,6,4,2,3]=>[7,5,2,6,1,4,3]=>{{1,7},{2,5},{3},{4,6}}
[7,2,6,4,5,3,1]=>[3,5,7,6,4,1,2]=>[7,5,3,6,1,4,2]=>{{1,7},{2,5},{3},{4,6}}
[7,2,6,5,1,3,4]=>[5,6,1,2,7,3,4]=>[7,6,2,3,5,4,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,5,1,4,3]=>[5,6,4,1,7,3,2]=>[6,4,7,3,5,1,2]=>{{1,6},{2,4},{3,7},{5}}
[7,2,6,5,3,1,4]=>[3,5,6,1,7,2,4]=>[7,6,3,2,5,4,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,5,3,4,1]=>[4,7,5,3,6,2,1]=>[7,4,5,1,6,2,3]=>{{1,7},{2,4},{3,5,6}}
[7,2,6,5,4,1,3]=>[4,5,1,6,7,2,3]=>[7,6,2,4,5,3,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,2,6,5,4,3,1]=>[3,4,5,6,7,1,2]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}
[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[7,1,3,2,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,3,1,2,4,6,5]=>[3,1,7,2,6,4,5]=>[6,1,3,2,7,5,4]=>{{1,6},{2},{3},{4},{5,7}}
[7,3,1,2,5,4,6]=>[3,1,7,5,2,4,6]=>[5,1,3,7,4,2,6]=>{{1,5},{2},{3},{4,7},{6}}
[7,3,1,2,5,6,4]=>[3,1,7,6,2,5,4]=>[6,1,3,7,4,2,5]=>{{1,6},{2},{3},{4,7},{5}}
[7,3,1,2,6,4,5]=>[3,1,7,6,4,2,5]=>[6,1,3,7,2,5,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,3,1,2,6,5,4]=>[3,1,7,5,6,2,4]=>[5,1,3,7,6,4,2]=>{{1,5,6},{2},{3},{4,7}}
[7,3,1,4,2,5,6]=>[3,7,4,2,1,5,6]=>[7,3,4,1,2,5,6]=>{{1,7},{2,3,4},{5},{6}}
[7,3,1,4,2,6,5]=>[3,7,4,2,6,1,5]=>[6,3,4,1,7,5,2]=>{{1,6},{2,3,4},{5,7}}
[7,3,1,4,5,2,6]=>[3,7,5,1,2,4,6]=>[7,3,5,2,4,1,6]=>{{1,7},{2,3,5},{4},{6}}
[7,3,1,4,5,6,2]=>[3,7,6,1,2,5,4]=>[7,3,6,2,4,1,5]=>{{1,7},{2,3,6},{4},{5}}
[7,3,1,4,6,2,5]=>[3,7,6,1,4,2,5]=>[7,3,6,2,1,5,4]=>{{1,7},{2,3,6},{4},{5}}
[7,3,1,4,6,5,2]=>[3,7,5,1,6,2,4]=>[7,3,5,2,6,4,1]=>{{1,7},{2,3,5,6},{4}}
[7,3,1,5,2,4,6]=>[3,7,5,2,4,1,6]=>[7,3,5,1,2,4,6]=>{{1,7},{2,3,5},{4},{6}}
[7,3,1,5,2,6,4]=>[3,7,5,6,2,1,4]=>[7,3,5,6,2,4,1]=>{{1,7},{2,3,5},{4,6}}
[7,3,1,5,4,2,6]=>[3,7,4,5,2,1,6]=>[7,3,4,5,1,2,6]=>{{1,7},{2,3,4,5},{6}}
[7,3,1,5,4,6,2]=>[3,7,6,5,1,2,4]=>[6,3,5,7,4,2,1]=>{{1,6},{2,3,5},{4,7}}
[7,3,1,5,6,2,4]=>[3,7,6,2,1,4,5]=>[7,3,6,1,4,5,2]=>{{1,7},{2,3,6},{4},{5}}
[7,3,1,5,6,4,2]=>[3,7,4,6,1,2,5]=>[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,6},{5}}
[7,3,1,6,2,4,5]=>[3,7,6,2,4,5,1]=>[7,3,6,1,2,4,5]=>{{1,7},{2,3,6},{4},{5}}
[7,3,1,6,2,5,4]=>[3,7,6,5,2,4,1]=>[6,3,5,7,2,1,4]=>{{1,6},{2,3,5},{4,7}}
[7,3,1,6,4,2,5]=>[3,7,4,6,2,5,1]=>[7,3,4,6,1,2,5]=>{{1,7},{2,3,4,6},{5}}
[7,3,1,6,4,5,2]=>[3,7,5,6,4,2,1]=>[7,3,5,6,1,2,4]=>{{1,7},{2,3,5},{4,6}}
[7,3,1,6,5,2,4]=>[3,7,5,2,6,4,1]=>[7,3,5,1,6,2,4]=>{{1,7},{2,3,5,6},{4}}
[7,3,1,6,5,4,2]=>[3,7,4,5,6,2,1]=>[7,3,4,5,6,1,2]=>{{1,7},{2,3,4,5,6}}
[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,3,2,1,4,6,5]=>[2,3,7,1,6,4,5]=>[6,2,3,1,7,5,4]=>{{1,6},{2},{3},{4},{5,7}}
[7,3,2,1,5,4,6]=>[2,3,7,5,1,4,6]=>[5,2,3,7,4,1,6]=>{{1,5},{2},{3},{4,7},{6}}
[7,3,2,1,5,6,4]=>[2,3,7,6,1,5,4]=>[6,2,3,7,4,1,5]=>{{1,6},{2},{3},{4,7},{5}}
[7,3,2,1,6,4,5]=>[2,3,7,6,4,1,5]=>[6,2,3,7,1,5,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,3,2,1,6,5,4]=>[2,3,7,5,6,1,4]=>[5,2,3,7,6,4,1]=>{{1,5,6},{2},{3},{4,7}}
[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[4,7,3,1,2,5,6]=>{{1,4},{2,7},{3},{5},{6}}
[7,3,2,4,1,6,5]=>[4,3,7,2,6,1,5]=>[4,6,3,1,7,5,2]=>{{1,4},{2,6},{3},{5,7}}
[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[5,7,3,1,2,4,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[6,7,3,1,2,4,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,4,6,1,5]=>[6,3,7,2,1,4,5]=>[6,7,3,1,4,5,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,4,6,5,1]=>[5,3,6,2,7,1,4]=>[6,7,3,1,5,4,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,5,1,4,6]=>[5,3,7,1,2,4,6]=>[5,7,3,2,4,1,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,3,2,5,1,6,4]=>[5,3,7,6,2,1,4]=>[5,7,3,6,2,4,1]=>{{1,5},{2,7},{3},{4,6}}
[7,3,2,5,4,1,6]=>[4,3,5,7,1,2,6]=>[5,7,3,4,2,1,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,3,2,5,4,6,1]=>[6,3,7,5,2,4,1]=>[5,6,3,7,2,1,4]=>{{1,5},{2,6},{3},{4,7}}
[7,3,2,5,6,1,4]=>[6,3,7,1,4,2,5]=>[6,7,3,2,1,5,4]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,5,6,4,1]=>[4,3,6,7,2,1,5]=>[6,7,3,4,1,5,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,6,1,4,5]=>[6,3,7,1,2,5,4]=>[6,7,3,2,4,1,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,6,1,5,4]=>[6,3,7,5,1,2,4]=>[5,6,3,7,4,2,1]=>{{1,5},{2,6},{3},{4,7}}
[7,3,2,6,4,1,5]=>[4,3,6,7,1,5,2]=>[6,7,3,4,2,1,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,6,4,5,1]=>[5,3,7,6,4,2,1]=>[5,7,3,6,1,2,4]=>{{1,5},{2,7},{3},{4,6}}
[7,3,2,6,5,1,4]=>[5,3,6,1,7,4,2]=>[6,7,3,2,5,1,4]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,2,6,5,4,1]=>[4,3,5,6,7,2,1]=>[6,7,3,4,5,1,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[7,1,4,2,3,5,6]=>{{1,7},{2},{3,4},{5},{6}}
[7,3,4,1,2,6,5]=>[4,1,7,3,6,2,5]=>[6,1,4,2,7,5,3]=>{{1,6},{2},{3,4},{5,7}}
[7,3,4,1,5,2,6]=>[4,5,7,3,1,2,6]=>[7,5,4,1,3,2,6]=>{{1,7},{2,5},{3,4},{6}}
[7,3,4,1,5,6,2]=>[4,6,7,3,2,1,5]=>[7,6,4,1,2,5,3]=>{{1,7},{2,6},{3,4},{5}}
[7,3,4,1,6,2,5]=>[4,6,7,3,1,5,2]=>[7,6,4,1,3,2,5]=>{{1,7},{2,6},{3,4},{5}}
[7,3,4,1,6,5,2]=>[4,5,6,3,7,2,1]=>[7,6,4,1,5,2,3]=>{{1,7},{2,6},{3,4},{5}}
[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[7,2,4,1,3,5,6]=>{{1,7},{2},{3,4},{5},{6}}
[7,3,4,2,1,6,5]=>[2,4,7,3,6,1,5]=>[6,2,4,1,7,5,3]=>{{1,6},{2},{3,4},{5,7}}
[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[5,7,4,1,2,3,6]=>{{1,5},{2,7},{3,4},{6}}
[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[6,7,4,1,2,3,5]=>{{1,6},{2,7},{3,4},{5}}
[7,3,4,2,6,1,5]=>[6,4,7,3,1,2,5]=>[6,7,4,1,3,5,2]=>{{1,6},{2,7},{3,4},{5}}
[7,3,4,2,6,5,1]=>[5,4,6,3,7,1,2]=>[6,7,4,1,5,3,2]=>{{1,6},{2,7},{3,4},{5}}
[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[7,1,5,2,3,4,6]=>{{1,7},{2},{3,5},{4},{6}}
[7,3,4,5,1,6,2]=>[5,6,7,3,4,1,2]=>[7,6,5,1,2,4,3]=>{{1,7},{2,6},{3,5},{4}}
[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[7,2,5,1,3,4,6]=>{{1,7},{2},{3,5},{4},{6}}
[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[6,7,5,1,2,3,4]=>{{1,6},{2,7},{3,5},{4}}
[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[7,1,6,2,3,4,5]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[7,2,6,1,3,4,5]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,4,6,1,2,5]=>[6,1,7,3,2,4,5]=>[7,1,6,2,4,5,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,4,6,1,5,2]=>[6,5,7,3,1,4,2]=>[6,7,5,1,4,2,3]=>{{1,6},{2,7},{3,5},{4}}
[7,3,4,6,2,1,5]=>[2,6,7,3,1,4,5]=>[7,2,6,1,4,5,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,4,6,2,5,1]=>[5,6,7,3,2,4,1]=>[7,6,5,1,3,2,4]=>{{1,7},{2,6},{3,5},{4}}
[7,3,4,6,5,1,2]=>[5,1,6,3,7,2,4]=>[7,1,6,2,5,4,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,4,6,5,2,1]=>[2,5,6,3,7,1,4]=>[7,2,6,1,5,4,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,5,1,2,4,6]=>[5,1,7,2,3,4,6]=>[7,1,5,3,4,2,6]=>{{1,7},{2},{3,5},{4},{6}}
[7,3,5,1,2,6,4]=>[5,1,7,6,3,2,4]=>[7,1,5,6,3,4,2]=>{{1,7},{2},{3,5},{4,6}}
[7,3,5,1,4,2,6]=>[5,4,7,1,3,2,6]=>[5,7,4,3,1,2,6]=>{{1,5},{2,7},{3,4},{6}}
[7,3,5,1,4,6,2]=>[5,6,7,1,3,4,2]=>[7,6,5,3,2,1,4]=>{{1,7},{2,6},{3,5},{4}}
[7,3,5,1,6,2,4]=>[5,6,7,2,4,3,1]=>[7,6,5,2,1,3,4]=>{{1,7},{2,6},{3,5},{4}}
[7,3,5,1,6,4,2]=>[5,4,6,7,3,2,1]=>[6,7,5,4,1,2,3]=>{{1,6},{2,7},{3,5},{4}}
[7,3,5,2,1,4,6]=>[2,5,7,1,3,4,6]=>[7,2,5,3,4,1,6]=>{{1,7},{2},{3,5},{4},{6}}
[7,3,5,2,1,6,4]=>[2,5,7,6,3,1,4]=>[7,2,5,6,3,4,1]=>{{1,7},{2},{3,5},{4,6}}
[7,3,5,2,4,1,6]=>[4,5,7,2,3,1,6]=>[7,5,4,2,1,3,6]=>{{1,7},{2,5},{3,4},{6}}
[7,3,5,2,4,6,1]=>[6,5,7,2,3,4,1]=>[6,7,5,2,3,1,4]=>{{1,6},{2,7},{3,5},{4}}
[7,3,5,2,6,1,4]=>[6,5,7,1,4,3,2]=>[6,7,5,3,1,2,4]=>{{1,6},{2,7},{3,5},{4}}
[7,3,5,2,6,4,1]=>[4,6,5,7,2,1,3]=>[7,5,6,4,2,3,1]=>{{1,7},{2,5},{3,6},{4}}
[7,3,5,4,1,2,6]=>[4,1,5,7,2,3,6]=>[7,1,5,4,3,2,6]=>{{1,7},{2},{3,5},{4},{6}}
[7,3,5,4,1,6,2]=>[4,5,6,7,3,1,2]=>[7,6,5,4,1,3,2]=>{{1,7},{2,6},{3,5},{4}}
[7,3,5,4,2,1,6]=>[2,4,5,7,1,3,6]=>[7,2,5,4,3,1,6]=>{{1,7},{2},{3,5},{4},{6}}
[7,3,5,4,2,6,1]=>[6,4,5,7,2,3,1]=>[5,7,6,4,2,1,3]=>{{1,5},{2,7},{3,6},{4}}
[7,3,5,4,6,1,2]=>[6,1,7,5,3,4,2]=>[6,1,5,7,3,2,4]=>{{1,6},{2},{3,5},{4,7}}
[7,3,5,4,6,2,1]=>[2,6,7,5,3,4,1]=>[6,2,5,7,3,1,4]=>{{1,6},{2},{3,5},{4,7}}
[7,3,5,6,1,2,4]=>[6,1,7,2,4,3,5]=>[7,1,6,3,2,5,4]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,5,6,1,4,2]=>[6,4,7,1,3,5,2]=>[6,7,4,3,1,2,5]=>{{1,6},{2,7},{3,4},{5}}
[7,3,5,6,2,1,4]=>[2,6,7,1,4,3,5]=>[7,2,6,3,1,5,4]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,5,6,2,4,1]=>[4,6,7,2,3,5,1]=>[7,6,4,2,1,3,5]=>{{1,7},{2,6},{3,4},{5}}
[7,3,5,6,4,1,2]=>[4,1,6,7,3,2,5]=>[7,1,6,4,2,5,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,5,6,4,2,1]=>[2,4,6,7,3,1,5]=>[7,2,6,4,1,5,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,1,2,4,5]=>[6,1,7,2,3,5,4]=>[7,1,6,3,4,2,5]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,1,2,5,4]=>[6,1,7,5,2,3,4]=>[6,1,5,7,4,3,2]=>{{1,6},{2},{3,5},{4,7}}
[7,3,6,1,4,2,5]=>[6,4,7,1,2,3,5]=>[6,7,4,3,2,5,1]=>{{1,6},{2,7},{3,4},{5}}
[7,3,6,1,4,5,2]=>[6,5,7,1,3,2,4]=>[6,7,5,3,2,4,1]=>{{1,6},{2,7},{3,5},{4}}
[7,3,6,1,5,2,4]=>[6,5,7,2,1,3,4]=>[6,7,5,2,4,3,1]=>{{1,6},{2,7},{3,5},{4}}
[7,3,6,1,5,4,2]=>[6,4,5,7,1,2,3]=>[5,7,6,4,3,2,1]=>{{1,5},{2,7},{3,6},{4}}
[7,3,6,2,1,4,5]=>[2,6,7,1,3,5,4]=>[7,2,6,3,4,1,5]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,2,1,5,4]=>[2,6,7,5,1,3,4]=>[6,2,5,7,4,3,1]=>{{1,6},{2},{3,5},{4,7}}
[7,3,6,2,4,1,5]=>[4,6,7,2,1,3,5]=>[7,6,4,2,3,5,1]=>{{1,7},{2,6},{3,4},{5}}
[7,3,6,2,4,5,1]=>[5,6,7,2,3,1,4]=>[7,6,5,2,3,4,1]=>{{1,7},{2,6},{3,5},{4}}
[7,3,6,2,5,1,4]=>[5,6,7,1,2,3,4]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,5},{4}}
[7,3,6,2,5,4,1]=>[4,5,6,7,1,2,3]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}
[7,3,6,4,1,2,5]=>[4,1,6,7,2,5,3]=>[7,1,6,4,3,2,5]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,4,1,5,2]=>[4,6,5,7,1,3,2]=>[7,5,6,4,3,1,2]=>{{1,7},{2,5},{3,6},{4}}
[7,3,6,4,2,1,5]=>[2,4,6,7,1,5,3]=>[7,2,6,4,3,1,5]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,4,2,5,1]=>[5,4,6,7,2,1,3]=>[6,7,5,4,2,3,1]=>{{1,6},{2,7},{3,5},{4}}
[7,3,6,4,5,1,2]=>[5,1,7,6,4,3,2]=>[7,1,5,6,2,3,4]=>{{1,7},{2},{3,5},{4,6}}
[7,3,6,4,5,2,1]=>[2,5,7,6,4,3,1]=>[7,2,5,6,1,3,4]=>{{1,7},{2},{3,5},{4,6}}
[7,3,6,5,1,2,4]=>[5,1,6,2,7,4,3]=>[7,1,6,3,5,2,4]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,5,1,4,2]=>[5,4,6,1,7,2,3]=>[6,7,4,3,5,2,1]=>{{1,6},{2,7},{3,4},{5}}
[7,3,6,5,2,1,4]=>[2,5,6,1,7,4,3]=>[7,2,6,3,5,1,4]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,5,2,4,1]=>[4,5,6,2,7,1,3]=>[7,6,4,2,5,3,1]=>{{1,7},{2,6},{3,4},{5}}
[7,3,6,5,4,1,2]=>[4,1,5,6,7,3,2]=>[7,1,6,4,5,2,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,3,6,5,4,2,1]=>[2,4,5,6,7,3,1]=>[7,2,6,4,5,1,3]=>{{1,7},{2},{3,6},{4},{5}}
[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[7,1,2,4,3,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,4,1,2,3,6,5]=>[4,1,2,7,6,3,5]=>[6,1,2,4,7,5,3]=>{{1,6},{2},{3},{4},{5,7}}
[7,4,1,2,5,3,6]=>[4,1,7,5,3,2,6]=>[7,1,4,5,2,3,6]=>{{1,7},{2},{3,4,5},{6}}
[7,4,1,2,5,6,3]=>[4,1,7,6,2,3,5]=>[7,1,4,6,3,5,2]=>{{1,7},{2},{3,4,6},{5}}
[7,4,1,2,6,3,5]=>[4,1,7,6,3,5,2]=>[7,1,4,6,2,3,5]=>{{1,7},{2},{3,4,6},{5}}
[7,4,1,2,6,5,3]=>[4,1,7,5,6,3,2]=>[7,1,4,5,6,2,3]=>{{1,7},{2},{3,4,5,6}}
[7,4,1,3,2,5,6]=>[4,3,1,7,2,5,6]=>[3,7,2,4,1,5,6]=>{{1,3},{2,7},{4},{5},{6}}
[7,4,1,3,2,6,5]=>[4,3,1,7,6,2,5]=>[3,6,2,4,7,5,1]=>{{1,3},{2,6},{4},{5,7}}
[7,4,1,3,5,2,6]=>[4,7,1,5,2,3,6]=>[7,4,2,5,3,1,6]=>{{1,7},{2,4,5},{3},{6}}
[7,4,1,3,5,6,2]=>[4,7,1,6,2,5,3]=>[7,4,2,6,3,1,5]=>{{1,7},{2,4,6},{3},{5}}
[7,4,1,3,6,2,5]=>[4,7,1,6,3,2,5]=>[7,4,2,6,1,5,3]=>{{1,7},{2,4,6},{3},{5}}
[7,4,1,3,6,5,2]=>[4,7,1,5,6,2,3]=>[7,4,2,5,6,3,1]=>{{1,7},{2,4,5,6},{3}}
[7,4,1,5,2,3,6]=>[4,7,2,5,3,1,6]=>[7,4,1,5,2,3,6]=>{{1,7},{2,4,5},{3},{6}}
[7,4,1,5,2,6,3]=>[4,7,5,6,1,2,3]=>[7,4,6,5,3,2,1]=>{{1,7},{2,4,5},{3,6}}
[7,4,1,5,3,2,6]=>[4,3,7,5,2,1,6]=>[4,7,3,5,1,2,6]=>{{1,4,5},{2,7},{3},{6}}
[7,4,1,5,3,6,2]=>[4,7,6,5,2,1,3]=>[7,4,5,6,2,3,1]=>{{1,7},{2,4,6},{3,5}}
[7,4,1,5,6,2,3]=>[4,7,2,6,1,3,5]=>[7,4,1,6,3,5,2]=>{{1,7},{2,4,6},{3},{5}}
[7,4,1,5,6,3,2]=>[4,3,7,6,1,2,5]=>[4,7,3,6,2,5,1]=>{{1,4,6},{2,7},{3},{5}}
[7,4,1,6,2,3,5]=>[4,7,2,6,3,5,1]=>[7,4,1,6,2,3,5]=>{{1,7},{2,4,6},{3},{5}}
[7,4,1,6,2,5,3]=>[4,7,6,5,3,2,1]=>[7,4,5,6,1,2,3]=>{{1,7},{2,4,6},{3,5}}
[7,4,1,6,3,2,5]=>[4,3,7,6,2,5,1]=>[4,7,3,6,1,2,5]=>{{1,4,6},{2,7},{3},{5}}
[7,4,1,6,3,5,2]=>[4,7,5,6,2,3,1]=>[7,4,6,5,2,1,3]=>{{1,7},{2,4,5},{3,6}}
[7,4,1,6,5,2,3]=>[4,7,2,5,6,3,1]=>[7,4,1,5,6,2,3]=>{{1,7},{2,4,5,6},{3}}
[7,4,1,6,5,3,2]=>[4,3,7,5,6,2,1]=>[4,7,3,5,6,1,2]=>{{1,4,5,6},{2,7},{3}}
[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[7,2,1,4,3,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,4,2,1,3,6,5]=>[2,4,1,7,6,3,5]=>[6,2,1,4,7,5,3]=>{{1,6},{2},{3},{4},{5,7}}
[7,4,2,1,5,3,6]=>[2,4,7,5,3,1,6]=>[7,2,4,5,1,3,6]=>{{1,7},{2},{3,4,5},{6}}
[7,4,2,1,5,6,3]=>[2,4,7,6,1,3,5]=>[7,2,4,6,3,5,1]=>{{1,7},{2},{3,4,6},{5}}
[7,4,2,1,6,3,5]=>[2,4,7,6,3,5,1]=>[7,2,4,6,1,3,5]=>{{1,7},{2},{3,4,6},{5}}
[7,4,2,1,6,5,3]=>[2,4,7,5,6,3,1]=>[7,2,4,5,6,1,3]=>{{1,7},{2},{3,4,5,6}}
[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[7,3,1,4,2,5,6]=>{{1,7},{2,3},{4},{5},{6}}
[7,4,2,3,1,6,5]=>[3,4,2,7,6,1,5]=>[6,3,1,4,7,5,2]=>{{1,6},{2,3},{4},{5,7}}
[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[5,7,1,4,2,3,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[6,7,1,4,2,3,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,4,2,3,6,1,5]=>[6,4,2,7,1,3,5]=>[6,7,1,4,3,5,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,4,2,3,6,5,1]=>[5,4,2,6,7,1,3]=>[6,7,1,4,5,3,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,4,2,5,1,3,6]=>[5,4,1,7,2,3,6]=>[5,7,2,4,3,1,6]=>{{1,5},{2,7},{3},{4},{6}}
[7,4,2,5,1,6,3]=>[5,4,7,6,2,3,1]=>[6,7,4,5,2,1,3]=>{{1,6},{2,7},{3,4,5}}
[7,4,2,5,3,1,6]=>[3,5,4,7,1,2,6]=>[7,3,5,4,2,1,6]=>{{1,7},{2,3,5},{4},{6}}
[7,4,2,5,3,6,1]=>[6,4,7,5,3,2,1]=>[5,7,4,6,1,2,3]=>{{1,5},{2,7},{3,4,6}}
[7,4,2,5,6,1,3]=>[6,4,1,7,3,2,5]=>[6,7,2,4,1,5,3]=>{{1,6},{2,7},{3},{4},{5}}
[7,4,2,5,6,3,1]=>[3,6,4,7,2,1,5]=>[7,3,6,4,1,5,2]=>{{1,7},{2,3,6},{4},{5}}
[7,4,2,6,1,3,5]=>[6,4,1,7,2,5,3]=>[6,7,2,4,3,1,5]=>{{1,6},{2,7},{3},{4},{5}}
[7,4,2,6,1,5,3]=>[6,4,7,5,1,3,2]=>[5,7,4,6,3,1,2]=>{{1,5},{2,7},{3,4,6}}
[7,4,2,6,3,1,5]=>[3,6,4,7,1,5,2]=>[7,3,6,4,2,1,5]=>{{1,7},{2,3,6},{4},{5}}
[7,4,2,6,3,5,1]=>[5,4,7,6,3,1,2]=>[6,7,4,5,1,3,2]=>{{1,6},{2,7},{3,4,5}}
[7,4,2,6,5,1,3]=>[5,4,1,6,7,3,2]=>[6,7,2,4,5,1,3]=>{{1,6},{2,7},{3},{4},{5}}
[7,4,2,6,5,3,1]=>[3,5,4,6,7,2,1]=>[7,3,6,4,5,1,2]=>{{1,7},{2,3,6},{4},{5}}
[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[7,1,3,4,2,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,4,3,1,2,6,5]=>[3,1,4,7,6,2,5]=>[6,1,3,4,7,5,2]=>{{1,6},{2},{3},{4},{5,7}}
[7,4,3,1,5,2,6]=>[3,4,7,5,1,2,6]=>[7,4,3,5,2,1,6]=>{{1,7},{2,4,5},{3},{6}}
[7,4,3,1,5,6,2]=>[3,4,7,6,1,5,2]=>[7,4,3,6,2,1,5]=>{{1,7},{2,4,6},{3},{5}}
[7,4,3,1,6,2,5]=>[3,4,7,6,2,1,5]=>[7,4,3,6,1,5,2]=>{{1,7},{2,4,6},{3},{5}}
[7,4,3,1,6,5,2]=>[3,4,7,5,6,1,2]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}
[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,4,3,2,1,6,5]=>[2,3,4,7,6,1,5]=>[6,2,3,4,7,5,1]=>{{1,6},{2},{3},{4},{5,7}}
[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[3,7,5,4,1,2,6]=>{{1,3,5},{2,7},{4},{6}}
[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[3,7,6,4,1,2,5]=>{{1,3,6},{2,7},{4},{5}}
[7,4,3,2,6,1,5]=>[6,3,4,7,1,2,5]=>[3,7,6,4,2,5,1]=>{{1,3,6},{2,7},{4},{5}}
[7,4,3,2,6,5,1]=>[5,3,4,6,7,1,2]=>[3,7,6,4,5,2,1]=>{{1,3,6},{2,7},{4},{5}}
[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[5,1,7,4,2,3,6]=>{{1,5},{2},{3,7},{4},{6}}
[7,4,3,5,1,6,2]=>[5,6,4,7,3,1,2]=>[6,5,7,4,1,3,2]=>{{1,6},{2,5},{3,7},{4}}
[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[5,2,7,4,1,3,6]=>{{1,5},{2},{3,7},{4},{6}}
[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[5,6,7,4,1,2,3]=>{{1,5},{2,6},{3,7},{4}}
[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[6,1,7,4,2,3,5]=>{{1,6},{2},{3,7},{4},{5}}
[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[6,2,7,4,1,3,5]=>{{1,6},{2},{3,7},{4},{5}}
[7,4,3,6,1,2,5]=>[6,1,4,7,2,3,5]=>[6,1,7,4,3,5,2]=>{{1,6},{2},{3,7},{4},{5}}
[7,4,3,6,1,5,2]=>[6,5,4,7,1,3,2]=>[5,6,7,4,3,1,2]=>{{1,5},{2,6},{3,7},{4}}
[7,4,3,6,2,1,5]=>[2,6,4,7,1,3,5]=>[6,2,7,4,3,5,1]=>{{1,6},{2},{3,7},{4},{5}}
[7,4,3,6,2,5,1]=>[5,6,4,7,2,3,1]=>[6,5,7,4,2,1,3]=>{{1,6},{2,5},{3,7},{4}}
[7,4,3,6,5,1,2]=>[5,1,4,6,7,2,3]=>[6,1,7,4,5,3,2]=>{{1,6},{2},{3,7},{4},{5}}
[7,4,3,6,5,2,1]=>[2,5,4,6,7,1,3]=>[6,2,7,4,5,3,1]=>{{1,6},{2},{3,7},{4},{5}}
[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[7,1,2,5,3,4,6]=>{{1,7},{2},{3},{4,5},{6}}
[7,4,5,1,2,6,3]=>[5,1,6,7,4,2,3]=>[7,1,6,5,2,4,3]=>{{1,7},{2},{3,6},{4,5}}
[7,4,5,1,3,2,6]=>[5,3,1,7,4,2,6]=>[3,7,2,5,1,4,6]=>{{1,3},{2,7},{4,5},{6}}
[7,4,5,1,3,6,2]=>[5,6,1,7,4,3,2]=>[7,6,2,5,1,3,4]=>{{1,7},{2,6},{3},{4,5}}
[7,4,5,1,6,2,3]=>[5,6,2,7,4,1,3]=>[7,6,1,5,2,4,3]=>{{1,7},{2,6},{3},{4,5}}
[7,4,5,1,6,3,2]=>[5,3,6,7,4,1,2]=>[6,7,3,5,1,4,2]=>{{1,6},{2,7},{3},{4,5}}
[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[7,2,1,5,3,4,6]=>{{1,7},{2},{3},{4,5},{6}}
[7,4,5,2,1,6,3]=>[2,5,6,7,4,1,3]=>[7,2,6,5,1,4,3]=>{{1,7},{2},{3,6},{4,5}}
[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[7,3,1,5,2,4,6]=>{{1,7},{2,3},{4,5},{6}}
[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[6,7,1,5,2,3,4]=>{{1,6},{2,7},{3},{4,5}}
[7,4,5,2,6,1,3]=>[6,5,1,7,4,2,3]=>[6,7,2,5,1,4,3]=>{{1,6},{2,7},{3},{4,5}}
[7,4,5,2,6,3,1]=>[3,6,5,7,4,1,2]=>[7,3,6,5,1,4,2]=>{{1,7},{2,3,6},{4,5}}
[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[7,1,3,5,2,4,6]=>{{1,7},{2},{3},{4,5},{6}}
[7,4,5,3,1,6,2]=>[3,5,6,7,4,2,1]=>[7,6,3,5,1,2,4]=>{{1,7},{2,6},{3},{4,5}}
[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[7,2,3,5,1,4,6]=>{{1,7},{2},{3},{4,5},{6}}
[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[3,7,6,5,1,2,4]=>{{1,3,6},{2,7},{4,5}}
[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[6,1,7,5,2,3,4]=>{{1,6},{2},{3,7},{4,5}}
[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[6,2,7,5,1,3,4]=>{{1,6},{2},{3,7},{4,5}}
[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[7,1,2,6,3,4,5]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,5,6,1,3,2]=>[6,3,1,7,4,5,2]=>[3,7,2,6,1,4,5]=>{{1,3},{2,7},{4,6},{5}}
[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[7,2,1,6,3,4,5]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[7,3,1,6,2,4,5]=>{{1,7},{2,3},{4,6},{5}}
[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[7,1,3,6,2,4,5]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[7,2,3,6,1,4,5]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,1,2,3,5]=>[6,1,2,7,3,4,5]=>[7,1,2,6,4,5,3]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,1,2,5,3]=>[6,1,5,7,2,4,3]=>[6,1,7,5,4,2,3]=>{{1,6},{2},{3,7},{4,5}}
[7,4,6,1,3,2,5]=>[6,3,1,7,2,4,5]=>[3,7,2,6,4,5,1]=>{{1,3},{2,7},{4,6},{5}}
[7,4,6,1,3,5,2]=>[6,5,1,7,3,4,2]=>[6,7,2,5,3,1,4]=>{{1,6},{2,7},{3},{4,5}}
[7,4,6,1,5,2,3]=>[6,5,2,7,1,4,3]=>[6,7,1,5,4,2,3]=>{{1,6},{2,7},{3},{4,5}}
[7,4,6,1,5,3,2]=>[6,3,5,7,1,4,2]=>[3,7,6,5,4,1,2]=>{{1,3,6},{2,7},{4,5}}
[7,4,6,2,1,3,5]=>[2,6,1,7,3,4,5]=>[7,2,1,6,4,5,3]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,2,1,5,3]=>[2,6,5,7,1,4,3]=>[6,2,7,5,4,1,3]=>{{1,6},{2},{3,7},{4,5}}
[7,4,6,2,3,1,5]=>[3,6,2,7,1,4,5]=>[7,3,1,6,4,5,2]=>{{1,7},{2,3},{4,6},{5}}
[7,4,6,2,3,5,1]=>[5,6,2,7,3,4,1]=>[7,6,1,5,3,2,4]=>{{1,7},{2,6},{3},{4,5}}
[7,4,6,2,5,1,3]=>[5,6,1,7,2,4,3]=>[7,6,2,5,4,1,3]=>{{1,7},{2,6},{3},{4,5}}
[7,4,6,2,5,3,1]=>[3,5,6,7,1,4,2]=>[7,6,3,5,4,1,2]=>{{1,7},{2,6},{3},{4,5}}
[7,4,6,3,1,2,5]=>[3,1,6,7,2,4,5]=>[7,1,3,6,4,5,2]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,3,1,5,2]=>[3,6,5,7,2,4,1]=>[7,3,6,5,2,1,4]=>{{1,7},{2,3,6},{4,5}}
[7,4,6,3,2,1,5]=>[2,3,6,7,1,4,5]=>[7,2,3,6,4,5,1]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,3,2,5,1]=>[5,3,6,7,2,4,1]=>[6,7,3,5,2,1,4]=>{{1,6},{2,7},{3},{4,5}}
[7,4,6,3,5,1,2]=>[5,1,6,7,3,4,2]=>[7,1,6,5,3,2,4]=>{{1,7},{2},{3,6},{4,5}}
[7,4,6,3,5,2,1]=>[2,5,6,7,3,4,1]=>[7,2,6,5,3,1,4]=>{{1,7},{2},{3,6},{4,5}}
[7,4,6,5,1,2,3]=>[5,1,2,6,7,3,4]=>[7,1,2,6,5,4,3]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,5,1,3,2]=>[5,3,1,6,7,2,4]=>[3,7,2,6,5,4,1]=>{{1,3},{2,7},{4,6},{5}}
[7,4,6,5,2,1,3]=>[2,5,1,6,7,3,4]=>[7,2,1,6,5,4,3]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,5,2,3,1]=>[3,5,2,6,7,1,4]=>[7,3,1,6,5,4,2]=>{{1,7},{2,3},{4,6},{5}}
[7,4,6,5,3,1,2]=>[3,1,5,6,7,2,4]=>[7,1,3,6,5,4,2]=>{{1,7},{2},{3},{4,6},{5}}
[7,4,6,5,3,2,1]=>[2,3,5,6,7,1,4]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}}
[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[7,1,2,3,5,4,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,1,2,3,6,4]=>[5,1,2,7,6,4,3]=>[7,1,2,5,6,3,4]=>{{1,7},{2},{3},{4,5,6}}
[7,5,1,2,4,3,6]=>[5,1,4,2,7,3,6]=>[4,1,7,3,5,2,6]=>{{1,4},{2},{3,7},{5},{6}}
[7,5,1,2,4,6,3]=>[5,1,7,2,6,3,4]=>[7,1,5,3,6,4,2]=>{{1,7},{2},{3,5,6},{4}}
[7,5,1,2,6,3,4]=>[5,1,7,3,6,4,2]=>[7,1,5,2,6,3,4]=>{{1,7},{2},{3,5,6},{4}}
[7,5,1,2,6,4,3]=>[5,1,4,7,6,3,2]=>[5,1,7,4,6,2,3]=>{{1,5,6},{2},{3,7},{4}}
[7,5,1,3,2,4,6]=>[5,3,1,2,7,4,6]=>[3,7,2,1,5,4,6]=>{{1,3},{2,7},{4},{5},{6}}
[7,5,1,3,2,6,4]=>[5,3,1,7,6,4,2]=>[3,7,2,5,6,1,4]=>{{1,3},{2,7},{4,5,6}}
[7,5,1,3,4,2,6]=>[5,4,1,3,7,2,6]=>[4,7,2,1,5,3,6]=>{{1,4},{2,7},{3},{5},{6}}
[7,5,1,3,4,6,2]=>[5,7,1,2,6,4,3]=>[7,5,2,3,6,1,4]=>{{1,7},{2,5,6},{3},{4}}
[7,5,1,3,6,2,4]=>[5,7,1,3,6,2,4]=>[7,5,2,1,6,4,3]=>{{1,7},{2,5,6},{3},{4}}
[7,5,1,3,6,4,2]=>[5,4,1,7,6,2,3]=>[5,7,2,4,6,3,1]=>{{1,5,6},{2,7},{3},{4}}
[7,5,1,4,2,3,6]=>[5,4,2,1,7,3,6]=>[4,7,1,3,5,2,6]=>{{1,4},{2,7},{3},{5},{6}}
[7,5,1,4,2,6,3]=>[5,4,7,1,6,3,2]=>[5,7,4,3,6,1,2]=>{{1,5,6},{2,7},{3,4}}
[7,5,1,4,3,2,6]=>[5,3,4,1,7,2,6]=>[3,7,4,2,5,1,6]=>{{1,3,4},{2,7},{5},{6}}
[7,5,1,4,3,6,2]=>[5,7,4,1,6,2,3]=>[5,4,7,3,6,2,1]=>{{1,5,6},{2,4},{3,7}}
[7,5,1,4,6,2,3]=>[5,7,2,1,6,3,4]=>[7,5,1,3,6,4,2]=>{{1,7},{2,5,6},{3},{4}}
[7,5,1,4,6,3,2]=>[5,3,7,1,6,2,4]=>[5,7,3,2,6,4,1]=>{{1,5,6},{2,7},{3},{4}}
[7,5,1,6,2,3,4]=>[5,7,2,3,6,4,1]=>[7,5,1,2,6,3,4]=>{{1,7},{2,5,6},{3},{4}}
[7,5,1,6,2,4,3]=>[5,7,4,2,6,3,1]=>[5,4,7,2,6,1,3]=>{{1,5,6},{2,4},{3,7}}
[7,5,1,6,3,2,4]=>[5,3,7,2,6,4,1]=>[5,7,3,1,6,2,4]=>{{1,5,6},{2,7},{3},{4}}
[7,5,1,6,3,4,2]=>[5,4,7,3,6,2,1]=>[5,7,4,1,6,2,3]=>{{1,5,6},{2,7},{3,4}}
[7,5,1,6,4,2,3]=>[5,4,2,7,6,3,1]=>[5,7,1,4,6,2,3]=>{{1,5,6},{2,7},{3},{4}}
[7,5,1,6,4,3,2]=>[5,3,4,7,6,2,1]=>[3,7,5,4,6,1,2]=>{{1,3,5,6},{2,7},{4}}
[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[7,2,1,3,5,4,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,2,1,3,6,4]=>[2,5,1,7,6,4,3]=>[7,2,1,5,6,3,4]=>{{1,7},{2},{3},{4,5,6}}
[7,5,2,1,4,3,6]=>[2,5,4,1,7,3,6]=>[4,2,7,3,5,1,6]=>{{1,4},{2},{3,7},{5},{6}}
[7,5,2,1,4,6,3]=>[2,5,7,1,6,3,4]=>[7,2,5,3,6,4,1]=>{{1,7},{2},{3,5,6},{4}}
[7,5,2,1,6,3,4]=>[2,5,7,3,6,4,1]=>[7,2,5,1,6,3,4]=>{{1,7},{2},{3,5,6},{4}}
[7,5,2,1,6,4,3]=>[2,5,4,7,6,3,1]=>[5,2,7,4,6,1,3]=>{{1,5,6},{2},{3,7},{4}}
[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[7,3,1,2,5,4,6]=>{{1,7},{2,3},{4},{5},{6}}
[7,5,2,3,1,6,4]=>[3,5,2,7,6,4,1]=>[7,3,1,5,6,2,4]=>{{1,7},{2,3},{4,5,6}}
[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[7,4,1,2,5,3,6]=>{{1,7},{2,4},{3},{5},{6}}
[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[6,7,1,2,5,3,4]=>{{1,6},{2,7},{3},{4},{5}}
[7,5,2,3,6,1,4]=>[6,5,2,1,7,3,4]=>[6,7,1,3,5,4,2]=>{{1,6},{2,7},{3},{4},{5}}
[7,5,2,3,6,4,1]=>[4,6,2,5,7,1,3]=>[7,4,1,6,5,3,2]=>{{1,7},{2,4,6},{3},{5}}
[7,5,2,4,1,3,6]=>[4,5,1,2,7,3,6]=>[7,4,2,3,5,1,6]=>{{1,7},{2,4},{3},{5},{6}}
[7,5,2,4,1,6,3]=>[4,5,7,2,6,3,1]=>[7,5,4,2,6,1,3]=>{{1,7},{2,5,6},{3,4}}
[7,5,2,4,3,1,6]=>[3,4,5,1,7,2,6]=>[7,4,3,2,5,1,6]=>{{1,7},{2,4},{3},{5},{6}}
[7,5,2,4,3,6,1]=>[6,5,4,2,7,3,1]=>[4,6,7,2,5,1,3]=>{{1,4},{2,6},{3,7},{5}}
[7,5,2,4,6,1,3]=>[6,5,1,3,7,2,4]=>[6,7,2,1,5,4,3]=>{{1,6},{2,7},{3},{4},{5}}
[7,5,2,4,6,3,1]=>[3,6,5,2,7,1,4]=>[7,3,6,1,5,4,2]=>{{1,7},{2,3,6},{4},{5}}
[7,5,2,6,1,3,4]=>[6,5,1,2,7,4,3]=>[6,7,2,3,5,1,4]=>{{1,6},{2,7},{3},{4},{5}}
[7,5,2,6,1,4,3]=>[6,5,4,1,7,2,3]=>[4,6,7,3,5,2,1]=>{{1,4},{2,6},{3,7},{5}}
[7,5,2,6,3,1,4]=>[3,6,5,1,7,4,2]=>[7,3,6,2,5,1,4]=>{{1,7},{2,3,6},{4},{5}}
[7,5,2,6,3,4,1]=>[4,5,7,3,6,1,2]=>[7,5,4,1,6,3,2]=>{{1,7},{2,5,6},{3,4}}
[7,5,2,6,4,1,3]=>[4,6,1,5,7,3,2]=>[7,4,2,6,5,1,3]=>{{1,7},{2,4,6},{3},{5}}
[7,5,2,6,4,3,1]=>[3,4,6,5,7,2,1]=>[7,4,3,6,5,1,2]=>{{1,7},{2,4,6},{3},{5}}
[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[7,1,3,2,5,4,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,3,1,2,6,4]=>[3,1,5,7,6,4,2]=>[7,1,3,5,6,2,4]=>{{1,7},{2},{3},{4,5,6}}
[7,5,3,1,4,2,6]=>[3,5,4,2,7,1,6]=>[7,3,4,1,5,2,6]=>{{1,7},{2,3,4},{5},{6}}
[7,5,3,1,4,6,2]=>[3,5,7,1,6,4,2]=>[7,5,3,2,6,1,4]=>{{1,7},{2,5,6},{3},{4}}
[7,5,3,1,6,2,4]=>[3,5,7,2,6,1,4]=>[7,5,3,1,6,4,2]=>{{1,7},{2,5,6},{3},{4}}
[7,5,3,1,6,4,2]=>[3,5,4,7,6,1,2]=>[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}}
[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[7,2,3,1,5,4,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,3,2,1,6,4]=>[2,3,5,7,6,4,1]=>[7,2,3,5,6,1,4]=>{{1,7},{2},{3},{4,5,6}}
[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[4,7,3,1,5,2,6]=>{{1,4},{2,7},{3},{5},{6}}
[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[3,7,6,1,5,2,4]=>{{1,3,6},{2,7},{4},{5}}
[7,5,3,2,6,1,4]=>[6,3,5,1,7,2,4]=>[3,7,6,2,5,4,1]=>{{1,3,6},{2,7},{4},{5}}
[7,5,3,2,6,4,1]=>[4,3,6,5,7,1,2]=>[4,7,3,6,5,2,1]=>{{1,4,6},{2,7},{3},{5}}
[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[7,1,4,2,5,3,6]=>{{1,7},{2},{3,4},{5},{6}}
[7,5,3,4,1,6,2]=>[4,6,5,3,7,1,2]=>[7,4,6,1,5,3,2]=>{{1,7},{2,4},{3,6},{5}}
[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[7,2,4,1,5,3,6]=>{{1,7},{2},{3,4},{5},{6}}
[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[4,7,6,1,5,2,3]=>{{1,4},{2,7},{3,6},{5}}
[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[6,1,7,2,5,3,4]=>{{1,6},{2},{3,7},{4},{5}}
[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[6,2,7,1,5,3,4]=>{{1,6},{2},{3,7},{4},{5}}
[7,5,3,6,1,2,4]=>[6,1,5,2,7,3,4]=>[6,1,7,3,5,4,2]=>{{1,6},{2},{3,7},{4},{5}}
[7,5,3,6,1,4,2]=>[6,4,5,1,7,3,2]=>[4,7,6,3,5,1,2]=>{{1,4},{2,7},{3,6},{5}}
[7,5,3,6,2,1,4]=>[2,6,5,1,7,3,4]=>[6,2,7,3,5,4,1]=>{{1,6},{2},{3,7},{4},{5}}
[7,5,3,6,2,4,1]=>[4,6,5,2,7,3,1]=>[7,4,6,2,5,1,3]=>{{1,7},{2,4},{3,6},{5}}
[7,5,3,6,4,1,2]=>[4,1,6,5,7,2,3]=>[7,1,4,6,5,3,2]=>{{1,7},{2},{3,4,6},{5}}
[7,5,3,6,4,2,1]=>[2,4,6,5,7,1,3]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}}
[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[7,1,2,4,5,3,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,4,1,2,6,3]=>[4,1,5,7,6,2,3]=>[7,1,5,4,6,3,2]=>{{1,7},{2},{3,5,6},{4}}
[7,5,4,1,3,2,6]=>[4,3,1,5,7,2,6]=>[3,7,2,4,5,1,6]=>{{1,3},{2,7},{4},{5},{6}}
[7,5,4,1,3,6,2]=>[4,5,1,7,6,3,2]=>[7,5,2,4,6,1,3]=>{{1,7},{2,5,6},{3},{4}}
[7,5,4,1,6,2,3]=>[4,5,2,7,6,1,3]=>[7,5,1,4,6,3,2]=>{{1,7},{2,5,6},{3},{4}}
[7,5,4,1,6,3,2]=>[4,3,5,7,6,1,2]=>[5,7,3,4,6,2,1]=>{{1,5,6},{2,7},{3},{4}}
[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[7,2,1,4,5,3,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,4,2,1,6,3]=>[2,4,5,7,6,1,3]=>[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}}
[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[7,3,1,4,5,2,6]=>{{1,7},{2,3},{4},{5},{6}}
[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[4,7,1,6,5,2,3]=>{{1,4,6},{2,7},{3},{5}}
[7,5,4,2,6,1,3]=>[6,4,1,5,7,2,3]=>[4,7,2,6,5,3,1]=>{{1,4,6},{2,7},{3},{5}}
[7,5,4,2,6,3,1]=>[3,6,4,5,7,1,2]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[7,1,3,4,5,2,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,4,3,1,6,2]=>[3,4,5,7,6,2,1]=>[7,5,3,4,6,1,2]=>{{1,7},{2,5,6},{3},{4}}
[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>{{1,7},{2},{3},{4},{5},{6}}
[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[3,7,4,6,5,1,2]=>{{1,3,4,6},{2,7},{5}}
[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[4,1,7,6,5,2,3]=>{{1,4,6},{2},{3,7},{5}}
[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[4,2,7,6,5,1,3]=>{{1,4,6},{2},{3,7},{5}}
[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[6,1,2,7,5,3,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,5,4,6,1,3,2]=>[6,3,1,5,7,4,2]=>[3,6,2,7,5,1,4]=>{{1,3},{2,6},{4,7},{5}}
[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[6,2,1,7,5,3,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[6,3,1,7,5,2,4]=>{{1,6},{2,3},{4,7},{5}}
[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[6,1,3,7,5,2,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[6,2,3,7,5,1,4]=>{{1,6},{2},{3},{4,7},{5}}
[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[7,1,2,3,6,4,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,1,2,4,3]=>[6,1,4,2,7,5,3]=>[4,1,7,3,6,2,5]=>{{1,4},{2},{3,7},{5,6}}
[7,5,6,1,3,2,4]=>[6,3,1,2,7,5,4]=>[3,7,2,1,6,4,5]=>{{1,3},{2,7},{4},{5,6}}
[7,5,6,1,3,4,2]=>[6,4,1,3,7,5,2]=>[4,7,2,1,6,3,5]=>{{1,4},{2,7},{3},{5,6}}
[7,5,6,1,4,2,3]=>[6,4,2,1,7,5,3]=>[4,7,1,3,6,2,5]=>{{1,4},{2,7},{3},{5,6}}
[7,5,6,1,4,3,2]=>[6,3,4,1,7,5,2]=>[3,7,4,2,6,1,5]=>{{1,3,4},{2,7},{5,6}}
[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[7,2,1,3,6,4,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,2,1,4,3]=>[2,6,4,1,7,5,3]=>[4,2,7,3,6,1,5]=>{{1,4},{2},{3,7},{5,6}}
[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[7,3,1,2,6,4,5]=>{{1,7},{2,3},{4},{5,6}}
[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[7,4,1,2,6,3,5]=>{{1,7},{2,4},{3},{5,6}}
[7,5,6,2,4,1,3]=>[4,6,1,2,7,5,3]=>[7,4,2,3,6,1,5]=>{{1,7},{2,4},{3},{5,6}}
[7,5,6,2,4,3,1]=>[3,4,6,1,7,5,2]=>[7,4,3,2,6,1,5]=>{{1,7},{2,4},{3},{5,6}}
[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[7,1,3,2,6,4,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,3,1,4,2]=>[3,6,4,2,7,5,1]=>[7,3,4,1,6,2,5]=>{{1,7},{2,3,4},{5,6}}
[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[7,2,3,1,6,4,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[4,7,3,1,6,2,5]=>{{1,4},{2,7},{3},{5,6}}
[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[7,1,4,2,6,3,5]=>{{1,7},{2},{3,4},{5,6}}
[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[7,2,4,1,6,3,5]=>{{1,7},{2},{3,4},{5,6}}
[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[7,1,2,4,6,3,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,4,1,3,2]=>[4,3,1,6,7,5,2]=>[3,7,2,4,6,1,5]=>{{1,3},{2,7},{4},{5,6}}
[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[7,2,1,4,6,3,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[7,3,1,4,6,2,5]=>{{1,7},{2,3},{4},{5,6}}
[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[7,1,3,4,6,2,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>{{1,7},{2},{3},{4},{5,6}}
[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[7,1,2,3,4,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,1,2,3,5,4]=>[6,1,2,5,3,7,4]=>[5,1,2,7,4,6,3]=>{{1,5},{2},{3},{4,7},{6}}
[7,6,1,2,4,3,5]=>[6,1,4,2,3,7,5]=>[4,1,7,3,2,6,5]=>{{1,4},{2},{3,7},{5},{6}}
[7,6,1,2,4,5,3]=>[6,1,5,2,4,7,3]=>[5,1,7,3,2,6,4]=>{{1,5},{2},{3,7},{4},{6}}
[7,6,1,2,5,3,4]=>[6,1,5,3,2,7,4]=>[5,1,7,2,4,6,3]=>{{1,5},{2},{3,7},{4},{6}}
[7,6,1,2,5,4,3]=>[6,1,4,5,2,7,3]=>[4,1,7,5,3,6,2]=>{{1,4,5},{2},{3,7},{6}}
[7,6,1,3,2,4,5]=>[6,3,1,2,4,7,5]=>[3,7,2,1,4,6,5]=>{{1,3},{2,7},{4},{5},{6}}
[7,6,1,3,2,5,4]=>[6,3,1,5,2,7,4]=>[3,5,2,7,4,6,1]=>{{1,3},{2,5},{4,7},{6}}
[7,6,1,3,4,2,5]=>[6,4,1,3,2,7,5]=>[4,7,2,1,3,6,5]=>{{1,4},{2,7},{3},{5},{6}}
[7,6,1,3,4,5,2]=>[6,5,1,2,3,7,4]=>[5,7,2,3,4,6,1]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,1,3,5,2,4]=>[6,5,1,3,4,7,2]=>[5,7,2,1,3,6,4]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,1,3,5,4,2]=>[6,4,1,5,3,7,2]=>[4,7,2,5,1,6,3]=>{{1,4,5},{2,7},{3},{6}}
[7,6,1,4,2,3,5]=>[6,4,2,1,3,7,5]=>[4,7,1,3,2,6,5]=>{{1,4},{2,7},{3},{5},{6}}
[7,6,1,4,2,5,3]=>[6,4,5,1,2,7,3]=>[4,7,5,3,2,6,1]=>{{1,4},{2,7},{3,5},{6}}
[7,6,1,4,3,2,5]=>[6,3,4,1,2,7,5]=>[3,7,4,2,1,6,5]=>{{1,3,4},{2,7},{5},{6}}
[7,6,1,4,3,5,2]=>[6,5,4,1,3,7,2]=>[4,5,7,3,1,6,2]=>{{1,4},{2,5},{3,7},{6}}
[7,6,1,4,5,2,3]=>[6,5,2,1,4,7,3]=>[5,7,1,3,2,6,4]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,1,4,5,3,2]=>[6,3,5,1,4,7,2]=>[3,7,5,2,1,6,4]=>{{1,3,5},{2,7},{4},{6}}
[7,6,1,5,2,3,4]=>[6,5,2,3,1,7,4]=>[5,7,1,2,4,6,3]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,1,5,2,4,3]=>[6,5,4,2,1,7,3]=>[4,5,7,2,3,6,1]=>{{1,4},{2,5},{3,7},{6}}
[7,6,1,5,3,2,4]=>[6,3,5,2,1,7,4]=>[3,7,5,1,4,6,2]=>{{1,3,5},{2,7},{4},{6}}
[7,6,1,5,3,4,2]=>[6,4,5,3,1,7,2]=>[4,7,5,1,3,6,2]=>{{1,4},{2,7},{3,5},{6}}
[7,6,1,5,4,2,3]=>[6,4,2,5,1,7,3]=>[4,7,1,5,3,6,2]=>{{1,4,5},{2,7},{3},{6}}
[7,6,1,5,4,3,2]=>[6,3,4,5,1,7,2]=>[3,7,4,5,2,6,1]=>{{1,3,4,5},{2,7},{6}}
[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[7,2,1,3,4,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,2,1,3,5,4]=>[2,6,1,5,3,7,4]=>[5,2,1,7,4,6,3]=>{{1,5},{2},{3},{4,7},{6}}
[7,6,2,1,4,3,5]=>[2,6,4,1,3,7,5]=>[4,2,7,3,1,6,5]=>{{1,4},{2},{3,7},{5},{6}}
[7,6,2,1,4,5,3]=>[2,6,5,1,4,7,3]=>[5,2,7,3,1,6,4]=>{{1,5},{2},{3,7},{4},{6}}
[7,6,2,1,5,3,4]=>[2,6,5,3,1,7,4]=>[5,2,7,1,4,6,3]=>{{1,5},{2},{3,7},{4},{6}}
[7,6,2,1,5,4,3]=>[2,6,4,5,1,7,3]=>[4,2,7,5,3,6,1]=>{{1,4,5},{2},{3,7},{6}}
[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[7,3,1,2,4,6,5]=>{{1,7},{2,3},{4},{5},{6}}
[7,6,2,3,1,5,4]=>[3,6,2,5,1,7,4]=>[5,3,1,7,4,6,2]=>{{1,5},{2,3},{4,7},{6}}
[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[7,4,1,2,3,6,5]=>{{1,7},{2,4},{3},{5},{6}}
[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[7,5,1,2,3,6,4]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,3,5,1,4]=>[5,6,2,1,3,7,4]=>[7,5,1,3,4,6,2]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,3,5,4,1]=>[4,5,2,6,1,7,3]=>[7,5,1,4,3,6,2]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,4,1,3,5]=>[4,6,1,2,3,7,5]=>[7,4,2,3,1,6,5]=>{{1,7},{2,4},{3},{5},{6}}
[7,6,2,4,1,5,3]=>[4,6,5,2,1,7,3]=>[7,4,5,2,3,6,1]=>{{1,7},{2,4},{3,5},{6}}
[7,6,2,4,3,1,5]=>[3,4,6,1,2,7,5]=>[7,4,3,2,1,6,5]=>{{1,7},{2,4},{3},{5},{6}}
[7,6,2,4,3,5,1]=>[5,6,4,2,3,7,1]=>[5,4,7,2,1,6,3]=>{{1,5},{2,4},{3,7},{6}}
[7,6,2,4,5,1,3]=>[5,6,1,3,2,7,4]=>[7,5,2,1,4,6,3]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,4,5,3,1]=>[3,5,6,2,1,7,4]=>[7,5,3,1,4,6,2]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,5,1,3,4]=>[5,6,1,2,4,7,3]=>[7,5,2,3,1,6,4]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,5,1,4,3]=>[5,6,4,1,2,7,3]=>[5,4,7,3,2,6,1]=>{{1,5},{2,4},{3,7},{6}}
[7,6,2,5,3,1,4]=>[3,5,6,1,4,7,2]=>[7,5,3,2,1,6,4]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,5,3,4,1]=>[4,6,5,3,2,7,1]=>[7,4,5,1,2,6,3]=>{{1,7},{2,4},{3,5},{6}}
[7,6,2,5,4,1,3]=>[4,5,1,6,3,7,2]=>[7,5,2,4,1,6,3]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,2,5,4,3,1]=>[3,4,5,6,2,7,1]=>[7,5,3,4,1,6,2]=>{{1,7},{2,5},{3},{4},{6}}
[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[7,1,3,2,4,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,3,1,2,5,4]=>[3,1,6,5,2,7,4]=>[5,1,3,7,4,6,2]=>{{1,5},{2},{3},{4,7},{6}}
[7,6,3,1,4,2,5]=>[3,6,4,2,1,7,5]=>[7,3,4,1,2,6,5]=>{{1,7},{2,3,4},{5},{6}}
[7,6,3,1,4,5,2]=>[3,6,5,1,2,7,4]=>[7,3,5,2,4,6,1]=>{{1,7},{2,3,5},{4},{6}}
[7,6,3,1,5,2,4]=>[3,6,5,2,4,7,1]=>[7,3,5,1,2,6,4]=>{{1,7},{2,3,5},{4},{6}}
[7,6,3,1,5,4,2]=>[3,6,4,5,2,7,1]=>[7,3,4,5,1,6,2]=>{{1,7},{2,3,4,5},{6}}
[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[7,2,3,1,4,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,3,2,1,5,4]=>[2,3,6,5,1,7,4]=>[5,2,3,7,4,6,1]=>{{1,5},{2},{3},{4,7},{6}}
[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[4,7,3,1,2,6,5]=>{{1,4},{2,7},{3},{5},{6}}
[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[5,7,3,1,2,6,4]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,3,2,5,1,4]=>[5,3,6,1,2,7,4]=>[5,7,3,2,4,6,1]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,3,2,5,4,1]=>[4,3,5,6,1,7,2]=>[5,7,3,4,2,6,1]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[7,1,4,2,3,6,5]=>{{1,7},{2},{3,4},{5},{6}}
[7,6,3,4,1,5,2]=>[4,5,6,3,1,7,2]=>[7,5,4,1,3,6,2]=>{{1,7},{2,5},{3,4},{6}}
[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[7,2,4,1,3,6,5]=>{{1,7},{2},{3,4},{5},{6}}
[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[5,7,4,1,2,6,3]=>{{1,5},{2,7},{3,4},{6}}
[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[7,1,5,2,3,6,4]=>{{1,7},{2},{3,5},{4},{6}}
[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[7,2,5,1,3,6,4]=>{{1,7},{2},{3,5},{4},{6}}
[7,6,3,5,1,2,4]=>[5,1,6,2,3,7,4]=>[7,1,5,3,4,6,2]=>{{1,7},{2},{3,5},{4},{6}}
[7,6,3,5,1,4,2]=>[5,4,6,1,3,7,2]=>[5,7,4,3,1,6,2]=>{{1,5},{2,7},{3,4},{6}}
[7,6,3,5,2,1,4]=>[2,5,6,1,3,7,4]=>[7,2,5,3,4,6,1]=>{{1,7},{2},{3,5},{4},{6}}
[7,6,3,5,2,4,1]=>[4,5,6,2,3,7,1]=>[7,5,4,2,1,6,3]=>{{1,7},{2,5},{3,4},{6}}
[7,6,3,5,4,1,2]=>[4,1,5,6,2,7,3]=>[7,1,5,4,3,6,2]=>{{1,7},{2},{3,5},{4},{6}}
[7,6,3,5,4,2,1]=>[2,4,5,6,1,7,3]=>[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}}
[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[7,1,2,4,3,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,4,1,2,5,3]=>[4,1,6,5,3,7,2]=>[7,1,4,5,2,6,3]=>{{1,7},{2},{3,4,5},{6}}
[7,6,4,1,3,2,5]=>[4,3,1,6,2,7,5]=>[3,7,2,4,1,6,5]=>{{1,3},{2,7},{4},{5},{6}}
[7,6,4,1,3,5,2]=>[4,6,1,5,2,7,3]=>[7,4,2,5,3,6,1]=>{{1,7},{2,4,5},{3},{6}}
[7,6,4,1,5,2,3]=>[4,6,2,5,3,7,1]=>[7,4,1,5,2,6,3]=>{{1,7},{2,4,5},{3},{6}}
[7,6,4,1,5,3,2]=>[4,3,6,5,2,7,1]=>[4,7,3,5,1,6,2]=>{{1,4,5},{2,7},{3},{6}}
[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[7,2,1,4,3,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,4,2,1,5,3]=>[2,4,6,5,3,7,1]=>[7,2,4,5,1,6,3]=>{{1,7},{2},{3,4,5},{6}}
[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[7,3,1,4,2,6,5]=>{{1,7},{2,3},{4},{5},{6}}
[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[5,7,1,4,2,6,3]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,4,2,5,1,3]=>[5,4,1,6,2,7,3]=>[5,7,2,4,3,6,1]=>{{1,5},{2,7},{3},{4},{6}}
[7,6,4,2,5,3,1]=>[3,5,4,6,1,7,2]=>[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}
[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[7,1,3,4,2,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,4,3,1,5,2]=>[3,4,6,5,1,7,2]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}
[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[7,2,3,4,1,6,5]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[3,7,5,4,1,6,2]=>{{1,3,5},{2,7},{4},{6}}
[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[5,1,7,4,2,6,3]=>{{1,5},{2},{3,7},{4},{6}}
[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[5,2,7,4,1,6,3]=>{{1,5},{2},{3,7},{4},{6}}
[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[7,1,2,5,3,6,4]=>{{1,7},{2},{3},{4,5},{6}}
[7,6,4,5,1,3,2]=>[5,3,1,6,4,7,2]=>[3,7,2,5,1,6,4]=>{{1,3},{2,7},{4,5},{6}}
[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[7,2,1,5,3,6,4]=>{{1,7},{2},{3},{4,5},{6}}
[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[7,3,1,5,2,6,4]=>{{1,7},{2,3},{4,5},{6}}
[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[7,1,3,5,2,6,4]=>{{1,7},{2},{3},{4,5},{6}}
[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,6,4]=>{{1,7},{2},{3},{4,5},{6}}
[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[7,1,2,3,5,6,4]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,1,2,4,3]=>[5,1,4,2,6,7,3]=>[4,1,7,3,5,6,2]=>{{1,4},{2},{3,7},{5},{6}}
[7,6,5,1,3,2,4]=>[5,3,1,2,6,7,4]=>[3,7,2,1,5,6,4]=>{{1,3},{2,7},{4},{5},{6}}
[7,6,5,1,3,4,2]=>[5,4,1,3,6,7,2]=>[4,7,2,1,5,6,3]=>{{1,4},{2,7},{3},{5},{6}}
[7,6,5,1,4,2,3]=>[5,4,2,1,6,7,3]=>[4,7,1,3,5,6,2]=>{{1,4},{2,7},{3},{5},{6}}
[7,6,5,1,4,3,2]=>[5,3,4,1,6,7,2]=>[3,7,4,2,5,6,1]=>{{1,3,4},{2,7},{5},{6}}
[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[7,2,1,3,5,6,4]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,2,1,4,3]=>[2,5,4,1,6,7,3]=>[4,2,7,3,5,6,1]=>{{1,4},{2},{3,7},{5},{6}}
[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[7,3,1,2,5,6,4]=>{{1,7},{2,3},{4},{5},{6}}
[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[7,4,1,2,5,6,3]=>{{1,7},{2,4},{3},{5},{6}}
[7,6,5,2,4,1,3]=>[4,5,1,2,6,7,3]=>[7,4,2,3,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[7,6,5,2,4,3,1]=>[3,4,5,1,6,7,2]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[7,1,3,2,5,6,4]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,3,1,4,2]=>[3,5,4,2,6,7,1]=>[7,3,4,1,5,6,2]=>{{1,7},{2,3,4},{5},{6}}
[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[7,2,3,1,5,6,4]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[4,7,3,1,5,6,2]=>{{1,4},{2,7},{3},{5},{6}}
[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[7,1,4,2,5,6,3]=>{{1,7},{2},{3,4},{5},{6}}
[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[7,2,4,1,5,6,3]=>{{1,7},{2},{3,4},{5},{6}}
[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[7,1,2,4,5,6,3]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,4,1,3,2]=>[4,3,1,5,6,7,2]=>[3,7,2,4,5,6,1]=>{{1,3},{2,7},{4},{5},{6}}
[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[7,2,1,4,5,6,3]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[7,3,1,4,5,6,2]=>{{1,7},{2,3},{4},{5},{6}}
[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[7,1,3,4,5,6,2]=>{{1,7},{2},{3},{4},{5},{6}}
[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}
[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[5,2,3,4,6,7,8,1]=>{{1,5,6,7,8},{2},{3},{4}}
[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[8,2,3,5,1,6,7,4]=>{{1,8},{2},{3},{4,5},{6},{7}}
[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[5,2,3,6,7,1,8,4]=>{{1,5,7,8},{2},{3},{4,6}}
[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[4,2,3,5,6,7,8,1]=>{{1,4,5,6,7,8},{2},{3}}
[6,5,7,8,3,4,2,1]=>[2,4,8,3,6,5,7,1]=>[6,2,4,1,7,3,8,5]=>{{1,6},{2},{3,4},{5,7,8}}
[8,7,6,4,3,5,2,1]=>[2,5,4,6,3,7,8,1]=>[5,2,8,4,1,6,7,3]=>{{1,5},{2},{3,8},{4},{6},{7}}
[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[5,2,7,4,1,8,3,6]=>{{1,5},{2},{3,7},{4},{6,8}}
[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[6,2,5,1,3,7,8,4]=>{{1,6,7,8},{2},{3,5},{4}}
[8,7,5,3,4,6,2,1]=>[2,6,5,3,7,4,8,1]=>[6,2,8,1,5,3,7,4]=>{{1,6},{2},{3,8},{4},{5},{7}}
[8,6,4,3,5,7,2,1]=>[2,7,4,6,3,8,5,1]=>[4,2,8,7,1,6,3,5]=>{{1,4,7},{2},{3,8},{5},{6}}
[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>[4,2,5,6,7,8,1,3]=>{{1,4,6,8},{2},{3,5,7}}
[7,6,4,3,5,8,2,1]=>[2,8,4,6,3,7,5,1]=>[4,2,8,6,1,7,3,5]=>{{1,4,6,7},{2},{3,8},{5}}
[7,6,3,4,5,8,2,1]=>[2,8,6,3,4,7,5,1]=>[6,2,8,1,3,7,4,5]=>{{1,6,7},{2},{3,8},{4},{5}}
[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>[3,2,4,5,6,7,8,1]=>{{1,3,4,5,6,7,8},{2}}
[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[8,3,1,5,2,7,4,6]=>{{1,8},{2,3},{4,5},{6,7}}
[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[7,3,1,5,2,8,4,6]=>{{1,7},{2,3},{4,5},{6,8}}
[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[6,3,1,5,2,7,8,4]=>{{1,6,7,8},{2,3},{4,5}}
[8,7,4,5,6,2,3,1]=>[3,6,2,7,4,5,8,1]=>[8,3,1,6,2,4,7,5]=>{{1,8},{2,3},{4,6},{5},{7}}
[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[7,3,1,6,2,4,8,5]=>{{1,7,8},{2,3},{4,6},{5}}
[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[7,3,1,8,6,2,4,5]=>{{1,7},{2,3},{4,8},{5,6}}
[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[6,3,1,8,7,2,4,5]=>{{1,6},{2,3},{4,8},{5,7}}
[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[6,3,1,7,8,2,4,5]=>{{1,6},{2,3},{4,7},{5,8}}
[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[4,3,1,5,6,7,8,2]=>{{1,4,5,6,7,8},{2,3}}
[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[4,8,3,1,7,2,5,6]=>{{1,4},{2,8},{3},{5,7},{6}}
[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>[8,4,1,2,7,3,5,6]=>{{1,8},{2,4},{3},{5,7},{6}}
[7,6,5,8,2,3,4,1]=>[4,8,2,3,6,7,5,1]=>[6,4,1,2,8,7,3,5]=>{{1,6,7},{2,4},{3},{5,8}}
[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[5,4,1,2,6,7,8,3]=>{{1,5,6,7,8},{2,4},{3}}
[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[5,8,4,1,2,7,3,6]=>{{1,5},{2,8},{3,4},{6,7}}
[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[5,7,4,1,2,8,3,6]=>{{1,5},{2,7},{3,4},{6,8}}
[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[4,7,6,1,5,2,8,3]=>{{1,4},{2,7,8},{3,6},{5}}
[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[4,8,7,1,6,2,3,5]=>{{1,4},{2,8},{3,7},{5,6}}
[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[6,7,8,5,1,2,3,4]=>{{1,6},{2,7},{3,8},{4,5}}
[8,4,3,5,6,2,7,1]=>[7,6,4,8,3,5,2,1]=>[6,7,8,4,1,2,3,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[8,3,4,5,6,2,7,1]=>[7,6,8,3,4,5,2,1]=>[7,8,6,1,2,3,4,5]=>{{1,7},{2,8},{3,6},{4},{5}}
[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[3,8,4,7,5,1,2,6]=>{{1,3,4,7},{2,8},{5},{6}}
[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[7,8,5,1,2,3,4,6]=>{{1,7},{2,8},{3,5},{4},{6}}
[8,2,3,4,5,6,7,1]=>[7,8,2,3,4,5,6,1]=>[8,7,1,2,3,4,5,6]=>{{1,8},{2,7},{3},{4},{5},{6}}
[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[4,8,6,1,7,2,3,5]=>{{1,4},{2,8},{3,6},{5,7}}
[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>[4,7,6,1,8,2,3,5]=>{{1,4},{2,7},{3,6},{5,8}}
[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[4,5,8,7,6,1,2,3]=>{{1,4,7},{2,5,6},{3,8}}
[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>[5,7,8,6,1,2,3,4]=>{{1,5},{2,7},{3,8},{4,6}}
[7,3,4,5,6,2,8,1]=>[8,6,7,3,4,5,2,1]=>[6,8,7,1,2,3,4,5]=>{{1,6},{2,8},{3,7},{4},{5}}
[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[5,6,8,7,1,2,3,4]=>{{1,5},{2,6},{3,8},{4,7}}
[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[5,6,7,8,1,2,3,4]=>{{1,5},{2,6},{3,7},{4,8}}
[6,3,4,5,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>[6,7,8,1,2,3,4,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>[3,4,5,6,7,8,1,2]=>{{1,3,5,7},{2,4,6,8}}
[7,6,4,5,2,3,8,1]=>[8,5,2,6,4,7,3,1]=>[5,8,1,6,2,7,3,4]=>{{1,5},{2,8},{3},{4,6,7}}
[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[5,7,1,6,2,8,3,4]=>{{1,5},{2,7},{3},{4,6,8}}
[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>[6,8,1,7,2,3,4,5]=>{{1,6},{2,8},{3},{4,7},{5}}
[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>[6,7,1,8,2,3,4,5]=>{{1,6},{2,7},{3},{4,8},{5}}
[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>[5,8,1,2,6,7,3,4]=>{{1,5,6,7},{2,8},{3},{4}}
[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>[4,8,1,6,2,7,3,5]=>{{1,4,6,7},{2,8},{3},{5}}
[7,6,3,2,4,5,8,1]=>[8,3,6,2,4,7,5,1]=>[3,8,6,1,2,7,4,5]=>{{1,3,6,7},{2,8},{4},{5}}
[7,5,4,2,3,6,8,1]=>[8,4,2,5,7,3,6,1]=>[4,8,1,5,7,2,3,6]=>{{1,4,5,7},{2,8},{3},{6}}
[7,4,2,3,5,6,8,1]=>[8,4,2,7,3,5,6,1]=>[4,8,1,7,2,3,5,6]=>{{1,4,7},{2,8},{3},{5},{6}}
[7,2,3,4,5,6,8,1]=>[8,7,2,3,4,5,6,1]=>[7,8,1,2,3,4,5,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[3,4,5,6,7,1,8,2]=>{{1,3,5,7,8},{2,4,6}}
[6,2,3,4,5,7,8,1]=>[8,6,2,3,4,5,7,1]=>[6,7,1,2,3,4,8,5]=>{{1,6},{2,7,8},{3},{4},{5}}
[5,2,3,4,6,7,8,1]=>[8,5,2,3,4,6,7,1]=>[5,6,1,2,3,7,8,4]=>{{1,5},{2,6,7,8},{3},{4}}
[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[3,4,1,5,6,7,8,2]=>{{1,3},{2,4,5,6,7,8}}
[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[2,3,4,5,6,7,8,1]=>{{1,2,3,4,5,6,7,8}}
[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[8,1,3,4,5,6,7,2]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>[6,1,3,4,5,7,8,2]=>{{1,6,7,8},{2},{3},{4},{5}}
[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[8,1,4,2,5,6,7,3]=>{{1,8},{2},{3,4},{5},{6},{7}}
[7,8,6,5,3,4,1,2]=>[4,1,5,3,6,8,7,2]=>[7,1,4,2,5,6,8,3]=>{{1,7,8},{2},{3,4},{5},{6}}
[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[8,1,4,2,6,3,7,5]=>{{1,8},{2},{3,4},{5,6},{7}}
[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[7,1,4,2,6,3,8,5]=>{{1,7,8},{2},{3,4},{5,6}}
[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[6,1,4,2,7,3,8,5]=>{{1,6},{2},{3,4},{5,7,8}}
[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[5,1,4,2,6,7,8,3]=>{{1,5,6,7,8},{2},{3,4}}
[8,5,4,3,6,7,1,2]=>[7,1,4,5,8,3,6,2]=>[4,1,8,7,5,2,3,6]=>{{1,4,7},{2},{3,8},{5},{6}}
[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[8,1,7,2,3,4,5,6]=>{{1,8},{2},{3,7},{4},{5},{6}}
[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>[6,1,7,8,2,3,4,5]=>{{1,6},{2},{3,7},{4,8},{5}}
[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>[5,1,8,2,7,3,4,6]=>{{1,5,7},{2},{3,8},{4},{6}}
[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[7,1,8,2,3,4,5,6]=>{{1,7},{2},{3,8},{4},{5},{6}}
[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>[3,1,4,5,6,7,8,2]=>{{1,3,4,5,6,7,8},{2}}
[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[7,2,1,4,6,3,8,5]=>{{1,7,8},{2},{3},{4},{5,6}}
[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>[6,2,1,4,8,7,3,5]=>{{1,6,7},{2},{3},{4},{5,8}}
[8,6,5,4,7,2,1,3]=>[2,7,1,5,6,8,4,3]=>[5,2,1,8,7,6,3,4]=>{{1,5,7},{2},{3},{4,8},{6}}
[5,6,7,4,8,2,1,3]=>[2,8,1,7,5,6,4,3]=>[5,2,1,6,7,8,3,4]=>{{1,5,7},{2},{3},{4,6,8}}
[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[7,1,2,8,5,3,4,6]=>{{1,7},{2},{3},{4,8},{5},{6}}
[8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,3]=>[8,1,2,7,3,4,5,6]=>{{1,8},{2},{3},{4,7},{5},{6}}
[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[7,1,2,8,3,4,5,6]=>{{1,7},{2},{3},{4,8},{5},{6}}
[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[4,1,2,5,6,7,8,3]=>{{1,4,5,6,7,8},{2},{3}}
[6,5,7,8,3,2,1,4]=>[2,3,8,1,6,5,7,4]=>[6,2,3,1,7,4,8,5]=>{{1,6},{2},{3},{4},{5,7,8}}
[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[8,3,1,2,5,6,7,4]=>{{1,8},{2,3},{4},{5},{6},{7}}
[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[8,1,3,2,6,4,7,5]=>{{1,8},{2},{3},{4},{5,6},{7}}
[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[7,1,3,2,6,4,8,5]=>{{1,7,8},{2},{3},{4},{5,6}}
[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>[7,2,1,3,8,6,4,5]=>{{1,7},{2},{3},{4},{5,8},{6}}
[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[6,2,1,3,7,8,4,5]=>{{1,6,8},{2},{3},{4},{5,7}}
[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[8,1,2,3,5,6,7,4]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[7,1,2,3,5,6,8,4]=>{{1,7,8},{2},{3},{4},{5},{6}}
[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[6,1,2,3,5,7,8,4]=>{{1,6,7,8},{2},{3},{4},{5}}
[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[8,1,2,3,7,4,5,6]=>{{1,8},{2},{3},{4},{5,7},{6}}
[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[6,1,2,3,8,7,4,5]=>{{1,6,7},{2},{3},{4},{5,8}}
[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[6,1,2,3,7,8,4,5]=>{{1,6,8},{2},{3},{4},{5,7}}
[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[5,1,2,3,6,7,8,4]=>{{1,5,6,7,8},{2},{3},{4}}
[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[6,2,3,4,1,7,8,5]=>{{1,6,7,8},{2},{3},{4},{5}}
[6,7,8,3,4,2,1,5]=>[2,4,8,3,1,6,7,5]=>[6,2,4,1,3,7,8,5]=>{{1,6,7,8},{2},{3,4},{5}}
[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>[8,1,3,4,2,6,7,5]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>[8,1,4,2,3,7,5,6]=>{{1,8},{2},{3,4},{5},{6,7}}
[6,7,8,4,2,1,3,5]=>[2,4,1,8,3,6,7,5]=>[6,2,1,4,3,7,8,5]=>{{1,6,7,8},{2},{3},{4},{5}}
[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>[8,3,1,2,4,7,5,6]=>{{1,8},{2,3},{4},{5},{6,7}}
[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[8,1,2,3,4,7,5,6]=>{{1,8},{2},{3},{4},{5},{6,7}}
[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[7,1,2,3,4,8,5,6]=>{{1,7},{2},{3},{4},{5},{6,8}}
[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[6,1,2,3,4,7,8,5]=>{{1,6,7,8},{2},{3},{4},{5}}
[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[8,2,4,1,5,3,7,6]=>{{1,8},{2},{3,4},{5},{6},{7}}
[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[8,3,1,5,2,4,7,6]=>{{1,8},{2,3},{4,5},{6},{7}}
[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[8,1,4,2,5,3,7,6]=>{{1,8},{2},{3,4},{5},{6},{7}}
[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[7,1,4,2,5,3,8,6]=>{{1,7,8},{2},{3,4},{5},{6}}
[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[8,2,3,1,5,4,7,6]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[8,1,3,2,5,4,7,6]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[7,1,3,2,5,4,8,6]=>{{1,7,8},{2},{3},{4},{5},{6}}
[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[7,2,3,1,4,5,8,6]=>{{1,7,8},{2},{3},{4},{5},{6}}
[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[7,3,1,2,4,5,8,6]=>{{1,7,8},{2,3},{4},{5},{6}}
[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[8,1,2,3,4,5,7,6]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[7,1,2,3,4,5,8,6]=>{{1,7,8},{2},{3},{4},{5},{6}}
[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[8,2,4,1,6,3,5,7]=>{{1,8},{2},{3,4},{5,6},{7}}
[8,4,3,5,6,2,1,7]=>[2,6,4,8,3,5,1,7]=>[6,2,8,4,1,3,5,7]=>{{1,6},{2},{3,8},{4},{5},{7}}
[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[8,1,4,2,6,3,5,7]=>{{1,8},{2},{3,4},{5,6},{7}}
[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>[8,2,1,4,6,3,5,7]=>{{1,8},{2},{3},{4},{5,6},{7}}
[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]=>[8,2,3,1,5,6,4,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>[8,3,1,2,6,4,5,7]=>{{1,8},{2,3},{4},{5,6},{7}}
[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[8,2,4,1,3,6,5,7]=>{{1,8},{2},{3,4},{5},{6},{7}}
[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[8,2,1,4,3,6,5,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[8,1,2,4,3,6,5,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[8,1,3,2,5,4,6,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[8,4,1,2,3,5,6,7]=>{{1,8},{2,4},{3},{5},{6},{7}}
[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[8,3,1,2,4,5,6,7]=>{{1,8},{2,3},{4},{5},{6},{7}}
[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>{{1,8},{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]=>{{1,8},{2},{3},{4},{5},{6},{7}}
[6,7,4,3,5,2,1,8]=>[2,5,4,7,3,6,1,8]=>[5,2,6,4,1,7,3,8]=>{{1,5},{2},{3,6,7},{4},{8}}
[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>[5,2,6,7,1,3,4,8]=>{{1,5},{2},{3,6},{4,7},{8}}
[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>[3,2,4,5,6,7,1,8]=>{{1,3,4,5,6,7},{2},{8}}
[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>[7,3,1,5,2,6,4,8]=>{{1,7},{2,3},{4,5},{6},{8}}
[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>[5,3,1,6,7,2,4,8]=>{{1,5,7},{2,3},{4,6},{8}}
[6,5,7,3,2,4,1,8]=>[4,3,7,2,6,5,1,8]=>[4,6,3,1,7,2,5,8]=>{{1,4},{2,6},{3},{5,7},{8}}
[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[6,4,1,2,5,7,3,8]=>{{1,6,7},{2,4},{3},{5},{8}}
[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[6,4,1,2,7,3,5,8]=>{{1,6},{2,4},{3},{5,7},{8}}
[7,6,3,2,4,5,1,8]=>[5,3,6,2,4,7,1,8]=>[5,7,3,1,2,6,4,8]=>{{1,5},{2,7},{3},{4},{6},{8}}
[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[5,6,7,4,1,2,3,8]=>{{1,5},{2,6},{3,7},{4},{8}}
[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>[4,6,5,1,7,2,3,8]=>{{1,4},{2,6},{3,5,7},{8}}
[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>[5,7,6,1,2,3,4,8]=>{{1,5},{2,7},{3,6},{4},{8}}
[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[4,5,6,7,1,2,3,8]=>{{1,4,7},{2,5},{3,6},{8}}
[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[4,7,1,6,2,3,5,8]=>{{1,4,6},{2,7},{3},{5},{8}}
[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>[6,7,1,2,3,4,5,8]=>{{1,6},{2,7},{3},{4},{5},{8}}
[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[2,3,4,5,6,7,1,8]=>{{1,2,3,4,5,6,7},{8}}
[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[7,1,4,2,6,3,5,8]=>{{1,7},{2},{3,4},{5,6},{8}}
[6,7,3,2,4,1,5,8]=>[4,3,7,2,1,6,5,8]=>[4,6,3,1,2,7,5,8]=>{{1,4},{2,6,7},{3},{5},{8}}
[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[7,2,1,4,3,6,5,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}
[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>[7,5,1,2,3,4,6,8]=>{{1,7},{2,5},{3},{4},{6},{8}}
[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}
[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>{{1,7},{2},{3},{4},{5},{6},{8}}
[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>[4,2,3,5,6,1,7,8]=>{{1,4,5,6},{2},{3},{7},{8}}
[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>[4,5,6,1,2,3,7,8]=>{{1,4},{2,5},{3,6},{7},{8}}
[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[2,3,4,5,6,1,7,8]=>{{1,2,3,4,5,6},{7},{8}}
[4,5,6,2,1,3,7,8]=>[2,6,1,4,5,3,7,8]=>[4,2,1,5,6,3,7,8]=>{{1,4,5,6},{2},{3},{7},{8}}
[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]=>[6,1,2,3,5,4,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}
[6,3,2,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>[6,2,3,1,4,5,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}
[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>{{1,6},{2},{3},{4},{5},{7},{8}}
[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}
[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[4,2,5,1,3,6,7,8]=>{{1,4},{2},{3,5},{6},{7},{8}}
[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>{{1,2,3,4,5},{6},{7},{8}}
[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}
[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>[5,3,1,2,4,6,7,8]=>{{1,5},{2,3},{4},{6},{7},{8}}
[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>{{1,5},{2},{3},{4},{6},{7},{8}}
[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}
[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>{{1,3},{2,4},{5},{6},{7},{8}}
[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>{{1,2,3,4},{5},{6},{7},{8}}
[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}}
[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>{{1,3,4},{2},{5},{6},{7},{8}}
[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>{{1,4},{2},{3},{5},{6},{7},{8}}
[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}
[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>{{1,3},{2},{4},{5},{6},{7},{8}}
[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>{{1,2},{3},{4},{5},{6},{7},{8}}
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>[3,2,5,4,7,6,8,1]=>{{1,3,5,7,8},{2},{4},{6}}
[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>[3,2,6,4,7,8,1,5]=>{{1,3,6,8},{2},{4},{5,7}}
[3,5,4,7,8,6,2,1]=>[2,6,3,5,4,8,7,1]=>[3,2,5,7,1,6,8,4]=>{{1,3,5},{2},{4,7,8},{6}}
[3,4,5,7,8,6,2,1]=>[2,6,3,4,5,8,7,1]=>[3,2,4,5,7,6,8,1]=>{{1,3,4,5,7,8},{2},{6}}
[5,6,4,3,8,7,2,1]=>[2,7,4,6,5,3,8,1]=>[4,2,6,5,8,1,7,3]=>{{1,4,5,8},{2},{3,6},{7}}
[4,5,6,3,8,7,2,1]=>[2,7,6,4,5,3,8,1]=>[4,2,5,6,8,1,7,3]=>{{1,4,6},{2},{3,5,8},{7}}
[4,3,6,5,8,7,2,1]=>[2,7,4,3,6,5,8,1]=>[4,2,6,1,8,3,7,5]=>{{1,4},{2},{3,6},{5,8},{7}}
[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]=>[4,2,5,6,1,8,7,3]=>{{1,4,6,8},{2},{3,5},{7}}
[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]=>[4,2,5,7,1,8,3,6]=>{{1,4,7},{2},{3,5},{6,8}}
[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]=>[2,8,3,4,5,6,7,1]=>{{1,2,8},{3},{4},{5},{6},{7}}
[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]=>[2,4,3,6,5,8,7,1]=>{{1,2,4,6,8},{3},{5},{7}}
[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]=>[2,4,3,6,5,7,8,1]=>{{1,2,4,6,7,8},{3},{5}}
[2,5,4,7,8,6,3,1]=>[3,2,6,5,4,8,7,1]=>[2,5,3,7,1,6,8,4]=>{{1,2,5},{3},{4,7,8},{6}}
[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]=>[2,4,3,6,8,1,7,5]=>{{1,2,4,6},{3},{5,8},{7}}
[2,6,5,4,7,8,3,1]=>[3,2,8,5,6,4,7,1]=>[2,5,3,7,6,1,8,4]=>{{1,2,5,6},{3},{4,7,8}}
[2,3,5,7,8,6,4,1]=>[4,2,3,6,5,8,7,1]=>[2,3,5,4,7,6,8,1]=>{{1,2,3,5,7,8},{4},{6}}
[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>[3,4,8,1,5,6,7,2]=>{{1,3,8},{2,4},{5},{6},{7}}
[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]=>[2,4,6,1,5,8,7,3]=>{{1,2,4},{3,6,8},{5},{7}}
[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]=>[3,4,1,8,5,6,7,2]=>{{1,3},{2,4,8},{5},{6},{7}}
[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]=>[2,3,4,8,5,6,7,1]=>{{1,2,3,4,8},{5},{6},{7}}
[2,4,5,6,3,8,7,1]=>[7,2,6,4,5,3,8,1]=>[2,4,5,6,8,1,7,3]=>{{1,2,4,6},{3,5,8},{7}}
[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]=>[2,4,6,1,8,3,7,5]=>{{1,2,4},{3,6},{5,8},{7}}
[2,3,4,5,6,8,7,1]=>[7,2,3,4,5,6,8,1]=>[2,3,4,5,6,8,7,1]=>{{1,2,3,4,5,6,8},{7}}
[4,6,7,5,3,2,8,1]=>[8,3,5,4,7,6,2,1]=>[3,5,4,7,6,8,1,2]=>{{1,3,4,7},{2,5,6,8}}
[4,3,6,7,5,2,8,1]=>[8,5,4,3,7,6,2,1]=>[4,5,7,1,6,8,2,3]=>{{1,4},{2,5,6,8},{3,7}}
[3,6,5,4,7,2,8,1]=>[8,7,3,5,6,4,2,1]=>[3,5,6,8,7,1,2,4]=>{{1,3,6},{2,5,7},{4,8}}
[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[3,5,6,7,8,1,2,4]=>{{1,3,6},{2,5,8},{4,7}}
[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[4,6,7,1,8,2,3,5]=>{{1,4},{2,6},{3,7},{5,8}}
[2,5,4,7,6,3,8,1]=>[8,2,6,5,4,7,3,1]=>[2,5,6,8,1,7,3,4]=>{{1,2,5},{3,6,7},{4,8}}
[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>[2,4,5,6,7,8,1,3]=>{{1,2,4,6,8},{3,5,7}}
[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[3,6,1,7,8,2,4,5]=>{{1,3},{2,6},{4,7},{5,8}}
[2,3,5,6,7,4,8,1]=>[8,2,3,7,5,6,4,1]=>[2,3,5,6,7,8,1,4]=>{{1,2,3,5,7},{4,6,8}}
[3,4,2,7,6,5,8,1]=>[8,4,3,2,6,7,5,1]=>[3,4,6,1,8,7,2,5]=>{{1,3,6,7},{2,4},{5,8}}
[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]=>[3,4,6,1,7,8,2,5]=>{{1,3,6,8},{2,4},{5,7}}
[2,3,4,6,7,5,8,1]=>[8,2,3,4,7,6,5,1]=>[2,3,4,6,7,8,1,5]=>{{1,2,3,4,6,8},{5,7}}
[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[4,5,7,1,2,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}
[2,5,4,3,7,6,8,1]=>[8,2,4,5,3,7,6,1]=>[2,4,7,5,1,8,3,6]=>{{1,2,4,5},{3,7},{6,8}}
[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[3,5,1,7,2,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}
[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]=>[2,3,4,5,7,8,1,6]=>{{1,2,3,4,5,7},{6,8}}
[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]=>[2,4,5,6,7,1,8,3]=>{{1,2,4,6},{3,5,7,8}}
[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>[3,4,6,1,7,2,8,5]=>{{1,3,6},{2,4},{5,7,8}}
[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>[2,4,6,1,7,3,8,5]=>{{1,2,4},{3,6},{5,7,8}}
[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]=>[2,4,5,6,1,7,8,3]=>{{1,2,4,6,7,8},{3,5}}
[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]=>[2,3,5,6,1,7,8,4]=>{{1,2,3,5},{4,6,7,8}}
[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]=>[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}}
[1,4,5,6,7,8,3,2]=>[1,3,8,4,5,6,7,2]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>[1,4,7,2,5,8,3,6]=>{{1},{2,4},{3,7},{5},{6,8}}
[1,4,3,6,5,8,7,2]=>[1,7,4,3,6,5,8,2]=>[1,4,6,2,8,3,7,5]=>{{1},{2,4},{3,6},{5,8},{7}}
[1,3,4,5,6,8,7,2]=>[1,7,3,4,5,6,8,2]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>[1,5,6,7,8,2,3,4]=>{{1},{2,5,8},{3,6},{4,7}}
[1,3,5,6,7,4,8,2]=>[1,8,3,7,5,6,4,2]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>[2,1,7,4,5,8,3,6]=>{{1,2},{3,7},{4},{5},{6,8}}
[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>[2,1,5,4,7,6,8,3]=>{{1,2},{3,5,7,8},{4},{6}}
[2,1,7,6,5,8,4,3]=>[2,1,4,8,6,7,5,3]=>[2,1,6,4,8,7,3,5]=>{{1,2},{3,6,7},{4},{5,8}}
[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>[2,1,6,4,7,3,8,5]=>{{1,2},{3,6},{4},{5,7,8}}
[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]=>[2,1,4,6,5,8,7,3]=>{{1,2},{3,4,6,8},{5},{7}}
[2,1,5,4,7,8,6,3]=>[2,1,6,5,4,8,7,3]=>[2,1,5,7,3,6,8,4]=>{{1,2},{3,5},{4,7,8},{6}}
[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]=>[2,1,4,5,8,6,7,3]=>{{1,2},{3,4,5,8},{6},{7}}
[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]=>[2,1,4,6,8,3,7,5]=>{{1,2},{3,4,6},{5,8},{7}}
[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[2,1,6,7,8,3,4,5]=>{{1,2},{3,6},{4,7},{5,8}}
[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[2,1,5,6,7,8,3,4]=>{{1,2},{3,5,7},{4,6,8}}
[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[2,1,5,7,3,8,4,6]=>{{1,2},{3,5},{4,7},{6,8}}
[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[2,1,4,5,6,7,8,3]=>{{1,2},{3,4,5,6,7,8}}
[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,4,5,8,7,6,3]=>[1,2,6,4,5,7,8,3]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>{{1,3},{2},{4,8},{5},{6},{7}}
[3,2,1,6,8,7,5,4]=>[2,3,1,5,7,6,8,4]=>[3,2,1,6,5,8,7,4]=>{{1,3},{2},{4,6,8},{5},{7}}
[3,2,1,6,7,8,5,4]=>[2,3,1,5,8,6,7,4]=>[3,2,1,6,5,7,8,4]=>{{1,3},{2},{4,6,7,8},{5}}
[3,2,1,5,7,8,6,4]=>[2,3,1,6,5,8,7,4]=>[3,2,1,5,7,6,8,4]=>{{1,3},{2},{4,5,7,8},{6}}
[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>[3,2,1,6,7,8,4,5]=>{{1,3},{2},{4,6,8},{5,7}}
[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[3,2,1,5,6,7,8,4]=>{{1,3},{2},{4,5,6,7,8}}
[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>[2,3,1,6,7,8,4,5]=>{{1,2,3},{4,6,8},{5,7}}
[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}}
[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[4,2,3,1,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}}
[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>{{1,3,4},{2},{5,8},{6},{7}}
[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}}
[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,6,8,7,5]=>{{1,3,4},{2},{5,6,8},{7}}
[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,7,8,5,6]=>{{1,3,4},{2},{5,7},{6,8}}
[3,4,2,1,6,7,8,5]=>[2,4,3,1,8,6,7,5]=>[3,2,4,1,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}
[2,4,3,1,7,8,6,5]=>[3,2,4,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}}
[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>[2,4,3,1,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}
[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[2,4,3,1,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}
[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[3,4,1,2,7,6,8,5]=>{{1,3},{2,4},{5,7,8},{6}}
[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[3,4,1,2,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}
[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[3,4,1,2,6,7,8,5]=>{{1,3},{2,4},{5,6,7,8}}
[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>{{1,2,3,4},{5,8},{6},{7}}
[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>{{1,2,3,4},{5,7,8},{6}}
[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>[2,3,4,1,6,8,7,5]=>{{1,2,3,4},{5,6,8},{7}}
[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[2,3,4,1,7,8,5,6]=>{{1,2,3,4},{5,7},{6,8}}
[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[2,3,4,1,6,7,8,5]=>{{1,2,3,4},{5,6,7,8}}
[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}
[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>{{1,2},{3,4},{5,8},{6},{7}}
[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>{{1,2},{3,4},{5,7,8},{6}}
[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,6,8,7,5]=>{{1,2},{3,4},{5,6,8},{7}}
[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,7,8,5,6]=>{{1,2},{3,4},{5,7},{6,8}}
[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[2,1,4,3,6,7,8,5]=>{{1,2},{3,4},{5,6,7,8}}
[1,2,4,3,7,8,6,5]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}
[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>{{1,2,3},{4},{5,7,8},{6}}
[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,7,8,5,6]=>{{1,2,3},{4},{5,7},{6,8}}
[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[2,3,1,4,6,7,8,5]=>{{1,2,3},{4},{5,6,7,8}}
[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[2,1,3,4,6,7,8,5]=>{{1,2},{3},{4},{5,6,7,8}}
[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>{{1,5},{2},{3},{4},{6,8},{7}}
[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>{{1,3,5},{2},{4},{6,8},{7}}
[2,4,5,3,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}
[2,3,5,4,1,8,7,6]=>[4,2,3,5,1,7,8,6]=>[2,3,5,4,1,8,7,6]=>{{1,2,3,5},{4},{6,8},{7}}
[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>[3,4,5,1,2,8,7,6]=>{{1,3,5},{2,4},{6,8},{7}}
[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>{{1,2,3,4,5},{6,8},{7}}
[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>{{1,2,3,4},{5},{6,8},{7}}
[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>{{1,2,3,4},{5},{6,7,8}}
[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>{{1,3},{2},{4},{5},{6,8},{7}}
[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>{{1,2,3},{4},{5},{6,7,8}}
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>[3,2,5,4,6,1,8,7]=>{{1,3,5,6},{2},{4},{7,8}}
[5,4,3,6,2,1,8,7]=>[2,6,4,5,3,1,8,7]=>[4,2,6,5,1,3,8,7]=>{{1,4,5},{2},{3,6},{7,8}}
[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]=>[4,2,5,6,1,3,8,7]=>{{1,4,6},{2},{3,5},{7,8}}
[4,3,5,6,2,1,8,7]=>[2,6,4,3,5,1,8,7]=>[4,2,5,1,6,3,8,7]=>{{1,4},{2},{3,5,6},{7,8}}
[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]=>[2,4,3,6,5,1,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[3,2,6,5,4,1,8,7]=>[4,3,2,5,6,1,8,7]=>[3,6,1,4,5,2,8,7]=>{{1,3},{2,6},{4},{5},{7,8}}
[3,2,5,6,4,1,8,7]=>[4,3,2,6,5,1,8,7]=>[3,5,1,4,6,2,8,7]=>{{1,3},{2,5,6},{4},{7,8}}
[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]=>[2,3,6,4,5,1,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]=>[2,4,6,1,5,3,8,7]=>{{1,2,4},{3,6},{5},{7,8}}
[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[4,5,6,1,2,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[3,5,1,6,2,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}
[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[2,3,4,5,6,1,8,7]=>{{1,2,3,4,5,6},{7,8}}
[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>{{1,2},{3,6},{4},{5},{7,8}}
[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>{{1,2},{3,5,6},{4},{7,8}}
[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>[2,1,4,6,5,3,8,7]=>{{1,2},{3,4,6},{5},{7,8}}
[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[2,1,5,6,3,4,8,7]=>{{1,2},{3,5},{4,6},{7,8}}
[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[2,1,4,5,6,3,8,7]=>{{1,2},{3,4,5,6},{7,8}}
[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}
[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}
[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}
[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}
[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>{{1,2,3,4},{5,6},{7,8}}
[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>{{1,2},{3,4},{5,6},{7,8}}
[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>{{1,2},{3,5},{4},{6},{7,8}}
[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>{{1,2},{3},{4},{5},{6},{7,8}}
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]=>[3,2,5,4,7,6,1,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[2,3,4,5,7,6,1,8]=>[6,2,3,4,5,7,1,8]=>[2,3,4,5,7,6,1,8]=>{{1,2,3,4,5,7},{6},{8}}
[1,5,4,7,6,3,2,8]=>[1,3,6,5,4,7,2,8]=>[1,5,3,7,2,6,4,8]=>{{1},{2,5},{3},{4,7},{6},{8}}
[1,3,7,6,5,4,2,8]=>[1,4,3,5,6,7,2,8]=>[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[1,4,5,3,6,7,2,8]=>[1,7,5,4,3,6,2,8]=>[1,4,5,6,2,7,3,8]=>{{1},{2,4,6,7},{3,5},{8}}
[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[3,2,1,7,6,5,4,8]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>{{1,3},{2},{4,7},{5},{6},{8}}
[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[2,3,1,5,6,7,4,8]=>{{1,2,3},{4,5,6,7},{8}}
[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>{{1,2,3,4},{5,6,7},{8}}
[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}}
[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>{{1,3},{2},{4},{5,7},{6},{8}}
[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>{{1,3},{2},{4,5},{6,7},{8}}
[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>{{1,2,3},{4,5},{6,7},{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},{4,5},{6,7},{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},{4,5},{6,7},{8}}
[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>{{1,2,3,4},{5},{6,7},{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},{6,7},{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},{6,7},{8}}
[2,3,4,6,5,1,7,8]=>[5,2,3,4,6,1,7,8]=>[2,3,4,6,5,1,7,8]=>{{1,2,3,4,6},{5},{7},{8}}
[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>{{1,2,3,4},{5,6},{7},{8}}
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>{{1,3,5},{2},{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},{4,5},{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},{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},{2,3},{4},{5},{6},{7},{8}}
[1,2,3,8,5,7,6,4]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,7,6,5,4]=>{{1},{2},{3},{4,8},{5,7},{6}}
[1,2,5,4,8,6,7,3]=>[1,2,7,5,4,8,6,3]=>[1,2,5,8,3,7,4,6]=>{{1},{2},{3,5},{4,8},{6,7}}
[1,2,8,4,5,6,7,3]=>[1,2,7,8,4,5,6,3]=>[1,2,8,7,3,4,5,6]=>{{1},{2},{3,8},{4,7},{5},{6}}
[1,2,8,4,6,7,5,3]=>[1,2,5,7,8,4,3,6]=>[1,2,8,7,5,3,6,4]=>{{1},{2},{3,8},{4,7},{5},{6}}
[1,2,7,5,4,6,8,3]=>[1,2,8,5,7,4,6,3]=>[1,2,5,8,7,3,4,6]=>{{1},{2},{3,5,7},{4,8},{6}}
[1,3,2,8,5,7,6,4]=>[1,3,2,6,7,8,4,5]=>[1,3,2,8,7,6,5,4]=>{{1},{2,3},{4,8},{5,7},{6}}
[1,3,8,4,5,6,7,2]=>[1,7,3,8,4,5,6,2]=>[1,3,8,7,2,4,5,6]=>{{1},{2,3,8},{4,7},{5},{6}}
[1,3,8,5,6,7,4,2]=>[1,4,3,7,8,5,6,2]=>[1,3,8,4,7,2,5,6]=>{{1},{2,3,8},{4},{5,7},{6}}
[1,5,3,4,2,6,7,8]=>[1,4,5,3,2,6,7,8]=>[1,5,4,2,3,6,7,8]=>{{1},{2,5},{3,4},{6},{7},{8}}
[1,7,3,4,5,6,8,2]=>[1,8,7,3,4,5,6,2]=>[1,7,8,2,3,4,5,6]=>{{1},{2,7},{3,8},{4},{5},{6}}
[1,7,4,5,6,3,8,2]=>[1,8,6,7,4,5,3,2]=>[1,6,8,7,2,3,4,5]=>{{1},{2,6},{3,8},{4,7},{5}}
[1,8,4,7,6,5,3,2]=>[1,3,5,6,7,8,4,2]=>[1,8,3,7,5,6,2,4]=>{{1},{2,8},{3},{4,7},{5},{6}}
[1,8,5,4,6,7,3,2]=>[1,3,7,5,8,4,6,2]=>[1,7,3,8,5,2,4,6]=>{{1},{2,7},{3},{4,8},{5},{6}}
[1,8,6,4,5,3,7,2]=>[1,7,5,6,4,8,3,2]=>[1,5,8,7,2,6,3,4]=>{{1},{2,5},{3,8},{4,7},{6}}
[1,8,6,5,4,7,3,2]=>[1,3,7,5,6,8,4,2]=>[1,5,3,8,7,6,2,4]=>{{1},{2,5,7},{3},{4,8},{6}}
[2,1,3,8,5,7,6,4]=>[2,1,3,6,7,8,4,5]=>[2,1,3,8,7,6,5,4]=>{{1,2},{3},{4,8},{5,7},{6}}
[2,1,4,3,8,6,7,5]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,7,5,6]=>{{1,2},{3,4},{5,8},{6,7}}
[2,1,4,5,8,6,7,3]=>[2,1,7,4,5,8,6,3]=>[2,1,4,5,8,7,3,6]=>{{1,2},{3,4,5,8},{6,7}}
[2,1,4,8,5,7,6,3]=>[2,1,6,4,7,8,3,5]=>[2,1,4,8,7,6,5,3]=>{{1,2},{3,4,8},{5,7},{6}}
[2,1,5,4,8,6,7,3]=>[2,1,7,5,4,8,6,3]=>[2,1,5,8,3,7,4,6]=>{{1,2},{3,5},{4,8},{6,7}}
[2,1,6,4,5,3,8,7]=>[2,1,5,6,4,3,8,7]=>[2,1,6,5,3,4,8,7]=>{{1,2},{3,6},{4,5},{7,8}}
[2,1,6,4,5,8,7,3]=>[2,1,7,6,4,5,8,3]=>[2,1,6,8,3,4,7,5]=>{{1,2},{3,6},{4,8},{5},{7}}
[2,1,8,4,5,6,7,3]=>[2,1,7,8,4,5,6,3]=>[2,1,8,7,3,4,5,6]=>{{1,2},{3,8},{4,7},{5},{6}}
[2,1,7,4,6,5,8,3]=>[2,1,8,7,6,4,5,3]=>[2,1,6,7,8,4,3,5]=>{{1,2},{3,6},{4,7},{5,8}}
[2,1,8,4,6,5,7,3]=>[2,1,7,8,6,4,5,3]=>[2,1,7,6,8,4,3,5]=>{{1,2},{3,7},{4,6},{5,8}}
[2,1,8,4,7,6,5,3]=>[2,1,5,6,7,8,4,3]=>[2,1,8,7,5,6,3,4]=>{{1,2},{3,8},{4,7},{5},{6}}
[2,1,7,5,4,6,8,3]=>[2,1,8,5,7,4,6,3]=>[2,1,5,8,7,3,4,6]=>{{1,2},{3,5,7},{4,8},{6}}
[2,1,8,5,4,7,6,3]=>[2,1,6,5,7,8,3,4]=>[2,1,7,8,5,6,4,3]=>{{1,2},{3,7},{4,8},{5},{6}}
[2,1,7,5,6,4,8,3]=>[2,1,8,6,7,5,4,3]=>[2,1,6,8,7,3,4,5]=>{{1,2},{3,6},{4,8},{5,7}}
[2,1,8,5,6,4,7,3]=>[2,1,7,6,8,5,4,3]=>[2,1,7,8,6,3,4,5]=>{{1,2},{3,7},{4,8},{5,6}}
[2,1,8,7,5,6,4,3]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,6,3,7,5]=>{{1,2},{3,8},{4},{5,6},{7}}
[2,3,4,1,8,6,7,5]=>[4,2,3,1,7,8,6,5]=>[2,3,4,1,8,7,5,6]=>{{1,2,3,4},{5,8},{6,7}}
[2,3,4,5,8,6,7,1]=>[7,2,3,4,5,8,6,1]=>[2,3,4,5,8,7,1,6]=>{{1,2,3,4,5,8},{6,7}}
[2,3,4,8,5,6,7,1]=>[7,2,3,4,8,5,6,1]=>[2,3,4,8,7,1,5,6]=>{{1,2,3,4,8},{5,7},{6}}
[2,3,4,8,5,7,6,1]=>[6,2,3,4,7,8,1,5]=>[2,3,4,8,7,6,5,1]=>{{1,2,3,4,8},{5,7},{6}}
[2,3,4,8,6,7,5,1]=>[5,2,3,4,7,8,6,1]=>[2,3,4,8,5,7,1,6]=>{{1,2,3,4,8},{5},{6,7}}
[2,3,6,4,5,1,8,7]=>[5,2,3,6,4,1,8,7]=>[2,3,6,5,1,4,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[2,3,7,4,5,6,8,1]=>[8,2,3,7,4,5,6,1]=>[2,3,7,8,1,4,5,6]=>{{1,2,3,7},{4,8},{5},{6}}
[2,3,8,4,5,6,7,1]=>[7,2,3,8,4,5,6,1]=>[2,3,8,7,1,4,5,6]=>{{1,2,3,8},{4,7},{5},{6}}
[2,4,3,8,5,6,7,1]=>[7,2,4,3,8,5,6,1]=>[2,4,8,1,7,3,5,6]=>{{1,2,4},{3,8},{5,7},{6}}
[2,5,3,4,1,8,7,6]=>[4,2,5,3,1,7,8,6]=>[2,5,4,1,3,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}}
[2,8,3,4,5,6,7,1]=>[7,2,8,3,4,5,6,1]=>[2,8,7,1,3,4,5,6]=>{{1,2,8},{3,7},{4},{5},{6}}
[2,8,3,5,7,6,4,1]=>[4,2,6,7,3,8,5,1]=>[2,8,7,4,1,6,3,5]=>{{1,2,8},{3,7},{4},{5},{6}}
[2,7,4,3,5,6,8,1]=>[8,2,4,7,3,5,6,1]=>[2,4,8,7,1,3,5,6]=>{{1,2,4,7},{3,8},{5},{6}}
[2,8,4,5,6,3,7,1]=>[7,2,6,8,4,5,3,1]=>[2,7,8,6,1,3,4,5]=>{{1,2,7},{3,8},{4,6},{5}}
[2,8,4,7,6,5,3,1]=>[3,2,5,6,7,8,4,1]=>[2,8,3,7,5,6,1,4]=>{{1,2,8},{3},{4,7},{5},{6}}
[3,2,1,7,5,6,4,8]=>[2,3,1,6,7,5,4,8]=>[3,2,1,7,6,4,5,8]=>{{1,3},{2},{4,7},{5,6},{8}}
[3,2,1,8,5,6,7,4]=>[2,3,1,7,8,5,6,4]=>[3,2,1,8,7,4,5,6]=>{{1,3},{2},{4,8},{5,7},{6}}
[3,2,1,8,5,7,6,4]=>[2,3,1,6,7,8,4,5]=>[3,2,1,8,7,6,5,4]=>{{1,3},{2},{4,8},{5,7},{6}}
[3,2,4,1,8,6,7,5]=>[4,3,2,1,7,8,6,5]=>[3,4,1,2,8,7,5,6]=>{{1,3},{2,4},{5,8},{6,7}}
[3,2,5,4,8,6,7,1]=>[7,3,2,5,4,8,6,1]=>[3,5,1,8,2,7,4,6]=>{{1,3},{2,5},{4,8},{6,7}}
[3,2,6,4,5,1,8,7]=>[5,3,2,6,4,1,8,7]=>[3,6,1,5,2,4,8,7]=>{{1,3},{2,6},{4,5},{7,8}}
[3,2,7,4,6,5,8,1]=>[8,3,2,7,6,4,5,1]=>[3,6,1,7,8,4,2,5]=>{{1,3},{2,6},{4,7},{5,8}}
[3,2,8,4,6,5,7,1]=>[7,3,2,8,6,4,5,1]=>[3,7,1,6,8,4,2,5]=>{{1,3},{2,7},{4,6},{5,8}}
[3,2,7,5,6,4,8,1]=>[8,3,2,6,7,5,4,1]=>[3,6,1,8,7,2,4,5]=>{{1,3},{2,6},{4,8},{5,7}}
[3,2,8,5,6,4,7,1]=>[7,3,2,6,8,5,4,1]=>[3,7,1,8,6,2,4,5]=>{{1,3},{2,7},{4,8},{5,6}}
[4,2,3,1,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}
[4,2,3,1,6,7,8,5]=>[3,4,2,1,8,6,7,5]=>[4,3,1,2,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}}
[4,2,3,1,7,6,8,5]=>[3,4,2,1,8,7,6,5]=>[4,3,1,2,7,8,5,6]=>{{1,4},{2,3},{5,7},{6,8}}
[4,2,3,1,8,6,7,5]=>[3,4,2,1,7,8,6,5]=>[4,3,1,2,8,7,5,6]=>{{1,4},{2,3},{5,8},{6,7}}
[4,2,3,5,1,8,7,6]=>[5,4,2,3,1,7,8,6]=>[4,5,1,2,3,8,7,6]=>{{1,4},{2,5},{3},{6,8},{7}}
[4,2,3,5,6,1,8,7]=>[6,4,2,3,5,1,8,7]=>[4,5,1,2,6,3,8,7]=>{{1,4},{2,5,6},{3},{7,8}}
[4,2,3,5,6,8,7,1]=>[7,4,2,3,5,6,8,1]=>[4,5,1,2,6,8,7,3]=>{{1,4},{2,5,6,8},{3},{7}}
[4,2,3,5,7,6,1,8]=>[6,4,2,3,5,7,1,8]=>[4,5,1,2,7,6,3,8]=>{{1,4},{2,5,7},{3},{6},{8}}
[4,2,3,7,5,6,8,1]=>[8,4,2,3,7,5,6,1]=>[4,7,1,2,8,3,5,6]=>{{1,4},{2,7},{3},{5,8},{6}}
[4,2,3,7,6,5,8,1]=>[8,4,2,3,6,7,5,1]=>[4,6,1,2,8,7,3,5]=>{{1,4},{2,6,7},{3},{5,8}}
[4,2,3,8,7,6,5,1]=>[5,4,2,3,6,7,8,1]=>[4,8,1,2,5,6,7,3]=>{{1,4},{2,8},{3},{5},{6},{7}}
[5,2,3,4,1,8,7,6]=>[4,5,2,3,1,7,8,6]=>[5,4,1,2,3,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}}
[5,2,3,4,8,6,7,1]=>[7,5,2,3,4,8,6,1]=>[5,8,1,2,3,7,4,6]=>{{1,5},{2,8},{3},{4},{6,7}}
[6,2,3,4,5,8,7,1]=>[7,6,2,3,4,5,8,1]=>[6,8,1,2,3,4,7,5]=>{{1,6},{2,8},{3},{4},{5},{7}}
[8,2,3,4,5,7,6,1]=>[6,7,2,3,4,8,1,5]=>[8,7,1,2,3,6,5,4]=>{{1,8},{2,7},{3},{4},{5},{6}}
[6,2,3,5,4,1,7,8]=>[4,5,2,6,1,3,7,8]=>[6,5,1,4,3,2,7,8]=>{{1,6},{2,5},{3},{4},{7},{8}}
[8,2,3,5,7,6,4,1]=>[4,6,2,7,3,8,5,1]=>[8,7,1,4,2,6,3,5]=>{{1,8},{2,7},{3},{4},{5},{6}}
[5,2,4,3,1,6,7,8]=>[3,4,5,1,2,6,7,8]=>[5,4,3,2,1,6,7,8]=>{{1,5},{2,4},{3},{6},{7},{8}}
[5,2,4,3,1,6,8,7]=>[3,4,5,1,2,6,8,7]=>[5,4,3,2,1,6,8,7]=>{{1,5},{2,4},{3},{6},{7,8}}
[5,2,4,3,1,8,7,6]=>[3,4,5,1,2,7,8,6]=>[5,4,3,2,1,8,7,6]=>{{1,5},{2,4},{3},{6,8},{7}}
[5,2,4,3,6,1,8,7]=>[6,5,4,2,3,1,8,7]=>[4,5,6,2,1,3,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[5,2,4,3,7,6,8,1]=>[8,5,4,2,3,7,6,1]=>[4,5,7,2,1,8,3,6]=>{{1,4},{2,5},{3,7},{6,8}}
[6,2,4,3,5,1,8,7]=>[5,6,4,2,3,1,8,7]=>[5,4,6,2,1,3,8,7]=>{{1,5},{2,4},{3,6},{7,8}}
[7,2,4,3,6,5,8,1]=>[8,7,4,2,6,3,5,1]=>[4,6,7,2,8,3,1,5]=>{{1,4},{2,6},{3,7},{5,8}}
[6,2,4,5,3,1,8,7]=>[3,5,6,2,1,4,8,7]=>[6,5,3,1,4,2,8,7]=>{{1,6},{2,5},{3},{4},{7,8}}
[7,2,4,5,3,6,8,1]=>[8,7,5,2,4,3,6,1]=>[5,7,8,2,1,3,4,6]=>{{1,5},{2,7},{3,8},{4},{6}}
[8,2,5,4,3,7,6,1]=>[6,7,4,5,2,8,1,3]=>[5,4,8,7,2,6,3,1]=>{{1,5},{2,4,7},{3,8},{6}}
[7,2,5,4,6,3,8,1]=>[8,7,6,5,2,4,3,1]=>[5,6,7,8,3,1,2,4]=>{{1,5},{2,6},{3,7},{4,8}}
[8,2,6,5,4,7,3,1]=>[3,7,8,5,6,2,1,4]=>[6,5,3,8,7,2,4,1]=>{{1,6},{2,5,7},{3},{4,8}}
[5,3,2,4,6,1,8,7]=>[6,3,5,2,4,1,8,7]=>[3,6,5,1,2,4,8,7]=>{{1,3,5},{2,6},{4},{7,8}}
[8,3,2,4,6,5,7,1]=>[7,3,8,2,6,4,5,1]=>[6,7,3,1,8,4,2,5]=>{{1,6},{2,7},{3},{4},{5,8}}
[7,3,2,5,4,6,1,8]=>[6,3,7,5,2,4,1,8]=>[5,6,3,7,2,1,4,8]=>{{1,5},{2,6},{3},{4,7},{8}}
[8,3,2,5,4,7,6,1]=>[6,3,7,5,2,8,1,4]=>[5,7,3,8,2,6,4,1]=>{{1,5},{2,7},{3},{4,8},{6}}
[8,3,2,5,7,6,4,1]=>[4,3,6,7,2,8,5,1]=>[7,8,3,4,1,6,2,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[5,3,4,2,6,1,8,7]=>[6,4,5,3,2,1,8,7]=>[4,6,5,1,2,3,8,7]=>{{1,4},{2,6},{3,5},{7,8}}
[5,3,4,2,7,6,8,1]=>[8,4,5,3,2,7,6,1]=>[4,7,5,1,2,8,3,6]=>{{1,4},{2,7},{3,5},{6,8}}
[5,3,4,2,8,6,7,1]=>[7,4,5,3,2,8,6,1]=>[4,8,5,1,2,7,3,6]=>{{1,4},{2,8},{3,5},{6,7}}
[6,3,4,2,5,1,8,7]=>[5,4,6,3,2,1,8,7]=>[5,6,4,1,2,3,8,7]=>{{1,5},{2,6},{3,4},{7,8}}
[7,3,4,2,6,5,8,1]=>[8,4,7,3,6,2,5,1]=>[4,7,6,1,8,3,2,5]=>{{1,4},{2,7},{3,6},{5,8}}
[8,3,4,2,6,5,7,1]=>[7,4,8,3,6,2,5,1]=>[6,7,4,1,8,3,2,5]=>{{1,6},{2,7},{3,4},{5,8}}
[6,3,5,4,2,7,1,8]=>[7,4,5,6,2,3,1,8]=>[4,7,6,5,2,1,3,8]=>{{1,4,5},{2,7},{3,6},{8}}
[8,3,5,4,2,7,6,1]=>[6,4,5,7,2,8,1,3]=>[5,8,7,4,2,6,3,1]=>{{1,5},{2,8},{3,7},{4},{6}}
[7,3,6,4,5,2,8,1]=>[8,5,7,6,4,3,2,1]=>[5,8,6,7,1,2,3,4]=>{{1,5},{2,8},{3,6},{4,7}}
[8,3,6,4,5,2,7,1]=>[7,5,8,6,4,3,2,1]=>[6,8,5,7,1,2,3,4]=>{{1,6},{2,8},{3,5},{4,7}}
[8,3,7,5,6,4,2,1]=>[2,4,6,8,7,5,1,3]=>[8,2,6,4,7,1,5,3]=>{{1,8},{2},{3,6},{4},{5,7}}
[8,4,3,2,6,7,5,1]=>[5,3,4,7,8,2,1,6]=>[3,8,7,4,5,1,6,2]=>{{1,3,7},{2,8},{4},{5},{6}}
[8,4,3,5,2,7,6,1]=>[6,5,4,7,3,8,1,2]=>[5,7,8,4,1,6,3,2]=>{{1,5},{2,7},{3,8},{4},{6}}
[8,4,3,7,6,5,2,1]=>[2,5,4,6,7,8,3,1]=>[7,2,8,4,5,6,1,3]=>{{1,7},{2},{3,8},{4},{5},{6}}
[6,5,3,4,2,1,8,7]=>[2,4,5,3,6,1,8,7]=>[6,2,4,1,5,3,8,7]=>{{1,6},{2},{3,4},{5},{7,8}}
[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>{{1,2,4},{3},{5,6},{7,8}}
[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>{{1,2},{3,4,6},{5},{7,8}}
[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>[2,4,1,6,3,5,8,7]=>{{1,2,4,6},{3},{5},{7,8}}
[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>{{1,2},{3,4},{5,6,8},{7}}
[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>{{1,2,4},{3},{5,6,8},{7}}
[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>[2,1,4,6,3,8,5,7]=>{{1,2},{3,4,6,8},{5},{7}}
[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[2,4,1,6,3,8,5,7]=>{{1,2,4,6,8},{3},{5},{7}}
[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]=>[2,4,1,6,3,7,5,8]=>{{1,2,4,6,7},{3},{5},{8}}
[2,4,1,3,6,7,8,5]=>[4,2,1,3,8,6,7,5]=>[2,4,1,3,6,7,8,5]=>{{1,2,4},{3},{5,6,7,8}}
[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,7,6,5]=>{{1,2},{3,4},{5,8},{6,7}}
[2,4,1,3,7,5,8,6]=>[4,2,1,3,7,8,5,6]=>[2,4,1,3,8,7,6,5]=>{{1,2,4},{3},{5,8},{6,7}}
[2,1,4,7,3,5,8,6]=>[2,1,7,4,3,8,5,6]=>[2,1,4,8,3,7,6,5]=>{{1,2},{3,4,8},{5},{6,7}}
[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[2,1,4,3,7,5,8,6]=>{{1,2},{3,4},{5,7,8},{6}}
[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]=>[2,4,1,3,7,5,8,6]=>{{1,2,4},{3},{5,7,8},{6}}
[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[2,1,4,5,8,7,6,3]=>{{1,2},{3,4,5,8},{6,7}}
[2,4,1,5,7,3,8,6]=>[4,2,7,1,5,8,3,6]=>[2,5,4,3,8,7,6,1]=>{{1,2,5,8},{3,4},{6,7}}
[2,4,5,7,1,3,8,6]=>[7,2,1,4,5,8,3,6]=>[2,4,1,5,8,7,6,3]=>{{1,2,4,5,8},{3},{6,7}}
[2,1,4,5,7,8,3,6]=>[2,1,8,4,5,3,7,6]=>[2,1,4,5,7,3,8,6]=>{{1,2},{3,4,5,7,8},{6}}
[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>{{1,2},{3,4},{5,8},{6},{7}}
[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>{{1,2,4},{3},{5,8},{6},{7}}
[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[2,1,4,5,8,3,6,7]=>{{1,2},{3,4,5,8},{6},{7}}
[2,4,5,1,3,6,7,8]=>[5,2,1,4,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>{{1,2,4,5},{3},{6},{7},{8}}
[2,4,5,6,1,3,7,8]=>[6,2,1,4,5,3,7,8]=>[2,4,1,5,6,3,7,8]=>{{1,2,4,5,6},{3},{7},{8}}
[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[2,5,4,3,6,7,8,1]=>{{1,2,5,6,7,8},{3,4}}
[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[2,5,4,6,7,3,8,1]=>{{1,2,5,7,8},{3,4,6}}
[2,4,5,6,7,8,1,3]=>[8,2,1,4,5,6,7,3]=>[2,4,1,5,6,7,8,3]=>{{1,2,4,5,6,7,8},{3}}
[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[2,1,6,5,4,3,8,7]=>{{1,2},{3,6},{4,5},{7,8}}
[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[2,1,5,3,6,4,8,7]=>{{1,2},{3,5,6},{4},{7,8}}
[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[2,1,6,5,7,4,8,3]=>{{1,2},{3,6},{4,5,7,8}}
[2,1,5,6,7,3,8,4]=>[2,1,7,8,5,6,3,4]=>[2,1,6,5,7,8,4,3]=>{{1,2},{3,6,8},{4,5,7}}
[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[2,7,6,5,4,8,3,1]=>{{1,2,7},{3,6,8},{4,5}}
[2,5,6,7,1,8,3,4]=>[7,2,8,3,5,6,1,4]=>[2,6,5,1,7,8,4,3]=>{{1,2,6,8},{3,5,7},{4}}
[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[2,1,8,5,4,7,6,3]=>{{1,2},{3,8},{4,5},{6,7}}
[2,1,5,7,3,4,8,6]=>[2,1,7,3,5,8,4,6]=>[2,1,5,3,8,7,6,4]=>{{1,2},{3,5,8},{4},{6,7}}
[2,5,1,3,7,8,4,6]=>[5,2,1,8,3,4,7,6]=>[2,7,1,5,4,3,8,6]=>{{1,2,7,8},{3},{4,5},{6}}
[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[2,1,5,3,7,4,8,6]=>{{1,2},{3,5,7,8},{4},{6}}
[2,3,5,1,8,4,6,7]=>[5,2,3,8,1,4,6,7]=>[2,3,8,5,4,1,6,7]=>{{1,2,3,8},{4,5},{6},{7}}
[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[2,3,6,5,4,1,8,7]=>{{1,2,3,6},{4,5},{7,8}}
[2,3,5,6,1,4,7,8]=>[6,2,3,1,5,4,7,8]=>[2,3,5,1,6,4,7,8]=>{{1,2,3,5,6},{4},{7},{8}}
[2,3,5,6,7,8,1,4]=>[8,2,3,1,5,6,7,4]=>[2,3,5,1,6,7,8,4]=>{{1,2,3,5,6,7,8},{4}}
[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[2,1,8,7,6,5,4,3]=>{{1,2},{3,8},{4,7},{5,6}}
[2,1,6,7,3,8,4,5]=>[2,1,7,8,4,6,3,5]=>[2,1,7,6,3,8,5,4]=>{{1,2},{3,7},{4,6,8},{5}}
[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[2,1,6,3,4,7,8,5]=>{{1,2},{3,6,7,8},{4},{5}}
[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[2,3,1,6,4,8,5,7]=>{{1,2,3},{4,6,8},{5},{7}}
[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>{{1,2},{3,6},{4},{5},{7,8}}
[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[2,3,6,1,4,5,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[2,3,4,1,6,8,5,7]=>[4,2,3,1,8,6,5,7]=>[2,3,4,1,6,8,5,7]=>{{1,2,3,4},{5,6,8},{7}}
[2,3,4,6,1,8,5,7]=>[6,2,3,4,8,1,5,7]=>[2,3,4,8,6,5,1,7]=>{{1,2,3,4,8},{5,6},{7}}
[2,3,4,6,7,1,5,8]=>[7,2,3,4,1,6,5,8]=>[2,3,4,6,1,7,5,8]=>{{1,2,3,4,6,7},{5},{8}}
[2,3,4,6,1,7,8,5]=>[6,2,3,4,8,1,7,5]=>[2,3,4,7,6,5,8,1]=>{{1,2,3,4,7,8},{5,6}}
[2,1,7,3,4,8,5,6]=>[2,1,7,3,8,5,4,6]=>[2,1,8,3,7,4,6,5]=>{{1,2},{3,8},{4},{5,7},{6}}
[2,1,7,3,4,5,8,6]=>[2,1,7,3,4,8,5,6]=>[2,1,8,3,4,7,6,5]=>{{1,2},{3,8},{4},{5},{6,7}}
[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,7,6,5]=>{{1,2},{3},{4},{5,8},{6,7}}
[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[2,3,4,1,8,7,6,5]=>{{1,2,3,4},{5,8},{6,7}}
[2,3,4,7,1,5,8,6]=>[7,2,3,4,1,8,5,6]=>[2,3,4,8,1,7,6,5]=>{{1,2,3,4,8},{5},{6,7}}
[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[2,3,4,1,7,5,8,6]=>{{1,2,3,4},{5,7,8},{6}}
[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>{{1,2,7},{3},{4},{5},{6},{8}}
[2,3,4,5,7,8,1,6]=>[8,2,3,4,5,1,7,6]=>[2,3,4,5,7,1,8,6]=>{{1,2,3,4,5,7,8},{6}}
[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>{{1,2},{3,8},{4},{5},{6},{7}}
[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>{{1,2,8},{3},{4},{5},{6},{7}}
[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>{{1,2},{3},{4,8},{5},{6},{7}}
[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>{{1,2},{3},{4},{5,8},{6},{7}}
[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>{{1,2,3},{4},{5,8},{6},{7}}
[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]=>{{1,2,3,4},{5,8},{6},{7}}
[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>{{1,2,3,4,8},{5},{6},{7}}
[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,6,7]=>[2,3,4,1,5,8,6,7]=>{{1,2,3,4},{5},{6,8},{7}}
[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,8,6,7]=>[2,3,4,5,1,8,6,7]=>{{1,2,3,4,5},{6,8},{7}}
[2,3,4,5,8,1,6,7]=>[8,2,3,4,5,1,6,7]=>[2,3,4,5,8,1,6,7]=>{{1,2,3,4,5,8},{6},{7}}
[2,3,4,5,6,8,1,7]=>[8,2,3,4,5,6,1,7]=>[2,3,4,5,6,8,1,7]=>{{1,2,3,4,5,6,8},{7}}
[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>{{1,4},{2,3},{5,6},{7,8}}
[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>{{1,3,4},{2},{5,6},{7,8}}
[3,1,4,2,6,8,5,7]=>[3,4,1,2,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>{{1,4},{2,3},{5,6,8},{7}}
[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>{{1,3,4},{2},{5,6,8},{7}}
[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>{{1,4},{2,3},{5,6},{7},{8}}
[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>{{1,4},{2,3},{5,6,7},{8}}
[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[4,3,2,1,6,7,8,5]=>{{1,4},{2,3},{5,6,7,8}}
[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[3,1,4,2,6,7,8,5]=>{{1,3,4},{2},{5,6,7,8}}
[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[4,3,7,2,6,5,8,1]=>{{1,4},{2,3,7,8},{5,6}}
[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[4,3,7,2,6,8,5,1]=>{{1,4},{2,3,7},{5,6,8}}
[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[4,3,2,1,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}
[3,4,1,2,7,5,8,6]=>[4,1,3,2,7,8,5,6]=>[3,1,4,2,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}
[3,1,4,2,7,8,5,6]=>[3,4,1,2,8,5,7,6]=>[4,3,2,1,7,5,8,6]=>{{1,4},{2,3},{5,7,8},{6}}
[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[3,1,4,2,7,5,8,6]=>{{1,3,4},{2},{5,7,8},{6}}
[3,4,7,1,8,2,5,6]=>[7,8,3,4,2,5,1,6]=>[4,3,7,8,1,2,6,5]=>{{1,4,8},{2,3,7},{5},{6}}
[3,1,4,2,7,5,6,8]=>[3,4,1,2,7,5,6,8]=>[4,3,2,1,7,5,6,8]=>{{1,4},{2,3},{5,7},{6},{8}}
[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>{{1,4},{2,3},{5},{6,7,8}}
[3,1,4,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>{{1,4},{2,3},{5,8},{6},{7}}
[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>{{1,3,4},{2},{5,8},{6},{7}}
[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,8,6,7]=>[4,3,2,1,5,8,6,7]=>{{1,4},{2,3},{5},{6,8},{7}}
[3,4,1,5,2,8,6,7]=>[4,5,3,1,2,8,6,7]=>[4,3,5,2,1,8,6,7]=>{{1,4},{2,3,5},{6,8},{7}}
[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[4,3,2,5,6,1,8,7]=>{{1,4,5,6},{2,3},{7,8}}
[3,4,1,5,6,2,8,7]=>[4,6,3,1,5,2,8,7]=>[4,3,5,2,6,1,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[3,4,5,1,6,2,8,7]=>[5,6,3,4,1,2,8,7]=>[4,3,5,6,2,1,8,7]=>{{1,4,6},{2,3,5},{7,8}}
[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>{{1,4},{2,3},{5},{6},{7},{8}}
[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[4,3,2,5,6,7,8,1]=>{{1,4,5,6,7,8},{2,3}}
[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[4,3,5,6,7,8,2,1]=>{{1,4,6,8},{2,3,5,7}}
[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[6,3,2,5,4,1,8,7]=>{{1,6},{2,3},{4,5},{7,8}}
[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[3,1,5,2,6,4,8,7]=>{{1,3,5,6},{2},{4},{7,8}}
[3,5,1,2,6,8,4,7]=>[5,1,3,8,2,6,4,7]=>[3,1,6,5,4,8,2,7]=>{{1,3,6,8},{2},{4,5},{7}}
[3,5,1,6,8,2,4,7]=>[5,8,3,2,1,6,4,7]=>[5,3,6,1,4,8,2,7]=>{{1,5},{2,3,6,8},{4},{7}}
[3,5,1,6,7,8,2,4]=>[5,8,3,2,1,6,7,4]=>[5,3,6,1,4,7,8,2]=>{{1,5},{2,3,6,7,8},{4}}
[3,5,6,1,7,8,2,4]=>[6,8,3,2,5,1,7,4]=>[5,3,6,1,7,4,8,2]=>{{1,5,7,8},{2,3,6},{4}}
[3,5,6,7,1,8,2,4]=>[7,8,3,2,5,6,1,4]=>[5,3,6,1,7,8,4,2]=>{{1,5,7},{2,3,6,8},{4}}
[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[8,3,2,5,4,7,6,1]=>{{1,8},{2,3},{4,5},{6,7}}
[3,1,5,7,2,4,8,6]=>[3,7,1,2,5,8,4,6]=>[5,3,2,1,8,7,6,4]=>{{1,5,8},{2,3},{4},{6,7}}
[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[3,1,5,2,7,4,8,6]=>{{1,3,5,7,8},{2},{4},{6}}
[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[3,1,5,2,7,4,6,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[1,3,5,2,7,4,6,8]=>[1,5,3,7,2,4,6,8]=>[1,3,7,5,4,2,6,8]=>{{1},{2,3,7},{4,5},{6},{8}}
[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[1,3,5,2,7,4,8,6]=>{{1},{2,3,5,7,8},{4},{6}}
[3,5,1,2,8,4,6,7]=>[5,1,3,8,2,4,6,7]=>[3,1,8,5,4,2,6,7]=>{{1,3,8},{2},{4,5},{6},{7}}
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>{{1},{2,3},{4,5},{6,8},{7}}
[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]=>[1,3,2,5,8,4,6,7]=>{{1},{2,3},{4,5,8},{6},{7}}
[1,3,5,6,8,2,4,7]=>[1,8,3,2,5,6,4,7]=>[1,3,5,2,6,8,4,7]=>{{1},{2,3,5,6,8},{4},{7}}
[1,3,5,6,7,2,4,8]=>[1,7,3,2,5,6,4,8]=>[1,3,5,2,6,7,4,8]=>{{1},{2,3,5,6,7},{4},{8}}
[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>[1,3,6,5,7,8,4,2]=>{{1},{2,3,6,8},{4,5,7}}
[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[8,3,2,7,6,5,4,1]=>{{1,8},{2,3},{4,7},{5,6}}
[3,1,6,7,2,4,5,8]=>[3,7,1,2,4,6,5,8]=>[6,3,2,1,4,7,5,8]=>{{1,6,7},{2,3},{4},{5},{8}}
[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,4,7,5,8]=>{{1},{2,3},{4,6,7},{5},{8}}
[1,3,6,7,8,2,4,5]=>[1,8,3,2,4,6,7,5]=>[1,3,6,2,4,7,8,5]=>{{1},{2,3,6,7,8},{4},{5}}
[3,1,6,2,4,8,5,7]=>[3,6,1,2,8,4,5,7]=>[8,3,2,1,6,5,4,7]=>{{1,8},{2,3},{4},{5,6},{7}}
[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,4,8,5,7]=>{{1},{2,3},{4,6,8},{5},{7}}
[3,1,6,2,4,5,8,7]=>[3,6,1,2,4,5,8,7]=>[6,3,2,1,4,5,8,7]=>{{1,6},{2,3},{4},{5},{7,8}}
[3,6,1,2,4,5,8,7]=>[6,1,3,2,4,5,8,7]=>[3,1,6,2,4,5,8,7]=>{{1,3,6},{2},{4},{5},{7,8}}
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>{{1},{2,3},{4,6},{5},{7},{8}}
[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[3,1,2,4,6,7,8,5]=>{{1,3},{2},{4},{5,6,7,8}}
[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,7},{5,6,8}}
[3,7,1,2,4,8,5,6]=>[7,1,3,2,8,5,4,6]=>[3,1,8,2,7,4,6,5]=>{{1,3,8},{2},{4},{5,7},{6}}
[3,7,1,2,4,5,8,6]=>[7,1,3,2,4,8,5,6]=>[3,1,8,2,4,7,6,5]=>{{1,3,8},{2},{4},{5},{6,7}}
[3,1,2,4,7,5,8,6]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}}
[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,7,6,5]=>{{1},{2,3},{4},{5,8},{6,7}}
[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[1,3,4,2,8,7,6,5]=>{{1},{2,3,4},{5,8},{6,7}}
[1,3,4,7,2,5,8,6]=>[1,7,3,4,2,8,5,6]=>[1,3,4,8,2,7,6,5]=>{{1},{2,3,4,8},{5},{6,7}}
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>{{1},{2,3},{4,7},{5},{6},{8}}
[3,1,8,2,4,5,6,7]=>[3,8,1,2,4,5,6,7]=>[8,3,2,1,4,5,6,7]=>{{1,8},{2,3},{4},{5},{6},{7}}
[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>{{1,3,8},{2},{4},{5},{6},{7}}
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>{{1},{2,3},{4,8},{5},{6},{7}}
[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>{{1,3},{2},{4},{5,8},{6},{7}}
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>{{1},{2,3},{4},{5,8},{6},{7}}
[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>{{1},{2,3,4},{5,8},{6},{7}}
[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>{{1,3},{2},{4},{5},{6,8},{7}}
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>{{1},{2,3},{4},{5},{6,8},{7}}
[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[6,5,4,3,2,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[4,5,1,6,2,3,8,7]=>[5,6,2,4,1,3,8,7]=>[5,4,1,6,3,2,8,7]=>{{1,5},{2,4,6},{3},{7,8}}
[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[4,1,2,5,6,3,8,7]=>{{1,4,5,6},{2},{3},{7,8}}
[4,1,5,2,6,8,3,7]=>[4,5,8,1,2,6,3,7]=>[6,5,4,3,2,8,1,7]=>{{1,6,8},{2,5},{3,4},{7}}
[4,5,1,6,2,8,3,7]=>[5,6,8,4,1,2,3,7]=>[6,5,4,8,3,2,1,7]=>{{1,6},{2,5},{3,4,8},{7}}
[4,1,5,6,8,2,3,7]=>[4,8,2,1,5,6,3,7]=>[5,4,1,3,6,8,2,7]=>{{1,5,6,8},{2,4},{3},{7}}
[4,1,5,2,6,3,7,8]=>[4,5,6,1,2,3,7,8]=>[6,5,4,3,2,1,7,8]=>{{1,6},{2,5},{3,4},{7},{8}}
[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[6,5,4,7,3,2,1,8]=>{{1,6},{2,5},{3,4,7},{8}}
[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[8,5,4,3,2,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}
[4,1,5,2,7,8,3,6]=>[4,5,8,1,2,3,7,6]=>[7,5,4,3,2,1,8,6]=>{{1,7,8},{2,5},{3,4},{6}}
[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>{{1},{2,4,5},{3},{6,7},{8}}
[1,4,5,7,2,3,8,6]=>[1,7,2,4,5,8,3,6]=>[1,4,2,5,8,7,6,3]=>{{1},{2,4,5,8},{3},{6,7}}
[4,5,1,2,8,3,6,7]=>[5,1,8,4,2,3,6,7]=>[5,1,4,8,3,2,6,7]=>{{1,5},{2},{3,4,8},{6},{7}}
[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>{{1},{2,4,5},{3},{6,8},{7}}
[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>{{1},{2,4,5},{3},{6},{7},{8}}
[1,4,5,6,7,2,3,8]=>[1,7,2,4,5,6,3,8]=>[1,4,2,5,6,7,3,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[1,5,4,3,6,7,8,2]=>{{1},{2,5,6,7,8},{3,4}}
[1,4,5,6,7,8,2,3]=>[1,8,2,4,5,6,7,3]=>[1,4,2,5,6,7,8,3]=>{{1},{2,4,5,6,7,8},{3}}
[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[8,7,4,3,6,5,2,1]=>{{1,8},{2,7},{3,4},{5,6}}
[1,4,6,7,2,3,5,8]=>[1,7,2,4,3,6,5,8]=>[1,4,2,6,3,7,5,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[4,1,2,6,3,8,5,7]=>{{1,4,6,8},{2},{3},{5},{7}}
[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,2,6,3,8,5,7]=>{{1},{2,4,6,8},{3},{5},{7}}
[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}
[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>{{1,4},{2},{3},{5,6,8},{7}}
[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>{{1,4},{2},{3},{5,6},{7},{8}}
[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>{{1,4},{2},{3},{5,6,7},{8}}
[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[4,1,2,3,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}}
[4,1,7,8,2,3,5,6]=>[4,8,2,1,3,5,7,6]=>[7,4,1,3,2,5,8,6]=>{{1,7,8},{2,4},{3},{5},{6}}
[4,1,7,2,3,8,5,6]=>[4,7,2,1,8,5,3,6]=>[8,4,1,3,7,2,6,5]=>{{1,8},{2,4},{3},{5,7},{6}}
[1,4,7,2,3,8,5,6]=>[1,7,2,4,8,5,3,6]=>[1,4,2,8,7,3,6,5]=>{{1},{2,4,8},{3},{5,7},{6}}
[1,4,2,7,8,3,5,6]=>[1,4,8,2,3,5,7,6]=>[1,7,4,3,2,5,8,6]=>{{1},{2,7,8},{3,4},{5},{6}}
[4,1,2,7,3,5,8,6]=>[4,1,7,2,3,8,5,6]=>[8,1,4,3,2,7,6,5]=>{{1,8},{2},{3,4},{5},{6,7}}
[1,4,7,2,3,5,8,6]=>[1,7,2,4,3,8,5,6]=>[1,4,2,8,3,7,6,5]=>{{1},{2,4,8},{3},{5},{6,7}}
[4,1,2,3,7,5,8,6]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}}
[1,4,2,3,7,5,8,6]=>[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}}
[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,7,6,5]=>{{1},{2},{3,4},{5,8},{6,7}}
[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[4,1,2,3,7,5,8,6]=>{{1,4},{2},{3},{5,7,8},{6}}
[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>{{1},{2,4,7},{3},{5},{6},{8}}
[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>{{1,4},{2},{3},{5,7},{6},{8}}
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>{{1},{2,4},{3},{5,7},{6},{8}}
[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>{{1,4},{2},{3},{5},{6,7},{8}}
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>{{1},{2,4},{3},{5},{6,7},{8}}
[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>{{1,4},{2},{3},{5},{6,7,8}}
[1,2,4,5,7,8,3,6]=>[1,2,8,4,5,3,7,6]=>[1,2,4,5,7,3,8,6]=>{{1},{2},{3,4,5,7,8},{6}}
[4,1,2,8,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>[8,1,4,3,2,5,6,7]=>{{1,8},{2},{3,4},{5},{6},{7}}
[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>{{1},{2,4,8},{3},{5},{6},{7}}
[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>{{1},{2,4},{3},{5,8},{6},{7}}
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>{{1},{2},{3,4},{5,8},{6},{7}}
[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>{{1,4},{2},{3},{5},{6,8},{7}}
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>{{1},{2,4},{3},{5},{6,8},{7}}
[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>{{1,4},{2},{3},{5},{6},{7,8}}
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[8,7,6,5,4,3,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[5,6,1,2,7,8,3,4]=>[6,1,8,3,5,2,7,4]=>[6,1,5,2,7,4,8,3]=>{{1,6},{2},{3,5,7,8},{4}}
[5,6,1,7,2,8,3,4]=>[6,7,8,3,5,1,2,4]=>[7,6,5,1,8,4,3,2]=>{{1,7},{2,6},{3,5,8},{4}}
[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[7,6,5,1,4,3,2,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[1,5,6,7,8,2,3,4]=>[1,8,2,3,5,6,7,4]=>[1,5,2,3,6,7,8,4]=>{{1},{2,5,6,7,8},{3},{4}}
[5,6,1,8,2,3,4,7]=>[6,8,2,3,5,1,4,7]=>[6,5,1,2,8,4,3,7]=>{{1,6},{2,5,8},{3},{4},{7}}
[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]=>[1,2,5,3,6,4,7,8]=>{{1},{2},{3,5,6},{4},{7},{8}}
[1,5,2,3,6,7,4,8]=>[1,5,2,7,3,6,4,8]=>[1,6,2,5,4,7,3,8]=>{{1},{2,6,7},{3},{4,5},{8}}
[5,1,2,3,6,7,8,4]=>[5,1,2,8,3,6,7,4]=>[6,1,2,5,4,7,8,3]=>{{1,6,7,8},{2},{3},{4,5}}
[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[1,2,6,5,4,7,8,3]=>{{1},{2},{3,6,7,8},{4,5}}
[1,2,5,6,7,8,3,4]=>[1,2,8,3,5,6,7,4]=>[1,2,5,3,6,7,8,4]=>{{1},{2},{3,5,6,7,8},{4}}
[5,7,1,2,3,4,8,6]=>[7,1,2,3,5,8,4,6]=>[5,1,2,3,8,7,6,4]=>{{1,5,8},{2},{3},{4},{6,7}}
[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[1,2,5,3,8,7,6,4]=>{{1},{2},{3,5,8},{4},{6,7}}
[1,5,7,2,3,4,6,8]=>[1,7,2,3,5,4,6,8]=>[1,5,2,3,7,4,6,8]=>{{1},{2,5,7},{3},{4},{6},{8}}
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>{{1},{2,5},{3},{4},{6,7},{8}}
[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[1,2,3,5,8,7,6,4]=>{{1},{2},{3},{4,5,8},{6,7}}
[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>[5,1,2,3,8,4,6,7]=>{{1,5,8},{2},{3},{4},{6},{7}}
[1,2,5,3,8,4,6,7]=>[1,2,5,8,3,4,6,7]=>[1,2,8,5,4,3,6,7]=>{{1},{2},{3,8},{4,5},{6},{7}}
[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>[1,2,5,3,8,4,6,7]=>{{1},{2},{3,5,8},{4},{6},{7}}
[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>{{1},{2,5},{3},{4},{6,8},{7}}
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>{{1},{2},{3},{4,5},{6,8},{7}}
[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>{{1,5},{2},{3},{4},{6},{7,8}}
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[8,7,1,6,2,5,4,3]=>{{1,8},{2,7},{3},{4,6},{5}}
[6,7,1,2,3,4,8,5]=>[7,1,2,3,8,6,4,5]=>[7,1,2,3,6,8,5,4]=>{{1,7},{2},{3},{4},{5,6,8}}
[1,2,6,7,3,8,4,5]=>[1,2,7,8,4,6,3,5]=>[1,2,7,6,3,8,5,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[1,2,6,7,8,3,4,5]=>[1,2,8,3,4,6,7,5]=>[1,2,6,3,4,7,8,5]=>{{1},{2},{3,6,7,8},{4},{5}}
[1,6,7,2,3,4,5,8]=>[1,7,2,3,4,6,5,8]=>[1,6,2,3,4,7,5,8]=>{{1},{2,6,7},{3},{4},{5},{8}}
[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,4,7,5,8]=>{{1},{2},{3},{4,6,7},{5},{8}}
[6,1,2,3,4,7,8,5]=>[6,1,2,3,8,4,7,5]=>[7,1,2,3,6,5,8,4]=>{{1,7,8},{2},{3},{4},{5,6}}
[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[1,2,3,7,6,5,8,4]=>{{1},{2},{3},{4,7,8},{5,6}}
[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,7},{5,6,8}}
[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,4,7,8,5]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,6,8,2,3,4,5,7]=>[1,8,2,3,4,6,5,7]=>[1,6,2,3,4,8,5,7]=>{{1},{2,6,8},{3},{4},{5},{7}}
[1,6,2,3,8,4,5,7]=>[1,6,2,8,4,3,5,7]=>[1,8,2,6,3,5,4,7]=>{{1},{2,8},{3},{4,6},{5},{7}}
[1,2,6,8,3,4,5,7]=>[1,2,8,3,4,6,5,7]=>[1,2,6,3,4,8,5,7]=>{{1},{2},{3,6,8},{4},{5},{7}}
[6,1,2,3,4,8,5,7]=>[6,1,2,3,8,4,5,7]=>[8,1,2,3,6,5,4,7]=>{{1,8},{2},{3},{4},{5,6},{7}}
[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,4,8,5,7]=>{{1},{2},{3},{4,6,8},{5},{7}}
[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>{{1},{2,6},{3},{4},{5},{7},{8}}
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}}
[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]=>[1,7,2,3,4,5,8,6]=>{{1},{2,7,8},{3},{4},{5},{6}}
[7,1,2,3,8,4,5,6]=>[7,1,2,8,4,5,3,6]=>[8,1,2,7,3,4,6,5]=>{{1,8},{2},{3},{4,7},{5},{6}}
[1,2,7,8,3,4,5,6]=>[1,2,8,3,4,5,7,6]=>[1,2,7,3,4,5,8,6]=>{{1},{2},{3,7,8},{4},{5},{6}}
[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[1,2,3,7,4,5,8,6]=>{{1},{2},{3},{4,7,8},{5},{6}}
[7,1,2,3,4,5,8,6]=>[7,1,2,3,4,8,5,6]=>[8,1,2,3,4,7,6,5]=>{{1,8},{2},{3},{4},{5},{6,7}}
[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,7,6,5]=>{{1},{2},{3},{4},{5,8},{6,7}}
[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,5,8,6]=>{{1},{2},{3},{4},{5,7,8},{6}}
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>{{1},{2},{3},{4},{5,8},{6},{7}}
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[6,4,5,2,3,1,8,7]=>[3,5,2,6,4,1,8,7]=>[6,3,1,5,2,4,8,7]=>{{1,6},{2,3},{4,5},{7,8}}
[8,6,4,3,7,2,5,1]=>[5,7,4,6,2,8,3,1]=>[7,4,8,5,2,6,1,3]=>{{1,7},{2,4,5},{3,8},{6}}
[5,8,4,3,1,7,6,2]=>[3,4,8,6,5,7,1,2]=>[6,4,3,5,8,7,2,1]=>{{1,6,7},{2,4,5,8},{3}}
[6,8,4,3,7,1,5,2]=>[7,5,4,8,1,6,3,2]=>[5,6,7,4,3,8,1,2]=>{{1,5},{2,6,8},{3,7},{4}}
[4,8,6,1,7,3,5,2]=>[6,5,8,4,3,7,2,1]=>[5,6,4,8,1,7,2,3]=>{{1,5},{2,6,7},{3,4,8}}
[3,8,1,6,7,4,5,2]=>[8,5,3,7,4,1,6,2]=>[3,5,8,7,1,4,2,6]=>{{1,3,8},{2,5},{4,7},{6}}
[2,1,8,6,7,4,5,3]=>[2,1,5,7,4,8,6,3]=>[2,1,8,5,3,7,4,6]=>{{1,2},{3,8},{4,5},{6,7}}
[4,7,6,1,8,3,2,5]=>[6,3,7,4,2,8,5,1]=>[4,7,3,8,1,6,2,5]=>{{1,4,8},{2,7},{3},{5},{6}}
[5,7,6,8,1,3,2,4]=>[8,3,1,2,5,7,6,4]=>[3,5,2,1,7,8,4,6]=>{{1,3},{2,5,7},{4},{6,8}}
[8,4,6,2,7,3,5,1]=>[5,6,7,8,3,4,2,1]=>[8,7,6,5,2,1,3,4]=>{{1,8},{2,7},{3,6},{4,5}}
[7,3,2,6,8,4,1,5]=>[4,3,8,7,1,5,6,2]=>[4,8,3,7,2,1,5,6]=>{{1,4,7},{2,8},{3},{5},{6}}
[4,3,2,1,7,8,5,6]=>[2,3,4,1,8,5,7,6]=>[4,2,3,1,7,5,8,6]=>{{1,4},{2},{3},{5,7,8},{6}}
[3,4,1,2,8,7,6,5]=>[4,1,3,2,6,7,8,5]=>[3,1,4,2,8,6,7,5]=>{{1,3,4},{2},{5,8},{6},{7}}
[4,6,8,1,7,2,5,3]=>[8,7,5,4,2,6,1,3]=>[4,5,6,7,2,8,3,1]=>{{1,4,7},{2,5},{3,6,8}}
[6,5,8,7,2,1,4,3]=>[2,7,4,1,6,5,8,3]=>[4,2,6,3,8,1,7,5]=>{{1,4},{2},{3,6},{5,8},{7}}
[3,7,1,8,6,5,2,4]=>[7,5,3,2,6,8,1,4]=>[3,5,8,1,7,6,4,2]=>{{1,3,8},{2,5,7},{4},{6}}
[3,8,1,7,6,5,4,2]=>[8,4,3,5,6,7,1,2]=>[3,4,8,5,6,7,2,1]=>{{1,3,8},{2,4,5,6,7}}
[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,10}}
[4,2,5,1,3,6,7,8]=>[5,4,1,2,3,6,7,8]=>[4,5,2,3,1,6,7,8]=>{{1,4},{2,5},{3},{6},{7},{8}}
[5,4,8,1,2,3,6,7]=>[8,1,2,5,4,3,6,7]=>[5,1,2,8,3,4,6,7]=>{{1,5},{2},{3},{4,8},{6},{7}}
[7,5,8,1,2,3,4,6]=>[8,1,2,3,7,4,5,6]=>[7,1,2,3,8,5,6,4]=>{{1,7},{2},{3},{4},{5,8},{6}}
[8,5,7,1,2,3,4,6]=>[7,1,2,3,8,4,5,6]=>[8,1,2,3,7,5,6,4]=>{{1,8},{2},{3},{4},{5,7},{6}}
[6,3,5,8,1,2,4,7]=>[8,1,6,2,4,3,5,7]=>[6,1,8,3,2,5,4,7]=>{{1,6},{2},{3,8},{4},{5},{7}}
[6,4,5,8,1,2,3,7]=>[8,1,2,6,4,5,3,7]=>[6,1,2,8,3,4,5,7]=>{{1,6},{2},{3},{4,8},{5},{7}}
[6,2,7,8,1,3,4,5]=>[8,6,1,2,3,4,7,5]=>[6,7,2,3,4,5,8,1]=>{{1,6},{2,7,8},{3},{4},{5}}
[7,2,4,8,1,3,5,6]=>[8,7,1,3,2,4,5,6]=>[7,8,2,1,4,5,6,3]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,4,6,8,1,2,3,5]=>[8,1,2,7,3,5,4,6]=>[7,1,2,8,4,3,6,5]=>{{1,7},{2},{3},{4,8},{5},{6}}
[8,2,4,6,1,3,5,7]=>[6,8,1,3,2,5,4,7]=>[8,6,2,1,4,3,5,7]=>{{1,8},{2,6},{3},{4},{5},{7}}
[8,3,5,6,1,2,4,7]=>[6,1,8,2,4,3,5,7]=>[8,1,6,3,2,5,4,7]=>{{1,8},{2},{3,6},{4},{5},{7}}
[8,2,4,7,1,3,5,6]=>[7,8,1,3,2,4,5,6]=>[8,7,2,1,4,5,6,3]=>{{1,8},{2,7},{3},{4},{5},{6}}
[8,2,6,7,1,3,4,5]=>[7,8,1,2,3,5,4,6]=>[8,7,2,3,4,1,6,5]=>{{1,8},{2,7},{3},{4},{5},{6}}
[5,8,2,4,1,3,6,7]=>[4,8,1,2,5,3,6,7]=>[5,4,2,3,8,1,6,7]=>{{1,5,8},{2,4},{3},{6},{7}}
[5,8,3,4,1,2,6,7]=>[4,1,8,3,5,2,6,7]=>[5,1,4,2,8,3,6,7]=>{{1,5,8},{2},{3,4},{6},{7}}
[4,8,2,6,1,3,5,7]=>[6,8,1,4,2,5,3,7]=>[6,4,2,8,3,1,5,7]=>{{1,6},{2,4,8},{3},{5},{7}}
[6,8,3,4,1,2,5,7]=>[4,1,8,3,2,6,5,7]=>[6,1,4,2,3,8,5,7]=>{{1,6,8},{2},{3,4},{5},{7}}
[7,8,3,5,1,2,4,6]=>[5,1,8,2,3,4,7,6]=>[7,1,5,3,4,2,8,6]=>{{1,7,8},{2},{3,5},{4},{6}}
[6,4,2,8,1,3,5,7]=>[8,4,1,6,2,5,3,7]=>[4,8,2,6,3,1,5,7]=>{{1,4,6},{2,8},{3},{5},{7}}
[8,7,3,5,1,2,4,6]=>[5,1,7,2,3,4,8,6]=>[8,1,5,3,4,2,7,6]=>{{1,8},{2},{3,5},{4},{6},{7}}
[8,7,3,6,1,2,4,5]=>[6,1,7,2,3,5,8,4]=>[8,1,6,3,4,2,7,5]=>{{1,8},{2},{3,6},{4},{5},{7}}
[5,8,3,6,7,1,2,4]=>[7,1,8,2,5,4,3,6]=>[7,1,5,3,8,2,6,4]=>{{1,7},{2},{3,5,8},{4},{6}}
[4,3,2,6,8,1,5,7]=>[8,3,4,2,1,6,5,7]=>[3,6,4,1,2,8,5,7]=>{{1,3,4},{2,6,8},{5},{7}}
[6,4,3,5,8,1,2,7]=>[8,1,4,6,3,5,2,7]=>[4,1,8,6,2,3,5,7]=>{{1,4,6},{2},{3,8},{5},{7}}
[5,3,2,7,8,1,4,6]=>[8,3,5,1,2,4,7,6]=>[3,7,5,2,4,1,8,6]=>{{1,3,5},{2,7,8},{4},{6}}
[5,4,2,7,8,1,3,6]=>[8,4,1,5,2,3,7,6]=>[4,7,2,5,3,1,8,6]=>{{1,4,5},{2,7,8},{3},{6}}
[5,4,3,7,8,1,2,6]=>[8,1,4,5,3,2,7,6]=>[4,1,7,5,2,3,8,6]=>{{1,4,5},{2},{3,7,8},{6}}
[6,4,2,7,8,1,3,5]=>[8,4,1,6,2,5,7,3]=>[4,7,2,6,3,1,8,5]=>{{1,4,6},{2,7,8},{3},{5}}
[7,4,2,5,8,1,3,6]=>[8,4,1,7,3,2,6,5]=>[4,8,2,7,1,5,3,6]=>{{1,4,7},{2,8},{3},{5},{6}}
[7,5,3,4,8,1,2,6]=>[8,1,5,3,7,2,4,6]=>[5,1,8,2,7,4,6,3]=>{{1,5,7},{2},{3,8},{4},{6}}
[8,3,2,5,7,1,4,6]=>[7,3,8,1,4,2,6,5]=>[7,8,3,2,1,5,4,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[5,3,7,2,6,1,4,8]=>[6,7,5,1,3,2,4,8]=>[6,5,7,3,2,4,1,8]=>{{1,6},{2,5},{3,7},{4},{8}}
[6,3,7,2,5,1,4,8]=>[5,7,6,1,2,3,4,8]=>[7,5,6,3,4,2,1,8]=>{{1,7},{2,5},{3,6},{4},{8}}
[6,5,8,3,4,1,2,7]=>[4,1,8,3,6,5,2,7]=>[6,1,4,2,8,3,5,7]=>{{1,6},{2},{3,4},{5,8},{7}}
[6,4,8,3,7,1,2,5]=>[7,1,8,6,2,4,3,5]=>[7,1,6,8,4,3,5,2]=>{{1,7},{2},{3,6},{4,8},{5}}
[8,6,4,2,7,1,3,5]=>[7,4,1,6,2,8,5,3]=>[4,8,2,7,3,6,1,5]=>{{1,4,7},{2,8},{3},{5},{6}}
[8,6,5,3,7,1,2,4]=>[7,1,5,2,6,8,3,4]=>[5,1,8,3,7,6,4,2]=>{{1,5,7},{2},{3,8},{4},{6}}
[5,8,4,7,3,6,1,2]=>[6,1,7,8,5,3,4,2]=>[7,1,6,5,8,3,2,4]=>{{1,7},{2},{3,6},{4,5,8}}
[6,8,3,7,2,5,1,4]=>[5,7,8,1,2,6,3,4]=>[7,6,5,3,4,8,2,1]=>{{1,7},{2,6,8},{3,5},{4}}
[8,1,2,3,6,7,4,5]=>[8,1,2,7,4,3,6,5]=>[7,1,2,8,3,5,4,6]=>{{1,7},{2},{3},{4,8},{5},{6}}
[8,1,2,6,3,7,4,5]=>[8,1,6,7,4,2,3,5]=>[6,1,8,7,2,5,4,3]=>{{1,6},{2},{3,8},{4,7},{5}}
[4,1,2,8,6,3,5,7]=>[4,1,6,2,3,8,5,7]=>[8,1,4,3,2,6,5,7]=>{{1,8},{2},{3,4},{5},{6},{7}}
[4,1,2,8,7,3,5,6]=>[4,1,7,2,3,5,8,6]=>[8,1,4,3,2,5,7,6]=>{{1,8},{2},{3,4},{5},{6},{7}}
[8,1,2,7,6,3,4,5]=>[8,1,6,3,4,7,2,5]=>[6,1,8,2,3,7,5,4]=>{{1,6,7},{2},{3,8},{4},{5}}
[7,1,2,5,6,3,8,4]=>[7,1,6,8,2,4,5,3]=>[7,1,8,6,4,3,2,5]=>{{1,7},{2},{3,8},{4,6},{5}}
[7,1,4,2,6,3,8,5]=>[7,4,6,1,8,2,3,5]=>[4,8,7,3,6,5,2,1]=>{{1,4},{2,8},{3,7},{5,6}}
[8,1,5,2,6,7,3,4]=>[8,5,7,3,1,2,6,4]=>[5,8,7,1,4,3,2,6]=>{{1,5},{2,8},{3,7},{4},{6}}
[3,1,8,5,2,4,6,7]=>[3,5,1,2,8,4,6,7]=>[8,3,2,1,5,4,6,7]=>{{1,8},{2,3},{4},{5},{6},{7}}
[3,1,8,6,2,4,5,7]=>[3,6,1,2,4,8,5,7]=>[8,3,2,1,4,6,5,7]=>{{1,8},{2,3},{4},{5},{6},{7}}
[7,1,8,6,2,3,4,5]=>[7,6,2,3,4,8,1,5]=>[7,8,1,2,3,6,5,4]=>{{1,7},{2,8},{3},{4},{5},{6}}
[8,1,4,5,7,2,3,6]=>[8,7,2,1,3,5,4,6]=>[7,8,1,3,4,2,6,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[8,1,7,5,6,2,3,4]=>[8,6,2,3,7,5,1,4]=>[6,8,1,2,7,3,5,4]=>{{1,6},{2,8},{3},{4},{5,7}}
[2,8,1,3,6,7,4,5]=>[8,2,1,7,4,3,6,5]=>[2,7,1,8,3,5,4,6]=>{{1,2,7},{3},{4,8},{5},{6}}
[2,8,1,5,6,3,4,7]=>[8,2,6,3,1,5,4,7]=>[2,6,8,1,4,3,5,7]=>{{1,2,6},{3,8},{4},{5},{7}}
[2,8,1,7,6,3,4,5]=>[8,2,6,3,4,7,1,5]=>[2,6,8,1,3,7,5,4]=>{{1,2,6,7},{3,8},{4},{5}}
[6,3,1,2,4,8,5,7]=>[3,1,6,2,8,4,5,7]=>[8,1,3,2,6,5,4,7]=>{{1,8},{2},{3},{4},{5,6},{7}}
[5,3,1,2,7,4,8,6]=>[3,1,5,7,2,8,4,6]=>[8,1,3,5,4,7,6,2]=>{{1,8},{2},{3},{4,5},{6,7}}
[5,3,1,2,6,7,8,4]=>[3,1,5,8,2,6,7,4]=>[6,1,3,5,4,7,8,2]=>{{1,6,7,8},{2},{3},{4,5}}
[4,3,1,8,2,7,5,6]=>[3,4,8,2,7,5,1,6]=>[7,4,3,1,8,2,6,5]=>{{1,7},{2,4},{3},{5,8},{6}}
[8,3,1,5,2,7,4,6]=>[3,8,5,7,2,4,1,6]=>[8,3,5,7,2,1,6,4]=>{{1,8},{2,3,5},{4,7},{6}}
[7,4,1,5,2,3,8,6]=>[4,7,2,5,3,8,1,6]=>[8,4,1,5,2,7,6,3]=>{{1,8},{2,4,5},{3},{6,7}}
[8,4,1,6,2,3,5,7]=>[4,8,2,6,3,5,1,7]=>[8,4,1,6,2,3,5,7]=>{{1,8},{2,4,6},{3},{5},{7}}
[4,3,1,8,7,2,5,6]=>[3,4,7,2,1,5,8,6]=>[8,4,3,1,2,5,7,6]=>{{1,8},{2,4},{3},{5},{6},{7}}
[4,3,1,7,6,2,8,5]=>[3,4,6,2,7,8,5,1]=>[8,4,3,1,7,6,2,5]=>{{1,8},{2,4},{3},{5,7},{6}}
[8,4,1,7,6,2,3,5]=>[4,8,2,6,3,7,5,1]=>[8,4,1,6,2,7,3,5]=>{{1,8},{2,4,6,7},{3},{5}}
[4,3,1,5,6,8,2,7]=>[3,4,8,2,5,6,1,7]=>[5,4,3,1,6,8,2,7]=>{{1,5,6,8},{2,4},{3},{7}}
[2,7,4,1,3,5,8,6]=>[4,2,1,7,3,8,5,6]=>[2,8,1,4,3,7,6,5]=>{{1,2,8},{3},{4},{5},{6,7}}
[2,8,7,1,3,4,5,6]=>[7,2,1,3,4,5,8,6]=>[2,8,1,3,4,5,7,6]=>{{1,2,8},{3},{4},{5},{6},{7}}
[2,8,5,1,7,3,4,6]=>[5,2,8,3,7,4,6,1]=>[2,8,5,1,7,3,4,6]=>{{1,2,8},{3,5,7},{4},{6}}
[7,3,4,1,2,5,8,6]=>[4,1,7,3,2,8,5,6]=>[8,1,4,2,3,7,6,5]=>{{1,8},{2},{3,4},{5},{6,7}}
[6,3,4,1,2,7,8,5]=>[4,1,6,3,8,2,7,5]=>[7,1,4,2,6,5,8,3]=>{{1,7,8},{2},{3,4},{5,6}}
[6,3,8,1,2,7,4,5]=>[8,1,6,7,4,3,2,5]=>[6,1,8,7,2,4,5,3]=>{{1,6},{2},{3,8},{4,7},{5}}
[7,3,4,1,6,2,8,5]=>[4,6,7,3,8,1,2,5]=>[8,7,4,1,6,5,3,2]=>{{1,8},{2,7},{3,4},{5,6}}
[7,3,8,1,6,2,4,5]=>[8,6,7,2,3,1,5,4]=>[6,8,7,2,3,5,1,4]=>{{1,6},{2,8},{3,7},{4},{5}}
[7,3,5,1,6,2,8,4]=>[5,6,7,8,3,1,2,4]=>[8,7,6,5,2,4,3,1]=>{{1,8},{2,7},{3,6},{4,5}}
[8,5,4,1,7,2,3,6]=>[4,5,2,8,7,3,1,6]=>[8,5,1,4,7,2,6,3]=>{{1,8},{2,5,7},{3},{4},{6}}
[7,8,4,1,6,2,3,5]=>[4,8,2,6,3,5,7,1]=>[7,4,1,6,2,3,8,5]=>{{1,7,8},{2,4,6},{3},{5}}
[5,3,4,1,8,7,2,6]=>[4,7,5,3,1,2,8,6]=>[8,4,5,1,3,2,7,6]=>{{1,8},{2,4},{3,5},{6},{7}}
[8,3,5,1,6,7,2,4]=>[5,7,8,2,4,3,6,1]=>[8,7,5,2,1,3,4,6]=>{{1,8},{2,7},{3,5},{4},{6}}
[8,5,4,1,6,7,2,3]=>[4,5,2,8,7,1,6,3]=>[8,5,1,4,7,3,2,6]=>{{1,8},{2,5,7},{3},{4},{6}}
[2,3,7,6,1,4,8,5]=>[6,2,3,1,7,8,5,4]=>[2,3,8,1,7,6,4,5]=>{{1,2,3,8},{4},{5,7},{6}}
[2,3,8,6,1,7,4,5]=>[6,2,3,8,4,7,5,1]=>[2,3,8,6,1,7,4,5]=>{{1,2,3,8},{4,6,7},{5}}
[2,8,4,5,1,7,3,6]=>[5,2,7,8,4,1,6,3]=>[2,8,7,5,1,4,3,6]=>{{1,2,8},{3,7},{4,5},{6}}
[7,3,4,6,1,2,8,5]=>[6,1,7,3,8,4,2,5]=>[8,1,7,2,6,4,5,3]=>{{1,8},{2},{3,7},{4},{5,6}}
[7,3,8,5,1,2,4,6]=>[5,1,8,2,7,3,4,6]=>[8,1,5,3,7,4,6,2]=>{{1,8},{2},{3,5,7},{4},{6}}
[7,3,6,5,1,2,8,4]=>[5,1,6,7,8,2,4,3]=>[8,1,7,6,5,4,2,3]=>{{1,8},{2},{3,7},{4,6},{5}}
[6,3,4,5,1,8,2,7]=>[5,8,6,3,4,1,2,7]=>[8,5,6,1,2,4,3,7]=>{{1,8},{2,5},{3,6},{4},{7}}
[8,3,4,6,1,7,2,5]=>[6,7,8,3,2,5,4,1]=>[8,7,6,1,3,2,4,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[2,3,4,8,6,1,5,7]=>[6,2,3,4,1,8,5,7]=>[2,3,4,8,1,6,5,7]=>{{1,2,3,4,8},{5},{6},{7}}
[2,3,4,8,7,1,5,6]=>[7,2,3,4,1,5,8,6]=>[2,3,4,8,1,5,7,6]=>{{1,2,3,4,8},{5},{6},{7}}
[2,3,4,7,6,1,8,5]=>[6,2,3,4,7,8,5,1]=>[2,3,4,8,7,6,1,5]=>{{1,2,3,4,8},{5,7},{6}}
[2,3,8,7,6,1,4,5]=>[6,2,3,1,4,7,8,5]=>[2,3,8,1,4,6,7,5]=>{{1,2,3,8},{4},{5},{6},{7}}
[2,8,4,5,7,1,3,6]=>[7,2,1,8,4,3,5,6]=>[2,8,1,7,3,5,6,4]=>{{1,2,8},{3},{4,7},{5},{6}}
[2,8,4,7,6,1,3,5]=>[6,2,1,7,3,8,5,4]=>[2,8,1,7,4,6,3,5]=>{{1,2,8},{3},{4,7},{5},{6}}
[2,8,7,5,6,1,3,4]=>[6,2,1,3,7,5,8,4]=>[2,8,1,3,6,4,7,5]=>{{1,2,8},{3},{4},{5,6},{7}}
[2,7,4,5,6,1,8,3]=>[6,2,8,7,4,5,1,3]=>[2,8,6,7,1,3,5,4]=>{{1,2,8},{3,6},{4,7},{5}}
[8,3,7,5,6,1,2,4]=>[6,1,8,2,7,5,3,4]=>[8,1,6,3,7,2,5,4]=>{{1,8},{2},{3,6},{4},{5,7}}
[2,3,4,8,6,7,1,5]=>[7,2,3,4,1,8,6,5]=>[2,3,4,8,1,7,5,6]=>{{1,2,3,4,8},{5},{6,7}}
[2,8,4,5,6,7,1,3]=>[7,2,1,8,4,5,6,3]=>[2,8,1,7,3,4,5,6]=>{{1,2,8},{3},{4,7},{5},{6}}
[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>{{1,2,9},{3},{4},{5},{6},{7},{8}}
[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>[8,1,2,3,4,5,6,9,7]=>{{1,8,9},{2},{3},{4},{5},{6},{7}}
[9,7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,9,7,6]=>[9,1,2,3,4,5,8,6,7]=>{{1,9},{2},{3},{4},{5},{6},{7,8}}
[2,3,4,5,6,7,9,1,8]=>[9,2,3,4,5,6,7,1,8]=>[2,3,4,5,6,7,9,1,8]=>{{1,2,3,4,5,6,7,9},{8}}
[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[2,3,4,5,6,7,8,9,1]=>{{1,2,3,4,5,6,7,8,9}}
[3,5,2,6,4,1,8,7]=>[4,6,3,5,1,2,8,7]=>[4,3,6,5,2,1,8,7]=>{{1,4,5},{2,3,6},{7,8}}
[4,5,7,2,3,8,1,6]=>[8,7,2,4,5,1,3,6]=>[4,5,1,7,8,3,6,2]=>{{1,4,7},{2,5,8},{3},{6}}
[4,5,7,1,3,8,2,6]=>[7,8,1,4,5,3,6,2]=>[5,4,2,7,8,1,3,6]=>{{1,5,8},{2,4,7},{3},{6}}
[3,5,1,7,4,8,2,6]=>[5,8,3,7,1,2,4,6]=>[5,3,8,7,4,2,6,1]=>{{1,5},{2,3,8},{4,7},{6}}
[2,1,5,7,4,8,6,3]=>[2,1,6,8,5,7,3,4]=>[2,1,6,5,8,7,4,3]=>{{1,2},{3,6,7},{4,5,8}}
[5,6,7,8,3,1,4,2]=>[3,8,4,2,5,6,7,1]=>[5,3,4,1,6,7,8,2]=>{{1,5,6,7,8},{2,3,4}}
[4,6,7,1,8,3,2,5]=>[7,3,8,4,2,6,1,5]=>[4,6,3,7,1,8,5,2]=>{{1,4,7},{2,6,8},{3},{5}}
[4,6,7,2,8,1,3,5]=>[8,7,1,4,2,6,5,3]=>[4,6,2,7,3,8,1,5]=>{{1,4,7},{2,6,8},{3},{5}}
[4,6,7,2,8,3,5,1]=>[5,7,8,4,3,6,2,1]=>[6,5,4,7,1,8,2,3]=>{{1,6,8},{2,5},{3,4,7}}
[3,6,2,7,8,4,1,5]=>[4,8,3,6,1,5,7,2]=>[4,3,7,6,2,1,8,5]=>{{1,4,6},{2,3,7,8},{5}}
[3,4,2,1,7,8,5,6]=>[2,4,3,1,8,5,7,6]=>[3,2,4,1,7,5,8,6]=>{{1,3,4},{2},{5,7,8},{6}}
[3,4,1,2,7,8,6,5]=>[4,1,3,2,6,8,7,5]=>[3,1,4,2,7,6,8,5]=>{{1,3,4},{2},{5,7,8},{6}}
[4,6,7,2,8,5,3,1]=>[3,5,8,4,7,6,2,1]=>[5,4,3,7,6,8,1,2]=>{{1,5,6,8},{2,4,7},{3}}
[4,6,7,2,8,1,5,3]=>[8,7,5,4,1,6,2,3]=>[4,5,6,7,3,8,2,1]=>{{1,4,7},{2,5},{3,6,8}}
[4,6,7,1,8,2,5,3]=>[7,8,5,4,2,6,1,3]=>[5,4,6,7,2,8,3,1]=>{{1,5},{2,4,7},{3,6,8}}
[5,6,7,8,2,4,3,1]=>[3,4,8,1,5,6,7,2]=>[5,4,3,2,6,7,8,1]=>{{1,5,6,7,8},{2,4},{3}}
[6,5,8,7,3,4,1,2]=>[4,1,7,3,6,5,8,2]=>[6,1,4,2,8,3,7,5]=>{{1,6},{2},{3,4},{5,8},{7}}
[1,6,7,4,5,2,3,8]=>[1,5,2,7,4,6,3,8]=>[1,6,2,5,3,7,4,8]=>{{1},{2,6,7},{3},{4,5},{8}}
[1,5,4,7,6,2,3,8]=>[1,6,2,5,4,7,3,8]=>[1,5,2,7,3,6,4,8]=>{{1},{2,5},{3},{4,7},{6},{8}}
[3,5,4,7,6,8,1,2]=>[8,1,3,5,4,7,6,2]=>[3,1,5,7,2,8,4,6]=>{{1,3,5},{2},{4,7},{6,8}}
[6,2,8,4,5,1,7,3]=>[5,6,7,8,4,2,1,3]=>[8,7,6,5,1,3,4,2]=>{{1,8},{2,7},{3,6},{4,5}}
[6,1,8,3,2,5,4,7]=>[6,3,8,5,2,1,4,7]=>[5,6,3,8,2,4,1,7]=>{{1,5},{2,6},{3},{4,8},{7}}
[2,6,7,3,1,5,8,4]=>[3,2,7,8,1,6,5,4]=>[2,7,3,6,4,8,1,5]=>{{1,2,7},{3},{4,6,8},{5}}
[5,4,1,8,7,2,3,6]=>[4,5,2,7,3,1,8,6]=>[8,5,1,4,2,3,7,6]=>{{1,8},{2,5},{3},{4},{6},{7}}
[5,3,1,8,2,7,4,6]=>[3,5,8,7,2,4,1,6]=>[8,5,3,7,2,1,6,4]=>{{1,8},{2,5},{3},{4,7},{6}}
[4,3,1,2,8,7,5,6]=>[3,1,4,2,7,5,8,6]=>[4,1,3,2,8,5,7,6]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,3,1,2,6,5,8,7]=>[3,1,4,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}
[5,3,1,6,2,4,8,7]=>[3,5,6,2,4,1,8,7]=>[6,5,3,1,2,4,8,7]=>{{1,6},{2,5},{3},{4},{7,8}}
[6,3,1,5,2,4,8,7]=>[3,6,5,2,4,1,8,7]=>[6,3,5,1,2,4,8,7]=>{{1,6},{2,3,5},{4},{7,8}}
[7,3,1,5,2,8,4,6]=>[3,7,5,8,2,4,1,6]=>[8,3,7,5,2,1,6,4]=>{{1,8},{2,3,7},{4,5},{6}}
[2,1,6,5,3,4,8,7]=>[2,1,5,3,6,4,8,7]=>[2,1,6,3,5,4,8,7]=>{{1,2},{3,6},{4},{5},{7,8}}
[4,6,5,1,2,3,8,7]=>[5,1,2,4,6,3,8,7]=>[4,1,2,6,5,3,8,7]=>{{1,4,6},{2},{3},{5},{7,8}}
[5,6,4,1,2,3,8,7]=>[4,1,2,6,5,3,8,7]=>[5,1,2,4,6,3,8,7]=>{{1,5,6},{2},{3},{4},{7,8}}
[6,5,4,1,2,3,8,7]=>[4,1,2,5,6,3,8,7]=>[6,1,2,4,5,3,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}
[7,6,4,1,8,2,3,5]=>[4,6,2,7,3,8,1,5]=>[8,7,1,4,2,6,5,3]=>{{1,8},{2,7},{3},{4},{5},{6}}
[6,7,4,1,8,2,3,5]=>[4,7,2,8,3,6,5,1]=>[7,6,1,4,2,8,3,5]=>{{1,7},{2,6,8},{3},{4},{5}}
[2,1,7,5,3,8,4,6]=>[2,1,5,7,8,4,6,3]=>[2,1,8,7,5,3,4,6]=>{{1,2},{3,8},{4,7},{5},{6}}
[2,1,8,5,3,7,4,6]=>[2,1,5,8,7,4,6,3]=>[2,1,8,5,7,3,4,6]=>{{1,2},{3,8},{4,5,7},{6}}
[4,8,5,1,2,7,3,6]=>[5,1,8,4,7,3,6,2]=>[5,1,4,8,7,2,3,6]=>{{1,5,7},{2},{3,4,8},{6}}
[5,8,6,7,1,2,3,4]=>[7,1,2,3,5,8,6,4]=>[5,1,2,3,8,7,4,6]=>{{1,5,8},{2},{3},{4},{6,7}}
[4,7,6,1,8,2,3,5]=>[6,7,2,4,3,8,5,1]=>[7,4,1,8,2,6,3,5]=>{{1,7},{2,4,8},{3},{5},{6}}
[4,3,1,2,7,8,5,6]=>[3,1,4,2,8,5,7,6]=>[4,1,3,2,7,5,8,6]=>{{1,4},{2},{3},{5,7,8},{6}}
[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,8,5,7,6]=>{{1,2},{3,4},{5,8},{6},{7}}
[3,4,1,2,8,7,5,6]=>[4,1,3,2,7,5,8,6]=>[3,1,4,2,8,5,7,6]=>{{1,3,4},{2},{5,8},{6},{7}}
[6,3,1,8,7,2,4,5]=>[3,6,7,2,4,5,8,1]=>[8,6,3,1,2,4,7,5]=>{{1,8},{2,6},{3},{4},{5},{7}}
[7,4,8,1,6,2,3,5]=>[8,6,2,7,3,1,4,5]=>[6,8,1,7,3,5,4,2]=>{{1,6},{2,8},{3},{4,7},{5}}
[5,4,8,1,2,7,3,6]=>[8,1,7,5,4,3,2,6]=>[5,1,7,8,2,3,6,4]=>{{1,5},{2},{3,7},{4,8},{6}}
[4,5,8,1,2,7,3,6]=>[8,1,7,4,5,3,2,6]=>[4,1,5,7,8,2,6,3]=>{{1,4,7},{2},{3,5,8},{6}}
[2,1,6,8,7,3,4,5]=>[2,1,7,3,4,6,8,5]=>[2,1,6,3,4,8,7,5]=>{{1,2},{3,6,8},{4},{5},{7}}
[5,6,8,7,1,2,3,4]=>[7,1,2,3,5,6,8,4]=>[5,1,2,3,6,8,7,4]=>{{1,5,6,8},{2},{3},{4},{7}}
[7,5,8,6,1,2,3,4]=>[6,1,2,3,8,7,4,5]=>[8,1,2,3,6,7,5,4]=>{{1,8},{2},{3},{4},{5,6,7}}
[8,5,7,6,1,2,3,4]=>[6,1,2,3,7,8,4,5]=>[8,1,2,3,7,6,5,4]=>{{1,8},{2},{3},{4},{5,7},{6}}
[5,7,8,6,1,2,3,4]=>[6,1,2,3,5,8,7,4]=>[5,1,2,3,7,6,8,4]=>{{1,5,7,8},{2},{3},{4},{6}}
[3,7,1,8,6,2,4,5]=>[7,6,3,2,4,8,1,5]=>[3,7,8,1,2,6,5,4]=>{{1,3,8},{2,7},{4},{5},{6}}
[2,1,7,8,6,3,4,5]=>[2,1,6,3,4,8,7,5]=>[2,1,7,3,4,6,8,5]=>{{1,2},{3,7,8},{4},{5},{6}}
[2,1,8,7,6,3,4,5]=>[2,1,6,3,4,7,8,5]=>[2,1,8,3,4,6,7,5]=>{{1,2},{3,8},{4},{5},{6},{7}}
[3,8,1,7,6,2,4,5]=>[8,6,3,2,4,7,1,5]=>[3,6,8,1,2,7,5,4]=>{{1,3,8},{2,6,7},{4},{5}}
[5,8,7,6,1,2,3,4]=>[6,1,2,3,5,7,8,4]=>[5,1,2,3,8,6,7,4]=>{{1,5,8},{2},{3},{4},{6},{7}}
[6,8,7,5,1,2,3,4]=>[5,1,2,3,7,6,8,4]=>[6,1,2,3,5,8,7,4]=>{{1,6,8},{2},{3},{4},{5},{7}}
[5,4,2,7,6,1,8,3]=>[6,4,5,7,3,8,2,1]=>[5,8,7,4,1,6,2,3]=>{{1,5},{2,8},{3,7},{4},{6}}
[5,4,2,6,7,1,8,3]=>[7,4,5,8,3,6,1,2]=>[5,7,6,4,1,8,3,2]=>{{1,5},{2,7},{3,6,8},{4}}
[5,3,2,6,1,7,4,8]=>[6,3,5,7,2,1,4,8]=>[3,7,6,5,2,4,1,8]=>{{1,3,6},{2,7},{4,5},{8}}
[5,4,2,6,8,1,7,3]=>[8,4,5,7,3,6,1,2]=>[4,7,6,5,1,8,3,2]=>{{1,4,5},{2,7},{3,6,8}}
[5,3,2,6,1,8,4,7]=>[6,3,5,8,2,1,4,7]=>[3,8,6,5,2,4,1,7]=>{{1,3,6},{2,8},{4,5},{7}}
[6,3,8,2,1,5,7,4]=>[2,8,6,7,1,3,5,4]=>[6,2,8,7,4,5,1,3]=>{{1,6},{2},{3,8},{4,7},{5}}
[5,3,2,8,1,6,7,4]=>[8,3,5,7,2,1,6,4]=>[3,8,5,7,2,4,1,6]=>{{1,3,5},{2,8},{4,7},{6}}
[6,5,7,8,2,1,4,3]=>[2,8,4,1,6,5,7,3]=>[4,2,6,3,7,1,8,5]=>{{1,4},{2},{3,6},{5,7,8}}
[4,3,2,1,8,7,5,6]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,8,5,7,6]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,3,2,1,7,5,8,6]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}}
[4,3,2,1,8,5,6,7]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[7,8,5,6,1,2,4,3]=>[6,1,4,2,8,5,7,3]=>[4,1,7,3,6,2,8,5]=>{{1,4},{2},{3,7,8},{5,6}}
[2,6,8,4,7,1,5,3]=>[7,2,5,8,1,6,4,3]=>[2,6,7,5,4,8,1,3]=>{{1,2,6,8},{3,7},{4,5}}
[5,3,4,8,7,6,1,2]=>[6,1,5,3,4,7,8,2]=>[5,1,8,2,3,6,7,4]=>{{1,5},{2},{3,8},{4},{6},{7}}
[4,1,2,3,8,7,6,5]=>[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,3,1,2,8,7,6,5]=>[3,1,4,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>{{1,4},{2},{3},{5,8},{6},{7}}
[5,3,1,8,2,7,6,4]=>[3,5,8,6,2,7,1,4]=>[8,5,3,6,2,7,4,1]=>{{1,8},{2,5},{3},{4,6,7}}
[1,5,3,8,2,7,6,4]=>[1,8,5,6,3,7,2,4]=>[1,5,8,6,3,7,4,2]=>{{1},{2,5},{3,8},{4,6,7}}
[1,5,4,8,7,2,6,3]=>[1,7,6,5,4,2,8,3]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,6},{4,8},{7}}
[6,5,8,7,1,2,4,3]=>[7,1,4,2,6,5,8,3]=>[4,1,6,3,8,2,7,5]=>{{1,4},{2},{3,6},{5,8},{7}}
[4,6,8,2,7,1,5,3]=>[7,8,5,4,1,6,2,3]=>[5,4,6,7,3,8,2,1]=>{{1,5},{2,4,7},{3,6,8}}
[3,1,4,2,8,7,6,5]=>[3,4,1,2,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>{{1,4},{2,3},{5,8},{6},{7}}
[4,3,5,8,7,6,1,2]=>[6,1,4,3,5,7,8,2]=>[4,1,5,2,8,6,7,3]=>{{1,4},{2},{3,5,8},{6},{7}}
[3,4,5,8,7,6,1,2]=>[6,1,3,4,5,7,8,2]=>[3,1,4,5,8,6,7,2]=>{{1,3,4,5,8},{2},{6},{7}}
[2,3,5,8,1,7,6,4]=>[8,2,3,6,5,7,1,4]=>[2,3,5,6,8,7,4,1]=>{{1,2,3,5,8},{4,6,7}}
[4,1,3,2,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[3,4,2,1,6,5,8,7]=>{{1,3},{2,4},{5,6},{7,8}}
[6,1,3,2,5,4,8,7]=>[6,3,1,5,2,4,8,7]=>[3,5,2,6,4,1,8,7]=>{{1,3},{2,5},{4,6},{7,8}}
[8,1,3,2,5,4,7,6]=>[8,3,1,5,2,7,4,6]=>[3,5,2,7,4,8,6,1]=>{{1,3},{2,5},{4,7},{6,8}}
[5,1,4,2,6,3,8,7]=>[5,4,6,1,2,3,8,7]=>[5,6,4,3,2,1,8,7]=>{{1,5},{2,6},{3,4},{7,8}}
[2,1,6,3,5,4,8,7]=>[2,1,6,5,3,4,8,7]=>[2,1,5,6,4,3,8,7]=>{{1,2},{3,5},{4,6},{7,8}}
[5,2,6,1,4,3,8,7]=>[6,5,4,1,2,3,8,7]=>[4,5,6,3,2,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[5,2,8,1,4,3,7,6]=>[8,5,4,1,2,7,3,6]=>[4,5,7,3,2,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}
[2,1,8,3,5,4,7,6]=>[2,1,8,5,3,7,4,6]=>[2,1,5,7,4,8,6,3]=>{{1,2},{3,5},{4,7},{6,8}}
[8,1,4,3,7,2,6,5]=>[8,7,4,1,6,3,5,2]=>[4,6,7,3,8,2,1,5]=>{{1,4},{2,6},{3,7},{5,8}}
[8,2,6,1,5,3,7,4]=>[6,8,5,7,1,2,3,4]=>[7,5,8,6,4,3,2,1]=>{{1,7},{2,5},{3,8},{4,6}}
[7,2,6,1,5,3,8,4]=>[6,7,5,8,1,2,3,4]=>[7,6,8,5,4,3,2,1]=>{{1,7},{2,6},{3,8},{4,5}}
[6,2,7,1,5,3,8,4]=>[7,6,5,8,1,2,3,4]=>[6,7,8,5,4,3,2,1]=>{{1,6},{2,7},{3,8},{4,5}}
[8,1,5,2,6,3,7,4]=>[8,5,6,7,1,2,3,4]=>[5,8,7,6,4,3,2,1]=>{{1,5},{2,8},{3,7},{4,6}}
[6,1,5,2,7,3,8,4]=>[6,5,7,8,1,2,3,4]=>[7,8,6,5,4,3,2,1]=>{{1,7},{2,8},{3,6},{4,5}}
[6,1,3,2,7,4,8,5]=>[6,3,1,7,8,2,4,5]=>[3,8,2,7,6,5,4,1]=>{{1,3},{2,8},{4,7},{5,6}}
[4,1,3,2,7,5,8,6]=>[4,3,1,2,7,8,5,6]=>[3,4,2,1,8,7,6,5]=>{{1,3},{2,4},{5,8},{6,7}}
[2,1,4,3,8,5,7,6]=>[2,1,4,3,8,7,5,6]=>[2,1,4,3,7,8,6,5]=>{{1,2},{3,4},{5,7},{6,8}}
[3,1,4,2,8,5,7,6]=>[3,4,1,2,8,7,5,6]=>[4,3,2,1,7,8,6,5]=>{{1,4},{2,3},{5,7},{6,8}}
[4,1,3,2,8,5,7,6]=>[4,3,1,2,8,7,5,6]=>[3,4,2,1,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}
[5,1,3,2,8,4,7,6]=>[5,3,1,8,2,7,4,6]=>[3,7,2,5,4,8,6,1]=>{{1,3},{2,7},{4,5},{6,8}}
[7,4,8,1,3,2,6,5]=>[8,3,1,7,6,2,4,5]=>[3,6,2,7,8,5,4,1]=>{{1,3},{2,6},{4,7},{5,8}}
[6,1,5,2,8,3,7,4]=>[6,5,8,7,1,2,3,4]=>[7,8,5,6,4,3,2,1]=>{{1,7},{2,8},{3,5},{4,6}}
[7,3,8,1,5,2,6,4]=>[8,5,7,6,1,2,3,4]=>[5,8,6,7,4,3,2,1]=>{{1,5},{2,8},{3,6},{4,7}}
[8,3,7,2,6,1,5,4]=>[6,7,8,5,1,2,3,4]=>[7,6,5,8,4,3,2,1]=>{{1,7},{2,6},{3,5},{4,8}}
[2,1,7,4,8,3,6,5]=>[2,1,8,7,6,3,4,5]=>[2,1,6,7,8,5,4,3]=>{{1,2},{3,6},{4,7},{5,8}}
[7,3,8,2,6,1,5,4]=>[6,8,7,5,1,2,3,4]=>[7,5,6,8,4,3,2,1]=>{{1,7},{2,5},{3,6},{4,8}}
[7,2,6,3,8,1,5,4]=>[8,7,6,5,1,4,2,3]=>[5,6,7,8,4,1,3,2]=>{{1,5},{2,6},{3,7},{4,8}}
[5,3,6,2,4,8,1,7]=>[8,6,5,2,3,4,1,7]=>[5,6,8,2,3,1,4,7]=>{{1,5},{2,6},{3,8},{4},{7}}
[5,3,1,6,8,2,4,7]=>[3,5,8,2,4,6,1,7]=>[6,5,3,1,2,8,4,7]=>{{1,6,8},{2,5},{3},{4},{7}}
[3,5,6,1,4,8,2,7]=>[6,8,3,1,5,4,2,7]=>[5,3,6,2,8,1,4,7]=>{{1,5,8},{2,3,6},{4},{7}}
[6,7,4,8,3,2,5,1]=>[5,3,8,7,2,6,4,1]=>[5,7,3,6,2,8,1,4]=>{{1,5},{2,7},{3},{4,6,8}}
[6,7,4,1,8,3,2,5]=>[4,3,7,8,2,6,5,1]=>[6,7,3,4,1,8,2,5]=>{{1,6,8},{2,7},{3},{4},{5}}
[7,3,5,8,1,4,6,2]=>[8,6,7,1,4,3,2,5]=>[6,8,7,3,1,4,5,2]=>{{1,6},{2,8},{3,7},{4},{5}}
[6,7,4,8,3,1,5,2]=>[3,8,5,7,2,6,4,1]=>[7,3,5,6,2,8,1,4]=>{{1,7},{2,3,5},{4,6,8}}
[6,7,4,8,3,5,2,1]=>[2,5,8,7,3,6,4,1]=>[7,2,5,6,3,8,1,4]=>{{1,7},{2},{3,5},{4,6,8}}
[5,6,2,7,3,8,4,1]=>[4,8,6,7,5,3,1,2]=>[7,4,6,5,8,1,3,2]=>{{1,7},{2,4,5,8},{3,6}}
[7,4,2,5,1,8,3,6]=>[5,4,7,8,2,3,6,1]=>[7,8,5,4,2,1,3,6]=>{{1,7},{2,8},{3,5},{4},{6}}
[3,7,8,1,4,6,2,5]=>[8,6,3,1,4,5,7,2]=>[3,6,7,2,1,4,8,5]=>{{1,3,7,8},{2,6},{4},{5}}
[5,1,6,2,7,8,4,3]=>[5,6,4,8,1,2,7,3]=>[6,5,7,4,3,2,8,1]=>{{1,6},{2,5},{3,7,8},{4}}
[5,6,2,1,7,8,4,3]=>[2,6,4,8,5,1,7,3]=>[5,2,6,4,7,3,8,1]=>{{1,5,7,8},{2},{3,6},{4}}
[5,6,7,2,8,4,3,1]=>[3,4,8,7,5,6,2,1]=>[6,4,3,5,7,8,1,2]=>{{1,6,8},{2,4,5,7},{3}}
[5,6,1,7,2,8,4,3]=>[6,7,4,8,5,1,2,3]=>[6,5,7,4,8,3,2,1]=>{{1,6},{2,5,8},{3,7},{4}}
[8,6,1,3,4,2,5,7]=>[6,4,1,3,2,8,5,7]=>[4,8,2,1,3,6,5,7]=>{{1,4},{2,8},{3},{5},{6},{7}}
[8,3,2,5,1,6,4,7]=>[5,3,8,6,2,1,4,7]=>[5,8,3,6,2,4,1,7]=>{{1,5},{2,8},{3},{4,6},{7}}
[7,2,4,5,8,3,6,1]=>[6,7,8,2,3,5,4,1]=>[8,7,6,2,3,1,4,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[8,4,1,5,6,3,2,7]=>[4,3,8,6,1,2,5,7]=>[4,8,3,6,2,5,1,7]=>{{1,4,6},{2,8},{3},{5},{7}}
[4,5,3,7,2,1,8,6]=>[2,7,5,4,3,8,1,6]=>[4,2,5,8,1,7,6,3]=>{{1,4,8},{2},{3,5},{6,7}}
[4,1,5,3,7,2,8,6]=>[4,7,5,1,3,8,2,6]=>[8,4,5,3,1,7,6,2]=>{{1,8},{2,4},{3,5},{6,7}}
[1,6,4,7,8,3,5,2]=>[1,5,8,6,3,4,7,2]=>[1,7,5,6,3,2,8,4]=>{{1},{2,7,8},{3,5},{4,6}}
[4,3,6,7,8,1,2,5]=>[8,1,4,3,2,6,7,5]=>[4,1,6,2,3,7,8,5]=>{{1,4},{2},{3,6,7,8},{5}}
[3,5,6,7,8,2,1,4]=>[2,8,3,1,5,6,7,4]=>[3,2,5,1,6,7,8,4]=>{{1,3,5,6,7,8},{2},{4}}
[4,2,6,7,8,3,1,5]=>[3,8,4,1,2,6,7,5]=>[6,3,4,2,1,7,8,5]=>{{1,6,7,8},{2,3,4},{5}}
[3,2,1,6,4,7,8,5]=>[2,3,1,6,8,4,7,5]=>[3,2,1,7,6,5,8,4]=>{{1,3},{2},{4,7,8},{5,6}}
[7,8,1,3,4,2,6,5]=>[8,4,1,3,6,2,7,5]=>[4,6,2,1,7,5,8,3]=>{{1,4},{2,6},{3},{5,7,8}}
[7,8,3,4,2,1,6,5]=>[2,4,8,3,6,1,7,5]=>[6,2,4,1,7,5,8,3]=>{{1,6},{2},{3,4},{5,7,8}}
[3,6,2,7,1,8,5,4]=>[7,6,3,5,8,2,1,4]=>[3,6,7,8,5,2,4,1]=>{{1,3,7},{2,6},{4,8},{5}}
[4,6,2,7,8,1,5,3]=>[8,6,5,4,1,2,7,3]=>[4,5,6,7,3,2,8,1]=>{{1,4,7,8},{2,5},{3,6}}
[4,5,2,3,7,6,1,8]=>[6,5,2,4,3,7,1,8]=>[4,5,1,7,2,6,3,8]=>{{1,4,7},{2,5},{3},{6},{8}}
[5,7,6,2,4,3,1,8]=>[3,4,6,1,5,7,2,8]=>[5,4,3,2,7,6,1,8]=>{{1,5,7},{2,4},{3},{6},{8}}
[7,1,5,4,8,2,6,3]=>[7,8,6,5,1,4,3,2]=>[6,5,7,8,4,1,2,3]=>{{1,6},{2,5},{3,7},{4,8}}
[1,7,6,8,4,3,5,2]=>[1,5,4,8,3,7,6,2]=>[1,5,7,4,2,8,3,6]=>{{1},{2,5},{3,7},{4},{6,8}}
[7,6,8,1,3,2,4,5]=>[8,3,1,2,4,7,6,5]=>[3,7,2,1,4,8,5,6]=>{{1,3},{2,7},{4},{5},{6,8}}
[7,5,8,3,1,2,4,6]=>[3,1,8,2,7,4,5,6]=>[7,1,3,2,8,5,6,4]=>{{1,7},{2},{3},{4},{5,8},{6}}
[8,5,7,3,1,4,2,6]=>[3,7,4,2,8,1,5,6]=>[8,3,4,1,7,5,6,2]=>{{1,8},{2,3,4},{5,7},{6}}
[5,6,1,2,3,8,7,4]=>[6,1,2,7,5,3,8,4]=>[6,1,2,5,8,4,7,3]=>{{1,6},{2},{3},{4,5,8},{7}}
[7,6,1,8,3,2,5,4]=>[6,3,7,5,2,8,4,1]=>[5,7,3,8,2,6,1,4]=>{{1,5},{2,7},{3},{4,8},{6}}
[1,6,8,7,3,5,4,2]=>[1,4,5,7,2,6,8,3]=>[1,6,5,4,3,8,7,2]=>{{1},{2,6,8},{3,5},{4},{7}}
[5,8,1,2,7,6,3,4]=>[8,1,6,3,5,7,2,4]=>[5,1,6,2,8,7,4,3]=>{{1,5,8},{2},{3,6,7},{4}}
[4,8,2,1,7,6,3,5]=>[2,8,6,4,3,7,1,5]=>[4,2,6,8,1,7,5,3]=>{{1,4,8},{2},{3,6,7},{5}}
[7,1,5,2,8,4,6,3]=>[7,5,6,8,1,4,2,3]=>[6,8,7,5,4,1,3,2]=>{{1,6},{2,8},{3,7},{4,5}}
[8,1,5,2,7,4,6,3]=>[8,5,6,7,1,4,2,3]=>[5,8,7,6,4,1,3,2]=>{{1,5},{2,8},{3,7},{4,6}}
[8,4,1,7,2,3,5,6]=>[4,8,2,7,3,5,6,1]=>[8,4,1,7,2,3,5,6]=>{{1,8},{2,4,7},{3},{5},{6}}
[7,4,1,6,2,3,5,8]=>[4,7,2,6,3,5,1,8]=>[7,4,1,6,2,3,5,8]=>{{1,7},{2,4,6},{3},{5},{8}}
[8,1,6,7,2,4,5,3]=>[8,7,5,2,4,1,6,3]=>[5,7,8,2,1,4,3,6]=>{{1,5},{2,7},{3,8},{4},{6}}
[3,1,2,7,8,5,6,4]=>[3,1,2,6,8,5,7,4]=>[3,1,2,7,6,4,8,5]=>{{1,3},{2},{4,7,8},{5,6}}
[4,8,1,2,7,3,6,5]=>[8,1,7,4,6,3,2,5]=>[4,1,6,7,8,3,5,2]=>{{1,4,7},{2},{3,6},{5,8}}
[6,8,1,7,2,3,5,4]=>[8,7,2,5,3,6,1,4]=>[5,6,1,7,3,8,4,2]=>{{1,5},{2,6,8},{3},{4,7}}
[5,8,7,1,2,3,4,6]=>[7,1,2,3,5,4,8,6]=>[5,1,2,3,8,4,7,6]=>{{1,5,8},{2},{3},{4},{6},{7}}
[7,1,8,6,2,4,5,3]=>[7,6,5,2,4,8,1,3]=>[5,7,8,2,1,6,4,3]=>{{1,5},{2,7},{3,8},{4},{6}}
[3,2,5,1,6,4,8,7]=>[5,3,2,6,1,4,8,7]=>[3,6,1,5,4,2,8,7]=>{{1,3},{2,6},{4,5},{7,8}}
[3,2,5,4,7,1,8,6]=>[7,3,2,5,4,8,1,6]=>[3,5,1,8,2,7,6,4]=>{{1,3},{2,5},{4,8},{6,7}}
[4,2,5,3,7,6,8,1]=>[8,4,5,2,3,7,6,1]=>[4,7,5,2,1,8,3,6]=>{{1,4},{2,7},{3,5},{6,8}}
[4,2,5,3,7,1,8,6]=>[7,4,5,2,3,8,1,6]=>[4,8,5,2,1,7,6,3]=>{{1,4},{2,8},{3,5},{6,7}}
[4,2,5,3,6,1,8,7]=>[6,4,5,2,3,1,8,7]=>[4,6,5,2,1,3,8,7]=>{{1,4},{2,6},{3,5},{7,8}}
[4,2,5,1,6,3,8,7]=>[5,4,6,2,1,3,8,7]=>[5,6,4,2,3,1,8,7]=>{{1,5},{2,6},{3,4},{7,8}}
[3,1,5,4,6,2,8,7]=>[3,6,1,5,4,2,8,7]=>[5,3,2,6,1,4,8,7]=>{{1,5},{2,3},{4,6},{7,8}}
[4,1,5,3,6,2,8,7]=>[4,6,5,1,3,2,8,7]=>[6,4,5,3,1,2,8,7]=>{{1,6},{2,4},{3,5},{7,8}}
[4,3,5,1,6,2,8,7]=>[5,6,4,3,1,2,8,7]=>[5,4,6,1,3,2,8,7]=>{{1,5},{2,4},{3,6},{7,8}}
[4,3,5,2,7,1,8,6]=>[7,5,4,3,2,8,1,6]=>[4,5,8,1,2,7,6,3]=>{{1,4},{2,5},{3,8},{6,7}}
[4,3,6,2,7,5,8,1]=>[8,6,4,3,7,2,5,1]=>[4,6,8,1,7,3,2,5]=>{{1,4},{2,6},{3,8},{5,7}}
[4,3,6,2,7,1,8,5]=>[7,6,4,3,8,2,1,5]=>[4,7,8,1,6,3,5,2]=>{{1,4},{2,7},{3,8},{5,6}}
[4,3,6,1,7,2,8,5]=>[6,7,4,3,8,1,2,5]=>[7,4,8,1,6,5,3,2]=>{{1,7},{2,4},{3,8},{5,6}}
[4,3,5,1,7,2,8,6]=>[5,7,4,3,1,8,2,6]=>[5,4,8,1,3,7,6,2]=>{{1,5},{2,4},{3,8},{6,7}}
[3,1,5,4,7,2,8,6]=>[3,7,1,5,4,8,2,6]=>[5,3,2,8,1,7,6,4]=>{{1,5},{2,3},{4,8},{6,7}}
[2,1,5,4,7,3,8,6]=>[2,1,7,5,4,8,3,6]=>[2,1,5,8,3,7,6,4]=>{{1,2},{3,5},{4,8},{6,7}}
[3,1,5,4,7,6,8,2]=>[3,8,1,5,4,7,6,2]=>[5,3,2,7,1,8,4,6]=>{{1,5},{2,3},{4,7},{6,8}}
[4,1,5,3,7,6,8,2]=>[4,8,5,1,3,7,6,2]=>[7,4,5,3,1,8,2,6]=>{{1,7},{2,4},{3,5},{6,8}}
[4,3,5,1,7,6,8,2]=>[5,8,4,3,1,7,6,2]=>[5,4,7,1,3,8,2,6]=>{{1,5},{2,4},{3,7},{6,8}}
[4,3,6,1,7,5,8,2]=>[6,8,4,3,7,1,5,2]=>[6,4,8,1,7,5,2,3]=>{{1,6},{2,4},{3,8},{5,7}}
[4,3,6,5,7,1,8,2]=>[7,8,4,3,6,5,1,2]=>[6,4,7,1,8,2,5,3]=>{{1,6},{2,4},{3,7},{5,8}}
[5,3,6,4,7,2,8,1]=>[8,7,5,6,3,4,2,1]=>[5,6,8,7,2,1,3,4]=>{{1,5},{2,6},{3,8},{4,7}}
[5,3,6,4,7,1,8,2]=>[7,8,5,6,3,4,1,2]=>[6,5,8,7,2,1,4,3]=>{{1,6},{2,5},{3,8},{4,7}}
[5,3,6,1,7,4,8,2]=>[6,8,5,7,3,1,4,2]=>[7,5,8,6,2,4,1,3]=>{{1,7},{2,5},{3,8},{4,6}}
[5,1,6,3,7,4,8,2]=>[5,8,6,7,1,3,4,2]=>[8,5,7,6,4,2,1,3]=>{{1,8},{2,5},{3,7},{4,6}}
[4,1,6,3,7,5,8,2]=>[4,8,6,1,7,3,5,2]=>[8,4,6,3,7,2,1,5]=>{{1,8},{2,4},{3,6},{5,7}}
[3,1,6,4,7,5,8,2]=>[3,8,1,6,7,4,5,2]=>[6,3,2,8,7,4,1,5]=>{{1,6},{2,3},{4,8},{5,7}}
[2,1,6,4,7,5,8,3]=>[2,1,8,6,7,4,5,3]=>[2,1,6,8,7,4,3,5]=>{{1,2},{3,6},{4,8},{5,7}}
[2,1,6,4,7,3,8,5]=>[2,1,7,6,8,4,3,5]=>[2,1,7,8,6,4,5,3]=>{{1,2},{3,7},{4,8},{5,6}}
[3,1,6,4,7,2,8,5]=>[3,7,1,6,8,4,2,5]=>[7,3,2,8,6,4,5,1]=>{{1,7},{2,3},{4,8},{5,6}}
[4,1,6,3,7,2,8,5]=>[4,7,6,1,8,3,2,5]=>[8,4,7,3,6,2,5,1]=>{{1,8},{2,4},{3,7},{5,6}}
[5,1,6,3,7,2,8,4]=>[5,7,6,8,1,3,2,4]=>[8,6,7,5,4,2,3,1]=>{{1,8},{2,6},{3,7},{4,5}}
[5,3,6,1,7,2,8,4]=>[6,7,5,8,3,1,2,4]=>[7,6,8,5,2,4,3,1]=>{{1,7},{2,6},{3,8},{4,5}}
[5,3,6,2,7,1,8,4]=>[7,6,5,8,3,2,1,4]=>[6,7,8,5,2,3,4,1]=>{{1,6},{2,7},{3,8},{4,5}}
[5,3,6,2,7,4,8,1]=>[8,6,5,7,3,2,4,1]=>[5,7,8,6,2,3,1,4]=>{{1,5},{2,7},{3,8},{4,6}}
[5,2,6,3,7,4,8,1]=>[8,5,6,7,2,3,4,1]=>[5,8,7,6,3,2,1,4]=>{{1,5},{2,8},{3,7},{4,6}}
[5,2,6,3,7,1,8,4]=>[7,5,6,8,2,3,1,4]=>[6,8,7,5,3,2,4,1]=>{{1,6},{2,8},{3,7},{4,5}}
[5,2,6,1,7,3,8,4]=>[6,5,7,8,2,1,3,4]=>[7,8,6,5,3,4,2,1]=>{{1,7},{2,8},{3,6},{4,5}}
[4,2,5,1,7,3,8,6]=>[5,4,7,2,1,8,3,6]=>[5,8,4,2,3,7,6,1]=>{{1,5},{2,8},{3,4},{6,7}}
[4,2,6,1,7,3,8,5]=>[6,4,7,2,8,1,3,5]=>[7,8,4,2,6,5,3,1]=>{{1,7},{2,8},{3,4},{5,6}}
[4,2,6,3,7,1,8,5]=>[7,4,6,2,8,3,1,5]=>[4,8,7,2,6,3,5,1]=>{{1,4},{2,8},{3,7},{5,6}}
[4,2,6,3,7,5,8,1]=>[8,4,6,2,7,3,5,1]=>[4,8,6,2,7,3,1,5]=>{{1,4},{2,8},{3,6},{5,7}}
[3,2,6,4,7,5,8,1]=>[8,3,2,6,7,4,5,1]=>[3,6,1,8,7,4,2,5]=>{{1,3},{2,6},{4,8},{5,7}}
[3,2,6,4,7,1,8,5]=>[7,3,2,6,8,4,1,5]=>[3,7,1,8,6,4,5,2]=>{{1,3},{2,7},{4,8},{5,6}}
[3,2,6,1,7,4,8,5]=>[6,3,2,7,8,1,4,5]=>[3,8,1,7,6,5,4,2]=>{{1,3},{2,8},{4,7},{5,6}}
[3,2,5,1,7,4,8,6]=>[5,3,2,7,1,8,4,6]=>[3,8,1,5,4,7,6,2]=>{{1,3},{2,8},{4,5},{6,7}}
[3,2,4,1,7,5,8,6]=>[4,3,2,1,7,8,5,6]=>[3,4,1,2,8,7,6,5]=>{{1,3},{2,4},{5,8},{6,7}}
[3,1,4,2,7,6,8,5]=>[3,4,1,2,8,7,6,5]=>[4,3,2,1,7,8,5,6]=>{{1,4},{2,3},{5,7},{6,8}}
[3,2,5,1,7,6,8,4]=>[5,3,2,8,1,7,6,4]=>[3,7,1,5,4,8,2,6]=>{{1,3},{2,7},{4,5},{6,8}}
[3,2,6,1,7,5,8,4]=>[6,3,2,8,7,1,5,4]=>[3,8,1,6,7,5,2,4]=>{{1,3},{2,8},{4,6},{5,7}}
[3,2,6,5,7,1,8,4]=>[7,3,2,8,6,5,1,4]=>[3,7,1,6,8,2,5,4]=>{{1,3},{2,7},{4,6},{5,8}}
[4,2,6,5,7,3,8,1]=>[8,4,7,2,6,5,3,1]=>[4,7,6,2,8,1,3,5]=>{{1,4},{2,7},{3,6},{5,8}}
[4,2,6,5,7,1,8,3]=>[7,4,8,2,6,5,1,3]=>[6,7,4,2,8,1,5,3]=>{{1,6},{2,7},{3,4},{5,8}}
[4,2,6,1,7,5,8,3]=>[6,4,8,2,7,1,5,3]=>[6,8,4,2,7,5,1,3]=>{{1,6},{2,8},{3,4},{5,7}}
[4,2,5,1,7,6,8,3]=>[5,4,8,2,1,7,6,3]=>[5,7,4,2,3,8,1,6]=>{{1,5},{2,7},{3,4},{6,8}}
[4,1,5,2,7,6,8,3]=>[4,5,8,1,2,7,6,3]=>[7,5,4,3,2,8,1,6]=>{{1,7},{2,5},{3,4},{6,8}}
[3,1,5,2,7,6,8,4]=>[3,5,1,8,2,7,6,4]=>[7,3,2,5,4,8,1,6]=>{{1,7},{2,3},{4,5},{6,8}}
[2,1,5,3,7,6,8,4]=>[2,1,5,8,3,7,6,4]=>[2,1,7,5,4,8,3,6]=>{{1,2},{3,7},{4,5},{6,8}}
[2,1,6,3,7,5,8,4]=>[2,1,6,8,7,3,5,4]=>[2,1,8,6,7,5,3,4]=>{{1,2},{3,8},{4,6},{5,7}}
[3,1,6,2,7,5,8,4]=>[3,6,1,8,7,2,5,4]=>[8,3,2,6,7,5,1,4]=>{{1,8},{2,3},{4,6},{5,7}}
[4,1,6,2,7,5,8,3]=>[4,6,8,1,7,2,5,3]=>[8,6,4,3,7,5,1,2]=>{{1,8},{2,6},{3,4},{5,7}}
[5,1,6,2,7,4,8,3]=>[5,6,8,7,1,2,4,3]=>[8,7,5,6,4,3,1,2]=>{{1,8},{2,7},{3,5},{4,6}}
[5,2,6,1,7,4,8,3]=>[6,5,8,7,2,1,4,3]=>[7,8,5,6,3,4,1,2]=>{{1,7},{2,8},{3,5},{4,6}}
[5,2,6,4,7,1,8,3]=>[7,5,8,6,2,4,1,3]=>[6,8,5,7,3,1,4,2]=>{{1,6},{2,8},{3,5},{4,7}}
[5,2,6,4,7,3,8,1]=>[8,5,7,6,2,4,3,1]=>[5,8,6,7,3,1,2,4]=>{{1,5},{2,8},{3,6},{4,7}}
[5,4,6,2,7,3,8,1]=>[8,6,7,5,4,2,3,1]=>[5,7,6,8,1,3,2,4]=>{{1,5},{2,7},{3,6},{4,8}}
[5,4,6,2,7,1,8,3]=>[7,6,8,5,4,2,1,3]=>[6,7,5,8,1,3,4,2]=>{{1,6},{2,7},{3,5},{4,8}}
[5,4,6,1,7,2,8,3]=>[6,7,8,5,4,1,2,3]=>[7,6,5,8,1,4,3,2]=>{{1,7},{2,6},{3,5},{4,8}}
[5,1,6,4,7,2,8,3]=>[5,7,8,6,1,4,2,3]=>[8,6,5,7,4,1,3,2]=>{{1,8},{2,6},{3,5},{4,7}}
[4,1,6,5,7,2,8,3]=>[4,7,8,1,6,5,2,3]=>[7,6,4,3,8,1,5,2]=>{{1,7},{2,6},{3,4},{5,8}}
[3,1,6,5,7,2,8,4]=>[3,7,1,8,6,5,2,4]=>[7,3,2,6,8,1,5,4]=>{{1,7},{2,3},{4,6},{5,8}}
[2,1,6,5,7,3,8,4]=>[2,1,7,8,6,5,3,4]=>[2,1,7,6,8,3,5,4]=>{{1,2},{3,7},{4,6},{5,8}}
[3,1,6,5,7,4,8,2]=>[3,8,1,7,6,5,4,2]=>[6,3,2,7,8,1,4,5]=>{{1,6},{2,3},{4,7},{5,8}}
[4,1,6,5,7,3,8,2]=>[4,8,7,1,6,5,3,2]=>[7,4,6,3,8,1,2,5]=>{{1,7},{2,4},{3,6},{5,8}}
[5,1,6,4,7,3,8,2]=>[5,8,7,6,1,4,3,2]=>[8,5,6,7,4,1,2,3]=>{{1,8},{2,5},{3,6},{4,7}}
[5,4,6,1,7,3,8,2]=>[6,8,7,5,4,1,3,2]=>[7,5,6,8,1,4,2,3]=>{{1,7},{2,5},{3,6},{4,8}}
[5,4,6,3,7,1,8,2]=>[7,8,6,5,4,3,1,2]=>[6,5,7,8,1,2,4,3]=>{{1,6},{2,5},{3,7},{4,8}}
[1,4,6,7,3,2,8,5]=>[1,3,7,4,8,6,2,5]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,7},{3},{5,6,8}}
[1,7,4,8,6,3,5,2]=>[1,5,6,8,3,7,2,4]=>[1,8,6,5,3,7,4,2]=>{{1},{2,8},{3,6,7},{4,5}}
[1,3,6,7,5,8,2,4]=>[1,8,3,2,7,6,5,4]=>[1,3,6,2,7,8,4,5]=>{{1},{2,3,6,8},{4},{5,7}}
[3,7,6,5,8,2,1,4]=>[2,8,3,1,6,7,5,4]=>[3,2,6,1,8,7,4,5]=>{{1,3,6,7},{2},{4},{5,8}}
[2,1,6,5,7,8,3,4]=>[2,1,8,3,6,5,7,4]=>[2,1,6,3,7,4,8,5]=>{{1,2},{3,6},{4},{5,7,8}}
[3,8,2,4,6,7,5,1]=>[5,7,3,2,8,4,1,6]=>[7,3,8,1,5,2,6,4]=>{{1,7},{2,3,8},{4},{5},{6}}
[2,1,7,8,5,6,4,3]=>[2,1,4,6,8,5,7,3]=>[2,1,7,4,6,3,8,5]=>{{1,2},{3,7,8},{4},{5,6}}
[1,7,4,8,2,6,5,3]=>[1,8,5,6,7,2,3,4]=>[1,5,8,7,6,4,3,2]=>{{1},{2,5,6},{3,8},{4,7}}
[8,4,7,6,5,1,3,2]=>[5,3,1,6,7,8,4,2]=>[3,8,2,7,5,6,1,4]=>{{1,3},{2,8},{4,7},{5},{6}}
[6,5,3,1,2,4,8,7]=>[3,1,5,2,6,4,8,7]=>[6,1,3,2,5,4,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}
[6,8,1,4,5,7,3,2]=>[8,3,7,1,2,6,4,5]=>[3,7,6,2,4,8,5,1]=>{{1,3,6,8},{2,7},{4},{5}}
[8,7,2,4,5,1,3,6]=>[5,7,1,3,2,4,8,6]=>[8,5,2,1,4,3,7,6]=>{{1,8},{2,5},{3},{4},{6},{7}}
[5,6,3,2,1,4,8,7]=>[2,3,6,1,5,4,8,7]=>[5,2,3,1,6,4,8,7]=>{{1,5,6},{2},{3},{4},{7,8}}
[6,3,1,4,5,2,8,7]=>[3,6,5,1,2,4,8,7]=>[6,3,5,2,4,1,8,7]=>{{1,6},{2,3,5},{4},{7,8}}
[3,1,6,4,5,2,8,7]=>[3,5,1,6,4,2,8,7]=>[6,3,2,5,1,4,8,7]=>{{1,6},{2,3},{4,5},{7,8}}
[5,8,7,4,2,6,3,1]=>[3,6,4,7,5,1,8,2]=>[6,3,5,4,8,2,7,1]=>{{1,6},{2,3,5,8},{4},{7}}
[2,1,8,7,5,3,4,6]=>[2,1,5,3,7,4,8,6]=>[2,1,8,3,5,4,7,6]=>{{1,2},{3,8},{4},{5},{6},{7}}
[7,6,1,4,5,8,3,2]=>[6,3,7,1,2,8,5,4]=>[7,8,3,2,4,6,1,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[2,4,8,3,5,6,7,1]=>[7,2,8,4,3,5,6,1]=>[2,7,4,8,1,3,5,6]=>{{1,2,7},{3,4,8},{5},{6}}
[7,3,8,4,2,6,1,5]=>[6,4,8,7,1,2,5,3]=>[7,8,4,6,3,5,1,2]=>{{1,7},{2,8},{3,4,6},{5}}
[4,8,2,3,5,6,7,1]=>[7,8,2,4,3,5,6,1]=>[7,4,1,8,2,3,5,6]=>{{1,7},{2,4,8},{3},{5},{6}}
[2,1,7,8,5,4,3,6]=>[2,1,4,5,8,3,7,6]=>[2,1,7,4,5,3,8,6]=>{{1,2},{3,7,8},{4},{5},{6}}
[5,7,8,4,3,6,2,1]=>[2,6,4,8,5,3,7,1]=>[5,2,6,4,7,1,8,3]=>{{1,5,7,8},{2},{3,6},{4}}
[4,8,3,6,2,1,7,5]=>[2,6,8,4,7,3,1,5]=>[6,2,4,8,7,3,5,1]=>{{1,6},{2},{3,4,8},{5,7}}
[8,6,3,1,4,2,7,5]=>[3,6,4,2,8,7,5,1]=>[8,3,4,1,6,7,2,5]=>{{1,8},{2,3,4},{5,6,7}}
[2,4,3,1,8,5,7,6]=>[3,2,4,1,8,7,5,6]=>[2,4,3,1,7,8,6,5]=>{{1,2,4},{3},{5,7},{6,8}}
[4,1,3,2,6,8,7,5]=>[4,3,1,2,7,6,8,5]=>[3,4,2,1,6,8,7,5]=>{{1,3},{2,4},{5,6,8},{7}}
[2,1,8,5,3,6,7,4]=>[2,1,5,8,7,3,4,6]=>[2,1,8,5,7,4,6,3]=>{{1,2},{3,8},{4,5,7},{6}}
[3,4,2,8,5,6,7,1]=>[7,4,3,2,8,5,6,1]=>[3,4,8,1,7,2,5,6]=>{{1,3,8},{2,4},{5,7},{6}}
[2,1,5,3,8,6,7,4]=>[2,1,5,7,3,8,6,4]=>[2,1,8,5,4,7,3,6]=>{{1,2},{3,8},{4,5},{6,7}}
[3,1,4,8,5,6,7,2]=>[3,7,1,4,8,5,6,2]=>[4,3,2,8,7,1,5,6]=>{{1,4,8},{2,3},{5,7},{6}}
[5,7,1,4,8,6,2,3]=>[7,6,2,1,5,8,4,3]=>[5,7,1,3,8,6,2,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[5,4,3,8,2,7,6,1]=>[6,7,4,5,3,8,1,2]=>[5,4,8,7,1,6,3,2]=>{{1,5},{2,4,7},{3,8},{6}}
[4,3,7,6,2,1,8,5]=>[2,6,4,3,7,8,5,1]=>[4,2,8,1,7,6,3,5]=>{{1,4},{2},{3,8},{5,7},{6}}
[1,4,7,5,8,3,2,6]=>[1,3,8,4,7,2,5,6]=>[1,4,3,7,8,5,6,2]=>{{1},{2,4,7},{3},{5,8},{6}}
[2,8,5,7,4,6,1,3]=>[6,2,1,7,8,4,5,3]=>[2,8,1,7,6,4,3,5]=>{{1,2,8},{3},{4,7},{5,6}}
[7,3,1,6,8,4,2,5]=>[3,7,4,8,2,1,5,6]=>[8,3,7,4,1,5,6,2]=>{{1,8},{2,3,7},{4},{5},{6}}
[6,1,7,5,3,2,8,4]=>[6,3,5,7,8,1,4,2]=>[3,8,7,6,5,4,1,2]=>{{1,3,7},{2,8},{4,6},{5}}
[3,8,6,2,4,7,5,1]=>[5,7,3,2,6,8,1,4]=>[5,3,8,1,7,6,4,2]=>{{1,5,7},{2,3,8},{4},{6}}
[7,3,6,2,4,1,8,5]=>[4,6,7,2,8,3,1,5]=>[8,7,4,2,6,3,5,1]=>{{1,8},{2,7},{3,4},{5,6}}
[3,6,8,1,7,5,2,4]=>[8,5,3,2,7,6,1,4]=>[3,5,7,1,6,8,4,2]=>{{1,3,7},{2,5,6,8},{4}}
[7,8,3,1,6,5,2,4]=>[3,8,5,2,6,4,7,1]=>[7,3,5,1,6,2,8,4]=>{{1,7,8},{2,3,5,6},{4}}
[5,8,6,2,3,1,4,7]=>[3,6,2,1,5,8,4,7]=>[5,3,1,2,8,6,4,7]=>{{1,5,8},{2,3},{4},{6},{7}}
[4,8,2,6,3,1,5,7]=>[3,6,8,4,1,5,2,7]=>[6,4,3,8,2,1,5,7]=>{{1,6},{2,4,8},{3},{5},{7}}
[7,1,5,2,8,3,4,6]=>[7,5,8,3,1,4,2,6]=>[7,8,5,1,4,2,6,3]=>{{1,7},{2,8},{3,5},{4},{6}}
[1,8,5,2,7,3,4,6]=>[1,5,8,3,7,4,6,2]=>[1,8,5,2,7,3,4,6]=>{{1},{2,8},{3,5,7},{4},{6}}
[1,8,6,7,2,3,4,5]=>[1,7,2,3,4,8,6,5]=>[1,8,2,3,4,7,5,6]=>{{1},{2,8},{3},{4},{5},{6,7}}
[1,7,6,8,2,3,4,5]=>[1,8,2,3,4,7,6,5]=>[1,7,2,3,4,8,5,6]=>{{1},{2,7},{3},{4},{5},{6,8}}
[6,5,8,2,3,1,4,7]=>[3,8,2,1,6,5,4,7]=>[6,3,1,2,8,4,5,7]=>{{1,6},{2,3},{4},{5,8},{7}}
[7,4,2,1,8,3,5,6]=>[2,4,7,8,3,5,6,1]=>[8,2,7,4,1,3,5,6]=>{{1,8},{2},{3,7},{4},{5},{6}}
[8,5,1,2,7,3,4,6]=>[5,1,8,3,7,4,6,2]=>[8,1,5,2,7,3,4,6]=>{{1,8},{2},{3,5,7},{4},{6}}
[8,6,1,7,2,3,4,5]=>[6,8,2,3,4,7,5,1]=>[8,6,1,2,3,7,4,5]=>{{1,8},{2,6,7},{3},{4},{5}}
[4,8,2,1,7,3,5,6]=>[2,8,7,4,3,5,1,6]=>[4,2,7,8,1,3,6,5]=>{{1,4,8},{2},{3,7},{5},{6}}
[6,3,5,1,2,4,8,7]=>[5,1,6,2,3,4,8,7]=>[6,1,5,3,4,2,8,7]=>{{1,6},{2},{3,5},{4},{7,8}}
[4,3,5,6,1,2,8,7]=>[6,1,4,3,5,2,8,7]=>[4,1,5,2,6,3,8,7]=>{{1,4},{2},{3,5,6},{7,8}}
[5,7,4,6,2,8,3,1]=>[3,8,6,7,5,4,1,2]=>[7,3,5,6,8,1,4,2]=>{{1,7},{2,3,5,8},{4,6}}
[8,1,4,7,2,6,3,5]=>[8,7,6,1,4,5,3,2]=>[6,7,8,3,1,2,4,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[2,1,8,5,7,3,4,6]=>[2,1,7,3,8,4,5,6]=>[2,1,8,3,7,5,6,4]=>{{1,2},{3,8},{4},{5,7},{6}}
[6,5,8,4,1,7,3,2]=>[4,3,8,7,6,5,2,1]=>[4,7,3,6,8,1,2,5]=>{{1,4,6},{2,7},{3},{5,8}}
[6,3,7,4,1,8,2,5]=>[4,7,8,6,2,1,5,3]=>[8,6,4,7,2,5,1,3]=>{{1,8},{2,6},{3,4,7},{5}}
[4,3,7,2,6,8,5,1]=>[5,8,4,3,7,2,1,6]=>[5,4,8,1,7,2,6,3]=>{{1,5,7},{2,4},{3,8},{6}}
[4,7,2,3,8,5,6,1]=>[6,7,2,4,8,5,3,1]=>[7,4,1,8,6,2,3,5]=>{{1,7},{2,4,8},{3},{5,6}}
[4,3,8,7,2,1,6,5]=>[2,7,4,3,6,1,8,5]=>[4,2,6,1,8,5,7,3]=>{{1,4},{2},{3,6},{5,8},{7}}
[2,3,4,1,8,5,7,6]=>[4,2,3,1,8,7,5,6]=>[2,3,4,1,7,8,6,5]=>{{1,2,3,4},{5,7},{6,8}}
[4,1,3,2,6,7,8,5]=>[4,3,1,2,8,6,7,5]=>[3,4,2,1,6,7,8,5]=>{{1,3},{2,4},{5,6,7,8}}
[2,8,6,5,4,7,1,3]=>[7,2,1,5,6,8,4,3]=>[2,5,1,8,7,6,3,4]=>{{1,2,5,7},{3},{4,8},{6}}
[8,1,6,4,5,7,2,3]=>[8,7,2,6,4,1,5,3]=>[6,7,1,8,2,5,3,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[2,4,1,5,8,7,6,3]=>[4,2,6,1,5,7,8,3]=>[2,5,4,3,8,6,7,1]=>{{1,2,5,8},{3,4},{6},{7}}
[6,7,2,3,4,8,5,1]=>[5,8,2,3,7,6,1,4]=>[7,5,1,2,6,8,4,3]=>{{1,7},{2,5,6,8},{3},{4}}
[5,1,7,3,8,4,6,2]=>[5,6,7,8,1,4,3,2]=>[8,7,6,5,4,1,2,3]=>{{1,8},{2,7},{3,6},{4,5}}
[7,6,1,3,5,8,4,2]=>[6,4,1,7,2,8,5,3]=>[7,8,2,4,3,6,1,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[5,6,3,7,4,8,1,2]=>[8,1,6,7,5,3,4,2]=>[5,1,7,6,8,3,2,4]=>{{1,5,8},{2},{3,7},{4,6}}
[2,1,6,7,4,8,5,3]=>[2,1,5,8,7,6,3,4]=>[2,1,7,5,6,8,4,3]=>{{1,2},{3,7},{4,5,6,8}}
[7,1,6,5,4,8,2,3]=>[7,8,2,5,6,1,4,3]=>[6,5,1,8,7,4,2,3]=>{{1,6},{2,5,7},{3},{4,8}}
[5,6,2,1,8,7,3,4]=>[2,6,7,3,5,1,8,4]=>[6,2,5,1,8,4,7,3]=>{{1,6},{2},{3,5,8},{4},{7}}
[4,1,2,3,6,8,7,5]=>[4,1,2,3,7,6,8,5]=>[4,1,2,3,6,8,7,5]=>{{1,4},{2},{3},{5,6,8},{7}}
[2,4,3,1,8,5,6,7]=>[3,2,4,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>{{1,2,4},{3},{5,8},{6},{7}}
[5,6,2,8,4,3,1,7]=>[3,4,8,6,5,2,1,7]=>[6,4,3,5,8,1,2,7]=>{{1,6},{2,4,5,8},{3},{7}}
[5,7,8,6,3,4,1,2]=>[4,1,6,3,5,8,7,2]=>[5,1,4,2,7,6,8,3]=>{{1,5,7,8},{2},{3,4},{6}}
[6,5,3,8,4,1,2,7]=>[4,1,8,5,6,2,3,7]=>[8,1,4,5,6,3,2,7]=>{{1,8},{2},{3,4,5,6},{7}}
[2,4,8,3,5,6,1,7]=>[6,2,8,4,3,5,1,7]=>[2,6,4,8,1,3,5,7]=>{{1,2,6},{3,4,8},{5},{7}}
[2,8,1,3,4,5,7,6]=>[8,2,1,3,4,7,5,6]=>[2,7,1,3,4,8,6,5]=>{{1,2,7},{3},{4},{5},{6,8}}
[2,8,4,1,6,5,3,7]=>[4,2,8,5,6,3,1,7]=>[2,8,4,5,6,1,3,7]=>{{1,2,8},{3,4,5,6},{7}}
[2,8,5,3,4,1,7,6]=>[4,2,5,3,8,7,1,6]=>[2,7,4,1,5,8,6,3]=>{{1,2,7},{3,4},{5},{6,8}}
[4,1,2,3,7,6,8,5]=>[4,1,2,3,8,7,6,5]=>[4,1,2,3,7,8,5,6]=>{{1,4},{2},{3},{5,7},{6,8}}
[6,5,2,7,3,4,8,1]=>[8,5,6,3,7,4,2,1]=>[5,8,7,1,6,2,3,4]=>{{1,5,6},{2,8},{3,7},{4}}
[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,5,8,6]=>[4,1,2,3,8,5,7,6]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,1,2,3,8,6,5,7]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[4,1,2,3,8,6,7,5]=>[4,1,2,3,7,8,6,5]=>[4,1,2,3,8,7,5,6]=>{{1,4},{2},{3},{5,8},{6,7}}
[4,1,2,3,7,6,5,8]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>{{1,4},{2},{3},{5,7},{6},{8}}
[4,1,2,3,8,5,7,6]=>[4,1,2,3,8,7,5,6]=>[4,1,2,3,7,8,6,5]=>{{1,4},{2},{3},{5,7},{6,8}}
[4,1,8,3,6,5,7,2]=>[4,7,8,1,6,3,5,2]=>[7,6,4,3,8,2,1,5]=>{{1,7},{2,6},{3,4},{5,8}}
[4,1,8,3,6,2,7,5]=>[4,6,8,1,7,3,2,5]=>[8,6,4,3,7,2,5,1]=>{{1,8},{2,6},{3,4},{5,7}}
[4,1,2,3,5,8,7,6]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>{{1,4},{2},{3},{5},{6,8},{7}}
[4,1,2,3,7,8,6,5]=>[4,1,2,3,6,8,7,5]=>[4,1,2,3,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}}
[2,1,8,7,5,4,3,6]=>[2,1,4,5,7,3,8,6]=>[2,1,8,4,5,3,7,6]=>{{1,2},{3,8},{4},{5},{6},{7}}
[5,2,8,1,4,7,3,6]=>[8,5,7,1,2,4,6,3]=>[5,8,7,3,4,1,2,6]=>{{1,5},{2,8},{3,7},{4},{6}}
[4,5,7,6,1,8,3,2]=>[6,3,7,4,5,8,2,1]=>[4,5,3,7,8,6,1,2]=>{{1,4,7},{2,5,8},{3},{6}}
[5,1,4,2,7,6,8,3]=>[5,4,8,1,2,7,6,3]=>[5,7,4,3,2,8,1,6]=>{{1,5},{2,7},{3,4},{6,8}}
[4,3,7,5,6,8,1,2]=>[8,1,4,3,7,5,6,2]=>[4,1,7,2,8,3,5,6]=>{{1,4},{2},{3,7},{5,8},{6}}
[3,7,8,5,1,2,4,6]=>[5,1,3,2,8,4,7,6]=>[3,1,7,2,5,4,8,6]=>{{1,3,7,8},{2},{4},{5},{6}}
[7,5,3,6,1,8,2,4]=>[6,8,5,2,7,4,3,1]=>[7,5,8,2,6,1,3,4]=>{{1,7},{2,5,6},{3,8},{4}}
[3,6,5,8,1,2,4,7]=>[8,1,3,2,6,5,4,7]=>[3,1,6,2,8,4,5,7]=>{{1,3,6},{2},{4},{5,8},{7}}
[5,4,6,7,2,8,1,3]=>[8,7,1,5,4,6,2,3]=>[5,6,2,7,1,8,4,3]=>{{1,5},{2,6,8},{3},{4,7}}
[5,4,7,3,8,1,2,6]=>[8,1,7,5,4,2,3,6]=>[5,1,7,8,2,4,6,3]=>{{1,5},{2},{3,7},{4,8},{6}}
[4,7,1,5,8,6,2,3]=>[7,6,2,4,1,8,5,3]=>[4,7,1,8,3,6,2,5]=>{{1,4,8},{2,7},{3},{5},{6}}
[7,6,1,8,5,2,3,4]=>[6,5,2,3,7,8,4,1]=>[7,8,1,2,5,6,3,4]=>{{1,7},{2,8},{3},{4},{5},{6}}
[5,7,2,8,1,6,3,4]=>[8,7,6,3,5,1,2,4]=>[5,6,7,1,8,4,3,2]=>{{1,5,8},{2,6},{3,7},{4}}
[5,3,8,7,1,2,4,6]=>[7,1,5,2,3,4,8,6]=>[5,1,8,3,4,2,7,6]=>{{1,5},{2},{3,8},{4},{6},{7}}
[3,5,8,7,1,2,4,6]=>[7,1,3,2,5,4,8,6]=>[3,1,5,2,8,4,7,6]=>{{1,3,5,8},{2},{4},{6},{7}}
[2,1,7,8,5,3,6,4]=>[2,1,5,8,6,4,7,3]=>[2,1,7,5,6,3,8,4]=>{{1,2},{3,7,8},{4,5,6}}
[5,7,3,8,1,2,6,4]=>[8,1,7,6,5,2,3,4]=>[5,1,6,7,8,4,3,2]=>{{1,5,8},{2},{3,6},{4,7}}
[2,7,8,4,1,6,5,3]=>[4,2,8,5,6,3,7,1]=>[2,7,4,5,6,1,8,3]=>{{1,2,7,8},{3,4,5,6}}
[7,1,8,4,2,6,5,3]=>[7,4,8,5,6,3,1,2]=>[5,8,4,6,7,1,3,2]=>{{1,5,7},{2,8},{3,4,6}}
[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[2,3,4,5,6,7,8,1,9]=>{{1,2,3,4,5,6,7,8},{9}}
[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>[3,1,4,5,6,7,8,9,2]=>{{1,3,4,5,6,7,8,9},{2}}
[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[2,3,4,5,6,7,8,9,10,1]=>{{1,2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>{{1,2,3,4,5,6,7,8,9},{10}}
[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>{{1,2,3,4,5,6,7},{8},{9}}
[2,3,4,5,6,7,8,10,1,9]=>[10,2,3,4,5,6,7,8,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>{{1,2,3,4,5,6,7,8,10},{9}}
[1,4,5,6,7,8,9,2,3]=>[1,9,2,4,5,6,7,8,3]=>[1,4,2,5,6,7,8,9,3]=>{{1},{2,4,5,6,7,8,9},{3}}
[3,4,5,6,7,8,9,10,1,2]=>[10,1,3,4,5,6,7,8,9,2]=>[3,1,4,5,6,7,8,9,10,2]=>{{1,3,4,5,6,7,8,9,10},{2}}
[3,6,4,5,7,2,8,1]=>[8,7,3,6,4,5,2,1]=>[3,6,7,8,1,2,4,5]=>{{1,3,7},{2,6},{4,8},{5}}
[6,3,2,5,1,8,4,7]=>[5,3,6,8,2,1,4,7]=>[6,8,3,5,2,4,1,7]=>{{1,6},{2,8},{3},{4,5},{7}}
[7,2,6,3,4,5,8,1]=>[8,7,6,3,4,2,5,1]=>[6,7,8,1,2,4,3,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[6,2,7,3,4,5,8,1]=>[8,6,7,3,4,2,5,1]=>[6,8,7,1,2,4,3,5]=>{{1,6},{2,8},{3,7},{4},{5}}
[3,6,2,7,4,5,8,1]=>[8,6,3,7,4,2,5,1]=>[3,6,8,7,1,4,2,5]=>{{1,3,8},{2,6},{4,7},{5}}
[2,7,6,3,4,5,8,1]=>[8,2,6,3,4,7,5,1]=>[2,6,8,1,3,7,4,5]=>{{1,2,6,7},{3,8},{4},{5}}
[8,5,2,1,7,3,4,6]=>[2,5,8,3,7,4,6,1]=>[8,2,5,1,7,3,4,6]=>{{1,8},{2},{3,5,7},{4},{6}}
[6,3,7,1,2,8,4,5]=>[7,1,6,8,4,3,2,5]=>[7,1,8,6,2,4,5,3]=>{{1,7},{2},{3,8},{4,6},{5}}
[3,2,1,5,8,4,6,7]=>[2,3,1,8,5,4,6,7]=>[3,2,1,5,8,4,6,7]=>{{1,3},{2},{4,5,8},{6},{7}}
[6,5,3,4,8,7,1,2]=>[7,1,5,3,6,4,8,2]=>[5,1,8,2,6,3,7,4]=>{{1,5,6},{2},{3,8},{4},{7}}
[8,5,3,7,6,1,2,4]=>[6,1,5,2,7,8,4,3]=>[7,1,8,3,5,6,2,4]=>{{1,7},{2},{3,8},{4},{5},{6}}
[2,3,8,7,1,4,5,6]=>[7,2,3,1,4,5,8,6]=>[2,3,8,1,4,5,7,6]=>{{1,2,3,8},{4},{5},{6},{7}}
[8,1,6,7,3,2,5,4]=>[8,3,7,5,2,1,6,4]=>[3,7,5,8,2,4,1,6]=>{{1,3,5},{2,7},{4,8},{6}}
[8,1,4,3,2,7,6,5]=>[8,3,4,1,6,7,2,5]=>[3,6,4,2,8,7,5,1]=>{{1,3,4},{2,6,7},{5,8}}
[7,6,1,8,3,2,4,5]=>[6,3,7,2,4,8,5,1]=>[7,8,3,1,2,6,4,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,6,1,8,4,5,2,3]=>[6,5,2,7,4,8,3,1]=>[7,8,1,5,2,6,3,4]=>{{1,7},{2,8},{3},{4,5},{6}}
[7,6,8,1,3,2,5,4]=>[8,3,1,5,2,7,6,4]=>[3,5,2,7,4,8,1,6]=>{{1,3},{2,5},{4,7},{6,8}}
[6,5,3,8,1,2,7,4]=>[8,1,5,6,7,4,2,3]=>[5,1,8,7,6,2,4,3]=>{{1,5,6},{2},{3,8},{4,7}}
[7,5,1,6,8,3,4,2]=>[5,4,7,3,8,1,2,6]=>[7,8,4,1,5,3,6,2]=>{{1,7},{2,8},{3,4},{5},{6}}
[6,5,2,1,8,7,4,3]=>[2,5,4,6,7,3,8,1]=>[6,2,8,4,5,1,7,3]=>{{1,6},{2},{3,8},{4},{5},{7}}
[1,6,2,7,3,5,4,8]=>[1,6,7,5,3,2,4,8]=>[1,6,5,7,3,4,2,8]=>{{1},{2,6},{3,5},{4,7},{8}}
[1,8,2,5,3,6,4,7]=>[1,8,5,6,2,3,4,7]=>[1,5,8,6,4,3,2,7]=>{{1},{2,5},{3,8},{4,6},{7}}
[1,8,2,3,4,6,5,7]=>[1,8,2,3,6,4,5,7]=>[1,6,2,3,8,5,4,7]=>{{1},{2,6},{3},{4},{5,8},{7}}
[1,7,2,4,3,8,5,6]=>[1,7,4,2,8,5,3,6]=>[1,4,8,3,7,2,6,5]=>{{1},{2,4},{3,8},{5,7},{6}}
[1,6,2,5,3,8,4,7]=>[1,6,5,8,2,3,4,7]=>[1,6,8,5,4,3,2,7]=>{{1},{2,6},{3,8},{4,5},{7}}
[5,6,7,2,4,3,1,8]=>[3,4,7,1,5,6,2,8]=>[5,4,3,2,6,7,1,8]=>{{1,5,6,7},{2,4},{3},{8}}
[3,2,6,8,5,1,7,4]=>[5,3,2,8,7,6,4,1]=>[3,7,1,5,6,8,2,4]=>{{1,3},{2,7},{4,5,6,8}}
[5,7,8,4,1,3,2,6]=>[4,3,1,8,5,2,7,6]=>[3,5,2,4,7,1,8,6]=>{{1,3},{2,5,7,8},{4},{6}}
[5,7,8,2,1,6,3,4]=>[2,8,6,3,5,1,7,4]=>[5,2,6,1,7,4,8,3]=>{{1,5,7,8},{2},{3,6},{4}}
[4,7,2,8,1,6,3,5]=>[8,7,6,4,3,1,2,5]=>[4,6,7,8,1,5,3,2]=>{{1,4,8},{2,6},{3,7},{5}}
[5,7,8,2,1,6,4,3]=>[2,8,4,6,5,1,7,3]=>[4,2,6,5,7,3,8,1]=>{{1,4,5,7,8},{2},{3,6}}
[5,7,8,2,1,4,6,3]=>[2,8,6,1,5,4,7,3]=>[5,2,6,3,7,1,8,4]=>{{1,5,7,8},{2},{3,6},{4}}
[5,7,8,3,1,4,6,2]=>[3,8,6,1,5,2,7,4]=>[6,3,5,2,7,4,8,1]=>{{1,6},{2,3,5,7,8},{4}}
[5,7,8,3,1,6,4,2]=>[3,8,4,6,5,2,7,1]=>[6,3,4,5,7,1,8,2]=>{{1,6},{2,3,4,5,7,8}}
[5,7,8,3,1,6,2,4]=>[3,8,6,2,5,4,7,1]=>[6,3,5,1,7,2,8,4]=>{{1,6},{2,3,5,7,8},{4}}
[4,6,3,8,2,1,7,5]=>[2,8,6,4,7,3,1,5]=>[4,2,6,8,7,3,5,1]=>{{1,4,8},{2},{3,6},{5,7}}
[3,2,5,4,8,1,7,6]=>[8,3,2,5,4,7,1,6]=>[3,5,1,7,2,8,6,4]=>{{1,3},{2,5},{4,7},{6,8}}
[5,7,8,3,1,2,4,6]=>[3,1,8,2,5,4,7,6]=>[5,1,3,2,7,4,8,6]=>{{1,5,7,8},{2},{3},{4},{6}}
[5,7,8,2,1,4,3,6]=>[2,8,4,1,5,3,7,6]=>[4,2,5,3,7,1,8,6]=>{{1,4},{2},{3,5,7,8},{6}}
[6,7,8,1,2,5,3,4]=>[8,1,5,3,2,6,7,4]=>[5,1,6,2,4,7,8,3]=>{{1,5},{2},{3,6,7,8},{4}}
[3,4,2,1,7,5,8,6]=>[2,4,3,1,7,8,5,6]=>[3,2,4,1,8,7,6,5]=>{{1,3,4},{2},{5,8},{6,7}}
[3,6,5,7,1,4,8,2]=>[7,8,3,1,6,5,4,2]=>[6,3,7,2,8,1,4,5]=>{{1,6},{2,3,7},{4},{5,8}}
[5,3,1,8,6,4,7,2]=>[3,5,7,6,2,8,4,1]=>[8,5,3,7,2,6,1,4]=>{{1,8},{2,5},{3},{4,7},{6}}
[1,5,2,7,4,6,3,8]=>[1,5,6,7,2,4,3,8]=>[1,7,6,5,4,2,3,8]=>{{1},{2,7},{3,6},{4,5},{8}}
[7,1,3,8,4,6,2,5]=>[7,6,1,8,3,5,2,4]=>[7,8,2,6,3,1,5,4]=>{{1,7},{2,8},{3},{4,6},{5}}
[2,3,4,8,6,1,7,5]=>[6,2,3,4,8,7,5,1]=>[2,3,4,8,6,7,1,5]=>{{1,2,3,4,8},{5,6,7}}
[2,3,4,8,6,5,1,7]=>[5,2,3,4,6,8,1,7]=>[2,3,4,8,5,6,1,7]=>{{1,2,3,4,8},{5},{6},{7}}
[5,3,6,1,4,8,2,7]=>[6,8,5,1,3,4,2,7]=>[6,5,8,3,2,1,4,7]=>{{1,6},{2,5},{3,8},{4},{7}}
[7,3,5,6,8,4,2,1]=>[2,4,8,7,3,5,1,6]=>[8,2,4,7,1,3,6,5]=>{{1,8},{2},{3,4,7},{5},{6}}
[6,3,5,1,8,2,7,4]=>[5,8,6,7,3,1,2,4]=>[8,5,7,6,2,4,3,1]=>{{1,8},{2,5},{3,7},{4,6}}
[2,7,6,5,8,3,4,1]=>[4,2,8,3,6,7,5,1]=>[2,6,4,1,8,7,3,5]=>{{1,2,6,7},{3,4},{5,8}}
[3,1,4,2,7,8,6,5]=>[3,4,1,2,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}}
[3,6,4,7,8,2,5,1]=>[5,8,3,6,2,4,7,1]=>[5,3,7,6,2,1,8,4]=>{{1,5},{2,3,7,8},{4,6}}
[2,7,8,5,6,3,4,1]=>[4,2,6,3,8,5,7,1]=>[2,7,4,1,6,3,8,5]=>{{1,2,7,8},{3,4},{5,6}}
[2,4,8,6,1,7,3,5]=>[6,2,8,4,3,7,5,1]=>[2,6,4,8,1,7,3,5]=>{{1,2,6,7},{3,4,8},{5}}
[3,2,1,8,6,7,4,5]=>[2,3,1,7,4,8,6,5]=>[3,2,1,8,4,7,5,6]=>{{1,3},{2},{4,8},{5},{6,7}}
[5,3,7,1,6,8,4,2]=>[7,4,8,5,2,1,6,3]=>[5,8,4,7,2,3,1,6]=>{{1,5},{2,8},{3,4,7},{6}}
[1,8,6,5,7,3,2,4]=>[1,3,7,2,6,8,5,4]=>[1,7,3,2,8,6,4,5]=>{{1},{2,7},{3},{4},{5,8},{6}}
[5,2,1,4,3,8,7,6]=>[2,5,4,1,3,7,8,6]=>[4,2,5,3,1,8,7,6]=>{{1,4},{2},{3,5},{6,8},{7}}
[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>{{1,2},{3,4},{5,6},{7,8},{9,10},{11,12}}
[7,4,6,1,8,3,5,2]=>[6,5,8,7,3,4,1,2]=>[7,8,5,6,2,1,4,3]=>{{1,7},{2,8},{3,5},{4,6}}
[3,6,8,4,1,7,5,2]=>[4,8,3,5,7,6,2,1]=>[4,3,7,5,6,8,1,2]=>{{1,4,5,6,8},{2,3,7}}
[3,6,7,5,1,8,4,2]=>[5,4,3,7,8,6,2,1]=>[3,6,7,4,5,8,1,2]=>{{1,3,7},{2,6,8},{4},{5}}
[3,4,6,5,7,1,8,2]=>[7,8,3,4,6,5,1,2]=>[4,3,6,7,8,1,5,2]=>{{1,4,7},{2,3,6},{5,8}}
[4,7,5,6,1,8,3,2]=>[6,3,8,4,7,5,1,2]=>[4,6,3,8,7,1,5,2]=>{{1,4,8},{2,6},{3},{5,7}}
[8,4,2,1,6,7,5,3]=>[2,4,8,5,7,1,3,6]=>[8,2,4,5,7,3,6,1]=>{{1,8},{2},{3,4,5,7},{6}}
[2,7,5,1,6,8,4,3]=>[5,2,4,7,8,1,3,6]=>[2,7,8,4,5,3,6,1]=>{{1,2,7},{3,8},{4},{5},{6}}
[3,6,7,1,5,8,2,4]=>[7,8,3,2,1,6,5,4]=>[6,3,7,1,4,8,2,5]=>{{1,6,8},{2,3,7},{4},{5}}
[8,4,1,6,7,5,2,3]=>[4,8,2,5,7,1,3,6]=>[8,4,1,5,7,3,6,2]=>{{1,8},{2,4,5,7},{3},{6}}
[6,2,5,1,7,4,8,3]=>[5,6,8,7,2,1,4,3]=>[8,7,5,6,3,4,1,2]=>{{1,8},{2,7},{3,5},{4,6}}
[7,1,6,4,8,2,5,3]=>[7,8,5,6,2,1,4,3]=>[6,5,8,7,3,4,1,2]=>{{1,6},{2,5},{3,8},{4,7}}
[1,8,3,5,7,6,2,4]=>[1,6,7,2,4,8,5,3]=>[1,8,7,3,2,6,4,5]=>{{1},{2,8},{3,7},{4},{5},{6}}
[3,6,8,2,5,7,1,4]=>[7,8,3,1,4,6,2,5]=>[6,3,7,2,1,8,5,4]=>{{1,6,8},{2,3,7},{4},{5}}
[4,1,3,2,7,6,8,5]=>[4,3,1,2,8,7,6,5]=>[3,4,2,1,7,8,5,6]=>{{1,3},{2,4},{5,7},{6,8}}
[4,2,1,3,7,6,8,5]=>[2,4,1,3,8,7,6,5]=>[4,2,1,3,7,8,5,6]=>{{1,4},{2},{3},{5,7},{6,8}}
[2,4,1,3,7,6,8,5]=>[4,2,1,3,8,7,6,5]=>[2,4,1,3,7,8,5,6]=>{{1,2,4},{3},{5,7},{6,8}}
[8,1,3,5,6,2,7,4]=>[8,6,1,7,2,3,5,4]=>[6,8,2,7,4,5,1,3]=>{{1,6},{2,8},{3},{4,7},{5}}
[2,6,5,8,7,3,4,1]=>[4,2,7,3,6,5,8,1]=>[2,6,4,1,8,3,7,5]=>{{1,2,6},{3,4},{5,8},{7}}
[5,6,3,8,1,2,7,4]=>[8,1,6,7,5,3,2,4]=>[5,1,7,6,8,3,4,2]=>{{1,5,8},{2},{3,7},{4,6}}
[1,8,7,3,5,4,6,2]=>[1,6,7,5,3,4,8,2]=>[1,6,5,8,3,2,7,4]=>{{1},{2,6},{3,5},{4,8},{7}}
[8,2,5,4,7,1,6,3]=>[7,8,6,5,2,1,4,3]=>[6,5,7,8,3,4,1,2]=>{{1,6},{2,5},{3,7},{4,8}}
[8,7,6,2,4,3,1,5]=>[3,4,6,1,2,7,8,5]=>[8,4,3,2,1,6,7,5]=>{{1,8},{2,4},{3},{5},{6},{7}}
[4,8,5,7,1,6,2,3]=>[7,6,2,4,8,1,5,3]=>[4,7,1,8,6,5,2,3]=>{{1,4,8},{2,7},{3},{5,6}}
[8,5,4,2,1,7,3,6]=>[2,4,5,8,7,3,1,6]=>[8,2,5,4,7,1,6,3]=>{{1,8},{2},{3,5,7},{4},{6}}
[6,5,4,2,3,1,8,7]=>[3,4,2,5,6,1,8,7]=>[6,3,1,4,5,2,8,7]=>{{1,6},{2,3},{4},{5},{7,8}}
[6,3,2,5,1,4,8,7]=>[5,3,6,1,2,4,8,7]=>[5,6,3,2,4,1,8,7]=>{{1,5},{2,6},{3},{4},{7,8}}
[6,5,4,1,3,2,8,7]=>[4,3,1,5,6,2,8,7]=>[3,6,2,4,5,1,8,7]=>{{1,3},{2,6},{4},{5},{7,8}}
[8,7,4,1,6,5,3,2]=>[4,3,7,5,6,2,8,1]=>[4,8,3,5,6,1,7,2]=>{{1,4,5,6},{2,8},{3},{7}}
[2,1,8,7,6,4,5,3]=>[2,1,5,6,4,7,8,3]=>[2,1,8,5,3,6,7,4]=>{{1,2},{3,8},{4,5},{6},{7}}
[8,3,2,7,6,4,5,1]=>[5,3,8,6,4,7,2,1]=>[5,8,3,6,1,7,2,4]=>{{1,5},{2,8},{3},{4,6,7}}
[8,3,1,7,6,5,4,2]=>[3,8,4,5,6,7,2,1]=>[8,3,4,5,6,7,1,2]=>{{1,8},{2,3,4,5,6,7}}
[8,3,1,5,4,7,6,2]=>[3,8,6,5,1,7,2,4]=>[6,3,5,8,4,7,2,1]=>{{1,6,7},{2,3,5},{4,8}}
[8,3,1,7,6,5,2,4]=>[3,8,5,2,6,7,4,1]=>[8,3,5,1,6,7,2,4]=>{{1,8},{2,3,5,6,7},{4}}
[8,3,2,5,4,7,1,6]=>[7,3,8,5,2,1,4,6]=>[5,7,3,8,2,4,6,1]=>{{1,5},{2,7},{3},{4,8},{6}}
[2,1,8,5,4,7,3,6]=>[2,1,7,5,8,3,4,6]=>[2,1,7,8,5,4,6,3]=>{{1,2},{3,7},{4,8},{5},{6}}
[8,7,6,5,3,1,4,2]=>[3,5,4,2,6,7,8,1]=>[8,3,4,1,5,6,7,2]=>{{1,8},{2,3,4},{5},{6},{7}}
[8,7,6,5,1,3,2,4]=>[5,3,1,2,6,7,8,4]=>[3,8,2,1,5,6,7,4]=>{{1,3},{2,8},{4},{5},{6},{7}}
[8,7,6,5,1,3,4,2]=>[5,4,1,3,6,7,8,2]=>[4,8,2,1,5,6,7,3]=>{{1,4},{2,8},{3},{5},{6},{7}}
[8,7,6,5,1,4,3,2]=>[5,3,4,1,6,7,8,2]=>[3,8,4,2,5,6,7,1]=>{{1,3,4},{2,8},{5},{6},{7}}
[8,7,4,3,6,1,5,2]=>[6,5,4,7,1,3,8,2]=>[5,6,8,4,3,1,7,2]=>{{1,5},{2,6},{3,8},{4},{7}}
[2,1,8,7,6,3,5,4]=>[2,1,6,5,3,7,8,4]=>[2,1,5,8,4,6,7,3]=>{{1,2},{3,5},{4,8},{6},{7}}
[8,7,6,5,1,4,2,3]=>[5,4,2,1,6,7,8,3]=>[4,8,1,3,5,6,7,2]=>{{1,4},{2,8},{3},{5},{6},{7}}
[8,7,6,5,1,2,4,3]=>[5,1,4,2,6,7,8,3]=>[4,1,8,3,5,6,7,2]=>{{1,4},{2},{3,8},{5},{6},{7}}
[7,3,5,1,8,4,6,2]=>[5,6,7,8,3,4,1,2]=>[8,7,6,5,2,1,4,3]=>{{1,8},{2,7},{3,6},{4,5}}
[7,3,4,1,8,5,6,2]=>[4,6,7,3,8,5,1,2]=>[8,7,4,1,6,2,5,3]=>{{1,8},{2,7},{3,4},{5,6}}
[6,5,1,2,8,4,3,7]=>[5,1,4,6,8,3,2,7]=>[6,1,8,4,5,2,3,7]=>{{1,6},{2},{3,8},{4},{5},{7}}
[4,3,1,2,8,6,5,7]=>[3,1,4,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[2,6,1,5,7,8,3,4]=>[6,2,8,3,1,5,7,4]=>[2,7,6,1,4,3,8,5]=>{{1,2,7,8},{3,6},{4},{5}}
[7,4,1,6,8,5,2,3]=>[4,7,2,5,8,1,3,6]=>[8,4,1,7,5,3,6,2]=>{{1,8},{2,4,7},{3},{5},{6}}
[5,2,3,1,8,6,7,4]=>[3,5,2,7,1,8,6,4]=>[8,3,1,5,4,7,2,6]=>{{1,8},{2,3},{4,5},{6,7}}
[3,5,2,1,6,8,7,4]=>[2,5,3,7,1,6,8,4]=>[3,2,6,5,4,8,7,1]=>{{1,3,6,8},{2},{4,5},{7}}
[6,2,1,5,8,7,3,4]=>[2,6,7,3,1,5,8,4]=>[8,2,6,1,4,3,7,5]=>{{1,8},{2},{3,6},{4},{5},{7}}
[6,2,4,1,8,5,7,3]=>[4,6,7,2,8,1,5,3]=>[8,7,4,2,6,5,1,3]=>{{1,8},{2,7},{3,4},{5,6}}
[6,2,5,1,8,4,7,3]=>[5,6,7,8,2,1,4,3]=>[8,7,6,5,3,4,1,2]=>{{1,8},{2,7},{3,6},{4,5}}
[5,2,1,3,8,7,4,6]=>[2,5,1,7,3,4,8,6]=>[8,2,1,5,4,3,7,6]=>{{1,8},{2},{3},{4,5},{6},{7}}
[7,6,1,4,8,3,2,5]=>[6,3,7,1,4,8,2,5]=>[7,8,3,2,1,6,5,4]=>{{1,7},{2,8},{3},{4},{5},{6}}
[4,2,1,3,8,7,5,6]=>[2,4,1,3,7,5,8,6]=>[4,2,1,3,8,5,7,6]=>{{1,4},{2},{3},{5,8},{6},{7}}
[7,1,3,5,8,2,4,6]=>[7,8,1,3,2,5,4,6]=>[8,7,2,1,4,3,6,5]=>{{1,8},{2,7},{3},{4},{5},{6}}
[5,2,3,1,6,4,8,7]=>[3,5,2,6,1,4,8,7]=>[6,3,1,5,4,2,8,7]=>{{1,6},{2,3},{4,5},{7,8}}
[7,4,5,2,3,1,8,6]=>[3,5,2,7,4,8,1,6]=>[8,3,1,5,2,7,6,4]=>{{1,8},{2,3},{4,5},{6,7}}
[8,6,7,3,5,2,4,1]=>[4,5,7,2,3,8,6,1]=>[8,5,4,2,1,7,3,6]=>{{1,8},{2,5},{3,4},{6,7}}
[7,3,5,2,4,1,8,6]=>[4,5,7,2,3,8,1,6]=>[8,5,4,2,1,7,6,3]=>{{1,8},{2,5},{3,4},{6,7}}
[6,3,5,2,4,1,8,7]=>[4,5,6,2,3,1,8,7]=>[6,5,4,2,1,3,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[5,2,4,1,6,3,8,7]=>[4,5,6,2,1,3,8,7]=>[6,5,4,2,3,1,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[4,1,6,3,5,2,8,7]=>[4,5,6,1,3,2,8,7]=>[6,5,4,3,1,2,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[6,3,4,1,5,2,8,7]=>[4,5,6,3,1,2,8,7]=>[6,5,4,1,3,2,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[5,2,6,3,4,1,8,7]=>[4,5,6,3,2,1,8,7]=>[6,5,4,1,2,3,8,7]=>{{1,6},{2,5},{3,4},{7,8}}
[5,2,7,3,4,1,8,6]=>[4,5,7,3,2,8,1,6]=>[8,5,4,1,2,7,6,3]=>{{1,8},{2,5},{3,4},{6,7}}
[5,2,8,6,7,3,4,1]=>[4,5,7,3,2,8,6,1]=>[8,5,4,1,2,7,3,6]=>{{1,8},{2,5},{3,4},{6,7}}
[6,2,8,5,7,3,4,1]=>[4,6,7,3,8,2,5,1]=>[8,7,4,1,6,3,2,5]=>{{1,8},{2,7},{3,4},{5,6}}
[6,2,7,3,4,1,8,5]=>[4,6,7,3,8,2,1,5]=>[8,7,4,1,6,3,5,2]=>{{1,8},{2,7},{3,4},{5,6}}
[7,3,4,1,5,2,8,6]=>[4,5,7,3,1,8,2,6]=>[8,5,4,1,3,7,6,2]=>{{1,8},{2,5},{3,4},{6,7}}
[4,1,7,3,5,2,8,6]=>[4,5,7,1,3,8,2,6]=>[8,5,4,3,1,7,6,2]=>{{1,8},{2,5},{3,4},{6,7}}
[3,1,7,4,5,2,8,6]=>[3,5,1,7,4,8,2,6]=>[8,3,2,5,1,7,6,4]=>{{1,8},{2,3},{4,5},{6,7}}
[2,1,7,4,5,3,8,6]=>[2,1,5,7,4,8,3,6]=>[2,1,8,5,3,7,6,4]=>{{1,2},{3,8},{4,5},{6,7}}
[3,1,8,6,7,4,5,2]=>[3,5,1,7,4,8,6,2]=>[8,3,2,5,1,7,4,6]=>{{1,8},{2,3},{4,5},{6,7}}
[4,1,8,6,7,3,5,2]=>[4,5,7,1,3,8,6,2]=>[8,5,4,3,1,7,2,6]=>{{1,8},{2,5},{3,4},{6,7}}
[8,6,7,3,4,1,5,2]=>[4,5,7,3,1,8,6,2]=>[8,5,4,1,3,7,2,6]=>{{1,8},{2,5},{3,4},{6,7}}
[8,5,7,3,4,1,6,2]=>[4,6,7,3,8,1,5,2]=>[8,7,4,1,6,5,2,3]=>{{1,8},{2,7},{3,4},{5,6}}
[8,5,6,2,7,3,4,1]=>[4,6,7,3,8,5,2,1]=>[8,7,4,1,6,2,3,5]=>{{1,8},{2,7},{3,4},{5,6}}
[8,4,7,3,5,1,6,2]=>[5,6,7,8,3,1,4,2]=>[8,7,6,5,2,4,1,3]=>{{1,8},{2,7},{3,6},{4,5}}
[5,1,8,4,7,3,6,2]=>[5,6,7,8,1,3,4,2]=>[8,7,6,5,4,2,1,3]=>{{1,8},{2,7},{3,6},{4,5}}
[4,1,8,5,7,3,6,2]=>[4,6,7,1,8,3,5,2]=>[8,7,4,3,6,2,1,5]=>{{1,8},{2,7},{3,4},{5,6}}
[3,1,8,5,7,4,6,2]=>[3,6,1,7,8,4,5,2]=>[8,3,2,7,6,4,1,5]=>{{1,8},{2,3},{4,7},{5,6}}
[2,1,8,5,7,4,6,3]=>[2,1,6,7,8,4,5,3]=>[2,1,8,7,6,4,3,5]=>{{1,2},{3,8},{4,7},{5,6}}
[2,1,7,4,6,3,8,5]=>[2,1,6,7,8,4,3,5]=>[2,1,8,7,6,4,5,3]=>{{1,2},{3,8},{4,7},{5,6}}
[3,1,7,4,6,2,8,5]=>[3,6,1,7,8,4,2,5]=>[8,3,2,7,6,4,5,1]=>{{1,8},{2,3},{4,7},{5,6}}
[4,1,7,3,6,2,8,5]=>[4,6,7,1,8,3,2,5]=>[8,7,4,3,6,2,5,1]=>{{1,8},{2,7},{3,4},{5,6}}
[5,1,7,3,6,2,8,4]=>[5,6,7,8,1,3,2,4]=>[8,7,6,5,4,2,3,1]=>{{1,8},{2,7},{3,6},{4,5}}
[6,2,7,3,5,1,8,4]=>[5,6,7,8,3,2,1,4]=>[8,7,6,5,2,3,4,1]=>{{1,8},{2,7},{3,6},{4,5}}
[6,2,8,4,7,3,5,1]=>[5,6,7,8,3,2,4,1]=>[8,7,6,5,2,3,1,4]=>{{1,8},{2,7},{3,6},{4,5}}
[8,4,7,3,6,2,5,1]=>[5,6,7,8,2,3,4,1]=>[8,7,6,5,3,2,1,4]=>{{1,8},{2,7},{3,6},{4,5}}
[7,3,6,2,5,1,8,4]=>[5,6,7,8,2,3,1,4]=>[8,7,6,5,3,2,4,1]=>{{1,8},{2,7},{3,6},{4,5}}
[6,2,5,1,7,3,8,4]=>[5,6,7,8,2,1,3,4]=>[8,7,6,5,3,4,2,1]=>{{1,8},{2,7},{3,6},{4,5}}
[5,2,4,1,7,3,8,6]=>[4,5,7,2,1,8,3,6]=>[8,5,4,2,3,7,6,1]=>{{1,8},{2,5},{3,4},{6,7}}
[6,2,4,1,7,3,8,5]=>[4,6,7,2,8,1,3,5]=>[8,7,4,2,6,5,3,1]=>{{1,8},{2,7},{3,4},{5,6}}
[8,5,7,3,6,2,4,1]=>[4,6,7,2,8,3,5,1]=>[8,7,4,2,6,3,1,5]=>{{1,8},{2,7},{3,4},{5,6}}
[8,5,7,4,6,2,3,1]=>[3,6,2,7,8,4,5,1]=>[8,3,1,7,6,4,2,5]=>{{1,8},{2,3},{4,7},{5,6}}
[7,4,6,2,3,1,8,5]=>[3,6,2,7,8,4,1,5]=>[8,3,1,7,6,4,5,2]=>{{1,8},{2,3},{4,7},{5,6}}
[6,2,3,1,7,4,8,5]=>[3,6,2,7,8,1,4,5]=>[8,3,1,7,6,5,4,2]=>{{1,8},{2,3},{4,7},{5,6}}
[5,2,3,1,7,4,8,6]=>[3,5,2,7,1,8,4,6]=>[8,3,1,5,4,7,6,2]=>{{1,8},{2,3},{4,5},{6,7}}
[4,2,3,1,7,5,8,6]=>[3,4,2,1,7,8,5,6]=>[4,3,1,2,8,7,6,5]=>{{1,4},{2,3},{5,8},{6,7}}
[3,1,4,2,8,6,7,5]=>[3,4,1,2,7,8,6,5]=>[4,3,2,1,8,7,5,6]=>{{1,4},{2,3},{5,8},{6,7}}
[6,2,3,1,8,5,7,4]=>[3,6,2,7,8,1,5,4]=>[8,3,1,7,6,5,2,4]=>{{1,8},{2,3},{4,7},{5,6}}
[8,5,6,2,3,1,7,4]=>[3,6,2,7,8,5,1,4]=>[8,3,1,7,6,2,5,4]=>{{1,8},{2,3},{4,7},{5,6}}
[7,4,8,5,6,2,3,1]=>[3,6,2,7,8,5,4,1]=>[8,3,1,7,6,2,4,5]=>{{1,8},{2,3},{4,7},{5,6}}
[7,3,8,5,6,2,4,1]=>[4,6,7,2,8,5,3,1]=>[8,7,4,2,6,1,3,5]=>{{1,8},{2,7},{3,4},{5,6}}
[8,5,6,2,4,1,7,3]=>[4,6,7,2,8,5,1,3]=>[8,7,4,2,6,1,5,3]=>{{1,8},{2,7},{3,4},{5,6}}
[5,2,4,1,8,6,7,3]=>[4,5,7,2,1,8,6,3]=>[8,5,4,2,3,7,1,6]=>{{1,8},{2,5},{3,4},{6,7}}
[4,1,5,2,8,6,7,3]=>[4,5,7,1,2,8,6,3]=>[8,5,4,3,2,7,1,6]=>{{1,8},{2,5},{3,4},{6,7}}
[3,1,5,2,8,6,7,4]=>[3,5,1,7,2,8,6,4]=>[8,3,2,5,4,7,1,6]=>{{1,8},{2,3},{4,5},{6,7}}
[2,1,6,3,8,5,7,4]=>[2,1,6,7,8,3,5,4]=>[2,1,8,7,6,5,3,4]=>{{1,2},{3,8},{4,7},{5,6}}
[3,1,6,2,8,5,7,4]=>[3,6,1,7,8,2,5,4]=>[8,3,2,7,6,5,1,4]=>{{1,8},{2,3},{4,7},{5,6}}
[4,1,6,2,8,5,7,3]=>[4,6,7,1,8,2,5,3]=>[8,7,4,3,6,5,1,2]=>{{1,8},{2,7},{3,4},{5,6}}
[5,1,6,2,8,4,7,3]=>[5,6,7,8,1,2,4,3]=>[8,7,6,5,4,3,1,2]=>{{1,8},{2,7},{3,6},{4,5}}
[8,4,6,2,5,1,7,3]=>[5,6,7,8,2,4,1,3]=>[8,7,6,5,3,1,4,2]=>{{1,8},{2,7},{3,6},{4,5}}
[7,3,8,4,6,2,5,1]=>[5,6,7,8,2,4,3,1]=>[8,7,6,5,3,1,2,4]=>{{1,8},{2,7},{3,6},{4,5}}
[6,2,7,3,8,4,5,1]=>[5,6,7,8,4,2,3,1]=>[8,7,6,5,1,3,2,4]=>{{1,8},{2,7},{3,6},{4,5}}
[8,4,5,1,6,2,7,3]=>[5,6,7,8,4,3,1,2]=>[8,7,6,5,1,2,4,3]=>{{1,8},{2,7},{3,6},{4,5}}
[5,1,8,4,6,2,7,3]=>[5,6,7,8,1,4,2,3]=>[8,7,6,5,4,1,3,2]=>{{1,8},{2,7},{3,6},{4,5}}
[4,1,8,5,6,2,7,3]=>[4,6,7,1,8,5,2,3]=>[8,7,4,3,6,1,5,2]=>{{1,8},{2,7},{3,4},{5,6}}
[3,1,8,5,6,2,7,4]=>[3,6,1,7,8,5,2,4]=>[8,3,2,7,6,1,5,4]=>{{1,8},{2,3},{4,7},{5,6}}
[2,1,8,5,6,3,7,4]=>[2,1,6,7,8,5,3,4]=>[2,1,8,7,6,3,5,4]=>{{1,2},{3,8},{4,7},{5,6}}
[2,1,7,4,8,5,6,3]=>[2,1,6,7,8,5,4,3]=>[2,1,8,7,6,3,4,5]=>{{1,2},{3,8},{4,7},{5,6}}
[3,1,7,4,8,5,6,2]=>[3,6,1,7,8,5,4,2]=>[8,3,2,7,6,1,4,5]=>{{1,8},{2,3},{4,7},{5,6}}
[4,1,7,3,8,5,6,2]=>[4,6,7,1,8,5,3,2]=>[8,7,4,3,6,1,2,5]=>{{1,8},{2,7},{3,4},{5,6}}
[7,3,8,4,5,1,6,2]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>{{1,8},{2,7},{3,6},{4,5}}
[8,4,5,1,7,3,6,2]=>[5,6,7,8,4,1,2,3]=>[8,7,6,5,1,4,3,2]=>{{1,8},{2,7},{3,6},{4,5}}
[7,3,6,2,8,4,5,1]=>[5,6,7,8,4,1,3,2]=>[8,7,6,5,1,4,2,3]=>{{1,8},{2,7},{3,6},{4,5}}
[7,8,1,3,6,2,5,4]=>[8,6,1,5,3,4,7,2]=>[5,6,2,7,3,1,8,4]=>{{1,5},{2,6},{3},{4,7,8}}
[2,6,4,8,3,7,1,5]=>[7,2,8,6,1,4,3,5]=>[2,7,6,8,4,3,5,1]=>{{1,2,7},{3,6},{4,8},{5}}
[4,6,2,5,3,1,8,7]=>[3,5,6,4,1,2,8,7]=>[5,4,3,6,2,1,8,7]=>{{1,5},{2,4,6},{3},{7,8}}
[3,5,6,7,8,1,4,2]=>[8,4,3,1,5,6,7,2]=>[3,4,5,2,6,7,8,1]=>{{1,3,5,6,7,8},{2,4}}
[2,7,5,6,8,4,1,3]=>[4,2,1,8,7,5,6,3]=>[2,7,1,4,8,3,5,6]=>{{1,2,7},{3},{4},{5,8},{6}}
[4,3,7,8,1,2,6,5]=>[8,1,4,3,6,2,7,5]=>[4,1,6,2,7,5,8,3]=>{{1,4},{2},{3,6},{5,7,8}}
[1,7,3,8,5,2,6,4]=>[1,5,8,7,6,3,4,2]=>[1,8,5,6,7,3,2,4]=>{{1},{2,8},{3,5,7},{4,6}}
[5,7,8,6,3,2,1,4]=>[2,3,6,1,5,8,7,4]=>[5,2,3,1,7,6,8,4]=>{{1,5,7,8},{2},{3},{4},{6}}
[7,1,5,3,4,2,8,6]=>[7,4,5,3,1,8,2,6]=>[4,8,5,1,3,7,6,2]=>{{1,4},{2,8},{3,5},{6,7}}
[7,1,3,5,6,4,2,8]=>[7,4,1,6,2,3,5,8]=>[4,7,2,6,3,5,1,8]=>{{1,4,6},{2,7},{3},{5},{8}}
[5,8,2,3,7,6,4,1]=>[4,6,2,7,5,8,3,1]=>[7,5,1,4,8,6,2,3]=>{{1,7},{2,5,8},{3},{4},{6}}
[3,5,6,1,8,4,7,2]=>[6,7,3,8,5,1,4,2]=>[6,3,7,5,8,4,1,2]=>{{1,6},{2,3,7},{4,5,8}}
[3,4,7,5,1,8,6,2]=>[5,7,3,4,6,8,2,1]=>[4,3,5,8,7,6,1,2]=>{{1,4,8},{2,3,5,7},{6}}
[2,6,3,7,5,8,1,4]=>[8,2,6,1,7,3,5,4]=>[2,6,8,3,7,5,1,4]=>{{1,2,6},{3,8},{4},{5,7}}
[5,2,1,7,8,3,4,6]=>[2,5,8,3,1,4,7,6]=>[7,2,5,1,4,3,8,6]=>{{1,7,8},{2},{3,5},{4},{6}}
[8,4,1,3,6,2,5,7]=>[4,8,1,6,3,2,5,7]=>[8,4,2,6,1,5,3,7]=>{{1,8},{2,4,6},{3},{5},{7}}
[3,8,2,4,6,7,1,5]=>[7,8,3,2,1,5,4,6]=>[7,3,8,1,4,2,6,5]=>{{1,7},{2,3,8},{4},{5},{6}}
[3,5,6,8,2,7,1,4]=>[7,8,3,1,5,6,2,4]=>[5,3,6,2,7,8,4,1]=>{{1,5,7},{2,3,6,8},{4}}
[5,8,7,3,4,1,2,6]=>[4,1,7,3,5,2,8,6]=>[5,1,4,2,8,3,7,6]=>{{1,5,8},{2},{3,4},{6},{7}}
[6,8,4,7,2,5,3,1]=>[3,5,7,8,1,6,4,2]=>[7,6,3,5,4,8,1,2]=>{{1,7},{2,6,8},{3},{4,5}}
[3,5,8,7,6,1,2,4]=>[6,1,3,2,5,7,8,4]=>[3,1,5,2,8,6,7,4]=>{{1,3,5,8},{2},{4},{6},{7}}
[4,5,8,7,6,1,2,3]=>[6,1,2,4,5,7,8,3]=>[4,1,2,5,8,6,7,3]=>{{1,4,5,8},{2},{3},{6},{7}}
[1,4,2,8,7,6,5,3]=>[1,4,5,2,6,7,8,3]=>[1,8,4,3,5,6,7,2]=>{{1},{2,8},{3,4},{5},{6},{7}}
[3,4,1,8,7,6,5,2]=>[4,5,3,1,6,7,8,2]=>[4,3,8,2,5,6,7,1]=>{{1,4},{2,3,8},{5},{6},{7}}
[8,5,6,1,2,4,3,7]=>[6,1,4,2,8,5,3,7]=>[4,1,8,3,6,2,5,7]=>{{1,4},{2},{3,8},{5,6},{7}}
[5,1,8,3,7,6,4,2]=>[5,4,6,7,1,8,3,2]=>[7,8,5,4,3,6,1,2]=>{{1,7},{2,8},{3,5},{4},{6}}
[4,1,3,8,7,6,5,2]=>[4,5,1,3,6,7,8,2]=>[8,4,2,1,5,6,7,3]=>{{1,8},{2,4},{3},{5},{6},{7}}
[1,4,2,6,5,8,3,7]=>[1,4,8,2,6,5,3,7]=>[1,6,4,3,8,2,5,7]=>{{1},{2,6},{3,4},{5,8},{7}}
[1,2,5,4,7,3,8,6]=>[1,2,7,5,4,8,3,6]=>[1,2,5,8,3,7,6,4]=>{{1},{2},{3,5},{4,8},{6,7}}
[1,2,5,3,8,7,6,4]=>[1,2,5,6,3,7,8,4]=>[1,2,8,5,4,6,7,3]=>{{1},{2},{3,8},{4,5},{6},{7}}
[1,7,5,2,6,3,8,4]=>[1,5,7,6,8,2,3,4]=>[1,8,6,7,5,4,3,2]=>{{1},{2,8},{3,6},{4,7},{5}}
[1,2,6,5,3,8,7,4]=>[1,2,5,6,7,4,8,3]=>[1,2,8,6,5,3,7,4]=>{{1},{2},{3,8},{4,6},{5},{7}}
[1,6,2,7,3,8,5,4]=>[1,6,7,5,8,2,3,4]=>[1,7,6,8,5,4,3,2]=>{{1},{2,7},{3,6},{4,8},{5}}
[1,2,8,7,5,3,6,4]=>[1,2,5,7,6,4,8,3]=>[1,2,8,5,6,3,7,4]=>{{1},{2},{3,8},{4,5,6},{7}}
[6,1,4,8,3,5,7,2]=>[6,7,8,1,4,5,3,2]=>[8,7,6,3,1,2,4,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[7,1,8,6,3,4,5,2]=>[7,5,6,3,4,8,1,2]=>[5,8,7,1,2,6,4,3]=>{{1,5},{2,8},{3,7},{4},{6}}
[2,3,4,1,8,6,5,7]=>[4,2,3,1,6,8,5,7]=>[2,3,4,1,8,6,5,7]=>{{1,2,3,4},{5,8},{6},{7}}
[8,4,5,6,3,1,7,2]=>[3,6,7,8,4,5,2,1]=>[8,7,3,6,1,2,4,5]=>{{1,8},{2,7},{3},{4,6},{5}}
[2,3,4,1,8,7,5,6]=>[4,2,3,1,7,5,8,6]=>[2,3,4,1,8,5,7,6]=>{{1,2,3,4},{5,8},{6},{7}}
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}
[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>{{1,2},{3},{4},{5},{6},{7},{8},{9}}
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>{{1,7},{2},{3},{4},{5},{6},{8,9}}
[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>{{1,2},{3,9},{4},{5},{6},{7},{8}}
[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>{{1,2,8},{3},{4},{5},{6},{7},{9}}
[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>{{1,2,10},{3},{4},{5},{6},{7},{8},{9}}
[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>{{1,2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[8,5,6,3,4,1,7,2]=>[4,7,6,3,8,5,1,2]=>[8,4,7,1,6,2,5,3]=>{{1,8},{2,4},{3,7},{5,6}}
[1,7,6,5,4,2,3,8]=>[1,4,2,5,6,7,3,8]=>[1,7,2,4,5,6,3,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[8,1,7,2,6,3,5,4]=>[8,7,6,5,3,2,1,4]=>[5,6,7,8,2,3,4,1]=>{{1,5},{2,6},{3,7},{4,8}}
[5,8,7,2,1,6,4,3]=>[2,7,4,6,5,1,8,3]=>[4,2,6,5,8,3,7,1]=>{{1,4,5,8},{2},{3,6},{7}}
[7,8,6,1,5,3,4,2]=>[6,4,5,3,1,8,7,2]=>[4,7,5,1,3,6,8,2]=>{{1,4},{2,7,8},{3,5},{6}}
[7,6,8,1,4,3,5,2]=>[8,5,4,1,3,7,6,2]=>[4,5,7,3,1,8,2,6]=>{{1,4},{2,5},{3,7},{6,8}}
[1,5,4,2,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[8,5,1,4,2,3,7,6]=>[5,4,2,1,8,7,3,6]=>[4,7,1,3,5,8,6,2]=>{{1,4},{2,7},{3},{5},{6,8}}
[1,7,2,3,6,4,5,8]=>[1,7,2,6,4,3,5,8]=>[1,6,2,7,3,5,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[8,7,1,2,3,6,5,4]=>[7,1,2,5,6,3,8,4]=>[5,1,2,8,6,4,7,3]=>{{1,5,6},{2},{3},{4,8},{7}}
[3,2,8,1,4,5,7,6]=>[8,3,2,1,4,7,5,6]=>[3,7,1,2,4,8,6,5]=>{{1,3},{2,7},{4},{5},{6,8}}
[6,7,4,5,1,8,3,2]=>[5,3,8,7,4,6,1,2]=>[5,7,3,6,1,8,4,2]=>{{1,5},{2,7},{3},{4,6,8}}
[1,4,8,6,2,3,7,5]=>[1,6,2,4,8,7,5,3]=>[1,4,2,8,6,7,3,5]=>{{1},{2,4,8},{3},{5,6,7}}
[1,5,6,8,2,3,7,4]=>[1,8,2,7,5,6,3,4]=>[1,5,2,6,7,8,4,3]=>{{1},{2,5,7},{3},{4,6,8}}
[5,1,7,8,2,3,6,4]=>[5,8,2,6,1,3,7,4]=>[7,5,1,6,4,3,8,2]=>{{1,7,8},{2,5},{3},{4,6}}
[5,2,7,4,8,1,6,3]=>[8,5,6,7,2,1,4,3]=>[5,8,7,6,3,4,1,2]=>{{1,5},{2,8},{3,7},{4,6}}
[5,7,2,3,8,1,6,4]=>[8,7,2,6,5,1,3,4]=>[5,6,1,7,8,4,3,2]=>{{1,5,8},{2,6},{3},{4,7}}
[5,7,3,1,8,2,6,4]=>[3,7,8,6,5,2,4,1]=>[6,5,3,7,8,2,1,4]=>{{1,6},{2,5,8},{3},{4,7}}
[5,7,1,3,8,6,2,4]=>[7,6,1,3,5,8,4,2]=>[5,7,2,1,8,6,3,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[5,7,3,1,8,6,2,4]=>[3,7,6,2,5,8,4,1]=>[7,3,5,1,8,6,2,4]=>{{1,7},{2,3,5,8},{4},{6}}
[6,7,8,3,1,4,2,5]=>[3,8,4,2,1,6,7,5]=>[6,3,4,1,2,7,8,5]=>{{1,6,7,8},{2,3,4},{5}}
[4,1,2,7,8,6,5,3]=>[4,1,5,2,6,8,7,3]=>[7,1,4,3,5,6,8,2]=>{{1,7,8},{2},{3,4},{5},{6}}
[6,2,7,8,5,1,4,3]=>[5,8,4,1,6,3,7,2]=>[5,4,7,3,6,1,8,2]=>{{1,5,6},{2,4},{3,7,8}}
[5,7,1,2,8,6,3,4]=>[7,1,6,3,5,8,2,4]=>[5,1,7,2,8,6,4,3]=>{{1,5,8},{2},{3,7},{4},{6}}
[6,1,7,8,2,5,4,3]=>[6,8,4,5,2,1,7,3]=>[5,4,7,6,2,3,8,1]=>{{1,5},{2,4,6},{3,7,8}}
[6,7,8,2,4,3,1,5]=>[3,4,8,1,2,6,7,5]=>[6,4,3,2,1,7,8,5]=>{{1,6,7,8},{2,4},{3},{5}}
[6,3,4,5,8,7,2,1]=>[2,7,6,3,4,5,8,1]=>[6,2,8,1,3,4,7,5]=>{{1,6},{2},{3,8},{4},{5},{7}}
[3,4,7,1,8,6,5,2]=>[7,5,3,4,6,8,1,2]=>[3,4,5,8,7,6,2,1]=>{{1,3,5,7},{2,4,8},{6}}
[7,8,3,5,1,4,6,2]=>[5,6,8,1,3,4,7,2]=>[7,6,5,3,2,1,8,4]=>{{1,7,8},{2,6},{3,5},{4}}
[3,8,6,7,1,4,5,2]=>[7,5,3,1,4,8,6,2]=>[3,5,8,2,1,7,4,6]=>{{1,3,8},{2,5},{4},{6,7}}
[8,3,6,1,2,5,7,4]=>[6,1,8,7,2,3,5,4]=>[8,1,6,7,4,5,2,3]=>{{1,8},{2},{3,6},{4,7},{5}}
[7,2,6,3,5,4,8,1]=>[8,7,6,5,3,2,4,1]=>[5,6,7,8,2,3,1,4]=>{{1,5},{2,6},{3,7},{4,8}}
[5,4,6,3,1,8,2,7]=>[3,6,8,5,4,2,1,7]=>[6,5,3,8,1,2,4,7]=>{{1,6},{2,5},{3},{4,8},{7}}
[5,8,2,6,4,7,3,1]=>[3,7,8,6,5,2,1,4]=>[6,5,3,7,8,2,4,1]=>{{1,6},{2,5,8},{3},{4,7}}
[8,7,5,2,6,4,3,1]=>[3,4,6,5,7,2,8,1]=>[8,4,3,6,5,1,7,2]=>{{1,8},{2,4,6},{3},{5},{7}}
[7,6,1,8,4,3,2,5]=>[6,3,4,7,2,8,5,1]=>[3,8,7,4,1,6,2,5]=>{{1,3,7},{2,8},{4},{5},{6}}
[8,3,1,4,7,5,6,2]=>[3,8,6,1,7,5,2,4]=>[8,3,6,2,7,1,5,4]=>{{1,8},{2,3,6},{4},{5,7}}
[5,4,8,1,7,2,6,3]=>[8,7,6,5,4,2,1,3]=>[5,6,7,8,1,3,4,2]=>{{1,5},{2,6},{3,7},{4,8}}
[5,7,3,8,2,6,4,1]=>[4,6,8,7,5,1,2,3]=>[7,6,4,5,8,3,2,1]=>{{1,7},{2,6},{3,4,5,8}}
[5,4,6,8,2,7,3,1]=>[3,7,8,5,4,6,1,2]=>[6,5,3,7,1,8,4,2]=>{{1,6,8},{2,5},{3},{4,7}}
[2,1,8,7,5,6,3,4]=>[2,1,6,3,7,5,8,4]=>[2,1,8,3,6,4,7,5]=>{{1,2},{3,8},{4},{5,6},{7}}
[8,2,7,6,3,5,4,1]=>[4,5,8,6,3,7,2,1]=>[8,6,4,5,1,7,2,3]=>{{1,8},{2,6,7},{3,4,5}}
[7,1,8,6,5,3,2,4]=>[7,3,5,2,6,8,1,4]=>[3,8,5,1,7,6,4,2]=>{{1,3,5,7},{2,8},{4},{6}}
[1,2,8,7,6,3,4,5]=>[1,2,6,3,4,7,8,5]=>[1,2,8,3,4,6,7,5]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[2,8,7,6,5,3,4,1]=>[4,2,5,3,6,7,8,1]=>[2,8,4,1,5,6,7,3]=>{{1,2,8},{3,4},{5},{6},{7}}
[5,8,6,7,3,4,1,2]=>[4,1,7,3,5,8,6,2]=>[5,1,4,2,8,7,3,6]=>{{1,5,8},{2},{3,4},{6,7}}
[4,8,6,7,3,5,1,2]=>[5,1,7,4,3,8,6,2]=>[5,1,4,8,2,7,3,6]=>{{1,5},{2},{3,4,8},{6,7}}
[1,8,6,7,4,5,2,3]=>[1,5,2,7,4,8,6,3]=>[1,8,2,5,3,7,4,6]=>{{1},{2,8},{3},{4,5},{6,7}}
[5,8,3,7,4,6,1,2]=>[6,1,8,7,5,4,3,2]=>[7,1,5,6,8,2,3,4]=>{{1,7},{2},{3,5,8},{4,6}}
[4,7,1,8,5,6,2,3]=>[7,6,2,4,8,5,1,3]=>[4,7,1,8,6,2,5,3]=>{{1,4,8},{2,7},{3},{5,6}}
[6,8,1,7,4,5,2,3]=>[8,5,2,7,4,6,1,3]=>[5,7,1,6,2,8,4,3]=>{{1,5},{2,7},{3},{4,6,8}}
[2,8,6,7,3,5,1,4]=>[5,2,7,1,3,8,6,4]=>[2,8,5,3,4,7,1,6]=>{{1,2,8},{3,5},{4},{6,7}}
[1,6,2,8,5,7,3,4]=>[1,6,7,3,8,2,5,4]=>[1,8,7,2,6,5,3,4]=>{{1},{2,8},{3,7},{4},{5,6}}
[3,8,5,7,1,6,2,4]=>[7,6,3,2,8,1,5,4]=>[3,7,8,1,6,5,2,4]=>{{1,3,8},{2,7},{4},{5,6}}
[5,8,2,6,1,7,3,4]=>[6,8,7,3,5,2,1,4]=>[7,5,6,1,8,3,4,2]=>{{1,7},{2,5,8},{3,6},{4}}
[2,7,3,6,1,8,4,5]=>[6,2,7,8,4,3,1,5]=>[2,8,7,6,1,4,5,3]=>{{1,2,8},{3,7},{4,6},{5}}
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[1,2,3,4,5,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[1,2,3,4,5,6,8,9,10,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[1,2,3,4,5,7,8,9,10,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[1,2,3,4,6,7,8,9,10,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,10,3]=>{{1},{2},{3,4,5,6,7,8,9,10}}
[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[5,6,4,8,2,3,1,7]=>[3,8,2,6,5,4,1,7]=>[5,3,1,6,8,2,4,7]=>{{1,5,8},{2,3},{4,6},{7}}
[5,7,4,8,2,6,1,3]=>[6,8,1,7,5,2,4,3]=>[7,5,2,6,8,4,1,3]=>{{1,7},{2,5,8},{3},{4,6}}
[4,7,3,5,2,6,1,8]=>[6,5,7,4,3,2,1,8]=>[5,6,4,7,1,2,3,8]=>{{1,5},{2,6},{3,4,7},{8}}
[4,5,3,7,2,6,1,8]=>[6,7,5,4,3,2,1,8]=>[5,4,6,7,1,2,3,8]=>{{1,5},{2,4,7},{3,6},{8}}
[4,5,3,6,2,8,1,7]=>[8,6,5,4,3,2,1,7]=>[4,5,6,8,1,2,3,7]=>{{1,4,8},{2,5},{3,6},{7}}
[5,6,4,2,3,1,8,7]=>[3,4,2,6,5,1,8,7]=>[5,3,1,4,6,2,8,7]=>{{1,5,6},{2,3},{4},{7,8}}
[5,4,6,1,3,2,8,7]=>[6,3,1,5,4,2,8,7]=>[3,5,2,6,1,4,8,7]=>{{1,3},{2,5},{4,6},{7,8}}
[6,3,2,8,7,4,1,5]=>[4,3,7,6,1,5,8,2]=>[4,8,3,6,2,1,7,5]=>{{1,4,6},{2,8},{3},{5},{7}}
[2,1,7,8,6,4,5,3]=>[2,1,5,6,4,8,7,3]=>[2,1,7,5,3,6,8,4]=>{{1,2},{3,7,8},{4,5},{6}}
[7,3,2,8,6,4,5,1]=>[5,3,7,6,4,8,2,1]=>[5,8,3,7,1,6,2,4]=>{{1,5},{2,8},{3},{4,7},{6}}
[5,7,8,6,2,3,1,4]=>[3,6,2,1,5,8,7,4]=>[5,3,1,2,7,6,8,4]=>{{1,5,7,8},{2,3},{4},{6}}
[5,8,7,6,3,2,1,4]=>[2,3,6,1,5,7,8,4]=>[5,2,3,1,8,6,7,4]=>{{1,5,8},{2},{3},{4},{6},{7}}
[4,7,6,2,8,1,3,5]=>[8,6,1,4,2,7,5,3]=>[4,6,2,8,3,7,1,5]=>{{1,4,8},{2,6,7},{3},{5}}
[8,3,2,6,7,5,1,4]=>[5,3,7,1,8,4,6,2]=>[7,8,3,2,5,1,4,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[8,6,4,3,7,5,1,2]=>[5,1,4,7,6,8,2,3]=>[5,1,8,4,7,6,3,2]=>{{1,5,7},{2},{3,8},{4},{6}}
[7,6,4,3,8,1,5,2]=>[8,5,4,6,1,7,3,2]=>[4,6,8,5,3,7,1,2]=>{{1,4,5},{2,6,7},{3,8}}
[2,1,7,6,8,3,5,4]=>[2,1,8,5,3,7,6,4]=>[2,1,5,7,4,8,3,6]=>{{1,2},{3,5},{4,7},{6,8}}
[6,5,7,8,1,2,4,3]=>[8,1,4,2,6,5,7,3]=>[4,1,6,3,7,2,8,5]=>{{1,4},{2},{3,6},{5,7,8}}
[6,1,5,4,3,8,7,2]=>[6,7,4,5,1,3,8,2]=>[5,4,8,6,3,1,7,2]=>{{1,5},{2,4,6},{3,8},{7}}
[7,1,4,3,5,6,8,2]=>[7,8,4,1,2,3,6,5]=>[7,4,8,3,2,5,1,6]=>{{1,7},{2,4},{3,8},{5},{6}}
[8,4,7,2,5,6,1,3]=>[6,7,1,8,3,2,4,5]=>[8,7,2,6,3,5,4,1]=>{{1,8},{2,7},{3},{4,6},{5}}
[3,5,8,7,2,4,1,6]=>[4,7,3,2,5,1,8,6]=>[4,3,5,1,8,2,7,6]=>{{1,4},{2,3,5,8},{6},{7}}
[2,5,8,3,1,7,4,6]=>[3,2,8,7,5,4,1,6]=>[2,5,3,7,8,1,6,4]=>{{1,2,5,8},{3},{4,7},{6}}
[1,7,3,8,5,2,4,6]=>[1,5,8,2,7,3,4,6]=>[1,8,5,3,7,4,6,2]=>{{1},{2,8},{3,5,7},{4},{6}}
[8,2,5,1,7,3,4,6]=>[5,8,7,3,2,4,1,6]=>[8,5,7,1,3,2,6,4]=>{{1,8},{2,5},{3,7},{4},{6}}
[6,2,4,8,5,7,1,3]=>[7,6,1,3,8,2,5,4]=>[7,8,2,1,6,5,3,4]=>{{1,7},{2,8},{3},{4},{5,6}}
[1,7,5,3,4,6,8,2]=>[1,8,5,3,7,4,6,2]=>[1,5,8,2,7,3,4,6]=>{{1},{2,5,7},{3,8},{4},{6}}
[1,2,8,4,3,5,6,7]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[1,7,4,2,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[1,8,3,2,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[8,3,1,6,2,5,4,7]=>[3,8,6,5,2,4,1,7]=>[6,3,5,8,2,1,4,7]=>{{1,6},{2,3,5},{4,8},{7}}
[5,1,4,8,2,7,3,6]=>[5,8,7,1,4,3,2,6]=>[8,5,7,3,1,2,6,4]=>{{1,8},{2,5},{3,7},{4},{6}}
[1,4,6,8,2,7,3,5]=>[1,8,7,4,3,6,2,5]=>[1,4,6,7,2,8,5,3]=>{{1},{2,4,7},{3,6,8},{5}}
[5,1,4,2,7,8,3,6]=>[5,4,8,1,2,3,7,6]=>[5,7,4,3,2,1,8,6]=>{{1,5},{2,7,8},{3,4},{6}}
[3,1,7,8,2,6,4,5]=>[3,8,1,6,4,2,7,5]=>[6,3,2,7,1,5,8,4]=>{{1,6},{2,3},{4,7,8},{5}}
[1,2,3,7,5,8,6,4]=>[1,2,3,6,8,7,4,5]=>[1,2,3,8,6,7,5,4]=>{{1},{2},{3},{4,8},{5,6,7}}
[2,1,7,8,3,4,6,5]=>[2,1,8,3,6,4,7,5]=>[2,1,6,3,7,5,8,4]=>{{1,2},{3,6},{4},{5,7,8}}
[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>{{1,11},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[5,7,8,3,2,1,4,6]=>[2,3,8,1,5,4,7,6]=>[5,2,3,1,7,4,8,6]=>{{1,5,7,8},{2},{3},{4},{6}}
[8,6,3,7,2,1,4,5]=>[2,7,6,1,3,8,5,4]=>[7,2,8,3,4,6,1,5]=>{{1,7},{2},{3,8},{4},{5},{6}}
[6,4,3,2,1,7,5,8]=>[2,3,4,6,7,1,5,8]=>[7,2,3,4,6,5,1,8]=>{{1,7},{2},{3},{4},{5,6},{8}}
[8,5,4,2,7,6,1,3]=>[6,4,1,5,7,8,3,2]=>[4,8,2,7,5,6,1,3]=>{{1,4,7},{2,8},{3},{5},{6}}
[7,5,4,2,8,6,1,3]=>[6,4,1,5,8,7,3,2]=>[4,8,2,6,5,7,1,3]=>{{1,4,6,7},{2,8},{3},{5}}
[3,6,4,7,2,8,1,5]=>[8,7,3,6,1,4,2,5]=>[3,6,7,8,4,2,5,1]=>{{1,3,7},{2,6},{4,8},{5}}
[2,6,4,7,3,8,5,1]=>[5,2,8,7,6,1,4,3]=>[2,8,5,6,7,4,1,3]=>{{1,2,8},{3,5,7},{4,6}}
[5,6,3,4,1,2,8,7]=>[4,1,6,3,5,2,8,7]=>[5,1,4,2,6,3,8,7]=>{{1,5,6},{2},{3,4},{7,8}}
[8,5,3,7,2,6,4,1]=>[4,6,7,5,8,1,2,3]=>[8,6,4,7,5,3,2,1]=>{{1,8},{2,6},{3,4,7},{5}}
[2,1,7,8,5,6,3,4]=>[2,1,6,3,8,5,7,4]=>[2,1,7,3,6,4,8,5]=>{{1,2},{3,7,8},{4},{5,6}}
[4,1,5,8,3,2,6,7]=>[4,3,8,1,5,2,6,7]=>[4,5,3,2,8,1,6,7]=>{{1,4},{2,5,8},{3},{6},{7}}
[5,3,6,2,1,4,7,8]=>[2,6,5,1,3,4,7,8]=>[5,2,6,3,4,1,7,8]=>{{1,5},{2},{3,6},{4},{7},{8}}
[3,2,6,1,5,7,4,8]=>[6,3,2,7,1,5,4,8]=>[3,7,1,6,4,2,5,8]=>{{1,3},{2,7},{4,6},{5},{8}}
[6,4,2,1,5,3,7,8]=>[2,4,6,5,3,1,7,8]=>[6,2,4,5,1,3,7,8]=>{{1,6},{2},{3,4,5},{7},{8}}
[6,5,2,1,4,7,8,3]=>[2,5,6,1,8,3,7,4]=>[7,2,6,3,5,4,8,1]=>{{1,7,8},{2},{3,6},{4},{5}}
[2,4,1,5,8,3,7,6]=>[4,2,8,1,5,7,3,6]=>[2,5,4,3,7,8,6,1]=>{{1,2,5,7},{3,4},{6,8}}
[2,4,1,5,3,8,7,6]=>[4,2,5,1,3,7,8,6]=>[2,5,4,3,1,8,7,6]=>{{1,2,5},{3,4},{6,8},{7}}
[3,5,6,2,7,1,4,8]=>[7,6,3,1,5,2,4,8]=>[3,5,6,2,7,4,1,8]=>{{1,3,6},{2,5,7},{4},{8}}
[3,4,6,8,2,7,1,5]=>[7,8,3,4,1,6,2,5]=>[4,3,6,7,2,8,5,1]=>{{1,4,7},{2,3,6,8},{5}}
[3,5,6,2,7,8,4,1]=>[4,8,3,6,5,1,7,2]=>[4,3,6,5,7,2,8,1]=>{{1,4,5,7,8},{2,3,6}}
[2,5,8,6,7,3,4,1]=>[4,2,7,3,5,8,6,1]=>[2,5,4,1,8,7,3,6]=>{{1,2,5,8},{3,4},{6,7}}
[3,5,6,8,7,2,1,4]=>[2,7,3,1,5,6,8,4]=>[3,2,5,1,6,8,7,4]=>{{1,3,5,6,8},{2},{4},{7}}
[4,5,6,7,8,1,3,2]=>[8,3,1,4,5,6,7,2]=>[3,4,2,5,6,7,8,1]=>{{1,3},{2,4,5,6,7,8}}
[5,8,6,1,7,3,4,2]=>[6,4,8,3,5,7,2,1]=>[5,6,4,1,8,7,2,3]=>{{1,5,8},{2,6,7},{3,4}}
[3,2,4,1,8,5,6,7]=>[4,3,2,1,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>{{1,3},{2,4},{5,8},{6},{7}}
[3,2,4,1,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>[3,4,1,2,6,8,5,7]=>{{1,3},{2,4},{5,6,8},{7}}
[3,2,4,1,8,5,7,6]=>[4,3,2,1,8,7,5,6]=>[3,4,1,2,7,8,6,5]=>{{1,3},{2,4},{5,7},{6,8}}
[8,5,6,1,7,3,4,2]=>[6,4,7,3,8,5,1,2]=>[7,8,4,1,6,2,5,3]=>{{1,7},{2,8},{3,4},{5,6}}
[3,2,4,1,8,6,5,7]=>[4,3,2,1,6,8,5,7]=>[3,4,1,2,8,6,5,7]=>{{1,3},{2,4},{5,8},{6},{7}}
[4,3,7,5,1,8,6,2]=>[5,7,4,3,6,8,2,1]=>[5,4,8,1,7,6,2,3]=>{{1,5,7},{2,4},{3,8},{6}}
[5,4,8,3,6,1,7,2]=>[6,7,8,5,4,3,1,2]=>[7,6,5,8,1,2,4,3]=>{{1,7},{2,6},{3,5},{4,8}}
[5,4,3,6,7,1,8,2]=>[7,8,4,5,3,6,1,2]=>[5,4,7,6,1,8,3,2]=>{{1,5},{2,4,6,8},{3,7}}
[2,4,1,7,5,3,8,6]=>[4,2,5,1,7,8,3,6]=>[2,8,4,3,5,7,6,1]=>{{1,2,8},{3,4},{5},{6,7}}
[3,2,7,1,5,8,6,4]=>[7,3,2,6,1,8,5,4]=>[3,7,1,8,4,6,2,5]=>{{1,3},{2,7},{4,8},{5},{6}}
[4,3,2,6,7,1,5,8]=>[7,3,4,2,1,6,5,8]=>[3,6,4,1,2,7,5,8]=>{{1,3,4},{2,6,7},{5},{8}}
[3,2,5,7,1,6,8,4]=>[7,3,2,8,5,1,6,4]=>[3,7,1,5,8,4,2,6]=>{{1,3},{2,7},{4,5,8},{6}}
[4,8,3,2,7,1,5,6]=>[7,3,8,4,1,2,6,5]=>[4,7,3,8,2,5,1,6]=>{{1,4,8},{2,7},{3},{5},{6}}
[3,2,1,4,7,5,8,6]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,7,6,5]=>{{1,3},{2},{4},{5,8},{6,7}}
[6,2,3,1,5,4,8,7]=>[3,6,2,5,1,4,8,7]=>[5,3,1,6,4,2,8,7]=>{{1,5},{2,3},{4,6},{7,8}}
[8,6,7,2,5,3,4,1]=>[4,7,5,3,2,8,6,1]=>[8,4,5,1,2,7,3,6]=>{{1,8},{2,4},{3,5},{6,7}}
[6,2,5,3,4,1,8,7]=>[4,6,5,3,2,1,8,7]=>[6,4,5,1,2,3,8,7]=>{{1,6},{2,4},{3,5},{7,8}}
[6,1,5,2,4,3,8,7]=>[6,5,4,2,1,3,8,7]=>[4,5,6,2,3,1,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[6,1,5,3,4,2,8,7]=>[6,4,5,3,1,2,8,7]=>[4,6,5,1,3,2,8,7]=>{{1,4},{2,6},{3,5},{7,8}}
[6,3,5,1,4,2,8,7]=>[5,4,6,1,3,2,8,7]=>[5,6,4,3,1,2,8,7]=>{{1,5},{2,6},{3,4},{7,8}}
[2,1,8,4,5,3,7,6]=>[2,1,5,8,4,7,3,6]=>[2,1,7,5,3,8,6,4]=>{{1,2},{3,7},{4,5},{6,8}}
[8,3,7,5,6,1,4,2]=>[6,4,8,1,7,5,3,2]=>[6,8,4,3,7,1,2,5]=>{{1,6},{2,8},{3,4},{5,7}}
[8,3,7,1,6,4,5,2]=>[7,5,8,6,4,1,3,2]=>[6,8,5,7,1,4,2,3]=>{{1,6},{2,8},{3,5},{4,7}}
[2,1,8,4,7,5,6,3]=>[2,1,6,8,7,5,4,3]=>[2,1,8,6,7,3,4,5]=>{{1,2},{3,8},{4,6},{5,7}}
[8,2,7,3,6,4,5,1]=>[5,8,7,6,4,3,2,1]=>[8,5,6,7,1,2,3,4]=>{{1,8},{2,5},{3,6},{4,7}}
[8,1,7,2,4,3,6,5]=>[8,7,4,2,6,3,1,5]=>[4,6,7,2,8,3,5,1]=>{{1,4},{2,6},{3,7},{5,8}}
[8,1,3,2,7,4,6,5]=>[8,3,1,7,6,4,2,5]=>[3,6,2,7,8,4,5,1]=>{{1,3},{2,6},{4,7},{5,8}}
[2,1,8,3,7,4,6,5]=>[2,1,8,7,6,4,3,5]=>[2,1,6,7,8,4,5,3]=>{{1,2},{3,6},{4,7},{5,8}}
[8,1,5,2,4,3,7,6]=>[8,5,4,2,1,7,3,6]=>[4,5,7,2,3,8,6,1]=>{{1,4},{2,5},{3,7},{6,8}}
[8,2,7,1,4,3,6,5]=>[7,8,4,1,6,2,5,3]=>[6,4,7,3,8,5,1,2]=>{{1,6},{2,4},{3,7},{5,8}}
[8,2,7,5,6,3,4,1]=>[4,8,6,3,7,5,2,1]=>[8,4,6,1,7,2,3,5]=>{{1,8},{2,4},{3,6},{5,7}}
[8,4,7,5,6,2,3,1]=>[3,6,2,8,7,5,4,1]=>[8,3,1,6,7,2,4,5]=>{{1,8},{2,3},{4,6},{5,7}}
[8,2,3,1,7,5,6,4]=>[3,8,2,6,7,5,1,4]=>[6,3,1,8,7,2,5,4]=>{{1,6},{2,3},{4,8},{5,7}}
[2,1,8,3,7,5,6,4]=>[2,1,8,6,7,5,3,4]=>[2,1,6,8,7,3,5,4]=>{{1,2},{3,6},{4,8},{5,7}}
[8,1,7,5,6,2,4,3]=>[8,6,4,2,7,5,1,3]=>[4,6,8,2,7,1,5,3]=>{{1,4},{2,6},{3,8},{5,7}}
[2,1,8,5,7,3,6,4]=>[2,1,7,6,8,3,5,4]=>[2,1,7,8,6,5,3,4]=>{{1,2},{3,7},{4,8},{5,6}}
[8,1,7,4,6,3,5,2]=>[8,5,6,7,3,4,1,2]=>[5,8,7,6,2,1,4,3]=>{{1,5},{2,8},{3,7},{4,6}}
[6,5,8,1,3,2,7,4]=>[8,3,1,7,6,5,2,4]=>[3,6,2,7,8,1,5,4]=>{{1,3},{2,6},{4,7},{5,8}}
[6,5,8,7,3,1,2,4]=>[3,1,7,2,6,5,8,4]=>[6,1,3,2,8,4,7,5]=>{{1,6},{2},{3},{4},{5,8},{7}}
[4,2,1,3,8,5,6,7]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[2,8,3,5,4,1,6,7]=>[4,2,5,8,1,3,6,7]=>[2,8,5,4,3,1,6,7]=>{{1,2,8},{3,5},{4},{6},{7}}
[4,3,1,2,8,5,6,7]=>[3,1,4,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[3,4,2,1,8,5,6,7]=>[2,4,3,1,8,5,6,7]=>[3,2,4,1,8,5,6,7]=>{{1,3,4},{2},{5,8},{6},{7}}
[3,7,1,8,5,4,6,2]=>[7,6,3,5,8,4,1,2]=>[3,6,7,8,5,1,4,2]=>{{1,3,7},{2,6},{4,8},{5}}
[5,7,8,4,3,6,1,2]=>[6,1,4,8,5,3,7,2]=>[5,1,6,4,7,2,8,3]=>{{1,5,7,8},{2},{3,6},{4}}
[2,8,7,4,1,6,5,3]=>[4,2,7,5,6,3,8,1]=>[2,8,4,5,6,1,7,3]=>{{1,2,8},{3,4,5,6},{7}}
[2,8,5,4,3,1,6,7]=>[3,2,4,5,8,1,6,7]=>[2,8,3,4,5,1,6,7]=>{{1,2,8},{3},{4},{5},{6},{7}}
[4,1,3,2,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>{{1,3},{2,4},{5,8},{6},{7}}
[1,4,3,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>{{1},{2,4},{3},{5,8},{6},{7}}
[7,3,2,8,5,4,6,1]=>[6,3,7,5,8,4,2,1]=>[6,7,3,8,5,1,2,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[6,2,8,4,5,3,1,7]=>[3,5,6,8,4,1,2,7]=>[8,6,3,5,1,4,2,7]=>{{1,8},{2,6},{3},{4,5},{7}}
[7,2,3,8,5,4,6,1]=>[6,7,2,5,8,4,3,1]=>[7,6,1,8,5,2,3,4]=>{{1,7},{2,6},{3},{4,8},{5}}
[4,2,3,1,8,5,6,7]=>[3,4,2,1,8,5,6,7]=>[4,3,1,2,8,5,6,7]=>{{1,4},{2,3},{5,8},{6},{7}}
[3,2,1,4,8,5,6,7]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>{{1,3},{2},{4},{5,8},{6},{7}}
[1,2,8,4,5,3,7,6]=>[1,2,5,8,4,7,3,6]=>[1,2,7,5,3,8,6,4]=>{{1},{2},{3,7},{4,5},{6,8}}
[1,5,2,8,4,3,6,7]=>[1,5,4,8,2,3,6,7]=>[1,5,8,4,3,2,6,7]=>{{1},{2,5},{3,8},{4},{6},{7}}
[1,2,5,4,3,8,6,7]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>{{1},{2},{3,5},{4},{6,8},{7}}
[1,2,7,4,8,5,3,6]=>[1,2,5,8,7,3,6,4]=>[1,2,8,5,7,4,3,6]=>{{1},{2},{3,8},{4,5,7},{6}}
[1,2,4,8,7,5,3,6]=>[1,2,5,4,7,3,8,6]=>[1,2,4,8,5,3,7,6]=>{{1},{2},{3,4,8},{5},{6},{7}}
[1,6,7,2,8,4,3,5]=>[1,7,4,8,3,6,2,5]=>[1,6,7,4,2,8,5,3]=>{{1},{2,6,8},{3,7},{4},{5}}
[5,8,1,3,7,2,4,6]=>[8,7,1,3,5,4,6,2]=>[5,7,2,1,8,3,4,6]=>{{1,5,8},{2,7},{3},{4},{6}}
[1,2,5,8,7,3,4,6]=>[1,2,7,3,5,4,8,6]=>[1,2,5,3,8,4,7,6]=>{{1},{2},{3,5,8},{4},{6},{7}}
[4,2,8,1,7,3,6,5]=>[8,4,7,2,6,3,1,5]=>[4,7,6,2,8,3,5,1]=>{{1,4},{2,7},{3,6},{5,8}}
[7,1,2,8,4,3,6,5]=>[7,1,4,8,6,3,2,5]=>[6,1,7,4,8,3,5,2]=>{{1,6},{2},{3,7},{4},{5,8}}
[7,1,2,8,6,4,3,5]=>[7,1,4,6,3,8,2,5]=>[4,1,8,7,2,6,5,3]=>{{1,4,7},{2},{3,8},{5},{6}}
[2,8,1,7,6,4,3,5]=>[8,2,4,6,3,7,1,5]=>[2,4,8,6,1,7,5,3]=>{{1,2,4,6,7},{3,8},{5}}
[6,8,3,4,1,7,2,5]=>[4,7,8,3,1,6,5,2]=>[7,6,4,1,3,8,2,5]=>{{1,7},{2,6,8},{3,4},{5}}
[5,8,3,4,1,7,2,6]=>[4,7,8,3,5,1,6,2]=>[7,5,4,1,8,3,2,6]=>{{1,7},{2,5,8},{3,4},{6}}
[4,6,2,8,3,5,1,7]=>[5,6,8,4,3,2,1,7]=>[6,5,4,8,1,2,3,7]=>{{1,6},{2,5},{3,4,8},{7}}
[4,5,1,7,3,8,2,6]=>[5,8,7,4,1,2,3,6]=>[7,4,5,8,3,2,6,1]=>{{1,7},{2,4,8},{3,5},{6}}
[4,6,2,8,3,7,1,5]=>[7,6,8,4,1,2,3,5]=>[6,7,4,8,3,5,2,1]=>{{1,6},{2,7},{3,4,8},{5}}
[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>{{1,9},{2},{3},{4},{5},{6},{7},{8}}
[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,2,3,1,4,5,6,7,8]=>[3,9,2,1,4,5,6,7,8]=>[9,3,1,2,4,5,6,7,8]=>{{1,9},{2,3},{4},{5},{6},{7},{8}}
[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>{{1,2,3,4,5,6,7,8,9,10,11}}
[6,5,3,2,1,4,8,7]=>[2,3,5,1,6,4,8,7]=>[6,2,3,1,5,4,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}
[2,8,7,4,5,1,3,6]=>[5,2,1,7,4,3,8,6]=>[2,8,1,5,3,4,7,6]=>{{1,2,8},{3},{4,5},{6},{7}}
[8,7,3,5,2,1,4,6]=>[2,5,7,1,3,4,8,6]=>[8,2,5,3,4,1,7,6]=>{{1,8},{2},{3,5},{4},{6},{7}}
[3,4,1,8,5,6,7,2]=>[4,7,3,1,8,5,6,2]=>[4,3,8,2,7,1,5,6]=>{{1,4},{2,3,8},{5,7},{6}}
[2,4,6,8,10,1,3,5,7,9]=>[10,2,1,4,3,6,5,8,7,9]=>[2,4,1,6,3,8,5,10,7,9]=>{{1,2,4,6,8,10},{3},{5},{7},{9}}
[3,5,7,2,6,4,8,1]=>[8,7,3,6,5,2,4,1]=>[3,5,6,7,8,2,1,4]=>{{1,3,6},{2,5,8},{4,7}}
[2,5,7,3,6,4,8,1]=>[8,2,7,6,5,3,4,1]=>[2,5,6,7,8,3,1,4]=>{{1,2,5,8},{3,6},{4,7}}
[8,4,3,7,6,1,5,2]=>[6,5,4,7,1,8,2,3]=>[5,7,8,4,3,6,2,1]=>{{1,5},{2,7},{3,8},{4},{6}}
[5,2,7,3,6,4,8,1]=>[8,5,7,6,2,3,4,1]=>[5,8,6,7,3,2,1,4]=>{{1,5},{2,8},{3,6},{4,7}}
[5,1,7,3,6,8,4,2]=>[5,4,8,7,1,3,2,6]=>[7,8,4,5,3,1,6,2]=>{{1,7},{2,8},{3,4,5},{6}}
[2,8,4,7,1,6,5,3]=>[7,2,5,6,8,1,3,4]=>[2,6,8,7,5,4,3,1]=>{{1,2,6},{3,8},{4,7},{5}}
[5,4,7,6,8,1,3,2]=>[8,3,1,5,4,7,6,2]=>[3,5,2,7,1,8,4,6]=>{{1,3},{2,5},{4,7},{6,8}}
[8,2,1,3,7,6,5,4]=>[2,8,1,5,6,7,3,4]=>[5,2,1,8,6,7,4,3]=>{{1,5,6,7},{2},{3},{4,8}}
[3,8,1,2,7,6,5,4]=>[8,1,3,5,6,7,2,4]=>[3,1,5,8,6,7,4,2]=>{{1,3,5,6,7},{2},{4,8}}
[2,3,4,5,6,7,8,9,11,1,10]=>[11,2,3,4,5,6,7,8,9,1,10]=>[2,3,4,5,6,7,8,9,11,1,10]=>{{1,2,3,4,5,6,7,8,9,11},{10}}
[2,3,4,5,6,7,8,9,10,12,1,11]=>[12,2,3,4,5,6,7,8,9,10,1,11]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>{{1,2,3,4,5,6,7,8,9,10,12},{11}}
[3,4,6,1,2,8,7,5]=>[6,1,3,4,7,2,8,5]=>[3,1,4,8,6,5,7,2]=>{{1,3,4,8},{2},{5,6},{7}}
[8,1,3,5,7,2,6,4]=>[8,7,1,6,2,5,3,4]=>[6,7,2,8,4,1,5,3]=>{{1,6},{2,7},{3},{4,8},{5}}
[6,2,5,1,8,3,7,4]=>[5,6,8,7,2,1,3,4]=>[8,7,5,6,3,4,2,1]=>{{1,8},{2,7},{3,5},{4,6}}
[8,1,3,4,2,7,6,5]=>[8,4,1,3,6,7,2,5]=>[4,6,2,1,8,7,5,3]=>{{1,4},{2,6,7},{3},{5,8}}
[2,4,3,6,1,5,8,7]=>[6,2,4,3,1,5,8,7]=>[2,4,6,1,3,5,8,7]=>{{1,2,4},{3,6},{5},{7,8}}
[2,4,3,6,5,8,1,7]=>[8,2,4,3,6,5,1,7]=>[2,4,6,1,8,3,5,7]=>{{1,2,4},{3,6},{5,8},{7}}
[2,4,6,3,5,8,7,1]=>[7,2,6,4,3,5,8,1]=>[2,4,6,8,1,3,7,5]=>{{1,2,4,8},{3,6},{5},{7}}
[2,1,4,6,5,8,3,7]=>[2,1,8,4,6,5,3,7]=>[2,1,4,6,8,3,5,7]=>{{1,2},{3,4,6},{5,8},{7}}
[2,4,6,8,1,5,7,3]=>[8,2,7,4,1,6,5,3]=>[2,4,6,7,3,8,1,5]=>{{1,2,4,7},{3,6,8},{5}}
[2,4,6,8,3,1,5,7]=>[3,2,8,4,1,6,5,7]=>[2,4,3,6,1,8,5,7]=>{{1,2,4,6,8},{3},{5},{7}}
[2,4,6,3,8,1,5,7]=>[8,2,6,4,1,3,5,7]=>[2,4,6,8,3,5,1,7]=>{{1,2,4,8},{3,6},{5},{7}}
[2,4,3,6,8,5,1,7]=>[5,2,4,3,8,6,1,7]=>[2,4,6,1,5,8,3,7]=>{{1,2,4},{3,6,8},{5},{7}}
[2,4,3,6,8,1,5,7]=>[8,2,4,3,1,6,5,7]=>[2,4,6,1,3,8,5,7]=>{{1,2,4},{3,6,8},{5},{7}}
[2,4,3,1,6,8,5,7]=>[3,2,4,1,8,6,5,7]=>[2,4,3,1,6,8,5,7]=>{{1,2,4},{3},{5,6,8},{7}}
[2,4,1,3,6,8,7,5]=>[4,2,1,3,7,6,8,5]=>[2,4,1,3,6,8,7,5]=>{{1,2,4},{3},{5,6,8},{7}}
[2,6,4,8,1,7,5,3]=>[8,2,5,7,6,3,1,4]=>[2,5,8,6,7,3,4,1]=>{{1,2,5,7},{3,8},{4,6}}
[1,6,4,7,3,8,2,5]=>[1,8,7,6,2,4,3,5]=>[1,6,7,8,4,3,5,2]=>{{1},{2,6},{3,7},{4,8},{5}}
[5,2,4,7,3,6,8,1]=>[8,5,7,2,4,3,6,1]=>[5,8,7,2,1,3,4,6]=>{{1,5},{2,8},{3,7},{4},{6}}
[5,1,2,4,8,3,6,7]=>[5,1,8,2,4,3,6,7]=>[8,1,5,3,2,4,6,7]=>{{1,8},{2},{3,5},{4},{6},{7}}
[2,6,4,8,7,1,3,5]=>[7,2,1,6,3,4,8,5]=>[2,6,1,8,4,5,7,3]=>{{1,2,6},{3},{4,8},{5},{7}}
[3,8,2,1,4,5,7,6]=>[2,8,3,1,4,7,5,6]=>[3,2,7,1,4,8,6,5]=>{{1,3,7},{2},{4},{5},{6,8}}
[3,7,2,1,4,5,8,6]=>[2,7,3,1,4,8,5,6]=>[3,2,8,1,4,7,6,5]=>{{1,3,8},{2},{4},{5},{6,7}}
[3,8,2,1,4,7,5,6]=>[2,8,3,1,7,5,4,6]=>[3,2,7,1,8,4,6,5]=>{{1,3,7},{2},{4},{5,8},{6}}
[3,7,2,1,4,8,5,6]=>[2,7,3,1,8,5,4,6]=>[3,2,8,1,7,4,6,5]=>{{1,3,8},{2},{4},{5,7},{6}}
[3,2,1,7,5,8,6,4]=>[2,3,1,6,8,7,4,5]=>[3,2,1,8,6,7,5,4]=>{{1,3},{2},{4,8},{5,6,7}}
[3,2,8,1,7,4,6,5]=>[8,3,2,7,6,4,1,5]=>[3,6,1,7,8,4,5,2]=>{{1,3},{2,6},{4,7},{5,8}}
[5,7,8,3,4,1,2,6]=>[4,1,8,3,5,2,7,6]=>[5,1,4,2,7,3,8,6]=>{{1,5,7,8},{2},{3,4},{6}}
[3,6,8,5,4,7,1,2]=>[7,1,3,5,8,6,4,2]=>[3,1,6,7,5,8,2,4]=>{{1,3,6,8},{2},{4,7},{5}}
[7,8,1,2,4,6,5,3]=>[8,1,5,2,6,4,7,3]=>[5,1,7,3,6,2,8,4]=>{{1,5,6},{2},{3,7,8},{4}}
[3,4,6,1,5,8,2,7]=>[6,8,3,4,1,5,2,7]=>[4,3,6,8,2,1,5,7]=>{{1,4,8},{2,3,6},{5},{7}}
[2,1,7,5,6,3,8,4]=>[2,1,6,8,7,5,3,4]=>[2,1,8,6,7,3,5,4]=>{{1,2},{3,8},{4,6},{5,7}}
[4,2,1,5,6,3,7,8]=>[2,4,6,1,5,3,7,8]=>[5,2,4,3,6,1,7,8]=>{{1,5,6},{2},{3,4},{7},{8}}
[6,4,1,5,2,3,7,8]=>[4,6,2,5,3,1,7,8]=>[6,4,1,5,2,3,7,8]=>{{1,6},{2,4,5},{3},{7},{8}}
[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}
[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>[7,1,2,3,4,5,8,9,6]=>{{1,7,8,9},{2},{3},{4},{5},{6}}
[6,7,8,9,1,2,3,4,5]=>[9,1,2,3,4,6,7,8,5]=>[6,1,2,3,4,7,8,9,5]=>{{1,6,7,8,9},{2},{3},{4},{5}}
[9,6,7,8,1,2,3,4,5]=>[8,1,2,3,4,9,6,7,5]=>[9,1,2,3,4,8,5,6,7]=>{{1,9},{2},{3},{4},{5},{6,8},{7}}
[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>[9,1,2,3,4,5,6,7,10,8]=>{{1,9,10},{2},{3},{4},{5},{6},{7},{8}}
[8,9,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,8,9,7]=>[8,1,2,3,4,5,6,9,10,7]=>{{1,8,9,10},{2},{3},{4},{5},{6},{7}}
[10,8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,10,8,7]=>[10,1,2,3,4,5,6,9,7,8]=>{{1,10},{2},{3},{4},{5},{6},{7},{8,9}}
[10,7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,10,7,8,6]=>[10,1,2,3,4,5,9,6,7,8]=>{{1,10},{2},{3},{4},{5},{6},{7,9},{8}}
[3,7,5,8,2,1,4,6]=>[2,8,3,1,7,4,5,6]=>[3,2,7,1,8,5,6,4]=>{{1,3,7},{2},{4},{5,8},{6}}
[5,4,7,2,1,8,6,3]=>[2,7,6,5,4,8,1,3]=>[5,2,7,8,1,6,4,3]=>{{1,5},{2},{3,7},{4,8},{6}}
[2,1,5,7,8,6,3,4]=>[2,1,6,3,5,8,7,4]=>[2,1,5,3,7,6,8,4]=>{{1,2},{3,5,7,8},{4},{6}}
[5,7,1,6,2,8,3,4]=>[7,6,8,3,5,1,2,4]=>[6,7,5,1,8,4,3,2]=>{{1,6},{2,7},{3,5,8},{4}}
[2,3,6,5,1,4,8,7]=>[5,2,3,1,6,4,8,7]=>[2,3,6,1,5,4,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[2,3,6,4,1,5,8,7]=>[4,2,3,6,1,5,8,7]=>[2,3,6,4,1,5,8,7]=>{{1,2,3,6},{4},{5},{7,8}}
[2,7,6,4,1,8,3,5]=>[4,2,6,7,3,8,1,5]=>[2,8,7,4,1,6,5,3]=>{{1,2,8},{3,7},{4},{5},{6}}
[2,3,4,8,7,6,1,5]=>[6,2,3,4,1,7,8,5]=>[2,3,4,8,1,6,7,5]=>{{1,2,3,4,8},{5},{6},{7}}
[2,3,4,8,5,7,1,6]=>[7,2,3,4,8,1,5,6]=>[2,3,4,8,7,5,6,1]=>{{1,2,3,4,8},{5,7},{6}}
[2,1,4,5,8,7,3,6]=>[2,1,7,4,5,3,8,6]=>[2,1,4,5,8,3,7,6]=>{{1,2},{3,4,5,8},{6},{7}}
[2,3,4,8,7,5,6,1]=>[6,2,3,4,7,5,8,1]=>[2,3,4,8,6,1,7,5]=>{{1,2,3,4,8},{5,6},{7}}
[2,3,4,8,7,5,1,6]=>[5,2,3,4,7,1,8,6]=>[2,3,4,8,5,1,7,6]=>{{1,2,3,4,8},{5},{6},{7}}
[2,7,6,5,4,8,1,3]=>[8,2,1,5,6,7,4,3]=>[2,5,1,8,6,7,3,4]=>{{1,2,5,6,7},{3},{4,8}}
[7,3,5,6,8,1,2,4]=>[8,1,7,2,4,5,3,6]=>[7,1,8,3,2,4,6,5]=>{{1,7},{2},{3,8},{4},{5},{6}}
[6,4,1,5,8,3,2,7]=>[4,3,6,8,1,2,5,7]=>[6,8,3,4,2,5,1,7]=>{{1,6},{2,8},{3},{4},{5},{7}}
[5,7,3,6,1,8,4,2]=>[6,4,8,7,5,3,2,1]=>[6,7,4,5,8,1,2,3]=>{{1,6},{2,7},{3,4,5,8}}
[2,1,4,5,8,6,3,7]=>[2,1,6,4,5,8,3,7]=>[2,1,4,5,8,6,3,7]=>{{1,2},{3,4,5,8},{6},{7}}
[2,3,4,8,5,6,1,7]=>[6,2,3,4,8,5,1,7]=>[2,3,4,8,6,1,5,7]=>{{1,2,3,4,8},{5,6},{7}}
[6,3,5,4,8,2,7,1]=>[7,8,6,5,3,4,2,1]=>[6,5,7,8,2,1,3,4]=>{{1,6},{2,5},{3,7},{4,8}}
[2,1,4,5,8,3,7,6]=>[2,1,8,4,5,7,3,6]=>[2,1,4,5,7,8,6,3]=>{{1,2},{3,4,5,7},{6,8}}
[2,3,4,8,5,1,6,7]=>[5,2,3,4,8,1,6,7]=>[2,3,4,8,5,1,6,7]=>{{1,2,3,4,8},{5},{6},{7}}
[1,8,2,7,4,6,3,5]=>[1,8,6,7,3,4,2,5]=>[1,6,8,7,3,4,5,2]=>{{1},{2,6},{3,8},{4,7},{5}}
[4,8,1,7,5,6,2,3]=>[8,6,2,4,7,5,1,3]=>[4,6,1,8,7,2,5,3]=>{{1,4,8},{2,6},{3},{5,7}}
[3,8,1,7,5,6,2,4]=>[8,6,3,2,7,5,1,4]=>[3,6,8,1,7,2,5,4]=>{{1,3,8},{2,6},{4},{5,7}}
[3,8,2,7,5,6,1,4]=>[6,8,3,1,7,5,2,4]=>[6,3,8,2,7,1,5,4]=>{{1,6},{2,3,8},{4},{5,7}}
[6,8,1,7,4,2,5,3]=>[8,4,7,5,3,6,1,2]=>[4,7,5,6,1,8,3,2]=>{{1,4,6,8},{2,7},{3,5}}
[2,6,3,7,8,4,5,1]=>[5,2,6,8,4,3,7,1]=>[2,7,6,5,1,3,8,4]=>{{1,2,7,8},{3,6},{4,5}}
[2,4,7,3,6,8,5,1]=>[5,2,8,4,7,3,1,6]=>[2,5,4,8,7,1,6,3]=>{{1,2,5,7},{3,4,8},{6}}
[3,1,5,4,7,8,2,6]=>[3,8,1,5,4,2,7,6]=>[5,3,2,7,1,4,8,6]=>{{1,5},{2,3},{4,7,8},{6}}
[4,8,1,3,6,7,2,5]=>[8,7,1,4,3,2,5,6]=>[4,7,2,8,1,5,6,3]=>{{1,4,8},{2,7},{3},{5},{6}}
[6,3,8,1,4,7,2,5]=>[8,7,6,1,3,5,4,2]=>[6,7,8,3,2,1,4,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[1,5,7,4,2,6,8,3]=>[1,4,7,8,5,2,3,6]=>[1,7,5,4,8,3,6,2]=>{{1},{2,7},{3,5,8},{4},{6}}
[6,5,3,1,4,2,8,7]=>[3,5,4,2,6,1,8,7]=>[6,3,4,1,5,2,8,7]=>{{1,6},{2,3,4},{5},{7,8}}
[5,3,6,8,4,7,2,1]=>[2,7,5,8,3,6,4,1]=>[6,2,7,5,3,8,1,4]=>{{1,6,8},{2},{3,7},{4,5}}
[5,2,6,8,4,3,7,1]=>[7,5,4,8,2,6,3,1]=>[5,6,7,4,2,8,1,3]=>{{1,5},{2,6,8},{3,7},{4}}
[4,1,6,5,8,3,2,7]=>[4,3,8,1,6,5,2,7]=>[4,6,3,2,8,1,5,7]=>{{1,4},{2,6},{3},{5,8},{7}}
[8,5,6,7,1,3,2,4]=>[7,3,1,2,8,5,6,4]=>[3,8,2,1,7,4,5,6]=>{{1,3},{2,8},{4},{5,7},{6}}
[8,3,6,1,4,7,2,5]=>[6,7,8,1,3,5,4,2]=>[8,7,6,3,2,1,4,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[2,7,6,1,4,3,8,5]=>[6,2,4,1,7,8,5,3]=>[2,4,8,3,7,6,1,5]=>{{1,2,4},{3,8},{5,7},{6}}
[4,7,6,2,8,3,5,1]=>[5,6,7,4,3,8,1,2]=>[7,5,4,8,1,6,3,2]=>{{1,7},{2,5},{3,4,8},{6}}
[8,3,6,2,4,7,5,1]=>[5,7,6,2,8,4,1,3]=>[8,6,7,2,5,1,4,3]=>{{1,8},{2,6},{3,7},{4},{5}}
[4,7,3,5,8,6,2,1]=>[2,6,8,4,3,7,1,5]=>[6,2,4,8,1,7,5,3]=>{{1,6,7},{2},{3,4,8},{5}}
[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>{{1,8},{2},{3},{4},{5},{6},{7},{9}}
[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>{{1},{2,9},{3},{4},{5},{6},{7},{8}}
[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>{{1,9},{2},{3},{4},{5},{6},{7},{8},{10}}
[1,8,9,2,3,4,5,6,7]=>[1,9,2,3,4,5,6,8,7]=>[1,8,2,3,4,5,6,9,7]=>{{1},{2,8,9},{3},{4},{5},{6},{7}}
[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>{{1,10},{2},{3},{4},{5},{6},{7},{8},{9},{11}}
[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>{{1},{2,11},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,4,7,2,5,8,6,3]=>[1,7,6,4,2,8,5,3]=>[1,4,7,8,3,6,2,5]=>{{1},{2,4,8},{3,7},{5},{6}}
[7,3,8,4,5,6,1,2]=>[6,1,7,8,4,5,3,2]=>[8,1,7,6,2,3,4,5]=>{{1,8},{2},{3,7},{4,6},{5}}
[1,8,5,2,7,3,6,4]=>[1,5,8,7,6,4,3,2]=>[1,8,5,6,7,2,3,4]=>{{1},{2,8},{3,5,7},{4,6}}
[1,8,3,5,4,2,7,6]=>[1,4,5,8,2,7,3,6]=>[1,7,5,4,3,8,6,2]=>{{1},{2,7},{3,5},{4},{6,8}}
[6,1,4,2,8,5,7,3]=>[6,4,7,1,8,2,5,3]=>[7,8,4,3,6,5,1,2]=>{{1,7},{2,8},{3,4},{5,6}}
[4,8,6,5,3,2,7,1]=>[7,3,5,4,6,8,2,1]=>[3,5,4,8,7,6,1,2]=>{{1,3,4,8},{2,5,7},{6}}
[1,7,5,8,2,6,4,3]=>[1,8,4,6,7,2,5,3]=>[1,4,8,6,7,5,2,3]=>{{1},{2,4,6},{3,8},{5,7}}
[1,3,8,5,7,6,2,4]=>[1,6,3,2,7,8,4,5]=>[1,3,8,2,7,6,5,4]=>{{1},{2,3,8},{4},{5,7},{6}}
[3,8,6,5,7,1,2,4]=>[7,1,3,2,6,8,5,4]=>[3,1,7,2,8,6,4,5]=>{{1,3,7},{2},{4},{5,8},{6}}
[3,2,8,5,7,6,1,4]=>[6,3,2,1,7,8,4,5]=>[3,8,1,2,7,6,5,4]=>{{1,3},{2,8},{4},{5,7},{6}}
[4,2,1,3,6,7,8,5]=>[2,4,1,3,8,6,7,5]=>[4,2,1,3,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}}
[7,2,6,5,4,1,8,3]=>[4,5,6,7,8,1,3,2]=>[8,7,6,4,5,3,1,2]=>{{1,8},{2,7},{3,6},{4},{5}}
[8,5,2,6,3,7,1,4]=>[7,5,8,1,6,4,3,2]=>[6,8,5,3,7,1,2,4]=>{{1,6},{2,8},{3,5,7},{4}}
[4,3,1,2,6,7,8,5]=>[3,1,4,2,8,6,7,5]=>[4,1,3,2,6,7,8,5]=>{{1,4},{2},{3},{5,6,7,8}}
[3,8,1,6,5,7,2,4]=>[8,7,3,2,6,1,5,4]=>[3,6,7,1,8,5,2,4]=>{{1,3,7},{2,6},{4},{5,8}}
[4,3,6,2,5,1,8,7]=>[5,6,4,3,2,1,8,7]=>[5,4,6,1,2,3,8,7]=>{{1,5},{2,4},{3,6},{7,8}}
[1,8,3,6,7,4,5,2]=>[1,5,8,7,4,2,3,6]=>[1,8,5,7,2,4,6,3]=>{{1},{2,8},{3,5},{4,7},{6}}
[4,2,1,3,6,5,8,7]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>{{1,4},{2},{3},{5,6},{7,8}}
[5,6,1,7,4,8,2,3]=>[6,8,2,7,5,1,4,3]=>[7,5,1,6,8,4,2,3]=>{{1,7},{2,5,8},{3},{4,6}}
[2,5,6,1,7,4,8,3]=>[6,2,8,7,5,1,4,3]=>[2,7,5,6,8,4,1,3]=>{{1,2,7},{3,5,8},{4,6}}
[1,7,6,5,4,8,2,3]=>[1,8,2,5,6,7,4,3]=>[1,5,2,8,6,7,3,4]=>{{1},{2,5,6,7},{3},{4,8}}
[8,1,6,5,7,2,4,3]=>[8,7,4,2,6,1,5,3]=>[4,6,7,2,8,5,1,3]=>{{1,4},{2,6},{3,7},{5,8}}
[3,8,6,4,2,7,5,1]=>[5,4,3,7,6,8,1,2]=>[3,5,8,4,7,6,2,1]=>{{1,3,8},{2,5,7},{4},{6}}
[5,4,7,1,8,3,2,6]=>[7,3,8,5,4,2,1,6]=>[5,7,3,8,1,2,6,4]=>{{1,5},{2,7},{3},{4,8},{6}}
[6,4,3,1,5,8,2,7]=>[3,4,6,8,1,5,2,7]=>[8,6,3,4,2,1,5,7]=>{{1,8},{2,6},{3},{4},{5},{7}}
[1,3,8,7,5,6,2,4]=>[1,6,3,2,7,5,8,4]=>[1,3,8,2,6,4,7,5]=>{{1},{2,3,8},{4},{5,6},{7}}
[3,1,8,5,7,6,2,4]=>[3,6,1,2,7,8,4,5]=>[8,3,2,1,7,6,5,4]=>{{1,8},{2,3},{4},{5,7},{6}}
[2,1,6,4,3,5,8,7]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>{{1,2},{3,6},{4},{5},{7,8}}
[2,6,1,4,3,5,8,7]=>[6,2,4,1,3,5,8,7]=>[2,4,6,3,1,5,8,7]=>{{1,2,4},{3,6},{5},{7,8}}
[2,6,4,1,3,5,8,7]=>[4,2,1,6,3,5,8,7]=>[2,6,1,4,3,5,8,7]=>{{1,2,6},{3},{4},{5},{7,8}}
[4,6,2,1,3,5,8,7]=>[2,6,1,4,3,5,8,7]=>[4,2,1,6,3,5,8,7]=>{{1,4,6},{2},{3},{5},{7,8}}
[6,4,2,1,3,5,8,7]=>[2,4,1,6,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>{{1,6},{2},{3},{4},{5},{7,8}}
[8,4,2,1,6,3,5,7]=>[2,4,8,6,3,5,1,7]=>[8,2,4,6,1,3,5,7]=>{{1,8},{2},{3,4,6},{5},{7}}
[6,4,2,1,8,3,5,7]=>[2,4,6,8,3,5,1,7]=>[8,2,6,4,1,3,5,7]=>{{1,8},{2},{3,6},{4},{5},{7}}
[2,6,1,4,3,8,5,7]=>[6,2,4,1,8,3,5,7]=>[2,4,8,3,6,5,1,7]=>{{1,2,4},{3,8},{5,6},{7}}
[2,8,1,4,3,6,5,7]=>[8,2,4,1,6,3,5,7]=>[2,4,6,3,8,5,1,7]=>{{1,2,4},{3,6},{5,8},{7}}
[4,2,1,3,6,8,5,7]=>[2,4,1,3,8,6,5,7]=>[4,2,1,3,6,8,5,7]=>{{1,4},{2},{3},{5,6,8},{7}}
[2,1,4,3,8,6,5,7]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>{{1,2},{3,4},{5,8},{6},{7}}
[2,4,1,3,8,6,5,7]=>[4,2,1,3,6,8,5,7]=>[2,4,1,3,8,6,5,7]=>{{1,2,4},{3},{5,8},{6},{7}}
[4,2,1,3,8,6,5,7]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>{{1,4},{2},{3},{5,8},{6},{7}}
[2,4,8,1,3,6,5,7]=>[8,2,1,4,6,3,5,7]=>[2,4,1,6,8,5,3,7]=>{{1,2,4,6},{3},{5,8},{7}}
[2,1,4,8,3,6,5,7]=>[2,1,8,4,6,3,5,7]=>[2,1,4,6,8,5,3,7]=>{{1,2},{3,4,6},{5,8},{7}}
[2,1,4,8,6,3,5,7]=>[2,1,6,4,3,8,5,7]=>[2,1,4,8,3,6,5,7]=>{{1,2},{3,4,8},{5},{6},{7}}
[2,4,8,6,1,3,5,7]=>[6,2,1,4,3,8,5,7]=>[2,4,1,8,3,6,5,7]=>{{1,2,4,8},{3},{5},{6},{7}}
[4,6,8,2,1,3,5,7]=>[2,8,1,4,3,6,5,7]=>[4,2,1,6,3,8,5,7]=>{{1,4,6,8},{2},{3},{5},{7}}
[2,6,8,4,1,3,5,7]=>[4,2,1,8,3,6,5,7]=>[2,6,1,4,3,8,5,7]=>{{1,2,6,8},{3},{4},{5},{7}}
[2,6,8,1,4,3,5,7]=>[8,2,4,1,3,6,5,7]=>[2,4,6,3,1,8,5,7]=>{{1,2,4},{3,6,8},{5},{7}}
[2,1,6,8,4,3,5,7]=>[2,1,4,8,3,6,5,7]=>[2,1,6,4,3,8,5,7]=>{{1,2},{3,6,8},{4},{5},{7}}
[2,1,8,6,4,3,5,7]=>[2,1,4,6,3,8,5,7]=>[2,1,8,4,3,6,5,7]=>{{1,2},{3,8},{4},{5},{6},{7}}
[2,8,6,4,1,3,5,7]=>[4,2,1,6,3,8,5,7]=>[2,8,1,4,3,6,5,7]=>{{1,2,8},{3},{4},{5},{6},{7}}
[4,8,6,2,1,3,5,7]=>[2,6,1,4,3,8,5,7]=>[4,2,1,8,3,6,5,7]=>{{1,4,8},{2},{3},{5},{6},{7}}
[6,8,4,2,1,3,5,7]=>[2,4,1,8,3,6,5,7]=>[6,2,1,4,3,8,5,7]=>{{1,6,8},{2},{3},{4},{5},{7}}
[3,2,6,1,5,4,8,7]=>[6,3,2,5,1,4,8,7]=>[3,5,1,6,4,2,8,7]=>{{1,3},{2,5},{4,6},{7,8}}
[5,2,4,3,8,1,7,6]=>[8,5,4,2,3,7,1,6]=>[4,5,7,2,1,8,6,3]=>{{1,4},{2,5},{3,7},{6,8}}
[6,2,4,1,5,3,8,7]=>[4,6,5,2,1,3,8,7]=>[6,4,5,2,3,1,8,7]=>{{1,6},{2,4},{3,5},{7,8}}
[4,3,6,1,5,2,8,7]=>[6,5,4,3,1,2,8,7]=>[4,5,6,1,3,2,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[4,3,5,2,8,1,7,6]=>[8,5,4,3,2,7,1,6]=>[4,5,7,1,2,8,6,3]=>{{1,4},{2,5},{3,7},{6,8}}
[4,3,7,2,6,5,8,1]=>[8,7,4,3,6,2,5,1]=>[4,6,7,1,8,3,2,5]=>{{1,4},{2,6},{3,7},{5,8}}
[4,3,8,2,6,1,7,5]=>[6,8,4,3,7,2,1,5]=>[6,4,8,1,7,3,5,2]=>{{1,6},{2,4},{3,8},{5,7}}
[4,3,8,1,7,2,6,5]=>[8,7,4,3,6,2,1,5]=>[4,6,7,1,8,3,5,2]=>{{1,4},{2,6},{3,7},{5,8}}
[4,3,8,1,5,2,7,6]=>[8,5,4,3,1,7,2,6]=>[4,5,7,1,3,8,6,2]=>{{1,4},{2,5},{3,7},{6,8}}
[5,4,8,1,3,2,7,6]=>[8,3,1,5,4,7,2,6]=>[3,5,2,7,1,8,6,4]=>{{1,3},{2,5},{4,7},{6,8}}
[2,1,5,4,8,3,7,6]=>[2,1,8,5,4,7,3,6]=>[2,1,5,7,3,8,6,4]=>{{1,2},{3,5},{4,7},{6,8}}
[4,3,7,6,8,1,5,2]=>[8,5,4,3,1,7,6,2]=>[4,5,7,1,3,8,2,6]=>{{1,4},{2,5},{3,7},{6,8}}
[4,3,6,5,8,1,7,2]=>[8,7,4,3,6,5,1,2]=>[4,6,7,1,8,2,5,3]=>{{1,4},{2,6},{3,7},{5,8}}
[6,3,5,4,7,2,8,1]=>[8,7,6,5,3,4,2,1]=>[5,6,7,8,2,1,3,4]=>{{1,5},{2,6},{3,7},{4,8}}
[6,3,5,4,8,1,7,2]=>[8,7,6,5,3,4,1,2]=>[5,6,7,8,2,1,4,3]=>{{1,5},{2,6},{3,7},{4,8}}
[7,4,6,5,8,1,3,2]=>[8,3,1,7,6,4,5,2]=>[3,6,2,7,8,4,1,5]=>{{1,3},{2,6},{4,7},{5,8}}
[2,1,8,4,6,3,7,5]=>[2,1,6,8,7,4,3,5]=>[2,1,8,6,7,4,5,3]=>{{1,2},{3,8},{4,6},{5,7}}
[8,1,6,3,7,2,5,4]=>[8,7,6,5,2,1,3,4]=>[5,6,7,8,3,4,2,1]=>{{1,5},{2,6},{3,7},{4,8}}
[3,2,8,4,6,1,7,5]=>[6,3,2,8,7,4,1,5]=>[3,8,1,6,7,4,5,2]=>{{1,3},{2,8},{4,6},{5,7}}
[3,2,8,1,5,4,7,6]=>[8,3,2,5,1,7,4,6]=>[3,5,1,7,4,8,6,2]=>{{1,3},{2,5},{4,7},{6,8}}
[3,2,7,6,8,1,5,4]=>[8,3,2,5,1,7,6,4]=>[3,5,1,7,4,8,2,6]=>{{1,3},{2,5},{4,7},{6,8}}
[3,2,6,5,8,1,7,4]=>[8,3,2,7,6,5,1,4]=>[3,6,1,7,8,2,5,4]=>{{1,3},{2,6},{4,7},{5,8}}
[6,5,7,2,4,3,8,1]=>[8,7,4,2,6,5,3,1]=>[4,6,7,2,8,1,3,5]=>{{1,4},{2,6},{3,7},{5,8}}
[7,2,4,1,8,5,6,3]=>[4,7,6,2,8,5,1,3]=>[8,4,7,2,6,1,5,3]=>{{1,8},{2,4},{3,7},{5,6}}
[7,6,8,2,4,1,5,3]=>[4,8,5,2,1,7,6,3]=>[7,4,5,2,3,8,1,6]=>{{1,7},{2,4},{3,5},{6,8}}
[7,6,8,1,5,2,4,3]=>[8,5,4,2,1,7,6,3]=>[4,5,7,2,3,8,1,6]=>{{1,4},{2,5},{3,7},{6,8}}
[7,2,8,1,5,4,6,3]=>[8,7,6,5,1,2,3,4]=>[5,6,7,8,4,3,2,1]=>{{1,5},{2,6},{3,7},{4,8}}
[5,4,7,2,6,3,8,1]=>[8,7,6,5,4,2,3,1]=>[5,6,7,8,1,3,2,4]=>{{1,5},{2,6},{3,7},{4,8}}
[6,5,8,1,7,2,4,3]=>[8,7,4,2,6,5,1,3]=>[4,6,7,2,8,1,5,3]=>{{1,4},{2,6},{3,7},{5,8}}
[2,1,6,5,8,3,7,4]=>[2,1,8,7,6,5,3,4]=>[2,1,6,7,8,3,5,4]=>{{1,2},{3,6},{4,7},{5,8}}
[6,5,7,4,8,1,3,2]=>[8,3,1,7,6,5,4,2]=>[3,6,2,7,8,1,4,5]=>{{1,3},{2,6},{4,7},{5,8}}
[6,1,7,4,8,3,5,2]=>[6,5,8,7,3,1,4,2]=>[7,8,5,6,2,4,1,3]=>{{1,7},{2,8},{3,5},{4,6}}
[5,4,6,3,8,1,7,2]=>[8,7,6,5,4,3,1,2]=>[5,6,7,8,1,2,4,3]=>{{1,5},{2,6},{3,7},{4,8}}
[2,4,8,3,5,7,6,1]=>[6,2,7,4,3,8,1,5]=>[2,7,4,8,1,6,5,3]=>{{1,2,7},{3,4,8},{5},{6}}
[7,6,4,1,3,8,2,5]=>[4,6,1,7,3,8,5,2]=>[8,7,2,4,1,6,3,5]=>{{1,8},{2,7},{3},{4},{5},{6}}
[6,2,4,8,3,7,5,1]=>[5,7,6,2,8,3,1,4]=>[8,6,7,2,5,3,4,1]=>{{1,8},{2,6},{3,7},{4},{5}}
[7,2,6,3,4,1,8,5]=>[4,7,6,3,8,2,1,5]=>[8,4,7,1,6,3,5,2]=>{{1,8},{2,4},{3,7},{5,6}}
[8,7,1,6,4,5,3,2]=>[7,3,5,6,4,1,8,2]=>[3,8,5,6,1,4,7,2]=>{{1,3,5},{2,8},{4,6},{7}}
[6,3,5,2,1,4,8,7]=>[2,5,6,1,3,4,8,7]=>[6,2,5,3,4,1,8,7]=>{{1,6},{2},{3,5},{4},{7,8}}
[2,1,8,5,7,4,3,6]=>[2,1,4,7,8,3,5,6]=>[2,1,8,4,7,5,6,3]=>{{1,2},{3,8},{4},{5,7},{6}}
[6,5,1,4,7,8,3,2]=>[5,3,6,1,8,2,7,4]=>[6,7,3,2,5,4,8,1]=>{{1,6},{2,7,8},{3},{4},{5}}
[2,1,6,7,5,8,3,4]=>[2,1,8,3,7,6,5,4]=>[2,1,6,3,7,8,4,5]=>{{1,2},{3,6,8},{4},{5,7}}
[5,7,3,6,1,2,8,4]=>[6,1,7,8,5,3,2,4]=>[7,1,6,5,8,3,4,2]=>{{1,7},{2},{3,6},{4,5,8}}
[4,6,2,1,8,7,5,3]=>[2,6,5,4,7,1,8,3]=>[4,2,6,8,5,3,7,1]=>{{1,4,8},{2},{3,6},{5},{7}}
[3,4,6,1,5,7,8,2]=>[6,8,3,4,1,5,7,2]=>[4,3,6,7,2,1,8,5]=>{{1,4,7,8},{2,3,6},{5}}
[4,8,7,2,6,5,3,1]=>[3,5,6,4,7,2,8,1]=>[6,4,3,8,5,1,7,2]=>{{1,6},{2,4,8},{3},{5},{7}}
[5,8,7,6,3,4,2,1]=>[2,4,6,3,5,7,8,1]=>[5,2,4,1,8,6,7,3]=>{{1,5,8},{2},{3,4},{6},{7}}
[5,8,7,6,3,1,4,2]=>[3,6,4,2,5,7,8,1]=>[5,3,4,1,8,6,7,2]=>{{1,5,8},{2,3,4},{6},{7}}
[5,8,7,6,2,4,3,1]=>[3,4,6,1,5,7,8,2]=>[5,4,3,2,8,6,7,1]=>{{1,5,8},{2,4},{3},{6},{7}}
[6,3,5,2,7,4,8,1]=>[8,5,6,7,3,2,4,1]=>[5,8,7,6,2,3,1,4]=>{{1,5},{2,8},{3,7},{4,6}}
[1,4,6,7,3,8,2,5]=>[1,8,7,4,2,6,3,5]=>[1,4,6,7,3,8,5,2]=>{{1},{2,4,7},{3,6,8},{5}}
[3,2,1,5,7,4,8,6]=>[2,3,1,7,5,8,4,6]=>[3,2,1,5,8,7,6,4]=>{{1,3},{2},{4,5,8},{6,7}}
[5,4,6,7,1,8,3,2]=>[7,3,8,5,4,6,1,2]=>[5,6,3,7,1,8,4,2]=>{{1,5},{2,6,8},{3},{4,7}}
[5,3,6,2,7,8,4,1]=>[4,8,6,5,1,3,7,2]=>[7,4,5,6,3,1,8,2]=>{{1,7,8},{2,4,6},{3,5}}
[1,5,6,7,8,2,4,3]=>[1,8,4,2,5,6,7,3]=>[1,4,5,3,6,7,8,2]=>{{1},{2,4},{3,5,6,7,8}}
[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>{{1,2},{3,4},{5,6},{7,8},{9}}
[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>{{1},{2,3},{4,5},{6,7},{8,9}}
[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>{{1,7},{2},{3},{4},{5},{6},{8},{9}}
[1,2,5,3,8,4,7,6]=>[1,2,5,8,3,7,4,6]=>[1,2,7,5,4,8,6,3]=>{{1},{2},{3,7},{4,5},{6,8}}
[2,4,8,1,3,7,6,5]=>[8,2,1,4,6,7,3,5]=>[2,4,1,6,8,7,5,3]=>{{1,2,4,6,7},{3},{5,8}}
[3,1,5,4,8,2,7,6]=>[3,8,1,5,4,7,2,6]=>[5,3,2,7,1,8,6,4]=>{{1,5},{2,3},{4,7},{6,8}}
[5,3,8,1,2,4,7,6]=>[8,1,5,2,3,7,4,6]=>[5,1,7,3,4,8,6,2]=>{{1,5},{2},{3,7},{4},{6,8}}
[5,4,8,1,2,7,6,3]=>[8,1,6,5,4,7,2,3]=>[5,1,6,8,2,7,4,3]=>{{1,5},{2},{3,6,7},{4,8}}
[3,4,8,7,1,2,6,5]=>[7,1,3,4,6,2,8,5]=>[3,1,4,6,8,5,7,2]=>{{1,3,4,6},{2},{5,8},{7}}
[4,2,5,8,1,7,6,3]=>[8,4,6,2,5,7,1,3]=>[4,6,5,2,8,7,3,1]=>{{1,4},{2,6,7},{3,5,8}}
[3,1,4,2,5,8,7,6]=>[3,4,1,2,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>{{1,4},{2,3},{5},{6,8},{7}}
[7,8,1,5,4,2,6,3]=>[8,4,5,6,1,3,7,2]=>[4,7,6,5,3,1,8,2]=>{{1,4,5},{2,7,8},{3,6}}
[6,4,2,1,7,3,8,5]=>[2,4,6,7,8,3,1,5]=>[8,2,7,4,6,3,5,1]=>{{1,8},{2},{3,7},{4},{5,6}}
[4,2,7,1,8,3,6,5]=>[7,4,8,2,6,3,1,5]=>[6,7,4,2,8,3,5,1]=>{{1,6},{2,7},{3,4},{5,8}}
[1,2,6,3,4,8,7,5]=>[1,2,6,3,7,4,8,5]=>[1,2,8,3,6,5,7,4]=>{{1},{2},{3,8},{4},{5,6},{7}}
[3,2,8,5,4,6,1,7]=>[6,3,2,5,8,4,1,7]=>[3,6,1,8,5,2,4,7]=>{{1,3},{2,6},{4,8},{5},{7}}
[8,2,5,1,3,7,6,4]=>[5,8,1,6,2,7,3,4]=>[8,5,2,6,4,7,3,1]=>{{1,8},{2,5},{3},{4,6,7}}
[2,6,5,8,4,1,3,7]=>[4,2,1,8,6,5,3,7]=>[2,6,1,4,8,3,5,7]=>{{1,2,6},{3},{4},{5,8},{7}}
[4,3,6,8,2,1,5,7]=>[2,8,4,3,1,6,5,7]=>[4,2,6,1,3,8,5,7]=>{{1,4},{2},{3,6,8},{5},{7}}
[6,5,2,1,7,8,3,4]=>[2,5,6,3,8,4,7,1]=>[7,2,6,1,5,3,8,4]=>{{1,7,8},{2},{3,6},{4},{5}}
[5,7,3,8,1,6,4,2]=>[8,4,6,7,5,1,2,3]=>[4,7,6,5,8,3,2,1]=>{{1,4,5,8},{2,7},{3,6}}
[3,8,7,6,5,1,4,2]=>[5,4,3,1,6,7,8,2]=>[3,4,8,2,5,6,7,1]=>{{1,3,8},{2,4},{5},{6},{7}}
[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>{{1,3},{2},{4},{5},{6},{7},{8},{9}}
[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>{{1,3},{2},{4},{5},{6},{7},{8},{9},{10}}
[3,6,5,1,2,4,8,7]=>[5,1,3,2,6,4,8,7]=>[3,1,6,2,5,4,8,7]=>{{1,3,6},{2},{4},{5},{7,8}}
[3,7,5,8,2,4,1,6]=>[4,8,3,2,7,1,5,6]=>[4,3,7,1,8,5,6,2]=>{{1,4},{2,3,7},{5,8},{6}}
[4,1,5,7,8,3,2,6]=>[4,3,8,1,5,2,7,6]=>[4,5,3,2,7,1,8,6]=>{{1,4},{2,5,7,8},{3},{6}}
[4,1,5,8,7,3,2,6]=>[4,3,7,1,5,2,8,6]=>[4,5,3,2,8,1,7,6]=>{{1,4},{2,5,8},{3},{6},{7}}
[2,1,5,8,7,3,4,6]=>[2,1,7,3,5,4,8,6]=>[2,1,5,3,8,4,7,6]=>{{1,2},{3,5,8},{4},{6},{7}}
[6,1,2,3,7,5,8,4]=>[6,1,2,8,7,3,5,4]=>[8,1,2,6,7,5,3,4]=>{{1,8},{2},{3},{4,6},{5,7}}
[3,6,8,1,4,2,7,5]=>[8,4,3,1,7,6,2,5]=>[3,4,6,2,7,8,5,1]=>{{1,3,6,8},{2,4},{5,7}}
[3,5,7,8,2,4,1,6]=>[4,8,3,2,5,1,7,6]=>[4,3,5,1,7,2,8,6]=>{{1,4},{2,3,5,7,8},{6}}
[7,6,2,8,3,1,4,5]=>[3,8,6,1,2,7,4,5]=>[8,3,6,2,4,7,5,1]=>{{1,8},{2,3,6,7},{4},{5}}
[1,2,8,5,4,7,3,6]=>[1,2,7,5,8,3,4,6]=>[1,2,7,8,5,4,6,3]=>{{1},{2},{3,7},{4,8},{5},{6}}
[6,2,8,1,7,3,5,4]=>[8,6,7,5,3,2,1,4]=>[5,7,6,8,2,3,4,1]=>{{1,5},{2,7},{3,6},{4,8}}
[2,4,8,7,6,5,1,3]=>[5,2,1,4,6,7,8,3]=>[2,4,1,8,5,6,7,3]=>{{1,2,4,8},{3},{5},{6},{7}}
[6,3,1,8,7,2,5,4]=>[3,6,7,5,2,4,8,1]=>[6,5,3,8,2,1,7,4]=>{{1,6},{2,5},{3},{4,8},{7}}
[5,1,8,4,7,2,6,3]=>[5,7,6,8,1,2,4,3]=>[8,6,7,5,4,3,1,2]=>{{1,8},{2,6},{3,7},{4,5}}
[5,6,3,1,2,4,8,7]=>[3,1,6,2,5,4,8,7]=>[5,1,3,2,6,4,8,7]=>{{1,5,6},{2},{3},{4},{7,8}}
[5,6,1,2,4,3,8,7]=>[6,1,4,2,5,3,8,7]=>[4,1,5,3,6,2,8,7]=>{{1,4},{2},{3,5,6},{7,8}}
[4,5,8,1,7,2,6,3]=>[8,7,6,4,5,2,1,3]=>[4,5,6,7,8,2,3,1]=>{{1,4,7},{2,5,8},{3,6}}
[3,4,8,7,6,5,1,2]=>[5,1,3,4,6,7,8,2]=>[3,1,4,8,5,6,7,2]=>{{1,3,4,8},{2},{5},{6},{7}}
[8,4,7,2,3,6,1,5]=>[6,7,2,8,1,3,4,5]=>[8,7,1,6,4,5,3,2]=>{{1,8},{2,7},{3},{4,6},{5}}
[5,8,7,1,3,6,2,4]=>[7,6,1,3,5,4,8,2]=>[5,6,2,1,8,3,7,4]=>{{1,5,8},{2,6},{3},{4},{7}}
[8,5,4,7,1,2,6,3]=>[7,1,6,5,8,2,4,3]=>[6,1,7,8,5,4,2,3]=>{{1,6},{2},{3,7},{4,8},{5}}
[6,8,4,2,7,1,5,3]=>[7,4,8,5,1,6,3,2]=>[5,7,4,6,3,8,1,2]=>{{1,5},{2,7},{3,4,6,8}}
[8,4,2,5,7,1,6,3]=>[7,4,8,6,2,1,3,5]=>[6,8,4,7,2,5,3,1]=>{{1,6},{2,8},{3,4,7},{5}}
[8,7,3,4,5,1,6,2]=>[5,6,7,3,4,1,8,2]=>[8,6,5,1,2,4,7,3]=>{{1,8},{2,6},{3,5},{4},{7}}
[5,7,3,2,6,4,8,1]=>[8,3,7,6,5,2,4,1]=>[3,6,5,7,8,2,1,4]=>{{1,3,5,8},{2,6},{4,7}}
[6,7,3,2,5,4,1,8]=>[4,3,5,7,1,6,2,8]=>[5,6,3,4,2,7,1,8]=>{{1,5},{2,6,7},{3},{4},{8}}
[4,6,5,7,2,8,1,3]=>[8,7,1,4,6,5,2,3]=>[4,6,2,7,8,1,5,3]=>{{1,4,7},{2,6},{3},{5,8}}
[6,4,5,7,1,8,2,3]=>[7,8,2,6,4,5,1,3]=>[7,6,1,8,2,3,5,4]=>{{1,7},{2,6},{3},{4,8},{5}}
[2,1,4,6,8,7,3,5]=>[2,1,7,4,3,6,8,5]=>[2,1,4,6,3,8,7,5]=>{{1,2},{3,4,6,8},{5},{7}}
[4,3,1,6,8,7,2,5]=>[3,4,7,2,1,6,8,5]=>[6,4,3,1,2,8,7,5]=>{{1,6,8},{2,4},{3},{5},{7}}
[1,3,2,8,6,7,4,5]=>[1,3,2,7,4,8,6,5]=>[1,3,2,8,4,7,5,6]=>{{1},{2,3},{4,8},{5},{6,7}}
[7,2,1,8,6,5,4,3]=>[2,7,4,5,6,8,1,3]=>[4,2,8,5,7,6,3,1]=>{{1,4,5,7},{2},{3,8},{6}}
[5,3,1,7,2,4,6,8]=>[3,5,7,2,4,1,6,8]=>[7,5,3,1,2,4,6,8]=>{{1,7},{2,5},{3},{4},{6},{8}}
[8,5,1,2,6,7,3,4]=>[5,1,8,3,7,2,4,6]=>[8,1,5,2,7,4,6,3]=>{{1,8},{2},{3,5,7},{4},{6}}
[7,1,4,5,2,8,6,3]=>[7,5,6,1,3,8,4,2]=>[5,8,7,3,2,6,1,4]=>{{1,5},{2,8},{3,7},{4},{6}}
[3,1,7,2,6,4,5,8]=>[3,7,1,6,4,2,5,8]=>[6,3,2,7,1,5,4,8]=>{{1,6},{2,3},{4,7},{5},{8}}
[1,2,3,5,8,4,7,6]=>[1,2,3,8,5,7,4,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,7},{6,8}}
[1,2,3,6,8,5,4,7]=>[1,2,3,5,8,6,4,7]=>[1,2,3,6,5,8,4,7]=>{{1},{2},{3},{4,6,8},{5},{7}}
[7,8,5,6,3,1,4,2]=>[3,6,4,2,8,5,7,1]=>[7,3,4,1,6,2,8,5]=>{{1,7,8},{2,3,4},{5,6}}
[7,5,8,3,1,4,2,6]=>[3,8,4,2,7,1,5,6]=>[7,3,4,1,8,5,6,2]=>{{1,7},{2,3,4},{5,8},{6}}
[7,8,5,3,1,4,2,6]=>[3,5,4,2,8,1,7,6]=>[7,3,4,1,5,2,8,6]=>{{1,7,8},{2,3,4},{5},{6}}
[7,5,3,6,1,2,8,4]=>[6,1,5,7,8,3,4,2]=>[7,1,8,6,5,3,2,4]=>{{1,7},{2},{3,8},{4,6},{5}}
[7,5,3,6,1,4,8,2]=>[6,8,5,1,7,3,4,2]=>[7,5,8,3,6,2,1,4]=>{{1,7},{2,5,6},{3,8},{4}}
[7,5,3,8,4,6,1,2]=>[6,1,5,7,8,4,2,3]=>[7,1,8,6,5,2,4,3]=>{{1,7},{2},{3,8},{4,6},{5}}
[7,5,3,1,4,6,2,8]=>[3,5,7,1,6,4,2,8]=>[7,5,3,2,6,1,4,8]=>{{1,7},{2,5,6},{3},{4},{8}}
[7,5,3,1,2,8,6,4]=>[3,1,5,7,6,8,4,2]=>[8,1,3,5,7,6,2,4]=>{{1,8},{2},{3},{4,5,7},{6}}
[5,4,8,3,2,7,6,1]=>[6,3,7,5,4,8,1,2]=>[5,7,3,8,1,6,4,2]=>{{1,5},{2,7},{3},{4,8},{6}}
[5,8,4,3,2,7,6,1]=>[6,3,4,7,5,8,1,2]=>[3,7,5,4,8,6,2,1]=>{{1,3,5,8},{2,7},{4},{6}}
[2,1,5,8,4,7,6,3]=>[2,1,6,7,5,8,3,4]=>[2,1,7,5,8,6,4,3]=>{{1,2},{3,7},{4,5,8},{6}}
[3,7,2,8,6,5,4,1]=>[4,5,3,6,8,7,1,2]=>[6,3,8,4,5,7,2,1]=>{{1,6,7},{2,3,8},{4},{5}}
[3,6,2,8,7,5,4,1]=>[4,5,3,7,6,2,8,1]=>[5,3,8,4,6,1,7,2]=>{{1,5,6},{2,3,8},{4},{7}}
[6,4,7,3,8,5,2,1]=>[2,5,8,7,6,1,4,3]=>[8,2,5,6,7,4,1,3]=>{{1,8},{2},{3,5,7},{4,6}}
[6,4,8,3,7,5,2,1]=>[2,5,7,8,6,1,4,3]=>[8,2,6,5,7,4,1,3]=>{{1,8},{2},{3,6},{4,5,7}}
[7,4,5,3,2,8,6,1]=>[6,3,5,8,4,7,1,2]=>[3,8,6,5,1,7,4,2]=>{{1,3,6,7},{2,8},{4,5}}
[2,1,7,5,4,8,6,3]=>[2,1,6,5,8,7,3,4]=>[2,1,6,8,5,7,4,3]=>{{1,2},{3,6,7},{4,8},{5}}
[7,8,4,3,6,5,2,1]=>[2,5,4,6,8,1,7,3]=>[6,2,7,4,5,3,8,1]=>{{1,6},{2},{3,7,8},{4},{5}}
[5,3,6,8,4,7,1,2]=>[7,1,5,8,3,6,4,2]=>[6,1,7,5,3,8,2,4]=>{{1,6,8},{2},{3,7},{4,5}}
[4,2,1,7,3,8,5,6]=>[2,4,7,1,8,5,3,6]=>[8,2,4,3,7,1,6,5]=>{{1,8},{2},{3,4},{5,7},{6}}
[5,1,4,3,2,8,7,6]=>[5,3,4,1,2,7,8,6]=>[3,5,4,2,1,8,7,6]=>{{1,3,4},{2,5},{6,8},{7}}
[8,6,1,7,4,3,2,5]=>[6,3,4,8,2,7,5,1]=>[3,8,6,4,1,7,2,5]=>{{1,3,6,7},{2,8},{4},{5}}
[7,3,6,8,5,1,2,4]=>[5,1,8,2,7,4,6,3]=>[8,1,5,3,7,2,4,6]=>{{1,8},{2},{3,5,7},{4},{6}}
[3,6,5,7,2,4,1,8]=>[4,7,3,2,6,5,1,8]=>[4,3,6,1,7,2,5,8]=>{{1,4},{2,3,6},{5,7},{8}}
[7,3,8,2,1,6,4,5]=>[2,8,7,6,4,1,3,5]=>[6,2,7,8,1,5,4,3]=>{{1,6},{2},{3,7},{4,8},{5}}
[1,2,5,7,8,4,3,6]=>[1,2,4,8,5,3,7,6]=>[1,2,5,4,7,3,8,6]=>{{1},{2},{3,5,7,8},{4},{6}}
[7,1,6,4,5,2,3,8]=>[7,5,2,6,4,1,3,8]=>[5,7,1,6,2,4,3,8]=>{{1,5},{2,7},{3},{4,6},{8}}
[3,5,1,4,8,6,2,7]=>[5,6,3,1,4,8,2,7]=>[5,3,8,2,1,6,4,7]=>{{1,5},{2,3,8},{4},{6},{7}}
[3,4,1,7,5,6,8,2]=>[4,8,3,1,7,5,6,2]=>[4,3,7,2,8,1,5,6]=>{{1,4},{2,3,7},{5,8},{6}}
[1,5,8,2,4,6,7,3]=>[1,8,7,2,5,3,4,6]=>[1,5,7,3,8,4,6,2]=>{{1},{2,5,8},{3,7},{4},{6}}
[1,5,7,2,4,6,8,3]=>[1,7,8,2,5,3,4,6]=>[1,7,5,3,8,4,6,2]=>{{1},{2,7},{3,5,8},{4},{6}}
[1,5,8,3,2,4,6,7]=>[1,3,8,2,5,4,6,7]=>[1,5,3,2,8,4,6,7]=>{{1},{2,5,8},{3},{4},{6},{7}}
[1,6,8,4,2,3,7,5]=>[1,4,2,8,7,6,3,5]=>[1,6,2,4,7,8,5,3]=>{{1},{2,6,8},{3},{4},{5,7}}
[8,6,1,4,2,7,5,3]=>[6,4,5,1,8,7,3,2]=>[4,8,6,3,5,7,1,2]=>{{1,4},{2,8},{3,6,7},{5}}
[1,6,7,4,3,5,8,2]=>[1,8,4,7,3,6,5,2]=>[1,4,7,6,2,8,3,5]=>{{1},{2,4,6,8},{3,7},{5}}
[6,1,7,4,3,5,8,2]=>[6,8,4,7,3,1,5,2]=>[7,4,8,6,1,5,2,3]=>{{1,7},{2,4,6},{3,8},{5}}
[4,8,1,3,7,2,5,6]=>[8,7,1,4,3,5,6,2]=>[4,7,2,8,1,3,5,6]=>{{1,4,8},{2,7},{3},{5},{6}}
[4,7,1,8,2,5,6,3]=>[7,8,6,4,2,5,1,3]=>[6,4,7,8,2,1,5,3]=>{{1,6},{2,4,8},{3,7},{5}}
[2,4,3,8,5,6,1,7]=>[6,2,4,3,8,5,1,7]=>[2,4,8,1,6,3,5,7]=>{{1,2,4},{3,8},{5,6},{7}}
[8,5,7,6,3,2,1,4]=>[2,3,6,1,7,8,4,5]=>[8,2,3,1,7,6,5,4]=>{{1,8},{2},{3},{4},{5,7},{6}}
[1,5,4,7,6,8,2,3]=>[1,8,2,5,4,7,6,3]=>[1,5,2,7,3,8,4,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[1,5,2,7,6,8,3,4]=>[1,5,8,3,2,7,6,4]=>[1,7,5,2,4,8,3,6]=>{{1},{2,7},{3,5},{4},{6,8}}
[7,8,2,1,4,3,6,5]=>[2,8,4,1,6,3,7,5]=>[4,2,6,3,7,5,8,1]=>{{1,4},{2},{3,6},{5,7,8}}
[4,3,6,5,8,7,1,2]=>[7,1,4,3,6,5,8,2]=>[4,1,6,2,8,3,7,5]=>{{1,4},{2},{3,6},{5,8},{7}}
[1,7,4,3,2,8,6,5]=>[1,3,4,7,6,8,2,5]=>[1,7,3,4,8,6,5,2]=>{{1},{2,7},{3},{4},{5,8},{6}}
[1,2,6,5,3,7,8,4]=>[1,2,5,6,8,4,7,3]=>[1,2,7,6,5,3,8,4]=>{{1},{2},{3,7,8},{4,6},{5}}
[1,7,5,3,2,8,6,4]=>[1,3,5,7,6,8,4,2]=>[1,8,3,5,7,6,2,4]=>{{1},{2,8},{3},{4,5,7},{6}}
[7,6,5,1,3,8,4,2]=>[5,4,1,6,7,8,3,2]=>[7,8,2,4,5,6,1,3]=>{{1,7},{2,8},{3},{4},{5},{6}}
[8,4,6,5,2,1,7,3]=>[2,5,6,7,8,4,1,3]=>[8,2,7,6,5,1,4,3]=>{{1,8},{2},{3,7},{4,6},{5}}
[4,8,7,5,6,1,3,2]=>[6,3,1,4,7,5,8,2]=>[3,4,2,8,6,1,7,5]=>{{1,3},{2,4,8},{5,6},{7}}
[3,6,5,2,4,1,8,7]=>[4,5,3,2,6,1,8,7]=>[4,3,6,1,5,2,8,7]=>{{1,4},{2,3,6},{5},{7,8}}
[4,3,7,6,8,2,5,1]=>[5,8,4,3,2,7,6,1]=>[5,4,7,1,2,8,3,6]=>{{1,5},{2,4},{3,7},{6,8}}
[2,1,5,8,7,4,6,3]=>[2,1,6,7,5,4,8,3]=>[2,1,6,5,8,3,7,4]=>{{1,2},{3,6},{4,5,8},{7}}
[4,2,7,1,8,5,6,3]=>[7,4,6,2,8,5,1,3]=>[4,8,7,2,6,1,5,3]=>{{1,4},{2,8},{3,7},{5,6}}
[4,1,7,2,8,5,6,3]=>[4,7,6,1,8,5,2,3]=>[8,4,7,3,6,1,5,2]=>{{1,8},{2,4},{3,7},{5,6}}
[3,4,7,2,8,5,6,1]=>[6,7,3,4,8,5,2,1]=>[4,3,7,8,6,1,2,5]=>{{1,4,8},{2,3,7},{5,6}}
[7,2,3,4,8,5,6,1]=>[6,7,2,3,8,5,4,1]=>[8,7,1,2,6,3,4,5]=>{{1,8},{2,7},{3},{4},{5,6}}
[2,6,3,5,8,7,1,4]=>[7,2,6,1,4,3,8,5]=>[2,6,8,3,1,5,7,4]=>{{1,2,6},{3,8},{4},{5},{7}}
[4,5,2,7,6,1,8,3]=>[6,5,7,4,2,8,3,1]=>[5,7,4,8,2,6,1,3]=>{{1,5},{2,7},{3,4,8},{6}}
[6,4,8,7,1,3,2,5]=>[7,3,1,6,2,4,8,5]=>[3,6,2,8,4,5,7,1]=>{{1,3},{2,6},{4,8},{5},{7}}
[5,8,4,3,7,6,1,2]=>[6,1,4,7,5,8,2,3]=>[5,1,7,4,8,6,3,2]=>{{1,5,8},{2},{3,7},{4},{6}}
[4,1,3,8,5,6,7,2]=>[4,7,1,3,8,5,6,2]=>[8,4,2,1,7,3,5,6]=>{{1,8},{2,4},{3},{5,7},{6}}
[1,4,8,2,3,6,7,5]=>[1,8,2,4,7,3,6,5]=>[1,4,2,7,8,5,3,6]=>{{1},{2,4,7},{3},{5,8},{6}}
[3,1,2,7,8,6,4,5]=>[3,1,2,6,4,8,7,5]=>[3,1,2,7,4,6,8,5]=>{{1,3},{2},{4,7,8},{5},{6}}
[4,2,7,1,8,6,3,5]=>[7,4,6,2,3,8,1,5]=>[4,8,7,2,1,6,5,3]=>{{1,4},{2,8},{3,7},{5},{6}}
[5,8,3,6,7,4,1,2]=>[4,1,7,8,5,3,2,6]=>[7,1,5,4,8,2,6,3]=>{{1,7},{2},{3,5,8},{4},{6}}
[2,4,3,7,1,8,5,6]=>[7,2,4,3,8,5,1,6]=>[2,4,8,1,7,3,6,5]=>{{1,2,4},{3,8},{5,7},{6}}
[2,7,1,4,3,8,5,6]=>[7,2,4,1,8,5,3,6]=>[2,4,8,3,7,1,6,5]=>{{1,2,4},{3,8},{5,7},{6}}
[6,1,5,3,8,7,2,4]=>[6,7,5,2,1,3,8,4]=>[6,5,8,2,4,3,7,1]=>{{1,6},{2,5},{3,8},{4},{7}}
[5,1,4,8,2,6,7,3]=>[5,8,7,1,4,2,6,3]=>[8,5,7,3,1,4,2,6]=>{{1,8},{2,5},{3,7},{4},{6}}
[7,6,1,2,8,3,5,4]=>[6,1,7,5,3,8,4,2]=>[7,1,5,8,3,6,2,4]=>{{1,7},{2},{3,5},{4,8},{6}}
[8,1,6,4,7,3,5,2]=>[8,5,7,6,3,1,4,2]=>[5,8,6,7,2,4,1,3]=>{{1,5},{2,8},{3,6},{4,7}}
[8,1,7,2,5,4,6,3]=>[8,7,6,5,2,4,1,3]=>[5,6,7,8,3,1,4,2]=>{{1,5},{2,6},{3,7},{4,8}}
[7,4,1,5,3,6,2,8]=>[4,7,6,5,2,1,3,8]=>[7,4,5,6,2,3,1,8]=>{{1,7},{2,4,6},{3,5},{8}}
[4,5,3,8,6,7,1,2]=>[7,1,5,4,3,8,6,2]=>[4,1,5,8,2,7,3,6]=>{{1,4,8},{2},{3,5},{6,7}}
[2,8,3,4,1,6,5,7]=>[4,2,8,3,6,1,5,7]=>[2,6,4,1,8,5,3,7]=>{{1,2,6},{3,4},{5,8},{7}}
[1,6,4,8,2,7,3,5]=>[1,8,7,6,3,4,2,5]=>[1,6,7,8,3,4,5,2]=>{{1},{2,6},{3,7},{4,8},{5}}
[1,7,2,8,4,6,3,5]=>[1,7,6,8,3,4,2,5]=>[1,7,8,6,3,4,5,2]=>{{1},{2,7},{3,8},{4,6},{5}}
[8,6,1,7,3,2,5,4]=>[6,3,8,5,2,7,4,1]=>[5,6,3,8,2,7,1,4]=>{{1,5},{2,6,7},{3},{4,8}}
[8,5,2,3,1,7,6,4]=>[3,5,2,8,6,7,4,1]=>[8,3,1,5,6,7,2,4]=>{{1,8},{2,3},{4,5,6,7}}
[8,6,1,3,7,2,5,4]=>[6,8,1,5,3,7,2,4]=>[6,5,2,8,3,7,4,1]=>{{1,6,7},{2,5},{3},{4,8}}
[8,1,6,4,7,2,5,3]=>[8,7,5,6,2,1,4,3]=>[5,6,8,7,3,4,1,2]=>{{1,5},{2,6},{3,8},{4,7}}
[5,2,8,6,4,1,3,7]=>[4,6,1,5,3,8,2,7]=>[8,4,2,5,1,6,3,7]=>{{1,8},{2,4,5},{3},{6},{7}}
[8,4,7,2,1,5,6,3]=>[2,7,6,8,1,4,3,5]=>[7,2,8,6,4,3,5,1]=>{{1,7},{2},{3,8},{4,6},{5}}
[3,6,5,4,1,2,8,7]=>[4,1,3,5,6,2,8,7]=>[3,1,6,4,5,2,8,7]=>{{1,3,6},{2},{4},{5},{7,8}}
[4,8,5,7,6,3,1,2]=>[3,1,6,4,7,8,2,5]=>[4,1,3,8,7,6,5,2]=>{{1,4,8},{2},{3},{5,7},{6}}
[6,2,1,5,3,4,8,7]=>[2,6,5,3,1,4,8,7]=>[5,2,6,1,4,3,8,7]=>{{1,5},{2},{3,6},{4},{7,8}}
[5,8,1,3,7,6,4,2]=>[8,4,1,6,5,7,3,2]=>[4,6,2,5,8,7,1,3]=>{{1,4,5,8},{2,6,7},{3}}
[2,1,5,8,7,6,3,4]=>[2,1,6,3,5,7,8,4]=>[2,1,5,3,8,6,7,4]=>{{1,2},{3,5,8},{4},{6},{7}}
[2,1,6,5,8,4,7,3]=>[2,1,7,8,6,5,4,3]=>[2,1,7,6,8,3,4,5]=>{{1,2},{3,7},{4,6},{5,8}}
[7,4,8,6,3,2,5,1]=>[5,3,6,8,2,7,1,4]=>[6,8,3,5,2,7,4,1]=>{{1,6,7},{2,8},{3},{4,5}}
[2,1,8,4,3,7,5,6]=>[2,1,4,8,7,5,3,6]=>[2,1,7,4,8,3,6,5]=>{{1,2},{3,7},{4},{5,8},{6}}
[5,8,2,4,3,1,6,7]=>[3,4,8,1,5,2,6,7]=>[5,4,3,2,8,1,6,7]=>{{1,5,8},{2,4},{3},{6},{7}}
[1,3,8,2,4,5,7,6]=>[1,8,3,2,4,7,5,6]=>[1,3,7,2,4,8,6,5]=>{{1},{2,3,7},{4},{5},{6,8}}
[1,8,2,3,5,4,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,2,8,4,3,6,7]=>{{1},{2,5},{3},{4,8},{6},{7}}
[1,8,2,3,6,4,5,7]=>[1,8,2,6,4,3,5,7]=>[1,6,2,8,3,5,4,7]=>{{1},{2,6},{3},{4,8},{5},{7}}
[5,7,6,4,1,8,2,3]=>[4,6,2,7,5,8,1,3]=>[7,5,1,4,8,6,3,2]=>{{1,7},{2,5,8},{3},{4},{6}}
[6,3,8,1,5,2,7,4]=>[8,5,6,7,1,3,2,4]=>[5,8,7,6,4,2,3,1]=>{{1,5},{2,8},{3,7},{4,6}}
[6,5,8,4,1,2,7,3]=>[4,1,8,7,6,5,3,2]=>[7,1,4,6,8,2,3,5]=>{{1,7},{2},{3,4,6},{5,8}}
[4,5,8,6,7,1,2,3]=>[7,1,2,4,5,8,6,3]=>[4,1,2,5,8,7,3,6]=>{{1,4,5,8},{2},{3},{6,7}}
[4,8,5,6,7,1,2,3]=>[7,1,2,4,8,5,6,3]=>[4,1,2,8,7,3,5,6]=>{{1,4,8},{2},{3},{5,7},{6}}
[4,7,5,6,8,1,2,3]=>[8,1,2,4,7,5,6,3]=>[4,1,2,7,8,3,5,6]=>{{1,4,7},{2},{3},{5,8},{6}}
[4,6,5,7,8,1,2,3]=>[8,1,2,4,6,5,7,3]=>[4,1,2,6,7,3,8,5]=>{{1,4,6},{2},{3},{5,7,8}}
[5,8,3,1,6,7,2,4]=>[3,8,7,2,5,1,4,6]=>[7,3,5,1,8,4,6,2]=>{{1,7},{2,3,5,8},{4},{6}}
[5,6,3,1,7,8,2,4]=>[3,6,8,2,5,4,7,1]=>[6,5,3,1,7,2,8,4]=>{{1,6},{2,5,7,8},{3},{4}}
[5,4,6,8,1,7,2,3]=>[8,7,2,5,4,6,1,3]=>[5,6,1,7,2,8,4,3]=>{{1,5},{2,6,8},{3},{4,7}}
[4,5,6,8,7,1,2,3]=>[7,1,2,4,5,6,8,3]=>[4,1,2,5,6,8,7,3]=>{{1,4,5,6,8},{2},{3},{7}}
[4,6,8,7,5,1,2,3]=>[5,1,2,4,7,6,8,3]=>[4,1,2,6,5,8,7,3]=>{{1,4,6,8},{2},{3},{5},{7}}
[1,2,7,6,3,4,8,5]=>[1,2,6,3,7,8,5,4]=>[1,2,8,3,7,6,4,5]=>{{1},{2},{3,8},{4},{5,7},{6}}
[1,2,3,7,4,8,6,5]=>[1,2,3,7,6,8,4,5]=>[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,7},{5,8},{6}}
[1,2,3,6,4,8,7,5]=>[1,2,3,6,7,4,8,5]=>[1,2,3,8,6,5,7,4]=>{{1},{2},{3},{4,8},{5,6},{7}}
[7,1,8,4,2,3,5,6]=>[7,4,2,8,3,5,1,6]=>[7,8,1,4,2,3,6,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[1,2,3,8,4,7,6,5]=>[1,2,3,8,6,7,4,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,6,7},{5,8}}
[1,2,7,3,4,8,6,5]=>[1,2,7,3,6,8,4,5]=>[1,2,7,3,8,6,5,4]=>{{1},{2},{3,7},{4},{5,8},{6}}
[1,2,3,8,7,4,6,5]=>[1,2,3,7,6,4,8,5]=>[1,2,3,6,8,5,7,4]=>{{1},{2},{3},{4,6},{5,8},{7}}
[2,4,3,8,1,6,5,7]=>[8,2,4,3,6,1,5,7]=>[2,4,6,1,8,5,3,7]=>{{1,2,4},{3,6},{5,8},{7}}
[2,4,8,1,3,5,7,6]=>[8,2,1,4,3,7,5,6]=>[2,4,1,7,3,8,6,5]=>{{1,2,4,7},{3},{5},{6,8}}
[5,8,6,7,1,4,3,2]=>[7,3,4,1,5,8,6,2]=>[3,5,4,2,8,7,1,6]=>{{1,3,4},{2,5,8},{6,7}}
[5,8,6,7,2,4,3,1]=>[3,4,7,1,5,8,6,2]=>[5,4,3,2,8,7,1,6]=>{{1,5,8},{2,4},{3},{6,7}}
[4,8,6,7,3,1,2,5]=>[3,1,7,4,2,8,6,5]=>[4,1,3,8,2,7,5,6]=>{{1,4,8},{2},{3},{5},{6,7}}
[3,4,1,7,5,6,2,8]=>[4,6,3,1,7,5,2,8]=>[4,3,7,2,6,1,5,8]=>{{1,4},{2,3,7},{5,6},{8}}
[5,8,6,7,3,1,4,2]=>[3,7,4,2,5,8,6,1]=>[5,3,4,1,8,7,2,6]=>{{1,5,8},{2,3,4},{6,7}}
[6,1,7,3,8,4,2,5]=>[6,4,8,7,2,1,5,3]=>[7,8,4,6,2,5,1,3]=>{{1,7},{2,8},{3,4,6},{5}}
[8,4,2,6,7,5,3,1]=>[3,5,4,7,8,2,6,1]=>[8,3,7,4,5,1,2,6]=>{{1,8},{2,3,7},{4},{5},{6}}
[1,3,8,6,2,7,5,4]=>[1,6,3,5,8,7,4,2]=>[1,3,6,8,5,7,2,4]=>{{1},{2,3,6,7},{4,8},{5}}
[4,7,2,6,8,1,5,3]=>[8,7,5,4,1,3,2,6]=>[4,5,7,8,3,1,6,2]=>{{1,4,8},{2,5},{3,7},{6}}
[1,8,6,4,5,2,3,7]=>[1,5,2,6,4,8,3,7]=>[1,8,2,5,3,6,4,7]=>{{1},{2,8},{3},{4,5},{6},{7}}
[8,3,7,4,5,2,6,1]=>[6,5,8,7,4,3,1,2]=>[7,8,5,6,1,2,4,3]=>{{1,7},{2,8},{3,5},{4,6}}
[8,2,7,5,4,3,6,1]=>[6,8,4,5,7,3,2,1]=>[5,4,8,7,6,1,2,3]=>{{1,5,6},{2,4,7},{3,8}}
[3,8,4,5,6,1,2,7]=>[6,1,3,8,4,5,2,7]=>[3,1,8,6,2,4,5,7]=>{{1,3,8},{2},{4,6},{5},{7}}
[1,4,3,5,7,8,2,6]=>[1,8,4,3,5,2,7,6]=>[1,4,5,2,7,3,8,6]=>{{1},{2,4},{3,5,7,8},{6}}
[3,6,7,2,4,8,1,5]=>[8,7,3,2,1,6,4,5]=>[3,6,7,1,4,8,5,2]=>{{1,3,7},{2,6,8},{4},{5}}
[6,1,5,2,8,4,7,3]=>[6,5,7,8,1,2,4,3]=>[7,8,6,5,4,3,1,2]=>{{1,7},{2,8},{3,6},{4,5}}
[3,6,8,1,5,7,2,4]=>[8,7,3,2,1,6,5,4]=>[3,6,7,1,4,8,2,5]=>{{1,3,7},{2,6,8},{4},{5}}
[7,6,8,1,2,3,5,4]=>[8,1,2,5,3,7,6,4]=>[5,1,2,7,4,8,3,6]=>{{1,5},{2},{3},{4,7},{6,8}}
[7,1,4,2,8,5,6,3]=>[7,4,6,1,8,5,2,3]=>[4,8,7,3,6,1,5,2]=>{{1,4},{2,8},{3,7},{5,6}}
[1,7,6,8,3,2,5,4]=>[1,3,8,5,2,7,6,4]=>[1,5,3,7,4,8,2,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[8,1,4,5,3,7,2,6]=>[8,7,5,1,2,4,6,3]=>[5,7,8,3,4,1,2,6]=>{{1,5},{2,7},{3,8},{4},{6}}
[7,3,1,5,4,8,2,6]=>[3,7,8,5,1,4,2,6]=>[7,5,3,8,4,1,6,2]=>{{1,7},{2,5},{3},{4,8},{6}}
[5,6,2,8,1,4,7,3]=>[8,6,7,1,5,2,4,3]=>[5,7,6,3,8,4,1,2]=>{{1,5,8},{2,7},{3,6},{4}}
[8,1,6,3,2,5,7,4]=>[8,3,6,7,2,1,5,4]=>[3,8,6,7,2,5,1,4]=>{{1,3,6},{2,8},{4,7},{5}}
[5,2,6,3,8,1,7,4]=>[8,5,6,7,2,3,1,4]=>[5,8,7,6,3,2,4,1]=>{{1,5},{2,8},{3,7},{4,6}}
[5,8,2,3,6,1,7,4]=>[6,8,2,7,5,3,1,4]=>[7,5,1,6,8,3,4,2]=>{{1,7},{2,5,8},{3},{4,6}}
[5,4,1,3,7,2,6,8]=>[4,5,1,7,2,3,6,8]=>[7,5,2,4,3,1,6,8]=>{{1,7},{2,5},{3},{4},{6},{8}}
[5,4,8,7,3,2,1,6]=>[2,3,7,5,4,1,8,6]=>[5,2,3,8,1,4,7,6]=>{{1,5},{2},{3},{4,8},{6},{7}}
[4,3,8,2,7,5,6,1]=>[6,8,4,3,7,5,2,1]=>[6,4,8,1,7,2,3,5]=>{{1,6},{2,4},{3,8},{5,7}}
[1,4,8,3,7,5,6,2]=>[1,6,8,4,7,5,3,2]=>[1,6,4,8,7,2,3,5]=>{{1},{2,6},{3,4,8},{5,7}}
[7,3,8,1,5,4,6,2]=>[8,6,7,5,1,3,2,4]=>[5,7,6,8,4,2,3,1]=>{{1,5},{2,7},{3,6},{4,8}}
[3,4,8,2,7,5,6,1]=>[6,8,3,4,7,5,2,1]=>[4,3,6,8,7,1,2,5]=>{{1,4,8},{2,3,6},{5,7}}
[3,4,2,1,8,6,5,7]=>[2,4,3,1,6,8,5,7]=>[3,2,4,1,8,6,5,7]=>{{1,3,4},{2},{5,8},{6},{7}}
[4,2,3,1,8,6,5,7]=>[3,4,2,1,6,8,5,7]=>[4,3,1,2,8,6,5,7]=>{{1,4},{2,3},{5,8},{6},{7}}
[7,6,2,8,3,5,4,1]=>[4,5,6,7,3,8,1,2]=>[8,7,5,4,1,6,3,2]=>{{1,8},{2,7},{3,5},{4},{6}}
[7,3,8,6,2,4,1,5]=>[4,6,8,2,1,7,5,3]=>[8,6,4,2,3,7,1,5]=>{{1,8},{2,6,7},{3,4},{5}}
[7,3,8,2,6,4,5,1]=>[5,8,7,6,4,2,3,1]=>[8,5,6,7,1,3,2,4]=>{{1,8},{2,5},{3,6},{4,7}}
[3,1,4,2,8,6,5,7]=>[3,4,1,2,6,8,5,7]=>[4,3,2,1,8,6,5,7]=>{{1,4},{2,3},{5,8},{6},{7}}
[2,8,4,5,7,3,6,1]=>[6,2,7,8,4,3,5,1]=>[2,8,7,6,1,4,3,5]=>{{1,2,8},{3,7},{4,6},{5}}
[7,6,1,3,4,2,8,5]=>[6,4,1,3,7,8,5,2]=>[4,8,2,1,7,6,3,5]=>{{1,4},{2,8},{3},{5,7},{6}}
[4,2,1,3,7,5,8,6]=>[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,7,6,5]=>{{1,4},{2},{3},{5,8},{6,7}}
[6,2,8,1,5,7,4,3]=>[8,6,4,7,1,2,5,3]=>[4,7,8,6,3,5,1,2]=>{{1,4,6},{2,7},{3,8},{5}}
[5,7,8,2,6,1,4,3]=>[6,8,4,1,5,2,7,3]=>[5,4,6,3,7,2,8,1]=>{{1,5,7,8},{2,4},{3,6}}
[7,4,8,1,6,2,5,3]=>[8,6,5,7,2,1,4,3]=>[5,7,8,6,3,4,1,2]=>{{1,5},{2,7},{3,8},{4,6}}
[8,6,7,5,1,4,3,2]=>[5,3,4,1,7,8,6,2]=>[3,8,4,2,5,7,1,6]=>{{1,3,4},{2,8},{5},{6,7}}
[6,3,7,8,2,1,4,5]=>[2,8,6,1,3,5,7,4]=>[6,2,7,3,4,1,8,5]=>{{1,6},{2},{3,7,8},{4},{5}}
[3,8,7,6,2,1,4,5]=>[2,6,3,1,4,7,8,5]=>[3,2,8,1,4,6,7,5]=>{{1,3,8},{2},{4},{5},{6},{7}}
[4,3,7,2,5,1,8,6]=>[5,7,4,3,2,8,1,6]=>[5,4,8,1,2,7,6,3]=>{{1,5},{2,4},{3,8},{6,7}}
[2,8,7,6,5,1,3,4]=>[5,2,1,3,6,7,8,4]=>[2,8,1,3,5,6,7,4]=>{{1,2,8},{3},{4},{5},{6},{7}}
[5,3,7,6,1,4,8,2]=>[6,7,5,1,3,8,2,4]=>[7,5,8,3,2,6,4,1]=>{{1,7},{2,5},{3,8},{4},{6}}
[3,8,7,2,1,4,5,6]=>[2,7,3,1,4,5,8,6]=>[3,2,8,1,4,5,7,6]=>{{1,3,8},{2},{4},{5},{6},{7}}
[5,4,7,1,6,8,3,2]=>[7,3,8,5,4,1,6,2]=>[5,7,3,8,1,4,2,6]=>{{1,5},{2,7},{3},{4,8},{6}}
[5,8,2,1,6,4,3,7]=>[2,8,4,6,5,1,3,7]=>[4,2,6,5,8,3,1,7]=>{{1,4,5,8},{2},{3,6},{7}}
[5,3,1,6,7,4,8,2]=>[3,5,8,7,2,6,4,1]=>[7,5,3,6,2,8,1,4]=>{{1,7},{2,5},{3},{4,6,8}}
[3,8,1,6,5,4,7,2]=>[8,7,3,5,6,1,4,2]=>[3,5,6,8,7,4,1,2]=>{{1,3,6},{2,5,7},{4,8}}
[4,1,7,6,5,8,3,2]=>[4,3,8,1,6,7,5,2]=>[4,6,3,2,8,7,1,5]=>{{1,4},{2,6,7},{3},{5,8}}
[8,1,7,5,4,2,3,6]=>[8,4,2,5,7,3,1,6]=>[4,8,1,5,7,2,6,3]=>{{1,4,5,7},{2,8},{3},{6}}
[8,7,6,3,2,1,5,4]=>[2,3,6,5,1,7,8,4]=>[5,2,3,8,4,6,7,1]=>{{1,5},{2},{3},{4,8},{6},{7}}
[2,1,8,5,7,6,3,4]=>[2,1,6,3,7,8,4,5]=>[2,1,8,3,7,6,5,4]=>{{1,2},{3,8},{4},{5,7},{6}}
[6,3,8,1,5,7,4,2]=>[8,4,7,6,1,2,5,3]=>[4,8,6,7,3,5,1,2]=>{{1,4,7},{2,8},{3,6},{5}}
[6,2,3,1,4,5,8,7]=>[3,6,2,1,4,5,8,7]=>[6,3,1,2,4,5,8,7]=>{{1,6},{2,3},{4},{5},{7,8}}
[5,8,1,6,3,7,4,2]=>[8,4,7,6,5,1,2,3]=>[4,7,5,6,8,3,2,1]=>{{1,4,6},{2,7},{3,5,8}}
[1,3,5,7,8,6,2,4]=>[1,6,3,2,5,8,7,4]=>[1,3,5,2,7,6,8,4]=>{{1},{2,3,5,7,8},{4},{6}}
[2,3,5,6,8,1,7,4]=>[8,2,3,7,5,6,1,4]=>[2,3,5,6,7,8,4,1]=>{{1,2,3,5,7},{4,6,8}}
[1,6,7,5,2,8,3,4]=>[1,5,7,3,8,6,4,2]=>[1,7,6,2,5,8,3,4]=>{{1},{2,7},{3,6,8},{4},{5}}
[6,7,2,5,3,8,1,4]=>[8,7,5,1,4,6,2,3]=>[5,6,7,3,1,8,4,2]=>{{1,5},{2,6,8},{3,7},{4}}
[2,5,7,8,6,3,1,4]=>[3,2,6,1,5,8,7,4]=>[2,5,3,1,7,6,8,4]=>{{1,2,5,7,8},{3},{4},{6}}
[1,6,3,7,5,8,2,4]=>[1,8,6,2,7,3,5,4]=>[1,6,8,3,7,5,2,4]=>{{1},{2,6},{3,8},{4},{5,7}}
[6,2,3,7,5,8,1,4]=>[8,6,2,1,7,3,5,4]=>[6,8,1,3,7,5,2,4]=>{{1,6},{2,8},{3},{4},{5,7}}
[4,5,1,6,3,2,8,7]=>[5,3,6,4,1,2,8,7]=>[4,5,3,6,2,1,8,7]=>{{1,4,6},{2,5},{3},{7,8}}
[2,6,7,4,1,8,3,5]=>[4,2,7,8,3,6,5,1]=>[2,7,6,4,1,8,3,5]=>{{1,2,7},{3,6,8},{4},{5}}
[2,1,6,7,3,8,5,4]=>[2,1,7,5,8,6,3,4]=>[2,1,6,7,5,8,4,3]=>{{1,2},{3,6,8},{4,7},{5}}
[1,6,3,7,4,8,5,2]=>[1,5,8,6,7,4,2,3]=>[1,8,5,7,6,2,4,3]=>{{1},{2,8},{3,5,6},{4,7}}
[6,3,7,2,8,4,5,1]=>[5,7,6,8,4,3,2,1]=>[8,6,7,5,1,2,3,4]=>{{1,8},{2,6},{3,7},{4,5}}
[5,7,3,8,2,1,6,4]=>[2,8,7,6,5,1,3,4]=>[5,2,6,7,8,4,3,1]=>{{1,5,8},{2},{3,6},{4,7}}
[4,1,3,6,8,2,5,7]=>[4,8,1,3,2,6,5,7]=>[6,4,2,1,3,8,5,7]=>{{1,6,8},{2,4},{3},{5},{7}}
[2,4,6,5,8,1,3,7]=>[8,2,1,4,6,5,3,7]=>[2,4,1,6,8,3,5,7]=>{{1,2,4,6},{3},{5,8},{7}}
[5,3,2,1,6,8,4,7]=>[2,3,5,8,1,6,4,7]=>[6,2,3,5,4,8,1,7]=>{{1,6,8},{2},{3},{4,5},{7}}
[1,6,3,4,5,8,2,7]=>[1,8,6,3,4,5,2,7]=>[1,6,8,2,3,4,5,7]=>{{1},{2,6},{3,8},{4},{5},{7}}
[1,5,3,2,8,7,4,6]=>[1,3,5,7,2,4,8,6]=>[1,8,3,5,4,2,7,6]=>{{1},{2,8},{3},{4,5},{6},{7}}
[5,2,6,8,7,1,3,4]=>[7,5,1,2,4,6,8,3]=>[5,6,2,3,1,8,7,4]=>{{1,5},{2,6,8},{3},{4},{7}}
[8,4,2,1,6,5,3,7]=>[2,4,8,5,6,3,1,7]=>[8,2,4,5,6,1,3,7]=>{{1,8},{2},{3,4,5,6},{7}}
[8,6,4,2,1,5,3,7]=>[2,4,6,5,3,8,1,7]=>[8,2,4,5,1,6,3,7]=>{{1,8},{2},{3,4,5},{6},{7}}
[8,2,6,3,4,5,1,7]=>[5,8,6,3,4,2,1,7]=>[8,5,6,1,2,3,4,7]=>{{1,8},{2,5},{3,6},{4},{7}}
[8,6,4,1,3,2,7,5]=>[4,3,1,6,8,7,5,2]=>[3,8,2,4,6,7,1,5]=>{{1,3},{2,8},{4},{5,6,7}}
[5,8,3,2,6,7,1,4]=>[7,3,8,1,5,4,2,6]=>[5,7,3,2,8,1,6,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[6,3,5,8,7,2,1,4]=>[2,7,6,1,4,3,8,5]=>[6,2,8,3,1,5,7,4]=>{{1,6},{2},{3,8},{4},{5},{7}}
[5,8,6,2,1,3,7,4]=>[2,6,1,8,5,7,4,3]=>[6,2,1,5,8,7,3,4]=>{{1,6,7},{2},{3},{4,5,8}}
[3,8,1,4,5,6,7,2]=>[8,7,3,1,2,4,6,5]=>[3,7,8,2,4,5,1,6]=>{{1,3,8},{2,7},{4},{5},{6}}
[3,5,7,2,8,4,6,1]=>[6,7,3,8,5,4,2,1]=>[6,3,7,5,8,1,2,4]=>{{1,6},{2,3,7},{4,5,8}}
[3,6,7,2,4,8,5,1]=>[5,8,3,2,7,6,1,4]=>[5,3,7,1,6,8,4,2]=>{{1,5,6,8},{2,3,7},{4}}
[3,6,8,2,4,5,1,7]=>[5,8,3,2,4,6,1,7]=>[5,3,6,1,2,8,4,7]=>{{1,5},{2,3,6,8},{4},{7}}
[3,7,2,8,4,5,6,1]=>[6,7,3,8,4,5,2,1]=>[7,3,8,6,1,2,4,5]=>{{1,7},{2,3,8},{4,6},{5}}
[4,1,6,8,3,5,2,7]=>[4,5,8,1,3,6,2,7]=>[6,5,4,3,1,8,2,7]=>{{1,6,8},{2,5},{3,4},{7}}
[4,1,7,3,2,8,6,5]=>[4,3,7,1,6,8,2,5]=>[4,7,3,2,8,6,5,1]=>{{1,4},{2,7},{3},{5,8},{6}}
[4,5,6,3,8,1,2,7]=>[8,1,6,4,5,3,2,7]=>[4,1,5,6,8,2,3,7]=>{{1,4,6},{2},{3,5,8},{7}}
[5,6,2,3,8,4,1,7]=>[4,8,2,6,5,1,3,7]=>[6,4,1,5,8,3,2,7]=>{{1,6},{2,4,5,8},{3},{7}}
[5,7,2,3,4,8,6,1]=>[6,8,2,3,5,7,1,4]=>[6,5,1,2,8,7,4,3]=>{{1,6,7},{2,5,8},{3},{4}}
[5,8,2,3,4,1,6,7]=>[4,8,2,3,5,1,6,7]=>[5,4,1,2,8,3,6,7]=>{{1,5,8},{2,4},{3},{6},{7}}
[7,1,2,3,4,8,6,5]=>[7,1,2,3,6,8,4,5]=>[7,1,2,3,8,6,5,4]=>{{1,7},{2},{3},{4},{5,8},{6}}
[8,2,6,5,4,7,1,3]=>[7,8,1,5,6,3,2,4]=>[6,5,2,8,7,3,4,1]=>{{1,6},{2,5,7},{3},{4,8}}
[7,8,2,5,3,1,6,4]=>[3,5,8,6,1,2,7,4]=>[7,5,3,6,4,2,8,1]=>{{1,7,8},{2,5},{3},{4,6}}
[7,3,2,6,5,1,8,4]=>[5,3,6,7,8,1,4,2]=>[7,8,3,6,5,4,1,2]=>{{1,7},{2,8},{3},{4,6},{5}}
[8,4,7,2,5,6,3,1]=>[3,6,7,8,2,1,4,5]=>[8,7,3,6,2,5,4,1]=>{{1,8},{2,7},{3},{4,6},{5}}
[7,2,6,8,5,3,1,4]=>[3,5,8,1,7,4,2,6]=>[8,5,3,2,7,1,6,4]=>{{1,8},{2,5,7},{3},{4},{6}}
[6,3,7,1,5,8,4,2]=>[7,4,8,6,1,2,5,3]=>[6,8,4,7,3,5,1,2]=>{{1,6},{2,8},{3,4,7},{5}}
[6,2,5,4,8,1,3,7]=>[8,6,1,5,3,2,4,7]=>[5,6,2,8,3,4,1,7]=>{{1,5},{2,6},{3},{4,8},{7}}
[5,4,6,8,1,2,7,3]=>[8,1,7,5,4,6,2,3]=>[5,1,6,7,2,8,4,3]=>{{1,5},{2},{3,6,8},{4,7}}
[7,4,3,6,8,2,5,1]=>[5,8,4,7,2,3,6,1]=>[7,4,8,5,2,1,3,6]=>{{1,7},{2,4,5},{3,8},{6}}
[6,5,4,8,7,2,1,3]=>[2,7,1,5,6,4,8,3]=>[5,2,1,8,6,3,7,4]=>{{1,5,6},{2},{3},{4,8},{7}}
[1,4,7,3,5,6,8,2]=>[1,8,7,4,3,5,6,2]=>[1,4,7,8,2,3,5,6]=>{{1},{2,4,8},{3,7},{5},{6}}
[5,1,2,6,8,4,7,3]=>[5,1,7,8,2,6,4,3]=>[7,1,6,5,4,8,2,3]=>{{1,7},{2},{3,6,8},{4,5}}
[1,2,7,4,8,6,5,3]=>[1,2,5,6,8,7,4,3]=>[1,2,8,6,5,7,3,4]=>{{1},{2},{3,8},{4,6,7},{5}}
[1,2,6,4,8,7,3,5]=>[1,2,7,6,3,4,8,5]=>[1,2,6,8,4,5,7,3]=>{{1},{2},{3,6},{4,8},{5},{7}}
[1,5,2,7,8,4,6,3]=>[1,5,6,8,2,4,7,3]=>[1,7,6,5,4,2,8,3]=>{{1},{2,7,8},{3,6},{4,5}}
[1,6,7,3,4,8,5,2]=>[1,5,8,3,7,6,2,4]=>[1,7,5,2,6,8,4,3]=>{{1},{2,7},{3,5,6,8},{4}}
[3,8,4,1,5,7,2,6]=>[4,8,3,7,1,5,2,6]=>[4,3,8,7,2,1,6,5]=>{{1,4,7},{2,3,8},{5},{6}}
[1,2,7,4,8,3,6,5]=>[1,2,8,7,6,3,4,5]=>[1,2,6,7,8,5,4,3]=>{{1},{2},{3,6},{4,7},{5,8}}
[1,4,8,6,7,2,3,5]=>[1,7,2,4,3,8,6,5]=>[1,4,2,8,3,7,5,6]=>{{1},{2,4,8},{3},{5},{6,7}}
[1,5,7,8,6,2,3,4]=>[1,6,2,3,5,8,7,4]=>[1,5,2,3,7,6,8,4]=>{{1},{2,5,7,8},{3},{4},{6}}
[1,4,7,6,8,2,3,5]=>[1,8,2,4,3,7,6,5]=>[1,4,2,7,3,8,5,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[3,6,4,1,5,8,7,2]=>[4,6,3,7,1,2,8,5]=>[6,3,8,4,2,5,7,1]=>{{1,6},{2,3,8},{4},{5},{7}}
[1,2,3,8,5,4,7,6]=>[1,2,3,5,8,7,4,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,7},{5},{6,8}}
[1,2,3,8,6,4,5,7]=>[1,2,3,6,4,8,5,7]=>[1,2,3,8,4,6,5,7]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[2,5,4,3,1,8,6,7]=>[3,2,4,5,1,8,6,7]=>[2,5,3,4,1,8,6,7]=>{{1,2,5},{3},{4},{6,8},{7}}
[1,2,3,8,6,7,4,5]=>[1,2,3,7,4,8,6,5]=>[1,2,3,8,4,7,5,6]=>{{1},{2},{3},{4,8},{5},{6,7}}
[1,2,3,8,5,7,4,6]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,7,5,6,4]=>{{1},{2},{3},{4,8},{5,7},{6}}
[8,3,7,6,5,1,4,2]=>[5,4,6,1,7,8,3,2]=>[7,8,4,3,5,6,1,2]=>{{1,7},{2,8},{3,4},{5},{6}}
[6,8,2,5,3,7,1,4]=>[7,8,5,1,4,6,2,3]=>[6,5,7,3,1,8,4,2]=>{{1,6,8},{2,5},{3,7},{4}}
[2,6,5,8,1,4,3,7]=>[8,2,4,1,6,5,3,7]=>[2,4,6,3,8,1,5,7]=>{{1,2,4},{3,6},{5,8},{7}}
[3,7,6,8,2,5,1,4]=>[5,8,3,1,2,7,6,4]=>[5,3,7,2,4,8,1,6]=>{{1,5},{2,3,7},{4},{6,8}}
[4,7,5,8,2,6,1,3]=>[6,8,1,4,7,2,5,3]=>[6,4,2,8,7,5,1,3]=>{{1,6},{2,4,8},{3},{5,7}}
[3,7,5,8,2,6,1,4]=>[6,8,3,1,7,2,5,4]=>[6,3,8,2,7,5,1,4]=>{{1,6},{2,3,8},{4},{5,7}}
[4,7,3,6,5,8,1,2]=>[8,1,7,4,6,3,5,2]=>[4,1,6,7,8,3,2,5]=>{{1,4,7},{2},{3,6},{5,8}}
[4,8,3,6,2,5,7,1]=>[7,6,8,4,2,3,5,1]=>[6,7,4,8,2,3,1,5]=>{{1,6},{2,7},{3,4,8},{5}}
[6,4,2,5,1,8,7,3]=>[5,4,6,7,2,3,8,1]=>[6,8,5,4,2,1,7,3]=>{{1,6},{2,8},{3,5},{4},{7}}
[6,4,3,5,8,2,1,7]=>[2,8,4,6,3,5,1,7]=>[4,2,8,6,1,3,5,7]=>{{1,4,6},{2},{3,8},{5},{7}}
[5,8,3,7,2,6,4,1]=>[4,6,7,8,5,1,2,3]=>[7,6,5,4,8,3,2,1]=>{{1,7},{2,6},{3,5,8},{4}}
[5,7,3,4,8,2,1,6]=>[2,8,7,3,5,1,4,6]=>[5,2,7,1,8,4,6,3]=>{{1,5,8},{2},{3,7},{4},{6}}
[5,8,4,2,3,1,6,7]=>[3,4,2,8,5,1,6,7]=>[5,3,1,4,8,2,6,7]=>{{1,5,8},{2,3},{4},{6},{7}}
[6,4,5,3,7,1,8,2]=>[7,8,5,6,4,3,1,2]=>[6,5,8,7,1,2,4,3]=>{{1,6},{2,5},{3,8},{4,7}}
[5,3,4,7,2,6,1,8]=>[6,7,5,3,4,2,1,8]=>[6,5,7,1,2,3,4,8]=>{{1,6},{2,5},{3,7},{4},{8}}
[4,6,3,5,7,8,2,1]=>[2,8,6,4,3,5,7,1]=>[4,2,6,7,1,3,8,5]=>{{1,4,7,8},{2},{3,6},{5}}
[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>[4,2,3,5,6,7,8,9,1]=>{{1,4,5,6,7,8,9},{2},{3}}
[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>[3,2,4,5,6,7,8,9,1]=>{{1,3,4,5,6,7,8,9},{2}}
[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>[3,2,4,5,6,7,8,9,10,1]=>{{1,3,4,5,6,7,8,9,10},{2}}
[1,6,8,2,3,5,4,7]=>[1,8,2,5,3,6,4,7]=>[1,5,2,6,4,8,3,7]=>{{1},{2,5},{3},{4,6,8},{7}}
[5,3,6,1,2,4,8,7]=>[6,1,5,2,3,4,8,7]=>[5,1,6,3,4,2,8,7]=>{{1,5},{2},{3,6},{4},{7,8}}
[8,1,4,7,5,2,3,6]=>[8,5,2,1,7,4,6,3]=>[5,8,1,3,7,2,4,6]=>{{1,5,7},{2,8},{3},{4},{6}}
[2,1,7,5,8,3,4,6]=>[2,1,8,3,7,4,5,6]=>[2,1,7,3,8,5,6,4]=>{{1,2},{3,7},{4},{5,8},{6}}
[7,8,3,1,2,4,6,5]=>[3,1,8,2,6,4,7,5]=>[6,1,3,2,7,5,8,4]=>{{1,6},{2},{3},{4},{5,7,8}}
[2,1,7,8,5,3,4,6]=>[2,1,5,3,8,4,7,6]=>[2,1,7,3,5,4,8,6]=>{{1,2},{3,7,8},{4},{5},{6}}
[4,1,3,7,5,6,8,2]=>[4,8,1,3,7,5,6,2]=>[7,4,2,1,8,3,5,6]=>{{1,7},{2,4},{3},{5,8},{6}}
[8,2,4,3,7,5,6,1]=>[6,8,4,2,7,5,3,1]=>[6,4,8,2,7,1,3,5]=>{{1,6},{2,4},{3,8},{5,7}}
[2,5,6,3,4,8,7,1]=>[7,2,6,3,5,4,8,1]=>[2,5,6,1,8,3,7,4]=>{{1,2,5,8},{3,6},{4},{7}}
[7,2,5,6,4,8,1,3]=>[8,7,1,6,3,5,2,4]=>[6,7,2,8,3,1,5,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[4,1,3,8,2,6,7,5]=>[4,8,1,3,7,2,6,5]=>[7,4,2,1,8,5,3,6]=>{{1,7},{2,4},{3},{5,8},{6}}
[3,1,7,2,8,5,4,6]=>[3,7,1,5,8,4,2,6]=>[7,3,2,8,5,1,6,4]=>{{1,7},{2,3},{4,8},{5},{6}}
[6,2,7,4,5,8,1,3]=>[8,6,1,7,4,2,5,3]=>[6,8,2,7,1,5,3,4]=>{{1,6},{2,8},{3},{4,7},{5}}
[3,6,8,4,7,2,5,1]=>[5,7,3,8,2,6,4,1]=>[6,3,7,5,2,8,1,4]=>{{1,6,8},{2,3,7},{4,5}}
[2,8,3,6,4,5,7,1]=>[7,2,8,6,4,3,5,1]=>[2,7,6,8,1,4,3,5]=>{{1,2,7},{3,6},{4,8},{5}}
[2,1,5,6,8,3,7,4]=>[2,1,8,7,5,6,3,4]=>[2,1,5,6,7,8,4,3]=>{{1,2},{3,5,7},{4,6,8}}
[5,4,8,3,6,2,7,1]=>[7,6,8,5,4,3,2,1]=>[6,7,5,8,1,2,3,4]=>{{1,6},{2,7},{3,5},{4,8}}
[1,5,6,4,8,2,7,3]=>[1,8,7,6,5,4,2,3]=>[1,5,6,7,8,2,4,3]=>{{1},{2,5,8},{3,6},{4,7}}
[2,4,6,3,1,7,8,5]=>[3,2,6,4,8,1,7,5]=>[2,4,3,7,6,5,8,1]=>{{1,2,4,7,8},{3},{5,6}}
[4,7,2,5,3,8,6,1]=>[6,8,5,4,2,7,1,3]=>[5,4,6,8,2,7,3,1]=>{{1,5},{2,4,8},{3,6,7}}
[1,2,7,3,6,8,5,4]=>[1,2,7,5,8,3,6,4]=>[1,2,7,8,5,4,3,6]=>{{1},{2},{3,7},{4,8},{5},{6}}
[3,1,5,4,8,7,6,2]=>[3,6,1,5,4,7,8,2]=>[5,3,2,8,1,6,7,4]=>{{1,5},{2,3},{4,8},{6},{7}}
[2,3,6,7,5,8,1,4]=>[8,2,3,1,7,6,5,4]=>[2,3,6,1,7,8,4,5]=>{{1,2,3,6,8},{4},{5,7}}
[1,3,7,5,6,8,2,4]=>[1,8,3,2,7,5,6,4]=>[1,3,7,2,8,4,5,6]=>{{1},{2,3,7},{4},{5,8},{6}}
[3,5,4,6,8,1,2,7]=>[8,1,3,5,4,6,2,7]=>[3,1,5,6,2,8,4,7]=>{{1,3,5},{2},{4,6,8},{7}}
[1,2,5,8,4,7,6,3]=>[1,2,6,7,5,8,3,4]=>[1,2,7,5,8,6,4,3]=>{{1},{2},{3,7},{4,5,8},{6}}
[6,4,5,7,2,8,1,3]=>[8,7,1,6,4,5,2,3]=>[6,7,2,8,1,3,5,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[5,3,6,2,7,1,4,8]=>[7,6,5,1,3,2,4,8]=>[5,6,7,3,2,4,1,8]=>{{1,5},{2,6},{3,7},{4},{8}}
[8,2,7,3,4,5,6,1]=>[6,8,7,3,4,5,2,1]=>[8,6,7,1,2,3,4,5]=>{{1,8},{2,6},{3,7},{4},{5}}
[7,2,8,3,4,5,6,1]=>[6,7,8,3,4,5,2,1]=>[8,7,6,1,2,3,4,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[2,5,7,1,8,3,6,4]=>[7,2,8,6,5,3,1,4]=>[2,6,5,7,8,3,4,1]=>{{1,2,6},{3,5,8},{4,7}}
[1,8,3,7,2,4,5,6]=>[1,7,8,2,3,4,5,6]=>[1,8,7,3,4,5,6,2]=>{{1},{2,8},{3,7},{4},{5},{6}}
[6,8,2,3,5,1,4,7]=>[5,8,2,1,3,6,4,7]=>[6,5,1,3,4,8,2,7]=>{{1,6,8},{2,5},{3},{4},{7}}
[1,7,6,2,3,4,5,8]=>[1,6,2,3,4,7,5,8]=>[1,7,2,3,4,6,5,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[1,8,6,2,3,4,5,7]=>[1,6,2,3,4,8,5,7]=>[1,8,2,3,4,6,5,7]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[7,8,3,6,2,4,5,1]=>[5,6,8,2,3,1,7,4]=>[7,6,5,2,3,4,8,1]=>{{1,7,8},{2,6},{3,5},{4}}
[5,2,7,4,1,3,6,8]=>[4,7,1,5,3,2,6,8]=>[7,4,2,5,1,3,6,8]=>{{1,7},{2,4,5},{3},{6},{8}}
[5,4,8,1,6,3,2,7]=>[8,3,6,5,4,1,2,7]=>[3,6,5,8,1,4,2,7]=>{{1,3,5},{2,6},{4,8},{7}}
[1,4,8,3,7,6,5,2]=>[1,5,6,4,7,8,3,2]=>[1,7,4,8,5,6,2,3]=>{{1},{2,7},{3,4,8},{5},{6}}
[4,3,8,2,1,6,5,7]=>[2,8,4,3,6,1,5,7]=>[4,2,6,1,8,5,3,7]=>{{1,4},{2},{3,6},{5,8},{7}}
[3,8,4,2,7,1,5,6]=>[7,4,3,8,1,2,6,5]=>[3,7,8,4,2,5,1,6]=>{{1,3,8},{2,7},{4},{5},{6}}
[8,1,7,6,2,4,3,5]=>[8,6,4,2,3,7,1,5]=>[4,6,8,2,1,7,5,3]=>{{1,4},{2,6,7},{3,8},{5}}
[1,8,6,5,7,3,4,2]=>[1,4,7,3,6,8,5,2]=>[1,7,4,2,8,6,3,5]=>{{1},{2,7},{3,4},{5,8},{6}}
[1,2,5,8,6,7,3,4]=>[1,2,7,3,5,8,6,4]=>[1,2,5,3,8,7,4,6]=>{{1},{2},{3,5,8},{4},{6,7}}
[4,2,1,5,8,7,3,6]=>[2,4,7,1,5,3,8,6]=>[5,2,4,3,8,1,7,6]=>{{1,5,8},{2},{3,4},{6},{7}}
[1,7,3,6,5,2,8,4]=>[1,5,6,7,8,2,4,3]=>[1,8,7,6,5,4,2,3]=>{{1},{2,8},{3,7},{4,6},{5}}
[1,3,4,7,6,2,8,5]=>[1,6,3,4,7,8,5,2]=>[1,3,4,8,7,6,2,5]=>{{1},{2,3,4,8},{5,7},{6}}
[1,2,4,7,3,8,6,5]=>[1,2,7,4,6,8,3,5]=>[1,2,4,7,8,6,5,3]=>{{1},{2},{3,4,7},{5,8},{6}}
[4,8,7,5,1,6,3,2]=>[5,3,7,4,6,2,8,1]=>[4,5,3,8,6,1,7,2]=>{{1,4,8},{2,5,6},{3},{7}}
[5,6,3,8,4,1,7,2]=>[4,8,7,6,5,1,2,3]=>[7,4,5,6,8,3,2,1]=>{{1,7},{2,4,6},{3,5,8}}
[8,6,1,7,4,5,2,3]=>[6,5,2,8,4,7,3,1]=>[6,8,1,5,2,7,3,4]=>{{1,6,7},{2,8},{3},{4,5}}
[5,4,8,2,7,3,1,6]=>[3,7,8,5,4,1,6,2]=>[7,5,3,8,1,4,2,6]=>{{1,7},{2,5},{3},{4,8},{6}}
[6,8,2,4,7,5,1,3]=>[5,7,1,3,8,6,4,2]=>[7,6,2,1,5,8,3,4]=>{{1,7},{2,6,8},{3},{4},{5}}
[4,6,8,2,7,3,1,5]=>[3,7,8,4,1,6,5,2]=>[6,4,3,7,2,8,1,5]=>{{1,6,8},{2,4,7},{3},{5}}
[2,6,8,7,3,4,1,5]=>[4,2,7,3,1,6,8,5]=>[2,6,4,1,3,8,7,5]=>{{1,2,6,8},{3,4},{5},{7}}
[3,8,7,4,5,6,1,2]=>[6,1,3,7,4,5,8,2]=>[3,1,8,6,2,4,7,5]=>{{1,3,8},{2},{4,6},{5},{7}}
[6,8,3,2,5,4,7,1]=>[7,3,8,5,2,6,4,1]=>[5,6,3,7,2,8,1,4]=>{{1,5},{2,6,8},{3},{4,7}}
[6,8,4,5,2,3,7,1]=>[7,5,2,8,4,6,3,1]=>[6,7,1,5,2,8,3,4]=>{{1,6,8},{2,7},{3},{4,5}}
[6,3,8,1,5,4,7,2]=>[8,7,6,5,1,3,4,2]=>[5,6,7,8,4,2,1,3]=>{{1,5},{2,6},{3,7},{4,8}}
[4,8,5,7,6,1,3,2]=>[6,3,1,4,7,8,2,5]=>[3,4,2,8,7,6,5,1]=>{{1,3},{2,4,8},{5,7},{6}}
[2,4,6,8,1,3,5,7,9]=>[8,2,1,4,3,6,5,7,9]=>[2,4,1,6,3,8,5,7,9]=>{{1,2,4,6,8},{3},{5},{7},{9}}
[6,1,8,2,5,3,7,4]=>[6,8,5,7,2,1,3,4]=>[7,5,8,6,3,4,2,1]=>{{1,7},{2,5},{3,8},{4,6}}
[8,1,6,2,5,3,7,4]=>[8,6,5,7,2,1,3,4]=>[5,7,8,6,3,4,2,1]=>{{1,5},{2,7},{3,8},{4,6}}
[1,8,6,4,7,2,3,5]=>[1,7,2,6,3,8,4,5]=>[1,7,2,8,4,6,5,3]=>{{1},{2,7},{3},{4,8},{5},{6}}
[7,6,3,8,5,4,1,2]=>[4,1,5,8,6,7,3,2]=>[8,1,5,4,6,7,2,3]=>{{1,8},{2},{3,5,6,7},{4}}
[7,2,8,6,3,1,4,5]=>[3,6,8,1,2,7,5,4]=>[8,6,3,2,4,7,1,5]=>{{1,8},{2,6,7},{3},{4},{5}}
[4,3,1,2,7,8,6,5]=>[3,1,4,2,6,8,7,5]=>[4,1,3,2,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}}
[4,5,2,8,6,1,7,3]=>[6,5,8,4,2,7,3,1]=>[5,6,4,8,2,7,1,3]=>{{1,5},{2,6,7},{3,4,8}}
[6,1,8,3,2,4,7,5]=>[6,3,8,2,7,1,4,5]=>[6,8,3,1,7,5,4,2]=>{{1,6},{2,8},{3},{4},{5,7}}
[4,3,5,7,6,8,1,2]=>[8,1,4,3,5,7,6,2]=>[4,1,5,2,7,8,3,6]=>{{1,4},{2},{3,5,7},{6,8}}
[7,6,5,4,1,8,3,2]=>[4,3,5,6,7,8,2,1]=>[7,8,3,4,5,6,1,2]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,8,1,3,2,4,5,6]=>[8,3,1,2,4,5,7,6]=>[3,7,2,1,4,5,8,6]=>{{1,3},{2,7,8},{4},{5},{6}}
[1,5,4,6,7,2,3,8]=>[1,7,2,5,4,6,3,8]=>[1,5,2,6,3,7,4,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[4,5,2,6,7,1,3,8]=>[7,5,1,4,2,6,3,8]=>[4,5,2,6,3,7,1,8]=>{{1,4,6,7},{2,5},{3},{8}}
[7,3,2,5,1,6,4,8]=>[5,3,7,6,2,1,4,8]=>[5,7,3,6,2,4,1,8]=>{{1,5},{2,7},{3},{4,6},{8}}
[6,3,4,5,8,1,7,2]=>[8,7,6,3,4,5,1,2]=>[6,7,8,1,2,3,5,4]=>{{1,6},{2,7},{3,8},{4},{5}}
[5,3,1,4,2,7,8,6]=>[3,5,4,2,1,8,7,6]=>[5,3,4,1,2,7,8,6]=>{{1,5},{2,3,4},{6,7,8}}
[1,3,4,5,8,2,7,6]=>[1,8,3,4,5,7,2,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,7},{6,8}}
[6,3,4,5,8,2,7,1]=>[7,8,6,3,4,5,2,1]=>[7,6,8,1,2,3,4,5]=>{{1,7},{2,6},{3,8},{4},{5}}
[7,3,2,5,6,8,4,1]=>[4,3,8,7,2,5,1,6]=>[4,8,3,7,1,2,6,5]=>{{1,4,7},{2,8},{3},{5},{6}}
[7,6,4,2,8,3,5,1]=>[5,4,6,7,3,8,2,1]=>[7,8,5,4,1,6,2,3]=>{{1,7},{2,8},{3,5},{4},{6}}
[2,1,8,6,3,5,4,7]=>[2,1,6,5,3,8,4,7]=>[2,1,5,8,4,6,3,7]=>{{1,2},{3,5},{4,8},{6},{7}}
[3,2,1,5,7,8,4,6]=>[2,3,1,8,5,4,7,6]=>[3,2,1,5,7,4,8,6]=>{{1,3},{2},{4,5,7,8},{6}}
[2,1,8,3,7,4,5,6]=>[2,1,8,7,4,5,3,6]=>[2,1,7,8,3,4,6,5]=>{{1,2},{3,7},{4,8},{5},{6}}
[1,6,8,3,7,2,4,5]=>[1,7,8,2,3,6,5,4]=>[1,7,6,3,4,8,2,5]=>{{1},{2,7},{3,6,8},{4},{5}}
[5,3,8,4,7,6,1,2]=>[6,1,5,7,3,8,2,4]=>[7,1,8,5,3,6,4,2]=>{{1,7},{2},{3,8},{4,5},{6}}
[6,1,8,2,7,4,5,3]=>[6,8,5,7,4,1,2,3]=>[7,5,8,6,1,4,3,2]=>{{1,7},{2,5},{3,8},{4,6}}
[1,2,3,7,5,4,8,6]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,7,6,4]=>{{1},{2},{3},{4,8},{5},{6,7}}
[2,8,7,6,5,1,4,3]=>[5,2,4,1,6,7,8,3]=>[2,4,8,3,5,6,7,1]=>{{1,2,4},{3,8},{5},{6},{7}}
[1,8,4,3,6,5,2,7]=>[1,5,4,6,8,2,3,7]=>[1,6,8,4,5,3,2,7]=>{{1},{2,6},{3,8},{4},{5},{7}}
[2,4,8,1,6,3,7,5]=>[8,2,6,4,7,1,3,5]=>[2,4,6,8,7,5,3,1]=>{{1,2,4,8},{3,6},{5,7}}
[2,7,4,8,5,3,6,1]=>[6,2,5,8,7,3,1,4]=>[2,7,8,5,6,3,4,1]=>{{1,2,7},{3,8},{4,5,6}}
[7,3,2,5,8,4,6,1]=>[6,3,7,8,2,5,1,4]=>[7,8,3,6,2,1,5,4]=>{{1,7},{2,8},{3},{4,6},{5}}
[3,5,6,8,2,4,1,7]=>[4,8,3,2,5,6,1,7]=>[4,3,5,1,6,8,2,7]=>{{1,4},{2,3,5,6,8},{7}}
[3,6,7,8,1,4,2,5]=>[8,4,3,1,2,6,7,5]=>[3,4,6,2,1,7,8,5]=>{{1,3,6,7,8},{2,4},{5}}
[5,4,7,2,8,1,6,3]=>[8,7,6,5,4,1,2,3]=>[5,6,7,8,1,4,3,2]=>{{1,5},{2,6},{3,7},{4,8}}
[4,8,6,2,1,5,7,3]=>[2,6,8,4,1,7,3,5]=>[6,2,4,8,3,7,5,1]=>{{1,6,7},{2},{3,4,8},{5}}
[8,4,1,2,7,5,3,6]=>[4,1,8,5,7,3,6,2]=>[8,1,4,5,7,2,3,6]=>{{1,8},{2},{3,4,5,7},{6}}
[3,8,4,5,6,1,7,2]=>[6,7,3,8,4,5,1,2]=>[7,3,8,6,1,2,5,4]=>{{1,7},{2,3,8},{4,6},{5}}
[7,2,3,4,8,1,6,5]=>[8,7,2,3,6,1,4,5]=>[6,7,1,2,8,5,4,3]=>{{1,6},{2,7},{3},{4},{5,8}}
[7,2,3,5,8,1,4,6]=>[8,7,2,1,4,3,6,5]=>[7,8,1,3,2,5,4,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,2,3,8,4,1,6,5]=>[4,8,2,7,6,1,5,3]=>[7,4,1,6,8,5,2,3]=>{{1,7},{2,4,6},{3},{5,8}}
[3,6,4,2,1,7,8,5]=>[2,4,3,6,8,1,7,5]=>[3,2,7,4,6,5,8,1]=>{{1,3,7,8},{2},{4},{5,6}}
[7,6,5,1,8,2,4,3]=>[5,6,4,2,7,8,1,3]=>[7,4,8,2,5,6,3,1]=>{{1,7},{2,4},{3,8},{5},{6}}
[6,8,7,1,3,2,4,5]=>[7,3,1,2,4,6,8,5]=>[3,6,2,1,4,8,7,5]=>{{1,3},{2,6,8},{4},{5},{7}}
[6,4,5,1,7,8,3,2]=>[5,3,8,6,4,1,7,2]=>[5,7,3,6,1,4,8,2]=>{{1,5},{2,7,8},{3},{4,6}}
[4,2,3,1,7,8,6,5]=>[3,4,2,1,6,8,7,5]=>[4,3,1,2,7,6,8,5]=>{{1,4},{2,3},{5,7,8},{6}}
[3,4,2,1,8,6,7,5]=>[2,4,3,1,7,8,6,5]=>[3,2,4,1,8,7,5,6]=>{{1,3,4},{2},{5,8},{6,7}}
[3,6,8,1,5,2,4,7]=>[8,5,3,2,1,6,4,7]=>[3,5,6,1,4,8,2,7]=>{{1,3,6,8},{2,5},{4},{7}}
[7,6,8,3,5,1,4,2]=>[5,4,8,1,3,7,6,2]=>[5,7,4,3,1,8,2,6]=>{{1,5},{2,7},{3,4},{6,8}}
[4,1,8,5,6,3,2,7]=>[4,3,6,1,8,5,2,7]=>[4,8,3,2,6,1,5,7]=>{{1,4},{2,8},{3},{5,6},{7}}
[6,1,8,5,3,7,4,2]=>[6,4,7,5,8,1,2,3]=>[6,8,4,7,5,3,2,1]=>{{1,6},{2,8},{3,4,7},{5}}
[8,6,3,5,1,7,2,4]=>[5,7,6,2,4,8,3,1]=>[8,5,7,2,1,6,3,4]=>{{1,8},{2,5},{3,7},{4},{6}}
[3,8,7,5,6,1,2,4]=>[6,1,3,2,7,5,8,4]=>[3,1,8,2,6,4,7,5]=>{{1,3,8},{2},{4},{5,6},{7}}
[7,5,4,1,2,6,8,3]=>[4,1,5,7,8,2,6,3]=>[8,1,7,4,5,3,2,6]=>{{1,8},{2},{3,7},{4},{5},{6}}
[7,1,4,3,5,2,8,6]=>[7,5,4,1,3,8,2,6]=>[4,5,8,3,1,7,6,2]=>{{1,4},{2,5},{3,8},{6,7}}
[8,3,2,6,1,4,7,5]=>[6,3,8,1,7,2,4,5]=>[6,8,3,2,7,5,4,1]=>{{1,6},{2,8},{3},{4},{5,7}}
[8,5,2,1,6,3,7,4]=>[2,5,8,6,7,1,3,4]=>[8,2,5,7,6,4,3,1]=>{{1,8},{2},{3,5,6},{4,7}}
[5,4,8,2,7,3,6,1]=>[6,8,7,5,4,3,2,1]=>[7,5,6,8,1,2,3,4]=>{{1,7},{2,5},{3,6},{4,8}}
[6,4,8,1,3,2,5,7]=>[8,3,1,6,2,4,5,7]=>[3,6,2,8,4,5,1,7]=>{{1,3},{2,6},{4,8},{5},{7}}
[1,4,8,5,2,6,7,3]=>[1,5,8,4,7,2,3,6]=>[1,5,4,8,7,3,6,2]=>{{1},{2,5,7},{3,4,8},{6}}
[8,6,3,7,4,1,2,5]=>[4,1,7,6,2,8,5,3]=>[8,1,4,7,3,6,2,5]=>{{1,8},{2},{3,4,7},{5},{6}}
[3,2,8,1,6,5,7,4]=>[8,3,2,7,6,1,5,4]=>[3,6,1,7,8,5,2,4]=>{{1,3},{2,6},{4,7},{5,8}}
[3,6,7,2,5,1,4,8]=>[5,7,3,1,2,6,4,8]=>[5,3,6,2,4,7,1,8]=>{{1,5},{2,3,6,7},{4},{8}}
[7,5,1,8,2,3,6,4]=>[5,7,2,8,6,4,3,1]=>[8,6,1,5,7,2,3,4]=>{{1,8},{2,6},{3},{4,5,7}}
[4,5,2,7,1,6,8,3]=>[7,5,8,4,2,1,6,3]=>[5,7,4,8,2,3,1,6]=>{{1,5},{2,7},{3,4,8},{6}}
[7,3,1,4,8,5,6,2]=>[3,7,6,1,8,5,2,4]=>[8,3,7,2,6,1,5,4]=>{{1,8},{2,3,7},{4},{5,6}}
[5,3,8,7,6,4,1,2]=>[4,1,6,5,2,7,8,3]=>[8,1,4,5,3,6,7,2]=>{{1,8},{2},{3,4,5},{6},{7}}
[6,2,8,7,1,5,4,3]=>[7,6,4,5,1,2,8,3]=>[4,5,8,6,3,2,7,1]=>{{1,4,6},{2,5},{3,8},{7}}
[8,2,3,6,1,4,5,7]=>[6,8,2,1,3,5,4,7]=>[8,6,1,3,4,2,5,7]=>{{1,8},{2,6},{3},{4},{5},{7}}
[8,2,3,6,4,1,5,7]=>[4,6,2,8,1,5,3,7]=>[8,6,1,4,3,2,5,7]=>{{1,8},{2,6},{3},{4},{5},{7}}
[6,1,8,7,4,2,3,5]=>[6,4,2,7,3,1,8,5]=>[6,8,1,4,2,5,7,3]=>{{1,6},{2,8},{3},{4},{5},{7}}
[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[10,9,8,7,6,5,4,3,2,1]=>{{1,10},{2,9},{3,8},{4,7},{5,6}}
[8,2,6,7,5,3,4,1]=>[4,8,5,3,7,1,2,6]=>[8,4,5,1,7,3,6,2]=>{{1,8},{2,4},{3,5,7},{6}}
[4,2,1,6,3,5,7,8]=>[2,4,6,1,3,5,7,8]=>[6,2,4,3,1,5,7,8]=>{{1,6},{2},{3,4},{5},{7},{8}}
[8,1,4,3,6,5,7,2]=>[8,7,4,1,6,2,3,5]=>[4,6,7,3,8,5,2,1]=>{{1,4},{2,6},{3,7},{5,8}}
[8,4,6,1,3,5,7,2]=>[6,7,1,8,2,5,4,3]=>[8,7,2,6,4,1,3,5]=>{{1,8},{2,7},{3},{4,6},{5}}
[2,1,8,3,6,5,7,4]=>[2,1,8,7,6,3,5,4]=>[2,1,6,7,8,5,3,4]=>{{1,2},{3,6},{4,7},{5,8}}
[2,8,4,1,3,5,7,6]=>[4,2,1,8,3,7,5,6]=>[2,7,1,4,3,8,6,5]=>{{1,2,7},{3},{4},{5},{6,8}}
[1,8,6,4,3,5,7,2]=>[1,7,4,6,3,8,5,2]=>[1,4,8,7,2,6,3,5]=>{{1},{2,4,7},{3,8},{5},{6}}
[8,4,2,1,3,5,7,6]=>[2,4,1,8,3,7,5,6]=>[7,2,1,4,3,8,6,5]=>{{1,7},{2},{3},{4},{5},{6,8}}
[5,8,1,4,6,3,7,2]=>[8,7,6,1,5,2,4,3]=>[5,6,7,3,8,4,1,2]=>{{1,5,8},{2,6},{3,7},{4}}
[5,6,4,2,7,3,8,1]=>[8,4,6,7,5,3,2,1]=>[4,7,6,5,8,1,2,3]=>{{1,4,5,8},{2,7},{3,6}}
[5,4,7,2,8,3,6,1]=>[6,7,8,5,4,3,2,1]=>[7,6,5,8,1,2,3,4]=>{{1,7},{2,6},{3,5},{4,8}}
[3,8,1,5,4,7,2,6]=>[8,7,3,5,1,4,6,2]=>[3,5,7,8,4,1,2,6]=>{{1,3,7},{2,5},{4,8},{6}}
[7,8,3,1,4,6,5,2]=>[3,8,5,1,6,2,7,4]=>[7,3,5,2,6,4,8,1]=>{{1,7,8},{2,3,5,6},{4}}
[3,4,1,2,8,5,7,6]=>[4,1,3,2,8,7,5,6]=>[3,1,4,2,7,8,6,5]=>{{1,3,4},{2},{5,7},{6,8}}
[3,4,1,2,5,8,7,6]=>[4,1,3,2,5,7,8,6]=>[3,1,4,2,5,8,7,6]=>{{1,3,4},{2},{5},{6,8},{7}}
[6,7,3,1,4,5,8,2]=>[3,7,8,1,2,6,5,4]=>[7,6,3,2,4,8,1,5]=>{{1,7},{2,6,8},{3},{4},{5}}
[8,5,4,7,3,2,1,6]=>[2,3,7,5,8,1,4,6]=>[7,2,3,8,5,4,6,1]=>{{1,7},{2},{3},{4,8},{5},{6}}
[8,7,3,6,5,2,1,4]=>[2,5,6,1,7,4,8,3]=>[8,2,6,3,5,1,7,4]=>{{1,8},{2},{3,6},{4},{5},{7}}
[5,8,6,2,3,4,7,1]=>[7,6,2,3,5,8,4,1]=>[5,7,1,2,8,6,3,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[4,3,7,8,6,5,1,2]=>[5,1,4,3,6,8,7,2]=>[4,1,7,2,5,6,8,3]=>{{1,4},{2},{3,7,8},{5},{6}}
[7,5,4,3,8,2,1,6]=>[2,8,4,5,7,1,3,6]=>[4,2,8,5,7,3,6,1]=>{{1,4,5,7},{2},{3,8},{6}}
[5,7,8,6,1,2,4,3]=>[6,1,4,2,5,8,7,3]=>[4,1,5,3,7,6,8,2]=>{{1,4},{2},{3,5,7,8},{6}}
[2,4,8,6,1,5,7,3]=>[6,2,8,4,1,7,3,5]=>[2,6,4,8,3,7,5,1]=>{{1,2,6,7},{3,4,8},{5}}
[2,5,8,3,1,4,7,6]=>[3,2,8,1,5,7,4,6]=>[2,5,3,1,7,8,6,4]=>{{1,2,5,7},{3},{4},{6,8}}
[7,3,5,1,6,8,4,2]=>[5,4,8,7,3,2,6,1]=>[7,8,4,5,1,2,3,6]=>{{1,7},{2,8},{3,4,5},{6}}
[6,3,5,4,7,1,8,2]=>[7,8,6,5,3,4,1,2]=>[6,5,7,8,2,1,4,3]=>{{1,6},{2,5},{3,7},{4,8}}
[2,3,1,8,6,4,7,5]=>[3,2,1,6,8,7,5,4]=>[2,3,1,8,6,7,4,5]=>{{1,2,3},{4,8},{5,6,7}}
[2,3,4,7,5,1,8,6]=>[5,2,3,4,7,8,1,6]=>[2,3,4,8,5,7,6,1]=>{{1,2,3,4,8},{5},{6,7}}
[2,3,4,7,1,6,8,5]=>[7,2,3,4,8,1,6,5]=>[2,3,4,8,7,5,1,6]=>{{1,2,3,4,8},{5,7},{6}}
[2,3,4,6,1,8,7,5]=>[6,2,3,4,7,1,8,5]=>[2,3,4,8,6,5,7,1]=>{{1,2,3,4,8},{5,6},{7}}
[1,8,4,5,2,3,6,7]=>[1,5,2,8,4,3,6,7]=>[1,8,2,5,3,4,6,7]=>{{1},{2,8},{3},{4,5},{6},{7}}
[6,3,5,8,4,2,1,7]=>[2,4,8,6,3,1,5,7]=>[8,2,4,6,1,5,3,7]=>{{1,8},{2},{3,4,6},{5},{7}}
[2,5,7,4,6,3,8,1]=>[8,2,6,7,5,4,3,1]=>[2,5,7,6,8,1,3,4]=>{{1,2,5,8},{3,7},{4,6}}
[5,4,2,7,8,3,6,1]=>[6,4,5,8,3,2,7,1]=>[5,7,6,4,1,2,8,3]=>{{1,5},{2,7,8},{3,6},{4}}
[5,1,4,6,8,3,2,7]=>[5,3,8,1,4,6,2,7]=>[5,6,3,2,1,8,4,7]=>{{1,5},{2,6,8},{3},{4},{7}}
[8,1,3,5,4,6,2,7]=>[8,6,1,5,2,3,4,7]=>[5,6,2,8,4,3,1,7]=>{{1,5},{2,6},{3},{4,8},{7}}
[6,8,3,2,4,7,5,1]=>[5,3,7,2,8,6,1,4]=>[6,7,3,1,5,8,4,2]=>{{1,6,8},{2,7},{3},{4},{5}}
[8,7,2,4,5,6,3,1]=>[3,6,7,2,4,1,8,5]=>[8,6,3,1,2,5,7,4]=>{{1,8},{2,6},{3},{4},{5},{7}}
[5,3,6,2,4,8,7,1]=>[7,6,5,2,3,4,8,1]=>[5,6,8,2,3,1,7,4]=>{{1,5},{2,6},{3,8},{4},{7}}
[7,5,4,1,3,8,2,6]=>[4,5,1,7,8,3,6,2]=>[8,7,2,4,5,1,3,6]=>{{1,8},{2,7},{3},{4},{5},{6}}
[8,6,5,1,3,4,2,7]=>[5,4,1,3,6,8,2,7]=>[4,8,2,1,5,6,3,7]=>{{1,4},{2,8},{3},{5},{6},{7}}
[3,4,7,6,1,8,5,2]=>[6,5,3,4,7,8,2,1]=>[3,4,7,8,5,6,1,2]=>{{1,3,7},{2,4,8},{5},{6}}
[6,8,4,2,5,1,7,3]=>[5,4,8,7,2,6,3,1]=>[6,7,4,5,2,8,1,3]=>{{1,6,8},{2,7},{3,4,5}}
[8,3,6,4,7,1,2,5]=>[7,1,8,6,2,5,3,4]=>[7,1,6,8,4,2,5,3]=>{{1,7},{2},{3,6},{4,8},{5}}
[7,3,6,4,8,2,1,5]=>[2,8,7,6,1,5,3,4]=>[6,2,7,8,4,1,5,3]=>{{1,6},{2},{3,7},{4,8},{5}}
[5,1,7,4,2,8,6,3]=>[5,4,7,6,1,8,3,2]=>[7,8,4,5,3,6,1,2]=>{{1,7},{2,8},{3,4,5},{6}}
[8,6,4,7,1,5,2,3]=>[7,5,2,6,1,8,4,3]=>[5,8,1,7,4,6,2,3]=>{{1,5},{2,8},{3},{4,7},{6}}
[4,2,3,7,8,5,1,6]=>[5,4,2,3,8,1,7,6]=>[4,7,1,2,5,3,8,6]=>{{1,4},{2,7,8},{3},{5},{6}}
[5,1,6,4,2,3,7,8]=>[5,4,2,6,1,3,7,8]=>[5,6,1,4,3,2,7,8]=>{{1,5},{2,6},{3},{4},{7},{8}}
[8,4,7,6,1,5,2,3]=>[6,5,2,7,1,8,3,4]=>[7,8,1,5,4,6,3,2]=>{{1,7},{2,8},{3},{4,5},{6}}
[8,2,7,1,5,3,4,6]=>[7,8,5,3,1,2,6,4]=>[7,5,8,1,4,3,2,6]=>{{1,7},{2,5},{3,8},{4},{6}}
[6,3,7,1,5,4,2,8]=>[7,4,5,6,1,2,3,8]=>[4,7,6,5,3,2,1,8]=>{{1,4,5},{2,7},{3,6},{8}}
[7,1,6,4,5,8,3,2]=>[7,3,8,6,4,1,5,2]=>[6,7,3,8,1,5,2,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[3,5,1,4,7,6,8,2]=>[5,8,3,1,4,7,6,2]=>[5,3,7,2,1,8,4,6]=>{{1,5},{2,3,7},{4},{6,8}}
[5,3,1,8,4,6,7,2]=>[3,5,7,8,2,4,6,1]=>[8,7,3,5,2,1,4,6]=>{{1,8},{2,7},{3},{4,5},{6}}
[4,2,1,5,6,3,8,7]=>[2,4,6,1,5,3,8,7]=>[5,2,4,3,6,1,8,7]=>{{1,5,6},{2},{3,4},{7,8}}
[5,7,6,8,1,4,3,2]=>[8,3,4,1,5,7,6,2]=>[3,5,4,2,7,8,1,6]=>{{1,3,4},{2,5,7},{6,8}}
[3,1,4,5,2,8,7,6]=>[3,5,1,4,2,7,8,6]=>[4,3,2,5,1,8,7,6]=>{{1,4,5},{2,3},{6,8},{7}}
[4,8,3,5,6,7,1,2]=>[7,1,8,4,3,5,6,2]=>[7,1,4,8,2,3,5,6]=>{{1,7},{2},{3,4,8},{5},{6}}
[1,8,3,5,6,7,2,4]=>[1,7,8,2,4,5,3,6]=>[1,8,7,3,2,4,6,5]=>{{1},{2,8},{3,7},{4},{5},{6}}
[5,3,8,4,1,7,2,6]=>[4,8,7,5,1,3,2,6]=>[8,4,5,7,3,1,6,2]=>{{1,8},{2,4,7},{3,5},{6}}
[7,8,4,3,6,2,1,5]=>[2,6,4,8,1,3,7,5]=>[6,2,7,4,3,5,8,1]=>{{1,6},{2},{3,7,8},{4},{5}}
[7,3,6,1,8,2,4,5]=>[6,8,7,2,3,5,1,4]=>[8,6,7,2,3,1,5,4]=>{{1,8},{2,6},{3,7},{4},{5}}
[1,7,6,5,8,3,4,2]=>[1,4,8,3,6,7,5,2]=>[1,6,4,2,8,7,3,5]=>{{1},{2,6,7},{3,4},{5,8}}
[8,4,1,5,6,7,3,2]=>[4,3,8,7,1,2,6,5]=>[4,8,3,7,2,5,1,6]=>{{1,4,7},{2,8},{3},{5},{6}}
[4,1,8,5,6,7,3,2]=>[4,3,7,1,8,5,6,2]=>[4,8,3,2,7,1,5,6]=>{{1,4},{2,8},{3},{5,7},{6}}
[1,2,8,5,6,7,3,4]=>[1,2,7,3,8,5,6,4]=>[1,2,8,3,7,4,5,6]=>{{1},{2},{3,8},{4},{5,7},{6}}
[5,3,4,6,2,8,1,7]=>[8,6,5,3,4,2,1,7]=>[5,6,8,1,2,3,4,7]=>{{1,5},{2,6},{3,8},{4},{7}}
[8,5,6,4,1,7,2,3]=>[4,6,2,7,8,5,3,1]=>[8,7,1,4,6,2,3,5]=>{{1,8},{2,7},{3},{4},{5,6}}
[6,7,5,4,1,8,2,3]=>[4,5,2,7,8,6,1,3]=>[7,6,1,4,5,8,3,2]=>{{1,7},{2,6,8},{3},{4},{5}}
[4,2,1,6,3,7,8,5]=>[2,4,6,1,8,3,7,5]=>[7,2,4,3,6,5,8,1]=>{{1,7,8},{2},{3,4},{5,6}}
[4,2,1,3,7,8,6,5]=>[2,4,1,3,6,8,7,5]=>[4,2,1,3,7,6,8,5]=>{{1,4},{2},{3},{5,7,8},{6}}
[3,7,8,6,2,1,4,5]=>[2,6,3,1,4,8,7,5]=>[3,2,7,1,4,6,8,5]=>{{1,3,7,8},{2},{4},{5},{6}}
[7,3,4,2,6,8,5,1]=>[5,4,8,3,7,2,1,6]=>[5,8,4,1,7,2,6,3]=>{{1,5,7},{2,8},{3,4},{6}}
[3,6,7,5,2,4,1,8]=>[4,5,3,2,7,6,1,8]=>[4,3,6,1,5,7,2,8]=>{{1,4},{2,3,6,7},{5},{8}}
[4,2,1,3,8,6,7,5]=>[2,4,1,3,7,8,6,5]=>[4,2,1,3,8,7,5,6]=>{{1,4},{2},{3},{5,8},{6,7}}
[4,7,5,2,1,3,6,8]=>[2,5,1,4,7,3,6,8]=>[4,2,1,7,5,3,6,8]=>{{1,4,7},{2},{3},{5},{6},{8}}
[3,2,8,5,7,1,6,4]=>[7,3,2,6,8,1,5,4]=>[3,7,1,8,6,5,2,4]=>{{1,3},{2,7},{4,8},{5,6}}
[8,2,7,1,5,4,6,3]=>[7,8,6,5,1,2,3,4]=>[6,5,7,8,4,3,2,1]=>{{1,6},{2,5},{3,7},{4,8}}
[7,2,5,3,6,8,1,4]=>[8,7,5,1,4,3,2,6]=>[5,7,8,3,1,2,6,4]=>{{1,5},{2,7},{3,8},{4},{6}}
[1,2,3,4,8,5,7,6]=>[1,2,3,4,8,7,5,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,7},{6,8}}
[7,5,1,2,3,4,8,6]=>[5,1,2,3,7,8,4,6]=>[8,1,2,3,5,7,6,4]=>{{1,8},{2},{3},{4},{5},{6,7}}
[5,4,7,1,2,8,6,3]=>[7,1,6,5,4,8,2,3]=>[5,1,7,8,2,6,4,3]=>{{1,5},{2},{3,7},{4,8},{6}}
[8,6,5,1,2,3,7,4]=>[5,1,2,6,8,7,3,4]=>[8,1,2,6,5,7,4,3]=>{{1,8},{2},{3},{4,6,7},{5}}
[1,8,3,4,2,7,5,6]=>[1,4,8,3,7,5,2,6]=>[1,7,4,2,8,3,6,5]=>{{1},{2,7},{3,4},{5,8},{6}}
[8,7,2,3,1,6,5,4]=>[3,7,2,5,6,1,8,4]=>[5,3,1,8,6,4,7,2]=>{{1,5,6},{2,3},{4,8},{7}}
[6,2,3,1,5,4,7,8]=>[3,6,2,5,1,4,7,8]=>[5,3,1,6,4,2,7,8]=>{{1,5},{2,3},{4,6},{7},{8}}
[8,2,3,1,4,5,7,6]=>[3,8,2,1,4,7,5,6]=>[7,3,1,2,4,8,6,5]=>{{1,7},{2,3},{4},{5},{6,8}}
[1,6,5,7,2,3,8,4]=>[1,7,2,8,6,5,3,4]=>[1,7,2,6,8,3,5,4]=>{{1},{2,7},{3},{4,6},{5,8}}
[1,4,8,3,5,7,6,2]=>[1,6,7,4,3,8,2,5]=>[1,7,4,8,2,6,5,3]=>{{1},{2,7},{3,4,8},{5},{6}}
[1,4,8,2,3,5,7,6]=>[1,8,2,4,3,7,5,6]=>[1,4,2,7,3,8,6,5]=>{{1},{2,4,7},{3},{5},{6,8}}
[3,4,7,1,8,6,2,5]=>[7,6,3,4,2,8,1,5]=>[3,4,7,8,1,6,5,2]=>{{1,3,7},{2,4,8},{5},{6}}
[1,5,6,8,3,4,2,7]=>[1,4,8,3,5,6,2,7]=>[1,5,4,2,6,8,3,7]=>{{1},{2,5,6,8},{3,4},{7}}
[4,5,1,6,8,3,2,7]=>[5,3,8,4,1,6,2,7]=>[4,5,3,6,2,8,1,7]=>{{1,4,6,8},{2,5},{3},{7}}
[7,1,8,3,4,2,5,6]=>[7,4,8,3,2,5,1,6]=>[7,8,4,1,2,3,6,5]=>{{1,7},{2,8},{3,4},{5},{6}}
[2,5,7,8,1,6,3,4]=>[8,2,6,3,5,1,7,4]=>[2,5,6,1,7,4,8,3]=>{{1,2,5,7,8},{3,6},{4}}
[1,6,4,7,8,2,5,3]=>[1,8,5,6,2,4,7,3]=>[1,5,7,6,4,2,8,3]=>{{1},{2,5},{3,7,8},{4,6}}
[5,6,1,2,7,8,4,3]=>[6,1,4,8,5,2,7,3]=>[5,1,6,4,7,3,8,2]=>{{1,5,7,8},{2},{3,6},{4}}
[1,8,2,4,6,3,7,5]=>[1,8,6,2,7,4,3,5]=>[1,6,8,3,7,4,5,2]=>{{1},{2,6},{3,8},{4},{5,7}}
[6,2,5,4,8,3,7,1]=>[7,6,8,5,2,4,3,1]=>[6,7,5,8,3,1,2,4]=>{{1,6},{2,7},{3,5},{4,8}}
[4,5,3,7,1,6,2,8]=>[7,6,5,4,3,1,2,8]=>[4,5,6,7,1,3,2,8]=>{{1,4,7},{2,5},{3,6},{8}}
[1,3,7,2,8,6,4,5]=>[1,7,3,6,4,8,2,5]=>[1,3,7,8,2,6,5,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[4,3,6,5,7,8,1,2]=>[8,1,4,3,6,5,7,2]=>[4,1,6,2,7,3,8,5]=>{{1,4},{2},{3,6},{5,7,8}}
[8,2,6,7,4,5,3,1]=>[3,5,8,7,4,1,6,2]=>[8,5,3,7,1,4,2,6]=>{{1,8},{2,5},{3},{4,7},{6}}
[4,2,3,6,8,7,5,1]=>[5,4,2,3,7,6,8,1]=>[4,6,1,2,5,8,7,3]=>{{1,4},{2,6,8},{3},{5},{7}}
[4,6,8,2,7,5,3,1]=>[3,5,7,4,8,6,2,1]=>[6,4,3,7,5,8,1,2]=>{{1,6,8},{2,4,7},{3},{5}}
[2,1,6,8,4,7,5,3]=>[2,1,5,7,8,6,3,4]=>[2,1,7,6,5,8,4,3]=>{{1,2},{3,7},{4,6,8},{5}}
[2,8,6,4,7,5,3,1]=>[3,2,5,7,6,8,1,4]=>[2,8,3,5,7,6,4,1]=>{{1,2,8},{3},{4,5,7},{6}}
[4,8,6,2,7,5,3,1]=>[3,5,7,4,6,8,2,1]=>[5,4,3,8,7,6,1,2]=>{{1,5,7},{2,4,8},{3},{6}}
[7,1,6,3,5,8,4,2]=>[7,4,8,6,3,1,2,5]=>[6,8,4,7,1,5,3,2]=>{{1,6},{2,8},{3,4,7},{5}}
[7,3,1,2,5,8,6,4]=>[3,1,7,6,2,8,5,4]=>[7,1,3,8,4,6,2,5]=>{{1,7},{2},{3},{4,8},{5},{6}}
[8,1,6,3,4,5,7,2]=>[8,7,6,3,4,1,5,2]=>[6,7,8,1,2,5,3,4]=>{{1,6},{2,7},{3,8},{4},{5}}
[3,6,4,2,8,5,7,1]=>[7,4,3,6,8,2,5,1]=>[3,4,8,7,6,2,1,5]=>{{1,3,8},{2,4,7},{5,6}}
[3,7,8,5,6,1,2,4]=>[6,1,3,2,8,5,7,4]=>[3,1,7,2,6,4,8,5]=>{{1,3,7,8},{2},{4},{5,6}}
[4,7,8,1,3,2,6,5]=>[8,3,1,4,6,2,7,5]=>[3,4,2,6,7,5,8,1]=>{{1,3},{2,4,6},{5,7,8}}
[3,2,5,4,8,7,1,6]=>[7,3,2,5,4,1,8,6]=>[3,5,1,8,2,4,7,6]=>{{1,3},{2,5},{4,8},{6},{7}}
[5,4,2,1,3,8,7,6]=>[2,4,1,5,3,7,8,6]=>[5,2,1,4,3,8,7,6]=>{{1,5},{2},{3},{4},{6,8},{7}}
[5,4,1,3,2,8,7,6]=>[4,3,1,5,2,7,8,6]=>[3,5,2,4,1,8,7,6]=>{{1,3},{2,5},{4},{6,8},{7}}
[3,1,5,4,8,7,2,6]=>[3,7,1,5,4,2,8,6]=>[5,3,2,8,1,4,7,6]=>{{1,5},{2,3},{4,8},{6},{7}}
[3,4,1,5,8,7,2,6]=>[4,7,3,1,5,2,8,6]=>[4,3,5,2,8,1,7,6]=>{{1,4},{2,3,5,8},{6},{7}}
[4,3,6,8,2,1,7,5]=>[2,8,4,3,7,6,1,5]=>[4,2,6,1,7,8,5,3]=>{{1,4},{2},{3,6,8},{5,7}}
[5,3,1,4,2,8,7,6]=>[3,5,4,2,1,7,8,6]=>[5,3,4,1,2,8,7,6]=>{{1,5},{2,3,4},{6,8},{7}}
[3,4,2,5,8,7,1,6]=>[7,4,3,2,5,1,8,6]=>[3,4,5,1,8,2,7,6]=>{{1,3,5,8},{2,4},{6},{7}}
[8,3,5,6,2,4,1,7]=>[4,6,8,2,3,5,1,7]=>[8,6,4,2,1,3,5,7]=>{{1,8},{2,6},{3,4},{5},{7}}
[8,1,3,7,6,4,2,5]=>[8,4,1,6,3,7,5,2]=>[4,8,2,6,1,7,3,5]=>{{1,4,6,7},{2,8},{3},{5}}
[8,2,6,4,7,1,3,5]=>[7,8,1,6,2,5,4,3]=>[7,6,2,8,4,1,3,5]=>{{1,7},{2,6},{3},{4,8},{5}}
[2,5,7,6,3,1,8,4]=>[3,2,6,7,5,8,4,1]=>[2,7,3,5,8,6,1,4]=>{{1,2,7},{3},{4,5,8},{6}}
[4,2,1,8,7,5,6,3]=>[2,4,6,1,7,5,8,3]=>[8,2,4,3,6,1,7,5]=>{{1,8},{2},{3,4},{5,6},{7}}
[8,2,1,3,4,5,7,6]=>[2,8,1,3,4,7,5,6]=>[7,2,1,3,4,8,6,5]=>{{1,7},{2},{3},{4},{5},{6,8}}
[2,6,8,5,4,1,3,7]=>[4,2,1,5,8,6,3,7]=>[2,6,1,4,5,8,3,7]=>{{1,2,6,8},{3},{4},{5},{7}}
[5,4,8,7,3,2,6,1]=>[6,3,7,5,4,2,8,1]=>[5,6,3,8,1,2,7,4]=>{{1,5},{2,6},{3},{4,8},{7}}
[1,5,4,8,3,7,6,2]=>[1,6,7,5,4,8,2,3]=>[1,7,5,8,2,6,4,3]=>{{1},{2,7},{3,5},{4,8},{6}}
[3,7,6,2,5,8,1,4]=>[8,6,3,1,4,7,2,5]=>[3,6,8,2,1,7,5,4]=>{{1,3,8},{2,6,7},{4},{5}}
[6,3,2,8,7,5,1,4]=>[5,3,7,1,6,4,8,2]=>[5,8,3,2,6,1,7,4]=>{{1,5,6},{2,8},{3},{4},{7}}
[4,5,1,2,7,6,8,3]=>[5,1,8,4,2,7,6,3]=>[5,1,4,7,3,8,2,6]=>{{1,5},{2},{3,4,7},{6,8}}
[4,6,1,3,8,5,2,7]=>[6,5,1,4,8,3,2,7]=>[4,6,2,8,5,1,3,7]=>{{1,4,8},{2,6},{3},{5},{7}}
[3,4,2,6,8,7,1,5]=>[7,4,3,2,1,6,8,5]=>[3,4,6,1,2,8,7,5]=>{{1,3,6,8},{2,4},{5},{7}}
[8,4,2,3,6,5,7,1]=>[7,4,2,8,6,3,5,1]=>[6,7,1,4,8,3,2,5]=>{{1,6},{2,7},{3},{4},{5,8}}
[2,7,8,3,4,5,1,6]=>[5,2,8,3,4,1,7,6]=>[2,7,5,1,3,4,8,6]=>{{1,2,7,8},{3,5},{4},{6}}
[2,8,6,5,3,7,1,4]=>[7,2,5,1,6,8,3,4]=>[2,5,8,3,7,6,4,1]=>{{1,2,5,7},{3,8},{4},{6}}
[3,8,2,5,4,6,7,1]=>[7,8,3,5,2,4,6,1]=>[5,3,7,8,2,1,4,6]=>{{1,5},{2,3,7},{4,8},{6}}
[4,2,7,5,6,3,8,1]=>[8,4,6,2,7,5,3,1]=>[4,8,6,2,7,1,3,5]=>{{1,4},{2,8},{3,6},{5,7}}
[4,2,7,5,6,1,8,3]=>[6,4,8,2,7,5,1,3]=>[6,8,4,2,7,1,5,3]=>{{1,6},{2,8},{3,4},{5,7}}
[5,4,2,3,7,6,8,1]=>[8,4,2,5,3,7,6,1]=>[4,7,1,5,2,8,3,6]=>{{1,4,5},{2,7},{3},{6,8}}
[4,5,7,1,2,6,8,3]=>[7,1,8,4,5,2,6,3]=>[5,1,4,7,8,3,2,6]=>{{1,5,8},{2},{3,4,7},{6}}
[4,8,3,6,5,2,1,7]=>[2,5,6,4,8,1,3,7]=>[6,2,4,8,5,3,1,7]=>{{1,6},{2},{3,4,8},{5},{7}}
[7,5,6,1,2,8,4,3]=>[6,1,4,8,7,5,2,3]=>[6,1,8,4,7,2,5,3]=>{{1,6},{2},{3,8},{4},{5,7}}
[5,1,6,8,4,2,7,3]=>[5,4,8,7,1,6,3,2]=>[6,7,4,5,3,8,1,2]=>{{1,6,8},{2,7},{3,4,5}}
[7,6,8,3,2,5,4,1]=>[4,3,5,8,1,7,6,2]=>[5,7,3,4,2,8,1,6]=>{{1,5},{2,7},{3},{4},{6,8}}
[5,8,2,6,3,1,4,7]=>[3,6,8,1,5,4,2,7]=>[6,5,3,2,8,1,4,7]=>{{1,6},{2,5,8},{3},{4},{7}}
[8,1,3,5,4,2,6,7]=>[8,4,1,5,3,2,6,7]=>[4,8,2,5,1,3,6,7]=>{{1,4,5},{2,8},{3},{6},{7}}
[8,1,5,6,2,3,7,4]=>[8,6,2,7,1,4,5,3]=>[6,8,1,7,4,3,2,5]=>{{1,6},{2,8},{3},{4,7},{5}}
[7,3,1,6,2,5,4,8]=>[3,7,6,5,2,4,1,8]=>[6,3,5,7,2,1,4,8]=>{{1,6},{2,3,5},{4,7},{8}}
[5,7,6,4,1,3,8,2]=>[4,6,1,7,5,8,3,2]=>[7,5,2,4,8,6,1,3]=>{{1,7},{2,5,8},{3},{4},{6}}
[3,4,8,6,7,1,5,2]=>[7,5,3,4,1,8,6,2]=>[3,4,5,8,2,7,1,6]=>{{1,3,5},{2,4,8},{6,7}}
[8,1,7,2,5,6,3,4]=>[8,7,6,3,2,5,1,4]=>[6,7,8,1,3,2,5,4]=>{{1,6},{2,7},{3,8},{4},{5}}
[8,7,2,1,5,6,3,4]=>[2,7,6,3,1,5,8,4]=>[6,2,8,1,4,3,7,5]=>{{1,6},{2},{3,8},{4},{5},{7}}
[7,5,6,2,1,8,4,3]=>[2,6,4,8,7,5,1,3]=>[6,2,8,4,7,1,5,3]=>{{1,6},{2},{3,8},{4},{5,7}}
[8,7,5,2,1,6,4,3]=>[2,5,4,7,6,3,8,1]=>[5,2,8,4,6,1,7,3]=>{{1,5,6},{2},{3,8},{4},{7}}
[4,5,3,6,8,2,7,1]=>[7,8,5,4,3,6,2,1]=>[5,4,6,7,1,8,2,3]=>{{1,5},{2,4,7},{3,6,8}}
[4,6,8,1,5,3,7,2]=>[8,7,5,4,1,6,3,2]=>[4,5,6,7,3,8,1,2]=>{{1,4,7},{2,5},{3,6,8}}
[6,7,8,3,5,1,2,4]=>[5,1,8,2,3,6,7,4]=>[6,1,5,3,4,7,8,2]=>{{1,6,7,8},{2},{3,5},{4}}
[2,6,5,4,1,3,8,7]=>[4,2,1,5,6,3,8,7]=>[2,6,1,4,5,3,8,7]=>{{1,2,6},{3},{4},{5},{7,8}}
[6,2,3,5,1,4,8,7]=>[5,6,2,1,3,4,8,7]=>[6,5,1,3,4,2,8,7]=>{{1,6},{2,5},{3},{4},{7,8}}
[2,1,4,8,7,6,3,5]=>[2,1,6,4,3,7,8,5]=>[2,1,4,8,3,6,7,5]=>{{1,2},{3,4,8},{5},{6},{7}}
[7,4,6,8,5,3,2,1]=>[2,3,5,8,7,4,1,6]=>[8,2,3,5,7,1,6,4]=>{{1,8},{2},{3},{4,5,7},{6}}
[7,4,6,8,5,1,3,2]=>[5,3,1,8,7,4,2,6]=>[3,8,2,5,7,1,6,4]=>{{1,3},{2,8},{4,5,7},{6}}
[3,6,8,2,4,1,7,5]=>[4,8,3,2,7,6,1,5]=>[4,3,6,1,7,8,5,2]=>{{1,4},{2,3,6,8},{5,7}}
[5,8,4,1,6,7,2,3]=>[4,8,2,7,5,1,3,6]=>[7,4,1,5,8,3,6,2]=>{{1,7},{2,4,5,8},{3},{6}}
[8,3,6,2,5,4,1,7]=>[4,5,6,8,1,2,3,7]=>[8,6,5,4,3,2,1,7]=>{{1,8},{2,6},{3,5},{4},{7}}
[2,8,7,3,5,1,4,6]=>[5,2,7,1,3,4,8,6]=>[2,8,5,3,4,1,7,6]=>{{1,2,8},{3,5},{4},{6},{7}}
[2,1,6,8,5,4,7,3]=>[2,1,7,5,8,6,4,3]=>[2,1,6,7,5,8,3,4]=>{{1,2},{3,6,8},{4,7},{5}}
[8,3,1,6,7,2,5,4]=>[3,8,7,5,2,1,4,6]=>[7,3,5,8,2,4,6,1]=>{{1,7},{2,3,5},{4,8},{6}}
[7,3,6,1,2,5,4,8]=>[6,1,7,5,2,3,4,8]=>[6,1,5,7,4,3,2,8]=>{{1,6},{2},{3,5},{4,7},{8}}
[1,5,2,6,8,4,7,3]=>[1,5,7,8,2,6,4,3]=>[1,7,6,5,4,8,2,3]=>{{1},{2,7},{3,6,8},{4,5}}
[6,4,7,5,8,1,2,3]=>[8,1,2,6,7,4,5,3]=>[6,1,2,8,7,4,3,5]=>{{1,6},{2},{3},{4,8},{5,7}}
[7,4,8,1,6,3,5,2]=>[8,5,6,7,3,1,4,2]=>[5,8,7,6,2,4,1,3]=>{{1,5},{2,8},{3,7},{4,6}}
[1,6,4,5,2,3,7,8]=>[1,5,2,6,4,3,7,8]=>[1,6,2,5,3,4,7,8]=>{{1},{2,6},{3},{4,5},{7},{8}}
[1,7,4,5,2,3,6,8]=>[1,5,2,7,4,3,6,8]=>[1,7,2,5,3,4,6,8]=>{{1},{2,7},{3},{4,5},{6},{8}}
[1,7,3,4,2,5,6,8]=>[1,4,7,3,2,5,6,8]=>[1,7,4,2,3,5,6,8]=>{{1},{2,7},{3,4},{5},{6},{8}}
[1,7,3,4,2,6,5,8]=>[1,4,7,3,6,2,5,8]=>[1,6,4,2,7,5,3,8]=>{{1},{2,6},{3,4},{5,7},{8}}
[1,5,2,8,4,7,3,6]=>[1,5,7,8,2,3,4,6]=>[1,8,7,5,4,3,6,2]=>{{1},{2,8},{3,7},{4,5},{6}}
[1,8,4,7,3,5,2,6]=>[1,5,7,8,3,2,4,6]=>[1,8,7,5,3,4,6,2]=>{{1},{2,8},{3,7},{4,5},{6}}
[3,4,5,6,7,8,9,10,11,12,1,2]=>[12,1,3,4,5,6,7,8,9,10,11,2]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>{{1,3,4,5,6,7,8,9,10,11,12},{2}}
[8,6,4,7,2,1,3,5]=>[2,7,1,6,3,8,4,5]=>[7,2,1,8,4,6,5,3]=>{{1,7},{2},{3},{4,8},{5},{6}}
[1,6,4,7,2,8,3,5]=>[1,7,8,6,3,4,2,5]=>[1,7,6,8,3,4,5,2]=>{{1},{2,7},{3,6},{4,8},{5}}
[6,1,3,7,4,8,2,5]=>[6,8,1,7,3,5,4,2]=>[8,6,2,7,3,1,4,5]=>{{1,8},{2,6},{3},{4,7},{5}}
[3,8,7,5,1,2,4,6]=>[5,1,3,2,7,4,8,6]=>[3,1,8,2,5,4,7,6]=>{{1,3,8},{2},{4},{5},{6},{7}}
[8,6,2,3,1,7,4,5]=>[3,6,2,8,4,7,5,1]=>[8,3,1,6,2,7,4,5]=>{{1,8},{2,3},{4,6,7},{5}}
[1,5,8,7,2,3,4,6]=>[1,7,2,3,5,4,8,6]=>[1,5,2,3,8,4,7,6]=>{{1},{2,5,8},{3},{4},{6},{7}}
[5,7,1,3,8,2,4,6]=>[7,8,1,3,5,4,6,2]=>[7,5,2,1,8,3,4,6]=>{{1,7},{2,5,8},{3},{4},{6}}
[3,4,7,1,6,8,5,2]=>[7,5,3,4,8,1,6,2]=>[3,4,7,8,5,2,1,6]=>{{1,3,7},{2,4,8},{5},{6}}
[6,8,5,1,3,7,2,4]=>[5,8,1,3,7,6,2,4]=>[7,5,2,1,6,8,4,3]=>{{1,7},{2,5,6,8},{3},{4}}
[5,4,7,3,6,2,8,1]=>[8,6,7,5,4,3,2,1]=>[5,7,6,8,1,2,3,4]=>{{1,5},{2,7},{3,6},{4,8}}
[5,4,7,2,6,1,8,3]=>[6,7,8,5,4,2,1,3]=>[7,6,5,8,1,3,4,2]=>{{1,7},{2,6},{3,5},{4,8}}
[6,2,4,3,1,5,8,7]=>[3,4,6,1,2,5,8,7]=>[6,4,3,2,1,5,8,7]=>{{1,6},{2,4},{3},{5},{7,8}}
[5,4,7,3,6,2,1,8]=>[2,6,7,5,4,3,1,8]=>[6,2,5,7,1,3,4,8]=>{{1,6},{2},{3,5},{4,7},{8}}
[6,5,2,8,4,3,1,7]=>[3,4,8,5,6,2,1,7]=>[8,4,3,5,6,1,2,7]=>{{1,8},{2,4,5,6},{3},{7}}
[4,3,7,8,5,1,2,6]=>[5,1,4,3,8,2,7,6]=>[4,1,7,2,5,3,8,6]=>{{1,4},{2},{3,7,8},{5},{6}}
[5,3,2,8,6,4,1,7]=>[4,3,6,5,1,8,2,7]=>[4,8,3,5,2,6,1,7]=>{{1,4,5},{2,8},{3},{6},{7}}
[8,7,5,3,6,2,4,1]=>[4,6,5,2,7,3,8,1]=>[8,4,6,2,5,1,7,3]=>{{1,8},{2,4},{3,6},{5},{7}}
[6,4,5,3,8,2,7,1]=>[7,8,5,6,4,3,2,1]=>[6,5,8,7,1,2,3,4]=>{{1,6},{2,5},{3,8},{4,7}}
[6,5,8,3,4,2,7,1]=>[7,4,8,3,6,5,2,1]=>[6,7,4,1,8,2,3,5]=>{{1,6},{2,7},{3,4},{5,8}}
[7,4,8,3,5,2,6,1]=>[6,5,8,7,3,2,4,1]=>[7,8,5,6,2,3,1,4]=>{{1,7},{2,8},{3,5},{4,6}}
[6,5,8,4,7,2,3,1]=>[3,7,2,8,6,5,4,1]=>[7,3,1,6,8,2,4,5]=>{{1,7},{2,3},{4,6},{5,8}}
[5,4,6,3,8,2,7,1]=>[7,8,6,5,4,3,2,1]=>[6,5,7,8,1,2,3,4]=>{{1,6},{2,5},{3,7},{4,8}}
[3,2,1,8,5,7,4,6]=>[2,3,1,7,8,4,5,6]=>[3,2,1,8,7,5,6,4]=>{{1,3},{2},{4,8},{5,7},{6}}
[5,2,6,1,8,3,4,7]=>[6,5,8,3,2,1,4,7]=>[6,8,5,1,3,4,2,7]=>{{1,6},{2,8},{3,5},{4},{7}}
[3,2,1,8,6,4,7,5]=>[2,3,1,6,8,7,5,4]=>[3,2,1,8,6,7,4,5]=>{{1,3},{2},{4,8},{5,6,7}}
[3,2,1,8,4,6,5,7]=>[2,3,1,8,6,4,5,7]=>[3,2,1,6,8,5,4,7]=>{{1,3},{2},{4,6},{5,8},{7}}
[3,2,1,8,4,7,6,5]=>[2,3,1,8,6,7,4,5]=>[3,2,1,6,8,7,5,4]=>{{1,3},{2},{4,6,7},{5,8}}
[3,2,1,8,7,4,6,5]=>[2,3,1,7,6,4,8,5]=>[3,2,1,6,8,5,7,4]=>{{1,3},{2},{4,6},{5,8},{7}}
[7,3,8,4,5,6,2,1]=>[2,6,7,8,4,5,3,1]=>[8,2,7,6,1,3,4,5]=>{{1,8},{2},{3,7},{4,6},{5}}
[5,7,4,2,6,8,1,3]=>[8,4,1,7,5,3,2,6]=>[4,7,2,5,8,1,6,3]=>{{1,4,5,8},{2,7},{3},{6}}
[6,3,7,2,4,5,1,8]=>[5,7,6,2,3,1,4,8]=>[7,5,6,2,3,4,1,8]=>{{1,7},{2,5},{3,6},{4},{8}}
[5,6,3,4,2,1,8,7]=>[2,4,6,3,5,1,8,7]=>[5,2,4,1,6,3,8,7]=>{{1,5,6},{2},{3,4},{7,8}}
[6,3,4,2,1,5,8,7]=>[2,4,6,3,1,5,8,7]=>[6,2,4,1,3,5,8,7]=>{{1,6},{2},{3,4},{5},{7,8}}
[4,2,1,5,7,8,6,3]=>[2,4,6,1,5,8,7,3]=>[5,2,4,3,7,6,8,1]=>{{1,5,7,8},{2},{3,4},{6}}
[2,1,8,5,6,4,3,7]=>[2,1,4,6,8,5,3,7]=>[2,1,8,4,6,3,5,7]=>{{1,2},{3,8},{4},{5,6},{7}}
[7,6,2,4,1,8,5,3]=>[4,6,5,2,7,8,3,1]=>[8,4,7,2,5,6,1,3]=>{{1,8},{2,4},{3,7},{5},{6}}
[2,1,6,4,3,7,8,5]=>[2,1,4,6,8,3,7,5]=>[2,1,7,4,6,5,8,3]=>{{1,2},{3,7,8},{4},{5,6}}
[5,7,6,2,3,8,4,1]=>[4,8,2,6,5,7,1,3]=>[6,4,1,5,8,7,3,2]=>{{1,6,7},{2,4,5,8},{3}}
[8,4,2,3,7,5,6,1]=>[6,4,2,8,7,5,3,1]=>[6,8,1,4,7,2,3,5]=>{{1,6},{2,8},{3},{4},{5,7}}
[4,8,5,7,6,2,1,3]=>[2,6,1,4,7,8,3,5]=>[4,2,1,8,7,6,5,3]=>{{1,4,8},{2},{3},{5,7},{6}}
[7,5,6,1,8,4,2,3]=>[6,4,2,8,7,5,1,3]=>[6,8,1,4,7,2,5,3]=>{{1,6},{2,8},{3},{4},{5,7}}
[3,2,1,7,5,4,8,6]=>[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,7,6,4]=>{{1,3},{2},{4,8},{5},{6,7}}
[6,5,8,2,3,1,7,4]=>[3,8,2,7,6,5,1,4]=>[6,3,1,7,8,2,5,4]=>{{1,6},{2,3},{4,7},{5,8}}
[1,4,7,6,3,2,5,8]=>[1,3,6,4,2,7,5,8]=>[1,4,3,7,2,6,5,8]=>{{1},{2,4,7},{3},{5},{6},{8}}
[4,8,3,2,7,6,1,5]=>[6,3,7,4,1,8,5,2]=>[4,7,3,8,2,6,1,5]=>{{1,4,8},{2,7},{3},{5},{6}}
[2,6,7,8,3,4,1,5]=>[4,2,8,3,1,6,7,5]=>[2,6,4,1,3,7,8,5]=>{{1,2,6,7,8},{3,4},{5}}
[3,7,8,2,6,4,1,5]=>[4,6,3,8,1,5,7,2]=>[6,3,7,4,2,1,8,5]=>{{1,6},{2,3,7,8},{4},{5}}
[3,2,7,4,8,1,6,5]=>[8,3,2,7,6,1,4,5]=>[3,6,1,7,8,5,4,2]=>{{1,3},{2,6},{4,7},{5,8}}
[1,3,5,4,7,2,8,6]=>[1,7,3,5,4,8,2,6]=>[1,3,5,8,2,7,6,4]=>{{1},{2,3,5},{4,8},{6,7}}
[1,4,7,3,5,2,8,6]=>[1,5,7,4,3,8,2,6]=>[1,5,4,8,2,7,6,3]=>{{1},{2,5},{3,4,8},{6,7}}
[1,4,7,2,3,8,6,5]=>[1,7,2,4,6,8,3,5]=>[1,4,2,7,8,6,5,3]=>{{1},{2,4,7},{3},{5,8},{6}}
[1,3,5,2,8,7,6,4]=>[1,5,3,6,2,7,8,4]=>[1,3,8,5,4,6,7,2]=>{{1},{2,3,8},{4,5},{6},{7}}
[2,5,1,6,8,4,7,3]=>[5,2,7,8,1,6,4,3]=>[2,7,6,5,4,8,1,3]=>{{1,2,7},{3,6,8},{4,5}}
[4,6,7,8,2,3,1,5]=>[3,8,2,4,1,6,7,5]=>[4,3,1,6,2,7,8,5]=>{{1,4,6,7,8},{2,3},{5}}
[7,4,6,8,2,3,1,5]=>[3,8,2,7,1,5,4,6]=>[7,3,1,8,4,2,6,5]=>{{1,7},{2,3},{4,8},{5},{6}}
[7,6,4,8,2,3,1,5]=>[3,8,2,6,1,7,4,5]=>[6,3,1,8,4,7,5,2]=>{{1,6,7},{2,3},{4,8},{5}}
[3,1,7,6,4,2,8,5]=>[3,4,1,6,7,8,5,2]=>[8,3,2,4,7,6,1,5]=>{{1,8},{2,3},{4},{5,7},{6}}
[4,6,3,1,5,8,7,2]=>[3,6,7,4,1,2,8,5]=>[6,4,3,8,2,5,7,1]=>{{1,6},{2,4,8},{3},{5},{7}}
[2,6,5,3,8,1,7,4]=>[8,2,5,6,7,4,1,3]=>[2,5,8,7,6,1,4,3]=>{{1,2,5,6},{3,8},{4,7}}
[4,6,8,1,5,7,3,2]=>[8,3,7,4,1,6,5,2]=>[3,6,4,7,2,8,1,5]=>{{1,3,4,7},{2,6,8},{5}}
[4,6,1,8,5,7,3,2]=>[6,3,7,4,8,1,5,2]=>[4,7,3,8,6,5,1,2]=>{{1,4,8},{2,7},{3},{5,6}}
[6,5,2,8,7,3,1,4]=>[3,7,5,1,6,4,8,2]=>[8,3,5,2,6,1,7,4]=>{{1,8},{2,3,5,6},{4},{7}}
[4,1,6,8,3,7,5,2]=>[4,5,7,1,8,6,2,3]=>[7,6,4,3,5,8,2,1]=>{{1,7},{2,6,8},{3,4},{5}}
[6,4,1,8,7,3,5,2]=>[4,6,5,7,2,3,8,1]=>[8,5,6,4,2,1,7,3]=>{{1,8},{2,5},{3,6},{4},{7}}
[2,5,6,7,4,8,1,3]=>[8,2,1,7,5,6,4,3]=>[2,5,1,6,7,8,3,4]=>{{1,2,5,7},{3},{4,6,8}}
[2,6,7,3,4,8,5,1]=>[5,2,8,3,7,6,1,4]=>[2,7,5,1,6,8,4,3]=>{{1,2,7},{3,5,6,8},{4}}
[4,7,2,3,5,6,1,8]=>[6,7,2,4,3,5,1,8]=>[6,4,1,7,2,3,5,8]=>{{1,6},{2,4,7},{3},{5},{8}}
[4,6,2,3,5,7,1,8]=>[7,6,2,4,3,5,1,8]=>[4,6,1,7,2,3,5,8]=>{{1,4,7},{2,6},{3},{5},{8}}
[3,5,2,1,8,6,4,7]=>[2,5,3,6,1,8,4,7]=>[3,2,8,5,4,6,1,7]=>{{1,3,8},{2},{4,5},{6},{7}}
[4,1,8,2,3,5,7,6]=>[4,8,2,1,3,7,5,6]=>[7,4,1,3,2,8,6,5]=>{{1,7},{2,4},{3},{5},{6,8}}
[6,1,2,3,4,8,7,5]=>[6,1,2,3,7,4,8,5]=>[8,1,2,3,6,5,7,4]=>{{1,8},{2},{3},{4},{5,6},{7}}
[3,8,2,1,5,6,4,7]=>[2,8,3,6,1,5,4,7]=>[3,2,6,8,4,1,5,7]=>{{1,3,6},{2},{4,8},{5},{7}}
[2,4,7,8,1,5,3,6]=>[8,2,5,4,1,3,7,6]=>[2,4,5,7,3,1,8,6]=>{{1,2,4,7,8},{3,5},{6}}
[1,8,7,3,5,4,2,6]=>[1,4,5,7,2,3,8,6]=>[1,8,5,4,3,2,7,6]=>{{1},{2,8},{3,5},{4},{6},{7}}
[7,3,2,8,4,5,1,6]=>[5,3,7,8,4,2,6,1]=>[7,8,3,5,1,2,4,6]=>{{1,7},{2,8},{3},{4,5},{6}}
[7,1,8,3,5,4,2,6]=>[7,4,5,8,2,3,1,6]=>[5,8,7,4,2,1,6,3]=>{{1,5},{2,8},{3,7},{4},{6}}
[8,3,2,7,4,5,1,6]=>[5,3,8,7,4,2,6,1]=>[5,8,3,7,1,2,4,6]=>{{1,5},{2,8},{3},{4,7},{6}}
[8,6,2,3,4,7,1,5]=>[7,6,2,3,1,8,4,5]=>[7,8,1,2,4,6,5,3]=>{{1,7},{2,8},{3},{4},{5},{6}}
[5,8,7,3,4,6,1,2]=>[6,1,7,3,5,4,8,2]=>[6,1,5,2,8,3,7,4]=>{{1,6},{2},{3,5,8},{4},{7}}
[5,2,8,1,6,3,7,4]=>[8,5,6,7,2,1,3,4]=>[5,8,7,6,3,4,2,1]=>{{1,5},{2,8},{3,7},{4,6}}
[7,8,4,1,2,6,5,3]=>[4,1,8,5,6,3,7,2]=>[7,1,4,5,6,2,8,3]=>{{1,7,8},{2},{3,4,5,6}}
[7,8,6,5,1,2,4,3]=>[5,1,4,2,6,8,7,3]=>[4,1,7,3,5,6,8,2]=>{{1,4},{2},{3,7,8},{5},{6}}
[1,5,8,3,4,6,7,2]=>[1,7,8,3,5,4,6,2]=>[1,7,5,2,8,3,4,6]=>{{1},{2,7},{3,5,8},{4},{6}}
[8,1,4,7,2,5,3,6]=>[8,7,5,1,4,3,6,2]=>[5,7,8,3,1,2,4,6]=>{{1,5},{2,7},{3,8},{4},{6}}
[6,1,2,7,5,3,8,4]=>[6,1,5,7,8,2,4,3]=>[7,1,8,6,5,4,2,3]=>{{1,7},{2},{3,8},{4,6},{5}}
[8,1,6,3,5,7,2,4]=>[8,7,6,2,4,1,3,5]=>[6,7,8,2,1,5,4,3]=>{{1,6},{2,7},{3,8},{4},{5}}
[2,3,8,7,6,5,1,4]=>[5,2,3,1,6,7,8,4]=>[2,3,8,1,5,6,7,4]=>{{1,2,3,8},{4},{5},{6},{7}}
[3,2,8,4,7,6,1,5]=>[6,3,2,7,1,8,5,4]=>[3,8,1,7,4,6,2,5]=>{{1,3},{2,8},{4,7},{5},{6}}
[2,1,8,4,3,7,6,5]=>[2,1,4,8,6,7,3,5]=>[2,1,6,4,8,7,5,3]=>{{1,2},{3,6,7},{4},{5,8}}
[7,1,4,8,6,2,5,3]=>[7,6,5,1,4,8,3,2]=>[5,7,8,3,1,6,2,4]=>{{1,5},{2,7},{3,8},{4},{6}}
[7,2,4,8,3,6,1,5]=>[6,7,8,2,1,4,5,3]=>[8,7,6,2,4,3,1,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[3,4,2,6,7,8,1,5]=>[8,4,3,2,1,6,7,5]=>[3,4,6,1,2,7,8,5]=>{{1,3,6,7,8},{2,4},{5}}
[3,1,4,2,6,8,7,5]=>[3,4,1,2,7,6,8,5]=>[4,3,2,1,6,8,7,5]=>{{1,4},{2,3},{5,6,8},{7}}
[3,2,8,7,6,5,1,4]=>[5,3,2,1,6,7,8,4]=>[3,8,1,2,5,6,7,4]=>{{1,3},{2,8},{4},{5},{6},{7}}
[7,8,1,5,3,2,4,6]=>[8,3,5,2,1,4,7,6]=>[3,7,5,1,4,2,8,6]=>{{1,3,5},{2,7,8},{4},{6}}
[5,7,6,1,8,2,3,4]=>[6,7,2,3,5,8,4,1]=>[7,5,1,2,8,6,3,4]=>{{1,7},{2,5,8},{3},{4},{6}}
[6,7,3,8,1,2,4,5]=>[8,1,7,2,3,6,5,4]=>[6,1,7,3,4,8,2,5]=>{{1,6,8},{2},{3,7},{4},{5}}
[8,3,1,7,4,6,2,5]=>[3,8,6,7,2,5,1,4]=>[8,3,6,7,2,1,5,4]=>{{1,8},{2,3,6},{4,7},{5}}
[8,7,5,2,3,1,6,4]=>[3,5,2,7,6,4,8,1]=>[8,3,1,5,6,2,7,4]=>{{1,8},{2,3},{4,5,6},{7}}
[4,3,5,2,6,8,1,7]=>[8,5,4,3,2,6,1,7]=>[4,5,6,1,2,8,3,7]=>{{1,4},{2,5},{3,6,8},{7}}
[4,6,3,5,1,7,8,2]=>[5,8,6,4,3,1,7,2]=>[6,4,5,7,1,3,8,2]=>{{1,6},{2,4,7,8},{3,5}}
[4,6,3,5,7,2,8,1]=>[8,7,6,4,3,5,2,1]=>[4,6,7,8,1,2,3,5]=>{{1,4,8},{2,6},{3,7},{5}}
[5,2,3,6,7,4,8,1]=>[8,5,2,7,3,6,4,1]=>[5,7,1,6,3,8,2,4]=>{{1,5},{2,7},{3},{4,6,8}}
[6,3,7,2,4,5,8,1]=>[8,7,6,2,3,5,4,1]=>[6,7,8,2,3,1,4,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,2,4,6,8,1,3,5]=>[8,7,1,3,2,5,6,4]=>[7,8,2,1,4,3,5,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[3,7,2,4,6,8,1,5]=>[8,7,3,2,1,5,4,6]=>[3,7,8,1,4,2,6,5]=>{{1,3,8},{2,7},{4},{5},{6}}
[6,3,7,2,5,8,1,4]=>[8,7,6,1,3,5,2,4]=>[6,7,8,3,2,1,5,4]=>{{1,6},{2,7},{3,8},{4},{5}}
[6,3,5,7,2,8,1,4]=>[8,7,6,1,4,3,2,5]=>[6,7,8,3,1,4,5,2]=>{{1,6},{2,7},{3,8},{4},{5}}
[5,4,6,3,1,7,8,2]=>[3,6,8,5,4,2,7,1]=>[6,5,3,7,1,2,8,4]=>{{1,6},{2,5},{3},{4,7,8}}
[5,6,3,7,4,1,8,2]=>[4,7,8,6,5,1,2,3]=>[7,5,4,6,8,3,2,1]=>{{1,7},{2,5,8},{3,4,6}}
[5,6,3,7,8,1,2,4]=>[8,1,6,2,5,3,7,4]=>[5,1,6,3,7,4,8,2]=>{{1,5,7,8},{2},{3,6},{4}}
[7,4,5,2,6,1,8,3]=>[6,5,8,7,4,3,2,1]=>[7,8,5,6,1,2,3,4]=>{{1,7},{2,8},{3,5},{4,6}}
[7,4,5,6,1,2,8,3]=>[6,1,8,7,4,5,2,3]=>[8,1,6,7,2,3,5,4]=>{{1,8},{2},{3,6},{4,7},{5}}
[6,7,3,5,1,2,8,4]=>[5,1,7,8,3,6,2,4]=>[7,1,6,5,3,8,4,2]=>{{1,7},{2},{3,6,8},{4,5}}
[5,4,6,7,3,1,8,2]=>[3,7,8,5,4,6,2,1]=>[6,5,3,7,1,8,2,4]=>{{1,6,8},{2,5},{3},{4,7}}
[3,7,8,5,6,4,1,2]=>[4,1,3,6,8,5,7,2]=>[3,1,7,4,6,2,8,5]=>{{1,3,7,8},{2},{4},{5,6}}
[1,7,5,8,6,3,4,2]=>[1,4,6,3,8,7,2,5]=>[1,8,4,2,6,7,5,3]=>{{1},{2,8},{3,4},{5,6,7}}
[7,3,8,5,6,4,1,2]=>[4,1,6,7,8,5,2,3]=>[8,1,7,4,6,2,5,3]=>{{1,8},{2},{3,7},{4},{5,6}}
[3,5,7,8,6,4,1,2]=>[4,1,3,6,5,8,7,2]=>[3,1,5,4,7,6,8,2]=>{{1,3,5,7,8},{2},{4},{6}}
[7,3,5,8,6,1,4,2]=>[6,4,8,1,3,7,2,5]=>[6,8,4,3,1,7,5,2]=>{{1,6,7},{2,8},{3,4},{5}}
[5,1,7,8,3,6,4,2]=>[5,4,6,8,1,2,7,3]=>[6,7,5,4,3,2,8,1]=>{{1,6},{2,7,8},{3,5},{4}}
[7,8,1,5,3,6,4,2]=>[8,4,6,5,1,2,7,3]=>[4,7,5,6,3,2,8,1]=>{{1,4,6},{2,7,8},{3,5}}
[1,7,3,5,8,6,4,2]=>[1,4,6,8,3,7,5,2]=>[1,8,6,4,2,7,3,5]=>{{1},{2,8},{3,6,7},{4},{5}}
[5,7,3,4,1,8,6,2]=>[4,6,8,3,5,7,2,1]=>[6,5,4,1,8,7,2,3]=>{{1,6,7},{2,5,8},{3,4}}
[5,7,3,1,4,8,2,6]=>[3,7,8,1,5,4,2,6]=>[7,5,3,2,8,1,6,4]=>{{1,7},{2,5,8},{3},{4},{6}}
[6,1,4,3,5,2,8,7]=>[6,5,4,1,3,2,8,7]=>[4,5,6,3,1,2,8,7]=>{{1,4},{2,5},{3,6},{7,8}}
[5,1,4,6,3,2,8,7]=>[5,3,6,1,4,2,8,7]=>[5,6,3,2,1,4,8,7]=>{{1,5},{2,6},{3},{4},{7,8}}
[3,5,6,2,4,1,8,7]=>[4,6,3,2,5,1,8,7]=>[4,3,5,1,6,2,8,7]=>{{1,4},{2,3,5,6},{7,8}}
[5,4,7,6,2,8,1,3]=>[8,6,1,5,4,7,2,3]=>[5,6,2,8,1,7,4,3]=>{{1,5},{2,6,7},{3},{4,8}}
[2,1,8,4,6,7,3,5]=>[2,1,7,8,3,5,4,6]=>[2,1,8,7,4,3,6,5]=>{{1,2},{3,8},{4,7},{5},{6}}
[2,1,7,3,6,8,5,4]=>[2,1,7,5,8,3,6,4]=>[2,1,7,8,5,4,3,6]=>{{1,2},{3,7},{4,8},{5},{6}}
[2,1,5,7,8,4,6,3]=>[2,1,6,8,5,4,7,3]=>[2,1,6,5,7,3,8,4]=>{{1,2},{3,6},{4,5,7,8}}
[6,8,3,4,2,1,7,5]=>[2,4,8,3,7,6,1,5]=>[6,2,4,1,7,8,5,3]=>{{1,6,8},{2},{3,4},{5,7}}
[6,5,8,3,7,4,1,2]=>[4,1,7,8,6,5,2,3]=>[7,1,6,4,8,2,5,3]=>{{1,7},{2},{3,6},{4},{5,8}}
[4,8,6,3,1,5,7,2]=>[3,6,8,4,1,7,5,2]=>[6,4,3,8,2,7,1,5]=>{{1,6,7},{2,4,8},{3},{5}}
[3,5,7,2,8,6,1,4]=>[6,8,3,1,5,7,4,2]=>[5,3,6,2,8,7,1,4]=>{{1,5,8},{2,3,6,7},{4}}
[1,2,4,6,3,8,7,5]=>[1,2,6,4,7,3,8,5]=>[1,2,4,8,6,5,7,3]=>{{1},{2},{3,4,8},{5,6},{7}}
[5,6,3,1,8,7,4,2]=>[3,6,4,7,5,2,8,1]=>[6,3,5,4,8,1,7,2]=>{{1,6},{2,3,5,8},{4},{7}}
[7,4,2,5,1,8,6,3]=>[5,4,7,6,2,8,3,1]=>[7,8,4,5,2,6,1,3]=>{{1,7},{2,8},{3,4,5},{6}}
[2,4,8,7,1,3,6,5]=>[7,2,1,4,6,3,8,5]=>[2,4,1,6,8,5,7,3]=>{{1,2,4,6},{3},{5,8},{7}}
[7,4,1,2,8,6,5,3]=>[4,1,7,5,6,8,3,2]=>[8,1,4,5,7,6,2,3]=>{{1,8},{2},{3,4,5,7},{6}}
[5,2,8,1,3,7,6,4]=>[8,5,1,6,2,7,3,4]=>[5,8,2,6,4,7,3,1]=>{{1,5},{2,8},{3},{4,6,7}}
[2,1,7,4,8,6,3,5]=>[2,1,6,8,3,7,5,4]=>[2,1,8,6,4,7,3,5]=>{{1,2},{3,8},{4,6,7},{5}}
[5,8,3,1,7,4,6,2]=>[3,8,6,7,5,4,2,1]=>[7,3,5,6,8,1,2,4]=>{{1,7},{2,3,5,8},{4,6}}
[4,6,3,7,5,2,8,1]=>[8,5,7,4,6,2,3,1]=>[4,6,5,8,7,2,1,3]=>{{1,4,8},{2,6},{3,5,7}}
[3,5,7,8,2,6,1,4]=>[6,8,3,1,5,2,7,4]=>[5,3,6,2,7,4,8,1]=>{{1,5,7,8},{2,3,6},{4}}
[1,8,4,2,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[8,7,2,5,1,4,6,3]=>[5,7,6,1,2,4,8,3]=>[8,5,6,3,4,1,7,2]=>{{1,8},{2,5},{3,6},{4},{7}}
[1,6,4,8,5,2,7,3]=>[1,5,8,7,6,2,3,4]=>[1,8,5,6,7,4,3,2]=>{{1},{2,8},{3,5,7},{4,6}}
[7,1,8,5,6,2,3,4]=>[7,6,2,3,8,5,1,4]=>[7,8,1,2,6,3,5,4]=>{{1,7},{2,8},{3},{4},{5,6}}
[3,5,8,7,1,6,2,4]=>[7,6,3,2,5,1,8,4]=>[3,5,6,1,8,4,7,2]=>{{1,3,6},{2,5,8},{4},{7}}
[7,1,8,2,3,5,6,4]=>[7,8,2,6,3,5,1,4]=>[7,6,1,8,3,2,5,4]=>{{1,7},{2,6},{3},{4,8},{5}}
[8,3,7,4,5,1,6,2]=>[5,6,8,7,4,3,2,1]=>[8,7,5,6,1,2,3,4]=>{{1,8},{2,7},{3,5},{4,6}}
[8,7,4,2,5,6,1,3]=>[6,4,1,7,3,2,8,5]=>[6,8,2,4,1,5,7,3]=>{{1,6},{2,8},{3},{4},{5},{7}}
[2,8,7,3,5,6,1,4]=>[6,2,7,1,4,3,8,5]=>[2,8,6,3,1,5,7,4]=>{{1,2,8},{3,6},{4},{5},{7}}
[8,3,1,6,7,5,2,4]=>[3,8,5,2,7,1,4,6]=>[8,3,5,1,7,4,6,2]=>{{1,8},{2,3,5,7},{4},{6}}
[8,1,2,7,3,6,4,5]=>[8,1,7,6,4,3,2,5]=>[6,1,7,8,2,4,5,3]=>{{1,6},{2},{3,7},{4,8},{5}}
[8,1,7,2,6,3,4,5]=>[8,7,6,3,4,2,1,5]=>[6,7,8,1,2,4,5,3]=>{{1,6},{2,7},{3,8},{4},{5}}
[2,8,6,4,3,5,7,1]=>[7,2,4,6,3,8,5,1]=>[2,4,8,7,1,6,3,5]=>{{1,2,4,7},{3,8},{5},{6}}
[4,1,7,6,2,3,5,8]=>[4,6,2,1,3,7,5,8]=>[7,4,1,3,2,6,5,8]=>{{1,7},{2,4},{3},{5},{6},{8}}
[7,8,3,6,2,5,4,1]=>[4,5,6,8,1,2,7,3]=>[7,6,5,4,3,2,8,1]=>{{1,7,8},{2,6},{3,5},{4}}
[7,5,2,3,1,4,8,6]=>[3,5,2,1,7,8,4,6]=>[8,3,1,2,5,7,6,4]=>{{1,8},{2,3},{4},{5},{6,7}}
[5,4,8,7,3,1,2,6]=>[3,1,7,5,4,2,8,6]=>[5,1,3,8,2,4,7,6]=>{{1,5},{2},{3},{4,8},{6},{7}}
[6,5,3,4,1,2,8,7]=>[4,1,5,3,6,2,8,7]=>[6,1,4,2,5,3,8,7]=>{{1,6},{2},{3,4},{5},{7,8}}
[5,7,8,4,6,2,1,3]=>[2,6,1,8,5,4,7,3]=>[6,2,1,5,7,3,8,4]=>{{1,6},{2},{3},{4,5,7,8}}
[5,3,8,6,2,7,4,1]=>[4,7,6,5,1,8,3,2]=>[8,4,5,7,3,6,1,2]=>{{1,8},{2,4,7},{3,5},{6}}
[5,4,6,8,2,7,1,3]=>[7,8,1,5,4,6,2,3]=>[6,5,2,7,1,8,4,3]=>{{1,6,8},{2,5},{3},{4,7}}
[5,2,7,4,6,8,1,3]=>[8,5,1,7,2,4,6,3]=>[5,8,2,7,4,1,3,6]=>{{1,5},{2,8},{3},{4,7},{6}}
[5,3,6,7,1,8,4,2]=>[7,4,8,5,2,6,1,3]=>[5,7,4,6,2,8,3,1]=>{{1,5},{2,7},{3,4,6,8}}
[6,4,1,2,7,3,8,5]=>[4,1,6,7,8,3,2,5]=>[8,1,7,4,6,3,5,2]=>{{1,8},{2},{3,7},{4},{5,6}}
[7,8,2,4,1,5,3,6]=>[4,8,5,2,1,3,7,6]=>[7,4,5,2,3,1,8,6]=>{{1,7,8},{2,4},{3,5},{6}}
[4,5,2,6,1,7,3,8]=>[6,5,7,4,2,1,3,8]=>[5,6,4,7,2,3,1,8]=>{{1,5},{2,6},{3,4,7},{8}}
[4,5,3,7,6,8,1,2]=>[8,1,5,4,3,7,6,2]=>[4,1,5,7,2,8,3,6]=>{{1,4,7},{2},{3,5},{6,8}}
[3,5,2,7,6,4,8,1]=>[8,5,3,6,2,7,4,1]=>[3,5,8,6,2,7,1,4]=>{{1,3,8},{2,5},{4,6,7}}
[2,1,5,6,8,4,7,3]=>[2,1,7,8,5,6,4,3]=>[2,1,6,5,7,8,3,4]=>{{1,2},{3,6,8},{4,5,7}}
[2,1,5,6,8,7,3,4]=>[2,1,7,3,5,6,8,4]=>[2,1,5,3,6,8,7,4]=>{{1,2},{3,5,6,8},{4},{7}}
[5,3,2,1,6,4,7,8]=>[2,3,5,6,1,4,7,8]=>[6,2,3,5,4,1,7,8]=>{{1,6},{2},{3},{4,5},{7},{8}}
[3,5,7,2,8,6,4,1]=>[4,6,3,8,5,7,2,1]=>[5,3,6,4,8,7,1,2]=>{{1,5,8},{2,3,6,7},{4}}
[5,1,6,2,7,4,3,8]=>[5,6,4,7,1,2,3,8]=>[6,5,7,4,3,2,1,8]=>{{1,6},{2,5},{3,7},{4},{8}}
[5,4,1,6,2,7,3,8]=>[4,5,6,7,2,3,1,8]=>[7,6,5,4,2,1,3,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[5,3,2,6,7,4,1,8]=>[4,3,7,5,1,6,2,8]=>[4,6,3,5,2,7,1,8]=>{{1,4,5},{2,6,7},{3},{8}}
[3,4,2,6,7,1,5,8]=>[7,4,3,2,1,6,5,8]=>[3,4,6,1,2,7,5,8]=>{{1,3,6,7},{2,4},{5},{8}}
[3,5,6,2,4,7,1,8]=>[7,6,3,2,5,4,1,8]=>[3,5,6,1,7,2,4,8]=>{{1,3,6},{2,5,7},{4},{8}}
[3,5,8,7,2,4,6,1]=>[6,7,3,2,5,4,8,1]=>[5,3,6,1,8,2,7,4]=>{{1,5,8},{2,3,6},{4},{7}}
[2,5,6,4,7,1,3,8]=>[7,2,1,6,5,4,3,8]=>[2,5,1,6,7,3,4,8]=>{{1,2,5,7},{3},{4,6},{8}}
[1,4,5,3,7,8,2,6]=>[1,8,5,4,3,2,7,6]=>[1,4,5,7,2,3,8,6]=>{{1},{2,4,7,8},{3,5},{6}}
[1,4,8,2,7,6,3,5]=>[1,8,6,4,3,7,2,5]=>[1,4,6,8,2,7,5,3]=>{{1},{2,4,8},{3,6,7},{5}}
[4,7,3,5,1,8,6,2]=>[5,6,8,4,3,7,2,1]=>[6,5,4,8,1,7,2,3]=>{{1,6,7},{2,5},{3,4,8}}
[1,4,6,7,3,5,8,2]=>[1,8,7,4,3,6,5,2]=>[1,4,6,7,2,8,3,5]=>{{1},{2,4,7},{3,6,8},{5}}
[2,5,4,8,3,6,1,7]=>[6,2,8,5,4,3,1,7]=>[2,6,5,8,1,3,4,7]=>{{1,2,6},{3,5},{4,8},{7}}
[4,6,2,7,1,5,3,8]=>[7,6,5,4,1,2,3,8]=>[4,5,6,7,3,2,1,8]=>{{1,4,7},{2,5},{3,6},{8}}
[4,7,1,6,2,5,3,8]=>[7,6,5,4,2,1,3,8]=>[4,5,6,7,2,3,1,8]=>{{1,4,7},{2,5},{3,6},{8}}
[4,7,1,5,3,6,2,8]=>[7,6,5,4,1,3,2,8]=>[4,5,6,7,3,1,2,8]=>{{1,4,7},{2,5},{3,6},{8}}
[5,7,1,6,4,8,2,3]=>[7,8,2,6,5,1,4,3]=>[6,5,1,7,8,4,2,3]=>{{1,6},{2,5,8},{3},{4,7}}
[3,7,1,4,2,8,5,6]=>[7,4,3,1,8,5,2,6]=>[3,4,8,2,7,1,6,5]=>{{1,3,8},{2,4},{5,7},{6}}
[3,4,2,7,1,8,5,6]=>[7,4,3,2,8,5,1,6]=>[3,4,8,1,7,2,6,5]=>{{1,3,8},{2,4},{5,7},{6}}
[7,4,5,2,8,6,3,1]=>[3,6,5,8,4,7,2,1]=>[8,3,6,5,1,7,2,4]=>{{1,8},{2,3,6,7},{4,5}}
[1,5,8,2,7,3,6,4]=>[1,8,7,6,5,3,2,4]=>[1,5,6,7,8,3,4,2]=>{{1},{2,5,8},{3,6},{4,7}}
[5,8,4,7,2,3,6,1]=>[6,7,2,8,5,3,4,1]=>[7,6,1,5,8,3,2,4]=>{{1,7},{2,6},{3},{4,5,8}}
[7,5,3,8,2,6,4,1]=>[4,6,8,5,7,1,2,3]=>[8,5,4,7,6,3,2,1]=>{{1,8},{2,5,6},{3,4,7}}
[1,6,8,4,5,2,3,7]=>[1,5,2,8,4,6,3,7]=>[1,6,2,5,3,8,4,7]=>{{1},{2,6,8},{3},{4,5},{7}}
[1,6,8,2,3,7,4,5]=>[1,8,2,7,4,6,3,5]=>[1,6,2,7,3,8,5,4]=>{{1},{2,6,8},{3},{4,7},{5}}
[7,8,1,2,3,4,6,5]=>[8,1,2,3,6,4,7,5]=>[6,1,2,3,7,5,8,4]=>{{1,6},{2},{3},{4},{5,7,8}}
[2,8,5,3,1,4,6,7]=>[3,2,5,1,8,4,6,7]=>[2,8,3,1,5,4,6,7]=>{{1,2,8},{3},{4},{5},{6},{7}}
[6,1,2,4,7,3,8,5]=>[6,1,7,2,8,4,3,5]=>[8,1,7,3,6,4,5,2]=>{{1,8},{2},{3,7},{4},{5,6}}
[4,1,5,7,3,2,6,8]=>[4,3,7,1,5,2,6,8]=>[4,5,3,2,7,1,6,8]=>{{1,4},{2,5,7},{3},{6},{8}}
[4,1,7,8,6,2,3,5]=>[4,6,2,1,3,8,7,5]=>[7,4,1,3,2,6,8,5]=>{{1,7,8},{2,4},{3},{5},{6}}
[6,7,2,4,3,1,5,8]=>[3,4,7,1,2,6,5,8]=>[6,4,3,2,1,7,5,8]=>{{1,6,7},{2,4},{3},{5},{8}}
[7,6,2,4,3,1,5,8]=>[3,4,6,1,2,7,5,8]=>[7,4,3,2,1,6,5,8]=>{{1,7},{2,4},{3},{5},{6},{8}}
[1,5,7,3,4,6,8,2]=>[1,8,7,3,5,4,6,2]=>[1,5,7,2,8,3,4,6]=>{{1},{2,5,8},{3,7},{4},{6}}
[5,1,2,3,8,6,4,7]=>[5,1,2,6,3,8,4,7]=>[8,1,2,5,4,6,3,7]=>{{1,8},{2},{3},{4,5},{6},{7}}
[7,3,4,6,8,5,1,2]=>[5,1,8,3,7,4,2,6]=>[8,1,5,2,7,3,6,4]=>{{1,8},{2},{3,5,7},{4},{6}}
[2,1,7,6,8,5,3,4]=>[2,1,5,3,8,7,6,4]=>[2,1,7,3,5,8,4,6]=>{{1,2},{3,7},{4},{5},{6,8}}
[4,8,2,3,5,6,1,7]=>[6,8,2,4,3,5,1,7]=>[6,4,1,8,2,3,5,7]=>{{1,6},{2,4,8},{3},{5},{7}}
[7,2,8,1,3,6,5,4]=>[8,7,1,5,6,2,4,3]=>[5,6,2,8,7,4,1,3]=>{{1,5,7},{2,6},{3},{4,8}}
[8,2,4,3,5,1,7,6]=>[5,8,4,2,3,7,1,6]=>[5,4,7,2,1,8,6,3]=>{{1,5},{2,4},{3,7},{6,8}}
[5,7,8,4,2,6,3,1]=>[3,6,4,8,5,1,7,2]=>[6,3,5,4,7,2,8,1]=>{{1,6},{2,3,5,7,8},{4}}
[5,6,1,4,7,8,3,2]=>[6,3,8,1,5,4,7,2]=>[5,6,3,2,7,1,8,4]=>{{1,5,7,8},{2,6},{3},{4}}
[5,3,2,8,6,7,4,1]=>[4,3,7,5,1,8,6,2]=>[4,8,3,5,2,7,1,6]=>{{1,4,5},{2,8},{3},{6,7}}
[4,6,3,2,8,7,5,1]=>[5,3,7,4,6,1,8,2]=>[4,5,3,8,6,2,7,1]=>{{1,4,8},{2,5,6},{3},{7}}
[5,3,2,7,6,8,4,1]=>[4,3,8,5,1,7,6,2]=>[4,7,3,5,2,8,1,6]=>{{1,4,5},{2,7},{3},{6,8}}
[6,2,7,5,1,4,8,3]=>[5,7,6,1,8,3,2,4]=>[8,6,7,3,5,2,4,1]=>{{1,8},{2,6},{3,7},{4},{5}}
[2,5,8,4,3,7,6,1]=>[6,2,4,7,5,8,1,3]=>[2,5,7,4,8,6,3,1]=>{{1,2,5,8},{3,7},{4},{6}}
[2,6,8,4,7,3,5,1]=>[5,2,7,8,3,6,4,1]=>[2,7,6,5,3,8,1,4]=>{{1,2,7},{3,6,8},{4,5}}
[7,2,8,4,5,1,3,6]=>[5,7,1,8,4,3,2,6]=>[8,7,2,5,1,3,6,4]=>{{1,8},{2,7},{3},{4,5},{6}}
[2,6,5,8,3,4,1,7]=>[4,2,8,3,6,5,1,7]=>[2,6,4,1,8,3,5,7]=>{{1,2,6},{3,4},{5,8},{7}}
[6,2,5,7,4,1,3,8]=>[4,7,1,6,3,5,2,8]=>[7,4,2,6,1,3,5,8]=>{{1,7},{2,4,6},{3},{5},{8}}
[6,2,5,8,4,1,3,7]=>[4,8,1,6,3,5,2,7]=>[8,4,2,6,1,3,5,7]=>{{1,8},{2,4,6},{3},{5},{7}}
[3,5,6,2,1,7,8,4]=>[2,6,3,8,5,1,7,4]=>[3,2,6,5,7,4,8,1]=>{{1,3,6},{2},{4,5,7,8}}
[8,1,6,3,4,7,2,5]=>[8,7,6,3,2,1,4,5]=>[6,7,8,1,3,5,4,2]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,2,1,5,4,8,3,6]=>[2,7,8,5,1,4,6,3]=>[7,2,5,8,4,1,3,6]=>{{1,7},{2},{3,5},{4,8},{6}}
[3,2,7,5,4,8,1,6]=>[8,3,2,5,7,1,4,6]=>[3,5,1,8,7,4,6,2]=>{{1,3},{2,5,7},{4,8},{6}}
[1,8,5,4,7,3,2,6]=>[1,3,7,5,8,2,4,6]=>[1,7,3,8,5,4,6,2]=>{{1},{2,7},{3},{4,8},{5},{6}}
[8,6,4,2,7,5,1,3]=>[5,4,1,7,6,8,3,2]=>[5,8,2,4,7,6,1,3]=>{{1,5,7},{2,8},{3},{4},{6}}
[4,1,3,2,7,8,5,6]=>[4,3,1,2,8,5,7,6]=>[3,4,2,1,7,5,8,6]=>{{1,3},{2,4},{5,7,8},{6}}
[8,2,5,4,7,3,1,6]=>[3,7,8,5,2,1,6,4]=>[7,5,3,8,2,4,1,6]=>{{1,7},{2,5},{3},{4,8},{6}}
[7,2,3,5,4,8,1,6]=>[8,7,2,5,3,1,4,6]=>[5,7,1,8,3,4,6,2]=>{{1,5},{2,7},{3},{4,8},{6}}
[3,2,1,4,7,8,5,6]=>[2,3,1,4,8,5,7,6]=>[3,2,1,4,7,5,8,6]=>{{1,3},{2},{4},{5,7,8},{6}}
[6,4,2,5,1,8,3,7]=>[5,4,6,8,2,3,1,7]=>[6,8,5,4,2,1,3,7]=>{{1,6},{2,8},{3,5},{4},{7}}
[2,3,6,8,1,4,7,5]=>[8,2,3,1,7,6,4,5]=>[2,3,6,1,7,8,5,4]=>{{1,2,3,6,8},{4},{5,7}}
[2,6,8,1,5,7,3,4]=>[8,2,7,3,1,6,5,4]=>[2,6,7,1,4,8,3,5]=>{{1,2,6,8},{3,7},{4},{5}}
[7,3,6,1,2,8,4,5]=>[6,1,7,8,4,3,2,5]=>[8,1,7,6,2,4,5,3]=>{{1,8},{2},{3,7},{4,6},{5}}
[4,6,8,5,1,7,2,3]=>[5,8,2,4,7,6,3,1]=>[5,4,1,7,6,8,2,3]=>{{1,5,6,8},{2,4,7},{3}}
[5,8,4,1,7,2,3,6]=>[4,8,2,7,5,3,6,1]=>[7,4,1,5,8,2,3,6]=>{{1,7},{2,4,5,8},{3},{6}}
[6,5,1,7,2,3,8,4]=>[5,6,2,7,8,3,4,1]=>[8,7,1,6,5,3,2,4]=>{{1,8},{2,7},{3},{4,6},{5}}
[5,6,2,7,1,4,8,3]=>[7,6,8,1,5,2,4,3]=>[6,7,5,3,8,4,1,2]=>{{1,6},{2,7},{3,5,8},{4}}
[2,6,8,3,4,7,1,5]=>[7,2,8,3,1,6,4,5]=>[2,7,6,1,4,8,5,3]=>{{1,2,7},{3,6,8},{4},{5}}
[4,6,2,7,5,1,3,8]=>[5,7,1,4,6,3,2,8]=>[5,4,2,7,6,1,3,8]=>{{1,5,6},{2,4,7},{3},{8}}
[4,1,8,2,5,7,3,6]=>[4,8,7,1,2,5,6,3]=>[8,4,7,3,2,1,5,6]=>{{1,8},{2,4},{3,7},{5},{6}}
[2,6,4,1,5,3,8,7]=>[4,2,6,5,3,1,8,7]=>[2,6,4,5,1,3,8,7]=>{{1,2,6},{3,4,5},{7,8}}
[5,3,1,7,2,6,8,4]=>[3,5,7,8,2,1,6,4]=>[8,7,3,5,2,4,1,6]=>{{1,8},{2,7},{3},{4,5},{6}}
[6,1,8,4,2,7,3,5]=>[6,4,8,7,3,1,5,2]=>[7,8,4,6,1,5,2,3]=>{{1,7},{2,8},{3,4,6},{5}}
[3,8,6,4,5,7,1,2]=>[7,1,3,6,4,8,5,2]=>[3,1,7,8,2,6,4,5]=>{{1,3,7},{2},{4,8},{5},{6}}
[5,2,8,3,7,4,6,1]=>[6,5,8,7,2,4,3,1]=>[7,8,5,6,3,1,2,4]=>{{1,7},{2,8},{3,5},{4,6}}
[6,4,3,8,1,2,7,5]=>[8,1,4,6,7,3,2,5]=>[4,1,8,6,7,3,5,2]=>{{1,4,6},{2},{3,8},{5,7}}
[5,3,2,7,8,4,6,1]=>[6,3,5,8,2,4,7,1]=>[3,7,6,5,2,1,8,4]=>{{1,3,6},{2,7,8},{4,5}}
[8,1,3,7,4,2,5,6]=>[8,4,1,7,3,5,6,2]=>[4,8,2,7,1,3,5,6]=>{{1,4,7},{2,8},{3},{5},{6}}
[3,5,6,7,1,4,8,2]=>[7,8,3,1,5,6,4,2]=>[5,3,6,2,7,8,1,4]=>{{1,5,7},{2,3,6,8},{4}}
[1,4,5,2,8,6,7,3]=>[1,5,7,4,2,8,6,3]=>[1,5,4,8,3,7,2,6]=>{{1},{2,5},{3,4,8},{6,7}}
[5,4,1,2,8,6,7,3]=>[4,1,5,7,3,8,6,2]=>[8,1,5,4,2,7,3,6]=>{{1,8},{2},{3,5},{4},{6,7}}
[1,4,7,6,5,8,2,3]=>[1,8,2,4,6,7,5,3]=>[1,4,2,6,8,7,3,5]=>{{1},{2,4,6,7},{3},{5,8}}
[3,6,7,4,8,1,2,5]=>[8,1,3,7,2,6,4,5]=>[3,1,6,7,4,8,5,2]=>{{1,3,6,8},{2},{4,7},{5}}
[8,4,5,2,7,6,1,3]=>[6,5,1,7,4,8,3,2]=>[7,8,2,5,1,6,3,4]=>{{1,7},{2,8},{3},{4,5},{6}}
[5,7,2,3,6,8,1,4]=>[8,7,2,1,5,4,3,6]=>[5,7,1,3,8,2,6,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[7,5,2,8,4,1,3,6]=>[4,8,1,5,7,2,3,6]=>[8,4,2,5,7,3,6,1]=>{{1,8},{2,4,5,7},{3},{6}}
[3,7,6,4,1,8,2,5]=>[4,6,3,7,2,8,1,5]=>[7,3,8,4,1,6,5,2]=>{{1,7},{2,3,8},{4},{5},{6}}
[2,4,1,3,8,6,7,5]=>[4,2,1,3,7,8,6,5]=>[2,4,1,3,8,7,5,6]=>{{1,2,4},{3},{5,8},{6,7}}
[7,1,2,5,3,6,8,4]=>[7,1,5,8,2,3,6,4]=>[7,1,8,5,4,3,2,6]=>{{1,7},{2},{3,8},{4,5},{6}}
[6,1,5,8,2,3,7,4]=>[6,8,2,7,1,5,3,4]=>[8,6,1,7,4,2,5,3]=>{{1,8},{2,6},{3},{4,7},{5}}
[3,7,8,2,4,1,5,6]=>[4,8,3,2,1,5,7,6]=>[4,3,7,1,2,5,8,6]=>{{1,4},{2,3,7,8},{5},{6}}
[3,6,8,2,4,5,7,1]=>[7,8,3,2,4,6,5,1]=>[6,3,7,1,2,8,4,5]=>{{1,6,8},{2,3,7},{4},{5}}
[3,6,7,2,4,5,8,1]=>[8,7,3,2,4,6,5,1]=>[3,6,7,1,2,8,4,5]=>{{1,3,7},{2,6,8},{4},{5}}
[8,6,1,7,2,5,4,3]=>[6,8,4,5,2,7,3,1]=>[5,4,8,6,2,7,1,3]=>{{1,5},{2,4,6,7},{3,8}}
[5,2,1,8,7,3,4,6]=>[2,5,7,3,1,4,8,6]=>[8,2,5,1,4,3,7,6]=>{{1,8},{2},{3,5},{4},{6},{7}}
[6,5,2,7,4,3,8,1]=>[8,5,4,6,7,3,2,1]=>[4,7,8,5,6,1,2,3]=>{{1,4,5,6},{2,7},{3,8}}
[6,3,8,7,4,5,1,2]=>[5,1,6,7,4,3,8,2]=>[8,1,6,5,2,3,7,4]=>{{1,8},{2},{3,6},{4,5},{7}}
[4,8,7,6,5,2,3,1]=>[3,5,2,4,6,7,8,1]=>[4,3,1,8,5,6,7,2]=>{{1,4,8},{2,3},{5},{6},{7}}
[7,2,5,4,6,1,8,3]=>[6,7,8,5,2,3,4,1]=>[7,6,5,8,3,2,1,4]=>{{1,7},{2,6},{3,5},{4,8}}
[8,5,6,2,7,3,1,4]=>[3,7,6,1,8,5,4,2]=>[8,3,7,2,6,1,4,5]=>{{1,8},{2,3,7},{4},{5,6}}
[5,4,2,1,3,7,8,6]=>[2,4,1,5,3,8,7,6]=>[5,2,1,4,3,7,8,6]=>{{1,5},{2},{3},{4},{6,7,8}}
[5,8,6,4,1,3,2,7]=>[4,3,1,6,5,8,2,7]=>[3,5,2,4,8,6,1,7]=>{{1,3},{2,5,8},{4},{6},{7}}
[6,8,5,7,4,2,3,1]=>[3,4,2,7,8,6,5,1]=>[7,3,1,4,6,8,2,5]=>{{1,7},{2,3},{4},{5,6,8}}
[3,5,8,7,4,1,2,6]=>[4,1,3,7,5,2,8,6]=>[3,1,5,4,8,2,7,6]=>{{1,3,5,8},{2},{4},{6},{7}}
[3,8,5,2,4,6,7,1]=>[7,5,3,2,8,4,6,1]=>[3,7,8,1,5,2,4,6]=>{{1,3,8},{2,7},{4},{5},{6}}
[5,8,3,2,7,6,1,4]=>[6,3,7,1,5,8,4,2]=>[5,7,3,2,8,6,1,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[4,8,6,1,5,2,7,3]=>[6,5,8,4,1,7,3,2]=>[5,6,4,8,3,7,1,2]=>{{1,5},{2,6,7},{3,4,8}}
[2,6,4,8,5,1,7,3]=>[5,2,8,7,6,1,3,4]=>[2,8,5,6,7,4,3,1]=>{{1,2,8},{3,5,7},{4,6}}
[3,4,8,6,5,2,7,1]=>[7,5,3,4,6,8,2,1]=>[3,4,5,8,7,6,1,2]=>{{1,3,5,7},{2,4,8},{6}}
[6,1,5,7,2,4,8,3]=>[6,7,8,2,1,5,4,3]=>[8,7,6,2,4,1,3,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[8,4,6,5,7,1,3,2]=>[7,3,1,8,6,4,5,2]=>[3,7,2,6,8,4,1,5]=>{{1,3},{2,7},{4,6},{5,8}}
[7,2,1,4,5,8,3,6]=>[2,7,8,1,3,5,4,6]=>[8,2,7,3,4,1,6,5]=>{{1,8},{2},{3,7},{4},{5},{6}}
[7,6,1,5,4,8,3,2]=>[6,3,7,5,1,8,2,4]=>[5,7,3,8,4,6,2,1]=>{{1,5},{2,7},{3},{4,8},{6}}
[8,6,2,3,5,7,1,4]=>[7,6,2,1,4,8,3,5]=>[7,8,1,3,2,6,5,4]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,8,2,4,3,1,5,6]=>[3,4,8,1,2,5,7,6]=>[7,4,3,2,1,5,8,6]=>{{1,7,8},{2,4},{3},{5},{6}}
[7,2,4,1,6,3,8,5]=>[4,7,6,2,8,1,3,5]=>[8,4,7,2,6,5,3,1]=>{{1,8},{2,4},{3,7},{5,6}}
[6,3,2,1,4,8,5,7]=>[2,3,6,1,8,4,5,7]=>[8,2,3,1,6,5,4,7]=>{{1,8},{2},{3},{4},{5,6},{7}}
[7,1,8,3,5,4,6,2]=>[7,6,8,5,3,4,1,2]=>[6,7,5,8,2,1,4,3]=>{{1,6},{2,7},{3,5},{4,8}}
[7,6,1,8,5,4,3,2]=>[6,3,4,5,7,8,2,1]=>[3,8,4,7,5,6,1,2]=>{{1,3,4,7},{2,8},{5},{6}}
[8,3,7,4,5,6,1,2]=>[6,1,8,7,4,5,3,2]=>[8,1,6,7,2,3,4,5]=>{{1,8},{2},{3,6},{4,7},{5}}
[6,8,4,2,3,1,5,7]=>[3,4,2,8,1,6,5,7]=>[6,3,1,4,2,8,5,7]=>{{1,6,8},{2,3},{4},{5},{7}}
[6,5,8,1,3,7,2,4]=>[8,7,1,3,6,5,4,2]=>[6,7,2,1,8,3,4,5]=>{{1,6},{2,7},{3},{4},{5,8}}
[4,7,3,1,8,2,5,6]=>[3,7,8,4,2,5,6,1]=>[7,4,3,8,1,2,5,6]=>{{1,7},{2,4,8},{3},{5},{6}}
[8,3,1,7,2,4,5,6]=>[3,8,7,2,4,5,6,1]=>[8,3,7,1,2,4,5,6]=>{{1,8},{2,3,7},{4},{5},{6}}
[4,5,1,8,2,7,6,3]=>[5,8,6,4,1,7,2,3]=>[6,4,5,8,3,7,2,1]=>{{1,6,7},{2,4,8},{3,5}}
[4,8,5,3,1,7,6,2]=>[3,5,8,4,6,7,1,2]=>[5,4,3,8,6,7,2,1]=>{{1,5,6,7},{2,4,8},{3}}
[5,6,1,7,8,2,4,3]=>[6,8,4,2,5,1,7,3]=>[5,4,6,2,7,3,8,1]=>{{1,5,7,8},{2,4},{3,6}}
[4,8,6,1,7,5,3,2]=>[6,3,5,4,8,7,2,1]=>[3,6,4,8,5,7,1,2]=>{{1,3,4,8},{2,6,7},{5}}
[5,6,7,1,3,8,2,4]=>[7,8,1,3,5,6,4,2]=>[6,5,2,1,7,8,3,4]=>{{1,6,8},{2,5,7},{3},{4}}
[7,5,4,2,3,8,1,6]=>[8,4,2,5,7,1,3,6]=>[4,8,1,5,7,3,6,2]=>{{1,4,5,7},{2,8},{3},{6}}
[7,1,3,8,5,6,2,4]=>[7,6,1,3,8,5,4,2]=>[7,8,2,1,6,3,4,5]=>{{1,7},{2,8},{3},{4},{5,6}}
[3,7,1,5,8,6,2,4]=>[7,6,3,2,1,8,5,4]=>[3,7,8,1,4,6,2,5]=>{{1,3,8},{2,7},{4},{5},{6}}
[5,3,7,8,4,6,1,2]=>[6,1,5,8,3,4,7,2]=>[6,1,7,5,3,2,8,4]=>{{1,6},{2},{3,7,8},{4,5}}
[1,5,3,7,8,4,2,6]=>[1,4,8,5,2,3,7,6]=>[1,7,4,5,3,2,8,6]=>{{1},{2,7,8},{3,4,5},{6}}
[6,4,2,5,1,3,8,7]=>[5,4,1,6,2,3,8,7]=>[5,6,2,4,3,1,8,7]=>{{1,5},{2,6},{3},{4},{7,8}}
[4,2,3,8,1,5,6,7]=>[8,4,2,3,1,5,6,7]=>[4,8,1,2,3,5,6,7]=>{{1,4},{2,8},{3},{5},{6},{7}}
[5,7,4,3,8,1,6,2]=>[8,6,4,7,5,1,3,2]=>[4,6,7,5,8,3,1,2]=>{{1,4,5,8},{2,6},{3,7}}
[2,1,6,7,5,3,8,4]=>[2,1,5,7,8,6,4,3]=>[2,1,7,6,5,8,3,4]=>{{1,2},{3,7},{4,6,8},{5}}
[1,4,8,5,7,6,2,3]=>[1,6,2,4,7,8,3,5]=>[1,4,2,8,7,6,5,3]=>{{1},{2,4,8},{3},{5,7},{6}}
[7,8,3,2,6,1,4,5]=>[6,3,8,1,2,5,7,4]=>[6,7,3,2,4,1,8,5]=>{{1,6},{2,7,8},{3},{4},{5}}
[7,8,1,4,5,6,3,2]=>[8,3,6,1,2,4,7,5]=>[3,7,6,2,4,5,8,1]=>{{1,3,6},{2,7,8},{4},{5}}
[6,2,4,8,1,5,3,7]=>[8,6,5,2,1,4,3,7]=>[5,6,8,2,4,1,3,7]=>{{1,5},{2,6},{3,8},{4},{7}}
[2,4,1,8,6,5,3,7]=>[4,2,5,1,6,8,3,7]=>[2,8,4,3,5,6,1,7]=>{{1,2,8},{3,4},{5},{6},{7}}
[3,2,7,8,5,1,4,6]=>[5,3,2,1,8,4,7,6]=>[3,7,1,2,5,4,8,6]=>{{1,3},{2,7,8},{4},{5},{6}}
[1,8,7,5,3,2,4,6]=>[1,3,5,2,7,4,8,6]=>[1,8,3,2,5,4,7,6]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[1,8,7,4,2,5,3,6]=>[1,4,7,5,3,2,8,6]=>[1,8,4,5,2,3,7,6]=>{{1},{2,8},{3,4,5},{6},{7}}
[1,5,3,8,7,4,2,6]=>[1,4,7,5,2,3,8,6]=>[1,8,4,5,3,2,7,6]=>{{1},{2,8},{3,4,5},{6},{7}}
[2,3,1,8,7,5,4,6]=>[3,2,1,5,7,4,8,6]=>[2,3,1,8,5,4,7,6]=>{{1,2,3},{4,8},{5},{6},{7}}
[8,6,3,5,7,4,2,1]=>[2,4,7,6,3,8,1,5]=>[8,2,4,7,1,6,5,3]=>{{1,8},{2},{3,4,7},{5},{6}}
[1,8,6,3,5,7,4,2]=>[1,4,7,6,3,8,2,5]=>[1,8,4,7,2,6,5,3]=>{{1},{2,8},{3,4,7},{5},{6}}
[1,8,6,3,2,4,7,5]=>[1,3,6,2,8,7,5,4]=>[1,8,3,2,6,7,4,5]=>{{1},{2,8},{3},{4},{5,6,7}}
[2,4,5,1,3,8,7,6]=>[5,2,1,4,3,7,8,6]=>[2,4,1,5,3,8,7,6]=>{{1,2,4,5},{3},{6,8},{7}}
[1,7,5,8,6,3,2,4]=>[1,3,6,2,8,7,4,5]=>[1,8,3,2,6,7,5,4]=>{{1},{2,8},{3},{4},{5,6,7}}
[4,1,8,6,3,2,7,5]=>[4,3,6,1,8,7,5,2]=>[4,8,3,2,6,7,1,5]=>{{1,4},{2,8},{3},{5,6,7}}
[7,4,6,3,1,8,5,2]=>[3,6,5,8,7,4,1,2]=>[8,3,7,5,6,1,4,2]=>{{1,8},{2,3,7},{4,5,6}}
[6,3,1,7,4,8,5,2]=>[3,6,5,8,7,2,1,4]=>[8,3,7,5,6,2,4,1]=>{{1,8},{2,3,7},{4,5,6}}
[3,6,5,2,1,4,8,7]=>[2,5,3,1,6,4,8,7]=>[3,2,6,1,5,4,8,7]=>{{1,3,6},{2},{4},{5},{7,8}}
[2,1,5,8,7,4,3,6]=>[2,1,4,7,5,3,8,6]=>[2,1,5,4,8,3,7,6]=>{{1,2},{3,5,8},{4},{6},{7}}
[5,1,7,4,8,3,2,6]=>[5,3,8,7,1,2,4,6]=>[5,8,3,7,4,2,6,1]=>{{1,5},{2,8},{3},{4,7},{6}}
[3,7,8,2,4,1,6,5]=>[4,8,3,2,6,1,7,5]=>[4,3,6,1,7,5,8,2]=>{{1,4},{2,3,6},{5,7,8}}
[6,2,8,4,1,7,3,5]=>[4,8,6,7,3,5,2,1]=>[8,4,7,6,1,2,3,5]=>{{1,8},{2,4,6},{3,7},{5}}
[7,3,4,8,1,6,2,5]=>[8,6,7,3,2,1,4,5]=>[6,8,7,1,3,5,4,2]=>{{1,6},{2,8},{3,7},{4},{5}}
[6,3,4,8,1,7,2,5]=>[8,7,6,3,2,4,1,5]=>[6,7,8,1,3,4,5,2]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,2,8,5,6,1,3,4]=>[6,7,1,2,8,5,4,3]=>[8,7,2,3,6,1,4,5]=>{{1,8},{2,7},{3},{4},{5,6}}
[1,8,5,7,6,2,3,4]=>[1,6,2,3,7,8,4,5]=>[1,8,2,3,7,6,5,4]=>{{1},{2,8},{3},{4},{5,7},{6}}
[6,3,8,7,5,1,2,4]=>[5,1,7,2,6,4,8,3]=>[8,1,5,3,6,2,7,4]=>{{1,8},{2},{3,5,6},{4},{7}}
[3,7,6,8,1,5,2,4]=>[8,5,3,2,1,7,6,4]=>[3,5,7,1,4,8,2,6]=>{{1,3,7},{2,5},{4},{6,8}}
[3,7,2,1,8,6,4,5]=>[2,7,3,6,4,8,1,5]=>[3,2,7,8,1,6,5,4]=>{{1,3,7},{2},{4,8},{5},{6}}
[3,6,5,8,1,4,7,2]=>[8,7,3,1,6,5,4,2]=>[3,6,7,2,8,1,4,5]=>{{1,3,7},{2,6},{4},{5,8}}
[3,5,1,6,8,4,7,2]=>[5,7,3,8,1,6,4,2]=>[6,3,7,5,4,8,1,2]=>{{1,6,8},{2,3,7},{4,5}}
[8,3,2,5,1,6,7,4]=>[5,3,8,7,2,1,6,4]=>[5,8,3,7,2,4,1,6]=>{{1,5},{2,8},{3},{4,7},{6}}
[2,5,8,1,6,4,7,3]=>[8,2,7,6,5,1,4,3]=>[2,5,6,7,8,4,1,3]=>{{1,2,5,8},{3,6},{4,7}}
[3,6,5,8,4,1,7,2]=>[4,8,3,7,6,5,2,1]=>[4,3,7,6,8,1,2,5]=>{{1,4,6},{2,3,7},{5,8}}
[7,1,8,6,2,4,3,5]=>[7,6,4,2,3,8,1,5]=>[4,7,8,2,1,6,5,3]=>{{1,4},{2,7},{3,8},{5},{6}}
[7,1,6,2,8,5,3,4]=>[7,6,5,3,8,1,2,4]=>[6,7,8,1,5,4,3,2]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,2,4,3,5,1,8,6]=>[5,7,4,2,3,8,1,6]=>[5,4,8,2,1,7,6,3]=>{{1,5},{2,4},{3,8},{6,7}}
[6,2,1,5,3,8,4,7]=>[2,6,5,8,1,3,4,7]=>[6,2,8,5,4,3,1,7]=>{{1,6},{2},{3,8},{4,5},{7}}
[7,1,6,3,4,2,8,5]=>[7,4,6,3,8,1,2,5]=>[4,8,7,1,6,5,3,2]=>{{1,4},{2,8},{3,7},{5,6}}
[7,4,1,5,8,3,2,6]=>[4,3,7,8,1,5,2,6]=>[7,8,3,4,2,1,6,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[4,6,7,1,5,8,3,2]=>[7,3,8,4,1,6,5,2]=>[4,6,3,7,2,8,1,5]=>{{1,4,7},{2,6,8},{3},{5}}
[7,6,4,8,3,2,5,1]=>[5,3,8,6,2,7,4,1]=>[5,8,3,6,2,7,1,4]=>{{1,5},{2,8},{3},{4,6,7}}
[3,6,8,2,1,5,7,4]=>[2,8,3,7,1,6,5,4]=>[3,2,6,7,4,8,1,5]=>{{1,3,6,8},{2},{4,7},{5}}
[8,7,3,6,4,2,1,5]=>[2,4,6,7,1,5,8,3]=>[8,2,6,4,3,1,7,5]=>{{1,8},{2},{3,6},{4},{5},{7}}
[3,7,8,5,4,1,2,6]=>[4,1,3,5,8,2,7,6]=>[3,1,7,4,5,2,8,6]=>{{1,3,7,8},{2},{4},{5},{6}}
[7,8,3,6,2,1,4,5]=>[2,6,8,1,3,5,7,4]=>[7,2,6,3,4,1,8,5]=>{{1,7,8},{2},{3,6},{4},{5}}
[6,5,7,3,8,2,1,4]=>[2,8,7,1,6,5,3,4]=>[6,2,7,3,8,1,5,4]=>{{1,6},{2},{3,7},{4},{5,8}}
[8,1,4,7,2,5,6,3]=>[8,7,6,1,3,4,5,2]=>[6,7,8,3,2,4,1,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[2,3,6,5,8,1,4,7]=>[8,2,3,1,6,5,4,7]=>[2,3,6,1,8,4,5,7]=>{{1,2,3,6},{4},{5,8},{7}}
[1,2,3,7,6,8,4,5]=>[1,2,3,8,4,7,6,5]=>[1,2,3,7,4,8,5,6]=>{{1},{2},{3},{4,7},{5},{6,8}}
[1,2,3,7,8,4,6,5]=>[1,2,3,8,6,4,7,5]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,6},{5,7,8}}
[1,2,3,6,8,4,7,5]=>[1,2,3,8,7,6,4,5]=>[1,2,3,6,7,8,5,4]=>{{1},{2},{3},{4,6,8},{5,7}}
[7,4,3,8,6,2,5,1]=>[5,6,4,8,2,7,1,3]=>[6,5,8,4,2,7,3,1]=>{{1,6,7},{2,5},{3,8},{4}}
[2,6,8,5,4,7,3,1]=>[3,2,7,5,8,6,4,1]=>[2,6,3,7,5,8,1,4]=>{{1,2,6,8},{3},{4,7},{5}}
[4,3,7,8,5,6,2,1]=>[2,6,4,3,8,5,7,1]=>[4,2,7,1,6,3,8,5]=>{{1,4},{2},{3,7,8},{5,6}}
[3,2,8,6,7,4,5,1]=>[5,3,2,7,4,8,6,1]=>[3,8,1,5,2,7,4,6]=>{{1,3},{2,8},{4,5},{6,7}}
[2,6,8,4,5,7,3,1]=>[3,2,7,8,4,6,5,1]=>[2,7,3,6,1,8,4,5]=>{{1,2,7},{3},{4,6,8},{5}}
[4,2,7,1,3,8,5,6]=>[7,4,1,2,8,5,3,6]=>[4,8,2,3,7,1,6,5]=>{{1,4},{2,8},{3},{5,7},{6}}
[4,2,5,1,3,8,6,7]=>[5,4,1,2,3,8,6,7]=>[4,5,2,3,1,8,6,7]=>{{1,4},{2,5},{3},{6,8},{7}}
[8,5,7,1,3,4,6,2]=>[7,6,1,2,8,3,5,4]=>[7,8,2,3,6,5,1,4]=>{{1,7},{2,8},{3},{4},{5,6}}
[6,8,1,3,7,4,5,2]=>[8,5,1,7,4,6,3,2]=>[5,7,2,6,1,8,3,4]=>{{1,5},{2,7},{3},{4,6,8}}
[7,2,8,1,6,3,4,5]=>[8,7,6,3,4,1,2,5]=>[6,7,8,1,2,5,4,3]=>{{1,6},{2,7},{3,8},{4},{5}}
[3,8,7,1,2,4,6,5]=>[7,1,3,2,6,4,8,5]=>[3,1,6,2,8,5,7,4]=>{{1,3,6},{2},{4},{5,8},{7}}
[4,8,7,1,2,3,6,5]=>[7,1,2,4,6,3,8,5]=>[4,1,2,6,8,5,7,3]=>{{1,4,6},{2},{3},{5,8},{7}}
[1,2,8,7,5,4,3,6]=>[1,2,4,5,7,3,8,6]=>[1,2,8,4,5,3,7,6]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[3,4,8,7,5,6,1,2]=>[6,1,3,4,7,5,8,2]=>[3,1,4,8,6,2,7,5]=>{{1,3,4,8},{2},{5,6},{7}}
[4,6,7,5,2,1,8,3]=>[2,5,7,4,8,6,3,1]=>[6,2,4,7,5,8,1,3]=>{{1,6,8},{2},{3,4,7},{5}}
[3,8,6,5,2,7,1,4]=>[7,5,3,1,6,8,2,4]=>[3,5,8,2,7,6,4,1]=>{{1,3,8},{2,5,7},{4},{6}}
[8,6,1,4,2,3,7,5]=>[6,4,2,1,8,7,5,3]=>[4,8,1,3,6,7,2,5]=>{{1,4},{2,8},{3},{5,6,7}}
[1,4,7,3,6,2,8,5]=>[1,6,7,4,8,3,2,5]=>[1,7,4,8,6,3,5,2]=>{{1},{2,7},{3,4,8},{5,6}}
[6,1,8,3,4,2,7,5]=>[6,4,8,3,7,1,2,5]=>[6,8,4,1,7,5,3,2]=>{{1,6},{2,8},{3,4},{5,7}}
[3,8,6,5,4,2,1,7]=>[2,4,3,5,6,8,1,7]=>[3,2,8,4,5,6,1,7]=>{{1,3,8},{2},{4},{5},{6},{7}}
[7,3,8,1,2,6,4,5]=>[8,1,7,6,4,2,3,5]=>[6,1,7,8,2,5,4,3]=>{{1,6},{2},{3,7},{4,8},{5}}
[2,1,8,7,5,3,6,4]=>[2,1,5,7,6,4,8,3]=>[2,1,8,5,6,3,7,4]=>{{1,2},{3,8},{4,5,6},{7}}
[6,1,7,4,5,8,3,2]=>[6,3,8,7,4,1,5,2]=>[6,8,3,7,1,5,2,4]=>{{1,6},{2,8},{3},{4,7},{5}}
[5,4,2,6,1,3,8,7]=>[6,4,1,5,2,3,8,7]=>[4,6,2,5,3,1,8,7]=>{{1,4,5},{2,6},{3},{7,8}}
[5,2,7,3,8,6,1,4]=>[6,5,8,1,2,7,4,3]=>[6,8,5,3,4,7,1,2]=>{{1,6,7},{2,8},{3,5},{4}}
[4,1,3,7,2,6,8,5]=>[4,7,1,3,8,2,6,5]=>[8,4,2,1,7,5,3,6]=>{{1,8},{2,4},{3},{5,7},{6}}
[3,5,8,1,7,2,6,4]=>[8,7,3,6,5,2,1,4]=>[3,5,6,7,8,2,4,1]=>{{1,3,6},{2,5,8},{4,7}}
[3,4,1,8,6,2,7,5]=>[4,6,3,1,8,7,5,2]=>[4,3,8,2,6,7,1,5]=>{{1,4},{2,3,8},{5,6,7}}
[7,3,6,5,2,8,4,1]=>[4,8,5,6,7,3,1,2]=>[8,4,7,5,6,1,3,2]=>{{1,8},{2,4,5,6},{3,7}}
[7,1,5,3,8,4,6,2]=>[7,6,5,8,1,4,3,2]=>[6,7,8,5,4,1,2,3]=>{{1,6},{2,7},{3,8},{4,5}}
[8,5,2,6,1,7,3,4]=>[6,5,8,3,7,2,4,1]=>[7,8,5,1,6,3,2,4]=>{{1,7},{2,8},{3,5,6},{4}}
[2,4,8,1,5,6,3,7]=>[8,2,6,4,1,5,3,7]=>[2,4,6,8,3,1,5,7]=>{{1,2,4,8},{3,6},{5},{7}}
[4,8,1,2,5,3,6,7]=>[8,1,5,4,2,3,6,7]=>[4,1,5,8,3,2,6,7]=>{{1,4,8},{2},{3,5},{6},{7}}
[3,8,7,6,5,2,4,1]=>[4,5,3,2,6,7,8,1]=>[4,3,8,1,5,6,7,2]=>{{1,4},{2,3,8},{5},{6},{7}}
[3,5,4,7,6,1,8,2]=>[6,7,3,5,4,8,2,1]=>[5,3,7,8,1,6,2,4]=>{{1,5},{2,3,7},{4,8},{6}}
[3,5,7,2,6,1,4,8]=>[6,7,3,1,5,2,4,8]=>[5,3,6,2,7,4,1,8]=>{{1,5,7},{2,3,6},{4},{8}}
[3,5,2,7,6,1,4,8]=>[6,5,3,1,2,7,4,8]=>[3,5,7,2,4,6,1,8]=>{{1,3,7},{2,5},{4},{6},{8}}
[5,3,7,6,4,1,8,2]=>[4,6,7,5,1,8,3,2]=>[8,5,4,7,3,6,1,2]=>{{1,8},{2,5},{3,4,7},{6}}
[3,7,5,1,4,8,6,2]=>[5,7,3,1,6,8,2,4]=>[5,3,8,2,7,6,4,1]=>{{1,5,7},{2,3,8},{4},{6}}
[5,3,7,1,6,2,4,8]=>[7,6,5,2,3,1,4,8]=>[5,6,7,2,3,4,1,8]=>{{1,5},{2,6},{3,7},{4},{8}}
[3,5,7,1,4,6,2,8]=>[7,6,3,1,5,4,2,8]=>[3,5,6,2,7,1,4,8]=>{{1,3,6},{2,5,7},{4},{8}}
[3,5,7,2,1,4,6,8]=>[2,7,3,1,5,4,6,8]=>[3,2,5,1,7,4,6,8]=>{{1,3,5,7},{2},{4},{6},{8}}
[3,5,2,7,1,4,6,8]=>[7,5,3,1,2,4,6,8]=>[3,5,7,2,4,1,6,8]=>{{1,3,7},{2,5},{4},{6},{8}}
[3,5,4,7,1,6,8,2]=>[7,8,3,5,4,1,6,2]=>[5,3,7,8,1,4,2,6]=>{{1,5},{2,3,7},{4,8},{6}}
[3,5,4,7,2,1,8,6]=>[2,7,3,5,4,8,1,6]=>[3,2,5,8,1,7,6,4]=>{{1,3,5},{2},{4,8},{6,7}}
[3,5,4,7,1,2,8,6]=>[7,1,3,5,4,8,2,6]=>[3,1,5,8,2,7,6,4]=>{{1,3,5},{2},{4,8},{6,7}}
[5,7,6,3,1,8,4,2]=>[3,6,4,7,5,8,1,2]=>[7,3,5,4,8,6,2,1]=>{{1,7},{2,3,5,8},{4},{6}}
[5,7,6,3,1,8,2,4]=>[3,6,7,2,5,8,1,4]=>[7,5,3,1,8,6,4,2]=>{{1,7},{2,5,8},{3},{4},{6}}
[3,5,2,7,1,4,8,6]=>[7,5,3,1,2,8,4,6]=>[3,5,8,2,4,7,6,1]=>{{1,3,8},{2,5},{4},{6,7}}
[3,5,7,2,1,4,8,6]=>[2,7,3,1,5,8,4,6]=>[3,2,5,1,8,7,6,4]=>{{1,3,5,8},{2},{4},{6,7}}
[6,3,2,7,4,1,8,5]=>[4,3,7,6,8,1,2,5]=>[4,8,3,7,6,5,2,1]=>{{1,4,7},{2,8},{3},{5,6}}
[3,8,4,1,7,6,5,2]=>[4,8,3,5,6,7,2,1]=>[4,3,8,5,6,7,1,2]=>{{1,4,5,6,7},{2,3,8}}
[5,4,7,6,8,2,3,1]=>[3,8,2,5,4,7,6,1]=>[5,3,1,7,2,8,4,6]=>{{1,5},{2,3},{4,7},{6,8}}
[6,4,2,7,3,5,8,1]=>[8,4,6,7,3,5,2,1]=>[4,8,7,6,1,2,3,5]=>{{1,4,6},{2,8},{3,7},{5}}
[5,7,8,2,4,3,1,6]=>[3,4,8,1,5,2,7,6]=>[5,4,3,2,7,1,8,6]=>{{1,5,7,8},{2,4},{3},{6}}
[5,1,3,2,4,7,6,8]=>[5,3,1,2,4,7,6,8]=>[3,5,2,1,4,7,6,8]=>{{1,3},{2,5},{4},{6,7},{8}}
[5,3,2,1,7,4,6,8]=>[2,3,5,7,1,4,6,8]=>[7,2,3,5,4,1,6,8]=>{{1,7},{2},{3},{4,5},{6},{8}}
[7,3,1,5,2,4,6,8]=>[3,7,5,2,4,1,6,8]=>[7,3,5,1,2,4,6,8]=>{{1,7},{2,3,5},{4},{6},{8}}
[5,7,1,3,2,4,6,8]=>[7,3,1,2,5,4,6,8]=>[3,5,2,1,7,4,6,8]=>{{1,3},{2,5,7},{4},{6},{8}}
[3,5,6,1,4,7,8,2]=>[6,8,3,1,5,4,7,2]=>[5,3,6,2,7,1,8,4]=>{{1,5,7,8},{2,3,6},{4}}
[3,5,6,8,1,7,2,4]=>[8,7,3,2,5,6,1,4]=>[3,5,6,1,7,8,4,2]=>{{1,3,6,8},{2,5,7},{4}}
[4,1,5,6,3,2,8,7]=>[4,3,6,1,5,2,8,7]=>[4,5,3,2,6,1,8,7]=>{{1,4},{2,5,6},{3},{7,8}}
[4,5,3,7,1,2,8,6]=>[7,1,5,4,3,8,2,6]=>[4,1,5,8,2,7,6,3]=>{{1,4,8},{2},{3,5},{6,7}}
[3,6,1,7,2,5,8,4]=>[6,7,3,8,2,1,5,4]=>[7,3,8,6,2,5,1,4]=>{{1,7},{2,3,8},{4,6},{5}}
[3,6,1,7,5,4,2,8]=>[6,4,3,5,7,1,2,8]=>[3,4,7,6,5,2,1,8]=>{{1,3,7},{2,4,6},{5},{8}}
[4,6,2,3,5,1,8,7]=>[5,6,2,4,3,1,8,7]=>[5,4,1,6,2,3,8,7]=>{{1,5},{2,4,6},{3},{7,8}}
[6,2,4,5,1,8,3,7]=>[5,6,8,2,3,4,1,7]=>[8,6,5,2,3,1,4,7]=>{{1,8},{2,6},{3,5},{4},{7}}
[6,8,4,5,7,2,3,1]=>[3,7,2,8,4,6,5,1]=>[7,3,1,6,2,8,4,5]=>{{1,7},{2,3},{4,6,8},{5}}
[4,2,3,1,6,8,5,7]=>[3,4,2,1,8,6,5,7]=>[4,3,1,2,6,8,5,7]=>{{1,4},{2,3},{5,6,8},{7}}
[6,4,5,8,2,3,7,1]=>[7,8,2,6,4,5,3,1]=>[7,6,1,8,2,3,4,5]=>{{1,7},{2,6},{3},{4,8},{5}}
[2,4,8,1,3,6,7,5]=>[8,2,1,4,7,3,6,5]=>[2,4,1,7,8,5,3,6]=>{{1,2,4,7},{3},{5,8},{6}}
[6,4,8,2,5,3,7,1]=>[7,8,5,6,2,4,3,1]=>[6,5,8,7,3,1,2,4]=>{{1,6},{2,5},{3,8},{4,7}}
[2,1,6,8,4,5,7,3]=>[2,1,7,8,4,6,5,3]=>[2,1,7,6,3,8,4,5]=>{{1,2},{3,7},{4,6,8},{5}}
[2,4,7,3,5,8,6,1]=>[6,2,8,4,3,7,1,5]=>[2,6,4,8,1,7,5,3]=>{{1,2,6,7},{3,4,8},{5}}
[5,8,1,3,6,4,7,2]=>[8,7,1,6,5,2,3,4]=>[5,6,2,7,8,4,3,1]=>{{1,5,8},{2,6},{3},{4,7}}
[6,4,5,3,8,1,7,2]=>[8,7,5,6,4,3,1,2]=>[5,6,8,7,1,2,4,3]=>{{1,5},{2,6},{3,8},{4,7}}
[3,5,2,4,6,1,8,7]=>[6,5,3,2,4,1,8,7]=>[3,5,6,1,2,4,8,7]=>{{1,3,6},{2,5},{4},{7,8}}
[7,2,8,3,4,1,5,6]=>[4,7,8,3,2,5,6,1]=>[8,7,4,1,2,3,5,6]=>{{1,8},{2,7},{3,4},{5},{6}}
[6,2,8,3,4,7,5,1]=>[5,7,6,3,8,4,1,2]=>[8,6,7,1,5,2,4,3]=>{{1,8},{2,6},{3,7},{4},{5}}
[7,6,3,1,4,2,5,8]=>[3,6,4,2,1,7,5,8]=>[7,3,4,1,2,6,5,8]=>{{1,7},{2,3,4},{5},{6},{8}}
[4,2,7,6,3,1,5,8]=>[3,6,4,1,2,7,5,8]=>[7,3,4,2,1,6,5,8]=>{{1,7},{2,3,4},{5},{6},{8}}
[7,5,2,4,6,3,1,8]=>[3,6,5,2,7,1,4,8]=>[7,3,6,1,5,4,2,8]=>{{1,7},{2,3,6},{4},{5},{8}}
[8,3,6,4,7,5,2,1]=>[2,5,7,8,6,4,1,3]=>[8,2,6,5,7,1,4,3]=>{{1,8},{2},{3,6},{4,5,7}}
[3,1,6,8,2,7,4,5]=>[3,8,1,7,4,6,2,5]=>[6,3,2,7,1,8,5,4]=>{{1,6,8},{2,3},{4,7},{5}}
[6,3,7,2,8,1,5,4]=>[8,7,6,5,1,3,2,4]=>[5,6,7,8,4,2,3,1]=>{{1,5},{2,6},{3,7},{4,8}}
[4,5,7,2,8,1,6,3]=>[8,7,6,4,5,1,2,3]=>[4,5,6,7,8,3,2,1]=>{{1,4,7},{2,5,8},{3,6}}
[7,8,1,2,4,3,6,5]=>[8,1,4,2,6,3,7,5]=>[4,1,6,3,7,5,8,2]=>{{1,4},{2},{3,6},{5,7,8}}
[4,1,3,6,5,7,8,2]=>[4,8,1,3,6,5,7,2]=>[6,4,2,1,7,3,8,5]=>{{1,6},{2,4},{3},{5,7,8}}
[8,1,4,3,5,7,6,2]=>[8,6,4,1,2,7,3,5]=>[4,6,8,3,2,7,5,1]=>{{1,4},{2,6,7},{3,8},{5}}
[2,7,6,3,1,8,4,5]=>[3,2,6,7,4,8,5,1]=>[2,8,3,7,1,6,4,5]=>{{1,2,8},{3},{4,7},{5},{6}}
[1,6,5,8,3,4,2,7]=>[1,4,8,3,6,5,2,7]=>[1,6,4,2,8,3,5,7]=>{{1},{2,6},{3,4},{5,8},{7}}
[8,1,5,4,7,2,6,3]=>[8,7,6,5,1,4,3,2]=>[5,6,7,8,4,1,2,3]=>{{1,5},{2,6},{3,7},{4,8}}
[3,8,7,5,6,4,2,1]=>[2,4,3,6,7,5,8,1]=>[3,2,8,4,6,1,7,5]=>{{1,3,8},{2},{4},{5,6},{7}}
[5,1,8,4,2,7,6,3]=>[5,4,8,6,1,7,3,2]=>[6,8,4,5,3,7,1,2]=>{{1,6,7},{2,8},{3,4,5}}
[6,8,3,7,1,5,4,2]=>[7,4,5,8,1,6,2,3]=>[5,7,6,4,3,8,2,1]=>{{1,5},{2,7},{3,6,8},{4}}
[6,3,7,1,2,8,5,4]=>[7,1,6,5,8,3,2,4]=>[6,1,7,8,5,3,4,2]=>{{1,6},{2},{3,7},{4,8},{5}}
[3,5,8,4,7,2,6,1]=>[6,7,3,8,5,2,4,1]=>[6,3,7,5,8,2,1,4]=>{{1,6},{2,3,7},{4,5,8}}
[2,8,5,4,6,3,1,7]=>[3,2,6,5,8,4,1,7]=>[2,6,3,8,5,1,4,7]=>{{1,2,6},{3},{4,8},{5},{7}}
[7,1,3,4,8,6,5,2]=>[7,5,1,2,6,8,3,4]=>[5,8,2,3,7,6,4,1]=>{{1,5,7},{2,8},{3},{4},{6}}
[1,5,8,4,7,6,2,3]=>[1,6,2,7,5,8,3,4]=>[1,7,2,5,8,6,4,3]=>{{1},{2,7},{3},{4,5,8},{6}}
[3,2,6,5,8,4,7,1]=>[7,3,2,8,6,5,4,1]=>[3,7,1,6,8,2,4,5]=>{{1,3},{2,7},{4,6},{5,8}}
[5,4,8,1,6,3,7,2]=>[8,7,6,5,4,1,3,2]=>[5,6,7,8,1,4,2,3]=>{{1,5},{2,6},{3,7},{4,8}}
[4,2,7,3,8,5,6,1]=>[6,4,7,2,8,5,3,1]=>[7,8,4,2,6,1,3,5]=>{{1,7},{2,8},{3,4},{5,6}}
[4,5,2,6,8,3,7,1]=>[7,5,8,4,2,6,3,1]=>[5,6,4,7,2,8,1,3]=>{{1,5},{2,6,8},{3,4,7}}
[6,8,5,4,2,3,7,1]=>[7,4,2,5,8,6,3,1]=>[4,7,1,6,5,8,2,3]=>{{1,4,6,8},{2,7},{3},{5}}
[10,1,3,2,5,4,7,6,9,8]=>[10,3,1,5,2,7,4,9,6,8]=>[3,5,2,7,4,9,6,10,8,1]=>{{1,3},{2,5},{4,7},{6,9},{8,10}}
[12,1,3,2,5,4,7,6,9,8,11,10]=>[12,3,1,5,2,7,4,9,6,11,8,10]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>{{1,3},{2,5},{4,7},{6,9},{8,11},{10,12}}
[5,1,2,7,3,6,8,4]=>[5,1,7,8,2,3,6,4]=>[8,1,7,5,4,3,2,6]=>{{1,8},{2},{3,7},{4,5},{6}}
[5,8,1,2,3,4,7,6]=>[8,1,2,3,5,7,4,6]=>[5,1,2,3,7,8,6,4]=>{{1,5,7},{2},{3},{4},{6,8}}
[7,1,2,8,3,6,4,5]=>[7,1,8,6,4,3,2,5]=>[7,1,6,8,2,4,5,3]=>{{1,7},{2},{3,6},{4,8},{5}}
[6,1,8,2,3,5,7,4]=>[6,8,2,7,3,1,5,4]=>[8,6,1,7,3,5,2,4]=>{{1,8},{2,6},{3},{4,7},{5}}
[4,3,8,7,5,6,2,1]=>[2,6,4,3,7,5,8,1]=>[4,2,8,1,6,3,7,5]=>{{1,4},{2},{3,8},{5,6},{7}}
[8,1,6,2,3,5,7,4]=>[8,6,2,7,3,1,5,4]=>[6,8,1,7,3,5,2,4]=>{{1,6},{2,8},{3},{4,7},{5}}
[8,1,7,2,3,5,6,4]=>[8,7,2,6,3,5,1,4]=>[6,7,1,8,3,2,5,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[8,7,1,2,3,4,6,5]=>[7,1,2,3,6,4,8,5]=>[6,1,2,3,8,5,7,4]=>{{1,6},{2},{3},{4},{5,8},{7}}
[8,6,1,2,3,4,7,5]=>[6,1,2,3,8,7,5,4]=>[8,1,2,3,6,7,4,5]=>{{1,8},{2},{3},{4},{5,6,7}}
[2,4,6,3,7,8,5,1]=>[5,2,8,4,6,1,7,3]=>[2,5,4,7,6,3,8,1]=>{{1,2,5,6},{3,4,7,8}}
[2,8,4,1,7,5,3,6]=>[4,2,8,5,7,3,6,1]=>[2,8,4,5,7,1,3,6]=>{{1,2,8},{3,4,5,7},{6}}
[8,2,6,3,5,4,1,7]=>[4,5,8,6,3,2,1,7]=>[8,6,4,5,1,2,3,7]=>{{1,8},{2,6},{3,4,5},{7}}
[8,3,2,5,7,4,1,6]=>[4,3,7,8,2,1,6,5]=>[7,8,3,4,1,5,2,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[6,1,3,8,7,5,4,2]=>[6,4,1,5,7,3,8,2]=>[4,8,2,6,5,1,7,3]=>{{1,4,6},{2,8},{3},{5},{7}}
[2,4,8,5,7,6,3,1]=>[3,2,6,4,7,8,1,5]=>[2,4,3,8,7,6,5,1]=>{{1,2,4,8},{3},{5,7},{6}}
[8,2,7,3,5,1,4,6]=>[5,8,7,1,3,4,2,6]=>[8,5,7,3,2,1,6,4]=>{{1,8},{2,5},{3,7},{4},{6}}
[6,2,1,8,7,5,4,3]=>[2,6,4,5,7,1,8,3]=>[4,2,8,6,5,3,7,1]=>{{1,4,6},{2},{3,8},{5},{7}}
[5,7,6,3,2,4,1,8]=>[4,3,6,2,5,7,1,8]=>[4,5,3,1,7,6,2,8]=>{{1,4},{2,5,7},{3},{6},{8}}
[5,8,1,3,2,7,4,6]=>[8,3,1,7,5,4,2,6]=>[3,5,2,7,8,1,6,4]=>{{1,3},{2,5,8},{4,7},{6}}
[1,5,4,8,2,3,7,6]=>[1,8,2,5,4,7,3,6]=>[1,5,2,7,3,8,6,4]=>{{1},{2,5},{3},{4,7},{6,8}}
[1,7,4,3,6,8,5,2]=>[1,5,4,8,7,3,2,6]=>[1,5,8,4,7,2,6,3]=>{{1},{2,5,7},{3,8},{4},{6}}
[1,7,6,3,2,8,4,5]=>[1,3,6,7,4,8,5,2]=>[1,8,3,7,2,6,4,5]=>{{1},{2,8},{3},{4,7},{5},{6}}
[7,2,6,3,4,5,1,8]=>[5,7,6,3,4,2,1,8]=>[7,5,6,1,2,3,4,8]=>{{1,7},{2,5},{3,6},{4},{8}}
[7,5,2,3,8,4,1,6]=>[4,8,2,5,7,1,6,3]=>[8,4,1,5,7,3,2,6]=>{{1,8},{2,4,5,7},{3},{6}}
[8,1,7,5,2,3,4,6]=>[8,5,2,3,7,4,1,6]=>[5,8,1,2,7,3,6,4]=>{{1,5,7},{2,8},{3},{4},{6}}
[9,2,3,4,5,6,7,8,1]=>[8,9,2,3,4,5,6,7,1]=>[9,8,1,2,3,4,5,6,7]=>{{1,9},{2,8},{3},{4},{5},{6},{7}}
[4,7,3,8,6,5,2,1]=>[2,5,6,4,8,7,3,1]=>[6,2,4,8,5,7,1,3]=>{{1,6,7},{2},{3,4,8},{5}}
[3,6,7,2,5,8,1,4]=>[8,7,3,1,4,6,2,5]=>[3,6,7,2,1,8,5,4]=>{{1,3,7},{2,6,8},{4},{5}}
[6,1,5,8,3,4,7,2]=>[6,7,8,3,1,5,4,2]=>[8,7,6,1,4,2,3,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[2,8,5,6,3,4,7,1]=>[7,2,6,3,8,5,4,1]=>[2,7,8,1,6,3,4,5]=>{{1,2,7},{3,8},{4},{5,6}}
[8,1,6,3,5,4,7,2]=>[8,7,6,5,3,1,4,2]=>[5,6,7,8,2,4,1,3]=>{{1,5},{2,6},{3,7},{4,8}}
[3,1,7,8,5,4,6,2]=>[3,6,1,5,8,4,7,2]=>[6,3,2,7,5,1,8,4]=>{{1,6},{2,3},{4,7,8},{5}}
[2,7,6,3,5,8,1,4]=>[8,2,6,1,4,7,3,5]=>[2,6,8,3,1,7,5,4]=>{{1,2,6,7},{3,8},{4},{5}}
[6,7,2,8,1,3,4,5]=>[8,7,1,2,3,6,4,5]=>[6,7,2,3,4,8,5,1]=>{{1,6,8},{2,7},{3},{4},{5}}
[7,2,5,4,8,1,6,3]=>[8,7,6,5,2,1,4,3]=>[5,6,7,8,3,4,1,2]=>{{1,5},{2,6},{3,7},{4,8}}
[3,8,7,6,5,1,2,4]=>[5,1,3,2,6,7,8,4]=>[3,1,8,2,5,6,7,4]=>{{1,3,8},{2},{4},{5},{6},{7}}
[7,2,4,8,6,1,5,3]=>[6,8,5,2,1,7,3,4]=>[6,5,8,2,4,7,3,1]=>{{1,6,7},{2,5},{3,8},{4}}
[5,8,4,3,1,6,7,2]=>[3,4,8,7,5,1,6,2]=>[7,4,3,5,8,2,1,6]=>{{1,7},{2,4,5,8},{3},{6}}
[6,3,7,2,5,4,8,1]=>[8,7,6,5,2,3,4,1]=>[5,6,7,8,3,2,1,4]=>{{1,5},{2,6},{3,7},{4,8}}
[3,6,5,7,2,8,4,1]=>[4,8,3,7,6,5,1,2]=>[4,3,7,6,8,1,5,2]=>{{1,4,6},{2,3,7},{5,8}}
[2,7,3,1,4,6,8,5]=>[3,2,7,1,8,4,6,5]=>[2,8,3,1,7,5,4,6]=>{{1,2,8},{3},{4},{5,7},{6}}
[4,7,2,8,6,3,1,5]=>[3,6,8,4,1,7,2,5]=>[6,4,3,8,2,7,5,1]=>{{1,6,7},{2,4,8},{3},{5}}
[1,8,4,2,5,7,6,3]=>[1,4,8,6,2,7,3,5]=>[1,8,4,6,3,7,5,2]=>{{1},{2,8},{3,4,6,7},{5}}
[1,8,2,4,5,7,6,3]=>[1,8,6,2,3,7,4,5]=>[1,6,8,3,4,7,5,2]=>{{1},{2,6,7},{3,8},{4},{5}}
[2,6,3,8,7,5,1,4]=>[5,2,7,1,6,4,8,3]=>[2,8,5,3,6,1,7,4]=>{{1,2,8},{3,5,6},{4},{7}}
[1,5,8,4,6,2,3,7]=>[1,6,2,8,5,4,3,7]=>[1,6,2,5,8,3,4,7]=>{{1},{2,6},{3},{4,5,8},{7}}
[1,7,3,2,4,6,8,5]=>[1,3,7,2,8,4,6,5]=>[1,8,3,2,7,5,4,6]=>{{1},{2,8},{3},{4},{5,7},{6}}
[5,1,2,6,8,7,3,4]=>[5,1,7,3,2,6,8,4]=>[6,1,5,2,4,8,7,3]=>{{1,6,8},{2},{3,5},{4},{7}}
[5,7,8,1,2,6,3,4]=>[8,1,6,3,5,2,7,4]=>[5,1,6,2,7,4,8,3]=>{{1,5,7,8},{2},{3,6},{4}}
[1,5,4,8,6,3,7,2]=>[1,7,6,5,4,8,3,2]=>[1,5,7,8,2,6,3,4]=>{{1},{2,5},{3,7},{4,8},{6}}
[3,8,4,5,2,6,7,1]=>[7,5,3,8,4,2,6,1]=>[3,7,8,5,1,2,4,6]=>{{1,3,8},{2,7},{4,5},{6}}
[4,3,7,2,1,8,6,5]=>[2,7,4,3,6,8,1,5]=>[4,2,7,1,8,6,5,3]=>{{1,4},{2},{3,7},{5,8},{6}}
[3,1,5,4,7,8,6,2]=>[3,6,1,5,4,8,7,2]=>[5,3,2,7,1,6,8,4]=>{{1,5},{2,3},{4,7,8},{6}}
[7,3,5,1,4,2,8,6]=>[5,4,7,1,3,8,2,6]=>[5,8,4,3,1,7,6,2]=>{{1,5},{2,8},{3,4},{6,7}}
[5,4,7,1,3,2,8,6]=>[7,3,1,5,4,8,2,6]=>[3,5,2,8,1,7,6,4]=>{{1,3},{2,5},{4,8},{6,7}}
[7,6,8,2,5,3,4,1]=>[4,8,5,3,2,7,6,1]=>[7,4,5,1,2,8,3,6]=>{{1,7},{2,4},{3,5},{6,8}}
[6,4,1,7,5,2,8,3]=>[4,6,5,7,8,2,1,3]=>[8,6,7,4,5,2,3,1]=>{{1,8},{2,6},{3,7},{4},{5}}
[2,6,4,5,7,3,8,1]=>[8,2,7,6,4,5,3,1]=>[2,6,7,8,1,3,4,5]=>{{1,2,6},{3,7},{4,8},{5}}
[4,5,7,2,6,8,1,3]=>[8,7,1,4,5,3,2,6]=>[4,5,2,7,8,1,6,3]=>{{1,4,7},{2,5,8},{3},{6}}
[1,2,5,3,8,6,7,4]=>[1,2,5,7,3,8,6,4]=>[1,2,8,5,4,7,3,6]=>{{1},{2},{3,8},{4,5},{6,7}}
[8,7,2,4,6,1,5,3]=>[6,7,5,2,1,4,8,3]=>[6,5,8,2,4,1,7,3]=>{{1,6},{2,5},{3,8},{4},{7}}
[5,4,8,6,7,2,3,1]=>[3,7,2,5,4,8,6,1]=>[5,3,1,8,2,7,4,6]=>{{1,5},{2,3},{4,8},{6,7}}
[5,4,8,6,3,1,2,7]=>[3,1,6,5,4,8,2,7]=>[5,1,3,8,2,6,4,7]=>{{1,5},{2},{3},{4,8},{6},{7}}
[5,4,8,7,2,1,3,6]=>[2,7,1,5,4,3,8,6]=>[5,2,1,8,3,4,7,6]=>{{1,5},{2},{3},{4,8},{6},{7}}
[2,5,4,7,8,1,3,6]=>[8,2,1,5,4,3,7,6]=>[2,5,1,7,3,4,8,6]=>{{1,2,5},{3},{4,7,8},{6}}
[5,3,6,4,8,2,7,1]=>[7,8,5,6,3,4,2,1]=>[6,5,8,7,2,1,3,4]=>{{1,6},{2,5},{3,8},{4,7}}
[4,5,6,2,7,3,8,1]=>[8,6,7,4,5,2,3,1]=>[4,6,5,7,8,2,1,3]=>{{1,4,7},{2,6},{3,5,8}}
[4,2,5,1,3,8,7,6]=>[5,4,1,2,3,7,8,6]=>[4,5,2,3,1,8,7,6]=>{{1,4},{2,5},{3},{6,8},{7}}
[8,5,2,6,1,3,7,4]=>[6,5,1,8,7,2,4,3]=>[7,8,2,5,6,4,1,3]=>{{1,7},{2,8},{3},{4,5,6}}
[6,4,1,5,3,2,8,7]=>[4,3,6,5,2,1,8,7]=>[4,6,3,5,1,2,8,7]=>{{1,4,5},{2,6},{3},{7,8}}
[2,1,8,6,3,7,5,4]=>[2,1,6,5,8,7,4,3]=>[2,1,6,8,5,7,3,4]=>{{1,2},{3,6,7},{4,8},{5}}
[5,2,1,4,3,8,6,7]=>[2,5,4,1,3,8,6,7]=>[4,2,5,3,1,8,6,7]=>{{1,4},{2},{3,5},{6,8},{7}}
[4,3,7,2,8,5,6,1]=>[6,7,4,3,8,5,2,1]=>[7,4,8,1,6,2,3,5]=>{{1,7},{2,4},{3,8},{5,6}}
[5,3,1,2,4,8,6,7]=>[3,1,5,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>{{1,5},{2},{3},{4},{6,8},{7}}
[3,5,2,8,1,6,7,4]=>[8,5,3,7,2,1,6,4]=>[3,5,8,7,2,4,1,6]=>{{1,3,8},{2,5},{4,7},{6}}
[3,1,7,8,2,5,4,6]=>[3,8,1,5,2,4,7,6]=>[5,3,2,7,4,1,8,6]=>{{1,5},{2,3},{4,7,8},{6}}
[4,8,1,3,5,6,2,7]=>[8,6,1,4,2,3,5,7]=>[4,6,2,8,3,5,1,7]=>{{1,4,8},{2,6},{3},{5},{7}}
[1,3,2,6,4,8,7,5]=>[1,3,2,6,7,4,8,5]=>[1,3,2,8,6,5,7,4]=>{{1},{2,3},{4,8},{5,6},{7}}
[2,5,1,4,3,8,7,6]=>[5,2,4,1,3,7,8,6]=>[2,4,5,3,1,8,7,6]=>{{1,2,4},{3,5},{6,8},{7}}
[1,7,2,6,3,8,5,4]=>[1,7,6,5,8,2,3,4]=>[1,6,7,8,5,4,3,2]=>{{1},{2,6},{3,7},{4,8},{5}}
[1,8,4,7,3,6,5,2]=>[1,5,6,7,8,2,3,4]=>[1,8,7,6,5,4,3,2]=>{{1},{2,8},{3,7},{4,6},{5}}
[8,6,4,1,5,3,2,7]=>[4,3,6,5,2,8,1,7]=>[4,8,3,5,1,6,2,7]=>{{1,4,5},{2,8},{3},{6},{7}}
[4,8,5,3,1,2,7,6]=>[3,1,5,4,8,7,2,6]=>[4,1,3,7,5,8,6,2]=>{{1,4,7},{2},{3},{5},{6,8}}
[4,8,7,6,5,1,3,2]=>[5,3,1,4,6,7,8,2]=>[3,4,2,8,5,6,7,1]=>{{1,3},{2,4,8},{5},{6},{7}}
[5,8,4,6,1,2,7,3]=>[6,1,7,8,5,4,2,3]=>[7,1,6,5,8,2,4,3]=>{{1,7},{2},{3,6},{4,5,8}}
[6,2,7,4,8,5,3,1]=>[3,5,8,6,7,4,2,1]=>[8,5,3,7,6,1,2,4]=>{{1,8},{2,5,6},{3},{4,7}}
[3,5,2,4,8,1,7,6]=>[8,5,3,2,4,7,1,6]=>[3,5,7,1,2,8,6,4]=>{{1,3,7},{2,5},{4},{6,8}}
[6,3,8,2,4,1,7,5]=>[4,8,6,2,7,3,1,5]=>[8,4,6,2,7,3,5,1]=>{{1,8},{2,4},{3,6},{5,7}}
[7,2,8,1,4,3,6,5]=>[8,7,4,1,6,2,5,3]=>[4,6,7,3,8,5,1,2]=>{{1,4},{2,6},{3,7},{5,8}}
[1,7,4,5,6,8,2,3]=>[1,8,2,7,4,5,6,3]=>[1,7,2,8,3,4,5,6]=>{{1},{2,7},{3},{4,8},{5},{6}}
[1,6,4,2,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>{{1},{2,6},{3},{4},{5},{7},{8}}
[1,8,7,2,3,4,5,6]=>[1,7,2,3,4,5,8,6]=>[1,8,2,3,4,5,7,6]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[1,3,2,7,6,4,5,8]=>[1,3,2,6,4,7,5,8]=>[1,3,2,7,4,6,5,8]=>{{1},{2,3},{4,7},{5},{6},{8}}
[1,2,3,7,6,4,5,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,7,4,6,5,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[1,5,4,2,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>{{1},{2,5},{3},{4},{6,7},{8}}
[1,5,4,2,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>{{1},{2,5},{3},{4},{6,8},{7}}
[1,3,2,8,6,4,5,7]=>[1,3,2,6,4,8,5,7]=>[1,3,2,8,4,6,5,7]=>{{1},{2,3},{4,8},{5},{6},{7}}
[4,7,3,1,8,6,5,2]=>[3,7,5,4,6,8,2,1]=>[5,3,4,8,7,6,1,2]=>{{1,5,7},{2,3,4,8},{6}}
[2,7,5,3,1,8,6,4]=>[3,2,5,7,6,8,4,1]=>[2,8,3,5,7,6,1,4]=>{{1,2,8},{3},{4,5,7},{6}}
[4,5,3,6,8,2,1,7]=>[2,8,5,4,3,6,1,7]=>[4,2,5,6,1,8,3,7]=>{{1,4,6,8},{2},{3,5},{7}}
[7,5,8,4,1,3,6,2]=>[4,8,1,6,7,2,5,3]=>[8,4,2,6,7,5,1,3]=>{{1,8},{2,4,6},{3},{5,7}}
[7,8,5,3,6,2,4,1]=>[4,6,5,2,8,3,7,1]=>[7,4,6,2,5,1,8,3]=>{{1,7,8},{2,4},{3,6},{5}}
[5,4,3,8,2,1,7,6]=>[2,8,4,5,3,7,1,6]=>[4,2,7,5,1,8,6,3]=>{{1,4,5},{2},{3,7},{6,8}}
[5,2,3,8,6,4,7,1]=>[7,5,2,6,3,8,4,1]=>[5,8,1,7,3,6,2,4]=>{{1,5},{2,8},{3},{4,7},{6}}
[7,2,3,4,5,8,1,6]=>[8,7,2,3,4,1,5,6]=>[7,8,1,2,3,5,6,4]=>{{1,7},{2,8},{3},{4},{5},{6}}
[8,5,4,7,1,3,6,2]=>[7,6,1,5,8,3,4,2]=>[6,7,2,8,5,3,1,4]=>{{1,6},{2,7},{3},{4,8},{5}}
[7,3,6,2,8,1,5,4]=>[8,6,7,5,1,4,3,2]=>[5,7,6,8,4,1,2,3]=>{{1,5},{2,7},{3,6},{4,8}}
[3,7,2,8,4,5,1,6]=>[5,7,3,8,4,2,6,1]=>[7,3,8,5,1,2,4,6]=>{{1,7},{2,3,8},{4,5},{6}}
[4,2,7,5,8,1,3,6]=>[8,4,1,2,7,3,5,6]=>[4,7,2,3,8,5,6,1]=>{{1,4},{2,7},{3},{5,8},{6}}
[5,3,8,4,1,6,2,7]=>[4,8,6,5,1,2,3,7]=>[8,4,5,6,3,2,1,7]=>{{1,8},{2,4,6},{3,5},{7}}
[7,8,4,1,6,5,2,3]=>[4,8,2,5,6,3,7,1]=>[7,4,1,5,6,2,8,3]=>{{1,7,8},{2,4,5,6},{3}}
[5,1,6,2,7,3,8,4,9]=>[5,6,7,8,1,2,3,4,9]=>[8,7,6,5,4,3,2,1,9]=>{{1,8},{2,7},{3,6},{4,5},{9}}
[4,8,1,3,7,5,2,6]=>[8,5,1,4,7,3,6,2]=>[4,5,2,8,7,1,3,6]=>{{1,4,8},{2,5,7},{3},{6}}
[4,2,8,5,1,3,6,7]=>[5,4,1,2,8,3,6,7]=>[4,8,2,3,5,1,6,7]=>{{1,4},{2,8},{3},{5},{6},{7}}
[7,2,8,5,6,3,4,1]=>[4,7,6,3,8,5,2,1]=>[8,4,7,1,6,2,3,5]=>{{1,8},{2,4},{3,7},{5,6}}
[4,8,5,1,3,7,2,6]=>[5,8,1,4,7,3,2,6]=>[5,4,2,8,7,1,6,3]=>{{1,5,7},{2,4,8},{3},{6}}
[4,3,7,5,6,2,8,1]=>[8,6,4,3,7,5,2,1]=>[4,6,8,1,7,2,3,5]=>{{1,4},{2,6},{3,8},{5,7}}
[4,5,1,8,6,7,3,2]=>[5,3,7,4,1,8,6,2]=>[4,5,3,8,2,7,1,6]=>{{1,4,8},{2,5},{3},{6,7}}
[5,3,8,6,4,7,2,1]=>[2,7,5,6,3,8,4,1]=>[5,2,8,7,3,6,1,4]=>{{1,5},{2},{3,8},{4,7},{6}}
[6,7,3,2,8,4,5,1]=>[5,3,7,8,4,6,2,1]=>[6,7,3,5,1,8,2,4]=>{{1,6,8},{2,7},{3},{4,5}}
[6,7,1,8,4,5,3,2]=>[7,3,5,8,4,6,1,2]=>[3,7,6,5,1,8,4,2]=>{{1,3,6,8},{2,7},{4,5}}
[8,3,4,2,7,5,6,1]=>[6,4,8,3,7,5,2,1]=>[6,8,4,1,7,2,3,5]=>{{1,6},{2,8},{3,4},{5,7}}
[8,3,5,2,7,4,6,1]=>[6,5,8,7,3,4,2,1]=>[7,8,5,6,2,1,3,4]=>{{1,7},{2,8},{3,5},{4,6}}
[8,5,3,2,7,6,4,1]=>[4,3,6,5,7,8,2,1]=>[4,8,3,7,5,6,1,2]=>{{1,4,7},{2,8},{3},{5},{6}}
[2,7,4,6,1,5,8,3]=>[6,2,8,7,1,4,5,3]=>[2,8,6,7,4,3,1,5]=>{{1,2,8},{3,6},{4,7},{5}}
[1,3,7,6,4,8,5,2]=>[1,5,3,8,6,7,2,4]=>[1,3,8,5,6,7,4,2]=>{{1},{2,3,8},{4,5,6,7}}
[5,4,1,8,6,3,2,7]=>[4,3,5,6,2,8,1,7]=>[5,8,3,4,1,6,2,7]=>{{1,5},{2,8},{3},{4},{6},{7}}
[5,4,1,7,6,3,2,8]=>[4,3,5,6,2,7,1,8]=>[5,7,3,4,1,6,2,8]=>{{1,5},{2,7},{3},{4},{6},{8}}
[8,4,1,7,5,3,2,6]=>[4,3,8,5,7,2,6,1]=>[4,8,3,5,7,1,2,6]=>{{1,4,5,7},{2,8},{3},{6}}
[5,8,6,1,4,3,2,7]=>[6,3,4,1,5,8,2,7]=>[3,5,4,2,8,6,1,7]=>{{1,3,4},{2,5,8},{6},{7}}
[3,1,6,4,5,8,7,2]=>[3,7,1,6,4,5,8,2]=>[6,3,2,8,1,4,7,5]=>{{1,6},{2,3},{4,8},{5},{7}}
[8,2,7,6,1,4,3,5]=>[6,7,4,1,2,8,3,5]=>[7,4,8,3,2,6,5,1]=>{{1,7},{2,4},{3,8},{5},{6}}
[5,2,3,4,7,1,6,8]=>[7,5,2,3,4,1,6,8]=>[5,7,1,2,3,4,6,8]=>{{1,5},{2,7},{3},{4},{6},{8}}
[3,6,7,1,4,2,5,8]=>[7,4,3,1,2,6,5,8]=>[3,4,6,2,1,7,5,8]=>{{1,3,6,7},{2,4},{5},{8}}
[4,7,5,8,2,1,3,6]=>[2,8,1,4,7,3,5,6]=>[4,2,1,7,8,5,6,3]=>{{1,4,7},{2},{3},{5,8},{6}}
[3,4,6,8,1,5,7,2]=>[8,7,3,4,1,6,5,2]=>[3,4,6,7,2,8,1,5]=>{{1,3,6,8},{2,4,7},{5}}
[8,4,1,6,5,2,7,3]=>[4,8,5,6,7,2,1,3]=>[8,4,7,5,6,2,3,1]=>{{1,8},{2,4,5,6},{3,7}}
[8,6,4,1,5,7,3,2]=>[4,3,6,8,1,7,5,2]=>[6,8,3,4,2,7,1,5]=>{{1,6,7},{2,8},{3},{4},{5}}
[3,2,1,7,5,8,4,6]=>[2,3,1,8,7,4,5,6]=>[3,2,1,7,8,5,6,4]=>{{1,3},{2},{4,7},{5,8},{6}}
[8,4,6,5,1,2,7,3]=>[5,1,6,7,8,4,2,3]=>[8,1,7,6,5,2,4,3]=>{{1,8},{2},{3,7},{4,6},{5}}
[4,5,3,8,2,1,7,6]=>[2,8,5,4,3,7,1,6]=>[4,2,5,7,1,8,6,3]=>{{1,4,7},{2},{3,5},{6,8}}
[6,4,1,3,2,5,8,7]=>[4,3,1,6,2,5,8,7]=>[3,6,2,4,1,5,8,7]=>{{1,3},{2,6},{4},{5},{7,8}}
[8,5,3,6,7,2,1,4]=>[2,7,5,1,8,4,3,6]=>[7,2,8,3,5,1,6,4]=>{{1,7},{2},{3,8},{4},{5},{6}}
[1,2,8,4,3,6,7,5]=>[1,2,4,8,7,3,6,5]=>[1,2,7,4,8,5,3,6]=>{{1},{2},{3,7},{4},{5,8},{6}}
[8,2,7,1,4,3,5,6]=>[7,8,4,1,2,3,5,6]=>[7,4,8,3,2,5,6,1]=>{{1,7},{2,4},{3,8},{5},{6}}
[6,3,8,7,1,5,4,2]=>[7,4,5,6,1,2,8,3]=>[4,8,6,5,3,2,7,1]=>{{1,4,5},{2,8},{3,6},{7}}
[8,6,4,7,1,5,3,2]=>[7,3,5,6,1,8,4,2]=>[3,8,5,7,4,6,1,2]=>{{1,3,5},{2,8},{4,7},{6}}
[4,5,2,6,1,3,8,7]=>[6,5,1,4,2,3,8,7]=>[4,5,2,6,3,1,8,7]=>{{1,4,6},{2,5},{3},{7,8}}
[3,4,6,7,2,5,8,1]=>[8,7,3,4,2,6,5,1]=>[3,4,6,7,1,8,2,5]=>{{1,3,6,8},{2,4,7},{5}}
[3,7,6,2,4,8,1,5]=>[8,6,3,2,1,7,4,5]=>[3,6,8,1,4,7,5,2]=>{{1,3,8},{2,6,7},{4},{5}}
[4,2,1,5,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>[5,2,4,3,1,6,7,8]=>{{1,5},{2},{3,4},{6},{7},{8}}
[4,1,5,2,6,3,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>{{1,6},{2,5},{3,4},{7},{8},{9}}
[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>{{1,4},{2,3},{5},{6},{7},{8},{9}}
[5,1,6,2,7,3,8,4,9,10]=>[5,6,7,8,1,2,3,4,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>{{1,8},{2,7},{3,6},{4,5},{9},{10}}
[4,1,5,2,6,3,7,8,9,10]=>[4,5,6,1,2,3,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>{{1,6},{2,5},{3,4},{7},{8},{9},{10}}
[3,1,4,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>{{1,4},{2,3},{5},{6},{7},{8},{9},{10}}
[6,2,5,4,1,8,7,3]=>[4,5,6,7,1,3,8,2]=>[8,6,5,4,3,1,7,2]=>{{1,8},{2,6},{3,5},{4},{7}}
[8,4,3,2,7,6,1,5]=>[6,3,4,7,1,8,5,2]=>[3,8,7,4,2,6,1,5]=>{{1,3,7},{2,8},{4},{5},{6}}
[8,4,3,6,5,2,1,7]=>[2,5,4,6,8,1,3,7]=>[6,2,8,4,5,3,1,7]=>{{1,6},{2},{3,8},{4},{5},{7}}
[3,6,1,4,8,7,2,5]=>[6,7,3,1,4,5,8,2]=>[6,3,8,2,1,4,7,5]=>{{1,6},{2,3,8},{4},{5},{7}}
[4,7,5,1,8,2,6,3]=>[5,7,8,4,6,3,2,1]=>[6,5,4,8,7,1,2,3]=>{{1,6},{2,5,7},{3,4,8}}
[7,2,5,1,8,3,6,4]=>[5,7,8,6,2,3,1,4]=>[8,6,5,7,3,2,4,1]=>{{1,8},{2,6},{3,5},{4,7}}
[8,3,6,4,1,7,5,2]=>[4,6,5,7,8,3,2,1]=>[8,6,7,4,5,1,2,3]=>{{1,8},{2,6},{3,7},{4},{5}}
[7,1,6,4,8,3,5,2]=>[7,5,8,6,3,1,4,2]=>[6,8,5,7,2,4,1,3]=>{{1,6},{2,8},{3,5},{4,7}}
[8,5,3,6,1,7,4,2]=>[6,4,7,5,8,3,2,1]=>[6,8,4,7,5,1,2,3]=>{{1,6},{2,8},{3,4,7},{5}}
[1,8,3,6,7,2,4,5]=>[1,7,8,2,3,5,6,4]=>[1,8,7,3,4,2,5,6]=>{{1},{2,8},{3,7},{4},{5},{6}}
[3,7,1,8,2,5,4,6]=>[7,8,3,5,2,4,1,6]=>[5,3,7,8,2,1,6,4]=>{{1,5},{2,3,7},{4,8},{6}}
[4,6,7,1,5,3,8,2]=>[7,8,5,4,1,6,3,2]=>[5,4,6,7,3,8,1,2]=>{{1,5},{2,4,7},{3,6,8}}
[3,7,8,4,6,2,5,1]=>[5,6,3,8,2,4,7,1]=>[6,3,7,5,2,1,8,4]=>{{1,6},{2,3,7,8},{4,5}}
[5,1,3,7,6,4,8,2]=>[5,8,1,6,3,7,4,2]=>[8,5,2,6,3,7,1,4]=>{{1,8},{2,5},{3},{4,6,7}}
[7,2,8,3,6,4,5,1]=>[5,7,8,6,4,3,2,1]=>[8,6,5,7,1,2,3,4]=>{{1,8},{2,6},{3,5},{4,7}}
[3,7,8,1,2,5,6,4]=>[8,1,3,6,2,5,7,4]=>[3,1,6,7,4,2,8,5]=>{{1,3,6},{2},{4,7,8},{5}}
[1,5,4,2,6,8,7,3]=>[1,4,5,7,3,6,8,2]=>[1,6,5,4,2,8,7,3]=>{{1},{2,6,8},{3,5},{4},{7}}
[8,7,3,2,1,4,6,5]=>[2,3,7,1,6,4,8,5]=>[6,2,3,1,8,5,7,4]=>{{1,6},{2},{3},{4},{5,8},{7}}
[8,3,5,1,7,4,2,6]=>[5,4,7,8,3,1,2,6]=>[7,8,5,4,1,3,6,2]=>{{1,7},{2,8},{3,5},{4},{6}}
[2,8,6,3,4,1,7,5]=>[4,2,6,3,8,7,5,1]=>[2,8,4,1,6,7,3,5]=>{{1,2,8},{3,4},{5,6,7}}
[2,8,3,7,5,1,6,4]=>[5,2,7,8,6,3,4,1]=>[2,8,6,5,7,3,1,4]=>{{1,2,8},{3,6},{4,5,7}}
[7,3,2,5,6,1,8,4]=>[6,3,7,8,2,4,5,1]=>[7,8,3,6,2,4,1,5]=>{{1,7},{2,8},{3},{4,6},{5}}
[1,2,6,5,3,4,7,8]=>[1,2,5,3,6,4,7,8]=>[1,2,6,3,5,4,7,8]=>{{1},{2},{3,6},{4},{5},{7},{8}}
[3,7,6,1,2,4,8,5]=>[6,1,3,2,7,8,5,4]=>[3,1,8,2,7,6,4,5]=>{{1,3,8},{2},{4},{5,7},{6}}
[8,1,3,7,2,4,5,6]=>[8,7,1,3,4,5,6,2]=>[7,8,2,1,3,4,5,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[1,3,8,7,4,2,6,5]=>[1,4,3,7,6,2,8,5]=>[1,3,6,4,8,5,7,2]=>{{1},{2,3,6},{4},{5,8},{7}}
[8,1,4,5,7,6,3,2]=>[8,3,6,1,2,7,4,5]=>[3,8,6,2,4,7,5,1]=>{{1,3,6,7},{2,8},{4},{5}}
[8,2,7,3,1,6,5,4]=>[3,7,8,5,6,1,4,2]=>[6,5,3,8,7,4,1,2]=>{{1,6},{2,5,7},{3},{4,8}}
[3,1,8,2,7,5,6,4]=>[3,8,1,6,7,5,2,4]=>[6,3,2,8,7,1,5,4]=>{{1,6},{2,3},{4,8},{5,7}}
[1,8,4,7,6,5,2,3]=>[1,5,2,6,7,8,4,3]=>[1,8,2,7,5,6,3,4]=>{{1},{2,8},{3},{4,7},{5},{6}}
[3,8,1,2,5,6,4,7]=>[8,1,3,6,2,5,4,7]=>[3,1,6,8,4,2,5,7]=>{{1,3,6},{2},{4,8},{5},{7}}
[2,8,6,4,7,3,1,5]=>[3,2,7,6,1,8,4,5]=>[2,7,3,8,4,6,5,1]=>{{1,2,7},{3},{4,8},{5},{6}}
[8,3,1,5,2,6,7,4]=>[3,8,5,7,2,1,6,4]=>[8,3,5,7,2,4,1,6]=>{{1,8},{2,3,5},{4,7},{6}}
[4,8,1,5,7,6,3,2]=>[8,3,6,4,1,7,5,2]=>[3,6,4,8,2,7,1,5]=>{{1,3,4,8},{2,6,7},{5}}
[4,7,1,6,8,3,2,5]=>[7,3,8,4,2,1,6,5]=>[4,7,3,8,1,5,2,6]=>{{1,4,8},{2,7},{3},{5},{6}}
[3,7,5,2,8,6,1,4]=>[6,5,3,1,8,7,4,2]=>[3,6,8,2,5,7,1,4]=>{{1,3,8},{2,6,7},{4},{5}}
[7,2,4,5,6,8,1,3]=>[8,7,1,3,4,5,2,6]=>[7,8,2,1,3,4,6,5]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,1,3,5,6,2,8,4]=>[7,6,1,8,2,3,5,4]=>[7,8,2,6,4,5,1,3]=>{{1,7},{2,8},{3},{4,6},{5}}
[7,2,4,8,1,5,6,3]=>[8,7,6,2,1,4,3,5]=>[6,7,8,2,4,3,5,1]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,3,8,5,6,2,1,4]=>[2,6,7,1,8,5,3,4]=>[8,2,7,3,6,1,5,4]=>{{1,8},{2},{3,7},{4},{5,6}}
[2,6,3,5,8,7,4,1]=>[4,2,7,6,3,1,8,5]=>[2,8,4,6,1,5,7,3]=>{{1,2,8},{3,4,6},{5},{7}}
[8,6,5,3,7,2,1,4]=>[2,7,5,1,6,8,3,4]=>[5,2,8,3,7,6,4,1]=>{{1,5,7},{2},{3,8},{4},{6}}
[7,4,8,6,5,3,2,1]=>[2,3,5,6,8,7,4,1]=>[8,2,3,6,5,7,1,4]=>{{1,8},{2},{3},{4,6,7},{5}}
[4,3,5,8,7,1,2,6]=>[7,1,4,3,5,2,8,6]=>[4,1,5,2,8,3,7,6]=>{{1,4},{2},{3,5,8},{6},{7}}
[5,6,4,3,7,1,8,2]=>[7,8,4,6,5,3,1,2]=>[5,4,7,6,8,1,3,2]=>{{1,5,8},{2,4,6},{3,7}}
[5,2,6,4,1,7,8,3]=>[4,6,5,8,3,2,7,1]=>[7,5,6,4,1,2,8,3]=>{{1,7,8},{2,5},{3,6},{4}}
[7,5,6,2,8,3,4,1]=>[4,6,8,3,7,5,2,1]=>[8,6,4,1,7,2,3,5]=>{{1,8},{2,6},{3,4},{5,7}}
[2,4,6,3,8,7,1,5]=>[7,2,6,4,1,3,8,5]=>[2,4,6,8,3,5,7,1]=>{{1,2,4,8},{3,6},{5},{7}}
[2,4,6,8,3,7,1,5]=>[7,2,8,4,1,6,3,5]=>[2,6,4,7,3,8,5,1]=>{{1,2,6,8},{3,4,7},{5}}
[2,4,6,8,5,1,3,7]=>[5,2,1,4,8,6,3,7]=>[2,4,1,6,5,8,3,7]=>{{1,2,4,6,8},{3},{5},{7}}
[2,4,6,5,8,3,1,7]=>[3,2,8,4,6,5,1,7]=>[2,4,3,6,8,1,5,7]=>{{1,2,4,6},{3},{5,8},{7}}
[2,4,6,8,5,3,1,7]=>[3,2,5,4,8,6,1,7]=>[2,4,3,6,5,8,1,7]=>{{1,2,4,6,8},{3},{5},{7}}
[2,4,6,8,7,3,1,5]=>[3,2,7,4,1,6,8,5]=>[2,4,3,6,1,8,7,5]=>{{1,2,4,6,8},{3},{5},{7}}
[6,1,2,7,8,4,5,3]=>[6,1,5,8,4,2,7,3]=>[6,1,7,5,2,4,8,3]=>{{1,6},{2},{3,7,8},{4,5}}
[1,8,6,2,3,7,4,5]=>[1,6,2,8,4,7,5,3]=>[1,8,2,6,3,7,4,5]=>{{1},{2,8},{3},{4,6,7},{5}}
[1,7,2,3,8,5,4,6]=>[1,7,2,5,8,4,3,6]=>[1,7,2,8,5,3,6,4]=>{{1},{2,7},{3},{4,8},{5},{6}}
[8,2,3,4,5,6,7,9,1]=>[9,8,2,3,4,5,6,7,1]=>[8,9,1,2,3,4,5,6,7]=>{{1,8},{2,9},{3},{4},{5},{6},{7}}
[9,2,3,4,5,6,7,8,10,1]=>[10,9,2,3,4,5,6,7,8,1]=>[9,10,1,2,3,4,5,6,7,8]=>{{1,9},{2,10},{3},{4},{5},{6},{7},{8}}
[6,2,3,5,8,1,7,4]=>[8,6,2,7,3,5,1,4]=>[6,8,1,7,3,2,5,4]=>{{1,6},{2,8},{3},{4,7},{5}}
[1,3,7,5,6,8,4,2]=>[1,4,3,8,7,5,6,2]=>[1,3,7,4,8,2,5,6]=>{{1},{2,3,7},{4},{5,8},{6}}
[1,3,7,5,2,8,6,4]=>[1,5,3,7,6,8,4,2]=>[1,3,8,5,7,6,2,4]=>{{1},{2,3,8},{4,5,7},{6}}
[1,5,7,3,6,4,8,2]=>[1,8,7,6,5,3,4,2]=>[1,5,6,7,8,3,2,4]=>{{1},{2,5,8},{3,6},{4,7}}
[4,6,3,5,8,2,1,7]=>[2,8,6,4,3,5,1,7]=>[4,2,6,8,1,3,5,7]=>{{1,4,8},{2},{3,6},{5},{7}}
[7,5,2,3,1,8,6,4]=>[3,5,2,7,6,8,4,1]=>[8,3,1,5,7,6,2,4]=>{{1,8},{2,3},{4,5,7},{6}}
[6,2,7,3,5,4,1,8]=>[4,5,6,7,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[3,5,7,8,2,4,6,1]=>[6,8,3,2,5,4,7,1]=>[5,3,6,1,7,2,8,4]=>{{1,5,7,8},{2,3,6},{4}}
[2,5,7,8,4,6,1,3]=>[6,2,1,8,5,4,7,3]=>[2,6,1,5,7,3,8,4]=>{{1,2,6},{3},{4,5,7,8}}
[6,7,4,3,8,2,5,1]=>[5,8,4,7,2,6,3,1]=>[6,4,7,5,2,8,1,3]=>{{1,6,8},{2,4,5},{3,7}}
[3,7,8,6,5,2,4,1]=>[4,5,3,2,6,8,7,1]=>[4,3,7,1,5,6,8,2]=>{{1,4},{2,3,7,8},{5},{6}}
[4,1,5,6,3,2,7,8]=>[4,3,6,1,5,2,7,8]=>[4,5,3,2,6,1,7,8]=>{{1,4},{2,5,6},{3},{7},{8}}
[4,3,5,6,1,7,8,2]=>[6,8,4,3,5,1,7,2]=>[5,4,6,1,7,3,8,2]=>{{1,5,7,8},{2,4},{3,6}}
[3,1,4,6,7,5,8,2]=>[3,8,1,4,7,6,5,2]=>[4,3,2,6,7,8,1,5]=>{{1,4,6,8},{2,3},{5,7}}
[3,8,1,4,7,2,6,5]=>[8,7,3,1,6,4,5,2]=>[3,6,7,2,8,4,1,5]=>{{1,3,7},{2,6},{4},{5,8}}
[4,3,8,1,2,7,6,5]=>[8,1,4,3,6,7,2,5]=>[4,1,6,2,8,7,5,3]=>{{1,4},{2},{3,6,7},{5,8}}
[8,3,5,6,1,7,2,4]=>[6,7,8,2,4,5,3,1]=>[8,7,6,2,1,3,4,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[4,5,8,1,2,6,7,3]=>[8,1,7,4,5,2,6,3]=>[4,1,5,7,8,3,2,6]=>{{1,4,7},{2},{3,5,8},{6}}
[8,4,5,2,6,1,7,3]=>[6,5,7,8,4,3,2,1]=>[7,8,6,5,1,2,3,4]=>{{1,7},{2,8},{3,6},{4,5}}
[8,1,2,5,3,6,7,4]=>[8,1,5,7,2,3,6,4]=>[5,1,8,7,4,3,2,6]=>{{1,5},{2},{3,8},{4,7},{6}}
[2,5,3,8,4,1,6,7]=>[4,2,8,5,1,3,6,7]=>[2,8,4,5,3,1,6,7]=>{{1,2,8},{3,4,5},{6},{7}}
[1,8,3,7,4,2,5,6]=>[1,4,7,8,2,3,5,6]=>[1,8,7,4,3,5,6,2]=>{{1},{2,8},{3,7},{4},{5},{6}}
[6,7,8,5,3,1,4,2]=>[3,5,4,2,8,6,7,1]=>[6,3,4,1,5,7,8,2]=>{{1,6,7,8},{2,3,4},{5}}
[1,7,3,5,2,8,6,4]=>[1,5,7,6,3,8,2,4]=>[1,8,5,7,3,6,4,2]=>{{1},{2,8},{3,5},{4,7},{6}}
[1,7,2,4,8,6,5,3]=>[1,7,5,2,6,8,4,3]=>[1,5,8,3,7,6,2,4]=>{{1},{2,5,7},{3,8},{4},{6}}
[8,4,1,3,5,6,2,7]=>[4,8,1,6,2,5,3,7]=>[8,4,2,6,3,1,5,7]=>{{1,8},{2,4,6},{3},{5},{7}}
[7,1,4,8,3,6,5,2]=>[7,5,6,1,8,4,3,2]=>[6,8,7,3,5,1,2,4]=>{{1,6},{2,8},{3,7},{4},{5}}
[7,6,3,4,1,8,5,2]=>[4,5,8,3,6,7,2,1]=>[8,5,4,1,6,7,2,3]=>{{1,8},{2,5,6,7},{3,4}}
[8,7,3,1,6,2,5,4]=>[3,7,6,5,2,4,8,1]=>[6,3,5,8,2,1,7,4]=>{{1,6},{2,3,5},{4,8},{7}}
[8,7,3,2,6,1,5,4]=>[6,3,7,5,1,2,8,4]=>[5,6,3,8,4,2,7,1]=>{{1,5},{2,6},{3},{4,8},{7}}
[6,5,7,2,8,3,4,1]=>[4,7,8,3,6,5,2,1]=>[7,6,4,1,8,2,3,5]=>{{1,7},{2,6},{3,4},{5,8}}
[6,5,7,2,8,1,4,3]=>[8,7,4,1,6,5,2,3]=>[4,6,7,3,8,1,5,2]=>{{1,4},{2,6},{3,7},{5,8}}
[6,2,7,5,8,1,4,3]=>[8,6,4,1,7,2,5,3]=>[4,6,8,3,7,5,1,2]=>{{1,4},{2,6},{3,8},{5,7}}
[6,5,7,3,8,1,4,2]=>[8,4,7,1,6,5,3,2]=>[4,7,6,3,8,1,2,5]=>{{1,4},{2,7},{3,6},{5,8}}
[2,6,5,1,4,3,8,7]=>[5,2,4,1,6,3,8,7]=>[2,4,6,3,5,1,8,7]=>{{1,2,4},{3,6},{5},{7,8}}
[6,5,1,2,4,3,8,7]=>[5,1,4,2,6,3,8,7]=>[4,1,6,3,5,2,8,7]=>{{1,4},{2},{3,6},{5},{7,8}}
[2,1,4,8,7,3,6,5]=>[2,1,7,4,6,3,8,5]=>[2,1,4,6,8,5,7,3]=>{{1,2},{3,4,6},{5,8},{7}}
[8,7,3,4,1,2,6,5]=>[4,1,7,3,6,2,8,5]=>[6,1,4,2,8,5,7,3]=>{{1,6},{2},{3,4},{5,8},{7}}
[8,7,1,2,4,3,6,5]=>[7,1,4,2,6,3,8,5]=>[4,1,6,3,8,5,7,2]=>{{1,4},{2},{3,6},{5,8},{7}}
[2,1,8,7,3,4,6,5]=>[2,1,7,3,6,4,8,5]=>[2,1,6,3,8,5,7,4]=>{{1,2},{3,6},{4},{5,8},{7}}
[2,8,7,1,4,3,6,5]=>[7,2,4,1,6,3,8,5]=>[2,4,6,3,8,5,7,1]=>{{1,2,4},{3,6},{5,8},{7}}
[2,8,7,3,4,1,6,5]=>[4,2,7,3,6,1,8,5]=>[2,6,4,1,8,5,7,3]=>{{1,2,6},{3,4},{5,8},{7}}
[2,8,7,5,6,3,4,1]=>[4,2,6,3,7,5,8,1]=>[2,8,4,1,6,3,7,5]=>{{1,2,8},{3,4},{5,6},{7}}
[2,4,8,7,3,1,6,5]=>[3,2,7,4,6,1,8,5]=>[2,4,3,6,8,5,7,1]=>{{1,2,4,6},{3},{5,8},{7}}
[2,4,3,1,8,7,5,6]=>[3,2,4,1,7,5,8,6]=>[2,4,3,1,8,5,7,6]=>{{1,2,4},{3},{5,8},{6},{7}}
[4,3,1,2,6,8,7,5]=>[3,1,4,2,7,6,8,5]=>[4,1,3,2,6,8,7,5]=>{{1,4},{2},{3},{5,6,8},{7}}
[2,8,7,5,6,1,4,3]=>[6,2,4,1,7,5,8,3]=>[2,4,8,3,6,1,7,5]=>{{1,2,4},{3,8},{5,6},{7}}
[2,6,8,7,5,1,4,3]=>[5,2,4,1,7,6,8,3]=>[2,4,6,3,5,8,7,1]=>{{1,2,4},{3,6,8},{5},{7}}
[8,7,5,6,1,2,4,3]=>[6,1,4,2,7,5,8,3]=>[4,1,8,3,6,2,7,5]=>{{1,4},{2},{3,8},{5,6},{7}}
[8,6,1,3,2,4,5,7]=>[6,3,1,2,4,8,5,7]=>[3,8,2,1,4,6,5,7]=>{{1,3},{2,8},{4},{5},{6},{7}}
[6,7,8,2,4,5,1,3]=>[5,8,1,3,2,6,7,4]=>[6,5,2,1,4,7,8,3]=>{{1,6,7,8},{2,5},{3},{4}}
[5,8,6,1,7,3,2,4]=>[6,3,8,2,5,7,4,1]=>[5,6,3,1,8,7,2,4]=>{{1,5,8},{2,6,7},{3},{4}}
[2,5,7,1,8,4,3,6]=>[7,2,4,8,5,3,1,6]=>[2,5,7,4,8,1,6,3]=>{{1,2,5,8},{3,7},{4},{6}}
[1,5,7,8,6,3,2,4]=>[1,3,6,2,5,8,7,4]=>[1,5,3,2,7,6,8,4]=>{{1},{2,5,7,8},{3},{4},{6}}
[8,3,7,5,6,2,1,4]=>[2,6,8,1,7,5,3,4]=>[8,2,6,3,7,1,5,4]=>{{1,8},{2},{3,6},{4},{5,7}}
[1,5,8,4,3,7,6,2]=>[1,6,4,7,5,8,2,3]=>[1,5,7,4,8,6,3,2]=>{{1},{2,5,8},{3,7},{4},{6}}
[7,3,4,1,6,5,8,2]=>[4,8,7,3,6,2,1,5]=>[7,4,6,1,8,3,5,2]=>{{1,7},{2,4},{3,6},{5,8}}
[3,7,4,2,5,8,6,1]=>[6,4,3,8,2,7,1,5]=>[3,6,8,4,1,7,5,2]=>{{1,3,8},{2,6,7},{4},{5}}
[8,3,7,5,1,2,6,4]=>[5,1,7,8,6,3,4,2]=>[8,1,6,5,7,3,2,4]=>{{1,8},{2},{3,6},{4,5,7}}
[8,7,3,1,4,5,2,6]=>[3,7,5,1,2,4,8,6]=>[8,3,5,2,4,1,7,6]=>{{1,8},{2,3,5},{4},{6},{7}}
[6,4,7,3,1,5,2,8]=>[3,7,5,6,2,4,1,8]=>[7,3,5,6,2,1,4,8]=>{{1,7},{2,3,5},{4,6},{8}}
[8,7,4,1,5,2,3,6]=>[4,7,2,5,3,1,8,6]=>[8,4,1,5,2,3,7,6]=>{{1,8},{2,4,5},{3},{6},{7}}
[8,7,5,1,2,6,3,4]=>[5,1,7,3,6,4,8,2]=>[8,1,5,2,6,3,7,4]=>{{1,8},{2},{3,5,6},{4},{7}}
[5,2,1,3,7,6,4,8]=>[2,5,1,6,3,7,4,8]=>[7,2,1,5,4,6,3,8]=>{{1,7},{2},{3},{4,5},{6},{8}}
[2,3,7,1,8,6,4,5]=>[7,2,3,6,4,8,1,5]=>[2,3,7,8,1,6,5,4]=>{{1,2,3,7},{4,8},{5},{6}}
[3,2,1,6,8,4,7,5]=>[2,3,1,8,7,6,4,5]=>[3,2,1,6,7,8,5,4]=>{{1,3},{2},{4,6,8},{5,7}}
[2,1,5,8,6,4,7,3]=>[2,1,7,6,5,8,4,3]=>[2,1,5,7,8,6,3,4]=>{{1,2},{3,5,8},{4,7},{6}}
[5,7,1,2,3,8,6,4]=>[7,1,2,6,5,8,3,4]=>[5,1,2,7,8,6,4,3]=>{{1,5,8},{2},{3},{4,7},{6}}
[1,8,6,4,2,5,7,3]=>[1,4,6,8,2,7,5,3]=>[1,8,6,4,3,7,2,5]=>{{1},{2,8},{3,6,7},{4},{5}}
[8,3,2,5,6,1,7,4]=>[6,3,8,7,2,4,5,1]=>[6,8,3,7,2,4,1,5]=>{{1,6},{2,8},{3},{4,7},{5}}
[1,7,8,5,2,6,3,4]=>[1,5,8,3,6,4,7,2]=>[1,7,5,2,6,3,8,4]=>{{1},{2,7,8},{3,5,6},{4}}
[6,7,2,1,5,3,8,4]=>[2,7,5,8,1,6,3,4]=>[6,2,7,5,4,8,3,1]=>{{1,6,8},{2},{3,7},{4,5}}
[4,8,3,1,7,6,5,2]=>[3,8,5,4,6,7,2,1]=>[5,3,4,8,6,7,1,2]=>{{1,5,6,7},{2,3,4,8}}
[3,8,7,2,6,5,1,4]=>[5,6,3,1,7,4,8,2]=>[6,3,8,2,5,1,7,4]=>{{1,6},{2,3,8},{4},{5},{7}}
[8,5,6,1,4,7,2,3]=>[6,7,2,1,8,5,4,3]=>[8,7,1,3,6,2,4,5]=>{{1,8},{2,7},{3},{4},{5,6}}
[1,6,7,5,8,3,2,4]=>[1,3,8,2,7,6,5,4]=>[1,6,3,2,7,8,4,5]=>{{1},{2,6,8},{3},{4},{5,7}}
[3,6,7,5,8,2,1,4]=>[2,8,3,1,7,6,5,4]=>[3,2,6,1,7,8,4,5]=>{{1,3,6,8},{2},{4},{5,7}}
[2,7,5,3,6,4,8,1]=>[8,2,5,7,6,4,3,1]=>[2,5,8,6,7,1,3,4]=>{{1,2,5,7},{3,8},{4,6}}
[2,7,5,8,6,3,4,1]=>[4,2,6,3,8,7,1,5]=>[2,8,4,1,6,7,5,3]=>{{1,2,8},{3,4},{5,6,7}}
[4,7,5,3,6,8,1,2]=>[8,1,5,4,7,3,6,2]=>[4,1,5,8,7,2,3,6]=>{{1,4,8},{2},{3,5,7},{6}}
[5,7,6,1,8,3,2,4]=>[6,3,7,2,5,8,4,1]=>[5,7,3,1,8,6,2,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[7,4,5,1,3,8,6,2]=>[5,6,1,8,4,7,2,3]=>[8,6,2,5,1,7,4,3]=>{{1,8},{2,6,7},{3},{4,5}}
[1,8,4,6,3,2,7,5]=>[1,3,6,8,7,4,2,5]=>[1,8,3,6,7,4,5,2]=>{{1},{2,8},{3},{4,6},{5,7}}
[7,1,3,2,4,6,8,5]=>[7,3,1,2,8,4,6,5]=>[3,8,2,1,7,5,4,6]=>{{1,3},{2,8},{4},{5,7},{6}}
[3,6,7,8,2,1,4,5]=>[2,8,3,1,4,6,7,5]=>[3,2,6,1,4,7,8,5]=>{{1,3,6,7,8},{2},{4},{5}}
[8,1,6,2,3,4,7,5]=>[8,6,2,3,7,1,4,5]=>[6,8,1,2,7,5,4,3]=>{{1,6},{2,8},{3},{4},{5,7}}
[4,5,8,6,3,7,2,1]=>[2,7,6,4,5,8,3,1]=>[4,2,5,7,8,6,1,3]=>{{1,4,7},{2},{3,5,8},{6}}
[6,1,2,8,4,7,5,3]=>[6,1,5,7,8,2,3,4]=>[7,1,8,6,5,4,3,2]=>{{1,7},{2},{3,8},{4,6},{5}}
[7,2,1,8,6,4,5,3]=>[2,7,5,6,4,8,1,3]=>[5,2,8,7,1,6,4,3]=>{{1,5},{2},{3,8},{4,7},{6}}
[2,4,8,5,7,6,1,3]=>[6,2,1,4,7,8,3,5]=>[2,4,1,8,7,6,5,3]=>{{1,2,4,8},{3},{5,7},{6}}
[1,3,8,6,4,7,2,5]=>[1,7,3,6,2,8,4,5]=>[1,3,7,8,4,6,5,2]=>{{1},{2,3,7},{4,8},{5},{6}}
[1,8,4,7,6,2,3,5]=>[1,6,2,7,3,8,5,4]=>[1,8,2,7,4,6,3,5]=>{{1},{2,8},{3},{4,7},{5},{6}}
[7,2,3,8,4,5,6,1]=>[6,7,2,8,4,5,3,1]=>[8,7,1,6,2,3,4,5]=>{{1,8},{2,7},{3},{4,6},{5}}
[6,5,1,8,7,2,4,3]=>[5,6,4,2,7,3,8,1]=>[6,4,8,2,5,1,7,3]=>{{1,6},{2,4},{3,8},{5},{7}}
[4,1,8,7,6,5,2,3]=>[4,5,2,1,6,7,8,3]=>[8,4,1,3,5,6,7,2]=>{{1,8},{2,4},{3},{5},{6},{7}}
[7,6,5,2,8,4,3,1]=>[3,4,8,5,6,7,2,1]=>[8,4,3,5,6,7,1,2]=>{{1,8},{2,4,5,6,7},{3}}
[4,5,3,1,8,7,2,6]=>[3,5,7,4,2,1,8,6]=>[5,4,3,8,1,2,7,6]=>{{1,5},{2,4,8},{3},{6},{7}}
[3,1,8,5,7,2,6,4]=>[3,7,1,6,8,2,5,4]=>[7,3,2,8,6,5,1,4]=>{{1,7},{2,3},{4,8},{5,6}}
[8,5,2,6,4,3,1,7]=>[3,4,6,5,8,2,1,7]=>[8,4,3,6,5,1,2,7]=>{{1,8},{2,4,6},{3},{5},{7}}
[4,3,5,2,8,6,7,1]=>[7,5,4,3,2,8,6,1]=>[4,5,8,1,2,7,3,6]=>{{1,4},{2,5},{3,8},{6,7}}
[5,6,7,4,2,8,3,1]=>[3,8,4,7,5,6,1,2]=>[6,3,4,5,7,8,2,1]=>{{1,6,8},{2,3,4,5,7}}
[6,4,1,8,5,2,7,3]=>[4,6,5,8,7,2,1,3]=>[8,5,7,4,6,2,3,1]=>{{1,8},{2,5,6},{3,7},{4}}
[7,5,6,1,2,3,8,4]=>[6,1,2,8,7,5,3,4]=>[8,1,2,6,7,3,5,4]=>{{1,8},{2},{3},{4,6},{5,7}}
[7,4,8,5,6,1,2,3]=>[6,1,2,7,8,5,4,3]=>[8,1,2,7,6,3,4,5]=>{{1,8},{2},{3},{4,7},{5,6}}
[4,2,7,5,1,8,3,6]=>[5,4,7,2,8,3,6,1]=>[7,8,4,2,5,1,3,6]=>{{1,7},{2,8},{3,4},{5},{6}}
[2,7,5,4,8,3,1,6]=>[3,2,8,5,7,1,4,6]=>[2,5,3,8,7,4,6,1]=>{{1,2,5,7},{3},{4,8},{6}}
[4,7,8,5,6,2,3,1]=>[3,6,2,4,8,5,7,1]=>[4,3,1,7,6,2,8,5]=>{{1,4,7,8},{2,3},{5,6}}
[2,7,8,5,6,1,4,3]=>[6,2,4,1,8,5,7,3]=>[2,4,7,3,6,1,8,5]=>{{1,2,4},{3,7,8},{5,6}}
[5,8,1,6,7,4,2,3]=>[8,4,2,7,5,1,6,3]=>[4,7,1,5,8,3,2,6]=>{{1,4,5,8},{2,7},{3},{6}}
[7,1,8,4,2,5,3,6]=>[7,4,8,5,3,2,1,6]=>[5,8,4,7,1,2,6,3]=>{{1,5},{2,8},{3,4,7},{6}}
[8,6,3,5,7,4,1,2]=>[4,1,7,6,3,8,2,5]=>[8,1,4,7,2,6,5,3]=>{{1,8},{2},{3,4,7},{5},{6}}
[1,8,5,7,6,3,2,4]=>[1,3,6,2,7,8,4,5]=>[1,8,3,2,7,6,5,4]=>{{1},{2,8},{3},{4},{5,7},{6}}
[1,4,7,3,6,8,5,2]=>[1,5,8,4,7,3,2,6]=>[1,5,4,8,7,2,6,3]=>{{1},{2,5,7},{3,4,8},{6}}
[8,4,2,7,1,6,3,5]=>[7,4,8,6,3,1,5,2]=>[6,8,4,7,1,5,2,3]=>{{1,6},{2,8},{3,4,7},{5}}
[5,7,8,3,4,6,1,2]=>[6,1,8,3,5,4,7,2]=>[6,1,5,2,7,3,8,4]=>{{1,6},{2},{3,5,7,8},{4}}
[7,5,1,3,4,2,6,8]=>[5,4,1,3,7,2,6,8]=>[4,7,2,1,5,3,6,8]=>{{1,4},{2,7},{3},{5},{6},{8}}
[1,7,3,8,2,5,6,4]=>[1,8,7,6,2,3,4,5]=>[1,6,7,8,4,5,3,2]=>{{1},{2,6},{3,7},{4,8},{5}}
[1,5,7,3,8,2,6,4]=>[1,8,7,6,5,2,3,4]=>[1,5,6,7,8,4,3,2]=>{{1},{2,5,8},{3,6},{4,7}}
[7,1,5,3,6,2,4,8]=>[7,6,5,2,1,3,4,8]=>[5,6,7,2,4,3,1,8]=>{{1,5},{2,6},{3,7},{4},{8}}
[3,1,2,7,5,8,4,6]=>[3,1,2,8,7,4,5,6]=>[3,1,2,7,8,5,6,4]=>{{1,3},{2},{4,7},{5,8},{6}}
[5,3,1,7,4,6,8,2]=>[3,5,8,7,2,4,6,1]=>[8,5,3,7,2,1,4,6]=>{{1,8},{2,5},{3},{4,7},{6}}
[8,1,5,4,6,3,7,2]=>[8,7,6,5,1,2,4,3]=>[5,6,7,8,4,3,1,2]=>{{1,5},{2,6},{3,7},{4,8}}
[1,4,8,6,2,3,5,7]=>[1,6,2,4,3,8,5,7]=>[1,4,2,8,3,6,5,7]=>{{1},{2,4,8},{3},{5},{6},{7}}
[1,8,4,5,6,7,2,3]=>[1,7,2,8,4,5,6,3]=>[1,8,2,7,3,4,5,6]=>{{1},{2,8},{3},{4,7},{5},{6}}
[1,8,6,7,4,2,3,5]=>[1,4,2,7,3,8,6,5]=>[1,8,2,4,3,7,5,6]=>{{1},{2,8},{3},{4},{5},{6,7}}
[1,8,4,5,6,2,3,7]=>[1,6,2,8,4,5,3,7]=>[1,8,2,6,3,4,5,7]=>{{1},{2,8},{3},{4,6},{5},{7}}
[3,1,8,4,6,2,7,5]=>[3,6,1,8,7,4,2,5]=>[8,3,2,6,7,4,5,1]=>{{1,8},{2,3},{4,6},{5,7}}
[7,3,5,2,8,4,6,1]=>[6,5,7,8,3,4,2,1]=>[7,8,6,5,2,1,3,4]=>{{1,7},{2,8},{3,6},{4,5}}
[8,4,5,6,1,3,7,2]=>[6,7,1,8,4,5,3,2]=>[8,7,2,6,1,3,4,5]=>{{1,8},{2,7},{3},{4,6},{5}}
[2,1,3,4,8,5,7,6]=>[2,1,3,4,8,7,5,6]=>[2,1,3,4,7,8,6,5]=>{{1,2},{3},{4},{5,7},{6,8}}
[8,3,5,6,1,4,7,2]=>[6,7,8,1,4,3,5,2]=>[8,7,6,3,1,4,2,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[5,7,2,1,8,4,3,6]=>[2,7,4,8,5,3,1,6]=>[5,2,7,4,8,1,6,3]=>{{1,5,8},{2},{3,7},{4},{6}}
[6,2,8,4,7,5,1,3]=>[5,7,1,6,8,4,3,2]=>[8,6,2,7,5,1,3,4]=>{{1,8},{2,6},{3},{4,7},{5}}
[3,5,7,6,2,8,4,1]=>[4,8,3,6,5,7,1,2]=>[4,3,6,5,8,7,2,1]=>{{1,4,5,8},{2,3,6,7}}
[5,3,6,2,8,7,4,1]=>[4,7,6,5,1,3,8,2]=>[8,4,5,6,3,1,7,2]=>{{1,8},{2,4,6},{3,5},{7}}
[2,8,4,1,3,7,6,5]=>[4,2,1,8,6,7,3,5]=>[2,6,1,4,8,7,5,3]=>{{1,2,6,7},{3},{4},{5,8}}
[7,2,6,8,1,4,3,5]=>[8,7,4,1,2,5,6,3]=>[4,7,8,3,2,1,5,6]=>{{1,4},{2,7},{3,8},{5},{6}}
[6,2,5,3,7,4,1,8]=>[4,7,6,5,3,1,2,8]=>[7,4,5,6,1,3,2,8]=>{{1,7},{2,4,6},{3,5},{8}}
[7,3,6,2,5,4,1,8]=>[4,5,6,7,1,2,3,8]=>[7,6,5,4,3,2,1,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[7,3,1,4,6,5,2,8]=>[3,7,5,1,6,2,4,8]=>[7,3,5,2,6,4,1,8]=>{{1,7},{2,3,5,6},{4},{8}}
[8,3,7,2,6,4,1,5]=>[4,6,7,8,1,3,5,2]=>[8,7,6,4,3,2,1,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[8,3,7,4,1,5,2,6]=>[4,7,5,8,1,2,3,6]=>[8,5,7,4,3,2,6,1]=>{{1,8},{2,5},{3,7},{4},{6}}
[6,3,5,2,4,8,1,7]=>[8,5,6,2,3,4,1,7]=>[5,8,6,2,3,1,4,7]=>{{1,5},{2,8},{3,6},{4},{7}}
[1,2,3,7,5,8,4,6]=>[1,2,3,8,7,4,5,6]=>[1,2,3,7,8,5,6,4]=>{{1},{2},{3},{4,7},{5,8},{6}}
[3,6,7,1,8,4,2,5]=>[7,4,3,8,2,6,1,5]=>[3,6,7,4,1,8,5,2]=>{{1,3,7},{2,6,8},{4},{5}}
[2,7,3,8,4,5,6,1]=>[6,2,7,8,4,5,3,1]=>[2,8,7,6,1,3,4,5]=>{{1,2,8},{3,7},{4,6},{5}}
[7,2,5,8,1,6,3,4]=>[8,7,6,3,2,1,5,4]=>[6,7,8,1,3,5,2,4]=>{{1,6},{2,7},{3,8},{4},{5}}
[1,2,8,4,7,3,5,6]=>[1,2,7,8,3,4,6,5]=>[1,2,8,7,4,5,3,6]=>{{1},{2},{3,8},{4,7},{5},{6}}
[7,2,4,8,6,3,5,1]=>[5,7,6,2,4,8,1,3]=>[8,5,7,2,1,6,4,3]=>{{1,8},{2,5},{3,7},{4},{6}}
[7,1,8,6,2,5,4,3]=>[7,6,4,5,2,8,1,3]=>[4,5,8,7,2,6,3,1]=>{{1,4,7},{2,5},{3,8},{6}}
[1,5,8,2,6,4,7,3]=>[1,8,7,6,5,2,4,3]=>[1,5,6,7,8,4,2,3]=>{{1},{2,5,8},{3,6},{4,7}}
[1,6,4,5,7,3,8,2]=>[1,8,7,6,4,5,3,2]=>[1,6,7,8,2,3,4,5]=>{{1},{2,6},{3,7},{4,8},{5}}
[6,8,2,7,5,4,3,1]=>[3,4,5,7,8,6,1,2]=>[7,6,3,4,5,8,2,1]=>{{1,7},{2,6,8},{3},{4},{5}}
[3,4,5,6,7,8,9,10,11,1,2]=>[11,1,3,4,5,6,7,8,9,10,2]=>[3,1,4,5,6,7,8,9,10,11,2]=>{{1,3,4,5,6,7,8,9,10,11},{2}}
[8,1,6,3,7,4,2,5]=>[8,4,7,6,2,1,5,3]=>[4,8,6,7,2,5,1,3]=>{{1,4,7},{2,8},{3,6},{5}}
[4,6,7,3,1,8,5,2]=>[3,7,5,4,8,6,2,1]=>[6,3,4,7,5,8,1,2]=>{{1,6,8},{2,3,4,7},{5}}
[4,8,1,5,6,3,7,2]=>[8,7,6,4,1,2,5,3]=>[4,6,7,8,3,5,1,2]=>{{1,4,8},{2,6},{3,7},{5}}
[3,8,1,7,2,6,5,4]=>[8,7,3,5,6,2,1,4]=>[3,5,6,8,7,2,4,1]=>{{1,3,6},{2,5,7},{4,8}}
[8,1,4,2,3,5,7,6]=>[8,4,2,1,3,7,5,6]=>[4,7,1,3,2,8,6,5]=>{{1,4},{2,7},{3},{5},{6,8}}
[3,6,8,5,2,4,7,1]=>[7,5,3,2,8,6,4,1]=>[3,6,7,1,5,8,2,4]=>{{1,3,7},{2,6,8},{4},{5}}
[6,2,3,5,8,4,1,7]=>[4,8,2,6,3,1,5,7]=>[8,4,1,6,2,5,3,7]=>{{1,8},{2,4,6},{3},{5},{7}}
[4,7,3,8,6,2,5,1]=>[5,6,8,4,2,7,1,3]=>[6,5,4,8,2,7,3,1]=>{{1,6,7},{2,5},{3,4,8}}
[5,4,7,3,8,2,1,6]=>[2,8,7,5,4,1,3,6]=>[5,2,7,8,1,4,6,3]=>{{1,5},{2},{3,7},{4,8},{6}}
[5,8,4,2,7,3,6,1]=>[6,4,8,7,5,3,1,2]=>[6,7,4,5,8,1,3,2]=>{{1,6},{2,7},{3,4,5,8}}
[8,2,7,3,4,5,1,6]=>[5,8,7,3,4,2,6,1]=>[8,5,7,1,2,3,4,6]=>{{1,8},{2,5},{3,7},{4},{6}}
[8,1,5,2,4,6,3,7]=>[8,5,6,2,1,4,3,7]=>[5,8,6,2,4,1,3,7]=>{{1,5},{2,8},{3,6},{4},{7}}
[3,5,8,2,1,4,7,6]=>[2,8,3,1,5,7,4,6]=>[3,2,5,1,7,8,6,4]=>{{1,3,5,7},{2},{4},{6,8}}
[8,7,3,2,5,4,6,1]=>[6,3,7,5,2,4,8,1]=>[5,6,3,8,2,1,7,4]=>{{1,5},{2,6},{3},{4,8},{7}}
[7,5,6,1,8,3,2,4]=>[6,3,8,2,7,5,1,4]=>[6,8,3,1,7,2,5,4]=>{{1,6},{2,8},{3},{4},{5,7}}
[5,4,7,3,2,8,1,6]=>[8,3,7,5,4,1,2,6]=>[3,7,5,8,1,4,6,2]=>{{1,3,5},{2,7},{4,8},{6}}
[5,8,3,4,6,1,2,7]=>[6,1,8,3,5,4,2,7]=>[6,1,5,2,8,3,4,7]=>{{1,6},{2},{3,5,8},{4},{7}}
[6,4,8,5,1,2,3,7]=>[5,1,2,8,6,3,4,7]=>[8,1,2,5,6,4,3,7]=>{{1,8},{2},{3},{4,5,6},{7}}
[5,4,8,3,2,7,1,6]=>[7,3,8,5,4,1,2,6]=>[5,7,3,8,1,4,6,2]=>{{1,5},{2,7},{3},{4,8},{6}}
[6,2,8,1,7,4,5,3]=>[8,6,5,7,4,2,1,3]=>[5,7,8,6,1,3,4,2]=>{{1,5},{2,7},{3,8},{4,6}}
[3,5,8,7,4,6,2,1]=>[2,6,3,7,5,4,8,1]=>[3,2,6,5,8,1,7,4]=>{{1,3,6},{2},{4,5,8},{7}}
[1,5,2,8,7,6,4,3]=>[1,5,4,6,2,7,8,3]=>[1,5,8,4,3,6,7,2]=>{{1},{2,5},{3,8},{4},{6},{7}}
[3,5,7,6,8,4,1,2]=>[4,1,3,8,5,7,6,2]=>[3,1,5,4,7,8,2,6]=>{{1,3,5,7},{2},{4},{6,8}}
[6,7,3,1,5,2,4,8]=>[3,7,5,2,4,6,1,8]=>[6,3,5,1,2,7,4,8]=>{{1,6,7},{2,3,5},{4},{8}}
[2,1,7,4,3,8,5,6]=>[2,1,4,7,8,5,3,6]=>[2,1,8,4,7,3,6,5]=>{{1,2},{3,8},{4},{5,7},{6}}
[1,4,6,7,3,5,2,8]=>[1,5,7,4,3,6,2,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,8,6,3,5,7,4,1]=>[4,2,7,6,3,8,1,5]=>[2,8,4,7,1,6,5,3]=>{{1,2,8},{3,4,7},{5},{6}}
[3,1,4,7,5,2,8,6]=>[3,5,1,4,7,8,2,6]=>[4,3,2,8,5,7,6,1]=>{{1,4,8},{2,3},{5},{6,7}}
[8,2,6,3,4,1,7,5]=>[4,8,6,3,7,2,1,5]=>[8,4,6,1,7,3,5,2]=>{{1,8},{2,4},{3,6},{5,7}}
[1,7,6,4,2,3,5,8]=>[1,4,2,6,3,7,5,8]=>[1,7,2,4,3,6,5,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[8,2,5,3,1,7,4,6]=>[3,5,8,7,1,4,2,6]=>[8,5,3,7,4,1,6,2]=>{{1,8},{2,5},{3},{4,7},{6}}
[1,7,3,8,2,4,6,5]=>[1,8,7,2,6,3,5,4]=>[1,6,7,3,8,5,2,4]=>{{1},{2,6},{3,7},{4},{5,8}}
[5,8,1,2,4,3,6,7]=>[8,1,4,2,5,3,6,7]=>[4,1,5,3,8,2,6,7]=>{{1,4},{2},{3,5,8},{6},{7}}
[6,3,8,1,2,5,4,7]=>[8,1,6,5,2,3,4,7]=>[5,1,6,8,4,3,2,7]=>{{1,5},{2},{3,6},{4,8},{7}}
[7,5,4,8,6,3,2,1]=>[2,3,6,5,8,7,1,4]=>[6,2,3,8,5,7,4,1]=>{{1,6,7},{2},{3},{4,8},{5}}
[1,5,3,2,6,8,7,4]=>[1,3,5,7,2,6,8,4]=>[1,6,3,5,4,8,7,2]=>{{1},{2,6,8},{3},{4,5},{7}}
[1,6,3,2,8,5,4,7]=>[1,3,6,5,8,2,4,7]=>[1,6,3,8,5,4,2,7]=>{{1},{2,6},{3},{4,8},{5},{7}}
[8,5,2,4,6,7,3,1]=>[3,7,5,2,8,4,1,6]=>[8,3,7,1,5,2,6,4]=>{{1,8},{2,3,7},{4},{5},{6}}
[5,2,8,6,4,7,1,3]=>[7,5,1,6,2,8,4,3]=>[5,8,2,7,4,6,1,3]=>{{1,5},{2,8},{3},{4,7},{6}}
[8,6,4,2,7,1,5,3]=>[7,4,6,5,1,8,3,2]=>[4,8,5,7,3,6,1,2]=>{{1,4,7},{2,8},{3,5},{6}}
[1,5,8,2,6,7,4,3]=>[1,8,4,7,5,2,6,3]=>[1,4,7,5,8,3,2,6]=>{{1},{2,4,5,8},{3,7},{6}}
[2,7,3,6,5,1,8,4]=>[5,2,6,7,8,1,4,3]=>[2,8,7,6,5,4,1,3]=>{{1,2,8},{3,7},{4,6},{5}}
[2,4,3,8,7,1,6,5]=>[7,2,4,3,6,1,8,5]=>[2,4,6,1,8,5,7,3]=>{{1,2,4},{3,6},{5,8},{7}}
[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>[5,6,7,8,1,2,3,4,9]=>{{1,5},{2,6},{3,7},{4,8},{9}}
[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>[6,7,8,9,10,1,2,3,4,5]=>{{1,6},{2,7},{3,8},{4,9},{5,10}}
[6,1,8,5,2,7,3,4]=>[6,5,8,3,7,1,4,2]=>[7,8,5,1,6,4,2,3]=>{{1,7},{2,8},{3,5,6},{4}}
[8,3,4,7,6,2,1,5]=>[2,6,7,3,1,8,5,4]=>[8,2,7,1,4,6,3,5]=>{{1,8},{2},{3,7},{4},{5},{6}}
[3,2,8,5,6,7,1,4]=>[7,3,2,1,8,5,6,4]=>[3,8,1,2,7,4,5,6]=>{{1,3},{2,8},{4},{5,7},{6}}
[3,7,8,2,5,6,1,4]=>[6,8,3,1,4,2,7,5]=>[6,3,7,2,1,5,8,4]=>{{1,6},{2,3,7,8},{4},{5}}
[1,8,3,7,4,5,6,2]=>[1,6,8,7,4,5,3,2]=>[1,8,6,7,2,3,4,5]=>{{1},{2,8},{3,6},{4,7},{5}}
[1,7,3,4,6,8,5,2]=>[1,5,8,3,7,4,2,6]=>[1,8,5,2,7,3,6,4]=>{{1},{2,8},{3,5,7},{4},{6}}
[1,7,3,8,4,5,6,2]=>[1,6,7,8,4,5,3,2]=>[1,8,7,6,2,3,4,5]=>{{1},{2,8},{3,7},{4,6},{5}}
[8,6,5,1,2,4,3,7]=>[5,1,4,2,6,8,3,7]=>[4,1,8,3,5,6,2,7]=>{{1,4},{2},{3,8},{5},{6},{7}}
[8,4,1,2,5,3,6,7]=>[4,1,8,5,3,2,6,7]=>[8,1,4,5,2,3,6,7]=>{{1,8},{2},{3,4,5},{6},{7}}
[7,2,4,1,3,6,8,5]=>[4,7,1,2,8,3,6,5]=>[8,4,2,3,7,5,1,6]=>{{1,8},{2,4},{3},{5,7},{6}}
[5,2,7,6,1,8,4,3]=>[6,5,4,7,2,8,3,1]=>[5,7,8,4,2,6,1,3]=>{{1,5},{2,7},{3,8},{4},{6}}
[6,8,7,1,4,5,2,3]=>[7,5,2,1,4,6,8,3]=>[5,6,1,3,2,8,7,4]=>{{1,5},{2,6,8},{3},{4},{7}}
[7,5,6,2,4,3,8,1]=>[8,6,4,2,7,5,3,1]=>[4,6,8,2,7,1,3,5]=>{{1,4},{2,6},{3,8},{5,7}}
[8,1,7,4,5,6,2,3]=>[8,6,2,7,4,5,1,3]=>[6,8,1,7,2,3,5,4]=>{{1,6},{2,8},{3},{4,7},{5}}
[2,1,7,8,4,5,6,3]=>[2,1,6,8,4,5,7,3]=>[2,1,7,6,3,4,8,5]=>{{1,2},{3,7,8},{4,6},{5}}
[5,4,1,6,2,8,3,7]=>[4,5,6,8,2,3,1,7]=>[8,6,5,4,2,1,3,7]=>{{1,8},{2,6},{3,5},{4},{7}}
[7,3,5,1,6,4,8,2]=>[5,8,7,6,3,2,1,4]=>[8,5,6,7,2,3,4,1]=>{{1,8},{2,5},{3,6},{4,7}}
[5,4,7,1,3,8,6,2]=>[7,6,1,5,4,8,3,2]=>[5,7,2,8,1,6,3,4]=>{{1,5},{2,7},{3},{4,8},{6}}
[8,1,4,2,5,7,3,6]=>[8,4,7,1,2,5,6,3]=>[4,8,7,3,2,1,5,6]=>{{1,4},{2,8},{3,7},{5},{6}}
[7,1,8,5,3,4,6,2]=>[7,6,5,3,8,4,1,2]=>[6,7,8,1,5,2,4,3]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,1,3,6,8,2,5,4]=>[7,8,1,5,3,2,4,6]=>[7,5,2,8,3,4,6,1]=>{{1,7},{2,5},{3},{4,8},{6}}
[3,6,7,5,8,2,4,1]=>[4,8,3,2,7,6,5,1]=>[4,3,6,1,7,8,2,5]=>{{1,4},{2,3,6,8},{5,7}}
[1,7,4,5,2,8,6,3]=>[1,5,6,8,4,7,3,2]=>[1,8,6,5,2,7,3,4]=>{{1},{2,8},{3,6,7},{4,5}}
[3,6,2,1,7,5,4,8]=>[2,6,3,5,7,1,4,8]=>[3,2,6,7,5,4,1,8]=>{{1,3,6},{2},{4,7},{5},{8}}
[7,2,8,5,6,4,3,1]=>[3,4,6,7,8,5,2,1]=>[8,7,3,4,6,1,2,5]=>{{1,8},{2,7},{3},{4},{5,6}}
[3,1,8,4,6,5,7,2]=>[3,7,1,8,6,4,5,2]=>[7,3,2,6,8,4,1,5]=>{{1,7},{2,3},{4,6},{5,8}}
[8,6,7,4,2,5,1,3]=>[5,4,1,7,2,8,6,3]=>[5,8,2,4,3,7,1,6]=>{{1,5},{2,8},{3},{4},{6,7}}
[8,6,4,1,5,2,3,7]=>[4,6,2,5,3,8,1,7]=>[8,4,1,5,2,6,3,7]=>{{1,8},{2,4,5},{3},{6},{7}}
[8,6,4,7,2,1,5,3]=>[2,7,5,6,1,8,4,3]=>[5,2,8,7,4,6,1,3]=>{{1,5},{2},{3,8},{4,7},{6}}
[8,6,4,2,5,7,1,3]=>[7,4,1,6,3,8,2,5]=>[4,8,2,7,1,6,5,3]=>{{1,4,7},{2,8},{3},{5},{6}}
[8,7,1,4,6,5,2,3]=>[7,5,2,1,6,4,8,3]=>[5,8,1,3,6,2,7,4]=>{{1,5,6},{2,8},{3},{4},{7}}
[7,4,5,1,2,8,6,3]=>[5,1,6,8,4,7,3,2]=>[8,1,6,5,2,7,3,4]=>{{1,8},{2},{3,6,7},{4,5}}
[3,8,2,5,1,7,4,6]=>[5,8,3,7,2,4,1,6]=>[5,3,8,7,2,1,6,4]=>{{1,5},{2,3,8},{4,7},{6}}
[4,8,5,2,1,7,3,6]=>[2,5,8,4,7,3,6,1]=>[5,2,4,8,7,1,3,6]=>{{1,5,7},{2},{3,4,8},{6}}
[8,6,4,1,7,3,2,5]=>[4,3,6,8,2,7,1,5]=>[6,8,3,4,1,7,5,2]=>{{1,6,7},{2,8},{3},{4},{5}}
[7,2,1,5,3,8,4,6]=>[2,7,5,8,1,4,3,6]=>[7,2,8,5,4,1,6,3]=>{{1,7},{2},{3,8},{4,5},{6}}
[3,6,8,4,5,1,7,2]=>[5,7,3,8,4,6,1,2]=>[6,3,7,5,1,8,4,2]=>{{1,6,8},{2,3,7},{4,5}}
[8,4,1,7,3,2,5,6]=>[4,3,8,7,2,5,6,1]=>[4,8,3,7,1,2,5,6]=>{{1,4,7},{2,8},{3},{5},{6}}
[3,5,8,4,2,1,6,7]=>[2,4,3,8,5,1,6,7]=>[3,2,5,4,8,1,6,7]=>{{1,3,5,8},{2},{4},{6},{7}}
[2,4,6,7,8,3,5,1]=>[5,2,8,4,3,6,7,1]=>[2,5,4,6,1,7,8,3]=>{{1,2,5},{3,4,6,7,8}}
[1,8,4,7,5,2,6,3]=>[1,5,7,6,8,2,4,3]=>[1,8,6,7,5,4,2,3]=>{{1},{2,8},{3,6},{4,7},{5}}
[1,6,3,2,7,5,4,8]=>[1,3,6,5,7,2,4,8]=>[1,6,3,7,5,4,2,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[1,8,3,7,5,2,4,6]=>[1,5,7,2,8,3,4,6]=>[1,8,7,3,5,4,6,2]=>{{1},{2,8},{3,7},{4},{5},{6}}
[5,7,1,4,8,2,3,6]=>[7,8,2,1,5,4,6,3]=>[7,5,1,3,8,2,4,6]=>{{1,7},{2,5,8},{3},{4},{6}}
[4,8,3,5,7,6,1,2]=>[6,1,7,4,3,8,2,5]=>[7,1,4,8,2,6,5,3]=>{{1,7},{2},{3,4,8},{5},{6}}
[7,4,1,6,2,5,3,8]=>[4,7,6,5,3,2,1,8]=>[7,4,5,6,1,2,3,8]=>{{1,7},{2,4,6},{3,5},{8}}
[5,3,1,8,2,6,4,7]=>[3,5,8,6,2,1,4,7]=>[8,5,3,6,2,4,1,7]=>{{1,8},{2,5},{3},{4,6},{7}}
[8,4,2,3,1,6,5,7]=>[3,4,2,8,6,1,5,7]=>[6,3,1,4,8,5,2,7]=>{{1,6},{2,3},{4},{5,8},{7}}
[6,4,5,2,8,1,7,3]=>[8,5,7,6,4,2,1,3]=>[5,8,6,7,1,3,4,2]=>{{1,5},{2,8},{3,6},{4,7}}
[6,4,2,3,5,8,1,7]=>[8,4,2,6,3,5,1,7]=>[4,8,1,6,2,3,5,7]=>{{1,4,6},{2,8},{3},{5},{7}}
[8,2,4,6,7,1,5,3]=>[7,8,5,2,1,4,6,3]=>[7,5,8,2,4,1,3,6]=>{{1,7},{2,5},{3,8},{4},{6}}
[1,7,4,6,3,8,2,5]=>[1,8,6,7,2,5,4,3]=>[1,6,8,7,4,2,3,5]=>{{1},{2,6},{3,8},{4,7},{5}}
[7,2,8,1,4,5,6,3]=>[8,7,6,1,2,4,5,3]=>[6,7,8,3,4,2,1,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,5,2,3,6,8,4,1]=>[4,8,2,5,7,3,1,6]=>[8,4,1,5,7,2,6,3]=>{{1,8},{2,4,5,7},{3},{6}}
[6,7,8,4,1,5,2,3]=>[4,8,2,5,3,6,7,1]=>[6,4,1,5,2,7,8,3]=>{{1,6,7,8},{2,4,5},{3}}
[7,4,5,6,1,8,2,3]=>[6,8,2,7,4,5,1,3]=>[8,6,1,7,2,3,5,4]=>{{1,8},{2,6},{3},{4,7},{5}}
[1,5,8,2,3,6,7,4]=>[1,8,2,7,5,3,6,4]=>[1,5,2,7,8,4,3,6]=>{{1},{2,5,8},{3},{4,7},{6}}
[1,3,2,6,8,5,4,7]=>[1,3,2,5,8,6,4,7]=>[1,3,2,6,5,8,4,7]=>{{1},{2,3},{4,6,8},{5},{7}}
[1,8,4,2,3,6,5,7]=>[1,4,2,8,6,3,5,7]=>[1,6,2,4,8,5,3,7]=>{{1},{2,6},{3},{4},{5,8},{7}}
[1,7,4,8,3,2,5,6]=>[1,3,8,7,2,4,6,5]=>[1,7,3,8,4,5,2,6]=>{{1},{2,7},{3},{4,8},{5},{6}}
[8,2,3,7,4,5,6,1]=>[6,8,2,7,4,5,3,1]=>[8,6,1,7,2,3,4,5]=>{{1,8},{2,6},{3},{4,7},{5}}
[7,1,5,3,6,4,8,2]=>[7,8,5,6,1,2,3,4]=>[6,5,8,7,4,3,2,1]=>{{1,6},{2,5},{3,8},{4,7}}
[4,8,5,3,6,7,1,2]=>[7,1,5,4,8,3,6,2]=>[4,1,7,8,5,2,3,6]=>{{1,4,8},{2},{3,7},{5},{6}}
[8,7,2,4,1,5,3,6]=>[4,7,5,2,1,3,8,6]=>[8,4,5,2,3,1,7,6]=>{{1,8},{2,4},{3,5},{6},{7}}
[4,8,7,2,6,3,1,5]=>[3,6,7,4,1,5,8,2]=>[6,4,3,8,2,1,7,5]=>{{1,6},{2,4,8},{3},{5},{7}}
[4,2,8,7,6,5,1,3]=>[5,4,1,2,6,7,8,3]=>[4,8,2,3,5,6,7,1]=>{{1,4},{2,8},{3},{5},{6},{7}}
[6,3,8,7,4,5,2,1]=>[2,5,6,7,4,3,8,1]=>[8,2,6,5,1,3,7,4]=>{{1,8},{2},{3,6},{4,5},{7}}
[6,8,4,1,7,5,2,3]=>[4,8,2,5,7,6,3,1]=>[7,4,1,5,6,8,2,3]=>{{1,7},{2,4,5,6,8},{3}}
[8,1,4,6,7,2,5,3]=>[8,7,5,1,4,2,3,6]=>[5,7,8,3,1,4,6,2]=>{{1,5},{2,7},{3,8},{4},{6}}
[4,8,1,2,6,7,5,3]=>[8,1,5,4,7,2,6,3]=>[4,1,5,8,7,3,2,6]=>{{1,4,8},{2},{3,5,7},{6}}
[4,5,3,6,7,1,8,2]=>[7,8,5,4,3,6,1,2]=>[5,4,6,7,1,8,3,2]=>{{1,5},{2,4,7},{3,6,8}}
[4,5,1,8,6,3,7,2]=>[5,7,6,4,1,8,3,2]=>[7,4,5,8,3,6,1,2]=>{{1,7},{2,4,8},{3,5},{6}}
[2,6,3,5,7,8,1,4]=>[8,2,6,1,4,3,7,5]=>[2,6,7,3,1,5,8,4]=>{{1,2,6},{3,7,8},{4},{5}}
[2,5,6,8,1,3,7,4]=>[8,2,1,7,5,6,3,4]=>[2,5,1,6,7,8,4,3]=>{{1,2,5,7},{3},{4,6,8}}
[4,7,5,8,3,6,2,1]=>[2,6,8,4,7,3,5,1]=>[6,2,4,8,7,3,1,5]=>{{1,6},{2},{3,4,8},{5,7}}
[3,8,7,5,1,2,6,4]=>[5,1,3,7,6,4,8,2]=>[3,1,8,5,6,2,7,4]=>{{1,3,8},{2},{4,5,6},{7}}
[5,3,8,2,4,6,1,7]=>[6,8,5,2,3,4,1,7]=>[6,5,8,2,3,1,4,7]=>{{1,6},{2,5},{3,8},{4},{7}}
[8,4,5,3,1,6,7,2]=>[3,5,7,8,4,2,6,1]=>[8,7,3,5,1,2,4,6]=>{{1,8},{2,7},{3},{4,5},{6}}
[6,2,8,4,5,3,7,1]=>[7,6,5,8,4,2,3,1]=>[6,7,8,5,1,3,2,4]=>{{1,6},{2,7},{3,8},{4,5}}
[3,5,1,4,6,2,7,8]=>[5,6,3,1,4,2,7,8]=>[5,3,6,2,1,4,7,8]=>{{1,5},{2,3,6},{4},{7},{8}}
[3,6,8,4,1,2,5,7]=>[4,1,3,8,2,6,5,7]=>[3,1,6,4,2,8,5,7]=>{{1,3,6,8},{2},{4},{5},{7}}
[3,1,8,5,4,7,2,6]=>[3,7,1,5,8,2,4,6]=>[7,3,2,8,5,4,6,1]=>{{1,7},{2,3},{4,8},{5},{6}}
[8,5,7,6,2,1,3,4]=>[2,6,1,3,7,8,4,5]=>[8,2,1,3,7,6,5,4]=>{{1,8},{2},{3},{4},{5,7},{6}}
[7,5,2,4,8,3,6,1]=>[6,5,7,2,8,4,3,1]=>[7,8,6,2,5,1,3,4]=>{{1,7},{2,8},{3,6},{4},{5}}
[7,8,2,6,3,5,4,1]=>[4,5,8,6,3,2,7,1]=>[7,6,4,5,1,2,8,3]=>{{1,7,8},{2,6},{3,4,5}}
[3,6,2,4,7,8,5,1]=>[5,8,3,2,6,1,7,4]=>[5,3,7,1,6,4,8,2]=>{{1,5,6},{2,3,7,8},{4}}
[8,4,6,1,3,7,2,5]=>[6,7,1,8,3,4,5,2]=>[8,7,2,6,3,4,1,5]=>{{1,8},{2,7},{3},{4,6},{5}}
[2,1,6,7,4,8,3,5]=>[2,1,8,7,3,6,4,5]=>[2,1,6,7,4,8,5,3]=>{{1,2},{3,6,8},{4,7},{5}}
[7,2,6,8,4,5,3,1]=>[3,5,7,8,4,1,6,2]=>[8,7,3,5,1,4,2,6]=>{{1,8},{2,7},{3},{4,5},{6}}
[7,3,8,1,6,4,5,2]=>[8,5,7,6,4,1,3,2]=>[5,8,6,7,1,4,2,3]=>{{1,5},{2,8},{3,6},{4,7}}
[3,7,8,2,6,5,1,4]=>[5,6,3,1,8,4,7,2]=>[6,3,7,2,5,1,8,4]=>{{1,6},{2,3,7,8},{4},{5}}
[6,7,8,3,1,5,4,2]=>[3,8,4,5,2,6,7,1]=>[6,3,4,5,1,7,8,2]=>{{1,6,7,8},{2,3,4,5}}
[7,8,1,6,2,5,4,3]=>[8,6,4,5,2,1,7,3]=>[4,5,7,6,2,3,8,1]=>{{1,4,6},{2,5},{3,7,8}}
[7,1,6,8,5,4,3,2]=>[7,3,4,5,8,1,6,2]=>[3,8,4,7,5,2,1,6]=>{{1,3,4,7},{2,8},{5},{6}}
[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,9,6,8,7]=>[1,2,3,4,5,8,6,9,7]=>{{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,2,4,6,8,3,7,5]=>[1,2,8,4,7,6,3,5]=>[1,2,4,6,7,8,5,3]=>{{1},{2},{3,4,6,8},{5,7}}
[1,6,5,7,8,4,2,3]=>[1,4,2,8,6,5,7,3]=>[1,6,2,4,7,3,8,5]=>{{1},{2,6},{3},{4},{5,7,8}}
[3,1,8,5,4,6,2,7]=>[3,6,1,5,8,4,2,7]=>[6,3,2,8,5,1,4,7]=>{{1,6},{2,3},{4,8},{5},{7}}
[6,3,8,4,5,2,1,7]=>[2,5,6,8,4,3,1,7]=>[8,2,6,5,1,3,4,7]=>{{1,8},{2},{3,6},{4,5},{7}}
[6,5,8,7,2,3,4,1]=>[4,7,2,3,6,5,8,1]=>[6,4,1,2,8,3,7,5]=>{{1,6},{2,4},{3},{5,8},{7}}
[6,3,8,4,5,2,7,1]=>[7,5,6,8,4,3,2,1]=>[6,8,7,5,1,2,3,4]=>{{1,6},{2,8},{3,7},{4,5}}
[2,1,6,8,5,3,7,4]=>[2,1,5,8,7,6,4,3]=>[2,1,7,5,6,8,3,4]=>{{1,2},{3,7},{4,5,6,8}}
[6,2,8,4,5,7,1,3]=>[7,6,1,8,4,2,5,3]=>[7,8,2,6,1,5,3,4]=>{{1,7},{2,8},{3},{4,6},{5}}
[6,1,8,4,5,7,3,2]=>[6,3,7,8,4,1,5,2]=>[7,8,3,6,1,5,2,4]=>{{1,7},{2,8},{3},{4,6},{5}}
[3,5,1,8,4,7,6,2]=>[5,6,3,7,1,8,2,4]=>[7,3,8,5,4,6,2,1]=>{{1,7},{2,3,8},{4,5},{6}}
[2,4,8,3,7,6,5,1]=>[5,2,6,4,7,8,3,1]=>[2,7,4,8,5,6,1,3]=>{{1,2,7},{3,4,8},{5},{6}}
[4,6,8,3,2,5,7,1]=>[7,3,8,4,2,6,5,1]=>[4,6,3,7,1,8,2,5]=>{{1,4,7},{2,6,8},{3},{5}}
[1,5,4,8,6,2,3,7]=>[1,6,2,5,4,8,3,7]=>[1,5,2,8,3,6,4,7]=>{{1},{2,5},{3},{4,8},{6},{7}}
[5,3,2,4,7,8,1,6]=>[8,3,5,2,4,1,7,6]=>[3,7,5,1,2,4,8,6]=>{{1,3,5},{2,7,8},{4},{6}}
[2,3,7,8,5,1,6,4]=>[5,2,3,8,6,4,7,1]=>[2,3,7,5,6,1,8,4]=>{{1,2,3,7,8},{4,5,6}}
[4,1,7,6,2,3,8,5]=>[4,6,2,1,7,8,5,3]=>[8,4,1,3,7,6,2,5]=>{{1,8},{2,4},{3},{5,7},{6}}
[3,4,8,2,5,6,1,7]=>[6,8,3,4,2,5,1,7]=>[4,3,6,8,1,2,5,7]=>{{1,4,8},{2,3,6},{5},{7}}
[4,6,1,3,8,2,7,5]=>[6,8,1,4,7,3,2,5]=>[6,4,2,8,7,3,5,1]=>{{1,6},{2,4,8},{3},{5,7}}
[5,4,6,2,3,1,8,7]=>[3,6,2,5,4,1,8,7]=>[5,3,1,6,2,4,8,7]=>{{1,5},{2,3},{4,6},{7,8}}
[2,1,7,6,8,4,5,3]=>[2,1,5,8,4,7,6,3]=>[2,1,7,5,3,8,4,6]=>{{1,2},{3,7},{4,5},{6,8}}
[1,7,4,8,6,5,3,2]=>[1,3,5,6,8,7,4,2]=>[1,8,3,6,5,7,2,4]=>{{1},{2,8},{3},{4,6,7},{5}}
[3,8,5,2,6,1,7,4]=>[6,5,3,8,7,2,4,1]=>[3,7,8,5,6,2,1,4]=>{{1,3,8},{2,7},{4,5,6}}
[6,8,7,1,3,4,2,5]=>[7,4,1,3,2,6,8,5]=>[4,6,2,1,3,8,7,5]=>{{1,4},{2,6,8},{3},{5},{7}}
[6,2,8,4,7,1,3,5]=>[7,6,1,8,2,5,4,3]=>[7,8,2,6,4,1,3,5]=>{{1,7},{2,8},{3},{4,6},{5}}
[4,3,8,5,7,1,6,2]=>[7,6,4,3,8,1,5,2]=>[4,7,8,1,6,5,2,3]=>{{1,4},{2,7},{3,8},{5,6}}
[5,3,8,4,7,1,6,2]=>[7,6,5,8,3,1,4,2]=>[6,7,8,5,2,4,1,3]=>{{1,6},{2,7},{3,8},{4,5}}
[3,5,8,7,4,1,6,2]=>[4,7,3,6,5,2,8,1]=>[4,3,6,5,8,1,7,2]=>{{1,4,5,8},{2,3,6},{7}}
[6,1,5,3,8,4,7,2]=>[6,7,5,8,1,3,4,2]=>[7,6,8,5,4,2,1,3]=>{{1,7},{2,6},{3,8},{4,5}}
[6,8,2,7,5,1,4,3]=>[5,7,4,1,8,6,3,2]=>[6,4,7,3,5,8,1,2]=>{{1,6,8},{2,4},{3,7},{5}}
[5,2,7,6,8,3,1,4]=>[3,8,5,1,4,7,6,2]=>[7,3,5,2,1,8,4,6]=>{{1,7},{2,3,5},{4},{6,8}}
[2,4,8,3,7,5,6,1]=>[6,2,8,4,7,5,3,1]=>[2,6,4,8,7,1,3,5]=>{{1,2,6},{3,4,8},{5,7}}
[4,8,3,7,5,6,2,1]=>[2,6,8,4,7,5,3,1]=>[6,2,4,8,7,1,3,5]=>{{1,6},{2},{3,4,8},{5,7}}
[6,7,3,2,8,4,1,5]=>[4,3,8,7,1,6,5,2]=>[4,7,3,6,2,8,1,5]=>{{1,4,6,8},{2,7},{3},{5}}
[4,7,8,3,1,5,2,6]=>[3,8,5,4,2,1,7,6]=>[5,3,4,7,1,2,8,6]=>{{1,5},{2,3,4,7,8},{6}}
[5,7,8,3,4,6,2,1]=>[2,6,8,3,5,4,7,1]=>[6,2,5,1,7,3,8,4]=>{{1,6},{2},{3,5,7,8},{4}}
[3,7,5,8,2,6,4,1]=>[4,6,3,8,7,1,5,2]=>[6,3,8,4,7,5,1,2]=>{{1,6},{2,3,8},{4},{5,7}}
[4,1,5,7,6,3,2,8]=>[4,3,6,1,5,7,2,8]=>[4,5,3,2,7,6,1,8]=>{{1,4},{2,5,7},{3},{6},{8}}
[4,5,1,7,6,3,2,8]=>[5,3,6,4,1,7,2,8]=>[4,5,3,7,2,6,1,8]=>{{1,4,7},{2,5},{3},{6},{8}}
[6,2,1,5,4,3,8,7]=>[2,6,4,5,1,3,8,7]=>[4,2,6,5,3,1,8,7]=>{{1,4,5},{2},{3,6},{7,8}}
[2,3,4,7,5,8,6,1]=>[6,2,3,4,8,7,1,5]=>[2,3,4,8,6,7,5,1]=>{{1,2,3,4,8},{5,6,7}}
[8,1,3,2,6,5,7,4]=>[8,3,1,7,6,2,5,4]=>[3,6,2,7,8,5,1,4]=>{{1,3},{2,6},{4,7},{5,8}}
[4,3,7,2,8,1,6,5]=>[8,7,4,3,6,1,2,5]=>[4,6,7,1,8,5,3,2]=>{{1,4},{2,6},{3,7},{5,8}}
[8,1,4,3,5,2,7,6]=>[8,5,4,1,3,7,2,6]=>[4,5,7,3,1,8,6,2]=>{{1,4},{2,5},{3,7},{6,8}}
[6,4,8,5,7,1,3,2]=>[7,3,1,6,8,4,5,2]=>[3,7,2,8,6,4,1,5]=>{{1,3},{2,7},{4,8},{5,6}}
[5,3,4,1,6,2,8,7]=>[4,6,5,3,1,2,8,7]=>[6,4,5,1,3,2,8,7]=>{{1,6},{2,4},{3,5},{7,8}}
[5,2,7,6,8,1,4,3]=>[8,5,4,1,2,7,6,3]=>[4,5,7,3,2,8,1,6]=>{{1,4},{2,5},{3,7},{6,8}}
[7,5,6,1,8,2,4,3]=>[6,8,4,2,7,5,1,3]=>[6,4,8,2,7,1,5,3]=>{{1,6},{2,4},{3,8},{5,7}}
[7,3,6,1,8,2,5,4]=>[6,8,7,5,2,4,3,1]=>[7,5,6,8,3,1,2,4]=>{{1,7},{2,5},{3,6},{4,8}}
[7,2,8,1,6,3,5,4]=>[8,7,6,5,3,1,2,4]=>[5,6,7,8,2,4,3,1]=>{{1,5},{2,6},{3,7},{4,8}}
[3,6,5,2,4,1,7,8]=>[4,5,3,2,6,1,7,8]=>[4,3,6,1,5,2,7,8]=>{{1,4},{2,3,6},{5},{7},{8}}
[7,8,5,1,2,4,3,6]=>[5,1,4,2,8,3,7,6]=>[4,1,7,3,5,2,8,6]=>{{1,4},{2},{3,7,8},{5},{6}}
[6,1,3,4,2,5,8,7]=>[6,4,1,3,2,5,8,7]=>[4,6,2,1,3,5,8,7]=>{{1,4},{2,6},{3},{5},{7,8}}
[5,3,7,6,1,8,4,2]=>[6,4,7,5,2,8,3,1]=>[5,8,4,7,2,6,1,3]=>{{1,5},{2,8},{3,4,7},{6}}
[7,3,5,6,1,8,4,2]=>[6,4,8,7,3,5,2,1]=>[7,8,4,6,1,2,3,5]=>{{1,7},{2,8},{3,4,6},{5}}
[7,8,5,1,3,2,4,6]=>[5,3,1,2,8,4,7,6]=>[3,7,2,1,5,4,8,6]=>{{1,3},{2,7,8},{4},{5},{6}}
[3,1,5,4,7,2,6,8]=>[3,7,1,5,4,2,6,8]=>[5,3,2,7,1,4,6,8]=>{{1,5},{2,3},{4,7},{6},{8}}
[1,5,3,8,4,2,7,6]=>[1,4,8,5,2,7,3,6]=>[1,7,4,5,3,8,6,2]=>{{1},{2,7},{3,4,5},{6,8}}
[1,5,2,8,3,6,7,4]=>[1,5,8,7,2,3,6,4]=>[1,8,5,7,4,3,2,6]=>{{1},{2,8},{3,5},{4,7},{6}}
[3,8,4,1,7,2,5,6]=>[4,8,3,7,2,5,6,1]=>[4,3,8,7,1,2,5,6]=>{{1,4,7},{2,3,8},{5},{6}}
[8,2,4,1,3,6,7,5]=>[4,8,1,2,7,3,6,5]=>[7,4,2,3,8,5,1,6]=>{{1,7},{2,4},{3},{5,8},{6}}
[8,1,3,6,2,5,7,4]=>[8,6,1,7,3,4,5,2]=>[6,8,2,7,3,4,1,5]=>{{1,6},{2,8},{3},{4,7},{5}}
[7,8,1,5,6,4,2,3]=>[8,4,2,6,1,5,7,3]=>[4,7,1,6,3,2,8,5]=>{{1,4,6},{2,7,8},{3},{5}}
[8,1,3,5,6,7,2,4]=>[8,7,1,3,2,4,6,5]=>[7,8,2,1,4,5,3,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[3,1,5,4,6,8,7,2]=>[3,7,1,5,4,6,8,2]=>[5,3,2,6,1,8,7,4]=>{{1,5},{2,3},{4,6,8},{7}}
[3,5,6,2,1,4,7,8]=>[2,6,3,1,5,4,7,8]=>[3,2,5,1,6,4,7,8]=>{{1,3,5,6},{2},{4},{7},{8}}
[1,2,5,6,8,3,7,4]=>[1,2,8,7,5,6,3,4]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,5,7},{4,6,8}}
[5,3,8,4,6,2,7,1]=>[7,6,5,8,3,4,2,1]=>[6,7,8,5,2,1,3,4]=>{{1,6},{2,7},{3,8},{4,5}}
[5,6,8,1,2,4,7,3]=>[8,1,7,2,5,6,4,3]=>[5,1,6,3,7,8,2,4]=>{{1,5,7},{2},{3,6,8},{4}}
[6,8,1,4,5,7,2,3]=>[8,7,2,1,3,6,4,5]=>[6,7,1,3,4,8,5,2]=>{{1,6,8},{2,7},{3},{4},{5}}
[3,2,8,1,7,5,6,4]=>[8,3,2,6,7,5,1,4]=>[3,6,1,8,7,2,5,4]=>{{1,3},{2,6},{4,8},{5,7}}
[4,5,6,3,8,1,7,2]=>[8,7,6,4,5,3,1,2]=>[4,5,6,7,8,1,3,2]=>{{1,4,7},{2,5,8},{3,6}}
[2,8,7,6,3,5,1,4]=>[5,2,6,1,3,7,8,4]=>[2,8,5,3,4,6,7,1]=>{{1,2,8},{3,5},{4},{6},{7}}
[3,6,7,5,8,4,1,2]=>[4,1,3,8,7,6,5,2]=>[3,1,6,4,7,8,2,5]=>{{1,3,6,8},{2},{4},{5,7}}
[6,8,7,3,2,4,5,1]=>[5,3,7,2,4,6,8,1]=>[5,6,3,1,2,8,7,4]=>{{1,5},{2,6,8},{3},{4},{7}}
[7,5,8,6,4,1,3,2]=>[4,3,1,6,8,7,2,5]=>[3,8,2,4,6,7,5,1]=>{{1,3},{2,8},{4},{5,6,7}}
[2,3,1,7,6,8,4,5]=>[3,2,1,8,4,7,6,5]=>[2,3,1,7,4,8,5,6]=>{{1,2,3},{4,7},{5},{6,8}}
[4,3,1,7,6,2,5,8]=>[3,4,6,2,1,7,5,8]=>[7,4,3,1,2,6,5,8]=>{{1,7},{2,4},{3},{5},{6},{8}}
[8,4,6,5,7,2,3,1]=>[3,7,2,8,6,4,5,1]=>[7,3,1,6,8,4,2,5]=>{{1,7},{2,3},{4,6},{5,8}}
[8,2,5,3,6,7,4,1]=>[4,7,8,5,3,2,1,6]=>[8,5,4,7,1,2,6,3]=>{{1,8},{2,5},{3,4,7},{6}}
[1,2,8,3,4,7,6,5]=>[1,2,8,3,6,7,4,5]=>[1,2,6,3,8,7,5,4]=>{{1},{2},{3,6,7},{4},{5,8}}
[1,6,8,3,5,2,4,7]=>[1,5,8,2,3,6,4,7]=>[1,6,5,3,4,8,2,7]=>{{1},{2,6,8},{3,5},{4},{7}}
[1,4,7,3,2,8,6,5]=>[1,3,7,4,6,8,2,5]=>[1,4,3,7,8,6,5,2]=>{{1},{2,4,7},{3},{5,8},{6}}
[7,3,2,6,1,5,8,4]=>[6,3,7,8,1,2,5,4]=>[7,8,3,6,4,5,1,2]=>{{1,7},{2,8},{3},{4,6},{5}}
[3,5,6,2,8,7,1,4]=>[7,6,3,1,5,2,8,4]=>[3,5,6,2,8,4,7,1]=>{{1,3,6},{2,5,8},{4},{7}}
[6,1,2,4,3,7,8,5]=>[6,1,4,2,8,3,7,5]=>[4,1,7,3,6,5,8,2]=>{{1,4},{2},{3,7,8},{5,6}}
[7,5,6,1,2,4,8,3]=>[6,1,8,2,7,5,4,3]=>[8,1,6,3,7,2,4,5]=>{{1,8},{2},{3,6},{4},{5,7}}
[6,1,4,7,8,2,3,5]=>[6,8,2,1,4,5,7,3]=>[7,6,1,3,2,4,8,5]=>{{1,7,8},{2,6},{3},{4},{5}}
[4,3,8,5,6,2,7,1]=>[7,6,4,3,8,5,2,1]=>[4,7,8,1,6,2,3,5]=>{{1,4},{2,7},{3,8},{5,6}}
[4,3,8,6,7,2,5,1]=>[5,7,4,3,2,8,6,1]=>[5,4,8,1,2,7,3,6]=>{{1,5},{2,4},{3,8},{6,7}}
[7,6,8,1,5,3,4,2]=>[8,4,5,3,1,7,6,2]=>[4,7,5,1,3,8,2,6]=>{{1,4},{2,7},{3,5},{6,8}}
[7,4,6,1,5,3,8,2]=>[6,8,5,7,1,4,3,2]=>[7,5,8,6,4,1,2,3]=>{{1,7},{2,5},{3,8},{4,6}}
[6,3,8,1,7,2,5,4]=>[8,7,6,5,2,3,1,4]=>[5,6,7,8,3,2,4,1]=>{{1,5},{2,6},{3,7},{4,8}}
[3,5,8,6,2,1,4,7]=>[2,6,3,1,5,8,4,7]=>[3,2,5,1,8,6,4,7]=>{{1,3,5,8},{2},{4},{6},{7}}
[2,4,8,5,6,1,3,7]=>[6,2,1,4,8,5,3,7]=>[2,4,1,8,6,3,5,7]=>{{1,2,4,8},{3},{5,6},{7}}
[8,7,2,4,6,3,1,5]=>[3,6,7,2,1,5,8,4]=>[8,6,3,1,4,2,7,5]=>{{1,8},{2,6},{3},{4},{5},{7}}
[8,7,1,4,5,3,6,2]=>[7,6,5,1,2,4,8,3]=>[5,6,8,3,4,1,7,2]=>{{1,5},{2,6},{3,8},{4},{7}}
[7,3,8,6,2,1,4,5]=>[2,6,8,1,3,7,4,5]=>[8,2,6,3,4,7,5,1]=>{{1,8},{2},{3,6,7},{4},{5}}
[6,5,8,1,3,4,2,7]=>[8,4,1,3,6,5,2,7]=>[4,6,2,1,8,3,5,7]=>{{1,4},{2,6},{3},{5,8},{7}}
[3,2,7,6,8,4,5,1]=>[5,3,2,8,4,7,6,1]=>[3,7,1,5,2,8,4,6]=>{{1,3},{2,7},{4,5},{6,8}}
[3,6,5,2,1,4,7,8]=>[2,5,3,1,6,4,7,8]=>[3,2,6,1,5,4,7,8]=>{{1,3,6},{2},{4},{5},{7},{8}}
[5,4,1,6,3,7,2,8]=>[4,5,7,6,2,1,3,8]=>[7,6,4,5,2,3,1,8]=>{{1,7},{2,6},{3,4,5},{8}}
[3,6,5,7,1,4,2,8]=>[7,4,3,1,6,5,2,8]=>[3,4,6,2,7,1,5,8]=>{{1,3,6},{2,4},{5,7},{8}}
[4,2,5,7,6,1,3,8]=>[6,4,1,2,5,7,3,8]=>[4,5,2,3,7,6,1,8]=>{{1,4},{2,5,7},{3},{6},{8}}
[4,2,5,7,6,3,8,1]=>[8,4,6,2,5,7,3,1]=>[4,6,5,2,8,7,1,3]=>{{1,4},{2,6,7},{3,5,8}}
[3,5,8,2,1,4,6,7]=>[2,8,3,1,5,4,6,7]=>[3,2,5,1,8,4,6,7]=>{{1,3,5,8},{2},{4},{6},{7}}
[3,5,8,2,4,6,7,1]=>[7,8,3,2,5,4,6,1]=>[5,3,7,1,8,2,4,6]=>{{1,5,8},{2,3,7},{4},{6}}
[5,8,2,1,4,3,6,7]=>[2,8,4,1,5,3,6,7]=>[4,2,5,3,8,1,6,7]=>{{1,4},{2},{3,5,8},{6},{7}}
[1,8,6,4,5,7,2,3]=>[1,7,2,6,4,8,5,3]=>[1,7,2,8,3,6,4,5]=>{{1},{2,7},{3},{4,8},{5},{6}}
[1,8,6,4,2,3,5,7]=>[1,4,2,6,3,8,5,7]=>[1,8,2,4,3,6,5,7]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[3,2,1,6,7,4,8,5]=>[2,3,1,7,8,6,4,5]=>[3,2,1,7,6,8,5,4]=>{{1,3},{2},{4,7},{5,6,8}}
[3,2,5,6,8,1,4,7]=>[8,3,2,1,5,6,4,7]=>[3,5,1,2,6,8,4,7]=>{{1,3},{2,5,6,8},{4},{7}}
[8,5,4,6,1,7,3,2]=>[6,3,7,5,8,4,1,2]=>[6,7,3,8,5,1,4,2]=>{{1,6},{2,7},{3},{4,8},{5}}
[3,7,4,5,6,8,2,1]=>[2,8,3,7,4,5,6,1]=>[3,2,7,8,1,4,5,6]=>{{1,3,7},{2},{4,8},{5},{6}}
[4,6,8,3,7,1,5,2]=>[7,5,8,4,1,6,3,2]=>[5,6,4,7,3,8,1,2]=>{{1,5},{2,6,8},{3,4,7}}
[3,6,7,2,5,1,8,4]=>[5,7,3,8,2,6,1,4]=>[6,3,7,5,2,8,4,1]=>{{1,6,8},{2,3,7},{4,5}}
[6,1,3,2,8,5,7,4]=>[6,3,1,7,8,2,5,4]=>[3,8,2,7,6,5,1,4]=>{{1,3},{2,8},{4,7},{5,6}}
[3,8,5,7,6,1,2,4]=>[6,1,3,2,7,8,4,5]=>[3,1,8,2,7,6,5,4]=>{{1,3,8},{2},{4},{5,7},{6}}
[3,8,6,4,7,2,1,5]=>[2,7,3,6,1,8,4,5]=>[3,2,7,8,4,6,5,1]=>{{1,3,7},{2},{4,8},{5},{6}}
[2,5,6,4,8,1,7,3]=>[8,2,7,6,5,4,1,3]=>[2,5,6,7,8,1,4,3]=>{{1,2,5,8},{3,6},{4,7}}
[3,5,6,7,4,1,8,2]=>[4,7,3,8,5,6,2,1]=>[5,3,6,4,7,8,1,2]=>{{1,5,7},{2,3,6,8},{4}}
[1,8,4,2,3,7,5,6]=>[1,4,2,8,7,5,3,6]=>[1,7,2,4,8,3,6,5]=>{{1},{2,7},{3},{4},{5,8},{6}}
[8,6,2,4,5,7,1,3]=>[7,6,1,3,4,8,2,5]=>[7,8,2,1,3,6,5,4]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,6,3,2,5,1,8,4]=>[5,3,6,7,2,8,4,1]=>[7,8,3,5,2,6,1,4]=>{{1,7},{2,8},{3},{4,5},{6}}
[7,2,3,4,1,8,5,6]=>[4,7,2,3,8,5,1,6]=>[8,4,1,2,7,3,6,5]=>{{1,8},{2,4},{3},{5,7},{6}}
[8,6,5,1,7,4,2,3]=>[5,4,2,6,8,7,1,3]=>[6,8,1,4,5,7,3,2]=>{{1,6,7},{2,8},{3},{4},{5}}
[1,4,6,8,2,5,7,3]=>[1,8,7,4,2,6,5,3]=>[1,4,6,7,3,8,2,5]=>{{1},{2,4,7},{3,6,8},{5}}
[7,4,6,1,8,5,2,3]=>[6,5,2,8,7,4,3,1]=>[7,8,1,5,6,2,3,4]=>{{1,7},{2,8},{3},{4,5,6}}
[5,1,7,3,2,8,4,6]=>[5,3,7,8,1,4,2,6]=>[7,8,3,5,4,1,6,2]=>{{1,7},{2,8},{3},{4,5},{6}}
[1,7,4,8,3,6,2,5]=>[1,6,8,7,2,3,4,5]=>[1,8,6,7,4,5,3,2]=>{{1},{2,8},{3,6},{4,7},{5}}
[5,6,3,7,8,2,1,4]=>[2,8,6,1,5,3,7,4]=>[5,2,6,3,7,4,8,1]=>{{1,5,7,8},{2},{3,6},{4}}
[4,5,1,6,7,3,2,8]=>[5,3,7,4,1,6,2,8]=>[4,5,3,6,2,7,1,8]=>{{1,4,6,7},{2,5},{3},{8}}
[8,5,6,3,7,2,1,4]=>[2,7,6,1,8,5,3,4]=>[7,2,8,3,6,1,5,4]=>{{1,7},{2},{3,8},{4},{5,6}}
[9,3,4,5,6,7,8,10,1,2]=>[10,1,9,3,4,5,6,7,8,2]=>[9,1,10,2,3,4,5,6,7,8]=>{{1,9},{2},{3,10},{4},{5},{6},{7},{8}}
[2,5,4,8,6,7,3,1]=>[3,2,7,5,4,8,6,1]=>[2,5,3,8,1,7,4,6]=>{{1,2,5},{3},{4,8},{6,7}}
[7,5,4,1,6,8,2,3]=>[4,5,2,7,8,1,6,3]=>[8,7,1,4,5,3,2,6]=>{{1,8},{2,7},{3},{4},{5},{6}}
[7,3,6,4,5,8,1,2]=>[8,1,7,6,4,3,5,2]=>[6,1,7,8,2,4,3,5]=>{{1,6},{2},{3,7},{4,8},{5}}
[8,1,4,5,3,6,2,7]=>[8,6,5,1,2,4,3,7]=>[5,6,8,3,4,1,2,7]=>{{1,5},{2,6},{3,8},{4},{7}}
[1,5,4,7,3,8,6,2]=>[1,6,8,5,4,7,2,3]=>[1,6,5,8,2,7,4,3]=>{{1},{2,6,7},{3,5},{4,8}}
[2,1,8,4,7,6,3,5]=>[2,1,6,7,3,8,5,4]=>[2,1,8,7,4,6,3,5]=>{{1,2},{3,8},{4,7},{5},{6}}
[1,6,2,7,4,5,8,3]=>[1,6,8,7,4,2,5,3]=>[1,8,6,7,2,5,3,4]=>{{1},{2,8},{3,6},{4,7},{5}}
[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>{{1,3},{2,4},{5},{6},{7},{8},{9}}
[4,3,1,6,5,2,7,8]=>[3,4,5,2,6,1,7,8]=>[6,4,3,1,5,2,7,8]=>{{1,6},{2,4},{3},{5},{7},{8}}
[4,2,6,3,5,1,7,8]=>[5,4,6,2,3,1,7,8]=>[5,6,4,2,1,3,7,8]=>{{1,5},{2,6},{3,4},{7},{8}}
[3,4,7,6,5,1,2,8]=>[5,1,3,4,6,7,2,8]=>[3,1,4,7,5,6,2,8]=>{{1,3,4,7},{2},{5},{6},{8}}
[4,5,2,7,1,3,6,8]=>[7,5,1,4,2,3,6,8]=>[4,5,2,7,3,1,6,8]=>{{1,4,7},{2,5},{3},{6},{8}}
[5,2,7,1,6,4,8,3]=>[7,5,8,6,2,1,4,3]=>[6,8,5,7,3,4,1,2]=>{{1,6},{2,8},{3,5},{4,7}}
[4,2,8,3,6,7,5,1]=>[5,4,7,2,8,3,1,6]=>[7,8,4,2,5,1,6,3]=>{{1,7},{2,8},{3,4},{5},{6}}
[1,2,4,5,8,7,3,6]=>[1,2,7,4,5,3,8,6]=>[1,2,4,5,8,3,7,6]=>{{1},{2},{3,4,5,8},{6},{7}}
[3,6,4,1,7,2,8,5]=>[4,6,3,7,8,2,1,5]=>[7,3,8,4,6,2,5,1]=>{{1,7},{2,3,8},{4},{5,6}}
[2,4,1,3,7,8,6,5]=>[4,2,1,3,6,8,7,5]=>[2,4,1,3,7,6,8,5]=>{{1,2,4},{3},{5,7,8},{6}}
[5,7,4,8,1,2,6,3]=>[8,1,6,7,5,2,4,3]=>[5,1,7,6,8,4,2,3]=>{{1,5,8},{2},{3,7},{4,6}}
[3,7,5,6,8,2,4,1]=>[4,8,3,2,7,5,6,1]=>[4,3,7,1,8,2,5,6]=>{{1,4},{2,3,7},{5,8},{6}}
[4,3,8,1,6,5,7,2]=>[8,7,4,3,6,1,5,2]=>[4,6,7,1,8,5,2,3]=>{{1,4},{2,6},{3,7},{5,8}}
[2,6,5,1,3,4,8,7]=>[5,2,1,3,6,4,8,7]=>[2,6,1,3,5,4,8,7]=>{{1,2,6},{3},{4},{5},{7,8}}
[2,5,8,1,7,6,3,4]=>[8,2,6,3,5,7,1,4]=>[2,5,6,1,8,7,4,3]=>{{1,2,5,8},{3,6,7},{4}}
[2,8,4,7,6,3,1,5]=>[3,2,6,7,1,8,5,4]=>[2,8,3,7,4,6,1,5]=>{{1,2,8},{3},{4,7},{5},{6}}
[1,8,2,4,6,7,5,3]=>[1,8,5,2,7,3,4,6]=>[1,5,8,3,7,4,6,2]=>{{1},{2,5,7},{3,8},{4},{6}}
[3,4,2,8,1,7,6,5]=>[8,4,3,2,6,7,1,5]=>[3,4,6,1,8,7,5,2]=>{{1,3,6,7},{2,4},{5,8}}
[1,5,2,8,6,4,7,3]=>[1,5,7,6,2,8,4,3]=>[1,8,5,7,4,6,2,3]=>{{1},{2,8},{3,5},{4,7},{6}}
[1,6,5,2,7,4,8,3]=>[1,5,6,8,7,3,2,4]=>[1,8,7,5,6,3,4,2]=>{{1},{2,8},{3,7},{4,5,6}}
[5,7,8,1,2,4,3,6]=>[8,1,4,2,5,3,7,6]=>[4,1,5,3,7,2,8,6]=>{{1,4},{2},{3,5,7,8},{6}}
[8,5,2,3,1,6,4,7]=>[3,5,2,8,6,4,1,7]=>[8,3,1,5,6,2,4,7]=>{{1,8},{2,3},{4,5,6},{7}}
[4,2,3,8,1,7,5,6]=>[8,4,2,3,7,5,1,6]=>[4,7,1,2,8,3,6,5]=>{{1,4},{2,7},{3},{5,8},{6}}
[4,2,1,5,3,7,6,8]=>[2,4,5,1,3,7,6,8]=>[5,2,4,3,1,7,6,8]=>{{1,5},{2},{3,4},{6,7},{8}}
[6,2,7,3,4,5,1,8]=>[5,6,7,3,4,2,1,8]=>[7,6,5,1,2,3,4,8]=>{{1,7},{2,6},{3,5},{4},{8}}
[4,5,7,2,8,3,6,1]=>[6,7,8,4,5,3,2,1]=>[6,5,4,7,8,1,2,3]=>{{1,6},{2,5,8},{3,4,7}}
[4,5,3,7,8,1,6,2]=>[8,6,5,4,3,1,7,2]=>[4,5,6,7,1,3,8,2]=>{{1,4,7,8},{2,5},{3,6}}
[4,6,3,5,2,7,8,1]=>[8,5,6,4,3,2,7,1]=>[4,6,5,7,1,2,8,3]=>{{1,4,7,8},{2,6},{3,5}}
[7,2,5,8,6,1,4,3]=>[6,8,4,1,3,7,5,2]=>[6,4,8,3,1,7,2,5]=>{{1,6,7},{2,4},{3,8},{5}}
[6,2,7,1,4,5,3,8]=>[7,6,5,1,2,3,4,8]=>[5,6,7,3,4,2,1,8]=>{{1,5},{2,6},{3,7},{4},{8}}
[7,4,5,6,2,1,8,3]=>[2,6,8,7,4,5,1,3]=>[8,2,6,7,1,3,5,4]=>{{1,8},{2},{3,6},{4,7},{5}}
[6,8,1,5,4,2,3,7]=>[8,4,2,5,1,6,3,7]=>[4,6,1,5,3,8,2,7]=>{{1,4,5},{2,6,8},{3},{7}}
[7,5,6,1,4,8,2,3]=>[6,8,2,1,7,5,4,3]=>[8,6,1,3,7,2,4,5]=>{{1,8},{2,6},{3},{4},{5,7}}
[6,5,8,2,7,3,4,1]=>[4,8,7,3,6,5,2,1]=>[7,4,6,1,8,2,3,5]=>{{1,7},{2,4},{3,6},{5,8}}
[2,4,6,5,7,8,1,3]=>[8,2,1,4,6,5,7,3]=>[2,4,1,6,7,3,8,5]=>{{1,2,4,6},{3},{5,7,8}}
[5,8,7,4,6,1,3,2]=>[6,3,1,7,5,4,8,2]=>[3,6,2,5,8,1,7,4]=>{{1,3},{2,6},{4,5,8},{7}}
[8,6,3,7,1,4,2,5]=>[7,4,6,1,2,8,3,5]=>[4,8,7,3,2,6,5,1]=>{{1,4},{2,8},{3,7},{5},{6}}
[3,1,2,8,7,6,4,5]=>[3,1,2,6,4,7,8,5]=>[3,1,2,8,4,6,7,5]=>{{1,3},{2},{4,8},{5},{6},{7}}
[4,6,1,3,2,7,8,5]=>[6,3,1,4,8,2,7,5]=>[3,4,2,7,6,5,8,1]=>{{1,3},{2,4,7,8},{5,6}}
[3,4,6,7,1,5,8,2]=>[7,8,3,4,1,6,5,2]=>[4,3,6,7,2,8,1,5]=>{{1,4,7},{2,3,6,8},{5}}
[2,5,4,7,3,8,1,6]=>[8,2,7,5,4,1,3,6]=>[2,5,7,8,1,4,6,3]=>{{1,2,5},{3,7},{4,8},{6}}
[1,4,7,6,3,8,2,5]=>[1,8,6,4,2,7,3,5]=>[1,4,6,8,3,7,5,2]=>{{1},{2,4,8},{3,6,7},{5}}
[1,3,6,8,2,4,7,5]=>[1,8,3,2,7,6,4,5]=>[1,3,6,2,7,8,5,4]=>{{1},{2,3,6,8},{4},{5,7}}
[1,6,4,7,3,8,5,2]=>[1,5,8,7,6,2,4,3]=>[1,8,5,6,7,4,2,3]=>{{1},{2,8},{3,5,7},{4,6}}
[2,6,8,5,4,3,1,7]=>[3,2,4,5,8,6,1,7]=>[2,6,3,4,5,8,1,7]=>{{1,2,6,8},{3},{4},{5},{7}}
[8,3,6,1,2,7,4,5]=>[6,1,8,7,4,3,2,5]=>[8,1,6,7,2,4,5,3]=>{{1,8},{2},{3,6},{4,7},{5}}
[6,8,1,5,4,7,2,3]=>[8,7,2,5,1,6,4,3]=>[5,6,1,7,4,8,2,3]=>{{1,5},{2,6,8},{3},{4,7}}
[6,7,2,5,4,8,1,3]=>[8,7,1,5,3,6,2,4]=>[5,6,2,7,3,8,4,1]=>{{1,5},{2,6,8},{3},{4,7}}
[4,7,5,2,6,3,8,1]=>[8,5,7,4,6,3,2,1]=>[4,6,5,8,7,1,2,3]=>{{1,4,8},{2,6},{3,5,7}}
[8,5,2,7,3,6,4,1]=>[4,6,5,8,7,3,1,2]=>[8,5,7,4,6,1,3,2]=>{{1,8},{2,5,6},{3,7},{4}}
[4,1,3,8,5,6,2,7]=>[4,6,1,3,8,5,2,7]=>[8,4,2,1,6,3,5,7]=>{{1,8},{2,4},{3},{5,6},{7}}
[3,2,7,4,8,5,6,1]=>[6,3,2,7,8,5,4,1]=>[3,8,1,7,6,2,4,5]=>{{1,3},{2,8},{4,7},{5,6}}
[7,2,5,1,6,3,8,4]=>[5,7,6,8,2,1,3,4]=>[8,6,7,5,3,4,2,1]=>{{1,8},{2,6},{3,7},{4,5}}
[7,3,1,8,4,5,6,2]=>[3,7,6,8,4,5,2,1]=>[8,3,7,6,1,2,4,5]=>{{1,8},{2,3,7},{4,6},{5}}
[8,4,1,2,7,6,5,3]=>[4,1,8,5,6,7,3,2]=>[8,1,4,5,6,7,2,3]=>{{1,8},{2},{3,4,5,6,7}}
[4,8,3,2,7,6,5,1]=>[5,3,6,4,7,8,2,1]=>[4,7,3,8,5,6,1,2]=>{{1,4,8},{2,7},{3},{5},{6}}
[8,5,7,3,1,2,4,6]=>[3,1,7,2,8,4,5,6]=>[8,1,3,2,7,5,6,4]=>{{1,8},{2},{3},{4},{5,7},{6}}
[6,2,3,8,1,5,7,4]=>[8,6,2,7,1,3,5,4]=>[6,8,1,7,4,5,2,3]=>{{1,6},{2,8},{3},{4,7},{5}}
[1,4,8,5,2,3,6,7]=>[1,5,2,4,8,3,6,7]=>[1,4,2,8,5,3,6,7]=>{{1},{2,4,8},{3},{5},{6},{7}}
[1,4,8,5,2,3,7,6]=>[1,5,2,4,8,7,3,6]=>[1,4,2,7,5,8,6,3]=>{{1},{2,4,7},{3},{5},{6,8}}
[6,8,4,3,2,7,5,1]=>[5,3,4,7,8,6,1,2]=>[3,7,6,4,5,8,2,1]=>{{1,3,6,8},{2,7},{4},{5}}
[1,3,7,6,4,8,2,5]=>[1,8,3,6,2,7,4,5]=>[1,3,6,8,4,7,5,2]=>{{1},{2,3,6,7},{4,8},{5}}
[6,3,1,8,4,5,2,7]=>[3,6,5,8,4,2,1,7]=>[8,3,6,5,1,2,4,7]=>{{1,8},{2,3,6},{4,5},{7}}
[6,5,8,1,4,3,7,2]=>[8,7,4,1,6,5,3,2]=>[4,6,7,3,8,1,2,5]=>{{1,4},{2,6},{3,7},{5,8}}
[8,5,7,6,1,3,2,4]=>[6,3,1,2,7,8,4,5]=>[3,8,2,1,7,6,5,4]=>{{1,3},{2,8},{4},{5,7},{6}}
[2,7,5,6,1,8,4,3]=>[6,2,4,8,7,5,1,3]=>[2,6,8,4,7,1,5,3]=>{{1,2,6},{3,8},{4},{5,7}}
[8,5,1,2,7,4,3,6]=>[5,1,4,8,7,3,6,2]=>[5,1,8,4,7,2,3,6]=>{{1,5,7},{2},{3,8},{4},{6}}
[4,5,7,2,6,3,8,1]=>[8,7,6,4,5,2,3,1]=>[4,5,6,7,8,2,1,3]=>{{1,4,7},{2,5,8},{3,6}}
[2,1,5,7,4,6,8,3]=>[2,1,8,7,5,4,6,3]=>[2,1,5,7,8,3,4,6]=>{{1,2},{3,5,8},{4,7},{6}}
[1,7,5,2,3,8,6,4]=>[1,5,2,7,6,8,4,3]=>[1,8,2,5,7,6,3,4]=>{{1},{2,8},{3},{4,5,7},{6}}
[3,1,5,4,6,7,8,2]=>[3,8,1,5,4,6,7,2]=>[5,3,2,6,1,7,8,4]=>{{1,5},{2,3},{4,6,7,8}}
[2,6,8,7,3,1,4,5]=>[3,2,7,1,4,6,8,5]=>[2,6,3,1,4,8,7,5]=>{{1,2,6,8},{3},{4},{5},{7}}
[3,8,4,1,5,2,7,6]=>[4,8,3,5,2,7,1,6]=>[4,3,7,5,1,8,6,2]=>{{1,4,5},{2,3,7},{6,8}}
[5,1,7,8,3,2,6,4]=>[5,3,8,6,1,2,7,4]=>[5,7,3,6,4,2,8,1]=>{{1,5},{2,7,8},{3},{4,6}}
[1,4,5,6,7,8,9,3,2]=>[1,3,9,4,5,6,7,8,2]=>[1,4,3,5,6,7,8,9,2]=>{{1},{2,4,5,6,7,8,9},{3}}
[1,2,5,7,8,6,3,4]=>[1,2,6,3,5,8,7,4]=>[1,2,5,3,7,6,8,4]=>{{1},{2},{3,5,7,8},{4},{6}}
[7,3,2,8,6,1,5,4]=>[6,3,8,5,1,7,4,2]=>[5,6,3,8,4,7,1,2]=>{{1,5},{2,6,7},{3},{4,8}}
[8,4,6,7,3,1,5,2]=>[3,7,5,8,2,4,6,1]=>[8,3,7,5,2,1,4,6]=>{{1,8},{2,3,7},{4,5},{6}}
[4,1,3,6,8,5,2,7]=>[4,5,1,3,8,6,2,7]=>[6,4,2,1,5,8,3,7]=>{{1,6,8},{2,4},{3},{5},{7}}
[1,7,6,8,4,2,3,5]=>[1,4,2,8,3,7,6,5]=>[1,7,2,4,3,8,5,6]=>{{1},{2,7},{3},{4},{5},{6,8}}
[2,8,3,1,7,5,6,4]=>[3,2,8,6,7,5,1,4]=>[2,6,3,8,7,1,5,4]=>{{1,2,6},{3},{4,8},{5,7}}
[2,5,1,8,4,6,7,3]=>[5,2,7,8,1,4,6,3]=>[2,8,7,5,4,1,3,6]=>{{1,2,8},{3,7},{4,5},{6}}
[5,2,8,4,6,7,1,3]=>[7,5,1,8,2,4,6,3]=>[7,8,2,5,4,1,3,6]=>{{1,7},{2,8},{3},{4,5},{6}}
[6,5,8,3,4,2,1,7]=>[2,4,8,3,6,5,1,7]=>[6,2,4,1,8,3,5,7]=>{{1,6},{2},{3,4},{5,8},{7}}
[7,2,8,3,4,5,1,6]=>[5,7,8,3,4,2,6,1]=>[8,7,5,1,2,3,4,6]=>{{1,8},{2,7},{3,5},{4},{6}}
[6,1,5,3,8,2,4,7]=>[6,8,5,2,1,3,4,7]=>[6,5,8,2,4,3,1,7]=>{{1,6},{2,5},{3,8},{4},{7}}
[1,4,6,8,5,7,2,3]=>[1,7,2,4,8,6,5,3]=>[1,4,2,7,6,8,3,5]=>{{1},{2,4,7},{3},{5,6,8}}
[2,5,3,8,6,7,4,1]=>[4,2,7,5,1,8,6,3]=>[2,8,4,5,3,7,1,6]=>{{1,2,8},{3,4,5},{6,7}}
[7,4,5,8,1,6,2,3]=>[8,6,2,7,4,1,5,3]=>[6,8,1,7,2,5,3,4]=>{{1,6},{2,8},{3},{4,7},{5}}
[6,3,8,7,2,1,5,4]=>[2,7,6,5,1,3,8,4]=>[5,2,6,8,4,3,7,1]=>{{1,5},{2},{3,6},{4,8},{7}}
[7,2,5,6,3,4,8,1]=>[8,7,6,3,2,5,4,1]=>[6,7,8,1,3,2,4,5]=>{{1,6},{2,7},{3,8},{4},{5}}
[7,4,5,2,8,1,6,3]=>[8,5,6,7,4,1,2,3]=>[5,8,7,6,1,4,3,2]=>{{1,5},{2,8},{3,7},{4,6}}
[7,2,8,3,6,1,4,5]=>[6,7,8,1,2,5,4,3]=>[8,7,6,3,4,1,2,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[7,4,5,2,8,3,6,1]=>[6,5,8,7,4,2,1,3]=>[7,8,5,6,1,3,4,2]=>{{1,7},{2,8},{3,5},{4,6}}
[3,1,5,4,7,6,2,8]=>[3,6,1,5,4,7,2,8]=>[5,3,2,7,1,6,4,8]=>{{1,5},{2,3},{4,7},{6},{8}}
[5,1,3,2,4,6,8,7]=>[5,3,1,2,4,6,8,7]=>[3,5,2,1,4,6,8,7]=>{{1,3},{2,5},{4},{6},{7,8}}
[7,4,8,3,6,5,1,2]=>[5,1,6,8,7,2,3,4]=>[8,1,7,5,6,4,3,2]=>{{1,8},{2},{3,7},{4,5,6}}
[4,2,6,8,5,7,1,3]=>[7,4,1,2,8,6,5,3]=>[4,7,2,3,6,8,1,5]=>{{1,4},{2,7},{3},{5,6,8}}
[3,5,6,2,4,7,8,1]=>[8,6,3,2,5,4,7,1]=>[3,5,6,1,7,2,8,4]=>{{1,3,6},{2,5,7,8},{4}}
[3,5,6,7,2,4,8,1]=>[8,7,3,2,5,6,4,1]=>[3,5,6,1,7,8,2,4]=>{{1,3,6,8},{2,5,7},{4}}
[3,5,4,7,2,6,8,1]=>[8,7,3,5,4,2,6,1]=>[3,5,7,8,1,2,4,6]=>{{1,3,7},{2,5},{4,8},{6}}
[3,5,7,8,2,6,4,1]=>[4,6,3,8,5,1,7,2]=>[5,3,6,4,7,2,8,1]=>{{1,5,7,8},{2,3,6},{4}}
[5,1,6,4,8,2,3,7]=>[5,8,2,6,1,4,3,7]=>[8,5,1,6,4,2,3,7]=>{{1,8},{2,5},{3},{4,6},{7}}
[7,3,2,4,6,8,1,5]=>[8,3,7,2,1,5,4,6]=>[3,8,7,1,4,2,6,5]=>{{1,3,7},{2,8},{4},{5},{6}}
[3,5,6,8,2,1,4,7]=>[2,8,3,1,5,6,4,7]=>[3,2,5,1,6,8,4,7]=>{{1,3,5,6,8},{2},{4},{7}}
[7,3,1,8,2,6,5,4]=>[3,7,8,5,6,2,4,1]=>[6,5,3,8,7,2,1,4]=>{{1,6},{2,5,7},{3},{4,8}}
[5,8,7,2,4,3,1,6]=>[3,4,7,1,5,2,8,6]=>[5,4,3,2,8,1,7,6]=>{{1,5,8},{2,4},{3},{6},{7}}
[7,5,8,3,4,2,1,6]=>[2,4,8,3,7,1,5,6]=>[7,2,4,1,8,5,6,3]=>{{1,7},{2},{3,4},{5,8},{6}}
[5,6,2,7,4,8,3,1]=>[3,8,6,7,5,1,4,2]=>[7,3,5,6,8,4,1,2]=>{{1,7},{2,3,5,8},{4,6}}
[2,7,8,1,4,3,6,5]=>[8,2,4,1,6,3,7,5]=>[2,4,6,3,7,5,8,1]=>{{1,2,4},{3,6},{5,7,8}}
[2,6,8,4,5,1,7,3]=>[5,2,7,8,4,6,1,3]=>[2,7,6,5,1,8,4,3]=>{{1,2,7},{3,6,8},{4,5}}
[5,3,2,1,7,8,4,6]=>[2,3,5,8,1,4,7,6]=>[7,2,3,5,4,1,8,6]=>{{1,7,8},{2},{3},{4,5},{6}}
[6,2,5,3,4,8,1,7]=>[8,6,5,3,2,4,1,7]=>[5,6,8,1,3,2,4,7]=>{{1,5},{2,6},{3,8},{4},{7}}
[2,5,3,6,8,4,1,7]=>[4,2,8,5,1,6,3,7]=>[2,6,4,5,3,8,1,7]=>{{1,2,6,8},{3,4,5},{7}}
[2,1,7,4,8,5,3,6]=>[2,1,5,8,7,3,6,4]=>[2,1,8,5,7,4,3,6]=>{{1,2},{3,8},{4,5,7},{6}}
[2,4,6,5,7,1,8,3]=>[7,2,8,4,6,5,1,3]=>[2,6,4,7,8,1,5,3]=>{{1,2,6},{3,4,7},{5,8}}
[6,3,8,5,7,1,4,2]=>[7,4,6,1,8,3,5,2]=>[4,8,7,3,6,2,1,5]=>{{1,4},{2,8},{3,7},{5,6}}
[2,5,6,3,4,1,8,7]=>[4,2,6,3,5,1,8,7]=>[2,5,4,1,6,3,8,7]=>{{1,2,5,6},{3,4},{7,8}}
[3,7,8,5,1,4,6,2]=>[5,8,3,1,6,2,7,4]=>[5,3,7,2,6,4,8,1]=>{{1,5,6},{2,3,7,8},{4}}
[8,5,3,6,4,2,1,7]=>[2,4,6,5,8,1,3,7]=>[8,2,4,6,5,3,1,7]=>{{1,8},{2},{3,4,6},{5},{7}}
[7,2,6,5,3,1,4,8]=>[3,5,6,1,7,2,4,8]=>[7,6,3,2,5,4,1,8]=>{{1,7},{2,6},{3},{4},{5},{8}}
[4,3,6,1,8,5,2,7]=>[6,5,4,3,8,1,2,7]=>[4,6,8,1,5,3,2,7]=>{{1,4},{2,6},{3,8},{5},{7}}
[4,6,7,3,1,5,8,2]=>[3,7,8,4,1,6,2,5]=>[6,4,3,7,2,8,5,1]=>{{1,6,8},{2,4,7},{3},{5}}
[4,2,3,6,7,5,1,8]=>[5,4,2,3,7,6,1,8]=>[4,6,1,2,5,7,3,8]=>{{1,4},{2,6,7},{3},{5},{8}}
[6,2,4,1,5,7,8,3]=>[4,6,8,2,1,5,7,3]=>[7,6,4,2,3,1,8,5]=>{{1,7,8},{2,6},{3,4},{5}}
[2,5,4,7,3,1,8,6]=>[3,2,7,5,4,8,1,6]=>[2,5,3,8,1,7,6,4]=>{{1,2,5},{3},{4,8},{6,7}}
[5,8,7,3,1,2,4,6]=>[3,1,7,2,5,4,8,6]=>[5,1,3,2,8,4,7,6]=>{{1,5,8},{2},{3},{4},{6},{7}}
[6,1,2,4,3,8,7,5]=>[6,1,4,2,7,3,8,5]=>[4,1,8,3,6,5,7,2]=>{{1,4},{2},{3,8},{5,6},{7}}
[3,7,8,1,2,4,6,5]=>[8,1,3,2,6,4,7,5]=>[3,1,6,2,7,5,8,4]=>{{1,3,6},{2},{4},{5,7,8}}
[3,8,2,7,4,5,1,6]=>[5,8,3,7,4,2,6,1]=>[5,3,8,7,1,2,4,6]=>{{1,5},{2,3,8},{4,7},{6}}
[8,2,6,1,3,5,4,7]=>[6,8,1,5,2,4,3,7]=>[6,5,2,8,4,1,3,7]=>{{1,6},{2,5},{3},{4,8},{7}}
[8,3,4,7,2,6,5,1]=>[5,6,7,3,8,1,2,4]=>[8,7,6,1,5,4,3,2]=>{{1,8},{2,7},{3,6},{4},{5}}
[8,4,1,7,5,6,2,3]=>[4,8,2,6,7,5,3,1]=>[8,4,1,6,7,2,3,5]=>{{1,8},{2,4,6},{3},{5,7}}
[1,4,7,6,2,3,5,8]=>[1,6,2,4,3,7,5,8]=>[1,4,2,7,3,6,5,8]=>{{1},{2,4,7},{3},{5},{6},{8}}
[1,7,6,2,3,8,4,5]=>[1,6,2,7,4,8,5,3]=>[1,8,2,7,3,6,4,5]=>{{1},{2,8},{3},{4,7},{5},{6}}
[5,4,8,6,3,7,2,1]=>[2,7,6,5,4,8,3,1]=>[5,2,7,8,1,6,3,4]=>{{1,5},{2},{3,7},{4,8},{6}}
[4,5,7,2,8,6,3,1]=>[3,6,8,4,5,7,2,1]=>[5,4,3,6,8,7,1,2]=>{{1,5,8},{2,4,6,7},{3}}
[3,7,4,5,1,6,8,2]=>[5,8,3,7,4,2,1,6]=>[5,3,8,7,1,2,6,4]=>{{1,5},{2,3,8},{4,7},{6}}
[4,6,8,1,2,5,7,3]=>[8,1,7,4,2,6,5,3]=>[4,1,6,7,3,8,2,5]=>{{1,4,7},{2},{3,6,8},{5}}
[3,7,4,5,2,8,6,1]=>[6,5,3,8,4,7,1,2]=>[3,6,8,5,1,7,4,2]=>{{1,3,8},{2,6,7},{4,5}}
[3,2,7,4,6,1,8,5]=>[6,3,2,7,8,4,1,5]=>[3,8,1,7,6,4,5,2]=>{{1,3},{2,8},{4,7},{5,6}}
[5,2,3,8,7,1,6,4]=>[7,5,2,6,3,1,8,4]=>[5,8,1,6,3,4,7,2]=>{{1,5},{2,8},{3},{4,6},{7}}
[7,2,6,8,5,1,3,4]=>[5,8,1,2,7,4,3,6]=>[8,5,2,3,7,1,6,4]=>{{1,8},{2,5,7},{3},{4},{6}}
[4,7,6,2,5,8,1,3]=>[8,6,1,4,3,7,2,5]=>[4,6,2,8,1,7,5,3]=>{{1,4,8},{2,6,7},{3},{5}}
[3,7,4,8,6,2,5,1]=>[5,6,3,8,2,7,1,4]=>[6,3,8,5,2,7,4,1]=>{{1,6,7},{2,3,8},{4,5}}
[1,2,6,8,7,4,5,3]=>[1,2,5,7,4,6,8,3]=>[1,2,6,5,3,8,7,4]=>{{1},{2},{3,6,8},{4,5},{7}}
[4,7,8,2,1,3,5,6]=>[2,8,1,4,3,5,7,6]=>[4,2,1,7,3,5,8,6]=>{{1,4,7,8},{2},{3},{5},{6}}
[2,5,6,1,3,8,7,4]=>[6,2,1,7,5,3,8,4]=>[2,6,1,5,8,4,7,3]=>{{1,2,6},{3},{4,5,8},{7}}
[2,3,5,4,7,1,8,6]=>[7,2,3,5,4,8,1,6]=>[2,3,5,8,1,7,6,4]=>{{1,2,3,5},{4,8},{6,7}}
[5,2,7,6,8,3,4,1]=>[4,5,8,3,2,7,6,1]=>[7,5,4,1,2,8,3,6]=>{{1,7},{2,5},{3,4},{6,8}}
[6,3,7,4,5,2,8,1]=>[8,5,6,7,4,3,2,1]=>[5,8,7,6,1,2,3,4]=>{{1,5},{2,8},{3,7},{4,6}}
[7,3,4,2,8,5,6,1]=>[6,4,7,3,8,5,2,1]=>[7,8,4,1,6,2,3,5]=>{{1,7},{2,8},{3,4},{5,6}}
[4,3,6,5,8,2,7,1]=>[7,8,4,3,6,5,2,1]=>[6,4,7,1,8,2,3,5]=>{{1,6},{2,4},{3,7},{5,8}}
[8,2,7,4,5,3,6,1]=>[6,8,5,7,4,3,2,1]=>[7,5,8,6,1,2,3,4]=>{{1,7},{2,5},{3,8},{4,6}}
[7,2,8,4,5,3,6,1]=>[6,7,5,8,4,3,2,1]=>[7,6,8,5,1,2,3,4]=>{{1,7},{2,6},{3,8},{4,5}}
[6,3,8,2,7,4,5,1]=>[5,8,6,7,4,3,2,1]=>[8,5,7,6,1,2,3,4]=>{{1,8},{2,5},{3,7},{4,6}}
[3,2,8,4,7,5,6,1]=>[6,3,2,8,7,5,4,1]=>[3,8,1,6,7,2,4,5]=>{{1,3},{2,8},{4,6},{5,7}}
[5,6,8,2,4,7,1,3]=>[7,8,1,3,5,6,2,4]=>[6,5,2,1,7,8,4,3]=>{{1,6,8},{2,5,7},{3},{4}}
[5,8,7,3,2,4,6,1]=>[6,3,7,2,5,4,8,1]=>[5,6,3,1,8,2,7,4]=>{{1,5,8},{2,6},{3},{4},{7}}
[3,4,2,1,6,8,5,7]=>[2,4,3,1,8,6,5,7]=>[3,2,4,1,6,8,5,7]=>{{1,3,4},{2},{5,6,8},{7}}
[8,1,7,4,2,5,3,6]=>[8,4,7,5,3,2,1,6]=>[4,8,5,7,1,2,6,3]=>{{1,4,7},{2,8},{3,5},{6}}
[8,6,4,7,1,3,5,2]=>[7,5,1,6,3,8,4,2]=>[5,8,2,7,3,6,1,4]=>{{1,5},{2,8},{3},{4,7},{6}}
[1,7,8,5,4,6,2,3]=>[1,6,2,5,8,4,7,3]=>[1,6,2,7,5,3,8,4]=>{{1},{2,6},{3},{4,7,8},{5}}
[2,3,7,5,8,6,1,4]=>[6,2,3,1,8,7,4,5]=>[2,3,8,1,6,7,5,4]=>{{1,2,3,8},{4},{5,6,7}}
[5,6,2,8,1,7,3,4]=>[8,6,7,3,5,2,1,4]=>[5,7,6,1,8,3,4,2]=>{{1,5,8},{2,7},{3,6},{4}}
[6,2,5,3,7,4,8,1]=>[8,6,5,7,2,3,4,1]=>[5,7,8,6,3,2,1,4]=>{{1,5},{2,7},{3,8},{4,6}}
[7,3,5,4,8,2,6,1]=>[6,8,7,5,3,2,4,1]=>[7,5,6,8,2,3,1,4]=>{{1,7},{2,5},{3,6},{4,8}}
[1,2,7,4,8,5,6,3]=>[1,2,6,7,8,5,4,3]=>[1,2,8,7,6,3,4,5]=>{{1},{2},{3,8},{4,7},{5,6}}
[8,3,7,2,4,5,6,1]=>[6,7,8,2,3,4,5,1]=>[8,7,6,2,3,4,1,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[4,6,1,3,5,7,2,8]=>[6,7,1,4,2,3,5,8]=>[6,4,2,7,3,5,1,8]=>{{1,6},{2,4,7},{3},{5},{8}}
[3,4,5,8,6,1,7,2]=>[6,8,3,4,5,7,2,1]=>[4,3,5,6,8,7,1,2]=>{{1,4,6,7},{2,3,5,8}}
[6,8,1,3,2,5,7,4]=>[8,3,1,7,2,6,5,4]=>[3,6,2,7,4,8,1,5]=>{{1,3},{2,6,8},{4,7},{5}}
[8,4,2,3,5,7,6,1]=>[6,4,2,7,3,8,1,5]=>[7,8,1,4,2,6,5,3]=>{{1,7},{2,8},{3},{4},{5},{6}}
[7,2,5,4,8,6,3,1]=>[3,6,8,5,2,7,4,1]=>[6,5,3,8,2,7,1,4]=>{{1,6,7},{2,5},{3},{4,8}}
[1,4,3,6,8,5,2,7]=>[1,5,4,3,8,6,2,7]=>[1,4,6,2,5,8,3,7]=>{{1},{2,4},{3,6,8},{5},{7}}
[8,5,7,1,4,2,6,3]=>[7,4,6,1,8,2,5,3]=>[4,8,7,3,6,5,1,2]=>{{1,4},{2,8},{3,7},{5,6}}
[8,1,5,7,4,6,2,3]=>[8,6,2,7,1,5,3,4]=>[6,8,1,7,4,2,5,3]=>{{1,6},{2,8},{3},{4,7},{5}}
[2,7,1,5,6,8,4,3]=>[7,2,4,8,1,3,5,6]=>[2,7,8,4,3,5,6,1]=>{{1,2,7},{3,8},{4},{5},{6}}
[4,5,6,8,3,2,7,1]=>[7,3,8,4,5,6,2,1]=>[4,5,3,6,7,8,1,2]=>{{1,4,6,8},{2,5,7},{3}}
[5,6,2,4,7,8,3,1]=>[3,8,6,2,5,1,7,4]=>[6,3,5,1,7,4,8,2]=>{{1,6},{2,3,5,7,8},{4}}
[5,6,3,2,8,4,7,1]=>[7,3,6,8,5,2,4,1]=>[3,7,6,5,8,2,1,4]=>{{1,3,6},{2,7},{4,5,8}}
[3,7,4,8,1,6,5,2]=>[8,5,3,6,7,1,2,4]=>[3,5,8,7,6,4,2,1]=>{{1,3,8},{2,5,6},{4,7}}
[5,2,4,8,6,7,3,1]=>[3,7,5,2,1,8,6,4]=>[8,3,5,1,4,7,2,6]=>{{1,8},{2,3,5},{4},{6,7}}
[5,8,6,1,7,2,3,4]=>[6,8,2,3,5,7,4,1]=>[6,5,1,2,8,7,3,4]=>{{1,6,7},{2,5,8},{3},{4}}
[8,7,5,1,6,3,2,4]=>[5,3,7,2,6,4,8,1]=>[5,8,3,1,6,2,7,4]=>{{1,5,6},{2,8},{3},{4},{7}}
[3,5,8,6,1,7,4,2]=>[6,4,3,8,5,7,2,1]=>[3,5,6,4,8,7,1,2]=>{{1,3,6,7},{2,5,8},{4}}
[1,4,8,6,7,3,5,2]=>[1,5,7,4,3,8,6,2]=>[1,5,4,8,2,7,3,6]=>{{1},{2,5},{3,4,8},{6,7}}
[7,4,5,3,1,8,6,2]=>[3,5,6,8,4,7,1,2]=>[8,6,3,5,1,7,4,2]=>{{1,8},{2,6,7},{3},{4,5}}
[5,6,8,7,2,4,3,1]=>[3,4,7,1,5,6,8,2]=>[5,4,3,2,6,8,7,1]=>{{1,5,6,8},{2,4},{3},{7}}
[2,8,3,4,1,7,6,5]=>[4,2,8,3,6,7,1,5]=>[2,6,4,1,8,7,5,3]=>{{1,2,6,7},{3,4},{5,8}}
[6,2,8,3,4,5,1,7]=>[5,6,8,3,4,2,1,7]=>[8,6,5,1,2,3,4,7]=>{{1,8},{2,6},{3,5},{4},{7}}
[8,7,3,2,5,1,6,4]=>[5,3,7,6,2,1,8,4]=>[5,8,3,6,2,4,7,1]=>{{1,5},{2,8},{3},{4,6},{7}}
[6,3,1,4,2,5,8,7]=>[3,6,4,2,1,5,8,7]=>[6,3,4,1,2,5,8,7]=>{{1,6},{2,3,4},{5},{7,8}}
[3,5,1,7,6,2,8,4]=>[5,6,3,7,1,8,4,2]=>[7,3,8,5,4,6,1,2]=>{{1,7},{2,3,8},{4,5},{6}}
[8,4,2,6,5,3,7,1]=>[7,4,8,5,6,3,2,1]=>[5,8,4,6,7,1,2,3]=>{{1,5,7},{2,8},{3,4,6}}
[5,8,4,1,2,3,6,7]=>[4,1,2,8,5,3,6,7]=>[5,1,2,4,8,3,6,7]=>{{1,5,8},{2},{3},{4},{6},{7}}
[8,4,2,5,3,6,7,1]=>[7,4,8,5,3,2,6,1]=>[5,8,4,7,1,2,3,6]=>{{1,5},{2,8},{3,4,7},{6}}
[2,8,5,4,6,7,1,3]=>[7,2,1,5,8,4,6,3]=>[2,7,1,8,5,3,4,6]=>{{1,2,7},{3},{4,8},{5},{6}}
[4,5,1,6,8,2,7,3]=>[5,8,7,4,1,6,2,3]=>[6,4,5,7,3,8,2,1]=>{{1,6,8},{2,4,7},{3,5}}
[4,3,1,6,7,2,5,8]=>[3,4,7,2,1,6,5,8]=>[6,4,3,1,2,7,5,8]=>{{1,6,7},{2,4},{3},{5},{8}}
[3,7,6,4,1,5,8,2]=>[4,6,3,7,1,8,5,2]=>[7,3,8,4,2,6,1,5]=>{{1,7},{2,3,8},{4},{5},{6}}
[7,1,6,5,4,2,8,3]=>[7,4,5,6,8,1,2,3]=>[4,8,7,6,5,3,2,1]=>{{1,4,6},{2,8},{3,7},{5}}
[4,7,1,3,5,6,2,8]=>[7,6,1,4,2,3,5,8]=>[4,6,2,7,3,5,1,8]=>{{1,4,7},{2,6},{3},{5},{8}}
[4,8,5,7,1,2,3,6]=>[7,1,2,4,8,3,5,6]=>[4,1,2,8,7,5,6,3]=>{{1,4,8},{2},{3},{5,7},{6}}
[4,2,3,7,6,1,8,5]=>[6,4,2,3,7,8,5,1]=>[4,8,1,2,7,6,3,5]=>{{1,4},{2,8},{3},{5,7},{6}}
[5,6,4,7,3,8,2,10,1,9]=>[10,8,7,6,5,4,3,2,1,9]=>[5,6,7,8,10,1,2,3,4,9]=>{{1,5,10},{2,6},{3,7},{4,8},{9}}
[5,1,7,3,6,4,2,8]=>[5,4,6,7,1,2,3,8]=>[6,7,5,4,3,2,1,8]=>{{1,6},{2,7},{3,5},{4},{8}}
[5,6,2,8,3,1,7,4]=>[3,8,6,7,5,1,2,4]=>[7,3,5,6,8,4,2,1]=>{{1,7},{2,3,5,8},{4,6}}
[8,1,5,7,6,3,2,4]=>[8,3,6,2,1,7,5,4]=>[3,8,6,1,4,7,2,5]=>{{1,3,6,7},{2,8},{4},{5}}
[1,8,7,6,3,5,4,2]=>[1,4,5,6,2,7,8,3]=>[1,8,5,4,3,6,7,2]=>{{1},{2,8},{3,5},{4},{6},{7}}
[1,6,2,7,3,8,4,9,5]=>[1,6,7,8,9,2,3,4,5]=>[1,9,8,7,6,5,4,3,2]=>{{1},{2,9},{3,8},{4,7},{5,6}}
[3,6,1,4,7,8,2,5]=>[6,8,3,1,4,5,7,2]=>[6,3,7,2,1,4,8,5]=>{{1,6},{2,3,7,8},{4},{5}}
[2,5,7,1,3,6,4,8]=>[7,2,1,6,5,3,4,8]=>[2,5,1,6,7,4,3,8]=>{{1,2,5,7},{3},{4,6},{8}}
[3,2,8,1,7,5,4,6]=>[8,3,2,5,7,4,1,6]=>[3,5,1,8,7,2,6,4]=>{{1,3},{2,5,7},{4,8},{6}}
[7,4,1,5,6,8,3,2]=>[4,3,7,8,1,2,6,5]=>[7,8,3,4,2,5,1,6]=>{{1,7},{2,8},{3},{4},{5},{6}}
[4,1,2,6,7,8,5,3]=>[4,1,5,2,8,6,7,3]=>[6,1,4,3,5,7,8,2]=>{{1,6,7,8},{2},{3,4},{5}}
[2,1,4,3,6,5,10,7,9,8]=>[2,1,4,3,6,5,10,9,7,8]=>[2,1,4,3,6,5,9,10,8,7]=>{{1,2},{3,4},{5,6},{7,9},{8,10}}
[2,1,4,3,8,5,7,6,10,9]=>[2,1,4,3,8,7,5,6,10,9]=>[2,1,4,3,7,8,6,5,10,9]=>{{1,2},{3,4},{5,7},{6,8},{9,10}}
[2,1,6,3,5,4,8,7,10,9]=>[2,1,6,5,3,4,8,7,10,9]=>[2,1,5,6,4,3,8,7,10,9]=>{{1,2},{3,5},{4,6},{7,8},{9,10}}
[2,1,6,3,5,4,10,7,9,8]=>[2,1,6,5,3,4,10,9,7,8]=>[2,1,5,6,4,3,9,10,8,7]=>{{1,2},{3,5},{4,6},{7,9},{8,10}}
[4,1,3,2,6,5,8,7,10,9]=>[4,3,1,2,6,5,8,7,10,9]=>[3,4,2,1,6,5,8,7,10,9]=>{{1,3},{2,4},{5,6},{7,8},{9,10}}
[4,1,3,2,6,5,10,7,9,8]=>[4,3,1,2,6,5,10,9,7,8]=>[3,4,2,1,6,5,9,10,8,7]=>{{1,3},{2,4},{5,6},{7,9},{8,10}}
[4,1,3,2,8,5,7,6,10,9]=>[4,3,1,2,8,7,5,6,10,9]=>[3,4,2,1,7,8,6,5,10,9]=>{{1,3},{2,4},{5,7},{6,8},{9,10}}
[2,1,4,3,6,5,8,7,12,9,11,10]=>[2,1,4,3,6,5,8,7,12,11,9,10]=>[2,1,4,3,6,5,8,7,11,12,10,9]=>{{1,2},{3,4},{5,6},{7,8},{9,11},{10,12}}
[2,1,4,3,6,5,10,7,9,8,12,11]=>[2,1,4,3,6,5,10,9,7,8,12,11]=>[2,1,4,3,6,5,9,10,8,7,12,11]=>{{1,2},{3,4},{5,6},{7,9},{8,10},{11,12}}
[2,1,4,3,8,5,7,6,10,9,12,11]=>[2,1,4,3,8,7,5,6,10,9,12,11]=>[2,1,4,3,7,8,6,5,10,9,12,11]=>{{1,2},{3,4},{5,7},{6,8},{9,10},{11,12}}
[2,1,4,3,8,5,7,6,12,9,11,10]=>[2,1,4,3,8,7,5,6,12,11,9,10]=>[2,1,4,3,7,8,6,5,11,12,10,9]=>{{1,2},{3,4},{5,7},{6,8},{9,11},{10,12}}
[2,1,6,3,5,4,8,7,10,9,12,11]=>[2,1,6,5,3,4,8,7,10,9,12,11]=>[2,1,5,6,4,3,8,7,10,9,12,11]=>{{1,2},{3,5},{4,6},{7,8},{9,10},{11,12}}
[2,1,6,3,5,4,8,7,12,9,11,10]=>[2,1,6,5,3,4,8,7,12,11,9,10]=>[2,1,5,6,4,3,8,7,11,12,10,9]=>{{1,2},{3,5},{4,6},{7,8},{9,11},{10,12}}
[2,1,6,3,5,4,10,7,9,8,12,11]=>[2,1,6,5,3,4,10,9,7,8,12,11]=>[2,1,5,6,4,3,9,10,8,7,12,11]=>{{1,2},{3,5},{4,6},{7,9},{8,10},{11,12}}
[4,1,3,2,6,5,8,7,10,9,12,11]=>[4,3,1,2,6,5,8,7,10,9,12,11]=>[3,4,2,1,6,5,8,7,10,9,12,11]=>{{1,3},{2,4},{5,6},{7,8},{9,10},{11,12}}
[4,1,3,2,6,5,8,7,12,9,11,10]=>[4,3,1,2,6,5,8,7,12,11,9,10]=>[3,4,2,1,6,5,8,7,11,12,10,9]=>{{1,3},{2,4},{5,6},{7,8},{9,11},{10,12}}
[4,1,3,2,6,5,10,7,9,8,12,11]=>[4,3,1,2,6,5,10,9,7,8,12,11]=>[3,4,2,1,6,5,9,10,8,7,12,11]=>{{1,3},{2,4},{5,6},{7,9},{8,10},{11,12}}
[4,1,3,2,8,5,7,6,10,9,12,11]=>[4,3,1,2,8,7,5,6,10,9,12,11]=>[3,4,2,1,7,8,6,5,10,9,12,11]=>{{1,3},{2,4},{5,7},{6,8},{9,10},{11,12}}
[4,1,3,2,8,5,7,6,12,9,11,10]=>[4,3,1,2,8,7,5,6,12,11,9,10]=>[3,4,2,1,7,8,6,5,11,12,10,9]=>{{1,3},{2,4},{5,7},{6,8},{9,11},{10,12}}
[1,7,4,5,6,8,3,2]=>[1,3,8,7,4,5,6,2]=>[1,7,3,8,2,4,5,6]=>{{1},{2,7},{3},{4,8},{5},{6}}
[5,4,3,6,8,1,7,2]=>[8,7,4,5,3,6,1,2]=>[4,5,7,6,1,8,3,2]=>{{1,4,6,8},{2,5},{3,7}}
[4,7,3,5,1,2,8,6]=>[5,1,7,4,3,8,2,6]=>[5,1,4,8,2,7,6,3]=>{{1,5},{2},{3,4,8},{6,7}}
[4,3,5,2,6,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>{{1,4},{2,5},{3,6},{7},{8},{9}}
[3,2,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>{{1,3},{2,4},{5},{6},{7},{8},{9},{10}}
[4,3,5,2,6,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[4,5,6,1,2,3,7,8,9,10]=>{{1,4},{2,5},{3,6},{7},{8},{9},{10}}
[5,4,6,3,7,2,8,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[5,6,7,8,1,2,3,4,9,10]=>{{1,5},{2,6},{3,7},{4,8},{9},{10}}
[4,3,7,8,2,1,6,5]=>[2,8,4,3,6,1,7,5]=>[4,2,6,1,7,5,8,3]=>{{1,4},{2},{3,6},{5,7,8}}
[8,7,1,3,2,4,5,6]=>[7,3,1,2,4,5,8,6]=>[3,8,2,1,4,5,7,6]=>{{1,3},{2,8},{4},{5},{6},{7}}
[4,2,7,3,6,8,5,1]=>[5,4,8,2,7,3,1,6]=>[5,8,4,2,7,1,6,3]=>{{1,5,7},{2,8},{3,4},{6}}
[1,5,4,8,7,3,2,6]=>[1,3,7,5,4,2,8,6]=>[1,5,3,8,2,4,7,6]=>{{1},{2,5},{3},{4,8},{6},{7}}
[3,8,6,4,1,5,7,2]=>[4,6,3,8,1,7,5,2]=>[6,3,8,4,2,7,1,5]=>{{1,6,7},{2,3,8},{4},{5}}
[8,7,1,4,5,2,3,6]=>[7,5,2,1,4,3,8,6]=>[5,8,1,3,2,4,7,6]=>{{1,5},{2,8},{3},{4},{6},{7}}
[4,7,2,5,6,8,1,3]=>[8,7,1,4,3,5,2,6]=>[4,7,2,8,1,3,6,5]=>{{1,4,8},{2,7},{3},{5},{6}}
[1,4,7,2,6,5,8,3]=>[1,7,8,4,6,2,5,3]=>[1,6,4,7,8,5,2,3]=>{{1},{2,6},{3,4,7},{5,8}}
[7,2,4,6,1,8,3,5]=>[6,7,8,2,4,3,5,1]=>[8,7,6,2,1,4,3,5]=>{{1,8},{2,7},{3,6},{4},{5}}
[6,5,1,8,3,4,7,2]=>[5,6,7,3,8,2,1,4]=>[8,7,6,1,5,3,4,2]=>{{1,8},{2,7},{3,6},{4},{5}}
[3,1,8,2,6,5,7,4]=>[3,8,1,7,6,2,5,4]=>[6,3,2,7,8,5,1,4]=>{{1,6},{2,3},{4,7},{5,8}}
[1,5,8,3,4,6,2,7]=>[1,6,8,3,5,4,2,7]=>[1,6,5,2,8,3,4,7]=>{{1},{2,6},{3,5,8},{4},{7}}
[1,4,7,6,2,3,8,5]=>[1,6,2,4,7,8,5,3]=>[1,4,2,8,7,6,3,5]=>{{1},{2,4,8},{3},{5,7},{6}}
[1,4,2,3,7,8,6,5]=>[1,4,2,3,6,8,7,5]=>[1,4,2,3,7,6,8,5]=>{{1},{2,4},{3},{5,7,8},{6}}
[4,5,8,1,6,3,7,2]=>[8,7,6,4,5,1,3,2]=>[4,5,6,7,8,3,1,2]=>{{1,4,7},{2,5,8},{3,6}}
[5,2,6,8,1,4,3,7]=>[8,5,4,1,2,6,3,7]=>[4,5,6,3,2,8,1,7]=>{{1,4},{2,5},{3,6,8},{7}}
[5,3,8,1,4,6,2,7]=>[8,6,5,1,3,4,2,7]=>[5,6,8,3,2,1,4,7]=>{{1,5},{2,6},{3,8},{4},{7}}
[1,6,8,5,3,2,7,4]=>[1,3,5,8,7,6,4,2]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[7,2,1,6,4,3,8,5]=>[2,7,4,6,8,1,3,5]=>[4,2,8,7,6,5,3,1]=>{{1,4,7},{2},{3,8},{5,6}}
[1,8,6,2,7,4,3,5]=>[1,6,4,8,3,7,5,2]=>[1,6,8,4,2,7,3,5]=>{{1},{2,6,7},{3,8},{4},{5}}
[8,5,1,3,7,6,4,2]=>[5,4,1,8,6,7,2,3]=>[5,8,2,4,6,7,3,1]=>{{1,5,6,7},{2,8},{3},{4}}
[1,6,7,5,8,4,2,3]=>[1,4,2,8,7,6,5,3]=>[1,6,2,4,7,8,3,5]=>{{1},{2,6,8},{3},{4},{5,7}}
[6,8,4,7,3,2,5,1]=>[5,3,7,8,2,6,4,1]=>[6,7,3,5,2,8,1,4]=>{{1,6,8},{2,7},{3},{4,5}}
[7,3,6,4,2,1,8,5]=>[2,4,6,7,8,1,3,5]=>[8,2,7,4,6,5,3,1]=>{{1,8},{2},{3,7},{4},{5,6}}
[7,1,2,6,4,3,8,5]=>[7,1,4,6,8,2,3,5]=>[4,1,8,7,6,5,3,2]=>{{1,4,7},{2},{3,8},{5,6}}
[8,7,2,4,3,1,5,6]=>[3,4,7,1,2,5,8,6]=>[8,4,3,2,1,5,7,6]=>{{1,8},{2,4},{3},{5},{6},{7}}
[2,1,4,3,10,5,7,6,9,8]=>[2,1,4,3,10,7,5,9,6,8]=>[2,1,4,3,7,9,6,10,8,5]=>{{1,2},{3,4},{5,7},{6,9},{8,10}}
[2,1,4,3,9,6,10,5,8,7]=>[2,1,4,3,10,9,8,5,6,7]=>[2,1,4,3,8,9,10,7,6,5]=>{{1,2},{3,4},{5,8},{6,9},{7,10}}
[2,1,8,3,5,4,7,6,10,9]=>[2,1,8,5,3,7,4,6,10,9]=>[2,1,5,7,4,8,6,3,10,9]=>{{1,2},{3,5},{4,7},{6,8},{9,10}}
[2,1,10,3,5,4,7,6,9,8]=>[2,1,10,5,3,7,4,9,6,8]=>[2,1,5,7,4,9,6,10,8,3]=>{{1,2},{3,5},{4,7},{6,9},{8,10}}
[2,1,9,6,10,3,5,4,8,7]=>[2,1,10,5,3,9,8,4,6,7]=>[2,1,5,8,4,9,10,7,6,3]=>{{1,2},{3,5},{4,8},{6,9},{7,10}}
[2,1,7,4,8,3,6,5,10,9]=>[2,1,8,7,6,3,4,5,10,9]=>[2,1,6,7,8,5,4,3,10,9]=>{{1,2},{3,6},{4,7},{5,8},{9,10}}
[2,1,7,4,10,3,6,5,9,8]=>[2,1,10,7,6,3,4,9,5,8]=>[2,1,6,7,9,5,4,10,8,3]=>{{1,2},{3,6},{4,7},{5,9},{8,10}}
[4,1,3,2,10,5,7,6,9,8]=>[4,3,1,2,10,7,5,9,6,8]=>[3,4,2,1,7,9,6,10,8,5]=>{{1,3},{2,4},{5,7},{6,9},{8,10}}
[4,1,3,2,9,6,10,5,8,7]=>[4,3,1,2,10,9,8,5,6,7]=>[3,4,2,1,8,9,10,7,6,5]=>{{1,3},{2,4},{5,8},{6,9},{7,10}}
[6,1,3,2,5,4,8,7,10,9]=>[6,3,1,5,2,4,8,7,10,9]=>[3,5,2,6,4,1,8,7,10,9]=>{{1,3},{2,5},{4,6},{7,8},{9,10}}
[6,1,3,2,5,4,10,7,9,8]=>[6,3,1,5,2,4,10,9,7,8]=>[3,5,2,6,4,1,9,10,8,7]=>{{1,3},{2,5},{4,6},{7,9},{8,10}}
[8,1,3,2,5,4,7,6,10,9]=>[8,3,1,5,2,7,4,6,10,9]=>[3,5,2,7,4,8,6,1,10,9]=>{{1,3},{2,5},{4,7},{6,8},{9,10}}
[9,6,10,1,3,2,5,4,8,7]=>[10,3,1,5,2,9,8,4,6,7]=>[3,5,2,8,4,9,10,7,6,1]=>{{1,3},{2,5},{4,8},{6,9},{7,10}}
[7,4,8,1,3,2,6,5,10,9]=>[8,3,1,7,6,2,4,5,10,9]=>[3,6,2,7,8,5,4,1,10,9]=>{{1,3},{2,6},{4,7},{5,8},{9,10}}
[7,4,10,1,3,2,6,5,9,8]=>[10,3,1,7,6,2,4,9,5,8]=>[3,6,2,7,9,5,4,10,8,1]=>{{1,3},{2,6},{4,7},{5,9},{8,10}}
[5,2,6,1,4,3,8,7,10,9]=>[6,5,4,1,2,3,8,7,10,9]=>[4,5,6,3,2,1,8,7,10,9]=>{{1,4},{2,5},{3,6},{7,8},{9,10}}
[5,2,6,1,4,3,10,7,9,8]=>[6,5,4,1,2,3,10,9,7,8]=>[4,5,6,3,2,1,9,10,8,7]=>{{1,4},{2,5},{3,6},{7,9},{8,10}}
[5,2,8,1,4,3,7,6,10,9]=>[8,5,4,1,2,7,3,6,10,9]=>[4,5,7,3,2,8,6,1,10,9]=>{{1,4},{2,5},{3,7},{6,8},{9,10}}
[5,2,10,1,4,3,7,6,9,8]=>[10,5,4,1,2,7,3,9,6,8]=>[4,5,7,3,2,9,6,10,8,1]=>{{1,4},{2,5},{3,7},{6,9},{8,10}}
[5,2,9,6,10,1,4,3,8,7]=>[10,5,4,1,2,9,8,3,6,7]=>[4,5,8,3,2,9,10,7,6,1]=>{{1,4},{2,5},{3,8},{6,9},{7,10}}
[2,1,4,3,6,5,12,7,9,8,11,10]=>[2,1,4,3,6,5,12,9,7,11,8,10]=>[2,1,4,3,6,5,9,11,8,12,10,7]=>{{1,2},{3,4},{5,6},{7,9},{8,11},{10,12}}
[2,1,4,3,6,5,11,8,12,7,10,9]=>[2,1,4,3,6,5,12,11,10,7,8,9]=>[2,1,4,3,6,5,10,11,12,9,8,7]=>{{1,2},{3,4},{5,6},{7,10},{8,11},{9,12}}
[2,1,4,3,10,5,7,6,9,8,12,11]=>[2,1,4,3,10,7,5,9,6,8,12,11]=>[2,1,4,3,7,9,6,10,8,5,12,11]=>{{1,2},{3,4},{5,7},{6,9},{8,10},{11,12}}
[2,1,4,3,12,5,7,6,9,8,11,10]=>[2,1,4,3,12,7,5,9,6,11,8,10]=>[2,1,4,3,7,9,6,11,8,12,10,5]=>{{1,2},{3,4},{5,7},{6,9},{8,11},{10,12}}
[2,1,4,3,11,8,12,5,7,6,10,9]=>[2,1,4,3,12,7,5,11,10,6,8,9]=>[2,1,4,3,7,10,6,11,12,9,8,5]=>{{1,2},{3,4},{5,7},{6,10},{8,11},{9,12}}
[2,1,4,3,9,6,10,5,8,7,12,11]=>[2,1,4,3,10,9,8,5,6,7,12,11]=>[2,1,4,3,8,9,10,7,6,5,12,11]=>{{1,2},{3,4},{5,8},{6,9},{7,10},{11,12}}
[2,1,4,3,9,6,12,5,8,7,11,10]=>[2,1,4,3,12,9,8,5,6,11,7,10]=>[2,1,4,3,8,9,11,7,6,12,10,5]=>{{1,2},{3,4},{5,8},{6,9},{7,11},{10,12}}
[2,1,6,3,5,4,12,7,9,8,11,10]=>[2,1,6,5,3,4,12,9,7,11,8,10]=>[2,1,5,6,4,3,9,11,8,12,10,7]=>{{1,2},{3,5},{4,6},{7,9},{8,11},{10,12}}
[2,1,6,3,5,4,11,8,12,7,10,9]=>[2,1,6,5,3,4,12,11,10,7,8,9]=>[2,1,5,6,4,3,10,11,12,9,8,7]=>{{1,2},{3,5},{4,6},{7,10},{8,11},{9,12}}
[2,1,8,3,5,4,7,6,10,9,12,11]=>[2,1,8,5,3,7,4,6,10,9,12,11]=>[2,1,5,7,4,8,6,3,10,9,12,11]=>{{1,2},{3,5},{4,7},{6,8},{9,10},{11,12}}
[2,1,8,3,5,4,7,6,12,9,11,10]=>[2,1,8,5,3,7,4,6,12,11,9,10]=>[2,1,5,7,4,8,6,3,11,12,10,9]=>{{1,2},{3,5},{4,7},{6,8},{9,11},{10,12}}
[2,1,10,3,5,4,7,6,9,8,12,11]=>[2,1,10,5,3,7,4,9,6,8,12,11]=>[2,1,5,7,4,9,6,10,8,3,12,11]=>{{1,2},{3,5},{4,7},{6,9},{8,10},{11,12}}
[2,1,12,3,5,4,7,6,9,8,11,10]=>[2,1,12,5,3,7,4,9,6,11,8,10]=>[2,1,5,7,4,9,6,11,8,12,10,3]=>{{1,2},{3,5},{4,7},{6,9},{8,11},{10,12}}
[2,1,11,8,12,3,5,4,7,6,10,9]=>[2,1,12,5,3,7,4,11,10,6,8,9]=>[2,1,5,7,4,10,6,11,12,9,8,3]=>{{1,2},{3,5},{4,7},{6,10},{8,11},{9,12}}
[2,1,9,6,10,3,5,4,8,7,12,11]=>[2,1,10,5,3,9,8,4,6,7,12,11]=>[2,1,5,8,4,9,10,7,6,3,12,11]=>{{1,2},{3,5},{4,8},{6,9},{7,10},{11,12}}
[2,1,9,6,12,3,5,4,8,7,11,10]=>[2,1,12,5,3,9,8,4,6,11,7,10]=>[2,1,5,8,4,9,11,7,6,12,10,3]=>{{1,2},{3,5},{4,8},{6,9},{7,11},{10,12}}
[2,1,7,4,8,3,6,5,10,9,12,11]=>[2,1,8,7,6,3,4,5,10,9,12,11]=>[2,1,6,7,8,5,4,3,10,9,12,11]=>{{1,2},{3,6},{4,7},{5,8},{9,10},{11,12}}
[2,1,7,4,8,3,6,5,12,9,11,10]=>[2,1,8,7,6,3,4,5,12,11,9,10]=>[2,1,6,7,8,5,4,3,11,12,10,9]=>{{1,2},{3,6},{4,7},{5,8},{9,11},{10,12}}
[2,1,7,4,10,3,6,5,9,8,12,11]=>[2,1,10,7,6,3,4,9,5,8,12,11]=>[2,1,6,7,9,5,4,10,8,3,12,11]=>{{1,2},{3,6},{4,7},{5,9},{8,10},{11,12}}
[2,1,7,4,12,3,6,5,9,8,11,10]=>[2,1,12,7,6,3,4,9,5,11,8,10]=>[2,1,6,7,9,5,4,11,8,12,10,3]=>{{1,2},{3,6},{4,7},{5,9},{8,11},{10,12}}
[2,1,7,4,11,8,12,3,6,5,10,9]=>[2,1,12,7,6,3,4,11,10,5,8,9]=>[2,1,6,7,10,5,4,11,12,9,8,3]=>{{1,2},{3,6},{4,7},{5,10},{8,11},{9,12}}
[4,1,3,2,6,5,12,7,9,8,11,10]=>[4,3,1,2,6,5,12,9,7,11,8,10]=>[3,4,2,1,6,5,9,11,8,12,10,7]=>{{1,3},{2,4},{5,6},{7,9},{8,11},{10,12}}
[4,1,3,2,6,5,11,8,12,7,10,9]=>[4,3,1,2,6,5,12,11,10,7,8,9]=>[3,4,2,1,6,5,10,11,12,9,8,7]=>{{1,3},{2,4},{5,6},{7,10},{8,11},{9,12}}
[4,1,3,2,10,5,7,6,9,8,12,11]=>[4,3,1,2,10,7,5,9,6,8,12,11]=>[3,4,2,1,7,9,6,10,8,5,12,11]=>{{1,3},{2,4},{5,7},{6,9},{8,10},{11,12}}
[4,1,3,2,12,5,7,6,9,8,11,10]=>[4,3,1,2,12,7,5,9,6,11,8,10]=>[3,4,2,1,7,9,6,11,8,12,10,5]=>{{1,3},{2,4},{5,7},{6,9},{8,11},{10,12}}
[4,1,3,2,11,8,12,5,7,6,10,9]=>[4,3,1,2,12,7,5,11,10,6,8,9]=>[3,4,2,1,7,10,6,11,12,9,8,5]=>{{1,3},{2,4},{5,7},{6,10},{8,11},{9,12}}
[4,1,3,2,9,6,10,5,8,7,12,11]=>[4,3,1,2,10,9,8,5,6,7,12,11]=>[3,4,2,1,8,9,10,7,6,5,12,11]=>{{1,3},{2,4},{5,8},{6,9},{7,10},{11,12}}
[4,1,3,2,9,6,12,5,8,7,11,10]=>[4,3,1,2,12,9,8,5,6,11,7,10]=>[3,4,2,1,8,9,11,7,6,12,10,5]=>{{1,3},{2,4},{5,8},{6,9},{7,11},{10,12}}
[6,1,3,2,5,4,8,7,10,9,12,11]=>[6,3,1,5,2,4,8,7,10,9,12,11]=>[3,5,2,6,4,1,8,7,10,9,12,11]=>{{1,3},{2,5},{4,6},{7,8},{9,10},{11,12}}
[6,1,3,2,5,4,8,7,12,9,11,10]=>[6,3,1,5,2,4,8,7,12,11,9,10]=>[3,5,2,6,4,1,8,7,11,12,10,9]=>{{1,3},{2,5},{4,6},{7,8},{9,11},{10,12}}
[6,1,3,2,5,4,10,7,9,8,12,11]=>[6,3,1,5,2,4,10,9,7,8,12,11]=>[3,5,2,6,4,1,9,10,8,7,12,11]=>{{1,3},{2,5},{4,6},{7,9},{8,10},{11,12}}
[6,1,3,2,5,4,12,7,9,8,11,10]=>[6,3,1,5,2,4,12,9,7,11,8,10]=>[3,5,2,6,4,1,9,11,8,12,10,7]=>{{1,3},{2,5},{4,6},{7,9},{8,11},{10,12}}
[6,1,3,2,5,4,11,8,12,7,10,9]=>[6,3,1,5,2,4,12,11,10,7,8,9]=>[3,5,2,6,4,1,10,11,12,9,8,7]=>{{1,3},{2,5},{4,6},{7,10},{8,11},{9,12}}
[8,1,3,2,5,4,7,6,10,9,12,11]=>[8,3,1,5,2,7,4,6,10,9,12,11]=>[3,5,2,7,4,8,6,1,10,9,12,11]=>{{1,3},{2,5},{4,7},{6,8},{9,10},{11,12}}
[8,1,3,2,5,4,7,6,12,9,11,10]=>[8,3,1,5,2,7,4,6,12,11,9,10]=>[3,5,2,7,4,8,6,1,11,12,10,9]=>{{1,3},{2,5},{4,7},{6,8},{9,11},{10,12}}
[10,1,3,2,5,4,7,6,9,8,12,11]=>[10,3,1,5,2,7,4,9,6,8,12,11]=>[3,5,2,7,4,9,6,10,8,1,12,11]=>{{1,3},{2,5},{4,7},{6,9},{8,10},{11,12}}
[11,8,12,1,3,2,5,4,7,6,10,9]=>[12,3,1,5,2,7,4,11,10,6,8,9]=>[3,5,2,7,4,10,6,11,12,9,8,1]=>{{1,3},{2,5},{4,7},{6,10},{8,11},{9,12}}
[9,6,10,1,3,2,5,4,8,7,12,11]=>[10,3,1,5,2,9,8,4,6,7,12,11]=>[3,5,2,8,4,9,10,7,6,1,12,11]=>{{1,3},{2,5},{4,8},{6,9},{7,10},{11,12}}
[9,6,12,1,3,2,5,4,8,7,11,10]=>[12,3,1,5,2,9,8,4,6,11,7,10]=>[3,5,2,8,4,9,11,7,6,12,10,1]=>{{1,3},{2,5},{4,8},{6,9},{7,11},{10,12}}
[7,4,8,1,3,2,6,5,10,9,12,11]=>[8,3,1,7,6,2,4,5,10,9,12,11]=>[3,6,2,7,8,5,4,1,10,9,12,11]=>{{1,3},{2,6},{4,7},{5,8},{9,10},{11,12}}
[7,4,8,1,3,2,6,5,12,9,11,10]=>[8,3,1,7,6,2,4,5,12,11,9,10]=>[3,6,2,7,8,5,4,1,11,12,10,9]=>{{1,3},{2,6},{4,7},{5,8},{9,11},{10,12}}
[7,4,10,1,3,2,6,5,9,8,12,11]=>[10,3,1,7,6,2,4,9,5,8,12,11]=>[3,6,2,7,9,5,4,10,8,1,12,11]=>{{1,3},{2,6},{4,7},{5,9},{8,10},{11,12}}
[7,4,12,1,3,2,6,5,9,8,11,10]=>[12,3,1,7,6,2,4,9,5,11,8,10]=>[3,6,2,7,9,5,4,11,8,12,10,1]=>{{1,3},{2,6},{4,7},{5,9},{8,11},{10,12}}
[7,4,11,8,12,1,3,2,6,5,10,9]=>[12,3,1,7,6,2,4,11,10,5,8,9]=>[3,6,2,7,10,5,4,11,12,9,8,1]=>{{1,3},{2,6},{4,7},{5,10},{8,11},{9,12}}
[5,2,6,1,4,3,8,7,10,9,12,11]=>[6,5,4,1,2,3,8,7,10,9,12,11]=>[4,5,6,3,2,1,8,7,10,9,12,11]=>{{1,4},{2,5},{3,6},{7,8},{9,10},{11,12}}
[5,2,6,1,4,3,8,7,12,9,11,10]=>[6,5,4,1,2,3,8,7,12,11,9,10]=>[4,5,6,3,2,1,8,7,11,12,10,9]=>{{1,4},{2,5},{3,6},{7,8},{9,11},{10,12}}
[5,2,6,1,4,3,10,7,9,8,12,11]=>[6,5,4,1,2,3,10,9,7,8,12,11]=>[4,5,6,3,2,1,9,10,8,7,12,11]=>{{1,4},{2,5},{3,6},{7,9},{8,10},{11,12}}
[5,2,6,1,4,3,12,7,9,8,11,10]=>[6,5,4,1,2,3,12,9,7,11,8,10]=>[4,5,6,3,2,1,9,11,8,12,10,7]=>{{1,4},{2,5},{3,6},{7,9},{8,11},{10,12}}
[5,2,6,1,4,3,11,8,12,7,10,9]=>[6,5,4,1,2,3,12,11,10,7,8,9]=>[4,5,6,3,2,1,10,11,12,9,8,7]=>{{1,4},{2,5},{3,6},{7,10},{8,11},{9,12}}
[5,2,8,1,4,3,7,6,10,9,12,11]=>[8,5,4,1,2,7,3,6,10,9,12,11]=>[4,5,7,3,2,8,6,1,10,9,12,11]=>{{1,4},{2,5},{3,7},{6,8},{9,10},{11,12}}
[5,2,8,1,4,3,7,6,12,9,11,10]=>[8,5,4,1,2,7,3,6,12,11,9,10]=>[4,5,7,3,2,8,6,1,11,12,10,9]=>{{1,4},{2,5},{3,7},{6,8},{9,11},{10,12}}
[5,2,10,1,4,3,7,6,9,8,12,11]=>[10,5,4,1,2,7,3,9,6,8,12,11]=>[4,5,7,3,2,9,6,10,8,1,12,11]=>{{1,4},{2,5},{3,7},{6,9},{8,10},{11,12}}
[5,2,12,1,4,3,7,6,9,8,11,10]=>[12,5,4,1,2,7,3,9,6,11,8,10]=>[4,5,7,3,2,9,6,11,8,12,10,1]=>{{1,4},{2,5},{3,7},{6,9},{8,11},{10,12}}
[5,2,11,8,12,1,4,3,7,6,10,9]=>[12,5,4,1,2,7,3,11,10,6,8,9]=>[4,5,7,3,2,10,6,11,12,9,8,1]=>{{1,4},{2,5},{3,7},{6,10},{8,11},{9,12}}
[5,2,9,6,10,1,4,3,8,7,12,11]=>[10,5,4,1,2,9,8,3,6,7,12,11]=>[4,5,8,3,2,9,10,7,6,1,12,11]=>{{1,4},{2,5},{3,8},{6,9},{7,10},{11,12}}
[5,2,9,6,12,1,4,3,8,7,11,10]=>[12,5,4,1,2,9,8,3,6,11,7,10]=>[4,5,8,3,2,9,11,7,6,12,10,1]=>{{1,4},{2,5},{3,8},{6,9},{7,11},{10,12}}
[1,5,2,6,8,7,4,3]=>[1,5,4,7,2,6,8,3]=>[1,5,6,4,3,8,7,2]=>{{1},{2,5},{3,6,8},{4},{7}}
[1,8,3,7,5,2,6,4]=>[1,5,7,8,6,3,4,2]=>[1,8,6,5,7,3,2,4]=>{{1},{2,8},{3,6},{4,5,7}}
[8,1,3,6,5,2,7,4]=>[8,5,1,6,7,2,3,4]=>[5,8,2,7,6,4,3,1]=>{{1,5,6},{2,8},{3},{4,7}}
[7,1,3,8,5,2,6,4]=>[7,5,1,8,6,4,3,2]=>[6,8,2,5,7,1,3,4]=>{{1,6},{2,8},{3},{4,5,7}}
[8,4,1,5,6,2,7,3]=>[4,8,6,7,1,2,3,5]=>[8,4,7,6,3,5,2,1]=>{{1,8},{2,4,6},{3,7},{5}}
[4,1,7,2,5,8,3,6]=>[4,7,8,1,2,5,6,3]=>[8,7,4,3,2,1,5,6]=>{{1,8},{2,7},{3,4},{5},{6}}
[3,2,8,1,5,6,4,7]=>[8,3,2,6,1,5,4,7]=>[3,6,1,8,4,2,5,7]=>{{1,3},{2,6},{4,8},{5},{7}}
[3,4,7,1,5,8,2,6]=>[7,8,3,4,1,5,6,2]=>[4,3,7,8,2,1,5,6]=>{{1,4,8},{2,3,7},{5},{6}}
[7,3,1,6,8,4,5,2]=>[3,7,5,8,4,1,2,6]=>[8,3,7,5,1,4,6,2]=>{{1,8},{2,3,7},{4,5},{6}}
[1,5,7,2,8,4,6,3]=>[1,7,6,8,5,4,2,3]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,7},{4,5,8}}
[1,8,7,5,2,6,3,4]=>[1,5,7,3,6,4,8,2]=>[1,8,5,2,6,3,7,4]=>{{1},{2,8},{3,5,6},{4},{7}}
[1,4,3,2,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,8,7,6,5]=>{{1},{2,4},{3},{5,8},{6,7}}
[7,6,2,8,4,5,3,1]=>[3,5,6,7,4,8,2,1]=>[8,7,3,5,1,6,2,4]=>{{1,8},{2,7},{3},{4,5},{6}}
[2,3,8,7,4,5,1,6]=>[5,2,3,7,4,1,8,6]=>[2,3,8,5,1,4,7,6]=>{{1,2,3,8},{4,5},{6},{7}}
[7,1,2,4,8,6,5,3]=>[7,1,5,2,6,8,4,3]=>[5,1,8,3,7,6,2,4]=>{{1,5,7},{2},{3,8},{4},{6}}
[1,6,7,2,5,8,3,4]=>[1,7,8,3,2,6,5,4]=>[1,7,6,2,4,8,3,5]=>{{1},{2,7},{3,6,8},{4},{5}}
[4,2,8,5,7,1,6,3]=>[7,4,6,2,8,1,5,3]=>[4,8,7,2,6,5,1,3]=>{{1,4},{2,8},{3,7},{5,6}}
[8,4,7,3,1,5,2,6]=>[3,7,5,8,2,1,4,6]=>[8,3,7,5,2,4,6,1]=>{{1,8},{2,3,7},{4,5},{6}}
[5,8,1,3,4,7,2,6]=>[8,7,1,2,5,4,3,6]=>[5,7,2,3,8,1,6,4]=>{{1,5,8},{2,7},{3},{4},{6}}
[6,4,7,2,3,8,5,1]=>[5,8,2,7,6,1,4,3]=>[8,5,1,6,7,4,2,3]=>{{1,8},{2,5,7},{3},{4,6}}
[7,1,5,6,3,4,8,2]=>[7,8,6,3,1,2,5,4]=>[7,6,8,1,4,5,2,3]=>{{1,7},{2,6},{3,8},{4},{5}}
[7,6,1,5,4,2,8,3]=>[6,4,5,7,1,8,2,3]=>[5,8,7,4,3,6,2,1]=>{{1,5},{2,8},{3,7},{4},{6}}
[2,8,5,7,6,1,3,4]=>[6,2,1,3,7,8,4,5]=>[2,8,1,3,7,6,5,4]=>{{1,2,8},{3},{4},{5,7},{6}}
[2,8,6,7,5,3,1,4]=>[3,2,5,1,7,8,6,4]=>[2,8,3,1,5,7,4,6]=>{{1,2,8},{3},{4},{5},{6,7}}
[8,6,3,4,5,1,7,2]=>[5,7,6,3,4,8,1,2]=>[8,5,7,1,2,6,4,3]=>{{1,8},{2,5},{3,7},{4},{6}}
[7,2,4,1,5,3,8,6]=>[4,7,5,2,1,8,3,6]=>[8,4,5,2,3,7,6,1]=>{{1,8},{2,4},{3,5},{6,7}}
[2,7,1,8,6,5,3,4]=>[7,2,5,3,6,8,1,4]=>[2,5,8,1,7,6,4,3]=>{{1,2,5,7},{3,8},{4},{6}}
[7,6,8,2,4,3,5,1]=>[5,8,4,2,3,7,6,1]=>[5,4,7,2,1,8,3,6]=>{{1,5},{2,4},{3,7},{6,8}}
[7,4,5,3,8,1,6,2]=>[8,6,5,7,4,1,3,2]=>[5,7,8,6,1,4,2,3]=>{{1,5},{2,7},{3,8},{4,6}}
[1,4,8,5,7,6,3,2]=>[1,3,6,4,7,8,2,5]=>[1,4,3,8,7,6,5,2]=>{{1},{2,4,8},{3},{5,7},{6}}
[7,3,2,5,1,6,8,4]=>[5,3,7,8,2,1,6,4]=>[7,8,3,5,2,4,1,6]=>{{1,7},{2,8},{3},{4,5},{6}}
[8,6,7,1,4,3,5,2]=>[7,5,4,1,3,8,6,2]=>[4,5,8,3,1,7,2,6]=>{{1,4},{2,5},{3,8},{6,7}}
[8,5,6,1,7,4,2,3]=>[6,4,2,7,8,5,1,3]=>[7,8,1,4,6,2,5,3]=>{{1,7},{2,8},{3},{4},{5,6}}
[3,5,6,8,1,2,7,4]=>[8,1,3,7,5,6,2,4]=>[3,1,5,6,7,8,4,2]=>{{1,3,5,7},{2},{4,6,8}}
[4,5,6,1,3,8,2,7]=>[6,8,1,4,5,3,2,7]=>[5,4,2,6,8,1,3,7]=>{{1,5,8},{2,4,6},{3},{7}}
[1,3,8,6,5,2,7,4]=>[1,5,3,6,8,7,2,4]=>[1,3,8,6,5,7,4,2]=>{{1},{2,3,8},{4,6,7},{5}}
[2,6,1,8,4,7,5,3]=>[6,2,5,7,8,1,3,4]=>[2,7,8,6,5,4,3,1]=>{{1,2,7},{3,8},{4,6},{5}}
[5,4,7,2,1,3,8,6]=>[2,7,1,5,4,8,3,6]=>[5,2,1,8,3,7,6,4]=>{{1,5},{2},{3},{4,8},{6,7}}
[2,6,4,5,7,1,8,3]=>[7,2,8,6,4,5,1,3]=>[2,7,6,8,1,3,5,4]=>{{1,2,7},{3,6},{4,8},{5}}
[4,6,7,5,8,2,1,3]=>[2,8,1,4,7,6,5,3]=>[4,2,1,6,7,8,3,5]=>{{1,4,6,8},{2},{3},{5,7}}
[4,8,3,5,1,2,7,6]=>[5,1,8,4,3,7,2,6]=>[5,1,4,7,2,8,6,3]=>{{1,5},{2},{3,4,7},{6,8}}
[6,8,2,5,4,7,3,1]=>[3,7,8,5,2,6,1,4]=>[6,5,3,7,2,8,4,1]=>{{1,6,8},{2,5},{3},{4,7}}
[5,6,4,2,8,7,1,3]=>[7,4,1,6,5,2,8,3]=>[4,6,2,5,8,3,7,1]=>{{1,4,5,8},{2,6},{3},{7}}
[5,4,7,1,6,2,8,3]=>[7,6,8,5,4,1,2,3]=>[6,7,5,8,1,4,3,2]=>{{1,6},{2,7},{3,5},{4,8}}
[6,5,1,2,7,4,8,3]=>[5,1,6,8,7,3,2,4]=>[8,1,7,5,6,3,4,2]=>{{1,8},{2},{3,7},{4,5,6}}
[3,6,5,7,8,2,4,1]=>[4,8,3,2,6,5,7,1]=>[4,3,6,1,7,2,8,5]=>{{1,4},{2,3,6},{5,7,8}}
[4,1,7,6,8,2,5,3]=>[4,8,5,1,2,7,6,3]=>[7,4,5,3,2,8,1,6]=>{{1,7},{2,4},{3,5},{6,8}}
[7,2,6,4,1,5,3,8]=>[4,6,7,5,2,3,1,8]=>[7,5,4,6,2,1,3,8]=>{{1,7},{2,5},{3,4,6},{8}}
[8,3,2,6,5,1,7,4]=>[5,3,6,8,7,1,4,2]=>[7,8,3,5,6,4,1,2]=>{{1,7},{2,8},{3},{4,5,6}}
[5,2,8,6,3,1,4,7]=>[3,6,5,1,4,8,2,7]=>[8,3,5,2,1,6,4,7]=>{{1,8},{2,3,5},{4},{6},{7}}
[6,3,7,8,1,2,5,4]=>[8,1,6,5,2,3,7,4]=>[5,1,6,7,4,3,8,2]=>{{1,5},{2},{3,6},{4,7,8}}
[7,4,1,6,5,2,3,8]=>[4,7,2,5,6,3,1,8]=>[7,4,1,5,6,2,3,8]=>{{1,7},{2,4,5,6},{3},{8}}
[5,8,6,2,4,7,3,1]=>[3,7,6,2,5,8,1,4]=>[7,3,5,1,8,6,4,2]=>{{1,7},{2,3,5,8},{4},{6}}
[8,5,6,2,4,7,3,1]=>[3,7,6,2,8,5,1,4]=>[8,3,7,1,6,2,5,4]=>{{1,8},{2,3,7},{4},{5,6}}
[4,3,1,6,2,5,8,7]=>[3,4,6,2,1,5,8,7]=>[6,4,3,1,2,5,8,7]=>{{1,6},{2,4},{3},{5},{7,8}}
[1,2,3,4,5,8,9,7,6]=>[1,2,3,4,5,7,9,8,6]=>[1,2,3,4,5,8,7,9,6]=>{{1},{2},{3},{4},{5},{6,8,9},{7}}
[2,1,6,5,8,7,3,4]=>[2,1,7,3,6,5,8,4]=>[2,1,6,3,8,4,7,5]=>{{1,2},{3,6},{4},{5,8},{7}}
[4,1,3,6,5,2,8,7]=>[4,5,1,3,6,2,8,7]=>[6,4,2,1,5,3,8,7]=>{{1,6},{2,4},{3},{5},{7,8}}
[8,5,6,1,3,2,7,4]=>[6,3,1,7,8,5,2,4]=>[3,8,2,7,6,1,5,4]=>{{1,3},{2,8},{4,7},{5,6}}
[8,6,3,2,7,4,5,1]=>[5,3,6,8,4,7,1,2]=>[6,8,3,5,1,7,4,2]=>{{1,6,7},{2,8},{3},{4,5}}
[3,8,2,6,4,7,1,5]=>[7,8,3,6,1,5,2,4]=>[6,3,7,8,4,1,5,2]=>{{1,6},{2,3,7},{4,8},{5}}
[2,7,1,5,3,6,8,4]=>[7,2,5,8,1,3,6,4]=>[2,7,8,5,4,3,1,6]=>{{1,2,7},{3,8},{4,5},{6}}
[1,7,2,4,8,5,6,3]=>[1,7,6,2,8,5,4,3]=>[1,7,8,3,6,2,4,5]=>{{1},{2,7},{3,8},{4},{5,6}}
[2,8,6,1,5,7,4,3]=>[6,2,4,8,1,7,3,5]=>[2,6,8,4,3,7,5,1]=>{{1,2,6,7},{3,8},{4},{5}}
[8,6,2,4,3,5,1,7]=>[5,6,4,2,3,8,1,7]=>[5,4,8,2,1,6,3,7]=>{{1,5},{2,4},{3,8},{6},{7}}
[6,8,1,5,7,3,2,4]=>[8,3,7,2,1,6,5,4]=>[3,7,6,1,4,8,2,5]=>{{1,3,6,8},{2,7},{4},{5}}
[3,7,6,2,1,4,5,8]=>[2,6,3,1,4,7,5,8]=>[3,2,7,1,4,6,5,8]=>{{1,3,7},{2},{4},{5},{6},{8}}
[6,7,2,4,5,3,1,8]=>[3,5,7,2,1,6,4,8]=>[6,5,3,1,4,7,2,8]=>{{1,6,7},{2,5},{3},{4},{8}}
[4,8,6,2,5,7,1,3]=>[7,6,1,4,3,8,2,5]=>[4,7,2,8,1,6,5,3]=>{{1,4,8},{2,7},{3},{5},{6}}
[6,2,8,5,1,4,7,3]=>[5,8,6,1,7,3,2,4]=>[8,5,7,3,6,2,4,1]=>{{1,8},{2,5,6},{3,7},{4}}
[7,4,2,8,5,6,3,1]=>[3,6,4,7,8,5,1,2]=>[8,3,7,4,6,1,5,2]=>{{1,8},{2,3,7},{4},{5,6}}
[4,1,3,8,6,2,5,7]=>[4,6,1,3,2,8,5,7]=>[8,4,2,1,3,6,5,7]=>{{1,8},{2,4},{3},{5},{6},{7}}
[7,1,5,4,6,3,8,2]=>[7,8,6,5,1,2,4,3]=>[6,5,7,8,4,3,1,2]=>{{1,6},{2,5},{3,7},{4,8}}
[6,2,5,4,1,8,3,7]=>[4,5,6,8,1,3,2,7]=>[8,6,5,4,3,1,2,7]=>{{1,8},{2,6},{3,5},{4},{7}}
[4,2,6,3,5,8,1,7]=>[8,4,6,2,3,5,1,7]=>[4,8,6,2,1,3,5,7]=>{{1,4},{2,8},{3,6},{5},{7}}
[7,3,4,1,6,8,5,2]=>[4,5,8,3,7,2,6,1]=>[8,5,4,1,7,2,3,6]=>{{1,8},{2,5,7},{3,4},{6}}
[8,6,2,3,5,7,4,1]=>[4,7,2,6,3,8,1,5]=>[8,4,1,7,2,6,5,3]=>{{1,8},{2,4,7},{3},{5},{6}}
[1,4,5,7,6,8,2,3]=>[1,8,2,4,5,7,6,3]=>[1,4,2,5,7,8,3,6]=>{{1},{2,4,5,7},{3},{6,8}}
[6,8,2,1,5,4,3,7]=>[2,8,4,5,1,6,3,7]=>[4,2,6,5,3,8,1,7]=>{{1,4,5},{2},{3,6,8},{7}}
[4,8,2,6,7,1,5,3]=>[7,8,5,4,1,3,2,6]=>[5,4,7,8,3,1,6,2]=>{{1,5},{2,4,8},{3,7},{6}}
[6,5,8,3,7,1,4,2]=>[7,4,8,1,6,5,3,2]=>[6,7,4,3,8,1,2,5]=>{{1,6},{2,7},{3,4},{5,8}}
[8,1,2,4,6,3,5,7]=>[8,1,6,2,4,5,3,7]=>[6,1,8,3,2,4,5,7]=>{{1,6},{2},{3,8},{4},{5},{7}}
[6,4,8,7,3,2,5,1]=>[5,3,7,6,2,4,8,1]=>[5,8,3,6,2,1,7,4]=>{{1,5},{2,8},{3},{4,6},{7}}
[5,6,2,8,7,4,3,1]=>[3,4,7,6,5,2,8,1]=>[6,4,3,5,8,1,7,2]=>{{1,6},{2,4,5,8},{3},{7}}
[3,7,5,6,4,2,8,1]=>[8,4,3,6,7,5,2,1]=>[3,4,8,6,7,1,2,5]=>{{1,3,8},{2,4,6},{5,7}}
[5,1,3,6,4,2,7,8]=>[5,4,1,6,3,2,7,8]=>[5,6,2,4,1,3,7,8]=>{{1,5},{2,6},{3},{4},{7},{8}}
[7,8,5,1,2,6,3,4]=>[5,1,8,3,6,4,7,2]=>[7,1,5,2,6,3,8,4]=>{{1,7,8},{2},{3,5,6},{4}}
[6,4,5,1,8,7,3,2]=>[5,3,7,6,4,1,8,2]=>[5,8,3,6,1,4,7,2]=>{{1,5},{2,8},{3},{4,6},{7}}
[1,7,6,8,2,5,4,3]=>[1,8,4,5,2,7,6,3]=>[1,4,7,5,3,8,2,6]=>{{1},{2,4,5},{3,7},{6,8}}
[4,6,5,7,1,8,2,3]=>[7,8,2,4,6,5,1,3]=>[6,4,1,7,8,2,5,3]=>{{1,6},{2,4,7},{3},{5,8}}
[7,5,3,6,8,4,2,1]=>[2,4,8,5,7,3,1,6]=>[8,2,4,5,7,1,6,3]=>{{1,8},{2},{3,4,5,7},{6}}
[2,6,7,5,3,4,1,8]=>[4,2,5,3,7,6,1,8]=>[2,6,4,1,5,7,3,8]=>{{1,2,6,7},{3,4},{5},{8}}
[5,6,1,4,3,8,7,2]=>[6,7,4,1,5,3,8,2]=>[5,4,6,3,8,1,7,2]=>{{1,5,8},{2,4},{3,6},{7}}
[5,8,6,4,3,1,7,2]=>[3,4,6,8,5,7,2,1]=>[6,5,3,4,8,7,1,2]=>{{1,6,7},{2,5,8},{3},{4}}
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
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
Corteel
Description
Corteel's map interchanging the number of crossings and the number of nestings of a permutation.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
This involution creates a labelled bicoloured Motzkin path, using the Foata-Zeilberger map. In the corresponding bump diagram, each label records the number of arcs nesting the given arc. Then each label is replaced by its complement, and the inverse of the Foata-Zeilberger map is applied.
Map
weak exceedance partition
Description
The set partition induced by the weak exceedances of a permutation.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
This is the coarsest set partition that contains all arcs $(i, \pi(i))$ with $i\leq\pi(i)$.
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