Identifier
Mp00326:
Permutations
—weak order rowmotion⟶
Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00069: Permutations —complement⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0009;cc-rep-3
[1]=>[1]=>[1]=>{{1}}
[1,2]=>[2,1]=>[1,2]=>{{1},{2}}
[2,1]=>[1,2]=>[2,1]=>{{1,2}}
[1,2,3]=>[3,2,1]=>[1,2,3]=>{{1},{2},{3}}
[1,3,2]=>[2,3,1]=>[2,1,3]=>{{1,2},{3}}
[2,1,3]=>[3,1,2]=>[1,3,2]=>{{1},{2,3}}
[2,3,1]=>[2,1,3]=>[2,3,1]=>{{1,2,3}}
[3,1,2]=>[1,3,2]=>[3,1,2]=>{{1,2,3}}
[3,2,1]=>[1,2,3]=>[3,2,1]=>{{1,3},{2}}
[1,2,3,4]=>[4,3,2,1]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[1,2,4,3]=>[3,4,2,1]=>[2,1,3,4]=>{{1,2},{3},{4}}
[1,3,2,4]=>[4,2,3,1]=>[1,3,2,4]=>{{1},{2,3},{4}}
[1,3,4,2]=>[3,2,4,1]=>[2,3,1,4]=>{{1,2,3},{4}}
[1,4,2,3]=>[2,4,3,1]=>[3,1,2,4]=>{{1,2,3},{4}}
[1,4,3,2]=>[2,3,4,1]=>[3,2,1,4]=>{{1,3},{2},{4}}
[2,1,3,4]=>[4,3,1,2]=>[1,2,4,3]=>{{1},{2},{3,4}}
[2,1,4,3]=>[3,4,1,2]=>[2,1,4,3]=>{{1,2},{3,4}}
[2,3,1,4]=>[4,2,1,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[2,3,4,1]=>[3,2,1,4]=>[2,3,4,1]=>{{1,2,3,4}}
[2,4,1,3]=>[2,1,4,3]=>[3,4,1,2]=>{{1,3},{2,4}}
[2,4,3,1]=>[2,1,3,4]=>[3,4,2,1]=>{{1,2,3,4}}
[3,1,2,4]=>[4,1,3,2]=>[1,4,2,3]=>{{1},{2,3,4}}
[3,1,4,2]=>[1,3,2,4]=>[4,2,3,1]=>{{1,4},{2},{3}}
[3,2,1,4]=>[4,1,2,3]=>[1,4,3,2]=>{{1},{2,4},{3}}
[3,2,4,1]=>[2,3,1,4]=>[3,2,4,1]=>{{1,3,4},{2}}
[3,4,1,2]=>[3,1,4,2]=>[2,4,1,3]=>{{1,2,3,4}}
[3,4,2,1]=>[3,1,2,4]=>[2,4,3,1]=>{{1,2,4},{3}}
[4,1,2,3]=>[1,4,3,2]=>[4,1,2,3]=>{{1,2,3,4}}
[4,1,3,2]=>[1,4,2,3]=>[4,1,3,2]=>{{1,2,4},{3}}
[4,2,1,3]=>[1,2,4,3]=>[4,3,1,2]=>{{1,2,3,4}}
[4,2,3,1]=>[2,4,1,3]=>[3,1,4,2]=>{{1,2,3,4}}
[4,3,1,2]=>[1,3,4,2]=>[4,2,1,3]=>{{1,3,4},{2}}
[4,3,2,1]=>[1,2,3,4]=>[4,3,2,1]=>{{1,4},{2,3}}
[1,2,3,4,5]=>[5,4,3,2,1]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[1,2,3,5,4]=>[4,5,3,2,1]=>[2,1,3,4,5]=>{{1,2},{3},{4},{5}}
[1,2,4,3,5]=>[5,3,4,2,1]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[1,2,4,5,3]=>[4,3,5,2,1]=>[2,3,1,4,5]=>{{1,2,3},{4},{5}}
[1,2,5,3,4]=>[3,5,4,2,1]=>[3,1,2,4,5]=>{{1,2,3},{4},{5}}
[1,2,5,4,3]=>[3,4,5,2,1]=>[3,2,1,4,5]=>{{1,3},{2},{4},{5}}
[1,3,2,4,5]=>[5,4,2,3,1]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[1,3,2,5,4]=>[4,5,2,3,1]=>[2,1,4,3,5]=>{{1,2},{3,4},{5}}
[1,3,4,2,5]=>[5,3,2,4,1]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[1,3,4,5,2]=>[4,3,2,5,1]=>[2,3,4,1,5]=>{{1,2,3,4},{5}}
[1,3,5,2,4]=>[3,2,5,4,1]=>[3,4,1,2,5]=>{{1,3},{2,4},{5}}
[1,3,5,4,2]=>[3,2,4,5,1]=>[3,4,2,1,5]=>{{1,2,3,4},{5}}
[1,4,2,3,5]=>[5,2,4,3,1]=>[1,4,2,3,5]=>{{1},{2,3,4},{5}}
[1,4,2,5,3]=>[2,4,3,5,1]=>[4,2,3,1,5]=>{{1,4},{2},{3},{5}}
[1,4,3,2,5]=>[5,2,3,4,1]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[1,4,3,5,2]=>[3,4,2,5,1]=>[3,2,4,1,5]=>{{1,3,4},{2},{5}}
[1,4,5,2,3]=>[4,2,5,3,1]=>[2,4,1,3,5]=>{{1,2,3,4},{5}}
[1,4,5,3,2]=>[4,2,3,5,1]=>[2,4,3,1,5]=>{{1,2,4},{3},{5}}
[1,5,2,3,4]=>[2,5,4,3,1]=>[4,1,2,3,5]=>{{1,2,3,4},{5}}
[1,5,2,4,3]=>[2,5,3,4,1]=>[4,1,3,2,5]=>{{1,2,4},{3},{5}}
[1,5,3,2,4]=>[2,3,5,4,1]=>[4,3,1,2,5]=>{{1,2,3,4},{5}}
[1,5,3,4,2]=>[3,5,2,4,1]=>[3,1,4,2,5]=>{{1,2,3,4},{5}}
[1,5,4,2,3]=>[2,4,5,3,1]=>[4,2,1,3,5]=>{{1,3,4},{2},{5}}
[1,5,4,3,2]=>[2,3,4,5,1]=>[4,3,2,1,5]=>{{1,4},{2,3},{5}}
[2,1,3,4,5]=>[5,4,3,1,2]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[2,1,3,5,4]=>[4,5,3,1,2]=>[2,1,3,5,4]=>{{1,2},{3},{4,5}}
[2,1,4,3,5]=>[5,3,4,1,2]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[2,1,4,5,3]=>[4,3,5,1,2]=>[2,3,1,5,4]=>{{1,2,3},{4,5}}
[2,1,5,3,4]=>[3,5,4,1,2]=>[3,1,2,5,4]=>{{1,2,3},{4,5}}
[2,1,5,4,3]=>[3,4,5,1,2]=>[3,2,1,5,4]=>{{1,3},{2},{4,5}}
[2,3,1,4,5]=>[5,4,2,1,3]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[2,3,1,5,4]=>[4,5,2,1,3]=>[2,1,4,5,3]=>{{1,2},{3,4,5}}
[2,3,4,1,5]=>[5,3,2,1,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[2,3,4,5,1]=>[4,3,2,1,5]=>[2,3,4,5,1]=>{{1,2,3,4,5}}
[2,3,5,1,4]=>[3,2,1,5,4]=>[3,4,5,1,2]=>{{1,2,3,4,5}}
[2,3,5,4,1]=>[3,2,1,4,5]=>[3,4,5,2,1]=>{{1,3,5},{2,4}}
[2,4,1,3,5]=>[5,2,1,4,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[2,4,1,5,3]=>[2,1,4,3,5]=>[4,5,2,3,1]=>{{1,2,3,4,5}}
[2,4,3,1,5]=>[5,2,1,3,4]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[2,4,3,5,1]=>[3,4,2,1,5]=>[3,2,4,5,1]=>{{1,3,4,5},{2}}
[2,4,5,1,3]=>[4,2,1,5,3]=>[2,4,5,1,3]=>{{1,2,4},{3,5}}
[2,4,5,3,1]=>[4,2,1,3,5]=>[2,4,5,3,1]=>{{1,2,3,4,5}}
[2,5,1,3,4]=>[2,1,5,4,3]=>[4,5,1,2,3]=>{{1,2,3,4,5}}
[2,5,1,4,3]=>[2,1,5,3,4]=>[4,5,1,3,2]=>{{1,3,4},{2,5}}
[2,5,3,1,4]=>[2,1,3,5,4]=>[4,5,3,1,2]=>{{1,4},{2,5},{3}}
[2,5,3,4,1]=>[3,5,2,1,4]=>[3,1,4,5,2]=>{{1,2,3,4,5}}
[2,5,4,1,3]=>[2,1,4,5,3]=>[4,5,2,1,3]=>{{1,4},{2,3,5}}
[2,5,4,3,1]=>[2,1,3,4,5]=>[4,5,3,2,1]=>{{1,2,4,5},{3}}
[3,1,2,4,5]=>[5,4,1,3,2]=>[1,2,5,3,4]=>{{1},{2},{3,4,5}}
[3,1,2,5,4]=>[4,5,1,3,2]=>[2,1,5,3,4]=>{{1,2},{3,4,5}}
[3,1,4,2,5]=>[5,1,3,2,4]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}
[3,1,4,5,2]=>[4,1,3,2,5]=>[2,5,3,4,1]=>{{1,2,5},{3},{4}}
[3,1,5,2,4]=>[1,3,2,5,4]=>[5,3,4,1,2]=>{{1,2,3,4,5}}
[3,1,5,4,2]=>[1,3,2,4,5]=>[5,3,4,2,1]=>{{1,5},{2,3,4}}
[3,2,1,4,5]=>[5,4,1,2,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[3,2,1,5,4]=>[4,5,1,2,3]=>[2,1,5,4,3]=>{{1,2},{3,5},{4}}
[3,2,4,1,5]=>[5,2,3,1,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[3,2,4,5,1]=>[4,2,3,1,5]=>[2,4,3,5,1]=>{{1,2,4,5},{3}}
[3,2,5,1,4]=>[2,3,1,5,4]=>[4,3,5,1,2]=>{{1,4},{2,3,5}}
[3,2,5,4,1]=>[2,3,1,4,5]=>[4,3,5,2,1]=>{{1,2,3,4,5}}
[3,4,1,2,5]=>[5,3,1,4,2]=>[1,3,5,2,4]=>{{1},{2,3,4,5}}
[3,4,1,5,2]=>[3,1,4,2,5]=>[3,5,2,4,1]=>{{1,2,3,5},{4}}
[3,4,2,1,5]=>[5,3,1,2,4]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[3,4,2,5,1]=>[3,2,4,1,5]=>[3,4,2,5,1]=>{{1,2,3,4,5}}
[3,4,5,1,2]=>[4,3,1,5,2]=>[2,3,5,1,4]=>{{1,2,3,4,5}}
[3,4,5,2,1]=>[4,3,1,2,5]=>[2,3,5,4,1]=>{{1,2,3,5},{4}}
[3,5,1,2,4]=>[3,1,5,4,2]=>[3,5,1,2,4]=>{{1,3},{2,4,5}}
[3,5,1,4,2]=>[3,1,5,2,4]=>[3,5,1,4,2]=>{{1,3},{2,5},{4}}
[3,5,2,1,4]=>[3,1,2,5,4]=>[3,5,4,1,2]=>{{1,3,4},{2,5}}
[3,5,2,4,1]=>[3,2,5,1,4]=>[3,4,1,5,2]=>{{1,3},{2,4,5}}
[3,5,4,1,2]=>[3,1,4,5,2]=>[3,5,2,1,4]=>{{1,2,3,4,5}}
[3,5,4,2,1]=>[3,1,2,4,5]=>[3,5,4,2,1]=>{{1,2,3,4,5}}
[4,1,2,3,5]=>[5,1,4,3,2]=>[1,5,2,3,4]=>{{1},{2,3,4,5}}
[4,1,2,5,3]=>[1,4,3,5,2]=>[5,2,3,1,4]=>{{1,4,5},{2},{3}}
[4,1,3,2,5]=>[5,1,4,2,3]=>[1,5,2,4,3]=>{{1},{2,3,5},{4}}
[4,1,3,5,2]=>[1,4,3,2,5]=>[5,2,3,4,1]=>{{1,5},{2},{3},{4}}
[4,1,5,2,3]=>[1,4,2,5,3]=>[5,2,4,1,3]=>{{1,3,4,5},{2}}
[4,1,5,3,2]=>[1,4,2,3,5]=>[5,2,4,3,1]=>{{1,5},{2},{3,4}}
[4,2,1,3,5]=>[5,1,2,4,3]=>[1,5,4,2,3]=>{{1},{2,3,4,5}}
[4,2,1,5,3]=>[1,2,4,3,5]=>[5,4,2,3,1]=>{{1,5},{2,3,4}}
[4,2,3,1,5]=>[5,2,4,1,3]=>[1,4,2,5,3]=>{{1},{2,3,4,5}}
[4,2,3,5,1]=>[2,4,3,1,5]=>[4,2,3,5,1]=>{{1,4,5},{2},{3}}
[4,2,5,1,3]=>[2,4,1,5,3]=>[4,2,5,1,3]=>{{1,4},{2},{3,5}}
[4,2,5,3,1]=>[2,4,1,3,5]=>[4,2,5,3,1]=>{{1,3,4,5},{2}}
[4,3,1,2,5]=>[5,1,3,4,2]=>[1,5,3,2,4]=>{{1},{2,4,5},{3}}
[4,3,1,5,2]=>[1,3,4,2,5]=>[5,3,2,4,1]=>{{1,5},{2,3},{4}}
[4,3,2,1,5]=>[5,1,2,3,4]=>[1,5,4,3,2]=>{{1},{2,5},{3,4}}
[4,3,2,5,1]=>[2,3,4,1,5]=>[4,3,2,5,1]=>{{1,4,5},{2,3}}
[4,3,5,1,2]=>[3,4,1,5,2]=>[3,2,5,1,4]=>{{1,3,4,5},{2}}
[4,3,5,2,1]=>[3,4,1,2,5]=>[3,2,5,4,1]=>{{1,3,5},{2},{4}}
[4,5,1,2,3]=>[4,1,5,3,2]=>[2,5,1,3,4]=>{{1,2,3,4,5}}
[4,5,1,3,2]=>[4,1,5,2,3]=>[2,5,1,4,3]=>{{1,2,3,5},{4}}
[4,5,2,1,3]=>[4,1,2,5,3]=>[2,5,4,1,3]=>{{1,2,3,4,5}}
[4,5,2,3,1]=>[4,2,5,1,3]=>[2,4,1,5,3]=>{{1,2,3,4,5}}
[4,5,3,1,2]=>[4,1,3,5,2]=>[2,5,3,1,4]=>{{1,2,4,5},{3}}
[4,5,3,2,1]=>[4,1,2,3,5]=>[2,5,4,3,1]=>{{1,2,5},{3,4}}
[5,1,2,3,4]=>[1,5,4,3,2]=>[5,1,2,3,4]=>{{1,2,3,4,5}}
[5,1,2,4,3]=>[1,5,3,4,2]=>[5,1,3,2,4]=>{{1,2,4,5},{3}}
[5,1,3,2,4]=>[1,5,4,2,3]=>[5,1,2,4,3]=>{{1,2,3,5},{4}}
[5,1,3,4,2]=>[1,5,3,2,4]=>[5,1,3,4,2]=>{{1,2,5},{3},{4}}
[5,1,4,2,3]=>[1,5,2,4,3]=>[5,1,4,2,3]=>{{1,2,3,4,5}}
[5,1,4,3,2]=>[1,5,2,3,4]=>[5,1,4,3,2]=>{{1,2,5},{3,4}}
[5,2,1,3,4]=>[1,2,5,4,3]=>[5,4,1,2,3]=>{{1,3,5},{2,4}}
[5,2,1,4,3]=>[1,2,5,3,4]=>[5,4,1,3,2]=>{{1,2,3,4,5}}
[5,2,3,1,4]=>[2,5,4,1,3]=>[4,1,2,5,3]=>{{1,2,3,4,5}}
[5,2,3,4,1]=>[2,5,3,1,4]=>[4,1,3,5,2]=>{{1,2,4,5},{3}}
[5,2,4,1,3]=>[2,5,1,4,3]=>[4,1,5,2,3]=>{{1,2,4},{3,5}}
[5,2,4,3,1]=>[2,5,1,3,4]=>[4,1,5,3,2]=>{{1,2,3,4,5}}
[5,3,1,2,4]=>[1,3,5,4,2]=>[5,3,1,2,4]=>{{1,2,3,4,5}}
[5,3,1,4,2]=>[1,3,5,2,4]=>[5,3,1,4,2]=>{{1,2,3,5},{4}}
[5,3,2,1,4]=>[1,2,3,5,4]=>[5,4,3,1,2]=>{{1,2,4,5},{3}}
[5,3,2,4,1]=>[2,3,5,1,4]=>[4,3,1,5,2]=>{{1,2,3,4,5}}
[5,3,4,1,2]=>[3,5,1,4,2]=>[3,1,5,2,4]=>{{1,2,3,4,5}}
[5,3,4,2,1]=>[3,5,1,2,4]=>[3,1,5,4,2]=>{{1,2,3,5},{4}}
[5,4,1,2,3]=>[1,4,5,3,2]=>[5,2,1,3,4]=>{{1,3,4,5},{2}}
[5,4,1,3,2]=>[1,4,5,2,3]=>[5,2,1,4,3]=>{{1,3,5},{2},{4}}
[5,4,2,1,3]=>[1,2,4,5,3]=>[5,4,2,1,3]=>{{1,2,3,4,5}}
[5,4,2,3,1]=>[2,4,5,1,3]=>[4,2,1,5,3]=>{{1,3,4,5},{2}}
[5,4,3,1,2]=>[1,3,4,5,2]=>[5,3,2,1,4]=>{{1,4,5},{2,3}}
[5,4,3,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>{{1,5},{2,4},{3}}
[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>{{1,2},{3},{4},{5},{6}}
[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[1,2,3,5,6,4]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>{{1,2,3},{4},{5},{6}}
[1,2,3,6,4,5]=>[4,6,5,3,2,1]=>[3,1,2,4,5,6]=>{{1,2,3},{4},{5},{6}}
[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>{{1,3},{2},{4},{5},{6}}
[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>{{1,2},{3,4},{5},{6}}
[1,2,4,5,3,6]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[1,2,4,5,6,3]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>{{1,2,3,4},{5},{6}}
[1,2,4,6,3,5]=>[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>{{1,3},{2,4},{5},{6}}
[1,2,4,6,5,3]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>{{1,2,3,4},{5},{6}}
[1,2,5,3,4,6]=>[6,3,5,4,2,1]=>[1,4,2,3,5,6]=>{{1},{2,3,4},{5},{6}}
[1,2,5,3,6,4]=>[3,5,4,6,2,1]=>[4,2,3,1,5,6]=>{{1,4},{2},{3},{5},{6}}
[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[1,2,5,4,6,3]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>{{1,3,4},{2},{5},{6}}
[1,2,5,6,3,4]=>[5,3,6,4,2,1]=>[2,4,1,3,5,6]=>{{1,2,3,4},{5},{6}}
[1,2,5,6,4,3]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>{{1,2,4},{3},{5},{6}}
[1,2,6,3,4,5]=>[3,6,5,4,2,1]=>[4,1,2,3,5,6]=>{{1,2,3,4},{5},{6}}
[1,2,6,3,5,4]=>[3,6,4,5,2,1]=>[4,1,3,2,5,6]=>{{1,2,4},{3},{5},{6}}
[1,2,6,4,3,5]=>[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>{{1,2,3,4},{5},{6}}
[1,2,6,4,5,3]=>[4,6,3,5,2,1]=>[3,1,4,2,5,6]=>{{1,2,3,4},{5},{6}}
[1,2,6,5,3,4]=>[3,5,6,4,2,1]=>[4,2,1,3,5,6]=>{{1,3,4},{2},{5},{6}}
[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>{{1,4},{2,3},{5},{6}}
[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>{{1,2},{3},{4,5},{6}}
[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[1,3,2,5,6,4]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>{{1,2,3},{4,5},{6}}
[1,3,2,6,4,5]=>[4,6,5,2,3,1]=>[3,1,2,5,4,6]=>{{1,2,3},{4,5},{6}}
[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>{{1,3},{2},{4,5},{6}}
[1,3,4,2,5,6]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[1,3,4,2,6,5]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>{{1,2},{3,4,5},{6}}
[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,3,4,5,6,2]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>{{1,2,3,4,5},{6}}
[1,3,4,6,2,5]=>[4,3,2,6,5,1]=>[3,4,5,1,2,6]=>{{1,2,3,4,5},{6}}
[1,3,4,6,5,2]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>{{1,3,5},{2,4},{6}}
[1,3,5,2,4,6]=>[6,3,2,5,4,1]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[1,3,5,2,6,4]=>[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>{{1,2,3,4,5},{6}}
[1,3,5,4,2,6]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[1,3,5,4,6,2]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>{{1,3,4,5},{2},{6}}
[1,3,5,6,2,4]=>[5,3,2,6,4,1]=>[2,4,5,1,3,6]=>{{1,2,4},{3,5},{6}}
[1,3,5,6,4,2]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>{{1,2,3,4,5},{6}}
[1,3,6,2,4,5]=>[3,2,6,5,4,1]=>[4,5,1,2,3,6]=>{{1,2,3,4,5},{6}}
[1,3,6,2,5,4]=>[3,2,6,4,5,1]=>[4,5,1,3,2,6]=>{{1,3,4},{2,5},{6}}
[1,3,6,4,2,5]=>[3,2,4,6,5,1]=>[4,5,3,1,2,6]=>{{1,4},{2,5},{3},{6}}
[1,3,6,4,5,2]=>[4,6,3,2,5,1]=>[3,1,4,5,2,6]=>{{1,2,3,4,5},{6}}
[1,3,6,5,2,4]=>[3,2,5,6,4,1]=>[4,5,2,1,3,6]=>{{1,4},{2,3,5},{6}}
[1,3,6,5,4,2]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>{{1,2,4,5},{3},{6}}
[1,4,2,3,5,6]=>[6,5,2,4,3,1]=>[1,2,5,3,4,6]=>{{1},{2},{3,4,5},{6}}
[1,4,2,3,6,5]=>[5,6,2,4,3,1]=>[2,1,5,3,4,6]=>{{1,2},{3,4,5},{6}}
[1,4,2,5,3,6]=>[6,2,4,3,5,1]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[1,4,2,5,6,3]=>[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>{{1,2,5},{3},{4},{6}}
[1,4,2,6,3,5]=>[2,4,3,6,5,1]=>[5,3,4,1,2,6]=>{{1,2,3,4,5},{6}}
[1,4,2,6,5,3]=>[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>{{1,5},{2,3,4},{6}}
[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>{{1,2},{3,5},{4},{6}}
[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[1,4,3,5,6,2]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>{{1,2,4,5},{3},{6}}
[1,4,3,6,2,5]=>[3,4,2,6,5,1]=>[4,3,5,1,2,6]=>{{1,4},{2,3,5},{6}}
[1,4,3,6,5,2]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>{{1,2,3,4,5},{6}}
[1,4,5,2,3,6]=>[6,4,2,5,3,1]=>[1,3,5,2,4,6]=>{{1},{2,3,4,5},{6}}
[1,4,5,2,6,3]=>[4,2,5,3,6,1]=>[3,5,2,4,1,6]=>{{1,2,3,5},{4},{6}}
[1,4,5,3,2,6]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[1,4,5,3,6,2]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>{{1,2,3,4,5},{6}}
[1,4,5,6,2,3]=>[5,4,2,6,3,1]=>[2,3,5,1,4,6]=>{{1,2,3,4,5},{6}}
[1,4,5,6,3,2]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>{{1,2,3,5},{4},{6}}
[1,4,6,2,3,5]=>[4,2,6,5,3,1]=>[3,5,1,2,4,6]=>{{1,3},{2,4,5},{6}}
[1,4,6,2,5,3]=>[4,2,6,3,5,1]=>[3,5,1,4,2,6]=>{{1,3},{2,5},{4},{6}}
[1,4,6,3,2,5]=>[4,2,3,6,5,1]=>[3,5,4,1,2,6]=>{{1,3,4},{2,5},{6}}
[1,4,6,3,5,2]=>[4,3,6,2,5,1]=>[3,4,1,5,2,6]=>{{1,3},{2,4,5},{6}}
[1,4,6,5,2,3]=>[4,2,5,6,3,1]=>[3,5,2,1,4,6]=>{{1,2,3,4,5},{6}}
[1,4,6,5,3,2]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>{{1,2,3,4,5},{6}}
[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[1,5,2,3,4,6]=>{{1},{2,3,4,5},{6}}
[1,5,2,3,6,4]=>[2,5,4,6,3,1]=>[5,2,3,1,4,6]=>{{1,4,5},{2},{3},{6}}
[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[1,5,2,4,3,6]=>{{1},{2,3,5},{4},{6}}
[1,5,2,4,6,3]=>[2,5,4,3,6,1]=>[5,2,3,4,1,6]=>{{1,5},{2},{3},{4},{6}}
[1,5,2,6,3,4]=>[2,5,3,6,4,1]=>[5,2,4,1,3,6]=>{{1,3,4,5},{2},{6}}
[1,5,2,6,4,3]=>[2,5,3,4,6,1]=>[5,2,4,3,1,6]=>{{1,5},{2},{3,4},{6}}
[1,5,3,2,4,6]=>[6,2,3,5,4,1]=>[1,5,4,2,3,6]=>{{1},{2,3,4,5},{6}}
[1,5,3,2,6,4]=>[2,3,5,4,6,1]=>[5,4,2,3,1,6]=>{{1,5},{2,3,4},{6}}
[1,5,3,4,2,6]=>[6,3,5,2,4,1]=>[1,4,2,5,3,6]=>{{1},{2,3,4,5},{6}}
[1,5,3,4,6,2]=>[3,5,4,2,6,1]=>[4,2,3,5,1,6]=>{{1,4,5},{2},{3},{6}}
[1,5,3,6,2,4]=>[3,5,2,6,4,1]=>[4,2,5,1,3,6]=>{{1,4},{2},{3,5},{6}}
[1,5,3,6,4,2]=>[3,5,2,4,6,1]=>[4,2,5,3,1,6]=>{{1,3,4,5},{2},{6}}
[1,5,4,2,3,6]=>[6,2,4,5,3,1]=>[1,5,3,2,4,6]=>{{1},{2,4,5},{3},{6}}
[1,5,4,2,6,3]=>[2,4,5,3,6,1]=>[5,3,2,4,1,6]=>{{1,5},{2,3},{4},{6}}
[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>{{1},{2,5},{3,4},{6}}
[1,5,4,3,6,2]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>{{1,4,5},{2,3},{6}}
[1,5,4,6,2,3]=>[4,5,2,6,3,1]=>[3,2,5,1,4,6]=>{{1,3,4,5},{2},{6}}
[1,5,4,6,3,2]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>{{1,3,5},{2},{4},{6}}
[1,5,6,2,3,4]=>[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>{{1,2,3,4,5},{6}}
[1,5,6,2,4,3]=>[5,2,6,3,4,1]=>[2,5,1,4,3,6]=>{{1,2,3,5},{4},{6}}
[1,5,6,3,2,4]=>[5,2,3,6,4,1]=>[2,5,4,1,3,6]=>{{1,2,3,4,5},{6}}
[1,5,6,3,4,2]=>[5,3,6,2,4,1]=>[2,4,1,5,3,6]=>{{1,2,3,4,5},{6}}
[1,5,6,4,2,3]=>[5,2,4,6,3,1]=>[2,5,3,1,4,6]=>{{1,2,4,5},{3},{6}}
[1,5,6,4,3,2]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>{{1,2,5},{3,4},{6}}
[1,6,2,3,4,5]=>[2,6,5,4,3,1]=>[5,1,2,3,4,6]=>{{1,2,3,4,5},{6}}
[1,6,2,3,5,4]=>[2,6,4,5,3,1]=>[5,1,3,2,4,6]=>{{1,2,4,5},{3},{6}}
[1,6,2,4,3,5]=>[2,6,5,3,4,1]=>[5,1,2,4,3,6]=>{{1,2,3,5},{4},{6}}
[1,6,2,4,5,3]=>[2,6,4,3,5,1]=>[5,1,3,4,2,6]=>{{1,2,5},{3},{4},{6}}
[1,6,2,5,3,4]=>[2,6,3,5,4,1]=>[5,1,4,2,3,6]=>{{1,2,3,4,5},{6}}
[1,6,2,5,4,3]=>[2,6,3,4,5,1]=>[5,1,4,3,2,6]=>{{1,2,5},{3,4},{6}}
[1,6,3,2,4,5]=>[2,3,6,5,4,1]=>[5,4,1,2,3,6]=>{{1,3,5},{2,4},{6}}
[1,6,3,2,5,4]=>[2,3,6,4,5,1]=>[5,4,1,3,2,6]=>{{1,2,3,4,5},{6}}
[1,6,3,4,2,5]=>[3,6,5,2,4,1]=>[4,1,2,5,3,6]=>{{1,2,3,4,5},{6}}
[1,6,3,4,5,2]=>[3,6,4,2,5,1]=>[4,1,3,5,2,6]=>{{1,2,4,5},{3},{6}}
[1,6,3,5,2,4]=>[3,6,2,5,4,1]=>[4,1,5,2,3,6]=>{{1,2,4},{3,5},{6}}
[1,6,3,5,4,2]=>[3,6,2,4,5,1]=>[4,1,5,3,2,6]=>{{1,2,3,4,5},{6}}
[1,6,4,2,3,5]=>[2,4,6,5,3,1]=>[5,3,1,2,4,6]=>{{1,2,3,4,5},{6}}
[1,6,4,2,5,3]=>[2,4,6,3,5,1]=>[5,3,1,4,2,6]=>{{1,2,3,5},{4},{6}}
[1,6,4,3,2,5]=>[2,3,4,6,5,1]=>[5,4,3,1,2,6]=>{{1,2,4,5},{3},{6}}
[1,6,4,3,5,2]=>[3,4,6,2,5,1]=>[4,3,1,5,2,6]=>{{1,2,3,4,5},{6}}
[1,6,4,5,2,3]=>[4,6,2,5,3,1]=>[3,1,5,2,4,6]=>{{1,2,3,4,5},{6}}
[1,6,4,5,3,2]=>[4,6,2,3,5,1]=>[3,1,5,4,2,6]=>{{1,2,3,5},{4},{6}}
[1,6,5,2,3,4]=>[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>{{1,3,4,5},{2},{6}}
[1,6,5,2,4,3]=>[2,5,6,3,4,1]=>[5,2,1,4,3,6]=>{{1,3,5},{2},{4},{6}}
[1,6,5,3,2,4]=>[2,3,5,6,4,1]=>[5,4,2,1,3,6]=>{{1,2,3,4,5},{6}}
[1,6,5,3,4,2]=>[3,5,6,2,4,1]=>[4,2,1,5,3,6]=>{{1,3,4,5},{2},{6}}
[1,6,5,4,2,3]=>[2,4,5,6,3,1]=>[5,3,2,1,4,6]=>{{1,4,5},{2,3},{6}}
[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>{{1,5},{2,4},{3},{6}}
[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>{{1,2},{3},{4},{5,6}}
[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[2,1,3,5,6,4]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>{{1,2,3},{4},{5,6}}
[2,1,3,6,4,5]=>[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>{{1,2,3},{4},{5,6}}
[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>{{1,3},{2},{4},{5,6}}
[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>{{1,2},{3,4},{5,6}}
[2,1,4,5,3,6]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[2,1,4,5,6,3]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>{{1,2,3,4},{5,6}}
[2,1,4,6,3,5]=>[4,3,6,5,1,2]=>[3,4,1,2,6,5]=>{{1,3},{2,4},{5,6}}
[2,1,4,6,5,3]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>{{1,2,3,4},{5,6}}
[2,1,5,3,4,6]=>[6,3,5,4,1,2]=>[1,4,2,3,6,5]=>{{1},{2,3,4},{5,6}}
[2,1,5,3,6,4]=>[3,5,4,6,1,2]=>[4,2,3,1,6,5]=>{{1,4},{2},{3},{5,6}}
[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[2,1,5,4,6,3]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>{{1,3,4},{2},{5,6}}
[2,1,5,6,3,4]=>[5,3,6,4,1,2]=>[2,4,1,3,6,5]=>{{1,2,3,4},{5,6}}
[2,1,5,6,4,3]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>{{1,2,4},{3},{5,6}}
[2,1,6,3,4,5]=>[3,6,5,4,1,2]=>[4,1,2,3,6,5]=>{{1,2,3,4},{5,6}}
[2,1,6,3,5,4]=>[3,6,4,5,1,2]=>[4,1,3,2,6,5]=>{{1,2,4},{3},{5,6}}
[2,1,6,4,3,5]=>[3,4,6,5,1,2]=>[4,3,1,2,6,5]=>{{1,2,3,4},{5,6}}
[2,1,6,4,5,3]=>[4,6,3,5,1,2]=>[3,1,4,2,6,5]=>{{1,2,3,4},{5,6}}
[2,1,6,5,3,4]=>[3,5,6,4,1,2]=>[4,2,1,3,6,5]=>{{1,3,4},{2},{5,6}}
[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>{{1,4},{2,3},{5,6}}
[2,3,1,4,5,6]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[2,3,1,4,6,5]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>{{1,2},{3},{4,5,6}}
[2,3,1,5,4,6]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>{{1,2,3},{4,5,6}}
[2,3,1,6,4,5]=>[4,6,5,2,1,3]=>[3,1,2,5,6,4]=>{{1,2,3},{4,5,6}}
[2,3,1,6,5,4]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>{{1,3},{2},{4,5,6}}
[2,3,4,1,5,6]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[2,3,4,1,6,5]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>{{1,2},{3,4,5,6}}
[2,3,4,5,1,6]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>{{1,2,3,4,5,6}}
[2,3,4,6,1,5]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>{{1,3,5},{2,4,6}}
[2,3,4,6,5,1]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>{{1,2,3,4,5,6}}
[2,3,5,1,4,6]=>[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>{{1},{2,3,4,5,6}}
[2,3,5,1,6,4]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>{{1,2,3,4,5,6}}
[2,3,5,4,1,6]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>{{1},{2,4,6},{3,5}}
[2,3,5,4,6,1]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>{{1,3,4,5,6},{2}}
[2,3,5,6,1,4]=>[5,3,2,1,6,4]=>[2,4,5,6,1,3]=>{{1,2,3,4,5,6}}
[2,3,5,6,4,1]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>{{1,2,4,6},{3,5}}
[2,3,6,1,4,5]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>{{1,4},{2,5},{3,6}}
[2,3,6,1,5,4]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>{{1,4},{2,3,5,6}}
[2,3,6,4,1,5]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>{{1,2,3,4,5,6}}
[2,3,6,4,5,1]=>[4,6,3,2,1,5]=>[3,1,4,5,6,2]=>{{1,2,3,4,5,6}}
[2,3,6,5,1,4]=>[3,2,1,5,6,4]=>[4,5,6,2,1,3]=>{{1,2,4,5},{3,6}}
[2,3,6,5,4,1]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>{{1,3,4,6},{2,5}}
[2,4,1,3,5,6]=>[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[2,4,1,3,6,5]=>[5,6,2,1,4,3]=>[2,1,5,6,3,4]=>{{1,2},{3,5},{4,6}}
[2,4,1,5,3,6]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>{{1},{2,3,4,5,6}}
[2,4,1,5,6,3]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>{{1,2,3,4,5,6}}
[2,4,1,6,3,5]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>{{1,5},{2,6},{3},{4}}
[2,4,1,6,5,3]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>{{1,2,5,6},{3},{4}}
[2,4,3,1,5,6]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[2,4,3,1,6,5]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>{{1,2},{3,4,5,6}}
[2,4,3,5,1,6]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[2,4,3,5,6,1]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>{{1,2,4,5,6},{3}}
[2,4,3,6,1,5]=>[3,4,2,1,6,5]=>[4,3,5,6,1,2]=>{{1,2,3,4,5,6}}
[2,4,3,6,5,1]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>{{1,4,6},{2,3,5}}
[2,4,5,1,3,6]=>[6,4,2,1,5,3]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[2,4,5,1,6,3]=>[4,2,1,5,3,6]=>[3,5,6,2,4,1]=>{{1,3,6},{2,4,5}}
[2,4,5,3,1,6]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[2,4,5,3,6,1]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>{{1,2,3,4,5,6}}
[2,4,5,6,1,3]=>[5,4,2,1,6,3]=>[2,3,5,6,1,4]=>{{1,2,3,5},{4,6}}
[2,4,5,6,3,1]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>{{1,2,3,4,5,6}}
[2,4,6,1,3,5]=>[4,2,1,6,5,3]=>[3,5,6,1,2,4]=>{{1,3,4,6},{2,5}}
[2,4,6,1,5,3]=>[4,2,1,6,3,5]=>[3,5,6,1,4,2]=>{{1,2,3,4,5,6}}
[2,4,6,3,1,5]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>{{1,2,3,5,6},{4}}
[2,4,6,3,5,1]=>[4,3,6,2,1,5]=>[3,4,1,5,6,2]=>{{1,3},{2,4,5,6}}
[2,4,6,5,1,3]=>[4,2,1,5,6,3]=>[3,5,6,2,1,4]=>{{1,2,3,4,5,6}}
[2,4,6,5,3,1]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>{{1,3,6},{2,5},{4}}
[2,5,1,3,4,6]=>[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>{{1},{2,3,4,5,6}}
[2,5,1,3,6,4]=>[2,1,5,4,6,3]=>[5,6,2,3,1,4]=>{{1,5},{2,3,4,6}}
[2,5,1,4,3,6]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>{{1},{2,4,5},{3,6}}
[2,5,1,4,6,3]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>{{1,2,3,4,5,6}}
[2,5,1,6,3,4]=>[2,1,5,3,6,4]=>[5,6,2,4,1,3]=>{{1,5},{2,3,6},{4}}
[2,5,1,6,4,3]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>{{1,2,3,5,6},{4}}
[2,5,3,1,4,6]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[2,5,3,1,6,4]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>{{1,2,3,4,5,6}}
[2,5,3,4,1,6]=>[6,3,5,2,1,4]=>[1,4,2,5,6,3]=>{{1},{2,3,4,5,6}}
[2,5,3,4,6,1]=>[3,5,4,2,1,6]=>[4,2,3,5,6,1]=>{{1,4,5,6},{2},{3}}
[2,5,3,6,1,4]=>[3,5,2,1,6,4]=>[4,2,5,6,1,3]=>{{1,3,4,5,6},{2}}
[2,5,3,6,4,1]=>[3,5,2,1,4,6]=>[4,2,5,6,3,1]=>{{1,4,6},{2},{3,5}}
[2,5,4,1,3,6]=>[6,2,1,4,5,3]=>[1,5,6,3,2,4]=>{{1},{2,5},{3,4,6}}
[2,5,4,1,6,3]=>[2,1,4,5,3,6]=>[5,6,3,2,4,1]=>{{1,2,4,5,6},{3}}
[2,5,4,3,1,6]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[2,5,4,3,6,1]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>{{1,4,5,6},{2,3}}
[2,5,4,6,1,3]=>[4,5,2,1,6,3]=>[3,2,5,6,1,4]=>{{1,3,5},{2},{4,6}}
[2,5,4,6,3,1]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>{{1,3,4,5,6},{2}}
[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>[2,5,6,1,3,4]=>{{1,2,3,4,5,6}}
[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>[2,5,6,1,4,3]=>{{1,2,4,5},{3,6}}
[2,5,6,3,1,4]=>[5,2,1,3,6,4]=>[2,5,6,4,1,3]=>{{1,2,5},{3,6},{4}}
[2,5,6,3,4,1]=>[5,3,6,2,1,4]=>[2,4,1,5,6,3]=>{{1,2,3,4,5,6}}
[2,5,6,4,1,3]=>[5,2,1,4,6,3]=>[2,5,6,3,1,4]=>{{1,2,5},{3,4,6}}
[2,5,6,4,3,1]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>{{1,2,3,5,6},{4}}
[2,6,1,3,4,5]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>{{1,3,5},{2,4,6}}
[2,6,1,3,5,4]=>[2,1,6,4,5,3]=>[5,6,1,3,2,4]=>{{1,2,3,4,5,6}}
[2,6,1,4,3,5]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>{{1,2,3,4,5,6}}
[2,6,1,4,5,3]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>{{1,3,4,5},{2,6}}
[2,6,1,5,3,4]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>{{1,2,3,5,6},{4}}
[2,6,1,5,4,3]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>{{1,3,5},{2,6},{4}}
[2,6,3,1,4,5]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>{{1,2,3,4,5,6}}
[2,6,3,1,5,4]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>{{1,3,4,5},{2,6}}
[2,6,3,4,1,5]=>[3,6,5,2,1,4]=>[4,1,2,5,6,3]=>{{1,2,3,4,5,6}}
[2,6,3,4,5,1]=>[3,6,4,2,1,5]=>[4,1,3,5,6,2]=>{{1,2,4,5,6},{3}}
[2,6,3,5,1,4]=>[3,6,2,1,5,4]=>[4,1,5,6,2,3]=>{{1,2,3,4,5,6}}
[2,6,3,5,4,1]=>[3,6,2,1,4,5]=>[4,1,5,6,3,2]=>{{1,2,4,6},{3,5}}
[2,6,4,1,3,5]=>[2,1,4,6,5,3]=>[5,6,3,1,2,4]=>{{1,2,4,5,6},{3}}
[2,6,4,1,5,3]=>[2,1,4,6,3,5]=>[5,6,3,1,4,2]=>{{1,4,5},{2,6},{3}}
[2,6,4,3,1,5]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>{{1,5},{2,6},{3,4}}
[2,6,4,3,5,1]=>[3,4,6,2,1,5]=>[4,3,1,5,6,2]=>{{1,2,3,4,5,6}}
[2,6,4,5,1,3]=>[4,6,2,1,5,3]=>[3,1,5,6,2,4]=>{{1,2,3,5},{4,6}}
[2,6,4,5,3,1]=>[4,6,2,1,3,5]=>[3,1,5,6,4,2]=>{{1,2,3,4,5,6}}
[2,6,5,1,3,4]=>[2,1,5,6,4,3]=>[5,6,2,1,3,4]=>{{1,2,3,4,5,6}}
[2,6,5,1,4,3]=>[2,1,5,6,3,4]=>[5,6,2,1,4,3]=>{{1,4,5},{2,3,6}}
[2,6,5,3,1,4]=>[2,1,3,5,6,4]=>[5,6,4,2,1,3]=>{{1,5},{2,3,4,6}}
[2,6,5,3,4,1]=>[3,5,6,2,1,4]=>[4,2,1,5,6,3]=>{{1,3,4,5,6},{2}}
[2,6,5,4,1,3]=>[2,1,4,5,6,3]=>[5,6,3,2,1,4]=>{{1,5},{2,4,6},{3}}
[2,6,5,4,3,1]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>{{1,2,5,6},{3,4}}
[3,1,2,4,5,6]=>[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>{{1},{2},{3},{4,5,6}}
[3,1,2,4,6,5]=>[5,6,4,1,3,2]=>[2,1,3,6,4,5]=>{{1,2},{3},{4,5,6}}
[3,1,2,5,4,6]=>[6,4,5,1,3,2]=>[1,3,2,6,4,5]=>{{1},{2,3},{4,5,6}}
[3,1,2,5,6,4]=>[5,4,6,1,3,2]=>[2,3,1,6,4,5]=>{{1,2,3},{4,5,6}}
[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[3,1,2,6,4,5]=>{{1,2,3},{4,5,6}}
[3,1,2,6,5,4]=>[4,5,6,1,3,2]=>[3,2,1,6,4,5]=>{{1,3},{2},{4,5,6}}
[3,1,4,2,5,6]=>[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[3,1,4,2,6,5]=>[5,6,1,3,2,4]=>[2,1,6,4,5,3]=>{{1,2},{3,6},{4},{5}}
[3,1,4,5,2,6]=>[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[3,1,4,5,6,2]=>[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>{{1,2,3,6},{4},{5}}
[3,1,4,6,2,5]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>{{1,3,4,5},{2,6}}
[3,1,4,6,5,2]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>{{1,2,3,4,5,6}}
[3,1,5,2,4,6]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>{{1},{2,3,4,5,6}}
[3,1,5,2,6,4]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>{{1,6},{2,4},{3,5}}
[3,1,5,4,2,6]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>{{1},{2,6},{3,4,5}}
[3,1,5,4,6,2]=>[4,5,1,3,2,6]=>[3,2,6,4,5,1]=>{{1,3,6},{2},{4},{5}}
[3,1,5,6,2,4]=>[5,1,3,2,6,4]=>[2,6,4,5,1,3]=>{{1,2,3,4,5,6}}
[3,1,5,6,4,2]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>{{1,2,6},{3,4,5}}
[3,1,6,2,4,5]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>{{1,2,3,4,5,6}}
[3,1,6,2,5,4]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>{{1,2,4,6},{3,5}}
[3,1,6,4,2,5]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>{{1,2,3,4,5,6}}
[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>[3,1,6,4,5,2]=>{{1,2,3,6},{4},{5}}
[3,1,6,5,2,4]=>[1,3,2,5,6,4]=>[6,4,5,2,1,3]=>{{1,3,5,6},{2,4}}
[3,1,6,5,4,2]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>{{1,6},{2,3,4,5}}
[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>{{1,2},{3},{4,6},{5}}
[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[3,2,1,5,6,4]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>{{1,2,3},{4,6},{5}}
[3,2,1,6,4,5]=>[4,6,5,1,2,3]=>[3,1,2,6,5,4]=>{{1,2,3},{4,6},{5}}
[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>{{1,3},{2},{4,6},{5}}
[3,2,4,1,5,6]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[3,2,4,1,6,5]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>{{1,2},{3,5,6},{4}}
[3,2,4,5,1,6]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[3,2,4,5,6,1]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>{{1,2,3,5,6},{4}}
[3,2,4,6,1,5]=>[4,2,3,1,6,5]=>[3,5,4,6,1,2]=>{{1,2,3,4,5,6}}
[3,2,4,6,5,1]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>{{1,3,4,6},{2,5}}
[3,2,5,1,4,6]=>[6,2,3,1,5,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,2,5,1,6,4]=>[2,3,1,5,4,6]=>[5,4,6,2,3,1]=>{{1,3,5,6},{2,4}}
[3,2,5,4,1,6]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,2,5,4,6,1]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>{{1,3,5,6},{2},{4}}
[3,2,5,6,1,4]=>[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>{{1,2,5},{3,4,6}}
[3,2,5,6,4,1]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>{{1,2,3,4,5,6}}
[3,2,6,1,4,5]=>[2,3,1,6,5,4]=>[5,4,6,1,2,3]=>{{1,2,4,5},{3,6}}
[3,2,6,1,5,4]=>[2,3,1,6,4,5]=>[5,4,6,1,3,2]=>{{1,2,3,4,5,6}}
[3,2,6,4,1,5]=>[2,3,1,4,6,5]=>[5,4,6,3,1,2]=>{{1,5},{2,3,4,6}}
[3,2,6,4,5,1]=>[4,6,2,3,1,5]=>[3,1,5,4,6,2]=>{{1,2,3,5,6},{4}}
[3,2,6,5,1,4]=>[2,3,1,5,6,4]=>[5,4,6,2,1,3]=>{{1,5},{2,4},{3,6}}
[3,2,6,5,4,1]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>{{1,2,3,4,5,6}}
[3,4,1,2,5,6]=>[6,5,3,1,4,2]=>[1,2,4,6,3,5]=>{{1},{2},{3,4,5,6}}
[3,4,1,2,6,5]=>[5,6,3,1,4,2]=>[2,1,4,6,3,5]=>{{1,2},{3,4,5,6}}
[3,4,1,5,2,6]=>[6,3,1,4,2,5]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[3,4,1,5,6,2]=>[5,3,1,4,2,6]=>[2,4,6,3,5,1]=>{{1,2,3,4,6},{5}}
[3,4,1,6,2,5]=>[3,1,4,2,6,5]=>[4,6,3,5,1,2]=>{{1,4,5},{2,6},{3}}
[3,4,1,6,5,2]=>[3,1,4,2,5,6]=>[4,6,3,5,2,1]=>{{1,2,4,5,6},{3}}
[3,4,2,1,5,6]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[3,4,2,1,6,5]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>{{1,2},{3,4,6},{5}}
[3,4,2,5,1,6]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[3,4,2,5,6,1]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>{{1,2,3,4,5,6}}
[3,4,2,6,1,5]=>[3,2,4,1,6,5]=>[4,5,3,6,1,2]=>{{1,2,4,5,6},{3}}
[3,4,2,6,5,1]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>{{1,4,6},{2,5},{3}}
[3,4,5,1,2,6]=>[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>{{1},{2,3,4,5,6}}
[3,4,5,1,6,2]=>[4,3,1,5,2,6]=>[3,4,6,2,5,1]=>{{1,3,6},{2,4},{5}}
[3,4,5,2,1,6]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>{{1,3,5,6},{2,4}}
[3,4,5,6,1,2]=>[5,4,3,1,6,2]=>[2,3,4,6,1,5]=>{{1,2,3,4,5,6}}
[3,4,5,6,2,1]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>{{1,2,3,4,6},{5}}
[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>[3,4,6,1,2,5]=>{{1,2,3,4,5,6}}
[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>[3,4,6,1,5,2]=>{{1,2,3,4,6},{5}}
[3,4,6,2,1,5]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>{{1,2,3,4,5,6}}
[3,4,6,2,5,1]=>[4,3,2,6,1,5]=>[3,4,5,1,6,2]=>{{1,2,3,4,5,6}}
[3,4,6,5,1,2]=>[4,3,1,5,6,2]=>[3,4,6,2,1,5]=>{{1,3,5,6},{2,4}}
[3,4,6,5,2,1]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>{{1,3,6},{2,4,5}}
[3,5,1,2,4,6]=>[6,3,1,5,4,2]=>[1,4,6,2,3,5]=>{{1},{2,4},{3,5,6}}
[3,5,1,2,6,4]=>[3,1,5,4,6,2]=>[4,6,2,3,1,5]=>{{1,2,3,4,5,6}}
[3,5,1,4,2,6]=>[6,3,1,5,2,4]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[3,5,1,4,6,2]=>[3,1,5,4,2,6]=>[4,6,2,3,5,1]=>{{1,2,3,4,6},{5}}
[3,5,1,6,2,4]=>[3,1,5,2,6,4]=>[4,6,2,5,1,3]=>{{1,4,5},{2,3,6}}
[3,5,1,6,4,2]=>[3,1,5,2,4,6]=>[4,6,2,5,3,1]=>{{1,2,3,4,5,6}}
[3,5,2,1,4,6]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[3,5,2,1,6,4]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>{{1,2,4,6},{3,5}}
[3,5,2,4,1,6]=>[6,3,2,5,1,4]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[3,5,2,4,6,1]=>[3,2,5,4,1,6]=>[4,5,2,3,6,1]=>{{1,2,3,4,5,6}}
[3,5,2,6,1,4]=>[3,2,5,1,6,4]=>[4,5,2,6,1,3]=>{{1,2,3,4,5,6}}
[3,5,2,6,4,1]=>[3,2,5,1,4,6]=>[4,5,2,6,3,1]=>{{1,4,6},{2,3,5}}
[3,5,4,1,2,6]=>[6,3,1,4,5,2]=>[1,4,6,3,2,5]=>{{1},{2,3,4,5,6}}
[3,5,4,1,6,2]=>[3,1,4,5,2,6]=>[4,6,3,2,5,1]=>{{1,2,4,6},{3},{5}}
[3,5,4,2,1,6]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[3,5,4,2,6,1]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>{{1,2,4,5,6},{3}}
[3,5,4,6,1,2]=>[4,5,3,1,6,2]=>[3,2,4,6,1,5]=>{{1,3,4,5,6},{2}}
[3,5,4,6,2,1]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>{{1,3,4,6},{2},{5}}
[3,5,6,1,2,4]=>[5,3,1,6,4,2]=>[2,4,6,1,3,5]=>{{1,2,4},{3,5,6}}
[3,5,6,1,4,2]=>[5,3,1,6,2,4]=>[2,4,6,1,5,3]=>{{1,2,4},{3,6},{5}}
[3,5,6,2,1,4]=>[5,3,1,2,6,4]=>[2,4,6,5,1,3]=>{{1,2,4,5},{3,6}}
[3,5,6,2,4,1]=>[5,3,2,6,1,4]=>[2,4,5,1,6,3]=>{{1,2,4},{3,5,6}}
[3,5,6,4,1,2]=>[5,3,1,4,6,2]=>[2,4,6,3,1,5]=>{{1,2,3,4,5,6}}
[3,5,6,4,2,1]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>{{1,2,3,4,5,6}}
[3,6,1,2,4,5]=>[3,1,6,5,4,2]=>[4,6,1,2,3,5]=>{{1,2,3,4,5,6}}
[3,6,1,2,5,4]=>[3,1,6,4,5,2]=>[4,6,1,3,2,5]=>{{1,3,4},{2,5,6}}
[3,6,1,4,2,5]=>[3,1,6,5,2,4]=>[4,6,1,2,5,3]=>{{1,2,3,4,6},{5}}
[3,6,1,4,5,2]=>[3,1,6,4,2,5]=>[4,6,1,3,5,2]=>{{1,3,4},{2,6},{5}}
[3,6,1,5,2,4]=>[3,1,6,2,5,4]=>[4,6,1,5,2,3]=>{{1,2,3,4,5,6}}
[3,6,1,5,4,2]=>[3,1,6,2,4,5]=>[4,6,1,5,3,2]=>{{1,3,4,5},{2,6}}
[3,6,2,1,4,5]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>{{1,4},{2,3,5,6}}
[3,6,2,1,5,4]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>{{1,4},{2,6},{3,5}}
[3,6,2,4,1,5]=>[3,2,6,5,1,4]=>[4,5,1,2,6,3]=>{{1,2,3,4,5,6}}
[3,6,2,4,5,1]=>[3,2,6,4,1,5]=>[4,5,1,3,6,2]=>{{1,3,4},{2,5,6}}
[3,6,2,5,1,4]=>[3,2,6,1,5,4]=>[4,5,1,6,2,3]=>{{1,3,4,6},{2,5}}
[3,6,2,5,4,1]=>[3,2,6,1,4,5]=>[4,5,1,6,3,2]=>{{1,2,3,4,5,6}}
[3,6,4,1,2,5]=>[3,1,4,6,5,2]=>[4,6,3,1,2,5]=>{{1,4},{2,5,6},{3}}
[3,6,4,1,5,2]=>[3,1,4,6,2,5]=>[4,6,3,1,5,2]=>{{1,4},{2,6},{3},{5}}
[3,6,4,2,1,5]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>{{1,3,4,5},{2,6}}
[3,6,4,2,5,1]=>[3,2,4,6,1,5]=>[4,5,3,1,6,2]=>{{1,4},{2,5,6},{3}}
[3,6,4,5,1,2]=>[4,6,3,1,5,2]=>[3,1,4,6,2,5]=>{{1,2,3,4,5,6}}
[3,6,4,5,2,1]=>[4,6,3,1,2,5]=>[3,1,4,6,5,2]=>{{1,2,3,4,6},{5}}
[3,6,5,1,2,4]=>[3,1,5,6,4,2]=>[4,6,2,1,3,5]=>{{1,4},{2,3,5,6}}
[3,6,5,1,4,2]=>[3,1,5,6,2,4]=>[4,6,2,1,5,3]=>{{1,4},{2,3,6},{5}}
[3,6,5,2,1,4]=>[3,1,2,5,6,4]=>[4,6,5,2,1,3]=>{{1,2,3,4,5,6}}
[3,6,5,2,4,1]=>[3,2,5,6,1,4]=>[4,5,2,1,6,3]=>{{1,4},{2,3,5,6}}
[3,6,5,4,1,2]=>[3,1,4,5,6,2]=>[4,6,3,2,1,5]=>{{1,2,4,5,6},{3}}
[3,6,5,4,2,1]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>{{1,2,3,4,5,6}}
[4,1,2,3,5,6]=>[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>{{1},{2},{3,4,5,6}}
[4,1,2,3,6,5]=>[5,6,1,4,3,2]=>[2,1,6,3,4,5]=>{{1,2},{3,4,5,6}}
[4,1,2,5,3,6]=>[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>{{1},{2,5,6},{3},{4}}
[4,1,2,5,6,3]=>[5,1,4,3,6,2]=>[2,6,3,4,1,5]=>{{1,2,5,6},{3},{4}}
[4,1,2,6,3,5]=>[1,4,3,6,5,2]=>[6,3,4,1,2,5]=>{{1,2,3,4,5,6}}
[4,1,2,6,5,3]=>[1,4,3,5,6,2]=>[6,3,4,2,1,5]=>{{1,5,6},{2,3,4}}
[4,1,3,2,5,6]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>{{1},{2},{3,4,6},{5}}
[4,1,3,2,6,5]=>[5,6,1,4,2,3]=>[2,1,6,3,5,4]=>{{1,2},{3,4,6},{5}}
[4,1,3,5,2,6]=>[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}
[4,1,3,5,6,2]=>[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>{{1,2,6},{3},{4},{5}}
[4,1,3,6,2,5]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>{{1,2,3,4,5,6}}
[4,1,3,6,5,2]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>{{1,6},{2,3,4,5}}
[4,1,5,2,3,6]=>[6,1,4,2,5,3]=>[1,6,3,5,2,4]=>{{1},{2,4,5,6},{3}}
[4,1,5,2,6,3]=>[1,4,2,5,3,6]=>[6,3,5,2,4,1]=>{{1,6},{2,3,4,5}}
[4,1,5,3,2,6]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>{{1},{2,6},{3},{4,5}}
[4,1,5,3,6,2]=>[1,4,3,5,2,6]=>[6,3,4,2,5,1]=>{{1,6},{2,3,4},{5}}
[4,1,5,6,2,3]=>[5,1,4,2,6,3]=>[2,6,3,5,1,4]=>{{1,2,4,5,6},{3}}
[4,1,5,6,3,2]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>{{1,2,6},{3},{4,5}}
[4,1,6,2,3,5]=>[1,4,2,6,5,3]=>[6,3,5,1,2,4]=>{{1,4,6},{2,3,5}}
[4,1,6,2,5,3]=>[1,4,2,6,3,5]=>[6,3,5,1,4,2]=>{{1,2,3,4,5,6}}
[4,1,6,3,2,5]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>{{1,2,3,5,6},{4}}
[4,1,6,3,5,2]=>[1,4,3,6,2,5]=>[6,3,4,1,5,2]=>{{1,2,3,4,6},{5}}
[4,1,6,5,2,3]=>[1,4,2,5,6,3]=>[6,3,5,2,1,4]=>{{1,2,3,4,5,6}}
[4,1,6,5,3,2]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>{{1,6},{2,3,5},{4}}
[4,2,1,3,5,6]=>[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>{{1},{2},{3,4,5,6}}
[4,2,1,3,6,5]=>[5,6,1,2,4,3]=>[2,1,6,5,3,4]=>{{1,2},{3,4,5,6}}
[4,2,1,5,3,6]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>{{1},{2,6},{3,4,5}}
[4,2,1,5,6,3]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>{{1,2,6},{3,4,5}}
[4,2,1,6,3,5]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>{{1,2,5,6},{3},{4}}
[4,2,1,6,5,3]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>{{1,6},{2,5},{3},{4}}
[4,2,3,1,5,6]=>[6,5,2,4,1,3]=>[1,2,5,3,6,4]=>{{1},{2},{3,4,5,6}}
[4,2,3,1,6,5]=>[5,6,2,4,1,3]=>[2,1,5,3,6,4]=>{{1,2},{3,4,5,6}}
[4,2,3,5,1,6]=>[6,2,4,3,1,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[4,2,3,5,6,1]=>[5,2,4,3,1,6]=>[2,5,3,4,6,1]=>{{1,2,5,6},{3},{4}}
[4,2,3,6,1,5]=>[2,4,3,1,6,5]=>[5,3,4,6,1,2]=>{{1,5},{2,3,4,6}}
[4,2,3,6,5,1]=>[2,4,3,1,5,6]=>[5,3,4,6,2,1]=>{{1,2,3,4,5,6}}
[4,2,5,1,3,6]=>[6,2,4,1,5,3]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[4,2,5,1,6,3]=>[2,4,1,5,3,6]=>[5,3,6,2,4,1]=>{{1,2,3,4,5,6}}
[4,2,5,3,1,6]=>[6,2,4,1,3,5]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[4,2,5,3,6,1]=>[2,4,3,5,1,6]=>[5,3,4,2,6,1]=>{{1,5,6},{2,3,4}}
[4,2,5,6,1,3]=>[5,2,4,1,6,3]=>[2,5,3,6,1,4]=>{{1,2,5},{3},{4,6}}
[4,2,5,6,3,1]=>[5,2,4,1,3,6]=>[2,5,3,6,4,1]=>{{1,2,4,5,6},{3}}
[4,2,6,1,3,5]=>[2,4,1,6,5,3]=>[5,3,6,1,2,4]=>{{1,2,3,4,5,6}}
[4,2,6,1,5,3]=>[2,4,1,6,3,5]=>[5,3,6,1,4,2]=>{{1,4,5},{2,3,6}}
[4,2,6,3,1,5]=>[2,4,1,3,6,5]=>[5,3,6,4,1,2]=>{{1,5},{2,3,6},{4}}
[4,2,6,3,5,1]=>[2,4,3,6,1,5]=>[5,3,4,1,6,2]=>{{1,2,3,4,5,6}}
[4,2,6,5,1,3]=>[2,4,1,5,6,3]=>[5,3,6,2,1,4]=>{{1,5},{2,3,4,6}}
[4,2,6,5,3,1]=>[2,4,1,3,5,6]=>[5,3,6,4,2,1]=>{{1,2,3,5,6},{4}}
[4,3,1,2,5,6]=>[6,5,1,3,4,2]=>[1,2,6,4,3,5]=>{{1},{2},{3,5,6},{4}}
[4,3,1,2,6,5]=>[5,6,1,3,4,2]=>[2,1,6,4,3,5]=>{{1,2},{3,5,6},{4}}
[4,3,1,5,2,6]=>[6,1,3,4,2,5]=>[1,6,4,3,5,2]=>{{1},{2,6},{3,4},{5}}
[4,3,1,5,6,2]=>[5,1,3,4,2,6]=>[2,6,4,3,5,1]=>{{1,2,6},{3,4},{5}}
[4,3,1,6,2,5]=>[1,3,4,2,6,5]=>[6,4,3,5,1,2]=>{{1,2,4,5,6},{3}}
[4,3,1,6,5,2]=>[1,3,4,2,5,6]=>[6,4,3,5,2,1]=>{{1,6},{2,4,5},{3}}
[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>{{1},{2},{3,6},{4,5}}
[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>{{1,2},{3,6},{4,5}}
[4,3,2,5,1,6]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>{{1},{2,5,6},{3,4}}
[4,3,2,5,6,1]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>{{1,2,5,6},{3,4}}
[4,3,2,6,1,5]=>[2,3,4,1,6,5]=>[5,4,3,6,1,2]=>{{1,5},{2,4,6},{3}}
[4,3,2,6,5,1]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>{{1,2,4,5,6},{3}}
[4,3,5,1,2,6]=>[6,3,4,1,5,2]=>[1,4,3,6,2,5]=>{{1},{2,4,5,6},{3}}
[4,3,5,1,6,2]=>[3,4,1,5,2,6]=>[4,3,6,2,5,1]=>{{1,2,3,4,6},{5}}
[4,3,5,2,1,6]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>{{1,2,3,4,5,6}}
[4,3,5,6,1,2]=>[5,3,4,1,6,2]=>[2,4,3,6,1,5]=>{{1,2,4,5,6},{3}}
[4,3,5,6,2,1]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>{{1,2,4,6},{3},{5}}
[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>[4,3,6,1,2,5]=>{{1,4},{2,3,5,6}}
[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>[4,3,6,1,5,2]=>{{1,4},{2,3,6},{5}}
[4,3,6,2,1,5]=>[3,4,1,2,6,5]=>[4,3,6,5,1,2]=>{{1,4,5},{2,3,6}}
[4,3,6,2,5,1]=>[3,4,2,6,1,5]=>[4,3,5,1,6,2]=>{{1,4},{2,3,5,6}}
[4,3,6,5,1,2]=>[3,4,1,5,6,2]=>[4,3,6,2,1,5]=>{{1,2,3,4,5,6}}
[4,3,6,5,2,1]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>{{1,2,3,4,5,6}}
[4,5,1,2,3,6]=>[6,4,1,5,3,2]=>[1,3,6,2,4,5]=>{{1},{2,3,4,5,6}}
[4,5,1,2,6,3]=>[4,1,5,3,6,2]=>[3,6,2,4,1,5]=>{{1,2,3,5,6},{4}}
[4,5,1,3,2,6]=>[6,4,1,5,2,3]=>[1,3,6,2,5,4]=>{{1},{2,3,4,6},{5}}
[4,5,1,3,6,2]=>[4,1,5,3,2,6]=>[3,6,2,4,5,1]=>{{1,2,3,6},{4},{5}}
[4,5,1,6,2,3]=>[4,1,5,2,6,3]=>[3,6,2,5,1,4]=>{{1,2,3,4,5,6}}
[4,5,1,6,3,2]=>[4,1,5,2,3,6]=>[3,6,2,5,4,1]=>{{1,2,3,6},{4,5}}
[4,5,2,1,3,6]=>[6,4,1,2,5,3]=>[1,3,6,5,2,4]=>{{1},{2,3,4,5,6}}
[4,5,2,1,6,3]=>[4,1,2,5,3,6]=>[3,6,5,2,4,1]=>{{1,2,3,4,5,6}}
[4,5,2,3,1,6]=>[6,4,2,5,1,3]=>[1,3,5,2,6,4]=>{{1},{2,3,4,5,6}}
[4,5,2,3,6,1]=>[4,2,5,3,1,6]=>[3,5,2,4,6,1]=>{{1,2,3,5,6},{4}}
[4,5,2,6,1,3]=>[4,2,5,1,6,3]=>[3,5,2,6,1,4]=>{{1,2,3,5},{4,6}}
[4,5,2,6,3,1]=>[4,2,5,1,3,6]=>[3,5,2,6,4,1]=>{{1,2,3,4,5,6}}
[4,5,3,1,2,6]=>[6,4,1,3,5,2]=>[1,3,6,4,2,5]=>{{1},{2,3,5,6},{4}}
[4,5,3,1,6,2]=>[4,1,3,5,2,6]=>[3,6,4,2,5,1]=>{{1,2,3,4,6},{5}}
[4,5,3,2,1,6]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>{{1},{2,3,6},{4,5}}
[4,5,3,2,6,1]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>{{1,2,3,4,5,6}}
[4,5,3,6,1,2]=>[4,3,5,1,6,2]=>[3,4,2,6,1,5]=>{{1,2,3,4,5,6}}
[4,5,3,6,2,1]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>{{1,2,3,4,6},{5}}
[4,5,6,1,2,3]=>[5,4,1,6,3,2]=>[2,3,6,1,4,5]=>{{1,2,3,4,5,6}}
[4,5,6,1,3,2]=>[5,4,1,6,2,3]=>[2,3,6,1,5,4]=>{{1,2,3,4,6},{5}}
[4,5,6,2,1,3]=>[5,4,1,2,6,3]=>[2,3,6,5,1,4]=>{{1,2,3,4,5,6}}
[4,5,6,2,3,1]=>[5,4,2,6,1,3]=>[2,3,5,1,6,4]=>{{1,2,3,4,5,6}}
[4,5,6,3,1,2]=>[5,4,1,3,6,2]=>[2,3,6,4,1,5]=>{{1,2,3,5,6},{4}}
[4,5,6,3,2,1]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>{{1,2,3,6},{4,5}}
[4,6,1,2,3,5]=>[4,1,6,5,3,2]=>[3,6,1,2,4,5]=>{{1,3},{2,4,5,6}}
[4,6,1,2,5,3]=>[4,1,6,3,5,2]=>[3,6,1,4,2,5]=>{{1,3},{2,5,6},{4}}
[4,6,1,3,2,5]=>[4,1,6,5,2,3]=>[3,6,1,2,5,4]=>{{1,3},{2,4,6},{5}}
[4,6,1,3,5,2]=>[4,1,6,3,2,5]=>[3,6,1,4,5,2]=>{{1,3},{2,6},{4},{5}}
[4,6,1,5,2,3]=>[4,1,6,2,5,3]=>[3,6,1,5,2,4]=>{{1,3},{2,4,5,6}}
[4,6,1,5,3,2]=>[4,1,6,2,3,5]=>[3,6,1,5,4,2]=>{{1,3},{2,6},{4,5}}
[4,6,2,1,3,5]=>[4,1,2,6,5,3]=>[3,6,5,1,2,4]=>{{1,2,3,4,5,6}}
[4,6,2,1,5,3]=>[4,1,2,6,3,5]=>[3,6,5,1,4,2]=>{{1,3,4,5},{2,6}}
[4,6,2,3,1,5]=>[4,2,6,5,1,3]=>[3,5,1,2,6,4]=>{{1,3},{2,4,5,6}}
[4,6,2,3,5,1]=>[4,2,6,3,1,5]=>[3,5,1,4,6,2]=>{{1,3},{2,5,6},{4}}
[4,6,2,5,1,3]=>[4,2,6,1,5,3]=>[3,5,1,6,2,4]=>{{1,3},{2,5},{4,6}}
[4,6,2,5,3,1]=>[4,2,6,1,3,5]=>[3,5,1,6,4,2]=>{{1,3},{2,4,5,6}}
[4,6,3,1,2,5]=>[4,1,3,6,5,2]=>[3,6,4,1,2,5]=>{{1,3,4},{2,5,6}}
[4,6,3,1,5,2]=>[4,1,3,6,2,5]=>[3,6,4,1,5,2]=>{{1,3,4},{2,6},{5}}
[4,6,3,2,1,5]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>{{1,3,5},{2,6},{4}}
[4,6,3,2,5,1]=>[4,2,3,6,1,5]=>[3,5,4,1,6,2]=>{{1,3,4},{2,5,6}}
[4,6,3,5,1,2]=>[4,3,6,1,5,2]=>[3,4,1,6,2,5]=>{{1,3},{2,4,5,6}}
[4,6,3,5,2,1]=>[4,3,6,1,2,5]=>[3,4,1,6,5,2]=>{{1,3},{2,4,6},{5}}
[4,6,5,1,2,3]=>[4,1,5,6,3,2]=>[3,6,2,1,4,5]=>{{1,2,3,4,5,6}}
[4,6,5,1,3,2]=>[4,1,5,6,2,3]=>[3,6,2,1,5,4]=>{{1,2,3,4,6},{5}}
[4,6,5,2,1,3]=>[4,1,2,5,6,3]=>[3,6,5,2,1,4]=>{{1,3,5},{2,4,6}}
[4,6,5,2,3,1]=>[4,2,5,6,1,3]=>[3,5,2,1,6,4]=>{{1,2,3,4,5,6}}
[4,6,5,3,1,2]=>[4,1,3,5,6,2]=>[3,6,4,2,1,5]=>{{1,2,3,4,5,6}}
[4,6,5,3,2,1]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>{{1,2,3,5,6},{4}}
[5,1,2,3,4,6]=>[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>{{1},{2,3,4,5,6}}
[5,1,2,3,6,4]=>[1,5,4,6,3,2]=>[6,2,3,1,4,5]=>{{1,4,5,6},{2},{3}}
[5,1,2,4,3,6]=>[6,1,5,3,4,2]=>[1,6,2,4,3,5]=>{{1},{2,3,5,6},{4}}
[5,1,2,4,6,3]=>[1,5,4,3,6,2]=>[6,2,3,4,1,5]=>{{1,5,6},{2},{3},{4}}
[5,1,2,6,3,4]=>[1,5,3,6,4,2]=>[6,2,4,1,3,5]=>{{1,3,4,5,6},{2}}
[5,1,2,6,4,3]=>[1,5,3,4,6,2]=>[6,2,4,3,1,5]=>{{1,5,6},{2},{3,4}}
[5,1,3,2,4,6]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>{{1},{2,3,4,6},{5}}
[5,1,3,2,6,4]=>[1,5,4,6,2,3]=>[6,2,3,1,5,4]=>{{1,4,6},{2},{3},{5}}
[5,1,3,4,2,6]=>[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>{{1},{2,3,6},{4},{5}}
[5,1,3,4,6,2]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>{{1,6},{2},{3},{4},{5}}
[5,1,3,6,2,4]=>[1,5,3,2,6,4]=>[6,2,4,5,1,3]=>{{1,3,4,5,6},{2}}
[5,1,3,6,4,2]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>{{1,6},{2},{3,4,5}}
[5,1,4,2,3,6]=>[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>{{1},{2,3,4,5,6}}
[5,1,4,2,6,3]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>{{1,6},{2},{3,4,5}}
[5,1,4,3,2,6]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>{{1},{2,3,6},{4,5}}
[5,1,4,3,6,2]=>[1,5,3,4,2,6]=>[6,2,4,3,5,1]=>{{1,6},{2},{3,4},{5}}
[5,1,4,6,2,3]=>[1,5,4,2,6,3]=>[6,2,3,5,1,4]=>{{1,4,5,6},{2},{3}}
[5,1,4,6,3,2]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>{{1,6},{2},{3},{4,5}}
[5,1,6,2,3,4]=>[1,5,2,6,4,3]=>[6,2,5,1,3,4]=>{{1,4,6},{2},{3,5}}
[5,1,6,2,4,3]=>[1,5,2,6,3,4]=>[6,2,5,1,4,3]=>{{1,3,4,5,6},{2}}
[5,1,6,3,2,4]=>[1,5,2,3,6,4]=>[6,2,5,4,1,3]=>{{1,3,5,6},{2},{4}}
[5,1,6,3,4,2]=>[1,5,3,6,2,4]=>[6,2,4,1,5,3]=>{{1,3,4,6},{2},{5}}
[5,1,6,4,2,3]=>[1,5,2,4,6,3]=>[6,2,5,3,1,4]=>{{1,3,4,5,6},{2}}
[5,1,6,4,3,2]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>{{1,6},{2},{3,5},{4}}
[5,2,1,3,4,6]=>[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>{{1},{2,4,6},{3,5}}
[5,2,1,3,6,4]=>[1,2,5,4,6,3]=>[6,5,2,3,1,4]=>{{1,2,3,4,5,6}}
[5,2,1,4,3,6]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>{{1},{2,3,4,5,6}}
[5,2,1,4,6,3]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>{{1,6},{2,3,4,5}}
[5,2,1,6,3,4]=>[1,2,5,3,6,4]=>[6,5,2,4,1,3]=>{{1,2,3,5,6},{4}}
[5,2,1,6,4,3]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>{{1,6},{2,3,5},{4}}
[5,2,3,1,4,6]=>[6,2,5,4,1,3]=>[1,5,2,3,6,4]=>{{1},{2,3,4,5,6}}
[5,2,3,1,6,4]=>[2,5,4,6,1,3]=>[5,2,3,1,6,4]=>{{1,4,5,6},{2},{3}}
[5,2,3,4,1,6]=>[6,2,5,3,1,4]=>[1,5,2,4,6,3]=>{{1},{2,3,5,6},{4}}
[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>[5,2,3,4,6,1]=>{{1,5,6},{2},{3},{4}}
[5,2,3,6,1,4]=>[2,5,3,1,6,4]=>[5,2,4,6,1,3]=>{{1,5},{2},{3,4,6}}
[5,2,3,6,4,1]=>[2,5,3,1,4,6]=>[5,2,4,6,3,1]=>{{1,3,4,5,6},{2}}
[5,2,4,1,3,6]=>[6,2,5,1,4,3]=>[1,5,2,6,3,4]=>{{1},{2,3,5},{4,6}}
[5,2,4,1,6,3]=>[2,5,1,4,3,6]=>[5,2,6,3,4,1]=>{{1,3,4,5,6},{2}}
[5,2,4,3,1,6]=>[6,2,5,1,3,4]=>[1,5,2,6,4,3]=>{{1},{2,3,4,5,6}}
[5,2,4,3,6,1]=>[2,5,3,4,1,6]=>[5,2,4,3,6,1]=>{{1,5,6},{2},{3,4}}
[5,2,4,6,1,3]=>[2,5,4,1,6,3]=>[5,2,3,6,1,4]=>{{1,5},{2},{3},{4,6}}
[5,2,4,6,3,1]=>[2,5,4,1,3,6]=>[5,2,3,6,4,1]=>{{1,4,5,6},{2},{3}}
[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>[5,2,6,1,3,4]=>{{1,3,4,5,6},{2}}
[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>[5,2,6,1,4,3]=>{{1,4,5},{2},{3,6}}
[5,2,6,3,1,4]=>[2,5,1,3,6,4]=>[5,2,6,4,1,3]=>{{1,5},{2},{3,6},{4}}
[5,2,6,3,4,1]=>[2,5,3,6,1,4]=>[5,2,4,1,6,3]=>{{1,3,4,5,6},{2}}
[5,2,6,4,1,3]=>[2,5,1,4,6,3]=>[5,2,6,3,1,4]=>{{1,5},{2},{3,4,6}}
[5,2,6,4,3,1]=>[2,5,1,3,4,6]=>[5,2,6,4,3,1]=>{{1,3,5,6},{2},{4}}
[5,3,1,2,4,6]=>[6,1,3,5,4,2]=>[1,6,4,2,3,5]=>{{1},{2,3,4,5,6}}
[5,3,1,2,6,4]=>[1,3,5,4,6,2]=>[6,4,2,3,1,5]=>{{1,5,6},{2,3,4}}
[5,3,1,4,2,6]=>[6,1,3,5,2,4]=>[1,6,4,2,5,3]=>{{1},{2,3,4,6},{5}}
[5,3,1,4,6,2]=>[1,3,5,4,2,6]=>[6,4,2,3,5,1]=>{{1,6},{2,3,4},{5}}
[5,3,1,6,2,4]=>[1,3,5,2,6,4]=>[6,4,2,5,1,3]=>{{1,2,3,4,5,6}}
[5,3,1,6,4,2]=>[1,3,5,2,4,6]=>[6,4,2,5,3,1]=>{{1,6},{2,3,4,5}}
[5,3,2,1,4,6]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>{{1},{2,3,5,6},{4}}
[5,3,2,1,6,4]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>{{1,6},{2,3,4,5}}
[5,3,2,4,1,6]=>[6,2,3,5,1,4]=>[1,5,4,2,6,3]=>{{1},{2,3,4,5,6}}
[5,3,2,4,6,1]=>[2,3,5,4,1,6]=>[5,4,2,3,6,1]=>{{1,5,6},{2,3,4}}
[5,3,2,6,1,4]=>[2,3,5,1,6,4]=>[5,4,2,6,1,3]=>{{1,5},{2,3,4,6}}
[5,3,2,6,4,1]=>[2,3,5,1,4,6]=>[5,4,2,6,3,1]=>{{1,2,3,4,5,6}}
[5,3,4,1,2,6]=>[6,3,5,1,4,2]=>[1,4,2,6,3,5]=>{{1},{2,3,4,5,6}}
[5,3,4,1,6,2]=>[3,5,1,4,2,6]=>[4,2,6,3,5,1]=>{{1,3,4,6},{2},{5}}
[5,3,4,2,1,6]=>[6,3,5,1,2,4]=>[1,4,2,6,5,3]=>{{1},{2,3,4,6},{5}}
[5,3,4,2,6,1]=>[3,5,2,4,1,6]=>[4,2,5,3,6,1]=>{{1,3,4,5,6},{2}}
[5,3,4,6,1,2]=>[3,5,4,1,6,2]=>[4,2,3,6,1,5]=>{{1,4,5,6},{2},{3}}
[5,3,4,6,2,1]=>[3,5,4,1,2,6]=>[4,2,3,6,5,1]=>{{1,4,6},{2},{3},{5}}
[5,3,6,1,2,4]=>[3,5,1,6,4,2]=>[4,2,6,1,3,5]=>{{1,4},{2},{3,5,6}}
[5,3,6,1,4,2]=>[3,5,1,6,2,4]=>[4,2,6,1,5,3]=>{{1,4},{2},{3,6},{5}}
[5,3,6,2,1,4]=>[3,5,1,2,6,4]=>[4,2,6,5,1,3]=>{{1,4,5},{2},{3,6}}
[5,3,6,2,4,1]=>[3,5,2,6,1,4]=>[4,2,5,1,6,3]=>{{1,4},{2},{3,5,6}}
[5,3,6,4,1,2]=>[3,5,1,4,6,2]=>[4,2,6,3,1,5]=>{{1,3,4,5,6},{2}}
[5,3,6,4,2,1]=>[3,5,1,2,4,6]=>[4,2,6,5,3,1]=>{{1,3,4,5,6},{2}}
[5,4,1,2,3,6]=>[6,1,4,5,3,2]=>[1,6,3,2,4,5]=>{{1},{2,4,5,6},{3}}
[5,4,1,2,6,3]=>[1,4,5,3,6,2]=>[6,3,2,4,1,5]=>{{1,5,6},{2,3},{4}}
[5,4,1,3,2,6]=>[6,1,4,5,2,3]=>[1,6,3,2,5,4]=>{{1},{2,4,6},{3},{5}}
[5,4,1,3,6,2]=>[1,4,5,3,2,6]=>[6,3,2,4,5,1]=>{{1,6},{2,3},{4},{5}}
[5,4,1,6,2,3]=>[1,4,5,2,6,3]=>[6,3,2,5,1,4]=>{{1,4,5,6},{2,3}}
[5,4,1,6,3,2]=>[1,4,5,2,3,6]=>[6,3,2,5,4,1]=>{{1,6},{2,3},{4,5}}
[5,4,2,1,3,6]=>[6,1,2,4,5,3]=>[1,6,5,3,2,4]=>{{1},{2,3,4,5,6}}
[5,4,2,1,6,3]=>[1,2,4,5,3,6]=>[6,5,3,2,4,1]=>{{1,6},{2,4,5},{3}}
[5,4,2,3,1,6]=>[6,2,4,5,1,3]=>[1,5,3,2,6,4]=>{{1},{2,4,5,6},{3}}
[5,4,2,3,6,1]=>[2,4,5,3,1,6]=>[5,3,2,4,6,1]=>{{1,5,6},{2,3},{4}}
[5,4,2,6,1,3]=>[2,4,5,1,6,3]=>[5,3,2,6,1,4]=>{{1,5},{2,3},{4,6}}
[5,4,2,6,3,1]=>[2,4,5,1,3,6]=>[5,3,2,6,4,1]=>{{1,4,5,6},{2,3}}
[5,4,3,1,2,6]=>[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>{{1},{2,5,6},{3,4}}
[5,4,3,1,6,2]=>[1,3,4,5,2,6]=>[6,4,3,2,5,1]=>{{1,6},{2,4},{3},{5}}
[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>{{1},{2,6},{3,5},{4}}
[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>{{1,5,6},{2,4},{3}}
[5,4,3,6,1,2]=>[3,4,5,1,6,2]=>[4,3,2,6,1,5]=>{{1,4,5,6},{2,3}}
[5,4,3,6,2,1]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>{{1,4,6},{2,3},{5}}
[5,4,6,1,2,3]=>[4,5,1,6,3,2]=>[3,2,6,1,4,5]=>{{1,3,4,5,6},{2}}
[5,4,6,1,3,2]=>[4,5,1,6,2,3]=>[3,2,6,1,5,4]=>{{1,3,4,6},{2},{5}}
[5,4,6,2,1,3]=>[4,5,1,2,6,3]=>[3,2,6,5,1,4]=>{{1,3,4,5,6},{2}}
[5,4,6,2,3,1]=>[4,5,2,6,1,3]=>[3,2,5,1,6,4]=>{{1,3,4,5,6},{2}}
[5,4,6,3,1,2]=>[4,5,1,3,6,2]=>[3,2,6,4,1,5]=>{{1,3,5,6},{2},{4}}
[5,4,6,3,2,1]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>{{1,3,6},{2},{4,5}}
[5,6,1,2,3,4]=>[5,1,6,4,3,2]=>[2,6,1,3,4,5]=>{{1,2,3,4,5,6}}
[5,6,1,2,4,3]=>[5,1,6,3,4,2]=>[2,6,1,4,3,5]=>{{1,2,3,5,6},{4}}
[5,6,1,3,2,4]=>[5,1,6,4,2,3]=>[2,6,1,3,5,4]=>{{1,2,3,4,6},{5}}
[5,6,1,3,4,2]=>[5,1,6,3,2,4]=>[2,6,1,4,5,3]=>{{1,2,3,6},{4},{5}}
[5,6,1,4,2,3]=>[5,1,6,2,4,3]=>[2,6,1,5,3,4]=>{{1,2,3,4,5,6}}
[5,6,1,4,3,2]=>[5,1,6,2,3,4]=>[2,6,1,5,4,3]=>{{1,2,3,6},{4,5}}
[5,6,2,1,3,4]=>[5,1,2,6,4,3]=>[2,6,5,1,3,4]=>{{1,2,4,6},{3,5}}
[5,6,2,1,4,3]=>[5,1,2,6,3,4]=>[2,6,5,1,4,3]=>{{1,2,3,4,5,6}}
[5,6,2,3,1,4]=>[5,2,6,4,1,3]=>[2,5,1,3,6,4]=>{{1,2,3,4,5,6}}
[5,6,2,3,4,1]=>[5,2,6,3,1,4]=>[2,5,1,4,6,3]=>{{1,2,3,5,6},{4}}
[5,6,2,4,1,3]=>[5,2,6,1,4,3]=>[2,5,1,6,3,4]=>{{1,2,3,5},{4,6}}
[5,6,2,4,3,1]=>[5,2,6,1,3,4]=>[2,5,1,6,4,3]=>{{1,2,3,4,5,6}}
[5,6,3,1,2,4]=>[5,1,3,6,4,2]=>[2,6,4,1,3,5]=>{{1,2,3,4,5,6}}
[5,6,3,1,4,2]=>[5,1,3,6,2,4]=>[2,6,4,1,5,3]=>{{1,2,3,4,6},{5}}
[5,6,3,2,1,4]=>[5,1,2,3,6,4]=>[2,6,5,4,1,3]=>{{1,2,3,5,6},{4}}
[5,6,3,2,4,1]=>[5,2,3,6,1,4]=>[2,5,4,1,6,3]=>{{1,2,3,4,5,6}}
[5,6,3,4,1,2]=>[5,3,6,1,4,2]=>[2,4,1,6,3,5]=>{{1,2,3,4,5,6}}
[5,6,3,4,2,1]=>[5,3,6,1,2,4]=>[2,4,1,6,5,3]=>{{1,2,3,4,6},{5}}
[5,6,4,1,2,3]=>[5,1,4,6,3,2]=>[2,6,3,1,4,5]=>{{1,2,4,5,6},{3}}
[5,6,4,1,3,2]=>[5,1,4,6,2,3]=>[2,6,3,1,5,4]=>{{1,2,4,6},{3},{5}}
[5,6,4,2,1,3]=>[5,1,2,4,6,3]=>[2,6,5,3,1,4]=>{{1,2,3,4,5,6}}
[5,6,4,2,3,1]=>[5,2,4,6,1,3]=>[2,5,3,1,6,4]=>{{1,2,4,5,6},{3}}
[5,6,4,3,1,2]=>[5,1,3,4,6,2]=>[2,6,4,3,1,5]=>{{1,2,5,6},{3,4}}
[5,6,4,3,2,1]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>{{1,2,6},{3,5},{4}}
[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>{{1,2,3,4,5,6}}
[6,1,2,3,5,4]=>[1,6,4,5,3,2]=>[6,1,3,2,4,5]=>{{1,2,4,5,6},{3}}
[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[6,1,2,4,3,5]=>{{1,2,3,5,6},{4}}
[6,1,2,4,5,3]=>[1,6,4,3,5,2]=>[6,1,3,4,2,5]=>{{1,2,5,6},{3},{4}}
[6,1,2,5,3,4]=>[1,6,3,5,4,2]=>[6,1,4,2,3,5]=>{{1,2,3,4,5,6}}
[6,1,2,5,4,3]=>[1,6,3,4,5,2]=>[6,1,4,3,2,5]=>{{1,2,5,6},{3,4}}
[6,1,3,2,4,5]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>{{1,2,3,4,6},{5}}
[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[6,1,3,2,5,4]=>{{1,2,4,6},{3},{5}}
[6,1,3,4,2,5]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>{{1,2,3,6},{4},{5}}
[6,1,3,4,5,2]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>{{1,2,6},{3},{4},{5}}
[6,1,3,5,2,4]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>{{1,2,3,4,5,6}}
[6,1,3,5,4,2]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>{{1,2,6},{3,4,5}}
[6,1,4,2,3,5]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>{{1,2,3,4,5,6}}
[6,1,4,2,5,3]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>{{1,2,6},{3,4,5}}
[6,1,4,3,2,5]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>{{1,2,3,6},{4,5}}
[6,1,4,3,5,2]=>[1,6,3,4,2,5]=>[6,1,4,3,5,2]=>{{1,2,6},{3,4},{5}}
[6,1,4,5,2,3]=>[1,6,4,2,5,3]=>[6,1,3,5,2,4]=>{{1,2,4,5,6},{3}}
[6,1,4,5,3,2]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>{{1,2,6},{3},{4,5}}
[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>{{1,2,4,6},{3,5}}
[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>{{1,2,3,4,5,6}}
[6,1,5,3,2,4]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>{{1,2,3,5,6},{4}}
[6,1,5,3,4,2]=>[1,6,3,5,2,4]=>[6,1,4,2,5,3]=>{{1,2,3,4,6},{5}}
[6,1,5,4,2,3]=>[1,6,2,4,5,3]=>[6,1,5,3,2,4]=>{{1,2,3,4,5,6}}
[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>{{1,2,6},{3,5},{4}}
[6,2,1,3,4,5]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>{{1,2,3,4,5,6}}
[6,2,1,3,5,4]=>[1,2,6,4,5,3]=>[6,5,1,3,2,4]=>{{1,3,4,6},{2,5}}
[6,2,1,4,3,5]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>{{1,3,6},{2,4,5}}
[6,2,1,4,5,3]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>{{1,2,3,4,5,6}}
[6,2,1,5,3,4]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>{{1,3,6},{2,5},{4}}
[6,2,1,5,4,3]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>{{1,2,3,5,6},{4}}
[6,2,3,1,4,5]=>[2,6,5,4,1,3]=>[5,1,2,3,6,4]=>{{1,2,3,4,5,6}}
[6,2,3,1,5,4]=>[2,6,4,5,1,3]=>[5,1,3,2,6,4]=>{{1,2,4,5,6},{3}}
[6,2,3,4,1,5]=>[2,6,5,3,1,4]=>[5,1,2,4,6,3]=>{{1,2,3,5,6},{4}}
[6,2,3,4,5,1]=>[2,6,4,3,1,5]=>[5,1,3,4,6,2]=>{{1,2,5,6},{3},{4}}
[6,2,3,5,1,4]=>[2,6,3,1,5,4]=>[5,1,4,6,2,3]=>{{1,2,5},{3,4,6}}
[6,2,3,5,4,1]=>[2,6,3,1,4,5]=>[5,1,4,6,3,2]=>{{1,2,3,4,5,6}}
[6,2,4,1,3,5]=>[2,6,5,1,4,3]=>[5,1,2,6,3,4]=>{{1,2,3,5},{4,6}}
[6,2,4,1,5,3]=>[2,6,1,4,3,5]=>[5,1,6,3,4,2]=>{{1,2,3,4,5,6}}
[6,2,4,3,1,5]=>[2,6,5,1,3,4]=>[5,1,2,6,4,3]=>{{1,2,3,4,5,6}}
[6,2,4,3,5,1]=>[2,6,3,4,1,5]=>[5,1,4,3,6,2]=>{{1,2,5,6},{3,4}}
[6,2,4,5,1,3]=>[2,6,4,1,5,3]=>[5,1,3,6,2,4]=>{{1,2,5},{3},{4,6}}
[6,2,4,5,3,1]=>[2,6,4,1,3,5]=>[5,1,3,6,4,2]=>{{1,2,4,5,6},{3}}
[6,2,5,1,3,4]=>[2,6,1,5,4,3]=>[5,1,6,2,3,4]=>{{1,2,3,4,5,6}}
[6,2,5,1,4,3]=>[2,6,1,5,3,4]=>[5,1,6,2,4,3]=>{{1,2,4,5},{3,6}}
[6,2,5,3,1,4]=>[2,6,1,3,5,4]=>[5,1,6,4,2,3]=>{{1,2,5},{3,6},{4}}
[6,2,5,3,4,1]=>[2,6,3,5,1,4]=>[5,1,4,2,6,3]=>{{1,2,3,4,5,6}}
[6,2,5,4,1,3]=>[2,6,1,4,5,3]=>[5,1,6,3,2,4]=>{{1,2,5},{3,4,6}}
[6,2,5,4,3,1]=>[2,6,1,3,4,5]=>[5,1,6,4,3,2]=>{{1,2,3,5,6},{4}}
[6,3,1,2,4,5]=>[1,3,6,5,4,2]=>[6,4,1,2,3,5]=>{{1,3,5,6},{2,4}}
[6,3,1,2,5,4]=>[1,3,6,4,5,2]=>[6,4,1,3,2,5]=>{{1,2,3,4,5,6}}
[6,3,1,4,2,5]=>[1,3,6,5,2,4]=>[6,4,1,2,5,3]=>{{1,3,6},{2,4},{5}}
[6,3,1,4,5,2]=>[1,3,6,4,2,5]=>[6,4,1,3,5,2]=>{{1,2,3,4,6},{5}}
[6,3,1,5,2,4]=>[1,3,6,2,5,4]=>[6,4,1,5,2,3]=>{{1,3,6},{2,4,5}}
[6,3,1,5,4,2]=>[1,3,6,2,4,5]=>[6,4,1,5,3,2]=>{{1,2,3,4,5,6}}
[6,3,2,1,4,5]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>{{1,3,4,6},{2,5}}
[6,3,2,1,5,4]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>{{1,2,3,4,5,6}}
[6,3,2,4,1,5]=>[2,3,6,5,1,4]=>[5,4,1,2,6,3]=>{{1,3,5,6},{2,4}}
[6,3,2,4,5,1]=>[2,3,6,4,1,5]=>[5,4,1,3,6,2]=>{{1,2,3,4,5,6}}
[6,3,2,5,1,4]=>[2,3,6,1,5,4]=>[5,4,1,6,2,3]=>{{1,2,3,4,5,6}}
[6,3,2,5,4,1]=>[2,3,6,1,4,5]=>[5,4,1,6,3,2]=>{{1,3,5},{2,4,6}}
[6,3,4,1,2,5]=>[3,6,5,1,4,2]=>[4,1,2,6,3,5]=>{{1,2,3,4,5,6}}
[6,3,4,1,5,2]=>[3,6,1,4,2,5]=>[4,1,6,3,5,2]=>{{1,2,3,4,6},{5}}
[6,3,4,2,1,5]=>[3,6,5,1,2,4]=>[4,1,2,6,5,3]=>{{1,2,3,4,6},{5}}
[6,3,4,2,5,1]=>[3,6,2,4,1,5]=>[4,1,5,3,6,2]=>{{1,2,3,4,5,6}}
[6,3,4,5,1,2]=>[3,6,4,1,5,2]=>[4,1,3,6,2,5]=>{{1,2,4,5,6},{3}}
[6,3,4,5,2,1]=>[3,6,4,1,2,5]=>[4,1,3,6,5,2]=>{{1,2,4,6},{3},{5}}
[6,3,5,1,2,4]=>[3,6,1,5,4,2]=>[4,1,6,2,3,5]=>{{1,2,4},{3,5,6}}
[6,3,5,1,4,2]=>[3,6,1,5,2,4]=>[4,1,6,2,5,3]=>{{1,2,4},{3,6},{5}}
[6,3,5,2,1,4]=>[3,6,1,2,5,4]=>[4,1,6,5,2,3]=>{{1,2,4,5},{3,6}}
[6,3,5,2,4,1]=>[3,6,2,5,1,4]=>[4,1,5,2,6,3]=>{{1,2,4},{3,5,6}}
[6,3,5,4,1,2]=>[3,6,1,4,5,2]=>[4,1,6,3,2,5]=>{{1,2,3,4,5,6}}
[6,3,5,4,2,1]=>[3,6,1,2,4,5]=>[4,1,6,5,3,2]=>{{1,2,3,4,5,6}}
[6,4,1,2,3,5]=>[1,4,6,5,3,2]=>[6,3,1,2,4,5]=>{{1,2,3,4,5,6}}
[6,4,1,2,5,3]=>[1,4,6,3,5,2]=>[6,3,1,4,2,5]=>{{1,2,3,5,6},{4}}
[6,4,1,3,2,5]=>[1,4,6,5,2,3]=>[6,3,1,2,5,4]=>{{1,2,3,4,6},{5}}
[6,4,1,3,5,2]=>[1,4,6,3,2,5]=>[6,3,1,4,5,2]=>{{1,2,3,6},{4},{5}}
[6,4,1,5,2,3]=>[1,4,6,2,5,3]=>[6,3,1,5,2,4]=>{{1,2,3,4,5,6}}
[6,4,1,5,3,2]=>[1,4,6,2,3,5]=>[6,3,1,5,4,2]=>{{1,2,3,6},{4,5}}
[6,4,2,1,3,5]=>[1,2,4,6,5,3]=>[6,5,3,1,2,4]=>{{1,4,6},{2,5},{3}}
[6,4,2,1,5,3]=>[1,2,4,6,3,5]=>[6,5,3,1,4,2]=>{{1,2,4,5,6},{3}}
[6,4,2,3,1,5]=>[2,4,6,5,1,3]=>[5,3,1,2,6,4]=>{{1,2,3,4,5,6}}
[6,4,2,3,5,1]=>[2,4,6,3,1,5]=>[5,3,1,4,6,2]=>{{1,2,3,5,6},{4}}
[6,4,2,5,1,3]=>[2,4,6,1,5,3]=>[5,3,1,6,2,4]=>{{1,2,3,5},{4,6}}
[6,4,2,5,3,1]=>[2,4,6,1,3,5]=>[5,3,1,6,4,2]=>{{1,2,3,4,5,6}}
[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[6,4,3,1,2,5]=>{{1,2,4,5,6},{3}}
[6,4,3,1,5,2]=>[1,3,4,6,2,5]=>[6,4,3,1,5,2]=>{{1,2,4,6},{3},{5}}
[6,4,3,2,1,5]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>{{1,2,5,6},{3,4}}
[6,4,3,2,5,1]=>[2,3,4,6,1,5]=>[5,4,3,1,6,2]=>{{1,2,4,5,6},{3}}
[6,4,3,5,1,2]=>[3,4,6,1,5,2]=>[4,3,1,6,2,5]=>{{1,2,3,4,5,6}}
[6,4,3,5,2,1]=>[3,4,6,1,2,5]=>[4,3,1,6,5,2]=>{{1,2,3,4,6},{5}}
[6,4,5,1,2,3]=>[4,6,1,5,3,2]=>[3,1,6,2,4,5]=>{{1,2,3,4,5,6}}
[6,4,5,1,3,2]=>[4,6,1,5,2,3]=>[3,1,6,2,5,4]=>{{1,2,3,4,6},{5}}
[6,4,5,2,1,3]=>[4,6,1,2,5,3]=>[3,1,6,5,2,4]=>{{1,2,3,4,5,6}}
[6,4,5,2,3,1]=>[4,6,2,5,1,3]=>[3,1,5,2,6,4]=>{{1,2,3,4,5,6}}
[6,4,5,3,1,2]=>[4,6,1,3,5,2]=>[3,1,6,4,2,5]=>{{1,2,3,5,6},{4}}
[6,4,5,3,2,1]=>[4,6,1,2,3,5]=>[3,1,6,5,4,2]=>{{1,2,3,6},{4,5}}
[6,5,1,2,3,4]=>[1,5,6,4,3,2]=>[6,2,1,3,4,5]=>{{1,3,4,5,6},{2}}
[6,5,1,2,4,3]=>[1,5,6,3,4,2]=>[6,2,1,4,3,5]=>{{1,3,5,6},{2},{4}}
[6,5,1,3,2,4]=>[1,5,6,4,2,3]=>[6,2,1,3,5,4]=>{{1,3,4,6},{2},{5}}
[6,5,1,3,4,2]=>[1,5,6,3,2,4]=>[6,2,1,4,5,3]=>{{1,3,6},{2},{4},{5}}
[6,5,1,4,2,3]=>[1,5,6,2,4,3]=>[6,2,1,5,3,4]=>{{1,3,4,5,6},{2}}
[6,5,1,4,3,2]=>[1,5,6,2,3,4]=>[6,2,1,5,4,3]=>{{1,3,6},{2},{4,5}}
[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[6,5,2,1,3,4]=>{{1,4,6},{2,3,5}}
[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[6,5,2,1,4,3]=>{{1,2,3,4,5,6}}
[6,5,2,3,1,4]=>[2,5,6,4,1,3]=>[5,2,1,3,6,4]=>{{1,3,4,5,6},{2}}
[6,5,2,3,4,1]=>[2,5,6,3,1,4]=>[5,2,1,4,6,3]=>{{1,3,5,6},{2},{4}}
[6,5,2,4,1,3]=>[2,5,6,1,4,3]=>[5,2,1,6,3,4]=>{{1,3,5},{2},{4,6}}
[6,5,2,4,3,1]=>[2,5,6,1,3,4]=>[5,2,1,6,4,3]=>{{1,3,4,5,6},{2}}
[6,5,3,1,2,4]=>[1,3,5,6,4,2]=>[6,4,2,1,3,5]=>{{1,2,3,4,5,6}}
[6,5,3,1,4,2]=>[1,3,5,6,2,4]=>[6,4,2,1,5,3]=>{{1,2,3,4,6},{5}}
[6,5,3,2,1,4]=>[1,2,3,5,6,4]=>[6,5,4,2,1,3]=>{{1,2,3,4,5,6}}
[6,5,3,2,4,1]=>[2,3,5,6,1,4]=>[5,4,2,1,6,3]=>{{1,2,3,4,5,6}}
[6,5,3,4,1,2]=>[3,5,6,1,4,2]=>[4,2,1,6,3,5]=>{{1,3,4,5,6},{2}}
[6,5,3,4,2,1]=>[3,5,6,1,2,4]=>[4,2,1,6,5,3]=>{{1,3,4,6},{2},{5}}
[6,5,4,1,2,3]=>[1,4,5,6,3,2]=>[6,3,2,1,4,5]=>{{1,4,5,6},{2,3}}
[6,5,4,1,3,2]=>[1,4,5,6,2,3]=>[6,3,2,1,5,4]=>{{1,4,6},{2,3},{5}}
[6,5,4,2,1,3]=>[1,2,4,5,6,3]=>[6,5,3,2,1,4]=>{{1,2,4,5,6},{3}}
[6,5,4,2,3,1]=>[2,4,5,6,1,3]=>[5,3,2,1,6,4]=>{{1,4,5,6},{2,3}}
[6,5,4,3,1,2]=>[1,3,4,5,6,2]=>[6,4,3,2,1,5]=>{{1,5,6},{2,4},{3}}
[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>{{1,6},{2,5},{3,4}}
[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>{{1,2},{3},{4},{5},{6},{7}}
[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[1,2,3,4,6,7,5]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[1,2,3,4,7,5,6]=>[5,7,6,4,3,2,1]=>[3,1,2,4,5,6,7]=>{{1,2,3},{4},{5},{6},{7}}
[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>{{1,3},{2},{4},{5},{6},{7}}
[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>{{1,2},{3,4},{5},{6},{7}}
[1,2,3,5,6,4,7]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,2,3,5,6,7,4]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[1,2,3,5,7,4,6]=>[5,4,7,6,3,2,1]=>[3,4,1,2,5,6,7]=>{{1,3},{2,4},{5},{6},{7}}
[1,2,3,5,7,6,4]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[1,2,3,6,4,5,7]=>[7,4,6,5,3,2,1]=>[1,4,2,3,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,2,3,6,4,7,5]=>[4,6,5,7,3,2,1]=>[4,2,3,1,5,6,7]=>{{1,4},{2},{3},{5},{6},{7}}
[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[1,2,3,6,5,7,4]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[1,2,3,6,7,4,5]=>[6,4,7,5,3,2,1]=>[2,4,1,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[1,2,3,6,7,5,4]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[1,2,3,7,4,5,6]=>[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[1,2,3,7,4,6,5]=>[4,7,5,6,3,2,1]=>[4,1,3,2,5,6,7]=>{{1,2,4},{3},{5},{6},{7}}
[1,2,3,7,5,4,6]=>[4,5,7,6,3,2,1]=>[4,3,1,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[1,2,3,7,5,6,4]=>[5,7,4,6,3,2,1]=>[3,1,4,2,5,6,7]=>{{1,2,3,4},{5},{6},{7}}
[1,2,3,7,6,4,5]=>[4,6,7,5,3,2,1]=>[4,2,1,3,5,6,7]=>{{1,3,4},{2},{5},{6},{7}}
[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>{{1,4},{2,3},{5},{6},{7}}
[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>{{1,2},{3},{4,5},{6},{7}}
[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[1,2,4,3,6,7,5]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}
[1,2,4,3,7,5,6]=>[5,7,6,3,4,2,1]=>[3,1,2,5,4,6,7]=>{{1,2,3},{4,5},{6},{7}}
[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>{{1,3},{2},{4,5},{6},{7}}
[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,4,5,3,7,6]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>{{1,2},{3,4,5},{6},{7}}
[1,2,4,5,6,3,7]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,2,4,5,6,7,3]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,4,5,7,3,6]=>[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,4,5,7,6,3]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>{{1,3,5},{2,4},{6},{7}}
[1,2,4,6,3,5,7]=>[7,4,3,6,5,2,1]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[1,2,4,6,3,7,5]=>[4,3,6,5,7,2,1]=>[4,5,2,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,4,6,5,3,7]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,2,4,6,5,7,3]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[1,2,4,6,7,3,5]=>[6,4,3,7,5,2,1]=>[2,4,5,1,3,6,7]=>{{1,2,4},{3,5},{6},{7}}
[1,2,4,6,7,5,3]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,4,7,3,5,6]=>[4,3,7,6,5,2,1]=>[4,5,1,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,4,7,3,6,5]=>[4,3,7,5,6,2,1]=>[4,5,1,3,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[1,2,4,7,5,3,6]=>[4,3,5,7,6,2,1]=>[4,5,3,1,2,6,7]=>{{1,4},{2,5},{3},{6},{7}}
[1,2,4,7,5,6,3]=>[5,7,4,3,6,2,1]=>[3,1,4,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,4,7,6,3,5]=>[4,3,6,7,5,2,1]=>[4,5,2,1,3,6,7]=>{{1,4},{2,3,5},{6},{7}}
[1,2,4,7,6,5,3]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[1,2,5,3,4,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,5,3,4,7,6]=>[6,7,3,5,4,2,1]=>[2,1,5,3,4,6,7]=>{{1,2},{3,4,5},{6},{7}}
[1,2,5,3,6,4,7]=>[7,3,5,4,6,2,1]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,2,5,3,6,7,4]=>[6,3,5,4,7,2,1]=>[2,5,3,4,1,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[1,2,5,3,7,4,6]=>[3,5,4,7,6,2,1]=>[5,3,4,1,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,5,3,7,6,4]=>[3,5,4,6,7,2,1]=>[5,3,4,2,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>{{1,2},{3,5},{4},{6},{7}}
[1,2,5,4,6,3,7]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,2,5,4,6,7,3]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>{{1,2,4,5},{3},{6},{7}}
[1,2,5,4,7,3,6]=>[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>{{1,4},{2,3,5},{6},{7}}
[1,2,5,4,7,6,3]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,5,6,3,4,7]=>[7,5,3,6,4,2,1]=>[1,3,5,2,4,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,2,5,6,3,7,4]=>[5,3,6,4,7,2,1]=>[3,5,2,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[1,2,5,6,4,3,7]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,2,5,6,4,7,3]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,5,6,7,3,4]=>[6,5,3,7,4,2,1]=>[2,3,5,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,5,6,7,4,3]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>{{1,2,3,5},{4},{6},{7}}
[1,2,5,7,3,4,6]=>[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>{{1,3},{2,4,5},{6},{7}}
[1,2,5,7,3,6,4]=>[5,3,7,4,6,2,1]=>[3,5,1,4,2,6,7]=>{{1,3},{2,5},{4},{6},{7}}
[1,2,5,7,4,3,6]=>[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>{{1,3,4},{2,5},{6},{7}}
[1,2,5,7,4,6,3]=>[5,4,7,3,6,2,1]=>[3,4,1,5,2,6,7]=>{{1,3},{2,4,5},{6},{7}}
[1,2,5,7,6,3,4]=>[5,3,6,7,4,2,1]=>[3,5,2,1,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,5,7,6,4,3]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,6,3,4,5,7]=>[7,3,6,5,4,2,1]=>[1,5,2,3,4,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,2,6,3,4,7,5]=>[3,6,5,7,4,2,1]=>[5,2,3,1,4,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[1,2,6,3,5,4,7]=>[7,3,6,4,5,2,1]=>[1,5,2,4,3,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,2,6,3,5,7,4]=>[3,6,5,4,7,2,1]=>[5,2,3,4,1,6,7]=>{{1,5},{2},{3},{4},{6},{7}}
[1,2,6,3,7,4,5]=>[3,6,4,7,5,2,1]=>[5,2,4,1,3,6,7]=>{{1,3,4,5},{2},{6},{7}}
[1,2,6,3,7,5,4]=>[3,6,4,5,7,2,1]=>[5,2,4,3,1,6,7]=>{{1,5},{2},{3,4},{6},{7}}
[1,2,6,4,3,5,7]=>[7,3,4,6,5,2,1]=>[1,5,4,2,3,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,2,6,4,3,7,5]=>[3,4,6,5,7,2,1]=>[5,4,2,3,1,6,7]=>{{1,5},{2,3,4},{6},{7}}
[1,2,6,4,5,3,7]=>[7,4,6,3,5,2,1]=>[1,4,2,5,3,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,2,6,4,5,7,3]=>[4,6,5,3,7,2,1]=>[4,2,3,5,1,6,7]=>{{1,4,5},{2},{3},{6},{7}}
[1,2,6,4,7,3,5]=>[4,6,3,7,5,2,1]=>[4,2,5,1,3,6,7]=>{{1,4},{2},{3,5},{6},{7}}
[1,2,6,4,7,5,3]=>[4,6,3,5,7,2,1]=>[4,2,5,3,1,6,7]=>{{1,3,4,5},{2},{6},{7}}
[1,2,6,5,3,4,7]=>[7,3,5,6,4,2,1]=>[1,5,3,2,4,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,2,6,5,3,7,4]=>[3,5,6,4,7,2,1]=>[5,3,2,4,1,6,7]=>{{1,5},{2,3},{4},{6},{7}}
[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>{{1},{2,5},{3,4},{6},{7}}
[1,2,6,5,4,7,3]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>{{1,4,5},{2,3},{6},{7}}
[1,2,6,5,7,3,4]=>[5,6,3,7,4,2,1]=>[3,2,5,1,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[1,2,6,5,7,4,3]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[1,2,6,7,3,4,5]=>[6,3,7,5,4,2,1]=>[2,5,1,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,6,7,3,5,4]=>[6,3,7,4,5,2,1]=>[2,5,1,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}
[1,2,6,7,4,3,5]=>[6,3,4,7,5,2,1]=>[2,5,4,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,6,7,4,5,3]=>[6,4,7,3,5,2,1]=>[2,4,1,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,6,7,5,3,4]=>[6,3,5,7,4,2,1]=>[2,5,3,1,4,6,7]=>{{1,2,4,5},{3},{6},{7}}
[1,2,6,7,5,4,3]=>[6,3,4,5,7,2,1]=>[2,5,4,3,1,6,7]=>{{1,2,5},{3,4},{6},{7}}
[1,2,7,3,4,5,6]=>[3,7,6,5,4,2,1]=>[5,1,2,3,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,3,4,6,5]=>[3,7,5,6,4,2,1]=>[5,1,3,2,4,6,7]=>{{1,2,4,5},{3},{6},{7}}
[1,2,7,3,5,4,6]=>[3,7,6,4,5,2,1]=>[5,1,2,4,3,6,7]=>{{1,2,3,5},{4},{6},{7}}
[1,2,7,3,5,6,4]=>[3,7,5,4,6,2,1]=>[5,1,3,4,2,6,7]=>{{1,2,5},{3},{4},{6},{7}}
[1,2,7,3,6,4,5]=>[3,7,4,6,5,2,1]=>[5,1,4,2,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,3,6,5,4]=>[3,7,4,5,6,2,1]=>[5,1,4,3,2,6,7]=>{{1,2,5},{3,4},{6},{7}}
[1,2,7,4,3,5,6]=>[3,4,7,6,5,2,1]=>[5,4,1,2,3,6,7]=>{{1,3,5},{2,4},{6},{7}}
[1,2,7,4,3,6,5]=>[3,4,7,5,6,2,1]=>[5,4,1,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,4,5,3,6]=>[4,7,6,3,5,2,1]=>[4,1,2,5,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,4,5,6,3]=>[4,7,5,3,6,2,1]=>[4,1,3,5,2,6,7]=>{{1,2,4,5},{3},{6},{7}}
[1,2,7,4,6,3,5]=>[4,7,3,6,5,2,1]=>[4,1,5,2,3,6,7]=>{{1,2,4},{3,5},{6},{7}}
[1,2,7,4,6,5,3]=>[4,7,3,5,6,2,1]=>[4,1,5,3,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,5,3,4,6]=>[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,5,3,6,4]=>[3,5,7,4,6,2,1]=>[5,3,1,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}
[1,2,7,5,4,3,6]=>[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>{{1,2,4,5},{3},{6},{7}}
[1,2,7,5,4,6,3]=>[4,5,7,3,6,2,1]=>[4,3,1,5,2,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,5,6,3,4]=>[5,7,3,6,4,2,1]=>[3,1,5,2,4,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,5,6,4,3]=>[5,7,3,4,6,2,1]=>[3,1,5,4,2,6,7]=>{{1,2,3,5},{4},{6},{7}}
[1,2,7,6,3,4,5]=>[3,6,7,5,4,2,1]=>[5,2,1,3,4,6,7]=>{{1,3,4,5},{2},{6},{7}}
[1,2,7,6,3,5,4]=>[3,6,7,4,5,2,1]=>[5,2,1,4,3,6,7]=>{{1,3,5},{2},{4},{6},{7}}
[1,2,7,6,4,3,5]=>[3,4,6,7,5,2,1]=>[5,4,2,1,3,6,7]=>{{1,2,3,4,5},{6},{7}}
[1,2,7,6,4,5,3]=>[4,6,7,3,5,2,1]=>[4,2,1,5,3,6,7]=>{{1,3,4,5},{2},{6},{7}}
[1,2,7,6,5,3,4]=>[3,5,6,7,4,2,1]=>[5,3,2,1,4,6,7]=>{{1,4,5},{2,3},{6},{7}}
[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>{{1,5},{2,4},{3},{6},{7}}
[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>{{1,2},{3},{4},{5,6},{7}}
[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[1,3,2,4,6,7,5]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}
[1,3,2,4,7,5,6]=>[5,7,6,4,2,3,1]=>[3,1,2,4,6,5,7]=>{{1,2,3},{4},{5,6},{7}}
[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>{{1,3},{2},{4},{5,6},{7}}
[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>{{1,2},{3,4},{5,6},{7}}
[1,3,2,5,6,4,7]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,3,2,5,6,7,4]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[1,3,2,5,7,4,6]=>[5,4,7,6,2,3,1]=>[3,4,1,2,6,5,7]=>{{1,3},{2,4},{5,6},{7}}
[1,3,2,5,7,6,4]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[1,3,2,6,4,5,7]=>[7,4,6,5,2,3,1]=>[1,4,2,3,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,3,2,6,4,7,5]=>[4,6,5,7,2,3,1]=>[4,2,3,1,6,5,7]=>{{1,4},{2},{3},{5,6},{7}}
[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[1,3,2,6,5,7,4]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[1,3,2,6,7,4,5]=>[6,4,7,5,2,3,1]=>[2,4,1,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[1,3,2,6,7,5,4]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[1,3,2,7,4,5,6]=>[4,7,6,5,2,3,1]=>[4,1,2,3,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[1,3,2,7,4,6,5]=>[4,7,5,6,2,3,1]=>[4,1,3,2,6,5,7]=>{{1,2,4},{3},{5,6},{7}}
[1,3,2,7,5,4,6]=>[4,5,7,6,2,3,1]=>[4,3,1,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[1,3,2,7,5,6,4]=>[5,7,4,6,2,3,1]=>[3,1,4,2,6,5,7]=>{{1,2,3,4},{5,6},{7}}
[1,3,2,7,6,4,5]=>[4,6,7,5,2,3,1]=>[4,2,1,3,6,5,7]=>{{1,3,4},{2},{5,6},{7}}
[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>{{1,4},{2,3},{5,6},{7}}
[1,3,4,2,5,6,7]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,3,4,2,5,7,6]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>{{1,2},{3},{4,5,6},{7}}
[1,3,4,2,6,5,7]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[1,3,4,2,6,7,5]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}
[1,3,4,2,7,5,6]=>[5,7,6,3,2,4,1]=>[3,1,2,5,6,4,7]=>{{1,2,3},{4,5,6},{7}}
[1,3,4,2,7,6,5]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>{{1,3},{2},{4,5,6},{7}}
[1,3,4,5,2,6,7]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,3,4,5,2,7,6]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>{{1,2},{3,4,5,6},{7}}
[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,4,5,6,7,2]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,4,5,7,2,6]=>[5,4,3,2,7,6,1]=>[3,4,5,6,1,2,7]=>{{1,3,5},{2,4,6},{7}}
[1,3,4,5,7,6,2]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,4,6,2,5,7]=>[7,4,3,2,6,5,1]=>[1,4,5,6,2,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,4,6,2,7,5]=>[4,3,2,6,5,7,1]=>[4,5,6,2,3,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,4,6,5,2,7]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>{{1},{2,4,6},{3,5},{7}}
[1,3,4,6,5,7,2]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[1,3,4,6,7,2,5]=>[6,4,3,2,7,5,1]=>[2,4,5,6,1,3,7]=>{{1,2,3,4,5,6},{7}}
[1,3,4,6,7,5,2]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>{{1,2,4,6},{3,5},{7}}
[1,3,4,7,2,5,6]=>[4,3,2,7,6,5,1]=>[4,5,6,1,2,3,7]=>{{1,4},{2,5},{3,6},{7}}
[1,3,4,7,2,6,5]=>[4,3,2,7,5,6,1]=>[4,5,6,1,3,2,7]=>{{1,4},{2,3,5,6},{7}}
[1,3,4,7,5,2,6]=>[4,3,2,5,7,6,1]=>[4,5,6,3,1,2,7]=>{{1,2,3,4,5,6},{7}}
[1,3,4,7,5,6,2]=>[5,7,4,3,2,6,1]=>[3,1,4,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[1,3,4,7,6,2,5]=>[4,3,2,6,7,5,1]=>[4,5,6,2,1,3,7]=>{{1,2,4,5},{3,6},{7}}
[1,3,4,7,6,5,2]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[1,3,5,2,4,6,7]=>[7,6,3,2,5,4,1]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[1,3,5,2,4,7,6]=>[6,7,3,2,5,4,1]=>[2,1,5,6,3,4,7]=>{{1,2},{3,5},{4,6},{7}}
[1,3,5,2,6,4,7]=>[7,3,2,5,4,6,1]=>[1,5,6,3,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,5,2,6,7,4]=>[6,3,2,5,4,7,1]=>[2,5,6,3,4,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,5,2,7,4,6]=>[3,2,5,4,7,6,1]=>[5,6,3,4,1,2,7]=>{{1,5},{2,6},{3},{4},{7}}
[1,3,5,2,7,6,4]=>[3,2,5,4,6,7,1]=>[5,6,3,4,2,1,7]=>{{1,2,5,6},{3},{4},{7}}
[1,3,5,4,2,6,7]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,3,5,4,2,7,6]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>{{1,2},{3,4,5,6},{7}}
[1,3,5,4,6,2,7]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,5,4,6,7,2]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[1,3,5,4,7,2,6]=>[4,5,3,2,7,6,1]=>[4,3,5,6,1,2,7]=>{{1,2,3,4,5,6},{7}}
[1,3,5,4,7,6,2]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>{{1,4,6},{2,3,5},{7}}
[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,3,5,6,2,7,4]=>[5,3,2,6,4,7,1]=>[3,5,6,2,4,1,7]=>{{1,3,6},{2,4,5},{7}}
[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,5,6,4,7,2]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,5,6,7,2,4]=>[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}
[1,3,5,6,7,4,2]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,5,7,2,4,6]=>[5,3,2,7,6,4,1]=>[3,5,6,1,2,4,7]=>{{1,3,4,6},{2,5},{7}}
[1,3,5,7,2,6,4]=>[5,3,2,7,4,6,1]=>[3,5,6,1,4,2,7]=>{{1,2,3,4,5,6},{7}}
[1,3,5,7,4,2,6]=>[5,3,2,4,7,6,1]=>[3,5,6,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}
[1,3,5,7,4,6,2]=>[5,4,7,3,2,6,1]=>[3,4,1,5,6,2,7]=>{{1,3},{2,4,5,6},{7}}
[1,3,5,7,6,2,4]=>[5,3,2,6,7,4,1]=>[3,5,6,2,1,4,7]=>{{1,2,3,4,5,6},{7}}
[1,3,5,7,6,4,2]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>{{1,3,6},{2,5},{4},{7}}
[1,3,6,2,4,5,7]=>[7,3,2,6,5,4,1]=>[1,5,6,2,3,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,6,2,4,7,5]=>[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>{{1,5},{2,3,4,6},{7}}
[1,3,6,2,5,4,7]=>[7,3,2,6,4,5,1]=>[1,5,6,2,4,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,3,6,2,5,7,4]=>[3,2,6,5,4,7,1]=>[5,6,2,3,4,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,6,2,7,4,5]=>[3,2,6,4,7,5,1]=>[5,6,2,4,1,3,7]=>{{1,5},{2,3,6},{4},{7}}
[1,3,6,2,7,5,4]=>[3,2,6,4,5,7,1]=>[5,6,2,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}
[1,3,6,4,2,5,7]=>[7,3,2,4,6,5,1]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,3,6,4,2,7,5]=>[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>{{1,2,3,4,5,6},{7}}
[1,3,6,4,5,2,7]=>[7,4,6,3,2,5,1]=>[1,4,2,5,6,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,3,6,4,5,7,2]=>[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>{{1,4,5,6},{2},{3},{7}}
[1,3,6,4,7,2,5]=>[4,6,3,2,7,5,1]=>[4,2,5,6,1,3,7]=>{{1,3,4,5,6},{2},{7}}
[1,3,6,4,7,5,2]=>[4,6,3,2,5,7,1]=>[4,2,5,6,3,1,7]=>{{1,4,6},{2},{3,5},{7}}
[1,3,6,5,2,4,7]=>[7,3,2,5,6,4,1]=>[1,5,6,3,2,4,7]=>{{1},{2,5},{3,4,6},{7}}
[1,3,6,5,2,7,4]=>[3,2,5,6,4,7,1]=>[5,6,3,2,4,1,7]=>{{1,2,4,5,6},{3},{7}}
[1,3,6,5,4,2,7]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,3,6,5,4,7,2]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>{{1,4,5,6},{2,3},{7}}
[1,3,6,5,7,2,4]=>[5,6,3,2,7,4,1]=>[3,2,5,6,1,4,7]=>{{1,3,5},{2},{4,6},{7}}
[1,3,6,5,7,4,2]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>{{1,3,4,5,6},{2},{7}}
[1,3,6,7,2,4,5]=>[6,3,2,7,5,4,1]=>[2,5,6,1,3,4,7]=>{{1,2,3,4,5,6},{7}}
[1,3,6,7,2,5,4]=>[6,3,2,7,4,5,1]=>[2,5,6,1,4,3,7]=>{{1,2,4,5},{3,6},{7}}
[1,3,6,7,4,2,5]=>[6,3,2,4,7,5,1]=>[2,5,6,4,1,3,7]=>{{1,2,5},{3,6},{4},{7}}
[1,3,6,7,4,5,2]=>[6,4,7,3,2,5,1]=>[2,4,1,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[1,3,6,7,5,2,4]=>[6,3,2,5,7,4,1]=>[2,5,6,3,1,4,7]=>{{1,2,5},{3,4,6},{7}}
[1,3,6,7,5,4,2]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>{{1,2,3,5,6},{4},{7}}
[1,3,7,2,4,5,6]=>[3,2,7,6,5,4,1]=>[5,6,1,2,3,4,7]=>{{1,3,5},{2,4,6},{7}}
[1,3,7,2,4,6,5]=>[3,2,7,5,6,4,1]=>[5,6,1,3,2,4,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,2,5,4,6]=>[3,2,7,6,4,5,1]=>[5,6,1,2,4,3,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,2,5,6,4]=>[3,2,7,5,4,6,1]=>[5,6,1,3,4,2,7]=>{{1,3,4,5},{2,6},{7}}
[1,3,7,2,6,4,5]=>[3,2,7,4,6,5,1]=>[5,6,1,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}
[1,3,7,2,6,5,4]=>[3,2,7,4,5,6,1]=>[5,6,1,4,3,2,7]=>{{1,3,5},{2,6},{4},{7}}
[1,3,7,4,2,5,6]=>[3,2,4,7,6,5,1]=>[5,6,4,1,2,3,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,4,2,6,5]=>[3,2,4,7,5,6,1]=>[5,6,4,1,3,2,7]=>{{1,3,4,5},{2,6},{7}}
[1,3,7,4,5,2,6]=>[4,7,6,3,2,5,1]=>[4,1,2,5,6,3,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,4,5,6,2]=>[4,7,5,3,2,6,1]=>[4,1,3,5,6,2,7]=>{{1,2,4,5,6},{3},{7}}
[1,3,7,4,6,2,5]=>[4,7,3,2,6,5,1]=>[4,1,5,6,2,3,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,4,6,5,2]=>[4,7,3,2,5,6,1]=>[4,1,5,6,3,2,7]=>{{1,2,4,6},{3,5},{7}}
[1,3,7,5,2,4,6]=>[3,2,5,7,6,4,1]=>[5,6,3,1,2,4,7]=>{{1,2,4,5,6},{3},{7}}
[1,3,7,5,2,6,4]=>[3,2,5,7,4,6,1]=>[5,6,3,1,4,2,7]=>{{1,4,5},{2,6},{3},{7}}
[1,3,7,5,4,2,6]=>[3,2,4,5,7,6,1]=>[5,6,4,3,1,2,7]=>{{1,5},{2,6},{3,4},{7}}
[1,3,7,5,4,6,2]=>[4,5,7,3,2,6,1]=>[4,3,1,5,6,2,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,5,6,2,4]=>[5,7,3,2,6,4,1]=>[3,1,5,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}
[1,3,7,5,6,4,2]=>[5,7,3,2,4,6,1]=>[3,1,5,6,4,2,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,6,2,4,5]=>[3,2,6,7,5,4,1]=>[5,6,2,1,3,4,7]=>{{1,2,3,4,5,6},{7}}
[1,3,7,6,2,5,4]=>[3,2,6,7,4,5,1]=>[5,6,2,1,4,3,7]=>{{1,4,5},{2,3,6},{7}}
[1,3,7,6,4,2,5]=>[3,2,4,6,7,5,1]=>[5,6,4,2,1,3,7]=>{{1,5},{2,3,4,6},{7}}
[1,3,7,6,4,5,2]=>[4,6,7,3,2,5,1]=>[4,2,1,5,6,3,7]=>{{1,3,4,5,6},{2},{7}}
[1,3,7,6,5,2,4]=>[3,2,5,6,7,4,1]=>[5,6,3,2,1,4,7]=>{{1,5},{2,4,6},{3},{7}}
[1,3,7,6,5,4,2]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>{{1,2,5,6},{3,4},{7}}
[1,4,2,3,5,6,7]=>[7,6,5,2,4,3,1]=>[1,2,3,6,4,5,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,4,2,3,5,7,6]=>[6,7,5,2,4,3,1]=>[2,1,3,6,4,5,7]=>{{1,2},{3},{4,5,6},{7}}
[1,4,2,3,6,5,7]=>[7,5,6,2,4,3,1]=>[1,3,2,6,4,5,7]=>{{1},{2,3},{4,5,6},{7}}
[1,4,2,3,6,7,5]=>[6,5,7,2,4,3,1]=>[2,3,1,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}
[1,4,2,3,7,5,6]=>[5,7,6,2,4,3,1]=>[3,1,2,6,4,5,7]=>{{1,2,3},{4,5,6},{7}}
[1,4,2,3,7,6,5]=>[5,6,7,2,4,3,1]=>[3,2,1,6,4,5,7]=>{{1,3},{2},{4,5,6},{7}}
[1,4,2,5,3,6,7]=>[7,6,2,4,3,5,1]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,4,2,5,3,7,6]=>[6,7,2,4,3,5,1]=>[2,1,6,4,5,3,7]=>{{1,2},{3,6},{4},{5},{7}}
[1,4,2,5,6,3,7]=>[7,5,2,4,3,6,1]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,4,2,5,6,7,3]=>[6,5,2,4,3,7,1]=>[2,3,6,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[1,4,2,5,7,3,6]=>[5,2,4,3,7,6,1]=>[3,6,4,5,1,2,7]=>{{1,3,4,5},{2,6},{7}}
[1,4,2,5,7,6,3]=>[5,2,4,3,6,7,1]=>[3,6,4,5,2,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,2,6,3,5,7]=>[7,2,4,3,6,5,1]=>[1,6,4,5,2,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,2,6,3,7,5]=>[2,4,3,6,5,7,1]=>[6,4,5,2,3,1,7]=>{{1,6},{2,4},{3,5},{7}}
[1,4,2,6,5,3,7]=>[7,2,4,3,5,6,1]=>[1,6,4,5,3,2,7]=>{{1},{2,6},{3,4,5},{7}}
[1,4,2,6,5,7,3]=>[5,6,2,4,3,7,1]=>[3,2,6,4,5,1,7]=>{{1,3,6},{2},{4},{5},{7}}
[1,4,2,6,7,3,5]=>[6,2,4,3,7,5,1]=>[2,6,4,5,1,3,7]=>{{1,2,3,4,5,6},{7}}
[1,4,2,6,7,5,3]=>[6,2,4,3,5,7,1]=>[2,6,4,5,3,1,7]=>{{1,2,6},{3,4,5},{7}}
[1,4,2,7,3,5,6]=>[2,4,3,7,6,5,1]=>[6,4,5,1,2,3,7]=>{{1,2,3,4,5,6},{7}}
[1,4,2,7,3,6,5]=>[2,4,3,7,5,6,1]=>[6,4,5,1,3,2,7]=>{{1,2,4,6},{3,5},{7}}
[1,4,2,7,5,3,6]=>[2,4,3,5,7,6,1]=>[6,4,5,3,1,2,7]=>{{1,2,3,4,5,6},{7}}
[1,4,2,7,5,6,3]=>[5,7,2,4,3,6,1]=>[3,1,6,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}
[1,4,2,7,6,3,5]=>[2,4,3,6,7,5,1]=>[6,4,5,2,1,3,7]=>{{1,3,5,6},{2,4},{7}}
[1,4,2,7,6,5,3]=>[2,4,3,5,6,7,1]=>[6,4,5,3,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>{{1,2},{3},{4,6},{5},{7}}
[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[1,4,3,2,6,7,5]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}
[1,4,3,2,7,5,6]=>[5,7,6,2,3,4,1]=>[3,1,2,6,5,4,7]=>{{1,2,3},{4,6},{5},{7}}
[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>{{1,3},{2},{4,6},{5},{7}}
[1,4,3,5,2,6,7]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,4,3,5,2,7,6]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>{{1,2},{3,5,6},{4},{7}}
[1,4,3,5,6,2,7]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,3,5,6,7,2]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}
[1,4,3,5,7,2,6]=>[5,3,4,2,7,6,1]=>[3,5,4,6,1,2,7]=>{{1,2,3,4,5,6},{7}}
[1,4,3,5,7,6,2]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>{{1,3,4,6},{2,5},{7}}
[1,4,3,6,2,5,7]=>[7,3,4,2,6,5,1]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,4,3,6,2,7,5]=>[3,4,2,6,5,7,1]=>[5,4,6,2,3,1,7]=>{{1,3,5,6},{2,4},{7}}
[1,4,3,6,5,2,7]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,3,6,5,7,2]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>{{1,3,5,6},{2},{4},{7}}
[1,4,3,6,7,2,5]=>[6,3,4,2,7,5,1]=>[2,5,4,6,1,3,7]=>{{1,2,5},{3,4,6},{7}}
[1,4,3,6,7,5,2]=>[6,3,4,2,5,7,1]=>[2,5,4,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,3,7,2,5,6]=>[3,4,2,7,6,5,1]=>[5,4,6,1,2,3,7]=>{{1,2,4,5},{3,6},{7}}
[1,4,3,7,2,6,5]=>[3,4,2,7,5,6,1]=>[5,4,6,1,3,2,7]=>{{1,2,3,4,5,6},{7}}
[1,4,3,7,5,2,6]=>[3,4,2,5,7,6,1]=>[5,4,6,3,1,2,7]=>{{1,5},{2,3,4,6},{7}}
[1,4,3,7,5,6,2]=>[5,7,3,4,2,6,1]=>[3,1,5,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}
[1,4,3,7,6,2,5]=>[3,4,2,6,7,5,1]=>[5,4,6,2,1,3,7]=>{{1,5},{2,4},{3,6},{7}}
[1,4,3,7,6,5,2]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,5,2,3,6,7]=>[7,6,4,2,5,3,1]=>[1,2,4,6,3,5,7]=>{{1},{2},{3,4,5,6},{7}}
[1,4,5,2,3,7,6]=>[6,7,4,2,5,3,1]=>[2,1,4,6,3,5,7]=>{{1,2},{3,4,5,6},{7}}
[1,4,5,2,6,3,7]=>[7,4,2,5,3,6,1]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,4,5,2,6,7,3]=>[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[1,4,5,2,7,3,6]=>[4,2,5,3,7,6,1]=>[4,6,3,5,1,2,7]=>{{1,4,5},{2,6},{3},{7}}
[1,4,5,2,7,6,3]=>[4,2,5,3,6,7,1]=>[4,6,3,5,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[1,4,5,3,2,6,7]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,4,5,3,2,7,6]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>{{1,2},{3,4,6},{5},{7}}
[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,5,3,6,7,2]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,5,3,7,2,6]=>[4,3,5,2,7,6,1]=>[4,5,3,6,1,2,7]=>{{1,2,4,5,6},{3},{7}}
[1,4,5,3,7,6,2]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>{{1,4,6},{2,5},{3},{7}}
[1,4,5,6,2,3,7]=>[7,5,4,2,6,3,1]=>[1,3,4,6,2,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,5,6,2,7,3]=>[5,4,2,6,3,7,1]=>[3,4,6,2,5,1,7]=>{{1,3,6},{2,4},{5},{7}}
[1,4,5,6,3,2,7]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,4,5,6,3,7,2]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>{{1,3,5,6},{2,4},{7}}
[1,4,5,6,7,2,3]=>[6,5,4,2,7,3,1]=>[2,3,4,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[1,4,5,6,7,3,2]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[1,4,5,7,2,3,6]=>[5,4,2,7,6,3,1]=>[3,4,6,1,2,5,7]=>{{1,2,3,4,5,6},{7}}
[1,4,5,7,2,6,3]=>[5,4,2,7,3,6,1]=>[3,4,6,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[1,4,5,7,3,2,6]=>[5,4,2,3,7,6,1]=>[3,4,6,5,1,2,7]=>{{1,2,3,4,5,6},{7}}
[1,4,5,7,3,6,2]=>[5,4,3,7,2,6,1]=>[3,4,5,1,6,2,7]=>{{1,2,3,4,5,6},{7}}
[1,4,5,7,6,2,3]=>[5,4,2,6,7,3,1]=>[3,4,6,2,1,5,7]=>{{1,3,5,6},{2,4},{7}}
[1,4,5,7,6,3,2]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>{{1,3,6},{2,4,5},{7}}
[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>[1,4,6,2,3,5,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,6,2,3,7,5]=>[4,2,6,5,7,3,1]=>[4,6,2,3,1,5,7]=>{{1,2,3,4,5,6},{7}}
[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,4,6,2,5,7,3]=>[4,2,6,5,3,7,1]=>[4,6,2,3,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[1,4,6,2,7,3,5]=>[4,2,6,3,7,5,1]=>[4,6,2,5,1,3,7]=>{{1,4,5},{2,3,6},{7}}
[1,4,6,2,7,5,3]=>[4,2,6,3,5,7,1]=>[4,6,2,5,3,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,6,3,2,5,7]=>[7,4,2,3,6,5,1]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,4,6,3,2,7,5]=>[4,2,3,6,5,7,1]=>[4,6,5,2,3,1,7]=>{{1,2,4,6},{3,5},{7}}
[1,4,6,3,5,2,7]=>[7,4,3,6,2,5,1]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,6,3,5,7,2]=>[4,3,6,5,2,7,1]=>[4,5,2,3,6,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,6,3,7,2,5]=>[4,3,6,2,7,5,1]=>[4,5,2,6,1,3,7]=>{{1,2,3,4,5,6},{7}}
[1,4,6,3,7,5,2]=>[4,3,6,2,5,7,1]=>[4,5,2,6,3,1,7]=>{{1,4,6},{2,3,5},{7}}
[1,4,6,5,2,3,7]=>[7,4,2,5,6,3,1]=>[1,4,6,3,2,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,6,5,2,7,3]=>[4,2,5,6,3,7,1]=>[4,6,3,2,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,4,6,5,3,7,2]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>{{1,2,4,5,6},{3},{7}}
[1,4,6,5,7,2,3]=>[5,6,4,2,7,3,1]=>[3,2,4,6,1,5,7]=>{{1,3,4,5,6},{2},{7}}
[1,4,6,5,7,3,2]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>{{1,3,4,6},{2},{5},{7}}
[1,4,6,7,2,3,5]=>[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>{{1,2,4},{3,5,6},{7}}
[1,4,6,7,2,5,3]=>[6,4,2,7,3,5,1]=>[2,4,6,1,5,3,7]=>{{1,2,4},{3,6},{5},{7}}
[1,4,6,7,3,2,5]=>[6,4,2,3,7,5,1]=>[2,4,6,5,1,3,7]=>{{1,2,4,5},{3,6},{7}}
[1,4,6,7,3,5,2]=>[6,4,3,7,2,5,1]=>[2,4,5,1,6,3,7]=>{{1,2,4},{3,5,6},{7}}
[1,4,6,7,5,2,3]=>[6,4,2,5,7,3,1]=>[2,4,6,3,1,5,7]=>{{1,2,3,4,5,6},{7}}
[1,4,6,7,5,3,2]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,2,3,5,6]=>[4,2,7,6,5,3,1]=>[4,6,1,2,3,5,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,2,3,6,5]=>[4,2,7,5,6,3,1]=>[4,6,1,3,2,5,7]=>{{1,3,4},{2,5,6},{7}}
[1,4,7,2,5,3,6]=>[4,2,7,6,3,5,1]=>[4,6,1,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[1,4,7,2,5,6,3]=>[4,2,7,5,3,6,1]=>[4,6,1,3,5,2,7]=>{{1,3,4},{2,6},{5},{7}}
[1,4,7,2,6,3,5]=>[4,2,7,3,6,5,1]=>[4,6,1,5,2,3,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,2,6,5,3]=>[4,2,7,3,5,6,1]=>[4,6,1,5,3,2,7]=>{{1,3,4,5},{2,6},{7}}
[1,4,7,3,2,5,6]=>[4,2,3,7,6,5,1]=>[4,6,5,1,2,3,7]=>{{1,4},{2,3,5,6},{7}}
[1,4,7,3,2,6,5]=>[4,2,3,7,5,6,1]=>[4,6,5,1,3,2,7]=>{{1,4},{2,6},{3,5},{7}}
[1,4,7,3,5,2,6]=>[4,3,7,6,2,5,1]=>[4,5,1,2,6,3,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,3,5,6,2]=>[4,3,7,5,2,6,1]=>[4,5,1,3,6,2,7]=>{{1,3,4},{2,5,6},{7}}
[1,4,7,3,6,2,5]=>[4,3,7,2,6,5,1]=>[4,5,1,6,2,3,7]=>{{1,3,4,6},{2,5},{7}}
[1,4,7,3,6,5,2]=>[4,3,7,2,5,6,1]=>[4,5,1,6,3,2,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,5,2,3,6]=>[4,2,5,7,6,3,1]=>[4,6,3,1,2,5,7]=>{{1,4},{2,5,6},{3},{7}}
[1,4,7,5,2,6,3]=>[4,2,5,7,3,6,1]=>[4,6,3,1,5,2,7]=>{{1,4},{2,6},{3},{5},{7}}
[1,4,7,5,3,2,6]=>[4,2,3,5,7,6,1]=>[4,6,5,3,1,2,7]=>{{1,3,4,5},{2,6},{7}}
[1,4,7,5,3,6,2]=>[4,3,5,7,2,6,1]=>[4,5,3,1,6,2,7]=>{{1,4},{2,5,6},{3},{7}}
[1,4,7,5,6,2,3]=>[5,7,4,2,6,3,1]=>[3,1,4,6,2,5,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,5,6,3,2]=>[5,7,4,2,3,6,1]=>[3,1,4,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[1,4,7,6,2,3,5]=>[4,2,6,7,5,3,1]=>[4,6,2,1,3,5,7]=>{{1,4},{2,3,5,6},{7}}
[1,4,7,6,2,5,3]=>[4,2,6,7,3,5,1]=>[4,6,2,1,5,3,7]=>{{1,4},{2,3,6},{5},{7}}
[1,4,7,6,3,2,5]=>[4,2,3,6,7,5,1]=>[4,6,5,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[1,4,7,6,3,5,2]=>[4,3,6,7,2,5,1]=>[4,5,2,1,6,3,7]=>{{1,4},{2,3,5,6},{7}}
[1,4,7,6,5,2,3]=>[4,2,5,6,7,3,1]=>[4,6,3,2,1,5,7]=>{{1,2,4,5,6},{3},{7}}
[1,4,7,6,5,3,2]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,2,3,4,6,7]=>[7,6,2,5,4,3,1]=>[1,2,6,3,4,5,7]=>{{1},{2},{3,4,5,6},{7}}
[1,5,2,3,4,7,6]=>[6,7,2,5,4,3,1]=>[2,1,6,3,4,5,7]=>{{1,2},{3,4,5,6},{7}}
[1,5,2,3,6,4,7]=>[7,2,5,4,6,3,1]=>[1,6,3,4,2,5,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,2,3,6,7,4]=>[6,2,5,4,7,3,1]=>[2,6,3,4,1,5,7]=>{{1,2,5,6},{3},{4},{7}}
[1,5,2,3,7,4,6]=>[2,5,4,7,6,3,1]=>[6,3,4,1,2,5,7]=>{{1,2,3,4,5,6},{7}}
[1,5,2,3,7,6,4]=>[2,5,4,6,7,3,1]=>[6,3,4,2,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[1,5,2,4,3,6,7]=>[7,6,2,5,3,4,1]=>[1,2,6,3,5,4,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,5,2,4,3,7,6]=>[6,7,2,5,3,4,1]=>[2,1,6,3,5,4,7]=>{{1,2},{3,4,6},{5},{7}}
[1,5,2,4,6,3,7]=>[7,2,5,4,3,6,1]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,5,2,4,6,7,3]=>[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>{{1,2,6},{3},{4},{5},{7}}
[1,5,2,4,7,3,6]=>[2,5,4,3,7,6,1]=>[6,3,4,5,1,2,7]=>{{1,2,3,4,5,6},{7}}
[1,5,2,4,7,6,3]=>[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>{{1,6},{2,3,4,5},{7}}
[1,5,2,6,3,4,7]=>[7,2,5,3,6,4,1]=>[1,6,3,5,2,4,7]=>{{1},{2,4,5,6},{3},{7}}
[1,5,2,6,3,7,4]=>[2,5,3,6,4,7,1]=>[6,3,5,2,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[1,5,2,6,4,3,7]=>[7,2,5,3,4,6,1]=>[1,6,3,5,4,2,7]=>{{1},{2,6},{3},{4,5},{7}}
[1,5,2,6,4,7,3]=>[2,5,4,6,3,7,1]=>[6,3,4,2,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[1,5,2,6,7,3,4]=>[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>{{1,2,4,5,6},{3},{7}}
[1,5,2,6,7,4,3]=>[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>{{1,2,6},{3},{4,5},{7}}
[1,5,2,7,3,4,6]=>[2,5,3,7,6,4,1]=>[6,3,5,1,2,4,7]=>{{1,4,6},{2,3,5},{7}}
[1,5,2,7,3,6,4]=>[2,5,3,7,4,6,1]=>[6,3,5,1,4,2,7]=>{{1,2,3,4,5,6},{7}}
[1,5,2,7,4,3,6]=>[2,5,3,4,7,6,1]=>[6,3,5,4,1,2,7]=>{{1,2,3,5,6},{4},{7}}
[1,5,2,7,4,6,3]=>[2,5,4,7,3,6,1]=>[6,3,4,1,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[1,5,2,7,6,3,4]=>[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,2,7,6,4,3]=>[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>{{1,6},{2,3,5},{4},{7}}
[1,5,3,2,4,6,7]=>[7,6,2,3,5,4,1]=>[1,2,6,5,3,4,7]=>{{1},{2},{3,4,5,6},{7}}
[1,5,3,2,4,7,6]=>[6,7,2,3,5,4,1]=>[2,1,6,5,3,4,7]=>{{1,2},{3,4,5,6},{7}}
[1,5,3,2,6,4,7]=>[7,2,3,5,4,6,1]=>[1,6,5,3,4,2,7]=>{{1},{2,6},{3,4,5},{7}}
[1,5,3,2,6,7,4]=>[6,2,3,5,4,7,1]=>[2,6,5,3,4,1,7]=>{{1,2,6},{3,4,5},{7}}
[1,5,3,2,7,4,6]=>[2,3,5,4,7,6,1]=>[6,5,3,4,1,2,7]=>{{1,2,5,6},{3},{4},{7}}
[1,5,3,2,7,6,4]=>[2,3,5,4,6,7,1]=>[6,5,3,4,2,1,7]=>{{1,6},{2,5},{3},{4},{7}}
[1,5,3,4,2,6,7]=>[7,6,3,5,2,4,1]=>[1,2,5,3,6,4,7]=>{{1},{2},{3,4,5,6},{7}}
[1,5,3,4,2,7,6]=>[6,7,3,5,2,4,1]=>[2,1,5,3,6,4,7]=>{{1,2},{3,4,5,6},{7}}
[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,5,3,4,6,7,2]=>[6,3,5,4,2,7,1]=>[2,5,3,4,6,1,7]=>{{1,2,5,6},{3},{4},{7}}
[1,5,3,4,7,2,6]=>[3,5,4,2,7,6,1]=>[5,3,4,6,1,2,7]=>{{1,5},{2,3,4,6},{7}}
[1,5,3,4,7,6,2]=>[3,5,4,2,6,7,1]=>[5,3,4,6,2,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,5,3,6,2,7,4]=>[3,5,2,6,4,7,1]=>[5,3,6,2,4,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,5,3,6,4,7,2]=>[3,5,4,6,2,7,1]=>[5,3,4,2,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[1,5,3,6,7,2,4]=>[6,3,5,2,7,4,1]=>[2,5,3,6,1,4,7]=>{{1,2,5},{3},{4,6},{7}}
[1,5,3,6,7,4,2]=>[6,3,5,2,4,7,1]=>[2,5,3,6,4,1,7]=>{{1,2,4,5,6},{3},{7}}
[1,5,3,7,2,4,6]=>[3,5,2,7,6,4,1]=>[5,3,6,1,2,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,3,7,2,6,4]=>[3,5,2,7,4,6,1]=>[5,3,6,1,4,2,7]=>{{1,4,5},{2,3,6},{7}}
[1,5,3,7,4,2,6]=>[3,5,2,4,7,6,1]=>[5,3,6,4,1,2,7]=>{{1,5},{2,3,6},{4},{7}}
[1,5,3,7,4,6,2]=>[3,5,4,7,2,6,1]=>[5,3,4,1,6,2,7]=>{{1,2,3,4,5,6},{7}}
[1,5,3,7,6,2,4]=>[3,5,2,6,7,4,1]=>[5,3,6,2,1,4,7]=>{{1,5},{2,3,4,6},{7}}
[1,5,3,7,6,4,2]=>[3,5,2,4,6,7,1]=>[5,3,6,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}
[1,5,4,2,3,6,7]=>[7,6,2,4,5,3,1]=>[1,2,6,4,3,5,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,5,4,2,3,7,6]=>[6,7,2,4,5,3,1]=>[2,1,6,4,3,5,7]=>{{1,2},{3,5,6},{4},{7}}
[1,5,4,2,6,3,7]=>[7,2,4,5,3,6,1]=>[1,6,4,3,5,2,7]=>{{1},{2,6},{3,4},{5},{7}}
[1,5,4,2,6,7,3]=>[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>{{1,2,6},{3,4},{5},{7}}
[1,5,4,2,7,3,6]=>[2,4,5,3,7,6,1]=>[6,4,3,5,1,2,7]=>{{1,2,4,5,6},{3},{7}}
[1,5,4,2,7,6,3]=>[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>{{1,6},{2,4,5},{3},{7}}
[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>{{1},{2},{3,6},{4,5},{7}}
[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>{{1,2},{3,6},{4,5},{7}}
[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>{{1},{2,5,6},{3,4},{7}}
[1,5,4,3,6,7,2]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>{{1,2,5,6},{3,4},{7}}
[1,5,4,3,7,2,6]=>[3,4,5,2,7,6,1]=>[5,4,3,6,1,2,7]=>{{1,5},{2,4,6},{3},{7}}
[1,5,4,3,7,6,2]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>{{1,2,4,5,6},{3},{7}}
[1,5,4,6,2,3,7]=>[7,4,5,2,6,3,1]=>[1,4,3,6,2,5,7]=>{{1},{2,4,5,6},{3},{7}}
[1,5,4,6,2,7,3]=>[4,5,2,6,3,7,1]=>[4,3,6,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[1,5,4,6,3,2,7]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,5,4,6,3,7,2]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,4,6,7,2,3]=>[6,4,5,2,7,3,1]=>[2,4,3,6,1,5,7]=>{{1,2,4,5,6},{3},{7}}
[1,5,4,6,7,3,2]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>{{1,2,4,6},{3},{5},{7}}
[1,5,4,7,2,3,6]=>[4,5,2,7,6,3,1]=>[4,3,6,1,2,5,7]=>{{1,4},{2,3,5,6},{7}}
[1,5,4,7,2,6,3]=>[4,5,2,7,3,6,1]=>[4,3,6,1,5,2,7]=>{{1,4},{2,3,6},{5},{7}}
[1,5,4,7,3,2,6]=>[4,5,2,3,7,6,1]=>[4,3,6,5,1,2,7]=>{{1,4,5},{2,3,6},{7}}
[1,5,4,7,3,6,2]=>[4,5,3,7,2,6,1]=>[4,3,5,1,6,2,7]=>{{1,4},{2,3,5,6},{7}}
[1,5,4,7,6,2,3]=>[4,5,2,6,7,3,1]=>[4,3,6,2,1,5,7]=>{{1,2,3,4,5,6},{7}}
[1,5,4,7,6,3,2]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,2,3,4,7]=>[7,5,2,6,4,3,1]=>[1,3,6,2,4,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,6,2,3,7,4]=>[5,2,6,4,7,3,1]=>[3,6,2,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}
[1,5,6,2,4,3,7]=>[7,5,2,6,3,4,1]=>[1,3,6,2,5,4,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,2,4,7,3]=>[5,2,6,4,3,7,1]=>[3,6,2,4,5,1,7]=>{{1,2,3,6},{4},{5},{7}}
[1,5,6,2,7,3,4]=>[5,2,6,3,7,4,1]=>[3,6,2,5,1,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,2,7,4,3]=>[5,2,6,3,4,7,1]=>[3,6,2,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[1,5,6,3,2,4,7]=>[7,5,2,3,6,4,1]=>[1,3,6,5,2,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,6,3,2,7,4]=>[5,2,3,6,4,7,1]=>[3,6,5,2,4,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,3,4,2,7]=>[7,5,3,6,2,4,1]=>[1,3,5,2,6,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,5,6,3,4,7,2]=>[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>{{1,2,3,5,6},{4},{7}}
[1,5,6,3,7,2,4]=>[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>{{1,2,3,5},{4,6},{7}}
[1,5,6,3,7,4,2]=>[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,4,2,3,7]=>[7,5,2,4,6,3,1]=>[1,3,6,4,2,5,7]=>{{1},{2,3,5,6},{4},{7}}
[1,5,6,4,2,7,3]=>[5,2,4,6,3,7,1]=>[3,6,4,2,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[1,5,6,4,3,2,7]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>{{1},{2,3,6},{4,5},{7}}
[1,5,6,4,3,7,2]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,4,7,2,3]=>[5,4,6,2,7,3,1]=>[3,4,2,6,1,5,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,4,7,3,2]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>{{1,2,3,4,6},{5},{7}}
[1,5,6,7,2,3,4]=>[6,5,2,7,4,3,1]=>[2,3,6,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,7,2,4,3]=>[6,5,2,7,3,4,1]=>[2,3,6,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[1,5,6,7,3,2,4]=>[6,5,2,3,7,4,1]=>[2,3,6,5,1,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,7,3,4,2]=>[6,5,3,7,2,4,1]=>[2,3,5,1,6,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,6,7,4,2,3]=>[6,5,2,4,7,3,1]=>[2,3,6,4,1,5,7]=>{{1,2,3,5,6},{4},{7}}
[1,5,6,7,4,3,2]=>[6,5,2,3,4,7,1]=>[2,3,6,5,4,1,7]=>{{1,2,3,6},{4,5},{7}}
[1,5,7,2,3,4,6]=>[5,2,7,6,4,3,1]=>[3,6,1,2,4,5,7]=>{{1,3},{2,4,5,6},{7}}
[1,5,7,2,3,6,4]=>[5,2,7,4,6,3,1]=>[3,6,1,4,2,5,7]=>{{1,3},{2,5,6},{4},{7}}
[1,5,7,2,4,3,6]=>[5,2,7,6,3,4,1]=>[3,6,1,2,5,4,7]=>{{1,3},{2,4,6},{5},{7}}
[1,5,7,2,4,6,3]=>[5,2,7,4,3,6,1]=>[3,6,1,4,5,2,7]=>{{1,3},{2,6},{4},{5},{7}}
[1,5,7,2,6,3,4]=>[5,2,7,3,6,4,1]=>[3,6,1,5,2,4,7]=>{{1,3},{2,4,5,6},{7}}
[1,5,7,2,6,4,3]=>[5,2,7,3,4,6,1]=>[3,6,1,5,4,2,7]=>{{1,3},{2,6},{4,5},{7}}
[1,5,7,3,2,4,6]=>[5,2,3,7,6,4,1]=>[3,6,5,1,2,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,7,3,2,6,4]=>[5,2,3,7,4,6,1]=>[3,6,5,1,4,2,7]=>{{1,3,4,5},{2,6},{7}}
[1,5,7,3,4,2,6]=>[5,3,7,6,2,4,1]=>[3,5,1,2,6,4,7]=>{{1,3},{2,4,5,6},{7}}
[1,5,7,3,4,6,2]=>[5,3,7,4,2,6,1]=>[3,5,1,4,6,2,7]=>{{1,3},{2,5,6},{4},{7}}
[1,5,7,3,6,2,4]=>[5,3,7,2,6,4,1]=>[3,5,1,6,2,4,7]=>{{1,3},{2,5},{4,6},{7}}
[1,5,7,3,6,4,2]=>[5,3,7,2,4,6,1]=>[3,5,1,6,4,2,7]=>{{1,3},{2,4,5,6},{7}}
[1,5,7,4,2,3,6]=>[5,2,4,7,6,3,1]=>[3,6,4,1,2,5,7]=>{{1,3,4},{2,5,6},{7}}
[1,5,7,4,2,6,3]=>[5,2,4,7,3,6,1]=>[3,6,4,1,5,2,7]=>{{1,3,4},{2,6},{5},{7}}
[1,5,7,4,3,2,6]=>[5,2,3,4,7,6,1]=>[3,6,5,4,1,2,7]=>{{1,3,5},{2,6},{4},{7}}
[1,5,7,4,3,6,2]=>[5,3,4,7,2,6,1]=>[3,5,4,1,6,2,7]=>{{1,3,4},{2,5,6},{7}}
[1,5,7,4,6,2,3]=>[5,4,7,2,6,3,1]=>[3,4,1,6,2,5,7]=>{{1,3},{2,4,5,6},{7}}
[1,5,7,4,6,3,2]=>[5,4,7,2,3,6,1]=>[3,4,1,6,5,2,7]=>{{1,3},{2,4,6},{5},{7}}
[1,5,7,6,2,3,4]=>[5,2,6,7,4,3,1]=>[3,6,2,1,4,5,7]=>{{1,2,3,4,5,6},{7}}
[1,5,7,6,2,4,3]=>[5,2,6,7,3,4,1]=>[3,6,2,1,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[1,5,7,6,3,2,4]=>[5,2,3,6,7,4,1]=>[3,6,5,2,1,4,7]=>{{1,3,5},{2,4,6},{7}}
[1,5,7,6,3,4,2]=>[5,3,6,7,2,4,1]=>[3,5,2,1,6,4,7]=>{{1,2,3,4,5,6},{7}}
[1,5,7,6,4,2,3]=>[5,2,4,6,7,3,1]=>[3,6,4,2,1,5,7]=>{{1,2,3,4,5,6},{7}}
[1,5,7,6,4,3,2]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>{{1,2,3,5,6},{4},{7}}
[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[1,6,2,3,4,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,3,4,7,5]=>[2,6,5,7,4,3,1]=>[6,2,3,1,4,5,7]=>{{1,4,5,6},{2},{3},{7}}
[1,6,2,3,5,4,7]=>[7,2,6,4,5,3,1]=>[1,6,2,4,3,5,7]=>{{1},{2,3,5,6},{4},{7}}
[1,6,2,3,5,7,4]=>[2,6,5,4,7,3,1]=>[6,2,3,4,1,5,7]=>{{1,5,6},{2},{3},{4},{7}}
[1,6,2,3,7,4,5]=>[2,6,4,7,5,3,1]=>[6,2,4,1,3,5,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,2,3,7,5,4]=>[2,6,4,5,7,3,1]=>[6,2,4,3,1,5,7]=>{{1,5,6},{2},{3,4},{7}}
[1,6,2,4,3,5,7]=>[7,2,6,5,3,4,1]=>[1,6,2,3,5,4,7]=>{{1},{2,3,4,6},{5},{7}}
[1,6,2,4,3,7,5]=>[2,6,5,7,3,4,1]=>[6,2,3,1,5,4,7]=>{{1,4,6},{2},{3},{5},{7}}
[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>[1,6,2,4,5,3,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,6,2,4,5,7,3]=>[2,6,5,4,3,7,1]=>[6,2,3,4,5,1,7]=>{{1,6},{2},{3},{4},{5},{7}}
[1,6,2,4,7,3,5]=>[2,6,4,3,7,5,1]=>[6,2,4,5,1,3,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,2,4,7,5,3]=>[2,6,4,3,5,7,1]=>[6,2,4,5,3,1,7]=>{{1,6},{2},{3,4,5},{7}}
[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[1,6,2,5,3,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,5,3,7,4]=>[2,6,3,5,4,7,1]=>[6,2,5,3,4,1,7]=>{{1,6},{2},{3,4,5},{7}}
[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[1,6,2,5,4,3,7]=>{{1},{2,3,6},{4,5},{7}}
[1,6,2,5,4,7,3]=>[2,6,4,5,3,7,1]=>[6,2,4,3,5,1,7]=>{{1,6},{2},{3,4},{5},{7}}
[1,6,2,5,7,3,4]=>[2,6,5,3,7,4,1]=>[6,2,3,5,1,4,7]=>{{1,4,5,6},{2},{3},{7}}
[1,6,2,5,7,4,3]=>[2,6,5,3,4,7,1]=>[6,2,3,5,4,1,7]=>{{1,6},{2},{3},{4,5},{7}}
[1,6,2,7,3,4,5]=>[2,6,3,7,5,4,1]=>[6,2,5,1,3,4,7]=>{{1,4,6},{2},{3,5},{7}}
[1,6,2,7,3,5,4]=>[2,6,3,7,4,5,1]=>[6,2,5,1,4,3,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,2,7,4,3,5]=>[2,6,3,4,7,5,1]=>[6,2,5,4,1,3,7]=>{{1,3,5,6},{2},{4},{7}}
[1,6,2,7,4,5,3]=>[2,6,4,7,3,5,1]=>[6,2,4,1,5,3,7]=>{{1,3,4,6},{2},{5},{7}}
[1,6,2,7,5,3,4]=>[2,6,3,5,7,4,1]=>[6,2,5,3,1,4,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,2,7,5,4,3]=>[2,6,3,4,5,7,1]=>[6,2,5,4,3,1,7]=>{{1,6},{2},{3,5},{4},{7}}
[1,6,3,2,4,5,7]=>[7,2,3,6,5,4,1]=>[1,6,5,2,3,4,7]=>{{1},{2,4,6},{3,5},{7}}
[1,6,3,2,4,7,5]=>[2,3,6,5,7,4,1]=>[6,5,2,3,1,4,7]=>{{1,2,3,4,5,6},{7}}
[1,6,3,2,5,4,7]=>[7,2,3,6,4,5,1]=>[1,6,5,2,4,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,2,5,7,4]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,1,7]=>{{1,6},{2,3,4,5},{7}}
[1,6,3,2,7,4,5]=>[2,3,6,4,7,5,1]=>[6,5,2,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}
[1,6,3,2,7,5,4]=>[2,3,6,4,5,7,1]=>[6,5,2,4,3,1,7]=>{{1,6},{2,3,5},{4},{7}}
[1,6,3,4,2,5,7]=>[7,3,6,5,2,4,1]=>[1,5,2,3,6,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,4,2,7,5]=>[3,6,5,7,2,4,1]=>[5,2,3,1,6,4,7]=>{{1,4,5,6},{2},{3},{7}}
[1,6,3,4,5,2,7]=>[7,3,6,4,2,5,1]=>[1,5,2,4,6,3,7]=>{{1},{2,3,5,6},{4},{7}}
[1,6,3,4,5,7,2]=>[3,6,5,4,2,7,1]=>[5,2,3,4,6,1,7]=>{{1,5,6},{2},{3},{4},{7}}
[1,6,3,4,7,2,5]=>[3,6,4,2,7,5,1]=>[5,2,4,6,1,3,7]=>{{1,5},{2},{3,4,6},{7}}
[1,6,3,4,7,5,2]=>[3,6,4,2,5,7,1]=>[5,2,4,6,3,1,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,3,5,2,4,7]=>[7,3,6,2,5,4,1]=>[1,5,2,6,3,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,6,3,5,2,7,4]=>[3,6,2,5,4,7,1]=>[5,2,6,3,4,1,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,3,5,4,2,7]=>[7,3,6,2,4,5,1]=>[1,5,2,6,4,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,5,4,7,2]=>[3,6,4,5,2,7,1]=>[5,2,4,3,6,1,7]=>{{1,5,6},{2},{3,4},{7}}
[1,6,3,5,7,2,4]=>[3,6,5,2,7,4,1]=>[5,2,3,6,1,4,7]=>{{1,5},{2},{3},{4,6},{7}}
[1,6,3,5,7,4,2]=>[3,6,5,2,4,7,1]=>[5,2,3,6,4,1,7]=>{{1,4,5,6},{2},{3},{7}}
[1,6,3,7,2,4,5]=>[3,6,2,7,5,4,1]=>[5,2,6,1,3,4,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,3,7,2,5,4]=>[3,6,2,7,4,5,1]=>[5,2,6,1,4,3,7]=>{{1,4,5},{2},{3,6},{7}}
[1,6,3,7,4,2,5]=>[3,6,2,4,7,5,1]=>[5,2,6,4,1,3,7]=>{{1,5},{2},{3,6},{4},{7}}
[1,6,3,7,4,5,2]=>[3,6,4,7,2,5,1]=>[5,2,4,1,6,3,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,3,7,5,2,4]=>[3,6,2,5,7,4,1]=>[5,2,6,3,1,4,7]=>{{1,5},{2},{3,4,6},{7}}
[1,6,3,7,5,4,2]=>[3,6,2,4,5,7,1]=>[5,2,6,4,3,1,7]=>{{1,3,5,6},{2},{4},{7}}
[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[1,6,4,2,3,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,2,3,7,5]=>[2,4,6,5,7,3,1]=>[6,4,2,3,1,5,7]=>{{1,5,6},{2,3,4},{7}}
[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>[1,6,4,2,5,3,7]=>{{1},{2,3,4,6},{5},{7}}
[1,6,4,2,5,7,3]=>[2,4,6,5,3,7,1]=>[6,4,2,3,5,1,7]=>{{1,6},{2,3,4},{5},{7}}
[1,6,4,2,7,3,5]=>[2,4,6,3,7,5,1]=>[6,4,2,5,1,3,7]=>{{1,2,3,4,5,6},{7}}
[1,6,4,2,7,5,3]=>[2,4,6,3,5,7,1]=>[6,4,2,5,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[1,6,4,3,2,5,7]=>[7,2,3,4,6,5,1]=>[1,6,5,4,2,3,7]=>{{1},{2,3,5,6},{4},{7}}
[1,6,4,3,2,7,5]=>[2,3,4,6,5,7,1]=>[6,5,4,2,3,1,7]=>{{1,6},{2,3,4,5},{7}}
[1,6,4,3,5,2,7]=>[7,3,4,6,2,5,1]=>[1,5,4,2,6,3,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,3,5,7,2]=>[3,4,6,5,2,7,1]=>[5,4,2,3,6,1,7]=>{{1,5,6},{2,3,4},{7}}
[1,6,4,3,7,2,5]=>[3,4,6,2,7,5,1]=>[5,4,2,6,1,3,7]=>{{1,5},{2,3,4,6},{7}}
[1,6,4,3,7,5,2]=>[3,4,6,2,5,7,1]=>[5,4,2,6,3,1,7]=>{{1,2,3,4,5,6},{7}}
[1,6,4,5,2,3,7]=>[7,4,6,2,5,3,1]=>[1,4,2,6,3,5,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,5,2,7,3]=>[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>{{1,3,4,6},{2},{5},{7}}
[1,6,4,5,3,2,7]=>[7,4,6,2,3,5,1]=>[1,4,2,6,5,3,7]=>{{1},{2,3,4,6},{5},{7}}
[1,6,4,5,3,7,2]=>[4,6,3,5,2,7,1]=>[4,2,5,3,6,1,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,4,5,7,2,3]=>[4,6,5,2,7,3,1]=>[4,2,3,6,1,5,7]=>{{1,4,5,6},{2},{3},{7}}
[1,6,4,5,7,3,2]=>[4,6,5,2,3,7,1]=>[4,2,3,6,5,1,7]=>{{1,4,6},{2},{3},{5},{7}}
[1,6,4,7,2,3,5]=>[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>{{1,4},{2},{3,5,6},{7}}
[1,6,4,7,2,5,3]=>[4,6,2,7,3,5,1]=>[4,2,6,1,5,3,7]=>{{1,4},{2},{3,6},{5},{7}}
[1,6,4,7,3,2,5]=>[4,6,2,3,7,5,1]=>[4,2,6,5,1,3,7]=>{{1,4,5},{2},{3,6},{7}}
[1,6,4,7,3,5,2]=>[4,6,3,7,2,5,1]=>[4,2,5,1,6,3,7]=>{{1,4},{2},{3,5,6},{7}}
[1,6,4,7,5,2,3]=>[4,6,2,5,7,3,1]=>[4,2,6,3,1,5,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,4,7,5,3,2]=>[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,5,2,3,4,7]=>[7,2,5,6,4,3,1]=>[1,6,3,2,4,5,7]=>{{1},{2,4,5,6},{3},{7}}
[1,6,5,2,3,7,4]=>[2,5,6,4,7,3,1]=>[6,3,2,4,1,5,7]=>{{1,5,6},{2,3},{4},{7}}
[1,6,5,2,4,3,7]=>[7,2,5,6,3,4,1]=>[1,6,3,2,5,4,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,6,5,2,4,7,3]=>[2,5,6,4,3,7,1]=>[6,3,2,4,5,1,7]=>{{1,6},{2,3},{4},{5},{7}}
[1,6,5,2,7,3,4]=>[2,5,6,3,7,4,1]=>[6,3,2,5,1,4,7]=>{{1,4,5,6},{2,3},{7}}
[1,6,5,2,7,4,3]=>[2,5,6,3,4,7,1]=>[6,3,2,5,4,1,7]=>{{1,6},{2,3},{4,5},{7}}
[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[1,6,5,3,2,4,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,3,2,7,4]=>[2,3,5,6,4,7,1]=>[6,5,3,2,4,1,7]=>{{1,6},{2,4,5},{3},{7}}
[1,6,5,3,4,2,7]=>[7,3,5,6,2,4,1]=>[1,5,3,2,6,4,7]=>{{1},{2,4,5,6},{3},{7}}
[1,6,5,3,4,7,2]=>[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>{{1,5,6},{2,3},{4},{7}}
[1,6,5,3,7,2,4]=>[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>{{1,5},{2,3},{4,6},{7}}
[1,6,5,3,7,4,2]=>[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>{{1,4,5,6},{2,3},{7}}
[1,6,5,4,2,3,7]=>[7,2,4,5,6,3,1]=>[1,6,4,3,2,5,7]=>{{1},{2,5,6},{3,4},{7}}
[1,6,5,4,2,7,3]=>[2,4,5,6,3,7,1]=>[6,4,3,2,5,1,7]=>{{1,6},{2,4},{3},{5},{7}}
[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>{{1},{2,6},{3,5},{4},{7}}
[1,6,5,4,3,7,2]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>{{1,5,6},{2,4},{3},{7}}
[1,6,5,4,7,2,3]=>[4,5,6,2,7,3,1]=>[4,3,2,6,1,5,7]=>{{1,4,5,6},{2,3},{7}}
[1,6,5,4,7,3,2]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>{{1,4,6},{2,3},{5},{7}}
[1,6,5,7,2,3,4]=>[5,6,2,7,4,3,1]=>[3,2,6,1,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,5,7,2,4,3]=>[5,6,2,7,3,4,1]=>[3,2,6,1,5,4,7]=>{{1,3,4,6},{2},{5},{7}}
[1,6,5,7,3,2,4]=>[5,6,2,3,7,4,1]=>[3,2,6,5,1,4,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,5,7,3,4,2]=>[5,6,3,7,2,4,1]=>[3,2,5,1,6,4,7]=>{{1,3,4,5,6},{2},{7}}
[1,6,5,7,4,2,3]=>[5,6,2,4,7,3,1]=>[3,2,6,4,1,5,7]=>{{1,3,5,6},{2},{4},{7}}
[1,6,5,7,4,3,2]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>{{1,3,6},{2},{4,5},{7}}
[1,6,7,2,3,4,5]=>[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,2,3,5,4]=>[6,2,7,4,5,3,1]=>[2,6,1,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}
[1,6,7,2,4,3,5]=>[6,2,7,5,3,4,1]=>[2,6,1,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[1,6,7,2,4,5,3]=>[6,2,7,4,3,5,1]=>[2,6,1,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}
[1,6,7,2,5,3,4]=>[6,2,7,3,5,4,1]=>[2,6,1,5,3,4,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,2,5,4,3]=>[6,2,7,3,4,5,1]=>[2,6,1,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}
[1,6,7,3,2,4,5]=>[6,2,3,7,5,4,1]=>[2,6,5,1,3,4,7]=>{{1,2,4,6},{3,5},{7}}
[1,6,7,3,2,5,4]=>[6,2,3,7,4,5,1]=>[2,6,5,1,4,3,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,3,4,2,5]=>[6,3,7,5,2,4,1]=>[2,5,1,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,3,4,5,2]=>[6,3,7,4,2,5,1]=>[2,5,1,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}
[1,6,7,3,5,2,4]=>[6,3,7,2,5,4,1]=>[2,5,1,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}
[1,6,7,3,5,4,2]=>[6,3,7,2,4,5,1]=>[2,5,1,6,4,3,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,4,2,3,5]=>[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,4,2,5,3]=>[6,2,4,7,3,5,1]=>[2,6,4,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[1,6,7,4,3,2,5]=>[6,2,3,4,7,5,1]=>[2,6,5,4,1,3,7]=>{{1,2,3,5,6},{4},{7}}
[1,6,7,4,3,5,2]=>[6,3,4,7,2,5,1]=>[2,5,4,1,6,3,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,4,5,2,3]=>[6,4,7,2,5,3,1]=>[2,4,1,6,3,5,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,4,5,3,2]=>[6,4,7,2,3,5,1]=>[2,4,1,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[1,6,7,5,2,3,4]=>[6,2,5,7,4,3,1]=>[2,6,3,1,4,5,7]=>{{1,2,4,5,6},{3},{7}}
[1,6,7,5,2,4,3]=>[6,2,5,7,3,4,1]=>[2,6,3,1,5,4,7]=>{{1,2,4,6},{3},{5},{7}}
[1,6,7,5,3,2,4]=>[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>{{1,2,3,4,5,6},{7}}
[1,6,7,5,3,4,2]=>[6,3,5,7,2,4,1]=>[2,5,3,1,6,4,7]=>{{1,2,4,5,6},{3},{7}}
[1,6,7,5,4,2,3]=>[6,2,4,5,7,3,1]=>[2,6,4,3,1,5,7]=>{{1,2,5,6},{3,4},{7}}
[1,6,7,5,4,3,2]=>[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>{{1,2,6},{3,5},{4},{7}}
[1,7,2,3,4,5,6]=>[2,7,6,5,4,3,1]=>[6,1,2,3,4,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,2,3,4,6,5]=>[2,7,5,6,4,3,1]=>[6,1,3,2,4,5,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,2,3,5,4,6]=>[2,7,6,4,5,3,1]=>[6,1,2,4,3,5,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,2,3,5,6,4]=>[2,7,5,4,6,3,1]=>[6,1,3,4,2,5,7]=>{{1,2,5,6},{3},{4},{7}}
[1,7,2,3,6,4,5]=>[2,7,4,6,5,3,1]=>[6,1,4,2,3,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,2,3,6,5,4]=>[2,7,4,5,6,3,1]=>[6,1,4,3,2,5,7]=>{{1,2,5,6},{3,4},{7}}
[1,7,2,4,3,5,6]=>[2,7,6,5,3,4,1]=>[6,1,2,3,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,2,4,3,6,5]=>[2,7,5,6,3,4,1]=>[6,1,3,2,5,4,7]=>{{1,2,4,6},{3},{5},{7}}
[1,7,2,4,5,3,6]=>[2,7,6,4,3,5,1]=>[6,1,2,4,5,3,7]=>{{1,2,3,6},{4},{5},{7}}
[1,7,2,4,5,6,3]=>[2,7,5,4,3,6,1]=>[6,1,3,4,5,2,7]=>{{1,2,6},{3},{4},{5},{7}}
[1,7,2,4,6,3,5]=>[2,7,4,3,6,5,1]=>[6,1,4,5,2,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,2,4,6,5,3]=>[2,7,4,3,5,6,1]=>[6,1,4,5,3,2,7]=>{{1,2,6},{3,4,5},{7}}
[1,7,2,5,3,4,6]=>[2,7,6,3,5,4,1]=>[6,1,2,5,3,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,2,5,3,6,4]=>[2,7,3,5,4,6,1]=>[6,1,5,3,4,2,7]=>{{1,2,6},{3,4,5},{7}}
[1,7,2,5,4,3,6]=>[2,7,6,3,4,5,1]=>[6,1,2,5,4,3,7]=>{{1,2,3,6},{4,5},{7}}
[1,7,2,5,4,6,3]=>[2,7,4,5,3,6,1]=>[6,1,4,3,5,2,7]=>{{1,2,6},{3,4},{5},{7}}
[1,7,2,5,6,3,4]=>[2,7,5,3,6,4,1]=>[6,1,3,5,2,4,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,2,5,6,4,3]=>[2,7,5,3,4,6,1]=>[6,1,3,5,4,2,7]=>{{1,2,6},{3},{4,5},{7}}
[1,7,2,6,3,4,5]=>[2,7,3,6,5,4,1]=>[6,1,5,2,3,4,7]=>{{1,2,4,6},{3,5},{7}}
[1,7,2,6,3,5,4]=>[2,7,3,6,4,5,1]=>[6,1,5,2,4,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,2,6,4,3,5]=>[2,7,3,4,6,5,1]=>[6,1,5,4,2,3,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,2,6,4,5,3]=>[2,7,4,6,3,5,1]=>[6,1,4,2,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,2,6,5,3,4]=>[2,7,3,5,6,4,1]=>[6,1,5,3,2,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,2,6,5,4,3]=>[2,7,3,4,5,6,1]=>[6,1,5,4,3,2,7]=>{{1,2,6},{3,5},{4},{7}}
[1,7,3,2,4,5,6]=>[2,3,7,6,5,4,1]=>[6,5,1,2,3,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,2,4,6,5]=>[2,3,7,5,6,4,1]=>[6,5,1,3,2,4,7]=>{{1,3,4,6},{2,5},{7}}
[1,7,3,2,5,4,6]=>[2,3,7,6,4,5,1]=>[6,5,1,2,4,3,7]=>{{1,3,6},{2,4,5},{7}}
[1,7,3,2,5,6,4]=>[2,3,7,5,4,6,1]=>[6,5,1,3,4,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,2,6,4,5]=>[2,3,7,4,6,5,1]=>[6,5,1,4,2,3,7]=>{{1,3,6},{2,5},{4},{7}}
[1,7,3,2,6,5,4]=>[2,3,7,4,5,6,1]=>[6,5,1,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,3,4,2,5,6]=>[3,7,6,5,2,4,1]=>[5,1,2,3,6,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,4,2,6,5]=>[3,7,5,6,2,4,1]=>[5,1,3,2,6,4,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,3,4,5,2,6]=>[3,7,6,4,2,5,1]=>[5,1,2,4,6,3,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,3,4,5,6,2]=>[3,7,5,4,2,6,1]=>[5,1,3,4,6,2,7]=>{{1,2,5,6},{3},{4},{7}}
[1,7,3,4,6,2,5]=>[3,7,4,2,6,5,1]=>[5,1,4,6,2,3,7]=>{{1,2,5},{3,4,6},{7}}
[1,7,3,4,6,5,2]=>[3,7,4,2,5,6,1]=>[5,1,4,6,3,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,5,2,4,6]=>[3,7,6,2,5,4,1]=>[5,1,2,6,3,4,7]=>{{1,2,3,5},{4,6},{7}}
[1,7,3,5,2,6,4]=>[3,7,2,5,4,6,1]=>[5,1,6,3,4,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,5,4,2,6]=>[3,7,6,2,4,5,1]=>[5,1,2,6,4,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,5,4,6,2]=>[3,7,4,5,2,6,1]=>[5,1,4,3,6,2,7]=>{{1,2,5,6},{3,4},{7}}
[1,7,3,5,6,2,4]=>[3,7,5,2,6,4,1]=>[5,1,3,6,2,4,7]=>{{1,2,5},{3},{4,6},{7}}
[1,7,3,5,6,4,2]=>[3,7,5,2,4,6,1]=>[5,1,3,6,4,2,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,3,6,2,4,5]=>[3,7,2,6,5,4,1]=>[5,1,6,2,3,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,6,2,5,4]=>[3,7,2,6,4,5,1]=>[5,1,6,2,4,3,7]=>{{1,2,4,5},{3,6},{7}}
[1,7,3,6,4,2,5]=>[3,7,2,4,6,5,1]=>[5,1,6,4,2,3,7]=>{{1,2,5},{3,6},{4},{7}}
[1,7,3,6,4,5,2]=>[3,7,4,6,2,5,1]=>[5,1,4,2,6,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,3,6,5,2,4]=>[3,7,2,5,6,4,1]=>[5,1,6,3,2,4,7]=>{{1,2,5},{3,4,6},{7}}
[1,7,3,6,5,4,2]=>[3,7,2,4,5,6,1]=>[5,1,6,4,3,2,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,4,2,3,5,6]=>[2,4,7,6,5,3,1]=>[6,4,1,2,3,5,7]=>{{1,3,5,6},{2,4},{7}}
[1,7,4,2,3,6,5]=>[2,4,7,5,6,3,1]=>[6,4,1,3,2,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,2,5,3,6]=>[2,4,7,6,3,5,1]=>[6,4,1,2,5,3,7]=>{{1,3,6},{2,4},{5},{7}}
[1,7,4,2,5,6,3]=>[2,4,7,5,3,6,1]=>[6,4,1,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,4,2,6,3,5]=>[2,4,7,3,6,5,1]=>[6,4,1,5,2,3,7]=>{{1,3,6},{2,4,5},{7}}
[1,7,4,2,6,5,3]=>[2,4,7,3,5,6,1]=>[6,4,1,5,3,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,3,2,5,6]=>[2,3,4,7,6,5,1]=>[6,5,4,1,2,3,7]=>{{1,3,4,6},{2,5},{7}}
[1,7,4,3,2,6,5]=>[2,3,4,7,5,6,1]=>[6,5,4,1,3,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,3,5,2,6]=>[3,4,7,6,2,5,1]=>[5,4,1,2,6,3,7]=>{{1,3,5,6},{2,4},{7}}
[1,7,4,3,5,6,2]=>[3,4,7,5,2,6,1]=>[5,4,1,3,6,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,3,6,2,5]=>[3,4,7,2,6,5,1]=>[5,4,1,6,2,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,3,6,5,2]=>[3,4,7,2,5,6,1]=>[5,4,1,6,3,2,7]=>{{1,3,5},{2,4,6},{7}}
[1,7,4,5,2,3,6]=>[4,7,6,2,5,3,1]=>[4,1,2,6,3,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,5,2,6,3]=>[4,7,2,5,3,6,1]=>[4,1,6,3,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,4,5,3,2,6]=>[4,7,6,2,3,5,1]=>[4,1,2,6,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,4,5,3,6,2]=>[4,7,3,5,2,6,1]=>[4,1,5,3,6,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,5,6,2,3]=>[4,7,5,2,6,3,1]=>[4,1,3,6,2,5,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,4,5,6,3,2]=>[4,7,5,2,3,6,1]=>[4,1,3,6,5,2,7]=>{{1,2,4,6},{3},{5},{7}}
[1,7,4,6,2,3,5]=>[4,7,2,6,5,3,1]=>[4,1,6,2,3,5,7]=>{{1,2,4},{3,5,6},{7}}
[1,7,4,6,2,5,3]=>[4,7,2,6,3,5,1]=>[4,1,6,2,5,3,7]=>{{1,2,4},{3,6},{5},{7}}
[1,7,4,6,3,2,5]=>[4,7,2,3,6,5,1]=>[4,1,6,5,2,3,7]=>{{1,2,4,5},{3,6},{7}}
[1,7,4,6,3,5,2]=>[4,7,3,6,2,5,1]=>[4,1,5,2,6,3,7]=>{{1,2,4},{3,5,6},{7}}
[1,7,4,6,5,2,3]=>[4,7,2,5,6,3,1]=>[4,1,6,3,2,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,4,6,5,3,2]=>[4,7,2,3,5,6,1]=>[4,1,6,5,3,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,2,3,4,6]=>[2,5,7,6,4,3,1]=>[6,3,1,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,2,3,6,4]=>[2,5,7,4,6,3,1]=>[6,3,1,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,5,2,4,3,6]=>[2,5,7,6,3,4,1]=>[6,3,1,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,5,2,4,6,3]=>[2,5,7,4,3,6,1]=>[6,3,1,4,5,2,7]=>{{1,2,3,6},{4},{5},{7}}
[1,7,5,2,6,3,4]=>[2,5,7,3,6,4,1]=>[6,3,1,5,2,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,2,6,4,3]=>[2,5,7,3,4,6,1]=>[6,3,1,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}
[1,7,5,3,2,4,6]=>[2,3,5,7,6,4,1]=>[6,5,3,1,2,4,7]=>{{1,4,6},{2,5},{3},{7}}
[1,7,5,3,2,6,4]=>[2,3,5,7,4,6,1]=>[6,5,3,1,4,2,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,5,3,4,2,6]=>[3,5,7,6,2,4,1]=>[5,3,1,2,6,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,3,4,6,2]=>[3,5,7,4,2,6,1]=>[5,3,1,4,6,2,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,5,3,6,2,4]=>[3,5,7,2,6,4,1]=>[5,3,1,6,2,4,7]=>{{1,2,3,5},{4,6},{7}}
[1,7,5,3,6,4,2]=>[3,5,7,2,4,6,1]=>[5,3,1,6,4,2,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,4,2,3,6]=>[2,4,5,7,6,3,1]=>[6,4,3,1,2,5,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,5,4,2,6,3]=>[2,4,5,7,3,6,1]=>[6,4,3,1,5,2,7]=>{{1,2,4,6},{3},{5},{7}}
[1,7,5,4,3,2,6]=>[2,3,4,5,7,6,1]=>[6,5,4,3,1,2,7]=>{{1,2,5,6},{3,4},{7}}
[1,7,5,4,3,6,2]=>[3,4,5,7,2,6,1]=>[5,4,3,1,6,2,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,5,4,6,2,3]=>[4,5,7,2,6,3,1]=>[4,3,1,6,2,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,4,6,3,2]=>[4,5,7,2,3,6,1]=>[4,3,1,6,5,2,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,5,6,2,3,4]=>[5,7,2,6,4,3,1]=>[3,1,6,2,4,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,6,2,4,3]=>[5,7,2,6,3,4,1]=>[3,1,6,2,5,4,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,5,6,3,2,4]=>[5,7,2,3,6,4,1]=>[3,1,6,5,2,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,6,3,4,2]=>[5,7,3,6,2,4,1]=>[3,1,5,2,6,4,7]=>{{1,2,3,4,5,6},{7}}
[1,7,5,6,4,2,3]=>[5,7,2,4,6,3,1]=>[3,1,6,4,2,5,7]=>{{1,2,3,5,6},{4},{7}}
[1,7,5,6,4,3,2]=>[5,7,2,3,4,6,1]=>[3,1,6,5,4,2,7]=>{{1,2,3,6},{4,5},{7}}
[1,7,6,2,3,4,5]=>[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>{{1,3,4,5,6},{2},{7}}
[1,7,6,2,3,5,4]=>[2,6,7,4,5,3,1]=>[6,2,1,4,3,5,7]=>{{1,3,5,6},{2},{4},{7}}
[1,7,6,2,4,3,5]=>[2,6,7,5,3,4,1]=>[6,2,1,3,5,4,7]=>{{1,3,4,6},{2},{5},{7}}
[1,7,6,2,4,5,3]=>[2,6,7,4,3,5,1]=>[6,2,1,4,5,3,7]=>{{1,3,6},{2},{4},{5},{7}}
[1,7,6,2,5,3,4]=>[2,6,7,3,5,4,1]=>[6,2,1,5,3,4,7]=>{{1,3,4,5,6},{2},{7}}
[1,7,6,2,5,4,3]=>[2,6,7,3,4,5,1]=>[6,2,1,5,4,3,7]=>{{1,3,6},{2},{4,5},{7}}
[1,7,6,3,2,4,5]=>[2,3,6,7,5,4,1]=>[6,5,2,1,3,4,7]=>{{1,4,6},{2,3,5},{7}}
[1,7,6,3,2,5,4]=>[2,3,6,7,4,5,1]=>[6,5,2,1,4,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,6,3,4,2,5]=>[3,6,7,5,2,4,1]=>[5,2,1,3,6,4,7]=>{{1,3,4,5,6},{2},{7}}
[1,7,6,3,4,5,2]=>[3,6,7,4,2,5,1]=>[5,2,1,4,6,3,7]=>{{1,3,5,6},{2},{4},{7}}
[1,7,6,3,5,2,4]=>[3,6,7,2,5,4,1]=>[5,2,1,6,3,4,7]=>{{1,3,5},{2},{4,6},{7}}
[1,7,6,3,5,4,2]=>[3,6,7,2,4,5,1]=>[5,2,1,6,4,3,7]=>{{1,3,4,5,6},{2},{7}}
[1,7,6,4,2,3,5]=>[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>{{1,2,3,4,5,6},{7}}
[1,7,6,4,2,5,3]=>[2,4,6,7,3,5,1]=>[6,4,2,1,5,3,7]=>{{1,2,3,4,6},{5},{7}}
[1,7,6,4,3,2,5]=>[2,3,4,6,7,5,1]=>[6,5,4,2,1,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,6,4,3,5,2]=>[3,4,6,7,2,5,1]=>[5,4,2,1,6,3,7]=>{{1,2,3,4,5,6},{7}}
[1,7,6,4,5,2,3]=>[4,6,7,2,5,3,1]=>[4,2,1,6,3,5,7]=>{{1,3,4,5,6},{2},{7}}
[1,7,6,4,5,3,2]=>[4,6,7,2,3,5,1]=>[4,2,1,6,5,3,7]=>{{1,3,4,6},{2},{5},{7}}
[1,7,6,5,2,3,4]=>[2,5,6,7,4,3,1]=>[6,3,2,1,4,5,7]=>{{1,4,5,6},{2,3},{7}}
[1,7,6,5,2,4,3]=>[2,5,6,7,3,4,1]=>[6,3,2,1,5,4,7]=>{{1,4,6},{2,3},{5},{7}}
[1,7,6,5,3,2,4]=>[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>{{1,2,4,5,6},{3},{7}}
[1,7,6,5,3,4,2]=>[3,5,6,7,2,4,1]=>[5,3,2,1,6,4,7]=>{{1,4,5,6},{2,3},{7}}
[1,7,6,5,4,2,3]=>[2,4,5,6,7,3,1]=>[6,4,3,2,1,5,7]=>{{1,5,6},{2,4},{3},{7}}
[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>{{1,6},{2,5},{3,4},{7}}
[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>{{1,2},{3},{4},{5},{6,7}}
[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[2,1,3,4,6,7,5]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}
[2,1,3,4,7,5,6]=>[5,7,6,4,3,1,2]=>[3,1,2,4,5,7,6]=>{{1,2,3},{4},{5},{6,7}}
[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>{{1,3},{2},{4},{5},{6,7}}
[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>{{1,2},{3,4},{5},{6,7}}
[2,1,3,5,6,4,7]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[2,1,3,5,6,7,4]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,1,3,5,7,4,6]=>[5,4,7,6,3,1,2]=>[3,4,1,2,5,7,6]=>{{1,3},{2,4},{5},{6,7}}
[2,1,3,5,7,6,4]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,1,3,6,4,5,7]=>[7,4,6,5,3,1,2]=>[1,4,2,3,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[2,1,3,6,4,7,5]=>[4,6,5,7,3,1,2]=>[4,2,3,1,5,7,6]=>{{1,4},{2},{3},{5},{6,7}}
[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[2,1,3,6,5,7,4]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[2,1,3,6,7,4,5]=>[6,4,7,5,3,1,2]=>[2,4,1,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,1,3,6,7,5,4]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[2,1,3,7,4,5,6]=>[4,7,6,5,3,1,2]=>[4,1,2,3,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,1,3,7,4,6,5]=>[4,7,5,6,3,1,2]=>[4,1,3,2,5,7,6]=>{{1,2,4},{3},{5},{6,7}}
[2,1,3,7,5,4,6]=>[4,5,7,6,3,1,2]=>[4,3,1,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,1,3,7,5,6,4]=>[5,7,4,6,3,1,2]=>[3,1,4,2,5,7,6]=>{{1,2,3,4},{5},{6,7}}
[2,1,3,7,6,4,5]=>[4,6,7,5,3,1,2]=>[4,2,1,3,5,7,6]=>{{1,3,4},{2},{5},{6,7}}
[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>{{1,4},{2,3},{5},{6,7}}
[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>{{1,2},{3},{4,5},{6,7}}
[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[2,1,4,3,6,7,5]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}
[2,1,4,3,7,5,6]=>[5,7,6,3,4,1,2]=>[3,1,2,5,4,7,6]=>{{1,2,3},{4,5},{6,7}}
[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>{{1,3},{2},{4,5},{6,7}}
[2,1,4,5,3,6,7]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>{{1,2},{3,4,5},{6,7}}
[2,1,4,5,6,3,7]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,4,5,6,7,3]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,4,5,7,3,6]=>[5,4,3,7,6,1,2]=>[3,4,5,1,2,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,4,5,7,6,3]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>{{1,3,5},{2,4},{6,7}}
[2,1,4,6,3,5,7]=>[7,4,3,6,5,1,2]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[2,1,4,6,3,7,5]=>[4,3,6,5,7,1,2]=>[4,5,2,3,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,4,6,5,3,7]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,4,6,5,7,3]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>{{1,3,4,5},{2},{6,7}}
[2,1,4,6,7,3,5]=>[6,4,3,7,5,1,2]=>[2,4,5,1,3,7,6]=>{{1,2,4},{3,5},{6,7}}
[2,1,4,6,7,5,3]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,4,7,3,5,6]=>[4,3,7,6,5,1,2]=>[4,5,1,2,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,4,7,3,6,5]=>[4,3,7,5,6,1,2]=>[4,5,1,3,2,7,6]=>{{1,3,4},{2,5},{6,7}}
[2,1,4,7,5,3,6]=>[4,3,5,7,6,1,2]=>[4,5,3,1,2,7,6]=>{{1,4},{2,5},{3},{6,7}}
[2,1,4,7,5,6,3]=>[5,7,4,3,6,1,2]=>[3,1,4,5,2,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,4,7,6,3,5]=>[4,3,6,7,5,1,2]=>[4,5,2,1,3,7,6]=>{{1,4},{2,3,5},{6,7}}
[2,1,4,7,6,5,3]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,1,5,3,4,6,7]=>[7,6,3,5,4,1,2]=>[1,2,5,3,4,7,6]=>{{1},{2},{3,4,5},{6,7}}
[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[2,1,5,3,4,7,6]=>{{1,2},{3,4,5},{6,7}}
[2,1,5,3,6,4,7]=>[7,3,5,4,6,1,2]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[2,1,5,3,6,7,4]=>[6,3,5,4,7,1,2]=>[2,5,3,4,1,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,1,5,3,7,4,6]=>[3,5,4,7,6,1,2]=>[5,3,4,1,2,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,5,3,7,6,4]=>[3,5,4,6,7,1,2]=>[5,3,4,2,1,7,6]=>{{1,5},{2,3,4},{6,7}}
[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>{{1,2},{3,5},{4},{6,7}}
[2,1,5,4,6,3,7]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[2,1,5,4,6,7,3]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,1,5,4,7,3,6]=>[4,5,3,7,6,1,2]=>[4,3,5,1,2,7,6]=>{{1,4},{2,3,5},{6,7}}
[2,1,5,4,7,6,3]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,5,6,3,4,7]=>[7,5,3,6,4,1,2]=>[1,3,5,2,4,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,5,6,3,7,4]=>[5,3,6,4,7,1,2]=>[3,5,2,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,1,5,6,4,3,7]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[2,1,5,6,4,7,3]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,5,6,7,3,4]=>[6,5,3,7,4,1,2]=>[2,3,5,1,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,5,6,7,4,3]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,1,5,7,3,4,6]=>[5,3,7,6,4,1,2]=>[3,5,1,2,4,7,6]=>{{1,3},{2,4,5},{6,7}}
[2,1,5,7,3,6,4]=>[5,3,7,4,6,1,2]=>[3,5,1,4,2,7,6]=>{{1,3},{2,5},{4},{6,7}}
[2,1,5,7,4,3,6]=>[5,3,4,7,6,1,2]=>[3,5,4,1,2,7,6]=>{{1,3,4},{2,5},{6,7}}
[2,1,5,7,4,6,3]=>[5,4,7,3,6,1,2]=>[3,4,1,5,2,7,6]=>{{1,3},{2,4,5},{6,7}}
[2,1,5,7,6,3,4]=>[5,3,6,7,4,1,2]=>[3,5,2,1,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,5,7,6,4,3]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,6,3,4,5,7]=>[7,3,6,5,4,1,2]=>[1,5,2,3,4,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,6,3,4,7,5]=>[3,6,5,7,4,1,2]=>[5,2,3,1,4,7,6]=>{{1,4,5},{2},{3},{6,7}}
[2,1,6,3,5,4,7]=>[7,3,6,4,5,1,2]=>[1,5,2,4,3,7,6]=>{{1},{2,3,5},{4},{6,7}}
[2,1,6,3,5,7,4]=>[3,6,5,4,7,1,2]=>[5,2,3,4,1,7,6]=>{{1,5},{2},{3},{4},{6,7}}
[2,1,6,3,7,4,5]=>[3,6,4,7,5,1,2]=>[5,2,4,1,3,7,6]=>{{1,3,4,5},{2},{6,7}}
[2,1,6,3,7,5,4]=>[3,6,4,5,7,1,2]=>[5,2,4,3,1,7,6]=>{{1,5},{2},{3,4},{6,7}}
[2,1,6,4,3,5,7]=>[7,3,4,6,5,1,2]=>[1,5,4,2,3,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,6,4,3,7,5]=>[3,4,6,5,7,1,2]=>[5,4,2,3,1,7,6]=>{{1,5},{2,3,4},{6,7}}
[2,1,6,4,5,3,7]=>[7,4,6,3,5,1,2]=>[1,4,2,5,3,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,6,4,5,7,3]=>[4,6,5,3,7,1,2]=>[4,2,3,5,1,7,6]=>{{1,4,5},{2},{3},{6,7}}
[2,1,6,4,7,3,5]=>[4,6,3,7,5,1,2]=>[4,2,5,1,3,7,6]=>{{1,4},{2},{3,5},{6,7}}
[2,1,6,4,7,5,3]=>[4,6,3,5,7,1,2]=>[4,2,5,3,1,7,6]=>{{1,3,4,5},{2},{6,7}}
[2,1,6,5,3,4,7]=>[7,3,5,6,4,1,2]=>[1,5,3,2,4,7,6]=>{{1},{2,4,5},{3},{6,7}}
[2,1,6,5,3,7,4]=>[3,5,6,4,7,1,2]=>[5,3,2,4,1,7,6]=>{{1,5},{2,3},{4},{6,7}}
[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>{{1},{2,5},{3,4},{6,7}}
[2,1,6,5,4,7,3]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>{{1,4,5},{2,3},{6,7}}
[2,1,6,5,7,3,4]=>[5,6,3,7,4,1,2]=>[3,2,5,1,4,7,6]=>{{1,3,4,5},{2},{6,7}}
[2,1,6,5,7,4,3]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>{{1,3,5},{2},{4},{6,7}}
[2,1,6,7,3,4,5]=>[6,3,7,5,4,1,2]=>[2,5,1,3,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,6,7,3,5,4]=>[6,3,7,4,5,1,2]=>[2,5,1,4,3,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,1,6,7,4,3,5]=>[6,3,4,7,5,1,2]=>[2,5,4,1,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,6,7,4,5,3]=>[6,4,7,3,5,1,2]=>[2,4,1,5,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,6,7,5,3,4]=>[6,3,5,7,4,1,2]=>[2,5,3,1,4,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,1,6,7,5,4,3]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>{{1,2,5},{3,4},{6,7}}
[2,1,7,3,4,5,6]=>[3,7,6,5,4,1,2]=>[5,1,2,3,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,3,4,6,5]=>[3,7,5,6,4,1,2]=>[5,1,3,2,4,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,1,7,3,5,4,6]=>[3,7,6,4,5,1,2]=>[5,1,2,4,3,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,1,7,3,5,6,4]=>[3,7,5,4,6,1,2]=>[5,1,3,4,2,7,6]=>{{1,2,5},{3},{4},{6,7}}
[2,1,7,3,6,4,5]=>[3,7,4,6,5,1,2]=>[5,1,4,2,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,3,6,5,4]=>[3,7,4,5,6,1,2]=>[5,1,4,3,2,7,6]=>{{1,2,5},{3,4},{6,7}}
[2,1,7,4,3,5,6]=>[3,4,7,6,5,1,2]=>[5,4,1,2,3,7,6]=>{{1,3,5},{2,4},{6,7}}
[2,1,7,4,3,6,5]=>[3,4,7,5,6,1,2]=>[5,4,1,3,2,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,4,5,3,6]=>[4,7,6,3,5,1,2]=>[4,1,2,5,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,4,5,6,3]=>[4,7,5,3,6,1,2]=>[4,1,3,5,2,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,1,7,4,6,3,5]=>[4,7,3,6,5,1,2]=>[4,1,5,2,3,7,6]=>{{1,2,4},{3,5},{6,7}}
[2,1,7,4,6,5,3]=>[4,7,3,5,6,1,2]=>[4,1,5,3,2,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,5,3,4,6]=>[3,5,7,6,4,1,2]=>[5,3,1,2,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,5,3,6,4]=>[3,5,7,4,6,1,2]=>[5,3,1,4,2,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,1,7,5,4,3,6]=>[3,4,5,7,6,1,2]=>[5,4,3,1,2,7,6]=>{{1,2,4,5},{3},{6,7}}
[2,1,7,5,4,6,3]=>[4,5,7,3,6,1,2]=>[4,3,1,5,2,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,5,6,3,4]=>[5,7,3,6,4,1,2]=>[3,1,5,2,4,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,5,6,4,3]=>[5,7,3,4,6,1,2]=>[3,1,5,4,2,7,6]=>{{1,2,3,5},{4},{6,7}}
[2,1,7,6,3,4,5]=>[3,6,7,5,4,1,2]=>[5,2,1,3,4,7,6]=>{{1,3,4,5},{2},{6,7}}
[2,1,7,6,3,5,4]=>[3,6,7,4,5,1,2]=>[5,2,1,4,3,7,6]=>{{1,3,5},{2},{4},{6,7}}
[2,1,7,6,4,3,5]=>[3,4,6,7,5,1,2]=>[5,4,2,1,3,7,6]=>{{1,2,3,4,5},{6,7}}
[2,1,7,6,4,5,3]=>[4,6,7,3,5,1,2]=>[4,2,1,5,3,7,6]=>{{1,3,4,5},{2},{6,7}}
[2,1,7,6,5,3,4]=>[3,5,6,7,4,1,2]=>[5,3,2,1,4,7,6]=>{{1,4,5},{2,3},{6,7}}
[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>{{1,5},{2,4},{3},{6,7}}
[2,3,1,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[2,3,1,4,5,7,6]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>{{1,2},{3},{4},{5,6,7}}
[2,3,1,4,6,5,7]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}
[2,3,1,4,7,5,6]=>[5,7,6,4,2,1,3]=>[3,1,2,4,6,7,5]=>{{1,2,3},{4},{5,6,7}}
[2,3,1,4,7,6,5]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>{{1,3},{2},{4},{5,6,7}}
[2,3,1,5,4,6,7]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[2,3,1,5,4,7,6]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>{{1,2},{3,4},{5,6,7}}
[2,3,1,5,6,4,7]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[2,3,1,5,6,7,4]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,1,5,7,4,6]=>[5,4,7,6,2,1,3]=>[3,4,1,2,6,7,5]=>{{1,3},{2,4},{5,6,7}}
[2,3,1,5,7,6,4]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,1,6,4,5,7]=>[7,4,6,5,2,1,3]=>[1,4,2,3,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[2,3,1,6,4,7,5]=>[4,6,5,7,2,1,3]=>[4,2,3,1,6,7,5]=>{{1,4},{2},{3},{5,6,7}}
[2,3,1,6,5,4,7]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[2,3,1,6,5,7,4]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[2,3,1,6,7,4,5]=>[6,4,7,5,2,1,3]=>[2,4,1,3,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,1,6,7,5,4]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[2,3,1,7,4,5,6]=>[4,7,6,5,2,1,3]=>[4,1,2,3,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,1,7,4,6,5]=>[4,7,5,6,2,1,3]=>[4,1,3,2,6,7,5]=>{{1,2,4},{3},{5,6,7}}
[2,3,1,7,5,4,6]=>[4,5,7,6,2,1,3]=>[4,3,1,2,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,1,7,5,6,4]=>[5,7,4,6,2,1,3]=>[3,1,4,2,6,7,5]=>{{1,2,3,4},{5,6,7}}
[2,3,1,7,6,4,5]=>[4,6,7,5,2,1,3]=>[4,2,1,3,6,7,5]=>{{1,3,4},{2},{5,6,7}}
[2,3,1,7,6,5,4]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>{{1,4},{2,3},{5,6,7}}
[2,3,4,1,5,6,7]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[2,3,4,1,5,7,6]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>{{1,2},{3},{4,5,6,7}}
[2,3,4,1,6,5,7]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[2,3,4,1,6,7,5]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>{{1,2,3},{4,5,6,7}}
[2,3,4,1,7,5,6]=>[5,7,6,3,2,1,4]=>[3,1,2,5,6,7,4]=>{{1,2,3},{4,5,6,7}}
[2,3,4,1,7,6,5]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>{{1,3},{2},{4,5,6,7}}
[2,3,4,5,1,6,7]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,3,4,5,1,7,6]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>{{1,2},{3,4,5,6,7}}
[2,3,4,5,6,1,7]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,3,4,5,7,1,6]=>[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>{{1,2,3,4,5,6,7}}
[2,3,4,5,7,6,1]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>{{1,3,5,7},{2,4,6}}
[2,3,4,6,1,5,7]=>[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,3,4,6,1,7,5]=>[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>{{1,4,7},{2,5},{3,6}}
[2,3,4,6,5,1,7]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,6,5,7,1]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>{{1,3,4,5,6,7},{2}}
[2,3,4,6,7,1,5]=>[6,4,3,2,1,7,5]=>[2,4,5,6,7,1,3]=>{{1,2,4,6},{3,5,7}}
[2,3,4,6,7,5,1]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,1,5,6]=>[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,1,6,5]=>[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>{{1,2,4,5,7},{3,6}}
[2,3,4,7,5,1,6]=>[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,5,6,1]=>[5,7,4,3,2,1,6]=>[3,1,4,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[2,3,4,7,6,1,5]=>[4,3,2,1,6,7,5]=>[4,5,6,7,2,1,3]=>{{1,3,4,6,7},{2,5}}
[2,3,4,7,6,5,1]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>{{1,4,7},{2,3,5,6}}
[2,3,5,1,4,6,7]=>[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>{{1},{2},{3,4,5,6,7}}
[2,3,5,1,4,7,6]=>[6,7,3,2,1,5,4]=>[2,1,5,6,7,3,4]=>{{1,2},{3,4,5,6,7}}
[2,3,5,1,6,4,7]=>[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,1,6,7,4]=>[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>{{1,2,3,4,5,6,7}}
[2,3,5,1,7,4,6]=>[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>{{1,2,3,4,5,6,7}}
[2,3,5,1,7,6,4]=>[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>{{1,3,4,5,7},{2,6}}
[2,3,5,4,1,6,7]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>{{1},{2},{3,5,7},{4,6}}
[2,3,5,4,1,7,6]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>{{1,2},{3,5,7},{4,6}}
[2,3,5,4,6,1,7]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,3,5,4,6,7,1]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>{{1,2,4,5,6,7},{3}}
[2,3,5,4,7,1,6]=>[4,5,3,2,1,7,6]=>[4,3,5,6,7,1,2]=>{{1,4,6},{2,3,5,7}}
[2,3,5,4,7,6,1]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>{{1,2,3,4,5,6,7}}
[2,3,5,6,1,4,7]=>[7,5,3,2,1,6,4]=>[1,3,5,6,7,2,4]=>{{1},{2,3,4,5,6,7}}
[2,3,5,6,1,7,4]=>[5,3,2,1,6,4,7]=>[3,5,6,7,2,4,1]=>{{1,3,4,6,7},{2,5}}
[2,3,5,6,4,1,7]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>{{1},{2,3,5,7},{4,6}}
[2,3,5,6,4,7,1]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>[2,3,5,6,7,1,4]=>{{1,2,3,4,5,6,7}}
[2,3,5,6,7,4,1]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>{{1,2,3,5,7},{4,6}}
[2,3,5,7,1,4,6]=>[5,3,2,1,7,6,4]=>[3,5,6,7,1,2,4]=>{{1,2,3,5,6},{4,7}}
[2,3,5,7,1,6,4]=>[5,3,2,1,7,4,6]=>[3,5,6,7,1,4,2]=>{{1,2,3,4,5,6,7}}
[2,3,5,7,4,1,6]=>[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>{{1,3,6},{2,4,5,7}}
[2,3,5,7,4,6,1]=>[5,4,7,3,2,1,6]=>[3,4,1,5,6,7,2]=>{{1,3},{2,4,5,6,7}}
[2,3,5,7,6,1,4]=>[5,3,2,1,6,7,4]=>[3,5,6,7,2,1,4]=>{{1,3,6},{2,5},{4,7}}
[2,3,5,7,6,4,1]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>{{1,2,3,4,5,6,7}}
[2,3,6,1,4,5,7]=>[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,3,6,1,4,7,5]=>[3,2,1,6,5,7,4]=>[5,6,7,2,3,1,4]=>{{1,2,3,4,5,6,7}}
[2,3,6,1,5,4,7]=>[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,3,6,1,5,7,4]=>[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>{{1,3,5,7},{2,4,6}}
[2,3,6,1,7,4,5]=>[3,2,1,6,4,7,5]=>[5,6,7,2,4,1,3]=>{{1,2,4,5,6},{3,7}}
[2,3,6,1,7,5,4]=>[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>{{1,2,3,4,5,6,7}}
[2,3,6,4,1,5,7]=>[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>{{1},{2,3,4,5,6,7}}
[2,3,6,4,1,7,5]=>[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>{{1,2,3,5,6,7},{4}}
[2,3,6,4,5,1,7]=>[7,4,6,3,2,1,5]=>[1,4,2,5,6,7,3]=>{{1},{2,3,4,5,6,7}}
[2,3,6,4,5,7,1]=>[4,6,5,3,2,1,7]=>[4,2,3,5,6,7,1]=>{{1,4,5,6,7},{2},{3}}
[2,3,6,4,7,1,5]=>[4,6,3,2,1,7,5]=>[4,2,5,6,7,1,3]=>{{1,4,6},{2},{3,5,7}}
[2,3,6,4,7,5,1]=>[4,6,3,2,1,5,7]=>[4,2,5,6,7,3,1]=>{{1,3,4,5,6,7},{2}}
[2,3,6,5,1,4,7]=>[7,3,2,1,5,6,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,3,6,5,1,7,4]=>[3,2,1,5,6,4,7]=>[5,6,7,3,2,4,1]=>{{1,2,3,4,5,6,7}}
[2,3,6,5,4,1,7]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>{{1},{2,4,5,7},{3,6}}
[2,3,6,5,4,7,1]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>{{1,4,5,6,7},{2,3}}
[2,3,6,5,7,1,4]=>[5,6,3,2,1,7,4]=>[3,2,5,6,7,1,4]=>{{1,3,4,5,6,7},{2}}
[2,3,6,5,7,4,1]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>{{1,3,5,7},{2},{4,6}}
[2,3,6,7,1,4,5]=>[6,3,2,1,7,5,4]=>[2,5,6,7,1,3,4]=>{{1,2,5},{3,6},{4,7}}
[2,3,6,7,1,5,4]=>[6,3,2,1,7,4,5]=>[2,5,6,7,1,4,3]=>{{1,2,5},{3,4,6,7}}
[2,3,6,7,4,1,5]=>[6,3,2,1,4,7,5]=>[2,5,6,7,4,1,3]=>{{1,2,3,4,5,6,7}}
[2,3,6,7,4,5,1]=>[6,4,7,3,2,1,5]=>[2,4,1,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,3,6,7,5,1,4]=>[6,3,2,1,5,7,4]=>[2,5,6,7,3,1,4]=>{{1,2,3,5,6},{4,7}}
[2,3,6,7,5,4,1]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>{{1,2,4,5,7},{3,6}}
[2,3,7,1,4,5,6]=>[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>{{1,2,3,4,5,6,7}}
[2,3,7,1,4,6,5]=>[3,2,1,7,5,6,4]=>[5,6,7,1,3,2,4]=>{{1,3,4,5,7},{2,6}}
[2,3,7,1,5,4,6]=>[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>{{1,2,4,5,6},{3,7}}
[2,3,7,1,5,6,4]=>[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>{{1,2,3,4,5,6,7}}
[2,3,7,1,6,4,5]=>[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>{{1,4,5},{2,6},{3,7}}
[2,3,7,1,6,5,4]=>[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>{{1,4,5},{2,3,6,7}}
[2,3,7,4,1,5,6]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>{{1,5},{2,6},{3,7},{4}}
[2,3,7,4,1,6,5]=>[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>{{1,5},{2,3,6,7},{4}}
[2,3,7,4,5,1,6]=>[4,7,6,3,2,1,5]=>[4,1,2,5,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,3,7,4,5,6,1]=>[4,7,5,3,2,1,6]=>[4,1,3,5,6,7,2]=>{{1,2,4,5,6,7},{3}}
[2,3,7,4,6,1,5]=>[4,7,3,2,1,6,5]=>[4,1,5,6,7,2,3]=>{{1,2,4,6},{3,5,7}}
[2,3,7,4,6,5,1]=>[4,7,3,2,1,5,6]=>[4,1,5,6,7,3,2]=>{{1,2,3,4,5,6,7}}
[2,3,7,5,1,4,6]=>[3,2,1,5,7,6,4]=>[5,6,7,3,1,2,4]=>{{1,5},{2,6},{3,4,7}}
[2,3,7,5,1,6,4]=>[3,2,1,5,7,4,6]=>[5,6,7,3,1,4,2]=>{{1,5},{2,3,4,6,7}}
[2,3,7,5,4,1,6]=>[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>{{1,2,3,5,6,7},{4}}
[2,3,7,5,4,6,1]=>[4,5,7,3,2,1,6]=>[4,3,1,5,6,7,2]=>{{1,2,3,4,5,6,7}}
[2,3,7,5,6,1,4]=>[5,7,3,2,1,6,4]=>[3,1,5,6,7,2,4]=>{{1,2,3,4,5,6,7}}
[2,3,7,5,6,4,1]=>[5,7,3,2,1,4,6]=>[3,1,5,6,7,4,2]=>{{1,2,3,5,7},{4,6}}
[2,3,7,6,1,4,5]=>[3,2,1,6,7,5,4]=>[5,6,7,2,1,3,4]=>{{1,5},{2,3,4,6,7}}
[2,3,7,6,1,5,4]=>[3,2,1,6,7,4,5]=>[5,6,7,2,1,4,3]=>{{1,5},{2,4,6},{3,7}}
[2,3,7,6,4,1,5]=>[3,2,1,4,6,7,5]=>[5,6,7,4,2,1,3]=>{{1,2,5,6},{3,7},{4}}
[2,3,7,6,4,5,1]=>[4,6,7,3,2,1,5]=>[4,2,1,5,6,7,3]=>{{1,3,4,5,6,7},{2}}
[2,3,7,6,5,1,4]=>[3,2,1,5,6,7,4]=>[5,6,7,3,2,1,4]=>{{1,2,5,6},{3,4,7}}
[2,3,7,6,5,4,1]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>{{1,3,5,7},{2,6},{4}}
[2,4,1,3,5,6,7]=>[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[2,4,1,3,5,7,6]=>[6,7,5,2,1,4,3]=>[2,1,3,6,7,4,5]=>{{1,2},{3},{4,6},{5,7}}
[2,4,1,3,6,5,7]=>[7,5,6,2,1,4,3]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[2,4,1,3,6,7,5]=>[6,5,7,2,1,4,3]=>[2,3,1,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}
[2,4,1,3,7,5,6]=>[5,7,6,2,1,4,3]=>[3,1,2,6,7,4,5]=>{{1,2,3},{4,6},{5,7}}
[2,4,1,3,7,6,5]=>[5,6,7,2,1,4,3]=>[3,2,1,6,7,4,5]=>{{1,3},{2},{4,6},{5,7}}
[2,4,1,5,3,6,7]=>[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>{{1},{2},{3,4,5,6,7}}
[2,4,1,5,3,7,6]=>[6,7,2,1,4,3,5]=>[2,1,6,7,4,5,3]=>{{1,2},{3,4,5,6,7}}
[2,4,1,5,6,3,7]=>[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>{{1},{2,3,4,5,6,7}}
[2,4,1,5,6,7,3]=>[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>{{1,2,3,4,5,6,7}}
[2,4,1,5,7,3,6]=>[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>{{1,2,3,6,7},{4},{5}}
[2,4,1,5,7,6,3]=>[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>{{1,3,7},{2,6},{4},{5}}
[2,4,1,6,3,5,7]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[2,4,1,6,3,7,5]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>{{1,2,3,4,5,6,7}}
[2,4,1,6,5,3,7]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[2,4,1,6,5,7,3]=>[5,6,2,1,4,3,7]=>[3,2,6,7,4,5,1]=>{{1,3,4,5,6,7},{2}}
[2,4,1,6,7,3,5]=>[6,2,1,4,3,7,5]=>[2,6,7,4,5,1,3]=>{{1,2,6},{3,7},{4},{5}}
[2,4,1,6,7,5,3]=>[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>{{1,2,3,6,7},{4},{5}}
[2,4,1,7,3,5,6]=>[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>{{1,2,3,4,5,6,7}}
[2,4,1,7,3,6,5]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>{{1,3,4,5,6},{2,7}}
[2,4,1,7,5,3,6]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>{{1,6},{2,7},{3,4,5}}
[2,4,1,7,5,6,3]=>[5,7,2,1,4,3,6]=>[3,1,6,7,4,5,2]=>{{1,2,3,4,5,6,7}}
[2,4,1,7,6,3,5]=>[2,1,4,3,6,7,5]=>[6,7,4,5,2,1,3]=>{{1,6},{2,3,4,5,7}}
[2,4,1,7,6,5,3]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>{{1,2,6,7},{3,4,5}}
[2,4,3,1,5,6,7]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[2,4,3,1,5,7,6]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>{{1,2},{3},{4,5,6,7}}
[2,4,3,1,6,5,7]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[2,4,3,1,6,7,5]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>{{1,2,3},{4,5,6,7}}
[2,4,3,1,7,5,6]=>[5,7,6,2,1,3,4]=>[3,1,2,6,7,5,4]=>{{1,2,3},{4,5,6,7}}
[2,4,3,1,7,6,5]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>{{1,3},{2},{4,5,6,7}}
[2,4,3,5,1,6,7]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[2,4,3,5,1,7,6]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>{{1,2},{3,5,6,7},{4}}
[2,4,3,5,6,1,7]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,4,3,5,6,7,1]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[2,4,3,5,7,1,6]=>[5,3,4,2,1,7,6]=>[3,5,4,6,7,1,2]=>{{1,3,4,6},{2,5,7}}
[2,4,3,5,7,6,1]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>{{1,2,3,4,5,6,7}}
[2,4,3,6,1,5,7]=>[7,3,4,2,1,6,5]=>[1,5,4,6,7,2,3]=>{{1},{2,3,4,5,6,7}}
[2,4,3,6,1,7,5]=>[3,4,2,1,6,5,7]=>[5,4,6,7,2,3,1]=>{{1,2,4,5,7},{3,6}}
[2,4,3,6,5,1,7]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>{{1},{2,5,7},{3,4,6}}
[2,4,3,6,5,7,1]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>{{1,3,5,6,7},{2},{4}}
[2,4,3,6,7,1,5]=>[6,3,4,2,1,7,5]=>[2,5,4,6,7,1,3]=>{{1,2,3,4,5,6,7}}
[2,4,3,6,7,5,1]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>{{1,2,5,7},{3,4,6}}
[2,4,3,7,1,5,6]=>[3,4,2,1,7,6,5]=>[5,4,6,7,1,2,3]=>{{1,5},{2,3,4,6,7}}
[2,4,3,7,1,6,5]=>[3,4,2,1,7,5,6]=>[5,4,6,7,1,3,2]=>{{1,5},{2,4,7},{3,6}}
[2,4,3,7,5,1,6]=>[3,4,2,1,5,7,6]=>[5,4,6,7,3,1,2]=>{{1,3,5,6},{2,4,7}}
[2,4,3,7,5,6,1]=>[5,7,3,4,2,1,6]=>[3,1,5,4,6,7,2]=>{{1,2,3,5,6,7},{4}}
[2,4,3,7,6,1,5]=>[3,4,2,1,6,7,5]=>[5,4,6,7,2,1,3]=>{{1,2,3,4,5,6,7}}
[2,4,3,7,6,5,1]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[2,4,5,1,3,6,7]=>[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[2,4,5,1,3,7,6]=>[6,7,4,2,1,5,3]=>[2,1,4,6,7,3,5]=>{{1,2},{3,4,6},{5,7}}
[2,4,5,1,6,3,7]=>[7,4,2,1,5,3,6]=>[1,4,6,7,3,5,2]=>{{1},{2,4,7},{3,5,6}}
[2,4,5,1,6,7,3]=>[6,4,2,1,5,3,7]=>[2,4,6,7,3,5,1]=>{{1,2,4,7},{3,5,6}}
[2,4,5,1,7,3,6]=>[4,2,1,5,3,7,6]=>[4,6,7,3,5,1,2]=>{{1,2,3,4,6,7},{5}}
[2,4,5,1,7,6,3]=>[4,2,1,5,3,6,7]=>[4,6,7,3,5,2,1]=>{{1,3,4,7},{2,6},{5}}
[2,4,5,3,1,6,7]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[2,4,5,3,1,7,6]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>{{1,2},{3,4,5,6,7}}
[2,4,5,3,6,1,7]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,3,6,7,1]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,4,5,3,7,1,6]=>[4,3,5,2,1,7,6]=>[4,5,3,6,7,1,2]=>{{1,4,6},{2,5,7},{3}}
[2,4,5,3,7,6,1]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>{{1,2,4,5,6,7},{3}}
[2,4,5,6,1,3,7]=>[7,5,4,2,1,6,3]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,4,5,6,1,7,3]=>[5,4,2,1,6,3,7]=>[3,4,6,7,2,5,1]=>{{1,2,3,4,5,6,7}}
[2,4,5,6,3,1,7]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,6,3,7,1]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>{{1,3,5,6,7},{2,4}}
[2,4,5,6,7,1,3]=>[6,5,4,2,1,7,3]=>[2,3,4,6,7,1,5]=>{{1,2,3,4,6},{5,7}}
[2,4,5,6,7,3,1]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>{{1,2,3,4,5,6,7}}
[2,4,5,7,1,3,6]=>[5,4,2,1,7,6,3]=>[3,4,6,7,1,2,5]=>{{1,2,3,4,5,6,7}}
[2,4,5,7,1,6,3]=>[5,4,2,1,7,3,6]=>[3,4,6,7,1,5,2]=>{{1,3,5,6},{2,4,7}}
[2,4,5,7,3,1,6]=>[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>{{1,3,6},{2,4,7},{5}}
[2,4,5,7,3,6,1]=>[5,4,3,7,2,1,6]=>[3,4,5,1,6,7,2]=>{{1,2,3,4,5,6,7}}
[2,4,5,7,6,1,3]=>[5,4,2,1,6,7,3]=>[3,4,6,7,2,1,5]=>{{1,3,6},{2,4,5,7}}
[2,4,5,7,6,3,1]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>{{1,2,3,4,6,7},{5}}
[2,4,6,1,3,5,7]=>[7,4,2,1,6,5,3]=>[1,4,6,7,2,3,5]=>{{1},{2,4,5,7},{3,6}}
[2,4,6,1,3,7,5]=>[4,2,1,6,5,7,3]=>[4,6,7,2,3,1,5]=>{{1,2,4,6},{3,5,7}}
[2,4,6,1,5,3,7]=>[7,4,2,1,6,3,5]=>[1,4,6,7,2,5,3]=>{{1},{2,3,4,5,6,7}}
[2,4,6,1,5,7,3]=>[4,2,1,6,5,3,7]=>[4,6,7,2,3,5,1]=>{{1,2,3,4,5,6,7}}
[2,4,6,1,7,3,5]=>[4,2,1,6,3,7,5]=>[4,6,7,2,5,1,3]=>{{1,2,4,6},{3,7},{5}}
[2,4,6,1,7,5,3]=>[4,2,1,6,3,5,7]=>[4,6,7,2,5,3,1]=>{{1,2,3,4,6,7},{5}}
[2,4,6,3,1,5,7]=>[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>{{1},{2,3,4,6,7},{5}}
[2,4,6,3,1,7,5]=>[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>{{1,2,3,4,5,6,7}}
[2,4,6,3,5,1,7]=>[7,4,3,6,2,1,5]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,4,6,3,5,7,1]=>[4,3,6,5,2,1,7]=>[4,5,2,3,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,4,6,3,7,1,5]=>[4,3,6,2,1,7,5]=>[4,5,2,6,7,1,3]=>{{1,4,6},{2,3,5,7}}
[2,4,6,3,7,5,1]=>[4,3,6,2,1,5,7]=>[4,5,2,6,7,3,1]=>{{1,2,3,4,5,6,7}}
[2,4,6,5,1,3,7]=>[7,4,2,1,5,6,3]=>[1,4,6,7,3,2,5]=>{{1},{2,3,4,5,6,7}}
[2,4,6,5,1,7,3]=>[4,2,1,5,6,3,7]=>[4,6,7,3,2,5,1]=>{{1,3,4,7},{2,5,6}}
[2,4,6,5,3,1,7]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>{{1},{2,4,7},{3,6},{5}}
[2,4,6,5,3,7,1]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>{{1,2,4,5,6,7},{3}}
[2,4,6,5,7,1,3]=>[5,6,4,2,1,7,3]=>[3,2,4,6,7,1,5]=>{{1,3,4,6},{2},{5,7}}
[2,4,6,5,7,3,1]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>{{1,3,4,5,6,7},{2}}
[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>[2,4,6,7,1,3,5]=>{{1,2,4,5,7},{3,6}}
[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>[2,4,6,7,1,5,3]=>{{1,2,3,4,5,6,7}}
[2,4,6,7,3,1,5]=>[6,4,2,1,3,7,5]=>[2,4,6,7,5,1,3]=>{{1,2,3,4,6,7},{5}}
[2,4,6,7,3,5,1]=>[6,4,3,7,2,1,5]=>[2,4,5,1,6,7,3]=>{{1,2,4},{3,5,6,7}}
[2,4,6,7,5,1,3]=>[6,4,2,1,5,7,3]=>[2,4,6,7,3,1,5]=>{{1,2,3,4,5,6,7}}
[2,4,6,7,5,3,1]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>{{1,2,4,7},{3,6},{5}}
[2,4,7,1,3,5,6]=>[4,2,1,7,6,5,3]=>[4,6,7,1,2,3,5]=>{{1,4},{2,3,5,6,7}}
[2,4,7,1,3,6,5]=>[4,2,1,7,5,6,3]=>[4,6,7,1,3,2,5]=>{{1,4},{2,6},{3,5,7}}
[2,4,7,1,5,3,6]=>[4,2,1,7,6,3,5]=>[4,6,7,1,2,5,3]=>{{1,4},{2,5,6},{3,7}}
[2,4,7,1,5,6,3]=>[4,2,1,7,5,3,6]=>[4,6,7,1,3,5,2]=>{{1,4},{2,3,5,6,7}}
[2,4,7,1,6,3,5]=>[4,2,1,7,3,6,5]=>[4,6,7,1,5,2,3]=>{{1,4},{2,6},{3,7},{5}}
[2,4,7,1,6,5,3]=>[4,2,1,7,3,5,6]=>[4,6,7,1,5,3,2]=>{{1,4},{2,3,6,7},{5}}
[2,4,7,3,1,5,6]=>[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>{{1,4,5},{2,6},{3,7}}
[2,4,7,3,1,6,5]=>[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>{{1,4,5},{2,3,6,7}}
[2,4,7,3,5,1,6]=>[4,3,7,6,2,1,5]=>[4,5,1,2,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,4,7,3,5,6,1]=>[4,3,7,5,2,1,6]=>[4,5,1,3,6,7,2]=>{{1,3,4},{2,5,6,7}}
[2,4,7,3,6,1,5]=>[4,3,7,2,1,6,5]=>[4,5,1,6,7,2,3]=>{{1,2,3,4,5,6,7}}
[2,4,7,3,6,5,1]=>[4,3,7,2,1,5,6]=>[4,5,1,6,7,3,2]=>{{1,3,4,6},{2,5,7}}
[2,4,7,5,1,3,6]=>[4,2,1,5,7,6,3]=>[4,6,7,3,1,2,5]=>{{1,3,4,5,7},{2,6}}
[2,4,7,5,1,6,3]=>[4,2,1,5,7,3,6]=>[4,6,7,3,1,5,2]=>{{1,2,3,4,5,6,7}}
[2,4,7,5,3,1,6]=>[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>{{1,2,3,4,5,6,7}}
[2,4,7,5,3,6,1]=>[4,3,5,7,2,1,6]=>[4,5,3,1,6,7,2]=>{{1,4},{2,5,6,7},{3}}
[2,4,7,5,6,1,3]=>[5,7,4,2,1,6,3]=>[3,1,4,6,7,2,5]=>{{1,2,3,4,6},{5,7}}
[2,4,7,5,6,3,1]=>[5,7,4,2,1,3,6]=>[3,1,4,6,7,5,2]=>{{1,2,3,4,5,6,7}}
[2,4,7,6,1,3,5]=>[4,2,1,6,7,5,3]=>[4,6,7,2,1,3,5]=>{{1,2,3,4,5,6,7}}
[2,4,7,6,1,5,3]=>[4,2,1,6,7,3,5]=>[4,6,7,2,1,5,3]=>{{1,2,4,5,6},{3,7}}
[2,4,7,6,3,1,5]=>[4,2,1,3,6,7,5]=>[4,6,7,5,2,1,3]=>{{1,2,4,5,6},{3,7}}
[2,4,7,6,3,5,1]=>[4,3,6,7,2,1,5]=>[4,5,2,1,6,7,3]=>{{1,4},{2,3,5,6,7}}
[2,4,7,6,5,1,3]=>[4,2,1,5,6,7,3]=>[4,6,7,3,2,1,5]=>{{1,2,3,4,5,6,7}}
[2,4,7,6,5,3,1]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>{{1,3,4,5,7},{2,6}}
[2,5,1,3,4,6,7]=>[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>{{1},{2},{3,4,5,6,7}}
[2,5,1,3,4,7,6]=>[6,7,2,1,5,4,3]=>[2,1,6,7,3,4,5]=>{{1,2},{3,4,5,6,7}}
[2,5,1,3,6,4,7]=>[7,2,1,5,4,6,3]=>[1,6,7,3,4,2,5]=>{{1},{2,6},{3,4,5,7}}
[2,5,1,3,6,7,4]=>[6,2,1,5,4,7,3]=>[2,6,7,3,4,1,5]=>{{1,2,6},{3,4,5,7}}
[2,5,1,3,7,4,6]=>[2,1,5,4,7,6,3]=>[6,7,3,4,1,2,5]=>{{1,2,5,6,7},{3},{4}}
[2,5,1,3,7,6,4]=>[2,1,5,4,6,7,3]=>[6,7,3,4,2,1,5]=>{{1,6},{2,5,7},{3},{4}}
[2,5,1,4,3,6,7]=>[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>{{1},{2},{3,5,6},{4,7}}
[2,5,1,4,3,7,6]=>[6,7,2,1,5,3,4]=>[2,1,6,7,3,5,4]=>{{1,2},{3,5,6},{4,7}}
[2,5,1,4,6,3,7]=>[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>{{1},{2,3,4,5,6,7}}
[2,5,1,4,6,7,3]=>[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>{{1,2,3,4,5,6,7}}
[2,5,1,4,7,3,6]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>{{1,6},{2,7},{3},{4},{5}}
[2,5,1,4,7,6,3]=>[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>{{1,2,6,7},{3},{4},{5}}
[2,5,1,6,3,4,7]=>[7,2,1,5,3,6,4]=>[1,6,7,3,5,2,4]=>{{1},{2,6},{3,4,7},{5}}
[2,5,1,6,3,7,4]=>[2,1,5,3,6,4,7]=>[6,7,3,5,2,4,1]=>{{1,2,4,5,6,7},{3}}
[2,5,1,6,4,3,7]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[2,5,1,6,4,7,3]=>[2,1,5,4,6,3,7]=>[6,7,3,4,2,5,1]=>{{1,2,5,6,7},{3},{4}}
[2,5,1,6,7,3,4]=>[6,2,1,5,3,7,4]=>[2,6,7,3,5,1,4]=>{{1,2,6},{3,4,7},{5}}
[2,5,1,6,7,4,3]=>[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>{{1,2,3,4,6,7},{5}}
[2,5,1,7,3,4,6]=>[2,1,5,3,7,6,4]=>[6,7,3,5,1,2,4]=>{{1,2,4,5,6,7},{3}}
[2,5,1,7,3,6,4]=>[2,1,5,3,7,4,6]=>[6,7,3,5,1,4,2]=>{{1,4,5,6},{2,7},{3}}
[2,5,1,7,4,3,6]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>{{1,6},{2,7},{3},{4,5}}
[2,5,1,7,4,6,3]=>[2,1,5,4,7,3,6]=>[6,7,3,4,1,5,2]=>{{1,5,6},{2,7},{3},{4}}
[2,5,1,7,6,3,4]=>[2,1,5,3,6,7,4]=>[6,7,3,5,2,1,4]=>{{1,6},{2,4,5,7},{3}}
[2,5,1,7,6,4,3]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>{{1,2,6,7},{3},{4,5}}
[2,5,3,1,4,6,7]=>[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[2,5,3,1,4,7,6]=>[6,7,2,1,3,5,4]=>[2,1,6,7,5,3,4]=>{{1,2},{3,6},{4,7},{5}}
[2,5,3,1,6,4,7]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,1,6,7,4]=>[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>{{1,2,3,4,5,6,7}}
[2,5,3,1,7,4,6]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>{{1,6},{2,7},{3,4,5}}
[2,5,3,1,7,6,4]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>{{1,2,6,7},{3,4,5}}
[2,5,3,4,1,6,7]=>[7,6,3,5,2,1,4]=>[1,2,5,3,6,7,4]=>{{1},{2},{3,4,5,6,7}}
[2,5,3,4,1,7,6]=>[6,7,3,5,2,1,4]=>[2,1,5,3,6,7,4]=>{{1,2},{3,4,5,6,7}}
[2,5,3,4,6,1,7]=>[7,3,5,4,2,1,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[2,5,3,4,6,7,1]=>[6,3,5,4,2,1,7]=>[2,5,3,4,6,7,1]=>{{1,2,5,6,7},{3},{4}}
[2,5,3,4,7,1,6]=>[3,5,4,2,1,7,6]=>[5,3,4,6,7,1,2]=>{{1,2,3,4,5,6,7}}
[2,5,3,4,7,6,1]=>[3,5,4,2,1,6,7]=>[5,3,4,6,7,2,1]=>{{1,5,7},{2,3,4,6}}
[2,5,3,6,1,4,7]=>[7,3,5,2,1,6,4]=>[1,5,3,6,7,2,4]=>{{1},{2,4,5,6,7},{3}}
[2,5,3,6,1,7,4]=>[3,5,2,1,6,4,7]=>[5,3,6,7,2,4,1]=>{{1,2,3,4,5,6,7}}
[2,5,3,6,4,1,7]=>[7,3,5,2,1,4,6]=>[1,5,3,6,7,4,2]=>{{1},{2,5,7},{3},{4,6}}
[2,5,3,6,4,7,1]=>[3,5,4,6,2,1,7]=>[5,3,4,2,6,7,1]=>{{1,5,6,7},{2,3,4}}
[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>[2,5,3,6,7,1,4]=>{{1,2,4,5,6,7},{3}}
[2,5,3,6,7,4,1]=>[6,3,5,2,1,4,7]=>[2,5,3,6,7,4,1]=>{{1,2,5,7},{3},{4,6}}
[2,5,3,7,1,4,6]=>[3,5,2,1,7,6,4]=>[5,3,6,7,1,2,4]=>{{1,5},{2,3,6},{4,7}}
[2,5,3,7,1,6,4]=>[3,5,2,1,7,4,6]=>[5,3,6,7,1,4,2]=>{{1,5},{2,3,4,6,7}}
[2,5,3,7,4,1,6]=>[3,5,2,1,4,7,6]=>[5,3,6,7,4,1,2]=>{{1,2,3,4,5,6,7}}
[2,5,3,7,4,6,1]=>[3,5,4,7,2,1,6]=>[5,3,4,1,6,7,2]=>{{1,2,3,4,5,6,7}}
[2,5,3,7,6,1,4]=>[3,5,2,1,6,7,4]=>[5,3,6,7,2,1,4]=>{{1,2,3,5,6},{4,7}}
[2,5,3,7,6,4,1]=>[3,5,2,1,4,6,7]=>[5,3,6,7,4,2,1]=>{{1,4,5,7},{2,3,6}}
[2,5,4,1,3,6,7]=>[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>{{1},{2},{3,6},{4,5,7}}
[2,5,4,1,3,7,6]=>[6,7,2,1,4,5,3]=>[2,1,6,7,4,3,5]=>{{1,2},{3,6},{4,5,7}}
[2,5,4,1,6,3,7]=>[7,2,1,4,5,3,6]=>[1,6,7,4,3,5,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,4,1,6,7,3]=>[6,2,1,4,5,3,7]=>[2,6,7,4,3,5,1]=>{{1,2,3,5,6,7},{4}}
[2,5,4,1,7,3,6]=>[2,1,4,5,3,7,6]=>[6,7,4,3,5,1,2]=>{{1,6},{2,7},{3,4},{5}}
[2,5,4,1,7,6,3]=>[2,1,4,5,3,6,7]=>[6,7,4,3,5,2,1]=>{{1,2,6,7},{3,4},{5}}
[2,5,4,3,1,6,7]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[2,5,4,3,1,7,6]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>{{1,2},{3,4,6,7},{5}}
[2,5,4,3,6,1,7]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>{{1},{2,5,6,7},{3,4}}
[2,5,4,3,6,7,1]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>{{1,2,5,6,7},{3,4}}
[2,5,4,3,7,1,6]=>[3,4,5,2,1,7,6]=>[5,4,3,6,7,1,2]=>{{1,2,4,5,6,7},{3}}
[2,5,4,3,7,6,1]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>{{1,5,7},{2,4,6},{3}}
[2,5,4,6,1,3,7]=>[7,4,5,2,1,6,3]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[2,5,4,6,1,7,3]=>[4,5,2,1,6,3,7]=>[4,3,6,7,2,5,1]=>{{1,4,7},{2,3,5,6}}
[2,5,4,6,3,1,7]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,4,6,3,7,1]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,5,4,6,7,1,3]=>[6,4,5,2,1,7,3]=>[2,4,3,6,7,1,5]=>{{1,2,4,6},{3},{5,7}}
[2,5,4,6,7,3,1]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>{{1,2,4,5,6,7},{3}}
[2,5,4,7,1,3,6]=>[4,5,2,1,7,6,3]=>[4,3,6,7,1,2,5]=>{{1,4,5,7},{2,3,6}}
[2,5,4,7,1,6,3]=>[4,5,2,1,7,3,6]=>[4,3,6,7,1,5,2]=>{{1,2,3,4,5,6,7}}
[2,5,4,7,3,1,6]=>[4,5,2,1,3,7,6]=>[4,3,6,7,5,1,2]=>{{1,2,3,4,6,7},{5}}
[2,5,4,7,3,6,1]=>[4,5,3,7,2,1,6]=>[4,3,5,1,6,7,2]=>{{1,4},{2,3,5,6,7}}
[2,5,4,7,6,1,3]=>[4,5,2,1,6,7,3]=>[4,3,6,7,2,1,5]=>{{1,2,3,4,5,6,7}}
[2,5,4,7,6,3,1]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>{{1,4,7},{2,3,6},{5}}
[2,5,6,1,3,4,7]=>[7,5,2,1,6,4,3]=>[1,3,6,7,2,4,5]=>{{1},{2,3,4,5,6,7}}
[2,5,6,1,3,7,4]=>[5,2,1,6,4,7,3]=>[3,6,7,2,4,1,5]=>{{1,2,3,4,5,6,7}}
[2,5,6,1,4,3,7]=>[7,5,2,1,6,3,4]=>[1,3,6,7,2,5,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,6,1,4,7,3]=>[5,2,1,6,4,3,7]=>[3,6,7,2,4,5,1]=>{{1,3,7},{2,4,5,6}}
[2,5,6,1,7,3,4]=>[5,2,1,6,3,7,4]=>[3,6,7,2,5,1,4]=>{{1,2,3,4,6,7},{5}}
[2,5,6,1,7,4,3]=>[5,2,1,6,3,4,7]=>[3,6,7,2,5,4,1]=>{{1,3,7},{2,4,6},{5}}
[2,5,6,3,1,4,7]=>[7,5,2,1,3,6,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[2,5,6,3,1,7,4]=>[5,2,1,3,6,4,7]=>[3,6,7,5,2,4,1]=>{{1,3,7},{2,4,5,6}}
[2,5,6,3,4,1,7]=>[7,5,3,6,2,1,4]=>[1,3,5,2,6,7,4]=>{{1},{2,3,4,5,6,7}}
[2,5,6,3,4,7,1]=>[5,3,6,4,2,1,7]=>[3,5,2,4,6,7,1]=>{{1,2,3,5,6,7},{4}}
[2,5,6,3,7,1,4]=>[5,3,6,2,1,7,4]=>[3,5,2,6,7,1,4]=>{{1,2,3,4,5,6,7}}
[2,5,6,3,7,4,1]=>[5,3,6,2,1,4,7]=>[3,5,2,6,7,4,1]=>{{1,2,3,5,7},{4,6}}
[2,5,6,4,1,3,7]=>[7,5,2,1,4,6,3]=>[1,3,6,7,4,2,5]=>{{1},{2,3,6},{4,5,7}}
[2,5,6,4,1,7,3]=>[5,2,1,4,6,3,7]=>[3,6,7,4,2,5,1]=>{{1,3,7},{2,5,6},{4}}
[2,5,6,4,3,1,7]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[2,5,6,4,3,7,1]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>{{1,2,3,4,5,6,7}}
[2,5,6,4,7,1,3]=>[5,4,6,2,1,7,3]=>[3,4,2,6,7,1,5]=>{{1,2,3,4,6},{5,7}}
[2,5,6,4,7,3,1]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>{{1,2,3,4,5,6,7}}
[2,5,6,7,1,3,4]=>[6,5,2,1,7,4,3]=>[2,3,6,7,1,4,5]=>{{1,2,3,4,5,6,7}}
[2,5,6,7,1,4,3]=>[6,5,2,1,7,3,4]=>[2,3,6,7,1,5,4]=>{{1,2,3,5,6},{4,7}}
[2,5,6,7,3,1,4]=>[6,5,2,1,3,7,4]=>[2,3,6,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}
[2,5,6,7,3,4,1]=>[6,5,3,7,2,1,4]=>[2,3,5,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,5,6,7,4,1,3]=>[6,5,2,1,4,7,3]=>[2,3,6,7,4,1,5]=>{{1,2,3,6},{4,5,7}}
[2,5,6,7,4,3,1]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>{{1,2,3,4,6,7},{5}}
[2,5,7,1,3,4,6]=>[5,2,1,7,6,4,3]=>[3,6,7,1,2,4,5]=>{{1,2,3,4,5,6,7}}
[2,5,7,1,3,6,4]=>[5,2,1,7,4,6,3]=>[3,6,7,1,4,2,5]=>{{1,3,4,5,7},{2,6}}
[2,5,7,1,4,3,6]=>[5,2,1,7,6,3,4]=>[3,6,7,1,2,5,4]=>{{1,3,4,7},{2,5,6}}
[2,5,7,1,4,6,3]=>[5,2,1,7,4,3,6]=>[3,6,7,1,4,5,2]=>{{1,2,3,4,5,6,7}}
[2,5,7,1,6,3,4]=>[5,2,1,7,3,6,4]=>[3,6,7,1,5,2,4]=>{{1,3,4,7},{2,6},{5}}
[2,5,7,1,6,4,3]=>[5,2,1,7,3,4,6]=>[3,6,7,1,5,4,2]=>{{1,2,3,4,6,7},{5}}
[2,5,7,3,1,4,6]=>[5,2,1,3,7,6,4]=>[3,6,7,5,1,2,4]=>{{1,3,4,5,7},{2,6}}
[2,5,7,3,1,6,4]=>[5,2,1,3,7,4,6]=>[3,6,7,5,1,4,2]=>{{1,2,3,4,5,6,7}}
[2,5,7,3,4,1,6]=>[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>{{1,3},{2,4,5,6,7}}
[2,5,7,3,4,6,1]=>[5,3,7,4,2,1,6]=>[3,5,1,4,6,7,2]=>{{1,3},{2,5,6,7},{4}}
[2,5,7,3,6,1,4]=>[5,3,7,2,1,6,4]=>[3,5,1,6,7,2,4]=>{{1,3},{2,4,5,6,7}}
[2,5,7,3,6,4,1]=>[5,3,7,2,1,4,6]=>[3,5,1,6,7,4,2]=>{{1,3},{2,5,7},{4,6}}
[2,5,7,4,1,3,6]=>[5,2,1,4,7,6,3]=>[3,6,7,4,1,2,5]=>{{1,3,5,7},{2,6},{4}}
[2,5,7,4,1,6,3]=>[5,2,1,4,7,3,6]=>[3,6,7,4,1,5,2]=>{{1,2,3,5,6,7},{4}}
[2,5,7,4,3,1,6]=>[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>{{1,2,3,6,7},{4,5}}
[2,5,7,4,3,6,1]=>[5,3,4,7,2,1,6]=>[3,5,4,1,6,7,2]=>{{1,3,4},{2,5,6,7}}
[2,5,7,4,6,1,3]=>[5,4,7,2,1,6,3]=>[3,4,1,6,7,2,5]=>{{1,3},{2,4,6},{5,7}}
[2,5,7,4,6,3,1]=>[5,4,7,2,1,3,6]=>[3,4,1,6,7,5,2]=>{{1,3},{2,4,5,6,7}}
[2,5,7,6,1,3,4]=>[5,2,1,6,7,4,3]=>[3,6,7,2,1,4,5]=>{{1,3,5,7},{2,4,6}}
[2,5,7,6,1,4,3]=>[5,2,1,6,7,3,4]=>[3,6,7,2,1,5,4]=>{{1,2,3,4,5,6,7}}
[2,5,7,6,3,1,4]=>[5,2,1,3,6,7,4]=>[3,6,7,5,2,1,4]=>{{1,2,3,4,5,6,7}}
[2,5,7,6,3,4,1]=>[5,3,6,7,2,1,4]=>[3,5,2,1,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,5,7,6,4,1,3]=>[5,2,1,4,6,7,3]=>[3,6,7,4,2,1,5]=>{{1,2,3,5,6,7},{4}}
[2,5,7,6,4,3,1]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>{{1,3,7},{2,6},{4,5}}
[2,6,1,3,4,5,7]=>[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>{{1},{2,4,6},{3,5,7}}
[2,6,1,3,4,7,5]=>[2,1,6,5,7,4,3]=>[6,7,2,3,1,4,5]=>{{1,2,3,4,5,6,7}}
[2,6,1,3,5,4,7]=>[7,2,1,6,4,5,3]=>[1,6,7,2,4,3,5]=>{{1},{2,3,4,5,6,7}}
[2,6,1,3,5,7,4]=>[2,1,6,5,4,7,3]=>[6,7,2,3,4,1,5]=>{{1,6},{2,3,4,5,7}}
[2,6,1,3,7,4,5]=>[2,1,6,4,7,5,3]=>[6,7,2,4,1,3,5]=>{{1,2,3,5,6,7},{4}}
[2,6,1,3,7,5,4]=>[2,1,6,4,5,7,3]=>[6,7,2,4,3,1,5]=>{{1,6},{2,3,5,7},{4}}
[2,6,1,4,3,5,7]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>{{1},{2,3,4,5,6,7}}
[2,6,1,4,3,7,5]=>[2,1,6,5,7,3,4]=>[6,7,2,3,1,5,4]=>{{1,5,6},{2,3,4,7}}
[2,6,1,4,5,3,7]=>[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>{{1},{2,4,5,6},{3,7}}
[2,6,1,4,5,7,3]=>[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>{{1,2,3,4,5,6,7}}
[2,6,1,4,7,3,5]=>[2,1,6,4,3,7,5]=>[6,7,2,4,5,1,3]=>{{1,6},{2,3,7},{4},{5}}
[2,6,1,4,7,5,3]=>[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>{{1,2,3,6,7},{4},{5}}
[2,6,1,5,3,4,7]=>[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>{{1},{2,3,4,6,7},{5}}
[2,6,1,5,3,7,4]=>[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>{{1,2,3,4,5,6,7}}
[2,6,1,5,4,3,7]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>{{1},{2,4,6},{3,7},{5}}
[2,6,1,5,4,7,3]=>[2,1,6,4,5,3,7]=>[6,7,2,4,3,5,1]=>{{1,2,3,5,6,7},{4}}
[2,6,1,5,7,3,4]=>[2,1,6,5,3,7,4]=>[6,7,2,3,5,1,4]=>{{1,6},{2,3,4,7},{5}}
[2,6,1,5,7,4,3]=>[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>{{1,2,3,4,6,7},{5}}
[2,6,1,7,3,4,5]=>[2,1,6,3,7,5,4]=>[6,7,2,5,1,3,4]=>{{1,2,3,4,5,6,7}}
[2,6,1,7,3,5,4]=>[2,1,6,3,7,4,5]=>[6,7,2,5,1,4,3]=>{{1,4,5,6},{2,3,7}}
[2,6,1,7,4,3,5]=>[2,1,6,3,4,7,5]=>[6,7,2,5,4,1,3]=>{{1,6},{2,3,7},{4,5}}
[2,6,1,7,4,5,3]=>[2,1,6,4,7,3,5]=>[6,7,2,4,1,5,3]=>{{1,5,6},{2,3,7},{4}}
[2,6,1,7,5,3,4]=>[2,1,6,3,5,7,4]=>[6,7,2,5,3,1,4]=>{{1,6},{2,3,4,5,7}}
[2,6,1,7,5,4,3]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>{{1,2,3,6,7},{4,5}}
[2,6,3,1,4,5,7]=>[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>{{1},{2,3,4,5,6,7}}
[2,6,3,1,4,7,5]=>[2,1,3,6,5,7,4]=>[6,7,5,2,3,1,4]=>{{1,6},{2,4,7},{3,5}}
[2,6,3,1,5,4,7]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>{{1},{2,4,5,6},{3,7}}
[2,6,3,1,5,7,4]=>[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>{{1,2,4,6,7},{3,5}}
[2,6,3,1,7,4,5]=>[2,1,3,6,4,7,5]=>[6,7,5,2,4,1,3]=>{{1,6},{2,3,4,5,7}}
[2,6,3,1,7,5,4]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>{{1,2,3,4,5,6,7}}
[2,6,3,4,1,5,7]=>[7,3,6,5,2,1,4]=>[1,5,2,3,6,7,4]=>{{1},{2,3,4,5,6,7}}
[2,6,3,4,1,7,5]=>[3,6,5,7,2,1,4]=>[5,2,3,1,6,7,4]=>{{1,4,5,6,7},{2},{3}}
[2,6,3,4,5,1,7]=>[7,3,6,4,2,1,5]=>[1,5,2,4,6,7,3]=>{{1},{2,3,5,6,7},{4}}
[2,6,3,4,5,7,1]=>[3,6,5,4,2,1,7]=>[5,2,3,4,6,7,1]=>{{1,5,6,7},{2},{3},{4}}
[2,6,3,4,7,1,5]=>[3,6,4,2,1,7,5]=>[5,2,4,6,7,1,3]=>{{1,3,4,5,6,7},{2}}
[2,6,3,4,7,5,1]=>[3,6,4,2,1,5,7]=>[5,2,4,6,7,3,1]=>{{1,5,7},{2},{3,4,6}}
[2,6,3,5,1,4,7]=>[7,3,6,2,1,5,4]=>[1,5,2,6,7,3,4]=>{{1},{2,3,4,5,6,7}}
[2,6,3,5,1,7,4]=>[3,6,2,1,5,4,7]=>[5,2,6,7,3,4,1]=>{{1,3,4,5,6,7},{2}}
[2,6,3,5,4,1,7]=>[7,3,6,2,1,4,5]=>[1,5,2,6,7,4,3]=>{{1},{2,3,5,7},{4,6}}
[2,6,3,5,4,7,1]=>[3,6,4,5,2,1,7]=>[5,2,4,3,6,7,1]=>{{1,5,6,7},{2},{3,4}}
[2,6,3,5,7,1,4]=>[3,6,5,2,1,7,4]=>[5,2,3,6,7,1,4]=>{{1,4,5,6,7},{2},{3}}
[2,6,3,5,7,4,1]=>[3,6,5,2,1,4,7]=>[5,2,3,6,7,4,1]=>{{1,5,7},{2},{3},{4,6}}
[2,6,3,7,1,4,5]=>[3,6,2,1,7,5,4]=>[5,2,6,7,1,3,4]=>{{1,5},{2},{3,6},{4,7}}
[2,6,3,7,1,5,4]=>[3,6,2,1,7,4,5]=>[5,2,6,7,1,4,3]=>{{1,5},{2},{3,4,6,7}}
[2,6,3,7,4,1,5]=>[3,6,2,1,4,7,5]=>[5,2,6,7,4,1,3]=>{{1,3,4,5,6,7},{2}}
[2,6,3,7,4,5,1]=>[3,6,4,7,2,1,5]=>[5,2,4,1,6,7,3]=>{{1,3,4,5,6,7},{2}}
[2,6,3,7,5,1,4]=>[3,6,2,1,5,7,4]=>[5,2,6,7,3,1,4]=>{{1,3,5,6},{2},{4,7}}
[2,6,3,7,5,4,1]=>[3,6,2,1,4,5,7]=>[5,2,6,7,4,3,1]=>{{1,4,5,7},{2},{3,6}}
[2,6,4,1,3,5,7]=>[7,2,1,4,6,5,3]=>[1,6,7,4,2,3,5]=>{{1},{2,3,5,6,7},{4}}
[2,6,4,1,3,7,5]=>[2,1,4,6,5,7,3]=>[6,7,4,2,3,1,5]=>{{1,6},{2,3,4,5,7}}
[2,6,4,1,5,3,7]=>[7,2,1,4,6,3,5]=>[1,6,7,4,2,5,3]=>{{1},{2,5,6},{3,7},{4}}
[2,6,4,1,5,7,3]=>[2,1,4,6,5,3,7]=>[6,7,4,2,3,5,1]=>{{1,2,3,4,5,6,7}}
[2,6,4,1,7,3,5]=>[2,1,4,6,3,7,5]=>[6,7,4,2,5,1,3]=>{{1,6},{2,3,4,7},{5}}
[2,6,4,1,7,5,3]=>[2,1,4,6,3,5,7]=>[6,7,4,2,5,3,1]=>{{1,2,3,4,6,7},{5}}
[2,6,4,3,1,5,7]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>{{1},{2,6},{3,7},{4,5}}
[2,6,4,3,1,7,5]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>{{1,2,3,5,6,7},{4}}
[2,6,4,3,5,1,7]=>[7,3,4,6,2,1,5]=>[1,5,4,2,6,7,3]=>{{1},{2,3,4,5,6,7}}
[2,6,4,3,5,7,1]=>[3,4,6,5,2,1,7]=>[5,4,2,3,6,7,1]=>{{1,5,6,7},{2,3,4}}
[2,6,4,3,7,1,5]=>[3,4,6,2,1,7,5]=>[5,4,2,6,7,1,3]=>{{1,2,3,4,5,6,7}}
[2,6,4,3,7,5,1]=>[3,4,6,2,1,5,7]=>[5,4,2,6,7,3,1]=>{{1,5,7},{2,3,4,6}}
[2,6,4,5,1,3,7]=>[7,4,6,2,1,5,3]=>[1,4,2,6,7,3,5]=>{{1},{2,3,4,6},{5,7}}
[2,6,4,5,1,7,3]=>[4,6,2,1,5,3,7]=>[4,2,6,7,3,5,1]=>{{1,4,7},{2},{3,5,6}}
[2,6,4,5,3,1,7]=>[7,4,6,2,1,3,5]=>[1,4,2,6,7,5,3]=>{{1},{2,3,4,5,6,7}}
[2,6,4,5,3,7,1]=>[4,6,3,5,2,1,7]=>[4,2,5,3,6,7,1]=>{{1,3,4,5,6,7},{2}}
[2,6,4,5,7,1,3]=>[4,6,5,2,1,7,3]=>[4,2,3,6,7,1,5]=>{{1,4,6},{2},{3},{5,7}}
[2,6,4,5,7,3,1]=>[4,6,5,2,1,3,7]=>[4,2,3,6,7,5,1]=>{{1,4,5,6,7},{2},{3}}
[2,6,4,7,1,3,5]=>[4,6,2,1,7,5,3]=>[4,2,6,7,1,3,5]=>{{1,4,5,7},{2},{3,6}}
[2,6,4,7,1,5,3]=>[4,6,2,1,7,3,5]=>[4,2,6,7,1,5,3]=>{{1,3,4,5,6,7},{2}}
[2,6,4,7,3,1,5]=>[4,6,2,1,3,7,5]=>[4,2,6,7,5,1,3]=>{{1,3,4,6,7},{2},{5}}
[2,6,4,7,3,5,1]=>[4,6,3,7,2,1,5]=>[4,2,5,1,6,7,3]=>{{1,4},{2},{3,5,6,7}}
[2,6,4,7,5,1,3]=>[4,6,2,1,5,7,3]=>[4,2,6,7,3,1,5]=>{{1,3,4,5,6,7},{2}}
[2,6,4,7,5,3,1]=>[4,6,2,1,3,5,7]=>[4,2,6,7,5,3,1]=>{{1,4,7},{2},{3,6},{5}}
[2,6,5,1,3,4,7]=>[7,2,1,5,6,4,3]=>[1,6,7,3,2,4,5]=>{{1},{2,3,4,5,6,7}}
[2,6,5,1,3,7,4]=>[2,1,5,6,4,7,3]=>[6,7,3,2,4,1,5]=>{{1,6},{2,4,5,7},{3}}
[2,6,5,1,4,3,7]=>[7,2,1,5,6,3,4]=>[1,6,7,3,2,5,4]=>{{1},{2,5,6},{3,4,7}}
[2,6,5,1,4,7,3]=>[2,1,5,6,4,3,7]=>[6,7,3,2,4,5,1]=>{{1,2,4,5,6,7},{3}}
[2,6,5,1,7,3,4]=>[2,1,5,6,3,7,4]=>[6,7,3,2,5,1,4]=>{{1,6},{2,4,7},{3},{5}}
[2,6,5,1,7,4,3]=>[2,1,5,6,3,4,7]=>[6,7,3,2,5,4,1]=>{{1,2,4,6,7},{3},{5}}
[2,6,5,3,1,4,7]=>[7,2,1,3,5,6,4]=>[1,6,7,5,3,2,4]=>{{1},{2,6},{3,4,5,7}}
[2,6,5,3,1,7,4]=>[2,1,3,5,6,4,7]=>[6,7,5,3,2,4,1]=>{{1,2,3,4,5,6,7}}
[2,6,5,3,4,1,7]=>[7,3,5,6,2,1,4]=>[1,5,3,2,6,7,4]=>{{1},{2,4,5,6,7},{3}}
[2,6,5,3,4,7,1]=>[3,5,6,4,2,1,7]=>[5,3,2,4,6,7,1]=>{{1,5,6,7},{2,3},{4}}
[2,6,5,3,7,1,4]=>[3,5,6,2,1,7,4]=>[5,3,2,6,7,1,4]=>{{1,4,5,6,7},{2,3}}
[2,6,5,3,7,4,1]=>[3,5,6,2,1,4,7]=>[5,3,2,6,7,4,1]=>{{1,5,7},{2,3},{4,6}}
[2,6,5,4,1,3,7]=>[7,2,1,4,5,6,3]=>[1,6,7,4,3,2,5]=>{{1},{2,6},{3,5,7},{4}}
[2,6,5,4,1,7,3]=>[2,1,4,5,6,3,7]=>[6,7,4,3,2,5,1]=>{{1,2,5,6,7},{3,4}}
[2,6,5,4,3,1,7]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>{{1},{2,3,6,7},{4,5}}
[2,6,5,4,3,7,1]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>{{1,5,6,7},{2,4},{3}}
[2,6,5,4,7,1,3]=>[4,5,6,2,1,7,3]=>[4,3,2,6,7,1,5]=>{{1,4,6},{2,3},{5,7}}
[2,6,5,4,7,3,1]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>{{1,4,5,6,7},{2,3}}
[2,6,5,7,1,3,4]=>[5,6,2,1,7,4,3]=>[3,2,6,7,1,4,5]=>{{1,3,4,5,6,7},{2}}
[2,6,5,7,1,4,3]=>[5,6,2,1,7,3,4]=>[3,2,6,7,1,5,4]=>{{1,3,5,6},{2},{4,7}}
[2,6,5,7,3,1,4]=>[5,6,2,1,3,7,4]=>[3,2,6,7,5,1,4]=>{{1,3,6},{2},{4,7},{5}}
[2,6,5,7,3,4,1]=>[5,6,3,7,2,1,4]=>[3,2,5,1,6,7,4]=>{{1,3,4,5,6,7},{2}}
[2,6,5,7,4,1,3]=>[5,6,2,1,4,7,3]=>[3,2,6,7,4,1,5]=>{{1,3,6},{2},{4,5,7}}
[2,6,5,7,4,3,1]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>{{1,3,4,6,7},{2},{5}}
[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>[2,6,7,1,3,4,5]=>{{1,2,4,6},{3,5,7}}
[2,6,7,1,3,5,4]=>[6,2,1,7,4,5,3]=>[2,6,7,1,4,3,5]=>{{1,2,3,4,5,6,7}}
[2,6,7,1,4,3,5]=>[6,2,1,7,5,3,4]=>[2,6,7,1,3,5,4]=>{{1,2,3,4,5,6,7}}
[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>[2,6,7,1,4,5,3]=>{{1,2,4,5,6},{3,7}}
[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>[2,6,7,1,5,3,4]=>{{1,2,3,4,6,7},{5}}
[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>[2,6,7,1,5,4,3]=>{{1,2,4,6},{3,7},{5}}
[2,6,7,3,1,4,5]=>[6,2,1,3,7,5,4]=>[2,6,7,5,1,3,4]=>{{1,2,3,4,5,6,7}}
[2,6,7,3,1,5,4]=>[6,2,1,3,7,4,5]=>[2,6,7,5,1,4,3]=>{{1,2,4,5,6},{3,7}}
[2,6,7,3,4,1,5]=>[6,3,7,5,2,1,4]=>[2,5,1,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,6,7,3,4,5,1]=>[6,3,7,4,2,1,5]=>[2,5,1,4,6,7,3]=>{{1,2,3,5,6,7},{4}}
[2,6,7,3,5,1,4]=>[6,3,7,2,1,5,4]=>[2,5,1,6,7,3,4]=>{{1,2,3,4,5,6,7}}
[2,6,7,3,5,4,1]=>[6,3,7,2,1,4,5]=>[2,5,1,6,7,4,3]=>{{1,2,3,5,7},{4,6}}
[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>[2,6,7,4,1,3,5]=>{{1,2,3,5,6,7},{4}}
[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>[2,6,7,4,1,5,3]=>{{1,2,5,6},{3,7},{4}}
[2,6,7,4,3,1,5]=>[6,2,1,3,4,7,5]=>[2,6,7,5,4,1,3]=>{{1,2,6},{3,7},{4,5}}
[2,6,7,4,3,5,1]=>[6,3,4,7,2,1,5]=>[2,5,4,1,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,6,7,4,5,1,3]=>[6,4,7,2,1,5,3]=>[2,4,1,6,7,3,5]=>{{1,2,3,4,6},{5,7}}
[2,6,7,4,5,3,1]=>[6,4,7,2,1,3,5]=>[2,4,1,6,7,5,3]=>{{1,2,3,4,5,6,7}}
[2,6,7,5,1,3,4]=>[6,2,1,5,7,4,3]=>[2,6,7,3,1,4,5]=>{{1,2,3,4,5,6,7}}
[2,6,7,5,1,4,3]=>[6,2,1,5,7,3,4]=>[2,6,7,3,1,5,4]=>{{1,2,5,6},{3,4,7}}
[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>[2,6,7,5,3,1,4]=>{{1,2,6},{3,4,5,7}}
[2,6,7,5,3,4,1]=>[6,3,5,7,2,1,4]=>[2,5,3,1,6,7,4]=>{{1,2,4,5,6,7},{3}}
[2,6,7,5,4,1,3]=>[6,2,1,4,5,7,3]=>[2,6,7,4,3,1,5]=>{{1,2,6},{3,5,7},{4}}
[2,6,7,5,4,3,1]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>{{1,2,3,6,7},{4,5}}
[2,7,1,3,4,5,6]=>[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>{{1,2,3,4,5,6,7}}
[2,7,1,3,4,6,5]=>[2,1,7,5,6,4,3]=>[6,7,1,3,2,4,5]=>{{1,3,4,6},{2,5,7}}
[2,7,1,3,5,4,6]=>[2,1,7,6,4,5,3]=>[6,7,1,2,4,3,5]=>{{1,3,6},{2,4,5,7}}
[2,7,1,3,5,6,4]=>[2,1,7,5,4,6,3]=>[6,7,1,3,4,2,5]=>{{1,2,3,4,5,6,7}}
[2,7,1,3,6,4,5]=>[2,1,7,4,6,5,3]=>[6,7,1,4,2,3,5]=>{{1,3,6},{2,5,7},{4}}
[2,7,1,3,6,5,4]=>[2,1,7,4,5,6,3]=>[6,7,1,4,3,2,5]=>{{1,2,3,5,6,7},{4}}
[2,7,1,4,3,5,6]=>[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>{{1,3,5,6},{2,4,7}}
[2,7,1,4,3,6,5]=>[2,1,7,5,6,3,4]=>[6,7,1,3,2,5,4]=>{{1,2,3,4,5,6,7}}
[2,7,1,4,5,3,6]=>[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>{{1,2,3,4,5,6,7}}
[2,7,1,4,5,6,3]=>[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>{{1,3,4,5,6},{2,7}}
[2,7,1,4,6,3,5]=>[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>{{1,2,3,6,7},{4},{5}}
[2,7,1,4,6,5,3]=>[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>{{1,3,6},{2,7},{4},{5}}
[2,7,1,5,3,4,6]=>[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>{{1,3,6},{2,4,7},{5}}
[2,7,1,5,3,6,4]=>[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>{{1,3,4,5,6},{2,7}}
[2,7,1,5,4,3,6]=>[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>{{1,2,3,4,6,7},{5}}
[2,7,1,5,4,6,3]=>[2,1,7,4,5,3,6]=>[6,7,1,4,3,5,2]=>{{1,3,5,6},{2,7},{4}}
[2,7,1,5,6,3,4]=>[2,1,7,5,3,6,4]=>[6,7,1,3,5,2,4]=>{{1,2,3,4,6,7},{5}}
[2,7,1,5,6,4,3]=>[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>{{1,3,4,6},{2,7},{5}}
[2,7,1,6,3,4,5]=>[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>{{1,3,6},{2,4,5,7}}
[2,7,1,6,3,5,4]=>[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>{{1,2,3,4,5,6,7}}
[2,7,1,6,4,3,5]=>[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>{{1,2,3,6,7},{4,5}}
[2,7,1,6,4,5,3]=>[2,1,7,4,6,3,5]=>[6,7,1,4,2,5,3]=>{{1,2,3,5,6,7},{4}}
[2,7,1,6,5,3,4]=>[2,1,7,3,5,6,4]=>[6,7,1,5,3,2,4]=>{{1,2,3,4,5,6,7}}
[2,7,1,6,5,4,3]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>{{1,3,6},{2,7},{4,5}}
[2,7,3,1,4,5,6]=>[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>{{1,2,3,4,5,6,7}}
[2,7,3,1,4,6,5]=>[2,1,3,7,5,6,4]=>[6,7,5,1,3,2,4]=>{{1,2,4,6,7},{3,5}}
[2,7,3,1,5,4,6]=>[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>{{1,4,6},{2,3,5,7}}
[2,7,3,1,5,6,4]=>[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>{{1,4,6},{2,7},{3,5}}
[2,7,3,1,6,4,5]=>[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>{{1,2,3,4,5,6,7}}
[2,7,3,1,6,5,4]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>{{1,3,4,5,6},{2,7}}
[2,7,3,4,1,5,6]=>[3,7,6,5,2,1,4]=>[5,1,2,3,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,7,3,4,1,6,5]=>[3,7,5,6,2,1,4]=>[5,1,3,2,6,7,4]=>{{1,2,4,5,6,7},{3}}
[2,7,3,4,5,1,6]=>[3,7,6,4,2,1,5]=>[5,1,2,4,6,7,3]=>{{1,2,3,5,6,7},{4}}
[2,7,3,4,5,6,1]=>[3,7,5,4,2,1,6]=>[5,1,3,4,6,7,2]=>{{1,2,5,6,7},{3},{4}}
[2,7,3,4,6,1,5]=>[3,7,4,2,1,6,5]=>[5,1,4,6,7,2,3]=>{{1,2,3,4,5,6,7}}
[2,7,3,4,6,5,1]=>[3,7,4,2,1,5,6]=>[5,1,4,6,7,3,2]=>{{1,2,5,7},{3,4,6}}
[2,7,3,5,1,4,6]=>[3,7,6,2,1,5,4]=>[5,1,2,6,7,3,4]=>{{1,2,3,4,5,6,7}}
[2,7,3,5,1,6,4]=>[3,7,2,1,5,4,6]=>[5,1,6,7,3,4,2]=>{{1,2,3,4,5,6,7}}
[2,7,3,5,4,1,6]=>[3,7,6,2,1,4,5]=>[5,1,2,6,7,4,3]=>{{1,2,3,5,7},{4,6}}
[2,7,3,5,4,6,1]=>[3,7,4,5,2,1,6]=>[5,1,4,3,6,7,2]=>{{1,2,5,6,7},{3,4}}
[2,7,3,5,6,1,4]=>[3,7,5,2,1,6,4]=>[5,1,3,6,7,2,4]=>{{1,2,4,5,6,7},{3}}
[2,7,3,5,6,4,1]=>[3,7,5,2,1,4,6]=>[5,1,3,6,7,4,2]=>{{1,2,5,7},{3},{4,6}}
[2,7,3,6,1,4,5]=>[3,7,2,1,6,5,4]=>[5,1,6,7,2,3,4]=>{{1,2,5},{3,6},{4,7}}
[2,7,3,6,1,5,4]=>[3,7,2,1,6,4,5]=>[5,1,6,7,2,4,3]=>{{1,2,5},{3,4,6,7}}
[2,7,3,6,4,1,5]=>[3,7,2,1,4,6,5]=>[5,1,6,7,4,2,3]=>{{1,2,3,4,5,6,7}}
[2,7,3,6,4,5,1]=>[3,7,4,6,2,1,5]=>[5,1,4,2,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,7,3,6,5,1,4]=>[3,7,2,1,5,6,4]=>[5,1,6,7,3,2,4]=>{{1,2,3,5,6},{4,7}}
[2,7,3,6,5,4,1]=>[3,7,2,1,4,5,6]=>[5,1,6,7,4,3,2]=>{{1,2,4,5,7},{3,6}}
[2,7,4,1,3,5,6]=>[2,1,4,7,6,5,3]=>[6,7,4,1,2,3,5]=>{{1,3,4,6},{2,5,7}}
[2,7,4,1,3,6,5]=>[2,1,4,7,5,6,3]=>[6,7,4,1,3,2,5]=>{{1,2,3,4,5,6,7}}
[2,7,4,1,5,3,6]=>[2,1,4,7,6,3,5]=>[6,7,4,1,2,5,3]=>{{1,2,3,4,5,6,7}}
[2,7,4,1,5,6,3]=>[2,1,4,7,5,3,6]=>[6,7,4,1,3,5,2]=>{{1,3,4,5,6},{2,7}}
[2,7,4,1,6,3,5]=>[2,1,4,7,3,6,5]=>[6,7,4,1,5,2,3]=>{{1,2,3,4,6,7},{5}}
[2,7,4,1,6,5,3]=>[2,1,4,7,3,5,6]=>[6,7,4,1,5,3,2]=>{{1,3,4,6},{2,7},{5}}
[2,7,4,3,1,5,6]=>[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>{{1,2,3,5,6,7},{4}}
[2,7,4,3,1,6,5]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>{{1,3,5,6},{2,7},{4}}
[2,7,4,3,5,1,6]=>[3,4,7,6,2,1,5]=>[5,4,1,2,6,7,3]=>{{1,3,5,6,7},{2,4}}
[2,7,4,3,5,6,1]=>[3,4,7,5,2,1,6]=>[5,4,1,3,6,7,2]=>{{1,2,3,4,5,6,7}}
[2,7,4,3,6,1,5]=>[3,4,7,2,1,6,5]=>[5,4,1,6,7,2,3]=>{{1,3,5,7},{2,4,6}}
[2,7,4,3,6,5,1]=>[3,4,7,2,1,5,6]=>[5,4,1,6,7,3,2]=>{{1,2,3,4,5,6,7}}
[2,7,4,5,1,3,6]=>[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>{{1,2,3,4,6},{5,7}}
[2,7,4,5,1,6,3]=>[4,7,2,1,5,3,6]=>[4,1,6,7,3,5,2]=>{{1,2,4,7},{3,5,6}}
[2,7,4,5,3,1,6]=>[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>{{1,2,3,4,5,6,7}}
[2,7,4,5,3,6,1]=>[4,7,3,5,2,1,6]=>[4,1,5,3,6,7,2]=>{{1,2,3,4,5,6,7}}
[2,7,4,5,6,1,3]=>[4,7,5,2,1,6,3]=>[4,1,3,6,7,2,5]=>{{1,2,4,6},{3},{5,7}}
[2,7,4,5,6,3,1]=>[4,7,5,2,1,3,6]=>[4,1,3,6,7,5,2]=>{{1,2,4,5,6,7},{3}}
[2,7,4,6,1,3,5]=>[4,7,2,1,6,5,3]=>[4,1,6,7,2,3,5]=>{{1,2,4,5,7},{3,6}}
[2,7,4,6,1,5,3]=>[4,7,2,1,6,3,5]=>[4,1,6,7,2,5,3]=>{{1,2,3,4,5,6,7}}
[2,7,4,6,3,1,5]=>[4,7,2,1,3,6,5]=>[4,1,6,7,5,2,3]=>{{1,2,3,4,6,7},{5}}
[2,7,4,6,3,5,1]=>[4,7,3,6,2,1,5]=>[4,1,5,2,6,7,3]=>{{1,2,4},{3,5,6,7}}
[2,7,4,6,5,1,3]=>[4,7,2,1,5,6,3]=>[4,1,6,7,3,2,5]=>{{1,2,3,4,5,6,7}}
[2,7,4,6,5,3,1]=>[4,7,2,1,3,5,6]=>[4,1,6,7,5,3,2]=>{{1,2,4,7},{3,6},{5}}
[2,7,5,1,3,4,6]=>[2,1,5,7,6,4,3]=>[6,7,3,1,2,4,5]=>{{1,4,6},{2,5,7},{3}}
[2,7,5,1,3,6,4]=>[2,1,5,7,4,6,3]=>[6,7,3,1,4,2,5]=>{{1,2,4,5,6,7},{3}}
[2,7,5,1,4,3,6]=>[2,1,5,7,6,3,4]=>[6,7,3,1,2,5,4]=>{{1,2,4,5,6,7},{3}}
[2,7,5,1,4,6,3]=>[2,1,5,7,4,3,6]=>[6,7,3,1,4,5,2]=>{{1,4,5,6},{2,7},{3}}
[2,7,5,1,6,3,4]=>[2,1,5,7,3,6,4]=>[6,7,3,1,5,2,4]=>{{1,2,4,6,7},{3},{5}}
[2,7,5,1,6,4,3]=>[2,1,5,7,3,4,6]=>[6,7,3,1,5,4,2]=>{{1,4,6},{2,7},{3},{5}}
[2,7,5,3,1,4,6]=>[2,1,3,5,7,6,4]=>[6,7,5,3,1,2,4]=>{{1,2,3,4,5,6,7}}
[2,7,5,3,1,6,4]=>[2,1,3,5,7,4,6]=>[6,7,5,3,1,4,2]=>{{1,3,4,5,6},{2,7}}
[2,7,5,3,4,1,6]=>[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,7,5,3,4,6,1]=>[3,5,7,4,2,1,6]=>[5,3,1,4,6,7,2]=>{{1,2,3,5,6,7},{4}}
[2,7,5,3,6,1,4]=>[3,5,7,2,1,6,4]=>[5,3,1,6,7,2,4]=>{{1,2,3,4,5,6,7}}
[2,7,5,3,6,4,1]=>[3,5,7,2,1,4,6]=>[5,3,1,6,7,4,2]=>{{1,2,3,5,7},{4,6}}
[2,7,5,4,1,3,6]=>[2,1,4,5,7,6,3]=>[6,7,4,3,1,2,5]=>{{1,2,5,6,7},{3,4}}
[2,7,5,4,1,6,3]=>[2,1,4,5,7,3,6]=>[6,7,4,3,1,5,2]=>{{1,5,6},{2,7},{3,4}}
[2,7,5,4,3,1,6]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>{{1,6},{2,7},{3,5},{4}}
[2,7,5,4,3,6,1]=>[3,4,5,7,2,1,6]=>[5,4,3,1,6,7,2]=>{{1,2,4,5,6,7},{3}}
[2,7,5,4,6,1,3]=>[4,5,7,2,1,6,3]=>[4,3,1,6,7,2,5]=>{{1,2,3,4,6},{5,7}}
[2,7,5,4,6,3,1]=>[4,5,7,2,1,3,6]=>[4,3,1,6,7,5,2]=>{{1,2,3,4,5,6,7}}
[2,7,5,6,1,3,4]=>[5,7,2,1,6,4,3]=>[3,1,6,7,2,4,5]=>{{1,2,3,4,5,6,7}}
[2,7,5,6,1,4,3]=>[5,7,2,1,6,3,4]=>[3,1,6,7,2,5,4]=>{{1,2,3,5,6},{4,7}}
[2,7,5,6,3,1,4]=>[5,7,2,1,3,6,4]=>[3,1,6,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}
[2,7,5,6,3,4,1]=>[5,7,3,6,2,1,4]=>[3,1,5,2,6,7,4]=>{{1,2,3,4,5,6,7}}
[2,7,5,6,4,1,3]=>[5,7,2,1,4,6,3]=>[3,1,6,7,4,2,5]=>{{1,2,3,6},{4,5,7}}
[2,7,5,6,4,3,1]=>[5,7,2,1,3,4,6]=>[3,1,6,7,5,4,2]=>{{1,2,3,4,6,7},{5}}
[2,7,6,1,3,4,5]=>[2,1,6,7,5,4,3]=>[6,7,2,1,3,4,5]=>{{1,4,6},{2,3,5,7}}
[2,7,6,1,3,5,4]=>[2,1,6,7,4,5,3]=>[6,7,2,1,4,3,5]=>{{1,2,3,4,5,6,7}}
[2,7,6,1,4,3,5]=>[2,1,6,7,5,3,4]=>[6,7,2,1,3,5,4]=>{{1,2,3,4,5,6,7}}
[2,7,6,1,4,5,3]=>[2,1,6,7,4,3,5]=>[6,7,2,1,4,5,3]=>{{1,4,5,6},{2,3,7}}
[2,7,6,1,5,3,4]=>[2,1,6,7,3,5,4]=>[6,7,2,1,5,3,4]=>{{1,2,3,4,6,7},{5}}
[2,7,6,1,5,4,3]=>[2,1,6,7,3,4,5]=>[6,7,2,1,5,4,3]=>{{1,4,6},{2,3,7},{5}}
[2,7,6,3,1,4,5]=>[2,1,3,6,7,5,4]=>[6,7,5,2,1,3,4]=>{{1,3,5,6},{2,4,7}}
[2,7,6,3,1,5,4]=>[2,1,3,6,7,4,5]=>[6,7,5,2,1,4,3]=>{{1,2,3,4,5,6,7}}
[2,7,6,3,4,1,5]=>[3,6,7,5,2,1,4]=>[5,2,1,3,6,7,4]=>{{1,3,4,5,6,7},{2}}
[2,7,6,3,4,5,1]=>[3,6,7,4,2,1,5]=>[5,2,1,4,6,7,3]=>{{1,3,5,6,7},{2},{4}}
[2,7,6,3,5,1,4]=>[3,6,7,2,1,5,4]=>[5,2,1,6,7,3,4]=>{{1,3,4,5,6,7},{2}}
[2,7,6,3,5,4,1]=>[3,6,7,2,1,4,5]=>[5,2,1,6,7,4,3]=>{{1,3,5,7},{2},{4,6}}
[2,7,6,4,1,3,5]=>[2,1,4,6,7,5,3]=>[6,7,4,2,1,3,5]=>{{1,2,3,4,5,6,7}}
[2,7,6,4,1,5,3]=>[2,1,4,6,7,3,5]=>[6,7,4,2,1,5,3]=>{{1,5,6},{2,3,4,7}}
[2,7,6,4,3,1,5]=>[2,1,3,4,6,7,5]=>[6,7,5,4,2,1,3]=>{{1,6},{2,3,5,7},{4}}
[2,7,6,4,3,5,1]=>[3,4,6,7,2,1,5]=>[5,4,2,1,6,7,3]=>{{1,2,3,4,5,6,7}}
[2,7,6,4,5,1,3]=>[4,6,7,2,1,5,3]=>[4,2,1,6,7,3,5]=>{{1,3,4,6},{2},{5,7}}
[2,7,6,4,5,3,1]=>[4,6,7,2,1,3,5]=>[4,2,1,6,7,5,3]=>{{1,3,4,5,6,7},{2}}
[2,7,6,5,1,3,4]=>[2,1,5,6,7,4,3]=>[6,7,3,2,1,4,5]=>{{1,2,4,5,6,7},{3}}
[2,7,6,5,1,4,3]=>[2,1,5,6,7,3,4]=>[6,7,3,2,1,5,4]=>{{1,5,6},{2,4,7},{3}}
[2,7,6,5,3,1,4]=>[2,1,3,5,6,7,4]=>[6,7,5,3,2,1,4]=>{{1,6},{2,3,4,5,7}}
[2,7,6,5,3,4,1]=>[3,5,6,7,2,1,4]=>[5,3,2,1,6,7,4]=>{{1,4,5,6,7},{2,3}}
[2,7,6,5,4,1,3]=>[2,1,4,5,6,7,3]=>[6,7,4,3,2,1,5]=>{{1,6},{2,5,7},{3,4}}
[2,7,6,5,4,3,1]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>{{1,2,6,7},{3,5},{4}}
[3,1,2,4,5,6,7]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>{{1},{2},{3},{4},{5,6,7}}
[3,1,2,4,5,7,6]=>[6,7,5,4,1,3,2]=>[2,1,3,4,7,5,6]=>{{1,2},{3},{4},{5,6,7}}
[3,1,2,4,6,5,7]=>[7,5,6,4,1,3,2]=>[1,3,2,4,7,5,6]=>{{1},{2,3},{4},{5,6,7}}
[3,1,2,4,6,7,5]=>[6,5,7,4,1,3,2]=>[2,3,1,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}
[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[3,1,2,4,7,5,6]=>{{1,2,3},{4},{5,6,7}}
[3,1,2,4,7,6,5]=>[5,6,7,4,1,3,2]=>[3,2,1,4,7,5,6]=>{{1,3},{2},{4},{5,6,7}}
[3,1,2,5,4,6,7]=>[7,6,4,5,1,3,2]=>[1,2,4,3,7,5,6]=>{{1},{2},{3,4},{5,6,7}}
[3,1,2,5,4,7,6]=>[6,7,4,5,1,3,2]=>[2,1,4,3,7,5,6]=>{{1,2},{3,4},{5,6,7}}
[3,1,2,5,6,4,7]=>[7,5,4,6,1,3,2]=>[1,3,4,2,7,5,6]=>{{1},{2,3,4},{5,6,7}}
[3,1,2,5,6,7,4]=>[6,5,4,7,1,3,2]=>[2,3,4,1,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,2,5,7,4,6]=>[5,4,7,6,1,3,2]=>[3,4,1,2,7,5,6]=>{{1,3},{2,4},{5,6,7}}
[3,1,2,5,7,6,4]=>[5,4,6,7,1,3,2]=>[3,4,2,1,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,2,6,4,5,7]=>[7,4,6,5,1,3,2]=>[1,4,2,3,7,5,6]=>{{1},{2,3,4},{5,6,7}}
[3,1,2,6,4,7,5]=>[4,6,5,7,1,3,2]=>[4,2,3,1,7,5,6]=>{{1,4},{2},{3},{5,6,7}}
[3,1,2,6,5,4,7]=>[7,4,5,6,1,3,2]=>[1,4,3,2,7,5,6]=>{{1},{2,4},{3},{5,6,7}}
[3,1,2,6,5,7,4]=>[5,6,4,7,1,3,2]=>[3,2,4,1,7,5,6]=>{{1,3,4},{2},{5,6,7}}
[3,1,2,6,7,4,5]=>[6,4,7,5,1,3,2]=>[2,4,1,3,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,2,6,7,5,4]=>[6,4,5,7,1,3,2]=>[2,4,3,1,7,5,6]=>{{1,2,4},{3},{5,6,7}}
[3,1,2,7,4,5,6]=>[4,7,6,5,1,3,2]=>[4,1,2,3,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,2,7,4,6,5]=>[4,7,5,6,1,3,2]=>[4,1,3,2,7,5,6]=>{{1,2,4},{3},{5,6,7}}
[3,1,2,7,5,4,6]=>[4,5,7,6,1,3,2]=>[4,3,1,2,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,2,7,5,6,4]=>[5,7,4,6,1,3,2]=>[3,1,4,2,7,5,6]=>{{1,2,3,4},{5,6,7}}
[3,1,2,7,6,4,5]=>[4,6,7,5,1,3,2]=>[4,2,1,3,7,5,6]=>{{1,3,4},{2},{5,6,7}}
[3,1,2,7,6,5,4]=>[4,5,6,7,1,3,2]=>[4,3,2,1,7,5,6]=>{{1,4},{2,3},{5,6,7}}
[3,1,4,2,5,6,7]=>[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[3,1,4,2,5,7,6]=>[6,7,5,1,3,2,4]=>[2,1,3,7,5,6,4]=>{{1,2},{3},{4,7},{5},{6}}
[3,1,4,2,6,5,7]=>[7,5,6,1,3,2,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[3,1,4,2,6,7,5]=>[6,5,7,1,3,2,4]=>[2,3,1,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}
[3,1,4,2,7,5,6]=>[5,7,6,1,3,2,4]=>[3,1,2,7,5,6,4]=>{{1,2,3},{4,7},{5},{6}}
[3,1,4,2,7,6,5]=>[5,6,7,1,3,2,4]=>[3,2,1,7,5,6,4]=>{{1,3},{2},{4,7},{5},{6}}
[3,1,4,5,2,6,7]=>[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[3,1,4,5,2,7,6]=>[6,7,4,1,3,2,5]=>[2,1,4,7,5,6,3]=>{{1,2},{3,4,7},{5},{6}}
[3,1,4,5,6,2,7]=>[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,1,4,5,6,7,2]=>[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[3,1,4,5,7,2,6]=>[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>{{1,2,3,4,5,6,7}}
[3,1,4,5,7,6,2]=>[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>{{1,3,7},{2,4,5,6}}
[3,1,4,6,2,5,7]=>[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[3,1,4,6,2,7,5]=>[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>{{1,2,3,4,5,6,7}}
[3,1,4,6,5,2,7]=>[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,4,6,5,7,2]=>[5,6,4,1,3,2,7]=>[3,2,4,7,5,6,1]=>{{1,3,4,7},{2},{5},{6}}
[3,1,4,6,7,2,5]=>[6,4,1,3,2,7,5]=>[2,4,7,5,6,1,3]=>{{1,2,4,5,6},{3,7}}
[3,1,4,6,7,5,2]=>[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>{{1,2,3,4,5,6,7}}
[3,1,4,7,2,5,6]=>[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>{{1,2,3,4,5,6,7}}
[3,1,4,7,2,6,5]=>[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>{{1,3,4,5,6},{2,7}}
[3,1,4,7,5,2,6]=>[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>{{1,4,6},{2,7},{3,5}}
[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>[3,1,4,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[3,1,4,7,6,2,5]=>[4,1,3,2,6,7,5]=>[4,7,5,6,2,1,3]=>{{1,4,6},{2,3,5,7}}
[3,1,4,7,6,5,2]=>[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>{{1,2,4,6,7},{3,5}}
[3,1,5,2,4,6,7]=>[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>{{1},{2},{3,4,5,6,7}}
[3,1,5,2,4,7,6]=>[6,7,1,3,2,5,4]=>[2,1,7,5,6,3,4]=>{{1,2},{3,4,5,6,7}}
[3,1,5,2,6,4,7]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>{{1},{2,7},{3,5},{4,6}}
[3,1,5,2,6,7,4]=>[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>{{1,2,7},{3,5},{4,6}}
[3,1,5,2,7,4,6]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>{{1,2,3,4,5,6,7}}
[3,1,5,2,7,6,4]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>{{1,7},{2,3,4,5,6}}
[3,1,5,4,2,6,7]=>[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>{{1},{2},{3,7},{4,5,6}}
[3,1,5,4,2,7,6]=>[6,7,1,3,2,4,5]=>[2,1,7,5,6,4,3]=>{{1,2},{3,7},{4,5,6}}
[3,1,5,4,6,2,7]=>[7,4,5,1,3,2,6]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[3,1,5,4,6,7,2]=>[6,4,5,1,3,2,7]=>[2,4,3,7,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[3,1,5,4,7,2,6]=>[4,5,1,3,2,7,6]=>[4,3,7,5,6,1,2]=>{{1,4,5,6},{2,3,7}}
[3,1,5,4,7,6,2]=>[4,5,1,3,2,6,7]=>[4,3,7,5,6,2,1]=>{{1,2,3,4,5,6,7}}
[3,1,5,6,2,4,7]=>[7,5,1,3,2,6,4]=>[1,3,7,5,6,2,4]=>{{1},{2,3,4,5,6,7}}
[3,1,5,6,2,7,4]=>[5,1,3,2,6,4,7]=>[3,7,5,6,2,4,1]=>{{1,2,3,5,7},{4,6}}
[3,1,5,6,4,2,7]=>[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>{{1},{2,3,7},{4,5,6}}
[3,1,5,6,4,7,2]=>[5,4,6,1,3,2,7]=>[3,4,2,7,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[3,1,5,6,7,2,4]=>[6,5,1,3,2,7,4]=>[2,3,7,5,6,1,4]=>{{1,2,3,4,5,6,7}}
[3,1,5,6,7,4,2]=>[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[3,1,5,7,2,4,6]=>[5,1,3,2,7,6,4]=>[3,7,5,6,1,2,4]=>{{1,3,5},{2,4,6,7}}
[3,1,5,7,2,6,4]=>[5,1,3,2,7,4,6]=>[3,7,5,6,1,4,2]=>{{1,3,5},{2,7},{4,6}}
[3,1,5,7,4,2,6]=>[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>{{1,3,4,5,6},{2,7}}
[3,1,5,7,4,6,2]=>[5,4,7,1,3,2,6]=>[3,4,1,7,5,6,2]=>{{1,3},{2,4,7},{5},{6}}
[3,1,5,7,6,2,4]=>[5,1,3,2,6,7,4]=>[3,7,5,6,2,1,4]=>{{1,2,3,4,5,6,7}}
[3,1,5,7,6,4,2]=>[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>{{1,2,3,4,5,6,7}}
[3,1,6,2,4,5,7]=>[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>{{1},{2,3,4,5,6,7}}
[3,1,6,2,4,7,5]=>[1,3,2,6,5,7,4]=>[7,5,6,2,3,1,4]=>{{1,2,3,4,5,6,7}}
[3,1,6,2,5,4,7]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>{{1},{2,3,5,7},{4,6}}
[3,1,6,2,5,7,4]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>{{1,7},{2,3,4,5,6}}
[3,1,6,2,7,4,5]=>[1,3,2,6,4,7,5]=>[7,5,6,2,4,1,3]=>{{1,3,6,7},{2,4,5}}
[3,1,6,2,7,5,4]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>{{1,7},{2,4,5},{3,6}}
[3,1,6,4,2,5,7]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>{{1},{2,3,4,5,6,7}}
[3,1,6,4,2,7,5]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>{{1,7},{2,5},{3,6},{4}}
[3,1,6,4,5,2,7]=>[7,4,6,1,3,2,5]=>[1,4,2,7,5,6,3]=>{{1},{2,3,4,7},{5},{6}}
[3,1,6,4,5,7,2]=>[4,6,5,1,3,2,7]=>[4,2,3,7,5,6,1]=>{{1,4,7},{2},{3},{5},{6}}
[3,1,6,4,7,2,5]=>[4,6,1,3,2,7,5]=>[4,2,7,5,6,1,3]=>{{1,4,5,6},{2},{3,7}}
[3,1,6,4,7,5,2]=>[4,6,1,3,2,5,7]=>[4,2,7,5,6,3,1]=>{{1,3,4,5,6,7},{2}}
[3,1,6,5,2,4,7]=>[7,1,3,2,5,6,4]=>[1,7,5,6,3,2,4]=>{{1},{2,4,6,7},{3,5}}
[3,1,6,5,2,7,4]=>[1,3,2,5,6,4,7]=>[7,5,6,3,2,4,1]=>{{1,7},{2,5},{3,4,6}}
[3,1,6,5,4,2,7]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>{{1},{2,7},{3,4,5,6}}
[3,1,6,5,4,7,2]=>[4,5,6,1,3,2,7]=>[4,3,2,7,5,6,1]=>{{1,4,7},{2,3},{5},{6}}
[3,1,6,5,7,2,4]=>[5,6,1,3,2,7,4]=>[3,2,7,5,6,1,4]=>{{1,3,4,5,6,7},{2}}
[3,1,6,5,7,4,2]=>[5,6,1,3,2,4,7]=>[3,2,7,5,6,4,1]=>{{1,3,7},{2},{4,5,6}}
[3,1,6,7,2,4,5]=>[6,1,3,2,7,5,4]=>[2,7,5,6,1,3,4]=>{{1,2,3,4,5,6,7}}
[3,1,6,7,2,5,4]=>[6,1,3,2,7,4,5]=>[2,7,5,6,1,4,3]=>{{1,2,3,5,7},{4,6}}
[3,1,6,7,4,2,5]=>[6,1,3,2,4,7,5]=>[2,7,5,6,4,1,3]=>{{1,2,3,4,5,6,7}}
[3,1,6,7,4,5,2]=>[6,4,7,1,3,2,5]=>[2,4,1,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[3,1,6,7,5,2,4]=>[6,1,3,2,5,7,4]=>[2,7,5,6,3,1,4]=>{{1,2,4,6,7},{3,5}}
[3,1,6,7,5,4,2]=>[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>{{1,2,7},{3,4,5,6}}
[3,1,7,2,4,5,6]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>{{1,4,7},{2,5},{3,6}}
[3,1,7,2,4,6,5]=>[1,3,2,7,5,6,4]=>[7,5,6,1,3,2,4]=>{{1,4,7},{2,3,5,6}}
[3,1,7,2,5,4,6]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>{{1,3,4,6,7},{2,5}}
[3,1,7,2,5,6,4]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>{{1,2,3,4,5,6,7}}
[3,1,7,2,6,4,5]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>{{1,2,3,4,5,6,7}}
[3,1,7,2,6,5,4]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>{{1,2,4,5,7},{3,6}}
[3,1,7,4,2,5,6]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>{{1,2,3,5,6,7},{4}}
[3,1,7,4,2,6,5]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>{{1,2,5,7},{3,6},{4}}
[3,1,7,4,5,2,6]=>[4,7,6,1,3,2,5]=>[4,1,2,7,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[3,1,7,4,5,6,2]=>[4,7,5,1,3,2,6]=>[4,1,3,7,5,6,2]=>{{1,2,4,7},{3},{5},{6}}
[3,1,7,4,6,2,5]=>[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>{{1,2,4,5,6},{3,7}}
[3,1,7,4,6,5,2]=>[4,7,1,3,2,5,6]=>[4,1,7,5,6,3,2]=>{{1,2,3,4,5,6,7}}
[3,1,7,5,2,4,6]=>[1,3,2,5,7,6,4]=>[7,5,6,3,1,2,4]=>{{1,2,3,4,5,6,7}}
[3,1,7,5,2,6,4]=>[1,3,2,5,7,4,6]=>[7,5,6,3,1,4,2]=>{{1,2,5,7},{3,4,6}}
[3,1,7,5,4,2,6]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>{{1,2,3,5,6,7},{4}}
[3,1,7,5,4,6,2]=>[4,5,7,1,3,2,6]=>[4,3,1,7,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>[3,1,7,5,6,2,4]=>{{1,2,3,4,5,6,7}}
[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>[3,1,7,5,6,4,2]=>{{1,2,3,7},{4,5,6}}
[3,1,7,6,2,4,5]=>[1,3,2,6,7,5,4]=>[7,5,6,2,1,3,4]=>{{1,2,4,5,7},{3,6}}
[3,1,7,6,2,5,4]=>[1,3,2,6,7,4,5]=>[7,5,6,2,1,4,3]=>{{1,2,3,4,5,6,7}}
[3,1,7,6,4,2,5]=>[1,3,2,4,6,7,5]=>[7,5,6,4,2,1,3]=>{{1,3,6,7},{2,5},{4}}
[3,1,7,6,4,5,2]=>[4,6,7,1,3,2,5]=>[4,2,1,7,5,6,3]=>{{1,3,4,7},{2},{5},{6}}
[3,1,7,6,5,2,4]=>[1,3,2,5,6,7,4]=>[7,5,6,3,2,1,4]=>{{1,3,4,6,7},{2,5}}
[3,1,7,6,5,4,2]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>{{1,7},{2,3,5,6},{4}}
[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>{{1,2},{3},{4},{5,7},{6}}
[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[3,2,1,4,6,7,5]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}
[3,2,1,4,7,5,6]=>[5,7,6,4,1,2,3]=>[3,1,2,4,7,6,5]=>{{1,2,3},{4},{5,7},{6}}
[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>{{1,3},{2},{4},{5,7},{6}}
[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>{{1,2},{3,4},{5,7},{6}}
[3,2,1,5,6,4,7]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[3,2,1,5,6,7,4]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,2,1,5,7,4,6]=>[5,4,7,6,1,2,3]=>[3,4,1,2,7,6,5]=>{{1,3},{2,4},{5,7},{6}}
[3,2,1,5,7,6,4]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,2,1,6,4,5,7]=>[7,4,6,5,1,2,3]=>[1,4,2,3,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[3,2,1,6,4,7,5]=>[4,6,5,7,1,2,3]=>[4,2,3,1,7,6,5]=>{{1,4},{2},{3},{5,7},{6}}
[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[3,2,1,6,5,7,4]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[3,2,1,6,7,4,5]=>[6,4,7,5,1,2,3]=>[2,4,1,3,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,2,1,6,7,5,4]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[3,2,1,7,4,5,6]=>[4,7,6,5,1,2,3]=>[4,1,2,3,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,2,1,7,4,6,5]=>[4,7,5,6,1,2,3]=>[4,1,3,2,7,6,5]=>{{1,2,4},{3},{5,7},{6}}
[3,2,1,7,5,4,6]=>[4,5,7,6,1,2,3]=>[4,3,1,2,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,2,1,7,5,6,4]=>[5,7,4,6,1,2,3]=>[3,1,4,2,7,6,5]=>{{1,2,3,4},{5,7},{6}}
[3,2,1,7,6,4,5]=>[4,6,7,5,1,2,3]=>[4,2,1,3,7,6,5]=>{{1,3,4},{2},{5,7},{6}}
[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>{{1,4},{2,3},{5,7},{6}}
[3,2,4,1,5,6,7]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[3,2,4,1,5,7,6]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>{{1,2},{3},{4,6,7},{5}}
[3,2,4,1,6,5,7]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[3,2,4,1,6,7,5]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}
[3,2,4,1,7,5,6]=>[5,7,6,2,3,1,4]=>[3,1,2,6,5,7,4]=>{{1,2,3},{4,6,7},{5}}
[3,2,4,1,7,6,5]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>{{1,3},{2},{4,6,7},{5}}
[3,2,4,5,1,6,7]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,2,4,5,1,7,6]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>{{1,2},{3,4,6,7},{5}}
[3,2,4,5,6,1,7]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,4,5,6,7,1]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>{{1,2,3,4,6,7},{5}}
[3,2,4,5,7,1,6]=>[5,4,2,3,1,7,6]=>[3,4,6,5,7,1,2]=>{{1,3,6},{2,4,5,7}}
[3,2,4,5,7,6,1]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[3,2,4,6,1,5,7]=>[7,4,2,3,1,6,5]=>[1,4,6,5,7,2,3]=>{{1},{2,3,4,5,6,7}}
[3,2,4,6,1,7,5]=>[4,2,3,1,6,5,7]=>[4,6,5,7,2,3,1]=>{{1,4,7},{2,3,5,6}}
[3,2,4,6,5,1,7]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>{{1},{2,4,5,7},{3,6}}
[3,2,4,6,5,7,1]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>{{1,3,4,6,7},{2},{5}}
[3,2,4,6,7,1,5]=>[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>{{1,2,3,4,5,6,7}}
[3,2,4,6,7,5,1]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>{{1,2,4,5,7},{3,6}}
[3,2,4,7,1,5,6]=>[4,2,3,1,7,6,5]=>[4,6,5,7,1,2,3]=>{{1,3,4,5,7},{2,6}}
[3,2,4,7,1,6,5]=>[4,2,3,1,7,5,6]=>[4,6,5,7,1,3,2]=>{{1,2,3,4,5,6,7}}
[3,2,4,7,5,1,6]=>[4,2,3,1,5,7,6]=>[4,6,5,7,3,1,2]=>{{1,2,4,6,7},{3,5}}
[3,2,4,7,5,6,1]=>[5,7,4,2,3,1,6]=>[3,1,4,6,5,7,2]=>{{1,2,3,4,6,7},{5}}
[3,2,4,7,6,1,5]=>[4,2,3,1,6,7,5]=>[4,6,5,7,2,1,3]=>{{1,2,3,4,5,6,7}}
[3,2,4,7,6,5,1]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>{{1,4,7},{2,6},{3,5}}
[3,2,5,1,4,6,7]=>[7,6,2,3,1,5,4]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,2,5,1,4,7,6]=>[6,7,2,3,1,5,4]=>[2,1,6,5,7,3,4]=>{{1,2},{3,6},{4,5,7}}
[3,2,5,1,6,4,7]=>[7,2,3,1,5,4,6]=>[1,6,5,7,3,4,2]=>{{1},{2,4,6,7},{3,5}}
[3,2,5,1,6,7,4]=>[6,2,3,1,5,4,7]=>[2,6,5,7,3,4,1]=>{{1,2,4,6,7},{3,5}}
[3,2,5,1,7,4,6]=>[2,3,1,5,4,7,6]=>[6,5,7,3,4,1,2]=>{{1,6},{2,3,4,5,7}}
[3,2,5,1,7,6,4]=>[2,3,1,5,4,6,7]=>[6,5,7,3,4,2,1]=>{{1,2,3,4,5,6,7}}
[3,2,5,4,1,6,7]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,2,5,4,1,7,6]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>{{1,2},{3,4,5,6,7}}
[3,2,5,4,6,1,7]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[3,2,5,4,6,7,1]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[3,2,5,4,7,1,6]=>[4,5,2,3,1,7,6]=>[4,3,6,5,7,1,2]=>{{1,2,3,4,5,6,7}}
[3,2,5,4,7,6,1]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>{{1,4,5,7},{2,3,6}}
[3,2,5,6,1,4,7]=>[7,5,2,3,1,6,4]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,2,5,6,1,7,4]=>[5,2,3,1,6,4,7]=>[3,6,5,7,2,4,1]=>{{1,2,3,4,5,6,7}}
[3,2,5,6,4,1,7]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,6,4,7,1]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>{{1,2,3,4,6,7},{5}}
[3,2,5,6,7,1,4]=>[6,5,2,3,1,7,4]=>[2,3,6,5,7,1,4]=>{{1,2,3,6},{4,5,7}}
[3,2,5,6,7,4,1]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>{{1,2,3,4,5,6,7}}
[3,2,5,7,1,4,6]=>[5,2,3,1,7,6,4]=>[3,6,5,7,1,2,4]=>{{1,3,5},{2,6},{4,7}}
[3,2,5,7,1,6,4]=>[5,2,3,1,7,4,6]=>[3,6,5,7,1,4,2]=>{{1,3,5},{2,4,6,7}}
[3,2,5,7,4,1,6]=>[5,2,3,1,4,7,6]=>[3,6,5,7,4,1,2]=>{{1,2,3,4,5,6,7}}
[3,2,5,7,4,6,1]=>[5,4,7,2,3,1,6]=>[3,4,1,6,5,7,2]=>{{1,3},{2,4,6,7},{5}}
[3,2,5,7,6,1,4]=>[5,2,3,1,6,7,4]=>[3,6,5,7,2,1,4]=>{{1,2,3,5,6},{4,7}}
[3,2,5,7,6,4,1]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>{{1,3,4,5,7},{2,6}}
[3,2,6,1,4,5,7]=>[7,2,3,1,6,5,4]=>[1,6,5,7,2,3,4]=>{{1},{2,3,5,6},{4,7}}
[3,2,6,1,4,7,5]=>[2,3,1,6,5,7,4]=>[6,5,7,2,3,1,4]=>{{1,6},{2,3,4,5,7}}
[3,2,6,1,5,4,7]=>[7,2,3,1,6,4,5]=>[1,6,5,7,2,4,3]=>{{1},{2,3,4,5,6,7}}
[3,2,6,1,5,7,4]=>[2,3,1,6,5,4,7]=>[6,5,7,2,3,4,1]=>{{1,2,3,4,5,6,7}}
[3,2,6,1,7,4,5]=>[2,3,1,6,4,7,5]=>[6,5,7,2,4,1,3]=>{{1,6},{2,4,5},{3,7}}
[3,2,6,1,7,5,4]=>[2,3,1,6,4,5,7]=>[6,5,7,2,4,3,1]=>{{1,3,6,7},{2,4,5}}
[3,2,6,4,1,5,7]=>[7,2,3,1,4,6,5]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,6,4,1,7,5]=>[2,3,1,4,6,5,7]=>[6,5,7,4,2,3,1]=>{{1,3,6,7},{2,5},{4}}
[3,2,6,4,5,1,7]=>[7,4,6,2,3,1,5]=>[1,4,2,6,5,7,3]=>{{1},{2,3,4,6,7},{5}}
[3,2,6,4,5,7,1]=>[4,6,5,2,3,1,7]=>[4,2,3,6,5,7,1]=>{{1,4,6,7},{2},{3},{5}}
[3,2,6,4,7,1,5]=>[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>{{1,3,4,5,6,7},{2}}
[3,2,6,4,7,5,1]=>[4,6,2,3,1,5,7]=>[4,2,6,5,7,3,1]=>{{1,4,5,7},{2},{3,6}}
[3,2,6,5,1,4,7]=>[7,2,3,1,5,6,4]=>[1,6,5,7,3,2,4]=>{{1},{2,6},{3,5},{4,7}}
[3,2,6,5,1,7,4]=>[2,3,1,5,6,4,7]=>[6,5,7,3,2,4,1]=>{{1,3,4,6,7},{2,5}}
[3,2,6,5,4,1,7]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,5,4,7,1]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>{{1,4,6,7},{2,3},{5}}
[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>[3,2,6,5,7,1,4]=>{{1,3,6},{2},{4,5,7}}
[3,2,6,5,7,4,1]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>{{1,3,4,5,6,7},{2}}
[3,2,6,7,1,4,5]=>[6,2,3,1,7,5,4]=>[2,6,5,7,1,3,4]=>{{1,2,3,5,6},{4,7}}
[3,2,6,7,1,5,4]=>[6,2,3,1,7,4,5]=>[2,6,5,7,1,4,3]=>{{1,2,3,4,5,6,7}}
[3,2,6,7,4,1,5]=>[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>{{1,2,6},{3,4,5,7}}
[3,2,6,7,4,5,1]=>[6,4,7,2,3,1,5]=>[2,4,1,6,5,7,3]=>{{1,2,3,4,6,7},{5}}
[3,2,6,7,5,1,4]=>[6,2,3,1,5,7,4]=>[2,6,5,7,3,1,4]=>{{1,2,6},{3,5},{4,7}}
[3,2,6,7,5,4,1]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>{{1,2,3,4,5,6,7}}
[3,2,7,1,4,5,6]=>[2,3,1,7,6,5,4]=>[6,5,7,1,2,3,4]=>{{1,3,4,6,7},{2,5}}
[3,2,7,1,4,6,5]=>[2,3,1,7,5,6,4]=>[6,5,7,1,3,2,4]=>{{1,2,3,4,5,6,7}}
[3,2,7,1,5,4,6]=>[2,3,1,7,6,4,5]=>[6,5,7,1,2,4,3]=>{{1,4,6},{2,5},{3,7}}
[3,2,7,1,5,6,4]=>[2,3,1,7,5,4,6]=>[6,5,7,1,3,4,2]=>{{1,4,6},{2,3,5,7}}
[3,2,7,1,6,4,5]=>[2,3,1,7,4,6,5]=>[6,5,7,1,4,2,3]=>{{1,2,4,5,6},{3,7}}
[3,2,7,1,6,5,4]=>[2,3,1,7,4,5,6]=>[6,5,7,1,4,3,2]=>{{1,2,3,4,5,6,7}}
[3,2,7,4,1,5,6]=>[2,3,1,4,7,6,5]=>[6,5,7,4,1,2,3]=>{{1,2,5,6},{3,7},{4}}
[3,2,7,4,1,6,5]=>[2,3,1,4,7,5,6]=>[6,5,7,4,1,3,2]=>{{1,2,3,5,6,7},{4}}
[3,2,7,4,5,1,6]=>[4,7,6,2,3,1,5]=>[4,1,2,6,5,7,3]=>{{1,2,3,4,6,7},{5}}
[3,2,7,4,5,6,1]=>[4,7,5,2,3,1,6]=>[4,1,3,6,5,7,2]=>{{1,2,4,6,7},{3},{5}}
[3,2,7,4,6,1,5]=>[4,7,2,3,1,6,5]=>[4,1,6,5,7,2,3]=>{{1,2,3,4,5,6,7}}
[3,2,7,4,6,5,1]=>[4,7,2,3,1,5,6]=>[4,1,6,5,7,3,2]=>{{1,2,4,5,7},{3,6}}
[3,2,7,5,1,4,6]=>[2,3,1,5,7,6,4]=>[6,5,7,3,1,2,4]=>{{1,2,5,6},{3,4,7}}
[3,2,7,5,1,6,4]=>[2,3,1,5,7,4,6]=>[6,5,7,3,1,4,2]=>{{1,2,3,4,5,6,7}}
[3,2,7,5,4,1,6]=>[2,3,1,4,5,7,6]=>[6,5,7,4,3,1,2]=>{{1,6},{2,3,5,7},{4}}
[3,2,7,5,4,6,1]=>[4,5,7,2,3,1,6]=>[4,3,1,6,5,7,2]=>{{1,2,3,4,6,7},{5}}
[3,2,7,5,6,1,4]=>[5,7,2,3,1,6,4]=>[3,1,6,5,7,2,4]=>{{1,2,3,6},{4,5,7}}
[3,2,7,5,6,4,1]=>[5,7,2,3,1,4,6]=>[3,1,6,5,7,4,2]=>{{1,2,3,4,5,6,7}}
[3,2,7,6,1,4,5]=>[2,3,1,6,7,5,4]=>[6,5,7,2,1,3,4]=>{{1,2,3,4,5,6,7}}
[3,2,7,6,1,5,4]=>[2,3,1,6,7,4,5]=>[6,5,7,2,1,4,3]=>{{1,2,4,5,6},{3,7}}
[3,2,7,6,4,1,5]=>[2,3,1,4,6,7,5]=>[6,5,7,4,2,1,3]=>{{1,6},{2,5},{3,7},{4}}
[3,2,7,6,4,5,1]=>[4,6,7,2,3,1,5]=>[4,2,1,6,5,7,3]=>{{1,3,4,6,7},{2},{5}}
[3,2,7,6,5,1,4]=>[2,3,1,5,6,7,4]=>[6,5,7,3,2,1,4]=>{{1,6},{2,5},{3,4,7}}
[3,2,7,6,5,4,1]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>{{1,2,3,5,6,7},{4}}
[3,4,1,2,5,6,7]=>[7,6,5,3,1,4,2]=>[1,2,3,5,7,4,6]=>{{1},{2},{3},{4,5,6,7}}
[3,4,1,2,5,7,6]=>[6,7,5,3,1,4,2]=>[2,1,3,5,7,4,6]=>{{1,2},{3},{4,5,6,7}}
[3,4,1,2,6,5,7]=>[7,5,6,3,1,4,2]=>[1,3,2,5,7,4,6]=>{{1},{2,3},{4,5,6,7}}
[3,4,1,2,6,7,5]=>[6,5,7,3,1,4,2]=>[2,3,1,5,7,4,6]=>{{1,2,3},{4,5,6,7}}
[3,4,1,2,7,5,6]=>[5,7,6,3,1,4,2]=>[3,1,2,5,7,4,6]=>{{1,2,3},{4,5,6,7}}
[3,4,1,2,7,6,5]=>[5,6,7,3,1,4,2]=>[3,2,1,5,7,4,6]=>{{1,3},{2},{4,5,6,7}}
[3,4,1,5,2,6,7]=>[7,6,3,1,4,2,5]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,4,1,5,2,7,6]=>[6,7,3,1,4,2,5]=>[2,1,5,7,4,6,3]=>{{1,2},{3,4,5,7},{6}}
[3,4,1,5,6,2,7]=>[7,5,3,1,4,2,6]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,1,5,6,7,2]=>[6,5,3,1,4,2,7]=>[2,3,5,7,4,6,1]=>{{1,2,3,4,5,7},{6}}
[3,4,1,5,7,2,6]=>[5,3,1,4,2,7,6]=>[3,5,7,4,6,1,2]=>{{1,2,3,5,6,7},{4}}
[3,4,1,5,7,6,2]=>[5,3,1,4,2,6,7]=>[3,5,7,4,6,2,1]=>{{1,3,7},{2,5,6},{4}}
[3,4,1,6,2,5,7]=>[7,3,1,4,2,6,5]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[3,4,1,6,2,7,5]=>[3,1,4,2,6,5,7]=>[5,7,4,6,2,3,1]=>{{1,2,5,7},{3,4,6}}
[3,4,1,6,5,2,7]=>[7,3,1,4,2,5,6]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,4,1,6,5,7,2]=>[5,6,3,1,4,2,7]=>[3,2,5,7,4,6,1]=>{{1,3,4,5,7},{2},{6}}
[3,4,1,6,7,2,5]=>[6,3,1,4,2,7,5]=>[2,5,7,4,6,1,3]=>{{1,2,5,6},{3,7},{4}}
[3,4,1,6,7,5,2]=>[6,3,1,4,2,5,7]=>[2,5,7,4,6,3,1]=>{{1,2,3,5,6,7},{4}}
[3,4,1,7,2,5,6]=>[3,1,4,2,7,6,5]=>[5,7,4,6,1,2,3]=>{{1,5},{2,3,4,6,7}}
[3,4,1,7,2,6,5]=>[3,1,4,2,7,5,6]=>[5,7,4,6,1,3,2]=>{{1,5},{2,7},{3,4,6}}
[3,4,1,7,5,2,6]=>[3,1,4,2,5,7,6]=>[5,7,4,6,3,1,2]=>{{1,3,4,5,6},{2,7}}
[3,4,1,7,5,6,2]=>[5,7,3,1,4,2,6]=>[3,1,5,7,4,6,2]=>{{1,2,3,4,5,7},{6}}
[3,4,1,7,6,2,5]=>[3,1,4,2,6,7,5]=>[5,7,4,6,2,1,3]=>{{1,2,3,4,5,6,7}}
[3,4,1,7,6,5,2]=>[3,1,4,2,5,6,7]=>[5,7,4,6,3,2,1]=>{{1,2,3,4,5,6,7}}
[3,4,2,1,5,6,7]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[3,4,2,1,5,7,6]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>{{1,2},{3},{4,5,7},{6}}
[3,4,2,1,6,5,7]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[3,4,2,1,6,7,5]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}
[3,4,2,1,7,5,6]=>[5,7,6,3,1,2,4]=>[3,1,2,5,7,6,4]=>{{1,2,3},{4,5,7},{6}}
[3,4,2,1,7,6,5]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>{{1,3},{2},{4,5,7},{6}}
[3,4,2,5,1,6,7]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,2,5,1,7,6]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>{{1,2},{3,4,5,6,7}}
[3,4,2,5,6,1,7]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,5,6,7,1]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>{{1,2,3,4,5,6,7}}
[3,4,2,5,7,1,6]=>[5,3,2,4,1,7,6]=>[3,5,6,4,7,1,2]=>{{1,3,6},{2,5,7},{4}}
[3,4,2,5,7,6,1]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>{{1,2,3,5,6,7},{4}}
[3,4,2,6,1,5,7]=>[7,3,2,4,1,6,5]=>[1,5,6,4,7,2,3]=>{{1},{2,3,5,6,7},{4}}
[3,4,2,6,1,7,5]=>[3,2,4,1,6,5,7]=>[5,6,4,7,2,3,1]=>{{1,2,3,4,5,6,7}}
[3,4,2,6,5,1,7]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>{{1},{2,5,7},{3,6},{4}}
[3,4,2,6,5,7,1]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>{{1,3,4,5,6,7},{2}}
[3,4,2,6,7,1,5]=>[6,3,2,4,1,7,5]=>[2,5,6,4,7,1,3]=>{{1,2,3,5,6,7},{4}}
[3,4,2,6,7,5,1]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>{{1,2,5,7},{3,6},{4}}
[3,4,2,7,1,5,6]=>[3,2,4,1,7,6,5]=>[5,6,4,7,1,2,3]=>{{1,5},{2,6},{3,4,7}}
[3,4,2,7,1,6,5]=>[3,2,4,1,7,5,6]=>[5,6,4,7,1,3,2]=>{{1,5},{2,3,4,6,7}}
[3,4,2,7,5,1,6]=>[3,2,4,1,5,7,6]=>[5,6,4,7,3,1,2]=>{{1,2,3,4,5,6,7}}
[3,4,2,7,5,6,1]=>[5,7,3,2,4,1,6]=>[3,1,5,6,4,7,2]=>{{1,2,3,4,5,6,7}}
[3,4,2,7,6,1,5]=>[3,2,4,1,6,7,5]=>[5,6,4,7,2,1,3]=>{{1,2,5,6},{3,4,7}}
[3,4,2,7,6,5,1]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>{{1,3,4,5,7},{2,6}}
[3,4,5,1,2,6,7]=>[7,6,4,3,1,5,2]=>[1,2,4,5,7,3,6]=>{{1},{2},{3,4,5,6,7}}
[3,4,5,1,2,7,6]=>[6,7,4,3,1,5,2]=>[2,1,4,5,7,3,6]=>{{1,2},{3,4,5,6,7}}
[3,4,5,1,6,2,7]=>[7,4,3,1,5,2,6]=>[1,4,5,7,3,6,2]=>{{1},{2,4,7},{3,5},{6}}
[3,4,5,1,6,7,2]=>[6,4,3,1,5,2,7]=>[2,4,5,7,3,6,1]=>{{1,2,4,7},{3,5},{6}}
[3,4,5,1,7,2,6]=>[4,3,1,5,2,7,6]=>[4,5,7,3,6,1,2]=>{{1,2,3,4,5,6,7}}
[3,4,5,1,7,6,2]=>[4,3,1,5,2,6,7]=>[4,5,7,3,6,2,1]=>{{1,3,4,7},{2,5,6}}
[3,4,5,2,1,6,7]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,4,5,2,1,7,6]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>{{1,2},{3,4,5,7},{6}}
[3,4,5,2,6,1,7]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>{{1},{2,4,6,7},{3,5}}
[3,4,5,2,6,7,1]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>{{1,2,4,6,7},{3,5}}
[3,4,5,2,7,1,6]=>[4,3,2,5,1,7,6]=>[4,5,6,3,7,1,2]=>{{1,3,4,6},{2,5,7}}
[3,4,5,2,7,6,1]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[3,4,5,6,1,2,7]=>[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>{{1},{2,3,4,5,6,7}}
[3,4,5,6,1,7,2]=>[5,4,3,1,6,2,7]=>[3,4,5,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[3,4,5,6,2,1,7]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[3,4,5,6,7,1,2]=>[6,5,4,3,1,7,2]=>[2,3,4,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[3,4,5,6,7,2,1]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>[3,4,5,7,1,2,6]=>{{1,3,5},{2,4,6,7}}
[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>[3,4,5,7,1,6,2]=>{{1,3,5},{2,4,7},{6}}
[3,4,5,7,2,1,6]=>[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>{{1,3,5,6},{2,4,7}}
[3,4,5,7,2,6,1]=>[5,4,3,2,7,1,6]=>[3,4,5,6,1,7,2]=>{{1,3,5},{2,4,6,7}}
[3,4,5,7,6,1,2]=>[5,4,3,1,6,7,2]=>[3,4,5,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[3,4,5,7,6,2,1]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>{{1,2,3,4,5,6,7}}
[3,4,6,1,2,5,7]=>[7,4,3,1,6,5,2]=>[1,4,5,7,2,3,6]=>{{1},{2,3,4,5,6,7}}
[3,4,6,1,2,7,5]=>[4,3,1,6,5,7,2]=>[4,5,7,2,3,1,6]=>{{1,2,3,4,5,6,7}}
[3,4,6,1,5,2,7]=>[7,4,3,1,6,2,5]=>[1,4,5,7,2,6,3]=>{{1},{2,3,4,5,7},{6}}
[3,4,6,1,5,7,2]=>[4,3,1,6,5,2,7]=>[4,5,7,2,3,6,1]=>{{1,2,3,4,5,7},{6}}
[3,4,6,1,7,2,5]=>[4,3,1,6,2,7,5]=>[4,5,7,2,6,1,3]=>{{1,2,4,5,6},{3,7}}
[3,4,6,1,7,5,2]=>[4,3,1,6,2,5,7]=>[4,5,7,2,6,3,1]=>{{1,2,3,4,5,6,7}}
[3,4,6,2,1,5,7]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>{{1},{2,3,4,5,6,7}}
[3,4,6,2,1,7,5]=>[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>{{1,3,4,6,7},{2,5}}
[3,4,6,2,5,1,7]=>[7,4,3,2,6,1,5]=>[1,4,5,6,2,7,3]=>{{1},{2,3,4,5,6,7}}
[3,4,6,2,5,7,1]=>[4,3,2,6,5,1,7]=>[4,5,6,2,3,7,1]=>{{1,2,3,4,5,6,7}}
[3,4,6,2,7,1,5]=>[4,3,2,6,1,7,5]=>[4,5,6,2,7,1,3]=>{{1,2,3,4,5,6,7}}
[3,4,6,2,7,5,1]=>[4,3,2,6,1,5,7]=>[4,5,6,2,7,3,1]=>{{1,2,4,5,7},{3,6}}
[3,4,6,5,1,2,7]=>[7,4,3,1,5,6,2]=>[1,4,5,7,3,2,6]=>{{1},{2,4,6,7},{3,5}}
[3,4,6,5,1,7,2]=>[4,3,1,5,6,2,7]=>[4,5,7,3,2,6,1]=>{{1,3,4,7},{2,5},{6}}
[3,4,6,5,2,1,7]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>{{1},{2,4,7},{3,5,6}}
[3,4,6,5,2,7,1]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>{{1,3,4,6,7},{2,5}}
[3,4,6,5,7,1,2]=>[5,6,4,3,1,7,2]=>[3,2,4,5,7,1,6]=>{{1,3,4,5,6,7},{2}}
[3,4,6,5,7,2,1]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>{{1,3,4,5,7},{2},{6}}
[3,4,6,7,1,2,5]=>[6,4,3,1,7,5,2]=>[2,4,5,7,1,3,6]=>{{1,2,3,4,5,6,7}}
[3,4,6,7,1,5,2]=>[6,4,3,1,7,2,5]=>[2,4,5,7,1,6,3]=>{{1,2,3,4,5,7},{6}}
[3,4,6,7,2,1,5]=>[6,4,3,1,2,7,5]=>[2,4,5,7,6,1,3]=>{{1,2,3,4,5,6,7}}
[3,4,6,7,2,5,1]=>[6,4,3,2,7,1,5]=>[2,4,5,6,1,7,3]=>{{1,2,3,4,5,6,7}}
[3,4,6,7,5,1,2]=>[6,4,3,1,5,7,2]=>[2,4,5,7,3,1,6]=>{{1,2,4,6,7},{3,5}}
[3,4,6,7,5,2,1]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>{{1,2,4,7},{3,5,6}}
[3,4,7,1,2,5,6]=>[4,3,1,7,6,5,2]=>[4,5,7,1,2,3,6]=>{{1,4},{2,5},{3,6,7}}
[3,4,7,1,2,6,5]=>[4,3,1,7,5,6,2]=>[4,5,7,1,3,2,6]=>{{1,4},{2,3,5,6,7}}
[3,4,7,1,5,2,6]=>[4,3,1,7,6,2,5]=>[4,5,7,1,2,6,3]=>{{1,4},{2,5},{3,7},{6}}
[3,4,7,1,5,6,2]=>[4,3,1,7,5,2,6]=>[4,5,7,1,3,6,2]=>{{1,4},{2,3,5,7},{6}}
[3,4,7,1,6,2,5]=>[4,3,1,7,2,6,5]=>[4,5,7,1,6,2,3]=>{{1,4},{2,5,6},{3,7}}
[3,4,7,1,6,5,2]=>[4,3,1,7,2,5,6]=>[4,5,7,1,6,3,2]=>{{1,4},{2,3,5,6,7}}
[3,4,7,2,1,5,6]=>[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>{{1,2,4,5,6},{3,7}}
[3,4,7,2,1,6,5]=>[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>{{1,2,3,4,5,6,7}}
[3,4,7,2,5,1,6]=>[4,3,2,7,6,1,5]=>[4,5,6,1,2,7,3]=>{{1,4},{2,5},{3,6,7}}
[3,4,7,2,5,6,1]=>[4,3,2,7,5,1,6]=>[4,5,6,1,3,7,2]=>{{1,4},{2,3,5,6,7}}
[3,4,7,2,6,1,5]=>[4,3,2,7,1,6,5]=>[4,5,6,1,7,2,3]=>{{1,4},{2,3,5,6,7}}
[3,4,7,2,6,5,1]=>[4,3,2,7,1,5,6]=>[4,5,6,1,7,3,2]=>{{1,4},{2,5,7},{3,6}}
[3,4,7,5,1,2,6]=>[4,3,1,5,7,6,2]=>[4,5,7,3,1,2,6]=>{{1,2,3,4,5,6,7}}
[3,4,7,5,1,6,2]=>[4,3,1,5,7,2,6]=>[4,5,7,3,1,6,2]=>{{1,2,3,4,5,7},{6}}
[3,4,7,5,2,1,6]=>[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>{{1,4,6},{2,3,5,7}}
[3,4,7,5,2,6,1]=>[4,3,2,5,7,1,6]=>[4,5,6,3,1,7,2]=>{{1,2,3,4,5,6,7}}
[3,4,7,5,6,1,2]=>[5,7,4,3,1,6,2]=>[3,1,4,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[3,4,7,5,6,2,1]=>[5,7,4,3,1,2,6]=>[3,1,4,5,7,6,2]=>{{1,2,3,4,5,7},{6}}
[3,4,7,6,1,2,5]=>[4,3,1,6,7,5,2]=>[4,5,7,2,1,3,6]=>{{1,2,4,5},{3,6,7}}
[3,4,7,6,1,5,2]=>[4,3,1,6,7,2,5]=>[4,5,7,2,1,6,3]=>{{1,2,4,5},{3,7},{6}}
[3,4,7,6,2,1,5]=>[4,3,1,2,6,7,5]=>[4,5,7,6,2,1,3]=>{{1,4,6},{2,5},{3,7}}
[3,4,7,6,2,5,1]=>[4,3,2,6,7,1,5]=>[4,5,6,2,1,7,3]=>{{1,2,4,5},{3,6,7}}
[3,4,7,6,5,1,2]=>[4,3,1,5,6,7,2]=>[4,5,7,3,2,1,6]=>{{1,3,4,6,7},{2,5}}
[3,4,7,6,5,2,1]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>{{1,2,3,4,5,6,7}}
[3,5,1,2,4,6,7]=>[7,6,3,1,5,4,2]=>[1,2,5,7,3,4,6]=>{{1},{2},{3,5},{4,6,7}}
[3,5,1,2,4,7,6]=>[6,7,3,1,5,4,2]=>[2,1,5,7,3,4,6]=>{{1,2},{3,5},{4,6,7}}
[3,5,1,2,6,4,7]=>[7,3,1,5,4,6,2]=>[1,5,7,3,4,2,6]=>{{1},{2,3,4,5,6,7}}
[3,5,1,2,6,7,4]=>[6,3,1,5,4,7,2]=>[2,5,7,3,4,1,6]=>{{1,2,3,4,5,6,7}}
[3,5,1,2,7,4,6]=>[3,1,5,4,7,6,2]=>[5,7,3,4,1,2,6]=>{{1,5},{2,6,7},{3},{4}}
[3,5,1,2,7,6,4]=>[3,1,5,4,6,7,2]=>[5,7,3,4,2,1,6]=>{{1,2,5,6,7},{3},{4}}
[3,5,1,4,2,6,7]=>[7,6,3,1,5,2,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[3,5,1,4,2,7,6]=>[6,7,3,1,5,2,4]=>[2,1,5,7,3,6,4]=>{{1,2},{3,5},{4,7},{6}}
[3,5,1,4,6,2,7]=>[7,3,1,5,4,2,6]=>[1,5,7,3,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,1,4,6,7,2]=>[6,3,1,5,4,2,7]=>[2,5,7,3,4,6,1]=>{{1,2,3,4,5,7},{6}}
[3,5,1,4,7,2,6]=>[3,1,5,4,2,7,6]=>[5,7,3,4,6,1,2]=>{{1,5,6},{2,7},{3},{4}}
[3,5,1,4,7,6,2]=>[3,1,5,4,2,6,7]=>[5,7,3,4,6,2,1]=>{{1,2,5,6,7},{3},{4}}
[3,5,1,6,2,4,7]=>[7,3,1,5,2,6,4]=>[1,5,7,3,6,2,4]=>{{1},{2,5,6},{3,4,7}}
[3,5,1,6,2,7,4]=>[3,1,5,2,6,4,7]=>[5,7,3,6,2,4,1]=>{{1,2,5,7},{3},{4,6}}
[3,5,1,6,4,2,7]=>[7,3,1,5,2,4,6]=>[1,5,7,3,6,4,2]=>{{1},{2,3,4,5,6,7}}
[3,5,1,6,4,7,2]=>[3,1,5,4,6,2,7]=>[5,7,3,4,2,6,1]=>{{1,2,5,7},{3},{4},{6}}
[3,5,1,6,7,2,4]=>[6,3,1,5,2,7,4]=>[2,5,7,3,6,1,4]=>{{1,2,5,6},{3,4,7}}
[3,5,1,6,7,4,2]=>[6,3,1,5,2,4,7]=>[2,5,7,3,6,4,1]=>{{1,2,3,4,5,6,7}}
[3,5,1,7,2,4,6]=>[3,1,5,2,7,6,4]=>[5,7,3,6,1,2,4]=>{{1,5},{2,4,6,7},{3}}
[3,5,1,7,2,6,4]=>[3,1,5,2,7,4,6]=>[5,7,3,6,1,4,2]=>{{1,5},{2,7},{3},{4,6}}
[3,5,1,7,4,2,6]=>[3,1,5,2,4,7,6]=>[5,7,3,6,4,1,2]=>{{1,4,5,6},{2,7},{3}}
[3,5,1,7,4,6,2]=>[3,1,5,4,7,2,6]=>[5,7,3,4,1,6,2]=>{{1,5},{2,7},{3},{4},{6}}
[3,5,1,7,6,2,4]=>[3,1,5,2,6,7,4]=>[5,7,3,6,2,1,4]=>{{1,2,4,5,6,7},{3}}
[3,5,1,7,6,4,2]=>[3,1,5,2,4,6,7]=>[5,7,3,6,4,2,1]=>{{1,2,4,5,6,7},{3}}
[3,5,2,1,4,6,7]=>[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[3,5,2,1,4,7,6]=>[6,7,3,1,2,5,4]=>[2,1,5,7,6,3,4]=>{{1,2},{3,5,6},{4,7}}
[3,5,2,1,6,4,7]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>{{1},{2,3,5,7},{4,6}}
[3,5,2,1,6,7,4]=>[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>{{1,2,3,5,7},{4,6}}
[3,5,2,1,7,4,6]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>{{1,3,4,5,6},{2,7}}
[3,5,2,1,7,6,4]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>{{1,2,3,4,5,6,7}}
[3,5,2,4,1,6,7]=>[7,6,3,2,5,1,4]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,5,2,4,1,7,6]=>[6,7,3,2,5,1,4]=>[2,1,5,6,3,7,4]=>{{1,2},{3,5},{4,6,7}}
[3,5,2,4,6,1,7]=>[7,3,2,5,4,1,6]=>[1,5,6,3,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,4,6,7,1]=>[6,3,2,5,4,1,7]=>[2,5,6,3,4,7,1]=>{{1,2,3,4,5,6,7}}
[3,5,2,4,7,1,6]=>[3,2,5,4,1,7,6]=>[5,6,3,4,7,1,2]=>{{1,2,5,6,7},{3},{4}}
[3,5,2,4,7,6,1]=>[3,2,5,4,1,6,7]=>[5,6,3,4,7,2,1]=>{{1,5,7},{2,6},{3},{4}}
[3,5,2,6,1,4,7]=>[7,3,2,5,1,6,4]=>[1,5,6,3,7,2,4]=>{{1},{2,3,4,5,6,7}}
[3,5,2,6,1,7,4]=>[3,2,5,1,6,4,7]=>[5,6,3,7,2,4,1]=>{{1,2,4,5,6,7},{3}}
[3,5,2,6,4,1,7]=>[7,3,2,5,1,4,6]=>[1,5,6,3,7,4,2]=>{{1},{2,5,7},{3,4,6}}
[3,5,2,6,4,7,1]=>[3,2,5,4,6,1,7]=>[5,6,3,4,2,7,1]=>{{1,2,5,6,7},{3},{4}}
[3,5,2,6,7,1,4]=>[6,3,2,5,1,7,4]=>[2,5,6,3,7,1,4]=>{{1,2,3,4,5,6,7}}
[3,5,2,6,7,4,1]=>[6,3,2,5,1,4,7]=>[2,5,6,3,7,4,1]=>{{1,2,5,7},{3,4,6}}
[3,5,2,7,1,4,6]=>[3,2,5,1,7,6,4]=>[5,6,3,7,1,2,4]=>{{1,5},{2,6},{3},{4,7}}
[3,5,2,7,1,6,4]=>[3,2,5,1,7,4,6]=>[5,6,3,7,1,4,2]=>{{1,5},{2,4,6,7},{3}}
[3,5,2,7,4,1,6]=>[3,2,5,1,4,7,6]=>[5,6,3,7,4,1,2]=>{{1,2,4,5,6,7},{3}}
[3,5,2,7,4,6,1]=>[3,2,5,4,7,1,6]=>[5,6,3,4,1,7,2]=>{{1,5},{2,6,7},{3},{4}}
[3,5,2,7,6,1,4]=>[3,2,5,1,6,7,4]=>[5,6,3,7,2,1,4]=>{{1,2,5,6},{3},{4,7}}
[3,5,2,7,6,4,1]=>[3,2,5,1,4,6,7]=>[5,6,3,7,4,2,1]=>{{1,4,5,7},{2,6},{3}}
[3,5,4,1,2,6,7]=>[7,6,3,1,4,5,2]=>[1,2,5,7,4,3,6]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,1,2,7,6]=>[6,7,3,1,4,5,2]=>[2,1,5,7,4,3,6]=>{{1,2},{3,4,5,6,7}}
[3,5,4,1,6,2,7]=>[7,3,1,4,5,2,6]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,5,4,1,6,7,2]=>[6,3,1,4,5,2,7]=>[2,5,7,4,3,6,1]=>{{1,2,3,5,7},{4},{6}}
[3,5,4,1,7,2,6]=>[3,1,4,5,2,7,6]=>[5,7,4,3,6,1,2]=>{{1,5,6},{2,7},{3,4}}
[3,5,4,1,7,6,2]=>[3,1,4,5,2,6,7]=>[5,7,4,3,6,2,1]=>{{1,2,5,6,7},{3,4}}
[3,5,4,2,1,6,7]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,2,1,7,6]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>{{1,2},{3,4,5,6,7}}
[3,5,4,2,6,1,7]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,4,2,6,7,1]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>{{1,2,3,5,6,7},{4}}
[3,5,4,2,7,1,6]=>[3,2,4,5,1,7,6]=>[5,6,4,3,7,1,2]=>{{1,2,5,6,7},{3,4}}
[3,5,4,2,7,6,1]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>{{1,5,7},{2,6},{3,4}}
[3,5,4,6,1,2,7]=>[7,4,5,3,1,6,2]=>[1,4,3,5,7,2,6]=>{{1},{2,4,5,6,7},{3}}
[3,5,4,6,1,7,2]=>[4,5,3,1,6,2,7]=>[4,3,5,7,2,6,1]=>{{1,4,7},{2,3,5},{6}}
[3,5,4,6,2,1,7]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[3,5,4,6,2,7,1]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>{{1,4,6,7},{2,3,5}}
[3,5,4,6,7,1,2]=>[6,4,5,3,1,7,2]=>[2,4,3,5,7,1,6]=>{{1,2,4,5,6,7},{3}}
[3,5,4,6,7,2,1]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>{{1,2,4,5,7},{3},{6}}
[3,5,4,7,1,2,6]=>[4,5,3,1,7,6,2]=>[4,3,5,7,1,2,6]=>{{1,2,3,4,5,6,7}}
[3,5,4,7,1,6,2]=>[4,5,3,1,7,2,6]=>[4,3,5,7,1,6,2]=>{{1,2,3,4,5,7},{6}}
[3,5,4,7,2,1,6]=>[4,5,3,1,2,7,6]=>[4,3,5,7,6,1,2]=>{{1,2,3,4,5,6,7}}
[3,5,4,7,2,6,1]=>[4,5,3,2,7,1,6]=>[4,3,5,6,1,7,2]=>{{1,2,3,4,5,6,7}}
[3,5,4,7,6,1,2]=>[4,5,3,1,6,7,2]=>[4,3,5,7,2,1,6]=>{{1,4,6,7},{2,3,5}}
[3,5,4,7,6,2,1]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>{{1,4,7},{2,3,5,6}}
[3,5,6,1,2,4,7]=>[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>{{1},{2,3,5},{4,6,7}}
[3,5,6,1,2,7,4]=>[5,3,1,6,4,7,2]=>[3,5,7,2,4,1,6]=>{{1,3,6,7},{2,4,5}}
[3,5,6,1,4,2,7]=>[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[3,5,6,1,4,7,2]=>[5,3,1,6,4,2,7]=>[3,5,7,2,4,6,1]=>{{1,3,7},{2,4,5},{6}}
[3,5,6,1,7,2,4]=>[5,3,1,6,2,7,4]=>[3,5,7,2,6,1,4]=>{{1,2,3,4,5,6,7}}
[3,5,6,1,7,4,2]=>[5,3,1,6,2,4,7]=>[3,5,7,2,6,4,1]=>{{1,3,7},{2,4,5,6}}
[3,5,6,2,1,4,7]=>[7,5,3,1,2,6,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,5,6,2,1,7,4]=>[5,3,1,2,6,4,7]=>[3,5,7,6,2,4,1]=>{{1,3,7},{2,5},{4,6}}
[3,5,6,2,4,1,7]=>[7,5,3,2,6,1,4]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,5,6,2,4,7,1]=>[5,3,2,6,4,1,7]=>[3,5,6,2,4,7,1]=>{{1,3,6,7},{2,4,5}}
[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>[3,5,6,2,7,1,4]=>{{1,3,6},{2,4,5,7}}
[3,5,6,2,7,4,1]=>[5,3,2,6,1,4,7]=>[3,5,6,2,7,4,1]=>{{1,2,3,4,5,6,7}}
[3,5,6,4,1,2,7]=>[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>{{1},{2,3,4,5,6,7}}
[3,5,6,4,1,7,2]=>[5,3,1,4,6,2,7]=>[3,5,7,4,2,6,1]=>{{1,3,7},{2,5},{4},{6}}
[3,5,6,4,2,1,7]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,4,2,7,1]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>{{1,3,6,7},{2,5},{4}}
[3,5,6,4,7,1,2]=>[5,4,6,3,1,7,2]=>[3,4,2,5,7,1,6]=>{{1,2,3,4,5,6,7}}
[3,5,6,4,7,2,1]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>{{1,2,3,4,5,7},{6}}
[3,5,6,7,1,2,4]=>[6,5,3,1,7,4,2]=>[2,3,5,7,1,4,6]=>{{1,2,3,5},{4,6,7}}
[3,5,6,7,1,4,2]=>[6,5,3,1,7,2,4]=>[2,3,5,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}
[3,5,6,7,2,1,4]=>[6,5,3,1,2,7,4]=>[2,3,5,7,6,1,4]=>{{1,2,3,5,6},{4,7}}
[3,5,6,7,2,4,1]=>[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>{{1,2,3,5},{4,6,7}}
[3,5,6,7,4,1,2]=>[6,5,3,1,4,7,2]=>[2,3,5,7,4,1,6]=>{{1,2,3,4,5,6,7}}
[3,5,6,7,4,2,1]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>{{1,2,3,4,5,6,7}}
[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>[3,5,7,1,2,4,6]=>{{1,3,4,6,7},{2,5}}
[3,5,7,1,2,6,4]=>[5,3,1,7,4,6,2]=>[3,5,7,1,4,2,6]=>{{1,2,3,4,5,6,7}}
[3,5,7,1,4,2,6]=>[5,3,1,7,6,2,4]=>[3,5,7,1,2,6,4]=>{{1,3,4,7},{2,5},{6}}
[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>[3,5,7,1,4,6,2]=>{{1,2,3,4,5,7},{6}}
[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>[3,5,7,1,6,2,4]=>{{1,3,4,7},{2,5,6}}
[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>[3,5,7,1,6,4,2]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,1,4,6]=>[5,3,1,2,7,6,4]=>[3,5,7,6,1,2,4]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,1,6,4]=>[5,3,1,2,7,4,6]=>[3,5,7,6,1,4,2]=>{{1,2,3,5,7},{4,6}}
[3,5,7,2,4,1,6]=>[5,3,2,7,6,1,4]=>[3,5,6,1,2,7,4]=>{{1,3,4,6,7},{2,5}}
[3,5,7,2,4,6,1]=>[5,3,2,7,4,1,6]=>[3,5,6,1,4,7,2]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,6,1,4]=>[5,3,2,7,1,6,4]=>[3,5,6,1,7,2,4]=>{{1,2,3,4,5,6,7}}
[3,5,7,2,6,4,1]=>[5,3,2,7,1,4,6]=>[3,5,6,1,7,4,2]=>{{1,3,4,6},{2,5,7}}
[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>[3,5,7,4,1,2,6]=>{{1,2,3,5,6,7},{4}}
[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>[3,5,7,4,1,6,2]=>{{1,2,3,5,7},{4},{6}}
[3,5,7,4,2,1,6]=>[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>{{1,2,3,4,5,6,7}}
[3,5,7,4,2,6,1]=>[5,3,2,4,7,1,6]=>[3,5,6,4,1,7,2]=>{{1,2,3,5,6,7},{4}}
[3,5,7,4,6,1,2]=>[5,4,7,3,1,6,2]=>[3,4,1,5,7,2,6]=>{{1,3},{2,4,5,6,7}}
[3,5,7,4,6,2,1]=>[5,4,7,3,1,2,6]=>[3,4,1,5,7,6,2]=>{{1,3},{2,4,5,7},{6}}
[3,5,7,6,1,2,4]=>[5,3,1,6,7,4,2]=>[3,5,7,2,1,4,6]=>{{1,2,3,4,5,6,7}}
[3,5,7,6,1,4,2]=>[5,3,1,6,7,2,4]=>[3,5,7,2,1,6,4]=>{{1,2,3,4,5,7},{6}}
[3,5,7,6,2,1,4]=>[5,3,1,2,6,7,4]=>[3,5,7,6,2,1,4]=>{{1,3,4,6,7},{2,5}}
[3,5,7,6,2,4,1]=>[5,3,2,6,7,1,4]=>[3,5,6,2,1,7,4]=>{{1,2,3,4,5,6,7}}
[3,5,7,6,4,1,2]=>[5,3,1,4,6,7,2]=>[3,5,7,4,2,1,6]=>{{1,3,6,7},{2,5},{4}}
[3,5,7,6,4,2,1]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>{{1,3,7},{2,4,5,6}}
[3,6,1,2,4,5,7]=>[7,3,1,6,5,4,2]=>[1,5,7,2,3,4,6]=>{{1},{2,3,4,5,6,7}}
[3,6,1,2,4,7,5]=>[3,1,6,5,7,4,2]=>[5,7,2,3,1,4,6]=>{{1,5},{2,3,4,6,7}}
[3,6,1,2,5,4,7]=>[7,3,1,6,4,5,2]=>[1,5,7,2,4,3,6]=>{{1},{2,4,5},{3,6,7}}
[3,6,1,2,5,7,4]=>[3,1,6,5,4,7,2]=>[5,7,2,3,4,1,6]=>{{1,2,3,4,5,6,7}}
[3,6,1,2,7,4,5]=>[3,1,6,4,7,5,2]=>[5,7,2,4,1,3,6]=>{{1,5},{2,3,6,7},{4}}
[3,6,1,2,7,5,4]=>[3,1,6,4,5,7,2]=>[5,7,2,4,3,1,6]=>{{1,2,3,5,6,7},{4}}
[3,6,1,4,2,5,7]=>[7,3,1,6,5,2,4]=>[1,5,7,2,3,6,4]=>{{1},{2,3,4,5,7},{6}}
[3,6,1,4,2,7,5]=>[3,1,6,5,7,2,4]=>[5,7,2,3,1,6,4]=>{{1,5},{2,3,4,7},{6}}
[3,6,1,4,5,2,7]=>[7,3,1,6,4,2,5]=>[1,5,7,2,4,6,3]=>{{1},{2,4,5},{3,7},{6}}
[3,6,1,4,5,7,2]=>[3,1,6,5,4,2,7]=>[5,7,2,3,4,6,1]=>{{1,2,3,4,5,7},{6}}
[3,6,1,4,7,2,5]=>[3,1,6,4,2,7,5]=>[5,7,2,4,6,1,3]=>{{1,5,6},{2,3,7},{4}}
[3,6,1,4,7,5,2]=>[3,1,6,4,2,5,7]=>[5,7,2,4,6,3,1]=>{{1,2,3,5,6,7},{4}}
[3,6,1,5,2,4,7]=>[7,3,1,6,2,5,4]=>[1,5,7,2,6,3,4]=>{{1},{2,3,4,5,6,7}}
[3,6,1,5,2,7,4]=>[3,1,6,2,5,4,7]=>[5,7,2,6,3,4,1]=>{{1,2,3,5,7},{4,6}}
[3,6,1,5,4,2,7]=>[7,3,1,6,2,4,5]=>[1,5,7,2,6,4,3]=>{{1},{2,4,5,6},{3,7}}
[3,6,1,5,4,7,2]=>[3,1,6,4,5,2,7]=>[5,7,2,4,3,6,1]=>{{1,2,3,5,7},{4},{6}}
[3,6,1,5,7,2,4]=>[3,1,6,5,2,7,4]=>[5,7,2,3,6,1,4]=>{{1,5,6},{2,3,4,7}}
[3,6,1,5,7,4,2]=>[3,1,6,5,2,4,7]=>[5,7,2,3,6,4,1]=>{{1,2,3,4,5,6,7}}
[3,6,1,7,2,4,5]=>[3,1,6,2,7,5,4]=>[5,7,2,6,1,3,4]=>{{1,5},{2,3,4,6,7}}
[3,6,1,7,2,5,4]=>[3,1,6,2,7,4,5]=>[5,7,2,6,1,4,3]=>{{1,5},{2,3,7},{4,6}}
[3,6,1,7,4,2,5]=>[3,1,6,2,4,7,5]=>[5,7,2,6,4,1,3]=>{{1,4,5,6},{2,3,7}}
[3,6,1,7,4,5,2]=>[3,1,6,4,7,2,5]=>[5,7,2,4,1,6,3]=>{{1,5},{2,3,7},{4},{6}}
[3,6,1,7,5,2,4]=>[3,1,6,2,5,7,4]=>[5,7,2,6,3,1,4]=>{{1,2,3,4,5,6,7}}
[3,6,1,7,5,4,2]=>[3,1,6,2,4,5,7]=>[5,7,2,6,4,3,1]=>{{1,2,3,4,5,6,7}}
[3,6,2,1,4,5,7]=>[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>{{1},{2,5},{3,4,6,7}}
[3,6,2,1,4,7,5]=>[3,1,2,6,5,7,4]=>[5,7,6,2,3,1,4]=>{{1,3,5,6},{2,4,7}}
[3,6,2,1,5,4,7]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>{{1},{2,5},{3,7},{4,6}}
[3,6,2,1,5,7,4]=>[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>{{1,2,3,4,5,6,7}}
[3,6,2,1,7,4,5]=>[3,1,2,6,4,7,5]=>[5,7,6,2,4,1,3]=>{{1,2,3,4,5,6,7}}
[3,6,2,1,7,5,4]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>{{1,2,4,5,7},{3,6}}
[3,6,2,4,1,5,7]=>[7,3,2,6,5,1,4]=>[1,5,6,2,3,7,4]=>{{1},{2,3,4,5,6,7}}
[3,6,2,4,1,7,5]=>[3,2,6,5,7,1,4]=>[5,6,2,3,1,7,4]=>{{1,5},{2,3,4,6,7}}
[3,6,2,4,5,1,7]=>[7,3,2,6,4,1,5]=>[1,5,6,2,4,7,3]=>{{1},{2,4,5},{3,6,7}}
[3,6,2,4,5,7,1]=>[3,2,6,5,4,1,7]=>[5,6,2,3,4,7,1]=>{{1,2,3,4,5,6,7}}
[3,6,2,4,7,1,5]=>[3,2,6,4,1,7,5]=>[5,6,2,4,7,1,3]=>{{1,2,3,5,6,7},{4}}
[3,6,2,4,7,5,1]=>[3,2,6,4,1,5,7]=>[5,6,2,4,7,3,1]=>{{1,5,7},{2,3,6},{4}}
[3,6,2,5,1,4,7]=>[7,3,2,6,1,5,4]=>[1,5,6,2,7,3,4]=>{{1},{2,4,5,7},{3,6}}
[3,6,2,5,1,7,4]=>[3,2,6,1,5,4,7]=>[5,6,2,7,3,4,1]=>{{1,2,3,4,5,6,7}}
[3,6,2,5,4,1,7]=>[7,3,2,6,1,4,5]=>[1,5,6,2,7,4,3]=>{{1},{2,3,4,5,6,7}}
[3,6,2,5,4,7,1]=>[3,2,6,4,5,1,7]=>[5,6,2,4,3,7,1]=>{{1,2,3,5,6,7},{4}}
[3,6,2,5,7,1,4]=>[3,2,6,5,1,7,4]=>[5,6,2,3,7,1,4]=>{{1,2,3,4,5,6,7}}
[3,6,2,5,7,4,1]=>[3,2,6,5,1,4,7]=>[5,6,2,3,7,4,1]=>{{1,5,7},{2,3,4,6}}
[3,6,2,7,1,4,5]=>[3,2,6,1,7,5,4]=>[5,6,2,7,1,3,4]=>{{1,5},{2,3,6},{4,7}}
[3,6,2,7,1,5,4]=>[3,2,6,1,7,4,5]=>[5,6,2,7,1,4,3]=>{{1,5},{2,3,4,6,7}}
[3,6,2,7,4,1,5]=>[3,2,6,1,4,7,5]=>[5,6,2,7,4,1,3]=>{{1,2,3,4,5,6,7}}
[3,6,2,7,4,5,1]=>[3,2,6,4,7,1,5]=>[5,6,2,4,1,7,3]=>{{1,5},{2,3,6,7},{4}}
[3,6,2,7,5,1,4]=>[3,2,6,1,5,7,4]=>[5,6,2,7,3,1,4]=>{{1,2,3,5,6},{4,7}}
[3,6,2,7,5,4,1]=>[3,2,6,1,4,5,7]=>[5,6,2,7,4,3,1]=>{{1,4,5,7},{2,3,6}}
[3,6,4,1,2,5,7]=>[7,3,1,4,6,5,2]=>[1,5,7,4,2,3,6]=>{{1},{2,5},{3,6,7},{4}}
[3,6,4,1,2,7,5]=>[3,1,4,6,5,7,2]=>[5,7,4,2,3,1,6]=>{{1,2,3,4,5,6,7}}
[3,6,4,1,5,2,7]=>[7,3,1,4,6,2,5]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[3,6,4,1,5,7,2]=>[3,1,4,6,5,2,7]=>[5,7,4,2,3,6,1]=>{{1,2,3,4,5,7},{6}}
[3,6,4,1,7,2,5]=>[3,1,4,6,2,7,5]=>[5,7,4,2,6,1,3]=>{{1,5,6},{2,3,4,7}}
[3,6,4,1,7,5,2]=>[3,1,4,6,2,5,7]=>[5,7,4,2,6,3,1]=>{{1,2,3,4,5,6,7}}
[3,6,4,2,1,5,7]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>{{1},{2,4,5,6},{3,7}}
[3,6,4,2,1,7,5]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>{{1,2,5,7},{3,6},{4}}
[3,6,4,2,5,1,7]=>[7,3,2,4,6,1,5]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[3,6,4,2,5,7,1]=>[3,2,4,6,5,1,7]=>[5,6,4,2,3,7,1]=>{{1,2,3,4,5,6,7}}
[3,6,4,2,7,1,5]=>[3,2,4,6,1,7,5]=>[5,6,4,2,7,1,3]=>{{1,2,3,4,5,6,7}}
[3,6,4,2,7,5,1]=>[3,2,4,6,1,5,7]=>[5,6,4,2,7,3,1]=>{{1,5,7},{2,3,4,6}}
[3,6,4,5,1,2,7]=>[7,4,6,3,1,5,2]=>[1,4,2,5,7,3,6]=>{{1},{2,3,4,5,6,7}}
[3,6,4,5,1,7,2]=>[4,6,3,1,5,2,7]=>[4,2,5,7,3,6,1]=>{{1,4,7},{2},{3,5},{6}}
[3,6,4,5,2,1,7]=>[7,4,6,3,1,2,5]=>[1,4,2,5,7,6,3]=>{{1},{2,3,4,5,7},{6}}
[3,6,4,5,2,7,1]=>[4,6,3,2,5,1,7]=>[4,2,5,6,3,7,1]=>{{1,4,6,7},{2},{3,5}}
[3,6,4,5,7,1,2]=>[4,6,5,3,1,7,2]=>[4,2,3,5,7,1,6]=>{{1,4,5,6,7},{2},{3}}
[3,6,4,5,7,2,1]=>[4,6,5,3,1,2,7]=>[4,2,3,5,7,6,1]=>{{1,4,5,7},{2},{3},{6}}
[3,6,4,7,1,2,5]=>[4,6,3,1,7,5,2]=>[4,2,5,7,1,3,6]=>{{1,3,4,5,6,7},{2}}
[3,6,4,7,1,5,2]=>[4,6,3,1,7,2,5]=>[4,2,5,7,1,6,3]=>{{1,3,4,5,7},{2},{6}}
[3,6,4,7,2,1,5]=>[4,6,3,1,2,7,5]=>[4,2,5,7,6,1,3]=>{{1,3,4,5,6,7},{2}}
[3,6,4,7,2,5,1]=>[4,6,3,2,7,1,5]=>[4,2,5,6,1,7,3]=>{{1,3,4,5,6,7},{2}}
[3,6,4,7,5,1,2]=>[4,6,3,1,5,7,2]=>[4,2,5,7,3,1,6]=>{{1,4,6,7},{2},{3,5}}
[3,6,4,7,5,2,1]=>[4,6,3,1,2,5,7]=>[4,2,5,7,6,3,1]=>{{1,4,7},{2},{3,5,6}}
[3,6,5,1,2,4,7]=>[7,3,1,5,6,4,2]=>[1,5,7,3,2,4,6]=>{{1},{2,5},{3,4,6,7}}
[3,6,5,1,2,7,4]=>[3,1,5,6,4,7,2]=>[5,7,3,2,4,1,6]=>{{1,2,4,5,6,7},{3}}
[3,6,5,1,4,2,7]=>[7,3,1,5,6,2,4]=>[1,5,7,3,2,6,4]=>{{1},{2,5},{3,4,7},{6}}
[3,6,5,1,4,7,2]=>[3,1,5,6,4,2,7]=>[5,7,3,2,4,6,1]=>{{1,2,4,5,7},{3},{6}}
[3,6,5,1,7,2,4]=>[3,1,5,6,2,7,4]=>[5,7,3,2,6,1,4]=>{{1,5,6},{2,4,7},{3}}
[3,6,5,1,7,4,2]=>[3,1,5,6,2,4,7]=>[5,7,3,2,6,4,1]=>{{1,2,4,5,6,7},{3}}
[3,6,5,2,1,4,7]=>[7,3,1,2,5,6,4]=>[1,5,7,6,3,2,4]=>{{1},{2,3,4,5,6,7}}
[3,6,5,2,1,7,4]=>[3,1,2,5,6,4,7]=>[5,7,6,3,2,4,1]=>{{1,2,5,7},{3,4,6}}
[3,6,5,2,4,1,7]=>[7,3,2,5,6,1,4]=>[1,5,6,3,2,7,4]=>{{1},{2,5},{3,4,6,7}}
[3,6,5,2,4,7,1]=>[3,2,5,6,4,1,7]=>[5,6,3,2,4,7,1]=>{{1,2,4,5,6,7},{3}}
[3,6,5,2,7,1,4]=>[3,2,5,6,1,7,4]=>[5,6,3,2,7,1,4]=>{{1,2,4,5,6,7},{3}}
[3,6,5,2,7,4,1]=>[3,2,5,6,1,4,7]=>[5,6,3,2,7,4,1]=>{{1,5,7},{2,4,6},{3}}
[3,6,5,4,1,2,7]=>[7,3,1,4,5,6,2]=>[1,5,7,4,3,2,6]=>{{1},{2,3,5,6,7},{4}}
[3,6,5,4,1,7,2]=>[3,1,4,5,6,2,7]=>[5,7,4,3,2,6,1]=>{{1,2,5,7},{3,4},{6}}
[3,6,5,4,2,1,7]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,4,2,7,1]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>{{1,2,5,6,7},{3,4}}
[3,6,5,4,7,1,2]=>[4,5,6,3,1,7,2]=>[4,3,2,5,7,1,6]=>{{1,4,5,6,7},{2,3}}
[3,6,5,4,7,2,1]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>{{1,4,5,7},{2,3},{6}}
[3,6,5,7,1,2,4]=>[5,6,3,1,7,4,2]=>[3,2,5,7,1,4,6]=>{{1,3,5},{2},{4,6,7}}
[3,6,5,7,1,4,2]=>[5,6,3,1,7,2,4]=>[3,2,5,7,1,6,4]=>{{1,3,5},{2},{4,7},{6}}
[3,6,5,7,2,1,4]=>[5,6,3,1,2,7,4]=>[3,2,5,7,6,1,4]=>{{1,3,5,6},{2},{4,7}}
[3,6,5,7,2,4,1]=>[5,6,3,2,7,1,4]=>[3,2,5,6,1,7,4]=>{{1,3,5},{2},{4,6,7}}
[3,6,5,7,4,1,2]=>[5,6,3,1,4,7,2]=>[3,2,5,7,4,1,6]=>{{1,3,4,5,6,7},{2}}
[3,6,5,7,4,2,1]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>{{1,3,4,5,6,7},{2}}
[3,6,7,1,2,4,5]=>[6,3,1,7,5,4,2]=>[2,5,7,1,3,4,6]=>{{1,2,3,4,5,6,7}}
[3,6,7,1,2,5,4]=>[6,3,1,7,4,5,2]=>[2,5,7,1,4,3,6]=>{{1,2,4,5},{3,6,7}}
[3,6,7,1,4,2,5]=>[6,3,1,7,5,2,4]=>[2,5,7,1,3,6,4]=>{{1,2,3,4,5,7},{6}}
[3,6,7,1,4,5,2]=>[6,3,1,7,4,2,5]=>[2,5,7,1,4,6,3]=>{{1,2,4,5},{3,7},{6}}
[3,6,7,1,5,2,4]=>[6,3,1,7,2,5,4]=>[2,5,7,1,6,3,4]=>{{1,2,3,4,5,6,7}}
[3,6,7,1,5,4,2]=>[6,3,1,7,2,4,5]=>[2,5,7,1,6,4,3]=>{{1,2,4,5,6},{3,7}}
[3,6,7,2,1,4,5]=>[6,3,1,2,7,5,4]=>[2,5,7,6,1,3,4]=>{{1,2,5},{3,4,6,7}}
[3,6,7,2,1,5,4]=>[6,3,1,2,7,4,5]=>[2,5,7,6,1,4,3]=>{{1,2,5},{3,7},{4,6}}
[3,6,7,2,4,1,5]=>[6,3,2,7,5,1,4]=>[2,5,6,1,3,7,4]=>{{1,2,3,4,5,6,7}}
[3,6,7,2,4,5,1]=>[6,3,2,7,4,1,5]=>[2,5,6,1,4,7,3]=>{{1,2,4,5},{3,6,7}}
[3,6,7,2,5,1,4]=>[6,3,2,7,1,5,4]=>[2,5,6,1,7,3,4]=>{{1,2,4,5,7},{3,6}}
[3,6,7,2,5,4,1]=>[6,3,2,7,1,4,5]=>[2,5,6,1,7,4,3]=>{{1,2,3,4,5,6,7}}
[3,6,7,4,1,2,5]=>[6,3,1,4,7,5,2]=>[2,5,7,4,1,3,6]=>{{1,2,5},{3,6,7},{4}}
[3,6,7,4,1,5,2]=>[6,3,1,4,7,2,5]=>[2,5,7,4,1,6,3]=>{{1,2,5},{3,7},{4},{6}}
[3,6,7,4,2,1,5]=>[6,3,1,2,4,7,5]=>[2,5,7,6,4,1,3]=>{{1,2,4,5,6},{3,7}}
[3,6,7,4,2,5,1]=>[6,3,2,4,7,1,5]=>[2,5,6,4,1,7,3]=>{{1,2,5},{3,6,7},{4}}
[3,6,7,4,5,1,2]=>[6,4,7,3,1,5,2]=>[2,4,1,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[3,6,7,4,5,2,1]=>[6,4,7,3,1,2,5]=>[2,4,1,5,7,6,3]=>{{1,2,3,4,5,7},{6}}
[3,6,7,5,1,2,4]=>[6,3,1,5,7,4,2]=>[2,5,7,3,1,4,6]=>{{1,2,5},{3,4,6,7}}
[3,6,7,5,1,4,2]=>[6,3,1,5,7,2,4]=>[2,5,7,3,1,6,4]=>{{1,2,5},{3,4,7},{6}}
[3,6,7,5,2,1,4]=>[6,3,1,2,5,7,4]=>[2,5,7,6,3,1,4]=>{{1,2,3,4,5,6,7}}
[3,6,7,5,2,4,1]=>[6,3,2,5,7,1,4]=>[2,5,6,3,1,7,4]=>{{1,2,5},{3,4,6,7}}
[3,6,7,5,4,1,2]=>[6,3,1,4,5,7,2]=>[2,5,7,4,3,1,6]=>{{1,2,3,5,6,7},{4}}
[3,6,7,5,4,2,1]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>{{1,2,3,4,5,6,7}}
[3,7,1,2,4,5,6]=>[3,1,7,6,5,4,2]=>[5,7,1,2,3,4,6]=>{{1,3,5},{2,4,6,7}}
[3,7,1,2,4,6,5]=>[3,1,7,5,6,4,2]=>[5,7,1,3,2,4,6]=>{{1,2,3,4,5,6,7}}
[3,7,1,2,5,4,6]=>[3,1,7,6,4,5,2]=>[5,7,1,2,4,3,6]=>{{1,2,3,4,5,6,7}}
[3,7,1,2,5,6,4]=>[3,1,7,5,4,6,2]=>[5,7,1,3,4,2,6]=>{{1,3,4,5},{2,6,7}}
[3,7,1,2,6,4,5]=>[3,1,7,4,6,5,2]=>[5,7,1,4,2,3,6]=>{{1,2,3,5,6,7},{4}}
[3,7,1,2,6,5,4]=>[3,1,7,4,5,6,2]=>[5,7,1,4,3,2,6]=>{{1,3,5},{2,6,7},{4}}
[3,7,1,4,2,5,6]=>[3,1,7,6,5,2,4]=>[5,7,1,2,3,6,4]=>{{1,3,5},{2,4,7},{6}}
[3,7,1,4,2,6,5]=>[3,1,7,5,6,2,4]=>[5,7,1,3,2,6,4]=>{{1,2,3,4,5,7},{6}}
[3,7,1,4,5,2,6]=>[3,1,7,6,4,2,5]=>[5,7,1,2,4,6,3]=>{{1,2,3,4,5,7},{6}}
[3,7,1,4,5,6,2]=>[3,1,7,5,4,2,6]=>[5,7,1,3,4,6,2]=>{{1,3,4,5},{2,7},{6}}
[3,7,1,4,6,2,5]=>[3,1,7,4,2,6,5]=>[5,7,1,4,6,2,3]=>{{1,2,3,5,6,7},{4}}
[3,7,1,4,6,5,2]=>[3,1,7,4,2,5,6]=>[5,7,1,4,6,3,2]=>{{1,3,5,6},{2,7},{4}}
[3,7,1,5,2,4,6]=>[3,1,7,6,2,5,4]=>[5,7,1,2,6,3,4]=>{{1,3,5,6},{2,4,7}}
[3,7,1,5,2,6,4]=>[3,1,7,2,5,4,6]=>[5,7,1,6,3,4,2]=>{{1,3,5},{2,7},{4,6}}
[3,7,1,5,4,2,6]=>[3,1,7,6,2,4,5]=>[5,7,1,2,6,4,3]=>{{1,2,3,4,5,6,7}}
[3,7,1,5,4,6,2]=>[3,1,7,4,5,2,6]=>[5,7,1,4,3,6,2]=>{{1,3,5},{2,7},{4},{6}}
[3,7,1,5,6,2,4]=>[3,1,7,5,2,6,4]=>[5,7,1,3,6,2,4]=>{{1,2,3,4,5,6,7}}
[3,7,1,5,6,4,2]=>[3,1,7,5,2,4,6]=>[5,7,1,3,6,4,2]=>{{1,3,4,5,6},{2,7}}
[3,7,1,6,2,4,5]=>[3,1,7,2,6,5,4]=>[5,7,1,6,2,3,4]=>{{1,2,3,4,5,6,7}}
[3,7,1,6,2,5,4]=>[3,1,7,2,6,4,5]=>[5,7,1,6,2,4,3]=>{{1,2,3,5,7},{4,6}}
[3,7,1,6,4,2,5]=>[3,1,7,2,4,6,5]=>[5,7,1,6,4,2,3]=>{{1,2,3,4,5,6,7}}
[3,7,1,6,4,5,2]=>[3,1,7,4,6,2,5]=>[5,7,1,4,2,6,3]=>{{1,2,3,5,7},{4},{6}}
[3,7,1,6,5,2,4]=>[3,1,7,2,5,6,4]=>[5,7,1,6,3,2,4]=>{{1,3,5},{2,4,6,7}}
[3,7,1,6,5,4,2]=>[3,1,7,2,4,5,6]=>[5,7,1,6,4,3,2]=>{{1,3,4,5,6},{2,7}}
[3,7,2,1,4,5,6]=>[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>{{1,2,4,5,7},{3,6}}
[3,7,2,1,4,6,5]=>[3,1,2,7,5,6,4]=>[5,7,6,1,3,2,4]=>{{1,2,3,4,5,6,7}}
[3,7,2,1,5,4,6]=>[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>{{1,2,3,4,5,6,7}}
[3,7,2,1,5,6,4]=>[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>{{1,3,4,5,6},{2,7}}
[3,7,2,1,6,4,5]=>[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>{{1,4,5},{2,3,6,7}}
[3,7,2,1,6,5,4]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>{{1,4,5},{2,7},{3,6}}
[3,7,2,4,1,5,6]=>[3,2,7,6,5,1,4]=>[5,6,1,2,3,7,4]=>{{1,3,5},{2,4,6,7}}
[3,7,2,4,1,6,5]=>[3,2,7,5,6,1,4]=>[5,6,1,3,2,7,4]=>{{1,2,3,4,5,6,7}}
[3,7,2,4,5,1,6]=>[3,2,7,6,4,1,5]=>[5,6,1,2,4,7,3]=>{{1,2,3,4,5,6,7}}
[3,7,2,4,5,6,1]=>[3,2,7,5,4,1,6]=>[5,6,1,3,4,7,2]=>{{1,3,4,5},{2,6,7}}
[3,7,2,4,6,1,5]=>[3,2,7,4,1,6,5]=>[5,6,1,4,7,2,3]=>{{1,3,5,7},{2,6},{4}}
[3,7,2,4,6,5,1]=>[3,2,7,4,1,5,6]=>[5,6,1,4,7,3,2]=>{{1,2,3,5,6,7},{4}}
[3,7,2,5,1,4,6]=>[3,2,7,6,1,5,4]=>[5,6,1,2,7,3,4]=>{{1,2,3,4,5,6,7}}
[3,7,2,5,1,6,4]=>[3,2,7,1,5,4,6]=>[5,6,1,7,3,4,2]=>{{1,3,5},{2,4,6,7}}
[3,7,2,5,4,1,6]=>[3,2,7,6,1,4,5]=>[5,6,1,2,7,4,3]=>{{1,3,5,7},{2,4,6}}
[3,7,2,5,4,6,1]=>[3,2,7,4,5,1,6]=>[5,6,1,4,3,7,2]=>{{1,3,5},{2,6,7},{4}}
[3,7,2,5,6,1,4]=>[3,2,7,5,1,6,4]=>[5,6,1,3,7,2,4]=>{{1,3,4,5,7},{2,6}}
[3,7,2,5,6,4,1]=>[3,2,7,5,1,4,6]=>[5,6,1,3,7,4,2]=>{{1,2,3,4,5,6,7}}
[3,7,2,6,1,4,5]=>[3,2,7,1,6,5,4]=>[5,6,1,7,2,3,4]=>{{1,2,3,5,6},{4,7}}
[3,7,2,6,1,5,4]=>[3,2,7,1,6,4,5]=>[5,6,1,7,2,4,3]=>{{1,2,3,4,5,6,7}}
[3,7,2,6,4,1,5]=>[3,2,7,1,4,6,5]=>[5,6,1,7,4,2,3]=>{{1,3,4,5,7},{2,6}}
[3,7,2,6,4,5,1]=>[3,2,7,4,6,1,5]=>[5,6,1,4,2,7,3]=>{{1,2,3,5,6,7},{4}}
[3,7,2,6,5,1,4]=>[3,2,7,1,5,6,4]=>[5,6,1,7,3,2,4]=>{{1,3,5},{2,6},{4,7}}
[3,7,2,6,5,4,1]=>[3,2,7,1,4,5,6]=>[5,6,1,7,4,3,2]=>{{1,2,3,4,5,6,7}}
[3,7,4,1,2,5,6]=>[3,1,4,7,6,5,2]=>[5,7,4,1,2,3,6]=>{{1,2,3,4,5,6,7}}
[3,7,4,1,2,6,5]=>[3,1,4,7,5,6,2]=>[5,7,4,1,3,2,6]=>{{1,3,4,5},{2,6,7}}
[3,7,4,1,5,2,6]=>[3,1,4,7,6,2,5]=>[5,7,4,1,2,6,3]=>{{1,2,3,4,5,7},{6}}
[3,7,4,1,5,6,2]=>[3,1,4,7,5,2,6]=>[5,7,4,1,3,6,2]=>{{1,3,4,5},{2,7},{6}}
[3,7,4,1,6,2,5]=>[3,1,4,7,2,6,5]=>[5,7,4,1,6,2,3]=>{{1,2,3,4,5,6,7}}
[3,7,4,1,6,5,2]=>[3,1,4,7,2,5,6]=>[5,7,4,1,6,3,2]=>{{1,3,4,5,6},{2,7}}
[3,7,4,2,1,5,6]=>[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>{{1,5},{2,3,6,7},{4}}
[3,7,4,2,1,6,5]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>{{1,5},{2,7},{3,6},{4}}
[3,7,4,2,5,1,6]=>[3,2,4,7,6,1,5]=>[5,6,4,1,2,7,3]=>{{1,2,3,4,5,6,7}}
[3,7,4,2,5,6,1]=>[3,2,4,7,5,1,6]=>[5,6,4,1,3,7,2]=>{{1,3,4,5},{2,6,7}}
[3,7,4,2,6,1,5]=>[3,2,4,7,1,6,5]=>[5,6,4,1,7,2,3]=>{{1,3,4,5,7},{2,6}}
[3,7,4,2,6,5,1]=>[3,2,4,7,1,5,6]=>[5,6,4,1,7,3,2]=>{{1,2,3,4,5,6,7}}
[3,7,4,5,1,2,6]=>[4,7,6,3,1,5,2]=>[4,1,2,5,7,3,6]=>{{1,2,3,4,5,6,7}}
[3,7,4,5,1,6,2]=>[4,7,3,1,5,2,6]=>[4,1,5,7,3,6,2]=>{{1,2,4,7},{3,5},{6}}
[3,7,4,5,2,1,6]=>[4,7,6,3,1,2,5]=>[4,1,2,5,7,6,3]=>{{1,2,3,4,5,7},{6}}
[3,7,4,5,2,6,1]=>[4,7,3,2,5,1,6]=>[4,1,5,6,3,7,2]=>{{1,2,4,6,7},{3,5}}
[3,7,4,5,6,1,2]=>[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>{{1,2,4,5,6,7},{3}}
[3,7,4,5,6,2,1]=>[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>{{1,2,4,5,7},{3},{6}}
[3,7,4,6,1,2,5]=>[4,7,3,1,6,5,2]=>[4,1,5,7,2,3,6]=>{{1,2,3,4,5,6,7}}
[3,7,4,6,1,5,2]=>[4,7,3,1,6,2,5]=>[4,1,5,7,2,6,3]=>{{1,2,3,4,5,7},{6}}
[3,7,4,6,2,1,5]=>[4,7,3,1,2,6,5]=>[4,1,5,7,6,2,3]=>{{1,2,3,4,5,6,7}}
[3,7,4,6,2,5,1]=>[4,7,3,2,6,1,5]=>[4,1,5,6,2,7,3]=>{{1,2,3,4,5,6,7}}
[3,7,4,6,5,1,2]=>[4,7,3,1,5,6,2]=>[4,1,5,7,3,2,6]=>{{1,2,4,6,7},{3,5}}
[3,7,4,6,5,2,1]=>[4,7,3,1,2,5,6]=>[4,1,5,7,6,3,2]=>{{1,2,4,7},{3,5,6}}
[3,7,5,1,2,4,6]=>[3,1,5,7,6,4,2]=>[5,7,3,1,2,4,6]=>{{1,2,4,5,6,7},{3}}
[3,7,5,1,2,6,4]=>[3,1,5,7,4,6,2]=>[5,7,3,1,4,2,6]=>{{1,4,5},{2,6,7},{3}}
[3,7,5,1,4,2,6]=>[3,1,5,7,6,2,4]=>[5,7,3,1,2,6,4]=>{{1,2,4,5,7},{3},{6}}
[3,7,5,1,4,6,2]=>[3,1,5,7,4,2,6]=>[5,7,3,1,4,6,2]=>{{1,4,5},{2,7},{3},{6}}
[3,7,5,1,6,2,4]=>[3,1,5,7,2,6,4]=>[5,7,3,1,6,2,4]=>{{1,2,4,5,6,7},{3}}
[3,7,5,1,6,4,2]=>[3,1,5,7,2,4,6]=>[5,7,3,1,6,4,2]=>{{1,4,5,6},{2,7},{3}}
[3,7,5,2,1,4,6]=>[3,1,2,5,7,6,4]=>[5,7,6,3,1,2,4]=>{{1,5},{2,3,4,6,7}}
[3,7,5,2,1,6,4]=>[3,1,2,5,7,4,6]=>[5,7,6,3,1,4,2]=>{{1,5},{2,7},{3,4,6}}
[3,7,5,2,4,1,6]=>[3,2,5,7,6,1,4]=>[5,6,3,1,2,7,4]=>{{1,2,4,5,6,7},{3}}
[3,7,5,2,4,6,1]=>[3,2,5,7,4,1,6]=>[5,6,3,1,4,7,2]=>{{1,4,5},{2,6,7},{3}}
[3,7,5,2,6,1,4]=>[3,2,5,7,1,6,4]=>[5,6,3,1,7,2,4]=>{{1,4,5,7},{2,6},{3}}
[3,7,5,2,6,4,1]=>[3,2,5,7,1,4,6]=>[5,6,3,1,7,4,2]=>{{1,2,4,5,6,7},{3}}
[3,7,5,4,1,2,6]=>[3,1,4,5,7,6,2]=>[5,7,4,3,1,2,6]=>{{1,5},{2,6,7},{3,4}}
[3,7,5,4,1,6,2]=>[3,1,4,5,7,2,6]=>[5,7,4,3,1,6,2]=>{{1,5},{2,7},{3,4},{6}}
[3,7,5,4,2,1,6]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>{{1,3,5,6},{2,7},{4}}
[3,7,5,4,2,6,1]=>[3,2,4,5,7,1,6]=>[5,6,4,3,1,7,2]=>{{1,5},{2,6,7},{3,4}}
[3,7,5,4,6,1,2]=>[4,5,7,3,1,6,2]=>[4,3,1,5,7,2,6]=>{{1,2,3,4,5,6,7}}
[3,7,5,4,6,2,1]=>[4,5,7,3,1,2,6]=>[4,3,1,5,7,6,2]=>{{1,2,3,4,5,7},{6}}
[3,7,5,6,1,2,4]=>[5,7,3,1,6,4,2]=>[3,1,5,7,2,4,6]=>{{1,2,3,5},{4,6,7}}
[3,7,5,6,1,4,2]=>[5,7,3,1,6,2,4]=>[3,1,5,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}
[3,7,5,6,2,1,4]=>[5,7,3,1,2,6,4]=>[3,1,5,7,6,2,4]=>{{1,2,3,5,6},{4,7}}
[3,7,5,6,2,4,1]=>[5,7,3,2,6,1,4]=>[3,1,5,6,2,7,4]=>{{1,2,3,5},{4,6,7}}
[3,7,5,6,4,1,2]=>[5,7,3,1,4,6,2]=>[3,1,5,7,4,2,6]=>{{1,2,3,4,5,6,7}}
[3,7,5,6,4,2,1]=>[5,7,3,1,2,4,6]=>[3,1,5,7,6,4,2]=>{{1,2,3,4,5,6,7}}
[3,7,6,1,2,4,5]=>[3,1,6,7,5,4,2]=>[5,7,2,1,3,4,6]=>{{1,2,3,4,5,6,7}}
[3,7,6,1,2,5,4]=>[3,1,6,7,4,5,2]=>[5,7,2,1,4,3,6]=>{{1,4,5},{2,3,6,7}}
[3,7,6,1,4,2,5]=>[3,1,6,7,5,2,4]=>[5,7,2,1,3,6,4]=>{{1,2,3,4,5,7},{6}}
[3,7,6,1,4,5,2]=>[3,1,6,7,4,2,5]=>[5,7,2,1,4,6,3]=>{{1,4,5},{2,3,7},{6}}
[3,7,6,1,5,2,4]=>[3,1,6,7,2,5,4]=>[5,7,2,1,6,3,4]=>{{1,2,3,4,5,6,7}}
[3,7,6,1,5,4,2]=>[3,1,6,7,2,4,5]=>[5,7,2,1,6,4,3]=>{{1,4,5,6},{2,3,7}}
[3,7,6,2,1,4,5]=>[3,1,2,6,7,5,4]=>[5,7,6,2,1,3,4]=>{{1,5},{2,4,7},{3,6}}
[3,7,6,2,1,5,4]=>[3,1,2,6,7,4,5]=>[5,7,6,2,1,4,3]=>{{1,5},{2,3,4,6,7}}
[3,7,6,2,4,1,5]=>[3,2,6,7,5,1,4]=>[5,6,2,1,3,7,4]=>{{1,2,3,4,5,6,7}}
[3,7,6,2,4,5,1]=>[3,2,6,7,4,1,5]=>[5,6,2,1,4,7,3]=>{{1,4,5},{2,3,6,7}}
[3,7,6,2,5,1,4]=>[3,2,6,7,1,5,4]=>[5,6,2,1,7,3,4]=>{{1,4,5,7},{2,3,6}}
[3,7,6,2,5,4,1]=>[3,2,6,7,1,4,5]=>[5,6,2,1,7,4,3]=>{{1,2,3,4,5,6,7}}
[3,7,6,4,1,2,5]=>[3,1,4,6,7,5,2]=>[5,7,4,2,1,3,6]=>{{1,5},{2,3,4,6,7}}
[3,7,6,4,1,5,2]=>[3,1,4,6,7,2,5]=>[5,7,4,2,1,6,3]=>{{1,5},{2,3,4,7},{6}}
[3,7,6,4,2,1,5]=>[3,1,2,4,6,7,5]=>[5,7,6,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[3,7,6,4,2,5,1]=>[3,2,4,6,7,1,5]=>[5,6,4,2,1,7,3]=>{{1,5},{2,3,4,6,7}}
[3,7,6,4,5,1,2]=>[4,6,7,3,1,5,2]=>[4,2,1,5,7,3,6]=>{{1,3,4,5,6,7},{2}}
[3,7,6,4,5,2,1]=>[4,6,7,3,1,2,5]=>[4,2,1,5,7,6,3]=>{{1,3,4,5,7},{2},{6}}
[3,7,6,5,1,2,4]=>[3,1,5,6,7,4,2]=>[5,7,3,2,1,4,6]=>{{1,5},{2,4,6,7},{3}}
[3,7,6,5,1,4,2]=>[3,1,5,6,7,2,4]=>[5,7,3,2,1,6,4]=>{{1,5},{2,4,7},{3},{6}}
[3,7,6,5,2,1,4]=>[3,1,2,5,6,7,4]=>[5,7,6,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[3,7,6,5,2,4,1]=>[3,2,5,6,7,1,4]=>[5,6,3,2,1,7,4]=>{{1,5},{2,4,6,7},{3}}
[3,7,6,5,4,1,2]=>[3,1,4,5,6,7,2]=>[5,7,4,3,2,1,6]=>{{1,2,5,6,7},{3,4}}
[3,7,6,5,4,2,1]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>{{1,2,3,5,6,7},{4}}
[4,1,2,3,5,6,7]=>[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>{{1},{2},{3},{4,5,6,7}}
[4,1,2,3,5,7,6]=>[6,7,5,1,4,3,2]=>[2,1,3,7,4,5,6]=>{{1,2},{3},{4,5,6,7}}
[4,1,2,3,6,5,7]=>[7,5,6,1,4,3,2]=>[1,3,2,7,4,5,6]=>{{1},{2,3},{4,5,6,7}}
[4,1,2,3,6,7,5]=>[6,5,7,1,4,3,2]=>[2,3,1,7,4,5,6]=>{{1,2,3},{4,5,6,7}}
[4,1,2,3,7,5,6]=>[5,7,6,1,4,3,2]=>[3,1,2,7,4,5,6]=>{{1,2,3},{4,5,6,7}}
[4,1,2,3,7,6,5]=>[5,6,7,1,4,3,2]=>[3,2,1,7,4,5,6]=>{{1,3},{2},{4,5,6,7}}
[4,1,2,5,3,6,7]=>[7,6,1,4,3,5,2]=>[1,2,7,4,5,3,6]=>{{1},{2},{3,6,7},{4},{5}}
[4,1,2,5,3,7,6]=>[6,7,1,4,3,5,2]=>[2,1,7,4,5,3,6]=>{{1,2},{3,6,7},{4},{5}}
[4,1,2,5,6,3,7]=>[7,5,1,4,3,6,2]=>[1,3,7,4,5,2,6]=>{{1},{2,3,6,7},{4},{5}}
[4,1,2,5,6,7,3]=>[6,5,1,4,3,7,2]=>[2,3,7,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}
[4,1,2,5,7,3,6]=>[5,1,4,3,7,6,2]=>[3,7,4,5,1,2,6]=>{{1,3,4,5},{2,6,7}}
[4,1,2,5,7,6,3]=>[5,1,4,3,6,7,2]=>[3,7,4,5,2,1,6]=>{{1,2,3,4,5,6,7}}
[4,1,2,6,3,5,7]=>[7,1,4,3,6,5,2]=>[1,7,4,5,2,3,6]=>{{1},{2,3,4,5,6,7}}
[4,1,2,6,3,7,5]=>[1,4,3,6,5,7,2]=>[7,4,5,2,3,1,6]=>{{1,6,7},{2,4},{3,5}}
[4,1,2,6,5,3,7]=>[7,1,4,3,5,6,2]=>[1,7,4,5,3,2,6]=>{{1},{2,6,7},{3,4,5}}
[4,1,2,6,5,7,3]=>[5,6,1,4,3,7,2]=>[3,2,7,4,5,1,6]=>{{1,3,6,7},{2},{4},{5}}
[4,1,2,6,7,3,5]=>[6,1,4,3,7,5,2]=>[2,7,4,5,1,3,6]=>{{1,2,3,4,5,6,7}}
[4,1,2,6,7,5,3]=>[6,1,4,3,5,7,2]=>[2,7,4,5,3,1,6]=>{{1,2,6,7},{3,4,5}}
[4,1,2,7,3,5,6]=>[1,4,3,7,6,5,2]=>[7,4,5,1,2,3,6]=>{{1,2,3,4,5,6,7}}
[4,1,2,7,3,6,5]=>[1,4,3,7,5,6,2]=>[7,4,5,1,3,2,6]=>{{1,2,4,6,7},{3,5}}
[4,1,2,7,5,3,6]=>[1,4,3,5,7,6,2]=>[7,4,5,3,1,2,6]=>{{1,2,3,4,5,6,7}}
[4,1,2,7,5,6,3]=>[5,7,1,4,3,6,2]=>[3,1,7,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}
[4,1,2,7,6,3,5]=>[1,4,3,6,7,5,2]=>[7,4,5,2,1,3,6]=>{{1,3,5,6,7},{2,4}}
[4,1,2,7,6,5,3]=>[1,4,3,5,6,7,2]=>[7,4,5,3,2,1,6]=>{{1,6,7},{2,3,4,5}}
[4,1,3,2,5,6,7]=>[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>{{1},{2},{3},{4,5,7},{6}}
[4,1,3,2,5,7,6]=>[6,7,5,1,4,2,3]=>[2,1,3,7,4,6,5]=>{{1,2},{3},{4,5,7},{6}}
[4,1,3,2,6,5,7]=>[7,5,6,1,4,2,3]=>[1,3,2,7,4,6,5]=>{{1},{2,3},{4,5,7},{6}}
[4,1,3,2,6,7,5]=>[6,5,7,1,4,2,3]=>[2,3,1,7,4,6,5]=>{{1,2,3},{4,5,7},{6}}
[4,1,3,2,7,5,6]=>[5,7,6,1,4,2,3]=>[3,1,2,7,4,6,5]=>{{1,2,3},{4,5,7},{6}}
[4,1,3,2,7,6,5]=>[5,6,7,1,4,2,3]=>[3,2,1,7,4,6,5]=>{{1,3},{2},{4,5,7},{6}}
[4,1,3,5,2,6,7]=>[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[4,1,3,5,2,7,6]=>[6,7,1,4,3,2,5]=>[2,1,7,4,5,6,3]=>{{1,2},{3,7},{4},{5},{6}}
[4,1,3,5,6,2,7]=>[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[4,1,3,5,6,7,2]=>[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[4,1,3,5,7,2,6]=>[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>{{1,3,4,5,6},{2,7}}
[4,1,3,5,7,6,2]=>[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>{{1,2,3,4,5,6,7}}
[4,1,3,6,2,5,7]=>[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>{{1},{2,3,4,5,6,7}}
[4,1,3,6,2,7,5]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>{{1,7},{2,3,4,5,6}}
[4,1,3,6,5,2,7]=>[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>{{1},{2,7},{3,4,5,6}}
[4,1,3,6,5,7,2]=>[5,6,1,4,3,2,7]=>[3,2,7,4,5,6,1]=>{{1,3,7},{2},{4},{5},{6}}
[4,1,3,6,7,2,5]=>[6,1,4,3,2,7,5]=>[2,7,4,5,6,1,3]=>{{1,2,3,4,5,6,7}}
[4,1,3,6,7,5,2]=>[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>{{1,2,7},{3,4,5,6}}
[4,1,3,7,2,5,6]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>{{1,3,5,7},{2,4,6}}
[4,1,3,7,2,6,5]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>{{1,2,3,4,5,6,7}}
[4,1,3,7,5,2,6]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>{{1,2,4,6,7},{3,5}}
[4,1,3,7,5,6,2]=>[5,7,1,4,3,2,6]=>[3,1,7,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}
[4,1,3,7,6,2,5]=>[1,4,3,2,6,7,5]=>[7,4,5,6,2,1,3]=>{{1,2,3,4,5,6,7}}
[4,1,3,7,6,5,2]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>{{1,7},{2,4,6},{3,5}}
[4,1,5,2,3,6,7]=>[7,6,1,4,2,5,3]=>[1,2,7,4,6,3,5]=>{{1},{2},{3,5,6,7},{4}}
[4,1,5,2,3,7,6]=>[6,7,1,4,2,5,3]=>[2,1,7,4,6,3,5]=>{{1,2},{3,5,6,7},{4}}
[4,1,5,2,6,3,7]=>[7,1,4,2,5,3,6]=>[1,7,4,6,3,5,2]=>{{1},{2,7},{3,4,5,6}}
[4,1,5,2,6,7,3]=>[6,1,4,2,5,3,7]=>[2,7,4,6,3,5,1]=>{{1,2,7},{3,4,5,6}}
[4,1,5,2,7,3,6]=>[1,4,2,5,3,7,6]=>[7,4,6,3,5,1,2]=>{{1,2,3,4,6,7},{5}}
[4,1,5,2,7,6,3]=>[1,4,2,5,3,6,7]=>[7,4,6,3,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[4,1,5,3,2,6,7]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>{{1},{2},{3,7},{4},{5,6}}
[4,1,5,3,2,7,6]=>[6,7,1,4,2,3,5]=>[2,1,7,4,6,5,3]=>{{1,2},{3,7},{4},{5,6}}
[4,1,5,3,6,2,7]=>[7,1,4,3,5,2,6]=>[1,7,4,5,3,6,2]=>{{1},{2,7},{3,4,5},{6}}
[4,1,5,3,6,7,2]=>[6,1,4,3,5,2,7]=>[2,7,4,5,3,6,1]=>{{1,2,7},{3,4,5},{6}}
[4,1,5,3,7,2,6]=>[1,4,3,5,2,7,6]=>[7,4,5,3,6,1,2]=>{{1,2,3,4,5,6,7}}
[4,1,5,3,7,6,2]=>[1,4,3,5,2,6,7]=>[7,4,5,3,6,2,1]=>{{1,7},{2,3,4,5,6}}
[4,1,5,6,2,3,7]=>[7,5,1,4,2,6,3]=>[1,3,7,4,6,2,5]=>{{1},{2,3,5,6,7},{4}}
[4,1,5,6,2,7,3]=>[5,1,4,2,6,3,7]=>[3,7,4,6,2,5,1]=>{{1,2,3,4,5,6,7}}
[4,1,5,6,3,2,7]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>{{1},{2,3,7},{4},{5,6}}
[4,1,5,6,3,7,2]=>[5,1,4,3,6,2,7]=>[3,7,4,5,2,6,1]=>{{1,2,3,4,5,7},{6}}
[4,1,5,6,7,2,3]=>[6,5,1,4,2,7,3]=>[2,3,7,4,6,1,5]=>{{1,2,3,5,6,7},{4}}
[4,1,5,6,7,3,2]=>[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}
[4,1,5,7,2,3,6]=>[5,1,4,2,7,6,3]=>[3,7,4,6,1,2,5]=>{{1,2,3,4,5,6,7}}
[4,1,5,7,2,6,3]=>[5,1,4,2,7,3,6]=>[3,7,4,6,1,5,2]=>{{1,3,4,5,6},{2,7}}
[4,1,5,7,3,2,6]=>[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>{{1,3,4,6},{2,7},{5}}
[4,1,5,7,3,6,2]=>[5,1,4,3,7,2,6]=>[3,7,4,5,1,6,2]=>{{1,3,4,5},{2,7},{6}}
[4,1,5,7,6,2,3]=>[5,1,4,2,6,7,3]=>[3,7,4,6,2,1,5]=>{{1,3,4,6},{2,5,7}}
[4,1,5,7,6,3,2]=>[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>{{1,2,3,4,6,7},{5}}
[4,1,6,2,3,5,7]=>[7,1,4,2,6,5,3]=>[1,7,4,6,2,3,5]=>{{1},{2,5,7},{3,4,6}}
[4,1,6,2,3,7,5]=>[1,4,2,6,5,7,3]=>[7,4,6,2,3,1,5]=>{{1,3,5,6,7},{2,4}}
[4,1,6,2,5,3,7]=>[7,1,4,2,6,3,5]=>[1,7,4,6,2,5,3]=>{{1},{2,3,4,5,6,7}}
[4,1,6,2,5,7,3]=>[1,4,2,6,5,3,7]=>[7,4,6,2,3,5,1]=>{{1,7},{2,4},{3,5,6}}
[4,1,6,2,7,3,5]=>[1,4,2,6,3,7,5]=>[7,4,6,2,5,1,3]=>{{1,3,6,7},{2,4},{5}}
[4,1,6,2,7,5,3]=>[1,4,2,6,3,5,7]=>[7,4,6,2,5,3,1]=>{{1,7},{2,4},{3,6},{5}}
[4,1,6,3,2,5,7]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>{{1},{2,3,4,6,7},{5}}
[4,1,6,3,2,7,5]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>{{1,7},{2,4,5},{3,6}}
[4,1,6,3,5,2,7]=>[7,1,4,3,6,2,5]=>[1,7,4,5,2,6,3]=>{{1},{2,3,4,5,7},{6}}
[4,1,6,3,5,7,2]=>[1,4,3,6,5,2,7]=>[7,4,5,2,3,6,1]=>{{1,7},{2,4},{3,5},{6}}
[4,1,6,3,7,2,5]=>[1,4,3,6,2,7,5]=>[7,4,5,2,6,1,3]=>{{1,3,5,6,7},{2,4}}
[4,1,6,3,7,5,2]=>[1,4,3,6,2,5,7]=>[7,4,5,2,6,3,1]=>{{1,7},{2,4},{3,5,6}}
[4,1,6,5,2,3,7]=>[7,1,4,2,5,6,3]=>[1,7,4,6,3,2,5]=>{{1},{2,3,4,5,6,7}}
[4,1,6,5,2,7,3]=>[1,4,2,5,6,3,7]=>[7,4,6,3,2,5,1]=>{{1,7},{2,3,4,5,6}}
[4,1,6,5,3,2,7]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>{{1},{2,7},{3,4,6},{5}}
[4,1,6,5,3,7,2]=>[1,4,3,5,6,2,7]=>[7,4,5,3,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[4,1,6,5,7,2,3]=>[5,6,1,4,2,7,3]=>[3,2,7,4,6,1,5]=>{{1,3,5,6,7},{2},{4}}
[4,1,6,5,7,3,2]=>[5,6,1,4,2,3,7]=>[3,2,7,4,6,5,1]=>{{1,3,7},{2},{4},{5,6}}
[4,1,6,7,2,3,5]=>[6,1,4,2,7,5,3]=>[2,7,4,6,1,3,5]=>{{1,2,5,7},{3,4,6}}
[4,1,6,7,2,5,3]=>[6,1,4,2,7,3,5]=>[2,7,4,6,1,5,3]=>{{1,2,3,4,5,6,7}}
[4,1,6,7,3,2,5]=>[6,1,4,2,3,7,5]=>[2,7,4,6,5,1,3]=>{{1,2,3,4,6,7},{5}}
[4,1,6,7,3,5,2]=>[6,1,4,3,7,2,5]=>[2,7,4,5,1,6,3]=>{{1,2,3,4,5,7},{6}}
[4,1,6,7,5,2,3]=>[6,1,4,2,5,7,3]=>[2,7,4,6,3,1,5]=>{{1,2,3,4,5,6,7}}
[4,1,6,7,5,3,2]=>[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>{{1,2,7},{3,4,6},{5}}
[4,1,7,2,3,5,6]=>[1,4,2,7,6,5,3]=>[7,4,6,1,2,3,5]=>{{1,2,4,5,7},{3,6}}
[4,1,7,2,3,6,5]=>[1,4,2,7,5,6,3]=>[7,4,6,1,3,2,5]=>{{1,2,3,4,5,6,7}}
[4,1,7,2,5,3,6]=>[1,4,2,7,6,3,5]=>[7,4,6,1,2,5,3]=>{{1,2,3,4,5,6,7}}
[4,1,7,2,5,6,3]=>[1,4,2,7,5,3,6]=>[7,4,6,1,3,5,2]=>{{1,2,4,7},{3,5,6}}
[4,1,7,2,6,3,5]=>[1,4,2,7,3,6,5]=>[7,4,6,1,5,2,3]=>{{1,2,3,4,6,7},{5}}
[4,1,7,2,6,5,3]=>[1,4,2,7,3,5,6]=>[7,4,6,1,5,3,2]=>{{1,2,4,7},{3,6},{5}}
[4,1,7,3,2,5,6]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>{{1,2,3,4,5,6,7}}
[4,1,7,3,2,6,5]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>{{1,2,4,5,7},{3,6}}
[4,1,7,3,5,2,6]=>[1,4,3,7,6,2,5]=>[7,4,5,1,2,6,3]=>{{1,2,3,4,5,7},{6}}
[4,1,7,3,5,6,2]=>[1,4,3,7,5,2,6]=>[7,4,5,1,3,6,2]=>{{1,2,4,7},{3,5},{6}}
[4,1,7,3,6,2,5]=>[1,4,3,7,2,6,5]=>[7,4,5,1,6,2,3]=>{{1,2,3,4,5,6,7}}
[4,1,7,3,6,5,2]=>[1,4,3,7,2,5,6]=>[7,4,5,1,6,3,2]=>{{1,2,4,7},{3,5,6}}
[4,1,7,5,2,3,6]=>[1,4,2,5,7,6,3]=>[7,4,6,3,1,2,5]=>{{1,5,7},{2,3,4,6}}
[4,1,7,5,2,6,3]=>[1,4,2,5,7,3,6]=>[7,4,6,3,1,5,2]=>{{1,2,3,4,5,6,7}}
[4,1,7,5,3,2,6]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>{{1,2,3,4,5,6,7}}
[4,1,7,5,3,6,2]=>[1,4,3,5,7,2,6]=>[7,4,5,3,1,6,2]=>{{1,2,3,4,5,7},{6}}
[4,1,7,5,6,2,3]=>[5,7,1,4,2,6,3]=>[3,1,7,4,6,2,5]=>{{1,2,3,5,6,7},{4}}
[4,1,7,5,6,3,2]=>[5,7,1,4,2,3,6]=>[3,1,7,4,6,5,2]=>{{1,2,3,7},{4},{5,6}}
[4,1,7,6,2,3,5]=>[1,4,2,6,7,5,3]=>[7,4,6,2,1,3,5]=>{{1,5,7},{2,4},{3,6}}
[4,1,7,6,2,5,3]=>[1,4,2,6,7,3,5]=>[7,4,6,2,1,5,3]=>{{1,3,5,6,7},{2,4}}
[4,1,7,6,3,2,5]=>[1,4,2,3,6,7,5]=>[7,4,6,5,2,1,3]=>{{1,3,6,7},{2,4,5}}
[4,1,7,6,3,5,2]=>[1,4,3,6,7,2,5]=>[7,4,5,2,1,6,3]=>{{1,3,5,7},{2,4},{6}}
[4,1,7,6,5,2,3]=>[1,4,2,5,6,7,3]=>[7,4,6,3,2,1,5]=>{{1,2,3,4,5,6,7}}
[4,1,7,6,5,3,2]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>{{1,7},{2,3,4,5,6}}
[4,2,1,3,5,6,7]=>[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>{{1},{2},{3},{4,5,6,7}}
[4,2,1,3,5,7,6]=>[6,7,5,1,2,4,3]=>[2,1,3,7,6,4,5]=>{{1,2},{3},{4,5,6,7}}
[4,2,1,3,6,5,7]=>[7,5,6,1,2,4,3]=>[1,3,2,7,6,4,5]=>{{1},{2,3},{4,5,6,7}}
[4,2,1,3,6,7,5]=>[6,5,7,1,2,4,3]=>[2,3,1,7,6,4,5]=>{{1,2,3},{4,5,6,7}}
[4,2,1,3,7,5,6]=>[5,7,6,1,2,4,3]=>[3,1,2,7,6,4,5]=>{{1,2,3},{4,5,6,7}}
[4,2,1,3,7,6,5]=>[5,6,7,1,2,4,3]=>[3,2,1,7,6,4,5]=>{{1,3},{2},{4,5,6,7}}
[4,2,1,5,3,6,7]=>[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>{{1},{2},{3,7},{4,5,6}}
[4,2,1,5,3,7,6]=>[6,7,1,2,4,3,5]=>[2,1,7,6,4,5,3]=>{{1,2},{3,7},{4,5,6}}
[4,2,1,5,6,3,7]=>[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>{{1},{2,3,7},{4,5,6}}
[4,2,1,5,6,7,3]=>[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>{{1,2,3,7},{4,5,6}}
[4,2,1,5,7,3,6]=>[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>{{1,3,6},{2,7},{4},{5}}
[4,2,1,5,7,6,3]=>[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>{{1,2,3,6,7},{4},{5}}
[4,2,1,6,3,5,7]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>{{1},{2,3,6,7},{4},{5}}
[4,2,1,6,3,7,5]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>{{1,7},{2,3,4,5,6}}
[4,2,1,6,5,3,7]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>{{1},{2,7},{3,6},{4},{5}}
[4,2,1,6,5,7,3]=>[5,6,1,2,4,3,7]=>[3,2,7,6,4,5,1]=>{{1,3,7},{2},{4,5,6}}
[4,2,1,6,7,3,5]=>[6,1,2,4,3,7,5]=>[2,7,6,4,5,1,3]=>{{1,2,3,6,7},{4},{5}}
[4,2,1,6,7,5,3]=>[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>{{1,2,7},{3,6},{4},{5}}
[4,2,1,7,3,5,6]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>{{1,3,4,5,7},{2,6}}
[4,2,1,7,3,6,5]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>{{1,2,3,4,5,6,7}}
[4,2,1,7,5,3,6]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>{{1,2,6,7},{3,4,5}}
[4,2,1,7,5,6,3]=>[5,7,1,2,4,3,6]=>[3,1,7,6,4,5,2]=>{{1,2,3,7},{4,5,6}}
[4,2,1,7,6,3,5]=>[1,2,4,3,6,7,5]=>[7,6,4,5,2,1,3]=>{{1,2,3,4,5,6,7}}
[4,2,1,7,6,5,3]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>{{1,7},{2,6},{3,4,5}}
[4,2,3,1,5,6,7]=>[7,6,5,2,4,1,3]=>[1,2,3,6,4,7,5]=>{{1},{2},{3},{4,5,6,7}}
[4,2,3,1,5,7,6]=>[6,7,5,2,4,1,3]=>[2,1,3,6,4,7,5]=>{{1,2},{3},{4,5,6,7}}
[4,2,3,1,6,5,7]=>[7,5,6,2,4,1,3]=>[1,3,2,6,4,7,5]=>{{1},{2,3},{4,5,6,7}}
[4,2,3,1,6,7,5]=>[6,5,7,2,4,1,3]=>[2,3,1,6,4,7,5]=>{{1,2,3},{4,5,6,7}}
[4,2,3,1,7,5,6]=>[5,7,6,2,4,1,3]=>[3,1,2,6,4,7,5]=>{{1,2,3},{4,5,6,7}}
[4,2,3,1,7,6,5]=>[5,6,7,2,4,1,3]=>[3,2,1,6,4,7,5]=>{{1,3},{2},{4,5,6,7}}
[4,2,3,5,1,6,7]=>[7,6,2,4,3,1,5]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[4,2,3,5,1,7,6]=>[6,7,2,4,3,1,5]=>[2,1,6,4,5,7,3]=>{{1,2},{3,6,7},{4},{5}}
[4,2,3,5,6,1,7]=>[7,5,2,4,3,1,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[4,2,3,5,6,7,1]=>[6,5,2,4,3,1,7]=>[2,3,6,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[4,2,3,5,7,1,6]=>[5,2,4,3,1,7,6]=>[3,6,4,5,7,1,2]=>{{1,2,3,4,5,6,7}}
[4,2,3,5,7,6,1]=>[5,2,4,3,1,6,7]=>[3,6,4,5,7,2,1]=>{{1,3,4,5,7},{2,6}}
[4,2,3,6,1,5,7]=>[7,2,4,3,1,6,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,3,6,1,7,5]=>[2,4,3,1,6,5,7]=>[6,4,5,7,2,3,1]=>{{1,2,3,4,5,6,7}}
[4,2,3,6,5,1,7]=>[7,2,4,3,1,5,6]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,6,5,7,1]=>[5,6,2,4,3,1,7]=>[3,2,6,4,5,7,1]=>{{1,3,6,7},{2},{4},{5}}
[4,2,3,6,7,1,5]=>[6,2,4,3,1,7,5]=>[2,6,4,5,7,1,3]=>{{1,2,6},{3,4,5,7}}
[4,2,3,6,7,5,1]=>[6,2,4,3,1,5,7]=>[2,6,4,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[4,2,3,7,1,5,6]=>[2,4,3,1,7,6,5]=>[6,4,5,7,1,2,3]=>{{1,2,3,4,5,6,7}}
[4,2,3,7,1,6,5]=>[2,4,3,1,7,5,6]=>[6,4,5,7,1,3,2]=>{{1,3,5,6},{2,4,7}}
[4,2,3,7,5,1,6]=>[2,4,3,1,5,7,6]=>[6,4,5,7,3,1,2]=>{{1,6},{2,4,7},{3,5}}
[4,2,3,7,5,6,1]=>[5,7,2,4,3,1,6]=>[3,1,6,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}
[4,2,3,7,6,1,5]=>[2,4,3,1,6,7,5]=>[6,4,5,7,2,1,3]=>{{1,6},{2,3,4,5,7}}
[4,2,3,7,6,5,1]=>[2,4,3,1,5,6,7]=>[6,4,5,7,3,2,1]=>{{1,2,4,6,7},{3,5}}
[4,2,5,1,3,6,7]=>[7,6,2,4,1,5,3]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[4,2,5,1,3,7,6]=>[6,7,2,4,1,5,3]=>[2,1,6,4,7,3,5]=>{{1,2},{3,6},{4},{5,7}}
[4,2,5,1,6,3,7]=>[7,2,4,1,5,3,6]=>[1,6,4,7,3,5,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,1,6,7,3]=>[6,2,4,1,5,3,7]=>[2,6,4,7,3,5,1]=>{{1,2,3,4,5,6,7}}
[4,2,5,1,7,3,6]=>[2,4,1,5,3,7,6]=>[6,4,7,3,5,1,2]=>{{1,6},{2,3,4,7},{5}}
[4,2,5,1,7,6,3]=>[2,4,1,5,3,6,7]=>[6,4,7,3,5,2,1]=>{{1,2,3,4,6,7},{5}}
[4,2,5,3,1,6,7]=>[7,6,2,4,1,3,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[4,2,5,3,1,7,6]=>[6,7,2,4,1,3,5]=>[2,1,6,4,7,5,3]=>{{1,2},{3,5,6,7},{4}}
[4,2,5,3,6,1,7]=>[7,2,4,3,5,1,6]=>[1,6,4,5,3,7,2]=>{{1},{2,6,7},{3,4,5}}
[4,2,5,3,6,7,1]=>[6,2,4,3,5,1,7]=>[2,6,4,5,3,7,1]=>{{1,2,6,7},{3,4,5}}
[4,2,5,3,7,1,6]=>[2,4,3,5,1,7,6]=>[6,4,5,3,7,1,2]=>{{1,6},{2,3,4,5,7}}
[4,2,5,3,7,6,1]=>[2,4,3,5,1,6,7]=>[6,4,5,3,7,2,1]=>{{1,2,3,4,5,6,7}}
[4,2,5,6,1,3,7]=>[7,5,2,4,1,6,3]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[4,2,5,6,1,7,3]=>[5,2,4,1,6,3,7]=>[3,6,4,7,2,5,1]=>{{1,3,4,7},{2,5,6}}
[4,2,5,6,3,1,7]=>[7,5,2,4,1,3,6]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[4,2,5,6,3,7,1]=>[5,2,4,3,6,1,7]=>[3,6,4,5,2,7,1]=>{{1,2,3,4,5,6,7}}
[4,2,5,6,7,1,3]=>[6,5,2,4,1,7,3]=>[2,3,6,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}
[4,2,5,6,7,3,1]=>[6,5,2,4,1,3,7]=>[2,3,6,4,7,5,1]=>{{1,2,3,5,6,7},{4}}
[4,2,5,7,1,3,6]=>[5,2,4,1,7,6,3]=>[3,6,4,7,1,2,5]=>{{1,3,4,5,7},{2,6}}
[4,2,5,7,1,6,3]=>[5,2,4,1,7,3,6]=>[3,6,4,7,1,5,2]=>{{1,2,3,4,5,6,7}}
[4,2,5,7,3,1,6]=>[5,2,4,1,3,7,6]=>[3,6,4,7,5,1,2]=>{{1,2,3,4,6,7},{5}}
[4,2,5,7,3,6,1]=>[5,2,4,3,7,1,6]=>[3,6,4,5,1,7,2]=>{{1,3,4,5},{2,6,7}}
[4,2,5,7,6,1,3]=>[5,2,4,1,6,7,3]=>[3,6,4,7,2,1,5]=>{{1,2,3,4,5,6,7}}
[4,2,5,7,6,3,1]=>[5,2,4,1,3,6,7]=>[3,6,4,7,5,2,1]=>{{1,3,4,7},{2,6},{5}}
[4,2,6,1,3,5,7]=>[7,2,4,1,6,5,3]=>[1,6,4,7,2,3,5]=>{{1},{2,3,4,5,6,7}}
[4,2,6,1,3,7,5]=>[2,4,1,6,5,7,3]=>[6,4,7,2,3,1,5]=>{{1,6},{2,4},{3,5,7}}
[4,2,6,1,5,3,7]=>[7,2,4,1,6,3,5]=>[1,6,4,7,2,5,3]=>{{1},{2,5,6},{3,4,7}}
[4,2,6,1,5,7,3]=>[2,4,1,6,5,3,7]=>[6,4,7,2,3,5,1]=>{{1,3,5,6,7},{2,4}}
[4,2,6,1,7,3,5]=>[2,4,1,6,3,7,5]=>[6,4,7,2,5,1,3]=>{{1,6},{2,4},{3,7},{5}}
[4,2,6,1,7,5,3]=>[2,4,1,6,3,5,7]=>[6,4,7,2,5,3,1]=>{{1,3,6,7},{2,4},{5}}
[4,2,6,3,1,5,7]=>[7,2,4,1,3,6,5]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,2,6,3,1,7,5]=>[2,4,1,3,6,5,7]=>[6,4,7,5,2,3,1]=>{{1,3,6,7},{2,4,5}}
[4,2,6,3,5,1,7]=>[7,2,4,3,6,1,5]=>[1,6,4,5,2,7,3]=>{{1},{2,3,4,5,6,7}}
[4,2,6,3,5,7,1]=>[2,4,3,6,5,1,7]=>[6,4,5,2,3,7,1]=>{{1,6,7},{2,4},{3,5}}
[4,2,6,3,7,1,5]=>[2,4,3,6,1,7,5]=>[6,4,5,2,7,1,3]=>{{1,6},{2,4},{3,5,7}}
[4,2,6,3,7,5,1]=>[2,4,3,6,1,5,7]=>[6,4,5,2,7,3,1]=>{{1,3,5,6,7},{2,4}}
[4,2,6,5,1,3,7]=>[7,2,4,1,5,6,3]=>[1,6,4,7,3,2,5]=>{{1},{2,6},{3,4,5,7}}
[4,2,6,5,1,7,3]=>[2,4,1,5,6,3,7]=>[6,4,7,3,2,5,1]=>{{1,2,3,4,5,6,7}}
[4,2,6,5,3,1,7]=>[7,2,4,1,3,5,6]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,6,5,3,7,1]=>[2,4,3,5,6,1,7]=>[6,4,5,3,2,7,1]=>{{1,6,7},{2,3,4,5}}
[4,2,6,5,7,1,3]=>[5,6,2,4,1,7,3]=>[3,2,6,4,7,1,5]=>{{1,3,6},{2},{4},{5,7}}
[4,2,6,5,7,3,1]=>[5,6,2,4,1,3,7]=>[3,2,6,4,7,5,1]=>{{1,3,5,6,7},{2},{4}}
[4,2,6,7,1,3,5]=>[6,2,4,1,7,5,3]=>[2,6,4,7,1,3,5]=>{{1,2,3,4,5,6,7}}
[4,2,6,7,1,5,3]=>[6,2,4,1,7,3,5]=>[2,6,4,7,1,5,3]=>{{1,2,5,6},{3,4,7}}
[4,2,6,7,3,1,5]=>[6,2,4,1,3,7,5]=>[2,6,4,7,5,1,3]=>{{1,2,6},{3,4,7},{5}}
[4,2,6,7,3,5,1]=>[6,2,4,3,7,1,5]=>[2,6,4,5,1,7,3]=>{{1,2,3,4,5,6,7}}
[4,2,6,7,5,1,3]=>[6,2,4,1,5,7,3]=>[2,6,4,7,3,1,5]=>{{1,2,6},{3,4,5,7}}
[4,2,6,7,5,3,1]=>[6,2,4,1,3,5,7]=>[2,6,4,7,5,3,1]=>{{1,2,3,4,6,7},{5}}
[4,2,7,1,3,5,6]=>[2,4,1,7,6,5,3]=>[6,4,7,1,2,3,5]=>{{1,2,3,4,5,6,7}}
[4,2,7,1,3,6,5]=>[2,4,1,7,5,6,3]=>[6,4,7,1,3,2,5]=>{{1,2,4,6},{3,5,7}}
[4,2,7,1,5,3,6]=>[2,4,1,7,6,3,5]=>[6,4,7,1,2,5,3]=>{{1,2,4,5,6},{3,7}}
[4,2,7,1,5,6,3]=>[2,4,1,7,5,3,6]=>[6,4,7,1,3,5,2]=>{{1,2,3,4,5,6,7}}
[4,2,7,1,6,3,5]=>[2,4,1,7,3,6,5]=>[6,4,7,1,5,2,3]=>{{1,2,4,6},{3,7},{5}}
[4,2,7,1,6,5,3]=>[2,4,1,7,3,5,6]=>[6,4,7,1,5,3,2]=>{{1,2,3,4,6,7},{5}}
[4,2,7,3,1,5,6]=>[2,4,1,3,7,6,5]=>[6,4,7,5,1,2,3]=>{{1,2,4,5,6},{3,7}}
[4,2,7,3,1,6,5]=>[2,4,1,3,7,5,6]=>[6,4,7,5,1,3,2]=>{{1,2,3,4,5,6,7}}
[4,2,7,3,5,1,6]=>[2,4,3,7,6,1,5]=>[6,4,5,1,2,7,3]=>{{1,2,3,4,5,6,7}}
[4,2,7,3,5,6,1]=>[2,4,3,7,5,1,6]=>[6,4,5,1,3,7,2]=>{{1,2,4,6,7},{3,5}}
[4,2,7,3,6,1,5]=>[2,4,3,7,1,6,5]=>[6,4,5,1,7,2,3]=>{{1,2,4,6},{3,5,7}}
[4,2,7,3,6,5,1]=>[2,4,3,7,1,5,6]=>[6,4,5,1,7,3,2]=>{{1,2,3,4,5,6,7}}
[4,2,7,5,1,3,6]=>[2,4,1,5,7,6,3]=>[6,4,7,3,1,2,5]=>{{1,2,3,4,5,6,7}}
[4,2,7,5,1,6,3]=>[2,4,1,5,7,3,6]=>[6,4,7,3,1,5,2]=>{{1,5,6},{2,3,4,7}}
[4,2,7,5,3,1,6]=>[2,4,1,3,5,7,6]=>[6,4,7,5,3,1,2]=>{{1,6},{2,3,4,5,7}}
[4,2,7,5,3,6,1]=>[2,4,3,5,7,1,6]=>[6,4,5,3,1,7,2]=>{{1,2,3,4,5,6,7}}
[4,2,7,5,6,1,3]=>[5,7,2,4,1,6,3]=>[3,1,6,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}
[4,2,7,5,6,3,1]=>[5,7,2,4,1,3,6]=>[3,1,6,4,7,5,2]=>{{1,2,3,5,6,7},{4}}
[4,2,7,6,1,3,5]=>[2,4,1,6,7,5,3]=>[6,4,7,2,1,3,5]=>{{1,3,5,6,7},{2,4}}
[4,2,7,6,1,5,3]=>[2,4,1,6,7,3,5]=>[6,4,7,2,1,5,3]=>{{1,5,6},{2,4},{3,7}}
[4,2,7,6,3,1,5]=>[2,4,1,3,6,7,5]=>[6,4,7,5,2,1,3]=>{{1,6},{2,4,5},{3,7}}
[4,2,7,6,3,5,1]=>[2,4,3,6,7,1,5]=>[6,4,5,2,1,7,3]=>{{1,3,5,6,7},{2,4}}
[4,2,7,6,5,1,3]=>[2,4,1,5,6,7,3]=>[6,4,7,3,2,1,5]=>{{1,6},{2,3,4,5,7}}
[4,2,7,6,5,3,1]=>[2,4,1,3,5,6,7]=>[6,4,7,5,3,2,1]=>{{1,2,3,4,5,6,7}}
[4,3,1,2,5,6,7]=>[7,6,5,1,3,4,2]=>[1,2,3,7,5,4,6]=>{{1},{2},{3},{4,6,7},{5}}
[4,3,1,2,5,7,6]=>[6,7,5,1,3,4,2]=>[2,1,3,7,5,4,6]=>{{1,2},{3},{4,6,7},{5}}
[4,3,1,2,6,5,7]=>[7,5,6,1,3,4,2]=>[1,3,2,7,5,4,6]=>{{1},{2,3},{4,6,7},{5}}
[4,3,1,2,6,7,5]=>[6,5,7,1,3,4,2]=>[2,3,1,7,5,4,6]=>{{1,2,3},{4,6,7},{5}}
[4,3,1,2,7,5,6]=>[5,7,6,1,3,4,2]=>[3,1,2,7,5,4,6]=>{{1,2,3},{4,6,7},{5}}
[4,3,1,2,7,6,5]=>[5,6,7,1,3,4,2]=>[3,2,1,7,5,4,6]=>{{1,3},{2},{4,6,7},{5}}
[4,3,1,5,2,6,7]=>[7,6,1,3,4,2,5]=>[1,2,7,5,4,6,3]=>{{1},{2},{3,7},{4,5},{6}}
[4,3,1,5,2,7,6]=>[6,7,1,3,4,2,5]=>[2,1,7,5,4,6,3]=>{{1,2},{3,7},{4,5},{6}}
[4,3,1,5,6,2,7]=>[7,5,1,3,4,2,6]=>[1,3,7,5,4,6,2]=>{{1},{2,3,7},{4,5},{6}}
[4,3,1,5,6,7,2]=>[6,5,1,3,4,2,7]=>[2,3,7,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[4,3,1,5,7,2,6]=>[5,1,3,4,2,7,6]=>[3,7,5,4,6,1,2]=>{{1,3,5,6},{2,7},{4}}
[4,3,1,5,7,6,2]=>[5,1,3,4,2,6,7]=>[3,7,5,4,6,2,1]=>{{1,2,3,5,6,7},{4}}
[4,3,1,6,2,5,7]=>[7,1,3,4,2,6,5]=>[1,7,5,4,6,2,3]=>{{1},{2,3,5,6,7},{4}}
[4,3,1,6,2,7,5]=>[1,3,4,2,6,5,7]=>[7,5,4,6,2,3,1]=>{{1,7},{2,5},{3,4,6}}
[4,3,1,6,5,2,7]=>[7,1,3,4,2,5,6]=>[1,7,5,4,6,3,2]=>{{1},{2,7},{3,5,6},{4}}
[4,3,1,6,5,7,2]=>[5,6,1,3,4,2,7]=>[3,2,7,5,4,6,1]=>{{1,3,7},{2},{4,5},{6}}
[4,3,1,6,7,2,5]=>[6,1,3,4,2,7,5]=>[2,7,5,4,6,1,3]=>{{1,2,3,5,6,7},{4}}
[4,3,1,6,7,5,2]=>[6,1,3,4,2,5,7]=>[2,7,5,4,6,3,1]=>{{1,2,7},{3,5,6},{4}}
[4,3,1,7,2,5,6]=>[1,3,4,2,7,6,5]=>[7,5,4,6,1,2,3]=>{{1,2,3,4,5,6,7}}
[4,3,1,7,2,6,5]=>[1,3,4,2,7,5,6]=>[7,5,4,6,1,3,2]=>{{1,2,5,7},{3,4,6}}
[4,3,1,7,5,2,6]=>[1,3,4,2,5,7,6]=>[7,5,4,6,3,1,2]=>{{1,2,3,4,5,6,7}}
[4,3,1,7,5,6,2]=>[5,7,1,3,4,2,6]=>[3,1,7,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}
[4,3,1,7,6,2,5]=>[1,3,4,2,6,7,5]=>[7,5,4,6,2,1,3]=>{{1,3,4,6,7},{2,5}}
[4,3,1,7,6,5,2]=>[1,3,4,2,5,6,7]=>[7,5,4,6,3,2,1]=>{{1,7},{2,3,4,5,6}}
[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>{{1},{2},{3},{4,7},{5,6}}
[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>{{1,2},{3},{4,7},{5,6}}
[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>{{1},{2,3},{4,7},{5,6}}
[4,3,2,1,6,7,5]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}
[4,3,2,1,7,5,6]=>[5,7,6,1,2,3,4]=>[3,1,2,7,6,5,4]=>{{1,2,3},{4,7},{5,6}}
[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>{{1,3},{2},{4,7},{5,6}}
[4,3,2,5,1,6,7]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>{{1},{2},{3,6,7},{4,5}}
[4,3,2,5,1,7,6]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>{{1,2},{3,6,7},{4,5}}
[4,3,2,5,6,1,7]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>{{1},{2,3,6,7},{4,5}}
[4,3,2,5,6,7,1]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>{{1,2,3,6,7},{4,5}}
[4,3,2,5,7,1,6]=>[5,2,3,4,1,7,6]=>[3,6,5,4,7,1,2]=>{{1,2,3,5,6,7},{4}}
[4,3,2,5,7,6,1]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>{{1,3,5,7},{2,6},{4}}
[4,3,2,6,1,5,7]=>[7,2,3,4,1,6,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[4,3,2,6,1,7,5]=>[2,3,4,1,6,5,7]=>[6,5,4,7,2,3,1]=>{{1,3,4,6,7},{2,5}}
[4,3,2,6,5,1,7]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[4,3,2,6,5,7,1]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>{{1,3,6,7},{2},{4,5}}
[4,3,2,6,7,1,5]=>[6,2,3,4,1,7,5]=>[2,6,5,4,7,1,3]=>{{1,2,6},{3,5,7},{4}}
[4,3,2,6,7,5,1]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>{{1,2,3,5,6,7},{4}}
[4,3,2,7,1,5,6]=>[2,3,4,1,7,6,5]=>[6,5,4,7,1,2,3]=>{{1,2,5,6},{3,4,7}}
[4,3,2,7,1,6,5]=>[2,3,4,1,7,5,6]=>[6,5,4,7,1,3,2]=>{{1,2,3,4,5,6,7}}
[4,3,2,7,5,1,6]=>[2,3,4,1,5,7,6]=>[6,5,4,7,3,1,2]=>{{1,6},{2,3,4,5,7}}
[4,3,2,7,5,6,1]=>[5,7,2,3,4,1,6]=>[3,1,6,5,4,7,2]=>{{1,2,3,6,7},{4,5}}
[4,3,2,7,6,1,5]=>[2,3,4,1,6,7,5]=>[6,5,4,7,2,1,3]=>{{1,6},{2,5},{3,4,7}}
[4,3,2,7,6,5,1]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>{{1,2,3,4,5,6,7}}
[4,3,5,1,2,6,7]=>[7,6,3,4,1,5,2]=>[1,2,5,4,7,3,6]=>{{1},{2},{3,5,6,7},{4}}
[4,3,5,1,2,7,6]=>[6,7,3,4,1,5,2]=>[2,1,5,4,7,3,6]=>{{1,2},{3,5,6,7},{4}}
[4,3,5,1,6,2,7]=>[7,3,4,1,5,2,6]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,5,1,6,7,2]=>[6,3,4,1,5,2,7]=>[2,5,4,7,3,6,1]=>{{1,2,3,4,5,7},{6}}
[4,3,5,1,7,2,6]=>[3,4,1,5,2,7,6]=>[5,4,7,3,6,1,2]=>{{1,5,6},{2,3,4,7}}
[4,3,5,1,7,6,2]=>[3,4,1,5,2,6,7]=>[5,4,7,3,6,2,1]=>{{1,2,3,4,5,6,7}}
[4,3,5,2,1,6,7]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[4,3,5,2,1,7,6]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>{{1,2},{3,5,7},{4},{6}}
[4,3,5,2,6,1,7]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,2,6,7,1]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[4,3,5,2,7,1,6]=>[3,4,2,5,1,7,6]=>[5,4,6,3,7,1,2]=>{{1,2,3,4,5,6,7}}
[4,3,5,2,7,6,1]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>{{1,5,7},{2,3,4,6}}
[4,3,5,6,1,2,7]=>[7,5,3,4,1,6,2]=>[1,3,5,4,7,2,6]=>{{1},{2,3,5,6,7},{4}}
[4,3,5,6,1,7,2]=>[5,3,4,1,6,2,7]=>[3,5,4,7,2,6,1]=>{{1,3,4,7},{2,5},{6}}
[4,3,5,6,2,1,7]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[4,3,5,6,2,7,1]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>{{1,3,4,6,7},{2,5}}
[4,3,5,6,7,1,2]=>[6,5,3,4,1,7,2]=>[2,3,5,4,7,1,6]=>{{1,2,3,5,6,7},{4}}
[4,3,5,6,7,2,1]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}
[4,3,5,7,1,2,6]=>[5,3,4,1,7,6,2]=>[3,5,4,7,1,2,6]=>{{1,2,3,4,5,6,7}}
[4,3,5,7,1,6,2]=>[5,3,4,1,7,2,6]=>[3,5,4,7,1,6,2]=>{{1,2,3,4,5,7},{6}}
[4,3,5,7,2,1,6]=>[5,3,4,1,2,7,6]=>[3,5,4,7,6,1,2]=>{{1,2,3,4,5,6,7}}
[4,3,5,7,2,6,1]=>[5,3,4,2,7,1,6]=>[3,5,4,6,1,7,2]=>{{1,2,3,4,5,6,7}}
[4,3,5,7,6,1,2]=>[5,3,4,1,6,7,2]=>[3,5,4,7,2,1,6]=>{{1,3,4,6,7},{2,5}}
[4,3,5,7,6,2,1]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>{{1,3,4,7},{2,5,6}}
[4,3,6,1,2,5,7]=>[7,3,4,1,6,5,2]=>[1,5,4,7,2,3,6]=>{{1},{2,5},{3,4,6,7}}
[4,3,6,1,2,7,5]=>[3,4,1,6,5,7,2]=>[5,4,7,2,3,1,6]=>{{1,3,5,6,7},{2,4}}
[4,3,6,1,5,2,7]=>[7,3,4,1,6,2,5]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,3,6,1,5,7,2]=>[3,4,1,6,5,2,7]=>[5,4,7,2,3,6,1]=>{{1,3,5,7},{2,4},{6}}
[4,3,6,1,7,2,5]=>[3,4,1,6,2,7,5]=>[5,4,7,2,6,1,3]=>{{1,5,6},{2,4},{3,7}}
[4,3,6,1,7,5,2]=>[3,4,1,6,2,5,7]=>[5,4,7,2,6,3,1]=>{{1,3,5,6,7},{2,4}}
[4,3,6,2,1,5,7]=>[7,3,4,1,2,6,5]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,3,6,2,1,7,5]=>[3,4,1,2,6,5,7]=>[5,4,7,6,2,3,1]=>{{1,2,3,4,5,6,7}}
[4,3,6,2,5,1,7]=>[7,3,4,2,6,1,5]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,3,6,2,5,7,1]=>[3,4,2,6,5,1,7]=>[5,4,6,2,3,7,1]=>{{1,3,5,6,7},{2,4}}
[4,3,6,2,7,1,5]=>[3,4,2,6,1,7,5]=>[5,4,6,2,7,1,3]=>{{1,3,5,6,7},{2,4}}
[4,3,6,2,7,5,1]=>[3,4,2,6,1,5,7]=>[5,4,6,2,7,3,1]=>{{1,5,7},{2,4},{3,6}}
[4,3,6,5,1,2,7]=>[7,3,4,1,5,6,2]=>[1,5,4,7,3,2,6]=>{{1},{2,3,4,5,6,7}}
[4,3,6,5,1,7,2]=>[3,4,1,5,6,2,7]=>[5,4,7,3,2,6,1]=>{{1,2,3,4,5,7},{6}}
[4,3,6,5,2,1,7]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,5,2,7,1]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[4,3,6,5,7,1,2]=>[5,6,3,4,1,7,2]=>[3,2,5,4,7,1,6]=>{{1,3,5,6,7},{2},{4}}
[4,3,6,5,7,2,1]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>{{1,3,5,7},{2},{4},{6}}
[4,3,6,7,1,2,5]=>[6,3,4,1,7,5,2]=>[2,5,4,7,1,3,6]=>{{1,2,5},{3,4,6,7}}
[4,3,6,7,1,5,2]=>[6,3,4,1,7,2,5]=>[2,5,4,7,1,6,3]=>{{1,2,5},{3,4,7},{6}}
[4,3,6,7,2,1,5]=>[6,3,4,1,2,7,5]=>[2,5,4,7,6,1,3]=>{{1,2,5,6},{3,4,7}}
[4,3,6,7,2,5,1]=>[6,3,4,2,7,1,5]=>[2,5,4,6,1,7,3]=>{{1,2,5},{3,4,6,7}}
[4,3,6,7,5,1,2]=>[6,3,4,1,5,7,2]=>[2,5,4,7,3,1,6]=>{{1,2,3,4,5,6,7}}
[4,3,6,7,5,2,1]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>{{1,2,3,4,5,6,7}}
[4,3,7,1,2,5,6]=>[3,4,1,7,6,5,2]=>[5,4,7,1,2,3,6]=>{{1,2,4,5},{3,6,7}}
[4,3,7,1,2,6,5]=>[3,4,1,7,5,6,2]=>[5,4,7,1,3,2,6]=>{{1,2,3,4,5,6,7}}
[4,3,7,1,5,2,6]=>[3,4,1,7,6,2,5]=>[5,4,7,1,2,6,3]=>{{1,2,4,5},{3,7},{6}}
[4,3,7,1,5,6,2]=>[3,4,1,7,5,2,6]=>[5,4,7,1,3,6,2]=>{{1,2,3,4,5,7},{6}}
[4,3,7,1,6,2,5]=>[3,4,1,7,2,6,5]=>[5,4,7,1,6,2,3]=>{{1,2,4,5,6},{3,7}}
[4,3,7,1,6,5,2]=>[3,4,1,7,2,5,6]=>[5,4,7,1,6,3,2]=>{{1,2,3,4,5,6,7}}
[4,3,7,2,1,5,6]=>[3,4,1,2,7,6,5]=>[5,4,7,6,1,2,3]=>{{1,5},{2,4,6},{3,7}}
[4,3,7,2,1,6,5]=>[3,4,1,2,7,5,6]=>[5,4,7,6,1,3,2]=>{{1,5},{2,3,4,6,7}}
[4,3,7,2,5,1,6]=>[3,4,2,7,6,1,5]=>[5,4,6,1,2,7,3]=>{{1,2,4,5},{3,6,7}}
[4,3,7,2,5,6,1]=>[3,4,2,7,5,1,6]=>[5,4,6,1,3,7,2]=>{{1,2,3,4,5,6,7}}
[4,3,7,2,6,1,5]=>[3,4,2,7,1,6,5]=>[5,4,6,1,7,2,3]=>{{1,2,3,4,5,6,7}}
[4,3,7,2,6,5,1]=>[3,4,2,7,1,5,6]=>[5,4,6,1,7,3,2]=>{{1,2,4,5,7},{3,6}}
[4,3,7,5,1,2,6]=>[3,4,1,5,7,6,2]=>[5,4,7,3,1,2,6]=>{{1,5},{2,3,4,6,7}}
[4,3,7,5,1,6,2]=>[3,4,1,5,7,2,6]=>[5,4,7,3,1,6,2]=>{{1,5},{2,3,4,7},{6}}
[4,3,7,5,2,1,6]=>[3,4,1,2,5,7,6]=>[5,4,7,6,3,1,2]=>{{1,2,3,4,5,6,7}}
[4,3,7,5,2,6,1]=>[3,4,2,5,7,1,6]=>[5,4,6,3,1,7,2]=>{{1,5},{2,3,4,6,7}}
[4,3,7,5,6,1,2]=>[5,7,3,4,1,6,2]=>[3,1,5,4,7,2,6]=>{{1,2,3,5,6,7},{4}}
[4,3,7,5,6,2,1]=>[5,7,3,4,1,2,6]=>[3,1,5,4,7,6,2]=>{{1,2,3,5,7},{4},{6}}
[4,3,7,6,1,2,5]=>[3,4,1,6,7,5,2]=>[5,4,7,2,1,3,6]=>{{1,5},{2,4},{3,6,7}}
[4,3,7,6,1,5,2]=>[3,4,1,6,7,2,5]=>[5,4,7,2,1,6,3]=>{{1,5},{2,4},{3,7},{6}}
[4,3,7,6,2,1,5]=>[3,4,1,2,6,7,5]=>[5,4,7,6,2,1,3]=>{{1,2,4,5,6},{3,7}}
[4,3,7,6,2,5,1]=>[3,4,2,6,7,1,5]=>[5,4,6,2,1,7,3]=>{{1,5},{2,4},{3,6,7}}
[4,3,7,6,5,1,2]=>[3,4,1,5,6,7,2]=>[5,4,7,3,2,1,6]=>{{1,2,3,4,5,6,7}}
[4,3,7,6,5,2,1]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>{{1,3,5,7},{2,4,6}}
[4,5,1,2,3,6,7]=>[7,6,4,1,5,3,2]=>[1,2,4,7,3,5,6]=>{{1},{2},{3,4,5,6,7}}
[4,5,1,2,3,7,6]=>[6,7,4,1,5,3,2]=>[2,1,4,7,3,5,6]=>{{1,2},{3,4,5,6,7}}
[4,5,1,2,6,3,7]=>[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>{{1},{2,3,4,6,7},{5}}
[4,5,1,2,6,7,3]=>[6,4,1,5,3,7,2]=>[2,4,7,3,5,1,6]=>{{1,2,3,4,6,7},{5}}
[4,5,1,2,7,3,6]=>[4,1,5,3,7,6,2]=>[4,7,3,5,1,2,6]=>{{1,4,5},{2,6,7},{3}}
[4,5,1,2,7,6,3]=>[4,1,5,3,6,7,2]=>[4,7,3,5,2,1,6]=>{{1,2,4,5,6,7},{3}}
[4,5,1,3,2,6,7]=>[7,6,4,1,5,2,3]=>[1,2,4,7,3,6,5]=>{{1},{2},{3,4,5,7},{6}}
[4,5,1,3,2,7,6]=>[6,7,4,1,5,2,3]=>[2,1,4,7,3,6,5]=>{{1,2},{3,4,5,7},{6}}
[4,5,1,3,6,2,7]=>[7,4,1,5,3,2,6]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,5,1,3,6,7,2]=>[6,4,1,5,3,2,7]=>[2,4,7,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[4,5,1,3,7,2,6]=>[4,1,5,3,2,7,6]=>[4,7,3,5,6,1,2]=>{{1,4,5,6},{2,7},{3}}
[4,5,1,3,7,6,2]=>[4,1,5,3,2,6,7]=>[4,7,3,5,6,2,1]=>{{1,2,4,5,6,7},{3}}
[4,5,1,6,2,3,7]=>[7,4,1,5,2,6,3]=>[1,4,7,3,6,2,5]=>{{1},{2,3,4,5,6,7}}
[4,5,1,6,2,7,3]=>[4,1,5,2,6,3,7]=>[4,7,3,6,2,5,1]=>{{1,2,4,5,6,7},{3}}
[4,5,1,6,3,2,7]=>[7,4,1,5,2,3,6]=>[1,4,7,3,6,5,2]=>{{1},{2,3,4,7},{5,6}}
[4,5,1,6,3,7,2]=>[4,1,5,3,6,2,7]=>[4,7,3,5,2,6,1]=>{{1,2,4,5,7},{3},{6}}
[4,5,1,6,7,2,3]=>[6,4,1,5,2,7,3]=>[2,4,7,3,6,1,5]=>{{1,2,3,4,5,6,7}}
[4,5,1,6,7,3,2]=>[6,4,1,5,2,3,7]=>[2,4,7,3,6,5,1]=>{{1,2,3,4,7},{5,6}}
[4,5,1,7,2,3,6]=>[4,1,5,2,7,6,3]=>[4,7,3,6,1,2,5]=>{{1,2,4,5,6,7},{3}}
[4,5,1,7,2,6,3]=>[4,1,5,2,7,3,6]=>[4,7,3,6,1,5,2]=>{{1,4,5,6},{2,7},{3}}
[4,5,1,7,3,2,6]=>[4,1,5,2,3,7,6]=>[4,7,3,6,5,1,2]=>{{1,4,6},{2,7},{3},{5}}
[4,5,1,7,3,6,2]=>[4,1,5,3,7,2,6]=>[4,7,3,5,1,6,2]=>{{1,4,5},{2,7},{3},{6}}
[4,5,1,7,6,2,3]=>[4,1,5,2,6,7,3]=>[4,7,3,6,2,1,5]=>{{1,4,6},{2,5,7},{3}}
[4,5,1,7,6,3,2]=>[4,1,5,2,3,6,7]=>[4,7,3,6,5,2,1]=>{{1,2,4,6,7},{3},{5}}
[4,5,2,1,3,6,7]=>[7,6,4,1,2,5,3]=>[1,2,4,7,6,3,5]=>{{1},{2},{3,4,5,6,7}}
[4,5,2,1,3,7,6]=>[6,7,4,1,2,5,3]=>[2,1,4,7,6,3,5]=>{{1,2},{3,4,5,6,7}}
[4,5,2,1,6,3,7]=>[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,1,6,7,3]=>[6,4,1,2,5,3,7]=>[2,4,7,6,3,5,1]=>{{1,2,3,4,5,6,7}}
[4,5,2,1,7,3,6]=>[4,1,2,5,3,7,6]=>[4,7,6,3,5,1,2]=>{{1,3,4,6},{2,7},{5}}
[4,5,2,1,7,6,3]=>[4,1,2,5,3,6,7]=>[4,7,6,3,5,2,1]=>{{1,2,3,4,6,7},{5}}
[4,5,2,3,1,6,7]=>[7,6,4,2,5,1,3]=>[1,2,4,6,3,7,5]=>{{1},{2},{3,4,5,6,7}}
[4,5,2,3,1,7,6]=>[6,7,4,2,5,1,3]=>[2,1,4,6,3,7,5]=>{{1,2},{3,4,5,6,7}}
[4,5,2,3,6,1,7]=>[7,4,2,5,3,1,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,5,2,3,6,7,1]=>[6,4,2,5,3,1,7]=>[2,4,6,3,5,7,1]=>{{1,2,3,4,6,7},{5}}
[4,5,2,3,7,1,6]=>[4,2,5,3,1,7,6]=>[4,6,3,5,7,1,2]=>{{1,2,4,5,6,7},{3}}
[4,5,2,3,7,6,1]=>[4,2,5,3,1,6,7]=>[4,6,3,5,7,2,1]=>{{1,4,5,7},{2,6},{3}}
[4,5,2,6,1,3,7]=>[7,4,2,5,1,6,3]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,5,2,6,1,7,3]=>[4,2,5,1,6,3,7]=>[4,6,3,7,2,5,1]=>{{1,4,7},{2,5,6},{3}}
[4,5,2,6,3,1,7]=>[7,4,2,5,1,3,6]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,6,3,7,1]=>[4,2,5,3,6,1,7]=>[4,6,3,5,2,7,1]=>{{1,2,4,5,6,7},{3}}
[4,5,2,6,7,1,3]=>[6,4,2,5,1,7,3]=>[2,4,6,3,7,1,5]=>{{1,2,3,4,6},{5,7}}
[4,5,2,6,7,3,1]=>[6,4,2,5,1,3,7]=>[2,4,6,3,7,5,1]=>{{1,2,3,4,5,6,7}}
[4,5,2,7,1,3,6]=>[4,2,5,1,7,6,3]=>[4,6,3,7,1,2,5]=>{{1,4,5,7},{2,6},{3}}
[4,5,2,7,1,6,3]=>[4,2,5,1,7,3,6]=>[4,6,3,7,1,5,2]=>{{1,2,4,5,6,7},{3}}
[4,5,2,7,3,1,6]=>[4,2,5,1,3,7,6]=>[4,6,3,7,5,1,2]=>{{1,2,4,6,7},{3},{5}}
[4,5,2,7,3,6,1]=>[4,2,5,3,7,1,6]=>[4,6,3,5,1,7,2]=>{{1,4,5},{2,6,7},{3}}
[4,5,2,7,6,1,3]=>[4,2,5,1,6,7,3]=>[4,6,3,7,2,1,5]=>{{1,2,4,5,6,7},{3}}
[4,5,2,7,6,3,1]=>[4,2,5,1,3,6,7]=>[4,6,3,7,5,2,1]=>{{1,4,7},{2,6},{3},{5}}
[4,5,3,1,2,6,7]=>[7,6,4,1,3,5,2]=>[1,2,4,7,5,3,6]=>{{1},{2},{3,4,6,7},{5}}
[4,5,3,1,2,7,6]=>[6,7,4,1,3,5,2]=>[2,1,4,7,5,3,6]=>{{1,2},{3,4,6,7},{5}}
[4,5,3,1,6,2,7]=>[7,4,1,3,5,2,6]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,3,1,6,7,2]=>[6,4,1,3,5,2,7]=>[2,4,7,5,3,6,1]=>{{1,2,3,4,5,7},{6}}
[4,5,3,1,7,2,6]=>[4,1,3,5,2,7,6]=>[4,7,5,3,6,1,2]=>{{1,3,4,5,6},{2,7}}
[4,5,3,1,7,6,2]=>[4,1,3,5,2,6,7]=>[4,7,5,3,6,2,1]=>{{1,2,3,4,5,6,7}}
[4,5,3,2,1,6,7]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>{{1},{2},{3,4,7},{5,6}}
[4,5,3,2,1,7,6]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>{{1,2},{3,4,7},{5,6}}
[4,5,3,2,6,1,7]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,2,6,7,1]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>{{1,2,3,4,5,6,7}}
[4,5,3,2,7,1,6]=>[4,2,3,5,1,7,6]=>[4,6,5,3,7,1,2]=>{{1,2,3,4,5,6,7}}
[4,5,3,2,7,6,1]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>{{1,3,4,5,7},{2,6}}
[4,5,3,6,1,2,7]=>[7,4,3,5,1,6,2]=>[1,4,5,3,7,2,6]=>{{1},{2,3,4,5,6,7}}
[4,5,3,6,1,7,2]=>[4,3,5,1,6,2,7]=>[4,5,3,7,2,6,1]=>{{1,4,7},{2,5},{3},{6}}
[4,5,3,6,2,1,7]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>{{1,4,6,7},{2,5},{3}}
[4,5,3,6,7,1,2]=>[6,4,3,5,1,7,2]=>[2,4,5,3,7,1,6]=>{{1,2,3,4,5,6,7}}
[4,5,3,6,7,2,1]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>{{1,2,3,4,5,7},{6}}
[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>[4,5,3,7,1,2,6]=>{{1,2,4,5,6,7},{3}}
[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>[4,5,3,7,1,6,2]=>{{1,2,4,5,7},{3},{6}}
[4,5,3,7,2,1,6]=>[4,3,5,1,2,7,6]=>[4,5,3,7,6,1,2]=>{{1,2,4,5,6,7},{3}}
[4,5,3,7,2,6,1]=>[4,3,5,2,7,1,6]=>[4,5,3,6,1,7,2]=>{{1,2,4,5,6,7},{3}}
[4,5,3,7,6,1,2]=>[4,3,5,1,6,7,2]=>[4,5,3,7,2,1,6]=>{{1,4,6,7},{2,5},{3}}
[4,5,3,7,6,2,1]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>{{1,4,7},{2,5,6},{3}}
[4,5,6,1,2,3,7]=>[7,5,4,1,6,3,2]=>[1,3,4,7,2,5,6]=>{{1},{2,3,4,5,6,7}}
[4,5,6,1,2,7,3]=>[5,4,1,6,3,7,2]=>[3,4,7,2,5,1,6]=>{{1,3,6,7},{2,4},{5}}
[4,5,6,1,3,2,7]=>[7,5,4,1,6,2,3]=>[1,3,4,7,2,6,5]=>{{1},{2,3,4,5,7},{6}}
[4,5,6,1,3,7,2]=>[5,4,1,6,3,2,7]=>[3,4,7,2,5,6,1]=>{{1,3,7},{2,4},{5},{6}}
[4,5,6,1,7,2,3]=>[5,4,1,6,2,7,3]=>[3,4,7,2,6,1,5]=>{{1,3,5,6,7},{2,4}}
[4,5,6,1,7,3,2]=>[5,4,1,6,2,3,7]=>[3,4,7,2,6,5,1]=>{{1,3,7},{2,4},{5,6}}
[4,5,6,2,1,3,7]=>[7,5,4,1,2,6,3]=>[1,3,4,7,6,2,5]=>{{1},{2,3,4,5,6,7}}
[4,5,6,2,1,7,3]=>[5,4,1,2,6,3,7]=>[3,4,7,6,2,5,1]=>{{1,3,7},{2,4,5,6}}
[4,5,6,2,3,1,7]=>[7,5,4,2,6,1,3]=>[1,3,4,6,2,7,5]=>{{1},{2,3,4,5,6,7}}
[4,5,6,2,3,7,1]=>[5,4,2,6,3,1,7]=>[3,4,6,2,5,7,1]=>{{1,3,6,7},{2,4},{5}}
[4,5,6,2,7,1,3]=>[5,4,2,6,1,7,3]=>[3,4,6,2,7,1,5]=>{{1,3,6},{2,4},{5,7}}
[4,5,6,2,7,3,1]=>[5,4,2,6,1,3,7]=>[3,4,6,2,7,5,1]=>{{1,3,5,6,7},{2,4}}
[4,5,6,3,1,2,7]=>[7,5,4,1,3,6,2]=>[1,3,4,7,5,2,6]=>{{1},{2,3,4,6,7},{5}}
[4,5,6,3,1,7,2]=>[5,4,1,3,6,2,7]=>[3,4,7,5,2,6,1]=>{{1,3,7},{2,4,5},{6}}
[4,5,6,3,2,1,7]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>{{1},{2,3,4,7},{5,6}}
[4,5,6,3,2,7,1]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>{{1,3,6,7},{2,4,5}}
[4,5,6,3,7,1,2]=>[5,4,3,6,1,7,2]=>[3,4,5,2,7,1,6]=>{{1,3,5,6,7},{2,4}}
[4,5,6,3,7,2,1]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>{{1,3,5,7},{2,4},{6}}
[4,5,6,7,1,2,3]=>[6,5,4,1,7,3,2]=>[2,3,4,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[4,5,6,7,1,3,2]=>[6,5,4,1,7,2,3]=>[2,3,4,7,1,6,5]=>{{1,2,3,4,5,7},{6}}
[4,5,6,7,2,1,3]=>[6,5,4,1,2,7,3]=>[2,3,4,7,6,1,5]=>{{1,2,3,4,5,6,7}}
[4,5,6,7,2,3,1]=>[6,5,4,2,7,1,3]=>[2,3,4,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[4,5,6,7,3,1,2]=>[6,5,4,1,3,7,2]=>[2,3,4,7,5,1,6]=>{{1,2,3,4,6,7},{5}}
[4,5,6,7,3,2,1]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[4,5,7,1,2,3,6]=>[5,4,1,7,6,3,2]=>[3,4,7,1,2,5,6]=>{{1,2,3,4,5,6,7}}
[4,5,7,1,2,6,3]=>[5,4,1,7,3,6,2]=>[3,4,7,1,5,2,6]=>{{1,2,3,4,6,7},{5}}
[4,5,7,1,3,2,6]=>[5,4,1,7,6,2,3]=>[3,4,7,1,2,6,5]=>{{1,2,3,4,5,7},{6}}
[4,5,7,1,3,6,2]=>[5,4,1,7,3,2,6]=>[3,4,7,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[4,5,7,1,6,2,3]=>[5,4,1,7,2,6,3]=>[3,4,7,1,6,2,5]=>{{1,2,3,4,5,6,7}}
[4,5,7,1,6,3,2]=>[5,4,1,7,2,3,6]=>[3,4,7,1,6,5,2]=>{{1,2,3,4,7},{5,6}}
[4,5,7,2,1,3,6]=>[5,4,1,2,7,6,3]=>[3,4,7,6,1,2,5]=>{{1,3,5,7},{2,4,6}}
[4,5,7,2,1,6,3]=>[5,4,1,2,7,3,6]=>[3,4,7,6,1,5,2]=>{{1,2,3,4,5,6,7}}
[4,5,7,2,3,1,6]=>[5,4,2,7,6,1,3]=>[3,4,6,1,2,7,5]=>{{1,2,3,4,5,6,7}}
[4,5,7,2,3,6,1]=>[5,4,2,7,3,1,6]=>[3,4,6,1,5,7,2]=>{{1,2,3,4,6,7},{5}}
[4,5,7,2,6,1,3]=>[5,4,2,7,1,6,3]=>[3,4,6,1,7,2,5]=>{{1,2,3,4,6},{5,7}}
[4,5,7,2,6,3,1]=>[5,4,2,7,1,3,6]=>[3,4,6,1,7,5,2]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,1,2,6]=>[5,4,1,3,7,6,2]=>[3,4,7,5,1,2,6]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,1,6,2]=>[5,4,1,3,7,2,6]=>[3,4,7,5,1,6,2]=>{{1,2,3,4,5,7},{6}}
[4,5,7,3,2,1,6]=>[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>{{1,2,3,4,6,7},{5}}
[4,5,7,3,2,6,1]=>[5,4,2,3,7,1,6]=>[3,4,6,5,1,7,2]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,6,1,2]=>[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>{{1,2,3,4,5,6,7}}
[4,5,7,3,6,2,1]=>[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>{{1,2,3,4,5,7},{6}}
[4,5,7,6,1,2,3]=>[5,4,1,6,7,3,2]=>[3,4,7,2,1,5,6]=>{{1,3,5,6,7},{2,4}}
[4,5,7,6,1,3,2]=>[5,4,1,6,7,2,3]=>[3,4,7,2,1,6,5]=>{{1,3,5,7},{2,4},{6}}
[4,5,7,6,2,1,3]=>[5,4,1,2,6,7,3]=>[3,4,7,6,2,1,5]=>{{1,2,3,4,5,6,7}}
[4,5,7,6,2,3,1]=>[5,4,2,6,7,1,3]=>[3,4,6,2,1,7,5]=>{{1,3,5,6,7},{2,4}}
[4,5,7,6,3,1,2]=>[5,4,1,3,6,7,2]=>[3,4,7,5,2,1,6]=>{{1,3,6,7},{2,4,5}}
[4,5,7,6,3,2,1]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>{{1,3,7},{2,4,6},{5}}
[4,6,1,2,3,5,7]=>[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>{{1},{2,4},{3,5,6,7}}
[4,6,1,2,3,7,5]=>[4,1,6,5,7,3,2]=>[4,7,2,3,1,5,6]=>{{1,2,3,4,5,6,7}}
[4,6,1,2,5,3,7]=>[7,4,1,6,3,5,2]=>[1,4,7,2,5,3,6]=>{{1},{2,4},{3,6,7},{5}}
[4,6,1,2,5,7,3]=>[4,1,6,5,3,7,2]=>[4,7,2,3,5,1,6]=>{{1,2,3,4,6,7},{5}}
[4,6,1,2,7,3,5]=>[4,1,6,3,7,5,2]=>[4,7,2,5,1,3,6]=>{{1,4,5},{2,3,6,7}}
[4,6,1,2,7,5,3]=>[4,1,6,3,5,7,2]=>[4,7,2,5,3,1,6]=>{{1,2,3,4,5,6,7}}
[4,6,1,3,2,5,7]=>[7,4,1,6,5,2,3]=>[1,4,7,2,3,6,5]=>{{1},{2,4},{3,5,7},{6}}
[4,6,1,3,2,7,5]=>[4,1,6,5,7,2,3]=>[4,7,2,3,1,6,5]=>{{1,2,3,4,5,7},{6}}
[4,6,1,3,5,2,7]=>[7,4,1,6,3,2,5]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[4,6,1,3,5,7,2]=>[4,1,6,5,3,2,7]=>[4,7,2,3,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[4,6,1,3,7,2,5]=>[4,1,6,3,2,7,5]=>[4,7,2,5,6,1,3]=>{{1,4,5,6},{2,3,7}}
[4,6,1,3,7,5,2]=>[4,1,6,3,2,5,7]=>[4,7,2,5,6,3,1]=>{{1,2,3,4,5,6,7}}
[4,6,1,5,2,3,7]=>[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>{{1},{2,4},{3,5,6,7}}
[4,6,1,5,2,7,3]=>[4,1,6,2,5,3,7]=>[4,7,2,6,3,5,1]=>{{1,2,3,4,5,6,7}}
[4,6,1,5,3,2,7]=>[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>{{1},{2,4},{3,7},{5,6}}
[4,6,1,5,3,7,2]=>[4,1,6,3,5,2,7]=>[4,7,2,5,3,6,1]=>{{1,2,3,4,5,7},{6}}
[4,6,1,5,7,2,3]=>[4,1,6,5,2,7,3]=>[4,7,2,3,6,1,5]=>{{1,2,3,4,5,6,7}}
[4,6,1,5,7,3,2]=>[4,1,6,5,2,3,7]=>[4,7,2,3,6,5,1]=>{{1,2,3,4,7},{5,6}}
[4,6,1,7,2,3,5]=>[4,1,6,2,7,5,3]=>[4,7,2,6,1,3,5]=>{{1,2,3,4,5,6,7}}
[4,6,1,7,2,5,3]=>[4,1,6,2,7,3,5]=>[4,7,2,6,1,5,3]=>{{1,4,5,6},{2,3,7}}
[4,6,1,7,3,2,5]=>[4,1,6,2,3,7,5]=>[4,7,2,6,5,1,3]=>{{1,4,6},{2,3,7},{5}}
[4,6,1,7,3,5,2]=>[4,1,6,3,7,2,5]=>[4,7,2,5,1,6,3]=>{{1,4,5},{2,3,7},{6}}
[4,6,1,7,5,2,3]=>[4,1,6,2,5,7,3]=>[4,7,2,6,3,1,5]=>{{1,4,6},{2,3,5,7}}
[4,6,1,7,5,3,2]=>[4,1,6,2,3,5,7]=>[4,7,2,6,5,3,1]=>{{1,2,3,4,6,7},{5}}
[4,6,2,1,3,5,7]=>[7,4,1,2,6,5,3]=>[1,4,7,6,2,3,5]=>{{1},{2,3,4,5,6,7}}
[4,6,2,1,3,7,5]=>[4,1,2,6,5,7,3]=>[4,7,6,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[4,6,2,1,5,3,7]=>[7,4,1,2,6,3,5]=>[1,4,7,6,2,5,3]=>{{1},{2,4,5,6},{3,7}}
[4,6,2,1,5,7,3]=>[4,1,2,6,5,3,7]=>[4,7,6,2,3,5,1]=>{{1,2,4,7},{3,5,6}}
[4,6,2,1,7,3,5]=>[4,1,2,6,3,7,5]=>[4,7,6,2,5,1,3]=>{{1,2,3,4,6,7},{5}}
[4,6,2,1,7,5,3]=>[4,1,2,6,3,5,7]=>[4,7,6,2,5,3,1]=>{{1,2,4,7},{3,6},{5}}
[4,6,2,3,1,5,7]=>[7,4,2,6,5,1,3]=>[1,4,6,2,3,7,5]=>{{1},{2,4},{3,5,6,7}}
[4,6,2,3,1,7,5]=>[4,2,6,5,7,1,3]=>[4,6,2,3,1,7,5]=>{{1,2,3,4,5,6,7}}
[4,6,2,3,5,1,7]=>[7,4,2,6,3,1,5]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[4,6,2,3,5,7,1]=>[4,2,6,5,3,1,7]=>[4,6,2,3,5,7,1]=>{{1,2,3,4,6,7},{5}}
[4,6,2,3,7,1,5]=>[4,2,6,3,1,7,5]=>[4,6,2,5,7,1,3]=>{{1,2,3,4,5,6,7}}
[4,6,2,3,7,5,1]=>[4,2,6,3,1,5,7]=>[4,6,2,5,7,3,1]=>{{1,4,5,7},{2,3,6}}
[4,6,2,5,1,3,7]=>[7,4,2,6,1,5,3]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[4,6,2,5,1,7,3]=>[4,2,6,1,5,3,7]=>[4,6,2,7,3,5,1]=>{{1,4,7},{2,3,5,6}}
[4,6,2,5,3,1,7]=>[7,4,2,6,1,3,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[4,6,2,5,3,7,1]=>[4,2,6,3,5,1,7]=>[4,6,2,5,3,7,1]=>{{1,2,3,4,5,6,7}}
[4,6,2,5,7,1,3]=>[4,2,6,5,1,7,3]=>[4,6,2,3,7,1,5]=>{{1,2,3,4,6},{5,7}}
[4,6,2,5,7,3,1]=>[4,2,6,5,1,3,7]=>[4,6,2,3,7,5,1]=>{{1,2,3,4,5,6,7}}
[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>[4,6,2,7,1,3,5]=>{{1,4,5,7},{2,3,6}}
[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>[4,6,2,7,1,5,3]=>{{1,2,3,4,5,6,7}}
[4,6,2,7,3,1,5]=>[4,2,6,1,3,7,5]=>[4,6,2,7,5,1,3]=>{{1,2,3,4,6,7},{5}}
[4,6,2,7,3,5,1]=>[4,2,6,3,7,1,5]=>[4,6,2,5,1,7,3]=>{{1,4,5},{2,3,6,7}}
[4,6,2,7,5,1,3]=>[4,2,6,1,5,7,3]=>[4,6,2,7,3,1,5]=>{{1,2,3,4,5,6,7}}
[4,6,2,7,5,3,1]=>[4,2,6,1,3,5,7]=>[4,6,2,7,5,3,1]=>{{1,4,7},{2,3,6},{5}}
[4,6,3,1,2,5,7]=>[7,4,1,3,6,5,2]=>[1,4,7,5,2,3,6]=>{{1},{2,4,5},{3,6,7}}
[4,6,3,1,2,7,5]=>[4,1,3,6,5,7,2]=>[4,7,5,2,3,1,6]=>{{1,2,4,6,7},{3,5}}
[4,6,3,1,5,2,7]=>[7,4,1,3,6,2,5]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[4,6,3,1,5,7,2]=>[4,1,3,6,5,2,7]=>[4,7,5,2,3,6,1]=>{{1,2,4,7},{3,5},{6}}
[4,6,3,1,7,2,5]=>[4,1,3,6,2,7,5]=>[4,7,5,2,6,1,3]=>{{1,2,3,4,5,6,7}}
[4,6,3,1,7,5,2]=>[4,1,3,6,2,5,7]=>[4,7,5,2,6,3,1]=>{{1,2,4,7},{3,5,6}}
[4,6,3,2,1,5,7]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[4,6,3,2,1,7,5]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>{{1,2,4,5,7},{3,6}}
[4,6,3,2,5,1,7]=>[7,4,2,3,6,1,5]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[4,6,3,2,5,7,1]=>[4,2,3,6,5,1,7]=>[4,6,5,2,3,7,1]=>{{1,2,4,6,7},{3,5}}
[4,6,3,2,7,1,5]=>[4,2,3,6,1,7,5]=>[4,6,5,2,7,1,3]=>{{1,2,4,6},{3,5,7}}
[4,6,3,2,7,5,1]=>[4,2,3,6,1,5,7]=>[4,6,5,2,7,3,1]=>{{1,2,3,4,5,6,7}}
[4,6,3,5,1,2,7]=>[7,4,3,6,1,5,2]=>[1,4,5,2,7,3,6]=>{{1},{2,4},{3,5,6,7}}
[4,6,3,5,1,7,2]=>[4,3,6,1,5,2,7]=>[4,5,2,7,3,6,1]=>{{1,4,7},{2,3,5},{6}}
[4,6,3,5,2,1,7]=>[7,4,3,6,1,2,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[4,6,3,5,2,7,1]=>[4,3,6,2,5,1,7]=>[4,5,2,6,3,7,1]=>{{1,4,6,7},{2,3,5}}
[4,6,3,5,7,1,2]=>[4,3,6,5,1,7,2]=>[4,5,2,3,7,1,6]=>{{1,2,3,4,5,6,7}}
[4,6,3,5,7,2,1]=>[4,3,6,5,1,2,7]=>[4,5,2,3,7,6,1]=>{{1,2,3,4,5,7},{6}}
[4,6,3,7,1,2,5]=>[4,3,6,1,7,5,2]=>[4,5,2,7,1,3,6]=>{{1,2,3,4,5,6,7}}
[4,6,3,7,1,5,2]=>[4,3,6,1,7,2,5]=>[4,5,2,7,1,6,3]=>{{1,2,3,4,5,7},{6}}
[4,6,3,7,2,1,5]=>[4,3,6,1,2,7,5]=>[4,5,2,7,6,1,3]=>{{1,2,3,4,5,6,7}}
[4,6,3,7,2,5,1]=>[4,3,6,2,7,1,5]=>[4,5,2,6,1,7,3]=>{{1,2,3,4,5,6,7}}
[4,6,3,7,5,1,2]=>[4,3,6,1,5,7,2]=>[4,5,2,7,3,1,6]=>{{1,4,6,7},{2,3,5}}
[4,6,3,7,5,2,1]=>[4,3,6,1,2,5,7]=>[4,5,2,7,6,3,1]=>{{1,4,7},{2,3,5,6}}
[4,6,5,1,2,3,7]=>[7,4,1,5,6,3,2]=>[1,4,7,3,2,5,6]=>{{1},{2,3,4,5,6,7}}
[4,6,5,1,2,7,3]=>[4,1,5,6,3,7,2]=>[4,7,3,2,5,1,6]=>{{1,2,4,6,7},{3},{5}}
[4,6,5,1,3,2,7]=>[7,4,1,5,6,2,3]=>[1,4,7,3,2,6,5]=>{{1},{2,3,4,5,7},{6}}
[4,6,5,1,3,7,2]=>[4,1,5,6,3,2,7]=>[4,7,3,2,5,6,1]=>{{1,2,4,7},{3},{5},{6}}
[4,6,5,1,7,2,3]=>[4,1,5,6,2,7,3]=>[4,7,3,2,6,1,5]=>{{1,2,4,5,6,7},{3}}
[4,6,5,1,7,3,2]=>[4,1,5,6,2,3,7]=>[4,7,3,2,6,5,1]=>{{1,2,4,7},{3},{5,6}}
[4,6,5,2,1,3,7]=>[7,4,1,2,5,6,3]=>[1,4,7,6,3,2,5]=>{{1},{2,4,6},{3,5,7}}
[4,6,5,2,1,7,3]=>[4,1,2,5,6,3,7]=>[4,7,6,3,2,5,1]=>{{1,2,3,4,5,6,7}}
[4,6,5,2,3,1,7]=>[7,4,2,5,6,1,3]=>[1,4,6,3,2,7,5]=>{{1},{2,3,4,5,6,7}}
[4,6,5,2,3,7,1]=>[4,2,5,6,3,1,7]=>[4,6,3,2,5,7,1]=>{{1,2,4,6,7},{3},{5}}
[4,6,5,2,7,1,3]=>[4,2,5,6,1,7,3]=>[4,6,3,2,7,1,5]=>{{1,2,4,6},{3},{5,7}}
[4,6,5,2,7,3,1]=>[4,2,5,6,1,3,7]=>[4,6,3,2,7,5,1]=>{{1,2,4,5,6,7},{3}}
[4,6,5,3,1,2,7]=>[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>{{1},{2,3,4,5,6,7}}
[4,6,5,3,1,7,2]=>[4,1,3,5,6,2,7]=>[4,7,5,3,2,6,1]=>{{1,2,3,4,5,7},{6}}
[4,6,5,3,2,1,7]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,5,3,2,7,1]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>{{1,2,3,4,5,6,7}}
[4,6,5,3,7,1,2]=>[4,3,5,6,1,7,2]=>[4,5,3,2,7,1,6]=>{{1,2,4,5,6,7},{3}}
[4,6,5,3,7,2,1]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>{{1,2,4,5,7},{3},{6}}
[4,6,5,7,1,2,3]=>[5,6,4,1,7,3,2]=>[3,2,4,7,1,5,6]=>{{1,3,4,5,6,7},{2}}
[4,6,5,7,1,3,2]=>[5,6,4,1,7,2,3]=>[3,2,4,7,1,6,5]=>{{1,3,4,5,7},{2},{6}}
[4,6,5,7,2,1,3]=>[5,6,4,1,2,7,3]=>[3,2,4,7,6,1,5]=>{{1,3,4,5,6,7},{2}}
[4,6,5,7,2,3,1]=>[5,6,4,2,7,1,3]=>[3,2,4,6,1,7,5]=>{{1,3,4,5,6,7},{2}}
[4,6,5,7,3,1,2]=>[5,6,4,1,3,7,2]=>[3,2,4,7,5,1,6]=>{{1,3,4,6,7},{2},{5}}
[4,6,5,7,3,2,1]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>{{1,3,4,7},{2},{5,6}}
[4,6,7,1,2,3,5]=>[6,4,1,7,5,3,2]=>[2,4,7,1,3,5,6]=>{{1,2,4},{3,5,6,7}}
[4,6,7,1,2,5,3]=>[6,4,1,7,3,5,2]=>[2,4,7,1,5,3,6]=>{{1,2,4},{3,6,7},{5}}
[4,6,7,1,3,2,5]=>[6,4,1,7,5,2,3]=>[2,4,7,1,3,6,5]=>{{1,2,4},{3,5,7},{6}}
[4,6,7,1,3,5,2]=>[6,4,1,7,3,2,5]=>[2,4,7,1,5,6,3]=>{{1,2,4},{3,7},{5},{6}}
[4,6,7,1,5,2,3]=>[6,4,1,7,2,5,3]=>[2,4,7,1,6,3,5]=>{{1,2,4},{3,5,6,7}}
[4,6,7,1,5,3,2]=>[6,4,1,7,2,3,5]=>[2,4,7,1,6,5,3]=>{{1,2,4},{3,7},{5,6}}
[4,6,7,2,1,3,5]=>[6,4,1,2,7,5,3]=>[2,4,7,6,1,3,5]=>{{1,2,3,4,5,6,7}}
[4,6,7,2,1,5,3]=>[6,4,1,2,7,3,5]=>[2,4,7,6,1,5,3]=>{{1,2,4,5,6},{3,7}}
[4,6,7,2,3,1,5]=>[6,4,2,7,5,1,3]=>[2,4,6,1,3,7,5]=>{{1,2,4},{3,5,6,7}}
[4,6,7,2,3,5,1]=>[6,4,2,7,3,1,5]=>[2,4,6,1,5,7,3]=>{{1,2,4},{3,6,7},{5}}
[4,6,7,2,5,1,3]=>[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>{{1,2,4},{3,6},{5,7}}
[4,6,7,2,5,3,1]=>[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>{{1,2,4},{3,5,6,7}}
[4,6,7,3,1,2,5]=>[6,4,1,3,7,5,2]=>[2,4,7,5,1,3,6]=>{{1,2,4,5},{3,6,7}}
[4,6,7,3,1,5,2]=>[6,4,1,3,7,2,5]=>[2,4,7,5,1,6,3]=>{{1,2,4,5},{3,7},{6}}
[4,6,7,3,2,1,5]=>[6,4,1,2,3,7,5]=>[2,4,7,6,5,1,3]=>{{1,2,4,6},{3,7},{5}}
[4,6,7,3,2,5,1]=>[6,4,2,3,7,1,5]=>[2,4,6,5,1,7,3]=>{{1,2,4,5},{3,6,7}}
[4,6,7,3,5,1,2]=>[6,4,3,7,1,5,2]=>[2,4,5,1,7,3,6]=>{{1,2,4},{3,5,6,7}}
[4,6,7,3,5,2,1]=>[6,4,3,7,1,2,5]=>[2,4,5,1,7,6,3]=>{{1,2,4},{3,5,7},{6}}
[4,6,7,5,1,2,3]=>[6,4,1,5,7,3,2]=>[2,4,7,3,1,5,6]=>{{1,2,3,4,5,6,7}}
[4,6,7,5,1,3,2]=>[6,4,1,5,7,2,3]=>[2,4,7,3,1,6,5]=>{{1,2,3,4,5,7},{6}}
[4,6,7,5,2,1,3]=>[6,4,1,2,5,7,3]=>[2,4,7,6,3,1,5]=>{{1,2,4,6},{3,5,7}}
[4,6,7,5,2,3,1]=>[6,4,2,5,7,1,3]=>[2,4,6,3,1,7,5]=>{{1,2,3,4,5,6,7}}
[4,6,7,5,3,1,2]=>[6,4,1,3,5,7,2]=>[2,4,7,5,3,1,6]=>{{1,2,3,4,5,6,7}}
[4,6,7,5,3,2,1]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>{{1,2,3,4,6,7},{5}}
[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>[4,7,1,2,3,5,6]=>{{1,2,3,4,5,6,7}}
[4,7,1,2,3,6,5]=>[4,1,7,5,6,3,2]=>[4,7,1,3,2,5,6]=>{{1,3,4},{2,5,6,7}}
[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>[4,7,1,2,5,3,6]=>{{1,2,3,4,6,7},{5}}
[4,7,1,2,5,6,3]=>[4,1,7,5,3,6,2]=>[4,7,1,3,5,2,6]=>{{1,3,4},{2,6,7},{5}}
[4,7,1,2,6,3,5]=>[4,1,7,3,6,5,2]=>[4,7,1,5,2,3,6]=>{{1,2,3,4,5,6,7}}
[4,7,1,2,6,5,3]=>[4,1,7,3,5,6,2]=>[4,7,1,5,3,2,6]=>{{1,3,4,5},{2,6,7}}
[4,7,1,3,2,5,6]=>[4,1,7,6,5,2,3]=>[4,7,1,2,3,6,5]=>{{1,2,3,4,5,7},{6}}
[4,7,1,3,2,6,5]=>[4,1,7,5,6,2,3]=>[4,7,1,3,2,6,5]=>{{1,3,4},{2,5,7},{6}}
[4,7,1,3,5,2,6]=>[4,1,7,6,3,2,5]=>[4,7,1,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>[4,7,1,3,5,6,2]=>{{1,3,4},{2,7},{5},{6}}
[4,7,1,3,6,2,5]=>[4,1,7,3,2,6,5]=>[4,7,1,5,6,2,3]=>{{1,2,3,4,5,6,7}}
[4,7,1,3,6,5,2]=>[4,1,7,3,2,5,6]=>[4,7,1,5,6,3,2]=>{{1,3,4,5,6},{2,7}}
[4,7,1,5,2,3,6]=>[4,1,7,6,2,5,3]=>[4,7,1,2,6,3,5]=>{{1,2,3,4,5,6,7}}
[4,7,1,5,2,6,3]=>[4,1,7,2,5,3,6]=>[4,7,1,6,3,5,2]=>{{1,3,4,5,6},{2,7}}
[4,7,1,5,3,2,6]=>[4,1,7,6,2,3,5]=>[4,7,1,2,6,5,3]=>{{1,2,3,4,7},{5,6}}
[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>[4,7,1,5,3,6,2]=>{{1,3,4,5},{2,7},{6}}
[4,7,1,5,6,2,3]=>[4,1,7,5,2,6,3]=>[4,7,1,3,6,2,5]=>{{1,3,4},{2,5,6,7}}
[4,7,1,5,6,3,2]=>[4,1,7,5,2,3,6]=>[4,7,1,3,6,5,2]=>{{1,3,4},{2,7},{5,6}}
[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>[4,7,1,6,2,3,5]=>{{1,3,4,6},{2,5,7}}
[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>[4,7,1,6,2,5,3]=>{{1,2,3,4,5,6,7}}
[4,7,1,6,3,2,5]=>[4,1,7,2,3,6,5]=>[4,7,1,6,5,2,3]=>{{1,2,3,4,6,7},{5}}
[4,7,1,6,3,5,2]=>[4,1,7,3,6,2,5]=>[4,7,1,5,2,6,3]=>{{1,2,3,4,5,7},{6}}
[4,7,1,6,5,2,3]=>[4,1,7,2,5,6,3]=>[4,7,1,6,3,2,5]=>{{1,2,3,4,5,6,7}}
[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>[4,7,1,6,5,3,2]=>{{1,3,4,6},{2,7},{5}}
[4,7,2,1,3,5,6]=>[4,1,2,7,6,5,3]=>[4,7,6,1,2,3,5]=>{{1,4},{2,5,7},{3,6}}
[4,7,2,1,3,6,5]=>[4,1,2,7,5,6,3]=>[4,7,6,1,3,2,5]=>{{1,4},{2,3,5,6,7}}
[4,7,2,1,5,3,6]=>[4,1,2,7,6,3,5]=>[4,7,6,1,2,5,3]=>{{1,4},{2,3,5,6,7}}
[4,7,2,1,5,6,3]=>[4,1,2,7,5,3,6]=>[4,7,6,1,3,5,2]=>{{1,4},{2,7},{3,5,6}}
[4,7,2,1,6,3,5]=>[4,1,2,7,3,6,5]=>[4,7,6,1,5,2,3]=>{{1,4},{2,3,6,7},{5}}
[4,7,2,1,6,5,3]=>[4,1,2,7,3,5,6]=>[4,7,6,1,5,3,2]=>{{1,4},{2,7},{3,6},{5}}
[4,7,2,3,1,5,6]=>[4,2,7,6,5,1,3]=>[4,6,1,2,3,7,5]=>{{1,2,3,4,5,6,7}}
[4,7,2,3,1,6,5]=>[4,2,7,5,6,1,3]=>[4,6,1,3,2,7,5]=>{{1,3,4},{2,5,6,7}}
[4,7,2,3,5,1,6]=>[4,2,7,6,3,1,5]=>[4,6,1,2,5,7,3]=>{{1,2,3,4,6,7},{5}}
[4,7,2,3,5,6,1]=>[4,2,7,5,3,1,6]=>[4,6,1,3,5,7,2]=>{{1,3,4},{2,6,7},{5}}
[4,7,2,3,6,1,5]=>[4,2,7,3,1,6,5]=>[4,6,1,5,7,2,3]=>{{1,3,4,5,7},{2,6}}
[4,7,2,3,6,5,1]=>[4,2,7,3,1,5,6]=>[4,6,1,5,7,3,2]=>{{1,2,3,4,5,6,7}}
[4,7,2,5,1,3,6]=>[4,2,7,6,1,5,3]=>[4,6,1,2,7,3,5]=>{{1,2,3,4,6},{5,7}}
[4,7,2,5,1,6,3]=>[4,2,7,1,5,3,6]=>[4,6,1,7,3,5,2]=>{{1,2,3,4,5,6,7}}
[4,7,2,5,3,1,6]=>[4,2,7,6,1,3,5]=>[4,6,1,2,7,5,3]=>{{1,2,3,4,5,6,7}}
[4,7,2,5,3,6,1]=>[4,2,7,3,5,1,6]=>[4,6,1,5,3,7,2]=>{{1,3,4,5},{2,6,7}}
[4,7,2,5,6,1,3]=>[4,2,7,5,1,6,3]=>[4,6,1,3,7,2,5]=>{{1,3,4},{2,6},{5,7}}
[4,7,2,5,6,3,1]=>[4,2,7,5,1,3,6]=>[4,6,1,3,7,5,2]=>{{1,3,4},{2,5,6,7}}
[4,7,2,6,1,3,5]=>[4,2,7,1,6,5,3]=>[4,6,1,7,2,3,5]=>{{1,2,3,4,5,6,7}}
[4,7,2,6,1,5,3]=>[4,2,7,1,6,3,5]=>[4,6,1,7,2,5,3]=>{{1,3,4,7},{2,5,6}}
[4,7,2,6,3,1,5]=>[4,2,7,1,3,6,5]=>[4,6,1,7,5,2,3]=>{{1,3,4,7},{2,6},{5}}
[4,7,2,6,3,5,1]=>[4,2,7,3,6,1,5]=>[4,6,1,5,2,7,3]=>{{1,2,3,4,5,6,7}}
[4,7,2,6,5,1,3]=>[4,2,7,1,5,6,3]=>[4,6,1,7,3,2,5]=>{{1,3,4,5,7},{2,6}}
[4,7,2,6,5,3,1]=>[4,2,7,1,3,5,6]=>[4,6,1,7,5,3,2]=>{{1,2,3,4,6,7},{5}}
[4,7,3,1,2,5,6]=>[4,1,3,7,6,5,2]=>[4,7,5,1,2,3,6]=>{{1,4},{2,3,5,6,7}}
[4,7,3,1,2,6,5]=>[4,1,3,7,5,6,2]=>[4,7,5,1,3,2,6]=>{{1,4},{2,6,7},{3,5}}
[4,7,3,1,5,2,6]=>[4,1,3,7,6,2,5]=>[4,7,5,1,2,6,3]=>{{1,4},{2,3,5,7},{6}}
[4,7,3,1,5,6,2]=>[4,1,3,7,5,2,6]=>[4,7,5,1,3,6,2]=>{{1,4},{2,7},{3,5},{6}}
[4,7,3,1,6,2,5]=>[4,1,3,7,2,6,5]=>[4,7,5,1,6,2,3]=>{{1,4},{2,3,5,6,7}}
[4,7,3,1,6,5,2]=>[4,1,3,7,2,5,6]=>[4,7,5,1,6,3,2]=>{{1,4},{2,7},{3,5,6}}
[4,7,3,2,1,5,6]=>[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>{{1,4,5},{2,3,6,7}}
[4,7,3,2,1,6,5]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>{{1,4,5},{2,7},{3,6}}
[4,7,3,2,5,1,6]=>[4,2,3,7,6,1,5]=>[4,6,5,1,2,7,3]=>{{1,4},{2,3,5,6,7}}
[4,7,3,2,5,6,1]=>[4,2,3,7,5,1,6]=>[4,6,5,1,3,7,2]=>{{1,4},{2,6,7},{3,5}}
[4,7,3,2,6,1,5]=>[4,2,3,7,1,6,5]=>[4,6,5,1,7,2,3]=>{{1,4},{2,6},{3,5,7}}
[4,7,3,2,6,5,1]=>[4,2,3,7,1,5,6]=>[4,6,5,1,7,3,2]=>{{1,4},{2,3,5,6,7}}
[4,7,3,5,1,2,6]=>[4,3,7,6,1,5,2]=>[4,5,1,2,7,3,6]=>{{1,2,3,4,5,6,7}}
[4,7,3,5,1,6,2]=>[4,3,7,1,5,2,6]=>[4,5,1,7,3,6,2]=>{{1,2,3,4,5,7},{6}}
[4,7,3,5,2,1,6]=>[4,3,7,6,1,2,5]=>[4,5,1,2,7,6,3]=>{{1,2,3,4,5,7},{6}}
[4,7,3,5,2,6,1]=>[4,3,7,2,5,1,6]=>[4,5,1,6,3,7,2]=>{{1,2,3,4,5,6,7}}
[4,7,3,5,6,1,2]=>[4,3,7,5,1,6,2]=>[4,5,1,3,7,2,6]=>{{1,3,4},{2,5,6,7}}
[4,7,3,5,6,2,1]=>[4,3,7,5,1,2,6]=>[4,5,1,3,7,6,2]=>{{1,3,4},{2,5,7},{6}}
[4,7,3,6,1,2,5]=>[4,3,7,1,6,5,2]=>[4,5,1,7,2,3,6]=>{{1,3,4,6,7},{2,5}}
[4,7,3,6,1,5,2]=>[4,3,7,1,6,2,5]=>[4,5,1,7,2,6,3]=>{{1,3,4,7},{2,5},{6}}
[4,7,3,6,2,1,5]=>[4,3,7,1,2,6,5]=>[4,5,1,7,6,2,3]=>{{1,3,4,7},{2,5,6}}
[4,7,3,6,2,5,1]=>[4,3,7,2,6,1,5]=>[4,5,1,6,2,7,3]=>{{1,3,4,6,7},{2,5}}
[4,7,3,6,5,1,2]=>[4,3,7,1,5,6,2]=>[4,5,1,7,3,2,6]=>{{1,2,3,4,5,6,7}}
[4,7,3,6,5,2,1]=>[4,3,7,1,2,5,6]=>[4,5,1,7,6,3,2]=>{{1,2,3,4,5,6,7}}
[4,7,5,1,2,3,6]=>[4,1,5,7,6,3,2]=>[4,7,3,1,2,5,6]=>{{1,4},{2,5,6,7},{3}}
[4,7,5,1,2,6,3]=>[4,1,5,7,3,6,2]=>[4,7,3,1,5,2,6]=>{{1,4},{2,6,7},{3},{5}}
[4,7,5,1,3,2,6]=>[4,1,5,7,6,2,3]=>[4,7,3,1,2,6,5]=>{{1,4},{2,5,7},{3},{6}}
[4,7,5,1,3,6,2]=>[4,1,5,7,3,2,6]=>[4,7,3,1,5,6,2]=>{{1,4},{2,7},{3},{5},{6}}
[4,7,5,1,6,2,3]=>[4,1,5,7,2,6,3]=>[4,7,3,1,6,2,5]=>{{1,4},{2,5,6,7},{3}}
[4,7,5,1,6,3,2]=>[4,1,5,7,2,3,6]=>[4,7,3,1,6,5,2]=>{{1,4},{2,7},{3},{5,6}}
[4,7,5,2,1,3,6]=>[4,1,2,5,7,6,3]=>[4,7,6,3,1,2,5]=>{{1,2,3,4,5,6,7}}
[4,7,5,2,1,6,3]=>[4,1,2,5,7,3,6]=>[4,7,6,3,1,5,2]=>{{1,3,4,5,6},{2,7}}
[4,7,5,2,3,1,6]=>[4,2,5,7,6,1,3]=>[4,6,3,1,2,7,5]=>{{1,4},{2,5,6,7},{3}}
[4,7,5,2,3,6,1]=>[4,2,5,7,3,1,6]=>[4,6,3,1,5,7,2]=>{{1,4},{2,6,7},{3},{5}}
[4,7,5,2,6,1,3]=>[4,2,5,7,1,6,3]=>[4,6,3,1,7,2,5]=>{{1,4},{2,6},{3},{5,7}}
[4,7,5,2,6,3,1]=>[4,2,5,7,1,3,6]=>[4,6,3,1,7,5,2]=>{{1,4},{2,5,6,7},{3}}
[4,7,5,3,1,2,6]=>[4,1,3,5,7,6,2]=>[4,7,5,3,1,2,6]=>{{1,3,4,5},{2,6,7}}
[4,7,5,3,1,6,2]=>[4,1,3,5,7,2,6]=>[4,7,5,3,1,6,2]=>{{1,3,4,5},{2,7},{6}}
[4,7,5,3,2,1,6]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>{{1,3,4,5,6},{2,7}}
[4,7,5,3,2,6,1]=>[4,2,3,5,7,1,6]=>[4,6,5,3,1,7,2]=>{{1,3,4,5},{2,6,7}}
[4,7,5,3,6,1,2]=>[4,3,5,7,1,6,2]=>[4,5,3,1,7,2,6]=>{{1,4},{2,5,6,7},{3}}
[4,7,5,3,6,2,1]=>[4,3,5,7,1,2,6]=>[4,5,3,1,7,6,2]=>{{1,4},{2,5,7},{3},{6}}
[4,7,5,6,1,2,3]=>[5,7,4,1,6,3,2]=>[3,1,4,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[4,7,5,6,1,3,2]=>[5,7,4,1,6,2,3]=>[3,1,4,7,2,6,5]=>{{1,2,3,4,5,7},{6}}
[4,7,5,6,2,1,3]=>[5,7,4,1,2,6,3]=>[3,1,4,7,6,2,5]=>{{1,2,3,4,5,6,7}}
[4,7,5,6,2,3,1]=>[5,7,4,2,6,1,3]=>[3,1,4,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[4,7,5,6,3,1,2]=>[5,7,4,1,3,6,2]=>[3,1,4,7,5,2,6]=>{{1,2,3,4,6,7},{5}}
[4,7,5,6,3,2,1]=>[5,7,4,1,2,3,6]=>[3,1,4,7,6,5,2]=>{{1,2,3,4,7},{5,6}}
[4,7,6,1,2,3,5]=>[4,1,6,7,5,3,2]=>[4,7,2,1,3,5,6]=>{{1,4},{2,3,5,6,7}}
[4,7,6,1,2,5,3]=>[4,1,6,7,3,5,2]=>[4,7,2,1,5,3,6]=>{{1,4},{2,3,6,7},{5}}
[4,7,6,1,3,2,5]=>[4,1,6,7,5,2,3]=>[4,7,2,1,3,6,5]=>{{1,4},{2,3,5,7},{6}}
[4,7,6,1,3,5,2]=>[4,1,6,7,3,2,5]=>[4,7,2,1,5,6,3]=>{{1,4},{2,3,7},{5},{6}}
[4,7,6,1,5,2,3]=>[4,1,6,7,2,5,3]=>[4,7,2,1,6,3,5]=>{{1,4},{2,3,5,6,7}}
[4,7,6,1,5,3,2]=>[4,1,6,7,2,3,5]=>[4,7,2,1,6,5,3]=>{{1,4},{2,3,7},{5,6}}
[4,7,6,2,1,3,5]=>[4,1,2,6,7,5,3]=>[4,7,6,2,1,3,5]=>{{1,2,4,5,7},{3,6}}
[4,7,6,2,1,5,3]=>[4,1,2,6,7,3,5]=>[4,7,6,2,1,5,3]=>{{1,2,3,4,5,6,7}}
[4,7,6,2,3,1,5]=>[4,2,6,7,5,1,3]=>[4,6,2,1,3,7,5]=>{{1,4},{2,3,5,6,7}}
[4,7,6,2,3,5,1]=>[4,2,6,7,3,1,5]=>[4,6,2,1,5,7,3]=>{{1,4},{2,3,6,7},{5}}
[4,7,6,2,5,1,3]=>[4,2,6,7,1,5,3]=>[4,6,2,1,7,3,5]=>{{1,4},{2,3,6},{5,7}}
[4,7,6,2,5,3,1]=>[4,2,6,7,1,3,5]=>[4,6,2,1,7,5,3]=>{{1,4},{2,3,5,6,7}}
[4,7,6,3,1,2,5]=>[4,1,3,6,7,5,2]=>[4,7,5,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[4,7,6,3,1,5,2]=>[4,1,3,6,7,2,5]=>[4,7,5,2,1,6,3]=>{{1,2,3,4,5,7},{6}}
[4,7,6,3,2,1,5]=>[4,1,2,3,6,7,5]=>[4,7,6,5,2,1,3]=>{{1,2,3,4,5,6,7}}
[4,7,6,3,2,5,1]=>[4,2,3,6,7,1,5]=>[4,6,5,2,1,7,3]=>{{1,2,3,4,5,6,7}}
[4,7,6,3,5,1,2]=>[4,3,6,7,1,5,2]=>[4,5,2,1,7,3,6]=>{{1,4},{2,3,5,6,7}}
[4,7,6,3,5,2,1]=>[4,3,6,7,1,2,5]=>[4,5,2,1,7,6,3]=>{{1,4},{2,3,5,7},{6}}
[4,7,6,5,1,2,3]=>[4,1,5,6,7,3,2]=>[4,7,3,2,1,5,6]=>{{1,2,4,5,6,7},{3}}
[4,7,6,5,1,3,2]=>[4,1,5,6,7,2,3]=>[4,7,3,2,1,6,5]=>{{1,2,4,5,7},{3},{6}}
[4,7,6,5,2,1,3]=>[4,1,2,5,6,7,3]=>[4,7,6,3,2,1,5]=>{{1,3,4,6},{2,5,7}}
[4,7,6,5,2,3,1]=>[4,2,5,6,7,1,3]=>[4,6,3,2,1,7,5]=>{{1,2,4,5,6,7},{3}}
[4,7,6,5,3,1,2]=>[4,1,3,5,6,7,2]=>[4,7,5,3,2,1,6]=>{{1,2,3,4,5,6,7}}
[4,7,6,5,3,2,1]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>{{1,2,3,4,5,6,7}}
[5,1,2,3,4,6,7]=>[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>{{1},{2},{3,4,5,6,7}}
[5,1,2,3,4,7,6]=>[6,7,1,5,4,3,2]=>[2,1,7,3,4,5,6]=>{{1,2},{3,4,5,6,7}}
[5,1,2,3,6,4,7]=>[7,1,5,4,6,3,2]=>[1,7,3,4,2,5,6]=>{{1},{2,5,6,7},{3},{4}}
[5,1,2,3,6,7,4]=>[6,1,5,4,7,3,2]=>[2,7,3,4,1,5,6]=>{{1,2,5,6,7},{3},{4}}
[5,1,2,3,7,4,6]=>[1,5,4,7,6,3,2]=>[7,3,4,1,2,5,6]=>{{1,2,3,4,5,6,7}}
[5,1,2,3,7,6,4]=>[1,5,4,6,7,3,2]=>[7,3,4,2,1,5,6]=>{{1,5,6,7},{2,3,4}}
[5,1,2,4,3,6,7]=>[7,6,1,5,3,4,2]=>[1,2,7,3,5,4,6]=>{{1},{2},{3,4,6,7},{5}}
[5,1,2,4,3,7,6]=>[6,7,1,5,3,4,2]=>[2,1,7,3,5,4,6]=>{{1,2},{3,4,6,7},{5}}
[5,1,2,4,6,3,7]=>[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>{{1},{2,6,7},{3},{4},{5}}
[5,1,2,4,6,7,3]=>[6,1,5,4,3,7,2]=>[2,7,3,4,5,1,6]=>{{1,2,6,7},{3},{4},{5}}
[5,1,2,4,7,3,6]=>[1,5,4,3,7,6,2]=>[7,3,4,5,1,2,6]=>{{1,2,3,4,5,6,7}}
[5,1,2,4,7,6,3]=>[1,5,4,3,6,7,2]=>[7,3,4,5,2,1,6]=>{{1,6,7},{2,3,4,5}}
[5,1,2,6,3,4,7]=>[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>{{1},{2,4,5,6,7},{3}}
[5,1,2,6,3,7,4]=>[1,5,3,6,4,7,2]=>[7,3,5,2,4,1,6]=>{{1,6,7},{2,3,4,5}}
[5,1,2,6,4,3,7]=>[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>{{1},{2,6,7},{3},{4,5}}
[5,1,2,6,4,7,3]=>[1,5,4,6,3,7,2]=>[7,3,4,2,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[5,1,2,6,7,3,4]=>[6,1,5,3,7,4,2]=>[2,7,3,5,1,4,6]=>{{1,2,4,5,6,7},{3}}
[5,1,2,6,7,4,3]=>[6,1,5,3,4,7,2]=>[2,7,3,5,4,1,6]=>{{1,2,6,7},{3},{4,5}}
[5,1,2,7,3,4,6]=>[1,5,3,7,6,4,2]=>[7,3,5,1,2,4,6]=>{{1,4,6,7},{2,3,5}}
[5,1,2,7,3,6,4]=>[1,5,3,7,4,6,2]=>[7,3,5,1,4,2,6]=>{{1,2,3,4,5,6,7}}
[5,1,2,7,4,3,6]=>[1,5,3,4,7,6,2]=>[7,3,5,4,1,2,6]=>{{1,2,3,5,6,7},{4}}
[5,1,2,7,4,6,3]=>[1,5,4,7,3,6,2]=>[7,3,4,1,5,2,6]=>{{1,2,3,4,6,7},{5}}
[5,1,2,7,6,3,4]=>[1,5,3,6,7,4,2]=>[7,3,5,2,1,4,6]=>{{1,2,3,4,5,6,7}}
[5,1,2,7,6,4,3]=>[1,5,3,4,6,7,2]=>[7,3,5,4,2,1,6]=>{{1,6,7},{2,3,5},{4}}
[5,1,3,2,4,6,7]=>[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>{{1},{2},{3,4,5,7},{6}}
[5,1,3,2,4,7,6]=>[6,7,1,5,4,2,3]=>[2,1,7,3,4,6,5]=>{{1,2},{3,4,5,7},{6}}
[5,1,3,2,6,4,7]=>[7,1,5,4,6,2,3]=>[1,7,3,4,2,6,5]=>{{1},{2,5,7},{3},{4},{6}}
[5,1,3,2,6,7,4]=>[6,1,5,4,7,2,3]=>[2,7,3,4,1,6,5]=>{{1,2,5,7},{3},{4},{6}}
[5,1,3,2,7,4,6]=>[1,5,4,7,6,2,3]=>[7,3,4,1,2,6,5]=>{{1,2,3,4,5,7},{6}}
[5,1,3,2,7,6,4]=>[1,5,4,6,7,2,3]=>[7,3,4,2,1,6,5]=>{{1,5,7},{2,3,4},{6}}
[5,1,3,4,2,6,7]=>[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>{{1},{2},{3,4,7},{5},{6}}
[5,1,3,4,2,7,6]=>[6,7,1,5,3,2,4]=>[2,1,7,3,5,6,4]=>{{1,2},{3,4,7},{5},{6}}
[5,1,3,4,6,2,7]=>[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}
[5,1,3,4,6,7,2]=>[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>{{1,2,7},{3},{4},{5},{6}}
[5,1,3,4,7,2,6]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>{{1,2,3,4,5,6,7}}
[5,1,3,4,7,6,2]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>{{1,7},{2,3,4,5,6}}
[5,1,3,6,2,4,7]=>[7,1,5,3,2,6,4]=>[1,7,3,5,6,2,4]=>{{1},{2,4,5,6,7},{3}}
[5,1,3,6,2,7,4]=>[1,5,3,2,6,4,7]=>[7,3,5,6,2,4,1]=>{{1,7},{2,3,5},{4,6}}
[5,1,3,6,4,2,7]=>[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>{{1},{2,7},{3},{4,5,6}}
[5,1,3,6,4,7,2]=>[1,5,4,6,3,2,7]=>[7,3,4,2,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[5,1,3,6,7,2,4]=>[6,1,5,3,2,7,4]=>[2,7,3,5,6,1,4]=>{{1,2,4,5,6,7},{3}}
[5,1,3,6,7,4,2]=>[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>{{1,2,7},{3},{4,5,6}}
[5,1,3,7,2,4,6]=>[1,5,3,2,7,6,4]=>[7,3,5,6,1,2,4]=>{{1,2,3,4,5,6,7}}
[5,1,3,7,2,6,4]=>[1,5,3,2,7,4,6]=>[7,3,5,6,1,4,2]=>{{1,2,3,5,7},{4,6}}
[5,1,3,7,4,2,6]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>{{1,2,3,4,5,6,7}}
[5,1,3,7,4,6,2]=>[1,5,4,7,3,2,6]=>[7,3,4,1,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[5,1,3,7,6,2,4]=>[1,5,3,2,6,7,4]=>[7,3,5,6,2,1,4]=>{{1,4,6,7},{2,3,5}}
[5,1,3,7,6,4,2]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>{{1,7},{2,3,4,5,6}}
[5,1,4,2,3,6,7]=>[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>{{1},{2},{3,4,5,6,7}}
[5,1,4,2,3,7,6]=>[6,7,1,5,2,4,3]=>[2,1,7,3,6,4,5]=>{{1,2},{3,4,5,6,7}}
[5,1,4,2,6,3,7]=>[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>{{1},{2,7},{3},{4,5,6}}
[5,1,4,2,6,7,3]=>[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>{{1,2,7},{3},{4,5,6}}
[5,1,4,2,7,3,6]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>{{1,2,3,6,7},{4},{5}}
[5,1,4,2,7,6,3]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>{{1,7},{2,3,6},{4},{5}}
[5,1,4,3,2,6,7]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>{{1},{2},{3,4,7},{5,6}}
[5,1,4,3,2,7,6]=>[6,7,1,5,2,3,4]=>[2,1,7,3,6,5,4]=>{{1,2},{3,4,7},{5,6}}
[5,1,4,3,6,2,7]=>[7,1,5,3,4,2,6]=>[1,7,3,5,4,6,2]=>{{1},{2,7},{3},{4,5},{6}}
[5,1,4,3,6,7,2]=>[6,1,5,3,4,2,7]=>[2,7,3,5,4,6,1]=>{{1,2,7},{3},{4,5},{6}}
[5,1,4,3,7,2,6]=>[1,5,3,4,2,7,6]=>[7,3,5,4,6,1,2]=>{{1,2,3,5,6,7},{4}}
[5,1,4,3,7,6,2]=>[1,5,3,4,2,6,7]=>[7,3,5,4,6,2,1]=>{{1,7},{2,3,5,6},{4}}
[5,1,4,6,2,3,7]=>[7,1,5,4,2,6,3]=>[1,7,3,4,6,2,5]=>{{1},{2,5,6,7},{3},{4}}
[5,1,4,6,2,7,3]=>[1,5,4,2,6,3,7]=>[7,3,4,6,2,5,1]=>{{1,7},{2,3,4,5,6}}
[5,1,4,6,3,2,7]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>{{1},{2,7},{3},{4},{5,6}}
[5,1,4,6,3,7,2]=>[1,5,4,3,6,2,7]=>[7,3,4,5,2,6,1]=>{{1,7},{2,3,4,5},{6}}
[5,1,4,6,7,2,3]=>[6,1,5,4,2,7,3]=>[2,7,3,4,6,1,5]=>{{1,2,5,6,7},{3},{4}}
[5,1,4,6,7,3,2]=>[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>{{1,2,7},{3},{4},{5,6}}
[5,1,4,7,2,3,6]=>[1,5,4,2,7,6,3]=>[7,3,4,6,1,2,5]=>{{1,5,7},{2,3,4,6}}
[5,1,4,7,2,6,3]=>[1,5,4,2,7,3,6]=>[7,3,4,6,1,5,2]=>{{1,2,3,4,5,6,7}}
[5,1,4,7,3,2,6]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>{{1,2,3,4,6,7},{5}}
[5,1,4,7,3,6,2]=>[1,5,4,3,7,2,6]=>[7,3,4,5,1,6,2]=>{{1,2,3,4,5,7},{6}}
[5,1,4,7,6,2,3]=>[1,5,4,2,6,7,3]=>[7,3,4,6,2,1,5]=>{{1,2,3,4,5,6,7}}
[5,1,4,7,6,3,2]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>{{1,7},{2,3,4,6},{5}}
[5,1,6,2,3,4,7]=>[7,1,5,2,6,4,3]=>[1,7,3,6,2,4,5]=>{{1},{2,5,7},{3},{4,6}}
[5,1,6,2,3,7,4]=>[1,5,2,6,4,7,3]=>[7,3,6,2,4,1,5]=>{{1,2,3,4,5,6,7}}
[5,1,6,2,4,3,7]=>[7,1,5,2,6,3,4]=>[1,7,3,6,2,5,4]=>{{1},{2,4,5,6,7},{3}}
[5,1,6,2,4,7,3]=>[1,5,2,6,4,3,7]=>[7,3,6,2,4,5,1]=>{{1,7},{2,3,4,5,6}}
[5,1,6,2,7,3,4]=>[1,5,2,6,3,7,4]=>[7,3,6,2,5,1,4]=>{{1,2,3,4,6,7},{5}}
[5,1,6,2,7,4,3]=>[1,5,2,6,3,4,7]=>[7,3,6,2,5,4,1]=>{{1,7},{2,3,4,6},{5}}
[5,1,6,3,2,4,7]=>[7,1,5,2,3,6,4]=>[1,7,3,6,5,2,4]=>{{1},{2,4,6,7},{3},{5}}
[5,1,6,3,2,7,4]=>[1,5,2,3,6,4,7]=>[7,3,6,5,2,4,1]=>{{1,7},{2,3,4,5,6}}
[5,1,6,3,4,2,7]=>[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>{{1},{2,4,5,7},{3},{6}}
[5,1,6,3,4,7,2]=>[1,5,3,6,4,2,7]=>[7,3,5,2,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[5,1,6,3,7,2,4]=>[1,5,3,6,2,7,4]=>[7,3,5,2,6,1,4]=>{{1,2,3,4,5,6,7}}
[5,1,6,3,7,4,2]=>[1,5,3,6,2,4,7]=>[7,3,5,2,6,4,1]=>{{1,7},{2,3,4,5,6}}
[5,1,6,4,2,3,7]=>[7,1,5,2,4,6,3]=>[1,7,3,6,4,2,5]=>{{1},{2,4,5,6,7},{3}}
[5,1,6,4,2,7,3]=>[1,5,2,4,6,3,7]=>[7,3,6,4,2,5,1]=>{{1,7},{2,3,5,6},{4}}
[5,1,6,4,3,2,7]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>{{1},{2,7},{3},{4,6},{5}}
[5,1,6,4,3,7,2]=>[1,5,3,4,6,2,7]=>[7,3,5,4,2,6,1]=>{{1,7},{2,3,5},{4},{6}}
[5,1,6,4,7,2,3]=>[1,5,4,6,2,7,3]=>[7,3,4,2,6,1,5]=>{{1,5,6,7},{2,3,4}}
[5,1,6,4,7,3,2]=>[1,5,4,6,2,3,7]=>[7,3,4,2,6,5,1]=>{{1,7},{2,3,4},{5,6}}
[5,1,6,7,2,3,4]=>[6,1,5,2,7,4,3]=>[2,7,3,6,1,4,5]=>{{1,2,5,7},{3},{4,6}}
[5,1,6,7,2,4,3]=>[6,1,5,2,7,3,4]=>[2,7,3,6,1,5,4]=>{{1,2,4,5,6,7},{3}}
[5,1,6,7,3,2,4]=>[6,1,5,2,3,7,4]=>[2,7,3,6,5,1,4]=>{{1,2,4,6,7},{3},{5}}
[5,1,6,7,3,4,2]=>[6,1,5,3,7,2,4]=>[2,7,3,5,1,6,4]=>{{1,2,4,5,7},{3},{6}}
[5,1,6,7,4,2,3]=>[6,1,5,2,4,7,3]=>[2,7,3,6,4,1,5]=>{{1,2,4,5,6,7},{3}}
[5,1,6,7,4,3,2]=>[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>{{1,2,7},{3},{4,6},{5}}
[5,1,7,2,3,4,6]=>[1,5,2,7,6,4,3]=>[7,3,6,1,2,4,5]=>{{1,2,3,4,5,6,7}}
[5,1,7,2,3,6,4]=>[1,5,2,7,4,6,3]=>[7,3,6,1,4,2,5]=>{{1,4,5,7},{2,3,6}}
[5,1,7,2,4,3,6]=>[1,5,2,7,6,3,4]=>[7,3,6,1,2,5,4]=>{{1,4,7},{2,3,5,6}}
[5,1,7,2,4,6,3]=>[1,5,2,7,4,3,6]=>[7,3,6,1,4,5,2]=>{{1,2,3,4,5,6,7}}
[5,1,7,2,6,3,4]=>[1,5,2,7,3,6,4]=>[7,3,6,1,5,2,4]=>{{1,4,7},{2,3,6},{5}}
[5,1,7,2,6,4,3]=>[1,5,2,7,3,4,6]=>[7,3,6,1,5,4,2]=>{{1,2,3,4,6,7},{5}}
[5,1,7,3,2,4,6]=>[1,5,2,3,7,6,4]=>[7,3,6,5,1,2,4]=>{{1,4,5,7},{2,3,6}}
[5,1,7,3,2,6,4]=>[1,5,2,3,7,4,6]=>[7,3,6,5,1,4,2]=>{{1,2,3,4,5,6,7}}
[5,1,7,3,4,2,6]=>[1,5,3,7,6,2,4]=>[7,3,5,1,2,6,4]=>{{1,4,7},{2,3,5},{6}}
[5,1,7,3,4,6,2]=>[1,5,3,7,4,2,6]=>[7,3,5,1,4,6,2]=>{{1,2,3,4,5,7},{6}}
[5,1,7,3,6,2,4]=>[1,5,3,7,2,6,4]=>[7,3,5,1,6,2,4]=>{{1,4,7},{2,3,5,6}}
[5,1,7,3,6,4,2]=>[1,5,3,7,2,4,6]=>[7,3,5,1,6,4,2]=>{{1,2,3,4,5,6,7}}
[5,1,7,4,2,3,6]=>[1,5,2,4,7,6,3]=>[7,3,6,4,1,2,5]=>{{1,5,7},{2,3,6},{4}}
[5,1,7,4,2,6,3]=>[1,5,2,4,7,3,6]=>[7,3,6,4,1,5,2]=>{{1,2,3,5,6,7},{4}}
[5,1,7,4,3,2,6]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>{{1,2,3,6,7},{4,5}}
[5,1,7,4,3,6,2]=>[1,5,3,4,7,2,6]=>[7,3,5,4,1,6,2]=>{{1,2,3,5,7},{4},{6}}
[5,1,7,4,6,2,3]=>[1,5,4,7,2,6,3]=>[7,3,4,1,6,2,5]=>{{1,2,3,4,5,6,7}}
[5,1,7,4,6,3,2]=>[1,5,4,7,2,3,6]=>[7,3,4,1,6,5,2]=>{{1,2,3,4,7},{5,6}}
[5,1,7,6,2,3,4]=>[1,5,2,6,7,4,3]=>[7,3,6,2,1,4,5]=>{{1,5,7},{2,3,4,6}}
[5,1,7,6,2,4,3]=>[1,5,2,6,7,3,4]=>[7,3,6,2,1,5,4]=>{{1,2,3,4,5,6,7}}
[5,1,7,6,3,2,4]=>[1,5,2,3,6,7,4]=>[7,3,6,5,2,1,4]=>{{1,2,3,4,5,6,7}}
[5,1,7,6,3,4,2]=>[1,5,3,6,7,2,4]=>[7,3,5,2,1,6,4]=>{{1,2,3,4,5,7},{6}}
[5,1,7,6,4,2,3]=>[1,5,2,4,6,7,3]=>[7,3,6,4,2,1,5]=>{{1,2,3,5,6,7},{4}}
[5,1,7,6,4,3,2]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>{{1,7},{2,3,6},{4,5}}
[5,2,1,3,4,6,7]=>[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>{{1},{2},{3,5,7},{4,6}}
[5,2,1,3,4,7,6]=>[6,7,1,2,5,4,3]=>[2,1,7,6,3,4,5]=>{{1,2},{3,5,7},{4,6}}
[5,2,1,3,6,4,7]=>[7,1,2,5,4,6,3]=>[1,7,6,3,4,2,5]=>{{1},{2,3,4,5,6,7}}
[5,2,1,3,6,7,4]=>[6,1,2,5,4,7,3]=>[2,7,6,3,4,1,5]=>{{1,2,3,4,5,6,7}}
[5,2,1,3,7,4,6]=>[1,2,5,4,7,6,3]=>[7,6,3,4,1,2,5]=>{{1,5,7},{2,6},{3},{4}}
[5,2,1,3,7,6,4]=>[1,2,5,4,6,7,3]=>[7,6,3,4,2,1,5]=>{{1,2,5,6,7},{3},{4}}
[5,2,1,4,3,6,7]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>{{1},{2},{3,4,5,6,7}}
[5,2,1,4,3,7,6]=>[6,7,1,2,5,3,4]=>[2,1,7,6,3,5,4]=>{{1,2},{3,4,5,6,7}}
[5,2,1,4,6,3,7]=>[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>{{1},{2,7},{3,4,5,6}}
[5,2,1,4,6,7,3]=>[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>{{1,2,7},{3,4,5,6}}
[5,2,1,4,7,3,6]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>{{1,2,6,7},{3},{4},{5}}
[5,2,1,4,7,6,3]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>{{1,7},{2,6},{3},{4},{5}}
[5,2,1,6,3,4,7]=>[7,1,2,5,3,6,4]=>[1,7,6,3,5,2,4]=>{{1},{2,3,4,6,7},{5}}
[5,2,1,6,3,7,4]=>[1,2,5,3,6,4,7]=>[7,6,3,5,2,4,1]=>{{1,7},{2,4,5,6},{3}}
[5,2,1,6,4,3,7]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>{{1},{2,7},{3,4,6},{5}}
[5,2,1,6,4,7,3]=>[1,2,5,4,6,3,7]=>[7,6,3,4,2,5,1]=>{{1,7},{2,5,6},{3},{4}}
[5,2,1,6,7,3,4]=>[6,1,2,5,3,7,4]=>[2,7,6,3,5,1,4]=>{{1,2,3,4,6,7},{5}}
[5,2,1,6,7,4,3]=>[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>{{1,2,7},{3,4,6},{5}}
[5,2,1,7,3,4,6]=>[1,2,5,3,7,6,4]=>[7,6,3,5,1,2,4]=>{{1,4,5,7},{2,6},{3}}
[5,2,1,7,3,6,4]=>[1,2,5,3,7,4,6]=>[7,6,3,5,1,4,2]=>{{1,2,4,5,6,7},{3}}
[5,2,1,7,4,3,6]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>{{1,2,6,7},{3},{4,5}}
[5,2,1,7,4,6,3]=>[1,2,5,4,7,3,6]=>[7,6,3,4,1,5,2]=>{{1,2,5,6,7},{3},{4}}
[5,2,1,7,6,3,4]=>[1,2,5,3,6,7,4]=>[7,6,3,5,2,1,4]=>{{1,2,4,5,6,7},{3}}
[5,2,1,7,6,4,3]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>{{1,7},{2,6},{3},{4,5}}
[5,2,3,1,4,6,7]=>[7,6,2,5,4,1,3]=>[1,2,6,3,4,7,5]=>{{1},{2},{3,4,5,6,7}}
[5,2,3,1,4,7,6]=>[6,7,2,5,4,1,3]=>[2,1,6,3,4,7,5]=>{{1,2},{3,4,5,6,7}}
[5,2,3,1,6,4,7]=>[7,2,5,4,6,1,3]=>[1,6,3,4,2,7,5]=>{{1},{2,5,6,7},{3},{4}}
[5,2,3,1,6,7,4]=>[6,2,5,4,7,1,3]=>[2,6,3,4,1,7,5]=>{{1,2,5,6,7},{3},{4}}
[5,2,3,1,7,4,6]=>[2,5,4,7,6,1,3]=>[6,3,4,1,2,7,5]=>{{1,2,3,4,5,6,7}}
[5,2,3,1,7,6,4]=>[2,5,4,6,7,1,3]=>[6,3,4,2,1,7,5]=>{{1,5,6,7},{2,3,4}}
[5,2,3,4,1,6,7]=>[7,6,2,5,3,1,4]=>[1,2,6,3,5,7,4]=>{{1},{2},{3,4,6,7},{5}}
[5,2,3,4,1,7,6]=>[6,7,2,5,3,1,4]=>[2,1,6,3,5,7,4]=>{{1,2},{3,4,6,7},{5}}
[5,2,3,4,6,1,7]=>[7,2,5,4,3,1,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[5,2,3,4,6,7,1]=>[6,2,5,4,3,1,7]=>[2,6,3,4,5,7,1]=>{{1,2,6,7},{3},{4},{5}}
[5,2,3,4,7,1,6]=>[2,5,4,3,1,7,6]=>[6,3,4,5,7,1,2]=>{{1,6},{2,3,4,5,7}}
[5,2,3,4,7,6,1]=>[2,5,4,3,1,6,7]=>[6,3,4,5,7,2,1]=>{{1,2,3,4,5,6,7}}
[5,2,3,6,1,4,7]=>[7,2,5,3,1,6,4]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,2,3,6,1,7,4]=>[2,5,3,1,6,4,7]=>[6,3,5,7,2,4,1]=>{{1,4,6,7},{2,3,5}}
[5,2,3,6,4,1,7]=>[7,2,5,3,1,4,6]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,3,6,4,7,1]=>[2,5,4,6,3,1,7]=>[6,3,4,2,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[5,2,3,6,7,1,4]=>[6,2,5,3,1,7,4]=>[2,6,3,5,7,1,4]=>{{1,2,6},{3},{4,5,7}}
[5,2,3,6,7,4,1]=>[6,2,5,3,1,4,7]=>[2,6,3,5,7,4,1]=>{{1,2,4,5,6,7},{3}}
[5,2,3,7,1,4,6]=>[2,5,3,1,7,6,4]=>[6,3,5,7,1,2,4]=>{{1,2,3,5,6},{4,7}}
[5,2,3,7,1,6,4]=>[2,5,3,1,7,4,6]=>[6,3,5,7,1,4,2]=>{{1,2,3,4,5,6,7}}
[5,2,3,7,4,1,6]=>[2,5,3,1,4,7,6]=>[6,3,5,7,4,1,2]=>{{1,6},{2,3,4,5,7}}
[5,2,3,7,4,6,1]=>[2,5,4,7,3,1,6]=>[6,3,4,1,5,7,2]=>{{1,2,3,4,6,7},{5}}
[5,2,3,7,6,1,4]=>[2,5,3,1,6,7,4]=>[6,3,5,7,2,1,4]=>{{1,6},{2,3,5},{4,7}}
[5,2,3,7,6,4,1]=>[2,5,3,1,4,6,7]=>[6,3,5,7,4,2,1]=>{{1,2,3,4,5,6,7}}
[5,2,4,1,3,6,7]=>[7,6,2,5,1,4,3]=>[1,2,6,3,7,4,5]=>{{1},{2},{3,4,6},{5,7}}
[5,2,4,1,3,7,6]=>[6,7,2,5,1,4,3]=>[2,1,6,3,7,4,5]=>{{1,2},{3,4,6},{5,7}}
[5,2,4,1,6,3,7]=>[7,2,5,1,4,3,6]=>[1,6,3,7,4,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,4,1,6,7,3]=>[6,2,5,1,4,3,7]=>[2,6,3,7,4,5,1]=>{{1,2,4,5,6,7},{3}}
[5,2,4,1,7,3,6]=>[2,5,1,4,3,7,6]=>[6,3,7,4,5,1,2]=>{{1,6},{2,3,7},{4},{5}}
[5,2,4,1,7,6,3]=>[2,5,1,4,3,6,7]=>[6,3,7,4,5,2,1]=>{{1,2,3,6,7},{4},{5}}
[5,2,4,3,1,6,7]=>[7,6,2,5,1,3,4]=>[1,2,6,3,7,5,4]=>{{1},{2},{3,4,5,6,7}}
[5,2,4,3,1,7,6]=>[6,7,2,5,1,3,4]=>[2,1,6,3,7,5,4]=>{{1,2},{3,4,5,6,7}}
[5,2,4,3,6,1,7]=>[7,2,5,3,4,1,6]=>[1,6,3,5,4,7,2]=>{{1},{2,6,7},{3},{4,5}}
[5,2,4,3,6,7,1]=>[6,2,5,3,4,1,7]=>[2,6,3,5,4,7,1]=>{{1,2,6,7},{3},{4,5}}
[5,2,4,3,7,1,6]=>[2,5,3,4,1,7,6]=>[6,3,5,4,7,1,2]=>{{1,6},{2,3,5,7},{4}}
[5,2,4,3,7,6,1]=>[2,5,3,4,1,6,7]=>[6,3,5,4,7,2,1]=>{{1,2,3,5,6,7},{4}}
[5,2,4,6,1,3,7]=>[7,2,5,4,1,6,3]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[5,2,4,6,1,7,3]=>[2,5,4,1,6,3,7]=>[6,3,4,7,2,5,1]=>{{1,2,3,4,5,6,7}}
[5,2,4,6,3,1,7]=>[7,2,5,4,1,3,6]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[5,2,4,6,3,7,1]=>[2,5,4,3,6,1,7]=>[6,3,4,5,2,7,1]=>{{1,6,7},{2,3,4,5}}
[5,2,4,6,7,1,3]=>[6,2,5,4,1,7,3]=>[2,6,3,4,7,1,5]=>{{1,2,6},{3},{4},{5,7}}
[5,2,4,6,7,3,1]=>[6,2,5,4,1,3,7]=>[2,6,3,4,7,5,1]=>{{1,2,5,6,7},{3},{4}}
[5,2,4,7,1,3,6]=>[2,5,4,1,7,6,3]=>[6,3,4,7,1,2,5]=>{{1,2,3,4,5,6,7}}
[5,2,4,7,1,6,3]=>[2,5,4,1,7,3,6]=>[6,3,4,7,1,5,2]=>{{1,5,6},{2,3,4,7}}
[5,2,4,7,3,1,6]=>[2,5,4,1,3,7,6]=>[6,3,4,7,5,1,2]=>{{1,6},{2,3,4,7},{5}}
[5,2,4,7,3,6,1]=>[2,5,4,3,7,1,6]=>[6,3,4,5,1,7,2]=>{{1,2,3,4,5,6,7}}
[5,2,4,7,6,1,3]=>[2,5,4,1,6,7,3]=>[6,3,4,7,2,1,5]=>{{1,6},{2,3,4,5,7}}
[5,2,4,7,6,3,1]=>[2,5,4,1,3,6,7]=>[6,3,4,7,5,2,1]=>{{1,2,3,4,6,7},{5}}
[5,2,6,1,3,4,7]=>[7,2,5,1,6,4,3]=>[1,6,3,7,2,4,5]=>{{1},{2,4,5,6,7},{3}}
[5,2,6,1,3,7,4]=>[2,5,1,6,4,7,3]=>[6,3,7,2,4,1,5]=>{{1,6},{2,3,4,5,7}}
[5,2,6,1,4,3,7]=>[7,2,5,1,6,3,4]=>[1,6,3,7,2,5,4]=>{{1},{2,5,6},{3},{4,7}}
[5,2,6,1,4,7,3]=>[2,5,1,6,4,3,7]=>[6,3,7,2,4,5,1]=>{{1,2,3,4,5,6,7}}
[5,2,6,1,7,3,4]=>[2,5,1,6,3,7,4]=>[6,3,7,2,5,1,4]=>{{1,6},{2,3,4,7},{5}}
[5,2,6,1,7,4,3]=>[2,5,1,6,3,4,7]=>[6,3,7,2,5,4,1]=>{{1,2,3,4,6,7},{5}}
[5,2,6,3,1,4,7]=>[7,2,5,1,3,6,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[5,2,6,3,1,7,4]=>[2,5,1,3,6,4,7]=>[6,3,7,5,2,4,1]=>{{1,2,3,4,5,6,7}}
[5,2,6,3,4,1,7]=>[7,2,5,3,6,1,4]=>[1,6,3,5,2,7,4]=>{{1},{2,4,5,6,7},{3}}
[5,2,6,3,4,7,1]=>[2,5,3,6,4,1,7]=>[6,3,5,2,4,7,1]=>{{1,6,7},{2,3,4,5}}
[5,2,6,3,7,1,4]=>[2,5,3,6,1,7,4]=>[6,3,5,2,7,1,4]=>{{1,6},{2,3,4,5,7}}
[5,2,6,3,7,4,1]=>[2,5,3,6,1,4,7]=>[6,3,5,2,7,4,1]=>{{1,2,3,4,5,6,7}}
[5,2,6,4,1,3,7]=>[7,2,5,1,4,6,3]=>[1,6,3,7,4,2,5]=>{{1},{2,6},{3},{4,5,7}}
[5,2,6,4,1,7,3]=>[2,5,1,4,6,3,7]=>[6,3,7,4,2,5,1]=>{{1,2,3,5,6,7},{4}}
[5,2,6,4,3,1,7]=>[7,2,5,1,3,4,6]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[5,2,6,4,3,7,1]=>[2,5,3,4,6,1,7]=>[6,3,5,4,2,7,1]=>{{1,6,7},{2,3,5},{4}}
[5,2,6,4,7,1,3]=>[2,5,4,6,1,7,3]=>[6,3,4,2,7,1,5]=>{{1,6},{2,3,4},{5,7}}
[5,2,6,4,7,3,1]=>[2,5,4,6,1,3,7]=>[6,3,4,2,7,5,1]=>{{1,5,6,7},{2,3,4}}
[5,2,6,7,1,3,4]=>[6,2,5,1,7,4,3]=>[2,6,3,7,1,4,5]=>{{1,2,4,5,6,7},{3}}
[5,2,6,7,1,4,3]=>[6,2,5,1,7,3,4]=>[2,6,3,7,1,5,4]=>{{1,2,5,6},{3},{4,7}}
[5,2,6,7,3,1,4]=>[6,2,5,1,3,7,4]=>[2,6,3,7,5,1,4]=>{{1,2,6},{3},{4,7},{5}}
[5,2,6,7,3,4,1]=>[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>{{1,2,4,5,6,7},{3}}
[5,2,6,7,4,1,3]=>[6,2,5,1,4,7,3]=>[2,6,3,7,4,1,5]=>{{1,2,6},{3},{4,5,7}}
[5,2,6,7,4,3,1]=>[6,2,5,1,3,4,7]=>[2,6,3,7,5,4,1]=>{{1,2,4,6,7},{3},{5}}
[5,2,7,1,3,4,6]=>[2,5,1,7,6,4,3]=>[6,3,7,1,2,4,5]=>{{1,4,6},{2,3,5,7}}
[5,2,7,1,3,6,4]=>[2,5,1,7,4,6,3]=>[6,3,7,1,4,2,5]=>{{1,2,3,4,5,6,7}}
[5,2,7,1,4,3,6]=>[2,5,1,7,6,3,4]=>[6,3,7,1,2,5,4]=>{{1,2,3,4,5,6,7}}
[5,2,7,1,4,6,3]=>[2,5,1,7,4,3,6]=>[6,3,7,1,4,5,2]=>{{1,4,5,6},{2,3,7}}
[5,2,7,1,6,3,4]=>[2,5,1,7,3,6,4]=>[6,3,7,1,5,2,4]=>{{1,2,3,4,6,7},{5}}
[5,2,7,1,6,4,3]=>[2,5,1,7,3,4,6]=>[6,3,7,1,5,4,2]=>{{1,4,6},{2,3,7},{5}}
[5,2,7,3,1,4,6]=>[2,5,1,3,7,6,4]=>[6,3,7,5,1,2,4]=>{{1,2,3,4,5,6,7}}
[5,2,7,3,1,6,4]=>[2,5,1,3,7,4,6]=>[6,3,7,5,1,4,2]=>{{1,4,5,6},{2,3,7}}
[5,2,7,3,4,1,6]=>[2,5,3,7,6,1,4]=>[6,3,5,1,2,7,4]=>{{1,4,6,7},{2,3,5}}
[5,2,7,3,4,6,1]=>[2,5,3,7,4,1,6]=>[6,3,5,1,4,7,2]=>{{1,2,3,4,5,6,7}}
[5,2,7,3,6,1,4]=>[2,5,3,7,1,6,4]=>[6,3,5,1,7,2,4]=>{{1,2,3,4,5,6,7}}
[5,2,7,3,6,4,1]=>[2,5,3,7,1,4,6]=>[6,3,5,1,7,4,2]=>{{1,4,6},{2,3,5,7}}
[5,2,7,4,1,3,6]=>[2,5,1,4,7,6,3]=>[6,3,7,4,1,2,5]=>{{1,2,3,5,6,7},{4}}
[5,2,7,4,1,6,3]=>[2,5,1,4,7,3,6]=>[6,3,7,4,1,5,2]=>{{1,5,6},{2,3,7},{4}}
[5,2,7,4,3,1,6]=>[2,5,1,3,4,7,6]=>[6,3,7,5,4,1,2]=>{{1,6},{2,3,7},{4,5}}
[5,2,7,4,3,6,1]=>[2,5,3,4,7,1,6]=>[6,3,5,4,1,7,2]=>{{1,2,3,5,6,7},{4}}
[5,2,7,4,6,1,3]=>[2,5,4,7,1,6,3]=>[6,3,4,1,7,2,5]=>{{1,2,3,4,6},{5,7}}
[5,2,7,4,6,3,1]=>[2,5,4,7,1,3,6]=>[6,3,4,1,7,5,2]=>{{1,2,3,4,5,6,7}}
[5,2,7,6,1,3,4]=>[2,5,1,6,7,4,3]=>[6,3,7,2,1,4,5]=>{{1,2,3,4,5,6,7}}
[5,2,7,6,1,4,3]=>[2,5,1,6,7,3,4]=>[6,3,7,2,1,5,4]=>{{1,5,6},{2,3,4,7}}
[5,2,7,6,3,1,4]=>[2,5,1,3,6,7,4]=>[6,3,7,5,2,1,4]=>{{1,6},{2,3,4,5,7}}
[5,2,7,6,3,4,1]=>[2,5,3,6,7,1,4]=>[6,3,5,2,1,7,4]=>{{1,2,3,4,5,6,7}}
[5,2,7,6,4,1,3]=>[2,5,1,4,6,7,3]=>[6,3,7,4,2,1,5]=>{{1,6},{2,3,5,7},{4}}
[5,2,7,6,4,3,1]=>[2,5,1,3,4,6,7]=>[6,3,7,5,4,2,1]=>{{1,2,3,6,7},{4,5}}
[5,3,1,2,4,6,7]=>[7,6,1,3,5,4,2]=>[1,2,7,5,3,4,6]=>{{1},{2},{3,4,5,6,7}}
[5,3,1,2,4,7,6]=>[6,7,1,3,5,4,2]=>[2,1,7,5,3,4,6]=>{{1,2},{3,4,5,6,7}}
[5,3,1,2,6,4,7]=>[7,1,3,5,4,6,2]=>[1,7,5,3,4,2,6]=>{{1},{2,6,7},{3,4,5}}
[5,3,1,2,6,7,4]=>[6,1,3,5,4,7,2]=>[2,7,5,3,4,1,6]=>{{1,2,6,7},{3,4,5}}
[5,3,1,2,7,4,6]=>[1,3,5,4,7,6,2]=>[7,5,3,4,1,2,6]=>{{1,2,5,6,7},{3},{4}}
[5,3,1,2,7,6,4]=>[1,3,5,4,6,7,2]=>[7,5,3,4,2,1,6]=>{{1,6,7},{2,5},{3},{4}}
[5,3,1,4,2,6,7]=>[7,6,1,3,5,2,4]=>[1,2,7,5,3,6,4]=>{{1},{2},{3,4,5,7},{6}}
[5,3,1,4,2,7,6]=>[6,7,1,3,5,2,4]=>[2,1,7,5,3,6,4]=>{{1,2},{3,4,5,7},{6}}
[5,3,1,4,6,2,7]=>[7,1,3,5,4,2,6]=>[1,7,5,3,4,6,2]=>{{1},{2,7},{3,4,5},{6}}
[5,3,1,4,6,7,2]=>[6,1,3,5,4,2,7]=>[2,7,5,3,4,6,1]=>{{1,2,7},{3,4,5},{6}}
[5,3,1,4,7,2,6]=>[1,3,5,4,2,7,6]=>[7,5,3,4,6,1,2]=>{{1,2,5,6,7},{3},{4}}
[5,3,1,4,7,6,2]=>[1,3,5,4,2,6,7]=>[7,5,3,4,6,2,1]=>{{1,7},{2,5,6},{3},{4}}
[5,3,1,6,2,4,7]=>[7,1,3,5,2,6,4]=>[1,7,5,3,6,2,4]=>{{1},{2,3,4,5,6,7}}
[5,3,1,6,2,7,4]=>[1,3,5,2,6,4,7]=>[7,5,3,6,2,4,1]=>{{1,7},{2,5},{3},{4,6}}
[5,3,1,6,4,2,7]=>[7,1,3,5,2,4,6]=>[1,7,5,3,6,4,2]=>{{1},{2,7},{3,4,5,6}}
[5,3,1,6,4,7,2]=>[1,3,5,4,6,2,7]=>[7,5,3,4,2,6,1]=>{{1,7},{2,5},{3},{4},{6}}
[5,3,1,6,7,2,4]=>[6,1,3,5,2,7,4]=>[2,7,5,3,6,1,4]=>{{1,2,3,4,5,6,7}}
[5,3,1,6,7,4,2]=>[6,1,3,5,2,4,7]=>[2,7,5,3,6,4,1]=>{{1,2,7},{3,4,5,6}}
[5,3,1,7,2,4,6]=>[1,3,5,2,7,6,4]=>[7,5,3,6,1,2,4]=>{{1,2,4,5,6,7},{3}}
[5,3,1,7,2,6,4]=>[1,3,5,2,7,4,6]=>[7,5,3,6,1,4,2]=>{{1,2,5,7},{3},{4,6}}
[5,3,1,7,4,2,6]=>[1,3,5,2,4,7,6]=>[7,5,3,6,4,1,2]=>{{1,2,4,5,6,7},{3}}
[5,3,1,7,4,6,2]=>[1,3,5,4,7,2,6]=>[7,5,3,4,1,6,2]=>{{1,2,5,7},{3},{4},{6}}
[5,3,1,7,6,2,4]=>[1,3,5,2,6,7,4]=>[7,5,3,6,2,1,4]=>{{1,4,6,7},{2,5},{3}}
[5,3,1,7,6,4,2]=>[1,3,5,2,4,6,7]=>[7,5,3,6,4,2,1]=>{{1,7},{2,4,5,6},{3}}
[5,3,2,1,4,6,7]=>[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>{{1},{2},{3,4,6,7},{5}}
[5,3,2,1,4,7,6]=>[6,7,1,2,3,5,4]=>[2,1,7,6,5,3,4]=>{{1,2},{3,4,6,7},{5}}
[5,3,2,1,6,4,7]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>{{1},{2,7},{3,4,5,6}}
[5,3,2,1,6,7,4]=>[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>{{1,2,7},{3,4,5,6}}
[5,3,2,1,7,4,6]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>{{1,2,6,7},{3,4,5}}
[5,3,2,1,7,6,4]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>{{1,7},{2,6},{3,4,5}}
[5,3,2,4,1,6,7]=>[7,6,2,3,5,1,4]=>[1,2,6,5,3,7,4]=>{{1},{2},{3,4,5,6,7}}
[5,3,2,4,1,7,6]=>[6,7,2,3,5,1,4]=>[2,1,6,5,3,7,4]=>{{1,2},{3,4,5,6,7}}
[5,3,2,4,6,1,7]=>[7,2,3,5,4,1,6]=>[1,6,5,3,4,7,2]=>{{1},{2,6,7},{3,4,5}}
[5,3,2,4,6,7,1]=>[6,2,3,5,4,1,7]=>[2,6,5,3,4,7,1]=>{{1,2,6,7},{3,4,5}}
[5,3,2,4,7,1,6]=>[2,3,5,4,1,7,6]=>[6,5,3,4,7,1,2]=>{{1,6},{2,5,7},{3},{4}}
[5,3,2,4,7,6,1]=>[2,3,5,4,1,6,7]=>[6,5,3,4,7,2,1]=>{{1,2,5,6,7},{3},{4}}
[5,3,2,6,1,4,7]=>[7,2,3,5,1,6,4]=>[1,6,5,3,7,2,4]=>{{1},{2,6},{3,4,5,7}}
[5,3,2,6,1,7,4]=>[2,3,5,1,6,4,7]=>[6,5,3,7,2,4,1]=>{{1,4,6,7},{2,5},{3}}
[5,3,2,6,4,1,7]=>[7,2,3,5,1,4,6]=>[1,6,5,3,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,6,4,7,1]=>[2,3,5,4,6,1,7]=>[6,5,3,4,2,7,1]=>{{1,6,7},{2,5},{3},{4}}
[5,3,2,6,7,1,4]=>[6,2,3,5,1,7,4]=>[2,6,5,3,7,1,4]=>{{1,2,6},{3,4,5,7}}
[5,3,2,6,7,4,1]=>[6,2,3,5,1,4,7]=>[2,6,5,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[5,3,2,7,1,4,6]=>[2,3,5,1,7,6,4]=>[6,5,3,7,1,2,4]=>{{1,2,5,6},{3},{4,7}}
[5,3,2,7,1,6,4]=>[2,3,5,1,7,4,6]=>[6,5,3,7,1,4,2]=>{{1,2,4,5,6,7},{3}}
[5,3,2,7,4,1,6]=>[2,3,5,1,4,7,6]=>[6,5,3,7,4,1,2]=>{{1,6},{2,4,5,7},{3}}
[5,3,2,7,4,6,1]=>[2,3,5,4,7,1,6]=>[6,5,3,4,1,7,2]=>{{1,2,5,6,7},{3},{4}}
[5,3,2,7,6,1,4]=>[2,3,5,1,6,7,4]=>[6,5,3,7,2,1,4]=>{{1,6},{2,5},{3},{4,7}}
[5,3,2,7,6,4,1]=>[2,3,5,1,4,6,7]=>[6,5,3,7,4,2,1]=>{{1,2,4,5,6,7},{3}}
[5,3,4,1,2,6,7]=>[7,6,3,5,1,4,2]=>[1,2,5,3,7,4,6]=>{{1},{2},{3,4,5,6,7}}
[5,3,4,1,2,7,6]=>[6,7,3,5,1,4,2]=>[2,1,5,3,7,4,6]=>{{1,2},{3,4,5,6,7}}
[5,3,4,1,6,2,7]=>[7,3,5,1,4,2,6]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,3,4,1,6,7,2]=>[6,3,5,1,4,2,7]=>[2,5,3,7,4,6,1]=>{{1,2,4,5,7},{3},{6}}
[5,3,4,1,7,2,6]=>[3,5,1,4,2,7,6]=>[5,3,7,4,6,1,2]=>{{1,5,6},{2,3,7},{4}}
[5,3,4,1,7,6,2]=>[3,5,1,4,2,6,7]=>[5,3,7,4,6,2,1]=>{{1,2,3,5,6,7},{4}}
[5,3,4,2,1,6,7]=>[7,6,3,5,1,2,4]=>[1,2,5,3,7,6,4]=>{{1},{2},{3,4,5,7},{6}}
[5,3,4,2,1,7,6]=>[6,7,3,5,1,2,4]=>[2,1,5,3,7,6,4]=>{{1,2},{3,4,5,7},{6}}
[5,3,4,2,6,1,7]=>[7,3,5,2,4,1,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,3,4,2,6,7,1]=>[6,3,5,2,4,1,7]=>[2,5,3,6,4,7,1]=>{{1,2,4,5,6,7},{3}}
[5,3,4,2,7,1,6]=>[3,5,2,4,1,7,6]=>[5,3,6,4,7,1,2]=>{{1,2,3,5,6,7},{4}}
[5,3,4,2,7,6,1]=>[3,5,2,4,1,6,7]=>[5,3,6,4,7,2,1]=>{{1,5,7},{2,3,6},{4}}
[5,3,4,6,1,2,7]=>[7,3,5,4,1,6,2]=>[1,5,3,4,7,2,6]=>{{1},{2,5,6,7},{3},{4}}
[5,3,4,6,1,7,2]=>[3,5,4,1,6,2,7]=>[5,3,4,7,2,6,1]=>{{1,2,3,4,5,7},{6}}
[5,3,4,6,2,1,7]=>[7,3,5,4,1,2,6]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>[5,3,4,6,2,7,1]=>{{1,2,3,4,5,6,7}}
[5,3,4,6,7,1,2]=>[6,3,5,4,1,7,2]=>[2,5,3,4,7,1,6]=>{{1,2,5,6,7},{3},{4}}
[5,3,4,6,7,2,1]=>[6,3,5,4,1,2,7]=>[2,5,3,4,7,6,1]=>{{1,2,5,7},{3},{4},{6}}
[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>[5,3,4,7,1,2,6]=>{{1,5},{2,3,4,6,7}}
[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>[5,3,4,7,1,6,2]=>{{1,5},{2,3,4,7},{6}}
[5,3,4,7,2,1,6]=>[3,5,4,1,2,7,6]=>[5,3,4,7,6,1,2]=>{{1,5,6},{2,3,4,7}}
[5,3,4,7,2,6,1]=>[3,5,4,2,7,1,6]=>[5,3,4,6,1,7,2]=>{{1,5},{2,3,4,6,7}}
[5,3,4,7,6,1,2]=>[3,5,4,1,6,7,2]=>[5,3,4,7,2,1,6]=>{{1,2,3,4,5,6,7}}
[5,3,4,7,6,2,1]=>[3,5,4,1,2,6,7]=>[5,3,4,7,6,2,1]=>{{1,2,3,4,5,6,7}}
[5,3,6,1,2,4,7]=>[7,3,5,1,6,4,2]=>[1,5,3,7,2,4,6]=>{{1},{2,5},{3},{4,6,7}}
[5,3,6,1,2,7,4]=>[3,5,1,6,4,7,2]=>[5,3,7,2,4,1,6]=>{{1,2,3,4,5,6,7}}
[5,3,6,1,4,2,7]=>[7,3,5,1,6,2,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[5,3,6,1,4,7,2]=>[3,5,1,6,4,2,7]=>[5,3,7,2,4,6,1]=>{{1,2,3,4,5,7},{6}}
[5,3,6,1,7,2,4]=>[3,5,1,6,2,7,4]=>[5,3,7,2,6,1,4]=>{{1,5,6},{2,3,4,7}}
[5,3,6,1,7,4,2]=>[3,5,1,6,2,4,7]=>[5,3,7,2,6,4,1]=>{{1,2,3,4,5,6,7}}
[5,3,6,2,1,4,7]=>[7,3,5,1,2,6,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[5,3,6,2,1,7,4]=>[3,5,1,2,6,4,7]=>[5,3,7,6,2,4,1]=>{{1,2,3,5,7},{4,6}}
[5,3,6,2,4,1,7]=>[7,3,5,2,6,1,4]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[5,3,6,2,4,7,1]=>[3,5,2,6,4,1,7]=>[5,3,6,2,4,7,1]=>{{1,2,3,4,5,6,7}}
[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>[5,3,6,2,7,1,4]=>{{1,2,3,4,5,6,7}}
[5,3,6,2,7,4,1]=>[3,5,2,6,1,4,7]=>[5,3,6,2,7,4,1]=>{{1,5,7},{2,3,4,6}}
[5,3,6,4,1,2,7]=>[7,3,5,1,4,6,2]=>[1,5,3,7,4,2,6]=>{{1},{2,4,5,6,7},{3}}
[5,3,6,4,1,7,2]=>[3,5,1,4,6,2,7]=>[5,3,7,4,2,6,1]=>{{1,2,3,5,7},{4},{6}}
[5,3,6,4,2,1,7]=>[7,3,5,1,2,4,6]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,3,6,4,2,7,1]=>[3,5,2,4,6,1,7]=>[5,3,6,4,2,7,1]=>{{1,2,3,5,6,7},{4}}
[5,3,6,4,7,1,2]=>[3,5,4,6,1,7,2]=>[5,3,4,2,7,1,6]=>{{1,5,6,7},{2,3,4}}
[5,3,6,4,7,2,1]=>[3,5,4,6,1,2,7]=>[5,3,4,2,7,6,1]=>{{1,5,7},{2,3,4},{6}}
[5,3,6,7,1,2,4]=>[6,3,5,1,7,4,2]=>[2,5,3,7,1,4,6]=>{{1,2,5},{3},{4,6,7}}
[5,3,6,7,1,4,2]=>[6,3,5,1,7,2,4]=>[2,5,3,7,1,6,4]=>{{1,2,5},{3},{4,7},{6}}
[5,3,6,7,2,1,4]=>[6,3,5,1,2,7,4]=>[2,5,3,7,6,1,4]=>{{1,2,5,6},{3},{4,7}}
[5,3,6,7,2,4,1]=>[6,3,5,2,7,1,4]=>[2,5,3,6,1,7,4]=>{{1,2,5},{3},{4,6,7}}
[5,3,6,7,4,1,2]=>[6,3,5,1,4,7,2]=>[2,5,3,7,4,1,6]=>{{1,2,4,5,6,7},{3}}
[5,3,6,7,4,2,1]=>[6,3,5,1,2,4,7]=>[2,5,3,7,6,4,1]=>{{1,2,4,5,6,7},{3}}
[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>[5,3,7,1,2,4,6]=>{{1,2,3,4,5,6,7}}
[5,3,7,1,2,6,4]=>[3,5,1,7,4,6,2]=>[5,3,7,1,4,2,6]=>{{1,4,5},{2,3,6,7}}
[5,3,7,1,4,2,6]=>[3,5,1,7,6,2,4]=>[5,3,7,1,2,6,4]=>{{1,2,3,4,5,7},{6}}
[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>[5,3,7,1,4,6,2]=>{{1,4,5},{2,3,7},{6}}
[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>[5,3,7,1,6,2,4]=>{{1,2,3,4,5,6,7}}
[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>[5,3,7,1,6,4,2]=>{{1,4,5,6},{2,3,7}}
[5,3,7,2,1,4,6]=>[3,5,1,2,7,6,4]=>[5,3,7,6,1,2,4]=>{{1,5},{2,3,4,6,7}}
[5,3,7,2,1,6,4]=>[3,5,1,2,7,4,6]=>[5,3,7,6,1,4,2]=>{{1,5},{2,3,7},{4,6}}
[5,3,7,2,4,1,6]=>[3,5,2,7,6,1,4]=>[5,3,6,1,2,7,4]=>{{1,2,3,4,5,6,7}}
[5,3,7,2,4,6,1]=>[3,5,2,7,4,1,6]=>[5,3,6,1,4,7,2]=>{{1,4,5},{2,3,6,7}}
[5,3,7,2,6,1,4]=>[3,5,2,7,1,6,4]=>[5,3,6,1,7,2,4]=>{{1,4,5,7},{2,3,6}}
[5,3,7,2,6,4,1]=>[3,5,2,7,1,4,6]=>[5,3,6,1,7,4,2]=>{{1,2,3,4,5,6,7}}
[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>[5,3,7,4,1,2,6]=>{{1,5},{2,3,6,7},{4}}
[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>[5,3,7,4,1,6,2]=>{{1,5},{2,3,7},{4},{6}}
[5,3,7,4,2,1,6]=>[3,5,1,2,4,7,6]=>[5,3,7,6,4,1,2]=>{{1,4,5,6},{2,3,7}}
[5,3,7,4,2,6,1]=>[3,5,2,4,7,1,6]=>[5,3,6,4,1,7,2]=>{{1,5},{2,3,6,7},{4}}
[5,3,7,4,6,1,2]=>[3,5,4,7,1,6,2]=>[5,3,4,1,7,2,6]=>{{1,2,3,4,5,6,7}}
[5,3,7,4,6,2,1]=>[3,5,4,7,1,2,6]=>[5,3,4,1,7,6,2]=>{{1,2,3,4,5,7},{6}}
[5,3,7,6,1,2,4]=>[3,5,1,6,7,4,2]=>[5,3,7,2,1,4,6]=>{{1,5},{2,3,4,6,7}}
[5,3,7,6,1,4,2]=>[3,5,1,6,7,2,4]=>[5,3,7,2,1,6,4]=>{{1,5},{2,3,4,7},{6}}
[5,3,7,6,2,1,4]=>[3,5,1,2,6,7,4]=>[5,3,7,6,2,1,4]=>{{1,2,3,4,5,6,7}}
[5,3,7,6,2,4,1]=>[3,5,2,6,7,1,4]=>[5,3,6,2,1,7,4]=>{{1,5},{2,3,4,6,7}}
[5,3,7,6,4,1,2]=>[3,5,1,4,6,7,2]=>[5,3,7,4,2,1,6]=>{{1,2,3,5,6,7},{4}}
[5,3,7,6,4,2,1]=>[3,5,1,2,4,6,7]=>[5,3,7,6,4,2,1]=>{{1,2,3,4,5,6,7}}
[5,4,1,2,3,6,7]=>[7,6,1,4,5,3,2]=>[1,2,7,4,3,5,6]=>{{1},{2},{3,5,6,7},{4}}
[5,4,1,2,3,7,6]=>[6,7,1,4,5,3,2]=>[2,1,7,4,3,5,6]=>{{1,2},{3,5,6,7},{4}}
[5,4,1,2,6,3,7]=>[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>{{1},{2,6,7},{3,4},{5}}
[5,4,1,2,6,7,3]=>[6,1,4,5,3,7,2]=>[2,7,4,3,5,1,6]=>{{1,2,6,7},{3,4},{5}}
[5,4,1,2,7,3,6]=>[1,4,5,3,7,6,2]=>[7,4,3,5,1,2,6]=>{{1,2,4,5,6,7},{3}}
[5,4,1,2,7,6,3]=>[1,4,5,3,6,7,2]=>[7,4,3,5,2,1,6]=>{{1,6,7},{2,4,5},{3}}
[5,4,1,3,2,6,7]=>[7,6,1,4,5,2,3]=>[1,2,7,4,3,6,5]=>{{1},{2},{3,5,7},{4},{6}}
[5,4,1,3,2,7,6]=>[6,7,1,4,5,2,3]=>[2,1,7,4,3,6,5]=>{{1,2},{3,5,7},{4},{6}}
[5,4,1,3,6,2,7]=>[7,1,4,5,3,2,6]=>[1,7,4,3,5,6,2]=>{{1},{2,7},{3,4},{5},{6}}
[5,4,1,3,6,7,2]=>[6,1,4,5,3,2,7]=>[2,7,4,3,5,6,1]=>{{1,2,7},{3,4},{5},{6}}
[5,4,1,3,7,2,6]=>[1,4,5,3,2,7,6]=>[7,4,3,5,6,1,2]=>{{1,2,4,5,6,7},{3}}
[5,4,1,3,7,6,2]=>[1,4,5,3,2,6,7]=>[7,4,3,5,6,2,1]=>{{1,7},{2,4,5,6},{3}}
[5,4,1,6,2,3,7]=>[7,1,4,5,2,6,3]=>[1,7,4,3,6,2,5]=>{{1},{2,5,6,7},{3,4}}
[5,4,1,6,2,7,3]=>[1,4,5,2,6,3,7]=>[7,4,3,6,2,5,1]=>{{1,7},{2,4,5,6},{3}}
[5,4,1,6,3,2,7]=>[7,1,4,5,2,3,6]=>[1,7,4,3,6,5,2]=>{{1},{2,7},{3,4},{5,6}}
[5,4,1,6,3,7,2]=>[1,4,5,3,6,2,7]=>[7,4,3,5,2,6,1]=>{{1,7},{2,4,5},{3},{6}}
[5,4,1,6,7,2,3]=>[6,1,4,5,2,7,3]=>[2,7,4,3,6,1,5]=>{{1,2,5,6,7},{3,4}}
[5,4,1,6,7,3,2]=>[6,1,4,5,2,3,7]=>[2,7,4,3,6,5,1]=>{{1,2,7},{3,4},{5,6}}
[5,4,1,7,2,3,6]=>[1,4,5,2,7,6,3]=>[7,4,3,6,1,2,5]=>{{1,5,7},{2,4,6},{3}}
[5,4,1,7,2,6,3]=>[1,4,5,2,7,3,6]=>[7,4,3,6,1,5,2]=>{{1,2,4,5,6,7},{3}}
[5,4,1,7,3,2,6]=>[1,4,5,2,3,7,6]=>[7,4,3,6,5,1,2]=>{{1,2,4,6,7},{3},{5}}
[5,4,1,7,3,6,2]=>[1,4,5,3,7,2,6]=>[7,4,3,5,1,6,2]=>{{1,2,4,5,7},{3},{6}}
[5,4,1,7,6,2,3]=>[1,4,5,2,6,7,3]=>[7,4,3,6,2,1,5]=>{{1,2,4,5,6,7},{3}}
[5,4,1,7,6,3,2]=>[1,4,5,2,3,6,7]=>[7,4,3,6,5,2,1]=>{{1,7},{2,4,6},{3},{5}}
[5,4,2,1,3,6,7]=>[7,6,1,2,4,5,3]=>[1,2,7,6,4,3,5]=>{{1},{2},{3,4,5,6,7}}
[5,4,2,1,3,7,6]=>[6,7,1,2,4,5,3]=>[2,1,7,6,4,3,5]=>{{1,2},{3,4,5,6,7}}
[5,4,2,1,6,3,7]=>[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>{{1},{2,7},{3,5,6},{4}}
[5,4,2,1,6,7,3]=>[6,1,2,4,5,3,7]=>[2,7,6,4,3,5,1]=>{{1,2,7},{3,5,6},{4}}
[5,4,2,1,7,3,6]=>[1,2,4,5,3,7,6]=>[7,6,4,3,5,1,2]=>{{1,2,6,7},{3,4},{5}}
[5,4,2,1,7,6,3]=>[1,2,4,5,3,6,7]=>[7,6,4,3,5,2,1]=>{{1,7},{2,6},{3,4},{5}}
[5,4,2,3,1,6,7]=>[7,6,2,4,5,1,3]=>[1,2,6,4,3,7,5]=>{{1},{2},{3,5,6,7},{4}}
[5,4,2,3,1,7,6]=>[6,7,2,4,5,1,3]=>[2,1,6,4,3,7,5]=>{{1,2},{3,5,6,7},{4}}
[5,4,2,3,6,1,7]=>[7,2,4,5,3,1,6]=>[1,6,4,3,5,7,2]=>{{1},{2,6,7},{3,4},{5}}
[5,4,2,3,6,7,1]=>[6,2,4,5,3,1,7]=>[2,6,4,3,5,7,1]=>{{1,2,6,7},{3,4},{5}}
[5,4,2,3,7,1,6]=>[2,4,5,3,1,7,6]=>[6,4,3,5,7,1,2]=>{{1,6},{2,4,5,7},{3}}
[5,4,2,3,7,6,1]=>[2,4,5,3,1,6,7]=>[6,4,3,5,7,2,1]=>{{1,2,4,5,6,7},{3}}
[5,4,2,6,1,3,7]=>[7,2,4,5,1,6,3]=>[1,6,4,3,7,2,5]=>{{1},{2,6},{3,4},{5,7}}
[5,4,2,6,1,7,3]=>[2,4,5,1,6,3,7]=>[6,4,3,7,2,5,1]=>{{1,2,4,5,6,7},{3}}
[5,4,2,6,3,1,7]=>[7,2,4,5,1,3,6]=>[1,6,4,3,7,5,2]=>{{1},{2,5,6,7},{3,4}}
[5,4,2,6,3,7,1]=>[2,4,5,3,6,1,7]=>[6,4,3,5,2,7,1]=>{{1,6,7},{2,4,5},{3}}
[5,4,2,6,7,1,3]=>[6,2,4,5,1,7,3]=>[2,6,4,3,7,1,5]=>{{1,2,6},{3,4},{5,7}}
[5,4,2,6,7,3,1]=>[6,2,4,5,1,3,7]=>[2,6,4,3,7,5,1]=>{{1,2,5,6,7},{3,4}}
[5,4,2,7,1,3,6]=>[2,4,5,1,7,6,3]=>[6,4,3,7,1,2,5]=>{{1,2,4,5,6,7},{3}}
[5,4,2,7,1,6,3]=>[2,4,5,1,7,3,6]=>[6,4,3,7,1,5,2]=>{{1,5,6},{2,4,7},{3}}
[5,4,2,7,3,1,6]=>[2,4,5,1,3,7,6]=>[6,4,3,7,5,1,2]=>{{1,6},{2,4,7},{3},{5}}
[5,4,2,7,3,6,1]=>[2,4,5,3,7,1,6]=>[6,4,3,5,1,7,2]=>{{1,2,4,5,6,7},{3}}
[5,4,2,7,6,1,3]=>[2,4,5,1,6,7,3]=>[6,4,3,7,2,1,5]=>{{1,6},{2,4,5,7},{3}}
[5,4,2,7,6,3,1]=>[2,4,5,1,3,6,7]=>[6,4,3,7,5,2,1]=>{{1,2,4,6,7},{3},{5}}
[5,4,3,1,2,6,7]=>[7,6,1,3,4,5,2]=>[1,2,7,5,4,3,6]=>{{1},{2},{3,6,7},{4,5}}
[5,4,3,1,2,7,6]=>[6,7,1,3,4,5,2]=>[2,1,7,5,4,3,6]=>{{1,2},{3,6,7},{4,5}}
[5,4,3,1,6,2,7]=>[7,1,3,4,5,2,6]=>[1,7,5,4,3,6,2]=>{{1},{2,7},{3,5},{4},{6}}
[5,4,3,1,6,7,2]=>[6,1,3,4,5,2,7]=>[2,7,5,4,3,6,1]=>{{1,2,7},{3,5},{4},{6}}
[5,4,3,1,7,2,6]=>[1,3,4,5,2,7,6]=>[7,5,4,3,6,1,2]=>{{1,2,5,6,7},{3,4}}
[5,4,3,1,7,6,2]=>[1,3,4,5,2,6,7]=>[7,5,4,3,6,2,1]=>{{1,7},{2,5,6},{3,4}}
[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>{{1},{2},{3,7},{4,6},{5}}
[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>{{1,2},{3,7},{4,6},{5}}
[5,4,3,2,6,1,7]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>{{1},{2,6,7},{3,5},{4}}
[5,4,3,2,6,7,1]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>{{1,2,6,7},{3,5},{4}}
[5,4,3,2,7,1,6]=>[2,3,4,5,1,7,6]=>[6,5,4,3,7,1,2]=>{{1,6},{2,5,7},{3,4}}
[5,4,3,2,7,6,1]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>{{1,2,5,6,7},{3,4}}
[5,4,3,6,1,2,7]=>[7,3,4,5,1,6,2]=>[1,5,4,3,7,2,6]=>{{1},{2,5,6,7},{3,4}}
[5,4,3,6,1,7,2]=>[3,4,5,1,6,2,7]=>[5,4,3,7,2,6,1]=>{{1,2,4,5,7},{3},{6}}
[5,4,3,6,2,1,7]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>{{1},{2,5,7},{3,4},{6}}
[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>{{1,2,4,5,6,7},{3}}
[5,4,3,6,7,1,2]=>[6,3,4,5,1,7,2]=>[2,5,4,3,7,1,6]=>{{1,2,5,6,7},{3,4}}
[5,4,3,6,7,2,1]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>{{1,2,5,7},{3,4},{6}}
[5,4,3,7,1,2,6]=>[3,4,5,1,7,6,2]=>[5,4,3,7,1,2,6]=>{{1,5},{2,4,6,7},{3}}
[5,4,3,7,1,6,2]=>[3,4,5,1,7,2,6]=>[5,4,3,7,1,6,2]=>{{1,5},{2,4,7},{3},{6}}
[5,4,3,7,2,1,6]=>[3,4,5,1,2,7,6]=>[5,4,3,7,6,1,2]=>{{1,5,6},{2,4,7},{3}}
[5,4,3,7,2,6,1]=>[3,4,5,2,7,1,6]=>[5,4,3,6,1,7,2]=>{{1,5},{2,4,6,7},{3}}
[5,4,3,7,6,1,2]=>[3,4,5,1,6,7,2]=>[5,4,3,7,2,1,6]=>{{1,2,4,5,6,7},{3}}
[5,4,3,7,6,2,1]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>{{1,2,4,5,6,7},{3}}
[5,4,6,1,2,3,7]=>[7,4,5,1,6,3,2]=>[1,4,3,7,2,5,6]=>{{1},{2,4,5,6,7},{3}}
[5,4,6,1,2,7,3]=>[4,5,1,6,3,7,2]=>[4,3,7,2,5,1,6]=>{{1,2,3,4,6,7},{5}}
[5,4,6,1,3,2,7]=>[7,4,5,1,6,2,3]=>[1,4,3,7,2,6,5]=>{{1},{2,4,5,7},{3},{6}}
[5,4,6,1,3,7,2]=>[4,5,1,6,3,2,7]=>[4,3,7,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[5,4,6,1,7,2,3]=>[4,5,1,6,2,7,3]=>[4,3,7,2,6,1,5]=>{{1,2,3,4,5,6,7}}
[5,4,6,1,7,3,2]=>[4,5,1,6,2,3,7]=>[4,3,7,2,6,5,1]=>{{1,2,3,4,7},{5,6}}
[5,4,6,2,1,3,7]=>[7,4,5,1,2,6,3]=>[1,4,3,7,6,2,5]=>{{1},{2,4,5,6,7},{3}}
[5,4,6,2,1,7,3]=>[4,5,1,2,6,3,7]=>[4,3,7,6,2,5,1]=>{{1,2,3,4,5,6,7}}
[5,4,6,2,3,1,7]=>[7,4,5,2,6,1,3]=>[1,4,3,6,2,7,5]=>{{1},{2,4,5,6,7},{3}}
[5,4,6,2,3,7,1]=>[4,5,2,6,3,1,7]=>[4,3,6,2,5,7,1]=>{{1,2,3,4,6,7},{5}}
[5,4,6,2,7,1,3]=>[4,5,2,6,1,7,3]=>[4,3,6,2,7,1,5]=>{{1,2,3,4,6},{5,7}}
[5,4,6,2,7,3,1]=>[4,5,2,6,1,3,7]=>[4,3,6,2,7,5,1]=>{{1,2,3,4,5,6,7}}
[5,4,6,3,1,2,7]=>[7,4,5,1,3,6,2]=>[1,4,3,7,5,2,6]=>{{1},{2,4,6,7},{3},{5}}
[5,4,6,3,1,7,2]=>[4,5,1,3,6,2,7]=>[4,3,7,5,2,6,1]=>{{1,2,3,4,5,7},{6}}
[5,4,6,3,2,1,7]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>{{1},{2,4,7},{3},{5,6}}
[5,4,6,3,2,7,1]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>{{1,2,3,4,5,6,7}}
[5,4,6,3,7,1,2]=>[4,5,3,6,1,7,2]=>[4,3,5,2,7,1,6]=>{{1,2,3,4,5,6,7}}
[5,4,6,3,7,2,1]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>{{1,2,3,4,5,7},{6}}
[5,4,6,7,1,2,3]=>[6,4,5,1,7,3,2]=>[2,4,3,7,1,5,6]=>{{1,2,4,5,6,7},{3}}
[5,4,6,7,1,3,2]=>[6,4,5,1,7,2,3]=>[2,4,3,7,1,6,5]=>{{1,2,4,5,7},{3},{6}}
[5,4,6,7,2,1,3]=>[6,4,5,1,2,7,3]=>[2,4,3,7,6,1,5]=>{{1,2,4,5,6,7},{3}}
[5,4,6,7,2,3,1]=>[6,4,5,2,7,1,3]=>[2,4,3,6,1,7,5]=>{{1,2,4,5,6,7},{3}}
[5,4,6,7,3,1,2]=>[6,4,5,1,3,7,2]=>[2,4,3,7,5,1,6]=>{{1,2,4,6,7},{3},{5}}
[5,4,6,7,3,2,1]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>{{1,2,4,7},{3},{5,6}}
[5,4,7,1,2,3,6]=>[4,5,1,7,6,3,2]=>[4,3,7,1,2,5,6]=>{{1,4},{2,3,5,6,7}}
[5,4,7,1,2,6,3]=>[4,5,1,7,3,6,2]=>[4,3,7,1,5,2,6]=>{{1,4},{2,3,6,7},{5}}
[5,4,7,1,3,2,6]=>[4,5,1,7,6,2,3]=>[4,3,7,1,2,6,5]=>{{1,4},{2,3,5,7},{6}}
[5,4,7,1,3,6,2]=>[4,5,1,7,3,2,6]=>[4,3,7,1,5,6,2]=>{{1,4},{2,3,7},{5},{6}}
[5,4,7,1,6,2,3]=>[4,5,1,7,2,6,3]=>[4,3,7,1,6,2,5]=>{{1,4},{2,3,5,6,7}}
[5,4,7,1,6,3,2]=>[4,5,1,7,2,3,6]=>[4,3,7,1,6,5,2]=>{{1,4},{2,3,7},{5,6}}
[5,4,7,2,1,3,6]=>[4,5,1,2,7,6,3]=>[4,3,7,6,1,2,5]=>{{1,2,3,4,5,6,7}}
[5,4,7,2,1,6,3]=>[4,5,1,2,7,3,6]=>[4,3,7,6,1,5,2]=>{{1,4,5,6},{2,3,7}}
[5,4,7,2,3,1,6]=>[4,5,2,7,6,1,3]=>[4,3,6,1,2,7,5]=>{{1,4},{2,3,5,6,7}}
[5,4,7,2,3,6,1]=>[4,5,2,7,3,1,6]=>[4,3,6,1,5,7,2]=>{{1,4},{2,3,6,7},{5}}
[5,4,7,2,6,1,3]=>[4,5,2,7,1,6,3]=>[4,3,6,1,7,2,5]=>{{1,4},{2,3,6},{5,7}}
[5,4,7,2,6,3,1]=>[4,5,2,7,1,3,6]=>[4,3,6,1,7,5,2]=>{{1,4},{2,3,5,6,7}}
[5,4,7,3,1,2,6]=>[4,5,1,3,7,6,2]=>[4,3,7,5,1,2,6]=>{{1,4,5},{2,3,6,7}}
[5,4,7,3,1,6,2]=>[4,5,1,3,7,2,6]=>[4,3,7,5,1,6,2]=>{{1,4,5},{2,3,7},{6}}
[5,4,7,3,2,1,6]=>[4,5,1,2,3,7,6]=>[4,3,7,6,5,1,2]=>{{1,4,6},{2,3,7},{5}}
[5,4,7,3,2,6,1]=>[4,5,2,3,7,1,6]=>[4,3,6,5,1,7,2]=>{{1,4,5},{2,3,6,7}}
[5,4,7,3,6,1,2]=>[4,5,3,7,1,6,2]=>[4,3,5,1,7,2,6]=>{{1,4},{2,3,5,6,7}}
[5,4,7,3,6,2,1]=>[4,5,3,7,1,2,6]=>[4,3,5,1,7,6,2]=>{{1,4},{2,3,5,7},{6}}
[5,4,7,6,1,2,3]=>[4,5,1,6,7,3,2]=>[4,3,7,2,1,5,6]=>{{1,2,3,4,5,6,7}}
[5,4,7,6,1,3,2]=>[4,5,1,6,7,2,3]=>[4,3,7,2,1,6,5]=>{{1,2,3,4,5,7},{6}}
[5,4,7,6,2,1,3]=>[4,5,1,2,6,7,3]=>[4,3,7,6,2,1,5]=>{{1,4,6},{2,3,5,7}}
[5,4,7,6,2,3,1]=>[4,5,2,6,7,1,3]=>[4,3,6,2,1,7,5]=>{{1,2,3,4,5,6,7}}
[5,4,7,6,3,1,2]=>[4,5,1,3,6,7,2]=>[4,3,7,5,2,1,6]=>{{1,2,3,4,5,6,7}}
[5,4,7,6,3,2,1]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>{{1,2,3,4,6,7},{5}}
[5,6,1,2,3,4,7]=>[7,5,1,6,4,3,2]=>[1,3,7,2,4,5,6]=>{{1},{2,3,4,5,6,7}}
[5,6,1,2,3,7,4]=>[5,1,6,4,7,3,2]=>[3,7,2,4,1,5,6]=>{{1,2,3,5,6,7},{4}}
[5,6,1,2,4,3,7]=>[7,5,1,6,3,4,2]=>[1,3,7,2,5,4,6]=>{{1},{2,3,4,6,7},{5}}
[5,6,1,2,4,7,3]=>[5,1,6,4,3,7,2]=>[3,7,2,4,5,1,6]=>{{1,2,3,6,7},{4},{5}}
[5,6,1,2,7,3,4]=>[5,1,6,3,7,4,2]=>[3,7,2,5,1,4,6]=>{{1,2,3,4,5,6,7}}
[5,6,1,2,7,4,3]=>[5,1,6,3,4,7,2]=>[3,7,2,5,4,1,6]=>{{1,2,3,6,7},{4,5}}
[5,6,1,3,2,4,7]=>[7,5,1,6,4,2,3]=>[1,3,7,2,4,6,5]=>{{1},{2,3,4,5,7},{6}}
[5,6,1,3,2,7,4]=>[5,1,6,4,7,2,3]=>[3,7,2,4,1,6,5]=>{{1,2,3,5,7},{4},{6}}
[5,6,1,3,4,2,7]=>[7,5,1,6,3,2,4]=>[1,3,7,2,5,6,4]=>{{1},{2,3,4,7},{5},{6}}
[5,6,1,3,4,7,2]=>[5,1,6,4,3,2,7]=>[3,7,2,4,5,6,1]=>{{1,2,3,7},{4},{5},{6}}
[5,6,1,3,7,2,4]=>[5,1,6,3,2,7,4]=>[3,7,2,5,6,1,4]=>{{1,2,3,4,5,6,7}}
[5,6,1,3,7,4,2]=>[5,1,6,3,2,4,7]=>[3,7,2,5,6,4,1]=>{{1,2,3,7},{4,5,6}}
[5,6,1,4,2,3,7]=>[7,5,1,6,2,4,3]=>[1,3,7,2,6,4,5]=>{{1},{2,3,4,5,6,7}}
[5,6,1,4,2,7,3]=>[5,1,6,2,4,3,7]=>[3,7,2,6,4,5,1]=>{{1,2,3,7},{4,5,6}}
[5,6,1,4,3,2,7]=>[7,5,1,6,2,3,4]=>[1,3,7,2,6,5,4]=>{{1},{2,3,4,7},{5,6}}
[5,6,1,4,3,7,2]=>[5,1,6,3,4,2,7]=>[3,7,2,5,4,6,1]=>{{1,2,3,7},{4,5},{6}}
[5,6,1,4,7,2,3]=>[5,1,6,4,2,7,3]=>[3,7,2,4,6,1,5]=>{{1,2,3,5,6,7},{4}}
[5,6,1,4,7,3,2]=>[5,1,6,4,2,3,7]=>[3,7,2,4,6,5,1]=>{{1,2,3,7},{4},{5,6}}
[5,6,1,7,2,3,4]=>[5,1,6,2,7,4,3]=>[3,7,2,6,1,4,5]=>{{1,2,3,5,7},{4,6}}
[5,6,1,7,2,4,3]=>[5,1,6,2,7,3,4]=>[3,7,2,6,1,5,4]=>{{1,2,3,4,5,6,7}}
[5,6,1,7,3,2,4]=>[5,1,6,2,3,7,4]=>[3,7,2,6,5,1,4]=>{{1,2,3,4,6,7},{5}}
[5,6,1,7,3,4,2]=>[5,1,6,3,7,2,4]=>[3,7,2,5,1,6,4]=>{{1,2,3,4,5,7},{6}}
[5,6,1,7,4,2,3]=>[5,1,6,2,4,7,3]=>[3,7,2,6,4,1,5]=>{{1,2,3,4,5,6,7}}
[5,6,1,7,4,3,2]=>[5,1,6,2,3,4,7]=>[3,7,2,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[5,6,2,1,3,4,7]=>[7,5,1,2,6,4,3]=>[1,3,7,6,2,4,5]=>{{1},{2,3,5,7},{4,6}}
[5,6,2,1,3,7,4]=>[5,1,2,6,4,7,3]=>[3,7,6,2,4,1,5]=>{{1,3,6},{2,4,5,7}}
[5,6,2,1,4,3,7]=>[7,5,1,2,6,3,4]=>[1,3,7,6,2,5,4]=>{{1},{2,3,4,5,6,7}}
[5,6,2,1,4,7,3]=>[5,1,2,6,4,3,7]=>[3,7,6,2,4,5,1]=>{{1,2,3,4,5,6,7}}
[5,6,2,1,7,3,4]=>[5,1,2,6,3,7,4]=>[3,7,6,2,5,1,4]=>{{1,3,6},{2,4,7},{5}}
[5,6,2,1,7,4,3]=>[5,1,2,6,3,4,7]=>[3,7,6,2,5,4,1]=>{{1,2,3,4,6,7},{5}}
[5,6,2,3,1,4,7]=>[7,5,2,6,4,1,3]=>[1,3,6,2,4,7,5]=>{{1},{2,3,4,5,6,7}}
[5,6,2,3,1,7,4]=>[5,2,6,4,7,1,3]=>[3,6,2,4,1,7,5]=>{{1,2,3,5,6,7},{4}}
[5,6,2,3,4,1,7]=>[7,5,2,6,3,1,4]=>[1,3,6,2,5,7,4]=>{{1},{2,3,4,6,7},{5}}
[5,6,2,3,4,7,1]=>[5,2,6,4,3,1,7]=>[3,6,2,4,5,7,1]=>{{1,2,3,6,7},{4},{5}}
[5,6,2,3,7,1,4]=>[5,2,6,3,1,7,4]=>[3,6,2,5,7,1,4]=>{{1,2,3,6},{4,5,7}}
[5,6,2,3,7,4,1]=>[5,2,6,3,1,4,7]=>[3,6,2,5,7,4,1]=>{{1,2,3,4,5,6,7}}
[5,6,2,4,1,3,7]=>[7,5,2,6,1,4,3]=>[1,3,6,2,7,4,5]=>{{1},{2,3,4,6},{5,7}}
[5,6,2,4,1,7,3]=>[5,2,6,1,4,3,7]=>[3,6,2,7,4,5,1]=>{{1,2,3,4,5,6,7}}
[5,6,2,4,3,1,7]=>[7,5,2,6,1,3,4]=>[1,3,6,2,7,5,4]=>{{1},{2,3,4,5,6,7}}
[5,6,2,4,3,7,1]=>[5,2,6,3,4,1,7]=>[3,6,2,5,4,7,1]=>{{1,2,3,6,7},{4,5}}
[5,6,2,4,7,1,3]=>[5,2,6,4,1,7,3]=>[3,6,2,4,7,1,5]=>{{1,2,3,6},{4},{5,7}}
[5,6,2,4,7,3,1]=>[5,2,6,4,1,3,7]=>[3,6,2,4,7,5,1]=>{{1,2,3,5,6,7},{4}}
[5,6,2,7,1,3,4]=>[5,2,6,1,7,4,3]=>[3,6,2,7,1,4,5]=>{{1,2,3,4,5,6,7}}
[5,6,2,7,1,4,3]=>[5,2,6,1,7,3,4]=>[3,6,2,7,1,5,4]=>{{1,2,3,5,6},{4,7}}
[5,6,2,7,3,1,4]=>[5,2,6,1,3,7,4]=>[3,6,2,7,5,1,4]=>{{1,2,3,6},{4,7},{5}}
[5,6,2,7,3,4,1]=>[5,2,6,3,7,1,4]=>[3,6,2,5,1,7,4]=>{{1,2,3,4,5,6,7}}
[5,6,2,7,4,1,3]=>[5,2,6,1,4,7,3]=>[3,6,2,7,4,1,5]=>{{1,2,3,6},{4,5,7}}
[5,6,2,7,4,3,1]=>[5,2,6,1,3,4,7]=>[3,6,2,7,5,4,1]=>{{1,2,3,4,6,7},{5}}
[5,6,3,1,2,4,7]=>[7,5,1,3,6,4,2]=>[1,3,7,5,2,4,6]=>{{1},{2,3,4,5,6,7}}
[5,6,3,1,2,7,4]=>[5,1,3,6,4,7,2]=>[3,7,5,2,4,1,6]=>{{1,2,3,4,5,6,7}}
[5,6,3,1,4,2,7]=>[7,5,1,3,6,2,4]=>[1,3,7,5,2,6,4]=>{{1},{2,3,4,5,7},{6}}
[5,6,3,1,4,7,2]=>[5,1,3,6,4,2,7]=>[3,7,5,2,4,6,1]=>{{1,2,3,4,5,7},{6}}
[5,6,3,1,7,2,4]=>[5,1,3,6,2,7,4]=>[3,7,5,2,6,1,4]=>{{1,3,5,6},{2,4,7}}
[5,6,3,1,7,4,2]=>[5,1,3,6,2,4,7]=>[3,7,5,2,6,4,1]=>{{1,2,3,4,5,6,7}}
[5,6,3,2,1,4,7]=>[7,5,1,2,3,6,4]=>[1,3,7,6,5,2,4]=>{{1},{2,3,4,6,7},{5}}
[5,6,3,2,1,7,4]=>[5,1,2,3,6,4,7]=>[3,7,6,5,2,4,1]=>{{1,2,3,4,5,6,7}}
[5,6,3,2,4,1,7]=>[7,5,2,3,6,1,4]=>[1,3,6,5,2,7,4]=>{{1},{2,3,4,5,6,7}}
[5,6,3,2,4,7,1]=>[5,2,3,6,4,1,7]=>[3,6,5,2,4,7,1]=>{{1,2,3,4,5,6,7}}
[5,6,3,2,7,1,4]=>[5,2,3,6,1,7,4]=>[3,6,5,2,7,1,4]=>{{1,2,3,4,5,6,7}}
[5,6,3,2,7,4,1]=>[5,2,3,6,1,4,7]=>[3,6,5,2,7,4,1]=>{{1,3,5,7},{2,4,6}}
[5,6,3,4,1,2,7]=>[7,5,3,6,1,4,2]=>[1,3,5,2,7,4,6]=>{{1},{2,3,4,5,6,7}}
[5,6,3,4,1,7,2]=>[5,3,6,1,4,2,7]=>[3,5,2,7,4,6,1]=>{{1,2,3,4,5,7},{6}}
[5,6,3,4,2,1,7]=>[7,5,3,6,1,2,4]=>[1,3,5,2,7,6,4]=>{{1},{2,3,4,5,7},{6}}
[5,6,3,4,2,7,1]=>[5,3,6,2,4,1,7]=>[3,5,2,6,4,7,1]=>{{1,2,3,4,5,6,7}}
[5,6,3,4,7,1,2]=>[5,3,6,4,1,7,2]=>[3,5,2,4,7,1,6]=>{{1,2,3,5,6,7},{4}}
[5,6,3,4,7,2,1]=>[5,3,6,4,1,2,7]=>[3,5,2,4,7,6,1]=>{{1,2,3,5,7},{4},{6}}
[5,6,3,7,1,2,4]=>[5,3,6,1,7,4,2]=>[3,5,2,7,1,4,6]=>{{1,2,3,5},{4,6,7}}
[5,6,3,7,1,4,2]=>[5,3,6,1,7,2,4]=>[3,5,2,7,1,6,4]=>{{1,2,3,5},{4,7},{6}}
[5,6,3,7,2,1,4]=>[5,3,6,1,2,7,4]=>[3,5,2,7,6,1,4]=>{{1,2,3,5,6},{4,7}}
[5,6,3,7,2,4,1]=>[5,3,6,2,7,1,4]=>[3,5,2,6,1,7,4]=>{{1,2,3,5},{4,6,7}}
[5,6,3,7,4,1,2]=>[5,3,6,1,4,7,2]=>[3,5,2,7,4,1,6]=>{{1,2,3,4,5,6,7}}
[5,6,3,7,4,2,1]=>[5,3,6,1,2,4,7]=>[3,5,2,7,6,4,1]=>{{1,2,3,4,5,6,7}}
[5,6,4,1,2,3,7]=>[7,5,1,4,6,3,2]=>[1,3,7,4,2,5,6]=>{{1},{2,3,5,6,7},{4}}
[5,6,4,1,2,7,3]=>[5,1,4,6,3,7,2]=>[3,7,4,2,5,1,6]=>{{1,2,3,4,6,7},{5}}
[5,6,4,1,3,2,7]=>[7,5,1,4,6,2,3]=>[1,3,7,4,2,6,5]=>{{1},{2,3,5,7},{4},{6}}
[5,6,4,1,3,7,2]=>[5,1,4,6,3,2,7]=>[3,7,4,2,5,6,1]=>{{1,2,3,4,7},{5},{6}}
[5,6,4,1,7,2,3]=>[5,1,4,6,2,7,3]=>[3,7,4,2,6,1,5]=>{{1,2,3,4,5,6,7}}
[5,6,4,1,7,3,2]=>[5,1,4,6,2,3,7]=>[3,7,4,2,6,5,1]=>{{1,2,3,4,7},{5,6}}
[5,6,4,2,1,3,7]=>[7,5,1,2,4,6,3]=>[1,3,7,6,4,2,5]=>{{1},{2,3,4,5,6,7}}
[5,6,4,2,1,7,3]=>[5,1,2,4,6,3,7]=>[3,7,6,4,2,5,1]=>{{1,2,3,5,6,7},{4}}
[5,6,4,2,3,1,7]=>[7,5,2,4,6,1,3]=>[1,3,6,4,2,7,5]=>{{1},{2,3,5,6,7},{4}}
[5,6,4,2,3,7,1]=>[5,2,4,6,3,1,7]=>[3,6,4,2,5,7,1]=>{{1,2,3,4,6,7},{5}}
[5,6,4,2,7,1,3]=>[5,2,4,6,1,7,3]=>[3,6,4,2,7,1,5]=>{{1,2,3,4,6},{5,7}}
[5,6,4,2,7,3,1]=>[5,2,4,6,1,3,7]=>[3,6,4,2,7,5,1]=>{{1,2,3,4,5,6,7}}
[5,6,4,3,1,2,7]=>[7,5,1,3,4,6,2]=>[1,3,7,5,4,2,6]=>{{1},{2,3,6,7},{4,5}}
[5,6,4,3,1,7,2]=>[5,1,3,4,6,2,7]=>[3,7,5,4,2,6,1]=>{{1,2,3,5,7},{4},{6}}
[5,6,4,3,2,1,7]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>{{1},{2,3,7},{4,6},{5}}
[5,6,4,3,2,7,1]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>{{1,2,3,5,6,7},{4}}
[5,6,4,3,7,1,2]=>[5,3,4,6,1,7,2]=>[3,5,4,2,7,1,6]=>{{1,2,3,4,5,6,7}}
[5,6,4,3,7,2,1]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>{{1,2,3,4,5,7},{6}}
[5,6,4,7,1,2,3]=>[5,4,6,1,7,3,2]=>[3,4,2,7,1,5,6]=>{{1,2,3,4,5,6,7}}
[5,6,4,7,1,3,2]=>[5,4,6,1,7,2,3]=>[3,4,2,7,1,6,5]=>{{1,2,3,4,5,7},{6}}
[5,6,4,7,2,1,3]=>[5,4,6,1,2,7,3]=>[3,4,2,7,6,1,5]=>{{1,2,3,4,5,6,7}}
[5,6,4,7,2,3,1]=>[5,4,6,2,7,1,3]=>[3,4,2,6,1,7,5]=>{{1,2,3,4,5,6,7}}
[5,6,4,7,3,1,2]=>[5,4,6,1,3,7,2]=>[3,4,2,7,5,1,6]=>{{1,2,3,4,6,7},{5}}
[5,6,4,7,3,2,1]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>{{1,2,3,4,7},{5,6}}
[5,6,7,1,2,3,4]=>[6,5,1,7,4,3,2]=>[2,3,7,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[5,6,7,1,2,4,3]=>[6,5,1,7,3,4,2]=>[2,3,7,1,5,4,6]=>{{1,2,3,4,6,7},{5}}
[5,6,7,1,3,2,4]=>[6,5,1,7,4,2,3]=>[2,3,7,1,4,6,5]=>{{1,2,3,4,5,7},{6}}
[5,6,7,1,3,4,2]=>[6,5,1,7,3,2,4]=>[2,3,7,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[5,6,7,1,4,2,3]=>[6,5,1,7,2,4,3]=>[2,3,7,1,6,4,5]=>{{1,2,3,4,5,6,7}}
[5,6,7,1,4,3,2]=>[6,5,1,7,2,3,4]=>[2,3,7,1,6,5,4]=>{{1,2,3,4,7},{5,6}}
[5,6,7,2,1,3,4]=>[6,5,1,2,7,4,3]=>[2,3,7,6,1,4,5]=>{{1,2,3,5,7},{4,6}}
[5,6,7,2,1,4,3]=>[6,5,1,2,7,3,4]=>[2,3,7,6,1,5,4]=>{{1,2,3,4,5,6,7}}
[5,6,7,2,3,1,4]=>[6,5,2,7,4,1,3]=>[2,3,6,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[5,6,7,2,3,4,1]=>[6,5,2,7,3,1,4]=>[2,3,6,1,5,7,4]=>{{1,2,3,4,6,7},{5}}
[5,6,7,2,4,1,3]=>[6,5,2,7,1,4,3]=>[2,3,6,1,7,4,5]=>{{1,2,3,4,6},{5,7}}
[5,6,7,2,4,3,1]=>[6,5,2,7,1,3,4]=>[2,3,6,1,7,5,4]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,1,2,4]=>[6,5,1,3,7,4,2]=>[2,3,7,5,1,4,6]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,1,4,2]=>[6,5,1,3,7,2,4]=>[2,3,7,5,1,6,4]=>{{1,2,3,4,5,7},{6}}
[5,6,7,3,2,1,4]=>[6,5,1,2,3,7,4]=>[2,3,7,6,5,1,4]=>{{1,2,3,4,6,7},{5}}
[5,6,7,3,2,4,1]=>[6,5,2,3,7,1,4]=>[2,3,6,5,1,7,4]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,4,1,2]=>[6,5,3,7,1,4,2]=>[2,3,5,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[5,6,7,3,4,2,1]=>[6,5,3,7,1,2,4]=>[2,3,5,1,7,6,4]=>{{1,2,3,4,5,7},{6}}
[5,6,7,4,1,2,3]=>[6,5,1,4,7,3,2]=>[2,3,7,4,1,5,6]=>{{1,2,3,5,6,7},{4}}
[5,6,7,4,1,3,2]=>[6,5,1,4,7,2,3]=>[2,3,7,4,1,6,5]=>{{1,2,3,5,7},{4},{6}}
[5,6,7,4,2,1,3]=>[6,5,1,2,4,7,3]=>[2,3,7,6,4,1,5]=>{{1,2,3,4,5,6,7}}
[5,6,7,4,2,3,1]=>[6,5,2,4,7,1,3]=>[2,3,6,4,1,7,5]=>{{1,2,3,5,6,7},{4}}
[5,6,7,4,3,1,2]=>[6,5,1,3,4,7,2]=>[2,3,7,5,4,1,6]=>{{1,2,3,6,7},{4,5}}
[5,6,7,4,3,2,1]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>{{1,2,3,7},{4,6},{5}}
[5,7,1,2,3,4,6]=>[5,1,7,6,4,3,2]=>[3,7,1,2,4,5,6]=>{{1,3},{2,4,5,6,7}}
[5,7,1,2,3,6,4]=>[5,1,7,4,6,3,2]=>[3,7,1,4,2,5,6]=>{{1,3},{2,5,6,7},{4}}
[5,7,1,2,4,3,6]=>[5,1,7,6,3,4,2]=>[3,7,1,2,5,4,6]=>{{1,3},{2,4,6,7},{5}}
[5,7,1,2,4,6,3]=>[5,1,7,4,3,6,2]=>[3,7,1,4,5,2,6]=>{{1,3},{2,6,7},{4},{5}}
[5,7,1,2,6,3,4]=>[5,1,7,3,6,4,2]=>[3,7,1,5,2,4,6]=>{{1,3},{2,4,5,6,7}}
[5,7,1,2,6,4,3]=>[5,1,7,3,4,6,2]=>[3,7,1,5,4,2,6]=>{{1,3},{2,6,7},{4,5}}
[5,7,1,3,2,4,6]=>[5,1,7,6,4,2,3]=>[3,7,1,2,4,6,5]=>{{1,3},{2,4,5,7},{6}}
[5,7,1,3,2,6,4]=>[5,1,7,4,6,2,3]=>[3,7,1,4,2,6,5]=>{{1,3},{2,5,7},{4},{6}}
[5,7,1,3,4,2,6]=>[5,1,7,6,3,2,4]=>[3,7,1,2,5,6,4]=>{{1,3},{2,4,7},{5},{6}}
[5,7,1,3,4,6,2]=>[5,1,7,4,3,2,6]=>[3,7,1,4,5,6,2]=>{{1,3},{2,7},{4},{5},{6}}
[5,7,1,3,6,2,4]=>[5,1,7,3,2,6,4]=>[3,7,1,5,6,2,4]=>{{1,3},{2,4,5,6,7}}
[5,7,1,3,6,4,2]=>[5,1,7,3,2,4,6]=>[3,7,1,5,6,4,2]=>{{1,3},{2,7},{4,5,6}}
[5,7,1,4,2,3,6]=>[5,1,7,6,2,4,3]=>[3,7,1,2,6,4,5]=>{{1,3},{2,4,5,6,7}}
[5,7,1,4,2,6,3]=>[5,1,7,2,4,3,6]=>[3,7,1,6,4,5,2]=>{{1,3},{2,7},{4,5,6}}
[5,7,1,4,3,2,6]=>[5,1,7,6,2,3,4]=>[3,7,1,2,6,5,4]=>{{1,3},{2,4,7},{5,6}}
[5,7,1,4,3,6,2]=>[5,1,7,3,4,2,6]=>[3,7,1,5,4,6,2]=>{{1,3},{2,7},{4,5},{6}}
[5,7,1,4,6,2,3]=>[5,1,7,4,2,6,3]=>[3,7,1,4,6,2,5]=>{{1,3},{2,5,6,7},{4}}
[5,7,1,4,6,3,2]=>[5,1,7,4,2,3,6]=>[3,7,1,4,6,5,2]=>{{1,3},{2,7},{4},{5,6}}
[5,7,1,6,2,3,4]=>[5,1,7,2,6,4,3]=>[3,7,1,6,2,4,5]=>{{1,3},{2,5,7},{4,6}}
[5,7,1,6,2,4,3]=>[5,1,7,2,6,3,4]=>[3,7,1,6,2,5,4]=>{{1,3},{2,4,5,6,7}}
[5,7,1,6,3,2,4]=>[5,1,7,2,3,6,4]=>[3,7,1,6,5,2,4]=>{{1,3},{2,4,6,7},{5}}
[5,7,1,6,3,4,2]=>[5,1,7,3,6,2,4]=>[3,7,1,5,2,6,4]=>{{1,3},{2,4,5,7},{6}}
[5,7,1,6,4,2,3]=>[5,1,7,2,4,6,3]=>[3,7,1,6,4,2,5]=>{{1,3},{2,4,5,6,7}}
[5,7,1,6,4,3,2]=>[5,1,7,2,3,4,6]=>[3,7,1,6,5,4,2]=>{{1,3},{2,7},{4,6},{5}}
[5,7,2,1,3,4,6]=>[5,1,2,7,6,4,3]=>[3,7,6,1,2,4,5]=>{{1,3,4,6},{2,5,7}}
[5,7,2,1,3,6,4]=>[5,1,2,7,4,6,3]=>[3,7,6,1,4,2,5]=>{{1,2,3,4,5,6,7}}
[5,7,2,1,4,3,6]=>[5,1,2,7,6,3,4]=>[3,7,6,1,2,5,4]=>{{1,2,3,4,5,6,7}}
[5,7,2,1,4,6,3]=>[5,1,2,7,4,3,6]=>[3,7,6,1,4,5,2]=>{{1,3,4,5,6},{2,7}}
[5,7,2,1,6,3,4]=>[5,1,2,7,3,6,4]=>[3,7,6,1,5,2,4]=>{{1,2,3,4,6,7},{5}}
[5,7,2,1,6,4,3]=>[5,1,2,7,3,4,6]=>[3,7,6,1,5,4,2]=>{{1,3,4,6},{2,7},{5}}
[5,7,2,3,1,4,6]=>[5,2,7,6,4,1,3]=>[3,6,1,2,4,7,5]=>{{1,3},{2,4,5,6,7}}
[5,7,2,3,1,6,4]=>[5,2,7,4,6,1,3]=>[3,6,1,4,2,7,5]=>{{1,3},{2,5,6,7},{4}}
[5,7,2,3,4,1,6]=>[5,2,7,6,3,1,4]=>[3,6,1,2,5,7,4]=>{{1,3},{2,4,6,7},{5}}
[5,7,2,3,4,6,1]=>[5,2,7,4,3,1,6]=>[3,6,1,4,5,7,2]=>{{1,3},{2,6,7},{4},{5}}
[5,7,2,3,6,1,4]=>[5,2,7,3,1,6,4]=>[3,6,1,5,7,2,4]=>{{1,3},{2,6},{4,5,7}}
[5,7,2,3,6,4,1]=>[5,2,7,3,1,4,6]=>[3,6,1,5,7,4,2]=>{{1,3},{2,4,5,6,7}}
[5,7,2,4,1,3,6]=>[5,2,7,6,1,4,3]=>[3,6,1,2,7,4,5]=>{{1,3},{2,4,6},{5,7}}
[5,7,2,4,1,6,3]=>[5,2,7,1,4,3,6]=>[3,6,1,7,4,5,2]=>{{1,3},{2,4,5,6,7}}
[5,7,2,4,3,1,6]=>[5,2,7,6,1,3,4]=>[3,6,1,2,7,5,4]=>{{1,3},{2,4,5,6,7}}
[5,7,2,4,3,6,1]=>[5,2,7,3,4,1,6]=>[3,6,1,5,4,7,2]=>{{1,3},{2,6,7},{4,5}}
[5,7,2,4,6,1,3]=>[5,2,7,4,1,6,3]=>[3,6,1,4,7,2,5]=>{{1,3},{2,6},{4},{5,7}}
[5,7,2,4,6,3,1]=>[5,2,7,4,1,3,6]=>[3,6,1,4,7,5,2]=>{{1,3},{2,5,6,7},{4}}
[5,7,2,6,1,3,4]=>[5,2,7,1,6,4,3]=>[3,6,1,7,2,4,5]=>{{1,3},{2,4,5,6,7}}
[5,7,2,6,1,4,3]=>[5,2,7,1,6,3,4]=>[3,6,1,7,2,5,4]=>{{1,3},{2,5,6},{4,7}}
[5,7,2,6,3,1,4]=>[5,2,7,1,3,6,4]=>[3,6,1,7,5,2,4]=>{{1,3},{2,6},{4,7},{5}}
[5,7,2,6,3,4,1]=>[5,2,7,3,6,1,4]=>[3,6,1,5,2,7,4]=>{{1,3},{2,4,5,6,7}}
[5,7,2,6,4,1,3]=>[5,2,7,1,4,6,3]=>[3,6,1,7,4,2,5]=>{{1,3},{2,6},{4,5,7}}
[5,7,2,6,4,3,1]=>[5,2,7,1,3,4,6]=>[3,6,1,7,5,4,2]=>{{1,3},{2,4,6,7},{5}}
[5,7,3,1,2,4,6]=>[5,1,3,7,6,4,2]=>[3,7,5,1,2,4,6]=>{{1,2,3,4,5,6,7}}
[5,7,3,1,2,6,4]=>[5,1,3,7,4,6,2]=>[3,7,5,1,4,2,6]=>{{1,3,4,5},{2,6,7}}
[5,7,3,1,4,2,6]=>[5,1,3,7,6,2,4]=>[3,7,5,1,2,6,4]=>{{1,2,3,4,5,7},{6}}
[5,7,3,1,4,6,2]=>[5,1,3,7,4,2,6]=>[3,7,5,1,4,6,2]=>{{1,3,4,5},{2,7},{6}}
[5,7,3,1,6,2,4]=>[5,1,3,7,2,6,4]=>[3,7,5,1,6,2,4]=>{{1,2,3,4,5,6,7}}
[5,7,3,1,6,4,2]=>[5,1,3,7,2,4,6]=>[3,7,5,1,6,4,2]=>{{1,3,4,5,6},{2,7}}
[5,7,3,2,1,4,6]=>[5,1,2,3,7,6,4]=>[3,7,6,5,1,2,4]=>{{1,2,3,4,5,6,7}}
[5,7,3,2,1,6,4]=>[5,1,2,3,7,4,6]=>[3,7,6,5,1,4,2]=>{{1,3,4,5,6},{2,7}}
[5,7,3,2,4,1,6]=>[5,2,3,7,6,1,4]=>[3,6,5,1,2,7,4]=>{{1,2,3,4,5,6,7}}
[5,7,3,2,4,6,1]=>[5,2,3,7,4,1,6]=>[3,6,5,1,4,7,2]=>{{1,3,4,5},{2,6,7}}
[5,7,3,2,6,1,4]=>[5,2,3,7,1,6,4]=>[3,6,5,1,7,2,4]=>{{1,3,4,5,7},{2,6}}
[5,7,3,2,6,4,1]=>[5,2,3,7,1,4,6]=>[3,6,5,1,7,4,2]=>{{1,2,3,4,5,6,7}}
[5,7,3,4,1,2,6]=>[5,3,7,6,1,4,2]=>[3,5,1,2,7,4,6]=>{{1,3},{2,4,5,6,7}}
[5,7,3,4,1,6,2]=>[5,3,7,1,4,2,6]=>[3,5,1,7,4,6,2]=>{{1,3},{2,4,5,7},{6}}
[5,7,3,4,2,1,6]=>[5,3,7,6,1,2,4]=>[3,5,1,2,7,6,4]=>{{1,3},{2,4,5,7},{6}}
[5,7,3,4,2,6,1]=>[5,3,7,2,4,1,6]=>[3,5,1,6,4,7,2]=>{{1,3},{2,4,5,6,7}}
[5,7,3,4,6,1,2]=>[5,3,7,4,1,6,2]=>[3,5,1,4,7,2,6]=>{{1,3},{2,5,6,7},{4}}
[5,7,3,4,6,2,1]=>[5,3,7,4,1,2,6]=>[3,5,1,4,7,6,2]=>{{1,3},{2,5,7},{4},{6}}
[5,7,3,6,1,2,4]=>[5,3,7,1,6,4,2]=>[3,5,1,7,2,4,6]=>{{1,3},{2,5},{4,6,7}}
[5,7,3,6,1,4,2]=>[5,3,7,1,6,2,4]=>[3,5,1,7,2,6,4]=>{{1,3},{2,5},{4,7},{6}}
[5,7,3,6,2,1,4]=>[5,3,7,1,2,6,4]=>[3,5,1,7,6,2,4]=>{{1,3},{2,5,6},{4,7}}
[5,7,3,6,2,4,1]=>[5,3,7,2,6,1,4]=>[3,5,1,6,2,7,4]=>{{1,3},{2,5},{4,6,7}}
[5,7,3,6,4,1,2]=>[5,3,7,1,4,6,2]=>[3,5,1,7,4,2,6]=>{{1,3},{2,4,5,6,7}}
[5,7,3,6,4,2,1]=>[5,3,7,1,2,4,6]=>[3,5,1,7,6,4,2]=>{{1,3},{2,4,5,6,7}}
[5,7,4,1,2,3,6]=>[5,1,4,7,6,3,2]=>[3,7,4,1,2,5,6]=>{{1,3,4},{2,5,6,7}}
[5,7,4,1,2,6,3]=>[5,1,4,7,3,6,2]=>[3,7,4,1,5,2,6]=>{{1,3,4},{2,6,7},{5}}
[5,7,4,1,3,2,6]=>[5,1,4,7,6,2,3]=>[3,7,4,1,2,6,5]=>{{1,3,4},{2,5,7},{6}}
[5,7,4,1,3,6,2]=>[5,1,4,7,3,2,6]=>[3,7,4,1,5,6,2]=>{{1,3,4},{2,7},{5},{6}}
[5,7,4,1,6,2,3]=>[5,1,4,7,2,6,3]=>[3,7,4,1,6,2,5]=>{{1,3,4},{2,5,6,7}}
[5,7,4,1,6,3,2]=>[5,1,4,7,2,3,6]=>[3,7,4,1,6,5,2]=>{{1,3,4},{2,7},{5,6}}
[5,7,4,2,1,3,6]=>[5,1,2,4,7,6,3]=>[3,7,6,4,1,2,5]=>{{1,2,3,5,6,7},{4}}
[5,7,4,2,1,6,3]=>[5,1,2,4,7,3,6]=>[3,7,6,4,1,5,2]=>{{1,3,5,6},{2,7},{4}}
[5,7,4,2,3,1,6]=>[5,2,4,7,6,1,3]=>[3,6,4,1,2,7,5]=>{{1,3,4},{2,5,6,7}}
[5,7,4,2,3,6,1]=>[5,2,4,7,3,1,6]=>[3,6,4,1,5,7,2]=>{{1,3,4},{2,6,7},{5}}
[5,7,4,2,6,1,3]=>[5,2,4,7,1,6,3]=>[3,6,4,1,7,2,5]=>{{1,3,4},{2,6},{5,7}}
[5,7,4,2,6,3,1]=>[5,2,4,7,1,3,6]=>[3,6,4,1,7,5,2]=>{{1,3,4},{2,5,6,7}}
[5,7,4,3,1,2,6]=>[5,1,3,4,7,6,2]=>[3,7,5,4,1,2,6]=>{{1,3,5},{2,6,7},{4}}
[5,7,4,3,1,6,2]=>[5,1,3,4,7,2,6]=>[3,7,5,4,1,6,2]=>{{1,3,5},{2,7},{4},{6}}
[5,7,4,3,2,1,6]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>{{1,3,6},{2,7},{4,5}}
[5,7,4,3,2,6,1]=>[5,2,3,4,7,1,6]=>[3,6,5,4,1,7,2]=>{{1,3,5},{2,6,7},{4}}
[5,7,4,3,6,1,2]=>[5,3,4,7,1,6,2]=>[3,5,4,1,7,2,6]=>{{1,3,4},{2,5,6,7}}
[5,7,4,3,6,2,1]=>[5,3,4,7,1,2,6]=>[3,5,4,1,7,6,2]=>{{1,3,4},{2,5,7},{6}}
[5,7,4,6,1,2,3]=>[5,4,7,1,6,3,2]=>[3,4,1,7,2,5,6]=>{{1,3},{2,4,5,6,7}}
[5,7,4,6,1,3,2]=>[5,4,7,1,6,2,3]=>[3,4,1,7,2,6,5]=>{{1,3},{2,4,5,7},{6}}
[5,7,4,6,2,1,3]=>[5,4,7,1,2,6,3]=>[3,4,1,7,6,2,5]=>{{1,3},{2,4,5,6,7}}
[5,7,4,6,2,3,1]=>[5,4,7,2,6,1,3]=>[3,4,1,6,2,7,5]=>{{1,3},{2,4,5,6,7}}
[5,7,4,6,3,1,2]=>[5,4,7,1,3,6,2]=>[3,4,1,7,5,2,6]=>{{1,3},{2,4,6,7},{5}}
[5,7,4,6,3,2,1]=>[5,4,7,1,2,3,6]=>[3,4,1,7,6,5,2]=>{{1,3},{2,4,7},{5,6}}
[5,7,6,1,2,3,4]=>[5,1,6,7,4,3,2]=>[3,7,2,1,4,5,6]=>{{1,2,3,4,5,6,7}}
[5,7,6,1,2,4,3]=>[5,1,6,7,3,4,2]=>[3,7,2,1,5,4,6]=>{{1,2,3,4,6,7},{5}}
[5,7,6,1,3,2,4]=>[5,1,6,7,4,2,3]=>[3,7,2,1,4,6,5]=>{{1,2,3,4,5,7},{6}}
[5,7,6,1,3,4,2]=>[5,1,6,7,3,2,4]=>[3,7,2,1,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[5,7,6,1,4,2,3]=>[5,1,6,7,2,4,3]=>[3,7,2,1,6,4,5]=>{{1,2,3,4,5,6,7}}
[5,7,6,1,4,3,2]=>[5,1,6,7,2,3,4]=>[3,7,2,1,6,5,4]=>{{1,2,3,4,7},{5,6}}
[5,7,6,2,1,3,4]=>[5,1,2,6,7,4,3]=>[3,7,6,2,1,4,5]=>{{1,2,3,4,5,6,7}}
[5,7,6,2,1,4,3]=>[5,1,2,6,7,3,4]=>[3,7,6,2,1,5,4]=>{{1,3,5,6},{2,4,7}}
[5,7,6,2,3,1,4]=>[5,2,6,7,4,1,3]=>[3,6,2,1,4,7,5]=>{{1,2,3,4,5,6,7}}
[5,7,6,2,3,4,1]=>[5,2,6,7,3,1,4]=>[3,6,2,1,5,7,4]=>{{1,2,3,4,6,7},{5}}
[5,7,6,2,4,1,3]=>[5,2,6,7,1,4,3]=>[3,6,2,1,7,4,5]=>{{1,2,3,4,6},{5,7}}
[5,7,6,2,4,3,1]=>[5,2,6,7,1,3,4]=>[3,6,2,1,7,5,4]=>{{1,2,3,4,5,6,7}}
[5,7,6,3,1,2,4]=>[5,1,3,6,7,4,2]=>[3,7,5,2,1,4,6]=>{{1,3,5},{2,4,6,7}}
[5,7,6,3,1,4,2]=>[5,1,3,6,7,2,4]=>[3,7,5,2,1,6,4]=>{{1,3,5},{2,4,7},{6}}
[5,7,6,3,2,1,4]=>[5,1,2,3,6,7,4]=>[3,7,6,5,2,1,4]=>{{1,3,6},{2,4,5,7}}
[5,7,6,3,2,4,1]=>[5,2,3,6,7,1,4]=>[3,6,5,2,1,7,4]=>{{1,3,5},{2,4,6,7}}
[5,7,6,3,4,1,2]=>[5,3,6,7,1,4,2]=>[3,5,2,1,7,4,6]=>{{1,2,3,4,5,6,7}}
[5,7,6,3,4,2,1]=>[5,3,6,7,1,2,4]=>[3,5,2,1,7,6,4]=>{{1,2,3,4,5,7},{6}}
[5,7,6,4,1,2,3]=>[5,1,4,6,7,3,2]=>[3,7,4,2,1,5,6]=>{{1,2,3,4,5,6,7}}
[5,7,6,4,1,3,2]=>[5,1,4,6,7,2,3]=>[3,7,4,2,1,6,5]=>{{1,2,3,4,5,7},{6}}
[5,7,6,4,2,1,3]=>[5,1,2,4,6,7,3]=>[3,7,6,4,2,1,5]=>{{1,3,6},{2,5,7},{4}}
[5,7,6,4,2,3,1]=>[5,2,4,6,7,1,3]=>[3,6,4,2,1,7,5]=>{{1,2,3,4,5,6,7}}
[5,7,6,4,3,1,2]=>[5,1,3,4,6,7,2]=>[3,7,5,4,2,1,6]=>{{1,2,3,5,6,7},{4}}
[5,7,6,4,3,2,1]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>{{1,2,3,6,7},{4,5}}
[6,1,2,3,4,5,7]=>[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>{{1},{2,3,4,5,6,7}}
[6,1,2,3,4,7,5]=>[1,6,5,7,4,3,2]=>[7,2,3,1,4,5,6]=>{{1,4,5,6,7},{2},{3}}
[6,1,2,3,5,4,7]=>[7,1,6,4,5,3,2]=>[1,7,2,4,3,5,6]=>{{1},{2,3,5,6,7},{4}}
[6,1,2,3,5,7,4]=>[1,6,5,4,7,3,2]=>[7,2,3,4,1,5,6]=>{{1,5,6,7},{2},{3},{4}}
[6,1,2,3,7,4,5]=>[1,6,4,7,5,3,2]=>[7,2,4,1,3,5,6]=>{{1,3,4,5,6,7},{2}}
[6,1,2,3,7,5,4]=>[1,6,4,5,7,3,2]=>[7,2,4,3,1,5,6]=>{{1,5,6,7},{2},{3,4}}
[6,1,2,4,3,5,7]=>[7,1,6,5,3,4,2]=>[1,7,2,3,5,4,6]=>{{1},{2,3,4,6,7},{5}}
[6,1,2,4,3,7,5]=>[1,6,5,7,3,4,2]=>[7,2,3,1,5,4,6]=>{{1,4,6,7},{2},{3},{5}}
[6,1,2,4,5,3,7]=>[7,1,6,4,3,5,2]=>[1,7,2,4,5,3,6]=>{{1},{2,3,6,7},{4},{5}}
[6,1,2,4,5,7,3]=>[1,6,5,4,3,7,2]=>[7,2,3,4,5,1,6]=>{{1,6,7},{2},{3},{4},{5}}
[6,1,2,4,7,3,5]=>[1,6,4,3,7,5,2]=>[7,2,4,5,1,3,6]=>{{1,3,4,5,6,7},{2}}
[6,1,2,4,7,5,3]=>[1,6,4,3,5,7,2]=>[7,2,4,5,3,1,6]=>{{1,6,7},{2},{3,4,5}}
[6,1,2,5,3,4,7]=>[7,1,6,3,5,4,2]=>[1,7,2,5,3,4,6]=>{{1},{2,3,4,5,6,7}}
[6,1,2,5,3,7,4]=>[1,6,3,5,4,7,2]=>[7,2,5,3,4,1,6]=>{{1,6,7},{2},{3,4,5}}
[6,1,2,5,4,3,7]=>[7,1,6,3,4,5,2]=>[1,7,2,5,4,3,6]=>{{1},{2,3,6,7},{4,5}}
[6,1,2,5,4,7,3]=>[1,6,4,5,3,7,2]=>[7,2,4,3,5,1,6]=>{{1,6,7},{2},{3,4},{5}}
[6,1,2,5,7,3,4]=>[1,6,5,3,7,4,2]=>[7,2,3,5,1,4,6]=>{{1,4,5,6,7},{2},{3}}
[6,1,2,5,7,4,3]=>[1,6,5,3,4,7,2]=>[7,2,3,5,4,1,6]=>{{1,6,7},{2},{3},{4,5}}
[6,1,2,7,3,4,5]=>[1,6,3,7,5,4,2]=>[7,2,5,1,3,4,6]=>{{1,4,6,7},{2},{3,5}}
[6,1,2,7,3,5,4]=>[1,6,3,7,4,5,2]=>[7,2,5,1,4,3,6]=>{{1,3,4,5,6,7},{2}}
[6,1,2,7,4,3,5]=>[1,6,3,4,7,5,2]=>[7,2,5,4,1,3,6]=>{{1,3,5,6,7},{2},{4}}
[6,1,2,7,4,5,3]=>[1,6,4,7,3,5,2]=>[7,2,4,1,5,3,6]=>{{1,3,4,6,7},{2},{5}}
[6,1,2,7,5,3,4]=>[1,6,3,5,7,4,2]=>[7,2,5,3,1,4,6]=>{{1,3,4,5,6,7},{2}}
[6,1,2,7,5,4,3]=>[1,6,3,4,5,7,2]=>[7,2,5,4,3,1,6]=>{{1,6,7},{2},{3,5},{4}}
[6,1,3,2,4,5,7]=>[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>{{1},{2,3,4,5,7},{6}}
[6,1,3,2,4,7,5]=>[1,6,5,7,4,2,3]=>[7,2,3,1,4,6,5]=>{{1,4,5,7},{2},{3},{6}}
[6,1,3,2,5,4,7]=>[7,1,6,4,5,2,3]=>[1,7,2,4,3,6,5]=>{{1},{2,3,5,7},{4},{6}}
[6,1,3,2,5,7,4]=>[1,6,5,4,7,2,3]=>[7,2,3,4,1,6,5]=>{{1,5,7},{2},{3},{4},{6}}
[6,1,3,2,7,4,5]=>[1,6,4,7,5,2,3]=>[7,2,4,1,3,6,5]=>{{1,3,4,5,7},{2},{6}}
[6,1,3,2,7,5,4]=>[1,6,4,5,7,2,3]=>[7,2,4,3,1,6,5]=>{{1,5,7},{2},{3,4},{6}}
[6,1,3,4,2,5,7]=>[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>{{1},{2,3,4,7},{5},{6}}
[6,1,3,4,2,7,5]=>[1,6,5,7,3,2,4]=>[7,2,3,1,5,6,4]=>{{1,4,7},{2},{3},{5},{6}}
[6,1,3,4,5,2,7]=>[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>{{1},{2,3,7},{4},{5},{6}}
[6,1,3,4,5,7,2]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>{{1,7},{2},{3},{4},{5},{6}}
[6,1,3,4,7,2,5]=>[1,6,4,3,2,7,5]=>[7,2,4,5,6,1,3]=>{{1,3,4,5,6,7},{2}}
[6,1,3,4,7,5,2]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>{{1,7},{2},{3,4,5,6}}
[6,1,3,5,2,4,7]=>[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>{{1},{2,3,4,5,6,7}}
[6,1,3,5,2,7,4]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>{{1,7},{2},{3,5},{4,6}}
[6,1,3,5,4,2,7]=>[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>{{1},{2,3,7},{4,5,6}}
[6,1,3,5,4,7,2]=>[1,6,4,5,3,2,7]=>[7,2,4,3,5,6,1]=>{{1,7},{2},{3,4},{5},{6}}
[6,1,3,5,7,2,4]=>[1,6,5,3,2,7,4]=>[7,2,3,5,6,1,4]=>{{1,4,5,6,7},{2},{3}}
[6,1,3,5,7,4,2]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>{{1,7},{2},{3},{4,5,6}}
[6,1,3,7,2,4,5]=>[1,6,3,2,7,5,4]=>[7,2,5,6,1,3,4]=>{{1,3,4,5,6,7},{2}}
[6,1,3,7,2,5,4]=>[1,6,3,2,7,4,5]=>[7,2,5,6,1,4,3]=>{{1,3,5,7},{2},{4,6}}
[6,1,3,7,4,2,5]=>[1,6,3,2,4,7,5]=>[7,2,5,6,4,1,3]=>{{1,3,4,5,6,7},{2}}
[6,1,3,7,4,5,2]=>[1,6,4,7,3,2,5]=>[7,2,4,1,5,6,3]=>{{1,3,4,7},{2},{5},{6}}
[6,1,3,7,5,2,4]=>[1,6,3,2,5,7,4]=>[7,2,5,6,3,1,4]=>{{1,4,6,7},{2},{3,5}}
[6,1,3,7,5,4,2]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>{{1,7},{2},{3,4,5,6}}
[6,1,4,2,3,5,7]=>[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>{{1},{2,3,4,5,6,7}}
[6,1,4,2,3,7,5]=>[1,6,5,7,2,4,3]=>[7,2,3,1,6,4,5]=>{{1,4,5,6,7},{2},{3}}
[6,1,4,2,5,3,7]=>[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>{{1},{2,3,7},{4,5,6}}
[6,1,4,2,5,7,3]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>{{1,7},{2},{3},{4,5,6}}
[6,1,4,2,7,3,5]=>[1,6,2,4,3,7,5]=>[7,2,6,4,5,1,3]=>{{1,3,6,7},{2},{4},{5}}
[6,1,4,2,7,5,3]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>{{1,7},{2},{3,6},{4},{5}}
[6,1,4,3,2,5,7]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>{{1},{2,3,4,7},{5,6}}
[6,1,4,3,2,7,5]=>[1,6,5,7,2,3,4]=>[7,2,3,1,6,5,4]=>{{1,4,7},{2},{3},{5,6}}
[6,1,4,3,5,2,7]=>[7,1,6,3,4,2,5]=>[1,7,2,5,4,6,3]=>{{1},{2,3,7},{4,5},{6}}
[6,1,4,3,5,7,2]=>[1,6,5,3,4,2,7]=>[7,2,3,5,4,6,1]=>{{1,7},{2},{3},{4,5},{6}}
[6,1,4,3,7,2,5]=>[1,6,3,4,2,7,5]=>[7,2,5,4,6,1,3]=>{{1,3,5,6,7},{2},{4}}
[6,1,4,3,7,5,2]=>[1,6,3,4,2,5,7]=>[7,2,5,4,6,3,1]=>{{1,7},{2},{3,5,6},{4}}
[6,1,4,5,2,3,7]=>[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>{{1},{2,3,5,6,7},{4}}
[6,1,4,5,2,7,3]=>[1,6,4,2,5,3,7]=>[7,2,4,6,3,5,1]=>{{1,7},{2},{3,4,5,6}}
[6,1,4,5,3,2,7]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>{{1},{2,3,7},{4},{5,6}}
[6,1,4,5,3,7,2]=>[1,6,4,3,5,2,7]=>[7,2,4,5,3,6,1]=>{{1,7},{2},{3,4,5},{6}}
[6,1,4,5,7,2,3]=>[1,6,5,4,2,7,3]=>[7,2,3,4,6,1,5]=>{{1,5,6,7},{2},{3},{4}}
[6,1,4,5,7,3,2]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>{{1,7},{2},{3},{4},{5,6}}
[6,1,4,7,2,3,5]=>[1,6,4,2,7,5,3]=>[7,2,4,6,1,3,5]=>{{1,5,7},{2},{3,4,6}}
[6,1,4,7,2,5,3]=>[1,6,4,2,7,3,5]=>[7,2,4,6,1,5,3]=>{{1,3,4,5,6,7},{2}}
[6,1,4,7,3,2,5]=>[1,6,4,2,3,7,5]=>[7,2,4,6,5,1,3]=>{{1,3,4,6,7},{2},{5}}
[6,1,4,7,3,5,2]=>[1,6,4,3,7,2,5]=>[7,2,4,5,1,6,3]=>{{1,3,4,5,7},{2},{6}}
[6,1,4,7,5,2,3]=>[1,6,4,2,5,7,3]=>[7,2,4,6,3,1,5]=>{{1,3,4,5,6,7},{2}}
[6,1,4,7,5,3,2]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>{{1,7},{2},{3,4,6},{5}}
[6,1,5,2,3,4,7]=>[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>{{1},{2,3,5,7},{4,6}}
[6,1,5,2,3,7,4]=>[1,6,2,5,4,7,3]=>[7,2,6,3,4,1,5]=>{{1,3,4,5,6,7},{2}}
[6,1,5,2,4,3,7]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>{{1},{2,3,4,5,6,7}}
[6,1,5,2,4,7,3]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>{{1,7},{2},{3,4,5,6}}
[6,1,5,2,7,3,4]=>[1,6,2,5,3,7,4]=>[7,2,6,3,5,1,4]=>{{1,3,4,6,7},{2},{5}}
[6,1,5,2,7,4,3]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>{{1,7},{2},{3,4,6},{5}}
[6,1,5,3,2,4,7]=>[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>{{1},{2,3,4,6,7},{5}}
[6,1,5,3,2,7,4]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>{{1,7},{2},{3,4,5,6}}
[6,1,5,3,4,2,7]=>[7,1,6,3,5,2,4]=>[1,7,2,5,3,6,4]=>{{1},{2,3,4,5,7},{6}}
[6,1,5,3,4,7,2]=>[1,6,3,5,4,2,7]=>[7,2,5,3,4,6,1]=>{{1,7},{2},{3,4,5},{6}}
[6,1,5,3,7,2,4]=>[1,6,3,5,2,7,4]=>[7,2,5,3,6,1,4]=>{{1,3,4,5,6,7},{2}}
[6,1,5,3,7,4,2]=>[1,6,3,5,2,4,7]=>[7,2,5,3,6,4,1]=>{{1,7},{2},{3,4,5,6}}
[6,1,5,4,2,3,7]=>[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>{{1},{2,3,4,5,6,7}}
[6,1,5,4,2,7,3]=>[1,6,2,4,5,3,7]=>[7,2,6,4,3,5,1]=>{{1,7},{2},{3,5,6},{4}}
[6,1,5,4,3,2,7]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>{{1},{2,3,7},{4,6},{5}}
[6,1,5,4,3,7,2]=>[1,6,3,4,5,2,7]=>[7,2,5,4,3,6,1]=>{{1,7},{2},{3,5},{4},{6}}
[6,1,5,4,7,2,3]=>[1,6,4,5,2,7,3]=>[7,2,4,3,6,1,5]=>{{1,5,6,7},{2},{3,4}}
[6,1,5,4,7,3,2]=>[1,6,4,5,2,3,7]=>[7,2,4,3,6,5,1]=>{{1,7},{2},{3,4},{5,6}}
[6,1,5,7,2,3,4]=>[1,6,5,2,7,4,3]=>[7,2,3,6,1,4,5]=>{{1,5,7},{2},{3},{4,6}}
[6,1,5,7,2,4,3]=>[1,6,5,2,7,3,4]=>[7,2,3,6,1,5,4]=>{{1,4,5,6,7},{2},{3}}
[6,1,5,7,3,2,4]=>[1,6,5,2,3,7,4]=>[7,2,3,6,5,1,4]=>{{1,4,6,7},{2},{3},{5}}
[6,1,5,7,3,4,2]=>[1,6,5,3,7,2,4]=>[7,2,3,5,1,6,4]=>{{1,4,5,7},{2},{3},{6}}
[6,1,5,7,4,2,3]=>[1,6,5,2,4,7,3]=>[7,2,3,6,4,1,5]=>{{1,4,5,6,7},{2},{3}}
[6,1,5,7,4,3,2]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>{{1,7},{2},{3},{4,6},{5}}
[6,1,7,2,3,4,5]=>[1,6,2,7,5,4,3]=>[7,2,6,1,3,4,5]=>{{1,3,4,5,6,7},{2}}
[6,1,7,2,3,5,4]=>[1,6,2,7,4,5,3]=>[7,2,6,1,4,3,5]=>{{1,4,5,7},{2},{3,6}}
[6,1,7,2,4,3,5]=>[1,6,2,7,5,3,4]=>[7,2,6,1,3,5,4]=>{{1,4,7},{2},{3,5,6}}
[6,1,7,2,4,5,3]=>[1,6,2,7,4,3,5]=>[7,2,6,1,4,5,3]=>{{1,3,4,5,6,7},{2}}
[6,1,7,2,5,3,4]=>[1,6,2,7,3,5,4]=>[7,2,6,1,5,3,4]=>{{1,4,7},{2},{3,6},{5}}
[6,1,7,2,5,4,3]=>[1,6,2,7,3,4,5]=>[7,2,6,1,5,4,3]=>{{1,3,4,6,7},{2},{5}}
[6,1,7,3,2,4,5]=>[1,6,2,3,7,5,4]=>[7,2,6,5,1,3,4]=>{{1,4,5,7},{2},{3,6}}
[6,1,7,3,2,5,4]=>[1,6,2,3,7,4,5]=>[7,2,6,5,1,4,3]=>{{1,3,4,5,6,7},{2}}
[6,1,7,3,4,2,5]=>[1,6,3,7,5,2,4]=>[7,2,5,1,3,6,4]=>{{1,4,7},{2},{3,5},{6}}
[6,1,7,3,4,5,2]=>[1,6,3,7,4,2,5]=>[7,2,5,1,4,6,3]=>{{1,3,4,5,7},{2},{6}}
[6,1,7,3,5,2,4]=>[1,6,3,7,2,5,4]=>[7,2,5,1,6,3,4]=>{{1,4,7},{2},{3,5,6}}
[6,1,7,3,5,4,2]=>[1,6,3,7,2,4,5]=>[7,2,5,1,6,4,3]=>{{1,3,4,5,6,7},{2}}
[6,1,7,4,2,3,5]=>[1,6,2,4,7,5,3]=>[7,2,6,4,1,3,5]=>{{1,5,7},{2},{3,6},{4}}
[6,1,7,4,2,5,3]=>[1,6,2,4,7,3,5]=>[7,2,6,4,1,5,3]=>{{1,3,5,6,7},{2},{4}}
[6,1,7,4,3,2,5]=>[1,6,2,3,4,7,5]=>[7,2,6,5,4,1,3]=>{{1,3,6,7},{2},{4,5}}
[6,1,7,4,3,5,2]=>[1,6,3,4,7,2,5]=>[7,2,5,4,1,6,3]=>{{1,3,5,7},{2},{4},{6}}
[6,1,7,4,5,2,3]=>[1,6,4,7,2,5,3]=>[7,2,4,1,6,3,5]=>{{1,3,4,5,6,7},{2}}
[6,1,7,4,5,3,2]=>[1,6,4,7,2,3,5]=>[7,2,4,1,6,5,3]=>{{1,3,4,7},{2},{5,6}}
[6,1,7,5,2,3,4]=>[1,6,2,5,7,4,3]=>[7,2,6,3,1,4,5]=>{{1,5,7},{2},{3,4,6}}
[6,1,7,5,2,4,3]=>[1,6,2,5,7,3,4]=>[7,2,6,3,1,5,4]=>{{1,3,4,5,6,7},{2}}
[6,1,7,5,3,2,4]=>[1,6,2,3,5,7,4]=>[7,2,6,5,3,1,4]=>{{1,3,4,5,6,7},{2}}
[6,1,7,5,3,4,2]=>[1,6,3,5,7,2,4]=>[7,2,5,3,1,6,4]=>{{1,3,4,5,7},{2},{6}}
[6,1,7,5,4,2,3]=>[1,6,2,4,5,7,3]=>[7,2,6,4,3,1,5]=>{{1,3,5,6,7},{2},{4}}
[6,1,7,5,4,3,2]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>{{1,7},{2},{3,6},{4,5}}
[6,2,1,3,4,5,7]=>[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>{{1},{2,3,4,5,6,7}}
[6,2,1,3,4,7,5]=>[1,2,6,5,7,4,3]=>[7,6,2,3,1,4,5]=>{{1,5,7},{2,3,4,6}}
[6,2,1,3,5,4,7]=>[7,1,2,6,4,5,3]=>[1,7,6,2,4,3,5]=>{{1},{2,4,5,7},{3,6}}
[6,2,1,3,5,7,4]=>[1,2,6,5,4,7,3]=>[7,6,2,3,4,1,5]=>{{1,2,3,4,5,6,7}}
[6,2,1,3,7,4,5]=>[1,2,6,4,7,5,3]=>[7,6,2,4,1,3,5]=>{{1,5,7},{2,3,6},{4}}
[6,2,1,3,7,5,4]=>[1,2,6,4,5,7,3]=>[7,6,2,4,3,1,5]=>{{1,2,3,5,6,7},{4}}
[6,2,1,4,3,5,7]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>{{1},{2,4,7},{3,5,6}}
[6,2,1,4,3,7,5]=>[1,2,6,5,7,3,4]=>[7,6,2,3,1,5,4]=>{{1,2,3,4,5,6,7}}
[6,2,1,4,5,3,7]=>[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>{{1},{2,3,4,5,6,7}}
[6,2,1,4,5,7,3]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>{{1,7},{2,3,4,5,6}}
[6,2,1,4,7,3,5]=>[1,2,6,4,3,7,5]=>[7,6,2,4,5,1,3]=>{{1,2,3,6,7},{4},{5}}
[6,2,1,4,7,5,3]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>{{1,7},{2,3,6},{4},{5}}
[6,2,1,5,3,4,7]=>[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>{{1},{2,4,7},{3,6},{5}}
[6,2,1,5,3,7,4]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>{{1,7},{2,3,4,5,6}}
[6,2,1,5,4,3,7]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>{{1},{2,3,4,6,7},{5}}
[6,2,1,5,4,7,3]=>[1,2,6,4,5,3,7]=>[7,6,2,4,3,5,1]=>{{1,7},{2,3,5,6},{4}}
[6,2,1,5,7,3,4]=>[1,2,6,5,3,7,4]=>[7,6,2,3,5,1,4]=>{{1,2,3,4,6,7},{5}}
[6,2,1,5,7,4,3]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>{{1,7},{2,3,4,6},{5}}
[6,2,1,7,3,4,5]=>[1,2,6,3,7,5,4]=>[7,6,2,5,1,3,4]=>{{1,4,5,7},{2,3,6}}
[6,2,1,7,3,5,4]=>[1,2,6,3,7,4,5]=>[7,6,2,5,1,4,3]=>{{1,2,3,4,5,6,7}}
[6,2,1,7,4,3,5]=>[1,2,6,3,4,7,5]=>[7,6,2,5,4,1,3]=>{{1,2,3,6,7},{4,5}}
[6,2,1,7,4,5,3]=>[1,2,6,4,7,3,5]=>[7,6,2,4,1,5,3]=>{{1,2,3,5,6,7},{4}}
[6,2,1,7,5,3,4]=>[1,2,6,3,5,7,4]=>[7,6,2,5,3,1,4]=>{{1,2,3,4,5,6,7}}
[6,2,1,7,5,4,3]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>{{1,7},{2,3,6},{4,5}}
[6,2,3,1,4,5,7]=>[7,2,6,5,4,1,3]=>[1,6,2,3,4,7,5]=>{{1},{2,3,4,5,6,7}}
[6,2,3,1,4,7,5]=>[2,6,5,7,4,1,3]=>[6,2,3,1,4,7,5]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,1,5,4,7]=>[7,2,6,4,5,1,3]=>[1,6,2,4,3,7,5]=>{{1},{2,3,5,6,7},{4}}
[6,2,3,1,5,7,4]=>[2,6,5,4,7,1,3]=>[6,2,3,4,1,7,5]=>{{1,5,6,7},{2},{3},{4}}
[6,2,3,1,7,4,5]=>[2,6,4,7,5,1,3]=>[6,2,4,1,3,7,5]=>{{1,3,4,5,6,7},{2}}
[6,2,3,1,7,5,4]=>[2,6,4,5,7,1,3]=>[6,2,4,3,1,7,5]=>{{1,5,6,7},{2},{3,4}}
[6,2,3,4,1,5,7]=>[7,2,6,5,3,1,4]=>[1,6,2,3,5,7,4]=>{{1},{2,3,4,6,7},{5}}
[6,2,3,4,1,7,5]=>[2,6,5,7,3,1,4]=>[6,2,3,1,5,7,4]=>{{1,4,6,7},{2},{3},{5}}
[6,2,3,4,5,1,7]=>[7,2,6,4,3,1,5]=>[1,6,2,4,5,7,3]=>{{1},{2,3,6,7},{4},{5}}
[6,2,3,4,5,7,1]=>[2,6,5,4,3,1,7]=>[6,2,3,4,5,7,1]=>{{1,6,7},{2},{3},{4},{5}}
[6,2,3,4,7,1,5]=>[2,6,4,3,1,7,5]=>[6,2,4,5,7,1,3]=>{{1,6},{2},{3,4,5,7}}
[6,2,3,4,7,5,1]=>[2,6,4,3,1,5,7]=>[6,2,4,5,7,3,1]=>{{1,3,4,5,6,7},{2}}
[6,2,3,5,1,4,7]=>[7,2,6,3,1,5,4]=>[1,6,2,5,7,3,4]=>{{1},{2,3,6},{4,5,7}}
[6,2,3,5,1,7,4]=>[2,6,3,1,5,4,7]=>[6,2,5,7,3,4,1]=>{{1,4,6,7},{2},{3,5}}
[6,2,3,5,4,1,7]=>[7,2,6,3,1,4,5]=>[1,6,2,5,7,4,3]=>{{1},{2,3,4,5,6,7}}
[6,2,3,5,4,7,1]=>[2,6,4,5,3,1,7]=>[6,2,4,3,5,7,1]=>{{1,6,7},{2},{3,4},{5}}
[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>[6,2,3,5,7,1,4]=>{{1,6},{2},{3},{4,5,7}}
[6,2,3,5,7,4,1]=>[2,6,5,3,1,4,7]=>[6,2,3,5,7,4,1]=>{{1,4,5,6,7},{2},{3}}
[6,2,3,7,1,4,5]=>[2,6,3,1,7,5,4]=>[6,2,5,7,1,3,4]=>{{1,3,5,6},{2},{4,7}}
[6,2,3,7,1,5,4]=>[2,6,3,1,7,4,5]=>[6,2,5,7,1,4,3]=>{{1,3,4,5,6,7},{2}}
[6,2,3,7,4,1,5]=>[2,6,3,1,4,7,5]=>[6,2,5,7,4,1,3]=>{{1,6},{2},{3,4,5,7}}
[6,2,3,7,4,5,1]=>[2,6,4,7,3,1,5]=>[6,2,4,1,5,7,3]=>{{1,3,4,6,7},{2},{5}}
[6,2,3,7,5,1,4]=>[2,6,3,1,5,7,4]=>[6,2,5,7,3,1,4]=>{{1,6},{2},{3,5},{4,7}}
[6,2,3,7,5,4,1]=>[2,6,3,1,4,5,7]=>[6,2,5,7,4,3,1]=>{{1,3,4,5,6,7},{2}}
[6,2,4,1,3,5,7]=>[7,2,6,5,1,4,3]=>[1,6,2,3,7,4,5]=>{{1},{2,3,4,6},{5,7}}
[6,2,4,1,3,7,5]=>[2,6,5,7,1,4,3]=>[6,2,3,1,7,4,5]=>{{1,4,6},{2},{3},{5,7}}
[6,2,4,1,5,3,7]=>[7,2,6,1,4,3,5]=>[1,6,2,7,4,5,3]=>{{1},{2,3,4,5,6,7}}
[6,2,4,1,5,7,3]=>[2,6,5,1,4,3,7]=>[6,2,3,7,4,5,1]=>{{1,4,5,6,7},{2},{3}}
[6,2,4,1,7,3,5]=>[2,6,1,4,3,7,5]=>[6,2,7,4,5,1,3]=>{{1,6},{2},{3,7},{4},{5}}
[6,2,4,1,7,5,3]=>[2,6,1,4,3,5,7]=>[6,2,7,4,5,3,1]=>{{1,3,6,7},{2},{4},{5}}
[6,2,4,3,1,5,7]=>[7,2,6,5,1,3,4]=>[1,6,2,3,7,5,4]=>{{1},{2,3,4,5,6,7}}
[6,2,4,3,1,7,5]=>[2,6,5,7,1,3,4]=>[6,2,3,1,7,5,4]=>{{1,4,5,6,7},{2},{3}}
[6,2,4,3,5,1,7]=>[7,2,6,3,4,1,5]=>[1,6,2,5,4,7,3]=>{{1},{2,3,6,7},{4,5}}
[6,2,4,3,5,7,1]=>[2,6,5,3,4,1,7]=>[6,2,3,5,4,7,1]=>{{1,6,7},{2},{3},{4,5}}
[6,2,4,3,7,1,5]=>[2,6,3,4,1,7,5]=>[6,2,5,4,7,1,3]=>{{1,6},{2},{3,5,7},{4}}
[6,2,4,3,7,5,1]=>[2,6,3,4,1,5,7]=>[6,2,5,4,7,3,1]=>{{1,3,5,6,7},{2},{4}}
[6,2,4,5,1,3,7]=>[7,2,6,4,1,5,3]=>[1,6,2,4,7,3,5]=>{{1},{2,3,6},{4},{5,7}}
[6,2,4,5,1,7,3]=>[2,6,4,1,5,3,7]=>[6,2,4,7,3,5,1]=>{{1,3,4,5,6,7},{2}}
[6,2,4,5,3,1,7]=>[7,2,6,4,1,3,5]=>[1,6,2,4,7,5,3]=>{{1},{2,3,5,6,7},{4}}
[6,2,4,5,3,7,1]=>[2,6,4,3,5,1,7]=>[6,2,4,5,3,7,1]=>{{1,6,7},{2},{3,4,5}}
[6,2,4,5,7,1,3]=>[2,6,5,4,1,7,3]=>[6,2,3,4,7,1,5]=>{{1,6},{2},{3},{4},{5,7}}
[6,2,4,5,7,3,1]=>[2,6,5,4,1,3,7]=>[6,2,3,4,7,5,1]=>{{1,5,6,7},{2},{3},{4}}
[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>[6,2,4,7,1,3,5]=>{{1,3,4,5,6,7},{2}}
[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>[6,2,4,7,1,5,3]=>{{1,5,6},{2},{3,4,7}}
[6,2,4,7,3,1,5]=>[2,6,4,1,3,7,5]=>[6,2,4,7,5,1,3]=>{{1,6},{2},{3,4,7},{5}}
[6,2,4,7,3,5,1]=>[2,6,4,3,7,1,5]=>[6,2,4,5,1,7,3]=>{{1,3,4,5,6,7},{2}}
[6,2,4,7,5,1,3]=>[2,6,4,1,5,7,3]=>[6,2,4,7,3,1,5]=>{{1,6},{2},{3,4,5,7}}
[6,2,4,7,5,3,1]=>[2,6,4,1,3,5,7]=>[6,2,4,7,5,3,1]=>{{1,3,4,6,7},{2},{5}}
[6,2,5,1,3,4,7]=>[7,2,6,1,5,4,3]=>[1,6,2,7,3,4,5]=>{{1},{2,3,4,5,6,7}}
[6,2,5,1,3,7,4]=>[2,6,1,5,4,7,3]=>[6,2,7,3,4,1,5]=>{{1,6},{2},{3,4,5,7}}
[6,2,5,1,4,3,7]=>[7,2,6,1,5,3,4]=>[1,6,2,7,3,5,4]=>{{1},{2,3,5,6},{4,7}}
[6,2,5,1,4,7,3]=>[2,6,1,5,4,3,7]=>[6,2,7,3,4,5,1]=>{{1,3,4,5,6,7},{2}}
[6,2,5,1,7,3,4]=>[2,6,1,5,3,7,4]=>[6,2,7,3,5,1,4]=>{{1,6},{2},{3,4,7},{5}}
[6,2,5,1,7,4,3]=>[2,6,1,5,3,4,7]=>[6,2,7,3,5,4,1]=>{{1,3,4,6,7},{2},{5}}
[6,2,5,3,1,4,7]=>[7,2,6,1,3,5,4]=>[1,6,2,7,5,3,4]=>{{1},{2,3,6},{4,7},{5}}
[6,2,5,3,1,7,4]=>[2,6,1,3,5,4,7]=>[6,2,7,5,3,4,1]=>{{1,3,4,5,6,7},{2}}
[6,2,5,3,4,1,7]=>[7,2,6,3,5,1,4]=>[1,6,2,5,3,7,4]=>{{1},{2,3,4,5,6,7}}
[6,2,5,3,4,7,1]=>[2,6,3,5,4,1,7]=>[6,2,5,3,4,7,1]=>{{1,6,7},{2},{3,4,5}}
[6,2,5,3,7,1,4]=>[2,6,3,5,1,7,4]=>[6,2,5,3,7,1,4]=>{{1,6},{2},{3,4,5,7}}
[6,2,5,3,7,4,1]=>[2,6,3,5,1,4,7]=>[6,2,5,3,7,4,1]=>{{1,3,4,5,6,7},{2}}
[6,2,5,4,1,3,7]=>[7,2,6,1,4,5,3]=>[1,6,2,7,4,3,5]=>{{1},{2,3,6},{4,5,7}}
[6,2,5,4,1,7,3]=>[2,6,1,4,5,3,7]=>[6,2,7,4,3,5,1]=>{{1,3,5,6,7},{2},{4}}
[6,2,5,4,3,1,7]=>[7,2,6,1,3,4,5]=>[1,6,2,7,5,4,3]=>{{1},{2,3,4,6,7},{5}}
[6,2,5,4,3,7,1]=>[2,6,3,4,5,1,7]=>[6,2,5,4,3,7,1]=>{{1,6,7},{2},{3,5},{4}}
[6,2,5,4,7,1,3]=>[2,6,4,5,1,7,3]=>[6,2,4,3,7,1,5]=>{{1,6},{2},{3,4},{5,7}}
[6,2,5,4,7,3,1]=>[2,6,4,5,1,3,7]=>[6,2,4,3,7,5,1]=>{{1,5,6,7},{2},{3,4}}
[6,2,5,7,1,3,4]=>[2,6,5,1,7,4,3]=>[6,2,3,7,1,4,5]=>{{1,4,5,6,7},{2},{3}}
[6,2,5,7,1,4,3]=>[2,6,5,1,7,3,4]=>[6,2,3,7,1,5,4]=>{{1,5,6},{2},{3},{4,7}}
[6,2,5,7,3,1,4]=>[2,6,5,1,3,7,4]=>[6,2,3,7,5,1,4]=>{{1,6},{2},{3},{4,7},{5}}
[6,2,5,7,3,4,1]=>[2,6,5,3,7,1,4]=>[6,2,3,5,1,7,4]=>{{1,4,5,6,7},{2},{3}}
[6,2,5,7,4,1,3]=>[2,6,5,1,4,7,3]=>[6,2,3,7,4,1,5]=>{{1,6},{2},{3},{4,5,7}}
[6,2,5,7,4,3,1]=>[2,6,5,1,3,4,7]=>[6,2,3,7,5,4,1]=>{{1,4,6,7},{2},{3},{5}}
[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>[6,2,7,1,3,4,5]=>{{1,4,6},{2},{3,5,7}}
[6,2,7,1,3,5,4]=>[2,6,1,7,4,5,3]=>[6,2,7,1,4,3,5]=>{{1,3,4,5,6,7},{2}}
[6,2,7,1,4,3,5]=>[2,6,1,7,5,3,4]=>[6,2,7,1,3,5,4]=>{{1,3,4,5,6,7},{2}}
[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>[6,2,7,1,4,5,3]=>{{1,4,5,6},{2},{3,7}}
[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>[6,2,7,1,5,3,4]=>{{1,3,4,6,7},{2},{5}}
[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>[6,2,7,1,5,4,3]=>{{1,4,6},{2},{3,7},{5}}
[6,2,7,3,1,4,5]=>[2,6,1,3,7,5,4]=>[6,2,7,5,1,3,4]=>{{1,3,4,5,6,7},{2}}
[6,2,7,3,1,5,4]=>[2,6,1,3,7,4,5]=>[6,2,7,5,1,4,3]=>{{1,4,5,6},{2},{3,7}}
[6,2,7,3,4,1,5]=>[2,6,3,7,5,1,4]=>[6,2,5,1,3,7,4]=>{{1,4,6,7},{2},{3,5}}
[6,2,7,3,4,5,1]=>[2,6,3,7,4,1,5]=>[6,2,5,1,4,7,3]=>{{1,3,4,5,6,7},{2}}
[6,2,7,3,5,1,4]=>[2,6,3,7,1,5,4]=>[6,2,5,1,7,3,4]=>{{1,3,4,5,6,7},{2}}
[6,2,7,3,5,4,1]=>[2,6,3,7,1,4,5]=>[6,2,5,1,7,4,3]=>{{1,4,6},{2},{3,5,7}}
[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>[6,2,7,4,1,3,5]=>{{1,3,5,6,7},{2},{4}}
[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>[6,2,7,4,1,5,3]=>{{1,5,6},{2},{3,7},{4}}
[6,2,7,4,3,1,5]=>[2,6,1,3,4,7,5]=>[6,2,7,5,4,1,3]=>{{1,6},{2},{3,7},{4,5}}
[6,2,7,4,3,5,1]=>[2,6,3,4,7,1,5]=>[6,2,5,4,1,7,3]=>{{1,3,5,6,7},{2},{4}}
[6,2,7,4,5,1,3]=>[2,6,4,7,1,5,3]=>[6,2,4,1,7,3,5]=>{{1,3,4,6},{2},{5,7}}
[6,2,7,4,5,3,1]=>[2,6,4,7,1,3,5]=>[6,2,4,1,7,5,3]=>{{1,3,4,5,6,7},{2}}
[6,2,7,5,1,3,4]=>[2,6,1,5,7,4,3]=>[6,2,7,3,1,4,5]=>{{1,3,4,5,6,7},{2}}
[6,2,7,5,1,4,3]=>[2,6,1,5,7,3,4]=>[6,2,7,3,1,5,4]=>{{1,5,6},{2},{3,4,7}}
[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>[6,2,7,5,3,1,4]=>{{1,6},{2},{3,4,5,7}}
[6,2,7,5,3,4,1]=>[2,6,3,5,7,1,4]=>[6,2,5,3,1,7,4]=>{{1,3,4,5,6,7},{2}}
[6,2,7,5,4,1,3]=>[2,6,1,4,5,7,3]=>[6,2,7,4,3,1,5]=>{{1,6},{2},{3,5,7},{4}}
[6,2,7,5,4,3,1]=>[2,6,1,3,4,5,7]=>[6,2,7,5,4,3,1]=>{{1,3,6,7},{2},{4,5}}
[6,3,1,2,4,5,7]=>[7,1,3,6,5,4,2]=>[1,7,5,2,3,4,6]=>{{1},{2,4,6,7},{3,5}}
[6,3,1,2,4,7,5]=>[1,3,6,5,7,4,2]=>[7,5,2,3,1,4,6]=>{{1,2,3,4,5,6,7}}
[6,3,1,2,5,4,7]=>[7,1,3,6,4,5,2]=>[1,7,5,2,4,3,6]=>{{1},{2,3,4,5,6,7}}
[6,3,1,2,5,7,4]=>[1,3,6,5,4,7,2]=>[7,5,2,3,4,1,6]=>{{1,6,7},{2,3,4,5}}
[6,3,1,2,7,4,5]=>[1,3,6,4,7,5,2]=>[7,5,2,4,1,3,6]=>{{1,2,3,5,6,7},{4}}
[6,3,1,2,7,5,4]=>[1,3,6,4,5,7,2]=>[7,5,2,4,3,1,6]=>{{1,6,7},{2,3,5},{4}}
[6,3,1,4,2,5,7]=>[7,1,3,6,5,2,4]=>[1,7,5,2,3,6,4]=>{{1},{2,4,7},{3,5},{6}}
[6,3,1,4,2,7,5]=>[1,3,6,5,7,2,4]=>[7,5,2,3,1,6,4]=>{{1,2,3,4,5,7},{6}}
[6,3,1,4,5,2,7]=>[7,1,3,6,4,2,5]=>[1,7,5,2,4,6,3]=>{{1},{2,3,4,5,7},{6}}
[6,3,1,4,5,7,2]=>[1,3,6,5,4,2,7]=>[7,5,2,3,4,6,1]=>{{1,7},{2,3,4,5},{6}}
[6,3,1,4,7,2,5]=>[1,3,6,4,2,7,5]=>[7,5,2,4,6,1,3]=>{{1,2,3,5,6,7},{4}}
[6,3,1,4,7,5,2]=>[1,3,6,4,2,5,7]=>[7,5,2,4,6,3,1]=>{{1,7},{2,3,5,6},{4}}
[6,3,1,5,2,4,7]=>[7,1,3,6,2,5,4]=>[1,7,5,2,6,3,4]=>{{1},{2,4,7},{3,5,6}}
[6,3,1,5,2,7,4]=>[1,3,6,2,5,4,7]=>[7,5,2,6,3,4,1]=>{{1,7},{2,3,5},{4,6}}
[6,3,1,5,4,2,7]=>[7,1,3,6,2,4,5]=>[1,7,5,2,6,4,3]=>{{1},{2,3,4,5,6,7}}
[6,3,1,5,4,7,2]=>[1,3,6,4,5,2,7]=>[7,5,2,4,3,6,1]=>{{1,7},{2,3,5},{4},{6}}
[6,3,1,5,7,2,4]=>[1,3,6,5,2,7,4]=>[7,5,2,3,6,1,4]=>{{1,2,3,4,5,6,7}}
[6,3,1,5,7,4,2]=>[1,3,6,5,2,4,7]=>[7,5,2,3,6,4,1]=>{{1,7},{2,3,4,5,6}}
[6,3,1,7,2,4,5]=>[1,3,6,2,7,5,4]=>[7,5,2,6,1,3,4]=>{{1,2,3,4,5,6,7}}
[6,3,1,7,2,5,4]=>[1,3,6,2,7,4,5]=>[7,5,2,6,1,4,3]=>{{1,2,3,5,7},{4,6}}
[6,3,1,7,4,2,5]=>[1,3,6,2,4,7,5]=>[7,5,2,6,4,1,3]=>{{1,2,3,4,5,6,7}}
[6,3,1,7,4,5,2]=>[1,3,6,4,7,2,5]=>[7,5,2,4,1,6,3]=>{{1,2,3,5,7},{4},{6}}
[6,3,1,7,5,2,4]=>[1,3,6,2,5,7,4]=>[7,5,2,6,3,1,4]=>{{1,4,6,7},{2,3,5}}
[6,3,1,7,5,4,2]=>[1,3,6,2,4,5,7]=>[7,5,2,6,4,3,1]=>{{1,7},{2,3,4,5,6}}
[6,3,2,1,4,5,7]=>[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>{{1},{2,4,5,7},{3,6}}
[6,3,2,1,4,7,5]=>[1,2,3,6,5,7,4]=>[7,6,5,2,3,1,4]=>{{1,2,4,6,7},{3,5}}
[6,3,2,1,5,4,7]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>{{1},{2,3,4,5,6,7}}
[6,3,2,1,5,7,4]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>{{1,7},{2,4,6},{3,5}}
[6,3,2,1,7,4,5]=>[1,2,3,6,4,7,5]=>[7,6,5,2,4,1,3]=>{{1,2,3,4,5,6,7}}
[6,3,2,1,7,5,4]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>{{1,7},{2,3,4,5,6}}
[6,3,2,4,1,5,7]=>[7,2,3,6,5,1,4]=>[1,6,5,2,3,7,4]=>{{1},{2,4,6,7},{3,5}}
[6,3,2,4,1,7,5]=>[2,3,6,5,7,1,4]=>[6,5,2,3,1,7,4]=>{{1,2,3,4,5,6,7}}
[6,3,2,4,5,1,7]=>[7,2,3,6,4,1,5]=>[1,6,5,2,4,7,3]=>{{1},{2,3,4,5,6,7}}
[6,3,2,4,5,7,1]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,7,1]=>{{1,6,7},{2,3,4,5}}
[6,3,2,4,7,1,5]=>[2,3,6,4,1,7,5]=>[6,5,2,4,7,1,3]=>{{1,6},{2,3,5,7},{4}}
[6,3,2,4,7,5,1]=>[2,3,6,4,1,5,7]=>[6,5,2,4,7,3,1]=>{{1,2,3,5,6,7},{4}}
[6,3,2,5,1,4,7]=>[7,2,3,6,1,5,4]=>[1,6,5,2,7,3,4]=>{{1},{2,3,4,5,6,7}}
[6,3,2,5,1,7,4]=>[2,3,6,1,5,4,7]=>[6,5,2,7,3,4,1]=>{{1,4,6,7},{2,3,5}}
[6,3,2,5,4,1,7]=>[7,2,3,6,1,4,5]=>[1,6,5,2,7,4,3]=>{{1},{2,4,6},{3,5,7}}
[6,3,2,5,4,7,1]=>[2,3,6,4,5,1,7]=>[6,5,2,4,3,7,1]=>{{1,6,7},{2,3,5},{4}}
[6,3,2,5,7,1,4]=>[2,3,6,5,1,7,4]=>[6,5,2,3,7,1,4]=>{{1,6},{2,3,4,5,7}}
[6,3,2,5,7,4,1]=>[2,3,6,5,1,4,7]=>[6,5,2,3,7,4,1]=>{{1,2,3,4,5,6,7}}
[6,3,2,7,1,4,5]=>[2,3,6,1,7,5,4]=>[6,5,2,7,1,3,4]=>{{1,2,3,5,6},{4,7}}
[6,3,2,7,1,5,4]=>[2,3,6,1,7,4,5]=>[6,5,2,7,1,4,3]=>{{1,2,3,4,5,6,7}}
[6,3,2,7,4,1,5]=>[2,3,6,1,4,7,5]=>[6,5,2,7,4,1,3]=>{{1,6},{2,3,4,5,7}}
[6,3,2,7,4,5,1]=>[2,3,6,4,7,1,5]=>[6,5,2,4,1,7,3]=>{{1,2,3,5,6,7},{4}}
[6,3,2,7,5,1,4]=>[2,3,6,1,5,7,4]=>[6,5,2,7,3,1,4]=>{{1,6},{2,3,5},{4,7}}
[6,3,2,7,5,4,1]=>[2,3,6,1,4,5,7]=>[6,5,2,7,4,3,1]=>{{1,2,3,4,5,6,7}}
[6,3,4,1,2,5,7]=>[7,3,6,5,1,4,2]=>[1,5,2,3,7,4,6]=>{{1},{2,3,4,5,6,7}}
[6,3,4,1,2,7,5]=>[3,6,5,7,1,4,2]=>[5,2,3,1,7,4,6]=>{{1,4,5,6,7},{2},{3}}
[6,3,4,1,5,2,7]=>[7,3,6,1,4,2,5]=>[1,5,2,7,4,6,3]=>{{1},{2,3,4,5,7},{6}}
[6,3,4,1,5,7,2]=>[3,6,5,1,4,2,7]=>[5,2,3,7,4,6,1]=>{{1,4,5,7},{2},{3},{6}}
[6,3,4,1,7,2,5]=>[3,6,1,4,2,7,5]=>[5,2,7,4,6,1,3]=>{{1,5,6},{2},{3,7},{4}}
[6,3,4,1,7,5,2]=>[3,6,1,4,2,5,7]=>[5,2,7,4,6,3,1]=>{{1,3,5,6,7},{2},{4}}
[6,3,4,2,1,5,7]=>[7,3,6,5,1,2,4]=>[1,5,2,3,7,6,4]=>{{1},{2,3,4,5,7},{6}}
[6,3,4,2,1,7,5]=>[3,6,5,7,1,2,4]=>[5,2,3,1,7,6,4]=>{{1,4,5,7},{2},{3},{6}}
[6,3,4,2,5,1,7]=>[7,3,6,2,4,1,5]=>[1,5,2,6,4,7,3]=>{{1},{2,3,4,5,6,7}}
[6,3,4,2,5,7,1]=>[3,6,5,2,4,1,7]=>[5,2,3,6,4,7,1]=>{{1,4,5,6,7},{2},{3}}
[6,3,4,2,7,1,5]=>[3,6,2,4,1,7,5]=>[5,2,6,4,7,1,3]=>{{1,3,5,6,7},{2},{4}}
[6,3,4,2,7,5,1]=>[3,6,2,4,1,5,7]=>[5,2,6,4,7,3,1]=>{{1,5,7},{2},{3,6},{4}}
[6,3,4,5,1,2,7]=>[7,3,6,4,1,5,2]=>[1,5,2,4,7,3,6]=>{{1},{2,3,5,6,7},{4}}
[6,3,4,5,1,7,2]=>[3,6,4,1,5,2,7]=>[5,2,4,7,3,6,1]=>{{1,3,4,5,7},{2},{6}}
[6,3,4,5,2,1,7]=>[7,3,6,4,1,2,5]=>[1,5,2,4,7,6,3]=>{{1},{2,3,5,7},{4},{6}}
[6,3,4,5,2,7,1]=>[3,6,4,2,5,1,7]=>[5,2,4,6,3,7,1]=>{{1,3,4,5,6,7},{2}}
[6,3,4,5,7,1,2]=>[3,6,5,4,1,7,2]=>[5,2,3,4,7,1,6]=>{{1,5,6,7},{2},{3},{4}}
[6,3,4,5,7,2,1]=>[3,6,5,4,1,2,7]=>[5,2,3,4,7,6,1]=>{{1,5,7},{2},{3},{4},{6}}
[6,3,4,7,1,2,5]=>[3,6,4,1,7,5,2]=>[5,2,4,7,1,3,6]=>{{1,5},{2},{3,4,6,7}}
[6,3,4,7,1,5,2]=>[3,6,4,1,7,2,5]=>[5,2,4,7,1,6,3]=>{{1,5},{2},{3,4,7},{6}}
[6,3,4,7,2,1,5]=>[3,6,4,1,2,7,5]=>[5,2,4,7,6,1,3]=>{{1,5,6},{2},{3,4,7}}
[6,3,4,7,2,5,1]=>[3,6,4,2,7,1,5]=>[5,2,4,6,1,7,3]=>{{1,5},{2},{3,4,6,7}}
[6,3,4,7,5,1,2]=>[3,6,4,1,5,7,2]=>[5,2,4,7,3,1,6]=>{{1,3,4,5,6,7},{2}}
[6,3,4,7,5,2,1]=>[3,6,4,1,2,5,7]=>[5,2,4,7,6,3,1]=>{{1,3,4,5,6,7},{2}}
[6,3,5,1,2,4,7]=>[7,3,6,1,5,4,2]=>[1,5,2,7,3,4,6]=>{{1},{2,3,5},{4,6,7}}
[6,3,5,1,2,7,4]=>[3,6,1,5,4,7,2]=>[5,2,7,3,4,1,6]=>{{1,3,4,5,6,7},{2}}
[6,3,5,1,4,2,7]=>[7,3,6,1,5,2,4]=>[1,5,2,7,3,6,4]=>{{1},{2,3,5},{4,7},{6}}
[6,3,5,1,4,7,2]=>[3,6,1,5,4,2,7]=>[5,2,7,3,4,6,1]=>{{1,3,4,5,7},{2},{6}}
[6,3,5,1,7,2,4]=>[3,6,1,5,2,7,4]=>[5,2,7,3,6,1,4]=>{{1,5,6},{2},{3,4,7}}
[6,3,5,1,7,4,2]=>[3,6,1,5,2,4,7]=>[5,2,7,3,6,4,1]=>{{1,3,4,5,6,7},{2}}
[6,3,5,2,1,4,7]=>[7,3,6,1,2,5,4]=>[1,5,2,7,6,3,4]=>{{1},{2,3,5,6},{4,7}}
[6,3,5,2,1,7,4]=>[3,6,1,2,5,4,7]=>[5,2,7,6,3,4,1]=>{{1,3,5,7},{2},{4,6}}
[6,3,5,2,4,1,7]=>[7,3,6,2,5,1,4]=>[1,5,2,6,3,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,3,5,2,4,7,1]=>[3,6,2,5,4,1,7]=>[5,2,6,3,4,7,1]=>{{1,3,4,5,6,7},{2}}
[6,3,5,2,7,1,4]=>[3,6,2,5,1,7,4]=>[5,2,6,3,7,1,4]=>{{1,3,4,5,6,7},{2}}
[6,3,5,2,7,4,1]=>[3,6,2,5,1,4,7]=>[5,2,6,3,7,4,1]=>{{1,5,7},{2},{3,4,6}}
[6,3,5,4,1,2,7]=>[7,3,6,1,4,5,2]=>[1,5,2,7,4,3,6]=>{{1},{2,3,4,5,6,7}}
[6,3,5,4,1,7,2]=>[3,6,1,4,5,2,7]=>[5,2,7,4,3,6,1]=>{{1,3,5,7},{2},{4},{6}}
[6,3,5,4,2,1,7]=>[7,3,6,1,2,4,5]=>[1,5,2,7,6,4,3]=>{{1},{2,3,4,5,6,7}}
[6,3,5,4,2,7,1]=>[3,6,2,4,5,1,7]=>[5,2,6,4,3,7,1]=>{{1,3,5,6,7},{2},{4}}
[6,3,5,4,7,1,2]=>[3,6,4,5,1,7,2]=>[5,2,4,3,7,1,6]=>{{1,5,6,7},{2},{3,4}}
[6,3,5,4,7,2,1]=>[3,6,4,5,1,2,7]=>[5,2,4,3,7,6,1]=>{{1,5,7},{2},{3,4},{6}}
[6,3,5,7,1,2,4]=>[3,6,5,1,7,4,2]=>[5,2,3,7,1,4,6]=>{{1,5},{2},{3},{4,6,7}}
[6,3,5,7,1,4,2]=>[3,6,5,1,7,2,4]=>[5,2,3,7,1,6,4]=>{{1,5},{2},{3},{4,7},{6}}
[6,3,5,7,2,1,4]=>[3,6,5,1,2,7,4]=>[5,2,3,7,6,1,4]=>{{1,5,6},{2},{3},{4,7}}
[6,3,5,7,2,4,1]=>[3,6,5,2,7,1,4]=>[5,2,3,6,1,7,4]=>{{1,5},{2},{3},{4,6,7}}
[6,3,5,7,4,1,2]=>[3,6,5,1,4,7,2]=>[5,2,3,7,4,1,6]=>{{1,4,5,6,7},{2},{3}}
[6,3,5,7,4,2,1]=>[3,6,5,1,2,4,7]=>[5,2,3,7,6,4,1]=>{{1,4,5,6,7},{2},{3}}
[6,3,7,1,2,4,5]=>[3,6,1,7,5,4,2]=>[5,2,7,1,3,4,6]=>{{1,3,4,5,6,7},{2}}
[6,3,7,1,2,5,4]=>[3,6,1,7,4,5,2]=>[5,2,7,1,4,3,6]=>{{1,4,5},{2},{3,6,7}}
[6,3,7,1,4,2,5]=>[3,6,1,7,5,2,4]=>[5,2,7,1,3,6,4]=>{{1,3,4,5,7},{2},{6}}
[6,3,7,1,4,5,2]=>[3,6,1,7,4,2,5]=>[5,2,7,1,4,6,3]=>{{1,4,5},{2},{3,7},{6}}
[6,3,7,1,5,2,4]=>[3,6,1,7,2,5,4]=>[5,2,7,1,6,3,4]=>{{1,3,4,5,6,7},{2}}
[6,3,7,1,5,4,2]=>[3,6,1,7,2,4,5]=>[5,2,7,1,6,4,3]=>{{1,4,5,6},{2},{3,7}}
[6,3,7,2,1,4,5]=>[3,6,1,2,7,5,4]=>[5,2,7,6,1,3,4]=>{{1,5},{2},{3,4,6,7}}
[6,3,7,2,1,5,4]=>[3,6,1,2,7,4,5]=>[5,2,7,6,1,4,3]=>{{1,5},{2},{3,7},{4,6}}
[6,3,7,2,4,1,5]=>[3,6,2,7,5,1,4]=>[5,2,6,1,3,7,4]=>{{1,3,4,5,6,7},{2}}
[6,3,7,2,4,5,1]=>[3,6,2,7,4,1,5]=>[5,2,6,1,4,7,3]=>{{1,4,5},{2},{3,6,7}}
[6,3,7,2,5,1,4]=>[3,6,2,7,1,5,4]=>[5,2,6,1,7,3,4]=>{{1,4,5,7},{2},{3,6}}
[6,3,7,2,5,4,1]=>[3,6,2,7,1,4,5]=>[5,2,6,1,7,4,3]=>{{1,3,4,5,6,7},{2}}
[6,3,7,4,1,2,5]=>[3,6,1,4,7,5,2]=>[5,2,7,4,1,3,6]=>{{1,5},{2},{3,6,7},{4}}
[6,3,7,4,1,5,2]=>[3,6,1,4,7,2,5]=>[5,2,7,4,1,6,3]=>{{1,5},{2},{3,7},{4},{6}}
[6,3,7,4,2,1,5]=>[3,6,1,2,4,7,5]=>[5,2,7,6,4,1,3]=>{{1,4,5,6},{2},{3,7}}
[6,3,7,4,2,5,1]=>[3,6,2,4,7,1,5]=>[5,2,6,4,1,7,3]=>{{1,5},{2},{3,6,7},{4}}
[6,3,7,4,5,1,2]=>[3,6,4,7,1,5,2]=>[5,2,4,1,7,3,6]=>{{1,3,4,5,6,7},{2}}
[6,3,7,4,5,2,1]=>[3,6,4,7,1,2,5]=>[5,2,4,1,7,6,3]=>{{1,3,4,5,7},{2},{6}}
[6,3,7,5,1,2,4]=>[3,6,1,5,7,4,2]=>[5,2,7,3,1,4,6]=>{{1,5},{2},{3,4,6,7}}
[6,3,7,5,1,4,2]=>[3,6,1,5,7,2,4]=>[5,2,7,3,1,6,4]=>{{1,5},{2},{3,4,7},{6}}
[6,3,7,5,2,1,4]=>[3,6,1,2,5,7,4]=>[5,2,7,6,3,1,4]=>{{1,3,4,5,6,7},{2}}
[6,3,7,5,2,4,1]=>[3,6,2,5,7,1,4]=>[5,2,6,3,1,7,4]=>{{1,5},{2},{3,4,6,7}}
[6,3,7,5,4,1,2]=>[3,6,1,4,5,7,2]=>[5,2,7,4,3,1,6]=>{{1,3,5,6,7},{2},{4}}
[6,3,7,5,4,2,1]=>[3,6,1,2,4,5,7]=>[5,2,7,6,4,3,1]=>{{1,3,4,5,6,7},{2}}
[6,4,1,2,3,5,7]=>[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>{{1},{2,3,4,5,6,7}}
[6,4,1,2,3,7,5]=>[1,4,6,5,7,3,2]=>[7,4,2,3,1,5,6]=>{{1,5,6,7},{2,3,4}}
[6,4,1,2,5,3,7]=>[7,1,4,6,3,5,2]=>[1,7,4,2,5,3,6]=>{{1},{2,3,4,6,7},{5}}
[6,4,1,2,5,7,3]=>[1,4,6,5,3,7,2]=>[7,4,2,3,5,1,6]=>{{1,6,7},{2,3,4},{5}}
[6,4,1,2,7,3,5]=>[1,4,6,3,7,5,2]=>[7,4,2,5,1,3,6]=>{{1,2,3,4,5,6,7}}
[6,4,1,2,7,5,3]=>[1,4,6,3,5,7,2]=>[7,4,2,5,3,1,6]=>{{1,6,7},{2,3,4,5}}
[6,4,1,3,2,5,7]=>[7,1,4,6,5,2,3]=>[1,7,4,2,3,6,5]=>{{1},{2,3,4,5,7},{6}}
[6,4,1,3,2,7,5]=>[1,4,6,5,7,2,3]=>[7,4,2,3,1,6,5]=>{{1,5,7},{2,3,4},{6}}
[6,4,1,3,5,2,7]=>[7,1,4,6,3,2,5]=>[1,7,4,2,5,6,3]=>{{1},{2,3,4,7},{5},{6}}
[6,4,1,3,5,7,2]=>[1,4,6,5,3,2,7]=>[7,4,2,3,5,6,1]=>{{1,7},{2,3,4},{5},{6}}
[6,4,1,3,7,2,5]=>[1,4,6,3,2,7,5]=>[7,4,2,5,6,1,3]=>{{1,2,3,4,5,6,7}}
[6,4,1,3,7,5,2]=>[1,4,6,3,2,5,7]=>[7,4,2,5,6,3,1]=>{{1,7},{2,3,4,5,6}}
[6,4,1,5,2,3,7]=>[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>{{1},{2,3,4,5,6,7}}
[6,4,1,5,2,7,3]=>[1,4,6,2,5,3,7]=>[7,4,2,6,3,5,1]=>{{1,7},{2,3,4,5,6}}
[6,4,1,5,3,2,7]=>[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>{{1},{2,3,4,7},{5,6}}
[6,4,1,5,3,7,2]=>[1,4,6,3,5,2,7]=>[7,4,2,5,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[6,4,1,5,7,2,3]=>[1,4,6,5,2,7,3]=>[7,4,2,3,6,1,5]=>{{1,5,6,7},{2,3,4}}
[6,4,1,5,7,3,2]=>[1,4,6,5,2,3,7]=>[7,4,2,3,6,5,1]=>{{1,7},{2,3,4},{5,6}}
[6,4,1,7,2,3,5]=>[1,4,6,2,7,5,3]=>[7,4,2,6,1,3,5]=>{{1,5,7},{2,3,4,6}}
[6,4,1,7,2,5,3]=>[1,4,6,2,7,3,5]=>[7,4,2,6,1,5,3]=>{{1,2,3,4,5,6,7}}
[6,4,1,7,3,2,5]=>[1,4,6,2,3,7,5]=>[7,4,2,6,5,1,3]=>{{1,2,3,4,6,7},{5}}
[6,4,1,7,3,5,2]=>[1,4,6,3,7,2,5]=>[7,4,2,5,1,6,3]=>{{1,2,3,4,5,7},{6}}
[6,4,1,7,5,2,3]=>[1,4,6,2,5,7,3]=>[7,4,2,6,3,1,5]=>{{1,2,3,4,5,6,7}}
[6,4,1,7,5,3,2]=>[1,4,6,2,3,5,7]=>[7,4,2,6,5,3,1]=>{{1,7},{2,3,4,6},{5}}
[6,4,2,1,3,5,7]=>[7,1,2,4,6,5,3]=>[1,7,6,4,2,3,5]=>{{1},{2,5,7},{3,6},{4}}
[6,4,2,1,3,7,5]=>[1,2,4,6,5,7,3]=>[7,6,4,2,3,1,5]=>{{1,2,3,4,5,6,7}}
[6,4,2,1,5,3,7]=>[7,1,2,4,6,3,5]=>[1,7,6,4,2,5,3]=>{{1},{2,3,5,6,7},{4}}
[6,4,2,1,5,7,3]=>[1,2,4,6,5,3,7]=>[7,6,4,2,3,5,1]=>{{1,7},{2,3,4,5,6}}
[6,4,2,1,7,3,5]=>[1,2,4,6,3,7,5]=>[7,6,4,2,5,1,3]=>{{1,2,3,4,6,7},{5}}
[6,4,2,1,7,5,3]=>[1,2,4,6,3,5,7]=>[7,6,4,2,5,3,1]=>{{1,7},{2,3,4,6},{5}}
[6,4,2,3,1,5,7]=>[7,2,4,6,5,1,3]=>[1,6,4,2,3,7,5]=>{{1},{2,3,4,5,6,7}}
[6,4,2,3,1,7,5]=>[2,4,6,5,7,1,3]=>[6,4,2,3,1,7,5]=>{{1,5,6,7},{2,3,4}}
[6,4,2,3,5,1,7]=>[7,2,4,6,3,1,5]=>[1,6,4,2,5,7,3]=>{{1},{2,3,4,6,7},{5}}
[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>[6,4,2,3,5,7,1]=>{{1,6,7},{2,3,4},{5}}
[6,4,2,3,7,1,5]=>[2,4,6,3,1,7,5]=>[6,4,2,5,7,1,3]=>{{1,6},{2,3,4,5,7}}
[6,4,2,3,7,5,1]=>[2,4,6,3,1,5,7]=>[6,4,2,5,7,3,1]=>{{1,2,3,4,5,6,7}}
[6,4,2,5,1,3,7]=>[7,2,4,6,1,5,3]=>[1,6,4,2,7,3,5]=>{{1},{2,3,4,6},{5,7}}
[6,4,2,5,1,7,3]=>[2,4,6,1,5,3,7]=>[6,4,2,7,3,5,1]=>{{1,2,3,4,5,6,7}}
[6,4,2,5,3,1,7]=>[7,2,4,6,1,3,5]=>[1,6,4,2,7,5,3]=>{{1},{2,3,4,5,6,7}}
[6,4,2,5,3,7,1]=>[2,4,6,3,5,1,7]=>[6,4,2,5,3,7,1]=>{{1,6,7},{2,3,4,5}}
[6,4,2,5,7,1,3]=>[2,4,6,5,1,7,3]=>[6,4,2,3,7,1,5]=>{{1,6},{2,3,4},{5,7}}
[6,4,2,5,7,3,1]=>[2,4,6,5,1,3,7]=>[6,4,2,3,7,5,1]=>{{1,5,6,7},{2,3,4}}
[6,4,2,7,1,3,5]=>[2,4,6,1,7,5,3]=>[6,4,2,7,1,3,5]=>{{1,2,3,4,5,6,7}}
[6,4,2,7,1,5,3]=>[2,4,6,1,7,3,5]=>[6,4,2,7,1,5,3]=>{{1,5,6},{2,3,4,7}}
[6,4,2,7,3,1,5]=>[2,4,6,1,3,7,5]=>[6,4,2,7,5,1,3]=>{{1,6},{2,3,4,7},{5}}
[6,4,2,7,3,5,1]=>[2,4,6,3,7,1,5]=>[6,4,2,5,1,7,3]=>{{1,2,3,4,5,6,7}}
[6,4,2,7,5,1,3]=>[2,4,6,1,5,7,3]=>[6,4,2,7,3,1,5]=>{{1,6},{2,3,4,5,7}}
[6,4,2,7,5,3,1]=>[2,4,6,1,3,5,7]=>[6,4,2,7,5,3,1]=>{{1,2,3,4,6,7},{5}}
[6,4,3,1,2,5,7]=>[7,1,3,4,6,5,2]=>[1,7,5,4,2,3,6]=>{{1},{2,3,5,6,7},{4}}
[6,4,3,1,2,7,5]=>[1,3,4,6,5,7,2]=>[7,5,4,2,3,1,6]=>{{1,6,7},{2,3,4,5}}
[6,4,3,1,5,2,7]=>[7,1,3,4,6,2,5]=>[1,7,5,4,2,6,3]=>{{1},{2,3,5,7},{4},{6}}
[6,4,3,1,5,7,2]=>[1,3,4,6,5,2,7]=>[7,5,4,2,3,6,1]=>{{1,7},{2,3,4,5},{6}}
[6,4,3,1,7,2,5]=>[1,3,4,6,2,7,5]=>[7,5,4,2,6,1,3]=>{{1,2,3,4,5,6,7}}
[6,4,3,1,7,5,2]=>[1,3,4,6,2,5,7]=>[7,5,4,2,6,3,1]=>{{1,7},{2,3,4,5,6}}
[6,4,3,2,1,5,7]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>{{1},{2,3,6,7},{4,5}}
[6,4,3,2,1,7,5]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>{{1,7},{2,3,5,6},{4}}
[6,4,3,2,5,1,7]=>[7,2,3,4,6,1,5]=>[1,6,5,4,2,7,3]=>{{1},{2,3,5,6,7},{4}}
[6,4,3,2,5,7,1]=>[2,3,4,6,5,1,7]=>[6,5,4,2,3,7,1]=>{{1,6,7},{2,3,4,5}}
[6,4,3,2,7,1,5]=>[2,3,4,6,1,7,5]=>[6,5,4,2,7,1,3]=>{{1,6},{2,3,4,5,7}}
[6,4,3,2,7,5,1]=>[2,3,4,6,1,5,7]=>[6,5,4,2,7,3,1]=>{{1,2,3,4,5,6,7}}
[6,4,3,5,1,2,7]=>[7,3,4,6,1,5,2]=>[1,5,4,2,7,3,6]=>{{1},{2,3,4,5,6,7}}
[6,4,3,5,1,7,2]=>[3,4,6,1,5,2,7]=>[5,4,2,7,3,6,1]=>{{1,2,3,4,5,7},{6}}
[6,4,3,5,2,1,7]=>[7,3,4,6,1,2,5]=>[1,5,4,2,7,6,3]=>{{1},{2,3,4,5,7},{6}}
[6,4,3,5,2,7,1]=>[3,4,6,2,5,1,7]=>[5,4,2,6,3,7,1]=>{{1,2,3,4,5,6,7}}
[6,4,3,5,7,1,2]=>[3,4,6,5,1,7,2]=>[5,4,2,3,7,1,6]=>{{1,5,6,7},{2,3,4}}
[6,4,3,5,7,2,1]=>[3,4,6,5,1,2,7]=>[5,4,2,3,7,6,1]=>{{1,5,7},{2,3,4},{6}}
[6,4,3,7,1,2,5]=>[3,4,6,1,7,5,2]=>[5,4,2,7,1,3,6]=>{{1,5},{2,3,4,6,7}}
[6,4,3,7,1,5,2]=>[3,4,6,1,7,2,5]=>[5,4,2,7,1,6,3]=>{{1,5},{2,3,4,7},{6}}
[6,4,3,7,2,1,5]=>[3,4,6,1,2,7,5]=>[5,4,2,7,6,1,3]=>{{1,5,6},{2,3,4,7}}
[6,4,3,7,2,5,1]=>[3,4,6,2,7,1,5]=>[5,4,2,6,1,7,3]=>{{1,5},{2,3,4,6,7}}
[6,4,3,7,5,1,2]=>[3,4,6,1,5,7,2]=>[5,4,2,7,3,1,6]=>{{1,2,3,4,5,6,7}}
[6,4,3,7,5,2,1]=>[3,4,6,1,2,5,7]=>[5,4,2,7,6,3,1]=>{{1,2,3,4,5,6,7}}
[6,4,5,1,2,3,7]=>[7,4,6,1,5,3,2]=>[1,4,2,7,3,5,6]=>{{1},{2,3,4,5,6,7}}
[6,4,5,1,2,7,3]=>[4,6,1,5,3,7,2]=>[4,2,7,3,5,1,6]=>{{1,3,4,6,7},{2},{5}}
[6,4,5,1,3,2,7]=>[7,4,6,1,5,2,3]=>[1,4,2,7,3,6,5]=>{{1},{2,3,4,5,7},{6}}
[6,4,5,1,3,7,2]=>[4,6,1,5,3,2,7]=>[4,2,7,3,5,6,1]=>{{1,3,4,7},{2},{5},{6}}
[6,4,5,1,7,2,3]=>[4,6,1,5,2,7,3]=>[4,2,7,3,6,1,5]=>{{1,3,4,5,6,7},{2}}
[6,4,5,1,7,3,2]=>[4,6,1,5,2,3,7]=>[4,2,7,3,6,5,1]=>{{1,3,4,7},{2},{5,6}}
[6,4,5,2,1,3,7]=>[7,4,6,1,2,5,3]=>[1,4,2,7,6,3,5]=>{{1},{2,3,4,5,6,7}}
[6,4,5,2,1,7,3]=>[4,6,1,2,5,3,7]=>[4,2,7,6,3,5,1]=>{{1,3,4,5,6,7},{2}}
[6,4,5,2,3,1,7]=>[7,4,6,2,5,1,3]=>[1,4,2,6,3,7,5]=>{{1},{2,3,4,5,6,7}}
[6,4,5,2,3,7,1]=>[4,6,2,5,3,1,7]=>[4,2,6,3,5,7,1]=>{{1,3,4,6,7},{2},{5}}
[6,4,5,2,7,1,3]=>[4,6,2,5,1,7,3]=>[4,2,6,3,7,1,5]=>{{1,3,4,6},{2},{5,7}}
[6,4,5,2,7,3,1]=>[4,6,2,5,1,3,7]=>[4,2,6,3,7,5,1]=>{{1,3,4,5,6,7},{2}}
[6,4,5,3,1,2,7]=>[7,4,6,1,3,5,2]=>[1,4,2,7,5,3,6]=>{{1},{2,3,4,6,7},{5}}
[6,4,5,3,1,7,2]=>[4,6,1,3,5,2,7]=>[4,2,7,5,3,6,1]=>{{1,3,4,5,7},{2},{6}}
[6,4,5,3,2,1,7]=>[7,4,6,1,2,3,5]=>[1,4,2,7,6,5,3]=>{{1},{2,3,4,7},{5,6}}
[6,4,5,3,2,7,1]=>[4,6,2,3,5,1,7]=>[4,2,6,5,3,7,1]=>{{1,3,4,5,6,7},{2}}
[6,4,5,3,7,1,2]=>[4,6,3,5,1,7,2]=>[4,2,5,3,7,1,6]=>{{1,3,4,5,6,7},{2}}
[6,4,5,3,7,2,1]=>[4,6,3,5,1,2,7]=>[4,2,5,3,7,6,1]=>{{1,3,4,5,7},{2},{6}}
[6,4,5,7,1,2,3]=>[4,6,5,1,7,3,2]=>[4,2,3,7,1,5,6]=>{{1,4,5,6,7},{2},{3}}
[6,4,5,7,1,3,2]=>[4,6,5,1,7,2,3]=>[4,2,3,7,1,6,5]=>{{1,4,5,7},{2},{3},{6}}
[6,4,5,7,2,1,3]=>[4,6,5,1,2,7,3]=>[4,2,3,7,6,1,5]=>{{1,4,5,6,7},{2},{3}}
[6,4,5,7,2,3,1]=>[4,6,5,2,7,1,3]=>[4,2,3,6,1,7,5]=>{{1,4,5,6,7},{2},{3}}
[6,4,5,7,3,1,2]=>[4,6,5,1,3,7,2]=>[4,2,3,7,5,1,6]=>{{1,4,6,7},{2},{3},{5}}
[6,4,5,7,3,2,1]=>[4,6,5,1,2,3,7]=>[4,2,3,7,6,5,1]=>{{1,4,7},{2},{3},{5,6}}
[6,4,7,1,2,3,5]=>[4,6,1,7,5,3,2]=>[4,2,7,1,3,5,6]=>{{1,4},{2},{3,5,6,7}}
[6,4,7,1,2,5,3]=>[4,6,1,7,3,5,2]=>[4,2,7,1,5,3,6]=>{{1,4},{2},{3,6,7},{5}}
[6,4,7,1,3,2,5]=>[4,6,1,7,5,2,3]=>[4,2,7,1,3,6,5]=>{{1,4},{2},{3,5,7},{6}}
[6,4,7,1,3,5,2]=>[4,6,1,7,3,2,5]=>[4,2,7,1,5,6,3]=>{{1,4},{2},{3,7},{5},{6}}
[6,4,7,1,5,2,3]=>[4,6,1,7,2,5,3]=>[4,2,7,1,6,3,5]=>{{1,4},{2},{3,5,6,7}}
[6,4,7,1,5,3,2]=>[4,6,1,7,2,3,5]=>[4,2,7,1,6,5,3]=>{{1,4},{2},{3,7},{5,6}}
[6,4,7,2,1,3,5]=>[4,6,1,2,7,5,3]=>[4,2,7,6,1,3,5]=>{{1,3,4,5,6,7},{2}}
[6,4,7,2,1,5,3]=>[4,6,1,2,7,3,5]=>[4,2,7,6,1,5,3]=>{{1,4,5,6},{2},{3,7}}
[6,4,7,2,3,1,5]=>[4,6,2,7,5,1,3]=>[4,2,6,1,3,7,5]=>{{1,4},{2},{3,5,6,7}}
[6,4,7,2,3,5,1]=>[4,6,2,7,3,1,5]=>[4,2,6,1,5,7,3]=>{{1,4},{2},{3,6,7},{5}}
[6,4,7,2,5,1,3]=>[4,6,2,7,1,5,3]=>[4,2,6,1,7,3,5]=>{{1,4},{2},{3,6},{5,7}}
[6,4,7,2,5,3,1]=>[4,6,2,7,1,3,5]=>[4,2,6,1,7,5,3]=>{{1,4},{2},{3,5,6,7}}
[6,4,7,3,1,2,5]=>[4,6,1,3,7,5,2]=>[4,2,7,5,1,3,6]=>{{1,4,5},{2},{3,6,7}}
[6,4,7,3,1,5,2]=>[4,6,1,3,7,2,5]=>[4,2,7,5,1,6,3]=>{{1,4,5},{2},{3,7},{6}}
[6,4,7,3,2,1,5]=>[4,6,1,2,3,7,5]=>[4,2,7,6,5,1,3]=>{{1,4,6},{2},{3,7},{5}}
[6,4,7,3,2,5,1]=>[4,6,2,3,7,1,5]=>[4,2,6,5,1,7,3]=>{{1,4,5},{2},{3,6,7}}
[6,4,7,3,5,1,2]=>[4,6,3,7,1,5,2]=>[4,2,5,1,7,3,6]=>{{1,4},{2},{3,5,6,7}}
[6,4,7,3,5,2,1]=>[4,6,3,7,1,2,5]=>[4,2,5,1,7,6,3]=>{{1,4},{2},{3,5,7},{6}}
[6,4,7,5,1,2,3]=>[4,6,1,5,7,3,2]=>[4,2,7,3,1,5,6]=>{{1,3,4,5,6,7},{2}}
[6,4,7,5,1,3,2]=>[4,6,1,5,7,2,3]=>[4,2,7,3,1,6,5]=>{{1,3,4,5,7},{2},{6}}
[6,4,7,5,2,1,3]=>[4,6,1,2,5,7,3]=>[4,2,7,6,3,1,5]=>{{1,4,6},{2},{3,5,7}}
[6,4,7,5,2,3,1]=>[4,6,2,5,7,1,3]=>[4,2,6,3,1,7,5]=>{{1,3,4,5,6,7},{2}}
[6,4,7,5,3,1,2]=>[4,6,1,3,5,7,2]=>[4,2,7,5,3,1,6]=>{{1,3,4,5,6,7},{2}}
[6,4,7,5,3,2,1]=>[4,6,1,2,3,5,7]=>[4,2,7,6,5,3,1]=>{{1,3,4,6,7},{2},{5}}
[6,5,1,2,3,4,7]=>[7,1,5,6,4,3,2]=>[1,7,3,2,4,5,6]=>{{1},{2,4,5,6,7},{3}}
[6,5,1,2,3,7,4]=>[1,5,6,4,7,3,2]=>[7,3,2,4,1,5,6]=>{{1,5,6,7},{2,3},{4}}
[6,5,1,2,4,3,7]=>[7,1,5,6,3,4,2]=>[1,7,3,2,5,4,6]=>{{1},{2,4,6,7},{3},{5}}
[6,5,1,2,4,7,3]=>[1,5,6,4,3,7,2]=>[7,3,2,4,5,1,6]=>{{1,6,7},{2,3},{4},{5}}
[6,5,1,2,7,3,4]=>[1,5,6,3,7,4,2]=>[7,3,2,5,1,4,6]=>{{1,4,5,6,7},{2,3}}
[6,5,1,2,7,4,3]=>[1,5,6,3,4,7,2]=>[7,3,2,5,4,1,6]=>{{1,6,7},{2,3},{4,5}}
[6,5,1,3,2,4,7]=>[7,1,5,6,4,2,3]=>[1,7,3,2,4,6,5]=>{{1},{2,4,5,7},{3},{6}}
[6,5,1,3,2,7,4]=>[1,5,6,4,7,2,3]=>[7,3,2,4,1,6,5]=>{{1,5,7},{2,3},{4},{6}}
[6,5,1,3,4,2,7]=>[7,1,5,6,3,2,4]=>[1,7,3,2,5,6,4]=>{{1},{2,4,7},{3},{5},{6}}
[6,5,1,3,4,7,2]=>[1,5,6,4,3,2,7]=>[7,3,2,4,5,6,1]=>{{1,7},{2,3},{4},{5},{6}}
[6,5,1,3,7,2,4]=>[1,5,6,3,2,7,4]=>[7,3,2,5,6,1,4]=>{{1,4,5,6,7},{2,3}}
[6,5,1,3,7,4,2]=>[1,5,6,3,2,4,7]=>[7,3,2,5,6,4,1]=>{{1,7},{2,3},{4,5,6}}
[6,5,1,4,2,3,7]=>[7,1,5,6,2,4,3]=>[1,7,3,2,6,4,5]=>{{1},{2,4,5,6,7},{3}}
[6,5,1,4,2,7,3]=>[1,5,6,2,4,3,7]=>[7,3,2,6,4,5,1]=>{{1,7},{2,3},{4,5,6}}
[6,5,1,4,3,2,7]=>[7,1,5,6,2,3,4]=>[1,7,3,2,6,5,4]=>{{1},{2,4,7},{3},{5,6}}
[6,5,1,4,3,7,2]=>[1,5,6,3,4,2,7]=>[7,3,2,5,4,6,1]=>{{1,7},{2,3},{4,5},{6}}
[6,5,1,4,7,2,3]=>[1,5,6,4,2,7,3]=>[7,3,2,4,6,1,5]=>{{1,5,6,7},{2,3},{4}}
[6,5,1,4,7,3,2]=>[1,5,6,4,2,3,7]=>[7,3,2,4,6,5,1]=>{{1,7},{2,3},{4},{5,6}}
[6,5,1,7,2,3,4]=>[1,5,6,2,7,4,3]=>[7,3,2,6,1,4,5]=>{{1,5,7},{2,3},{4,6}}
[6,5,1,7,2,4,3]=>[1,5,6,2,7,3,4]=>[7,3,2,6,1,5,4]=>{{1,4,5,6,7},{2,3}}
[6,5,1,7,3,2,4]=>[1,5,6,2,3,7,4]=>[7,3,2,6,5,1,4]=>{{1,4,6,7},{2,3},{5}}
[6,5,1,7,3,4,2]=>[1,5,6,3,7,2,4]=>[7,3,2,5,1,6,4]=>{{1,4,5,7},{2,3},{6}}
[6,5,1,7,4,2,3]=>[1,5,6,2,4,7,3]=>[7,3,2,6,4,1,5]=>{{1,4,5,6,7},{2,3}}
[6,5,1,7,4,3,2]=>[1,5,6,2,3,4,7]=>[7,3,2,6,5,4,1]=>{{1,7},{2,3},{4,6},{5}}
[6,5,2,1,3,4,7]=>[7,1,2,5,6,4,3]=>[1,7,6,3,2,4,5]=>{{1},{2,5,7},{3,4,6}}
[6,5,2,1,3,7,4]=>[1,2,5,6,4,7,3]=>[7,6,3,2,4,1,5]=>{{1,2,4,5,6,7},{3}}
[6,5,2,1,4,3,7]=>[7,1,2,5,6,3,4]=>[1,7,6,3,2,5,4]=>{{1},{2,3,4,5,6,7}}
[6,5,2,1,4,7,3]=>[1,2,5,6,4,3,7]=>[7,6,3,2,4,5,1]=>{{1,7},{2,4,5,6},{3}}
[6,5,2,1,7,3,4]=>[1,2,5,6,3,7,4]=>[7,6,3,2,5,1,4]=>{{1,2,4,6,7},{3},{5}}
[6,5,2,1,7,4,3]=>[1,2,5,6,3,4,7]=>[7,6,3,2,5,4,1]=>{{1,7},{2,4,6},{3},{5}}
[6,5,2,3,1,4,7]=>[7,2,5,6,4,1,3]=>[1,6,3,2,4,7,5]=>{{1},{2,4,5,6,7},{3}}
[6,5,2,3,1,7,4]=>[2,5,6,4,7,1,3]=>[6,3,2,4,1,7,5]=>{{1,5,6,7},{2,3},{4}}
[6,5,2,3,4,1,7]=>[7,2,5,6,3,1,4]=>[1,6,3,2,5,7,4]=>{{1},{2,4,6,7},{3},{5}}
[6,5,2,3,4,7,1]=>[2,5,6,4,3,1,7]=>[6,3,2,4,5,7,1]=>{{1,6,7},{2,3},{4},{5}}
[6,5,2,3,7,1,4]=>[2,5,6,3,1,7,4]=>[6,3,2,5,7,1,4]=>{{1,6},{2,3},{4,5,7}}
[6,5,2,3,7,4,1]=>[2,5,6,3,1,4,7]=>[6,3,2,5,7,4,1]=>{{1,4,5,6,7},{2,3}}
[6,5,2,4,1,3,7]=>[7,2,5,6,1,4,3]=>[1,6,3,2,7,4,5]=>{{1},{2,4,6},{3},{5,7}}
[6,5,2,4,1,7,3]=>[2,5,6,1,4,3,7]=>[6,3,2,7,4,5,1]=>{{1,4,5,6,7},{2,3}}
[6,5,2,4,3,1,7]=>[7,2,5,6,1,3,4]=>[1,6,3,2,7,5,4]=>{{1},{2,4,5,6,7},{3}}
[6,5,2,4,3,7,1]=>[2,5,6,3,4,1,7]=>[6,3,2,5,4,7,1]=>{{1,6,7},{2,3},{4,5}}
[6,5,2,4,7,1,3]=>[2,5,6,4,1,7,3]=>[6,3,2,4,7,1,5]=>{{1,6},{2,3},{4},{5,7}}
[6,5,2,4,7,3,1]=>[2,5,6,4,1,3,7]=>[6,3,2,4,7,5,1]=>{{1,5,6,7},{2,3},{4}}
[6,5,2,7,1,3,4]=>[2,5,6,1,7,4,3]=>[6,3,2,7,1,4,5]=>{{1,4,5,6,7},{2,3}}
[6,5,2,7,1,4,3]=>[2,5,6,1,7,3,4]=>[6,3,2,7,1,5,4]=>{{1,5,6},{2,3},{4,7}}
[6,5,2,7,3,1,4]=>[2,5,6,1,3,7,4]=>[6,3,2,7,5,1,4]=>{{1,6},{2,3},{4,7},{5}}
[6,5,2,7,3,4,1]=>[2,5,6,3,7,1,4]=>[6,3,2,5,1,7,4]=>{{1,4,5,6,7},{2,3}}
[6,5,2,7,4,1,3]=>[2,5,6,1,4,7,3]=>[6,3,2,7,4,1,5]=>{{1,6},{2,3},{4,5,7}}
[6,5,2,7,4,3,1]=>[2,5,6,1,3,4,7]=>[6,3,2,7,5,4,1]=>{{1,4,6,7},{2,3},{5}}
[6,5,3,1,2,4,7]=>[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>{{1},{2,3,4,5,6,7}}
[6,5,3,1,2,7,4]=>[1,3,5,6,4,7,2]=>[7,5,3,2,4,1,6]=>{{1,6,7},{2,4,5},{3}}
[6,5,3,1,4,2,7]=>[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>{{1},{2,3,4,5,7},{6}}
[6,5,3,1,4,7,2]=>[1,3,5,6,4,2,7]=>[7,5,3,2,4,6,1]=>{{1,7},{2,4,5},{3},{6}}
[6,5,3,1,7,2,4]=>[1,3,5,6,2,7,4]=>[7,5,3,2,6,1,4]=>{{1,2,4,5,6,7},{3}}
[6,5,3,1,7,4,2]=>[1,3,5,6,2,4,7]=>[7,5,3,2,6,4,1]=>{{1,7},{2,4,5,6},{3}}
[6,5,3,2,1,4,7]=>[7,1,2,3,5,6,4]=>[1,7,6,5,3,2,4]=>{{1},{2,3,4,5,6,7}}
[6,5,3,2,1,7,4]=>[1,2,3,5,6,4,7]=>[7,6,5,3,2,4,1]=>{{1,7},{2,3,4,5,6}}
[6,5,3,2,4,1,7]=>[7,2,3,5,6,1,4]=>[1,6,5,3,2,7,4]=>{{1},{2,3,4,5,6,7}}
[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>[6,5,3,2,4,7,1]=>{{1,6,7},{2,4,5},{3}}
[6,5,3,2,7,1,4]=>[2,3,5,6,1,7,4]=>[6,5,3,2,7,1,4]=>{{1,6},{2,4,5,7},{3}}
[6,5,3,2,7,4,1]=>[2,3,5,6,1,4,7]=>[6,5,3,2,7,4,1]=>{{1,2,4,5,6,7},{3}}
[6,5,3,4,1,2,7]=>[7,3,5,6,1,4,2]=>[1,5,3,2,7,4,6]=>{{1},{2,4,5,6,7},{3}}
[6,5,3,4,1,7,2]=>[3,5,6,1,4,2,7]=>[5,3,2,7,4,6,1]=>{{1,4,5,7},{2,3},{6}}
[6,5,3,4,2,1,7]=>[7,3,5,6,1,2,4]=>[1,5,3,2,7,6,4]=>{{1},{2,4,5,7},{3},{6}}
[6,5,3,4,2,7,1]=>[3,5,6,2,4,1,7]=>[5,3,2,6,4,7,1]=>{{1,4,5,6,7},{2,3}}
[6,5,3,4,7,1,2]=>[3,5,6,4,1,7,2]=>[5,3,2,4,7,1,6]=>{{1,5,6,7},{2,3},{4}}
[6,5,3,4,7,2,1]=>[3,5,6,4,1,2,7]=>[5,3,2,4,7,6,1]=>{{1,5,7},{2,3},{4},{6}}
[6,5,3,7,1,2,4]=>[3,5,6,1,7,4,2]=>[5,3,2,7,1,4,6]=>{{1,5},{2,3},{4,6,7}}
[6,5,3,7,1,4,2]=>[3,5,6,1,7,2,4]=>[5,3,2,7,1,6,4]=>{{1,5},{2,3},{4,7},{6}}
[6,5,3,7,2,1,4]=>[3,5,6,1,2,7,4]=>[5,3,2,7,6,1,4]=>{{1,5,6},{2,3},{4,7}}
[6,5,3,7,2,4,1]=>[3,5,6,2,7,1,4]=>[5,3,2,6,1,7,4]=>{{1,5},{2,3},{4,6,7}}
[6,5,3,7,4,1,2]=>[3,5,6,1,4,7,2]=>[5,3,2,7,4,1,6]=>{{1,4,5,6,7},{2,3}}
[6,5,3,7,4,2,1]=>[3,5,6,1,2,4,7]=>[5,3,2,7,6,4,1]=>{{1,4,5,6,7},{2,3}}
[6,5,4,1,2,3,7]=>[7,1,4,5,6,3,2]=>[1,7,4,3,2,5,6]=>{{1},{2,5,6,7},{3,4}}
[6,5,4,1,2,7,3]=>[1,4,5,6,3,7,2]=>[7,4,3,2,5,1,6]=>{{1,6,7},{2,4},{3},{5}}
[6,5,4,1,3,2,7]=>[7,1,4,5,6,2,3]=>[1,7,4,3,2,6,5]=>{{1},{2,5,7},{3,4},{6}}
[6,5,4,1,3,7,2]=>[1,4,5,6,3,2,7]=>[7,4,3,2,5,6,1]=>{{1,7},{2,4},{3},{5},{6}}
[6,5,4,1,7,2,3]=>[1,4,5,6,2,7,3]=>[7,4,3,2,6,1,5]=>{{1,5,6,7},{2,4},{3}}
[6,5,4,1,7,3,2]=>[1,4,5,6,2,3,7]=>[7,4,3,2,6,5,1]=>{{1,7},{2,4},{3},{5,6}}
[6,5,4,2,1,3,7]=>[7,1,2,4,5,6,3]=>[1,7,6,4,3,2,5]=>{{1},{2,3,5,6,7},{4}}
[6,5,4,2,1,7,3]=>[1,2,4,5,6,3,7]=>[7,6,4,3,2,5,1]=>{{1,7},{2,5,6},{3,4}}
[6,5,4,2,3,1,7]=>[7,2,4,5,6,1,3]=>[1,6,4,3,2,7,5]=>{{1},{2,5,6,7},{3,4}}
[6,5,4,2,3,7,1]=>[2,4,5,6,3,1,7]=>[6,4,3,2,5,7,1]=>{{1,6,7},{2,4},{3},{5}}
[6,5,4,2,7,1,3]=>[2,4,5,6,1,7,3]=>[6,4,3,2,7,1,5]=>{{1,6},{2,4},{3},{5,7}}
[6,5,4,2,7,3,1]=>[2,4,5,6,1,3,7]=>[6,4,3,2,7,5,1]=>{{1,5,6,7},{2,4},{3}}
[6,5,4,3,1,2,7]=>[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>{{1},{2,6,7},{3,5},{4}}
[6,5,4,3,1,7,2]=>[1,3,4,5,6,2,7]=>[7,5,4,3,2,6,1]=>{{1,7},{2,5},{3,4},{6}}
[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>{{1},{2,7},{3,6},{4,5}}
[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>{{1,6,7},{2,5},{3,4}}
[6,5,4,3,7,1,2]=>[3,4,5,6,1,7,2]=>[5,4,3,2,7,1,6]=>{{1,5,6,7},{2,4},{3}}
[6,5,4,3,7,2,1]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>{{1,5,7},{2,4},{3},{6}}
[6,5,4,7,1,2,3]=>[4,5,6,1,7,3,2]=>[4,3,2,7,1,5,6]=>{{1,4,5,6,7},{2,3}}
[6,5,4,7,1,3,2]=>[4,5,6,1,7,2,3]=>[4,3,2,7,1,6,5]=>{{1,4,5,7},{2,3},{6}}
[6,5,4,7,2,1,3]=>[4,5,6,1,2,7,3]=>[4,3,2,7,6,1,5]=>{{1,4,5,6,7},{2,3}}
[6,5,4,7,2,3,1]=>[4,5,6,2,7,1,3]=>[4,3,2,6,1,7,5]=>{{1,4,5,6,7},{2,3}}
[6,5,4,7,3,1,2]=>[4,5,6,1,3,7,2]=>[4,3,2,7,5,1,6]=>{{1,4,6,7},{2,3},{5}}
[6,5,4,7,3,2,1]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>{{1,4,7},{2,3},{5,6}}
[6,5,7,1,2,3,4]=>[5,6,1,7,4,3,2]=>[3,2,7,1,4,5,6]=>{{1,3,4,5,6,7},{2}}
[6,5,7,1,2,4,3]=>[5,6,1,7,3,4,2]=>[3,2,7,1,5,4,6]=>{{1,3,4,6,7},{2},{5}}
[6,5,7,1,3,2,4]=>[5,6,1,7,4,2,3]=>[3,2,7,1,4,6,5]=>{{1,3,4,5,7},{2},{6}}
[6,5,7,1,3,4,2]=>[5,6,1,7,3,2,4]=>[3,2,7,1,5,6,4]=>{{1,3,4,7},{2},{5},{6}}
[6,5,7,1,4,2,3]=>[5,6,1,7,2,4,3]=>[3,2,7,1,6,4,5]=>{{1,3,4,5,6,7},{2}}
[6,5,7,1,4,3,2]=>[5,6,1,7,2,3,4]=>[3,2,7,1,6,5,4]=>{{1,3,4,7},{2},{5,6}}
[6,5,7,2,1,3,4]=>[5,6,1,2,7,4,3]=>[3,2,7,6,1,4,5]=>{{1,3,5,7},{2},{4,6}}
[6,5,7,2,1,4,3]=>[5,6,1,2,7,3,4]=>[3,2,7,6,1,5,4]=>{{1,3,4,5,6,7},{2}}
[6,5,7,2,3,1,4]=>[5,6,2,7,4,1,3]=>[3,2,6,1,4,7,5]=>{{1,3,4,5,6,7},{2}}
[6,5,7,2,3,4,1]=>[5,6,2,7,3,1,4]=>[3,2,6,1,5,7,4]=>{{1,3,4,6,7},{2},{5}}
[6,5,7,2,4,1,3]=>[5,6,2,7,1,4,3]=>[3,2,6,1,7,4,5]=>{{1,3,4,6},{2},{5,7}}
[6,5,7,2,4,3,1]=>[5,6,2,7,1,3,4]=>[3,2,6,1,7,5,4]=>{{1,3,4,5,6,7},{2}}
[6,5,7,3,1,2,4]=>[5,6,1,3,7,4,2]=>[3,2,7,5,1,4,6]=>{{1,3,4,5,6,7},{2}}
[6,5,7,3,1,4,2]=>[5,6,1,3,7,2,4]=>[3,2,7,5,1,6,4]=>{{1,3,4,5,7},{2},{6}}
[6,5,7,3,2,1,4]=>[5,6,1,2,3,7,4]=>[3,2,7,6,5,1,4]=>{{1,3,4,6,7},{2},{5}}
[6,5,7,3,2,4,1]=>[5,6,2,3,7,1,4]=>[3,2,6,5,1,7,4]=>{{1,3,4,5,6,7},{2}}
[6,5,7,3,4,1,2]=>[5,6,3,7,1,4,2]=>[3,2,5,1,7,4,6]=>{{1,3,4,5,6,7},{2}}
[6,5,7,3,4,2,1]=>[5,6,3,7,1,2,4]=>[3,2,5,1,7,6,4]=>{{1,3,4,5,7},{2},{6}}
[6,5,7,4,1,2,3]=>[5,6,1,4,7,3,2]=>[3,2,7,4,1,5,6]=>{{1,3,5,6,7},{2},{4}}
[6,5,7,4,1,3,2]=>[5,6,1,4,7,2,3]=>[3,2,7,4,1,6,5]=>{{1,3,5,7},{2},{4},{6}}
[6,5,7,4,2,1,3]=>[5,6,1,2,4,7,3]=>[3,2,7,6,4,1,5]=>{{1,3,4,5,6,7},{2}}
[6,5,7,4,2,3,1]=>[5,6,2,4,7,1,3]=>[3,2,6,4,1,7,5]=>{{1,3,5,6,7},{2},{4}}
[6,5,7,4,3,1,2]=>[5,6,1,3,4,7,2]=>[3,2,7,5,4,1,6]=>{{1,3,6,7},{2},{4,5}}
[6,5,7,4,3,2,1]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>{{1,3,7},{2},{4,6},{5}}
[6,7,1,2,3,4,5]=>[6,1,7,5,4,3,2]=>[2,7,1,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[6,7,1,2,3,5,4]=>[6,1,7,4,5,3,2]=>[2,7,1,4,3,5,6]=>{{1,2,3,5,6,7},{4}}
[6,7,1,2,4,3,5]=>[6,1,7,5,3,4,2]=>[2,7,1,3,5,4,6]=>{{1,2,3,4,6,7},{5}}
[6,7,1,2,4,5,3]=>[6,1,7,4,3,5,2]=>[2,7,1,4,5,3,6]=>{{1,2,3,6,7},{4},{5}}
[6,7,1,2,5,3,4]=>[6,1,7,3,5,4,2]=>[2,7,1,5,3,4,6]=>{{1,2,3,4,5,6,7}}
[6,7,1,2,5,4,3]=>[6,1,7,3,4,5,2]=>[2,7,1,5,4,3,6]=>{{1,2,3,6,7},{4,5}}
[6,7,1,3,2,4,5]=>[6,1,7,5,4,2,3]=>[2,7,1,3,4,6,5]=>{{1,2,3,4,5,7},{6}}
[6,7,1,3,2,5,4]=>[6,1,7,4,5,2,3]=>[2,7,1,4,3,6,5]=>{{1,2,3,5,7},{4},{6}}
[6,7,1,3,4,2,5]=>[6,1,7,5,3,2,4]=>[2,7,1,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[6,7,1,3,4,5,2]=>[6,1,7,4,3,2,5]=>[2,7,1,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}
[6,7,1,3,5,2,4]=>[6,1,7,3,2,5,4]=>[2,7,1,5,6,3,4]=>{{1,2,3,4,5,6,7}}
[6,7,1,3,5,4,2]=>[6,1,7,3,2,4,5]=>[2,7,1,5,6,4,3]=>{{1,2,3,7},{4,5,6}}
[6,7,1,4,2,3,5]=>[6,1,7,5,2,4,3]=>[2,7,1,3,6,4,5]=>{{1,2,3,4,5,6,7}}
[6,7,1,4,2,5,3]=>[6,1,7,2,4,3,5]=>[2,7,1,6,4,5,3]=>{{1,2,3,7},{4,5,6}}
[6,7,1,4,3,2,5]=>[6,1,7,5,2,3,4]=>[2,7,1,3,6,5,4]=>{{1,2,3,4,7},{5,6}}
[6,7,1,4,3,5,2]=>[6,1,7,3,4,2,5]=>[2,7,1,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}
[6,7,1,4,5,2,3]=>[6,1,7,4,2,5,3]=>[2,7,1,4,6,3,5]=>{{1,2,3,5,6,7},{4}}
[6,7,1,4,5,3,2]=>[6,1,7,4,2,3,5]=>[2,7,1,4,6,5,3]=>{{1,2,3,7},{4},{5,6}}
[6,7,1,5,2,3,4]=>[6,1,7,2,5,4,3]=>[2,7,1,6,3,4,5]=>{{1,2,3,5,7},{4,6}}
[6,7,1,5,2,4,3]=>[6,1,7,2,5,3,4]=>[2,7,1,6,3,5,4]=>{{1,2,3,4,5,6,7}}
[6,7,1,5,3,2,4]=>[6,1,7,2,3,5,4]=>[2,7,1,6,5,3,4]=>{{1,2,3,4,6,7},{5}}
[6,7,1,5,3,4,2]=>[6,1,7,3,5,2,4]=>[2,7,1,5,3,6,4]=>{{1,2,3,4,5,7},{6}}
[6,7,1,5,4,2,3]=>[6,1,7,2,4,5,3]=>[2,7,1,6,4,3,5]=>{{1,2,3,4,5,6,7}}
[6,7,1,5,4,3,2]=>[6,1,7,2,3,4,5]=>[2,7,1,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}
[6,7,2,1,3,4,5]=>[6,1,2,7,5,4,3]=>[2,7,6,1,3,4,5]=>{{1,2,3,4,5,6,7}}
[6,7,2,1,3,5,4]=>[6,1,2,7,4,5,3]=>[2,7,6,1,4,3,5]=>{{1,2,4,5,7},{3,6}}
[6,7,2,1,4,3,5]=>[6,1,2,7,5,3,4]=>[2,7,6,1,3,5,4]=>{{1,2,4,7},{3,5,6}}
[6,7,2,1,4,5,3]=>[6,1,2,7,4,3,5]=>[2,7,6,1,4,5,3]=>{{1,2,3,4,5,6,7}}
[6,7,2,1,5,3,4]=>[6,1,2,7,3,5,4]=>[2,7,6,1,5,3,4]=>{{1,2,4,7},{3,6},{5}}
[6,7,2,1,5,4,3]=>[6,1,2,7,3,4,5]=>[2,7,6,1,5,4,3]=>{{1,2,3,4,6,7},{5}}
[6,7,2,3,1,4,5]=>[6,2,7,5,4,1,3]=>[2,6,1,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[6,7,2,3,1,5,4]=>[6,2,7,4,5,1,3]=>[2,6,1,4,3,7,5]=>{{1,2,3,5,6,7},{4}}
[6,7,2,3,4,1,5]=>[6,2,7,5,3,1,4]=>[2,6,1,3,5,7,4]=>{{1,2,3,4,6,7},{5}}
[6,7,2,3,4,5,1]=>[6,2,7,4,3,1,5]=>[2,6,1,4,5,7,3]=>{{1,2,3,6,7},{4},{5}}
[6,7,2,3,5,1,4]=>[6,2,7,3,1,5,4]=>[2,6,1,5,7,3,4]=>{{1,2,3,6},{4,5,7}}
[6,7,2,3,5,4,1]=>[6,2,7,3,1,4,5]=>[2,6,1,5,7,4,3]=>{{1,2,3,4,5,6,7}}
[6,7,2,4,1,3,5]=>[6,2,7,5,1,4,3]=>[2,6,1,3,7,4,5]=>{{1,2,3,4,6},{5,7}}
[6,7,2,4,1,5,3]=>[6,2,7,1,4,3,5]=>[2,6,1,7,4,5,3]=>{{1,2,3,4,5,6,7}}
[6,7,2,4,3,1,5]=>[6,2,7,5,1,3,4]=>[2,6,1,3,7,5,4]=>{{1,2,3,4,5,6,7}}
[6,7,2,4,3,5,1]=>[6,2,7,3,4,1,5]=>[2,6,1,5,4,7,3]=>{{1,2,3,6,7},{4,5}}
[6,7,2,4,5,1,3]=>[6,2,7,4,1,5,3]=>[2,6,1,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}
[6,7,2,4,5,3,1]=>[6,2,7,4,1,3,5]=>[2,6,1,4,7,5,3]=>{{1,2,3,5,6,7},{4}}
[6,7,2,5,1,3,4]=>[6,2,7,1,5,4,3]=>[2,6,1,7,3,4,5]=>{{1,2,3,4,5,6,7}}
[6,7,2,5,1,4,3]=>[6,2,7,1,5,3,4]=>[2,6,1,7,3,5,4]=>{{1,2,3,5,6},{4,7}}
[6,7,2,5,3,1,4]=>[6,2,7,1,3,5,4]=>[2,6,1,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}
[6,7,2,5,3,4,1]=>[6,2,7,3,5,1,4]=>[2,6,1,5,3,7,4]=>{{1,2,3,4,5,6,7}}
[6,7,2,5,4,1,3]=>[6,2,7,1,4,5,3]=>[2,6,1,7,4,3,5]=>{{1,2,3,6},{4,5,7}}
[6,7,2,5,4,3,1]=>[6,2,7,1,3,4,5]=>[2,6,1,7,5,4,3]=>{{1,2,3,4,6,7},{5}}
[6,7,3,1,2,4,5]=>[6,1,3,7,5,4,2]=>[2,7,5,1,3,4,6]=>{{1,2,4,6,7},{3,5}}
[6,7,3,1,2,5,4]=>[6,1,3,7,4,5,2]=>[2,7,5,1,4,3,6]=>{{1,2,3,4,5,6,7}}
[6,7,3,1,4,2,5]=>[6,1,3,7,5,2,4]=>[2,7,5,1,3,6,4]=>{{1,2,4,7},{3,5},{6}}
[6,7,3,1,4,5,2]=>[6,1,3,7,4,2,5]=>[2,7,5,1,4,6,3]=>{{1,2,3,4,5,7},{6}}
[6,7,3,1,5,2,4]=>[6,1,3,7,2,5,4]=>[2,7,5,1,6,3,4]=>{{1,2,4,7},{3,5,6}}
[6,7,3,1,5,4,2]=>[6,1,3,7,2,4,5]=>[2,7,5,1,6,4,3]=>{{1,2,3,4,5,6,7}}
[6,7,3,2,1,4,5]=>[6,1,2,3,7,5,4]=>[2,7,6,5,1,3,4]=>{{1,2,4,5,7},{3,6}}
[6,7,3,2,1,5,4]=>[6,1,2,3,7,4,5]=>[2,7,6,5,1,4,3]=>{{1,2,3,4,5,6,7}}
[6,7,3,2,4,1,5]=>[6,2,3,7,5,1,4]=>[2,6,5,1,3,7,4]=>{{1,2,4,6,7},{3,5}}
[6,7,3,2,4,5,1]=>[6,2,3,7,4,1,5]=>[2,6,5,1,4,7,3]=>{{1,2,3,4,5,6,7}}
[6,7,3,2,5,1,4]=>[6,2,3,7,1,5,4]=>[2,6,5,1,7,3,4]=>{{1,2,3,4,5,6,7}}
[6,7,3,2,5,4,1]=>[6,2,3,7,1,4,5]=>[2,6,5,1,7,4,3]=>{{1,2,4,6},{3,5,7}}
[6,7,3,4,1,2,5]=>[6,3,7,5,1,4,2]=>[2,5,1,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[6,7,3,4,1,5,2]=>[6,3,7,1,4,2,5]=>[2,5,1,7,4,6,3]=>{{1,2,3,4,5,7},{6}}
[6,7,3,4,2,1,5]=>[6,3,7,5,1,2,4]=>[2,5,1,3,7,6,4]=>{{1,2,3,4,5,7},{6}}
[6,7,3,4,2,5,1]=>[6,3,7,2,4,1,5]=>[2,5,1,6,4,7,3]=>{{1,2,3,4,5,6,7}}
[6,7,3,4,5,1,2]=>[6,3,7,4,1,5,2]=>[2,5,1,4,7,3,6]=>{{1,2,3,5,6,7},{4}}
[6,7,3,4,5,2,1]=>[6,3,7,4,1,2,5]=>[2,5,1,4,7,6,3]=>{{1,2,3,5,7},{4},{6}}
[6,7,3,5,1,2,4]=>[6,3,7,1,5,4,2]=>[2,5,1,7,3,4,6]=>{{1,2,3,5},{4,6,7}}
[6,7,3,5,1,4,2]=>[6,3,7,1,5,2,4]=>[2,5,1,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}
[6,7,3,5,2,1,4]=>[6,3,7,1,2,5,4]=>[2,5,1,7,6,3,4]=>{{1,2,3,5,6},{4,7}}
[6,7,3,5,2,4,1]=>[6,3,7,2,5,1,4]=>[2,5,1,6,3,7,4]=>{{1,2,3,5},{4,6,7}}
[6,7,3,5,4,1,2]=>[6,3,7,1,4,5,2]=>[2,5,1,7,4,3,6]=>{{1,2,3,4,5,6,7}}
[6,7,3,5,4,2,1]=>[6,3,7,1,2,4,5]=>[2,5,1,7,6,4,3]=>{{1,2,3,4,5,6,7}}
[6,7,4,1,2,3,5]=>[6,1,4,7,5,3,2]=>[2,7,4,1,3,5,6]=>{{1,2,3,4,5,6,7}}
[6,7,4,1,2,5,3]=>[6,1,4,7,3,5,2]=>[2,7,4,1,5,3,6]=>{{1,2,3,4,6,7},{5}}
[6,7,4,1,3,2,5]=>[6,1,4,7,5,2,3]=>[2,7,4,1,3,6,5]=>{{1,2,3,4,5,7},{6}}
[6,7,4,1,3,5,2]=>[6,1,4,7,3,2,5]=>[2,7,4,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[6,7,4,1,5,2,3]=>[6,1,4,7,2,5,3]=>[2,7,4,1,6,3,5]=>{{1,2,3,4,5,6,7}}
[6,7,4,1,5,3,2]=>[6,1,4,7,2,3,5]=>[2,7,4,1,6,5,3]=>{{1,2,3,4,7},{5,6}}
[6,7,4,2,1,3,5]=>[6,1,2,4,7,5,3]=>[2,7,6,4,1,3,5]=>{{1,2,5,7},{3,6},{4}}
[6,7,4,2,1,5,3]=>[6,1,2,4,7,3,5]=>[2,7,6,4,1,5,3]=>{{1,2,3,5,6,7},{4}}
[6,7,4,2,3,1,5]=>[6,2,4,7,5,1,3]=>[2,6,4,1,3,7,5]=>{{1,2,3,4,5,6,7}}
[6,7,4,2,3,5,1]=>[6,2,4,7,3,1,5]=>[2,6,4,1,5,7,3]=>{{1,2,3,4,6,7},{5}}
[6,7,4,2,5,1,3]=>[6,2,4,7,1,5,3]=>[2,6,4,1,7,3,5]=>{{1,2,3,4,6},{5,7}}
[6,7,4,2,5,3,1]=>[6,2,4,7,1,3,5]=>[2,6,4,1,7,5,3]=>{{1,2,3,4,5,6,7}}
[6,7,4,3,1,2,5]=>[6,1,3,4,7,5,2]=>[2,7,5,4,1,3,6]=>{{1,2,3,5,6,7},{4}}
[6,7,4,3,1,5,2]=>[6,1,3,4,7,2,5]=>[2,7,5,4,1,6,3]=>{{1,2,3,5,7},{4},{6}}
[6,7,4,3,2,1,5]=>[6,1,2,3,4,7,5]=>[2,7,6,5,4,1,3]=>{{1,2,3,6,7},{4,5}}
[6,7,4,3,2,5,1]=>[6,2,3,4,7,1,5]=>[2,6,5,4,1,7,3]=>{{1,2,3,5,6,7},{4}}
[6,7,4,3,5,1,2]=>[6,3,4,7,1,5,2]=>[2,5,4,1,7,3,6]=>{{1,2,3,4,5,6,7}}
[6,7,4,3,5,2,1]=>[6,3,4,7,1,2,5]=>[2,5,4,1,7,6,3]=>{{1,2,3,4,5,7},{6}}
[6,7,4,5,1,2,3]=>[6,4,7,1,5,3,2]=>[2,4,1,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[6,7,4,5,1,3,2]=>[6,4,7,1,5,2,3]=>[2,4,1,7,3,6,5]=>{{1,2,3,4,5,7},{6}}
[6,7,4,5,2,1,3]=>[6,4,7,1,2,5,3]=>[2,4,1,7,6,3,5]=>{{1,2,3,4,5,6,7}}
[6,7,4,5,2,3,1]=>[6,4,7,2,5,1,3]=>[2,4,1,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[6,7,4,5,3,1,2]=>[6,4,7,1,3,5,2]=>[2,4,1,7,5,3,6]=>{{1,2,3,4,6,7},{5}}
[6,7,4,5,3,2,1]=>[6,4,7,1,2,3,5]=>[2,4,1,7,6,5,3]=>{{1,2,3,4,7},{5,6}}
[6,7,5,1,2,3,4]=>[6,1,5,7,4,3,2]=>[2,7,3,1,4,5,6]=>{{1,2,4,5,6,7},{3}}
[6,7,5,1,2,4,3]=>[6,1,5,7,3,4,2]=>[2,7,3,1,5,4,6]=>{{1,2,4,6,7},{3},{5}}
[6,7,5,1,3,2,4]=>[6,1,5,7,4,2,3]=>[2,7,3,1,4,6,5]=>{{1,2,4,5,7},{3},{6}}
[6,7,5,1,3,4,2]=>[6,1,5,7,3,2,4]=>[2,7,3,1,5,6,4]=>{{1,2,4,7},{3},{5},{6}}
[6,7,5,1,4,2,3]=>[6,1,5,7,2,4,3]=>[2,7,3,1,6,4,5]=>{{1,2,4,5,6,7},{3}}
[6,7,5,1,4,3,2]=>[6,1,5,7,2,3,4]=>[2,7,3,1,6,5,4]=>{{1,2,4,7},{3},{5,6}}
[6,7,5,2,1,3,4]=>[6,1,2,5,7,4,3]=>[2,7,6,3,1,4,5]=>{{1,2,5,7},{3,4,6}}
[6,7,5,2,1,4,3]=>[6,1,2,5,7,3,4]=>[2,7,6,3,1,5,4]=>{{1,2,3,4,5,6,7}}
[6,7,5,2,3,1,4]=>[6,2,5,7,4,1,3]=>[2,6,3,1,4,7,5]=>{{1,2,4,5,6,7},{3}}
[6,7,5,2,3,4,1]=>[6,2,5,7,3,1,4]=>[2,6,3,1,5,7,4]=>{{1,2,4,6,7},{3},{5}}
[6,7,5,2,4,1,3]=>[6,2,5,7,1,4,3]=>[2,6,3,1,7,4,5]=>{{1,2,4,6},{3},{5,7}}
[6,7,5,2,4,3,1]=>[6,2,5,7,1,3,4]=>[2,6,3,1,7,5,4]=>{{1,2,4,5,6,7},{3}}
[6,7,5,3,1,2,4]=>[6,1,3,5,7,4,2]=>[2,7,5,3,1,4,6]=>{{1,2,3,4,5,6,7}}
[6,7,5,3,1,4,2]=>[6,1,3,5,7,2,4]=>[2,7,5,3,1,6,4]=>{{1,2,3,4,5,7},{6}}
[6,7,5,3,2,1,4]=>[6,1,2,3,5,7,4]=>[2,7,6,5,3,1,4]=>{{1,2,3,4,5,6,7}}
[6,7,5,3,2,4,1]=>[6,2,3,5,7,1,4]=>[2,6,5,3,1,7,4]=>{{1,2,3,4,5,6,7}}
[6,7,5,3,4,1,2]=>[6,3,5,7,1,4,2]=>[2,5,3,1,7,4,6]=>{{1,2,4,5,6,7},{3}}
[6,7,5,3,4,2,1]=>[6,3,5,7,1,2,4]=>[2,5,3,1,7,6,4]=>{{1,2,4,5,7},{3},{6}}
[6,7,5,4,1,2,3]=>[6,1,4,5,7,3,2]=>[2,7,4,3,1,5,6]=>{{1,2,5,6,7},{3,4}}
[6,7,5,4,1,3,2]=>[6,1,4,5,7,2,3]=>[2,7,4,3,1,6,5]=>{{1,2,5,7},{3,4},{6}}
[6,7,5,4,2,1,3]=>[6,1,2,4,5,7,3]=>[2,7,6,4,3,1,5]=>{{1,2,3,5,6,7},{4}}
[6,7,5,4,2,3,1]=>[6,2,4,5,7,1,3]=>[2,6,4,3,1,7,5]=>{{1,2,5,6,7},{3,4}}
[6,7,5,4,3,1,2]=>[6,1,3,4,5,7,2]=>[2,7,5,4,3,1,6]=>{{1,2,6,7},{3,5},{4}}
[6,7,5,4,3,2,1]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>{{1,2,7},{3,6},{4,5}}
[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,3,4,6,5]=>[1,7,5,6,4,3,2]=>[7,1,3,2,4,5,6]=>{{1,2,4,5,6,7},{3}}
[7,1,2,3,5,4,6]=>[1,7,6,4,5,3,2]=>[7,1,2,4,3,5,6]=>{{1,2,3,5,6,7},{4}}
[7,1,2,3,5,6,4]=>[1,7,5,4,6,3,2]=>[7,1,3,4,2,5,6]=>{{1,2,5,6,7},{3},{4}}
[7,1,2,3,6,4,5]=>[1,7,4,6,5,3,2]=>[7,1,4,2,3,5,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,3,6,5,4]=>[1,7,4,5,6,3,2]=>[7,1,4,3,2,5,6]=>{{1,2,5,6,7},{3,4}}
[7,1,2,4,3,5,6]=>[1,7,6,5,3,4,2]=>[7,1,2,3,5,4,6]=>{{1,2,3,4,6,7},{5}}
[7,1,2,4,3,6,5]=>[1,7,5,6,3,4,2]=>[7,1,3,2,5,4,6]=>{{1,2,4,6,7},{3},{5}}
[7,1,2,4,5,3,6]=>[1,7,6,4,3,5,2]=>[7,1,2,4,5,3,6]=>{{1,2,3,6,7},{4},{5}}
[7,1,2,4,5,6,3]=>[1,7,5,4,3,6,2]=>[7,1,3,4,5,2,6]=>{{1,2,6,7},{3},{4},{5}}
[7,1,2,4,6,3,5]=>[1,7,4,3,6,5,2]=>[7,1,4,5,2,3,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,4,6,5,3]=>[1,7,4,3,5,6,2]=>[7,1,4,5,3,2,6]=>{{1,2,6,7},{3,4,5}}
[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[7,1,2,5,3,4,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,5,3,6,4]=>[1,7,3,5,4,6,2]=>[7,1,5,3,4,2,6]=>{{1,2,6,7},{3,4,5}}
[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[7,1,2,5,4,3,6]=>{{1,2,3,6,7},{4,5}}
[7,1,2,5,4,6,3]=>[1,7,4,5,3,6,2]=>[7,1,4,3,5,2,6]=>{{1,2,6,7},{3,4},{5}}
[7,1,2,5,6,3,4]=>[1,7,5,3,6,4,2]=>[7,1,3,5,2,4,6]=>{{1,2,4,5,6,7},{3}}
[7,1,2,5,6,4,3]=>[1,7,5,3,4,6,2]=>[7,1,3,5,4,2,6]=>{{1,2,6,7},{3},{4,5}}
[7,1,2,6,3,4,5]=>[1,7,3,6,5,4,2]=>[7,1,5,2,3,4,6]=>{{1,2,4,6,7},{3,5}}
[7,1,2,6,3,5,4]=>[1,7,3,6,4,5,2]=>[7,1,5,2,4,3,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,6,4,3,5]=>[1,7,3,4,6,5,2]=>[7,1,5,4,2,3,6]=>{{1,2,3,5,6,7},{4}}
[7,1,2,6,4,5,3]=>[1,7,4,6,3,5,2]=>[7,1,4,2,5,3,6]=>{{1,2,3,4,6,7},{5}}
[7,1,2,6,5,3,4]=>[1,7,3,5,6,4,2]=>[7,1,5,3,2,4,6]=>{{1,2,3,4,5,6,7}}
[7,1,2,6,5,4,3]=>[1,7,3,4,5,6,2]=>[7,1,5,4,3,2,6]=>{{1,2,6,7},{3,5},{4}}
[7,1,3,2,4,5,6]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>{{1,2,3,4,5,7},{6}}
[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[7,1,3,2,4,6,5]=>{{1,2,4,5,7},{3},{6}}
[7,1,3,2,5,4,6]=>[1,7,6,4,5,2,3]=>[7,1,2,4,3,6,5]=>{{1,2,3,5,7},{4},{6}}
[7,1,3,2,5,6,4]=>[1,7,5,4,6,2,3]=>[7,1,3,4,2,6,5]=>{{1,2,5,7},{3},{4},{6}}
[7,1,3,2,6,4,5]=>[1,7,4,6,5,2,3]=>[7,1,4,2,3,6,5]=>{{1,2,3,4,5,7},{6}}
[7,1,3,2,6,5,4]=>[1,7,4,5,6,2,3]=>[7,1,4,3,2,6,5]=>{{1,2,5,7},{3,4},{6}}
[7,1,3,4,2,5,6]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[7,1,3,4,2,6,5]=>[1,7,5,6,3,2,4]=>[7,1,3,2,5,6,4]=>{{1,2,4,7},{3},{5},{6}}
[7,1,3,4,5,2,6]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>{{1,2,3,7},{4},{5},{6}}
[7,1,3,4,5,6,2]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>{{1,2,7},{3},{4},{5},{6}}
[7,1,3,4,6,2,5]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>{{1,2,3,4,5,6,7}}
[7,1,3,4,6,5,2]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>{{1,2,7},{3,4,5,6}}
[7,1,3,5,2,4,6]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>{{1,2,3,4,5,6,7}}
[7,1,3,5,2,6,4]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>{{1,2,7},{3,5},{4,6}}
[7,1,3,5,4,2,6]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>{{1,2,3,7},{4,5,6}}
[7,1,3,5,4,6,2]=>[1,7,4,5,3,2,6]=>[7,1,4,3,5,6,2]=>{{1,2,7},{3,4},{5},{6}}
[7,1,3,5,6,2,4]=>[1,7,5,3,2,6,4]=>[7,1,3,5,6,2,4]=>{{1,2,4,5,6,7},{3}}
[7,1,3,5,6,4,2]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>{{1,2,7},{3},{4,5,6}}
[7,1,3,6,2,4,5]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>{{1,2,3,4,5,6,7}}
[7,1,3,6,2,5,4]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>{{1,2,3,5,7},{4,6}}
[7,1,3,6,4,2,5]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>{{1,2,3,4,5,6,7}}
[7,1,3,6,4,5,2]=>[1,7,4,6,3,2,5]=>[7,1,4,2,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[7,1,3,6,5,2,4]=>[1,7,3,2,5,6,4]=>[7,1,5,6,3,2,4]=>{{1,2,4,6,7},{3,5}}
[7,1,3,6,5,4,2]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>{{1,2,7},{3,4,5,6}}
[7,1,4,2,3,5,6]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>{{1,2,3,4,5,6,7}}
[7,1,4,2,3,6,5]=>[1,7,5,6,2,4,3]=>[7,1,3,2,6,4,5]=>{{1,2,4,5,6,7},{3}}
[7,1,4,2,5,3,6]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>{{1,2,3,7},{4,5,6}}
[7,1,4,2,5,6,3]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>{{1,2,7},{3},{4,5,6}}
[7,1,4,2,6,3,5]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>{{1,2,3,6,7},{4},{5}}
[7,1,4,2,6,5,3]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>{{1,2,7},{3,6},{4},{5}}
[7,1,4,3,2,5,6]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>{{1,2,3,4,7},{5,6}}
[7,1,4,3,2,6,5]=>[1,7,5,6,2,3,4]=>[7,1,3,2,6,5,4]=>{{1,2,4,7},{3},{5,6}}
[7,1,4,3,5,2,6]=>[1,7,6,3,4,2,5]=>[7,1,2,5,4,6,3]=>{{1,2,3,7},{4,5},{6}}
[7,1,4,3,5,6,2]=>[1,7,5,3,4,2,6]=>[7,1,3,5,4,6,2]=>{{1,2,7},{3},{4,5},{6}}
[7,1,4,3,6,2,5]=>[1,7,3,4,2,6,5]=>[7,1,5,4,6,2,3]=>{{1,2,3,5,6,7},{4}}
[7,1,4,3,6,5,2]=>[1,7,3,4,2,5,6]=>[7,1,5,4,6,3,2]=>{{1,2,7},{3,5,6},{4}}
[7,1,4,5,2,3,6]=>[1,7,6,4,2,5,3]=>[7,1,2,4,6,3,5]=>{{1,2,3,5,6,7},{4}}
[7,1,4,5,2,6,3]=>[1,7,4,2,5,3,6]=>[7,1,4,6,3,5,2]=>{{1,2,7},{3,4,5,6}}
[7,1,4,5,3,2,6]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>{{1,2,3,7},{4},{5,6}}
[7,1,4,5,3,6,2]=>[1,7,4,3,5,2,6]=>[7,1,4,5,3,6,2]=>{{1,2,7},{3,4,5},{6}}
[7,1,4,5,6,2,3]=>[1,7,5,4,2,6,3]=>[7,1,3,4,6,2,5]=>{{1,2,5,6,7},{3},{4}}
[7,1,4,5,6,3,2]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>{{1,2,7},{3},{4},{5,6}}
[7,1,4,6,2,3,5]=>[1,7,4,2,6,5,3]=>[7,1,4,6,2,3,5]=>{{1,2,5,7},{3,4,6}}
[7,1,4,6,2,5,3]=>[1,7,4,2,6,3,5]=>[7,1,4,6,2,5,3]=>{{1,2,3,4,5,6,7}}
[7,1,4,6,3,2,5]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>{{1,2,3,4,6,7},{5}}
[7,1,4,6,3,5,2]=>[1,7,4,3,6,2,5]=>[7,1,4,5,2,6,3]=>{{1,2,3,4,5,7},{6}}
[7,1,4,6,5,2,3]=>[1,7,4,2,5,6,3]=>[7,1,4,6,3,2,5]=>{{1,2,3,4,5,6,7}}
[7,1,4,6,5,3,2]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>{{1,2,7},{3,4,6},{5}}
[7,1,5,2,3,4,6]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>{{1,2,3,5,7},{4,6}}
[7,1,5,2,3,6,4]=>[1,7,2,5,4,6,3]=>[7,1,6,3,4,2,5]=>{{1,2,3,4,5,6,7}}
[7,1,5,2,4,3,6]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>{{1,2,3,4,5,6,7}}
[7,1,5,2,4,6,3]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>{{1,2,7},{3,4,5,6}}
[7,1,5,2,6,3,4]=>[1,7,2,5,3,6,4]=>[7,1,6,3,5,2,4]=>{{1,2,3,4,6,7},{5}}
[7,1,5,2,6,4,3]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>{{1,2,7},{3,4,6},{5}}
[7,1,5,3,2,4,6]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>{{1,2,3,4,6,7},{5}}
[7,1,5,3,2,6,4]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>{{1,2,7},{3,4,5,6}}
[7,1,5,3,4,2,6]=>[1,7,6,3,5,2,4]=>[7,1,2,5,3,6,4]=>{{1,2,3,4,5,7},{6}}
[7,1,5,3,4,6,2]=>[1,7,3,5,4,2,6]=>[7,1,5,3,4,6,2]=>{{1,2,7},{3,4,5},{6}}
[7,1,5,3,6,2,4]=>[1,7,3,5,2,6,4]=>[7,1,5,3,6,2,4]=>{{1,2,3,4,5,6,7}}
[7,1,5,3,6,4,2]=>[1,7,3,5,2,4,6]=>[7,1,5,3,6,4,2]=>{{1,2,7},{3,4,5,6}}
[7,1,5,4,2,3,6]=>[1,7,6,2,4,5,3]=>[7,1,2,6,4,3,5]=>{{1,2,3,4,5,6,7}}
[7,1,5,4,2,6,3]=>[1,7,2,4,5,3,6]=>[7,1,6,4,3,5,2]=>{{1,2,7},{3,5,6},{4}}
[7,1,5,4,3,2,6]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>{{1,2,3,7},{4,6},{5}}
[7,1,5,4,3,6,2]=>[1,7,3,4,5,2,6]=>[7,1,5,4,3,6,2]=>{{1,2,7},{3,5},{4},{6}}
[7,1,5,4,6,2,3]=>[1,7,4,5,2,6,3]=>[7,1,4,3,6,2,5]=>{{1,2,5,6,7},{3,4}}
[7,1,5,4,6,3,2]=>[1,7,4,5,2,3,6]=>[7,1,4,3,6,5,2]=>{{1,2,7},{3,4},{5,6}}
[7,1,5,6,2,3,4]=>[1,7,5,2,6,4,3]=>[7,1,3,6,2,4,5]=>{{1,2,5,7},{3},{4,6}}
[7,1,5,6,2,4,3]=>[1,7,5,2,6,3,4]=>[7,1,3,6,2,5,4]=>{{1,2,4,5,6,7},{3}}
[7,1,5,6,3,2,4]=>[1,7,5,2,3,6,4]=>[7,1,3,6,5,2,4]=>{{1,2,4,6,7},{3},{5}}
[7,1,5,6,3,4,2]=>[1,7,5,3,6,2,4]=>[7,1,3,5,2,6,4]=>{{1,2,4,5,7},{3},{6}}
[7,1,5,6,4,2,3]=>[1,7,5,2,4,6,3]=>[7,1,3,6,4,2,5]=>{{1,2,4,5,6,7},{3}}
[7,1,5,6,4,3,2]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>{{1,2,7},{3},{4,6},{5}}
[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>{{1,2,3,4,5,6,7}}
[7,1,6,2,3,5,4]=>[1,7,2,6,4,5,3]=>[7,1,6,2,4,3,5]=>{{1,2,4,5,7},{3,6}}
[7,1,6,2,4,3,5]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>{{1,2,4,7},{3,5,6}}
[7,1,6,2,4,5,3]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>{{1,2,3,4,5,6,7}}
[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>{{1,2,4,7},{3,6},{5}}
[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>{{1,2,3,4,6,7},{5}}
[7,1,6,3,2,4,5]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>{{1,2,4,5,7},{3,6}}
[7,1,6,3,2,5,4]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>{{1,2,3,4,5,6,7}}
[7,1,6,3,4,2,5]=>[1,7,3,6,5,2,4]=>[7,1,5,2,3,6,4]=>{{1,2,4,7},{3,5},{6}}
[7,1,6,3,4,5,2]=>[1,7,3,6,4,2,5]=>[7,1,5,2,4,6,3]=>{{1,2,3,4,5,7},{6}}
[7,1,6,3,5,2,4]=>[1,7,3,6,2,5,4]=>[7,1,5,2,6,3,4]=>{{1,2,4,7},{3,5,6}}
[7,1,6,3,5,4,2]=>[1,7,3,6,2,4,5]=>[7,1,5,2,6,4,3]=>{{1,2,3,4,5,6,7}}
[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[7,1,6,4,2,3,5]=>{{1,2,5,7},{3,6},{4}}
[7,1,6,4,2,5,3]=>[1,7,2,4,6,3,5]=>[7,1,6,4,2,5,3]=>{{1,2,3,5,6,7},{4}}
[7,1,6,4,3,2,5]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>{{1,2,3,6,7},{4,5}}
[7,1,6,4,3,5,2]=>[1,7,3,4,6,2,5]=>[7,1,5,4,2,6,3]=>{{1,2,3,5,7},{4},{6}}
[7,1,6,4,5,2,3]=>[1,7,4,6,2,5,3]=>[7,1,4,2,6,3,5]=>{{1,2,3,4,5,6,7}}
[7,1,6,4,5,3,2]=>[1,7,4,6,2,3,5]=>[7,1,4,2,6,5,3]=>{{1,2,3,4,7},{5,6}}
[7,1,6,5,2,3,4]=>[1,7,2,5,6,4,3]=>[7,1,6,3,2,4,5]=>{{1,2,5,7},{3,4,6}}
[7,1,6,5,2,4,3]=>[1,7,2,5,6,3,4]=>[7,1,6,3,2,5,4]=>{{1,2,3,4,5,6,7}}
[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[7,1,6,5,3,2,4]=>{{1,2,3,4,5,6,7}}
[7,1,6,5,3,4,2]=>[1,7,3,5,6,2,4]=>[7,1,5,3,2,6,4]=>{{1,2,3,4,5,7},{6}}
[7,1,6,5,4,2,3]=>[1,7,2,4,5,6,3]=>[7,1,6,4,3,2,5]=>{{1,2,3,5,6,7},{4}}
[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>{{1,2,7},{3,6},{4,5}}
[7,2,1,3,4,5,6]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>{{1,3,5,7},{2,4,6}}
[7,2,1,3,4,6,5]=>[1,2,7,5,6,4,3]=>[7,6,1,3,2,4,5]=>{{1,2,3,4,5,6,7}}
[7,2,1,3,5,4,6]=>[1,2,7,6,4,5,3]=>[7,6,1,2,4,3,5]=>{{1,2,3,4,5,6,7}}
[7,2,1,3,5,6,4]=>[1,2,7,5,4,6,3]=>[7,6,1,3,4,2,5]=>{{1,3,4,5,7},{2,6}}
[7,2,1,3,6,4,5]=>[1,2,7,4,6,5,3]=>[7,6,1,4,2,3,5]=>{{1,2,3,5,6,7},{4}}
[7,2,1,3,6,5,4]=>[1,2,7,4,5,6,3]=>[7,6,1,4,3,2,5]=>{{1,3,5,7},{2,6},{4}}
[7,2,1,4,3,5,6]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>{{1,2,3,4,5,6,7}}
[7,2,1,4,3,6,5]=>[1,2,7,5,6,3,4]=>[7,6,1,3,2,5,4]=>{{1,3,4,7},{2,5,6}}
[7,2,1,4,5,3,6]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>{{1,3,7},{2,4,5,6}}
[7,2,1,4,5,6,3]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>{{1,2,3,4,5,6,7}}
[7,2,1,4,6,3,5]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>{{1,3,7},{2,6},{4},{5}}
[7,2,1,4,6,5,3]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>{{1,2,3,6,7},{4},{5}}
[7,2,1,5,3,4,6]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>{{1,2,3,4,6,7},{5}}
[7,2,1,5,3,6,4]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>{{1,2,3,4,5,6,7}}
[7,2,1,5,4,3,6]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>{{1,3,7},{2,4,6},{5}}
[7,2,1,5,4,6,3]=>[1,2,7,4,5,3,6]=>[7,6,1,4,3,5,2]=>{{1,2,3,5,6,7},{4}}
[7,2,1,5,6,3,4]=>[1,2,7,5,3,6,4]=>[7,6,1,3,5,2,4]=>{{1,3,4,7},{2,6},{5}}
[7,2,1,5,6,4,3]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>{{1,2,3,4,6,7},{5}}
[7,2,1,6,3,4,5]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>{{1,2,3,4,5,6,7}}
[7,2,1,6,3,5,4]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>{{1,3,7},{2,4,5,6}}
[7,2,1,6,4,3,5]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>{{1,3,7},{2,6},{4,5}}
[7,2,1,6,4,5,3]=>[1,2,7,4,6,3,5]=>[7,6,1,4,2,5,3]=>{{1,3,7},{2,5,6},{4}}
[7,2,1,6,5,3,4]=>[1,2,7,3,5,6,4]=>[7,6,1,5,3,2,4]=>{{1,3,4,5,7},{2,6}}
[7,2,1,6,5,4,3]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>{{1,2,3,6,7},{4,5}}
[7,2,3,1,4,5,6]=>[2,7,6,5,4,1,3]=>[6,1,2,3,4,7,5]=>{{1,2,3,4,5,6,7}}
[7,2,3,1,4,6,5]=>[2,7,5,6,4,1,3]=>[6,1,3,2,4,7,5]=>{{1,2,4,5,6,7},{3}}
[7,2,3,1,5,4,6]=>[2,7,6,4,5,1,3]=>[6,1,2,4,3,7,5]=>{{1,2,3,5,6,7},{4}}
[7,2,3,1,5,6,4]=>[2,7,5,4,6,1,3]=>[6,1,3,4,2,7,5]=>{{1,2,5,6,7},{3},{4}}
[7,2,3,1,6,4,5]=>[2,7,4,6,5,1,3]=>[6,1,4,2,3,7,5]=>{{1,2,3,4,5,6,7}}
[7,2,3,1,6,5,4]=>[2,7,4,5,6,1,3]=>[6,1,4,3,2,7,5]=>{{1,2,5,6,7},{3,4}}
[7,2,3,4,1,5,6]=>[2,7,6,5,3,1,4]=>[6,1,2,3,5,7,4]=>{{1,2,3,4,6,7},{5}}
[7,2,3,4,1,6,5]=>[2,7,5,6,3,1,4]=>[6,1,3,2,5,7,4]=>{{1,2,4,6,7},{3},{5}}
[7,2,3,4,5,1,6]=>[2,7,6,4,3,1,5]=>[6,1,2,4,5,7,3]=>{{1,2,3,6,7},{4},{5}}
[7,2,3,4,5,6,1]=>[2,7,5,4,3,1,6]=>[6,1,3,4,5,7,2]=>{{1,2,6,7},{3},{4},{5}}
[7,2,3,4,6,1,5]=>[2,7,4,3,1,6,5]=>[6,1,4,5,7,2,3]=>{{1,2,6},{3,4,5,7}}
[7,2,3,4,6,5,1]=>[2,7,4,3,1,5,6]=>[6,1,4,5,7,3,2]=>{{1,2,3,4,5,6,7}}
[7,2,3,5,1,4,6]=>[2,7,6,3,1,5,4]=>[6,1,2,5,7,3,4]=>{{1,2,3,6},{4,5,7}}
[7,2,3,5,1,6,4]=>[2,7,3,1,5,4,6]=>[6,1,5,7,3,4,2]=>{{1,2,4,6,7},{3,5}}
[7,2,3,5,4,1,6]=>[2,7,6,3,1,4,5]=>[6,1,2,5,7,4,3]=>{{1,2,3,4,5,6,7}}
[7,2,3,5,4,6,1]=>[2,7,4,5,3,1,6]=>[6,1,4,3,5,7,2]=>{{1,2,6,7},{3,4},{5}}
[7,2,3,5,6,1,4]=>[2,7,5,3,1,6,4]=>[6,1,3,5,7,2,4]=>{{1,2,6},{3},{4,5,7}}
[7,2,3,5,6,4,1]=>[2,7,5,3,1,4,6]=>[6,1,3,5,7,4,2]=>{{1,2,4,5,6,7},{3}}
[7,2,3,6,1,4,5]=>[2,7,3,1,6,5,4]=>[6,1,5,7,2,3,4]=>{{1,2,3,5,6},{4,7}}
[7,2,3,6,1,5,4]=>[2,7,3,1,6,4,5]=>[6,1,5,7,2,4,3]=>{{1,2,3,4,5,6,7}}
[7,2,3,6,4,1,5]=>[2,7,3,1,4,6,5]=>[6,1,5,7,4,2,3]=>{{1,2,6},{3,4,5,7}}
[7,2,3,6,4,5,1]=>[2,7,4,6,3,1,5]=>[6,1,4,2,5,7,3]=>{{1,2,3,4,6,7},{5}}
[7,2,3,6,5,1,4]=>[2,7,3,1,5,6,4]=>[6,1,5,7,3,2,4]=>{{1,2,6},{3,5},{4,7}}
[7,2,3,6,5,4,1]=>[2,7,3,1,4,5,6]=>[6,1,5,7,4,3,2]=>{{1,2,3,4,5,6,7}}
[7,2,4,1,3,5,6]=>[2,7,6,5,1,4,3]=>[6,1,2,3,7,4,5]=>{{1,2,3,4,6},{5,7}}
[7,2,4,1,3,6,5]=>[2,7,5,6,1,4,3]=>[6,1,3,2,7,4,5]=>{{1,2,4,6},{3},{5,7}}
[7,2,4,1,5,3,6]=>[2,7,6,1,4,3,5]=>[6,1,2,7,4,5,3]=>{{1,2,3,4,5,6,7}}
[7,2,4,1,5,6,3]=>[2,7,5,1,4,3,6]=>[6,1,3,7,4,5,2]=>{{1,2,4,5,6,7},{3}}
[7,2,4,1,6,3,5]=>[2,7,1,4,3,6,5]=>[6,1,7,4,5,2,3]=>{{1,2,6},{3,7},{4},{5}}
[7,2,4,1,6,5,3]=>[2,7,1,4,3,5,6]=>[6,1,7,4,5,3,2]=>{{1,2,3,6,7},{4},{5}}
[7,2,4,3,1,5,6]=>[2,7,6,5,1,3,4]=>[6,1,2,3,7,5,4]=>{{1,2,3,4,5,6,7}}
[7,2,4,3,1,6,5]=>[2,7,5,6,1,3,4]=>[6,1,3,2,7,5,4]=>{{1,2,4,5,6,7},{3}}
[7,2,4,3,5,1,6]=>[2,7,6,3,4,1,5]=>[6,1,2,5,4,7,3]=>{{1,2,3,6,7},{4,5}}
[7,2,4,3,5,6,1]=>[2,7,5,3,4,1,6]=>[6,1,3,5,4,7,2]=>{{1,2,6,7},{3},{4,5}}
[7,2,4,3,6,1,5]=>[2,7,3,4,1,6,5]=>[6,1,5,4,7,2,3]=>{{1,2,6},{3,5,7},{4}}
[7,2,4,3,6,5,1]=>[2,7,3,4,1,5,6]=>[6,1,5,4,7,3,2]=>{{1,2,3,5,6,7},{4}}
[7,2,4,5,1,3,6]=>[2,7,6,4,1,5,3]=>[6,1,2,4,7,3,5]=>{{1,2,3,6},{4},{5,7}}
[7,2,4,5,1,6,3]=>[2,7,4,1,5,3,6]=>[6,1,4,7,3,5,2]=>{{1,2,3,4,5,6,7}}
[7,2,4,5,3,1,6]=>[2,7,6,4,1,3,5]=>[6,1,2,4,7,5,3]=>{{1,2,3,5,6,7},{4}}
[7,2,4,5,3,6,1]=>[2,7,4,3,5,1,6]=>[6,1,4,5,3,7,2]=>{{1,2,6,7},{3,4,5}}
[7,2,4,5,6,1,3]=>[2,7,5,4,1,6,3]=>[6,1,3,4,7,2,5]=>{{1,2,6},{3},{4},{5,7}}
[7,2,4,5,6,3,1]=>[2,7,5,4,1,3,6]=>[6,1,3,4,7,5,2]=>{{1,2,5,6,7},{3},{4}}
[7,2,4,6,1,3,5]=>[2,7,4,1,6,5,3]=>[6,1,4,7,2,3,5]=>{{1,2,3,4,5,6,7}}
[7,2,4,6,1,5,3]=>[2,7,4,1,6,3,5]=>[6,1,4,7,2,5,3]=>{{1,2,5,6},{3,4,7}}
[7,2,4,6,3,1,5]=>[2,7,4,1,3,6,5]=>[6,1,4,7,5,2,3]=>{{1,2,6},{3,4,7},{5}}
[7,2,4,6,3,5,1]=>[2,7,4,3,6,1,5]=>[6,1,4,5,2,7,3]=>{{1,2,3,4,5,6,7}}
[7,2,4,6,5,1,3]=>[2,7,4,1,5,6,3]=>[6,1,4,7,3,2,5]=>{{1,2,6},{3,4,5,7}}
[7,2,4,6,5,3,1]=>[2,7,4,1,3,5,6]=>[6,1,4,7,5,3,2]=>{{1,2,3,4,6,7},{5}}
[7,2,5,1,3,4,6]=>[2,7,6,1,5,4,3]=>[6,1,2,7,3,4,5]=>{{1,2,3,4,5,6,7}}
[7,2,5,1,3,6,4]=>[2,7,1,5,4,6,3]=>[6,1,7,3,4,2,5]=>{{1,2,6},{3,4,5,7}}
[7,2,5,1,4,3,6]=>[2,7,6,1,5,3,4]=>[6,1,2,7,3,5,4]=>{{1,2,3,5,6},{4,7}}
[7,2,5,1,4,6,3]=>[2,7,1,5,4,3,6]=>[6,1,7,3,4,5,2]=>{{1,2,3,4,5,6,7}}
[7,2,5,1,6,3,4]=>[2,7,1,5,3,6,4]=>[6,1,7,3,5,2,4]=>{{1,2,6},{3,4,7},{5}}
[7,2,5,1,6,4,3]=>[2,7,1,5,3,4,6]=>[6,1,7,3,5,4,2]=>{{1,2,3,4,6,7},{5}}
[7,2,5,3,1,4,6]=>[2,7,6,1,3,5,4]=>[6,1,2,7,5,3,4]=>{{1,2,3,6},{4,7},{5}}
[7,2,5,3,1,6,4]=>[2,7,1,3,5,4,6]=>[6,1,7,5,3,4,2]=>{{1,2,3,4,5,6,7}}
[7,2,5,3,4,1,6]=>[2,7,6,3,5,1,4]=>[6,1,2,5,3,7,4]=>{{1,2,3,4,5,6,7}}
[7,2,5,3,4,6,1]=>[2,7,3,5,4,1,6]=>[6,1,5,3,4,7,2]=>{{1,2,6,7},{3,4,5}}
[7,2,5,3,6,1,4]=>[2,7,3,5,1,6,4]=>[6,1,5,3,7,2,4]=>{{1,2,6},{3,4,5,7}}
[7,2,5,3,6,4,1]=>[2,7,3,5,1,4,6]=>[6,1,5,3,7,4,2]=>{{1,2,3,4,5,6,7}}
[7,2,5,4,1,3,6]=>[2,7,6,1,4,5,3]=>[6,1,2,7,4,3,5]=>{{1,2,3,6},{4,5,7}}
[7,2,5,4,1,6,3]=>[2,7,1,4,5,3,6]=>[6,1,7,4,3,5,2]=>{{1,2,3,5,6,7},{4}}
[7,2,5,4,3,1,6]=>[2,7,6,1,3,4,5]=>[6,1,2,7,5,4,3]=>{{1,2,3,4,6,7},{5}}
[7,2,5,4,3,6,1]=>[2,7,3,4,5,1,6]=>[6,1,5,4,3,7,2]=>{{1,2,6,7},{3,5},{4}}
[7,2,5,4,6,1,3]=>[2,7,4,5,1,6,3]=>[6,1,4,3,7,2,5]=>{{1,2,6},{3,4},{5,7}}
[7,2,5,4,6,3,1]=>[2,7,4,5,1,3,6]=>[6,1,4,3,7,5,2]=>{{1,2,5,6,7},{3,4}}
[7,2,5,6,1,3,4]=>[2,7,5,1,6,4,3]=>[6,1,3,7,2,4,5]=>{{1,2,4,5,6,7},{3}}
[7,2,5,6,1,4,3]=>[2,7,5,1,6,3,4]=>[6,1,3,7,2,5,4]=>{{1,2,5,6},{3},{4,7}}
[7,2,5,6,3,1,4]=>[2,7,5,1,3,6,4]=>[6,1,3,7,5,2,4]=>{{1,2,6},{3},{4,7},{5}}
[7,2,5,6,3,4,1]=>[2,7,5,3,6,1,4]=>[6,1,3,5,2,7,4]=>{{1,2,4,5,6,7},{3}}
[7,2,5,6,4,1,3]=>[2,7,5,1,4,6,3]=>[6,1,3,7,4,2,5]=>{{1,2,6},{3},{4,5,7}}
[7,2,5,6,4,3,1]=>[2,7,5,1,3,4,6]=>[6,1,3,7,5,4,2]=>{{1,2,4,6,7},{3},{5}}
[7,2,6,1,3,4,5]=>[2,7,1,6,5,4,3]=>[6,1,7,2,3,4,5]=>{{1,2,4,6},{3,5,7}}
[7,2,6,1,3,5,4]=>[2,7,1,6,4,5,3]=>[6,1,7,2,4,3,5]=>{{1,2,3,4,5,6,7}}
[7,2,6,1,4,3,5]=>[2,7,1,6,5,3,4]=>[6,1,7,2,3,5,4]=>{{1,2,3,4,5,6,7}}
[7,2,6,1,4,5,3]=>[2,7,1,6,4,3,5]=>[6,1,7,2,4,5,3]=>{{1,2,4,5,6},{3,7}}
[7,2,6,1,5,3,4]=>[2,7,1,6,3,5,4]=>[6,1,7,2,5,3,4]=>{{1,2,3,4,6,7},{5}}
[7,2,6,1,5,4,3]=>[2,7,1,6,3,4,5]=>[6,1,7,2,5,4,3]=>{{1,2,4,6},{3,7},{5}}
[7,2,6,3,1,4,5]=>[2,7,1,3,6,5,4]=>[6,1,7,5,2,3,4]=>{{1,2,3,4,5,6,7}}
[7,2,6,3,1,5,4]=>[2,7,1,3,6,4,5]=>[6,1,7,5,2,4,3]=>{{1,2,4,5,6},{3,7}}
[7,2,6,3,4,1,5]=>[2,7,3,6,5,1,4]=>[6,1,5,2,3,7,4]=>{{1,2,4,6,7},{3,5}}
[7,2,6,3,4,5,1]=>[2,7,3,6,4,1,5]=>[6,1,5,2,4,7,3]=>{{1,2,3,4,5,6,7}}
[7,2,6,3,5,1,4]=>[2,7,3,6,1,5,4]=>[6,1,5,2,7,3,4]=>{{1,2,3,4,5,6,7}}
[7,2,6,3,5,4,1]=>[2,7,3,6,1,4,5]=>[6,1,5,2,7,4,3]=>{{1,2,4,6},{3,5,7}}
[7,2,6,4,1,3,5]=>[2,7,1,4,6,5,3]=>[6,1,7,4,2,3,5]=>{{1,2,3,5,6,7},{4}}
[7,2,6,4,1,5,3]=>[2,7,1,4,6,3,5]=>[6,1,7,4,2,5,3]=>{{1,2,5,6},{3,7},{4}}
[7,2,6,4,3,1,5]=>[2,7,1,3,4,6,5]=>[6,1,7,5,4,2,3]=>{{1,2,6},{3,7},{4,5}}
[7,2,6,4,3,5,1]=>[2,7,3,4,6,1,5]=>[6,1,5,4,2,7,3]=>{{1,2,3,5,6,7},{4}}
[7,2,6,4,5,1,3]=>[2,7,4,6,1,5,3]=>[6,1,4,2,7,3,5]=>{{1,2,3,4,6},{5,7}}
[7,2,6,4,5,3,1]=>[2,7,4,6,1,3,5]=>[6,1,4,2,7,5,3]=>{{1,2,3,4,5,6,7}}
[7,2,6,5,1,3,4]=>[2,7,1,5,6,4,3]=>[6,1,7,3,2,4,5]=>{{1,2,3,4,5,6,7}}
[7,2,6,5,1,4,3]=>[2,7,1,5,6,3,4]=>[6,1,7,3,2,5,4]=>{{1,2,5,6},{3,4,7}}
[7,2,6,5,3,1,4]=>[2,7,1,3,5,6,4]=>[6,1,7,5,3,2,4]=>{{1,2,6},{3,4,5,7}}
[7,2,6,5,3,4,1]=>[2,7,3,5,6,1,4]=>[6,1,5,3,2,7,4]=>{{1,2,3,4,5,6,7}}
[7,2,6,5,4,1,3]=>[2,7,1,4,5,6,3]=>[6,1,7,4,3,2,5]=>{{1,2,6},{3,5,7},{4}}
[7,2,6,5,4,3,1]=>[2,7,1,3,4,5,6]=>[6,1,7,5,4,3,2]=>{{1,2,3,6,7},{4,5}}
[7,3,1,2,4,5,6]=>[1,3,7,6,5,4,2]=>[7,5,1,2,3,4,6]=>{{1,2,3,4,5,6,7}}
[7,3,1,2,4,6,5]=>[1,3,7,5,6,4,2]=>[7,5,1,3,2,4,6]=>{{1,3,4,6,7},{2,5}}
[7,3,1,2,5,4,6]=>[1,3,7,6,4,5,2]=>[7,5,1,2,4,3,6]=>{{1,3,6,7},{2,4,5}}
[7,3,1,2,5,6,4]=>[1,3,7,5,4,6,2]=>[7,5,1,3,4,2,6]=>{{1,2,3,4,5,6,7}}
[7,3,1,2,6,4,5]=>[1,3,7,4,6,5,2]=>[7,5,1,4,2,3,6]=>{{1,3,6,7},{2,5},{4}}
[7,3,1,2,6,5,4]=>[1,3,7,4,5,6,2]=>[7,5,1,4,3,2,6]=>{{1,2,3,5,6,7},{4}}
[7,3,1,4,2,5,6]=>[1,3,7,6,5,2,4]=>[7,5,1,2,3,6,4]=>{{1,2,3,4,5,7},{6}}
[7,3,1,4,2,6,5]=>[1,3,7,5,6,2,4]=>[7,5,1,3,2,6,4]=>{{1,3,4,7},{2,5},{6}}
[7,3,1,4,5,2,6]=>[1,3,7,6,4,2,5]=>[7,5,1,2,4,6,3]=>{{1,3,7},{2,4,5},{6}}
[7,3,1,4,5,6,2]=>[1,3,7,5,4,2,6]=>[7,5,1,3,4,6,2]=>{{1,2,3,4,5,7},{6}}
[7,3,1,4,6,2,5]=>[1,3,7,4,2,6,5]=>[7,5,1,4,6,2,3]=>{{1,3,7},{2,5,6},{4}}
[7,3,1,4,6,5,2]=>[1,3,7,4,2,5,6]=>[7,5,1,4,6,3,2]=>{{1,2,3,5,6,7},{4}}
[7,3,1,5,2,4,6]=>[1,3,7,6,2,5,4]=>[7,5,1,2,6,3,4]=>{{1,2,3,4,5,6,7}}
[7,3,1,5,2,6,4]=>[1,3,7,2,5,4,6]=>[7,5,1,6,3,4,2]=>{{1,2,3,5,7},{4,6}}
[7,3,1,5,4,2,6]=>[1,3,7,6,2,4,5]=>[7,5,1,2,6,4,3]=>{{1,3,7},{2,4,5,6}}
[7,3,1,5,4,6,2]=>[1,3,7,4,5,2,6]=>[7,5,1,4,3,6,2]=>{{1,2,3,5,7},{4},{6}}
[7,3,1,5,6,2,4]=>[1,3,7,5,2,6,4]=>[7,5,1,3,6,2,4]=>{{1,3,4,7},{2,5,6}}
[7,3,1,5,6,4,2]=>[1,3,7,5,2,4,6]=>[7,5,1,3,6,4,2]=>{{1,2,3,4,5,6,7}}
[7,3,1,6,2,4,5]=>[1,3,7,2,6,5,4]=>[7,5,1,6,2,3,4]=>{{1,3,4,6,7},{2,5}}
[7,3,1,6,2,5,4]=>[1,3,7,2,6,4,5]=>[7,5,1,6,2,4,3]=>{{1,3,7},{2,5},{4,6}}
[7,3,1,6,4,2,5]=>[1,3,7,2,4,6,5]=>[7,5,1,6,4,2,3]=>{{1,3,7},{2,4,5,6}}
[7,3,1,6,4,5,2]=>[1,3,7,4,6,2,5]=>[7,5,1,4,2,6,3]=>{{1,3,7},{2,5},{4},{6}}
[7,3,1,6,5,2,4]=>[1,3,7,2,5,6,4]=>[7,5,1,6,3,2,4]=>{{1,2,3,4,5,6,7}}
[7,3,1,6,5,4,2]=>[1,3,7,2,4,5,6]=>[7,5,1,6,4,3,2]=>{{1,2,3,4,5,6,7}}
[7,3,2,1,4,5,6]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>{{1,4,7},{2,3,5,6}}
[7,3,2,1,4,6,5]=>[1,2,3,7,5,6,4]=>[7,6,5,1,3,2,4]=>{{1,4,7},{2,6},{3,5}}
[7,3,2,1,5,4,6]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>{{1,2,3,4,5,6,7}}
[7,3,2,1,5,6,4]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>{{1,2,4,6,7},{3,5}}
[7,3,2,1,6,4,5]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>{{1,3,4,5,7},{2,6}}
[7,3,2,1,6,5,4]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>{{1,2,3,4,5,6,7}}
[7,3,2,4,1,5,6]=>[2,3,7,6,5,1,4]=>[6,5,1,2,3,7,4]=>{{1,2,3,4,5,6,7}}
[7,3,2,4,1,6,5]=>[2,3,7,5,6,1,4]=>[6,5,1,3,2,7,4]=>{{1,3,4,6,7},{2,5}}
[7,3,2,4,5,1,6]=>[2,3,7,6,4,1,5]=>[6,5,1,2,4,7,3]=>{{1,3,6,7},{2,4,5}}
[7,3,2,4,5,6,1]=>[2,3,7,5,4,1,6]=>[6,5,1,3,4,7,2]=>{{1,2,3,4,5,6,7}}
[7,3,2,4,6,1,5]=>[2,3,7,4,1,6,5]=>[6,5,1,4,7,2,3]=>{{1,2,3,5,6,7},{4}}
[7,3,2,4,6,5,1]=>[2,3,7,4,1,5,6]=>[6,5,1,4,7,3,2]=>{{1,3,6},{2,5,7},{4}}
[7,3,2,5,1,4,6]=>[2,3,7,6,1,5,4]=>[6,5,1,2,7,3,4]=>{{1,3,6},{2,4,5,7}}
[7,3,2,5,1,6,4]=>[2,3,7,1,5,4,6]=>[6,5,1,7,3,4,2]=>{{1,2,3,4,5,6,7}}
[7,3,2,5,4,1,6]=>[2,3,7,6,1,4,5]=>[6,5,1,2,7,4,3]=>{{1,2,3,4,5,6,7}}
[7,3,2,5,4,6,1]=>[2,3,7,4,5,1,6]=>[6,5,1,4,3,7,2]=>{{1,2,3,5,6,7},{4}}
[7,3,2,5,6,1,4]=>[2,3,7,5,1,6,4]=>[6,5,1,3,7,2,4]=>{{1,2,3,4,5,6,7}}
[7,3,2,5,6,4,1]=>[2,3,7,5,1,4,6]=>[6,5,1,3,7,4,2]=>{{1,3,4,6},{2,5,7}}
[7,3,2,6,1,4,5]=>[2,3,7,1,6,5,4]=>[6,5,1,7,2,3,4]=>{{1,3,6},{2,5},{4,7}}
[7,3,2,6,1,5,4]=>[2,3,7,1,6,4,5]=>[6,5,1,7,2,4,3]=>{{1,3,4,6,7},{2,5}}
[7,3,2,6,4,1,5]=>[2,3,7,1,4,6,5]=>[6,5,1,7,4,2,3]=>{{1,2,3,4,5,6,7}}
[7,3,2,6,4,5,1]=>[2,3,7,4,6,1,5]=>[6,5,1,4,2,7,3]=>{{1,3,6,7},{2,5},{4}}
[7,3,2,6,5,1,4]=>[2,3,7,1,5,6,4]=>[6,5,1,7,3,2,4]=>{{1,2,3,5,6},{4,7}}
[7,3,2,6,5,4,1]=>[2,3,7,1,4,5,6]=>[6,5,1,7,4,3,2]=>{{1,3,6},{2,4,5,7}}
[7,3,4,1,2,5,6]=>[3,7,6,5,1,4,2]=>[5,1,2,3,7,4,6]=>{{1,2,3,4,5,6,7}}
[7,3,4,1,2,6,5]=>[3,7,5,6,1,4,2]=>[5,1,3,2,7,4,6]=>{{1,2,4,5,6,7},{3}}
[7,3,4,1,5,2,6]=>[3,7,6,1,4,2,5]=>[5,1,2,7,4,6,3]=>{{1,2,3,4,5,7},{6}}
[7,3,4,1,5,6,2]=>[3,7,5,1,4,2,6]=>[5,1,3,7,4,6,2]=>{{1,2,4,5,7},{3},{6}}
[7,3,4,1,6,2,5]=>[3,7,1,4,2,6,5]=>[5,1,7,4,6,2,3]=>{{1,2,5,6},{3,7},{4}}
[7,3,4,1,6,5,2]=>[3,7,1,4,2,5,6]=>[5,1,7,4,6,3,2]=>{{1,2,3,5,6,7},{4}}
[7,3,4,2,1,5,6]=>[3,7,6,5,1,2,4]=>[5,1,2,3,7,6,4]=>{{1,2,3,4,5,7},{6}}
[7,3,4,2,1,6,5]=>[3,7,5,6,1,2,4]=>[5,1,3,2,7,6,4]=>{{1,2,4,5,7},{3},{6}}
[7,3,4,2,5,1,6]=>[3,7,6,2,4,1,5]=>[5,1,2,6,4,7,3]=>{{1,2,3,4,5,6,7}}
[7,3,4,2,5,6,1]=>[3,7,5,2,4,1,6]=>[5,1,3,6,4,7,2]=>{{1,2,4,5,6,7},{3}}
[7,3,4,2,6,1,5]=>[3,7,2,4,1,6,5]=>[5,1,6,4,7,2,3]=>{{1,2,3,5,6,7},{4}}
[7,3,4,2,6,5,1]=>[3,7,2,4,1,5,6]=>[5,1,6,4,7,3,2]=>{{1,2,5,7},{3,6},{4}}
[7,3,4,5,1,2,6]=>[3,7,6,4,1,5,2]=>[5,1,2,4,7,3,6]=>{{1,2,3,5,6,7},{4}}
[7,3,4,5,1,6,2]=>[3,7,4,1,5,2,6]=>[5,1,4,7,3,6,2]=>{{1,2,3,4,5,7},{6}}
[7,3,4,5,2,1,6]=>[3,7,6,4,1,2,5]=>[5,1,2,4,7,6,3]=>{{1,2,3,5,7},{4},{6}}
[7,3,4,5,2,6,1]=>[3,7,4,2,5,1,6]=>[5,1,4,6,3,7,2]=>{{1,2,3,4,5,6,7}}
[7,3,4,5,6,1,2]=>[3,7,5,4,1,6,2]=>[5,1,3,4,7,2,6]=>{{1,2,5,6,7},{3},{4}}
[7,3,4,5,6,2,1]=>[3,7,5,4,1,2,6]=>[5,1,3,4,7,6,2]=>{{1,2,5,7},{3},{4},{6}}
[7,3,4,6,1,2,5]=>[3,7,4,1,6,5,2]=>[5,1,4,7,2,3,6]=>{{1,2,5},{3,4,6,7}}
[7,3,4,6,1,5,2]=>[3,7,4,1,6,2,5]=>[5,1,4,7,2,6,3]=>{{1,2,5},{3,4,7},{6}}
[7,3,4,6,2,1,5]=>[3,7,4,1,2,6,5]=>[5,1,4,7,6,2,3]=>{{1,2,5,6},{3,4,7}}
[7,3,4,6,2,5,1]=>[3,7,4,2,6,1,5]=>[5,1,4,6,2,7,3]=>{{1,2,5},{3,4,6,7}}
[7,3,4,6,5,1,2]=>[3,7,4,1,5,6,2]=>[5,1,4,7,3,2,6]=>{{1,2,3,4,5,6,7}}
[7,3,4,6,5,2,1]=>[3,7,4,1,2,5,6]=>[5,1,4,7,6,3,2]=>{{1,2,3,4,5,6,7}}
[7,3,5,1,2,4,6]=>[3,7,6,1,5,4,2]=>[5,1,2,7,3,4,6]=>{{1,2,3,5},{4,6,7}}
[7,3,5,1,2,6,4]=>[3,7,1,5,4,6,2]=>[5,1,7,3,4,2,6]=>{{1,2,3,4,5,6,7}}
[7,3,5,1,4,2,6]=>[3,7,6,1,5,2,4]=>[5,1,2,7,3,6,4]=>{{1,2,3,5},{4,7},{6}}
[7,3,5,1,4,6,2]=>[3,7,1,5,4,2,6]=>[5,1,7,3,4,6,2]=>{{1,2,3,4,5,7},{6}}
[7,3,5,1,6,2,4]=>[3,7,1,5,2,6,4]=>[5,1,7,3,6,2,4]=>{{1,2,5,6},{3,4,7}}
[7,3,5,1,6,4,2]=>[3,7,1,5,2,4,6]=>[5,1,7,3,6,4,2]=>{{1,2,3,4,5,6,7}}
[7,3,5,2,1,4,6]=>[3,7,6,1,2,5,4]=>[5,1,2,7,6,3,4]=>{{1,2,3,5,6},{4,7}}
[7,3,5,2,1,6,4]=>[3,7,1,2,5,4,6]=>[5,1,7,6,3,4,2]=>{{1,2,3,5,7},{4,6}}
[7,3,5,2,4,1,6]=>[3,7,6,2,5,1,4]=>[5,1,2,6,3,7,4]=>{{1,2,3,5},{4,6,7}}
[7,3,5,2,4,6,1]=>[3,7,2,5,4,1,6]=>[5,1,6,3,4,7,2]=>{{1,2,3,4,5,6,7}}
[7,3,5,2,6,1,4]=>[3,7,2,5,1,6,4]=>[5,1,6,3,7,2,4]=>{{1,2,3,4,5,6,7}}
[7,3,5,2,6,4,1]=>[3,7,2,5,1,4,6]=>[5,1,6,3,7,4,2]=>{{1,2,5,7},{3,4,6}}
[7,3,5,4,1,2,6]=>[3,7,6,1,4,5,2]=>[5,1,2,7,4,3,6]=>{{1,2,3,4,5,6,7}}
[7,3,5,4,1,6,2]=>[3,7,1,4,5,2,6]=>[5,1,7,4,3,6,2]=>{{1,2,3,5,7},{4},{6}}
[7,3,5,4,2,1,6]=>[3,7,6,1,2,4,5]=>[5,1,2,7,6,4,3]=>{{1,2,3,4,5,6,7}}
[7,3,5,4,2,6,1]=>[3,7,2,4,5,1,6]=>[5,1,6,4,3,7,2]=>{{1,2,3,5,6,7},{4}}
[7,3,5,4,6,1,2]=>[3,7,4,5,1,6,2]=>[5,1,4,3,7,2,6]=>{{1,2,5,6,7},{3,4}}
[7,3,5,4,6,2,1]=>[3,7,4,5,1,2,6]=>[5,1,4,3,7,6,2]=>{{1,2,5,7},{3,4},{6}}
[7,3,5,6,1,2,4]=>[3,7,5,1,6,4,2]=>[5,1,3,7,2,4,6]=>{{1,2,5},{3},{4,6,7}}
[7,3,5,6,1,4,2]=>[3,7,5,1,6,2,4]=>[5,1,3,7,2,6,4]=>{{1,2,5},{3},{4,7},{6}}
[7,3,5,6,2,1,4]=>[3,7,5,1,2,6,4]=>[5,1,3,7,6,2,4]=>{{1,2,5,6},{3},{4,7}}
[7,3,5,6,2,4,1]=>[3,7,5,2,6,1,4]=>[5,1,3,6,2,7,4]=>{{1,2,5},{3},{4,6,7}}
[7,3,5,6,4,1,2]=>[3,7,5,1,4,6,2]=>[5,1,3,7,4,2,6]=>{{1,2,4,5,6,7},{3}}
[7,3,5,6,4,2,1]=>[3,7,5,1,2,4,6]=>[5,1,3,7,6,4,2]=>{{1,2,4,5,6,7},{3}}
[7,3,6,1,2,4,5]=>[3,7,1,6,5,4,2]=>[5,1,7,2,3,4,6]=>{{1,2,3,4,5,6,7}}
[7,3,6,1,2,5,4]=>[3,7,1,6,4,5,2]=>[5,1,7,2,4,3,6]=>{{1,2,4,5},{3,6,7}}
[7,3,6,1,4,2,5]=>[3,7,1,6,5,2,4]=>[5,1,7,2,3,6,4]=>{{1,2,3,4,5,7},{6}}
[7,3,6,1,4,5,2]=>[3,7,1,6,4,2,5]=>[5,1,7,2,4,6,3]=>{{1,2,4,5},{3,7},{6}}
[7,3,6,1,5,2,4]=>[3,7,1,6,2,5,4]=>[5,1,7,2,6,3,4]=>{{1,2,3,4,5,6,7}}
[7,3,6,1,5,4,2]=>[3,7,1,6,2,4,5]=>[5,1,7,2,6,4,3]=>{{1,2,4,5,6},{3,7}}
[7,3,6,2,1,4,5]=>[3,7,1,2,6,5,4]=>[5,1,7,6,2,3,4]=>{{1,2,5},{3,4,6,7}}
[7,3,6,2,1,5,4]=>[3,7,1,2,6,4,5]=>[5,1,7,6,2,4,3]=>{{1,2,5},{3,7},{4,6}}
[7,3,6,2,4,1,5]=>[3,7,2,6,5,1,4]=>[5,1,6,2,3,7,4]=>{{1,2,3,4,5,6,7}}
[7,3,6,2,4,5,1]=>[3,7,2,6,4,1,5]=>[5,1,6,2,4,7,3]=>{{1,2,4,5},{3,6,7}}
[7,3,6,2,5,1,4]=>[3,7,2,6,1,5,4]=>[5,1,6,2,7,3,4]=>{{1,2,4,5,7},{3,6}}
[7,3,6,2,5,4,1]=>[3,7,2,6,1,4,5]=>[5,1,6,2,7,4,3]=>{{1,2,3,4,5,6,7}}
[7,3,6,4,1,2,5]=>[3,7,1,4,6,5,2]=>[5,1,7,4,2,3,6]=>{{1,2,5},{3,6,7},{4}}
[7,3,6,4,1,5,2]=>[3,7,1,4,6,2,5]=>[5,1,7,4,2,6,3]=>{{1,2,5},{3,7},{4},{6}}
[7,3,6,4,2,1,5]=>[3,7,1,2,4,6,5]=>[5,1,7,6,4,2,3]=>{{1,2,4,5,6},{3,7}}
[7,3,6,4,2,5,1]=>[3,7,2,4,6,1,5]=>[5,1,6,4,2,7,3]=>{{1,2,5},{3,6,7},{4}}
[7,3,6,4,5,1,2]=>[3,7,4,6,1,5,2]=>[5,1,4,2,7,3,6]=>{{1,2,3,4,5,6,7}}
[7,3,6,4,5,2,1]=>[3,7,4,6,1,2,5]=>[5,1,4,2,7,6,3]=>{{1,2,3,4,5,7},{6}}
[7,3,6,5,1,2,4]=>[3,7,1,5,6,4,2]=>[5,1,7,3,2,4,6]=>{{1,2,5},{3,4,6,7}}
[7,3,6,5,1,4,2]=>[3,7,1,5,6,2,4]=>[5,1,7,3,2,6,4]=>{{1,2,5},{3,4,7},{6}}
[7,3,6,5,2,1,4]=>[3,7,1,2,5,6,4]=>[5,1,7,6,3,2,4]=>{{1,2,3,4,5,6,7}}
[7,3,6,5,2,4,1]=>[3,7,2,5,6,1,4]=>[5,1,6,3,2,7,4]=>{{1,2,5},{3,4,6,7}}
[7,3,6,5,4,1,2]=>[3,7,1,4,5,6,2]=>[5,1,7,4,3,2,6]=>{{1,2,3,5,6,7},{4}}
[7,3,6,5,4,2,1]=>[3,7,1,2,4,5,6]=>[5,1,7,6,4,3,2]=>{{1,2,3,4,5,6,7}}
[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[7,4,1,2,3,5,6]=>{{1,3,5,6,7},{2,4}}
[7,4,1,2,3,6,5]=>[1,4,7,5,6,3,2]=>[7,4,1,3,2,5,6]=>{{1,2,3,4,5,6,7}}
[7,4,1,2,5,3,6]=>[1,4,7,6,3,5,2]=>[7,4,1,2,5,3,6]=>{{1,3,6,7},{2,4},{5}}
[7,4,1,2,5,6,3]=>[1,4,7,5,3,6,2]=>[7,4,1,3,5,2,6]=>{{1,2,3,4,6,7},{5}}
[7,4,1,2,6,3,5]=>[1,4,7,3,6,5,2]=>[7,4,1,5,2,3,6]=>{{1,3,6,7},{2,4,5}}
[7,4,1,2,6,5,3]=>[1,4,7,3,5,6,2]=>[7,4,1,5,3,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,1,3,2,5,6]=>[1,4,7,6,5,2,3]=>[7,4,1,2,3,6,5]=>{{1,3,5,7},{2,4},{6}}
[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[7,4,1,3,2,6,5]=>{{1,2,3,4,5,7},{6}}
[7,4,1,3,5,2,6]=>[1,4,7,6,3,2,5]=>[7,4,1,2,5,6,3]=>{{1,3,7},{2,4},{5},{6}}
[7,4,1,3,5,6,2]=>[1,4,7,5,3,2,6]=>[7,4,1,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[7,4,1,3,6,2,5]=>[1,4,7,3,2,6,5]=>[7,4,1,5,6,2,3]=>{{1,3,7},{2,4,5,6}}
[7,4,1,3,6,5,2]=>[1,4,7,3,2,5,6]=>[7,4,1,5,6,3,2]=>{{1,2,3,4,5,6,7}}
[7,4,1,5,2,3,6]=>[1,4,7,6,2,5,3]=>[7,4,1,2,6,3,5]=>{{1,3,5,6,7},{2,4}}
[7,4,1,5,2,6,3]=>[1,4,7,2,5,3,6]=>[7,4,1,6,3,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,1,5,3,2,6]=>[1,4,7,6,2,3,5]=>[7,4,1,2,6,5,3]=>{{1,3,7},{2,4},{5,6}}
[7,4,1,5,3,6,2]=>[1,4,7,3,5,2,6]=>[7,4,1,5,3,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,1,5,6,2,3]=>[1,4,7,5,2,6,3]=>[7,4,1,3,6,2,5]=>{{1,2,3,4,5,6,7}}
[7,4,1,5,6,3,2]=>[1,4,7,5,2,3,6]=>[7,4,1,3,6,5,2]=>{{1,2,3,4,7},{5,6}}
[7,4,1,6,2,3,5]=>[1,4,7,2,6,5,3]=>[7,4,1,6,2,3,5]=>{{1,2,3,4,5,6,7}}
[7,4,1,6,2,5,3]=>[1,4,7,2,6,3,5]=>[7,4,1,6,2,5,3]=>{{1,3,7},{2,4,5,6}}
[7,4,1,6,3,2,5]=>[1,4,7,2,3,6,5]=>[7,4,1,6,5,2,3]=>{{1,3,7},{2,4,6},{5}}
[7,4,1,6,3,5,2]=>[1,4,7,3,6,2,5]=>[7,4,1,5,2,6,3]=>{{1,3,7},{2,4,5},{6}}
[7,4,1,6,5,2,3]=>[1,4,7,2,5,6,3]=>[7,4,1,6,3,2,5]=>{{1,3,5,7},{2,4,6}}
[7,4,1,6,5,3,2]=>[1,4,7,2,3,5,6]=>[7,4,1,6,5,3,2]=>{{1,2,3,4,6,7},{5}}
[7,4,2,1,3,5,6]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,3,5]=>{{1,2,3,4,5,6,7}}
[7,4,2,1,3,6,5]=>[1,2,4,7,5,6,3]=>[7,6,4,1,3,2,5]=>{{1,3,4,5,7},{2,6}}
[7,4,2,1,5,3,6]=>[1,2,4,7,6,3,5]=>[7,6,4,1,2,5,3]=>{{1,3,4,7},{2,5,6}}
[7,4,2,1,5,6,3]=>[1,2,4,7,5,3,6]=>[7,6,4,1,3,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,2,1,6,3,5]=>[1,2,4,7,3,6,5]=>[7,6,4,1,5,2,3]=>{{1,3,4,7},{2,6},{5}}
[7,4,2,1,6,5,3]=>[1,2,4,7,3,5,6]=>[7,6,4,1,5,3,2]=>{{1,2,3,4,6,7},{5}}
[7,4,2,3,1,5,6]=>[2,4,7,6,5,1,3]=>[6,4,1,2,3,7,5]=>{{1,3,5,6,7},{2,4}}
[7,4,2,3,1,6,5]=>[2,4,7,5,6,1,3]=>[6,4,1,3,2,7,5]=>{{1,2,3,4,5,6,7}}
[7,4,2,3,5,1,6]=>[2,4,7,6,3,1,5]=>[6,4,1,2,5,7,3]=>{{1,3,6,7},{2,4},{5}}
[7,4,2,3,5,6,1]=>[2,4,7,5,3,1,6]=>[6,4,1,3,5,7,2]=>{{1,2,3,4,6,7},{5}}
[7,4,2,3,6,1,5]=>[2,4,7,3,1,6,5]=>[6,4,1,5,7,2,3]=>{{1,2,3,4,5,6,7}}
[7,4,2,3,6,5,1]=>[2,4,7,3,1,5,6]=>[6,4,1,5,7,3,2]=>{{1,3,6},{2,4,5,7}}
[7,4,2,5,1,3,6]=>[2,4,7,6,1,5,3]=>[6,4,1,2,7,3,5]=>{{1,3,6},{2,4},{5,7}}
[7,4,2,5,1,6,3]=>[2,4,7,1,5,3,6]=>[6,4,1,7,3,5,2]=>{{1,3,5,6},{2,4,7}}
[7,4,2,5,3,1,6]=>[2,4,7,6,1,3,5]=>[6,4,1,2,7,5,3]=>{{1,3,5,6,7},{2,4}}
[7,4,2,5,3,6,1]=>[2,4,7,3,5,1,6]=>[6,4,1,5,3,7,2]=>{{1,2,3,4,5,6,7}}
[7,4,2,5,6,1,3]=>[2,4,7,5,1,6,3]=>[6,4,1,3,7,2,5]=>{{1,2,3,4,6},{5,7}}
[7,4,2,5,6,3,1]=>[2,4,7,5,1,3,6]=>[6,4,1,3,7,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,2,6,1,3,5]=>[2,4,7,1,6,5,3]=>[6,4,1,7,2,3,5]=>{{1,3,6},{2,4,5,7}}
[7,4,2,6,1,5,3]=>[2,4,7,1,6,3,5]=>[6,4,1,7,2,5,3]=>{{1,2,3,4,5,6,7}}
[7,4,2,6,3,1,5]=>[2,4,7,1,3,6,5]=>[6,4,1,7,5,2,3]=>{{1,2,3,4,6,7},{5}}
[7,4,2,6,3,5,1]=>[2,4,7,3,6,1,5]=>[6,4,1,5,2,7,3]=>{{1,3,6,7},{2,4,5}}
[7,4,2,6,5,1,3]=>[2,4,7,1,5,6,3]=>[6,4,1,7,3,2,5]=>{{1,2,3,4,5,6,7}}
[7,4,2,6,5,3,1]=>[2,4,7,1,3,5,6]=>[6,4,1,7,5,3,2]=>{{1,3,6},{2,4,7},{5}}
[7,4,3,1,2,5,6]=>[1,3,4,7,6,5,2]=>[7,5,4,1,2,3,6]=>{{1,3,4,6,7},{2,5}}
[7,4,3,1,2,6,5]=>[1,3,4,7,5,6,2]=>[7,5,4,1,3,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,3,1,5,2,6]=>[1,3,4,7,6,2,5]=>[7,5,4,1,2,6,3]=>{{1,3,4,7},{2,5},{6}}
[7,4,3,1,5,6,2]=>[1,3,4,7,5,2,6]=>[7,5,4,1,3,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,3,1,6,2,5]=>[1,3,4,7,2,6,5]=>[7,5,4,1,6,2,3]=>{{1,3,4,7},{2,5,6}}
[7,4,3,1,6,5,2]=>[1,3,4,7,2,5,6]=>[7,5,4,1,6,3,2]=>{{1,2,3,4,5,6,7}}
[7,4,3,2,1,5,6]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>{{1,3,5,7},{2,6},{4}}
[7,4,3,2,1,6,5]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>{{1,2,3,5,6,7},{4}}
[7,4,3,2,5,1,6]=>[2,3,4,7,6,1,5]=>[6,5,4,1,2,7,3]=>{{1,3,4,6,7},{2,5}}
[7,4,3,2,5,6,1]=>[2,3,4,7,5,1,6]=>[6,5,4,1,3,7,2]=>{{1,2,3,4,5,6,7}}
[7,4,3,2,6,1,5]=>[2,3,4,7,1,6,5]=>[6,5,4,1,7,2,3]=>{{1,2,3,4,5,6,7}}
[7,4,3,2,6,5,1]=>[2,3,4,7,1,5,6]=>[6,5,4,1,7,3,2]=>{{1,3,4,6},{2,5,7}}
[7,4,3,5,1,2,6]=>[3,4,7,6,1,5,2]=>[5,4,1,2,7,3,6]=>{{1,3,5,6,7},{2,4}}
[7,4,3,5,1,6,2]=>[3,4,7,1,5,2,6]=>[5,4,1,7,3,6,2]=>{{1,3,5},{2,4,7},{6}}
[7,4,3,5,2,1,6]=>[3,4,7,6,1,2,5]=>[5,4,1,2,7,6,3]=>{{1,3,5,7},{2,4},{6}}
[7,4,3,5,2,6,1]=>[3,4,7,2,5,1,6]=>[5,4,1,6,3,7,2]=>{{1,3,5},{2,4,6,7}}
[7,4,3,5,6,1,2]=>[3,4,7,5,1,6,2]=>[5,4,1,3,7,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,3,5,6,2,1]=>[3,4,7,5,1,2,6]=>[5,4,1,3,7,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,3,6,1,2,5]=>[3,4,7,1,6,5,2]=>[5,4,1,7,2,3,6]=>{{1,2,3,4,5,6,7}}
[7,4,3,6,1,5,2]=>[3,4,7,1,6,2,5]=>[5,4,1,7,2,6,3]=>{{1,2,3,4,5,7},{6}}
[7,4,3,6,2,1,5]=>[3,4,7,1,2,6,5]=>[5,4,1,7,6,2,3]=>{{1,2,3,4,5,6,7}}
[7,4,3,6,2,5,1]=>[3,4,7,2,6,1,5]=>[5,4,1,6,2,7,3]=>{{1,2,3,4,5,6,7}}
[7,4,3,6,5,1,2]=>[3,4,7,1,5,6,2]=>[5,4,1,7,3,2,6]=>{{1,3,5},{2,4,6,7}}
[7,4,3,6,5,2,1]=>[3,4,7,1,2,5,6]=>[5,4,1,7,6,3,2]=>{{1,3,5,6},{2,4,7}}
[7,4,5,1,2,3,6]=>[4,7,6,1,5,3,2]=>[4,1,2,7,3,5,6]=>{{1,2,3,4,5,6,7}}
[7,4,5,1,2,6,3]=>[4,7,1,5,3,6,2]=>[4,1,7,3,5,2,6]=>{{1,2,3,4,6,7},{5}}
[7,4,5,1,3,2,6]=>[4,7,6,1,5,2,3]=>[4,1,2,7,3,6,5]=>{{1,2,3,4,5,7},{6}}
[7,4,5,1,3,6,2]=>[4,7,1,5,3,2,6]=>[4,1,7,3,5,6,2]=>{{1,2,3,4,7},{5},{6}}
[7,4,5,1,6,2,3]=>[4,7,1,5,2,6,3]=>[4,1,7,3,6,2,5]=>{{1,2,3,4,5,6,7}}
[7,4,5,1,6,3,2]=>[4,7,1,5,2,3,6]=>[4,1,7,3,6,5,2]=>{{1,2,3,4,7},{5,6}}
[7,4,5,2,1,3,6]=>[4,7,6,1,2,5,3]=>[4,1,2,7,6,3,5]=>{{1,2,3,4,5,6,7}}
[7,4,5,2,1,6,3]=>[4,7,1,2,5,3,6]=>[4,1,7,6,3,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,5,2,3,1,6]=>[4,7,6,2,5,1,3]=>[4,1,2,6,3,7,5]=>{{1,2,3,4,5,6,7}}
[7,4,5,2,3,6,1]=>[4,7,2,5,3,1,6]=>[4,1,6,3,5,7,2]=>{{1,2,3,4,6,7},{5}}
[7,4,5,2,6,1,3]=>[4,7,2,5,1,6,3]=>[4,1,6,3,7,2,5]=>{{1,2,3,4,6},{5,7}}
[7,4,5,2,6,3,1]=>[4,7,2,5,1,3,6]=>[4,1,6,3,7,5,2]=>{{1,2,3,4,5,6,7}}
[7,4,5,3,1,2,6]=>[4,7,6,1,3,5,2]=>[4,1,2,7,5,3,6]=>{{1,2,3,4,6,7},{5}}
[7,4,5,3,1,6,2]=>[4,7,1,3,5,2,6]=>[4,1,7,5,3,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,5,3,2,1,6]=>[4,7,6,1,2,3,5]=>[4,1,2,7,6,5,3]=>{{1,2,3,4,7},{5,6}}
[7,4,5,3,2,6,1]=>[4,7,2,3,5,1,6]=>[4,1,6,5,3,7,2]=>{{1,2,3,4,5,6,7}}
[7,4,5,3,6,1,2]=>[4,7,3,5,1,6,2]=>[4,1,5,3,7,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,5,3,6,2,1]=>[4,7,3,5,1,2,6]=>[4,1,5,3,7,6,2]=>{{1,2,3,4,5,7},{6}}
[7,4,5,6,1,2,3]=>[4,7,5,1,6,3,2]=>[4,1,3,7,2,5,6]=>{{1,2,4,5,6,7},{3}}
[7,4,5,6,1,3,2]=>[4,7,5,1,6,2,3]=>[4,1,3,7,2,6,5]=>{{1,2,4,5,7},{3},{6}}
[7,4,5,6,2,1,3]=>[4,7,5,1,2,6,3]=>[4,1,3,7,6,2,5]=>{{1,2,4,5,6,7},{3}}
[7,4,5,6,2,3,1]=>[4,7,5,2,6,1,3]=>[4,1,3,6,2,7,5]=>{{1,2,4,5,6,7},{3}}
[7,4,5,6,3,1,2]=>[4,7,5,1,3,6,2]=>[4,1,3,7,5,2,6]=>{{1,2,4,6,7},{3},{5}}
[7,4,5,6,3,2,1]=>[4,7,5,1,2,3,6]=>[4,1,3,7,6,5,2]=>{{1,2,4,7},{3},{5,6}}
[7,4,6,1,2,3,5]=>[4,7,1,6,5,3,2]=>[4,1,7,2,3,5,6]=>{{1,2,4},{3,5,6,7}}
[7,4,6,1,2,5,3]=>[4,7,1,6,3,5,2]=>[4,1,7,2,5,3,6]=>{{1,2,4},{3,6,7},{5}}
[7,4,6,1,3,2,5]=>[4,7,1,6,5,2,3]=>[4,1,7,2,3,6,5]=>{{1,2,4},{3,5,7},{6}}
[7,4,6,1,3,5,2]=>[4,7,1,6,3,2,5]=>[4,1,7,2,5,6,3]=>{{1,2,4},{3,7},{5},{6}}
[7,4,6,1,5,2,3]=>[4,7,1,6,2,5,3]=>[4,1,7,2,6,3,5]=>{{1,2,4},{3,5,6,7}}
[7,4,6,1,5,3,2]=>[4,7,1,6,2,3,5]=>[4,1,7,2,6,5,3]=>{{1,2,4},{3,7},{5,6}}
[7,4,6,2,1,3,5]=>[4,7,1,2,6,5,3]=>[4,1,7,6,2,3,5]=>{{1,2,3,4,5,6,7}}
[7,4,6,2,1,5,3]=>[4,7,1,2,6,3,5]=>[4,1,7,6,2,5,3]=>{{1,2,4,5,6},{3,7}}
[7,4,6,2,3,1,5]=>[4,7,2,6,5,1,3]=>[4,1,6,2,3,7,5]=>{{1,2,4},{3,5,6,7}}
[7,4,6,2,3,5,1]=>[4,7,2,6,3,1,5]=>[4,1,6,2,5,7,3]=>{{1,2,4},{3,6,7},{5}}
[7,4,6,2,5,1,3]=>[4,7,2,6,1,5,3]=>[4,1,6,2,7,3,5]=>{{1,2,4},{3,6},{5,7}}
[7,4,6,2,5,3,1]=>[4,7,2,6,1,3,5]=>[4,1,6,2,7,5,3]=>{{1,2,4},{3,5,6,7}}
[7,4,6,3,1,2,5]=>[4,7,1,3,6,5,2]=>[4,1,7,5,2,3,6]=>{{1,2,4,5},{3,6,7}}
[7,4,6,3,1,5,2]=>[4,7,1,3,6,2,5]=>[4,1,7,5,2,6,3]=>{{1,2,4,5},{3,7},{6}}
[7,4,6,3,2,1,5]=>[4,7,1,2,3,6,5]=>[4,1,7,6,5,2,3]=>{{1,2,4,6},{3,7},{5}}
[7,4,6,3,2,5,1]=>[4,7,2,3,6,1,5]=>[4,1,6,5,2,7,3]=>{{1,2,4,5},{3,6,7}}
[7,4,6,3,5,1,2]=>[4,7,3,6,1,5,2]=>[4,1,5,2,7,3,6]=>{{1,2,4},{3,5,6,7}}
[7,4,6,3,5,2,1]=>[4,7,3,6,1,2,5]=>[4,1,5,2,7,6,3]=>{{1,2,4},{3,5,7},{6}}
[7,4,6,5,1,2,3]=>[4,7,1,5,6,3,2]=>[4,1,7,3,2,5,6]=>{{1,2,3,4,5,6,7}}
[7,4,6,5,1,3,2]=>[4,7,1,5,6,2,3]=>[4,1,7,3,2,6,5]=>{{1,2,3,4,5,7},{6}}
[7,4,6,5,2,1,3]=>[4,7,1,2,5,6,3]=>[4,1,7,6,3,2,5]=>{{1,2,4,6},{3,5,7}}
[7,4,6,5,2,3,1]=>[4,7,2,5,6,1,3]=>[4,1,6,3,2,7,5]=>{{1,2,3,4,5,6,7}}
[7,4,6,5,3,1,2]=>[4,7,1,3,5,6,2]=>[4,1,7,5,3,2,6]=>{{1,2,3,4,5,6,7}}
[7,4,6,5,3,2,1]=>[4,7,1,2,3,5,6]=>[4,1,7,6,5,3,2]=>{{1,2,3,4,6,7},{5}}
[7,5,1,2,3,4,6]=>[1,5,7,6,4,3,2]=>[7,3,1,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[7,5,1,2,3,6,4]=>[1,5,7,4,6,3,2]=>[7,3,1,4,2,5,6]=>{{1,2,3,5,6,7},{4}}
[7,5,1,2,4,3,6]=>[1,5,7,6,3,4,2]=>[7,3,1,2,5,4,6]=>{{1,2,3,4,6,7},{5}}
[7,5,1,2,4,6,3]=>[1,5,7,4,3,6,2]=>[7,3,1,4,5,2,6]=>{{1,2,3,6,7},{4},{5}}
[7,5,1,2,6,3,4]=>[1,5,7,3,6,4,2]=>[7,3,1,5,2,4,6]=>{{1,2,3,4,5,6,7}}
[7,5,1,2,6,4,3]=>[1,5,7,3,4,6,2]=>[7,3,1,5,4,2,6]=>{{1,2,3,6,7},{4,5}}
[7,5,1,3,2,4,6]=>[1,5,7,6,4,2,3]=>[7,3,1,2,4,6,5]=>{{1,2,3,4,5,7},{6}}
[7,5,1,3,2,6,4]=>[1,5,7,4,6,2,3]=>[7,3,1,4,2,6,5]=>{{1,2,3,5,7},{4},{6}}
[7,5,1,3,4,2,6]=>[1,5,7,6,3,2,4]=>[7,3,1,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[7,5,1,3,4,6,2]=>[1,5,7,4,3,2,6]=>[7,3,1,4,5,6,2]=>{{1,2,3,7},{4},{5},{6}}
[7,5,1,3,6,2,4]=>[1,5,7,3,2,6,4]=>[7,3,1,5,6,2,4]=>{{1,2,3,4,5,6,7}}
[7,5,1,3,6,4,2]=>[1,5,7,3,2,4,6]=>[7,3,1,5,6,4,2]=>{{1,2,3,7},{4,5,6}}
[7,5,1,4,2,3,6]=>[1,5,7,6,2,4,3]=>[7,3,1,2,6,4,5]=>{{1,2,3,4,5,6,7}}
[7,5,1,4,2,6,3]=>[1,5,7,2,4,3,6]=>[7,3,1,6,4,5,2]=>{{1,2,3,7},{4,5,6}}
[7,5,1,4,3,2,6]=>[1,5,7,6,2,3,4]=>[7,3,1,2,6,5,4]=>{{1,2,3,4,7},{5,6}}
[7,5,1,4,3,6,2]=>[1,5,7,3,4,2,6]=>[7,3,1,5,4,6,2]=>{{1,2,3,7},{4,5},{6}}
[7,5,1,4,6,2,3]=>[1,5,7,4,2,6,3]=>[7,3,1,4,6,2,5]=>{{1,2,3,5,6,7},{4}}
[7,5,1,4,6,3,2]=>[1,5,7,4,2,3,6]=>[7,3,1,4,6,5,2]=>{{1,2,3,7},{4},{5,6}}
[7,5,1,6,2,3,4]=>[1,5,7,2,6,4,3]=>[7,3,1,6,2,4,5]=>{{1,2,3,5,7},{4,6}}
[7,5,1,6,2,4,3]=>[1,5,7,2,6,3,4]=>[7,3,1,6,2,5,4]=>{{1,2,3,4,5,6,7}}
[7,5,1,6,3,2,4]=>[1,5,7,2,3,6,4]=>[7,3,1,6,5,2,4]=>{{1,2,3,4,6,7},{5}}
[7,5,1,6,3,4,2]=>[1,5,7,3,6,2,4]=>[7,3,1,5,2,6,4]=>{{1,2,3,4,5,7},{6}}
[7,5,1,6,4,2,3]=>[1,5,7,2,4,6,3]=>[7,3,1,6,4,2,5]=>{{1,2,3,4,5,6,7}}
[7,5,1,6,4,3,2]=>[1,5,7,2,3,4,6]=>[7,3,1,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}
[7,5,2,1,3,4,6]=>[1,2,5,7,6,4,3]=>[7,6,3,1,2,4,5]=>{{1,2,4,5,6,7},{3}}
[7,5,2,1,3,6,4]=>[1,2,5,7,4,6,3]=>[7,6,3,1,4,2,5]=>{{1,4,5,7},{2,6},{3}}
[7,5,2,1,4,3,6]=>[1,2,5,7,6,3,4]=>[7,6,3,1,2,5,4]=>{{1,4,7},{2,5,6},{3}}
[7,5,2,1,4,6,3]=>[1,2,5,7,4,3,6]=>[7,6,3,1,4,5,2]=>{{1,2,4,5,6,7},{3}}
[7,5,2,1,6,3,4]=>[1,2,5,7,3,6,4]=>[7,6,3,1,5,2,4]=>{{1,4,7},{2,6},{3},{5}}
[7,5,2,1,6,4,3]=>[1,2,5,7,3,4,6]=>[7,6,3,1,5,4,2]=>{{1,2,4,6,7},{3},{5}}
[7,5,2,3,1,4,6]=>[2,5,7,6,4,1,3]=>[6,3,1,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[7,5,2,3,1,6,4]=>[2,5,7,4,6,1,3]=>[6,3,1,4,2,7,5]=>{{1,2,3,5,6,7},{4}}
[7,5,2,3,4,1,6]=>[2,5,7,6,3,1,4]=>[6,3,1,2,5,7,4]=>{{1,2,3,4,6,7},{5}}
[7,5,2,3,4,6,1]=>[2,5,7,4,3,1,6]=>[6,3,1,4,5,7,2]=>{{1,2,3,6,7},{4},{5}}
[7,5,2,3,6,1,4]=>[2,5,7,3,1,6,4]=>[6,3,1,5,7,2,4]=>{{1,2,3,6},{4,5,7}}
[7,5,2,3,6,4,1]=>[2,5,7,3,1,4,6]=>[6,3,1,5,7,4,2]=>{{1,2,3,4,5,6,7}}
[7,5,2,4,1,3,6]=>[2,5,7,6,1,4,3]=>[6,3,1,2,7,4,5]=>{{1,2,3,4,6},{5,7}}
[7,5,2,4,1,6,3]=>[2,5,7,1,4,3,6]=>[6,3,1,7,4,5,2]=>{{1,2,3,4,5,6,7}}
[7,5,2,4,3,1,6]=>[2,5,7,6,1,3,4]=>[6,3,1,2,7,5,4]=>{{1,2,3,4,5,6,7}}
[7,5,2,4,3,6,1]=>[2,5,7,3,4,1,6]=>[6,3,1,5,4,7,2]=>{{1,2,3,6,7},{4,5}}
[7,5,2,4,6,1,3]=>[2,5,7,4,1,6,3]=>[6,3,1,4,7,2,5]=>{{1,2,3,6},{4},{5,7}}
[7,5,2,4,6,3,1]=>[2,5,7,4,1,3,6]=>[6,3,1,4,7,5,2]=>{{1,2,3,5,6,7},{4}}
[7,5,2,6,1,3,4]=>[2,5,7,1,6,4,3]=>[6,3,1,7,2,4,5]=>{{1,2,3,4,5,6,7}}
[7,5,2,6,1,4,3]=>[2,5,7,1,6,3,4]=>[6,3,1,7,2,5,4]=>{{1,2,3,5,6},{4,7}}
[7,5,2,6,3,1,4]=>[2,5,7,1,3,6,4]=>[6,3,1,7,5,2,4]=>{{1,2,3,6},{4,7},{5}}
[7,5,2,6,3,4,1]=>[2,5,7,3,6,1,4]=>[6,3,1,5,2,7,4]=>{{1,2,3,4,5,6,7}}
[7,5,2,6,4,1,3]=>[2,5,7,1,4,6,3]=>[6,3,1,7,4,2,5]=>{{1,2,3,6},{4,5,7}}
[7,5,2,6,4,3,1]=>[2,5,7,1,3,4,6]=>[6,3,1,7,5,4,2]=>{{1,2,3,4,6,7},{5}}
[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[7,5,3,1,2,4,6]=>{{1,4,6,7},{2,5},{3}}
[7,5,3,1,2,6,4]=>[1,3,5,7,4,6,2]=>[7,5,3,1,4,2,6]=>{{1,2,4,5,6,7},{3}}
[7,5,3,1,4,2,6]=>[1,3,5,7,6,2,4]=>[7,5,3,1,2,6,4]=>{{1,4,7},{2,5},{3},{6}}
[7,5,3,1,4,6,2]=>[1,3,5,7,4,2,6]=>[7,5,3,1,4,6,2]=>{{1,2,4,5,7},{3},{6}}
[7,5,3,1,6,2,4]=>[1,3,5,7,2,6,4]=>[7,5,3,1,6,2,4]=>{{1,4,7},{2,5,6},{3}}
[7,5,3,1,6,4,2]=>[1,3,5,7,2,4,6]=>[7,5,3,1,6,4,2]=>{{1,2,4,5,6,7},{3}}
[7,5,3,2,1,4,6]=>[1,2,3,5,7,6,4]=>[7,6,5,3,1,2,4]=>{{1,3,4,5,7},{2,6}}
[7,5,3,2,1,6,4]=>[1,2,3,5,7,4,6]=>[7,6,5,3,1,4,2]=>{{1,2,3,4,5,6,7}}
[7,5,3,2,4,1,6]=>[2,3,5,7,6,1,4]=>[6,5,3,1,2,7,4]=>{{1,4,6,7},{2,5},{3}}
[7,5,3,2,4,6,1]=>[2,3,5,7,4,1,6]=>[6,5,3,1,4,7,2]=>{{1,2,4,5,6,7},{3}}
[7,5,3,2,6,1,4]=>[2,3,5,7,1,6,4]=>[6,5,3,1,7,2,4]=>{{1,2,4,5,6,7},{3}}
[7,5,3,2,6,4,1]=>[2,3,5,7,1,4,6]=>[6,5,3,1,7,4,2]=>{{1,4,6},{2,5,7},{3}}
[7,5,3,4,1,2,6]=>[3,5,7,6,1,4,2]=>[5,3,1,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[7,5,3,4,1,6,2]=>[3,5,7,1,4,2,6]=>[5,3,1,7,4,6,2]=>{{1,2,3,4,5,7},{6}}
[7,5,3,4,2,1,6]=>[3,5,7,6,1,2,4]=>[5,3,1,2,7,6,4]=>{{1,2,3,4,5,7},{6}}
[7,5,3,4,2,6,1]=>[3,5,7,2,4,1,6]=>[5,3,1,6,4,7,2]=>{{1,2,3,4,5,6,7}}
[7,5,3,4,6,1,2]=>[3,5,7,4,1,6,2]=>[5,3,1,4,7,2,6]=>{{1,2,3,5,6,7},{4}}
[7,5,3,4,6,2,1]=>[3,5,7,4,1,2,6]=>[5,3,1,4,7,6,2]=>{{1,2,3,5,7},{4},{6}}
[7,5,3,6,1,2,4]=>[3,5,7,1,6,4,2]=>[5,3,1,7,2,4,6]=>{{1,2,3,5},{4,6,7}}
[7,5,3,6,1,4,2]=>[3,5,7,1,6,2,4]=>[5,3,1,7,2,6,4]=>{{1,2,3,5},{4,7},{6}}
[7,5,3,6,2,1,4]=>[3,5,7,1,2,6,4]=>[5,3,1,7,6,2,4]=>{{1,2,3,5,6},{4,7}}
[7,5,3,6,2,4,1]=>[3,5,7,2,6,1,4]=>[5,3,1,6,2,7,4]=>{{1,2,3,5},{4,6,7}}
[7,5,3,6,4,1,2]=>[3,5,7,1,4,6,2]=>[5,3,1,7,4,2,6]=>{{1,2,3,4,5,6,7}}
[7,5,3,6,4,2,1]=>[3,5,7,1,2,4,6]=>[5,3,1,7,6,4,2]=>{{1,2,3,4,5,6,7}}
[7,5,4,1,2,3,6]=>[1,4,5,7,6,3,2]=>[7,4,3,1,2,5,6]=>{{1,2,4,5,6,7},{3}}
[7,5,4,1,2,6,3]=>[1,4,5,7,3,6,2]=>[7,4,3,1,5,2,6]=>{{1,2,4,6,7},{3},{5}}
[7,5,4,1,3,2,6]=>[1,4,5,7,6,2,3]=>[7,4,3,1,2,6,5]=>{{1,2,4,5,7},{3},{6}}
[7,5,4,1,3,6,2]=>[1,4,5,7,3,2,6]=>[7,4,3,1,5,6,2]=>{{1,2,4,7},{3},{5},{6}}
[7,5,4,1,6,2,3]=>[1,4,5,7,2,6,3]=>[7,4,3,1,6,2,5]=>{{1,2,4,5,6,7},{3}}
[7,5,4,1,6,3,2]=>[1,4,5,7,2,3,6]=>[7,4,3,1,6,5,2]=>{{1,2,4,7},{3},{5,6}}
[7,5,4,2,1,3,6]=>[1,2,4,5,7,6,3]=>[7,6,4,3,1,2,5]=>{{1,5,7},{2,6},{3,4}}
[7,5,4,2,1,6,3]=>[1,2,4,5,7,3,6]=>[7,6,4,3,1,5,2]=>{{1,2,5,6,7},{3,4}}
[7,5,4,2,3,1,6]=>[2,4,5,7,6,1,3]=>[6,4,3,1,2,7,5]=>{{1,2,4,5,6,7},{3}}
[7,5,4,2,3,6,1]=>[2,4,5,7,3,1,6]=>[6,4,3,1,5,7,2]=>{{1,2,4,6,7},{3},{5}}
[7,5,4,2,6,1,3]=>[2,4,5,7,1,6,3]=>[6,4,3,1,7,2,5]=>{{1,2,4,6},{3},{5,7}}
[7,5,4,2,6,3,1]=>[2,4,5,7,1,3,6]=>[6,4,3,1,7,5,2]=>{{1,2,4,5,6,7},{3}}
[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[7,5,4,3,1,2,6]=>{{1,2,5,6,7},{3,4}}
[7,5,4,3,1,6,2]=>[1,3,4,5,7,2,6]=>[7,5,4,3,1,6,2]=>{{1,2,5,7},{3,4},{6}}
[7,5,4,3,2,1,6]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>{{1,2,6,7},{3,5},{4}}
[7,5,4,3,2,6,1]=>[2,3,4,5,7,1,6]=>[6,5,4,3,1,7,2]=>{{1,2,5,6,7},{3,4}}
[7,5,4,3,6,1,2]=>[3,4,5,7,1,6,2]=>[5,4,3,1,7,2,6]=>{{1,2,4,5,6,7},{3}}
[7,5,4,3,6,2,1]=>[3,4,5,7,1,2,6]=>[5,4,3,1,7,6,2]=>{{1,2,4,5,7},{3},{6}}
[7,5,4,6,1,2,3]=>[4,5,7,1,6,3,2]=>[4,3,1,7,2,5,6]=>{{1,2,3,4,5,6,7}}
[7,5,4,6,1,3,2]=>[4,5,7,1,6,2,3]=>[4,3,1,7,2,6,5]=>{{1,2,3,4,5,7},{6}}
[7,5,4,6,2,1,3]=>[4,5,7,1,2,6,3]=>[4,3,1,7,6,2,5]=>{{1,2,3,4,5,6,7}}
[7,5,4,6,2,3,1]=>[4,5,7,2,6,1,3]=>[4,3,1,6,2,7,5]=>{{1,2,3,4,5,6,7}}
[7,5,4,6,3,1,2]=>[4,5,7,1,3,6,2]=>[4,3,1,7,5,2,6]=>{{1,2,3,4,6,7},{5}}
[7,5,4,6,3,2,1]=>[4,5,7,1,2,3,6]=>[4,3,1,7,6,5,2]=>{{1,2,3,4,7},{5,6}}
[7,5,6,1,2,3,4]=>[5,7,1,6,4,3,2]=>[3,1,7,2,4,5,6]=>{{1,2,3,4,5,6,7}}
[7,5,6,1,2,4,3]=>[5,7,1,6,3,4,2]=>[3,1,7,2,5,4,6]=>{{1,2,3,4,6,7},{5}}
[7,5,6,1,3,2,4]=>[5,7,1,6,4,2,3]=>[3,1,7,2,4,6,5]=>{{1,2,3,4,5,7},{6}}
[7,5,6,1,3,4,2]=>[5,7,1,6,3,2,4]=>[3,1,7,2,5,6,4]=>{{1,2,3,4,7},{5},{6}}
[7,5,6,1,4,2,3]=>[5,7,1,6,2,4,3]=>[3,1,7,2,6,4,5]=>{{1,2,3,4,5,6,7}}
[7,5,6,1,4,3,2]=>[5,7,1,6,2,3,4]=>[3,1,7,2,6,5,4]=>{{1,2,3,4,7},{5,6}}
[7,5,6,2,1,3,4]=>[5,7,1,2,6,4,3]=>[3,1,7,6,2,4,5]=>{{1,2,3,5,7},{4,6}}
[7,5,6,2,1,4,3]=>[5,7,1,2,6,3,4]=>[3,1,7,6,2,5,4]=>{{1,2,3,4,5,6,7}}
[7,5,6,2,3,1,4]=>[5,7,2,6,4,1,3]=>[3,1,6,2,4,7,5]=>{{1,2,3,4,5,6,7}}
[7,5,6,2,3,4,1]=>[5,7,2,6,3,1,4]=>[3,1,6,2,5,7,4]=>{{1,2,3,4,6,7},{5}}
[7,5,6,2,4,1,3]=>[5,7,2,6,1,4,3]=>[3,1,6,2,7,4,5]=>{{1,2,3,4,6},{5,7}}
[7,5,6,2,4,3,1]=>[5,7,2,6,1,3,4]=>[3,1,6,2,7,5,4]=>{{1,2,3,4,5,6,7}}
[7,5,6,3,1,2,4]=>[5,7,1,3,6,4,2]=>[3,1,7,5,2,4,6]=>{{1,2,3,4,5,6,7}}
[7,5,6,3,1,4,2]=>[5,7,1,3,6,2,4]=>[3,1,7,5,2,6,4]=>{{1,2,3,4,5,7},{6}}
[7,5,6,3,2,1,4]=>[5,7,1,2,3,6,4]=>[3,1,7,6,5,2,4]=>{{1,2,3,4,6,7},{5}}
[7,5,6,3,2,4,1]=>[5,7,2,3,6,1,4]=>[3,1,6,5,2,7,4]=>{{1,2,3,4,5,6,7}}
[7,5,6,3,4,1,2]=>[5,7,3,6,1,4,2]=>[3,1,5,2,7,4,6]=>{{1,2,3,4,5,6,7}}
[7,5,6,3,4,2,1]=>[5,7,3,6,1,2,4]=>[3,1,5,2,7,6,4]=>{{1,2,3,4,5,7},{6}}
[7,5,6,4,1,2,3]=>[5,7,1,4,6,3,2]=>[3,1,7,4,2,5,6]=>{{1,2,3,5,6,7},{4}}
[7,5,6,4,1,3,2]=>[5,7,1,4,6,2,3]=>[3,1,7,4,2,6,5]=>{{1,2,3,5,7},{4},{6}}
[7,5,6,4,2,1,3]=>[5,7,1,2,4,6,3]=>[3,1,7,6,4,2,5]=>{{1,2,3,4,5,6,7}}
[7,5,6,4,2,3,1]=>[5,7,2,4,6,1,3]=>[3,1,6,4,2,7,5]=>{{1,2,3,5,6,7},{4}}
[7,5,6,4,3,1,2]=>[5,7,1,3,4,6,2]=>[3,1,7,5,4,2,6]=>{{1,2,3,6,7},{4,5}}
[7,5,6,4,3,2,1]=>[5,7,1,2,3,4,6]=>[3,1,7,6,5,4,2]=>{{1,2,3,7},{4,6},{5}}
[7,6,1,2,3,4,5]=>[1,6,7,5,4,3,2]=>[7,2,1,3,4,5,6]=>{{1,3,4,5,6,7},{2}}
[7,6,1,2,3,5,4]=>[1,6,7,4,5,3,2]=>[7,2,1,4,3,5,6]=>{{1,3,5,6,7},{2},{4}}
[7,6,1,2,4,3,5]=>[1,6,7,5,3,4,2]=>[7,2,1,3,5,4,6]=>{{1,3,4,6,7},{2},{5}}
[7,6,1,2,4,5,3]=>[1,6,7,4,3,5,2]=>[7,2,1,4,5,3,6]=>{{1,3,6,7},{2},{4},{5}}
[7,6,1,2,5,3,4]=>[1,6,7,3,5,4,2]=>[7,2,1,5,3,4,6]=>{{1,3,4,5,6,7},{2}}
[7,6,1,2,5,4,3]=>[1,6,7,3,4,5,2]=>[7,2,1,5,4,3,6]=>{{1,3,6,7},{2},{4,5}}
[7,6,1,3,2,4,5]=>[1,6,7,5,4,2,3]=>[7,2,1,3,4,6,5]=>{{1,3,4,5,7},{2},{6}}
[7,6,1,3,2,5,4]=>[1,6,7,4,5,2,3]=>[7,2,1,4,3,6,5]=>{{1,3,5,7},{2},{4},{6}}
[7,6,1,3,4,2,5]=>[1,6,7,5,3,2,4]=>[7,2,1,3,5,6,4]=>{{1,3,4,7},{2},{5},{6}}
[7,6,1,3,4,5,2]=>[1,6,7,4,3,2,5]=>[7,2,1,4,5,6,3]=>{{1,3,7},{2},{4},{5},{6}}
[7,6,1,3,5,2,4]=>[1,6,7,3,2,5,4]=>[7,2,1,5,6,3,4]=>{{1,3,4,5,6,7},{2}}
[7,6,1,3,5,4,2]=>[1,6,7,3,2,4,5]=>[7,2,1,5,6,4,3]=>{{1,3,7},{2},{4,5,6}}
[7,6,1,4,2,3,5]=>[1,6,7,5,2,4,3]=>[7,2,1,3,6,4,5]=>{{1,3,4,5,6,7},{2}}
[7,6,1,4,2,5,3]=>[1,6,7,2,4,3,5]=>[7,2,1,6,4,5,3]=>{{1,3,7},{2},{4,5,6}}
[7,6,1,4,3,2,5]=>[1,6,7,5,2,3,4]=>[7,2,1,3,6,5,4]=>{{1,3,4,7},{2},{5,6}}
[7,6,1,4,3,5,2]=>[1,6,7,3,4,2,5]=>[7,2,1,5,4,6,3]=>{{1,3,7},{2},{4,5},{6}}
[7,6,1,4,5,2,3]=>[1,6,7,4,2,5,3]=>[7,2,1,4,6,3,5]=>{{1,3,5,6,7},{2},{4}}
[7,6,1,4,5,3,2]=>[1,6,7,4,2,3,5]=>[7,2,1,4,6,5,3]=>{{1,3,7},{2},{4},{5,6}}
[7,6,1,5,2,3,4]=>[1,6,7,2,5,4,3]=>[7,2,1,6,3,4,5]=>{{1,3,5,7},{2},{4,6}}
[7,6,1,5,2,4,3]=>[1,6,7,2,5,3,4]=>[7,2,1,6,3,5,4]=>{{1,3,4,5,6,7},{2}}
[7,6,1,5,3,2,4]=>[1,6,7,2,3,5,4]=>[7,2,1,6,5,3,4]=>{{1,3,4,6,7},{2},{5}}
[7,6,1,5,3,4,2]=>[1,6,7,3,5,2,4]=>[7,2,1,5,3,6,4]=>{{1,3,4,5,7},{2},{6}}
[7,6,1,5,4,2,3]=>[1,6,7,2,4,5,3]=>[7,2,1,6,4,3,5]=>{{1,3,4,5,6,7},{2}}
[7,6,1,5,4,3,2]=>[1,6,7,2,3,4,5]=>[7,2,1,6,5,4,3]=>{{1,3,7},{2},{4,6},{5}}
[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[7,6,2,1,3,4,5]=>{{1,2,3,4,5,6,7}}
[7,6,2,1,3,5,4]=>[1,2,6,7,4,5,3]=>[7,6,2,1,4,3,5]=>{{1,4,5,7},{2,3,6}}
[7,6,2,1,4,3,5]=>[1,2,6,7,5,3,4]=>[7,6,2,1,3,5,4]=>{{1,4,7},{2,3,5,6}}
[7,6,2,1,4,5,3]=>[1,2,6,7,4,3,5]=>[7,6,2,1,4,5,3]=>{{1,2,3,4,5,6,7}}
[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[7,6,2,1,5,3,4]=>{{1,4,7},{2,3,6},{5}}
[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[7,6,2,1,5,4,3]=>{{1,2,3,4,6,7},{5}}
[7,6,2,3,1,4,5]=>[2,6,7,5,4,1,3]=>[6,2,1,3,4,7,5]=>{{1,3,4,5,6,7},{2}}
[7,6,2,3,1,5,4]=>[2,6,7,4,5,1,3]=>[6,2,1,4,3,7,5]=>{{1,3,5,6,7},{2},{4}}
[7,6,2,3,4,1,5]=>[2,6,7,5,3,1,4]=>[6,2,1,3,5,7,4]=>{{1,3,4,6,7},{2},{5}}
[7,6,2,3,4,5,1]=>[2,6,7,4,3,1,5]=>[6,2,1,4,5,7,3]=>{{1,3,6,7},{2},{4},{5}}
[7,6,2,3,5,1,4]=>[2,6,7,3,1,5,4]=>[6,2,1,5,7,3,4]=>{{1,3,6},{2},{4,5,7}}
[7,6,2,3,5,4,1]=>[2,6,7,3,1,4,5]=>[6,2,1,5,7,4,3]=>{{1,3,4,5,6,7},{2}}
[7,6,2,4,1,3,5]=>[2,6,7,5,1,4,3]=>[6,2,1,3,7,4,5]=>{{1,3,4,6},{2},{5,7}}
[7,6,2,4,1,5,3]=>[2,6,7,1,4,3,5]=>[6,2,1,7,4,5,3]=>{{1,3,4,5,6,7},{2}}
[7,6,2,4,3,1,5]=>[2,6,7,5,1,3,4]=>[6,2,1,3,7,5,4]=>{{1,3,4,5,6,7},{2}}
[7,6,2,4,3,5,1]=>[2,6,7,3,4,1,5]=>[6,2,1,5,4,7,3]=>{{1,3,6,7},{2},{4,5}}
[7,6,2,4,5,1,3]=>[2,6,7,4,1,5,3]=>[6,2,1,4,7,3,5]=>{{1,3,6},{2},{4},{5,7}}
[7,6,2,4,5,3,1]=>[2,6,7,4,1,3,5]=>[6,2,1,4,7,5,3]=>{{1,3,5,6,7},{2},{4}}
[7,6,2,5,1,3,4]=>[2,6,7,1,5,4,3]=>[6,2,1,7,3,4,5]=>{{1,3,4,5,6,7},{2}}
[7,6,2,5,1,4,3]=>[2,6,7,1,5,3,4]=>[6,2,1,7,3,5,4]=>{{1,3,5,6},{2},{4,7}}
[7,6,2,5,3,1,4]=>[2,6,7,1,3,5,4]=>[6,2,1,7,5,3,4]=>{{1,3,6},{2},{4,7},{5}}
[7,6,2,5,3,4,1]=>[2,6,7,3,5,1,4]=>[6,2,1,5,3,7,4]=>{{1,3,4,5,6,7},{2}}
[7,6,2,5,4,1,3]=>[2,6,7,1,4,5,3]=>[6,2,1,7,4,3,5]=>{{1,3,6},{2},{4,5,7}}
[7,6,2,5,4,3,1]=>[2,6,7,1,3,4,5]=>[6,2,1,7,5,4,3]=>{{1,3,4,6,7},{2},{5}}
[7,6,3,1,2,4,5]=>[1,3,6,7,5,4,2]=>[7,5,2,1,3,4,6]=>{{1,4,6,7},{2,3,5}}
[7,6,3,1,2,5,4]=>[1,3,6,7,4,5,2]=>[7,5,2,1,4,3,6]=>{{1,2,3,4,5,6,7}}
[7,6,3,1,4,2,5]=>[1,3,6,7,5,2,4]=>[7,5,2,1,3,6,4]=>{{1,4,7},{2,3,5},{6}}
[7,6,3,1,4,5,2]=>[1,3,6,7,4,2,5]=>[7,5,2,1,4,6,3]=>{{1,2,3,4,5,7},{6}}
[7,6,3,1,5,2,4]=>[1,3,6,7,2,5,4]=>[7,5,2,1,6,3,4]=>{{1,4,7},{2,3,5,6}}
[7,6,3,1,5,4,2]=>[1,3,6,7,2,4,5]=>[7,5,2,1,6,4,3]=>{{1,2,3,4,5,6,7}}
[7,6,3,2,1,4,5]=>[1,2,3,6,7,5,4]=>[7,6,5,2,1,3,4]=>{{1,2,3,4,5,6,7}}
[7,6,3,2,1,5,4]=>[1,2,3,6,7,4,5]=>[7,6,5,2,1,4,3]=>{{1,3,5,7},{2,4,6}}
[7,6,3,2,4,1,5]=>[2,3,6,7,5,1,4]=>[6,5,2,1,3,7,4]=>{{1,4,6,7},{2,3,5}}
[7,6,3,2,4,5,1]=>[2,3,6,7,4,1,5]=>[6,5,2,1,4,7,3]=>{{1,2,3,4,5,6,7}}
[7,6,3,2,5,1,4]=>[2,3,6,7,1,5,4]=>[6,5,2,1,7,3,4]=>{{1,2,3,4,5,6,7}}
[7,6,3,2,5,4,1]=>[2,3,6,7,1,4,5]=>[6,5,2,1,7,4,3]=>{{1,4,6},{2,3,5,7}}
[7,6,3,4,1,2,5]=>[3,6,7,5,1,4,2]=>[5,2,1,3,7,4,6]=>{{1,3,4,5,6,7},{2}}
[7,6,3,4,1,5,2]=>[3,6,7,1,4,2,5]=>[5,2,1,7,4,6,3]=>{{1,3,4,5,7},{2},{6}}
[7,6,3,4,2,1,5]=>[3,6,7,5,1,2,4]=>[5,2,1,3,7,6,4]=>{{1,3,4,5,7},{2},{6}}
[7,6,3,4,2,5,1]=>[3,6,7,2,4,1,5]=>[5,2,1,6,4,7,3]=>{{1,3,4,5,6,7},{2}}
[7,6,3,4,5,1,2]=>[3,6,7,4,1,5,2]=>[5,2,1,4,7,3,6]=>{{1,3,5,6,7},{2},{4}}
[7,6,3,4,5,2,1]=>[3,6,7,4,1,2,5]=>[5,2,1,4,7,6,3]=>{{1,3,5,7},{2},{4},{6}}
[7,6,3,5,1,2,4]=>[3,6,7,1,5,4,2]=>[5,2,1,7,3,4,6]=>{{1,3,5},{2},{4,6,7}}
[7,6,3,5,1,4,2]=>[3,6,7,1,5,2,4]=>[5,2,1,7,3,6,4]=>{{1,3,5},{2},{4,7},{6}}
[7,6,3,5,2,1,4]=>[3,6,7,1,2,5,4]=>[5,2,1,7,6,3,4]=>{{1,3,5,6},{2},{4,7}}
[7,6,3,5,2,4,1]=>[3,6,7,2,5,1,4]=>[5,2,1,6,3,7,4]=>{{1,3,5},{2},{4,6,7}}
[7,6,3,5,4,1,2]=>[3,6,7,1,4,5,2]=>[5,2,1,7,4,3,6]=>{{1,3,4,5,6,7},{2}}
[7,6,3,5,4,2,1]=>[3,6,7,1,2,4,5]=>[5,2,1,7,6,4,3]=>{{1,3,4,5,6,7},{2}}
[7,6,4,1,2,3,5]=>[1,4,6,7,5,3,2]=>[7,4,2,1,3,5,6]=>{{1,2,3,4,5,6,7}}
[7,6,4,1,2,5,3]=>[1,4,6,7,3,5,2]=>[7,4,2,1,5,3,6]=>{{1,2,3,4,6,7},{5}}
[7,6,4,1,3,2,5]=>[1,4,6,7,5,2,3]=>[7,4,2,1,3,6,5]=>{{1,2,3,4,5,7},{6}}
[7,6,4,1,3,5,2]=>[1,4,6,7,3,2,5]=>[7,4,2,1,5,6,3]=>{{1,2,3,4,7},{5},{6}}
[7,6,4,1,5,2,3]=>[1,4,6,7,2,5,3]=>[7,4,2,1,6,3,5]=>{{1,2,3,4,5,6,7}}
[7,6,4,1,5,3,2]=>[1,4,6,7,2,3,5]=>[7,4,2,1,6,5,3]=>{{1,2,3,4,7},{5,6}}
[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[7,6,4,2,1,3,5]=>{{1,5,7},{2,3,4,6}}
[7,6,4,2,1,5,3]=>[1,2,4,6,7,3,5]=>[7,6,4,2,1,5,3]=>{{1,2,3,4,5,6,7}}
[7,6,4,2,3,1,5]=>[2,4,6,7,5,1,3]=>[6,4,2,1,3,7,5]=>{{1,2,3,4,5,6,7}}
[7,6,4,2,3,5,1]=>[2,4,6,7,3,1,5]=>[6,4,2,1,5,7,3]=>{{1,2,3,4,6,7},{5}}
[7,6,4,2,5,1,3]=>[2,4,6,7,1,5,3]=>[6,4,2,1,7,3,5]=>{{1,2,3,4,6},{5,7}}
[7,6,4,2,5,3,1]=>[2,4,6,7,1,3,5]=>[6,4,2,1,7,5,3]=>{{1,2,3,4,5,6,7}}
[7,6,4,3,1,2,5]=>[1,3,4,6,7,5,2]=>[7,5,4,2,1,3,6]=>{{1,2,3,4,5,6,7}}
[7,6,4,3,1,5,2]=>[1,3,4,6,7,2,5]=>[7,5,4,2,1,6,3]=>{{1,2,3,4,5,7},{6}}
[7,6,4,3,2,1,5]=>[1,2,3,4,6,7,5]=>[7,6,5,4,2,1,3]=>{{1,2,3,5,6,7},{4}}
[7,6,4,3,2,5,1]=>[2,3,4,6,7,1,5]=>[6,5,4,2,1,7,3]=>{{1,2,3,4,5,6,7}}
[7,6,4,3,5,1,2]=>[3,4,6,7,1,5,2]=>[5,4,2,1,7,3,6]=>{{1,2,3,4,5,6,7}}
[7,6,4,3,5,2,1]=>[3,4,6,7,1,2,5]=>[5,4,2,1,7,6,3]=>{{1,2,3,4,5,7},{6}}
[7,6,4,5,1,2,3]=>[4,6,7,1,5,3,2]=>[4,2,1,7,3,5,6]=>{{1,3,4,5,6,7},{2}}
[7,6,4,5,1,3,2]=>[4,6,7,1,5,2,3]=>[4,2,1,7,3,6,5]=>{{1,3,4,5,7},{2},{6}}
[7,6,4,5,2,1,3]=>[4,6,7,1,2,5,3]=>[4,2,1,7,6,3,5]=>{{1,3,4,5,6,7},{2}}
[7,6,4,5,2,3,1]=>[4,6,7,2,5,1,3]=>[4,2,1,6,3,7,5]=>{{1,3,4,5,6,7},{2}}
[7,6,4,5,3,1,2]=>[4,6,7,1,3,5,2]=>[4,2,1,7,5,3,6]=>{{1,3,4,6,7},{2},{5}}
[7,6,4,5,3,2,1]=>[4,6,7,1,2,3,5]=>[4,2,1,7,6,5,3]=>{{1,3,4,7},{2},{5,6}}
[7,6,5,1,2,3,4]=>[1,5,6,7,4,3,2]=>[7,3,2,1,4,5,6]=>{{1,4,5,6,7},{2,3}}
[7,6,5,1,2,4,3]=>[1,5,6,7,3,4,2]=>[7,3,2,1,5,4,6]=>{{1,4,6,7},{2,3},{5}}
[7,6,5,1,3,2,4]=>[1,5,6,7,4,2,3]=>[7,3,2,1,4,6,5]=>{{1,4,5,7},{2,3},{6}}
[7,6,5,1,3,4,2]=>[1,5,6,7,3,2,4]=>[7,3,2,1,5,6,4]=>{{1,4,7},{2,3},{5},{6}}
[7,6,5,1,4,2,3]=>[1,5,6,7,2,4,3]=>[7,3,2,1,6,4,5]=>{{1,4,5,6,7},{2,3}}
[7,6,5,1,4,3,2]=>[1,5,6,7,2,3,4]=>[7,3,2,1,6,5,4]=>{{1,4,7},{2,3},{5,6}}
[7,6,5,2,1,3,4]=>[1,2,5,6,7,4,3]=>[7,6,3,2,1,4,5]=>{{1,5,7},{2,4,6},{3}}
[7,6,5,2,1,4,3]=>[1,2,5,6,7,3,4]=>[7,6,3,2,1,5,4]=>{{1,2,4,5,6,7},{3}}
[7,6,5,2,3,1,4]=>[2,5,6,7,4,1,3]=>[6,3,2,1,4,7,5]=>{{1,4,5,6,7},{2,3}}
[7,6,5,2,3,4,1]=>[2,5,6,7,3,1,4]=>[6,3,2,1,5,7,4]=>{{1,4,6,7},{2,3},{5}}
[7,6,5,2,4,1,3]=>[2,5,6,7,1,4,3]=>[6,3,2,1,7,4,5]=>{{1,4,6},{2,3},{5,7}}
[7,6,5,2,4,3,1]=>[2,5,6,7,1,3,4]=>[6,3,2,1,7,5,4]=>{{1,4,5,6,7},{2,3}}
[7,6,5,3,1,2,4]=>[1,3,5,6,7,4,2]=>[7,5,3,2,1,4,6]=>{{1,2,4,5,6,7},{3}}
[7,6,5,3,1,4,2]=>[1,3,5,6,7,2,4]=>[7,5,3,2,1,6,4]=>{{1,2,4,5,7},{3},{6}}
[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[7,6,5,3,2,1,4]=>{{1,2,3,4,5,6,7}}
[7,6,5,3,2,4,1]=>[2,3,5,6,7,1,4]=>[6,5,3,2,1,7,4]=>{{1,2,4,5,6,7},{3}}
[7,6,5,3,4,1,2]=>[3,5,6,7,1,4,2]=>[5,3,2,1,7,4,6]=>{{1,4,5,6,7},{2,3}}
[7,6,5,3,4,2,1]=>[3,5,6,7,1,2,4]=>[5,3,2,1,7,6,4]=>{{1,4,5,7},{2,3},{6}}
[7,6,5,4,1,2,3]=>[1,4,5,6,7,3,2]=>[7,4,3,2,1,5,6]=>{{1,5,6,7},{2,4},{3}}
[7,6,5,4,1,3,2]=>[1,4,5,6,7,2,3]=>[7,4,3,2,1,6,5]=>{{1,5,7},{2,4},{3},{6}}
[7,6,5,4,2,1,3]=>[1,2,4,5,6,7,3]=>[7,6,4,3,2,1,5]=>{{1,2,5,6,7},{3,4}}
[7,6,5,4,2,3,1]=>[2,4,5,6,7,1,3]=>[6,4,3,2,1,7,5]=>{{1,5,6,7},{2,4},{3}}
[7,6,5,4,3,1,2]=>[1,3,4,5,6,7,2]=>[7,5,4,3,2,1,6]=>{{1,6,7},{2,5},{3,4}}
[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>{{1,7},{2,6},{3,5},{4}}
Map
weak order rowmotion
Description
Return the reversal of the permutation obtained by inverting the corresponding Laguerre heap.
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
This map is the composite of Mp00241invert Laguerre heap and Mp00064reverse.
Conjecturally, it is also the rowmotion on the weak order:
Any semidistributive lattice $L$ has a canonical labeling of the edges of its Hasse diagram by its join irreducible elements (see [1] and [2]). Rowmotion on this lattice is the bijection which takes an element $x \in L$ with a given set of down-labels to the unique element $y \in L$ which has that set as its up-labels (see [2] and [3]). For example, if the lattice is the distributive lattice $J(P)$ of order ideals of a finite poset $P$, then this reduces to ordinary rowmotion on the order ideals of $P$.
The weak order (a.k.a. permutohedral order) on the permutations in $S_n$ is a semidistributive lattice. In this way, we obtain an action of rowmotion on the set of permutations in $S_n$.
Note that the dynamics of weak order rowmotion is poorly understood. A collection of nontrivial homomesies is described in Corollary 6.14 of [4].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
Map
to cycle type
Description
Let $\pi=c_1\dots c_r$ a permutation of size $n$ decomposed in its cyclic parts. The associated set partition of $[n]$ then is $S=S_1\cup\dots\cup S_r$ such that $S_i$ is the set of integers in the cycle $c_i$.
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
A permutation is cyclic [1] if and only if its cycle type is a hook partition [2].
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