Identifier
Mp00223:
Permutations
—runsort⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00151: Permutations —to cycle type⟶ Set partitions
Images
=>
Cc0009;cc-rep-3
[1]=>[1]=>[1]=>{{1}}
[1,2]=>[1,2]=>[1,2]=>{{1},{2}}
[2,1]=>[1,2]=>[1,2]=>{{1},{2}}
[1,2,3]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[1,3,2]=>[1,3,2]=>[1,3,2]=>{{1},{2,3}}
[2,1,3]=>[1,3,2]=>[1,3,2]=>{{1},{2,3}}
[2,3,1]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[3,1,2]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[3,2,1]=>[1,2,3]=>[1,2,3]=>{{1},{2},{3}}
[1,2,3,4]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[1,2,4,3]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}}
[1,3,2,4]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}}
[1,3,4,2]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}}
[1,4,2,3]=>[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[1,4,3,2]=>[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[2,1,3,4]=>[1,3,4,2]=>[1,4,3,2]=>{{1},{2,4},{3}}
[2,1,4,3]=>[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[2,3,1,4]=>[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[2,3,4,1]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[2,4,1,3]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}}
[2,4,3,1]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}}
[3,1,2,4]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}}
[3,1,4,2]=>[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[3,2,1,4]=>[1,4,2,3]=>[1,3,4,2]=>{{1},{2,3,4}}
[3,2,4,1]=>[1,2,4,3]=>[1,2,4,3]=>{{1},{2},{3,4}}
[3,4,1,2]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[3,4,2,1]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[4,1,2,3]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[4,1,3,2]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}}
[4,2,1,3]=>[1,3,2,4]=>[1,3,2,4]=>{{1},{2,3},{4}}
[4,2,3,1]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[4,3,1,2]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[4,3,2,1]=>[1,2,3,4]=>[1,2,3,4]=>{{1},{2},{3},{4}}
[1,2,3,4,5]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[1,2,3,5,4]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[1,2,4,3,5]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[1,2,4,5,3]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[1,2,5,3,4]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[1,2,5,4,3]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[1,3,2,4,5]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[1,3,2,5,4]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[1,3,4,2,5]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[1,3,4,5,2]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}
[1,3,5,2,4]=>[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[1,3,5,4,2]=>[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[1,4,2,3,5]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[1,4,2,5,3]=>[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[1,4,3,2,5]=>[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[1,4,3,5,2]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[1,4,5,2,3]=>[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[1,4,5,3,2]=>[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[1,5,2,3,4]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[1,5,2,4,3]=>[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[1,5,3,2,4]=>[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[1,5,3,4,2]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[1,5,4,2,3]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[1,5,4,3,2]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[2,1,3,4,5]=>[1,3,4,5,2]=>[1,5,3,4,2]=>{{1},{2,5},{3},{4}}
[2,1,3,5,4]=>[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[2,1,4,3,5]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[2,1,4,5,3]=>[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[2,1,5,3,4]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[2,1,5,4,3]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[2,3,1,4,5]=>[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[2,3,1,5,4]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[2,3,4,1,5]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[2,3,4,5,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[2,3,5,1,4]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[2,3,5,4,1]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[2,4,1,3,5]=>[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[2,4,1,5,3]=>[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[2,4,3,1,5]=>[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[2,4,3,5,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[2,4,5,1,3]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[2,4,5,3,1]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[2,5,1,3,4]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[2,5,1,4,3]=>[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[2,5,3,1,4]=>[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[2,5,3,4,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[2,5,4,1,3]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[2,5,4,3,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[3,1,2,4,5]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[3,1,2,5,4]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[3,1,4,2,5]=>[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[3,1,4,5,2]=>[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[3,1,5,2,4]=>[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[3,1,5,4,2]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[3,2,1,4,5]=>[1,4,5,2,3]=>[1,3,5,4,2]=>{{1},{2,3,5},{4}}
[3,2,1,5,4]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[3,2,4,1,5]=>[1,5,2,4,3]=>[1,4,5,3,2]=>{{1},{2,3,4,5}}
[3,2,4,5,1]=>[1,2,4,5,3]=>[1,2,5,4,3]=>{{1},{2},{3,5},{4}}
[3,2,5,1,4]=>[1,4,2,5,3]=>[1,4,5,2,3]=>{{1},{2,4},{3,5}}
[3,2,5,4,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[3,4,1,2,5]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[3,4,1,5,2]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[3,4,2,1,5]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[3,4,2,5,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[3,4,5,1,2]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[3,4,5,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[3,5,1,2,4]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[3,5,1,4,2]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[3,5,2,1,4]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[3,5,2,4,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[3,5,4,1,2]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[3,5,4,2,1]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[4,1,2,3,5]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[4,1,2,5,3]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[4,1,3,2,5]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[4,1,3,5,2]=>[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[4,1,5,2,3]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[4,1,5,3,2]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[4,2,1,3,5]=>[1,3,5,2,4]=>[1,4,3,5,2]=>{{1},{2,4,5},{3}}
[4,2,1,5,3]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[4,2,3,1,5]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[4,2,3,5,1]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[4,2,5,1,3]=>[1,3,2,5,4]=>[1,3,2,5,4]=>{{1},{2,3},{4,5}}
[4,2,5,3,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[4,3,1,2,5]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[4,3,1,5,2]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[4,3,2,1,5]=>[1,5,2,3,4]=>[1,3,4,5,2]=>{{1},{2,3,4,5}}
[4,3,2,5,1]=>[1,2,5,3,4]=>[1,2,4,5,3]=>{{1},{2},{3,4,5}}
[4,3,5,1,2]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[4,3,5,2,1]=>[1,2,3,5,4]=>[1,2,3,5,4]=>{{1},{2},{3},{4,5}}
[4,5,1,2,3]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[4,5,1,3,2]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[4,5,2,1,3]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[4,5,2,3,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[4,5,3,1,2]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[4,5,3,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,1,2,3,4]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,1,2,4,3]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[5,1,3,2,4]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[5,1,3,4,2]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[5,1,4,2,3]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[5,1,4,3,2]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[5,2,1,3,4]=>[1,3,4,2,5]=>[1,4,3,2,5]=>{{1},{2,4},{3},{5}}
[5,2,1,4,3]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[5,2,3,1,4]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[5,2,3,4,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,2,4,1,3]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[5,2,4,3,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[5,3,1,2,4]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[5,3,1,4,2]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[5,3,2,1,4]=>[1,4,2,3,5]=>[1,3,4,2,5]=>{{1},{2,3,4},{5}}
[5,3,2,4,1]=>[1,2,4,3,5]=>[1,2,4,3,5]=>{{1},{2},{3,4},{5}}
[5,3,4,1,2]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,3,4,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,4,1,2,3]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,4,1,3,2]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[5,4,2,1,3]=>[1,3,2,4,5]=>[1,3,2,4,5]=>{{1},{2,3},{4},{5}}
[5,4,2,3,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,4,3,1,2]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[5,4,3,2,1]=>[1,2,3,4,5]=>[1,2,3,4,5]=>{{1},{2},{3},{4},{5}}
[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[1,2,3,5,6,4]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[1,2,4,5,3,6]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[1,2,4,5,6,3]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[1,2,4,6,3,5]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[1,2,4,6,5,3]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[1,2,5,3,6,4]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[1,2,5,4,3,6]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[1,2,5,4,6,3]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[1,2,5,6,3,4]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[1,2,5,6,4,3]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[1,2,6,3,5,4]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[1,2,6,4,3,5]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[1,2,6,4,5,3]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[1,2,6,5,3,4]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[1,3,2,5,6,4]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[1,3,4,2,5,6]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[1,3,4,2,6,5]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[1,3,4,5,2,6]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[1,3,4,5,6,2]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}
[1,3,4,6,2,5]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[1,3,4,6,5,2]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[1,3,5,2,4,6]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[1,3,5,2,6,4]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[1,3,5,4,2,6]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[1,3,5,4,6,2]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[1,3,5,6,2,4]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[1,3,5,6,4,2]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[1,3,6,2,4,5]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[1,3,6,2,5,4]=>[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[1,3,6,4,2,5]=>[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[1,3,6,4,5,2]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[1,3,6,5,2,4]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[1,3,6,5,4,2]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[1,4,2,5,3,6]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[1,4,2,5,6,3]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[1,4,2,6,3,5]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[1,4,2,6,5,3]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[1,4,3,2,5,6]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[1,4,3,2,6,5]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[1,4,3,5,2,6]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[1,4,3,5,6,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[1,4,3,6,2,5]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[1,4,3,6,5,2]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[1,4,5,2,3,6]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[1,4,5,2,6,3]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[1,4,5,3,2,6]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[1,4,5,3,6,2]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[1,4,5,6,2,3]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[1,4,5,6,3,2]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[1,4,6,2,3,5]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[1,4,6,2,5,3]=>[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[1,4,6,3,2,5]=>[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[1,4,6,3,5,2]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[1,4,6,5,2,3]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[1,4,6,5,3,2]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,5,2,3,6,4]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[1,5,2,4,3,6]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[1,5,2,4,6,3]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[1,5,2,6,3,4]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,2,6,4,3]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,3,2,4,6]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[1,5,3,2,6,4]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,3,4,2,6]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,3,4,6,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,5,3,6,2,4]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[1,5,3,6,4,2]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[1,5,4,2,3,6]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[1,5,4,2,6,3]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,4,3,2,6]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[1,5,4,3,6,2]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[1,5,4,6,2,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,5,4,6,3,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[1,5,6,2,3,4]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[1,5,6,2,4,3]=>[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[1,5,6,3,2,4]=>[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[1,5,6,3,4,2]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[1,5,6,4,2,3]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[1,5,6,4,3,2]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,2,3,5,4]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[1,6,2,4,3,5]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[1,6,2,4,5,3]=>[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[1,6,2,5,3,4]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,6,2,5,4,3]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,6,3,2,4,5]=>[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[1,6,3,2,5,4]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,6,3,4,2,5]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,6,3,4,5,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,3,5,2,4]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[1,6,3,5,4,2]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[1,6,4,2,3,5]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[1,6,4,2,5,3]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,6,4,3,2,5]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[1,6,4,3,5,2]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[1,6,4,5,2,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,4,5,3,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,5,2,3,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,5,2,4,3]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[1,6,5,3,2,4]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[1,6,5,3,4,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,5,4,2,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,1,3,4,5,6]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>{{1},{2,6},{3},{4},{5}}
[2,1,3,4,6,5]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[2,1,3,5,4,6]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[2,1,3,5,6,4]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[2,1,3,6,4,5]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[2,1,3,6,5,4]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[2,1,4,3,5,6]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[2,1,4,3,6,5]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[2,1,4,5,3,6]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[2,1,4,5,6,3]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[2,1,4,6,3,5]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[2,1,4,6,5,3]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[2,1,5,3,4,6]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[2,1,5,3,6,4]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[2,1,5,4,3,6]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[2,1,5,4,6,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[2,1,5,6,3,4]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[2,1,5,6,4,3]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[2,1,6,3,4,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,1,6,3,5,4]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[2,1,6,4,3,5]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[2,1,6,4,5,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,1,6,5,3,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,1,6,5,4,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,3,1,4,5,6]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[2,3,1,4,6,5]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[2,3,1,5,4,6]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[2,3,1,5,6,4]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[2,3,1,6,4,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,3,1,6,5,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,3,4,1,5,6]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[2,3,4,1,6,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,3,4,5,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[2,3,4,6,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[2,3,4,6,5,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[2,3,5,1,4,6]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[2,3,5,1,6,4]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[2,3,5,4,1,6]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[2,3,5,4,6,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[2,3,5,6,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[2,3,5,6,4,1]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[2,3,6,1,4,5]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[2,3,6,1,5,4]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[2,3,6,4,1,5]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[2,3,6,4,5,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[2,3,6,5,1,4]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[2,3,6,5,4,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[2,4,1,3,5,6]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[2,4,1,3,6,5]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[2,4,1,5,3,6]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[2,4,1,5,6,3]=>[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[2,4,1,6,3,5]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[2,4,1,6,5,3]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[2,4,3,1,5,6]=>[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[2,4,3,1,6,5]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[2,4,3,5,1,6]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[2,4,3,5,6,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[2,4,3,6,1,5]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[2,4,3,6,5,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[2,4,5,1,3,6]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[2,4,5,1,6,3]=>[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[2,4,5,3,1,6]=>[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[2,4,5,3,6,1]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[2,4,5,6,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[2,4,5,6,3,1]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[2,4,6,1,3,5]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[2,4,6,1,5,3]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[2,4,6,3,1,5]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[2,4,6,3,5,1]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[2,4,6,5,1,3]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[2,4,6,5,3,1]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[2,5,1,3,4,6]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[2,5,1,3,6,4]=>[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[2,5,1,4,3,6]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[2,5,1,4,6,3]=>[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[2,5,1,6,3,4]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[2,5,1,6,4,3]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[2,5,3,1,4,6]=>[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[2,5,3,1,6,4]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[2,5,3,4,1,6]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[2,5,3,4,6,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[2,5,3,6,1,4]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[2,5,3,6,4,1]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[2,5,4,1,3,6]=>[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[2,5,4,1,6,3]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[2,5,4,3,1,6]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[2,5,4,3,6,1]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[2,5,4,6,1,3]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[2,5,4,6,3,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[2,5,6,1,3,4]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[2,5,6,1,4,3]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[2,5,6,3,1,4]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[2,5,6,3,4,1]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[2,5,6,4,1,3]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[2,5,6,4,3,1]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[2,6,1,3,4,5]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[2,6,1,3,5,4]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[2,6,1,4,3,5]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[2,6,1,4,5,3]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[2,6,1,5,3,4]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[2,6,1,5,4,3]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[2,6,3,1,4,5]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[2,6,3,1,5,4]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[2,6,3,4,1,5]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[2,6,3,4,5,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[2,6,3,5,1,4]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[2,6,3,5,4,1]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[2,6,4,1,3,5]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[2,6,4,1,5,3]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[2,6,4,3,1,5]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[2,6,4,3,5,1]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[2,6,4,5,1,3]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[2,6,4,5,3,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[2,6,5,1,3,4]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[2,6,5,1,4,3]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[2,6,5,3,1,4]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[2,6,5,3,4,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[2,6,5,4,1,3]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[2,6,5,4,3,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,1,2,4,5,6]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[3,1,2,4,6,5]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[3,1,2,5,4,6]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[3,1,2,5,6,4]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[3,1,2,6,4,5]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,1,2,6,5,4]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,1,4,2,5,6]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[3,1,4,2,6,5]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[3,1,4,5,2,6]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[3,1,4,5,6,2]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[3,1,4,6,2,5]=>[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[3,1,4,6,5,2]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[3,1,5,2,4,6]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[3,1,5,2,6,4]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,1,5,4,2,6]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,1,5,4,6,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[3,1,5,6,2,4]=>[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[3,1,5,6,4,2]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[3,1,6,2,4,5]=>[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[3,1,6,2,5,4]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,1,6,4,2,5]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,1,6,4,5,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,1,6,5,2,4]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[3,1,6,5,4,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,2,1,4,5,6]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>{{1},{2,3,6},{4},{5}}
[3,2,1,4,6,5]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[3,2,1,5,4,6]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[3,2,1,5,6,4]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[3,2,1,6,4,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,2,1,6,5,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,2,4,1,5,6]=>[1,5,6,2,4,3]=>[1,4,6,3,5,2]=>{{1},{2,3,4,6},{5}}
[3,2,4,1,6,5]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[3,2,4,5,1,6]=>[1,6,2,4,5,3]=>[1,4,6,5,3,2]=>{{1},{2,3,4,5,6}}
[3,2,4,5,6,1]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>{{1},{2},{3,6},{4},{5}}
[3,2,4,6,1,5]=>[1,5,2,4,6,3]=>[1,4,6,5,2,3]=>{{1},{2,4,5},{3,6}}
[3,2,4,6,5,1]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[3,2,5,1,4,6]=>[1,4,6,2,5,3]=>[1,5,6,4,3,2]=>{{1},{2,3,5,6},{4}}
[3,2,5,1,6,4]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,2,5,4,1,6]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,2,5,4,6,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[3,2,5,6,1,4]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>{{1},{2,4},{3,6},{5}}
[3,2,5,6,4,1]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[3,2,6,1,4,5]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>{{1},{2,5},{3,6},{4}}
[3,2,6,1,5,4]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,2,6,4,1,5]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,2,6,4,5,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,2,6,5,1,4]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[3,2,6,5,4,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,4,1,2,5,6]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[3,4,1,2,6,5]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,4,1,5,2,6]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,4,1,5,6,2]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[3,4,1,6,2,5]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,4,1,6,5,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,4,2,1,5,6]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[3,4,2,1,6,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,4,2,5,1,6]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[3,4,2,5,6,1]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[3,4,2,6,1,5]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[3,4,2,6,5,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,4,5,1,2,6]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,4,5,1,6,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,4,5,2,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[3,4,5,2,6,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[3,4,5,6,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[3,4,5,6,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[3,4,6,1,2,5]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[3,4,6,1,5,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[3,4,6,2,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[3,4,6,2,5,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[3,4,6,5,1,2]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[3,4,6,5,2,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[3,5,1,2,4,6]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[3,5,1,2,6,4]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[3,5,1,4,2,6]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[3,5,1,4,6,2]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[3,5,1,6,2,4]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[3,5,1,6,4,2]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[3,5,2,1,4,6]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[3,5,2,1,6,4]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[3,5,2,4,1,6]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[3,5,2,4,6,1]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[3,5,2,6,1,4]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[3,5,2,6,4,1]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[3,5,4,1,2,6]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[3,5,4,1,6,2]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[3,5,4,2,1,6]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[3,5,4,2,6,1]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[3,5,4,6,1,2]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[3,5,4,6,2,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[3,5,6,1,2,4]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[3,5,6,1,4,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[3,5,6,2,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[3,5,6,2,4,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[3,5,6,4,1,2]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[3,5,6,4,2,1]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[3,6,1,2,4,5]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[3,6,1,2,5,4]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[3,6,1,4,2,5]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[3,6,1,4,5,2]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[3,6,1,5,2,4]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[3,6,1,5,4,2]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[3,6,2,1,4,5]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[3,6,2,1,5,4]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[3,6,2,4,1,5]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[3,6,2,4,5,1]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[3,6,2,5,1,4]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[3,6,2,5,4,1]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[3,6,4,1,2,5]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[3,6,4,1,5,2]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[3,6,4,2,1,5]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[3,6,4,2,5,1]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[3,6,4,5,1,2]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[3,6,4,5,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[3,6,5,1,2,4]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[3,6,5,1,4,2]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[3,6,5,2,1,4]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[3,6,5,2,4,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[3,6,5,4,1,2]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[3,6,5,4,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,1,2,3,5,6]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[4,1,2,3,6,5]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,1,2,5,3,6]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[4,1,2,5,6,3]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[4,1,2,6,3,5]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[4,1,2,6,5,3]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,1,3,2,5,6]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[4,1,3,2,6,5]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[4,1,3,5,2,6]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[4,1,3,5,6,2]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[4,1,3,6,2,5]=>[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[4,1,3,6,5,2]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[4,1,5,2,3,6]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[4,1,5,2,6,3]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[4,1,5,3,2,6]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[4,1,5,3,6,2]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[4,1,5,6,2,3]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[4,1,5,6,3,2]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[4,1,6,2,3,5]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[4,1,6,2,5,3]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[4,1,6,3,2,5]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[4,1,6,3,5,2]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[4,1,6,5,2,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,1,6,5,3,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,2,1,3,5,6]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>{{1},{2,4,6},{3},{5}}
[4,2,1,3,6,5]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[4,2,1,5,3,6]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[4,2,1,5,6,3]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[4,2,1,6,3,5]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[4,2,1,6,5,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,2,3,1,5,6]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[4,2,3,1,6,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,2,3,5,1,6]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[4,2,3,5,6,1]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[4,2,3,6,1,5]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[4,2,3,6,5,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,2,5,1,3,6]=>[1,3,6,2,5,4]=>[1,5,3,6,4,2]=>{{1},{2,4,5,6},{3}}
[4,2,5,1,6,3]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[4,2,5,3,1,6]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[4,2,5,3,6,1]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[4,2,5,6,1,3]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>{{1},{2,3},{4,6},{5}}
[4,2,5,6,3,1]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[4,2,6,1,3,5]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>{{1},{2,5},{3},{4,6}}
[4,2,6,1,5,3]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[4,2,6,3,1,5]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[4,2,6,3,5,1]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[4,2,6,5,1,3]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[4,2,6,5,3,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,3,1,2,5,6]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[4,3,1,2,6,5]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,3,1,5,2,6]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[4,3,1,5,6,2]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[4,3,1,6,2,5]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[4,3,1,6,5,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,3,2,1,5,6]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>{{1},{2,3,4,6},{5}}
[4,3,2,1,6,5]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,3,2,5,1,6]=>[1,6,2,5,3,4]=>[1,5,4,6,3,2]=>{{1},{2,3,4,5,6}}
[4,3,2,5,6,1]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>{{1},{2},{3,4,6},{5}}
[4,3,2,6,1,5]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>{{1},{2,5},{3,4,6}}
[4,3,2,6,5,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,3,5,1,2,6]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[4,3,5,1,6,2]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[4,3,5,2,1,6]=>[1,6,2,3,5,4]=>[1,3,5,6,4,2]=>{{1},{2,3,4,5,6}}
[4,3,5,2,6,1]=>[1,2,6,3,5,4]=>[1,2,5,6,4,3]=>{{1},{2},{3,4,5,6}}
[4,3,5,6,1,2]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[4,3,5,6,2,1]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>{{1},{2},{3},{4,6},{5}}
[4,3,6,1,2,5]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[4,3,6,1,5,2]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[4,3,6,2,1,5]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>{{1},{2,3,5},{4,6}}
[4,3,6,2,5,1]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>{{1},{2},{3,5},{4,6}}
[4,3,6,5,1,2]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,3,6,5,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,5,1,2,3,6]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,5,1,2,6,3]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,5,1,3,2,6]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[4,5,1,3,6,2]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[4,5,1,6,2,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,5,1,6,3,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,5,2,1,3,6]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[4,5,2,1,6,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,5,2,3,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,5,2,3,6,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,5,2,6,1,3]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[4,5,2,6,3,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,5,3,1,2,6]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,5,3,1,6,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,5,3,2,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[4,5,3,2,6,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[4,5,3,6,1,2]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,5,3,6,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[4,5,6,1,2,3]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[4,5,6,1,3,2]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[4,5,6,2,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[4,5,6,2,3,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[4,5,6,3,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[4,5,6,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[4,6,1,2,3,5]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[4,6,1,2,5,3]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[4,6,1,3,2,5]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[4,6,1,3,5,2]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[4,6,1,5,2,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[4,6,1,5,3,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[4,6,2,1,3,5]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[4,6,2,1,5,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[4,6,2,3,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[4,6,2,3,5,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[4,6,2,5,1,3]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[4,6,2,5,3,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[4,6,3,1,2,5]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[4,6,3,1,5,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[4,6,3,2,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[4,6,3,2,5,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[4,6,3,5,1,2]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[4,6,3,5,2,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[4,6,5,1,2,3]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[4,6,5,2,1,3]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[4,6,5,2,3,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[4,6,5,3,1,2]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[4,6,5,3,2,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,1,2,3,4,6]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,1,2,3,6,4]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,1,2,4,3,6]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[5,1,2,4,6,3]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[5,1,2,6,3,4]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,1,2,6,4,3]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,1,3,2,4,6]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[5,1,3,2,6,4]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[5,1,3,4,2,6]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[5,1,3,4,6,2]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[5,1,3,6,2,4]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[5,1,3,6,4,2]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[5,1,4,2,3,6]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[5,1,4,2,6,3]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[5,1,4,3,2,6]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[5,1,4,3,6,2]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[5,1,4,6,2,3]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[5,1,4,6,3,2]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[5,1,6,2,3,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,1,6,2,4,3]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[5,1,6,3,2,4]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[5,1,6,3,4,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,1,6,4,2,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,1,6,4,3,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,2,1,3,4,6]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>{{1},{2,5,6},{3},{4}}
[5,2,1,3,6,4]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[5,2,1,4,3,6]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[5,2,1,4,6,3]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[5,2,1,6,3,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,2,1,6,4,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,2,3,1,4,6]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[5,2,3,1,6,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,2,3,4,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,2,3,4,6,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,2,3,6,1,4]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[5,2,3,6,4,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,2,4,1,3,6]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[5,2,4,1,6,3]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[5,2,4,3,1,6]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[5,2,4,3,6,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[5,2,4,6,1,3]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[5,2,4,6,3,1]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[5,2,6,1,3,4]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>{{1},{2,4},{3},{5,6}}
[5,2,6,1,4,3]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[5,2,6,3,1,4]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[5,2,6,3,4,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,2,6,4,1,3]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[5,2,6,4,3,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,3,1,2,4,6]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[5,3,1,2,6,4]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,3,1,4,2,6]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[5,3,1,4,6,2]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[5,3,1,6,2,4]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[5,3,1,6,4,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,3,2,1,4,6]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>{{1},{2,3,5,6},{4}}
[5,3,2,1,6,4]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,3,2,4,1,6]=>[1,6,2,4,3,5]=>[1,4,5,3,6,2]=>{{1},{2,3,4,5,6}}
[5,3,2,4,6,1]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>{{1},{2},{3,5,6},{4}}
[5,3,2,6,1,4]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>{{1},{2,4},{3,5,6}}
[5,3,2,6,4,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,3,4,1,2,6]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,3,4,1,6,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,3,4,2,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,3,4,2,6,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,3,4,6,1,2]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,3,4,6,2,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,3,6,1,2,4]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[5,3,6,1,4,2]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[5,3,6,2,1,4]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>{{1},{2,3,4},{5,6}}
[5,3,6,2,4,1]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>{{1},{2},{3,4},{5,6}}
[5,3,6,4,1,2]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,3,6,4,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,4,1,2,3,6]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,4,1,2,6,3]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,4,1,3,2,6]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[5,4,1,3,6,2]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[5,4,1,6,2,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,4,1,6,3,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,4,2,1,3,6]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>{{1},{2,4,5,6},{3}}
[5,4,2,1,6,3]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,4,2,3,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,4,2,3,6,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,4,2,6,1,3]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>{{1},{2,3},{4,5,6}}
[5,4,2,6,3,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,4,3,1,2,6]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,4,3,1,6,2]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,4,3,2,1,6]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>{{1},{2,3,4,5,6}}
[5,4,3,2,6,1]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>{{1},{2},{3,4,5,6}}
[5,4,3,6,1,2]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,4,3,6,2,1]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>{{1},{2},{3},{4,5,6}}
[5,4,6,1,2,3]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,4,6,1,3,2]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[5,4,6,2,1,3]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>{{1},{2,3},{4},{5,6}}
[5,4,6,2,3,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,4,6,3,1,2]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,4,6,3,2,1]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>{{1},{2},{3},{4},{5,6}}
[5,6,1,2,3,4]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,1,2,4,3]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[5,6,1,3,2,4]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[5,6,1,3,4,2]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[5,6,1,4,2,3]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[5,6,1,4,3,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[5,6,2,1,3,4]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[5,6,2,1,4,3]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[5,6,2,3,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[5,6,2,3,4,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,2,4,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[5,6,2,4,3,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[5,6,3,1,2,4]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[5,6,3,1,4,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[5,6,3,2,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[5,6,3,2,4,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[5,6,3,4,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,3,4,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,4,1,2,3]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,4,1,3,2]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[5,6,4,2,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[5,6,4,2,3,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,4,3,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[5,6,4,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,1,2,3,4,5]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,1,2,3,5,4]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,1,2,4,3,5]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,1,2,4,5,3]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[6,1,2,5,3,4]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,1,2,5,4,3]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,1,3,2,4,5]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,1,3,2,5,4]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[6,1,3,4,2,5]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[6,1,3,4,5,2]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[6,1,3,5,2,4]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[6,1,3,5,4,2]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[6,1,4,2,3,5]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,1,4,2,5,3]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[6,1,4,3,2,5]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[6,1,4,3,5,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,1,4,5,2,3]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[6,1,4,5,3,2]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[6,1,5,2,3,4]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,1,5,2,4,3]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[6,1,5,3,2,4]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[6,1,5,3,4,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,1,5,4,2,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,1,5,4,3,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,1,3,4,5]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>{{1},{2,5},{3},{4},{6}}
[6,2,1,3,5,4]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[6,2,1,4,3,5]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,2,1,4,5,3]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[6,2,1,5,3,4]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,1,5,4,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,3,1,4,5]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[6,2,3,1,5,4]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,3,4,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,3,4,5,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,2,3,5,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,2,3,5,4,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,2,4,1,3,5]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[6,2,4,1,5,3]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,4,3,1,5]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[6,2,4,3,5,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,2,4,5,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,2,4,5,3,1]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[6,2,5,1,3,4]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[6,2,5,1,4,3]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[6,2,5,3,1,4]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[6,2,5,3,4,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,2,5,4,1,3]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[6,2,5,4,3,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,3,1,2,4,5]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[6,3,1,2,5,4]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,3,1,4,2,5]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[6,3,1,4,5,2]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[6,3,1,5,2,4]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[6,3,1,5,4,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,3,2,1,4,5]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>{{1},{2,3,5},{4},{6}}
[6,3,2,1,5,4]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,3,2,4,1,5]=>[1,5,2,4,3,6]=>[1,4,5,3,2,6]=>{{1},{2,3,4,5},{6}}
[6,3,2,4,5,1]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>{{1},{2},{3,5},{4},{6}}
[6,3,2,5,1,4]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>{{1},{2,4},{3,5},{6}}
[6,3,2,5,4,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,3,4,1,2,5]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,3,4,1,5,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,3,4,2,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,3,4,2,5,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,3,4,5,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,3,4,5,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,3,5,1,2,4]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,3,5,1,4,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,3,5,2,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,3,5,2,4,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,3,5,4,1,2]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,3,5,4,2,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,4,1,2,3,5]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,4,1,2,5,3]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,4,1,3,2,5]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[6,4,1,3,5,2]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[6,4,1,5,2,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,4,1,5,3,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,4,2,1,3,5]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>{{1},{2,4,5},{3},{6}}
[6,4,2,1,5,3]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,4,2,3,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,4,2,3,5,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,4,2,5,1,3]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>{{1},{2,3},{4,5},{6}}
[6,4,2,5,3,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,4,3,1,2,5]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,4,3,1,5,2]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,4,3,2,1,5]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>{{1},{2,3,4,5},{6}}
[6,4,3,2,5,1]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>{{1},{2},{3,4,5},{6}}
[6,4,3,5,1,2]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,4,3,5,2,1]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>{{1},{2},{3},{4,5},{6}}
[6,4,5,1,2,3]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,4,5,1,3,2]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,4,5,2,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,4,5,2,3,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,4,5,3,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,4,5,3,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,1,2,3,4]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,1,2,4,3]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,5,1,3,2,4]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,5,1,3,4,2]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[6,5,1,4,2,3]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,5,1,4,3,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,5,2,1,3,4]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>{{1},{2,4},{3},{5},{6}}
[6,5,2,1,4,3]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,5,2,3,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,5,2,3,4,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,2,4,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,5,2,4,3,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,5,3,1,2,4]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,5,3,1,4,2]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,5,3,2,1,4]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>{{1},{2,3,4},{5},{6}}
[6,5,3,2,4,1]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>{{1},{2},{3,4},{5},{6}}
[6,5,3,4,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,3,4,2,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,4,1,2,3]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,4,1,3,2]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,5,4,2,1,3]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>{{1},{2,3},{4},{5},{6}}
[6,5,4,2,3,1]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{1},{2},{3},{4},{5},{6}}
[6,5,4,3,1,2]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>{{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},{5},{6}}
[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[1,2,3,4,6,7,5]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[1,2,3,5,6,4,7]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[1,2,3,5,6,7,4]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[1,2,3,5,7,4,6]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[1,2,3,5,7,6,4]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,2,3,6,4,7,5]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[1,2,3,6,5,7,4]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[1,2,3,6,7,4,5]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[1,2,3,6,7,5,4]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,4,6,5]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,5,4,6]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,5,6,4]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,6,4,5]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[1,2,4,3,6,7,5]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[1,2,4,5,3,6,7]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[1,2,4,5,3,7,6]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[1,2,4,5,6,7,3]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[1,2,4,5,7,3,6]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,4,5,7,6,3]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[1,2,4,6,3,5,7]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,2,4,6,3,7,5]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,4,6,5,3,7]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[1,2,4,6,5,7,3]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[1,2,4,6,7,3,5]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,4,6,7,5,3]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[1,2,4,7,3,5,6]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,4,7,3,6,5]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,4,7,5,3,6]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,4,7,5,6,3]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,4,7,6,3,5]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,4,7,6,5,3]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[1,2,5,3,6,4,7]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[1,2,5,3,6,7,4]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,5,3,7,4,6]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,3,7,6,4]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,4,3,6,7]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[1,2,5,4,3,7,6]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,4,6,3,7]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[1,2,5,4,6,7,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[1,2,5,4,7,3,6]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[1,2,5,4,7,6,3]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[1,2,5,6,3,4,7]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,2,5,6,3,7,4]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,5,6,4,3,7]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[1,2,5,6,4,7,3]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[1,2,5,6,7,3,4]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,5,6,7,4,3]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[1,2,5,7,3,4,6]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,5,7,3,6,4]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,5,7,4,3,6]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,5,7,4,6,3]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,5,7,6,3,4]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,5,7,6,4,3]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,3,4,7,5]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,6,3,5,4,7]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,3,5,7,4]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[1,2,6,3,7,4,5]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,3,7,5,4]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,4,3,5,7]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[1,2,6,4,3,7,5]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,4,5,3,7]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,4,5,7,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,4,7,3,5]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,4,7,5,3]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,6,5,3,4,7]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,6,5,3,7,4]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,5,4,3,7]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[1,2,6,5,4,7,3]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[1,2,6,5,7,3,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,5,7,4,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[1,2,6,7,3,4,5]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,6,7,3,5,4]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,6,7,4,3,5]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,6,7,4,5,3]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,6,7,5,3,4]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,6,7,5,4,3]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,4,6,5]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,5,4,6]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,5,6,4]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,6,4,5]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,3,6,5,4]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,4,3,5,6]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,4,3,6,5]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,4,5,3,6]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,4,5,6,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,4,6,3,5]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,4,6,5,3]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,3,4,6]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,3,6,4]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,4,3,6]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,4,6,3]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,6,3,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,5,6,4,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,3,4,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,3,5,4]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,4,3,5]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,4,5,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,5,3,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,2,7,6,5,4,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[1,3,2,4,6,7,5]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[1,3,2,4,7,6,5]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[1,3,2,5,6,4,7]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[1,3,2,5,6,7,4]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[1,3,2,5,7,4,6]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[1,3,2,5,7,6,4]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[1,3,2,6,4,7,5]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[1,3,2,6,5,4,7]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[1,3,2,6,5,7,4]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[1,3,2,6,7,4,5]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[1,3,2,6,7,5,4]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,4,6,5]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,5,4,6]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,5,6,4]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,6,4,5]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[1,3,4,2,5,6,7]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[1,3,4,2,5,7,6]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[1,3,4,2,6,5,7]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[1,3,4,2,7,5,6]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[1,3,4,2,7,6,5]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[1,3,4,5,2,6,7]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[1,3,4,5,2,7,6]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[1,3,4,5,6,2,7]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[1,3,4,5,6,7,2]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}
[1,3,4,5,7,2,6]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[1,3,4,5,7,6,2]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[1,3,4,6,2,5,7]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,3,4,6,2,7,5]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,3,4,6,5,2,7]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[1,3,4,6,5,7,2]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[1,3,4,6,7,2,5]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[1,3,4,6,7,5,2]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[1,3,4,7,2,5,6]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[1,3,4,7,2,6,5]=>[1,3,4,7,2,6,5]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[1,3,4,7,5,2,6]=>[1,3,4,7,2,6,5]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[1,3,4,7,5,6,2]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[1,3,4,7,6,2,5]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[1,3,4,7,6,5,2]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[1,3,5,2,4,6,7]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,3,5,2,4,7,6]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[1,3,5,2,6,4,7]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,3,5,2,6,7,4]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[1,3,5,2,7,4,6]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,3,5,2,7,6,4]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,3,5,4,2,6,7]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[1,3,5,4,2,7,6]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,3,5,4,6,2,7]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[1,3,5,4,6,7,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[1,3,5,4,7,2,6]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[1,3,5,4,7,6,2]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[1,3,5,6,2,4,7]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,3,5,6,2,7,4]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,3,5,6,4,2,7]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[1,3,5,6,4,7,2]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[1,3,5,6,7,2,4]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[1,3,5,6,7,4,2]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[1,3,5,7,2,4,6]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[1,3,5,7,2,6,4]=>[1,3,5,7,2,6,4]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[1,3,5,7,4,2,6]=>[1,3,5,7,2,6,4]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[1,3,5,7,4,6,2]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[1,3,5,7,6,2,4]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[1,3,5,7,6,4,2]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[1,3,6,2,4,5,7]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,6,2,4,7,5]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[1,3,6,2,5,4,7]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,6,2,5,7,4]=>[1,3,6,2,5,7,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[1,3,6,2,7,4,5]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,3,6,2,7,5,4]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,3,6,4,2,5,7]=>[1,3,6,2,5,7,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[1,3,6,4,2,7,5]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,3,6,4,5,2,7]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,3,6,4,5,7,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,6,4,7,2,5]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,6,4,7,5,2]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[1,3,6,5,2,4,7]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[1,3,6,5,2,7,4]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,3,6,5,4,2,7]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[1,3,6,5,4,7,2]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[1,3,6,5,7,2,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,6,5,7,4,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[1,3,6,7,2,4,5]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,3,6,7,2,5,4]=>[1,3,6,7,2,5,4]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,3,6,7,4,2,5]=>[1,3,6,7,2,5,4]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,3,6,7,4,5,2]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,3,6,7,5,2,4]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,3,6,7,5,4,2]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[1,3,7,2,4,5,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,2,4,6,5]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,2,5,4,6]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,2,5,6,4]=>[1,3,7,2,5,6,4]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,2,6,4,5]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,2,6,5,4]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,4,2,5,6]=>[1,3,7,2,5,6,4]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,4,2,6,5]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,4,5,2,6]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,4,5,6,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,4,6,2,5]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,4,6,5,2]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,5,2,4,6]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,5,2,6,4]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,5,4,2,6]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,5,4,6,2]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,5,6,2,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,5,6,4,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,6,2,4,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,6,2,5,4]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,6,4,2,5]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,6,4,5,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,6,5,2,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,3,7,6,5,4,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,4,2,3,6,7,5]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,4,2,3,7,6,5]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,4,2,5,3,6,7]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[1,4,2,5,3,7,6]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[1,4,2,5,6,3,7]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,4,2,5,6,7,3]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,2,5,7,3,6]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[1,4,2,5,7,6,3]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[1,4,2,6,3,5,7]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,2,6,3,7,5]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[1,4,2,6,5,3,7]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[1,4,2,6,5,7,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,2,6,7,3,5]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[1,4,2,6,7,5,3]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[1,4,2,7,3,5,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,2,7,3,6,5]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,2,7,5,3,6]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,2,7,5,6,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,2,7,6,3,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,2,7,6,5,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,2,5,6,7]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[1,4,3,2,5,7,6]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[1,4,3,2,6,5,7]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,3,2,6,7,5]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[1,4,3,2,7,5,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,2,7,6,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,5,2,6,7]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[1,4,3,5,2,7,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,5,6,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,5,6,7,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[1,4,3,5,7,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[1,4,3,5,7,6,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[1,4,3,6,2,5,7]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[1,4,3,6,2,7,5]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,6,5,2,7]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[1,4,3,6,5,7,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[1,4,3,6,7,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[1,4,3,6,7,5,2]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[1,4,3,7,2,5,6]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[1,4,3,7,2,6,5]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[1,4,3,7,5,2,6]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[1,4,3,7,5,6,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,4,3,7,6,2,5]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[1,4,3,7,6,5,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[1,4,5,2,3,6,7]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,4,5,2,3,7,6]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[1,4,5,2,6,3,7]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,4,5,2,6,7,3]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[1,4,5,2,7,3,6]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,4,5,2,7,6,3]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,4,5,3,2,6,7]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[1,4,5,3,2,7,6]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,4,5,3,6,2,7]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[1,4,5,3,6,7,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[1,4,5,3,7,2,6]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[1,4,5,3,7,6,2]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[1,4,5,6,2,3,7]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,4,5,6,2,7,3]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,4,5,6,3,2,7]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[1,4,5,6,3,7,2]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[1,4,5,6,7,2,3]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[1,4,5,6,7,3,2]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[1,4,5,7,2,3,6]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[1,4,5,7,2,6,3]=>[1,4,5,7,2,6,3]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[1,4,5,7,3,2,6]=>[1,4,5,7,2,6,3]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[1,4,5,7,3,6,2]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[1,4,5,7,6,2,3]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[1,4,5,7,6,3,2]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[1,4,6,2,3,5,7]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,6,2,3,7,5]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[1,4,6,2,5,3,7]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,6,2,5,7,3]=>[1,4,6,2,5,7,3]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[1,4,6,2,7,3,5]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,4,6,2,7,5,3]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,4,6,3,2,5,7]=>[1,4,6,2,5,7,3]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[1,4,6,3,2,7,5]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,4,6,3,5,2,7]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,4,6,3,5,7,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,6,3,7,2,5]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,6,3,7,5,2]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[1,4,6,5,2,3,7]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[1,4,6,5,2,7,3]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,4,6,5,3,2,7]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[1,4,6,5,3,7,2]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[1,4,6,5,7,2,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,6,5,7,3,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[1,4,6,7,2,3,5]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,4,6,7,2,5,3]=>[1,4,6,7,2,5,3]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,4,6,7,3,2,5]=>[1,4,6,7,2,5,3]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,4,6,7,3,5,2]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,4,6,7,5,2,3]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,4,6,7,5,3,2]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[1,4,7,2,3,5,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,2,3,6,5]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,2,5,3,6]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,2,5,6,3]=>[1,4,7,2,5,6,3]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,2,6,3,5]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,2,6,5,3]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,3,2,5,6]=>[1,4,7,2,5,6,3]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,3,2,6,5]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,3,5,2,6]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,3,5,6,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,3,6,2,5]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,3,6,5,2]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,5,2,3,6]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,5,2,6,3]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,5,3,2,6]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,5,3,6,2]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,5,6,2,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,5,6,3,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,6,2,3,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,6,2,5,3]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,6,3,2,5]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,6,3,5,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,6,5,2,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,4,7,6,5,3,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,2,3,6,4,7]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,5,2,3,6,7,4]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,5,2,3,7,4,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,2,3,7,6,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,2,4,3,6,7]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,2,4,3,7,6]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,2,4,6,3,7]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,5,2,4,6,7,3]=>[1,5,2,4,6,7,3]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[1,5,2,4,7,3,6]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,5,2,4,7,6,3]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,5,2,6,3,4,7]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,2,6,3,7,4]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,2,6,4,3,7]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,2,6,4,7,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,2,6,7,3,4]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,2,6,7,4,3]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,2,7,3,6,4]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,2,7,4,3,6]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,2,7,4,6,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,2,7,6,3,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,2,7,6,4,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,2,4,6,7]=>[1,5,2,4,6,7,3]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[1,5,3,2,4,7,6]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,5,3,2,6,4,7]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,3,2,6,7,4]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,3,2,7,4,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,2,7,6,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,4,2,6,7]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,4,6,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,4,6,7,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,3,4,7,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,3,4,7,6,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,3,6,2,4,7]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[1,5,3,6,2,7,4]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,6,4,2,7]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,3,6,4,7,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,5,3,6,7,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,3,6,7,4,2]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,5,3,7,2,4,6]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[1,5,3,7,2,6,4]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,3,7,4,2,6]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,3,7,4,6,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,3,7,6,2,4]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,3,7,6,4,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,4,2,3,6,7]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,5,4,2,3,7,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,4,2,6,3,7]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,4,2,6,7,3]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,4,2,7,3,6]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,2,7,6,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,3,2,6,7]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[1,5,4,3,2,7,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,3,6,2,7]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,3,6,7,2]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[1,5,4,3,7,2,6]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[1,5,4,3,7,6,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,4,6,2,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,4,6,2,7,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,6,3,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[1,5,4,6,3,7,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[1,5,4,6,7,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,4,6,7,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[1,5,4,7,2,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,5,4,7,2,6,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,4,7,3,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[1,5,4,7,3,6,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[1,5,4,7,6,2,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,4,7,6,3,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[1,5,6,2,3,4,7]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,2,3,7,4]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[1,5,6,2,4,3,7]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,2,4,7,3]=>[1,5,6,2,4,7,3]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[1,5,6,2,7,3,4]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,5,6,2,7,4,3]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,5,6,3,2,4,7]=>[1,5,6,2,4,7,3]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[1,5,6,3,2,7,4]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,5,6,3,4,2,7]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,5,6,3,4,7,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,3,7,2,4]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,3,7,4,2]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[1,5,6,4,2,3,7]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[1,5,6,4,2,7,3]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,5,6,4,3,2,7]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[1,5,6,4,3,7,2]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[1,5,6,4,7,2,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,4,7,3,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[1,5,6,7,2,3,4]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,5,6,7,2,4,3]=>[1,5,6,7,2,4,3]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,5,6,7,3,2,4]=>[1,5,6,7,2,4,3]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,5,6,7,3,4,2]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,5,6,7,4,2,3]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,5,6,7,4,3,2]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[1,5,7,2,3,4,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,2,3,6,4]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,2,4,3,6]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,2,4,6,3]=>[1,5,7,2,4,6,3]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,2,6,3,4]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,2,6,4,3]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,3,2,4,6]=>[1,5,7,2,4,6,3]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,3,2,6,4]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,3,4,2,6]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,3,4,6,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,3,6,2,4]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,3,6,4,2]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,4,2,3,6]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,4,2,6,3]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,4,3,2,6]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,4,3,6,2]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,4,6,2,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,4,6,3,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,6,2,3,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,6,2,4,3]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,6,3,2,4]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,6,3,4,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,6,4,2,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,5,7,6,4,3,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,3,4,7,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,2,3,5,4,7]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,3,5,7,4]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,2,3,7,4,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,2,3,7,5,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,2,4,3,5,7]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,4,3,7,5]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,2,4,5,3,7]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,4,5,7,3]=>[1,6,2,4,5,7,3]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[1,6,2,4,7,3,5]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,2,4,7,5,3]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,2,5,3,4,7]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,5,3,7,4]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,2,5,4,3,7]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,2,5,4,7,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,2,5,7,3,4]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,2,5,7,4,3]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,2,7,3,4,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,2,7,3,5,4]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,2,7,4,3,5]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,2,7,4,5,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,2,7,5,3,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,2,7,5,4,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,2,4,5,7]=>[1,6,2,4,5,7,3]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[1,6,3,2,4,7,5]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,3,2,5,4,7]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,2,5,7,4]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,3,2,7,4,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,2,7,5,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,4,2,5,7]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,3,4,2,7,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,4,5,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,4,5,7,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,4,7,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,4,7,5,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,3,5,2,4,7]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,3,5,2,7,4]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,5,4,2,7]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,3,5,4,7,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,5,7,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,5,7,4,2]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,3,7,2,4,5]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,3,7,2,5,4]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,3,7,4,2,5]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,3,7,4,5,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,3,7,5,2,4]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,3,7,5,4,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,4,2,3,5,7]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,4,2,3,7,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,4,2,5,3,7]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,4,2,5,7,3]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,4,2,7,3,5]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,2,7,5,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,3,2,5,7]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[1,6,4,3,2,7,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,3,5,2,7]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,3,5,7,2]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,4,3,7,2,5]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[1,6,4,3,7,5,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,4,5,2,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,4,5,2,7,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,5,3,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,4,5,3,7,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,4,5,7,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,5,7,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,7,2,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,7,2,5,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,7,3,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,7,3,5,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,4,7,5,2,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,4,7,5,3,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,2,3,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,2,3,7,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,5,2,4,3,7]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,2,4,7,3]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,5,2,7,3,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,2,7,4,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,3,2,4,7]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[1,6,5,3,2,7,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,3,4,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,3,4,7,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,3,7,2,4]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,3,7,4,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,5,4,2,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,5,4,2,7,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,4,3,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[1,6,5,4,3,7,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[1,6,5,4,7,2,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,4,7,3,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[1,6,5,7,2,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,7,2,4,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,7,3,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,7,3,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,7,4,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,5,7,4,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[1,6,7,2,3,4,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,2,3,5,4]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,2,4,3,5]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,2,4,5,3]=>[1,6,7,2,4,5,3]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,2,5,3,4]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,2,5,4,3]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,3,2,4,5]=>[1,6,7,2,4,5,3]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,3,2,5,4]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,3,4,2,5]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,3,4,5,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,3,5,2,4]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,3,5,4,2]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,4,2,3,5]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,4,2,5,3]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,4,3,2,5]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,4,3,5,2]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,4,5,3,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,5,2,3,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,5,2,4,3]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,5,3,2,4]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,5,3,4,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,5,4,2,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,6,7,5,4,3,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,4,6,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,5,4,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,5,6,4]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,6,4,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,3,6,5,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,4,3,5,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,4,3,6,5]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,4,5,3,6]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,4,5,6,3]=>[1,7,2,4,5,6,3]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,4,6,3,5]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,4,6,5,3]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,3,4,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,3,6,4]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,4,3,6]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,4,6,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,6,3,4]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,5,6,4,3]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,3,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,3,5,4]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,4,3,5]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,4,5,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,5,3,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,2,6,5,4,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,2,4,5,6]=>[1,7,2,4,5,6,3]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,2,4,6,5]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,2,5,4,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,2,5,6,4]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,2,6,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,2,6,5,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,4,2,5,6]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,4,2,6,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,4,5,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,4,5,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,4,6,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,4,6,5,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,5,2,4,6]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,5,2,6,4]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,5,4,2,6]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,5,4,6,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,5,6,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,5,6,4,2]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,6,2,4,5]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,6,2,5,4]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,6,4,2,5]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,6,4,5,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,6,5,2,4]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,3,6,5,4,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,3,5,6]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,3,6,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,5,3,6]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,5,6,3]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,6,3,5]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,2,6,5,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,3,2,5,6]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,3,2,6,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,3,5,2,6]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,3,5,6,2]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,3,6,2,5]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,3,6,5,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,2,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,2,6,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,3,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,3,6,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,6,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,5,6,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,2,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,2,5,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,3,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,3,5,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,5,2,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,4,6,5,3,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,3,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,3,6,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,4,3,6]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,4,6,3]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,6,3,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,2,6,4,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,2,4,6]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,2,6,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,4,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,4,6,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,6,2,4]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,3,6,4,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,4,2,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,4,2,6,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,4,3,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,4,3,6,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,4,6,2,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,4,6,3,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,2,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,2,4,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,3,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,4,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,5,6,4,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,3,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,3,5,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,4,3,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,4,5,3]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,5,3,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,2,5,4,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,2,4,5]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,2,5,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,4,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,4,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,5,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,3,5,4,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,4,2,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,4,2,5,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,4,3,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,4,3,5,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,4,5,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,4,5,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,2,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,2,4,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,3,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,3,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,4,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,3,4,5,6,7]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>{{1},{2,7},{3},{4},{5},{6}}
[2,1,3,4,5,7,6]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[2,1,3,4,6,5,7]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[2,1,3,4,6,7,5]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[2,1,3,4,7,5,6]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[2,1,3,4,7,6,5]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[2,1,3,5,4,6,7]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[2,1,3,5,4,7,6]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[2,1,3,5,6,4,7]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[2,1,3,5,6,7,4]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[2,1,3,5,7,4,6]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[2,1,3,5,7,6,4]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[2,1,3,6,4,5,7]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[2,1,3,6,4,7,5]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[2,1,3,6,5,4,7]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[2,1,3,6,5,7,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[2,1,3,6,7,4,5]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[2,1,3,6,7,5,4]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[2,1,3,7,4,5,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,1,3,7,4,6,5]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[2,1,3,7,5,4,6]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[2,1,3,7,5,6,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,1,3,7,6,4,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,1,3,7,6,5,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,1,4,3,5,6,7]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[2,1,4,3,5,7,6]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[2,1,4,3,6,5,7]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[2,1,4,3,6,7,5]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[2,1,4,3,7,5,6]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[2,1,4,3,7,6,5]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[2,1,4,5,3,6,7]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[2,1,4,5,3,7,6]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[2,1,4,5,6,3,7]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[2,1,4,5,6,7,3]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[2,1,4,5,7,3,6]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[2,1,4,5,7,6,3]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[2,1,4,6,3,5,7]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[2,1,4,6,3,7,5]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[2,1,4,6,5,3,7]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[2,1,4,6,5,7,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[2,1,4,6,7,3,5]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[2,1,4,6,7,5,3]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[2,1,4,7,3,5,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,1,4,7,3,6,5]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[2,1,4,7,5,3,6]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[2,1,4,7,5,6,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,1,4,7,6,3,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,1,4,7,6,5,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,1,5,3,4,6,7]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[2,1,5,3,4,7,6]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,5,3,6,4,7]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[2,1,5,3,6,7,4]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[2,1,5,3,7,4,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,1,5,3,7,6,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,1,5,4,3,6,7]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[2,1,5,4,3,7,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,1,5,4,6,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,1,5,4,6,7,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[2,1,5,4,7,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[2,1,5,4,7,6,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,1,5,6,3,4,7]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[2,1,5,6,3,7,4]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[2,1,5,6,4,3,7]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[2,1,5,6,4,7,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[2,1,5,6,7,3,4]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[2,1,5,6,7,4,3]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[2,1,5,7,3,4,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,1,5,7,3,6,4]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[2,1,5,7,4,3,6]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[2,1,5,7,4,6,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,1,5,7,6,3,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,1,5,7,6,4,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,1,6,3,4,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,1,6,3,4,7,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,1,6,3,5,4,7]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,1,6,3,5,7,4]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,1,6,3,7,4,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,1,6,3,7,5,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,1,6,4,3,5,7]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,1,6,4,3,7,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,1,6,4,5,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,1,6,4,5,7,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,1,6,4,7,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,1,6,4,7,5,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,1,6,5,3,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,1,6,5,3,7,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,1,6,5,4,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,1,6,5,4,7,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,1,6,5,7,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,1,6,5,7,4,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,1,6,7,3,4,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,1,6,7,3,5,4]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,1,6,7,4,3,5]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,1,6,7,4,5,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,1,6,7,5,3,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,1,6,7,5,4,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,1,7,3,4,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,3,4,6,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,3,5,4,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,3,5,6,4]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,3,6,4,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,3,6,5,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,4,3,5,6]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,4,3,6,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,4,5,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,4,5,6,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,4,6,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,4,6,5,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,5,3,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,5,3,6,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,5,4,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,5,4,6,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,5,6,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,5,6,4,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,6,3,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,6,3,5,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,6,4,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,6,4,5,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,6,5,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,1,7,6,5,4,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,1,4,5,6,7]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[2,3,1,4,5,7,6]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[2,3,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[2,3,1,4,6,7,5]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[2,3,1,4,7,5,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,3,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,3,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[2,3,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,3,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[2,3,1,5,6,7,4]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[2,3,1,5,7,4,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,3,1,5,7,6,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,3,1,6,4,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,3,1,6,4,7,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,3,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,3,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,3,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,3,1,6,7,5,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,3,1,7,4,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,1,7,4,6,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,3,1,7,5,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,3,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,1,7,6,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,1,5,6,7]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[2,3,4,1,5,7,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,3,4,1,6,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,3,4,1,6,7,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,3,4,1,7,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,1,7,6,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,5,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,3,4,5,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,5,6,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[2,3,4,5,7,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,3,4,5,7,6,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[2,3,4,6,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,3,4,6,1,7,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,6,5,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,3,4,6,5,7,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[2,3,4,6,7,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[2,3,4,6,7,5,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[2,3,4,7,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[2,3,4,7,1,6,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,3,4,7,5,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,3,4,7,5,6,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[2,3,4,7,6,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,3,4,7,6,5,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[2,3,5,1,4,6,7]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[2,3,5,1,4,7,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,3,5,1,6,4,7]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,3,5,1,6,7,4]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,3,5,1,7,4,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,1,7,6,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,4,1,6,7]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,3,5,4,1,7,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,4,6,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,4,6,7,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[2,3,5,4,7,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,3,5,4,7,6,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[2,3,5,6,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,3,5,6,1,7,4]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,6,4,1,7]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,5,6,4,7,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[2,3,5,6,7,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[2,3,5,6,7,4,1]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[2,3,5,7,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[2,3,5,7,1,6,4]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,3,5,7,4,1,6]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,3,5,7,4,6,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[2,3,5,7,6,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[2,3,5,7,6,4,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[2,3,6,1,4,5,7]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[2,3,6,1,4,7,5]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[2,3,6,1,5,4,7]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[2,3,6,1,5,7,4]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[2,3,6,1,7,4,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,6,1,7,5,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,6,4,1,5,7]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[2,3,6,4,1,7,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,6,4,5,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,6,4,5,7,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[2,3,6,4,7,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[2,3,6,4,7,5,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[2,3,6,5,1,4,7]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[2,3,6,5,1,7,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,6,5,4,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[2,3,6,5,4,7,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[2,3,6,5,7,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[2,3,6,5,7,4,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[2,3,6,7,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[2,3,6,7,1,5,4]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[2,3,6,7,4,1,5]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[2,3,6,7,4,5,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[2,3,6,7,5,1,4]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[2,3,6,7,5,4,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[2,3,7,1,4,5,6]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[2,3,7,1,4,6,5]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[2,3,7,1,5,4,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,3,7,1,5,6,4]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[2,3,7,1,6,4,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,3,7,1,6,5,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,3,7,4,1,5,6]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[2,3,7,4,1,6,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,3,7,4,5,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,3,7,4,5,6,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[2,3,7,4,6,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,3,7,4,6,5,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[2,3,7,5,1,4,6]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[2,3,7,5,1,6,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,3,7,5,4,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[2,3,7,5,4,6,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[2,3,7,5,6,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[2,3,7,5,6,4,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[2,3,7,6,1,4,5]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[2,3,7,6,1,5,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,3,7,6,4,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[2,3,7,6,4,5,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[2,3,7,6,5,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[2,3,7,6,5,4,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[2,4,1,3,5,6,7]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[2,4,1,3,5,7,6]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[2,4,1,3,6,5,7]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[2,4,1,3,6,7,5]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[2,4,1,3,7,5,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,4,1,3,7,6,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,4,1,5,3,6,7]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[2,4,1,5,3,7,6]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,4,1,5,6,3,7]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[2,4,1,5,6,7,3]=>[1,5,6,7,2,4,3]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[2,4,1,5,7,3,6]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,4,1,5,7,6,3]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,4,1,6,3,5,7]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,4,1,6,3,7,5]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,4,1,6,5,3,7]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,4,1,6,5,7,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,4,1,6,7,3,5]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,4,1,6,7,5,3]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,4,1,7,3,5,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,1,7,3,6,5]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,4,1,7,5,3,6]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,4,1,7,5,6,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,1,7,6,3,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,1,7,6,5,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,1,5,6,7]=>[1,5,6,7,2,4,3]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[2,4,3,1,5,7,6]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,4,3,1,6,5,7]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,4,3,1,6,7,5]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,4,3,1,7,5,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,1,7,6,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,5,1,6,7]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,4,3,5,1,7,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,5,6,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,5,6,7,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[2,4,3,5,7,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,4,3,5,7,6,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[2,4,3,6,1,5,7]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[2,4,3,6,1,7,5]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,6,5,1,7]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[2,4,3,6,5,7,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[2,4,3,6,7,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[2,4,3,6,7,5,1]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[2,4,3,7,1,5,6]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[2,4,3,7,1,6,5]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,4,3,7,5,1,6]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[2,4,3,7,5,6,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[2,4,3,7,6,1,5]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[2,4,3,7,6,5,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[2,4,5,1,3,6,7]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[2,4,5,1,3,7,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,4,5,1,6,3,7]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,4,5,1,6,7,3]=>[1,6,7,2,4,5,3]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,4,5,1,7,3,6]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,1,7,6,3]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,3,1,6,7]=>[1,6,7,2,4,5,3]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,4,5,3,1,7,6]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,3,6,1,7]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,3,6,7,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[2,4,5,3,7,1,6]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,4,5,3,7,6,1]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[2,4,5,6,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,4,5,6,1,7,3]=>[1,7,2,4,5,6,3]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,6,3,1,7]=>[1,7,2,4,5,6,3]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,5,6,3,7,1]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[2,4,5,6,7,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[2,4,5,6,7,3,1]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[2,4,5,7,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[2,4,5,7,1,6,3]=>[1,6,2,4,5,7,3]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[2,4,5,7,3,1,6]=>[1,6,2,4,5,7,3]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[2,4,5,7,3,6,1]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[2,4,5,7,6,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[2,4,5,7,6,3,1]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[2,4,6,1,3,5,7]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[2,4,6,1,3,7,5]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[2,4,6,1,5,3,7]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[2,4,6,1,5,7,3]=>[1,5,7,2,4,6,3]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,4,6,1,7,3,5]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,6,1,7,5,3]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,6,3,1,5,7]=>[1,5,7,2,4,6,3]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,4,6,3,1,7,5]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,6,3,5,1,7]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,6,3,5,7,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[2,4,6,3,7,1,5]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[2,4,6,3,7,5,1]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[2,4,6,5,1,3,7]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[2,4,6,5,1,7,3]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,6,5,3,1,7]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,4,6,5,3,7,1]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[2,4,6,5,7,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[2,4,6,5,7,3,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[2,4,6,7,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[2,4,6,7,1,5,3]=>[1,5,2,4,6,7,3]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[2,4,6,7,3,1,5]=>[1,5,2,4,6,7,3]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[2,4,6,7,3,5,1]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[2,4,6,7,5,1,3]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[2,4,6,7,5,3,1]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[2,4,7,1,3,5,6]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[2,4,7,1,3,6,5]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[2,4,7,1,5,3,6]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[2,4,7,1,5,6,3]=>[1,5,6,2,4,7,3]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[2,4,7,1,6,3,5]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,4,7,1,6,5,3]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,4,7,3,1,5,6]=>[1,5,6,2,4,7,3]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[2,4,7,3,1,6,5]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,4,7,3,5,1,6]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,4,7,3,5,6,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[2,4,7,3,6,1,5]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[2,4,7,3,6,5,1]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[2,4,7,5,1,3,6]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[2,4,7,5,1,6,3]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,4,7,5,3,1,6]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[2,4,7,5,3,6,1]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[2,4,7,5,6,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[2,4,7,5,6,3,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[2,4,7,6,1,3,5]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[2,4,7,6,1,5,3]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[2,4,7,6,3,1,5]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[2,4,7,6,3,5,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[2,4,7,6,5,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[2,4,7,6,5,3,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[2,5,1,3,4,6,7]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[2,5,1,3,4,7,6]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[2,5,1,3,6,4,7]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[2,5,1,3,6,7,4]=>[1,3,6,7,2,5,4]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[2,5,1,3,7,4,6]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,1,3,7,6,4]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,1,4,3,6,7]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[2,5,1,4,3,7,6]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[2,5,1,4,6,3,7]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[2,5,1,4,6,7,3]=>[1,4,6,7,2,5,3]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[2,5,1,4,7,3,6]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,1,4,7,6,3]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,1,6,3,4,7]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,5,1,6,3,7,4]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,1,6,4,3,7]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,1,6,4,7,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,5,1,6,7,3,4]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,5,1,6,7,4,3]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,5,1,7,3,4,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,1,7,3,6,4]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,1,7,4,3,6]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,1,7,4,6,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,1,7,6,3,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,1,7,6,4,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,1,4,6,7]=>[1,4,6,7,2,5,3]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[2,5,3,1,4,7,6]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,3,1,6,4,7]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,5,3,1,6,7,4]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,5,3,1,7,4,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,1,7,6,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,4,1,6,7]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,5,3,4,1,7,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,4,6,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,4,6,7,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[2,5,3,4,7,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,5,3,4,7,6,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[2,5,3,6,1,4,7]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,3,6,1,7,4]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,6,4,1,7]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,3,6,4,7,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[2,5,3,6,7,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[2,5,3,6,7,4,1]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[2,5,3,7,1,4,6]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[2,5,3,7,1,6,4]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,3,7,4,1,6]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,3,7,4,6,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[2,5,3,7,6,1,4]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[2,5,3,7,6,4,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[2,5,4,1,3,6,7]=>[1,3,6,7,2,5,4]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[2,5,4,1,3,7,6]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,4,1,6,3,7]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,4,1,6,7,3]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,5,4,1,7,3,6]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,4,1,7,6,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,4,3,1,6,7]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[2,5,4,3,1,7,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,4,3,6,1,7]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[2,5,4,3,6,7,1]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[2,5,4,3,7,1,6]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[2,5,4,3,7,6,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[2,5,4,6,1,3,7]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,4,6,1,7,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,4,6,3,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[2,5,4,6,3,7,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[2,5,4,6,7,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[2,5,4,6,7,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[2,5,4,7,1,3,6]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[2,5,4,7,1,6,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,5,4,7,3,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[2,5,4,7,3,6,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[2,5,4,7,6,1,3]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[2,5,4,7,6,3,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[2,5,6,1,3,4,7]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[2,5,6,1,3,7,4]=>[1,3,7,2,5,6,4]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,6,1,4,3,7]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[2,5,6,1,4,7,3]=>[1,4,7,2,5,6,3]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,6,1,7,3,4]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,5,6,1,7,4,3]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,5,6,3,1,4,7]=>[1,4,7,2,5,6,3]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,5,6,3,1,7,4]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,5,6,3,4,1,7]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,5,6,3,4,7,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[2,5,6,3,7,1,4]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[2,5,6,3,7,4,1]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[2,5,6,4,1,3,7]=>[1,3,7,2,5,6,4]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,5,6,4,1,7,3]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,5,6,4,3,1,7]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[2,5,6,4,3,7,1]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[2,5,6,4,7,1,3]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[2,5,6,4,7,3,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[2,5,6,7,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[2,5,6,7,1,4,3]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[2,5,6,7,3,1,4]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[2,5,6,7,3,4,1]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[2,5,6,7,4,1,3]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[2,5,6,7,4,3,1]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[2,5,7,1,3,4,6]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[2,5,7,1,3,6,4]=>[1,3,6,2,5,7,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[2,5,7,1,4,3,6]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[2,5,7,1,4,6,3]=>[1,4,6,2,5,7,3]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[2,5,7,1,6,3,4]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[2,5,7,1,6,4,3]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[2,5,7,3,1,4,6]=>[1,4,6,2,5,7,3]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[2,5,7,3,1,6,4]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[2,5,7,3,4,1,6]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[2,5,7,3,4,6,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[2,5,7,3,6,1,4]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[2,5,7,3,6,4,1]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[2,5,7,4,1,3,6]=>[1,3,6,2,5,7,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[2,5,7,4,1,6,3]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[2,5,7,4,3,1,6]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[2,5,7,4,3,6,1]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[2,5,7,4,6,1,3]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[2,5,7,4,6,3,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[2,5,7,6,1,3,4]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[2,5,7,6,1,4,3]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[2,5,7,6,3,1,4]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[2,5,7,6,3,4,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[2,5,7,6,4,1,3]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[2,5,7,6,4,3,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[2,6,1,3,4,5,7]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[2,6,1,3,4,7,5]=>[1,3,4,7,2,6,5]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[2,6,1,3,5,4,7]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[2,6,1,3,5,7,4]=>[1,3,5,7,2,6,4]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[2,6,1,3,7,4,5]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,6,1,3,7,5,4]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,6,1,4,3,5,7]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[2,6,1,4,3,7,5]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[2,6,1,4,5,3,7]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[2,6,1,4,5,7,3]=>[1,4,5,7,2,6,3]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[2,6,1,4,7,3,5]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,6,1,4,7,5,3]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,6,1,5,3,4,7]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[2,6,1,5,3,7,4]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,6,1,5,4,3,7]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,6,1,5,4,7,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[2,6,1,5,7,3,4]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,6,1,5,7,4,3]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,6,1,7,3,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,1,7,3,5,4]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,1,7,4,3,5]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,1,7,4,5,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,1,7,5,3,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,1,7,5,4,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,1,4,5,7]=>[1,4,5,7,2,6,3]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[2,6,3,1,4,7,5]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,6,3,1,5,4,7]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[2,6,3,1,5,7,4]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,6,3,1,7,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,1,7,5,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,4,1,5,7]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,6,3,4,1,7,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,4,5,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,4,5,7,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[2,6,3,4,7,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[2,6,3,4,7,5,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[2,6,3,5,1,4,7]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,6,3,5,1,7,4]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,5,4,1,7]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,3,5,4,7,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[2,6,3,5,7,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[2,6,3,5,7,4,1]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[2,6,3,7,1,4,5]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[2,6,3,7,1,5,4]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,6,3,7,4,1,5]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,6,3,7,4,5,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[2,6,3,7,5,1,4]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[2,6,3,7,5,4,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[2,6,4,1,3,5,7]=>[1,3,5,7,2,6,4]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[2,6,4,1,3,7,5]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,6,4,1,5,3,7]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,6,4,1,5,7,3]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,6,4,1,7,3,5]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,4,1,7,5,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,4,3,1,5,7]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[2,6,4,3,1,7,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,4,3,5,1,7]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,4,3,5,7,1]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[2,6,4,3,7,1,5]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[2,6,4,3,7,5,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[2,6,4,5,1,3,7]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,6,4,5,1,7,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,4,5,3,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,4,5,3,7,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[2,6,4,5,7,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[2,6,4,5,7,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[2,6,4,7,1,3,5]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[2,6,4,7,1,5,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[2,6,4,7,3,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[2,6,4,7,3,5,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[2,6,4,7,5,1,3]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[2,6,4,7,5,3,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[2,6,5,1,3,4,7]=>[1,3,4,7,2,6,5]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[2,6,5,1,3,7,4]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,6,5,1,4,3,7]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[2,6,5,1,4,7,3]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,6,5,1,7,3,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,5,1,7,4,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,5,3,1,4,7]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[2,6,5,3,1,7,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,5,3,4,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,5,3,4,7,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[2,6,5,3,7,1,4]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[2,6,5,3,7,4,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[2,6,5,4,1,3,7]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[2,6,5,4,1,7,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,5,4,3,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[2,6,5,4,3,7,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[2,6,5,4,7,1,3]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[2,6,5,4,7,3,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[2,6,5,7,1,3,4]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[2,6,5,7,1,4,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[2,6,5,7,3,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[2,6,5,7,3,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[2,6,5,7,4,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[2,6,5,7,4,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[2,6,7,1,3,4,5]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[2,6,7,1,3,5,4]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[2,6,7,1,4,3,5]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[2,6,7,1,4,5,3]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[2,6,7,1,5,3,4]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[2,6,7,1,5,4,3]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[2,6,7,3,1,4,5]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[2,6,7,3,1,5,4]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[2,6,7,3,4,1,5]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[2,6,7,3,4,5,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[2,6,7,3,5,1,4]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[2,6,7,3,5,4,1]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[2,6,7,4,1,3,5]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[2,6,7,4,1,5,3]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[2,6,7,4,3,1,5]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[2,6,7,4,3,5,1]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[2,6,7,4,5,1,3]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[2,6,7,4,5,3,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[2,6,7,5,1,3,4]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[2,6,7,5,1,4,3]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[2,6,7,5,3,1,4]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[2,6,7,5,3,4,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[2,6,7,5,4,1,3]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[2,6,7,5,4,3,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[2,7,1,3,4,5,6]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[2,7,1,3,4,6,5]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[2,7,1,3,5,4,6]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[2,7,1,3,5,6,4]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[2,7,1,3,6,4,5]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[2,7,1,3,6,5,4]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[2,7,1,4,3,5,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,1,4,3,6,5]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,1,4,5,3,6]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[2,7,1,4,5,6,3]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[2,7,1,4,6,3,5]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[2,7,1,4,6,5,3]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[2,7,1,5,3,4,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,1,5,3,6,4]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,1,5,4,3,6]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,1,5,4,6,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,1,5,6,3,4]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[2,7,1,5,6,4,3]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[2,7,1,6,3,4,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,1,6,3,5,4]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,1,6,4,3,5]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,1,6,4,5,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,1,6,5,3,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,1,6,5,4,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,1,4,5,6]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[2,7,3,1,4,6,5]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[2,7,3,1,5,4,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,3,1,5,6,4]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[2,7,3,1,6,4,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,1,6,5,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,4,1,5,6]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[2,7,3,4,1,6,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,4,5,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,4,5,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,3,4,6,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,3,4,6,5,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,3,5,1,4,6]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[2,7,3,5,1,6,4]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,5,4,1,6]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,3,5,4,6,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,3,5,6,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,3,5,6,4,1]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,3,6,1,4,5]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[2,7,3,6,1,5,4]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,3,6,4,1,5]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,3,6,4,5,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,3,6,5,1,4]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,3,6,5,4,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,4,1,3,5,6]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[2,7,4,1,3,6,5]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[2,7,4,1,5,3,6]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,4,1,5,6,3]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[2,7,4,1,6,3,5]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,4,1,6,5,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,4,3,1,5,6]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[2,7,4,3,1,6,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,4,3,5,1,6]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,4,3,5,6,1]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,4,3,6,1,5]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,4,3,6,5,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,4,5,1,3,6]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[2,7,4,5,1,6,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,4,5,3,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,4,5,3,6,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,4,5,6,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[2,7,4,5,6,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,4,6,1,3,5]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[2,7,4,6,1,5,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,4,6,3,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,4,6,3,5,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,4,6,5,1,3]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[2,7,4,6,5,3,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,5,1,3,4,6]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[2,7,5,1,3,6,4]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[2,7,5,1,4,3,6]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,5,1,4,6,3]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[2,7,5,1,6,3,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,5,1,6,4,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,5,3,1,4,6]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[2,7,5,3,1,6,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,5,3,4,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,5,3,4,6,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,5,3,6,1,4]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,5,3,6,4,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,5,4,1,3,6]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[2,7,5,4,1,6,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,5,4,3,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[2,7,5,4,3,6,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,5,4,6,1,3]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[2,7,5,4,6,3,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,5,6,1,3,4]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[2,7,5,6,1,4,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,5,6,3,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,5,6,3,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,5,6,4,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[2,7,5,6,4,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,6,1,3,4,5]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[2,7,6,1,3,5,4]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[2,7,6,1,4,3,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,6,1,4,5,3]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[2,7,6,1,5,3,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,6,1,5,4,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,6,3,1,4,5]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[2,7,6,3,1,5,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,6,3,4,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,6,3,4,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,6,3,5,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,6,3,5,4,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,6,4,1,3,5]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[2,7,6,4,1,5,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,6,4,3,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[2,7,6,4,3,5,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,6,4,5,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[2,7,6,4,5,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,6,5,1,3,4]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[2,7,6,5,1,4,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,6,5,3,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[2,7,6,5,3,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[2,7,6,5,4,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[2,7,6,5,4,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,2,4,5,6,7]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[3,1,2,4,5,7,6]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[3,1,2,4,6,5,7]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[3,1,2,4,6,7,5]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[3,1,2,4,7,5,6]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,1,2,4,7,6,5]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,1,2,5,4,6,7]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[3,1,2,5,4,7,6]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[3,1,2,5,6,4,7]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[3,1,2,5,6,7,4]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[3,1,2,5,7,4,6]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,1,2,5,7,6,4]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,1,2,6,4,5,7]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,1,2,6,4,7,5]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,1,2,6,5,4,7]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,1,2,6,5,7,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,1,2,6,7,4,5]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,1,2,6,7,5,4]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,1,2,7,4,5,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,2,7,4,6,5]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,2,7,5,4,6]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,2,7,5,6,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,2,7,6,4,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,2,7,6,5,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,1,4,2,5,6,7]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[3,1,4,2,5,7,6]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[3,1,4,2,6,5,7]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[3,1,4,2,6,7,5]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[3,1,4,2,7,5,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,1,4,2,7,6,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,1,4,5,2,6,7]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[3,1,4,5,2,7,6]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[3,1,4,5,6,2,7]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[3,1,4,5,6,7,2]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[3,1,4,5,7,2,6]=>[1,4,5,7,2,6,3]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[3,1,4,5,7,6,2]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[3,1,4,6,2,5,7]=>[1,4,6,2,5,7,3]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[3,1,4,6,2,7,5]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[3,1,4,6,5,2,7]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[3,1,4,6,5,7,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[3,1,4,6,7,2,5]=>[1,4,6,7,2,5,3]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,1,4,6,7,5,2]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,1,4,7,2,5,6]=>[1,4,7,2,5,6,3]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,1,4,7,2,6,5]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,1,4,7,5,2,6]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,1,4,7,5,6,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,1,4,7,6,2,5]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,1,4,7,6,5,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,1,5,2,4,6,7]=>[1,5,2,4,6,7,3]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[3,1,5,2,4,7,6]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[3,1,5,2,6,4,7]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[3,1,5,2,6,7,4]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[3,1,5,2,7,4,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,1,5,2,7,6,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,1,5,4,2,6,7]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[3,1,5,4,2,7,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,1,5,4,6,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,1,5,4,6,7,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[3,1,5,4,7,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[3,1,5,4,7,6,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[3,1,5,6,2,4,7]=>[1,5,6,2,4,7,3]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[3,1,5,6,2,7,4]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[3,1,5,6,4,2,7]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[3,1,5,6,4,7,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[3,1,5,6,7,2,4]=>[1,5,6,7,2,4,3]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,1,5,6,7,4,2]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,1,5,7,2,4,6]=>[1,5,7,2,4,6,3]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,1,5,7,2,6,4]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,1,5,7,4,2,6]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,1,5,7,4,6,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,1,5,7,6,2,4]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,1,5,7,6,4,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,1,6,2,4,5,7]=>[1,6,2,4,5,7,3]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[3,1,6,2,4,7,5]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[3,1,6,2,5,4,7]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,1,6,2,5,7,4]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[3,1,6,2,7,4,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,1,6,2,7,5,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,1,6,4,2,5,7]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[3,1,6,4,2,7,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,1,6,4,5,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,1,6,4,5,7,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,1,6,4,7,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,1,6,4,7,5,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,1,6,5,2,4,7]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[3,1,6,5,2,7,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,1,6,5,4,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,1,6,5,4,7,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,1,6,5,7,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,1,6,5,7,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,1,6,7,2,4,5]=>[1,6,7,2,4,5,3]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,1,6,7,2,5,4]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,1,6,7,4,2,5]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,1,6,7,4,5,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,1,6,7,5,2,4]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,1,6,7,5,4,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,1,7,2,4,5,6]=>[1,7,2,4,5,6,3]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,2,4,6,5]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,2,5,4,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,2,5,6,4]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,2,6,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,2,6,5,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,4,2,5,6]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,4,2,6,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,4,5,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,4,5,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,4,6,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,4,6,5,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,5,2,4,6]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,5,2,6,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,5,4,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,5,4,6,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,5,6,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,5,6,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,6,2,4,5]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,6,2,5,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,6,4,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,6,4,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,6,5,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,1,7,6,5,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,1,4,5,6,7]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>{{1},{2,3,7},{4},{5},{6}}
[3,2,1,4,5,7,6]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[3,2,1,4,6,5,7]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[3,2,1,4,6,7,5]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,2,1,4,7,5,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,2,1,4,7,6,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,2,1,5,4,6,7]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[3,2,1,5,4,7,6]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[3,2,1,5,6,4,7]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[3,2,1,5,6,7,4]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,2,1,5,7,4,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,1,5,7,6,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,1,6,4,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,2,1,6,4,7,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,2,1,6,5,7,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,2,1,6,7,4,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,2,1,6,7,5,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,2,1,7,4,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,1,7,4,6,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,2,1,7,5,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,2,1,7,5,6,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,1,7,6,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,1,5,6,7]=>[1,5,6,7,2,4,3]=>[1,4,7,3,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,2,4,1,5,7,6]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,4,1,6,5,7]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,2,4,1,6,7,5]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,2,4,1,7,5,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,1,7,6,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,5,1,6,7]=>[1,6,7,2,4,5,3]=>[1,4,7,5,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,2,4,5,1,7,6]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,5,6,1,7]=>[1,7,2,4,5,6,3]=>[1,4,7,5,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,5,6,7,1]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>{{1},{2},{3,7},{4},{5},{6}}
[3,2,4,5,7,1,6]=>[1,6,2,4,5,7,3]=>[1,4,7,5,6,2,3]=>{{1},{2,4,5,6},{3,7}}
[3,2,4,5,7,6,1]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[3,2,4,6,1,5,7]=>[1,5,7,2,4,6,3]=>[1,4,7,6,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,4,6,1,7,5]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,6,5,1,7]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,4,6,5,7,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[3,2,4,6,7,1,5]=>[1,5,2,4,6,7,3]=>[1,4,7,5,2,6,3]=>{{1},{2,4,5},{3,7},{6}}
[3,2,4,6,7,5,1]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[3,2,4,7,1,5,6]=>[1,5,6,2,4,7,3]=>[1,4,7,6,5,2,3]=>{{1},{2,4,6},{3,7},{5}}
[3,2,4,7,1,6,5]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[3,2,4,7,5,1,6]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[3,2,4,7,5,6,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,2,4,7,6,1,5]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[3,2,4,7,6,5,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,2,5,1,4,6,7]=>[1,4,6,7,2,5,3]=>[1,5,7,4,3,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,2,5,1,4,7,6]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,2,5,1,6,4,7]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,2,5,1,6,7,4]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,2,5,1,7,4,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,1,7,6,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,4,1,6,7]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,2,5,4,1,7,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,4,6,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,4,6,7,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[3,2,5,4,7,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,2,5,4,7,6,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[3,2,5,6,1,4,7]=>[1,4,7,2,5,6,3]=>[1,5,7,4,6,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,2,5,6,1,7,4]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,6,4,1,7]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,5,6,4,7,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[3,2,5,6,7,1,4]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>{{1},{2,4},{3,7},{5},{6}}
[3,2,5,6,7,4,1]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[3,2,5,7,1,4,6]=>[1,4,6,2,5,7,3]=>[1,5,7,4,6,2,3]=>{{1},{2,5,6},{3,7},{4}}
[3,2,5,7,1,6,4]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[3,2,5,7,4,1,6]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[3,2,5,7,4,6,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,2,5,7,6,1,4]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[3,2,5,7,6,4,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,2,6,1,4,5,7]=>[1,4,5,7,2,6,3]=>[1,6,7,4,5,3,2]=>{{1},{2,3,6,7},{4},{5}}
[3,2,6,1,4,7,5]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,2,6,1,5,4,7]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[3,2,6,1,5,7,4]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,6,1,7,4,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,1,7,5,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,4,1,5,7]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,2,6,4,1,7,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,4,5,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,4,5,7,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,2,6,4,7,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[3,2,6,4,7,5,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,2,6,5,1,4,7]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,2,6,5,1,7,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,5,4,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,2,6,5,4,7,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,2,6,5,7,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[3,2,6,5,7,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,2,6,7,1,4,5]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>{{1},{2,5},{3,7},{4},{6}}
[3,2,6,7,1,5,4]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[3,2,6,7,4,1,5]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[3,2,6,7,4,5,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,2,6,7,5,1,4]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[3,2,6,7,5,4,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,2,7,1,4,5,6]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>{{1},{2,6},{3,7},{4},{5}}
[3,2,7,1,4,6,5]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[3,2,7,1,5,4,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,2,7,1,5,6,4]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[3,2,7,1,6,4,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,7,1,6,5,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,7,4,1,5,6]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[3,2,7,4,1,6,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,7,4,5,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,7,4,5,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,2,7,4,6,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,2,7,4,6,5,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,2,7,5,1,4,6]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[3,2,7,5,1,6,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,7,5,4,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,2,7,5,4,6,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,2,7,5,6,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,2,7,5,6,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,2,7,6,1,4,5]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[3,2,7,6,1,5,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,2,7,6,4,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,2,7,6,4,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,2,7,6,5,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,2,7,6,5,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,1,2,5,6,7]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[3,4,1,2,5,7,6]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,4,1,2,6,5,7]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,4,1,2,6,7,5]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,4,1,2,7,5,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,1,2,7,6,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,1,5,2,6,7]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[3,4,1,5,2,7,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,4,1,5,6,2,7]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[3,4,1,5,6,7,2]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,4,1,5,7,2,6]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,4,1,5,7,6,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,4,1,6,2,5,7]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[3,4,1,6,2,7,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,4,1,6,5,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,4,1,6,5,7,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,4,1,6,7,2,5]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,1,6,7,5,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,1,7,2,5,6]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,1,7,2,6,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,1,7,5,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,1,7,5,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,1,7,6,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,1,7,6,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[3,4,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,4,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,4,2,1,6,7,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,2,1,7,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,5,1,6,7]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,2,5,1,7,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,5,6,1,7]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,5,6,7,1]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[3,4,2,5,7,1,6]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[3,4,2,5,7,6,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,4,2,6,1,5,7]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[3,4,2,6,1,7,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,6,5,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,4,2,6,7,1,5]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[3,4,2,6,7,5,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,4,2,7,1,5,6]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[3,4,2,7,1,6,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,4,2,7,5,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,4,2,7,5,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,2,7,6,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,4,2,7,6,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,5,1,2,6,7]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,4,5,1,2,7,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,5,1,6,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,4,5,1,6,7,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,5,1,7,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,5,1,7,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,5,2,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,4,5,2,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,5,2,6,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,4,5,2,6,7,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,4,5,2,7,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,4,5,2,7,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,5,6,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,5,6,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,5,6,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,5,6,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[3,4,5,6,7,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[3,4,5,7,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,4,5,7,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,4,5,7,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,4,5,7,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,4,5,7,6,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[3,4,5,7,6,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[3,4,6,1,2,5,7]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,4,6,1,2,7,5]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,6,1,5,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,4,6,1,5,7,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,4,6,1,7,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,6,1,7,5,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,4,6,2,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,4,6,2,1,7,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,4,6,2,5,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,4,6,2,5,7,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[3,4,6,2,7,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[3,4,6,2,7,5,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,6,5,1,2,7]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,6,5,1,7,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,4,6,5,2,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,4,6,5,2,7,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[3,4,6,5,7,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[3,4,6,5,7,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[3,4,6,7,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[3,4,6,7,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[3,4,6,7,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[3,4,6,7,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[3,4,6,7,5,1,2]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[3,4,6,7,5,2,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[3,4,7,1,2,5,6]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[3,4,7,1,2,6,5]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,4,7,1,5,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[3,4,7,1,5,6,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[3,4,7,1,6,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,4,7,1,6,5,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,4,7,2,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[3,4,7,2,1,6,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,4,7,2,5,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,4,7,2,5,6,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[3,4,7,2,6,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[3,4,7,2,6,5,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,4,7,5,1,2,6]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,4,7,5,1,6,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,4,7,5,2,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,4,7,5,2,6,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[3,4,7,5,6,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[3,4,7,5,6,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[3,4,7,6,1,2,5]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[3,4,7,6,1,5,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[3,4,7,6,2,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[3,4,7,6,2,5,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[3,4,7,6,5,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[3,4,7,6,5,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[3,5,1,2,4,6,7]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[3,5,1,2,4,7,6]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,5,1,2,6,4,7]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,5,1,2,6,7,4]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,5,1,2,7,4,6]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,1,2,7,6,4]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,1,4,2,6,7]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[3,5,1,4,2,7,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,5,1,4,6,2,7]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[3,5,1,4,6,7,2]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,5,1,4,7,2,6]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,1,4,7,6,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,1,6,2,4,7]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[3,5,1,6,2,7,4]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,5,1,6,4,2,7]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,5,1,6,4,7,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,5,1,6,7,2,4]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,1,6,7,4,2]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,1,7,2,4,6]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,1,7,2,6,4]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,1,7,4,2,6]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,1,7,4,6,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,1,7,6,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,1,7,6,4,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,1,4,6,7]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[3,5,2,1,4,7,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,2,1,6,4,7]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,5,2,1,6,7,4]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,2,1,7,4,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,1,7,6,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,4,1,6,7]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,2,4,1,7,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,4,6,1,7]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,4,6,7,1]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[3,5,2,4,7,1,6]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[3,5,2,4,7,6,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,5,2,6,1,4,7]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,2,6,1,7,4]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,6,4,1,7]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,2,6,4,7,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,5,2,6,7,1,4]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[3,5,2,6,7,4,1]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,5,2,7,1,4,6]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[3,5,2,7,1,6,4]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,5,2,7,4,1,6]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,5,2,7,4,6,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,2,7,6,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,5,2,7,6,4,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,1,2,6,7]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,5,4,1,2,7,6]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,1,6,2,7]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,5,4,1,6,7,2]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,4,1,7,2,6]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,4,1,7,6,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,4,2,1,6,7]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[3,5,4,2,1,7,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,4,2,6,1,7]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[3,5,4,2,6,7,1]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[3,5,4,2,7,1,6]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[3,5,4,2,7,6,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,6,1,2,7]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,6,1,7,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,4,6,2,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,4,6,2,7,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,4,6,7,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[3,5,4,6,7,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[3,5,4,7,1,2,6]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,5,4,7,1,6,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,5,4,7,2,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,5,4,7,2,6,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[3,5,4,7,6,1,2]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[3,5,4,7,6,2,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[3,5,6,1,2,4,7]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,5,6,1,2,7,4]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,6,1,4,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,5,6,1,4,7,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,6,1,7,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,1,7,4,2]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,2,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,5,6,2,1,7,4]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,2,4,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,2,4,7,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[3,5,6,2,7,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[3,5,6,2,7,4,1]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,6,4,1,2,7]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,6,4,1,7,2]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,4,2,1,7]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[3,5,6,4,2,7,1]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,5,6,4,7,1,2]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[3,5,6,4,7,2,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[3,5,6,7,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[3,5,6,7,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[3,5,6,7,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[3,5,6,7,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[3,5,6,7,4,1,2]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[3,5,6,7,4,2,1]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[3,5,7,1,2,4,6]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[3,5,7,1,2,6,4]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[3,5,7,1,4,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[3,5,7,1,4,6,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[3,5,7,1,6,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,5,7,1,6,4,2]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,5,7,2,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[3,5,7,2,1,6,4]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,5,7,2,4,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,5,7,2,4,6,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[3,5,7,2,6,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[3,5,7,2,6,4,1]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[3,5,7,4,1,2,6]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[3,5,7,4,1,6,2]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,5,7,4,2,1,6]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,5,7,4,2,6,1]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[3,5,7,4,6,1,2]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[3,5,7,4,6,2,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[3,5,7,6,1,2,4]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[3,5,7,6,1,4,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[3,5,7,6,2,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[3,5,7,6,2,4,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[3,5,7,6,4,1,2]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[3,5,7,6,4,2,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[3,6,1,2,4,5,7]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[3,6,1,2,4,7,5]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[3,6,1,2,5,4,7]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[3,6,1,2,5,7,4]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[3,6,1,2,7,4,5]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,1,2,7,5,4]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,1,4,2,5,7]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[3,6,1,4,2,7,5]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[3,6,1,4,5,2,7]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[3,6,1,4,5,7,2]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[3,6,1,4,7,2,5]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,6,1,4,7,5,2]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[3,6,1,5,2,4,7]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[3,6,1,5,2,7,4]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[3,6,1,5,4,2,7]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[3,6,1,5,4,7,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[3,6,1,5,7,2,4]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,6,1,5,7,4,2]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[3,6,1,7,2,4,5]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,6,1,7,2,5,4]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,1,7,4,2,5]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,1,7,4,5,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,1,7,5,2,4]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,6,1,7,5,4,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,1,4,5,7]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[3,6,2,1,4,7,5]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[3,6,2,1,5,4,7]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[3,6,2,1,5,7,4]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[3,6,2,1,7,4,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,1,7,5,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,4,1,5,7]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[3,6,2,4,1,7,5]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,4,5,1,7]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,4,5,7,1]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[3,6,2,4,7,1,5]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[3,6,2,4,7,5,1]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[3,6,2,5,1,4,7]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[3,6,2,5,1,7,4]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,5,4,1,7]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,2,5,4,7,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[3,6,2,5,7,1,4]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[3,6,2,5,7,4,1]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[3,6,2,7,1,4,5]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[3,6,2,7,1,5,4]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[3,6,2,7,4,1,5]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[3,6,2,7,4,5,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,2,7,5,1,4]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[3,6,2,7,5,4,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,4,1,2,5,7]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[3,6,4,1,2,7,5]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,4,1,5,2,7]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[3,6,4,1,5,7,2]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[3,6,4,1,7,2,5]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,4,1,7,5,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,4,2,1,5,7]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[3,6,4,2,1,7,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,4,2,5,1,7]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,4,2,5,7,1]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[3,6,4,2,7,1,5]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[3,6,4,2,7,5,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,4,5,1,2,7]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,4,5,1,7,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,4,5,2,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,4,5,2,7,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,4,5,7,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[3,6,4,5,7,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[3,6,4,7,1,2,5]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[3,6,4,7,1,5,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[3,6,4,7,2,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[3,6,4,7,2,5,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[3,6,4,7,5,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[3,6,4,7,5,2,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[3,6,5,1,2,4,7]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[3,6,5,1,2,7,4]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,5,1,4,2,7]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[3,6,5,1,4,7,2]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[3,6,5,1,7,2,4]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,1,7,4,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,2,1,4,7]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[3,6,5,2,1,7,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,2,4,1,7]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,2,4,7,1]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[3,6,5,2,7,1,4]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[3,6,5,2,7,4,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,5,4,1,2,7]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,5,4,1,7,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,4,2,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[3,6,5,4,2,7,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[3,6,5,4,7,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[3,6,5,4,7,2,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[3,6,5,7,1,2,4]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[3,6,5,7,1,4,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[3,6,5,7,2,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[3,6,5,7,2,4,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[3,6,5,7,4,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[3,6,5,7,4,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[3,6,7,1,2,4,5]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[3,6,7,1,2,5,4]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[3,6,7,1,4,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[3,6,7,1,4,5,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[3,6,7,1,5,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[3,6,7,1,5,4,2]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[3,6,7,2,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[3,6,7,2,1,5,4]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[3,6,7,2,4,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[3,6,7,2,4,5,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[3,6,7,2,5,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[3,6,7,2,5,4,1]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[3,6,7,4,1,2,5]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[3,6,7,4,1,5,2]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[3,6,7,4,2,1,5]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[3,6,7,4,2,5,1]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[3,6,7,4,5,1,2]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[3,6,7,4,5,2,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[3,6,7,5,1,2,4]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[3,6,7,5,1,4,2]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[3,6,7,5,2,1,4]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[3,6,7,5,2,4,1]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[3,6,7,5,4,1,2]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[3,6,7,5,4,2,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[3,7,1,2,4,5,6]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[3,7,1,2,4,6,5]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[3,7,1,2,5,4,6]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,1,2,5,6,4]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[3,7,1,2,6,4,5]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,1,2,6,5,4]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,1,4,2,5,6]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[3,7,1,4,2,6,5]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[3,7,1,4,5,2,6]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[3,7,1,4,5,6,2]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[3,7,1,4,6,2,5]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[3,7,1,4,6,5,2]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[3,7,1,5,2,4,6]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[3,7,1,5,2,6,4]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[3,7,1,5,4,2,6]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[3,7,1,5,4,6,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,1,5,6,2,4]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[3,7,1,5,6,4,2]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[3,7,1,6,2,4,5]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,7,1,6,2,5,4]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,7,1,6,4,2,5]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,7,1,6,4,5,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,1,6,5,2,4]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,7,1,6,5,4,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,2,1,4,5,6]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[3,7,2,1,4,6,5]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[3,7,2,1,5,4,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,2,1,5,6,4]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[3,7,2,1,6,4,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,2,1,6,5,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,2,4,1,5,6]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[3,7,2,4,1,6,5]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,7,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[3,7,2,4,5,6,1]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[3,7,2,4,6,1,5]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[3,7,2,4,6,5,1]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[3,7,2,5,1,4,6]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[3,7,2,5,1,6,4]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,7,2,5,4,1,6]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,7,2,5,4,6,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,2,5,6,1,4]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[3,7,2,5,6,4,1]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[3,7,2,6,1,4,5]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[3,7,2,6,1,5,4]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[3,7,2,6,4,1,5]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[3,7,2,6,4,5,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,2,6,5,1,4]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[3,7,2,6,5,4,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,4,1,2,5,6]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[3,7,4,1,2,6,5]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,4,1,5,2,6]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[3,7,4,1,5,6,2]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[3,7,4,1,6,2,5]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,7,4,1,6,5,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,4,2,1,5,6]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[3,7,4,2,1,6,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,4,2,5,1,6]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[3,7,4,2,5,6,1]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[3,7,4,2,6,1,5]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[3,7,4,2,6,5,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,4,5,1,2,6]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,4,5,1,6,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,4,5,2,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,4,5,2,6,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,4,5,6,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,4,5,6,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,4,6,1,2,5]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,4,6,1,5,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,4,6,2,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,4,6,2,5,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,4,6,5,1,2]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,4,6,5,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,5,1,2,4,6]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[3,7,5,1,2,6,4]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,5,1,4,2,6]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[3,7,5,1,4,6,2]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[3,7,5,1,6,2,4]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,7,5,1,6,4,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,5,2,1,4,6]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[3,7,5,2,1,6,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,5,2,4,1,6]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[3,7,5,2,4,6,1]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[3,7,5,2,6,1,4]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[3,7,5,2,6,4,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,5,4,1,2,6]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,5,4,1,6,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,5,4,2,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[3,7,5,4,2,6,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[3,7,5,4,6,1,2]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,5,4,6,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,5,6,1,2,4]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[3,7,5,6,1,4,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[3,7,5,6,2,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[3,7,5,6,2,4,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[3,7,5,6,4,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,5,6,4,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,6,1,2,4,5]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[3,7,6,1,2,5,4]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,6,1,4,2,5]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[3,7,6,1,4,5,2]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[3,7,6,1,5,2,4]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[3,7,6,1,5,4,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,6,2,1,4,5]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[3,7,6,2,1,5,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,6,2,4,1,5]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[3,7,6,2,4,5,1]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[3,7,6,2,5,1,4]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[3,7,6,2,5,4,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,6,4,1,2,5]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,6,4,1,5,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,6,4,2,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[3,7,6,4,2,5,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[3,7,6,4,5,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,6,4,5,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,6,5,1,2,4]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[3,7,6,5,1,4,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[3,7,6,5,2,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[3,7,6,5,2,4,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[3,7,6,5,4,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[3,7,6,5,4,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,1,2,3,5,6,7]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[4,1,2,3,5,7,6]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,1,2,3,6,5,7]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,1,2,3,6,7,5]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,1,2,3,7,5,6]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,1,2,3,7,6,5]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,1,2,5,3,6,7]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[4,1,2,5,3,7,6]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,1,2,5,6,3,7]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[4,1,2,5,6,7,3]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[4,1,2,5,7,3,6]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[4,1,2,5,7,6,3]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,1,2,6,3,5,7]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[4,1,2,6,3,7,5]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,1,2,6,5,3,7]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,1,2,6,5,7,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,1,2,6,7,3,5]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,1,2,6,7,5,3]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,1,2,7,3,5,6]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,1,2,7,3,6,5]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,1,2,7,5,3,6]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,1,2,7,5,6,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,1,2,7,6,3,5]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,1,2,7,6,5,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,1,3,2,5,6,7]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[4,1,3,2,5,7,6]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[4,1,3,2,6,5,7]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[4,1,3,2,6,7,5]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[4,1,3,2,7,5,6]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,1,3,2,7,6,5]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,1,3,5,2,6,7]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[4,1,3,5,2,7,6]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[4,1,3,5,6,2,7]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[4,1,3,5,6,7,2]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[4,1,3,5,7,2,6]=>[1,3,5,7,2,6,4]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[4,1,3,5,7,6,2]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[4,1,3,6,2,5,7]=>[1,3,6,2,5,7,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[4,1,3,6,2,7,5]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[4,1,3,6,5,2,7]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[4,1,3,6,5,7,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[4,1,3,6,7,2,5]=>[1,3,6,7,2,5,4]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[4,1,3,6,7,5,2]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[4,1,3,7,2,5,6]=>[1,3,7,2,5,6,4]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,1,3,7,2,6,5]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,1,3,7,5,2,6]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,1,3,7,5,6,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,1,3,7,6,2,5]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,1,3,7,6,5,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,1,5,2,3,6,7]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[4,1,5,2,3,7,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,1,5,2,6,3,7]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[4,1,5,2,6,7,3]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,1,5,2,7,3,6]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[4,1,5,2,7,6,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,1,5,3,2,6,7]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,1,5,3,2,7,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,1,5,3,6,2,7]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[4,1,5,3,6,7,2]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[4,1,5,3,7,2,6]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[4,1,5,3,7,6,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,1,5,6,2,3,7]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[4,1,5,6,2,7,3]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,1,5,6,3,2,7]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,1,5,6,3,7,2]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[4,1,5,6,7,2,3]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,1,5,6,7,3,2]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,1,5,7,2,3,6]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[4,1,5,7,2,6,3]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,1,5,7,3,2,6]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,1,5,7,3,6,2]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[4,1,5,7,6,2,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,1,5,7,6,3,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,1,6,2,3,5,7]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,1,6,2,3,7,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,1,6,2,5,3,7]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,1,6,2,5,7,3]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,1,6,2,7,3,5]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,1,6,2,7,5,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,1,6,3,2,5,7]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,1,6,3,2,7,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,1,6,3,5,2,7]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,1,6,3,5,7,2]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,1,6,3,7,2,5]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,1,6,3,7,5,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,1,6,5,2,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,1,6,5,2,7,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,1,6,5,3,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,1,6,5,3,7,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,1,6,5,7,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,1,6,5,7,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,1,6,7,2,3,5]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,1,6,7,2,5,3]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,1,6,7,3,2,5]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,1,6,7,3,5,2]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,1,6,7,5,2,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,1,6,7,5,3,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,1,7,2,3,5,6]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,2,3,6,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,2,5,3,6]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,2,5,6,3]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,2,6,3,5]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,2,6,5,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,3,2,5,6]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,3,2,6,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,3,5,2,6]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,3,5,6,2]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,3,6,2,5]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,3,6,5,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,5,2,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,5,2,6,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,5,3,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,5,3,6,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,5,6,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,5,6,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,6,2,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,6,2,5,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,6,3,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,6,3,5,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,6,5,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,1,7,6,5,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,1,3,5,6,7]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>{{1},{2,4,7},{3},{5},{6}}
[4,2,1,3,5,7,6]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[4,2,1,3,6,5,7]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[4,2,1,3,6,7,5]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[4,2,1,3,7,5,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,2,1,3,7,6,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,2,1,5,3,6,7]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[4,2,1,5,3,7,6]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,2,1,5,6,3,7]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[4,2,1,5,6,7,3]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,2,1,5,7,3,6]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,1,5,7,6,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,1,6,3,5,7]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,2,1,6,3,7,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,2,1,6,5,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,2,1,6,5,7,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,2,1,6,7,3,5]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,2,1,6,7,5,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,2,1,7,3,5,6]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,1,7,3,6,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,1,7,5,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,1,7,5,6,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,1,7,6,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,1,7,6,5,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,1,5,6,7]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,2,3,1,5,7,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,3,1,6,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,2,3,1,6,7,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,2,3,1,7,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,1,7,6,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,5,1,6,7]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,2,3,5,1,7,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,5,6,1,7]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,5,6,7,1]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[4,2,3,5,7,1,6]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,2,3,5,7,6,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,2,3,6,1,5,7]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,3,6,1,7,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,6,5,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,3,6,5,7,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,2,3,6,7,1,5]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[4,2,3,6,7,5,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,2,3,7,1,5,6]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[4,2,3,7,1,6,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,2,3,7,5,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,2,3,7,5,6,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,2,3,7,6,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,2,3,7,6,5,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,2,5,1,3,6,7]=>[1,3,6,7,2,5,4]=>[1,5,3,7,4,6,2]=>{{1},{2,4,5,7},{3},{6}}
[4,2,5,1,3,7,6]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,2,5,1,6,3,7]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,2,5,1,6,7,3]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,2,5,1,7,3,6]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,1,7,6,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,3,1,6,7]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,2,5,3,1,7,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,3,6,1,7]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,3,6,7,1]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[4,2,5,3,7,1,6]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,2,5,3,7,6,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,2,5,6,1,3,7]=>[1,3,7,2,5,6,4]=>[1,5,3,7,6,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,2,5,6,1,7,3]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,6,3,1,7]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,5,6,3,7,1]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[4,2,5,6,7,1,3]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>{{1},{2,3},{4,7},{5},{6}}
[4,2,5,6,7,3,1]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[4,2,5,7,1,3,6]=>[1,3,6,2,5,7,4]=>[1,5,3,7,6,2,4]=>{{1},{2,5,6},{3},{4,7}}
[4,2,5,7,1,6,3]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,2,5,7,3,1,6]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,2,5,7,3,6,1]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[4,2,5,7,6,1,3]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[4,2,5,7,6,3,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,2,6,1,3,5,7]=>[1,3,5,7,2,6,4]=>[1,6,3,7,5,4,2]=>{{1},{2,4,6,7},{3},{5}}
[4,2,6,1,3,7,5]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,2,6,1,5,3,7]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[4,2,6,1,5,7,3]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,6,1,7,3,5]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,6,1,7,5,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,6,3,1,5,7]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,2,6,3,1,7,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,6,3,5,1,7]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,6,3,5,7,1]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[4,2,6,3,7,1,5]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[4,2,6,3,7,5,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,2,6,5,1,3,7]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,2,6,5,1,7,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,6,5,3,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,2,6,5,3,7,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,2,6,5,7,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[4,2,6,5,7,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,2,6,7,1,3,5]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>{{1},{2,5},{3},{4,7},{6}}
[4,2,6,7,1,5,3]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,2,6,7,3,1,5]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,2,6,7,3,5,1]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,2,6,7,5,1,3]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[4,2,6,7,5,3,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,2,7,1,3,5,6]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>{{1},{2,6},{3},{4,7},{5}}
[4,2,7,1,3,6,5]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[4,2,7,1,5,3,6]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[4,2,7,1,5,6,3]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,2,7,1,6,3,5]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,7,3,1,5,6]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,2,7,3,1,6,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,7,3,5,1,6]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,7,3,5,6,1]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,2,7,3,6,1,5]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[4,2,7,3,6,5,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,2,7,5,1,3,6]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[4,2,7,5,1,6,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,7,5,3,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,2,7,5,3,6,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,2,7,5,6,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,2,7,5,6,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,2,7,6,1,3,5]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[4,2,7,6,1,5,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,2,7,6,3,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,2,7,6,3,5,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,2,7,6,5,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,2,7,6,5,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,1,2,5,6,7]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[4,3,1,2,5,7,6]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,3,1,2,6,5,7]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,3,1,2,6,7,5]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,3,1,2,7,5,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,1,2,7,6,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,1,5,2,6,7]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,3,1,5,2,7,6]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,3,1,5,6,2,7]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,3,1,5,6,7,2]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,3,1,5,7,2,6]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,3,1,5,7,6,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,3,1,6,2,5,7]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,3,1,6,2,7,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,3,1,6,5,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,3,1,6,5,7,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,3,1,6,7,2,5]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,1,6,7,5,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,1,7,2,5,6]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,1,7,2,6,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,1,7,5,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,1,7,5,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,1,7,6,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,1,7,6,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,1,5,6,7]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>{{1},{2,3,4,7},{5},{6}}
[4,3,2,1,5,7,6]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,3,2,1,6,7,5]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,2,1,7,5,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,5,1,6,7]=>[1,6,7,2,5,3,4]=>[1,5,4,7,3,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,2,5,1,7,6]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,5,6,1,7]=>[1,7,2,5,6,3,4]=>[1,5,4,7,6,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,5,6,7,1]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>{{1},{2},{3,4,7},{5},{6}}
[4,3,2,5,7,1,6]=>[1,6,2,5,7,3,4]=>[1,5,4,7,6,2,3]=>{{1},{2,5,6},{3,4,7}}
[4,3,2,5,7,6,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,3,2,6,1,5,7]=>[1,5,7,2,6,3,4]=>[1,6,4,7,5,3,2]=>{{1},{2,3,4,6,7},{5}}
[4,3,2,6,1,7,5]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,6,5,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,2,6,5,7,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,3,2,6,7,1,5]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>{{1},{2,5},{3,4,7},{6}}
[4,3,2,6,7,5,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,3,2,7,1,5,6]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>{{1},{2,6},{3,4,7},{5}}
[4,3,2,7,1,6,5]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,3,2,7,5,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,3,2,7,5,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,2,7,6,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,3,2,7,6,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,5,1,2,6,7]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,3,5,1,2,7,6]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,5,1,6,2,7]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,3,5,1,6,7,2]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,5,1,7,2,6]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,1,7,6,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,2,1,6,7]=>[1,6,7,2,3,5,4]=>[1,3,5,7,4,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,3,5,2,1,7,6]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,2,6,1,7]=>[1,7,2,6,3,5,4]=>[1,6,5,7,4,3,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,2,6,7,1]=>[1,2,6,7,3,5,4]=>[1,2,5,7,4,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,3,5,2,7,1,6]=>[1,6,2,7,3,5,4]=>[1,6,5,7,4,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,3,5,2,7,6,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,5,6,1,2,7]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,5,6,1,7,2]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,6,2,1,7]=>[1,7,2,3,5,6,4]=>[1,3,5,7,6,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,5,6,2,7,1]=>[1,2,7,3,5,6,4]=>[1,2,5,7,6,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,5,6,7,1,2]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[4,3,5,6,7,2,1]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>{{1},{2},{3},{4,7},{5},{6}}
[4,3,5,7,1,2,6]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[4,3,5,7,1,6,2]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,3,5,7,2,1,6]=>[1,6,2,3,5,7,4]=>[1,3,5,7,6,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,3,5,7,2,6,1]=>[1,2,6,3,5,7,4]=>[1,2,5,7,6,3,4]=>{{1},{2},{3,5,6},{4,7}}
[4,3,5,7,6,1,2]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,3,5,7,6,2,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,3,6,1,2,5,7]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[4,3,6,1,2,7,5]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,6,1,5,2,7]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[4,3,6,1,5,7,2]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[4,3,6,1,7,2,5]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,1,7,5,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,2,1,5,7]=>[1,5,7,2,3,6,4]=>[1,3,6,7,5,4,2]=>{{1},{2,3,4,6,7},{5}}
[4,3,6,2,1,7,5]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,2,5,1,7]=>[1,7,2,5,3,6,4]=>[1,5,6,7,3,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,2,5,7,1]=>[1,2,5,7,3,6,4]=>[1,2,6,7,5,4,3]=>{{1},{2},{3,4,6,7},{5}}
[4,3,6,2,7,1,5]=>[1,5,2,7,3,6,4]=>[1,5,6,7,2,4,3]=>{{1},{2,5},{3,4,6,7}}
[4,3,6,2,7,5,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,6,5,1,2,7]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,6,5,1,7,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,5,2,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,3,6,5,2,7,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,3,6,5,7,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,3,6,5,7,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,3,6,7,1,2,5]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[4,3,6,7,1,5,2]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[4,3,6,7,2,1,5]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>{{1},{2,3,5},{4,7},{6}}
[4,3,6,7,2,5,1]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>{{1},{2},{3,5},{4,7},{6}}
[4,3,6,7,5,1,2]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,3,6,7,5,2,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,3,7,1,2,5,6]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[4,3,7,1,2,6,5]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,3,7,1,5,2,6]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[4,3,7,1,5,6,2]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[4,3,7,1,6,2,5]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,3,7,1,6,5,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,3,7,2,1,5,6]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>{{1},{2,3,6},{4,7},{5}}
[4,3,7,2,1,6,5]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,3,7,2,5,1,6]=>[1,6,2,5,3,7,4]=>[1,5,6,7,3,2,4]=>{{1},{2,3,5,6},{4,7}}
[4,3,7,2,5,6,1]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>{{1},{2},{3,6},{4,7},{5}}
[4,3,7,2,6,1,5]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>{{1},{2,5},{3,6},{4,7}}
[4,3,7,2,6,5,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,3,7,5,1,2,6]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,3,7,5,1,6,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,3,7,5,2,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,3,7,5,2,6,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,3,7,5,6,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,3,7,5,6,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,3,7,6,1,2,5]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,3,7,6,1,5,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,3,7,6,2,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,3,7,6,2,5,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,3,7,6,5,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,3,7,6,5,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,1,2,3,6,7]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,5,1,2,3,7,6]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,1,2,6,3,7]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,5,1,2,6,7,3]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,5,1,2,7,3,6]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,1,2,7,6,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,1,3,2,6,7]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[4,5,1,3,2,7,6]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,5,1,3,6,2,7]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[4,5,1,3,6,7,2]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[4,5,1,3,7,2,6]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,5,1,3,7,6,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,5,1,6,2,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,5,1,6,2,7,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,5,1,6,3,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,5,1,6,3,7,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,5,1,6,7,2,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,1,6,7,3,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,1,7,2,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,5,1,7,2,6,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,5,1,7,3,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,5,1,7,3,6,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,5,1,7,6,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,1,7,6,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,1,3,6,7]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[4,5,2,1,3,7,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,5,2,1,6,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,5,2,1,6,7,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,2,1,7,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,1,7,6,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,3,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,2,3,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,3,6,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,3,6,7,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,5,2,3,7,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,5,2,3,7,6,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,2,6,1,3,7]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[4,5,2,6,1,7,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,6,3,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,5,2,6,3,7,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,5,2,6,7,1,3]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[4,5,2,6,7,3,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,5,2,7,1,3,6]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[4,5,2,7,1,6,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,5,2,7,3,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,5,2,7,3,6,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,2,7,6,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,5,2,7,6,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,3,1,2,6,7]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,5,3,1,2,7,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,3,1,6,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,5,3,1,6,7,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,3,1,7,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,1,7,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[4,5,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,2,6,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,2,6,7,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[4,5,3,2,7,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[4,5,3,2,7,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,3,6,1,2,7]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,3,6,1,7,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,6,2,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[4,5,3,6,2,7,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,3,6,7,1,2]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,5,3,6,7,2,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[4,5,3,7,1,2,6]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,5,3,7,1,6,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,5,3,7,2,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[4,5,3,7,2,6,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[4,5,3,7,6,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,3,7,6,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,6,1,2,3,7]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,6,1,2,7,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,6,1,3,2,7]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,5,6,1,3,7,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,5,6,1,7,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,6,1,7,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,6,2,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,5,6,2,1,7,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,6,2,3,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,6,2,3,7,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,6,2,7,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[4,5,6,2,7,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,6,3,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,6,3,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,6,3,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[4,5,6,3,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,5,6,3,7,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,6,3,7,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[4,5,6,7,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[4,5,6,7,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[4,5,6,7,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[4,5,6,7,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[4,5,6,7,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[4,5,6,7,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[4,5,7,1,2,3,6]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,5,7,1,2,6,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,5,7,1,3,2,6]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[4,5,7,1,3,6,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[4,5,7,1,6,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,5,7,1,6,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,5,7,2,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[4,5,7,2,1,6,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,5,7,2,3,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,5,7,2,3,6,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,5,7,2,6,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[4,5,7,2,6,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,5,7,3,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,5,7,3,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,5,7,3,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,5,7,3,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,5,7,3,6,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,5,7,3,6,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[4,5,7,6,1,2,3]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[4,5,7,6,1,3,2]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[4,5,7,6,2,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[4,5,7,6,2,3,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[4,5,7,6,3,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[4,5,7,6,3,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[4,6,1,2,3,5,7]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,6,1,2,3,7,5]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,1,2,5,3,7]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,6,1,2,5,7,3]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,6,1,2,7,3,5]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,1,2,7,5,3]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,1,3,2,5,7]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[4,6,1,3,2,7,5]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[4,6,1,3,5,2,7]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[4,6,1,3,5,7,2]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[4,6,1,3,7,2,5]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,6,1,3,7,5,2]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[4,6,1,5,2,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,6,1,5,2,7,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,6,1,5,3,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,6,1,5,3,7,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,6,1,5,7,2,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,1,5,7,3,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,1,7,2,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,1,7,2,5,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,1,7,3,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,1,7,3,5,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,1,7,5,2,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,1,7,5,3,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,1,3,5,7]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[4,6,2,1,3,7,5]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[4,6,2,1,5,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,6,2,1,5,7,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,2,1,7,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,1,7,5,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,3,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,2,3,1,7,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,3,5,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,3,5,7,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,6,2,3,7,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,6,2,3,7,5,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,2,5,1,3,7]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[4,6,2,5,1,7,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,5,3,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,2,5,3,7,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,6,2,5,7,1,3]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[4,6,2,5,7,3,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,6,2,7,1,3,5]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[4,6,2,7,1,5,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,6,2,7,3,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,6,2,7,3,5,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,2,7,5,1,3]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[4,6,2,7,5,3,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,3,1,2,5,7]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,6,3,1,2,7,5]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,6,3,1,5,7,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,3,1,7,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,3,1,7,5,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,3,2,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[4,6,3,2,1,7,5]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,3,2,5,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,3,2,5,7,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[4,6,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[4,6,3,2,7,5,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,3,5,1,2,7]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,3,5,1,7,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,3,5,2,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[4,6,3,5,2,7,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,3,5,7,1,2]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,6,3,5,7,2,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[4,6,3,7,1,2,5]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,6,3,7,1,5,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,6,3,7,2,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[4,6,3,7,2,5,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[4,6,3,7,5,1,2]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,3,7,5,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,5,1,2,3,7]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,5,1,2,7,3]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,5,1,3,2,7]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[4,6,5,1,3,7,2]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[4,6,5,1,7,2,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,5,1,7,3,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,5,2,1,3,7]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[4,6,5,2,1,7,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,5,2,3,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,5,2,3,7,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,5,2,7,1,3]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[4,6,5,2,7,3,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,5,3,1,2,7]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,5,3,1,7,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,5,3,2,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[4,6,5,3,2,7,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[4,6,5,3,7,1,2]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,5,3,7,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[4,6,5,7,1,2,3]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[4,6,5,7,1,3,2]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[4,6,5,7,2,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[4,6,5,7,2,3,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[4,6,5,7,3,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[4,6,5,7,3,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[4,6,7,1,2,3,5]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[4,6,7,1,2,5,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[4,6,7,1,3,2,5]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[4,6,7,1,3,5,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[4,6,7,1,5,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[4,6,7,1,5,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[4,6,7,2,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[4,6,7,2,1,5,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[4,6,7,2,3,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[4,6,7,2,3,5,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[4,6,7,2,5,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[4,6,7,2,5,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[4,6,7,3,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[4,6,7,3,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[4,6,7,3,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[4,6,7,3,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[4,6,7,3,5,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[4,6,7,3,5,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[4,6,7,5,1,2,3]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[4,6,7,5,1,3,2]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[4,6,7,5,2,1,3]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[4,6,7,5,2,3,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[4,6,7,5,3,1,2]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[4,6,7,5,3,2,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[4,7,1,2,3,5,6]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[4,7,1,2,3,6,5]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,1,2,5,3,6]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[4,7,1,2,5,6,3]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[4,7,1,2,6,3,5]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,7,1,2,6,5,3]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,1,3,2,5,6]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[4,7,1,3,2,6,5]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[4,7,1,3,5,2,6]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[4,7,1,3,5,6,2]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[4,7,1,3,6,2,5]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[4,7,1,3,6,5,2]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[4,7,1,5,2,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[4,7,1,5,2,6,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[4,7,1,5,3,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[4,7,1,5,3,6,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[4,7,1,5,6,2,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[4,7,1,5,6,3,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[4,7,1,6,2,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,1,6,2,5,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,1,6,3,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,1,6,3,5,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,1,6,5,2,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,1,6,5,3,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,2,1,3,5,6]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[4,7,2,1,3,6,5]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[4,7,2,1,5,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[4,7,2,1,5,6,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[4,7,2,1,6,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,2,1,6,5,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,2,3,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[4,7,2,3,1,6,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,2,3,5,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,2,3,5,6,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[4,7,2,3,6,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[4,7,2,3,6,5,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,2,5,1,3,6]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[4,7,2,5,1,6,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,2,5,3,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,2,5,3,6,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[4,7,2,5,6,1,3]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[4,7,2,5,6,3,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[4,7,2,6,1,3,5]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[4,7,2,6,1,5,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[4,7,2,6,3,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[4,7,2,6,3,5,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,7,2,6,5,1,3]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[4,7,2,6,5,3,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,3,1,2,5,6]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[4,7,3,1,2,6,5]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,3,1,5,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[4,7,3,1,5,6,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[4,7,3,1,6,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,3,1,6,5,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,3,2,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[4,7,3,2,1,6,5]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,3,2,5,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,3,2,5,6,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[4,7,3,2,6,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[4,7,3,2,6,5,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,3,5,1,2,6]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,7,3,5,1,6,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,3,5,2,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[4,7,3,5,2,6,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[4,7,3,5,6,1,2]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[4,7,3,5,6,2,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[4,7,3,6,1,2,5]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[4,7,3,6,1,5,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[4,7,3,6,2,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[4,7,3,6,2,5,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[4,7,3,6,5,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,3,6,5,2,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,5,1,2,3,6]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,5,1,2,6,3]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,5,1,3,2,6]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[4,7,5,1,3,6,2]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[4,7,5,1,6,2,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,5,1,6,3,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,5,2,1,3,6]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[4,7,5,2,1,6,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,5,2,3,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,5,2,3,6,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,5,2,6,1,3]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[4,7,5,2,6,3,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,5,3,1,2,6]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,5,3,1,6,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,5,3,2,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[4,7,5,3,2,6,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[4,7,5,3,6,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,5,3,6,2,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[4,7,5,6,1,2,3]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,5,6,1,3,2]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[4,7,5,6,2,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[4,7,5,6,2,3,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,5,6,3,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,5,6,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,6,1,2,3,5]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[4,7,6,1,2,5,3]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[4,7,6,1,3,2,5]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[4,7,6,1,3,5,2]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[4,7,6,1,5,2,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[4,7,6,1,5,3,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[4,7,6,2,1,3,5]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[4,7,6,2,1,5,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[4,7,6,2,3,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[4,7,6,2,3,5,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[4,7,6,2,5,1,3]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[4,7,6,2,5,3,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[4,7,6,3,1,2,5]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[4,7,6,3,1,5,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[4,7,6,3,2,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[4,7,6,3,2,5,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[4,7,6,3,5,1,2]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[4,7,6,3,5,2,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[4,7,6,5,1,2,3]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,6,5,1,3,2]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[4,7,6,5,2,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[4,7,6,5,2,3,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,6,5,3,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[4,7,6,5,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,1,2,3,4,6,7]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,1,2,3,4,7,6]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,1,2,3,6,4,7]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,1,2,3,6,7,4]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,1,2,3,7,4,6]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,1,2,3,7,6,4]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,1,2,4,3,6,7]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[5,1,2,4,3,7,6]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,1,2,4,6,3,7]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[5,1,2,4,6,7,3]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[5,1,2,4,7,3,6]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[5,1,2,4,7,6,3]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,1,2,6,3,4,7]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,1,2,6,3,7,4]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,1,2,6,4,3,7]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,1,2,6,4,7,3]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,1,2,6,7,3,4]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,1,2,6,7,4,3]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,1,2,7,3,4,6]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,1,2,7,3,6,4]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,1,2,7,4,3,6]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,1,2,7,4,6,3]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,1,2,7,6,3,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,1,2,7,6,4,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,1,3,2,4,6,7]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[5,1,3,2,4,7,6]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,1,3,2,6,4,7]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[5,1,3,2,6,7,4]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[5,1,3,2,7,4,6]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[5,1,3,2,7,6,4]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,1,3,4,2,6,7]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[5,1,3,4,2,7,6]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[5,1,3,4,6,2,7]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[5,1,3,4,6,7,2]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[5,1,3,4,7,2,6]=>[1,3,4,7,2,6,5]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[5,1,3,4,7,6,2]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[5,1,3,6,2,4,7]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[5,1,3,6,2,7,4]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,1,3,6,4,2,7]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,1,3,6,4,7,2]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[5,1,3,6,7,2,4]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,1,3,6,7,4,2]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,1,3,7,2,4,6]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,1,3,7,2,6,4]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,1,3,7,4,2,6]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,1,3,7,4,6,2]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,1,3,7,6,2,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,1,3,7,6,4,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,1,4,2,3,6,7]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[5,1,4,2,3,7,6]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,1,4,2,6,3,7]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[5,1,4,2,6,7,3]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[5,1,4,2,7,3,6]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[5,1,4,2,7,6,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,1,4,3,2,6,7]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[5,1,4,3,2,7,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,1,4,3,6,2,7]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[5,1,4,3,6,7,2]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[5,1,4,3,7,2,6]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[5,1,4,3,7,6,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,1,4,6,2,3,7]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[5,1,4,6,2,7,3]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[5,1,4,6,3,2,7]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[5,1,4,6,3,7,2]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[5,1,4,6,7,2,3]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[5,1,4,6,7,3,2]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[5,1,4,7,2,3,6]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[5,1,4,7,2,6,3]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[5,1,4,7,3,2,6]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[5,1,4,7,3,6,2]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[5,1,4,7,6,2,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,1,4,7,6,3,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,1,6,2,3,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,1,6,2,3,7,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,1,6,2,4,3,7]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,1,6,2,4,7,3]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[5,1,6,2,7,3,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,1,6,2,7,4,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,1,6,3,2,4,7]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[5,1,6,3,2,7,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,1,6,3,4,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,1,6,3,4,7,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,1,6,3,7,2,4]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,1,6,3,7,4,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,1,6,4,2,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,1,6,4,2,7,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,1,6,4,3,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,1,6,4,3,7,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,1,6,4,7,2,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,1,6,4,7,3,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,1,6,7,2,3,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,1,6,7,2,4,3]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,1,6,7,3,2,4]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,1,6,7,3,4,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,1,6,7,4,2,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,1,6,7,4,3,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,1,7,2,3,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,2,3,6,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,2,4,3,6]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,2,4,6,3]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,2,6,3,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,2,6,4,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,3,2,4,6]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,3,2,6,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,3,4,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,3,4,6,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,3,6,2,4]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,3,6,4,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,4,2,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,4,2,6,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,4,3,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,4,3,6,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,4,6,2,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,4,6,3,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,6,2,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,6,2,4,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,6,3,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,6,3,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,6,4,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,1,7,6,4,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,1,3,4,6,7]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>{{1},{2,5,7},{3},{4},{6}}
[5,2,1,3,4,7,6]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[5,2,1,3,6,4,7]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[5,2,1,3,6,7,4]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,2,1,3,7,4,6]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,1,3,7,6,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,1,4,3,6,7]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[5,2,1,4,3,7,6]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,2,1,4,6,3,7]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[5,2,1,4,6,7,3]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[5,2,1,4,7,3,6]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[5,2,1,4,7,6,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,2,1,6,3,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,2,1,6,3,7,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,2,1,6,4,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,2,1,6,4,7,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,2,1,6,7,3,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,2,1,6,7,4,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,2,1,7,3,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,2,1,7,3,6,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,2,1,7,4,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,2,1,7,4,6,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,2,1,7,6,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,1,7,6,4,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,1,4,6,7]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[5,2,3,1,4,7,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,2,3,1,6,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,2,3,1,6,7,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,2,3,1,7,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,1,7,6,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,4,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,2,3,4,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,4,6,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,4,6,7,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,2,3,4,7,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,2,3,4,7,6,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,2,3,6,1,4,7]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[5,2,3,6,1,7,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,6,4,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,2,3,6,4,7,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,2,3,6,7,1,4]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[5,2,3,6,7,4,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,2,3,7,1,4,6]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,2,3,7,4,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,2,3,7,4,6,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,2,3,7,6,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,2,3,7,6,4,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,2,4,1,3,6,7]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,2,4,1,3,7,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,4,1,6,3,7]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,2,4,1,6,7,3]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,2,4,1,7,3,6]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,2,4,1,7,6,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,4,3,1,6,7]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,2,4,3,1,7,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,2,4,3,6,1,7]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,2,4,3,6,7,1]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[5,2,4,3,7,1,6]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,2,4,3,7,6,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,2,4,6,1,3,7]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,4,6,1,7,3]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,4,6,3,1,7]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,4,6,3,7,1]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[5,2,4,6,7,1,3]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[5,2,4,6,7,3,1]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[5,2,4,7,1,3,6]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[5,2,4,7,1,6,3]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[5,2,4,7,3,1,6]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[5,2,4,7,3,6,1]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[5,2,4,7,6,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,2,4,7,6,3,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,2,6,1,3,4,7]=>[1,3,4,7,2,6,5]=>[1,6,3,4,7,5,2]=>{{1},{2,5,6,7},{3},{4}}
[5,2,6,1,3,7,4]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,6,1,4,3,7]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[5,2,6,1,4,7,3]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[5,2,6,1,7,3,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,6,1,7,4,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,6,3,1,4,7]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[5,2,6,3,1,7,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,6,3,4,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,6,3,4,7,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,2,6,3,7,1,4]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[5,2,6,3,7,4,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,2,6,4,1,3,7]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,2,6,4,1,7,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,6,4,3,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,2,6,4,3,7,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,2,6,4,7,1,3]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[5,2,6,4,7,3,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,2,6,7,1,3,4]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>{{1},{2,4},{3},{5,7},{6}}
[5,2,6,7,1,4,3]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[5,2,6,7,3,1,4]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[5,2,6,7,3,4,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,2,6,7,4,1,3]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[5,2,6,7,4,3,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,2,7,1,3,4,6]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>{{1},{2,6},{3},{4},{5,7}}
[5,2,7,1,3,6,4]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,2,7,1,4,3,6]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[5,2,7,1,4,6,3]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[5,2,7,1,6,3,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,2,7,1,6,4,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,2,7,3,1,4,6]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[5,2,7,3,1,6,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,2,7,3,4,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,2,7,3,4,6,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,2,7,3,6,1,4]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[5,2,7,3,6,4,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,2,7,4,1,3,6]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,2,7,4,3,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,2,7,4,3,6,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,2,7,4,6,1,3]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[5,2,7,4,6,3,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,2,7,6,1,3,4]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[5,2,7,6,1,4,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,2,7,6,3,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,2,7,6,3,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,2,7,6,4,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,2,7,6,4,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,1,2,4,6,7]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[5,3,1,2,4,7,6]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,3,1,2,6,4,7]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,3,1,2,6,7,4]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,3,1,2,7,4,6]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,1,2,7,6,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,1,4,2,6,7]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[5,3,1,4,2,7,6]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,3,1,4,6,2,7]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[5,3,1,4,6,7,2]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[5,3,1,4,7,2,6]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[5,3,1,4,7,6,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,3,1,6,2,4,7]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[5,3,1,6,2,7,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,3,1,6,4,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,3,1,6,4,7,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,3,1,6,7,2,4]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,3,1,6,7,4,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,3,1,7,2,4,6]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,1,7,2,6,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,1,7,4,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,1,7,4,6,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,3,1,7,6,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,3,1,7,6,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,1,4,6,7]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>{{1},{2,3,5,7},{4},{6}}
[5,3,2,1,4,7,6]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,3,2,1,6,4,7]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,3,2,1,6,7,4]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,3,2,1,7,4,6]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,1,7,6,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,4,1,6,7]=>[1,6,7,2,4,3,5]=>[1,4,5,3,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,3,2,4,1,7,6]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,4,6,1,7]=>[1,7,2,4,6,3,5]=>[1,4,5,6,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,4,6,7,1]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>{{1},{2},{3,5,7},{4},{6}}
[5,3,2,4,7,1,6]=>[1,6,2,4,7,3,5]=>[1,4,5,6,7,2,3]=>{{1},{2,4,6},{3,5,7}}
[5,3,2,4,7,6,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,3,2,6,1,4,7]=>[1,4,7,2,6,3,5]=>[1,6,5,4,7,3,2]=>{{1},{2,3,5,6,7},{4}}
[5,3,2,6,1,7,4]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,6,4,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,2,6,4,7,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,3,2,6,7,1,4]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>{{1},{2,4},{3,5,7},{6}}
[5,3,2,6,7,4,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,3,2,7,1,4,6]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>{{1},{2,6},{3,5,7},{4}}
[5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,3,2,7,4,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,3,2,7,4,6,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,2,7,6,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,3,2,7,6,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,4,1,2,6,7]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,3,4,1,2,7,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,4,1,6,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,3,4,1,6,7,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,3,4,1,7,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,4,1,7,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,3,4,2,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,3,4,2,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,3,4,2,6,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,3,4,2,6,7,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,3,4,2,7,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,3,4,2,7,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,4,6,1,2,7]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,4,6,1,7,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,3,4,6,2,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,3,4,6,2,7,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,4,6,7,1,2]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,3,4,6,7,2,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,3,4,7,1,2,6]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,3,4,7,1,6,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,3,4,7,2,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,3,4,7,2,6,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,3,4,7,6,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,3,4,7,6,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,3,6,1,2,4,7]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[5,3,6,1,2,7,4]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,6,1,4,2,7]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[5,3,6,1,4,7,2]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[5,3,6,1,7,2,4]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,3,6,1,7,4,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,3,6,2,1,4,7]=>[1,4,7,2,3,6,5]=>[1,3,6,4,7,5,2]=>{{1},{2,3,5,6,7},{4}}
[5,3,6,2,1,7,4]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,3,6,2,4,1,7]=>[1,7,2,4,3,6,5]=>[1,4,6,3,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,3,6,2,4,7,1]=>[1,2,4,7,3,6,5]=>[1,2,6,4,7,5,3]=>{{1},{2},{3,5,6,7},{4}}
[5,3,6,2,7,1,4]=>[1,4,2,7,3,6,5]=>[1,4,6,2,7,5,3]=>{{1},{2,4},{3,5,6,7}}
[5,3,6,2,7,4,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,6,4,1,2,7]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,6,4,1,7,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,3,6,4,2,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,3,6,4,2,7,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,3,6,4,7,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,3,6,4,7,2,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,3,6,7,1,2,4]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[5,3,6,7,1,4,2]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[5,3,6,7,2,1,4]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>{{1},{2,3,4},{5,7},{6}}
[5,3,6,7,2,4,1]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>{{1},{2},{3,4},{5,7},{6}}
[5,3,6,7,4,1,2]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,3,6,7,4,2,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,3,7,1,2,4,6]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[5,3,7,1,2,6,4]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,3,7,1,4,2,6]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[5,3,7,1,4,6,2]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[5,3,7,1,6,2,4]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,3,7,1,6,4,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,3,7,2,1,4,6]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>{{1},{2,3,6},{4},{5,7}}
[5,3,7,2,1,6,4]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,3,7,2,4,1,6]=>[1,6,2,4,3,7,5]=>[1,4,6,3,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,3,7,2,4,6,1]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>{{1},{2},{3,6},{4},{5,7}}
[5,3,7,2,6,1,4]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>{{1},{2,4},{3,6},{5,7}}
[5,3,7,2,6,4,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,3,7,4,1,2,6]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,3,7,4,1,6,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,3,7,4,2,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,3,7,4,2,6,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,3,7,4,6,1,2]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,3,7,4,6,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,3,7,6,1,2,4]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,3,7,6,1,4,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,3,7,6,2,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,3,7,6,2,4,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,3,7,6,4,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,3,7,6,4,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,1,2,3,6,7]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,4,1,2,3,7,6]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,1,2,6,3,7]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,4,1,2,6,7,3]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,4,1,2,7,3,6]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,1,2,7,6,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,1,3,2,6,7]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[5,4,1,3,2,7,6]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,4,1,3,6,2,7]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,4,1,3,6,7,2]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,4,1,3,7,2,6]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,4,1,3,7,6,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,4,1,6,2,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,4,1,6,2,7,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,4,1,6,3,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,4,1,6,3,7,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,4,1,6,7,2,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,4,1,6,7,3,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,4,1,7,2,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,4,1,7,2,6,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,4,1,7,3,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,4,1,7,3,6,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,4,1,7,6,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,4,1,7,6,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,1,3,6,7]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>{{1},{2,4,5,7},{3},{6}}
[5,4,2,1,3,7,6]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,4,2,1,6,3,7]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,4,2,1,6,7,3]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,4,2,1,7,3,6]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,1,7,6,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,3,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,4,2,3,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,3,6,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,3,6,7,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,4,2,3,7,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,4,2,3,7,6,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,2,6,1,3,7]=>[1,3,7,2,6,4,5]=>[1,6,3,5,7,4,2]=>{{1},{2,4,5,6,7},{3}}
[5,4,2,6,1,7,3]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,6,3,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,4,2,6,3,7,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,4,2,6,7,1,3]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>{{1},{2,3},{4,5,7},{6}}
[5,4,2,6,7,3,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,4,2,7,1,3,6]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>{{1},{2,6},{3},{4,5,7}}
[5,4,2,7,1,6,3]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,4,2,7,3,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,4,2,7,3,6,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,2,7,6,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,4,2,7,6,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,3,1,2,6,7]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,4,3,1,2,7,6]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,3,1,6,2,7]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,4,3,1,6,7,2]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,4,3,1,7,2,6]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,4,3,1,7,6,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,4,3,2,1,6,7]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>{{1},{2,3,4,5,7},{6}}
[5,4,3,2,1,7,6]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,4,3,2,6,1,7]=>[1,7,2,6,3,4,5]=>[1,6,4,5,7,3,2]=>{{1},{2,3,4,5,6,7}}
[5,4,3,2,6,7,1]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>{{1},{2},{3,4,5,7},{6}}
[5,4,3,2,7,1,6]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>{{1},{2,6},{3,4,5,7}}
[5,4,3,2,7,6,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,3,6,1,2,7]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,3,6,1,7,2]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,4,3,6,2,1,7]=>[1,7,2,3,6,4,5]=>[1,3,6,5,7,4,2]=>{{1},{2,3,4,5,6,7}}
[5,4,3,6,2,7,1]=>[1,2,7,3,6,4,5]=>[1,2,6,5,7,4,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,3,6,7,1,2]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,4,3,6,7,2,1]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>{{1},{2},{3},{4,5,7},{6}}
[5,4,3,7,1,2,6]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,4,3,7,1,6,2]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,4,3,7,2,1,6]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>{{1},{2,3,6},{4,5,7}}
[5,4,3,7,2,6,1]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>{{1},{2},{3,6},{4,5,7}}
[5,4,3,7,6,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,3,7,6,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,6,1,2,3,7]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,6,1,2,7,3]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,6,1,3,2,7]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[5,4,6,1,3,7,2]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,4,6,1,7,2,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,4,6,1,7,3,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,4,6,2,1,3,7]=>[1,3,7,2,4,6,5]=>[1,4,3,6,7,5,2]=>{{1},{2,4,5,6,7},{3}}
[5,4,6,2,1,7,3]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,4,6,2,3,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,4,6,2,3,7,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,6,2,7,1,3]=>[1,3,2,7,4,6,5]=>[1,3,2,6,7,5,4]=>{{1},{2,3},{4,5,6,7}}
[5,4,6,2,7,3,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,6,3,1,2,7]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,6,3,1,7,2]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,4,6,3,2,1,7]=>[1,7,2,3,4,6,5]=>[1,3,4,6,7,5,2]=>{{1},{2,3,4,5,6,7}}
[5,4,6,3,2,7,1]=>[1,2,7,3,4,6,5]=>[1,2,4,6,7,5,3]=>{{1},{2},{3,4,5,6,7}}
[5,4,6,3,7,1,2]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,6,3,7,2,1]=>[1,2,3,7,4,6,5]=>[1,2,3,6,7,5,4]=>{{1},{2},{3},{4,5,6,7}}
[5,4,6,7,1,2,3]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,4,6,7,1,3,2]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[5,4,6,7,2,1,3]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>{{1},{2,3},{4},{5,7},{6}}
[5,4,6,7,2,3,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,4,6,7,3,1,2]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,4,6,7,3,2,1]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>{{1},{2},{3},{4},{5,7},{6}}
[5,4,7,1,2,3,6]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,4,7,1,2,6,3]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,4,7,1,3,2,6]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[5,4,7,1,3,6,2]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[5,4,7,1,6,2,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,4,7,1,6,3,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,4,7,2,1,3,6]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>{{1},{2,4,6},{3},{5,7}}
[5,4,7,2,1,6,3]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,4,7,2,3,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,4,7,2,3,6,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,4,7,2,6,1,3]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>{{1},{2,3},{4,6},{5,7}}
[5,4,7,2,6,3,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,4,7,3,1,2,6]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,4,7,3,1,6,2]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,4,7,3,2,1,6]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>{{1},{2,3,4,6},{5,7}}
[5,4,7,3,2,6,1]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>{{1},{2},{3,4,6},{5,7}}
[5,4,7,3,6,1,2]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,4,7,3,6,2,1]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>{{1},{2},{3},{4,6},{5,7}}
[5,4,7,6,1,2,3]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,4,7,6,1,3,2]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,4,7,6,2,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,4,7,6,2,3,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,4,7,6,3,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,4,7,6,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,1,2,3,4,7]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,1,2,3,7,4]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,1,2,4,3,7]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,6,1,2,4,7,3]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,6,1,2,7,3,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,1,2,7,4,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,1,3,2,4,7]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,6,1,3,2,7,4]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,6,1,3,4,2,7]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[5,6,1,3,4,7,2]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[5,6,1,3,7,2,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,6,1,3,7,4,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,6,1,4,2,3,7]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,6,1,4,2,7,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,6,1,4,3,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,6,1,4,3,7,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,6,1,4,7,2,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,6,1,4,7,3,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,6,1,7,2,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,1,7,2,4,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,1,7,3,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,1,7,3,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,1,7,4,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,1,7,4,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,1,3,4,7]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[5,6,2,1,3,7,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,6,2,1,4,3,7]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,6,2,1,4,7,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,6,2,1,7,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,1,7,4,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,3,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,6,2,3,1,7,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,3,4,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,3,4,7,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,2,3,7,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,6,2,3,7,4,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,2,4,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,6,2,4,1,7,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,4,3,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,2,4,3,7,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,6,2,4,7,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,6,2,4,7,3,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,6,2,7,1,3,4]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[5,6,2,7,1,4,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,6,2,7,3,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,6,2,7,3,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,2,7,4,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,6,2,7,4,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,3,1,2,4,7]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,6,3,1,2,7,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,3,1,4,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,6,3,1,4,7,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,6,3,1,7,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,3,1,7,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,3,2,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[5,6,3,2,1,7,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,3,2,4,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,3,2,4,7,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[5,6,3,2,7,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[5,6,3,2,7,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,3,4,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,3,4,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,3,4,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,3,4,7,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,3,4,7,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,3,7,1,2,4]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,6,3,7,1,4,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,6,3,7,2,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[5,6,3,7,2,4,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[5,6,3,7,4,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,3,7,4,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,4,1,2,3,7]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,4,1,2,7,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,4,1,3,2,7]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,6,4,1,3,7,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,6,4,1,7,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,4,1,7,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,4,2,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[5,6,4,2,1,7,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,4,2,3,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,4,2,3,7,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,4,2,7,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[5,6,4,2,7,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,4,3,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,4,3,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[5,6,4,3,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[5,6,4,3,7,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,4,3,7,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[5,6,4,7,1,2,3]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,4,7,1,3,2]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,6,4,7,2,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[5,6,4,7,2,3,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,4,7,3,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,4,7,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,1,2,4,3]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[5,6,7,1,3,2,4]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[5,6,7,1,3,4,2]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[5,6,7,1,4,2,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[5,6,7,1,4,3,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[5,6,7,2,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[5,6,7,2,1,4,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[5,6,7,2,3,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,2,4,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[5,6,7,2,4,3,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[5,6,7,3,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[5,6,7,3,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[5,6,7,3,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[5,6,7,3,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[5,6,7,3,4,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,3,4,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,4,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[5,6,7,4,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[5,6,7,4,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,4,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,6,7,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[5,7,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,1,2,3,6,4]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,1,2,4,3,6]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[5,7,1,2,4,6,3]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[5,7,1,2,6,3,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,1,2,6,4,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,1,3,2,4,6]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[5,7,1,3,2,6,4]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[5,7,1,3,4,2,6]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[5,7,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[5,7,1,3,6,2,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[5,7,1,3,6,4,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[5,7,1,4,2,3,6]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[5,7,1,4,2,6,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[5,7,1,4,3,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[5,7,1,4,3,6,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[5,7,1,4,6,2,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[5,7,1,4,6,3,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[5,7,1,6,2,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,1,6,3,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,1,6,4,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,1,6,4,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[5,7,2,1,3,6,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[5,7,2,1,4,3,6]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[5,7,2,1,4,6,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[5,7,2,1,6,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,1,6,4,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,3,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[5,7,2,3,1,6,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,3,4,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,2,3,6,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[5,7,2,3,6,4,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,2,4,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[5,7,2,4,1,6,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,4,3,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,2,4,3,6,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[5,7,2,4,6,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[5,7,2,4,6,3,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[5,7,2,6,1,3,4]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[5,7,2,6,1,4,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[5,7,2,6,3,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[5,7,2,6,3,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,2,6,4,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[5,7,2,6,4,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,3,1,2,4,6]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[5,7,3,1,2,6,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,3,1,4,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[5,7,3,1,4,6,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[5,7,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,3,1,6,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,3,2,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[5,7,3,2,1,6,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,3,2,4,6,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[5,7,3,2,6,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[5,7,3,2,6,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,3,4,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,3,4,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,3,4,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,3,4,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,3,6,1,2,4]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[5,7,3,6,1,4,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[5,7,3,6,2,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[5,7,3,6,2,4,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[5,7,3,6,4,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,3,6,4,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,4,1,2,3,6]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,4,1,2,6,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,4,1,3,2,6]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[5,7,4,1,3,6,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[5,7,4,1,6,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,4,1,6,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,4,2,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[5,7,4,2,1,6,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,4,2,3,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,4,2,3,6,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,4,2,6,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[5,7,4,2,6,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,4,3,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,4,3,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,4,3,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[5,7,4,3,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[5,7,4,3,6,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,4,3,6,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[5,7,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,4,6,1,3,2]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[5,7,4,6,2,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[5,7,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[5,7,6,1,2,3,4]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,1,2,4,3]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[5,7,6,1,3,2,4]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[5,7,6,1,3,4,2]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[5,7,6,1,4,2,3]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[5,7,6,1,4,3,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[5,7,6,2,1,3,4]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[5,7,6,2,1,4,3]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[5,7,6,2,3,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[5,7,6,2,3,4,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,2,4,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[5,7,6,2,4,3,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[5,7,6,3,1,2,4]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[5,7,6,3,1,4,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[5,7,6,3,2,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[5,7,6,3,2,4,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[5,7,6,3,4,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,3,4,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,4,1,2,3]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,4,1,3,2]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[5,7,6,4,2,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[5,7,6,4,2,3,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,4,3,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[5,7,6,4,3,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,1,2,3,4,5,7]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,1,2,3,4,7,5]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,1,2,3,5,4,7]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,1,2,3,5,7,4]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,1,2,3,7,4,5]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,1,2,3,7,5,4]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,1,2,4,3,5,7]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,1,2,4,3,7,5]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,1,2,4,5,3,7]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[6,1,2,4,5,7,3]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[6,1,2,4,7,3,5]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,1,2,4,7,5,3]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,1,2,5,3,4,7]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,1,2,5,3,7,4]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,1,2,5,4,3,7]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,1,2,5,4,7,3]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,1,2,5,7,3,4]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,1,2,5,7,4,3]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,1,2,7,3,4,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,1,2,7,3,5,4]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,1,2,7,4,3,5]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,1,2,7,4,5,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,1,2,7,5,3,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,1,2,7,5,4,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,1,3,2,4,5,7]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,1,3,2,4,7,5]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,1,3,2,5,4,7]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[6,1,3,2,5,7,4]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[6,1,3,2,7,4,5]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,1,3,2,7,5,4]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,1,3,4,2,5,7]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[6,1,3,4,2,7,5]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[6,1,3,4,5,2,7]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[6,1,3,4,5,7,2]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[6,1,3,4,7,2,5]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[6,1,3,4,7,5,2]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[6,1,3,5,2,4,7]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[6,1,3,5,2,7,4]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[6,1,3,5,4,2,7]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[6,1,3,5,4,7,2]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[6,1,3,5,7,2,4]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[6,1,3,5,7,4,2]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[6,1,3,7,2,4,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,1,3,7,2,5,4]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,1,3,7,4,2,5]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,1,3,7,4,5,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,1,3,7,5,2,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,1,3,7,5,4,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,1,4,2,3,5,7]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,1,4,2,3,7,5]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,1,4,2,5,3,7]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[6,1,4,2,5,7,3]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[6,1,4,2,7,3,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,1,4,2,7,5,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,1,4,3,2,5,7]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[6,1,4,3,2,7,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,1,4,3,5,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,1,4,3,5,7,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,1,4,3,7,2,5]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[6,1,4,3,7,5,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,1,4,5,2,3,7]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[6,1,4,5,2,7,3]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[6,1,4,5,3,2,7]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[6,1,4,5,3,7,2]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[6,1,4,5,7,2,3]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[6,1,4,5,7,3,2]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[6,1,4,7,2,3,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,1,4,7,2,5,3]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,1,4,7,3,2,5]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,1,4,7,3,5,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,1,4,7,5,2,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,1,4,7,5,3,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,1,5,2,3,4,7]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,1,5,2,3,7,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,1,5,2,4,3,7]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,1,5,2,4,7,3]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[6,1,5,2,7,3,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,1,5,2,7,4,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,1,5,3,2,4,7]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[6,1,5,3,2,7,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,1,5,3,4,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,1,5,3,4,7,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,1,5,3,7,2,4]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,1,5,3,7,4,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,1,5,4,2,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,1,5,4,2,7,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,1,5,4,3,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,1,5,4,3,7,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,1,5,4,7,2,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,1,5,4,7,3,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,1,5,7,2,3,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,1,5,7,2,4,3]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,1,5,7,3,2,4]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,1,5,7,3,4,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,1,5,7,4,2,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,1,5,7,4,3,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,1,7,2,3,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,2,3,5,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,2,4,3,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,2,4,5,3]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,2,5,3,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,2,5,4,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,3,2,4,5]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,3,2,5,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,3,4,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,3,4,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,3,5,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,3,5,4,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,4,2,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,4,2,5,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,4,3,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,4,3,5,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,4,5,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,4,5,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,5,2,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,5,2,4,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,5,3,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,5,3,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,5,4,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,1,7,5,4,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,1,3,4,5,7]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>{{1},{2,6,7},{3},{4},{5}}
[6,2,1,3,4,7,5]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[6,2,1,3,5,4,7]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[6,2,1,3,5,7,4]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[6,2,1,3,7,4,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,2,1,3,7,5,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,2,1,4,3,5,7]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,2,1,4,3,7,5]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,2,1,4,5,3,7]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[6,2,1,4,5,7,3]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[6,2,1,4,7,3,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,2,1,4,7,5,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,2,1,5,3,4,7]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,2,1,5,3,7,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,2,1,5,4,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,2,1,5,4,7,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,2,1,5,7,3,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,2,1,5,7,4,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,2,1,7,3,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,1,7,3,5,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,1,7,4,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,1,7,4,5,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,1,7,5,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,1,7,5,4,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,1,4,5,7]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[6,2,3,1,4,7,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,2,3,1,5,4,7]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,2,3,1,5,7,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,2,3,1,7,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,1,7,5,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,4,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,2,3,4,1,7,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,4,5,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,4,5,7,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,2,3,4,7,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,2,3,4,7,5,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,2,3,5,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,2,3,5,1,7,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,5,4,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,3,5,4,7,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,2,3,5,7,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,2,3,5,7,4,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,2,3,7,1,4,5]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[6,2,3,7,1,5,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,2,3,7,4,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,2,3,7,4,5,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,2,3,7,5,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,2,3,7,5,4,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,2,4,1,3,5,7]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[6,2,4,1,3,7,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,2,4,1,5,3,7]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,2,4,1,5,7,3]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,2,4,1,7,3,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,4,1,7,5,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,4,3,1,5,7]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,2,4,3,1,7,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,4,3,5,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,4,3,5,7,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,2,4,3,7,1,5]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,2,4,3,7,5,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,2,4,5,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,2,4,5,1,7,3]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,4,5,3,1,7]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,4,5,3,7,1]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[6,2,4,5,7,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,2,4,5,7,3,1]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[6,2,4,7,1,3,5]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[6,2,4,7,1,5,3]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[6,2,4,7,3,1,5]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[6,2,4,7,3,5,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,2,4,7,5,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,2,4,7,5,3,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,2,5,1,3,4,7]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[6,2,5,1,3,7,4]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,2,5,1,4,3,7]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[6,2,5,1,4,7,3]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,2,5,1,7,3,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,5,1,7,4,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,5,3,1,4,7]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,2,5,3,1,7,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,5,3,4,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,5,3,4,7,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,2,5,3,7,1,4]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[6,2,5,3,7,4,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,2,5,4,1,3,7]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,2,5,4,1,7,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,5,4,3,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,2,5,4,3,7,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,2,5,4,7,1,3]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[6,2,5,4,7,3,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,2,5,7,1,3,4]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[6,2,5,7,1,4,3]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[6,2,5,7,3,1,4]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[6,2,5,7,3,4,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,2,5,7,4,1,3]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[6,2,5,7,4,3,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,2,7,1,3,4,5]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>{{1},{2,5},{3},{4},{6,7}}
[6,2,7,1,3,5,4]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[6,2,7,1,4,3,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,2,7,1,4,5,3]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[6,2,7,1,5,3,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,2,7,1,5,4,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,2,7,3,1,4,5]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[6,2,7,3,1,5,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,2,7,3,4,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,2,7,3,4,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,2,7,3,5,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,2,7,3,5,4,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,2,7,4,1,3,5]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[6,2,7,4,1,5,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,2,7,4,3,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,2,7,4,3,5,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,2,7,4,5,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,2,7,4,5,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,2,7,5,1,3,4]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[6,2,7,5,1,4,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,2,7,5,3,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,2,7,5,3,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,2,7,5,4,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,2,7,5,4,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,1,2,4,5,7]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[6,3,1,2,4,7,5]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,3,1,2,5,4,7]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,3,1,2,5,7,4]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,3,1,2,7,4,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,1,2,7,5,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,1,4,2,5,7]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[6,3,1,4,2,7,5]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,3,1,4,5,2,7]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[6,3,1,4,5,7,2]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[6,3,1,4,7,2,5]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,3,1,4,7,5,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,3,1,5,2,4,7]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[6,3,1,5,2,7,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,3,1,5,4,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,3,1,5,4,7,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,3,1,5,7,2,4]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,3,1,5,7,4,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,3,1,7,2,4,5]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,1,7,2,5,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,1,7,4,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,1,7,4,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,1,7,5,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,1,7,5,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,1,4,5,7]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>{{1},{2,3,6,7},{4},{5}}
[6,3,2,1,4,7,5]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,3,2,1,5,4,7]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,3,2,1,5,7,4]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,3,2,1,7,4,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,1,7,5,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,4,1,5,7]=>[1,5,7,2,4,3,6]=>[1,4,6,3,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,3,2,4,1,7,5]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,4,5,1,7]=>[1,7,2,4,5,3,6]=>[1,4,6,5,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,4,5,7,1]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>{{1},{2},{3,6,7},{4},{5}}
[6,3,2,4,7,1,5]=>[1,5,2,4,7,3,6]=>[1,4,6,5,2,7,3]=>{{1},{2,4,5},{3,6,7}}
[6,3,2,4,7,5,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,3,2,5,1,4,7]=>[1,4,7,2,5,3,6]=>[1,5,6,4,3,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,3,2,5,1,7,4]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,5,4,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,2,5,4,7,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,3,2,5,7,1,4]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>{{1},{2,4},{3,6,7},{5}}
[6,3,2,5,7,4,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,3,2,7,1,4,5]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>{{1},{2,5},{3,6,7},{4}}
[6,3,2,7,1,5,4]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,3,2,7,4,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,3,2,7,4,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,2,7,5,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,3,2,7,5,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,4,1,2,5,7]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,3,4,1,2,7,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,4,1,5,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,3,4,1,5,7,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,3,4,1,7,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,4,1,7,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,4,2,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,3,4,2,1,7,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,4,2,5,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,4,2,5,7,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,3,4,2,7,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,3,4,2,7,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,4,5,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,4,5,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,4,5,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,4,5,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,4,5,7,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,3,4,5,7,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,3,4,7,1,2,5]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,3,4,7,1,5,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,3,4,7,2,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,3,4,7,2,5,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,3,4,7,5,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,3,4,7,5,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,3,5,1,2,4,7]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,3,5,1,2,7,4]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,5,1,4,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,3,5,1,4,7,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,3,5,1,7,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,5,1,7,4,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,5,2,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,3,5,2,1,7,4]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,5,2,4,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,5,2,4,7,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,3,5,2,7,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,3,5,2,7,4,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,5,4,1,2,7]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,5,4,1,7,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,5,4,2,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,3,5,4,2,7,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,3,5,4,7,1,2]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,3,5,4,7,2,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,3,5,7,1,2,4]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,3,5,7,1,4,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,3,5,7,2,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,3,5,7,2,4,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,3,5,7,4,1,2]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,3,5,7,4,2,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,3,7,1,2,4,5]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[6,3,7,1,2,5,4]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,3,7,1,4,2,5]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[6,3,7,1,4,5,2]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[6,3,7,1,5,2,4]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,3,7,1,5,4,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,3,7,2,1,4,5]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>{{1},{2,3,5},{4},{6,7}}
[6,3,7,2,1,5,4]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,3,7,2,4,1,5]=>[1,5,2,4,3,7,6]=>[1,4,5,3,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,3,7,2,4,5,1]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>{{1},{2},{3,5},{4},{6,7}}
[6,3,7,2,5,1,4]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>{{1},{2,4},{3,5},{6,7}}
[6,3,7,2,5,4,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,3,7,4,1,2,5]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,3,7,4,1,5,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,3,7,4,2,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,3,7,4,2,5,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,3,7,4,5,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,3,7,4,5,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,3,7,5,1,2,4]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,3,7,5,1,4,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,3,7,5,2,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,3,7,5,2,4,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,3,7,5,4,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,3,7,5,4,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,1,2,3,5,7]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,4,1,2,3,7,5]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,1,2,5,3,7]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,4,1,2,5,7,3]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,4,1,2,7,3,5]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,1,2,7,5,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,1,3,2,5,7]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[6,4,1,3,2,7,5]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,4,1,3,5,2,7]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[6,4,1,3,5,7,2]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[6,4,1,3,7,2,5]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,4,1,3,7,5,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,4,1,5,2,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,4,1,5,2,7,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,4,1,5,3,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,4,1,5,3,7,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,4,1,5,7,2,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,4,1,5,7,3,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,4,1,7,2,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,1,7,2,5,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,1,7,3,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,1,7,3,5,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,1,7,5,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,1,7,5,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,1,3,5,7]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>{{1},{2,4,6,7},{3},{5}}
[6,4,2,1,3,7,5]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,4,2,1,5,3,7]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,4,2,1,5,7,3]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,4,2,1,7,3,5]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,1,7,5,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,3,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,4,2,3,1,7,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,3,5,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,3,5,7,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,4,2,3,7,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,4,2,3,7,5,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,2,5,1,3,7]=>[1,3,7,2,5,4,6]=>[1,5,3,6,4,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,4,2,5,1,7,3]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,5,3,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,2,5,3,7,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,4,2,5,7,1,3]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>{{1},{2,3},{4,6,7},{5}}
[6,4,2,5,7,3,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,4,2,7,1,3,5]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>{{1},{2,5},{3},{4,6,7}}
[6,4,2,7,1,5,3]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,4,2,7,3,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,4,2,7,3,5,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,2,7,5,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,4,2,7,5,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,3,1,2,5,7]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,4,3,1,2,7,5]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,3,1,5,2,7]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,4,3,1,5,7,2]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,4,3,1,7,2,5]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,3,1,7,5,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,3,2,1,5,7]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>{{1},{2,3,4,6,7},{5}}
[6,4,3,2,1,7,5]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,3,2,5,1,7]=>[1,7,2,5,3,4,6]=>[1,5,4,6,3,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,3,2,5,7,1]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>{{1},{2},{3,4,6,7},{5}}
[6,4,3,2,7,1,5]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>{{1},{2,5},{3,4,6,7}}
[6,4,3,2,7,5,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,3,5,1,2,7]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,3,5,1,7,2]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,3,5,2,1,7]=>[1,7,2,3,5,4,6]=>[1,3,5,6,4,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,3,5,2,7,1]=>[1,2,7,3,5,4,6]=>[1,2,5,6,4,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,3,5,7,1,2]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,4,3,5,7,2,1]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>{{1},{2},{3},{4,6,7},{5}}
[6,4,3,7,1,2,5]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,4,3,7,1,5,2]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,4,3,7,2,1,5]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>{{1},{2,3,5},{4,6,7}}
[6,4,3,7,2,5,1]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>{{1},{2},{3,5},{4,6,7}}
[6,4,3,7,5,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,3,7,5,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,5,1,2,3,7]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,5,1,2,7,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,5,1,3,2,7]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,4,5,1,3,7,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,4,5,1,7,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,5,1,7,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,5,2,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,4,5,2,1,7,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,5,2,3,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,5,2,3,7,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,5,2,7,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,4,5,2,7,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,5,3,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,5,3,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,5,3,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,4,5,3,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,4,5,3,7,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,5,3,7,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,4,5,7,1,2,3]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,4,5,7,1,3,2]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,4,5,7,2,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,4,5,7,2,3,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,4,5,7,3,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,4,5,7,3,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,4,7,1,2,3,5]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,4,7,1,2,5,3]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,4,7,1,3,2,5]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[6,4,7,1,3,5,2]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[6,4,7,1,5,2,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,4,7,1,5,3,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,4,7,2,1,3,5]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>{{1},{2,4,5},{3},{6,7}}
[6,4,7,2,1,5,3]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,4,7,2,3,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,4,7,2,3,5,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,4,7,2,5,1,3]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>{{1},{2,3},{4,5},{6,7}}
[6,4,7,2,5,3,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,4,7,3,1,2,5]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,4,7,3,1,5,2]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,4,7,3,2,1,5]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>{{1},{2,3,4,5},{6,7}}
[6,4,7,3,2,5,1]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>{{1},{2},{3,4,5},{6,7}}
[6,4,7,3,5,1,2]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,4,7,3,5,2,1]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>{{1},{2},{3},{4,5},{6,7}}
[6,4,7,5,1,2,3]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,4,7,5,1,3,2]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,4,7,5,2,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,4,7,5,2,3,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,4,7,5,3,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,4,7,5,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,1,2,3,4,7]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,1,2,3,7,4]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,1,2,4,3,7]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,5,1,2,4,7,3]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,5,1,2,7,3,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,1,2,7,4,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,1,3,2,4,7]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,5,1,3,2,7,4]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,5,1,3,4,2,7]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[6,5,1,3,4,7,2]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[6,5,1,3,7,2,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,5,1,3,7,4,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,5,1,4,2,3,7]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,5,1,4,2,7,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,5,1,4,3,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,5,1,4,3,7,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,5,1,4,7,2,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,5,1,4,7,3,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,5,1,7,2,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,1,7,2,4,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,1,7,3,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,1,7,3,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,1,7,4,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,1,7,4,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,1,3,4,7]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>{{1},{2,5,6,7},{3},{4}}
[6,5,2,1,3,7,4]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,5,2,1,4,3,7]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,5,2,1,4,7,3]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,5,2,1,7,3,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,1,7,4,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,3,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,5,2,3,1,7,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,3,4,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,3,4,7,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,2,3,7,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,5,2,3,7,4,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,2,4,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,5,2,4,1,7,3]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,4,3,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,2,4,3,7,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,5,2,4,7,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,5,2,4,7,3,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,5,2,7,1,3,4]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>{{1},{2,4},{3},{5,6,7}}
[6,5,2,7,1,4,3]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,5,2,7,3,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,5,2,7,3,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,2,7,4,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,5,2,7,4,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,3,1,2,4,7]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,5,3,1,2,7,4]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,3,1,4,2,7]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,5,3,1,4,7,2]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,5,3,1,7,2,4]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,3,1,7,4,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,3,2,1,4,7]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>{{1},{2,3,5,6,7},{4}}
[6,5,3,2,1,7,4]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,3,2,4,1,7]=>[1,7,2,4,3,5,6]=>[1,4,5,3,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,3,2,4,7,1]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>{{1},{2},{3,5,6,7},{4}}
[6,5,3,2,7,1,4]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>{{1},{2,4},{3,5,6,7}}
[6,5,3,2,7,4,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,3,4,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,3,4,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,3,4,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,3,4,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,3,4,7,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,3,4,7,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,3,7,1,2,4]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,5,3,7,1,4,2]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,5,3,7,2,1,4]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>{{1},{2,3,4},{5,6,7}}
[6,5,3,7,2,4,1]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>{{1},{2},{3,4},{5,6,7}}
[6,5,3,7,4,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,3,7,4,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,4,1,2,3,7]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,4,1,2,7,3]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,4,1,3,2,7]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,5,4,1,3,7,2]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,5,4,1,7,2,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,4,1,7,3,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,4,2,1,3,7]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>{{1},{2,4,5,6,7},{3}}
[6,5,4,2,1,7,3]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,4,2,3,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,4,2,3,7,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,4,2,7,1,3]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>{{1},{2,3},{4,5,6,7}}
[6,5,4,2,7,3,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,4,3,1,2,7]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,4,3,1,7,2]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>{{1},{2,3,4,5,6,7}}
[6,5,4,3,2,7,1]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>{{1},{2},{3,4,5,6,7}}
[6,5,4,3,7,1,2]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,4,3,7,2,1]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>{{1},{2},{3},{4,5,6,7}}
[6,5,4,7,1,2,3]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,4,7,1,3,2]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,5,4,7,2,1,3]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>{{1},{2,3},{4},{5,6,7}}
[6,5,4,7,2,3,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,4,7,3,1,2]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,4,7,3,2,1]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>{{1},{2},{3},{4},{5,6,7}}
[6,5,7,1,2,3,4]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,1,2,4,3]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,5,7,1,3,2,4]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,5,7,1,3,4,2]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[6,5,7,1,4,2,3]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,5,7,1,4,3,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,5,7,2,1,3,4]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>{{1},{2,4},{3},{5},{6,7}}
[6,5,7,2,1,4,3]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,5,7,2,3,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,5,7,2,3,4,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,2,4,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,5,7,2,4,3,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,5,7,3,1,2,4]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,5,7,3,1,4,2]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,5,7,3,2,1,4]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>{{1},{2,3,4},{5},{6,7}}
[6,5,7,3,2,4,1]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>{{1},{2},{3,4},{5},{6,7}}
[6,5,7,3,4,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,3,4,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,4,1,2,3]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,4,1,3,2]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,5,7,4,2,1,3]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>{{1},{2,3},{4},{5},{6,7}}
[6,5,7,4,2,3,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,4,3,1,2]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,5,7,4,3,2,1]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>{{1},{2},{3},{4},{5},{6,7}}
[6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,1,2,3,5,4]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,1,2,4,3,5]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,1,2,4,5,3]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[6,7,1,2,5,3,4]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,1,2,5,4,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,1,3,2,5,4]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[6,7,1,3,4,2,5]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[6,7,1,3,4,5,2]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[6,7,1,3,5,2,4]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[6,7,1,3,5,4,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[6,7,1,4,2,3,5]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,1,4,2,5,3]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[6,7,1,4,3,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[6,7,1,4,3,5,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,1,4,5,2,3]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[6,7,1,4,5,3,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[6,7,1,5,2,3,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,1,5,2,4,3]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,1,5,3,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,1,5,3,4,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,1,5,4,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,1,5,4,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,1,3,4,5]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[6,7,2,1,3,5,4]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[6,7,2,1,4,3,5]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,2,1,4,5,3]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[6,7,2,1,5,3,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,1,5,4,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,3,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[6,7,2,3,1,5,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,3,4,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,2,3,5,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,2,3,5,4,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,2,4,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[6,7,2,4,1,5,3]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,4,3,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,2,4,3,5,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,2,4,5,3,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[6,7,2,5,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[6,7,2,5,1,4,3]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[6,7,2,5,3,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[6,7,2,5,3,4,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,2,5,4,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[6,7,2,5,4,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,3,1,2,4,5]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[6,7,3,1,2,5,4]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,3,1,4,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[6,7,3,1,4,5,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[6,7,3,1,5,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,3,1,5,4,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,3,2,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[6,7,3,2,1,5,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,3,2,4,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,3,2,4,5,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[6,7,3,2,5,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[6,7,3,2,5,4,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,3,4,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,3,4,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,3,4,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,3,4,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,3,5,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,3,5,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,3,5,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,3,5,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,3,5,4,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,3,5,4,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,4,1,2,3,5]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,4,1,2,5,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,4,1,3,2,5]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[6,7,4,1,3,5,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[6,7,4,1,5,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,4,1,5,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,4,2,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[6,7,4,2,1,5,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,4,2,3,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,4,2,3,5,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,4,2,5,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[6,7,4,2,5,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,4,3,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,4,3,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,4,3,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[6,7,4,3,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[6,7,4,3,5,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,4,3,5,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[6,7,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[6,7,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[6,7,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[6,7,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[6,7,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,1,2,3,4,6,5]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,1,2,3,5,4,6]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,1,2,3,5,6,4]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,1,2,3,6,4,5]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,1,2,3,6,5,4]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,1,2,4,3,5,6]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,1,2,4,3,6,5]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,1,2,4,5,3,6]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,1,2,4,5,6,3]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[7,1,2,4,6,3,5]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,1,2,4,6,5,3]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,1,2,5,3,4,6]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,1,2,5,3,6,4]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,1,2,5,4,3,6]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,1,2,5,4,6,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,1,2,5,6,3,4]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,1,2,5,6,4,3]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,1,2,6,3,4,5]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,1,2,6,3,5,4]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,1,2,6,4,3,5]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,1,2,6,4,5,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,1,2,6,5,3,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,1,2,6,5,4,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,1,3,2,4,5,6]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,1,3,2,4,6,5]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,1,3,2,5,4,6]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,1,3,2,5,6,4]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[7,1,3,2,6,4,5]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,1,3,2,6,5,4]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,1,3,4,2,5,6]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,1,3,4,2,6,5]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[7,1,3,4,5,2,6]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[7,1,3,4,5,6,2]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[7,1,3,4,6,2,5]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[7,1,3,4,6,5,2]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[7,1,3,5,2,4,6]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,1,3,5,2,6,4]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[7,1,3,5,4,2,6]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[7,1,3,5,4,6,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,1,3,5,6,2,4]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[7,1,3,5,6,4,2]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[7,1,3,6,2,4,5]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,1,3,6,2,5,4]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,1,3,6,4,2,5]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,1,3,6,4,5,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,1,3,6,5,2,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,1,3,6,5,4,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,1,4,2,3,5,6]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,1,4,2,3,6,5]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,1,4,2,5,3,6]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,1,4,2,5,6,3]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[7,1,4,2,6,3,5]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,1,4,2,6,5,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,1,4,3,2,5,6]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[7,1,4,3,2,6,5]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,1,4,3,5,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,1,4,3,5,6,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,1,4,3,6,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,1,4,3,6,5,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,1,4,5,2,3,6]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,1,4,5,2,6,3]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[7,1,4,5,3,2,6]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[7,1,4,5,3,6,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,1,4,5,6,2,3]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[7,1,4,5,6,3,2]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[7,1,4,6,2,3,5]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,1,4,6,2,5,3]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,1,4,6,3,2,5]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,1,4,6,3,5,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,1,4,6,5,2,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,1,4,6,5,3,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,1,5,2,3,4,6]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,1,5,2,3,6,4]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,1,5,2,4,3,6]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,1,5,2,4,6,3]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[7,1,5,2,6,3,4]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,1,5,2,6,4,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,1,5,3,2,4,6]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[7,1,5,3,2,6,4]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,1,5,3,4,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,1,5,3,4,6,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,1,5,3,6,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,1,5,3,6,4,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,1,5,4,2,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,1,5,4,2,6,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,1,5,4,3,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,1,5,4,3,6,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,1,5,4,6,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,1,5,4,6,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,1,5,6,2,3,4]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,1,5,6,2,4,3]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,1,5,6,3,2,4]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,1,5,6,3,4,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,1,5,6,4,2,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,1,5,6,4,3,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,1,6,2,3,4,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,2,3,5,4]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,2,4,3,5]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,2,4,5,3]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,2,5,3,4]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,2,5,4,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,3,2,4,5]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,3,2,5,4]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,3,4,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,3,4,5,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,3,5,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,3,5,4,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,4,2,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,4,2,5,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,4,3,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,4,3,5,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,4,5,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,4,5,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,5,2,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,5,2,4,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,5,3,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,5,3,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,5,4,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,1,6,5,4,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,1,3,4,5,6]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>{{1},{2,6},{3},{4},{5},{7}}
[7,2,1,3,4,6,5]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[7,2,1,3,5,4,6]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,2,1,3,5,6,4]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[7,2,1,3,6,4,5]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,2,1,3,6,5,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,2,1,4,3,5,6]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,2,1,4,3,6,5]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,2,1,4,5,3,6]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,2,1,4,5,6,3]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[7,2,1,4,6,3,5]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,2,1,4,6,5,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,2,1,5,3,4,6]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,2,1,5,3,6,4]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,2,1,5,4,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,2,1,5,4,6,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,2,1,5,6,3,4]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,2,1,5,6,4,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,2,1,6,3,4,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,1,6,3,5,4]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,1,6,4,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,1,6,4,5,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,1,6,5,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,1,6,5,4,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,1,4,5,6]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[7,2,3,1,4,6,5]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,2,3,1,5,4,6]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,2,3,1,5,6,4]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,2,3,1,6,4,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,1,6,5,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,4,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,2,3,4,1,6,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,4,5,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,4,5,6,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,2,3,4,6,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,2,3,4,6,5,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,2,3,5,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,2,3,5,1,6,4]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,5,4,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,3,5,4,6,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,2,3,5,6,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,2,3,5,6,4,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,2,3,6,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,2,3,6,1,5,4]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,2,3,6,4,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,2,3,6,4,5,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,2,3,6,5,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,2,3,6,5,4,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,2,4,1,3,5,6]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[7,2,4,1,3,6,5]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,2,4,1,5,3,6]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,2,4,1,5,6,3]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,2,4,1,6,3,5]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,4,1,6,5,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,4,3,1,5,6]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,2,4,3,1,6,5]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,4,3,5,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,4,3,5,6,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,2,4,3,6,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,2,4,3,6,5,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,2,4,5,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,2,4,5,1,6,3]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,4,5,3,1,6]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,4,5,3,6,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,2,4,5,6,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,2,4,5,6,3,1]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[7,2,4,6,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,2,4,6,1,5,3]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[7,2,4,6,3,1,5]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[7,2,4,6,3,5,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,2,4,6,5,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,2,4,6,5,3,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,2,5,1,3,4,6]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[7,2,5,1,3,6,4]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,2,5,1,4,3,6]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,2,5,1,4,6,3]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,2,5,1,6,3,4]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,5,1,6,4,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,5,3,1,4,6]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,2,5,3,1,6,4]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,5,3,4,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,5,3,4,6,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,2,5,3,6,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,2,5,3,6,4,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,2,5,4,1,3,6]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,2,5,4,1,6,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,5,4,3,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,2,5,4,3,6,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,2,5,4,6,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,2,5,4,6,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,2,5,6,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,2,5,6,1,4,3]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[7,2,5,6,3,1,4]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[7,2,5,6,3,4,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,2,5,6,4,1,3]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[7,2,5,6,4,3,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,2,6,1,3,4,5]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[7,2,6,1,3,5,4]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[7,2,6,1,4,3,5]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,2,6,1,4,5,3]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[7,2,6,1,5,3,4]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,2,6,1,5,4,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,2,6,3,1,4,5]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[7,2,6,3,1,5,4]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,2,6,3,4,5,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,2,6,3,5,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,2,6,3,5,4,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,2,6,4,1,3,5]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[7,2,6,4,1,5,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,2,6,4,3,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,2,6,4,3,5,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,2,6,4,5,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,2,6,4,5,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,2,6,5,1,3,4]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[7,2,6,5,1,4,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,2,6,5,3,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,2,6,5,3,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,2,6,5,4,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,2,6,5,4,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,1,2,4,5,6]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[7,3,1,2,4,6,5]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,3,1,2,5,4,6]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,3,1,2,5,6,4]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,3,1,2,6,4,5]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,1,2,6,5,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,1,4,2,5,6]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[7,3,1,4,2,6,5]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,3,1,4,5,2,6]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[7,3,1,4,5,6,2]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[7,3,1,4,6,2,5]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,3,1,4,6,5,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,3,1,5,2,4,6]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[7,3,1,5,2,6,4]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,3,1,5,4,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,3,1,5,4,6,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,3,1,5,6,2,4]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,3,1,5,6,4,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,3,1,6,2,4,5]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,1,6,2,5,4]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,1,6,4,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,1,6,4,5,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,1,6,5,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,1,6,5,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,1,4,5,6]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>{{1},{2,3,6},{4},{5},{7}}
[7,3,2,1,4,6,5]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,3,2,1,5,4,6]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,3,2,1,5,6,4]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,3,2,1,6,4,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,1,6,5,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,4,1,5,6]=>[1,5,6,2,4,3,7]=>[1,4,6,3,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,3,2,4,1,6,5]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,4,5,1,6]=>[1,6,2,4,5,3,7]=>[1,4,6,5,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,4,5,6,1]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>{{1},{2},{3,6},{4},{5},{7}}
[7,3,2,4,6,1,5]=>[1,5,2,4,6,3,7]=>[1,4,6,5,2,3,7]=>{{1},{2,4,5},{3,6},{7}}
[7,3,2,4,6,5,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,3,2,5,1,4,6]=>[1,4,6,2,5,3,7]=>[1,5,6,4,3,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,3,2,5,1,6,4]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,5,4,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,2,5,4,6,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,3,2,5,6,1,4]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>{{1},{2,4},{3,6},{5},{7}}
[7,3,2,5,6,4,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,3,2,6,1,4,5]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>{{1},{2,5},{3,6},{4},{7}}
[7,3,2,6,1,5,4]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,3,2,6,4,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,3,2,6,4,5,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,2,6,5,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,3,2,6,5,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,4,1,2,5,6]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,3,4,1,2,6,5]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,4,1,5,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,3,4,1,5,6,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,3,4,1,6,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,4,1,6,5,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,4,2,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,3,4,2,1,6,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,4,2,5,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,4,2,5,6,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,3,4,2,6,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,3,4,2,6,5,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,4,5,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,4,5,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,4,5,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,4,5,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,4,5,6,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,3,4,5,6,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,3,4,6,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,3,4,6,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,3,4,6,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,3,4,6,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,3,4,6,5,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,3,4,6,5,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,3,5,1,2,4,6]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,3,5,1,2,6,4]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,5,1,4,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,3,5,1,4,6,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,3,5,1,6,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,5,1,6,4,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,5,2,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,3,5,2,1,6,4]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,5,2,4,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,5,2,4,6,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,3,5,2,6,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,3,5,2,6,4,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,5,4,1,2,6]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,5,4,1,6,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,5,4,2,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,3,5,4,2,6,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,3,5,4,6,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,3,5,4,6,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,3,5,6,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,3,5,6,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,3,5,6,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,3,5,6,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,3,5,6,4,1,2]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,3,5,6,4,2,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,3,6,1,2,4,5]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,3,6,1,2,5,4]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,3,6,1,4,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,3,6,1,4,5,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,3,6,1,5,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,3,6,1,5,4,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,3,6,2,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,3,6,2,1,5,4]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,3,6,2,4,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,3,6,2,4,5,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,3,6,2,5,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,3,6,2,5,4,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,3,6,4,1,2,5]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,3,6,4,1,5,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,3,6,4,2,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,3,6,4,2,5,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,3,6,4,5,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,3,6,4,5,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,3,6,5,1,2,4]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,3,6,5,1,4,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,3,6,5,2,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,3,6,5,2,4,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,3,6,5,4,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,3,6,5,4,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,1,2,3,5,6]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,4,1,2,3,6,5]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,1,2,5,3,6]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,4,1,2,5,6,3]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,4,1,2,6,3,5]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,1,2,6,5,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,1,3,2,5,6]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[7,4,1,3,2,6,5]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,4,1,3,5,2,6]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[7,4,1,3,5,6,2]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[7,4,1,3,6,2,5]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,4,1,3,6,5,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,4,1,5,2,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,4,1,5,2,6,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,4,1,5,3,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,4,1,5,3,6,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,4,1,5,6,2,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,4,1,5,6,3,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,4,1,6,2,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,1,6,2,5,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,1,6,3,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,1,6,3,5,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,1,6,5,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,1,6,5,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,1,3,5,6]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>{{1},{2,4,6},{3},{5},{7}}
[7,4,2,1,3,6,5]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,4,2,1,5,3,6]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,4,2,1,5,6,3]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,4,2,1,6,3,5]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,1,6,5,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,3,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,4,2,3,1,6,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,3,5,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,3,5,6,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,4,2,3,6,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,4,2,3,6,5,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,2,5,1,3,6]=>[1,3,6,2,5,4,7]=>[1,5,3,6,4,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,4,2,5,1,6,3]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,5,3,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,2,5,3,6,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,4,2,5,6,1,3]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>{{1},{2,3},{4,6},{5},{7}}
[7,4,2,5,6,3,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,4,2,6,1,3,5]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>{{1},{2,5},{3},{4,6},{7}}
[7,4,2,6,1,5,3]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,4,2,6,3,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,4,2,6,3,5,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,2,6,5,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,4,2,6,5,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,3,1,2,5,6]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,4,3,1,2,6,5]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,3,1,5,2,6]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,4,3,1,5,6,2]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,4,3,1,6,2,5]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,3,1,6,5,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,3,2,1,5,6]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>{{1},{2,3,4,6},{5},{7}}
[7,4,3,2,1,6,5]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,3,2,5,1,6]=>[1,6,2,5,3,4,7]=>[1,5,4,6,3,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,3,2,5,6,1]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>{{1},{2},{3,4,6},{5},{7}}
[7,4,3,2,6,1,5]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>{{1},{2,5},{3,4,6},{7}}
[7,4,3,2,6,5,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,3,5,1,2,6]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,3,5,1,6,2]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,3,5,2,1,6]=>[1,6,2,3,5,4,7]=>[1,3,5,6,4,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,3,5,2,6,1]=>[1,2,6,3,5,4,7]=>[1,2,5,6,4,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,3,5,6,1,2]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,4,3,5,6,2,1]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>{{1},{2},{3},{4,6},{5},{7}}
[7,4,3,6,1,2,5]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,4,3,6,1,5,2]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,4,3,6,2,1,5]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>{{1},{2,3,5},{4,6},{7}}
[7,4,3,6,2,5,1]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>{{1},{2},{3,5},{4,6},{7}}
[7,4,3,6,5,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,3,6,5,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,5,1,2,3,6]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,5,1,2,6,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,5,1,3,2,6]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,4,5,1,3,6,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,4,5,1,6,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,5,1,6,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,5,2,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,4,5,2,1,6,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,5,2,3,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,5,2,3,6,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,5,2,6,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,4,5,2,6,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,5,3,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,5,3,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,5,3,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,4,5,3,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,4,5,3,6,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,5,3,6,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,4,5,6,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,4,5,6,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,4,5,6,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,4,5,6,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,4,5,6,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,4,6,1,2,3,5]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,4,6,1,2,5,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,4,6,1,3,2,5]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,4,6,1,3,5,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,4,6,1,5,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,4,6,1,5,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,4,6,2,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,4,6,2,1,5,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,4,6,2,3,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,4,6,2,3,5,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,4,6,2,5,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,4,6,2,5,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,4,6,3,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,4,6,3,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,4,6,3,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,4,6,3,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,4,6,3,5,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,4,6,3,5,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,4,6,5,1,2,3]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,4,6,5,1,3,2]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,4,6,5,2,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,4,6,5,2,3,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,4,6,5,3,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,4,6,5,3,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,1,2,3,4,6]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,1,2,3,6,4]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,1,2,4,3,6]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,5,1,2,4,6,3]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,5,1,2,6,3,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,1,2,6,4,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,1,3,2,4,6]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,5,1,3,2,6,4]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,5,1,3,4,2,6]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[7,5,1,3,4,6,2]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[7,5,1,3,6,2,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,5,1,3,6,4,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,5,1,4,2,3,6]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,5,1,4,2,6,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,5,1,4,3,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,5,1,4,3,6,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,5,1,4,6,2,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,5,1,4,6,3,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,5,1,6,2,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,1,6,2,4,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,1,6,3,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,1,6,3,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,1,6,4,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,1,6,4,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,1,3,4,6]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>{{1},{2,5,6},{3},{4},{7}}
[7,5,2,1,3,6,4]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,5,2,1,4,3,6]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,5,2,1,4,6,3]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,5,2,1,6,3,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,1,6,4,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,3,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,5,2,3,1,6,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,3,4,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,3,4,6,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,2,3,6,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,5,2,3,6,4,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,2,4,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,5,2,4,1,6,3]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,4,3,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,2,4,3,6,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,5,2,4,6,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,5,2,4,6,3,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,5,2,6,1,3,4]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>{{1},{2,4},{3},{5,6},{7}}
[7,5,2,6,1,4,3]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,5,2,6,3,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,5,2,6,3,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,2,6,4,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,5,2,6,4,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,3,1,2,4,6]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,5,3,1,2,6,4]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,3,1,4,2,6]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,5,3,1,4,6,2]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,5,3,1,6,2,4]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,3,1,6,4,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,3,2,1,4,6]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>{{1},{2,3,5,6},{4},{7}}
[7,5,3,2,1,6,4]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,3,2,4,1,6]=>[1,6,2,4,3,5,7]=>[1,4,5,3,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,3,2,4,6,1]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>{{1},{2},{3,5,6},{4},{7}}
[7,5,3,2,6,1,4]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>{{1},{2,4},{3,5,6},{7}}
[7,5,3,2,6,4,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,3,4,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,3,4,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,3,4,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,3,4,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,3,4,6,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,3,4,6,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,3,6,1,2,4]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,5,3,6,1,4,2]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,5,3,6,2,1,4]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>{{1},{2,3,4},{5,6},{7}}
[7,5,3,6,2,4,1]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>{{1},{2},{3,4},{5,6},{7}}
[7,5,3,6,4,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,3,6,4,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,4,1,2,3,6]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,4,1,2,6,3]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,4,1,3,2,6]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,5,4,1,3,6,2]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,5,4,1,6,2,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,4,1,6,3,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,4,2,1,3,6]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>{{1},{2,4,5,6},{3},{7}}
[7,5,4,2,1,6,3]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,4,2,3,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,4,2,3,6,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,4,2,6,1,3]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>{{1},{2,3},{4,5,6},{7}}
[7,5,4,2,6,3,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,4,3,1,2,6]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,4,3,1,6,2]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,4,3,2,1,6]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>{{1},{2,3,4,5,6},{7}}
[7,5,4,3,2,6,1]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>{{1},{2},{3,4,5,6},{7}}
[7,5,4,3,6,1,2]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,4,3,6,2,1]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>{{1},{2},{3},{4,5,6},{7}}
[7,5,4,6,1,2,3]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,4,6,1,3,2]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,5,4,6,2,1,3]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>{{1},{2,3},{4},{5,6},{7}}
[7,5,4,6,2,3,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,4,6,3,1,2]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,4,6,3,2,1]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>{{1},{2},{3},{4},{5,6},{7}}
[7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,1,2,4,3]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,5,6,1,3,2,4]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,5,6,1,3,4,2]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,5,6,1,4,2,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,5,6,1,4,3,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,5,6,2,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,5,6,2,1,4,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,5,6,2,3,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,5,6,2,3,4,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,5,6,2,4,3,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,5,6,3,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,5,6,3,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,5,6,3,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,5,6,3,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,4,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,4,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,5,6,4,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,5,6,4,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,1,2,3,5,4]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,1,2,4,3,5]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,1,2,4,5,3]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,6,1,2,5,3,4]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,1,2,5,4,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,1,3,2,5,4]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,6,1,3,4,2,5]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,6,1,3,4,5,2]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[7,6,1,3,5,2,4]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,6,1,3,5,4,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,6,1,4,2,3,5]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,1,4,2,5,3]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,6,1,4,3,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,6,1,4,3,5,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,1,4,5,2,3]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,6,1,4,5,3,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,6,1,5,2,3,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,1,5,2,4,3]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,1,5,3,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,1,5,3,4,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,1,5,4,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,1,5,4,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,1,3,4,5]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>{{1},{2,5},{3},{4},{6},{7}}
[7,6,2,1,3,5,4]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,6,2,1,4,3,5]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,2,1,4,5,3]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,6,2,1,5,3,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,1,5,4,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,3,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,6,2,3,1,5,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,3,4,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,3,4,5,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,2,3,5,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,2,3,5,4,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,2,4,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,6,2,4,1,5,3]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,4,3,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,2,4,3,5,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,2,4,5,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,2,4,5,3,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,6,2,5,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,6,2,5,1,4,3]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,6,2,5,3,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,6,2,5,3,4,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,2,5,4,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,6,2,5,4,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,3,1,2,4,5]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,6,3,1,2,5,4]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,3,1,4,2,5]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,6,3,1,4,5,2]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,6,3,1,5,2,4]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,3,1,5,4,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,3,2,1,4,5]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>{{1},{2,3,5},{4},{6},{7}}
[7,6,3,2,1,5,4]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,3,2,4,1,5]=>[1,5,2,4,3,6,7]=>[1,4,5,3,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,3,2,4,5,1]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>{{1},{2},{3,5},{4},{6},{7}}
[7,6,3,2,5,1,4]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>{{1},{2,4},{3,5},{6},{7}}
[7,6,3,2,5,4,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,3,4,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,3,4,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,3,4,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,3,4,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,3,4,5,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,3,4,5,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,3,5,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,3,5,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,3,5,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,3,5,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,3,5,4,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,3,5,4,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,4,1,2,3,5]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,4,1,2,5,3]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,4,1,3,2,5]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,6,4,1,3,5,2]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,6,4,1,5,2,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,4,1,5,3,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,4,2,1,3,5]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>{{1},{2,4,5},{3},{6},{7}}
[7,6,4,2,1,5,3]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,4,2,3,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,4,2,3,5,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,4,2,5,1,3]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>{{1},{2,3},{4,5},{6},{7}}
[7,6,4,2,5,3,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,4,3,1,2,5]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,4,3,1,5,2]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,4,3,2,1,5]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>{{1},{2,3,4,5},{6},{7}}
[7,6,4,3,2,5,1]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>{{1},{2},{3,4,5},{6},{7}}
[7,6,4,3,5,1,2]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,4,3,5,2,1]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>{{1},{2},{3},{4,5},{6},{7}}
[7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,4,5,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,4,5,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,1,2,4,3]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,5,1,3,4,2]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,5,2,1,3,4]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>{{1},{2,4},{3},{5},{6},{7}}
[7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,5,2,4,3,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,5,3,1,2,4]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>{{1},{2,3,4},{5},{6},{7}}
[7,6,5,3,2,4,1]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>{{1},{2},{3,4},{5},{6},{7}}
[7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>{{1},{2,3},{4},{5},{6},{7}}
[7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{1},{2},{3},{4},{5},{6},{7}}
[7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>{{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},{6},{7}}
[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,5,6,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,5,8,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,5,6,8,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,5,7,8,4,3,2,1]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,6,7,8,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,4,5,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,5,4,8,3,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,5,7,4,8,3,2,1]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,6,4,5,8,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,5,4,6,8,3,2,1]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[7,4,5,6,8,3,2,1]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[4,5,6,7,8,3,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,5,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,5,6,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[5,6,7,8,3,4,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,7,8,3,4,5,2,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,5,4,3,6,2,1]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,6,5,4,3,8,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,4,5,7,3,8,2,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,6,7,3,8,2,1]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,5,6,7,3,8,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,6,5,3,4,8,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,6,4,3,5,8,2,1]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[7,6,3,4,5,8,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,3,4,5,7,8,2,1]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[4,3,5,6,7,8,2,1]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[8,7,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,5,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,5,6,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[5,6,7,8,4,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,4,5,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,4,5,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[4,5,6,7,8,2,3,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,5,3,2,4,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[8,6,5,7,3,2,4,1]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>{{1},{2},{3,4},{5},{6,7},{8}}
[5,6,7,8,3,2,4,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[8,7,6,5,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,7,8,5,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,5,6,7,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[5,6,7,8,2,3,4,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,3,2,4,5,6,1]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>{{1},{2},{3,6},{4},{5},{7},{8}}
[7,6,5,4,3,2,8,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,7,5,4,3,2,8,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,7,4,3,2,8,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,5,7,3,2,8,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,5,6,7,3,2,8,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,4,3,7,2,8,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,4,6,3,7,2,8,1]=>[1,2,8,3,7,4,6,5]=>[1,2,7,6,8,5,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,5,4,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,7,4,5,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,4,5,7,2,3,8,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,5,6,7,2,3,8,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,6,5,3,2,4,8,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[7,6,5,2,3,4,8,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,7,2,3,4,5,8,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,4,3,2,6,7,8,1]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[3,4,5,2,6,7,8,1]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[5,2,3,4,6,7,8,1]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>{{1},{2},{3},{4},{5,8},{6},{7}}
[4,3,2,5,6,7,8,1]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[3,4,2,5,6,7,8,1]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[4,2,3,5,6,7,8,1]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[3,2,4,5,6,7,8,1]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,5,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,5,6,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,5,7,8,4,3,1,2]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,6,7,8,4,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,4,5,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,4,5,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[4,5,6,7,8,3,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,5,8,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,7,5,8,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,5,6,8,3,4,1,2]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,5,7,8,3,4,1,2]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,6,7,8,3,4,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,5,4,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,8,4,5,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,8,5,3,4,6,1,2]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[7,8,4,3,5,6,1,2]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}}
[7,8,3,4,5,6,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,4,3,5,6,7,1,2]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[8,3,4,5,6,7,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,5,4,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,5,7,4,3,8,1,2]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,7,4,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,7,4,5,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,4,7,3,8,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,6,7,3,8,1,2]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,5,6,7,3,8,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,6,3,7,8,1,2]=>[1,2,3,7,8,4,6,5]=>[1,2,3,6,8,5,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[5,6,3,4,7,8,1,2]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[6,4,3,5,7,8,1,2]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[6,3,4,5,7,8,1,2]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,4,3,6,7,8,1,2]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[4,5,3,6,7,8,1,2]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[4,3,5,6,7,8,1,2]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[3,4,5,6,7,8,1,2]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,5,4,2,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[7,6,8,5,4,2,1,3]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>{{1},{2,3},{4},{5},{6},{7,8}}
[5,6,7,8,4,2,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[4,5,6,7,8,2,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,7,8,5,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,5,6,7,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,5,7,8,4,1,2,3]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,6,7,8,4,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[6,7,4,5,8,1,2,3]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,5,4,7,8,1,2,3]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[4,5,6,7,8,1,2,3]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,5,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[7,8,5,6,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[7,6,5,8,3,2,1,4]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[5,6,7,8,3,2,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,5,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[7,8,5,6,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[6,7,5,8,2,3,1,4]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[7,5,6,8,2,3,1,4]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[5,6,7,8,2,3,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,5,3,1,2,4]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[7,8,5,6,3,1,2,4]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[6,7,5,8,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[7,5,6,8,3,1,2,4]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[5,6,7,8,3,1,2,4]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[8,7,6,5,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[7,8,6,5,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[6,7,8,5,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[7,8,5,6,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[6,5,7,8,2,1,3,4]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>{{1},{2,4},{3},{5},{6,8},{7}}
[5,6,7,8,2,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,8,5,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,7,8,5,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,5,7,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,5,8,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,7,5,8,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,5,6,8,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,5,7,8,1,2,3,4]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,7,6,4,3,2,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,4,3,2,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,3,4,2,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,3,4,2,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,4,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,4,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,3,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,3,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,2,3,4,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,2,3,4,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,4,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[6,7,8,4,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[8,7,6,3,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}}
[6,7,8,3,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}}
[8,7,6,2,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[6,7,8,2,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,8,1,2,3,4,5]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,5,4,3,2,1,6]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,4,5,2,3,1,6]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,3,4,2,5,1,6]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,5,4,2,1,3,6]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[7,8,5,4,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,8,4,5,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[8,7,5,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[7,8,5,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[7,8,3,4,1,2,5,6]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[7,8,4,2,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[8,7,4,1,2,3,5,6]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}}
[7,8,2,1,3,4,5,6]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>{{1},{2,6},{3},{4},{5},{7},{8}}
[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[8,6,5,4,3,2,1,7]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,4,5,6,3,2,1,7]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,5,4,3,1,2,7]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,5,6,3,4,1,2,7]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,3,4,5,6,1,2,7]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,6,4,5,1,2,3,7]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[8,5,6,2,1,3,4,7]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[8,6,5,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[8,5,6,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[8,6,4,2,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[8,4,1,2,3,5,6,7]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[8,3,2,1,4,5,6,7]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[8,2,3,1,4,5,6,7]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[8,2,1,3,4,5,6,7]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[7,6,5,4,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,5,4,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,4,3,2,1,8]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,4,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,4,5,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,5,6,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,4,7,3,2,1,8]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,7,3,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,6,3,4,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,3,4,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,3,4,5,2,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,5,4,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,4,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,4,5,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,4,5,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,5,6,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,4,7,2,3,1,8]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,7,2,3,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,3,2,4,1,8]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,3,2,4,1,8]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,5,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,5,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,6,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,2,3,4,1,8]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,2,3,4,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,4,2,5,1,8]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,3,4,2,7,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,3,6,2,7,1,8]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,3,2,6,7,1,8]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,6,7,1,8]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,5,4,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,5,6,4,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,5,6,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,5,6,7,3,1,2,8]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,5,4,2,1,3,8]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,5,7,4,2,1,3,8]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,4,5,6,2,1,3,8]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,5,6,7,2,1,3,8]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,6,5,4,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,7,4,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,4,5,6,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,4,7,1,2,3,8]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,6,7,1,2,3,8]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,5,6,7,1,2,3,8]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,7,3,1,2,4,8]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[5,6,7,2,1,3,4,8]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[7,6,5,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,7,5,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,5,6,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,5,7,1,2,3,4,8]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,6,7,1,2,3,4,8]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,6,4,3,2,1,5,8]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,7,1,2,3,4,5,8]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,5,3,1,2,4,6,8]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[7,5,1,2,3,4,6,8]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[7,3,1,2,4,5,6,8]=>[1,2,4,5,6,8,3,7]=>[1,2,7,4,5,6,8,3]=>{{1},{2},{3,7,8},{4},{5},{6}}
[7,2,1,3,4,5,6,8]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>{{1},{2,7,8},{3},{4},{5},{6}}
[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,5,4,3,2,1,7,8]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,2,3,5,6,1,7,8]=>[1,7,8,2,3,5,6,4]=>[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,3,4,5,6,1,7,8]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,6,4,3,1,2,7,8]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,4,6,3,1,2,7,8]=>[1,2,7,8,3,4,6,5]=>[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,6,3,4,1,2,7,8]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,4,6,2,1,3,7,8]=>[1,3,7,8,2,4,6,5]=>[1,4,3,6,8,5,7,2]=>{{1},{2,4,5,6,8},{3},{7}}
[4,5,6,1,2,3,7,8]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[6,4,3,1,2,5,7,8]=>[1,2,5,7,8,3,4,6]=>[1,2,4,6,5,8,7,3]=>{{1},{2},{3,4,6,8},{5},{7}}
[6,4,1,2,3,5,7,8]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[6,2,3,1,4,5,7,8]=>[1,4,5,7,8,2,3,6]=>[1,3,6,4,5,8,7,2]=>{{1},{2,3,6,8},{4},{5},{7}}
[6,1,2,3,4,5,7,8]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,4,3,2,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[4,5,2,3,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[5,2,3,4,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,3,4,5,1,6,7,8]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[5,3,1,2,4,6,7,8]=>[1,2,4,6,7,8,3,5]=>[1,2,5,4,8,6,7,3]=>{{1},{2},{3,5,8},{4},{6},{7}}
[5,1,2,3,4,6,7,8]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>{{1},{2},{3},{4},{5,8},{6},{7}}
[4,3,2,1,5,6,7,8]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[2,3,4,1,5,6,7,8]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[3,4,1,2,5,6,7,8]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[4,1,2,3,5,6,7,8]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[3,2,1,4,5,6,7,8]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>{{1},{2,3,8},{4},{5},{6},{7}}
[3,1,2,4,5,6,7,8]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[2,1,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>{{1},{2},{3},{4},{5},{6},{7},{8}}
[5,8,7,6,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,5,8,7,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,8,7,6,5,3,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[4,7,6,5,8,3,2,1]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[3,7,6,8,5,4,2,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[3,5,8,7,6,4,2,1]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[3,5,6,8,7,4,2,1]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[3,5,6,7,8,4,2,1]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[3,4,8,7,6,5,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[3,4,5,8,7,6,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,3,6,5,8,7,2,1]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[5,7,6,4,3,8,2,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,7,8,6,5,4,3,1]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[2,5,6,7,8,4,3,1]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[2,4,8,7,6,5,3,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[2,4,6,8,7,5,3,1]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[2,7,6,5,4,8,3,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[2,3,5,6,8,7,4,1]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[2,3,5,6,7,8,4,1]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[4,3,2,8,7,6,5,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,4,2,8,7,6,5,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,4,3,8,7,6,5,1]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[3,2,4,8,7,6,5,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[2,3,4,8,7,6,5,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,4,3,2,8,7,6,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,4,3,2,7,8,6,1]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[2,5,4,3,8,7,6,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[2,5,4,3,7,8,6,1]=>[1,2,5,3,7,8,4,6]=>[1,2,5,6,3,8,7,4]=>{{1},{2},{3,5},{4,6,8},{7}}
[2,4,5,3,7,8,6,1]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>{{1},{2},{3,5},{4},{6,8},{7}}
[3,4,2,5,7,8,6,1]=>[1,2,5,7,8,3,4,6]=>[1,2,4,6,5,8,7,3]=>{{1},{2},{3,4,6,8},{5},{7}}
[2,4,3,6,5,8,7,1]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}}
[2,5,4,3,6,8,7,1]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>{{1},{2},{3,5},{4,7,8},{6}}
[2,4,3,5,6,8,7,1]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[2,3,4,5,6,8,7,1]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[2,5,4,7,6,3,8,1]=>[1,2,5,3,8,4,7,6]=>[1,2,5,7,3,8,6,4]=>{{1},{2},{3,5},{4,6,7,8}}
[2,5,4,6,7,3,8,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[4,3,2,7,6,5,8,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[3,4,2,7,6,5,8,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[2,4,3,7,6,5,8,1]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>{{1},{2},{3,4},{5,7},{6,8}}
[3,2,4,7,6,5,8,1]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>{{1},{2},{3,5,7},{4},{6,8}}
[2,3,4,7,6,5,8,1]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[5,4,3,2,7,6,8,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,3,5,2,7,6,8,1]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[2,5,4,3,7,6,8,1]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[3,2,5,4,7,6,8,1]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}}
[2,3,5,4,7,6,8,1]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[2,4,3,6,5,7,8,1]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[2,5,4,3,6,7,8,1]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>{{1},{2},{3,5},{4,8},{6},{7}}
[1,8,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,8,6,5,4,3,2]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,8,7,5,4,3,2]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,6,8,5,4,3,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,8,5,4,3,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[1,5,8,7,6,4,3,2]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,7,6,5,8,4,3,2]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,5,6,7,8,4,3,2]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[1,3,5,7,8,6,4,2]=>[1,3,5,7,8,2,4,6]=>[1,4,3,6,5,8,7,2]=>{{1},{2,4,6,8},{3},{5},{7}}
[1,3,6,5,7,8,4,2]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,3,5,6,7,8,4,2]=>[1,3,5,6,7,8,2,4]=>[1,4,3,8,5,6,7,2]=>{{1},{2,4,8},{3},{5},{6},{7}}
[1,4,3,8,7,6,5,2]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[1,4,3,7,8,6,5,2]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[1,4,3,7,6,8,5,2]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[1,3,4,8,7,6,5,2]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[1,3,4,7,6,8,5,2]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[1,3,4,5,7,8,6,2]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>{{1},{2,6,8},{3},{4},{5},{7}}
[1,5,6,4,3,8,7,2]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[1,4,3,6,5,8,7,2]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[1,3,4,5,6,8,7,2]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>{{1},{2,7,8},{3},{4},{5},{6}}
[1,5,4,3,6,7,8,2]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>{{1},{2,3,5},{4,8},{6},{7}}
[1,4,3,5,6,7,8,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[1,3,4,5,6,7,8,2]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>{{1},{2,8},{3},{4},{5},{6},{7}}
[2,1,8,7,6,5,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,7,8,5,4,3]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,1,6,5,8,7,4,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,1,7,6,5,8,4,3]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,1,6,7,5,8,4,3]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,1,6,5,7,8,4,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,1,5,6,7,8,4,3]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[2,1,4,5,8,7,6,3]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[2,1,4,5,7,8,6,3]=>[1,4,5,7,8,2,3,6]=>[1,3,6,4,5,8,7,2]=>{{1},{2,3,6,8},{4},{5},{7}}
[2,1,6,5,7,4,8,3]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,1,5,4,7,6,8,3]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[2,1,4,5,6,7,8,3]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>{{1},{2,3,8},{4},{5},{6},{7}}
[1,2,6,7,8,5,4,3]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[1,2,5,6,7,8,4,3]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[1,2,4,8,7,6,5,3]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,4,7,8,6,5,3]=>[1,2,4,7,8,3,5,6]=>[1,2,5,4,6,8,7,3]=>{{1},{2},{3,5,6,8},{4},{7}}
[1,2,4,6,7,8,5,3]=>[1,2,4,6,7,8,3,5]=>[1,2,5,4,8,6,7,3]=>{{1},{2},{3,5,8},{4},{6},{7}}
[1,2,6,5,4,7,8,3]=>[1,2,6,3,4,7,8,5]=>[1,2,4,6,8,3,7,5]=>{{1},{2},{3,4,6},{5,8},{7}}
[1,2,5,6,4,7,8,3]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[1,2,4,5,6,7,8,3]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>{{1},{2},{3,8},{4},{5},{6},{7}}
[3,2,1,8,7,6,5,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,1,7,8,6,5,4]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,2,1,6,8,7,5,4]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,2,1,7,6,8,5,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,1,6,7,8,5,4]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[3,2,1,5,8,7,6,4]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,2,1,6,5,8,7,4]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[3,2,1,7,6,5,8,4]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,2,1,6,7,5,8,4]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[3,2,1,6,5,7,8,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,2,1,5,6,7,8,4]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[2,3,1,8,7,6,5,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,2,8,7,6,5,4]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[2,1,3,8,7,6,5,4]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,2,3,8,7,6,5,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,7,8,6,5,4]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,6,8,7,5,4]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[1,2,3,7,6,8,5,4]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,2,3,6,7,8,5,4]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[1,2,3,5,8,7,6,4]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,2,3,5,7,8,6,4]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[1,2,3,6,5,8,7,4]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[1,2,3,5,6,8,7,4]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[1,2,3,7,6,5,8,4]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[1,2,3,6,7,5,8,4]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[1,2,3,5,7,6,8,4]=>[1,2,3,5,7,4,6,8]=>[1,2,3,6,5,7,4,8]=>{{1},{2},{3},{4,6,7},{5},{8}}
[1,2,3,6,5,7,8,4]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[1,2,3,5,6,7,8,4]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[4,3,2,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,3,2,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,3,2,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,3,2,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[3,4,2,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,2,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,4,2,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,4,2,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,4,2,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,4,3,1,8,7,6,5]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,3,1,7,8,6,5]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,4,3,1,7,6,8,5]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,4,1,8,7,6,5]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,4,1,7,8,6,5]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,2,4,1,7,6,8,5]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,3,4,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,1,7,8,6,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,3,4,1,6,8,7,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,3,4,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,3,4,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[1,4,3,2,8,7,6,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,4,3,2,7,6,8,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[1,4,3,2,6,7,8,5]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>{{1},{2,4},{3,5,8},{6},{7}}
[1,3,4,2,8,7,6,5]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[1,3,4,2,7,6,8,5]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>{{1},{2,4},{3},{5,6,7},{8}}
[1,3,4,2,6,7,8,5]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>{{1},{2,4},{3},{5,8},{6},{7}}
[2,1,4,3,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,1,4,3,7,8,6,5]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[2,1,4,3,6,8,7,5]=>[1,4,2,3,6,8,5,7]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}
[2,1,4,3,7,6,8,5]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[2,1,4,3,6,7,8,5]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>{{1},{2,3,4},{5,8},{6},{7}}
[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[1,2,4,3,7,6,8,5]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[1,2,4,3,6,7,8,5]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>{{1},{2},{3,4},{5,8},{6},{7}}
[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[1,3,2,4,6,7,8,5]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>{{1},{2,3},{4},{5,8},{6},{7}}
[2,1,3,4,8,7,6,5]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,1,3,4,7,6,8,5]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[2,1,3,4,6,7,8,5]=>[1,3,4,6,7,8,2,5]=>[1,5,3,4,8,6,7,2]=>{{1},{2,5,8},{3},{4},{6},{7}}
[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,2,3,4,7,8,6,5]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[1,2,3,4,7,6,8,5]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,2,3,4,6,7,8,5]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>{{1},{2},{3},{4},{5,8},{6},{7}}
[5,4,3,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,3,2,1,7,8,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,5,3,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,5,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,4,3,1,8,7,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,5,4,1,8,7,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,5,1,8,7,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,2,5,1,8,7,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,3,5,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,1,5,8,7,6]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,2,4,1,5,7,8,6]=>[1,5,7,8,2,4,3,6]=>[1,4,6,3,5,8,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[2,3,4,1,5,8,7,6]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,2,1,4,5,8,7,6]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[2,3,1,4,5,7,8,6]=>[1,4,5,7,8,2,3,6]=>[1,3,6,4,5,8,7,2]=>{{1},{2,3,6,8},{4},{5},{7}}
[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[6,5,4,3,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,4,3,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,3,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,3,6,5,1,8,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,3,2,6,1,8,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,3,2,6,1,8,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,5,2,6,1,8,7]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,5,4,6,1,8,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,6,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,5,6,4,3,8,7]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[2,1,4,6,5,3,8,7]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[2,1,5,4,6,3,8,7]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[2,1,4,5,6,3,8,7]=>[1,4,5,6,2,3,8,7]=>[1,3,6,4,5,2,8,7]=>{{1},{2,3,6},{4},{5},{7,8}}
[4,3,2,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[3,4,2,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,3,4,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,1,4,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[5,4,3,2,1,6,8,7]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,2,4,1,5,6,8,7]=>[1,5,6,8,2,4,3,7]=>[1,4,7,3,5,6,8,2]=>{{1},{2,3,4,7,8},{5},{6}}
[2,1,3,4,5,6,8,7]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>{{1},{2,7,8},{3},{4},{5},{6}}
[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[5,7,6,4,3,2,1,8]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,6,5,3,2,1,8]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,7,6,5,2,1,8]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,7,6,5,4,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,6,7,5,4,1,8]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,3,2,7,6,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,3,2,7,6,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,4,2,7,6,1,8]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,5,4,7,6,1,8]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,7,6,1,8]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,3,4,6,7,5,2,8]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>{{1},{2,7},{3},{4},{5,8},{6}}
[1,3,4,5,7,6,2,8]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>{{1},{2,7},{3},{4},{5},{6,8}}
[2,1,6,7,5,4,3,8]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[4,3,2,1,7,6,5,8]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,3,2,1,6,7,5,8]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[3,2,4,1,7,6,5,8]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,3,4,1,7,6,5,8]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,3,4,1,6,7,5,8]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,4,3,2,7,6,5,8]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[1,3,4,2,6,7,5,8]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}}
[5,4,3,2,1,7,6,8]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,1,5,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[2,3,1,5,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}
[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[1,2,4,6,5,3,7,8]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>{{1},{2},{3,6},{4},{5,8},{7}}
[4,3,2,1,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,2,4,1,6,5,7,8]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,3,4,1,6,5,7,8]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[1,2,3,4,8,6,7,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,2,3,5,8,6,7,4]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,2,3,7,5,6,8,4]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,2,3,8,5,6,7,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,5,7,6,4]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,6,5,7,4]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,8,6,7,5,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,4,5,8,6,7,3]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[1,2,4,8,6,5,7,3]=>[1,2,4,8,3,5,7,6]=>[1,2,5,4,7,8,6,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,2,6,4,5,7,8,3]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,2,8,5,4,6,7,3]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,2,8,6,5,7,4]=>[1,3,2,8,4,5,7,6]=>[1,3,2,5,7,8,6,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,3,7,4,5,6,2,8]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[1,3,8,5,4,6,7,2]=>[1,3,8,2,4,6,7,5]=>[1,4,3,6,8,7,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,8,5,6,7,4,2]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,8,6,5,7,4,2]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,3,4,6,7,8,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,8,4,7,6,5,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,4,7,6,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,4,5,6,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,4,6,5,3,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,5,4,7,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,5,4,6,3,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,5,6,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,3,8,5,7,6,4]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,1,4,3,8,6,7,5]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,1,4,5,8,6,7,3]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[2,1,7,4,6,5,8,3]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,8,5,4,7,6,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,8,7,5,6,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,1,8,6,7,5,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,1,8,6,7,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,8,5,6,7,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[2,3,4,8,5,7,6,1]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[2,3,4,8,6,5,7,1]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[2,3,4,8,6,7,5,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[2,3,7,4,5,6,8,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[2,5,3,4,1,8,7,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,3,4,8,6,7,1]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[2,8,3,4,5,6,7,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,8,3,5,4,7,6,1]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,8,3,5,7,6,4,1]=>[1,2,8,3,5,7,4,6]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,5,4,3,8,6,7,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[2,8,4,3,5,7,6,1]=>[1,2,8,3,5,7,4,6]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,2,1,5,8,6,7,4]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,2,1,7,5,6,4,8]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,2,1,7,5,6,8,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,1,8,5,6,7,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,1,8,5,7,6,4]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,1,8,6,5,7,4]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,1,8,6,7,5,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,4,1,8,6,7,5]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,7,4,6,5,8,1]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,2,7,5,4,6,1,8]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,3,1,6,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[4,2,3,1,6,7,8,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[4,2,3,1,7,6,8,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,2,3,1,8,6,7,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,3,1,8,7,6,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,3,7,5,6,8,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[4,2,3,7,6,5,8,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[4,2,3,8,7,6,5,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,2,3,4,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,3,4,6,5,1,8]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,4,3,1,7,6,8]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,2,4,3,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,4,3,6,1,7,8]=>[1,7,8,2,4,3,6,5]=>[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,2,4,3,6,1,8,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,4,3,7,6,8,1]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[7,2,4,3,6,5,8,1]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}}
[8,2,7,4,6,5,3,1]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,3,2,1,8,6,7,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,7,5,6,8,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,3,2,8,5,7,6,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,3,2,4,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,2,5,4,1,8,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,2,5,4,7,6,1]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}}
[8,3,2,7,6,5,4,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,3,4,2,1,7,8,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,3,4,2,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,7,4,6,5,2,1]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,4,3,2,8,6,7,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,3,4,2,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,3,5,4,6,2,1]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[8,7,3,6,5,4,2,1]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[8,5,4,3,2,7,6,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,7,4,3,6,5,2,1]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[2,4,6,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[2,1,4,3,6,8,5,7]=>[1,4,2,3,6,8,5,7]=>[1,3,4,2,7,6,8,5]=>{{1},{2,3,4},{5,7,8},{6}}
[2,1,4,6,3,8,5,7]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[2,4,1,6,3,8,5,7]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,1,4,6,8,3,5,7]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[2,4,6,1,8,3,5,7]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,6,8,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[2,4,1,6,3,7,5,8]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[2,4,1,3,6,7,8,5]=>[1,3,6,7,8,2,4,5]=>[1,4,3,5,8,6,7,2]=>{{1},{2,4,5,8},{3},{6},{7}}
[2,4,1,6,7,3,8,5]=>[1,6,7,2,4,3,8,5]=>[1,4,7,3,8,6,2,5]=>{{1},{2,3,4,7},{5,8},{6}}
[2,1,4,3,7,5,8,6]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[2,4,1,3,7,5,8,6]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[2,1,4,3,7,8,5,6]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[2,4,7,1,3,8,5,6]=>[1,3,8,2,4,7,5,6]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,4,7,8,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[2,4,1,5,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[2,1,4,5,7,3,8,6]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[2,4,5,7,1,3,8,6]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,1,4,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,4,1,3,8,5,6,7]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,4,1,5,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[2,1,4,5,8,3,6,7]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[2,4,1,5,3,6,8,7]=>[1,5,2,4,3,6,8,7]=>[1,4,5,3,2,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[2,4,1,5,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[2,4,5,6,7,8,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[2,1,5,3,6,4,8,7]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[2,5,6,8,1,3,4,7]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>{{1},{2,5,6,7},{3},{4},{8}}
[2,5,1,6,7,3,4,8]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,5,1,6,7,3,8,4]=>[1,6,7,2,5,3,8,4]=>[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[2,1,5,6,7,8,3,4]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[2,5,6,1,7,8,3,4]=>[1,7,8,2,5,6,3,4]=>[1,5,4,8,6,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,5,6,7,8,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[2,1,5,3,7,4,8,6]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[2,1,5,7,3,8,4,6]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[2,5,7,1,8,3,4,6]=>[1,8,2,5,7,3,4,6]=>[1,5,4,6,7,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,5,1,7,4,8,6]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,3,5,1,6,4,7,8]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,3,5,6,1,7,8,4]=>[1,7,8,2,3,5,6,4]=>[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,3,5,6,7,8,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[2,1,6,3,7,4,8,5]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[2,6,1,3,7,4,8,5]=>[1,3,7,2,6,4,8,5]=>[1,6,3,7,8,4,2,5]=>{{1},{2,4,6,7},{3},{5,8}}
[2,6,7,1,3,4,8,5]=>[1,3,4,8,2,6,7,5]=>[1,6,3,4,8,7,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,6,1,7,3,8,4,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[2,1,6,7,8,3,4,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,6,7,8,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[2,1,6,3,7,4,5,8]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[2,3,1,6,4,7,5,8]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[2,3,6,1,4,7,5,8]=>[1,4,7,2,3,6,5,8]=>[1,3,6,4,7,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[2,1,3,6,7,8,4,5]=>[1,3,6,7,8,2,4,5]=>[1,4,3,5,8,6,7,2]=>{{1},{2,4,5,8},{3},{6},{7}}
[2,3,1,6,7,8,4,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,1,6,3,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,3,1,6,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,3,1,6,8,4,5,7]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,1,6,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,3,6,1,4,5,8,7]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[2,3,4,1,6,8,5,7]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,6,1,3,4,5,7,8]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>{{1},{2,6,8},{3},{4},{5},{7}}
[2,3,4,6,1,7,5,8]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,3,4,6,7,8,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[2,1,7,8,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,7,1,8,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,8,1,3,4,5,6]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>{{1},{2,6},{3},{4},{5},{7},{8}}
[2,3,1,7,4,8,5,6]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,3,7,1,4,8,5,6]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[2,3,4,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,3,4,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,3,4,7,1,8,5,6]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,1,3,4,5,6,8]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>{{1},{2,7,8},{3},{4},{5},{6}}
[2,3,4,1,7,5,6,8]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,3,4,5,7,1,8,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,7,8,1,6]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,1,8,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,1,3,4,5,6,7]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[2,1,3,8,4,5,6,7]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,1,3,4,8,5,6,7]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,3,4,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,1,5,8,6,7]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,3,4,5,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,8,1,6,7]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,3,4,5,6,8,1,7]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,4,2,6,5,8,7]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[3,4,1,2,6,5,8,7]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[3,1,4,6,8,2,5,7]=>[1,4,6,8,2,5,7,3]=>[1,5,8,4,7,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[3,4,6,1,2,7,5,8]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,1,4,2,6,7,8,5]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>{{1},{2,4},{3,5,8},{6},{7}}
[3,4,1,2,6,7,8,5]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[3,4,6,1,2,7,8,5]=>[1,2,7,8,3,4,6,5]=>[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[3,4,6,7,1,2,8,5]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,4,6,7,1,8,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,4,2,7,5,8,6]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[3,4,1,2,7,8,5,6]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[3,4,7,8,1,2,5,6]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[3,4,5,7,1,2,8,6]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,4,2,8,5,6,7]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[3,4,1,2,8,5,6,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,4,1,5,8,2,6,7]=>[1,5,8,2,6,7,3,4]=>[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,1,4,2,5,6,7,8]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>{{1},{2,4},{3,8},{5},{6},{7}}
[3,1,4,5,6,7,8,2]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>{{1},{2,3,8},{4},{5},{6},{7}}
[3,4,1,5,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[3,4,5,6,7,1,8,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,1,6,2,4,8,7]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[3,5,6,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[3,5,1,2,6,8,4,7]=>[1,2,6,8,3,5,4,7]=>[1,2,5,7,4,6,8,3]=>{{1},{2},{3,4,5,7,8},{6}}
[3,5,6,8,1,2,4,7]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[3,5,6,1,7,2,4,8]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[3,5,6,1,7,2,8,4]=>[1,7,2,8,3,5,6,4]=>[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,5,6,1,7,8,2,4]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,5,6,7,8,1,2,4]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[3,1,5,2,7,4,8,6]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[3,1,5,7,2,8,4,6]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[3,5,1,7,2,8,4,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,1,5,2,7,4,6,8]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,3,5,2,7,4,8,6]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[3,1,5,2,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[1,3,2,5,8,4,6,7]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[1,3,5,8,2,4,6,7]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[1,3,5,2,6,7,4,8]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>{{1},{2,5},{3},{4,7},{6},{8}}
[1,3,5,6,2,7,4,8]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[1,3,5,6,7,8,2,4]=>[1,3,5,6,7,8,2,4]=>[1,4,3,8,5,6,7,2]=>{{1},{2,4,8},{3},{5},{6},{7}}
[3,1,6,2,7,4,8,5]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[3,6,1,7,2,8,4,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,6,7,1,2,8,4,5]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,1,7,8,2,4,5]=>[1,7,8,2,4,5,3,6]=>[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,6,7,8,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}}
[3,1,6,2,7,4,5,8]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[3,1,6,7,2,4,5,8]=>[1,6,7,2,4,5,8,3]=>[1,4,8,5,7,6,2,3]=>{{1},{2,4,5,7},{3,8},{6}}
[3,6,1,2,4,7,5,8]=>[1,2,4,7,3,6,5,8]=>[1,2,6,4,7,5,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[1,3,2,6,4,7,5,8]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[3,1,2,6,7,4,8,5]=>[1,2,6,7,3,4,8,5]=>[1,2,4,7,8,6,3,5]=>{{1},{2},{3,4,7},{5,8},{6}}
[3,1,6,2,8,4,5,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,1,6,8,2,4,5,7]=>[1,6,8,2,4,5,7,3]=>[1,4,8,5,7,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,3,2,6,4,8,5,7]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[3,1,6,2,4,5,8,7]=>[1,6,2,4,5,8,3,7]=>[1,4,7,5,6,2,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[3,1,6,2,4,5,7,8]=>[1,6,2,4,5,7,8,3]=>[1,4,8,5,6,2,7,3]=>{{1},{2,4,5,6},{3,8},{7}}
[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[3,1,2,4,6,7,8,5]=>[1,2,4,6,7,8,3,5]=>[1,2,5,4,8,6,7,3]=>{{1},{2},{3,5,8},{4},{6},{7}}
[1,3,4,6,7,2,8,5]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>{{1},{2,7},{3},{4},{5,8},{6}}
[1,3,2,7,4,8,5,6]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[1,3,7,2,8,4,5,6]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[3,7,1,2,4,5,6,8]=>[1,2,4,5,6,8,3,7]=>[1,2,7,4,5,6,8,3]=>{{1},{2},{3,7,8},{4},{5},{6}}
[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,3,4,5,7,8,2,6]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>{{1},{2,6,8},{3},{4},{5},{7}}
[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[3,1,2,4,8,5,6,7]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[1,3,4,2,8,5,6,7]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[3,1,2,4,5,8,6,7]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[4,1,5,2,6,3,8,7]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[4,5,1,2,6,3,8,7]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,5,6,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,1,5,2,6,8,3,7]=>[1,5,2,6,8,3,7,4]=>[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[4,5,1,6,2,8,3,7]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,5,6,1,2,8,3,7]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,5,6,8,2,3,7]=>[1,5,6,8,2,3,7,4]=>[1,3,7,8,5,6,4,2]=>{{1},{2,3,4,7,8},{5},{6}}
[4,5,6,8,1,2,3,7]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[4,5,1,6,2,7,3,8]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[4,5,6,1,7,2,3,8]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,5,6,7,1,2,8,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,5,6,7,8,2,3]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[4,5,6,7,1,8,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,2,7,3,8,6]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[4,5,1,7,2,3,8,6]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,1,5,2,7,8,3,6]=>[1,5,2,7,8,3,6,4]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[4,1,5,7,2,8,3,6]=>[1,5,7,2,8,3,6,4]=>[1,7,6,8,5,4,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[4,5,1,7,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,5,7,8,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[4,5,1,2,7,3,6,8]=>[1,2,7,3,6,8,4,5]=>[1,2,6,5,8,7,3,4]=>{{1},{2},{3,6,7},{4,5,8}}
[1,4,2,5,3,7,6,8]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}
[4,1,2,5,7,3,6,8]=>[1,2,5,7,3,6,8,4]=>[1,2,6,8,5,7,3,4]=>{{1},{2},{3,6,7},{4,8},{5}}
[1,4,2,5,7,3,8,6]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>{{1},{2,4},{3,7},{5},{6,8}}
[1,4,5,2,7,3,8,6]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>{{1},{2,5},{3,7},{4},{6,8}}
[1,4,5,7,2,3,8,6]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[4,5,1,2,8,3,6,7]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,4,2,5,3,8,6,7]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[4,1,2,5,6,3,8,7]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>{{1},{2},{3,6},{4,7,8},{5}}
[1,4,2,5,3,6,7,8]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[1,4,5,2,6,3,7,8]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>{{1},{2,5},{3,6},{4},{7},{8}}
[1,4,2,5,6,7,3,8]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>{{1},{2,4},{3,7},{5},{6},{8}}
[1,4,5,6,2,7,3,8]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>{{1},{2,6},{3,7},{4},{5},{8}}
[1,4,5,6,7,2,3,8]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[4,1,2,5,6,7,8,3]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[1,4,2,5,6,7,8,3]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>{{1},{2,4},{3,8},{5},{6},{7}}
[1,4,5,2,6,7,8,3]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>{{1},{2,5},{3,8},{4},{6},{7}}
[1,4,5,6,7,8,2,3]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>{{1},{2,3,8},{4},{5},{6},{7}}
[4,1,6,2,7,3,8,5]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[4,6,7,8,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[4,6,1,7,2,3,5,8]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[4,6,1,2,3,7,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,4,2,6,3,7,5,8]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[4,1,2,6,7,3,8,5]=>[1,2,6,7,3,8,4,5]=>[1,2,7,5,8,6,3,4]=>{{1},{2},{3,7},{4,5,8},{6}}
[1,4,6,2,7,3,8,5]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>{{1},{2,6},{3,7},{4},{5,8}}
[1,4,2,6,7,8,3,5]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>{{1},{2,4},{3,5,8},{6},{7}}
[1,4,6,2,7,8,3,5]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>{{1},{2,6},{3,5,8},{4},{7}}
[1,4,6,7,2,8,3,5]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>{{1},{2,7},{3,5,8},{4},{6}}
[4,1,6,2,8,3,5,7]=>[1,6,2,8,3,5,7,4]=>[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,6,1,8,2,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,2,6,3,8,5,7]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[1,4,2,6,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[4,1,2,3,6,5,8,7]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[4,1,2,3,6,8,5,7]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[4,6,1,2,3,5,7,8]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[1,4,2,6,3,5,7,8]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[4,1,2,3,6,5,7,8]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[4,1,2,3,6,7,5,8]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[4,1,2,3,6,7,8,5]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[1,4,2,3,6,7,8,5]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>{{1},{2,3,4},{5,8},{6},{7}}
[1,2,4,6,7,8,3,5]=>[1,2,4,6,7,8,3,5]=>[1,2,5,4,8,6,7,3]=>{{1},{2},{3,5,8},{4},{6},{7}}
[4,1,7,2,8,3,5,6]=>[1,7,2,8,3,5,6,4]=>[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,7,1,2,8,3,5,6]=>[1,2,8,3,5,6,4,7]=>[1,2,5,7,6,4,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,7,8,2,3,5,6]=>[1,7,8,2,3,5,6,4]=>[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,4,2,7,3,8,5,6]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[1,4,2,7,8,3,5,6]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[4,1,2,3,7,5,8,6]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[4,1,2,3,7,8,5,6]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[4,1,7,2,3,5,6,8]=>[1,7,2,3,5,6,8,4]=>[1,3,5,8,6,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[4,7,1,2,3,5,6,8]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[1,4,2,7,3,5,6,8]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[4,1,2,3,7,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[4,1,2,3,5,7,6,8]=>[1,2,3,5,7,4,6,8]=>[1,2,3,6,5,7,4,8]=>{{1},{2},{3},{4,6,7},{5},{8}}
[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[4,1,2,3,5,7,8,6]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[1,2,4,5,7,3,8,6]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>{{1},{2},{3,7},{4},{5},{6,8}}
[4,8,1,2,3,5,6,7]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[1,4,2,8,3,5,6,7]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,1,2,3,8,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[4,1,2,3,5,8,6,7]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[4,1,2,3,5,6,8,7]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[5,1,6,2,7,3,8,4]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[5,6,1,2,7,8,3,4]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[1,5,2,6,3,7,4,8]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[5,6,1,2,3,7,8,4]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,5,6,7,8,2,3,4]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[5,6,8,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[5,6,1,2,3,8,4,7]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,5,2,6,3,8,4,7]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[1,5,6,2,3,8,4,7]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[1,5,2,6,3,4,7,8]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[1,5,2,3,6,4,7,8]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[1,2,5,3,6,4,7,8]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[1,2,5,6,3,4,7,8]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[1,2,5,3,6,7,4,8]=>[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>{{1},{2},{3,5},{4,7},{6},{8}}
[5,1,2,3,6,7,8,4]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[1,5,2,3,6,7,8,4]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>{{1},{2,3,5},{4,8},{6},{7}}
[1,2,5,3,6,7,8,4]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>{{1},{2},{3,5},{4,8},{6},{7}}
[1,2,5,6,3,7,8,4]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>{{1},{2},{3,6},{4,8},{5},{7}}
[1,2,5,6,7,3,8,4]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>{{1},{2},{3,7},{4,8},{5},{6}}
[1,2,5,6,7,8,3,4]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[5,7,8,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[1,5,2,7,3,8,4,6]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[1,5,7,2,8,3,4,6]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[5,1,2,7,3,4,8,6]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[5,7,1,2,3,4,6,8]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[1,5,2,7,3,4,6,8]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,5,2,3,7,4,6,8]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[5,1,2,8,3,4,6,7]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,5,2,8,3,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,5,8,2,3,4,6,7]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,1,2,3,8,4,6,7]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,5,3,8,4,6,7]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[5,1,2,3,4,6,8,7]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,1,7,8,2,3,4,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,7,1,8,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,2,7,3,8,4,5]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[1,6,7,8,2,3,4,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[6,7,1,2,3,4,8,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,1,2,3,7,8,4,5]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[6,1,7,2,3,4,5,8]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,1,2,7,3,4,5,8]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[1,6,2,7,3,4,5,8]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,6,7,2,3,4,5,8]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,6,2,3,4,7,5,8]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,2,3,6,4,7,5,8]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[6,1,2,3,4,7,8,5]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[1,2,6,3,4,7,8,5]=>[1,2,6,3,4,7,8,5]=>[1,2,4,6,8,3,7,5]=>{{1},{2},{3,4,6},{5,8},{7}}
[1,2,3,6,4,7,8,5]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>{{1},{2},{3},{4,6},{5,8},{7}}
[1,2,3,6,7,4,8,5]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>{{1},{2},{3},{4,7},{5,8},{6}}
[6,1,8,2,3,4,5,7]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,2,8,3,4,5,7]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,6,2,8,3,4,5,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,6,8,2,3,4,5,7]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,6,2,3,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[1,2,3,6,4,8,5,7]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[6,1,2,3,4,5,8,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,1,8,2,3,4,5,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,2,8,3,4,5,6]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,2,8,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,7,8,2,3,4,5,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,7,2,3,8,4,5,6]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,1,2,3,4,8,5,6]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,7,2,3,4,8,5,6]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,2,3,7,4,8,5,6]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[7,1,2,3,4,5,8,6]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[1,7,2,3,4,5,8,6]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[1,2,3,7,4,5,8,6]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[1,2,3,4,7,8,5,6]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,3,2,5,4,8,1,6]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[8,4,5,2,3,7,6,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[6,4,5,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,1,5,4,2,8,7]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,6,5,1,3,2,8,7]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,6,4,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,5,4,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,6,4,3,7,2,5,1]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[7,6,4,3,8,2,1,5]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,7,4,3,8,1,2,5]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[5,7,4,3,1,8,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,1,5,4,8,2,6]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[4,8,5,1,3,7,6,2]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[5,8,4,3,1,7,6,2]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,8,4,3,7,1,5,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[7,8,4,3,6,5,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[6,8,5,7,3,1,4,2]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[5,8,6,7,1,3,4,2]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}}
[4,8,6,1,7,3,5,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,8,1,6,7,4,5,2]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[2,1,8,6,7,4,5,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,6,8,4,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,7,1,6,8,4,2,5]=>[1,6,8,2,5,3,7,4]=>[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,7,6,1,8,3,2,5]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,6,8,1,3,2,4]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[7,4,6,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,4,6,2,7,3,5,1]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[7,3,2,6,8,4,1,5]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>{{1},{2,5},{3,4,7,8},{6}}
[6,3,2,7,8,1,4,5]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>{{1},{2,5},{3,6,8},{4},{7}}
[5,3,2,7,1,8,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,4,1,2,8,7,6,5]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,3,2,8,1,7,6,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,3,2,8,7,1,5,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,3,2,8,6,5,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[7,4,8,2,6,5,1,3]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[6,4,8,2,7,1,5,3]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[5,4,8,2,1,7,6,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,5,8,1,2,7,6,3]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[3,5,1,8,2,7,6,4]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,8,7,3,5,4]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,6,1,8,7,2,5,4]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,8,1,7,2,5,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,8,7,1,2,4,3]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[6,5,8,7,2,1,4,3]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[7,5,8,6,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[8,5,7,6,2,4,3,1]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>{{1},{2},{3,4},{5},{6,7},{8}}
[3,7,1,8,6,5,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,8,6,5,3,4]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,8,1,7,6,5,4,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,8,7,1,6,5,3,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,8,7,6,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[6,8,7,5,4,1,3,2]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>{{1},{2,3},{4},{5},{6},{7,8}}
[2,1,4,3,6,5,8,7,10,9]=>[1,4,2,3,6,5,8,7,10,9]=>[1,3,4,2,6,5,8,7,10,9]=>{{1},{2,3,4},{5,6},{7,8},{9,10}}
[8,7,6,5,4,3,2,1,10,9]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,9,6,5,4,3,8,7,2,1]=>[1,2,3,8,4,5,6,7,9,10]=>[1,2,3,5,6,7,8,4,9,10]=>{{1},{2},{3},{4,5,6,7,8},{9},{10}}
[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[6,5,4,3,2,1,10,9,8,7]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,9,4,3,8,7,6,5,2,1]=>[1,2,3,8,4,5,6,7,9,10]=>[1,2,3,5,6,7,8,4,9,10]=>{{1},{2},{3},{4,5,6,7,8},{9},{10}}
[4,3,2,1,10,9,8,7,6,5]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[2,1,10,9,8,7,6,5,4,3]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[6,3,5,1,2,4,7,8]=>[1,2,4,7,8,3,5,6]=>[1,2,5,4,6,8,7,3]=>{{1},{2},{3,5,6,8},{4},{7}}
[7,3,5,1,2,4,6,8]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[6,2,8,1,3,4,5,7]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>{{1},{2,7},{3},{4},{5},{6,8}}
[6,5,8,1,2,3,4,7]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[7,5,8,1,2,3,4,6]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[8,3,7,1,2,4,5,6]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>{{1},{2},{3,6},{4},{5},{7},{8}}
[8,5,7,1,2,3,4,6]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[5,2,6,7,1,3,4,8]=>[1,3,4,8,2,6,7,5]=>[1,6,3,4,8,7,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[5,3,6,7,1,2,4,8]=>[1,2,4,8,3,6,7,5]=>[1,2,6,4,8,7,5,3]=>{{1},{2},{3,5,6,7,8},{4}}
[6,2,5,7,1,3,4,8]=>[1,3,4,8,2,5,7,6]=>[1,5,3,4,7,8,6,2]=>{{1},{2,5,6,7,8},{3},{4}}
[6,3,5,7,1,2,4,8]=>[1,2,4,8,3,5,7,6]=>[1,2,5,4,7,8,6,3]=>{{1},{2},{3,5,6,7,8},{4}}
[4,2,6,8,1,3,5,7]=>[1,3,5,7,2,6,8,4]=>[1,6,3,8,5,7,2,4]=>{{1},{2,6,7},{3},{4,8},{5}}
[4,3,6,8,1,2,5,7]=>[1,2,5,7,3,6,8,4]=>[1,2,6,8,5,7,3,4]=>{{1},{2},{3,6,7},{4,8},{5}}
[6,2,4,8,1,3,5,7]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[6,3,5,8,1,2,4,7]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>{{1},{2},{3,5,7},{4},{6,8}}
[3,2,7,8,1,4,5,6]=>[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>{{1},{2,6},{3,8},{4},{5},{7}}
[8,2,4,6,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[4,8,2,5,1,3,6,7]=>[1,3,6,7,2,5,4,8]=>[1,5,3,7,4,6,2,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[4,8,2,6,1,3,5,7]=>[1,3,5,7,2,6,4,8]=>[1,6,3,7,5,4,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[6,8,2,4,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[3,8,2,7,1,4,5,6]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>{{1},{2,6},{3,7},{4},{5},{8}}
[4,8,2,7,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[4,8,3,7,1,2,5,6]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>{{1},{2},{3,6},{4,7},{5},{8}}
[5,8,3,7,1,2,4,6]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>{{1},{2},{3,6},{4},{5,7},{8}}
[5,8,4,7,1,2,3,6]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[6,8,5,7,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[7,8,2,4,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[7,8,4,6,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[4,3,2,6,1,5,7,8]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[5,3,2,7,1,4,6,8]=>[1,4,6,8,2,7,3,5]=>[1,7,5,4,8,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[4,3,2,8,1,5,6,7]=>[1,5,6,7,2,8,3,4]=>[1,7,4,8,5,6,2,3]=>{{1},{2,7},{3,4,8},{5},{6}}
[5,3,2,8,1,4,6,7]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>{{1},{2,7},{3,5,8},{4},{6}}
[6,4,2,8,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[6,5,4,8,1,2,3,7]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[7,4,3,8,1,2,5,6]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>{{1},{2},{3,6},{4,7,8},{5}}
[8,4,2,5,1,3,6,7]=>[1,3,6,7,2,5,4,8]=>[1,5,3,7,4,6,2,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[8,4,2,6,1,3,5,7]=>[1,3,5,7,2,6,4,8]=>[1,6,3,7,5,4,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[8,6,2,4,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[8,4,2,7,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[8,5,4,7,1,2,3,6]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[8,7,2,4,1,3,5,6]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>{{1},{2,4,6},{3},{5},{7},{8}}
[8,7,2,6,1,3,4,5]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[8,7,3,6,1,2,4,5]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}}
[8,7,4,6,1,2,3,5]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[5,6,2,4,8,1,3,7]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[5,7,2,4,8,1,3,6]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[4,7,3,6,8,1,2,5]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>{{1},{2},{3,5},{4,7,8},{6}}
[6,7,3,4,8,1,2,5]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[4,8,3,5,7,1,2,6]=>[1,2,6,3,5,7,4,8]=>[1,2,5,7,6,3,4,8]=>{{1},{2},{3,5,6},{4,7},{8}}
[5,8,4,6,7,1,2,3]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>{{1},{2},{3},{4},{5,7},{6},{8}}
[6,8,2,5,7,1,3,4]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>{{1},{2,4},{3},{5},{6,7},{8}}
[6,4,3,5,8,1,2,7]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[6,5,2,4,8,1,3,7]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[4,3,2,7,8,1,5,6]=>[1,5,6,2,7,8,3,4]=>[1,6,4,8,5,2,7,3]=>{{1},{2,6},{3,4,8},{5},{7}}
[4,3,7,2,6,1,5,8]=>[1,5,8,2,6,3,7,4]=>[1,6,7,8,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,3,7,2,5,1,4,8]=>[1,4,8,2,5,3,7,6]=>[1,5,7,4,3,8,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,4,7,2,5,1,3,8]=>[1,3,8,2,5,4,7,6]=>[1,5,3,7,4,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,4,8,2,5,1,3,7]=>[1,3,7,2,5,4,8,6]=>[1,5,3,7,4,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[4,3,8,2,7,1,5,6]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>{{1},{2,6},{3,7},{4,8},{5}}
[6,4,8,2,7,1,3,5]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[6,5,8,2,7,1,3,4]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>{{1},{2,4},{3},{5,7},{6,8}}
[7,5,8,4,6,1,2,3]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[8,3,7,2,6,1,4,5]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>{{1},{2,5},{3,6},{4},{7},{8}}
[8,4,7,2,6,1,3,5]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[8,4,7,3,6,1,2,5]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[8,6,7,2,5,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[6,4,3,2,7,1,5,8]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[7,6,5,3,8,1,2,4]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[8,5,3,2,7,1,4,6]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>{{1},{2,6},{3,5,7},{4},{8}}
[8,6,5,3,7,1,2,4]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[8,7,4,2,6,1,3,5]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[8,7,4,3,6,1,2,5]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[8,7,5,3,6,1,2,4]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[4,8,3,7,2,6,1,5]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[5,8,3,7,2,6,1,4]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[5,8,4,7,2,6,1,3]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[5,8,4,7,3,6,1,2]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[6,8,3,7,2,5,1,4]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}
[6,8,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}
[6,8,4,7,3,5,1,2]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[6,8,5,7,2,4,1,3]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[6,8,5,7,3,4,1,2]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[7,8,3,6,2,5,1,4]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[7,8,4,6,2,5,1,3]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[7,8,4,6,3,5,1,2]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[7,8,5,6,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[6,4,3,8,2,7,1,5]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[6,5,3,8,2,7,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[7,5,3,8,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[7,6,4,8,2,5,1,3]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[8,5,3,7,2,6,1,4]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[8,5,4,7,2,6,1,3]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[8,5,4,7,3,6,1,2]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[8,6,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}
[8,7,5,6,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[6,5,4,3,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[8,5,4,3,2,7,1,6]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,7,5,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[8,7,6,5,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[8,1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,1,2,3,8,7,4,6]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[8,1,2,3,6,7,4,5]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[4,1,2,8,7,3,5,6]=>[1,2,8,3,5,6,4,7]=>[1,2,5,7,6,4,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,2,7,6,3,8,5]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[8,1,2,5,6,3,4,7]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[8,1,2,7,6,3,4,5]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[7,1,2,5,6,3,8,4]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>{{1},{2},{3,6},{4,7,8},{5}}
[3,1,8,2,6,7,4,5]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,4,2,3,8,5,7]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[8,1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[8,1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,1,4,2,8,3,6,7]=>[1,4,2,8,3,6,7,5]=>[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,1,4,2,7,3,8,6]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[8,1,4,2,6,3,5,7]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[7,1,4,2,6,3,8,5]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[8,1,5,2,7,3,4,6]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[7,1,5,2,6,3,8,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[5,1,4,2,8,7,3,6]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,1,4,2,6,7,8,3]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>{{1},{2,4},{3,5,8},{6},{7}}
[3,1,8,6,2,7,4,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,8,5,2,3,4,6]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,8,6,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,6,5,2,7,3,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,1,4,5,2,7,8,3]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>{{1},{2,5},{3,6,8},{4},{7}}
[3,1,7,5,6,2,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[8,1,4,5,7,2,3,6]=>[1,4,5,7,2,3,6,8]=>[1,3,6,4,5,7,2,8]=>{{1},{2,3,6,7},{4},{5},{8}}
[8,1,7,5,6,2,3,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,1,4,5,6,2,8,3]=>[1,4,5,6,2,8,3,7]=>[1,6,7,4,5,2,8,3]=>{{1},{2,6},{3,7,8},{4},{5}}
[3,1,4,5,8,7,2,6]=>[1,4,5,8,2,6,3,7]=>[1,6,7,4,5,3,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[3,1,8,5,6,7,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,4,5,6,7,2,3]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>{{1},{2,3,7},{4},{5},{6},{8}}
[2,4,1,8,6,3,5,7]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,1,2,4,5,8,6]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[8,3,1,2,4,7,5,6]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[8,3,1,2,6,4,5,7]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[7,6,1,2,3,4,8,5]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,8,1,2,3,7,4,6]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[8,6,1,2,3,7,4,5]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,4,1,2,8,3,6,7]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,1,2,6,3,8,5]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[5,8,1,2,7,3,4,6]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,7,1,2,6,3,4,5]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[5,7,1,2,6,3,8,4]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[5,4,1,2,6,7,8,3]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[4,3,1,6,2,8,5,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,3,1,6,2,4,8,5]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[8,3,1,5,2,7,4,6]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,3,1,6,2,7,4,5]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[7,4,1,5,2,3,8,6]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[8,7,1,5,2,3,4,6]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,1,6,2,3,4,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,7,1,5,2,3,8,4]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,4,1,5,2,8,3,7]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,4,1,5,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,4,1,6,2,7,3,5]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,8,1,5,2,7,3,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[4,3,1,7,6,2,8,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[8,4,1,5,7,2,3,6]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[8,4,1,7,6,2,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,3,1,5,8,7,2,6]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,3,1,8,6,7,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,1,5,6,7,8,2]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[2,3,8,1,6,7,4,5]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[2,6,4,1,3,8,5,7]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,7,5,1,3,4,8,6]=>[1,3,4,8,2,7,5,6]=>[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,8,4,1,6,3,5,7]=>[1,6,2,8,3,5,7,4]=>[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,4,1,7,3,5,6]=>[1,7,2,8,3,5,6,4]=>[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,7,4,1,6,3,8,5]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[2,7,5,1,6,3,8,4]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[2,5,4,1,8,7,3,6]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,4,1,6,7,3,5]=>[1,6,7,2,8,3,5,4]=>[1,7,5,8,4,6,2,3]=>{{1},{2,7},{3,4,5,8},{6}}
[6,3,4,1,2,7,8,5]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[7,3,5,1,2,4,8,6]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[8,3,5,1,2,7,4,6]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,3,8,1,2,7,4,5]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[7,5,4,1,2,3,8,6]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,7,4,1,2,3,8,5]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,8,5,1,2,3,4,7]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[6,7,5,1,2,3,8,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,8,4,1,2,7,3,5]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,8,5,1,2,7,3,4]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,5,4,1,2,7,8,3]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[7,3,4,1,6,2,8,5]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,3,5,1,6,2,4,7]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[8,3,5,1,7,2,4,6]=>[1,7,2,4,6,3,5,8]=>[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,3,5,1,6,2,8,4]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,5,4,1,6,2,3,7]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[8,5,4,1,7,2,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,8,4,1,6,2,3,5]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,5,1,6,2,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,5,4,1,6,2,8,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,3,4,1,8,7,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,4,1,6,7,2,5]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[8,5,4,1,6,7,2,3]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[5,3,4,1,6,7,8,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,3,4,8,1,7,5,6]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,3,7,6,1,4,8,5]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[2,3,8,5,1,7,4,6]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,3,8,6,1,7,4,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,8,4,6,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[2,7,4,8,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[2,7,4,6,1,3,8,5]=>[1,3,8,2,7,4,6,5]=>[1,7,3,6,8,5,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,7,8,5,1,3,4,6]=>[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>{{1},{2,6},{3},{4},{5,8},{7}}
[2,7,8,6,1,3,4,5]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>{{1},{2,5},{3},{4},{6,8},{7}}
[2,7,6,5,1,3,8,4]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,6,4,5,1,8,3,7]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,4,5,1,7,3,6]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,4,6,1,7,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,6,5,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[8,3,6,5,1,2,4,7]=>[1,2,4,7,3,6,5,8]=>[1,2,6,4,7,5,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[7,3,8,5,1,2,4,6]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[7,3,8,6,1,2,4,5]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>{{1},{2},{3,5},{4},{6,7,8}}
[7,6,4,5,1,2,8,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,3,4,5,1,8,2,7]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,4,5,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,4,6,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,6,5,1,7,2,4]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,4,5,1,7,2,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,3,4,5,1,7,8,2]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,3,4,8,6,1,5,7]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[2,3,4,7,6,1,8,5]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,5,6,1,4,7]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[2,3,8,5,7,1,4,6]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[2,3,8,7,6,1,4,5]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}}
[2,3,7,5,6,1,8,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,4,5,6,1,3,7]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[2,8,4,5,7,1,3,6]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[2,8,7,5,6,1,3,4]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[2,7,4,5,6,1,8,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,4,5,7,1,2,6]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,3,4,7,6,1,2,5]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}}
[8,3,7,5,6,1,2,4]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[7,3,4,5,6,1,8,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,5,8,7,1,6]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,3,4,8,6,7,1,5]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[2,3,8,5,6,7,1,4]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,8,4,5,6,7,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[8,1,2,3,4,5,6,9,7]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[9,1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,7,8,6,9]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}
[7,1,2,3,4,5,8,9,6]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,7,9,8,6]=>{{1},{2},{3},{4},{5},{6,7,9},{8}}
[8,1,2,3,9,4,5,6,7]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[9,1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>{{1},{2,3,4,5,6,7,8},{9}}
[9,1,8,5,6,7,2,3,4]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>{{1},{2,3,4,5,6,7,8},{9}}
[3,1,4,5,6,7,8,9,2]=>[1,4,5,6,7,8,9,2,3]=>[1,3,9,4,5,6,7,8,2]=>{{1},{2,3,9},{4},{5},{6},{7},{8}}
[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,7,4,5,6,1,2,3,8]=>[1,2,3,8,4,5,6,7,9]=>[1,2,3,5,6,7,8,4,9]=>{{1},{2},{3},{4,5,6,7,8},{9}}
[2,3,4,5,6,7,9,1,8]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>{{1},{2,3,4,5,6,7,8},{9}}
[2,3,4,5,6,7,8,9,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[3,5,2,6,4,1,8,7]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,2,7,4,8,1,6]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,5,7,2,3,8,6,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,5,6,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,2,1,3,8,7]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[3,5,1,6,4,2,8,7]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,5,6,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,5,6,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,5,7,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,5,7,3,2,8,6,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,6,7,3,8,2,5,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[4,6,7,3,8,2,1,5]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[4,6,7,3,8,1,2,5]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[4,5,7,3,1,8,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,7,1,3,8,2,6]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[3,5,1,7,4,8,2,6]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,5,7,4,8,3,6]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[2,1,5,7,4,8,6,3]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[3,5,1,7,4,8,6,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,5,7,1,3,8,6,2]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,5,7,3,1,8,6,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,7,3,8,1,5,2]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[4,6,7,3,8,5,1,2]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,6,7,3,8,5,2,1]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,7,8,3,1,4,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[5,6,7,8,1,3,4,2]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[2,1,6,7,8,4,5,3]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[4,6,7,1,8,3,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,8,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[4,6,7,2,8,1,3,5]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[4,6,7,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,6,7,2,8,3,5,1]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,2,7,8,4,1,5]=>[1,5,2,7,8,3,6,4]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[3,6,2,7,8,1,4,5]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>{{1},{2,5},{3,6,8},{4},{7}}
[3,5,2,7,1,8,4,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,2,1,7,8,5,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,4,1,2,7,8,6,5]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[3,5,2,7,1,8,6,4]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,2,7,8,1,5,4]=>[1,5,2,7,8,3,6,4]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[3,6,2,7,8,5,1,4]=>[1,4,2,7,8,3,6,5]=>[1,4,6,2,8,5,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[4,6,7,2,8,5,3,1]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,6,7,2,8,5,1,3]=>[1,3,2,8,4,6,7,5]=>[1,3,2,6,8,7,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,6,7,2,8,1,5,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,5,7,2,1,8,6,3]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,7,1,2,8,6,3]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,5,1,7,2,8,6,4]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,1,5,7,3,8,6,4]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[4,6,7,1,8,2,5,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,8,1,2,4,3]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[5,6,7,8,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[5,6,7,8,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[5,6,7,8,2,4,3,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[5,6,7,8,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[3,6,1,7,8,5,2,4]=>[1,7,8,2,4,3,6,5]=>[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,1,6,7,8,5,3,4]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[5,6,7,8,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[5,6,7,8,4,1,3,2]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[5,6,7,8,4,3,2,1,10,9]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[4,5,6,3,2,1,9,10,8,7]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[6,5,8,7,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[3,6,7,4,5,8,1,2]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[2,6,7,4,5,1,8,3]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,7,4,5,2,3,8]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[2,5,4,7,6,1,8,3]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,4,7,6,8,1,2]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[4,5,3,7,8,6,1,2]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[5,4,3,8,7,6,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,4,8,3,7,5,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[6,3,8,4,5,7,1,2]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,3,4,8,6,7,1,2]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[4,3,5,6,8,7,1,2]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[4,2,5,6,8,1,7,3]=>[1,7,2,5,6,8,3,4]=>[1,5,4,8,6,7,2,3]=>{{1},{2,5,6,7},{3,4,8}}
[5,2,4,8,6,1,7,3]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[6,2,8,4,5,1,7,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,8,2,4,5,1,6,3]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,1,8,4,5,2,3,7]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,4,8,6,2,3,7]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[4,1,3,2,8,6,5,7]=>[1,3,2,8,4,5,7,6]=>[1,3,2,5,7,8,6,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,1,8,3,2,5,4,7]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,3,2,5,4,6]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[6,2,8,3,1,5,7,4]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[5,2,3,8,1,6,7,4]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[6,3,8,2,1,7,5,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,8,3,2,1,6,5,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,4,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[5,4,2,8,7,1,6,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,5,3,7,1,6,8,4]=>[1,6,8,2,5,3,7,4]=>[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,5,3,7,2,6,4,8]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[1,6,7,3,2,5,4,8]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,6,7,3,1,5,8,4]=>[1,5,8,2,6,7,3,4]=>[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[7,8,5,6,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[6,5,8,7,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,4,8,1,7,2,3,5]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[7,8,3,1,2,6,4,5]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[5,3,1,8,2,7,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,1,2,8,7,5,6]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,2,1,3,8,5,7,6]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,2,1,8,3,4,7,6]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,1,2,6,5,8,7]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[5,3,1,6,2,4,8,7]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[7,3,1,5,2,8,4,6]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,4,5,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,6,1,2,3,8,7]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,1,6,5,3,4,8,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[4,6,5,1,2,3,8,7]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,4,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,5,4,1,2,3,8,7]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[8,6,4,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,5,1,2,8,3,6]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,7,1,5,2,8,4,6]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,1,7,5,3,8,4,6]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,8,1,5,2,7,4,6]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[4,8,5,1,2,7,3,6]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[6,8,4,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,4,1,6,2,3,5]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,8,6,7,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,8,6,1,7,2,3,5]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,1,8,6,7,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,6,8,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,6,1,8,2,3,5]=>[1,8,2,3,5,4,7,6]=>[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,6,8,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[5,4,7,1,2,8,3,6]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,7,1,8,2,3,5]=>[1,8,2,3,5,4,7,6]=>[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,6,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,3,1,7,8,2,4,5]=>[1,7,8,2,4,5,3,6]=>[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,3,1,2,7,8,5,6]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[2,1,4,3,8,7,5,6]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[3,4,1,2,8,7,5,6]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,4,7,1,6,2,3,5]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,4,8,1,2,7,3,6]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[3,5,1,8,2,7,4,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,8,7,3,4,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,6,8,1,7,2,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,8,7,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[7,5,8,6,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[8,5,7,6,1,2,3,4]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[5,7,8,6,1,2,3,4]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[4,7,8,1,6,2,3,5]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,1,7,8,6,3,4,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,1,8,7,6,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,7,6,2,4,5]=>[1,7,2,4,5,3,8,6]=>[1,4,7,5,3,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[5,8,7,6,1,2,3,4]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,8,7,5,1,2,3,4]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[6,4,7,3,8,5,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,4,7,3,5,8,1,2]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[6,4,7,2,5,1,8,3]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,7,6,1,3,8]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,4,2,7,6,1,8,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,3,7,6,8,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,4,3,7,8,6,1,2]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[6,4,8,3,5,7,1,2]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>{{1},{2},{3},{4,7},{5},{6,8}}
[5,4,3,8,6,7,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,3,6,8,7,1,2]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[5,4,2,6,7,1,8,3]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,6,7,1,3,8]=>[1,3,8,2,6,7,4,5]=>[1,6,3,5,8,7,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,3,2,6,1,8,7,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,8,6,1,7,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,8,4,2,5,1,6,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,4,2,5,1,3,6]=>[1,3,6,2,5,4,7,8]=>[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[5,4,2,8,6,1,3,7]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[5,3,2,6,1,8,4,7]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,1,6,8,5,7]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,3,2,1,8,6,5,7]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,2,8,1,6,4,7]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,8,3,2,1,5,4,6]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,3,8,2,1,5,7,4]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[5,3,2,7,1,8,6,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,2,7,1,6,4,8]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[6,3,7,2,1,5,4,8]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[6,3,7,2,1,8,5,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,8,7,2,1,3,4]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}}
[6,3,7,2,1,8,4,5]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,7,2,1,4,8,5]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,3,7,2,1,4,5,8]=>[1,4,5,8,2,3,7,6]=>[1,3,7,4,5,8,6,2]=>{{1},{2,3,6,7,8},{4},{5}}
[5,4,2,8,7,1,3,6]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[7,8,4,2,6,1,3,5]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[7,8,3,2,1,6,4,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,3,8,2,1,7,4,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,3,2,1,8,7,5,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,3,2,1,7,5,6,8]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,3,2,1,8,5,7,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,8,2,1,4,7,5]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[6,3,8,2,1,4,5,7]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[4,3,2,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,2,1,5,8,6,7]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[7,8,5,6,1,2,4,3]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[7,8,4,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,1,4,6,2,5,3]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[6,1,8,4,7,2,5,3]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,4,7,2,5,3]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,1,8,3,2,7,5,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,3,2,6,5,4]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[7,8,3,1,2,6,5,4]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[7,8,3,4,6,5,1,2]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[7,8,2,3,1,6,5,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,2,1,3,6,5,4]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[7,8,1,2,3,6,5,4]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[6,1,8,2,3,7,5,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,2,3,7,5,4]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,5,2,8,3,7,6,4]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,1,2,8,3,7,6,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,2,1,8,3,7,6,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,8,1,3,7,5,4]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[6,2,8,3,1,7,5,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,3,8,4,7,5,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,6,8,4,7,5,1,2]=>[1,2,3,6,8,4,7,5]=>[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[2,6,8,4,7,1,5,3]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>{{1},{2,5},{3,4,7,8},{6}}
[2,5,1,8,3,7,6,4]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,5,8,3,7,6,4]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[2,4,1,3,8,7,6,5]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,5,3,8,1,7,6,4]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[2,5,4,8,7,1,6,3]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[3,5,4,8,7,6,1,2]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[5,3,4,8,7,6,1,2]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,2,4,8,7,1,6,3]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[5,2,3,8,1,7,6,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,2,1,3,8,7,6,5]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,1,2,3,8,7,6,5]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,4,2,3,8,7,6,5]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[4,1,3,2,8,7,6,5]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,3,1,2,8,7,6,5]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,3,8,1,2,7,5,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[5,3,1,8,2,7,6,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,3,8,2,7,6,4]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,3,8,2,7,6,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,4,1,8,7,2,6,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,8,7,1,2,4,3]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[5,6,8,7,3,4,1,2]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[5,6,8,7,2,1,4,3]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[4,5,1,8,7,2,6,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,8,7,2,6,3]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,4,5,8,7,2,6,3]=>[1,4,5,8,2,6,3,7]=>[1,6,7,4,5,3,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[3,1,5,8,2,7,6,4]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,6,8,1,2,7,5,4]=>[1,2,7,3,6,8,4,5]=>[1,2,6,5,8,7,3,4]=>{{1},{2},{3,6,7},{4,5,8}}
[4,6,8,2,7,1,5,3]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[4,6,8,3,7,5,1,2]=>[1,2,3,7,4,6,8,5]=>[1,2,3,6,8,7,4,5]=>{{1},{2},{3},{4,6,7},{5,8}}
[4,5,3,8,7,6,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,5,2,8,7,1,6,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,5,2,8,1,7,6,4]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,1,4,2,8,7,6,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[3,1,2,4,8,7,6,5]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[3,2,5,8,1,7,6,4]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[4,2,5,8,7,1,6,3]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[4,3,5,8,7,6,1,2]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[3,4,5,8,7,6,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[2,4,5,8,7,1,6,3]=>[1,6,2,4,5,8,3,7]=>[1,4,7,5,6,2,8,3]=>{{1},{2,4,5,6},{3,7,8}}
[2,3,5,8,1,7,6,4]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[5,1,3,2,6,4,8,7]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[6,1,3,2,5,4,8,7]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[7,1,3,2,5,4,8,6]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[8,1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>{{1},{2,3},{4,5},{6,7},{8}}
[8,1,4,2,5,3,7,6]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}
[7,1,4,2,5,3,8,6]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[6,1,4,2,5,3,8,7]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[5,1,4,2,6,3,8,7]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[3,1,6,2,5,4,8,7]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[4,1,6,2,5,3,8,7]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[6,2,5,1,4,3,8,7]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[5,2,6,1,4,3,8,7]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[5,2,7,1,4,3,8,6]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[5,2,8,1,4,3,7,6]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,2,8,1,4,3,7,5]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,2,7,1,4,3,8,5]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[7,2,6,1,4,3,8,5]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[7,2,5,1,4,3,8,6]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[4,1,7,2,5,3,8,6]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[2,1,7,3,5,4,8,6]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,1,8,3,5,4,7,6]=>[1,8,2,3,5,4,7,6]=>[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,8,2,5,4,7,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,2,5,3,7,6]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,5,1,4,3,7,6]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}
[8,2,6,1,4,3,7,5]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[7,1,4,3,8,2,6,5]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[8,1,4,3,7,2,6,5]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[8,1,5,3,7,2,6,4]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[7,1,5,3,8,2,6,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[8,2,6,1,5,3,7,4]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[5,1,8,2,6,3,7,4]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,2,6,3,7,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,8,2,6,4,7,5]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,7,2,6,3,8,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[5,1,7,2,6,3,8,4]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[7,2,6,1,5,3,8,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[6,2,7,1,5,3,8,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[6,2,8,1,5,3,7,4]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,1,5,2,6,3,7,4]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[6,1,5,2,7,3,8,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[6,1,4,2,7,3,8,5]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[8,1,4,2,6,3,7,5]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[8,1,3,2,6,4,7,5]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[7,1,3,2,6,4,8,5]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[6,1,3,2,7,4,8,5]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[5,1,3,2,7,4,8,6]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[4,1,3,2,7,5,8,6]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>{{1},{2,3},{4,5,7},{6,8}}
[2,1,4,3,8,5,7,6]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[4,1,3,2,8,5,7,6]=>[1,3,2,8,4,5,7,6]=>[1,3,2,5,7,8,6,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,1,3,2,8,4,7,6]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,1,3,2,8,4,7,5]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[8,4,7,1,3,2,6,5]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[7,4,8,1,3,2,6,5]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[7,3,8,1,4,2,6,5]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[8,3,7,1,4,2,6,5]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[6,1,4,2,8,3,7,5]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,1,4,2,8,3,7,6]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,1,5,2,8,3,7,6]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,1,6,2,8,4,7,5]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,1,6,2,8,3,7,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,1,6,2,8,3,7,4]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,1,5,2,8,3,7,4]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,3,7,1,5,2,6,4]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[7,3,8,1,5,2,6,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[6,2,7,3,8,1,5,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[6,2,8,3,7,1,5,4]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,3,7,2,6,1,5,4]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[5,1,8,3,7,2,6,4]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,3,7,2,6,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,8,4,7,2,6,5]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,7,3,8,2,6,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[5,1,7,3,8,2,6,4]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[7,3,8,2,6,1,5,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[8,2,6,3,7,1,5,4]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[7,2,6,3,8,1,5,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[5,7,3,8,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,7,3,8,2,4,6,1]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[7,4,2,5,8,3,1,6]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[4,5,2,6,3,8,1,7]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,5,2,1,6,8,3,7]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,1,5,6,3,8,2,7]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>{{1},{2,6},{3,7},{4,8},{5}}
[4,5,1,6,3,8,2,7]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[4,5,6,3,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,4,5,3,8,2,6,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[6,7,4,8,3,2,5,1]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[6,7,4,8,3,2,1,5]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[6,7,4,1,8,3,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,5,3,1,8,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,1,5,8,3,2,6]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,3,7,8,1,4,2,6]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>{{1},{2,4},{3,6},{5,8},{7}}
[7,5,8,2,4,6,1,3]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>{{1},{2,3},{4},{5,6},{7,8}}
[6,7,4,3,8,1,5,2]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,7,4,8,3,1,5,2]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[6,7,4,8,3,5,2,1]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[5,6,7,3,8,4,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,7,3,1,8,4,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,1,7,3,8,4,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,1,6,7,3,8,4,2]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[6,4,7,1,8,3,5,2]=>[1,8,2,3,5,4,7,6]=>[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,2,8,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,7,2,8,4,1,3,5]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[5,6,1,7,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,6,7,3,2,1,8,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,3,2,8,4,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,6,2,7,3,8,4,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[5,6,2,7,3,1,8,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,1,7,3,8,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,1,7,4,2,8,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,7,2,1,8,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,2,1,3,4,6]=>[1,3,4,6,2,5,8,7]=>[1,5,3,4,6,2,8,7]=>{{1},{2,5,6},{3},{4},{7,8}}
[5,7,3,1,8,2,4,6]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,1,5,2,8,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,4,2,5,1,8,3,6]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,4,2,8,3,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,7,4,2,8,3,5,1]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,7,2,8,4,5,1]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,7,2,8,4,1,5]=>[1,5,2,8,3,6,7,4]=>[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,7,3,8,2,1,4,6]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[3,7,8,1,4,6,2,5]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[3,4,7,8,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[5,7,3,8,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[3,6,7,2,8,5,1,4]=>[1,4,2,8,3,6,7,5]=>[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[3,6,7,8,5,2,1,4]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>{{1},{2,3,4},{5,8},{6},{7}}
[3,6,7,8,5,2,4,1]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>{{1},{2},{3,4},{5,8},{6},{7}}
[6,4,7,8,2,5,3,1]=>[1,2,5,3,4,7,8,6]=>[1,2,4,5,3,8,7,6]=>{{1},{2},{3,4,5},{6,8},{7}}
[6,4,7,8,2,1,5,3]=>[1,5,2,3,4,7,8,6]=>[1,3,4,5,2,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[4,1,5,7,8,2,6,3]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[6,7,2,8,5,1,3,4]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[5,6,2,1,7,8,4,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,6,2,7,1,8,4,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,7,8,4,3,1]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,6,7,2,8,4,3,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,6,7,2,1,8,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,1,7,2,8,4,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,4,7,1,8,2,5,3]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,8,5,2,4,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[6,7,8,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[4,6,7,8,1,5,3,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[5,1,6,7,8,4,3,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[5,6,1,7,8,4,3,2]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,6,7,1,8,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,1,3,4,2,5,7]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>{{1},{2,4},{3},{5},{6,7},{8}}
[8,3,2,5,1,6,4,7]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,3,6,2,4,1,7]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,3,2,7,4,1,8,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,3,8,2,4,6,1]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[7,2,4,5,8,3,6,1]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[8,1,2,4,5,6,3,7]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>{{1},{2},{3,6},{4},{5},{7},{8}}
[8,2,5,1,3,6,4,7]=>[1,3,6,2,5,4,7,8]=>[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[8,5,6,2,1,4,3,7]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[8,4,1,5,6,3,2,7]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>{{1},{2,6},{3,4,7},{5},{8}}
[8,1,4,5,6,3,2,7]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>{{1},{2,6},{3,7},{4},{5},{8}}
[4,5,3,7,2,1,8,6]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,5,8,3,2,6,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[4,3,6,7,2,8,5,1]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,3,6,7,2,8,1,5]=>[1,5,2,8,3,6,7,4]=>[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,4,3,6,7,2,8,5]=>[1,4,2,8,3,6,7,5]=>[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,5,3,7,1,8,2,6]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,3,7,2,8,6]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,4,5,8,3,6,1,2]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[4,3,6,7,8,1,5,2]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>{{1},{2,3,5},{4,8},{6},{7}}
[1,6,4,7,8,3,5,2]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,4,7,8,3,5,2,1]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>{{1},{2},{3},{4,5},{6,8},{7}}
[3,5,6,7,8,4,1,2]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>{{1},{2},{3},{4,8},{5},{6},{7}}
[3,1,5,6,7,8,4,2]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[3,6,7,1,4,8,5,2]=>[1,4,8,2,3,6,7,5]=>[1,3,6,4,8,7,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,2,4,1,7,8,5,3]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,3,6,7,8,1,2,5]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>{{1},{2},{3,5},{4,8},{6},{7}}
[1,5,3,6,7,8,2,4]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[3,5,6,7,8,2,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[3,5,6,7,8,2,4,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[5,2,7,1,3,8,4,6]=>[1,3,8,2,7,4,6,5]=>[1,7,3,6,8,5,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,6,7,8,3,1,5]=>[1,5,2,6,7,8,3,4]=>[1,5,4,8,2,6,7,3]=>{{1},{2,5},{3,4,8},{6},{7}}
[3,6,2,7,4,8,5,1]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[3,6,2,7,4,8,1,5]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,7,3,4,2,5,8,6]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[7,8,4,2,1,3,6,5]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[7,8,3,4,2,1,6,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,3,2,7,1,8,5,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,2,7,1,8,5,4]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,8,2,5,4,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[6,4,7,8,5,2,3,1]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[2,6,4,7,8,1,5,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,4,5,8,6,2,1,3]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[7,4,1,5,8,6,2,3]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[7,5,3,8,6,1,2,4]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[7,5,8,2,1,6,3,4]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[6,2,7,1,3,8,5,4]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,1,2,6,7,8,4,3]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[5,2,6,7,8,4,3,1]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[1,5,2,6,7,8,4,3]=>[1,5,2,6,7,8,3,4]=>[1,5,4,8,2,6,7,3]=>{{1},{2,5},{3,4,8},{6},{7}}
[2,6,7,1,3,8,5,4]=>[1,3,8,2,6,7,4,5]=>[1,6,3,5,8,7,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,7,8,2,1,5,4,3]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,3,8,5,1,4,2]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[6,4,7,8,5,3,1,2]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[4,5,2,3,7,6,1,8]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,7,2,5,1,8]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,2,7,3,5,1,8]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,6,7,4,5,1,8]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,2,6,5,3,1,8]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,6,2,4,3,1,8]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,5,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[5,8,6,2,4,1,3,7]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[4,8,2,6,5,1,3,7]=>[1,3,7,2,6,4,8,5]=>[1,6,3,7,8,4,2,5]=>{{1},{2,4,6,7},{3},{5,8}}
[4,1,2,6,5,8,7,3]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[5,1,6,2,4,8,7,3]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[6,1,5,4,2,8,7,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,1,5,4,7,6,2,3]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[1,8,6,7,4,5,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,6,7,4,5,2,3]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[7,1,6,8,4,2,5,3]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,1,7,8,2,4,5,3]=>[1,7,8,2,4,5,3,6]=>[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,1,2,7,8,5,6,3]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[3,2,1,7,8,5,6,4]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,2,8,7,1,5,4,6]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,8,2,7,1,5,3,6]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[5,8,7,2,1,4,3,6]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[6,8,7,1,2,4,3,5]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[7,8,6,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,1,4,3,2,5]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[1,7,6,8,4,3,5,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,8,3,4,5,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[8,6,7,1,3,4,2,5]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[7,6,8,1,3,2,4,5]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>{{1},{2,3},{4},{5},{6},{7,8}}
[4,6,2,8,3,1,5,7]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[8,5,7,3,1,4,2,6]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[1,5,7,3,8,4,6,2]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[1,4,3,7,8,5,6,2]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[8,4,3,7,1,5,2,6]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[6,4,3,8,2,1,5,7]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[4,5,2,3,8,1,6,7]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[3,2,5,4,8,1,6,7]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[4,5,2,3,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,1,2,8,7,5]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,3,1,8,2,6,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,3,1,7,6,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,1,3,8,2,6,4]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,5,1,3,2,8,7,4]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,6,1,2,3,8,7,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,2,7,1,8,4,6,5]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,1,8,3,2,5,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,1,7,3,5,2,4]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,8,7,3,5,4,2]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,8,6,5,3,4,2]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[8,7,1,6,5,3,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,1,6,5,2,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,8,1,7,2,5,3,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,1,2,7,6,3,4]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[4,8,2,1,7,6,3,5]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,2,8,1,7,6,4,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,1,2,8,7,6,5,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,8,2,7,6,4,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,8,7,2,5,4,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,8,6,5,2,4,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,7,6,5,4,2,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,2,6,5,8,7,4]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[3,1,6,2,4,8,7,5]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[4,5,1,2,3,8,7,6]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,6,1,2,3,8,7,5]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,6,5,3,4,8,7,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,5,1,2,3,8,7,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,4,1,2,3,8,7,5]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,1,2,3,8,7,6]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,4,1,2,7,3,6,8]=>[1,2,7,3,6,8,4,5]=>[1,2,6,5,8,7,3,4]=>{{1},{2},{3,6,7},{4,5,8}}
[6,4,1,7,2,3,5,8]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[6,4,1,8,2,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,5,2,8,4,6,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,7,5,3,8,4,6,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[8,1,5,2,7,4,6,3]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,4,1,7,2,3,5,6]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,1,7,2,3,5,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,6,7,3,4,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,8,3,4,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,1,2,8,3,6,5]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,2,7,8,5,6,4]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[1,4,3,8,7,5,6,2]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[4,1,2,8,7,5,6,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,2,8,7,5,6,4]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,8,2,7,4,6,5]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,8,1,7,2,3,5,6]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,8,1,2,7,3,6,5]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[5,1,8,2,7,4,6,3]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,8,7,3,4,5,2]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,1,7,2,3,5,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,7,1,2,3,4,5]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>{{1},{2},{3},{4},{5},{6},{7,8}}
[5,8,7,1,2,3,4,6]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[5,8,6,1,2,3,4,7]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[5,7,6,1,2,3,4,8]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,8,1,6,2,3,5,4]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,7,8,6,3,4,5,2]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,8,7,6,3,4,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,1,6,2,3,5,4]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,2,5,1,6,4,8,7]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[3,2,5,4,7,1,8,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,5,3,7,6,8,1]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[4,2,5,3,7,1,8,6]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,5,3,6,1,8,7]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,5,1,6,3,8,7]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[3,1,5,4,6,2,8,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,1,5,3,6,2,8,7]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,3,5,1,6,2,8,7]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,3,5,2,7,1,8,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,6,2,7,1,8,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,6,1,7,2,8,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,3,5,1,7,2,8,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,1,5,4,7,6,8,2]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[4,1,5,3,7,6,8,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[4,3,5,1,7,6,8,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,3,6,1,7,5,8,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,3,6,4,7,2,8,1]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,6,3,7,4,8,2]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[4,1,6,3,7,5,8,2]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[3,1,6,4,7,5,8,2]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[2,1,6,4,7,5,8,3]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[3,1,6,4,7,2,8,5]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,1,6,3,7,2,8,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,1,6,3,7,2,8,4]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,3,6,1,7,2,8,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,3,6,2,7,1,8,4]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,6,2,7,4,8,1]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[5,2,6,3,7,4,8,1]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[5,2,6,3,7,1,8,4]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,6,1,7,3,8,4]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,2,5,1,7,3,8,6]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[4,2,6,1,7,3,8,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,2,6,3,7,1,8,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,6,4,7,1,8,5]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,4,1,7,5,8,6]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,1,4,2,7,6,8,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[3,2,5,1,7,6,8,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,6,1,7,5,8,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,6,5,7,1,8,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,5,7,3,8,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,2,6,5,7,1,8,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,1,7,5,8,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,2,5,1,7,6,8,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,1,5,2,7,6,8,3]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[3,1,5,2,7,6,8,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,1,5,3,7,6,8,4]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[2,1,6,3,7,5,8,4]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[3,1,6,2,7,5,8,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,1,6,2,7,5,8,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[5,1,6,2,7,4,8,3]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[5,2,6,4,7,1,8,3]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,6,4,7,3,8,1]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[5,4,6,2,7,1,8,3]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,6,4,7,2,8,3]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,1,6,5,7,2,8,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,1,6,5,7,2,8,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,1,6,5,7,4,8,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,4,6,1,7,3,8,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[8,3,5,2,1,6,4,7]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,6,3,5,2,4,1,7]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,7,5,2,4,1,8,6]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,7,5,2,4,6,1]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>{{1},{2},{3,6},{4},{5,7},{8}}
[8,2,4,6,5,3,1,7]=>[1,7,2,4,6,3,5,8]=>[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,5,4,6,1,3,7]=>[1,3,7,2,5,4,6,8]=>[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[8,6,3,5,1,4,2,7]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,1,5,6,4,3,2,7]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>{{1},{2,6},{3,4,7},{5},{8}}
[5,7,4,3,2,1,8,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,7,4,3,2,6,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,4,6,7,3,2,8,5]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>{{1},{2,7},{3,5,8},{4},{6}}
[5,4,7,3,1,8,2,6]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,5,3,2,8,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,7,5,1,4,2,8,6]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,7,4,2,1,3,8,6]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[8,5,7,4,2,1,6,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,3,7,5,1,4,6,2]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[8,4,1,7,5,3,6,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,6,3,8,7,1,5,2]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[1,7,4,8,6,3,5,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[8,4,7,6,3,5,2,1]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[3,6,5,8,7,4,1,2]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[3,1,5,8,6,7,4,2]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,6,8,1,4,3,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[3,7,1,6,4,8,2,5]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[1,7,3,5,6,8,2,4]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,6,7,5,8,2,4]=>[1,3,6,7,2,4,5,8]=>[1,4,3,5,7,6,2,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[3,7,6,5,8,2,1,4]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[3,6,8,5,7,2,4,1]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}
[2,3,5,7,6,8,1,4]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[2,1,6,5,7,8,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[4,2,7,6,8,3,1,5]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[4,2,6,8,7,3,5,1]=>[1,2,6,8,3,5,4,7]=>[1,2,5,7,4,6,8,3]=>{{1},{2},{3,4,5,7,8},{6}}
[3,8,2,4,6,7,5,1]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>{{1},{2},{3,7},{4},{5,8},{6}}
[3,7,2,6,4,8,1,5]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[8,7,6,1,3,4,2,5]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[8,5,7,3,2,1,6,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,3,6,7,2,1,5,4]=>[1,5,2,3,6,7,4,8]=>[1,3,5,7,2,6,4,8]=>{{1},{2,3,5},{4,7},{6},{8}}
[8,7,6,3,5,2,4,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[2,7,4,8,1,6,5,3]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[8,4,1,5,7,2,6,3]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[8,5,3,7,1,6,2,4]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,5,7,2,1,3,6,4]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[8,2,6,7,1,3,5,4]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>{{1},{2,5},{3},{4,7},{6},{8}}
[8,3,6,1,7,5,2,4]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,6,1,8,7,2,5,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,6,5,7,4,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[2,1,7,8,5,6,4,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,7,6,8,5,4,1,3]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,7,2,5,8,6,4,3]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[2,7,8,6,1,3,5,4]=>[1,3,5,2,7,8,4,6]=>[1,5,3,6,2,8,7,4]=>{{1},{2,5},{3},{4,6,8},{7}}
[8,7,6,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,1,6,7,5,4,3,2]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[6,5,3,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[4,6,3,5,1,2,8,7]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,5,3,7,2,1,4,6]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[6,8,1,4,5,7,3,2]=>[1,4,5,7,2,3,6,8]=>[1,3,6,4,5,7,2,8]=>{{1},{2,3,6,7},{4},{5},{8}}
[8,7,2,4,5,1,3,6]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[6,1,2,4,5,3,8,7]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>{{1},{2},{3,5},{4},{6,7,8}}
[3,1,6,4,5,2,8,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,8,7,4,2,6,3,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[2,8,7,4,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,1,7,4,2,6,3,5]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,7,8,4,5,1,2,6]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[2,1,8,7,5,3,4,6]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,8,5,7,3,4]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,6,3,8,1,7,2,4]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[7,6,1,4,5,8,3,2]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[3,7,6,4,5,8,2,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[8,5,7,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,1,8,4,7,6,2,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,8,4,7,6,1,3]=>[1,3,2,5,8,4,7,6]=>[1,3,2,7,5,8,6,4]=>{{1},{2,3},{4,6,7,8},{5}}
[2,4,8,3,5,6,7,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[3,8,4,2,5,6,7,1]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>{{1},{2},{3,7},{4,8},{5},{6}}
[7,5,8,4,3,6,1,2]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[6,5,3,8,4,1,7,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,1,5,8,4,6,7,3]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,1,4,8,3,6,7,5]=>[1,4,8,2,3,6,7,5]=>[1,3,6,4,8,7,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,4,3,8,2,1,7,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,3,8,4,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[2,3,8,1,5,6,7,4]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[4,3,8,2,5,6,7,1]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>{{1},{2},{3,7},{4,8},{5},{6}}
[4,8,2,3,5,6,7,1]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[3,8,2,1,5,6,7,4]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[2,8,1,3,5,6,7,4]=>[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>{{1},{2,7},{3},{4,8},{5},{6}}
[8,1,2,3,5,6,7,4]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>{{1},{2},{3},{4,7},{5},{6},{8}}
[7,8,2,4,3,6,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,8,3,2,4,1,7,5]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,7,3,8,1,4,2,6]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[7,1,8,4,5,3,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,1,4,3,6,2,5]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[3,8,7,4,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[5,7,8,4,3,6,2,1]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[5,6,3,8,4,2,7,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[8,6,3,1,4,2,7,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[7,5,3,8,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,4,3,1,8,5,7,6]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,3,6,2,8,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[8,6,3,5,1,2,7,4]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,8,3,2,6,1,7,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,5,3,8,6,2,7,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[3,5,8,4,7,6,2,1]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[5,8,2,4,7,6,1,3]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>{{1},{2,3},{4},{5,7},{6,8}}
[8,7,5,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,7,6,4,5,8,1,3]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>{{1},{2,3},{4,5,7},{6,8}}
[7,1,6,4,5,8,2,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[5,7,3,6,1,8,2,4]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,6,5,8,3,4]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,8,3,5,2,1,7,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,8,5,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[8,1,4,2,5,6,7,3]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>{{1},{2,4},{3,7},{5},{6},{8}}
[2,8,4,1,5,6,7,3]=>[1,5,6,7,2,8,3,4]=>[1,7,4,8,5,6,2,3]=>{{1},{2,7},{3,4,8},{5},{6}}
[3,4,2,8,5,6,7,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,4,1,8,5,6,7,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,2,8,5,6,7,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,5,2,4,8,6,1,3]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[6,5,3,2,8,1,7,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,1,5,3,8,6,7,4]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,4,3,5,8,1,7,2]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[7,3,5,4,8,6,1,2]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[4,3,1,8,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,7,2,8,4,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,3,7,4,5,8,2,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[6,7,2,4,5,8,3,1]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[5,1,7,4,8,6,3,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,3,7,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,5,4,8,6,2,1]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[5,6,3,1,8,2,7,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,3,5,8,2,7,1]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[3,2,5,1,6,8,4,7]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,6,2,5,4,8,1,7]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,5,8,2,4,7,6,1]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>{{1},{2},{3,5,7},{4},{6,8}}
[4,2,5,8,3,7,6,1]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[4,2,6,5,3,8,1,7]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[5,4,2,1,6,8,3,7]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,6,1,5,3,8,2,7]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,1,6,4,3,8,2,7]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[5,4,3,2,7,1,8,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,3,8,2,7,6,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,3,7,6,2,1,8,5]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,1,7,2,8,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,5,4,3,1,8,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,5,7,4,6,1,3]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,4,5,8,7,3,6,2]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[1,5,4,8,7,3,6,2]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[6,4,3,8,1,7,5,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,3,7,1,8,6,5,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,8,3,7,6,5,2,1]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[5,3,8,7,6,4,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,5,3,1,8,6,4,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,5,3,7,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,8,7,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[7,6,2,8,4,1,3,5]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[7,3,1,6,8,4,2,5]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,1,6,3,2,8,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,1,7,5,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,6,5,3,2,1,8,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,2,8,7,4,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,2,6,3,8,7,4,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[5,2,7,6,3,1,8,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,2,1,7,3,8,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,2,7,4,1,8,3,6]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,2,6,3,1,8,5]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,6,2,4,1,8,5]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,7,2,1,4,8,5]=>[1,4,8,2,3,6,7,5]=>[1,3,6,4,8,7,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[4,3,7,8,2,1,5,6]=>[1,5,6,2,3,7,8,4]=>[1,3,6,8,5,2,7,4]=>{{1},{2,3,6},{4,8},{5},{7}}
[8,3,7,1,4,6,2,5]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[3,8,2,5,7,1,6,4]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[8,3,6,2,7,1,5,4]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[7,8,3,6,2,1,5,4]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[8,7,3,6,2,5,4,1]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[5,4,8,2,7,1,6,3]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[4,8,1,5,7,2,6,3]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[5,8,3,7,1,6,2,4]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,6,2,7,5,1,3,4]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>{{1},{2,4},{3},{5,6,7},{8}}
[6,5,2,8,1,7,4,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,2,7,1,8,6,4,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,2,7,6,4,3,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[6,2,8,7,5,4,3,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,2,1,8,5,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,2,8,5,4,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,5,1,8,2,6,4,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,1,8,6,2,5,3]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,3,1,6,5,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,4,6,1,5,3,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,5,7,1,6,4,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,8,1,7,5,4,3,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,1,8,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,3,7,6,1,8]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,2,7,3,5,1,8]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,2,6,3,5,1,8]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,2,6,3,1,5,7]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[3,2,7,6,4,5,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,2,6,3,5,1,8]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,6,2,3,4,1,8]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,8,2,6,3,1,5,7]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[3,2,8,6,4,1,5,7]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[3,2,1,6,4,8,5,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[7,1,5,2,8,3,4,6]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,8,5,2,7,3,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,7,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,6,7,2,3,4,5]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[7,1,6,8,2,3,4,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,2,1,7,8,4,5,6]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,2,8,7,1,4,5,6]=>[1,4,5,6,2,8,3,7]=>[1,6,7,4,5,2,8,3]=>{{1},{2,6},{3,7,8},{4},{5}}
[5,8,7,2,1,3,4,6]=>[1,3,4,6,2,5,8,7]=>[1,5,3,4,6,2,8,7]=>{{1},{2,5,6},{3},{4},{7,8}}
[1,7,6,8,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,4,2,8,3,1,5,7]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[5,4,2,3,8,1,6,7]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[3,2,5,4,1,8,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,2,3,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,3,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,2,1,3,8,5,7]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[8,4,2,1,7,3,5,6]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,2,8,7,3,5,6]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,5,8,2,7,3,4,6]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[8,5,1,2,7,3,4,6]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,5,1,2,3,8,4,7]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,2,7,1,8,4,5,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,1,8,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,1,7,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,8,7,2,3,4,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,7,8,6,2,3,4,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,8,1,6,2,3,4,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,8,1,7,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,8,2,1,7,3,5,6]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,8,1,7,4,5,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,2,1,8,7,4,5,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,8,2,7,3,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,8,7,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,7,6,2,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,7,6,2,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,5,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[4,3,5,6,1,2,8,7]=>[1,2,8,3,5,6,4,7]=>[1,2,5,7,6,4,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,3,7,5,2,1,4,6]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[6,3,7,5,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,2,7,1,8,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,1,5,4,3,8,7]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[6,4,3,5,1,2,8,7]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,1,8,5,7,3,4,6]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,3,5,1,7,4,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,4,8,6,5,7,1,2]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,5,4,8,1,6,3,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,1,4,6,8,2,7,3]=>[1,4,6,8,2,7,3,5]=>[1,7,5,4,8,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[2,5,4,6,7,1,8,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,6,3,7,5,8,1]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>{{1},{2},{3,6},{4},{5,7},{8}}
[3,7,4,2,8,6,5,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,1,3,5,8,6,2]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[6,5,8,4,1,7,3,2]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[8,5,3,7,4,1,6,2]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[2,1,4,8,3,7,6,5]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,3,7,4,1,8,2,5]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,8,2,7,6,5,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,1,6,7,5,4]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[4,3,7,2,6,8,5,1]=>[1,2,6,8,3,7,4,5]=>[1,2,7,5,8,6,4,3]=>{{1},{2},{3,4,5,7,8},{6}}
[4,7,2,3,8,5,6,1]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,8,2,1,7,5,6,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,8,1,3,6,5,7,4]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[8,7,1,6,3,4,2,5]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,8,6,7,2,4,1,5]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[5,3,8,7,4,2,6,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[8,3,6,1,4,2,7,5]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[2,3,4,1,8,5,7,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,5,6,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[5,3,6,1,8,7,2,4]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,8,7,4,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[7,8,5,6,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[2,8,6,5,4,7,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[8,1,6,4,5,7,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,8,3,6,1,7,2,4]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,8,6,5,7,3,4]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,4,2,5,6,8,3]=>[1,4,2,5,6,8,3,7]=>[1,4,7,2,5,6,8,3]=>{{1},{2,4},{3,7,8},{5},{6}}
[2,7,4,1,6,5,8,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,6,1,2,8,7,3,5]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,2,1,5,8,7,3]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[8,5,2,4,6,1,7,3]=>[1,7,2,4,6,3,5,8]=>[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,1,4,5,6,8,7,2]=>[1,4,5,6,8,2,3,7]=>[1,3,7,4,5,6,8,2]=>{{1},{2,3,7,8},{4},{5},{6}}
[4,5,2,6,3,1,8,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,2,1,4,3,8,7]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[6,5,2,7,4,8,3,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[8,5,2,7,4,1,6,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,3,7,5,2,1,6,4]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[6,3,7,5,2,8,4,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,6,5,4,2,8,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,6,3,2,4,1,8,7]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,2,3,4,8,5,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[8,7,2,3,4,1,6,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,1,7,3,8,4,6,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,5,7,3,8,6,4,1]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[7,6,1,3,5,8,4,2]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[5,6,3,7,4,8,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[3,8,7,4,1,2,6,5]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[7,8,1,3,5,2,6,4]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[5,8,7,3,2,6,1,4]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[2,8,6,3,1,5,7,4]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[8,1,6,3,2,5,4,7]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,8,4,1,6,3,7,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,8,4,2,5,7,1,6]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[6,8,3,5,2,7,4,1]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[2,1,5,3,8,7,6,4]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,5,3,2,8,7,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[7,5,2,4,8,1,6,3]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[3,4,2,8,5,7,6,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,4,1,8,7,6,5,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,2,1,7,5,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,3,1,8,6,7,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,6,5,4,8,2,3]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[3,7,5,6,8,4,2,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[8,6,2,5,1,7,4,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,2,1,8,7,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,2,5,8,3,7,1]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[7,5,2,6,3,8,1,4]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[4,1,2,3,6,8,7,5]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[2,4,3,1,8,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,8,4,3,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,7,2,8,1,5,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,7,8,6,3,4,1,2]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[5,7,3,8,1,4,6,2]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[6,5,3,8,4,1,2,7]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[7,5,8,4,3,6,2,1]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[2,4,8,3,5,6,1,7]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[4,1,8,3,6,5,2,7]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,1,4,6,7,5]=>[1,4,6,7,2,3,8,5]=>[1,3,7,4,8,6,2,5]=>{{1},{2,3,7},{4},{5,8},{6}}
[4,3,8,2,5,1,7,6]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[6,3,8,4,2,5,7,1]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[7,4,3,8,2,5,1,6]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[6,8,2,4,3,5,1,7]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,8,2,1,4,6,5,7]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[2,8,1,3,4,5,7,6]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>{{1},{2,7},{3},{4},{5},{6,8}}
[2,8,4,1,6,5,3,7]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,4,1,6,5,7,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,7,6,1,4,3,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,8,5,6,7,4,3,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,5,8,6,1,4,2,3]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[2,8,5,3,4,1,7,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,5,3,6,1,7,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,5,6,7,4,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[2,8,5,3,4,7,1,6]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,5,3,4,6,7,1]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,5,7,2,4,6,1,8]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,2,8,3,1,7,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,5,8,6,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[6,5,8,2,1,3,7,4]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[3,5,7,2,4,1,8,6]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,7,2,4,6,8,1]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[6,5,2,7,3,1,8,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,2,3,7,6,8,5]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[6,5,2,7,3,4,8,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[5,1,6,7,4,3,8,2]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[5,1,6,8,7,3,4,2]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,5,2,8,3,7,4,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,2,3,8,7,5,6]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,1,2,3,8,6,5,7]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,1,2,3,8,6,7,5]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,1,2,3,7,6,5,8]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[4,1,2,3,8,5,7,6]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,1,6,8,4,3,5,2]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,1,2,8,4,5,7,3]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,6,8,2,3,1,7,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,5,8,2,4,3,1,7]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,5,8,2,4,3,7,1]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>{{1},{2},{3,4},{5,7},{6,8}}
[7,5,2,8,3,4,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,5,2,8,3,7,1,4]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,5,2,7,3,4,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,6,8,4,3,2,5]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,8,6,3,4,2,1]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>{{1},{2},{3},{4},{5},{6,8},{7}}
[4,1,8,3,6,2,7,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,6,5,7,3,2,8]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,5,2,6,3,7,1,8]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,2,7,3,8,1,6]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[3,5,6,2,4,8,7,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[3,5,6,2,4,8,1,7]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[3,7,5,6,8,4,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[3,6,5,2,8,1,7,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,1,2,5,8,4,7,3]=>[1,2,5,8,3,4,7,6]=>[1,2,4,7,5,8,6,3]=>{{1},{2},{3,4,6,7,8},{5}}
[7,1,6,5,8,3,4,2]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[7,5,2,6,3,8,4,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,1,2,3,5,8,7,6]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[4,1,2,3,7,8,6,5]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[4,5,2,7,3,8,6,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,1,2,5,6,8,7,3]=>[1,2,5,6,8,3,4,7]=>[1,2,4,7,5,6,8,3]=>{{1},{2},{3,4,7,8},{5},{6}}
[4,5,2,6,3,7,8,1]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[7,8,5,6,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[7,8,4,2,1,5,3,6]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[7,8,2,1,6,5,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,4,1,2,5,7,3,8]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[7,8,3,4,5,1,6,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,3,5,4,2,1,6]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,4,1,2,3,6,5]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,8,3,6,5,4,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,8,2,1,5,3,4,6]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[7,8,2,6,4,1,3,5]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[7,8,2,5,6,4,1,3]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>{{1},{2,3},{4,6},{5},{7},{8}}
[7,8,1,6,5,4,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,2,1,7,5,4,3,8]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,3,7,1,6,4,8,2]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[5,3,6,2,7,4,1,8]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,1,8,4,2,7,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,2,1,5,3,8,7]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,4,3,7,5,8,1,2]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[4,3,8,7,5,6,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,4,7,1,5,3,6,8]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[1,3,7,6,4,2,8,5]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[2,1,7,5,6,8,4,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,7,2,8,6,4,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,8,1,7,6,4,5,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,7,5,8,3,6,1,4]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[5,6,7,3,8,4,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,6,7,5,2,1,3,8]=>[1,3,8,2,4,6,7,5]=>[1,4,3,6,8,7,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,5,6,7,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,5,7,6,1,8,3,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,6,2,7,3,4]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,6,5,8,3,2,7,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,7,5,6,3,1,8,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,6,3,4,2,8,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,7,1,4,2,3,8,6]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[5,7,6,4,3,8,1,2]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,3,4,5,8,7,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,2,4,1,8,3,7,5]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,3,5,4,8,1,7]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[5,1,4,2,7,6,8,3]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[1,6,2,4,7,8,3,5]=>[1,6,2,4,7,8,3,5]=>[1,4,5,6,8,2,7,3]=>{{1},{2,4,6},{3,5,8},{7}}
[5,7,2,4,1,6,3,8]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,1,4,2,8,5,3,7]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,7,5,8,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[5,8,7,6,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,8,7,6,2,3,1,4]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[4,1,7,2,6,5,3,8]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,8,2,1,5,6,3,7]=>[1,5,6,2,3,7,4,8]=>[1,3,6,7,5,2,4,8]=>{{1},{2,3,6},{4,7},{5},{8}}
[2,1,8,7,6,5,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,7,4,5,6,8,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,2,7,1,6,3,8,5]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[4,3,7,5,6,8,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[4,8,6,3,5,7,1,2]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>{{1},{2},{3},{4,7},{5},{6,8}}
[4,8,1,2,5,3,7,6]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>{{1},{2},{3,5},{4,7},{6,8}}
[3,8,6,5,2,4,1,7]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,8,5,6,1,4,7,2]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[5,2,8,7,1,6,4,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,6,7,8,5,1,4,2]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>{{1},{2,3,4},{5,8},{6},{7}}
[3,7,6,8,5,2,1,4]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[3,7,8,5,1,2,4,6]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>{{1},{2},{3,6},{4},{5,8},{7}}
[3,7,1,6,4,2,5,8]=>[1,6,2,5,8,3,7,4]=>[1,5,7,8,6,2,4,3]=>{{1},{2,5,6},{3,4,7,8}}
[4,1,8,6,2,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,8,6,3,5,1,2]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>{{1},{2},{3},{4,5},{6,8},{7}}
[3,8,7,6,5,4,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,1,7,6,5,3,4,8]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,8,1,6,4,5,3,7]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,7,5,1,4,3,6]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,8,6,7,5,1,3,4]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[6,3,1,2,7,4,8,5]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[6,4,2,7,1,3,8,5]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,5,3,6,1,8,2,4]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,3,6,1,7,2,4]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,6,2,4,7,1,5]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[4,3,7,1,2,5,8,6]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[3,6,2,7,1,4,8,5]=>[1,4,8,2,7,3,6,5]=>[1,7,6,4,8,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[5,3,6,7,1,2,8,4]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,3,7,4,1,2,8,5]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,4,2,3,8,1,5]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[8,6,4,2,3,7,1,5]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[4,7,6,3,8,1,2,5]=>[1,2,5,3,8,4,7,6]=>[1,2,5,7,3,8,6,4]=>{{1},{2},{3,5},{4,6,7,8}}
[3,7,6,1,4,8,2,5]=>[1,4,8,2,5,3,7,6]=>[1,5,7,4,3,8,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[5,7,2,6,1,8,3,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,7,5,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[7,4,8,5,2,6,1,3]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[5,8,2,6,3,7,1,4]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[3,8,6,1,2,7,4,5]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[3,8,6,2,4,7,1,5]=>[1,5,2,4,7,3,8,6]=>[1,4,7,5,2,8,3,6]=>{{1},{2,4,5},{3,7},{6,8}}
[6,8,4,3,7,1,2,5]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[6,8,5,3,7,1,2,4]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[3,8,5,7,1,2,4,6]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[4,8,6,2,7,1,3,5]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[7,3,8,5,6,1,2,4]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[6,3,7,5,8,1,2,4]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>{{1},{2},{3,4},{5,7},{6,8}}
[2,7,6,4,8,1,3,5]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>{{1},{2,5},{3},{4,7},{6,8}}
[3,6,5,8,1,2,4,7]=>[1,2,4,7,3,6,5,8]=>[1,2,6,4,7,5,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[5,4,6,7,2,8,1,3]=>[1,3,2,8,4,6,7,5]=>[1,3,2,6,8,7,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,6,3,7,1,8,2,5]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,7,3,8,1,2,6]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[7,4,6,3,8,1,2,5]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[8,4,6,3,7,1,2,5]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[7,4,1,6,8,2,3,5]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,5,3,7,1,8,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,1,2,7,8,3,4]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,3,6,4,7,8,1,2]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>{{1},{2},{3},{4,6},{5,8},{7}}
[6,3,7,4,8,5,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[7,5,1,2,8,6,3,4]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,5,3,8,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[7,6,1,8,5,2,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,1,7,5,2,3,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,7,2,8,1,6,3,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,4,7,8,2,5,1,3]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>{{1},{2,3},{4,5},{6,8},{7}}
[6,3,7,8,5,1,2,4]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,6,8,7,5]=>{{1},{2},{3,4},{5,6,8},{7}}
[4,3,8,7,1,2,5,6]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>{{1},{2},{3,6},{4,7,8},{5}}
[5,3,8,7,1,2,4,6]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[8,4,7,6,1,2,3,5]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[5,4,8,7,1,2,3,6]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[2,5,8,7,1,3,4,6]=>[1,3,4,6,2,5,8,7]=>[1,5,3,4,6,2,8,7]=>{{1},{2,5,6},{3},{4},{7,8}}
[4,6,8,2,7,1,3,5]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[4,7,1,8,6,2,3,5]=>[1,8,2,3,5,4,7,6]=>[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,6,4,1,2,3]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[6,8,4,7,5,1,2,3]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[5,8,7,1,6,2,3,4]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[2,8,7,6,1,3,4,5]=>[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,7,8,6]=>{{1},{2,5},{3},{4},{6,7,8}}
[3,8,7,6,1,2,4,5]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>{{1},{2},{3,5},{4},{6,7,8}}
[4,8,7,6,1,2,3,5]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[5,6,3,1,4,2,8,7]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,7,1,4,5,8,2,3]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[5,7,3,8,1,2,6,4]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[8,7,1,4,5,3,2,6]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>{{1},{2,5},{3,6},{4},{7},{8}}
[7,1,8,4,2,6,5,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,1,8,4,7,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,8,1,5,7,2]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[8,7,1,4,2,6,5,3]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[2,3,4,5,6,7,8,1,9]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[2,3,4,5,6,8,9,1,7]=>[1,7,2,3,4,5,6,8,9]=>[1,3,4,5,6,7,2,8,9]=>{{1},{2,3,4,5,6,7},{8},{9}}
[2,3,4,6,7,8,9,1,5]=>[1,5,2,3,4,6,7,8,9]=>[1,3,4,5,2,6,7,8,9]=>{{1},{2,3,4,5},{6},{7},{8},{9}}
[2,3,5,6,7,8,9,1,4]=>[1,4,2,3,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}}
[2,4,5,6,7,8,9,1,3]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>{{1},{2,3},{4},{5},{6},{7},{8},{9}}
[3,4,5,6,7,8,9,1,2]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[2,3,4,5,6,7,8,9,10,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[2,3,4,5,6,7,8,9,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[2,3,4,5,6,7,1,8,9]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}
[2,3,4,5,6,7,8,10,1,9]=>[1,9,2,3,4,5,6,7,8,10]=>[1,3,4,5,6,7,8,9,2,10]=>{{1},{2,3,4,5,6,7,8,9},{10}}
[2,3,4,5,6,1,9,7,8]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[2,3,4,5,1,8,9,6,7]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}
[2,3,5,6,7,8,9,10,1,4]=>[1,4,2,3,5,6,7,8,9,10]=>[1,3,4,2,5,6,7,8,9,10]=>{{1},{2,3,4},{5},{6},{7},{8},{9},{10}}
[1,4,5,6,7,8,9,2,3]=>[1,4,5,6,7,8,9,2,3]=>[1,3,9,4,5,6,7,8,2]=>{{1},{2,3,9},{4},{5},{6},{7},{8}}
[2,4,5,6,7,8,9,10,1,3]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>{{1},{2,3},{4},{5},{6},{7},{8},{9},{10}}
[3,4,5,6,7,8,9,10,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[7,5,3,6,2,4,8,1]=>[1,2,4,8,3,6,5,7]=>[1,2,6,4,7,5,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[6,3,2,5,1,8,4,7]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,3,6,2,7,1,4]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,2,6,3,4,7,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,2,6,3,4,5,8,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[6,2,7,3,4,5,8,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[4,2,5,7,3,6,8,1]=>[1,2,5,7,3,6,8,4]=>[1,2,6,8,5,7,3,4]=>{{1},{2},{3,6,7},{4,8},{5}}
[5,4,7,6,2,3,8,1]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,7,3,5,2,4,8,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[2,7,6,3,4,5,8,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[8,6,5,2,3,7,1,4]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[8,5,2,1,7,3,4,6]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,2,1,8,3,4,6]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,3,2,8,4,5,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,6,2,3,1,8,4,7]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,5,1,8,3,7]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,8,6,2,7,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[6,8,3,5,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[6,8,2,1,7,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,7,3,4,5,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,1,7,3,4,5,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,8,6,1,7,2,4,5]=>[1,7,2,4,5,3,8,6]=>[1,4,7,5,3,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,8,1,5,7,2,3,6]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[4,1,7,5,8,2,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,6,2,7,1,8,4,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,7,1,2,8,4,5]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,2,6,1,8,3,4,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,6,1,7,3,4,5]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,1,5,8,4,6,7]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,4,1,3,6,8,2,7]=>[1,3,6,8,2,7,4,5]=>[1,7,3,5,8,6,4,2]=>{{1},{2,4,5,7,8},{3},{6}}
[1,5,3,4,6,8,2,7]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[4,3,5,1,6,8,2,7]=>[1,6,8,2,7,3,5,4]=>[1,7,5,8,4,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,4,6,3,8,7,1,2]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,6,4,5,8,7,1,2]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[6,5,3,4,8,7,1,2]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[5,3,1,8,7,2,4,6]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,3,7,6,1,2,4]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[6,3,8,1,7,2,4,5]=>[1,7,2,4,5,3,8,6]=>[1,4,7,5,3,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[7,6,8,2,3,5,1,4]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[6,7,3,8,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[5,4,7,8,2,6,1,3]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>{{1},{2,3},{4,6},{5,8},{7}}
[3,7,8,1,6,2,4,5]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,3,8,7,1,4,5,6]=>[1,4,5,6,2,3,8,7]=>[1,3,6,4,5,2,8,7]=>{{1},{2,3,6},{4},{5},{7,8}}
[7,2,8,6,1,3,4,5]=>[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,7,8,6]=>{{1},{2,5},{3},{4},{6,7,8}}
[2,1,8,7,3,4,5,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,7,3,4,5,6]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,8,7,2,4,5,6]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,7,8,3,6,2,4,5]=>[1,7,8,2,4,5,3,6]=>[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,4,8,7,6,1,2,3]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,8,3,7,5,1,2,4]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[7,8,6,2,5,1,3,4]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[8,1,6,7,3,2,5,4]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[8,1,5,3,6,2,4,7]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[7,5,1,3,6,2,4,8]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[7,5,8,3,6,2,4,1]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}}
[8,1,4,3,2,6,5,7]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[8,1,4,3,2,7,5,6]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,1,4,3,2,7,6,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,1,5,4,6,7,2,3]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,1,5,3,6,2,7,4]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,1,4,3,2,5,6,7]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>{{1},{2,4},{3,7},{5},{6},{8}}
[7,4,1,3,2,5,6,8]=>[1,3,2,5,6,8,4,7]=>[1,3,2,7,5,6,8,4]=>{{1},{2,3},{4,7,8},{5},{6}}
[6,4,3,8,2,5,7,1]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[7,4,1,3,2,5,8,6]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[7,5,1,3,6,2,8,4]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[7,5,1,4,6,8,2,3]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[7,5,8,3,6,2,1,4]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[7,4,8,3,2,5,1,6]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[6,4,3,8,2,5,1,7]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[6,4,3,7,2,5,8,1]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[5,4,3,2,8,6,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,4,3,2,8,7,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,5,3,8,7,2,1,4]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[6,5,4,8,7,1,2,3]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,5,4,1,7,8,2,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,5,3,1,7,2,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,4,3,1,2,7,8,5]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,4,3,2,1,8,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,1,8,2,7,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,4,1,8,7,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,1,3,2,8,6,5]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[7,4,1,3,2,8,5,6]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,4,3,1,2,8,5,7]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,3,1,2,7,5,8]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[6,4,3,8,2,7,5,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[6,5,3,8,7,2,4,1]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[6,5,3,1,7,2,4,8]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[7,6,1,8,4,5,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,7,8,2,4,1]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,6,8,7,5]=>{{1},{2},{3,4},{5,6,8},{7}}
[6,4,3,7,2,8,5,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,8,3,2,1,6,5]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[7,5,8,3,1,2,6,4]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[7,5,8,4,1,6,2,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[6,5,4,8,1,7,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[6,5,3,8,1,2,7,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[5,4,3,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,4,3,7,2,1,8,5]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,7,1,2,8,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,4,7,1,8,2,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,3,7,8,2,1,4]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[6,4,3,7,2,8,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,6,2,1,3,4,8,7]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[5,3,7,8,2,1,4,6]=>[1,4,6,2,3,7,8,5]=>[1,3,6,4,8,2,7,5]=>{{1},{2,3,6},{4},{5,8},{7}}
[2,1,7,8,4,3,5,6]=>[1,7,8,2,3,5,6,4]=>[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[8,3,7,4,1,5,6,2]=>[1,5,6,2,3,7,4,8]=>[1,3,6,7,5,2,4,8]=>{{1},{2,3,6},{4,7},{5},{8}}
[8,4,1,3,7,6,2,5]=>[1,3,7,2,5,4,6,8]=>[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[5,8,7,4,2,1,6,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[7,5,1,6,8,3,4,2]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,5,2,1,8,7,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,8,6,1,2,5,4]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[3,4,7,1,8,2,6,5]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,4,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,4,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,2,4,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,5,2,4,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,6,2,5,3,4,7,8]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,7,2,5,3,4,6,8]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,5,3,4,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,6,3,4,5,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,6,3,4,5,8]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,7,3,5,4,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,8,3,5,4,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,6,2,8,3,5,4,7]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,5,2,8,3,6,4,7]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,4,2,8,3,6,5,7]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,3,2,8,4,6,5,7]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,2,3,8,4,6,5,7]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,3,7,4,6,5,8]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[1,3,2,7,4,6,5,8]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,5,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,4,2,7,3,6,5,8]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[1,5,2,7,3,6,4,8]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,6,2,7,3,5,4,8]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,7,2,6,3,5,4,8]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,6,3,5,4,7]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,5,3,6,4,7]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,5,3,6,4,8]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,2,5,3,7,4,8]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[1,5,2,4,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[1,6,2,4,3,7,5,8]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,7,2,4,3,6,5,8]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,4,3,6,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,3,4,6,5,7]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,3,4,6,5,8]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,2,3,4,7,5,6]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,4,3,7,5,6]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,4,3,8,5,6]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,6,2,4,3,8,5,7]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[1,5,2,4,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,6,2,5,3,8,4,7]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[1,7,2,5,3,8,4,6]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,8,2,5,3,7,4,6]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,6,3,7,4,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,2,6,3,8,4,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[1,2,3,8,4,7,5,6]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,3,2,8,4,7,5,6]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,4,2,8,3,7,5,6]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,5,2,8,3,7,4,6]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,6,2,8,3,7,4,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,7,2,8,3,6,4,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,8,2,7,3,6,4,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,3,7,2,5,1,8]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,3,8,5,1,7,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,6,8,3,4,1,2,7]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,6,8,3,4,1,7,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,6,2,7,5,3,1,8]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,2,4,3,1,8]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,8,4,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,8,4,3,1,2,7]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,7,8,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,7,8,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,7,8,4,1,3,6,2]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[5,6,8,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,8,2,4,1,7,3]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,7,8,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[5,7,8,4,1,2,6,3]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[5,7,8,4,1,2,3,6]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[6,7,8,1,5,2,3,4]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,1,5,2,4,3]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,1,5,3,2,4]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[5,7,8,2,1,6,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[4,7,2,8,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,7,2,8,1,6,5,3]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,7,8,2,1,6,4,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,7,8,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,1,5,4,3,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,1,5,4,2,3]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,8,1,4,3,5,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[6,7,8,1,3,4,5,2]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>{{1},{2,5},{3},{4},{6},{7},{8}}
[3,2,7,8,1,5,6,4]=>[1,5,6,2,7,8,3,4]=>[1,6,4,8,5,2,7,3]=>{{1},{2,6},{3,4,8},{5},{7}}
[5,6,8,3,2,1,7,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,7,8,3,1,6,4,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,7,8,3,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[4,7,3,8,1,6,2,5]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[4,7,3,8,1,5,6,2]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[4,6,3,8,2,1,7,5]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,5,3,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,5,2,3,8,1,7,6]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,6,3,8,2,1,5,7]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[4,7,3,8,1,5,2,6]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[4,7,3,8,1,2,6,5]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,7,3,8,1,2,5,6]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>{{1},{2},{3,6},{4,7,8},{5}}
[5,7,8,3,1,2,6,4]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[5,7,8,3,1,4,2,6]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[6,7,8,1,3,4,2,5]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[6,7,8,1,4,3,2,5]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[6,7,8,1,4,2,5,3]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[6,7,8,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[6,7,8,1,2,4,5,3]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>{{1},{2},{3,5},{4},{6},{7},{8}}
[6,7,8,1,3,2,5,4]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[5,7,8,2,1,3,6,4]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[3,2,7,8,1,4,6,5]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>{{1},{2,6},{3,5,8},{4},{7}}
[6,7,8,1,3,2,4,5]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[6,7,8,1,2,4,3,5]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[6,7,8,1,2,3,5,4]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[7,2,8,5,1,6,4,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,3,7,5,2,6,4,8]=>[1,3,7,2,6,4,8,5]=>[1,6,3,7,8,4,2,5]=>{{1},{2,4,6,7},{3},{5,8}}
[7,2,8,5,4,1,6,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,5,4,3,1,7,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,4,5,6,1,7,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,4,5,3,7,1,6]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,4,3,5,6,1,7]=>[1,7,2,8,3,5,6,4]=>[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,2,8,4,5,6,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,2,3,8,5,1,7,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,4,8,5,2,1,3,6]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[6,4,8,5,1,3,7,2]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[6,3,7,5,2,1,8,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,7,5,1,2,8,6]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,3,7,1,5,6,8,2]=>[1,5,6,8,2,3,7,4]=>[1,3,7,8,5,6,4,2]=>{{1},{2,3,4,7,8},{5},{6}}
[3,6,1,7,5,2,8,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,4,1,2,7,6,8,5]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,4,2,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,6,5,7,1,4,8,2]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,5,2,7,4,1,8,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,1,8,6,4,7,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,1,8,7,2,4,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,5,8,2,7,4,1]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[6,5,8,4,2,3,7,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[6,2,5,8,3,7,1,4]=>[1,4,2,5,8,3,7,6]=>[1,4,7,2,5,8,6,3]=>{{1},{2,4},{3,6,7,8},{5}}
[1,6,5,7,3,4,2,8]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,5,2,7,4,6,3,8]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,2,1,8,7,6,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,8,6,1,7,5]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,3,4,8,6,5,1,7]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,7,3,5,8,6,1,4]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[3,2,4,7,8,6,1,5]=>[1,5,2,4,7,8,3,6]=>[1,4,6,5,2,8,7,3]=>{{1},{2,4,5},{3,6,8},{7}}
[1,5,4,6,2,7,3,8]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,2,4,7,1,8,3,6]=>[1,8,2,4,7,3,6,5]=>[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,6,1,4,8,2,7]=>[1,4,8,2,7,3,6,5]=>[1,7,6,4,8,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[7,3,5,6,8,4,2,1]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[6,3,5,1,8,2,7,4]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,1,5,8,4,7,3]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,6,5,8,3,4,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[3,2,4,1,7,8,5,6]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,1,4,2,7,8,6,5]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[3,6,4,7,8,2,5,1]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[3,1,4,6,8,5,7,2]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[6,3,4,5,7,1,8,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,1,4,3,6,5,8]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[7,3,4,1,2,6,5,8]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[7,4,3,2,1,6,5,8]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[7,6,3,2,5,4,1,8]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,2,5,4,8,1]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[1,8,3,2,5,4,7,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,5,2,3,7,6]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,5,1,6,2,4,8]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[7,3,6,1,5,4,2,8]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,4,6,5,1,3,2,8]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,8,5,4,3,2,7,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,4,3,7,2,5]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,4,3,1,8,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,7,5,1,3,8,2]=>[1,3,8,2,4,7,5,6]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,3,7,1,5,4,8,2]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[6,2,1,7,5,4,8,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,2,1,8,5,4,7,6]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,8,5,1,3,7,6]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[2,5,8,4,3,1,7,6]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[2,6,8,4,3,7,1,5]=>[1,5,2,6,8,3,7,4]=>[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[1,8,7,5,6,3,4,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,8,5,6,3,4,1]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[2,5,8,6,7,1,3,4]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}}
[2,4,8,6,1,7,3,5]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[3,2,1,8,6,7,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,1,7,6,8,4,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,3,7,1,6,8,4,2]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,4,7,6,1,8,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,7,6,8,1,3,2]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[4,6,7,5,8,3,1,2]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>{{1},{2},{3},{4},{5,7},{6},{8}}
[1,8,6,5,7,3,2,4]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,6,7,2,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,5,6,8,2,3,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[4,6,5,7,8,2,1,3]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>{{1},{2,3},{4},{5,6},{7},{8}}
[5,3,6,1,7,8,2,4]=>[1,7,8,2,4,3,6,5]=>[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,2,1,6,7,8,3,4]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[6,2,1,5,7,3,8,4]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[6,3,5,1,7,2,8,4]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,4,5,7,1,2,8,3]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,4,7,2,1,8,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,4,7,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,8,4,6,2,7,3,5]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,2,6,7,4,5]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,3,2,7,8,1,4]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[6,5,3,2,7,1,8,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,2,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,2,1,4,3,7,8,5]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[5,2,1,4,3,8,7,6]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[5,3,4,1,2,8,7,6]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,6,3,2,8,7,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,8,3,2,7,6,5,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,7,2,6,5,3]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,4,8,2,6,5,1]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[3,6,4,8,2,7,1,5]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[3,5,4,8,2,1,7,6]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,4,5,8,1,2,7,6]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[4,3,5,1,8,2,7,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,1,6,8,7,3,5]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,3,6,1,8,7,2,5]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,8,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,5,6,8,7,1,2,4]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[3,6,5,8,7,2,1,4]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[3,7,5,8,6,2,4,1]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>{{1},{2},{3,4},{5,7},{6,8}}
[1,8,5,7,6,2,4,3]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,7,5,4,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,7,8,5,4,1,2]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[4,2,1,7,8,6,5,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,3,8,1,7,6,5,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,4,8,7,1,6,5,3]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[2,1,12,11,10,9,8,7,6,5,4,3]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[4,3,2,1,12,11,10,9,8,7,6,5]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[6,5,4,3,2,1,12,11,10,9,8,7]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[8,7,6,5,4,3,2,1,12,11,10,9]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[10,9,8,7,6,5,4,3,2,1,12,11]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[12,11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[8,3,5,1,7,4,6,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,4,1,7,5,6,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,8,3,1,7,5,6,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,6,2,1,7,5,8,3]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,6,2,7,5,8,3]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>{{1},{2,6},{3,5,7},{4},{8}}
[7,5,2,1,6,8,4,3]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,4,3,1,7,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,6,1,8,3,4,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,5,7,1,8,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,5,6,1,8,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,5,1,8,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,4,1,7,5,3,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,7,5,3,1,8,4,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,2,1,6,7,5,3]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[1,8,4,2,6,7,5,3]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,3,2,7,6,8,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[5,3,2,1,7,6,8,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,5,3,1,7,6,8,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,4,6,1,7,5,8,3]=>[1,7,2,4,6,3,5,8]=>[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,1,6,5,8,2,3]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[4,8,2,6,5,7,1,3]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[4,6,1,2,7,5,8,3]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,3,1,2,7,6,8,4]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,3,7,6,8,4]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[4,3,1,2,7,6,8,5]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,5,1,2,7,6,8,4]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,7,1,5,8,2,3,4]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,6,1,5,8,3,4]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,3,5,1,7,6,8,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,1,6,8,4,2,3]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,4,1,6,7,5,2,3]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[5,2,3,1,7,6,8,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,5,2,1,7,6,8,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,5,2,7,6,8,4]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[1,7,6,2,5,8,3,4]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[7,6,2,1,5,8,3,4]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,2,4,1,7,5,8,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[7,1,6,4,8,2,5,3]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[8,2,6,4,7,1,5,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[6,1,5,2,7,4,8,3]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[8,3,5,7,6,2,1,4]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[1,8,3,5,7,6,2,4]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,2,3,7,6,8,4]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[8,4,2,6,7,5,1,3]=>[1,3,2,6,7,4,5,8]=>[1,3,2,5,7,6,4,8]=>{{1},{2,3},{4,5,7},{6},{8}}
[6,1,4,2,7,5,8,3]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[8,2,6,5,7,1,4,3]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[5,1,3,2,7,6,8,4]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[4,1,3,2,7,6,8,5]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[1,4,2,3,7,6,8,5]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[2,5,1,3,7,6,8,4]=>[1,3,7,2,5,4,6,8]=>[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[6,8,2,3,5,7,1,4]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[6,7,1,3,5,8,2,4]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[8,3,5,7,6,1,2,4]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>{{1},{2},{3,4},{5},{6,7},{8}}
[5,1,2,3,7,6,8,4]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[3,1,2,4,7,6,8,5]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[10,8,9,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,7,8,5,6,9,1,2,3,4]=>[1,2,3,4,5,6,9,7,8,10]=>[1,2,3,4,5,6,8,9,7,10]=>{{1},{2},{3},{4},{5},{6},{7,8,9},{10}}
[9,8,10,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[9,7,10,5,6,8,1,2,3,4]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>{{1},{2},{3},{4},{5},{6},{7,8},{9,10}}
[8,1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[8,1,3,5,6,2,7,4]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[8,1,3,4,2,6,7,5]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>{{1},{2,4},{3},{5,7},{6},{8}}
[8,1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[2,7,8,3,4,5,6,1]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[2,6,3,8,4,5,7,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[6,3,2,1,4,5,8,7]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[4,7,8,5,6,1,2,3]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[3,7,8,5,6,2,1,4]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[3,7,8,4,2,6,1,5]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>{{1},{2,5},{3,6},{4,8},{7}}
[3,7,8,2,4,5,1,6]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,6,2,8,4,5,1,7]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,3,6,7,4,5,8,1]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[3,5,2,4,8,6,1,7]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[3,5,4,2,8,7,1,6]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,6,5,8,7,1,2,3]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[6,4,5,1,7,8,2,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,4,1,2,3,8,5,6]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,2,4,1,3,7,5,8]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[2,6,4,8,3,7,5,1]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[2,6,5,8,7,3,4,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[6,5,2,1,8,3,4,7]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,6,7,8,3,4,1]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>{{1},{2},{3,4,8},{5},{6},{7}}
[2,4,6,7,3,8,5,1]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>{{1},{2},{3,7},{4},{5,8},{6}}
[4,2,6,7,3,1,5,8]=>[1,5,8,2,6,7,3,4]=>[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,6,4,8,1,7,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,3,8,1,2,7,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,2,5,3,7,1,6,8]=>[1,6,8,2,5,3,7,4]=>[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,4,6,7,2,8,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,4,2,5,6,8,1,7]=>[1,7,2,5,6,8,3,4]=>[1,5,4,8,6,7,2,3]=>{{1},{2,5,6,7},{3,4,8}}
[5,1,2,7,8,6,4,3]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[4,7,1,8,6,5,2,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,7,1,5,3,2,4]=>[1,5,2,4,3,6,8,7]=>[1,4,5,3,2,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[6,8,7,3,5,1,2,4]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[7,8,1,6,3,5,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,1,3,6,5,2,4]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,7,3,4,8,6,5,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,2,7,1,8,6,5,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,7,1,6,2,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,7,1,2,6,3,4]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[6,8,2,7,1,3,5,4]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[1,6,8,3,7,4,5,2]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,2,4,8,1,7,5,3]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[6,8,7,2,3,5,1,4]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[6,8,2,1,7,3,5,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,7,2,1,6,3,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,7,1,2,3,6,4]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[8,7,6,2,1,4,3,5]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,5,7,2,3,1,6,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,8,4,2,7,1,6,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,8,7,5,3,4,6,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,5,4,7,1,6,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,2,7,3,1,6,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,7,6,2,4,3,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,1,2,4,3,5]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[8,7,6,1,4,2,3,5]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,4,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[5,8,4,7,2,1,6,3]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,6,8,4,3,7,5,2]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,1,7,3,2,5,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,7,3,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,7,1,3,2,6,4]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[8,5,7,3,1,2,6,4]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[5,8,4,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,4,7,1,6,2,3]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,1,2,6,5,7,4,3]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[4,8,5,7,1,6,2,3]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[8,5,3,1,7,2,6,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,1,3,7,2,5,4]=>[1,3,7,2,5,4,6,8]=>[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,6,4,8,3,7,5,2]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[4,8,5,7,2,1,6,3]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[8,5,3,7,2,1,6,4]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[8,7,6,3,1,4,2,5]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[8,7,6,1,3,2,4,5]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,5,3,2,7,1,6,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,8,5,2,7,1,6,3]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[1,8,7,3,4,5,6,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,2,3,7,1,6,4]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[6,3,1,5,4,2,8,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,3,1,5,2,7,6,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,5,4,2,1,7,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,4,2,1,7,6,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,5,4,2,1,3,8,7]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,5,4,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,4,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,4,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[8,5,4,1,2,7,6,3]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,7,4,1,6,3,2,5]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,4,1,6,3,5,2]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,4,1,6,5,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,4,3,1,7,6,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,2,5,1,7,6,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,8,5,3,7,6,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,2,5,1,7,4,6]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,4,3,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,4,1,6,5,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,4,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,6,5,2,1,4,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,4,3,6,2,1,5]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[8,3,2,7,6,4,1,5]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,1,8,7,6,4,5,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,2,7,6,4,5,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,7,4,3,6,2,5,1]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[8,7,6,5,2,4,3,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[8,5,4,2,3,7,6,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[8,7,4,2,6,5,3,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,7,4,2,6,3,5,1]=>[1,2,6,3,5,4,7,8]=>[1,2,5,6,4,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,7,4,2,6,3,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[8,3,1,7,6,4,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,1,7,6,4,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,1,7,6,5,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,1,5,4,7,6,2]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[8,3,1,5,4,7,2,6]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[8,3,1,7,6,5,2,4]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,1,7,6,2,5,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,4,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[8,7,4,2,6,5,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[8,5,4,2,3,7,1,6]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[8,3,2,5,4,7,1,6]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,3,2,7,6,5,1,4]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,7,4,3,6,5,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[8,7,6,5,3,1,4,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,5,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,7,6,5,1,3,4,2]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[8,7,6,5,1,4,3,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,5,4,1,3,2]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,7,4,3,6,1,5,2]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[8,3,2,7,6,1,5,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,7,6,5,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,7,6,5,1,2,4,3]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[7,3,4,1,8,5,6,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,2,1,8,7,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,2,7,4,3,8]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[7,4,3,1,8,6,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,5,1,8,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,4,1,8,5,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,2,1,8,7,5,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,4,2,7,5,3,8]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[1,5,3,2,7,6,4,8]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[5,3,2,1,8,7,6,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,7,1,6,8,2,3]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,5,1,2,8,4,3,7]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,1,2,8,5,3,7]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,3,1,2,8,6,5,7]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,2,5,8,3,4,7]=>[1,2,5,8,3,4,7,6]=>[1,2,4,7,5,8,6,3]=>{{1},{2},{3,4,6,7,8},{5}}
[7,1,3,4,8,2,5,6]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,6,1,5,7,8,3,4]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[7,4,1,6,8,5,2,3]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,2,3,1,8,6,7,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,2,1,6,8,7,4]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,6,2,5,7,3,4,8]=>[1,6,2,5,7,3,4,8]=>[1,5,4,7,6,2,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[6,2,1,5,8,7,3,4]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,2,4,1,8,5,7,3]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,5,1,8,4,7,3]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,2,4,7,3,5,8]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[7,4,1,3,8,5,2,6]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,5,1,3,8,4,2,6]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,1,3,8,7,5,6]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,1,4,6,8,2,3,5]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[7,1,3,5,8,2,4,6]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[6,1,2,4,8,3,5,7]=>[1,2,4,8,3,5,7,6]=>[1,2,5,4,7,8,6,3]=>{{1},{2},{3,5,6,7,8},{4}}
[5,2,3,1,6,4,8,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[7,4,5,2,3,1,8,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,7,3,5,2,4,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[7,3,5,2,4,1,8,6]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,5,2,4,1,8,7]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,4,1,6,3,8,7]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[4,1,6,3,5,2,8,7]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,3,4,1,5,2,8,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,2,6,3,4,1,8,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,7,3,4,1,8,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,8,6,7,3,4,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,2,8,5,7,3,4,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,2,7,3,4,1,8,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,4,1,5,2,8,6]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,1,7,3,5,2,8,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,1,7,4,5,2,8,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,1,7,4,5,3,8,6]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,1,8,6,7,4,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,7,3,4,1,5,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,5,7,3,4,1,6,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,6,2,7,3,4,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,4,7,3,5,1,6,2]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,1,8,5,7,4,6,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,8,5,7,4,6,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,4,6,3,8,5]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,1,7,3,6,2,8,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,1,7,3,6,2,8,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,2,7,3,5,1,8,4]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,8,4,7,3,5,1]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,4,7,3,6,2,5,1]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>{{1},{2},{3,5},{4,6},{7},{8}}
[7,3,6,2,5,1,8,4]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,5,1,7,3,8,4]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[5,2,4,1,7,3,8,6]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[6,2,4,1,7,3,8,5]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[8,5,7,3,6,2,4,1]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>{{1},{2},{3,4},{5,6},{7},{8}}
[8,5,7,4,6,2,3,1]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[7,4,6,2,3,1,8,5]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,3,1,7,4,8,5]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,2,3,1,7,4,8,6]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,2,3,1,7,5,8,6]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,1,4,2,8,6,7,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,2,3,1,8,5,7,4]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,6,2,3,1,7,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,4,8,5,6,2,3,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,3,8,5,6,2,4,1]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[8,5,6,2,4,1,7,3]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,2,4,1,8,6,7,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,2,8,6,7,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,1,5,2,8,6,7,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,1,6,2,8,5,7,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,1,6,2,8,5,7,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,1,6,2,8,4,7,3]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,4,6,2,5,1,7,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,3,8,4,6,2,5,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[6,2,7,3,8,4,5,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[8,4,5,1,6,2,7,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[5,1,8,4,6,2,7,3]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,5,6,2,7,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,8,5,6,2,7,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,8,5,6,3,7,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,4,8,5,6,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,1,7,4,8,5,6,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,1,7,3,8,5,6,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[8,4,5,1,7,3,6,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,8,5,6,1,3,4,2]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>{{1},{2,4},{3},{5},{6},{7},{8}}
[7,8,1,3,6,2,5,4]=>[1,3,6,2,5,4,7,8]=>[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,3,8,4,7,2,5,6]=>[1,3,8,2,5,6,4,7]=>[1,5,3,7,6,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,6,1,2,5,7,3,8]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[1,4,8,2,5,7,3,6]=>[1,4,8,2,5,7,3,6]=>[1,5,6,4,7,8,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[7,8,2,4,5,6,1,3]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[7,8,1,5,4,6,3,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[7,8,2,1,6,3,4,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,3,5,6,4,1,2]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}}
[7,8,5,1,4,2,6,3]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[7,8,4,5,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,5,8,4,3,2,7,6]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,6,1,4,3,2,7,8]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[2,6,4,8,3,7,1,5]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[3,5,8,4,7,6,1,2]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[1,6,2,4,7,3,8,5]=>[1,6,2,4,7,3,8,5]=>[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[4,6,2,5,3,1,8,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,5,1,3,6,8,2]=>[1,3,6,8,2,4,7,5]=>[1,4,3,7,8,6,5,2]=>{{1},{2,4,5,7,8},{3},{6}}
[7,5,3,6,2,4,1,8]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,3,6,1,4,8,2]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,1,7,5,2,4,8,3]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[6,3,1,2,4,5,8,7]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>{{1},{2},{3,6,7,8},{4},{5}}
[4,6,7,8,3,5,1,2]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[3,5,6,7,8,1,4,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[5,2,7,6,1,4,3,8]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[2,5,7,6,8,1,3,4]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>{{1},{2,4},{3},{5},{6,7},{8}}
[2,7,5,6,8,4,1,3]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[2,1,6,8,4,5,3,7]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,7,1,8,5,3,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,6,8,5,4,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[4,3,8,5,6,7,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,2,8,1,6,3,7,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,2,8,4,5,6,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,4,2,8,6,1,7,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,4,7,1,5,2,6,8]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>{{1},{2,5},{3,4,7,8},{6}}
[4,3,7,8,1,2,6,5]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[1,7,3,8,5,2,6,4]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[5,7,8,6,1,3,4,2]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>{{1},{2,4},{3},{5},{6,8},{7}}
[7,6,5,8,1,3,4,2]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}}
[1,6,4,3,8,2,5,7]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[2,4,5,1,7,8,6,3]=>[1,7,8,2,4,5,3,6]=>[1,4,6,5,3,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,6,3,4,5,8,1,7]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,6,4,1,8,3,7,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,6,4,8,5,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[6,5,2,7,1,8,4,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,7,4,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,7,6,4,1,8,3,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,1,5,2,8,3,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,7,5,3,8,4,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,1,5,3,4,2,8,6]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,6,1,5,3,2,8,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,5,6,4,1,2,8,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,7,5,4,3,1,8,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,6,1,2,5,3,8]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,6,4,2,5,7,3,8]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[1,6,3,7,5,4,2,8]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,3,1,6,4,5,2,8]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,4,2,6,5,1,3,8]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,4,6,3,1,5,2,8]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,2,4,1,5,3,6,8]=>[1,5,2,4,3,6,8,7]=>[1,4,5,3,2,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[7,2,3,5,4,1,6,8]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,1,2,3,4,7,5]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,5,7,2,3,8,6,4]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[5,8,2,3,7,6,4,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[6,2,8,1,3,7,4,5]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[6,8,2,3,5,4,7,1]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[6,8,3,1,2,4,7,5]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[2,5,3,6,8,4,7,1]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>{{1},{2},{3,5},{4,7,8},{6}}
[2,5,3,7,6,1,8,4]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,7,4,1,6,2,8]=>[1,6,2,8,3,5,7,4]=>[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,3,4,1,8,6,7,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,1,8,6,3,7,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,8,6,5,3,7,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,2,8,5,7,6,3,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,4,2,7,5,8,6,3]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[4,1,8,6,7,5,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,8,7,6,2,4,1]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[5,8,4,7,6,2,1,3]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>{{1},{2,3},{4},{5,7},{6,8}}
[5,8,7,4,3,6,1,2]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[6,4,2,8,7,1,3,5]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[6,3,8,7,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[5,8,3,7,1,6,4,2]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[5,1,3,8,6,7,2,4]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,7,6,4,2,8,3]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[5,8,7,4,1,6,2,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[6,8,5,1,2,3,7,4]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[6,8,5,2,4,3,7,1]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[6,8,5,3,1,2,7,4]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,5,1,2,7,6,3,8]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[3,5,7,1,2,8,6,4]=>[1,2,8,3,5,7,4,6]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,2,7,5,1,4,8]=>[1,4,8,2,7,3,6,5]=>[1,7,6,4,8,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[4,6,3,1,2,7,5,8]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,5,3,1,7,6,2,8]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,2,5,7,1,6,3,8]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[3,4,6,5,8,7,1,2]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[3,1,4,5,8,6,7,2]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[3,5,6,2,8,4,7,1]=>[1,2,8,3,5,6,4,7]=>[1,2,5,7,6,4,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,5,3,1,6,8,7,2]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,1,7,5,8,6,4,3]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[1,2,7,5,3,8,6,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,1,2,7,3,8,6,5]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[6,4,1,7,5,2,3,8]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,1,3,7,5,2,4,8]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[3,1,2,6,8,5,4,7]=>[1,2,6,8,3,4,7,5]=>[1,2,4,7,8,6,5,3]=>{{1},{2},{3,4,5,7,8},{6}}
[3,7,1,2,5,4,8,6]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>{{1},{2},{3,5},{4,7},{6,8}}
[1,3,7,2,4,8,6,5]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[2,4,1,7,8,6,5,3]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,4,7,5,1,8,6,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,4,1,5,8,6,3]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,8,6,4,1,5,7,3]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[6,3,7,4,5,1,8,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,3,7,5,8,1,4]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[5,2,7,3,6,8,1,4]=>[1,4,2,7,3,6,8,5]=>[1,4,6,2,8,7,3,5]=>{{1},{2,4},{3,6,7},{5,8}}
[5,7,4,6,2,8,1,3]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,7,3,4,6,1,8,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,8,4,6,1,7,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,2,8,3,6,7,1,5]=>[1,5,2,8,3,6,7,4]=>[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,4,8,1,7,3,5,6]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[5,2,8,4,7,1,6,3]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,8,4,7,3,1,6,2]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[6,3,8,2,7,1,5,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,3,8,1,2,6,4,7]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[5,1,8,4,2,7,3,6]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,2,8,5,3,7,4]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,8,5,3,1,7,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,3,7,2,8,4,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,3,2,7,8,5,1,4]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[4,5,7,8,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[4,7,2,5,8,1,6,3]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[3,8,2,4,6,7,1,5]=>[1,5,2,4,6,7,3,8]=>[1,4,7,5,2,6,3,8]=>{{1},{2,4,5},{3,7},{6},{8}}
[3,5,6,8,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[2,4,5,6,8,1,7,3]=>[1,7,2,4,5,6,8,3]=>[1,4,8,5,6,7,2,3]=>{{1},{2,4,5,6,7},{3,8}}
[4,8,3,5,6,1,7,2]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,2,3,7,8,1,4]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[5,8,7,3,4,1,2,6]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[6,8,4,7,1,5,3,2]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[6,8,4,7,2,5,3,1]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>{{1},{2},{3,4,5},{6,7},{8}}
[5,4,8,7,1,6,3,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,3,8,7,6,1,2,4]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[4,3,8,7,6,1,2,5]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[4,8,3,7,5,1,2,6]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[8,3,4,6,5,1,2,7]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[3,8,4,7,5,1,2,6]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[3,4,8,7,6,1,2,5]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[3,5,8,7,6,1,2,4]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[4,5,8,7,6,1,2,3]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,5,8,7,1,6,3,2]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[4,5,8,7,2,6,3,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[3,5,8,2,7,6,4,1]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[3,5,8,1,7,6,4,2]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[2,5,8,1,7,6,4,3]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[2,5,8,7,1,6,3,4]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[2,4,8,7,1,6,3,5]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[2,8,4,7,1,5,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,1,4,6,2,5,3,7]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[1,8,4,7,2,5,3,6]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,8,7,2,6,3,4]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,5,8,2,7,6,4,3]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,5,8,3,7,6,4,1]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[1,4,2,8,7,6,5,3]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,3,8,2,7,6,4,5]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,8,3,2,7,5,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,3,2,6,5,4,7]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[8,2,3,1,6,5,4,7]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[2,3,8,1,7,6,4,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,4,1,8,7,6,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,1,8,7,6,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,1,8,7,6,5,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,2,1,7,5,4,6]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[8,3,2,1,6,5,4,7]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,4,2,6,1,5,3,7]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[4,2,8,7,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,2,8,7,1,6,3,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,2,8,1,7,6,4,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,3,8,1,7,6,4,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,3,8,2,7,6,4,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[6,8,3,2,7,5,4,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,8,3,1,7,5,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,2,1,7,5,4,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,2,7,1,5,3,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[6,8,7,2,1,4,3,5]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[8,5,6,1,2,4,3,7]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[5,8,7,1,2,4,3,6]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}}
[6,8,1,2,7,5,4,3]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,8,2,3,7,5,4,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,2,8,3,7,6,4,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,8,3,7,6,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,8,7,2,6,3,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,7,2,6,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,8,1,7,2,5,3,6]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,4,1,6,2,5,3,7]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[3,1,8,2,7,6,4,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,2,8,7,6,5,4]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,3,8,7,6,5,2]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,1,8,3,7,6,4,5]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,2,3,6,5,4,7]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[1,2,8,3,7,6,4,5]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,6,2,5,8,4,7]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[1,4,5,2,8,3,7,6]=>[1,4,5,2,8,3,7,6]=>[1,5,7,4,2,8,6,3]=>{{1},{2,5},{3,6,7,8},{4}}
[1,4,2,6,5,8,3,7]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[1,5,4,2,6,8,3,7]=>[1,5,2,6,8,3,7,4]=>[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[3,1,6,5,8,2,4,7]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[1,6,4,2,5,8,3,7]=>[1,6,2,5,8,3,7,4]=>[1,5,7,8,6,2,4,3]=>{{1},{2,5,6},{3,4,7,8}}
[1,5,2,6,4,8,3,7]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[1,2,6,5,4,8,3,7]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[1,2,5,4,7,3,8,6]=>[1,2,5,3,8,4,7,6]=>[1,2,5,7,3,8,6,4]=>{{1},{2},{3,5},{4,6,7,8}}
[4,1,2,6,3,8,7,5]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[7,1,5,4,2,8,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,1,3,5,2,8,4,6]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[7,2,5,1,8,3,4,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,4,2,8,3,7,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,4,2,8,3,7,6,5]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,2,5,3,8,7,6,4]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,2,8,6,5,3,7,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,5,2,8,6,3,7,4]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,6,4,2,8,7,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,2,1,8,7,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,2,1,8,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,1,6,2,8,4,5]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,7,6,4,2,8,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,7,5,2,6,3,8,4]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[1,6,2,7,5,3,8,4]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[1,2,7,6,5,3,8,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[1,2,6,5,3,8,7,4]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[1,5,2,6,3,8,7,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[1,5,2,7,6,3,8,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[1,6,5,2,7,3,8,4]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[1,5,7,4,2,8,3,6]=>[1,5,7,2,8,3,6,4]=>[1,7,6,8,5,4,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[4,1,2,8,6,3,7,5]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,3,7,1,8,2,5,6]=>[1,8,2,5,6,3,7,4]=>[1,5,7,8,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,1,6,2,4,7,5]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[7,1,8,3,2,4,6,5]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,3,2,4,6,5]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,2,8,7,3,6,5]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,7,4,2,8,3,6,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[8,1,5,4,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,4,8,5,2,7,3,6]=>[1,4,8,2,7,3,6,5]=>[1,7,6,4,8,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[8,5,3,1,7,2,4,6]=>[1,7,2,4,6,3,5,8]=>[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,2,1,7,3,4,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,6,4,2,7,3,5]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,2,6,3,7,4]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,5,2,7,3,8,6,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[1,2,8,5,3,7,6,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,6,3,8,7,5,4]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[1,2,7,6,3,8,5,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[1,6,2,7,3,8,5,4]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[1,7,2,8,5,3,6,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,7,4,2,8,6,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,1,8,3,2,6,4,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,1,8,6,3,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,3,2,6,4,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,4,2,8,7,6,3,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,2,8,6,3,7,5,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,7,3,8,6,5,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,1,7,3,6,5,8,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,1,8,7,6,2,4,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,7,6,3,4,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,7,8,6,2,4,1,3]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>{{1},{2,3},{4},{5},{6,8},{7}}
[5,7,1,6,2,4,3,8]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,4,1,5,2,7,3,8]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[8,1,4,5,3,7,6,2]=>[1,4,5,2,3,7,6,8]=>[1,3,5,4,2,7,6,8]=>{{1},{2,3,5},{4},{6,7},{8}}
[6,1,4,5,3,8,7,2]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}}
[5,1,7,8,6,2,4,3]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,1,8,6,3,4,5,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,4,5,3,8,6,2]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}}
[7,4,1,5,2,6,3,8]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[6,3,5,8,2,1,7,4]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[6,3,5,7,2,1,8,4]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,5,7,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[6,4,5,8,3,7,2,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[5,8,7,6,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[5,4,8,6,3,1,7,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,4,1,8,2,3,7,6]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,1,6,2,4,3,7]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,4,1,5,2,6,3,7]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[2,3,4,1,8,6,5,7]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,5,1,4,7,6]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[2,3,8,6,1,5,7,4]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[2,8,6,7,1,3,5,4]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[2,3,8,5,6,1,7,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,4,5,6,3,1,8,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,5,6,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,3,5,6,2,8,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,7,6,5,1,3,4,8]=>[1,3,4,8,2,7,5,6]=>[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,7,6,8,1,3,5,4]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>{{1},{2,5},{3},{4,6,7},{8}}
[2,7,6,5,8,3,1,4]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[8,7,5,6,1,4,2,3]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[2,6,4,1,8,5,7,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,1,3,8,5,7,4]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,7,6,8,4,3,1,5]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,7,6,1,8,3,4,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,6,1,4,3,5,8]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[7,3,5,1,2,8,4,6]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,4,1,5,2,3,7,6]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[7,8,1,6,3,4,2,5]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,4,1,8,3,2,7,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,6,4,1,7,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,8,6,7,4,3,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,3,5,7,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,3,4,1,8,7,5,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,6,1,7,3,4,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,3,8,1,4,5,7,6]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}
[2,1,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>{{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[2,1,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[9,1,2,3,4,5,6,7,10,8]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[1,8,2,3,4,5,6,9,7]=>[1,8,2,3,4,5,6,9,7]=>[1,3,4,5,6,8,9,2,7]=>{{1},{2,3,4,5,6,8},{7,9}}
[7,1,2,3,4,5,6,9,8]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[2,1,9,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[2,8,1,3,4,5,6,7,9]=>[1,3,4,5,6,7,9,2,8]=>[1,8,3,4,5,6,7,9,2]=>{{1},{2,8,9},{3},{4},{5},{6},{7}}
[8,4,3,6,5,1,7,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,6,3,4,1,7,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,5,4,3,1,7,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,6,5,4,2,3,8]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[1,8,6,5,2,7,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,5,4,1,6,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,5,4,1,3,6,2]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[6,8,5,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,6,2,4,1,7,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,2,8,6,5,1,7,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,2,1,7,6,4,5,8]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,1,3,7,6,2,5,8]=>[1,3,7,2,5,8,4,6]=>[1,5,3,6,7,8,2,4]=>{{1},{2,5,7},{3},{4,6,8}}
[6,1,7,5,3,2,4,8]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[7,1,6,5,2,4,3,8]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[8,1,6,5,2,3,7,4]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[1,2,7,6,3,4,5,8]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[1,2,8,3,7,4,5,6]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,1,7,2,6,3,5,4]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,1,8,2,6,4,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,8,3,2,7,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,3,8,2,7,5,6]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[3,2,1,8,4,7,5,6]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,8,7,1,6,5,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,8,2,7,1,6,5,3]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[5,8,7,2,1,6,4,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[7,8,6,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,6,1,5,4,3,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[1,8,7,2,6,5,3,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,8,2,5,6,3,4]=>[1,7,8,2,5,6,3,4]=>[1,5,4,8,6,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,6,8,1,4,3,5,2]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[6,5,8,3,2,1,7,4]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[8,5,7,3,1,6,4,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,6,8,4,2,7,3,5]=>[1,6,8,2,7,3,5,4]=>[1,7,5,8,4,6,3,2]=>{{1},{2,3,4,5,7,8},{6}}
[1,5,4,8,2,7,3,6]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,4,3,7,1,6,5,2]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[7,4,3,8,1,5,6,2]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[7,4,3,1,2,6,5,8]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[1,5,4,2,3,6,7,8]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>{{1},{2,3,5},{4,8},{6},{7}}
[8,5,1,4,2,3,7,6]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[7,5,1,4,2,6,3,8]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[6,5,1,4,3,2,7,8]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[5,6,1,3,4,2,7,8]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,6,8,7,5]=>{{1},{2,4},{3},{5,6,8},{7}}
[3,2,6,1,5,4,7,8]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[3,2,7,1,4,6,5,8]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>{{1},{2,6},{3,5,7},{4},{8}}
[5,7,1,3,2,6,4,8]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[6,7,1,2,4,5,3,8]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>{{1},{2},{3,5},{4},{6,7,8}}
[7,6,1,2,5,4,3,8]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[8,6,1,2,5,3,7,4]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[1,7,2,3,6,4,5,8]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,1,2,3,6,5,4]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,8,1,2,3,5,6,4]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>{{1},{2},{3},{4,6},{5},{7},{8}}
[6,8,1,2,4,3,7,5]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[5,8,1,3,2,4,7,6]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>{{1},{2,3},{4},{5,7},{6,8}}
[4,8,2,1,3,5,7,6]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[5,1,2,4,3,6,7,8]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>{{1},{2},{3,4},{5,8},{6},{7}}
[6,1,2,3,5,4,7,8]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>{{1},{2},{3},{4,5},{6,8},{7}}
[7,1,2,3,4,6,5,8]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[8,1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[6,7,3,8,5,1,2,4]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[6,7,4,5,1,8,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,7,6,8,1,2,3]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[5,3,7,8,6,1,2,4]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,6,8,7,5]=>{{1},{2},{3,4},{5,6,8},{7}}
[3,8,4,5,7,1,2,6]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[3,4,8,6,7,1,2,5]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[4,5,6,7,1,8,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,1,7,8,4,2]=>[1,7,8,2,3,5,6,4]=>[1,3,5,8,6,4,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,5,6,8,1,7,3,4]=>[1,7,2,5,6,8,3,4]=>[1,5,4,8,6,7,2,3]=>{{1},{2,5,6,7},{3,4,8}}
[8,2,4,5,1,6,3,7]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,4,8,6,2,3,7,5]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,5,6,8,2,3,7,4]=>[1,5,6,8,2,3,7,4]=>[1,3,7,8,5,6,4,2]=>{{1},{2,3,4,7,8},{5},{6}}
[2,5,6,3,4,7,8,1]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[8,1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[2,8,3,1,5,7,4,6]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[3,4,1,6,7,8,5,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[4,3,1,7,6,8,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,3,7,2,6,4,8,1]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[6,7,3,1,5,8,4,2]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,7,2,1,8,5,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,2,8,1,5,3,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,7,8,2,1,4,3,5]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[6,7,1,2,8,4,5,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,7,1,3,4,8,5,2]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[5,1,7,3,4,8,6,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,8,1,2,7,4,5,6]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,1,3,7,5,8,6,2]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[3,1,4,5,7,8,6,2]=>[1,4,5,7,8,2,3,6]=>[1,3,6,4,5,8,7,2]=>{{1},{2,3,6,8},{4},{5},{7}}
[2,1,8,3,4,7,6,5]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,3,4,5,7,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,3,4,6,7,5]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,2,1,6,5,8,7,3]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[5,2,6,4,1,8,7,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,7,4,8,1,6,3]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[5,2,7,4,8,6,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[5,7,2,3,8,6,1,4]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[5,6,2,3,1,8,7,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,1,3,8,7,4]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,1,6,4,2,8,7,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,6,1,3,2,8,7,4]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,6,3,1,2,8,7,4]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,6,3,2,1,8,7,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,3,2,8,1,6,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,7,3,8,2,1,5,4]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,7,3,8,1,2,5,4]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[5,7,3,1,8,2,6,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,3,8,2,6,4]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,7,4,8,3,6,2]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[1,5,7,4,8,6,3,2]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[5,1,7,4,8,6,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,7,1,3,8,6,2,4]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,7,3,1,8,6,2,4]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,8,1,5,2,4]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[6,7,3,8,5,2,1,4]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[6,7,8,3,1,4,2,5]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[6,7,1,8,3,5,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,8,4,5,2,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,7,8,4,5,3,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[6,7,1,8,3,2,5,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,2,8,1,3,5,4]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[6,7,2,8,3,1,5,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,7,2,8,3,5,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,2,7,8,1,4,5,3]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>{{1},{2,5},{3,6,8},{4},{7}}
[5,2,7,1,8,4,6,3]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,1,7,8,5,6,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[4,1,2,7,8,6,5,3]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[6,2,7,8,5,1,4,3]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[6,7,2,8,5,3,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,7,2,1,8,6,3,4]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,1,2,8,6,3,4]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,7,2,8,6,4,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,5,7,3,8,6,4,2]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[6,7,1,8,2,5,3,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,8,2,4,3,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,7,1,8,5,2,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,8,5,2,4,3]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[1,6,7,8,5,3,4,2]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[6,1,7,8,5,4,2,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,7,1,8,5,3,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,8,4,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[6,3,8,5,2,7,4,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[6,3,4,5,8,7,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,8,1,4,7,2,3,6]=>[1,4,7,2,3,6,5,8]=>[1,3,6,4,7,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[3,6,4,8,5,7,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[5,1,4,8,6,3,7,2]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[3,4,7,1,8,6,5,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,8,4,2,7,1,5]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[4,3,8,5,6,7,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,8,1,7,6,2,4,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,6,1,2,7,8,5,3]=>[1,2,7,8,3,4,6,5]=>[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[6,3,7,5,2,8,1,4]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,5,2,7,4,8,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[5,8,1,4,6,7,2,3]=>[1,4,6,7,2,3,5,8]=>[1,3,5,4,7,6,2,8]=>{{1},{2,3,5,7},{4},{6},{8}}
[6,5,8,4,3,7,2,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[6,3,7,4,2,8,5,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,7,1,6,2,4,5,3]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,8,6,7,1,4,5,2]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}}
[5,3,8,7,4,1,2,6]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,3,8,7,1,5,6,2]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[8,3,6,1,2,5,7,4]=>[1,2,5,7,3,6,4,8]=>[1,2,6,7,5,4,3,8]=>{{1},{2},{3,4,6,7},{5},{8}}
[5,6,1,8,7,3,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,2,7,3,6,8,1]=>[1,2,7,3,6,8,4,5]=>[1,2,6,5,8,7,3,4]=>{{1},{2},{3,6,7},{4,5,8}}
[6,4,1,5,3,8,2,7]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[6,2,7,4,3,5,8,1]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[3,7,6,4,5,2,8,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,7,6,5,3,4,8,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[6,5,4,3,1,8,2,7]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,5,4,2,7,3,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,5,4,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,4,1,8,3,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,5,2,8,3,4,7]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,6,5,3,4,8,2,7]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[5,4,6,3,1,8,2,7]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,8,4,2,7,3,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[3,8,6,2,5,7,4,1]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[7,8,5,3,2,6,4,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[6,8,3,1,7,2,5,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,6,3,7,5,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,5,2,6,4,3,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,7,1,6,2,5,4,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,1,6,3,2,5,4]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,8,1,7,3,5,6,4]=>[1,7,2,8,3,5,6,4]=>[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,8,6,1,7,4,5,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,8,1,3,7,2,6,5]=>[1,3,7,2,6,4,8,5]=>[1,6,3,7,8,4,2,5]=>{{1},{2,4,6,7},{3},{5,8}}
[5,1,7,6,8,3,2,4]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,7,1,5,8,4,2,6]=>[1,5,8,2,6,3,7,4]=>[1,6,7,8,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,7,3,1,8,4,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,8,4,5,2,6]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[7,6,1,8,4,3,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,1,7,4,2,5,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,2,7,3,4,6,5]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[7,1,2,8,3,5,4,6]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,2,6,1,8,4,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,6,1,7,3,5,4]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,3,1,5,8,4,2,6]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,4,2,7,1,8,3,6]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,5,6,8,3,2,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[6,5,4,8,2,7,3,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[6,5,2,8,7,3,4,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,1,8,7,4,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,4,7,5,3,2,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[5,1,8,3,7,6,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,3,2,6,4,1]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[3,6,8,2,4,7,5,1]=>[1,2,4,7,3,6,8,5]=>[1,2,6,4,8,7,3,5]=>{{1},{2},{3,6,7},{4},{5,8}}
[5,7,3,8,2,6,4,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,7,2,8,6,3,5,1]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,8,1,7,2,5,4]=>[1,7,2,5,3,6,8,4]=>[1,5,6,8,3,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[2,3,8,7,4,5,6,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,2,8,6,4,3,5,1]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,1,8,7,5,6,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,7,6,3,5,4,1]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,1,7,6,5,2,4,3]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,1,8,6,5,3,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,8,7,6,3,4,5]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,5,8,3,7,6,2,4]=>[1,5,8,2,4,3,7,6]=>[1,4,7,3,5,8,6,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,1,6,8,7,4,2,3]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,4,7,5,3,2,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[3,8,7,6,4,5,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,8,7,6,5,3,4,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,8,7,6,5,4,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,6,7,3,4,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,8,6,7,3,5,1,2]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[3,8,6,7,4,5,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,8,6,7,4,5,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,8,6,7,4,5,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,7,4,6,2,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,5,7,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,8,5,7,3,6,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[7,8,3,6,4,5,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[6,8,3,7,4,5,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,8,3,7,4,6,1,2]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[3,7,4,8,5,6,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[4,7,3,8,5,6,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,7,2,8,5,6,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,7,1,8,5,6,2,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,1,8,5,6,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,2,8,5,6,1,4]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,7,3,8,5,6,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[2,7,4,8,5,6,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[5,8,2,7,4,6,1,3]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,5,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[6,8,2,7,4,5,1,3]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[7,8,2,6,4,5,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[7,8,1,6,4,5,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,8,1,7,4,5,2,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,1,7,4,6,2,3]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,4,8,5,6,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,7,3,8,5,6,2,4]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,8,5,6,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,8,5,6,2,7,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,3,8,4,6,2,5]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[4,8,1,7,3,6,2,5]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,1,7,3,6,2,4]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,1,7,3,5,2,4]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,8,2,6,3,5,1,4]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[6,8,2,7,3,5,1,4]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[5,8,2,7,3,6,1,4]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[4,8,2,7,3,6,1,5]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,7,3,8,4,6,1,5]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[3,7,2,8,4,6,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,7,1,8,4,6,2,5]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,7,3,6,2,5]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,4,7,3,6,1,5]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,8,4,7,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[4,8,5,7,2,6,1,3]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[3,8,5,7,2,6,1,4]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[2,8,5,7,3,6,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,8,5,7,3,6,2,4]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,7,3,5,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,6,7,3,5,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[3,8,6,7,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[4,8,6,7,2,5,1,3]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[5,8,6,7,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[6,8,5,7,1,4,2,3]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[5,8,6,7,1,4,2,3]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[4,8,6,7,1,5,2,3]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[3,8,6,7,1,5,2,4]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,5,2,8,6,7,3,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,5,1,8,6,7,3,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,1,8,5,7,3,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,2,8,5,7,3,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,8,5,7,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,8,4,7,1,5,2,3]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[7,8,4,6,1,5,2,3]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[7,8,3,6,1,5,2,4]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,8,3,7,1,5,2,4]=>[1,5,2,4,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[4,8,3,7,1,6,2,5]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[3,8,4,7,1,6,2,5]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[1,6,2,8,4,7,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,6,1,8,4,7,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,2,6,1,8,4,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,1,6,2,8,4,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,8,1,6,2,7,3,5]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[5,8,1,6,2,7,3,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[7,8,1,5,2,6,3,4]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,8,2,5,1,6,3,4]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,8,2,5,1,7,3,4]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,2,6,1,7,3,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,8,2,6,1,7,3,5]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,7,3,6,2,8,4,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,7,3,6,1,8,4,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>{{1},{2},{3},{4},{5},{6,9},{7},{8}}
[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>{{1},{2},{3},{4},{5,9},{6},{7},{8}}
[1,2,3,5,6,7,8,9,4]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>{{1},{2},{3},{4,9},{5},{6},{7},{8}}
[1,2,4,5,6,7,8,9,3]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>{{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,3,4,5,6,7,8,9,2]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>{{1},{2,9},{3},{4},{5},{6},{7},{8}}
[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,10},{9}}
[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,7,8,6,9]=>{{1},{2},{3},{4},{5},{6,7,8},{9}}
[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,10},{8},{9}}
[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,10},{7},{8},{9}}
[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>{{1},{2},{3},{4},{5,10},{6},{7},{8},{9}}
[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>{{1},{2},{3},{4,10},{5},{6},{7},{8},{9}}
[1,4,3,5,6,7,8,9,2]=>[1,4,2,3,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>{{1},{2,3,4},{5},{6},{7},{8},{9}}
[1,2,4,5,6,7,8,9,10,3]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[3,2,4,5,6,7,8,9,1]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>{{1},{2},{3,9},{4},{5},{6},{7},{8}}
[1,3,4,5,6,7,8,9,10,2]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>{{1},{2,10},{3},{4},{5},{6},{7},{8},{9}}
[6,7,4,8,3,5,1,2]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[6,7,4,5,2,8,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,7,4,6,2,3,1,8]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,4,6,3,8,1,2]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,7,4,8,3,6,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[6,8,4,5,3,7,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,8,4,6,3,7,1,2]=>[1,2,3,7,4,6,5,8]=>[1,2,3,6,7,5,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,6,4,8,3,7,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[5,6,3,7,2,4,1,8]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,3,7,2,8,1,4]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,6,3,8,2,7,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[5,6,4,8,2,7,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[5,8,4,6,2,7,1,3]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,5,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[6,8,4,5,2,7,1,3]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[7,8,4,5,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[6,8,4,5,2,3,1,7]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,4,6,2,3,1,7]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,4,8,2,3,1,7]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,3,8,2,4,1,7]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,3,4,2,8,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,6,3,5,2,7,1,8]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,3,5,2,8,1,7]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,6,3,8,2,5,1,7]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[4,8,3,6,2,5,1,7]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,3,6,2,4,1,7]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,3,5,2,4,1,7]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,8,3,5,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,3,5,2,6,1,4]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[5,8,3,6,2,7,1,4]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[4,8,3,6,2,7,1,5]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[4,6,3,8,2,7,1,5]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[4,6,3,7,2,8,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,7,3,6,2,5,1,8]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,3,6,2,8,1,5]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,7,3,8,2,6,1,5]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[5,7,4,8,2,6,1,3]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[5,7,3,6,2,8,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,7,3,6,2,4,1,8]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,5,2,4,1,8]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,3,5,2,8,1,4]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,7,4,8,2,5,1,3]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>{{1},{2,3},{4,5},{6,7,8}}
[6,7,5,8,2,4,1,3]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[6,8,5,7,2,3,1,4]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[6,7,4,8,2,3,1,5]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[6,7,3,8,2,4,1,5]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[6,7,3,4,2,8,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,7,3,4,2,6,1,8]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,3,4,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,7,4,8,2,3,1,6]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,8,4,7,2,3,1,6]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[6,8,4,7,2,3,1,5]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[7,8,4,6,2,3,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[7,8,3,6,2,4,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[6,8,3,7,2,4,1,5]=>[1,5,2,4,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[5,8,3,7,2,4,1,6]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[4,8,3,7,2,5,1,6]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[4,7,3,8,2,5,1,6]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[4,7,3,5,2,8,1,6]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,7,3,5,2,6,1,8]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,3,7,2,6,1,8]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,3,7,2,8,1,6]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,5,3,8,2,7,1,6]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[4,8,3,5,2,7,1,6]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[5,8,3,4,2,7,1,6]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,8,3,4,2,7,1,5]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[7,8,3,4,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[6,8,3,4,2,5,1,7]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,3,4,2,6,1,7]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,8,3,5,2,6,1,7]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,5,3,8,2,6,1,7]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,5,3,6,2,8,1,7]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,8,5,2,1,7,6,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,4,2,3,1,8,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,5,3,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,4,6,1,3,2,8,7]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,6,8,1,7,3,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,8,1,6,3,5,2]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,4,8,1,6,5,3,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,4,8,1,3,7,6,2]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[8,4,5,3,1,7,6,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,4,8,1,7,5,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,8,7,2,1,3,4]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>{{1},{2,4},{3},{5},{6},{7,8}}
[8,5,7,6,4,2,1,3]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[8,4,6,3,7,2,1,5]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[6,3,2,8,7,4,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,1,6,8,7,4,3,5]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,1,7,8,6,4,5,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,3,2,8,6,4,5,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,8,5,2,4,3,1]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[5,8,7,6,3,2,1,4]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[6,8,7,5,3,2,4,1]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[5,8,4,2,3,7,6,1]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[7,8,4,2,6,5,3,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[4,8,6,2,7,3,1,5]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[3,6,1,8,7,4,2,5]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,1,8,6,4,5,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,6,7,5,2,4]=>[1,6,7,2,4,3,8,5]=>[1,4,7,3,8,6,2,5]=>{{1},{2,3,4,7},{5,8},{6}}
[3,7,1,6,8,2,5,4]=>[1,6,8,2,5,3,7,4]=>[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,7,4,2,8,1,5,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,8,4,2,7,5,1,3]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[2,1,8,6,7,5,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,4,3,7,5,1,2]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,8,6,7,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[6,7,5,8,1,3,4,2]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>{{1},{2,4},{3},{5},{6,7,8}}
[7,6,5,8,1,4,3,2]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[8,6,5,7,4,1,3,2]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[7,6,4,3,8,1,5,2]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[7,3,2,6,8,1,5,4]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>{{1},{2,5},{3,4,7,8},{6}}
[2,1,7,6,8,3,5,4]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,6,8,1,4,2,3]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[6,5,7,8,1,2,4,3]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>{{1},{2},{3,4},{5},{6,8},{7}}
[5,2,8,7,4,6,1,3]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,6,2,5,4,7,3,8]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[6,2,7,5,4,8,3,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[8,1,3,5,4,7,6,2]=>[1,3,5,2,4,7,6,8]=>[1,4,3,5,2,7,6,8]=>{{1},{2,4,5},{3},{6,7},{8}}
[6,1,5,4,3,8,7,2]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,1,8,3,4,5,7,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,5,3,4,8,6,2]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[7,1,4,3,5,6,8,2]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[8,1,3,4,5,6,7,2]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>{{1},{2,7},{3},{4},{5},{6},{8}}
[6,3,2,7,5,1,8,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,7,2,5,6,1,3]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>{{1},{2,3},{4,6},{5},{7},{8}}
[6,5,8,2,4,7,3,1]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>{{1},{2},{3,5,7},{4},{6,8}}
[8,5,2,1,4,3,7,6]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[6,5,2,8,4,1,3,7]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[5,6,2,1,4,8,3,7]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[3,6,1,8,5,2,4,7]=>[1,8,2,4,7,3,6,5]=>[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,3,5,4,7,8]=>[1,2,6,3,5,4,7,8]=>[1,2,5,6,4,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[3,4,1,2,8,6,5,7]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,8,1,6,3,2,4,7]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[6,3,8,5,2,1,4,7]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[8,3,1,5,2,4,7,6]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[3,8,6,7,2,1,5,4]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[8,5,6,4,2,1,7,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,2,5,8,3,1,6,4]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[1,7,5,6,3,2,4,8]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[6,1,2,3,8,5,7,4]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,1,2,3,6,5,8,4]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[7,2,1,3,8,6,4,5]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,7,3,2,4,6,8]=>[1,5,7,2,4,6,8,3]=>[1,4,8,6,5,7,2,3]=>{{1},{2,4,6,7},{3,8},{5}}
[5,2,7,3,1,8,4,6]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,2,4,1,3,7,6]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[8,7,2,6,3,4,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[4,8,1,6,3,2,7,5]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[3,1,8,6,4,2,7,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,6,7,4,3,2,5]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,4,1,3,8,7,5,6]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,5,8,3,1,7,4,6]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[8,7,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}
[8,7,6,9,5,4,3,2,1]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[8,7,6,5,9,4,3,2,1]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[8,7,6,5,4,9,3,2,1]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[8,7,6,5,4,3,9,2,1]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[8,7,6,5,4,3,2,9,1]=>[1,2,9,3,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[8,7,6,5,4,3,2,1,9]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[9,10,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[7,8,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[8,6,7,9,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}
[9,8,7,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[8,7,5,6,9,4,3,2,1]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[9,8,7,6,10,5,4,3,2,1]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,8,9,10,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9,10}}
[8,7,6,4,5,9,3,2,1]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,7,8,9,6]=>{{1},{2},{3},{4},{5},{6,7,8,9}}
[9,8,7,6,5,10,4,3,2,1]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,7,8,9,10,6]=>{{1},{2},{3},{4},{5},{6,7,8,9,10}}
[8,7,6,5,3,4,9,2,1]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[9,8,7,6,5,4,10,3,2,1]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,6,7,8,9,10,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[8,7,6,5,4,2,3,9,1]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>{{1},{2},{3},{4,5,6,7,8,9}}
[9,8,7,6,5,4,3,10,2,1]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,5,6,7,8,9,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[8,7,6,5,4,3,1,2,9]=>[1,2,9,3,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[9,8,7,6,5,4,3,2,10,1]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,4,5,6,7,8,9,10,3]=>{{1},{2},{3,4,5,6,7,8,9,10}}
[9,8,7,6,5,4,3,2,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,4,2,7,8,6,3,5]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[1,6,2,4,7,5,3,8]=>[1,6,2,4,7,3,8,5]=>[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[1,7,3,2,8,6,4,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,2,5,7,8,6,1,3]=>[1,3,2,5,7,8,4,6]=>[1,3,2,6,5,8,7,4]=>{{1},{2,3},{4,6,8},{5},{7}}
[7,2,3,1,8,5,6,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,5,1,7,3,4,6]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,2,1,8,3,4,7,5]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,8,3,5,1,7,4]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,3,6,4,8,5,7,2]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[6,2,4,7,5,8,1,3]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>{{1},{2,3},{4},{5,7},{6,8}}
[7,8,2,1,4,3,5,6]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[7,6,4,2,3,1,8,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,2,3,1,6,8,4]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,2,5,4,6,7,1,3]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[5,2,6,3,1,8,7,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,6,4,3,1,7,5]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,7,4,1,3,5,6]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>{{1},{2,6},{3},{4,7},{5},{8}}
[1,2,8,4,3,5,6,7]=>[1,2,8,3,5,6,7,4]=>[1,2,5,8,6,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,4,2,3,5,6,8]=>[1,7,2,3,5,6,8,4]=>[1,3,5,8,6,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[6,8,4,1,3,2,5,7]=>[1,3,2,5,7,4,6,8]=>[1,3,2,6,5,7,4,8]=>{{1},{2,3},{4,6,7},{5},{8}}
[1,6,3,8,2,4,7,5]=>[1,6,2,4,7,3,8,5]=>[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[5,1,8,3,2,6,4,7]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,5,4,2,6,3,8]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[1,5,8,4,2,7,3,6]=>[1,5,8,2,7,3,6,4]=>[1,7,6,8,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,4,6,2,8,3,7,5]=>[1,4,6,2,8,3,7,5]=>[1,6,7,4,8,2,5,3]=>{{1},{2,6},{3,5,7,8},{4}}
[5,3,6,1,2,8,4,7]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,4,5,3,8,6,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,3,1,4,2,7,5,8]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[8,6,3,2,4,1,7,5]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,2,3,4,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,2,3,1,4,5,8,6]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[8,3,1,6,5,2,4,7]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[3,7,5,1,8,2,4,6]=>[1,8,2,4,6,3,7,5]=>[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,5,2,8,7,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,1,2,4,6,5,3,7]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>{{1},{2},{3,6},{4},{5,7},{8}}
[8,1,2,5,4,6,3,7]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[8,3,1,6,2,5,4,7]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,1,2,5,6,4,3,7]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>{{1},{2},{3,6},{4,7},{5},{8}}
[1,7,5,4,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,1,4,8,2,7,3,6]=>[1,4,8,2,7,3,6,5]=>[1,7,6,4,8,5,3,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,4,6,8,2,7,3,5]=>[1,4,6,8,2,7,3,5]=>[1,7,5,4,8,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[1,7,4,5,2,8,3,6]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,7,5,1,2,8,4,6]=>[1,2,8,3,7,4,6,5]=>[1,2,7,6,8,5,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,5,8,2,7,3,6]=>[1,5,8,2,7,3,6,4]=>[1,7,6,8,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,4,2,8,6,7,3,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,1,7,6,3,4,8,5]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,2,3,6,8,5,7,4]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[5,1,4,2,7,8,3,6]=>[1,4,2,7,8,3,6,5]=>[1,4,6,2,8,5,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[1,4,2,7,6,8,3,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[3,1,2,8,4,6,7,5]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,1,2,7,6,4,8,5]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[5,3,7,1,8,2,4,6]=>[1,8,2,4,6,3,7,5]=>[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,3,2,5,8,6]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[1,4,2,7,8,3,6,5]=>[1,4,2,7,8,3,6,5]=>[1,4,6,2,8,5,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[2,1,8,6,3,4,7,5]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,3,7,8,5,6,4]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[1,2,3,7,5,8,6,4]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[1,4,2,7,3,8,6,5]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[3,1,7,2,8,6,4,5]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,2,3,8,7,5,6,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8,10]=>[1,2,3,4,5,6,8,9,7,10]=>{{1},{2},{3},{4},{5},{6},{7,8,9},{10}}
[9,1,2,3,4,10,5,6,7,8]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,6,7,8,9,10,5]=>{{1},{2},{3},{4},{5,6,7,8,9,10}}
[9,1,10,2,3,4,5,6,7,8]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[10,1,2,3,4,5,6,7,8,11,9]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,10,11,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10,11}}
[8,1,2,3,4,5,6,9,10,7]=>[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,8,10,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,10},{9}}
[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[4,7,8,5,6,2,1,3]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,6,8,7,5]=>{{1},{2,3},{4},{5,6,8},{7}}
[5,7,8,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[6,7,8,4,2,5,1,3]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[8,6,3,7,2,1,5,4]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[7,6,3,8,2,1,5,4]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[6,7,8,3,2,1,5,4]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[5,7,8,3,2,1,6,4]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,6,3,8,2,1,4,5]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>{{1},{2,3,5},{4},{6,7,8}}
[8,6,3,7,2,1,4,5]=>[1,4,5,2,3,7,6,8]=>[1,3,5,4,2,7,6,8]=>{{1},{2,3,5},{4},{6,7},{8}}
[5,6,3,8,2,1,4,7]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[3,6,4,8,2,5,1,7]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,6,4,8,3,5,7,1]=>[1,2,6,3,5,7,4,8]=>[1,2,5,7,6,3,4,8]=>{{1},{2},{3,5,6},{4,7},{8}}
[3,6,4,7,2,5,1,8]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,3,7,2,1,4,8]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[8,4,3,2,1,6,5,7]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,4,3,2,1,7,5,8]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,5,4,2,8,6,1,7]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,4,3,2,1,8,5,7]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,3,2,1,8,5,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,3,2,1,7,5,6]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,4,3,2,1,7,6,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,4,3,2,1,8,6,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,2,1,8,7,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,3,8,2,1,7,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,5,3,2,8,1,6,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,5,4,2,7,6,1,3]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[7,5,4,2,8,6,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,5,4,2,8,7,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,6,5,8,7,2,1,3]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>{{1},{2,3},{4},{5,6},{7,8}}
[2,6,5,7,8,3,4,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,5,4,2,6,7,1,3]=>[1,3,2,6,7,4,5,8]=>[1,3,2,5,7,6,4,8]=>{{1},{2,3},{4,5,7},{6},{8}}
[8,5,3,2,6,1,7,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,5,3,2,6,1,8,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,3,7,2,1,8,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,4,7,2,8,1,5]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,6,4,7,3,8,5,1]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,5,3,2,7,1,8,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,3,2,1,6,8,5]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,4,3,2,1,6,7,5]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[7,4,3,2,1,5,8,6]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,4,3,2,1,5,8,7]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,6,3,4,1,2,8,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,5,7,4,2,6,3,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[2,1,7,8,5,6,3,4]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,8,3,7,5,1,4,2]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[5,7,3,8,1,6,2,4]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[3,2,5,8,4,6,1,7]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[3,5,2,4,1,7,6,8]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,2,1,5,7,3,6,8]=>[1,5,7,2,3,6,8,4]=>[1,3,6,8,5,7,2,4]=>{{1},{2,3,6,7},{4,8},{5}}
[4,5,2,3,7,1,6,8]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,2,5,3,8,1,6,7]=>[1,6,7,2,5,3,8,4]=>[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[4,2,5,8,3,1,6,7]=>[1,6,7,2,5,8,3,4]=>[1,5,4,8,7,6,2,3]=>{{1},{2,5,7},{3,4,8},{6}}
[3,1,5,4,2,8,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,1,5,3,8,2,6,7]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>{{1},{2,5},{3,7},{4,8},{6}}
[4,1,5,8,3,2,6,7]=>[1,5,8,2,6,7,3,4]=>[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,3,8,5,2,1,6,7]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[4,7,3,5,2,1,6,8]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[4,6,7,1,3,2,5,8]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[3,5,1,4,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[5,2,1,4,3,7,8,6]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[5,3,1,4,2,7,6,8]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[4,3,6,1,5,2,7,8]=>[1,5,2,7,8,3,6,4]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[6,3,4,1,2,7,5,8]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[4,6,3,1,7,2,5,8]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[5,6,2,7,1,3,4,8]=>[1,3,4,8,2,7,5,6]=>[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[4,6,7,2,3,1,5,8]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,6,2,1,7,3,5,8]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[3,6,2,1,4,7,5,8]=>[1,4,7,2,3,6,5,8]=>[1,3,6,4,7,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[3,5,2,7,4,6,1,8]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,1,4,6,3,8,5]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[3,2,6,1,5,7,4,8]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[3,6,2,1,5,7,4,8]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[6,3,2,1,5,7,4,8]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[4,2,6,1,5,3,7,8]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>{{1},{2,5},{3,6},{4,8},{7}}
[7,4,1,5,6,2,3,8]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[6,4,5,1,7,2,3,8]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,6,5,1,7,2,3,8]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,6,5,1,2,7,4,8]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[2,3,1,8,5,4,7,6]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,1,5,8,3,7,6]=>[1,5,8,2,4,3,7,6]=>[1,4,7,3,5,8,6,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,4,1,5,3,8,7,6]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[3,4,5,1,2,8,7,6]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,4,5,1,8,2,7,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,4,5,3,2,7,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,8,5,3,1,7,6]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[3,4,5,8,2,1,7,6]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,4,5,2,8,1,7,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,4,6,2,1,7,5,8]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,5,6,2,7,1,8,4]=>[1,8,2,7,3,5,6,4]=>[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,2,7,8,1,4]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[3,4,6,2,8,7,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,4,6,8,2,7,1,5]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[2,4,8,6,3,7,1,5]=>[1,5,2,4,8,3,7,6]=>[1,4,7,5,2,8,6,3]=>{{1},{2,4,5},{3,6,7,8}}
[1,8,4,6,3,7,2,5]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,2,7,4,1,8]=>[1,8,2,7,3,5,6,4]=>[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,7,2,8,3,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,5,6,8,7,2,4,1]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[1,8,5,6,7,3,4,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,6,7,3,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,8,7,2,1,4]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[4,5,6,7,2,1,8,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,1,8,7,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,1,8,6,7,4,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,2,6,7,5,4]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,1,6,7,4,8,3]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,5,1,6,7,4,3,8]=>[1,6,7,2,5,3,8,4]=>[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[3,5,6,1,7,4,2,8]=>[1,7,2,8,3,5,6,4]=>[1,7,5,8,6,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,5,6,1,7,4,8,2]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,4,6,1,8,7,5,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,8,6,1,7,5,3]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[1,8,4,6,2,7,5,3]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,6,7,2,4,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,8,7,1,4,2]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[4,5,6,7,8,1,3,2]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[4,5,6,7,1,3,8,2]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,5,6,7,1,3,2,8]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,5,6,7,3,1,8,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,8,7,4,1,2]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[2,5,8,6,7,4,1,3]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[1,8,5,6,7,4,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,6,7,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,5,3,7,1,6,4]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[8,2,4,3,7,1,6,5]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[5,8,2,4,3,7,1,6]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[4,2,5,6,1,8,3,7]=>[1,8,2,5,6,3,7,4]=>[1,5,7,8,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,8,3,2,4,7]=>[1,5,8,2,4,7,3,6]=>[1,4,6,7,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,6,8,2,4,7,1,5]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[3,7,1,5,6,8,2,4]=>[1,5,6,8,2,4,3,7]=>[1,4,7,3,5,6,8,2]=>{{1},{2,3,4,7,8},{5},{6}}
[3,2,5,1,7,4,6,8]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,5,1,8,4,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,7,8,3,2,4]=>[1,5,7,8,2,4,3,6]=>[1,4,6,3,5,8,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[4,2,5,6,1,7,8,3]=>[1,7,8,2,5,6,3,4]=>[1,5,4,8,6,3,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,7,6,1,8,3,4,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,6,1,7,3,4,2]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,2,5,1,8,7,4,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,5,1,6,4,7,8]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,2,4,1,8,7,5,6]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,5,1,6,8,7,4]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,8,6,5,1,7,4,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,7,6,5,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,1,7,8,4,2,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,2,4,1,8,5,6,7]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,4,1,7,5,6,8]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,4,1,8,5,7,6]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,2,4,7,6,1,5]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[3,2,5,1,8,4,7,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,5,1,6,7,4,8]=>[1,6,7,2,5,3,4,8]=>[1,5,4,7,3,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[6,5,1,7,4,2,3,8]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,5,1,8,4,2,3,7]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,2,3,7,5,1,6]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[4,2,6,1,8,3,7,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,6,1,8,3,7,4]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,6,1,7,3,5,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,2,6,1,8,4,7,3]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,1,6,4,2,3,7]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[3,2,5,1,8,6,4,7]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,1,8,5,7,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,6,1,7,3,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,1,6,7,4,2,3]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[3,2,5,1,8,6,7,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,4,1,8,6,5,7]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,5,1,6,4,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,8,5,1,7,6,4,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,7,5,1,8,6,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,5,1,6,4,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,2,5,1,8,7,6,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,3,1,8,4,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,1,7,5,3,8]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[2,5,7,4,1,6,3,8]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[4,3,7,5,1,8,6,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,3,8,5,1,7,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,8,4,3,6,1,7,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,5,4,6,1,7,3,8]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[3,2,5,8,1,6,7,4]=>[1,6,7,2,5,8,3,4]=>[1,5,4,8,7,6,2,3]=>{{1},{2,5,7},{3,4,8},{6}}
[2,5,4,6,8,1,7,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,6,2,1,8,5,7,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,1,7,5,8,6,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,4,1,7,5,3,8,6]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,6,4,1,8,5,3,7]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,8,2,1,6,3,7]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[2,5,8,4,1,6,3,7]=>[1,6,2,5,8,3,7,4]=>[1,5,7,8,6,2,4,3]=>{{1},{2,5,6},{3,4,7,8}}
[4,8,3,2,6,1,5,7]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[3,5,2,8,1,6,4,7]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,2,7,1,5,4,8,6]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[3,2,7,1,5,8,6,4]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,8,2,5,1,6,7,4]=>[1,6,7,2,5,3,8,4]=>[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[4,8,3,2,6,7,1,5]=>[1,5,2,6,7,3,4,8]=>[1,5,4,7,2,6,3,8]=>{{1},{2,5},{3,4,7},{6},{8}}
[4,3,8,2,6,7,1,5]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>{{1},{2,5},{3,7},{4,8},{6}}
[4,3,2,6,7,8,1,5]=>[1,5,2,6,7,8,3,4]=>[1,5,4,8,2,6,7,3]=>{{1},{2,5},{3,4,8},{6},{7}}
[4,3,2,6,7,1,5,8]=>[1,5,8,2,6,7,3,4]=>[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,3,7,2,6,8,1,5]=>[1,5,2,6,8,3,7,4]=>[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[4,3,7,8,2,6,1,5]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>{{1},{2,5},{3,6},{4,8},{7}}
[2,5,7,4,8,1,6,3]=>[1,6,2,5,7,3,4,8]=>[1,5,4,7,6,2,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[3,2,5,7,8,1,6,4]=>[1,6,2,5,7,8,3,4]=>[1,5,4,8,6,2,7,3]=>{{1},{2,5,6},{3,4,8},{7}}
[3,2,5,7,1,6,4,8]=>[1,6,2,5,7,3,4,8]=>[1,5,4,7,6,2,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[6,3,2,7,1,5,4,8]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[6,3,2,7,1,5,8,4]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,5,2,1,7,8,4,3]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,1,7,5,3,8,6,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,2,1,8,5,3,7,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,2,1,7,4,6,8]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,4,2,1,7,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,4,1,7,3,8,6,5]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,5,8,2,1,7,4,6]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[4,8,3,7,2,1,5,6]=>[1,5,6,2,3,7,4,8]=>[1,3,6,7,5,2,4,8]=>{{1},{2,3,6},{4,7},{5},{8}}
[4,3,7,2,1,5,6,8]=>[1,5,6,8,2,3,7,4]=>[1,3,7,8,5,6,4,2]=>{{1},{2,3,4,7,8},{5},{6}}
[4,8,3,2,7,1,5,6]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>{{1},{2,6},{3,4,7},{5},{8}}
[3,5,2,8,1,7,4,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,3,8,2,1,5,6,7]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[1,9,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[8,7,6,4,5,3,2,1,9]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,9,8,7,5,6,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,10,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,9,8,7,6,5,4,3,2,1,11]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>{{1},{2,3,4,5,6,7,8,9,10,11}}
[9,8,7,5,6,4,3,2,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,10,9,8,6,7,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>{{1},{2,3,4,5,6,7,8,9,10,11}}
[6,2,3,1,5,4,8,7]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[8,4,5,2,3,1,7,6]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,5,3,4,1,7,6]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,2,5,3,4,1,8,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,2,4,3,8,7]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[6,4,5,1,3,2,8,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,1,5,3,4,2,8,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,3,5,1,4,2,8,7]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[8,3,5,2,4,1,7,6]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,7,5,6,2,4,1]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[8,3,7,2,4,1,6,5]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,3,5,1,4,2,7,6]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,1,5,3,4,2,7,6]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,4,5,1,3,2,7,6]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[2,1,8,4,5,3,7,6]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,6,7,4,5,1,3,2]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,6,7,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,6,7,3,5,1,4,2]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[8,3,7,5,6,1,4,2]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[8,3,7,4,6,2,5,1]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[8,3,7,4,6,1,5,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[8,3,7,1,6,4,5,2]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[8,1,7,3,6,4,5,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,7,5,6,3,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,8,4,7,5,6,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,7,3,4,2,6,5]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,7,3,6,2,5,4]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,7,1,6,2,5,4]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[8,2,7,3,6,1,5,4]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,2,7,1,6,3,5,4]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,1,7,2,4,3,6,5]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,3,2,7,4,6,5]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,5,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[8,1,5,2,4,3,7,6]=>[1,5,2,4,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[8,2,7,1,4,3,6,5]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,2,7,3,4,1,6,5]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,2,7,5,6,3,4,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,4,7,5,6,2,3,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[8,4,7,2,3,1,6,5]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[8,2,3,1,7,4,6,5]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,3,1,5,4,7,6]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[4,2,3,1,8,5,7,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,3,2,8,6,7,5]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[8,6,7,2,3,1,5,4]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,2,3,1,7,5,6,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,7,2,6,3,4,1]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,5,7,2,6,1,4,3]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[8,2,7,5,6,1,4,3]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,6,7,2,5,1,4,3]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>{{1},{2,4},{3,5},{6},{7},{8}}
[8,6,7,1,5,2,4,3]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,6,7,1,3,2,5,4]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[2,1,8,3,7,5,6,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,3,2,7,5,6,4]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[8,1,7,5,6,2,4,3]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,7,2,6,4,5,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,7,1,6,4,5,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,2,7,4,6,1,5,3]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,2,7,4,6,3,5,1]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,4,7,2,6,3,5,1]=>[1,2,6,3,5,4,7,8]=>[1,2,5,6,4,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,4,7,2,6,1,5,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[8,4,7,1,6,2,5,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,1,7,4,6,2,5,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,5,7,1,6,2,4,3]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,5,7,4,6,1,3,2]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>{{1},{2,3},{4},{5,6},{7},{8}}
[8,5,7,1,6,3,4,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,1,7,4,6,3,5,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,4,7,1,6,3,5,2]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,4,7,3,6,1,5,2]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[6,5,8,1,3,2,7,4]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>{{1},{2,3},{4,5,7},{6,8}}
[4,5,8,6,3,2,7,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[6,5,8,7,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[6,7,2,8,4,1,5,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,6,1,8,4,5,7,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,4,6,1,5,7,3]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[6,3,1,8,4,5,7,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,6,8,4,5,7,2]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,3,6,8,4,5,7,1]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[1,3,7,8,4,6,5,2]=>[1,3,7,8,2,4,6,5]=>[1,4,3,6,8,5,7,2]=>{{1},{2,4,5,6,8},{3},{7}}
[3,6,7,8,4,2,5,1]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>{{1},{2},{3,5},{4,8},{6},{7}}
[7,6,1,8,4,2,5,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,8,7,3,2,1,4]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[2,8,3,7,1,6,5,4]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,2,8,7,3,6,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[7,2,1,8,4,6,5,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,7,8,4,6,5,1]=>[1,2,7,8,3,4,6,5]=>[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,2,7,8,1,4,6,3]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>{{1},{2,6},{3,5,8},{4},{7}}
[1,2,7,8,5,4,6,3]=>[1,2,7,8,3,4,6,5]=>[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[4,2,1,3,8,5,6,7]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,2,8,5,4,3,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,3,5,4,1,6,7]=>[1,6,7,2,8,3,5,4]=>[1,7,5,8,4,6,2,3]=>{{1},{2,7},{3,4,5,8},{6}}
[6,4,8,5,2,3,1,7]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,3,1,2,8,5,6,7]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,4,2,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,6,8,4,3,5,1]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[5,7,1,8,3,4,6,2]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,5,8,1,4,6,2]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[1,7,5,8,3,4,6,2]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,6,8,5,1,3,2,7]=>[1,3,2,7,4,6,8,5]=>[1,3,2,6,8,7,4,5]=>{{1},{2,3},{4,6,7},{5,8}}
[5,6,8,1,4,3,2,7]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[7,5,8,6,3,4,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,1,8,3,5,6,2,7]=>[1,8,2,7,3,5,6,4]=>[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,8,4,1,3,2,7]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[4,6,8,1,5,3,2,7]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[1,7,3,8,5,4,6,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[5,7,8,4,3,6,1,2]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[2,8,7,4,1,6,5,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,5,8,4,2,3,1,7]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,1,3,2,8,5,6,7]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,4,3,2,8,5,6,7]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,8,4,3,5,1,6,7]=>[1,6,7,2,8,3,5,4]=>[1,7,5,8,4,6,2,3]=>{{1},{2,7},{3,4,5,8},{6}}
[6,2,8,4,5,3,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,2,3,8,5,4,6,1]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,2,3,1,8,5,6,7]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,3,2,4,8,6,7]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[1,2,8,4,5,3,7,6]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,4,2,8,5,3,6,7]=>[1,4,2,8,3,6,7,5]=>[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[8,1,5,3,2,4,6,7]=>[1,5,2,4,6,7,3,8]=>[1,4,7,5,2,6,3,8]=>{{1},{2,4,5},{3,7},{6},{8}}
[3,8,1,5,2,4,6,7]=>[1,5,2,4,6,7,3,8]=>[1,4,7,5,2,6,3,8]=>{{1},{2,4,5},{3,7},{6},{8}}
[1,5,2,8,4,3,6,7]=>[1,5,2,8,3,6,7,4]=>[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,2,8,5,4,3,6,7]=>[1,2,8,3,6,7,4,5]=>[1,2,6,5,8,7,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,2,5,4,3,8,6,7]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,2,7,4,8,5,3,6]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[1,5,2,7,8,4,3,6]=>[1,5,2,7,8,3,6,4]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[5,1,2,7,4,8,3,6]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[2,8,1,5,4,7,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,2,4,8,7,5,3,6]=>[1,2,4,8,3,6,5,7]=>[1,2,6,4,7,5,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[2,8,1,4,3,7,6,5]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,1,2,8,7,4,3,5]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,1,2,8,7,3,5]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,4,8,1,7,2,5]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,6,1,4,2,8,3,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[7,1,6,2,8,4,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,6,7,2,8,4,3,5]=>[1,6,7,2,8,3,5,4]=>[1,7,5,8,4,6,2,3]=>{{1},{2,7},{3,4,5,8},{6}}
[6,7,1,4,2,8,3,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,3,7,1,4,8,2,5]=>[1,4,8,2,5,3,7,6]=>[1,5,7,4,3,8,6,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,7,2,8,4,5,3,6]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,4,2,7,8,5,3,6]=>[1,4,2,7,8,3,6,5]=>[1,4,6,2,8,5,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[6,1,2,8,4,3,7,5]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,4,1,2,8,3,7,5]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,6,1,3,2,4,8,5]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[6,7,1,3,2,4,8,5]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[1,2,7,3,5,8,4,6]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[1,2,7,5,8,3,4,6]=>[1,2,7,3,4,6,5,8]=>[1,2,4,6,7,5,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,5,8,3,7,4,6]=>[1,2,5,8,3,7,4,6]=>[1,2,7,6,5,8,4,3]=>{{1},{2},{3,4,6,7,8},{5}}
[2,8,1,7,3,5,4,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,2,8,1,7,3,6,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,1,7,4,3,6,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,2,8,4,7,5,3,6]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,6,1,4,2,7,3,5]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[8,1,6,2,7,4,3,5]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[7,1,2,8,6,4,3,5]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,4,1,2,8,6,3,5]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,7,4,8,1,6,2,5]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[3,4,8,7,1,6,2,5]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[4,2,8,1,7,6,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,1,7,6,4,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,8,3,4,1,5,2,6]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,8,3,4,1,6,2,5]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,8,3,4,1,7,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,7,3,4,1,8,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,3,4,1,8,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,3,4,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,3,4,1,6,2,7]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,8,3,4,1,5,2,7]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[6,7,3,4,1,5,2,8]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[5,7,3,4,1,6,2,8]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,6,2,8,3,4,1,7]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,6,2,7,3,4,1,8]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,2,8,3,5,1,7]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,7,3,5,1,6,2,8]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,8,3,5,1,6,2,7]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,8,3,5,1,7,2,6]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,3,5,1,8,2,6]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,3,1,7,4,8]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,6,2,4,1,8,3,7]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,2,4,1,7,3,8]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,6,2,5,1,7,3,8]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[4,6,2,5,1,8,3,7]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,1,8,3,7,2,6]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,1,7,3,8,2,6]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,6,2,7,3,8,1,5]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,6,2,7,3,8,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[5,6,2,7,4,8,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[5,6,3,8,4,7,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,6,2,8,4,7,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[5,6,2,8,3,7,1,4]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,6,2,8,3,7,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,5,1,7,3,6,2,8]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,5,1,8,3,6,2,7]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,3,5,6,7,8,9,1]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>{{1},{2},{3},{4,9},{5},{6},{7},{8}}
[3,2,4,5,6,7,8,9,10,1]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>{{1},{2},{3,10},{4},{5},{6},{7},{8},{9}}
[2,3,4,5,6,7,8,9,10,11,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11}}
[8,7,3,5,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,2,4,5,3,1,6]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,3,7,4,5,2,1,6]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[6,3,8,4,5,7,2,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,8,7,4,3,6,2,1]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[2,8,7,4,3,6,1,5]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,1,7,4,3,6,2,5]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,7,3,5,1,4,2,6]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[2,1,6,8,5,7,4,3]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,3,5,1,7,4,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,1,8,4,7,6,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,8,4,7,6,3,1]=>[1,2,5,8,3,4,7,6]=>[1,2,4,7,5,8,6,3]=>{{1},{2},{3,4,6,7,8},{5}}
[4,3,8,1,5,6,7,2]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>{{1},{2,3,7},{4,8},{5},{6}}
[5,8,7,4,1,6,3,2]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[5,8,3,6,1,4,7,2]=>[1,4,7,2,3,6,5,8]=>[1,3,6,4,7,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[4,8,3,6,1,2,7,5]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[3,8,7,4,1,6,2,5]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[3,8,1,2,5,6,7,4]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>{{1},{2},{3,7},{4,8},{5},{6}}
[8,7,1,4,2,6,3,5]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[8,6,3,1,2,4,7,5]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[8,1,7,4,5,2,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,8,7,4,5,1,3,6]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[8,7,2,4,1,6,3,5]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,8,3,6,2,4,7,1]=>[1,2,4,7,3,6,5,8]=>[1,2,6,4,7,5,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[5,8,3,6,2,1,7,4]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,1,8,4,5,7,2,3]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,3,5,1,7,2,4]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,3,1,6,2,7,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,5,3,8,6,1,7,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,4,1,8,5,6,7,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,7,8,9,10,1,2,3,4,6]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>{{1},{2},{3},{4},{5,6},{7},{8},{9},{10}}
[7,8,9,10,11,12,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[4,5,7,6,2,3,8,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,5,7,2,6,4,8,1]=>[1,2,6,3,5,7,4,8]=>[1,2,5,7,6,3,4,8]=>{{1},{2},{3,5,6},{4,7},{8}}
[2,5,7,3,6,4,8,1]=>[1,2,5,7,3,6,4,8]=>[1,2,6,7,5,4,3,8]=>{{1},{2},{3,4,6,7},{5},{8}}
[1,5,7,3,6,8,4,2]=>[1,5,7,2,3,6,8,4]=>[1,3,6,8,5,7,2,4]=>{{1},{2,3,6,7},{4,8},{5}}
[8,4,3,7,6,1,5,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[6,7,2,3,5,4,8,1]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[5,2,7,3,6,4,8,1]=>[1,2,7,3,6,4,8,5]=>[1,2,6,7,8,4,3,5]=>{{1},{2},{3,4,6,7},{5,8}}
[8,3,4,7,6,1,5,2]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[8,2,4,7,1,6,5,3]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[6,7,1,3,5,8,4,2]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[5,8,7,3,6,1,4,2]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[4,8,3,7,6,1,5,2]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[2,8,4,7,1,6,5,3]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[2,8,3,1,7,6,5,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,8,2,1,7,6,5,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,7,1,2,8,5,4,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,2,3,1,7,6,5,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,2,1,7,6,5,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,4,1,7,6,8,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,4,2,7,8,6,5,3]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[8,4,2,7,1,6,5,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,5,7,2,1,6,4,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,5,7,2,8,6,4,3]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[2,5,7,1,8,6,4,3]=>[1,8,2,5,7,3,4,6]=>[1,5,4,6,7,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,7,1,6,8,4,2]=>[1,6,8,2,3,5,7,4]=>[1,3,5,8,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,7,4,5,8,1,3,2]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[2,5,7,8,1,6,4,3]=>[1,6,2,5,7,8,3,4]=>[1,5,4,8,6,2,7,3]=>{{1},{2,5,6},{3,4,8},{7}}
[1,5,7,8,2,6,4,3]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[8,5,7,1,2,6,4,3]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[8,4,1,7,2,6,5,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,4,8,7,6,1,5,2]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[4,3,8,7,6,1,5,2]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[5,3,7,8,6,1,4,2]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>{{1},{2,3,4},{5,6,8},{7}}
[6,7,2,8,1,5,4,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,2,8,7,1,6,5,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,2,8,1,7,6,5,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,3,8,2,7,6,5,4]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[8,3,1,2,7,6,5,4]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,2,8,3,7,6,5,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,1,8,3,7,6,5,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,8,7,2,6,5,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,1,8,2,5,4,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,7,1,2,6,4,3]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>{{1},{2},{3,4,5,6},{7,8}}
[3,8,1,2,7,6,5,4]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[2,8,1,3,7,6,5,4]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[1,8,2,3,7,6,5,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[6,7,1,8,4,5,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,1,5,8,2,6,4]=>[1,5,8,2,6,3,7,4]=>[1,6,7,8,5,3,4,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,1,5,8,3,6,4]=>[1,5,8,2,7,3,6,4]=>[1,7,6,8,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,6,5,1,8,3,7,4]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,5,1,8,2,7,4]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,5,1,8,7,2,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,4,1,8,7,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,4,5,7,6,2,3]=>[1,4,5,7,2,3,6,8]=>[1,3,6,4,5,7,2,8]=>{{1},{2,3,6,7},{4},{5},{8}}
[6,4,5,1,8,7,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,6,1,8,7,2,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,6,1,8,7,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,6,1,8,2,7,4]=>[1,8,2,7,3,5,6,4]=>[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,6,1,8,3,7,4]=>[1,8,2,5,6,3,7,4]=>[1,5,7,8,6,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,6,1,8,2,7,4]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,1,5,8,2,6,4]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[8,1,3,5,7,2,6,4]=>[1,3,5,7,2,6,4,8]=>[1,6,3,7,5,4,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[8,1,2,5,7,3,6,4]=>[1,2,5,7,3,6,4,8]=>[1,2,6,7,5,4,3,8]=>{{1},{2},{3,4,6,7},{5},{8}}
[6,2,5,1,8,3,7,4]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,1,3,8,7,5]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,3,6,1,4,8,7,5]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[4,2,5,3,1,8,7,6]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,4,1,3,8,7,5]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,2,1,4,3,8,6,5]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[8,1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[8,1,3,4,2,7,6,5]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>{{1},{2,4},{3},{5,6,7},{8}}
[7,3,1,4,2,8,6,5]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,3,4,1,2,8,7,5]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,6,4,1,3,8,7,5]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[2,7,1,4,3,8,6,5]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[3,7,1,4,2,8,6,5]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,7,1,3,2,8,6,5]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,7,1,2,3,8,6,5]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,7,1,3,4,8,6,5]=>[1,3,4,8,2,7,5,6]=>[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[3,6,2,1,4,8,7,5]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[5,6,2,1,8,3,7,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,2,1,8,3,7,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,5,2,7,3,6,4]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,1,4,2,3,7,6,5]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>{{1},{2,3,4},{5,6,7},{8}}
[7,4,1,2,3,8,6,5]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,4,2,1,3,8,7,5]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,4,2,3,1,8,7,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,2,4,1,8,7,6]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,1,2,4,8,6,5]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[8,1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[7,2,1,3,4,8,6,5]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[2,4,3,6,5,8,1,7]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,4,6,3,5,8,1,7]=>[1,7,2,4,6,3,5,8]=>[1,4,5,6,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,4,6,3,5,1,8,7]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,1,6,5,3,8,7]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[4,2,6,5,3,1,8,7]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,5,1,3,8,7]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,6,5,1,8,7,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,6,5,8,1,7,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,2,6,5,8,3,1,7]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,4,1,6,5,8,3,7]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[2,1,4,6,5,8,3,7]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[4,2,6,5,3,8,7,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[2,6,4,3,8,7,1,5]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[2,6,4,3,8,7,5,1]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,2,6,8,5,3,7,1]=>[1,2,6,8,3,7,4,5]=>[1,2,7,5,8,6,4,3]=>{{1},{2},{3,4,5,7,8},{6}}
[2,4,6,8,1,5,7,3]=>[1,5,7,2,4,6,8,3]=>[1,4,8,6,5,7,2,3]=>{{1},{2,4,6,7},{3,8},{5}}
[2,4,6,1,8,5,7,3]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,4,6,8,5,7,3]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[2,4,6,1,8,5,3,7]=>[1,8,2,4,6,3,7,5]=>[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,6,8,1,5,3,7]=>[1,5,2,4,6,8,3,7]=>[1,4,7,5,2,6,8,3]=>{{1},{2,4,5},{3,7,8},{6}}
[2,4,6,8,3,5,7,1]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>{{1},{2},{3,5,7,8},{4},{6}}
[2,4,6,8,3,5,1,7]=>[1,7,2,4,6,8,3,5]=>[1,4,5,6,8,7,2,3]=>{{1},{2,4,6,7},{3,5,8}}
[2,4,6,8,3,1,5,7]=>[1,5,7,2,4,6,8,3]=>[1,4,8,6,5,7,2,3]=>{{1},{2,4,6,7},{3,8},{5}}
[2,4,6,3,1,8,5,7]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,6,3,8,5,7,1]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[2,4,3,6,8,5,7,1]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}
[2,4,3,6,1,8,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,3,6,1,8,7,5]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,5,2,8,7,1,3]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,6,2,5,8,7,1,3]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[2,4,6,3,1,8,7,5]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,1,6,3,8,7,5]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,1,4,6,3,8,7,5]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>{{1},{2,3,6},{4},{5,7,8}}
[2,4,6,1,8,3,7,5]=>[1,8,2,4,6,3,7,5]=>[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,6,8,3,1,7,5]=>[1,7,2,4,6,8,3,5]=>[1,4,5,6,8,7,2,3]=>{{1},{2,4,6,7},{3,5,8}}
[4,6,2,8,5,7,1,3]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,4,2,8,7,5,3,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,6,4,1,8,7,5,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,4,8,7,5,3]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,6,4,1,8,7,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,4,8,1,7,3,5]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,4,2,8,7,5,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,2,4,8,7,3,5,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[1,6,4,7,3,8,2,5]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[5,2,4,7,3,6,8,1]=>[1,2,4,7,3,6,8,5]=>[1,2,6,4,8,7,3,5]=>{{1},{2},{3,6,7},{4},{5,8}}
[8,1,6,3,7,2,4,5]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,1,7,4,5,8,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,1,4,7,3,8,2,6]=>[1,4,7,2,6,3,8,5]=>[1,6,7,4,8,3,2,5]=>{{1},{2,3,6,7},{4},{5,8}}
[4,3,1,7,5,8,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,8,6,3,7,1,4,5]=>[1,4,5,2,8,3,7,6]=>[1,5,7,4,2,8,6,3]=>{{1},{2,5},{3,6,7,8},{4}}
[5,8,2,1,7,3,4,6]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,7,2,1,8,3,4,6]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,1,3,8,2,4,5]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[5,1,2,4,8,3,6,7]=>[1,2,4,8,3,6,7,5]=>[1,2,6,4,8,7,5,3]=>{{1},{2},{3,5,6,7,8},{4}}
[4,3,6,1,5,8,2,7]=>[1,5,8,2,7,3,6,4]=>[1,7,6,8,5,4,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,6,1,4,5,8,3,7]=>[1,4,5,8,2,6,3,7]=>[1,6,7,4,5,3,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[6,5,1,3,4,8,2,7]=>[1,3,4,8,2,7,5,6]=>[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[1,6,2,4,8,3,5,7]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[1,5,3,2,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,5,3,4,1,8,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,8,3,6,1,4,5]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>{{1},{2,5},{3,6,8},{4},{7}}
[5,2,4,8,7,1,3,6]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[6,2,8,3,7,1,4,5]=>[1,4,5,2,8,3,7,6]=>[1,5,7,4,2,8,6,3]=>{{1},{2,5},{3,6,7,8},{4}}
[5,1,4,8,7,2,3,6]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[4,8,2,5,1,3,7,6]=>[1,3,7,2,5,4,8,6]=>[1,5,3,7,4,8,2,6]=>{{1},{2,4,5,7},{3},{6,8}}
[4,7,2,5,1,3,8,6]=>[1,3,8,2,5,4,7,6]=>[1,5,3,7,4,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[3,7,2,1,5,4,8,6]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[8,3,2,1,5,4,6,7]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,3,2,1,6,4,5,7]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,4,2,5,1,6,3,7]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[3,8,2,1,4,5,7,6]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>{{1},{2,3,7},{4},{5},{6,8}}
[3,7,2,1,4,5,8,6]=>[1,4,5,8,2,3,7,6]=>[1,3,7,4,5,8,6,2]=>{{1},{2,3,6,7,8},{4},{5}}
[3,2,7,1,4,6,8,5]=>[1,4,6,8,2,7,3,5]=>[1,7,5,4,8,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[3,2,8,1,4,6,7,5]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>{{1},{2,7},{3,5,8},{4},{6}}
[3,8,2,1,4,7,5,6]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[3,8,2,1,5,7,4,6]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[4,8,2,5,1,7,3,6]=>[1,7,2,5,3,6,4,8]=>[1,5,6,7,3,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,7,2,5,1,8,3,6]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,2,1,4,8,5,6]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[3,2,1,7,5,8,6,4]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[4,2,7,6,1,8,3,5]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,7,6,8,1,2,5]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>{{1},{2},{3,5},{4,6,7},{8}}
[4,3,8,6,7,1,2,5]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[4,2,8,6,1,7,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[3,2,1,8,7,5,6,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,2,1,7,4,5,6]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[3,2,8,1,6,4,7,5]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[3,2,7,1,6,4,8,5]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[4,2,7,6,1,3,8,5]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,8,6,1,3,7,5]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[4,2,8,7,1,3,6,5]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[5,7,8,3,4,1,2,6]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[4,2,6,7,1,3,8,5]=>[1,3,8,2,6,7,4,5]=>[1,6,3,5,8,7,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[3,2,6,1,8,4,7,5]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,2,1,8,4,5,6]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,3,8,5,1,2,6]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,3,7,8,6,1,2,5]=>[1,2,5,3,7,8,4,6]=>[1,2,5,6,3,8,7,4]=>{{1},{2},{3,5},{4,6,8},{7}}
[3,2,7,1,8,6,4,5]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,1,6,8,5,7,4]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,2,6,1,8,7,4,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,6,8,7,1,2,5]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>{{1},{2},{3,5},{4,7,8},{6}}
[3,4,6,8,7,5,1,2]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>{{1},{2},{3},{4},{5,7,8},{6}}
[5,3,6,4,8,7,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[1,4,6,2,7,8,5,3]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>{{1},{2,6},{3,5,8},{4},{7}}
[3,1,8,5,4,2,6,7]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,7,5,4,8,6,3]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[6,3,7,5,4,8,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[7,3,8,5,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,8,7,5,4,6,1,2]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,3,6,7,8,5,1,2]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>{{1},{2},{3},{4,5,8},{6},{7}}
[4,5,6,3,8,7,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,6,8,5,4,7,1,2]=>[1,2,3,6,8,4,7,5]=>[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[6,8,3,5,4,7,1,2]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[7,6,3,5,4,8,1,2]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[1,6,2,5,4,8,7,3]=>[1,6,2,5,3,4,8,7]=>[1,5,4,6,3,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[6,2,1,5,4,8,7,3]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[4,1,6,2,8,7,5,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,8,3,1,4,2,6,5]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[4,3,6,1,8,2,7,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,8,5,4,1,6,7]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>{{1},{2,3,7},{4,5,8},{6}}
[4,8,1,5,2,3,7,6]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[7,5,1,6,4,3,2,8]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,8,1,6,4,3,2,7]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,1,5,7,4,3,2,8]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[1,5,8,6,4,3,2,7]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,4,6,1,5,8,2,7]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[7,8,4,1,5,3,2,6]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,8,5,1,6,3,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,6,8,7,4,3,2,5]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,1,7,4,3,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,1,7,4,3,2,8]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,1,7,6,4,3,2,8]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,1,8,6,4,3,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,7,6,4,3,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,5,6,3,8,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,8,1,6,5,3,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,8,1,5,4,6,7,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,2,8,5,6,3,7,4]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,1,2,5,7,3,8,4]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[4,2,1,5,6,3,7,8]=>[1,5,6,2,3,7,8,4]=>[1,3,6,8,5,2,7,4]=>{{1},{2,3,6},{4,8},{5},{7}}
[4,3,6,1,5,7,2,8]=>[1,5,7,2,8,3,6,4]=>[1,7,6,8,5,4,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[2,4,6,3,7,1,8,5]=>[1,8,2,4,6,3,7,5]=>[1,4,7,6,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,6,7,3,8,2,5]=>[1,6,7,2,5,3,8,4]=>[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[4,1,7,5,2,3,8,6]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,8,3,5,4,1,7,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,2,6,3,8,1,7,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[7,8,2,3,4,1,6,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,1,4,6,3,2,5]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[3,1,6,4,7,8,2,5]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,8,5,7,4,3,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,5,8,4,3,2,6]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,1,8,7,4,3,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,1,8,4,3,2,7]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,1,4,3,2,6]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[5,8,7,1,4,3,2,6]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[1,5,7,8,4,3,2,6]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[2,4,7,5,1,3,8,6]=>[1,3,8,2,4,7,5,6]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,8,4,6,1,3,2,5]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[7,8,5,4,1,3,2,6]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[3,5,6,4,1,8,2,7]=>[1,8,2,7,3,5,6,4]=>[1,7,5,8,6,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,4,5,1,3,8,7]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,6,5,8,4,3,2,7]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[6,8,5,1,4,3,2,7]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[7,6,5,1,4,3,2,8]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>{{1},{2},{3},{4},{5},{6,8},{7,9}}
[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,9,5,8,6]=>{{1},{2},{3},{4},{5,7},{6,9},{8}}
[1,2,3,6,4,7,8,9,5]=>[1,2,3,6,4,7,8,9,5]=>[1,2,3,6,9,4,7,8,5]=>{{1},{2},{3},{4,6},{5,9},{7},{8}}
[1,2,5,3,6,7,8,9,4]=>[1,2,5,3,6,7,8,9,4]=>[1,2,5,9,3,6,7,8,4]=>{{1},{2},{3,5},{4,9},{6},{7},{8}}
[1,4,2,5,6,7,8,9,3]=>[1,4,2,5,6,7,8,9,3]=>[1,4,9,2,5,6,7,8,3]=>{{1},{2,4},{3,9},{5},{6},{7},{8}}
[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[8,9,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[8,9,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[7,8,9,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[8,9,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9}}
[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,10,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,6,7,8,9,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,10,6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,6,7,8,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,8,9,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,6,7,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,10,5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,5,6,7,8,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[8,9,10,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,5,6,7,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,10,7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,7,8,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,5,6,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,7,8,9,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,10,7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,7,8,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,4,5,6,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,8,9,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,6,7,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,6,4,5,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[9,10,7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,7,8,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,5,6,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,6,5,3,4,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10}}
[3,4,6,2,7,1,5,8]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,3,6,2,8,1,5,7]=>[1,5,7,2,8,3,6,4]=>[1,7,6,8,5,4,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[6,1,2,5,4,7,8,3]=>[1,2,5,3,4,7,8,6]=>[1,2,4,5,3,8,7,6]=>{{1},{2},{3,4,5},{6,8},{7}}
[4,2,8,5,1,3,7,6]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[4,3,6,8,1,7,2,5]=>[1,7,2,5,3,6,8,4]=>[1,5,6,8,3,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[5,3,6,4,1,7,2,8]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,4,6,3,7,5,8,2]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[4,6,7,2,5,8,1,3]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[2,7,5,4,1,6,3,8]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[7,5,4,6,2,8,1,3]=>[1,3,2,8,4,6,5,7]=>[1,3,2,6,7,5,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[1,7,5,4,3,8,6,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,5,4,1,6,7,3,8]=>[1,6,7,2,5,3,8,4]=>[1,5,7,8,3,6,2,4]=>{{1},{2,3,5,7},{4,8},{6}}
[5,6,3,2,7,1,8,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,6,3,2,7,1,4]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[2,4,1,7,8,5,3,6]=>[1,7,8,2,4,3,6,5]=>[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[2,5,4,1,6,3,8,7]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[5,6,3,2,1,8,4,7]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,5,2,1,6,4,7,8]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,7,5,8,2,1,4,6]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>{{1},{2,3,6},{4},{5,7},{8}}
[7,3,2,8,5,1,6,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,4,6,3,2,1,7,5]=>[1,7,2,3,4,6,5,8]=>[1,3,4,6,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,6,4,3,2,1,7,5]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,6,4,3,2,1,8,5]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,4,3,2,1,6,5]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,4,7,2,1,8,6,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,8,3,2,6,1,4]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[5,7,3,2,1,6,8,4]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[5,7,3,2,1,6,4,8]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,3,7,2,5,1,8,4]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,7,8,3,5,2,1,4]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>{{1},{2,3,4},{5},{6},{7},{8}}
[6,2,5,7,8,4,1,3]=>[1,3,2,5,7,8,4,6]=>[1,3,2,6,5,8,7,4]=>{{1},{2,3},{4,6,8},{5},{7}}
[6,3,7,2,8,1,4,5]=>[1,4,5,2,8,3,7,6]=>[1,5,7,4,2,8,6,3]=>{{1},{2,5},{3,6,7,8},{4}}
[3,2,6,1,7,4,5,8]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,5,8,4,1,3,7,6]=>[1,3,7,2,5,8,4,6]=>[1,5,3,6,7,8,2,4]=>{{1},{2,5,7},{3},{4,6,8}}
[2,4,1,7,8,3,6,5]=>[1,7,8,2,4,3,6,5]=>[1,4,6,3,8,5,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[3,7,2,8,6,1,4,5]=>[1,4,5,2,8,3,7,6]=>[1,5,7,4,2,8,6,3]=>{{1},{2,5},{3,6,7,8},{4}}
[5,3,8,2,1,4,7,6]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[3,5,2,1,4,6,8,7]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>{{1},{2,3,5,7,8},{4},{6}}
[7,8,6,5,4,3,2,1,9]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[1,8,9,7,6,5,4,3,2]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}
[8,9,7,6,5,4,3,2,1,10]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[1,8,7,9,6,5,4,3,2]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>{{1},{2,3,4,5,6,7,8},{9}}
[1,7,9,8,6,5,4,3,2]=>[1,7,9,2,3,4,5,6,8]=>[1,3,4,5,6,8,7,9,2]=>{{1},{2,3,4,5,6,8,9},{7}}
[1,9,10,8,7,6,5,4,3,2]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[7,8,3,5,4,6,1,2]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>{{1},{2},{3},{4,5},{6},{7},{8}}
[8,6,3,7,5,2,4,1]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>{{1},{2},{3,4},{5,6,7},{8}}
[5,4,1,6,3,2,8,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,7,1,6,2,8,3,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,7,1,6,2,8,4,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,7,6,5,1,8,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,6,5,1,8,4,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,6,5,1,4,8,7]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[2,3,6,1,5,4,8,7]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[7,3,5,1,8,4,2,6]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,6,1,5,8,4,3]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[2,7,6,4,1,8,5,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,6,3,8,5,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,1,7,6,3,8,4,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,7,6,4,1,8,3,5]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,5,1,8,6,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,3,4,8,7,6,1,5]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[2,3,4,8,5,7,1,6]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,4,3,5,8,7,2,1]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[2,1,4,5,8,7,3,6]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>{{1},{2,3,6,7,8},{4},{5}}
[6,4,3,5,8,7,1,2]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[2,3,4,8,7,5,6,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[2,3,4,8,7,5,1,6]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,7,6,5,4,8,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[7,3,5,6,8,4,1,2]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[7,3,5,6,8,1,4,2]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[7,3,5,6,8,1,2,4]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>{{1},{2},{3,4},{5},{6},{7,8}}
[6,4,1,5,8,7,2,3]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,4,1,5,8,7,3,2]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,7,1,6,3,8,2,4]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[6,4,1,5,8,3,2,7]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[7,4,1,5,8,2,6,3]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,3,5,7,8,2,4,1]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>{{1},{2},{3,4},{5},{6,8},{7}}
[2,7,6,4,5,8,3,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[2,1,4,5,8,6,3,7]=>[1,4,5,8,2,3,7,6]=>[1,3,7,4,5,8,6,2]=>{{1},{2,3,6,7,8},{4},{5}}
[7,3,5,4,8,6,2,1]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>{{1},{2},{3},{4,5},{6,7,8}}
[2,3,4,8,5,6,1,7]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,3,4,8,7,1,6,5]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,3,4,8,1,7,6,5]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,3,4,8,5,1,7,6]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,1,4,5,8,3,7,6]=>[1,4,5,8,2,3,7,6]=>[1,3,7,4,5,8,6,2]=>{{1},{2,3,6,7,8},{4},{5}}
[6,3,5,4,8,2,1,7]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,3,4,8,1,6,5,7]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,3,4,8,1,5,7,6]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[7,8,2,6,1,5,3,4]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,8,1,6,2,5,3,4]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,8,6,7,2,5,3,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,5,7,2,6,3,4]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,1,7,2,6,3,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,2,7,1,6,3,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[2,8,6,7,1,5,3,4]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,8,5,7,1,6,3,4]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,1,7,5,6,3,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,8,2,7,5,6,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,2,7,4,6,3,5]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,1,7,4,6,3,5]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,8,4,7,1,6,3,5]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,8,2,7,1,6,3,5]=>[1,6,2,7,3,5,4,8]=>[1,6,5,7,4,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[4,8,1,7,2,6,3,5]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,4,7,2,6,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,8,1,7,5,6,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[1,8,4,7,5,6,2,3]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,7,5,6,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,7,5,6,2,4]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,8,1,7,4,6,2,5]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[1,8,3,7,4,6,2,5]=>[1,8,2,5,3,7,4,6]=>[1,5,7,6,3,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,3,7,2,6,4,5]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,7,2,6,4,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[3,8,2,7,1,6,4,5]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[3,8,2,7,4,6,1,5]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[3,8,2,7,5,6,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[4,8,2,7,5,6,1,3]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[4,8,3,7,5,6,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[3,8,4,7,5,6,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,8,4,7,5,6,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[2,8,3,7,5,6,1,4]=>[1,4,2,8,3,7,5,6]=>[1,4,7,2,6,8,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,8,3,7,4,6,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,8,3,7,1,6,4,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,1,7,3,6,4,5]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,5,2,8,6,4,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[7,5,1,8,6,2,3,4]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,8,6,1,5,2,3]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[7,1,8,4,5,2,6,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,1,7,4,2,5,3]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,6,7,3,8,5,2,4]=>[1,6,7,2,4,3,8,5]=>[1,4,7,3,8,6,2,5]=>{{1},{2,3,4,7},{5,8},{6}}
[7,1,8,3,5,6,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,8,6,2,5,1,4]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[7,4,2,8,6,1,3,5]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[7,2,8,4,1,5,3,6]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[7,2,8,3,5,1,6,4]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,2,8,3,4,6,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[1,5,7,8,2,6,3,4]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[6,2,3,8,5,7,4,1]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,2,4,8,5,3,1,7]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[2,6,3,7,8,5,4,1]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[2,6,3,7,8,4,5,1]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[2,4,7,3,5,6,8,1]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[2,4,7,3,6,8,5,1]=>[1,2,4,7,3,6,8,5]=>[1,2,6,4,8,7,3,5]=>{{1},{2},{3,6,7},{4},{5,8}}
[3,1,5,4,7,8,2,6]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[5,2,4,8,6,1,3,7]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[5,2,3,8,4,6,7,1]=>[1,2,3,8,4,6,7,5]=>[1,2,3,6,8,7,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,4,7,8,3,6,2,5]=>[1,4,7,8,2,5,3,6]=>[1,5,6,4,3,8,7,2]=>{{1},{2,3,5,6,8},{4},{7}}
[4,8,1,3,6,7,2,5]=>[1,3,6,7,2,5,4,8]=>[1,5,3,7,4,6,2,8]=>{{1},{2,4,5,7},{3},{6},{8}}
[5,3,8,2,4,7,1,6]=>[1,6,2,4,7,3,8,5]=>[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[5,4,3,8,1,2,7,6]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[6,4,2,8,1,3,7,5]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>{{1},{2,7},{3},{4,5,6,8}}
[6,3,8,2,5,1,7,4]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[5,8,1,4,2,6,3,7]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[5,8,4,1,2,7,6,3]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[6,5,1,2,8,7,3,4]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,3,1,4,2,8,7]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,2,6,4,1,7,3,8]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,5,1,7,2,6,3,8]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[3,5,6,1,2,8,7,4]=>[1,2,8,3,5,6,4,7]=>[1,2,5,7,6,4,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,5,7,1,8,6,2,4]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[3,6,2,7,5,1,8,4]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,5,7,1,8,6,3]=>[1,8,2,5,7,3,4,6]=>[1,5,4,6,7,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,5,8,2,7,1,6]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[3,4,6,2,8,1,5,7]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[4,2,5,6,1,3,8,7]=>[1,3,8,2,5,6,4,7]=>[1,5,3,7,6,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,3,1,2,5,6,8,7]=>[1,2,5,6,8,3,4,7]=>[1,2,4,7,5,6,8,3]=>{{1},{2},{3,4,7,8},{5},{6}}
[5,3,6,8,4,7,2,1]=>[1,2,3,6,8,4,7,5]=>[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[3,7,2,5,4,8,6,1]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>{{1},{2},{3,5},{4,7},{6,8}}
[8,4,2,5,7,3,6,1]=>[1,2,5,7,3,6,4,8]=>[1,2,6,7,5,4,3,8]=>{{1},{2},{3,4,6,7},{5},{8}}
[5,2,6,8,4,3,7,1]=>[1,2,6,8,3,7,4,5]=>[1,2,7,5,8,6,4,3]=>{{1},{2},{3,4,5,7,8},{6}}
[3,1,6,5,4,8,2,7]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[4,1,6,5,8,3,2,7]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,5,4,7,6,3,2,1]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[5,7,1,8,4,3,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,1,5,4,3,8,6]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[8,2,1,5,4,3,7,6]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[8,4,1,5,7,3,2,6]=>[1,5,7,2,6,3,4,8]=>[1,6,4,7,5,3,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[8,5,6,7,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[8,4,6,1,7,3,2,5]=>[1,7,2,5,3,4,6,8]=>[1,5,4,6,3,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,7,6,1,4,3,8,5]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[6,7,8,5,1,3,2,4]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>{{1},{2,3},{4},{5},{6},{7},{8}}
[5,7,6,8,2,3,4,1]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[6,7,8,2,4,3,5,1]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>{{1},{2},{3,4},{5},{6},{7},{8}}
[4,7,6,2,8,3,5,1]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,3,6,2,4,7,5,1]=>[1,2,4,7,3,6,5,8]=>[1,2,6,4,7,5,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[5,7,3,8,4,6,2,1]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,7,3,5,8,6,2,1]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[8,7,3,1,4,6,2,5]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[8,7,3,5,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,2,5,1,3,6,4]=>[1,3,6,2,5,4,7,8]=>[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[8,4,6,5,7,1,2,3]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>{{1},{2},{3},{4},{5,6},{7},{8}}
[5,7,6,8,4,1,2,3]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[4,7,6,5,8,1,2,3]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[3,7,6,5,1,8,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9}}
[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>{{1},{2,3,4,5,6,7,8,9}}
[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9,10}}
[7,8,1,2,3,4,5,6,9]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>{{1},{2},{3},{4},{5},{6},{7,8,9}}
[1,8,9,2,3,4,5,6,7]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}
[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>{{1},{2,3,4,5,6,7,8,9,10}}
[10,1,2,3,4,5,6,7,8,9,11]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10,11}}
[8,9,1,2,3,4,5,6,7,10]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,9,10,8]=>{{1},{2},{3},{4},{5},{6},{7},{8,9,10}}
[7,1,8,2,3,4,5,6,9]=>[1,8,2,3,4,5,6,9,7]=>[1,3,4,5,6,8,9,2,7]=>{{1},{2,3,4,5,6,8},{7,9}}
[6,8,1,2,3,4,5,7,9]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,8,7,9,6]=>{{1},{2},{3},{4},{5},{6,8,9},{7}}
[1,8,2,9,3,4,5,6,7]=>[1,8,2,9,3,4,5,6,7]=>[1,8,4,5,6,7,9,2,3]=>{{1},{2,8},{3,4,5,6,7,9}}
[1,7,9,2,3,4,5,6,8]=>[1,7,9,2,3,4,5,6,8]=>[1,3,4,5,6,8,7,9,2]=>{{1},{2,3,4,5,6,8,9},{7}}
[1,9,10,2,3,4,5,6,7,8]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>{{1},{2,3,4,5,6,7,8,9,10,11}}
[3,6,4,8,7,5,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[5,6,4,3,8,7,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,6,2,4,7,8,5,3]=>[1,6,2,4,7,8,3,5]=>[1,4,5,6,8,2,7,3]=>{{1},{2,4,6},{3,5,8},{7}}
[3,4,7,2,8,1,6,5]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,3,8,4,5,6,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,5,6,4,8,7,1,2]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>{{1},{2},{3},{4,6},{5},{7,8}}
[4,6,8,5,3,7,1,2]=>[1,2,3,7,4,6,8,5]=>[1,2,3,6,8,7,4,5]=>{{1},{2},{3},{4,6,7},{5,8}}
[6,8,5,3,4,7,1,2]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>{{1},{2},{3},{4},{5,6,7},{8}}
[1,6,5,4,2,8,7,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,8,5,2,7,3,6,4]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,7,5,1,8,6,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,4,2,6,5,3]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[6,5,1,3,4,2,8,7]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>{{1},{2,4},{3},{5,6,7,8}}
[7,4,5,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,8,3,6,1,4,2,7]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[2,5,8,6,4,1,3,7]=>[1,3,7,2,5,8,4,6]=>[1,5,3,6,7,8,2,4]=>{{1},{2,5,7},{3},{4,6,8}}
[1,6,8,7,4,2,3,5]=>[1,6,8,2,3,5,4,7]=>[1,3,5,7,4,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,1,7,8,2,4,3,5]=>[1,7,8,2,4,3,5,6]=>[1,4,5,3,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,1,8,6,3,4,2,5]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,1,4,5,6,8,3]=>[1,4,5,6,8,2,3,7]=>[1,3,7,4,5,6,8,2]=>{{1},{2,3,7,8},{4},{5},{6}}
[6,1,3,2,7,5,8,4]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>{{1},{2,3},{4,5,7},{6,8}}
[1,6,3,8,5,7,2,4]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[2,6,4,1,7,5,8,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,6,5,8,1,4,2,3]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[5,8,6,7,3,2,1,4]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[1,6,4,3,7,2,8,5]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,1,3,4,5,2,8,6]=>[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,7,8,6]=>{{1},{2,5},{3},{4},{6,7,8}}
[1,8,3,5,4,2,7,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[4,1,6,3,8,2,7,5]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[3,2,6,4,7,8,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[2,8,5,7,4,3,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,2,5,8,3,4,1,6]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[5,3,8,7,1,2,6,4]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[6,5,3,8,2,1,7,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,5,8,4,1,2,3,6]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[3,5,7,8,4,1,2,6]=>[1,2,6,3,5,7,8,4]=>[1,2,5,8,6,3,7,4]=>{{1},{2},{3,5,6},{4,8},{7}}
[1,4,7,5,3,8,2,6]=>[1,4,7,2,6,3,8,5]=>[1,6,7,4,8,3,2,5]=>{{1},{2,3,6,7},{4},{5,8}}
[2,6,4,5,3,8,1,7]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[3,6,5,8,4,2,1,7]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,8,4,2,3,1,7]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,5,4,3,1,2,7]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[4,8,6,5,3,2,7,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[8,6,5,1,2,4,7,3]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[6,7,5,8,2,1,4,3]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[1,7,5,8,2,6,4,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,8,5,7,6,2,4]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,3,8,5,7,1,2,4]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,6,5]=>{{1},{2},{3,4},{5,6,7,8}}
[8,3,1,5,6,2,7,4]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>{{1},{2,6},{3,4,7},{5},{8}}
[8,1,2,5,6,3,7,4]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>{{1},{2},{3,6},{4,7},{5},{8}}
[1,8,2,5,7,6,3,4]=>[1,8,2,5,7,3,4,6]=>[1,5,4,6,7,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,8,6,2,7,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,8,6,1,7,3,4]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[3,8,6,5,7,1,2,4]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,6,5]=>{{1},{2},{3,4},{5,6,7,8}}
[7,6,5,8,1,2,4,3]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[5,1,7,6,8,4,2,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,2,5,8,1,6,4,3]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[5,2,8,6,1,7,3,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,2,8,6,5,7,3,4]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,2,1,3,6,7,8,5]=>[1,3,6,7,8,2,4,5]=>[1,4,3,5,8,6,7,2]=>{{1},{2,4,5,8},{3},{6},{7}}
[8,2,5,6,3,7,1,4]=>[1,4,2,5,6,3,7,8]=>[1,4,6,2,5,3,7,8]=>{{1},{2,4},{3,6},{5},{7},{8}}
[7,2,6,5,4,1,8,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,3,4,7,8,2]=>[1,5,2,3,4,7,8,6]=>[1,3,4,5,2,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[7,5,6,2,4,1,8,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,2,6,3,7,1,4]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[4,3,1,2,6,7,8,5]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>{{1},{2},{3,4,5,8},{6},{7}}
[8,1,6,5,7,3,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,5,8,6,2,7,1,4]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>{{1},{2,4},{3,5,7},{6,8}}
[5,8,1,6,3,7,2,4]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,8,5,6,3,7,2,4]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,5,4,2,8,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[7,1,4,2,6,5,8,3]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[4,1,7,3,5,6,8,2]=>[1,7,2,3,5,6,8,4]=>[1,3,5,8,6,7,2,4]=>{{1},{2,3,5,6,7},{4,8}}
[5,7,6,4,1,2,8,3]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,7,6,4,5,2,8,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,8,3,6,5,7,2,4]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,1,6,5,7,2,4]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[8,1,3,5,7,6,2,4]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[7,8,5,4,1,6,2,3]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,5,6,4,2,1,8,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,3,2,6,5,7,1,4]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[7,4,6,2,5,1,8,3]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,3,4,5,7,8,2]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>{{1},{2,6,8},{3},{4},{5},{7}}
[7,2,6,4,5,1,8,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,7,3,6,8,1,2]=>[1,2,3,6,8,4,7,5]=>[1,2,3,7,8,6,5,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[3,4,7,8,5,6,1,2]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>{{1},{2},{3},{4},{5,6,8},{7}}
[3,4,7,2,5,1,6,8]=>[1,6,8,2,5,3,4,7]=>[1,5,4,7,3,6,8,2]=>{{1},{2,3,4,5,7,8},{6}}
[3,6,2,4,7,1,5,8]=>[1,5,8,2,4,7,3,6]=>[1,4,6,7,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[6,8,3,4,5,7,1,2]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[4,3,6,7,5,8,1,2]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[6,3,7,5,8,4,1,2]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[7,3,8,6,4,5,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,2,7,6,5,8,3,4]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[4,8,2,6,1,5,3,7]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[2,3,8,6,4,1,5,7]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[4,3,6,2,5,1,8,7]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,3,2,5,1,4,6]=>[1,4,6,2,5,3,7,8]=>[1,5,6,4,3,2,7,8]=>{{1},{2,3,5,6},{4},{7},{8}}
[7,8,1,2,5,6,3,4]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>{{1},{2},{3,4,6},{5},{7},{8}}
[4,1,6,2,5,7,3,8]=>[1,6,2,5,7,3,8,4]=>[1,5,7,8,6,2,3,4]=>{{1},{2,5,6},{3,7},{4,8}}
[2,1,8,6,4,7,3,5]=>[1,8,2,3,5,4,7,6]=>[1,3,5,7,4,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,7,4,2,8,3]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[3,1,6,4,7,2,5,8]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[2,4,7,5,1,8,3,6]=>[1,8,2,4,7,3,6,5]=>[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,5,7,1,4,2,3,8]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[6,8,5,1,3,4,2,7]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>{{1},{2,4},{3},{5,6,7},{8}}
[2,8,3,4,5,1,7,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,2,4,3,1,5,7,8]=>[1,5,7,8,2,4,3,6]=>[1,4,6,3,5,8,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[4,2,8,3,1,7,5,6]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[5,3,7,4,1,6,2,8]=>[1,6,2,8,3,7,4,5]=>[1,6,7,5,8,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,4,7,3,6,1,8,5]=>[1,8,2,4,7,3,6,5]=>[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,7,6,3,1,2,4]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[7,5,6,8,1,4,3,2]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>{{1},{2,3,4},{5},{6},{7,8}}
[2,4,7,1,6,5,3,8]=>[1,6,2,4,7,3,8,5]=>[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[6,3,1,2,8,4,5,7]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[2,8,1,4,5,6,3,7]=>[1,4,5,6,2,8,3,7]=>[1,6,7,4,5,2,8,3]=>{{1},{2,6},{3,7,8},{4},{5}}
[7,2,1,5,4,6,3,8]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[4,2,6,1,8,5,3,7]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,4,1,5,3,6,2]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[3,4,6,1,5,8,7,2]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,8,1,6,3,4,7,2]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[6,5,1,8,2,7,4,3]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,8,1,7,5,2,3,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,6,1,8,5,3,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,1,7,4,8,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,6,1,5,7,4,2,8]=>[1,5,7,2,8,3,6,4]=>[1,7,6,8,5,4,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[3,1,7,5,6,4,8,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,1,7,6,4,8,3,2]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[6,1,7,8,5,3,4,2]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[7,1,8,6,5,4,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,4,7,5,8,2,3]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,3,7,4,6,8,2,5]=>[1,3,7,2,5,4,6,8]=>[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[1,7,6,5,4,8,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[8,1,6,5,7,2,4,3]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[1,2,7,6,8,3,4,5]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[6,1,7,5,3,8,2,4]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[2,1,7,5,6,8,3,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,4,1,7,6,8,2,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,8,5,6,2,7,3,1]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[3,8,6,4,2,7,5,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[2,8,6,3,7,4,5,1]=>[1,2,8,3,7,4,5,6]=>[1,2,7,5,6,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,8,1,6,2,4,5,3]=>[1,6,2,4,5,3,7,8]=>[1,4,6,5,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,8,4,1,7,2,6,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[5,4,7,1,8,3,2,6]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,4,1,8,5,2,6]=>[1,8,2,6,3,7,4,5]=>[1,6,7,5,8,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,1,8,4,5,3,6]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,2,8,4,3,5,7]=>[1,2,8,3,5,7,4,6]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,1,4,3,8,2,7]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[1,6,2,5,8,3,4,7]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[8,4,2,1,7,3,6,5]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,5,4,2,8,3,6,7]=>[1,5,2,8,3,6,7,4]=>[1,5,6,8,2,7,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,4,3,1,5,8,2,7]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[3,7,6,8,4,5,2,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[2,7,6,8,5,3,4,1]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,7,6,8,5,4,2,3]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,4,8,6,7,3,5,1]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[7,3,8,5,4,6,2,1]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[3,4,8,5,6,7,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,3,5,8,4,7,2,1]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[5,4,3,8,6,7,2,1]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,3,8,7,5,6,2,4]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[3,1,8,5,7,6,2,4]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,5,8,7,4,2,3]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,4,1,8,7,6,2,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,6,7,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[4,8,7,5,6,3,2,1]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[6,2,1,4,3,5,8,7]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[6,2,1,4,3,8,5,7]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[8,2,4,1,3,6,5,7]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[6,2,4,1,3,8,5,7]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,2,4,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[2,6,1,4,3,5,8,7]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[4,6,2,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[6,4,2,1,3,5,8,7]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[8,4,2,1,3,6,5,7]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[6,4,2,1,8,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,2,1,8,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,1,4,3,8,5,7]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[2,8,1,4,3,6,5,7]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[2,8,4,1,3,6,5,7]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[4,8,2,1,3,6,5,7]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[6,8,2,1,4,3,5,7]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[8,6,2,1,4,3,5,7]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>{{1},{2,3,4},{5},{6,7},{8}}
[2,1,8,4,6,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,4,1,8,3,5,7]=>[1,8,2,6,3,5,7,4]=>[1,6,5,8,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,4,8,1,3,5,7]=>[1,3,5,7,2,6,4,8]=>[1,6,3,7,5,4,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[4,6,2,8,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[4,2,6,1,3,8,5,7]=>[1,3,8,2,6,4,5,7]=>[1,6,3,5,7,4,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,6,1,8,3,5,7]=>[1,8,2,6,3,5,7,4]=>[1,6,5,8,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,4,1,8,3,5,7]=>[1,8,2,4,3,5,7,6]=>[1,4,5,3,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,4,1,6,3,5,7]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[4,2,1,6,8,3,5,7]=>[1,6,8,2,3,5,7,4]=>[1,3,5,8,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,1,4,3,8,6,5,7]=>[1,4,2,3,8,5,7,6]=>[1,3,4,2,7,8,6,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,4,1,3,8,6,5,7]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,1,3,8,6,5,7]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,2,1,8,6,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,2,1,8,4,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[8,2,6,1,4,3,5,7]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>{{1},{2,4},{3,5,6},{7},{8}}
[4,2,8,1,6,3,5,7]=>[1,6,2,8,3,5,7,4]=>[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,2,8,1,3,6,5,7]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[2,4,8,1,3,6,5,7]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>{{1},{2,4,6},{3},{5,7,8}}
[2,4,1,8,3,6,5,7]=>[1,8,2,4,3,6,5,7]=>[1,4,6,3,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,4,8,3,6,5,7]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[2,4,8,1,6,3,5,7]=>[1,6,2,4,8,3,5,7]=>[1,4,5,6,7,2,8,3]=>{{1},{2,4,6},{3,5,7,8}}
[2,4,8,6,1,3,5,7]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[4,2,8,6,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[6,2,8,4,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[8,2,6,4,1,3,5,7]=>[1,3,5,7,2,6,4,8]=>[1,6,3,7,5,4,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[8,4,6,2,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[6,4,8,2,1,3,5,7]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[4,6,8,2,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[2,6,8,4,1,3,5,7]=>[1,3,5,7,2,6,8,4]=>[1,6,3,8,5,7,2,4]=>{{1},{2,6,7},{3},{4,8},{5}}
[2,6,1,8,4,3,5,7]=>[1,8,2,6,3,5,7,4]=>[1,6,5,8,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,8,4,3,5,7]=>[1,6,8,2,3,5,7,4]=>[1,3,5,8,7,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[2,1,8,6,4,3,5,7]=>[1,8,2,3,5,7,4,6]=>[1,3,5,6,7,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,1,6,4,3,5,7]=>[1,6,2,8,3,5,7,4]=>[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,8,6,4,1,3,5,7]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>{{1},{2,7},{3},{4,6,8},{5}}
[4,8,6,2,1,3,5,7]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>{{1},{2,4,7},{3},{5},{6,8}}
[6,8,4,2,1,3,5,7]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>{{1},{2,4,6,7},{3},{5},{8}}
[5,2,4,3,8,1,7,6]=>[1,7,2,4,3,8,5,6]=>[1,4,7,3,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[6,2,4,1,5,3,8,7]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[4,3,6,1,5,2,8,7]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[4,3,5,2,8,1,7,6]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,3,8,2,6,1,7,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,3,8,1,7,2,6,5]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,3,8,1,5,2,7,6]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[5,1,8,3,4,2,7,6]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,8,1,3,2,7,6]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>{{1},{2,3},{4,7},{5,6,8}}
[2,1,5,4,8,3,7,6]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[5,1,7,6,8,3,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,3,7,6,8,1,5,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[4,3,7,1,8,5,6,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,6,5,8,1,7,2]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,3,5,4,7,2,8,1]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,3,5,4,8,1,7,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[7,4,6,5,8,1,3,2]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>{{1},{2,3},{4},{5,6},{7,8}}
[8,4,6,1,3,2,7,5]=>[1,3,2,7,4,6,5,8]=>[1,3,2,6,7,5,4,8]=>{{1},{2,3},{4,5,6,7},{8}}
[8,1,6,3,4,2,7,5]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,1,6,3,7,2,5,4]=>[1,6,2,5,3,7,4,8]=>[1,5,6,7,3,2,4,8]=>{{1},{2,3,5,6},{4,7},{8}}
[8,3,5,1,7,2,6,4]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,3,5,2,6,1,7,4]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,6,3,5,1,7,4]=>[1,7,2,6,3,5,4,8]=>[1,6,5,7,4,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,7,1,5,3,6,4]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,2,4,1,5,3,7,6]=>[1,5,2,4,3,7,6,8]=>[1,4,5,3,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[8,2,4,1,7,3,6,5]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,2,4,3,6,1,7,5]=>[1,7,2,4,3,6,5,8]=>[1,4,6,3,7,5,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[3,2,7,6,8,1,5,4]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[3,2,7,1,8,5,6,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,6,5,8,1,7,4]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,5,7,2,4,3,8,1]=>[1,2,4,3,8,5,7,6]=>[1,2,4,3,7,8,6,5]=>{{1},{2},{3,4},{5,6,7,8}}
[6,5,8,2,4,1,7,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[7,2,4,1,8,5,6,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,6,8,2,4,1,5,3]=>[1,5,2,4,3,6,8,7]=>[1,4,5,3,2,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[7,6,8,1,5,2,4,3]=>[1,5,2,4,3,6,8,7]=>[1,4,5,3,2,6,8,7]=>{{1},{2,3,4,5},{6},{7,8}}
[2,1,7,3,8,5,6,4]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[7,1,3,2,8,5,6,4]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[7,1,8,5,6,2,4,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,8,2,6,4,5,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,8,1,5,4,6,3]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,2,7,4,5,3,8,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[5,4,7,2,6,3,8,1]=>[1,2,6,3,8,4,7,5]=>[1,2,6,7,8,3,5,4]=>{{1},{2},{3,6},{4,5,7,8}}
[6,5,8,1,7,2,4,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,1,6,5,8,3,7,4]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[6,5,7,1,8,3,4,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,7,4,8,3,5,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[5,4,6,3,8,1,7,2]=>[1,7,2,3,8,4,6,5]=>[1,3,7,6,8,5,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[6,7,8,9,10,5,4,3,2,1,12,11]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>{{1},{2,3,4,5,6,7,8,9,10,11,12}}
[7,8,9,10,11,12,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>[1,2,3,4,5,6,7,8,9,10,11,12]=>{{1},{2},{3},{4},{5},{6},{7},{8},{9},{10},{11},{12}}
[2,8,3,1,5,4,6,7]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[2,5,3,4,7,1,8,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[2,4,8,3,5,7,6,1]=>[1,2,4,8,3,5,7,6]=>[1,2,5,4,7,8,6,3]=>{{1},{2},{3,5,6,7,8},{4}}
[4,2,5,3,1,8,6,7]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,1,3,8,2,6,7]=>[1,3,8,2,6,7,4,5]=>[1,6,3,5,8,7,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,8,4,3,2,6,7]=>[1,5,8,2,6,7,3,4]=>[1,6,4,8,5,7,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,8,5,4,3,2,6,7]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,4,3,8,5,2,6]=>[1,7,2,6,3,8,4,5]=>[1,6,7,5,8,3,2,4]=>{{1},{2,3,6,7},{4,5,8}}
[4,8,1,5,7,3,6,2]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[8,1,5,3,7,4,6,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[3,8,4,7,6,5,2,1]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[1,6,8,5,3,7,4,2]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,8,1,7,4,3,5,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,4,8,1,7,3,5,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,4,8,7,1,5,2,3]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,7,5,6,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[2,7,4,6,3,1,8,5]=>[1,8,2,7,3,4,6,5]=>[1,7,4,6,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,6,8,4,3,7,5,1]=>[1,2,6,8,3,7,4,5]=>[1,2,7,5,8,6,4,3]=>{{1},{2},{3,4,5,7,8},{6}}
[7,2,6,3,4,1,8,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,1,8,3,5,4,6]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,7,3,5,8,4,6]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[8,7,1,3,6,2,4,5]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[8,2,1,7,3,5,6,4]=>[1,7,2,3,5,6,4,8]=>[1,3,5,7,6,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,8,2,6,3,1,5,4]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[8,7,2,6,3,5,4,1]=>[1,2,6,3,5,4,7,8]=>[1,2,5,6,4,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,2,8,7,4,5,6,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,6,1,2,7,5,3,4]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[8,1,6,2,7,4,5,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,8,5,2,6,7,4,3]=>[1,8,2,6,7,3,4,5]=>[1,6,4,5,8,7,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,2,1,8,6,7,4,3]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,8,5,7,6,4,3,1]=>[1,2,8,3,4,5,7,6]=>[1,2,4,5,7,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[7,8,1,6,4,2,5,3]=>[1,6,2,5,3,4,7,8]=>[1,5,4,6,3,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,6,1,5,3,2,4]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[7,3,8,6,1,5,2,4]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[8,7,6,1,5,3,4,2]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[8,7,1,6,4,5,3,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,1,7,5,6,4,3,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,8,6,7,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,5,7,2,8,4,1]=>[1,2,8,3,5,7,4,6]=>[1,2,5,6,7,8,4,3]=>{{1},{2},{3,4,5,6,7,8}}
[8,5,2,7,4,3,1,6]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,3,4,5,7,2,1,6]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[5,7,4,6,3,8,2,1]=>[1,2,3,8,4,6,5,7]=>[1,2,3,6,7,5,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[2,8,4,6,3,7,1,5]=>[1,5,2,8,3,7,4,6]=>[1,5,7,6,2,8,4,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,5,3,7,1,4,2,6]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[6,5,3,7,1,8,4,2]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,4,7,5,8,1,2]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>{{1},{2},{3},{4},{5,7},{6,8}}
[4,8,3,7,1,2,6,5]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>{{1},{2},{3,6},{4,7},{5,8}}
[3,8,6,4,1,7,2,5]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[3,8,1,2,5,7,6,4]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>{{1},{2},{3,7},{4,6,8},{5}}
[2,8,7,5,4,1,3,6]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[8,7,2,6,4,1,3,5]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>{{1},{2,5},{3},{4,6},{7},{8}}
[3,8,6,7,4,2,1,5]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[5,7,6,8,4,2,3,1]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>{{1},{2},{3},{4},{5},{6,7},{8}}
[5,3,7,8,2,4,6,1]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>{{1},{2},{3,6},{4},{5,8},{7}}
[8,3,6,2,1,4,7,5]=>[1,4,7,2,3,6,5,8]=>[1,3,6,4,7,5,2,8]=>{{1},{2,3,5,6,7},{4},{8}}
[5,3,7,6,2,1,8,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[5,3,6,2,8,7,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[5,7,8,6,4,2,1,3]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>{{1},{2,3},{4},{5},{6,8},{7}}
[6,1,7,4,5,8,2,3]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,7,3,5,1,8,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,1,6,7,5,8,3,4]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>{{1},{2,3,4,5,7},{6},{8}}
[2,1,5,7,3,6,8,4]=>[1,5,7,2,3,6,8,4]=>[1,3,6,8,5,7,2,4]=>{{1},{2,3,6,7},{4,8},{5}}
[4,1,7,2,5,6,8,3]=>[1,7,2,5,6,8,3,4]=>[1,5,4,8,6,7,2,3]=>{{1},{2,5,6,7},{3,4,8}}
[2,4,7,1,6,5,8,3]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[4,6,2,1,8,7,5,3]=>[1,8,2,3,4,6,5,7]=>[1,3,4,6,7,5,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,4,6,2,7,8,5,1]=>[1,2,7,8,3,4,6,5]=>[1,2,4,6,8,5,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[5,6,3,1,8,7,2,4]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,2,7,1,6,5,4]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[3,8,2,7,6,1,5,4]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>{{1},{2,5},{3,7},{4,6,8}}
[3,8,2,7,6,5,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[3,8,2,7,6,5,4,1]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>{{1},{2},{3,7},{4,5,6,8}}
[4,8,7,2,6,5,1,3]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>{{1},{2,3},{4,6},{5,7,8}}
[4,8,7,2,1,6,5,3]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[4,8,7,3,1,6,5,2]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[4,8,7,3,2,1,6,5]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[4,8,7,3,6,2,5,1]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>{{1},{2},{3,5},{4,6},{7,8}}
[4,8,7,3,6,2,1,5]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[4,8,7,3,6,1,5,2]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>{{1},{2,3,5},{4,6},{7,8}}
[4,8,7,3,6,5,1,2]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[4,8,7,3,6,5,2,1]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[5,8,7,6,3,4,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,8,7,6,3,1,4,2]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[5,8,7,6,3,2,4,1]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[5,8,7,6,2,4,3,1]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>{{1},{2},{3,4},{5},{6,7,8}}
[5,8,7,6,2,1,4,3]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>{{1},{2,3,4},{5},{6,7,8}}
[5,8,7,6,4,2,3,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,8,7,6,4,2,1,3]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[5,8,7,6,4,1,3,2]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>{{1},{2,3},{4},{5},{6,7,8}}
[5,8,7,6,4,3,1,2]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[7,3,4,2,1,6,5,8]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>{{1},{2,3,4,5,6},{7,8}}
[7,3,5,2,6,4,1,8]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,1,5,6,4,3,8]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>{{1},{2,3,6},{4,7,8},{5}}
[7,3,5,1,6,4,2,8]=>[1,6,2,8,3,5,4,7]=>[1,6,5,7,4,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,4,5,6,1,3,2,8]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[6,4,5,7,3,1,8,2]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,5,7,1,3,8,2]=>[1,3,8,2,4,5,7,6]=>[1,4,3,5,7,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[6,3,5,1,7,4,8,2]=>[1,7,2,3,5,4,8,6]=>[1,3,5,7,4,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[6,2,1,5,7,4,8,3]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[3,2,1,5,7,4,8,6]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>{{1},{2,3,4,7},{5},{6,8}}
[2,4,6,7,3,8,1,5]=>[1,5,2,4,6,7,3,8]=>[1,4,7,5,2,6,3,8]=>{{1},{2,4,5},{3,7},{6},{8}}
[1,4,6,7,3,8,5,2]=>[1,4,6,7,2,3,8,5]=>[1,3,7,4,8,6,2,5]=>{{1},{2,3,7},{4},{5,8},{6}}
[1,5,6,7,8,3,4,2]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[2,5,6,7,8,3,1,4]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>{{1},{2,4},{3,8},{5},{6},{7}}
[3,2,1,6,7,8,4,5]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[5,2,1,6,7,8,4,3]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[6,4,5,7,2,1,8,3]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[5,4,6,7,2,8,3,1]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,3,6,2,7,8,1,4]=>[1,4,2,7,8,3,6,5]=>[1,4,6,2,8,5,7,3]=>{{1},{2,4},{3,5,6,8},{7}}
[6,3,5,2,7,1,8,4]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,3,4,2,1,7,8,5]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[5,3,4,1,2,7,8,6]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>{{1},{2},{3,4,5,6,8},{7}}
[4,3,6,2,7,8,1,5]=>[1,5,2,7,8,3,6,4]=>[1,5,6,8,2,4,7,3]=>{{1},{2,5},{3,4,6,8},{7}}
[1,4,6,7,2,8,5,3]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>{{1},{2,7},{3,5,8},{4},{6}}
[3,4,6,7,2,8,5,1]=>[1,2,8,3,4,6,7,5]=>[1,2,4,6,8,7,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,4,5,7,2,1,8,6]=>[1,8,2,3,4,5,7,6]=>[1,3,4,5,7,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[4,2,1,5,7,3,8,6]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>{{1},{2,3,7},{4,6,8},{5}}
[1,5,6,7,8,4,2,3]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>{{1},{2,3,4,8},{5},{6},{7}}
[4,2,1,6,7,8,5,3]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>{{1},{2,3,4,5,8},{6},{7}}
[2,5,6,7,8,1,4,3]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>{{1},{2,4},{3,8},{5},{6},{7}}
[2,1,4,3,6,5,8,7,9]=>[1,4,2,3,6,5,8,7,9]=>[1,3,4,2,6,5,8,7,9]=>{{1},{2,3,4},{5,6},{7,8},{9}}
[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>{{1},{2,3},{4,5},{6,7},{8,9}}
[1,4,2,5,3,7,6,9,8]=>[1,4,2,5,3,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>{{1},{2,4},{3,5},{6,7},{8,9}}
[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>{{1},{2,3},{4,5},{6,7},{8,9},{10}}
[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>{{1},{2},{3},{4},{5},{6},{7,9},{8}}
[1,4,3,7,2,5,6,8]=>[1,4,2,5,6,8,3,7]=>[1,4,7,2,5,6,8,3]=>{{1},{2,4},{3,7,8},{5},{6}}
[1,4,3,7,6,8,2,5]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}
[1,4,3,7,5,8,2,6]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[1,4,3,7,2,6,5,8]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[1,5,3,7,4,8,2,6]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[1,3,2,6,5,8,4,7]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>{{1},{2,3},{4,6},{5,7},{8}}
[1,5,4,8,2,6,3,7]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[1,5,4,8,3,7,2,6]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>{{1},{2,5},{3,6},{4,7},{8}}
[1,2,3,6,5,8,4,7]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>{{1},{2},{3},{4,6},{5,7},{8}}
[6,8,2,4,5,7,1,3]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>{{1},{2,3},{4},{5},{6,7},{8}}
[3,7,8,4,5,2,6,1]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[4,8,3,6,1,5,7,2]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[5,8,3,1,6,4,7,2]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[7,5,1,8,6,2,4,3]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,4,1,8,2,6,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,1,8,4,2,6,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[1,6,3,8,5,2,4,7]=>[1,6,2,4,7,3,8,5]=>[1,4,7,6,8,2,3,5]=>{{1},{2,4,6},{3,7},{5,8}}
[6,1,3,8,5,2,4,7]=>[1,3,8,2,4,7,5,6]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,1,8,3,6,2,5,4]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,3,1,8,4,2,6,5]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,2,8,4,1,6,5,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,2,8,3,6,5,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[7,2,8,3,6,1,5,4]=>[1,5,2,8,3,6,4,7]=>[1,5,6,7,2,4,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[6,1,2,8,3,5,4,7]=>[1,2,8,3,5,4,7,6]=>[1,2,5,7,4,8,6,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,1,2,3,8,4,7,6]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,2,3,8,1,4,7,6]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>{{1},{2,3,7},{4},{5,6,8}}
[6,2,4,1,8,7,3,5]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,1,6,4,2,8,5,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[2,6,3,8,7,1,5,4]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>{{1},{2,5},{3,6},{4,7,8}}
[2,6,3,8,5,1,4,7]=>[1,4,7,2,6,3,8,5]=>[1,6,7,4,8,3,2,5]=>{{1},{2,3,6,7},{4},{5,8}}
[2,5,1,8,3,4,7,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,1,3,8,4,7,6]=>[1,3,8,2,5,4,7,6]=>[1,5,3,7,4,8,6,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,2,5,3,8,4,7,6]=>[1,2,5,3,8,4,7,6]=>[1,2,5,7,3,8,6,4]=>{{1},{2},{3,5},{4,6,7,8}}
[2,4,8,1,3,7,6,5]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>{{1},{2,4,7},{3},{5,6,8}}
[2,4,8,3,7,6,1,5]=>[1,5,2,4,8,3,7,6]=>[1,4,7,5,2,8,6,3]=>{{1},{2,4,5},{3,6,7,8}}
[2,5,3,8,1,7,4,6]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[3,1,5,4,8,2,7,6]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[4,8,2,3,7,6,1,5]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>{{1},{2,3,5},{4,7},{6,8}}
[4,8,2,3,7,1,6,5]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>{{1},{2,3,6},{4,7},{5,8}}
[4,8,1,2,3,7,6,5]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[1,4,8,2,3,7,6,5]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[1,4,8,3,7,2,6,5]=>[1,4,8,2,6,3,7,5]=>[1,6,7,4,8,3,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[6,3,8,1,5,2,4,7]=>[1,5,2,4,7,3,8,6]=>[1,4,7,5,2,8,3,6]=>{{1},{2,4,5},{3,7},{6,8}}
[5,1,3,8,2,4,7,6]=>[1,3,8,2,4,7,5,6]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,3,8,2,4,7,6]=>[1,5,2,4,7,3,8,6]=>[1,4,7,5,2,8,3,6]=>{{1},{2,4,5},{3,7},{6,8}}
[1,5,4,8,2,7,6,3]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[5,4,8,1,2,7,6,3]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[6,5,1,2,8,7,4,3]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[5,3,1,6,4,2,8,7]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[5,1,6,2,8,7,4,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[4,1,5,8,2,7,6,3]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,3,5,2,8,7,4,6]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>{{1},{2,5},{3},{4,6,7,8}}
[3,5,1,2,8,7,4,6]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[3,6,2,8,7,5,1,4]=>[1,4,2,8,3,6,5,7]=>[1,4,6,2,7,5,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[4,2,6,1,8,7,3,5]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,1,5,8,2,7,6]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[1,3,4,8,2,7,6,5]=>[1,3,4,8,2,7,5,6]=>[1,7,3,4,6,8,5,2]=>{{1},{2,5,6,7,8},{3},{4}}
[3,4,8,1,2,7,6,5]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>{{1},{2},{3,4,7},{5,6,8}}
[3,4,8,2,7,1,6,5]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>{{1},{2,6},{3,4,7},{5,8}}
[3,4,8,2,7,6,1,5]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>{{1},{2,5},{3,4,7},{6,8}}
[4,2,5,8,1,7,6,3]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[7,8,2,1,5,3,6,4]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[6,4,1,2,7,3,5,8]=>[1,2,7,3,5,8,4,6]=>[1,2,5,6,7,8,3,4]=>{{1},{2},{3,5,7},{4,6,8}}
[2,3,7,5,4,1,8,6]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,1,5,4,2,6,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[7,8,3,5,4,1,6,2]=>[1,6,2,3,5,4,7,8]=>[1,3,5,6,4,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[7,8,2,5,4,1,3,6]=>[1,3,6,2,5,4,7,8]=>[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[7,8,2,5,4,6,1,3]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>{{1},{2,3},{4,5},{6},{7},{8}}
[5,3,6,2,4,7,1,8]=>[1,8,2,4,7,3,6,5]=>[1,4,6,7,8,5,3,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,2,1,7,3,8,5]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,3,7,5,8,6,1,2]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[4,2,7,1,8,3,6,5]=>[1,8,2,7,3,6,4,5]=>[1,7,6,5,8,4,3,2]=>{{1},{2,3,4,5,6,7,8}}
[3,2,6,7,4,8,1,5]=>[1,5,2,6,7,3,4,8]=>[1,5,4,7,2,6,3,8]=>{{1},{2,5},{3,4,7},{6},{8}}
[1,7,6,5,3,8,4,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[2,7,6,5,3,8,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[1,7,6,5,2,4,8,3]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[3,7,6,4,8,5,1,2]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[5,7,6,3,8,4,1,2]=>[1,2,3,8,4,5,7,6]=>[1,2,3,5,7,8,6,4]=>{{1},{2},{3},{4,5,6,7,8}}
[4,7,6,5,2,1,3,8]=>[1,3,8,2,4,7,5,6]=>[1,4,3,7,6,8,5,2]=>{{1},{2,4,5,6,7,8},{3}}
[4,7,6,5,2,8,1,3]=>[1,3,2,8,4,7,5,6]=>[1,3,2,7,6,8,5,4]=>{{1},{2,3},{4,5,6,7,8}}
[4,7,6,5,1,8,3,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,5,2,8,3,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,7,6,5,3,2,8,4]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[4,7,6,5,3,1,8,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,1,6,2,4,7,8,3]=>[1,6,2,4,7,8,3,5]=>[1,4,5,6,8,2,7,3]=>{{1},{2,4,6},{3,5,8},{7}}
[4,1,8,2,6,3,5,7]=>[1,8,2,6,3,5,7,4]=>[1,6,5,8,7,3,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,2,6,7,4,8,5,3]=>[1,2,6,7,3,4,8,5]=>[1,2,4,7,8,6,3,5]=>{{1},{2},{3,4,7},{5,8},{6}}
[4,7,6,3,5,8,1,2]=>[1,2,3,5,8,4,7,6]=>[1,2,3,7,5,8,6,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[4,7,1,2,5,3,8,6]=>[1,2,5,3,8,4,7,6]=>[1,2,5,7,3,8,6,4]=>{{1},{2},{3,5},{4,6,7,8}}
[3,7,6,5,2,4,1,8]=>[1,8,2,4,3,7,5,6]=>[1,4,7,3,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[3,7,6,5,1,4,8,2]=>[1,4,8,2,3,7,5,6]=>[1,3,7,4,6,8,5,2]=>{{1},{2,3,5,6,7,8},{4}}
[3,7,6,5,2,1,8,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,7,6,5,8,2,4,3]=>[1,7,2,4,3,5,8,6]=>[1,4,5,3,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[3,7,6,5,8,1,4,2]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[4,7,6,8,3,5,1,2]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>{{1},{2},{3},{4,5},{6,7},{8}}
[2,7,6,5,1,4,3,8]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[2,7,6,5,8,1,3,4]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>{{1},{2,4},{3},{5,7},{6,8}}
[2,7,6,5,8,4,1,3]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>{{1},{2,3},{4,5,7},{6,8}}
[6,3,2,1,7,4,8,5]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[4,2,1,7,3,5,8,6]=>[1,7,2,3,5,8,4,6]=>[1,3,5,6,7,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[7,3,1,5,4,2,8,6]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[8,4,1,5,2,7,6,3]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,2,5,1,3,7,6,4]=>[1,3,7,2,5,4,6,8]=>[1,5,3,6,4,7,2,8]=>{{1},{2,4,5,6,7},{3},{8}}
[6,3,7,4,2,1,8,5]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,7,2,5,3,1,8,6]=>[1,8,2,5,3,4,7,6]=>[1,5,4,7,3,8,6,2]=>{{1},{2,3,4,5,6,7,8}}
[2,7,5,4,1,3,8,6]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[7,5,4,3,2,1,8,6]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,5,3,2,1,7,6,4]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,5,2,1,8,4,3,7]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[4,6,3,2,8,1,5,7]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>{{1},{2,7},{3,4,6,8},{5}}
[5,7,4,3,2,8,1,6]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,7,6,2,4,8,3,5]=>[1,7,2,4,8,3,5,6]=>[1,4,5,7,6,8,2,3]=>{{1},{2,4,7},{3,5,6,8}}
[2,7,3,6,4,8,1,5]=>[1,5,2,7,3,6,4,8]=>[1,5,6,7,2,4,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[6,2,7,5,3,8,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[5,8,1,6,2,7,4,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[1,8,6,2,3,7,5,4]=>[1,8,2,3,7,4,5,6]=>[1,3,7,5,6,8,4,2]=>{{1},{2,3,4,5,6,7,8}}
[1,8,6,3,2,7,5,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,3,2,7,1,6,4]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,7,3,1,6,5,4,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,2,6,1,5,4,3]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[1,8,5,7,2,4,6,3]=>[1,8,2,4,6,3,5,7]=>[1,4,5,6,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[3,8,6,1,7,2,5,4]=>[1,7,2,5,3,8,4,6]=>[1,5,7,6,3,8,2,4]=>{{1},{2,3,5,7},{4,6,8}}
[5,8,4,6,7,1,3,2]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>{{1},{2,3},{4},{5,7},{6},{8}}
[7,2,8,5,6,1,4,3]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>{{1},{2,4},{3,5,6,7,8}}
[6,3,7,5,8,2,1,4]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[3,7,2,6,8,4,1,5]=>[1,5,2,6,8,3,7,4]=>[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[3,6,5,8,1,4,2,7]=>[1,4,2,7,3,6,5,8]=>[1,4,6,2,7,5,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[6,5,4,8,3,2,1,7]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[8,4,3,7,2,1,6,5]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>{{1},{2,3,6},{4,5,7},{8}}
[6,2,5,8,1,4,3,7]=>[1,4,2,5,8,3,7,6]=>[1,4,7,2,5,8,6,3]=>{{1},{2,4},{3,6,7,8},{5}}
[4,3,6,8,2,1,5,7]=>[1,5,7,2,3,6,8,4]=>[1,3,6,8,5,7,2,4]=>{{1},{2,3,6,7},{4,8},{5}}
[6,3,5,1,8,4,2,7]=>[1,8,2,7,3,5,4,6]=>[1,7,5,6,4,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[8,4,1,5,7,3,6,2]=>[1,5,7,2,3,6,4,8]=>[1,3,6,7,5,4,2,8]=>{{1},{2,3,4,6,7},{5},{8}}
[6,4,2,5,8,3,1,7]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[5,4,1,6,8,2,3,7]=>[1,6,8,2,3,7,4,5]=>[1,3,7,5,8,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[6,5,2,1,7,8,3,4]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>{{1},{2,3,4,5,6,8},{7}}
[6,3,7,4,8,5,2,1]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>{{1},{2},{3},{4,7},{5,6,8}}
[4,7,2,5,8,6,3,1]=>[1,2,5,8,3,4,7,6]=>[1,2,4,7,5,8,6,3]=>{{1},{2},{3,4,6,7,8},{5}}
[6,3,1,8,4,7,5,2]=>[1,8,2,3,4,7,5,6]=>[1,3,4,7,6,8,5,2]=>{{1},{2,3,4,5,6,7,8}}
[6,4,2,8,7,3,5,1]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[6,5,3,8,7,4,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[8,5,3,7,6,4,2,1]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[5,4,8,1,7,6,2,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[5,2,8,1,7,3,6,4]=>[1,7,2,8,3,6,4,5]=>[1,7,6,5,8,4,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,4,8,2,1,7,5,3]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[3,6,8,1,4,7,5,2]=>[1,4,7,2,3,6,8,5]=>[1,3,6,4,8,7,2,5]=>{{1},{2,3,6,7},{4},{5,8}}
[6,4,7,8,1,5,3,2]=>[1,5,2,3,4,7,8,6]=>[1,3,4,5,2,8,7,6]=>{{1},{2,3,4,5},{6,8},{7}}
[6,3,7,8,5,2,4,1]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,6,8,7,5]=>{{1},{2},{3,4},{5,6,8},{7}}
[8,3,7,6,1,5,4,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[8,2,7,6,5,1,4,3]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>{{1},{2,4},{3,5,6,7},{8}}
[4,3,8,7,6,2,1,5]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[3,5,8,7,2,6,1,4]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[4,7,3,8,6,5,1,2]=>[1,2,3,8,4,7,5,6]=>[1,2,3,7,6,8,5,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,5,8,6,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>{{1},{2},{3},{4},{5},{6,7,8}}
[5,8,7,3,6,4,2,1]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>{{1},{2},{3},{4,5,6},{7,8}}
[4,8,7,6,2,5,3,1]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[3,8,7,6,5,1,4,2]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>{{1},{2,3,4},{5,6,7,8}}
[2,8,7,6,5,4,1,3]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>{{1},{2,3},{4,5,6,7,8}}
[3,2,1,4,5,6,7,8,9]=>[1,4,5,6,7,8,9,2,3]=>[1,3,9,4,5,6,7,8,2]=>{{1},{2,3,9},{4},{5},{6},{7},{8}}
[5,6,7,8,1,2,3,4,9]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>{{1},{2},{3},{4},{5,6,7,8,9}}
[7,8,5,6,3,4,1,2,9]=>[1,2,9,3,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>{{1},{2},{3,4,5,6,7,8,9}}
[7,6,5,4,3,2,1,8,9]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>{{1},{2,3,4,5,6,7,9},{8}}
[8,6,9,4,7,2,5,1,3]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>{{1},{2,3},{4,5},{6,7},{8,9}}
[7,8,9,4,5,6,1,2,3,10]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,5,6,7,8,9,10,4]=>{{1},{2},{3},{4,5,6,7,8,9,10}}
[8,7,6,5,4,3,2,1,9,10]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>{{1},{2,3,4,5,6,7,8,10},{9}}
[3,6,5,1,2,4,8,7]=>[1,2,4,8,3,6,5,7]=>[1,2,6,4,7,5,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[3,7,5,8,2,4,1,6]=>[1,6,2,4,3,7,5,8]=>[1,4,6,3,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[3,8,5,7,2,4,1,6]=>[1,6,2,4,3,8,5,7]=>[1,4,6,3,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[5,1,2,6,4,3,8,7]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[6,1,2,5,4,3,8,7]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[5,1,2,4,6,3,8,7]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>{{1},{2},{3,6},{4},{5,7,8}}
[4,1,2,6,5,3,8,7]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>{{1},{2},{3,6},{4,5,7,8}}
[4,1,5,7,8,3,2,6]=>[1,5,7,8,2,6,3,4]=>[1,6,4,8,5,3,7,2]=>{{1},{2,3,4,6,8},{5},{7}}
[4,1,5,8,7,3,2,6]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,7,1,8,3,6,2,5]=>[1,8,2,5,3,6,4,7]=>[1,5,6,7,3,4,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,5,3,8,1,4,2,6]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[2,1,5,8,7,3,4,6]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[4,7,1,6,3,2,8,5]=>[1,6,2,8,3,4,7,5]=>[1,6,4,7,8,2,5,3]=>{{1},{2,6},{3,4,5,7,8}}
[6,1,2,3,7,5,8,4]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>{{1},{2},{3},{4,5,7},{6,8}}
[7,1,2,3,8,6,5,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[7,1,2,3,5,8,6,4]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[6,8,1,4,3,7,2,5]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>{{1},{2,4},{3,5},{6,7},{8}}
[8,7,3,2,4,1,6,5]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[2,1,7,3,4,8,6,5]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>{{1},{2,3,4,7},{5,6,8}}
[7,8,3,2,4,1,6,5]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,7,1,4,3,8,2,5]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>{{1},{2,4},{3,5},{6,7,8}}
[8,1,2,3,5,7,6,4]=>[1,2,3,5,7,4,6,8]=>[1,2,3,6,5,7,4,8]=>{{1},{2},{3},{4,6,7},{5},{8}}
[8,1,2,3,6,7,5,4]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>{{1},{2},{3},{4,5,7},{6},{8}}
[7,1,2,3,6,8,5,4]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[7,1,2,3,8,5,6,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[8,1,2,3,7,5,6,4]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>{{1},{2},{3},{4,5,6,7},{8}}
[8,1,2,3,6,5,7,4]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>{{1},{2},{3},{4,5,6},{7},{8}}
[7,1,8,5,4,3,2,6]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[7,8,2,6,3,4,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[6,8,2,7,3,4,1,5]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[6,7,2,8,3,4,1,5]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>{{1},{2,5},{3,4,6,7,8}}
[3,8,7,1,4,2,6,5]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>{{1},{2,4},{3,6},{5,7,8}}
[3,7,8,1,4,2,6,5]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>{{1},{2,4},{3,6},{5,8},{7}}
[3,6,8,1,4,2,7,5]=>[1,4,2,7,3,6,8,5]=>[1,4,6,2,8,7,3,5]=>{{1},{2,4},{3,6,7},{5,8}}
[3,5,7,8,2,4,1,6]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[3,6,7,1,4,2,8,5]=>[1,4,2,8,3,6,7,5]=>[1,4,6,2,8,7,5,3]=>{{1},{2,4},{3,5,6,7,8}}
[8,1,7,5,4,3,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[8,1,7,4,5,3,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,8,3,7,1,4,2,6]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>{{1},{2,4},{3,6},{5,7},{8}}
[6,7,3,2,4,1,8,5]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[8,7,2,4,3,6,1,5]=>[1,5,2,4,3,6,7,8]=>[1,4,5,3,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
[7,1,2,3,5,6,8,4]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>{{1},{2},{3},{4,7,8},{5},{6}}
[6,1,2,3,8,7,4,5]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,1,2,3,7,8,6,4]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>{{1},{2},{3},{4,5,6,8},{7}}
[5,1,2,3,8,7,6,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[5,1,2,3,8,6,7,4]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,1,2,3,5,8,7,4]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>{{1},{2},{3},{4,6,7,8},{5}}
[8,6,2,4,3,1,7,5]=>[1,7,2,4,3,5,6,8]=>[1,4,5,3,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,1,6,3,4,8,7,5]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>{{1},{2,3,4,6},{5,7,8}}
[8,6,3,2,4,7,1,5]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[7,6,2,4,3,1,8,5]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[6,1,2,3,5,7,8,4]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>{{1},{2},{3},{4,6,8},{5},{7}}
[5,1,2,3,6,8,7,4]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>{{1},{2},{3},{4,5,7,8},{6}}
[7,8,1,2,6,3,5,4]=>[1,2,6,3,5,4,7,8]=>[1,2,5,6,4,3,7,8]=>{{1},{2},{3,4,5,6},{7},{8}}
[1,2,8,5,4,7,3,6]=>[1,2,8,3,6,4,7,5]=>[1,2,6,7,8,4,5,3]=>{{1},{2},{3,4,5,6,7,8}}
[1,3,8,5,4,2,7,6]=>[1,3,8,2,7,4,5,6]=>[1,7,3,5,6,8,4,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,3,6,8,4,7,5,2]=>[1,3,6,8,2,4,7,5]=>[1,4,3,7,8,6,5,2]=>{{1},{2,4,5,7,8},{3},{6}}
[3,4,8,5,7,6,1,2]=>[1,2,3,4,8,5,7,6]=>[1,2,3,4,7,8,6,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[7,5,1,2,4,3,6,8]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,6,8,5]=>{{1},{2},{3,4},{5,7,8},{6}}
[7,4,6,1,5,2,3,8]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>{{1},{2,3,5},{4,6,7,8}}
[7,1,4,2,6,3,5,8]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[1,6,4,2,8,3,5,7]=>[1,6,2,8,3,5,7,4]=>[1,6,5,8,7,2,4,3]=>{{1},{2,6},{3,4,5,7,8}}
[1,6,3,8,5,4,2,7]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>{{1},{2,6},{3,7},{4,5,8}}
[6,8,1,7,3,5,4,2]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[7,1,3,6,5,4,2,8]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[7,3,1,6,5,4,2,8]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[7,2,3,6,5,1,4,8]=>[1,4,8,2,3,6,5,7]=>[1,3,6,4,7,5,8,2]=>{{1},{2,3,5,6,7,8},{4}}
[7,1,2,3,6,5,4,8]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>{{1},{2},{3},{4,6},{5,7,8}}
[6,8,1,2,7,3,5,4]=>[1,2,7,3,5,4,6,8]=>[1,2,5,6,4,7,3,8]=>{{1},{2},{3,4,5,6,7},{8}}
[1,5,8,2,7,6,3,4]=>[1,5,8,2,7,3,4,6]=>[1,7,4,6,5,8,3,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,1,8,2,7,6,3,4]=>[1,8,2,7,3,4,5,6]=>[1,7,4,5,6,8,3,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,2,7,6,3,4,1]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[6,2,8,1,7,3,5,4]=>[1,7,2,8,3,5,4,6]=>[1,7,5,6,4,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[6,8,2,1,7,4,3,5]=>[1,7,2,3,5,4,6,8]=>[1,3,5,6,4,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[2,5,1,8,7,6,3,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[2,5,3,8,7,4,6,1]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[1,2,5,3,8,7,4,6]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>{{1},{2},{3,5},{4,6,7,8}}
[2,4,8,7,6,5,1,3]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>{{1},{2,3},{4},{5,6,7,8}}
[2,5,3,8,7,1,6,4]=>[1,6,2,5,3,8,4,7]=>[1,5,6,7,3,2,8,4]=>{{1},{2,3,5,6},{4,7,8}}
[2,5,8,4,1,7,6,3]=>[1,7,2,5,8,3,4,6]=>[1,5,4,6,7,8,2,3]=>{{1},{2,5,7},{3,4,6,8}}
[3,5,8,7,1,4,2,6]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>{{1},{2,4},{3,5,6},{7,8}}
[5,3,8,4,1,7,6,2]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>{{1},{2,3,7},{4,5,6,8}}
[4,2,8,7,6,3,5,1]=>[1,2,8,3,5,4,6,7]=>[1,2,5,6,4,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,2,8,7,6,5,3,1]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>{{1},{2},{3,4,5,6,7,8}}
[4,1,8,7,6,5,3,2]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,3,8,7,6,5,1,2]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>{{1},{2},{3},{4,5,6,7,8}}
[6,3,1,8,7,2,5,4]=>[1,8,2,5,3,4,6,7]=>[1,5,4,6,3,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,3,7,6,1,4,2]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>{{1},{2,3,4},{5,7},{6,8}}
[5,1,3,8,7,6,2,4]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>{{1},{2,4,5,6,7,8},{3}}
[1,5,3,8,7,6,2,4]=>[1,5,2,4,3,8,6,7]=>[1,4,5,3,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[1,5,8,4,7,2,6,3]=>[1,5,8,2,6,3,4,7]=>[1,6,4,7,5,3,8,2]=>{{1},{2,3,4,6,7,8},{5}}
[5,1,8,4,7,2,6,3]=>[1,8,2,6,3,4,7,5]=>[1,6,4,7,8,3,5,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,7,4,6,1,2,3]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>{{1},{2},{3},{4},{5,6},{7,8}}
[6,8,5,1,2,4,7,3]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>{{1},{2},{3,5,6,7},{4},{8}}
[5,6,3,1,2,4,8,7]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>{{1},{2},{3,5,6,7,8},{4}}
[5,6,2,4,3,1,8,7]=>[1,8,2,4,3,5,6,7]=>[1,4,5,3,6,7,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,6,1,2,4,3,8,7]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>{{1},{2},{3,4},{5,6,7,8}}
[4,5,8,1,7,2,3,6]=>[1,7,2,3,6,4,5,8]=>[1,3,6,5,7,4,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,5,8,1,7,2,6,3]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[1,3,2,5,8,7,4,6]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>{{1},{2,3},{4,6,7,8},{5}}
[3,5,1,8,7,2,6,4]=>[1,8,2,6,3,5,4,7]=>[1,6,5,7,4,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[4,5,8,3,1,7,2,6]=>[1,7,2,6,3,4,5,8]=>[1,6,4,5,7,3,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[4,5,2,8,7,1,3,6]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>{{1},{2,6},{3},{4,5,7,8}}
[3,2,5,8,7,1,6,4]=>[1,6,2,5,8,3,4,7]=>[1,5,4,7,6,2,8,3]=>{{1},{2,5,6},{3,4,7,8}}
[3,4,8,7,6,2,1,5]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>{{1},{2,3,4,5},{6,7,8}}
[3,4,8,7,6,5,1,2]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>{{1},{2},{3},{4},{5,6,7,8}}
[1,3,4,8,7,6,2,5]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>{{1},{2,5,6,7,8},{3},{4}}
[3,4,8,7,6,2,5,1]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>{{1},{2},{3,4,5},{6,7,8}}
[4,5,8,3,1,7,6,2]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>{{1},{2,3,4,5,7},{6,8}}
[2,1,3,5,8,7,4,6]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>{{1},{2,4,6,7,8},{3},{5}}
[1,2,7,5,8,6,4,3]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>{{1},{2},{3,4,5,7},{6,8}}
[3,7,8,1,2,6,5,4]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>{{1},{2},{3,6},{4,5,8},{7}}
[2,8,1,6,7,3,5,4]=>[1,6,7,2,8,3,5,4]=>[1,7,5,8,4,6,2,3]=>{{1},{2,7},{3,4,5,8},{6}}
[2,6,8,3,7,1,5,4]=>[1,5,2,6,8,3,7,4]=>[1,5,7,8,2,6,4,3]=>{{1},{2,5},{3,4,7,8},{6}}
[6,8,3,4,1,7,5,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[6,8,3,7,4,1,5,2]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>{{1},{2,3,5},{4,6,7},{8}}
[8,2,5,7,1,6,3,4]=>[1,6,2,5,7,3,4,8]=>[1,5,4,7,6,2,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[8,4,7,2,3,6,1,5]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>{{1},{2,3,5},{4,6},{7},{8}}
[8,5,7,4,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[8,5,2,4,7,1,6,3]=>[1,6,2,4,7,3,5,8]=>[1,4,5,6,7,2,3,8]=>{{1},{2,4,6},{3,5,7},{8}}
[8,2,4,7,3,6,1,5]=>[1,5,2,4,7,3,6,8]=>[1,4,6,5,2,7,3,8]=>{{1},{2,4,5},{3,6,7},{8}}
[8,2,7,1,4,6,3,5]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>{{1},{2,6},{3,5,7},{4},{8}}
[8,4,7,1,3,6,2,5]=>[1,3,6,2,5,4,7,8]=>[1,5,3,6,4,2,7,8]=>{{1},{2,4,5,6},{3},{7},{8}}
[1,6,8,3,7,2,5,4]=>[1,6,8,2,5,3,7,4]=>[1,5,7,8,3,6,4,2]=>{{1},{2,3,4,5,7,8},{6}}
[8,3,5,7,1,2,6,4]=>[1,2,6,3,5,7,4,8]=>[1,2,5,7,6,3,4,8]=>{{1},{2},{3,5,6},{4,7},{8}}
[8,5,4,7,1,6,2,3]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>{{1},{2,3,4,6},{5,7},{8}}
[1,4,6,8,2,7,5,3]=>[1,4,6,8,2,7,3,5]=>[1,7,5,4,8,6,3,2]=>{{1},{2,3,5,7,8},{4},{6}}
[1,6,5,8,2,7,4,3]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>{{1},{2,6},{3,4,5,7},{8}}
[8,5,6,3,1,7,4,2]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>{{1},{2,3,4,5,6,7},{8}}
[5,6,2,8,1,7,4,3]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>{{1},{2,7},{3,4,5,6,8}}
[1,8,4,5,7,2,6,3]=>[1,8,2,6,3,4,5,7]=>[1,6,4,5,7,3,8,2]=>{{1},{2,3,4,5,6,7,8}}
[5,8,7,3,6,1,2,4]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>{{1},{2},{3,4},{5,6},{7,8}}
[8,3,5,7,1,6,2,4]=>[1,6,2,4,3,5,7,8]=>[1,4,5,3,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[6,3,8,2,7,5,1,4]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>{{1},{2,4},{3,7},{5,6,8}}
[6,8,4,2,7,1,5,3]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>{{1},{2,5},{3,4,6,7},{8}}
[8,6,4,7,3,1,5,2]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>{{1},{2,3,4,5},{6,7},{8}}
[8,4,5,7,3,1,6,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,4,2,5,7,1,6,3]=>[1,6,2,5,7,3,4,8]=>[1,5,4,7,6,2,3,8]=>{{1},{2,5,6},{3,4,7},{8}}
[8,3,4,7,2,6,1,5]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>{{1},{2,5},{3,4,6},{7},{8}}
[2,8,4,5,7,1,6,3]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>{{1},{2,6},{3,4,5,7,8}}
[8,7,3,4,5,1,6,2]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>{{1},{2,3,4,5,6},{7},{8}}
[8,7,4,5,2,6,1,3]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>{{1},{2,3},{4,5,6},{7},{8}}
[5,8,7,2,3,6,1,4]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>{{1},{2,3,4},{5,6},{7,8}}
[8,7,2,3,4,6,1,5]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>{{1},{2,3,4,5},{6},{7},{8}}
Map
runsort
Description
The permutation obtained by sorting the increasing runs lexicographically.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
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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